Full list of non-zero Kazhdan-Lusztig-Vogan polynomials:

   0:    0: 1

   1:    1: 1

   2:    2: 1

   3:    3: 1

   4:    4: 1

   5:    5: 1

   6:    6: 1

   7:    7: 1

   8:    8: 1

   9:    9: 1

  10:    0: 1
         1: 1
        10: 1

  11:    3: 1
         5: 1
        11: 1

  12:    4: 1
         6: 1
        12: 1

  13:    0: 1
         2: 1
        13: 1

  14:    4: 1
         7: 1
        14: 1

  15:    5: 1
         8: 1
        15: 1

  16:    0: 1
         3: 1
        16: 1

  17:    1: 1
         5: 1
        17: 1

  18:    7: 1
         9: 1
        18: 1

  19:    0: 1
         4: 1
        19: 1

  20:    1: 1
         6: 1
        20: 1

  21:    2: 1
         7: 1
        21: 1

  22:    0: 1
         5: 1
        22: 1

  23:    1: 1
         3: 1
        23: 1

  24:    2: 1
         8: 1
        24: 1

  25:    0: 1
         5: 1
        25: 1

  26:    1: 1
         3: 1
        26: 1

  27:    2: 1
         8: 1
        27: 1

  28:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        28: 1

  29:    0: 1
         1: 1
         4: 1
         6: 1
        10: 1
        12: 1
        19: 1
        20: 1
        29: 1

  30:    0: 1
         2: 1
         4: 1
         7: 1
        13: 1
        14: 1
        19: 1
        21: 1
        30: 1

  31:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        22: 1
        23: 1
        31: 1

  32:    0: 1
         2: 1
         5: 1
         8: 1
        13: 1
        15: 1
        22: 1
        24: 1
        32: 1

  33:    0: 1
         1: 1
         3: 1
         5: 1
        16: 1
        17: 1
        22: 1
        23: 1
        33: 1

  34:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        25: 1
        26: 1
        34: 1

  35:    0: 1
         2: 1
         5: 1
         8: 1
        13: 1
        15: 1
        25: 1
        27: 1
        35: 1

  36:    0: 1
         1: 1
         3: 1
         5: 1
        16: 1
        17: 1
        25: 1
        26: 1
        36: 1

  37:    0: 1
         5: 1
        22: 1
        25: 1
        37: 1

  38:    0: 1
         5: 1
        22: 1
        25: 1
        38: 1

  39:    1: 1
         3: 1
        23: 1
        26: 1
        39: 1

  40:    1: 1
         3: 1
        23: 1
        26: 1
        40: 1

  41:    2: 1
         8: 1
        24: 1
        27: 1
        41: 1

  42:    2: 1
         8: 1
        24: 1
        27: 1
        42: 1

  43:    0: 1
         1: 1
         2: 1
        10: 1
        13: 1
        43: 1

  44:    4: 1
         6: 1
         7: 1
        12: 1
        14: 1
        44: 1

  45:    3: 1
         5: 1
         8: 1
        11: 1
        15: 1
        45: 1

  46:    0: 1
         2: 1
         3: 1
        13: 1
        16: 1
        46: 1

  47:    1: 1
         5: 1
         8: 1
        15: 1
        17: 1
        47: 1

  48:    4: 1
         7: 1
         9: 1
        14: 1
        18: 1
        48: 1

  49:    0: 1
         3: 1
         4: 1
        16: 1
        19: 1
        49: 1

  50:    1: 1
         5: 1
         6: 1
        17: 1
        20: 1
        50: 1

  51:    2: 1
         7: 1
         9: 1
        18: 1
        21: 1
        51: 1

  52:    0: 1
         4: 1
         5: 1
        19: 1
        22: 1
        52: 1

  53:    1: 1
         3: 1
         6: 1
        20: 1
        23: 1
        53: 1

  54:    2: 1
         7: 1
         8: 1
        21: 1
        24: 1
        54: 1

  55:    0: 1
         4: 1
         5: 1
        19: 1
        25: 1
        55: 1

  56:    1: 1
         3: 1
         6: 1
        20: 1
        26: 1
        56: 1

  57:    2: 1
         7: 1
         8: 1
        21: 1
        27: 1
        57: 1

  58:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        28: 1
        31: 1
        33: 1
        58: 1

  59:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        28: 1
        31: 1
        33: 1
        59: 1

  60:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        25: 1
        26: 1
        28: 1
        34: 1
        36: 1
        60: 1

  61:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        25: 1
        26: 1
        28: 1
        34: 1
        36: 1
        61: 1

  62:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        22: 1
        23: 1
        25: 1
        26: 1
        31: 1
        34: 1
        37: 1
        39: 1
        62: 1

  63:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        22: 1
        23: 1
        25: 1
        26: 1
        31: 1
        34: 1
        38: 1
        40: 1
        63: 1

  64:    0: 1
         2: 1
         5: 1
         8: 1
        13: 1
        15: 1
        22: 1
        24: 1
        25: 1
        27: 1
        32: 1
        35: 1
        37: 1
        41: 1
        64: 1

  65:    0: 1
         2: 1
         5: 1
         8: 1
        13: 1
        15: 1
        22: 1
        24: 1
        25: 1
        27: 1
        32: 1
        35: 1
        38: 1
        42: 1
        65: 1

  66:    0: 1
         1: 1
         3: 1
         5: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        66: 1

  67:    0: 1
         1: 1
         3: 1
         5: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        67: 1

  68:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        28: 1
        43: 1
        45: 1
        46: 1
        47: 1
        68: 1

  69:    0: 1
         2: q+1
         3: 1
         4: q+1
         7: 1
         9: 1
        13: 1
        14: 1
        16: 1
        18: 1
        19: 1
        21: 1
        30: 1
        46: 1
        48: 1
        49: 1
        51: 1
        69: 1

  70:    0: 1
         1: 1
         2: 1
         4: 1
         6: 1
         7: 1
        10: 1
        12: 1
        13: 1
        14: 1
        19: 1
        20: 1
        21: 1
        29: 1
        30: 1
        43: 1
        44: 1
        70: 1

  71:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        28: 1
        29: 1
        49: 1
        50: 1
        71: 1

  72:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        72: 1

  73:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        73: 1

  74:    0: 1
         4: 1
         5: q+1
        19: 1
        22: 1
        25: 1
        37: 1
        52: 1
        55: 1
        74: 1

  75:    0: 1
         4: 1
         5: q+1
        19: 1
        22: 1
        25: 1
        38: 1
        52: 1
        55: 1
        75: 1

  76:    1: 1
         3: q+1
         6: 1
        20: 1
        23: 1
        26: 1
        39: 1
        53: 1
        56: 1
        76: 1

  77:    1: 1
         3: q+1
         6: 1
        20: 1
        23: 1
        26: 1
        40: 1
        53: 1
        56: 1
        77: 1

  78:    2: 1
         7: 1
         8: q+1
        21: 1
        24: 1
        27: 1
        41: 1
        54: 1
        57: 1
        78: 1

  79:    2: 1
         7: 1
         8: q+1
        21: 1
        24: 1
        27: 1
        42: 1
        54: 1
        57: 1
        79: 1

  80:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        22: 1
        23: 1
        24: 1
        31: 1
        32: 1
        43: 1
        45: 1
        80: 1

  81:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        32: 1
        33: 1
        46: 1
        47: 1
        81: 1

  82:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        19: 1
        20: 1
        22: 1
        23: 1
        29: 1
        31: 1
        52: 1
        53: 1
        82: 1

  83:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        19: 1
        21: 1
        22: 1
        24: 1
        30: 1
        32: 1
        52: 1
        54: 1
        83: 1

  84:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        25: 1
        26: 1
        27: 1
        34: 1
        35: 1
        43: 1
        45: 1
        84: 1

  85:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        25: 1
        26: 1
        27: 1
        35: 1
        36: 1
        46: 1
        47: 1
        85: 1

  86:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        19: 1
        20: 1
        25: 1
        26: 1
        29: 1
        34: 1
        55: 1
        56: 1
        86: 1

  87:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        19: 1
        21: 1
        25: 1
        27: 1
        30: 1
        35: 1
        55: 1
        57: 1
        87: 1

  88:    0: 1
         1: 1
         2: q+1
         3: 1
         5: 1
        10: 1
        11: 1
        13: 1
        16: 1
        17: 1
        28: 1
        43: 1
        46: 1
        88: 1

  89:    0: 1
         1: 1
         3: 1
         5: 1
         8: q+1
        10: 1
        11: 1
        15: 1
        16: 1
        17: 1
        28: 1
        45: 1
        47: 1
        89: 1

  90:    4: 1
         6: 1
         7: 1
         9: 1
        12: 1
        14: 1
        18: 1
        44: 1
        48: 1
        90: 1

  91:    0: 1
         2: 1
         3: q+1
         4: 1
         7: 1
        13: 1
        14: 1
        16: 1
        19: 1
        21: 1
        30: 1
        46: 1
        49: 1
        91: 1

  92:    1: 1
         5: 1
         6: 1
         8: 1
        15: 1
        17: 1
        20: 1
        47: 1
        50: 1
        92: 1

  93:    0: 1
         2: 1
         4: 1
         7: 1
         9: q+1
        13: 1
        14: 1
        18: 1
        19: 1
        21: 1
        30: 1
        48: 1
        51: 1
        93: 1

  94:    0: 1
         1: 1
         3: 1
         4: q+1
         5: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        33: 1
        49: 1
        52: 1
        94: 1

  95:    0: 1
         1: 1
         3: 1
         5: 1
         6: q+1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        33: 1
        50: 1
        53: 1
        95: 1

  96:    2: 1
         7: 1
         8: 1
         9: 1
        18: 1
        21: 1
        24: 1
        51: 1
        54: 1
        96: 1

  97:    0: 1
         1: 1
         3: 1
         4: q+1
         5: 1
        16: 1
        17: 1
        19: 1
        25: 1
        26: 1
        36: 1
        49: 1
        55: 1
        97: 1

  98:    0: 1
         1: 1
         3: 1
         5: 1
         6: q+1
        16: 1
        17: 1
        20: 1
        25: 1
        26: 1
        36: 1
        50: 1
        56: 1
        98: 1

  99:    2: 1
         7: 1
         8: 1
         9: 1
        18: 1
        21: 1
        27: 1
        51: 1
        57: 1
        99: 1

 100:    0: 2
         4: q+1
         5: 2
        19: 1
        22: 2
        25: 2
        37: 1
        38: 1
        52: 1
        55: 1
       100: 1

 101:    1: 2
         3: 2
         6: q+1
        20: 1
        23: 2
        26: 2
        39: 1
        40: 1
        53: 1
        56: 1
       101: 1

 102:    2: 2
         7: q+1
         8: 2
        21: 1
        24: 2
        27: 2
        41: 1
        42: 1
        54: 1
        57: 1
       102: 1

 103:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        58: 1
        60: 1
        62: 1
        66: 1
       103: 1

 104:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        59: 1
        60: 1
        63: 1
        67: 1
       104: 1

 105:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        58: 1
        61: 1
        63: 1
        67: 1
       105: 1

 106:    0: 1
         1: 1
         3: 1
         5: 1
        10: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        59: 1
        61: 1
        62: 1
        66: 1
       106: 1

 107:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        28: 1
        29: 1
        34: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        60: 1
        71: 1
        72: 1
        86: 1
       107: 1

 108:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        28: 1
        29: 1
        34: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        61: 1
        71: 1
        72: 1
        86: 1
       108: 1

 109:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        28: 1
        29: 1
        31: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        58: 1
        71: 1
        73: 1
        82: 1
       109: 1

 110:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        28: 1
        29: 1
        31: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        59: 1
        71: 1
        73: 1
        82: 1
       110: 1

 111:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
       111: 1

 112:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
       112: 1

 113:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        29: 1
        31: 1
        34: 1
        37: 1
        39: 1
        52: 1
        53: 1
        55: 1
        56: 1
        62: 1
        74: 1
        76: 1
        82: 1
        86: 1
       113: 1

 114:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        29: 1
        31: 1
        34: 1
        38: 1
        40: 1
        52: 1
        53: 1
        55: 1
        56: 1
        63: 1
        75: 1
        77: 1
        82: 1
        86: 1
       114: 1

 115:    0: 1
         2: 1
         4: 1
         5: q+1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        37: 1
        41: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        74: 1
        78: 1
        83: 1
        87: 1
       115: 1

 116:    0: 1
         2: 1
         4: 1
         5: q+1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        38: 1
        42: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        75: 1
        79: 1
        83: 1
        87: 1
       116: 1

 117:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        31: 1
        32: 1
        33: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        68: 1
        80: 1
        81: 1
       117: 1

 118:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        31: 1
        32: 1
        33: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        68: 1
        80: 1
        81: 1
       118: 1

 119:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        34: 1
        35: 1
        36: 1
        43: 1
        45: 1
        46: 1
        47: 1
        60: 1
        68: 1
        84: 1
        85: 1
       119: 1

 120:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        34: 1
        35: 1
        36: 1
        43: 1
        45: 1
        46: 1
        47: 1
        61: 1
        68: 1
        84: 1
        85: 1
       120: 1

 121:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        31: 1
        32: 1
        34: 1
        35: 1
        37: 1
        39: 1
        41: 1
        43: 1
        45: 1
        62: 1
        64: 1
        80: 1
        84: 1
       121: 1

 122:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        31: 1
        32: 1
        34: 1
        35: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        63: 1
        65: 1
        80: 1
        84: 1
       122: 1

 123:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        64: 1
        66: 1
        81: 1
        85: 1
       123: 1

 124:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        65: 1
        67: 1
        81: 1
        85: 1
       124: 1

 125:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        28: 1
        43: 1
        45: 1
        46: 1
        47: 1
        68: 1
        88: 1
        89: 1
       125: 1

 126:    0: 1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: 1
         6: q+1
         7: 1
         9: 1
        10: 1
        11: 1
        12: q+1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        46: 1
        48: 1
        49: 1
        50: 1
        51: 1
        69: 1
        70: 1
        71: 1
        88: 1
        90: 1
       126: 1

 127:    0: 1
         1: q+1
         3: 1
         4: q+1
         5: q+1
        16: 1
        17: q+1
        19: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        52: 1
        55: 1
        66: 1
        74: 1
        94: 1
        97: 1
       127: 1

 128:    0: 1
         1: q+1
         3: 1
         4: q+1
         5: q+1
        16: 1
        17: q+1
        19: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        52: 1
        55: 1
        67: 1
        75: 1
        94: 1
        97: 1
       128: 1

 129:    0: q+1
         1: 1
         3: q+1
         5: 1
         6: q+1
        16: q+1
        17: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        50: 1
        53: 1
        56: 1
        66: 1
        76: 1
        95: 1
        98: 1
       129: 1

 130:    0: q+1
         1: 1
         3: q+1
         5: 1
         6: q+1
        16: q+1
        17: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        50: 1
        53: 1
        56: 1
        67: 1
        77: 1
        95: 1
        98: 1
       130: 1

 131:    2: 1
         7: 1
         8: q+1
         9: 1
        18: 1
        21: 1
        24: 1
        27: 1
        41: 1
        51: 1
        54: 1
        57: 1
        78: 1
        96: 1
        99: 1
       131: 1

 132:    2: 1
         7: 1
         8: q+1
         9: 1
        18: 1
        21: 1
        24: 1
        27: 1
        42: 1
        51: 1
        54: 1
        57: 1
        79: 1
        96: 1
        99: 1
       132: 1

 133:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        68: 1
        70: 1
        71: 1
        91: 1
        92: 1
       133: 1

 134:    0: 1
         2: 1
         3: 1
         4: 1
         7: 1
         9: 1
        13: 1
        14: 1
        16: 1
        18: 1
        19: 1
        21: 1
        30: 1
        46: 1
        48: 1
        49: 1
        51: 1
        69: 1
        91: 1
        93: 1
       134: 1

 135:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: 1
        57: 1
        72: 1
        85: 1
        87: 1
        91: 1
        92: 1
       135: 1

 136:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        73: 1
        81: 1
        83: 1
        91: 1
        92: 1
       136: 1

 137:    0: 2
         1: 2
         2: q+1
         3: 2
         5: 2
         8: q+1
        10: 2
        11: 2
        13: 1
        15: 1
        16: 2
        17: 2
        22: 2
        23: 2
        24: q+1
        28: 2
        31: 2
        32: 1
        33: 2
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        59: 1
        80: 1
        81: 1
        88: 1
        89: 1
       137: 1

 138:    0: 1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: 1
         7: 1
         8: q+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        54: 1
        69: 1
        81: 1
        83: 1
        94: 1
        96: 1
       138: 1

 139:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        28: 2
        29: 1
        31: 2
        33: 2
        49: 1
        50: 1
        52: 1
        53: 1
        58: 1
        59: 1
        71: 1
        82: 1
        94: 1
        95: 1
       139: 1

 140:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: q+2
        23: q+2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        67: 1
        72: 1
        94: 1
        95: 1
       100: 1
       101: 1
       140: 1

 141:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        29: 1
        30: 1
        31: 1
        32: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        54: 1
        70: 1
        80: 1
        82: 1
        83: 1
       141: 1

 142:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        73: 1
        94: 1
        95: 1
       142: 1

 143:    0: 2
         1: 2
         2: q+1
         3: 2
         5: 2
         8: q+1
        10: 2
        11: 2
        13: 1
        15: 1
        16: 2
        17: 2
        25: 2
        26: 2
        27: q+1
        28: 2
        34: 2
        35: 1
        36: 2
        43: 1
        45: 1
        46: 1
        47: 1
        60: 1
        61: 1
        84: 1
        85: 1
        88: 1
        89: 1
       143: 1

 144:    0: 1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: 1
         7: 1
         8: q+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        27: q+1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        55: 1
        57: 1
        69: 1
        85: 1
        87: 1
        97: 1
        99: 1
       144: 1

 145:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        25: 2
        26: 2
        28: 2
        29: 1
        34: 2
        36: 2
        49: 1
        50: 1
        55: 1
        56: 1
        60: 1
        61: 1
        71: 1
        86: 1
        97: 1
        98: 1
       145: 1

 146:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        34: 1
        35: 1
        43: 1
        44: 1
        45: 1
        55: 1
        56: 1
        57: 1
        70: 1
        84: 1
        86: 1
        87: 1
       146: 1

 147:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        72: 1
        97: 1
        98: 1
       147: 1

 148:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: q+2
        26: q+2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        67: 1
        73: 1
        97: 1
        98: 1
       100: 1
       101: 1
       148: 1

 149:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        29: 1
        31: 2
        34: 2
        37: 1
        38: 1
        39: 1
        40: 1
        52: 1
        53: 1
        55: 1
        56: 1
        62: 1
        63: 1
        82: 1
        86: 1
       100: 1
       101: 1
       149: 1

 150:    0: 2
         2: 2
         4: q+1
         5: 2
         7: q+1
         8: 2
        13: 2
        14: q+1
        15: 2
        19: 1
        21: 1
        22: 2
        24: 2
        25: 2
        27: 2
        30: 1
        32: 2
        35: 2
        37: 1
        38: 1
        41: 1
        42: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        65: 1
        83: 1
        87: 1
       100: 1
       102: 1
       150: 1

 151:    0: 1
         4: 1
         5: 1
        19: 1
        22: 1
        25: 1
        37: 1
        52: 1
        55: 1
        74: 1
       100: 1
       151: 1

 152:    0: 1
         4: 1
         5: 1
        19: 1
        22: 1
        25: 1
        38: 1
        52: 1
        55: 1
        75: 1
       100: 1
       152: 1

 153:    1: 1
         3: 1
         6: 1
        20: 1
        23: 1
        26: 1
        39: 1
        53: 1
        56: 1
        76: 1
       101: 1
       153: 1

 154:    1: 1
         3: 1
         6: 1
        20: 1
        23: 1
        26: 1
        40: 1
        53: 1
        56: 1
        77: 1
       101: 1
       154: 1

 155:    2: 1
         7: 1
         8: 1
        21: 1
        24: 1
        27: 1
        41: 1
        54: 1
        57: 1
        78: 1
       102: 1
       155: 1

 156:    2: 1
         7: 1
         8: 1
        21: 1
        24: 1
        27: 1
        42: 1
        54: 1
        57: 1
        79: 1
       102: 1
       156: 1

 157:    0: 1
         1: 1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: q+1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        46: 1
        49: 1
        50: 1
        70: 1
        71: 1
        88: 1
        91: 1
       157: 1

 158:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: q+1
        10: 1
        11: 1
        12: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        28: 1
        29: 1
        45: 1
        47: 1
        49: 1
        50: 1
        71: 1
        89: 1
        92: 1
       158: 1

 159:    0: 1
         1: 1
         2: 1
         4: 1
         6: 1
         7: 1
         9: q+1
        10: 1
        12: 1
        13: 1
        14: 1
        18: 1
        19: 1
        20: 1
        21: 1
        29: 1
        30: 1
        43: 1
        44: 1
        48: 1
        51: 1
        70: 1
        90: 1
        93: 1
       159: 1

 160:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: q+1
         8: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        49: 1
        52: 1
        54: 1
        81: 1
        83: 1
        91: 1
        94: 1
       160: 1

 161:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: q+1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        24: 1
        32: 1
        33: 1
        46: 1
        47: 1
        50: 1
        53: 1
        81: 1
        92: 1
        95: 1
       161: 1

 162:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: q+1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        30: 1
        32: 1
        48: 1
        51: 1
        52: 1
        54: 1
        83: 1
        93: 1
        96: 1
       162: 1

 163:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: q+1
         8: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        49: 1
        55: 1
        57: 1
        85: 1
        87: 1
        91: 1
        97: 1
       163: 1

 164:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: q+1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        20: 1
        25: 1
        26: 1
        27: 1
        35: 1
        36: 1
        46: 1
        47: 1
        50: 1
        56: 1
        85: 1
        92: 1
        98: 1
       164: 1

 165:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: q+1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        21: 1
        25: 1
        27: 1
        30: 1
        35: 1
        48: 1
        51: 1
        55: 1
        57: 1
        87: 1
        93: 1
        99: 1
       165: 1

 166:    0: 2
         1: 2
         3: 2
         4: 2q+1
         5: 2
        16: 2
        17: 2
        19: 1
        22: 2
        23: 2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        52: 1
        55: 1
        66: 1
        67: 1
        94: 1
        97: 1
       100: 1
       166: 1

 167:    0: 2
         1: 2
         3: 2
         5: 2
         6: 2q+1
        16: 2
        17: 2
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        50: 1
        53: 1
        56: 1
        66: 1
        67: 1
        95: 1
        98: 1
       101: 1
       167: 1

 168:    2: 2
         7: q+1
         8: 2
         9: q+1
        18: q+1
        21: 1
        24: 2
        27: 2
        41: 1
        42: 1
        51: 1
        54: 1
        57: 1
        96: 1
        99: 1
       102: 1
       168: 1

 169:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        60: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       169: 1

 170:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        60: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       170: 1

 171:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        61: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       171: 1

 172:    0: 1
         1: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
        10: 1
        11: q+1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        61: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       172: 1

 173:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
       103: 1
       117: 1
       119: 1
       121: 1
       123: 1
       173: 1

 174:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
       104: 1
       118: 1
       119: 1
       122: 1
       124: 1
       174: 1

 175:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
       105: 1
       117: 1
       120: 1
       122: 1
       124: 1
       175: 1

 176:    0: 1
         1: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
       106: 1
       118: 1
       120: 1
       121: 1
       123: 1
       176: 1

 177:    0: 1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: 1
         8: q^2+2q+1
         9: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        46: 1
        47: q+1
        48: 1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        69: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        94: 1
        96: 1
        97: 1
        99: 1
       115: 1
       123: 1
       127: 1
       131: 1
       138: 1
       144: 1
       177: 1

 178:    0: 1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: 1
         8: q^2+2q+1
         9: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: q+1
        46: 1
        47: q+1
        48: 1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        69: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        94: 1
        96: 1
        97: 1
        99: 1
       116: 1
       124: 1
       128: 1
       132: 1
       138: 1
       144: 1
       178: 1

 179:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: q+2
        17: q+2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: q+2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 2
        39: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        66: 2
        71: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       106: 1
       113: 1
       127: 1
       129: 1
       139: 1
       145: 1
       179: 1

 180:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: q+2
        17: q+2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: q+2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        38: 2
        40: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        67: 2
        71: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       105: 1
       114: 1
       128: 1
       130: 1
       139: 1
       145: 1
       180: 1

 181:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       111: 1
       127: 1
       129: 1
       142: 1
       147: 1
       181: 1

 182:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       112: 1
       128: 1
       130: 1
       142: 1
       147: 1
       182: 1

 183:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        60: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       107: 1
       119: 1
       133: 1
       135: 1
       146: 1
       183: 1

 184:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        61: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       108: 1
       120: 1
       133: 1
       135: 1
       146: 1
       184: 1

 185:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        58: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        91: 1
        92: 1
       109: 1
       117: 1
       133: 1
       136: 1
       141: 1
       185: 1

 186:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        59: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        91: 1
        92: 1
       110: 1
       118: 1
       133: 1
       136: 1
       141: 1
       186: 1

 187:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
       111: 1
       115: 1
       123: 1
       135: 1
       136: 1
       187: 1

 188:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
       112: 1
       116: 1
       124: 1
       135: 1
       136: 1
       188: 1

 189:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        64: 1
        70: 1
        74: 1
        76: 1
        78: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
       113: 1
       115: 1
       121: 1
       141: 1
       146: 1
       189: 1

 190:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        63: 1
        65: 1
        70: 1
        75: 1
        77: 1
        79: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
       114: 1
       116: 1
       122: 1
       141: 1
       146: 1
       190: 1

 191:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        28: 1
        31: 1
        32: 1
        33: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        68: 1
        80: 1
        81: 1
        88: 1
        89: 1
       117: 1
       125: 1
       137: 1
       191: 1

 192:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        28: 1
        31: 1
        32: 1
        33: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        68: 1
        80: 1
        81: 1
        88: 1
        89: 1
       118: 1
       125: 1
       137: 1
       192: 1

 193:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: q+2
        23: q+2
        25: 2
        26: 2
        28: 2
        29: 1
        31: q+2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        72: 1
        82: 1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       103: 1
       104: 1
       107: 1
       139: 1
       140: 1
       149: 1
       193: 1

 194:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: q+2
        23: q+2
        25: 2
        26: 2
        28: 2
        29: 1
        31: q+2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        72: 1
        82: 1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       105: 1
       106: 1
       108: 1
       139: 1
       140: 1
       149: 1
       194: 1

 195:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        28: 1
        29: 1
        31: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        58: 1
        71: 1
        73: 1
        82: 1
        94: 1
        95: 1
       109: 1
       139: 1
       142: 1
       195: 1

 196:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        28: 1
        29: 1
        31: 1
        33: 1
        49: 1
        50: 1
        52: 1
        53: 1
        59: 1
        71: 1
        73: 1
        82: 1
        94: 1
        95: 1
       110: 1
       139: 1
       142: 1
       196: 1

 197:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
       100: 1
       101: 1
       111: 1
       140: 1
       142: 1
       151: 1
       153: 1
       197: 1

 198:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
       100: 1
       101: 1
       112: 1
       140: 1
       142: 1
       152: 1
       154: 1
       198: 1

 199:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        25: 1
        26: 1
        27: 1
        28: 1
        34: 1
        35: 1
        36: 1
        43: 1
        45: 1
        46: 1
        47: 1
        60: 1
        68: 1
        84: 1
        85: 1
        88: 1
        89: 1
       119: 1
       125: 1
       143: 1
       199: 1

 200:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        25: 1
        26: 1
        27: 1
        28: 1
        34: 1
        35: 1
        36: 1
        43: 1
        45: 1
        46: 1
        47: 1
        61: 1
        68: 1
        84: 1
        85: 1
        88: 1
        89: 1
       120: 1
       125: 1
       143: 1
       200: 1

 201:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        28: 1
        29: 1
        34: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        60: 1
        71: 1
        72: 1
        86: 1
        97: 1
        98: 1
       107: 1
       145: 1
       147: 1
       201: 1

 202:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        25: 1
        26: 1
        28: 1
        29: 1
        34: 1
        36: 1
        49: 1
        50: 1
        55: 1
        56: 1
        61: 1
        71: 1
        72: 1
        86: 1
        97: 1
        98: 1
       108: 1
       145: 1
       147: 1
       202: 1

 203:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: q+2
        26: q+2
        28: 2
        29: 1
        31: 2
        33: 2
        34: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        73: 1
        82: 1
        86: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       105: 1
       109: 1
       145: 1
       148: 1
       149: 1
       203: 1

 204:    0: q+2
         1: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
        10: q+2
        11: q+2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: q+2
        26: q+2
        28: 2
        29: 1
        31: 2
        33: 2
        34: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        73: 1
        82: 1
        86: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       106: 1
       110: 1
       145: 1
       148: 1
       149: 1
       204: 1

 205:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        97: 1
        98: 1
       100: 1
       101: 1
       111: 1
       147: 1
       148: 1
       151: 1
       153: 1
       205: 1

 206:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        97: 1
        98: 1
       100: 1
       101: 1
       112: 1
       147: 1
       148: 1
       152: 1
       154: 1
       206: 1

 207:    0: 2
         1: 2
         2: q+1
         3: 2
         5: 2
         8: q+1
        10: 2
        11: 2
        13: 1
        15: 1
        16: 2
        17: 2
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       103: 1
       106: 1
       121: 1
       123: 1
       137: 1
       143: 1
       207: 1

 208:    0: 2
         1: 2
         2: q+1
         3: 2
         5: 2
         8: q+1
        10: 2
        11: 2
        13: 1
        15: 1
        16: 2
        17: 2
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       104: 1
       105: 1
       122: 1
       124: 1
       137: 1
       143: 1
       208: 1

 209:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        29: 1
        31: 1
        34: 1
        37: 1
        39: 1
        52: 1
        53: 1
        55: 1
        56: 1
        62: 1
        74: 1
        76: 1
        82: 1
        86: 1
       100: 1
       101: 1
       113: 1
       149: 1
       151: 1
       153: 1
       209: 1

 210:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        29: 1
        31: 1
        34: 1
        38: 1
        40: 1
        52: 1
        53: 1
        55: 1
        56: 1
        63: 1
        75: 1
        77: 1
        82: 1
        86: 1
       100: 1
       101: 1
       114: 1
       149: 1
       152: 1
       154: 1
       210: 1

 211:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        37: 1
        41: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        74: 1
        78: 1
        83: 1
        87: 1
       100: 1
       102: 1
       115: 1
       150: 1
       151: 1
       155: 1
       211: 1

 212:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        38: 1
        42: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        75: 1
        79: 1
        83: 1
        87: 1
       100: 1
       102: 1
       116: 1
       150: 1
       152: 1
       156: 1
       212: 1

 213:    0: 1
         1: q^2+2q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        19: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: 1
        47: q+1
        49: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        94: 1
        97: 1
       115: 1
       123: 1
       127: 1
       160: 1
       163: 1
       213: 1

 214:    0: 1
         1: q^2+2q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        19: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: 1
        47: q+1
        49: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        94: 1
        97: 1
       116: 1
       124: 1
       128: 1
       160: 1
       163: 1
       214: 1

 215:    0: q+1
         1: 1
         2: q+1
         3: q+1
         5: 1
         6: q^2+q+1
         8: 1
        13: q+1
        15: 1
        16: q+1
        17: 1
        20: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: q+1
        47: 1
        50: 1
        53: 1
        56: 1
        64: 1
        66: 1
        76: 1
        81: 1
        85: 1
        92: 1
        95: 1
        98: 1
       123: 1
       129: 1
       161: 1
       164: 1
       215: 1

 216:    0: q+1
         1: 1
         2: q+1
         3: q+1
         5: 1
         6: q^2+q+1
         8: 1
        13: q+1
        15: 1
        16: q+1
        17: 1
        20: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: q+1
        47: 1
        50: 1
        53: 1
        56: 1
        65: 1
        67: 1
        77: 1
        81: 1
        85: 1
        92: 1
        95: 1
        98: 1
       124: 1
       130: 1
       161: 1
       164: 1
       216: 1

 217:    0: 1
         2: 1
         4: 1
         5: q+1
         7: 1
         8: q+1
         9: q+1
        13: 1
        14: 1
        15: q+1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        37: 1
        41: 1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        74: 1
        78: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       115: 1
       131: 1
       162: 1
       165: 1
       217: 1

 218:    0: 1
         2: 1
         4: 1
         5: q+1
         7: 1
         8: q+1
         9: q+1
        13: 1
        14: 1
        15: q+1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        38: 1
        42: 1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        75: 1
        79: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       116: 1
       132: 1
       162: 1
       165: 1
       218: 1

 219:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q^2+1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        68: 1
        69: 1
        70: 1
        71: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       125: 1
       126: 1
       133: 1
       134: 1
       219: 1

 220:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        68: 1
        70: 1
        71: 1
        88: 1
        89: 1
        91: 1
        92: 1
       125: 1
       133: 1
       157: 1
       158: 1
       220: 1

 221:    0: 1
         1: 1
         2: q+1
         3: 1
         4: 1
         5: 1
         6: 1
         7: q+1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: q+1
        19: 1
        20: 1
        21: q+1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        46: 1
        48: 1
        49: 1
        50: 1
        51: q+1
        69: 1
        70: 1
        71: 1
        88: 1
        90: 1
        91: 1
        93: 1
       126: 1
       134: 1
       157: 1
       159: 1
       221: 1

 222:    0: 2
         1: 2
         2: q+1
         3: 2q+2
         4: 2
         5: 2q+2
         6: 2
         7: q+1
         8: q^2+2q+1
        10: 2
        11: 2q+2
        12: 2
        13: 1
        14: 1
        15: q+1
        16: 2
        17: 2
        19: 2
        20: 2
        21: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        34: 2
        35: 1
        36: 2
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        55: 2
        56: 2
        57: q+1
        60: 1
        61: 1
        70: 1
        71: 2
        72: 2
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       107: 1
       108: 1
       135: 1
       143: 1
       146: 1
       157: 1
       158: 1
       222: 1

 223:    0: q+1
         1: 1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: 1
        19: q+1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        69: 1
        72: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       134: 1
       135: 1
       144: 1
       147: 1
       223: 1

 224:    0: 2
         1: 2
         2: q+1
         3: 2q+2
         4: 2
         5: 2q+2
         6: 2
         7: q+1
         8: q^2+2q+1
        10: 2
        11: 2q+2
        12: 2
        13: 1
        14: 1
        15: q+1
        16: 2
        17: 2
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        58: 1
        59: 1
        70: 1
        71: 2
        73: 2
        80: 1
        81: 1
        82: 2
        83: 1
        88: 1
        89: 1
        91: 1
        92: 1
       109: 1
       110: 1
       136: 1
       137: 1
       141: 1
       157: 1
       158: 1
       224: 1

 225:    0: q+1
         1: 1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        69: 1
        73: 1
        81: 1
        83: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       134: 1
       136: 1
       138: 1
       142: 1
       225: 1

 226:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: 1
         8: q+1
         9: 1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: 1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        59: 1
        69: 1
        70: 1
        71: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        94: 1
        95: 1
        96: 1
       126: 1
       137: 1
       138: 1
       139: 1
       141: 1
       226: 1

 227:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        58: 1
        59: 1
        68: 2
        70: 1
        71: 1
        80: 2
        81: 2
        82: 1
        83: 1
        91: 1
        92: 1
        94: 1
        95: 1
       117: 1
       118: 1
       133: 1
       139: 1
       141: 1
       160: 1
       161: 1
       227: 1

 228:    0: 1
         1: 1
         2: 1
         3: 1
         4: q+1
         5: 1
         7: q+1
         8: 1
         9: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        18: q+1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        69: 1
        81: 1
        83: 1
        91: 1
        93: 1
        94: 1
        96: 1
       134: 1
       138: 1
       160: 1
       162: 1
       228: 1

 229:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        30: 1
        32: q+2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        72: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       135: 1
       140: 1
       150: 1
       160: 1
       161: 1
       229: 1

 230:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        73: 1
        81: 1
        83: 1
        91: 1
        92: 1
        94: 1
        95: 1
       136: 1
       142: 1
       160: 1
       161: 1
       230: 1

 231:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: 1
         8: q+1
         9: 1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: 1
        19: 1
        20: 1
        21: 1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        34: 2
        35: 1
        36: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        69: 1
        70: 1
        71: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        97: 1
        98: 1
        99: 1
       126: 1
       143: 1
       144: 1
       145: 1
       146: 1
       231: 1

 232:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        34: 2
        35: 2
        36: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        60: 1
        61: 1
        68: 2
        70: 1
        71: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       119: 1
       120: 1
       133: 1
       145: 1
       146: 1
       163: 1
       164: 1
       232: 1

 233:    0: 1
         1: 1
         2: 1
         3: 1
         4: q+1
         5: 1
         7: q+1
         8: 1
         9: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        18: q+1
        19: 1
        21: 1
        25: 1
        26: 1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        51: 1
        55: 1
        57: 1
        69: 1
        85: 1
        87: 1
        91: 1
        93: 1
        97: 1
        99: 1
       134: 1
       144: 1
       163: 1
       165: 1
       233: 1

 234:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        72: 1
        85: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       135: 1
       147: 1
       163: 1
       164: 1
       234: 1

 235:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        30: 1
        32: 2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        73: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       136: 1
       148: 1
       150: 1
       163: 1
       164: 1
       235: 1

 236:    0: 2
         1: 2
         2: 2q+2
         3: 2
         4: q^2+2q+1
         5: 2
         7: q+1
         8: 2q+2
         9: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        21: 1
        22: 2
        23: 2
        24: 2q+2
        25: 2
        26: 2
        27: 2q+2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        46: 2
        47: 2
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        81: 2
        83: 1
        85: 2
        87: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       123: 1
       124: 1
       138: 1
       144: 1
       150: 1
       166: 1
       168: 1
       236: 1

 237:    0: 1
         1: 1
         3: 1
         4: q+1
         5: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        52: 1
        55: 1
        66: 1
        74: 1
        94: 1
        97: 1
       100: 1
       127: 1
       151: 1
       166: 1
       237: 1

 238:    0: 1
         1: 1
         3: 1
         4: q+1
         5: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        52: 1
        55: 1
        67: 1
        75: 1
        94: 1
        97: 1
       100: 1
       128: 1
       152: 1
       166: 1
       238: 1

 239:    0: 1
         1: 1
         3: 1
         5: 1
         6: q+1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        50: 1
        53: 1
        56: 1
        66: 1
        76: 1
        95: 1
        98: 1
       101: 1
       129: 1
       153: 1
       167: 1
       239: 1

 240:    0: 1
         1: 1
         3: 1
         5: 1
         6: q+1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        50: 1
        53: 1
        56: 1
        67: 1
        77: 1
        95: 1
        98: 1
       101: 1
       130: 1
       154: 1
       167: 1
       240: 1

 241:    2: q+1
         7: 1
         8: q+1
         9: 1
        18: 1
        21: 1
        24: q+1
        27: q+1
        41: q+1
        51: 1
        54: 1
        57: 1
        78: 1
        96: 1
        99: 1
       102: 1
       131: 1
       155: 1
       168: 1
       241: 1

 242:    2: q+1
         7: 1
         8: q+1
         9: 1
        18: 1
        21: 1
        24: q+1
        27: q+1
        42: q+1
        51: 1
        54: 1
        57: 1
        79: 1
        96: 1
        99: 1
       102: 1
       132: 1
       156: 1
       168: 1
       242: 1

 243:    0: 4
         1: 4
         3: 4
         4: 2q+1
         5: 4
         6: 2q+1
        10: 4
        11: 4
        12: 2q+1
        16: 4
        17: 4
        19: 1
        20: 1
        22: 4
        23: 4
        25: 4
        26: 4
        28: 4
        29: 1
        31: 4
        33: 4
        34: 4
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        66: 2
        67: 2
        71: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       139: 1
       145: 1
       149: 1
       166: 1
       167: 1
       243: 1

 244:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        67: 1
        72: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       140: 1
       147: 1
       166: 1
       167: 1
       244: 1

 245:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        67: 1
        73: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       142: 1
       148: 1
       166: 1
       167: 1
       245: 1

 246:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        29: 1
        30: 1
        31: 2
        32: 2
        34: 2
        35: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        63: 1
        64: 1
        65: 1
        70: 1
        80: 2
        82: 1
        83: 1
        84: 2
        86: 1
        87: 1
       100: 1
       101: 1
       102: 1
       121: 1
       122: 1
       141: 1
       146: 1
       149: 1
       150: 1
       246: 1

 247:    0: 3q+2
         1: 2
         3: 2q+2
         4: 3q+2
         5: 2q+2
         6: 2
        16: q+2
        17: 2
        19: 3q+2
        20: 2
        22: q+2
        23: 2
        25: q+2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: q+2
        50: 2
        52: q+2
        53: 2
        55: q+2
        56: 2
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2
       111: 1
       112: 1
       142: 1
       147: 1
       151: 1
       152: 1
       166: 1
       247: 1

 248:    0: 2
         1: 3q+2
         3: 2q+2
         4: 2
         5: 2q+2
         6: 3q+2
        16: 2
        17: q+2
        19: 2
        20: 3q+2
        22: 2
        23: q+2
        25: 2
        26: q+2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: q+2
        52: 2
        53: q+2
        55: 2
        56: q+2
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       101: 2
       111: 1
       112: 1
       142: 1
       147: 1
       153: 1
       154: 1
       167: 1
       248: 1

 249:    2: 2
         7: 2
         8: 2
         9: q^2+1
        18: 1
        21: 2
        24: 2
        27: 2
        41: 1
        42: 1
        51: 1
        54: 2
        57: 2
        78: 1
        79: 1
        96: 1
        99: 1
       102: 2
       155: 1
       156: 1
       168: 1
       249: 1

 250:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        28: 2
        29: 1
        30: 1
        31: q+2
        32: 1
        33: 2
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        58: 1
        59: 1
        70: 1
        71: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
       137: 1
       139: 1
       141: 1
       157: 1
       160: 1
       250: 1

 251:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         8: q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        24: q+1
        28: 2
        29: 1
        31: 2
        32: 1
        33: 2
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        58: 1
        59: 1
        71: 1
        80: 1
        81: 1
        82: 1
        88: 1
        89: 1
        92: 1
        94: 1
        95: 1
       137: 1
       139: 1
       158: 1
       161: 1
       251: 1

 252:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        29: 1
        30: 1
        31: 1
        32: 1
        43: 1
        44: 1
        45: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        70: 1
        80: 1
        82: 1
        83: 1
        90: 1
        93: 1
        96: 1
       141: 1
       159: 1
       162: 1
       252: 1

 253:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        21: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: 1
        30: 1
        34: q+2
        35: 1
        36: 2
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        70: 1
        71: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        97: 1
        98: 1
       143: 1
       145: 1
       146: 1
       157: 1
       163: 1
       253: 1

 254:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         8: q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        34: 2
        35: 1
        36: 2
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: 1
        60: 1
        61: 1
        71: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        92: 1
        97: 1
        98: 1
       143: 1
       145: 1
       158: 1
       164: 1
       254: 1

 255:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        34: 1
        35: 1
        43: 1
        44: 1
        45: 1
        48: 1
        51: 1
        55: 1
        56: 1
        57: 1
        70: 1
        84: 1
        86: 1
        87: 1
        90: 1
        93: 1
        99: 1
       146: 1
       159: 1
       165: 1
       255: 1

 256:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: 2q+1
         5: 2
         7: 2q+1
         8: 2
        13: 2
        14: 2q+1
        15: 2
        16: 2
        17: 2
        19: 1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        94: 1
        97: 1
       100: 1
       102: 1
       123: 1
       124: 1
       150: 1
       160: 1
       163: 1
       166: 1
       256: 1

 257:    0: 2
         1: 2
         2: 2
         3: 2
         5: 2
         6: q^2+2q+1
         8: 2
        13: 2
        15: 2
        16: 2
        17: 2
        20: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        50: 1
        53: 1
        56: 1
        64: 1
        65: 1
        66: 1
        67: 1
        81: 2
        85: 2
        92: 1
        95: 1
        98: 1
       101: 1
       123: 1
       124: 1
       161: 1
       164: 1
       167: 1
       257: 1

 258:    0: 2
         2: 2
         4: q+1
         5: 2
         7: q+1
         8: 2
         9: q^2+2q+1
        13: 2
        14: q+1
        15: 2
        18: q+1
        19: 1
        21: 1
        22: 2
        24: 2
        25: 2
        27: 2
        30: 1
        32: 2
        35: 2
        37: 1
        38: 1
        41: 1
        42: 1
        48: q+1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        65: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       100: 1
       102: 1
       150: 1
       162: 1
       165: 1
       168: 1
       258: 1

 259:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        60: 1
        62: 1
        66: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: 1
       147: 1
       169: 1
       179: 1
       181: 1
       195: 1
       201: 1
       259: 1

 260:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        60: 1
        63: 1
        67: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: 1
       147: 1
       170: 1
       180: 1
       182: 1
       196: 1
       201: 1
       260: 1

 261:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        61: 1
        63: 1
        67: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: 1
       147: 1
       171: 1
       180: 1
       182: 1
       195: 1
       202: 1
       261: 1

 262:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        61: 1
        62: 1
        66: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: 1
       147: 1
       172: 1
       179: 1
       181: 1
       196: 1
       202: 1
       262: 1

 263:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       141: 1
       146: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       263: 1

 264:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       141: 1
       146: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       264: 1

 265:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       141: 1
       146: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       265: 1

 266:    0: 1
         1: q+1
         2: 1
         3: q^2+2q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       141: 1
       146: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       266: 1

 267:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: 1
        60: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       139: 1
       140: 1
       142: 1
       149: 1
       151: 1
       153: 1
       169: 1
       193: 1
       195: 1
       197: 1
       209: 1
       267: 1

 268:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        59: 1
        60: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       139: 1
       140: 1
       142: 1
       149: 1
       152: 1
       154: 1
       170: 1
       193: 1
       196: 1
       198: 1
       210: 1
       268: 1

 269:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        59: 1
        61: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       139: 1
       140: 1
       142: 1
       149: 1
       151: 1
       153: 1
       172: 1
       194: 1
       196: 1
       197: 1
       209: 1
       269: 1

 270:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: 1
        61: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: 1
        95: 1
       100: 1
       101: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       139: 1
       140: 1
       142: 1
       149: 1
       152: 1
       154: 1
       171: 1
       194: 1
       195: 1
       198: 1
       210: 1
       270: 1

 271:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: 1
        60: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       169: 1
       201: 1
       203: 1
       205: 1
       209: 1
       271: 1

 272:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: 1
        61: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       171: 1
       202: 1
       203: 1
       206: 1
       210: 1
       272: 1

 273:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: 1
        61: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       172: 1
       202: 1
       204: 1
       205: 1
       209: 1
       273: 1

 274:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: 1
        60: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       170: 1
       201: 1
       204: 1
       206: 1
       210: 1
       274: 1

 275:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       103: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       137: 1
       143: 1
       173: 1
       191: 1
       199: 1
       207: 1
       275: 1

 276:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       104: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       137: 1
       143: 1
       174: 1
       192: 1
       199: 1
       208: 1
       276: 1

 277:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       105: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       137: 1
       143: 1
       175: 1
       191: 1
       200: 1
       208: 1
       277: 1

 278:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        13: 1
        15: 1
        16: 1
        17: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        45: 1
        46: 1
        47: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        80: 1
        81: 1
        84: 1
        85: 1
        88: 1
        89: 1
       106: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       137: 1
       143: 1
       176: 1
       192: 1
       200: 1
       207: 1
       278: 1

 279:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2q+2
        41: 2
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: q+2
        70: 1
        71: 1
        74: 1
        76: q+1
        78: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       127: 1
       129: 1
       133: 1
       139: 1
       141: 1
       145: 1
       146: 1
       160: 1
       161: 1
       163: 1
       164: 1
       173: 1
       176: 1
       179: 1
       189: 1
       213: 1
       215: 1
       227: 1
       232: 1
       279: 1

 280:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2q+2
        42: 2
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: q+2
        70: 1
        71: 1
        75: 1
        77: q+1
        79: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       128: 1
       130: 1
       133: 1
       139: 1
       141: 1
       145: 1
       146: 1
       160: 1
       161: 1
       163: 1
       164: 1
       174: 1
       175: 1
       180: 1
       190: 1
       214: 1
       216: 1
       227: 1
       232: 1
       280: 1

 281:    0: 1
         1: q+1
         2: 1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        69: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       115: 1
       123: 1
       127: 1
       131: 1
       134: 1
       138: 1
       144: 1
       160: 1
       162: 1
       163: 1
       165: 1
       177: 1
       213: 1
       217: 1
       228: 1
       233: 1
       281: 1

 282:    0: 1
         1: q+1
         2: 1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        69: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       116: 1
       124: 1
       128: 1
       132: 1
       134: 1
       138: 1
       144: 1
       160: 1
       162: 1
       163: 1
       165: 1
       178: 1
       214: 1
       218: 1
       228: 1
       233: 1
       282: 1

 283:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        34: q+1
        35: q+1
        36: 2q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        55: 1
        56: q+1
        57: 1
        60: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: q+1
        99: 1
       107: 1
       119: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       183: 1
       199: 1
       201: 1
       219: 1
       223: 1
       231: 1
       283: 1

 284:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        34: q+1
        35: q+1
        36: 2q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        55: 1
        56: q+1
        57: 1
        61: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: q+1
        99: 1
       108: 1
       120: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       184: 1
       200: 1
       202: 1
       219: 1
       223: 1
       231: 1
       284: 1

 285:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        58: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
       109: 1
       117: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       185: 1
       191: 1
       195: 1
       219: 1
       225: 1
       226: 1
       285: 1

 286:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        59: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
       110: 1
       118: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       186: 1
       192: 1
       196: 1
       219: 1
       225: 1
       226: 1
       286: 1

 287:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+2
        17: q+2
        18: 1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       126: 1
       127: 1
       129: 1
       131: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       177: 1
       179: 1
       189: 1
       207: 1
       226: 1
       231: 1
       287: 1

 288:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+2
        17: q+2
        18: 1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       126: 1
       128: 1
       130: 1
       132: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       178: 1
       180: 1
       190: 1
       208: 1
       226: 1
       231: 1
       288: 1

 289:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: 1
       142: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       181: 1
       187: 1
       213: 1
       215: 1
       230: 1
       234: 1
       289: 1

 290:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: 1
       142: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       182: 1
       188: 1
       214: 1
       216: 1
       230: 1
       234: 1
       290: 1

 291:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       177: 1
       181: 1
       187: 1
       223: 1
       225: 1
       291: 1

 292:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       178: 1
       182: 1
       188: 1
       223: 1
       225: 1
       292: 1

 293:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: 1
        57: 1
        60: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       107: 1
       119: 1
       125: 1
       133: 1
       135: 1
       143: 1
       146: 1
       157: 1
       158: 1
       183: 1
       199: 1
       220: 1
       222: 1
       293: 1

 294:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: 1
        57: 1
        61: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       108: 1
       120: 1
       125: 1
       133: 1
       135: 1
       143: 1
       146: 1
       157: 1
       158: 1
       184: 1
       200: 1
       220: 1
       222: 1
       294: 1

 295:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        58: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        91: 1
        92: 1
       109: 1
       117: 1
       125: 1
       133: 1
       136: 1
       137: 1
       141: 1
       157: 1
       158: 1
       185: 1
       191: 1
       220: 1
       224: 1
       295: 1

 296:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        59: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        91: 1
        92: 1
       110: 1
       118: 1
       125: 1
       133: 1
       136: 1
       137: 1
       141: 1
       157: 1
       158: 1
       186: 1
       192: 1
       220: 1
       224: 1
       296: 1

 297:    0: 2
         1: 2
         2: q+1
         3: 2q+2
         4: 2
         5: 2q+2
         6: 2
         7: q+1
         8: q^2+2q+1
        10: 2
        11: 2q+2
        12: 2
        13: 1
        14: 1
        15: q+1
        16: 2
        17: 2
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        70: 1
        71: 2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       169: 1
       172: 1
       187: 1
       189: 1
       207: 1
       222: 1
       224: 1
       297: 1

 298:    0: 2
         1: 2
         2: q+1
         3: 2q+2
         4: 2
         5: 2q+2
         6: 2
         7: q+1
         8: q^2+2q+1
        10: 2
        11: 2q+2
        12: 2
        13: 1
        14: 1
        15: q+1
        16: 2
        17: 2
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        70: 1
        71: 2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       170: 1
       171: 1
       188: 1
       190: 1
       208: 1
       222: 1
       224: 1
       298: 1

 299:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: q+2
        23: q^2+3q+2
        24: q+2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       135: 1
       139: 1
       140: 1
       141: 1
       146: 1
       149: 1
       150: 1
       160: 1
       161: 1
       173: 1
       174: 1
       183: 1
       193: 1
       227: 1
       229: 1
       246: 1
       299: 1

 300:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: q+2
        23: q^2+3q+2
        24: q+2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       135: 1
       139: 1
       140: 1
       141: 1
       146: 1
       149: 1
       150: 1
       160: 1
       161: 1
       175: 1
       176: 1
       184: 1
       194: 1
       227: 1
       229: 1
       246: 1
       300: 1

 301:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        33: 2q+1
        36: q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        66: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       140: 1
       142: 1
       147: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       197: 1
       237: 1
       239: 1
       244: 1
       301: 1

 302:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        33: 2q+1
        36: q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       140: 1
       142: 1
       147: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       198: 1
       238: 1
       240: 1
       244: 1
       302: 1

 303:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        58: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        91: 1
        92: 1
        94: 1
        95: 1
       109: 1
       117: 1
       133: 1
       136: 1
       139: 1
       141: 1
       142: 1
       160: 1
       161: 1
       185: 1
       195: 1
       227: 1
       230: 1
       303: 1

 304:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        59: 1
        68: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        91: 1
        92: 1
        94: 1
        95: 1
       110: 1
       118: 1
       133: 1
       136: 1
       139: 1
       141: 1
       142: 1
       160: 1
       161: 1
       186: 1
       196: 1
       227: 1
       230: 1
       304: 1

 305:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: q+1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: q+1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       135: 1
       136: 1
       140: 1
       142: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       187: 1
       197: 1
       211: 1
       229: 1
       230: 1
       305: 1

 306:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: q+1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: q+1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       135: 1
       136: 1
       140: 1
       142: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       188: 1
       198: 1
       212: 1
       229: 1
       230: 1
       306: 1

 307:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        60: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       107: 1
       119: 1
       133: 1
       135: 1
       145: 1
       146: 1
       147: 1
       163: 1
       164: 1
       183: 1
       201: 1
       232: 1
       234: 1
       307: 1

 308:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        55: 1
        56: q+1
        57: 1
        61: 1
        68: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       108: 1
       120: 1
       133: 1
       135: 1
       145: 1
       146: 1
       147: 1
       163: 1
       164: 1
       184: 1
       202: 1
       232: 1
       234: 1
       308: 1

 309:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: q+2
        26: q^2+3q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       136: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       163: 1
       164: 1
       173: 1
       175: 1
       185: 1
       203: 1
       232: 1
       235: 1
       246: 1
       309: 1

 310:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+1
         5: q+2
         6: q^2+2q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: q+2
        26: q^2+3q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       136: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       163: 1
       164: 1
       174: 1
       176: 1
       186: 1
       204: 1
       232: 1
       235: 1
       246: 1
       310: 1

 311:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        33: q+1
        36: 2q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        66: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       142: 1
       147: 1
       148: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       205: 1
       237: 1
       239: 1
       245: 1
       311: 1

 312:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        33: q+1
        36: 2q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       142: 1
       147: 1
       148: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       206: 1
       238: 1
       240: 1
       245: 1
       312: 1

 313:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       135: 1
       136: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       163: 1
       164: 1
       187: 1
       205: 1
       211: 1
       234: 1
       235: 1
       313: 1

 314:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       135: 1
       136: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       163: 1
       164: 1
       188: 1
       206: 1
       212: 1
       234: 1
       235: 1
       314: 1

 315:    0: 1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: 1
         7: 1
         8: q+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        69: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       115: 1
       123: 1
       127: 1
       131: 1
       138: 1
       144: 1
       150: 1
       151: 1
       155: 1
       166: 1
       168: 1
       177: 1
       211: 1
       236: 1
       237: 1
       241: 1
       315: 1

 316:    0: 1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: 1
         7: 1
         8: q+1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        69: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       116: 1
       124: 1
       128: 1
       132: 1
       138: 1
       144: 1
       150: 1
       152: 1
       156: 1
       166: 1
       168: 1
       178: 1
       212: 1
       236: 1
       238: 1
       242: 1
       316: 1

 317:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 2
        39: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        66: 2
        71: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       106: 1
       113: 1
       127: 1
       129: 1
       139: 1
       145: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       179: 1
       209: 1
       237: 1
       239: 1
       243: 1
       317: 1

 318:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        38: 2
        40: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        67: 2
        71: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       105: 1
       114: 1
       128: 1
       130: 1
       139: 1
       145: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       180: 1
       210: 1
       238: 1
       240: 1
       243: 1
       318: 1

 319:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        72: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       104: 1
       107: 1
       139: 1
       140: 1
       145: 1
       147: 1
       149: 1
       166: 1
       167: 1
       193: 1
       201: 1
       243: 1
       244: 1
       319: 1

 320:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        72: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       105: 1
       106: 1
       108: 1
       139: 1
       140: 1
       145: 1
       147: 1
       149: 1
       166: 1
       167: 1
       194: 1
       202: 1
       243: 1
       244: 1
       320: 1

 321:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        73: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       105: 1
       109: 1
       139: 1
       142: 1
       145: 1
       148: 1
       149: 1
       166: 1
       167: 1
       195: 1
       203: 1
       243: 1
       245: 1
       321: 1

 322:    0: 2
         1: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
        10: 2
        11: 2
        12: q+1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        25: 2
        26: 2
        28: 2
        29: 1
        31: 2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 1
        73: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       106: 1
       110: 1
       139: 1
       142: 1
       145: 1
       148: 1
       149: 1
       166: 1
       167: 1
       196: 1
       204: 1
       243: 1
       245: 1
       322: 1

 323:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        33: q+1
        36: q+1
        37: q+1
        38: q
        39: q+1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        66: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       111: 1
       140: 1
       142: 1
       147: 1
       148: 1
       151: 1
       153: 1
       166: 1
       167: 1
       197: 1
       205: 1
       244: 1
       245: 1
       323: 1

 324:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        33: q+1
        36: q+1
        37: q
        38: q+1
        39: q
        40: q+1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       112: 1
       140: 1
       142: 1
       147: 1
       148: 1
       152: 1
       154: 1
       166: 1
       167: 1
       198: 1
       206: 1
       244: 1
       245: 1
       324: 1

 325:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        64: 1
        70: 1
        74: 1
        76: 1
        78: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
       100: 1
       101: 1
       102: 1
       113: 1
       115: 1
       121: 1
       141: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       189: 1
       209: 1
       211: 1
       246: 1
       325: 1

 326:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        63: 1
        65: 1
        70: 1
        75: 1
        77: 1
        79: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
       100: 1
       101: 1
       102: 1
       114: 1
       116: 1
       122: 1
       141: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       190: 1
       210: 1
       212: 1
       246: 1
       326: 1

 327:    0: q^2+2q+2
         1: q^2+2q+2
         2: q+1
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+2
        17: q+2
        19: 1
        20: 1
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: 1
        71: 1
        74: 1
        76: 1
        78: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       127: 1
       129: 1
       137: 1
       139: 1
       141: 1
       143: 1
       145: 1
       146: 1
       157: 1
       160: 1
       163: 1
       179: 1
       189: 1
       207: 1
       213: 1
       250: 1
       253: 1
       327: 1

 328:    0: q^2+2q+2
         1: q^2+2q+2
         2: q+1
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+2
        17: q+2
        19: 1
        20: 1
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: 1
        71: 1
        75: 1
        77: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       128: 1
       130: 1
       137: 1
       139: 1
       141: 1
       143: 1
       145: 1
       146: 1
       157: 1
       160: 1
       163: 1
       180: 1
       190: 1
       208: 1
       214: 1
       250: 1
       253: 1
       328: 1

 329:    0: q+2
         1: q+2
         2: q^2+2q+1
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         8: q+1
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+1
        15: 1
        16: q+2
        17: q+2
        19: 1
        20: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        45: 1
        46: q+1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        71: 1
        74: 1
        76: 1
        80: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: q+1
        89: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       106: 1
       113: 1
       121: 1
       123: 1
       127: 1
       129: 1
       137: 1
       139: 1
       143: 1
       145: 1
       158: 1
       161: 1
       164: 1
       179: 1
       207: 1
       215: 1
       251: 1
       254: 1
       329: 1

 330:    0: q+2
         1: q+2
         2: q^2+2q+1
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         8: q+1
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+1
        15: 1
        16: q+2
        17: q+2
        19: 1
        20: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        71: 1
        75: 1
        77: 1
        80: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: q+1
        89: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       105: 1
       114: 1
       122: 1
       124: 1
       128: 1
       130: 1
       137: 1
       139: 1
       143: 1
       145: 1
       158: 1
       161: 1
       164: 1
       180: 1
       208: 1
       216: 1
       251: 1
       254: 1
       330: 1

 331:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: q^2+q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        64: 1
        70: 1
        74: 1
        76: 1
        78: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       113: 1
       115: 1
       121: 1
       131: 1
       141: 1
       146: 1
       159: 1
       162: 1
       165: 1
       189: 1
       217: 1
       252: 1
       255: 1
       331: 1

 332:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: q^2+q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        63: 1
        65: 1
        70: 1
        75: 1
        77: 1
        79: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       114: 1
       116: 1
       122: 1
       132: 1
       141: 1
       146: 1
       159: 1
       162: 1
       165: 1
       190: 1
       218: 1
       252: 1
       255: 1
       332: 1

 333:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        28: 1
        29: 1
        30: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        68: 1
        69: 1
        70: 1
        71: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       125: 1
       126: 1
       133: 1
       134: 1
       157: 1
       158: 1
       159: 1
       219: 1
       220: 1
       221: 1
       333: 1

 334:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: q+2
        17: q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: q+2
        30: 1
        34: 2
        35: 1
        36: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        55: 2
        56: 2
        57: q+1
        60: 1
        61: 1
        69: 1
        70: 1
        71: q+2
        72: 2
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 2
        98: 2
        99: q+1
       107: 1
       108: 1
       126: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: 1
       158: 1
       159: 1
       201: 1
       202: 1
       221: 1
       222: 1
       223: 1
       231: 1
       334: 1

 335:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: q+2
        17: q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        28: q+2
        29: q+2
        30: 1
        31: 2
        32: 1
        33: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        58: 1
        59: 1
        69: 1
        70: 1
        71: q+2
        73: 2
        80: 1
        81: 1
        82: 2
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
       109: 1
       110: 1
       126: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       157: 1
       158: 1
       159: 1
       195: 1
       196: 1
       221: 1
       224: 1
       225: 1
       226: 1
       335: 1

 336:    0: q^2+3q+2
         1: 2
         2: 4q+2
         3: 2q+2
         4: q^2+3q+2
         5: 2q+2
         6: 2
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: q+2
        17: 2
        18: 2q+1
        19: q^2+3q+2
        20: 2
        21: 4q+2
        22: q+2
        23: 2
        24: 3q+2
        25: q+2
        26: 2
        27: 3q+2
        30: 2q+2
        32: q+2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        46: 2
        47: 2
        48: q+1
        49: q+2
        50: 2
        51: 2q+1
        52: q+2
        53: 2
        54: 3q+2
        55: q+2
        56: 2
        57: 3q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: q+1
        79: q+1
        81: 2
        83: q+2
        85: 2
        87: q+2
        91: 2
        92: 2
        93: q+1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       142: 1
       144: 1
       147: 1
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       166: 1
       168: 1
       187: 1
       188: 1
       211: 1
       212: 1
       223: 1
       225: 1
       236: 1
       247: 1
       249: 1
       336: 1

 337:    0: 3q+4
         1: 3q+4
         3: 4q+4
         4: 3q+4
         5: 4q+4
         6: 3q+4
        10: 3q+4
        11: 4q+4
        12: 3q+4
        16: q+4
        17: q+4
        19: 3q+4
        20: 3q+4
        22: q+4
        23: q+4
        25: q+4
        26: q+4
        28: q+4
        29: 3q+4
        31: q+4
        33: 4
        34: q+4
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        49: q+4
        50: q+4
        52: q+4
        53: q+4
        55: q+4
        56: q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        66: 2
        67: 2
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        82: q+4
        86: q+4
        94: 2
        95: 2
        97: 2
        98: 2
       100: 2
       101: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       139: 2
       142: 2
       145: 2
       147: 2
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       169: 1
       170: 1
       171: 1
       172: 1
       195: 1
       196: 1
       201: 1
       202: 1
       209: 1
       210: 1
       243: 1
       247: 1
       248: 1
       337: 1

 338:    0: q+1
         1: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
        16: q+1
        17: 1
        19: q+1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       111: 1
       127: 1
       129: 1
       142: 1
       147: 1
       151: 1
       166: 1
       181: 1
       237: 1
       247: 1
       338: 1

 339:    0: q+1
         1: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
        16: q+1
        17: 1
        19: q+1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       112: 1
       128: 1
       130: 1
       142: 1
       147: 1
       152: 1
       166: 1
       182: 1
       238: 1
       247: 1
       339: 1

 340:    0: 1
         1: q+1
         3: 1
         4: 1
         5: q+1
         6: q+1
        16: 1
        17: q+1
        19: 1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       101: 1
       111: 1
       127: 1
       129: 1
       142: 1
       147: 1
       153: 1
       167: 1
       181: 1
       239: 1
       248: 1
       340: 1

 341:    0: 1
         1: q+1
         3: 1
         4: 1
         5: q+1
         6: q+1
        16: 1
        17: q+1
        19: 1
        20: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: q+1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       101: 1
       112: 1
       128: 1
       130: 1
       142: 1
       147: 1
       154: 1
       167: 1
       182: 1
       240: 1
       248: 1
       341: 1

 342:    2: 1
         7: 1
         8: 1
         9: 1
        18: 1
        21: 1
        24: 1
        27: 1
        41: 1
        51: 1
        54: 1
        57: 1
        78: 1
        96: 1
        99: 1
       102: 1
       131: 1
       155: 1
       168: 1
       241: 1
       249: 1
       342: 1

 343:    2: 1
         7: 1
         8: 1
         9: 1
        18: 1
        21: 1
        24: 1
        27: 1
        42: 1
        51: 1
        54: 1
        57: 1
        79: 1
        96: 1
        99: 1
       102: 1
       132: 1
       156: 1
       168: 1
       242: 1
       249: 1
       343: 1

 344:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q^2+q+1
         7: q+1
         8: q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: q+2
        33: q+2
        43: 2
        44: q+1
        45: 2
        46: q+2
        47: q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        59: 1
        68: 2
        69: 1
        70: 1
        71: 1
        80: 2
        81: q+2
        82: 1
        83: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       117: 1
       118: 1
       125: 2
       126: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       160: 1
       161: 1
       162: 1
       191: 1
       192: 1
       219: 1
       226: 1
       227: 1
       228: 1
       344: 1

 345:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        58: 1
        59: 1
        68: 2
        70: 1
        71: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
       117: 1
       118: 1
       125: 2
       133: 1
       137: 2
       139: 1
       141: 1
       157: 1
       158: 1
       160: 1
       161: 1
       191: 1
       192: 1
       220: 1
       227: 1
       250: 1
       251: 1
       345: 1

 346:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2
        23: 2
        24: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        58: 1
        59: 1
        69: 1
        70: 1
        71: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
       126: 1
       134: 1
       137: 1
       138: 1
       139: 1
       141: 1
       157: 1
       159: 1
       160: 1
       162: 1
       221: 1
       226: 1
       228: 1
       250: 1
       252: 1
       346: 1

 347:    0: 2q+4
         1: 2q+4
         2: q^2+3q+2
         3: 2q+4
         4: 2q+2
         5: 2q+4
         6: 2q+2
         7: q^2+2q+1
         8: q^2+3q+2
        10: 2q+4
        11: 2q+4
        12: 2q+2
        13: q+2
        14: q+1
        15: q+2
        16: 4
        17: 4
        19: 2
        20: 2
        21: q+1
        22: 2q+4
        23: 2q+4
        24: q^2+3q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 2
        30: 1
        31: 2q+4
        32: q+2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 1
        71: 2
        72: 2
        80: q+2
        81: 2
        82: 2
        83: 1
        84: 2
        85: 2
        86: 2
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 2
        95: 2
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 1
       137: 2
       139: 2
       140: 2
       141: 1
       143: 2
       146: 1
       149: 2
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       193: 1
       194: 1
       207: 1
       208: 1
       222: 1
       229: 1
       246: 1
       250: 1
       251: 1
       347: 1

 348:    0: q+2
         1: q+2
         2: q^2+2
         3: q+2
         4: q^2+2q+1
         5: q+2
         6: q+1
         7: q+1
         8: q^2+2
         9: q+1
        13: 2
        14: q+1
        15: 2
        16: q+2
        17: q+2
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q^2+2
        25: 2
        26: 2
        27: 2
        30: 1
        32: 2
        33: q+2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       134: 1
       135: 1
       138: 1
       140: 1
       144: 1
       147: 1
       150: 1
       160: 1
       161: 1
       162: 1
       166: 1
       167: 1
       168: 1
       223: 1
       228: 1
       229: 1
       236: 1
       244: 1
       348: 1

 349:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        28: 2
        29: q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        58: 1
        59: 1
        70: 1
        71: 2
        73: 2
        80: 1
        81: 1
        82: q+2
        83: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
       109: 1
       110: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       157: 1
       158: 1
       160: 1
       161: 1
       195: 1
       196: 1
       224: 1
       230: 1
       250: 1
       251: 1
       349: 1

 350:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        30: 1
        32: 1
        33: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        69: 1
        73: 1
        81: 1
        83: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       134: 1
       136: 1
       138: 1
       142: 1
       160: 1
       161: 1
       162: 1
       225: 1
       228: 1
       230: 1
       350: 1

 351:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: q+2
        23: q+2
        25: 2
        26: 2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        55: 2
        56: 2
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2
       111: 1
       112: 1
       140: 2
       142: 2
       147: 1
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       197: 1
       198: 1
       244: 1
       247: 1
       248: 1
       351: 1

 352:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q^2+q+1
         7: q+1
         8: q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        34: 2
        35: q+2
        36: q+2
        43: 2
        44: q+1
        45: 2
        46: q+2
        47: q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        68: 2
        69: 1
        70: 1
        71: 1
        84: 2
        85: q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       119: 1
       120: 1
       125: 2
       126: 1
       133: 1
       134: 1
       143: 2
       144: 1
       145: 1
       146: 1
       163: 1
       164: 1
       165: 1
       199: 1
       200: 1
       219: 1
       231: 1
       232: 1
       233: 1
       352: 1

 353:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        34: q+2
        35: q+2
        36: 2
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        68: 2
        70: 1
        71: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        97: 1
        98: 1
       119: 1
       120: 1
       125: 2
       133: 1
       143: 2
       145: 1
       146: 1
       157: 1
       158: 1
       163: 1
       164: 1
       199: 1
       200: 1
       220: 1
       232: 1
       253: 1
       254: 1
       353: 1

 354:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        34: 2
        35: 1
        36: 2
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        50: 1
        51: q+1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        69: 1
        70: 1
        71: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q+1
        91: 1
        93: 1
        97: 1
        98: 1
        99: q+1
       126: 1
       134: 1
       143: 1
       144: 1
       145: 1
       146: 1
       157: 1
       159: 1
       163: 1
       165: 1
       221: 1
       231: 1
       233: 1
       253: 1
       255: 1
       354: 1

 355:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: q+2
        30: 1
        34: q+2
        35: 1
        36: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        55: q+2
        56: q+2
        57: q+1
        60: 1
        61: 1
        70: 1
        71: 2
        72: 2
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 2
        98: 2
       107: 1
       108: 1
       135: 1
       143: 1
       145: 2
       146: 1
       147: 2
       157: 1
       158: 1
       163: 1
       164: 1
       201: 1
       202: 1
       222: 1
       234: 1
       253: 1
       254: 1
       355: 1

 356:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        30: 1
        35: 1
        36: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        69: 1
        72: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       134: 1
       135: 1
       144: 1
       147: 1
       163: 1
       164: 1
       165: 1
       223: 1
       233: 1
       234: 1
       356: 1

 357:    0: 2q+4
         1: 2q+4
         2: q^2+3q+2
         3: 2q+4
         4: 2q+2
         5: 2q+4
         6: 2q+2
         7: q^2+2q+1
         8: q^2+3q+2
        10: 2q+4
        11: 2q+4
        12: 2q+2
        13: q+2
        14: q+1
        15: q+2
        16: 4
        17: 4
        19: 2
        20: 2
        21: q+1
        22: 4
        23: 4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: q^2+3q+2
        28: 4
        29: 2
        30: 1
        31: 4
        32: 2
        33: 4
        34: 2q+4
        35: q+2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 1
        71: 2
        73: 2
        80: 2
        81: 2
        82: 2
        83: 1
        84: q+2
        85: 2
        86: 2
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        97: 2
        98: 2
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       121: 1
       122: 1
       123: 1
       124: 1
       136: 1
       137: 2
       141: 1
       143: 2
       145: 2
       146: 1
       148: 2
       149: 2
       150: 1
       157: 1
       158: 1
       163: 1
       164: 1
       203: 1
       204: 1
       207: 1
       208: 1
       224: 1
       235: 1
       246: 1
       253: 1
       254: 1
       357: 1

 358:    0: q+2
         1: q+2
         2: q^2+2
         3: q+2
         4: q^2+2q+1
         5: q+2
         6: q+1
         7: q+1
         8: q^2+2
         9: q+1
        13: 2
        14: q+1
        15: 2
        16: q+2
        17: q+2
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q^2+2
        30: 1
        32: 2
        33: 2
        35: 2
        36: q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        73: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       134: 1
       136: 1
       138: 1
       142: 1
       144: 1
       148: 1
       150: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       225: 1
       233: 1
       235: 1
       236: 1
       245: 1
       358: 1

 359:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: 2
        23: 2
        25: q+2
        26: q+2
        33: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: 2
        53: 2
        55: q+2
        56: q+2
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2
       111: 1
       112: 1
       142: 1
       147: 2
       148: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       205: 1
       206: 1
       245: 1
       247: 1
       248: 1
       359: 1

 360:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: q+1
         8: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: 1
        47: 1
        49: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        94: 1
        97: 1
       100: 1
       102: 1
       115: 1
       123: 1
       127: 1
       150: 1
       151: 1
       155: 1
       160: 1
       163: 1
       166: 1
       211: 1
       213: 1
       237: 1
       256: 1
       360: 1

 361:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: q+1
         8: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: 1
        47: 1
        49: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        94: 1
        97: 1
       100: 1
       102: 1
       116: 1
       124: 1
       128: 1
       150: 1
       152: 1
       156: 1
       160: 1
       163: 1
       166: 1
       212: 1
       214: 1
       238: 1
       256: 1
       361: 1

 362:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: q^2+q+1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        50: 1
        53: 1
        56: 1
        64: 1
        66: 1
        76: 1
        81: 1
        85: 1
        92: 1
        95: 1
        98: 1
       101: 1
       123: 1
       129: 1
       153: 1
       161: 1
       164: 1
       167: 1
       215: 1
       239: 1
       257: 1
       362: 1

 363:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: q^2+q+1
         8: 1
        13: 1
        15: 1
        16: 1
        17: 1
        20: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        50: 1
        53: 1
        56: 1
        65: 1
        67: 1
        77: 1
        81: 1
        85: 1
        92: 1
        95: 1
        98: 1
       101: 1
       124: 1
       130: 1
       154: 1
       161: 1
       164: 1
       167: 1
       216: 1
       240: 1
       257: 1
       363: 1

 364:    0: q+1
         2: q+1
         4: 1
         5: q+1
         7: 1
         8: q+1
         9: q+1
        13: q+1
        14: 1
        15: q+1
        18: 1
        19: 1
        21: 1
        22: q+1
        24: q+1
        25: q+1
        27: q+1
        30: 1
        32: q+1
        35: q+1
        37: q+1
        41: q+1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: q+1
        74: 1
        78: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       100: 1
       102: 1
       115: 1
       131: 1
       150: 1
       151: 1
       155: 1
       162: 1
       165: 1
       168: 1
       211: 1
       217: 1
       241: 1
       258: 1
       364: 1

 365:    0: q+1
         2: q+1
         4: 1
         5: q+1
         7: 1
         8: q+1
         9: q+1
        13: q+1
        14: 1
        15: q+1
        18: 1
        19: 1
        21: 1
        22: q+1
        24: q+1
        25: q+1
        27: q+1
        30: 1
        32: q+1
        35: q+1
        38: q+1
        42: q+1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: q+1
        75: 1
        79: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       100: 1
       102: 1
       116: 1
       132: 1
       150: 1
       152: 1
       156: 1
       162: 1
       165: 1
       168: 1
       212: 1
       218: 1
       242: 1
       258: 1
       365: 1

 366:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: q^2+2q+1
         5: 4
         6: q^2+2q+1
         7: q+1
         8: 2q+2
         9: q+1
        10: 4
        11: 4
        12: q^2+2q+1
        13: 2
        14: q+1
        15: 2
        16: 4
        17: 4
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 1
        30: 1
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       166: 1
       167: 1
       168: 1
       207: 1
       208: 1
       226: 1
       231: 1
       236: 1
       243: 1
       246: 1
       366: 1

 367:    0: 4
         1: 4q+4
         2: 4
         3: 4q+4
         4: 2q+1
         5: 4
         6: 2q^2+3q+1
         7: 2q+1
         8: 4
        10: 4
        11: 4
        12: 2q+1
        13: 4
        14: 2q+1
        15: 4
        16: 4
        17: 4
        19: 1
        20: q+1
        21: 1
        22: 4
        23: 4q+4
        24: 4
        25: 4
        26: 4q+4
        27: 4
        28: 4
        29: 1
        30: 1
        31: 4
        32: 4
        33: 4
        34: 4
        35: 4
        36: 4
        37: 2
        38: 2
        39: 2q+2
        40: 2q+2
        41: 2
        42: 2
        43: 4
        44: 2q+1
        45: 4
        46: 4
        47: 4
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: 4
        70: 1
        71: 1
        80: 4
        81: 4
        82: 1
        83: 1
        84: 4
        85: 4
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       133: 1
       139: 1
       141: 1
       145: 1
       146: 1
       149: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       174: 1
       175: 1
       176: 1
       227: 1
       232: 1
       243: 1
       246: 1
       256: 1
       257: 1
       367: 1

 368:    0: 2
         1: 2
         2: 2
         3: 2
         4: 2q+1
         5: 2
         7: 2q+1
         8: 2
         9: 2q+1
        13: 2
        14: 2q+1
        15: 2
        16: 2
        17: 2
        18: 2q+1
        19: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: 2q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       123: 1
       124: 1
       134: 1
       138: 1
       144: 1
       150: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       168: 1
       228: 1
       233: 1
       236: 1
       256: 1
       258: 1
       368: 1

 369:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        72: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       123: 1
       124: 1
       135: 1
       140: 1
       147: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       229: 1
       234: 1
       244: 1
       256: 1
       257: 1
       369: 1

 370:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        73: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       123: 1
       124: 1
       136: 1
       142: 1
       148: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       230: 1
       235: 1
       245: 1
       256: 1
       257: 1
       370: 1

 371:    0: 3q+2
         1: 2q+2
         2: 3q+2
         3: 2q^2+4q+2
         4: 3q+2
         5: 2q+2
         6: 2q+2
         7: 3q+2
         8: 2q+2
        13: 3q+2
        14: 3q+2
        15: 2q+2
        16: q+2
        17: 2
        19: 3q+2
        20: 2q+2
        21: 3q+2
        22: q+2
        23: 2q+2
        24: q+2
        25: q+2
        26: 2q+2
        27: q+2
        30: 3q+2
        32: q+2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: q+2
        47: 2
        49: q+2
        50: 2
        52: q+2
        53: 2q+2
        54: q+2
        55: q+2
        56: 2q+2
        57: q+2
        64: 1
        65: 1
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 2
        83: q+2
        85: 2
        87: q+2
        91: q+2
        92: 2
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       135: 2
       136: 2
       142: 1
       147: 1
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       187: 1
       188: 1
       211: 1
       212: 1
       230: 1
       234: 1
       247: 1
       256: 1
       371: 1

 372:    0: 2
         1: q^2+3q+2
         2: 2
         3: 2q+2
         4: 2
         5: 2q+2
         6: q^2+3q+2
         7: 2
         8: 2q+2
        13: 2
        14: 2
        15: 2q+2
        16: 2
        17: q+2
        19: 2
        20: q^2+3q+2
        21: 2
        22: 2
        23: q+2
        24: 2
        25: 2
        26: q+2
        27: 2
        30: 2
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: q+2
        49: 2
        50: q+2
        52: 2
        53: q+2
        54: 2
        55: 2
        56: q+2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: 2
        91: 2
        92: q+2
        94: 1
        95: 1
        97: 1
        98: 1
       101: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       135: 2
       136: 2
       142: 1
       147: 1
       153: 1
       154: 1
       160: 1
       161: 1
       163: 1
       164: 1
       167: 1
       187: 1
       188: 1
       230: 1
       234: 1
       248: 1
       257: 1
       372: 1

 373:    0: 2
         2: 2
         4: 2
         5: 2
         7: 2
         8: 2
         9: q^2+q+1
        13: 2
        14: 2
        15: 2
        18: 1
        19: 2
        21: 2
        22: 2
        24: 2
        25: 2
        27: 2
        30: 2
        32: 2
        35: 2
        37: 1
        38: 1
        41: 1
        42: 1
        48: 1
        51: 1
        52: 2
        54: 2
        55: 2
        57: 2
        64: 1
        65: 1
        74: 1
        75: 1
        78: 1
        79: 1
        83: 2
        87: 2
        93: 1
        96: 1
        99: 1
       100: 2
       102: 2
       115: 1
       116: 1
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       162: 1
       165: 1
       168: 1
       211: 1
       212: 1
       249: 1
       258: 1
       373: 1

 374:    0: 2q+4
         1: 2q+4
         2: 2q+2
         3: 2q+4
         4: 2q+1
         5: 2q+4
         6: 2q+1
         7: 2q^2+3q+1
         8: 2q+2
        10: 2q+4
        11: 2q+4
        12: 2q+1
        13: 2
        14: 2q+1
        15: 2
        16: 4
        17: 4
        19: 1
        20: 1
        21: q+1
        22: 2q+4
        23: 2q+4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: 2q+2
        28: 4
        29: 1
        30: 1
        31: 2q+4
        32: 2
        33: 4
        34: 2q+4
        35: 2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: 2
        44: 2q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 1
        71: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       121: 1
       122: 1
       123: 1
       124: 1
       137: 2
       139: 1
       141: 1
       143: 2
       145: 1
       146: 1
       149: 1
       150: 1
       157: 1
       160: 1
       163: 1
       166: 1
       167: 1
       207: 1
       208: 1
       243: 1
       246: 1
       250: 1
       253: 1
       256: 1
       374: 1

 375:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: q^2+2q+1
         5: 4
         6: q^2+2q+1
         8: 2q+2
        10: 4
        11: 4
        12: q^2+2q+1
        13: 2
        15: 2
        16: 4
        17: 4
        19: 1
        20: 1
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 1
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        71: 1
        80: 2
        81: 2
        82: 1
        84: 2
        85: 2
        86: 1
        88: 2
        89: 2
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       121: 1
       122: 1
       123: 1
       124: 1
       137: 2
       139: 1
       143: 2
       145: 1
       149: 1
       158: 1
       161: 1
       164: 1
       166: 1
       167: 1
       207: 1
       208: 1
       243: 1
       251: 1
       254: 1
       257: 1
       375: 1

 376:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: 2q^2+2q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        29: 1
        30: 1
        31: 2
        32: 2
        34: 2
        35: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        48: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        63: 1
        64: 1
        65: 1
        70: 1
        80: 2
        82: 1
        83: 1
        84: 2
        86: 1
        87: 1
        90: q+1
        93: 1
        96: 1
        99: 1
       100: 1
       101: 1
       102: 1
       121: 1
       122: 1
       141: 1
       146: 1
       149: 1
       150: 1
       159: 1
       162: 1
       165: 1
       168: 1
       246: 1
       252: 1
       255: 1
       258: 1
       376: 1

 377:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: q+1
        60: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: 1
       259: 1
       263: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       377: 1

 378:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: q+1
        60: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: 1
       260: 1
       264: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       378: 1

 379:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: q+1
        61: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: 1
       261: 1
       265: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       379: 1

 380:    0: q^2+3q+1
         1: 3q+1
         2: q+1
         3: q^2+3q+1
         4: q+1
         5: 3q+1
         6: q^2+2q+1
         7: 1
         8: q^2+2q+1
         9: 1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: 1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: 1
        19: q+1
        20: 2q+1
        21: 1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: 1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: q+1
        61: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: 1
       262: 1
       266: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       380: 1

 381:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       195: 1
       201: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: 1
       234: 1
       259: 1
       263: 1
       279: 1
       289: 1
       303: 1
       307: 1
       381: 1

 382:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       196: 1
       201: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: 1
       234: 1
       260: 1
       264: 1
       280: 1
       290: 1
       304: 1
       307: 1
       382: 1

 383:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       195: 1
       202: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: 1
       234: 1
       261: 1
       265: 1
       280: 1
       290: 1
       303: 1
       308: 1
       383: 1

 384:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: 1
       163: 1
       164: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       196: 1
       202: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: 1
       234: 1
       262: 1
       266: 1
       279: 1
       289: 1
       304: 1
       308: 1
       384: 1

 385:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       199: 1
       207: 1
       220: 1
       222: 1
       224: 1
       263: 1
       275: 1
       293: 1
       295: 1
       297: 1
       385: 1

 386:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       199: 1
       208: 1
       220: 1
       222: 1
       224: 1
       264: 1
       276: 1
       293: 1
       296: 1
       298: 1
       386: 1

 387:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       200: 1
       208: 1
       220: 1
       222: 1
       224: 1
       265: 1
       277: 1
       294: 1
       295: 1
       298: 1
       387: 1

 388:    0: 1
         1: 1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       146: 1
       157: 1
       158: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       200: 1
       207: 1
       220: 1
       222: 1
       224: 1
       266: 1
       278: 1
       294: 1
       296: 1
       297: 1
       388: 1

 389:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        28: 2q+1
        29: q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        36: q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q+1
        59: q
        60: q+1
        62: q+1
        66: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: q+1
       140: 1
       142: 1
       145: 1
       147: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       193: 1
       195: 1
       197: 1
       201: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       259: 1
       267: 1
       301: 1
       317: 1
       319: 1
       389: 1

 390:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        28: 2q+1
        29: q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        36: q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q
        59: q+1
        60: q+1
        63: q+1
        67: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: q+1
       140: 1
       142: 1
       145: 1
       147: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       193: 1
       196: 1
       198: 1
       201: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       260: 1
       268: 1
       302: 1
       318: 1
       319: 1
       390: 1

 391:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        28: 2q+1
        29: q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        36: q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q
        59: q+1
        61: q+1
        62: q+1
        66: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: q+1
       140: 1
       142: 1
       145: 1
       147: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       194: 1
       196: 1
       197: 1
       202: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       262: 1
       269: 1
       301: 1
       317: 1
       320: 1
       391: 1

 392:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: q+1
        26: q+1
        28: 2q+1
        29: q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        36: q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q+1
        59: q
        61: q+1
        63: q+1
        67: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: q+1
       140: 1
       142: 1
       145: 1
       147: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       194: 1
       195: 1
       198: 1
       202: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       261: 1
       270: 1
       302: 1
       318: 1
       320: 1
       392: 1

 393:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       193: 1
       195: 1
       197: 1
       209: 1
       211: 1
       227: 1
       229: 1
       230: 1
       246: 1
       263: 1
       267: 1
       299: 1
       303: 1
       305: 1
       325: 1
       393: 1

 394:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       193: 1
       196: 1
       198: 1
       210: 1
       212: 1
       227: 1
       229: 1
       230: 1
       246: 1
       264: 1
       268: 1
       299: 1
       304: 1
       306: 1
       326: 1
       394: 1

 395:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       194: 1
       195: 1
       198: 1
       210: 1
       212: 1
       227: 1
       229: 1
       230: 1
       246: 1
       265: 1
       270: 1
       300: 1
       303: 1
       306: 1
       326: 1
       395: 1

 396:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       194: 1
       196: 1
       197: 1
       209: 1
       211: 1
       227: 1
       229: 1
       230: 1
       246: 1
       266: 1
       269: 1
       300: 1
       304: 1
       305: 1
       325: 1
       396: 1

 397:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        28: 2q+1
        29: q+1
        31: q+1
        33: q+1
        34: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: q+1
        60: q+1
        61: q
        62: q+1
        66: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: q+1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       195: 1
       201: 1
       203: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       245: 1
       259: 1
       271: 1
       311: 1
       317: 1
       321: 1
       397: 1

 398:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        28: 2q+1
        29: q+1
        31: q+1
        33: q+1
        34: 2q+1
        36: 2q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: q+1
        60: q
        61: q+1
        63: q+1
        67: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: q+1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       195: 1
       202: 1
       203: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       245: 1
       261: 1
       272: 1
       312: 1
       318: 1
       321: 1
       398: 1

 399:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        28: 2q+1
        29: q+1
        31: q+1
        33: q+1
        34: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: q+1
        60: q
        61: q+1
        62: q+1
        66: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: q+1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       196: 1
       202: 1
       204: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       245: 1
       262: 1
       273: 1
       311: 1
       317: 1
       322: 1
       399: 1

 400:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        28: 2q+1
        29: q+1
        31: q+1
        33: q+1
        34: 2q+1
        36: 2q+1
        38: q+1
        40: q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q
        63: q+1
        67: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: q+1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       196: 1
       201: 1
       204: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       245: 1
       260: 1
       274: 1
       312: 1
       318: 1
       322: 1
       400: 1

 401:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       141: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       163: 1
       164: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       201: 1
       203: 1
       205: 1
       209: 1
       211: 1
       232: 1
       234: 1
       235: 1
       246: 1
       263: 1
       271: 1
       307: 1
       309: 1
       313: 1
       325: 1
       401: 1

 402:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       141: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       163: 1
       164: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       232: 1
       234: 1
       235: 1
       246: 1
       265: 1
       272: 1
       308: 1
       309: 1
       314: 1
       326: 1
       402: 1

 403:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       141: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       163: 1
       164: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       201: 1
       204: 1
       206: 1
       210: 1
       212: 1
       232: 1
       234: 1
       235: 1
       246: 1
       264: 1
       274: 1
       307: 1
       310: 1
       314: 1
       326: 1
       403: 1

 404:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       133: 1
       135: 1
       136: 1
       141: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       163: 1
       164: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       232: 1
       234: 1
       235: 1
       246: 1
       266: 1
       273: 1
       308: 1
       310: 1
       313: 1
       325: 1
       404: 1

 405:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        28: q+1
        29: q+1
        31: 2q+1
        33: q+1
        34: 2q+1
        36: q+1
        37: q+1
        38: q
        39: q+1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        58: q+1
        60: q+1
        62: q+1
        63: q
        66: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       243: 1
       244: 1
       245: 1
       267: 1
       271: 1
       319: 1
       321: 1
       323: 1
       405: 1

 406:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        28: q+1
        29: q+1
        31: 2q+1
        33: q+1
        34: 2q+1
        36: q+1
        37: q+1
        38: q
        39: q+1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        59: q+1
        61: q+1
        62: q+1
        63: q
        66: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       243: 1
       244: 1
       245: 1
       269: 1
       273: 1
       320: 1
       322: 1
       323: 1
       406: 1

 407:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        28: q+1
        29: q+1
        31: 2q+1
        33: q+1
        34: 2q+1
        36: q+1
        37: q
        38: q+1
        39: q
        40: q+1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        62: q
        63: q+1
        67: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       243: 1
       244: 1
       245: 1
       268: 1
       274: 1
       319: 1
       322: 1
       324: 1
       407: 1

 408:    0: 2q+1
         1: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        28: q+1
        29: q+1
        31: 2q+1
        33: q+1
        34: 2q+1
        36: q+1
        37: q
        38: q+1
        39: q
        40: q+1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        58: q+1
        61: q+1
        62: q
        63: q+1
        67: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       243: 1
       244: 1
       245: 1
       270: 1
       272: 1
       320: 1
       321: 1
       324: 1
       408: 1

 409:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: 2q+2
         4: q^2+q+1
         5: 2q+2
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+2
        10: q^2+2q+2
        11: 2q+2
        12: q^2+q+1
        13: q^2+2q+2
        14: q^2+q+1
        15: 2q+2
        16: q+2
        17: q+2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+2q+2
        44: q^2+q+1
        45: 2q+2
        46: q+2
        47: q+2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: q+2
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: q+2
       127: 1
       129: 1
       133: 1
       137: 2
       139: 1
       141: 1
       143: 2
       145: 1
       146: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       173: 1
       176: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       213: 1
       215: 1
       220: 1
       227: 1
       232: 1
       250: 1
       251: 1
       253: 1
       254: 1
       275: 1
       278: 1
       279: 1
       327: 1
       329: 1
       345: 1
       353: 1
       409: 1

 410:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: 2q+2
         4: q^2+q+1
         5: 2q+2
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+2
        10: q^2+2q+2
        11: 2q+2
        12: q^2+q+1
        13: q^2+2q+2
        14: q^2+q+1
        15: 2q+2
        16: q+2
        17: q+2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+2q+2
        44: q^2+q+1
        45: 2q+2
        46: q+2
        47: q+2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: q+2
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: q+2
       128: 1
       130: 1
       133: 1
       137: 2
       139: 1
       141: 1
       143: 2
       145: 1
       146: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       174: 1
       175: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       214: 1
       216: 1
       220: 1
       227: 1
       232: 1
       250: 1
       251: 1
       253: 1
       254: 1
       276: 1
       277: 1
       280: 1
       328: 1
       330: 1
       345: 1
       353: 1
       410: 1

 411:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       126: 1
       127: 1
       129: 1
       131: q+1
       134: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       177: 1
       179: 1
       189: 1
       207: 1
       213: 1
       217: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       250: 1
       252: 1
       253: 1
       255: 1
       281: 1
       287: 1
       327: 1
       331: 1
       346: 1
       354: 1
       411: 1

 412:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       126: 1
       128: 1
       130: 1
       132: q+1
       134: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       178: 1
       180: 1
       190: 1
       208: 1
       214: 1
       218: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       250: 1
       252: 1
       253: 1
       255: 1
       282: 1
       288: 1
       328: 1
       332: 1
       346: 1
       354: 1
       412: 1

 413:    0: 2q+2
         1: q^2+2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: q^2+2q+2
         6: q^2+q+1
         7: q+1
         8: q^2+2q+2
         9: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 2q+2
        14: q+1
        15: q^2+2q+2
        16: 2q+2
        17: q^2+2q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        37: q+2
        39: q+2
        41: q+2
        43: q+2
        44: q+1
        45: q+2
        46: 2q+2
        47: q^2+2q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: q+2
        66: q+2
        68: q+2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 2
        81: q+2
        82: 1
        83: 1
        84: 2
        85: q+2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: q+2
       125: q+2
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       173: 1
       176: 1
       177: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       213: 1
       215: 1
       217: 1
       219: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       275: 1
       278: 1
       279: 1
       281: 1
       287: 1
       344: 1
       352: 1
       413: 1

 414:    0: 2q+2
         1: q^2+2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: q^2+2q+2
         6: q^2+q+1
         7: q+1
         8: q^2+2q+2
         9: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 2q+2
        14: q+1
        15: q^2+2q+2
        16: 2q+2
        17: q^2+2q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        38: q+2
        40: q+2
        42: q+2
        43: q+2
        44: q+1
        45: q+2
        46: 2q+2
        47: q^2+2q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: q+2
        67: q+2
        68: q+2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 2
        81: q+2
        82: 1
        83: 1
        84: 2
        85: q+2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: q+2
       125: q+2
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       174: 1
       175: 1
       178: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       214: 1
       216: 1
       218: 1
       219: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       276: 1
       277: 1
       280: 1
       282: 1
       288: 1
       344: 1
       352: 1
       414: 1

 415:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2
        98: 2
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       213: 1
       215: 1
       222: 1
       224: 1
       230: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       259: 1
       262: 1
       289: 1
       297: 1
       327: 1
       329: 1
       349: 1
       355: 1
       415: 1

 416:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2
        98: 2
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       214: 1
       216: 1
       222: 1
       224: 1
       230: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       260: 1
       261: 1
       290: 1
       298: 1
       328: 1
       330: 1
       349: 1
       355: 1
       416: 1

 417:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       177: 1
       181: 1
       187: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       281: 1
       289: 1
       291: 1
       350: 1
       356: 1
       417: 1

 418:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       178: 1
       182: 1
       188: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       282: 1
       290: 1
       292: 1
       350: 1
       356: 1
       418: 1

 419:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       107: 1
       119: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       183: 1
       199: 1
       201: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       283: 1
       293: 1
       333: 1
       334: 1
       419: 1

 420:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        55: 1
        56: 1
        57: 1
        61: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       108: 1
       120: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       184: 1
       200: 1
       202: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       284: 1
       294: 1
       333: 1
       334: 1
       420: 1

 421:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
       109: 1
       117: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: q+1
       159: 1
       185: 1
       191: 1
       195: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       285: 1
       295: 1
       333: 1
       335: 1
       421: 1

 422:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        59: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
       110: 1
       118: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: q+1
       159: 1
       186: 1
       192: 1
       196: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       286: 1
       296: 1
       333: 1
       335: 1
       422: 1

 423:    0: 2q+2
         1: 2q+2
         2: q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q+1
         8: q^3+2q^2+2q+1
         9: q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: 1
       158: q+1
       159: 1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       259: 1
       262: 1
       287: 1
       291: 1
       297: 1
       334: 1
       335: 1
       423: 1

 424:    0: 2q+2
         1: 2q+2
         2: q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q+1
         8: q^3+2q^2+2q+1
         9: q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: 1
       158: q+1
       159: 1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       260: 1
       261: 1
       288: 1
       292: 1
       298: 1
       334: 1
       335: 1
       424: 1

 425:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q^2+q+1
         9: q+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        64: 1
        66: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q+1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       151: 1
       155: 1
       166: 1
       168: 1
       177: 1
       181: 1
       187: 1
       211: 1
       223: 1
       225: 1
       236: 1
       237: 1
       241: 1
       247: 1
       249: 1
       291: 1
       315: 1
       336: 1
       338: 1
       342: 1
       425: 1

 426:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q^2+q+1
         9: q+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: q+1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        65: 1
        67: 1
        69: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: q+1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       152: 1
       156: 1
       166: 1
       168: 1
       178: 1
       182: 1
       188: 1
       212: 1
       223: 1
       225: 1
       236: 1
       238: 1
       242: 1
       247: 1
       249: 1
       292: 1
       316: 1
       336: 1
       339: 1
       343: 1
       426: 1

 427:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: q+2
        17: q+2
        19: q+2
        20: q+2
        22: 2
        23: 2
        25: 2
        26: 2
        28: q+2
        29: q+2
        31: 2
        33: 2
        34: 2
        36: 2
        37: 2
        39: 2
        49: q+2
        50: q+2
        52: 2
        53: 2
        55: 2
        56: 2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        66: 2
        71: q+2
        72: 2
        73: 2
        74: 2
        76: 2
        82: 2
        86: 2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       127: 2
       129: 2
       139: 2
       142: 2
       145: 2
       147: 2
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       172: 1
       179: 2
       181: 2
       195: 1
       196: 1
       201: 1
       202: 1
       209: 1
       237: 1
       239: 1
       243: 1
       247: 1
       248: 1
       259: 1
       262: 1
       317: 1
       337: 1
       338: 1
       340: 1
       427: 1

 428:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: q+2
        17: q+2
        19: q+2
        20: q+2
        22: 2
        23: 2
        25: 2
        26: 2
        28: q+2
        29: q+2
        31: 2
        33: 2
        34: 2
        36: 2
        38: 2
        40: 2
        49: q+2
        50: q+2
        52: 2
        53: 2
        55: 2
        56: 2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        67: 2
        71: q+2
        72: 2
        73: 2
        75: 2
        77: 2
        82: 2
        86: 2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       128: 2
       130: 2
       139: 2
       142: 2
       145: 2
       147: 2
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       171: 1
       180: 2
       182: 2
       195: 1
       196: 1
       201: 1
       202: 1
       210: 1
       238: 1
       240: 1
       243: 1
       247: 1
       248: 1
       260: 1
       261: 1
       318: 1
       337: 1
       339: 1
       341: 1
       428: 1

 429:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+2q+1
         5: q^2+6q+2
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+3q+2
         9: q+1
        10: 4q+2
        11: 4q+2
        12: q^2+2q+1
        13: 3q+2
        14: q+1
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+1
        19: q+1
        20: 2q+1
        21: 1
        22: q^2+6q+2
        23: q^2+6q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: 2q+2
        28: 4q+2
        29: q+1
        30: 1
        31: 4q+2
        32: 3q+2
        33: q^2+6q+2
        34: 2q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+1
        49: q+1
        50: 2q+1
        51: 1
        52: q+1
        53: 2q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2q+1
        59: 2q+1
        60: 2q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: 1
        70: 1
        71: q+1
        72: 1
        80: q+2
        81: 3q+2
        82: q+1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 2q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: q+1
       104: q+1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: q+2
       138: 1
       139: q+1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       219: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       236: 1
       243: 1
       244: 1
       246: 1
       275: 1
       276: 1
       283: 1
       299: 1
       319: 1
       344: 1
       348: 1
       366: 1
       429: 1

 430:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+2q+1
         5: q^2+6q+2
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+3q+2
         9: q+1
        10: 4q+2
        11: 4q+2
        12: q^2+2q+1
        13: 3q+2
        14: q+1
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+1
        19: q+1
        20: 2q+1
        21: 1
        22: q^2+6q+2
        23: q^2+6q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: 2q+2
        28: 4q+2
        29: q+1
        30: 1
        31: 4q+2
        32: 3q+2
        33: q^2+6q+2
        34: 2q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+1
        49: q+1
        50: 2q+1
        51: 1
        52: q+1
        53: 2q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2q+1
        59: 2q+1
        61: 2q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: 1
        70: 1
        71: q+1
        72: 1
        80: q+2
        81: 3q+2
        82: q+1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 2q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: q+1
       106: q+1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: q+2
       138: 1
       139: q+1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       219: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       236: 1
       243: 1
       244: 1
       246: 1
       277: 1
       278: 1
       284: 1
       300: 1
       320: 1
       344: 1
       348: 1
       366: 1
       430: 1

 431:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        58: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
       109: 1
       117: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       160: 1
       161: q+1
       162: 1
       185: 1
       191: 1
       195: 1
       219: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       285: 1
       303: 1
       344: 1
       350: 1
       431: 1

 432:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        59: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
       110: 1
       118: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       160: 1
       161: q+1
       162: 1
       186: 1
       192: 1
       196: 1
       219: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       286: 1
       304: 1
       344: 1
       350: 1
       432: 1

 433:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 3q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        64: q+1
        66: q+1
        69: q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       211: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       291: 1
       301: 1
       305: 1
       315: 1
       348: 1
       350: 1
       433: 1

 434:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 3q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        65: q+1
        67: q+1
        69: q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       292: 1
       302: 1
       306: 1
       316: 1
       348: 1
       350: 1
       434: 1

 435:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        64: q+1
        66: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       181: 1
       187: 1
       197: 1
       211: 1
       213: 1
       215: 1
       229: 1
       230: 1
       234: 1
       237: 1
       239: 1
       244: 1
       256: 1
       257: 1
       289: 1
       301: 1
       305: 1
       360: 1
       362: 1
       369: 1
       435: 1

 436:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 2q+1
        35: q+1
        36: q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        65: q+1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       182: 1
       188: 1
       198: 1
       212: 1
       214: 1
       216: 1
       229: 1
       230: 1
       234: 1
       238: 1
       240: 1
       244: 1
       256: 1
       257: 1
       290: 1
       302: 1
       306: 1
       361: 1
       363: 1
       369: 1
       436: 1

 437:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       133: 1
       135: 1
       137: 2
       139: 1
       140: 1
       141: 1
       143: 2
       146: 1
       149: 1
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       207: 1
       208: 1
       220: 1
       222: 1
       227: 1
       229: 1
       246: 1
       250: 1
       251: 1
       275: 1
       276: 1
       293: 1
       299: 1
       345: 1
       347: 1
       437: 1

 438:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       133: 1
       135: 1
       137: 2
       139: 1
       140: 1
       141: 1
       143: 2
       146: 1
       149: 1
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       207: 1
       208: 1
       220: 1
       222: 1
       227: 1
       229: 1
       246: 1
       250: 1
       251: 1
       277: 1
       278: 1
       294: 1
       300: 1
       345: 1
       347: 1
       438: 1

 439:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        58: 1
        68: 1
        70: q+1
        71: 1
        73: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       109: 1
       117: 1
       125: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       157: 1
       158: 1
       160: 1
       161: 1
       185: 1
       191: 1
       195: 1
       220: 1
       224: 1
       227: 1
       230: 1
       250: 1
       251: 1
       295: 1
       303: 1
       345: 1
       349: 1
       439: 1

 440:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        59: 1
        68: 1
        70: q+1
        71: 1
        73: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       110: 1
       118: 1
       125: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       157: 1
       158: 1
       160: 1
       161: 1
       186: 1
       192: 1
       196: 1
       220: 1
       224: 1
       227: 1
       230: 1
       250: 1
       251: 1
       296: 1
       304: 1
       345: 1
       349: 1
       440: 1

 441:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: q+1
        81: 1
        82: 2q+2
        83: q+1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: 1
       146: 1
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       169: 1
       172: 1
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       207: 1
       209: 2
       211: 1
       222: 1
       224: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       267: 1
       269: 1
       297: 1
       305: 1
       325: 1
       347: 1
       349: 1
       441: 1

 442:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: q+1
        81: 1
        82: 2q+2
        83: q+1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: 1
       146: 1
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       170: 1
       171: 1
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       208: 1
       210: 2
       212: 1
       222: 1
       224: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       268: 1
       270: 1
       298: 1
       306: 1
       326: 1
       347: 1
       349: 1
       442: 1

 443:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: q+2
        23: q+2
        25: 2
        26: 2
        28: 2
        29: q+2
        31: q+2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        55: 2
        56: 2
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        82: q+2
        86: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       139: 2
       140: 2
       142: 2
       145: 1
       147: 1
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       169: 1
       170: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       201: 1
       209: 1
       210: 1
       243: 1
       244: 1
       247: 1
       248: 1
       267: 1
       268: 1
       319: 1
       337: 1
       351: 1
       443: 1

 444:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: q+2
        23: q+2
        25: 2
        26: 2
        28: 2
        29: q+2
        31: q+2
        33: 2
        34: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        55: 2
        56: 2
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        66: 1
        67: 1
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        82: q+2
        86: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       139: 2
       140: 2
       142: 2
       145: 1
       147: 1
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       171: 1
       172: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       202: 1
       209: 1
       210: 1
       243: 1
       244: 1
       247: 1
       248: 1
       269: 1
       270: 1
       320: 1
       337: 1
       351: 1
       444: 1

 445:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        33: q+1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        66: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       140: 1
       142: q+1
       147: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       197: 1
       237: 1
       239: 1
       244: 1
       247: 1
       248: 1
       301: 1
       338: 1
       340: 1
       351: 1
       445: 1

 446:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        33: q+1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        67: 1
        72: 1
        73: q+1
        75: 1
        77: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       140: 1
       142: q+1
       147: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       198: 1
       238: 1
       240: 1
       244: 1
       247: 1
       248: 1
       302: 1
       339: 1
       341: 1
       351: 1
       446: 1

 447:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        34: 1
        35: q+1
        36: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        55: 1
        56: q+1
        57: 1
        60: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: q+1
        99: 1
       107: 1
       119: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       163: 1
       164: q+1
       165: 1
       183: 1
       199: 1
       201: 1
       219: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       283: 1
       307: 1
       352: 1
       356: 1
       447: 1

 448:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        34: 1
        35: q+1
        36: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        55: 1
        56: q+1
        57: 1
        61: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: q+1
        99: 1
       108: 1
       120: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       163: 1
       164: q+1
       165: 1
       184: 1
       200: 1
       202: 1
       219: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       284: 1
       308: 1
       352: 1
       356: 1
       448: 1

 449:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+2q+1
         5: q^2+6q+2
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+3q+2
         9: q+1
        10: 4q+2
        11: 4q+2
        12: q^2+2q+1
        13: 3q+2
        14: q+1
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+1
        19: q+1
        20: 2q+1
        21: 1
        22: 4q+2
        23: 4q+2
        24: 2q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: q^2+3q+2
        28: 4q+2
        29: q+1
        30: 1
        31: 2q+2
        32: 2q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: 2q+1
        57: 1
        58: 2q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: q+2
        85: 3q+2
        86: q+1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: 2q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: q+1
       105: q+1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+2
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       150: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       219: 1
       225: 1
       226: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       275: 1
       277: 1
       285: 1
       309: 1
       321: 1
       352: 1
       358: 1
       366: 1
       449: 1

 450:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+2q+1
         5: q^2+6q+2
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+3q+2
         9: q+1
        10: 4q+2
        11: 4q+2
        12: q^2+2q+1
        13: 3q+2
        14: q+1
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+1
        19: q+1
        20: 2q+1
        21: 1
        22: 4q+2
        23: 4q+2
        24: 2q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: q^2+3q+2
        28: 4q+2
        29: q+1
        30: 1
        31: 2q+2
        32: 2q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+1
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+1
        49: q+1
        50: 2q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: 2q+1
        57: 1
        59: 2q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: q+2
        85: 3q+2
        86: q+1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: 2q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: q+1
       106: q+1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+2
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       150: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       219: 1
       225: 1
       226: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       276: 1
       278: 1
       286: 1
       310: 1
       322: 1
       352: 1
       358: 1
       366: 1
       450: 1

 451:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 3q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        64: q+1
        66: q+1
        69: q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       205: 1
       211: 1
       223: 1
       225: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       245: 1
       291: 1
       311: 1
       313: 1
       315: 1
       356: 1
       358: 1
       451: 1

 452:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 3q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        65: q+1
        67: q+1
        69: q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       206: 1
       212: 1
       223: 1
       225: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       245: 1
       292: 1
       312: 1
       314: 1
       316: 1
       356: 1
       358: 1
       452: 1

 453:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        34: q+1
        35: q+1
        36: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: q+1
        56: q+1
        57: q+1
        60: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       107: 1
       119: 1
       125: 1
       133: 1
       135: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: 1
       158: 1
       163: 1
       164: 1
       183: 1
       199: 1
       201: 1
       220: 1
       222: 1
       232: 1
       234: 1
       253: 1
       254: 1
       293: 1
       307: 1
       353: 1
       355: 1
       453: 1

 454:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        34: q+1
        35: q+1
        36: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        55: q+1
        56: q+1
        57: q+1
        61: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       108: 1
       120: 1
       125: 1
       133: 1
       135: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: 1
       158: 1
       163: 1
       164: 1
       184: 1
       200: 1
       202: 1
       220: 1
       222: 1
       232: 1
       234: 1
       253: 1
       254: 1
       294: 1
       308: 1
       353: 1
       355: 1
       454: 1

 455:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        64: q+1
        66: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       135: 1
       136: 1
       142: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       181: 1
       187: 1
       205: 1
       211: 1
       213: 1
       215: 1
       230: 1
       234: 1
       235: 1
       237: 1
       239: 1
       245: 1
       256: 1
       257: 1
       289: 1
       311: 1
       313: 1
       360: 1
       362: 1
       370: 1
       455: 1

 456:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        65: q+1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       135: 1
       136: 1
       142: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       182: 1
       188: 1
       206: 1
       212: 1
       214: 1
       216: 1
       230: 1
       234: 1
       235: 1
       238: 1
       240: 1
       245: 1
       256: 1
       257: 1
       290: 1
       312: 1
       314: 1
       361: 1
       363: 1
       370: 1
       456: 1

 457:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       133: 1
       136: 1
       137: 2
       141: 1
       143: 2
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       163: 1
       164: 1
       173: 1
       175: 1
       185: 1
       191: 2
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       220: 1
       224: 1
       232: 1
       235: 1
       246: 1
       253: 1
       254: 1
       275: 1
       277: 1
       295: 1
       309: 1
       353: 1
       357: 1
       457: 1

 458:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q+1
         8: q+2
        10: q+2
        11: q+2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       133: 1
       136: 1
       137: 2
       141: 1
       143: 2
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       163: 1
       164: 1
       174: 1
       176: 1
       186: 1
       192: 2
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       220: 1
       224: 1
       232: 1
       235: 1
       246: 1
       253: 1
       254: 1
       276: 1
       278: 1
       296: 1
       310: 1
       353: 1
       357: 1
       458: 1

 459:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: q+1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: q+1
        85: 1
        86: 2q+2
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 2
        98: 2
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: 1
       163: 1
       164: 1
       169: 1
       172: 1
       187: 1
       189: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: 2
       211: 1
       222: 1
       224: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       271: 1
       273: 1
       297: 1
       313: 1
       325: 1
       355: 1
       357: 1
       459: 1

 460:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: q+1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: q+1
        85: 1
        86: 2q+2
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 2
        98: 2
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: 1
       163: 1
       164: 1
       170: 1
       171: 1
       188: 1
       190: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       210: 2
       212: 1
       222: 1
       224: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       272: 1
       274: 1
       298: 1
       314: 1
       326: 1
       355: 1
       357: 1
       460: 1

 461:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: 2
        23: 2
        25: q+2
        26: q+2
        28: 2
        29: q+2
        31: 2
        33: 2
        34: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: 2
        53: 2
        55: q+2
        56: q+2
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        82: 2
        86: q+2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       139: 1
       142: 1
       145: 2
       147: 2
       148: 2
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       169: 1
       171: 1
       195: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       209: 1
       210: 1
       243: 1
       245: 1
       247: 1
       248: 1
       271: 1
       272: 1
       321: 1
       337: 1
       359: 1
       461: 1

 462:    0: q+2
         1: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
        10: q+2
        11: q+2
        12: q+2
        16: 2
        17: 2
        19: q+2
        20: q+2
        22: 2
        23: 2
        25: q+2
        26: q+2
        28: 2
        29: q+2
        31: 2
        33: 2
        34: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        49: 2
        50: 2
        52: 2
        53: 2
        55: q+2
        56: q+2
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        66: 1
        67: 1
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        82: 2
        86: q+2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       139: 1
       142: 1
       145: 2
       147: 2
       148: 2
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       166: 1
       167: 1
       170: 1
       172: 1
       196: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       209: 1
       210: 1
       243: 1
       245: 1
       247: 1
       248: 1
       273: 1
       274: 1
       322: 1
       337: 1
       359: 1
       462: 1

 463:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        33: 1
        36: q+1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        66: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       142: 1
       147: q+1
       148: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       205: 1
       237: 1
       239: 1
       245: 1
       247: 1
       248: 1
       311: 1
       338: 1
       340: 1
       359: 1
       463: 1

 464:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        33: 1
        36: q+1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        67: 1
        72: q+1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       142: 1
       147: q+1
       148: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       206: 1
       238: 1
       240: 1
       245: 1
       247: 1
       248: 1
       312: 1
       339: 1
       341: 1
       359: 1
       464: 1

 465:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2q+2
        41: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: 2
        70: 1
        71: 1
        74: 1
        76: q+1
        78: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       127: 1
       129: 1
       133: 1
       139: 1
       141: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       176: 1
       179: 1
       189: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       232: 1
       237: 1
       239: 1
       243: 1
       246: 1
       256: 1
       257: 1
       279: 1
       317: 1
       325: 1
       360: 1
       362: 1
       367: 1
       465: 1

 466:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2q+2
        42: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: 2
        70: 1
        71: 1
        75: 1
        77: q+1
        79: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       128: 1
       130: 1
       133: 1
       139: 1
       141: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       174: 1
       175: 1
       180: 1
       190: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       232: 1
       238: 1
       240: 1
       243: 1
       246: 1
       256: 1
       257: 1
       280: 1
       318: 1
       326: 1
       361: 1
       363: 1
       367: 1
       466: 1

 467:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: q+1
        66: q+1
        69: 1
        74: 1
        78: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       115: 1
       123: q+1
       127: 1
       131: 1
       134: 1
       138: 1
       144: 1
       150: 1
       151: 1
       155: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       168: 1
       177: 1
       211: 1
       213: 1
       217: 1
       228: 1
       233: 1
       236: 1
       237: 1
       241: 1
       256: 1
       258: 1
       281: 1
       315: 1
       360: 1
       364: 1
       368: 1
       467: 1

 468:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: q+1
        67: q+1
        69: 1
        75: 1
        79: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       116: 1
       124: q+1
       128: 1
       132: 1
       134: 1
       138: 1
       144: 1
       150: 1
       152: 1
       156: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       168: 1
       178: 1
       212: 1
       214: 1
       218: 1
       228: 1
       233: 1
       236: 1
       238: 1
       242: 1
       256: 1
       258: 1
       282: 1
       316: 1
       361: 1
       365: 1
       368: 1
       468: 1

 469:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: 1
         8: q+1
         9: 1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: 1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       126: 1
       127: 1
       129: 1
       131: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       166: 1
       167: 1
       168: 1
       177: 1
       179: 1
       189: 1
       207: 1
       209: 1
       211: 1
       226: 1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       287: 1
       315: 1
       317: 1
       325: 1
       366: 1
       469: 1

 470:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: 1
         8: q+1
         9: 1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: 1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       126: 1
       128: 1
       130: 1
       132: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       166: 1
       167: 1
       168: 1
       178: 1
       180: 1
       190: 1
       208: 1
       210: 1
       212: 1
       226: 1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       288: 1
       316: 1
       318: 1
       326: 1
       366: 1
       470: 1

 471:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       135: 1
       139: 1
       140: 1
       141: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       174: 1
       183: 1
       193: 1
       201: 1
       227: 1
       229: 1
       232: 1
       234: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       299: 1
       307: 1
       319: 1
       367: 1
       369: 1
       471: 1

 472:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       135: 1
       139: 1
       140: 1
       141: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       175: 1
       176: 1
       184: 1
       194: 1
       202: 1
       227: 1
       229: 1
       232: 1
       234: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       300: 1
       308: 1
       320: 1
       367: 1
       369: 1
       472: 1

 473:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       175: 1
       185: 1
       195: 1
       203: 1
       227: 1
       230: 1
       232: 1
       235: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       303: 1
       309: 1
       321: 1
       367: 1
       370: 1
       473: 1

 474:    0: 2
         1: 2q+2
         2: 2
         3: 2q+2
         4: q+1
         5: 2
         6: q^2+2q+1
         7: q+1
         8: 2
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        19: 1
        20: q+1
        21: 1
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       174: 1
       176: 1
       186: 1
       196: 1
       204: 1
       227: 1
       230: 1
       232: 1
       235: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       304: 1
       310: 1
       322: 1
       367: 1
       370: 1
       474: 1

 475:    0: 2q+1
         1: 3q+1
         2: 2q+1
         3: 3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: 2q+1
        21: q+1
        22: 2q+1
        23: 3q+1
        24: 2q+1
        25: 2q+1
        26: 3q+1
        27: 2q+1
        30: q+1
        32: 2q+1
        33: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: q
        39: 2q+1
        40: q
        41: q+1
        42: q
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: 2q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: q+1
        64: q+1
        65: q
        66: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: 2q+1
       102: q+1
       111: 1
       115: 1
       123: q+1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       187: 1
       197: 1
       205: 1
       211: 1
       229: 1
       230: 1
       234: 1
       235: 1
       244: 1
       245: 1
       256: 1
       257: 1
       305: 1
       313: 1
       323: 1
       369: 1
       370: 1
       475: 1

 476:    0: 2q+1
         1: 3q+1
         2: 2q+1
         3: 3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: 2q+1
        21: q+1
        22: 2q+1
        23: 3q+1
        24: 2q+1
        25: 2q+1
        26: 3q+1
        27: 2q+1
        30: q+1
        32: 2q+1
        33: q+1
        35: 2q+1
        36: q+1
        37: q
        38: q+1
        39: q
        40: 2q+1
        41: q
        42: q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: 2q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: q+1
        64: q
        65: q+1
        67: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: 2q+1
       102: q+1
       112: 1
       116: 1
       124: q+1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       188: 1
       198: 1
       206: 1
       212: 1
       229: 1
       230: 1
       234: 1
       235: 1
       244: 1
       245: 1
       256: 1
       257: 1
       306: 1
       314: 1
       324: 1
       369: 1
       370: 1
       476: 1

 477:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       140: 1
       142: 1
       147: 1
       148: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       197: 1
       205: 1
       237: 1
       239: 1
       244: 1
       245: 1
       301: 1
       311: 1
       323: 1
       477: 1

 478:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       140: 1
       142: 1
       147: 1
       148: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       198: 1
       206: 1
       238: 1
       240: 1
       244: 1
       245: 1
       302: 1
       312: 1
       324: 1
       478: 1

 479:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        33: 1
        36: 1
        37: 1
        38: q
        39: 1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        66: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: 1
        77: q
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       111: 1
       140: 1
       142: 1
       147: 1
       148: 1
       151: 1
       152: q
       153: 1
       154: q
       166: 1
       167: 1
       197: 1
       205: 1
       244: 1
       245: 1
       247: 1
       248: 1
       323: 1
       351: 1
       359: 1
       479: 1

 480:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        33: 1
        36: 1
        37: q
        38: 1
        39: q
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        67: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       112: 1
       140: 1
       142: 1
       147: 1
       148: 1
       151: q
       152: 1
       153: q
       154: 1
       166: 1
       167: 1
       198: 1
       206: 1
       244: 1
       245: 1
       247: 1
       248: 1
       324: 1
       351: 1
       359: 1
       480: 1

 481:    0: 3q+2
         1: q^2+3q+2
         2: 3q+2
         3: q^2+3q+2
         4: 3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: 3q+2
         8: q^2+3q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 3q+2
        14: 3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: 2q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: 2q+2
        30: 3q+2
        34: q+2
        35: 2q+2
        36: q+2
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: 2q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        55: 2q+2
        56: 2q+2
        57: 2q+2
        60: 1
        61: 1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        97: 2
        98: 2
        99: q+1
       107: 1
       108: 1
       119: 1
       120: 1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: q+2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: 2
       158: 2
       159: q+1
       163: 2
       164: 2
       165: q+1
       183: 1
       184: 1
       199: 1
       200: 1
       201: 1
       202: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       231: 1
       232: 2
       233: 1
       234: 2
       293: 1
       294: 1
       307: 1
       308: 1
       333: 1
       334: 1
       352: 1
       356: 1
       481: 1

 482:    0: 3q+2
         1: q^2+3q+2
         2: 3q+2
         3: q^2+3q+2
         4: 3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: 3q+2
         8: q^2+3q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 3q+2
        14: 3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: 2q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        28: q+2
        29: 2q+2
        30: 3q+2
        31: q+2
        32: 2q+2
        33: q+2
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: 2q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        58: 1
        59: 1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        73: q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
       109: 1
       110: 1
       117: 1
       118: 1
       125: 2
       126: 1
       133: q+2
       134: q+1
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       185: 1
       186: 1
       191: 1
       192: 1
       195: 1
       196: 1
       219: 1
       220: 2
       221: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       295: 1
       296: 1
       303: 1
       304: 1
       333: 1
       335: 1
       344: 1
       350: 1
       482: 1

 483:    0: q^2+3q+4
         1: q^2+3q+4
         2: 4q+2
         3: 4q+4
         4: q^2+3q+4
         5: 4q+4
         6: q^2+3q+4
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: q^2+3q+4
        11: 4q+4
        12: q^2+3q+4
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: q+4
        17: q+4
        18: 2q+1
        19: q^2+3q+4
        20: q^2+3q+4
        21: 4q+2
        22: q+4
        23: q+4
        24: 3q+2
        25: q+4
        26: q+4
        27: 3q+2
        28: q+4
        29: q^2+3q+4
        30: 2q+2
        31: q+4
        32: q+2
        33: 4
        34: q+4
        35: q+2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: q+4
        50: q+4
        51: 2q+1
        52: q+4
        53: q+4
        54: 3q+2
        55: q+4
        56: q+4
        57: 3q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 2q+2
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: q+4
        83: q+2
        84: q+2
        85: 2
        86: q+4
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       231: 1
       236: 1
       243: 1
       246: 2
       247: 1
       248: 1
       249: 1
       297: 1
       298: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 1
       366: 1
       483: 1

 484:    0: 3q+4
         1: 3q^2+7q+4
         2: 3q+4
         3: 4q^2+8q+4
         4: 3q+4
         5: 4q+4
         6: 3q^2+7q+4
         7: 3q+4
         8: 4q+4
        10: 3q+4
        11: 4q+4
        12: 3q+4
        13: 3q+4
        14: 3q+4
        15: 4q+4
        16: q+4
        17: q+4
        19: 3q+4
        20: 3q^2+7q+4
        21: 3q+4
        22: q+4
        23: q^2+5q+4
        24: q+4
        25: q+4
        26: q^2+5q+4
        27: q+4
        28: q+4
        29: 3q+4
        30: 3q+4
        31: q+4
        32: q+4
        33: 4
        34: q+4
        35: q+4
        36: 4
        37: 2
        38: 2
        39: 2q+2
        40: 2q+2
        41: 2
        42: 2
        43: 3q+4
        44: 3q+4
        45: 4q+4
        46: q+4
        47: q+4
        49: q+4
        50: q+4
        52: q+4
        53: q^2+5q+4
        54: q+4
        55: q+4
        56: q^2+5q+4
        57: q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: q+4
        70: 3q+4
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2q+2
        77: 2q+2
        78: 2
        79: 2
        80: q+4
        81: 4
        82: q+4
        83: q+4
        84: q+4
        85: 4
        86: q+4
        87: q+4
        91: q+4
        92: q+4
        94: 2
        95: 2
        97: 2
        98: 2
       100: 2
       101: 2q+2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 2
       116: 2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       133: q+4
       135: 4
       136: 4
       139: 2
       141: q+4
       142: 2
       145: 2
       146: q+4
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 2
       190: 2
       195: 1
       196: 1
       201: 1
       202: 1
       209: 1
       210: 1
       211: 1
       212: 1
       227: 2
       230: 2
       232: 2
       234: 2
       243: 1
       246: 2
       247: 1
       248: 1
       256: 1
       257: 1
       263: 1
       264: 1
       265: 1
       266: 1
       303: 1
       304: 1
       307: 1
       308: 1
       325: 1
       326: 1
       337: 1
       367: 1
       371: 1
       372: 1
       484: 1

 485:    0: q+1
         1: q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: 1
         6: q+1
         7: q+1
         8: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: q+1
        47: 1
        49: q+1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: 1
       142: 1
       147: 1
       150: 1
       151: 1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       181: 1
       187: 1
       211: 1
       213: 1
       215: 1
       230: 1
       234: 1
       237: 1
       247: 1
       256: 1
       289: 1
       338: 1
       360: 1
       371: 1
       485: 1

 486:    0: q+1
         1: q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: 1
         6: q+1
         7: q+1
         8: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: q+1
        47: 1
        49: q+1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: 1
       142: 1
       147: 1
       150: 1
       152: 1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       182: 1
       188: 1
       212: 1
       214: 1
       216: 1
       230: 1
       234: 1
       238: 1
       247: 1
       256: 1
       290: 1
       339: 1
       361: 1
       371: 1
       486: 1

 487:    0: 1
         1: q^2+2q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: q^2+2q+1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: q+1
        19: 1
        20: q^2+2q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: 1
        47: q+1
        49: 1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       101: q+1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: 1
       142: 1
       147: 1
       153: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       167: 1
       181: 1
       187: 1
       213: 1
       215: 1
       230: 1
       234: 1
       239: 1
       248: 1
       257: 1
       289: 1
       340: 1
       362: 1
       372: 1
       487: 1

 488:    0: 1
         1: q^2+2q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: q^2+2q+1
         7: 1
         8: q+1
        13: 1
        14: 1
        15: q+1
        16: 1
        17: q+1
        19: 1
        20: q^2+2q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: 1
        47: q+1
        49: 1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       101: q+1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: 1
       142: 1
       147: 1
       154: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       167: 1
       182: 1
       188: 1
       214: 1
       216: 1
       230: 1
       234: 1
       240: 1
       248: 1
       257: 1
       290: 1
       341: 1
       363: 1
       372: 1
       488: 1

 489:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: q+1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        37: 1
        41: 1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        74: 1
        78: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       100: 1
       102: 1
       115: 1
       131: 1
       150: 1
       151: 1
       155: 1
       162: 1
       165: 1
       168: 1
       211: 1
       217: 1
       241: 1
       249: 1
       258: 1
       342: 1
       364: 1
       373: 1
       489: 1

 490:    0: 1
         2: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: q+1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        32: 1
        35: 1
        38: 1
        42: 1
        48: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        75: 1
        79: 1
        83: 1
        87: 1
        93: 1
        96: 1
        99: 1
       100: 1
       102: 1
       116: 1
       132: 1
       150: 1
       152: 1
       156: 1
       162: 1
       165: 1
       168: 1
       212: 1
       218: 1
       242: 1
       249: 1
       258: 1
       343: 1
       365: 1
       373: 1
       490: 1

 491:    0: 3q+2
         1: 2
         2: 3q+2
         3: 2q+2
         4: 3q+2
         5: 2q+2
         6: 2
         7: 3q+2
         8: 2q+2
         9: 2q^2+3q+1
        13: 3q+2
        14: 3q+2
        15: 2q+2
        16: q+2
        17: 2
        18: 3q+1
        19: 3q+2
        20: 2
        21: 3q+2
        22: q+2
        23: 2
        24: q+2
        25: q+2
        26: 2
        27: q+2
        30: 3q+2
        32: q+2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: q+2
        47: 2
        48: 3q+1
        49: q+2
        50: 2
        51: 3q+1
        52: q+2
        53: 2
        54: q+2
        55: q+2
        56: 2
        57: q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: q+1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: q+2
        85: 2
        87: q+2
        91: q+2
        92: 2
        93: 3q+1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: q+1
       135: 2
       136: 2
       138: 1
       142: 1
       144: 1
       147: 1
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       168: 1
       187: 1
       188: 1
       211: 1
       212: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       247: 1
       249: 1
       256: 1
       258: 1
       336: 1
       350: 1
       356: 1
       368: 1
       371: 1
       373: 1
       491: 1

 492:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        59: 1
        68: 2
        69: 1
        70: 1
        71: 1
        80: 2
        81: 2
        82: 1
        83: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       117: 1
       118: 1
       125: 2
       126: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       191: 1
       192: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       250: 1
       251: 1
       252: 1
       333: 1
       344: 1
       345: 1
       346: 1
       492: 1

 493:    0: 2q+4
         1: 2q+4
         2: q^2+2q+2
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+2
         9: q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2
        14: q+1
        15: 2
        16: 2q+4
        17: 2q+4
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2q+4
        23: 2q+4
        24: q^2+2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 2q+4
        29: q+2
        30: 1
        31: 2q+4
        32: 2
        33: 2q+4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: q+2
        59: q+2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: q+2
        72: 2
        80: 2
        81: 2
        82: q+2
        83: 1
        84: 2
        85: 2
        86: 2
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: q+2
        95: q+2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: q+2
       140: 2
       141: 1
       143: 2
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       166: 2
       167: 2
       168: q+1
       193: 1
       194: 1
       201: 1
       202: 1
       207: 1
       208: 1
       221: 1
       222: 1
       223: 1
       226: 1
       228: 1
       229: 1
       231: 1
       236: 1
       243: 2
       244: 2
       246: 1
       250: 1
       251: 1
       252: 1
       319: 1
       320: 1
       334: 1
       346: 1
       347: 1
       348: 1
       366: 1
       493: 1

 494:    0: 2
         1: 2
         2: q+1
         3: 2
         4: 2
         5: 2
         6: 2
         7: q+1
         8: q+1
         9: q+1
        10: 2
        11: 2
        12: 2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: q+1
        58: 1
        59: 1
        69: 1
        70: 1
        71: 2
        73: 2
        80: 1
        81: 1
        82: 2
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
       109: 1
       110: 1
       126: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       195: 1
       196: 1
       221: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       250: 1
       251: 1
       252: 1
       335: 1
       346: 1
       349: 1
       350: 1
       494: 1

 495:    0: q^2+2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        13: q+2
        14: q+2
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: q^2+2q+2
        20: 2q+2
        21: q^2+q+2
        22: q^2+2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        30: q+2
        32: q+2
        33: q+2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: q^2+2q+2
        53: 2q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 2
        73: q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: q+2
        85: 2
        87: 2
        91: 2
        92: 2
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       140: 2
       142: q+2
       144: 1
       147: 1
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       160: 2
       161: 2
       162: q+1
       166: 1
       167: 1
       168: 1
       187: 1
       188: 1
       197: 1
       198: 1
       211: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 2
       230: 2
       236: 1
       244: 1
       247: 1
       248: 1
       249: 1
       305: 1
       306: 1
       336: 1
       348: 1
       350: 1
       351: 1
       495: 1

 496:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: q+2
        23: q^2+3q+2
        24: q+2
        25: 2
        26: 2q+2
        27: 2
        30: q+2
        32: q+2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 2
        50: 2
        52: q+2
        53: q^2+3q+2
        54: q+2
        55: 2
        56: 2q+2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 2
        83: q+2
        85: 2
        87: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2q+2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       135: 2
       136: 2
       140: 2
       142: 2
       147: 1
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2
       163: 1
       164: 1
       166: 1
       167: 1
       187: 1
       188: 1
       197: 1
       198: 1
       211: 1
       212: 1
       229: 2
       230: 2
       234: 1
       244: 1
       247: 1
       248: 1
       256: 1
       257: 1
       305: 1
       306: 1
       351: 1
       369: 1
       371: 1
       372: 1
       496: 1

 497:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        34: 2
        35: 2
        36: 2
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        68: 2
        69: 1
        70: 1
        71: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       119: 1
       120: 1
       125: 2
       126: 1
       133: 1
       134: 1
       143: 2
       144: 1
       145: 1
       146: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       199: 1
       200: 1
       219: 1
       220: 1
       221: 1
       231: 1
       232: 1
       233: 1
       253: 1
       254: 1
       255: 1
       333: 1
       352: 1
       353: 1
       354: 1
       497: 1

 498:    0: 2
         1: 2
         2: q+1
         3: 2
         4: 2
         5: 2
         6: 2
         7: q+1
         8: q+1
         9: q+1
        10: 2
        11: 2
        12: 2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: 2
        20: 2
        21: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        34: 2
        35: 1
        36: 2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        55: 2
        56: 2
        57: q+1
        60: 1
        61: 1
        69: 1
        70: 1
        71: 2
        72: 2
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 2
        98: 2
        99: q+1
       107: 1
       108: 1
       126: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       201: 1
       202: 1
       221: 1
       222: 1
       223: 1
       231: 1
       233: 1
       234: 1
       253: 1
       254: 1
       255: 1
       334: 1
       354: 1
       355: 1
       356: 1
       498: 1

 499:    0: 2q+4
         1: 2q+4
         2: q^2+2q+2
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+2
         9: q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2
        14: q+1
        15: 2
        16: 2q+4
        17: 2q+4
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q+1
        22: 4
        23: 4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: q^2+2q+2
        28: 2q+4
        29: q+2
        30: 1
        31: 4
        32: 2
        33: 4
        34: 2q+4
        35: 2
        36: 2q+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 2
        59: 2
        60: q+2
        61: q+2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: q+2
        73: 2
        80: 2
        81: 2
        82: 2
        83: 1
        84: 2
        85: 2
        86: q+2
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2
       144: 1
       145: q+2
       146: 1
       148: 2
       149: 2
       150: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       195: 1
       196: 1
       203: 1
       204: 1
       207: 1
       208: 1
       221: 1
       224: 1
       225: 1
       226: 1
       231: 1
       233: 1
       235: 1
       236: 1
       243: 2
       245: 2
       246: 1
       253: 1
       254: 1
       255: 1
       321: 1
       322: 1
       335: 1
       354: 1
       357: 1
       358: 1
       366: 1
       499: 1

 500:    0: q^2+2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        13: q+2
        14: q+2
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: q^2+2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: q^2+2q+2
        26: 2q+2
        27: q^2+q+2
        30: q+2
        32: 2
        33: 2
        35: q+2
        36: q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q^2+2q+2
        56: 2q+2
        57: q^2+q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: q+2
        91: 2
        92: 2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+2
        98: q+2
        99: q+1
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       142: 1
       144: 1
       147: q+2
       148: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       187: 1
       188: 1
       205: 1
       206: 1
       211: 1
       212: 1
       223: 1
       225: 1
       233: 1
       234: 2
       235: 2
       236: 1
       245: 1
       247: 1
       248: 1
       249: 1
       313: 1
       314: 1
       336: 1
       356: 1
       358: 1
       359: 1
       500: 1

 501:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2
        23: 2q+2
        24: 2
        25: q+2
        26: q^2+3q+2
        27: q+2
        30: q+2
        32: 2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2
        53: 2q+2
        54: 2
        55: q+2
        56: q^2+3q+2
        57: q+2
        64: 1
        65: 1
        66: 1
        67: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: q+2
        91: 2
        92: 2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2q+2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       135: 2
       136: 2
       142: 1
       147: 2
       148: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: 1
       163: 2
       164: 2
       166: 1
       167: 1
       187: 1
       188: 1
       205: 1
       206: 1
       211: 1
       212: 1
       230: 1
       234: 2
       235: 2
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       313: 1
       314: 1
       359: 1
       370: 1
       371: 1
       372: 1
       501: 1

 502:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: 1
        71: 1
        74: 1
        76: 1
        78: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: q+1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       127: 1
       129: 1
       137: 1
       139: 1
       141: 1
       143: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: 1
       160: 1
       163: 1
       166: 1
       167: 1
       179: 1
       189: 1
       207: 1
       209: 1
       211: 1
       213: 1
       237: 1
       239: 1
       243: 1
       246: 1
       250: 1
       253: 1
       256: 1
       317: 1
       325: 1
       327: 1
       360: 1
       374: 1
       502: 1

 503:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+1
         5: q+2
         6: q+1
         7: q^2+2q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: 1
        71: 1
        75: 1
        77: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: q+1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       128: 1
       130: 1
       137: 1
       139: 1
       141: 1
       143: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: 1
       160: 1
       163: 1
       166: 1
       167: 1
       180: 1
       190: 1
       208: 1
       210: 1
       212: 1
       214: 1
       238: 1
       240: 1
       243: 1
       246: 1
       250: 1
       253: 1
       256: 1
       318: 1
       326: 1
       328: 1
       361: 1
       374: 1
       503: 1

 504:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q^2+q+1
         5: 2
         6: q^2+q+1
         8: q+1
        10: 2
        11: 2
        12: q^2+q+1
        13: 1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        71: 1
        74: 1
        76: 1
        80: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       106: 1
       113: 1
       121: 1
       123: 1
       127: 1
       129: 1
       137: 1
       139: 1
       143: 1
       145: 1
       149: 1
       151: 1
       153: 1
       158: 1
       161: 1
       164: 1
       166: 1
       167: 1
       179: 1
       207: 1
       209: 1
       215: 1
       237: 1
       239: 1
       243: 1
       251: 1
       254: 1
       257: 1
       317: 1
       329: 1
       362: 1
       375: 1
       504: 1

 505:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q^2+q+1
         5: 2
         6: q^2+q+1
         8: q+1
        10: 2
        11: 2
        12: q^2+q+1
        13: 1
        15: 1
        16: 2
        17: 2
        19: 1
        20: 1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        71: 1
        75: 1
        77: 1
        80: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       105: 1
       114: 1
       122: 1
       124: 1
       128: 1
       130: 1
       137: 1
       139: 1
       143: 1
       145: 1
       149: 1
       152: 1
       154: 1
       158: 1
       161: 1
       164: 1
       166: 1
       167: 1
       180: 1
       208: 1
       210: 1
       216: 1
       238: 1
       240: 1
       243: 1
       251: 1
       254: 1
       257: 1
       318: 1
       330: 1
       363: 1
       375: 1
       505: 1

 506:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: 1
        15: q+1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        29: 1
        30: 1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: 1
        45: q+1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: q+1
        64: q+1
        70: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        82: 1
        83: 1
        84: q+1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       100: 1
       101: 1
       102: 1
       113: 1
       115: 1
       121: q+1
       131: 1
       141: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       159: 1
       162: 1
       165: 1
       168: 1
       189: 1
       209: 1
       211: 1
       217: 1
       241: 1
       246: 1
       252: 1
       255: 1
       258: 1
       325: 1
       331: 1
       364: 1
       376: 1
       506: 1

 507:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: 1
        15: q+1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        29: 1
        30: 1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        63: q+1
        65: q+1
        70: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        82: 1
        83: 1
        84: q+1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       100: 1
       101: 1
       102: 1
       114: 1
       116: 1
       122: q+1
       132: 1
       141: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       159: 1
       162: 1
       165: 1
       168: 1
       190: 1
       210: 1
       212: 1
       218: 1
       242: 1
       246: 1
       252: 1
       255: 1
       258: 1
       326: 1
       332: 1
       365: 1
       376: 1
       507: 1

 508:    0: 2q+4
         1: 2q+4
         2: 2q+4
         3: 2q+4
         4: 2q+1
         5: 2q+4
         6: q^3+q^2+2q+1
         7: 2q+1
         8: 2q+4
         9: 2q+1
        10: 4
        11: 4
        12: 2q+1
        13: 2q+4
        14: 2q+1
        15: 2q+4
        16: 2q+4
        17: 2q+4
        18: 2q+1
        19: 1
        20: 1
        21: 1
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: 1
        30: 1
        31: 4
        32: 2q+4
        33: 2q+4
        34: 4
        35: 2q+4
        36: 2q+4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 4
        44: 2q+1
        45: 4
        46: 2q+4
        47: 2q+4
        48: 2q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: q+2
        65: q+2
        66: q+2
        67: q+2
        68: 4
        69: 1
        70: 1
        71: 1
        80: 4
        81: 2q+4
        82: 1
        83: 1
        84: 4
        85: 2q+4
        86: 1
        87: 1
        88: 4
        89: 4
        90: 2q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: 1
       134: 1
       137: 4
       138: 1
       139: 1
       141: 1
       143: 4
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       174: 1
       175: 1
       176: 1
       191: 2
       192: 2
       199: 2
       200: 2
       207: 2
       208: 2
       219: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       243: 1
       246: 1
       256: 1
       257: 1
       258: 1
       275: 1
       276: 1
       277: 1
       278: 1
       344: 1
       352: 1
       366: 1
       367: 1
       368: 1
       508: 1

 509:    0: 2q+4
         1: 2q+4
         2: 2q+4
         3: 2q+4
         4: q^2+2q+1
         5: 2q+4
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+4
        10: 2q+4
        11: 2q+4
        12: q^2+2q+1
        13: 2q+4
        14: q^2+2q+1
        15: 2q+4
        16: 4
        17: 4
        19: 1
        20: 1
        21: 1
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: 1
        30: 1
        31: 2q+4
        32: 2q+4
        33: 4
        34: 2q+4
        35: 2q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 2q+4
        44: q^2+2q+1
        45: 2q+4
        46: 4
        47: 4
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: 4
        70: 1
        71: 1
        80: 2q+4
        81: 4
        82: 1
        83: 1
        84: 2q+4
        85: 4
        86: 1
        87: 1
        88: 4
        89: 4
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: 4
       133: 1
       137: 4
       139: 1
       141: 1
       143: 4
       145: 1
       146: 1
       149: 1
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       174: 1
       175: 1
       176: 1
       191: 2
       192: 2
       199: 2
       200: 2
       207: 2
       208: 2
       220: 1
       227: 1
       232: 1
       243: 1
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       275: 1
       276: 1
       277: 1
       278: 1
       345: 1
       353: 1
       367: 1
       374: 1
       375: 1
       509: 1

 510:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: 2q+1
         5: 4
         6: 2q+1
         7: 2q^2+3q+1
         8: 2q+2
         9: 2q^2+3q+1
        10: 4
        11: 4
        12: 2q+1
        13: 2
        14: 2q+1
        15: 2
        16: 4
        17: 4
        18: 2q^2+3q+1
        19: 1
        20: 1
        21: q+1
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 1
        30: 1
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: 2q+1
        45: 2
        46: 2
        47: 2
        48: 2q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: 2q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: 1
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       207: 1
       208: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       236: 1
       243: 1
       246: 1
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       346: 1
       354: 1
       366: 1
       368: 1
       374: 1
       376: 1
       510: 1

 511:    0: 2q+4
         1: 2q+4
         2: 2q+2
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+2q+1
         8: 2q+2
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2
        14: q+1
        15: 2
        16: 4
        17: 4
        19: q+2
        20: q+2
        21: q+1
        22: 2q+4
        23: 2q+4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: 2q+2
        28: 4
        29: q+2
        30: 1
        31: 2q+4
        32: 2
        33: 4
        34: 2q+4
        35: 2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 1
        71: 2
        72: 2
        80: 2
        81: 2
        82: q+2
        83: 1
        84: 2
        85: 2
        86: q+2
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 1
       137: 2
       139: 2
       140: 2
       141: 1
       143: 2
       145: 2
       146: 1
       147: 2
       149: q+2
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       193: 1
       194: 1
       201: 1
       202: 1
       207: 1
       208: 1
       222: 1
       229: 1
       234: 1
       243: 2
       244: 2
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       319: 1
       320: 1
       347: 1
       355: 1
       369: 1
       374: 1
       375: 1
       511: 1

 512:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       134: 1
       135: 1
       138: 1
       140: 1
       144: 1
       147: 1
       150: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       223: 1
       228: 1
       229: 1
       233: 1
       234: 1
       236: 1
       244: 1
       256: 1
       257: 1
       258: 1
       348: 1
       356: 1
       368: 1
       369: 1
       512: 1

 513:    0: 2q+4
         1: 2q+4
         2: 2q+2
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+2q+1
         8: 2q+2
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2
        14: q+1
        15: 2
        16: 4
        17: 4
        19: q+2
        20: q+2
        21: q+1
        22: 2q+4
        23: 2q+4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: 2q+2
        28: 4
        29: q+2
        30: 1
        31: 2q+4
        32: 2
        33: 4
        34: 2q+4
        35: 2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 1
        71: 2
        73: 2
        80: 2
        81: 2
        82: q+2
        83: 1
        84: 2
        85: 2
        86: q+2
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       121: 1
       122: 1
       123: 1
       124: 1
       136: 1
       137: 2
       139: 2
       141: 1
       142: 2
       143: 2
       145: 2
       146: 1
       148: 2
       149: q+2
       150: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       195: 1
       196: 1
       203: 1
       204: 1
       207: 1
       208: 1
       224: 1
       230: 1
       235: 1
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       321: 1
       322: 1
       349: 1
       357: 1
       370: 1
       374: 1
       375: 1
       513: 1

 514:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        30: 1
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        73: 1
        81: 2
        83: 1
        85: 2
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       123: 1
       124: 1
       134: 1
       136: 1
       138: 1
       142: 1
       144: 1
       148: 1
       150: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       225: 1
       228: 1
       230: 1
       233: 1
       235: 1
       236: 1
       245: 1
       256: 1
       257: 1
       258: 1
       350: 1
       358: 1
       368: 1
       370: 1
       514: 1

 515:    0: 3q^2+8q+2
         1: 6q+2
         2: 3q^2+5q+2
         3: 3q^2+8q+2
         4: 3q^2+5q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: 3q+2
         8: 2q^2+4q+2
         9: 3q+2
        13: q^2+5q+2
        14: 3q+2
        15: 4q+2
        16: 3q^2+8q+2
        17: 6q+2
        18: 3q+2
        19: q^2+5q+2
        20: 4q+2
        21: 3q+2
        22: 5q+2
        23: 5q+2
        24: q^2+3q+2
        25: 5q+2
        26: 5q+2
        27: q^2+3q+2
        30: 3q+2
        32: 3q+2
        33: 5q+2
        35: 3q+2
        36: 5q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        46: q^2+5q+2
        47: 4q+2
        48: 3q+2
        49: q^2+5q+2
        50: 4q+2
        51: 3q+2
        52: 2q+2
        53: 3q+2
        54: q+2
        55: 2q+2
        56: 3q+2
        57: q+2
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        69: 3q+2
        72: q+2
        73: q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 3q+2
        83: q+2
        85: 3q+2
        87: q+2
        91: q+2
        92: 2q+2
        93: q+2
        94: 2q+2
        95: 3q+2
        96: q+2
        97: 2q+2
        98: 3q+2
        99: q+2
       100: q+2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: q+1
       124: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: q+2
       135: 2
       136: 2
       138: q+2
       142: q+2
       144: q+2
       147: q+2
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       211: 1
       212: 1
       223: 2
       225: 2
       228: 1
       230: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       241: 1
       242: 1
       247: 2
       256: 1
       258: 1
       291: 1
       292: 1
       315: 1
       316: 1
       338: 1
       339: 1
       350: 1
       356: 1
       368: 1
       371: 1
       515: 1

 516:    0: 2q+2
         1: q^2+4q+2
         2: 2
         3: 2q+2
         4: 2q+2
         5: q^2+4q+2
         6: q^2+4q+2
         7: 2
         8: q^2+2q+2
         9: 2
        13: 2
        14: 2
        15: 2q+2
        16: 2q+2
        17: q^2+4q+2
        18: 2
        19: 2q+2
        20: q^2+4q+2
        21: 2
        22: q+2
        23: q+2
        24: 2
        25: q+2
        26: q+2
        27: 2
        30: 2
        32: 2
        33: q+2
        35: 2
        36: q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2q+2
        48: 2
        49: 2q+2
        50: q^2+4q+2
        51: 2
        52: q+2
        53: q+2
        54: 2
        55: q+2
        56: q+2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 2
        72: q+2
        73: q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: 2
        91: 2
        92: 2q+2
        93: 2
        94: q+2
        95: q+2
        96: 2
        97: q+2
        98: q+2
        99: 2
       101: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 2
       135: 2
       136: 2
       138: 2
       142: q+2
       144: 2
       147: q+2
       153: 1
       154: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       223: 2
       225: 2
       228: 1
       230: 1
       233: 1
       234: 1
       239: 1
       240: 1
       248: 2
       257: 1
       291: 1
       292: 1
       340: 1
       341: 1
       350: 1
       356: 1
       372: 1
       516: 1

 517:    0: 2
         1: 2
         2: 2q+2
         3: 2
         4: 2q+2
         5: 2
         7: q^2+2q+2
         8: 2q+2
         9: q^2+2q+2
        13: 2
        14: q+2
        15: 2
        16: 2
        17: 2
        18: q^2+2q+2
        19: 2
        21: q+2
        22: 2
        23: 2
        24: 2q+2
        25: 2
        26: 2
        27: 2q+2
        30: 2
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        46: 2
        47: 2
        48: q+2
        49: 2
        51: q+2
        52: 2
        54: q+2
        55: 2
        57: q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 2
        74: 1
        75: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: 2
        91: 1
        93: 1
        94: 2
        96: q+2
        97: 2
        99: q+2
       100: 2
       102: q+2
       115: 1
       116: 1
       123: 1
       124: 1
       127: 1
       128: 1
       131: 1
       132: 1
       134: 1
       138: 2
       144: 2
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 2
       168: q+2
       177: 1
       178: 1
       211: 1
       212: 1
       228: 1
       233: 1
       236: 2
       237: 1
       238: 1
       241: 1
       242: 1
       249: 2
       256: 1
       258: 1
       315: 1
       316: 1
       342: 1
       343: 1
       368: 1
       373: 1
       517: 1

 518:    0: 5q+4
         1: 5q+4
         2: 3q^2+5q+2
         3: 2q^2+6q+4
         4: 5q+4
         5: 2q^2+6q+4
         6: 5q+4
         7: 3q^2+5q+2
         8: 2q^2+4q+2
        10: 5q+4
        11: 2q^2+6q+4
        12: 5q+4
        13: 3q+2
        14: 3q+2
        15: 2q+2
        16: q+4
        17: q+4
        19: 5q+4
        20: 5q+4
        21: 3q^2+5q+2
        22: 3q+4
        23: 3q+4
        24: q^2+3q+2
        25: 3q+4
        26: 3q+4
        27: q^2+3q+2
        28: q+4
        29: 5q+4
        30: 3q+2
        31: 3q+4
        32: q+2
        33: 4
        34: 3q+4
        35: q+2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: 2q+2
        46: q+2
        47: 2
        49: q+4
        50: q+4
        52: 3q+4
        53: 3q+4
        54: q^2+3q+2
        55: 3q+4
        56: 3q+4
        57: q^2+3q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 3q+2
        71: q+4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: 3q+4
        83: q+2
        84: q+2
        85: 2
        86: 3q+4
        87: q+2
        88: q+2
        89: 2
        91: q+2
        92: 2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 2
       101: 2
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 2
       136: 2
       137: 2
       139: 2
       141: q+2
       142: 2
       143: 2
       145: 2
       146: q+2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+2
       158: 2
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       222: 2
       224: 2
       230: 1
       234: 1
       243: 1
       246: 2
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       297: 1
       298: 1
       325: 1
       326: 1
       337: 1
       349: 1
       355: 1
       371: 1
       374: 1
       518: 1

 519:    0: q^2+3q+4
         1: q^2+3q+4
         2: 2q+2
         3: 4q+4
         4: q^2+3q+4
         5: 4q+4
         6: q^2+3q+4
         7: 2q+2
         8: 2q^2+4q+2
        10: q^2+3q+4
        11: 4q+4
        12: q^2+3q+4
        13: 2
        14: 2
        15: 2q+2
        16: q+4
        17: q+4
        19: q^2+3q+4
        20: q^2+3q+4
        21: 2q+2
        22: q+4
        23: q+4
        24: 2q+2
        25: q+4
        26: q+4
        27: 2q+2
        28: q+4
        29: q^2+3q+4
        30: 2
        31: q+4
        32: 2
        33: 4
        34: q+4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: 2
        45: 2q+2
        46: 2
        47: q+2
        49: q+4
        50: q+4
        52: q+4
        53: q+4
        54: 2q+2
        55: q+4
        56: q+4
        57: 2q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        70: 2
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: q+4
        83: 2
        84: 2
        85: 2
        86: q+4
        87: 2
        88: 2
        89: q+2
        91: 2
        92: q+2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 2
       101: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 2
       136: 2
       137: 2
       139: 2
       141: 2
       142: 2
       143: 2
       145: 2
       146: 2
       147: 2
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       157: 2
       158: q+2
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       222: 2
       224: 2
       230: 1
       234: 1
       243: 1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       257: 1
       297: 1
       298: 1
       337: 1
       349: 1
       355: 1
       372: 1
       375: 1
       519: 1

 520:    0: 2
         1: 2
         2: 2
         3: 2
         4: 2
         5: 2
         6: 2
         7: 2
         8: 2
         9: 2q^2+q+1
        10: 2
        11: 2
        12: 2
        13: 2
        14: 2
        15: 2
        18: 1
        19: 2
        20: 2
        21: 2
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        29: 2
        30: 2
        31: 2
        32: 2
        34: 2
        35: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: 2
        45: 2
        48: 1
        51: 1
        52: 2
        53: 2
        54: 2
        55: 2
        56: 2
        57: 2
        62: 1
        63: 1
        64: 1
        65: 1
        70: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        82: 2
        83: 2
        84: 2
        86: 2
        87: 2
        90: 1
        93: 1
        96: 1
        99: 1
       100: 2
       101: 2
       102: 2
       113: 1
       114: 1
       115: 1
       116: 1
       121: 1
       122: 1
       141: 2
       146: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       159: 1
       162: 1
       165: 1
       168: 1
       189: 1
       190: 1
       209: 1
       210: 1
       211: 1
       212: 1
       246: 2
       249: 1
       252: 1
       255: 1
       258: 1
       325: 1
       326: 1
       373: 1
       376: 1
       520: 1

 521:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       259: 1
       263: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       303: 1
       307: 1
       344: 1
       350: 1
       352: 1
       356: 1
       377: 1
       381: 1
       413: 1
       417: 1
       431: 1
       447: 1
       521: 1

 522:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       260: 1
       264: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       304: 1
       307: 1
       344: 1
       350: 1
       352: 1
       356: 1
       378: 1
       382: 1
       414: 1
       418: 1
       432: 1
       447: 1
       522: 1

 523:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       261: 1
       265: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       303: 1
       308: 1
       344: 1
       350: 1
       352: 1
       356: 1
       379: 1
       383: 1
       414: 1
       418: 1
       431: 1
       448: 1
       523: 1

 524:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       262: 1
       266: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       304: 1
       308: 1
       344: 1
       350: 1
       352: 1
       356: 1
       380: 1
       384: 1
       413: 1
       417: 1
       432: 1
       448: 1
       524: 1

 525:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: 1
       119: 1
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       259: 1
       263: 1
       275: 1
       279: 1
       289: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       327: 1
       329: 1
       345: 1
       349: 1
       353: 1
       355: 1
       381: 1
       385: 1
       409: 1
       415: 1
       439: 1
       453: 1
       525: 1

 526:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: 1
       119: 1
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       260: 1
       264: 1
       276: 1
       280: 1
       290: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       328: 1
       330: 1
       345: 1
       349: 1
       353: 1
       355: 1
       382: 1
       386: 1
       410: 1
       416: 1
       440: 1
       453: 1
       526: 1

 527:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: 1
       120: 1
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       261: 1
       265: 1
       277: 1
       280: 1
       290: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       328: 1
       330: 1
       345: 1
       349: 1
       353: 1
       355: 1
       383: 1
       387: 1
       410: 1
       416: 1
       439: 1
       454: 1
       527: 1

 528:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: 1
       120: 1
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: 1
       234: 1
       250: 1
       251: 1
       253: 1
       254: 1
       262: 1
       266: 1
       278: 1
       279: 1
       289: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       327: 1
       329: 1
       345: 1
       349: 1
       353: 1
       355: 1
       384: 1
       388: 1
       409: 1
       415: 1
       440: 1
       454: 1
       528: 1

 529:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       259: 1
       263: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       293: 1
       295: 1
       297: 1
       333: 1
       334: 1
       335: 1
       377: 1
       385: 1
       419: 1
       421: 1
       423: 1
       529: 1

 530:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       260: 1
       264: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       293: 1
       296: 1
       298: 1
       333: 1
       334: 1
       335: 1
       378: 1
       386: 1
       419: 1
       422: 1
       424: 1
       530: 1

 531:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       261: 1
       265: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       294: 1
       295: 1
       298: 1
       333: 1
       334: 1
       335: 1
       379: 1
       387: 1
       420: 1
       421: 1
       424: 1
       531: 1

 532:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: 1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: q+1
       159: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       262: 1
       266: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       294: 1
       296: 1
       297: 1
       333: 1
       334: 1
       335: 1
       380: 1
       388: 1
       420: 1
       422: 1
       423: 1
       532: 1

 533:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 2q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       109: q+1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: q+1
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       259: 1
       263: 1
       267: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       315: 1
       317: 1
       319: 1
       325: 1
       344: 1
       348: 1
       350: 1
       366: 1
       377: 1
       389: 1
       393: 1
       429: 1
       431: 1
       433: 1
       469: 1
       533: 1

 534:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 2q+1
        60: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 1
       110: q+1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: q+1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       260: 1
       264: 1
       268: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       316: 1
       318: 1
       319: 1
       326: 1
       344: 1
       348: 1
       350: 1
       366: 1
       378: 1
       390: 1
       394: 1
       429: 1
       432: 1
       434: 1
       470: 1
       534: 1

 535:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 2q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: 1
       109: q+1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: q+1
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       261: 1
       265: 1
       270: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       316: 1
       318: 1
       320: 1
       326: 1
       344: 1
       348: 1
       350: 1
       366: 1
       379: 1
       392: 1
       395: 1
       430: 1
       431: 1
       434: 1
       470: 1
       535: 1

 536:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 2q+1
        61: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: 1
       110: q+1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: q+1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       262: 1
       266: 1
       269: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       315: 1
       317: 1
       320: 1
       325: 1
       344: 1
       348: 1
       350: 1
       366: 1
       380: 1
       391: 1
       396: 1
       430: 1
       432: 1
       433: 1
       469: 1
       536: 1

 537:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: q+1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       193: 1
       195: 1
       197: 1
       201: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       279: 1
       289: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       317: 1
       319: 1
       325: 1
       360: 1
       362: 1
       367: 1
       369: 1
       381: 1
       389: 1
       393: 1
       435: 1
       465: 1
       471: 1
       537: 1

 538:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: q+1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       193: 1
       196: 1
       198: 1
       201: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       280: 1
       290: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       318: 1
       319: 1
       326: 1
       361: 1
       363: 1
       367: 1
       369: 1
       382: 1
       390: 1
       394: 1
       436: 1
       466: 1
       471: 1
       538: 1

 539:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: q+1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       194: 1
       196: 1
       197: 1
       202: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       279: 1
       289: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       317: 1
       320: 1
       325: 1
       360: 1
       362: 1
       367: 1
       369: 1
       384: 1
       391: 1
       396: 1
       435: 1
       465: 1
       472: 1
       539: 1

 540:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: q+1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       194: 1
       195: 1
       198: 1
       202: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       280: 1
       290: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       318: 1
       320: 1
       326: 1
       361: 1
       363: 1
       367: 1
       369: 1
       383: 1
       392: 1
       395: 1
       436: 1
       466: 1
       472: 1
       540: 1

 541:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       160: 1
       161: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       207: 1
       209: 1
       211: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       263: 1
       267: 1
       275: 1
       293: 1
       295: 1
       297: 1
       299: 1
       303: 1
       305: 1
       325: 1
       345: 1
       347: 1
       349: 1
       385: 1
       393: 1
       437: 1
       439: 1
       441: 1
       541: 1

 542:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       161: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       208: 1
       210: 1
       212: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       264: 1
       268: 1
       276: 1
       293: 1
       296: 1
       298: 1
       299: 1
       304: 1
       306: 1
       326: 1
       345: 1
       347: 1
       349: 1
       386: 1
       394: 1
       437: 1
       440: 1
       442: 1
       542: 1

 543:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       160: 1
       161: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       207: 1
       209: 1
       211: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       266: 1
       269: 1
       278: 1
       294: 1
       296: 1
       297: 1
       300: 1
       304: 1
       305: 1
       325: 1
       345: 1
       347: 1
       349: 1
       388: 1
       396: 1
       438: 1
       440: 1
       441: 1
       543: 1

 544:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
       100: 1
       101: 1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       161: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       208: 1
       210: 1
       212: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       246: 1
       250: 1
       251: 1
       265: 1
       270: 1
       277: 1
       294: 1
       295: 1
       298: 1
       300: 1
       303: 1
       306: 1
       326: 1
       345: 1
       347: 1
       349: 1
       387: 1
       395: 1
       438: 1
       439: 1
       442: 1
       544: 1

 545:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: q+1
        33: q+1
        34: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: 1
        59: q
        60: 1
        62: 1
        66: 1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       110: q
       111: 1
       113: 1
       127: 1
       129: 1
       139: q+1
       140: 1
       142: q+1
       145: 1
       147: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       193: 1
       195: 1
       196: q
       197: 1
       201: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       247: 1
       248: 1
       259: 1
       267: 1
       301: 1
       317: 1
       319: 1
       337: 1
       338: 1
       340: 1
       351: 1
       389: 1
       427: 1
       443: 1
       445: 1
       545: 1

 546:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: q+1
        33: q+1
        34: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q
        59: 1
        60: 1
        63: 1
        67: 1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       107: 1
       109: q
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: q+1
       140: 1
       142: q+1
       145: 1
       147: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       193: 1
       195: q
       196: 1
       198: 1
       201: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       247: 1
       248: 1
       260: 1
       268: 1
       302: 1
       318: 1
       319: 1
       337: 1
       339: 1
       341: 1
       351: 1
       390: 1
       428: 1
       443: 1
       446: 1
       546: 1

 547:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: q+1
        33: q+1
        34: 1
        36: 1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: q
        59: 1
        61: 1
        62: 1
        66: 1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       106: 1
       108: 1
       109: q
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: q+1
       140: 1
       142: q+1
       145: 1
       147: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       194: 1
       195: q
       196: 1
       197: 1
       202: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       247: 1
       248: 1
       262: 1
       269: 1
       301: 1
       317: 1
       320: 1
       337: 1
       338: 1
       340: 1
       351: 1
       391: 1
       427: 1
       444: 1
       445: 1
       547: 1

 548:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        28: q+1
        29: q+1
        31: q+1
        33: q+1
        34: 1
        36: 1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        55: 1
        56: 1
        58: 1
        59: q
        61: 1
        63: 1
        67: 1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        82: q+1
        86: 1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: 1
       105: 1
       108: 1
       109: 1
       110: q
       112: 1
       114: 1
       128: 1
       130: 1
       139: q+1
       140: 1
       142: q+1
       145: 1
       147: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       194: 1
       195: 1
       196: q
       198: 1
       202: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       247: 1
       248: 1
       261: 1
       270: 1
       302: 1
       318: 1
       320: 1
       337: 1
       339: 1
       341: 1
       351: 1
       392: 1
       428: 1
       444: 1
       446: 1
       548: 1

 549:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q+1
        60: 2q+1
        61: q
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: q+1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: q+1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       259: 1
       263: 1
       271: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       352: 1
       356: 1
       358: 1
       366: 1
       377: 1
       397: 1
       401: 1
       447: 1
       449: 1
       451: 1
       469: 1
       549: 1

 550:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q+1
        60: q
        61: 2q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: q+1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: q+1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       261: 1
       265: 1
       272: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       352: 1
       356: 1
       358: 1
       366: 1
       379: 1
       398: 1
       402: 1
       448: 1
       449: 1
       452: 1
       470: 1
       550: 1

 551:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        59: q+1
        60: 2q+1
        61: q
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: q+1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: q+1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       260: 1
       264: 1
       274: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       352: 1
       356: 1
       358: 1
       366: 1
       378: 1
       400: 1
       403: 1
       447: 1
       450: 1
       452: 1
       470: 1
       551: 1

 552:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        59: q+1
        60: q
        61: 2q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: q+1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: q+1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       262: 1
       266: 1
       273: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       352: 1
       356: 1
       358: 1
       366: 1
       380: 1
       399: 1
       404: 1
       448: 1
       450: 1
       451: 1
       469: 1
       552: 1

 553:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        60: q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       120: q
       121: q+1
       123: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       169: 1
       173: q+1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       195: 1
       201: 1
       203: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       259: 1
       263: 1
       271: 1
       279: 1
       289: 1
       303: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       321: 1
       325: 1
       360: 1
       362: 1
       367: 1
       370: 1
       381: 1
       397: 1
       401: 1
       455: 1
       465: 1
       473: 1
       553: 1

 554:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        60: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       119: q
       120: q+1
       122: q+1
       124: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       171: 1
       175: q+1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       195: 1
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       261: 1
       265: 1
       272: 1
       280: 1
       290: 1
       303: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       321: 1
       326: 1
       361: 1
       363: 1
       367: 1
       370: 1
       383: 1
       398: 1
       402: 1
       456: 1
       466: 1
       473: 1
       554: 1

 555:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q^2+2q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        60: q
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       119: q
       120: q+1
       121: q+1
       123: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       172: 1
       176: q+1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       196: 1
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       262: 1
       266: 1
       273: 1
       279: 1
       289: 1
       304: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       322: 1
       325: 1
       360: 1
       362: 1
       367: 1
       370: 1
       384: 1
       399: 1
       404: 1
       455: 1
       465: 1
       474: 1
       555: 1

 556:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        60: q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       120: q
       122: q+1
       124: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       170: 1
       174: q+1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       196: 1
       201: 1
       204: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: 1
       260: 1
       264: 1
       274: 1
       280: 1
       290: 1
       304: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       322: 1
       326: 1
       361: 1
       363: 1
       367: 1
       370: 1
       382: 1
       400: 1
       403: 1
       456: 1
       466: 1
       474: 1
       556: 1

 557:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       163: 1
       164: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       220: 1
       222: 1
       224: 1
       232: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       263: 1
       271: 1
       275: 1
       293: 1
       295: 1
       297: 1
       307: 1
       309: 1
       313: 1
       325: 1
       353: 1
       355: 1
       357: 1
       385: 1
       401: 1
       453: 1
       457: 1
       459: 1
       557: 1

 558:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       163: 1
       164: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       220: 1
       222: 1
       224: 1
       232: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       265: 1
       272: 1
       277: 1
       294: 1
       295: 1
       298: 1
       308: 1
       309: 1
       314: 1
       326: 1
       353: 1
       355: 1
       357: 1
       387: 1
       402: 1
       454: 1
       457: 1
       460: 1
       558: 1

 559:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       163: 1
       164: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       220: 1
       222: 1
       224: 1
       232: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       266: 1
       273: 1
       278: 1
       294: 1
       296: 1
       297: 1
       308: 1
       310: 1
       313: 1
       325: 1
       353: 1
       355: 1
       357: 1
       388: 1
       404: 1
       454: 1
       458: 1
       459: 1
       559: 1

 560:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       141: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       163: 1
       164: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       220: 1
       222: 1
       224: 1
       232: 1
       234: 1
       235: 1
       246: 1
       253: 1
       254: 1
       264: 1
       274: 1
       276: 1
       293: 1
       296: 1
       298: 1
       307: 1
       310: 1
       314: 1
       326: 1
       353: 1
       355: 1
       357: 1
       386: 1
       403: 1
       453: 1
       458: 1
       460: 1
       560: 1

 561:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: q+1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: 1
        60: 1
        61: q
        62: 1
        66: 1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       103: 1
       107: 1
       108: q
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: q+1
       147: q+1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       195: 1
       201: 1
       202: q
       203: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       245: 1
       247: 1
       248: 1
       259: 1
       271: 1
       311: 1
       317: 1
       321: 1
       337: 1
       338: 1
       340: 1
       359: 1
       397: 1
       427: 1
       461: 1
       463: 1
       561: 1

 562:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: q+1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        58: 1
        60: q
        61: 1
        63: 1
        67: 1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       105: 1
       107: q
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: q+1
       147: q+1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       195: 1
       201: q
       202: 1
       203: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       245: 1
       247: 1
       248: 1
       261: 1
       272: 1
       312: 1
       318: 1
       321: 1
       337: 1
       339: 1
       341: 1
       359: 1
       398: 1
       428: 1
       461: 1
       464: 1
       562: 1

 563:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: q+1
        37: 1
        39: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: 1
        60: q
        61: 1
        62: 1
        66: 1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       106: 1
       107: q
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       142: 1
       145: q+1
       147: q+1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       196: 1
       201: q
       202: 1
       204: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       245: 1
       247: 1
       248: 1
       262: 1
       273: 1
       311: 1
       317: 1
       322: 1
       337: 1
       338: 1
       340: 1
       359: 1
       399: 1
       427: 1
       462: 1
       463: 1
       563: 1

 564:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        28: q+1
        29: q+1
        31: 1
        33: 1
        34: q+1
        36: q+1
        38: 1
        40: 1
        49: q+1
        50: q+1
        52: 1
        53: 1
        55: q+1
        56: q+1
        59: 1
        60: 1
        61: q
        63: 1
        67: 1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        82: 1
        86: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       104: 1
       107: 1
       108: q
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       142: 1
       145: q+1
       147: q+1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       196: 1
       201: 1
       202: q
       204: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       245: 1
       247: 1
       248: 1
       260: 1
       274: 1
       312: 1
       318: 1
       322: 1
       337: 1
       339: 1
       341: 1
       359: 1
       400: 1
       428: 1
       462: 1
       464: 1
       564: 1

 565:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: q
        39: q^2+2q+1
        40: q^2+q
        41: q+1
        42: q
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        60: q+1
        62: q+1
        63: q
        64: q+1
        65: q
        66: q+1
        68: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       121: q+1
       122: q
       123: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: q+1
       183: 1
       185: 1
       187: 1
       189: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       211: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       256: 1
       257: 1
       263: 1
       267: 1
       271: 1
       299: 1
       303: 1
       305: 1
       307: 1
       309: 1
       313: 1
       319: 1
       321: 1
       323: 1
       325: 1
       367: 1
       369: 1
       370: 1
       393: 1
       401: 1
       405: 1
       471: 1
       473: 1
       475: 1
       565: 1

 566:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        37: q
        38: q+1
        39: q^2+q
        40: q^2+2q+1
        41: q
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        60: q+1
        62: q
        63: q+1
        64: q
        65: q+1
        67: q+1
        68: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       121: q
       122: q+1
       124: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: q+1
       183: 1
       186: 1
       188: 1
       190: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       212: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       256: 1
       257: 1
       264: 1
       268: 1
       274: 1
       299: 1
       304: 1
       306: 1
       307: 1
       310: 1
       314: 1
       319: 1
       322: 1
       324: 1
       326: 1
       367: 1
       369: 1
       370: 1
       394: 1
       403: 1
       407: 1
       471: 1
       474: 1
       476: 1
       566: 1

 567:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        37: q
        38: q+1
        39: q^2+q
        40: q^2+2q+1
        41: q
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        61: q+1
        62: q
        63: q+1
        64: q
        65: q+1
        67: q+1
        68: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       120: q+1
       121: q
       122: q+1
       124: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: q+1
       184: 1
       185: 1
       188: 1
       190: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       256: 1
       257: 1
       265: 1
       270: 1
       272: 1
       300: 1
       303: 1
       306: 1
       308: 1
       309: 1
       314: 1
       320: 1
       321: 1
       324: 1
       326: 1
       367: 1
       369: 1
       370: 1
       395: 1
       402: 1
       408: 1
       472: 1
       473: 1
       476: 1
       567: 1

 568:    0: 2q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q+1
         6: q^3+2q^2+2q+1
         7: q^2+q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: q
        39: q^2+2q+1
        40: q^2+q
        41: q+1
        42: q
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        61: q+1
        62: q+1
        63: q
        64: q+1
        65: q
        66: q+1
        68: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       120: q+1
       121: q+1
       122: q
       123: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: q+1
       184: 1
       186: 1
       187: 1
       189: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       256: 1
       257: 1
       266: 1
       269: 1
       273: 1
       300: 1
       304: 1
       305: 1
       308: 1
       310: 1
       313: 1
       320: 1
       322: 1
       323: 1
       325: 1
       367: 1
       369: 1
       370: 1
       396: 1
       404: 1
       406: 1
       472: 1
       474: 1
       475: 1
       568: 1

 569:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        10: 1
        11: 1
        12: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        60: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       259: 1
       267: 1
       271: 1
       301: 1
       311: 1
       317: 1
       319: 1
       321: 1
       323: 1
       389: 1
       397: 1
       405: 1
       477: 1
       569: 1

 570:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        10: 1
        11: 1
        12: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        61: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       262: 1
       269: 1
       273: 1
       301: 1
       311: 1
       317: 1
       320: 1
       322: 1
       323: 1
       391: 1
       399: 1
       406: 1
       477: 1
       570: 1

 571:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        10: 1
        11: 1
        12: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        60: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       260: 1
       268: 1
       274: 1
       302: 1
       312: 1
       318: 1
       319: 1
       322: 1
       324: 1
       390: 1
       400: 1
       407: 1
       478: 1
       571: 1

 572:    0: 1
         1: 1
         3: 1
         4: q^3+1
         5: 1
         6: q^3+1
        10: 1
        11: 1
        12: q^3+1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        61: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       261: 1
       270: 1
       272: 1
       302: 1
       312: 1
       318: 1
       320: 1
       321: 1
       324: 1
       392: 1
       398: 1
       408: 1
       478: 1
       572: 1

 573:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: q+1
        36: 1
        37: 1
        38: q
        39: 1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        58: 1
        60: 1
        62: 1
        63: q
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: 1
        77: q
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       114: q
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: 1
       152: q
       153: 1
       154: q
       166: 1
       167: 1
       169: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       210: q
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       267: 1
       271: 1
       319: 1
       321: 1
       323: 1
       337: 1
       351: 1
       359: 1
       405: 1
       443: 1
       461: 1
       479: 1
       573: 1

 574:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: q+1
        36: 1
        37: q
        38: 1
        39: q
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        59: 1
        60: 1
        62: q
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q
        77: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       104: 1
       107: 1
       110: 1
       112: 1
       113: q
       114: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: q
       152: 1
       153: q
       154: 1
       166: 1
       167: 1
       170: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       209: q
       210: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       268: 1
       274: 1
       319: 1
       322: 1
       324: 1
       337: 1
       351: 1
       359: 1
       407: 1
       443: 1
       462: 1
       480: 1
       574: 1

 575:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: q+1
        36: 1
        37: 1
        38: q
        39: 1
        40: q
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        59: 1
        61: 1
        62: 1
        63: q
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: 1
        77: q
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       114: q
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: 1
       152: q
       153: 1
       154: q
       166: 1
       167: 1
       172: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       210: q
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       269: 1
       273: 1
       320: 1
       322: 1
       323: 1
       337: 1
       351: 1
       359: 1
       406: 1
       444: 1
       462: 1
       479: 1
       575: 1

 576:    0: q+1
         1: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
        10: q+1
        11: q+1
        12: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        28: 1
        29: q+1
        31: q+1
        33: 1
        34: q+1
        36: 1
        37: q
        38: 1
        39: q
        40: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        55: q+1
        56: q+1
        58: 1
        61: 1
        62: q
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q
        77: 1
        82: q+1
        86: q+1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       105: 1
       108: 1
       109: 1
       112: 1
       113: q
       114: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: q+1
       151: q
       152: 1
       153: q
       154: 1
       166: 1
       167: 1
       171: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       209: q
       210: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       270: 1
       272: 1
       320: 1
       321: 1
       324: 1
       337: 1
       351: 1
       359: 1
       408: 1
       444: 1
       461: 1
       480: 1
       576: 1

 577:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       111: 1
       127: 1
       129: 1
       140: 1
       142: 1
       147: 1
       148: 1
       151: 1
       153: 1
       166: 1
       167: 1
       181: 1
       197: 1
       205: 1
       237: 1
       239: 1
       244: 1
       245: 1
       247: 1
       248: 1
       301: 1
       311: 1
       323: 1
       338: 1
       340: 1
       351: 1
       359: 1
       445: 1
       463: 1
       477: 1
       479: 1
       577: 1

 578:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        33: 3q
        36: 3q
        37: q
        38: 2q
        39: q
        40: 2q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        66: q
        67: 2q
        72: q
        73: q
        75: q
        77: q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       128: q
       130: q
       140: q
       142: q
       147: q
       148: q
       152: q
       154: q
       166: 2q
       167: 2q
       238: q
       240: q
       244: q
       245: q
       247: 1
       248: 1
       339: 1
       341: 1
       351: 1
       359: 1
       446: 1
       464: 1
       479: 1
       578: 1

 579:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        33: q
        36: q
        37: q
        39: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        66: q
        72: q
        73: q
        74: q
        76: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       111: q
       127: q
       129: q
       140: q
       142: q
       147: q
       148: q
       151: q
       153: q
       181: q
       197: q
       205: q
       477: 1
       579: 1

 580:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        33: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q
        40: q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        66: 2q
        67: q
        72: q
        73: q
        74: q
        76: q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       127: q
       129: q
       140: q
       142: q
       147: q
       148: q
       151: q
       153: q
       166: 2q
       167: 2q
       237: q
       239: q
       244: q
       245: q
       247: 1
       248: 1
       338: 1
       340: 1
       351: 1
       359: 1
       445: 1
       463: 1
       480: 1
       580: 1

 581:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        33: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       112: 1
       128: 1
       130: 1
       140: 1
       142: 1
       147: 1
       148: 1
       152: 1
       154: 1
       166: 1
       167: 1
       182: 1
       198: 1
       206: 1
       238: 1
       240: 1
       244: 1
       245: 1
       247: 1
       248: 1
       302: 1
       312: 1
       324: 1
       339: 1
       341: 1
       351: 1
       359: 1
       446: 1
       464: 1
       478: 1
       480: 1
       581: 1

 582:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        33: q
        36: q
        38: q
        40: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        67: q
        72: q
        73: q
        75: q
        77: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       112: q
       128: q
       130: q
       140: q
       142: q
       147: q
       148: q
       152: q
       154: q
       182: q
       198: q
       206: q
       478: 1
       582: 1

 583:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         7: q^2+q+1
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+2
        14: q^2+q+1
        15: q+2
        16: q+2
        17: q+2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2
        41: 2
        43: q+2
        44: q^2+q+1
        45: q+2
        46: q+2
        47: q+2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: q+2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       125: q+2
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       173: 1
       176: 1
       177: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       275: 1
       278: 1
       279: 1
       281: 1
       287: 1
       327: 1
       329: 1
       331: 1
       333: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       409: 1
       411: 1
       413: 1
       492: 1
       497: 1
       583: 1

 584:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         7: q^2+q+1
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+2
        14: q^2+q+1
        15: q+2
        16: q+2
        17: q+2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: q+2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2
        42: 2
        43: q+2
        44: q^2+q+1
        45: q+2
        46: q+2
        47: q+2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: q+2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       125: q+2
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       174: 1
       175: 1
       178: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       276: 1
       277: 1
       280: 1
       282: 1
       288: 1
       328: 1
       330: 1
       332: 1
       333: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       410: 1
       412: 1
       414: 1
       492: 1
       497: 1
       584: 1

 585:    0: 4q+2
         1: 2q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: q^3+3q^2+4q+2
         6: 2q^2+4q+2
         7: 4q+2
         8: q^3+3q^2+4q+2
         9: q^2+2q+1
        10: 3q+2
        11: q^2+3q+2
        12: 3q+2
        13: 4q+2
        14: 4q+2
        15: q^3+3q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: 2q^2+4q+2
        21: 4q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 3q+2
        30: 4q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: q+2
        35: 2q+2
        36: q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 2q+2
        66: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: q+2
        73: q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+2
       113: q+2
       115: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: q+2
       125: q+2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: q+2
       158: q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: q+2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       213: 2
       215: 2
       217: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       333: 1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       381: 1
       384: 1
       385: 1
       388: 1
       413: 1
       417: 1
       423: 1
       481: 1
       482: 1
       585: 1

 586:    0: 4q+2
         1: 2q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: q^3+3q^2+4q+2
         6: 2q^2+4q+2
         7: 4q+2
         8: q^3+3q^2+4q+2
         9: q^2+2q+1
        10: 3q+2
        11: q^2+3q+2
        12: 3q+2
        13: 4q+2
        14: 4q+2
        15: q^3+3q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: 2q^2+4q+2
        21: 4q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 3q+2
        30: 4q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: q+2
        35: 2q+2
        36: q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 2q+2
        67: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: q+2
        73: q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+2
       114: q+2
       116: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: q+2
       125: q+2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: q+2
       158: q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: q+2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       333: 1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       382: 1
       383: 1
       386: 1
       387: 1
       414: 1
       418: 1
       424: 1
       481: 1
       482: 1
       586: 1

 587:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       259: 1
       262: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       411: 1
       415: 1
       417: 1
       423: 1
       494: 1
       498: 1
       587: 1

 588:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       260: 1
       261: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       412: 1
       416: 1
       418: 1
       424: 1
       494: 1
       498: 1
       588: 1

 589:    0: 1
         1: q^2+1
         2: 1
         3: 1
         4: 1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: q^2+1
        16: 1
        17: q^2+1
        18: 1
        19: 1
        20: q^2+1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+1
        93: 1
        97: 1
        98: 1
        99: 1
       107: 1
       119: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       183: 1
       199: 1
       201: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       283: 1
       293: 1
       307: 1
       333: 1
       334: 1
       352: 1
       356: 1
       419: 1
       447: 1
       481: 1
       589: 1

 590:    0: 1
         1: q^2+1
         2: 1
         3: 1
         4: 1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: q^2+1
        16: 1
        17: q^2+1
        18: 1
        19: 1
        20: q^2+1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        55: 1
        56: 1
        57: 1
        61: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+1
        93: 1
        97: 1
        98: 1
        99: 1
       108: 1
       120: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       184: 1
       200: 1
       202: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       284: 1
       294: 1
       308: 1
       333: 1
       334: 1
       352: 1
       356: 1
       420: 1
       448: 1
       481: 1
       590: 1

 591:    0: 3q^2+8q+2
         1: q^3+6q^2+8q+2
         2: q^2+5q+2
         3: q^3+7q^2+8q+2
         4: 3q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+6q^2+8q+2
         7: q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^2+2q+1
        10: 2q^2+6q+2
        11: 4q^2+6q+2
        12: 2q^2+6q+2
        13: 5q+2
        14: 5q+2
        15: 3q^2+5q+2
        16: 2q^2+7q+2
        17: 3q^2+7q+2
        18: 2q+1
        19: 3q^2+8q+2
        20: q^3+6q^2+8q+2
        21: q^2+5q+2
        22: 5q+2
        23: q^2+5q+2
        24: 3q+2
        25: 2q^2+7q+2
        26: 3q^2+7q+2
        27: q^2+4q+2
        28: q^2+5q+2
        29: 2q^2+6q+2
        30: 5q+2
        31: 3q+2
        32: 3q+2
        33: 5q+2
        34: q^2+5q+2
        35: 4q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 4q+2
        47: q^2+4q+2
        48: 2q+1
        49: 2q^2+7q+2
        50: 3q^2+7q+2
        51: 2q+1
        52: 5q+2
        53: q^2+5q+2
        54: 3q+2
        55: 2q^2+7q+2
        56: 3q^2+7q+2
        57: q^2+4q+2
        58: 3q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q^2+5q+2
        72: q^2+6q+2
        73: 5q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: 3q+2
        83: 3q+2
        84: 2q+2
        85: 3q+2
        86: q^2+5q+2
        87: 4q+2
        88: q+2
        89: q+2
        90: q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 3q+2
        98: 3q+2
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       103: q+1
       105: q+1
       107: 2q+1
       108: 2q+1
       109: 3q+2
       111: 2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+1
       141: q+2
       142: 2q+1
       143: q+2
       144: 1
       145: 2q+2
       146: 2q+2
       147: 3q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       171: q+1
       173: 1
       175: 1
       183: 1
       184: 1
       185: q+2
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 2
       195: q+1
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: q+1
       226: 1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       352: 1
       356: 1
       358: 1
       359: 1
       366: 1
       385: 1
       387: 1
       401: 1
       402: 1
       421: 1
       449: 1
       461: 1
       481: 1
       483: 1
       500: 1
       591: 1

 592:    0: 3q^2+8q+2
         1: q^3+6q^2+8q+2
         2: q^2+5q+2
         3: q^3+7q^2+8q+2
         4: 3q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+6q^2+8q+2
         7: q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^2+2q+1
        10: 2q^2+6q+2
        11: 4q^2+6q+2
        12: 2q^2+6q+2
        13: 5q+2
        14: 5q+2
        15: 3q^2+5q+2
        16: 2q^2+7q+2
        17: 3q^2+7q+2
        18: 2q+1
        19: 3q^2+8q+2
        20: q^3+6q^2+8q+2
        21: q^2+5q+2
        22: 5q+2
        23: q^2+5q+2
        24: 3q+2
        25: 2q^2+7q+2
        26: 3q^2+7q+2
        27: q^2+4q+2
        28: q^2+5q+2
        29: 2q^2+6q+2
        30: 5q+2
        31: 3q+2
        32: 3q+2
        33: 5q+2
        34: q^2+5q+2
        35: 4q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 4q+2
        47: q^2+4q+2
        48: 2q+1
        49: 2q^2+7q+2
        50: 3q^2+7q+2
        51: 2q+1
        52: 5q+2
        53: q^2+5q+2
        54: 3q+2
        55: 2q^2+7q+2
        56: 3q^2+7q+2
        57: q^2+4q+2
        59: 3q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q^2+5q+2
        72: q^2+6q+2
        73: 5q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: 3q+2
        83: 3q+2
        84: 2q+2
        85: 3q+2
        86: q^2+5q+2
        87: 4q+2
        88: q+2
        89: q+2
        90: q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 3q+2
        98: 3q+2
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       104: q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       110: 3q+2
       111: 2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: q+2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+1
       141: q+2
       142: 2q+1
       143: q+2
       144: 1
       145: 2q+2
       146: 2q+2
       147: 3q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: q+1
       172: q+1
       174: 1
       176: 1
       183: 1
       184: 1
       186: q+2
       187: q+1
       188: q+1
       189: 1
       190: 1
       192: 2
       196: q+1
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: q+1
       226: 1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       352: 1
       356: 1
       358: 1
       359: 1
       366: 1
       386: 1
       388: 1
       403: 1
       404: 1
       422: 1
       450: 1
       462: 1
       481: 1
       483: 1
       500: 1
       592: 1

 593:    0: 3q^2+8q+2
         1: q^3+6q^2+8q+2
         2: q^2+5q+2
         3: q^3+7q^2+8q+2
         4: 3q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+6q^2+8q+2
         7: q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^2+2q+1
        10: 2q^2+6q+2
        11: 4q^2+6q+2
        12: 2q^2+6q+2
        13: 5q+2
        14: 5q+2
        15: 3q^2+5q+2
        16: 2q^2+7q+2
        17: 3q^2+7q+2
        18: 2q+1
        19: 3q^2+8q+2
        20: q^3+6q^2+8q+2
        21: q^2+5q+2
        22: 2q^2+7q+2
        23: 3q^2+7q+2
        24: q^2+4q+2
        25: 5q+2
        26: q^2+5q+2
        27: 3q+2
        28: q^2+5q+2
        29: 2q^2+6q+2
        30: 5q+2
        31: q^2+5q+2
        32: 4q+2
        33: q^2+6q+2
        34: 3q+2
        35: 3q+2
        36: 5q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 4q+2
        47: q^2+4q+2
        48: 2q+1
        49: 2q^2+7q+2
        50: 3q^2+7q+2
        51: 2q+1
        52: 2q^2+7q+2
        53: 3q^2+7q+2
        54: q^2+4q+2
        55: 5q+2
        56: q^2+5q+2
        57: 3q+2
        58: 2q+1
        59: 2q+1
        60: 3q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q^2+5q+2
        72: 5q+2
        73: q^2+6q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 3q+2
        82: q^2+5q+2
        83: 4q+2
        84: q+2
        85: 3q+2
        86: 3q+2
        87: 3q+2
        88: q+2
        89: q+2
        90: q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 3q+2
        95: 3q+2
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       103: q+1
       104: q+1
       107: 3q+2
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: q+2
       138: 1
       139: 2q+2
       140: 2
       141: 2q+2
       142: 3q+2
       143: 2
       144: q+1
       145: q+1
       146: q+2
       147: 2q+1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       173: 1
       174: 1
       183: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: q+2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       319: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       348: 1
       350: 1
       351: 1
       366: 1
       385: 1
       386: 1
       393: 1
       394: 1
       419: 1
       429: 1
       443: 1
       482: 1
       483: 1
       495: 1
       593: 1

 594:    0: 3q^2+8q+2
         1: q^3+6q^2+8q+2
         2: q^2+5q+2
         3: q^3+7q^2+8q+2
         4: 3q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+6q^2+8q+2
         7: q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^2+2q+1
        10: 2q^2+6q+2
        11: 4q^2+6q+2
        12: 2q^2+6q+2
        13: 5q+2
        14: 5q+2
        15: 3q^2+5q+2
        16: 2q^2+7q+2
        17: 3q^2+7q+2
        18: 2q+1
        19: 3q^2+8q+2
        20: q^3+6q^2+8q+2
        21: q^2+5q+2
        22: 2q^2+7q+2
        23: 3q^2+7q+2
        24: q^2+4q+2
        25: 5q+2
        26: q^2+5q+2
        27: 3q+2
        28: q^2+5q+2
        29: 2q^2+6q+2
        30: 5q+2
        31: q^2+5q+2
        32: 4q+2
        33: q^2+6q+2
        34: 3q+2
        35: 3q+2
        36: 5q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: q^2+3q+2
        46: 4q+2
        47: q^2+4q+2
        48: 2q+1
        49: 2q^2+7q+2
        50: 3q^2+7q+2
        51: 2q+1
        52: 2q^2+7q+2
        53: 3q^2+7q+2
        54: q^2+4q+2
        55: 5q+2
        56: q^2+5q+2
        57: 3q+2
        58: 2q+1
        59: 2q+1
        61: 3q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q^2+5q+2
        72: 5q+2
        73: q^2+6q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 3q+2
        82: q^2+5q+2
        83: 4q+2
        84: q+2
        85: 3q+2
        86: 3q+2
        87: 3q+2
        88: q+2
        89: q+2
        90: q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 3q+2
        95: 3q+2
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       105: q+1
       106: q+1
       108: 3q+2
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: q+2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: q+2
       138: 1
       139: 2q+2
       140: 2
       141: 2q+2
       142: 3q+2
       143: 2
       144: q+1
       145: q+1
       146: q+2
       147: 2q+1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       166: 1
       167: q+1
       168: 1
       171: q+1
       172: q+1
       175: 1
       176: 1
       184: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: q+2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       320: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       348: 1
       350: 1
       351: 1
       366: 1
       387: 1
       388: 1
       395: 1
       396: 1
       420: 1
       430: 1
       444: 1
       482: 1
       483: 1
       495: 1
       594: 1

 595:    0: 1
         1: q^2+1
         2: 1
         3: 1
         4: 1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: q^2+1
        16: 1
        17: q^2+1
        18: 1
        19: 1
        20: q^2+1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: 1
        96: 1
       109: 1
       117: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       185: 1
       191: 1
       195: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       285: 1
       295: 1
       303: 1
       333: 1
       335: 1
       344: 1
       350: 1
       421: 1
       431: 1
       482: 1
       595: 1

 596:    0: 1
         1: q^2+1
         2: 1
         3: 1
         4: 1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: q^2+1
        16: 1
        17: q^2+1
        18: 1
        19: 1
        20: q^2+1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: 1
        54: 1
        59: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: 1
        96: 1
       110: 1
       118: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       186: 1
       192: 1
       196: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       286: 1
       296: 1
       304: 1
       333: 1
       335: 1
       344: 1
       350: 1
       422: 1
       432: 1
       482: 1
       596: 1

 597:    0: 3q+1
         1: q+1
         2: 3q+1
         3: q^2+2q+1
         4: 3q+1
         5: q^2+2q+1
         6: q+1
         7: 3q+1
         8: q^2+2q+1
         9: q^2+2q+1
        13: 3q+1
        14: 3q+1
        15: q^2+2q+1
        16: 2q+1
        17: q+1
        18: 2q+1
        19: 3q+1
        20: q+1
        21: 3q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        30: 3q+1
        32: 2q+1
        33: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        39: q+1
        41: 2q+1
        46: 2q+1
        47: q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        64: 2q+1
        66: q+1
        69: q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: q+1
        78: 2q+1
        81: q+1
        83: 2q+1
        85: q+1
        87: 2q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: q+1
       102: q+1
       111: q+1
       115: 2q+1
       123: q+1
       127: 1
       129: 1
       131: q+1
       134: q+1
       135: q+1
       136: q+1
       138: 1
       142: 1
       144: 1
       147: 1
       150: q+1
       151: q+1
       155: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       168: 1
       177: 1
       181: 1
       187: q+1
       211: q+1
       213: 1
       215: 1
       217: q+1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       237: 1
       241: 1
       247: 1
       249: 1
       256: 1
       258: 1
       281: 1
       289: 1
       291: 1
       315: 1
       336: 1
       338: 1
       342: 1
       350: 1
       356: 1
       360: 1
       364: 1
       368: 1
       371: 1
       373: 1
       417: 1
       425: 1
       467: 1
       485: 1
       489: 1
       491: 1
       597: 1

 598:    0: 3q+1
         1: q+1
         2: 3q+1
         3: q^2+2q+1
         4: 3q+1
         5: q^2+2q+1
         6: q+1
         7: 3q+1
         8: q^2+2q+1
         9: q^2+2q+1
        13: 3q+1
        14: 3q+1
        15: q^2+2q+1
        16: 2q+1
        17: q+1
        18: 2q+1
        19: 3q+1
        20: q+1
        21: 3q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        30: 3q+1
        32: 2q+1
        33: q+1
        35: 2q+1
        36: q+1
        38: 2q+1
        40: q+1
        42: 2q+1
        46: 2q+1
        47: q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        65: 2q+1
        67: q+1
        69: q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: q+1
        79: 2q+1
        81: q+1
        83: 2q+1
        85: q+1
        87: 2q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: q+1
       102: q+1
       112: q+1
       116: 2q+1
       124: q+1
       128: 1
       130: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       138: 1
       142: 1
       144: 1
       147: 1
       150: q+1
       152: q+1
       156: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       168: 1
       178: 1
       182: 1
       188: q+1
       212: q+1
       214: 1
       216: 1
       218: q+1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       238: 1
       242: 1
       247: 1
       249: 1
       256: 1
       258: 1
       282: 1
       290: 1
       292: 1
       316: 1
       336: 1
       339: 1
       343: 1
       350: 1
       356: 1
       361: 1
       365: 1
       368: 1
       371: 1
       373: 1
       418: 1
       426: 1
       468: 1
       486: 1
       490: 1
       491: 1
       598: 1

 599:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: q+2
        17: q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       166: 1
       167: 1
       168: 1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       209: 1
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       259: 1
       262: 1
       287: 1
       291: 1
       297: 1
       315: 1
       317: 1
       325: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       366: 1
       423: 1
       425: 1
       427: 1
       469: 1
       483: 1
       599: 1

 600:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: q+2
        17: q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       210: 1
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       260: 1
       261: 1
       288: 1
       292: 1
       298: 1
       316: 1
       318: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       366: 1
       424: 1
       426: 1
       428: 1
       470: 1
       483: 1
       600: 1

 601:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: q+2
        17: q+2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: q+2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2q+2
        41: 2
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        49: q+2
        50: q+2
        52: 2
        53: 2q+2
        54: 2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        74: 2
        76: 2q+2
        78: 2
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2
        85: 2
        86: 2
        87: 2
        91: q+2
        92: q+2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: q+1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 2
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       127: 2
       129: 2
       133: q+2
       135: 2
       136: 2
       139: 2
       141: 2
       142: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       172: 1
       173: 1
       176: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2
       195: 1
       196: 1
       201: 1
       202: 1
       209: 1
       211: 1
       213: 2
       215: 2
       227: 2
       230: 2
       232: 2
       234: 2
       237: 1
       239: 1
       243: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       259: 1
       262: 1
       263: 1
       266: 1
       279: 2
       289: 2
       303: 1
       304: 1
       307: 1
       308: 1
       317: 1
       325: 1
       337: 1
       338: 1
       340: 1
       360: 1
       362: 1
       367: 1
       371: 1
       372: 1
       381: 1
       384: 1
       427: 1
       465: 1
       484: 1
       485: 1
       487: 1
       601: 1

 602:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: q+2
        17: q+2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2
        23: 2q+2
        24: 2
        25: 2
        26: 2q+2
        27: 2
        28: q+2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2q+2
        42: 2
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        49: q+2
        50: q+2
        52: 2
        53: 2q+2
        54: 2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        75: 2
        77: 2q+2
        79: 2
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2
        85: 2
        86: 2
        87: 2
        91: q+2
        92: q+2
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: q+1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 2
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       128: 2
       130: 2
       133: q+2
       135: 2
       136: 2
       139: 2
       141: 2
       142: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       170: 1
       171: 1
       174: 1
       175: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2
       195: 1
       196: 1
       201: 1
       202: 1
       210: 1
       212: 1
       214: 2
       216: 2
       227: 2
       230: 2
       232: 2
       234: 2
       238: 1
       240: 1
       243: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       260: 1
       261: 1
       264: 1
       265: 1
       280: 2
       290: 2
       303: 1
       304: 1
       307: 1
       308: 1
       318: 1
       326: 1
       337: 1
       339: 1
       341: 1
       361: 1
       363: 1
       367: 1
       371: 1
       372: 1
       382: 1
       383: 1
       428: 1
       466: 1
       484: 1
       486: 1
       488: 1
       602: 1

 603:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q+1
         8: q^2+q+2
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: q+1
        30: 1
        31: 2q+2
        32: q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q+1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: q+1
        72: 1
        80: q+2
        81: q+2
        82: q+1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: q+2
       138: 1
       139: q+1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       275: 1
       276: 1
       283: 1
       293: 1
       299: 1
       319: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       366: 1
       419: 1
       429: 1
       437: 1
       492: 1
       493: 1
       603: 1

 604:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q+1
         8: q^2+q+2
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: q+1
        30: 1
        31: 2q+2
        32: q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q+1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: q+1
        72: 1
        80: q+2
        81: q+2
        82: q+1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: q+2
       138: 1
       139: q+1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       277: 1
       278: 1
       284: 1
       294: 1
       300: 1
       320: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       366: 1
       420: 1
       430: 1
       438: 1
       492: 1
       493: 1
       604: 1

 605:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        64: q+1
        66: q+1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 1
       136: 1
       138: q+1
       140: 1
       142: 1
       144: 1
       147: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: q+1
       229: 1
       230: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       315: 1
       348: 1
       350: 1
       356: 1
       360: 1
       362: 1
       364: 1
       368: 1
       369: 1
       417: 1
       433: 1
       435: 1
       467: 1
       512: 1
       605: 1

 606:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 2q+1
        33: 2q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        65: q+1
        67: q+1
        69: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 1
       136: 1
       138: q+1
       140: 1
       142: 1
       144: 1
       147: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: q+1
       229: 1
       230: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       316: 1
       348: 1
       350: 1
       356: 1
       361: 1
       363: 1
       365: 1
       368: 1
       369: 1
       418: 1
       434: 1
       436: 1
       468: 1
       512: 1
       606: 1

 607:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        58: 2q+1
        59: q
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        73: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
       109: q+1
       117: q+1
       125: q+1
       126: q+1
       133: 1
       134: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       185: 1
       191: q+1
       195: q+1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       250: 1
       251: q+1
       252: 1
       285: 1
       295: 1
       303: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       421: 1
       431: 1
       439: 1
       492: 1
       494: 1
       607: 1

 608:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        58: q
        59: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        73: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
       110: q+1
       118: q+1
       125: q+1
       126: q+1
       133: 1
       134: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       186: 1
       192: q+1
       196: q+1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       250: 1
       251: q+1
       252: 1
       286: 1
       296: 1
       304: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       422: 1
       432: 1
       440: 1
       492: 1
       494: 1
       608: 1

 609:    0: 6q+2
         1: 6q+2
         2: q^3+3q^2+3q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 6q+2
        23: 6q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 6q+2
        32: 2q+1
        33: 6q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 4q+2
        53: 4q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 3q+1
        59: 3q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: 4q+2
        72: 2
        73: 2q+2
        74: 2
        76: 2
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 4q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: 2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: 1
       202: 1
       207: q+1
       209: 2
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: 1
       250: 1
       251: q+1
       252: 1
       259: 1
       262: 1
       267: 1
       269: 1
       287: 1
       291: 1
       297: 1
       301: 2
       305: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       389: 1
       391: 1
       423: 1
       433: 1
       441: 1
       469: 1
       493: 1
       494: 1
       609: 1

 610:    0: 6q+2
         1: 6q+2
         2: q^3+3q^2+3q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 6q+2
        23: 6q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 6q+2
        32: 2q+1
        33: 6q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 4q+2
        53: 4q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 3q+1
        59: 3q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: 4q+2
        72: 2
        73: 2q+2
        75: 2
        77: 2
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 4q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: 2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: 1
       202: 1
       208: q+1
       210: 2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: 1
       250: 1
       251: q+1
       252: 1
       260: 1
       261: 1
       268: 1
       270: 1
       288: 1
       292: 1
       298: 1
       302: 2
       306: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       390: 1
       392: 1
       424: 1
       434: 1
       442: 1
       470: 1
       493: 1
       494: 1
       610: 1

 611:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+3q+1
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q^2+5q+2
        23: 2q^2+5q+2
        24: 2q^2+3q+1
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+1
        28: 4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q^2+5q+2
        32: 2q+1
        33: 4q+2
        34: q^2+3q+2
        35: q+1
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: 2q+2
        50: 2q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q+1
        66: 2q+2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 2q+1
        81: 2q+1
        82: q^2+3q+2
        83: q+1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 2q+2
        95: 2q+2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 2q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2
       143: q+1
       145: 2
       146: 1
       147: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       237: 2
       239: 2
       243: 2
       244: 2
       246: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       262: 1
       267: 1
       269: 1
       289: 1
       297: 1
       301: 2
       305: 1
       317: 2
       319: 1
       320: 1
       325: 1
       327: 1
       329: 1
       347: 1
       349: 1
       355: 1
       360: 1
       362: 1
       369: 1
       374: 1
       375: 1
       389: 1
       391: 1
       415: 1
       435: 1
       441: 1
       502: 1
       504: 1
       511: 1
       611: 1

 612:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+3q+1
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q^2+5q+2
        23: 2q^2+5q+2
        24: 2q^2+3q+1
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+1
        28: 4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q^2+5q+2
        32: 2q+1
        33: 4q+2
        34: q^2+3q+2
        35: q+1
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: 2q+2
        50: 2q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q+1
        67: 2q+2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 2q+1
        81: 2q+1
        82: q^2+3q+2
        83: q+1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 2q+2
        95: 2q+2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 2q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2
       143: q+1
       145: 2
       146: 1
       147: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       238: 2
       240: 2
       243: 2
       244: 2
       246: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       261: 1
       268: 1
       270: 1
       290: 1
       298: 1
       302: 2
       306: 1
       318: 2
       319: 1
       320: 1
       326: 1
       328: 1
       330: 1
       347: 1
       349: 1
       355: 1
       361: 1
       363: 1
       369: 1
       374: 1
       375: 1
       390: 1
       392: 1
       416: 1
       436: 1
       442: 1
       503: 1
       505: 1
       511: 1
       612: 1

 613:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: q+1
        23: q+1
        24: q^2+1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q+1
        53: q+1
        54: q^2+1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       162: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       211: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       247: 1
       248: 1
       249: 1
       291: 1
       301: 1
       305: 1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: 1
       351: 1
       425: 1
       433: 1
       445: 1
       495: 1
       613: 1

 614:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: q+1
        23: q+1
        24: q^2+1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q+1
        53: q+1
        54: q^2+1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: 1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       162: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       247: 1
       248: 1
       249: 1
       292: 1
       302: 1
       306: 1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: 1
       351: 1
       426: 1
       434: 1
       446: 1
       495: 1
       614: 1

 615:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: q+2
        23: q^2+3q+2
        24: q+2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q+2
        53: q^2+3q+2
        54: q+2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2q+2
       102: 2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 2
       135: 2
       136: 2
       139: 2
       140: 2
       141: q+2
       142: 2
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       201: 1
       209: 1
       210: 1
       211: 1
       212: 1
       227: 2
       229: 2
       230: 2
       232: 1
       234: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       256: 1
       257: 1
       263: 1
       264: 1
       267: 1
       268: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       319: 1
       325: 1
       326: 1
       337: 1
       351: 1
       367: 1
       369: 1
       371: 1
       372: 1
       393: 1
       394: 1
       443: 1
       471: 1
       484: 1
       496: 1
       615: 1

 616:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: q+2
        23: q^2+3q+2
        24: q+2
        25: 2
        26: 2q+2
        27: 2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q+2
        53: q^2+3q+2
        54: q+2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2
       101: 2q+2
       102: 2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       133: 2
       135: 2
       136: 2
       139: 2
       140: 2
       141: q+2
       142: 2
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       202: 1
       209: 1
       210: 1
       211: 1
       212: 1
       227: 2
       229: 2
       230: 2
       232: 1
       234: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       256: 1
       257: 1
       265: 1
       266: 1
       269: 1
       270: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       320: 1
       325: 1
       326: 1
       337: 1
       351: 1
       367: 1
       369: 1
       371: 1
       372: 1
       395: 1
       396: 1
       444: 1
       472: 1
       484: 1
       496: 1
       616: 1

 617:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: q+1
        85: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: q+1
       140: 1
       142: q+1
       147: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       181: 1
       187: 1
       197: 1
       211: 1
       213: 1
       215: 1
       229: 1
       230: q+1
       234: 1
       237: 1
       239: 1
       244: 1
       247: 1
       248: 1
       256: 1
       257: 1
       289: 1
       301: 1
       305: 1
       338: 1
       340: 1
       351: 1
       360: 1
       362: 1
       369: 1
       371: 1
       372: 1
       435: 1
       445: 1
       485: 1
       487: 1
       496: 1
       617: 1

 618:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        30: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: q+1
        85: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: q+1
       140: 1
       142: q+1
       147: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       182: 1
       188: 1
       198: 1
       212: 1
       214: 1
       216: 1
       229: 1
       230: q+1
       234: 1
       238: 1
       240: 1
       244: 1
       247: 1
       248: 1
       256: 1
       257: 1
       290: 1
       302: 1
       306: 1
       339: 1
       341: 1
       351: 1
       361: 1
       363: 1
       369: 1
       371: 1
       372: 1
       436: 1
       446: 1
       486: 1
       488: 1
       496: 1
       618: 1

 619:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        60: 2q+1
        61: q
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       107: q+1
       119: q+1
       125: q+1
       126: q+1
       133: 1
       134: 1
       135: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       183: 1
       199: q+1
       201: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       253: 1
       254: q+1
       255: 1
       283: 1
       293: 1
       307: 1
       333: 1
       334: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       419: 1
       447: 1
       453: 1
       497: 1
       498: 1
       619: 1

 620:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        60: q
        61: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       108: q+1
       120: q+1
       125: q+1
       126: q+1
       133: 1
       134: 1
       135: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       184: 1
       200: q+1
       202: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       253: 1
       254: q+1
       255: 1
       284: 1
       294: 1
       308: 1
       333: 1
       334: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       420: 1
       448: 1
       454: 1
       497: 1
       498: 1
       620: 1

 621:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q+1
         8: q^2+q+2
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2q+2
        26: 2q+2
        27: q^2+q+2
        28: 2q+2
        29: q+1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 1
        58: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: q+2
        86: q+1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+2
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       275: 1
       277: 1
       285: 1
       295: 1
       309: 1
       321: 1
       333: 1
       335: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       421: 1
       449: 1
       457: 1
       497: 1
       499: 1
       621: 1

 622:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q+1
         8: q^2+q+2
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: q+2
        14: q+1
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2q+2
        26: 2q+2
        27: q^2+q+2
        28: 2q+2
        29: q+1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+1
        45: q+2
        46: q+2
        47: q+2
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 1
        59: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: q+1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: q+2
        86: q+1
        87: 1
        88: q+2
        89: q+2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+2
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       276: 1
       278: 1
       286: 1
       296: 1
       310: 1
       322: 1
       333: 1
       335: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       422: 1
       450: 1
       458: 1
       497: 1
       499: 1
       622: 1

 623:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        64: q+1
        66: q+1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: 1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       205: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       245: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       311: 1
       313: 1
       315: 1
       350: 1
       356: 1
       358: 1
       360: 1
       362: 1
       364: 1
       368: 1
       370: 1
       417: 1
       451: 1
       455: 1
       467: 1
       514: 1
       623: 1

 624:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        30: q+1
        32: q+1
        33: q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        65: q+1
        67: q+1
        69: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: q+1
        83: 1
        85: 2q+1
        87: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: 1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       206: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       245: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       350: 1
       356: 1
       358: 1
       361: 1
       363: 1
       365: 1
       368: 1
       370: 1
       418: 1
       452: 1
       456: 1
       468: 1
       514: 1
       624: 1

 625:    0: 6q+2
         1: 6q+2
         2: q^3+3q^2+3q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 6q+2
        26: 6q+2
        27: q^3+3q^2+3q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 6q+2
        35: 2q+1
        36: 6q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 4q+2
        56: 4q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 3q+1
        61: 3q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: 4q+2
        72: 2q+2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: q+1
        81: q+1
        82: 2
        83: 1
        84: 2q+1
        85: 2q+1
        86: 4q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: q+1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: 2
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: 1
       253: 1
       254: q+1
       255: 1
       259: 1
       262: 1
       271: 1
       273: 1
       287: 1
       291: 1
       297: 1
       311: 2
       313: 1
       315: 1
       317: 2
       321: 1
       322: 1
       325: 1
       334: 1
       335: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       397: 1
       399: 1
       423: 1
       451: 1
       459: 1
       469: 1
       498: 1
       499: 1
       625: 1

 626:    0: 6q+2
         1: 6q+2
         2: q^3+3q^2+3q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 6q+2
        26: 6q+2
        27: q^3+3q^2+3q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 6q+2
        35: 2q+1
        36: 6q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 4q+2
        56: 4q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 3q+1
        61: 3q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: 4q+2
        72: 2q+2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: q+1
        81: q+1
        82: 2
        83: 1
        84: 2q+1
        85: 2q+1
        86: 4q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: q+1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: 2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: 1
       253: 1
       254: q+1
       255: 1
       260: 1
       261: 1
       272: 1
       274: 1
       288: 1
       292: 1
       298: 1
       312: 2
       314: 1
       316: 1
       318: 2
       321: 1
       322: 1
       326: 1
       334: 1
       335: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       398: 1
       400: 1
       424: 1
       452: 1
       460: 1
       470: 1
       498: 1
       499: 1
       626: 1

 627:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+3q+1
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+1
        25: 2q^2+5q+2
        26: 2q^2+5q+2
        27: 2q^2+3q+1
        28: 4q+2
        29: q^2+3q+2
        30: q+1
        31: q^2+3q+2
        32: q+1
        33: 2q+2
        34: 2q^2+5q+2
        35: 2q+1
        36: 4q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+2
        64: q+1
        66: 2q+2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: 2q+1
        85: 2q+1
        86: q^2+3q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2q+2
        98: 2q+2
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       127: 2
       129: 2
       135: 1
       136: 1
       137: q+1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       145: 2q+2
       146: q+1
       147: 2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: 1
       224: 1
       230: 1
       234: 1
       235: 1
       237: 2
       239: 2
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       259: 1
       262: 1
       271: 1
       273: 1
       289: 1
       297: 1
       311: 2
       313: 1
       317: 2
       321: 1
       322: 1
       325: 1
       327: 1
       329: 1
       349: 1
       355: 1
       357: 1
       360: 1
       362: 1
       370: 1
       374: 1
       375: 1
       397: 1
       399: 1
       415: 1
       455: 1
       459: 1
       502: 1
       504: 1
       513: 1
       627: 1

 628:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+3q+1
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+1
        25: 2q^2+5q+2
        26: 2q^2+5q+2
        27: 2q^2+3q+1
        28: 4q+2
        29: q^2+3q+2
        30: q+1
        31: q^2+3q+2
        32: q+1
        33: 2q+2
        34: 2q^2+5q+2
        35: 2q+1
        36: 4q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: q^2+3q+2
        65: q+1
        67: 2q+2
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: 2q+1
        85: 2q+1
        86: q^2+3q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2q+2
        98: 2q+2
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       128: 2
       130: 2
       135: 1
       136: 1
       137: q+1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       145: 2q+2
       146: q+1
       147: 2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: 1
       224: 1
       230: 1
       234: 1
       235: 1
       238: 2
       240: 2
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       260: 1
       261: 1
       272: 1
       274: 1
       290: 1
       298: 1
       312: 2
       314: 1
       318: 2
       321: 1
       322: 1
       326: 1
       328: 1
       330: 1
       349: 1
       355: 1
       357: 1
       361: 1
       363: 1
       370: 1
       374: 1
       375: 1
       398: 1
       400: 1
       416: 1
       456: 1
       460: 1
       503: 1
       505: 1
       513: 1
       628: 1

 629:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q^2+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: q+1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q^2+1
        64: 1
        66: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q^2+1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       205: 1
       211: 1
       223: 1
       225: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       245: 1
       247: 1
       248: 1
       249: 1
       291: 1
       311: 1
       313: 1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       356: 1
       358: 1
       359: 1
       425: 1
       451: 1
       463: 1
       500: 1
       629: 1

 630:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q^2+1
        30: 1
        32: 1
        33: 1
        35: 1
        36: q+1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q^2+1
        65: 1
        67: 1
        69: 1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q^2+1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       206: 1
       212: 1
       223: 1
       225: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       245: 1
       247: 1
       248: 1
       249: 1
       292: 1
       312: 1
       314: 1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       356: 1
       358: 1
       359: 1
       426: 1
       452: 1
       464: 1
       500: 1
       630: 1

 631:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2
        23: 2q+2
        24: 2
        25: q+2
        26: q^2+3q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2
        53: 2q+2
        54: 2
        55: q+2
        56: q^2+3q+2
        57: q+2
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        91: 2
        92: 2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2q+2
       102: 2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 2
       135: 2
       136: 2
       139: 1
       141: 2
       142: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: 1
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       209: 1
       210: 1
       211: 1
       212: 1
       227: 1
       230: 1
       232: 2
       234: 2
       235: 2
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       256: 1
       257: 1
       263: 1
       265: 1
       271: 1
       272: 1
       303: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       337: 1
       359: 1
       367: 1
       370: 1
       371: 1
       372: 1
       401: 1
       402: 1
       461: 1
       473: 1
       484: 1
       501: 1
       631: 1

 632:    0: q+2
         1: q^2+3q+2
         2: q+2
         3: q^2+3q+2
         4: q+2
         5: q+2
         6: q^2+3q+2
         7: q+2
         8: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2
        23: 2q+2
        24: 2
        25: q+2
        26: q^2+3q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2
        53: 2q+2
        54: 2
        55: q+2
        56: q^2+3q+2
        57: q+2
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        91: 2
        92: 2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2
       101: 2q+2
       102: 2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       133: 2
       135: 2
       136: 2
       139: 1
       141: 2
       142: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: 1
       163: 2
       164: 2
       166: 1
       167: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       196: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       209: 1
       210: 1
       211: 1
       212: 1
       227: 1
       230: 1
       232: 2
       234: 2
       235: 2
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       256: 1
       257: 1
       264: 1
       266: 1
       273: 1
       274: 1
       304: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       337: 1
       359: 1
       367: 1
       370: 1
       371: 1
       372: 1
       403: 1
       404: 1
       462: 1
       474: 1
       484: 1
       501: 1
       632: 1

 633:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        41: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        64: 1
        66: 1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: q+1
       136: 1
       142: 1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       181: 1
       187: 1
       205: 1
       211: 1
       213: 1
       215: 1
       230: 1
       234: q+1
       235: 1
       237: 1
       239: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       289: 1
       311: 1
       313: 1
       338: 1
       340: 1
       359: 1
       360: 1
       362: 1
       370: 1
       371: 1
       372: 1
       455: 1
       463: 1
       485: 1
       487: 1
       501: 1
       633: 1

 634:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: q+1
        38: 1
        40: q+1
        42: 1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        65: 1
        67: 1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: q+1
       136: 1
       142: 1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       182: 1
       188: 1
       206: 1
       212: 1
       214: 1
       216: 1
       230: 1
       234: q+1
       235: 1
       238: 1
       240: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       290: 1
       312: 1
       314: 1
       339: 1
       341: 1
       359: 1
       361: 1
       363: 1
       370: 1
       371: 1
       372: 1
       456: 1
       464: 1
       486: 1
       488: 1
       501: 1
       634: 1

 635:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         7: q^2+q+1
         8: q+2
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+2
        14: q^2+q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q+2
        44: q^2+q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: 2
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: 2
       127: 1
       129: 1
       133: 1
       137: 2
       139: 1
       141: 1
       143: 2
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       176: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       209: 1
       211: 1
       213: 1
       215: 1
       220: 1
       227: 1
       232: 1
       237: 1
       239: 1
       243: 1
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       275: 1
       278: 1
       279: 1
       317: 1
       325: 1
       327: 1
       329: 1
       345: 1
       353: 1
       360: 1
       362: 1
       367: 1
       374: 1
       375: 1
       409: 1
       465: 1
       502: 1
       504: 1
       509: 1
       635: 1

 636:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q^2+q+1
         5: q+2
         6: q^2+q+1
         7: q^2+q+1
         8: q+2
        10: q+2
        11: q+2
        12: q^2+q+1
        13: q+2
        14: q^2+q+1
        15: q+2
        16: 2
        17: 2
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q+2
        44: q^2+q+1
        45: q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: 2
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: q+2
        81: 2
        82: 1
        83: 1
        84: q+2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: 2
       128: 1
       130: 1
       133: 1
       137: 2
       139: 1
       141: 1
       143: 2
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       174: 1
       175: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       210: 1
       212: 1
       214: 1
       216: 1
       220: 1
       227: 1
       232: 1
       238: 1
       240: 1
       243: 1
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       276: 1
       277: 1
       280: 1
       318: 1
       326: 1
       328: 1
       330: 1
       345: 1
       353: 1
       361: 1
       363: 1
       367: 1
       374: 1
       375: 1
       410: 1
       466: 1
       503: 1
       505: 1
       509: 1
       636: 1

 637:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: 1
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: q+1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       113: 1
       115: 1
       121: q+1
       123: q+1
       126: 1
       127: 1
       129: 1
       131: q+1
       134: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       177: 1
       179: 1
       189: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       217: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: 1
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       281: 1
       287: 1
       315: 1
       317: 1
       325: 1
       327: 1
       331: 1
       346: 1
       354: 1
       360: 1
       364: 1
       366: 1
       368: 1
       374: 1
       376: 1
       411: 1
       467: 1
       469: 1
       502: 1
       506: 1
       510: 1
       637: 1

 638:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: 1
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: q+1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: 1
       102: q+1
       104: q+1
       105: q+1
       114: 1
       116: 1
       122: q+1
       124: q+1
       126: 1
       128: 1
       130: 1
       132: q+1
       134: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       178: 1
       180: 1
       190: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       218: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: 1
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       282: 1
       288: 1
       316: 1
       318: 1
       326: 1
       328: 1
       332: 1
       346: 1
       354: 1
       361: 1
       365: 1
       366: 1
       368: 1
       374: 1
       376: 1
       412: 1
       468: 1
       470: 1
       503: 1
       507: 1
       510: 1
       638: 1

 639:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q^2+q+1
         7: q+1
         8: q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        37: q+2
        39: q+2
        41: q+2
        43: 2
        44: q+1
        45: 2
        46: q+2
        47: q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: q+2
        66: q+2
        68: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 2
        81: q+2
        82: 1
        83: 1
        84: 2
        85: q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: q+2
       125: 2
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       176: 1
       177: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       256: 1
       257: 1
       258: 1
       275: 1
       278: 1
       279: 1
       281: 1
       287: 1
       315: 1
       317: 1
       325: 1
       344: 1
       352: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       413: 1
       465: 1
       467: 1
       469: 1
       508: 1
       639: 1

 640:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+1
         5: q+2
         6: q^2+q+1
         7: q+1
         8: q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q+2
        14: q+1
        15: q+2
        16: q+2
        17: q+2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        38: q+2
        40: q+2
        42: q+2
        43: 2
        44: q+1
        45: 2
        46: q+2
        47: q+2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: q+2
        67: q+2
        68: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 2
        81: q+2
        82: 1
        83: 1
        84: 2
        85: q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: q+2
       125: 2
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       174: 1
       175: 1
       178: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       256: 1
       257: 1
       258: 1
       276: 1
       277: 1
       280: 1
       282: 1
       288: 1
       316: 1
       318: 1
       326: 1
       344: 1
       352: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       414: 1
       466: 1
       468: 1
       470: 1
       508: 1
       640: 1

 641:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q^3+2q^2+2q+1
         7: q+1
         8: 2q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2q+2
        14: q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       219: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       275: 1
       276: 1
       283: 1
       299: 1
       307: 1
       319: 1
       344: 1
       348: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       429: 1
       447: 1
       471: 1
       508: 1
       512: 1
       641: 1

 642:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q^3+2q^2+2q+1
         7: q+1
         8: 2q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2q+2
        14: q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       219: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       277: 1
       278: 1
       284: 1
       300: 1
       308: 1
       320: 1
       344: 1
       348: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       430: 1
       448: 1
       472: 1
       508: 1
       512: 1
       642: 1

 643:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q^3+2q^2+2q+1
         7: q+1
         8: 2q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2q+2
        14: q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       219: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       275: 1
       277: 1
       285: 1
       303: 1
       309: 1
       321: 1
       344: 1
       350: 1
       352: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       431: 1
       449: 1
       473: 1
       508: 1
       514: 1
       643: 1

 644:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q+1
         5: 2q+2
         6: q^3+2q^2+2q+1
         7: q+1
         8: 2q+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2q+2
        14: q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2q+2
        82: 1
        83: 1
        84: 2
        85: 2q+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       219: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       276: 1
       278: 1
       286: 1
       304: 1
       310: 1
       322: 1
       344: 1
       350: 1
       352: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       432: 1
       450: 1
       474: 1
       508: 1
       514: 1
       644: 1

 645:    0: 5q+1
         1: 5q+1
         2: q^2+3q+1
         3: 5q+1
         4: q^3+2q^2+2q+1
         5: 5q+1
         6: q^3+3q^2+3q+1
         7: q^2+q+1
         8: q^2+3q+1
         9: q^2+q+1
        13: 3q+1
        14: q^2+q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: q^2+q+1
        19: 2q+1
        20: 3q+1
        21: q+1
        22: 5q+1
        23: 5q+1
        24: q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: q^2+3q+1
        30: q+1
        32: 3q+1
        33: 5q+1
        35: 3q+1
        36: 5q+1
        37: 3q+1
        38: 2q
        39: 3q+1
        40: 2q
        41: 2q+1
        42: q^2+q
        46: 3q+1
        47: 3q+1
        48: q^2+q+1
        49: 2q+1
        50: 3q+1
        51: q+1
        52: 2q+1
        53: 3q+1
        54: q+1
        55: 2q+1
        56: 3q+1
        57: q+1
        64: 2q+1
        65: q
        66: 3q+1
        67: 2q
        69: q+1
        72: q+1
        73: q+1
        74: 1
        76: q+1
        78: 1
        81: 3q+1
        83: q+1
        85: 3q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 3q+1
        96: q+1
        97: 2q+1
        98: 3q+1
        99: q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       111: 1
       115: 1
       123: 2q+1
       124: q
       127: 1
       129: q+1
       131: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       239: q+1
       241: 1
       244: q+1
       245: q+1
       256: 1
       257: q+1
       258: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       348: 1
       350: 1
       356: 1
       358: 1
       368: 1
       369: 1
       370: 1
       433: 1
       451: 1
       475: 1
       477: 1
       512: 1
       514: 1
       645: 1

 646:    0: 5q+1
         1: 5q+1
         2: q^2+3q+1
         3: 5q+1
         4: q^3+2q^2+2q+1
         5: 5q+1
         6: q^3+3q^2+3q+1
         7: q^2+q+1
         8: q^2+3q+1
         9: q^2+q+1
        13: 3q+1
        14: q^2+q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: q^2+q+1
        19: 2q+1
        20: 3q+1
        21: q+1
        22: 5q+1
        23: 5q+1
        24: q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: q^2+3q+1
        30: q+1
        32: 3q+1
        33: 5q+1
        35: 3q+1
        36: 5q+1
        37: 2q
        38: 3q+1
        39: 2q
        40: 3q+1
        41: q^2+q
        42: 2q+1
        46: 3q+1
        47: 3q+1
        48: q^2+q+1
        49: 2q+1
        50: 3q+1
        51: q+1
        52: 2q+1
        53: 3q+1
        54: q+1
        55: 2q+1
        56: 3q+1
        57: q+1
        64: q
        65: 2q+1
        66: 2q
        67: 3q+1
        69: q+1
        72: q+1
        73: q+1
        75: 1
        77: q+1
        79: 1
        81: 3q+1
        83: q+1
        85: 3q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 3q+1
        96: q+1
        97: 2q+1
        98: 3q+1
        99: q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       112: 1
       116: 1
       123: q
       124: 2q+1
       128: 1
       130: q+1
       132: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 3q+1
       168: q+1
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 1
       240: q+1
       242: 1
       244: q+1
       245: q+1
       256: 1
       257: q+1
       258: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       348: 1
       350: 1
       356: 1
       358: 1
       368: 1
       369: 1
       370: 1
       434: 1
       452: 1
       476: 1
       478: 1
       512: 1
       514: 1
       646: 1

 647:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+2
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: 2q+2
        14: q^2+2q+1
        15: 2q+2
        16: 2
        17: 2
        19: q+1
        20: q+1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q+1
        30: q+1
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: q^2+2q+1
        45: 2q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: 1
        60: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q+1
        71: 1
        72: 1
        80: 2q+2
        81: 2
        82: q+1
        83: q+1
        84: 2q+2
        85: 2
        86: q+1
        87: q+1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 1
       135: 1
       137: 2
       139: 1
       140: 1
       141: q+1
       143: 2
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       220: 1
       222: 1
       227: 1
       229: 1
       232: 1
       234: 1
       243: 1
       244: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       275: 1
       276: 1
       293: 1
       299: 1
       307: 1
       319: 1
       345: 1
       347: 1
       353: 1
       355: 1
       367: 1
       369: 1
       374: 1
       375: 1
       437: 1
       453: 1
       471: 1
       509: 1
       511: 1
       647: 1

 648:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+2
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: 2q+2
        14: q^2+2q+1
        15: 2q+2
        16: 2
        17: 2
        19: q+1
        20: q+1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q+1
        30: q+1
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: q^2+2q+1
        45: 2q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: 1
        61: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q+1
        71: 1
        72: 1
        80: 2q+2
        81: 2
        82: q+1
        83: q+1
        84: 2q+2
        85: 2
        86: q+1
        87: q+1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 1
       135: 1
       137: 2
       139: 1
       140: 1
       141: q+1
       143: 2
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       220: 1
       222: 1
       227: 1
       229: 1
       232: 1
       234: 1
       243: 1
       244: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       277: 1
       278: 1
       294: 1
       300: 1
       308: 1
       320: 1
       345: 1
       347: 1
       353: 1
       355: 1
       367: 1
       369: 1
       374: 1
       375: 1
       438: 1
       454: 1
       472: 1
       509: 1
       511: 1
       648: 1

 649:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+2
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: 2q+2
        14: q^2+2q+1
        15: 2q+2
        16: 2
        17: 2
        19: q+1
        20: q+1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q+1
        30: q+1
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: q^2+2q+1
        45: 2q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q+1
        71: 1
        73: 1
        80: 2q+2
        81: 2
        82: q+1
        83: q+1
        84: 2q+2
        85: 2
        86: q+1
        87: q+1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 1
       136: 1
       137: 2
       139: 1
       141: q+1
       142: 1
       143: 2
       145: 1
       146: q+1
       148: 1
       149: q+1
       150: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       220: 1
       224: 1
       227: 1
       230: 1
       232: 1
       235: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       275: 1
       277: 1
       295: 1
       303: 1
       309: 1
       321: 1
       345: 1
       349: 1
       353: 1
       357: 1
       367: 1
       370: 1
       374: 1
       375: 1
       439: 1
       457: 1
       473: 1
       509: 1
       513: 1
       649: 1

 650:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+2q+1
         5: 2q+2
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+2
        10: 2q+2
        11: 2q+2
        12: q^2+2q+1
        13: 2q+2
        14: q^2+2q+1
        15: 2q+2
        16: 2
        17: 2
        19: q+1
        20: q+1
        21: q+1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q+1
        30: q+1
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: q^2+2q+1
        45: 2q+2
        46: 2
        47: 2
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q+1
        71: 1
        73: 1
        80: 2q+2
        81: 2
        82: q+1
        83: q+1
        84: 2q+2
        85: 2
        86: q+1
        87: q+1
        88: 2
        89: 2
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 1
       136: 1
       137: 2
       139: 1
       141: q+1
       142: 1
       143: 2
       145: 1
       146: q+1
       148: 1
       149: q+1
       150: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       220: 1
       224: 1
       227: 1
       230: 1
       232: 1
       235: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       276: 1
       278: 1
       296: 1
       304: 1
       310: 1
       322: 1
       345: 1
       349: 1
       353: 1
       357: 1
       367: 1
       370: 1
       374: 1
       375: 1
       440: 1
       458: 1
       474: 1
       509: 1
       513: 1
       650: 1

 651:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^3+q+1
         7: q^3+1
         8: 1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: 1
       229: 1
       230: 1
       234: 1
       235: 1
       237: 1
       239: 1
       244: 1
       245: 1
       256: 1
       257: 1
       289: 1
       301: 1
       305: 1
       311: 1
       313: 1
       323: 1
       360: 1
       362: 1
       369: 1
       370: 1
       435: 1
       455: 1
       475: 1
       477: 1
       651: 1

 652:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^3+q+1
         7: q^3+1
         8: 1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: 1
       229: 1
       230: 1
       234: 1
       235: 1
       238: 1
       240: 1
       244: 1
       245: 1
       256: 1
       257: 1
       290: 1
       302: 1
       306: 1
       312: 1
       314: 1
       324: 1
       361: 1
       363: 1
       369: 1
       370: 1
       436: 1
       456: 1
       476: 1
       478: 1
       652: 1

 653:    0: 5q+2
         1: 5q+2
         2: 2q^2+3q+1
         3: 5q+2
         4: 2q^2+3q+2
         5: 5q+2
         6: 2q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 5q+2
        11: 5q+2
        12: 2q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+2
        17: 2q+2
        19: 3q+2
        20: 3q+2
        21: q^2+2q+1
        22: 5q+2
        23: 5q+2
        24: 2q^2+3q+1
        25: 5q+2
        26: 5q+2
        27: 2q^2+3q+1
        28: 2q+2
        29: 3q+2
        30: q+1
        31: 5q+2
        32: 2q+1
        33: 2q+2
        34: 5q+2
        35: 2q+1
        36: 2q+2
        37: 3q+2
        38: 2q
        39: 3q+2
        40: 2q
        41: q^2+2q+1
        42: q^2+q
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 2
        50: 2
        52: 3q+2
        53: 3q+2
        54: q^2+2q+1
        55: 3q+2
        56: 3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 3q+2
        63: 2q
        64: q+1
        65: q
        66: 2q+2
        70: q+1
        71: 2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 2q+1
        81: q+1
        82: 3q+2
        83: q+1
        84: 2q+1
        85: q+1
        86: 3q+2
        87: q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 3q+2
       101: 3q+2
       102: q^2+2q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       122: q
       123: q+1
       135: 1
       136: 1
       137: q+1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: q+1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 3q+2
       150: q+1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       243: 2
       244: 2
       245: 2
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       267: 1
       269: 1
       271: 1
       273: 1
       297: 1
       305: 1
       313: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       347: 1
       349: 1
       355: 1
       357: 1
       369: 1
       370: 1
       374: 1
       375: 1
       405: 1
       406: 1
       441: 1
       459: 1
       475: 1
       511: 1
       513: 1
       653: 1

 654:    0: 5q+2
         1: 5q+2
         2: 2q^2+3q+1
         3: 5q+2
         4: 2q^2+3q+2
         5: 5q+2
         6: 2q^2+3q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 5q+2
        11: 5q+2
        12: 2q^2+3q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+2
        17: 2q+2
        19: 3q+2
        20: 3q+2
        21: q^2+2q+1
        22: 5q+2
        23: 5q+2
        24: 2q^2+3q+1
        25: 5q+2
        26: 5q+2
        27: 2q^2+3q+1
        28: 2q+2
        29: 3q+2
        30: q+1
        31: 5q+2
        32: 2q+1
        33: 2q+2
        34: 5q+2
        35: 2q+1
        36: 2q+2
        37: 2q
        38: 3q+2
        39: 2q
        40: 3q+2
        41: q^2+q
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q+1
        47: q+1
        49: 2
        50: 2
        52: 3q+2
        53: 3q+2
        54: q^2+2q+1
        55: 3q+2
        56: 3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q
        63: 3q+2
        64: q
        65: q+1
        67: 2q+2
        70: q+1
        71: 2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 2q+1
        81: q+1
        82: 3q+2
        83: q+1
        84: 2q+1
        85: q+1
        86: 3q+2
        87: q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 3q+2
       101: 3q+2
       102: q^2+2q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       121: q
       122: q+1
       124: q+1
       135: 1
       136: 1
       137: q+1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: q+1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 3q+2
       150: q+1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       243: 2
       244: 2
       245: 2
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       268: 1
       270: 1
       272: 1
       274: 1
       298: 1
       306: 1
       314: 1
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       347: 1
       349: 1
       355: 1
       357: 1
       369: 1
       370: 1
       374: 1
       375: 1
       407: 1
       408: 1
       442: 1
       460: 1
       476: 1
       511: 1
       513: 1
       654: 1

 655:    0: q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: q+1
         5: q+1
         6: 2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: q+1
        30: q+1
        32: q+1
        33: 1
        35: q+1
        36: 1
        37: 1
        38: q
        39: q+1
        40: q
        41: 1
        42: q
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: 2q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: q+1
        64: 1
        65: q
        66: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: q+1
        77: q
        78: 1
        79: q
        81: 1
        83: q+1
        85: 1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: 2q+1
       102: q+1
       111: 1
       115: 1
       116: q
       123: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q
       155: 1
       156: q
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       187: 1
       197: 1
       205: 1
       211: 1
       212: q
       229: 1
       230: 1
       234: 1
       235: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       305: 1
       313: 1
       323: 1
       351: 1
       359: 1
       369: 1
       370: 1
       371: 1
       372: 1
       475: 1
       479: 1
       496: 1
       501: 1
       655: 1

 656:    0: q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: q+1
         5: q+1
         6: 2q+1
         7: q+1
         8: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: q+1
        30: q+1
        32: q+1
        33: 1
        35: q+1
        36: 1
        37: q
        38: 1
        39: q
        40: q+1
        41: q
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: 2q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: q+1
        64: q
        65: 1
        67: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q
        77: q+1
        78: q
        79: 1
        81: 1
        83: q+1
        85: 1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: 2q+1
       102: q+1
       112: 1
       115: q
       116: 1
       124: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: q+1
       151: q
       152: 1
       153: q
       154: q+1
       155: q
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       188: 1
       198: 1
       206: 1
       211: q
       212: 1
       229: 1
       230: 1
       234: 1
       235: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       306: 1
       314: 1
       324: 1
       351: 1
       359: 1
       369: 1
       370: 1
       371: 1
       372: 1
       476: 1
       480: 1
       496: 1
       501: 1
       656: 1

 657:    0: 5q^2+14q+4
         1: 4q^2+14q+4
         2: 3q^2+7q+4
         3: 5q^2+14q+4
         4: 3q^2+7q+4
         5: 4q^2+14q+4
         6: 3q^3+10q^2+11q+4
         7: 3q+4
         8: 4q^2+8q+4
         9: 3q+4
        10: q^2+10q+4
        11: q^2+10q+4
        12: 3q^2+7q+4
        13: q^2+7q+4
        14: 3q+4
        15: q^2+8q+4
        16: 5q^2+14q+4
        17: 4q^2+14q+4
        18: 3q+4
        19: q^2+7q+4
        20: 4q^2+11q+4
        21: 3q+4
        22: q^2+10q+4
        23: q^2+10q+4
        24: q^2+5q+4
        25: q^2+10q+4
        26: q^2+10q+4
        27: q^2+5q+4
        28: q^2+10q+4
        29: q^2+7q+4
        30: 3q+4
        31: 6q+4
        32: 5q+4
        33: q^2+10q+4
        34: 6q+4
        35: 5q+4
        36: q^2+10q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: 2q+2
        42: 2q+2
        43: 3q+4
        44: 3q+4
        45: 4q+4
        46: q^2+7q+4
        47: q^2+8q+4
        48: 3q+4
        49: q^2+7q+4
        50: 4q^2+11q+4
        51: 3q+4
        52: 3q+4
        53: q^2+7q+4
        54: q+4
        55: 3q+4
        56: q^2+7q+4
        57: q+4
        58: 3q+2
        59: 3q+2
        60: 3q+2
        61: 3q+2
        62: 2q+2
        63: 2q+2
        64: 2q+2
        65: 2q+2
        66: 4q+2
        67: 4q+2
        68: q+4
        69: 3q+4
        70: 3q+4
        71: q^2+7q+4
        72: 2q+4
        73: 2q+4
        74: 2
        75: 2
        76: 2q+2
        77: 2q+2
        78: 2
        79: 2
        80: q+4
        81: 5q+4
        82: 3q+4
        83: q+4
        84: q+4
        85: 5q+4
        86: 3q+4
        87: q+4
        88: 3q+4
        89: 4q+4
        90: 3q+4
        91: q+4
        92: q^2+5q+4
        93: q+4
        94: 3q+4
        95: q^2+7q+4
        96: q+4
        97: 3q+4
        98: q^2+7q+4
        99: q+4
       100: q+2
       101: 3q+2
       102: 2
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 2
       116: 2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2q+2
       124: 2q+2
       125: q+4
       126: 3q+4
       127: 2
       128: 2
       129: 2q+2
       130: 2q+2
       131: 2
       132: 2
       133: q+4
       134: q+4
       135: 4
       136: 4
       137: q+4
       138: q+4
       139: 3q+4
       141: q+4
       142: 2q+4
       143: q+4
       144: q+4
       145: 3q+4
       146: q+4
       147: 2q+4
       149: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: q+2
       167: 3q+2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 2
       178: 2
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 2
       190: 2
       191: 2
       192: 2
       195: q+2
       196: q+2
       199: 2
       200: 2
       201: q+2
       202: q+2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       219: q+4
       223: 4
       225: 4
       226: q+4
       227: 2
       228: 2
       230: 2
       231: q+4
       232: 2
       233: 2
       234: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+2
       246: 2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       283: 2
       284: 2
       285: 2
       286: 2
       287: 2
       288: 2
       291: 2
       292: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       350: 2
       352: 2
       356: 2
       366: 2
       367: 1
       368: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       380: 1
       427: 1
       428: 1
       431: 1
       432: 1
       447: 1
       448: 1
       469: 1
       470: 1
       484: 1
       508: 1
       515: 1
       516: 1
       657: 1

 658:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q^2+2q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: q+1
        66: q+1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: q+1
       131: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       151: 1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       177: 1
       181: 1
       187: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       237: 1
       241: 1
       247: 1
       256: 1
       258: 1
       281: 1
       289: 1
       291: 1
       315: 1
       338: 1
       350: 1
       356: 1
       360: 1
       364: 1
       368: 1
       371: 1
       417: 1
       467: 1
       485: 1
       515: 1
       658: 1

 659:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q^2+2q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: q+1
        67: q+1
        69: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: q+1
       132: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       152: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       178: 1
       182: 1
       188: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       238: 1
       242: 1
       247: 1
       256: 1
       258: 1
       282: 1
       290: 1
       292: 1
       316: 1
       339: 1
       350: 1
       356: 1
       361: 1
       365: 1
       368: 1
       371: 1
       418: 1
       468: 1
       486: 1
       515: 1
       659: 1

 660:    0: 1
         1: q^2+q+1
         2: 1
         3: 1
         4: 1
         5: q^2+q+1
         6: q^2+q+1
         7: 1
         8: q^2+q+1
         9: 1
        13: 1
        14: 1
        15: q^2+q+1
        16: 1
        17: q^2+q+1
        18: 1
        19: 1
        20: q^2+q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: q^2+q+1
        48: 1
        49: 1
        50: q^2+q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       101: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       153: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       177: 1
       181: 1
       187: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       239: 1
       248: 1
       257: 1
       281: 1
       289: 1
       291: 1
       340: 1
       350: 1
       356: 1
       362: 1
       372: 1
       417: 1
       487: 1
       516: 1
       660: 1

 661:    0: 1
         1: q^2+q+1
         2: 1
         3: 1
         4: 1
         5: q^2+q+1
         6: q^2+q+1
         7: 1
         8: q^2+q+1
         9: 1
        13: 1
        14: 1
        15: q^2+q+1
        16: 1
        17: q^2+q+1
        18: 1
        19: 1
        20: q^2+q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: q^2+q+1
        48: 1
        49: 1
        50: q^2+q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       101: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       154: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       178: 1
       182: 1
       188: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       240: 1
       248: 1
       257: 1
       282: 1
       290: 1
       292: 1
       341: 1
       350: 1
       356: 1
       363: 1
       372: 1
       418: 1
       488: 1
       516: 1
       661: 1

 662:    0: 1
         1: 1
         2: 1
         3: 1
         4: q+1
         5: 1
         7: q+1
         8: 1
         9: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        18: q+1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        64: 1
        66: 1
        69: 1
        74: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       115: 1
       123: 1
       127: 1
       131: 1
       134: 1
       138: 1
       144: 1
       150: 1
       151: 1
       155: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       168: 1
       177: 1
       211: 1
       213: 1
       217: 1
       228: 1
       233: 1
       236: 1
       237: 1
       241: 1
       249: 1
       256: 1
       258: 1
       281: 1
       315: 1
       342: 1
       360: 1
       364: 1
       368: 1
       373: 1
       467: 1
       489: 1
       517: 1
       662: 1

 663:    0: 1
         1: 1
         2: 1
         3: 1
         4: q+1
         5: 1
         7: q+1
         8: 1
         9: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: 1
        18: q+1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        51: 1
        52: 1
        54: 1
        55: 1
        57: 1
        65: 1
        67: 1
        69: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        93: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       116: 1
       124: 1
       128: 1
       132: 1
       134: 1
       138: 1
       144: 1
       150: 1
       152: 1
       156: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       168: 1
       178: 1
       212: 1
       214: 1
       218: 1
       228: 1
       233: 1
       236: 1
       238: 1
       242: 1
       249: 1
       256: 1
       258: 1
       282: 1
       316: 1
       343: 1
       361: 1
       365: 1
       368: 1
       373: 1
       468: 1
       490: 1
       517: 1
       663: 1

 664:    0: 2q+2
         1: 2
         2: 2q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2
         6: 2
         7: 2q^2+q+2
         8: 2q^2+2
         9: 2q^2+q+2
        13: q+2
        14: q+2
        15: 2
        16: 2q+2
        17: 2
        18: 2q^2+q+2
        19: 2q+2
        20: 2
        21: 2q^2+q+2
        22: 2
        23: 2
        24: q^2+2
        25: 2
        26: 2
        27: q^2+2
        30: q+2
        32: 2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: q+2
        47: 2
        48: q+2
        49: 2q+2
        50: 2
        51: 2q^2+q+2
        52: 2
        53: 2
        54: q^2+2
        55: 2
        56: 2
        57: q^2+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: q+2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: 2
        91: q+2
        92: 2
        93: q+2
        94: 2
        95: 2
        96: q^2+2
        97: 2
        98: 2
        99: q^2+2
       100: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+2
       135: 2
       136: 2
       138: 2
       142: 2
       144: 2
       147: 2
       150: 2
       151: 1
       152: 1
       155: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       211: 1
       212: 1
       223: 2
       225: 2
       228: 1
       230: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       241: 1
       242: 1
       247: 2
       249: 2
       256: 1
       258: 1
       291: 1
       292: 1
       315: 1
       316: 1
       336: 2
       338: 1
       339: 1
       342: 1
       343: 1
       350: 1
       356: 1
       368: 1
       371: 1
       373: 1
       425: 1
       426: 1
       491: 1
       515: 1
       517: 1
       664: 1

 665:    0: 5q+4
         1: q^3+q^2+5q+4
         2: 5q+4
         3: 2q^2+6q+4
         4: 5q+4
         5: 2q^2+6q+4
         6: q^3+q^2+5q+4
         7: 5q+4
         8: 2q^2+6q+4
         9: 2q^2+3q+1
        10: 3q+4
        11: 4q+4
        12: 3q+4
        13: 5q+4
        14: 5q+4
        15: 2q^2+6q+4
        16: 3q+4
        17: 3q+4
        18: 3q+1
        19: 5q+4
        20: q^3+q^2+5q+4
        21: 5q+4
        22: 3q+4
        23: 3q+4
        24: 3q+4
        25: 3q+4
        26: 3q+4
        27: 3q+4
        28: q+4
        29: 3q+4
        30: 5q+4
        31: q+4
        32: 3q+4
        33: 2q+4
        34: q+4
        35: 3q+4
        36: 2q+4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 3q+4
        44: 3q+4
        45: 4q+4
        46: 3q+4
        47: 3q+4
        48: 3q+1
        49: 3q+4
        50: 3q+4
        51: 3q+1
        52: 3q+4
        53: 3q+4
        54: 3q+4
        55: 3q+4
        56: 3q+4
        57: 3q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: q+2
        65: q+2
        66: q+2
        67: q+2
        68: q+4
        69: q+1
        70: 3q+4
        71: q+4
        72: 2q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: q+4
        81: 2q+4
        82: q+4
        83: 3q+4
        84: q+4
        85: 2q+4
        86: q+4
        87: 3q+4
        88: 4
        89: 4
        90: 2q+1
        91: 3q+4
        92: 3q+4
        93: 3q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: q+2
       112: q+2
       113: 2
       114: 2
       115: q+2
       116: q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: q+4
       134: q+1
       135: 2q+4
       136: 2q+4
       137: 4
       138: 1
       139: 2
       141: q+4
       142: 2
       143: 4
       144: 1
       145: 2
       146: q+4
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 4
       158: 4
       159: 2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: 2
       190: 2
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 4
       221: 1
       222: 4
       223: 1
       224: 4
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 1
       246: 2
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       350: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       385: 1
       386: 1
       387: 1
       388: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       508: 1
       665: 1

 666:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: q^2+2q+2
         4: 2q+2
         5: q^2+2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q+1
        10: 2q+2
        11: q^2+2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: 1
        16: q+2
        17: q+2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: 2q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: 1
        49: q+2
        50: q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: q+1
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: 1
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: q+1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       222: 1
       224: 1
       230: 1
       234: 1
       237: 1
       239: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       259: 1
       262: 1
       289: 1
       297: 1
       317: 1
       325: 1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       349: 1
       355: 1
       360: 1
       371: 1
       374: 1
       415: 1
       427: 1
       485: 1
       502: 1
       518: 1
       666: 1

 667:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: q^2+2q+2
         4: 2q+2
         5: q^2+2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q+1
        10: 2q+2
        11: q^2+2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: 1
        16: q+2
        17: q+2
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: 2q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: 1
        49: q+2
        50: q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: q+1
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 1
       101: 1
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       222: 1
       224: 1
       230: 1
       234: 1
       238: 1
       240: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       260: 1
       261: 1
       290: 1
       298: 1
       318: 1
       326: 1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       349: 1
       355: 1
       361: 1
       371: 1
       374: 1
       416: 1
       428: 1
       486: 1
       503: 1
       518: 1
       667: 1

 668:    0: q^2+2q+2
         1: q^2+2q+2
         2: q+1
         3: 2q+2
         4: q^2+2q+2
         5: 2q+2
         6: q^2+2q+2
         7: q+1
         8: q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q^2+2q+2
        13: 1
        14: 1
        15: q+1
        16: q+2
        17: q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: q^2+2q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        49: q+2
        50: q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: 1
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+1
       101: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       149: q+1
       151: q+1
       153: q+1
       157: 1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       209: q+1
       213: 1
       215: 1
       222: 1
       224: 1
       230: 1
       234: 1
       237: 1
       239: 1
       243: 1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       257: 1
       259: 1
       262: 1
       289: 1
       297: 1
       317: 1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       349: 1
       355: 1
       362: 1
       372: 1
       375: 1
       415: 1
       427: 1
       487: 1
       504: 1
       519: 1
       668: 1

 669:    0: q^2+2q+2
         1: q^2+2q+2
         2: q+1
         3: 2q+2
         4: q^2+2q+2
         5: 2q+2
         6: q^2+2q+2
         7: q+1
         8: q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q^2+2q+2
        13: 1
        14: 1
        15: q+1
        16: q+2
        17: q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: q+2
        29: q^2+2q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: 1
        44: 1
        45: q+1
        46: 1
        47: q+1
        49: q+2
        50: q+2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: 1
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+1
       101: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       149: q+1
       152: q+1
       154: q+1
       157: 1
       158: q+1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       210: q+1
       214: 1
       216: 1
       222: 1
       224: 1
       230: 1
       234: 1
       238: 1
       240: 1
       243: 1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       257: 1
       260: 1
       261: 1
       290: 1
       298: 1
       318: 1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       349: 1
       355: 1
       363: 1
       372: 1
       375: 1
       416: 1
       428: 1
       488: 1
       505: 1
       519: 1
       669: 1

 670:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        62: 1
        64: 1
        70: 1
        74: 1
        76: 1
        78: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       100: 1
       101: 1
       102: 1
       113: 1
       115: 1
       121: 1
       131: 1
       141: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       159: 1
       162: 1
       165: 1
       168: 1
       189: 1
       209: 1
       211: 1
       217: 1
       241: 1
       246: 1
       249: 1
       252: 1
       255: 1
       258: 1
       325: 1
       331: 1
       342: 1
       364: 1
       373: 1
       376: 1
       489: 1
       506: 1
       520: 1
       670: 1

 671:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        63: 1
        65: 1
        70: 1
        75: 1
        77: 1
        79: 1
        80: 1
        82: 1
        83: 1
        84: 1
        86: 1
        87: 1
        90: 1
        93: 1
        96: 1
        99: 1
       100: 1
       101: 1
       102: 1
       114: 1
       116: 1
       122: 1
       132: 1
       141: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       159: 1
       162: 1
       165: 1
       168: 1
       190: 1
       210: 1
       212: 1
       218: 1
       242: 1
       246: 1
       249: 1
       252: 1
       255: 1
       258: 1
       326: 1
       332: 1
       343: 1
       365: 1
       373: 1
       376: 1
       490: 1
       507: 1
       520: 1
       671: 1

 672:    0: q^2+5q+4
         1: q^2+5q+4
         2: q^2+5q+4
         3: 2q^2+6q+4
         4: q^2+5q+4
         5: 2q^2+6q+4
         6: q^2+5q+4
         7: q^2+5q+4
         8: 2q^2+6q+4
        10: q^2+5q+4
        11: 2q^2+6q+4
        12: q^2+5q+4
        13: q^2+5q+4
        14: q^2+5q+4
        15: 2q^2+6q+4
        16: q+4
        17: q+4
        19: q^2+5q+4
        20: q^2+5q+4
        21: q^2+5q+4
        22: 3q+4
        23: 3q+4
        24: 3q+4
        25: 3q+4
        26: 3q+4
        27: 3q+4
        28: q+4
        29: q^2+5q+4
        30: q^2+5q+4
        31: 3q+4
        32: 3q+4
        33: 4
        34: 3q+4
        35: 3q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: q^2+5q+4
        44: q^2+5q+4
        45: 2q^2+6q+4
        46: q+4
        47: q+4
        49: q+4
        50: q+4
        52: 3q+4
        53: 3q+4
        54: 3q+4
        55: 3q+4
        56: 3q+4
        57: 3q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: q+4
        70: q^2+5q+4
        71: q+4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 3q+4
        81: 4
        82: 3q+4
        83: 3q+4
        84: 3q+4
        85: 4
        86: 3q+4
        87: 3q+4
        88: q+4
        89: q+4
        91: q+4
        92: q+4
        94: 2
        95: 2
        97: 2
        98: 2
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: q+4
       133: q+4
       135: 4
       136: 4
       137: 4
       139: 2
       141: 3q+4
       142: 2
       143: 4
       145: 2
       146: 3q+4
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+4
       158: q+4
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       220: q+4
       222: 4
       224: 4
       227: 2
       230: 2
       232: 2
       234: 2
       243: 1
       246: 2
       247: 1
       248: 1
       250: 2
       251: 2
       253: 2
       254: 2
       256: 1
       257: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       325: 1
       326: 1
       337: 1
       345: 2
       349: 2
       353: 2
       355: 2
       367: 1
       371: 1
       372: 1
       374: 1
       375: 1
       385: 1
       386: 1
       387: 1
       388: 1
       439: 1
       440: 1
       453: 1
       454: 1
       484: 1
       509: 1
       518: 1
       519: 1
       672: 1

 673:    0: 3q+4
         1: 3q+4
         2: 3q^2+5q+2
         3: 4q+4
         4: 3q+4
         5: 4q+4
         6: 3q+4
         7: 3q^2+5q+2
         8: 2q^2+4q+2
         9: 2q^3+5q^2+4q+1
        10: 3q+4
        11: 4q+4
        12: 3q+4
        13: 3q+2
        14: 3q+2
        15: 2q+2
        16: q+4
        17: q+4
        18: 3q^2+4q+1
        19: 3q+4
        20: 3q+4
        21: 3q^2+5q+2
        22: q+4
        23: q+4
        24: q^2+3q+2
        25: q+4
        26: q+4
        27: q^2+3q+2
        28: q+4
        29: 3q+4
        30: 3q+2
        31: q+4
        32: q+2
        33: 4
        34: q+4
        35: q+2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 3q+2
        44: 3q+2
        45: 2q+2
        46: q+2
        47: 2
        48: 3q+1
        49: q+4
        50: q+4
        51: 3q^2+4q+1
        52: q+4
        53: q+4
        54: q^2+3q+2
        55: q+4
        56: q+4
        57: q^2+3q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: q+1
        70: 3q+2
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: q+4
        83: q+2
        84: q+2
        85: 2
        86: q+4
        87: q+2
        88: q+2
        89: 2
        90: 3q+1
        91: q+2
        92: 2
        93: 3q+1
        94: 2
        95: 2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q^2+2q+1
       100: 2
       101: 2
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: q+1
       134: q+1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+2
       158: 2
       159: 3q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       243: 1
       246: 2
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       258: 1
       297: 1
       298: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       366: 1
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       483: 1
       491: 1
       494: 1
       498: 1
       510: 1
       518: 1
       520: 1
       673: 1

 674:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: q^2+6q+2
        23: q^2+6q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: 2q+2
        30: q+2
        32: 3q+2
        33: q^2+6q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: 3q+2
        53: q^2+5q+2
        54: q+2
        55: q+2
        56: 3q+2
        57: 2
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        69: q+2
        72: q+2
        73: 2q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 3q+2
        83: q+2
        85: 2q+2
        87: 2
        91: 2
        92: 2q+2
        93: 2
        94: 3q+2
        95: q^2+5q+2
        96: q+2
        97: q+2
        98: 3q+2
        99: 2
       100: q+2
       101: 3q+2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: q+1
       124: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 2
       135: 2
       136: 2
       138: q+2
       140: q+2
       142: 2q+2
       144: 2
       147: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: 3q+2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       197: 1
       198: 1
       211: 1
       212: 1
       223: 2
       225: 2
       228: 2
       229: 2
       230: 2
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       291: 1
       292: 1
       301: 1
       302: 1
       305: 1
       306: 1
       315: 1
       316: 1
       338: 1
       339: 1
       340: 1
       341: 1
       348: 2
       350: 2
       351: 2
       356: 1
       368: 1
       369: 1
       371: 1
       372: 1
       433: 1
       434: 1
       445: 1
       446: 1
       496: 1
       512: 1
       515: 1
       516: 1
       674: 1

 675:    0: q^2+6q+4
         1: 2q^2+6q+4
         2: q^2+6q+4
         3: 2q^2+6q+4
         4: 3q^2+5q+2
         5: q^2+6q+4
         6: q^3+4q^2+5q+2
         7: 3q^2+5q+2
         8: q^2+6q+4
         9: q^3+3q^2+3q+1
        10: 4q+4
        11: 4q+4
        12: 2q^2+4q+2
        13: q^2+6q+4
        14: 3q^2+5q+2
        15: q^2+6q+4
        16: 4q+4
        17: 4q+4
        18: 2q^2+3q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        22: q^2+6q+4
        23: 2q^2+6q+4
        24: q^2+6q+4
        25: 4q+4
        26: 4q+4
        27: 4q+4
        28: 2q+4
        29: 2q+2
        30: 3q+2
        31: 4q+4
        32: q^2+6q+4
        33: 4q+4
        34: 2q+4
        35: 4q+4
        36: 2q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: 4q+4
        44: 2q^2+4q+2
        45: 4q+4
        46: 4q+4
        47: 4q+4
        48: 2q^2+3q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+2
        59: q+2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 2q+4
        69: q+1
        70: 2q+2
        71: q+2
        72: q+2
        80: 4q+4
        81: 4q+4
        82: 2q+2
        83: 3q+2
        84: 2q+4
        85: 2q+4
        86: q+2
        87: 2q+2
        88: 4
        89: 4
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        94: 2q+2
        95: 2q+2
        96: 2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       117: q+2
       118: q+2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: q+2
       134: q+1
       135: q+2
       137: 4
       138: q+1
       139: q+2
       140: q+2
       141: 2q+2
       143: 4
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 2q+2
       161: 2q+2
       162: 2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 1
       184: 1
       191: 2
       192: 2
       193: 1
       194: 1
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       226: 1
       227: q+2
       228: q+1
       229: q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 2
       244: 2
       246: q+2
       250: 2
       251: 2
       252: q+1
       256: 2
       257: 2
       258: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 1
       294: 1
       299: 1
       300: 1
       307: 1
       308: 1
       319: 1
       320: 1
       333: 1
       334: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       352: 1
       356: 1
       366: 1
       367: 2
       368: 1
       369: 2
       437: 1
       438: 1
       471: 1
       472: 1
       481: 1
       492: 1
       493: 1
       508: 1
       512: 1
       675: 1

 676:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        58: 1
        59: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        73: 2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
       109: 1
       110: 1
       117: 1
       118: 1
       125: 2
       126: 1
       133: 2
       134: 1
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       185: 1
       186: 1
       191: 1
       192: 1
       195: 1
       196: 1
       219: 1
       220: 2
       221: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       250: 2
       251: 2
       252: q+1
       295: 1
       296: 1
       303: 1
       304: 1
       333: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       439: 1
       440: 1
       482: 1
       492: 1
       494: 1
       676: 1

 677:    0: q^2+4q+4
         1: q^2+4q+4
         2: 2q^2+3q+2
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: 2q^2+3q+2
         8: 2q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 2q+4
        17: 2q+4
        18: q^2+2q+1
        19: q^2+4q+4
        20: q^2+4q+4
        21: 2q^2+3q+2
        22: q^2+4q+4
        23: q^2+4q+4
        24: 2q^2+3q+2
        25: 4
        26: 4
        27: 2q+2
        28: 2q+4
        29: q^2+4q+4
        30: q+2
        31: q^2+4q+4
        32: q+2
        33: 2q+4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2q+4
        50: 2q+4
        51: q^2+2q+1
        52: q^2+4q+4
        53: q^2+4q+4
        54: 2q^2+3q+2
        55: 4
        56: 4
        57: 2q+2
        58: q+2
        59: q+2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: q+2
        71: 2q+4
        72: 4
        73: 2q+4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: q^2+4q+4
        83: q+2
        84: 2
        85: 2
        86: 4
        87: 2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2q+4
        95: 2q+4
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2q+4
       140: 4
       141: q+2
       142: 2q+4
       143: 2
       144: 1
       145: 2
       146: 2
       147: 2
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       193: 2
       194: 2
       195: q+2
       196: q+2
       197: 2
       198: 2
       201: 1
       202: 1
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       228: 1
       229: 2
       230: 2
       231: 1
       236: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       297: 1
       298: 1
       305: 1
       306: 1
       319: 1
       320: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       366: 1
       441: 1
       442: 1
       443: 1
       444: 1
       483: 1
       493: 1
       494: 1
       495: 1
       677: 1

 678:    0: q^2+4q+4
         1: q^2+4q+4
         2: q^2+3q+2
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4
        17: 4
        19: q^2+4q+4
        20: q^2+4q+4
        21: q^2+3q+2
        22: q^2+4q+4
        23: q^2+4q+4
        24: q^2+3q+2
        25: 2q+4
        26: 2q+4
        27: 2q+2
        28: 4
        29: q^2+4q+4
        30: q+2
        31: q^2+4q+4
        32: q+2
        33: 4
        34: 2q+4
        35: 2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 4
        50: 4
        52: q^2+4q+4
        53: q^2+4q+4
        54: q^2+3q+2
        55: 2q+4
        56: 2q+4
        57: 2q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: q+2
        71: 4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: q^2+4q+4
        83: q+2
        84: 2
        85: 2
        86: 2q+4
        87: 2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 4
        95: 4
        97: 2
        98: 2
       100: 2q+4
       101: 2q+4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 2
       136: 2
       137: 2
       139: 4
       140: 4
       141: q+2
       142: 4
       143: 2
       145: 2
       146: 2
       147: 2
       149: 2q+4
       150: 2
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 2
       161: 2
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       193: 2
       194: 2
       195: 2
       196: 2
       197: 2
       198: 2
       201: 1
       202: 1
       207: 1
       208: 1
       209: q+2
       210: q+2
       211: 1
       212: 1
       222: 2
       224: 2
       229: 2
       230: 2
       234: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       250: 2
       251: 2
       253: 1
       254: 1
       256: 1
       257: 1
       267: 1
       268: 1
       269: 1
       270: 1
       297: 1
       298: 1
       305: 1
       306: 1
       319: 1
       320: 1
       325: 1
       326: 1
       337: 2
       347: 2
       349: 2
       351: 2
       355: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       441: 1
       442: 1
       443: 1
       444: 1
       496: 1
       511: 1
       518: 1
       519: 1
       678: 1

 679:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        30: q+2
        32: q+2
        33: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: 2
        56: 2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: q+2
        85: 2
        87: 2
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       140: 2
       142: 2
       144: 1
       147: 1
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       160: 2
       161: 2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       187: 1
       188: 1
       197: 1
       198: 1
       211: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 2
       230: 2
       233: 1
       234: 1
       236: 1
       244: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       305: 1
       306: 1
       336: 1
       348: 1
       350: 1
       351: 1
       356: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       491: 1
       495: 1
       496: 1
       512: 1
       679: 1

 680:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: 4q+2
        23: 4q+2
        24: 2q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: q^2+3q+2
        30: q+2
        32: 2q+2
        33: 4q+2
        35: 3q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: q+2
        53: 3q+2
        54: 2
        55: 3q+2
        56: q^2+5q+2
        57: q+2
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        69: q+2
        72: 2q+2
        73: q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        81: 2q+2
        83: 2
        85: 3q+2
        87: q+2
        91: 2
        92: 2q+2
        93: 2
        94: q+2
        95: 3q+2
        96: 2
        97: 3q+2
        98: q^2+5q+2
        99: q+2
       100: q+2
       101: 3q+2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: q+1
       124: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 2
       135: 2
       136: 2
       138: 2
       142: q+2
       144: q+2
       147: 2q+2
       148: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: q+2
       167: 3q+2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       205: 1
       206: 1
       211: 1
       212: 1
       223: 2
       225: 2
       228: 1
       230: 1
       233: 2
       234: 2
       235: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       245: q+2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       291: 1
       292: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       338: 1
       339: 1
       340: 1
       341: 1
       350: 1
       356: 2
       358: 2
       359: 2
       368: 1
       370: 1
       371: 1
       372: 1
       451: 1
       452: 1
       463: 1
       464: 1
       501: 1
       514: 1
       515: 1
       516: 1
       680: 1

 681:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        34: q+2
        35: q+2
        36: 2
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        55: q+2
        56: q+2
        57: q+2
        60: 1
        61: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        97: 2
        98: 2
        99: q+1
       107: 1
       108: 1
       119: 1
       120: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: 2
       158: 2
       159: q+1
       163: 2
       164: 2
       165: q+1
       183: 1
       184: 1
       199: 1
       200: 1
       201: 1
       202: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       231: 1
       232: 2
       233: 1
       234: 2
       253: 2
       254: 2
       255: q+1
       293: 1
       294: 1
       307: 1
       308: 1
       333: 1
       334: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       453: 1
       454: 1
       481: 1
       497: 1
       498: 1
       681: 1

 682:    0: q^2+6q+4
         1: 2q^2+6q+4
         2: q^2+6q+4
         3: 2q^2+6q+4
         4: 3q^2+5q+2
         5: q^2+6q+4
         6: q^3+4q^2+5q+2
         7: 3q^2+5q+2
         8: q^2+6q+4
         9: q^3+3q^2+3q+1
        10: 4q+4
        11: 4q+4
        12: 2q^2+4q+2
        13: q^2+6q+4
        14: 3q^2+5q+2
        15: q^2+6q+4
        16: 4q+4
        17: 4q+4
        18: 2q^2+3q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        22: 4q+4
        23: 4q+4
        24: 4q+4
        25: q^2+6q+4
        26: 2q^2+6q+4
        27: q^2+6q+4
        28: 2q+4
        29: 2q+2
        30: 3q+2
        31: 2q+4
        32: 4q+4
        33: 2q+4
        34: 4q+4
        35: q^2+6q+4
        36: 4q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: 4q+4
        44: 2q^2+4q+2
        45: 4q+4
        46: 4q+4
        47: 4q+4
        48: 2q^2+3q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: 2
        59: 2
        60: q+2
        61: q+2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 2q+4
        69: q+1
        70: 2q+2
        71: q+2
        73: q+2
        80: 2q+4
        81: 2q+4
        82: q+2
        83: 2q+2
        84: 4q+4
        85: 4q+4
        86: 2q+2
        87: 3q+2
        88: 4
        89: 4
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: 2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       117: 2
       118: 2
       119: q+2
       120: q+2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: q+2
       134: q+1
       136: q+2
       137: 4
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4
       144: q+1
       145: q+2
       146: 2q+2
       148: q+2
       149: q+2
       150: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2q+2
       164: 2q+2
       165: 2q+1
       166: 2
       167: 2
       168: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       185: 1
       186: 1
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       203: 1
       204: 1
       207: 2
       208: 2
       219: 1
       220: 2
       221: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: q+2
       233: q+1
       235: q+2
       236: 1
       243: 2
       245: 2
       246: q+2
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       295: 1
       296: 1
       303: 1
       304: 1
       309: 1
       310: 1
       321: 1
       322: 1
       333: 1
       335: 1
       344: 1
       350: 1
       352: 1
       353: 2
       354: 1
       357: 2
       358: 1
       366: 1
       367: 2
       368: 1
       370: 2
       457: 1
       458: 1
       473: 1
       474: 1
       482: 1
       497: 1
       499: 1
       508: 1
       514: 1
       682: 1

 683:    0: q^2+4q+4
         1: q^2+4q+4
         2: 2q^2+3q+2
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: 2q^2+3q+2
         8: 2q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 2q+4
        17: 2q+4
        18: q^2+2q+1
        19: q^2+4q+4
        20: q^2+4q+4
        21: 2q^2+3q+2
        22: 4
        23: 4
        24: 2q+2
        25: q^2+4q+4
        26: q^2+4q+4
        27: 2q^2+3q+2
        28: 2q+4
        29: q^2+4q+4
        30: q+2
        31: 4
        32: 2
        33: 4
        34: q^2+4q+4
        35: q+2
        36: 2q+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2q+4
        50: 2q+4
        51: q^2+2q+1
        52: 4
        53: 4
        54: 2q+2
        55: q^2+4q+4
        56: q^2+4q+4
        57: 2q^2+3q+2
        58: 2
        59: 2
        60: q+2
        61: q+2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: q+2
        71: 2q+4
        72: 2q+4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 4
        83: 2
        84: q+2
        85: 2
        86: q^2+4q+4
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+4
        98: 2q+4
        99: q^2+2q+1
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: 2
       142: 2
       143: 2
       144: 1
       145: 2q+4
       146: q+2
       147: 2q+4
       148: 4
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: q+2
       202: q+2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       231: 1
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: q+1
       253: 2
       254: 2
       255: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       297: 1
       298: 1
       313: 1
       314: 1
       321: 1
       322: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       459: 1
       460: 1
       461: 1
       462: 1
       483: 1
       498: 1
       499: 1
       500: 1
       683: 1

 684:    0: q^2+4q+4
         1: q^2+4q+4
         2: q^2+3q+2
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4
        17: 4
        19: q^2+4q+4
        20: q^2+4q+4
        21: q^2+3q+2
        22: 2q+4
        23: 2q+4
        24: 2q+2
        25: q^2+4q+4
        26: q^2+4q+4
        27: q^2+3q+2
        28: 4
        29: q^2+4q+4
        30: q+2
        31: 2q+4
        32: 2
        33: 4
        34: q^2+4q+4
        35: q+2
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        49: 4
        50: 4
        52: 2q+4
        53: 2q+4
        54: 2q+2
        55: q^2+4q+4
        56: q^2+4q+4
        57: q^2+3q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 1
        65: 1
        66: 2
        67: 2
        70: q+2
        71: 4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 2q+4
        83: 2
        84: q+2
        85: 2
        86: q^2+4q+4
        87: q+2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 4
        98: 4
       100: 2q+4
       101: 2q+4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       135: 2
       136: 2
       137: 2
       139: 2
       141: 2
       142: 2
       143: 2
       145: 4
       146: q+2
       147: 4
       148: 4
       149: 2q+4
       150: 2
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 1
       161: 1
       163: 2
       164: 2
       166: 2
       167: 2
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 2
       202: 2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 1
       208: 1
       209: q+2
       210: q+2
       211: 1
       212: 1
       222: 2
       224: 2
       230: 1
       234: 2
       235: 2
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       250: 1
       251: 1
       253: 2
       254: 2
       256: 1
       257: 1
       271: 1
       272: 1
       273: 1
       274: 1
       297: 1
       298: 1
       313: 1
       314: 1
       321: 1
       322: 1
       325: 1
       326: 1
       337: 2
       349: 1
       355: 2
       357: 2
       359: 2
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       459: 1
       460: 1
       461: 1
       462: 1
       501: 1
       513: 1
       518: 1
       519: 1
       684: 1

 685:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        30: q+2
        32: 2
        33: 2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q+2
        56: q+2
        57: q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: 1
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: 2
        87: q+2
        91: 2
        92: 2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       142: 1
       144: 1
       147: 2
       148: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       187: 1
       188: 1
       205: 1
       206: 1
       211: 1
       212: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 2
       235: 2
       236: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       313: 1
       314: 1
       336: 1
       350: 1
       356: 1
       358: 1
       359: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       491: 1
       500: 1
       501: 1
       514: 1
       685: 1

 686:    0: 4
         1: 4
         2: 4
         3: 4
         4: q^2+2q+1
         5: 4
         6: q^2+2q+1
         7: q^2+2q+1
         8: 4
         9: q^2+2q+1
        10: 4
        11: 4
        12: q^2+2q+1
        13: 4
        14: q^2+2q+1
        15: 4
        16: 4
        17: 4
        18: q^2+2q+1
        19: 1
        20: 1
        21: 1
        22: 4
        23: 4
        24: 4
        25: 4
        26: 4
        27: 4
        28: 4
        29: 1
        30: 1
        31: 4
        32: 4
        33: 4
        34: 4
        35: 4
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: 2
        42: 2
        43: 4
        44: q^2+2q+1
        45: 4
        46: 4
        47: 4
        48: q^2+2q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: 4
        69: 1
        70: 1
        71: 1
        80: 4
        81: 4
        82: 1
        83: 1
        84: 4
        85: 4
        86: 1
        87: 1
        88: 4
        89: 4
        90: q^2+2q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 1
       134: 1
       137: 4
       138: 1
       139: 1
       141: 1
       143: 4
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       174: 1
       175: 1
       176: 1
       191: 2
       192: 2
       199: 2
       200: 2
       207: 2
       208: 2
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       243: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: 1
       276: 1
       277: 1
       278: 1
       333: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       366: 1
       367: 1
       368: 1
       374: 1
       375: 1
       376: 1
       492: 1
       497: 1
       508: 1
       509: 1
       510: 1
       686: 1

 687:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: 2q+2
         5: 4
         6: 2q+2
         7: q^2+2q+1
         8: 2q+2
         9: q^2+2q+1
        10: 4
        11: 4
        12: 2q+2
        13: 2
        14: q+1
        15: 2
        16: 4
        17: 4
        18: q^2+2q+1
        19: 2
        20: 2
        21: q+1
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 2
        30: 1
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: 2
        72: 2
        80: 2
        81: 2
        82: 2
        83: 1
        84: 2
        85: 2
        86: 2
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 2
       140: 2
       141: 1
       143: 2
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       193: 1
       194: 1
       201: 1
       202: 1
       207: 1
       208: 1
       221: 1
       222: 1
       223: 1
       226: 1
       228: 1
       229: 1
       231: 1
       233: 1
       234: 1
       236: 1
       243: 2
       244: 2
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       319: 1
       320: 1
       334: 1
       346: 1
       347: 1
       348: 1
       354: 1
       355: 1
       356: 1
       366: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       493: 1
       498: 1
       510: 1
       511: 1
       512: 1
       687: 1

 688:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: 2q+2
         5: 4
         6: 2q+2
         7: q^2+2q+1
         8: 2q+2
         9: q^2+2q+1
        10: 4
        11: 4
        12: 2q+2
        13: 2
        14: q+1
        15: 2
        16: 4
        17: 4
        18: q^2+2q+1
        19: 2
        20: 2
        21: q+1
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 2
        30: 1
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: 1
        71: 2
        73: 2
        80: 2
        81: 2
        82: 2
        83: 1
        84: 2
        85: 2
        86: 2
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2
       144: 1
       145: 2
       146: 1
       148: 2
       149: 2
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       195: 1
       196: 1
       203: 1
       204: 1
       207: 1
       208: 1
       221: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       235: 1
       236: 1
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       321: 1
       322: 1
       335: 1
       346: 1
       349: 1
       350: 1
       354: 1
       357: 1
       358: 1
       366: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       494: 1
       499: 1
       510: 1
       513: 1
       514: 1
       688: 1

 689:    0: 2q^2+6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: q^3+3q^2+4q+2
         5: 2q^2+6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 4q+2
        17: 4q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 2q^2+6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 2q^2+6q+2
        26: 6q+2
        27: 2q^2+4q+2
        30: 3q+2
        32: 4q+2
        33: 4q+2
        35: 4q+2
        36: 4q+2
        37: q^2+3q+1
        38: q^2+3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: q^2+4q+2
        53: 4q+2
        54: q^2+3q+2
        55: q^2+4q+2
        56: 4q+2
        57: q^2+3q+2
        64: 2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        69: q+1
        72: q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        81: 2q+2
        83: 3q+2
        85: 2q+2
        87: 3q+2
        91: 2
        92: 2
        93: q+1
        94: 2q+2
        95: 2q+2
        96: 2q+1
        97: 2q+2
        98: 2q+2
        99: 2q+1
       100: q^2+4q+2
       101: 4q+2
       102: q^2+3q+2
       111: 1
       112: 1
       115: q+1
       116: q+1
       123: q+1
       124: q+1
       134: 1
       135: 2
       136: 2
       138: q+1
       140: q+2
       142: q+2
       144: q+1
       147: q+2
       148: q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2q+2
       167: 2q+2
       168: 2q+1
       187: 1
       188: 1
       197: 1
       198: 1
       205: 1
       206: 1
       211: q+1
       212: q+1
       223: 1
       225: 1
       228: 1
       229: 2
       230: 2
       233: 1
       234: 2
       235: 2
       236: q+1
       244: q+2
       245: q+2
       247: 2
       248: 2
       249: q+1
       256: 2
       257: 2
       258: q+1
       305: 1
       306: 1
       313: 1
       314: 1
       323: 1
       324: 1
       336: 1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 2
       370: 2
       475: 1
       476: 1
       479: 1
       480: 1
       495: 1
       500: 1
       512: 1
       514: 1
       689: 1

 690:    0: 3q^2+14q+4
         1: 3q^2+14q+4
         2: 3q^3+8q^2+7q+2
         3: 3q^2+14q+4
         4: 5q^2+9q+4
         5: 3q^2+14q+4
         6: 5q^2+9q+4
         7: 3q^2+5q+2
         8: 2q^3+6q^2+6q+2
         9: 3q^2+5q+2
        10: 3q^2+14q+4
        11: 3q^2+14q+4
        12: 5q^2+9q+4
        13: q^2+5q+2
        14: 3q+2
        15: 4q+2
        16: 3q^2+14q+4
        17: 3q^2+14q+4
        18: 3q^2+5q+2
        19: q^2+9q+4
        20: q^2+9q+4
        21: 3q^2+5q+2
        22: 10q+4
        23: 10q+4
        24: q^3+4q^2+5q+2
        25: 10q+4
        26: 10q+4
        27: q^3+4q^2+5q+2
        28: 3q^2+14q+4
        29: q^2+9q+4
        30: 3q+2
        31: 10q+4
        32: 3q+2
        33: 10q+4
        34: 10q+4
        35: 3q+2
        36: 10q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: 3q+2
        45: 4q+2
        46: q^2+5q+2
        47: 4q+2
        48: 3q+2
        49: q^2+9q+4
        50: q^2+9q+4
        51: 3q^2+5q+2
        52: 5q+4
        53: 5q+4
        54: q^2+3q+2
        55: 5q+4
        56: 5q+4
        57: q^2+3q+2
        58: 5q+2
        59: 5q+2
        60: 5q+2
        61: 5q+2
        62: 4q+2
        63: 4q+2
        64: q+1
        65: q+1
        66: 4q+2
        67: 4q+2
        69: 3q+2
        70: 3q+2
        71: q^2+9q+4
        72: 2q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: 3q+2
        81: 3q+2
        82: 5q+4
        83: q+2
        84: 3q+2
        85: 3q+2
        86: 5q+4
        87: q+2
        88: q^2+5q+2
        89: 4q+2
        90: 3q+2
        91: q+2
        92: 2q+2
        93: q+2
        94: 5q+4
        95: 5q+4
        96: q^2+3q+2
        97: 5q+4
        98: 5q+4
        99: q^2+3q+2
       100: q+2
       101: q+2
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       126: 3q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       134: q+2
       135: 2
       136: 2
       137: 3q+2
       138: q+2
       139: 5q+4
       141: q+2
       142: 2q+4
       143: 3q+2
       144: q+2
       145: 5q+4
       146: q+2
       147: 2q+4
       149: q+2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+2
       158: 2q+2
       159: q+2
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: q+2
       196: q+2
       201: q+2
       202: q+2
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       228: 1
       230: 1
       231: q+2
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: q+2
       246: 2
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       366: 2
       368: 1
       371: 1
       374: 1
       376: 1
       423: 1
       424: 1
       427: 1
       428: 1
       469: 1
       470: 1
       494: 1
       498: 1
       510: 1
       515: 1
       518: 1
       690: 1

 691:    0: q^2+6q+4
         1: q^2+6q+4
         2: 2q+2
         3: q^2+6q+4
         4: q^2+6q+4
         5: q^2+6q+4
         6: q^2+6q+4
         7: 2q+2
         8: q^3+3q^2+4q+2
         9: 2q+2
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: 2
        14: 2
        15: 2q+2
        16: q^2+6q+4
        17: q^2+6q+4
        18: 2q+2
        19: q^2+6q+4
        20: q^2+6q+4
        21: 2q+2
        22: 2q+4
        23: 2q+4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: 2q+2
        28: q^2+6q+4
        29: q^2+6q+4
        30: 2
        31: 2q+4
        32: 2
        33: 2q+4
        34: 2q+4
        35: 2
        36: 2q+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: 2
        45: 2q+2
        46: 2
        47: 2q+2
        48: 2
        49: q^2+6q+4
        50: q^2+6q+4
        51: 2q+2
        52: 2q+4
        53: 2q+4
        54: 2q+2
        55: 2q+4
        56: 2q+4
        57: 2q+2
        58: q+2
        59: q+2
        60: q+2
        61: q+2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 2
        70: 2
        71: q^2+6q+4
        72: 2q+4
        73: 2q+4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 2q+4
        83: 2
        84: 2
        85: 2
        86: 2q+4
        87: 2
        88: 2
        89: 2q+2
        90: 2
        91: 2
        92: 2q+2
        93: 2
        94: 2q+4
        95: 2q+4
        96: 2q+2
        97: 2q+4
        98: 2q+4
        99: 2q+2
       100: 2
       101: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       134: 2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 2q+4
       141: 2
       142: 2q+4
       143: 2
       144: 2
       145: 2q+4
       146: 2
       147: 2q+4
       149: 2
       151: 1
       152: 1
       153: 1
       154: 1
       157: 2
       158: 2q+2
       159: 2
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: q+2
       196: q+2
       201: q+2
       202: q+2
       207: 1
       208: 1
       209: 1
       210: 1
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2
       228: 1
       230: 1
       231: 2
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       243: 2
       247: 2
       248: 2
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       257: 1
       259: 1
       260: 1
       261: 1
       262: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       317: 1
       318: 1
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       372: 1
       375: 1
       423: 1
       424: 1
       427: 1
       428: 1
       494: 1
       498: 1
       516: 1
       519: 1
       691: 1

 692:    0: 4
         1: 4
         2: 2q+2
         3: 4
         4: 2q+2
         5: 4
         6: 2q+2
         7: 2q^2+2q+2
         8: 2q+2
         9: 2q^2+2q+2
        10: 4
        11: 4
        12: 2q+2
        13: 2
        14: q+2
        15: 2
        16: 4
        17: 4
        18: 2q^2+2q+2
        19: 2
        20: 2
        21: q+2
        22: 4
        23: 4
        24: 2q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 2
        30: 2
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: 2
        44: q+2
        45: 2
        46: 2
        47: 2
        48: q+2
        49: 2
        50: 2
        51: q+2
        52: 2
        53: 2
        54: q+2
        55: 2
        56: 2
        57: q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 2
        70: 2
        71: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2
        89: 2
        90: q+2
        91: 1
        93: 1
        94: 2
        95: 2
        96: q+2
        97: 2
        98: 2
        99: q+2
       100: 2
       101: 2
       102: q+2
       103: 1
       104: 1
       105: 1
       106: 1
       113: 1
       114: 1
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       137: 2
       138: 2
       139: 2
       141: 2
       143: 2
       144: 2
       145: 2
       146: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 2
       167: 2
       168: q+2
       177: 1
       178: 1
       179: 1
       180: 1
       189: 1
       190: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       226: 2
       228: 1
       231: 2
       233: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       249: 2
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       287: 1
       288: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       342: 1
       343: 1
       346: 1
       354: 1
       366: 2
       368: 1
       373: 1
       374: 1
       376: 1
       469: 1
       470: 1
       510: 1
       517: 1
       520: 1
       692: 1

 693:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        60: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       169: 1
       179: 1
       181: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       259: 1
       267: 1
       271: 1
       301: 1
       311: 1
       317: 1
       319: 1
       321: 1
       323: 1
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       389: 1
       397: 1
       405: 1
       427: 1
       443: 1
       445: 1
       461: 1
       463: 1
       477: 1
       479: 1
       545: 1
       561: 1
       569: 1
       573: 1
       577: 1
       693: 1

 694:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        28: 3q
        29: 2q
        31: 3q
        33: 3q
        34: 3q
        36: 3q
        37: q
        38: 2q
        39: q
        40: 2q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        58: 2q
        59: q
        60: 2q
        61: q
        62: q
        63: 2q
        66: q
        67: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q
        82: 2q
        86: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       103: q
       104: q
       105: q
       107: q
       109: q
       114: q
       128: q
       130: q
       139: 2q
       140: q
       142: q
       145: 2q
       147: q
       148: q
       149: 2q
       152: q
       154: q
       166: 2q
       167: 2q
       180: q
       193: q
       195: q
       201: q
       203: q
       210: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       247: 1
       248: 1
       318: q
       319: q
       321: q
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       428: 1
       443: 1
       446: 1
       461: 1
       464: 1
       479: 1
       546: 1
       562: 1
       573: 1
       578: 1
       694: 1

 695:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        10: q^3+q
        11: q
        12: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        28: q
        29: q^3+q
        31: q
        33: q
        34: q
        36: q
        37: q
        39: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        58: q
        60: q
        62: q
        66: q
        71: q
        72: q
        73: q
        74: q
        76: q
        82: q
        86: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       103: q
       107: q
       109: q
       111: q
       113: q
       127: q
       129: q
       139: q
       140: q
       142: q
       145: q
       147: q
       148: q
       149: q
       151: q
       153: q
       169: q
       179: q
       181: q
       193: q
       195: q
       197: q
       201: q
       203: q
       205: q
       209: q
       259: q
       267: q
       271: q
       477: 1
       569: 1
       579: 1
       695: 1

 696:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        28: 3q
        29: 2q
        31: 3q
        33: 3q
        34: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q
        40: q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        58: q
        59: 2q
        60: 2q
        61: q
        62: 2q
        63: q
        66: 2q
        67: q
        71: 2q
        72: q
        73: q
        74: q
        76: q
        82: 2q
        86: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       103: q
       104: q
       106: q
       107: q
       110: q
       113: q
       127: q
       129: q
       139: 2q
       140: q
       142: q
       145: 2q
       147: q
       148: q
       149: 2q
       151: q
       153: q
       166: 2q
       167: 2q
       179: q
       193: q
       196: q
       201: q
       204: q
       209: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       247: 1
       248: 1
       317: q
       319: q
       322: q
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       427: 1
       443: 1
       445: 1
       462: 1
       463: 1
       480: 1
       545: 1
       563: 1
       574: 1
       580: 1
       696: 1

 697:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        61: 1
        62: 1
        66: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       127: 1
       129: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       151: 1
       153: 1
       166: 1
       167: 1
       172: 1
       179: 1
       181: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       262: 1
       269: 1
       273: 1
       301: 1
       311: 1
       317: 1
       320: 1
       322: 1
       323: 1
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       391: 1
       399: 1
       406: 1
       427: 1
       444: 1
       445: 1
       462: 1
       463: 1
       477: 1
       479: 1
       547: 1
       563: 1
       570: 1
       575: 1
       577: 1
       697: 1

 698:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        28: 3q
        29: 2q
        31: 3q
        33: 3q
        34: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q
        40: q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        58: 2q
        59: q
        60: q
        61: 2q
        62: 2q
        63: q
        66: 2q
        67: q
        71: 2q
        72: q
        73: q
        74: q
        76: q
        82: 2q
        86: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       103: q
       105: q
       106: q
       108: q
       109: q
       113: q
       127: q
       129: q
       139: 2q
       140: q
       142: q
       145: 2q
       147: q
       148: q
       149: 2q
       151: q
       153: q
       166: 2q
       167: 2q
       179: q
       194: q
       195: q
       202: q
       203: q
       209: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       247: 1
       248: 1
       317: q
       320: q
       321: q
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       427: 1
       444: 1
       445: 1
       461: 1
       463: 1
       480: 1
       547: 1
       561: 1
       576: 1
       580: 1
       698: 1

 699:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        59: 1
        60: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       170: 1
       180: 1
       182: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       260: 1
       268: 1
       274: 1
       302: 1
       312: 1
       318: 1
       319: 1
       322: 1
       324: 1
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       390: 1
       400: 1
       407: 1
       428: 1
       443: 1
       446: 1
       462: 1
       464: 1
       478: 1
       480: 1
       546: 1
       564: 1
       571: 1
       574: 1
       581: 1
       699: 1

 700:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         6: 1
        10: 1
        11: 1
        12: 1
        16: 1
        17: 1
        19: 1
        20: 1
        22: 1
        23: 1
        25: 1
        26: 1
        28: 1
        29: 1
        31: 1
        33: 1
        34: 1
        36: 1
        38: 1
        40: 1
        49: 1
        50: 1
        52: 1
        53: 1
        55: 1
        56: 1
        58: 1
        61: 1
        63: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        82: 1
        86: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       128: 1
       130: 1
       139: 1
       140: 1
       142: 1
       145: 1
       147: 1
       148: 1
       149: 1
       152: 1
       154: 1
       166: 1
       167: 1
       171: 1
       180: 1
       182: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       261: 1
       270: 1
       272: 1
       302: 1
       312: 1
       318: 1
       320: 1
       321: 1
       324: 1
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       392: 1
       398: 1
       408: 1
       428: 1
       444: 1
       446: 1
       461: 1
       464: 1
       478: 1
       480: 1
       548: 1
       562: 1
       572: 1
       576: 1
       581: 1
       700: 1

 701:    0: 3q
         1: 3q
         3: 3q
         4: q^2+2q
         5: 3q
         6: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        16: 3q
        17: 3q
        19: 2q
        20: 2q
        22: 3q
        23: 3q
        25: 3q
        26: 3q
        28: 3q
        29: 2q
        31: 3q
        33: 3q
        34: 3q
        36: 3q
        37: q
        38: 2q
        39: q
        40: 2q
        49: 2q
        50: 2q
        52: 2q
        53: 2q
        55: 2q
        56: 2q
        58: q
        59: 2q
        60: q
        61: 2q
        62: q
        63: 2q
        66: q
        67: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q
        82: 2q
        86: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q
       104: q
       105: q
       106: q
       108: q
       110: q
       114: q
       128: q
       130: q
       139: 2q
       140: q
       142: q
       145: 2q
       147: q
       148: q
       149: 2q
       152: q
       154: q
       166: 2q
       167: 2q
       180: q
       194: q
       196: q
       202: q
       204: q
       210: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       247: 1
       248: 1
       318: q
       320: q
       322: q
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       428: 1
       444: 1
       446: 1
       462: 1
       464: 1
       479: 1
       548: 1
       564: 1
       575: 1
       578: 1
       701: 1

 702:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        10: q^3+q
        11: q
        12: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        28: q
        29: q^3+q
        31: q
        33: q
        34: q
        36: q
        37: q
        39: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        59: q
        61: q
        62: q
        66: q
        71: q
        72: q
        73: q
        74: q
        76: q
        82: q
        86: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       106: q
       108: q
       110: q
       111: q
       113: q
       127: q
       129: q
       139: q
       140: q
       142: q
       145: q
       147: q
       148: q
       149: q
       151: q
       153: q
       172: q
       179: q
       181: q
       194: q
       196: q
       197: q
       202: q
       204: q
       205: q
       209: q
       262: q
       269: q
       273: q
       477: 1
       570: 1
       579: 1
       702: 1

 703:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        10: q^3+q
        11: q
        12: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        28: q
        29: q^3+q
        31: q
        33: q
        34: q
        36: q
        38: q
        40: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        59: q
        60: q
        63: q
        67: q
        71: q
        72: q
        73: q
        75: q
        77: q
        82: q
        86: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       104: q
       107: q
       110: q
       112: q
       114: q
       128: q
       130: q
       139: q
       140: q
       142: q
       145: q
       147: q
       148: q
       149: q
       152: q
       154: q
       170: q
       180: q
       182: q
       193: q
       196: q
       198: q
       201: q
       204: q
       206: q
       210: q
       260: q
       268: q
       274: q
       478: 1
       571: 1
       582: 1
       703: 1

 704:    0: q^3+q
         1: q^3+q
         3: q
         4: q^3+q
         5: q
         6: q^3+q
        10: q^3+q
        11: q
        12: q^3+q
        16: q
        17: q
        19: q^3+q
        20: q^3+q
        22: q
        23: q
        25: q
        26: q
        28: q
        29: q^3+q
        31: q
        33: q
        34: q
        36: q
        38: q
        40: q
        49: q
        50: q
        52: q
        53: q
        55: q
        56: q
        58: q
        61: q
        63: q
        67: q
        71: q
        72: q
        73: q
        75: q
        77: q
        82: q
        86: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q
       105: q
       108: q
       109: q
       112: q
       114: q
       128: q
       130: q
       139: q
       140: q
       142: q
       145: q
       147: q
       148: q
       149: q
       152: q
       154: q
       171: q
       180: q
       182: q
       194: q
       195: q
       198: q
       202: q
       203: q
       206: q
       210: q
       261: q
       270: q
       272: q
       478: 1
       572: 1
       582: 1
       704: 1

 705:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       103: 2q+1
       106: q
       107: q+1
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       169: q+1
       173: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       195: q+1
       199: q+1
       201: q+1
       207: 2q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       259: q+1
       263: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       377: 1
       381: 1
       385: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       439: 1
       447: 1
       453: 1
       492: 1
       494: 1
       497: 1
       498: 1
       521: 1
       525: 1
       529: 1
       583: 1
       587: 1
       607: 1
       619: 1
       705: 1

 706:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       104: 2q+1
       105: q
       107: q+1
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       170: q+1
       174: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       196: q+1
       199: q+1
       201: q+1
       208: 2q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       260: q+1
       264: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       378: 1
       382: 1
       386: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       440: 1
       447: 1
       453: 1
       492: 1
       494: 1
       497: 1
       498: 1
       522: 1
       526: 1
       530: 1
       584: 1
       588: 1
       608: 1
       619: 1
       706: 1

 707:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       104: q
       105: 2q+1
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       171: q+1
       175: q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       195: q+1
       200: q+1
       202: q+1
       208: 2q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       261: q+1
       265: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       379: 1
       383: 1
       387: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       439: 1
       448: 1
       454: 1
       492: 1
       494: 1
       497: 1
       498: 1
       523: 1
       527: 1
       531: 1
       584: 1
       588: 1
       607: 1
       620: 1
       707: 1

 708:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       103: q
       106: 2q+1
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       172: q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       196: q+1
       200: q+1
       202: q+1
       207: 2q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       262: q+1
       266: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       380: 1
       384: 1
       388: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       440: 1
       448: 1
       454: 1
       492: 1
       494: 1
       497: 1
       498: 1
       524: 1
       528: 1
       532: 1
       583: 1
       587: 1
       608: 1
       620: 1
       708: 1

 709:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       259: 1
       263: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       377: 1
       381: 1
       385: 1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       447: 1
       481: 1
       482: 1
       521: 1
       529: 1
       585: 1
       589: 1
       595: 1
       709: 1

 710:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       260: 1
       264: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       378: 1
       382: 1
       386: 1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       447: 1
       481: 1
       482: 1
       522: 1
       530: 1
       586: 1
       589: 1
       596: 1
       710: 1

 711:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       261: 1
       265: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       379: 1
       383: 1
       387: 1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       448: 1
       481: 1
       482: 1
       523: 1
       531: 1
       586: 1
       590: 1
       595: 1
       711: 1

 712:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       262: 1
       266: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 1
       356: 1
       380: 1
       384: 1
       388: 1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       448: 1
       481: 1
       482: 1
       524: 1
       532: 1
       585: 1
       590: 1
       596: 1
       712: 1

 713:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^2+2q+1
        58: q+1
        60: 2q+1
        61: q
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+4q+1
        73: 2q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 2q+1
       108: q
       109: q+1
       111: 2q+1
       113: q+1
       115: q+1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       141: 1
       142: 2q+1
       143: q+1
       144: 2q+1
       145: 3q+1
       146: q+1
       147: q^2+4q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       173: 1
       177: q+1
       179: q+1
       181: 2q+1
       183: 1
       185: 1
       187: q+1
       189: 1
       191: 1
       195: q+1
       199: 1
       201: 2q+1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       259: q+1
       263: 1
       271: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: q+1
       293: 1
       295: 1
       297: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       366: 1
       377: 1
       385: 1
       397: 1
       401: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       447: 1
       449: 1
       451: 1
       461: 1
       463: 1
       469: 1
       481: 1
       483: 1
       500: 1
       529: 1
       549: 1
       561: 1
       589: 1
       591: 1
       599: 1
       629: 1
       713: 1

 714:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^2+2q+1
        58: q+1
        60: q
        61: 2q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+4q+1
        73: 2q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       105: q+1
       107: q
       108: 2q+1
       109: q+1
       112: 2q+1
       114: q+1
       116: q+1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       141: 1
       142: 2q+1
       143: q+1
       144: 2q+1
       145: 3q+1
       146: q+1
       147: q^2+4q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: q+1
       175: 1
       178: q+1
       180: q+1
       182: 2q+1
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       195: q+1
       200: 1
       201: q
       202: 2q+1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       261: q+1
       265: 1
       272: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: q+1
       294: 1
       295: 1
       298: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       366: 1
       379: 1
       387: 1
       398: 1
       402: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       448: 1
       449: 1
       452: 1
       461: 1
       464: 1
       470: 1
       481: 1
       483: 1
       500: 1
       531: 1
       550: 1
       562: 1
       590: 1
       591: 1
       600: 1
       630: 1
       714: 1

 715:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^2+2q+1
        59: q+1
        60: 2q+1
        61: q
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+4q+1
        73: 2q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 2q+1
       108: q
       110: q+1
       112: 2q+1
       114: q+1
       116: q+1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       141: 1
       142: 2q+1
       143: q+1
       144: 2q+1
       145: 3q+1
       146: q+1
       147: q^2+4q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: q+1
       174: 1
       178: q+1
       180: q+1
       182: 2q+1
       183: 1
       186: 1
       188: q+1
       190: 1
       192: 1
       196: q+1
       199: 1
       201: 2q+1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       260: q+1
       264: 1
       274: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: q+1
       293: 1
       296: 1
       298: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       366: 1
       378: 1
       386: 1
       400: 1
       403: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       447: 1
       450: 1
       452: 1
       462: 1
       464: 1
       470: 1
       481: 1
       483: 1
       500: 1
       530: 1
       551: 1
       564: 1
       589: 1
       592: 1
       600: 1
       630: 1
       715: 1

 716:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^2+2q+1
        59: q+1
        60: q
        61: 2q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+4q+1
        73: 2q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       106: q+1
       107: q
       108: 2q+1
       110: q+1
       111: 2q+1
       113: q+1
       115: q+1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       141: 1
       142: 2q+1
       143: q+1
       144: 2q+1
       145: 3q+1
       146: q+1
       147: q^2+4q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: q+1
       176: 1
       177: q+1
       179: q+1
       181: 2q+1
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       196: q+1
       200: 1
       201: q
       202: 2q+1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       262: q+1
       266: 1
       273: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: q+1
       294: 1
       296: 1
       297: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       366: 1
       380: 1
       388: 1
       399: 1
       404: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       448: 1
       450: 1
       451: 1
       462: 1
       463: 1
       469: 1
       481: 1
       483: 1
       500: 1
       532: 1
       552: 1
       563: 1
       590: 1
       592: 1
       599: 1
       629: 1
       716: 1

 717:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: 2q+1
        73: q^2+4q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: q+1
       109: 2q+1
       110: q
       111: 2q+1
       113: q+1
       115: q+1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 3q+1
       140: 1
       141: q+1
       142: q^2+4q+1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 2q+1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       173: 1
       177: q+1
       179: q+1
       181: 2q+1
       183: 1
       185: 1
       187: q+1
       189: 1
       191: 1
       193: 1
       195: 2q+1
       196: q
       197: 1
       199: 1
       201: q+1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       259: q+1
       263: 1
       267: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       366: 1
       377: 1
       385: 1
       389: 1
       393: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       443: 1
       445: 1
       469: 1
       482: 1
       483: 1
       495: 1
       529: 1
       533: 1
       545: 1
       593: 1
       595: 1
       599: 1
       613: 1
       717: 1

 718:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: 2q+1
        73: q^2+4q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: q+1
       109: q
       110: 2q+1
       112: 2q+1
       114: q+1
       116: q+1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 3q+1
       140: 1
       141: q+1
       142: q^2+4q+1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 2q+1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: q+1
       168: 1
       170: q+1
       174: 1
       178: q+1
       180: q+1
       182: 2q+1
       183: 1
       186: 1
       188: q+1
       190: 1
       192: 1
       193: 1
       195: q
       196: 2q+1
       198: 1
       199: 1
       201: q+1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       260: q+1
       264: 1
       268: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       366: 1
       378: 1
       386: 1
       390: 1
       394: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       443: 1
       446: 1
       470: 1
       482: 1
       483: 1
       495: 1
       530: 1
       534: 1
       546: 1
       593: 1
       596: 1
       600: 1
       614: 1
       718: 1

 719:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        38: 2q+1
        40: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: 2q+1
        73: q^2+4q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: q+1
       109: 2q+1
       110: q
       112: 2q+1
       114: q+1
       116: q+1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 3q+1
       140: 1
       141: q+1
       142: q^2+4q+1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 2q+1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: q+1
       168: 1
       171: q+1
       175: 1
       178: q+1
       180: q+1
       182: 2q+1
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       194: 1
       195: 2q+1
       196: q
       198: 1
       200: 1
       202: q+1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       261: q+1
       265: 1
       270: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       366: 1
       379: 1
       387: 1
       392: 1
       395: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       444: 1
       446: 1
       470: 1
       482: 1
       483: 1
       495: 1
       531: 1
       535: 1
       548: 1
       594: 1
       595: 1
       600: 1
       614: 1
       719: 1

 720:    0: 2q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^2+2q+1
         3: 2q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+4q+1
        20: q^3+3q^2+4q+1
        21: q^2+2q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+4q+1
        50: q^3+3q^2+4q+1
        51: q^2+2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        61: q+1
        62: q+1
        64: q+1
        66: 2q+1
        68: 1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: 2q+1
        73: q^2+4q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: q+1
       109: q
       110: 2q+1
       111: 2q+1
       113: q+1
       115: q+1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 3q+1
       140: 1
       141: q+1
       142: q^2+4q+1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 2q+1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: q+1
       168: 1
       172: q+1
       176: 1
       177: q+1
       179: q+1
       181: 2q+1
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       194: 1
       195: q
       196: 2q+1
       197: 1
       200: 1
       202: q+1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       262: q+1
       266: 1
       269: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       366: 1
       380: 1
       388: 1
       391: 1
       396: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       444: 1
       445: 1
       469: 1
       482: 1
       483: 1
       495: 1
       532: 1
       536: 1
       547: 1
       594: 1
       596: 1
       599: 1
       613: 1
       720: 1

 721:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q+1
        59: q
        60: q+1
        62: q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: 2q^2+3q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       118: q
       119: q+1
       121: q+1
       123: q^2+2q+1
       125: 2q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       192: q
       193: 1
       195: 1
       197: 1
       199: q+1
       201: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       344: q+1
       348: 1
       350: 1
       352: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       377: 1
       381: 1
       389: 1
       393: 1
       413: 1
       417: 1
       429: 1
       431: 1
       433: 1
       435: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       508: 1
       512: 1
       521: 1
       533: 1
       537: 1
       605: 1
       639: 1
       641: 1
       721: 1

 722:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: q+1
        60: q+1
        63: q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: 2q^2+3q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: q+1
       119: q+1
       122: q+1
       124: q^2+2q+1
       125: 2q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       191: q
       192: q+1
       193: 1
       196: 1
       198: 1
       199: q+1
       201: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       344: q+1
       348: 1
       350: 1
       352: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       378: 1
       382: 1
       390: 1
       394: 1
       414: 1
       418: 1
       429: 1
       432: 1
       434: 1
       436: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       508: 1
       512: 1
       522: 1
       534: 1
       538: 1
       606: 1
       640: 1
       641: 1
       722: 1

 723:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: q+1
        61: q+1
        62: q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: 2q^2+3q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: q+1
       120: q+1
       121: q+1
       123: q^2+2q+1
       125: 2q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       191: q
       192: q+1
       194: 1
       196: 1
       197: 1
       200: q+1
       202: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       344: q+1
       348: 1
       350: 1
       352: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       380: 1
       384: 1
       391: 1
       396: 1
       413: 1
       417: 1
       430: 1
       432: 1
       433: 1
       435: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       508: 1
       512: 1
       524: 1
       536: 1
       539: 1
       605: 1
       639: 1
       642: 1
       723: 1

 724:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q+1
        59: q
        61: q+1
        63: q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: 2q^2+3q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       118: q
       120: q+1
       122: q+1
       124: q^2+2q+1
       125: 2q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       192: q
       194: 1
       195: 1
       198: 1
       200: q+1
       202: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       344: q+1
       348: 1
       350: 1
       352: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       379: 1
       383: 1
       392: 1
       395: 1
       414: 1
       418: 1
       430: 1
       431: 1
       434: 1
       436: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       508: 1
       512: 1
       523: 1
       535: 1
       540: 1
       606: 1
       640: 1
       642: 1
       724: 1

 725:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 2q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: 1
       109: q+1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       121: q+1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       193: 1
       195: q+1
       197: 1
       199: q+1
       201: 1
       207: q+1
       209: 1
       211: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       259: 1
       263: 1
       267: 1
       275: q+1
       283: 1
       285: 1
       287: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       377: 1
       385: 1
       389: 1
       393: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       469: 1
       492: 1
       493: 1
       494: 1
       529: 1
       533: 1
       541: 1
       603: 1
       607: 1
       609: 1
       725: 1

 726:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 2q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: 1
       110: q+1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: q+1
       193: 1
       196: q+1
       198: 1
       199: q+1
       201: 1
       208: q+1
       210: 1
       212: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       260: 1
       264: 1
       268: 1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       378: 1
       386: 1
       390: 1
       394: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       470: 1
       492: 1
       493: 1
       494: 1
       530: 1
       534: 1
       542: 1
       603: 1
       608: 1
       610: 1
       726: 1

 727:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 2q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: 1
       110: q+1
       111: 1
       113: 1
       115: 1
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: q+1
       194: 1
       196: q+1
       197: 1
       200: q+1
       202: 1
       207: q+1
       209: 1
       211: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       262: 1
       266: 1
       269: 1
       278: q+1
       284: 1
       286: 1
       287: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       380: 1
       388: 1
       391: 1
       396: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       469: 1
       492: 1
       493: 1
       494: 1
       532: 1
       536: 1
       543: 1
       604: 1
       608: 1
       609: 1
       727: 1

 728:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 2q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: 1
       109: q+1
       112: 1
       114: 1
       116: 1
       117: q+1
       120: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       194: 1
       195: q+1
       198: 1
       200: q+1
       202: 1
       208: q+1
       210: 1
       212: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: q+1
       252: 1
       261: 1
       265: 1
       270: 1
       277: q+1
       284: 1
       285: 1
       288: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       366: 1
       379: 1
       387: 1
       392: 1
       395: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       470: 1
       492: 1
       493: 1
       494: 1
       531: 1
       535: 1
       544: 1
       604: 1
       607: 1
       610: 1
       728: 1

 729:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q
        60: q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q+1
       118: q
       119: q+1
       121: q^2+2q+1
       123: q+1
       125: 2q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: 2q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: 1
       143: q+1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: q+1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       192: q
       193: 1
       195: 1
       197: 1
       199: q+1
       201: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: q+1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       275: q+1
       279: 1
       289: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       317: 1
       319: 1
       325: q+1
       327: 1
       329: 1
       345: q+1
       347: 1
       349: 1
       353: 1
       355: 1
       360: 1
       362: 1
       367: 1
       369: 1
       374: 1
       375: 1
       381: 1
       385: 1
       389: 1
       393: 1
       409: 1
       415: 1
       435: 1
       437: 1
       439: 1
       441: 1
       453: 1
       465: 1
       471: 1
       502: 1
       504: 1
       509: 1
       511: 1
       525: 1
       537: 1
       541: 1
       611: 1
       635: 1
       647: 1
       729: 1

 730:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q+1
        60: q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: q+1
       119: q+1
       122: q^2+2q+1
       124: q+1
       125: 2q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: 2q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: 1
       143: q+1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: q+1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       191: q
       192: q+1
       193: 1
       196: 1
       198: 1
       199: q+1
       201: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: q+1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       276: q+1
       280: 1
       290: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       318: 1
       319: 1
       326: q+1
       328: 1
       330: 1
       345: q+1
       347: 1
       349: 1
       353: 1
       355: 1
       361: 1
       363: 1
       367: 1
       369: 1
       374: 1
       375: 1
       382: 1
       386: 1
       390: 1
       394: 1
       410: 1
       416: 1
       436: 1
       437: 1
       440: 1
       442: 1
       453: 1
       466: 1
       471: 1
       503: 1
       505: 1
       509: 1
       511: 1
       526: 1
       538: 1
       542: 1
       612: 1
       636: 1
       647: 1
       730: 1

 731:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q+1
        61: q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: q+1
       120: q+1
       121: q^2+2q+1
       123: q+1
       125: 2q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: 2q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: 1
       143: q+1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: q+1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       191: q
       192: q+1
       194: 1
       196: 1
       197: 1
       200: q+1
       202: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: q+1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       278: q+1
       279: 1
       289: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       317: 1
       320: 1
       325: q+1
       327: 1
       329: 1
       345: q+1
       347: 1
       349: 1
       353: 1
       355: 1
       360: 1
       362: 1
       367: 1
       369: 1
       374: 1
       375: 1
       384: 1
       388: 1
       391: 1
       396: 1
       409: 1
       415: 1
       435: 1
       438: 1
       440: 1
       441: 1
       454: 1
       465: 1
       472: 1
       502: 1
       504: 1
       509: 1
       511: 1
       528: 1
       539: 1
       543: 1
       611: 1
       635: 1
       648: 1
       731: 1

 732:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q
        61: q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q+1
       118: q
       120: q+1
       122: q^2+2q+1
       124: q+1
       125: 2q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: 2q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: 1
       143: q+1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: q+1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       192: q
       194: 1
       195: 1
       198: 1
       200: q+1
       202: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: q+1
       229: 1
       230: 1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: q+1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       277: q+1
       280: 1
       290: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       318: 1
       320: 1
       326: q+1
       328: 1
       330: 1
       345: q+1
       347: 1
       349: 1
       353: 1
       355: 1
       361: 1
       363: 1
       367: 1
       369: 1
       374: 1
       375: 1
       383: 1
       387: 1
       392: 1
       395: 1
       410: 1
       416: 1
       436: 1
       438: 1
       439: 1
       442: 1
       454: 1
       466: 1
       472: 1
       503: 1
       505: 1
       509: 1
       511: 1
       527: 1
       540: 1
       544: 1
       612: 1
       636: 1
       648: 1
       732: 1

 733:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q
        60: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       110: q
       111: 1
       113: 1
       115: 1
       117: 1
       118: q
       119: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       186: q
       187: 1
       189: 1
       193: 1
       195: 1
       196: q
       197: 1
       201: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       279: 1
       289: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       317: 1
       319: 1
       325: 1
       337: 1
       338: 1
       340: 1
       351: 1
       360: 1
       362: 1
       367: 1
       369: 1
       371: 1
       372: 1
       381: 1
       389: 1
       393: 1
       427: 1
       435: 1
       443: 1
       445: 1
       465: 1
       471: 1
       484: 1
       485: 1
       487: 1
       496: 1
       537: 1
       545: 1
       601: 1
       615: 1
       617: 1
       733: 1

 734:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       109: q
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       185: q
       186: 1
       188: 1
       190: 1
       193: 1
       195: q
       196: 1
       198: 1
       201: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       280: 1
       290: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       318: 1
       319: 1
       326: 1
       337: 1
       339: 1
       341: 1
       351: 1
       361: 1
       363: 1
       367: 1
       369: 1
       371: 1
       372: 1
       382: 1
       390: 1
       394: 1
       428: 1
       436: 1
       443: 1
       446: 1
       466: 1
       471: 1
       484: 1
       486: 1
       488: 1
       496: 1
       538: 1
       546: 1
       602: 1
       615: 1
       618: 1
       734: 1

 735:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       109: q
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: 1
       120: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       185: q
       186: 1
       187: 1
       189: 1
       194: 1
       195: q
       196: 1
       197: 1
       202: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       279: 1
       289: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       317: 1
       320: 1
       325: 1
       337: 1
       338: 1
       340: 1
       351: 1
       360: 1
       362: 1
       367: 1
       369: 1
       371: 1
       372: 1
       384: 1
       391: 1
       396: 1
       427: 1
       435: 1
       444: 1
       445: 1
       465: 1
       472: 1
       484: 1
       485: 1
       487: 1
       496: 1
       539: 1
       547: 1
       601: 1
       616: 1
       617: 1
       735: 1

 736:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       110: q
       112: 1
       114: 1
       116: 1
       117: 1
       118: q
       120: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       186: q
       188: 1
       190: 1
       194: 1
       195: 1
       196: q
       198: 1
       202: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       280: 1
       290: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       318: 1
       320: 1
       326: 1
       337: 1
       339: 1
       341: 1
       351: 1
       361: 1
       363: 1
       367: 1
       369: 1
       371: 1
       372: 1
       383: 1
       392: 1
       395: 1
       428: 1
       436: 1
       444: 1
       446: 1
       466: 1
       472: 1
       484: 1
       486: 1
       488: 1
       496: 1
       540: 1
       548: 1
       602: 1
       616: 1
       618: 1
       736: 1

 737:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        60: q+1
        61: q
        62: q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q^2+2q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q^2+3q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       120: q
       121: q+1
       123: q^2+2q+1
       125: 2q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       195: 1
       199: q+1
       200: q
       201: 1
       203: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       271: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       303: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       344: 1
       350: 1
       352: q+1
       356: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       377: 1
       381: 1
       397: 1
       401: 1
       413: 1
       417: 1
       431: 1
       447: 1
       449: 1
       451: 1
       455: 1
       465: 1
       467: 1
       469: 1
       473: 1
       508: 1
       514: 1
       521: 1
       549: 1
       553: 1
       623: 1
       639: 1
       643: 1
       737: 1

 738:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        60: q
        61: q+1
        63: q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q^2+2q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q^2+3q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       119: q
       120: q+1
       122: q+1
       124: q^2+2q+1
       125: 2q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       195: 1
       199: q
       200: q+1
       202: 1
       203: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       272: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       303: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       344: 1
       350: 1
       352: q+1
       356: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       379: 1
       383: 1
       398: 1
       402: 1
       414: 1
       418: 1
       431: 1
       448: 1
       449: 1
       452: 1
       456: 1
       466: 1
       468: 1
       470: 1
       473: 1
       508: 1
       514: 1
       523: 1
       550: 1
       554: 1
       624: 1
       640: 1
       643: 1
       738: 1

 739:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        60: q
        61: q+1
        62: q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q^2+2q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q^2+3q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       119: q
       120: q+1
       121: q+1
       123: q^2+2q+1
       125: 2q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: q+1
       196: 1
       199: q
       200: q+1
       202: 1
       204: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       273: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       304: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       344: 1
       350: 1
       352: q+1
       356: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       380: 1
       384: 1
       399: 1
       404: 1
       413: 1
       417: 1
       432: 1
       448: 1
       450: 1
       451: 1
       455: 1
       465: 1
       467: 1
       469: 1
       474: 1
       508: 1
       514: 1
       524: 1
       552: 1
       555: 1
       623: 1
       639: 1
       644: 1
       739: 1

 740:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+q+1
         5: 2q^2+3q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q^2+3q+1
        14: q^2+q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: q+1
        60: q+1
        61: q
        63: q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q^2+2q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q^2+3q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       120: q
       122: q+1
       124: q^2+2q+1
       125: 2q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: q+1
       196: 1
       199: q+1
       200: q
       201: 1
       204: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       274: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       304: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       344: 1
       350: 1
       352: q+1
       356: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       378: 1
       382: 1
       400: 1
       403: 1
       414: 1
       418: 1
       432: 1
       447: 1
       450: 1
       452: 1
       456: 1
       466: 1
       468: 1
       470: 1
       474: 1
       508: 1
       514: 1
       522: 1
       551: 1
       556: 1
       624: 1
       640: 1
       644: 1
       740: 1

 741:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        60: 2q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: q+1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       121: q+1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       195: 1
       199: q+1
       201: q+1
       203: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       259: 1
       263: 1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: 1
       291: 1
       293: 1
       295: 1
       297: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: 1
       334: 1
       335: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       377: 1
       385: 1
       397: 1
       401: 1
       419: 1
       421: 1
       423: 1
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       469: 1
       497: 1
       498: 1
       499: 1
       529: 1
       549: 1
       557: 1
       619: 1
       621: 1
       625: 1
       741: 1

 742:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        60: q
        61: 2q+1
        63: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: q+1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       120: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       195: 1
       200: q+1
       202: q+1
       203: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       261: 1
       265: 1
       272: 1
       277: q+1
       284: 1
       285: 1
       288: 1
       292: 1
       294: 1
       295: 1
       298: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: 1
       334: 1
       335: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       379: 1
       387: 1
       398: 1
       402: 1
       420: 1
       421: 1
       424: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       470: 1
       497: 1
       498: 1
       499: 1
       531: 1
       550: 1
       558: 1
       620: 1
       621: 1
       626: 1
       742: 1

 743:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        59: q+1
        60: q
        61: 2q+1
        62: q+1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: q+1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: q+1
       196: 1
       200: q+1
       202: q+1
       204: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       262: 1
       266: 1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: 1
       291: 1
       294: 1
       296: 1
       297: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: 1
       334: 1
       335: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       380: 1
       388: 1
       399: 1
       404: 1
       420: 1
       422: 1
       423: 1
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       469: 1
       497: 1
       498: 1
       499: 1
       532: 1
       552: 1
       559: 1
       620: 1
       622: 1
       625: 1
       743: 1

 744:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: 2q+1
        57: q+1
        59: q+1
        60: 2q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: q+1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: q+1
       159: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: q+1
       196: 1
       199: q+1
       201: q+1
       204: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: q+1
       255: 1
       260: 1
       264: 1
       274: 1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: 1
       293: 1
       296: 1
       298: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: 1
       334: 1
       335: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 1
       378: 1
       386: 1
       400: 1
       403: 1
       419: 1
       422: 1
       424: 1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       470: 1
       497: 1
       498: 1
       499: 1
       530: 1
       551: 1
       560: 1
       619: 1
       622: 1
       626: 1
       744: 1

 745:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        60: q+1
        61: q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       120: q
       121: q^2+2q+1
       123: q+1
       125: 2q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: q+1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       145: q+1
       146: q^2+2q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       169: 1
       173: q+1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       195: 1
       199: q+1
       200: q
       201: 1
       203: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       259: 1
       263: 1
       271: 1
       275: q+1
       279: 1
       289: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       321: 1
       325: q+1
       327: 1
       329: 1
       345: 1
       349: 1
       353: q+1
       355: 1
       357: 1
       360: 1
       362: 1
       367: 1
       370: 1
       374: 1
       375: 1
       381: 1
       385: 1
       397: 1
       401: 1
       409: 1
       415: 1
       439: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       473: 1
       502: 1
       504: 1
       509: 1
       513: 1
       525: 1
       553: 1
       557: 1
       627: 1
       635: 1
       649: 1
       745: 1

 746:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        60: q
        61: q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q+1
       119: q
       120: q+1
       122: q^2+2q+1
       124: q+1
       125: 2q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: q+1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       145: q+1
       146: q^2+2q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       171: 1
       175: q+1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       195: 1
       199: q
       200: q+1
       202: 1
       203: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       261: 1
       265: 1
       272: 1
       277: q+1
       280: 1
       290: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       321: 1
       326: q+1
       328: 1
       330: 1
       345: 1
       349: 1
       353: q+1
       355: 1
       357: 1
       361: 1
       363: 1
       367: 1
       370: 1
       374: 1
       375: 1
       383: 1
       387: 1
       398: 1
       402: 1
       410: 1
       416: 1
       439: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       473: 1
       503: 1
       505: 1
       509: 1
       513: 1
       527: 1
       554: 1
       558: 1
       628: 1
       636: 1
       649: 1
       746: 1

 747:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: q+1
        60: q
        61: q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: q+1
       119: q
       120: q+1
       121: q^2+2q+1
       123: q+1
       125: 2q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: 1
       137: q+1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       145: q+1
       146: q^2+2q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       172: 1
       176: q+1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       196: 1
       199: q
       200: q+1
       202: 1
       204: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       262: 1
       266: 1
       273: 1
       278: q+1
       279: 1
       289: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       322: 1
       325: q+1
       327: 1
       329: 1
       345: 1
       349: 1
       353: q+1
       355: 1
       357: 1
       360: 1
       362: 1
       367: 1
       370: 1
       374: 1
       375: 1
       384: 1
       388: 1
       399: 1
       404: 1
       409: 1
       415: 1
       440: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       474: 1
       502: 1
       504: 1
       509: 1
       513: 1
       528: 1
       555: 1
       559: 1
       627: 1
       635: 1
       650: 1
       747: 1

 748:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: 2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: q+1
        60: q+1
        61: q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q+1
        68: 2q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       120: q
       122: q^2+2q+1
       124: q+1
       125: 2q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: 1
       137: q+1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       145: q+1
       146: q^2+2q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       170: 1
       174: q+1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       196: 1
       199: q+1
       200: q
       201: 1
       204: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       260: 1
       264: 1
       274: 1
       276: q+1
       280: 1
       290: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       322: 1
       326: q+1
       328: 1
       330: 1
       345: 1
       349: 1
       353: q+1
       355: 1
       357: 1
       361: 1
       363: 1
       367: 1
       370: 1
       374: 1
       375: 1
       382: 1
       386: 1
       400: 1
       403: 1
       410: 1
       416: 1
       440: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       474: 1
       503: 1
       505: 1
       509: 1
       513: 1
       526: 1
       556: 1
       560: 1
       628: 1
       636: 1
       650: 1
       748: 1

 749:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: 1
        61: q
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       108: q
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       120: q
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: q+1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       184: q
       185: 1
       187: 1
       189: 1
       195: 1
       201: 1
       202: q
       203: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       259: 1
       263: 1
       271: 1
       279: 1
       289: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       317: 1
       321: 1
       325: 1
       337: 1
       338: 1
       340: 1
       359: 1
       360: 1
       362: 1
       367: 1
       370: 1
       371: 1
       372: 1
       381: 1
       397: 1
       401: 1
       427: 1
       455: 1
       461: 1
       463: 1
       465: 1
       473: 1
       484: 1
       485: 1
       487: 1
       501: 1
       553: 1
       561: 1
       601: 1
       631: 1
       633: 1
       749: 1

 750:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       105: 1
       107: q
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       119: q
       120: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: q+1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       183: q
       184: 1
       185: 1
       188: 1
       190: 1
       195: 1
       201: q
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       261: 1
       265: 1
       272: 1
       280: 1
       290: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       321: 1
       326: 1
       337: 1
       339: 1
       341: 1
       359: 1
       361: 1
       363: 1
       367: 1
       370: 1
       371: 1
       372: 1
       383: 1
       398: 1
       402: 1
       428: 1
       456: 1
       461: 1
       464: 1
       466: 1
       473: 1
       484: 1
       486: 1
       488: 1
       501: 1
       554: 1
       562: 1
       602: 1
       631: 1
       634: 1
       750: 1

 751:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: q
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       106: 1
       107: q
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       119: q
       120: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: q+1
       135: q+1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       183: q
       184: 1
       186: 1
       187: 1
       189: 1
       196: 1
       201: q
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       262: 1
       266: 1
       273: 1
       279: 1
       289: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       322: 1
       325: 1
       337: 1
       338: 1
       340: 1
       359: 1
       360: 1
       362: 1
       367: 1
       370: 1
       371: 1
       372: 1
       384: 1
       399: 1
       404: 1
       427: 1
       455: 1
       462: 1
       463: 1
       465: 1
       474: 1
       484: 1
       485: 1
       487: 1
       501: 1
       555: 1
       563: 1
       601: 1
       632: 1
       633: 1
       751: 1

 752:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        38: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: 1
        61: q
        63: 1
        65: 1
        67: 1
        68: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       108: q
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       120: q
       122: 1
       124: 1
       128: 1
       130: 1
       133: q+1
       135: q+1
       136: 1
       139: 1
       141: 1
       142: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       184: q
       186: 1
       188: 1
       190: 1
       196: 1
       201: 1
       202: q
       204: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       260: 1
       264: 1
       274: 1
       280: 1
       290: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       318: 1
       322: 1
       326: 1
       337: 1
       339: 1
       341: 1
       359: 1
       361: 1
       363: 1
       367: 1
       370: 1
       371: 1
       372: 1
       382: 1
       400: 1
       403: 1
       428: 1
       456: 1
       462: 1
       464: 1
       466: 1
       474: 1
       484: 1
       486: 1
       488: 1
       501: 1
       556: 1
       564: 1
       602: 1
       632: 1
       634: 1
       752: 1

 753:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: q^3+2q^2+2q+1
         5: 3q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^3+2q^2+2q+1
        13: q^2+3q+1
        14: q^2+q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^2+q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 2q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 2q^2+3q+1
        28: q^2+4q+1
        29: 2q+1
        30: q+1
        31: q^2+4q+1
        32: q^2+3q+1
        33: 3q^2+5q+1
        34: q^2+4q+1
        35: q^2+3q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q^2+3q+1
        59: q
        60: q^2+3q+1
        61: q
        62: q^2+2q+1
        63: 2q
        64: q^2+2q+1
        65: q
        66: 2q^2+3q+1
        67: q^2+2q
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q^2+2q+1
       104: q
       105: q
       107: q+1
       109: q+1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       121: q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       193: q+1
       195: q+1
       197: 1
       199: q+1
       201: q+1
       203: q+1
       205: 1
       207: q+1
       208: q
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       239: q+1
       241: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: 1
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: q+1
       321: q+1
       323: 1
       325: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       377: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       429: 1
       431: 1
       433: 1
       447: 1
       449: 1
       451: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       508: 1
       512: 1
       514: 1
       533: 1
       549: 1
       565: 1
       569: 1
       641: 1
       643: 1
       645: 1
       753: 1

 754:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: q^3+2q^2+2q+1
         5: 3q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^3+2q^2+2q+1
        13: q^2+3q+1
        14: q^2+q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^2+q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 2q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 2q^2+3q+1
        28: q^2+4q+1
        29: 2q+1
        30: q+1
        31: q^2+4q+1
        32: q^2+3q+1
        33: 3q^2+5q+1
        34: q^2+4q+1
        35: q^2+3q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q
        59: q^2+3q+1
        60: q^2+3q+1
        61: q
        62: 2q
        63: q^2+2q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: 2q^2+3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       104: q^2+2q+1
       106: q
       107: q+1
       110: q+1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       121: q
       122: q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: q+1
       193: q+1
       196: q+1
       198: 1
       199: q+1
       201: q+1
       204: q+1
       206: 1
       207: q
       208: q+1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 1
       240: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: q+1
       322: q+1
       324: 1
       326: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       378: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       429: 1
       432: 1
       434: 1
       447: 1
       450: 1
       452: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       508: 1
       512: 1
       514: 1
       534: 1
       551: 1
       566: 1
       571: 1
       641: 1
       644: 1
       646: 1
       754: 1

 755:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: q^3+2q^2+2q+1
         5: 3q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^3+2q^2+2q+1
        13: q^2+3q+1
        14: q^2+q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^2+q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 2q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 2q^2+3q+1
        28: q^2+4q+1
        29: 2q+1
        30: q+1
        31: q^2+4q+1
        32: q^2+3q+1
        33: 3q^2+5q+1
        34: q^2+4q+1
        35: q^2+3q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q^2+3q+1
        59: q
        60: q
        61: q^2+3q+1
        62: 2q
        63: q^2+2q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: 2q^2+3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       105: q^2+2q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       114: 1
       116: 1
       117: q+1
       120: q+1
       121: q
       122: q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       194: q+1
       195: q+1
       198: 1
       200: q+1
       202: q+1
       203: q+1
       206: 1
       207: q
       208: q+1
       210: 1
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 1
       240: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: q+1
       284: 1
       285: 1
       288: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: q+1
       321: q+1
       324: 1
       326: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       379: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       430: 1
       431: 1
       434: 1
       448: 1
       449: 1
       452: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       508: 1
       512: 1
       514: 1
       535: 1
       550: 1
       567: 1
       572: 1
       642: 1
       643: 1
       646: 1
       755: 1

 756:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: q^3+2q^2+2q+1
         5: 3q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^2+q+1
         8: 2q^2+3q+1
         9: q^2+q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^3+2q^2+2q+1
        13: q^2+3q+1
        14: q^2+q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^2+q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 2q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 2q^2+3q+1
        28: q^2+4q+1
        29: 2q+1
        30: q+1
        31: q^2+4q+1
        32: q^2+3q+1
        33: 3q^2+5q+1
        34: q^2+4q+1
        35: q^2+3q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q
        59: q^2+3q+1
        60: q
        61: q^2+3q+1
        62: q^2+2q+1
        63: 2q
        64: q^2+2q+1
        65: q
        66: 2q^2+3q+1
        67: q^2+2q
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       104: q
       105: q
       106: q^2+2q+1
       108: q+1
       110: q+1
       111: 1
       113: 1
       115: 1
       118: q+1
       120: q+1
       121: q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: q+1
       194: q+1
       196: q+1
       197: 1
       200: q+1
       202: q+1
       204: q+1
       205: 1
       207: q+1
       208: q
       209: 1
       211: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       239: q+1
       241: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: 1
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: q+1
       322: q+1
       323: 1
       325: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       380: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       430: 1
       432: 1
       433: 1
       448: 1
       450: 1
       451: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       508: 1
       512: 1
       514: 1
       536: 1
       552: 1
       568: 1
       570: 1
       642: 1
       644: 1
       645: 1
       756: 1

 757:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^4+q^3+q+1
         7: q^3+1
         8: 1
        10: 1
        11: 1
        12: q^3+1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       271: 1
       279: 1
       289: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       381: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       435: 1
       455: 1
       465: 1
       471: 1
       473: 1
       475: 1
       477: 1
       537: 1
       553: 1
       565: 1
       569: 1
       651: 1
       757: 1

 758:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^4+q^3+q+1
         7: q^3+1
         8: 1
        10: 1
        11: 1
        12: q^3+1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       273: 1
       279: 1
       289: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       384: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       435: 1
       455: 1
       465: 1
       472: 1
       474: 1
       475: 1
       477: 1
       539: 1
       555: 1
       568: 1
       570: 1
       651: 1
       758: 1

 759:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^4+q^3+q+1
         7: q^3+1
         8: 1
        10: 1
        11: 1
        12: q^3+1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       274: 1
       280: 1
       290: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       382: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       436: 1
       456: 1
       466: 1
       471: 1
       474: 1
       476: 1
       478: 1
       538: 1
       556: 1
       566: 1
       571: 1
       652: 1
       759: 1

 760:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: q^3+1
         5: 1
         6: q^4+q^3+q+1
         7: q^3+1
         8: 1
        10: 1
        11: 1
        12: q^3+1
        13: 1
        14: q^3+1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       272: 1
       280: 1
       290: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       383: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       436: 1
       456: 1
       466: 1
       472: 1
       473: 1
       476: 1
       478: 1
       540: 1
       554: 1
       567: 1
       572: 1
       652: 1
       760: 1

 761:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: q+1
        17: q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: 3q+1
        33: q+1
        34: 3q+1
        35: 3q+1
        36: q+1
        37: 2q+1
        38: q
        39: 2q+1
        40: q
        41: 2q+1
        42: q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        60: q+1
        62: 2q+1
        63: q
        64: 2q+1
        65: q
        66: q+1
        68: q+1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: q+1
       125: q+1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: q+1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       193: 1
       195: 1
       197: 1
       199: q+1
       201: 1
       203: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       303: 1
       305: 1
       307: 1
       309: 1
       313: 1
       319: 1
       321: 1
       323: 1
       325: q+1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       385: 1
       393: 1
       401: 1
       405: 1
       437: 1
       439: 1
       441: 1
       453: 1
       457: 1
       459: 1
       471: 1
       473: 1
       475: 1
       509: 1
       511: 1
       513: 1
       541: 1
       557: 1
       565: 1
       647: 1
       649: 1
       653: 1
       761: 1

 762:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: q+1
        17: q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: 3q+1
        33: q+1
        34: 3q+1
        35: 3q+1
        36: q+1
        37: 2q+1
        38: q
        39: 2q+1
        40: q
        41: 2q+1
        42: q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        59: q+1
        61: q+1
        62: 2q+1
        63: q
        64: 2q+1
        65: q
        66: q+1
        68: q+1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: q+1
       125: q+1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: q+1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       194: 1
       196: 1
       197: 1
       200: q+1
       202: 1
       204: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       266: 1
       269: 1
       273: 1
       278: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       304: 1
       305: 1
       308: 1
       310: 1
       313: 1
       320: 1
       322: 1
       323: 1
       325: q+1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       388: 1
       396: 1
       404: 1
       406: 1
       438: 1
       440: 1
       441: 1
       454: 1
       458: 1
       459: 1
       472: 1
       474: 1
       475: 1
       509: 1
       511: 1
       513: 1
       543: 1
       559: 1
       568: 1
       648: 1
       650: 1
       653: 1
       762: 1

 763:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: q+1
        17: q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: 3q+1
        33: q+1
        34: 3q+1
        35: 3q+1
        36: q+1
        37: q
        38: 2q+1
        39: q
        40: 2q+1
        41: q
        42: 2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        59: q+1
        60: q+1
        62: q
        63: 2q+1
        64: q
        65: 2q+1
        67: q+1
        68: q+1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       124: q+1
       125: q+1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: q+1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       193: 1
       196: 1
       198: 1
       199: q+1
       201: 1
       204: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       304: 1
       306: 1
       307: 1
       310: 1
       314: 1
       319: 1
       322: 1
       324: 1
       326: q+1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       386: 1
       394: 1
       403: 1
       407: 1
       437: 1
       440: 1
       442: 1
       453: 1
       458: 1
       460: 1
       471: 1
       474: 1
       476: 1
       509: 1
       511: 1
       513: 1
       542: 1
       560: 1
       566: 1
       647: 1
       650: 1
       654: 1
       763: 1

 764:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: q+1
        17: q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: 3q+1
        33: q+1
        34: 3q+1
        35: 3q+1
        36: q+1
        37: q
        38: 2q+1
        39: q
        40: 2q+1
        41: q
        42: 2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q+1
        47: q+1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        61: q+1
        62: q
        63: 2q+1
        64: q
        65: 2q+1
        67: q+1
        68: q+1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       124: q+1
       125: q+1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: q+1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       194: 1
       195: 1
       198: 1
       200: q+1
       202: 1
       203: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       265: 1
       270: 1
       272: 1
       277: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       303: 1
       306: 1
       308: 1
       309: 1
       314: 1
       320: 1
       321: 1
       324: 1
       326: q+1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       387: 1
       395: 1
       402: 1
       408: 1
       438: 1
       439: 1
       442: 1
       454: 1
       457: 1
       460: 1
       472: 1
       473: 1
       476: 1
       509: 1
       511: 1
       513: 1
       544: 1
       558: 1
       567: 1
       648: 1
       649: 1
       654: 1
       764: 1

 765:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        38: q
        39: q+1
        40: q^2+q
        41: 1
        42: q
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: 1
        62: 1
        63: q
        64: 1
        65: q
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: q+1
        77: q^2+q
        78: 1
        79: q
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       114: q
       115: 1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q^2+q
       155: 1
       156: q
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: 1
       190: q
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       210: q
       211: 1
       212: q
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       256: 1
       257: 1
       263: 1
       267: 1
       271: 1
       299: 1
       303: 1
       305: 1
       307: 1
       309: 1
       313: 1
       319: 1
       321: 1
       323: 1
       325: 1
       326: q
       337: 1
       351: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       393: 1
       401: 1
       405: 1
       443: 1
       461: 1
       471: 1
       473: 1
       475: 1
       479: 1
       484: 1
       496: 1
       501: 1
       565: 1
       573: 1
       615: 1
       631: 1
       655: 1
       765: 1

 766:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q
        38: 1
        39: q^2+q
        40: q+1
        41: q
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: 1
        62: q
        63: 1
        64: q
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q^2+q
        77: q+1
        78: q
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       104: 1
       107: 1
       110: 1
       112: 1
       113: q
       114: 1
       115: q
       116: 1
       118: 1
       119: 1
       121: q
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q
       152: 1
       153: q^2+q
       154: q+1
       155: q
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       189: q
       190: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       209: q
       210: 1
       211: q
       212: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       256: 1
       257: 1
       264: 1
       268: 1
       274: 1
       299: 1
       304: 1
       306: 1
       307: 1
       310: 1
       314: 1
       319: 1
       322: 1
       324: 1
       325: q
       326: 1
       337: 1
       351: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       394: 1
       403: 1
       407: 1
       443: 1
       462: 1
       471: 1
       474: 1
       476: 1
       480: 1
       484: 1
       496: 1
       501: 1
       566: 1
       574: 1
       615: 1
       632: 1
       656: 1
       766: 1

 767:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q
        38: 1
        39: q^2+q
        40: q+1
        41: q
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        61: 1
        62: q
        63: 1
        64: q
        65: 1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q
        75: 1
        76: q^2+q
        77: q+1
        78: q
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       112: 1
       113: q
       114: 1
       115: q
       116: 1
       117: 1
       120: 1
       121: q
       122: 1
       124: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q
       152: 1
       153: q^2+q
       154: q+1
       155: q
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       189: q
       190: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       209: q
       210: 1
       211: q
       212: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       256: 1
       257: 1
       265: 1
       270: 1
       272: 1
       300: 1
       303: 1
       306: 1
       308: 1
       309: 1
       314: 1
       320: 1
       321: 1
       324: 1
       325: q
       326: 1
       337: 1
       351: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       395: 1
       402: 1
       408: 1
       444: 1
       461: 1
       472: 1
       473: 1
       476: 1
       480: 1
       484: 1
       496: 1
       501: 1
       567: 1
       576: 1
       616: 1
       631: 1
       656: 1
       767: 1

 768:    0: q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: 1
        38: q
        39: q+1
        40: q^2+q
        41: 1
        42: q
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        61: 1
        62: 1
        63: q
        64: 1
        65: q
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q
        76: q+1
        77: q^2+q
        78: 1
        79: q
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q^2+2q+1
       102: q+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       114: q
       115: 1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q^2+q
       155: 1
       156: q
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: 1
       190: q
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       210: q
       211: 1
       212: q
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       256: 1
       257: 1
       266: 1
       269: 1
       273: 1
       300: 1
       304: 1
       305: 1
       308: 1
       310: 1
       313: 1
       320: 1
       322: 1
       323: 1
       325: 1
       326: q
       337: 1
       351: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       396: 1
       404: 1
       406: 1
       444: 1
       462: 1
       472: 1
       474: 1
       475: 1
       479: 1
       484: 1
       496: 1
       501: 1
       568: 1
       575: 1
       616: 1
       632: 1
       655: 1
       768: 1

 769:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: 1
        66: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: 1
       229: 1
       230: 1
       234: 1
       235: 1
       237: 1
       239: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       289: 1
       301: 1
       305: 1
       311: 1
       313: 1
       323: 1
       338: 1
       340: 1
       351: 1
       359: 1
       360: 1
       362: 1
       369: 1
       370: 1
       371: 1
       372: 1
       435: 1
       445: 1
       455: 1
       463: 1
       475: 1
       477: 1
       479: 1
       485: 1
       487: 1
       496: 1
       501: 1
       577: 1
       617: 1
       633: 1
       651: 1
       655: 1
       769: 1

 770:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        30: 2q
        32: 3q
        33: 3q
        35: 3q
        36: 3q
        37: q
        38: 2q
        39: q^2+q
        40: 2q^2+2q
        41: q
        42: 2q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        64: q
        65: 2q
        66: q
        67: 2q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        81: 3q
        83: 2q
        85: 3q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       116: q
       123: q
       124: 2q
       128: q
       130: q
       135: q
       136: q
       140: q
       142: q
       147: q
       148: q
       150: 2q
       152: q
       154: q^2+q
       156: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       212: q
       214: q
       216: q
       229: q
       230: q
       234: q
       235: q
       238: q
       240: q
       244: q
       245: q
       247: 1
       248: 1
       256: 2q
       257: 2q
       339: 1
       341: 1
       351: 1
       359: 1
       361: q
       363: q
       369: q
       370: q
       371: 1
       372: 1
       446: 1
       464: 1
       479: 1
       486: 1
       488: 1
       496: 1
       501: 1
       578: 1
       618: 1
       634: 1
       655: 1
       770: 1

 771:    0: q^3+q
         1: q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^3+q^2+q
         7: q^3+q
         8: q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        30: q^3+q
        32: q
        33: q
        35: q
        36: q
        37: q
        39: q^2+q
        41: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        64: q
        66: q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       111: q
       115: q
       123: q
       127: q
       129: q
       135: q
       136: q
       140: q
       142: q
       147: q
       148: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q
       163: q
       164: q
       181: q
       187: q
       197: q
       205: q
       211: q
       213: q
       215: q
       229: q
       230: q
       234: q
       235: q
       289: q
       305: q
       313: q
       477: 1
       579: 1
       651: 1
       771: 1

 772:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        30: 2q
        32: 3q
        33: 3q
        35: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q^2+2q
        40: q^2+q
        41: 2q
        42: q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        64: 2q
        65: q
        66: 2q
        67: q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        81: 3q
        83: 2q
        85: 3q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       115: q
       123: 2q
       124: q
       127: q
       129: q
       135: q
       136: q
       140: q
       142: q
       147: q
       148: q
       150: 2q
       151: q
       153: q^2+q
       155: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       211: q
       213: q
       215: q
       229: q
       230: q
       234: q
       235: q
       237: q
       239: q
       244: q
       245: q
       247: 1
       248: 1
       256: 2q
       257: 2q
       338: 1
       340: 1
       351: 1
       359: 1
       360: q
       362: q
       369: q
       370: q
       371: 1
       372: 1
       445: 1
       463: 1
       480: 1
       485: 1
       487: 1
       496: 1
       501: 1
       580: 1
       617: 1
       633: 1
       656: 1
       772: 1

 773:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: 1
        67: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       135: 1
       136: 1
       140: 1
       142: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: 1
       229: 1
       230: 1
       234: 1
       235: 1
       238: 1
       240: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: 1
       290: 1
       302: 1
       306: 1
       312: 1
       314: 1
       324: 1
       339: 1
       341: 1
       351: 1
       359: 1
       361: 1
       363: 1
       369: 1
       370: 1
       371: 1
       372: 1
       436: 1
       446: 1
       456: 1
       464: 1
       476: 1
       478: 1
       480: 1
       486: 1
       488: 1
       496: 1
       501: 1
       581: 1
       618: 1
       634: 1
       652: 1
       656: 1
       773: 1

 774:    0: q^3+q
         1: q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^3+q^2+q
         7: q^3+q
         8: q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        30: q^3+q
        32: q
        33: q
        35: q
        36: q
        38: q
        40: q^2+q
        42: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        65: q
        67: q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       112: q
       116: q
       124: q
       128: q
       130: q
       135: q
       136: q
       140: q
       142: q
       147: q
       148: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q
       163: q
       164: q
       182: q
       188: q
       198: q
       206: q
       212: q
       214: q
       216: q
       229: q
       230: q
       234: q
       235: q
       290: q
       306: q
       314: q
       478: 1
       582: 1
       652: 1
       774: 1

 775:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q+2
         5: q^2+3q+2
         6: q^3+3q^2+3q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q^2+3q+2
        14: q+2
        15: q^2+3q+2
        16: q^2+3q+2
        17: q^2+3q+2
        18: q+2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: q+2
        30: q+2
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: q+2
        44: q+2
        45: q+2
        46: q^2+3q+2
        47: q^2+3q+2
        48: q+2
        49: q+2
        50: q^2+3q+2
        51: q+2
        52: 2
        53: 2q+2
        54: 2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2q+2
        66: 2q+2
        68: q+2
        69: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        74: 2
        76: 2q+2
        78: 2
        80: 2
        81: 2q+2
        82: 2
        83: 2
        84: 2
        85: 2q+2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q^2+3q+2
        93: q+2
        94: 2
        95: 2q+2
        96: 2
        97: 2
        98: 2q+2
        99: 2
       100: 1
       101: q+1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 2
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2q+2
       125: q+2
       126: q+2
       127: 2
       129: 2q+2
       131: 2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: 1
       167: q+1
       168: 1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 2
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: 1
       211: 1
       213: 2
       215: 2q+2
       217: 2
       219: q+2
       223: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 2
       283: 1
       284: 1
       285: 1
       286: 1
       287: 2
       289: 2
       291: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: 2
       350: 2
       352: 2
       356: 2
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       377: 1
       380: 1
       381: 1
       384: 1
       413: 2
       417: 2
       427: 1
       431: 1
       432: 1
       447: 1
       448: 1
       465: 1
       467: 1
       469: 1
       484: 1
       485: 1
       487: 1
       508: 1
       515: 1
       516: 1
       521: 1
       524: 1
       601: 1
       639: 1
       657: 1
       658: 1
       660: 1
       775: 1

 776:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q+2
         5: q^2+3q+2
         6: q^3+3q^2+3q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: q+2
        11: q+2
        12: q+2
        13: q^2+3q+2
        14: q+2
        15: q^2+3q+2
        16: q^2+3q+2
        17: q^2+3q+2
        18: q+2
        19: q+2
        20: q^2+3q+2
        21: q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: q+2
        30: q+2
        31: 2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: q+2
        44: q+2
        45: q+2
        46: q^2+3q+2
        47: q^2+3q+2
        48: q+2
        49: q+2
        50: q^2+3q+2
        51: q+2
        52: 2
        53: 2q+2
        54: 2
        55: 2
        56: 2q+2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2q+2
        67: 2q+2
        68: q+2
        69: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        75: 2
        77: 2q+2
        79: 2
        80: 2
        81: 2q+2
        82: 2
        83: 2
        84: 2
        85: 2q+2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q^2+3q+2
        93: q+2
        94: 2
        95: 2q+2
        96: 2
        97: 2
        98: 2q+2
        99: 2
       100: 1
       101: q+1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 2
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2q+2
       125: q+2
       126: q+2
       128: 2
       130: 2q+2
       132: 2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: 1
       167: q+1
       168: 1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 2
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: 1
       212: 1
       214: 2
       216: 2q+2
       218: 2
       219: q+2
       223: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 2
       283: 1
       284: 1
       285: 1
       286: 1
       288: 2
       290: 2
       292: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: 2
       350: 2
       352: 2
       356: 2
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       378: 1
       379: 1
       382: 1
       383: 1
       414: 2
       418: 2
       428: 1
       431: 1
       432: 1
       447: 1
       448: 1
       466: 1
       468: 1
       470: 1
       484: 1
       486: 1
       488: 1
       508: 1
       515: 1
       516: 1
       522: 1
       523: 1
       602: 1
       640: 1
       657: 1
       659: 1
       661: 1
       776: 1

 777:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: 2q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       439: 1
       440: 1
       453: 1
       454: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       525: 1
       528: 1
       583: 1
       585: 1
       587: 1
       676: 1
       681: 1
       777: 1

 778:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: 2q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       439: 1
       440: 1
       453: 1
       454: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       526: 1
       527: 1
       584: 1
       586: 1
       588: 1
       676: 1
       681: 1
       778: 1

 779:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: 1
         9: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       151: 1
       155: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       168: 1
       177: 1
       181: 1
       187: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       237: 1
       241: 1
       247: 1
       249: 1
       256: 1
       258: 1
       281: 1
       289: 1
       291: 1
       315: 1
       336: 1
       338: 1
       342: 1
       350: 1
       356: 1
       360: 1
       364: 1
       368: 1
       371: 1
       373: 1
       417: 1
       425: 1
       467: 1
       485: 1
       489: 1
       491: 1
       515: 1
       517: 1
       597: 1
       658: 1
       662: 1
       664: 1
       779: 1

 780:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: 1
         9: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 1
       136: 1
       138: 1
       142: 1
       144: 1
       147: 1
       150: 1
       152: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       168: 1
       178: 1
       182: 1
       188: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       230: 1
       233: 1
       234: 1
       236: 1
       238: 1
       242: 1
       247: 1
       249: 1
       256: 1
       258: 1
       282: 1
       290: 1
       292: 1
       316: 1
       336: 1
       339: 1
       343: 1
       350: 1
       356: 1
       361: 1
       365: 1
       368: 1
       371: 1
       373: 1
       418: 1
       426: 1
       468: 1
       486: 1
       490: 1
       491: 1
       515: 1
       517: 1
       598: 1
       659: 1
       663: 1
       664: 1
       780: 1

 781:    0: 3q+2
         1: q^2+3q+2
         2: 3q+2
         3: q^2+3q+2
         4: 3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: 3q+2
         8: q^2+3q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 3q+2
        14: 3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: 2q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: 2q+2
        30: 3q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: q+2
        35: 2q+2
        36: q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: 2q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 2q+2
        66: q+2
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: q+2
        73: q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+2
       113: q+2
       115: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: q+2
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: q+2
       134: q+1
       135: q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: q+2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: q+1
       211: q+1
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       350: 1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       381: 1
       384: 1
       385: 1
       388: 1
       413: 1
       417: 1
       423: 1
       425: 1
       427: 1
       465: 1
       467: 1
       469: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       508: 1
       585: 1
       597: 1
       599: 1
       601: 1
       639: 1
       665: 1
       781: 1

 782:    0: 3q+2
         1: q^2+3q+2
         2: 3q+2
         3: q^2+3q+2
         4: 3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: 3q+2
         8: q^2+3q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 3q+2
        14: 3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: 2q+1
        19: 3q+2
        20: q^2+3q+2
        21: 3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: 2q+2
        30: 3q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: q+2
        35: 2q+2
        36: q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: 2q+1
        49: 2q+2
        50: 2q+2
        51: 2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 2q+2
        67: q+2
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: q+2
        73: q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2q+2
        92: 2q+2
        93: 2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+2
       114: q+2
       116: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: q+2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: q+2
       134: q+1
       135: q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: q+2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: q+1
       212: q+1
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       350: 1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       382: 1
       383: 1
       386: 1
       387: 1
       414: 1
       418: 1
       424: 1
       426: 1
       428: 1
       466: 1
       468: 1
       470: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       508: 1
       586: 1
       598: 1
       600: 1
       602: 1
       640: 1
       665: 1
       782: 1

 783:    0: 4q+2
         1: 4q+2
         2: 3q^2+4q+1
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: 4q+2
         7: 3q^2+4q+1
         8: q^3+3q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 4q+2
        11: 2q^2+4q+2
        12: 4q+2
        13: 3q+1
        14: 3q+1
        15: q^2+2q+1
        16: 3q+2
        17: 3q+2
        18: 2q^2+3q+1
        19: 4q+2
        20: 4q+2
        21: 3q^2+4q+1
        22: 3q+2
        23: 3q+2
        24: 2q^2+3q+1
        25: 3q+2
        26: 3q+2
        27: 2q^2+3q+1
        28: 3q+2
        29: 4q+2
        30: 3q+1
        31: 3q+2
        32: 2q+1
        33: 2q+2
        34: 3q+2
        35: 2q+1
        36: 2q+2
        37: 3q+2
        39: 3q+2
        41: 2q^2+3q+1
        43: 3q+1
        44: 3q+1
        45: q^2+2q+1
        46: 2q+1
        47: q+1
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q^2+3q+1
        52: 3q+2
        53: 3q+2
        54: 2q^2+3q+1
        55: 3q+2
        56: 3q+2
        57: 2q^2+3q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 3q+2
        64: 2q+1
        66: 2q+2
        69: q+1
        70: 3q+1
        71: 3q+2
        72: 2q+2
        73: 2q+2
        74: 3q+2
        76: 3q+2
        78: 2q^2+3q+1
        80: 2q+1
        81: q+1
        82: 3q+2
        83: 2q+1
        84: 2q+1
        85: q+1
        86: 3q+2
        87: 2q+1
        88: 2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 2
        95: 2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 3q+2
       115: 2q+1
       121: 2q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: 2
       141: 2q+1
       142: 2
       143: q+1
       144: 1
       145: 2
       146: 2q+1
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q^2+2q+1
       157: 2q+1
       158: q+1
       159: 2q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       172: q+1
       177: 1
       179: 2
       181: 2
       187: q+1
       189: 2q+1
       195: 1
       196: 1
       201: 1
       202: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       258: 1
       259: 1
       262: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: q+1
       315: 1
       317: 1
       325: q+1
       327: 1
       329: 1
       331: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q+1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       360: 1
       364: 1
       366: 1
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 1
       467: 1
       469: 1
       483: 1
       485: 1
       489: 1
       491: 1
       494: 1
       498: 1
       502: 1
       506: 1
       510: 1
       518: 1
       520: 1
       587: 1
       597: 1
       599: 1
       637: 1
       666: 1
       670: 1
       673: 1
       783: 1

 784:    0: 4q+2
         1: 4q+2
         2: 3q^2+4q+1
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: 4q+2
         7: 3q^2+4q+1
         8: q^3+3q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 4q+2
        11: 2q^2+4q+2
        12: 4q+2
        13: 3q+1
        14: 3q+1
        15: q^2+2q+1
        16: 3q+2
        17: 3q+2
        18: 2q^2+3q+1
        19: 4q+2
        20: 4q+2
        21: 3q^2+4q+1
        22: 3q+2
        23: 3q+2
        24: 2q^2+3q+1
        25: 3q+2
        26: 3q+2
        27: 2q^2+3q+1
        28: 3q+2
        29: 4q+2
        30: 3q+1
        31: 3q+2
        32: 2q+1
        33: 2q+2
        34: 3q+2
        35: 2q+1
        36: 2q+2
        38: 3q+2
        40: 3q+2
        42: 2q^2+3q+1
        43: 3q+1
        44: 3q+1
        45: q^2+2q+1
        46: 2q+1
        47: q+1
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q^2+3q+1
        52: 3q+2
        53: 3q+2
        54: 2q^2+3q+1
        55: 3q+2
        56: 3q+2
        57: 2q^2+3q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 3q+2
        65: 2q+1
        67: 2q+2
        69: q+1
        70: 3q+1
        71: 3q+2
        72: 2q+2
        73: 2q+2
        75: 3q+2
        77: 3q+2
        79: 2q^2+3q+1
        80: 2q+1
        81: q+1
        82: 3q+2
        83: 2q+1
        84: 2q+1
        85: q+1
        86: 3q+2
        87: 2q+1
        88: 2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 2
        95: 2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q^2+2q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 3q+2
       116: 2q+1
       122: 2q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: 2
       141: 2q+1
       142: 2
       143: q+1
       144: 1
       145: 2
       146: 2q+1
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q^2+2q+1
       157: 2q+1
       158: q+1
       159: 2q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: 1
       168: q+1
       170: q+1
       171: q+1
       178: 1
       180: 2
       182: 2
       188: q+1
       190: 2q+1
       195: 1
       196: 1
       201: 1
       202: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       258: 1
       260: 1
       261: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: q+1
       316: 1
       318: 1
       326: q+1
       328: 1
       330: 1
       332: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q+1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       361: 1
       365: 1
       366: 1
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 1
       468: 1
       470: 1
       483: 1
       486: 1
       490: 1
       491: 1
       494: 1
       498: 1
       503: 1
       507: 1
       510: 1
       518: 1
       520: 1
       588: 1
       598: 1
       600: 1
       638: 1
       667: 1
       671: 1
       673: 1
       784: 1

 785:    0: 4q+2
         1: q^3+3q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: q^3+3q^2+4q+2
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 4q+2
        14: 4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: q^3+3q^2+4q+2
        21: 4q+2
        22: 3q+2
        23: q^2+3q+2
        24: 3q+2
        25: 3q+2
        26: q^2+3q+2
        27: 3q+2
        28: q+2
        29: 2q+2
        30: 4q+2
        31: q+2
        32: 3q+2
        33: 2q+2
        34: q+2
        35: 3q+2
        36: 3q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: 1
        59: 1
        60: q+2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: 3q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 2q+2
        82: q+2
        83: 3q+2
        84: q+2
        85: 3q+2
        86: q+2
        87: 3q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: q+2
        95: q+2
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       103: 1
       104: 1
       107: q+2
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 2q+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: q+2
       143: 2
       144: q+1
       145: q+1
       146: q+2
       147: 2q+1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+1
       319: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       385: 1
       386: 1
       393: 1
       394: 1
       419: 1
       429: 1
       443: 1
       447: 1
       471: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       589: 1
       593: 1
       615: 1
       641: 1
       665: 1
       679: 1
       785: 1

 786:    0: 4q+2
         1: q^3+3q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: q^3+3q^2+4q+2
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 4q+2
        14: 4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: q^3+3q^2+4q+2
        21: 4q+2
        22: 3q+2
        23: q^2+3q+2
        24: 3q+2
        25: 3q+2
        26: q^2+3q+2
        27: 3q+2
        28: q+2
        29: 2q+2
        30: 4q+2
        31: q+2
        32: 3q+2
        33: 2q+2
        34: q+2
        35: 3q+2
        36: 3q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: 1
        59: 1
        61: q+2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: 3q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 2q+2
        82: q+2
        83: 3q+2
        84: q+2
        85: 3q+2
        86: q+2
        87: 3q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: q+2
        95: q+2
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       105: 1
       106: 1
       108: q+2
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: q+2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 2q+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: q+2
       143: 2
       144: q+1
       145: q+1
       146: q+2
       147: 2q+1
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+1
       320: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       387: 1
       388: 1
       395: 1
       396: 1
       420: 1
       430: 1
       444: 1
       448: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       590: 1
       594: 1
       616: 1
       642: 1
       665: 1
       679: 1
       786: 1

 787:    0: 4q+2
         1: q^3+3q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: q^3+3q^2+4q+2
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 4q+2
        14: 4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: q^3+3q^2+4q+2
        21: 4q+2
        22: 3q+2
        23: q^2+3q+2
        24: 3q+2
        25: 3q+2
        26: q^2+3q+2
        27: 3q+2
        28: q+2
        29: 2q+2
        30: 4q+2
        31: q+2
        32: 3q+2
        33: 3q+2
        34: q+2
        35: 3q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: q+2
        60: 1
        61: 1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: 2q+2
        73: 3q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: q+2
        83: 3q+2
        84: q+2
        85: 2q+2
        86: q+2
        87: 3q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       103: 1
       105: 1
       107: 1
       108: 1
       109: q+2
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 2q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+1
       141: q+2
       142: 2q+1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: q+2
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 2
       195: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: q+1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       350: q+1
       352: 1
       356: 1
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       385: 1
       387: 1
       401: 1
       402: 1
       421: 1
       431: 1
       449: 1
       461: 1
       473: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       591: 1
       595: 1
       631: 1
       643: 1
       665: 1
       685: 1
       787: 1

 788:    0: 4q+2
         1: q^3+3q^2+4q+2
         2: 4q+2
         3: 2q^2+4q+2
         4: 4q+2
         5: 2q^2+4q+2
         6: q^3+3q^2+4q+2
         7: 4q+2
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 4q+2
        14: 4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: q^2+3q+2
        18: 2q+1
        19: 4q+2
        20: q^3+3q^2+4q+2
        21: 4q+2
        22: 3q+2
        23: q^2+3q+2
        24: 3q+2
        25: 3q+2
        26: q^2+3q+2
        27: 3q+2
        28: q+2
        29: 2q+2
        30: 4q+2
        31: q+2
        32: 3q+2
        33: 3q+2
        34: q+2
        35: 3q+2
        36: 2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 3q+2
        47: q^2+3q+2
        48: 2q+1
        49: 3q+2
        50: q^2+3q+2
        51: 2q+1
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        59: q+2
        60: 1
        61: 1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 2q+2
        71: q+2
        72: 2q+2
        73: 3q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: q+2
        83: 3q+2
        84: q+2
        85: 2q+2
        86: q+2
        87: 3q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: q^2+3q+2
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2
       101: 2q+2
       102: 2
       104: 1
       106: 1
       107: 1
       108: 1
       110: q+2
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       118: q+2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 2q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+1
       141: q+2
       142: 2q+1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: q+2
       187: q+1
       188: q+1
       189: 1
       190: 1
       192: 2
       196: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: q+1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       350: q+1
       352: 1
       356: 1
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       386: 1
       388: 1
       403: 1
       404: 1
       422: 1
       432: 1
       450: 1
       462: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       592: 1
       596: 1
       632: 1
       644: 1
       665: 1
       685: 1
       788: 1

 789:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: q+2
        17: q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: q+2
        47: q+2
        49: q+2
        50: q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2q+2
        64: 2q+2
        66: 2
        68: q+2
        70: q^2+3q+2
        71: q+2
        72: 2
        73: 2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: q+2
        89: q+2
        91: q+2
        92: q+2
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+1
       101: q+1
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2q+2
       115: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2q+2
       123: 2
       125: q+2
       127: 2
       129: 2
       133: q+2
       135: 2
       136: 2
       137: 2
       139: 2
       141: 2q+2
       142: 2
       143: 2
       145: 2
       146: 2q+2
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+2
       158: q+2
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       172: 1
       173: 1
       176: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: q+1
       211: q+1
       213: 2
       215: 2
       220: q+2
       222: 2
       224: 2
       227: 2
       230: 2
       232: 2
       234: 2
       237: 1
       239: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       250: 2
       251: 2
       253: 2
       254: 2
       256: 1
       257: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       289: 2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       317: 1
       325: q+1
       327: 2
       329: 2
       337: 1
       338: 1
       340: 1
       345: 2
       349: 2
       353: 2
       355: 2
       360: 1
       362: 1
       367: 1
       371: 1
       372: 1
       374: 1
       375: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       415: 2
       427: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       484: 1
       485: 1
       487: 1
       502: 1
       504: 1
       509: 1
       518: 1
       519: 1
       525: 1
       528: 1
       601: 1
       635: 1
       666: 1
       668: 1
       672: 1
       789: 1

 790:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: q+2
        17: q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: q+2
        47: q+2
        49: q+2
        50: q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2q+2
        65: 2q+2
        67: 2
        68: q+2
        70: q^2+3q+2
        71: q+2
        72: 2
        73: 2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: q+2
        89: q+2
        91: q+2
        92: q+2
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2q+2
       116: 2q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2q+2
       124: 2
       125: q+2
       128: 2
       130: 2
       133: q+2
       135: 2
       136: 2
       137: 2
       139: 2
       141: 2q+2
       142: 2
       143: 2
       145: 2
       146: 2q+2
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+2
       158: q+2
       160: 2
       161: 2
       163: 2
       164: 2
       166: 1
       167: 1
       170: 1
       171: 1
       174: 1
       175: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: q+1
       212: q+1
       214: 2
       216: 2
       220: q+2
       222: 2
       224: 2
       227: 2
       230: 2
       232: 2
       234: 2
       238: 1
       240: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       250: 2
       251: 2
       253: 2
       254: 2
       256: 1
       257: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       290: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       318: 1
       326: q+1
       328: 2
       330: 2
       337: 1
       339: 1
       341: 1
       345: 2
       349: 2
       353: 2
       355: 2
       361: 1
       363: 1
       367: 1
       371: 1
       372: 1
       374: 1
       375: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       416: 2
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       466: 1
       484: 1
       486: 1
       488: 1
       503: 1
       505: 1
       509: 1
       518: 1
       519: 1
       526: 1
       527: 1
       602: 1
       636: 1
       667: 1
       669: 1
       672: 1
       790: 1

 791:    0: q^3+4q^2+6q+1
         1: q^3+6q^2+6q+1
         2: 3q^2+4q+1
         3: 5q^2+6q+1
         4: q^3+4q^2+6q+1
         5: 5q^2+6q+1
         6: q^3+6q^2+6q+1
         7: 3q^2+4q+1
         8: q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 3q^2+4q+1
        16: 2q^2+6q+1
        17: 3q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+4q^2+6q+1
        20: q^3+6q^2+6q+1
        21: 3q^2+4q+1
        22: 2q^2+6q+1
        23: 3q^2+6q+1
        24: 2q^2+4q+1
        25: 2q^2+6q+1
        26: 3q^2+6q+1
        27: 2q^2+4q+1
        30: 2q^2+4q+1
        32: q^2+4q+1
        33: q^2+6q+1
        35: q^2+4q+1
        36: q^2+6q+1
        37: 4q+1
        38: 2q
        39: q^2+4q+1
        40: 2q
        41: 3q+1
        42: q^2+q
        46: 4q+1
        47: q^2+4q+1
        48: q^2+2q+1
        49: 2q^2+6q+1
        50: 3q^2+6q+1
        51: 2q^2+2q+1
        52: 2q^2+6q+1
        53: 3q^2+6q+1
        54: 2q^2+4q+1
        55: 2q^2+6q+1
        56: 3q^2+6q+1
        57: 2q^2+4q+1
        64: 3q+1
        65: q
        66: 4q+1
        67: 2q
        69: 2q+1
        72: q^2+6q+1
        73: q^2+6q+1
        74: 4q+1
        75: 2q
        76: q^2+4q+1
        77: 2q
        78: 3q+1
        79: q^2+q
        81: 4q+1
        83: q^2+4q+1
        85: 4q+1
        87: q^2+4q+1
        91: 4q+1
        92: q^2+4q+1
        93: q^2+2q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: q^2+2q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: q^2+6q+1
       102: 3q+1
       111: 4q+1
       112: 2q
       115: 3q+1
       116: q
       123: 3q+1
       124: q
       127: 2q+1
       129: 2q+1
       131: q+1
       134: 2q+1
       135: 4q+1
       136: 4q+1
       138: 2q+1
       140: 3q+1
       142: q^2+5q+1
       144: 2q+1
       147: q^2+5q+1
       148: 3q+1
       150: 3q+1
       151: 3q+1
       152: 2q
       153: q^2+4q+1
       154: 2q
       155: 2q+1
       156: q
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: q+1
       181: 2q+1
       187: 3q+1
       188: q
       197: 2q+1
       198: q
       205: 2q+1
       206: q
       211: 2q+1
       212: q
       223: 2q+1
       225: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 1
       239: q+1
       241: 1
       244: q+1
       245: q+1
       247: 2q+1
       248: 3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       291: q+1
       301: 1
       305: q+1
       311: 1
       313: q+1
       315: 1
       323: 1
       336: q+1
       338: 1
       340: q+1
       342: 1
       348: 1
       350: q+1
       351: q+1
       356: q+1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       425: 1
       433: 1
       445: 1
       451: 1
       463: 1
       475: 1
       477: 2
       479: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       577: 1
       579: 1
       613: 1
       629: 1
       645: 1
       655: 1
       679: 1
       685: 1
       791: 1

 792:    0: q^3+4q^2+6q+1
         1: q^3+6q^2+6q+1
         2: 3q^2+4q+1
         3: 5q^2+6q+1
         4: q^3+4q^2+6q+1
         5: 5q^2+6q+1
         6: q^3+6q^2+6q+1
         7: 3q^2+4q+1
         8: q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 3q^2+4q+1
        16: 2q^2+6q+1
        17: 3q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+4q^2+6q+1
        20: q^3+6q^2+6q+1
        21: 3q^2+4q+1
        22: 2q^2+6q+1
        23: 3q^2+6q+1
        24: 2q^2+4q+1
        25: 2q^2+6q+1
        26: 3q^2+6q+1
        27: 2q^2+4q+1
        30: 2q^2+4q+1
        32: q^2+4q+1
        33: q^2+6q+1
        35: q^2+4q+1
        36: q^2+6q+1
        37: 2q
        38: 4q+1
        39: 2q
        40: q^2+4q+1
        41: q^2+q
        42: 3q+1
        46: 4q+1
        47: q^2+4q+1
        48: q^2+2q+1
        49: 2q^2+6q+1
        50: 3q^2+6q+1
        51: 2q^2+2q+1
        52: 2q^2+6q+1
        53: 3q^2+6q+1
        54: 2q^2+4q+1
        55: 2q^2+6q+1
        56: 3q^2+6q+1
        57: 2q^2+4q+1
        64: q
        65: 3q+1
        66: 2q
        67: 4q+1
        69: 2q+1
        72: q^2+6q+1
        73: q^2+6q+1
        74: 2q
        75: 4q+1
        76: 2q
        77: q^2+4q+1
        78: q^2+q
        79: 3q+1
        81: 4q+1
        83: q^2+4q+1
        85: 4q+1
        87: q^2+4q+1
        91: 4q+1
        92: q^2+4q+1
        93: q^2+2q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: q^2+2q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: q^2+6q+1
       102: 3q+1
       111: 2q
       112: 4q+1
       115: q
       116: 3q+1
       123: q
       124: 3q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       134: 2q+1
       135: 4q+1
       136: 4q+1
       138: 2q+1
       140: 3q+1
       142: q^2+5q+1
       144: 2q+1
       147: q^2+5q+1
       148: 3q+1
       150: 3q+1
       151: 2q
       152: 3q+1
       153: 2q
       154: q^2+4q+1
       155: q
       156: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 3q+1
       168: q+1
       178: q+1
       182: 2q+1
       187: q
       188: 3q+1
       197: q
       198: 2q+1
       205: q
       206: 2q+1
       211: q
       212: 2q+1
       223: 2q+1
       225: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 1
       240: q+1
       242: 1
       244: q+1
       245: q+1
       247: 2q+1
       248: 3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       292: q+1
       302: 1
       306: q+1
       312: 1
       314: q+1
       316: 1
       324: 1
       336: q+1
       339: 1
       341: q+1
       343: 1
       348: 1
       350: q+1
       351: q+1
       356: q+1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       426: 1
       434: 1
       446: 1
       452: 1
       464: 1
       476: 1
       478: 2
       480: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       581: 1
       582: 1
       614: 1
       630: 1
       646: 1
       656: 1
       679: 1
       685: 1
       792: 1

 793:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: q^2+6q+2
        23: q^2+6q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: 2q+2
        28: 4q+2
        29: 3q+2
        30: q+2
        31: 4q+2
        32: 3q+2
        33: q^2+6q+2
        34: 2q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: 3q+2
        53: q^2+5q+2
        54: q+2
        55: q+2
        56: 3q+2
        57: 2
        58: 2q+1
        59: 2q+1
        60: 2q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: q+2
        70: q+2
        71: 3q+2
        72: q+2
        73: 2q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: q+2
        81: 3q+2
        82: 3q+2
        83: q+2
        84: 2
        85: 2q+2
        86: q+2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: 3q+2
        95: q^2+5q+2
        96: q+2
        97: q+2
        98: 3q+2
        99: 2
       100: q+2
       101: 3q+2
       102: 2
       103: q+1
       104: q+1
       107: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 2
       134: 2
       135: 2
       136: 2
       137: q+2
       138: q+2
       139: 3q+2
       140: q+2
       141: q+2
       142: 2q+2
       143: 2
       144: 2
       145: q+2
       146: 2
       147: q+2
       149: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: 3q+2
       168: 2
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: q+2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       223: 2
       225: 2
       226: q+2
       227: 2
       228: 2
       229: 2
       230: 2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+2
       244: q+2
       246: 2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       299: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: q+2
       325: 1
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       348: 2
       350: 2
       351: 2
       352: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       377: 1
       378: 1
       389: 1
       390: 1
       393: 1
       394: 1
       427: 1
       428: 1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       443: 2
       445: 1
       446: 1
       447: 1
       469: 1
       470: 1
       471: 1
       484: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       533: 1
       534: 1
       545: 1
       546: 1
       615: 1
       641: 1
       657: 1
       674: 1
       793: 1

 794:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: q^2+6q+2
        23: q^2+6q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: 2q+2
        28: 4q+2
        29: 3q+2
        30: q+2
        31: 4q+2
        32: 3q+2
        33: q^2+6q+2
        34: 2q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: 3q+2
        53: q^2+5q+2
        54: q+2
        55: q+2
        56: 3q+2
        57: 2
        58: 2q+1
        59: 2q+1
        61: 2q+2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: q+2
        70: q+2
        71: 3q+2
        72: q+2
        73: 2q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: q+2
        81: 3q+2
        82: 3q+2
        83: q+2
        84: 2
        85: 2q+2
        86: q+2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: 3q+2
        95: q^2+5q+2
        96: q+2
        97: q+2
        98: 3q+2
        99: 2
       100: q+2
       101: 3q+2
       102: 2
       105: q+1
       106: q+1
       108: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 2
       134: 2
       135: 2
       136: 2
       137: q+2
       138: q+2
       139: 3q+2
       140: q+2
       141: q+2
       142: 2q+2
       143: 2
       144: 2
       145: q+2
       146: 2
       147: q+2
       149: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: 3q+2
       168: 2
       171: 1
       172: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: q+2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       223: 2
       225: 2
       226: q+2
       227: 2
       228: 2
       229: 2
       230: 2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+2
       244: q+2
       246: 2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       300: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: q+2
       325: 1
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       348: 2
       350: 2
       351: 2
       352: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       379: 1
       380: 1
       391: 1
       392: 1
       395: 1
       396: 1
       427: 1
       428: 1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       444: 2
       445: 1
       446: 1
       448: 1
       469: 1
       470: 1
       472: 1
       484: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       535: 1
       536: 1
       547: 1
       548: 1
       616: 1
       642: 1
       657: 1
       674: 1
       794: 1

 795:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        64: q+1
        66: q+1
        69: q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        81: q^2+2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: q+1
       131: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       223: 1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: 1
       234: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       244: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       315: 1
       338: 1
       340: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       369: 1
       371: 1
       372: 1
       417: 1
       433: 1
       435: 1
       445: 1
       467: 1
       485: 1
       487: 1
       496: 1
       512: 1
       515: 1
       516: 1
       605: 1
       617: 1
       658: 1
       660: 1
       674: 1
       795: 1

 796:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        65: q+1
        67: q+1
        69: q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        81: q^2+2q+1
        83: q+1
        85: q+1
        87: 1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: q+1
       132: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       223: 1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: 1
       234: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       244: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       316: 1
       339: 1
       341: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       369: 1
       371: 1
       372: 1
       418: 1
       434: 1
       436: 1
       446: 1
       468: 1
       486: 1
       488: 1
       496: 1
       512: 1
       515: 1
       516: 1
       606: 1
       618: 1
       659: 1
       661: 1
       674: 1
       796: 1

 797:    0: q^3+5q^2+8q+2
         1: 6q^2+8q+2
         2: q^3+5q^2+8q+2
         3: 6q^2+8q+2
         4: 4q^2+6q+2
         5: q^3+5q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: 4q^2+6q+2
         8: q^3+5q^2+8q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+7q+2
        11: 2q^2+7q+2
        12: 3q^2+5q+2
        13: q^3+5q^2+8q+2
        14: 4q^2+6q+2
        15: q^3+5q^2+8q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: q^3+5q^2+8q+2
        23: 6q^2+8q+2
        24: q^3+5q^2+8q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^3+5q^2+8q+2
        33: 2q^2+7q+2
        34: q^2+3q+2
        35: 2q^2+4q+2
        36: q^2+3q+2
        37: 2q^2+4q+2
        39: 2q^2+4q+2
        41: 2q^2+4q+2
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 2q^2+7q+2
        47: 2q^2+7q+2
        48: 2q^2+3q+1
        49: 5q+2
        50: q^2+5q+2
        51: q^2+3q+1
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 3q+1
        59: 3q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: 2q^2+4q+2
        66: q^2+3q+2
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: q+2
        73: 3q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 2q^2+7q+2
        81: 2q^2+7q+2
        82: q^2+5q+2
        83: 2q^2+6q+2
        84: q^2+3q+2
        85: q^2+3q+2
        86: q+2
        87: 2q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 5q+2
        95: q^2+5q+2
        96: q^2+3q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: q+2
       113: q+2
       115: 2q+2
       117: 3q+1
       118: 3q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: q^2+3q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 4q+2
       134: 2q+1
       135: q+2
       136: 3q+2
       137: 4q+2
       138: 2q+1
       139: 4q+2
       140: q+2
       141: q^2+5q+2
       142: 3q+2
       143: 2q+2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: 5q+2
       161: q^2+5q+2
       162: q^2+3q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: q+2
       189: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+2
       211: 2q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: 4q+2
       228: 2q+1
       229: q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q+2
       250: q+2
       251: q+2
       252: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       307: 1
       308: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q+2
       333: 1
       334: 1
       335: 1
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       352: 1
       356: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       413: 1
       417: 1
       423: 1
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       508: 1
       512: 1
       537: 1
       539: 1
       541: 1
       543: 1
       585: 1
       605: 1
       609: 1
       639: 1
       675: 1
       676: 1
       797: 1

 798:    0: q^3+5q^2+8q+2
         1: 6q^2+8q+2
         2: q^3+5q^2+8q+2
         3: 6q^2+8q+2
         4: 4q^2+6q+2
         5: q^3+5q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: 4q^2+6q+2
         8: q^3+5q^2+8q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+7q+2
        11: 2q^2+7q+2
        12: 3q^2+5q+2
        13: q^3+5q^2+8q+2
        14: 4q^2+6q+2
        15: q^3+5q^2+8q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: q^3+5q^2+8q+2
        23: 6q^2+8q+2
        24: q^3+5q^2+8q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^3+5q^2+8q+2
        33: 2q^2+7q+2
        34: q^2+3q+2
        35: 2q^2+4q+2
        36: q^2+3q+2
        38: 2q^2+4q+2
        40: 2q^2+4q+2
        42: 2q^2+4q+2
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 2q^2+7q+2
        47: 2q^2+7q+2
        48: 2q^2+3q+1
        49: 5q+2
        50: q^2+5q+2
        51: q^2+3q+1
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 3q+1
        59: 3q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: 2q^2+4q+2
        67: q^2+3q+2
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: q+2
        73: 3q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 2q^2+7q+2
        81: 2q^2+7q+2
        82: q^2+5q+2
        83: 2q^2+6q+2
        84: q^2+3q+2
        85: q^2+3q+2
        86: q+2
        87: 2q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 5q+2
        95: q^2+5q+2
        96: q^2+3q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: q+2
       114: q+2
       116: 2q+2
       117: 3q+1
       118: 3q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: q^2+3q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 4q+2
       134: 2q+1
       135: q+2
       136: 3q+2
       137: 4q+2
       138: 2q+1
       139: 4q+2
       140: q+2
       141: q^2+5q+2
       142: 3q+2
       143: 2q+2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: 5q+2
       161: q^2+5q+2
       162: q^2+3q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: q+2
       190: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+2
       212: 2q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: 4q+2
       228: 2q+1
       229: q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q+2
       250: q+2
       251: q+2
       252: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: q+2
       307: 1
       308: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q+2
       333: 1
       334: 1
       335: 1
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       352: 1
       356: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       414: 1
       418: 1
       424: 1
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       508: 1
       512: 1
       538: 1
       540: 1
       542: 1
       544: 1
       586: 1
       606: 1
       610: 1
       640: 1
       675: 1
       676: 1
       798: 1

 799:    0: 4q+2
         1: 4q+2
         2: 2q^2+3q+1
         3: 4q+2
         4: 2q^2+2q+2
         5: 4q+2
         6: 2q^2+2q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: 2q^2+2q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 4q+2
        23: 4q+2
        24: 2q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 4q+2
        29: 2q+2
        30: q+1
        31: 4q+2
        32: 2q+1
        33: 4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2
       143: q+1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       207: q+1
       209: 2
       211: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       411: 1
       415: 1
       417: 1
       423: 1
       433: 1
       435: 1
       441: 1
       467: 1
       469: 1
       493: 1
       494: 1
       498: 1
       502: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       587: 1
       605: 1
       609: 1
       611: 1
       637: 1
       687: 1
       799: 1

 800:    0: 4q+2
         1: 4q+2
         2: 2q^2+3q+1
         3: 4q+2
         4: 2q^2+2q+2
         5: 4q+2
         6: 2q^2+2q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: 2q^2+2q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 4q+2
        23: 4q+2
        24: 2q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 4q+2
        29: 2q+2
        30: q+1
        31: 4q+2
        32: 2q+1
        33: 4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2
       143: q+1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       208: q+1
       210: 2
       212: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       412: 1
       416: 1
       418: 1
       424: 1
       434: 1
       436: 1
       442: 1
       468: 1
       470: 1
       493: 1
       494: 1
       498: 1
       503: 1
       505: 1
       507: 1
       510: 1
       511: 1
       512: 1
       588: 1
       606: 1
       610: 1
       612: 1
       638: 1
       687: 1
       800: 1

 801:    0: q^2+2
         1: q^2+2
         2: q^2+2
         3: q^2+2
         4: q+1
         5: q^2+2
         6: q^3+q^2+q+1
         7: q+1
         8: q^2+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q^2+2
        14: q+1
        15: q^2+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: 1
        20: q^2+1
        21: 1
        22: q^2+2
        23: q^2+2
        24: q^2+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: q^2+2
        33: q^2+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: q^2+1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: q^2+2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: q^2+1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q^2+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: 1
       252: 1
       256: 1
       257: 1
       258: 1
       275: 1
       276: 1
       283: 1
       293: 1
       299: 1
       307: 1
       319: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       419: 1
       429: 1
       437: 1
       447: 1
       471: 1
       481: 1
       492: 1
       493: 1
       508: 1
       512: 1
       589: 1
       603: 1
       641: 1
       675: 1
       801: 1

 802:    0: q^2+2
         1: q^2+2
         2: q^2+2
         3: q^2+2
         4: q+1
         5: q^2+2
         6: q^3+q^2+q+1
         7: q+1
         8: q^2+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q^2+2
        14: q+1
        15: q^2+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: 1
        20: q^2+1
        21: 1
        22: q^2+2
        23: q^2+2
        24: q^2+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: q^2+2
        33: q^2+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: q^2+1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: q^2+2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: q^2+1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q^2+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: 1
       252: 1
       256: 1
       257: 1
       258: 1
       277: 1
       278: 1
       284: 1
       294: 1
       300: 1
       308: 1
       320: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       420: 1
       430: 1
       438: 1
       448: 1
       472: 1
       481: 1
       492: 1
       493: 1
       508: 1
       512: 1
       590: 1
       604: 1
       642: 1
       675: 1
       802: 1

 803:    0: q^3+14q^2+13q+2
         1: 3q^3+16q^2+13q+2
         2: q^3+8q^2+9q+2
         3: 3q^3+16q^2+13q+2
         4: 3q^3+10q^2+10q+2
         5: q^3+14q^2+13q+2
         6: q^4+7q^3+13q^2+10q+2
         7: q^3+6q^2+7q+2
         8: q^3+8q^2+9q+2
         9: q^3+3q^2+3q+1
        10: 8q^2+11q+2
        11: 8q^2+11q+2
        12: 2q^3+7q^2+8q+2
        13: 6q^2+9q+2
        14: 5q^2+7q+2
        15: 6q^2+9q+2
        16: 9q^2+11q+2
        17: 9q^2+11q+2
        18: 2q^2+3q+1
        19: 7q^2+10q+2
        20: 2q^3+10q^2+10q+2
        21: 4q^2+7q+2
        22: q^3+14q^2+13q+2
        23: 3q^3+16q^2+13q+2
        24: q^3+8q^2+9q+2
        25: 8q^2+12q+2
        26: 10q^2+12q+2
        27: 4q^2+8q+2
        28: 4q^2+9q+2
        29: 4q^2+8q+2
        30: 3q^2+7q+2
        31: 8q^2+11q+2
        32: 6q^2+9q+2
        33: 9q^2+11q+2
        34: 4q^2+10q+2
        35: 2q^2+8q+2
        36: 6q^2+10q+2
        37: 4q^2+6q+1
        38: 4q^2+6q+1
        39: 5q^2+6q+1
        40: 5q^2+6q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 4q^2+7q+2
        47: 4q^2+7q+2
        48: 2q^2+3q+1
        49: 3q^2+8q+2
        50: 4q^2+8q+2
        51: q^2+3q+1
        52: 7q^2+10q+2
        53: 2q^3+10q^2+10q+2
        54: 4q^2+7q+2
        55: 2q^2+9q+2
        56: 5q^2+9q+2
        57: q^2+6q+2
        58: 3q^2+7q+2
        59: q^2+2q
        60: q^2+4q+1
        61: q^2+4q+1
        62: 2q^2+5q+1
        63: 2q^2+5q+1
        64: q^2+4q+1
        65: q^2+4q+1
        66: 3q^2+5q+1
        67: 3q^2+5q+1
        68: q^2+3q+2
        69: q^2+2q+1
        70: q^2+5q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: 2q+1
        79: 2q+1
        80: 2q^2+7q+2
        81: 4q^2+7q+2
        82: 4q^2+8q+2
        83: 3q^2+7q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: q^2+7q+2
        87: 6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 3q^2+8q+2
        95: 4q^2+8q+2
        96: q^2+3q+1
        97: 4q+2
        98: q^2+4q+2
        99: 2q+1
       100: 2q^2+9q+2
       101: 5q^2+9q+2
       102: q^2+6q+2
       103: q^2+3q+1
       104: q
       105: q^2+3q+1
       106: q
       107: 2q+1
       108: 2q+1
       109: 4q+2
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q^2+3q+2
       119: q+1
       120: q+1
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: q^2+2q+1
       139: q^2+6q+2
       140: q^2+6q+2
       141: q^2+5q+2
       142: q^2+6q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: 3q+2
       148: q+2
       149: q^2+7q+2
       150: 6q+2
       151: 3q+1
       152: 3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+1
       160: 4q+2
       161: q^2+4q+2
       162: 2q+1
       163: q+2
       164: q+2
       165: q+1
       166: 4q+2
       167: q^2+4q+2
       168: 2q+1
       169: q+1
       171: q+1
       173: q+1
       175: q+1
       183: 1
       184: 1
       185: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+2
       193: 2q+1
       194: 2q+1
       195: 4q+2
       197: 2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 3q+2
       244: 3q+2
       245: q+2
       246: 4q+2
       247: q+2
       248: q+2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       265: 1
       267: q+1
       270: q+1
       271: 1
       272: 1
       275: q+1
       277: q+1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       303: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       319: q+1
       320: q+1
       321: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: q+2
       348: 1
       349: 2
       350: q+1
       351: q+2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       385: 1
       387: 1
       393: 1
       395: 1
       401: 1
       402: 1
       405: 1
       408: 1
       421: 1
       431: 1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 1
       444: 1
       449: 1
       461: 2
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       500: 1
       508: 1
       512: 1
       514: 1
       541: 1
       544: 1
       565: 1
       567: 1
       573: 1
       576: 1
       591: 1
       607: 1
       643: 1
       675: 1
       677: 1
       689: 1
       803: 1

 804:    0: q^3+14q^2+13q+2
         1: 3q^3+16q^2+13q+2
         2: q^3+8q^2+9q+2
         3: 3q^3+16q^2+13q+2
         4: 3q^3+10q^2+10q+2
         5: q^3+14q^2+13q+2
         6: q^4+7q^3+13q^2+10q+2
         7: q^3+6q^2+7q+2
         8: q^3+8q^2+9q+2
         9: q^3+3q^2+3q+1
        10: 8q^2+11q+2
        11: 8q^2+11q+2
        12: 2q^3+7q^2+8q+2
        13: 6q^2+9q+2
        14: 5q^2+7q+2
        15: 6q^2+9q+2
        16: 9q^2+11q+2
        17: 9q^2+11q+2
        18: 2q^2+3q+1
        19: 7q^2+10q+2
        20: 2q^3+10q^2+10q+2
        21: 4q^2+7q+2
        22: q^3+14q^2+13q+2
        23: 3q^3+16q^2+13q+2
        24: q^3+8q^2+9q+2
        25: 8q^2+12q+2
        26: 10q^2+12q+2
        27: 4q^2+8q+2
        28: 4q^2+9q+2
        29: 4q^2+8q+2
        30: 3q^2+7q+2
        31: 8q^2+11q+2
        32: 6q^2+9q+2
        33: 9q^2+11q+2
        34: 4q^2+10q+2
        35: 2q^2+8q+2
        36: 6q^2+10q+2
        37: 4q^2+6q+1
        38: 4q^2+6q+1
        39: 5q^2+6q+1
        40: 5q^2+6q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 4q^2+7q+2
        47: 4q^2+7q+2
        48: 2q^2+3q+1
        49: 3q^2+8q+2
        50: 4q^2+8q+2
        51: q^2+3q+1
        52: 7q^2+10q+2
        53: 2q^3+10q^2+10q+2
        54: 4q^2+7q+2
        55: 2q^2+9q+2
        56: 5q^2+9q+2
        57: q^2+6q+2
        58: q^2+2q
        59: 3q^2+7q+2
        60: q^2+4q+1
        61: q^2+4q+1
        62: 2q^2+5q+1
        63: 2q^2+5q+1
        64: q^2+4q+1
        65: q^2+4q+1
        66: 3q^2+5q+1
        67: 3q^2+5q+1
        68: q^2+3q+2
        69: q^2+2q+1
        70: q^2+5q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: 2q+1
        79: 2q+1
        80: 2q^2+7q+2
        81: 4q^2+7q+2
        82: 4q^2+8q+2
        83: 3q^2+7q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: q^2+7q+2
        87: 6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 3q^2+8q+2
        95: 4q^2+8q+2
        96: q^2+3q+1
        97: 4q+2
        98: q^2+4q+2
        99: 2q+1
       100: 2q^2+9q+2
       101: 5q^2+9q+2
       102: q^2+6q+2
       103: q
       104: q^2+3q+1
       105: q
       106: q^2+3q+1
       107: 2q+1
       108: 2q+1
       110: 4q+2
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       118: q^2+3q+2
       119: q+1
       120: q+1
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: q^2+2q+1
       139: q^2+6q+2
       140: q^2+6q+2
       141: q^2+5q+2
       142: q^2+6q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: 3q+2
       148: q+2
       149: q^2+7q+2
       150: 6q+2
       151: 3q+1
       152: 3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+1
       160: 4q+2
       161: q^2+4q+2
       162: 2q+1
       163: q+2
       164: q+2
       165: q+1
       166: 4q+2
       167: q^2+4q+2
       168: 2q+1
       170: q+1
       172: q+1
       174: q+1
       176: q+1
       183: 1
       184: 1
       186: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       192: 2q+2
       193: 2q+1
       194: 2q+1
       196: 4q+2
       197: 2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 3q+2
       244: 3q+2
       245: q+2
       246: 4q+2
       247: q+2
       248: q+2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       256: q+2
       257: q+2
       258: q+1
       264: 1
       266: 1
       268: q+1
       269: q+1
       273: 1
       274: 1
       276: q+1
       278: q+1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       304: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       319: q+1
       320: q+1
       322: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: q+2
       348: 1
       349: 2
       350: q+1
       351: q+2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       386: 1
       388: 1
       394: 1
       396: 1
       403: 1
       404: 1
       406: 1
       407: 1
       422: 1
       432: 1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 1
       444: 1
       450: 1
       462: 2
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       500: 1
       508: 1
       512: 1
       514: 1
       542: 1
       543: 1
       566: 1
       568: 1
       574: 1
       575: 1
       592: 1
       608: 1
       644: 1
       675: 1
       677: 1
       689: 1
       804: 1

 805:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: q^2+3q+2
        30: 2q+2
        31: q^2+3q+2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2q+2
        72: 2
        73: 2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2q+2
        81: q+2
        82: q^2+3q+2
        83: 2q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: q+2
       137: q+2
       138: 1
       139: 2q+2
       140: 2
       141: 2q+2
       142: 2q+2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: q+2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: q+2
       251: q+2
       252: q+1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       319: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 1
       366: 1
       385: 1
       386: 1
       393: 1
       394: 1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       541: 1
       542: 1
       593: 1
       603: 1
       676: 1
       677: 1
       805: 1

 806:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: q^2+3q+2
        30: 2q+2
        31: q^2+3q+2
        32: 2q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2q+2
        72: 2
        73: 2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2q+2
        81: q+2
        82: q^2+3q+2
        83: 2q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: q+2
       137: q+2
       138: 1
       139: 2q+2
       140: 2
       141: 2q+2
       142: 2q+2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       166: 1
       167: 1
       168: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: q+2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: q+2
       251: q+2
       252: q+1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       320: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 1
       366: 1
       387: 1
       388: 1
       395: 1
       396: 1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       543: 1
       544: 1
       594: 1
       604: 1
       676: 1
       677: 1
       806: 1

 807:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        58: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       109: 1
       117: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       185: 1
       191: 1
       195: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       250: 1
       251: 1
       252: 1
       285: 1
       295: 1
       303: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       421: 1
       431: 1
       439: 1
       482: 1
       492: 1
       494: 1
       595: 1
       607: 1
       676: 1
       807: 1

 808:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        59: 1
        68: 1
        69: 1
        70: 1
        71: 1
        73: 1
        80: 1
        81: 1
        82: 1
        83: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
       110: 1
       118: 1
       125: 1
       126: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       186: 1
       192: 1
       196: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       250: 1
       251: 1
       252: 1
       286: 1
       296: 1
       304: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       422: 1
       432: 1
       440: 1
       482: 1
       492: 1
       494: 1
       596: 1
       608: 1
       676: 1
       808: 1

 809:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        64: q+1
        66: q+1
        69: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: q+1
        78: q+1
        81: 2q+1
        83: q^2+2q+1
        85: q+1
        87: q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       111: q+1
       115: q+1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: q+1
       136: 2q+1
       138: q+1
       140: q+1
       142: 2q+1
       144: 1
       147: 1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: q+1
       197: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       223: 1
       225: q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: q+1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       360: 1
       362: 1
       364: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 1
       467: 1
       485: 1
       487: 1
       489: 1
       491: 1
       495: 1
       496: 1
       512: 1
       597: 1
       605: 1
       613: 1
       617: 1
       679: 1
       809: 1

 810:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        30: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        65: q+1
        67: q+1
        69: q+1
        72: q+1
        73: 2q+1
        75: q+1
        77: q+1
        79: q+1
        81: 2q+1
        83: q^2+2q+1
        85: q+1
        87: q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       112: q+1
       116: q+1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: q+1
       136: 2q+1
       138: q+1
       140: q+1
       142: 2q+1
       144: 1
       147: 1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: q+1
       198: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       223: 1
       225: q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: q+1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       361: 1
       363: 1
       365: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 1
       468: 1
       486: 1
       488: 1
       490: 1
       491: 1
       495: 1
       496: 1
       512: 1
       598: 1
       606: 1
       614: 1
       618: 1
       679: 1
       810: 1

 811:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2q+2
        23: 2q+2
        24: q^2+q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2q+2
        32: 1
        33: 2q+2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q+2
        53: 2q+2
        54: q^2+q+1
        55: 2
        56: 2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2
        73: 2q+2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2q+2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2
       141: 1
       142: 2q+2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: 1
       202: 1
       207: 1
       209: 2
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       259: 1
       262: 1
       267: 1
       269: 1
       287: 1
       291: 1
       297: 1
       301: 2
       305: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       366: 1
       389: 1
       391: 1
       423: 1
       425: 1
       427: 2
       433: 1
       441: 1
       443: 1
       444: 1
       445: 2
       469: 1
       483: 1
       493: 1
       494: 1
       495: 1
       545: 1
       547: 1
       599: 1
       609: 1
       613: 1
       677: 1
       811: 1

 812:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2q+2
        23: 2q+2
        24: q^2+q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2q+2
        32: 1
        33: 2q+2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q+2
        53: 2q+2
        54: q^2+q+1
        55: 2
        56: 2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2
        73: 2q+2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2q+2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2
       141: 1
       142: 2q+2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: 1
       202: 1
       208: 1
       210: 2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       260: 1
       261: 1
       268: 1
       270: 1
       288: 1
       292: 1
       298: 1
       302: 2
       306: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       366: 1
       390: 1
       392: 1
       424: 1
       426: 1
       428: 2
       434: 1
       442: 1
       443: 1
       444: 1
       446: 2
       470: 1
       483: 1
       493: 1
       494: 1
       495: 1
       546: 1
       548: 1
       600: 1
       610: 1
       614: 1
       677: 1
       812: 1

 813:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q^2+3q+2
        32: q+1
        33: 2q+2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: q+1
        71: 2q+2
        72: 2
        73: 2q+2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q^2+3q+2
        83: q+1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2q+2
        95: 2q+2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: q+1
       137: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: 1
       145: 2
       146: 1
       147: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: 1
       202: 1
       207: 1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: 1
       224: q+1
       229: 1
       230: q+1
       234: 1
       237: 2
       239: 2
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       262: 1
       267: 1
       269: 1
       289: 1
       297: 1
       301: 2
       305: 1
       317: 2
       319: 1
       320: 1
       325: 1
       327: 1
       329: 1
       337: 2
       338: 2
       340: 2
       347: 1
       349: q+1
       351: 2
       355: 1
       360: 1
       362: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       389: 1
       391: 1
       415: 1
       427: 2
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       485: 1
       487: 1
       496: 1
       502: 1
       504: 1
       511: 1
       518: 1
       519: 1
       545: 1
       547: 1
       611: 1
       617: 1
       666: 1
       668: 1
       678: 1
       813: 1

 814:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+2q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q^2+3q+2
        32: q+1
        33: 2q+2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: q+1
        71: 2q+2
        72: 2
        73: 2q+2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q^2+3q+2
        83: q+1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2q+2
        95: 2q+2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: q+1
       137: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: 1
       145: 2
       146: 1
       147: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: 1
       202: 1
       208: 1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: 1
       224: q+1
       229: 1
       230: q+1
       234: 1
       238: 2
       240: 2
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       261: 1
       268: 1
       270: 1
       290: 1
       298: 1
       302: 2
       306: 1
       318: 2
       319: 1
       320: 1
       326: 1
       328: 1
       330: 1
       337: 2
       339: 2
       341: 2
       347: 1
       349: q+1
       351: 2
       355: 1
       361: 1
       363: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       390: 1
       392: 1
       416: 1
       428: 2
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       486: 1
       488: 1
       496: 1
       503: 1
       505: 1
       511: 1
       518: 1
       519: 1
       546: 1
       548: 1
       612: 1
       618: 1
       667: 1
       669: 1
       678: 1
       814: 1

 815:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2
        17: 2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q^2+3q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q^2+3q+2
        81: 2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 2
       135: 2
       136: 2
       137: 2
       139: 2
       140: 2
       141: q^2+3q+2
       142: 2
       143: 2
       145: 1
       146: 2q+2
       147: 1
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 2
       161: 2
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       220: 2
       222: 2
       224: 2
       227: 2
       229: 2
       230: 2
       232: 1
       234: 1
       243: 1
       244: 1
       246: 2q+2
       247: 1
       248: 1
       250: 2
       251: 2
       253: 1
       254: 1
       256: 1
       257: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       319: 1
       325: q+1
       326: q+1
       337: 1
       345: 2
       347: 2
       349: 2
       351: 1
       353: 1
       355: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       385: 1
       386: 1
       393: 1
       394: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       453: 1
       471: 1
       484: 1
       496: 1
       509: 1
       511: 1
       518: 1
       519: 1
       541: 1
       542: 1
       615: 1
       647: 1
       672: 1
       678: 1
       815: 1

 816:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2
        17: 2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        61: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q^2+3q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q^2+3q+2
        81: 2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 2
        95: 2
        97: 1
        98: 1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 2
       135: 2
       136: 2
       137: 2
       139: 2
       140: 2
       141: q^2+3q+2
       142: 2
       143: 2
       145: 1
       146: 2q+2
       147: 1
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 2
       161: 2
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       220: 2
       222: 2
       224: 2
       227: 2
       229: 2
       230: 2
       232: 1
       234: 1
       243: 1
       244: 1
       246: 2q+2
       247: 1
       248: 1
       250: 2
       251: 2
       253: 1
       254: 1
       256: 1
       257: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       320: 1
       325: q+1
       326: q+1
       337: 1
       345: 2
       347: 2
       349: 2
       351: 1
       353: 1
       355: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       387: 1
       388: 1
       395: 1
       396: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       454: 1
       472: 1
       484: 1
       496: 1
       509: 1
       511: 1
       518: 1
       519: 1
       543: 1
       544: 1
       616: 1
       648: 1
       672: 1
       678: 1
       816: 1

 817:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: 4q+2
        23: 4q+2
        24: 2q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: q^2+3q+2
        28: 4q+2
        29: 3q+2
        30: q+2
        31: 2q+2
        32: 2q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: q+2
        53: 3q+2
        54: 2
        55: 3q+2
        56: q^2+5q+2
        57: q+2
        58: 2q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: q+2
        70: q+2
        71: 3q+2
        72: 2q+2
        73: q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: 2
        81: 2q+2
        82: q+2
        83: 2
        84: q+2
        85: 3q+2
        86: 3q+2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: q+2
        95: 3q+2
        96: 2
        97: 3q+2
        98: q^2+5q+2
        99: q+2
       100: q+2
       101: 3q+2
       102: 2
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 2
       134: 2
       135: 2
       136: 2
       137: 2
       138: 2
       139: q+2
       141: 2
       142: q+2
       143: q+2
       144: q+2
       145: 3q+2
       146: q+2
       147: 2q+2
       148: q+2
       149: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: q+2
       167: 3q+2
       168: 2
       169: 1
       171: 1
       173: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: q+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: q+2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       223: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: 2
       234: 2
       235: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+2
       245: q+2
       246: 2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       283: 1
       284: 1
       285: 2
       287: 1
       288: 1
       291: 1
       292: 1
       303: 1
       307: 1
       308: 1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       321: q+2
       325: 1
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       350: 1
       352: 2
       356: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       377: 1
       379: 1
       397: 1
       398: 1
       401: 1
       402: 1
       427: 1
       428: 1
       431: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       461: 2
       463: 1
       464: 1
       469: 1
       470: 1
       473: 1
       484: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       549: 1
       550: 1
       561: 1
       562: 1
       631: 1
       643: 1
       657: 1
       680: 1
       817: 1

 818:    0: q^2+6q+2
         1: q^2+6q+2
         2: q^2+3q+2
         3: q^2+6q+2
         4: q^2+3q+2
         5: q^2+6q+2
         6: q^3+4q^2+5q+2
         7: q+2
         8: q^2+3q+2
         9: q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 3q+2
        14: q+2
        15: 3q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: q+2
        19: 3q+2
        20: q^2+5q+2
        21: q+2
        22: 4q+2
        23: 4q+2
        24: 2q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: q^2+3q+2
        28: 4q+2
        29: 3q+2
        30: q+2
        31: 2q+2
        32: 2q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: q^2+6q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: 3q+2
        50: q^2+5q+2
        51: q+2
        52: q+2
        53: 3q+2
        54: 2
        55: 3q+2
        56: q^2+5q+2
        57: q+2
        59: 2q+2
        60: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2
        69: q+2
        70: q+2
        71: 3q+2
        72: 2q+2
        73: q+2
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: 1
        80: 2
        81: 2q+2
        82: q+2
        83: 2
        84: q+2
        85: 3q+2
        86: 3q+2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: q+2
        95: 3q+2
        96: 2
        97: 3q+2
        98: q^2+5q+2
        99: q+2
       100: q+2
       101: 3q+2
       102: 2
       104: q+1
       106: q+1
       107: q+1
       108: q+1
       110: q+2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 2
       134: 2
       135: 2
       136: 2
       137: 2
       138: 2
       139: q+2
       141: 2
       142: q+2
       143: q+2
       144: q+2
       145: 3q+2
       146: q+2
       147: 2q+2
       148: q+2
       149: q+2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: q+2
       167: 3q+2
       168: 2
       170: 1
       172: 1
       174: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: q+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: q+2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       223: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: 2
       234: 2
       235: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+2
       245: q+2
       246: 2
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       283: 1
       284: 1
       286: 2
       287: 1
       288: 1
       291: 1
       292: 1
       304: 1
       307: 1
       308: 1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: q+2
       325: 1
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       350: 1
       352: 2
       356: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       378: 1
       380: 1
       399: 1
       400: 1
       403: 1
       404: 1
       427: 1
       428: 1
       432: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       462: 2
       463: 1
       464: 1
       469: 1
       470: 1
       474: 1
       484: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       551: 1
       552: 1
       563: 1
       564: 1
       632: 1
       644: 1
       657: 1
       680: 1
       818: 1

 819:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        30: q+1
        32: q+1
        33: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        64: q+1
        66: q+1
        69: q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: 1
        85: q^2+2q+1
        87: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: q+1
       131: 1
       134: q+1
       135: q+1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       177: 1
       181: 1
       187: 1
       205: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       281: 1
       289: 1
       291: 1
       311: 1
       313: 1
       315: 1
       338: 1
       340: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       370: 1
       371: 1
       372: 1
       417: 1
       451: 1
       455: 1
       463: 1
       467: 1
       485: 1
       487: 1
       501: 1
       514: 1
       515: 1
       516: 1
       623: 1
       633: 1
       658: 1
       660: 1
       680: 1
       819: 1

 820:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        30: q+1
        32: q+1
        33: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        65: q+1
        67: q+1
        69: q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: 1
        85: q^2+2q+1
        87: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: q+1
       132: 1
       134: q+1
       135: q+1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       178: 1
       182: 1
       188: 1
       206: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       282: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       339: 1
       341: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       370: 1
       371: 1
       372: 1
       418: 1
       452: 1
       456: 1
       464: 1
       468: 1
       486: 1
       488: 1
       501: 1
       514: 1
       515: 1
       516: 1
       624: 1
       634: 1
       659: 1
       661: 1
       680: 1
       820: 1

 821:    0: q^3+5q^2+8q+2
         1: 6q^2+8q+2
         2: q^3+5q^2+8q+2
         3: 6q^2+8q+2
         4: 4q^2+6q+2
         5: q^3+5q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: 4q^2+6q+2
         8: q^3+5q^2+8q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+7q+2
        11: 2q^2+7q+2
        12: 3q^2+5q+2
        13: q^3+5q^2+8q+2
        14: 4q^2+6q+2
        15: q^3+5q^2+8q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: q^3+5q^2+8q+2
        26: 6q^2+8q+2
        27: q^3+5q^2+8q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: q^2+3q+2
        32: 2q^2+4q+2
        33: q^2+3q+2
        34: 2q^2+7q+2
        35: q^3+5q^2+8q+2
        36: 2q^2+7q+2
        37: 2q^2+4q+2
        39: 2q^2+4q+2
        41: 2q^2+4q+2
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 2q^2+7q+2
        47: 2q^2+7q+2
        48: 2q^2+3q+1
        49: 5q+2
        50: q^2+5q+2
        51: q^2+3q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: q+1
        59: q+1
        60: 3q+1
        61: 3q+1
        62: q^2+3q+2
        64: 2q^2+4q+2
        66: q^2+3q+2
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: 3q+2
        73: q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^2+3q+2
        81: q^2+3q+2
        82: q+2
        83: 2q+2
        84: 2q^2+7q+2
        85: 2q^2+7q+2
        86: q^2+5q+2
        87: 2q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 2
        95: 2
        96: q+1
        97: 5q+2
        98: q^2+5q+2
        99: q^2+3q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+2
       113: q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: 3q+1
       120: 3q+1
       121: q^2+3q+2
       123: q^2+3q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 4q+2
       134: 2q+1
       135: 3q+2
       136: q+2
       137: 2q+2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4q+2
       144: 2q+1
       145: 4q+2
       146: q^2+5q+2
       147: 3q+2
       148: q+2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 5q+2
       164: q^2+5q+2
       165: q^2+3q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: q+2
       189: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+2
       207: 2q+2
       209: q+2
       211: 2q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 4q+2
       233: 2q+1
       234: 3q+2
       235: q+2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q+2
       253: q+2
       254: q+2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: q+2
       315: 1
       317: 2
       321: 1
       322: 1
       325: q+2
       333: 1
       334: 1
       335: 1
       344: 1
       350: 1
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       413: 1
       417: 1
       423: 1
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       465: 2
       467: 1
       469: 1
       473: 1
       474: 1
       481: 1
       482: 1
       497: 1
       498: 1
       499: 1
       508: 1
       514: 1
       553: 1
       555: 1
       557: 1
       559: 1
       585: 1
       623: 1
       625: 1
       639: 1
       681: 1
       682: 1
       821: 1

 822:    0: q^3+5q^2+8q+2
         1: 6q^2+8q+2
         2: q^3+5q^2+8q+2
         3: 6q^2+8q+2
         4: 4q^2+6q+2
         5: q^3+5q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: 4q^2+6q+2
         8: q^3+5q^2+8q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+7q+2
        11: 2q^2+7q+2
        12: 3q^2+5q+2
        13: q^3+5q^2+8q+2
        14: 4q^2+6q+2
        15: q^3+5q^2+8q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: q^3+5q^2+8q+2
        26: 6q^2+8q+2
        27: q^3+5q^2+8q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: q^2+3q+2
        32: 2q^2+4q+2
        33: q^2+3q+2
        34: 2q^2+7q+2
        35: q^3+5q^2+8q+2
        36: 2q^2+7q+2
        38: 2q^2+4q+2
        40: 2q^2+4q+2
        42: 2q^2+4q+2
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 2q^2+7q+2
        47: 2q^2+7q+2
        48: 2q^2+3q+1
        49: 5q+2
        50: q^2+5q+2
        51: q^2+3q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: q+1
        59: q+1
        60: 3q+1
        61: 3q+1
        63: q^2+3q+2
        65: 2q^2+4q+2
        67: q^2+3q+2
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: 3q+2
        73: q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^2+3q+2
        81: q^2+3q+2
        82: q+2
        83: 2q+2
        84: 2q^2+7q+2
        85: 2q^2+7q+2
        86: q^2+5q+2
        87: 2q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 2
        95: 2
        96: q+1
        97: 5q+2
        98: q^2+5q+2
        99: q^2+3q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: q+2
       114: q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: 3q+1
       120: 3q+1
       122: q^2+3q+2
       124: q^2+3q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 4q+2
       134: 2q+1
       135: 3q+2
       136: q+2
       137: 2q+2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4q+2
       144: 2q+1
       145: 4q+2
       146: q^2+5q+2
       147: 3q+2
       148: q+2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 5q+2
       164: q^2+5q+2
       165: q^2+3q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: q+2
       190: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: q+2
       208: 2q+2
       210: q+2
       212: 2q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 4q+2
       233: 2q+1
       234: 3q+2
       235: q+2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q+2
       253: q+2
       254: q+2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: q+2
       316: 1
       318: 2
       321: 1
       322: 1
       326: q+2
       333: 1
       334: 1
       335: 1
       344: 1
       350: 1
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       414: 1
       418: 1
       424: 1
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       466: 2
       468: 1
       470: 1
       473: 1
       474: 1
       481: 1
       482: 1
       497: 1
       498: 1
       499: 1
       508: 1
       514: 1
       554: 1
       556: 1
       558: 1
       560: 1
       586: 1
       624: 1
       626: 1
       640: 1
       681: 1
       682: 1
       822: 1

 823:    0: 4q+2
         1: 4q+2
         2: 2q^2+3q+1
         3: 4q+2
         4: 2q^2+2q+2
         5: 4q+2
         6: 2q^2+2q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: 2q^2+2q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 4q+2
        26: 4q+2
        27: 2q^2+3q+1
        28: 4q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 4q+2
        35: 2q+1
        36: 4q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: q+1
        81: q+1
        82: 2
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: 2
       211: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       311: 2
       313: 1
       315: 1
       317: 2
       321: 1
       322: 1
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       397: 1
       399: 1
       411: 1
       415: 1
       417: 1
       423: 1
       451: 1
       455: 1
       459: 1
       467: 1
       469: 1
       494: 1
       498: 1
       499: 1
       502: 1
       504: 1
       506: 1
       510: 1
       513: 1
       514: 1
       587: 1
       623: 1
       625: 1
       627: 1
       637: 1
       688: 1
       823: 1

 824:    0: 4q+2
         1: 4q+2
         2: 2q^2+3q+1
         3: 4q+2
         4: 2q^2+2q+2
         5: 4q+2
         6: 2q^2+2q+2
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: 2q^2+2q+2
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 4q+2
        26: 4q+2
        27: 2q^2+3q+1
        28: 4q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 4q+2
        35: 2q+1
        36: 4q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: q+1
        81: q+1
        82: 2
        83: 1
        84: 2q+1
        85: 2q+1
        86: 2q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 2q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: 2
       212: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       312: 2
       314: 1
       316: 1
       318: 2
       321: 1
       322: 1
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       398: 1
       400: 1
       412: 1
       416: 1
       418: 1
       424: 1
       452: 1
       456: 1
       460: 1
       468: 1
       470: 1
       494: 1
       498: 1
       499: 1
       503: 1
       505: 1
       507: 1
       510: 1
       513: 1
       514: 1
       588: 1
       624: 1
       626: 1
       628: 1
       638: 1
       688: 1
       824: 1

 825:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        60: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       107: 1
       119: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       183: 1
       199: 1
       201: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       253: 1
       254: 1
       255: 1
       283: 1
       293: 1
       307: 1
       333: 1
       334: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       419: 1
       447: 1
       453: 1
       481: 1
       497: 1
       498: 1
       589: 1
       619: 1
       681: 1
       825: 1

 826:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        34: 1
        35: 1
        36: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        55: 1
        56: 1
        57: 1
        61: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       108: 1
       120: 1
       125: 1
       126: 1
       133: 1
       134: 1
       135: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       184: 1
       200: 1
       202: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       253: 1
       254: 1
       255: 1
       284: 1
       294: 1
       308: 1
       333: 1
       334: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       420: 1
       448: 1
       454: 1
       481: 1
       497: 1
       498: 1
       590: 1
       620: 1
       681: 1
       826: 1

 827:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+2
        22: 2
        23: 2
        24: 2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+2
        28: 2q+2
        29: q^2+3q+2
        30: 2q+2
        31: 2
        32: 2
        33: 2
        34: q^2+3q+2
        35: 2q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+2
        58: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2q+2
        72: 2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2q+2
        85: q+2
        86: q^2+3q+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 2q+2
        98: 2q+2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: q+1
       108: q+1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: q+2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: q+2
       144: 1
       145: 2q+2
       146: 2q+2
       147: 2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 1
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: 1
       226: 1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       253: q+2
       254: q+2
       255: q+1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       385: 1
       387: 1
       401: 1
       402: 1
       421: 1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 1
       481: 1
       483: 1
       497: 1
       498: 1
       499: 1
       500: 1
       557: 1
       558: 1
       591: 1
       621: 1
       681: 1
       683: 1
       827: 1

 828:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+2
        22: 2
        23: 2
        24: 2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+2
        28: 2q+2
        29: q^2+3q+2
        30: 2q+2
        31: 2
        32: 2
        33: 2
        34: q^2+3q+2
        35: 2q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+2
        59: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2q+2
        72: 2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2q+2
        85: q+2
        86: q^2+3q+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 2q+2
        98: 2q+2
        99: q+1
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: q+1
       108: q+1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: q+2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: q+2
       144: 1
       145: 2q+2
       146: 2q+2
       147: 2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 1
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: 1
       226: 1
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       253: q+2
       254: q+2
       255: q+1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       386: 1
       388: 1
       403: 1
       404: 1
       422: 1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 1
       481: 1
       483: 1
       497: 1
       498: 1
       499: 1
       500: 1
       559: 1
       560: 1
       592: 1
       622: 1
       681: 1
       683: 1
       828: 1

 829:    0: q^3+14q^2+13q+2
         1: 3q^3+16q^2+13q+2
         2: q^3+8q^2+9q+2
         3: 3q^3+16q^2+13q+2
         4: 3q^3+10q^2+10q+2
         5: q^3+14q^2+13q+2
         6: q^4+7q^3+13q^2+10q+2
         7: q^3+6q^2+7q+2
         8: q^3+8q^2+9q+2
         9: q^3+3q^2+3q+1
        10: 8q^2+11q+2
        11: 8q^2+11q+2
        12: 2q^3+7q^2+8q+2
        13: 6q^2+9q+2
        14: 5q^2+7q+2
        15: 6q^2+9q+2
        16: 9q^2+11q+2
        17: 9q^2+11q+2
        18: 2q^2+3q+1
        19: 7q^2+10q+2
        20: 2q^3+10q^2+10q+2
        21: 4q^2+7q+2
        22: 8q^2+12q+2
        23: 10q^2+12q+2
        24: 4q^2+8q+2
        25: q^3+14q^2+13q+2
        26: 3q^3+16q^2+13q+2
        27: q^3+8q^2+9q+2
        28: 4q^2+9q+2
        29: 4q^2+8q+2
        30: 3q^2+7q+2
        31: 4q^2+10q+2
        32: 2q^2+8q+2
        33: 6q^2+10q+2
        34: 8q^2+11q+2
        35: 6q^2+9q+2
        36: 9q^2+11q+2
        37: 4q^2+6q+1
        38: 4q^2+6q+1
        39: 5q^2+6q+1
        40: 5q^2+6q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 4q^2+7q+2
        47: 4q^2+7q+2
        48: 2q^2+3q+1
        49: 3q^2+8q+2
        50: 4q^2+8q+2
        51: q^2+3q+1
        52: 2q^2+9q+2
        53: 5q^2+9q+2
        54: q^2+6q+2
        55: 7q^2+10q+2
        56: 2q^3+10q^2+10q+2
        57: 4q^2+7q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: 3q^2+7q+2
        61: q^2+2q
        62: 2q^2+5q+1
        63: 2q^2+5q+1
        64: q^2+4q+1
        65: q^2+4q+1
        66: 3q^2+5q+1
        67: 3q^2+5q+1
        68: q^2+3q+2
        69: q^2+2q+1
        70: q^2+5q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: 2q+1
        79: 2q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: q^2+7q+2
        83: 6q+2
        84: 2q^2+7q+2
        85: 4q^2+7q+2
        86: 4q^2+8q+2
        87: 3q^2+7q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 4q+2
        95: q^2+4q+2
        96: 2q+1
        97: 3q^2+8q+2
        98: 4q^2+8q+2
        99: q^2+3q+1
       100: 2q^2+9q+2
       101: 5q^2+9q+2
       102: q^2+6q+2
       103: q^2+3q+1
       104: q^2+3q+1
       105: q
       106: q
       107: 4q+2
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q^2+3q+2
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: q+2
       141: 4q+2
       142: 3q+2
       143: 4q+2
       144: q^2+2q+1
       145: q^2+6q+2
       146: q^2+5q+2
       147: q^2+6q+2
       148: q^2+6q+2
       149: q^2+7q+2
       150: 6q+2
       151: 3q+1
       152: 3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 4q+2
       164: q^2+4q+2
       165: 2q+1
       166: 4q+2
       167: q^2+4q+2
       168: 2q+1
       169: q+1
       170: q+1
       173: q+1
       174: q+1
       183: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: 4q+2
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: q+2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       243: 3q+2
       244: q+2
       245: 3q+2
       246: 4q+2
       247: q+2
       248: q+2
       249: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       264: 1
       267: 1
       268: 1
       271: q+1
       274: q+1
       275: q+1
       276: q+1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       313: q+1
       314: q+1
       319: q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: q+2
       358: 1
       359: q+2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       385: 1
       386: 1
       393: 1
       394: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 1
       429: 1
       443: 2
       447: 1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       512: 1
       514: 1
       557: 1
       560: 1
       565: 1
       566: 1
       573: 1
       574: 1
       593: 1
       619: 1
       641: 1
       682: 1
       683: 1
       689: 1
       829: 1

 830:    0: q^3+14q^2+13q+2
         1: 3q^3+16q^2+13q+2
         2: q^3+8q^2+9q+2
         3: 3q^3+16q^2+13q+2
         4: 3q^3+10q^2+10q+2
         5: q^3+14q^2+13q+2
         6: q^4+7q^3+13q^2+10q+2
         7: q^3+6q^2+7q+2
         8: q^3+8q^2+9q+2
         9: q^3+3q^2+3q+1
        10: 8q^2+11q+2
        11: 8q^2+11q+2
        12: 2q^3+7q^2+8q+2
        13: 6q^2+9q+2
        14: 5q^2+7q+2
        15: 6q^2+9q+2
        16: 9q^2+11q+2
        17: 9q^2+11q+2
        18: 2q^2+3q+1
        19: 7q^2+10q+2
        20: 2q^3+10q^2+10q+2
        21: 4q^2+7q+2
        22: 8q^2+12q+2
        23: 10q^2+12q+2
        24: 4q^2+8q+2
        25: q^3+14q^2+13q+2
        26: 3q^3+16q^2+13q+2
        27: q^3+8q^2+9q+2
        28: 4q^2+9q+2
        29: 4q^2+8q+2
        30: 3q^2+7q+2
        31: 4q^2+10q+2
        32: 2q^2+8q+2
        33: 6q^2+10q+2
        34: 8q^2+11q+2
        35: 6q^2+9q+2
        36: 9q^2+11q+2
        37: 4q^2+6q+1
        38: 4q^2+6q+1
        39: 5q^2+6q+1
        40: 5q^2+6q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+7q+2
        44: 3q^2+5q+2
        45: 2q^2+7q+2
        46: 4q^2+7q+2
        47: 4q^2+7q+2
        48: 2q^2+3q+1
        49: 3q^2+8q+2
        50: 4q^2+8q+2
        51: q^2+3q+1
        52: 2q^2+9q+2
        53: 5q^2+9q+2
        54: q^2+6q+2
        55: 7q^2+10q+2
        56: 2q^3+10q^2+10q+2
        57: 4q^2+7q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+2q
        61: 3q^2+7q+2
        62: 2q^2+5q+1
        63: 2q^2+5q+1
        64: q^2+4q+1
        65: q^2+4q+1
        66: 3q^2+5q+1
        67: 3q^2+5q+1
        68: q^2+3q+2
        69: q^2+2q+1
        70: q^2+5q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: 2q+1
        79: 2q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: q^2+7q+2
        83: 6q+2
        84: 2q^2+7q+2
        85: 4q^2+7q+2
        86: 4q^2+8q+2
        87: 3q^2+7q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: q^2+4q+2
        93: 2q+1
        94: 4q+2
        95: q^2+4q+2
        96: 2q+1
        97: 3q^2+8q+2
        98: 4q^2+8q+2
        99: q^2+3q+1
       100: 2q^2+9q+2
       101: 5q^2+9q+2
       102: q^2+6q+2
       103: q
       104: q
       105: q^2+3q+1
       106: q^2+3q+1
       108: 4q+2
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       120: q^2+3q+2
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: q+2
       141: 4q+2
       142: 3q+2
       143: 4q+2
       144: q^2+2q+1
       145: q^2+6q+2
       146: q^2+5q+2
       147: q^2+6q+2
       148: q^2+6q+2
       149: q^2+7q+2
       150: 6q+2
       151: 3q+1
       152: 3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 4q+2
       164: q^2+4q+2
       165: 2q+1
       166: 4q+2
       167: q^2+4q+2
       168: 2q+1
       171: q+1
       172: q+1
       175: q+1
       176: q+1
       184: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: 4q+2
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: q+2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       243: 3q+2
       244: q+2
       245: 3q+2
       246: 4q+2
       247: q+2
       248: q+2
       249: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       265: 1
       266: 1
       269: 1
       270: 1
       272: q+1
       273: q+1
       277: q+1
       278: q+1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       313: q+1
       314: q+1
       320: q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: q+2
       358: 1
       359: q+2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       387: 1
       388: 1
       395: 1
       396: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 1
       430: 1
       444: 2
       448: 1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       512: 1
       514: 1
       558: 1
       559: 1
       567: 1
       568: 1
       575: 1
       576: 1
       594: 1
       620: 1
       642: 1
       682: 1
       683: 1
       689: 1
       830: 1

 831:    0: q^2+2
         1: q^2+2
         2: q^2+2
         3: q^2+2
         4: q+1
         5: q^2+2
         6: q^3+q^2+q+1
         7: q+1
         8: q^2+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q^2+2
        14: q+1
        15: q^2+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: 1
        20: q^2+1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q^2+2
        26: q^2+2
        27: q^2+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: q^2+2
        36: q^2+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q^2+1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: q^2+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: q^2+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q^2+1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: 1
       277: 1
       285: 1
       295: 1
       303: 1
       309: 1
       321: 1
       333: 1
       335: 1
       344: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       421: 1
       431: 1
       449: 1
       457: 1
       473: 1
       482: 1
       497: 1
       499: 1
       508: 1
       514: 1
       595: 1
       621: 1
       643: 1
       682: 1
       831: 1

 832:    0: q^2+2
         1: q^2+2
         2: q^2+2
         3: q^2+2
         4: q+1
         5: q^2+2
         6: q^3+q^2+q+1
         7: q+1
         8: q^2+2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: q^2+2
        14: q+1
        15: q^2+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: 1
        20: q^2+1
        21: 1
        22: 2
        23: 2
        24: 2
        25: q^2+2
        26: q^2+2
        27: q^2+2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: q^2+2
        36: q^2+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: 1
        50: q^2+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q^2+1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: q^2+2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: q^2+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: q^2+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q^2+1
       165: 1
       166: 1
       167: 1
       168: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       276: 1
       278: 1
       286: 1
       296: 1
       304: 1
       310: 1
       322: 1
       333: 1
       335: 1
       344: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       422: 1
       432: 1
       450: 1
       458: 1
       474: 1
       482: 1
       497: 1
       499: 1
       508: 1
       514: 1
       596: 1
       622: 1
       644: 1
       682: 1
       832: 1

 833:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        30: q^2+2q+1
        32: q+1
        33: q+1
        35: q^2+2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        64: q+1
        66: q+1
        69: q+1
        72: 2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        81: q+1
        83: q+1
        85: 2q+1
        87: q^2+2q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       111: q+1
       115: q+1
       123: q+1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 2q+1
       136: q+1
       138: 1
       142: 1
       144: q+1
       147: 2q+1
       148: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: q+1
       205: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: 1
       241: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       311: 1
       313: q+1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       451: 1
       455: 1
       463: 1
       467: 1
       485: 1
       487: 1
       489: 1
       491: 1
       500: 1
       501: 1
       514: 1
       597: 1
       623: 1
       629: 1
       633: 1
       685: 1
       833: 1

 834:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        30: q^2+2q+1
        32: q+1
        33: q+1
        35: q^2+2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        65: q+1
        67: q+1
        69: q+1
        72: 2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        81: q+1
        83: q+1
        85: 2q+1
        87: q^2+2q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       112: q+1
       116: q+1
       124: q+1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 2q+1
       136: q+1
       138: 1
       142: 1
       144: q+1
       147: 2q+1
       148: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: q+1
       206: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: 1
       242: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       312: 1
       314: q+1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       452: 1
       456: 1
       464: 1
       468: 1
       486: 1
       488: 1
       490: 1
       491: 1
       500: 1
       501: 1
       514: 1
       598: 1
       624: 1
       630: 1
       634: 1
       685: 1
       834: 1

 835:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: 1
        36: 2q+2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2q+2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2q+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2q+2
       146: 1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 1
       209: 2
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       253: 1
       254: 1
       255: 1
       259: 1
       262: 1
       271: 1
       273: 1
       287: 1
       291: 1
       297: 1
       311: 2
       313: 1
       315: 1
       317: 2
       321: 1
       322: 1
       325: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 1
       397: 1
       399: 1
       423: 1
       425: 1
       427: 2
       451: 1
       459: 1
       461: 1
       462: 1
       463: 2
       469: 1
       483: 1
       498: 1
       499: 1
       500: 1
       561: 1
       563: 1
       599: 1
       625: 1
       629: 1
       683: 1
       835: 1

 836:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: 1
        36: 2q+2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2q+2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2q+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2q+2
       146: 1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 1
       210: 2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       253: 1
       254: 1
       255: 1
       260: 1
       261: 1
       272: 1
       274: 1
       288: 1
       292: 1
       298: 1
       312: 2
       314: 1
       316: 1
       318: 2
       321: 1
       322: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 1
       398: 1
       400: 1
       424: 1
       426: 1
       428: 2
       452: 1
       460: 1
       461: 1
       462: 1
       464: 2
       470: 1
       483: 1
       498: 1
       499: 1
       500: 1
       562: 1
       564: 1
       600: 1
       626: 1
       630: 1
       683: 1
       836: 1

 837:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q^2+3q+2
        35: q+1
        36: 2q+2
        37: q+2
        39: q+2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: q+2
        64: 1
        66: 2
        70: q+1
        71: 2q+2
        72: 2q+2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q^2+3q+2
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2q+2
        98: 2q+2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: q+1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: q+1
       224: 1
       230: 1
       234: q+1
       235: 1
       237: 2
       239: 2
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       259: 1
       262: 1
       271: 1
       273: 1
       289: 1
       297: 1
       311: 2
       313: 1
       317: 2
       321: 1
       322: 1
       325: 1
       327: 1
       329: 1
       337: 2
       338: 2
       340: 2
       349: 1
       355: q+1
       357: 1
       359: 2
       360: 1
       362: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       397: 1
       399: 1
       415: 1
       427: 2
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       485: 1
       487: 1
       501: 1
       502: 1
       504: 1
       513: 1
       518: 1
       519: 1
       561: 1
       563: 1
       627: 1
       633: 1
       666: 1
       668: 1
       684: 1
       837: 1

 838:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+2q+1
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: q+2
        23: q+2
        24: q+1
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+2q+1
        28: 2q+2
        29: q^2+3q+2
        30: q+1
        31: q+2
        32: 1
        33: 2
        34: q^2+3q+2
        35: q+1
        36: 2q+2
        38: q+2
        40: q+2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        49: 2q+2
        50: 2q+2
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        63: q+2
        65: 1
        67: 2
        70: q+1
        71: 2q+2
        72: 2q+2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q^2+3q+2
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 2
        95: 2
        97: 2q+2
        98: 2q+2
       100: q+2
       101: q+2
       102: q+1
       104: 1
       105: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: q+1
       136: 1
       137: 1
       139: 2
       141: 1
       142: 2
       143: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: q+1
       224: 1
       230: 1
       234: q+1
       235: 1
       238: 2
       240: 2
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       260: 1
       261: 1
       272: 1
       274: 1
       290: 1
       298: 1
       312: 2
       314: 1
       318: 2
       321: 1
       322: 1
       326: 1
       328: 1
       330: 1
       337: 2
       339: 2
       341: 2
       349: 1
       355: q+1
       357: 1
       359: 2
       361: 1
       363: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       398: 1
       400: 1
       416: 1
       428: 2
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       486: 1
       488: 1
       501: 1
       503: 1
       505: 1
       513: 1
       518: 1
       519: 1
       562: 1
       564: 1
       628: 1
       634: 1
       667: 1
       669: 1
       684: 1
       838: 1

 839:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2
        17: 2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q^2+3q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 2
       135: 2
       136: 2
       137: 2
       139: 1
       141: 2q+2
       142: 1
       143: 2
       145: 2
       146: q^2+3q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 1
       161: 1
       163: 2
       164: 2
       166: 1
       167: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2
       195: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       220: 2
       222: 2
       224: 2
       227: 1
       230: 1
       232: 2
       234: 2
       235: 2
       243: 1
       245: 1
       246: 2q+2
       247: 1
       248: 1
       250: 1
       251: 1
       253: 2
       254: 2
       256: 1
       257: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: q+1
       326: q+1
       337: 1
       345: 1
       349: 1
       353: 2
       355: 2
       357: 2
       359: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       385: 1
       387: 1
       401: 1
       402: 1
       439: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 1
       473: 1
       484: 1
       501: 1
       509: 1
       513: 1
       518: 1
       519: 1
       557: 1
       558: 1
       631: 1
       649: 1
       672: 1
       684: 1
       839: 1

 840:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2
        17: 2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2
        47: 2
        49: 2
        50: 2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        59: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        70: q^2+3q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2
        89: 2
        91: 2
        92: 2
        94: 1
        95: 1
        97: 2
        98: 2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       133: 2
       135: 2
       136: 2
       137: 2
       139: 1
       141: 2q+2
       142: 1
       143: 2
       145: 2
       146: q^2+3q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       160: 1
       161: 1
       163: 2
       164: 2
       166: 1
       167: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       220: 2
       222: 2
       224: 2
       227: 1
       230: 1
       232: 2
       234: 2
       235: 2
       243: 1
       245: 1
       246: 2q+2
       247: 1
       248: 1
       250: 1
       251: 1
       253: 2
       254: 2
       256: 1
       257: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: q+1
       326: q+1
       337: 1
       345: 1
       349: 1
       353: 2
       355: 2
       357: 2
       359: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       386: 1
       388: 1
       403: 1
       404: 1
       440: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 1
       474: 1
       484: 1
       501: 1
       509: 1
       513: 1
       518: 1
       519: 1
       559: 1
       560: 1
       632: 1
       650: 1
       672: 1
       684: 1
       840: 1

 841:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+q+1
         5: 2q+2
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+2
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: q^2+q+1
        13: 2q+2
        14: q^2+q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 1
        30: 1
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 2q+2
        44: q^2+q+1
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: 2q+2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 2q+2
        81: 2q+2
        82: 1
        83: 1
        84: 2q+2
        85: 2q+2
        86: 1
        87: 1
        88: 2q+2
        89: 2q+2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: q+1
       106: q+1
       113: 1
       115: 1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: 2q+2
       125: 2q+2
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       137: 2q+2
       138: 1
       139: 1
       141: 1
       143: 2q+2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: q+1
       176: q+1
       177: 1
       179: 1
       189: 1
       191: q+1
       192: q+1
       199: q+1
       200: q+1
       207: 2q+2
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: q+1
       278: q+1
       279: 1
       281: 1
       287: 1
       315: 1
       317: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       374: 1
       375: 1
       376: 1
       409: 1
       411: 1
       413: 1
       465: 1
       467: 1
       469: 1
       492: 1
       497: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       583: 1
       635: 1
       637: 1
       639: 1
       686: 1
       841: 1

 842:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+q+1
         5: 2q+2
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+2
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: q^2+q+1
        13: 2q+2
        14: q^2+q+1
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 1
        30: 1
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 2q+2
        44: q^2+q+1
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: 2q+2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 2q+2
        81: 2q+2
        82: 1
        83: 1
        84: 2q+2
        85: 2q+2
        86: 1
        87: 1
        88: 2q+2
        89: 2q+2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       105: q+1
       114: 1
       116: 1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: 2q+2
       125: 2q+2
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       137: 2q+2
       138: 1
       139: 1
       141: 1
       143: 2q+2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       174: q+1
       175: q+1
       178: 1
       180: 1
       190: 1
       191: q+1
       192: q+1
       199: q+1
       200: q+1
       208: 2q+2
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       276: q+1
       277: q+1
       280: 1
       282: 1
       288: 1
       316: 1
       318: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       374: 1
       375: 1
       376: 1
       410: 1
       412: 1
       414: 1
       466: 1
       468: 1
       470: 1
       492: 1
       497: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       584: 1
       636: 1
       638: 1
       640: 1
       686: 1
       842: 1

 843:    0: 4q+1
         1: 4q+1
         2: q^2+2q+1
         3: 4q+1
         4: q^2+2q+1
         5: 4q+1
         6: 2q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 4q+1
        17: 4q+1
        18: q+1
        19: 2q+1
        20: 3q+1
        21: q+1
        22: 4q+1
        23: 4q+1
        24: q^2+2q+1
        25: 4q+1
        26: 4q+1
        27: q^2+2q+1
        30: q+1
        32: 2q+1
        33: 4q+1
        35: 2q+1
        36: 4q+1
        37: 2q+1
        38: 2q
        39: 2q+1
        40: 2q
        41: q+1
        42: q^2+q
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 3q+1
        51: q+1
        52: 2q+1
        53: 3q+1
        54: q+1
        55: 2q+1
        56: 3q+1
        57: q+1
        64: q+1
        65: q
        66: 2q+1
        67: 2q
        69: q+1
        72: q+1
        73: q+1
        74: 1
        75: q
        76: q+1
        77: q
        78: 1
        79: q
        81: 2q+1
        83: q+1
        85: 2q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 3q+1
        96: q+1
        97: 2q+1
        98: 3q+1
        99: q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       111: 1
       115: 1
       116: q
       123: q+1
       124: q
       127: 1
       128: q
       129: q+1
       130: q
       131: 1
       132: q
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q
       155: 1
       156: q
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: 1
       178: q
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       212: q
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q
       239: q+1
       240: q
       241: 1
       242: q
       244: q+1
       245: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       316: q
       323: 1
       338: 1
       339: 1
       340: 1
       341: 1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       433: 1
       445: 1
       446: 1
       451: 1
       463: 1
       464: 1
       475: 1
       477: 1
       479: 2
       496: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       577: 1
       578: 1
       645: 1
       655: 1
       674: 1
       680: 1
       843: 1

 844:    0: 4q+1
         1: 4q+1
         2: q^2+2q+1
         3: 4q+1
         4: q^2+2q+1
         5: 4q+1
         6: 2q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 4q+1
        17: 4q+1
        18: q+1
        19: 2q+1
        20: 3q+1
        21: q+1
        22: 4q+1
        23: 4q+1
        24: q^2+2q+1
        25: 4q+1
        26: 4q+1
        27: q^2+2q+1
        30: q+1
        32: 2q+1
        33: 4q+1
        35: 2q+1
        36: 4q+1
        37: 2q
        38: 2q+1
        39: 2q
        40: 2q+1
        41: q^2+q
        42: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 3q+1
        51: q+1
        52: 2q+1
        53: 3q+1
        54: q+1
        55: 2q+1
        56: 3q+1
        57: q+1
        64: q
        65: q+1
        66: 2q
        67: 2q+1
        69: q+1
        72: q+1
        73: q+1
        74: q
        75: 1
        76: q
        77: q+1
        78: q
        79: 1
        81: 2q+1
        83: q+1
        85: 2q+1
        87: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 3q+1
        96: q+1
        97: 2q+1
        98: 3q+1
        99: q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       112: 1
       115: q
       116: 1
       123: q
       124: q+1
       127: q
       128: 1
       129: q
       130: q+1
       131: q
       132: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       151: q
       152: 1
       153: q
       154: q+1
       155: q
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: q
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       211: q
       212: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q
       238: 1
       239: q
       240: q+1
       241: q
       242: 1
       244: q+1
       245: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       315: q
       316: 1
       324: 1
       338: 1
       339: 1
       340: 1
       341: 1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       434: 1
       445: 1
       446: 1
       452: 1
       463: 1
       464: 1
       476: 1
       478: 1
       480: 2
       496: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       580: 1
       581: 1
       646: 1
       656: 1
       674: 1
       680: 1
       844: 1

 845:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: q^3+3q^2+3q+1
         5: 6q+2
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: q^3+3q^2+3q+1
        13: 4q+2
        14: q^2+2q+1
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 2q+1
        30: q+1
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+2q+1
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 3q+1
        59: 3q+1
        60: 4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        80: 4q+2
        81: 4q+2
        82: 2q+1
        83: q+1
        84: 4q+2
        85: 4q+2
        86: 2q+1
        87: q+1
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 1
       134: 1
       135: 1
       137: 4q+2
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       143: 4q+2
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       173: q+1
       174: q+1
       183: 1
       191: q+1
       192: q+1
       193: q+1
       199: 2q+2
       201: q+1
       207: 2q+1
       208: 2q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       275: q+1
       276: q+1
       283: 1
       293: 1
       299: 1
       307: 1
       319: q+1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       419: 1
       429: 1
       437: 1
       447: 1
       453: 1
       471: 1
       492: 1
       493: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       603: 1
       619: 1
       641: 1
       647: 1
       686: 1
       687: 1
       845: 1

 846:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: q^3+3q^2+3q+1
         5: 6q+2
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: q^3+3q^2+3q+1
        13: 4q+2
        14: q^2+2q+1
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 2q+1
        30: q+1
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+2q+1
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 4q+2
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        80: 4q+2
        81: 4q+2
        82: 2q+1
        83: q+1
        84: 4q+2
        85: 4q+2
        86: 2q+1
        87: q+1
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 1
       134: 1
       135: 1
       137: 4q+2
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       143: 4q+2
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       175: q+1
       176: q+1
       184: 1
       191: q+1
       192: q+1
       194: q+1
       200: 2q+2
       202: q+1
       207: 2q+1
       208: 2q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       277: q+1
       278: q+1
       284: 1
       294: 1
       300: 1
       308: 1
       320: q+1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       420: 1
       430: 1
       438: 1
       448: 1
       454: 1
       472: 1
       492: 1
       493: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       604: 1
       620: 1
       642: 1
       648: 1
       686: 1
       687: 1
       846: 1

 847:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: q^3+3q^2+3q+1
         5: 6q+2
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: q^3+3q^2+3q+1
        13: 4q+2
        14: q^2+2q+1
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 2q+1
        30: q+1
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+2q+1
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: q+1
        71: 2q+1
        73: q+1
        80: 4q+2
        81: 4q+2
        82: 2q+1
        83: q+1
        84: 4q+2
        85: 4q+2
        86: 2q+1
        87: q+1
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       109: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 1
       134: 1
       136: 1
       137: 4q+2
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 4q+2
       144: q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: 2q+1
       150: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       173: q+1
       175: q+1
       185: 1
       191: 2q+2
       195: q+1
       199: q+1
       200: q+1
       203: q+1
       207: 2q+1
       208: 2q+1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       235: 1
       236: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       275: q+1
       277: q+1
       285: 1
       295: 1
       303: 1
       309: 1
       321: q+1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       421: 1
       431: 1
       439: 1
       449: 1
       457: 1
       473: 1
       492: 1
       494: 1
       497: 1
       499: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       607: 1
       621: 1
       643: 1
       649: 1
       686: 1
       688: 1
       847: 1

 848:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: q^3+3q^2+3q+1
         5: 6q+2
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+2
         9: q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: q^3+3q^2+3q+1
        13: 4q+2
        14: q^2+2q+1
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 2q+1
        30: q+1
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+2q+1
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q
        59: 4q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: q+1
        71: 2q+1
        73: q+1
        80: 4q+2
        81: 4q+2
        82: 2q+1
        83: q+1
        84: 4q+2
        85: 4q+2
        86: 2q+1
        87: q+1
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       110: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 1
       134: 1
       136: 1
       137: 4q+2
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 4q+2
       144: q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: 2q+1
       150: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       174: q+1
       176: q+1
       186: 1
       192: 2q+2
       196: q+1
       199: q+1
       200: q+1
       204: q+1
       207: 2q+1
       208: 2q+1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       235: 1
       236: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       276: q+1
       278: q+1
       286: 1
       296: 1
       304: 1
       310: 1
       322: q+1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       422: 1
       432: 1
       440: 1
       450: 1
       458: 1
       474: 1
       492: 1
       494: 1
       497: 1
       499: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       608: 1
       622: 1
       644: 1
       650: 1
       686: 1
       688: 1
       848: 1

 849:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: q+1
        66: q+1
        69: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: q+1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       244: 1
       245: 1
       256: 1
       257: q+1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       348: 1
       350: 1
       356: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       417: 1
       433: 1
       435: 1
       451: 1
       455: 1
       467: 1
       475: 1
       477: 1
       512: 1
       514: 1
       605: 1
       623: 1
       645: 1
       651: 1
       849: 1

 850:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: q+1
        67: q+1
        69: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: q+1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       244: 1
       245: 1
       256: 1
       257: q+1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       348: 1
       350: 1
       356: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       369: 1
       370: 1
       418: 1
       434: 1
       436: 1
       452: 1
       456: 1
       468: 1
       476: 1
       478: 1
       512: 1
       514: 1
       606: 1
       624: 1
       646: 1
       652: 1
       850: 1

 851:    0: 10q+2
         1: 10q+2
         2: q^3+4q^2+4q+1
         3: 10q+2
         4: 2q^3+5q^2+5q+2
         5: 10q+2
         6: 2q^3+5q^2+5q+2
         7: q^3+2q^2+2q+1
         8: q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 10q+2
        11: 10q+2
        12: 2q^3+5q^2+5q+2
        13: 3q+1
        14: q^2+q+1
        15: 3q+1
        16: 10q+2
        17: 10q+2
        18: q^3+2q^2+2q+1
        19: 5q+2
        20: 5q+2
        21: q^2+2q+1
        22: 10q+2
        23: 10q+2
        24: q^3+4q^2+4q+1
        25: 10q+2
        26: 10q+2
        27: q^3+4q^2+4q+1
        28: 10q+2
        29: 5q+2
        30: q+1
        31: 10q+2
        32: 3q+1
        33: 10q+2
        34: 10q+2
        35: 3q+1
        36: 10q+2
        37: 6q+2
        38: 4q
        39: 6q+2
        40: 4q
        41: 2q^2+3q+1
        42: q^3+2q^2+q
        43: 3q+1
        44: q^2+q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+q+1
        49: 5q+2
        50: 5q+2
        51: q^2+2q+1
        52: 5q+2
        53: 5q+2
        54: q^2+2q+1
        55: 5q+2
        56: 5q+2
        57: q^2+2q+1
        58: 5q+1
        59: 5q+1
        60: 5q+1
        61: 5q+1
        62: 6q+2
        63: 4q
        64: 2q+1
        65: q
        66: 6q+2
        67: 4q
        69: q+1
        70: q+1
        71: 5q+2
        72: 2q+2
        73: 2q+2
        74: q+2
        76: q+2
        78: q+1
        80: 3q+1
        81: 3q+1
        82: 5q+2
        83: q+1
        84: 3q+1
        85: 3q+1
        86: 5q+2
        87: q+1
        88: 3q+1
        89: 3q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 5q+2
        95: 5q+2
        96: q^2+2q+1
        97: 5q+2
        98: 5q+2
        99: q^2+2q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: 3q+1
       104: 2q
       105: 2q
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       115: 1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: q+1
       139: 5q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: 3q+1
       144: q+1
       145: 5q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: 2q+1
       208: q
       209: q+2
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+2
       239: q+2
       241: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       287: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       423: 1
       433: 1
       441: 1
       451: 1
       459: 1
       469: 1
       475: 1
       477: 2
       493: 1
       494: 1
       498: 1
       499: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       569: 1
       570: 1
       609: 1
       625: 1
       645: 1
       653: 1
       687: 1
       688: 1
       851: 1

 852:    0: 10q+2
         1: 10q+2
         2: q^3+4q^2+4q+1
         3: 10q+2
         4: 2q^3+5q^2+5q+2
         5: 10q+2
         6: 2q^3+5q^2+5q+2
         7: q^3+2q^2+2q+1
         8: q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 10q+2
        11: 10q+2
        12: 2q^3+5q^2+5q+2
        13: 3q+1
        14: q^2+q+1
        15: 3q+1
        16: 10q+2
        17: 10q+2
        18: q^3+2q^2+2q+1
        19: 5q+2
        20: 5q+2
        21: q^2+2q+1
        22: 10q+2
        23: 10q+2
        24: q^3+4q^2+4q+1
        25: 10q+2
        26: 10q+2
        27: q^3+4q^2+4q+1
        28: 10q+2
        29: 5q+2
        30: q+1
        31: 10q+2
        32: 3q+1
        33: 10q+2
        34: 10q+2
        35: 3q+1
        36: 10q+2
        37: 4q
        38: 6q+2
        39: 4q
        40: 6q+2
        41: q^3+2q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+q+1
        49: 5q+2
        50: 5q+2
        51: q^2+2q+1
        52: 5q+2
        53: 5q+2
        54: q^2+2q+1
        55: 5q+2
        56: 5q+2
        57: q^2+2q+1
        58: 5q+1
        59: 5q+1
        60: 5q+1
        61: 5q+1
        62: 4q
        63: 6q+2
        64: q
        65: 2q+1
        66: 4q
        67: 6q+2
        69: q+1
        70: q+1
        71: 5q+2
        72: 2q+2
        73: 2q+2
        75: q+2
        77: q+2
        79: q+1
        80: 3q+1
        81: 3q+1
        82: 5q+2
        83: q+1
        84: 3q+1
        85: 3q+1
        86: 5q+2
        87: q+1
        88: 3q+1
        89: 3q+1
        90: q^2+q+1
        91: 1
        92: q+1
        93: 1
        94: 5q+2
        95: 5q+2
        96: q^2+2q+1
        97: 5q+2
        98: 5q+2
        99: q^2+2q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: 2q
       104: 3q+1
       105: 3q+1
       106: 2q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       114: q+2
       116: 1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: q+1
       139: 5q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: 3q+1
       144: q+1
       145: 5q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       207: q
       208: 2q+1
       210: q+2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: q+2
       240: q+2
       242: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       288: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       326: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       424: 1
       434: 1
       442: 1
       452: 1
       460: 1
       470: 1
       476: 1
       478: 2
       493: 1
       494: 1
       498: 1
       499: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       571: 1
       572: 1
       610: 1
       626: 1
       646: 1
       654: 1
       687: 1
       688: 1
       852: 1

 853:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: 2q^3+q+2
         5: q+2
         6: 2q^3+q+2
         7: q^4+q^3+q+1
         8: q+1
        10: q+2
        11: q+2
        12: 2q^3+q+2
        13: 1
        14: q^3+1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: 1
        71: 2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       237: 2
       239: 2
       243: 2
       244: 2
       245: 2
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       289: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: 1
       347: 1
       349: 1
       355: 1
       357: 1
       360: 1
       362: 1
       369: 1
       370: 1
       374: 1
       375: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       415: 1
       435: 1
       441: 1
       455: 1
       459: 1
       475: 1
       477: 2
       502: 1
       504: 1
       511: 1
       513: 1
       569: 1
       570: 1
       611: 1
       627: 1
       651: 1
       653: 1
       853: 1

 854:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: 2q^3+q+2
         5: q+2
         6: 2q^3+q+2
         7: q^4+q^3+q+1
         8: q+1
        10: q+2
        11: q+2
        12: 2q^3+q+2
        13: 1
        14: q^3+1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: 1
        44: q^3+1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: 1
        71: 2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       238: 2
       240: 2
       243: 2
       244: 2
       245: 2
       246: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       290: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: 1
       347: 1
       349: 1
       355: 1
       357: 1
       361: 1
       363: 1
       369: 1
       370: 1
       374: 1
       375: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       416: 1
       436: 1
       442: 1
       456: 1
       460: 1
       476: 1
       478: 2
       503: 1
       505: 1
       511: 1
       513: 1
       571: 1
       572: 1
       612: 1
       628: 1
       652: 1
       654: 1
       854: 1

 855:    0: 3q+1
         1: 3q+1
         2: 2q^2+q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: 2q^2+q+1
         9: q^3+q^2+q+1
        13: q+1
        14: q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q^2+q+1
        19: 2q+1
        20: 2q+1
        21: q^2+q+1
        22: 3q+1
        23: 3q+1
        24: 2q^2+q+1
        25: 3q+1
        26: 3q+1
        27: 2q^2+q+1
        30: q+1
        32: q+1
        33: 3q+1
        35: q+1
        36: 3q+1
        37: 2q+1
        38: q
        39: 2q+1
        40: q
        41: q^2+q+1
        42: q^2
        46: q+1
        47: q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: 2q+1
        53: 2q+1
        54: q^2+q+1
        55: 2q+1
        56: 2q+1
        57: q^2+q+1
        64: q+1
        66: 2q+1
        67: q
        69: q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: 1
        92: 1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: 2q+1
       101: 2q+1
       102: q^2+q+1
       111: 1
       115: q+1
       123: q+1
       127: q+1
       129: q+1
       131: q+1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       177: q+1
       181: 1
       187: 1
       197: 1
       205: 1
       211: q+1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       244: q+1
       245: q+1
       247: 2
       248: 2
       249: q+1
       256: 1
       257: 1
       258: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: q+1
       323: 1
       336: 1
       338: 2
       340: 2
       342: q+1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 1
       370: 1
       425: 1
       433: 1
       445: 2
       451: 1
       463: 2
       475: 1
       477: 1
       479: 1
       480: 1
       495: 1
       500: 1
       512: 1
       514: 1
       577: 1
       580: 1
       613: 1
       629: 1
       645: 1
       689: 1
       855: 1

 856:    0: 3q+1
         1: 3q+1
         2: 2q^2+q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: 2q^2+q+1
         9: q^3+q^2+q+1
        13: q+1
        14: q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q^2+q+1
        19: 2q+1
        20: 2q+1
        21: q^2+q+1
        22: 3q+1
        23: 3q+1
        24: 2q^2+q+1
        25: 3q+1
        26: 3q+1
        27: 2q^2+q+1
        30: q+1
        32: q+1
        33: 3q+1
        35: q+1
        36: 3q+1
        37: q
        38: 2q+1
        39: q
        40: 2q+1
        41: q^2
        42: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: 2q+1
        53: 2q+1
        54: q^2+q+1
        55: 2q+1
        56: 2q+1
        57: q^2+q+1
        65: q+1
        66: q
        67: 2q+1
        69: q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: 1
        92: 1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: 2q+1
       101: 2q+1
       102: q^2+q+1
       112: 1
       116: q+1
       124: q+1
       128: q+1
       130: q+1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: q+1
       140: q+1
       142: q+1
       144: q+1
       147: q+1
       148: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       178: q+1
       182: 1
       188: 1
       198: 1
       206: 1
       212: q+1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       244: q+1
       245: q+1
       247: 2
       248: 2
       249: q+1
       256: 1
       257: 1
       258: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: q+1
       324: 1
       336: 1
       339: 2
       341: 2
       343: q+1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 1
       370: 1
       426: 1
       434: 1
       446: 2
       452: 1
       464: 2
       476: 1
       478: 1
       479: 1
       480: 1
       495: 1
       500: 1
       512: 1
       514: 1
       578: 1
       581: 1
       614: 1
       630: 1
       646: 1
       689: 1
       856: 1

 857:    0: 3q+2
         1: 3q+2
         2: q^2+2q+1
         3: 3q+2
         4: 3q+2
         5: 3q+2
         6: 3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 3q+2
        20: 3q+2
        21: q^2+2q+1
        22: 3q+2
        23: 3q+2
        24: q^2+2q+1
        25: 3q+2
        26: 3q+2
        27: q^2+2q+1
        28: 2
        29: 3q+2
        30: q+1
        31: 3q+2
        32: q+1
        33: 2
        34: 3q+2
        35: q+1
        36: 2
        37: q+2
        38: 2q
        39: q+2
        40: 2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 3q+2
        53: 3q+2
        54: q^2+2q+1
        55: 3q+2
        56: 3q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        63: 2q
        64: 1
        65: q
        66: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        74: q+2
        75: 2q
        76: q+2
        77: 2q
        78: q+1
        79: q^2+q
        80: q+1
        81: 1
        82: 3q+2
        83: q+1
        84: q+1
        85: 1
        86: 3q+2
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 3q+2
       101: 3q+2
       102: q^2+2q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       114: 2q
       115: 1
       116: q
       121: 1
       122: q
       123: 1
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: 1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 3q+2
       150: q+1
       151: q+2
       152: 2q
       153: q+2
       154: 2q
       155: q+1
       156: q^2+q
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       187: 1
       189: 1
       190: q
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: q+2
       210: 2q
       211: 1
       212: q
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       243: 2
       244: 2
       245: 2
       246: q+1
       247: 2
       248: 2
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       267: 1
       269: 1
       271: 1
       273: 1
       297: 1
       305: 1
       313: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       326: q
       337: 2
       347: 1
       349: 1
       351: 2
       355: 1
       357: 1
       359: 2
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       405: 1
       406: 1
       441: 1
       443: 1
       444: 1
       459: 1
       461: 1
       462: 1
       475: 1
       479: 2
       496: 1
       501: 1
       511: 1
       513: 1
       518: 1
       519: 1
       573: 1
       575: 1
       653: 1
       655: 1
       678: 1
       684: 1
       857: 1

 858:    0: 3q+2
         1: 3q+2
         2: q^2+2q+1
         3: 3q+2
         4: 3q+2
         5: 3q+2
         6: 3q+2
         7: q^2+2q+1
         8: q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2
        17: 2
        19: 3q+2
        20: 3q+2
        21: q^2+2q+1
        22: 3q+2
        23: 3q+2
        24: q^2+2q+1
        25: 3q+2
        26: 3q+2
        27: q^2+2q+1
        28: 2
        29: 3q+2
        30: q+1
        31: 3q+2
        32: q+1
        33: 2
        34: 3q+2
        35: q+1
        36: 2
        37: 2q
        38: q+2
        39: 2q
        40: q+2
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 2
        50: 2
        52: 3q+2
        53: 3q+2
        54: q^2+2q+1
        55: 3q+2
        56: 3q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2q
        63: q+2
        64: q
        65: 1
        67: 2
        70: q+1
        71: 2
        72: 2
        73: 2
        74: 2q
        75: q+2
        76: 2q
        77: q+2
        78: q^2+q
        79: q+1
        80: q+1
        81: 1
        82: 3q+2
        83: q+1
        84: q+1
        85: 1
        86: 3q+2
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: 3q+2
       101: 3q+2
       102: q^2+2q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       113: 2q
       114: q+2
       115: q
       116: 1
       121: q
       122: 1
       124: 1
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: q+1
       142: 2
       143: 1
       145: 2
       146: q+1
       147: 2
       148: 2
       149: 3q+2
       150: q+1
       151: 2q
       152: q+2
       153: 2q
       154: q+2
       155: q^2+q
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       188: 1
       189: q
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       209: 2q
       210: q+2
       211: q
       212: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       243: 2
       244: 2
       245: 2
       246: q+1
       247: 2
       248: 2
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       268: 1
       270: 1
       272: 1
       274: 1
       298: 1
       306: 1
       314: 1
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       325: q
       326: 1
       337: 2
       347: 1
       349: 1
       351: 2
       355: 1
       357: 1
       359: 2
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       407: 1
       408: 1
       442: 1
       443: 1
       444: 1
       460: 1
       461: 1
       462: 1
       476: 1
       480: 2
       496: 1
       501: 1
       511: 1
       513: 1
       518: 1
       519: 1
       574: 1
       576: 1
       654: 1
       656: 1
       678: 1
       684: 1
       858: 1

 859:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^3+3q^2+3q+1
         3: q^2+3q+2
         4: q^2+2q+2
         5: q^2+3q+2
         6: q^2+2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+2q+2
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+3q+2
        17: q^2+3q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: q^2+3q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       262: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       315: 1
       317: 1
       325: 1
       327: 1
       329: q+1
       331: 1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       360: 1
       364: 1
       366: 1
       368: 1
       371: 1
       374: 1
       376: 1
       411: 1
       415: 1
       417: 1
       423: 1
       427: 1
       467: 1
       469: 1
       485: 1
       494: 1
       498: 1
       502: 1
       506: 1
       510: 1
       515: 1
       518: 1
       587: 1
       637: 1
       658: 1
       666: 1
       690: 1
       859: 1

 860:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^3+3q^2+3q+1
         3: q^2+3q+2
         4: q^2+2q+2
         5: q^2+3q+2
         6: q^2+2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+2q+2
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+3q+2
        17: q^2+3q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: q^2+3q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 1
       101: 1
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       258: 1
       260: 1
       261: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       316: 1
       318: 1
       326: 1
       328: 1
       330: q+1
       332: 1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       361: 1
       365: 1
       366: 1
       368: 1
       371: 1
       374: 1
       376: 1
       412: 1
       416: 1
       418: 1
       424: 1
       428: 1
       468: 1
       470: 1
       486: 1
       494: 1
       498: 1
       503: 1
       507: 1
       510: 1
       515: 1
       518: 1
       588: 1
       638: 1
       659: 1
       667: 1
       690: 1
       860: 1

 861:    0: q^2+q+2
         1: q^2+q+2
         2: q+1
         3: q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^2+q+2
         7: q+1
         8: q^3+2q^2+2q+1
         9: q+1
        10: q^2+q+2
        11: q^2+q+2
        12: q^2+q+2
        13: 1
        14: 1
        15: q^2+q+1
        16: q^2+q+2
        17: q^2+q+2
        18: q+1
        19: q^2+q+2
        20: q^2+q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q^2+q+2
        29: q^2+q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: q^2+q+1
        46: 1
        47: q^2+q+1
        48: 1
        49: q^2+q+2
        50: q^2+q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: q^2+q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: q^2+q+1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       151: 1
       153: 1
       157: 1
       158: q^2+q+1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       209: 1
       213: 1
       215: 1
       217: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       237: 1
       239: 1
       243: 1
       247: 1
       248: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       257: 1
       259: 1
       262: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       317: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       362: 1
       372: 1
       375: 1
       411: 1
       415: 1
       417: 1
       423: 1
       427: 1
       487: 1
       494: 1
       498: 1
       504: 1
       516: 1
       519: 1
       587: 1
       660: 1
       668: 1
       691: 1
       861: 1

 862:    0: q^2+q+2
         1: q^2+q+2
         2: q+1
         3: q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^2+q+2
         7: q+1
         8: q^3+2q^2+2q+1
         9: q+1
        10: q^2+q+2
        11: q^2+q+2
        12: q^2+q+2
        13: 1
        14: 1
        15: q^2+q+1
        16: q^2+q+2
        17: q^2+q+2
        18: q+1
        19: q^2+q+2
        20: q^2+q+2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q^2+q+2
        29: q^2+q+2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: q^2+q+1
        46: 1
        47: q^2+q+1
        48: 1
        49: q^2+q+2
        50: q^2+q+2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: q^2+q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: q^2+q+1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       152: 1
       154: 1
       157: 1
       158: q^2+q+1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       210: 1
       214: 1
       216: 1
       218: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       238: 1
       240: 1
       243: 1
       247: 1
       248: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       257: 1
       260: 1
       261: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       318: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       363: 1
       372: 1
       375: 1
       412: 1
       416: 1
       418: 1
       424: 1
       428: 1
       488: 1
       494: 1
       498: 1
       505: 1
       516: 1
       519: 1
       588: 1
       661: 1
       669: 1
       691: 1
       862: 1

 863:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: 1
       102: q+1
       103: 1
       106: 1
       113: 1
       115: 1
       121: 1
       123: 1
       126: 1
       127: 1
       129: 1
       131: q+1
       134: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       177: 1
       179: 1
       189: 1
       207: 1
       209: 1
       211: 1
       213: 1
       217: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: 1
       249: q+1
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       281: 1
       287: 1
       315: 1
       317: 1
       325: 1
       327: 1
       331: 1
       342: q+1
       346: 1
       354: 1
       360: 1
       364: 1
       366: 1
       368: 1
       373: 1
       374: 1
       376: 1
       411: 1
       467: 1
       469: 1
       489: 1
       502: 1
       506: 1
       510: 1
       517: 1
       520: 1
       637: 1
       662: 1
       670: 1
       692: 1
       863: 1

 864:    0: 2
         1: 2
         2: q+1
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: 2
        11: 2
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 2
        17: 2
        18: q^2+2q+1
        19: 1
        20: 1
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 1
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        50: 1
        51: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q+1
        91: 1
        93: 1
        94: 1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: 1
       102: q+1
       104: 1
       105: 1
       114: 1
       116: 1
       122: 1
       124: 1
       126: 1
       128: 1
       130: 1
       132: q+1
       134: 1
       137: 1
       138: 1
       139: 1
       141: 1
       143: 1
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: 1
       159: 1
       160: 1
       162: 1
       163: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       178: 1
       180: 1
       190: 1
       208: 1
       210: 1
       212: 1
       214: 1
       218: 1
       221: 1
       226: 1
       228: 1
       231: 1
       233: 1
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: 1
       249: q+1
       250: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       282: 1
       288: 1
       316: 1
       318: 1
       326: 1
       328: 1
       332: 1
       343: q+1
       346: 1
       354: 1
       361: 1
       365: 1
       366: 1
       368: 1
       373: 1
       374: 1
       376: 1
       412: 1
       468: 1
       470: 1
       490: 1
       503: 1
       507: 1
       510: 1
       517: 1
       520: 1
       638: 1
       663: 1
       671: 1
       692: 1
       864: 1

 865:    0: 4q^2+14q+4
         1: 4q^2+14q+4
         2: q^3+6q^2+9q+4
         3: 4q^2+14q+4
         4: q^3+6q^2+9q+4
         5: 4q^2+14q+4
         6: q^3+6q^2+9q+4
         7: q^2+5q+4
         8: 2q^3+8q^2+10q+4
         9: q^2+5q+4
        10: 4q^2+14q+4
        11: 4q^2+14q+4
        12: q^3+6q^2+9q+4
        13: 2q^2+9q+4
        14: q^2+5q+4
        15: 3q^2+10q+4
        16: 4q^2+14q+4
        17: 4q^2+14q+4
        18: q^2+5q+4
        19: 2q^2+9q+4
        20: 2q^2+9q+4
        21: q^2+5q+4
        22: 10q+4
        23: 10q+4
        24: 3q^2+7q+4
        25: 10q+4
        26: 10q+4
        27: 3q^2+7q+4
        28: 4q^2+14q+4
        29: 2q^2+9q+4
        30: q^2+5q+4
        31: 10q+4
        32: 7q+4
        33: 10q+4
        34: 10q+4
        35: 7q+4
        36: 10q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+3q+2
        42: q^2+3q+2
        43: 2q^2+9q+4
        44: q^2+5q+4
        45: 3q^2+10q+4
        46: 2q^2+9q+4
        47: 3q^2+10q+4
        48: q^2+5q+4
        49: 2q^2+9q+4
        50: 2q^2+9q+4
        51: q^2+5q+4
        52: 5q+4
        53: 5q+4
        54: 3q+4
        55: 5q+4
        56: 5q+4
        57: 3q+4
        58: 5q+2
        59: 5q+2
        60: 5q+2
        61: 5q+2
        62: 4q+2
        63: 4q+2
        64: 3q+2
        65: 3q+2
        66: 4q+2
        67: 4q+2
        68: q^2+5q+4
        69: q^2+5q+4
        70: q^2+5q+4
        71: 2q^2+9q+4
        72: 2q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 7q+4
        81: 7q+4
        82: 5q+4
        83: 3q+4
        84: 7q+4
        85: 7q+4
        86: 5q+4
        87: 3q+4
        88: 2q^2+9q+4
        89: 3q^2+10q+4
        90: q^2+5q+4
        91: q+4
        92: q^2+5q+4
        93: q+4
        94: 5q+4
        95: 5q+4
        96: 3q+4
        97: 5q+4
        98: 5q+4
        99: 3q+4
       100: q+2
       101: q+2
       102: 2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2q+2
       118: 2q+2
       119: 2q+2
       120: 2q+2
       121: 3q+2
       122: 3q+2
       123: 3q+2
       124: 3q+2
       125: q^2+5q+4
       126: q^2+5q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q+4
       134: q+4
       135: 4
       136: 4
       137: 7q+4
       138: 3q+4
       139: 5q+4
       141: 3q+4
       142: 2q+4
       143: 7q+4
       144: 3q+4
       145: 5q+4
       146: 3q+4
       147: 2q+4
       149: q+2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+4
       158: q^2+5q+4
       159: q+4
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: q+2
       167: q+2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2q+2
       192: 2q+2
       195: q+2
       196: q+2
       199: 2q+2
       200: 2q+2
       201: q+2
       202: q+2
       207: 3q+2
       208: 3q+2
       209: 1
       210: 1
       211: 1
       212: 1
       219: q+4
       220: q+4
       221: q+4
       222: 4
       223: 4
       224: 4
       225: 4
       226: 3q+4
       227: 2
       228: 2
       230: 2
       231: 3q+4
       232: 2
       233: 2
       234: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+2
       246: 2
       247: 2
       248: 2
       250: 2
       251: 2q+2
       252: 2
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2
       284: 2
       285: 2
       286: 2
       287: q+2
       288: q+2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: q+4
       334: 4
       335: 4
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       345: 2
       346: 2
       349: 2
       350: 2
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       366: 2
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       427: 1
       428: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       469: 1
       470: 1
       484: 1
       492: 2
       494: 2
       497: 2
       498: 2
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       518: 1
       519: 1
       529: 1
       530: 1
       531: 1
       532: 1
       607: 1
       608: 1
       619: 1
       620: 1
       657: 1
       672: 1
       686: 1
       690: 1
       691: 1
       865: 1

 866:    0: 3q^2+8q+4
         1: q^3+4q^2+8q+4
         2: 3q^2+5q+4
         3: 3q^2+8q+4
         4: 3q^2+8q+4
         5: q^3+4q^2+8q+4
         6: q^3+4q^2+8q+4
         7: 3q^2+5q+4
         8: 2q^3+6q^2+6q+4
         9: 3q^2+5q+4
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: q^2+5q+4
        14: q^2+5q+4
        15: 3q^2+6q+4
        16: 3q^2+8q+4
        17: q^3+4q^2+8q+4
        18: 3q^2+5q+4
        19: 3q^2+8q+4
        20: q^3+4q^2+8q+4
        21: 3q^2+5q+4
        22: 4q+4
        23: 4q+4
        24: q^2+3q+4
        25: 4q+4
        26: 4q+4
        27: q^2+3q+4
        28: q^2+6q+4
        29: q^2+6q+4
        30: q^2+5q+4
        31: 2q+4
        32: 3q+4
        33: 4q+4
        34: 2q+4
        35: 3q+4
        36: 4q+4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 3q+4
        44: 3q+4
        45: 4q+4
        46: q^2+5q+4
        47: 3q^2+6q+4
        48: q^2+5q+4
        49: 3q^2+8q+4
        50: q^3+4q^2+8q+4
        51: 3q^2+5q+4
        52: 4q+4
        53: 4q+4
        54: q^2+3q+4
        55: 4q+4
        56: 4q+4
        57: q^2+3q+4
        58: q+2
        59: q+2
        60: q+2
        61: q+2
        62: 2
        63: 2
        64: q+2
        65: q+2
        66: q+2
        67: q+2
        68: q+4
        69: q^2+5q+4
        70: 3q+4
        71: q^2+6q+4
        72: 4q+4
        73: 4q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: q+4
        81: 3q+4
        82: 2q+4
        83: 3q+4
        84: q+4
        85: 3q+4
        86: 2q+4
        87: 3q+4
        88: 3q+4
        89: 4q+4
        90: 3q+4
        91: q^2+5q+4
        92: 3q^2+6q+4
        93: q^2+5q+4
        94: 4q+4
        95: 4q+4
        96: q^2+3q+4
        97: 4q+4
        98: 4q+4
        99: q^2+3q+4
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: 2
       114: 2
       115: q+2
       116: q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: q+2
       124: q+2
       125: q+4
       126: 3q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q+4
       134: q^2+5q+4
       135: 3q+4
       136: 3q+4
       137: q+4
       138: 3q+4
       139: 2q+4
       141: q+4
       142: 4q+4
       143: q+4
       144: 3q+4
       145: 2q+4
       146: q+4
       147: 4q+4
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 3q+4
       158: 4q+4
       159: 3q+4
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+2
       178: q+2
       179: 2
       180: 2
       181: q+2
       182: q+2
       183: 2
       184: 2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: 2
       190: 2
       191: 2
       192: 2
       195: q+2
       196: q+2
       199: 2
       200: 2
       201: q+2
       202: q+2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       219: q+4
       220: q+4
       221: 3q+4
       222: q+4
       223: 3q+4
       224: q+4
       225: 3q+4
       226: q+4
       227: 2
       228: q+2
       230: q+2
       231: q+4
       232: 2
       233: q+2
       234: q+2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       247: 2
       248: 2
       249: 2
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       283: 2
       284: 2
       285: 2
       286: 2
       287: 2
       288: 2
       291: q+2
       292: q+2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       350: q+2
       352: 2
       356: q+2
       366: 2
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       447: 1
       448: 1
       469: 1
       470: 1
       481: 2
       482: 2
       483: 2
       484: 1
       491: 1
       508: 1
       515: 1
       516: 1
       517: 1
       529: 1
       530: 1
       531: 1
       532: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       657: 1
       664: 1
       665: 1
       866: 1

 867:    0: 2q+4
         1: 2q+4
         2: 3q^2+3q+2
         3: 2q+4
         4: 2q+4
         5: 2q+4
         6: 2q+4
         7: 3q^2+3q+2
         8: 2q^2+2q+2
         9: 3q^2+3q+2
        10: 2q+4
        11: 2q+4
        12: 2q+4
        13: q+2
        14: q+2
        15: 2
        16: 2q+4
        17: 2q+4
        18: 3q^2+3q+2
        19: 2q+4
        20: 2q+4
        21: 3q^2+3q+2
        22: 4
        23: 4
        24: q^2+2q+2
        25: 4
        26: 4
        27: q^2+2q+2
        28: 2q+4
        29: 2q+4
        30: q+2
        31: 4
        32: 2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: 2
        46: q+2
        47: 2
        48: q+2
        49: 2q+4
        50: 2q+4
        51: 3q^2+3q+2
        52: 4
        53: 4
        54: q^2+2q+2
        55: 4
        56: 4
        57: q^2+2q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: q+2
        70: q+2
        71: 2q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 4
        83: 2
        84: 2
        85: 2
        86: 4
        87: 2
        88: q+2
        89: 2
        90: q+2
        91: q+2
        92: 2
        93: q+2
        94: 4
        95: 4
        96: q^2+2q+2
        97: 4
        98: 4
        99: q^2+2q+2
       100: 2
       101: 2
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       134: q+2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 4
       141: 2
       142: 4
       143: 2
       144: 2
       145: 4
       146: 2
       147: 4
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+2
       158: 2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: 2
       196: 2
       201: 2
       202: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2
       228: 1
       230: 1
       231: 2
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: 2
       246: 2
       247: 2
       248: 2
       249: 2q+2
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       334: 2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       366: 2
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       469: 1
       470: 1
       483: 2
       491: 1
       494: 1
       498: 1
       510: 1
       515: 1
       517: 1
       518: 1
       520: 1
       599: 1
       600: 1
       664: 1
       673: 1
       690: 1
       692: 1
       867: 1

 868:    0: q^2+3q+4
         1: q^2+3q+4
         2: q^2+3q+4
         3: 4q+4
         4: q^2+3q+4
         5: 4q+4
         6: q^2+3q+4
         7: q^2+3q+4
         8: 4q+4
         9: q^3+3q^2+3q+1
        10: q^2+3q+4
        11: 4q+4
        12: q^2+3q+4
        13: q^2+3q+4
        14: q^2+3q+4
        15: 4q+4
        16: q+4
        17: q+4
        18: q^2+3q+1
        19: q^2+3q+4
        20: q^2+3q+4
        21: q^2+3q+4
        22: q+4
        23: q+4
        24: q+4
        25: q+4
        26: q+4
        27: q+4
        28: q+4
        29: q^2+3q+4
        30: q^2+3q+4
        31: q+4
        32: q+4
        33: 4
        34: q+4
        35: q+4
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: 2
        42: 2
        43: q^2+3q+4
        44: q^2+3q+4
        45: 4q+4
        46: q+4
        47: q+4
        48: q^2+3q+1
        49: q+4
        50: q+4
        51: q^2+3q+1
        52: q+4
        53: q+4
        54: q+4
        55: q+4
        56: q+4
        57: q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: q+4
        69: q+1
        70: q^2+3q+4
        71: q+4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: 2
        79: 2
        80: q+4
        81: 4
        82: q+4
        83: q+4
        84: q+4
        85: 4
        86: q+4
        87: q+4
        88: q+4
        89: q+4
        90: q^2+3q+1
        91: q+4
        92: q+4
        93: q^2+3q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 2
       116: 2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       125: q+4
       126: q+1
       133: q+4
       134: q+1
       135: 4
       136: 4
       137: 4
       138: 1
       139: 2
       141: q+4
       142: 2
       143: 4
       144: 1
       145: 2
       146: q+4
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+4
       158: q+4
       159: q^2+3q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 2
       190: 2
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       219: q+1
       220: q+4
       221: q+1
       222: 4
       223: 1
       224: 4
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       325: 1
       326: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       385: 1
       386: 1
       387: 1
       388: 1
       439: 1
       440: 1
       453: 1
       454: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       518: 1
       519: 1
       520: 1
       665: 1
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       868: 1

 869:    0: 2q^2+12q+4
         1: 2q^2+12q+4
         2: q^3+4q^2+5q+2
         3: 2q^2+12q+4
         4: q^3+5q^2+8q+4
         5: 2q^2+12q+4
         6: q^3+5q^2+8q+4
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+12q+4
        11: 2q^2+12q+4
        12: q^3+5q^2+8q+4
        13: 3q+2
        14: q+2
        15: 3q+2
        16: 2q^2+12q+4
        17: 2q^2+12q+4
        18: q^2+3q+2
        19: q^2+8q+4
        20: q^2+8q+4
        21: q^2+3q+2
        22: 2q^2+12q+4
        23: 2q^2+12q+4
        24: q^3+4q^2+5q+2
        25: 8q+4
        26: 8q+4
        27: 2q^2+4q+2
        28: 2q^2+12q+4
        29: q^2+8q+4
        30: q+2
        31: 2q^2+12q+4
        32: 3q+2
        33: 2q^2+12q+4
        34: 8q+4
        35: 2q+2
        36: 8q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+2q+1
        42: q^2+2q+1
        43: 3q+2
        44: q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: q^2+8q+4
        50: q^2+8q+4
        51: q^2+3q+2
        52: q^2+8q+4
        53: q^2+8q+4
        54: q^2+3q+2
        55: 4q+4
        56: 4q+4
        57: 2q+2
        58: q^2+6q+2
        59: q^2+6q+2
        60: 4q+2
        61: 4q+2
        62: 4q+2
        63: 4q+2
        64: q+1
        65: q+1
        66: 4q+2
        67: 4q+2
        69: q+2
        70: q+2
        71: q^2+8q+4
        72: 2q+4
        73: 4q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: 3q+2
        81: 3q+2
        82: q^2+8q+4
        83: q+2
        84: 2q+2
        85: 2q+2
        86: 4q+4
        87: 2
        88: 3q+2
        89: 3q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: q^2+8q+4
        95: q^2+8q+4
        96: q^2+3q+2
        97: 4q+4
        98: 4q+4
        99: 2q+2
       100: 4q+4
       101: 4q+4
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       126: q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       134: 2
       135: 2
       136: 2
       137: 3q+2
       138: q+2
       139: q^2+8q+4
       140: 2q+4
       141: q+2
       142: 4q+4
       143: 2q+2
       144: 2
       145: 4q+4
       146: 2
       147: 2q+4
       149: 4q+4
       150: 2
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: 4q+4
       167: 4q+4
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       193: q+2
       194: q+2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       201: q+2
       202: q+2
       207: q+1
       208: q+1
       209: q+2
       210: q+2
       211: 1
       212: 1
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       228: 2
       229: 2
       230: 2
       231: 2
       233: 1
       234: 1
       236: 2
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+1
       242: q+1
       243: 4q+4
       244: 2q+4
       246: 2
       247: 4
       248: 4
       250: 2
       251: 2q+2
       252: 2
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       267: 1
       268: 1
       269: 1
       270: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       301: 2
       302: 2
       305: 1
       306: 1
       315: 1
       316: 1
       317: q+2
       318: q+2
       319: q+2
       320: q+2
       325: 1
       326: 1
       334: 2
       335: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       346: 2
       347: 2
       348: 2
       349: 2
       350: 2
       351: 4
       354: 1
       355: 1
       356: 1
       366: 2
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       390: 1
       391: 1
       392: 1
       423: 1
       424: 1
       427: 2
       428: 2
       433: 1
       434: 1
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       469: 1
       470: 1
       493: 2
       494: 2
       496: 1
       498: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       546: 1
       547: 1
       548: 1
       609: 1
       610: 1
       674: 1
       678: 1
       687: 1
       690: 1
       691: 1
       869: 1

 870:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        30: q+2
        32: q+2
        33: 2q+2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2q+2
        53: 2q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        64: 1
        65: 1
        66: 1
        67: 1
        69: q+2
        72: 2
        73: 2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: q+2
        83: q+2
        85: 2
        87: 2
        91: q+2
        92: q+2
        93: q+2
        94: 2q+2
        95: 2q+2
        96: q^2+q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+2
       135: 2
       136: q+2
       138: q+2
       140: 2
       142: 2q+2
       144: 2
       147: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       160: q+2
       161: q+2
       162: q+2
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       197: 1
       198: 1
       211: 1
       212: 1
       223: 2
       225: q+2
       228: q+2
       229: 2
       230: q+2
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 2
       247: 2
       248: 2
       249: 2
       256: 1
       257: 1
       258: 1
       291: 1
       292: 1
       301: 1
       302: 1
       305: 1
       306: 1
       315: 1
       316: 1
       336: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       348: 2
       350: q+2
       351: 2
       356: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       425: 1
       426: 1
       433: 1
       434: 1
       445: 1
       446: 1
       491: 1
       495: 2
       496: 1
       512: 1
       515: 1
       516: 1
       517: 1
       613: 1
       614: 1
       664: 1
       674: 1
       679: 1
       870: 1

 871:    0: 3q^2+8q+4
         1: q^3+4q^2+8q+4
         2: 3q^2+8q+4
         3: q^3+4q^2+8q+4
         4: 3q^2+8q+4
         5: 3q^2+8q+4
         6: q^3+4q^2+8q+4
         7: 3q^2+8q+4
         8: 3q^2+8q+4
         9: 2q^3+3q^2+3q+1
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: 3q^2+8q+4
        14: 3q^2+8q+4
        15: 3q^2+8q+4
        16: 4q+4
        17: 4q+4
        18: q^2+3q+1
        19: 3q^2+8q+4
        20: q^3+4q^2+8q+4
        21: 3q^2+8q+4
        22: 3q^2+8q+4
        23: q^3+4q^2+8q+4
        24: 3q^2+8q+4
        25: 4q+4
        26: 4q+4
        27: 4q+4
        28: 2q+4
        29: q^2+6q+4
        30: 3q^2+8q+4
        31: q^2+6q+4
        32: 3q^2+8q+4
        33: 4q+4
        34: 2q+4
        35: 4q+4
        36: 2q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+6q+4
        44: q^2+6q+4
        45: q^2+6q+4
        46: 4q+4
        47: 4q+4
        48: q^2+3q+1
        49: 4q+4
        50: 4q+4
        51: q^2+3q+1
        52: 3q^2+8q+4
        53: q^3+4q^2+8q+4
        54: 3q^2+8q+4
        55: 4q+4
        56: 4q+4
        57: 4q+4
        58: q+2
        59: q+2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 2q+4
        69: q+1
        70: q^2+6q+4
        71: 2q+4
        72: 2q+4
        73: 4q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: q^2+6q+4
        81: 4q+4
        82: q^2+6q+4
        83: 3q^2+8q+4
        84: 2q+4
        85: 2q+4
        86: 2q+4
        87: 4q+4
        88: 4
        89: 4
        90: 2q+1
        91: 4q+4
        92: 4q+4
        93: q^2+3q+1
        94: 4q+4
        95: 4q+4
        96: q^2+3q+1
        97: 2
        98: 2
        99: q+1
       100: 4q+4
       101: 4q+4
       102: 4q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: q+2
       118: q+2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: 2q+4
       134: q+1
       135: 2q+4
       136: 4q+4
       137: 4
       138: q+1
       139: 2q+4
       140: 2q+4
       141: q^2+6q+4
       142: 4q+4
       143: 4
       144: 1
       145: 2
       146: 2q+4
       147: 2
       149: 2q+4
       150: 4q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 4
       158: 4
       159: 2q+1
       160: 4q+4
       161: 4q+4
       162: q^2+3q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2
       192: 2
       193: 2
       194: 2
       195: q+2
       196: q+2
       197: q+2
       198: q+2
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       219: 1
       220: 4
       221: 1
       222: 4
       223: 1
       224: 4
       225: q+1
       226: 1
       227: 2q+4
       228: q+1
       229: 2q+4
       230: 4q+4
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 2
       244: 2
       246: 2q+4
       247: 2
       248: 2
       249: q+1
       250: 4
       251: 4
       252: 2q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       303: q+2
       304: q+2
       305: q+2
       306: q+2
       307: 1
       308: 1
       319: 1
       320: 1
       325: q+2
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 4
       346: 1
       347: 4
       348: 1
       349: 4
       350: q+1
       351: 2
       352: 1
       356: 1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       385: 1
       386: 1
       387: 1
       388: 1
       393: 1
       394: 1
       395: 1
       396: 1
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 1
       444: 1
       471: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       508: 1
       512: 1
       541: 1
       542: 1
       543: 1
       544: 1
       615: 1
       616: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       871: 1

 872:    0: 2q+4
         1: 2q+4
         2: q^2+3q+2
         3: 2q+4
         4: 2q+4
         5: 2q+4
         6: 2q+4
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: 2q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4
        17: 4
        18: q^2+2q+1
        19: 2q+4
        20: 2q+4
        21: q^2+3q+2
        22: 2q+4
        23: 2q+4
        24: q^2+3q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4
        29: 2q+4
        30: q+2
        31: 2q+4
        32: q+2
        33: 4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 4
        50: 4
        51: q^2+2q+1
        52: 2q+4
        53: 2q+4
        54: q^2+3q+2
        55: 4
        56: 4
        57: 2q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: q+2
        71: 4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: q+2
        81: 2
        82: 2q+4
        83: q+2
        84: 2
        85: 2
        86: 4
        87: 2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 4
        95: 4
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 4
       140: 4
       141: q+2
       142: 4
       143: 2
       144: 1
       145: 2
       146: 2
       147: 2
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       193: 2
       194: 2
       195: 2
       196: 2
       197: 2
       198: 2
       201: 1
       202: 1
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       228: 1
       229: 2
       230: 2
       231: 1
       233: 1
       234: 1
       236: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       267: 1
       268: 1
       269: 1
       270: 1
       297: 1
       298: 1
       305: 1
       306: 1
       319: 1
       320: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       441: 1
       442: 1
       443: 1
       444: 1
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       673: 1
       677: 1
       678: 1
       679: 1
       687: 1
       872: 1

 873:    0: 2q^2+12q+4
         1: 2q^2+12q+4
         2: q^3+4q^2+5q+2
         3: 2q^2+12q+4
         4: q^3+5q^2+8q+4
         5: 2q^2+12q+4
         6: q^3+5q^2+8q+4
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+12q+4
        11: 2q^2+12q+4
        12: q^3+5q^2+8q+4
        13: 3q+2
        14: q+2
        15: 3q+2
        16: 2q^2+12q+4
        17: 2q^2+12q+4
        18: q^2+3q+2
        19: q^2+8q+4
        20: q^2+8q+4
        21: q^2+3q+2
        22: 8q+4
        23: 8q+4
        24: 2q^2+4q+2
        25: 2q^2+12q+4
        26: 2q^2+12q+4
        27: q^3+4q^2+5q+2
        28: 2q^2+12q+4
        29: q^2+8q+4
        30: q+2
        31: 8q+4
        32: 2q+2
        33: 8q+4
        34: 2q^2+12q+4
        35: 3q+2
        36: 2q^2+12q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+2q+1
        42: q^2+2q+1
        43: 3q+2
        44: q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q+2
        49: q^2+8q+4
        50: q^2+8q+4
        51: q^2+3q+2
        52: 4q+4
        53: 4q+4
        54: 2q+2
        55: q^2+8q+4
        56: q^2+8q+4
        57: q^2+3q+2
        58: 4q+2
        59: 4q+2
        60: q^2+6q+2
        61: q^2+6q+2
        62: 4q+2
        63: 4q+2
        64: q+1
        65: q+1
        66: 4q+2
        67: 4q+2
        69: q+2
        70: q+2
        71: q^2+8q+4
        72: 4q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+1
        79: q+1
        80: 2q+2
        81: 2q+2
        82: 4q+4
        83: 2
        84: 3q+2
        85: 3q+2
        86: q^2+8q+4
        87: q+2
        88: 3q+2
        89: 3q+2
        90: q+2
        91: 2
        92: 2q+2
        93: 2
        94: 4q+4
        95: 4q+4
        96: 2q+2
        97: q^2+8q+4
        98: q^2+8q+4
        99: q^2+3q+2
       100: 4q+4
       101: 4q+4
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+2
       108: 2q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: 1
       116: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       126: q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       134: 2
       135: 2
       136: 2
       137: 2q+2
       138: 2
       139: 4q+4
       141: 2
       142: 2q+4
       143: 3q+2
       144: q+2
       145: q^2+8q+4
       146: q+2
       147: 4q+4
       148: 2q+4
       149: 4q+4
       150: 2
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: 4q+4
       167: 4q+4
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: q+2
       196: q+2
       201: 2q+2
       202: 2q+2
       203: q+2
       204: q+2
       205: 2
       206: 2
       207: q+1
       208: q+1
       209: q+2
       210: q+2
       211: 1
       212: 1
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2
       228: 1
       230: 1
       231: q+2
       233: 2
       234: 2
       235: 2
       236: 2
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+1
       242: q+1
       243: 4q+4
       245: 2q+4
       246: 2
       247: 4
       248: 4
       250: 1
       251: q+1
       252: 1
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       271: 1
       272: 1
       273: 1
       274: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       311: 2
       312: 2
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+2
       318: q+2
       321: q+2
       322: q+2
       325: 1
       326: 1
       334: 2
       335: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       346: 1
       349: 1
       350: 1
       354: 2
       355: 2
       356: 2
       357: 2
       358: 2
       359: 4
       366: 2
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       397: 1
       398: 1
       399: 1
       400: 1
       423: 1
       424: 1
       427: 2
       428: 2
       451: 1
       452: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: 1
       470: 1
       494: 1
       498: 2
       499: 2
       501: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       561: 1
       562: 1
       563: 1
       564: 1
       625: 1
       626: 1
       680: 1
       684: 1
       688: 1
       690: 1
       691: 1
       873: 1

 874:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: 2q+2
        26: 2q+2
        27: q^2+q+2
        30: q+2
        32: 2
        33: 2
        35: q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2
        53: 2
        54: 2
        55: 2q+2
        56: 2q+2
        57: q^2+q+2
        64: 1
        65: 1
        66: 1
        67: 1
        69: q+2
        72: 2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        81: 2
        83: 2
        85: q+2
        87: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 2
        95: 2
        96: 2
        97: 2q+2
        98: 2q+2
        99: q^2+q+2
       100: 2
       101: 2
       102: 2
       111: 1
       112: 1
       115: 1
       116: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+2
       135: q+2
       136: 2
       138: 2
       142: 2
       144: q+2
       147: 2q+2
       148: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: q+2
       164: q+2
       165: q+2
       166: 2
       167: 2
       168: 2
       177: 1
       178: 1
       181: 1
       182: 1
       187: 1
       188: 1
       205: 1
       206: 1
       211: 1
       212: 1
       223: q+2
       225: 2
       228: 1
       230: 1
       233: q+2
       234: q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       245: 2
       247: 2
       248: 2
       249: 2
       256: 1
       257: 1
       258: 1
       291: 1
       292: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       336: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       350: 1
       356: q+2
       358: 2
       359: 2
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       425: 1
       426: 1
       451: 1
       452: 1
       463: 1
       464: 1
       491: 1
       500: 2
       501: 1
       514: 1
       515: 1
       516: 1
       517: 1
       629: 1
       630: 1
       664: 1
       680: 1
       685: 1
       874: 1

 875:    0: 3q^2+8q+4
         1: q^3+4q^2+8q+4
         2: 3q^2+8q+4
         3: q^3+4q^2+8q+4
         4: 3q^2+8q+4
         5: 3q^2+8q+4
         6: q^3+4q^2+8q+4
         7: 3q^2+8q+4
         8: 3q^2+8q+4
         9: 2q^3+3q^2+3q+1
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: 3q^2+8q+4
        14: 3q^2+8q+4
        15: 3q^2+8q+4
        16: 4q+4
        17: 4q+4
        18: q^2+3q+1
        19: 3q^2+8q+4
        20: q^3+4q^2+8q+4
        21: 3q^2+8q+4
        22: 4q+4
        23: 4q+4
        24: 4q+4
        25: 3q^2+8q+4
        26: q^3+4q^2+8q+4
        27: 3q^2+8q+4
        28: 2q+4
        29: q^2+6q+4
        30: 3q^2+8q+4
        31: 2q+4
        32: 4q+4
        33: 2q+4
        34: q^2+6q+4
        35: 3q^2+8q+4
        36: 4q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+6q+4
        44: q^2+6q+4
        45: q^2+6q+4
        46: 4q+4
        47: 4q+4
        48: q^2+3q+1
        49: 4q+4
        50: 4q+4
        51: q^2+3q+1
        52: 4q+4
        53: 4q+4
        54: 4q+4
        55: 3q^2+8q+4
        56: q^3+4q^2+8q+4
        57: 3q^2+8q+4
        58: 2
        59: 2
        60: q+2
        61: q+2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 2q+4
        69: q+1
        70: q^2+6q+4
        71: 2q+4
        72: 4q+4
        73: 2q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: 2q+4
        81: 2q+4
        82: 2q+4
        83: 4q+4
        84: q^2+6q+4
        85: 4q+4
        86: q^2+6q+4
        87: 3q^2+8q+4
        88: 4
        89: 4
        90: 2q+1
        91: 4q+4
        92: 4q+4
        93: q^2+3q+1
        94: 2
        95: 2
        96: q+1
        97: 4q+4
        98: 4q+4
        99: q^2+3q+1
       100: 4q+4
       101: 4q+4
       102: 4q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: 2
       110: 2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 2
       118: 2
       119: q+2
       120: q+2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 4
       126: 1
       133: 2q+4
       134: q+1
       135: 4q+4
       136: 2q+4
       137: 4
       138: 1
       139: 2
       141: 2q+4
       142: 2
       143: 4
       144: q+1
       145: 2q+4
       146: q^2+6q+4
       147: 4q+4
       148: 2q+4
       149: 2q+4
       150: 4q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 4
       158: 4
       159: 2q+1
       160: 2
       161: 2
       162: q+1
       163: 4q+4
       164: 4q+4
       165: q^2+3q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: q+2
       184: q+2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       201: q+2
       202: q+2
       203: 2
       204: 2
       205: q+2
       206: q+2
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       219: 1
       220: 4
       221: 1
       222: 4
       223: q+1
       224: 4
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2q+4
       233: q+1
       234: 4q+4
       235: 2q+4
       236: 1
       243: 2
       245: 2
       246: 2q+4
       247: 2
       248: 2
       249: q+1
       253: 4
       254: 4
       255: 2q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: q+2
       308: q+2
       309: 2
       310: 2
       313: q+2
       314: q+2
       321: 1
       322: 1
       325: q+2
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       350: 1
       352: 1
       353: 4
       354: 1
       355: 4
       356: q+1
       357: 4
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       385: 1
       386: 1
       387: 1
       388: 1
       401: 1
       402: 1
       403: 1
       404: 1
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 1
       462: 1
       473: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       514: 1
       557: 1
       558: 1
       559: 1
       560: 1
       631: 1
       632: 1
       665: 1
       681: 1
       682: 1
       683: 1
       685: 1
       875: 1

 876:    0: 2q+4
         1: 2q+4
         2: q^2+3q+2
         3: 2q+4
         4: 2q+4
         5: 2q+4
         6: 2q+4
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: 2q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4
        17: 4
        18: q^2+2q+1
        19: 2q+4
        20: 2q+4
        21: q^2+3q+2
        22: 4
        23: 4
        24: 2q+2
        25: 2q+4
        26: 2q+4
        27: q^2+3q+2
        28: 4
        29: 2q+4
        30: q+2
        31: 4
        32: 2
        33: 4
        34: 2q+4
        35: q+2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 4
        50: 4
        51: q^2+2q+1
        52: 4
        53: 4
        54: 2q+2
        55: 2q+4
        56: 2q+4
        57: q^2+3q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: 1
        70: q+2
        71: 4
        72: 4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 4
        83: 2
        84: q+2
        85: 2
        86: 2q+4
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 4
        98: 4
        99: q^2+2q+1
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: 2
       142: 2
       143: 2
       144: 1
       145: 4
       146: q+2
       147: 4
       148: 4
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: 1
       190: 1
       195: 1
       196: 1
       201: 2
       202: 2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       271: 1
       272: 1
       273: 1
       274: 1
       297: 1
       298: 1
       313: 1
       314: 1
       321: 1
       322: 1
       325: 1
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2
       346: 1
       349: 1
       350: 1
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       459: 1
       460: 1
       461: 1
       462: 1
       483: 1
       491: 1
       494: 1
       498: 1
       499: 1
       500: 1
       501: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       673: 1
       683: 1
       684: 1
       685: 1
       688: 1
       876: 1

 877:    0: 2q+4
         1: 2q+4
         2: 2q+4
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+3q+2
         8: 2q+4
         9: q^3+2q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2q+4
        14: q^2+3q+2
        15: 2q+4
        16: 4
        17: 4
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q+2
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: q+2
        30: q+2
        31: 2q+4
        32: 2q+4
        33: 4
        34: 2q+4
        35: 2q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 2q+4
        44: q^2+3q+2
        45: 2q+4
        46: 4
        47: 4
        48: q^2+2q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: 4
        69: 1
        70: q+2
        71: 2
        72: 2
        80: 2q+4
        81: 4
        82: q+2
        83: q+2
        84: 2q+4
        85: 4
        86: q+2
        87: q+2
        88: 4
        89: 4
        90: q^2+2q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 2
       134: 1
       135: 2
       137: 4
       138: 1
       139: 2
       140: 2
       141: q+2
       143: 4
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 1
       184: 1
       191: 2
       192: 2
       193: 1
       194: 1
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       226: 1
       227: 2
       228: 1
       229: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 2
       244: 2
       246: q+2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 1
       294: 1
       299: 1
       300: 1
       307: 1
       308: 1
       319: 1
       320: 1
       333: 1
       334: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       366: 1
       367: 2
       368: 1
       369: 2
       374: 2
       375: 2
       376: q+1
       437: 1
       438: 1
       453: 1
       454: 1
       471: 1
       472: 1
       481: 1
       492: 1
       493: 1
       497: 1
       498: 1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       647: 1
       648: 1
       675: 1
       681: 1
       686: 1
       687: 1
       877: 1

 878:    0: 2q+4
         1: 2q+4
         2: 2q+4
         3: 2q+4
         4: q^2+3q+2
         5: 2q+4
         6: q^2+3q+2
         7: q^2+3q+2
         8: 2q+4
         9: q^3+2q^2+2q+1
        10: 2q+4
        11: 2q+4
        12: q^2+3q+2
        13: 2q+4
        14: q^2+3q+2
        15: 2q+4
        16: 4
        17: 4
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q+2
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: q+2
        30: q+2
        31: 2q+4
        32: 2q+4
        33: 4
        34: 2q+4
        35: 2q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 2q+4
        44: q^2+3q+2
        45: 2q+4
        46: 4
        47: 4
        48: q^2+2q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: 4
        69: 1
        70: q+2
        71: 2
        73: 2
        80: 2q+4
        81: 4
        82: q+2
        83: q+2
        84: 2q+4
        85: 4
        86: q+2
        87: q+2
        88: 4
        89: 4
        90: q^2+2q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       103: 1
       104: 1
       105: 1
       106: 1
       109: 1
       110: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 2
       134: 1
       136: 2
       137: 4
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4
       144: 1
       145: 2
       146: q+2
       148: 2
       149: q+2
       150: q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       185: 1
       186: 1
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       203: 1
       204: 1
       207: 2
       208: 2
       219: 1
       220: 2
       221: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       235: 2
       236: 1
       243: 2
       245: 2
       246: q+2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       295: 1
       296: 1
       303: 1
       304: 1
       309: 1
       310: 1
       321: 1
       322: 1
       333: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       357: 2
       358: 1
       366: 1
       367: 2
       368: 1
       370: 2
       374: 2
       375: 2
       376: q+1
       439: 1
       440: 1
       457: 1
       458: 1
       473: 1
       474: 1
       482: 1
       492: 1
       494: 1
       497: 1
       499: 1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       649: 1
       650: 1
       676: 1
       682: 1
       686: 1
       688: 1
       878: 1

 879:    0: 2q^2+12q+4
         1: 2q^2+12q+4
         2: 4q^2+6q+2
         3: 2q^2+12q+4
         4: q^3+5q^2+8q+4
         5: 2q^2+12q+4
         6: q^3+5q^2+8q+4
         7: 2q^3+3q^2+5q+2
         8: 4q^2+6q+2
         9: 3q^3+3q^2+3q+1
        10: 2q^2+12q+4
        11: 2q^2+12q+4
        12: q^3+5q^2+8q+4
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 8q+4
        17: 8q+4
        18: q^3+2q^2+3q+1
        19: q^2+8q+4
        20: q^2+8q+4
        21: 2q^2+5q+2
        22: 2q^2+12q+4
        23: 2q^2+12q+4
        24: 4q^2+6q+2
        25: 2q^2+12q+4
        26: 2q^2+12q+4
        27: 4q^2+6q+2
        28: 8q+4
        29: q^2+8q+4
        30: 3q+2
        31: 2q^2+12q+4
        32: 4q+2
        33: 8q+4
        34: 2q^2+12q+4
        35: 4q+2
        36: 8q+4
        37: q^2+6q+2
        38: q^2+6q+2
        39: q^2+6q+2
        40: q^2+6q+2
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 4q+4
        50: 4q+4
        51: q^2+3q+1
        52: q^2+8q+4
        53: q^2+8q+4
        54: 2q^2+5q+2
        55: q^2+8q+4
        56: q^2+8q+4
        57: 2q^2+5q+2
        58: 4q+2
        59: 4q+2
        60: 4q+2
        61: 4q+2
        62: q^2+6q+2
        63: q^2+6q+2
        64: 2q+1
        65: 2q+1
        66: 4q+2
        67: 4q+2
        69: q+1
        70: 3q+2
        71: 4q+4
        72: 2q+4
        73: 2q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+1
        79: 2q+1
        80: 4q+2
        81: 2q+2
        82: q^2+8q+4
        83: 3q+2
        84: 4q+2
        85: 2q+2
        86: q^2+8q+4
        87: 3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2
        92: 2
        93: q+1
        94: 4q+4
        95: 4q+4
        96: q^2+3q+1
        97: 4q+4
        98: 4q+4
        99: q^2+3q+1
       100: q^2+8q+4
       101: q^2+8q+4
       102: 2q^2+5q+2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: 2q+2
       114: 2q+2
       115: q+1
       116: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       126: q+1
       134: 1
       135: 2
       136: 2
       137: 2q+2
       138: q+1
       139: 4q+4
       140: 2q+4
       141: 3q+2
       142: 2q+4
       143: 2q+2
       144: q+1
       145: 4q+4
       146: 3q+2
       147: 2q+4
       148: 2q+4
       149: q^2+8q+4
       150: 3q+2
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+1
       156: 2q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 4q+4
       167: 4q+4
       168: q^2+3q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       193: q+2
       194: q+2
       195: q+2
       196: q+2
       197: 2
       198: 2
       201: q+2
       202: q+2
       203: q+2
       204: q+2
       205: 2
       206: 2
       207: q+1
       208: q+1
       209: 2q+2
       210: 2q+2
       211: q+1
       212: q+1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: q+1
       228: 1
       229: 2
       230: 2
       231: q+1
       233: 1
       234: 2
       235: 2
       236: q+1
       243: 4q+4
       244: 2q+4
       245: 2q+4
       246: 3q+2
       247: 4
       248: 4
       249: 2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       297: 1
       298: 1
       305: 1
       306: 1
       313: 1
       314: 1
       319: q+2
       320: q+2
       321: q+2
       322: q+2
       323: 2
       324: 2
       325: q+1
       326: q+1
       334: 1
       335: 1
       336: 1
       337: 4
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 4
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 4
       366: q+1
       368: 1
       369: 2
       370: 2
       374: 2
       375: 2
       376: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       441: 1
       442: 1
       443: 2
       444: 2
       459: 1
       460: 1
       461: 2
       462: 2
       475: 1
       476: 1
       479: 2
       480: 2
       483: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       573: 1
       574: 1
       575: 1
       576: 1
       653: 1
       654: 1
       677: 1
       683: 1
       687: 1
       688: 1
       689: 1
       879: 1

 880:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: 2q+2
         8: 2q+2
         9: q^3+q^2+q+1
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2
        17: 2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        30: 2q+2
        32: 2q+2
        33: 2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        64: q+1
        65: q+1
        66: 1
        67: 1
        69: 1
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        81: 2
        83: 2q+2
        85: 2
        87: 2q+2
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       111: 1
       112: 1
       115: q+1
       116: q+1
       123: 1
       124: 1
       134: 1
       135: 2
       136: 2
       138: 1
       140: 2
       142: 2
       144: 1
       147: 2
       148: 2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       187: 1
       188: 1
       197: 1
       198: 1
       205: 1
       206: 1
       211: q+1
       212: q+1
       223: 1
       225: 1
       228: 1
       229: 2
       230: 2
       233: 1
       234: 2
       235: 2
       236: 1
       244: 2
       245: 2
       247: 2
       248: 2
       249: q+1
       256: 2
       257: 2
       258: q+1
       305: 1
       306: 1
       313: 1
       314: 1
       323: 1
       324: 1
       336: 1
       348: 1
       350: 1
       351: 2
       356: 1
       358: 1
       359: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       475: 1
       476: 1
       479: 1
       480: 1
       491: 1
       495: 1
       496: 2
       500: 1
       501: 2
       512: 1
       514: 1
       655: 1
       656: 1
       679: 1
       685: 1
       689: 1
       880: 1

 881:    0: 4q^3+15q^2+18q+4
         1: 3q^3+17q^2+18q+4
         2: 4q^3+15q^2+18q+4
         3: 3q^3+17q^2+18q+4
         4: 11q^2+13q+4
         5: 2q^3+13q^2+18q+4
         6: 5q^3+14q^2+13q+4
         7: 11q^2+13q+4
         8: 2q^3+13q^2+18q+4
         9: 3q^3+8q^2+7q+2
        10: q^3+8q^2+16q+4
        11: 7q^2+16q+4
        12: 8q^2+11q+4
        13: 4q^3+15q^2+18q+4
        14: 11q^2+13q+4
        15: 2q^3+13q^2+18q+4
        16: q^3+8q^2+16q+4
        17: 7q^2+16q+4
        18: 6q^2+7q+2
        19: 7q^2+13q+4
        20: q^3+10q^2+13q+4
        21: 7q^2+13q+4
        22: q^3+7q^2+14q+4
        23: 10q^2+14q+4
        24: q^3+7q^2+14q+4
        25: q^3+7q^2+14q+4
        26: 10q^2+14q+4
        27: q^3+7q^2+14q+4
        28: 3q^2+14q+4
        29: 4q^2+11q+4
        30: 7q^2+13q+4
        31: 3q^2+12q+4
        32: q^3+7q^2+14q+4
        33: 3q^2+12q+4
        34: 3q^2+12q+4
        35: q^3+7q^2+14q+4
        36: 3q^2+12q+4
        37: 2q^2+6q+2
        38: 2q^2+6q+2
        39: 4q^2+6q+2
        40: 4q^2+6q+2
        41: 2q^2+6q+2
        42: 2q^2+6q+2
        43: q^3+8q^2+16q+4
        44: 8q^2+11q+4
        45: 7q^2+16q+4
        46: q^3+8q^2+16q+4
        47: 7q^2+16q+4
        48: 6q^2+7q+2
        49: 2q^2+11q+4
        50: 3q^2+11q+4
        51: 4q^2+7q+2
        52: 2q^2+9q+4
        53: 5q^2+9q+4
        54: 2q^2+9q+4
        55: 2q^2+9q+4
        56: 5q^2+9q+4
        57: 2q^2+9q+4
        58: 5q+2
        59: 5q+2
        60: 5q+2
        61: 5q+2
        62: q^2+5q+2
        63: q^2+5q+2
        64: 2q^2+6q+2
        65: 2q^2+6q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 3q^2+14q+4
        69: q^2+5q+2
        70: 4q^2+11q+4
        71: q^2+9q+4
        72: 4q+4
        73: 4q+4
        74: 3q+2
        75: 3q+2
        76: q^2+3q+2
        77: q^2+3q+2
        78: 3q+2
        79: 3q+2
        80: 3q^2+12q+4
        81: 3q^2+12q+4
        82: q^2+7q+4
        83: 2q^2+9q+4
        84: 3q^2+12q+4
        85: 3q^2+12q+4
        86: q^2+7q+4
        87: 2q^2+9q+4
        88: q^2+9q+4
        89: q^2+9q+4
        90: 3q^2+5q+2
        91: 2q^2+11q+4
        92: 3q^2+11q+4
        93: 4q^2+7q+2
        94: 6q+4
        95: q^2+6q+4
        96: q^2+4q+2
        97: 6q+4
        98: q^2+6q+4
        99: q^2+4q+2
       100: 5q+2
       101: q^2+3q+2
       102: 5q+2
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: 2q+2
       114: 2q+2
       115: 3q+2
       116: 3q+2
       117: 5q+2
       118: 5q+2
       119: 5q+2
       120: 5q+2
       121: q^2+5q+2
       122: q^2+5q+2
       123: q^2+5q+2
       124: q^2+5q+2
       125: q^2+9q+4
       126: 3q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       133: q^2+9q+4
       134: q^2+5q+2
       135: 4q+4
       136: 4q+4
       137: 6q+4
       138: 2q+2
       139: 5q+4
       141: q^2+7q+4
       142: 3q+4
       143: 6q+4
       144: 2q+2
       145: 5q+4
       146: q^2+7q+4
       147: 3q+4
       149: 3q+2
       150: 5q+2
       151: 2q+1
       152: 2q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 3q+4
       158: 3q+4
       159: q^2+3q+2
       160: 6q+4
       161: q^2+6q+4
       162: q^2+4q+2
       163: 6q+4
       164: q^2+6q+4
       165: q^2+4q+2
       166: 2q+2
       167: q+2
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: q+2
       184: q+2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: 2q+2
       190: 2q+2
       191: 3q+2
       192: 3q+2
       195: q+2
       196: q+2
       199: 3q+2
       200: 3q+2
       201: q+2
       202: q+2
       207: 2q+2
       208: 2q+2
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+1
       218: q+1
       219: 3q+2
       220: 3q+4
       221: q+2
       222: 4
       223: q+2
       224: 4
       225: q+2
       226: q+2
       227: 5q+4
       228: 2q+2
       230: 3q+4
       231: q+2
       232: 5q+4
       233: 2q+2
       234: 3q+4
       236: q+2
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: q+2
       246: 3q+2
       247: q+2
       248: 2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 2q+2
       257: q+2
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: q+2
       304: q+2
       307: q+2
       308: q+2
       315: 1
       316: 1
       317: 1
       318: 1
       325: q+1
       326: q+1
       333: q+2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: q+2
       345: q+2
       346: 1
       349: 2
       350: q+2
       352: q+2
       353: q+2
       354: 1
       355: 2
       356: q+2
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       366: 2
       367: q+2
       368: q+2
       371: q+2
       372: 2
       374: 1
       375: 1
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       427: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: 1
       494: 1
       497: 1
       498: 1
       508: 2
       509: 1
       510: 1
       515: 2
       518: 1
       519: 1
       585: 1
       586: 1
       601: 1
       602: 1
       639: 1
       640: 1
       658: 1
       659: 1
       672: 1
       676: 1
       681: 1
       686: 1
       690: 1
       881: 1

 882:    0: q^2+10q+4
         1: q^3+7q^2+10q+4
         2: q^2+10q+4
         3: q^3+7q^2+10q+4
         4: q^2+10q+4
         5: q^3+6q^2+10q+4
         6: q^3+7q^2+10q+4
         7: q^2+10q+4
         8: q^3+6q^2+10q+4
         9: 2q^2+4q+2
        10: q^2+8q+4
        11: 3q^2+8q+4
        12: q^2+8q+4
        13: q^2+10q+4
        14: q^2+10q+4
        15: q^3+6q^2+10q+4
        16: q^2+8q+4
        17: 3q^2+8q+4
        18: 4q+2
        19: q^2+10q+4
        20: q^3+7q^2+10q+4
        21: q^2+10q+4
        22: 6q+4
        23: 2q^2+6q+4
        24: 6q+4
        25: 6q+4
        26: 2q^2+6q+4
        27: 6q+4
        28: q^2+6q+4
        29: q^2+8q+4
        30: q^2+10q+4
        31: 4q+4
        32: 6q+4
        33: 4q+4
        34: 4q+4
        35: 6q+4
        36: 4q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+8q+4
        44: q^2+8q+4
        45: 3q^2+8q+4
        46: q^2+8q+4
        47: 3q^2+8q+4
        48: 4q+2
        49: q^2+8q+4
        50: 3q^2+8q+4
        51: 4q+2
        52: 6q+4
        53: 2q^2+6q+4
        54: 6q+4
        55: 6q+4
        56: 2q^2+6q+4
        57: 6q+4
        58: q+2
        59: q+2
        60: q+2
        61: q+2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: q^2+6q+4
        69: 2q+2
        70: q^2+8q+4
        71: q^2+6q+4
        72: 4q+4
        73: 4q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: 4q+4
        81: 4q+4
        82: 4q+4
        83: 6q+4
        84: 4q+4
        85: 4q+4
        86: 4q+4
        87: 6q+4
        88: 2q+4
        89: 2q+4
        90: 2q+2
        91: q^2+8q+4
        92: 3q^2+8q+4
        93: 4q+2
        94: 3q+4
        95: 3q+4
        96: 3q+2
        97: 3q+4
        98: 3q+4
        99: 3q+2
       100: 2
       101: 2q+2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: q+2
       118: q+2
       119: q+2
       120: q+2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 2q+4
       126: 2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       133: q^2+6q+4
       134: 2q+2
       135: 4q+4
       136: 4q+4
       137: 4
       138: q+2
       139: 2q+4
       141: 4q+4
       142: 3q+4
       143: 4
       144: q+2
       145: 2q+4
       146: 4q+4
       147: 3q+4
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 2q+4
       158: 2q+4
       159: 2q+2
       160: 3q+4
       161: 3q+4
       162: 3q+2
       163: 3q+4
       164: 3q+4
       165: 3q+2
       166: 2
       167: q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       183: q+2
       184: q+2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: q+2
       196: q+2
       199: 2
       200: 2
       201: q+2
       202: q+2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       213: 2
       214: 2
       215: 2
       216: 2
       217: q+1
       218: q+1
       219: 2
       220: 2q+4
       221: 2
       222: 4
       223: q+2
       224: 4
       225: q+2
       226: 2
       227: 2q+4
       228: q+2
       230: 3q+4
       231: 2
       232: 2q+4
       233: q+2
       234: 3q+4
       237: 1
       238: 1
       239: 1
       240: 1
       243: 2
       246: 2
       247: 2
       248: q+2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2
       280: 2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: q+2
       304: q+2
       307: q+2
       308: q+2
       317: 1
       318: 1
       325: 1
       326: 1
       333: 2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       345: 2
       346: 1
       349: 2
       350: q+2
       352: 2
       353: 2
       354: 1
       355: 2
       356: q+2
       360: 1
       361: 1
       362: 1
       363: 1
       367: 2
       371: 2
       372: q+2
       374: 1
       375: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       427: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       466: 1
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: 1
       494: 1
       497: 1
       498: 1
       509: 1
       516: 2
       518: 1
       519: 1
       585: 1
       586: 1
       601: 1
       602: 1
       660: 1
       661: 1
       672: 1
       676: 1
       681: 1
       691: 1
       882: 1

 883:    0: 2q+4
         1: 2q+4
         2: 2q+4
         3: 2q+4
         4: 3q^2+3q+2
         5: 2q+4
         6: 2q^2+2q+2
         7: 3q^2+3q+2
         8: 2q+4
         9: 3q^2+3q+2
        10: 4
        11: 4
        12: q^2+2q+2
        13: 2q+4
        14: 3q^2+3q+2
        15: 2q+4
        16: 2q+4
        17: 2q+4
        18: 3q^2+3q+2
        19: q+2
        20: 2
        21: q+2
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: 2
        30: q+2
        31: 4
        32: 2q+4
        33: 2q+4
        34: 4
        35: 2q+4
        36: 2q+4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: 4
        44: q^2+2q+2
        45: 4
        46: 2q+4
        47: 2q+4
        48: 3q^2+3q+2
        49: q+2
        50: 2
        51: q+2
        52: q+2
        53: 2
        54: q+2
        55: q+2
        56: 2
        57: q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: q+2
        65: q+2
        66: q+2
        67: q+2
        68: 4
        69: q+2
        70: 2
        71: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 4
        81: 2q+4
        82: 2
        83: q+2
        84: 4
        85: 2q+4
        86: 2
        87: q+2
        88: 4
        89: 4
        90: q^2+2q+2
        91: q+2
        92: 2
        93: q+2
        94: q+2
        95: 2
        96: q+2
        97: q+2
        98: 2
        99: q+2
       100: q+2
       101: 2
       102: q+2
       103: 1
       104: 1
       105: 1
       106: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: q+2
       124: q+2
       125: 4
       126: 2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q+2
       137: 4
       138: q+2
       139: 2
       141: 2
       143: 4
       144: q+2
       145: 2
       146: 2
       149: 2
       150: q+2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: q+2
       161: 2
       162: q+2
       163: q+2
       164: 2
       165: q+2
       166: q+2
       167: 2
       168: q+2
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       189: 1
       190: 1
       191: 2
       192: 2
       199: 2
       200: 2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 2
       220: 1
       221: 1
       226: 2
       227: 2
       228: q+2
       231: 2
       232: 2
       233: q+2
       236: q+2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       249: 2
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+2
       257: 2
       258: q+2
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       287: 1
       288: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: 1
       342: 1
       343: 1
       344: 2
       345: 1
       346: 1
       352: 2
       353: 1
       354: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: q+2
       373: 2
       374: 1
       375: 1
       376: 1
       413: 1
       414: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       489: 1
       490: 1
       492: 1
       497: 1
       508: 2
       509: 1
       510: 1
       517: 2
       520: 1
       639: 1
       640: 1
       662: 1
       663: 1
       686: 1
       692: 1
       883: 1

 884:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       193: 1
       195: 1
       197: 1
       201: 1
       203: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       271: 1
       279: 1
       289: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       381: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       427: 1
       435: 1
       443: 1
       445: 1
       455: 1
       461: 1
       463: 1
       465: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       537: 1
       545: 1
       553: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       601: 1
       615: 1
       617: 1
       631: 1
       633: 1
       651: 1
       655: 1
       693: 1
       733: 1
       749: 1
       757: 1
       765: 1
       769: 1
       884: 1

 885:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q
        33: 3q
        34: 3q
        35: 3q
        36: 3q
        37: q
        38: 2q
        39: q^2+q
        40: 2q^2+2q
        41: q
        42: 2q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: 2q
        59: q
        60: 2q
        61: q
        62: q
        63: 2q
        64: q
        65: 2q
        66: q
        67: 2q
        68: 3q
        70: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: 3q
        81: 3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q
        86: 2q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       104: q
       105: q
       107: q
       109: q
       114: q
       116: q
       117: 2q
       118: q
       119: 2q
       120: q
       121: q
       122: 2q
       123: q
       124: 2q
       128: q
       130: q
       133: 2q
       135: q
       136: q
       139: 2q
       140: q
       141: 2q
       142: q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       152: q
       154: q^2+q
       156: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       174: q
       175: q
       180: q
       183: q
       185: q
       190: q
       193: q
       195: q
       201: q
       203: q
       210: q
       212: q
       214: q
       216: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q
       280: q
       299: q
       303: q
       307: q
       309: q
       318: q
       319: q
       321: q
       326: q
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       361: q
       363: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       428: 1
       443: 1
       446: 1
       461: 1
       464: 1
       466: q
       471: q
       473: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       546: 1
       562: 1
       573: 1
       578: 1
       602: 1
       615: 1
       618: 1
       631: 1
       634: 1
       655: 1
       694: 1
       734: 1
       750: 1
       765: 1
       770: 1
       885: 1

 886:    0: q^3+q
         1: q^4+q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^4+q^3+q^2+q
         7: q^3+q
         8: q
        10: q^3+q
        11: q
        12: q^3+q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^4+q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        28: q
        29: q^3+q
        30: q^3+q
        31: q
        32: q
        33: q
        34: q
        35: q
        36: q
        37: q
        39: q^2+q
        41: q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        58: q
        60: q
        62: q
        64: q
        66: q
        68: q
        70: q^3+q
        71: q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: q
        81: q
        82: q
        83: q
        84: q
        85: q
        86: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       103: q
       107: q
       109: q
       111: q
       113: q
       115: q
       117: q
       119: q
       121: q
       123: q
       127: q
       129: q
       133: q
       135: q
       136: q
       139: q
       140: q
       141: q
       142: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q
       163: q
       164: q
       169: q
       173: q
       179: q
       181: q
       183: q
       185: q
       187: q
       189: q
       193: q
       195: q
       197: q
       201: q
       203: q
       205: q
       209: q
       211: q
       213: q
       215: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q
       259: q
       263: q
       267: q
       271: q
       279: q
       289: q
       299: q
       303: q
       305: q
       307: q
       309: q
       313: q
       325: q
       381: q
       393: q
       401: q
       477: 1
       569: 1
       579: 1
       651: 1
       695: 1
       757: 1
       771: 1
       886: 1

 887:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q
        33: 3q
        34: 3q
        35: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q^2+2q
        40: q^2+q
        41: 2q
        42: q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: q
        59: 2q
        60: 2q
        61: q
        62: 2q
        63: q
        64: 2q
        65: q
        66: 2q
        67: q
        68: 3q
        70: 2q
        71: 2q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: 3q
        81: 3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q
        86: 2q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       104: q
       106: q
       107: q
       110: q
       113: q
       115: q
       117: q
       118: 2q
       119: 2q
       120: q
       121: 2q
       122: q
       123: 2q
       124: q
       127: q
       129: q
       133: 2q
       135: q
       136: q
       139: 2q
       140: q
       141: 2q
       142: q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       151: q
       153: q^2+q
       155: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       174: q
       176: q
       179: q
       183: q
       186: q
       189: q
       193: q
       196: q
       201: q
       204: q
       209: q
       211: q
       213: q
       215: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q
       279: q
       299: q
       304: q
       307: q
       310: q
       317: q
       319: q
       322: q
       325: q
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       360: q
       362: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       427: 1
       443: 1
       445: 1
       462: 1
       463: 1
       465: q
       471: q
       474: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       545: 1
       563: 1
       574: 1
       580: 1
       601: 1
       615: 1
       617: 1
       632: 1
       633: 1
       656: 1
       696: 1
       733: 1
       751: 1
       766: 1
       772: 1
       887: 1

 888:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q
        33: 3q
        34: 3q
        35: 3q
        36: 3q
        37: 2q
        38: q
        39: 2q^2+2q
        40: q^2+q
        41: 2q
        42: q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: 2q
        59: q
        60: q
        61: 2q
        62: 2q
        63: q
        64: 2q
        65: q
        66: 2q
        67: q
        68: 3q
        70: 2q
        71: 2q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: 3q
        81: 3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q
        86: 2q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       105: q
       106: q
       108: q
       109: q
       113: q
       115: q
       117: 2q
       118: q
       119: q
       120: 2q
       121: 2q
       122: q
       123: 2q
       124: q
       127: q
       129: q
       133: 2q
       135: q
       136: q
       139: 2q
       140: q
       141: 2q
       142: q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       151: q
       153: q^2+q
       155: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       175: q
       176: q
       179: q
       184: q
       185: q
       189: q
       194: q
       195: q
       202: q
       203: q
       209: q
       211: q
       213: q
       215: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q
       279: q
       300: q
       303: q
       308: q
       309: q
       317: q
       320: q
       321: q
       325: q
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       360: q
       362: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       427: 1
       444: 1
       445: 1
       461: 1
       463: 1
       465: q
       472: q
       473: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       547: 1
       561: 1
       576: 1
       580: 1
       601: 1
       616: 1
       617: 1
       631: 1
       633: 1
       656: 1
       698: 1
       735: 1
       749: 1
       767: 1
       772: 1
       888: 1

 889:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: q+1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       194: 1
       196: 1
       197: 1
       202: 1
       204: 1
       205: 1
       209: 1
       211: 1
       213: 1
       215: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       273: 1
       279: 1
       289: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       337: 1
       338: 1
       340: 1
       351: 1
       359: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       384: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       427: 1
       435: 1
       444: 1
       445: 1
       455: 1
       462: 1
       463: 1
       465: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       539: 1
       547: 1
       555: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       601: 1
       616: 1
       617: 1
       632: 1
       633: 1
       651: 1
       655: 1
       697: 1
       735: 1
       751: 1
       758: 1
       768: 1
       769: 1
       889: 1

 890:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       193: 1
       196: 1
       198: 1
       201: 1
       204: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       274: 1
       280: 1
       290: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       382: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       428: 1
       436: 1
       443: 1
       446: 1
       456: 1
       462: 1
       464: 1
       466: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       538: 1
       546: 1
       556: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       602: 1
       615: 1
       618: 1
       632: 1
       634: 1
       652: 1
       656: 1
       699: 1
       734: 1
       752: 1
       759: 1
       766: 1
       773: 1
       890: 1

 891:    0: 1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       139: 1
       140: 1
       141: 1
       142: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       194: 1
       195: 1
       198: 1
       202: 1
       203: 1
       206: 1
       210: 1
       212: 1
       214: 1
       216: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       272: 1
       280: 1
       290: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       383: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       428: 1
       436: 1
       444: 1
       446: 1
       456: 1
       461: 1
       464: 1
       466: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       540: 1
       548: 1
       554: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       602: 1
       616: 1
       618: 1
       631: 1
       634: 1
       652: 1
       656: 1
       700: 1
       736: 1
       750: 1
       760: 1
       767: 1
       773: 1
       891: 1

 892:    0: 3q
         1: 3q^2+3q
         2: 3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q
         6: q^3+3q^2+2q
         7: q^2+2q
         8: 3q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 3q
        17: 3q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q
        23: 3q^2+3q
        24: 3q
        25: 3q
        26: 3q^2+3q
        27: 3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q
        33: 3q
        34: 3q
        35: 3q
        36: 3q
        37: q
        38: 2q
        39: q^2+q
        40: 2q^2+2q
        41: q
        42: 2q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: q
        59: 2q
        60: q
        61: 2q
        62: q
        63: 2q
        64: q
        65: 2q
        66: q
        67: 2q
        68: 3q
        70: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: 3q
        81: 3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q
        86: 2q
        87: 2q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       104: q
       105: q
       106: q
       108: q
       110: q
       114: q
       116: q
       117: q
       118: 2q
       119: q
       120: 2q
       121: q
       122: 2q
       123: q
       124: 2q
       128: q
       130: q
       133: 2q
       135: q
       136: q
       139: 2q
       140: q
       141: 2q
       142: q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       152: q
       154: q^2+q
       156: q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       174: q
       175: q
       176: q
       180: q
       184: q
       186: q
       190: q
       194: q
       196: q
       202: q
       204: q
       210: q
       212: q
       214: q
       216: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q
       280: q
       300: q
       304: q
       308: q
       310: q
       318: q
       320: q
       322: q
       326: q
       337: 1
       339: 1
       341: 1
       351: 1
       359: 1
       361: q
       363: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       428: 1
       444: 1
       446: 1
       462: 1
       464: 1
       466: q
       472: q
       474: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       548: 1
       564: 1
       575: 1
       578: 1
       602: 1
       616: 1
       618: 1
       632: 1
       634: 1
       655: 1
       701: 1
       736: 1
       752: 1
       768: 1
       770: 1
       892: 1

 893:    0: q^3+q
         1: q^4+q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^4+q^3+q^2+q
         7: q^3+q
         8: q
        10: q^3+q
        11: q
        12: q^3+q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^4+q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        28: q
        29: q^3+q
        30: q^3+q
        31: q
        32: q
        33: q
        34: q
        35: q
        36: q
        37: q
        39: q^2+q
        41: q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        59: q
        61: q
        62: q
        64: q
        66: q
        68: q
        70: q^3+q
        71: q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: q
        81: q
        82: q
        83: q
        84: q
        85: q
        86: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       106: q
       108: q
       110: q
       111: q
       113: q
       115: q
       118: q
       120: q
       121: q
       123: q
       127: q
       129: q
       133: q
       135: q
       136: q
       139: q
       140: q
       141: q
       142: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q
       163: q
       164: q
       172: q
       176: q
       179: q
       181: q
       184: q
       186: q
       187: q
       189: q
       194: q
       196: q
       197: q
       202: q
       204: q
       205: q
       209: q
       211: q
       213: q
       215: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q
       262: q
       266: q
       269: q
       273: q
       279: q
       289: q
       300: q
       304: q
       305: q
       308: q
       310: q
       313: q
       325: q
       384: q
       396: q
       404: q
       477: 1
       570: 1
       579: 1
       651: 1
       702: 1
       758: 1
       771: 1
       893: 1

 894:    0: q^3+q
         1: q^4+q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^4+q^3+q^2+q
         7: q^3+q
         8: q
        10: q^3+q
        11: q
        12: q^3+q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^4+q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        28: q
        29: q^3+q
        30: q^3+q
        31: q
        32: q
        33: q
        34: q
        35: q
        36: q
        38: q
        40: q^2+q
        42: q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        59: q
        60: q
        63: q
        65: q
        67: q
        68: q
        70: q^3+q
        71: q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: q
        81: q
        82: q
        83: q
        84: q
        85: q
        86: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       104: q
       107: q
       110: q
       112: q
       114: q
       116: q
       118: q
       119: q
       122: q
       124: q
       128: q
       130: q
       133: q
       135: q
       136: q
       139: q
       140: q
       141: q
       142: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q
       163: q
       164: q
       170: q
       174: q
       180: q
       182: q
       183: q
       186: q
       188: q
       190: q
       193: q
       196: q
       198: q
       201: q
       204: q
       206: q
       210: q
       212: q
       214: q
       216: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q
       260: q
       264: q
       268: q
       274: q
       280: q
       290: q
       299: q
       304: q
       306: q
       307: q
       310: q
       314: q
       326: q
       382: q
       394: q
       403: q
       478: 1
       571: 1
       582: 1
       652: 1
       703: 1
       759: 1
       774: 1
       894: 1

 895:    0: q^3+q
         1: q^4+q^3+q^2+q
         2: q^3+q
         3: q^2+q
         4: q^3+q
         5: q
         6: q^4+q^3+q^2+q
         7: q^3+q
         8: q
        10: q^3+q
        11: q
        12: q^3+q
        13: q^3+q
        14: q^3+q
        15: q
        16: q
        17: q
        19: q^3+q
        20: q^4+q^3+q^2+q
        21: q^3+q
        22: q
        23: q^2+q
        24: q
        25: q
        26: q^2+q
        27: q
        28: q
        29: q^3+q
        30: q^3+q
        31: q
        32: q
        33: q
        34: q
        35: q
        36: q
        38: q
        40: q^2+q
        42: q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: q
        50: q
        52: q
        53: q^2+q
        54: q
        55: q
        56: q^2+q
        57: q
        58: q
        61: q
        63: q
        65: q
        67: q
        68: q
        70: q^3+q
        71: q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: q
        81: q
        82: q
        83: q
        84: q
        85: q
        86: q
        87: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q
       101: q^2+q
       102: q
       105: q
       108: q
       109: q
       112: q
       114: q
       116: q
       117: q
       120: q
       122: q
       124: q
       128: q
       130: q
       133: q
       135: q
       136: q
       139: q
       140: q
       141: q
       142: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q
       163: q
       164: q
       171: q
       175: q
       180: q
       182: q
       184: q
       185: q
       188: q
       190: q
       194: q
       195: q
       198: q
       202: q
       203: q
       206: q
       210: q
       212: q
       214: q
       216: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q
       261: q
       265: q
       270: q
       272: q
       280: q
       290: q
       300: q
       303: q
       306: q
       308: q
       309: q
       314: q
       326: q
       383: q
       395: q
       402: q
       478: 1
       572: 1
       582: 1
       652: 1
       704: 1
       760: 1
       774: 1
       895: 1

 896:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: 1
       207: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       259: 1
       263: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       377: 1
       381: 1
       385: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       439: 1
       447: 1
       453: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       521: 1
       525: 1
       529: 1
       583: 1
       585: 1
       587: 1
       589: 1
       595: 1
       607: 1
       619: 1
       676: 1
       681: 1
       705: 1
       709: 1
       777: 1
       807: 1
       825: 1
       896: 1

 897:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: 1
       208: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       260: 1
       264: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       378: 1
       382: 1
       386: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       440: 1
       447: 1
       453: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       522: 1
       526: 1
       530: 1
       584: 1
       586: 1
       588: 1
       589: 1
       596: 1
       608: 1
       619: 1
       676: 1
       681: 1
       706: 1
       710: 1
       778: 1
       808: 1
       825: 1
       897: 1

 898:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       202: 1
       208: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       261: 1
       265: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       379: 1
       383: 1
       387: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       439: 1
       448: 1
       454: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       523: 1
       527: 1
       531: 1
       584: 1
       586: 1
       588: 1
       590: 1
       595: 1
       607: 1
       620: 1
       676: 1
       681: 1
       707: 1
       711: 1
       778: 1
       807: 1
       826: 1
       898: 1

 899:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       202: 1
       207: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       262: 1
       266: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       380: 1
       384: 1
       388: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       440: 1
       448: 1
       454: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: 1
       498: 1
       524: 1
       528: 1
       532: 1
       583: 1
       585: 1
       587: 1
       590: 1
       596: 1
       608: 1
       620: 1
       676: 1
       681: 1
       708: 1
       712: 1
       777: 1
       808: 1
       826: 1
       899: 1

 900:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+3q+1
        25: 3q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+4q+1
        36: 2q^2+4q+1
        37: q^2+3q+1
        39: 2q^2+3q+1
        41: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 3q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+4q+1
        58: 2q+1
        60: 2q+1
        61: q
        62: 2q+1
        64: q^2+3q+1
        66: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+4q+1
        73: q^2+3q+1
        74: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+4q+1
        86: q^2+3q+1
        87: 3q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: 2q+1
       107: 2q+1
       108: q
       109: 2q+1
       111: q^2+3q+1
       113: 2q+1
       115: q^2+3q+1
       117: 2q+1
       119: 2q+1
       120: q
       121: 2q+1
       123: q^2+3q+1
       125: 2q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+4q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       169: 2q+1
       173: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       183: 2q+1
       184: q
       185: 2q+1
       187: q^2+3q+1
       189: 2q+1
       191: q+1
       195: q+1
       199: q+1
       200: q
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 2q+1
       271: q+1
       275: q+1
       279: q+1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: 2q+1
       291: q+1
       293: q+1
       294: q
       295: q+1
       297: q+1
       303: q+1
       307: 2q+1
       308: q
       309: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       321: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       350: q+1
       352: q+1
       356: 2q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: q+1
       385: q+1
       397: 1
       401: q+1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       521: 1
       529: 1
       549: 1
       553: 1
       561: 1
       585: 1
       589: 1
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       643: 1
       665: 1
       685: 1
       709: 1
       713: 1
       737: 1
       749: 1
       781: 1
       787: 1
       833: 1
       900: 1

 901:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+3q+1
        25: 3q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+4q+1
        36: 2q^2+4q+1
        38: q^2+3q+1
        40: 2q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 3q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+4q+1
        58: 2q+1
        60: q
        61: 2q+1
        63: 2q+1
        65: q^2+3q+1
        67: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+4q+1
        73: q^2+3q+1
        75: q^2+3q+1
        77: 2q^2+3q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+4q+1
        86: q^2+3q+1
        87: 3q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       105: 2q+1
       107: q
       108: 2q+1
       109: 2q+1
       112: q^2+3q+1
       114: 2q+1
       116: q^2+3q+1
       117: 2q+1
       119: q
       120: 2q+1
       122: 2q+1
       124: q^2+3q+1
       125: 2q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+4q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       171: 2q+1
       175: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       183: q
       184: 2q+1
       185: 2q+1
       188: q^2+3q+1
       190: 2q+1
       191: q+1
       195: q+1
       199: q
       200: q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 2q+1
       272: q+1
       277: q+1
       280: q+1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: 2q+1
       292: q+1
       293: q
       294: q+1
       295: q+1
       298: q+1
       303: q+1
       307: q
       308: 2q+1
       309: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       321: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       350: q+1
       352: q+1
       356: 2q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: q+1
       387: q+1
       398: 1
       402: q+1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       523: 1
       531: 1
       550: 1
       554: 1
       562: 1
       586: 1
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       643: 1
       665: 1
       685: 1
       711: 1
       714: 1
       738: 1
       750: 1
       782: 1
       787: 1
       834: 1
       901: 1

 902:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+3q+1
        25: 3q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+4q+1
        36: 2q^2+4q+1
        37: q^2+3q+1
        39: 2q^2+3q+1
        41: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 3q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+4q+1
        59: 2q+1
        60: q
        61: 2q+1
        62: 2q+1
        64: q^2+3q+1
        66: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+4q+1
        73: q^2+3q+1
        74: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+4q+1
        86: q^2+3q+1
        87: 3q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       106: 2q+1
       107: q
       108: 2q+1
       110: 2q+1
       111: q^2+3q+1
       113: 2q+1
       115: q^2+3q+1
       118: 2q+1
       119: q
       120: 2q+1
       121: 2q+1
       123: q^2+3q+1
       125: 2q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+4q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       172: 2q+1
       176: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       183: q
       184: 2q+1
       186: 2q+1
       187: q^2+3q+1
       189: 2q+1
       192: q+1
       196: q+1
       199: q
       200: q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 2q+1
       273: q+1
       278: q+1
       279: q+1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: 2q+1
       291: q+1
       293: q
       294: q+1
       296: q+1
       297: q+1
       304: q+1
       307: q
       308: 2q+1
       310: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       322: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       350: q+1
       352: q+1
       356: 2q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: q+1
       388: q+1
       399: 1
       404: q+1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       524: 1
       532: 1
       552: 1
       555: 1
       563: 1
       585: 1
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       644: 1
       665: 1
       685: 1
       712: 1
       716: 1
       739: 1
       751: 1
       781: 1
       788: 1
       833: 1
       902: 1

 903:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+3q+1
        25: 3q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+4q+1
        36: 2q^2+4q+1
        38: q^2+3q+1
        40: 2q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 3q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+4q+1
        59: 2q+1
        60: 2q+1
        61: q
        63: 2q+1
        65: q^2+3q+1
        67: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+4q+1
        73: q^2+3q+1
        75: q^2+3q+1
        77: 2q^2+3q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+4q+1
        86: q^2+3q+1
        87: 3q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       104: 2q+1
       107: 2q+1
       108: q
       110: 2q+1
       112: q^2+3q+1
       114: 2q+1
       116: q^2+3q+1
       118: 2q+1
       119: 2q+1
       120: q
       122: 2q+1
       124: q^2+3q+1
       125: 2q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+4q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       170: 2q+1
       174: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       183: 2q+1
       184: q
       186: 2q+1
       188: q^2+3q+1
       190: 2q+1
       192: q+1
       196: q+1
       199: q+1
       200: q
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 2q+1
       274: q+1
       276: q+1
       280: q+1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: 2q+1
       292: q+1
       293: q+1
       294: q
       296: q+1
       298: q+1
       304: q+1
       307: 2q+1
       308: q
       310: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       322: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       350: q+1
       352: q+1
       356: 2q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: q+1
       386: q+1
       400: 1
       403: q+1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       522: 1
       530: 1
       551: 1
       556: 1
       564: 1
       586: 1
       589: 1
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       644: 1
       665: 1
       685: 1
       710: 1
       715: 1
       740: 1
       752: 1
       782: 1
       788: 1
       834: 1
       903: 1

 904:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: 3q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+4q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: q^2+3q+1
        32: 3q^2+4q+1
        33: 2q^2+4q+1
        34: 2q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        39: 2q^2+3q+1
        41: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: 3q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+4q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: 2q+1
        59: q
        60: 2q+1
        62: 2q+1
        64: q^2+3q+1
        66: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: 2q^2+4q+1
        74: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+4q+1
        82: q^2+3q+1
        83: 3q^2+4q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: 2q+1
       107: 2q+1
       109: 2q+1
       110: q
       111: q^2+3q+1
       113: 2q+1
       115: q^2+3q+1
       117: 2q+1
       118: q
       119: 2q+1
       121: 2q+1
       123: q^2+3q+1
       125: 2q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: q+1
       144: q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 2q+1
       173: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       183: 2q+1
       185: 2q+1
       186: q
       187: q^2+3q+1
       189: 2q+1
       191: q+1
       192: q
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q+1
       201: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 2q+1
       267: q+1
       275: q+1
       279: q+1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: 2q+1
       291: q+1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: q+1
       301: 1
       303: 2q+1
       304: q
       305: q+1
       307: q+1
       315: 1
       317: 1
       319: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: q+1
       348: 1
       350: 2q+1
       351: 1
       352: 1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: q+1
       385: q+1
       389: 1
       393: q+1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       585: 1
       589: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       639: 1
       641: 1
       665: 1
       679: 1
       709: 1
       717: 1
       721: 1
       733: 1
       781: 1
       785: 1
       809: 1
       904: 1

 905:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: 3q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+4q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: q^2+3q+1
        32: 3q^2+4q+1
        33: 2q^2+4q+1
        34: 2q+1
        35: q^2+3q+1
        36: q^2+3q+1
        38: q^2+3q+1
        40: 2q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: 3q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+4q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q
        59: 2q+1
        60: 2q+1
        63: 2q+1
        65: q^2+3q+1
        67: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: 2q^2+4q+1
        75: q^2+3q+1
        77: 2q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+4q+1
        82: q^2+3q+1
        83: 3q^2+4q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       104: 2q+1
       107: 2q+1
       109: q
       110: 2q+1
       112: q^2+3q+1
       114: 2q+1
       116: q^2+3q+1
       117: q
       118: 2q+1
       119: 2q+1
       122: 2q+1
       124: q^2+3q+1
       125: 2q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: q+1
       144: q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 2q+1
       174: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       183: 2q+1
       185: q
       186: 2q+1
       188: q^2+3q+1
       190: 2q+1
       191: q
       192: q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q+1
       201: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 2q+1
       268: q+1
       276: q+1
       280: q+1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: 2q+1
       292: q+1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: q+1
       302: 1
       303: q
       304: 2q+1
       306: q+1
       307: q+1
       316: 1
       318: 1
       319: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: q+1
       348: 1
       350: 2q+1
       351: 1
       352: 1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: q+1
       386: q+1
       390: 1
       394: q+1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       586: 1
       589: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       640: 1
       641: 1
       665: 1
       679: 1
       710: 1
       718: 1
       722: 1
       734: 1
       782: 1
       785: 1
       810: 1
       905: 1

 906:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: 3q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+4q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: q^2+3q+1
        32: 3q^2+4q+1
        33: 2q^2+4q+1
        34: 2q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        39: 2q^2+3q+1
        41: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: 3q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+4q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q
        59: 2q+1
        61: 2q+1
        62: 2q+1
        64: q^2+3q+1
        66: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: 2q^2+4q+1
        74: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+4q+1
        82: q^2+3q+1
        83: 3q^2+4q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       106: 2q+1
       108: 2q+1
       109: q
       110: 2q+1
       111: q^2+3q+1
       113: 2q+1
       115: q^2+3q+1
       117: q
       118: 2q+1
       120: 2q+1
       121: 2q+1
       123: q^2+3q+1
       125: 2q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: q+1
       144: q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: 2q+1
       176: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       184: 2q+1
       185: q
       186: 2q+1
       187: q^2+3q+1
       189: 2q+1
       191: q
       192: q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       200: q+1
       202: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 2q+1
       269: q+1
       278: q+1
       279: q+1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: 2q+1
       291: q+1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: q+1
       301: 1
       303: q
       304: 2q+1
       305: q+1
       308: q+1
       315: 1
       317: 1
       320: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: q+1
       348: 1
       350: 2q+1
       351: 1
       352: 1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: q+1
       388: q+1
       391: 1
       396: q+1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       585: 1
       590: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       639: 1
       642: 1
       665: 1
       679: 1
       712: 1
       720: 1
       723: 1
       735: 1
       781: 1
       786: 1
       809: 1
       906: 1

 907:    0: 4q^2+4q+1
         1: q^4+3q^3+6q^2+4q+1
         2: 4q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^4+3q^3+6q^2+4q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+2q+1
        19: 4q^2+4q+1
        20: q^4+3q^3+6q^2+4q+1
        21: 4q^2+4q+1
        22: 3q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+4q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: 4q^2+4q+1
        31: q^2+3q+1
        32: 3q^2+4q+1
        33: 2q^2+4q+1
        34: 2q+1
        35: q^2+3q+1
        36: q^2+3q+1
        38: q^2+3q+1
        40: 2q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^2+2q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+2q+1
        52: 3q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+4q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: 2q+1
        59: q
        61: 2q+1
        63: 2q+1
        65: q^2+3q+1
        67: q^2+3q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: 2q^2+4q+1
        75: q^2+3q+1
        77: 2q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+4q+1
        82: q^2+3q+1
        83: 3q^2+4q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       105: 2q+1
       108: 2q+1
       109: 2q+1
       110: q
       112: q^2+3q+1
       114: 2q+1
       116: q^2+3q+1
       117: 2q+1
       118: q
       120: 2q+1
       122: 2q+1
       124: q^2+3q+1
       125: 2q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: q+1
       144: q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 2q+1
       175: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       184: 2q+1
       185: 2q+1
       186: q
       188: q^2+3q+1
       190: 2q+1
       191: q+1
       192: q
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       200: q+1
       202: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 2q+1
       270: q+1
       277: q+1
       280: q+1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: 2q+1
       292: q+1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: q+1
       302: 1
       303: 2q+1
       304: q
       306: q+1
       308: q+1
       316: 1
       318: 1
       320: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: q+1
       348: 1
       350: 2q+1
       351: 1
       352: 1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: q+1
       387: q+1
       392: 1
       395: q+1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       586: 1
       590: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       640: 1
       642: 1
       665: 1
       679: 1
       711: 1
       719: 1
       724: 1
       736: 1
       782: 1
       786: 1
       810: 1
       907: 1

 908:    0: q^3+7q^2+6q+1
         1: q^4+4q^3+9q^2+6q+1
         2: 4q^2+4q+1
         3: 3q^3+8q^2+6q+1
         4: q^3+7q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: q^4+4q^3+9q^2+6q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 3q^2+4q+1
        14: 3q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 5q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+7q^2+6q+1
        20: q^4+4q^3+9q^2+6q+1
        21: 4q^2+4q+1
        22: 5q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 3q^2+4q+1
        25: 5q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 3q^2+4q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 3q^2+4q+1
        31: 3q^2+5q+1
        32: 2q^2+4q+1
        33: 4q^2+6q+1
        34: 3q^2+5q+1
        35: 2q^2+4q+1
        36: 4q^2+6q+1
        37: 2q^2+4q+1
        38: q^2+2q
        39: 3q^2+4q+1
        40: q^2+2q
        41: q^2+3q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 2q^2+2q+1
        52: 5q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 3q^2+4q+1
        55: 5q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 3q^2+4q+1
        58: 2q^2+4q+1
        59: q
        60: 2q^2+4q+1
        61: q
        62: q^2+3q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 2q^2+4q+1
        67: q^2+2q
        68: 2q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 2q^2+4q+1
        75: q^2+2q
        76: 3q^2+4q+1
        77: q^2+2q
        78: q^2+3q+1
        79: q^2+q
        80: q^2+3q+1
        81: q^2+4q+1
        82: 3q^2+5q+1
        83: 2q^2+4q+1
        84: q^2+3q+1
        85: q^2+4q+1
        86: 3q^2+5q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+4q+1
        92: 2q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+2q+1
        97: 2q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: 3q^2+6q+1
       102: 3q+1
       103: q^2+3q+1
       104: q
       105: q
       107: 2q^2+4q+1
       108: q
       109: 2q^2+4q+1
       110: q
       111: 2q^2+4q+1
       112: q^2+2q
       113: q^2+3q+1
       114: 2q
       115: q^2+3q+1
       116: q
       117: 2q+1
       119: 2q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 2q+1
       134: 2q+1
       135: q^2+4q+1
       136: q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^2+3q+1
       142: 2q^2+5q+1
       143: 2q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: 2q^2+5q+1
       148: 3q+1
       149: 5q+1
       150: 3q+1
       151: 3q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: 2q+1
       156: q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q^2+3q+1
       170: q
       171: q
       173: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       183: 2q+1
       185: 2q+1
       187: q^2+3q+1
       188: q
       189: 2q+1
       190: q
       191: q+1
       193: 3q+1
       195: q^2+3q+1
       196: q
       197: 2q+1
       198: q
       199: q+1
       201: q^2+3q+1
       202: q
       203: 3q+1
       205: 2q+1
       206: q
       207: q+1
       208: q
       209: 3q+1
       210: 2q
       211: 2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 1
       239: q+1
       241: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 2q+1
       267: 2q+1
       268: q
       271: 2q+1
       272: q
       275: q+1
       283: 1
       285: 1
       287: 1
       291: q+1
       293: q+1
       295: q+1
       297: q+1
       298: q
       299: q+1
       301: 1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       319: q+1
       321: q+1
       323: 1
       325: 2q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       443: q+1
       445: 1
       447: 1
       449: 1
       451: 1
       461: q+1
       463: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       529: 1
       533: 1
       545: 1
       549: 1
       561: 1
       565: 1
       569: 2
       573: 1
       577: 1
       579: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       613: 1
       615: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       665: 1
       679: 1
       685: 1
       693: 1
       695: 1
       713: 1
       717: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       908: 1

 909:    0: q^3+7q^2+6q+1
         1: q^4+4q^3+9q^2+6q+1
         2: 4q^2+4q+1
         3: 3q^3+8q^2+6q+1
         4: q^3+7q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: q^4+4q^3+9q^2+6q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 3q^2+4q+1
        14: 3q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 5q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+7q^2+6q+1
        20: q^4+4q^3+9q^2+6q+1
        21: 4q^2+4q+1
        22: 5q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 3q^2+4q+1
        25: 5q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 3q^2+4q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 3q^2+4q+1
        31: 3q^2+5q+1
        32: 2q^2+4q+1
        33: 4q^2+6q+1
        34: 3q^2+5q+1
        35: 2q^2+4q+1
        36: 4q^2+6q+1
        37: q^2+2q
        38: 2q^2+4q+1
        39: q^2+2q
        40: 3q^2+4q+1
        41: q^2+q
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 2q^2+2q+1
        52: 5q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 3q^2+4q+1
        55: 5q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 3q^2+4q+1
        58: q
        59: 2q^2+4q+1
        60: 2q^2+4q+1
        61: q
        62: 2q
        63: q^2+3q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: q^2+2q
        75: 2q^2+4q+1
        76: q^2+2q
        77: 3q^2+4q+1
        78: q^2+q
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+4q+1
        82: 3q^2+5q+1
        83: 2q^2+4q+1
        84: q^2+3q+1
        85: q^2+4q+1
        86: 3q^2+5q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+4q+1
        92: 2q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+2q+1
        97: 2q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: 3q^2+6q+1
       102: 3q+1
       103: q
       104: q^2+3q+1
       106: q
       107: 2q^2+4q+1
       108: q
       109: q
       110: 2q^2+4q+1
       111: q^2+2q
       112: 2q^2+4q+1
       113: 2q
       114: q^2+3q+1
       115: q
       116: q^2+3q+1
       118: 2q+1
       119: 2q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 2q+1
       134: 2q+1
       135: q^2+4q+1
       136: q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^2+3q+1
       142: 2q^2+5q+1
       143: 2q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: 2q^2+5q+1
       148: 3q+1
       149: 5q+1
       150: 3q+1
       151: 2q
       152: 3q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: q
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q
       170: q^2+3q+1
       172: q
       174: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       183: 2q+1
       186: 2q+1
       187: q
       188: q^2+3q+1
       189: q
       190: 2q+1
       192: q+1
       193: 3q+1
       195: q
       196: q^2+3q+1
       197: q
       198: 2q+1
       199: q+1
       201: q^2+3q+1
       202: q
       204: 3q+1
       205: q
       206: 2q+1
       207: q
       208: q+1
       209: 2q
       210: 3q+1
       211: q
       212: 2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 1
       240: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 2q+1
       267: q
       268: 2q+1
       273: q
       274: 2q+1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: q+1
       299: q+1
       302: 1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: 2q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       443: q+1
       446: 1
       447: 1
       450: 1
       452: 1
       462: q+1
       464: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       530: 1
       534: 1
       546: 1
       551: 1
       564: 1
       566: 1
       571: 2
       574: 1
       581: 1
       582: 1
       589: 1
       592: 1
       593: 1
       596: 1
       600: 1
       614: 1
       615: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       665: 1
       679: 1
       685: 1
       699: 1
       703: 1
       715: 1
       718: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       909: 1

 910:    0: q^3+7q^2+6q+1
         1: q^4+4q^3+9q^2+6q+1
         2: 4q^2+4q+1
         3: 3q^3+8q^2+6q+1
         4: q^3+7q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: q^4+4q^3+9q^2+6q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 3q^2+4q+1
        14: 3q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 5q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+7q^2+6q+1
        20: q^4+4q^3+9q^2+6q+1
        21: 4q^2+4q+1
        22: 5q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 3q^2+4q+1
        25: 5q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 3q^2+4q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 3q^2+4q+1
        31: 3q^2+5q+1
        32: 2q^2+4q+1
        33: 4q^2+6q+1
        34: 3q^2+5q+1
        35: 2q^2+4q+1
        36: 4q^2+6q+1
        37: q^2+2q
        38: 2q^2+4q+1
        39: q^2+2q
        40: 3q^2+4q+1
        41: q^2+q
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 2q^2+2q+1
        52: 5q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 3q^2+4q+1
        55: 5q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 3q^2+4q+1
        58: 2q^2+4q+1
        59: q
        60: q
        61: 2q^2+4q+1
        62: 2q
        63: q^2+3q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: q^2+2q
        75: 2q^2+4q+1
        76: q^2+2q
        77: 3q^2+4q+1
        78: q^2+q
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+4q+1
        82: 3q^2+5q+1
        83: 2q^2+4q+1
        84: q^2+3q+1
        85: q^2+4q+1
        86: 3q^2+5q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+4q+1
        92: 2q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+2q+1
        97: 2q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: 3q^2+6q+1
       102: 3q+1
       103: q
       105: q^2+3q+1
       106: q
       107: q
       108: 2q^2+4q+1
       109: 2q^2+4q+1
       110: q
       111: q^2+2q
       112: 2q^2+4q+1
       113: 2q
       114: q^2+3q+1
       115: q
       116: q^2+3q+1
       117: 2q+1
       120: 2q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 2q+1
       134: 2q+1
       135: q^2+4q+1
       136: q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^2+3q+1
       142: 2q^2+5q+1
       143: 2q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: 2q^2+5q+1
       148: 3q+1
       149: 5q+1
       150: 3q+1
       151: 2q
       152: 3q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: q
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q
       171: q^2+3q+1
       172: q
       175: 2q+1
       178: q+1
       180: q+1
       182: 2q+1
       184: 2q+1
       185: 2q+1
       187: q
       188: q^2+3q+1
       189: q
       190: 2q+1
       191: q+1
       194: 3q+1
       195: q^2+3q+1
       196: q
       197: q
       198: 2q+1
       200: q+1
       201: q
       202: q^2+3q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: q
       208: q+1
       209: 2q
       210: 3q+1
       211: q
       212: 2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 1
       240: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 2q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       277: q+1
       284: 1
       285: 1
       288: 1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: q+1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: 2q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       444: q+1
       446: 1
       448: 1
       449: 1
       452: 1
       461: q+1
       464: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       531: 1
       535: 1
       548: 1
       550: 1
       562: 1
       567: 1
       572: 2
       576: 1
       581: 1
       582: 1
       590: 1
       591: 1
       594: 1
       595: 1
       600: 1
       614: 1
       616: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       665: 1
       679: 1
       685: 1
       700: 1
       704: 1
       714: 1
       719: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       910: 1

 911:    0: q^3+7q^2+6q+1
         1: q^4+4q^3+9q^2+6q+1
         2: 4q^2+4q+1
         3: 3q^3+8q^2+6q+1
         4: q^3+7q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: q^4+4q^3+9q^2+6q+1
         7: 4q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+2q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 3q^2+4q+1
        14: 3q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 5q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 2q^2+2q+1
        19: q^3+7q^2+6q+1
        20: q^4+4q^3+9q^2+6q+1
        21: 4q^2+4q+1
        22: 5q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 3q^2+4q+1
        25: 5q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 3q^2+4q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 3q^2+4q+1
        31: 3q^2+5q+1
        32: 2q^2+4q+1
        33: 4q^2+6q+1
        34: 3q^2+5q+1
        35: 2q^2+4q+1
        36: 4q^2+6q+1
        37: 2q^2+4q+1
        38: q^2+2q
        39: 3q^2+4q+1
        40: q^2+2q
        41: q^2+3q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 2q^2+2q+1
        52: 5q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 3q^2+4q+1
        55: 5q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 3q^2+4q+1
        58: q
        59: 2q^2+4q+1
        60: q
        61: 2q^2+4q+1
        62: q^2+3q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 2q^2+4q+1
        67: q^2+2q
        68: 2q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 2q^2+4q+1
        75: q^2+2q
        76: 3q^2+4q+1
        77: q^2+2q
        78: q^2+3q+1
        79: q^2+q
        80: q^2+3q+1
        81: q^2+4q+1
        82: 3q^2+5q+1
        83: 2q^2+4q+1
        84: q^2+3q+1
        85: q^2+4q+1
        86: 3q^2+5q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+4q+1
        92: 2q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+2q+1
        97: 2q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+2q+1
       100: 5q+1
       101: 3q^2+6q+1
       102: 3q+1
       104: q
       105: q
       106: q^2+3q+1
       107: q
       108: 2q^2+4q+1
       109: q
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: q^2+2q
       113: q^2+3q+1
       114: 2q
       115: q^2+3q+1
       116: q
       118: 2q+1
       120: 2q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 2q+1
       134: 2q+1
       135: q^2+4q+1
       136: q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^2+3q+1
       142: 2q^2+5q+1
       143: 2q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: 2q^2+5q+1
       148: 3q+1
       149: 5q+1
       150: 3q+1
       151: 3q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: 2q+1
       156: q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       170: q
       171: q
       172: q^2+3q+1
       176: 2q+1
       177: q+1
       179: q+1
       181: 2q+1
       184: 2q+1
       186: 2q+1
       187: q^2+3q+1
       188: q
       189: 2q+1
       190: q
       192: q+1
       194: 3q+1
       195: q
       196: q^2+3q+1
       197: 2q+1
       198: q
       200: q+1
       201: q
       202: q^2+3q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: q+1
       208: q
       209: 3q+1
       210: 2q
       211: 2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 1
       239: q+1
       241: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 2q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: q
       278: q+1
       284: 1
       286: 1
       287: 1
       291: q+1
       294: q+1
       296: q+1
       297: q+1
       298: q
       300: q+1
       301: 1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       320: q+1
       322: q+1
       323: 1
       325: 2q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       444: q+1
       445: 1
       448: 1
       450: 1
       451: 1
       462: q+1
       463: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       532: 1
       536: 1
       547: 1
       552: 1
       563: 1
       568: 1
       570: 2
       575: 1
       577: 1
       579: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       613: 1
       616: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       665: 1
       679: 1
       685: 1
       697: 1
       702: 1
       716: 1
       720: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       911: 1

 912:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 5q^2+5q+1
        23: 5q^2+5q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: q^3+2q^2+3q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 5q^2+5q+1
        32: 3q^2+4q+1
        33: 5q^2+5q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: 2q^2+4q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q^2+3q+1
        59: 3q^2+2q
        60: q^2+3q+1
        61: q^2+q
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q^2+3q+1
       106: q^2+q
       107: q+1
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: 2q+1
       118: q^2+q
       119: 2q+1
       121: q^2+3q+1
       123: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 3q^2+4q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q+1
       143: q^2+3q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: 2q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 2q+1
       192: q^2+q
       193: q+1
       195: q+1
       197: q+1
       199: 2q+1
       201: q+1
       207: q^2+3q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       267: q+1
       275: 2q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: 1
       315: q+1
       317: 2q+1
       319: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       389: q+1
       393: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: 1
       453: 1
       465: 1
       467: 1
       469: q+1
       471: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       583: 1
       587: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       686: 1
       687: 1
       705: 1
       721: 1
       725: 1
       729: 1
       799: 1
       841: 1
       845: 1
       912: 1

 913:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 5q^2+5q+1
        23: 5q^2+5q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: q^3+2q^2+3q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 5q^2+5q+1
        32: 3q^2+4q+1
        33: 5q^2+5q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: 2q^2+4q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 3q^2+2q
        59: 2q^2+3q+1
        60: q^2+3q+1
        61: q^2+q
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q^2+3q+1
       105: q^2+q
       107: q+1
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q^2+q
       118: 2q+1
       119: 2q+1
       122: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 3q^2+4q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q+1
       143: q^2+3q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: 2q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       191: q^2+q
       192: 2q+1
       193: q+1
       196: q+1
       198: q+1
       199: 2q+1
       201: q+1
       208: q^2+3q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       268: q+1
       276: 2q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: 1
       316: q+1
       318: 2q+1
       319: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       390: q+1
       394: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: 1
       453: 1
       466: 1
       468: 1
       470: q+1
       471: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       584: 1
       588: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       686: 1
       687: 1
       706: 1
       722: 1
       726: 1
       730: 1
       800: 1
       842: 1
       845: 1
       913: 1

 914:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 5q^2+5q+1
        23: 5q^2+5q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: q^3+2q^2+3q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 5q^2+5q+1
        32: 3q^2+4q+1
        33: 5q^2+5q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: 2q^2+4q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 3q^2+2q
        59: 2q^2+3q+1
        60: q^2+q
        61: q^2+3q+1
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q^2+q
       106: q^2+3q+1
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q^2+q
       118: 2q+1
       120: 2q+1
       121: q^2+3q+1
       123: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 3q^2+4q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q+1
       143: q^2+3q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: 2q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       191: q^2+q
       192: 2q+1
       194: q+1
       196: q+1
       197: q+1
       200: 2q+1
       202: q+1
       207: q^2+3q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       269: q+1
       278: 2q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: 1
       315: q+1
       317: 2q+1
       320: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       391: q+1
       396: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       472: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       583: 1
       587: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       686: 1
       687: 1
       708: 1
       723: 1
       727: 1
       731: 1
       799: 1
       841: 1
       846: 1
       914: 1

 915:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 5q^2+5q+1
        23: 5q^2+5q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: q^3+2q^2+3q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 5q^2+5q+1
        32: 3q^2+4q+1
        33: 5q^2+5q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: 2q^2+4q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q^2+3q+1
        59: 3q^2+2q
        60: q^2+q
        61: q^2+3q+1
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: 2q+1
        87: q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q^2+q
       105: q^2+3q+1
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: 2q+1
       118: q^2+q
       120: 2q+1
       122: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 3q^2+4q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q+1
       143: q^2+3q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: 2q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 2q+1
       192: q^2+q
       194: q+1
       195: q+1
       198: q+1
       200: 2q+1
       202: q+1
       208: q^2+3q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       270: q+1
       277: 2q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: 1
       316: q+1
       318: 2q+1
       320: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       392: q+1
       395: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       472: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       584: 1
       588: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       686: 1
       687: 1
       707: 1
       724: 1
       728: 1
       732: 1
       800: 1
       842: 1
       846: 1
       915: 1

 916:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       110: q
       111: 1
       113: 1
       115: 1
       117: 1
       118: q
       119: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       186: q
       187: 1
       189: 1
       191: 1
       192: q
       193: 1
       195: 1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       286: q
       287: 1
       289: 1
       291: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       377: 1
       381: 1
       389: 1
       393: 1
       413: 1
       417: 1
       427: 1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       484: 1
       485: 1
       487: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       521: 1
       533: 1
       537: 1
       545: 1
       601: 1
       605: 1
       615: 1
       617: 1
       639: 1
       641: 1
       657: 1
       658: 1
       660: 1
       674: 1
       721: 1
       733: 1
       775: 1
       793: 1
       795: 1
       916: 1

 917:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       109: q
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: 1
       119: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       185: q
       186: 1
       188: 1
       190: 1
       191: q
       192: 1
       193: 1
       195: q
       196: 1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       276: 1
       280: 1
       282: 1
       283: 1
       285: q
       286: 1
       288: 1
       290: 1
       292: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       378: 1
       382: 1
       390: 1
       394: 1
       414: 1
       418: 1
       428: 1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       484: 1
       486: 1
       488: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       522: 1
       534: 1
       538: 1
       546: 1
       602: 1
       606: 1
       615: 1
       618: 1
       640: 1
       641: 1
       657: 1
       659: 1
       661: 1
       674: 1
       722: 1
       734: 1
       776: 1
       793: 1
       796: 1
       917: 1

 918:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: q
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        74: 1
        76: q+1
        78: 1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       109: q
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: 1
       120: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       185: q
       186: 1
       187: 1
       189: 1
       191: q
       192: 1
       194: 1
       195: q
       196: 1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       278: 1
       279: 1
       281: 1
       284: 1
       285: q
       286: 1
       287: 1
       289: 1
       291: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       380: 1
       384: 1
       391: 1
       396: 1
       413: 1
       417: 1
       427: 1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       484: 1
       485: 1
       487: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       524: 1
       536: 1
       539: 1
       547: 1
       601: 1
       605: 1
       616: 1
       617: 1
       639: 1
       642: 1
       657: 1
       658: 1
       660: 1
       674: 1
       723: 1
       735: 1
       775: 1
       794: 1
       795: 1
       918: 1

 919:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: q+1
        75: 1
        77: q+1
        79: 1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q^2+2q+1
        96: q+1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       110: q
       112: 1
       114: 1
       116: 1
       117: 1
       118: q
       120: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       186: q
       188: 1
       190: 1
       191: 1
       192: q
       194: 1
       195: 1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: q
       288: 1
       290: 1
       292: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       379: 1
       383: 1
       392: 1
       395: 1
       414: 1
       418: 1
       428: 1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       484: 1
       486: 1
       488: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       523: 1
       535: 1
       540: 1
       548: 1
       602: 1
       606: 1
       616: 1
       618: 1
       640: 1
       642: 1
       657: 1
       659: 1
       661: 1
       674: 1
       724: 1
       736: 1
       776: 1
       794: 1
       796: 1
       919: 1

 920:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 1
        56: 1
        57: 1
        58: 2q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        80: 3q+1
        81: q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: q^2+2q+1
        96: 2q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: 1
       109: q+1
       111: 1
       113: 1
       115: 1
       117: 2q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       125: 3q+1
       126: 2q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: 2q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: q+1
       187: 1
       189: 1
       191: 2q+1
       192: q
       193: 1
       195: q+1
       197: 1
       199: q+1
       201: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: q+1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: q+1
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: q+1
       334: 1
       335: 1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: q+1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: q+1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       508: 1
       512: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       585: 1
       589: 1
       595: 1
       603: 1
       605: 1
       607: 1
       609: 1
       639: 1
       641: 1
       675: 1
       676: 1
       709: 1
       721: 1
       725: 1
       797: 1
       801: 1
       807: 1
       920: 1

 921:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 2q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        80: 3q+1
        81: q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: q^2+2q+1
        96: 2q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: 1
       110: q+1
       112: 1
       114: 1
       116: 1
       117: q
       118: 2q+1
       119: q+1
       122: q+1
       124: q+1
       125: 3q+1
       126: 2q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: 2q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: q+1
       188: 1
       190: 1
       191: q
       192: 2q+1
       193: 1
       196: q+1
       198: 1
       199: q+1
       201: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: q+1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: q+1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: q+1
       334: 1
       335: 1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: q+1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: q+1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       508: 1
       512: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       586: 1
       589: 1
       596: 1
       603: 1
       606: 1
       608: 1
       610: 1
       640: 1
       641: 1
       675: 1
       676: 1
       710: 1
       722: 1
       726: 1
       798: 1
       801: 1
       808: 1
       921: 1

 922:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 2q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        80: 3q+1
        81: q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: q^2+2q+1
        96: 2q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: 1
       110: q+1
       111: 1
       113: 1
       115: 1
       117: q
       118: 2q+1
       120: q+1
       121: q+1
       123: q+1
       125: 3q+1
       126: 2q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: 2q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: q+1
       187: 1
       189: 1
       191: q
       192: 2q+1
       194: 1
       196: q+1
       197: 1
       200: q+1
       202: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: q+1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: q+1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: q+1
       334: 1
       335: 1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: q+1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: q+1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       508: 1
       512: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       585: 1
       590: 1
       596: 1
       604: 1
       605: 1
       608: 1
       609: 1
       639: 1
       642: 1
       675: 1
       676: 1
       712: 1
       723: 1
       727: 1
       797: 1
       802: 1
       808: 1
       922: 1

 923:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: q+1
        27: q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: 3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 1
        56: 1
        57: 1
        58: 2q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        80: 3q+1
        81: q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: q^2+2q+1
        96: 2q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: 1
       109: q+1
       112: 1
       114: 1
       116: 1
       117: 2q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       125: 3q+1
       126: 2q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: 2q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: q+1
       188: 1
       190: 1
       191: 2q+1
       192: q
       194: 1
       195: q+1
       198: 1
       200: q+1
       202: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       270: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: q+1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: q+1
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: q+1
       334: 1
       335: 1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: q+1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: q+1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       508: 1
       512: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       586: 1
       590: 1
       595: 1
       604: 1
       606: 1
       607: 1
       610: 1
       640: 1
       642: 1
       675: 1
       676: 1
       711: 1
       724: 1
       728: 1
       798: 1
       802: 1
       807: 1
       923: 1

 924:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: q^3+7q^2+7q+1
        23: q^3+7q^2+7q+1
        24: q^3+4q^2+4q+1
        25: 4q^2+7q+1
        26: 4q^2+7q+1
        27: 3q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: 3q^2+6q+1
        32: 2q^2+4q+1
        33: q^3+7q^2+7q+1
        34: q^2+6q+1
        35: q^2+4q+1
        36: 4q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: 4q^2+5q+1
        53: q^3+5q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: 2q^2+5q+1
        57: q^2+3q+1
        58: 2q^2+4q+1
        59: q^2+2q
        60: q^2+4q+1
        61: 2q
        62: q^2+4q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 3q^2+5q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: 2q^2+3q+1
        74: 3q+1
        76: q^2+3q+1
        78: 2q+1
        80: 3q+1
        81: 2q^2+4q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^2+4q+1
        86: 4q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 4q^2+5q+1
        95: q^3+5q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q
       105: q
       106: q
       107: 2q+1
       108: q
       109: q^2+2q+1
       111: 2q+1
       113: 2q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q^2+4q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: 3q+1
       145: 4q+1
       146: 2q+1
       147: q^2+4q+1
       148: q+1
       149: 4q+1
       150: 3q+1
       151: 3q+1
       153: q^2+3q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       169: q+1
       173: q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       183: 1
       185: 1
       187: q+1
       189: q+1
       191: q+1
       193: 2q+1
       194: q
       195: q^2+2q+1
       197: 2q+1
       199: q+1
       201: 2q+1
       202: q
       203: q+1
       205: 1
       207: 2q+1
       208: q
       209: 2q+1
       211: 2q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       263: 1
       267: q+1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 2q+1
       303: 1
       305: q+1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 2q+1
       317: 2q+1
       319: 2q+1
       320: q
       321: q+1
       323: 1
       325: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: 1
       350: q+1
       351: q+2
       352: 1
       356: q+1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       377: 1
       385: 1
       389: q+1
       393: 1
       397: 1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: 1
       433: q+1
       437: 1
       439: 1
       441: 1
       443: 1
       444: 1
       445: q+2
       447: 1
       449: 1
       451: 1
       461: 2
       463: 2
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       500: 1
       508: 1
       512: q+1
       514: 1
       529: 1
       533: 1
       541: 1
       545: 1
       547: 1
       549: 1
       561: 2
       565: 1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       589: 1
       591: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: 1
       629: 1
       641: 1
       643: 1
       645: 1
       675: 1
       677: 1
       689: 1
       693: 1
       698: 1
       713: 1
       725: 1
       753: 1
       801: 1
       803: 1
       811: 1
       855: 1
       924: 1

 925:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: q^3+7q^2+7q+1
        23: q^3+7q^2+7q+1
        24: q^3+4q^2+4q+1
        25: 4q^2+7q+1
        26: 4q^2+7q+1
        27: 3q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: 3q^2+6q+1
        32: 2q^2+4q+1
        33: q^3+7q^2+7q+1
        34: q^2+6q+1
        35: q^2+4q+1
        36: 4q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: 4q^2+5q+1
        53: q^3+5q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: 2q^2+5q+1
        57: q^2+3q+1
        58: 2q^2+4q+1
        59: q^2+2q
        60: 2q
        61: q^2+4q+1
        62: 2q
        63: q^2+4q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 3q^2+5q+1
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: 2q^2+3q+1
        75: 3q+1
        77: q^2+3q+1
        79: 2q+1
        80: 3q+1
        81: 2q^2+4q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^2+4q+1
        86: 4q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 4q^2+5q+1
        95: q^3+5q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q
       105: q^2+3q+1
       106: q
       107: q
       108: 2q+1
       109: q^2+2q+1
       112: 2q+1
       114: 2q+1
       116: 2q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q^2+4q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: 3q+1
       145: 4q+1
       146: 2q+1
       147: q^2+4q+1
       148: q+1
       149: 4q+1
       150: 3q+1
       152: 3q+1
       154: q^2+3q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       171: q+1
       175: q+1
       178: 2q+1
       180: 2q+1
       182: 2q+1
       184: 1
       185: 1
       188: q+1
       190: q+1
       191: q+1
       193: q
       194: 2q+1
       195: q^2+2q+1
       198: 2q+1
       200: q+1
       201: q
       202: 2q+1
       203: q+1
       206: 1
       207: q
       208: 2q+1
       210: 2q+1
       212: 2q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       261: q+1
       265: 1
       270: q+1
       272: 1
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 2q+1
       303: 1
       306: q+1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 2q+1
       318: 2q+1
       319: q
       320: 2q+1
       321: q+1
       324: 1
       326: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: 1
       350: q+1
       351: q+2
       352: 1
       356: q+1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       379: 1
       387: 1
       392: q+1
       395: 1
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: 1
       434: q+1
       438: 1
       439: 1
       442: 1
       443: 1
       444: 1
       446: q+2
       448: 1
       449: 1
       452: 1
       461: 2
       464: 2
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       500: 1
       508: 1
       512: q+1
       514: 1
       531: 1
       535: 1
       544: 1
       546: 1
       548: 1
       550: 1
       562: 2
       567: 1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       590: 1
       591: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: 1
       630: 1
       642: 1
       643: 1
       646: 1
       675: 1
       677: 1
       689: 1
       694: 1
       700: 1
       714: 1
       728: 1
       755: 1
       802: 1
       803: 1
       812: 1
       856: 1
       925: 1

 926:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: q^3+7q^2+7q+1
        23: q^3+7q^2+7q+1
        24: q^3+4q^2+4q+1
        25: 4q^2+7q+1
        26: 4q^2+7q+1
        27: 3q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: 3q^2+6q+1
        32: 2q^2+4q+1
        33: q^3+7q^2+7q+1
        34: q^2+6q+1
        35: q^2+4q+1
        36: 4q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: 4q^2+5q+1
        53: q^3+5q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: 2q^2+5q+1
        57: q^2+3q+1
        58: q^2+2q
        59: 2q^2+4q+1
        60: q^2+4q+1
        61: 2q
        62: 2q
        63: q^2+4q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 3q^2+5q+1
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: 2q^2+3q+1
        75: 3q+1
        77: q^2+3q+1
        79: 2q+1
        80: 3q+1
        81: 2q^2+4q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^2+4q+1
        86: 4q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 4q^2+5q+1
        95: q^3+5q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q^2+3q+1
       105: q
       106: q
       107: 2q+1
       108: q
       110: q^2+2q+1
       112: 2q+1
       114: 2q+1
       116: 2q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q^2+4q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: 3q+1
       145: 4q+1
       146: 2q+1
       147: q^2+4q+1
       148: q+1
       149: 4q+1
       150: 3q+1
       152: 3q+1
       154: q^2+3q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       170: q+1
       174: q+1
       178: 2q+1
       180: 2q+1
       182: 2q+1
       183: 1
       186: 1
       188: q+1
       190: q+1
       192: q+1
       193: 2q+1
       194: q
       196: q^2+2q+1
       198: 2q+1
       199: q+1
       201: 2q+1
       202: q
       204: q+1
       206: 1
       207: q
       208: 2q+1
       210: 2q+1
       212: 2q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q+1
       264: 1
       268: q+1
       274: 1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 2q+1
       304: 1
       306: q+1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 2q+1
       318: 2q+1
       319: 2q+1
       320: q
       322: q+1
       324: 1
       326: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: 1
       350: q+1
       351: q+2
       352: 1
       356: q+1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       378: 1
       386: 1
       390: q+1
       394: 1
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: 1
       434: q+1
       437: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: q+2
       447: 1
       450: 1
       452: 1
       462: 2
       464: 2
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       500: 1
       508: 1
       512: q+1
       514: 1
       530: 1
       534: 1
       542: 1
       546: 1
       548: 1
       551: 1
       564: 2
       566: 1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       589: 1
       592: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: 1
       630: 1
       641: 1
       644: 1
       646: 1
       675: 1
       677: 1
       689: 1
       699: 1
       701: 1
       715: 1
       726: 1
       754: 1
       801: 1
       804: 1
       812: 1
       856: 1
       926: 1

 927:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: q^3+7q^2+7q+1
        23: q^3+7q^2+7q+1
        24: q^3+4q^2+4q+1
        25: 4q^2+7q+1
        26: 4q^2+7q+1
        27: 3q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: 3q^2+6q+1
        32: 2q^2+4q+1
        33: q^3+7q^2+7q+1
        34: q^2+6q+1
        35: q^2+4q+1
        36: 4q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: 4q^2+5q+1
        53: q^3+5q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: 2q^2+5q+1
        57: q^2+3q+1
        58: q^2+2q
        59: 2q^2+4q+1
        60: 2q
        61: q^2+4q+1
        62: q^2+4q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 3q^2+5q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: 2q^2+3q+1
        74: 3q+1
        76: q^2+3q+1
        78: 2q+1
        80: 3q+1
        81: 2q^2+4q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^2+4q+1
        86: 4q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 4q^2+5q+1
        95: q^3+5q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q
       105: q
       106: q^2+3q+1
       107: q
       108: 2q+1
       110: q^2+2q+1
       111: 2q+1
       113: 2q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q^2+4q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: 3q+1
       145: 4q+1
       146: 2q+1
       147: q^2+4q+1
       148: q+1
       149: 4q+1
       150: 3q+1
       151: 3q+1
       153: q^2+3q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       172: q+1
       176: q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       184: 1
       186: 1
       187: q+1
       189: q+1
       192: q+1
       193: q
       194: 2q+1
       196: q^2+2q+1
       197: 2q+1
       200: q+1
       201: q
       202: 2q+1
       204: q+1
       205: 1
       207: 2q+1
       208: q
       209: 2q+1
       211: 2q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       262: q+1
       266: 1
       269: q+1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 2q+1
       304: 1
       305: q+1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 2q+1
       317: 2q+1
       319: q
       320: 2q+1
       322: q+1
       323: 1
       325: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: 1
       350: q+1
       351: q+2
       352: 1
       356: q+1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       380: 1
       388: 1
       391: q+1
       396: 1
       399: 1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: 1
       433: q+1
       438: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: q+2
       448: 1
       450: 1
       451: 1
       462: 2
       463: 2
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       500: 1
       508: 1
       512: q+1
       514: 1
       532: 1
       536: 1
       543: 1
       545: 1
       547: 1
       552: 1
       563: 2
       568: 1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       590: 1
       592: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: 1
       629: 1
       642: 1
       644: 1
       645: 1
       675: 1
       677: 1
       689: 1
       696: 1
       697: 1
       716: 1
       727: 1
       756: 1
       802: 1
       804: 1
       811: 1
       855: 1
       927: 1

 928:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q^2+q+1
        59: q
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: 1
        73: q^2+2q+1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: q^2+q+1
       110: q
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: q^2+q+1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       259: 1
       263: 1
       267: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       366: 1
       377: 1
       385: 1
       389: 1
       393: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       469: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       529: 1
       533: 1
       541: 1
       545: 1
       593: 1
       595: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: 1
       676: 1
       677: 1
       717: 1
       725: 1
       805: 1
       807: 1
       811: 1
       928: 1

 929:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q^2+q+1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: 1
        73: q^2+2q+1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       109: q
       110: q^2+q+1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       195: q
       196: q^2+q+1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       260: 1
       264: 1
       268: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       366: 1
       378: 1
       386: 1
       390: 1
       394: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       470: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       530: 1
       534: 1
       542: 1
       546: 1
       593: 1
       596: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: 1
       676: 1
       677: 1
       718: 1
       726: 1
       805: 1
       808: 1
       812: 1
       929: 1

 930:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q^2+q+1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: 1
        73: q^2+2q+1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       109: q
       110: q^2+q+1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       195: q
       196: q^2+q+1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       262: 1
       266: 1
       269: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       366: 1
       380: 1
       388: 1
       391: 1
       396: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       469: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       532: 1
       536: 1
       543: 1
       547: 1
       594: 1
       596: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: 1
       676: 1
       677: 1
       720: 1
       727: 1
       806: 1
       808: 1
       811: 1
       930: 1

 931:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q^2+q+1
        59: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: 1
        73: q^2+2q+1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       108: 1
       109: q^2+q+1
       110: q
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: q^2+q+1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       261: 1
       265: 1
       270: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       366: 1
       379: 1
       387: 1
       392: 1
       395: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 1
       446: 1
       470: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       531: 1
       535: 1
       544: 1
       548: 1
       594: 1
       595: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: 1
       676: 1
       677: 1
       719: 1
       728: 1
       806: 1
       807: 1
       812: 1
       931: 1

 932:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: q
        60: 1
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       110: q
       111: 1
       113: q+1
       115: q+1
       117: 1
       118: q
       119: 1
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       186: q
       187: 1
       189: q+1
       191: 1
       192: q
       193: 1
       195: 1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: q+1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       275: 1
       279: 1
       289: 1
       293: 1
       295: 1
       296: q
       297: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       317: 1
       319: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: q+1
       347: 1
       349: q+1
       351: 1
       353: 1
       355: 1
       360: 1
       362: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       381: 1
       385: 1
       389: 1
       393: 1
       409: 1
       415: 1
       427: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: 1
       445: 1
       453: 1
       465: 1
       471: 1
       484: 1
       485: 1
       487: 1
       496: 1
       502: 1
       504: 1
       509: 1
       511: 1
       518: 1
       519: 1
       525: 1
       537: 1
       541: 1
       545: 1
       601: 1
       611: 1
       615: 1
       617: 1
       635: 1
       647: 1
       666: 1
       668: 1
       672: 1
       678: 1
       729: 1
       733: 1
       789: 1
       813: 1
       815: 1
       932: 1

 933:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: 1
        60: 1
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       109: q
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: 1
       119: 1
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       185: q
       186: 1
       188: 1
       190: q+1
       191: q
       192: 1
       193: 1
       195: q
       196: 1
       198: 1
       199: 1
       201: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: q+1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       276: 1
       280: 1
       290: 1
       293: 1
       295: q
       296: 1
       298: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       318: 1
       319: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: q+1
       347: 1
       349: q+1
       351: 1
       353: 1
       355: 1
       361: 1
       363: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       382: 1
       386: 1
       390: 1
       394: 1
       410: 1
       416: 1
       428: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: 1
       446: 1
       453: 1
       466: 1
       471: 1
       484: 1
       486: 1
       488: 1
       496: 1
       503: 1
       505: 1
       509: 1
       511: 1
       518: 1
       519: 1
       526: 1
       538: 1
       542: 1
       546: 1
       602: 1
       612: 1
       615: 1
       618: 1
       636: 1
       647: 1
       667: 1
       669: 1
       672: 1
       678: 1
       730: 1
       734: 1
       790: 1
       814: 1
       815: 1
       933: 1

 934:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: 1
        61: 1
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       108: 1
       109: q
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: 1
       120: 1
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       185: q
       186: 1
       187: 1
       189: q+1
       191: q
       192: 1
       194: 1
       195: q
       196: 1
       197: 1
       200: 1
       202: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: 1
       224: q+1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       237: 1
       239: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       278: 1
       279: 1
       289: 1
       294: 1
       295: q
       296: 1
       297: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       317: 1
       320: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: q+1
       347: 1
       349: q+1
       351: 1
       353: 1
       355: 1
       360: 1
       362: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       384: 1
       388: 1
       391: 1
       396: 1
       409: 1
       415: 1
       427: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: 1
       445: 1
       454: 1
       465: 1
       472: 1
       484: 1
       485: 1
       487: 1
       496: 1
       502: 1
       504: 1
       509: 1
       511: 1
       518: 1
       519: 1
       528: 1
       539: 1
       543: 1
       547: 1
       601: 1
       611: 1
       616: 1
       617: 1
       635: 1
       648: 1
       666: 1
       668: 1
       672: 1
       678: 1
       731: 1
       735: 1
       789: 1
       813: 1
       816: 1
       934: 1

 935:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: q
        61: 1
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: 1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: q+1
        95: q+1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       110: q
       112: 1
       114: q+1
       116: q+1
       117: 1
       118: q
       120: 1
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       161: q+1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       186: q
       188: 1
       190: q+1
       191: 1
       192: q
       194: 1
       195: 1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: 1
       224: q+1
       227: q+1
       229: 1
       230: q+1
       232: 1
       234: 1
       238: 1
       240: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       253: 1
       254: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       277: 1
       280: 1
       290: 1
       294: 1
       295: 1
       296: q
       298: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       318: 1
       320: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: q+1
       347: 1
       349: q+1
       351: 1
       353: 1
       355: 1
       361: 1
       363: 1
       367: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: 1
       383: 1
       387: 1
       392: 1
       395: 1
       410: 1
       416: 1
       428: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: 1
       446: 1
       454: 1
       466: 1
       472: 1
       484: 1
       486: 1
       488: 1
       496: 1
       503: 1
       505: 1
       509: 1
       511: 1
       518: 1
       519: 1
       527: 1
       540: 1
       544: 1
       548: 1
       602: 1
       612: 1
       616: 1
       618: 1
       636: 1
       648: 1
       667: 1
       669: 1
       672: 1
       678: 1
       732: 1
       736: 1
       790: 1
       814: 1
       816: 1
       935: 1

 936:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: q^3+2q^2+3q+1
        25: 5q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+4q^2+4q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: 2q^2+4q+1
        34: 5q^2+5q+1
        35: 3q^2+4q+1
        36: 5q^2+5q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+3q+1
        59: q^2+q
        60: 2q^2+3q+1
        61: 3q^2+2q
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q^2+3q+1
       106: q^2+q
       107: q+1
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: 2q+1
       119: 2q+1
       120: q^2+q
       121: q^2+3q+1
       123: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+3q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 3q^2+4q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: 2q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 2q+1
       195: q+1
       199: 2q+1
       200: q^2+q
       201: q+1
       203: q+1
       205: q+1
       207: q^2+3q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       271: q+1
       275: 2q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       321: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       397: q+1
       401: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       439: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       467: 1
       469: q+1
       473: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: 1
       583: 1
       587: 1
       607: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       686: 1
       688: 1
       705: 1
       737: 1
       741: 1
       745: 1
       823: 1
       841: 1
       847: 1
       936: 1

 937:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: q^3+2q^2+3q+1
        25: 5q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+4q^2+4q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: 2q^2+4q+1
        34: 5q^2+5q+1
        35: 3q^2+4q+1
        36: 5q^2+5q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+3q+1
        59: q^2+q
        60: 3q^2+2q
        61: 2q^2+3q+1
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q^2+q
       105: q^2+3q+1
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: 2q+1
       119: q^2+q
       120: 2q+1
       122: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+3q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 3q^2+4q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: 2q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 2q+1
       195: q+1
       199: q^2+q
       200: 2q+1
       202: q+1
       203: q+1
       206: q+1
       208: q^2+3q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       272: q+1
       277: 2q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       321: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       398: q+1
       402: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       439: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       468: 1
       470: q+1
       473: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: 1
       584: 1
       588: 1
       607: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       686: 1
       688: 1
       707: 1
       738: 1
       742: 1
       746: 1
       824: 1
       842: 1
       847: 1
       937: 1

 938:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: q^3+2q^2+3q+1
        25: 5q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+4q^2+4q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: 2q^2+4q+1
        34: 5q^2+5q+1
        35: 3q^2+4q+1
        36: 5q^2+5q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+3q+1
        60: 3q^2+2q
        61: 2q^2+3q+1
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q^2+q
       106: q^2+3q+1
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       118: 2q+1
       119: q^2+q
       120: 2q+1
       121: q^2+3q+1
       123: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+3q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 3q^2+4q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: 2q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 2q+1
       196: q+1
       199: q^2+q
       200: 2q+1
       202: q+1
       204: q+1
       205: q+1
       207: q^2+3q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       273: q+1
       278: 2q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       322: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       399: q+1
       404: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       440: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       467: 1
       469: q+1
       474: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: 1
       583: 1
       587: 1
       608: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       686: 1
       688: 1
       708: 1
       739: 1
       743: 1
       747: 1
       823: 1
       841: 1
       848: 1
       938: 1

 939:    0: 5q^2+5q+1
         1: 5q^2+5q+1
         2: 2q^3+4q^2+4q+1
         3: 5q^2+5q+1
         4: q^4+3q^3+4q^2+3q+1
         5: 5q^2+5q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^3+4q^2+4q+1
         9: q^3+2q^2+2q+1
        10: 5q^2+5q+1
        11: 5q^2+5q+1
        12: q^4+3q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+2q^2+2q+1
        15: 3q^2+4q+1
        16: 5q^2+5q+1
        17: 5q^2+5q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: q^3+2q^2+3q+1
        25: 5q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+4q^2+4q+1
        28: 5q^2+5q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: 2q^2+4q+1
        34: 5q^2+5q+1
        35: 3q^2+4q+1
        36: 5q^2+5q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+2q^2+2q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+3q+1
        60: 2q^2+3q+1
        61: 3q^2+2q
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+2q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q^2+3q+1
       105: q^2+q
       107: q+1
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       118: 2q+1
       119: 2q+1
       120: q^2+q
       122: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+3q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 3q^2+4q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: 2q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: 2q+1
       196: q+1
       199: 2q+1
       200: q^2+q
       201: q+1
       204: q+1
       206: q+1
       208: q^2+3q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       274: q+1
       276: 2q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       322: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       400: q+1
       403: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       440: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       468: 1
       470: q+1
       474: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: 1
       584: 1
       588: 1
       608: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       686: 1
       688: 1
       706: 1
       740: 1
       744: 1
       748: 1
       824: 1
       842: 1
       848: 1
       939: 1

 940:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: 1
        61: q
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       108: q
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       120: q
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       184: q
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       200: q
       201: 1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       284: q
       285: 1
       287: 1
       289: 1
       291: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: 1
       350: 1
       352: q+1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       377: 1
       381: 1
       397: 1
       401: 1
       413: 1
       417: 1
       427: 1
       431: 1
       447: 1
       448: q
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       484: 1
       485: 1
       487: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       521: 1
       549: 1
       553: 1
       561: 1
       601: 1
       623: 1
       631: 1
       633: 1
       639: 1
       643: 1
       657: 1
       658: 1
       660: 1
       680: 1
       737: 1
       749: 1
       775: 1
       817: 1
       819: 1
       940: 1

 941:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: 1
        60: q
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: 1
       107: q
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       119: q
       120: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: q
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       199: q
       200: 1
       201: q
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       272: 1
       277: 1
       280: 1
       282: 1
       283: q
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: 1
       350: 1
       352: q+1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       379: 1
       383: 1
       398: 1
       402: 1
       414: 1
       418: 1
       428: 1
       431: 1
       447: q
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       484: 1
       486: 1
       488: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       523: 1
       550: 1
       554: 1
       562: 1
       602: 1
       624: 1
       631: 1
       634: 1
       640: 1
       643: 1
       657: 1
       659: 1
       661: 1
       680: 1
       738: 1
       750: 1
       776: 1
       817: 1
       820: 1
       941: 1

 942:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: q
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: 1
       107: q
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       119: q
       120: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: 1
       129: q+1
       131: 1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       183: q
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       199: q
       200: 1
       201: q
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       273: 1
       278: 1
       279: 1
       281: 1
       283: q
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: 1
       350: 1
       352: q+1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       380: 1
       384: 1
       399: 1
       404: 1
       413: 1
       417: 1
       427: 1
       432: 1
       447: q
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       484: 1
       485: 1
       487: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       524: 1
       552: 1
       555: 1
       563: 1
       601: 1
       623: 1
       632: 1
       633: 1
       639: 1
       644: 1
       657: 1
       658: 1
       660: 1
       680: 1
       739: 1
       751: 1
       775: 1
       818: 1
       819: 1
       942: 1

 943:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 1
        53: q+1
        54: 1
        55: q+1
        56: q^2+2q+1
        57: q+1
        59: 1
        60: 1
        61: q
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q^2+2q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       108: q
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       120: q
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: q+1
       132: 1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       184: q
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       200: q
       201: 1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       284: q
       286: 1
       288: 1
       290: 1
       292: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: 1
       350: 1
       352: q+1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       378: 1
       382: 1
       400: 1
       403: 1
       414: 1
       418: 1
       428: 1
       432: 1
       447: 1
       448: q
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       484: 1
       486: 1
       488: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       522: 1
       551: 1
       556: 1
       564: 1
       602: 1
       624: 1
       632: 1
       634: 1
       640: 1
       644: 1
       657: 1
       659: 1
       661: 1
       680: 1
       740: 1
       752: 1
       776: 1
       818: 1
       820: 1
       943: 1

 944:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q+1
        39: q+1
        41: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        60: 2q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: q+1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: 2q+1
       120: q
       121: q+1
       123: q+1
       125: 3q+1
       126: 2q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 3q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q+1
       185: 1
       187: 1
       189: 1
       191: q+1
       195: 1
       199: 2q+1
       200: q
       201: q+1
       203: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       271: 1
       275: q+1
       279: 1
       281: 1
       283: q+1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: q+1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       447: q+1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: 1
       482: 1
       497: q+1
       498: 1
       499: 1
       508: 1
       514: 1
       521: 1
       529: 1
       549: 1
       553: 1
       557: 1
       585: 1
       589: 1
       595: 1
       619: 1
       621: 1
       623: 1
       625: 1
       639: 1
       643: 1
       681: 1
       682: 1
       709: 1
       737: 1
       741: 1
       821: 1
       825: 1
       831: 1
       944: 1

 945:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        38: q+1
        40: q+1
        42: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        60: q
        61: 2q+1
        63: q+1
        65: q+1
        67: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: q+1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       119: q
       120: 2q+1
       122: q+1
       124: q+1
       125: 3q+1
       126: 2q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 3q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: q+1
       185: 1
       188: 1
       190: 1
       191: q+1
       195: 1
       199: q
       200: 2q+1
       202: q+1
       203: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       272: 1
       277: q+1
       280: 1
       282: 1
       284: q+1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: q+1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       448: q+1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: 1
       482: 1
       497: q+1
       498: 1
       499: 1
       508: 1
       514: 1
       523: 1
       531: 1
       550: 1
       554: 1
       558: 1
       586: 1
       590: 1
       595: 1
       620: 1
       621: 1
       624: 1
       626: 1
       640: 1
       643: 1
       681: 1
       682: 1
       711: 1
       738: 1
       742: 1
       822: 1
       826: 1
       831: 1
       945: 1

 946:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q+1
        39: q+1
        41: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        59: q+1
        60: q
        61: 2q+1
        62: q+1
        64: q+1
        66: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: q+1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       119: q
       120: 2q+1
       121: q+1
       123: q+1
       125: 3q+1
       126: 2q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 3q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: q+1
       186: 1
       187: 1
       189: 1
       192: q+1
       196: 1
       199: q
       200: 2q+1
       202: q+1
       204: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       273: 1
       278: q+1
       279: 1
       281: 1
       284: q+1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: q+1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       448: q+1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: 1
       482: 1
       497: q+1
       498: 1
       499: 1
       508: 1
       514: 1
       524: 1
       532: 1
       552: 1
       555: 1
       559: 1
       585: 1
       590: 1
       596: 1
       620: 1
       622: 1
       623: 1
       625: 1
       639: 1
       644: 1
       681: 1
       682: 1
       712: 1
       739: 1
       743: 1
       821: 1
       826: 1
       832: 1
       946: 1

 947:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: 2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        38: q+1
        40: q+1
        42: q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 1
        53: 1
        54: 1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        59: q+1
        60: 2q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: 3q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: q+1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: 2q+1
       120: q
       122: q+1
       124: q+1
       125: 3q+1
       126: 2q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 3q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q+1
       186: 1
       188: 1
       190: 1
       192: q+1
       196: 1
       199: 2q+1
       200: q
       201: q+1
       204: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       274: 1
       276: q+1
       280: 1
       282: 1
       283: q+1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: q+1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       350: 1
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       447: q+1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: 1
       482: 1
       497: q+1
       498: 1
       499: 1
       508: 1
       514: 1
       522: 1
       530: 1
       551: 1
       556: 1
       560: 1
       586: 1
       589: 1
       596: 1
       619: 1
       622: 1
       624: 1
       626: 1
       640: 1
       644: 1
       681: 1
       682: 1
       710: 1
       740: 1
       744: 1
       822: 1
       825: 1
       832: 1
       947: 1

 948:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: 1
        60: q^2+q+1
        61: q
        62: 1
        64: 1
        66: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       103: 1
       107: q^2+q+1
       108: q
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       201: q^2+q+1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       259: 1
       263: 1
       271: 1
       275: 1
       283: 1
       285: 1
       287: 1
       291: 1
       293: 1
       295: 1
       297: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       366: 1
       377: 1
       385: 1
       397: 1
       401: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 1
       463: 1
       469: 1
       481: 1
       483: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       529: 1
       549: 1
       557: 1
       561: 1
       589: 1
       591: 1
       599: 1
       619: 1
       621: 1
       625: 1
       629: 1
       681: 1
       683: 1
       713: 1
       741: 1
       825: 1
       827: 1
       835: 1
       948: 1

 949:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: 1
        60: q
        61: q^2+q+1
        63: 1
        65: 1
        67: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       105: 1
       107: q
       108: q^2+q+1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       200: 1
       201: q
       202: q^2+q+1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       261: 1
       265: 1
       272: 1
       277: 1
       284: 1
       285: 1
       288: 1
       292: 1
       294: 1
       295: 1
       298: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       366: 1
       379: 1
       387: 1
       398: 1
       402: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 1
       464: 1
       470: 1
       481: 1
       483: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       531: 1
       550: 1
       558: 1
       562: 1
       590: 1
       591: 1
       600: 1
       620: 1
       621: 1
       626: 1
       630: 1
       681: 1
       683: 1
       714: 1
       742: 1
       826: 1
       827: 1
       836: 1
       949: 1

 950:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        59: 1
        60: q
        61: q^2+q+1
        62: 1
        64: 1
        66: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       106: 1
       107: q
       108: q^2+q+1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       200: 1
       201: q
       202: q^2+q+1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       262: 1
       266: 1
       273: 1
       278: 1
       284: 1
       286: 1
       287: 1
       291: 1
       294: 1
       296: 1
       297: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       366: 1
       380: 1
       388: 1
       399: 1
       404: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 1
       463: 1
       469: 1
       481: 1
       483: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       532: 1
       552: 1
       559: 1
       563: 1
       590: 1
       592: 1
       599: 1
       620: 1
       622: 1
       625: 1
       629: 1
       681: 1
       683: 1
       716: 1
       743: 1
       826: 1
       828: 1
       835: 1
       950: 1

 951:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        59: 1
        60: q^2+q+1
        61: q
        63: 1
        65: 1
        67: 1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       104: 1
       107: q^2+q+1
       108: q
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       201: q^2+q+1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       260: 1
       264: 1
       274: 1
       276: 1
       283: 1
       286: 1
       288: 1
       292: 1
       293: 1
       296: 1
       298: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       366: 1
       378: 1
       386: 1
       400: 1
       403: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 1
       464: 1
       470: 1
       481: 1
       483: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       530: 1
       551: 1
       560: 1
       564: 1
       589: 1
       592: 1
       600: 1
       619: 1
       622: 1
       626: 1
       630: 1
       681: 1
       683: 1
       715: 1
       744: 1
       825: 1
       828: 1
       836: 1
       951: 1

 952:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: 4q^2+7q+1
        23: 4q^2+7q+1
        24: 3q^2+4q+1
        25: q^3+7q^2+7q+1
        26: q^3+7q^2+7q+1
        27: q^3+4q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: q^2+6q+1
        32: q^2+4q+1
        33: 4q^2+7q+1
        34: 3q^2+6q+1
        35: 2q^2+4q+1
        36: q^3+7q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: 2q^2+5q+1
        54: q^2+3q+1
        55: 4q^2+5q+1
        56: q^3+5q^2+5q+1
        57: 2q^2+3q+1
        58: q^2+4q+1
        59: 2q
        60: 2q^2+4q+1
        61: q^2+2q
        62: q^2+4q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 3q^2+5q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: 2q^2+3q+1
        73: q^2+4q+1
        74: 3q+1
        76: q^2+3q+1
        78: 2q+1
        80: 3q+1
        81: q^2+4q+1
        82: 4q+1
        83: 3q+1
        84: 3q+1
        85: 2q^2+4q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 4q^2+5q+1
        98: q^3+5q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q
       105: q
       106: q
       107: q^2+2q+1
       109: 2q+1
       110: q
       111: 2q+1
       113: 2q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: 3q+1
       138: 3q+1
       139: 4q+1
       140: q+1
       141: 2q+1
       142: q^2+4q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q+1
       147: 2q^2+3q+1
       148: q^2+4q+1
       149: 4q+1
       150: 3q+1
       151: 3q+1
       153: q^2+3q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       169: q+1
       173: q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       183: 1
       185: 1
       187: q+1
       189: q+1
       191: q+1
       193: q+1
       195: 2q+1
       196: q
       197: 1
       199: q+1
       201: q^2+2q+1
       203: 2q+1
       204: q
       205: 2q+1
       207: 2q+1
       208: q
       209: 2q+1
       211: 2q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: 2q+1
       234: q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q+1
       245: q^2+4q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       263: 1
       267: 1
       271: q+1
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 2q+1
       313: q+1
       315: 2q+1
       317: 2q+1
       319: q+1
       321: 2q+1
       322: q
       323: 1
       325: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       377: 1
       385: 1
       389: 1
       393: 1
       397: q+1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: 1
       433: 1
       443: 2
       445: 2
       447: 1
       449: 1
       451: q+1
       453: 1
       457: 1
       459: 1
       461: 1
       462: 1
       463: q+2
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       512: 1
       514: q+1
       529: 1
       533: 1
       545: 2
       549: 1
       557: 1
       561: 1
       563: 1
       565: 1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       593: 1
       595: 1
       599: 1
       613: 1
       619: 1
       621: 1
       625: 1
       629: 1
       641: 1
       643: 1
       645: 1
       682: 1
       683: 1
       689: 1
       693: 1
       696: 1
       717: 1
       741: 1
       753: 1
       829: 1
       831: 1
       835: 1
       855: 1
       952: 1

 953:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: 4q^2+7q+1
        23: 4q^2+7q+1
        24: 3q^2+4q+1
        25: q^3+7q^2+7q+1
        26: q^3+7q^2+7q+1
        27: q^3+4q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: q^2+6q+1
        32: q^2+4q+1
        33: 4q^2+7q+1
        34: 3q^2+6q+1
        35: 2q^2+4q+1
        36: q^3+7q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: 2q^2+5q+1
        54: q^2+3q+1
        55: 4q^2+5q+1
        56: q^3+5q^2+5q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+4q+1
        60: 2q^2+4q+1
        61: q^2+2q
        62: 2q
        63: q^2+4q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 3q^2+5q+1
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: 2q^2+3q+1
        73: q^2+4q+1
        75: 3q+1
        77: q^2+3q+1
        79: 2q+1
        80: 3q+1
        81: q^2+4q+1
        82: 4q+1
        83: 3q+1
        84: 3q+1
        85: 2q^2+4q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 4q^2+5q+1
        98: q^3+5q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q^2+3q+1
       105: q
       106: q
       107: q^2+2q+1
       109: q
       110: 2q+1
       112: 2q+1
       114: 2q+1
       116: 2q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: 3q+1
       138: 3q+1
       139: 4q+1
       140: q+1
       141: 2q+1
       142: q^2+4q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q+1
       147: 2q^2+3q+1
       148: q^2+4q+1
       149: 4q+1
       150: 3q+1
       152: 3q+1
       154: q^2+3q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       170: q+1
       174: q+1
       178: 2q+1
       180: 2q+1
       182: 2q+1
       183: 1
       186: 1
       188: q+1
       190: q+1
       192: q+1
       193: q+1
       195: q
       196: 2q+1
       198: 1
       199: q+1
       201: q^2+2q+1
       203: q
       204: 2q+1
       206: 2q+1
       207: q
       208: 2q+1
       210: 2q+1
       212: 2q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: 2q+1
       234: q+1
       235: 2q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q+1
       245: q^2+4q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q+1
       264: 1
       268: 1
       274: q+1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 2q+1
       314: q+1
       316: 2q+1
       318: 2q+1
       319: q+1
       321: q
       322: 2q+1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       378: 1
       386: 1
       390: 1
       394: 1
       400: q+1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: 1
       434: 1
       443: 2
       446: 2
       447: 1
       450: 1
       452: q+1
       453: 1
       458: 1
       460: 1
       461: 1
       462: 1
       464: q+2
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       512: 1
       514: q+1
       530: 1
       534: 1
       546: 2
       551: 1
       560: 1
       562: 1
       564: 1
       566: 1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       593: 1
       596: 1
       600: 1
       614: 1
       619: 1
       622: 1
       626: 1
       630: 1
       641: 1
       644: 1
       646: 1
       682: 1
       683: 1
       689: 1
       694: 1
       699: 1
       718: 1
       744: 1
       754: 1
       829: 1
       832: 1
       836: 1
       856: 1
       953: 1

 954:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: 4q^2+7q+1
        23: 4q^2+7q+1
        24: 3q^2+4q+1
        25: q^3+7q^2+7q+1
        26: q^3+7q^2+7q+1
        27: q^3+4q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: q^2+6q+1
        32: q^2+4q+1
        33: 4q^2+7q+1
        34: 3q^2+6q+1
        35: 2q^2+4q+1
        36: q^3+7q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: 2q^2+5q+1
        54: q^2+3q+1
        55: 4q^2+5q+1
        56: q^3+5q^2+5q+1
        57: 2q^2+3q+1
        58: q^2+4q+1
        59: 2q
        60: q^2+2q
        61: 2q^2+4q+1
        62: 2q
        63: q^2+4q+1
        64: q
        65: q^2+3q+1
        66: q^2+2q
        67: 3q^2+5q+1
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: 2q^2+3q+1
        73: q^2+4q+1
        75: 3q+1
        77: q^2+3q+1
        79: 2q+1
        80: 3q+1
        81: q^2+4q+1
        82: 4q+1
        83: 3q+1
        84: 3q+1
        85: 2q^2+4q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 4q^2+5q+1
        98: q^3+5q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q
       105: q^2+3q+1
       106: q
       108: q^2+2q+1
       109: 2q+1
       110: q
       112: 2q+1
       114: 2q+1
       116: 2q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: q^2+3q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: 3q+1
       138: 3q+1
       139: 4q+1
       140: q+1
       141: 2q+1
       142: q^2+4q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q+1
       147: 2q^2+3q+1
       148: q^2+4q+1
       149: 4q+1
       150: 3q+1
       152: 3q+1
       154: q^2+3q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       171: q+1
       175: q+1
       178: 2q+1
       180: 2q+1
       182: 2q+1
       184: 1
       185: 1
       188: q+1
       190: q+1
       191: q+1
       194: q+1
       195: 2q+1
       196: q
       198: 1
       200: q+1
       202: q^2+2q+1
       203: 2q+1
       204: q
       206: 2q+1
       207: q
       208: 2q+1
       210: 2q+1
       212: 2q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: 2q+1
       234: q+1
       235: 2q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q+1
       245: q^2+4q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: q+1
       265: 1
       270: 1
       272: q+1
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 2q+1
       314: q+1
       316: 2q+1
       318: 2q+1
       320: q+1
       321: 2q+1
       322: q
       324: 1
       326: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       379: 1
       387: 1
       392: 1
       395: 1
       398: q+1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: 1
       434: 1
       444: 2
       446: 2
       448: 1
       449: 1
       452: q+1
       454: 1
       457: 1
       460: 1
       461: 1
       462: 1
       464: q+2
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       512: 1
       514: q+1
       531: 1
       535: 1
       548: 2
       550: 1
       558: 1
       562: 1
       564: 1
       567: 1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       594: 1
       595: 1
       600: 1
       614: 1
       620: 1
       621: 1
       626: 1
       630: 1
       642: 1
       643: 1
       646: 1
       682: 1
       683: 1
       689: 1
       700: 1
       701: 1
       719: 1
       742: 1
       755: 1
       830: 1
       831: 1
       836: 1
       856: 1
       954: 1

 955:    0: q^3+7q^2+7q+1
         1: q^3+7q^2+7q+1
         2: q^3+4q^2+4q+1
         3: q^3+7q^2+7q+1
         4: 2q^3+6q^2+5q+1
         5: q^3+7q^2+7q+1
         6: q^4+4q^3+7q^2+5q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q^2+6q+1
        11: 3q^2+6q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+3q+1
        15: 2q^2+4q+1
        16: q^3+7q^2+7q+1
        17: q^3+7q^2+7q+1
        18: q^3+3q^2+3q+1
        19: 4q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 2q^2+3q+1
        22: 4q^2+7q+1
        23: 4q^2+7q+1
        24: 3q^2+4q+1
        25: q^3+7q^2+7q+1
        26: q^3+7q^2+7q+1
        27: q^3+4q^2+4q+1
        28: 3q^2+6q+1
        29: 2q^2+4q+1
        30: q^2+3q+1
        31: q^2+6q+1
        32: q^2+4q+1
        33: 4q^2+7q+1
        34: 3q^2+6q+1
        35: 2q^2+4q+1
        36: q^3+7q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: 2q^2+3q+1
        49: 4q^2+5q+1
        50: q^3+5q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: 2q^2+5q+1
        54: q^2+3q+1
        55: 4q^2+5q+1
        56: q^3+5q^2+5q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+4q+1
        60: q^2+2q
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 2q
        64: q^2+3q+1
        65: q
        66: 3q^2+5q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: 2q^2+3q+1
        73: q^2+4q+1
        74: 3q+1
        76: q^2+3q+1
        78: 2q+1
        80: 3q+1
        81: q^2+4q+1
        82: 4q+1
        83: 3q+1
        84: 3q+1
        85: 2q^2+4q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 4q^2+5q+1
        98: q^3+5q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: q^2+3q+1
       103: q
       104: q
       105: q
       106: q^2+3q+1
       108: q^2+2q+1
       109: q
       110: 2q+1
       111: 2q+1
       113: 2q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: q^2+3q+1
       124: q
       125: q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 1
       134: 2q+1
       135: q+1
       136: 2q+1
       137: 3q+1
       138: 3q+1
       139: 4q+1
       140: q+1
       141: 2q+1
       142: q^2+4q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q+1
       147: 2q^2+3q+1
       148: q^2+4q+1
       149: 4q+1
       150: 3q+1
       151: 3q+1
       153: q^2+3q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       172: q+1
       176: q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       184: 1
       186: 1
       187: q+1
       189: q+1
       192: q+1
       194: q+1
       195: q
       196: 2q+1
       197: 1
       200: q+1
       202: q^2+2q+1
       203: q
       204: 2q+1
       205: 2q+1
       207: 2q+1
       208: q
       209: 2q+1
       211: 2q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: 2q+1
       234: q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q+1
       245: q^2+4q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: q+1
       266: 1
       269: 1
       273: q+1
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 2q+1
       313: q+1
       315: 2q+1
       317: 2q+1
       320: q+1
       321: q
       322: 2q+1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       380: 1
       388: 1
       391: 1
       396: 1
       399: q+1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: 1
       433: 1
       444: 2
       445: 2
       448: 1
       450: 1
       451: q+1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: q+2
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       512: 1
       514: q+1
       532: 1
       536: 1
       547: 2
       552: 1
       559: 1
       561: 1
       563: 1
       568: 1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       594: 1
       596: 1
       599: 1
       613: 1
       620: 1
       622: 1
       625: 1
       629: 1
       642: 1
       644: 1
       645: 1
       682: 1
       683: 1
       689: 1
       697: 1
       698: 1
       720: 1
       743: 1
       756: 1
       830: 1
       832: 1
       835: 1
       855: 1
       955: 1

 956:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 1
        60: 1
        61: q
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       108: q
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: 1
       119: 1
       120: q
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: q+1
       145: q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       184: q
       185: 1
       187: 1
       189: q+1
       191: 1
       195: 1
       199: 1
       200: q
       201: 1
       202: q
       203: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: q+1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       259: 1
       263: 1
       271: 1
       275: 1
       279: 1
       289: 1
       293: 1
       294: q
       295: 1
       297: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       317: 1
       321: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: 1
       349: 1
       353: q+1
       355: q+1
       357: 1
       359: 1
       360: 1
       362: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       381: 1
       385: 1
       397: 1
       401: 1
       409: 1
       415: 1
       427: 1
       439: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       473: 1
       484: 1
       485: 1
       487: 1
       501: 1
       502: 1
       504: 1
       509: 1
       513: 1
       518: 1
       519: 1
       525: 1
       553: 1
       557: 1
       561: 1
       601: 1
       627: 1
       631: 1
       633: 1
       635: 1
       649: 1
       666: 1
       668: 1
       672: 1
       684: 1
       745: 1
       749: 1
       789: 1
       837: 1
       839: 1
       956: 1

 957:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 1
        60: q
        61: 1
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       107: q
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: 1
       119: q
       120: 1
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: q+1
       145: q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       183: q
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 1
       195: 1
       199: q
       200: 1
       201: q
       202: 1
       203: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: q+1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       261: 1
       265: 1
       272: 1
       277: 1
       280: 1
       290: 1
       293: q
       294: 1
       295: 1
       298: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       321: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: 1
       349: 1
       353: q+1
       355: q+1
       357: 1
       359: 1
       361: 1
       363: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       383: 1
       387: 1
       398: 1
       402: 1
       410: 1
       416: 1
       428: 1
       439: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       473: 1
       484: 1
       486: 1
       488: 1
       501: 1
       503: 1
       505: 1
       509: 1
       513: 1
       518: 1
       519: 1
       527: 1
       554: 1
       558: 1
       562: 1
       602: 1
       628: 1
       631: 1
       634: 1
       636: 1
       649: 1
       667: 1
       669: 1
       672: 1
       684: 1
       746: 1
       750: 1
       790: 1
       838: 1
       839: 1
       957: 1

 958:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: 1
        60: q
        61: 1
        62: q+1
        64: q+1
        66: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       107: q
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: 1
       119: q
       120: 1
       121: q+1
       123: 1
       125: q+1
       127: 1
       129: 1
       133: q+1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: q+1
       145: q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       183: q
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 1
       196: 1
       199: q
       200: 1
       201: q
       202: 1
       204: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: q+1
       222: q+1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       237: 1
       239: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       262: 1
       266: 1
       273: 1
       278: 1
       279: 1
       289: 1
       293: q
       294: 1
       296: 1
       297: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       322: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: 1
       349: 1
       353: q+1
       355: q+1
       357: 1
       359: 1
       360: 1
       362: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       384: 1
       388: 1
       399: 1
       404: 1
       409: 1
       415: 1
       427: 1
       440: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       474: 1
       484: 1
       485: 1
       487: 1
       501: 1
       502: 1
       504: 1
       509: 1
       513: 1
       518: 1
       519: 1
       528: 1
       555: 1
       559: 1
       563: 1
       601: 1
       627: 1
       632: 1
       633: 1
       635: 1
       650: 1
       666: 1
       668: 1
       672: 1
       684: 1
       747: 1
       751: 1
       789: 1
       837: 1
       840: 1
       958: 1

 959:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: 1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: 1
        60: 1
        61: q
        63: q+1
        65: q+1
        67: 1
        68: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        94: 1
        95: 1
        97: q+1
        98: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       108: q
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: 1
       119: 1
       120: q
       122: q+1
       124: 1
       125: q+1
       128: 1
       130: 1
       133: q+1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: q+1
       145: q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       184: q
       186: 1
       188: 1
       190: q+1
       192: 1
       196: 1
       199: 1
       200: q
       201: 1
       202: q
       204: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: q+1
       222: q+1
       224: 1
       227: 1
       230: 1
       232: q+1
       234: q+1
       235: 1
       238: 1
       240: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       260: 1
       264: 1
       274: 1
       276: 1
       280: 1
       290: 1
       293: 1
       294: q
       296: 1
       298: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       318: 1
       322: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: 1
       349: 1
       353: q+1
       355: q+1
       357: 1
       359: 1
       361: 1
       363: 1
       367: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       382: 1
       386: 1
       400: 1
       403: 1
       410: 1
       416: 1
       428: 1
       440: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       474: 1
       484: 1
       486: 1
       488: 1
       501: 1
       503: 1
       505: 1
       509: 1
       513: 1
       518: 1
       519: 1
       526: 1
       556: 1
       560: 1
       564: 1
       602: 1
       628: 1
       632: 1
       634: 1
       636: 1
       650: 1
       667: 1
       669: 1
       672: 1
       684: 1
       748: 1
       752: 1
       790: 1
       838: 1
       840: 1
       959: 1

 960:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^4+q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        10: 1
        11: 1
        12: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: q^3+1
        45: 1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       377: 1
       381: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: 1
       429: 1
       431: 1
       433: 1
       435: 1
       447: 1
       449: 1
       451: 1
       455: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       508: 1
       512: 1
       514: 1
       521: 1
       533: 1
       537: 1
       549: 1
       553: 1
       565: 1
       569: 1
       605: 1
       623: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       721: 1
       737: 1
       753: 1
       757: 1
       849: 1
       960: 1

 961:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^4+q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        10: 1
        11: 1
        12: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: q^3+1
        45: 1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       380: 1
       384: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: 1
       430: 1
       432: 1
       433: 1
       435: 1
       448: 1
       450: 1
       451: 1
       455: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       508: 1
       512: 1
       514: 1
       524: 1
       536: 1
       539: 1
       552: 1
       555: 1
       568: 1
       570: 1
       605: 1
       623: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       723: 1
       739: 1
       756: 1
       758: 1
       849: 1
       961: 1

 962:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^4+q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        10: 1
        11: 1
        12: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: q^3+1
        45: 1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       378: 1
       382: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       418: 1
       429: 1
       432: 1
       434: 1
       436: 1
       447: 1
       450: 1
       452: 1
       456: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       508: 1
       512: 1
       514: 1
       522: 1
       534: 1
       538: 1
       551: 1
       556: 1
       566: 1
       571: 1
       606: 1
       624: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       722: 1
       740: 1
       754: 1
       759: 1
       850: 1
       962: 1

 963:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+1
         5: q+1
         6: q^4+q^3+q^2+q+1
         7: q^3+1
         8: q+1
         9: q^3+1
        10: 1
        11: 1
        12: q^3+1
        13: q+1
        14: q^3+1
        15: q+1
        16: q+1
        17: q+1
        18: q^3+1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: q^3+1
        45: 1
        46: q+1
        47: q+1
        48: q^3+1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       344: 1
       348: 1
       350: 1
       352: 1
       356: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       379: 1
       383: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       418: 1
       430: 1
       431: 1
       434: 1
       436: 1
       448: 1
       449: 1
       452: 1
       456: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       508: 1
       512: 1
       514: 1
       523: 1
       535: 1
       540: 1
       550: 1
       554: 1
       567: 1
       572: 1
       606: 1
       624: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       724: 1
       738: 1
       755: 1
       760: 1
       850: 1
       963: 1

 964:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        38: q^2+2q
        39: 2q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: 2q+1
        59: q
        60: 2q+1
        61: q
        62: q+1
        63: 2q
        64: q+1
        65: q
        66: 2q+1
        67: q^2+2q
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: q
        76: q+1
        77: q^2+q
        78: 1
        79: q
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q+1
       104: q
       105: q
       107: q+1
       109: q+1
       111: 1
       113: 1
       114: q
       115: 1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: 1
       128: q
       129: q+1
       130: q^2+q
       131: 1
       132: q
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q^2+q
       155: 1
       156: q
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: 1
       173: 1
       177: 1
       178: q
       179: 1
       180: q
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       190: q
       191: 1
       193: q+1
       195: q+1
       197: 1
       199: 1
       201: q+1
       203: q+1
       205: 1
       207: 1
       208: q
       209: 1
       210: q
       211: 1
       212: q
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q
       239: q+1
       240: q^2+q
       241: 1
       242: q
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       316: q
       317: 1
       318: q
       319: q+1
       321: q+1
       323: 1
       325: 1
       326: q
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       377: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       443: 2
       445: 1
       446: 1
       447: 1
       449: 1
       451: 1
       461: 2
       463: 1
       464: 1
       469: 1
       470: q
       471: 1
       473: 1
       475: 1
       477: 1
       479: 2
       484: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       533: 1
       545: 1
       546: 1
       549: 1
       561: 1
       562: 1
       565: 1
       569: 1
       573: 2
       577: 1
       578: 1
       615: 1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       657: 1
       674: 1
       680: 1
       693: 1
       694: 1
       753: 1
       765: 1
       793: 1
       817: 1
       843: 1
       964: 1

 965:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: q^2+2q
        38: 2q+1
        39: q^2+2q
        40: 2q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q
        59: 2q+1
        60: 2q+1
        61: q
        62: 2q
        63: q+1
        64: q
        65: q+1
        66: q^2+2q
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: q
        75: 1
        76: q^2+q
        77: q+1
        78: q
        79: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       104: q+1
       106: q
       107: q+1
       110: q+1
       112: 1
       113: q
       114: 1
       115: q
       116: 1
       118: 1
       119: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q
       128: 1
       129: q^2+q
       130: q+1
       131: q
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q
       152: 1
       153: q^2+q
       154: q+1
       155: q
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       170: 1
       174: 1
       177: q
       178: 1
       179: q
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       189: q
       190: 1
       192: 1
       193: q+1
       196: q+1
       198: 1
       199: 1
       201: q+1
       204: q+1
       206: 1
       207: q
       208: 1
       209: q
       210: 1
       211: q
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q
       238: 1
       239: q^2+q
       240: q+1
       241: q
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       315: q
       316: 1
       317: q
       318: 1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       378: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       427: 1
       428: 1
       429: 1
       432: 1
       434: 1
       443: 2
       445: 1
       446: 1
       447: 1
       450: 1
       452: 1
       462: 2
       463: 1
       464: 1
       469: q
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 2
       484: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       534: 1
       545: 1
       546: 1
       551: 1
       563: 1
       564: 1
       566: 1
       571: 1
       574: 2
       580: 1
       581: 1
       615: 1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       657: 1
       674: 1
       680: 1
       696: 1
       699: 1
       754: 1
       766: 1
       793: 1
       818: 1
       844: 1
       965: 1

 966:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: q^2+2q
        38: 2q+1
        39: q^2+2q
        40: 2q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: 2q+1
        59: q
        60: q
        61: 2q+1
        62: 2q
        63: q+1
        64: q
        65: q+1
        66: q^2+2q
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: q
        75: 1
        76: q^2+q
        77: q+1
        78: q
        79: 1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       105: q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       113: q
       114: 1
       115: q
       116: 1
       117: 1
       120: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q
       128: 1
       129: q^2+q
       130: q+1
       131: q
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q
       152: 1
       153: q^2+q
       154: q+1
       155: q
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       171: 1
       175: 1
       177: q
       178: 1
       179: q
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       189: q
       190: 1
       191: 1
       194: q+1
       195: q+1
       198: 1
       200: 1
       202: q+1
       203: q+1
       206: 1
       207: q
       208: 1
       209: q
       210: 1
       211: q
       212: 1
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q
       238: 1
       239: q^2+q
       240: q+1
       241: q
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       315: q
       316: 1
       317: q
       318: 1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       379: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       427: 1
       428: 1
       430: 1
       431: 1
       434: 1
       444: 2
       445: 1
       446: 1
       448: 1
       449: 1
       452: 1
       461: 2
       463: 1
       464: 1
       469: q
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 2
       484: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       535: 1
       547: 1
       548: 1
       550: 1
       561: 1
       562: 1
       567: 1
       572: 1
       576: 2
       580: 1
       581: 1
       616: 1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       657: 1
       674: 1
       680: 1
       698: 1
       700: 1
       755: 1
       767: 1
       794: 1
       817: 1
       844: 1
       966: 1

 967:    0: q^2+4q+1
         1: q^2+4q+1
         2: q^2+2q+1
         3: q^2+4q+1
         4: q^2+2q+1
         5: q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q+1
        19: 2q+1
        20: q^2+3q+1
        21: q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+2q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: q^2+4q+1
        37: 2q+1
        38: q^2+2q
        39: 2q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: q^2+3q+1
        51: q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: 2q+1
        56: q^2+3q+1
        57: q+1
        58: q
        59: 2q+1
        60: q
        61: 2q+1
        62: q+1
        63: 2q
        64: q+1
        65: q
        66: 2q+1
        67: q^2+2q
        68: 1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: q
        76: q+1
        77: q^2+q
        78: 1
        79: q
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: q^2+3q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       104: q
       105: q
       106: q+1
       108: q+1
       110: q+1
       111: 1
       113: 1
       114: q
       115: 1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: 1
       128: q
       129: q+1
       130: q^2+q
       131: 1
       132: q
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       152: q
       153: q+1
       154: q^2+q
       155: 1
       156: q
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       172: 1
       176: 1
       177: 1
       178: q
       179: 1
       180: q
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       190: q
       192: 1
       194: q+1
       196: q+1
       197: 1
       200: 1
       202: q+1
       204: q+1
       205: 1
       207: 1
       208: q
       209: 1
       210: q
       211: 1
       212: q
       219: 1
       223: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q
       239: q+1
       240: q^2+q
       241: 1
       242: q
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2
       248: 2
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       316: q
       317: 1
       318: q
       320: q+1
       322: q+1
       323: 1
       325: 1
       326: q
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       356: 1
       358: 1
       359: 2
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       380: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       427: 1
       428: 1
       430: 1
       432: 1
       433: 1
       444: 2
       445: 1
       446: 1
       448: 1
       450: 1
       451: 1
       462: 2
       463: 1
       464: 1
       469: 1
       470: q
       472: 1
       474: 1
       475: 1
       477: 1
       479: 2
       484: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       536: 1
       547: 1
       548: 1
       552: 1
       563: 1
       564: 1
       568: 1
       570: 1
       575: 2
       577: 1
       578: 1
       616: 1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       657: 1
       674: 1
       680: 1
       697: 1
       701: 1
       756: 1
       768: 1
       794: 1
       818: 1
       843: 1
       967: 1

 968:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        64: q+1
        66: q+1
        69: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       111: 1
       115: 1
       123: q+1
       127: 1
       129: q+1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       338: 1
       340: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       417: 1
       433: 1
       435: 1
       445: 1
       451: 1
       455: 1
       463: 1
       467: 1
       475: 1
       477: 1
       479: 1
       485: 1
       487: 1
       496: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       577: 1
       605: 1
       617: 1
       623: 1
       633: 1
       645: 1
       651: 1
       655: 1
       658: 1
       660: 1
       674: 1
       680: 1
       769: 1
       795: 1
       819: 1
       843: 1
       849: 1
       968: 1

 969:    0: 2q^2+3q
         1: 2q^2+3q
         2: 2q^2+3q
         3: 2q^2+3q
         4: q^2+2q
         5: 2q^2+3q
         6: 2q^3+2q^2+2q
         7: q^2+2q
         8: 2q^2+3q
         9: q^2+2q
        13: 2q^2+3q
        14: q^2+2q
        15: 2q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^2+2q
        19: 2q
        20: q^2+2q
        21: 2q
        22: 2q^2+3q
        23: 2q^2+3q
        24: 2q^2+3q
        25: 2q^2+3q
        26: 2q^2+3q
        27: 2q^2+3q
        30: 2q
        32: 2q^2+3q
        33: 2q^2+3q
        35: 2q^2+3q
        36: 2q^2+3q
        37: q^2+q
        38: q^2+2q
        39: q^2+q
        40: q^2+2q
        41: q^2+q
        42: q^2+2q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^2+2q
        49: 2q
        50: q^2+2q
        51: 2q
        52: 2q
        53: q^2+2q
        54: 2q
        55: 2q
        56: q^2+2q
        57: 2q
        64: q^2+q
        65: q^2+2q
        66: q^2+q
        67: q^2+2q
        69: 2q
        72: q
        73: q
        75: q
        77: q
        79: q
        81: 2q^2+3q
        83: 2q
        85: 2q^2+3q
        87: 2q
        91: 2q
        92: q^2+2q
        93: 2q
        94: 2q
        95: q^2+2q
        96: 2q
        97: 2q
        98: q^2+2q
        99: 2q
       100: 2q
       101: q^2+2q
       102: 2q
       116: q
       123: q^2+q
       124: q^2+2q
       128: q
       130: q
       132: q
       134: 2q
       135: q
       136: q
       138: 2q
       140: q
       142: q
       144: 2q
       147: q
       148: q
       150: 2q
       152: q
       154: q
       156: q
       160: 2q
       161: q^2+2q
       162: 2q
       163: 2q
       164: q^2+2q
       165: 2q
       166: 2q
       167: q^2+2q
       168: 2q
       178: q
       212: q
       214: q
       216: q
       218: q
       223: q
       225: q
       228: 2q
       229: q
       230: q
       233: 2q
       234: q
       235: q
       236: 2q
       238: q
       240: q
       242: q
       244: q
       245: q
       247: 1
       248: 1
       256: 2q
       257: q^2+2q
       258: 2q
       282: q
       316: q
       339: 1
       341: 1
       348: q
       350: q
       351: 1
       356: q
       358: q
       359: 1
       361: q
       363: q
       365: q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       446: 1
       464: 1
       468: q
       479: 1
       486: 1
       488: 1
       496: 1
       501: 1
       512: q
       514: q
       515: 1
       516: 1
       578: 1
       618: 1
       634: 1
       655: 1
       659: 1
       661: 1
       674: 1
       680: 1
       770: 1
       796: 1
       820: 1
       843: 1
       969: 1

 970:    0: q^3+2q^2+q
         1: q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        30: q^3+q
        32: q^2+q
        33: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2+q
        39: 2q^2+q
        41: q^2+q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        64: q^2+q
        66: 2q^2+q
        69: q^3+q
        72: q^2+q
        73: q^2+q
        74: q^2+q
        76: 2q^2+q
        78: q
        81: q^2+q
        83: q
        85: q^2+q
        87: q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       111: q^2+q
       115: q
       123: q^2+q
       127: q^2+q
       129: 2q^2+q
       131: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q^2+q
       144: q
       147: q^2+q
       148: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       177: q
       181: q^2+q
       187: q
       197: q
       205: q
       211: q
       213: q
       215: q^2+q
       217: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       244: q
       245: q
       281: q
       289: q
       291: q
       301: q
       305: q
       311: q
       313: q
       315: q
       323: q
       348: q
       350: q
       356: q
       358: q
       417: q
       433: q
       451: q
       477: q
       651: 1
       771: 1
       849: 1
       970: 1

 971:    0: 2q^2+3q
         1: 2q^2+3q
         2: 2q^2+3q
         3: 2q^2+3q
         4: q^2+2q
         5: 2q^2+3q
         6: 2q^3+2q^2+2q
         7: q^2+2q
         8: 2q^2+3q
         9: q^2+2q
        13: 2q^2+3q
        14: q^2+2q
        15: 2q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^2+2q
        19: 2q
        20: q^2+2q
        21: 2q
        22: 2q^2+3q
        23: 2q^2+3q
        24: 2q^2+3q
        25: 2q^2+3q
        26: 2q^2+3q
        27: 2q^2+3q
        30: 2q
        32: 2q^2+3q
        33: 2q^2+3q
        35: 2q^2+3q
        36: 2q^2+3q
        37: q^2+2q
        38: q^2+q
        39: q^2+2q
        40: q^2+q
        41: q^2+2q
        42: q^2+q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^2+2q
        49: 2q
        50: q^2+2q
        51: 2q
        52: 2q
        53: q^2+2q
        54: 2q
        55: 2q
        56: q^2+2q
        57: 2q
        64: q^2+2q
        65: q^2+q
        66: q^2+2q
        67: q^2+q
        69: 2q
        72: q
        73: q
        74: q
        76: q
        78: q
        81: 2q^2+3q
        83: 2q
        85: 2q^2+3q
        87: 2q
        91: 2q
        92: q^2+2q
        93: 2q
        94: 2q
        95: q^2+2q
        96: 2q
        97: 2q
        98: q^2+2q
        99: 2q
       100: 2q
       101: q^2+2q
       102: 2q
       115: q
       123: q^2+2q
       124: q^2+q
       127: q
       129: q
       131: q
       134: 2q
       135: q
       136: q
       138: 2q
       140: q
       142: q
       144: 2q
       147: q
       148: q
       150: 2q
       151: q
       153: q
       155: q
       160: 2q
       161: q^2+2q
       162: 2q
       163: 2q
       164: q^2+2q
       165: 2q
       166: 2q
       167: q^2+2q
       168: 2q
       177: q
       211: q
       213: q
       215: q
       217: q
       223: q
       225: q
       228: 2q
       229: q
       230: q
       233: 2q
       234: q
       235: q
       236: 2q
       237: q
       239: q
       241: q
       244: q
       245: q
       247: 1
       248: 1
       256: 2q
       257: q^2+2q
       258: 2q
       281: q
       315: q
       338: 1
       340: 1
       348: q
       350: q
       351: 1
       356: q
       358: q
       359: 1
       360: q
       362: q
       364: q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       445: 1
       463: 1
       467: q
       480: 1
       485: 1
       487: 1
       496: 1
       501: 1
       512: q
       514: q
       515: 1
       516: 1
       580: 1
       617: 1
       633: 1
       656: 1
       658: 1
       660: 1
       674: 1
       680: 1
       772: 1
       795: 1
       819: 1
       844: 1
       971: 1

 972:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        65: q+1
        67: q+1
        69: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        81: q+1
        83: 1
        85: q+1
        87: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       112: 1
       116: 1
       124: q+1
       128: 1
       130: q+1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       244: 1
       245: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       339: 1
       341: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       418: 1
       434: 1
       436: 1
       446: 1
       452: 1
       456: 1
       464: 1
       468: 1
       476: 1
       478: 1
       480: 1
       486: 1
       488: 1
       496: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       581: 1
       606: 1
       618: 1
       624: 1
       634: 1
       646: 1
       652: 1
       656: 1
       659: 1
       661: 1
       674: 1
       680: 1
       773: 1
       796: 1
       820: 1
       844: 1
       850: 1
       972: 1

 973:    0: q^3+2q^2+q
         1: q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        30: q^3+q
        32: q^2+q
        33: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        38: 2q^2+q
        40: 2q^2+q
        42: q^2+q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        65: q^2+q
        67: 2q^2+q
        69: q^3+q
        72: q^2+q
        73: q^2+q
        75: q^2+q
        77: 2q^2+q
        79: q
        81: q^2+q
        83: q
        85: q^2+q
        87: q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       112: q^2+q
       116: q
       124: q^2+q
       128: q^2+q
       130: 2q^2+q
       132: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q^2+q
       144: q
       147: q^2+q
       148: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       178: q
       182: q^2+q
       188: q
       198: q
       206: q
       212: q
       214: q
       216: q^2+q
       218: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       244: q
       245: q
       282: q
       290: q
       292: q
       302: q
       306: q
       312: q
       314: q
       316: q
       324: q
       348: q
       350: q
       356: q
       358: q
       418: q
       434: q
       452: q
       478: q
       652: 1
       774: 1
       850: 1
       973: 1

 974:    0: 6q+1
         1: 6q+1
         2: 2q^2+4q+1
         3: 6q+1
         4: q^3+3q^2+3q+1
         5: 6q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+1
         9: q^2+2q+1
        10: 6q+1
        11: 6q+1
        12: q^3+3q^2+3q+1
        13: 4q+1
        14: q^2+2q+1
        15: 4q+1
        16: 6q+1
        17: 6q+1
        18: q^2+2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 6q+1
        23: 6q+1
        24: 2q^2+4q+1
        25: 6q+1
        26: 6q+1
        27: 2q^2+4q+1
        28: 6q+1
        29: 3q+1
        30: 2q+1
        31: 6q+1
        32: 4q+1
        33: 6q+1
        34: 6q+1
        35: 4q+1
        36: 6q+1
        37: 4q+1
        38: 2q
        39: 4q+1
        40: 2q
        41: q^2+3q+1
        42: q^2+q
        43: 4q+1
        44: q^2+2q+1
        45: 4q+1
        46: 4q+1
        47: 4q+1
        48: q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 4q+1
        59: 2q
        60: 4q+1
        61: 2q
        62: 4q+1
        63: 2q
        64: 3q+1
        65: q
        66: 4q+1
        67: 2q
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 4q+1
        81: 4q+1
        82: 3q+1
        83: 2q+1
        84: 4q+1
        85: 4q+1
        86: 3q+1
        87: 2q+1
        88: 4q+1
        89: 4q+1
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: 3q+1
       104: q
       105: q
       106: q
       107: q+1
       109: q+1
       111: 1
       113: q+1
       115: q+1
       117: 2q+1
       119: 2q+1
       121: 3q+1
       122: q
       123: 3q+1
       124: q
       125: 2q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 4q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 4q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: 1
       173: 2q+1
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 2q+1
       193: q+1
       195: q+1
       197: 1
       199: 2q+1
       201: q+1
       203: q+1
       205: 1
       207: 3q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 2q+1
       283: 1
       285: 1
       287: q+1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q+1
       321: q+1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       529: 1
       533: 1
       541: 1
       549: 1
       557: 1
       565: 1
       569: 1
       603: 1
       607: 1
       609: 1
       619: 1
       621: 1
       625: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       686: 1
       687: 1
       688: 1
       725: 1
       741: 1
       753: 1
       761: 1
       845: 1
       847: 1
       851: 1
       974: 1

 975:    0: 6q+1
         1: 6q+1
         2: 2q^2+4q+1
         3: 6q+1
         4: q^3+3q^2+3q+1
         5: 6q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+1
         9: q^2+2q+1
        10: 6q+1
        11: 6q+1
        12: q^3+3q^2+3q+1
        13: 4q+1
        14: q^2+2q+1
        15: 4q+1
        16: 6q+1
        17: 6q+1
        18: q^2+2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 6q+1
        23: 6q+1
        24: 2q^2+4q+1
        25: 6q+1
        26: 6q+1
        27: 2q^2+4q+1
        28: 6q+1
        29: 3q+1
        30: 2q+1
        31: 6q+1
        32: 4q+1
        33: 6q+1
        34: 6q+1
        35: 4q+1
        36: 6q+1
        37: 4q+1
        38: 2q
        39: 4q+1
        40: 2q
        41: q^2+3q+1
        42: q^2+q
        43: 4q+1
        44: q^2+2q+1
        45: 4q+1
        46: 4q+1
        47: 4q+1
        48: q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 2q
        59: 4q+1
        60: 2q
        61: 4q+1
        62: 4q+1
        63: 2q
        64: 3q+1
        65: q
        66: 4q+1
        67: 2q
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 4q+1
        81: 4q+1
        82: 3q+1
        83: 2q+1
        84: 4q+1
        85: 4q+1
        86: 3q+1
        87: 2q+1
        88: 4q+1
        89: 4q+1
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: q
       105: q
       106: 3q+1
       108: q+1
       110: q+1
       111: 1
       113: q+1
       115: q+1
       118: 2q+1
       120: 2q+1
       121: 3q+1
       122: q
       123: 3q+1
       124: q
       125: 2q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 4q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 4q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       172: 1
       176: 2q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 2q+1
       194: q+1
       196: q+1
       197: 1
       200: 2q+1
       202: q+1
       204: q+1
       205: 1
       207: 3q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 2q+1
       284: 1
       286: 1
       287: q+1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: q+1
       322: q+1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       532: 1
       536: 1
       543: 1
       552: 1
       559: 1
       568: 1
       570: 1
       604: 1
       608: 1
       609: 1
       620: 1
       622: 1
       625: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       686: 1
       687: 1
       688: 1
       727: 1
       743: 1
       756: 1
       762: 1
       846: 1
       848: 1
       851: 1
       975: 1

 976:    0: 6q+1
         1: 6q+1
         2: 2q^2+4q+1
         3: 6q+1
         4: q^3+3q^2+3q+1
         5: 6q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+1
         9: q^2+2q+1
        10: 6q+1
        11: 6q+1
        12: q^3+3q^2+3q+1
        13: 4q+1
        14: q^2+2q+1
        15: 4q+1
        16: 6q+1
        17: 6q+1
        18: q^2+2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 6q+1
        23: 6q+1
        24: 2q^2+4q+1
        25: 6q+1
        26: 6q+1
        27: 2q^2+4q+1
        28: 6q+1
        29: 3q+1
        30: 2q+1
        31: 6q+1
        32: 4q+1
        33: 6q+1
        34: 6q+1
        35: 4q+1
        36: 6q+1
        37: 2q
        38: 4q+1
        39: 2q
        40: 4q+1
        41: q^2+q
        42: q^2+3q+1
        43: 4q+1
        44: q^2+2q+1
        45: 4q+1
        46: 4q+1
        47: 4q+1
        48: q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 2q
        59: 4q+1
        60: 4q+1
        61: 2q
        62: 2q
        63: 4q+1
        64: q
        65: 3q+1
        66: 2q
        67: 4q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 4q+1
        81: 4q+1
        82: 3q+1
        83: 2q+1
        84: 4q+1
        85: 4q+1
        86: 3q+1
        87: 2q+1
        88: 4q+1
        89: 4q+1
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: 3q+1
       105: q
       106: q
       107: q+1
       110: q+1
       112: 1
       114: q+1
       116: q+1
       118: 2q+1
       119: 2q+1
       121: q
       122: 3q+1
       123: q
       124: 3q+1
       125: 2q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 4q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 4q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       170: 1
       174: 2q+1
       178: q+1
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: 2q+1
       193: q+1
       196: q+1
       198: 1
       199: 2q+1
       201: q+1
       204: q+1
       206: 1
       207: q
       208: 3q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 2q+1
       283: 1
       286: 1
       288: q+1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q+1
       322: q+1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       530: 1
       534: 1
       542: 1
       551: 1
       560: 1
       566: 1
       571: 1
       603: 1
       608: 1
       610: 1
       619: 1
       622: 1
       626: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       686: 1
       687: 1
       688: 1
       726: 1
       744: 1
       754: 1
       763: 1
       845: 1
       848: 1
       852: 1
       976: 1

 977:    0: 6q+1
         1: 6q+1
         2: 2q^2+4q+1
         3: 6q+1
         4: q^3+3q^2+3q+1
         5: 6q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+4q+1
         9: q^2+2q+1
        10: 6q+1
        11: 6q+1
        12: q^3+3q^2+3q+1
        13: 4q+1
        14: q^2+2q+1
        15: 4q+1
        16: 6q+1
        17: 6q+1
        18: q^2+2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 6q+1
        23: 6q+1
        24: 2q^2+4q+1
        25: 6q+1
        26: 6q+1
        27: 2q^2+4q+1
        28: 6q+1
        29: 3q+1
        30: 2q+1
        31: 6q+1
        32: 4q+1
        33: 6q+1
        34: 6q+1
        35: 4q+1
        36: 6q+1
        37: 2q
        38: 4q+1
        39: 2q
        40: 4q+1
        41: q^2+q
        42: q^2+3q+1
        43: 4q+1
        44: q^2+2q+1
        45: 4q+1
        46: 4q+1
        47: 4q+1
        48: q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 4q+1
        59: 2q
        60: 2q
        61: 4q+1
        62: 2q
        63: 4q+1
        64: q
        65: 3q+1
        66: 2q
        67: 4q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 4q+1
        81: 4q+1
        82: 3q+1
        83: 2q+1
        84: 4q+1
        85: 4q+1
        86: 3q+1
        87: 2q+1
        88: 4q+1
        89: 4q+1
        90: q^2+2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: q
       105: 3q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       114: q+1
       116: q+1
       117: 2q+1
       120: 2q+1
       121: q
       122: 3q+1
       123: q
       124: 3q+1
       125: 2q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 4q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 4q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       171: 1
       175: 2q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 2q+1
       194: q+1
       195: q+1
       198: 1
       200: 2q+1
       202: q+1
       203: q+1
       206: 1
       207: q
       208: 3q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 2q+1
       284: 1
       285: 1
       288: q+1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: q+1
       321: q+1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       531: 1
       535: 1
       544: 1
       550: 1
       558: 1
       567: 1
       572: 1
       604: 1
       607: 1
       610: 1
       620: 1
       621: 1
       626: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       686: 1
       687: 1
       688: 1
       728: 1
       742: 1
       755: 1
       764: 1
       846: 1
       847: 1
       852: 1
       977: 1

 978:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+q+1
         5: q+1
         6: q^3+q+1
         7: q^3+q+1
         8: q+1
        10: q+1
        11: q+1
        12: q^3+q+1
        13: q+1
        14: q^3+q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q^3+q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: q+1
        64: q+1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: 1
       119: 1
       121: q+1
       123: 1
       125: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       289: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q+1
       327: 1
       329: 1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: 1
       415: 1
       435: 1
       437: 1
       439: 1
       441: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       471: 1
       473: 1
       475: 1
       477: 1
       502: 1
       504: 1
       509: 1
       511: 1
       513: 1
       525: 1
       537: 1
       541: 1
       553: 1
       557: 1
       565: 1
       569: 1
       611: 1
       627: 1
       635: 1
       647: 1
       649: 1
       651: 1
       653: 1
       729: 1
       745: 1
       757: 1
       761: 1
       853: 1
       978: 1

 979:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+q+1
         5: q+1
         6: q^3+q+1
         7: q^3+q+1
         8: q+1
        10: q+1
        11: q+1
        12: q^3+q+1
        13: q+1
        14: q^3+q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q^3+q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: q+1
        64: q+1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: 1
       120: 1
       121: q+1
       123: 1
       125: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       289: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q+1
       327: 1
       329: 1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: 1
       415: 1
       435: 1
       438: 1
       440: 1
       441: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       472: 1
       474: 1
       475: 1
       477: 1
       502: 1
       504: 1
       509: 1
       511: 1
       513: 1
       528: 1
       539: 1
       543: 1
       555: 1
       559: 1
       568: 1
       570: 1
       611: 1
       627: 1
       635: 1
       648: 1
       650: 1
       651: 1
       653: 1
       731: 1
       747: 1
       758: 1
       762: 1
       853: 1
       979: 1

 980:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+q+1
         5: q+1
         6: q^3+q+1
         7: q^3+q+1
         8: q+1
        10: q+1
        11: q+1
        12: q^3+q+1
        13: q+1
        14: q^3+q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q^3+q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: q+1
        65: q+1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: 1
       119: 1
       122: q+1
       124: 1
       125: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       290: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q+1
       328: 1
       330: 1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: 1
       416: 1
       436: 1
       437: 1
       440: 1
       442: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       471: 1
       474: 1
       476: 1
       478: 1
       503: 1
       505: 1
       509: 1
       511: 1
       513: 1
       526: 1
       538: 1
       542: 1
       556: 1
       560: 1
       566: 1
       571: 1
       612: 1
       628: 1
       636: 1
       647: 1
       650: 1
       652: 1
       654: 1
       730: 1
       748: 1
       759: 1
       763: 1
       854: 1
       980: 1

 981:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q^3+q+1
         5: q+1
         6: q^3+q+1
         7: q^3+q+1
         8: q+1
        10: q+1
        11: q+1
        12: q^3+q+1
        13: q+1
        14: q^3+q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q^3+q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: q+1
        65: q+1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: 1
       120: 1
       122: q+1
       124: 1
       125: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       290: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q+1
       328: 1
       330: 1
       345: 1
       347: 1
       349: 1
       353: 1
       355: 1
       357: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       374: 1
       375: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: 1
       416: 1
       436: 1
       438: 1
       439: 1
       442: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       472: 1
       473: 1
       476: 1
       478: 1
       503: 1
       505: 1
       509: 1
       511: 1
       513: 1
       527: 1
       540: 1
       544: 1
       554: 1
       558: 1
       567: 1
       572: 1
       612: 1
       628: 1
       636: 1
       648: 1
       649: 1
       652: 1
       654: 1
       732: 1
       746: 1
       760: 1
       764: 1
       854: 1
       981: 1

 982:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        37: q+2
        39: q+2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: 1
        66: 2
        70: 1
        71: 2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: 1
       123: 1
       127: 2
       129: 2
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       169: 1
       172: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: q+2
       211: 1
       213: 1
       215: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       237: 2
       239: 2
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       289: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: 1
       337: 2
       338: 2
       340: 2
       347: 1
       349: 1
       351: 2
       355: 1
       357: 1
       359: 2
       360: 1
       362: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       415: 1
       427: 2
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       475: 1
       477: 2
       479: 2
       485: 1
       487: 1
       496: 1
       501: 1
       502: 1
       504: 1
       511: 1
       513: 1
       518: 1
       519: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       611: 1
       617: 1
       627: 1
       633: 1
       651: 1
       653: 1
       655: 1
       666: 1
       668: 1
       678: 1
       684: 1
       693: 1
       697: 1
       769: 1
       813: 1
       837: 1
       853: 1
       857: 1
       982: 1

 983:    0: 3q^2+6q
         1: 3q^2+6q
         2: 3q^2+3q
         3: 3q^2+6q
         4: q^3+4q^2+4q
         5: 3q^2+6q
         6: q^3+4q^2+4q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+6q
        11: 3q^2+6q
        12: q^3+4q^2+4q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 6q
        17: 6q
        19: 2q^2+4q
        20: 2q^2+4q
        21: 2q^2+2q
        22: 3q^2+6q
        23: 3q^2+6q
        24: 3q^2+3q
        25: 3q^2+6q
        26: 3q^2+6q
        27: 3q^2+3q
        28: 6q
        29: 2q^2+4q
        30: 2q
        31: 3q^2+6q
        32: 3q
        33: 6q
        34: 3q^2+6q
        35: 3q
        36: 6q
        37: q^2+2q
        38: 2q^2+4q
        39: q^2+2q
        40: 2q^2+4q
        41: q^2+q
        42: 2q^2+2q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 4q
        50: 4q
        52: 2q^2+4q
        53: 2q^2+4q
        54: 2q^2+2q
        55: 2q^2+4q
        56: 2q^2+4q
        57: 2q^2+2q
        58: 3q
        59: 3q
        60: 3q
        61: 3q
        62: q^2+2q
        63: 2q^2+4q
        64: q
        65: 2q
        66: 2q
        67: 4q
        70: 2q
        71: 4q
        72: 2q
        73: 2q
        75: q^2+2q
        77: q^2+2q
        79: q^2+q
        80: 3q
        81: 3q
        82: 2q^2+4q
        83: 2q
        84: 3q
        85: 3q
        86: 2q^2+4q
        87: 2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 4q
        95: 4q
        97: 4q
        98: 4q
       100: 2q^2+4q
       101: 2q^2+4q
       102: 2q^2+2q
       103: q
       104: 2q
       105: 2q
       106: q
       107: q
       108: q
       109: q
       110: q
       114: q^2+2q
       116: q
       121: q
       122: 2q
       123: q
       124: 2q
       128: 2q
       130: 2q
       135: q
       136: q
       137: 3q
       139: 4q
       140: 2q
       141: 2q
       142: 2q
       143: 3q
       145: 4q
       146: 2q
       147: 2q
       148: 2q
       149: 2q^2+4q
       150: 2q
       152: q^2+2q
       154: q^2+2q
       156: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 4q
       167: 4q
       180: 2q
       190: q
       193: q
       194: q
       195: q
       196: q
       201: q
       202: q
       203: q
       204: q
       207: q
       208: 2q
       210: q^2+2q
       212: q
       214: q
       216: q
       222: q
       224: q
       229: q
       230: q
       234: q
       235: q
       238: 2q
       240: 2q
       243: 4q
       244: 2q
       245: 2q
       246: 2q
       247: 2
       248: 2
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       318: 2q
       319: q
       320: q
       321: q
       322: q
       326: q
       328: q
       330: q
       337: 2
       339: 2
       341: 2
       347: q
       349: q
       351: 2
       355: q
       357: q
       359: 2
       361: q
       363: q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       428: 2
       443: 1
       444: 1
       446: 2
       461: 1
       462: 1
       464: 2
       479: 2
       486: 1
       488: 1
       496: 1
       501: 1
       503: q
       505: q
       511: q
       513: q
       518: 1
       519: 1
       546: 1
       548: 1
       562: 1
       564: 1
       573: 1
       575: 1
       578: 2
       618: 1
       634: 1
       655: 1
       667: 1
       669: 1
       678: 1
       684: 1
       694: 1
       701: 1
       770: 1
       814: 1
       838: 1
       857: 1
       983: 1

 984:    0: 2q^3+q^2+2q
         1: 2q^3+q^2+2q
         2: q^4+q^3+q^2+q
         3: q^2+2q
         4: 2q^3+q^2+2q
         5: q^2+2q
         6: 2q^3+q^2+2q
         7: q^4+q^3+q^2+q
         8: q^2+q
        10: 2q^3+q^2+2q
        11: q^2+2q
        12: 2q^3+q^2+2q
        13: q^3+q
        14: q^3+q
        15: q
        16: 2q
        17: 2q
        19: 2q^3+q^2+2q
        20: 2q^3+q^2+2q
        21: q^4+q^3+q^2+q
        22: q^2+2q
        23: q^2+2q
        24: q^2+q
        25: q^2+2q
        26: q^2+2q
        27: q^2+q
        28: 2q
        29: 2q^3+q^2+2q
        30: q^3+q
        31: q^2+2q
        32: q
        33: 2q
        34: q^2+2q
        35: q
        36: 2q
        37: q^2+2q
        39: q^2+2q
        41: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: 2q
        50: 2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+q
        55: q^2+2q
        56: q^2+2q
        57: q^2+q
        58: q
        59: q
        60: q
        61: q
        62: q^2+2q
        64: q
        66: 2q
        70: q^3+q
        71: 2q
        72: 2q
        73: 2q
        74: q^2+2q
        76: q^2+2q
        78: q^2+q
        80: q
        81: q
        82: q^2+2q
        83: q
        84: q
        85: q
        86: q^2+2q
        87: q
        88: q
        89: q
        91: q
        92: q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       103: q
       106: q
       107: q
       108: q
       109: q
       110: q
       111: 2q
       113: q^2+2q
       115: q
       121: q
       123: q
       127: 2q
       129: 2q
       135: q
       136: q
       137: q
       139: 2q
       140: 2q
       141: q
       142: 2q
       143: q
       145: 2q
       146: q
       147: 2q
       148: 2q
       149: q^2+2q
       150: q
       151: q^2+2q
       153: q^2+2q
       155: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       169: q
       172: q
       179: 2q
       181: 2q
       187: q
       189: q
       193: q
       194: q
       195: q
       196: q
       197: 2q
       201: q
       202: q
       203: q
       204: q
       205: 2q
       207: q
       209: q^2+2q
       211: q
       213: q
       215: q
       222: q
       224: q
       229: q
       230: q
       234: q
       235: q
       246: q
       250: q
       251: q
       253: q
       254: q
       259: q
       262: q
       267: q
       269: q
       271: q
       273: q
       289: q
       297: q
       305: q
       313: q
       325: q
       327: q
       329: q
       347: q
       349: q
       355: q
       357: q
       415: q
       441: q
       459: q
       477: 2
       569: 1
       570: 1
       579: 2
       651: 1
       695: 1
       702: 1
       771: 1
       853: 1
       984: 1

 985:    0: 3q^2+6q
         1: 3q^2+6q
         2: 3q^2+3q
         3: 3q^2+6q
         4: q^3+4q^2+4q
         5: 3q^2+6q
         6: q^3+4q^2+4q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+6q
        11: 3q^2+6q
        12: q^3+4q^2+4q
        13: 3q
        14: q^2+2q
        15: 3q
        16: 6q
        17: 6q
        19: 2q^2+4q
        20: 2q^2+4q
        21: 2q^2+2q
        22: 3q^2+6q
        23: 3q^2+6q
        24: 3q^2+3q
        25: 3q^2+6q
        26: 3q^2+6q
        27: 3q^2+3q
        28: 6q
        29: 2q^2+4q
        30: 2q
        31: 3q^2+6q
        32: 3q
        33: 6q
        34: 3q^2+6q
        35: 3q
        36: 6q
        37: 2q^2+4q
        38: q^2+2q
        39: 2q^2+4q
        40: q^2+2q
        41: 2q^2+2q
        42: q^2+q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q
        47: 3q
        49: 4q
        50: 4q
        52: 2q^2+4q
        53: 2q^2+4q
        54: 2q^2+2q
        55: 2q^2+4q
        56: 2q^2+4q
        57: 2q^2+2q
        58: 3q
        59: 3q
        60: 3q
        61: 3q
        62: 2q^2+4q
        63: q^2+2q
        64: 2q
        65: q
        66: 4q
        67: 2q
        70: 2q
        71: 4q
        72: 2q
        73: 2q
        74: q^2+2q
        76: q^2+2q
        78: q^2+q
        80: 3q
        81: 3q
        82: 2q^2+4q
        83: 2q
        84: 3q
        85: 3q
        86: 2q^2+4q
        87: 2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 4q
        95: 4q
        97: 4q
        98: 4q
       100: 2q^2+4q
       101: 2q^2+4q
       102: 2q^2+2q
       103: 2q
       104: q
       105: q
       106: 2q
       107: q
       108: q
       109: q
       110: q
       113: q^2+2q
       115: q
       121: 2q
       122: q
       123: 2q
       124: q
       127: 2q
       129: 2q
       135: q
       136: q
       137: 3q
       139: 4q
       140: 2q
       141: 2q
       142: 2q
       143: 3q
       145: 4q
       146: 2q
       147: 2q
       148: 2q
       149: 2q^2+4q
       150: 2q
       151: q^2+2q
       153: q^2+2q
       155: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 4q
       167: 4q
       179: 2q
       189: q
       193: q
       194: q
       195: q
       196: q
       201: q
       202: q
       203: q
       204: q
       207: 2q
       208: q
       209: q^2+2q
       211: q
       213: q
       215: q
       222: q
       224: q
       229: q
       230: q
       234: q
       235: q
       237: 2q
       239: 2q
       243: 4q
       244: 2q
       245: 2q
       246: 2q
       247: 2
       248: 2
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       317: 2q
       319: q
       320: q
       321: q
       322: q
       325: q
       327: q
       329: q
       337: 2
       338: 2
       340: 2
       347: q
       349: q
       351: 2
       355: q
       357: q
       359: 2
       360: q
       362: q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       427: 2
       443: 1
       444: 1
       445: 2
       461: 1
       462: 1
       463: 2
       480: 2
       485: 1
       487: 1
       496: 1
       501: 1
       502: q
       504: q
       511: q
       513: q
       518: 1
       519: 1
       545: 1
       547: 1
       561: 1
       563: 1
       574: 1
       576: 1
       580: 2
       617: 1
       633: 1
       656: 1
       666: 1
       668: 1
       678: 1
       684: 1
       696: 1
       698: 1
       772: 1
       813: 1
       837: 1
       858: 1
       985: 1

 986:    0: q+2
         1: q+2
         2: q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+1
         8: q+1
        10: q+2
        11: q+2
        12: q+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        19: q+2
        20: q+2
        21: q+1
        22: q+2
        23: q+2
        24: q+1
        25: q+2
        26: q+2
        27: q+1
        28: 2
        29: q+2
        30: 1
        31: q+2
        32: 1
        33: 2
        34: q+2
        35: 1
        36: 2
        38: q+2
        40: q+2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        49: 2
        50: 2
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: 1
        67: 2
        70: 1
        71: 2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: 1
        81: 1
        82: q+2
        83: 1
        84: 1
        85: 1
        86: q+2
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 2
        95: 2
        97: 2
        98: 2
       100: q+2
       101: q+2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: 1
       124: 1
       128: 2
       130: 2
       135: 1
       136: 1
       137: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 2
       167: 2
       170: 1
       171: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       210: q+2
       212: 1
       214: 1
       216: 1
       222: 1
       224: 1
       229: 1
       230: 1
       234: 1
       235: 1
       238: 2
       240: 2
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       290: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: 1
       337: 2
       339: 2
       341: 2
       347: 1
       349: 1
       351: 2
       355: 1
       357: 1
       359: 2
       361: 1
       363: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       416: 1
       428: 2
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       476: 1
       478: 2
       480: 2
       486: 1
       488: 1
       496: 1
       501: 1
       503: 1
       505: 1
       511: 1
       513: 1
       518: 1
       519: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       612: 1
       618: 1
       628: 1
       634: 1
       652: 1
       654: 1
       656: 1
       667: 1
       669: 1
       678: 1
       684: 1
       699: 1
       700: 1
       773: 1
       814: 1
       838: 1
       854: 1
       858: 1
       986: 1

 987:    0: 2q^3+q^2+2q
         1: 2q^3+q^2+2q
         2: q^4+q^3+q^2+q
         3: q^2+2q
         4: 2q^3+q^2+2q
         5: q^2+2q
         6: 2q^3+q^2+2q
         7: q^4+q^3+q^2+q
         8: q^2+q
        10: 2q^3+q^2+2q
        11: q^2+2q
        12: 2q^3+q^2+2q
        13: q^3+q
        14: q^3+q
        15: q
        16: 2q
        17: 2q
        19: 2q^3+q^2+2q
        20: 2q^3+q^2+2q
        21: q^4+q^3+q^2+q
        22: q^2+2q
        23: q^2+2q
        24: q^2+q
        25: q^2+2q
        26: q^2+2q
        27: q^2+q
        28: 2q
        29: 2q^3+q^2+2q
        30: q^3+q
        31: q^2+2q
        32: q
        33: 2q
        34: q^2+2q
        35: q
        36: 2q
        38: q^2+2q
        40: q^2+2q
        42: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q
        47: q
        49: 2q
        50: 2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+q
        55: q^2+2q
        56: q^2+2q
        57: q^2+q
        58: q
        59: q
        60: q
        61: q
        63: q^2+2q
        65: q
        67: 2q
        70: q^3+q
        71: 2q
        72: 2q
        73: 2q
        75: q^2+2q
        77: q^2+2q
        79: q^2+q
        80: q
        81: q
        82: q^2+2q
        83: q
        84: q
        85: q
        86: q^2+2q
        87: q
        88: q
        89: q
        91: q
        92: q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       104: q
       105: q
       107: q
       108: q
       109: q
       110: q
       112: 2q
       114: q^2+2q
       116: q
       122: q
       124: q
       128: 2q
       130: 2q
       135: q
       136: q
       137: q
       139: 2q
       140: 2q
       141: q
       142: 2q
       143: q
       145: 2q
       146: q
       147: 2q
       148: 2q
       149: q^2+2q
       150: q
       152: q^2+2q
       154: q^2+2q
       156: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       170: q
       171: q
       180: 2q
       182: 2q
       188: q
       190: q
       193: q
       194: q
       195: q
       196: q
       198: 2q
       201: q
       202: q
       203: q
       204: q
       206: 2q
       208: q
       210: q^2+2q
       212: q
       214: q
       216: q
       222: q
       224: q
       229: q
       230: q
       234: q
       235: q
       246: q
       250: q
       251: q
       253: q
       254: q
       260: q
       261: q
       268: q
       270: q
       272: q
       274: q
       290: q
       298: q
       306: q
       314: q
       326: q
       328: q
       330: q
       347: q
       349: q
       355: q
       357: q
       416: q
       442: q
       460: q
       478: 2
       571: 1
       572: 1
       582: 2
       652: 1
       703: 1
       704: 1
       774: 1
       854: 1
       987: 1

 988:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: 1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 1
        34: 2q+1
        35: 2q+1
        36: 1
        37: q+1
        38: q
        39: q+1
        40: q
        41: q+1
        42: q
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 1
        60: 1
        62: q+1
        63: q
        64: q+1
        65: q
        66: 1
        68: 1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: 2q+1
        81: 1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: 1
        86: 2q+1
        87: 2q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       117: 1
       119: 1
       121: q+1
       122: q
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: 1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       190: q
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: q+1
       210: q
       211: q+1
       212: q
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       263: 1
       267: 1
       271: 1
       275: 1
       293: 1
       295: 1
       297: 1
       299: 1
       303: 1
       305: 1
       307: 1
       309: 1
       313: 1
       319: 1
       321: 1
       323: 1
       325: q+1
       326: q
       337: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       385: 1
       393: 1
       401: 1
       405: 1
       437: 1
       439: 1
       441: 1
       443: 1
       453: 1
       457: 1
       459: 1
       461: 1
       471: 1
       473: 1
       475: 1
       479: 1
       484: 1
       496: 1
       501: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       541: 1
       557: 1
       565: 1
       573: 1
       615: 1
       631: 1
       647: 1
       649: 1
       653: 1
       655: 1
       672: 1
       678: 1
       684: 1
       761: 1
       765: 1
       815: 1
       839: 1
       857: 1
       988: 1

 989:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: 1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 1
        34: 2q+1
        35: 2q+1
        36: 1
        37: q
        38: q+1
        39: q
        40: q+1
        41: q
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        59: 1
        60: 1
        62: q
        63: q+1
        64: q
        65: q+1
        67: 1
        68: 1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: 2q+1
        81: 1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: 1
        86: 2q+1
        87: 2q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       104: 1
       107: 1
       110: 1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       118: 1
       119: 1
       121: q
       122: q+1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: 1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       183: 1
       186: 1
       188: 1
       189: q
       190: q+1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       209: q
       210: q+1
       211: q
       212: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       264: 1
       268: 1
       274: 1
       276: 1
       293: 1
       296: 1
       298: 1
       299: 1
       304: 1
       306: 1
       307: 1
       310: 1
       314: 1
       319: 1
       322: 1
       324: 1
       325: q
       326: q+1
       337: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       386: 1
       394: 1
       403: 1
       407: 1
       437: 1
       440: 1
       442: 1
       443: 1
       453: 1
       458: 1
       460: 1
       462: 1
       471: 1
       474: 1
       476: 1
       480: 1
       484: 1
       496: 1
       501: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       542: 1
       560: 1
       566: 1
       574: 1
       615: 1
       632: 1
       647: 1
       650: 1
       654: 1
       656: 1
       672: 1
       678: 1
       684: 1
       763: 1
       766: 1
       815: 1
       840: 1
       858: 1
       989: 1

 990:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: 1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 1
        34: 2q+1
        35: 2q+1
        36: 1
        37: q
        38: q+1
        39: q
        40: q+1
        41: q
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 1
        61: 1
        62: q
        63: q+1
        64: q
        65: q+1
        67: 1
        68: 1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: 2q+1
        81: 1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: 1
        86: 2q+1
        87: 2q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       105: 1
       108: 1
       109: 1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       117: 1
       120: 1
       121: q
       122: q+1
       124: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: 1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       184: 1
       185: 1
       188: 1
       189: q
       190: q+1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       209: q
       210: q+1
       211: q
       212: q+1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       265: 1
       270: 1
       272: 1
       277: 1
       294: 1
       295: 1
       298: 1
       300: 1
       303: 1
       306: 1
       308: 1
       309: 1
       314: 1
       320: 1
       321: 1
       324: 1
       325: q
       326: q+1
       337: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       387: 1
       395: 1
       402: 1
       408: 1
       438: 1
       439: 1
       442: 1
       444: 1
       454: 1
       457: 1
       460: 1
       461: 1
       472: 1
       473: 1
       476: 1
       480: 1
       484: 1
       496: 1
       501: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       544: 1
       558: 1
       567: 1
       576: 1
       616: 1
       631: 1
       648: 1
       649: 1
       654: 1
       656: 1
       672: 1
       678: 1
       684: 1
       764: 1
       767: 1
       816: 1
       839: 1
       858: 1
       990: 1

 991:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: 1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 1
        34: 2q+1
        35: 2q+1
        36: 1
        37: q+1
        38: q
        39: q+1
        40: q
        41: q+1
        42: q
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        59: 1
        61: 1
        62: q+1
        63: q
        64: q+1
        65: q
        66: 1
        68: 1
        70: 2q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: 2q+1
        81: 1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: 1
        86: 2q+1
        87: 2q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       118: 1
       120: 1
       121: q+1
       122: q
       123: 1
       125: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: 2q+1
       142: 1
       143: 1
       145: 1
       146: 2q+1
       147: 1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       190: q
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: q+1
       210: q
       211: q+1
       212: q
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       243: 1
       244: 1
       245: 1
       246: 2q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       266: 1
       269: 1
       273: 1
       278: 1
       294: 1
       296: 1
       297: 1
       300: 1
       304: 1
       305: 1
       308: 1
       310: 1
       313: 1
       320: 1
       322: 1
       323: 1
       325: q+1
       326: q
       337: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       388: 1
       396: 1
       404: 1
       406: 1
       438: 1
       440: 1
       441: 1
       444: 1
       454: 1
       458: 1
       459: 1
       462: 1
       472: 1
       474: 1
       475: 1
       479: 1
       484: 1
       496: 1
       501: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       543: 1
       559: 1
       568: 1
       575: 1
       616: 1
       632: 1
       648: 1
       650: 1
       653: 1
       655: 1
       672: 1
       678: 1
       684: 1
       762: 1
       768: 1
       816: 1
       840: 1
       857: 1
       991: 1

 992:    0: 3q^2+7q+2
         1: 3q^2+7q+2
         2: q^3+4q^2+5q+2
         3: 3q^2+7q+2
         4: q^3+4q^2+5q+2
         5: 3q^2+7q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 3q^2+7q+2
        11: 3q^2+7q+2
        12: q^3+4q^2+5q+2
        13: 2q^2+5q+2
        14: q^2+3q+2
        15: 2q^2+5q+2
        16: 3q^2+7q+2
        17: 3q^2+7q+2
        18: q^2+3q+2
        19: 2q^2+5q+2
        20: 2q^2+5q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 3q^2+7q+2
        29: 2q^2+5q+2
        30: q^2+3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 6q+2
        39: 6q+2
        41: 2q^2+4q+2
        43: 2q^2+5q+2
        44: q^2+3q+2
        45: 2q^2+5q+2
        46: 2q^2+5q+2
        47: 2q^2+5q+2
        48: q^2+3q+2
        49: 2q^2+5q+2
        50: 2q^2+5q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: 2q+2
        55: 4q+2
        56: 4q+2
        57: 2q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 6q+2
        64: 4q+2
        66: 6q+2
        68: q^2+3q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: 2q^2+5q+2
        72: 2q+2
        73: 2q+2
        74: 4q+2
        76: 4q+2
        78: 2q+2
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 2q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 2q+2
        88: 2q^2+5q+2
        89: 2q^2+5q+2
        90: q^2+3q+2
        91: q+2
        92: q^2+3q+2
        93: q+2
        94: 4q+2
        95: 4q+2
        96: 2q+2
        97: 4q+2
        98: 4q+2
        99: 2q+2
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 3q+1
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 4q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 4q+2
       123: 4q+2
       125: q^2+3q+2
       126: q^2+3q+2
       127: 4q+2
       129: 4q+2
       131: 2q+2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 4q+2
       138: 2q+2
       139: 4q+2
       141: 2q+2
       142: 2q+2
       143: 4q+2
       144: 2q+2
       145: 4q+2
       146: 2q+2
       147: 2q+2
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+2
       158: q^2+3q+2
       159: q+2
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: 2q+2
       179: 4q+2
       181: 2q+2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: q+1
       192: q+1
       195: q+1
       196: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       207: 4q+2
       209: 2q+1
       211: q+1
       213: 2
       215: 2q+2
       217: 2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2q+2
       227: 2
       228: 2
       230: 2
       231: 2q+2
       232: 2
       233: 2
       234: 2
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       246: q+1
       247: q+1
       248: q+1
       250: 2
       251: 2q+2
       252: 2
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       259: q+1
       262: q+1
       263: 1
       266: 1
       275: q+1
       278: q+1
       279: 2
       281: 2
       283: 1
       284: 1
       285: 1
       286: 1
       287: 2q+2
       289: 2
       291: 2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: q+1
       317: 2q+1
       325: q+1
       327: 2
       329: 2q+2
       331: 2
       333: q+2
       334: 2
       335: 2
       337: q+1
       338: q+1
       340: q+1
       344: 2
       345: 2
       346: 2
       349: 2
       350: 2
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       411: 2
       413: 2
       415: 2
       417: 2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       427: q+1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       484: 1
       485: 1
       487: 1
       492: 2
       494: 2
       497: 2
       498: 2
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       583: 2
       587: 2
       601: 1
       607: 1
       608: 1
       619: 1
       620: 1
       635: 1
       637: 1
       639: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       686: 1
       690: 1
       691: 1
       705: 1
       708: 1
       775: 1
       789: 1
       841: 1
       859: 1
       861: 1
       865: 1
       992: 1

 993:    0: 3q^2+7q+2
         1: 3q^2+7q+2
         2: q^3+4q^2+5q+2
         3: 3q^2+7q+2
         4: q^3+4q^2+5q+2
         5: 3q^2+7q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 3q^2+7q+2
        11: 3q^2+7q+2
        12: q^3+4q^2+5q+2
        13: 2q^2+5q+2
        14: q^2+3q+2
        15: 2q^2+5q+2
        16: 3q^2+7q+2
        17: 3q^2+7q+2
        18: q^2+3q+2
        19: 2q^2+5q+2
        20: 2q^2+5q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 3q^2+7q+2
        29: 2q^2+5q+2
        30: q^2+3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        38: 6q+2
        40: 6q+2
        42: 2q^2+4q+2
        43: 2q^2+5q+2
        44: q^2+3q+2
        45: 2q^2+5q+2
        46: 2q^2+5q+2
        47: 2q^2+5q+2
        48: q^2+3q+2
        49: 2q^2+5q+2
        50: 2q^2+5q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: 2q+2
        55: 4q+2
        56: 4q+2
        57: 2q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        63: 6q+2
        65: 4q+2
        67: 6q+2
        68: q^2+3q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: 2q^2+5q+2
        72: 2q+2
        73: 2q+2
        75: 4q+2
        77: 4q+2
        79: 2q+2
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 2q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 2q+2
        88: 2q^2+5q+2
        89: 2q^2+5q+2
        90: q^2+3q+2
        91: q+2
        92: q^2+3q+2
        93: q+2
        94: 4q+2
        95: 4q+2
        96: 2q+2
        97: 4q+2
        98: 4q+2
        99: 2q+2
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 3q+1
       105: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 4q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 4q+2
       124: 4q+2
       125: q^2+3q+2
       126: q^2+3q+2
       128: 4q+2
       130: 4q+2
       132: 2q+2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 4q+2
       138: 2q+2
       139: 4q+2
       141: 2q+2
       142: 2q+2
       143: 4q+2
       144: 2q+2
       145: 4q+2
       146: 2q+2
       147: 2q+2
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+2
       158: q^2+3q+2
       159: q+2
       160: 2
       161: 2q+2
       162: 2
       163: 2
       164: 2q+2
       165: 2
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: 2q+2
       180: 4q+2
       182: 2q+2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: q+1
       192: q+1
       195: q+1
       196: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       208: 4q+2
       210: 2q+1
       212: q+1
       214: 2
       216: 2q+2
       218: 2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2q+2
       227: 2
       228: 2
       230: 2
       231: 2q+2
       232: 2
       233: 2
       234: 2
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       246: q+1
       247: q+1
       248: q+1
       250: 2
       251: 2q+2
       252: 2
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       260: q+1
       261: q+1
       264: 1
       265: 1
       276: q+1
       277: q+1
       280: 2
       282: 2
       283: 1
       284: 1
       285: 1
       286: 1
       288: 2q+2
       290: 2
       292: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: q+1
       318: 2q+1
       326: q+1
       328: 2
       330: 2q+2
       332: 2
       333: q+2
       334: 2
       335: 2
       337: q+1
       339: q+1
       341: q+1
       344: 2
       345: 2
       346: 2
       349: 2
       350: 2
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       412: 2
       414: 2
       416: 2
       418: 2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       428: q+1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       484: 1
       486: 1
       488: 1
       492: 2
       494: 2
       497: 2
       498: 2
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       584: 2
       588: 2
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       636: 1
       638: 1
       640: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       686: 1
       690: 1
       691: 1
       706: 1
       707: 1
       776: 1
       790: 1
       842: 1
       860: 1
       862: 1
       865: 1
       993: 1

 994:    0: q^2+2q+2
         1: 2q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: 2q^2+2q+2
         6: 2q^2+2q+2
         7: q^2+2q+2
         8: 2q^2+2q+2
         9: q^2+2q+2
        10: q+2
        11: q+2
        12: q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: 2q^2+2q+2
        16: q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: 2q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: q+2
        30: q^2+2q+2
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        37: q+2
        39: q+2
        41: q+2
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: 2q^2+2q+2
        51: q^2+2q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: q+2
        66: q+2
        68: q+2
        69: q^2+2q+2
        70: q+2
        71: q+2
        72: q+2
        73: q+2
        74: q+2
        76: q+2
        78: q+2
        80: 2
        81: q+2
        82: 2
        83: q+2
        84: 2
        85: q+2
        86: 2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+2q+2
        92: 2q^2+2q+2
        93: q^2+2q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+2
       113: 2
       115: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: q+2
       125: q+2
       126: q+2
       127: q+2
       129: q+2
       131: q+2
       133: q+2
       134: q^2+2q+2
       135: q+2
       136: q+2
       137: 2
       138: q+2
       139: 2
       141: 2
       142: q+2
       143: 2
       144: q+2
       145: 2
       146: 2
       147: q+2
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 1
       167: 1
       168: 1
       169: 1
       172: 1
       173: 1
       176: 1
       177: q+2
       179: 2
       181: q+2
       183: 1
       184: 1
       185: 1
       186: 1
       187: q+2
       189: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: 1
       211: 1
       213: q+2
       215: q+2
       217: q+2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: q+2
       224: 2
       225: q+2
       226: 2
       227: 2
       228: q+2
       230: q+2
       231: 2
       232: 2
       233: q+2
       234: q+2
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       287: 2
       289: q+2
       291: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: 1
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 2
       350: q+2
       352: 2
       356: q+2
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       413: 2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 1
       431: 1
       432: 1
       447: 1
       448: 1
       465: 1
       467: 1
       469: 1
       481: 2
       482: 2
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       508: 1
       515: 1
       516: 1
       517: 1
       521: 1
       524: 1
       529: 1
       532: 1
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 1
       639: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       709: 1
       712: 1
       775: 1
       779: 1
       781: 1
       866: 1
       994: 1

 995:    0: q^2+2q+2
         1: 2q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: 2q^2+2q+2
         6: 2q^2+2q+2
         7: q^2+2q+2
         8: 2q^2+2q+2
         9: q^2+2q+2
        10: q+2
        11: q+2
        12: q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: 2q^2+2q+2
        16: q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: 2q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: q+2
        30: q^2+2q+2
        31: 2
        32: q+2
        33: q+2
        34: 2
        35: q+2
        36: q+2
        38: q+2
        40: q+2
        42: q+2
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: 2q^2+2q+2
        51: q^2+2q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: q+2
        67: q+2
        68: q+2
        69: q^2+2q+2
        70: q+2
        71: q+2
        72: q+2
        73: q+2
        75: q+2
        77: q+2
        79: q+2
        80: 2
        81: q+2
        82: 2
        83: q+2
        84: 2
        85: q+2
        86: 2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+2q+2
        92: 2q^2+2q+2
        93: q^2+2q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+2
       114: 2
       116: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: q+2
       125: q+2
       126: q+2
       128: q+2
       130: q+2
       132: q+2
       133: q+2
       134: q^2+2q+2
       135: q+2
       136: q+2
       137: 2
       138: q+2
       139: 2
       141: 2
       142: q+2
       143: 2
       144: q+2
       145: 2
       146: 2
       147: q+2
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       174: 1
       175: 1
       178: q+2
       180: 2
       182: q+2
       183: 1
       184: 1
       185: 1
       186: 1
       188: q+2
       190: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: 1
       212: 1
       214: q+2
       216: q+2
       218: q+2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: q+2
       224: 2
       225: q+2
       226: 2
       227: 2
       228: q+2
       230: q+2
       231: 2
       232: 2
       233: q+2
       234: q+2
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       288: 2
       290: q+2
       292: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: 1
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 2
       350: q+2
       352: 2
       356: q+2
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       414: 2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 1
       431: 1
       432: 1
       447: 1
       448: 1
       466: 1
       468: 1
       470: 1
       481: 2
       482: 2
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       508: 1
       515: 1
       516: 1
       517: 1
       522: 1
       523: 1
       530: 1
       531: 1
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 1
       640: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       710: 1
       711: 1
       776: 1
       780: 1
       782: 1
       866: 1
       995: 1

 996:    0: q+2
         1: q+2
         2: q^2+2q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+1
        14: q+1
        15: 1
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+2
        50: q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: q+1
        70: q+1
        71: q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       262: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       315: 1
       317: 1
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q+1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       360: 1
       364: 1
       366: 1
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 1
       467: 1
       469: 1
       483: 1
       485: 1
       489: 1
       491: 1
       494: 1
       498: 1
       502: 1
       506: 1
       510: 1
       515: 1
       517: 1
       518: 1
       520: 1
       587: 1
       597: 1
       599: 1
       637: 1
       658: 1
       662: 1
       664: 1
       666: 1
       670: 1
       673: 1
       690: 1
       692: 1
       779: 1
       783: 1
       859: 1
       863: 1
       867: 1
       996: 1

 997:    0: q+2
         1: q+2
         2: q^2+2q+1
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+1
        14: q+1
        15: 1
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: q+2
        20: q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: q+2
        29: q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+2
        50: q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: q+1
        70: q+1
        71: q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       260: 1
       261: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       316: 1
       318: 1
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q+1
       346: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       361: 1
       365: 1
       366: 1
       368: 1
       371: 1
       373: 1
       374: 1
       376: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 1
       468: 1
       470: 1
       483: 1
       486: 1
       490: 1
       491: 1
       494: 1
       498: 1
       503: 1
       507: 1
       510: 1
       515: 1
       517: 1
       518: 1
       520: 1
       588: 1
       598: 1
       600: 1
       638: 1
       659: 1
       663: 1
       664: 1
       667: 1
       671: 1
       673: 1
       690: 1
       692: 1
       780: 1
       784: 1
       860: 1
       864: 1
       867: 1
       997: 1

 998:    0: 2q^2+4q+2
         1: q^3+4q^2+4q+2
         2: q^2+3q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: q^3+4q^2+4q+2
         6: q^3+4q^2+4q+2
         7: q^2+3q+2
         8: q^3+3q^2+3q+2
         9: q^2+3q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: 3q+2
        14: 3q+2
        15: 2q^2+3q+2
        16: 2q^2+4q+2
        17: q^3+4q^2+4q+2
        18: q^2+3q+2
        19: 2q^2+4q+2
        20: q^3+4q^2+4q+2
        21: q^2+3q+2
        22: q^2+2q+2
        23: q^2+2q+2
        24: 2q+2
        25: q^2+4q+2
        26: q^2+4q+2
        27: q^2+3q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: 3q+2
        31: q^2+2
        32: 2q+2
        33: q^2+2q+2
        34: 2q+2
        35: 3q+2
        36: q^2+4q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 2q^2+3q+2
        48: 3q+2
        49: 2q^2+4q+2
        50: q^3+4q^2+4q+2
        51: q^2+3q+2
        52: q^2+2q+2
        53: q^2+2q+2
        54: 2q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+3q+2
        58: q^2+2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 3q+2
        70: q+2
        71: q^2+2q+2
        72: q^2+4q+2
        73: q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2
        81: 2q+2
        82: q^2+2
        83: 2q+2
        84: q+2
        85: 3q+2
        86: 2q+2
        87: 3q+2
        88: q+2
        89: q+2
        90: q+2
        91: 3q+2
        92: 2q^2+3q+2
        93: 3q+2
        94: q^2+2q+2
        95: q^2+2q+2
        96: 2q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+3q+2
       100: 2
       101: 2q+2
       102: 2
       103: 1
       105: 1
       107: q+1
       108: q+1
       109: q^2+2
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 3q+2
       135: 3q+2
       136: 2q+2
       137: 2
       138: 2q+2
       139: q^2+2
       141: 2
       142: q^2+2q+2
       143: q+2
       144: 3q+2
       145: 2q+2
       146: q+2
       147: q^2+4q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+1
       161: q+1
       162: q+1
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 2
       167: 2q+2
       168: 2
       169: 1
       171: 1
       173: 1
       175: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: 1
       185: 2
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 2
       195: q^2+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: 3q+2
       224: 2
       225: 2q+2
       226: 2
       227: 1
       228: q+1
       230: q+1
       231: q+2
       232: 2
       233: 2q+2
       234: 2q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2q+2
       249: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       283: 1
       284: 1
       285: 2
       287: 1
       288: 1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       321: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: 1
       343: 1
       344: 1
       350: q+1
       352: 2
       356: 2q+2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       379: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       431: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       461: 2
       463: 1
       464: 1
       469: 1
       470: 1
       473: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       500: 2
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       529: 1
       531: 1
       549: 1
       550: 1
       561: 1
       562: 1
       589: 1
       590: 1
       591: 2
       595: 1
       599: 1
       600: 1
       629: 1
       630: 1
       631: 1
       643: 1
       657: 1
       664: 1
       665: 1
       680: 1
       685: 1
       713: 1
       714: 1
       787: 1
       817: 1
       866: 1
       874: 1
       998: 1

 999:    0: 2q^2+4q+2
         1: q^3+4q^2+4q+2
         2: q^2+3q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: q^3+4q^2+4q+2
         6: q^3+4q^2+4q+2
         7: q^2+3q+2
         8: q^3+3q^2+3q+2
         9: q^2+3q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: 3q+2
        14: 3q+2
        15: 2q^2+3q+2
        16: 2q^2+4q+2
        17: q^3+4q^2+4q+2
        18: q^2+3q+2
        19: 2q^2+4q+2
        20: q^3+4q^2+4q+2
        21: q^2+3q+2
        22: q^2+2q+2
        23: q^2+2q+2
        24: 2q+2
        25: q^2+4q+2
        26: q^2+4q+2
        27: q^2+3q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: 3q+2
        31: q^2+2
        32: 2q+2
        33: q^2+2q+2
        34: 2q+2
        35: 3q+2
        36: q^2+4q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 2q^2+3q+2
        48: 3q+2
        49: 2q^2+4q+2
        50: q^3+4q^2+4q+2
        51: q^2+3q+2
        52: q^2+2q+2
        53: q^2+2q+2
        54: 2q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+3q+2
        59: q^2+2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 3q+2
        70: q+2
        71: q^2+2q+2
        72: q^2+4q+2
        73: q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2
        81: 2q+2
        82: q^2+2
        83: 2q+2
        84: q+2
        85: 3q+2
        86: 2q+2
        87: 3q+2
        88: q+2
        89: q+2
        90: q+2
        91: 3q+2
        92: 2q^2+3q+2
        93: 3q+2
        94: q^2+2q+2
        95: q^2+2q+2
        96: 2q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+3q+2
       100: 2
       101: 2q+2
       102: 2
       104: 1
       106: 1
       107: q+1
       108: q+1
       110: q^2+2
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 3q+2
       135: 3q+2
       136: 2q+2
       137: 2
       138: 2q+2
       139: q^2+2
       141: 2
       142: q^2+2q+2
       143: q+2
       144: 3q+2
       145: 2q+2
       146: q+2
       147: q^2+4q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+1
       161: q+1
       162: q+1
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 2
       167: 2q+2
       168: 2
       170: 1
       172: 1
       174: 1
       176: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: 1
       186: 2
       187: q+1
       188: q+1
       189: 1
       190: 1
       192: 2
       196: q^2+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: 3q+2
       224: 2
       225: 2q+2
       226: 2
       227: 1
       228: q+1
       230: q+1
       231: q+2
       232: 2
       233: 2q+2
       234: 2q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2q+2
       249: 2
       256: 1
       257: q+1
       258: 1
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       283: 1
       284: 1
       286: 2
       287: 1
       288: 1
       291: q+1
       292: q+1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: 1
       343: 1
       344: 1
       350: q+1
       352: 2
       356: 2q+2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       380: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       432: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       462: 2
       463: 1
       464: 1
       469: 1
       470: 1
       474: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       500: 2
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       530: 1
       532: 1
       551: 1
       552: 1
       563: 1
       564: 1
       589: 1
       590: 1
       592: 2
       596: 1
       599: 1
       600: 1
       629: 1
       630: 1
       632: 1
       644: 1
       657: 1
       664: 1
       665: 1
       680: 1
       685: 1
       715: 1
       716: 1
       788: 1
       818: 1
       866: 1
       874: 1
       999: 1

1000:    0: 2q^2+4q+2
         1: q^3+4q^2+4q+2
         2: q^2+3q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: q^3+4q^2+4q+2
         6: q^3+4q^2+4q+2
         7: q^2+3q+2
         8: q^3+3q^2+3q+2
         9: q^2+3q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: 3q+2
        14: 3q+2
        15: 2q^2+3q+2
        16: 2q^2+4q+2
        17: q^3+4q^2+4q+2
        18: q^2+3q+2
        19: 2q^2+4q+2
        20: q^3+4q^2+4q+2
        21: q^2+3q+2
        22: q^2+4q+2
        23: q^2+4q+2
        24: q^2+3q+2
        25: q^2+2q+2
        26: q^2+2q+2
        27: 2q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: 3q+2
        31: 2q+2
        32: 3q+2
        33: q^2+4q+2
        34: q^2+2
        35: 2q+2
        36: q^2+2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 2q^2+3q+2
        48: 3q+2
        49: 2q^2+4q+2
        50: q^3+4q^2+4q+2
        51: q^2+3q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+3q+2
        55: q^2+2q+2
        56: q^2+2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q^2+2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 3q+2
        70: q+2
        71: q^2+2q+2
        72: q^2+2q+2
        73: q^2+4q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: 2q+2
        83: 3q+2
        84: 2
        85: 2q+2
        86: q^2+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+2
        91: 3q+2
        92: 2q^2+3q+2
        93: 3q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+3q+2
        97: q^2+2q+2
        98: q^2+2q+2
        99: 2q+2
       100: 2
       101: 2q+2
       102: 2
       103: 1
       104: 1
       107: q^2+2
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 3q+2
       135: 2q+2
       136: 3q+2
       137: q+2
       138: 3q+2
       139: 2q+2
       140: 2
       141: q+2
       142: q^2+4q+2
       143: 2
       144: 2q+2
       145: q^2+2
       146: 2
       147: q^2+2q+2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2q+2
       168: 2
       169: 1
       170: 1
       173: 1
       174: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: q^2+2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2q+2
       224: q+2
       225: 3q+2
       226: q+2
       227: 2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 2
       232: 1
       233: q+1
       234: q+1
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2q+2
       249: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: q+1
       292: q+1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: 1
       343: 1
       344: 2
       348: 2
       350: 2q+2
       351: 2
       352: 1
       356: q+1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       443: 2
       445: 1
       446: 1
       447: 1
       469: 1
       470: 1
       471: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       495: 2
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       529: 1
       530: 1
       533: 1
       534: 1
       545: 1
       546: 1
       589: 1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       613: 1
       614: 1
       615: 1
       641: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       717: 1
       718: 1
       785: 1
       793: 1
       866: 1
       870: 1
      1000: 1

1001:    0: 2q^2+4q+2
         1: q^3+4q^2+4q+2
         2: q^2+3q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: q^3+4q^2+4q+2
         6: q^3+4q^2+4q+2
         7: q^2+3q+2
         8: q^3+3q^2+3q+2
         9: q^2+3q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: 3q+2
        14: 3q+2
        15: 2q^2+3q+2
        16: 2q^2+4q+2
        17: q^3+4q^2+4q+2
        18: q^2+3q+2
        19: 2q^2+4q+2
        20: q^3+4q^2+4q+2
        21: q^2+3q+2
        22: q^2+4q+2
        23: q^2+4q+2
        24: q^2+3q+2
        25: q^2+2q+2
        26: q^2+2q+2
        27: 2q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: 3q+2
        31: 2q+2
        32: 3q+2
        33: q^2+4q+2
        34: q^2+2
        35: 2q+2
        36: q^2+2q+2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: 3q+2
        47: 2q^2+3q+2
        48: 3q+2
        49: 2q^2+4q+2
        50: q^3+4q^2+4q+2
        51: q^2+3q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+3q+2
        55: q^2+2q+2
        56: q^2+2q+2
        57: 2q+2
        58: q+1
        59: q+1
        61: q^2+2
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: 2
        69: 3q+2
        70: q+2
        71: q^2+2q+2
        72: q^2+2q+2
        73: q^2+4q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+2
        81: 3q+2
        82: 2q+2
        83: 3q+2
        84: 2
        85: 2q+2
        86: q^2+2
        87: 2q+2
        88: q+2
        89: q+2
        90: q+2
        91: 3q+2
        92: 2q^2+3q+2
        93: 3q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+3q+2
        97: q^2+2q+2
        98: q^2+2q+2
        99: 2q+2
       100: 2
       101: 2q+2
       102: 2
       105: 1
       106: 1
       108: q^2+2
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: q+1
       124: q+1
       125: 2
       126: q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 3q+2
       135: 2q+2
       136: 3q+2
       137: q+2
       138: 3q+2
       139: 2q+2
       140: 2
       141: q+2
       142: q^2+4q+2
       143: 2
       144: 2q+2
       145: q^2+2
       146: 2
       147: q^2+2q+2
       149: 2
       150: 2
       151: 1
       152: 1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2q+2
       168: 2
       171: 1
       172: 1
       175: 1
       176: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       184: 2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: q^2+2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2q+2
       224: q+2
       225: 3q+2
       226: q+2
       227: 2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 2
       232: 1
       233: q+1
       234: q+1
       236: 2
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2q+2
       249: 2
       256: 1
       257: q+1
       258: 1
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: q+1
       292: q+1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: 1
       343: 1
       344: 2
       348: 2
       350: 2q+2
       351: 2
       352: 1
       356: q+1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       444: 2
       445: 1
       446: 1
       448: 1
       469: 1
       470: 1
       472: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       495: 2
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       531: 1
       532: 1
       535: 1
       536: 1
       547: 1
       548: 1
       590: 1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       613: 1
       614: 1
       616: 1
       642: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       719: 1
       720: 1
       786: 1
       794: 1
       866: 1
       870: 1
      1001: 1

1002:    0: q^2+4q+2
         1: q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: 2q^2+4q+2
         6: q^2+4q+2
         7: q^2+4q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: q^2+4q+2
        11: 2q^2+4q+2
        12: q^2+4q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 3q+2
        23: 3q+2
        24: 3q+2
        25: 3q+2
        26: 3q+2
        27: 3q+2
        28: 3q+2
        29: q^2+4q+2
        30: q^2+4q+2
        31: 3q+2
        32: 3q+2
        33: 2q+2
        34: 3q+2
        35: 3q+2
        36: 2q+2
        37: 3q+2
        39: 3q+2
        41: 3q+2
        43: q^2+4q+2
        44: q^2+4q+2
        45: 2q^2+4q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 3q+2
        53: 3q+2
        54: 3q+2
        55: 3q+2
        56: 3q+2
        57: 3q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 3q+2
        64: 3q+2
        66: 2q+2
        68: 3q+2
        69: q+1
        70: q^2+4q+2
        71: 3q+2
        72: 2q+2
        73: 2q+2
        74: 3q+2
        76: 3q+2
        78: 3q+2
        80: 3q+2
        81: 2q+2
        82: 3q+2
        83: 3q+2
        84: 3q+2
        85: 2q+2
        86: 3q+2
        87: 3q+2
        88: 3q+2
        89: 3q+2
        90: q^2+2q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 3q+2
       115: 3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 3q+2
       123: 2q+2
       125: 3q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 3q+2
       134: q+1
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: 1
       139: 2
       141: 3q+2
       142: 2
       143: 2q+2
       144: 1
       145: 2
       146: 3q+2
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 3q+2
       158: 3q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q+2
       189: 3q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+1
       211: q+1
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 3q+2
       221: q+1
       222: 2q+2
       223: 1
       224: 2q+2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       263: q+1
       266: q+1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2q+2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: q+1
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       381: 1
       384: 1
       385: q+1
       388: q+1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       518: 1
       519: 1
       520: 1
       525: 1
       528: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 1
       635: 1
       637: 1
       639: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       777: 1
       781: 1
       783: 1
       789: 1
       841: 1
       868: 1
      1002: 1

1003:    0: q^2+4q+2
         1: q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: 2q^2+4q+2
         6: q^2+4q+2
         7: q^2+4q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: q^2+4q+2
        11: 2q^2+4q+2
        12: q^2+4q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: 2q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 3q+2
        23: 3q+2
        24: 3q+2
        25: 3q+2
        26: 3q+2
        27: 3q+2
        28: 3q+2
        29: q^2+4q+2
        30: q^2+4q+2
        31: 3q+2
        32: 3q+2
        33: 2q+2
        34: 3q+2
        35: 3q+2
        36: 2q+2
        38: 3q+2
        40: 3q+2
        42: 3q+2
        43: q^2+4q+2
        44: q^2+4q+2
        45: 2q^2+4q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 3q+2
        53: 3q+2
        54: 3q+2
        55: 3q+2
        56: 3q+2
        57: 3q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 3q+2
        65: 3q+2
        67: 2q+2
        68: 3q+2
        69: q+1
        70: q^2+4q+2
        71: 3q+2
        72: 2q+2
        73: 2q+2
        75: 3q+2
        77: 3q+2
        79: 3q+2
        80: 3q+2
        81: 2q+2
        82: 3q+2
        83: 3q+2
        84: 3q+2
        85: 2q+2
        86: 3q+2
        87: 3q+2
        88: 3q+2
        89: 3q+2
        90: q^2+2q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 3q+2
       116: 3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 3q+2
       124: 2q+2
       125: 3q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 3q+2
       134: q+1
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: 1
       139: 2
       141: 3q+2
       142: 2
       143: 2q+2
       144: 1
       145: 2
       146: 3q+2
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 3q+2
       158: 3q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2q+2
       190: 3q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+1
       212: q+1
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 3q+2
       221: q+1
       222: 2q+2
       223: 1
       224: 2q+2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       264: q+1
       265: q+1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2q+2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: q+1
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       382: 1
       383: 1
       386: q+1
       387: q+1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       518: 1
       519: 1
       520: 1
       526: 1
       527: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 1
       636: 1
       638: 1
       640: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       778: 1
       782: 1
       784: 1
       790: 1
       842: 1
       868: 1
      1003: 1

1004:    0: q^3+5q^2+8q+2
         1: q^3+5q^2+8q+2
         2: 4q^2+6q+2
         3: 6q^2+8q+2
         4: q^3+5q^2+8q+2
         5: 6q^2+8q+2
         6: q^3+5q^2+8q+2
         7: 4q^2+6q+2
         8: 2q^3+6q^2+6q+2
         9: q^3+3q^2+3q+1
        10: q^3+5q^2+8q+2
        11: 6q^2+8q+2
        12: q^3+5q^2+8q+2
        13: 2q^2+6q+2
        14: 2q^2+6q+2
        15: 4q^2+6q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: q^3+5q^2+8q+2
        20: q^3+5q^2+8q+2
        21: 4q^2+6q+2
        22: 2q^2+7q+2
        23: 2q^2+7q+2
        24: 3q^2+5q+2
        25: 2q^2+7q+2
        26: 2q^2+7q+2
        27: 3q^2+5q+2
        28: 2q^2+7q+2
        29: q^3+5q^2+8q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^2+5q+2
        33: 6q+2
        34: 2q^2+7q+2
        35: q^2+5q+2
        36: q^2+7q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+6q+2
        44: 2q^2+6q+2
        45: 4q^2+6q+2
        46: 5q+2
        47: q^2+5q+2
        48: q^2+3q+1
        49: 2q^2+7q+2
        50: 2q^2+7q+2
        51: 2q^2+3q+1
        52: 2q^2+7q+2
        53: 2q^2+7q+2
        54: 3q^2+5q+2
        55: 2q^2+7q+2
        56: 2q^2+7q+2
        57: 3q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: q^2+5q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 3q+2
        69: 2q+1
        70: 2q^2+6q+2
        71: 2q^2+7q+2
        72: q^2+7q+2
        73: 6q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: 4q+2
        82: 2q^2+7q+2
        83: q^2+5q+2
        84: q^2+5q+2
        85: 5q+2
        86: 2q^2+7q+2
        87: q^2+5q+2
        88: 5q+2
        89: q^2+5q+2
        90: q^2+3q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q^2+5q+2
       108: 2q
       109: 3q+1
       110: 3q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 3q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 3q+2
       126: 2q+1
       133: 3q+2
       134: 2q+1
       135: 5q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q^2+5q+2
       142: 4q+2
       143: 5q+2
       144: 2q+1
       145: q^2+4q+1
       146: q^2+5q+2
       147: q^2+4q+1
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: 5q+2
       158: q^2+5q+2
       159: q^2+3q+1
       160: q+2
       161: q+2
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: q+1
       174: q+1
       183: 3q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       199: 3q+2
       201: q^2+3q+1
       202: q
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q+1
       220: 3q+2
       221: 2q+1
       222: 5q+2
       223: 2q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       243: 2q+1
       244: q+1
       246: 2q+2
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       263: q+1
       264: q+1
       267: q+1
       268: q+1
       275: q+1
       276: q+1
       283: q+1
       293: 3q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+1
       319: q+1
       325: q+1
       326: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: 2q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       385: q+1
       386: q+1
       393: 1
       394: 1
       419: q+1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       447: 1
       453: q+1
       471: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       541: 1
       542: 1
       589: 1
       593: 1
       603: 1
       615: 1
       619: 1
       641: 1
       647: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       785: 1
       805: 1
       815: 1
       825: 1
       845: 1
       868: 1
       872: 1
      1004: 1

1005:    0: q^3+5q^2+8q+2
         1: q^3+5q^2+8q+2
         2: 4q^2+6q+2
         3: 6q^2+8q+2
         4: q^3+5q^2+8q+2
         5: 6q^2+8q+2
         6: q^3+5q^2+8q+2
         7: 4q^2+6q+2
         8: 2q^3+6q^2+6q+2
         9: q^3+3q^2+3q+1
        10: q^3+5q^2+8q+2
        11: 6q^2+8q+2
        12: q^3+5q^2+8q+2
        13: 2q^2+6q+2
        14: 2q^2+6q+2
        15: 4q^2+6q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: q^3+5q^2+8q+2
        20: q^3+5q^2+8q+2
        21: 4q^2+6q+2
        22: 2q^2+7q+2
        23: 2q^2+7q+2
        24: 3q^2+5q+2
        25: 2q^2+7q+2
        26: 2q^2+7q+2
        27: 3q^2+5q+2
        28: 2q^2+7q+2
        29: q^3+5q^2+8q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^2+5q+2
        33: 6q+2
        34: 2q^2+7q+2
        35: q^2+5q+2
        36: q^2+7q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+6q+2
        44: 2q^2+6q+2
        45: 4q^2+6q+2
        46: 5q+2
        47: q^2+5q+2
        48: q^2+3q+1
        49: 2q^2+7q+2
        50: 2q^2+7q+2
        51: 2q^2+3q+1
        52: 2q^2+7q+2
        53: 2q^2+7q+2
        54: 3q^2+5q+2
        55: 2q^2+7q+2
        56: 2q^2+7q+2
        57: 3q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: q^2+5q+2
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 3q+2
        69: 2q+1
        70: 2q^2+6q+2
        71: 2q^2+7q+2
        72: q^2+7q+2
        73: 6q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: 4q+2
        82: 2q^2+7q+2
        83: q^2+5q+2
        84: q^2+5q+2
        85: 5q+2
        86: 2q^2+7q+2
        87: q^2+5q+2
        88: 5q+2
        89: q^2+5q+2
        90: q^2+3q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       107: 2q
       108: q^2+5q+2
       109: 3q+1
       110: 3q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       120: 3q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 3q+2
       126: 2q+1
       133: 3q+2
       134: 2q+1
       135: 5q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q^2+5q+2
       142: 4q+2
       143: 5q+2
       144: 2q+1
       145: q^2+4q+1
       146: q^2+5q+2
       147: q^2+4q+1
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: 5q+2
       158: q^2+5q+2
       159: q^2+3q+1
       160: q+2
       161: q+2
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       175: q+1
       176: q+1
       184: 3q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       200: 3q+2
       201: q
       202: q^2+3q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q+1
       220: 3q+2
       221: 2q+1
       222: 5q+2
       223: 2q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       243: 2q+1
       244: q+1
       246: 2q+2
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       265: q+1
       266: q+1
       269: q+1
       270: q+1
       277: q+1
       278: q+1
       284: q+1
       294: 3q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+1
       320: q+1
       325: q+1
       326: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: 2q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       387: q+1
       388: q+1
       395: 1
       396: 1
       420: q+1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: q+1
       448: 1
       454: q+1
       472: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       543: 1
       544: 1
       590: 1
       594: 1
       604: 1
       616: 1
       620: 1
       642: 1
       648: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       786: 1
       806: 1
       816: 1
       826: 1
       846: 1
       868: 1
       872: 1
      1005: 1

1006:    0: q^3+5q^2+8q+2
         1: q^3+5q^2+8q+2
         2: 4q^2+6q+2
         3: 6q^2+8q+2
         4: q^3+5q^2+8q+2
         5: 6q^2+8q+2
         6: q^3+5q^2+8q+2
         7: 4q^2+6q+2
         8: 2q^3+6q^2+6q+2
         9: q^3+3q^2+3q+1
        10: q^3+5q^2+8q+2
        11: 6q^2+8q+2
        12: q^3+5q^2+8q+2
        13: 2q^2+6q+2
        14: 2q^2+6q+2
        15: 4q^2+6q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: q^3+5q^2+8q+2
        20: q^3+5q^2+8q+2
        21: 4q^2+6q+2
        22: 2q^2+7q+2
        23: 2q^2+7q+2
        24: 3q^2+5q+2
        25: 2q^2+7q+2
        26: 2q^2+7q+2
        27: 3q^2+5q+2
        28: 2q^2+7q+2
        29: q^3+5q^2+8q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^2+5q+2
        33: q^2+7q+2
        34: 2q^2+7q+2
        35: q^2+5q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+6q+2
        44: 2q^2+6q+2
        45: 4q^2+6q+2
        46: 5q+2
        47: q^2+5q+2
        48: q^2+3q+1
        49: 2q^2+7q+2
        50: 2q^2+7q+2
        51: 2q^2+3q+1
        52: 2q^2+7q+2
        53: 2q^2+7q+2
        54: 3q^2+5q+2
        55: 2q^2+7q+2
        56: 2q^2+7q+2
        57: 3q^2+5q+2
        58: q^2+5q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 3q+2
        69: 2q+1
        70: 2q^2+6q+2
        71: 2q^2+7q+2
        72: 6q+2
        73: q^2+7q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: 5q+2
        82: 2q^2+7q+2
        83: q^2+5q+2
        84: q^2+5q+2
        85: 4q+2
        86: 2q^2+7q+2
        87: q^2+5q+2
        88: 5q+2
        89: q^2+5q+2
        90: q^2+3q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: 3q+1
       108: 3q+1
       109: q^2+5q+2
       110: 2q
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: 3q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 3q+2
       126: 2q+1
       133: 3q+2
       134: 2q+1
       135: 4q+2
       136: 5q+2
       137: 5q+2
       138: 2q+1
       139: q^2+4q+1
       141: q^2+5q+2
       142: q^2+4q+1
       143: 4q+2
       144: q+1
       145: 4q+2
       146: q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: 5q+2
       158: q^2+5q+2
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: q+1
       175: q+1
       183: q+1
       184: q+1
       185: 3q+2
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: 3q+2
       195: q^2+3q+1
       196: q
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q+1
       220: 3q+2
       221: 2q+1
       222: 4q+2
       223: q+1
       224: 5q+2
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 2q+1
       245: q+1
       246: 2q+2
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 1
       257: q+1
       258: 1
       263: q+1
       265: q+1
       271: q+1
       272: q+1
       275: q+1
       277: q+1
       285: q+1
       293: q+1
       294: q+1
       295: 3q+2
       297: 2q+1
       298: 2q+1
       303: q+1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: q+1
       325: q+1
       326: q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       385: q+1
       387: q+1
       401: 1
       402: 1
       421: q+1
       431: 1
       439: q+1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: q+1
       473: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       492: 1
       494: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       557: 1
       558: 1
       591: 1
       595: 1
       607: 1
       621: 1
       631: 1
       643: 1
       649: 1
       665: 1
       672: 1
       673: 1
       676: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       787: 1
       807: 1
       827: 1
       839: 1
       847: 1
       868: 1
       876: 1
      1006: 1

1007:    0: q^3+5q^2+8q+2
         1: q^3+5q^2+8q+2
         2: 4q^2+6q+2
         3: 6q^2+8q+2
         4: q^3+5q^2+8q+2
         5: 6q^2+8q+2
         6: q^3+5q^2+8q+2
         7: 4q^2+6q+2
         8: 2q^3+6q^2+6q+2
         9: q^3+3q^2+3q+1
        10: q^3+5q^2+8q+2
        11: 6q^2+8q+2
        12: q^3+5q^2+8q+2
        13: 2q^2+6q+2
        14: 2q^2+6q+2
        15: 4q^2+6q+2
        16: 2q^2+7q+2
        17: 2q^2+7q+2
        18: 2q^2+3q+1
        19: q^3+5q^2+8q+2
        20: q^3+5q^2+8q+2
        21: 4q^2+6q+2
        22: 2q^2+7q+2
        23: 2q^2+7q+2
        24: 3q^2+5q+2
        25: 2q^2+7q+2
        26: 2q^2+7q+2
        27: 3q^2+5q+2
        28: 2q^2+7q+2
        29: q^3+5q^2+8q+2
        30: 2q^2+6q+2
        31: 2q^2+7q+2
        32: q^2+5q+2
        33: q^2+7q+2
        34: 2q^2+7q+2
        35: q^2+5q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+6q+2
        44: 2q^2+6q+2
        45: 4q^2+6q+2
        46: 5q+2
        47: q^2+5q+2
        48: q^2+3q+1
        49: 2q^2+7q+2
        50: 2q^2+7q+2
        51: 2q^2+3q+1
        52: 2q^2+7q+2
        53: 2q^2+7q+2
        54: 3q^2+5q+2
        55: 2q^2+7q+2
        56: 2q^2+7q+2
        57: 3q^2+5q+2
        58: 2q
        59: q^2+5q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 3q+2
        69: 2q+1
        70: 2q^2+6q+2
        71: 2q^2+7q+2
        72: 6q+2
        73: q^2+7q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: 5q+2
        82: 2q^2+7q+2
        83: q^2+5q+2
        84: q^2+5q+2
        85: 4q+2
        86: 2q^2+7q+2
        87: q^2+5q+2
        88: 5q+2
        89: q^2+5q+2
        90: q^2+3q+1
        91: 5q+2
        92: q^2+5q+2
        93: q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: 3q+1
       108: 3q+1
       109: 2q
       110: q^2+5q+2
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       118: 3q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 3q+2
       126: 2q+1
       133: 3q+2
       134: 2q+1
       135: 4q+2
       136: 5q+2
       137: 5q+2
       138: 2q+1
       139: q^2+4q+1
       141: q^2+5q+2
       142: q^2+4q+1
       143: 4q+2
       144: q+1
       145: 4q+2
       146: q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: 5q+2
       158: q^2+5q+2
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       174: q+1
       176: q+1
       183: q+1
       184: q+1
       186: 3q+2
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       192: 3q+2
       195: q
       196: q^2+3q+1
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       204: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q+1
       220: 3q+2
       221: 2q+1
       222: 4q+2
       223: q+1
       224: 5q+2
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 2q+1
       245: q+1
       246: 2q+2
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 1
       257: q+1
       258: 1
       264: q+1
       266: q+1
       273: q+1
       274: q+1
       276: q+1
       278: q+1
       286: q+1
       293: q+1
       294: q+1
       296: 3q+2
       297: 2q+1
       298: 2q+1
       304: q+1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: q+1
       325: q+1
       326: q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       386: q+1
       388: q+1
       403: 1
       404: 1
       422: q+1
       432: 1
       440: q+1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: q+1
       474: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       492: 1
       494: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       559: 1
       560: 1
       592: 1
       596: 1
       608: 1
       622: 1
       632: 1
       644: 1
       650: 1
       665: 1
       672: 1
       673: 1
       676: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       788: 1
       808: 1
       828: 1
       840: 1
       848: 1
       868: 1
       876: 1
      1007: 1

1008:    0: 2q^3+10q^2+12q+2
         1: 2q^3+10q^2+12q+2
         2: 3q^3+7q^2+5q+1
         3: 10q^2+12q+2
         4: 2q^3+10q^2+12q+2
         5: 10q^2+12q+2
         6: 2q^3+10q^2+12q+2
         7: 3q^3+7q^2+5q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 2q^3+10q^2+12q+2
        11: 10q^2+12q+2
        12: 2q^3+10q^2+12q+2
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 3q^2+4q+1
        16: 5q^2+12q+2
        17: 5q^2+12q+2
        18: 2q^3+4q^2+3q+1
        19: 2q^3+10q^2+12q+2
        20: 2q^3+10q^2+12q+2
        21: 3q^3+7q^2+5q+1
        22: 5q^2+12q+2
        23: 5q^2+12q+2
        24: 2q^3+6q^2+5q+1
        25: 5q^2+12q+2
        26: 5q^2+12q+2
        27: 2q^3+6q^2+5q+1
        28: 5q^2+12q+2
        29: 2q^3+10q^2+12q+2
        30: 2q^2+4q+1
        31: 5q^2+12q+2
        32: q^2+4q+1
        33: 2q^2+12q+2
        34: 5q^2+12q+2
        35: q^2+4q+1
        36: 2q^2+12q+2
        37: q^2+8q+2
        38: 4q
        39: q^2+8q+2
        40: 4q
        41: 3q^2+4q+1
        42: q^3+2q^2+q
        43: 2q^2+4q+1
        44: 2q^2+4q+1
        45: 3q^2+4q+1
        46: 4q+1
        47: q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+12q+2
        50: 5q^2+12q+2
        51: 2q^3+4q^2+3q+1
        52: 5q^2+12q+2
        53: 5q^2+12q+2
        54: 2q^3+6q^2+5q+1
        55: 5q^2+12q+2
        56: 5q^2+12q+2
        57: 2q^3+6q^2+5q+1
        58: q^2+6q+1
        59: q^2+6q+1
        60: q^2+6q+1
        61: q^2+6q+1
        62: q^2+8q+2
        63: 4q
        64: 3q+1
        65: q
        66: 8q+2
        67: 4q
        69: 2q+1
        70: 2q^2+4q+1
        71: 5q^2+12q+2
        72: 2q^2+12q+2
        73: 2q^2+12q+2
        74: q^2+8q+2
        75: 4q
        76: q^2+8q+2
        77: 4q
        78: 3q^2+4q+1
        79: q^3+2q^2+q
        80: q^2+4q+1
        81: 4q+1
        82: 5q^2+12q+2
        83: q^2+4q+1
        84: q^2+4q+1
        85: 4q+1
        86: 5q^2+12q+2
        87: q^2+4q+1
        88: 4q+1
        89: q^2+4q+1
        90: q^2+2q+1
        91: 4q+1
        92: q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+10q+2
        95: 2q^2+10q+2
        96: q^3+3q^2+3q+1
        97: 2q^2+10q+2
        98: 2q^2+10q+2
        99: q^3+3q^2+3q+1
       100: q^2+11q+2
       101: q^2+11q+2
       102: 3q^2+4q+1
       103: 4q+1
       104: 2q
       105: 2q
       106: 4q+1
       107: q^2+6q+1
       108: q^2+6q+1
       109: q^2+6q+1
       110: q^2+6q+1
       111: 8q+2
       112: 4q
       113: q^2+8q+2
       114: 4q
       115: 3q+1
       116: q
       121: 3q+1
       122: q
       123: 3q+1
       124: q
       126: 2q+1
       127: 4q+2
       129: 4q+2
       131: q^2+2q+1
       134: 2q+1
       135: 4q+1
       136: 4q+1
       137: 4q+1
       138: 2q+1
       139: 2q^2+10q+2
       140: 6q+2
       141: q^2+4q+1
       142: 2q^2+10q+2
       143: 4q+1
       144: 2q+1
       145: 2q^2+10q+2
       146: q^2+4q+1
       147: 2q^2+10q+2
       148: 6q+2
       149: q^2+11q+2
       150: 3q+1
       151: q^2+7q+2
       152: 4q
       153: q^2+7q+2
       154: 4q
       155: 2q^2+3q+1
       156: q^2+q
       157: 4q+1
       158: q^2+4q+1
       159: q^2+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: 4q+1
       170: 2q
       171: 2q
       172: 4q+1
       177: q+1
       179: 4q+2
       181: 4q+2
       187: 3q+1
       188: q
       189: 3q+1
       190: q
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: 4q+2
       198: 2q
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 4q+2
       206: 2q
       207: 3q+1
       208: q
       209: q^2+7q+2
       210: 4q
       211: 2q+1
       212: q
       221: 2q+1
       222: 4q+1
       223: 2q+1
       224: 4q+1
       225: 2q+1
       226: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+2
       239: q+2
       241: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: 3q+1
       247: 5q+2
       248: 5q+2
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: 2q+1
       267: 2q+1
       268: q
       269: 2q+1
       270: q
       271: 2q+1
       272: q
       273: 2q+1
       274: q
       287: q+1
       291: q+1
       297: 3q+1
       298: q
       301: 2
       305: q+1
       311: 2
       313: q+1
       315: 1
       317: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 2q+1
       326: q
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 5q+2
       338: q+2
       340: q+2
       342: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2q+2
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2q+2
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       423: q+1
       425: 1
       427: q+2
       433: 1
       441: q+1
       443: q+1
       444: q+1
       445: 2
       451: 1
       459: q+1
       461: q+1
       462: q+1
       463: 2
       469: 1
       475: 1
       477: 4
       479: 2
       483: q+1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 2
       570: 2
       573: 1
       575: 1
       577: 2
       579: 2
       599: 1
       609: 1
       613: 1
       625: 1
       629: 1
       645: 1
       653: 1
       655: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       693: 1
       695: 1
       697: 1
       702: 1
       791: 1
       811: 1
       835: 1
       851: 1
       857: 1
       872: 1
       876: 1
      1008: 1

1009:    0: 2q^3+10q^2+12q+2
         1: 2q^3+10q^2+12q+2
         2: 3q^3+7q^2+5q+1
         3: 10q^2+12q+2
         4: 2q^3+10q^2+12q+2
         5: 10q^2+12q+2
         6: 2q^3+10q^2+12q+2
         7: 3q^3+7q^2+5q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 2q^3+10q^2+12q+2
        11: 10q^2+12q+2
        12: 2q^3+10q^2+12q+2
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 3q^2+4q+1
        16: 5q^2+12q+2
        17: 5q^2+12q+2
        18: 2q^3+4q^2+3q+1
        19: 2q^3+10q^2+12q+2
        20: 2q^3+10q^2+12q+2
        21: 3q^3+7q^2+5q+1
        22: 5q^2+12q+2
        23: 5q^2+12q+2
        24: 2q^3+6q^2+5q+1
        25: 5q^2+12q+2
        26: 5q^2+12q+2
        27: 2q^3+6q^2+5q+1
        28: 5q^2+12q+2
        29: 2q^3+10q^2+12q+2
        30: 2q^2+4q+1
        31: 5q^2+12q+2
        32: q^2+4q+1
        33: 2q^2+12q+2
        34: 5q^2+12q+2
        35: q^2+4q+1
        36: 2q^2+12q+2
        37: 4q
        38: q^2+8q+2
        39: 4q
        40: q^2+8q+2
        41: q^3+2q^2+q
        42: 3q^2+4q+1
        43: 2q^2+4q+1
        44: 2q^2+4q+1
        45: 3q^2+4q+1
        46: 4q+1
        47: q^2+4q+1
        48: q^2+2q+1
        49: 5q^2+12q+2
        50: 5q^2+12q+2
        51: 2q^3+4q^2+3q+1
        52: 5q^2+12q+2
        53: 5q^2+12q+2
        54: 2q^3+6q^2+5q+1
        55: 5q^2+12q+2
        56: 5q^2+12q+2
        57: 2q^3+6q^2+5q+1
        58: q^2+6q+1
        59: q^2+6q+1
        60: q^2+6q+1
        61: q^2+6q+1
        62: 4q
        63: q^2+8q+2
        64: q
        65: 3q+1
        66: 4q
        67: 8q+2
        69: 2q+1
        70: 2q^2+4q+1
        71: 5q^2+12q+2
        72: 2q^2+12q+2
        73: 2q^2+12q+2
        74: 4q
        75: q^2+8q+2
        76: 4q
        77: q^2+8q+2
        78: q^3+2q^2+q
        79: 3q^2+4q+1
        80: q^2+4q+1
        81: 4q+1
        82: 5q^2+12q+2
        83: q^2+4q+1
        84: q^2+4q+1
        85: 4q+1
        86: 5q^2+12q+2
        87: q^2+4q+1
        88: 4q+1
        89: q^2+4q+1
        90: q^2+2q+1
        91: 4q+1
        92: q^2+4q+1
        93: q^2+2q+1
        94: 2q^2+10q+2
        95: 2q^2+10q+2
        96: q^3+3q^2+3q+1
        97: 2q^2+10q+2
        98: 2q^2+10q+2
        99: q^3+3q^2+3q+1
       100: q^2+11q+2
       101: q^2+11q+2
       102: 3q^2+4q+1
       103: 2q
       104: 4q+1
       105: 4q+1
       106: 2q
       107: q^2+6q+1
       108: q^2+6q+1
       109: q^2+6q+1
       110: q^2+6q+1
       111: 4q
       112: 8q+2
       113: 4q
       114: q^2+8q+2
       115: q
       116: 3q+1
       121: q
       122: 3q+1
       123: q
       124: 3q+1
       126: 2q+1
       128: 4q+2
       130: 4q+2
       132: q^2+2q+1
       134: 2q+1
       135: 4q+1
       136: 4q+1
       137: 4q+1
       138: 2q+1
       139: 2q^2+10q+2
       140: 6q+2
       141: q^2+4q+1
       142: 2q^2+10q+2
       143: 4q+1
       144: 2q+1
       145: 2q^2+10q+2
       146: q^2+4q+1
       147: 2q^2+10q+2
       148: 6q+2
       149: q^2+11q+2
       150: 3q+1
       151: 4q
       152: q^2+7q+2
       153: 4q
       154: q^2+7q+2
       155: q^2+q
       156: 2q^2+3q+1
       157: 4q+1
       158: q^2+4q+1
       159: q^2+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: 2q
       170: 4q+1
       171: 4q+1
       172: 2q
       178: q+1
       180: 4q+2
       182: 4q+2
       187: q
       188: 3q+1
       189: q
       190: 3q+1
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: 2q
       198: 4q+2
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 2q
       206: 4q+2
       207: q
       208: 3q+1
       209: 4q
       210: q^2+7q+2
       211: q
       212: 2q+1
       221: 2q+1
       222: 4q+1
       223: 2q+1
       224: 4q+1
       225: 2q+1
       226: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: q+2
       240: q+2
       242: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: 3q+1
       247: 5q+2
       248: 5q+2
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: 2q+1
       267: q
       268: 2q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       273: q
       274: 2q+1
       288: q+1
       292: q+1
       297: q
       298: 3q+1
       302: 2
       306: q+1
       312: 2
       314: q+1
       316: 1
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       325: q
       326: 2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 5q+2
       339: q+2
       341: q+2
       343: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2q+2
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2q+2
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       424: q+1
       426: 1
       428: q+2
       434: 1
       442: q+1
       443: q+1
       444: q+1
       446: 2
       452: 1
       460: q+1
       461: q+1
       462: q+1
       464: 2
       470: 1
       476: 1
       478: 4
       480: 2
       483: q+1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 2
       572: 2
       574: 1
       576: 1
       581: 2
       582: 2
       600: 1
       610: 1
       614: 1
       626: 1
       630: 1
       646: 1
       654: 1
       656: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       699: 1
       700: 1
       703: 1
       704: 1
       792: 1
       812: 1
       836: 1
       852: 1
       858: 1
       872: 1
       876: 1
      1009: 1

1010:    0: q^3+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        30: q^3+2q+1
        32: 2q+1
        33: 2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: q^2+2q+1
        41: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        64: 2q+1
        66: 2q+1
        69: q+1
        72: 2q+1
        73: 2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        81: 2q+1
        83: 2q+1
        85: 2q+1
        87: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       111: 2q+1
       115: 2q+1
       123: 2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       138: q+1
       140: q+1
       142: 2q+1
       144: q+1
       147: 2q+1
       148: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       177: q+1
       181: 2q+1
       187: 2q+1
       197: q+1
       205: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       223: q+1
       225: q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       281: q+1
       289: 2q+1
       291: q+1
       301: 1
       305: q+1
       311: 1
       313: q+1
       315: 1
       323: 1
       336: 1
       338: 1
       340: q+1
       342: 1
       348: 1
       350: q+1
       351: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       417: q+1
       425: 1
       433: 1
       435: 1
       445: 1
       451: 1
       455: 1
       463: 1
       467: 1
       475: 1
       477: 2
       479: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       577: 1
       579: 1
       597: 1
       605: 1
       613: 1
       617: 1
       623: 1
       629: 1
       633: 1
       645: 1
       651: 2
       655: 1
       679: 1
       685: 1
       769: 1
       771: 1
       791: 1
       809: 1
       833: 1
       849: 1
      1010: 1

1011:    0: q^3+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        30: q^3+2q+1
        32: 2q+1
        33: 2q+1
        35: 2q+1
        36: 2q+1
        38: 2q+1
        40: q^2+2q+1
        42: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        65: 2q+1
        67: 2q+1
        69: q+1
        72: 2q+1
        73: 2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        81: 2q+1
        83: 2q+1
        85: 2q+1
        87: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       112: 2q+1
       116: 2q+1
       124: 2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       138: q+1
       140: q+1
       142: 2q+1
       144: q+1
       147: 2q+1
       148: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       178: q+1
       182: 2q+1
       188: 2q+1
       198: q+1
       206: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       223: q+1
       225: q+1
       228: q+1
       229: q+1
       230: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       282: q+1
       290: 2q+1
       292: q+1
       302: 1
       306: q+1
       312: 1
       314: q+1
       316: 1
       324: 1
       336: 1
       339: 1
       341: q+1
       343: 1
       348: 1
       350: q+1
       351: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       418: q+1
       426: 1
       434: 1
       436: 1
       446: 1
       452: 1
       456: 1
       464: 1
       468: 1
       476: 1
       478: 2
       480: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       581: 1
       582: 1
       598: 1
       606: 1
       614: 1
       618: 1
       624: 1
       630: 1
       634: 1
       646: 1
       652: 2
       656: 1
       679: 1
       685: 1
       773: 1
       774: 1
       792: 1
       810: 1
       834: 1
       850: 1
      1011: 1

1012:    0: 2q^2+3q+1
         1: 3q^2+3q+1
         2: q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 3q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 3q^2+3q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        30: 2q+1
        32: 2q+1
        33: q^2+3q+1
        35: 2q+1
        36: q^2+3q+1
        37: q+1
        38: 2q
        39: q+1
        40: 2q
        41: q+1
        42: q^2+q
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+3q+1
        50: 3q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        64: q+1
        65: q
        66: q+1
        67: 2q
        69: 2q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q
        76: q+1
        77: 2q
        78: q+1
        79: q^2+q
        81: 2q+1
        83: 2q+1
        85: 2q+1
        87: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       111: q+1
       112: 2q
       115: q+1
       116: q
       123: q+1
       124: q
       127: q+1
       128: 2q
       129: q+1
       130: 2q
       131: q+1
       132: q^2+q
       134: 2q+1
       135: 2q+1
       136: 2q+1
       138: 2q+1
       140: q+1
       142: q^2+3q+1
       144: 2q+1
       147: q^2+3q+1
       148: q+1
       150: q+1
       151: 1
       152: 2q
       153: q+1
       154: 2q
       155: 1
       156: q
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: q+1
       178: q
       181: q+1
       182: 2q
       187: q+1
       188: q
       197: 1
       198: q
       205: 1
       206: q
       211: 1
       212: q
       223: 2q+1
       225: 2q+1
       228: q+1
       229: 1
       230: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 1
       238: 2q
       239: q+1
       240: 2q
       241: 1
       242: q
       244: q+1
       245: q+1
       247: 2q+1
       248: 3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       291: q+1
       292: q
       301: 1
       302: q
       305: 1
       311: 1
       312: q
       313: 1
       315: 1
       316: q
       323: 1
       336: q+1
       338: 1
       339: 2q
       340: q+1
       341: 2q
       342: 1
       343: q
       348: 1
       350: q+1
       351: q+1
       356: q+1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       425: 1
       426: q
       433: 1
       445: 1
       446: q
       451: 1
       463: 1
       464: q
       475: 1
       477: 1
       479: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       577: 1
       613: 1
       629: 1
       645: 1
       655: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       791: 1
       843: 1
       870: 1
       874: 1
      1012: 1

1013:    0: 2q^2+3q+1
         1: 3q^2+3q+1
         2: q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 3q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 3q^2+3q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        30: 2q+1
        32: 2q+1
        33: q^2+3q+1
        35: 2q+1
        36: q^2+3q+1
        37: 2q
        38: q+1
        39: 2q
        40: q+1
        41: q^2+q
        42: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 2q^2+3q+1
        50: 3q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        64: q
        65: q+1
        66: 2q
        67: q+1
        69: 2q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q
        75: q+1
        76: 2q
        77: q+1
        78: q^2+q
        79: q+1
        81: 2q+1
        83: 2q+1
        85: 2q+1
        87: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 3q+1
       102: q+1
       111: 2q
       112: q+1
       115: q
       116: q+1
       123: q
       124: q+1
       127: 2q
       128: q+1
       129: 2q
       130: q+1
       131: q^2+q
       132: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       138: 2q+1
       140: q+1
       142: q^2+3q+1
       144: 2q+1
       147: q^2+3q+1
       148: q+1
       150: q+1
       151: 2q
       152: 1
       153: 2q
       154: q+1
       155: q
       156: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 3q+1
       168: q+1
       177: q
       178: q+1
       181: 2q
       182: q+1
       187: q
       188: q+1
       197: q
       198: 1
       205: q
       206: 1
       211: q
       212: 1
       223: 2q+1
       225: 2q+1
       228: q+1
       229: 1
       230: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q
       238: 1
       239: 2q
       240: q+1
       241: q
       242: 1
       244: q+1
       245: q+1
       247: 2q+1
       248: 3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       291: q
       292: q+1
       301: q
       302: 1
       306: 1
       311: q
       312: 1
       314: 1
       315: q
       316: 1
       324: 1
       336: q+1
       338: 2q
       339: 1
       340: 2q
       341: q+1
       342: q
       343: 1
       348: 1
       350: q+1
       351: q+1
       356: q+1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       425: q
       426: 1
       434: 1
       445: q
       446: 1
       452: 1
       463: q
       464: 1
       476: 1
       478: 1
       480: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       581: 1
       614: 1
       630: 1
       646: 1
       656: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       792: 1
       844: 1
       870: 1
       874: 1
      1013: 1

1014:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q^2+4q+2
        32: q^2+2q+1
        33: 2q^2+4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: q^2+3q+2
        72: 2
        73: 2q+2
        74: q+2
        76: q+2
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+3q+2
        83: q+1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+2q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       134: q+1
       135: 1
       136: q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+3q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: 1
       202: 1
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: q+1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       233: 1
       234: 1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       246: 1
       247: 2
       248: 2
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       315: 1
       317: q+2
       319: 1
       320: 1
       325: 1
       327: 1
       329: q+1
       331: 1
       334: 1
       335: q+1
       337: 2
       338: 2
       340: 2
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       411: 1
       415: 1
       417: 1
       423: 1
       427: 2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       467: 1
       469: 1
       485: 1
       487: 1
       493: 1
       494: q+1
       496: 1
       498: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       547: 1
       587: 1
       605: 1
       609: 1
       611: 1
       617: 1
       637: 1
       658: 1
       660: 1
       666: 1
       668: 1
       674: 1
       678: 1
       687: 1
       690: 1
       691: 1
       795: 1
       799: 1
       813: 1
       859: 1
       861: 1
       869: 1
      1014: 1

1015:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q^2+4q+2
        32: q^2+2q+1
        33: 2q^2+4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+2q+1
        55: q+2
        56: q+2
        57: q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: q^2+3q+2
        72: 2
        73: 2q+2
        75: q+2
        77: q+2
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+3q+2
        83: q+1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+2q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       134: q+1
       135: 1
       136: q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+3q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: 1
       202: 1
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: q+1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       233: 1
       234: 1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       246: 1
       247: 2
       248: 2
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       316: 1
       318: q+2
       319: 1
       320: 1
       326: 1
       328: 1
       330: q+1
       332: 1
       334: 1
       335: q+1
       337: 2
       339: 2
       341: 2
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       412: 1
       416: 1
       418: 1
       424: 1
       428: 2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       468: 1
       470: 1
       486: 1
       488: 1
       493: 1
       494: q+1
       496: 1
       498: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       546: 1
       548: 1
       588: 1
       606: 1
       610: 1
       612: 1
       618: 1
       638: 1
       659: 1
       661: 1
       667: 1
       669: 1
       674: 1
       678: 1
       687: 1
       690: 1
       691: 1
       796: 1
       800: 1
       814: 1
       860: 1
       862: 1
       869: 1
      1015: 1

1016:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: q^3+4q^2+5q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^2+5q+2
        14: q^2+3q+2
        15: q^2+5q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^2+3q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+3q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: q^3+4q^2+5q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 2q^2+8q+2
        29: q^2+5q+2
        30: q^2+3q+2
        31: 2q^2+8q+2
        32: q^2+5q+2
        33: 2q^2+8q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+3q+2
        45: q^2+5q+2
        46: q^2+5q+2
        47: q^2+5q+2
        48: q^2+3q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+3q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+3q+2
        55: 3q+2
        56: 3q+2
        57: 2q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: 4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+5q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q^2+5q+2
        81: q^2+5q+2
        82: q^2+5q+2
        83: q^2+3q+2
        84: 4q+2
        85: 4q+2
        86: 3q+2
        87: 2q+2
        88: q^2+5q+2
        89: q^2+5q+2
        90: q^2+3q+2
        91: 2
        92: 2q+2
        93: 2
        94: q^2+5q+2
        95: q^2+5q+2
        96: q^2+3q+2
        97: 3q+2
        98: 3q+2
        99: 2q+2
       100: 3q+2
       101: 3q+2
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 2
       135: 2
       136: 2
       137: q^2+5q+2
       138: q^2+3q+2
       139: q^2+5q+2
       140: q+2
       141: q^2+3q+2
       142: 2q+2
       143: 4q+2
       144: 2q+2
       145: 3q+2
       146: 2q+2
       147: q+2
       149: 3q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: 3q+2
       167: 3q+2
       168: 2q+2
       169: 1
       170: 1
       173: q+1
       174: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: q+2
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 2
       220: 2
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q^2+3q+2
       227: 2
       228: 2
       229: 2
       230: 2
       231: 2q+2
       232: 1
       233: 1
       234: 1
       236: 2q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       244: q+2
       246: 2q+2
       247: 2
       248: 2
       250: 2
       251: 2q+2
       252: 2
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: q+1
       276: q+1
       283: 2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+2
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       345: 2
       346: 2
       347: 2
       348: 2
       349: 2
       350: 2
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 2q+2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       427: 1
       428: 1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: 1
       453: 1
       469: q+1
       470: q+1
       471: 1
       484: 1
       492: 2
       493: 2
       494: 2
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 1
       546: 1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       615: 1
       619: 1
       641: 1
       647: 1
       657: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       725: 1
       726: 1
       793: 1
       815: 1
       845: 1
       865: 1
       869: 1
      1016: 1

1017:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: q^3+4q^2+5q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^2+5q+2
        14: q^2+3q+2
        15: q^2+5q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^2+3q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+3q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: q^3+4q^2+5q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 2q^2+8q+2
        29: q^2+5q+2
        30: q^2+3q+2
        31: 2q^2+8q+2
        32: q^2+5q+2
        33: 2q^2+8q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+3q+2
        45: q^2+5q+2
        46: q^2+5q+2
        47: q^2+5q+2
        48: q^2+3q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+3q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+3q+2
        55: 3q+2
        56: 3q+2
        57: 2q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: 2q
        61: 4q+2
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+5q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q^2+5q+2
        81: q^2+5q+2
        82: q^2+5q+2
        83: q^2+3q+2
        84: 4q+2
        85: 4q+2
        86: 3q+2
        87: 2q+2
        88: q^2+5q+2
        89: q^2+5q+2
        90: q^2+3q+2
        91: 2
        92: 2q+2
        93: 2
        94: q^2+5q+2
        95: q^2+5q+2
        96: q^2+3q+2
        97: 3q+2
        98: 3q+2
        99: 2q+2
       100: 3q+2
       101: 3q+2
       102: 2q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 2
       135: 2
       136: 2
       137: q^2+5q+2
       138: q^2+3q+2
       139: q^2+5q+2
       140: q+2
       141: q^2+3q+2
       142: 2q+2
       143: 4q+2
       144: 2q+2
       145: 3q+2
       146: 2q+2
       147: q+2
       149: 3q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 2
       161: 2q+2
       162: 2
       163: 1
       164: q+1
       165: 1
       166: 3q+2
       167: 3q+2
       168: 2q+2
       171: 1
       172: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: q+2
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 2
       220: 2
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q^2+3q+2
       227: 2
       228: 2
       229: 2
       230: 2
       231: 2q+2
       232: 1
       233: 1
       234: 1
       236: 2q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       244: q+2
       246: 2q+2
       247: 2
       248: 2
       250: 2
       251: 2q+2
       252: 2
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: q+1
       278: q+1
       284: 2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: q+2
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 2
       345: 2
       346: 2
       347: 2
       348: 2
       349: 2
       350: 2
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 2q+2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       427: 1
       428: 1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: 1
       454: 1
       469: q+1
       470: q+1
       472: 1
       484: 1
       492: 2
       493: 2
       494: 2
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 1
       548: 1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       616: 1
       620: 1
       642: 1
       648: 1
       657: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       727: 1
       728: 1
       794: 1
       816: 1
       846: 1
       865: 1
       869: 1
      1017: 1

1018:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+5q+2
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 2q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q^2+5q+2
        14: q^3+3q^2+3q+2
        15: 2q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+5q+2
        23: 2q^2+5q+2
        24: 2q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q^2+5q+2
        32: 2q^2+5q+2
        33: 4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 2q^2+5q+2
        44: q^3+3q^2+3q+2
        45: 2q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: q^3+2q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 4q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: 2q^2+5q+2
        81: 4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q^2+3q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 4q+2
        89: 4q+2
        90: q^3+2q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 4q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2
       143: 2q+2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+2
       211: q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q+2
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       453: 1
       454: 1
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       583: 1
       585: 1
       587: 1
       605: 1
       609: 1
       611: 2
       635: 2
       637: 1
       639: 1
       647: 1
       648: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       729: 1
       731: 1
       777: 1
       797: 1
       799: 1
       841: 1
       877: 1
      1018: 1

1019:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+5q+2
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 2q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q^2+5q+2
        14: q^3+3q^2+3q+2
        15: 2q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+5q+2
        23: 2q^2+5q+2
        24: 2q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q^2+5q+2
        32: 2q^2+5q+2
        33: 4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 2q^2+5q+2
        44: q^3+3q^2+3q+2
        45: 2q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: q^3+2q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 4q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: 2q^2+5q+2
        81: 4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q^2+3q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 4q+2
        89: 4q+2
        90: q^3+2q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 4q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2
       143: 2q+2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+2
       212: q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q+2
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       453: 1
       454: 1
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       584: 1
       586: 1
       588: 1
       606: 1
       610: 1
       612: 2
       636: 2
       638: 1
       640: 1
       647: 1
       648: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       730: 1
       732: 1
       778: 1
       798: 1
       800: 1
       842: 1
       877: 1
      1019: 1

1020:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: q+1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: 1
        81: q+1
        83: q+1
        85: 1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       360: 1
       362: 1
       364: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 1
       467: 1
       485: 1
       487: 1
       489: 1
       491: 1
       495: 1
       496: 1
       512: 1
       515: 1
       516: 1
       517: 1
       597: 1
       605: 1
       613: 1
       617: 1
       658: 1
       660: 1
       662: 1
       664: 1
       674: 1
       679: 1
       779: 1
       795: 1
       809: 1
       870: 1
      1020: 1

1021:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: q+1
        72: 1
        73: q+1
        75: 1
        77: 1
        79: 1
        81: q+1
        83: q+1
        85: 1
        87: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: 1
       147: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: q+1
       351: 1
       356: 1
       361: 1
       363: 1
       365: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 1
       468: 1
       486: 1
       488: 1
       490: 1
       491: 1
       495: 1
       496: 1
       512: 1
       515: 1
       516: 1
       517: 1
       598: 1
       606: 1
       614: 1
       618: 1
       659: 1
       661: 1
       663: 1
       664: 1
       674: 1
       679: 1
       780: 1
       796: 1
       810: 1
       870: 1
      1021: 1

1022:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: q^2+4q+2
        23: 2q^2+4q+2
        24: q^2+4q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: 3q+2
        32: q^2+4q+2
        33: 3q+2
        34: q+2
        35: 2q+2
        36: q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: q^2+4q+2
        53: 2q^2+4q+2
        54: q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+2
        64: 2q+2
        66: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: q+2
        73: 3q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+4q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       106: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: q+2
       113: q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: q+2
       123: q+2
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: q+2
       189: q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+2
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: q+2
       211: 2q+2
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       307: 1
       308: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: 2
       352: 1
       356: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       413: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       508: 1
       512: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       585: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: 2
       639: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       733: 1
       735: 1
       781: 1
       797: 1
       809: 1
       811: 1
       871: 1
      1022: 1

1023:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: q^2+4q+2
        23: 2q^2+4q+2
        24: q^2+4q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: 3q+2
        32: q^2+4q+2
        33: 3q+2
        34: q+2
        35: 2q+2
        36: q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: q^2+4q+2
        53: 2q^2+4q+2
        54: q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: 1
        61: 1
        63: q+2
        65: 2q+2
        67: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: q+2
        73: 3q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+4q+2
        84: q+2
        85: q+2
        86: q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: 1
       105: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: q+2
       114: q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: 1
       120: 1
       122: q+2
       124: q+2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: q+2
       190: q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+2
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: q+2
       212: 2q+2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: q+2
       307: 1
       308: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: 2
       352: 1
       356: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       414: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       508: 1
       512: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       586: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: 2
       640: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       734: 1
       736: 1
       782: 1
       798: 1
       810: 1
       812: 1
       871: 1
      1023: 1

1024:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+3q+1
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 4q+2
        29: 2q^2+4q+2
        30: q^2+2q+1
        31: 2q^2+4q+2
        32: q^2+2q+1
        33: 4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 4q+2
        50: 4q+2
        51: q^3+2q^2+2q+1
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: q^3+3q^2+3q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q^2+2q+1
        71: 4q+2
        72: 2q+2
        73: 4q+2
        74: 2q+2
        76: 2q+2
        78: q^2+2q+1
        80: q^2+2q+1
        81: 2q+1
        82: 2q^2+4q+2
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 4q+2
        95: 4q+2
        96: q^3+2q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: q^2+2q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       111: 2q+2
       113: 2q+2
       115: q+1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q^2+2q+1
       142: 4q+2
       143: q+1
       144: 1
       145: 2
       146: q+1
       147: 2
       149: 2q+2
       150: q+1
       151: 2q+2
       153: 2q+2
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: q+1
       172: q+1
       177: 1
       179: 2
       181: 2
       187: q+1
       189: q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       201: 1
       202: 1
       207: q+1
       209: 2q+2
       211: q+1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: q+1
       269: q+1
       281: 1
       287: 1
       289: 1
       291: 1
       297: q+1
       301: 2
       305: q+1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 1
       441: q+1
       443: 1
       444: 1
       445: 2
       467: 1
       469: 1
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: 1
       502: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       545: 1
       547: 1
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       637: 1
       666: 1
       668: 1
       670: 1
       673: 1
       677: 1
       678: 1
       679: 1
       687: 1
       783: 1
       799: 1
       809: 1
       811: 1
       813: 1
       872: 1
      1024: 1

1025:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+3q+1
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+3q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 4q+2
        29: 2q^2+4q+2
        30: q^2+2q+1
        31: 2q^2+4q+2
        32: q^2+2q+1
        33: 4q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 4q+2
        50: 4q+2
        51: q^3+2q^2+2q+1
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: q^3+3q^2+3q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q^2+2q+1
        71: 4q+2
        72: 2q+2
        73: 4q+2
        75: 2q+2
        77: 2q+2
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q+1
        82: 2q^2+4q+2
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 4q+2
        95: 4q+2
        96: q^3+2q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: q^2+2q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       112: 2q+2
       114: 2q+2
       116: q+1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q^2+2q+1
       142: 4q+2
       143: q+1
       144: 1
       145: 2
       146: q+1
       147: 2
       149: 2q+2
       150: q+1
       152: 2q+2
       154: 2q+2
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: q+1
       171: q+1
       178: 1
       180: 2
       182: 2
       188: q+1
       190: q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       201: 1
       202: 1
       208: q+1
       210: 2q+2
       212: q+1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: q+1
       270: q+1
       282: 1
       288: 1
       290: 1
       292: 1
       298: q+1
       302: 2
       306: q+1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 1
       442: q+1
       443: 1
       444: 1
       446: 2
       468: 1
       470: 1
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: 1
       503: 1
       505: 1
       507: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       546: 1
       548: 1
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       638: 1
       667: 1
       669: 1
       671: 1
       673: 1
       677: 1
       678: 1
       679: 1
       687: 1
       784: 1
       800: 1
       810: 1
       812: 1
       814: 1
       872: 1
      1025: 1

1026:    0: q^2+q+2
         1: q^3+q^2+q+2
         2: q^2+q+2
         3: q^3+q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^3+q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: q^2+q+2
        20: q^3+q^2+q+2
        21: q^2+q+2
        22: q^2+q+2
        23: q^3+q^2+q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: q+2
        30: q^2+q+2
        31: q+2
        32: q^2+q+2
        33: q^2+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: q^2+2
        50: q^2+2
        51: q+1
        52: q^2+q+2
        53: q^3+q^2+q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: q^2+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q^2+2
        82: q+2
        83: q^2+q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2
        89: 2
        90: q+1
        91: q^2+2
        92: q^2+2
        93: q+1
        94: q^2+2
        95: q^2+2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: q^2+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: q^2+2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: q^2+2
       161: q^2+2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q^2+2
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       256: 1
       257: 1
       258: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       319: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       385: 1
       386: 1
       393: 1
       394: 1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       447: 1
       471: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       508: 1
       512: 1
       541: 1
       542: 1
       589: 1
       593: 1
       603: 1
       615: 1
       641: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       785: 1
       801: 1
       805: 1
       871: 1
      1026: 1

1027:    0: q^2+q+2
         1: q^3+q^2+q+2
         2: q^2+q+2
         3: q^3+q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^3+q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: q^2+q+2
        20: q^3+q^2+q+2
        21: q^2+q+2
        22: q^2+q+2
        23: q^3+q^2+q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: q+2
        30: q^2+q+2
        31: q+2
        32: q^2+q+2
        33: q^2+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: q^2+2
        50: q^2+2
        51: q+1
        52: q^2+q+2
        53: q^3+q^2+q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: q^2+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q^2+2
        82: q+2
        83: q^2+q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2
        89: 2
        90: q+1
        91: q^2+2
        92: q^2+2
        93: q+1
        94: q^2+2
        95: q^2+2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: q^2+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: q^2+2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: q^2+2
       161: q^2+2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q^2+2
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       320: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 1
       352: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       387: 1
       388: 1
       395: 1
       396: 1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       448: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       508: 1
       512: 1
       543: 1
       544: 1
       590: 1
       594: 1
       604: 1
       616: 1
       642: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       786: 1
       802: 1
       806: 1
       871: 1
      1027: 1

1028:    0: q^2+5q+2
         1: q^3+3q^2+5q+2
         2: q^2+5q+2
         3: q^3+3q^2+5q+2
         4: q^2+5q+2
         5: q^2+5q+2
         6: q^3+3q^2+5q+2
         7: q^2+5q+2
         8: q^2+5q+2
         9: q^3+q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: q^2+5q+2
        16: 3q+2
        17: 3q+2
        18: 2q+1
        19: q^2+5q+2
        20: q^3+3q^2+5q+2
        21: q^2+5q+2
        22: q^2+5q+2
        23: q^3+3q^2+5q+2
        24: q^2+5q+2
        25: 4q+2
        26: 2q^2+4q+2
        27: 4q+2
        28: q+2
        29: 3q+2
        30: q^2+5q+2
        31: 3q+2
        32: q^2+5q+2
        33: 3q+2
        34: 2q+2
        35: 4q+2
        36: 2q+2
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q+1
        42: 2q+1
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^3+3q^2+5q+2
        54: q^2+5q+2
        55: 4q+2
        56: 2q^2+4q+2
        57: 4q+2
        58: q+2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: 2q+2
        73: 3q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+5q+2
        84: 2q+2
        85: 2q+2
        86: 2q+2
        87: 4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: 2q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: q+2
        98: q+2
        99: q+1
       100: 4q+2
       101: 2q^2+4q+2
       102: 4q+2
       103: 1
       105: 1
       107: 1
       108: 1
       109: q+2
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 2q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+2
       140: 2q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: q+2
       148: 2
       149: 2q+2
       150: 4q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: 2q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2
       193: 1
       194: 1
       195: q+2
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: q+2
       228: q+1
       229: 2q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 2
       244: q+2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: 2
       251: 2
       252: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       303: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       319: 1
       320: 1
       321: 2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: q+2
       352: 1
       356: 1
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       385: 1
       387: 1
       393: 1
       395: 1
       401: 1
       402: 1
       405: 1
       408: 1
       421: 1
       431: 1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 1
       444: 1
       449: 1
       461: 2
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 1
       512: 1
       514: 1
       541: 1
       544: 1
       565: 1
       567: 1
       573: 1
       576: 1
       591: 1
       595: 1
       607: 1
       615: 1
       616: 1
       631: 2
       643: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       765: 1
       767: 1
       787: 1
       803: 1
       807: 1
       871: 1
       880: 1
      1028: 1

1029:    0: q^2+5q+2
         1: q^3+3q^2+5q+2
         2: q^2+5q+2
         3: q^3+3q^2+5q+2
         4: q^2+5q+2
         5: q^2+5q+2
         6: q^3+3q^2+5q+2
         7: q^2+5q+2
         8: q^2+5q+2
         9: q^3+q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: q^2+5q+2
        16: 3q+2
        17: 3q+2
        18: 2q+1
        19: q^2+5q+2
        20: q^3+3q^2+5q+2
        21: q^2+5q+2
        22: q^2+5q+2
        23: q^3+3q^2+5q+2
        24: q^2+5q+2
        25: 4q+2
        26: 2q^2+4q+2
        27: 4q+2
        28: q+2
        29: 3q+2
        30: q^2+5q+2
        31: 3q+2
        32: q^2+5q+2
        33: 3q+2
        34: 2q+2
        35: 4q+2
        36: 2q+2
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q+1
        42: 2q+1
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^3+3q^2+5q+2
        54: q^2+5q+2
        55: 4q+2
        56: 2q^2+4q+2
        57: 4q+2
        59: q+2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: 2q+2
        73: 3q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+5q+2
        84: 2q+2
        85: 2q+2
        86: 2q+2
        87: 4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: 2q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: q+2
        98: q+2
        99: q+1
       100: 4q+2
       101: 2q^2+4q+2
       102: 4q+2
       104: 1
       106: 1
       107: 1
       108: 1
       110: q+2
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       118: q+2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 2q+2
       136: 3q+2
       137: 2
       138: q+1
       139: q+2
       140: 2q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: q+2
       148: 2
       149: 2q+2
       150: 4q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: 2q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       192: 2
       193: 1
       194: 1
       196: q+2
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: 1
       227: q+2
       228: q+1
       229: 2q+2
       230: 3q+2
       231: 1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: 1
       243: 2
       244: q+2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: 2
       251: 2
       252: q+1
       256: q+2
       257: q+2
       258: q+1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       304: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       319: 1
       320: 1
       322: 2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: q+2
       352: 1
       356: 1
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       386: 1
       388: 1
       394: 1
       396: 1
       403: 1
       404: 1
       406: 1
       407: 1
       422: 1
       432: 1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 1
       444: 1
       450: 1
       462: 2
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 1
       512: 1
       514: 1
       542: 1
       543: 1
       566: 1
       568: 1
       574: 1
       575: 1
       592: 1
       596: 1
       608: 1
       615: 1
       616: 1
       632: 2
       644: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       766: 1
       768: 1
       788: 1
       804: 1
       808: 1
       871: 1
       880: 1
      1029: 1

1030:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+3q+1
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q^2+4q+2
        35: q^2+2q+1
        36: 2q^2+4q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: q^2+3q+2
        72: 2q+2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+3q+2
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       134: q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: q+2
       141: 1
       142: 2
       143: q^2+2q+1
       144: q+1
       145: q^2+3q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: q+1
       217: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       311: 2
       313: 1
       315: 1
       317: q+2
       321: 1
       322: 1
       325: 1
       327: 1
       329: q+1
       331: 1
       334: q+1
       335: 1
       337: 2
       338: 2
       340: 2
       346: 1
       349: 1
       350: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       397: 1
       399: 1
       411: 1
       415: 1
       417: 1
       423: 1
       427: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       485: 1
       487: 1
       494: 1
       498: q+1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       561: 1
       563: 1
       587: 1
       623: 1
       625: 1
       627: 1
       633: 1
       637: 1
       658: 1
       660: 1
       666: 1
       668: 1
       680: 1
       684: 1
       688: 1
       690: 1
       691: 1
       819: 1
       823: 1
       837: 1
       859: 1
       861: 1
       873: 1
      1030: 1

1031:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+3q+1
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q^2+4q+2
        35: q^2+2q+1
        36: 2q^2+4q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+1
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: q^2+3q+2
        72: 2q+2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+3q+2
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       134: q+1
       135: q+1
       136: 1
       137: q+1
       138: 1
       139: q+2
       141: 1
       142: 2
       143: q^2+2q+1
       144: q+1
       145: q^2+3q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: q+1
       218: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       312: 2
       314: 1
       316: 1
       318: q+2
       321: 1
       322: 1
       326: 1
       328: 1
       330: q+1
       332: 1
       334: q+1
       335: 1
       337: 2
       339: 2
       341: 2
       346: 1
       349: 1
       350: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       398: 1
       400: 1
       412: 1
       416: 1
       418: 1
       424: 1
       428: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       486: 1
       488: 1
       494: 1
       498: q+1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       562: 1
       564: 1
       588: 1
       624: 1
       626: 1
       628: 1
       634: 1
       638: 1
       659: 1
       661: 1
       667: 1
       669: 1
       680: 1
       684: 1
       688: 1
       690: 1
       691: 1
       820: 1
       824: 1
       838: 1
       860: 1
       862: 1
       873: 1
      1031: 1

1032:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: q^3+4q^2+5q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^2+5q+2
        14: q^2+3q+2
        15: q^2+5q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^2+3q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: q^3+4q^2+5q+2
        28: 2q^2+8q+2
        29: q^2+5q+2
        30: q^2+3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: q^2+5q+2
        36: 2q^2+8q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+3q+2
        45: q^2+5q+2
        46: q^2+5q+2
        47: q^2+5q+2
        48: q^2+3q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+3q+2
        52: 3q+2
        53: 3q+2
        54: 2q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+3q+2
        58: 4q+2
        59: 2q
        60: q^2+4q+1
        61: q^2+4q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+5q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 3q+2
        83: 2q+2
        84: q^2+5q+2
        85: q^2+5q+2
        86: q^2+5q+2
        87: q^2+3q+2
        88: q^2+5q+2
        89: q^2+5q+2
        90: q^2+3q+2
        91: 2
        92: 2q+2
        93: 2
        94: 3q+2
        95: 3q+2
        96: 2q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: q^2+3q+2
       100: 3q+2
       101: 3q+2
       102: 2q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 2
       135: 2
       136: 2
       137: 4q+2
       138: 2q+2
       139: 3q+2
       141: 2q+2
       142: q+2
       143: q^2+5q+2
       144: q^2+3q+2
       145: q^2+5q+2
       146: q^2+3q+2
       147: 2q+2
       148: q+2
       149: 3q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: 3q+2
       167: 3q+2
       168: 2q+2
       169: 1
       171: 1
       173: q+1
       175: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q+2
       195: q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 2
       220: 2
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2q+2
       227: 1
       228: 1
       230: 1
       231: q^2+3q+2
       232: 2
       233: 2
       234: 2
       235: 2
       236: 2q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       245: q+2
       246: 2q+2
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       283: 1
       284: 1
       285: 2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       321: q+2
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       357: 2
       358: 2
       359: 2
       366: 2q+2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       379: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       427: 1
       428: 1
       431: 1
       439: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       463: 1
       464: 1
       469: q+1
       470: q+1
       473: 1
       484: 1
       492: 1
       494: 1
       497: 2
       498: 2
       499: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       529: 1
       531: 1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 1
       562: 1
       607: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       631: 1
       643: 1
       649: 1
       657: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       741: 1
       742: 1
       817: 1
       839: 1
       847: 1
       865: 1
       873: 1
      1032: 1

1033:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: q^3+4q^2+5q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^2+3q+2
         8: q^3+4q^2+5q+2
         9: q^2+3q+2
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^2+5q+2
        14: q^2+3q+2
        15: q^2+5q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^2+3q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: q^3+4q^2+5q+2
        28: 2q^2+8q+2
        29: q^2+5q+2
        30: q^2+3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: q^2+5q+2
        36: 2q^2+8q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+3q+2
        45: q^2+5q+2
        46: q^2+5q+2
        47: q^2+5q+2
        48: q^2+3q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+3q+2
        52: 3q+2
        53: 3q+2
        54: 2q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+3q+2
        58: 2q
        59: 4q+2
        60: q^2+4q+1
        61: q^2+4q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+5q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 3q+2
        83: 2q+2
        84: q^2+5q+2
        85: q^2+5q+2
        86: q^2+5q+2
        87: q^2+3q+2
        88: q^2+5q+2
        89: q^2+5q+2
        90: q^2+3q+2
        91: 2
        92: 2q+2
        93: 2
        94: 3q+2
        95: 3q+2
        96: 2q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: q^2+3q+2
       100: 3q+2
       101: 3q+2
       102: 2q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 2
       134: 2
       135: 2
       136: 2
       137: 4q+2
       138: 2q+2
       139: 3q+2
       141: 2q+2
       142: q+2
       143: q^2+5q+2
       144: q^2+3q+2
       145: q^2+5q+2
       146: q^2+3q+2
       147: 2q+2
       148: q+2
       149: 3q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2q+2
       159: 2
       160: 1
       161: q+1
       162: 1
       163: 2
       164: 2q+2
       165: 2
       166: 3q+2
       167: 3q+2
       168: 2q+2
       170: 1
       172: 1
       174: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2q+2
       196: q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 2
       220: 2
       221: 2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2q+2
       227: 1
       228: 1
       230: 1
       231: q^2+3q+2
       232: 2
       233: 2
       234: 2
       235: 2
       236: 2q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       245: q+2
       246: 2q+2
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 2
       254: 2q+2
       255: 2
       256: 1
       257: q+1
       258: 1
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       283: 1
       284: 1
       286: 2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       322: q+2
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       357: 2
       358: 2
       359: 2
       366: 2q+2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       380: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       427: 1
       428: 1
       432: 1
       440: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       463: 1
       464: 1
       469: q+1
       470: q+1
       474: 1
       484: 1
       492: 1
       494: 1
       497: 2
       498: 2
       499: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       530: 1
       532: 1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 1
       564: 1
       608: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       632: 1
       644: 1
       650: 1
       657: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       743: 1
       744: 1
       818: 1
       840: 1
       848: 1
       865: 1
       873: 1
      1033: 1

1034:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+5q+2
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 2q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q^2+5q+2
        14: q^3+3q^2+3q+2
        15: 2q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 2q^2+5q+2
        26: 2q^2+5q+2
        27: 2q^2+5q+2
        28: 4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: 2q^2+5q+2
        35: 2q^2+5q+2
        36: 4q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 2q^2+5q+2
        44: q^3+3q^2+3q+2
        45: 2q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: q^3+2q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 4q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q^2+3q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q^2+5q+2
        85: 4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^3+2q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       121: q^2+3q+2
       123: 2q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: q+2
       211: q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2
       235: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q+2
       250: 2
       251: 2
       252: q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: 2
       321: 1
       322: 1
       325: q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 2q+2
       354: q+1
       355: 2
       356: 1
       357: 2
       358: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       439: 1
       440: 1
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       465: 2
       467: 1
       469: 1
       473: 1
       474: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       525: 1
       528: 1
       553: 1
       555: 1
       557: 1
       559: 1
       583: 1
       585: 1
       587: 1
       623: 1
       625: 1
       627: 2
       635: 2
       637: 1
       639: 1
       649: 1
       650: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       745: 1
       747: 1
       777: 1
       821: 1
       823: 1
       841: 1
       878: 1
      1034: 1

1035:    0: 2q^2+5q+2
         1: 2q^2+5q+2
         2: 2q^2+5q+2
         3: 2q^2+5q+2
         4: q^3+3q^2+3q+2
         5: 2q^2+5q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 2q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+5q+2
        11: 2q^2+5q+2
        12: q^3+3q^2+3q+2
        13: 2q^2+5q+2
        14: q^3+3q^2+3q+2
        15: 2q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 2q^2+5q+2
        26: 2q^2+5q+2
        27: 2q^2+5q+2
        28: 4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: 2q^2+5q+2
        35: 2q^2+5q+2
        36: 4q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 2q^2+5q+2
        44: q^3+3q^2+3q+2
        45: 2q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: q^3+2q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 4q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q^2+3q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q^2+5q+2
        85: 4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^3+2q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       122: q^2+3q+2
       124: 2q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 4q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: q+2
       212: q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2
       235: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q+2
       250: 2
       251: 2
       252: q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: 2
       321: 1
       322: 1
       326: q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 2q+2
       354: q+1
       355: 2
       356: 1
       357: 2
       358: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       439: 1
       440: 1
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       466: 2
       468: 1
       470: 1
       473: 1
       474: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       526: 1
       527: 1
       554: 1
       556: 1
       558: 1
       560: 1
       584: 1
       586: 1
       588: 1
       624: 1
       626: 1
       628: 2
       636: 2
       638: 1
       640: 1
       649: 1
       650: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       746: 1
       748: 1
       778: 1
       822: 1
       824: 1
       842: 1
       878: 1
      1035: 1

1036:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: q+1
        37: 1
        39: 1
        41: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        64: 1
        66: 1
        69: q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: q+1
        87: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: q+1
       135: q+1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       205: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       311: 1
       313: 1
       315: 1
       336: 1
       338: 1
       340: 1
       342: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       451: 1
       455: 1
       463: 1
       467: 1
       485: 1
       487: 1
       489: 1
       491: 1
       500: 1
       501: 1
       514: 1
       515: 1
       516: 1
       517: 1
       597: 1
       623: 1
       629: 1
       633: 1
       658: 1
       660: 1
       662: 1
       664: 1
       680: 1
       685: 1
       779: 1
       819: 1
       833: 1
       874: 1
      1036: 1

1037:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: 1
        33: 1
        35: q+1
        36: q+1
        38: 1
        40: 1
        42: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        65: 1
        67: 1
        69: q+1
        72: q+1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: q+1
        87: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: q+1
       135: q+1
       136: 1
       138: 1
       142: 1
       144: q+1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       206: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: q+1
       225: 1
       228: 1
       230: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       336: 1
       339: 1
       341: 1
       343: 1
       350: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       452: 1
       456: 1
       464: 1
       468: 1
       486: 1
       488: 1
       490: 1
       491: 1
       500: 1
       501: 1
       514: 1
       515: 1
       516: 1
       517: 1
       598: 1
       624: 1
       630: 1
       634: 1
       659: 1
       661: 1
       663: 1
       664: 1
       680: 1
       685: 1
       780: 1
       820: 1
       834: 1
       874: 1
      1037: 1

1038:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: q^2+4q+2
        26: 2q^2+4q+2
        27: q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: 3q+2
        35: q^2+4q+2
        36: 3q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: q^2+4q+2
        56: 2q^2+4q+2
        57: q^2+4q+2
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: q+2
        64: 2q+2
        66: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: 3q+2
        73: q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+2
       113: q+2
       115: 2q+2
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+2
       123: q+2
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 3q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: q+1
       145: 2q+2
       146: 3q+2
       147: 3q+2
       148: q+2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: q+2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+2
       207: 2
       209: q+2
       211: 2q+2
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: q+2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: q+2
       315: 1
       317: 2
       321: 1
       322: 1
       325: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: 2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       413: 1
       417: 1
       423: 1
       425: 1
       427: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: 2
       467: 1
       469: 1
       473: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       514: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       585: 1
       597: 1
       599: 1
       601: 2
       623: 1
       625: 1
       629: 1
       631: 1
       632: 1
       633: 2
       639: 1
       665: 1
       681: 1
       682: 1
       683: 1
       685: 1
       749: 1
       751: 1
       781: 1
       821: 1
       833: 1
       835: 1
       875: 1
      1038: 1

1039:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: q^2+4q+2
        26: 2q^2+4q+2
        27: q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: q+2
        32: 2q+2
        33: q+2
        34: 3q+2
        35: q^2+4q+2
        36: 3q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: q^2+4q+2
        56: 2q^2+4q+2
        57: q^2+4q+2
        58: 1
        59: 1
        60: q+1
        61: q+1
        63: q+2
        65: 2q+2
        67: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: 3q+2
        73: q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q+2
        81: q+2
        82: q+2
        83: 2q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: 1
       105: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: q+2
       114: q+2
       116: 2q+2
       117: 1
       118: 1
       119: q+1
       120: q+1
       122: q+2
       124: q+2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 3q+2
       136: q+2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: q+1
       145: 2q+2
       146: 3q+2
       147: 3q+2
       148: q+2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: q+2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: q+2
       208: 2
       210: q+2
       212: 2q+2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: q+2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: q+2
       316: 1
       318: 2
       321: 1
       322: 1
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: 2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       414: 1
       418: 1
       424: 1
       426: 1
       428: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: 2
       468: 1
       470: 1
       473: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       514: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       586: 1
       598: 1
       600: 1
       602: 2
       624: 1
       626: 1
       630: 1
       631: 1
       632: 1
       634: 2
       640: 1
       665: 1
       681: 1
       682: 1
       683: 1
       685: 1
       750: 1
       752: 1
       782: 1
       822: 1
       834: 1
       836: 1
       875: 1
      1039: 1

1040:    0: q^2+5q+2
         1: q^3+3q^2+5q+2
         2: q^2+5q+2
         3: q^3+3q^2+5q+2
         4: q^2+5q+2
         5: q^2+5q+2
         6: q^3+3q^2+5q+2
         7: q^2+5q+2
         8: q^2+5q+2
         9: q^3+q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: q^2+5q+2
        16: 3q+2
        17: 3q+2
        18: 2q+1
        19: q^2+5q+2
        20: q^3+3q^2+5q+2
        21: q^2+5q+2
        22: 4q+2
        23: 2q^2+4q+2
        24: 4q+2
        25: q^2+5q+2
        26: q^3+3q^2+5q+2
        27: q^2+5q+2
        28: q+2
        29: 3q+2
        30: q^2+5q+2
        31: 2q+2
        32: 4q+2
        33: 2q+2
        34: 3q+2
        35: q^2+5q+2
        36: 3q+2
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q+1
        42: 2q+1
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: 4q+2
        53: 2q^2+4q+2
        54: 4q+2
        55: q^2+5q+2
        56: q^3+3q^2+5q+2
        57: q^2+5q+2
        58: 1
        59: 1
        60: q+2
        62: q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: 3q+2
        73: 2q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+2
        81: 2q+2
        82: 2q+2
        83: 4q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+5q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: 2q+1
        94: q+2
        95: q+2
        96: q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: 4q+2
       101: 2q^2+4q+2
       102: 4q+2
       103: 1
       104: 1
       107: q+2
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 1
       118: 1
       119: q+2
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 2q+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: q+2
       143: 2
       144: q+1
       145: q+2
       146: 3q+2
       147: 3q+2
       148: 2q+2
       149: 2q+2
       150: 4q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2
       158: 2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 3q+2
       164: 3q+2
       165: 2q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       170: 1
       173: 1
       174: 1
       183: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: q+2
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       232: q+2
       233: q+1
       234: 3q+2
       235: 2q+2
       236: 1
       243: 2
       244: 2
       245: q+2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       253: 2
       254: 2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       313: q+1
       314: q+1
       319: 2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: q+2
       366: 1
       367: 2
       368: 1
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       385: 1
       386: 1
       393: 1
       394: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 1
       429: 1
       443: 2
       447: 1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: q+2
       508: 1
       512: 1
       514: 1
       557: 1
       560: 1
       565: 1
       566: 1
       573: 1
       574: 1
       589: 1
       593: 1
       615: 2
       619: 1
       631: 1
       632: 1
       641: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       689: 1
       765: 1
       766: 1
       785: 1
       825: 1
       829: 1
       875: 1
       880: 1
      1040: 1

1041:    0: q^2+5q+2
         1: q^3+3q^2+5q+2
         2: q^2+5q+2
         3: q^3+3q^2+5q+2
         4: q^2+5q+2
         5: q^2+5q+2
         6: q^3+3q^2+5q+2
         7: q^2+5q+2
         8: q^2+5q+2
         9: q^3+q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: q^2+5q+2
        16: 3q+2
        17: 3q+2
        18: 2q+1
        19: q^2+5q+2
        20: q^3+3q^2+5q+2
        21: q^2+5q+2
        22: 4q+2
        23: 2q^2+4q+2
        24: 4q+2
        25: q^2+5q+2
        26: q^3+3q^2+5q+2
        27: q^2+5q+2
        28: q+2
        29: 3q+2
        30: q^2+5q+2
        31: 2q+2
        32: 4q+2
        33: 2q+2
        34: 3q+2
        35: q^2+5q+2
        36: 3q+2
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q+1
        42: 2q+1
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: 2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: 4q+2
        53: 2q^2+4q+2
        54: 4q+2
        55: q^2+5q+2
        56: q^3+3q^2+5q+2
        57: q^2+5q+2
        58: 1
        59: 1
        61: q+2
        62: q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: 3q+2
        73: 2q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+2
        81: 2q+2
        82: 2q+2
        83: 4q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+5q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: 2q+1
        94: q+2
        95: q+2
        96: q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: 4q+2
       101: 2q^2+4q+2
       102: 4q+2
       105: 1
       106: 1
       108: q+2
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 1
       118: 1
       120: q+2
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2
       126: 1
       133: q+2
       134: q+1
       135: 3q+2
       136: 2q+2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: q+2
       143: 2
       144: q+1
       145: q+2
       146: 3q+2
       147: 3q+2
       148: 2q+2
       149: 2q+2
       150: 4q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2
       158: 2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: 3q+2
       164: 3q+2
       165: 2q+1
       166: q+2
       167: q+2
       168: q+1
       171: 1
       172: 1
       175: 1
       176: 1
       184: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: q+2
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: 1
       232: q+2
       233: q+1
       234: 3q+2
       235: 2q+2
       236: 1
       243: 2
       244: 2
       245: q+2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       253: 2
       254: 2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       313: q+1
       314: q+1
       320: 2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       348: 1
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: q+2
       366: 1
       367: 2
       368: 1
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       387: 1
       388: 1
       395: 1
       396: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 1
       430: 1
       444: 2
       448: 1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: q+2
       508: 1
       512: 1
       514: 1
       558: 1
       559: 1
       567: 1
       568: 1
       575: 1
       576: 1
       590: 1
       594: 1
       616: 2
       620: 1
       631: 1
       632: 1
       642: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       689: 1
       767: 1
       768: 1
       786: 1
       826: 1
       830: 1
       875: 1
       880: 1
      1041: 1

1042:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+3q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+3q+1
        28: 4q+2
        29: 2q^2+4q+2
        30: q^2+2q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q^2+4q+2
        35: q^2+2q+1
        36: 4q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 4q+2
        50: 4q+2
        51: q^3+2q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: q^3+3q^2+3q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q^2+2q+1
        71: 4q+2
        72: 4q+2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: q^2+2q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: 2q^2+4q+2
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: q^3+2q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: q^2+2q+1
       103: q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 2q+2
       115: q+1
       121: q+1
       123: q+1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 2
       141: q+1
       142: 2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: q^2+2q+1
       147: 4q+2
       148: 2q+2
       149: 2q+2
       150: q+1
       151: 2q+2
       153: 2q+2
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2
       167: 2
       168: q+1
       169: q+1
       172: q+1
       177: 1
       179: 2
       181: 2
       187: q+1
       189: q+1
       195: 1
       196: 1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 2q+2
       207: q+1
       209: 2q+2
       211: q+1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q+1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       271: q+1
       273: q+1
       281: 1
       287: 1
       289: 1
       291: 1
       297: q+1
       311: 2
       313: q+1
       315: 1
       317: 2
       321: 1
       322: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       397: 1
       399: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       451: 1
       455: 1
       459: q+1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       494: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       561: 1
       563: 1
       587: 1
       597: 1
       599: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       666: 1
       668: 1
       670: 1
       673: 1
       683: 1
       684: 1
       685: 1
       688: 1
       783: 1
       823: 1
       833: 1
       835: 1
       837: 1
       876: 1
      1042: 1

1043:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 4q+2
        17: 4q+2
        18: q^3+2q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+3q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+3q+1
        28: 4q+2
        29: 2q^2+4q+2
        30: q^2+2q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q^2+4q+2
        35: q^2+2q+1
        36: 4q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 4q+2
        50: 4q+2
        51: q^3+2q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: q^3+3q^2+3q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q^2+2q+1
        71: 4q+2
        72: 4q+2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: 2q^2+4q+2
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: q^3+2q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: q^2+2q+1
       104: q+1
       105: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 2q+2
       116: q+1
       122: q+1
       124: q+1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 2
       141: q+1
       142: 2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: q^2+2q+1
       147: 4q+2
       148: 2q+2
       149: 2q+2
       150: q+1
       152: 2q+2
       154: 2q+2
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2
       167: 2
       168: q+1
       170: q+1
       171: q+1
       178: 1
       180: 2
       182: 2
       188: q+1
       190: q+1
       195: 1
       196: 1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       206: 2q+2
       208: q+1
       210: 2q+2
       212: q+1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q+1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       272: q+1
       274: q+1
       282: 1
       288: 1
       290: 1
       292: 1
       298: q+1
       312: 2
       314: q+1
       316: 1
       318: 2
       321: 1
       322: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       398: 1
       400: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       452: 1
       456: 1
       460: q+1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       494: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       562: 1
       564: 1
       588: 1
       598: 1
       600: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       667: 1
       669: 1
       671: 1
       673: 1
       683: 1
       684: 1
       685: 1
       688: 1
       784: 1
       824: 1
       834: 1
       836: 1
       838: 1
       876: 1
      1043: 1

1044:    0: q^2+q+2
         1: q^3+q^2+q+2
         2: q^2+q+2
         3: q^3+q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^3+q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: q^2+q+2
        20: q^3+q^2+q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: q^2+q+2
        26: q^3+q^2+q+2
        27: q^2+q+2
        28: 2
        29: q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q^2+q+2
        36: q^2+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: q^2+2
        50: q^2+2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q^2+q+2
        56: q^3+q^2+q+2
        57: q^2+q+2
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: q^2+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q^2+2
        86: q+2
        87: q^2+q+2
        88: 2
        89: 2
        90: q+1
        91: q^2+2
        92: q^2+2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2
        98: q^2+2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: q^2+2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: q^2+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2
       164: q^2+2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 2
       233: 1
       234: q^2+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       385: 1
       387: 1
       401: 1
       402: 1
       421: 1
       431: 1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 1
       473: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       557: 1
       558: 1
       591: 1
       595: 1
       621: 1
       631: 1
       643: 1
       665: 1
       681: 1
       682: 1
       683: 1
       685: 1
       787: 1
       827: 1
       831: 1
       875: 1
      1044: 1

1045:    0: q^2+q+2
         1: q^3+q^2+q+2
         2: q^2+q+2
         3: q^3+q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^3+q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+2
        17: q^2+2
        18: q+1
        19: q^2+q+2
        20: q^3+q^2+q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: q^2+q+2
        26: q^3+q^2+q+2
        27: q^2+q+2
        28: 2
        29: q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q^2+q+2
        36: q^2+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+2
        47: q^2+2
        48: q+1
        49: q^2+2
        50: q^2+2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q^2+q+2
        56: q^3+q^2+q+2
        57: q^2+q+2
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: q^2+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q^2+2
        86: q+2
        87: q^2+q+2
        88: 2
        89: 2
        90: q+1
        91: q^2+2
        92: q^2+2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q^2+2
        98: q^2+2
        99: q+1
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: q^2+2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: q^2+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2
       164: q^2+2
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 2
       233: 1
       234: q^2+2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       386: 1
       388: 1
       403: 1
       404: 1
       422: 1
       432: 1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       559: 1
       560: 1
       592: 1
       596: 1
       622: 1
       632: 1
       644: 1
       665: 1
       681: 1
       682: 1
       683: 1
       685: 1
       788: 1
       828: 1
       832: 1
       875: 1
      1045: 1

1046:    0: 8q+2
         1: 8q+2
         2: q^3+3q^2+3q+1
         3: 8q+2
         4: 3q^2+5q+2
         5: 8q+2
         6: 3q^2+5q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 8q+2
        11: 8q+2
        12: 3q^2+5q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 8q+2
        17: 8q+2
        18: q^2+2q+1
        19: 5q+2
        20: 5q+2
        21: q^2+2q+1
        22: 8q+2
        23: 8q+2
        24: q^3+3q^2+3q+1
        25: 8q+2
        26: 8q+2
        27: q^3+3q^2+3q+1
        28: 8q+2
        29: 5q+2
        30: q+1
        31: 8q+2
        32: 2q+1
        33: 8q+2
        34: 8q+2
        35: 2q+1
        36: 8q+2
        37: 4q+2
        38: 4q
        39: 4q+2
        40: 4q
        41: q^2+2q+1
        42: q^3+2q^2+q
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 5q+2
        50: 5q+2
        51: q^2+2q+1
        52: 5q+2
        53: 5q+2
        54: q^2+2q+1
        55: 5q+2
        56: 5q+2
        57: q^2+2q+1
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: 4q+2
        63: 4q
        64: q+1
        65: q
        66: 4q+2
        67: 4q
        69: q+1
        70: q+1
        71: 5q+2
        72: 2q+2
        73: 2q+2
        74: q+2
        75: 2q
        76: q+2
        77: 2q
        78: q+1
        79: q^2+q
        80: 2q+1
        81: 2q+1
        82: 5q+2
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 5q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 5q+2
        95: 5q+2
        96: q^2+2q+1
        97: 5q+2
        98: 5q+2
        99: q^2+2q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: 2q+1
       104: 2q
       105: 2q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       114: 2q
       115: 1
       116: q
       121: q+1
       122: q
       123: q+1
       124: q
       126: q+1
       127: q+2
       128: 2q
       129: q+2
       130: 2q
       131: q+1
       132: q^2+q
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 5q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: 2q+1
       144: q+1
       145: 5q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       151: q+2
       152: 2q
       153: q+2
       154: 2q
       155: q+1
       156: q^2+q
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: 1
       172: 1
       177: 1
       178: q
       179: q+2
       180: 2q
       181: 2
       187: 1
       189: 1
       190: q
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: q+1
       208: q
       209: q+2
       210: 2q
       211: 1
       212: q
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+2
       238: 2q
       239: q+2
       240: 2q
       241: q+1
       242: q^2+q
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 4
       248: 4
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       287: 1
       288: q
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       316: q
       317: q+2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 1
       326: q
       334: 1
       335: 1
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 4
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 4
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       423: 1
       427: 2
       428: 2
       433: 1
       441: 1
       443: 2
       444: 2
       445: 2
       446: 2
       451: 1
       459: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: 1
       470: q
       475: 1
       477: 2
       479: 4
       493: 1
       494: 1
       496: 1
       498: 1
       499: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       546: 1
       547: 1
       548: 1
       561: 1
       562: 1
       563: 1
       564: 1
       569: 1
       570: 1
       573: 2
       575: 2
       577: 2
       578: 2
       609: 1
       625: 1
       645: 1
       653: 1
       655: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       694: 1
       697: 1
       701: 1
       843: 1
       851: 1
       857: 1
       869: 1
       873: 1
      1046: 1

1047:    0: 8q+2
         1: 8q+2
         2: q^3+3q^2+3q+1
         3: 8q+2
         4: 3q^2+5q+2
         5: 8q+2
         6: 3q^2+5q+2
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 8q+2
        11: 8q+2
        12: 3q^2+5q+2
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 8q+2
        17: 8q+2
        18: q^2+2q+1
        19: 5q+2
        20: 5q+2
        21: q^2+2q+1
        22: 8q+2
        23: 8q+2
        24: q^3+3q^2+3q+1
        25: 8q+2
        26: 8q+2
        27: q^3+3q^2+3q+1
        28: 8q+2
        29: 5q+2
        30: q+1
        31: 8q+2
        32: 2q+1
        33: 8q+2
        34: 8q+2
        35: 2q+1
        36: 8q+2
        37: 4q
        38: 4q+2
        39: 4q
        40: 4q+2
        41: q^3+2q^2+q
        42: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 5q+2
        50: 5q+2
        51: q^2+2q+1
        52: 5q+2
        53: 5q+2
        54: q^2+2q+1
        55: 5q+2
        56: 5q+2
        57: q^2+2q+1
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: 4q
        63: 4q+2
        64: q
        65: q+1
        66: 4q
        67: 4q+2
        69: q+1
        70: q+1
        71: 5q+2
        72: 2q+2
        73: 2q+2
        74: 2q
        75: q+2
        76: 2q
        77: q+2
        78: q^2+q
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 5q+2
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 5q+2
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 5q+2
        95: 5q+2
        96: q^2+2q+1
        97: 5q+2
        98: 5q+2
        99: q^2+2q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: 2q
       104: 2q+1
       105: 2q+1
       106: 2q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       113: 2q
       114: q+2
       115: q
       116: 1
       121: q
       122: q+1
       123: q
       124: q+1
       126: q+1
       127: 2q
       128: q+2
       129: 2q
       130: q+2
       131: q^2+q
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 5q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: 2q+1
       144: q+1
       145: 5q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       151: 2q
       152: q+2
       153: 2q
       154: q+2
       155: q^2+q
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       170: 1
       171: 1
       177: q
       178: 1
       179: 2q
       180: q+2
       182: 2
       188: 1
       189: q
       190: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       207: q
       208: q+1
       209: 2q
       210: q+2
       211: q
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q
       238: q+2
       239: 2q
       240: q+2
       241: q^2+q
       242: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 4
       248: 4
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       287: q
       288: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       315: q
       316: 1
       317: 2q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       325: q
       326: 1
       334: 1
       335: 1
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 4
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 4
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       424: 1
       427: 2
       428: 2
       434: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       452: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: q
       470: 1
       476: 1
       478: 2
       480: 4
       493: 1
       494: 1
       496: 1
       498: 1
       499: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       546: 1
       547: 1
       548: 1
       561: 1
       562: 1
       563: 1
       564: 1
       571: 1
       572: 1
       574: 2
       576: 2
       580: 2
       581: 2
       610: 1
       626: 1
       646: 1
       654: 1
       656: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: 1
       688: 1
       690: 1
       691: 1
       696: 1
       698: 1
       699: 1
       700: 1
       844: 1
       852: 1
       858: 1
       869: 1
       873: 1
      1047: 1

1048:    0: q^3+7q^2+12q+2
         1: 10q^2+12q+2
         2: q^3+7q^2+12q+2
         3: 10q^2+12q+2
         4: 4q^3+7q^2+7q+2
         5: q^3+7q^2+12q+2
         6: 2q^4+7q^3+10q^2+7q+2
         7: 4q^3+7q^2+7q+2
         8: q^3+7q^2+12q+2
         9: q^4+3q^3+4q^2+3q+1
        10: 3q^2+11q+2
        11: 3q^2+11q+2
        12: 3q^3+6q^2+6q+2
        13: q^3+7q^2+12q+2
        14: 4q^3+7q^2+7q+2
        15: q^3+7q^2+12q+2
        16: 3q^2+11q+2
        17: 3q^2+11q+2
        18: 2q^3+3q^2+3q+1
        19: 2q^2+7q+2
        20: 5q^2+7q+2
        21: 2q^2+7q+2
        22: q^3+7q^2+12q+2
        23: 10q^2+12q+2
        24: q^3+7q^2+12q+2
        25: q^3+7q^2+12q+2
        26: 10q^2+12q+2
        27: q^3+7q^2+12q+2
        28: 10q+2
        29: q^2+6q+2
        30: 2q^2+7q+2
        31: 3q^2+11q+2
        32: q^3+7q^2+12q+2
        33: 3q^2+11q+2
        34: 3q^2+11q+2
        35: q^3+7q^2+12q+2
        36: 3q^2+11q+2
        37: 4q^2+8q+2
        38: q^3+3q^2+4q
        39: 6q^2+8q+2
        40: 4q^2+4q
        41: 4q^2+8q+2
        42: q^3+3q^2+4q
        43: 3q^2+11q+2
        44: 3q^3+6q^2+6q+2
        45: 3q^2+11q+2
        46: 3q^2+11q+2
        47: 3q^2+11q+2
        48: 2q^3+3q^2+3q+1
        49: 6q+2
        50: q^2+6q+2
        51: q^2+3q+1
        52: 2q^2+7q+2
        53: 5q^2+7q+2
        54: 2q^2+7q+2
        55: 2q^2+7q+2
        56: 5q^2+7q+2
        57: 2q^2+7q+2
        58: 5q+1
        59: 5q+1
        60: 5q+1
        61: 5q+1
        62: 2q^2+7q+2
        63: q^2+4q
        64: 4q^2+8q+2
        65: q^3+3q^2+4q
        66: 2q^2+7q+2
        67: q^2+4q
        68: 10q+2
        69: 2q+1
        70: q^2+6q+2
        71: 5q+2
        72: 3q+2
        73: 3q+2
        74: 3q+2
        76: q^2+3q+2
        78: 3q+2
        80: 3q^2+11q+2
        81: 3q^2+11q+2
        82: q^2+6q+2
        83: 2q^2+7q+2
        84: 3q^2+11q+2
        85: 3q^2+11q+2
        86: q^2+6q+2
        87: 2q^2+7q+2
        88: 6q+2
        89: 6q+2
        90: q^3+2q^2+2q+1
        91: 6q+2
        92: q^2+6q+2
        93: q^2+3q+1
        94: 6q+2
        95: q^2+6q+2
        96: q^2+3q+1
        97: 6q+2
        98: q^2+6q+2
        99: q^2+3q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: 3q+1
       104: 2q
       105: 2q
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       113: 2q+2
       115: 3q+2
       117: 5q+1
       118: 5q+1
       119: 5q+1
       120: 5q+1
       121: 2q^2+7q+2
       122: q^2+4q
       123: 2q^2+7q+2
       124: q^2+4q
       125: 6q+2
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       133: 5q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 6q+2
       138: 2q+1
       139: 5q+2
       140: 3q+2
       141: q^2+6q+2
       142: 3q+2
       143: 6q+2
       144: 2q+1
       145: 5q+2
       146: q^2+6q+2
       147: 3q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       151: 3q+2
       153: q^2+3q+2
       155: 3q+2
       157: q+2
       158: q+2
       159: q+1
       160: 6q+2
       161: q^2+6q+2
       162: q^2+3q+1
       163: 6q+2
       164: q^2+6q+2
       165: q^2+3q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: 1
       172: 1
       173: 3q+1
       174: 2q
       175: 2q
       176: 3q+1
       177: 1
       179: q+2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       189: 2q+2
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       207: 4q+2
       208: 2q
       209: 2q+2
       211: 3q+2
       213: q+2
       215: q+2
       217: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 5q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 5q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       237: q+2
       239: q+2
       241: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: 2q+1
       276: q
       277: q
       278: 2q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: q+2
       315: 1
       317: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: 2q+2
       333: 1
       334: 1
       335: 1
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       360: q+2
       362: q+2
       364: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       413: 1
       417: 1
       423: 1
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       465: q+2
       467: 1
       469: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: 2
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       537: 1
       539: 1
       541: 1
       543: 1
       553: 1
       555: 1
       557: 1
       559: 1
       565: 1
       568: 1
       569: 1
       570: 1
       585: 1
       605: 1
       609: 1
       623: 1
       625: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       675: 1
       676: 1
       681: 1
       682: 1
       686: 1
       687: 1
       688: 1
       757: 1
       758: 1
       761: 1
       762: 1
       797: 1
       821: 1
       849: 1
       851: 1
       877: 1
       878: 1
      1048: 1

1049:    0: q^3+7q^2+12q+2
         1: 10q^2+12q+2
         2: q^3+7q^2+12q+2
         3: 10q^2+12q+2
         4: 4q^3+7q^2+7q+2
         5: q^3+7q^2+12q+2
         6: 2q^4+7q^3+10q^2+7q+2
         7: 4q^3+7q^2+7q+2
         8: q^3+7q^2+12q+2
         9: q^4+3q^3+4q^2+3q+1
        10: 3q^2+11q+2
        11: 3q^2+11q+2
        12: 3q^3+6q^2+6q+2
        13: q^3+7q^2+12q+2
        14: 4q^3+7q^2+7q+2
        15: q^3+7q^2+12q+2
        16: 3q^2+11q+2
        17: 3q^2+11q+2
        18: 2q^3+3q^2+3q+1
        19: 2q^2+7q+2
        20: 5q^2+7q+2
        21: 2q^2+7q+2
        22: q^3+7q^2+12q+2
        23: 10q^2+12q+2
        24: q^3+7q^2+12q+2
        25: q^3+7q^2+12q+2
        26: 10q^2+12q+2
        27: q^3+7q^2+12q+2
        28: 10q+2
        29: q^2+6q+2
        30: 2q^2+7q+2
        31: 3q^2+11q+2
        32: q^3+7q^2+12q+2
        33: 3q^2+11q+2
        34: 3q^2+11q+2
        35: q^3+7q^2+12q+2
        36: 3q^2+11q+2
        37: q^3+3q^2+4q
        38: 4q^2+8q+2
        39: 4q^2+4q
        40: 6q^2+8q+2
        41: q^3+3q^2+4q
        42: 4q^2+8q+2
        43: 3q^2+11q+2
        44: 3q^3+6q^2+6q+2
        45: 3q^2+11q+2
        46: 3q^2+11q+2
        47: 3q^2+11q+2
        48: 2q^3+3q^2+3q+1
        49: 6q+2
        50: q^2+6q+2
        51: q^2+3q+1
        52: 2q^2+7q+2
        53: 5q^2+7q+2
        54: 2q^2+7q+2
        55: 2q^2+7q+2
        56: 5q^2+7q+2
        57: 2q^2+7q+2
        58: 5q+1
        59: 5q+1
        60: 5q+1
        61: 5q+1
        62: q^2+4q
        63: 2q^2+7q+2
        64: q^3+3q^2+4q
        65: 4q^2+8q+2
        66: q^2+4q
        67: 2q^2+7q+2
        68: 10q+2
        69: 2q+1
        70: q^2+6q+2
        71: 5q+2
        72: 3q+2
        73: 3q+2
        75: 3q+2
        77: q^2+3q+2
        79: 3q+2
        80: 3q^2+11q+2
        81: 3q^2+11q+2
        82: q^2+6q+2
        83: 2q^2+7q+2
        84: 3q^2+11q+2
        85: 3q^2+11q+2
        86: q^2+6q+2
        87: 2q^2+7q+2
        88: 6q+2
        89: 6q+2
        90: q^3+2q^2+2q+1
        91: 6q+2
        92: q^2+6q+2
        93: q^2+3q+1
        94: 6q+2
        95: q^2+6q+2
        96: q^2+3q+1
        97: 6q+2
        98: q^2+6q+2
        99: q^2+3q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: 2q
       104: 3q+1
       105: 3q+1
       106: 2q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+2
       114: 2q+2
       116: 3q+2
       117: 5q+1
       118: 5q+1
       119: 5q+1
       120: 5q+1
       121: q^2+4q
       122: 2q^2+7q+2
       123: q^2+4q
       124: 2q^2+7q+2
       125: 6q+2
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       133: 5q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 6q+2
       138: 2q+1
       139: 5q+2
       140: 3q+2
       141: q^2+6q+2
       142: 3q+2
       143: 6q+2
       144: 2q+1
       145: 5q+2
       146: q^2+6q+2
       147: 3q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       152: 3q+2
       154: q^2+3q+2
       156: 3q+2
       157: q+2
       158: q+2
       159: q+1
       160: 6q+2
       161: q^2+6q+2
       162: q^2+3q+1
       163: 6q+2
       164: q^2+6q+2
       165: q^2+3q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       170: 1
       171: 1
       173: 2q
       174: 3q+1
       175: 3q+1
       176: 2q
       178: 1
       180: q+2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: q+2
       190: 2q+2
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+2
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: q+2
       207: 2q
       208: 4q+2
       210: 2q+2
       212: 3q+2
       214: q+2
       216: q+2
       218: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 5q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 5q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       238: q+2
       240: q+2
       242: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       275: q
       276: 2q+1
       277: 2q+1
       278: q
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       314: q+2
       316: 1
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       326: 2q+2
       333: 1
       334: 1
       335: 1
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       361: q+2
       363: q+2
       365: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       414: 1
       418: 1
       424: 1
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       466: q+2
       468: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: 2
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       538: 1
       540: 1
       542: 1
       544: 1
       554: 1
       556: 1
       558: 1
       560: 1
       566: 1
       567: 1
       571: 1
       572: 1
       586: 1
       606: 1
       610: 1
       624: 1
       626: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       675: 1
       676: 1
       681: 1
       682: 1
       686: 1
       687: 1
       688: 1
       759: 1
       760: 1
       763: 1
       764: 1
       798: 1
       822: 1
       850: 1
       852: 1
       877: 1
       878: 1
      1049: 1

1050:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q^3+q^2+q+2
         5: 2q+2
         6: 2q^3+q^2+q+2
         7: q^4+q^3+q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: 2q+2
        11: 2q+2
        12: 2q^3+q^2+q+2
        13: q+1
        14: q^3+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^4+q^3+q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: q+2
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q+1
        44: q^3+1
        45: q+1
        46: q+1
        47: q+1
        48: q^3+1
        49: q+2
        50: q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       126: 1
       127: q+2
       129: q+2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       140: 2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: q+1
       217: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: q+1
       331: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: 1
       415: 1
       417: 1
       423: 1
       433: 1
       435: 1
       441: 1
       451: 1
       455: 1
       459: 1
       467: 1
       469: 1
       475: 1
       477: 2
       493: 1
       494: 1
       498: 1
       499: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       569: 1
       570: 1
       587: 1
       605: 1
       609: 1
       611: 1
       623: 1
       625: 1
       627: 1
       637: 1
       645: 1
       651: 1
       653: 1
       687: 1
       688: 1
       799: 1
       823: 1
       849: 1
       851: 1
       853: 1
      1050: 1

1051:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q^3+q^2+q+2
         5: 2q+2
         6: 2q^3+q^2+q+2
         7: q^4+q^3+q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: 2q+2
        11: 2q+2
        12: 2q^3+q^2+q+2
        13: q+1
        14: q^3+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^4+q^3+q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: q+2
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q+1
        44: q^3+1
        45: q+1
        46: q+1
        47: q+1
        48: q^3+1
        49: q+2
        50: q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        90: q^3+1
        91: 1
        92: q+1
        93: 1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       126: 1
       128: q+2
       130: q+2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       140: 2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: q+1
       218: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: q+1
       332: 1
       334: 1
       335: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: 1
       416: 1
       418: 1
       424: 1
       434: 1
       436: 1
       442: 1
       452: 1
       456: 1
       460: 1
       468: 1
       470: 1
       476: 1
       478: 2
       493: 1
       494: 1
       498: 1
       499: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       571: 1
       572: 1
       588: 1
       606: 1
       610: 1
       612: 1
       624: 1
       626: 1
       628: 1
       638: 1
       646: 1
       652: 1
       654: 1
       687: 1
       688: 1
       800: 1
       824: 1
       850: 1
       852: 1
       854: 1
      1051: 1

1052:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       107: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       174: 1
       183: 1
       191: 1
       192: 1
       193: 1
       199: 2
       201: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: 1
       276: 1
       283: 1
       293: 1
       299: 1
       307: 1
       319: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       419: 1
       429: 1
       437: 1
       447: 1
       453: 1
       471: 1
       481: 1
       492: 1
       493: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       589: 1
       603: 1
       619: 1
       641: 1
       647: 1
       675: 1
       681: 1
       686: 1
       687: 1
       801: 1
       825: 1
       845: 1
       877: 1
      1052: 1

1053:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        72: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       106: 1
       108: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       135: 1
       137: 2
       138: 1
       139: 1
       140: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       175: 1
       176: 1
       184: 1
       191: 1
       192: 1
       194: 1
       200: 2
       202: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       226: 1
       227: 1
       228: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       277: 1
       278: 1
       284: 1
       294: 1
       300: 1
       308: 1
       320: 1
       333: 1
       334: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       420: 1
       430: 1
       438: 1
       448: 1
       454: 1
       472: 1
       481: 1
       492: 1
       493: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       590: 1
       604: 1
       620: 1
       642: 1
       648: 1
       675: 1
       681: 1
       686: 1
       687: 1
       802: 1
       826: 1
       846: 1
       877: 1
      1053: 1

1054:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: 2q^2+6q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: 6q+2
        14: 2q^2+4q+2
        15: 6q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+4q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: 2q^2+6q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: q^2+5q+2
        30: 4q+2
        31: 2q^2+8q+2
        32: 6q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: 6q+2
        36: 6q+2
        37: q^2+4q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: q^2+4q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+4q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+4q+2
        58: 4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: q^2+4q+1
        63: q^2+4q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q+2
        71: 3q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 4q+2
        82: q^2+5q+2
        83: 4q+2
        84: 6q+2
        85: 4q+2
        86: q^2+5q+2
        87: 4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+4q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 3q+1
       122: 3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2
       134: 1
       135: q+2
       136: 2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: 2q+2
       141: 4q+2
       142: q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: 2q+2
       148: q+2
       149: q^2+5q+2
       150: 4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 3q+2
       167: 3q+2
       168: 2q+1
       169: 1
       171: 1
       173: q+1
       175: q+1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q+2
       193: q+1
       194: q+1
       195: q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: q+2
       230: 2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 3q+2
       244: 2q+2
       245: q+2
       246: 4q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       303: 2
       305: 1
       306: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       319: q+1
       320: q+1
       321: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: q+2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       374: q+2
       375: q+2
       376: q+1
       385: 1
       387: 1
       393: 1
       395: 1
       401: 1
       402: 1
       405: 1
       408: 1
       421: 1
       431: 1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 1
       444: 1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       509: 2
       510: 1
       511: q+2
       512: 1
       513: 2
       514: 1
       541: 1
       544: 1
       557: 1
       558: 1
       565: 1
       567: 1
       573: 1
       576: 1
       591: 1
       607: 1
       621: 1
       643: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       764: 1
       803: 1
       827: 1
       847: 1
       877: 1
       879: 1
      1054: 1

1055:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: 2q^2+6q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: 6q+2
        14: 2q^2+4q+2
        15: 6q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+4q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: 2q^2+6q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: q^2+5q+2
        30: 4q+2
        31: 2q^2+8q+2
        32: 6q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: 6q+2
        36: 6q+2
        37: q^2+4q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: q^2+4q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+4q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+4q+2
        58: 2q
        59: 4q+2
        60: 3q+1
        61: 3q+1
        62: q^2+4q+1
        63: q^2+4q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q+2
        71: 3q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 4q+2
        82: q^2+5q+2
        83: 4q+2
        84: 6q+2
        85: 4q+2
        86: q^2+5q+2
        87: 4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+4q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 3q+1
       122: 3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2
       134: 1
       135: q+2
       136: 2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: 2q+2
       141: 4q+2
       142: q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: 2q+2
       148: q+2
       149: q^2+5q+2
       150: 4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 3q+2
       167: 3q+2
       168: 2q+1
       170: 1
       172: 1
       174: q+1
       176: q+1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2q+2
       193: q+1
       194: q+1
       196: q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: q+2
       223: 1
       224: 2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: q+2
       230: 2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 3q+2
       244: 2q+2
       245: q+2
       246: 4q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       304: 2
       305: 1
       306: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       319: q+1
       320: q+1
       322: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: q+2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       374: q+2
       375: q+2
       376: q+1
       386: 1
       388: 1
       394: 1
       396: 1
       403: 1
       404: 1
       406: 1
       407: 1
       422: 1
       432: 1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 1
       444: 1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       509: 2
       510: 1
       511: q+2
       512: 1
       513: 2
       514: 1
       542: 1
       543: 1
       559: 1
       560: 1
       566: 1
       568: 1
       574: 1
       575: 1
       592: 1
       608: 1
       622: 1
       644: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       763: 1
       804: 1
       828: 1
       848: 1
       877: 1
       879: 1
      1055: 1

1056:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: 2q^2+6q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: 6q+2
        14: 2q^2+4q+2
        15: 6q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+4q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: 2q^2+6q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: q^2+5q+2
        30: 4q+2
        31: 2q^2+8q+2
        32: 6q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: 6q+2
        36: 6q+2
        37: q^2+4q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: q^2+4q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+4q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 4q+2
        61: 2q
        62: q^2+4q+1
        63: q^2+4q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q+2
        71: 3q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 4q+2
        82: q^2+5q+2
        83: 4q+2
        84: 6q+2
        85: 4q+2
        86: q^2+5q+2
        87: 4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+4q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 3q+1
       122: 3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2
       134: 1
       135: 2
       136: q+2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: q+2
       141: 4q+2
       142: 2q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: q+2
       148: 2q+2
       149: q^2+5q+2
       150: 4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 3q+2
       167: 3q+2
       168: 2q+1
       169: 1
       170: 1
       173: q+1
       174: q+1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: q+2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: 2
       233: 1
       234: 2
       235: q+2
       236: q+1
       243: 3q+2
       244: q+2
       245: 2q+2
       246: 4q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: q+1
       276: q+1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 2
       309: 1
       310: 1
       313: 1
       314: 1
       319: q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: q+2
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       374: q+2
       375: q+2
       376: q+1
       385: 1
       386: 1
       393: 1
       394: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       447: 1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: q+2
       514: 1
       541: 1
       542: 1
       557: 1
       560: 1
       565: 1
       566: 1
       573: 1
       574: 1
       593: 1
       603: 1
       619: 1
       641: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       763: 1
       805: 1
       829: 1
       845: 1
       878: 1
       879: 1
      1056: 1

1057:    0: 2q^2+8q+2
         1: 2q^2+8q+2
         2: 2q^2+6q+2
         3: 2q^2+8q+2
         4: q^3+4q^2+5q+2
         5: 2q^2+8q+2
         6: q^3+4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+8q+2
        11: 2q^2+8q+2
        12: q^3+4q^2+5q+2
        13: 6q+2
        14: 2q^2+4q+2
        15: 6q+2
        16: 6q+2
        17: 6q+2
        18: q^2+2q+1
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+4q+2
        22: 2q^2+8q+2
        23: 2q^2+8q+2
        24: 2q^2+6q+2
        25: 2q^2+8q+2
        26: 2q^2+8q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: q^2+5q+2
        30: 4q+2
        31: 2q^2+8q+2
        32: 6q+2
        33: 6q+2
        34: 2q^2+8q+2
        35: 6q+2
        36: 6q+2
        37: q^2+4q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: q^2+4q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: 2q+1
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+4q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 4q+2
        62: q^2+4q+1
        63: q^2+4q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q+2
        71: 3q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 4q+2
        82: q^2+5q+2
        83: 4q+2
        84: 6q+2
        85: 4q+2
        86: q^2+5q+2
        87: 4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q+1
        94: 3q+2
        95: 3q+2
        96: 2q+1
        97: 3q+2
        98: 3q+2
        99: 2q+1
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+4q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 3q+1
       122: 3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2
       134: 1
       135: 2
       136: q+2
       137: 4q+2
       138: q+1
       139: 3q+2
       140: q+2
       141: 4q+2
       142: 2q+2
       143: 4q+2
       144: q+1
       145: 3q+2
       146: 4q+2
       147: q+2
       148: 2q+2
       149: q^2+5q+2
       150: 4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 3q+2
       167: 3q+2
       168: 2q+1
       171: 1
       172: 1
       175: q+1
       176: q+1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: q+2
       225: 1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: 2
       233: 1
       234: 2
       235: q+2
       236: q+1
       243: 3q+2
       244: q+2
       245: 2q+2
       246: 4q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: q+1
       278: q+1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 2
       309: 1
       310: 1
       313: 1
       314: 1
       320: q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: q+2
       358: 1
       359: 2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       374: q+2
       375: q+2
       376: q+1
       387: 1
       388: 1
       395: 1
       396: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       448: 1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: q+2
       514: 1
       543: 1
       544: 1
       558: 1
       559: 1
       567: 1
       568: 1
       575: 1
       576: 1
       594: 1
       604: 1
       620: 1
       642: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       764: 1
       806: 1
       830: 1
       846: 1
       878: 1
       879: 1
      1057: 1

1058:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       109: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       175: 1
       185: 1
       191: 2
       195: 1
       199: 1
       200: 1
       203: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: 1
       277: 1
       285: 1
       295: 1
       303: 1
       309: 1
       321: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       421: 1
       431: 1
       439: 1
       449: 1
       457: 1
       473: 1
       482: 1
       492: 1
       494: 1
       497: 1
       499: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       595: 1
       607: 1
       621: 1
       643: 1
       649: 1
       676: 1
       682: 1
       686: 1
       688: 1
       807: 1
       831: 1
       847: 1
       878: 1
      1058: 1

1059:    0: 2
         1: 2
         2: 2
         3: 2
         4: q+1
         5: 2
         6: q+1
         7: q+1
         8: 2
         9: q+1
        10: 2
        11: 2
        12: q+1
        13: 2
        14: q+1
        15: 2
        16: 2
        17: 2
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2
        44: q+1
        45: 2
        46: 2
        47: 2
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 1
        71: 1
        73: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       106: 1
       110: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 1
       134: 1
       136: 1
       137: 2
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       150: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       174: 1
       176: 1
       186: 1
       192: 2
       196: 1
       199: 1
       200: 1
       204: 1
       207: 1
       208: 1
       219: 1
       220: 1
       221: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 1
       233: 1
       235: 1
       236: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       276: 1
       278: 1
       286: 1
       296: 1
       304: 1
       310: 1
       322: 1
       333: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       357: 1
       358: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       422: 1
       432: 1
       440: 1
       450: 1
       458: 1
       474: 1
       482: 1
       492: 1
       494: 1
       497: 1
       499: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       596: 1
       608: 1
       622: 1
       644: 1
       650: 1
       676: 1
       682: 1
       686: 1
       688: 1
       808: 1
       832: 1
       848: 1
       878: 1
      1059: 1

1060:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        30: 2q^2+3q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+q
        66: q^2+3q+1
        67: q
        69: 2q+1
        72: 2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        81: q^2+4q+1
        83: 2q^2+3q+1
        85: q^2+4q+1
        87: 2q^2+3q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       111: q+1
       115: q^2+2q+1
       123: q^2+3q+1
       124: q
       127: q+1
       129: q+1
       131: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       138: 2q+1
       140: 2q+1
       142: 2q+1
       144: 2q+1
       147: 2q+1
       148: 2q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       177: q+1
       181: 1
       187: q+1
       197: q+1
       205: q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       223: q+1
       225: q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       244: 2q+1
       245: 2q+1
       247: 2
       248: 2
       249: q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       281: q+1
       289: 1
       291: 1
       301: 1
       305: q+1
       311: 1
       313: q+1
       315: q+1
       323: q+1
       336: 1
       338: 2
       340: 2
       342: q+1
       348: q+1
       350: q+1
       351: 2
       356: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 2
       451: 1
       455: 1
       463: 2
       467: q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       485: 2
       487: 2
       489: q+1
       491: 1
       495: 1
       496: 2
       500: 1
       501: 2
       512: q+1
       514: q+1
       577: 1
       580: 1
       597: 1
       605: 1
       613: 1
       617: 2
       623: 1
       629: 1
       633: 2
       645: 1
       651: 1
       655: 1
       656: 1
       679: 1
       685: 1
       689: 1
       769: 1
       772: 1
       809: 1
       833: 1
       849: 1
       855: 1
       880: 1
      1060: 1

1061:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        30: 2q^2+3q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q
        67: q^2+3q+1
        69: 2q+1
        72: 2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        81: q^2+4q+1
        83: 2q^2+3q+1
        85: q^2+4q+1
        87: 2q^2+3q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       112: q+1
       116: q^2+2q+1
       123: q
       124: q^2+3q+1
       128: q+1
       130: q+1
       132: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       138: 2q+1
       140: 2q+1
       142: 2q+1
       144: 2q+1
       147: 2q+1
       148: 2q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       178: q+1
       182: 1
       188: q+1
       198: q+1
       206: q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       223: q+1
       225: q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       244: 2q+1
       245: 2q+1
       247: 2
       248: 2
       249: q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       282: q+1
       290: 1
       292: 1
       302: 1
       306: q+1
       312: 1
       314: q+1
       316: q+1
       324: q+1
       336: 1
       339: 2
       341: 2
       343: q+1
       348: q+1
       350: q+1
       351: 2
       356: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 2
       452: 1
       456: 1
       464: 2
       468: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       486: 2
       488: 2
       490: q+1
       491: 1
       495: 1
       496: 2
       500: 1
       501: 2
       512: q+1
       514: q+1
       578: 1
       581: 1
       598: 1
       606: 1
       614: 1
       618: 2
       624: 1
       630: 1
       634: 2
       646: 1
       652: 1
       655: 1
       656: 1
       679: 1
       685: 1
       689: 1
       770: 1
       773: 1
       810: 1
       834: 1
       850: 1
       856: 1
       880: 1
      1061: 1

1062:    0: 6q+2
         1: 6q+2
         2: 2q^2+2q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+q^2+2q+1
         8: 2q^2+2q+1
         9: q^3+q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: q+1
        14: q+1
        15: q+1
        16: 6q+2
        17: 6q+2
        18: q^3+q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+2q+1
        25: 6q+2
        26: 6q+2
        27: 2q^2+2q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 6q+2
        32: q+1
        33: 6q+2
        34: 6q+2
        35: q+1
        36: 6q+2
        37: 4q+2
        38: 2q
        39: 4q+2
        40: 2q
        41: q^2+2q+1
        42: q^2
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 4q+2
        53: 4q+2
        54: q^2+2q+1
        55: 4q+2
        56: 4q+2
        57: q^2+2q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 4q+2
        63: 2q
        64: q+1
        66: 4q+2
        67: 2q
        69: q+1
        70: q+1
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: 2q+1
        80: q+1
        81: q+1
        82: 4q+2
        83: q+1
        84: q+1
        85: q+1
        86: 4q+2
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: q^2+2q+1
       103: 2q+1
       104: q
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: 2q+2
       115: q+1
       121: q+1
       123: q+1
       126: q+1
       127: 2q+2
       129: 2q+2
       131: 2q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: q+1
       144: q+1
       145: 4q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: q+1
       151: 2q+2
       153: 2q+2
       155: 2q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       169: 1
       172: 1
       177: q+1
       179: 2q+2
       181: 2
       187: 1
       189: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: q+1
       209: 2q+2
       211: q+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q+2
       239: 2q+2
       241: 2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 4
       248: 4
       249: 2q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       287: q+1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: q+1
       317: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: q+1
       334: 1
       335: 1
       336: 1
       337: 4
       338: 4
       340: 4
       342: 2q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 4
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 4
       366: q+1
       368: 1
       369: 1
       370: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       423: 1
       425: 1
       427: 4
       433: 1
       441: 1
       443: 2
       444: 2
       445: 4
       451: 1
       459: 1
       461: 2
       462: 2
       463: 4
       469: q+1
       475: 1
       477: 2
       479: 2
       480: 2
       483: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       545: 2
       547: 2
       561: 2
       563: 2
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       599: 1
       609: 1
       613: 1
       625: 1
       629: 1
       645: 1
       653: 1
       677: 1
       683: 1
       687: 1
       688: 1
       689: 1
       693: 1
       696: 1
       697: 1
       698: 1
       811: 1
       835: 1
       851: 1
       855: 1
       879: 1
      1062: 1

1063:    0: 6q+2
         1: 6q+2
         2: 2q^2+2q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+q^2+2q+1
         8: 2q^2+2q+1
         9: q^3+q^2+2q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: q+1
        14: q+1
        15: q+1
        16: 6q+2
        17: 6q+2
        18: q^3+q^2+2q+1
        19: 4q+2
        20: 4q+2
        21: q^2+2q+1
        22: 6q+2
        23: 6q+2
        24: 2q^2+2q+1
        25: 6q+2
        26: 6q+2
        27: 2q^2+2q+1
        28: 6q+2
        29: 4q+2
        30: q+1
        31: 6q+2
        32: q+1
        33: 6q+2
        34: 6q+2
        35: q+1
        36: 6q+2
        37: 2q
        38: 4q+2
        39: 2q
        40: 4q+2
        41: q^2
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 4q+2
        50: 4q+2
        51: q^2+2q+1
        52: 4q+2
        53: 4q+2
        54: q^2+2q+1
        55: 4q+2
        56: 4q+2
        57: q^2+2q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 2q
        63: 4q+2
        65: q+1
        66: 2q
        67: 4q+2
        69: q+1
        70: q+1
        71: 4q+2
        72: 2q+2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: 2q+1
        80: q+1
        81: q+1
        82: 4q+2
        83: q+1
        84: q+1
        85: q+1
        86: 4q+2
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: 1
        93: 1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q+2
       101: 4q+2
       102: q^2+2q+1
       103: q
       104: 2q+1
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       114: 2q+2
       116: q+1
       122: q+1
       124: q+1
       126: q+1
       128: 2q+2
       130: 2q+2
       132: 2q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: q+1
       142: 2q+2
       143: q+1
       144: q+1
       145: 4q+2
       146: q+1
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: q+1
       152: 2q+2
       154: 2q+2
       156: 2q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       170: 1
       171: 1
       178: q+1
       180: 2q+2
       182: 2
       188: 1
       190: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       208: q+1
       210: 2q+2
       212: q+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 2q+2
       240: 2q+2
       242: 2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 4
       248: 4
       249: 2q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       288: q+1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: q+1
       318: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       326: q+1
       334: 1
       335: 1
       336: 1
       337: 4
       339: 4
       341: 4
       343: 2q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 4
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 4
       366: q+1
       368: 1
       369: 1
       370: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       424: 1
       426: 1
       428: 4
       434: 1
       442: 1
       443: 2
       444: 2
       446: 4
       452: 1
       460: 1
       461: 2
       462: 2
       464: 4
       470: q+1
       476: 1
       478: 2
       479: 2
       480: 2
       483: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       546: 2
       548: 2
       562: 2
       564: 2
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       600: 1
       610: 1
       614: 1
       626: 1
       630: 1
       646: 1
       654: 1
       677: 1
       683: 1
       687: 1
       688: 1
       689: 1
       694: 1
       699: 1
       700: 1
       701: 1
       812: 1
       836: 1
       852: 1
       856: 1
       879: 1
      1063: 1

1064:    0: q^2+q+1
         1: q^2+q+1
         2: 2q^2+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: 2q^2+1
         8: 2q^2+1
         9: q^4+q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q+1
        17: q+1
        18: q^2+1
        19: q^2+q+1
        20: q^2+q+1
        21: 2q^2+1
        22: q^2+q+1
        23: q^2+q+1
        24: 2q^2+1
        25: q^2+q+1
        26: q^2+q+1
        27: 2q^2+1
        30: q^2+1
        32: q^2+1
        33: q+1
        35: q^2+1
        36: q+1
        37: q^2+1
        38: q
        39: q^2+1
        40: q
        41: q^2+1
        42: q^2
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q^2+q+1
        53: q^2+q+1
        54: 2q^2+1
        55: q^2+q+1
        56: q^2+q+1
        57: 2q^2+1
        64: q^2+1
        66: 1
        67: q
        69: 1
        72: q+1
        73: q+1
        74: q^2+1
        75: q
        76: q^2+1
        77: q
        78: q^2+1
        79: q^2
        81: 1
        83: q^2+1
        85: 1
        87: q^2+1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: q+1
        98: q+1
        99: q^2+1
       100: q^2+q+1
       101: q^2+q+1
       102: 2q^2+1
       111: 1
       112: q
       115: q^2+1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: q+1
       142: q+1
       144: 1
       147: q+1
       148: q+1
       150: q^2+1
       151: q^2+1
       152: q
       153: q^2+1
       154: q
       155: q^2+1
       156: q^2
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q^2+1
       177: 1
       181: 1
       187: 1
       197: 1
       198: q
       205: 1
       206: q
       211: q^2+1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: q+1
       245: q+1
       247: q+1
       248: q+1
       249: q^2+1
       256: 1
       257: 1
       258: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       324: q
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: 1
       351: q+1
       356: 1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       425: 1
       433: 1
       445: 1
       451: 1
       463: 1
       475: 1
       477: 1
       479: 1
       480: q
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       577: 1
       613: 1
       629: 1
       645: 1
       655: 1
       679: 1
       685: 1
       689: 1
       791: 1
       855: 1
       880: 1
      1064: 1

1065:    0: q^2+q+1
         1: q^2+q+1
         2: 2q^2+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: 2q^2+1
         8: 2q^2+1
         9: q^4+q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q+1
        17: q+1
        18: q^2+1
        19: q^2+q+1
        20: q^2+q+1
        21: 2q^2+1
        22: q^2+q+1
        23: q^2+q+1
        24: 2q^2+1
        25: q^2+q+1
        26: q^2+q+1
        27: 2q^2+1
        30: q^2+1
        32: q^2+1
        33: q+1
        35: q^2+1
        36: q+1
        37: q
        38: q^2+1
        39: q
        40: q^2+1
        41: q^2
        42: q^2+1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q^2+q+1
        53: q^2+q+1
        54: 2q^2+1
        55: q^2+q+1
        56: q^2+q+1
        57: 2q^2+1
        65: q^2+1
        66: q
        67: 1
        69: 1
        72: q+1
        73: q+1
        74: q
        75: q^2+1
        76: q
        77: q^2+1
        78: q^2
        79: q^2+1
        81: 1
        83: q^2+1
        85: 1
        87: q^2+1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: q+1
        98: q+1
        99: q^2+1
       100: q^2+q+1
       101: q^2+q+1
       102: 2q^2+1
       111: q
       112: 1
       116: q^2+1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: q+1
       142: q+1
       144: 1
       147: q+1
       148: q+1
       150: q^2+1
       151: q
       152: q^2+1
       153: q
       154: q^2+1
       155: q^2
       156: q^2+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q^2+1
       178: 1
       182: 1
       188: 1
       197: q
       198: 1
       205: q
       206: 1
       212: q^2+1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: q+1
       245: q+1
       247: q+1
       248: q+1
       249: q^2+1
       256: 1
       257: 1
       258: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       323: q
       324: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: 1
       351: q+1
       356: 1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       426: 1
       434: 1
       446: 1
       452: 1
       464: 1
       476: 1
       478: 1
       479: q
       480: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       581: 1
       614: 1
       630: 1
       646: 1
       656: 1
       679: 1
       685: 1
       689: 1
       792: 1
       856: 1
       880: 1
      1065: 1

1066:    0: q^3+3q^2+4q+2
         1: q^3+3q^2+4q+2
         2: q^3+3q^2+4q+2
         3: 2q^2+4q+2
         4: 2q^2+3q+2
         5: 2q^2+4q+2
         6: 2q^2+3q+2
         7: 2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+3q+2
        13: q^3+3q^2+4q+2
        14: 2q^2+3q+2
        15: 2q^2+4q+2
        16: q^2+3q+2
        17: q^2+3q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: q^2+3q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: q^3+3q^2+4q+2
        44: 2q^2+3q+2
        45: 2q^2+4q+2
        46: q^2+3q+2
        47: q^2+3q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: q^2+3q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: q^2+3q+2
        89: q^2+3q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: q^2+3q+2
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: q+2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+1
       211: q+1
       213: q+2
       215: q+2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 1
       257: 1
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       275: q+1
       278: q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: q+1
       327: q+2
       329: q+2
       331: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       344: 1
       345: q+2
       346: 1
       349: 2
       350: 1
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       360: 1
       362: 1
       364: q+1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       409: q+2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       427: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: 1
       481: 1
       482: 1
       484: 1
       485: 1
       487: 1
       492: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: q+1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       525: 1
       528: 1
       583: 1
       585: 1
       587: 1
       601: 1
       635: 1
       637: 1
       639: 1
       658: 1
       666: 1
       668: 1
       672: 1
       676: 1
       681: 1
       686: 1
       690: 1
       777: 1
       789: 1
       841: 1
       859: 1
       881: 1
      1066: 1

1067:    0: q^3+3q^2+4q+2
         1: q^3+3q^2+4q+2
         2: q^3+3q^2+4q+2
         3: 2q^2+4q+2
         4: 2q^2+3q+2
         5: 2q^2+4q+2
         6: 2q^2+3q+2
         7: 2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+3q+2
        13: q^3+3q^2+4q+2
        14: 2q^2+3q+2
        15: 2q^2+4q+2
        16: q^2+3q+2
        17: q^2+3q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: q^2+3q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: q^3+3q^2+4q+2
        44: 2q^2+3q+2
        45: 2q^2+4q+2
        46: q^2+3q+2
        47: q^2+3q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: q^2+3q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: q^2+3q+2
        89: q^2+3q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: q^2+3q+2
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: q+2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+1
       212: q+1
       214: q+2
       216: q+2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 1
       257: 1
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       276: q+1
       277: q+1
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: q+1
       328: q+2
       330: q+2
       332: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       344: 1
       345: q+2
       346: 1
       349: 2
       350: 1
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       361: 1
       363: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       410: q+2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: 1
       481: 1
       482: 1
       484: 1
       486: 1
       488: 1
       492: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: q+1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       526: 1
       527: 1
       584: 1
       586: 1
       588: 1
       602: 1
       636: 1
       638: 1
       640: 1
       659: 1
       667: 1
       669: 1
       672: 1
       676: 1
       681: 1
       686: 1
       690: 1
       778: 1
       790: 1
       842: 1
       860: 1
       881: 1
      1067: 1

1068:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^3+2q^2+2q+2
         4: q^2+2q+2
         5: q^3+2q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^3+2q^2+2q+2
         9: q^2+q+1
        10: q^2+2q+2
        11: q^3+2q^2+2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^3+2q^2+2q+2
        16: q^2+q+2
        17: q^2+q+2
        18: q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q^2+q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^3+2q^2+2q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q+1
        49: q^2+q+2
        50: q^2+q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: q^2+q+2
        69: 1
        70: q^2+2q+2
        71: q^2+q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: q^2+q+2
        89: q^2+q+2
        90: q+1
        91: q^2+q+2
        92: q^2+q+2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: q^2+q+2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: q^2+q+2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+2
       158: q^2+q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: 1
       211: 1
       213: 2
       215: 2
       217: q+1
       219: 1
       220: q^2+q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       237: 1
       239: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       317: 1
       325: 1
       327: 2
       329: 2
       331: q+1
       333: 1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 1
       362: 1
       367: 1
       371: 1
       372: 1
       374: 1
       375: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       427: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       481: 1
       482: 1
       484: 1
       485: 1
       487: 1
       492: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       509: 1
       516: 1
       518: 1
       519: 1
       525: 1
       528: 1
       583: 1
       585: 1
       587: 1
       601: 1
       635: 1
       660: 1
       666: 1
       668: 1
       672: 1
       676: 1
       681: 1
       691: 1
       777: 1
       789: 1
       861: 1
       882: 1
      1068: 1

1069:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^3+2q^2+2q+2
         4: q^2+2q+2
         5: q^3+2q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^3+2q^2+2q+2
         9: q^2+q+1
        10: q^2+2q+2
        11: q^3+2q^2+2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^3+2q^2+2q+2
        16: q^2+q+2
        17: q^2+q+2
        18: q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q^2+q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^3+2q^2+2q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q+1
        49: q^2+q+2
        50: q^2+q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: q^2+q+2
        69: 1
        70: q^2+2q+2
        71: q^2+q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: q^2+q+2
        89: q^2+q+2
        90: q+1
        91: q^2+q+2
        92: q^2+q+2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: q^2+q+2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: q^2+q+2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+2
       158: q^2+q+2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: 1
       212: 1
       214: 2
       216: 2
       218: q+1
       219: 1
       220: q^2+q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       238: 1
       240: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       318: 1
       326: 1
       328: 2
       330: 2
       332: q+1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 1
       363: 1
       367: 1
       371: 1
       372: 1
       374: 1
       375: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       466: 1
       481: 1
       482: 1
       484: 1
       486: 1
       488: 1
       492: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       509: 1
       516: 1
       518: 1
       519: 1
       526: 1
       527: 1
       584: 1
       586: 1
       588: 1
       602: 1
       636: 1
       661: 1
       667: 1
       669: 1
       672: 1
       676: 1
       681: 1
       691: 1
       778: 1
       790: 1
       862: 1
       882: 1
      1069: 1

1070:    0: 2
         1: 2
         2: 2
         3: 2
         4: q^2+q+1
         5: 2
         6: q^2+q+1
         7: q^2+q+1
         8: 2
         9: q^2+q+1
        10: 2
        11: 2
        12: q^2+q+1
        13: 2
        14: q^2+q+1
        15: 2
        16: 2
        17: 2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2
        41: 2
        43: 2
        44: q^2+q+1
        45: 2
        46: 2
        47: 2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: 2
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       113: 1
       115: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       125: 2
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       173: 1
       176: 1
       177: 1
       179: 1
       189: 1
       191: 1
       192: 1
       199: 1
       200: 1
       207: 2
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       275: 1
       278: 1
       279: 1
       281: 1
       287: 1
       315: 1
       317: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       342: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       373: 1
       374: 1
       375: 1
       376: 1
       409: 1
       411: 1
       413: 1
       465: 1
       467: 1
       469: 1
       489: 1
       492: 1
       497: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       517: 1
       520: 1
       583: 1
       635: 1
       637: 1
       639: 1
       662: 1
       670: 1
       686: 1
       692: 1
       841: 1
       863: 1
       883: 1
      1070: 1

1071:    0: 2
         1: 2
         2: 2
         3: 2
         4: q^2+q+1
         5: 2
         6: q^2+q+1
         7: q^2+q+1
         8: 2
         9: q^2+q+1
        10: 2
        11: 2
        12: q^2+q+1
        13: 2
        14: q^2+q+1
        15: 2
        16: 2
        17: 2
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: 2
        29: 1
        30: 1
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2
        42: 2
        43: 2
        44: q^2+q+1
        45: 2
        46: 2
        47: 2
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: 2
        69: 1
        70: 1
        71: 1
        75: 1
        77: 1
        79: 1
        80: 2
        81: 2
        82: 1
        83: 1
        84: 2
        85: 2
        86: 1
        87: 1
        88: 2
        89: 2
        90: q^2+q+1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       125: 2
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       137: 2
       138: 1
       139: 1
       141: 1
       143: 2
       144: 1
       145: 1
       146: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       174: 1
       175: 1
       178: 1
       180: 1
       190: 1
       191: 1
       192: 1
       199: 1
       200: 1
       208: 2
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       226: 1
       227: 1
       228: 1
       231: 1
       232: 1
       233: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       276: 1
       277: 1
       280: 1
       282: 1
       288: 1
       316: 1
       318: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: 1
       343: 1
       344: 1
       345: 1
       346: 1
       352: 1
       353: 1
       354: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       373: 1
       374: 1
       375: 1
       376: 1
       410: 1
       412: 1
       414: 1
       466: 1
       468: 1
       470: 1
       490: 1
       492: 1
       497: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       517: 1
       520: 1
       584: 1
       636: 1
       638: 1
       640: 1
       663: 1
       671: 1
       686: 1
       692: 1
       842: 1
       864: 1
       883: 1
      1071: 1

1072:    0: q^3+7q^2+10q+4
         1: 2q^3+8q^2+10q+4
         2: q^3+7q^2+10q+4
         3: q^3+7q^2+10q+4
         4: 3q^2+8q+4
         5: 2q^3+8q^2+10q+4
         6: q^4+5q^3+7q^2+8q+4
         7: 3q^2+8q+4
         8: 2q^3+8q^2+10q+4
         9: 3q^2+8q+4
        10: 3q^2+10q+4
        11: 3q^2+10q+4
        12: 3q^2+8q+4
        13: q^3+7q^2+10q+4
        14: 3q^2+8q+4
        15: 2q^3+8q^2+10q+4
        16: q^3+7q^2+10q+4
        17: 2q^3+8q^2+10q+4
        18: 3q^2+8q+4
        19: q^2+8q+4
        20: q^3+5q^2+8q+4
        21: q^2+8q+4
        22: 3q^2+6q+4
        23: 3q^2+6q+4
        24: 3q^2+6q+4
        25: 3q^2+6q+4
        26: 3q^2+6q+4
        27: 3q^2+6q+4
        28: 3q^2+10q+4
        29: q^2+8q+4
        30: q^2+8q+4
        31: 6q+4
        32: 3q^2+6q+4
        33: 3q^2+6q+4
        34: 6q+4
        35: 3q^2+6q+4
        36: 3q^2+6q+4
        37: q^2+2q+2
        38: q^2+2q+2
        39: q^2+2q+2
        40: q^2+2q+2
        41: q^2+2q+2
        42: q^2+2q+2
        43: 3q^2+10q+4
        44: 3q^2+8q+4
        45: 3q^2+10q+4
        46: q^3+7q^2+10q+4
        47: 2q^3+8q^2+10q+4
        48: 3q^2+8q+4
        49: q^2+8q+4
        50: q^3+5q^2+8q+4
        51: q^2+8q+4
        52: 4q+4
        53: 2q^2+4q+4
        54: 4q+4
        55: 4q+4
        56: 2q^2+4q+4
        57: 4q+4
        58: 3q+2
        59: 3q+2
        60: 3q+2
        61: 3q+2
        62: 2q+2
        63: 2q+2
        64: q^2+2q+2
        65: q^2+2q+2
        66: q^2+2q+2
        67: q^2+2q+2
        68: 3q^2+10q+4
        69: q^2+8q+4
        70: q^2+8q+4
        71: q^2+8q+4
        72: 2q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 6q+4
        81: 3q^2+6q+4
        82: 4q+4
        83: 4q+4
        84: 6q+4
        85: 3q^2+6q+4
        86: 4q+4
        87: 4q+4
        88: 3q^2+10q+4
        89: 3q^2+10q+4
        90: 3q^2+8q+4
        91: q^2+8q+4
        92: q^3+5q^2+8q+4
        93: q^2+8q+4
        94: 4q+4
        95: 2q^2+4q+4
        96: 4q+4
        97: 4q+4
        98: 2q^2+4q+4
        99: 4q+4
       100: 2
       101: q^2+2
       102: 2
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 3q+2
       118: 3q+2
       119: 3q+2
       120: 3q+2
       121: 2q+2
       122: 2q+2
       123: q^2+2q+2
       124: q^2+2q+2
       125: 3q^2+10q+4
       126: q^2+8q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q^2+8q+4
       134: q^2+8q+4
       135: 2q+4
       136: 2q+4
       137: 6q+4
       138: 4q+4
       139: 4q+4
       141: 4q+4
       142: 2q+4
       143: 6q+4
       144: 4q+4
       145: 4q+4
       146: 4q+4
       147: 2q+4
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 4q+4
       158: 4q+4
       159: 4q+4
       160: 4q+4
       161: 2q^2+4q+4
       162: 4q+4
       163: 4q+4
       164: 2q^2+4q+4
       165: 4q+4
       166: 2
       167: q^2+2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: q+2
       184: q+2
       185: q+2
       186: q+2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 3q+2
       192: 3q+2
       195: q+2
       196: q+2
       199: 3q+2
       200: 3q+2
       201: q+2
       202: q+2
       207: 2q+2
       208: 2q+2
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+2
       218: q+2
       219: q^2+8q+4
       220: 4q+4
       221: 4q+4
       222: 4
       223: 2q+4
       224: 4
       225: 2q+4
       226: 4q+4
       227: 4q+4
       228: 4q+4
       230: 2q+4
       231: 4q+4
       232: 4q+4
       233: 4q+4
       234: 2q+4
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       247: 2
       248: 2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 2
       257: q^2+2
       258: 2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: q+2
       282: q+2
       283: q+2
       284: q+2
       285: q+2
       286: q+2
       287: q+2
       288: q+2
       289: 2
       290: 2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: q+2
       304: q+2
       307: q+2
       308: q+2
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: 4q+4
       334: 4
       335: 4
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 4q+4
       345: q+2
       346: q+2
       349: 2
       350: 2q+4
       352: 4q+4
       353: q+2
       354: q+2
       355: 2
       356: 2q+4
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       371: 2
       372: 2
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       413: q+2
       414: q+2
       417: 2
       418: 2
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       427: 1
       428: 1
       431: q+2
       432: q+2
       439: 1
       440: 1
       447: q+2
       448: q+2
       453: 1
       454: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       481: 4
       482: 4
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+2
       494: 2
       497: q+2
       498: 2
       508: 2
       509: 1
       510: 1
       515: 2
       516: 2
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       585: 2
       586: 2
       589: 2
       590: 2
       595: 2
       596: 2
       601: 1
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       639: 1
       640: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       709: 1
       710: 1
       711: 1
       712: 1
       775: 1
       776: 1
       807: 1
       808: 1
       825: 1
       826: 1
       865: 1
       881: 1
       882: 1
      1072: 1

1073:    0: 4q^2+6q+4
         1: 2q^2+6q+4
         2: 4q^2+6q+4
         3: 2q^2+6q+4
         4: 4q^2+6q+4
         5: 2q^2+6q+4
         6: 2q^2+6q+4
         7: 4q^2+6q+4
         8: 2q^2+6q+4
         9: 3q^3+6q^2+5q+2
        10: q^2+4q+4
        11: 4q+4
        12: q^2+4q+4
        13: 4q^2+6q+4
        14: 4q^2+6q+4
        15: 2q^2+6q+4
        16: q^2+4q+4
        17: 4q+4
        18: 4q^2+5q+2
        19: 4q^2+6q+4
        20: 2q^2+6q+4
        21: 4q^2+6q+4
        22: q^2+4q+4
        23: 4q+4
        24: q^2+4q+4
        25: q^2+4q+4
        26: 4q+4
        27: q^2+4q+4
        28: 2q+4
        29: q^2+4q+4
        30: 4q^2+6q+4
        31: 2q+4
        32: q^2+4q+4
        33: 2q+4
        34: 2q+4
        35: q^2+4q+4
        36: 2q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+4q+4
        44: q^2+4q+4
        45: 4q+4
        46: q^2+4q+4
        47: 4q+4
        48: 4q^2+5q+2
        49: q^2+4q+4
        50: 4q+4
        51: 4q^2+5q+2
        52: q^2+4q+4
        53: 4q+4
        54: q^2+4q+4
        55: q^2+4q+4
        56: 4q+4
        57: q^2+4q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 2q+4
        69: q^2+3q+2
        70: q^2+4q+4
        71: 2q+4
        72: 2q+4
        73: 2q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: 2q+4
        81: 2q+4
        82: 2q+4
        83: q^2+4q+4
        84: 2q+4
        85: 2q+4
        86: 2q+4
        87: q^2+4q+4
        88: q+4
        89: q+4
        90: q^2+3q+2
        91: q^2+4q+4
        92: 4q+4
        93: 4q^2+5q+2
        94: q+4
        95: q+4
        96: q^2+3q+2
        97: q+4
        98: q+4
        99: q^2+3q+2
       100: 4q+2
       101: 2q+2
       102: 4q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: q+4
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       133: 2q+4
       134: q^2+3q+2
       135: 2q+4
       136: 2q+4
       137: 4
       138: q+2
       139: 4
       141: 2q+4
       142: q+4
       143: 4
       144: q+2
       145: 4
       146: 2q+4
       147: q+4
       149: 2q+2
       150: 4q+2
       151: 2q+1
       152: 2q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: q+4
       158: q+4
       159: q^2+3q+2
       160: q+4
       161: q+4
       162: q^2+3q+2
       163: q+4
       164: q+4
       165: q^2+3q+2
       166: q+2
       167: 2
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: 2
       196: 2
       199: 2
       200: 2
       201: 2
       202: 2
       207: 2
       208: 2
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       213: 2
       214: 2
       215: 2
       216: 2
       217: q+1
       218: q+1
       219: q+2
       220: q+4
       221: q+2
       222: 4
       223: q+2
       224: 4
       225: q+2
       226: 2
       227: 4
       228: q+2
       230: q+4
       231: 2
       232: 4
       233: q+2
       234: q+4
       236: q+2
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: 2
       246: 2q+2
       247: q+2
       248: 2
       249: 3q+2
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: q+2
       257: 2
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2
       280: 2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 2
       304: 2
       307: 2
       308: 2
       315: 1
       316: 1
       317: 1
       318: 1
       325: q+1
       326: q+1
       333: q+2
       334: 2
       335: 2
       336: q+2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: 2
       345: 2
       346: 1
       349: 2
       350: q+2
       352: 2
       353: 2
       354: 1
       355: 2
       356: q+2
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       366: 2
       367: 2
       368: q+2
       371: q+2
       372: 2
       373: 3q+2
       374: 1
       375: 1
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       481: 2
       482: 2
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+2
       492: 1
       494: 1
       497: 1
       498: 1
       508: 2
       509: 1
       510: 1
       515: 2
       517: 2
       518: 1
       519: 1
       520: q+1
       585: 1
       586: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       639: 1
       640: 1
       658: 1
       659: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       690: 1
       692: 1
       779: 1
       780: 1
       781: 1
       782: 1
       867: 1
       868: 1
       881: 1
       883: 1
      1073: 1

1074:    0: q^2+6q+4
         1: q^2+6q+4
         2: q^3+3q^2+3q+4
         3: q^2+6q+4
         4: q^2+6q+4
         5: q^2+6q+4
         6: q^2+6q+4
         7: q^3+3q^2+3q+4
         8: 3q^2+4q+4
         9: q^3+3q^2+3q+4
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: q^2+3q+4
        14: q^2+3q+4
        15: 4q+4
        16: q^2+6q+4
        17: q^2+6q+4
        18: q^3+3q^2+3q+4
        19: q^2+6q+4
        20: q^2+6q+4
        21: q^3+3q^2+3q+4
        22: 2q+4
        23: 2q+4
        24: q^2+q+4
        25: 2q+4
        26: 2q+4
        27: q^2+q+4
        28: q^2+6q+4
        29: q^2+6q+4
        30: q^2+3q+4
        31: 2q+4
        32: q+4
        33: 2q+4
        34: 2q+4
        35: q+4
        36: 2q+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: 2
        42: 2
        43: q^2+3q+4
        44: q^2+3q+4
        45: 4q+4
        46: q^2+3q+4
        47: 4q+4
        48: q^2+3q+4
        49: q^2+6q+4
        50: q^2+6q+4
        51: q^3+3q^2+3q+4
        52: 2q+4
        53: 2q+4
        54: q^2+q+4
        55: 2q+4
        56: 2q+4
        57: q^2+q+4
        58: q+2
        59: q+2
        60: q+2
        61: q+2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: q+4
        69: q^2+3q+4
        70: q^2+3q+4
        71: q^2+6q+4
        72: 2q+4
        73: 2q+4
        74: 2
        75: 2
        76: 2
        77: 2
        78: 2
        79: 2
        80: q+4
        81: q+4
        82: 2q+4
        83: q+4
        84: q+4
        85: q+4
        86: 2q+4
        87: q+4
        88: q^2+3q+4
        89: 4q+4
        90: q^2+3q+4
        91: q^2+3q+4
        92: 4q+4
        93: q^2+3q+4
        94: 2q+4
        95: 2q+4
        96: q^2+q+4
        97: 2q+4
        98: 2q+4
        99: q^2+q+4
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 2
       116: 2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       125: q+4
       126: q^2+3q+4
       127: 2
       128: 2
       129: 2
       130: 2
       131: 2
       132: 2
       133: q+4
       134: q^2+3q+4
       135: q+4
       136: q+4
       137: q+4
       138: q+4
       139: 2q+4
       141: q+4
       142: 2q+4
       143: q+4
       144: q+4
       145: 2q+4
       146: q+4
       147: 2q+4
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q^2+3q+4
       158: 4q+4
       159: q^2+3q+4
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 2
       178: 2
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 2
       190: 2
       191: 2
       192: 2
       195: q+2
       196: q+2
       199: 2
       200: 2
       201: q+2
       202: q+2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       219: q+4
       220: q+4
       221: q^2+3q+4
       222: q+4
       223: q+4
       224: q+4
       225: q+4
       226: q+4
       227: 2
       228: q+2
       230: q+2
       231: q+4
       232: 2
       233: q+2
       234: q+2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       283: 2
       284: 2
       285: 2
       286: 2
       287: 2
       288: 2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 2
       346: q+2
       349: q+2
       350: q+2
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       366: 2
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       469: 1
       470: 1
       481: 2
       482: 2
       483: 2
       484: 1
       491: 1
       492: 2
       494: q+2
       497: 2
       498: q+2
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       529: 1
       530: 1
       531: 1
       532: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       607: 1
       608: 1
       619: 1
       620: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       807: 1
       808: 1
       825: 1
       826: 1
       865: 1
       866: 1
       867: 1
       868: 1
      1074: 1

1075:    0: q^3+9q^2+16q+4
         1: 2q^3+14q^2+16q+4
         2: q^3+9q^2+16q+4
         3: 2q^3+14q^2+16q+4
         4: q^3+7q^2+12q+4
         5: q^3+9q^2+16q+4
         6: q^4+6q^3+13q^2+12q+4
         7: q^3+7q^2+12q+4
         8: q^3+9q^2+16q+4
         9: q^3+4q^2+5q+2
        10: 5q^2+14q+4
        11: 5q^2+14q+4
        12: q^3+6q^2+10q+4
        13: q^3+9q^2+16q+4
        14: q^3+7q^2+12q+4
        15: q^3+9q^2+16q+4
        16: 5q^2+14q+4
        17: 5q^2+14q+4
        18: 2q^2+5q+2
        19: 3q^2+12q+4
        20: q^3+9q^2+12q+4
        21: 3q^2+12q+4
        22: q^3+9q^2+16q+4
        23: 2q^3+14q^2+16q+4
        24: q^3+9q^2+16q+4
        25: 4q^2+12q+4
        26: 8q^2+12q+4
        27: 4q^2+12q+4
        28: 2q^2+12q+4
        29: 2q^2+10q+4
        30: 3q^2+12q+4
        31: 5q^2+14q+4
        32: q^3+9q^2+16q+4
        33: 5q^2+14q+4
        34: 2q^2+10q+4
        35: 4q^2+12q+4
        36: 2q^2+10q+4
        37: 2q^2+6q+2
        38: 2q^2+6q+2
        39: 4q^2+6q+2
        40: 4q^2+6q+2
        41: 2q^2+6q+2
        42: 2q^2+6q+2
        43: 5q^2+14q+4
        44: q^3+6q^2+10q+4
        45: 5q^2+14q+4
        46: 5q^2+14q+4
        47: 5q^2+14q+4
        48: 2q^2+5q+2
        49: q^2+10q+4
        50: 3q^2+10q+4
        51: q^2+5q+2
        52: 3q^2+12q+4
        53: q^3+9q^2+12q+4
        54: 3q^2+12q+4
        55: 8q+4
        56: 4q^2+8q+4
        57: 8q+4
        58: q^2+6q+2
        59: q^2+6q+2
        60: 4q+2
        61: 4q+2
        62: q^2+5q+2
        63: q^2+5q+2
        64: 2q^2+6q+2
        65: 2q^2+6q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 2q^2+12q+4
        69: 3q+2
        70: 2q^2+10q+4
        71: q^2+8q+4
        72: 4q+4
        73: 6q+4
        74: 3q+2
        75: 3q+2
        76: q^2+3q+2
        77: q^2+3q+2
        78: 3q+2
        79: 3q+2
        80: 5q^2+14q+4
        81: 5q^2+14q+4
        82: 2q^2+10q+4
        83: 3q^2+12q+4
        84: 2q^2+10q+4
        85: 2q^2+10q+4
        86: 6q+4
        87: 8q+4
        88: 6q+4
        89: 6q+4
        90: q^2+3q+2
        91: q^2+10q+4
        92: 3q^2+10q+4
        93: q^2+5q+2
        94: q^2+10q+4
        95: 3q^2+10q+4
        96: q^2+5q+2
        97: 5q+4
        98: q^2+5q+4
        99: 3q+2
       100: 8q+4
       101: 4q^2+8q+4
       102: 8q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: 2q+2
       110: 2q+2
       111: q+2
       112: q+2
       113: 2q+2
       114: 2q+2
       115: 3q+2
       116: 3q+2
       117: q^2+6q+2
       118: q^2+6q+2
       119: 4q+2
       120: 4q+2
       121: q^2+5q+2
       122: q^2+5q+2
       123: q^2+5q+2
       124: q^2+5q+2
       125: 6q+4
       126: q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       133: q^2+8q+4
       134: 3q+2
       135: 4q+4
       136: 6q+4
       137: 6q+4
       138: 3q+2
       139: q^2+8q+4
       140: 4q+4
       141: 2q^2+10q+4
       142: 6q+4
       143: 4q+4
       144: q+2
       145: 4q+4
       146: 6q+4
       147: 3q+4
       149: 6q+4
       150: 8q+4
       151: 3q+2
       152: 3q+2
       153: q^2+3q+2
       154: q^2+3q+2
       155: 3q+2
       156: 3q+2
       157: 2q+4
       158: 2q+4
       159: 2q+2
       160: q^2+10q+4
       161: 3q^2+10q+4
       162: q^2+5q+2
       163: 5q+4
       164: q^2+5q+4
       165: 3q+2
       166: 5q+4
       167: q^2+5q+4
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: q+2
       184: q+2
       185: 2q+2
       186: 2q+2
       187: q+2
       188: q+2
       189: 2q+2
       190: 2q+2
       191: 3q+2
       192: 3q+2
       193: q+2
       194: q+2
       195: 2q+2
       196: 2q+2
       197: q+2
       198: q+2
       199: 2q+2
       200: 2q+2
       201: q+2
       202: q+2
       207: 2q+2
       208: 2q+2
       209: 2q+2
       210: 2q+2
       211: 3q+2
       212: 3q+2
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+1
       218: q+1
       219: q+2
       220: 2q+4
       221: 2
       222: 4
       223: q+2
       224: 4
       225: 2q+2
       226: q+2
       227: q^2+8q+4
       228: 3q+2
       229: 4q+4
       230: 6q+4
       231: 2
       232: 4q+4
       233: q+2
       234: 3q+4
       236: q+2
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+1
       242: q+1
       243: 4q+4
       244: 3q+4
       246: 6q+4
       247: q+4
       248: q+4
       250: 2q+4
       251: 2q+4
       252: 2q+2
       253: q+2
       254: q+2
       255: q+1
       256: 5q+4
       257: q^2+5q+4
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: q+2
       300: q+2
       301: 2
       302: 2
       303: 2q+2
       304: 2q+2
       305: q+2
       306: q+2
       307: q+2
       308: q+2
       315: 1
       316: 1
       317: q+2
       318: q+2
       319: q+2
       320: q+2
       325: 2q+2
       326: 2q+2
       333: 2
       334: 2
       335: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       344: q+2
       345: 2q+4
       346: 2
       347: 4
       348: q+2
       349: 4
       350: 2q+2
       351: q+4
       352: 2
       353: q+2
       354: 1
       355: 2
       356: q+2
       360: q+2
       361: q+2
       362: q+2
       363: q+2
       364: q+1
       365: q+1
       366: 2
       367: 4q+4
       368: q+2
       369: 3q+4
       371: q+4
       372: q+4
       374: q+2
       375: q+2
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       427: 2
       428: 2
       433: 1
       434: 1
       435: 2
       436: 2
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       453: 1
       454: 1
       465: q+2
       466: q+2
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+2
       472: q+2
       481: 2
       482: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       492: 2
       493: 2
       494: 2
       496: q+4
       497: 1
       498: 1
       508: 2
       509: q+2
       510: 1
       511: 2
       512: q+2
       515: 2
       516: 2
       518: 2
       519: 2
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       585: 1
       586: 1
       601: 2
       602: 2
       605: 1
       606: 1
       609: 1
       610: 1
       615: 2
       616: 2
       617: 2
       618: 2
       639: 1
       640: 1
       647: 1
       648: 1
       658: 1
       659: 1
       660: 1
       661: 1
       672: 2
       674: 2
       675: 2
       676: 2
       678: 2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       733: 1
       734: 1
       735: 1
       736: 1
       795: 1
       796: 1
       797: 1
       798: 1
       815: 1
       816: 1
       869: 1
       877: 1
       881: 1
       882: 1
      1075: 1

1076:    0: q^3+10q^2+16q+4
         1: q^3+10q^2+16q+4
         2: 3q^3+10q^2+12q+4
         3: q^3+10q^2+16q+4
         4: 3q^3+10q^2+12q+4
         5: q^3+10q^2+16q+4
         6: q^4+5q^3+11q^2+12q+4
         7: 3q^3+7q^2+9q+4
         8: 3q^3+10q^2+12q+4
         9: 3q^3+7q^2+9q+4
        10: 4q^2+14q+4
        11: 4q^2+14q+4
        12: q^3+7q^2+10q+4
        13: 6q^2+12q+4
        14: q^3+5q^2+9q+4
        15: 6q^2+12q+4
        16: q^3+10q^2+16q+4
        17: q^3+10q^2+16q+4
        18: 3q^3+7q^2+9q+4
        19: 6q^2+12q+4
        20: q^3+7q^2+12q+4
        21: q^3+5q^2+9q+4
        22: q^3+10q^2+16q+4
        23: q^3+10q^2+16q+4
        24: 3q^3+10q^2+12q+4
        25: 2q^2+10q+4
        26: 2q^2+10q+4
        27: 4q^2+8q+4
        28: 4q^2+14q+4
        29: 3q^2+10q+4
        30: 3q^2+9q+4
        31: 4q^2+14q+4
        32: 6q^2+12q+4
        33: q^3+10q^2+16q+4
        34: 8q+4
        35: 2q^2+8q+4
        36: 2q^2+10q+4
        37: q^2+5q+2
        38: q^2+5q+2
        39: q^2+5q+2
        40: q^2+5q+2
        41: 2q^2+4q+2
        42: 2q^2+4q+2
        43: q^2+10q+4
        44: 3q^2+7q+4
        45: q^2+10q+4
        46: 6q^2+12q+4
        47: 6q^2+12q+4
        48: q^3+5q^2+9q+4
        49: 6q^2+12q+4
        50: q^3+7q^2+12q+4
        51: q^3+5q^2+9q+4
        52: 6q^2+12q+4
        53: q^3+7q^2+12q+4
        54: q^3+5q^2+9q+4
        55: 6q+4
        56: 6q+4
        57: q^2+5q+4
        58: 2q^2+7q+2
        59: 2q^2+7q+2
        60: 4q+2
        61: 4q+2
        62: 4q+2
        63: 4q+2
        64: q^2+4q+2
        65: q^2+4q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 6q+4
        69: 3q^2+9q+4
        70: q^2+7q+4
        71: 3q^2+10q+4
        72: 4q+4
        73: 3q^2+8q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: q^2+10q+4
        81: 6q^2+12q+4
        82: 3q^2+10q+4
        83: 3q^2+9q+4
        84: 6q+4
        85: 2q^2+8q+4
        86: 4q+4
        87: 5q+4
        88: q^2+10q+4
        89: q^2+10q+4
        90: 3q^2+7q+4
        91: q^2+7q+4
        92: 3q^2+8q+4
        93: q^2+7q+4
        94: 6q^2+12q+4
        95: q^3+7q^2+12q+4
        96: q^3+5q^2+9q+4
        97: 6q+4
        98: 6q+4
        99: q^2+5q+4
       100: 6q+4
       101: 6q+4
       102: q^2+5q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q^2+3q+2
       110: q^2+3q+2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 3q+2
       118: 3q+2
       119: 2q+2
       120: 2q+2
       121: 3q+2
       122: 3q+2
       123: q^2+4q+2
       124: q^2+4q+2
       125: 6q+4
       126: q^2+7q+4
       127: 2q+2
       128: 2q+2
       129: 2q+2
       130: 2q+2
       131: 2q+2
       132: 2q+2
       133: 3q+4
       134: q^2+7q+4
       135: 3q+4
       136: 5q+4
       137: q^2+10q+4
       138: 3q^2+9q+4
       139: 3q^2+10q+4
       140: 4q+4
       141: q^2+7q+4
       142: 3q^2+8q+4
       143: 6q+4
       144: 5q+4
       145: 4q+4
       146: 3q+4
       147: 4q+4
       149: 4q+4
       150: 5q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 3q+4
       158: 4q+4
       159: 3q+4
       160: q^2+7q+4
       161: 3q^2+8q+4
       162: q^2+7q+4
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 6q+4
       167: 6q+4
       168: q^2+5q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: 2q+2
       178: 2q+2
       179: q+2
       180: q+2
       181: q+2
       182: q+2
       183: 2
       184: 2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 3q+2
       192: 3q+2
       193: q+2
       194: q+2
       195: q^2+3q+2
       196: q^2+3q+2
       197: q+2
       198: q+2
       199: 2q+2
       200: 2q+2
       201: q+2
       202: q+2
       207: 3q+2
       208: 3q+2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       219: 3q+4
       220: q+4
       221: 3q+4
       222: q+4
       223: 3q+4
       224: q+4
       225: 5q+4
       226: q^2+7q+4
       227: 3q+4
       228: q^2+7q+4
       229: 3q+4
       230: 5q+4
       231: 3q+4
       232: q+2
       233: 2q+2
       234: q+2
       236: 5q+4
       237: 2q+2
       238: 2q+2
       239: 2q+2
       240: 2q+2
       241: 2q+2
       242: 2q+2
       243: 4q+4
       244: 4q+4
       246: 3q+4
       247: 4
       248: 4
       249: 2q+2
       250: 3q+4
       251: 4q+4
       252: 3q+4
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2
       284: 2
       285: q+2
       286: q+2
       287: q+2
       288: q+2
       291: q+2
       292: q+2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       301: q+2
       302: q+2
       303: q+2
       304: q+2
       305: q+2
       306: q+2
       307: 1
       308: 1
       315: 2q+2
       316: 2q+2
       317: q+2
       318: q+2
       319: q+2
       320: q+2
       325: q+2
       326: q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 3q+4
       345: q+4
       346: 3q+4
       347: q+4
       348: 3q+4
       349: q+4
       350: 5q+4
       351: 4
       352: q+2
       356: q+2
       366: 3q+4
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       429: 2
       430: 2
       431: q+2
       432: q+2
       433: q+2
       434: q+2
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       469: q+2
       470: q+2
       471: 1
       472: 1
       481: 2
       482: 2
       483: 2
       484: 2
       491: 1
       492: q+4
       493: q+4
       494: q+4
       495: 2
       496: 2
       508: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       604: 2
       607: 2
       608: 2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 1
       616: 1
       641: 1
       642: 1
       657: 2
       664: 1
       665: 1
       674: 2
       675: 2
       676: 2
       677: 2
       679: 1
       725: 1
       726: 1
       727: 1
       728: 1
       793: 1
       794: 1
       801: 1
       802: 1
       807: 1
       808: 1
       811: 1
       812: 1
       866: 1
       870: 1
       871: 1
      1076: 1

1077:    0: 4q+4
         1: 4q+4
         2: q^3+2q^2+3q+2
         3: 4q+4
         4: 4q+4
         5: 4q+4
         6: 4q+4
         7: q^3+2q^2+3q+2
         8: q^3+2q^2+3q+2
         9: q^3+2q^2+3q+2
        10: 4q+4
        11: 4q+4
        12: 4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4q+4
        17: 4q+4
        18: q^3+2q^2+3q+2
        19: 4q+4
        20: 4q+4
        21: q^3+2q^2+3q+2
        22: 4q+4
        23: 4q+4
        24: q^3+2q^2+3q+2
        25: 4
        26: 4
        27: 2q+2
        28: 4q+4
        29: 4q+4
        30: q+2
        31: 4q+4
        32: q+2
        33: 4q+4
        34: 4
        35: 2
        36: 4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 4q+4
        50: 4q+4
        51: q^3+2q^2+3q+2
        52: 4q+4
        53: 4q+4
        54: q^3+2q^2+3q+2
        55: 4
        56: 4
        57: 2q+2
        58: 2q+2
        59: 2q+2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: q+2
        70: q+2
        71: 4q+4
        72: 4
        73: 4q+4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: q+2
        81: q+2
        82: 4q+4
        83: q+2
        84: 2
        85: 2
        86: 4
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 4q+4
        95: 4q+4
        96: q^3+2q^2+3q+2
        97: 4
        98: 4
        99: 2q+2
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       134: q+2
       135: 2
       136: q+2
       137: q+2
       138: q+2
       139: 4q+4
       140: 4
       141: q+2
       142: 4q+4
       143: 2
       144: 2
       145: 4
       146: 2
       147: 4
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: 1
       164: 1
       165: 1
       166: 4
       167: 4
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       193: 2
       194: 2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       201: 2
       202: 2
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: q+2
       222: 2
       223: 2
       224: q+2
       225: q+2
       226: q+2
       228: q+2
       229: 2
       230: q+2
       231: 2
       233: 1
       234: 1
       236: 2
       237: 2
       238: 2
       239: 2
       240: 2
       241: q+1
       242: q+1
       243: 4
       244: 4
       246: 2
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       267: 1
       268: 1
       269: 1
       270: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       301: 2
       302: 2
       305: 1
       306: 1
       315: 1
       316: 1
       317: 2
       318: 2
       319: 2
       320: 2
       325: 1
       326: 1
       334: 2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q+2
       351: 4
       354: 1
       355: 1
       356: 1
       366: 2
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       390: 1
       391: 1
       392: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       433: 1
       434: 1
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       469: 1
       470: 1
       483: 2
       491: 1
       493: 2
       494: q+2
       495: 2
       496: 1
       498: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       545: 1
       546: 1
       547: 1
       548: 1
       599: 1
       600: 1
       609: 1
       610: 1
       613: 1
       614: 1
       664: 1
       673: 1
       674: 1
       677: 2
       678: 1
       679: 1
       687: 1
       690: 1
       691: 1
       692: 1
       811: 1
       812: 1
       867: 1
       869: 1
       870: 1
       872: 1
      1077: 1

1078:    0: q^2+4q+4
         1: q^2+4q+4
         2: q^2+4q+4
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: q^2+4q+4
         8: q^2+4q+4
         9: q^4+2q^3+3q^2+2q+1
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q^2+4q+4
        14: q^2+4q+4
        15: q^2+4q+4
        16: 4
        17: 4
        18: q^2+2q+1
        19: q^2+4q+4
        20: q^2+4q+4
        21: q^2+4q+4
        22: q^2+4q+4
        23: q^2+4q+4
        24: q^2+4q+4
        25: 2q+4
        26: 2q+4
        27: 2q+4
        28: 4
        29: q^2+4q+4
        30: q^2+4q+4
        31: q^2+4q+4
        32: q^2+4q+4
        33: 4
        34: 2q+4
        35: 2q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: q^2+4q+4
        44: q^2+4q+4
        45: q^2+4q+4
        46: 4
        47: 4
        48: q^2+2q+1
        49: 4
        50: 4
        51: q^2+2q+1
        52: q^2+4q+4
        53: q^2+4q+4
        54: q^2+4q+4
        55: 2q+4
        56: 2q+4
        57: 2q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: 4
        69: 1
        70: q^2+4q+4
        71: 4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: q^2+4q+4
        81: 4
        82: q^2+4q+4
        83: q^2+4q+4
        84: 2q+4
        85: 4
        86: 2q+4
        87: 2q+4
        88: 4
        89: 4
        90: q^2+2q+1
        91: 4
        92: 4
        93: q^2+2q+1
        94: 4
        95: 4
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+4
       101: 2q+4
       102: 2q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 4
       134: 1
       135: 4
       136: 4
       137: 4
       138: 1
       139: 4
       140: 4
       141: q^2+4q+4
       142: 4
       143: 4
       144: 1
       145: 2
       146: 2q+4
       147: 2
       149: 2q+4
       150: 2q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: 4
       158: 4
       159: q^2+2q+1
       160: 4
       161: 4
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2
       192: 2
       193: 2
       194: 2
       195: 2
       196: 2
       197: 2
       198: 2
       199: 2
       200: 2
       201: 1
       202: 1
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       219: 1
       220: 4
       221: 1
       222: 4
       223: 1
       224: 4
       225: 1
       226: 1
       227: 4
       228: 1
       229: 4
       230: 4
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       243: 2
       244: 2
       246: 2q+4
       247: 2
       248: 2
       249: q+1
       250: 4
       251: 4
       252: q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       303: 2
       304: 2
       305: 2
       306: 2
       307: 1
       308: 1
       319: 1
       320: 1
       325: q+2
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 4
       346: 1
       347: 4
       348: 1
       349: 4
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       386: 1
       387: 1
       388: 1
       393: 1
       394: 1
       395: 1
       396: 1
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 1
       444: 1
       453: 1
       454: 1
       471: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       518: 2
       519: 2
       520: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       615: 1
       616: 1
       647: 1
       648: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       686: 1
       687: 1
       815: 1
       816: 1
       868: 1
       871: 1
       872: 1
       877: 1
      1078: 1

1079:    0: q^3+9q^2+16q+4
         1: 2q^3+14q^2+16q+4
         2: q^3+9q^2+16q+4
         3: 2q^3+14q^2+16q+4
         4: q^3+7q^2+12q+4
         5: q^3+9q^2+16q+4
         6: q^4+6q^3+13q^2+12q+4
         7: q^3+7q^2+12q+4
         8: q^3+9q^2+16q+4
         9: q^3+4q^2+5q+2
        10: 5q^2+14q+4
        11: 5q^2+14q+4
        12: q^3+6q^2+10q+4
        13: q^3+9q^2+16q+4
        14: q^3+7q^2+12q+4
        15: q^3+9q^2+16q+4
        16: 5q^2+14q+4
        17: 5q^2+14q+4
        18: 2q^2+5q+2
        19: 3q^2+12q+4
        20: q^3+9q^2+12q+4
        21: 3q^2+12q+4
        22: 4q^2+12q+4
        23: 8q^2+12q+4
        24: 4q^2+12q+4
        25: q^3+9q^2+16q+4
        26: 2q^3+14q^2+16q+4
        27: q^3+9q^2+16q+4
        28: 2q^2+12q+4
        29: 2q^2+10q+4
        30: 3q^2+12q+4
        31: 2q^2+10q+4
        32: 4q^2+12q+4
        33: 2q^2+10q+4
        34: 5q^2+14q+4
        35: q^3+9q^2+16q+4
        36: 5q^2+14q+4
        37: 2q^2+6q+2
        38: 2q^2+6q+2
        39: 4q^2+6q+2
        40: 4q^2+6q+2
        41: 2q^2+6q+2
        42: 2q^2+6q+2
        43: 5q^2+14q+4
        44: q^3+6q^2+10q+4
        45: 5q^2+14q+4
        46: 5q^2+14q+4
        47: 5q^2+14q+4
        48: 2q^2+5q+2
        49: q^2+10q+4
        50: 3q^2+10q+4
        51: q^2+5q+2
        52: 8q+4
        53: 4q^2+8q+4
        54: 8q+4
        55: 3q^2+12q+4
        56: q^3+9q^2+12q+4
        57: 3q^2+12q+4
        58: 4q+2
        59: 4q+2
        60: q^2+6q+2
        61: q^2+6q+2
        62: q^2+5q+2
        63: q^2+5q+2
        64: 2q^2+6q+2
        65: 2q^2+6q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 2q^2+12q+4
        69: 3q+2
        70: 2q^2+10q+4
        71: q^2+8q+4
        72: 6q+4
        73: 4q+4
        74: 3q+2
        75: 3q+2
        76: q^2+3q+2
        77: q^2+3q+2
        78: 3q+2
        79: 3q+2
        80: 2q^2+10q+4
        81: 2q^2+10q+4
        82: 6q+4
        83: 8q+4
        84: 5q^2+14q+4
        85: 5q^2+14q+4
        86: 2q^2+10q+4
        87: 3q^2+12q+4
        88: 6q+4
        89: 6q+4
        90: q^2+3q+2
        91: q^2+10q+4
        92: 3q^2+10q+4
        93: q^2+5q+2
        94: 5q+4
        95: q^2+5q+4
        96: 3q+2
        97: q^2+10q+4
        98: 3q^2+10q+4
        99: q^2+5q+2
       100: 8q+4
       101: 4q^2+8q+4
       102: 8q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+2
       108: 2q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: 2q+2
       114: 2q+2
       115: 3q+2
       116: 3q+2
       117: 4q+2
       118: 4q+2
       119: q^2+6q+2
       120: q^2+6q+2
       121: q^2+5q+2
       122: q^2+5q+2
       123: q^2+5q+2
       124: q^2+5q+2
       125: 6q+4
       126: q+2
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+1
       132: q+1
       133: q^2+8q+4
       134: 3q+2
       135: 6q+4
       136: 4q+4
       137: 4q+4
       138: q+2
       139: 4q+4
       141: 6q+4
       142: 3q+4
       143: 6q+4
       144: 3q+2
       145: q^2+8q+4
       146: 2q^2+10q+4
       147: 6q+4
       148: 4q+4
       149: 6q+4
       150: 8q+4
       151: 3q+2
       152: 3q+2
       153: q^2+3q+2
       154: q^2+3q+2
       155: 3q+2
       156: 3q+2
       157: 2q+4
       158: 2q+4
       159: 2q+2
       160: 5q+4
       161: q^2+5q+4
       162: 3q+2
       163: q^2+10q+4
       164: 3q^2+10q+4
       165: q^2+5q+2
       166: 5q+4
       167: q^2+5q+4
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: 1
       178: 1
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2q+2
       184: 2q+2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: 2q+2
       190: 2q+2
       191: 2q+2
       192: 2q+2
       195: q+2
       196: q+2
       199: 3q+2
       200: 3q+2
       201: 2q+2
       202: 2q+2
       203: q+2
       204: q+2
       205: q+2
       206: q+2
       207: 2q+2
       208: 2q+2
       209: 2q+2
       210: 2q+2
       211: 3q+2
       212: 3q+2
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+1
       218: q+1
       219: q+2
       220: 2q+4
       221: 2
       222: 4
       223: 2q+2
       224: 4
       225: q+2
       226: 2
       227: 4q+4
       228: q+2
       230: 3q+4
       231: q+2
       232: q^2+8q+4
       233: 3q+2
       234: 6q+4
       235: 4q+4
       236: q+2
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+1
       242: q+1
       243: 4q+4
       245: 3q+4
       246: 6q+4
       247: q+4
       248: q+4
       250: q+2
       251: q+2
       252: q+1
       253: 2q+4
       254: 2q+4
       255: 2q+2
       256: 5q+4
       257: q^2+5q+4
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: q+2
       304: q+2
       307: 2q+2
       308: 2q+2
       309: q+2
       310: q+2
       311: 2
       312: 2
       313: q+2
       314: q+2
       315: 1
       316: 1
       317: q+2
       318: q+2
       321: q+2
       322: q+2
       325: 2q+2
       326: 2q+2
       333: 2
       334: 2
       335: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       344: 2
       345: q+2
       346: 1
       349: 2
       350: q+2
       352: q+2
       353: 2q+4
       354: 2
       355: 4
       356: 2q+2
       357: 4
       358: q+2
       359: q+4
       360: q+2
       361: q+2
       362: q+2
       363: q+2
       364: q+1
       365: q+1
       366: 2
       367: 4q+4
       368: q+2
       370: 3q+4
       371: q+4
       372: q+4
       374: q+2
       375: q+2
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       427: 2
       428: 2
       439: 1
       440: 1
       451: 1
       452: 1
       453: 2
       454: 2
       455: 2
       456: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       465: q+2
       466: q+2
       467: 1
       468: 1
       469: 1
       470: 1
       473: q+2
       474: q+2
       481: 2
       482: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       492: 1
       494: 1
       497: 2
       498: 2
       499: 2
       501: q+4
       508: 2
       509: q+2
       510: 1
       513: 2
       514: q+2
       515: 2
       516: 2
       518: 2
       519: 2
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       585: 1
       586: 1
       601: 2
       602: 2
       623: 1
       624: 1
       625: 1
       626: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: 1
       640: 1
       649: 1
       650: 1
       658: 1
       659: 1
       660: 1
       661: 1
       672: 2
       676: 1
       680: 2
       681: 2
       682: 2
       684: 2
       686: 1
       688: 1
       690: 1
       691: 1
       749: 1
       750: 1
       751: 1
       752: 1
       819: 1
       820: 1
       821: 1
       822: 1
       839: 1
       840: 1
       873: 1
       878: 1
       881: 1
       882: 1
      1079: 1

1080:    0: q^3+10q^2+16q+4
         1: q^3+10q^2+16q+4
         2: 3q^3+10q^2+12q+4
         3: q^3+10q^2+16q+4
         4: 3q^3+10q^2+12q+4
         5: q^3+10q^2+16q+4
         6: q^4+5q^3+11q^2+12q+4
         7: 3q^3+7q^2+9q+4
         8: 3q^3+10q^2+12q+4
         9: 3q^3+7q^2+9q+4
        10: 4q^2+14q+4
        11: 4q^2+14q+4
        12: q^3+7q^2+10q+4
        13: 6q^2+12q+4
        14: q^3+5q^2+9q+4
        15: 6q^2+12q+4
        16: q^3+10q^2+16q+4
        17: q^3+10q^2+16q+4
        18: 3q^3+7q^2+9q+4
        19: 6q^2+12q+4
        20: q^3+7q^2+12q+4
        21: q^3+5q^2+9q+4
        22: 2q^2+10q+4
        23: 2q^2+10q+4
        24: 4q^2+8q+4
        25: q^3+10q^2+16q+4
        26: q^3+10q^2+16q+4
        27: 3q^3+10q^2+12q+4
        28: 4q^2+14q+4
        29: 3q^2+10q+4
        30: 3q^2+9q+4
        31: 8q+4
        32: 2q^2+8q+4
        33: 2q^2+10q+4
        34: 4q^2+14q+4
        35: 6q^2+12q+4
        36: q^3+10q^2+16q+4
        37: q^2+5q+2
        38: q^2+5q+2
        39: q^2+5q+2
        40: q^2+5q+2
        41: 2q^2+4q+2
        42: 2q^2+4q+2
        43: q^2+10q+4
        44: 3q^2+7q+4
        45: q^2+10q+4
        46: 6q^2+12q+4
        47: 6q^2+12q+4
        48: q^3+5q^2+9q+4
        49: 6q^2+12q+4
        50: q^3+7q^2+12q+4
        51: q^3+5q^2+9q+4
        52: 6q+4
        53: 6q+4
        54: q^2+5q+4
        55: 6q^2+12q+4
        56: q^3+7q^2+12q+4
        57: q^3+5q^2+9q+4
        58: 4q+2
        59: 4q+2
        60: 2q^2+7q+2
        61: 2q^2+7q+2
        62: 4q+2
        63: 4q+2
        64: q^2+4q+2
        65: q^2+4q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 6q+4
        69: 3q^2+9q+4
        70: q^2+7q+4
        71: 3q^2+10q+4
        72: 3q^2+8q+4
        73: 4q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: 6q+4
        81: 2q^2+8q+4
        82: 4q+4
        83: 5q+4
        84: q^2+10q+4
        85: 6q^2+12q+4
        86: 3q^2+10q+4
        87: 3q^2+9q+4
        88: q^2+10q+4
        89: q^2+10q+4
        90: 3q^2+7q+4
        91: q^2+7q+4
        92: 3q^2+8q+4
        93: q^2+7q+4
        94: 6q+4
        95: 6q+4
        96: q^2+5q+4
        97: 6q^2+12q+4
        98: q^3+7q^2+12q+4
        99: q^3+5q^2+9q+4
       100: 6q+4
       101: 6q+4
       102: q^2+5q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q^2+3q+2
       108: q^2+3q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 2q+2
       118: 2q+2
       119: 3q+2
       120: 3q+2
       121: 3q+2
       122: 3q+2
       123: q^2+4q+2
       124: q^2+4q+2
       125: 6q+4
       126: q^2+7q+4
       127: 2q+2
       128: 2q+2
       129: 2q+2
       130: 2q+2
       131: 2q+2
       132: 2q+2
       133: 3q+4
       134: q^2+7q+4
       135: 5q+4
       136: 3q+4
       137: 6q+4
       138: 5q+4
       139: 4q+4
       141: 3q+4
       142: 4q+4
       143: q^2+10q+4
       144: 3q^2+9q+4
       145: 3q^2+10q+4
       146: q^2+7q+4
       147: 3q^2+8q+4
       148: 4q+4
       149: 4q+4
       150: 5q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 3q+4
       158: 4q+4
       159: 3q+4
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q^2+7q+4
       164: 3q^2+8q+4
       165: q^2+7q+4
       166: 6q+4
       167: 6q+4
       168: q^2+5q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: 2q+2
       178: 2q+2
       179: q+2
       180: q+2
       181: q+2
       182: q+2
       183: q+2
       184: q+2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2q+2
       192: 2q+2
       195: q+2
       196: q+2
       199: 3q+2
       200: 3q+2
       201: q^2+3q+2
       202: q^2+3q+2
       203: q+2
       204: q+2
       205: q+2
       206: q+2
       207: 3q+2
       208: 3q+2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       219: 3q+4
       220: q+4
       221: 3q+4
       222: q+4
       223: 5q+4
       224: q+4
       225: 3q+4
       226: 3q+4
       227: q+2
       228: 2q+2
       230: q+2
       231: q^2+7q+4
       232: 3q+4
       233: q^2+7q+4
       234: 5q+4
       235: 3q+4
       236: 5q+4
       237: 2q+2
       238: 2q+2
       239: 2q+2
       240: 2q+2
       241: 2q+2
       242: 2q+2
       243: 4q+4
       245: 4q+4
       246: 3q+4
       247: 4
       248: 4
       249: 2q+2
       253: 3q+4
       254: 4q+4
       255: 3q+4
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: q+2
       284: q+2
       285: 2
       286: 2
       287: q+2
       288: q+2
       291: q+2
       292: q+2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: q+2
       308: q+2
       309: 2
       310: 2
       311: q+2
       312: q+2
       313: q+2
       314: q+2
       315: 2q+2
       316: 2q+2
       317: q+2
       318: q+2
       321: q+2
       322: q+2
       325: q+2
       326: q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       350: q+2
       352: 3q+4
       353: q+4
       354: 3q+4
       355: q+4
       356: 5q+4
       357: q+4
       358: 3q+4
       359: 4
       366: 3q+4
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       431: 1
       432: 1
       447: q+2
       448: q+2
       449: 2
       450: 2
       451: q+2
       452: q+2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+2
       470: q+2
       473: 1
       474: 1
       481: 2
       482: 2
       483: 2
       484: 2
       491: 1
       497: q+4
       498: q+4
       499: q+4
       500: 2
       501: 2
       508: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       549: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       619: 2
       620: 2
       621: 2
       622: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 1
       632: 1
       643: 1
       644: 1
       657: 2
       664: 1
       665: 1
       680: 2
       681: 2
       682: 2
       683: 2
       685: 1
       741: 1
       742: 1
       743: 1
       744: 1
       817: 1
       818: 1
       825: 1
       826: 1
       831: 1
       832: 1
       835: 1
       836: 1
       866: 1
       874: 1
       875: 1
      1080: 1

1081:    0: 4q+4
         1: 4q+4
         2: q^3+2q^2+3q+2
         3: 4q+4
         4: 4q+4
         5: 4q+4
         6: 4q+4
         7: q^3+2q^2+3q+2
         8: q^3+2q^2+3q+2
         9: q^3+2q^2+3q+2
        10: 4q+4
        11: 4q+4
        12: 4q+4
        13: q+2
        14: q+2
        15: q+2
        16: 4q+4
        17: 4q+4
        18: q^3+2q^2+3q+2
        19: 4q+4
        20: 4q+4
        21: q^3+2q^2+3q+2
        22: 4
        23: 4
        24: 2q+2
        25: 4q+4
        26: 4q+4
        27: q^3+2q^2+3q+2
        28: 4q+4
        29: 4q+4
        30: q+2
        31: 4
        32: 2
        33: 4
        34: 4q+4
        35: q+2
        36: 4q+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: q+1
        42: q+1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 4q+4
        50: 4q+4
        51: q^3+2q^2+3q+2
        52: 4
        53: 4
        54: 2q+2
        55: 4q+4
        56: 4q+4
        57: q^3+2q^2+3q+2
        58: 2
        59: 2
        60: 2q+2
        61: 2q+2
        62: 2
        63: 2
        64: 1
        65: 1
        66: 2
        67: 2
        69: q+2
        70: q+2
        71: 4q+4
        72: 4q+4
        73: 4
        74: 2
        75: 2
        76: 2
        77: 2
        78: q+1
        79: q+1
        80: 2
        81: 2
        82: 4
        83: 2
        84: q+2
        85: q+2
        86: 4q+4
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 4
        95: 4
        96: 2q+2
        97: 4q+4
        98: 4q+4
        99: q^3+2q^2+3q+2
       100: 4
       101: 4
       102: 2q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2q+2
       108: 2q+2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 1
       116: 1
       121: 1
       122: 1
       123: 1
       124: 1
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       134: q+2
       135: q+2
       136: 2
       137: 2
       138: 2
       139: 4
       141: 2
       142: 4
       143: q+2
       144: q+2
       145: 4q+4
       146: q+2
       147: 4q+4
       148: 4
       149: 4
       150: 2
       151: 2
       152: 2
       153: 2
       154: 2
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: q+2
       164: q+2
       165: q+2
       166: 4
       167: 4
       168: 2q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       187: 1
       188: 1
       189: 1
       190: 1
       195: 2
       196: 2
       201: 2q+2
       202: 2q+2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 1
       208: 1
       209: 2
       210: 2
       211: 1
       212: 1
       221: q+2
       222: q+2
       223: q+2
       224: 2
       225: 2
       226: 2
       228: 1
       230: 1
       231: q+2
       233: q+2
       234: q+2
       235: 2
       236: 2
       237: 2
       238: 2
       239: 2
       240: 2
       241: q+1
       242: q+1
       243: 4
       245: 4
       246: 2
       247: 4
       248: 4
       249: 2q+2
       250: 1
       251: 1
       252: 1
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       271: 1
       272: 1
       273: 1
       274: 1
       287: 1
       288: 1
       291: 1
       292: 1
       297: 1
       298: 1
       311: 2
       312: 2
       313: 1
       314: 1
       315: 1
       316: 1
       317: 2
       318: 2
       321: 2
       322: 2
       325: 1
       326: 1
       334: q+2
       335: 2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       346: 1
       349: 1
       350: 1
       354: q+2
       355: q+2
       356: q+2
       357: 2
       358: 2
       359: 4
       366: 2
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       397: 1
       398: 1
       399: 1
       400: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       451: 1
       452: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: 1
       470: 1
       483: 2
       491: 1
       494: 1
       498: q+2
       499: 2
       500: 2
       501: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       561: 1
       562: 1
       563: 1
       564: 1
       599: 1
       600: 1
       625: 1
       626: 1
       629: 1
       630: 1
       664: 1
       673: 1
       680: 1
       683: 2
       684: 1
       685: 1
       688: 1
       690: 1
       691: 1
       692: 1
       835: 1
       836: 1
       867: 1
       873: 1
       874: 1
       876: 1
      1081: 1

1082:    0: q^2+4q+4
         1: q^2+4q+4
         2: q^2+4q+4
         3: q^2+4q+4
         4: q^2+4q+4
         5: q^2+4q+4
         6: q^2+4q+4
         7: q^2+4q+4
         8: q^2+4q+4
         9: q^4+2q^3+3q^2+2q+1
        10: q^2+4q+4
        11: q^2+4q+4
        12: q^2+4q+4
        13: q^2+4q+4
        14: q^2+4q+4
        15: q^2+4q+4
        16: 4
        17: 4
        18: q^2+2q+1
        19: q^2+4q+4
        20: q^2+4q+4
        21: q^2+4q+4
        22: 2q+4
        23: 2q+4
        24: 2q+4
        25: q^2+4q+4
        26: q^2+4q+4
        27: q^2+4q+4
        28: 4
        29: q^2+4q+4
        30: q^2+4q+4
        31: 2q+4
        32: 2q+4
        33: 4
        34: q^2+4q+4
        35: q^2+4q+4
        36: 4
        37: q+2
        38: q+2
        39: q+2
        40: q+2
        41: q+2
        42: q+2
        43: q^2+4q+4
        44: q^2+4q+4
        45: q^2+4q+4
        46: 4
        47: 4
        48: q^2+2q+1
        49: 4
        50: 4
        51: q^2+2q+1
        52: 2q+4
        53: 2q+4
        54: 2q+4
        55: q^2+4q+4
        56: q^2+4q+4
        57: q^2+4q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: q+2
        65: q+2
        66: 2
        67: 2
        68: 4
        69: 1
        70: q^2+4q+4
        71: 4
        72: 4
        73: 4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 2q+4
        81: 4
        82: 2q+4
        83: 2q+4
        84: q^2+4q+4
        85: 4
        86: q^2+4q+4
        87: q^2+4q+4
        88: 4
        89: 4
        90: q^2+2q+1
        91: 4
        92: 4
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 4
        98: 4
        99: q^2+2q+1
       100: 2q+4
       101: 2q+4
       102: 2q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 4
       134: 1
       135: 4
       136: 4
       137: 4
       138: 1
       139: 2
       141: 2q+4
       142: 2
       143: 4
       144: 1
       145: 4
       146: q^2+4q+4
       147: 4
       148: 4
       149: 2q+4
       150: 2q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: 4
       158: 4
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 4
       164: 4
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: 1
       196: 1
       199: 2
       200: 2
       201: 2
       202: 2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       219: 1
       220: 4
       221: 1
       222: 4
       223: 1
       224: 4
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 4
       233: 1
       234: 4
       235: 4
       236: 1
       243: 2
       245: 2
       246: 2q+4
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 4
       254: 4
       255: q^2+2q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 2
       308: 2
       309: 2
       310: 2
       313: 2
       314: 2
       321: 1
       322: 1
       325: q+2
       326: q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 4
       354: 1
       355: 4
       356: 1
       357: 4
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       386: 1
       387: 1
       388: 1
       401: 1
       402: 1
       403: 1
       404: 1
       439: 1
       440: 1
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 1
       462: 1
       473: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       631: 1
       632: 1
       649: 1
       650: 1
       665: 1
       672: 2
       673: 1
       676: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       688: 1
       839: 1
       840: 1
       868: 1
       875: 1
       876: 1
       878: 1
      1082: 1

1083:    0: 6q^2+16q+4
         1: 2q^3+10q^2+16q+4
         2: 6q^2+16q+4
         3: 2q^3+10q^2+16q+4
         4: 3q^3+7q^2+12q+4
         5: 6q^2+16q+4
         6: q^4+5q^3+10q^2+12q+4
         7: 3q^3+7q^2+12q+4
         8: 6q^2+16q+4
         9: q^4+4q^3+5q^2+4q+1
        10: 2q^2+14q+4
        11: 2q^2+14q+4
        12: q^3+5q^2+10q+4
        13: 6q^2+16q+4
        14: 3q^3+7q^2+12q+4
        15: 6q^2+16q+4
        16: 2q^2+10q+4
        17: 2q^2+10q+4
        18: q^3+3q^2+4q+1
        19: 3q^2+12q+4
        20: q^3+6q^2+12q+4
        21: 3q^2+12q+4
        22: 6q^2+16q+4
        23: 2q^3+10q^2+16q+4
        24: 6q^2+16q+4
        25: 6q^2+16q+4
        26: 2q^3+10q^2+16q+4
        27: 6q^2+16q+4
        28: 8q+4
        29: q^2+10q+4
        30: 3q^2+12q+4
        31: 2q^2+14q+4
        32: 6q^2+16q+4
        33: 2q^2+10q+4
        34: 2q^2+14q+4
        35: 6q^2+16q+4
        36: 2q^2+10q+4
        37: 3q^2+8q+2
        38: 3q^2+8q+2
        39: q^3+5q^2+8q+2
        40: q^3+5q^2+8q+2
        41: 3q^2+8q+2
        42: 3q^2+8q+2
        43: 2q^2+14q+4
        44: q^3+5q^2+10q+4
        45: 2q^2+14q+4
        46: 2q^2+10q+4
        47: 2q^2+10q+4
        48: q^3+3q^2+4q+1
        49: 6q+4
        50: 6q+4
        51: q^2+4q+1
        52: 3q^2+12q+4
        53: q^3+6q^2+12q+4
        54: 3q^2+12q+4
        55: 3q^2+12q+4
        56: q^3+6q^2+12q+4
        57: 3q^2+12q+4
        58: 4q+2
        59: 4q+2
        60: 4q+2
        61: 4q+2
        62: q^2+7q+2
        63: q^2+7q+2
        64: 3q^2+8q+2
        65: 3q^2+8q+2
        66: q^2+5q+2
        67: q^2+5q+2
        68: 8q+4
        69: 2q+1
        70: q^2+10q+4
        71: 4q+4
        72: 4q+4
        73: 4q+4
        74: 4q+2
        75: 4q+2
        76: q^2+4q+2
        77: q^2+4q+2
        78: 4q+2
        79: 4q+2
        80: 2q^2+14q+4
        81: 2q^2+10q+4
        82: q^2+10q+4
        83: 3q^2+12q+4
        84: 2q^2+14q+4
        85: 2q^2+10q+4
        86: q^2+10q+4
        87: 3q^2+12q+4
        88: 4q+4
        89: 4q+4
        90: 2q^2+3q+1
        91: 6q+4
        92: 6q+4
        93: q^2+4q+1
        94: 6q+4
        95: 6q+4
        96: q^2+4q+1
        97: 6q+4
        98: 6q+4
        99: q^2+4q+1
       100: 3q^2+12q+4
       101: q^3+6q^2+12q+4
       102: 3q^2+12q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: q+2
       110: q+2
       111: q+2
       112: q+2
       113: 3q+2
       114: 3q+2
       115: 4q+2
       116: 4q+2
       117: 4q+2
       118: 4q+2
       119: 4q+2
       120: 4q+2
       121: q^2+7q+2
       122: q^2+7q+2
       123: q^2+5q+2
       124: q^2+5q+2
       125: 4q+4
       126: q+1
       133: 4q+4
       134: 2q+1
       135: 4q+4
       136: 4q+4
       137: 4q+4
       138: 2q+1
       139: 4q+4
       140: 4q+4
       141: q^2+10q+4
       142: 4q+4
       143: 4q+4
       144: 2q+1
       145: 4q+4
       146: q^2+10q+4
       147: 4q+4
       148: 4q+4
       149: q^2+10q+4
       150: 3q^2+12q+4
       151: 4q+2
       152: 4q+2
       153: q^2+4q+2
       154: q^2+4q+2
       155: 4q+2
       156: 4q+2
       157: 4
       158: 4
       159: 2q+1
       160: 6q+4
       161: 6q+4
       162: q^2+4q+1
       163: 6q+4
       164: 6q+4
       165: q^2+4q+1
       166: 6q+4
       167: 6q+4
       168: q^2+4q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       183: q+2
       184: q+2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: 3q+2
       190: 3q+2
       191: 2q+2
       192: 2q+2
       193: q+2
       194: q+2
       195: q+2
       196: q+2
       197: q+2
       198: q+2
       199: 2q+2
       200: 2q+2
       201: q+2
       202: q+2
       203: q+2
       204: q+2
       205: q+2
       206: q+2
       207: 2q+2
       208: 2q+2
       209: 3q+2
       210: 3q+2
       211: 4q+2
       212: 4q+2
       219: q+1
       220: 4
       221: 1
       222: 4
       223: q+1
       224: 4
       225: q+1
       226: q+1
       227: 4q+4
       228: 2q+1
       229: 4q+4
       230: 4q+4
       231: q+1
       232: 4q+4
       233: 2q+1
       234: 4q+4
       235: 4q+4
       236: 2q+1
       243: 4q+4
       244: 4q+4
       245: 4q+4
       246: q^2+10q+4
       247: 4
       248: 4
       249: 2q+1
       250: 4
       251: 4
       252: 2q+1
       253: 4
       254: 4
       255: 2q+1
       256: 6q+4
       257: 6q+4
       258: q^2+4q+1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: q+2
       300: q+2
       303: q+2
       304: q+2
       305: q+2
       306: q+2
       307: q+2
       308: q+2
       309: q+2
       310: q+2
       313: q+2
       314: q+2
       319: q+2
       320: q+2
       321: q+2
       322: q+2
       323: q+2
       324: q+2
       325: 3q+2
       326: 3q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 4
       344: q+1
       345: 4
       346: 1
       347: 4
       348: q+1
       349: 4
       350: q+1
       351: 4
       352: q+1
       353: 4
       354: 1
       355: 4
       356: q+1
       357: 4
       358: q+1
       359: 4
       366: q+1
       367: 4q+4
       368: 2q+1
       369: 4q+4
       370: 4q+4
       371: 4
       372: 4
       373: 2q+1
       374: 4
       375: 4
       376: 2q+1
       385: 1
       386: 1
       387: 1
       388: 1
       393: 1
       394: 1
       395: 1
       396: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 2
       444: 2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       471: q+2
       472: q+2
       473: q+2
       474: q+2
       475: q+2
       476: q+2
       479: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 4
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 4
       497: 1
       498: 1
       499: 1
       500: 1
       501: 4
       508: q+1
       509: 4
       510: 1
       511: 4
       512: q+1
       513: 4
       514: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       557: 1
       558: 1
       559: 1
       560: 1
       565: 1
       566: 1
       567: 1
       568: 1
       573: 1
       574: 1
       575: 1
       576: 1
       615: 2
       616: 2
       631: 2
       632: 2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 2
       656: 2
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
      1083: 1

1084:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^3+2q^2+3q+2
        19: 4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        30: 3q+2
        32: 4q+2
        33: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 4q+2
        50: 4q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        69: 3q+2
        72: 2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        81: 4q+2
        83: 3q+2
        85: 4q+2
        87: 3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: 4q+2
       101: 4q+2
       102: q^2+3q+2
       111: 1
       112: 1
       115: q+1
       116: q+1
       123: 2q+1
       124: 2q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: 2q+2
       135: q+2
       136: q+2
       138: 3q+2
       140: 2q+2
       142: 2q+2
       144: 3q+2
       147: 2q+2
       148: 2q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: q^2+3q+2
       177: q+1
       178: q+1
       181: 1
       182: 1
       187: 1
       188: 1
       197: 1
       198: 1
       205: 1
       206: 1
       211: q+1
       212: q+1
       223: q+2
       225: q+2
       228: 2q+2
       229: q+2
       230: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       244: 2q+2
       245: 2q+2
       247: 4
       248: 4
       249: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       291: 1
       292: 1
       301: 1
       302: 1
       305: 1
       306: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       323: 1
       324: 1
       336: 2
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       348: q+2
       350: q+2
       351: 4
       356: q+2
       358: q+2
       359: 4
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       425: 1
       426: 1
       433: 1
       434: 1
       445: 2
       446: 2
       451: 1
       452: 1
       463: 2
       464: 2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       491: 1
       495: 2
       496: 2
       500: 2
       501: 2
       512: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       577: 1
       578: 1
       580: 1
       581: 1
       613: 1
       614: 1
       629: 1
       630: 1
       645: 1
       646: 1
       655: 1
       656: 1
       664: 1
       674: 2
       679: 1
       680: 2
       685: 1
       689: 2
       843: 1
       844: 1
       855: 1
       856: 1
       870: 1
       874: 1
       880: 1
      1084: 1

1085:    0: 4q+4
         1: 4q+4
         2: 2q^2+4q+2
         3: 4q+4
         4: 4q+4
         5: 4q+4
         6: 4q+4
         7: 2q^2+4q+2
         8: 2q^2+4q+2
         9: q^4+2q^3+2q^2+2q+1
        10: 4q+4
        11: 4q+4
        12: 4q+4
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 4
        17: 4
        18: q^2+2q+1
        19: 4q+4
        20: 4q+4
        21: 2q^2+4q+2
        22: 4q+4
        23: 4q+4
        24: 2q^2+4q+2
        25: 4q+4
        26: 4q+4
        27: 2q^2+4q+2
        28: 4
        29: 4q+4
        30: 2q+2
        31: 4q+4
        32: 2q+2
        33: 4
        34: 4q+4
        35: 2q+2
        36: 4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: 4
        50: 4
        51: q^2+2q+1
        52: 4q+4
        53: 4q+4
        54: 2q^2+4q+2
        55: 4q+4
        56: 4q+4
        57: 2q^2+4q+2
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2q+2
        63: 2q+2
        64: q+1
        65: q+1
        66: 2
        67: 2
        69: 1
        70: 2q+2
        71: 4
        72: 4
        73: 4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+2
        81: 2
        82: 4q+4
        83: 2q+2
        84: 2q+2
        85: 2
        86: 4q+4
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 4
        95: 4
        96: q^2+2q+1
        97: 4
        98: 4
        99: q^2+2q+1
       100: 4q+4
       101: 4q+4
       102: 2q^2+4q+2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2q+2
       114: 2q+2
       115: q+1
       116: q+1
       121: q+1
       122: q+1
       123: 1
       124: 1
       126: 1
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 4
       140: 4
       141: 2q+2
       142: 4
       143: 2
       144: 1
       145: 4
       146: 2q+2
       147: 4
       148: 4
       149: 4q+4
       150: 2q+2
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: q^2+2q+1
       156: q^2+2q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 4
       167: 4
       168: q^2+2q+1
       169: 1
       170: 1
       171: 1
       172: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       193: 2
       194: 2
       195: 2
       196: 2
       197: 2
       198: 2
       201: 2
       202: 2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 1
       208: 1
       209: 2q+2
       210: 2q+2
       211: q+1
       212: q+1
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       228: 1
       229: 2
       230: 2
       231: 1
       233: 1
       234: 2
       235: 2
       236: 1
       243: 4
       244: 4
       245: 4
       246: 2q+2
       247: 4
       248: 4
       249: q^2+2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       297: 1
       298: 1
       305: 1
       306: 1
       313: 1
       314: 1
       319: 2
       320: 2
       321: 2
       322: 2
       323: 2
       324: 2
       325: q+1
       326: q+1
       334: 1
       335: 1
       336: 1
       337: 4
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 4
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 4
       366: 1
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       441: 1
       442: 1
       443: 2
       444: 2
       459: 1
       460: 1
       461: 2
       462: 2
       475: 1
       476: 1
       479: 2
       480: 2
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 2
       498: 1
       499: 1
       500: 1
       501: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       573: 1
       574: 1
       575: 1
       576: 1
       653: 1
       654: 1
       655: 1
       656: 1
       673: 1
       677: 1
       678: 2
       679: 1
       683: 1
       684: 2
       685: 1
       687: 1
       688: 1
       689: 1
       857: 1
       858: 1
       872: 1
       876: 1
       879: 1
       880: 1
      1085: 1

1086:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: 1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       377: 1
       381: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       521: 1
       533: 1
       537: 1
       545: 1
       549: 1
       553: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       601: 1
       605: 1
       615: 1
       617: 1
       623: 1
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: 1
       660: 1
       674: 1
       680: 1
       693: 1
       721: 1
       733: 1
       737: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       775: 1
       793: 1
       795: 1
       817: 1
       819: 1
       843: 1
       849: 1
       884: 1
       916: 1
       940: 1
       960: 1
       964: 1
       968: 1
      1086: 1

1087:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q^2+3q
         6: q^4+3q^3+3q^2+2q
         7: q^2+2q
         8: 3q^2+3q
         9: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q^2+3q
        14: q^2+2q
        15: 3q^2+3q
        16: 3q^2+3q
        17: 3q^2+3q
        18: q^2+2q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q^2+3q
        33: 3q^2+3q
        34: 3q
        35: 3q^2+3q
        36: 3q^2+3q
        37: q^2+q
        38: 2q^2+2q
        39: q^2+q
        40: 2q^2+2q
        41: q^2+q
        42: 2q^2+2q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q^2+3q
        47: 3q^2+3q
        48: q^2+2q
        49: 2q
        50: 2q^2+2q
        51: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: 2q
        59: q
        60: 2q
        61: q
        62: q
        63: 2q
        64: q^2+q
        65: 2q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: 3q
        69: 2q
        70: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: 3q
        81: 3q^2+3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q^2+3q
        86: 2q
        87: 2q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 2q
        95: 2q^2+2q
        96: 2q
        97: 2q
        98: 2q^2+2q
        99: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       104: q
       105: q
       107: q
       109: q
       114: q
       116: q
       117: 2q
       118: q
       119: 2q
       120: q
       121: q
       122: 2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q
       130: q^2+q
       132: q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 3q
       138: 2q
       139: 2q
       140: q
       141: 2q
       142: q
       143: 3q
       144: 2q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       152: q
       154: q^2+q
       156: q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 2q
       167: 2q^2+2q
       168: 2q
       173: q
       174: q
       175: q
       178: q
       180: q
       183: q
       185: q
       190: q
       191: 2q
       192: q
       193: q
       195: q
       199: 2q
       200: q
       201: q
       203: q
       207: q
       208: 2q
       210: q
       212: q
       214: q
       216: q^2+q
       218: q
       219: 2q
       223: q
       225: q
       226: 2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       238: q
       240: q^2+q
       242: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q
       276: q
       277: q
       280: q
       282: q
       283: q
       285: q
       288: q
       299: q
       303: q
       307: q
       309: q
       316: q
       318: q
       319: q
       321: q
       326: q
       337: 1
       339: 1
       341: 1
       344: 2q
       348: q
       350: q
       351: 1
       352: 2q
       356: q
       358: q
       359: 1
       361: q
       363: q^2+q
       365: q
       366: 2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       414: q
       428: 1
       429: q
       431: q
       443: 1
       446: 1
       447: q
       449: q
       461: 1
       464: 1
       466: q
       468: q
       470: q
       471: q
       473: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       508: 2q
       512: q
       514: q
       515: 1
       516: 1
       546: 1
       562: 1
       573: 1
       578: 1
       602: 1
       615: 1
       618: 1
       631: 1
       634: 1
       640: q
       641: q
       643: q
       655: 1
       657: 1
       659: 1
       661: 1
       674: 1
       680: 1
       694: 1
       734: 1
       750: 1
       765: 1
       770: 1
       776: 1
       793: 1
       796: 1
       817: 1
       820: 1
       843: 1
       885: 1
       917: 1
       941: 1
       964: 1
       969: 1
      1087: 1

1088:    0: q^3+2q^2+q
         1: q^4+q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^4+q^3+2q^2+q
         6: q^5+2q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^4+q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^4+q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^4+q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2+q
        39: 2q^2+q
        41: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^4+q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        58: q^2+q
        60: q^2+q
        62: q^2+q
        64: q^2+q
        66: 2q^2+q
        68: q
        69: q^3+q
        70: q^3+q
        71: q^3+q^2+q
        72: q^2+q
        73: q^2+q
        74: q^2+q
        76: 2q^2+q
        78: q
        80: q
        81: q^2+q
        82: q^2+q
        83: q
        84: q
        85: q^2+q
        86: q^2+q
        87: q
        88: q^3+q
        89: q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       103: q^2+q
       107: q^2+q
       109: q^2+q
       111: q^2+q
       113: q^2+q
       115: q
       117: q
       119: q
       121: q
       123: q^2+q
       125: q
       126: q^3+q
       127: q^2+q
       129: 2q^2+q
       131: q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^2+q
       140: q
       141: q
       142: q^2+q
       143: q
       144: q
       145: q^2+q
       146: q
       147: q^2+q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       169: q^2+q
       173: q
       177: q
       179: q^2+q
       181: q^2+q
       183: q
       185: q
       187: q
       189: q
       191: q
       193: q
       195: q^2+q
       197: q
       199: q
       201: q^2+q
       203: q
       205: q
       207: q
       209: q
       211: q
       213: q
       215: q^2+q
       217: q
       219: q
       223: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       243: q
       244: q
       245: q
       246: q
       259: q^2+q
       263: q
       267: q
       271: q
       275: q
       279: q
       281: q
       283: q
       285: q
       287: q
       289: q
       291: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q
       317: q
       319: q
       321: q
       323: q
       325: q
       344: q
       348: q
       350: q
       352: q
       356: q
       358: q
       366: q
       377: q
       381: q
       389: q
       393: q
       397: q
       401: q
       405: q
       413: q
       417: q
       429: q
       431: q
       433: q
       447: q
       449: q
       451: q
       469: q
       477: q
       521: q
       533: q
       549: q
       569: q
       651: 1
       757: 1
       771: 1
       849: 1
       886: 1
       960: 1
       970: 1
      1088: 1

1089:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q^2+3q
         6: q^4+3q^3+3q^2+2q
         7: q^2+2q
         8: 3q^2+3q
         9: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q^2+3q
        14: q^2+2q
        15: 3q^2+3q
        16: 3q^2+3q
        17: 3q^2+3q
        18: q^2+2q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q^2+3q
        33: 3q^2+3q
        34: 3q
        35: 3q^2+3q
        36: 3q^2+3q
        37: 2q^2+2q
        38: q^2+q
        39: 2q^2+2q
        40: q^2+q
        41: 2q^2+2q
        42: q^2+q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q^2+3q
        47: 3q^2+3q
        48: q^2+2q
        49: 2q
        50: 2q^2+2q
        51: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: q
        59: 2q
        60: 2q
        61: q
        62: 2q
        63: q
        64: 2q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: 3q
        69: 2q
        70: 2q
        71: 2q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: 3q
        81: 3q^2+3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q^2+3q
        86: 2q
        87: 2q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 2q
        95: 2q^2+2q
        96: 2q
        97: 2q
        98: 2q^2+2q
        99: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       104: q
       106: q
       107: q
       110: q
       113: q
       115: q
       117: q
       118: 2q
       119: 2q
       120: q
       121: 2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q
       129: q^2+q
       131: q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 3q
       138: 2q
       139: 2q
       140: q
       141: 2q
       142: q
       143: 3q
       144: 2q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       151: q
       153: q^2+q
       155: q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 2q
       167: 2q^2+2q
       168: 2q
       173: q
       174: q
       176: q
       177: q
       179: q
       183: q
       186: q
       189: q
       191: q
       192: 2q
       193: q
       196: q
       199: 2q
       200: q
       201: q
       204: q
       207: 2q
       208: q
       209: q
       211: q
       213: q
       215: q^2+q
       217: q
       219: 2q
       223: q
       225: q
       226: 2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       237: q
       239: q^2+q
       241: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q
       276: q
       278: q
       279: q
       281: q
       283: q
       286: q
       287: q
       299: q
       304: q
       307: q
       310: q
       315: q
       317: q
       319: q
       322: q
       325: q
       337: 1
       338: 1
       340: 1
       344: 2q
       348: q
       350: q
       351: 1
       352: 2q
       356: q
       358: q
       359: 1
       360: q
       362: q^2+q
       364: q
       366: 2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       413: q
       427: 1
       429: q
       432: q
       443: 1
       445: 1
       447: q
       450: q
       462: 1
       463: 1
       465: q
       467: q
       469: q
       471: q
       474: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       508: 2q
       512: q
       514: q
       515: 1
       516: 1
       545: 1
       563: 1
       574: 1
       580: 1
       601: 1
       615: 1
       617: 1
       632: 1
       633: 1
       639: q
       641: q
       644: q
       656: 1
       657: 1
       658: 1
       660: 1
       674: 1
       680: 1
       696: 1
       733: 1
       751: 1
       766: 1
       772: 1
       775: 1
       793: 1
       795: 1
       818: 1
       819: 1
       844: 1
       887: 1
       916: 1
       942: 1
       965: 1
       971: 1
      1089: 1

1090:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q^2+3q
         6: q^4+3q^3+3q^2+2q
         7: q^2+2q
         8: 3q^2+3q
         9: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q^2+3q
        14: q^2+2q
        15: 3q^2+3q
        16: 3q^2+3q
        17: 3q^2+3q
        18: q^2+2q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q^2+3q
        33: 3q^2+3q
        34: 3q
        35: 3q^2+3q
        36: 3q^2+3q
        37: 2q^2+2q
        38: q^2+q
        39: 2q^2+2q
        40: q^2+q
        41: 2q^2+2q
        42: q^2+q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q^2+3q
        47: 3q^2+3q
        48: q^2+2q
        49: 2q
        50: 2q^2+2q
        51: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: 2q
        59: q
        60: q
        61: 2q
        62: 2q
        63: q
        64: 2q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: 3q
        69: 2q
        70: 2q
        71: 2q
        72: q
        73: q
        74: q
        76: q^2+q
        78: q
        80: 3q
        81: 3q^2+3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q^2+3q
        86: 2q
        87: 2q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 2q
        95: 2q^2+2q
        96: 2q
        97: 2q
        98: 2q^2+2q
        99: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       103: q
       105: q
       106: q
       108: q
       109: q
       113: q
       115: q
       117: 2q
       118: q
       119: q
       120: 2q
       121: 2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q
       129: q^2+q
       131: q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 3q
       138: 2q
       139: 2q
       140: q
       141: 2q
       142: q
       143: 3q
       144: 2q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       151: q
       153: q^2+q
       155: q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 2q
       167: 2q^2+2q
       168: 2q
       173: q
       175: q
       176: q
       177: q
       179: q
       184: q
       185: q
       189: q
       191: 2q
       192: q
       194: q
       195: q
       199: q
       200: 2q
       202: q
       203: q
       207: 2q
       208: q
       209: q
       211: q
       213: q
       215: q^2+q
       217: q
       219: 2q
       223: q
       225: q
       226: 2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       237: q
       239: q^2+q
       241: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q
       277: q
       278: q
       279: q
       281: q
       284: q
       285: q
       287: q
       300: q
       303: q
       308: q
       309: q
       315: q
       317: q
       320: q
       321: q
       325: q
       337: 1
       338: 1
       340: 1
       344: 2q
       348: q
       350: q
       351: 1
       352: 2q
       356: q
       358: q
       359: 1
       360: q
       362: q^2+q
       364: q
       366: 2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       413: q
       427: 1
       430: q
       431: q
       444: 1
       445: 1
       448: q
       449: q
       461: 1
       463: 1
       465: q
       467: q
       469: q
       472: q
       473: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       508: 2q
       512: q
       514: q
       515: 1
       516: 1
       547: 1
       561: 1
       576: 1
       580: 1
       601: 1
       616: 1
       617: 1
       631: 1
       633: 1
       639: q
       642: q
       643: q
       656: 1
       657: 1
       658: 1
       660: 1
       674: 1
       680: 1
       698: 1
       735: 1
       749: 1
       767: 1
       772: 1
       775: 1
       794: 1
       795: 1
       817: 1
       819: 1
       844: 1
       888: 1
       918: 1
       940: 1
       966: 1
       971: 1
      1090: 1

1091:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: q+1
        78: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: 1
       129: q+1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: q+1
       217: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       337: 1
       338: 1
       340: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: 1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       380: 1
       384: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       524: 1
       536: 1
       539: 1
       547: 1
       552: 1
       555: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       601: 1
       605: 1
       616: 1
       617: 1
       623: 1
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: 1
       660: 1
       674: 1
       680: 1
       697: 1
       723: 1
       735: 1
       739: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       775: 1
       794: 1
       795: 1
       818: 1
       819: 1
       843: 1
       849: 1
       889: 1
       918: 1
       942: 1
       961: 1
       967: 1
       968: 1
      1091: 1

1092:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: 1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       378: 1
       382: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       418: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       522: 1
       534: 1
       538: 1
       546: 1
       551: 1
       556: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       602: 1
       606: 1
       615: 1
       618: 1
       624: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: 1
       661: 1
       674: 1
       680: 1
       699: 1
       722: 1
       734: 1
       740: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       776: 1
       793: 1
       796: 1
       818: 1
       820: 1
       844: 1
       850: 1
       890: 1
       917: 1
       943: 1
       962: 1
       965: 1
       972: 1
      1092: 1

1093:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q^2+q+1
         7: 1
         8: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: 1
        49: 1
        50: q+1
        51: 1
        52: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: q+1
        99: 1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: 1
       130: q+1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: q+1
       218: 1
       219: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       337: 1
       339: 1
       341: 1
       344: 1
       348: 1
       350: 1
       351: 1
       352: 1
       356: 1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       379: 1
       383: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       418: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: 1
       523: 1
       535: 1
       540: 1
       548: 1
       550: 1
       554: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       602: 1
       606: 1
       616: 1
       618: 1
       624: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: 1
       661: 1
       674: 1
       680: 1
       700: 1
       724: 1
       736: 1
       738: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       776: 1
       794: 1
       796: 1
       817: 1
       820: 1
       844: 1
       850: 1
       891: 1
       919: 1
       941: 1
       963: 1
       966: 1
       972: 1
      1093: 1

1094:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^2+2q
         5: 3q^2+3q
         6: q^4+3q^3+3q^2+2q
         7: q^2+2q
         8: 3q^2+3q
         9: q^2+2q
        10: 3q
        11: 3q
        12: q^2+2q
        13: 3q^2+3q
        14: q^2+2q
        15: 3q^2+3q
        16: 3q^2+3q
        17: 3q^2+3q
        18: q^2+2q
        19: 2q
        20: 2q^2+2q
        21: 2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q
        30: 2q
        31: 3q
        32: 3q^2+3q
        33: 3q^2+3q
        34: 3q
        35: 3q^2+3q
        36: 3q^2+3q
        37: q^2+q
        38: 2q^2+2q
        39: q^2+q
        40: 2q^2+2q
        41: q^2+q
        42: 2q^2+2q
        43: 3q
        44: q^2+2q
        45: 3q
        46: 3q^2+3q
        47: 3q^2+3q
        48: q^2+2q
        49: 2q
        50: 2q^2+2q
        51: 2q
        52: 2q
        53: 2q^2+2q
        54: 2q
        55: 2q
        56: 2q^2+2q
        57: 2q
        58: q
        59: 2q
        60: q
        61: 2q
        62: q
        63: 2q
        64: q^2+q
        65: 2q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: 3q
        69: 2q
        70: 2q
        71: 2q
        72: q
        73: q
        75: q
        77: q^2+q
        79: q
        80: 3q
        81: 3q^2+3q
        82: 2q
        83: 2q
        84: 3q
        85: 3q^2+3q
        86: 2q
        87: 2q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 2q
        95: 2q^2+2q
        96: 2q
        97: 2q
        98: 2q^2+2q
        99: 2q
       100: 2q
       101: 2q^2+2q
       102: 2q
       104: q
       105: q
       106: q
       108: q
       110: q
       114: q
       116: q
       117: q
       118: 2q
       119: q
       120: 2q
       121: q
       122: 2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q
       130: q^2+q
       132: q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 3q
       138: 2q
       139: 2q
       140: q
       141: 2q
       142: q
       143: 3q
       144: 2q
       145: 2q
       146: 2q
       147: q
       148: q
       149: 2q
       150: 2q
       152: q
       154: q^2+q
       156: q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 2q
       167: 2q^2+2q
       168: 2q
       174: q
       175: q
       176: q
       178: q
       180: q
       184: q
       186: q
       190: q
       191: q
       192: 2q
       194: q
       196: q
       199: q
       200: 2q
       202: q
       204: q
       207: q
       208: 2q
       210: q
       212: q
       214: q
       216: q^2+q
       218: q
       219: 2q
       223: q
       225: q
       226: 2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       238: q
       240: q^2+q
       242: q
       243: 2q
       244: q
       245: q
       246: 2q
       247: 1
       248: 1
       256: 2q
       257: 2q^2+2q
       258: 2q
       276: q
       277: q
       278: q
       280: q
       282: q
       284: q
       286: q
       288: q
       300: q
       304: q
       308: q
       310: q
       316: q
       318: q
       320: q
       322: q
       326: q
       337: 1
       339: 1
       341: 1
       344: 2q
       348: q
       350: q
       351: 1
       352: 2q
       356: q
       358: q
       359: 1
       361: q
       363: q^2+q
       365: q
       366: 2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       414: q
       428: 1
       430: q
       432: q
       444: 1
       446: 1
       448: q
       450: q
       462: 1
       464: 1
       466: q
       468: q
       470: q
       472: q
       474: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       508: 2q
       512: q
       514: q
       515: 1
       516: 1
       548: 1
       564: 1
       575: 1
       578: 1
       602: 1
       616: 1
       618: 1
       632: 1
       634: 1
       640: q
       642: q
       644: q
       655: 1
       657: 1
       659: 1
       661: 1
       674: 1
       680: 1
       701: 1
       736: 1
       752: 1
       768: 1
       770: 1
       776: 1
       794: 1
       796: 1
       818: 1
       820: 1
       843: 1
       892: 1
       919: 1
       943: 1
       967: 1
       969: 1
      1094: 1

1095:    0: q^3+2q^2+q
         1: q^4+q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^4+q^3+2q^2+q
         6: q^5+2q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^4+q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^4+q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^4+q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2+q
        39: 2q^2+q
        41: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^4+q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        59: q^2+q
        61: q^2+q
        62: q^2+q
        64: q^2+q
        66: 2q^2+q
        68: q
        69: q^3+q
        70: q^3+q
        71: q^3+q^2+q
        72: q^2+q
        73: q^2+q
        74: q^2+q
        76: 2q^2+q
        78: q
        80: q
        81: q^2+q
        82: q^2+q
        83: q
        84: q
        85: q^2+q
        86: q^2+q
        87: q
        88: q^3+q
        89: q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       106: q^2+q
       108: q^2+q
       110: q^2+q
       111: q^2+q
       113: q^2+q
       115: q
       118: q
       120: q
       121: q
       123: q^2+q
       125: q
       126: q^3+q
       127: q^2+q
       129: 2q^2+q
       131: q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^2+q
       140: q
       141: q
       142: q^2+q
       143: q
       144: q
       145: q^2+q
       146: q
       147: q^2+q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       172: q^2+q
       176: q
       177: q
       179: q^2+q
       181: q^2+q
       184: q
       186: q
       187: q
       189: q
       192: q
       194: q
       196: q^2+q
       197: q
       200: q
       202: q^2+q
       204: q
       205: q
       207: q
       209: q
       211: q
       213: q
       215: q^2+q
       217: q
       219: q
       223: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       243: q
       244: q
       245: q
       246: q
       262: q^2+q
       266: q
       269: q
       273: q
       278: q
       279: q
       281: q
       284: q
       286: q
       287: q
       289: q
       291: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q
       317: q
       320: q
       322: q
       323: q
       325: q
       344: q
       348: q
       350: q
       352: q
       356: q
       358: q
       366: q
       380: q
       384: q
       391: q
       396: q
       399: q
       404: q
       406: q
       413: q
       417: q
       430: q
       432: q
       433: q
       448: q
       450: q
       451: q
       469: q
       477: q
       524: q
       536: q
       552: q
       570: q
       651: 1
       758: 1
       771: 1
       849: 1
       893: 1
       961: 1
       970: 1
      1095: 1

1096:    0: q^3+2q^2+q
         1: q^4+q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^4+q^3+2q^2+q
         6: q^5+2q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^4+q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^4+q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^4+q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        38: 2q^2+q
        40: 2q^2+q
        42: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^4+q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        59: q^2+q
        60: q^2+q
        63: q^2+q
        65: q^2+q
        67: 2q^2+q
        68: q
        69: q^3+q
        70: q^3+q
        71: q^3+q^2+q
        72: q^2+q
        73: q^2+q
        75: q^2+q
        77: 2q^2+q
        79: q
        80: q
        81: q^2+q
        82: q^2+q
        83: q
        84: q
        85: q^2+q
        86: q^2+q
        87: q
        88: q^3+q
        89: q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       104: q^2+q
       107: q^2+q
       110: q^2+q
       112: q^2+q
       114: q^2+q
       116: q
       118: q
       119: q
       122: q
       124: q^2+q
       125: q
       126: q^3+q
       128: q^2+q
       130: 2q^2+q
       132: q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^2+q
       140: q
       141: q
       142: q^2+q
       143: q
       144: q
       145: q^2+q
       146: q
       147: q^2+q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       170: q^2+q
       174: q
       178: q
       180: q^2+q
       182: q^2+q
       183: q
       186: q
       188: q
       190: q
       192: q
       193: q
       196: q^2+q
       198: q
       199: q
       201: q^2+q
       204: q
       206: q
       208: q
       210: q
       212: q
       214: q
       216: q^2+q
       218: q
       219: q
       223: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       243: q
       244: q
       245: q
       246: q
       260: q^2+q
       264: q
       268: q
       274: q
       276: q
       280: q
       282: q
       283: q
       286: q
       288: q
       290: q
       292: q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q
       318: q
       319: q
       322: q
       324: q
       326: q
       344: q
       348: q
       350: q
       352: q
       356: q
       358: q
       366: q
       378: q
       382: q
       390: q
       394: q
       400: q
       403: q
       407: q
       414: q
       418: q
       429: q
       432: q
       434: q
       447: q
       450: q
       452: q
       470: q
       478: q
       522: q
       534: q
       551: q
       571: q
       652: 1
       759: 1
       774: 1
       850: 1
       894: 1
       962: 1
       973: 1
      1096: 1

1097:    0: q^3+2q^2+q
         1: q^4+q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^4+q^3+q^2+q
         5: q^4+q^3+2q^2+q
         6: q^5+2q^4+2q^3+2q^2+q
         7: q^3+q
         8: q^2+q
         9: q^3+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^4+q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: q^3+2q^2+q
        17: q^4+q^3+2q^2+q
        18: q^3+q
        19: q^3+q^2+q
        20: q^4+q^3+2q^2+q
        21: q^3+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        38: 2q^2+q
        40: 2q^2+q
        42: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: q^3+q^2+q
        50: q^4+q^3+2q^2+q
        51: q^3+q
        52: q^2+q
        53: 2q^2+q
        54: q
        55: q^2+q
        56: 2q^2+q
        57: q
        58: q^2+q
        61: q^2+q
        63: q^2+q
        65: q^2+q
        67: 2q^2+q
        68: q
        69: q^3+q
        70: q^3+q
        71: q^3+q^2+q
        72: q^2+q
        73: q^2+q
        75: q^2+q
        77: 2q^2+q
        79: q
        80: q
        81: q^2+q
        82: q^2+q
        83: q
        84: q
        85: q^2+q
        86: q^2+q
        87: q
        88: q^3+q
        89: q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: q^2+q
        95: 2q^2+q
        96: q
        97: q^2+q
        98: 2q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       105: q^2+q
       108: q^2+q
       109: q^2+q
       112: q^2+q
       114: q^2+q
       116: q
       117: q
       120: q
       122: q
       124: q^2+q
       125: q
       126: q^3+q
       128: q^2+q
       130: 2q^2+q
       132: q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^2+q
       140: q
       141: q
       142: q^2+q
       143: q
       144: q
       145: q^2+q
       146: q
       147: q^2+q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q
       167: q^2+q
       168: q
       171: q^2+q
       175: q
       178: q
       180: q^2+q
       182: q^2+q
       184: q
       185: q
       188: q
       190: q
       191: q
       194: q
       195: q^2+q
       198: q
       200: q
       202: q^2+q
       203: q
       206: q
       208: q
       210: q
       212: q
       214: q
       216: q^2+q
       218: q
       219: q
       223: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       243: q
       244: q
       245: q
       246: q
       261: q^2+q
       265: q
       270: q
       272: q
       277: q
       280: q
       282: q
       284: q
       285: q
       288: q
       290: q
       292: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q
       318: q
       320: q
       321: q
       324: q
       326: q
       344: q
       348: q
       350: q
       352: q
       356: q
       358: q
       366: q
       379: q
       383: q
       392: q
       395: q
       398: q
       402: q
       408: q
       414: q
       418: q
       430: q
       431: q
       434: q
       448: q
       449: q
       452: q
       470: q
       478: q
       523: q
       535: q
       550: q
       572: q
       652: 1
       760: 1
       774: 1
       850: 1
       895: 1
       963: 1
       973: 1
      1097: 1

1098:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: q+1
        64: q+1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: 1
       119: 1
       121: q+1
       123: 1
       125: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       169: 1
       173: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       289: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: 1
       415: 1
       427: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       502: 1
       504: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       525: 1
       537: 1
       541: 1
       545: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       601: 1
       611: 1
       615: 1
       617: 1
       627: 1
       631: 1
       633: 1
       635: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       666: 1
       668: 1
       672: 1
       678: 1
       684: 1
       693: 1
       729: 1
       733: 1
       745: 1
       749: 1
       757: 1
       761: 1
       765: 1
       769: 1
       789: 1
       813: 1
       815: 1
       837: 1
       839: 1
       853: 1
       857: 1
       884: 1
       932: 1
       956: 1
       978: 1
       982: 1
       988: 1
      1098: 1

1099:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^3+3q^2+2q
         5: 3q^2+3q
         6: q^3+3q^2+2q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+3q
        11: 3q^2+3q
        12: q^3+3q^2+2q
        13: 3q^2+3q
        14: q^3+3q^2+2q
        15: 3q^2+3q
        16: 3q
        17: 3q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+3q
        32: 3q^2+3q
        33: 3q
        34: 3q^2+3q
        35: 3q^2+3q
        36: 3q
        37: q^2+q
        38: 2q^2+2q
        39: q^2+q
        40: 2q^2+2q
        41: q^2+q
        42: 2q^2+2q
        43: 3q^2+3q
        44: q^3+3q^2+2q
        45: 3q^2+3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: 2q
        59: q
        60: 2q
        61: q
        62: q^2+q
        63: 2q^2+2q
        64: q^2+q
        65: 2q^2+2q
        66: q
        67: 2q
        68: 3q
        70: 2q^2+2q
        71: 2q
        72: q
        73: q
        75: q^2+q
        77: q^2+q
        79: q^2+q
        80: 3q^2+3q
        81: 3q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+3q
        85: 3q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q
       104: q
       105: q
       107: q
       109: q
       114: q^2+q
       116: q^2+q
       117: 2q
       118: q
       119: 2q
       120: q
       121: q^2+q
       122: 2q^2+2q
       123: q
       124: 2q
       125: 3q
       128: q
       130: q
       133: 2q
       135: q
       136: q
       137: 3q
       139: 2q
       140: q
       141: 2q^2+2q
       142: q
       143: 3q
       145: 2q
       146: 2q^2+2q
       147: q
       148: q
       149: 2q^2+2q
       150: 2q^2+2q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       174: q
       175: q
       180: q
       183: q
       185: q
       190: q^2+q
       191: 2q
       192: q
       193: q
       195: q
       199: 2q
       200: q
       201: q
       203: q
       207: q
       208: 2q
       210: q^2+q
       212: q^2+q
       214: q
       216: q
       220: 2q
       222: q
       224: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       246: 2q^2+2q
       247: 1
       248: 1
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       275: q
       276: q
       277: q
       280: q
       293: q
       295: q
       299: q
       303: q
       307: q
       309: q
       318: q
       319: q
       321: q
       326: q^2+q
       328: q
       330: q
       337: 1
       339: 1
       341: 1
       345: 2q
       347: q
       349: q
       351: 1
       353: 2q
       355: q
       357: q
       359: 1
       361: q
       363: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       410: q
       428: 1
       437: q
       439: q
       443: 1
       446: 1
       453: q
       457: q
       461: 1
       464: 1
       466: q
       471: q
       473: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       503: q
       505: q
       509: 2q
       511: q
       513: q
       518: 1
       519: 1
       546: 1
       562: 1
       573: 1
       578: 1
       602: 1
       615: 1
       618: 1
       631: 1
       634: 1
       636: q
       647: q
       649: q
       655: 1
       667: 1
       669: 1
       672: 1
       678: 1
       684: 1
       694: 1
       734: 1
       750: 1
       765: 1
       770: 1
       790: 1
       814: 1
       815: 1
       838: 1
       839: 1
       857: 1
       885: 1
       933: 1
       957: 1
       983: 1
       988: 1
      1099: 1

1100:    0: q^3+q^2+q
         1: q^3+q^2+q
         2: q^3+q^2+q
         3: q^2+q
         4: q^3+q^2+q
         5: q^2+q
         6: q^3+q^2+q
         7: q^3+q^2+q
         8: q^2+q
        10: q^3+q^2+q
        11: q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^2+q
        16: q
        17: q
        19: q^3+q^2+q
        20: q^3+q^2+q
        21: q^3+q^2+q
        22: q^2+q
        23: q^2+q
        24: q^2+q
        25: q^2+q
        26: q^2+q
        27: q^2+q
        28: q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: q
        34: q^2+q
        35: q^2+q
        36: q
        37: q^2+q
        39: q^2+q
        41: q^2+q
        43: q^3+q^2+q
        44: q^3+q^2+q
        45: q^2+q
        46: q
        47: q
        49: q
        50: q
        52: q^2+q
        53: q^2+q
        54: q^2+q
        55: q^2+q
        56: q^2+q
        57: q^2+q
        58: q
        60: q
        62: q^2+q
        64: q^2+q
        66: q
        68: q
        70: q^3+q^2+q
        71: q
        72: q
        73: q
        74: q^2+q
        76: q^2+q
        78: q^2+q
        80: q^2+q
        81: q
        82: q^2+q
        83: q^2+q
        84: q^2+q
        85: q
        86: q^2+q
        87: q^2+q
        88: q
        89: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q
       107: q
       109: q
       111: q
       113: q^2+q
       115: q^2+q
       117: q
       119: q
       121: q^2+q
       123: q
       125: q
       127: q
       129: q
       133: q
       135: q
       136: q
       137: q
       139: q
       140: q
       141: q^2+q
       142: q
       143: q
       145: q
       146: q^2+q
       147: q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       169: q
       173: q
       179: q
       181: q
       183: q
       185: q
       187: q
       189: q^2+q
       191: q
       193: q
       195: q
       197: q
       199: q
       201: q
       203: q
       205: q
       207: q
       209: q^2+q
       211: q^2+q
       213: q
       215: q
       220: q
       222: q
       224: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q^2+q
       250: q
       251: q
       253: q
       254: q
       259: q
       263: q
       267: q
       271: q
       275: q
       279: q
       289: q
       293: q
       295: q
       297: q
       299: q
       303: q
       305: q
       307: q
       309: q
       313: q
       325: q^2+q
       327: q
       329: q
       345: q
       347: q
       349: q
       353: q
       355: q
       357: q
       381: q
       385: q
       393: q
       401: q
       409: q
       415: q
       437: q
       439: q
       441: q
       453: q
       457: q
       459: q
       477: 1
       525: q
       541: q
       557: q
       569: 1
       579: 1
       651: 1
       695: 1
       757: 1
       771: 1
       853: 1
       886: 1
       978: 1
       984: 1
      1100: 1

1101:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^3+3q^2+2q
         5: 3q^2+3q
         6: q^3+3q^2+2q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+3q
        11: 3q^2+3q
        12: q^3+3q^2+2q
        13: 3q^2+3q
        14: q^3+3q^2+2q
        15: 3q^2+3q
        16: 3q
        17: 3q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+3q
        32: 3q^2+3q
        33: 3q
        34: 3q^2+3q
        35: 3q^2+3q
        36: 3q
        37: 2q^2+2q
        38: q^2+q
        39: 2q^2+2q
        40: q^2+q
        41: 2q^2+2q
        42: q^2+q
        43: 3q^2+3q
        44: q^3+3q^2+2q
        45: 3q^2+3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: q
        59: 2q
        60: 2q
        61: q
        62: 2q^2+2q
        63: q^2+q
        64: 2q^2+2q
        65: q^2+q
        66: 2q
        67: q
        68: 3q
        70: 2q^2+2q
        71: 2q
        72: q
        73: q
        74: q^2+q
        76: q^2+q
        78: q^2+q
        80: 3q^2+3q
        81: 3q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+3q
        85: 3q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q
       104: q
       106: q
       107: q
       110: q
       113: q^2+q
       115: q^2+q
       117: q
       118: 2q
       119: 2q
       120: q
       121: 2q^2+2q
       122: q^2+q
       123: 2q
       124: q
       125: 3q
       127: q
       129: q
       133: 2q
       135: q
       136: q
       137: 3q
       139: 2q
       140: q
       141: 2q^2+2q
       142: q
       143: 3q
       145: 2q
       146: 2q^2+2q
       147: q
       148: q
       149: 2q^2+2q
       150: 2q^2+2q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       174: q
       176: q
       179: q
       183: q
       186: q
       189: q^2+q
       191: q
       192: 2q
       193: q
       196: q
       199: 2q
       200: q
       201: q
       204: q
       207: 2q
       208: q
       209: q^2+q
       211: q^2+q
       213: q
       215: q
       220: 2q
       222: q
       224: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       246: 2q^2+2q
       247: 1
       248: 1
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       275: q
       276: q
       278: q
       279: q
       293: q
       296: q
       299: q
       304: q
       307: q
       310: q
       317: q
       319: q
       322: q
       325: q^2+q
       327: q
       329: q
       337: 1
       338: 1
       340: 1
       345: 2q
       347: q
       349: q
       351: 1
       353: 2q
       355: q
       357: q
       359: 1
       360: q
       362: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       409: q
       427: 1
       437: q
       440: q
       443: 1
       445: 1
       453: q
       458: q
       462: 1
       463: 1
       465: q
       471: q
       474: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       502: q
       504: q
       509: 2q
       511: q
       513: q
       518: 1
       519: 1
       545: 1
       563: 1
       574: 1
       580: 1
       601: 1
       615: 1
       617: 1
       632: 1
       633: 1
       635: q
       647: q
       650: q
       656: 1
       666: 1
       668: 1
       672: 1
       678: 1
       684: 1
       696: 1
       733: 1
       751: 1
       766: 1
       772: 1
       789: 1
       813: 1
       815: 1
       837: 1
       840: 1
       858: 1
       887: 1
       932: 1
       958: 1
       985: 1
       989: 1
      1101: 1

1102:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: q+1
        64: q+1
        66: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       118: 1
       120: 1
       121: q+1
       123: 1
       125: 1
       127: 1
       129: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       172: 1
       176: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: q+1
       211: q+1
       213: 1
       215: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       237: 1
       239: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       289: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q+1
       327: 1
       329: 1
       337: 1
       338: 1
       340: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       360: 1
       362: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: 1
       415: 1
       427: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       502: 1
       504: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       528: 1
       539: 1
       543: 1
       547: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       601: 1
       611: 1
       616: 1
       617: 1
       627: 1
       632: 1
       633: 1
       635: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       666: 1
       668: 1
       672: 1
       678: 1
       684: 1
       697: 1
       731: 1
       735: 1
       747: 1
       751: 1
       758: 1
       762: 1
       768: 1
       769: 1
       789: 1
       813: 1
       816: 1
       837: 1
       840: 1
       853: 1
       857: 1
       889: 1
       934: 1
       958: 1
       979: 1
       982: 1
       991: 1
      1102: 1

1103:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^3+3q^2+2q
         5: 3q^2+3q
         6: q^3+3q^2+2q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+3q
        11: 3q^2+3q
        12: q^3+3q^2+2q
        13: 3q^2+3q
        14: q^3+3q^2+2q
        15: 3q^2+3q
        16: 3q
        17: 3q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+3q
        32: 3q^2+3q
        33: 3q
        34: 3q^2+3q
        35: 3q^2+3q
        36: 3q
        37: 2q^2+2q
        38: q^2+q
        39: 2q^2+2q
        40: q^2+q
        41: 2q^2+2q
        42: q^2+q
        43: 3q^2+3q
        44: q^3+3q^2+2q
        45: 3q^2+3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: 2q
        59: q
        60: q
        61: 2q
        62: 2q^2+2q
        63: q^2+q
        64: 2q^2+2q
        65: q^2+q
        66: 2q
        67: q
        68: 3q
        70: 2q^2+2q
        71: 2q
        72: q
        73: q
        74: q^2+q
        76: q^2+q
        78: q^2+q
        80: 3q^2+3q
        81: 3q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+3q
        85: 3q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q
       105: q
       106: q
       108: q
       109: q
       113: q^2+q
       115: q^2+q
       117: 2q
       118: q
       119: q
       120: 2q
       121: 2q^2+2q
       122: q^2+q
       123: 2q
       124: q
       125: 3q
       127: q
       129: q
       133: 2q
       135: q
       136: q
       137: 3q
       139: 2q
       140: q
       141: 2q^2+2q
       142: q
       143: 3q
       145: 2q
       146: 2q^2+2q
       147: q
       148: q
       149: 2q^2+2q
       150: 2q^2+2q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       173: q
       175: q
       176: q
       179: q
       184: q
       185: q
       189: q^2+q
       191: 2q
       192: q
       194: q
       195: q
       199: q
       200: 2q
       202: q
       203: q
       207: 2q
       208: q
       209: q^2+q
       211: q^2+q
       213: q
       215: q
       220: 2q
       222: q
       224: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       237: q
       239: q
       243: 2q
       244: q
       245: q
       246: 2q^2+2q
       247: 1
       248: 1
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       275: q
       277: q
       278: q
       279: q
       294: q
       295: q
       300: q
       303: q
       308: q
       309: q
       317: q
       320: q
       321: q
       325: q^2+q
       327: q
       329: q
       337: 1
       338: 1
       340: 1
       345: 2q
       347: q
       349: q
       351: 1
       353: 2q
       355: q
       357: q
       359: 1
       360: q
       362: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       409: q
       427: 1
       438: q
       439: q
       444: 1
       445: 1
       454: q
       457: q
       461: 1
       463: 1
       465: q
       472: q
       473: q
       480: 1
       484: 1
       485: 1
       487: 1
       496: 1
       501: 1
       502: q
       504: q
       509: 2q
       511: q
       513: q
       518: 1
       519: 1
       547: 1
       561: 1
       576: 1
       580: 1
       601: 1
       616: 1
       617: 1
       631: 1
       633: 1
       635: q
       648: q
       649: q
       656: 1
       666: 1
       668: 1
       672: 1
       678: 1
       684: 1
       698: 1
       735: 1
       749: 1
       767: 1
       772: 1
       789: 1
       813: 1
       816: 1
       837: 1
       839: 1
       858: 1
       888: 1
       934: 1
       956: 1
       985: 1
       990: 1
      1103: 1

1104:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: q+1
        65: q+1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       118: 1
       119: 1
       122: q+1
       124: 1
       125: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       170: 1
       174: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       290: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: 1
       416: 1
       428: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       503: 1
       505: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       526: 1
       538: 1
       542: 1
       546: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       602: 1
       612: 1
       615: 1
       618: 1
       628: 1
       632: 1
       634: 1
       636: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       667: 1
       669: 1
       672: 1
       678: 1
       684: 1
       699: 1
       730: 1
       734: 1
       748: 1
       752: 1
       759: 1
       763: 1
       766: 1
       773: 1
       790: 1
       814: 1
       815: 1
       838: 1
       840: 1
       854: 1
       858: 1
       890: 1
       933: 1
       959: 1
       980: 1
       986: 1
       989: 1
      1104: 1

1105:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: 1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        49: 1
        50: 1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: q+1
        65: q+1
        67: 1
        68: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: q+1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: 1
       120: 1
       122: q+1
       124: 1
       125: 1
       128: 1
       130: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       145: 1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       160: 1
       161: 1
       163: 1
       164: 1
       166: 1
       167: 1
       171: 1
       175: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: q+1
       212: q+1
       214: 1
       216: 1
       220: 1
       222: 1
       224: 1
       227: 1
       229: 1
       230: 1
       232: 1
       234: 1
       235: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       290: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q+1
       328: 1
       330: 1
       337: 1
       339: 1
       341: 1
       345: 1
       347: 1
       349: 1
       351: 1
       353: 1
       355: 1
       357: 1
       359: 1
       361: 1
       363: 1
       367: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: 1
       416: 1
       428: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: 1
       446: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       503: 1
       505: 1
       509: 1
       511: 1
       513: 1
       518: 1
       519: 1
       527: 1
       540: 1
       544: 1
       548: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       602: 1
       612: 1
       616: 1
       618: 1
       628: 1
       631: 1
       634: 1
       636: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       667: 1
       669: 1
       672: 1
       678: 1
       684: 1
       700: 1
       732: 1
       736: 1
       746: 1
       750: 1
       760: 1
       764: 1
       767: 1
       773: 1
       790: 1
       814: 1
       816: 1
       838: 1
       839: 1
       854: 1
       858: 1
       891: 1
       935: 1
       957: 1
       981: 1
       986: 1
       990: 1
      1105: 1

1106:    0: 3q^2+3q
         1: 3q^2+3q
         2: 3q^2+3q
         3: 3q^2+3q
         4: q^3+3q^2+2q
         5: 3q^2+3q
         6: q^3+3q^2+2q
         7: q^3+3q^2+2q
         8: 3q^2+3q
        10: 3q^2+3q
        11: 3q^2+3q
        12: q^3+3q^2+2q
        13: 3q^2+3q
        14: q^3+3q^2+2q
        15: 3q^2+3q
        16: 3q
        17: 3q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+3q
        23: 3q^2+3q
        24: 3q^2+3q
        25: 3q^2+3q
        26: 3q^2+3q
        27: 3q^2+3q
        28: 3q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+3q
        32: 3q^2+3q
        33: 3q
        34: 3q^2+3q
        35: 3q^2+3q
        36: 3q
        37: q^2+q
        38: 2q^2+2q
        39: q^2+q
        40: 2q^2+2q
        41: q^2+q
        42: 2q^2+2q
        43: 3q^2+3q
        44: q^3+3q^2+2q
        45: 3q^2+3q
        46: 3q
        47: 3q
        49: 2q
        50: 2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: q
        59: 2q
        60: q
        61: 2q
        62: q^2+q
        63: 2q^2+2q
        64: q^2+q
        65: 2q^2+2q
        66: q
        67: 2q
        68: 3q
        70: 2q^2+2q
        71: 2q
        72: q
        73: q
        75: q^2+q
        77: q^2+q
        79: q^2+q
        80: 3q^2+3q
        81: 3q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+3q
        85: 3q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q
        89: 3q
        91: 2q
        92: 2q
        94: 2q
        95: 2q
        97: 2q
        98: 2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       104: q
       105: q
       106: q
       108: q
       110: q
       114: q^2+q
       116: q^2+q
       117: q
       118: 2q
       119: q
       120: 2q
       121: q^2+q
       122: 2q^2+2q
       123: q
       124: 2q
       125: 3q
       128: q
       130: q
       133: 2q
       135: q
       136: q
       137: 3q
       139: 2q
       140: q
       141: 2q^2+2q
       142: q
       143: 3q
       145: 2q
       146: 2q^2+2q
       147: q
       148: q
       149: 2q^2+2q
       150: 2q^2+2q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: 2q
       158: 2q
       160: 2q
       161: 2q
       163: 2q
       164: 2q
       166: 2q
       167: 2q
       174: q
       175: q
       176: q
       180: q
       184: q
       186: q
       190: q^2+q
       191: q
       192: 2q
       194: q
       196: q
       199: q
       200: 2q
       202: q
       204: q
       207: q
       208: 2q
       210: q^2+q
       212: q^2+q
       214: q
       216: q
       220: 2q
       222: q
       224: q
       227: 2q
       229: q
       230: q
       232: 2q
       234: q
       235: q
       238: q
       240: q
       243: 2q
       244: q
       245: q
       246: 2q^2+2q
       247: 1
       248: 1
       250: 2q
       251: 2q
       253: 2q
       254: 2q
       256: 2q
       257: 2q
       276: q
       277: q
       278: q
       280: q
       294: q
       296: q
       300: q
       304: q
       308: q
       310: q
       318: q
       320: q
       322: q
       326: q^2+q
       328: q
       330: q
       337: 1
       339: 1
       341: 1
       345: 2q
       347: q
       349: q
       351: 1
       353: 2q
       355: q
       357: q
       359: 1
       361: q
       363: q
       367: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q
       410: q
       428: 1
       438: q
       440: q
       444: 1
       446: 1
       454: q
       458: q
       462: 1
       464: 1
       466: q
       472: q
       474: q
       479: 1
       484: 1
       486: 1
       488: 1
       496: 1
       501: 1
       503: q
       505: q
       509: 2q
       511: q
       513: q
       518: 1
       519: 1
       548: 1
       564: 1
       575: 1
       578: 1
       602: 1
       616: 1
       618: 1
       632: 1
       634: 1
       636: q
       648: q
       650: q
       655: 1
       667: 1
       669: 1
       672: 1
       678: 1
       684: 1
       701: 1
       736: 1
       752: 1
       768: 1
       770: 1
       790: 1
       814: 1
       816: 1
       838: 1
       840: 1
       857: 1
       892: 1
       935: 1
       959: 1
       983: 1
       991: 1
      1106: 1

1107:    0: q^3+q^2+q
         1: q^3+q^2+q
         2: q^3+q^2+q
         3: q^2+q
         4: q^3+q^2+q
         5: q^2+q
         6: q^3+q^2+q
         7: q^3+q^2+q
         8: q^2+q
        10: q^3+q^2+q
        11: q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^2+q
        16: q
        17: q
        19: q^3+q^2+q
        20: q^3+q^2+q
        21: q^3+q^2+q
        22: q^2+q
        23: q^2+q
        24: q^2+q
        25: q^2+q
        26: q^2+q
        27: q^2+q
        28: q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: q
        34: q^2+q
        35: q^2+q
        36: q
        37: q^2+q
        39: q^2+q
        41: q^2+q
        43: q^3+q^2+q
        44: q^3+q^2+q
        45: q^2+q
        46: q
        47: q
        49: q
        50: q
        52: q^2+q
        53: q^2+q
        54: q^2+q
        55: q^2+q
        56: q^2+q
        57: q^2+q
        59: q
        61: q
        62: q^2+q
        64: q^2+q
        66: q
        68: q
        70: q^3+q^2+q
        71: q
        72: q
        73: q
        74: q^2+q
        76: q^2+q
        78: q^2+q
        80: q^2+q
        81: q
        82: q^2+q
        83: q^2+q
        84: q^2+q
        85: q
        86: q^2+q
        87: q^2+q
        88: q
        89: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       106: q
       108: q
       110: q
       111: q
       113: q^2+q
       115: q^2+q
       118: q
       120: q
       121: q^2+q
       123: q
       125: q
       127: q
       129: q
       133: q
       135: q
       136: q
       137: q
       139: q
       140: q
       141: q^2+q
       142: q
       143: q
       145: q
       146: q^2+q
       147: q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       172: q
       176: q
       179: q
       181: q
       184: q
       186: q
       187: q
       189: q^2+q
       192: q
       194: q
       196: q
       197: q
       200: q
       202: q
       204: q
       205: q
       207: q
       209: q^2+q
       211: q^2+q
       213: q
       215: q
       220: q
       222: q
       224: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q^2+q
       250: q
       251: q
       253: q
       254: q
       262: q
       266: q
       269: q
       273: q
       278: q
       279: q
       289: q
       294: q
       296: q
       297: q
       300: q
       304: q
       305: q
       308: q
       310: q
       313: q
       325: q^2+q
       327: q
       329: q
       345: q
       347: q
       349: q
       353: q
       355: q
       357: q
       384: q
       388: q
       396: q
       404: q
       409: q
       415: q
       438: q
       440: q
       441: q
       454: q
       458: q
       459: q
       477: 1
       528: q
       543: q
       559: q
       570: 1
       579: 1
       651: 1
       702: 1
       758: 1
       771: 1
       853: 1
       893: 1
       979: 1
       984: 1
      1107: 1

1108:    0: q^3+q^2+q
         1: q^3+q^2+q
         2: q^3+q^2+q
         3: q^2+q
         4: q^3+q^2+q
         5: q^2+q
         6: q^3+q^2+q
         7: q^3+q^2+q
         8: q^2+q
        10: q^3+q^2+q
        11: q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^2+q
        16: q
        17: q
        19: q^3+q^2+q
        20: q^3+q^2+q
        21: q^3+q^2+q
        22: q^2+q
        23: q^2+q
        24: q^2+q
        25: q^2+q
        26: q^2+q
        27: q^2+q
        28: q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: q
        34: q^2+q
        35: q^2+q
        36: q
        38: q^2+q
        40: q^2+q
        42: q^2+q
        43: q^3+q^2+q
        44: q^3+q^2+q
        45: q^2+q
        46: q
        47: q
        49: q
        50: q
        52: q^2+q
        53: q^2+q
        54: q^2+q
        55: q^2+q
        56: q^2+q
        57: q^2+q
        59: q
        60: q
        63: q^2+q
        65: q^2+q
        67: q
        68: q
        70: q^3+q^2+q
        71: q
        72: q
        73: q
        75: q^2+q
        77: q^2+q
        79: q^2+q
        80: q^2+q
        81: q
        82: q^2+q
        83: q^2+q
        84: q^2+q
        85: q
        86: q^2+q
        87: q^2+q
        88: q
        89: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q
       107: q
       110: q
       112: q
       114: q^2+q
       116: q^2+q
       118: q
       119: q
       122: q^2+q
       124: q
       125: q
       128: q
       130: q
       133: q
       135: q
       136: q
       137: q
       139: q
       140: q
       141: q^2+q
       142: q
       143: q
       145: q
       146: q^2+q
       147: q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       170: q
       174: q
       180: q
       182: q
       183: q
       186: q
       188: q
       190: q^2+q
       192: q
       193: q
       196: q
       198: q
       199: q
       201: q
       204: q
       206: q
       208: q
       210: q^2+q
       212: q^2+q
       214: q
       216: q
       220: q
       222: q
       224: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q^2+q
       250: q
       251: q
       253: q
       254: q
       260: q
       264: q
       268: q
       274: q
       276: q
       280: q
       290: q
       293: q
       296: q
       298: q
       299: q
       304: q
       306: q
       307: q
       310: q
       314: q
       326: q^2+q
       328: q
       330: q
       345: q
       347: q
       349: q
       353: q
       355: q
       357: q
       382: q
       386: q
       394: q
       403: q
       410: q
       416: q
       437: q
       440: q
       442: q
       453: q
       458: q
       460: q
       478: 1
       526: q
       542: q
       560: q
       571: 1
       582: 1
       652: 1
       703: 1
       759: 1
       774: 1
       854: 1
       894: 1
       980: 1
       987: 1
      1108: 1

1109:    0: q^3+q^2+q
         1: q^3+q^2+q
         2: q^3+q^2+q
         3: q^2+q
         4: q^3+q^2+q
         5: q^2+q
         6: q^3+q^2+q
         7: q^3+q^2+q
         8: q^2+q
        10: q^3+q^2+q
        11: q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^2+q
        16: q
        17: q
        19: q^3+q^2+q
        20: q^3+q^2+q
        21: q^3+q^2+q
        22: q^2+q
        23: q^2+q
        24: q^2+q
        25: q^2+q
        26: q^2+q
        27: q^2+q
        28: q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: q
        34: q^2+q
        35: q^2+q
        36: q
        38: q^2+q
        40: q^2+q
        42: q^2+q
        43: q^3+q^2+q
        44: q^3+q^2+q
        45: q^2+q
        46: q
        47: q
        49: q
        50: q
        52: q^2+q
        53: q^2+q
        54: q^2+q
        55: q^2+q
        56: q^2+q
        57: q^2+q
        58: q
        61: q
        63: q^2+q
        65: q^2+q
        67: q
        68: q
        70: q^3+q^2+q
        71: q
        72: q
        73: q
        75: q^2+q
        77: q^2+q
        79: q^2+q
        80: q^2+q
        81: q
        82: q^2+q
        83: q^2+q
        84: q^2+q
        85: q
        86: q^2+q
        87: q^2+q
        88: q
        89: q
        91: q
        92: q
        94: q
        95: q
        97: q
        98: q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       105: q
       108: q
       109: q
       112: q
       114: q^2+q
       116: q^2+q
       117: q
       120: q
       122: q^2+q
       124: q
       125: q
       128: q
       130: q
       133: q
       135: q
       136: q
       137: q
       139: q
       140: q
       141: q^2+q
       142: q
       143: q
       145: q
       146: q^2+q
       147: q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q
       158: q
       160: q
       161: q
       163: q
       164: q
       171: q
       175: q
       180: q
       182: q
       184: q
       185: q
       188: q
       190: q^2+q
       191: q
       194: q
       195: q
       198: q
       200: q
       202: q
       203: q
       206: q
       208: q
       210: q^2+q
       212: q^2+q
       214: q
       216: q
       220: q
       222: q
       224: q
       227: q
       229: q
       230: q
       232: q
       234: q
       235: q
       246: q^2+q
       250: q
       251: q
       253: q
       254: q
       261: q
       265: q
       270: q
       272: q
       277: q
       280: q
       290: q
       294: q
       295: q
       298: q
       300: q
       303: q
       306: q
       308: q
       309: q
       314: q
       326: q^2+q
       328: q
       330: q
       345: q
       347: q
       349: q
       353: q
       355: q
       357: q
       383: q
       387: q
       395: q
       402: q
       410: q
       416: q
       438: q
       439: q
       442: q
       454: q
       457: q
       460: q
       478: 1
       527: q
       544: q
       558: q
       572: 1
       582: 1
       652: 1
       704: 1
       760: 1
       774: 1
       854: 1
       895: 1
       981: 1
       987: 1
      1109: 1

1110:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 4q^2+5q+1
        23: 4q^2+5q+1
        24: q^3+3q^2+4q+1
        25: 2q^3+8q^2+6q+1
        26: 2q^3+8q^2+6q+1
        27: 3q^3+6q^2+5q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 4q^2+5q+1
        32: 2q^2+4q+1
        33: 3q^2+5q+1
        34: 2q^3+8q^2+6q+1
        35: q^3+5q^2+5q+1
        36: 6q^2+6q+1
        37: 4q^2+5q+1
        39: 4q^2+5q+1
        41: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 4q^2+5q+1
        53: 4q^2+5q+1
        54: q^3+3q^2+4q+1
        55: 2q^3+8q^2+6q+1
        56: 2q^3+8q^2+6q+1
        57: 3q^3+6q^2+5q+1
        58: 2q^2+4q+1
        59: q^2+q
        60: 3q^2+4q+1
        61: 3q^2+2q
        62: 4q^2+5q+1
        64: 2q^2+4q+1
        66: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 6q^2+6q+1
        73: 3q^2+5q+1
        74: 4q^2+5q+1
        76: 4q^2+5q+1
        78: q^3+3q^2+4q+1
        80: 2q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+5q+1
        83: 2q^2+4q+1
        84: q^3+5q^2+5q+1
        85: 3q^2+5q+1
        86: 2q^3+8q^2+6q+1
        87: q^3+5q^2+5q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 5q^2+6q+1
        98: 5q^2+6q+1
        99: q^3+3q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: 2q^2+4q+1
       106: q^2+q
       107: 3q^2+4q+1
       108: 3q^2+2q
       109: 2q^2+4q+1
       110: q^2+q
       111: 3q^2+5q+1
       113: 4q^2+5q+1
       115: 2q^2+4q+1
       117: 3q+1
       119: 3q+1
       120: q^2+q
       121: 2q^2+4q+1
       123: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+5q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: 3q^2+5q+1
       144: q^2+3q+1
       145: 5q^2+6q+1
       146: q^3+5q^2+5q+1
       147: 5q^2+6q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q^2+4q+1
       172: q^2+q
       173: 3q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       183: 3q+1
       184: q^2+q
       185: 3q+1
       187: q^2+4q+1
       189: 2q^2+4q+1
       191: 3q+1
       195: q^2+3q+1
       196: q
       199: 3q+1
       200: q^2+q
       201: 3q^2+4q+1
       202: 2q^2+2q
       203: q^2+2q+1
       205: q^2+2q+1
       207: q^2+4q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: q^2+4q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q^2+3q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       259: q^2+3q+1
       262: q
       263: 3q+1
       271: q^2+2q+1
       275: 3q+1
       279: q+1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       293: 3q+1
       294: q^2+q
       295: 3q+1
       297: q^2+4q+1
       303: q+1
       307: 2q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       321: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q^2+2q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: q+1
       353: 3q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: q+1
       385: 3q+1
       397: q+1
       401: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       431: 1
       439: q+1
       447: 1
       449: 1
       451: 1
       453: 2q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       473: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: q+1
       529: q+1
       549: 1
       553: 1
       557: q+1
       561: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       591: 1
       595: 1
       597: 1
       599: q+1
       601: 1
       607: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       705: 1
       709: 1
       713: 1
       737: 1
       741: 1
       745: 1
       749: 1
       777: 1
       781: 1
       783: 1
       787: 1
       789: 1
       807: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       847: 1
       868: 1
       876: 1
       896: 1
       900: 1
       936: 1
       948: 1
       956: 1
      1002: 1
      1006: 1
      1042: 1
      1110: 1

1111:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 4q^2+5q+1
        23: 4q^2+5q+1
        24: q^3+3q^2+4q+1
        25: 2q^3+8q^2+6q+1
        26: 2q^3+8q^2+6q+1
        27: 3q^3+6q^2+5q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 4q^2+5q+1
        32: 2q^2+4q+1
        33: 3q^2+5q+1
        34: 2q^3+8q^2+6q+1
        35: q^3+5q^2+5q+1
        36: 6q^2+6q+1
        38: 4q^2+5q+1
        40: 4q^2+5q+1
        42: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 4q^2+5q+1
        53: 4q^2+5q+1
        54: q^3+3q^2+4q+1
        55: 2q^3+8q^2+6q+1
        56: 2q^3+8q^2+6q+1
        57: 3q^3+6q^2+5q+1
        58: 2q^2+4q+1
        59: q^2+q
        60: 3q^2+2q
        61: 3q^2+4q+1
        63: 4q^2+5q+1
        65: 2q^2+4q+1
        67: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 6q^2+6q+1
        73: 3q^2+5q+1
        75: 4q^2+5q+1
        77: 4q^2+5q+1
        79: q^3+3q^2+4q+1
        80: 2q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+5q+1
        83: 2q^2+4q+1
        84: q^3+5q^2+5q+1
        85: 3q^2+5q+1
        86: 2q^3+8q^2+6q+1
        87: q^3+5q^2+5q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 5q^2+6q+1
        98: 5q^2+6q+1
        99: q^3+3q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: q^2+q
       105: 2q^2+4q+1
       107: 3q^2+2q
       108: 3q^2+4q+1
       109: 2q^2+4q+1
       110: q^2+q
       112: 3q^2+5q+1
       114: 4q^2+5q+1
       116: 2q^2+4q+1
       117: 3q+1
       119: q^2+q
       120: 3q+1
       122: 2q^2+4q+1
       124: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+5q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: 3q^2+5q+1
       144: q^2+3q+1
       145: 5q^2+6q+1
       146: q^3+5q^2+5q+1
       147: 5q^2+6q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+q
       171: 2q^2+4q+1
       175: 3q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       183: q^2+q
       184: 3q+1
       185: 3q+1
       188: q^2+4q+1
       190: 2q^2+4q+1
       191: 3q+1
       195: q^2+3q+1
       196: q
       199: q^2+q
       200: 3q+1
       201: 2q^2+2q
       202: 3q^2+4q+1
       203: q^2+2q+1
       206: q^2+2q+1
       208: q^2+4q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: q^2+4q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q^2+3q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: q^2+3q+1
       265: 3q+1
       272: q^2+2q+1
       277: 3q+1
       280: q+1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       293: q^2+q
       294: 3q+1
       295: 3q+1
       298: q^2+4q+1
       303: q+1
       307: q
       308: 2q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       321: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q^2+2q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: q+1
       353: 3q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: q+1
       387: 3q+1
       398: q+1
       402: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       431: 1
       439: q+1
       448: 1
       449: 1
       452: 1
       453: q
       454: 2q+1
       456: 1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       473: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: q+1
       531: q+1
       550: 1
       554: 1
       558: q+1
       562: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       591: 1
       595: 1
       598: 1
       600: q+1
       602: 1
       607: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       707: 1
       711: 1
       714: 1
       738: 1
       742: 1
       746: 1
       750: 1
       778: 1
       782: 1
       784: 1
       787: 1
       790: 1
       807: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       847: 1
       868: 1
       876: 1
       898: 1
       901: 1
       937: 1
       949: 1
       957: 1
      1003: 1
      1006: 1
      1043: 1
      1111: 1

1112:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 4q^2+5q+1
        23: 4q^2+5q+1
        24: q^3+3q^2+4q+1
        25: 2q^3+8q^2+6q+1
        26: 2q^3+8q^2+6q+1
        27: 3q^3+6q^2+5q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 4q^2+5q+1
        32: 2q^2+4q+1
        33: 3q^2+5q+1
        34: 2q^3+8q^2+6q+1
        35: q^3+5q^2+5q+1
        36: 6q^2+6q+1
        37: 4q^2+5q+1
        39: 4q^2+5q+1
        41: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 4q^2+5q+1
        53: 4q^2+5q+1
        54: q^3+3q^2+4q+1
        55: 2q^3+8q^2+6q+1
        56: 2q^3+8q^2+6q+1
        57: 3q^3+6q^2+5q+1
        58: q^2+q
        59: 2q^2+4q+1
        60: 3q^2+2q
        61: 3q^2+4q+1
        62: 4q^2+5q+1
        64: 2q^2+4q+1
        66: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 6q^2+6q+1
        73: 3q^2+5q+1
        74: 4q^2+5q+1
        76: 4q^2+5q+1
        78: q^3+3q^2+4q+1
        80: 2q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+5q+1
        83: 2q^2+4q+1
        84: q^3+5q^2+5q+1
        85: 3q^2+5q+1
        86: 2q^3+8q^2+6q+1
        87: q^3+5q^2+5q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 5q^2+6q+1
        98: 5q^2+6q+1
        99: q^3+3q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: q^2+q
       106: 2q^2+4q+1
       107: 3q^2+2q
       108: 3q^2+4q+1
       109: q^2+q
       110: 2q^2+4q+1
       111: 3q^2+5q+1
       113: 4q^2+5q+1
       115: 2q^2+4q+1
       118: 3q+1
       119: q^2+q
       120: 3q+1
       121: 2q^2+4q+1
       123: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+5q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: 3q^2+5q+1
       144: q^2+3q+1
       145: 5q^2+6q+1
       146: q^3+5q^2+5q+1
       147: 5q^2+6q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+q
       172: 2q^2+4q+1
       176: 3q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       183: q^2+q
       184: 3q+1
       186: 3q+1
       187: q^2+4q+1
       189: 2q^2+4q+1
       192: 3q+1
       195: q
       196: q^2+3q+1
       199: q^2+q
       200: 3q+1
       201: 2q^2+2q
       202: 3q^2+4q+1
       204: q^2+2q+1
       205: q^2+2q+1
       207: q^2+4q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: q^2+4q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q^2+3q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: q^2+3q+1
       266: 3q+1
       273: q^2+2q+1
       278: 3q+1
       279: q+1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       293: q^2+q
       294: 3q+1
       296: 3q+1
       297: q^2+4q+1
       304: q+1
       307: q
       308: 2q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       322: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q^2+2q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: q+1
       353: 3q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: q+1
       388: 3q+1
       399: q+1
       404: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       432: 1
       440: q+1
       448: 1
       450: 1
       451: 1
       453: q
       454: 2q+1
       455: 1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       474: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: q+1
       532: q+1
       552: 1
       555: 1
       559: q+1
       563: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       592: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       608: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       708: 1
       712: 1
       716: 1
       739: 1
       743: 1
       747: 1
       751: 1
       777: 1
       781: 1
       783: 1
       788: 1
       789: 1
       808: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       848: 1
       868: 1
       876: 1
       899: 1
       902: 1
       938: 1
       950: 1
       958: 1
      1002: 1
      1007: 1
      1042: 1
      1112: 1

1113:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 4q^2+5q+1
        23: 4q^2+5q+1
        24: q^3+3q^2+4q+1
        25: 2q^3+8q^2+6q+1
        26: 2q^3+8q^2+6q+1
        27: 3q^3+6q^2+5q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 4q^2+5q+1
        32: 2q^2+4q+1
        33: 3q^2+5q+1
        34: 2q^3+8q^2+6q+1
        35: q^3+5q^2+5q+1
        36: 6q^2+6q+1
        38: 4q^2+5q+1
        40: 4q^2+5q+1
        42: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 4q^2+5q+1
        53: 4q^2+5q+1
        54: q^3+3q^2+4q+1
        55: 2q^3+8q^2+6q+1
        56: 2q^3+8q^2+6q+1
        57: 3q^3+6q^2+5q+1
        58: q^2+q
        59: 2q^2+4q+1
        60: 3q^2+4q+1
        61: 3q^2+2q
        63: 4q^2+5q+1
        65: 2q^2+4q+1
        67: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 6q^2+6q+1
        73: 3q^2+5q+1
        75: 4q^2+5q+1
        77: 4q^2+5q+1
        79: q^3+3q^2+4q+1
        80: 2q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+5q+1
        83: 2q^2+4q+1
        84: q^3+5q^2+5q+1
        85: 3q^2+5q+1
        86: 2q^3+8q^2+6q+1
        87: q^3+5q^2+5q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: 5q^2+6q+1
        98: 5q^2+6q+1
        99: q^3+3q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: 2q^2+4q+1
       105: q^2+q
       107: 3q^2+4q+1
       108: 3q^2+2q
       109: q^2+q
       110: 2q^2+4q+1
       112: 3q^2+5q+1
       114: 4q^2+5q+1
       116: 2q^2+4q+1
       118: 3q+1
       119: 3q+1
       120: q^2+q
       122: 2q^2+4q+1
       124: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+5q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: 3q^2+5q+1
       144: q^2+3q+1
       145: 5q^2+6q+1
       146: q^3+5q^2+5q+1
       147: 5q^2+6q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: 2q^2+4q+1
       171: q^2+q
       174: 3q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       183: 3q+1
       184: q^2+q
       186: 3q+1
       188: q^2+4q+1
       190: 2q^2+4q+1
       192: 3q+1
       195: q
       196: q^2+3q+1
       199: 3q+1
       200: q^2+q
       201: 3q^2+4q+1
       202: 2q^2+2q
       204: q^2+2q+1
       206: q^2+2q+1
       208: q^2+4q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: q^2+4q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       230: 2q+1
       231: q^2+3q+1
       232: 3q+1
       233: 2q+1
       234: q^2+4q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       260: q^2+3q+1
       261: q
       264: 3q+1
       274: q^2+2q+1
       276: 3q+1
       280: q+1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       293: 3q+1
       294: q^2+q
       296: 3q+1
       298: q^2+4q+1
       304: q+1
       307: 2q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       322: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q^2+2q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       349: 2q+1
       350: q+1
       352: q+1
       353: 3q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: q+1
       386: 3q+1
       400: q+1
       403: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       432: 1
       440: q+1
       447: 1
       450: 1
       452: 1
       453: 2q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       474: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: q+1
       530: q+1
       551: 1
       556: 1
       560: q+1
       564: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       592: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       608: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       706: 1
       710: 1
       715: 1
       740: 1
       744: 1
       748: 1
       752: 1
       778: 1
       782: 1
       784: 1
       788: 1
       790: 1
       808: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       848: 1
       868: 1
       876: 1
       897: 1
       903: 1
       939: 1
       951: 1
       959: 1
      1003: 1
      1007: 1
      1043: 1
      1113: 1

1114:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 1
        60: 1
        61: q
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       108: q
       109: 1
       111: q+1
       113: 1
       115: q+1
       117: 1
       119: 1
       120: q
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       141: 1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: q+1
       179: 1
       181: q+1
       183: 1
       184: q
       185: 1
       187: q+1
       189: 1
       191: 1
       195: 1
       199: 1
       200: q
       201: 1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       271: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       284: q
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       294: q
       295: 1
       297: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       350: q+1
       352: q+1
       356: q^2+2q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       413: 1
       417: q+1
       419: 1
       420: q
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       447: 1
       448: q
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       521: 1
       529: 1
       549: 1
       553: 1
       561: 1
       585: 1
       589: 1
       590: q
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       643: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       680: 1
       685: 1
       709: 1
       713: 1
       737: 1
       749: 1
       775: 1
       779: 1
       781: 1
       787: 1
       817: 1
       819: 1
       833: 1
       866: 1
       874: 1
       900: 1
       940: 1
       994: 1
       998: 1
      1036: 1
      1114: 1

1115:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 1
        60: q
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       105: 1
       107: q
       108: 1
       109: 1
       112: q+1
       114: 1
       116: q+1
       117: 1
       119: q
       120: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       141: 1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       183: q
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       195: 1
       199: q
       200: 1
       201: q
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       272: 1
       277: 1
       280: 1
       282: q+1
       283: q
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       293: q
       294: 1
       295: 1
       298: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       350: q+1
       352: q+1
       356: q^2+2q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       414: 1
       418: q+1
       419: q
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       447: q
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       523: 1
       531: 1
       550: 1
       554: 1
       562: 1
       586: 1
       589: q
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       643: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       680: 1
       685: 1
       711: 1
       714: 1
       738: 1
       750: 1
       776: 1
       780: 1
       782: 1
       787: 1
       817: 1
       820: 1
       834: 1
       866: 1
       874: 1
       901: 1
       941: 1
       995: 1
       998: 1
      1037: 1
      1115: 1

1116:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: 1
        60: q
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       106: 1
       107: q
       108: 1
       110: 1
       111: q+1
       113: 1
       115: q+1
       118: 1
       119: q
       120: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       141: 1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: q+1
       179: 1
       181: q+1
       183: q
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       196: 1
       199: q
       200: 1
       201: q
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       273: 1
       278: 1
       279: 1
       281: q+1
       283: q
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       293: q
       294: 1
       296: 1
       297: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       350: q+1
       352: q+1
       356: q^2+2q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       413: 1
       417: q+1
       419: q
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       447: q
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       524: 1
       532: 1
       552: 1
       555: 1
       563: 1
       585: 1
       589: q
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       644: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       680: 1
       685: 1
       712: 1
       716: 1
       739: 1
       751: 1
       775: 1
       779: 1
       781: 1
       788: 1
       818: 1
       819: 1
       833: 1
       866: 1
       874: 1
       902: 1
       942: 1
       994: 1
       999: 1
      1036: 1
      1116: 1

1117:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: 1
        60: 1
        61: q
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       108: q
       110: 1
       112: q+1
       114: 1
       116: q+1
       118: 1
       119: 1
       120: q
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       141: 1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q+1
       146: q+1
       147: q^2+2q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: q+1
       180: 1
       182: q+1
       183: 1
       184: q
       186: 1
       188: q+1
       190: 1
       192: 1
       196: 1
       199: 1
       200: q
       201: 1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       274: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       284: q
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       294: q
       296: 1
       298: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       350: q+1
       352: q+1
       356: q^2+2q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       414: 1
       418: q+1
       419: 1
       420: q
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       447: 1
       448: q
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       522: 1
       530: 1
       551: 1
       556: 1
       564: 1
       586: 1
       589: 1
       590: q
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       644: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       680: 1
       685: 1
       710: 1
       715: 1
       740: 1
       752: 1
       776: 1
       780: 1
       782: 1
       788: 1
       818: 1
       820: 1
       834: 1
       866: 1
       874: 1
       903: 1
       943: 1
       995: 1
       999: 1
      1037: 1
      1117: 1

1118:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 2q^3+8q^2+6q+1
        23: 2q^3+8q^2+6q+1
        24: 3q^3+6q^2+5q+1
        25: 4q^2+5q+1
        26: 4q^2+5q+1
        27: q^3+3q^2+4q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 2q^3+8q^2+6q+1
        32: q^3+5q^2+5q+1
        33: 6q^2+6q+1
        34: 4q^2+5q+1
        35: 2q^2+4q+1
        36: 3q^2+5q+1
        37: 4q^2+5q+1
        39: 4q^2+5q+1
        41: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 2q^3+8q^2+6q+1
        53: 2q^3+8q^2+6q+1
        54: 3q^3+6q^2+5q+1
        55: 4q^2+5q+1
        56: 4q^2+5q+1
        57: q^3+3q^2+4q+1
        58: 3q^2+4q+1
        59: 3q^2+2q
        60: 2q^2+4q+1
        61: q^2+q
        62: 4q^2+5q+1
        64: 2q^2+4q+1
        66: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 3q^2+5q+1
        73: 6q^2+6q+1
        74: 4q^2+5q+1
        76: 4q^2+5q+1
        78: q^3+3q^2+4q+1
        80: q^3+5q^2+5q+1
        81: 3q^2+5q+1
        82: 2q^3+8q^2+6q+1
        83: q^3+5q^2+5q+1
        84: 2q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+5q+1
        87: 2q^2+4q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: 5q^2+6q+1
        95: 5q^2+6q+1
        96: q^3+3q^2+3q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: 2q^2+4q+1
       106: q^2+q
       107: 2q^2+4q+1
       108: q^2+q
       109: 3q^2+4q+1
       110: 3q^2+2q
       111: 3q^2+5q+1
       113: 4q^2+5q+1
       115: 2q^2+4q+1
       117: 3q+1
       118: q^2+q
       119: 3q+1
       121: 2q^2+4q+1
       123: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: q^2+4q+1
       136: 3q^2+5q+1
       137: 3q^2+5q+1
       138: q^2+3q+1
       139: 5q^2+6q+1
       140: q^2+2q+1
       141: q^3+5q^2+5q+1
       142: 5q^2+6q+1
       143: q^2+4q+1
       144: 2q+1
       145: q^2+4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q^2+4q+1
       172: q^2+q
       173: 3q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       183: 3q+1
       185: 3q+1
       186: q^2+q
       187: q^2+4q+1
       189: 2q^2+4q+1
       191: 3q+1
       192: q^2+q
       193: q^2+2q+1
       195: 3q^2+4q+1
       196: 2q^2+2q
       197: q^2+2q+1
       199: 3q+1
       201: q^2+3q+1
       202: q
       207: q^2+4q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: q^2+4q+1
       223: 2q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q^2+3q+1
       262: q
       263: 3q+1
       267: q^2+2q+1
       275: 3q+1
       279: q+1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       293: 3q+1
       295: 3q+1
       296: q^2+q
       297: q^2+4q+1
       299: q+1
       301: q+1
       303: 2q+1
       304: q
       305: q+1
       307: q+1
       315: q+1
       317: 2q+1
       319: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: q^2+4q+1
       350: 2q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: q+1
       385: 3q+1
       389: q+1
       393: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: 1
       453: q+1
       465: 1
       467: 1
       469: q+1
       471: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: q+1
       529: q+1
       533: 1
       537: 1
       541: q+1
       545: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       593: 1
       595: 1
       597: 1
       599: q+1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       777: 1
       781: 1
       783: 1
       785: 1
       789: 1
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       825: 1
       841: 1
       845: 1
       868: 1
       872: 1
       896: 1
       904: 1
       912: 1
       928: 1
       932: 1
      1002: 1
      1004: 1
      1024: 1
      1118: 1

1119:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 2q^3+8q^2+6q+1
        23: 2q^3+8q^2+6q+1
        24: 3q^3+6q^2+5q+1
        25: 4q^2+5q+1
        26: 4q^2+5q+1
        27: q^3+3q^2+4q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 2q^3+8q^2+6q+1
        32: q^3+5q^2+5q+1
        33: 6q^2+6q+1
        34: 4q^2+5q+1
        35: 2q^2+4q+1
        36: 3q^2+5q+1
        38: 4q^2+5q+1
        40: 4q^2+5q+1
        42: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 2q^3+8q^2+6q+1
        53: 2q^3+8q^2+6q+1
        54: 3q^3+6q^2+5q+1
        55: 4q^2+5q+1
        56: 4q^2+5q+1
        57: q^3+3q^2+4q+1
        58: 3q^2+2q
        59: 3q^2+4q+1
        60: 2q^2+4q+1
        61: q^2+q
        63: 4q^2+5q+1
        65: 2q^2+4q+1
        67: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 3q^2+5q+1
        73: 6q^2+6q+1
        75: 4q^2+5q+1
        77: 4q^2+5q+1
        79: q^3+3q^2+4q+1
        80: q^3+5q^2+5q+1
        81: 3q^2+5q+1
        82: 2q^3+8q^2+6q+1
        83: q^3+5q^2+5q+1
        84: 2q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+5q+1
        87: 2q^2+4q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: 5q^2+6q+1
        95: 5q^2+6q+1
        96: q^3+3q^2+3q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: 2q^2+4q+1
       105: q^2+q
       107: 2q^2+4q+1
       108: q^2+q
       109: 3q^2+2q
       110: 3q^2+4q+1
       112: 3q^2+5q+1
       114: 4q^2+5q+1
       116: 2q^2+4q+1
       117: q^2+q
       118: 3q+1
       119: 3q+1
       122: 2q^2+4q+1
       124: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: q^2+4q+1
       136: 3q^2+5q+1
       137: 3q^2+5q+1
       138: q^2+3q+1
       139: 5q^2+6q+1
       140: q^2+2q+1
       141: q^3+5q^2+5q+1
       142: 5q^2+6q+1
       143: q^2+4q+1
       144: 2q+1
       145: q^2+4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: 2q^2+4q+1
       171: q^2+q
       174: 3q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       183: 3q+1
       185: q^2+q
       186: 3q+1
       188: q^2+4q+1
       190: 2q^2+4q+1
       191: q^2+q
       192: 3q+1
       193: q^2+2q+1
       195: 2q^2+2q
       196: 3q^2+4q+1
       198: q^2+2q+1
       199: 3q+1
       201: q^2+3q+1
       202: q
       208: q^2+4q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: q^2+4q+1
       223: 2q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q^2+3q+1
       261: q
       264: 3q+1
       268: q^2+2q+1
       276: 3q+1
       280: q+1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       293: 3q+1
       295: q^2+q
       296: 3q+1
       298: q^2+4q+1
       299: q+1
       302: q+1
       303: q
       304: 2q+1
       306: q+1
       307: q+1
       316: q+1
       318: 2q+1
       319: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: q^2+4q+1
       350: 2q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: q+1
       386: 3q+1
       390: q+1
       394: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: q+1
       446: q+1
       447: 1
       453: q+1
       466: 1
       468: 1
       470: q+1
       471: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: q+1
       530: q+1
       534: 1
       538: 1
       542: q+1
       546: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       593: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       778: 1
       782: 1
       784: 1
       785: 1
       790: 1
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       842: 1
       845: 1
       868: 1
       872: 1
       897: 1
       905: 1
       913: 1
       929: 1
       933: 1
      1003: 1
      1004: 1
      1025: 1
      1119: 1

1120:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 2q^3+8q^2+6q+1
        23: 2q^3+8q^2+6q+1
        24: 3q^3+6q^2+5q+1
        25: 4q^2+5q+1
        26: 4q^2+5q+1
        27: q^3+3q^2+4q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 2q^3+8q^2+6q+1
        32: q^3+5q^2+5q+1
        33: 6q^2+6q+1
        34: 4q^2+5q+1
        35: 2q^2+4q+1
        36: 3q^2+5q+1
        37: 4q^2+5q+1
        39: 4q^2+5q+1
        41: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 2q^3+8q^2+6q+1
        53: 2q^3+8q^2+6q+1
        54: 3q^3+6q^2+5q+1
        55: 4q^2+5q+1
        56: 4q^2+5q+1
        57: q^3+3q^2+4q+1
        58: 3q^2+2q
        59: 3q^2+4q+1
        60: q^2+q
        61: 2q^2+4q+1
        62: 4q^2+5q+1
        64: 2q^2+4q+1
        66: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 3q^2+5q+1
        73: 6q^2+6q+1
        74: 4q^2+5q+1
        76: 4q^2+5q+1
        78: q^3+3q^2+4q+1
        80: q^3+5q^2+5q+1
        81: 3q^2+5q+1
        82: 2q^3+8q^2+6q+1
        83: q^3+5q^2+5q+1
        84: 2q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+5q+1
        87: 2q^2+4q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: 5q^2+6q+1
        95: 5q^2+6q+1
        96: q^3+3q^2+3q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: q^2+q
       106: 2q^2+4q+1
       107: q^2+q
       108: 2q^2+4q+1
       109: 3q^2+2q
       110: 3q^2+4q+1
       111: 3q^2+5q+1
       113: 4q^2+5q+1
       115: 2q^2+4q+1
       117: q^2+q
       118: 3q+1
       120: 3q+1
       121: 2q^2+4q+1
       123: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: q^2+4q+1
       136: 3q^2+5q+1
       137: 3q^2+5q+1
       138: q^2+3q+1
       139: 5q^2+6q+1
       140: q^2+2q+1
       141: q^3+5q^2+5q+1
       142: 5q^2+6q+1
       143: q^2+4q+1
       144: 2q+1
       145: q^2+4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+q
       172: 2q^2+4q+1
       176: 3q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       184: 3q+1
       185: q^2+q
       186: 3q+1
       187: q^2+4q+1
       189: 2q^2+4q+1
       191: q^2+q
       192: 3q+1
       194: q^2+2q+1
       195: 2q^2+2q
       196: 3q^2+4q+1
       197: q^2+2q+1
       200: 3q+1
       201: q
       202: q^2+3q+1
       207: q^2+4q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: q^2+4q+1
       223: 2q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: q^2+3q+1
       266: 3q+1
       269: q^2+2q+1
       278: 3q+1
       279: q+1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       294: 3q+1
       295: q^2+q
       296: 3q+1
       297: q^2+4q+1
       300: q+1
       301: q+1
       303: q
       304: 2q+1
       305: q+1
       308: q+1
       315: q+1
       317: 2q+1
       320: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: q^2+4q+1
       350: 2q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: q+1
       388: 3q+1
       391: q+1
       396: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: q+1
       445: q+1
       448: 1
       454: q+1
       465: 1
       467: 1
       469: q+1
       472: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: q+1
       532: q+1
       536: 1
       539: 1
       543: q+1
       547: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       594: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       777: 1
       781: 1
       783: 1
       786: 1
       789: 1
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       826: 1
       841: 1
       846: 1
       868: 1
       872: 1
       899: 1
       906: 1
       914: 1
       930: 1
       934: 1
      1002: 1
      1005: 1
      1024: 1
      1120: 1

1121:    0: q^4+5q^3+10q^2+6q+1
         1: q^4+5q^3+10q^2+6q+1
         2: 4q^3+7q^2+5q+1
         3: 5q^3+10q^2+6q+1
         4: q^4+5q^3+10q^2+6q+1
         5: 5q^3+10q^2+6q+1
         6: q^4+5q^3+10q^2+6q+1
         7: 4q^3+7q^2+5q+1
         8: 2q^4+6q^3+8q^2+5q+1
         9: q^4+3q^3+4q^2+3q+1
        10: q^4+5q^3+10q^2+6q+1
        11: 5q^3+10q^2+6q+1
        12: q^4+5q^3+10q^2+6q+1
        13: 2q^3+6q^2+5q+1
        14: 2q^3+6q^2+5q+1
        15: 3q^3+7q^2+5q+1
        16: 2q^3+8q^2+6q+1
        17: 2q^3+8q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+5q^3+10q^2+6q+1
        20: q^4+5q^3+10q^2+6q+1
        21: 4q^3+7q^2+5q+1
        22: 2q^3+8q^2+6q+1
        23: 2q^3+8q^2+6q+1
        24: 3q^3+6q^2+5q+1
        25: 4q^2+5q+1
        26: 4q^2+5q+1
        27: q^3+3q^2+4q+1
        28: 2q^3+8q^2+6q+1
        29: q^4+5q^3+10q^2+6q+1
        30: 2q^3+6q^2+5q+1
        31: 2q^3+8q^2+6q+1
        32: q^3+5q^2+5q+1
        33: 6q^2+6q+1
        34: 4q^2+5q+1
        35: 2q^2+4q+1
        36: 3q^2+5q+1
        38: 4q^2+5q+1
        40: 4q^2+5q+1
        42: q^3+3q^2+4q+1
        43: 2q^3+6q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 3q^3+7q^2+5q+1
        46: 4q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+8q^2+6q+1
        50: 2q^3+8q^2+6q+1
        51: 2q^3+4q^2+3q+1
        52: 2q^3+8q^2+6q+1
        53: 2q^3+8q^2+6q+1
        54: 3q^3+6q^2+5q+1
        55: 4q^2+5q+1
        56: 4q^2+5q+1
        57: q^3+3q^2+4q+1
        58: 3q^2+4q+1
        59: 3q^2+2q
        60: q^2+q
        61: 2q^2+4q+1
        63: 4q^2+5q+1
        65: 2q^2+4q+1
        67: 3q^2+5q+1
        68: 2q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^3+6q^2+5q+1
        71: 2q^3+8q^2+6q+1
        72: 3q^2+5q+1
        73: 6q^2+6q+1
        75: 4q^2+5q+1
        77: 4q^2+5q+1
        79: q^3+3q^2+4q+1
        80: q^3+5q^2+5q+1
        81: 3q^2+5q+1
        82: 2q^3+8q^2+6q+1
        83: q^3+5q^2+5q+1
        84: 2q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+5q+1
        87: 2q^2+4q+1
        88: 4q^2+5q+1
        89: q^3+5q^2+5q+1
        90: q^3+3q^2+3q+1
        91: 4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+3q^2+3q+1
        94: 5q^2+6q+1
        95: 5q^2+6q+1
        96: q^3+3q^2+3q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: q^2+q
       105: 2q^2+4q+1
       107: q^2+q
       108: 2q^2+4q+1
       109: 3q^2+4q+1
       110: 3q^2+2q
       112: 3q^2+5q+1
       114: 4q^2+5q+1
       116: 2q^2+4q+1
       117: 3q+1
       118: q^2+q
       120: 3q+1
       122: 2q^2+4q+1
       124: q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: q^2+4q+1
       136: 3q^2+5q+1
       137: 3q^2+5q+1
       138: q^2+3q+1
       139: 5q^2+6q+1
       140: q^2+2q+1
       141: q^3+5q^2+5q+1
       142: 5q^2+6q+1
       143: q^2+4q+1
       144: 2q+1
       145: q^2+4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+3q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^2+2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+q
       171: 2q^2+4q+1
       175: 3q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       184: 3q+1
       185: 3q+1
       186: q^2+q
       188: q^2+4q+1
       190: 2q^2+4q+1
       191: 3q+1
       192: q^2+q
       194: q^2+2q+1
       195: 3q^2+4q+1
       196: 2q^2+2q
       198: q^2+2q+1
       200: 3q+1
       201: q
       202: q^2+3q+1
       208: q^2+4q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q^2+2q+1
       220: 2q^2+4q+1
       221: 2q^2+3q+1
       222: q^2+4q+1
       223: 2q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: q^2+4q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: q^2+3q+1
       265: 3q+1
       270: q^2+2q+1
       277: 3q+1
       280: q+1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       294: 3q+1
       295: 3q+1
       296: q^2+q
       298: q^2+4q+1
       300: q+1
       302: q+1
       303: 2q+1
       304: q
       306: q+1
       308: q+1
       316: q+1
       318: 2q+1
       320: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: q^2+4q+1
       350: 2q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: q+1
       387: 3q+1
       392: q+1
       395: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       448: 1
       454: q+1
       466: 1
       468: 1
       470: q+1
       472: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: q+1
       531: q+1
       535: 1
       540: 1
       544: q+1
       548: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       594: 1
       595: 1
       598: 1
       600: q+1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       778: 1
       782: 1
       784: 1
       786: 1
       790: 1
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       826: 1
       842: 1
       846: 1
       868: 1
       872: 1
       898: 1
       907: 1
       915: 1
       931: 1
       935: 1
      1003: 1
      1005: 1
      1025: 1
      1121: 1

1122:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: q
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       110: q
       111: q+1
       113: 1
       115: q+1
       117: 1
       118: q
       119: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: q+1
       179: 1
       181: q+1
       183: 1
       185: 1
       186: q
       187: q+1
       189: 1
       191: 1
       192: q
       193: 1
       195: 1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       286: q
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       296: q
       297: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: q+1
       348: 1
       350: q^2+2q+1
       351: 1
       352: 1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       422: q
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       585: 1
       589: 1
       593: 1
       595: 1
       596: q
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       639: 1
       641: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       674: 1
       679: 1
       709: 1
       717: 1
       721: 1
       733: 1
       775: 1
       779: 1
       781: 1
       785: 1
       793: 1
       795: 1
       809: 1
       866: 1
       870: 1
       904: 1
       916: 1
       994: 1
      1000: 1
      1020: 1
      1122: 1

1123:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       109: q
       110: 1
       112: q+1
       114: 1
       116: q+1
       117: q
       118: 1
       119: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: q+1
       180: 1
       182: q+1
       183: 1
       185: q
       186: 1
       188: q+1
       190: 1
       191: q
       192: 1
       193: 1
       195: q
       196: 1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       285: q
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       295: q
       296: 1
       298: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: q+1
       348: 1
       350: q^2+2q+1
       351: 1
       352: 1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       414: 1
       418: q+1
       419: 1
       421: q
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       586: 1
       589: 1
       593: 1
       595: q
       596: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       640: 1
       641: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       674: 1
       679: 1
       710: 1
       718: 1
       722: 1
       734: 1
       776: 1
       780: 1
       782: 1
       785: 1
       793: 1
       796: 1
       810: 1
       866: 1
       870: 1
       905: 1
       917: 1
       995: 1
      1000: 1
      1021: 1
      1123: 1

1124:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       109: q
       110: 1
       111: q+1
       113: 1
       115: q+1
       117: q
       118: 1
       120: 1
       121: 1
       123: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: q+1
       179: 1
       181: q+1
       184: 1
       185: q
       186: 1
       187: q+1
       189: 1
       191: q
       192: 1
       194: 1
       195: q
       196: 1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       278: 1
       279: 1
       281: q+1
       284: 1
       285: q
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       295: q
       296: 1
       297: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: q+1
       348: 1
       350: q^2+2q+1
       351: 1
       352: 1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       413: 1
       417: q+1
       420: 1
       421: q
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       585: 1
       590: 1
       594: 1
       595: q
       596: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       639: 1
       642: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       674: 1
       679: 1
       712: 1
       720: 1
       723: 1
       735: 1
       775: 1
       779: 1
       781: 1
       786: 1
       794: 1
       795: 1
       809: 1
       866: 1
       870: 1
       906: 1
       918: 1
       994: 1
      1001: 1
      1020: 1
      1124: 1

1125:    0: q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: q
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       110: q
       112: q+1
       114: 1
       116: q+1
       117: 1
       118: q
       120: 1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       184: 1
       185: 1
       186: q
       188: q+1
       190: 1
       191: 1
       192: q
       194: 1
       195: 1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       286: q
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       296: q
       298: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: q+1
       348: 1
       350: q^2+2q+1
       351: 1
       352: 1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       422: q
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       586: 1
       590: 1
       594: 1
       595: 1
       596: q
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       640: 1
       642: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       674: 1
       679: 1
       711: 1
       719: 1
       724: 1
       736: 1
       776: 1
       780: 1
       782: 1
       786: 1
       794: 1
       796: 1
       810: 1
       866: 1
       870: 1
       907: 1
       919: 1
       995: 1
      1001: 1
      1021: 1
      1125: 1

1126:    0: q^3+2q+1
         1: q^4+q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^4+q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: q^3+q+1
        11: q+1
        12: q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^4+q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q+1
        29: q^3+q+1
        30: q^3+2q+1
        31: q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: q^2+2q+1
        41: 2q+1
        43: q^3+q+1
        44: q^3+q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        60: q+1
        62: q+1
        64: 2q+1
        66: 2q+1
        68: q+1
        69: q+1
        70: q^3+q+1
        71: q+1
        72: 2q+1
        73: 2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       107: q+1
       109: q+1
       111: 2q+1
       113: q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: q+1
       123: 2q+1
       125: 1
       126: 1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       173: q+1
       177: q+1
       179: q+1
       181: 2q+1
       183: q+1
       185: q+1
       187: 2q+1
       189: q+1
       191: 1
       193: q+1
       195: q+1
       197: q+1
       199: 1
       201: q+1
       203: q+1
       205: q+1
       207: 1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: q+1
       267: q+1
       271: q+1
       275: 1
       279: q+1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: 2q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: q+1
       301: 1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: q+1
       385: 1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       549: 1
       553: 1
       561: 1
       565: 1
       569: 2
       573: 1
       577: 1
       579: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 2
       655: 1
       665: 1
       679: 1
       685: 1
       693: 1
       695: 1
       709: 1
       713: 1
       717: 1
       721: 1
       733: 1
       737: 1
       749: 1
       753: 1
       757: 2
       765: 1
       769: 1
       771: 1
       781: 1
       785: 1
       787: 1
       791: 1
       809: 1
       833: 1
       849: 1
       884: 1
       886: 1
       900: 1
       904: 1
       908: 1
       960: 1
      1010: 1
      1126: 1

1127:    0: q^3+2q+1
         1: q^4+q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^4+q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: q^3+q+1
        11: q+1
        12: q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^4+q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q+1
        29: q^3+q+1
        30: q^3+2q+1
        31: q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: q^2+2q+1
        41: 2q+1
        43: q^3+q+1
        44: q^3+q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        59: q+1
        61: q+1
        62: q+1
        64: 2q+1
        66: 2q+1
        68: q+1
        69: q+1
        70: q^3+q+1
        71: q+1
        72: 2q+1
        73: 2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       106: q+1
       108: q+1
       110: q+1
       111: 2q+1
       113: q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: q+1
       123: 2q+1
       125: 1
       126: 1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q^2+2q+1
       155: q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: q+1
       176: q+1
       177: q+1
       179: q+1
       181: 2q+1
       184: q+1
       186: q+1
       187: 2q+1
       189: q+1
       192: 1
       194: q+1
       196: q+1
       197: q+1
       200: 1
       202: q+1
       204: q+1
       205: q+1
       207: 1
       209: q+1
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: q+1
       269: q+1
       273: q+1
       278: 1
       279: q+1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: 2q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: q+1
       301: 1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: q+1
       388: 1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       552: 1
       555: 1
       563: 1
       568: 1
       570: 2
       575: 1
       577: 1
       579: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 2
       655: 1
       665: 1
       679: 1
       685: 1
       697: 1
       702: 1
       712: 1
       716: 1
       720: 1
       723: 1
       735: 1
       739: 1
       751: 1
       756: 1
       758: 2
       768: 1
       769: 1
       771: 1
       781: 1
       786: 1
       788: 1
       791: 1
       809: 1
       833: 1
       849: 1
       889: 1
       893: 1
       902: 1
       906: 1
       911: 1
       961: 1
      1010: 1
      1127: 1

1128:    0: q^3+2q+1
         1: q^4+q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^4+q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: q^3+q+1
        11: q+1
        12: q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^4+q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q+1
        29: q^3+q+1
        30: q^3+2q+1
        31: q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        38: 2q+1
        40: q^2+2q+1
        42: 2q+1
        43: q^3+q+1
        44: q^3+q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        59: q+1
        60: q+1
        63: q+1
        65: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q^3+q+1
        71: q+1
        72: 2q+1
        73: 2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       104: q+1
       107: q+1
       110: q+1
       112: 2q+1
       114: q+1
       116: 2q+1
       118: q+1
       119: q+1
       122: q+1
       124: 2q+1
       125: 1
       126: 1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: q+1
       174: q+1
       178: q+1
       180: q+1
       182: 2q+1
       183: q+1
       186: q+1
       188: 2q+1
       190: q+1
       192: 1
       193: q+1
       196: q+1
       198: q+1
       199: 1
       201: q+1
       204: q+1
       206: q+1
       208: 1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: q+1
       268: q+1
       274: q+1
       276: 1
       280: q+1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: 2q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: q+1
       302: 1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: q+1
       386: 1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       551: 1
       556: 1
       564: 1
       566: 1
       571: 2
       574: 1
       581: 1
       582: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 2
       656: 1
       665: 1
       679: 1
       685: 1
       699: 1
       703: 1
       710: 1
       715: 1
       718: 1
       722: 1
       734: 1
       740: 1
       752: 1
       754: 1
       759: 2
       766: 1
       773: 1
       774: 1
       782: 1
       785: 1
       788: 1
       792: 1
       810: 1
       834: 1
       850: 1
       890: 1
       894: 1
       903: 1
       905: 1
       909: 1
       962: 1
      1011: 1
      1128: 1

1129:    0: q^3+2q+1
         1: q^4+q^3+2q^2+2q+1
         2: q^3+2q+1
         3: q^2+2q+1
         4: q^3+2q+1
         5: q^2+2q+1
         6: q^4+q^3+2q^2+2q+1
         7: q^3+2q+1
         8: q^2+2q+1
         9: q^4+q^3+q+1
        10: q^3+q+1
        11: q+1
        12: q^3+q+1
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^3+q+1
        19: q^3+2q+1
        20: q^4+q^3+2q^2+2q+1
        21: q^3+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q+1
        29: q^3+q+1
        30: q^3+2q+1
        31: q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        38: 2q+1
        40: q^2+2q+1
        42: 2q+1
        43: q^3+q+1
        44: q^3+q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^3+q+1
        52: 2q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        61: q+1
        63: q+1
        65: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q^3+q+1
        71: q+1
        72: 2q+1
        73: 2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       105: q+1
       108: q+1
       109: q+1
       112: 2q+1
       114: q+1
       116: 2q+1
       117: q+1
       120: q+1
       122: q+1
       124: 2q+1
       125: 1
       126: 1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q^2+2q+1
       156: q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: q+1
       175: q+1
       178: q+1
       180: q+1
       182: 2q+1
       184: q+1
       185: q+1
       188: 2q+1
       190: q+1
       191: 1
       194: q+1
       195: q+1
       198: q+1
       200: 1
       202: q+1
       203: q+1
       206: q+1
       208: 1
       210: q+1
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: q+1
       270: q+1
       272: q+1
       277: 1
       280: q+1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: 2q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: q+1
       387: 1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       550: 1
       554: 1
       562: 1
       567: 1
       572: 2
       576: 1
       581: 1
       582: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 2
       656: 1
       665: 1
       679: 1
       685: 1
       700: 1
       704: 1
       711: 1
       714: 1
       719: 1
       724: 1
       736: 1
       738: 1
       750: 1
       755: 1
       760: 2
       767: 1
       773: 1
       774: 1
       782: 1
       786: 1
       787: 1
       792: 1
       810: 1
       834: 1
       850: 1
       891: 1
       895: 1
       901: 1
       907: 1
       910: 1
       963: 1
      1011: 1
      1129: 1

1130:    0: 3q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^2+2q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 3q^2+3q+1
        17: q^3+4q^2+3q+1
        18: q^2+2q+1
        19: 3q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 3q^2+3q+1
        50: q^3+4q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: 2q+1
        70: q+1
        71: 2q^2+2q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: 2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q^2+2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: 1
       104: q
       105: q
       107: q^2+q+1
       108: q
       109: q^2+q+1
       110: q
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: 2q^2+3q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q^2+3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       152: 2q
       153: q+1
       154: q^2+2q
       155: 1
       156: q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: 1
       170: q
       171: q
       173: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       183: 1
       185: 1
       187: q+1
       188: q
       189: 1
       190: q
       191: 1
       193: q+1
       195: q^2+q+1
       196: q
       197: 1
       198: q
       199: 1
       201: q^2+q+1
       202: q
       203: q+1
       205: 1
       206: q
       207: 1
       208: q
       209: 1
       210: 2q
       211: 1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 1
       238: 2q
       239: q+1
       240: q^2+2q
       241: 1
       242: q
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       259: 1
       260: q
       261: q
       263: 1
       267: 1
       268: q
       271: 1
       272: q
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: q+1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: 1
       301: 1
       302: q
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       312: q
       313: 1
       315: 1
       316: q
       317: 1
       318: 2q
       319: q+1
       321: q+1
       323: 1
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 1
       339: 2q
       340: q+1
       341: q^2+2q
       342: 1
       343: q
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       385: 1
       389: 1
       390: q
       393: 1
       397: 1
       398: q
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       424: q
       425: 1
       426: q
       427: 1
       428: 2q
       429: 1
       431: 1
       433: 1
       443: q+1
       445: 1
       446: q
       447: 1
       449: 1
       451: 1
       461: q+1
       463: 1
       464: q
       469: 1
       470: q
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       529: 1
       533: 1
       545: 1
       546: q
       549: 1
       561: 1
       562: q
       565: 1
       569: 1
       573: 1
       577: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       613: 1
       615: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       693: 1
       713: 1
       717: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       817: 1
       843: 1
       866: 1
       870: 1
       874: 1
       908: 1
       964: 1
       998: 1
      1000: 1
      1012: 1
      1130: 1

1131:    0: 3q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^2+2q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 3q^2+3q+1
        17: q^3+4q^2+3q+1
        18: q^2+2q+1
        19: 3q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 3q^2+3q+1
        50: q^3+4q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q^2+q+1
        61: q
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: 2q+1
        70: q+1
        71: 2q^2+2q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: 2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q^2+2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       104: 1
       106: q
       107: q^2+q+1
       108: q
       109: q
       110: q^2+q+1
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       118: 1
       119: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: 2q^2+3q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q^2+3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q
       152: 1
       153: q^2+2q
       154: q+1
       155: q
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q
       170: 1
       172: q
       174: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       183: 1
       186: 1
       187: q
       188: q+1
       189: q
       190: 1
       192: 1
       193: q+1
       195: q
       196: q^2+q+1
       197: q
       198: 1
       199: 1
       201: q^2+q+1
       202: q
       204: q+1
       205: q
       206: 1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q
       238: 1
       239: q^2+2q
       240: q+1
       241: q
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       260: 1
       262: q
       264: 1
       267: q
       268: 1
       273: q
       274: 1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       291: q
       292: q+1
       293: 1
       296: 1
       297: q
       298: 1
       299: 1
       301: q
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       311: q
       312: 1
       314: 1
       315: q
       316: 1
       317: 2q
       318: 1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 2q
       339: 1
       340: q^2+2q
       341: q+1
       342: q
       343: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       386: 1
       389: q
       390: 1
       394: 1
       399: q
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: 1
       429: 1
       432: 1
       434: 1
       443: q+1
       445: q
       446: 1
       447: 1
       450: 1
       452: 1
       462: q+1
       463: q
       464: 1
       469: q
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       530: 1
       534: 1
       545: q
       546: 1
       551: 1
       563: q
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       614: 1
       615: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       699: 1
       715: 1
       718: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       818: 1
       844: 1
       866: 1
       870: 1
       874: 1
       909: 1
       965: 1
       999: 1
      1000: 1
      1013: 1
      1131: 1

1132:    0: 3q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^2+2q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 3q^2+3q+1
        17: q^3+4q^2+3q+1
        18: q^2+2q+1
        19: 3q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 3q^2+3q+1
        50: q^3+4q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: 2q+1
        70: q+1
        71: 2q^2+2q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: 2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q^2+2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       103: q
       105: 1
       106: q
       107: q
       108: q^2+q+1
       109: q^2+q+1
       110: q
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       117: 1
       120: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: 2q^2+3q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q^2+3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q
       152: 1
       153: q^2+2q
       154: q+1
       155: q
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q
       171: 1
       172: q
       175: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       184: 1
       185: 1
       187: q
       188: q+1
       189: q
       190: 1
       191: 1
       194: q+1
       195: q^2+q+1
       196: q
       197: q
       198: 1
       200: 1
       201: q
       202: q^2+q+1
       203: q+1
       205: q
       206: 1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q
       238: 1
       239: q^2+2q
       240: q+1
       241: q
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       261: 1
       262: q
       265: 1
       269: q
       270: 1
       271: q
       272: 1
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       291: q
       292: q+1
       294: 1
       295: 1
       297: q
       298: 1
       300: 1
       301: q
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       311: q
       312: 1
       314: 1
       315: q
       316: 1
       317: 2q
       318: 1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 2q
       339: 1
       340: q^2+2q
       341: q+1
       342: q
       343: 1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       387: 1
       391: q
       392: 1
       395: 1
       397: q
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: 1
       430: 1
       431: 1
       434: 1
       444: q+1
       445: q
       446: 1
       448: 1
       449: 1
       452: 1
       461: q+1
       463: q
       464: 1
       469: q
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       531: 1
       535: 1
       547: q
       548: 1
       550: 1
       561: q
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       614: 1
       616: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       700: 1
       714: 1
       719: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       817: 1
       844: 1
       866: 1
       870: 1
       874: 1
       910: 1
       966: 1
       998: 1
      1001: 1
      1013: 1
      1132: 1

1133:    0: 3q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^2+2q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 3q^2+3q+1
        17: q^3+4q^2+3q+1
        18: q^2+2q+1
        19: 3q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 3q^2+3q+1
        50: q^3+4q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q
        61: q^2+q+1
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: 2q+1
        70: q+1
        71: 2q^2+2q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: 2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: 2q+1
        86: q^2+2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+3q+1
       102: q+1
       104: q
       105: q
       106: 1
       107: q
       108: q^2+q+1
       109: q
       110: q^2+q+1
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: 2q^2+3q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q^2+3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       152: 2q
       153: q+1
       154: q^2+2q
       155: 1
       156: q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       170: q
       171: q
       172: 1
       176: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       184: 1
       186: 1
       187: q+1
       188: q
       189: 1
       190: q
       192: 1
       194: q+1
       195: q
       196: q^2+q+1
       197: 1
       198: q
       200: 1
       201: q
       202: q^2+q+1
       204: q+1
       205: 1
       206: q
       207: 1
       208: q
       209: 1
       210: 2q
       211: 1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 1
       238: 2q
       239: q+1
       240: q^2+2q
       241: 1
       242: q
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+3q+1
       249: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: q
       262: 1
       266: 1
       269: 1
       270: q
       273: 1
       274: q
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: q+1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: 1
       301: 1
       302: q
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       312: q
       313: 1
       315: 1
       316: q
       317: 1
       318: 2q
       320: q+1
       322: q+1
       323: 1
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 1
       339: 2q
       340: q+1
       341: q^2+2q
       342: 1
       343: q
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       388: 1
       391: 1
       392: q
       396: 1
       399: 1
       400: q
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       424: q
       425: 1
       426: q
       427: 1
       428: 2q
       430: 1
       432: 1
       433: 1
       444: q+1
       445: 1
       446: q
       448: 1
       450: 1
       451: 1
       462: q+1
       463: 1
       464: q
       469: 1
       470: q
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       532: 1
       536: 1
       547: 1
       548: q
       552: 1
       563: 1
       564: q
       568: 1
       570: 1
       575: 1
       577: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       613: 1
       616: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       657: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       697: 1
       716: 1
       720: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       818: 1
       843: 1
       866: 1
       870: 1
       874: 1
       911: 1
       967: 1
       999: 1
      1001: 1
      1012: 1
      1133: 1

1134:    0: q^3+6q^2+7q+1
         1: q^3+6q^2+7q+1
         2: 5q^2+5q+1
         3: 6q^2+7q+1
         4: q^3+6q^2+7q+1
         5: 6q^2+7q+1
         6: q^3+6q^2+7q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+3q^2+3q+1
        10: q^3+6q^2+7q+1
        11: 6q^2+7q+1
        12: q^3+6q^2+7q+1
        13: 3q^2+5q+1
        14: 3q^2+5q+1
        15: 4q^2+5q+1
        16: 3q^2+7q+1
        17: 3q^2+7q+1
        18: 3q^2+3q+1
        19: q^3+6q^2+7q+1
        20: q^3+6q^2+7q+1
        21: 5q^2+5q+1
        22: 3q^2+7q+1
        23: 3q^2+7q+1
        24: 4q^2+5q+1
        25: 3q^2+7q+1
        26: 3q^2+7q+1
        27: 4q^2+5q+1
        28: 3q^2+7q+1
        29: q^3+6q^2+7q+1
        30: 3q^2+5q+1
        31: 3q^2+7q+1
        32: 2q^2+5q+1
        33: q^2+7q+1
        34: 3q^2+7q+1
        35: 2q^2+5q+1
        36: q^2+7q+1
        37: q^2+5q+1
        38: 2q
        39: q^2+5q+1
        40: 2q
        41: 2q^2+4q+1
        42: q^2+q
        43: 3q^2+5q+1
        44: 3q^2+5q+1
        45: 4q^2+5q+1
        46: 5q+1
        47: q^2+5q+1
        48: q^2+3q+1
        49: 3q^2+7q+1
        50: 3q^2+7q+1
        51: 3q^2+3q+1
        52: 3q^2+7q+1
        53: 3q^2+7q+1
        54: 4q^2+5q+1
        55: 3q^2+7q+1
        56: 3q^2+7q+1
        57: 4q^2+5q+1
        58: q^2+5q+1
        59: 2q
        60: q^2+5q+1
        61: 2q
        62: q^2+5q+1
        63: 2q
        64: q^2+4q+1
        65: q
        66: 5q+1
        67: 2q
        68: 3q+1
        69: 3q+1
        70: 3q^2+5q+1
        71: 3q^2+7q+1
        72: q^2+7q+1
        73: q^2+7q+1
        74: q^2+5q+1
        75: 2q
        76: q^2+5q+1
        77: 2q
        78: 2q^2+4q+1
        79: q^2+q
        80: 2q^2+5q+1
        81: 5q+1
        82: 3q^2+7q+1
        83: 2q^2+5q+1
        84: 2q^2+5q+1
        85: 5q+1
        86: 3q^2+7q+1
        87: 2q^2+5q+1
        88: 5q+1
        89: q^2+5q+1
        90: q^2+3q+1
        91: 5q+1
        92: q^2+5q+1
        93: q^2+3q+1
        94: q^2+6q+1
        95: q^2+6q+1
        96: 2q^2+3q+1
        97: q^2+6q+1
        98: q^2+6q+1
        99: 2q^2+3q+1
       100: q^2+6q+1
       101: q^2+6q+1
       102: q^2+4q+1
       103: 4q+1
       104: q
       105: q
       106: q
       107: q^2+5q+1
       108: 2q
       109: q^2+5q+1
       110: 2q
       111: 5q+1
       112: 2q
       113: q^2+5q+1
       114: 2q
       115: q^2+4q+1
       116: q
       117: 3q+1
       119: 3q+1
       121: q^2+4q+1
       122: q
       123: 4q+1
       124: q
       125: 3q+1
       126: 3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q+1
       134: 3q+1
       135: 5q+1
       136: 5q+1
       137: 5q+1
       138: 3q+1
       139: q^2+6q+1
       140: 3q+1
       141: 2q^2+5q+1
       142: q^2+6q+1
       143: 5q+1
       144: 3q+1
       145: q^2+6q+1
       146: 2q^2+5q+1
       147: q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+4q+1
       151: q^2+4q+1
       152: 2q
       153: q^2+4q+1
       154: 2q
       155: q^2+3q+1
       156: q
       157: 5q+1
       158: q^2+5q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: 4q+1
       170: q
       171: q
       172: q
       173: 3q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: 3q+1
       185: 3q+1
       187: 4q+1
       188: q
       189: q^2+4q+1
       190: q
       191: 3q+1
       193: 3q+1
       195: q^2+4q+1
       196: 2q
       197: 2q+1
       198: q
       199: 3q+1
       201: q^2+4q+1
       202: 2q
       203: 3q+1
       205: 2q+1
       206: q
       207: 4q+1
       208: q
       209: q^2+4q+1
       210: 2q
       211: q^2+3q+1
       212: q
       219: q+1
       220: 3q+1
       221: 3q+1
       222: 5q+1
       223: 3q+1
       224: 5q+1
       225: 3q+1
       226: 3q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 3q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+4q+1
       247: 3q+1
       248: 3q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: q
       263: 3q+1
       267: 2q+1
       268: q
       271: 2q+1
       272: q
       275: 3q+1
       283: q+1
       285: q+1
       287: 2q+1
       291: 2q+1
       293: 3q+1
       295: 3q+1
       297: 4q+1
       298: q
       299: q+1
       301: 1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: q+1
       321: q+1
       323: 1
       325: q^2+3q+1
       326: q
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 3q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       385: 3q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: 1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: q+1
       429: 1
       431: 1
       433: 1
       437: q+1
       439: q+1
       441: q+1
       443: q+1
       445: 1
       447: 1
       449: 1
       451: 1
       453: q+1
       457: q+1
       459: q+1
       461: q+1
       463: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       529: q+1
       533: 1
       541: q+1
       545: 1
       549: 1
       557: q+1
       561: 1
       565: 1
       569: 2
       573: 1
       577: 1
       579: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: q+1
       603: 1
       607: 1
       609: 1
       613: 1
       615: 1
       619: 1
       621: 1
       625: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       693: 1
       695: 1
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       805: 1
       807: 1
       811: 1
       815: 1
       825: 1
       827: 1
       835: 1
       839: 1
       845: 1
       847: 1
       851: 1
       857: 1
       868: 1
       872: 1
       876: 1
       908: 1
       928: 1
       948: 1
       974: 1
       988: 1
      1004: 1
      1006: 1
      1008: 1
      1134: 1

1135:    0: q^3+6q^2+7q+1
         1: q^3+6q^2+7q+1
         2: 5q^2+5q+1
         3: 6q^2+7q+1
         4: q^3+6q^2+7q+1
         5: 6q^2+7q+1
         6: q^3+6q^2+7q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+3q^2+3q+1
        10: q^3+6q^2+7q+1
        11: 6q^2+7q+1
        12: q^3+6q^2+7q+1
        13: 3q^2+5q+1
        14: 3q^2+5q+1
        15: 4q^2+5q+1
        16: 3q^2+7q+1
        17: 3q^2+7q+1
        18: 3q^2+3q+1
        19: q^3+6q^2+7q+1
        20: q^3+6q^2+7q+1
        21: 5q^2+5q+1
        22: 3q^2+7q+1
        23: 3q^2+7q+1
        24: 4q^2+5q+1
        25: 3q^2+7q+1
        26: 3q^2+7q+1
        27: 4q^2+5q+1
        28: 3q^2+7q+1
        29: q^3+6q^2+7q+1
        30: 3q^2+5q+1
        31: 3q^2+7q+1
        32: 2q^2+5q+1
        33: q^2+7q+1
        34: 3q^2+7q+1
        35: 2q^2+5q+1
        36: q^2+7q+1
        37: q^2+5q+1
        38: 2q
        39: q^2+5q+1
        40: 2q
        41: 2q^2+4q+1
        42: q^2+q
        43: 3q^2+5q+1
        44: 3q^2+5q+1
        45: 4q^2+5q+1
        46: 5q+1
        47: q^2+5q+1
        48: q^2+3q+1
        49: 3q^2+7q+1
        50: 3q^2+7q+1
        51: 3q^2+3q+1
        52: 3q^2+7q+1
        53: 3q^2+7q+1
        54: 4q^2+5q+1
        55: 3q^2+7q+1
        56: 3q^2+7q+1
        57: 4q^2+5q+1
        58: 2q
        59: q^2+5q+1
        60: 2q
        61: q^2+5q+1
        62: q^2+5q+1
        63: 2q
        64: q^2+4q+1
        65: q
        66: 5q+1
        67: 2q
        68: 3q+1
        69: 3q+1
        70: 3q^2+5q+1
        71: 3q^2+7q+1
        72: q^2+7q+1
        73: q^2+7q+1
        74: q^2+5q+1
        75: 2q
        76: q^2+5q+1
        77: 2q
        78: 2q^2+4q+1
        79: q^2+q
        80: 2q^2+5q+1
        81: 5q+1
        82: 3q^2+7q+1
        83: 2q^2+5q+1
        84: 2q^2+5q+1
        85: 5q+1
        86: 3q^2+7q+1
        87: 2q^2+5q+1
        88: 5q+1
        89: q^2+5q+1
        90: q^2+3q+1
        91: 5q+1
        92: q^2+5q+1
        93: q^2+3q+1
        94: q^2+6q+1
        95: q^2+6q+1
        96: 2q^2+3q+1
        97: q^2+6q+1
        98: q^2+6q+1
        99: 2q^2+3q+1
       100: q^2+6q+1
       101: q^2+6q+1
       102: q^2+4q+1
       103: q
       104: q
       105: q
       106: 4q+1
       107: 2q
       108: q^2+5q+1
       109: 2q
       110: q^2+5q+1
       111: 5q+1
       112: 2q
       113: q^2+5q+1
       114: 2q
       115: q^2+4q+1
       116: q
       118: 3q+1
       120: 3q+1
       121: q^2+4q+1
       122: q
       123: 4q+1
       124: q
       125: 3q+1
       126: 3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q+1
       134: 3q+1
       135: 5q+1
       136: 5q+1
       137: 5q+1
       138: 3q+1
       139: q^2+6q+1
       140: 3q+1
       141: 2q^2+5q+1
       142: q^2+6q+1
       143: 5q+1
       144: 3q+1
       145: q^2+6q+1
       146: 2q^2+5q+1
       147: q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+4q+1
       151: q^2+4q+1
       152: 2q
       153: q^2+4q+1
       154: 2q
       155: q^2+3q+1
       156: q
       157: 5q+1
       158: q^2+5q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: q
       170: q
       171: q
       172: 4q+1
       176: 3q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: 3q+1
       186: 3q+1
       187: 4q+1
       188: q
       189: q^2+4q+1
       190: q
       192: 3q+1
       194: 3q+1
       195: 2q
       196: q^2+4q+1
       197: 2q+1
       198: q
       200: 3q+1
       201: 2q
       202: q^2+4q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: 4q+1
       208: q
       209: q^2+4q+1
       210: 2q
       211: q^2+3q+1
       212: q
       219: q+1
       220: 3q+1
       221: 3q+1
       222: 5q+1
       223: 3q+1
       224: 5q+1
       225: 3q+1
       226: 3q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 3q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+4q+1
       247: 3q+1
       248: 3q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: 2q+1
       266: 3q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: q
       278: 3q+1
       284: q+1
       286: q+1
       287: 2q+1
       291: 2q+1
       294: 3q+1
       296: 3q+1
       297: 4q+1
       298: q
       300: q+1
       301: 1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       320: q+1
       322: q+1
       323: 1
       325: q^2+3q+1
       326: q
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 3q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       388: 3q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: 1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: q+1
       430: 1
       432: 1
       433: 1
       438: q+1
       440: q+1
       441: q+1
       444: q+1
       445: 1
       448: 1
       450: 1
       451: 1
       454: q+1
       458: q+1
       459: q+1
       462: q+1
       463: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 2
       479: 1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       532: q+1
       536: 1
       543: q+1
       547: 1
       552: 1
       559: q+1
       563: 1
       568: 1
       570: 2
       575: 1
       577: 1
       579: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: q+1
       604: 1
       608: 1
       609: 1
       613: 1
       616: 1
       620: 1
       622: 1
       625: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       697: 1
       702: 1
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       806: 1
       808: 1
       811: 1
       816: 1
       826: 1
       828: 1
       835: 1
       840: 1
       846: 1
       848: 1
       851: 1
       857: 1
       868: 1
       872: 1
       876: 1
       911: 1
       930: 1
       950: 1
       975: 1
       991: 1
      1005: 1
      1007: 1
      1008: 1
      1135: 1

1136:    0: q^3+6q^2+7q+1
         1: q^3+6q^2+7q+1
         2: 5q^2+5q+1
         3: 6q^2+7q+1
         4: q^3+6q^2+7q+1
         5: 6q^2+7q+1
         6: q^3+6q^2+7q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+3q^2+3q+1
        10: q^3+6q^2+7q+1
        11: 6q^2+7q+1
        12: q^3+6q^2+7q+1
        13: 3q^2+5q+1
        14: 3q^2+5q+1
        15: 4q^2+5q+1
        16: 3q^2+7q+1
        17: 3q^2+7q+1
        18: 3q^2+3q+1
        19: q^3+6q^2+7q+1
        20: q^3+6q^2+7q+1
        21: 5q^2+5q+1
        22: 3q^2+7q+1
        23: 3q^2+7q+1
        24: 4q^2+5q+1
        25: 3q^2+7q+1
        26: 3q^2+7q+1
        27: 4q^2+5q+1
        28: 3q^2+7q+1
        29: q^3+6q^2+7q+1
        30: 3q^2+5q+1
        31: 3q^2+7q+1
        32: 2q^2+5q+1
        33: q^2+7q+1
        34: 3q^2+7q+1
        35: 2q^2+5q+1
        36: q^2+7q+1
        37: 2q
        38: q^2+5q+1
        39: 2q
        40: q^2+5q+1
        41: q^2+q
        42: 2q^2+4q+1
        43: 3q^2+5q+1
        44: 3q^2+5q+1
        45: 4q^2+5q+1
        46: 5q+1
        47: q^2+5q+1
        48: q^2+3q+1
        49: 3q^2+7q+1
        50: 3q^2+7q+1
        51: 3q^2+3q+1
        52: 3q^2+7q+1
        53: 3q^2+7q+1
        54: 4q^2+5q+1
        55: 3q^2+7q+1
        56: 3q^2+7q+1
        57: 4q^2+5q+1
        58: 2q
        59: q^2+5q+1
        60: q^2+5q+1
        61: 2q
        62: 2q
        63: q^2+5q+1
        64: q
        65: q^2+4q+1
        66: 2q
        67: 5q+1
        68: 3q+1
        69: 3q+1
        70: 3q^2+5q+1
        71: 3q^2+7q+1
        72: q^2+7q+1
        73: q^2+7q+1
        74: 2q
        75: q^2+5q+1
        76: 2q
        77: q^2+5q+1
        78: q^2+q
        79: 2q^2+4q+1
        80: 2q^2+5q+1
        81: 5q+1
        82: 3q^2+7q+1
        83: 2q^2+5q+1
        84: 2q^2+5q+1
        85: 5q+1
        86: 3q^2+7q+1
        87: 2q^2+5q+1
        88: 5q+1
        89: q^2+5q+1
        90: q^2+3q+1
        91: 5q+1
        92: q^2+5q+1
        93: q^2+3q+1
        94: q^2+6q+1
        95: q^2+6q+1
        96: 2q^2+3q+1
        97: q^2+6q+1
        98: q^2+6q+1
        99: 2q^2+3q+1
       100: q^2+6q+1
       101: q^2+6q+1
       102: q^2+4q+1
       103: q
       104: 4q+1
       105: q
       106: q
       107: q^2+5q+1
       108: 2q
       109: 2q
       110: q^2+5q+1
       111: 2q
       112: 5q+1
       113: 2q
       114: q^2+5q+1
       115: q
       116: q^2+4q+1
       118: 3q+1
       119: 3q+1
       121: q
       122: q^2+4q+1
       123: q
       124: 4q+1
       125: 3q+1
       126: 3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q+1
       134: 3q+1
       135: 5q+1
       136: 5q+1
       137: 5q+1
       138: 3q+1
       139: q^2+6q+1
       140: 3q+1
       141: 2q^2+5q+1
       142: q^2+6q+1
       143: 5q+1
       144: 3q+1
       145: q^2+6q+1
       146: 2q^2+5q+1
       147: q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+4q+1
       151: 2q
       152: q^2+4q+1
       153: 2q
       154: q^2+4q+1
       155: q
       156: q^2+3q+1
       157: 5q+1
       158: q^2+5q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: q
       170: 4q+1
       171: q
       172: q
       174: 3q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: 3q+1
       186: 3q+1
       187: q
       188: 4q+1
       189: q
       190: q^2+4q+1
       192: 3q+1
       193: 3q+1
       195: 2q
       196: q^2+4q+1
       197: q
       198: 2q+1
       199: 3q+1
       201: q^2+4q+1
       202: 2q
       204: 3q+1
       205: q
       206: 2q+1
       207: q
       208: 4q+1
       209: 2q
       210: q^2+4q+1
       211: q
       212: q^2+3q+1
       219: q+1
       220: 3q+1
       221: 3q+1
       222: 5q+1
       223: 3q+1
       224: 5q+1
       225: 3q+1
       226: 3q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 3q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+4q+1
       247: 3q+1
       248: 3q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: q
       264: 3q+1
       267: q
       268: 2q+1
       273: q
       274: 2q+1
       276: 3q+1
       283: q+1
       286: q+1
       288: 2q+1
       292: 2q+1
       293: 3q+1
       296: 3q+1
       297: q
       298: 4q+1
       299: q+1
       302: 1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: q^2+3q+1
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 3q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       386: 3q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: 1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: q+1
       429: 1
       432: 1
       434: 1
       437: q+1
       440: q+1
       442: q+1
       443: q+1
       446: 1
       447: 1
       450: 1
       452: 1
       453: q+1
       458: q+1
       460: q+1
       462: q+1
       464: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       530: q+1
       534: 1
       542: q+1
       546: 1
       551: 1
       560: q+1
       564: 1
       566: 1
       571: 2
       574: 1
       581: 1
       582: 1
       589: 1
       592: 1
       593: 1
       596: 1
       600: q+1
       603: 1
       608: 1
       610: 1
       614: 1
       615: 1
       619: 1
       622: 1
       626: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       699: 1
       703: 1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       805: 1
       808: 1
       812: 1
       815: 1
       825: 1
       828: 1
       836: 1
       840: 1
       845: 1
       848: 1
       852: 1
       858: 1
       868: 1
       872: 1
       876: 1
       909: 1
       929: 1
       951: 1
       976: 1
       989: 1
      1004: 1
      1007: 1
      1009: 1
      1136: 1

1137:    0: q^3+6q^2+7q+1
         1: q^3+6q^2+7q+1
         2: 5q^2+5q+1
         3: 6q^2+7q+1
         4: q^3+6q^2+7q+1
         5: 6q^2+7q+1
         6: q^3+6q^2+7q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+3q^2+3q+1
        10: q^3+6q^2+7q+1
        11: 6q^2+7q+1
        12: q^3+6q^2+7q+1
        13: 3q^2+5q+1
        14: 3q^2+5q+1
        15: 4q^2+5q+1
        16: 3q^2+7q+1
        17: 3q^2+7q+1
        18: 3q^2+3q+1
        19: q^3+6q^2+7q+1
        20: q^3+6q^2+7q+1
        21: 5q^2+5q+1
        22: 3q^2+7q+1
        23: 3q^2+7q+1
        24: 4q^2+5q+1
        25: 3q^2+7q+1
        26: 3q^2+7q+1
        27: 4q^2+5q+1
        28: 3q^2+7q+1
        29: q^3+6q^2+7q+1
        30: 3q^2+5q+1
        31: 3q^2+7q+1
        32: 2q^2+5q+1
        33: q^2+7q+1
        34: 3q^2+7q+1
        35: 2q^2+5q+1
        36: q^2+7q+1
        37: 2q
        38: q^2+5q+1
        39: 2q
        40: q^2+5q+1
        41: q^2+q
        42: 2q^2+4q+1
        43: 3q^2+5q+1
        44: 3q^2+5q+1
        45: 4q^2+5q+1
        46: 5q+1
        47: q^2+5q+1
        48: q^2+3q+1
        49: 3q^2+7q+1
        50: 3q^2+7q+1
        51: 3q^2+3q+1
        52: 3q^2+7q+1
        53: 3q^2+7q+1
        54: 4q^2+5q+1
        55: 3q^2+7q+1
        56: 3q^2+7q+1
        57: 4q^2+5q+1
        58: q^2+5q+1
        59: 2q
        60: 2q
        61: q^2+5q+1
        62: 2q
        63: q^2+5q+1
        64: q
        65: q^2+4q+1
        66: 2q
        67: 5q+1
        68: 3q+1
        69: 3q+1
        70: 3q^2+5q+1
        71: 3q^2+7q+1
        72: q^2+7q+1
        73: q^2+7q+1
        74: 2q
        75: q^2+5q+1
        76: 2q
        77: q^2+5q+1
        78: q^2+q
        79: 2q^2+4q+1
        80: 2q^2+5q+1
        81: 5q+1
        82: 3q^2+7q+1
        83: 2q^2+5q+1
        84: 2q^2+5q+1
        85: 5q+1
        86: 3q^2+7q+1
        87: 2q^2+5q+1
        88: 5q+1
        89: q^2+5q+1
        90: q^2+3q+1
        91: 5q+1
        92: q^2+5q+1
        93: q^2+3q+1
        94: q^2+6q+1
        95: q^2+6q+1
        96: 2q^2+3q+1
        97: q^2+6q+1
        98: q^2+6q+1
        99: 2q^2+3q+1
       100: q^2+6q+1
       101: q^2+6q+1
       102: q^2+4q+1
       103: q
       104: q
       105: 4q+1
       106: q
       107: 2q
       108: q^2+5q+1
       109: q^2+5q+1
       110: 2q
       111: 2q
       112: 5q+1
       113: 2q
       114: q^2+5q+1
       115: q
       116: q^2+4q+1
       117: 3q+1
       120: 3q+1
       121: q
       122: q^2+4q+1
       123: q
       124: 4q+1
       125: 3q+1
       126: 3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q+1
       134: 3q+1
       135: 5q+1
       136: 5q+1
       137: 5q+1
       138: 3q+1
       139: q^2+6q+1
       140: 3q+1
       141: 2q^2+5q+1
       142: q^2+6q+1
       143: 5q+1
       144: 3q+1
       145: q^2+6q+1
       146: 2q^2+5q+1
       147: q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+4q+1
       151: 2q
       152: q^2+4q+1
       153: 2q
       154: q^2+4q+1
       155: q
       156: q^2+3q+1
       157: 5q+1
       158: q^2+5q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: q
       170: q
       171: 4q+1
       172: q
       175: 3q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: 3q+1
       185: 3q+1
       187: q
       188: 4q+1
       189: q
       190: q^2+4q+1
       191: 3q+1
       194: 3q+1
       195: q^2+4q+1
       196: 2q
       197: q
       198: 2q+1
       200: 3q+1
       201: 2q
       202: q^2+4q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: q
       208: 4q+1
       209: 2q
       210: q^2+4q+1
       211: q
       212: q^2+3q+1
       219: q+1
       220: 3q+1
       221: 3q+1
       222: 5q+1
       223: 3q+1
       224: 5q+1
       225: 3q+1
       226: 3q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 3q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+4q+1
       247: 3q+1
       248: 3q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: 2q+1
       265: 3q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       277: 3q+1
       284: q+1
       285: q+1
       288: 2q+1
       292: 2q+1
       294: 3q+1
       295: 3q+1
       297: q
       298: 4q+1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: q^2+3q+1
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 3q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       387: 3q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: 1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: q+1
       430: 1
       431: 1
       434: 1
       438: q+1
       439: q+1
       442: q+1
       444: q+1
       446: 1
       448: 1
       449: 1
       452: 1
       454: q+1
       457: q+1
       460: q+1
       461: q+1
       464: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 2
       480: 1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       531: q+1
       535: 1
       544: q+1
       548: 1
       550: 1
       558: q+1
       562: 1
       567: 1
       572: 2
       576: 1
       581: 1
       582: 1
       590: 1
       591: 1
       594: 1
       595: 1
       600: q+1
       604: 1
       607: 1
       610: 1
       614: 1
       616: 1
       620: 1
       621: 1
       626: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       700: 1
       704: 1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       806: 1
       807: 1
       812: 1
       816: 1
       826: 1
       827: 1
       836: 1
       839: 1
       846: 1
       847: 1
       852: 1
       858: 1
       868: 1
       872: 1
       876: 1
       910: 1
       931: 1
       949: 1
       977: 1
       990: 1
      1005: 1
      1006: 1
      1009: 1
      1137: 1

1138:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        64: q+1
        66: q+1
        69: q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       111: q+1
       115: q+1
       123: q+1
       127: q+1
       129: q+1
       131: q+1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: q+1
       147: q+1
       148: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       177: q+1
       181: q+1
       187: q+1
       197: 1
       205: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       223: q+1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       281: q+1
       289: q+1
       291: q+1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       336: 1
       338: 1
       340: q+1
       342: 1
       348: 1
       350: q+1
       351: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       417: q+1
       425: 1
       433: 1
       435: 1
       445: 1
       451: 1
       455: 1
       463: 1
       467: 1
       475: 1
       477: 1
       479: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       577: 1
       597: 1
       605: 1
       613: 1
       617: 1
       623: 1
       629: 1
       633: 1
       645: 1
       651: 1
       655: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       769: 1
       779: 1
       791: 1
       795: 1
       809: 1
       819: 1
       833: 1
       843: 1
       849: 1
       870: 1
       874: 1
       968: 1
      1010: 1
      1012: 1
      1020: 1
      1036: 1
      1138: 1

1139:    0: 5q^2+3q
         1: 3q^3+5q^2+3q
         2: 5q^2+3q
         3: 2q^3+5q^2+3q
         4: 5q^2+3q
         5: 2q^3+5q^2+3q
         6: 3q^3+5q^2+3q
         7: 5q^2+3q
         8: 2q^3+5q^2+3q
         9: q^3+3q^2+2q
        13: 5q^2+3q
        14: 5q^2+3q
        15: 2q^3+5q^2+3q
        16: 4q^2+3q
        17: q^3+4q^2+3q
        18: 3q^2+2q
        19: 5q^2+3q
        20: 3q^3+5q^2+3q
        21: 5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        30: 5q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: q^2+q
        38: 2q^2+2q
        39: q^2+q
        40: 2q^2+2q
        41: q^2+q
        42: 2q^2+2q
        46: 4q^2+3q
        47: q^3+4q^2+3q
        48: 3q^2+2q
        49: 4q^2+3q
        50: q^3+4q^2+3q
        51: 3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        64: q^2+q
        65: 2q^2+2q
        66: q^2+q
        67: q^2+2q
        69: 2q^2+2q
        72: 3q^2+3q
        73: 3q^2+3q
        74: q^2+q
        75: 2q^2+2q
        76: q^2+q
        77: 2q^2+2q
        78: q^2+q
        79: 2q^2+2q
        81: 3q^2+3q
        83: 4q^2+3q
        85: 3q^2+3q
        87: 4q^2+3q
        91: 4q^2+3q
        92: q^3+4q^2+3q
        93: 3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: 3q^2+3q
       102: q^2+3q
       111: q^2+q
       112: q^2+2q
       115: q^2+q
       116: 2q^2+2q
       123: q^2+q
       124: q^2+2q
       128: 2q
       130: 2q
       132: q^2+q
       134: 2q^2+2q
       135: 3q^2+3q
       136: 3q^2+3q
       138: q^2+2q
       140: 2q
       142: 2q^2+3q
       144: q^2+2q
       147: 2q^2+3q
       148: 2q
       150: q^2+3q
       151: q
       152: q^2+2q
       153: q^2+q
       154: 2q^2+2q
       155: q
       156: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 3q
       167: q^2+3q
       168: 2q
       178: q
       182: 2q
       187: q^2+q
       188: q^2+2q
       197: q
       198: q
       205: q
       206: q
       211: q
       212: q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       223: q^2+2q
       225: q^2+2q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 2q
       238: 2q
       240: 2q
       242: q
       244: 2q
       245: 2q
       247: 3q
       248: q^2+3q
       249: 2q
       256: 3q
       257: q^2+3q
       258: 2q
       282: q
       290: 2q
       292: q
       302: q
       305: q
       306: q
       312: q
       313: q
       314: q
       316: q
       323: q
       336: 2q
       339: 2q
       341: 2q
       343: q
       348: q
       350: q^2+2q
       351: 2q
       356: q^2+2q
       358: q
       359: 2q
       361: 2q
       363: 2q
       365: q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: q^2+3q
       373: 2q
       418: q
       426: q
       436: q
       446: q
       456: q
       464: q
       468: q
       475: q
       479: q
       486: 2q
       488: 2q
       490: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       598: q
       618: q
       634: q
       655: q
       659: 1
       661: q+1
       663: 1
       664: 1
       674: 1
       679: q
       680: 1
       685: q
       780: 1
       796: 1
       820: 1
       843: 1
       870: 1
       874: 1
       969: 1
      1012: 1
      1021: 1
      1037: 1
      1139: 1

1140:    0: q^2+q
         1: q^3+q^2+q
         2: q^4+q
         3: q^2+q
         4: q^2+q
         5: q^3+q^2+q
         6: q^3+q^2+q
         7: q^4+q
         8: q
         9: q^4+q
        13: q
        14: q
        15: q
        16: q^2+q
        17: q^3+q^2+q
        18: q^4+q
        19: q^2+q
        20: q^3+q^2+q
        21: q^4+q
        22: q^2+q
        23: q^2+q
        24: q
        25: q^2+q
        26: q^2+q
        27: q
        30: q
        32: q
        33: q^2+q
        35: q
        36: q^2+q
        37: q^2+q
        39: q^2+q
        41: q
        46: q
        47: q
        48: q
        49: q^2+q
        50: q^3+q^2+q
        51: q^4+q
        52: q^2+q
        53: q^2+q
        54: q
        55: q^2+q
        56: q^2+q
        57: q
        64: q
        66: q^2+q
        69: q
        72: q^2+q
        73: q^2+q
        74: q^2+q
        76: q^2+q
        78: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        93: q
        94: q^2+q
        95: q^2+q
        96: q
        97: q^2+q
        98: q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       111: q^2+q
       115: q
       123: q
       127: q^2+q
       129: q^2+q
       131: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q^2+q
       144: q
       147: q^2+q
       148: q
       150: q
       151: q
       153: q^2+q
       155: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q
       167: q^2+q
       168: q
       177: q
       181: q^2+q
       187: q
       197: q
       205: q
       211: q
       213: q
       215: q
       217: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       244: q
       245: q
       247: q
       248: q^2+q
       249: q
       281: q
       289: q
       291: q
       301: q
       305: q
       311: q
       313: q
       315: q
       323: q
       336: q
       338: q
       340: q^2+q
       342: q
       348: q
       350: q
       351: q
       356: q
       358: q
       359: q
       417: q
       425: q
       433: q
       445: q
       451: q
       463: q
       477: q
       479: q
       495: q
       500: q
       577: q
       613: q
       629: q
       651: 1
       771: 1
       849: 1
       970: 1
      1010: 1
      1140: 1

1141:    0: 5q^2+3q
         1: 3q^3+5q^2+3q
         2: 5q^2+3q
         3: 2q^3+5q^2+3q
         4: 5q^2+3q
         5: 2q^3+5q^2+3q
         6: 3q^3+5q^2+3q
         7: 5q^2+3q
         8: 2q^3+5q^2+3q
         9: q^3+3q^2+2q
        13: 5q^2+3q
        14: 5q^2+3q
        15: 2q^3+5q^2+3q
        16: 4q^2+3q
        17: q^3+4q^2+3q
        18: 3q^2+2q
        19: 5q^2+3q
        20: 3q^3+5q^2+3q
        21: 5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        30: 5q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: 2q^2+2q
        38: q^2+q
        39: 2q^2+2q
        40: q^2+q
        41: 2q^2+2q
        42: q^2+q
        46: 4q^2+3q
        47: q^3+4q^2+3q
        48: 3q^2+2q
        49: 4q^2+3q
        50: q^3+4q^2+3q
        51: 3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        64: 2q^2+2q
        65: q^2+q
        66: q^2+2q
        67: q^2+q
        69: 2q^2+2q
        72: 3q^2+3q
        73: 3q^2+3q
        74: 2q^2+2q
        75: q^2+q
        76: 2q^2+2q
        77: q^2+q
        78: 2q^2+2q
        79: q^2+q
        81: 3q^2+3q
        83: 4q^2+3q
        85: 3q^2+3q
        87: 4q^2+3q
        91: 4q^2+3q
        92: q^3+4q^2+3q
        93: 3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: 3q^2+3q
       102: q^2+3q
       111: q^2+2q
       112: q^2+q
       115: 2q^2+2q
       116: q^2+q
       123: q^2+2q
       124: q^2+q
       127: 2q
       129: 2q
       131: q^2+q
       134: 2q^2+2q
       135: 3q^2+3q
       136: 3q^2+3q
       138: q^2+2q
       140: 2q
       142: 2q^2+3q
       144: q^2+2q
       147: 2q^2+3q
       148: 2q
       150: q^2+3q
       151: q^2+2q
       152: q
       153: 2q^2+2q
       154: q^2+q
       155: q^2+2q
       156: q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 3q
       167: q^2+3q
       168: 2q
       177: q
       181: 2q
       187: q^2+2q
       188: q^2+q
       197: q
       198: q
       205: q
       206: q
       211: q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       223: q^2+2q
       225: q^2+2q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 2q
       237: 2q
       239: 2q
       241: q
       244: 2q
       245: 2q
       247: 3q
       248: q^2+3q
       249: 2q
       256: 3q
       257: q^2+3q
       258: 2q
       281: q
       289: 2q
       291: q
       301: q
       305: q
       306: q
       311: q
       313: q
       314: q
       315: q
       324: q
       336: 2q
       338: 2q
       340: 2q
       342: q
       348: q
       350: q^2+2q
       351: 2q
       356: q^2+2q
       358: q
       359: 2q
       360: 2q
       362: 2q
       364: q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: q^2+3q
       373: 2q
       417: q
       425: q
       435: q
       445: q
       455: q
       463: q
       467: q
       476: q
       480: q
       485: 2q
       487: 2q
       489: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       597: q
       617: q
       633: q
       656: q
       658: 1
       660: q+1
       662: 1
       664: 1
       674: 1
       679: q
       680: 1
       685: q
       779: 1
       795: 1
       819: 1
       844: 1
       870: 1
       874: 1
       971: 1
      1013: 1
      1020: 1
      1036: 1
      1141: 1

1142:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        30: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        65: q+1
        67: q+1
        69: q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        81: q+1
        83: q+1
        85: q+1
        87: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       112: q+1
       116: q+1
       124: q+1
       128: q+1
       130: q+1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       140: 1
       142: q+1
       144: q+1
       147: q+1
       148: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       178: q+1
       182: q+1
       188: q+1
       198: 1
       206: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       223: q+1
       225: q+1
       228: q+1
       229: 1
       230: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       282: q+1
       290: q+1
       292: q+1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       336: 1
       339: 1
       341: q+1
       343: 1
       348: 1
       350: q+1
       351: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       418: q+1
       426: 1
       434: 1
       436: 1
       446: 1
       452: 1
       456: 1
       464: 1
       468: 1
       476: 1
       478: 1
       480: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       581: 1
       598: 1
       606: 1
       614: 1
       618: 1
       624: 1
       630: 1
       634: 1
       646: 1
       652: 1
       656: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       773: 1
       780: 1
       792: 1
       796: 1
       810: 1
       820: 1
       834: 1
       844: 1
       850: 1
       870: 1
       874: 1
       972: 1
      1011: 1
      1013: 1
      1021: 1
      1037: 1
      1142: 1

1143:    0: q^2+q
         1: q^3+q^2+q
         2: q^4+q
         3: q^2+q
         4: q^2+q
         5: q^3+q^2+q
         6: q^3+q^2+q
         7: q^4+q
         8: q
         9: q^4+q
        13: q
        14: q
        15: q
        16: q^2+q
        17: q^3+q^2+q
        18: q^4+q
        19: q^2+q
        20: q^3+q^2+q
        21: q^4+q
        22: q^2+q
        23: q^2+q
        24: q
        25: q^2+q
        26: q^2+q
        27: q
        30: q
        32: q
        33: q^2+q
        35: q
        36: q^2+q
        38: q^2+q
        40: q^2+q
        42: q
        46: q
        47: q
        48: q
        49: q^2+q
        50: q^3+q^2+q
        51: q^4+q
        52: q^2+q
        53: q^2+q
        54: q
        55: q^2+q
        56: q^2+q
        57: q
        65: q
        67: q^2+q
        69: q
        72: q^2+q
        73: q^2+q
        75: q^2+q
        77: q^2+q
        79: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        93: q
        94: q^2+q
        95: q^2+q
        96: q
        97: q^2+q
        98: q^2+q
        99: q
       100: q
       101: q^2+q
       102: q
       112: q^2+q
       116: q
       124: q
       128: q^2+q
       130: q^2+q
       132: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q^2+q
       144: q
       147: q^2+q
       148: q
       150: q
       152: q
       154: q^2+q
       156: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q
       167: q^2+q
       168: q
       178: q
       182: q^2+q
       188: q
       198: q
       206: q
       212: q
       214: q
       216: q
       218: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       244: q
       245: q
       247: q
       248: q^2+q
       249: q
       282: q
       290: q
       292: q
       302: q
       306: q
       312: q
       314: q
       316: q
       324: q
       336: q
       339: q
       341: q^2+q
       343: q
       348: q
       350: q
       351: q
       356: q
       358: q
       359: q
       418: q
       426: q
       434: q
       446: q
       452: q
       464: q
       478: q
       480: q
       495: q
       500: q
       581: q
       614: q
       630: q
       652: 1
       774: 1
       850: 1
       973: 1
      1011: 1
      1143: 1

1144:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q^2+2q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: q+1
       109: q+1
       110: q^2+q
       111: q+1
       113: 2q+1
       115: q+1
       117: q+1
       118: q^2+q
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       186: q
       187: 1
       189: q+1
       191: q+1
       192: q^2+q
       193: q+1
       195: q+1
       196: q^2+q
       197: q+1
       199: q+1
       201: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       267: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       286: q
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       296: q
       297: 1
       299: 1
       301: q+1
       303: 1
       304: q
       305: 1
       307: 1
       315: q+1
       317: 2q+1
       319: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: q+1
       337: q+1
       338: q+1
       340: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       389: q+1
       393: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       422: q
       423: 1
       427: q+1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: q+1
       445: q+1
       447: 1
       453: 1
       465: 1
       467: 1
       469: q+1
       471: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       493: 1
       494: q+1
       496: 1
       497: 1
       498: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: q+1
       583: 1
       587: 1
       601: 1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       705: 1
       721: 1
       725: 1
       729: 1
       733: 1
       775: 1
       789: 1
       793: 1
       795: 1
       799: 1
       813: 1
       815: 1
       841: 1
       845: 1
       859: 1
       861: 1
       865: 1
       869: 1
       912: 1
       916: 1
       932: 1
       992: 1
      1014: 1
      1016: 1
      1144: 1

1145:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q^2+2q
        59: q^2+2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q^2+2q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: q+1
       109: q^2+q
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q^2+q
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       185: q
       186: 1
       188: 1
       190: q+1
       191: q^2+q
       192: q+1
       193: q+1
       195: q^2+q
       196: q+1
       198: q+1
       199: q+1
       201: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       268: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       285: q
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       295: q
       296: 1
       298: 1
       299: 1
       302: q+1
       303: q
       304: 1
       306: 1
       307: 1
       316: q+1
       318: 2q+1
       319: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       337: q+1
       339: q+1
       341: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       390: q+1
       394: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       421: q
       422: 1
       424: 1
       428: q+1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: 1
       453: 1
       466: 1
       468: 1
       470: q+1
       471: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       493: 1
       494: q+1
       496: 1
       497: 1
       498: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: q+1
       584: 1
       588: 1
       602: 1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       706: 1
       722: 1
       726: 1
       730: 1
       734: 1
       776: 1
       790: 1
       793: 1
       796: 1
       800: 1
       814: 1
       815: 1
       842: 1
       845: 1
       860: 1
       862: 1
       865: 1
       869: 1
       913: 1
       917: 1
       933: 1
       993: 1
      1015: 1
      1016: 1
      1145: 1

1146:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q^2+2q
        59: q^2+2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q^2+2q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       108: q+1
       109: q^2+q
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q^2+q
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       185: q
       186: 1
       187: 1
       189: q+1
       191: q^2+q
       192: q+1
       194: q+1
       195: q^2+q
       196: q+1
       197: q+1
       200: q+1
       202: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       269: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       285: q
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       295: q
       296: 1
       297: 1
       300: 1
       301: q+1
       303: q
       304: 1
       305: 1
       308: 1
       315: q+1
       317: 2q+1
       320: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: 1
       335: q+1
       337: q+1
       338: q+1
       340: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       391: q+1
       396: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       421: q
       422: 1
       423: 1
       427: q+1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       472: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       493: 1
       494: q+1
       496: 1
       497: 1
       498: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: q+1
       583: 1
       587: 1
       601: 1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       708: 1
       723: 1
       727: 1
       731: 1
       735: 1
       775: 1
       789: 1
       794: 1
       795: 1
       799: 1
       813: 1
       816: 1
       841: 1
       846: 1
       859: 1
       861: 1
       865: 1
       869: 1
       914: 1
       918: 1
       934: 1
       992: 1
      1014: 1
      1017: 1
      1146: 1

1147:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q+1
        73: q^2+2q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+2q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       108: q+1
       109: q+1
       110: q^2+q
       112: q+1
       114: 2q+1
       116: q+1
       117: q+1
       118: q^2+q
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       186: q
       188: 1
       190: q+1
       191: q+1
       192: q^2+q
       194: q+1
       195: q+1
       196: q^2+q
       198: q+1
       200: q+1
       202: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       270: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       286: q
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       296: q
       298: 1
       300: 1
       302: q+1
       303: 1
       304: q
       306: 1
       308: 1
       316: q+1
       318: 2q+1
       320: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       337: q+1
       339: q+1
       341: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       392: q+1
       395: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       422: q
       424: 1
       428: q+1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: q+1
       446: q+1
       448: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       472: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       493: 1
       494: q+1
       496: 1
       497: 1
       498: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: q+1
       584: 1
       588: 1
       602: 1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       686: 1
       687: 1
       690: 1
       691: 1
       707: 1
       724: 1
       728: 1
       732: 1
       736: 1
       776: 1
       790: 1
       794: 1
       796: 1
       800: 1
       814: 1
       816: 1
       842: 1
       846: 1
       860: 1
       862: 1
       865: 1
       869: 1
       915: 1
       919: 1
       935: 1
       993: 1
      1015: 1
      1017: 1
      1147: 1

1148:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       192: q
       193: 1
       195: 1
       197: 1
       199: q+1
       201: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: 1
       453: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       583: 1
       585: 1
       587: 1
       589: 1
       595: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       705: 1
       709: 1
       721: 1
       725: 1
       729: 1
       777: 1
       797: 1
       799: 1
       801: 1
       807: 1
       825: 1
       841: 1
       845: 1
       877: 1
       896: 1
       912: 1
       920: 1
      1018: 1
      1052: 1
      1148: 1

1149:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       191: q
       192: q+1
       193: 1
       196: 1
       198: 1
       199: q+1
       201: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: 1
       453: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       584: 1
       586: 1
       588: 1
       589: 1
       596: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       706: 1
       710: 1
       722: 1
       726: 1
       730: 1
       778: 1
       798: 1
       800: 1
       801: 1
       808: 1
       825: 1
       842: 1
       845: 1
       877: 1
       897: 1
       913: 1
       921: 1
      1019: 1
      1052: 1
      1149: 1

1150:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       191: q
       192: q+1
       194: 1
       196: 1
       197: 1
       200: q+1
       202: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: 1
       454: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       583: 1
       585: 1
       587: 1
       590: 1
       596: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       708: 1
       712: 1
       723: 1
       727: 1
       731: 1
       777: 1
       797: 1
       799: 1
       802: 1
       808: 1
       826: 1
       841: 1
       846: 1
       877: 1
       899: 1
       914: 1
       922: 1
      1018: 1
      1053: 1
      1150: 1

1151:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 2q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: 1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       192: q
       194: 1
       195: 1
       198: 1
       200: q+1
       202: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       270: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: 1
       454: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       584: 1
       586: 1
       588: 1
       590: 1
       595: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       675: 1
       676: 1
       681: 1
       686: 1
       687: 1
       707: 1
       711: 1
       724: 1
       728: 1
       732: 1
       778: 1
       798: 1
       800: 1
       802: 1
       807: 1
       826: 1
       842: 1
       846: 1
       877: 1
       898: 1
       915: 1
       923: 1
      1019: 1
      1053: 1
      1151: 1

1152:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: 3q^3+11q^2+6q+1
        23: q^4+7q^3+12q^2+6q+1
        24: 3q^3+11q^2+6q+1
        25: q^3+8q^2+6q+1
        26: 4q^3+9q^2+6q+1
        27: q^3+8q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 6q^2+5q+1
        32: 3q^3+11q^2+6q+1
        33: 2q^3+9q^2+6q+1
        34: 4q^2+5q+1
        35: q^3+8q^2+6q+1
        36: q^3+6q^2+6q+1
        37: q^3+6q^2+5q+1
        38: 2q^2+q
        39: 3q^3+7q^2+5q+1
        40: q^3+2q^2+q
        41: q^3+6q^2+5q+1
        42: 2q^2+q
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: q^3+7q^2+5q+1
        53: q^4+5q^3+9q^2+5q+1
        54: q^3+7q^2+5q+1
        55: 4q^2+5q+1
        56: 2q^3+6q^2+5q+1
        57: 4q^2+5q+1
        58: 3q^2+4q+1
        59: q^2+q
        60: 2q^2+3q+1
        61: 2q
        62: 3q^2+4q+1
        63: q^2+q
        64: q^3+6q^2+5q+1
        65: 2q^2+q
        66: q^3+5q^2+5q+1
        67: q^2+q
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 2q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        78: 2q^2+4q+1
        80: 6q^2+5q+1
        81: 2q^3+9q^2+6q+1
        82: 4q^2+4q+1
        83: q^3+7q^2+5q+1
        84: 4q^2+5q+1
        85: q^3+6q^2+6q+1
        86: 2q^2+4q+1
        87: 4q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: 5q^2+5q+1
        95: q^3+6q^2+5q+1
        96: 3q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: 2q^2+3q+1
       105: q
       106: q
       107: 2q+1
       108: q
       109: q^2+3q+1
       111: q^2+3q+1
       113: q^2+3q+1
       115: 2q^2+4q+1
       117: 3q^2+4q+1
       118: q^2+q
       119: 2q^2+3q+1
       120: 2q
       121: 3q^2+4q+1
       122: q^2+q
       123: q^3+5q^2+5q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 2q^2+4q+1
       136: 3q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+3q+1
       139: 2q^2+4q+1
       140: 2q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: q^2+4q+1
       144: 3q+1
       145: 4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       148: 2q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       151: 2q^2+4q+1
       153: q^3+4q^2+4q+1
       155: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 5q^2+5q+1
       161: q^3+6q^2+5q+1
       162: 3q^2+3q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       169: 2q+1
       173: 2q^2+3q+1
       175: q
       176: q
       177: 2q+1
       179: 2q+1
       181: 2q+1
       183: 2q+1
       184: q
       185: q^2+3q+1
       187: q^2+3q+1
       189: q^2+3q+1
       191: q^2+3q+1
       192: q
       193: 2q+1
       194: q
       195: q^2+3q+1
       197: q^2+3q+1
       199: q^2+2q+1
       200: 2q
       201: 2q+1
       202: q
       203: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+3q+1
       211: 2q^2+4q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q^2+4q+1
       228: 2q^2+3q+1
       229: 2q^2+4q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: 2q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q+1
       263: 2q+1
       267: 2q+1
       271: q+1
       275: q^2+2q+1
       277: q
       278: q
       279: 2q+1
       281: 2q+1
       283: 1
       285: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q+1
       294: q
       295: q+1
       297: q+1
       299: 2q+1
       300: q
       301: 2q+1
       303: q^2+3q+1
       305: q^2+3q+1
       307: 2q+1
       308: q
       309: 2q+1
       311: 1
       313: q+1
       315: 2q+1
       317: 2q+1
       319: 2q+1
       320: q
       321: 2q+1
       323: q+1
       325: q^2+3q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: 2q+1
       358: q+1
       359: 2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       377: 1
       381: q+1
       385: q+1
       389: q+1
       393: 2q+1
       397: 1
       401: q+1
       405: q+1
       413: q+1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: q+1
       433: q+1
       435: 2q+1
       437: q+1
       438: q
       439: q+1
       441: q+1
       443: 1
       444: 1
       445: q+2
       447: 1
       449: q+1
       451: 1
       455: 1
       461: 2
       463: 2
       465: 2q+1
       467: 2q+1
       469: q+1
       471: 2q+1
       472: q
       473: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: 2q+1
       514: q+1
       521: 1
       529: 1
       533: 1
       537: q+1
       541: q+1
       545: 1
       547: 1
       549: 1
       553: 1
       561: 2
       565: q+1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       585: 1
       589: 1
       591: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: 1
       605: q+1
       607: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: q+2
       623: 1
       629: 1
       631: 2
       633: 2
       639: q+1
       641: 1
       643: q+1
       645: 1
       651: 1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       693: 1
       698: 1
       709: 1
       713: 1
       721: 1
       725: 1
       733: 1
       735: 1
       737: 1
       749: 2
       753: 1
       757: 1
       765: 1
       767: 1
       769: 1
       772: 1
       781: 1
       787: 1
       797: 1
       801: 1
       803: 1
       807: 1
       809: 1
       811: 1
       833: 1
       849: 1
       855: 1
       871: 1
       880: 1
       884: 1
       888: 1
       900: 1
       920: 1
       924: 1
       960: 1
      1022: 1
      1028: 1
      1060: 1
      1152: 1

1153:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: 3q^3+11q^2+6q+1
        23: q^4+7q^3+12q^2+6q+1
        24: 3q^3+11q^2+6q+1
        25: q^3+8q^2+6q+1
        26: 4q^3+9q^2+6q+1
        27: q^3+8q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 6q^2+5q+1
        32: 3q^3+11q^2+6q+1
        33: 2q^3+9q^2+6q+1
        34: 4q^2+5q+1
        35: q^3+8q^2+6q+1
        36: q^3+6q^2+6q+1
        37: 2q^2+q
        38: q^3+6q^2+5q+1
        39: q^3+2q^2+q
        40: 3q^3+7q^2+5q+1
        41: 2q^2+q
        42: q^3+6q^2+5q+1
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: q^3+7q^2+5q+1
        53: q^4+5q^3+9q^2+5q+1
        54: q^3+7q^2+5q+1
        55: 4q^2+5q+1
        56: 2q^3+6q^2+5q+1
        57: 4q^2+5q+1
        58: 3q^2+4q+1
        59: q^2+q
        60: 2q
        61: 2q^2+3q+1
        62: q^2+q
        63: 3q^2+4q+1
        64: 2q^2+q
        65: q^3+6q^2+5q+1
        66: q^2+q
        67: q^3+5q^2+5q+1
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 2q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        79: 2q^2+4q+1
        80: 6q^2+5q+1
        81: 2q^3+9q^2+6q+1
        82: 4q^2+4q+1
        83: q^3+7q^2+5q+1
        84: 4q^2+5q+1
        85: q^3+6q^2+6q+1
        86: 2q^2+4q+1
        87: 4q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: 5q^2+5q+1
        95: q^3+6q^2+5q+1
        96: 3q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: q
       104: q
       105: 2q^2+3q+1
       107: q
       108: 2q+1
       109: q^2+3q+1
       112: q^2+3q+1
       114: q^2+3q+1
       116: 2q^2+4q+1
       117: 3q^2+4q+1
       118: q^2+q
       119: 2q
       120: 2q^2+3q+1
       121: q^2+q
       122: 3q^2+4q+1
       123: q^2+q
       124: q^3+5q^2+5q+1
       125: q^2+4q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 2q^2+4q+1
       136: 3q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+3q+1
       139: 2q^2+4q+1
       140: 2q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: q^2+4q+1
       144: 3q+1
       145: 4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       148: 2q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       152: 2q^2+4q+1
       154: q^3+4q^2+4q+1
       156: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 5q^2+5q+1
       161: q^3+6q^2+5q+1
       162: 3q^2+3q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       171: 2q+1
       173: q
       174: q
       175: 2q^2+3q+1
       178: 2q+1
       180: 2q+1
       182: 2q+1
       183: q
       184: 2q+1
       185: q^2+3q+1
       188: q^2+3q+1
       190: q^2+3q+1
       191: q^2+3q+1
       192: q
       193: q
       194: 2q+1
       195: q^2+3q+1
       198: q^2+3q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: 2q+1
       203: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+3q+1
       212: 2q^2+4q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q^2+4q+1
       228: 2q^2+3q+1
       229: 2q^2+4q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: 2q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       261: q+1
       265: 2q+1
       270: 2q+1
       272: q+1
       275: q
       276: q
       277: q^2+2q+1
       280: 2q+1
       282: 2q+1
       284: 1
       285: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q
       294: q+1
       295: q+1
       298: q+1
       299: q
       300: 2q+1
       302: 2q+1
       303: q^2+3q+1
       306: q^2+3q+1
       307: q
       308: 2q+1
       309: 2q+1
       312: 1
       314: q+1
       316: 2q+1
       318: 2q+1
       319: q
       320: 2q+1
       321: 2q+1
       324: q+1
       326: q^2+3q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: 2q+1
       358: q+1
       359: 2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       379: 1
       383: q+1
       387: q+1
       392: q+1
       395: 2q+1
       398: 1
       402: q+1
       408: q+1
       414: q+1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: q+1
       434: q+1
       436: 2q+1
       437: q
       438: q+1
       439: q+1
       442: q+1
       443: 1
       444: 1
       446: q+2
       448: 1
       449: q+1
       452: 1
       456: 1
       461: 2
       464: 2
       466: 2q+1
       468: 2q+1
       470: q+1
       471: q
       472: 2q+1
       473: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: 2q+1
       514: q+1
       523: 1
       531: 1
       535: 1
       540: q+1
       544: q+1
       546: 1
       548: 1
       550: 1
       554: 1
       562: 2
       567: q+1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 2
       604: 1
       606: q+1
       607: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: q+2
       624: 1
       630: 1
       631: 2
       634: 2
       640: q+1
       642: 1
       643: q+1
       646: 1
       652: 1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       694: 1
       700: 1
       711: 1
       714: 1
       724: 1
       728: 1
       734: 1
       736: 1
       738: 1
       750: 2
       755: 1
       760: 1
       765: 1
       767: 1
       770: 1
       773: 1
       782: 1
       787: 1
       798: 1
       802: 1
       803: 1
       807: 1
       810: 1
       812: 1
       834: 1
       850: 1
       856: 1
       871: 1
       880: 1
       885: 1
       891: 1
       901: 1
       923: 1
       925: 1
       963: 1
      1023: 1
      1028: 1
      1061: 1
      1153: 1

1154:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: 3q^3+11q^2+6q+1
        23: q^4+7q^3+12q^2+6q+1
        24: 3q^3+11q^2+6q+1
        25: q^3+8q^2+6q+1
        26: 4q^3+9q^2+6q+1
        27: q^3+8q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 6q^2+5q+1
        32: 3q^3+11q^2+6q+1
        33: 2q^3+9q^2+6q+1
        34: 4q^2+5q+1
        35: q^3+8q^2+6q+1
        36: q^3+6q^2+6q+1
        37: q^3+6q^2+5q+1
        38: 2q^2+q
        39: 3q^3+7q^2+5q+1
        40: q^3+2q^2+q
        41: q^3+6q^2+5q+1
        42: 2q^2+q
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: q^3+7q^2+5q+1
        53: q^4+5q^3+9q^2+5q+1
        54: q^3+7q^2+5q+1
        55: 4q^2+5q+1
        56: 2q^3+6q^2+5q+1
        57: 4q^2+5q+1
        58: q^2+q
        59: 3q^2+4q+1
        60: 2q
        61: 2q^2+3q+1
        62: 3q^2+4q+1
        63: q^2+q
        64: q^3+6q^2+5q+1
        65: 2q^2+q
        66: q^3+5q^2+5q+1
        67: q^2+q
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 2q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        78: 2q^2+4q+1
        80: 6q^2+5q+1
        81: 2q^3+9q^2+6q+1
        82: 4q^2+4q+1
        83: q^3+7q^2+5q+1
        84: 4q^2+5q+1
        85: q^3+6q^2+6q+1
        86: 2q^2+4q+1
        87: 4q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: 5q^2+5q+1
        95: q^3+6q^2+5q+1
        96: 3q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: q
       104: q
       106: 2q^2+3q+1
       107: q
       108: 2q+1
       110: q^2+3q+1
       111: q^2+3q+1
       113: q^2+3q+1
       115: 2q^2+4q+1
       117: q^2+q
       118: 3q^2+4q+1
       119: 2q
       120: 2q^2+3q+1
       121: 3q^2+4q+1
       122: q^2+q
       123: q^3+5q^2+5q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 2q^2+4q+1
       136: 3q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+3q+1
       139: 2q^2+4q+1
       140: 2q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: q^2+4q+1
       144: 3q+1
       145: 4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       148: 2q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       151: 2q^2+4q+1
       153: q^3+4q^2+4q+1
       155: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 5q^2+5q+1
       161: q^3+6q^2+5q+1
       162: 3q^2+3q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       172: 2q+1
       173: q
       174: q
       176: 2q^2+3q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       183: q
       184: 2q+1
       186: q^2+3q+1
       187: q^2+3q+1
       189: q^2+3q+1
       191: q
       192: q^2+3q+1
       193: q
       194: 2q+1
       196: q^2+3q+1
       197: q^2+3q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: 2q+1
       204: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+3q+1
       211: 2q^2+4q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q^2+4q+1
       228: 2q^2+3q+1
       229: 2q^2+4q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: 2q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       262: q+1
       266: 2q+1
       269: 2q+1
       273: q+1
       275: q
       276: q
       278: q^2+2q+1
       279: 2q+1
       281: 2q+1
       284: 1
       286: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q
       294: q+1
       296: q+1
       297: q+1
       299: q
       300: 2q+1
       301: 2q+1
       304: q^2+3q+1
       305: q^2+3q+1
       307: q
       308: 2q+1
       310: 2q+1
       311: 1
       313: q+1
       315: 2q+1
       317: 2q+1
       319: q
       320: 2q+1
       322: 2q+1
       323: q+1
       325: q^2+3q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: 2q+1
       358: q+1
       359: 2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       380: 1
       384: q+1
       388: q+1
       391: q+1
       396: 2q+1
       399: 1
       404: q+1
       406: q+1
       413: q+1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: q+1
       433: q+1
       435: 2q+1
       437: q
       438: q+1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: q+2
       448: 1
       450: q+1
       451: 1
       455: 1
       462: 2
       463: 2
       465: 2q+1
       467: 2q+1
       469: q+1
       471: q
       472: 2q+1
       474: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: 2q+1
       514: q+1
       524: 1
       532: 1
       536: 1
       539: q+1
       543: q+1
       545: 1
       547: 1
       552: 1
       555: 1
       563: 2
       568: q+1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       585: 1
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 2
       604: 1
       605: q+1
       608: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: q+2
       623: 1
       629: 1
       632: 2
       633: 2
       639: q+1
       642: 1
       644: q+1
       645: 1
       651: 1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       696: 1
       697: 1
       712: 1
       716: 1
       723: 1
       727: 1
       733: 1
       735: 1
       739: 1
       751: 2
       756: 1
       758: 1
       766: 1
       768: 1
       769: 1
       772: 1
       781: 1
       788: 1
       797: 1
       802: 1
       804: 1
       808: 1
       809: 1
       811: 1
       833: 1
       849: 1
       855: 1
       871: 1
       880: 1
       887: 1
       889: 1
       902: 1
       922: 1
       927: 1
       961: 1
      1022: 1
      1029: 1
      1060: 1
      1154: 1

1155:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: 3q^3+11q^2+6q+1
        23: q^4+7q^3+12q^2+6q+1
        24: 3q^3+11q^2+6q+1
        25: q^3+8q^2+6q+1
        26: 4q^3+9q^2+6q+1
        27: q^3+8q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 6q^2+5q+1
        32: 3q^3+11q^2+6q+1
        33: 2q^3+9q^2+6q+1
        34: 4q^2+5q+1
        35: q^3+8q^2+6q+1
        36: q^3+6q^2+6q+1
        37: 2q^2+q
        38: q^3+6q^2+5q+1
        39: q^3+2q^2+q
        40: 3q^3+7q^2+5q+1
        41: 2q^2+q
        42: q^3+6q^2+5q+1
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: q^3+7q^2+5q+1
        53: q^4+5q^3+9q^2+5q+1
        54: q^3+7q^2+5q+1
        55: 4q^2+5q+1
        56: 2q^3+6q^2+5q+1
        57: 4q^2+5q+1
        58: q^2+q
        59: 3q^2+4q+1
        60: 2q^2+3q+1
        61: 2q
        62: q^2+q
        63: 3q^2+4q+1
        64: 2q^2+q
        65: q^3+6q^2+5q+1
        66: q^2+q
        67: q^3+5q^2+5q+1
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 2q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        79: 2q^2+4q+1
        80: 6q^2+5q+1
        81: 2q^3+9q^2+6q+1
        82: 4q^2+4q+1
        83: q^3+7q^2+5q+1
        84: 4q^2+5q+1
        85: q^3+6q^2+6q+1
        86: 2q^2+4q+1
        87: 4q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: 5q^2+5q+1
        95: q^3+6q^2+5q+1
        96: 3q^2+3q+1
        97: q^2+5q+1
        98: 2q^2+5q+1
        99: q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       104: 2q^2+3q+1
       105: q
       106: q
       107: 2q+1
       108: q
       110: q^2+3q+1
       112: q^2+3q+1
       114: q^2+3q+1
       116: 2q^2+4q+1
       117: q^2+q
       118: 3q^2+4q+1
       119: 2q^2+3q+1
       120: 2q
       121: q^2+q
       122: 3q^2+4q+1
       123: q^2+q
       124: q^3+5q^2+5q+1
       125: q^2+4q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 2q^2+4q+1
       136: 3q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+3q+1
       139: 2q^2+4q+1
       140: 2q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: q^2+4q+1
       144: 3q+1
       145: 4q+1
       146: 2q^2+4q+1
       147: q^2+4q+1
       148: 2q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       152: 2q^2+4q+1
       154: q^3+4q^2+4q+1
       156: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 5q^2+5q+1
       161: q^3+6q^2+5q+1
       162: 3q^2+3q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       170: 2q+1
       174: 2q^2+3q+1
       175: q
       176: q
       178: 2q+1
       180: 2q+1
       182: 2q+1
       183: 2q+1
       184: q
       186: q^2+3q+1
       188: q^2+3q+1
       190: q^2+3q+1
       191: q
       192: q^2+3q+1
       193: 2q+1
       194: q
       196: q^2+3q+1
       198: q^2+3q+1
       199: q^2+2q+1
       200: 2q
       201: 2q+1
       202: q
       204: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+3q+1
       212: 2q^2+4q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q^2+4q+1
       228: 2q^2+3q+1
       229: 2q^2+4q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: q^2+4q+1
       245: 2q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q+1
       264: 2q+1
       268: 2q+1
       274: q+1
       276: q^2+2q+1
       277: q
       278: q
       280: 2q+1
       282: 2q+1
       283: 1
       286: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q+1
       294: q
       296: q+1
       298: q+1
       299: 2q+1
       300: q
       302: 2q+1
       304: q^2+3q+1
       306: q^2+3q+1
       307: 2q+1
       308: q
       310: 2q+1
       312: 1
       314: q+1
       316: 2q+1
       318: 2q+1
       319: 2q+1
       320: q
       322: 2q+1
       324: q+1
       326: q^2+3q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: 2q+1
       358: q+1
       359: 2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       378: 1
       382: q+1
       386: q+1
       390: q+1
       394: 2q+1
       400: 1
       403: q+1
       407: q+1
       414: q+1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: q+1
       434: q+1
       436: 2q+1
       437: q+1
       438: q
       440: q+1
       442: q+1
       443: 1
       444: 1
       446: q+2
       447: 1
       450: q+1
       452: 1
       456: 1
       462: 2
       464: 2
       466: 2q+1
       468: 2q+1
       470: q+1
       471: 2q+1
       472: q
       474: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: 2q+1
       514: q+1
       522: 1
       530: 1
       534: 1
       538: q+1
       542: q+1
       546: 1
       548: 1
       551: 1
       556: 1
       564: 2
       566: q+1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       586: 1
       589: 1
       592: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       606: q+1
       608: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: q+2
       624: 1
       630: 1
       632: 2
       634: 2
       640: q+1
       641: 1
       644: q+1
       646: 1
       652: 1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       685: 1
       689: 1
       699: 1
       701: 1
       710: 1
       715: 1
       722: 1
       726: 1
       734: 1
       736: 1
       740: 1
       752: 2
       754: 1
       759: 1
       766: 1
       768: 1
       770: 1
       773: 1
       782: 1
       788: 1
       798: 1
       801: 1
       804: 1
       808: 1
       810: 1
       812: 1
       834: 1
       850: 1
       856: 1
       871: 1
       880: 1
       890: 1
       892: 1
       903: 1
       921: 1
       926: 1
       962: 1
      1023: 1
      1029: 1
      1061: 1
      1155: 1

1156:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: 3q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: 2q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: 3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: 3q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 3q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q+1
       109: q^2+q+1
       110: q
       111: q+1
       113: q+1
       115: q+1
       117: q^2+q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: q+1
       136: 2q^2+2q+1
       137: 2q+1
       138: q^2+q+1
       139: q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: q+1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q+1
       185: q^2+q+1
       186: q
       187: q+1
       189: q+1
       191: q+1
       192: q
       193: q+1
       195: q^2+q+1
       196: q
       197: q+1
       199: q+1
       201: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q^2+q+1
       226: q+1
       227: q^2+2q+1
       228: q^2+q+1
       229: q+1
       230: 2q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: q+1
       267: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: q+1
       301: 1
       303: q^2+q+1
       304: q
       305: q+1
       307: 1
       315: 1
       317: 1
       319: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: 1
       445: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 1
       585: 1
       589: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: 1
       617: 1
       639: 1
       641: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       709: 1
       717: 1
       721: 1
       725: 1
       733: 1
       781: 1
       785: 1
       797: 1
       801: 1
       805: 1
       807: 1
       809: 1
       811: 1
       871: 1
       904: 1
       920: 1
       928: 1
      1022: 1
      1026: 1
      1156: 1

1157:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: 3q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: 2q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: 3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: 3q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 3q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q+1
       109: q
       110: q^2+q+1
       112: q+1
       114: q+1
       116: q+1
       117: q
       118: q^2+q+1
       119: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: q+1
       136: 2q^2+2q+1
       137: 2q+1
       138: q^2+q+1
       139: q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: q+1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q+1
       185: q
       186: q^2+q+1
       188: q+1
       190: q+1
       191: q
       192: q+1
       193: q+1
       195: q
       196: q^2+q+1
       198: q+1
       199: q+1
       201: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q^2+q+1
       226: q+1
       227: q^2+2q+1
       228: q^2+q+1
       229: q+1
       230: 2q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: q+1
       268: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: q+1
       302: 1
       303: q
       304: q^2+q+1
       306: q+1
       307: 1
       316: 1
       318: 1
       319: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: 1
       446: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 1
       586: 1
       589: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: 1
       618: 1
       640: 1
       641: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       710: 1
       718: 1
       722: 1
       726: 1
       734: 1
       782: 1
       785: 1
       798: 1
       801: 1
       805: 1
       808: 1
       810: 1
       812: 1
       871: 1
       905: 1
       921: 1
       929: 1
      1023: 1
      1026: 1
      1157: 1

1158:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: 3q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: 2q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: 3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: 3q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 3q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       108: q+1
       109: q
       110: q^2+q+1
       111: q+1
       113: q+1
       115: q+1
       117: q
       118: q^2+q+1
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: q+1
       136: 2q^2+2q+1
       137: 2q+1
       138: q^2+q+1
       139: q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: q+1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: q+1
       185: q
       186: q^2+q+1
       187: q+1
       189: q+1
       191: q
       192: q+1
       194: q+1
       195: q
       196: q^2+q+1
       197: q+1
       200: q+1
       202: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q^2+q+1
       226: q+1
       227: q^2+2q+1
       228: q^2+q+1
       229: q+1
       230: 2q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: q+1
       269: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: q+1
       301: 1
       303: q
       304: q^2+q+1
       305: q+1
       308: 1
       315: 1
       317: 1
       320: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: 1
       445: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       547: 1
       585: 1
       590: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       616: 1
       617: 1
       639: 1
       642: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       712: 1
       720: 1
       723: 1
       727: 1
       735: 1
       781: 1
       786: 1
       797: 1
       802: 1
       806: 1
       808: 1
       809: 1
       811: 1
       871: 1
       906: 1
       922: 1
       930: 1
      1022: 1
      1027: 1
      1158: 1

1159:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: 3q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: 2q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: 3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: 3q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 3q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       108: q+1
       109: q^2+q+1
       110: q
       112: q+1
       114: q+1
       116: q+1
       117: q^2+q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: q+1
       136: 2q^2+2q+1
       137: 2q+1
       138: q^2+q+1
       139: q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: q+1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: q+1
       185: q^2+q+1
       186: q
       188: q+1
       190: q+1
       191: q+1
       192: q
       194: q+1
       195: q^2+q+1
       196: q
       198: q+1
       200: q+1
       202: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q^2+q+1
       226: q+1
       227: q^2+2q+1
       228: q^2+q+1
       229: q+1
       230: 2q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: q+1
       270: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: q+1
       302: 1
       303: q^2+q+1
       304: q
       306: q+1
       308: 1
       316: 1
       318: 1
       320: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: 1
       446: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       548: 1
       586: 1
       590: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       616: 1
       618: 1
       640: 1
       642: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       711: 1
       719: 1
       724: 1
       728: 1
       736: 1
       782: 1
       786: 1
       798: 1
       802: 1
       806: 1
       807: 1
       810: 1
       812: 1
       871: 1
       907: 1
       923: 1
       931: 1
      1023: 1
      1027: 1
      1159: 1

1160:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 3q^3+7q^2+4q+1
        23: q^4+4q^3+7q^2+4q+1
        24: 2q^3+5q^2+3q+1
        25: 4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+5q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q^2+2q+1
        38: q^2+2q
        39: q^3+3q^2+2q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 3q^3+7q^2+4q+1
        53: q^4+4q^3+7q^2+4q+1
        54: 2q^3+5q^2+3q+1
        55: 4q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+3q+1
        58: 2q^2+2q+1
        59: q
        60: q^2+2q+1
        61: q
        62: 2q^2+q+1
        63: 2q
        64: 2q^2+2q+1
        65: q
        66: 2q^2+2q+1
        67: q^2+2q
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: 3q^2+4q+1
        73: q^3+5q^2+4q+1
        74: 3q^2+2q+1
        75: q^2+2q
        76: q^3+3q^2+2q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+2q+1
        81: 2q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+2q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^3+5q^2+4q+1
        95: q^3+5q^2+4q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q^2+q+1
       104: q
       105: q
       107: q^2+2q+1
       108: q
       109: 2q^2+2q+1
       110: q
       111: 2q^2+2q+1
       112: q^2+2q
       113: 2q^2+q+1
       114: 2q
       115: 2q^2+2q+1
       116: q
       117: q+1
       119: q+1
       121: q^2+q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q^2+4q+1
       141: 2q^2+2q+1
       142: q^3+5q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 3q^2+2q+1
       152: q^2+2q
       153: q^3+3q^2+2q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q^2+q+1
       170: q
       171: q
       173: q+1
       177: q+1
       179: 1
       181: q+1
       183: q+1
       185: q+1
       187: q^2+2q+1
       188: q
       189: q^2+q+1
       190: q
       191: q+1
       193: q^2+2q+1
       194: q
       195: 2q^2+2q+1
       196: q
       197: 2q^2+2q+1
       198: q^2+2q
       199: q+1
       201: q+1
       202: q
       203: q+1
       205: 1
       206: q
       207: q+1
       208: q
       209: 2q^2+q+1
       210: 2q
       211: 2q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+3q+1
       230: 2q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: q+1
       267: q^2+q+1
       268: q
       270: q
       271: 1
       272: q
       275: q+1
       283: 1
       285: 1
       287: 1
       291: q+1
       293: q+1
       295: q+1
       297: q+1
       298: q
       299: q+1
       301: q+1
       303: q+1
       305: q^2+2q+1
       306: q
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       319: q+1
       320: q
       321: q+1
       323: 1
       324: q
       325: q^2+q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: 1
       405: 1
       408: q
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: q+1
       437: q+1
       439: q+1
       441: q+1
       442: q
       443: q+1
       444: q
       445: q+1
       447: 1
       449: 1
       451: 1
       461: q+1
       463: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       529: 1
       533: 1
       541: q+1
       545: 1
       549: 1
       561: 1
       565: 1
       569: 1
       573: 1
       576: q
       577: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: q+1
       615: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       685: 1
       689: 1
       693: 1
       713: 1
       717: 1
       725: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       855: 1
       871: 1
       880: 1
       908: 1
       924: 1
       928: 1
      1026: 1
      1028: 1
      1064: 1
      1160: 1

1161:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 3q^3+7q^2+4q+1
        23: q^4+4q^3+7q^2+4q+1
        24: 2q^3+5q^2+3q+1
        25: 4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+5q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: q^2+2q
        38: 3q^2+2q+1
        39: q^2+2q
        40: q^3+3q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 3q^3+7q^2+4q+1
        53: q^4+4q^3+7q^2+4q+1
        54: 2q^3+5q^2+3q+1
        55: 4q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+3q+1
        58: 2q^2+2q+1
        59: q
        60: q
        61: q^2+2q+1
        62: 2q
        63: 2q^2+q+1
        64: q
        65: 2q^2+2q+1
        66: q^2+2q
        67: 2q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: 3q^2+4q+1
        73: q^3+5q^2+4q+1
        74: q^2+2q
        75: 3q^2+2q+1
        76: q^2+2q
        77: q^3+3q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+2q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^3+5q^2+4q+1
        95: q^3+5q^2+4q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q
       105: q^2+q+1
       106: q
       107: q
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: q
       111: q^2+2q
       112: 2q^2+2q+1
       113: 2q
       114: 2q^2+q+1
       115: q
       116: 2q^2+2q+1
       117: q+1
       120: q+1
       121: q
       122: q^2+q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q^2+4q+1
       141: 2q^2+2q+1
       142: q^3+5q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q
       152: 3q^2+2q+1
       153: q^2+2q
       154: q^3+3q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       171: q^2+q+1
       172: q
       175: q+1
       178: q+1
       180: 1
       182: q+1
       184: q+1
       185: q+1
       187: q
       188: q^2+2q+1
       189: q
       190: q^2+q+1
       191: q+1
       193: q
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q
       197: q^2+2q
       198: 2q^2+2q+1
       200: q+1
       201: q
       202: q+1
       203: q+1
       205: q
       206: 1
       207: q
       208: q+1
       209: 2q
       210: 2q^2+q+1
       211: q
       212: 2q^2+2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+3q+1
       230: 2q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: q+1
       267: q
       269: q
       270: q^2+q+1
       271: q
       272: 1
       277: q+1
       284: 1
       285: 1
       288: 1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: q+1
       300: q+1
       302: q+1
       303: q+1
       305: q
       306: q^2+2q+1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       319: q
       320: q+1
       321: q+1
       323: q
       324: 1
       325: q
       326: q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: 1
       405: q
       408: 1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: q+1
       438: q+1
       439: q+1
       441: q
       442: q+1
       443: q
       444: q+1
       446: q+1
       448: 1
       449: 1
       452: 1
       461: q+1
       464: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       531: 1
       535: 1
       544: q+1
       548: 1
       550: 1
       562: 1
       567: 1
       572: 1
       573: q
       576: 1
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: q+1
       616: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       685: 1
       689: 1
       700: 1
       714: 1
       719: 1
       728: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       802: 1
       803: 1
       806: 1
       807: 1
       812: 1
       856: 1
       871: 1
       880: 1
       910: 1
       925: 1
       931: 1
      1027: 1
      1028: 1
      1065: 1
      1161: 1

1162:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 3q^3+7q^2+4q+1
        23: q^4+4q^3+7q^2+4q+1
        24: 2q^3+5q^2+3q+1
        25: 4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+5q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: q^2+2q
        38: 3q^2+2q+1
        39: q^2+2q
        40: q^3+3q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 3q^3+7q^2+4q+1
        53: q^4+4q^3+7q^2+4q+1
        54: 2q^3+5q^2+3q+1
        55: 4q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+3q+1
        58: q
        59: 2q^2+2q+1
        60: q^2+2q+1
        61: q
        62: 2q
        63: 2q^2+q+1
        64: q
        65: 2q^2+2q+1
        66: q^2+2q
        67: 2q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: 3q^2+4q+1
        73: q^3+5q^2+4q+1
        74: q^2+2q
        75: 3q^2+2q+1
        76: q^2+2q
        77: q^3+3q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+2q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^3+5q^2+4q+1
        95: q^3+5q^2+4q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q
       104: q^2+q+1
       106: q
       107: q^2+2q+1
       108: q
       109: q
       110: 2q^2+2q+1
       111: q^2+2q
       112: 2q^2+2q+1
       113: 2q
       114: 2q^2+q+1
       115: q
       116: 2q^2+2q+1
       118: q+1
       119: q+1
       121: q
       122: q^2+q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q^2+4q+1
       141: 2q^2+2q+1
       142: q^3+5q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q
       152: 3q^2+2q+1
       153: q^2+2q
       154: q^3+3q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       170: q^2+q+1
       172: q
       174: q+1
       178: q+1
       180: 1
       182: q+1
       183: q+1
       186: q+1
       187: q
       188: q^2+2q+1
       189: q
       190: q^2+q+1
       192: q+1
       193: q^2+2q+1
       194: q
       195: q
       196: 2q^2+2q+1
       197: q^2+2q
       198: 2q^2+2q+1
       199: q+1
       201: q+1
       202: q
       204: q+1
       205: q
       206: 1
       207: q
       208: q+1
       209: 2q
       210: 2q^2+q+1
       211: q
       212: 2q^2+2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+3q+1
       230: 2q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: q+1
       267: q
       268: q^2+q+1
       269: q
       273: q
       274: 1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: q+1
       299: q+1
       302: q+1
       304: q+1
       305: q
       306: q^2+2q+1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       319: q+1
       320: q
       322: q+1
       323: q
       324: 1
       325: q
       326: q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: 1
       406: q
       407: 1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: q+1
       437: q+1
       440: q+1
       441: q
       442: q+1
       443: q+1
       444: q
       446: q+1
       447: 1
       450: 1
       452: 1
       462: q+1
       464: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       530: 1
       534: 1
       542: q+1
       546: 1
       551: 1
       564: 1
       566: 1
       571: 1
       574: 1
       575: q
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: q+1
       615: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       685: 1
       689: 1
       699: 1
       715: 1
       718: 1
       726: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       801: 1
       804: 1
       805: 1
       808: 1
       812: 1
       856: 1
       871: 1
       880: 1
       909: 1
       926: 1
       929: 1
      1026: 1
      1029: 1
      1065: 1
      1162: 1

1163:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 3q^3+7q^2+4q+1
        23: q^4+4q^3+7q^2+4q+1
        24: 2q^3+5q^2+3q+1
        25: 4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+5q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q^2+2q+1
        38: q^2+2q
        39: q^3+3q^2+2q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 3q^3+7q^2+4q+1
        53: q^4+4q^3+7q^2+4q+1
        54: 2q^3+5q^2+3q+1
        55: 4q^2+4q+1
        56: q^3+4q^2+4q+1
        57: 3q^2+3q+1
        58: q
        59: 2q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 2q^2+q+1
        63: 2q
        64: 2q^2+2q+1
        65: q
        66: 2q^2+2q+1
        67: q^2+2q
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: 3q^2+4q+1
        73: q^3+5q^2+4q+1
        74: 3q^2+2q+1
        75: q^2+2q
        76: q^3+3q^2+2q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+2q+1
        81: 2q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+2q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^3+5q^2+4q+1
        95: q^3+5q^2+4q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       104: q
       105: q
       106: q^2+q+1
       107: q
       108: q^2+2q+1
       109: q
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+2q
       113: 2q^2+q+1
       114: 2q
       115: 2q^2+2q+1
       116: q
       118: q+1
       120: q+1
       121: q^2+q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q^2+4q+1
       141: 2q^2+2q+1
       142: q^3+5q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 3q^2+2q+1
       152: q^2+2q
       153: q^3+3q^2+2q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: q
       171: q
       172: q^2+q+1
       176: q+1
       177: q+1
       179: 1
       181: q+1
       184: q+1
       186: q+1
       187: q^2+2q+1
       188: q
       189: q^2+q+1
       190: q
       192: q+1
       193: q
       194: q^2+2q+1
       195: q
       196: 2q^2+2q+1
       197: 2q^2+2q+1
       198: q^2+2q
       200: q+1
       201: q
       202: q+1
       204: q+1
       205: 1
       206: q
       207: q+1
       208: q
       209: 2q^2+q+1
       210: 2q
       211: 2q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+3q+1
       230: 2q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: q+1
       268: q
       269: q^2+q+1
       270: q
       273: 1
       274: q
       278: q+1
       284: 1
       286: 1
       287: 1
       291: q+1
       294: q+1
       296: q+1
       297: q+1
       298: q
       300: q+1
       301: q+1
       304: q+1
       305: q^2+2q+1
       306: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       319: q
       320: q+1
       322: q+1
       323: 1
       324: q
       325: q^2+q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: 1
       406: 1
       407: q
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: q+1
       438: q+1
       440: q+1
       441: q+1
       442: q
       443: q
       444: q+1
       445: q+1
       448: 1
       450: 1
       451: 1
       462: q+1
       463: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       532: 1
       536: 1
       543: q+1
       547: 1
       552: 1
       563: 1
       568: 1
       570: 1
       574: q
       575: 1
       577: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: q+1
       616: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       685: 1
       689: 1
       697: 1
       716: 1
       720: 1
       727: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       855: 1
       871: 1
       880: 1
       911: 1
       927: 1
       930: 1
      1027: 1
      1029: 1
      1064: 1
      1163: 1

1164:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: q^2+2q+1
        61: 2q^2+2q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: q+1
       108: q^2+q
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q+1
       119: q+1
       120: q^2+q
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       184: q
       185: 1
       187: 1
       189: q+1
       191: q+1
       195: q+1
       199: q+1
       200: q^2+q
       201: q+1
       202: q^2+q
       203: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       284: q
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       294: q
       295: 1
       297: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       321: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: q+1
       335: 1
       337: q+1
       338: q+1
       340: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       397: q+1
       401: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       420: q
       421: 1
       423: 1
       427: q+1
       431: 1
       439: 1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       473: 1
       484: 1
       485: 1
       487: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: 1
       561: q+1
       583: 1
       587: 1
       601: 1
       607: 1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       705: 1
       737: 1
       741: 1
       745: 1
       749: 1
       775: 1
       789: 1
       817: 1
       819: 1
       823: 1
       837: 1
       839: 1
       841: 1
       847: 1
       859: 1
       861: 1
       865: 1
       873: 1
       936: 1
       940: 1
       956: 1
       992: 1
      1030: 1
      1032: 1
      1164: 1

1165:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: 2q^2+2q
        61: q^2+2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       107: q^2+q
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q+1
       119: q^2+q
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: q
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       195: q+1
       199: q^2+q
       200: q+1
       201: q^2+q
       202: q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       272: q+1
       277: q+1
       280: 1
       282: 1
       283: q
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       293: q
       294: 1
       295: 1
       298: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       321: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: q+1
       335: 1
       337: q+1
       339: q+1
       341: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       398: q+1
       402: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q
       420: 1
       421: 1
       424: 1
       428: q+1
       431: 1
       439: 1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       473: 1
       484: 1
       486: 1
       488: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: 1
       562: q+1
       584: 1
       588: 1
       602: 1
       607: 1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       707: 1
       738: 1
       742: 1
       746: 1
       750: 1
       776: 1
       790: 1
       817: 1
       820: 1
       824: 1
       838: 1
       839: 1
       842: 1
       847: 1
       860: 1
       862: 1
       865: 1
       873: 1
       937: 1
       941: 1
       957: 1
       993: 1
      1031: 1
      1032: 1
      1165: 1

1166:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: 2q^2+2q
        61: q^2+2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       107: q^2+q
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       118: q+1
       119: q^2+q
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: q
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       196: q+1
       199: q^2+q
       200: q+1
       201: q^2+q
       202: q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       273: q+1
       278: q+1
       279: 1
       281: 1
       283: q
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       293: q
       294: 1
       296: 1
       297: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       322: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: q+1
       334: q+1
       335: 1
       337: q+1
       338: q+1
       340: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       399: q+1
       404: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q
       420: 1
       422: 1
       423: 1
       427: q+1
       432: 1
       440: 1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       474: 1
       484: 1
       485: 1
       487: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: 1
       563: q+1
       583: 1
       587: 1
       601: 1
       608: 1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       708: 1
       739: 1
       743: 1
       747: 1
       751: 1
       775: 1
       789: 1
       818: 1
       819: 1
       823: 1
       837: 1
       840: 1
       841: 1
       848: 1
       859: 1
       861: 1
       865: 1
       873: 1
       938: 1
       942: 1
       958: 1
       992: 1
      1030: 1
      1033: 1
      1166: 1

1167:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+3q^2+3q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 3q^2+4q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: 3q^2+4q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: q^2+2q+1
        61: 2q^2+2q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: q+1
       108: q^2+q
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       118: q+1
       119: q+1
       120: q^2+q
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       184: q
       186: 1
       188: 1
       190: q+1
       192: q+1
       196: q+1
       199: q+1
       200: q^2+q
       201: q+1
       202: q^2+q
       204: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       284: q
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       294: q
       296: 1
       298: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       322: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: q+1
       334: q+1
       335: 1
       337: q+1
       339: q+1
       341: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       400: q+1
       403: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       420: q
       422: 1
       424: 1
       428: q+1
       432: 1
       440: 1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       474: 1
       484: 1
       486: 1
       488: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: 1
       564: q+1
       584: 1
       588: 1
       602: 1
       608: 1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       680: 1
       684: 1
       686: 1
       688: 1
       690: 1
       691: 1
       706: 1
       740: 1
       744: 1
       748: 1
       752: 1
       776: 1
       790: 1
       818: 1
       820: 1
       824: 1
       838: 1
       840: 1
       842: 1
       848: 1
       860: 1
       862: 1
       865: 1
       873: 1
       939: 1
       943: 1
       959: 1
       993: 1
      1031: 1
      1033: 1
      1167: 1

1168:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        60: q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       103: q+1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: q+1
       119: q+1
       120: q
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: q+1
       195: 1
       199: q+1
       200: q
       201: 1
       203: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       271: 1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       303: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       431: 1
       439: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: 1
       583: 1
       585: 1
       587: 1
       589: 1
       595: 1
       607: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       705: 1
       709: 1
       737: 1
       741: 1
       745: 1
       777: 1
       807: 1
       821: 1
       823: 1
       825: 1
       831: 1
       841: 1
       847: 1
       878: 1
       896: 1
       936: 1
       944: 1
      1034: 1
      1058: 1
      1168: 1

1169:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        60: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       105: q+1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: q+1
       119: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: q+1
       195: 1
       199: q
       200: q+1
       202: 1
       203: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       272: 1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       303: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       431: 1
       439: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: 1
       584: 1
       586: 1
       588: 1
       590: 1
       595: 1
       607: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       707: 1
       711: 1
       738: 1
       742: 1
       746: 1
       778: 1
       807: 1
       822: 1
       824: 1
       826: 1
       831: 1
       842: 1
       847: 1
       878: 1
       898: 1
       937: 1
       945: 1
      1035: 1
      1058: 1
      1169: 1

1170:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        59: q+1
        60: q
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       106: q+1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: q+1
       119: q
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: q+1
       196: 1
       199: q
       200: q+1
       202: 1
       204: 1
       205: 1
       207: q+1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       273: 1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       304: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       432: 1
       440: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: 1
       583: 1
       585: 1
       587: 1
       590: 1
       596: 1
       608: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       708: 1
       712: 1
       739: 1
       743: 1
       747: 1
       777: 1
       808: 1
       821: 1
       823: 1
       826: 1
       832: 1
       841: 1
       848: 1
       878: 1
       899: 1
       938: 1
       946: 1
      1034: 1
      1059: 1
      1170: 1

1171:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q^2+q+1
         5: 2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: 2q+1
        12: q^2+q+1
        13: 2q+1
        14: q^2+q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: q^2+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        59: q+1
        60: q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: 1
       102: 1
       104: q+1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: q+1
       119: q+1
       120: q
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: 1
       141: 1
       142: 1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: q+1
       196: 1
       199: q+1
       200: q
       201: 1
       204: 1
       206: 1
       208: q+1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       274: 1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       304: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       432: 1
       440: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: 1
       482: 1
       492: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: 1
       584: 1
       586: 1
       588: 1
       589: 1
       596: 1
       608: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       676: 1
       681: 1
       682: 1
       686: 1
       688: 1
       706: 1
       710: 1
       740: 1
       744: 1
       748: 1
       778: 1
       808: 1
       822: 1
       824: 1
       825: 1
       832: 1
       842: 1
       848: 1
       878: 1
       897: 1
       939: 1
       947: 1
      1035: 1
      1059: 1
      1171: 1

1172:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: 3q^2+2q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: 3q^2+2q+1
        58: q+1
        60: q^2+q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q^2+q+1
       108: q
       109: q+1
       111: q+1
       113: q+1
       115: q+1
       117: q+1
       119: q^2+q+1
       120: q
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q^2+q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+q+1
       166: 1
       167: 1
       168: 1
       169: q+1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q^2+q+1
       184: q
       185: q+1
       187: q+1
       189: q+1
       191: q+1
       195: 1
       199: q+1
       200: q
       201: q^2+q+1
       202: q
       203: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q+1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: q+1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: q+1
       294: q
       295: q+1
       297: q+1
       303: 1
       307: q^2+q+1
       308: q
       309: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       321: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       377: 1
       381: 1
       385: q+1
       397: 1
       401: q+1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       447: 1
       449: 1
       451: 1
       453: q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       521: 1
       529: 1
       549: 1
       553: 1
       557: q+1
       561: 1
       585: 1
       589: 1
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 1
       633: 1
       639: 1
       643: 1
       665: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       709: 1
       713: 1
       737: 1
       741: 1
       749: 1
       781: 1
       787: 1
       821: 1
       825: 1
       827: 1
       831: 1
       833: 1
       835: 1
       875: 1
       900: 1
       944: 1
       948: 1
      1038: 1
      1044: 1
      1172: 1

1173:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: 3q^2+2q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: 3q^2+2q+1
        58: q+1
        60: q
        61: q^2+q+1
        63: q+1
        65: q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       107: q
       108: q^2+q+1
       109: q+1
       112: q+1
       114: q+1
       116: q+1
       117: q+1
       119: q
       120: q^2+q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q^2+q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+q+1
       166: 1
       167: 1
       168: 1
       171: q+1
       175: q+1
       178: 1
       180: 1
       182: 1
       183: q
       184: q^2+q+1
       185: q+1
       188: q+1
       190: q+1
       191: q+1
       195: 1
       199: q
       200: q+1
       201: q
       202: q^2+q+1
       203: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q+1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: q+1
       272: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       293: q
       294: q+1
       295: q+1
       298: q+1
       303: 1
       307: q
       308: q^2+q+1
       309: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       321: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       379: 1
       383: 1
       387: q+1
       398: 1
       402: q+1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       448: 1
       449: 1
       452: 1
       453: q
       454: q+1
       456: 1
       457: q+1
       460: q+1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       523: 1
       531: 1
       550: 1
       554: 1
       558: q+1
       562: 1
       586: 1
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 1
       634: 1
       640: 1
       643: 1
       665: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       711: 1
       714: 1
       738: 1
       742: 1
       750: 1
       782: 1
       787: 1
       822: 1
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       875: 1
       901: 1
       945: 1
       949: 1
      1039: 1
      1044: 1
      1173: 1

1174:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: 3q^2+2q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: 3q^2+2q+1
        59: q+1
        60: q
        61: q^2+q+1
        62: q+1
        64: q+1
        66: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       107: q
       108: q^2+q+1
       110: q+1
       111: q+1
       113: q+1
       115: q+1
       118: q+1
       119: q
       120: q^2+q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q^2+q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+q+1
       166: 1
       167: 1
       168: 1
       172: q+1
       176: q+1
       177: 1
       179: 1
       181: 1
       183: q
       184: q^2+q+1
       186: q+1
       187: q+1
       189: q+1
       192: q+1
       196: 1
       199: q
       200: q+1
       201: q
       202: q^2+q+1
       204: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q+1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: q+1
       273: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       293: q
       294: q+1
       296: q+1
       297: q+1
       304: 1
       307: q
       308: q^2+q+1
       310: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       322: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       380: 1
       384: 1
       388: q+1
       399: 1
       404: q+1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       448: 1
       450: 1
       451: 1
       453: q
       454: q+1
       455: 1
       458: q+1
       459: q+1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       524: 1
       532: 1
       552: 1
       555: 1
       559: q+1
       563: 1
       585: 1
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 1
       633: 1
       639: 1
       644: 1
       665: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       712: 1
       716: 1
       739: 1
       743: 1
       751: 1
       781: 1
       788: 1
       821: 1
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       875: 1
       902: 1
       946: 1
       950: 1
      1038: 1
      1045: 1
      1174: 1

1175:    0: 3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+2q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+q+1
        19: 3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: 3q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: 3q^2+2q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: 3q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: 3q^2+2q+1
        59: q+1
        60: q^2+q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q^2+q+1
       108: q
       110: q+1
       112: q+1
       114: q+1
       116: q+1
       118: q+1
       119: q^2+q+1
       120: q
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q^2+q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+q+1
       166: 1
       167: 1
       168: 1
       170: q+1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q^2+q+1
       184: q
       186: q+1
       188: q+1
       190: q+1
       192: q+1
       196: 1
       199: q+1
       200: q
       201: q^2+q+1
       202: q
       204: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q+1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: q+1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: q+1
       294: q
       296: q+1
       298: q+1
       304: 1
       307: q^2+q+1
       308: q
       310: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       322: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       378: 1
       382: 1
       386: q+1
       400: 1
       403: q+1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       447: 1
       450: 1
       452: 1
       453: q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       522: 1
       530: 1
       551: 1
       556: 1
       560: q+1
       564: 1
       586: 1
       589: 1
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       632: 1
       634: 1
       640: 1
       644: 1
       665: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       710: 1
       715: 1
       740: 1
       744: 1
       752: 1
       782: 1
       788: 1
       822: 1
       825: 1
       828: 1
       832: 1
       834: 1
       836: 1
       875: 1
       903: 1
       947: 1
       951: 1
      1039: 1
      1045: 1
      1175: 1

1176:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: q^3+8q^2+6q+1
        23: 4q^3+9q^2+6q+1
        24: q^3+8q^2+6q+1
        25: 3q^3+11q^2+6q+1
        26: q^4+7q^3+12q^2+6q+1
        27: 3q^3+11q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 4q^2+5q+1
        32: q^3+8q^2+6q+1
        33: q^3+6q^2+6q+1
        34: 6q^2+5q+1
        35: 3q^3+11q^2+6q+1
        36: 2q^3+9q^2+6q+1
        37: q^3+6q^2+5q+1
        38: 2q^2+q
        39: 3q^3+7q^2+5q+1
        40: q^3+2q^2+q
        41: q^3+6q^2+5q+1
        42: 2q^2+q
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: 4q^2+5q+1
        53: 2q^3+6q^2+5q+1
        54: 4q^2+5q+1
        55: q^3+7q^2+5q+1
        56: q^4+5q^3+9q^2+5q+1
        57: q^3+7q^2+5q+1
        58: 2q^2+3q+1
        59: 2q
        60: 3q^2+4q+1
        61: q^2+q
        62: 3q^2+4q+1
        63: q^2+q
        64: q^3+6q^2+5q+1
        65: 2q^2+q
        66: q^3+5q^2+5q+1
        67: q^2+q
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 3q^2+4q+1
        73: 2q^2+4q+1
        74: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        78: 2q^2+4q+1
        80: 4q^2+5q+1
        81: q^3+6q^2+6q+1
        82: 2q^2+4q+1
        83: 4q^2+5q+1
        84: 6q^2+5q+1
        85: 2q^3+9q^2+6q+1
        86: 4q^2+4q+1
        87: q^3+7q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 5q^2+5q+1
        98: q^3+6q^2+5q+1
        99: 3q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: 2q^2+3q+1
       104: q
       106: q
       107: q^2+3q+1
       109: 2q+1
       110: q
       111: q^2+3q+1
       113: q^2+3q+1
       115: 2q^2+4q+1
       117: 2q^2+3q+1
       118: 2q
       119: 3q^2+4q+1
       120: q^2+q
       121: 3q^2+4q+1
       122: q^2+q
       123: q^3+5q^2+5q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+4q+1
       136: 2q^2+4q+1
       137: q^2+4q+1
       138: 3q+1
       139: 4q+1
       140: 2q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+3q+1
       145: 2q^2+4q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       151: 2q^2+4q+1
       153: q^3+4q^2+4q+1
       155: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 5q^2+5q+1
       164: q^3+6q^2+5q+1
       165: 3q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       169: 2q+1
       173: 2q^2+3q+1
       174: q
       176: q
       177: 2q+1
       179: 2q+1
       181: 2q+1
       183: q^2+3q+1
       185: 2q+1
       186: q
       187: q^2+3q+1
       189: q^2+3q+1
       191: q^2+2q+1
       192: 2q
       193: 2q+1
       195: 2q+1
       196: q
       197: q+1
       199: q^2+3q+1
       200: q
       201: q^2+3q+1
       203: 2q+1
       204: q
       205: q^2+3q+1
       207: q^2+3q+1
       208: q
       209: q^2+3q+1
       211: 2q^2+4q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 2q+1
       232: 2q^2+4q+1
       233: 2q^2+3q+1
       234: 3q^2+4q+1
       235: 2q^2+4q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: 2q+1
       245: q^2+4q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q+1
       263: 2q+1
       267: q+1
       271: 2q+1
       275: q^2+2q+1
       276: q
       278: q
       279: 2q+1
       281: 2q+1
       283: q+1
       285: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: 2q+1
       301: 1
       303: 2q+1
       304: q
       305: q+1
       307: q^2+3q+1
       309: 2q+1
       310: q
       311: 2q+1
       313: q^2+3q+1
       315: 2q+1
       317: 2q+1
       319: 2q+1
       321: 2q+1
       322: q
       323: q+1
       325: q^2+3q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       348: q+1
       350: 2q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       377: 1
       381: q+1
       385: q+1
       389: 1
       393: q+1
       397: q+1
       401: 2q+1
       405: q+1
       413: q+1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: q+1
       431: 1
       433: 1
       435: 1
       443: 2
       445: 2
       447: q+1
       449: 1
       451: q+1
       453: q+1
       455: 2q+1
       457: q+1
       458: q
       459: q+1
       461: 1
       462: 1
       463: q+2
       465: 2q+1
       467: 2q+1
       469: q+1
       471: 2q+1
       473: 2q+1
       474: q
       475: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: 2q+1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 2
       549: 1
       553: q+1
       557: q+1
       561: 1
       563: 1
       565: q+1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       585: 1
       589: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 2
       605: 1
       613: 1
       615: 2
       617: 2
       619: 1
       621: 1
       623: q+1
       625: 1
       629: 1
       631: 1
       632: 1
       633: q+2
       639: q+1
       641: q+1
       643: 1
       645: 1
       651: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       693: 1
       696: 1
       709: 1
       717: 1
       721: 1
       733: 2
       737: 1
       741: 1
       749: 1
       751: 1
       753: 1
       757: 1
       765: 1
       766: 1
       769: 1
       772: 1
       781: 1
       785: 1
       809: 1
       821: 1
       825: 1
       829: 1
       831: 1
       833: 1
       835: 1
       849: 1
       855: 1
       875: 1
       880: 1
       884: 1
       887: 1
       904: 1
       944: 1
       952: 1
       960: 1
      1038: 1
      1040: 1
      1060: 1
      1176: 1

1177:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: q^3+8q^2+6q+1
        23: 4q^3+9q^2+6q+1
        24: q^3+8q^2+6q+1
        25: 3q^3+11q^2+6q+1
        26: q^4+7q^3+12q^2+6q+1
        27: 3q^3+11q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 4q^2+5q+1
        32: q^3+8q^2+6q+1
        33: q^3+6q^2+6q+1
        34: 6q^2+5q+1
        35: 3q^3+11q^2+6q+1
        36: 2q^3+9q^2+6q+1
        37: 2q^2+q
        38: q^3+6q^2+5q+1
        39: q^3+2q^2+q
        40: 3q^3+7q^2+5q+1
        41: 2q^2+q
        42: q^3+6q^2+5q+1
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: 4q^2+5q+1
        53: 2q^3+6q^2+5q+1
        54: 4q^2+5q+1
        55: q^3+7q^2+5q+1
        56: q^4+5q^3+9q^2+5q+1
        57: q^3+7q^2+5q+1
        58: 2q
        59: 2q^2+3q+1
        60: 3q^2+4q+1
        61: q^2+q
        62: q^2+q
        63: 3q^2+4q+1
        64: 2q^2+q
        65: q^3+6q^2+5q+1
        66: q^2+q
        67: q^3+5q^2+5q+1
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 3q^2+4q+1
        73: 2q^2+4q+1
        75: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        79: 2q^2+4q+1
        80: 4q^2+5q+1
        81: q^3+6q^2+6q+1
        82: 2q^2+4q+1
        83: 4q^2+5q+1
        84: 6q^2+5q+1
        85: 2q^3+9q^2+6q+1
        86: 4q^2+4q+1
        87: q^3+7q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 5q^2+5q+1
        98: q^3+6q^2+5q+1
        99: 3q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: q
       104: 2q^2+3q+1
       105: q
       107: q^2+3q+1
       109: q
       110: 2q+1
       112: q^2+3q+1
       114: q^2+3q+1
       116: 2q^2+4q+1
       117: 2q
       118: 2q^2+3q+1
       119: 3q^2+4q+1
       120: q^2+q
       121: q^2+q
       122: 3q^2+4q+1
       123: q^2+q
       124: q^3+5q^2+5q+1
       125: q^2+4q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+4q+1
       136: 2q^2+4q+1
       137: q^2+4q+1
       138: 3q+1
       139: 4q+1
       140: 2q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+3q+1
       145: 2q^2+4q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       152: 2q^2+4q+1
       154: q^3+4q^2+4q+1
       156: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 5q^2+5q+1
       164: q^3+6q^2+5q+1
       165: 3q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       170: 2q+1
       173: q
       174: 2q^2+3q+1
       175: q
       178: 2q+1
       180: 2q+1
       182: 2q+1
       183: q^2+3q+1
       185: q
       186: 2q+1
       188: q^2+3q+1
       190: q^2+3q+1
       191: 2q
       192: q^2+2q+1
       193: 2q+1
       195: q
       196: 2q+1
       198: q+1
       199: q^2+3q+1
       200: q
       201: q^2+3q+1
       203: q
       204: 2q+1
       206: q^2+3q+1
       207: q
       208: q^2+3q+1
       210: q^2+3q+1
       212: 2q^2+4q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 2q+1
       232: 2q^2+4q+1
       233: 2q^2+3q+1
       234: 3q^2+4q+1
       235: 2q^2+4q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: 2q+1
       245: q^2+4q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q+1
       264: 2q+1
       268: q+1
       274: 2q+1
       275: q
       276: q^2+2q+1
       277: q
       280: 2q+1
       282: 2q+1
       283: q+1
       286: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: 2q+1
       302: 1
       303: q
       304: 2q+1
       306: q+1
       307: q^2+3q+1
       309: q
       310: 2q+1
       312: 2q+1
       314: q^2+3q+1
       316: 2q+1
       318: 2q+1
       319: 2q+1
       321: q
       322: 2q+1
       324: q+1
       326: q^2+3q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       348: q+1
       350: 2q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       378: 1
       382: q+1
       386: q+1
       390: 1
       394: q+1
       400: q+1
       403: 2q+1
       407: q+1
       414: q+1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: q+1
       432: 1
       434: 1
       436: 1
       443: 2
       446: 2
       447: q+1
       450: 1
       452: q+1
       453: q+1
       456: 2q+1
       457: q
       458: q+1
       460: q+1
       461: 1
       462: 1
       464: q+2
       466: 2q+1
       468: 2q+1
       470: q+1
       471: 2q+1
       473: q
       474: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: 2q+1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 2
       551: 1
       556: q+1
       560: q+1
       562: 1
       564: 1
       566: q+1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       586: 1
       589: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 2
       606: 1
       614: 1
       615: 2
       618: 2
       619: 1
       622: 1
       624: q+1
       626: 1
       630: 1
       631: 1
       632: 1
       634: q+2
       640: q+1
       641: q+1
       644: 1
       646: 1
       652: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       694: 1
       699: 1
       710: 1
       718: 1
       722: 1
       734: 2
       740: 1
       744: 1
       750: 1
       752: 1
       754: 1
       759: 1
       765: 1
       766: 1
       770: 1
       773: 1
       782: 1
       785: 1
       810: 1
       822: 1
       825: 1
       829: 1
       832: 1
       834: 1
       836: 1
       850: 1
       856: 1
       875: 1
       880: 1
       885: 1
       890: 1
       905: 1
       947: 1
       953: 1
       962: 1
      1039: 1
      1040: 1
      1061: 1
      1177: 1

1178:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: q^3+8q^2+6q+1
        23: 4q^3+9q^2+6q+1
        24: q^3+8q^2+6q+1
        25: 3q^3+11q^2+6q+1
        26: q^4+7q^3+12q^2+6q+1
        27: 3q^3+11q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 4q^2+5q+1
        32: q^3+8q^2+6q+1
        33: q^3+6q^2+6q+1
        34: 6q^2+5q+1
        35: 3q^3+11q^2+6q+1
        36: 2q^3+9q^2+6q+1
        37: q^3+6q^2+5q+1
        38: 2q^2+q
        39: 3q^3+7q^2+5q+1
        40: q^3+2q^2+q
        41: q^3+6q^2+5q+1
        42: 2q^2+q
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: 4q^2+5q+1
        53: 2q^3+6q^2+5q+1
        54: 4q^2+5q+1
        55: q^3+7q^2+5q+1
        56: q^4+5q^3+9q^2+5q+1
        57: q^3+7q^2+5q+1
        58: 2q
        59: 2q^2+3q+1
        60: q^2+q
        61: 3q^2+4q+1
        62: 3q^2+4q+1
        63: q^2+q
        64: q^3+6q^2+5q+1
        65: 2q^2+q
        66: q^3+5q^2+5q+1
        67: q^2+q
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 3q^2+4q+1
        73: 2q^2+4q+1
        74: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        78: 2q^2+4q+1
        80: 4q^2+5q+1
        81: q^3+6q^2+6q+1
        82: 2q^2+4q+1
        83: 4q^2+5q+1
        84: 6q^2+5q+1
        85: 2q^3+9q^2+6q+1
        86: 4q^2+4q+1
        87: q^3+7q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 5q^2+5q+1
        98: q^3+6q^2+5q+1
        99: 3q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       103: q
       105: q
       106: 2q^2+3q+1
       108: q^2+3q+1
       109: q
       110: 2q+1
       111: q^2+3q+1
       113: q^2+3q+1
       115: 2q^2+4q+1
       117: 2q
       118: 2q^2+3q+1
       119: q^2+q
       120: 3q^2+4q+1
       121: 3q^2+4q+1
       122: q^2+q
       123: q^3+5q^2+5q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 3q+1
       129: q^2+3q+1
       131: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+4q+1
       136: 2q^2+4q+1
       137: q^2+4q+1
       138: 3q+1
       139: 4q+1
       140: 2q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+3q+1
       145: 2q^2+4q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       151: 2q^2+4q+1
       153: q^3+4q^2+4q+1
       155: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 5q^2+5q+1
       164: q^3+6q^2+5q+1
       165: 3q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       172: 2q+1
       173: q
       175: q
       176: 2q^2+3q+1
       177: 2q+1
       179: 2q+1
       181: 2q+1
       184: q^2+3q+1
       185: q
       186: 2q+1
       187: q^2+3q+1
       189: q^2+3q+1
       191: 2q
       192: q^2+2q+1
       194: 2q+1
       195: q
       196: 2q+1
       197: q+1
       199: q
       200: q^2+3q+1
       202: q^2+3q+1
       203: q
       204: 2q+1
       205: q^2+3q+1
       207: q^2+3q+1
       208: q
       209: q^2+3q+1
       211: 2q^2+4q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 2q+1
       232: 2q^2+4q+1
       233: 2q^2+3q+1
       234: 3q^2+4q+1
       235: 2q^2+4q+1
       236: 3q+1
       237: 3q+1
       239: q^2+3q+1
       241: 2q+1
       243: 4q+1
       244: 2q+1
       245: q^2+4q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       262: q+1
       266: 2q+1
       269: q+1
       273: 2q+1
       275: q
       277: q
       278: q^2+2q+1
       279: 2q+1
       281: 2q+1
       284: q+1
       286: 1
       287: q+1
       289: 2q+1
       291: q+1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: 2q+1
       301: 1
       303: q
       304: 2q+1
       305: q+1
       308: q^2+3q+1
       309: q
       310: 2q+1
       311: 2q+1
       313: q^2+3q+1
       315: 2q+1
       317: 2q+1
       320: 2q+1
       321: q
       322: 2q+1
       323: q+1
       325: q^2+3q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       348: q+1
       350: 2q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       380: 1
       384: q+1
       388: q+1
       391: 1
       396: q+1
       399: q+1
       404: 2q+1
       406: q+1
       413: q+1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: q+1
       432: 1
       433: 1
       435: 1
       444: 2
       445: 2
       448: q+1
       450: 1
       451: q+1
       454: q+1
       455: 2q+1
       457: q
       458: q+1
       459: q+1
       461: 1
       462: 1
       463: q+2
       465: 2q+1
       467: 2q+1
       469: q+1
       472: 2q+1
       473: q
       474: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: 2q+1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 2
       552: 1
       555: q+1
       559: q+1
       561: 1
       563: 1
       568: q+1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       585: 1
       590: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 2
       605: 1
       613: 1
       616: 2
       617: 2
       620: 1
       622: 1
       623: q+1
       625: 1
       629: 1
       631: 1
       632: 1
       633: q+2
       639: q+1
       642: q+1
       644: 1
       645: 1
       651: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       697: 1
       698: 1
       712: 1
       720: 1
       723: 1
       735: 2
       739: 1
       743: 1
       749: 1
       751: 1
       756: 1
       758: 1
       767: 1
       768: 1
       769: 1
       772: 1
       781: 1
       786: 1
       809: 1
       821: 1
       826: 1
       830: 1
       832: 1
       833: 1
       835: 1
       849: 1
       855: 1
       875: 1
       880: 1
       888: 1
       889: 1
       906: 1
       946: 1
       955: 1
       961: 1
      1038: 1
      1041: 1
      1060: 1
      1178: 1

1179:    0: 3q^3+11q^2+6q+1
         1: q^4+7q^3+12q^2+6q+1
         2: 3q^3+11q^2+6q+1
         3: q^4+7q^3+12q^2+6q+1
         4: 4q^3+8q^2+5q+1
         5: 3q^3+11q^2+6q+1
         6: q^5+4q^4+9q^3+10q^2+5q+1
         7: 4q^3+8q^2+5q+1
         8: 3q^3+11q^2+6q+1
         9: q^4+3q^3+4q^2+3q+1
        10: 6q^2+5q+1
        11: 6q^2+5q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+11q^2+6q+1
        14: 4q^3+8q^2+5q+1
        15: 3q^3+11q^2+6q+1
        16: 2q^3+9q^2+6q+1
        17: 2q^3+9q^2+6q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+7q^2+5q+1
        20: q^4+5q^3+9q^2+5q+1
        21: q^3+7q^2+5q+1
        22: q^3+8q^2+6q+1
        23: 4q^3+9q^2+6q+1
        24: q^3+8q^2+6q+1
        25: 3q^3+11q^2+6q+1
        26: q^4+7q^3+12q^2+6q+1
        27: 3q^3+11q^2+6q+1
        28: 4q^2+5q+1
        29: 4q^2+4q+1
        30: q^3+7q^2+5q+1
        31: 4q^2+5q+1
        32: q^3+8q^2+6q+1
        33: q^3+6q^2+6q+1
        34: 6q^2+5q+1
        35: 3q^3+11q^2+6q+1
        36: 2q^3+9q^2+6q+1
        37: 2q^2+q
        38: q^3+6q^2+5q+1
        39: q^3+2q^2+q
        40: 3q^3+7q^2+5q+1
        41: 2q^2+q
        42: q^3+6q^2+5q+1
        43: 6q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: 6q^2+5q+1
        46: 2q^3+9q^2+6q+1
        47: 2q^3+9q^2+6q+1
        48: 2q^3+4q^2+3q+1
        49: 5q^2+5q+1
        50: q^3+6q^2+5q+1
        51: 3q^2+3q+1
        52: 4q^2+5q+1
        53: 2q^3+6q^2+5q+1
        54: 4q^2+5q+1
        55: q^3+7q^2+5q+1
        56: q^4+5q^3+9q^2+5q+1
        57: q^3+7q^2+5q+1
        58: 2q^2+3q+1
        59: 2q
        60: q^2+q
        61: 3q^2+4q+1
        62: q^2+q
        63: 3q^2+4q+1
        64: 2q^2+q
        65: q^3+6q^2+5q+1
        66: q^2+q
        67: q^3+5q^2+5q+1
        68: 4q^2+5q+1
        69: 2q^2+3q+1
        70: 4q^2+4q+1
        71: 2q^2+4q+1
        72: 3q^2+4q+1
        73: 2q^2+4q+1
        75: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        79: 2q^2+4q+1
        80: 4q^2+5q+1
        81: q^3+6q^2+6q+1
        82: 2q^2+4q+1
        83: 4q^2+5q+1
        84: 6q^2+5q+1
        85: 2q^3+9q^2+6q+1
        86: 4q^2+4q+1
        87: q^3+7q^2+5q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 5q^2+5q+1
        92: q^3+6q^2+5q+1
        93: 3q^2+3q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: q^2+3q+1
        97: 5q^2+5q+1
        98: q^3+6q^2+5q+1
        99: 3q^2+3q+1
       100: 4q^2+5q+1
       101: 2q^3+6q^2+5q+1
       102: 4q^2+5q+1
       104: q
       105: 2q^2+3q+1
       106: q
       108: q^2+3q+1
       109: 2q+1
       110: q
       112: q^2+3q+1
       114: q^2+3q+1
       116: 2q^2+4q+1
       117: 2q^2+3q+1
       118: 2q
       119: q^2+q
       120: 3q^2+4q+1
       121: q^2+q
       122: 3q^2+4q+1
       123: q^2+q
       124: q^3+5q^2+5q+1
       125: q^2+4q+1
       126: 2q+1
       128: 3q+1
       130: q^2+3q+1
       132: 2q+1
       133: 2q^2+4q+1
       134: 2q^2+3q+1
       135: 3q^2+4q+1
       136: 2q^2+4q+1
       137: q^2+4q+1
       138: 3q+1
       139: 4q+1
       140: 2q+1
       141: 2q^2+4q+1
       142: q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+3q+1
       145: 2q^2+4q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: 4q^2+5q+1
       152: 2q^2+4q+1
       154: q^3+4q^2+4q+1
       156: 2q^2+4q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 5q^2+5q+1
       164: q^3+6q^2+5q+1
       165: 3q^2+3q+1
       166: q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+3q+1
       171: 2q+1
       174: q
       175: 2q^2+3q+1
       176: q
       178: 2q+1
       180: 2q+1
       182: 2q+1
       184: q^2+3q+1
       185: 2q+1
       186: q
       188: q^2+3q+1
       190: q^2+3q+1
       191: q^2+2q+1
       192: 2q
       194: 2q+1
       195: 2q+1
       196: q
       198: q+1
       199: q
       200: q^2+3q+1
       202: q^2+3q+1
       203: 2q+1
       204: q
       206: q^2+3q+1
       207: q
       208: q^2+3q+1
       210: q^2+3q+1
       212: 2q^2+4q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 2q+1
       232: 2q^2+4q+1
       233: 2q^2+3q+1
       234: 3q^2+4q+1
       235: 2q^2+4q+1
       236: 3q+1
       238: 3q+1
       240: q^2+3q+1
       242: 2q+1
       243: 4q+1
       244: 2q+1
       245: q^2+4q+1
       246: 2q^2+4q+1
       247: q+2
       248: q+2
       249: q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       261: q+1
       265: 2q+1
       270: q+1
       272: 2q+1
       276: q
       277: q^2+2q+1
       278: q
       280: 2q+1
       282: 2q+1
       284: q+1
       285: 1
       288: q+1
       290: 2q+1
       292: q+1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: 2q+1
       302: 1
       303: 2q+1
       304: q
       306: q+1
       308: q^2+3q+1
       309: 2q+1
       310: q
       312: 2q+1
       314: q^2+3q+1
       316: 2q+1
       318: 2q+1
       320: 2q+1
       321: 2q+1
       322: q
       324: q+1
       326: q^2+3q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       348: q+1
       350: 2q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       379: 1
       383: q+1
       387: q+1
       392: 1
       395: q+1
       398: q+1
       402: 2q+1
       408: q+1
       414: q+1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: q+1
       431: 1
       434: 1
       436: 1
       444: 2
       446: 2
       448: q+1
       449: 1
       452: q+1
       454: q+1
       456: 2q+1
       457: q+1
       458: q
       460: q+1
       461: 1
       462: 1
       464: q+2
       466: 2q+1
       468: 2q+1
       470: q+1
       472: 2q+1
       473: 2q+1
       474: q
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: 2q+1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 2
       550: 1
       554: q+1
       558: q+1
       562: 1
       564: 1
       567: q+1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 2
       606: 1
       614: 1
       616: 2
       618: 2
       620: 1
       621: 1
       624: q+1
       626: 1
       630: 1
       631: 1
       632: 1
       634: q+2
       640: q+1
       642: q+1
       643: 1
       646: 1
       652: 1
       655: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       700: 1
       701: 1
       711: 1
       719: 1
       724: 1
       736: 2
       738: 1
       742: 1
       750: 1
       752: 1
       755: 1
       760: 1
       767: 1
       768: 1
       770: 1
       773: 1
       782: 1
       786: 1
       810: 1
       822: 1
       826: 1
       830: 1
       831: 1
       834: 1
       836: 1
       850: 1
       856: 1
       875: 1
       880: 1
       891: 1
       892: 1
       907: 1
       945: 1
       954: 1
       963: 1
      1039: 1
      1041: 1
      1061: 1
      1179: 1

1180:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+3q+1
        25: 3q^3+7q^2+4q+1
        26: q^4+4q^3+7q^2+4q+1
        27: 2q^3+5q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: q^3+5q^2+4q+1
        37: 3q^2+2q+1
        38: q^2+2q
        39: q^3+3q^2+2q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+3q+1
        55: 3q^3+7q^2+4q+1
        56: q^4+4q^3+7q^2+4q+1
        57: 2q^3+5q^2+3q+1
        58: q^2+2q+1
        59: q
        60: 2q^2+2q+1
        61: q
        62: 2q^2+q+1
        63: 2q
        64: 2q^2+2q+1
        65: q
        66: 2q^2+2q+1
        67: q^2+2q
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: 3q^2+2q+1
        75: q^2+2q
        76: q^3+3q^2+2q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+2q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+2q+1
        85: 2q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+3q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q^2+q+1
       104: q
       105: q
       107: 2q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: 2q^2+2q+1
       112: q^2+2q
       113: 2q^2+q+1
       114: 2q
       115: 2q^2+2q+1
       116: q
       117: q+1
       119: q+1
       121: q^2+q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: 2q^2+2q+1
       147: q^3+5q^2+4q+1
       148: 3q^2+4q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 3q^2+2q+1
       152: q^2+2q
       153: q^3+3q^2+2q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q^2+q+1
       170: q
       171: q
       173: q+1
       177: q+1
       179: 1
       181: q+1
       183: q+1
       185: q+1
       187: q^2+2q+1
       188: q
       189: q^2+q+1
       190: q
       191: q+1
       193: q+1
       195: q+1
       196: q
       197: 1
       198: q
       199: q+1
       201: 2q^2+2q+1
       202: q
       203: q^2+2q+1
       204: q
       205: 2q^2+2q+1
       206: q^2+2q
       207: q+1
       208: q
       209: 2q^2+q+1
       210: 2q
       211: 2q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: q+1
       267: 1
       268: q
       271: q^2+q+1
       272: q
       274: q
       275: q+1
       283: 1
       285: 1
       287: 1
       291: q+1
       293: q+1
       295: q+1
       297: q+1
       298: q
       299: 1
       301: 1
       303: 1
       305: 1
       307: q+1
       309: q+1
       311: q+1
       313: q^2+2q+1
       314: q
       315: q+1
       317: 1
       319: q+1
       321: q+1
       322: q
       323: 1
       324: q
       325: q^2+q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       385: q+1
       389: 1
       393: 1
       397: 1
       401: q+1
       405: 1
       407: q
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: 1
       443: q+1
       445: 1
       447: 1
       449: 1
       451: q+1
       453: q+1
       457: q+1
       459: q+1
       460: q
       461: q+1
       462: q
       463: q+1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       529: 1
       533: 1
       545: 1
       549: 1
       557: q+1
       561: 1
       565: 1
       569: 1
       573: 1
       574: q
       577: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       613: 1
       615: 1
       619: 1
       621: 1
       625: 1
       629: q+1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       693: 1
       713: 1
       717: 1
       741: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       855: 1
       875: 1
       880: 1
       908: 1
       948: 1
       952: 1
      1040: 1
      1044: 1
      1064: 1
      1180: 1

1181:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+3q+1
        25: 3q^3+7q^2+4q+1
        26: q^4+4q^3+7q^2+4q+1
        27: 2q^3+5q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: q^3+5q^2+4q+1
        37: q^2+2q
        38: 3q^2+2q+1
        39: q^2+2q
        40: q^3+3q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+3q+1
        55: 3q^3+7q^2+4q+1
        56: q^4+4q^3+7q^2+4q+1
        57: 2q^3+5q^2+3q+1
        58: q
        59: q^2+2q+1
        60: 2q^2+2q+1
        61: q
        62: 2q
        63: 2q^2+q+1
        64: q
        65: 2q^2+2q+1
        66: q^2+2q
        67: 2q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: q^2+2q
        75: 3q^2+2q+1
        76: q^2+2q
        77: q^3+3q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+2q+1
        85: 2q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+3q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q
       104: q^2+q+1
       106: q
       107: 2q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       111: q^2+2q
       112: 2q^2+2q+1
       113: 2q
       114: 2q^2+q+1
       115: q
       116: 2q^2+2q+1
       118: q+1
       119: q+1
       121: q
       122: q^2+q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: 2q^2+2q+1
       147: q^3+5q^2+4q+1
       148: 3q^2+4q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q
       152: 3q^2+2q+1
       153: q^2+2q
       154: q^3+3q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       170: q^2+q+1
       172: q
       174: q+1
       178: q+1
       180: 1
       182: q+1
       183: q+1
       186: q+1
       187: q
       188: q^2+2q+1
       189: q
       190: q^2+q+1
       192: q+1
       193: q+1
       195: q
       196: q+1
       197: q
       198: 1
       199: q+1
       201: 2q^2+2q+1
       202: q
       203: q
       204: q^2+2q+1
       205: q^2+2q
       206: 2q^2+2q+1
       207: q
       208: q+1
       209: 2q
       210: 2q^2+q+1
       211: q
       212: 2q^2+2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: q+1
       267: q
       268: 1
       271: q
       273: q
       274: q^2+q+1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: q+1
       299: 1
       302: 1
       304: 1
       306: 1
       307: q+1
       310: q+1
       312: q+1
       313: q
       314: q^2+2q+1
       316: q+1
       318: 1
       319: q+1
       321: q
       322: q+1
       323: q
       324: 1
       325: q
       326: q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       386: q+1
       390: 1
       394: 1
       400: 1
       403: q+1
       405: q
       407: 1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: 1
       443: q+1
       446: 1
       447: 1
       450: 1
       452: q+1
       453: q+1
       458: q+1
       459: q
       460: q+1
       461: q
       462: q+1
       464: q+1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       530: 1
       534: 1
       546: 1
       551: 1
       560: q+1
       564: 1
       566: 1
       571: 1
       573: q
       574: 1
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       600: 1
       614: 1
       615: 1
       619: 1
       622: 1
       626: 1
       630: q+1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       699: 1
       715: 1
       718: 1
       744: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       825: 1
       828: 1
       829: 1
       832: 1
       836: 1
       856: 1
       875: 1
       880: 1
       909: 1
       951: 1
       953: 1
      1040: 1
      1045: 1
      1065: 1
      1181: 1

1182:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+3q+1
        25: 3q^3+7q^2+4q+1
        26: q^4+4q^3+7q^2+4q+1
        27: 2q^3+5q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: q^3+5q^2+4q+1
        37: q^2+2q
        38: 3q^2+2q+1
        39: q^2+2q
        40: q^3+3q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+3q+1
        55: 3q^3+7q^2+4q+1
        56: q^4+4q^3+7q^2+4q+1
        57: 2q^3+5q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q
        61: 2q^2+2q+1
        62: 2q
        63: 2q^2+q+1
        64: q
        65: 2q^2+2q+1
        66: q^2+2q
        67: 2q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: q^2+2q
        75: 3q^2+2q+1
        76: q^2+2q
        77: q^3+3q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+2q+1
        85: 2q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+3q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       103: q
       105: q^2+q+1
       106: q
       107: q
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: q
       111: q^2+2q
       112: 2q^2+2q+1
       113: 2q
       114: 2q^2+q+1
       115: q
       116: 2q^2+2q+1
       117: q+1
       120: q+1
       121: q
       122: q^2+q+1
       123: q
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: 2q^2+2q+1
       147: q^3+5q^2+4q+1
       148: 3q^2+4q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q
       152: 3q^2+2q+1
       153: q^2+2q
       154: q^3+3q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       171: q^2+q+1
       172: q
       175: q+1
       178: q+1
       180: 1
       182: q+1
       184: q+1
       185: q+1
       187: q
       188: q^2+2q+1
       189: q
       190: q^2+q+1
       191: q+1
       194: q+1
       195: q+1
       196: q
       197: q
       198: 1
       200: q+1
       201: q
       202: 2q^2+2q+1
       203: q^2+2q+1
       204: q
       205: q^2+2q
       206: 2q^2+2q+1
       207: q
       208: q+1
       209: 2q
       210: 2q^2+q+1
       211: q
       212: 2q^2+2q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: q+1
       269: q
       270: 1
       271: q
       272: q^2+q+1
       273: q
       277: q+1
       284: 1
       285: 1
       288: 1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: q+1
       300: 1
       302: 1
       303: 1
       306: 1
       308: q+1
       309: q+1
       312: q+1
       313: q
       314: q^2+2q+1
       316: q+1
       318: 1
       320: q+1
       321: q+1
       322: q
       323: q
       324: 1
       325: q
       326: q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       387: q+1
       392: 1
       395: 1
       398: 1
       402: q+1
       406: q
       408: 1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: 1
       444: q+1
       446: 1
       448: 1
       449: 1
       452: q+1
       454: q+1
       457: q+1
       459: q
       460: q+1
       461: q+1
       462: q
       464: q+1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       531: 1
       535: 1
       548: 1
       550: 1
       558: q+1
       562: 1
       567: 1
       572: 1
       575: q
       576: 1
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       600: 1
       614: 1
       616: 1
       620: 1
       621: 1
       626: 1
       630: q+1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       700: 1
       714: 1
       719: 1
       742: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       826: 1
       827: 1
       830: 1
       831: 1
       836: 1
       856: 1
       875: 1
       880: 1
       910: 1
       949: 1
       954: 1
      1041: 1
      1044: 1
      1065: 1
      1182: 1

1183:    0: 3q^3+7q^2+4q+1
         1: q^4+4q^3+7q^2+4q+1
         2: 2q^3+5q^2+3q+1
         3: q^4+4q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: q^4+4q^3+7q^2+4q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+3q^2+2q+1
        19: 3q^3+7q^2+4q+1
        20: q^4+4q^3+7q^2+4q+1
        21: 2q^3+5q^2+3q+1
        22: 4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+3q+1
        25: 3q^3+7q^2+4q+1
        26: q^4+4q^3+7q^2+4q+1
        27: 2q^3+5q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: q^3+5q^2+4q+1
        37: 3q^2+2q+1
        38: q^2+2q
        39: q^3+3q^2+2q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: q^3+5q^2+4q+1
        50: q^3+5q^2+4q+1
        51: q^3+3q^2+2q+1
        52: 4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 3q^2+3q+1
        55: 3q^3+7q^2+4q+1
        56: q^4+4q^3+7q^2+4q+1
        57: 2q^3+5q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q
        61: 2q^2+2q+1
        62: 2q^2+q+1
        63: 2q
        64: 2q^2+2q+1
        65: q
        66: 2q^2+2q+1
        67: q^2+2q
        68: q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: 3q^2+2q+1
        75: q^2+2q
        76: q^3+3q^2+2q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+2q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+2q+1
        85: 2q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+3q^2+2q+1
       100: 4q^2+4q+1
       101: q^3+4q^2+4q+1
       102: 3q^2+3q+1
       104: q
       105: q
       106: q^2+q+1
       107: q
       108: 2q^2+2q+1
       109: q
       110: q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+2q
       113: 2q^2+q+1
       114: 2q
       115: 2q^2+2q+1
       116: q
       118: q+1
       120: q+1
       121: q^2+q+1
       122: q
       123: q^2+2q+1
       124: q
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: 2q^2+2q+1
       147: q^3+5q^2+4q+1
       148: 3q^2+4q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 3q^2+2q+1
       152: q^2+2q
       153: q^3+3q^2+2q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: q
       171: q
       172: q^2+q+1
       176: q+1
       177: q+1
       179: 1
       181: q+1
       184: q+1
       186: q+1
       187: q^2+2q+1
       188: q
       189: q^2+q+1
       190: q
       192: q+1
       194: q+1
       195: q
       196: q+1
       197: 1
       198: q
       200: q+1
       201: q
       202: 2q^2+2q+1
       203: q
       204: q^2+2q+1
       205: 2q^2+2q+1
       206: q^2+2q
       207: q+1
       208: q
       209: 2q^2+q+1
       210: 2q
       211: 2q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: q+1
       269: 1
       270: q
       272: q
       273: q^2+q+1
       274: q
       278: q+1
       284: 1
       286: 1
       287: 1
       291: q+1
       294: q+1
       296: q+1
       297: q+1
       298: q
       300: 1
       301: 1
       304: 1
       305: 1
       308: q+1
       310: q+1
       311: q+1
       313: q^2+2q+1
       314: q
       315: q+1
       317: 1
       320: q+1
       321: q
       322: q+1
       323: 1
       324: q
       325: q^2+q+1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       388: q+1
       391: 1
       396: 1
       399: 1
       404: q+1
       406: 1
       408: q
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: 1
       444: q+1
       445: 1
       448: 1
       450: 1
       451: q+1
       454: q+1
       458: q+1
       459: q+1
       460: q
       461: q
       462: q+1
       463: q+1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       532: 1
       536: 1
       547: 1
       552: 1
       559: q+1
       563: 1
       568: 1
       570: 1
       575: 1
       576: q
       577: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       613: 1
       616: 1
       620: 1
       622: 1
       625: 1
       629: q+1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       697: 1
       716: 1
       720: 1
       743: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       855: 1
       875: 1
       880: 1
       911: 1
       950: 1
       955: 1
      1041: 1
      1045: 1
      1064: 1
      1183: 1

1184:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^4+q^3+q^2+2q+1
         5: 3q+1
         6: q^4+q^3+q^2+2q+1
         7: q^3+q+1
         8: q^2+2q+1
         9: q^3+q+1
        10: 3q+1
        11: 3q+1
        12: q^4+q^3+q^2+2q+1
        13: 2q+1
        14: q^3+q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^3+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^3+q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^3+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: q+1
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       193: q+1
       195: q+1
       197: q+1
       199: q+1
       201: q+1
       203: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       267: q+1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       389: q+1
       393: 1
       397: q+1
       401: 1
       405: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: 1
       467: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       549: 1
       553: 1
       557: 1
       565: 1
       569: q+1
       583: 1
       587: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       686: 1
       687: 1
       688: 1
       705: 1
       721: 1
       725: 1
       729: 1
       737: 1
       741: 1
       745: 1
       753: 1
       757: 1
       761: 1
       799: 1
       823: 1
       841: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       912: 1
       936: 1
       960: 1
       974: 1
       978: 1
      1050: 1
      1184: 1

1185:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^4+q^3+q^2+2q+1
         5: 3q+1
         6: q^4+q^3+q^2+2q+1
         7: q^3+q+1
         8: q^2+2q+1
         9: q^3+q+1
        10: 3q+1
        11: 3q+1
        12: q^4+q^3+q^2+2q+1
        13: 2q+1
        14: q^3+q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: q^3+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^3+q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^3+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       194: q+1
       196: q+1
       197: q+1
       200: q+1
       202: q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       269: q+1
       273: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       391: q+1
       396: 1
       399: q+1
       404: 1
       406: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: 1
       467: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       552: 1
       555: 1
       559: 1
       568: 1
       570: q+1
       583: 1
       587: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       686: 1
       687: 1
       688: 1
       708: 1
       723: 1
       727: 1
       731: 1
       739: 1
       743: 1
       747: 1
       756: 1
       758: 1
       762: 1
       799: 1
       823: 1
       841: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       914: 1
       938: 1
       961: 1
       975: 1
       979: 1
      1050: 1
      1185: 1

1186:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^4+q^3+q^2+2q+1
         5: 3q+1
         6: q^4+q^3+q^2+2q+1
         7: q^3+q+1
         8: q^2+2q+1
         9: q^3+q+1
        10: 3q+1
        11: 3q+1
        12: q^4+q^3+q^2+2q+1
        13: 2q+1
        14: q^3+q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^3+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^3+q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^3+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: q+1
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       193: q+1
       196: q+1
       198: q+1
       199: q+1
       201: q+1
       204: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       268: q+1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       390: q+1
       394: 1
       400: q+1
       403: 1
       407: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: 1
       468: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       551: 1
       556: 1
       560: 1
       566: 1
       571: q+1
       584: 1
       588: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       686: 1
       687: 1
       688: 1
       706: 1
       722: 1
       726: 1
       730: 1
       740: 1
       744: 1
       748: 1
       754: 1
       759: 1
       763: 1
       800: 1
       824: 1
       842: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       913: 1
       939: 1
       962: 1
       976: 1
       980: 1
      1051: 1
      1186: 1

1187:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^4+q^3+q^2+2q+1
         5: 3q+1
         6: q^4+q^3+q^2+2q+1
         7: q^3+q+1
         8: q^2+2q+1
         9: q^3+q+1
        10: 3q+1
        11: 3q+1
        12: q^4+q^3+q^2+2q+1
        13: 2q+1
        14: q^3+q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q^3+q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^3+q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^3+q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^3+q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       194: q+1
       195: q+1
       198: q+1
       200: q+1
       202: q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       270: q+1
       272: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       392: q+1
       395: 1
       398: q+1
       402: 1
       408: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: 1
       468: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       550: 1
       554: 1
       558: 1
       567: 1
       572: q+1
       584: 1
       588: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       686: 1
       687: 1
       688: 1
       707: 1
       724: 1
       728: 1
       732: 1
       738: 1
       742: 1
       746: 1
       755: 1
       760: 1
       764: 1
       800: 1
       824: 1
       842: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       915: 1
       937: 1
       963: 1
       977: 1
       981: 1
      1051: 1
      1187: 1

1188:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: q^2+q+2
         5: 2q+2
         6: q^2+q+2
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+q+2
        13: q+1
        14: 1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: q+2
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: 1
       121: q+1
       123: q+1
       126: 1
       127: q+2
       129: q+2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       140: 2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: q+2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       213: 1
       215: q+1
       217: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: q+1
       331: 1
       334: 1
       335: 1
       337: 2
       338: 2
       340: 2
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: 1
       415: 1
       417: 1
       423: 1
       427: 2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       475: 1
       477: 2
       479: 2
       485: 1
       487: 1
       493: 1
       494: 1
       496: 1
       498: 1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       587: 1
       605: 1
       609: 1
       611: 1
       617: 1
       623: 1
       625: 1
       627: 1
       633: 1
       637: 1
       645: 1
       651: 1
       653: 1
       655: 1
       658: 1
       660: 1
       666: 1
       668: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       697: 1
       769: 1
       795: 1
       799: 1
       813: 1
       819: 1
       823: 1
       837: 1
       843: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: 1
       869: 1
       873: 1
       968: 1
       982: 1
      1014: 1
      1030: 1
      1046: 1
      1050: 1
      1188: 1

1189:    0: 4q^2+6q
         1: 4q^2+6q
         2: 2q^3+5q^2+3q
         3: 4q^2+6q
         4: 2q^3+3q^2+4q
         5: 4q^2+6q
         6: 2q^3+3q^2+4q
         7: q^3+3q^2+2q
         8: 2q^3+5q^2+3q
         9: q^3+3q^2+2q
        10: 4q^2+6q
        11: 4q^2+6q
        12: 2q^3+3q^2+4q
        13: 2q^2+3q
        14: q^2+2q
        15: 2q^2+3q
        16: 4q^2+6q
        17: 4q^2+6q
        18: q^3+3q^2+2q
        19: q^2+4q
        20: q^2+4q
        21: 2q^2+2q
        22: 4q^2+6q
        23: 4q^2+6q
        24: 2q^3+5q^2+3q
        25: 4q^2+6q
        26: 4q^2+6q
        27: 2q^3+5q^2+3q
        28: 4q^2+6q
        29: q^2+4q
        30: 2q
        31: 4q^2+6q
        32: 2q^2+3q
        33: 4q^2+6q
        34: 4q^2+6q
        35: 2q^2+3q
        36: 4q^2+6q
        37: 2q^2+2q
        38: 2q^2+4q
        39: 2q^2+2q
        40: 2q^2+4q
        41: q^3+2q^2+q
        42: q^3+3q^2+2q
        43: 2q^2+3q
        44: q^2+2q
        45: 2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^2+2q
        49: q^2+4q
        50: q^2+4q
        51: 2q^2+2q
        52: q^2+4q
        53: q^2+4q
        54: 2q^2+2q
        55: q^2+4q
        56: q^2+4q
        57: 2q^2+2q
        58: 2q^2+3q
        59: 2q^2+3q
        60: 2q^2+3q
        61: 2q^2+3q
        62: 2q^2+2q
        63: 2q^2+4q
        64: q^2+q
        65: q^2+2q
        66: 2q^2+2q
        67: 2q^2+4q
        69: 2q
        70: 2q
        71: q^2+4q
        72: 2q
        73: 2q
        75: 2q
        77: 2q
        79: q^2+q
        80: 2q^2+3q
        81: 2q^2+3q
        82: q^2+4q
        83: 2q
        84: 2q^2+3q
        85: 2q^2+3q
        86: q^2+4q
        87: 2q
        88: 2q^2+3q
        89: 2q^2+3q
        90: q^2+2q
        91: 2q
        92: q^2+2q
        93: 2q
        94: q^2+4q
        95: q^2+4q
        96: 2q^2+2q
        97: q^2+4q
        98: q^2+4q
        99: 2q^2+2q
       100: q^2+4q
       101: q^2+4q
       102: 2q^2+2q
       103: q^2+q
       104: q^2+2q
       105: q^2+2q
       106: q^2+q
       107: q
       108: q
       109: q
       110: q
       114: 2q
       116: q
       121: q^2+q
       122: q^2+2q
       123: q^2+q
       124: q^2+2q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       134: 2q
       135: q
       136: q
       137: 2q^2+3q
       138: 2q
       139: q^2+4q
       140: 2q
       141: 2q
       142: 2q
       143: 2q^2+3q
       144: 2q
       145: q^2+4q
       146: 2q
       147: 2q
       148: 2q
       149: q^2+4q
       150: 2q
       152: 2q
       154: 2q
       156: q^2+q
       157: 2q
       158: q^2+2q
       159: 2q
       160: 2q
       161: q^2+2q
       162: 2q
       163: 2q
       164: q^2+2q
       165: 2q
       166: q^2+4q
       167: q^2+4q
       168: 2q^2+2q
       178: q
       180: 2q
       190: q
       193: q
       194: q
       195: q
       196: q
       201: q
       202: q
       203: q
       204: q
       207: q^2+q
       208: q^2+2q
       210: 2q
       212: q
       214: q
       216: q
       218: q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       238: 2q
       240: 2q
       242: q^2+q
       243: q^2+4q
       244: 2q
       245: 2q
       246: 2q
       247: 2
       248: 2
       250: 2q
       251: q^2+2q
       252: 2q
       253: 2q
       254: q^2+2q
       255: 2q
       256: 2q
       257: q^2+2q
       258: 2q
       282: q
       288: q
       316: q
       318: 2q
       319: q
       320: q
       321: q
       322: q
       326: q
       328: q
       330: q
       332: q
       334: q
       335: q
       337: 2
       339: 2
       341: 2
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: 2
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: 2
       361: q
       363: q
       365: q
       366: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: q^2+2q
       376: 2q
       412: q
       428: 2
       443: 1
       444: 1
       446: 2
       461: 1
       462: 1
       464: 2
       468: q
       470: q
       479: 2
       486: 1
       488: 1
       493: q
       494: q
       496: 1
       498: q
       499: q
       501: 1
       503: q
       505: q
       507: q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       546: 1
       548: 1
       562: 1
       564: 1
       573: 1
       575: 1
       578: 2
       618: 1
       634: 1
       638: q
       655: 1
       659: 1
       661: 1
       667: 1
       669: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: q
       688: q
       690: 1
       691: 1
       694: 1
       701: 1
       770: 1
       796: 1
       814: 1
       820: 1
       838: 1
       843: 1
       857: 1
       860: 1
       862: 1
       869: 1
       873: 1
       969: 1
       983: 1
      1015: 1
      1031: 1
      1046: 1
      1189: 1

1190:    0: 2q^3+4q^2+2q
         1: 2q^3+4q^2+2q
         2: q^5+2q^4+2q^3+2q^2+q
         3: 2q^3+4q^2+2q
         4: 2q^4+3q^3+3q^2+2q
         5: 2q^3+4q^2+2q
         6: 2q^4+3q^3+3q^2+2q
         7: q^4+q^3+q^2+q
         8: q^3+2q^2+q
         9: q^4+q^3+q^2+q
        10: 2q^3+4q^2+2q
        11: 2q^3+4q^2+2q
        12: 2q^4+3q^3+3q^2+2q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: 2q^3+4q^2+2q
        17: 2q^3+4q^2+2q
        18: q^4+q^3+q^2+q
        19: 2q^3+3q^2+2q
        20: 2q^3+3q^2+2q
        21: q^4+q^3+q^2+q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+2q^2+q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+2q^2+q
        28: 2q^3+4q^2+2q
        29: 2q^3+3q^2+2q
        30: q^3+q
        31: 4q^2+2q
        32: q^2+q
        33: 4q^2+2q
        34: 4q^2+2q
        35: q^2+q
        36: 4q^2+2q
        37: 4q^2+2q
        39: 4q^2+2q
        41: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^3+q
        45: q^2+q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: 2q^3+3q^2+2q
        50: 2q^3+3q^2+2q
        51: q^4+q^3+q^2+q
        52: 3q^2+2q
        53: 3q^2+2q
        54: q^2+q
        55: 3q^2+2q
        56: 3q^2+2q
        57: q^2+q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        62: 4q^2+2q
        64: q^2+q
        66: 4q^2+2q
        69: q^3+q
        70: q^3+q
        71: 2q^3+3q^2+2q
        72: 2q^2+2q
        73: 2q^2+2q
        74: 3q^2+2q
        76: 3q^2+2q
        78: q^2+q
        80: q^2+q
        81: q^2+q
        82: 3q^2+2q
        83: q
        84: q^2+q
        85: q^2+q
        86: 3q^2+2q
        87: q
        88: q^3+q^2+q
        89: q^2+q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: 3q^2+2q
        95: 3q^2+2q
        96: q^2+q
        97: 3q^2+2q
        98: 3q^2+2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       103: 2q^2+q
       106: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       111: 2q^2+2q
       113: 3q^2+2q
       115: q
       121: q^2+q
       123: q^2+q
       126: q^3+q
       127: 3q^2+2q
       129: 3q^2+2q
       131: q^2+q
       134: q
       135: q
       136: q
       137: q^2+q
       138: q
       139: 3q^2+2q
       140: 2q
       141: q
       142: 2q^2+2q
       143: q^2+q
       144: q
       145: 3q^2+2q
       146: q
       147: 2q^2+2q
       148: 2q
       149: q^2+2q
       150: q
       151: q^2+2q
       153: q^2+2q
       155: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       169: q^2+q
       172: q^2+q
       177: q
       179: 3q^2+2q
       181: 2q^2+2q
       187: q
       189: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       197: 2q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       205: 2q
       207: q^2+q
       209: q^2+2q
       211: q
       213: q
       215: q^2+q
       217: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       259: q^2+q
       262: q^2+q
       267: q
       269: q
       271: q
       273: q
       281: q
       287: q
       289: q
       291: q
       297: q
       301: 2q
       305: q
       311: 2q
       313: q
       315: q
       317: q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: 2q
       325: q
       327: q
       329: q^2+q
       331: q
       334: q
       335: q
       346: q
       347: q
       348: q
       349: q
       350: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q
       389: q
       391: q
       397: q
       399: q
       405: q
       406: q
       411: q
       415: q
       417: q
       423: q
       433: q
       441: q
       451: q
       459: q
       469: q
       477: 2q
       493: q
       494: q
       498: q
       499: q
       569: q
       570: q
       587: q
       609: q
       625: q
       651: 1
       771: 1
       849: 1
       853: 1
       970: 1
       984: 1
      1050: 1
      1190: 1

1191:    0: 4q^2+6q
         1: 4q^2+6q
         2: 2q^3+5q^2+3q
         3: 4q^2+6q
         4: 2q^3+3q^2+4q
         5: 4q^2+6q
         6: 2q^3+3q^2+4q
         7: q^3+3q^2+2q
         8: 2q^3+5q^2+3q
         9: q^3+3q^2+2q
        10: 4q^2+6q
        11: 4q^2+6q
        12: 2q^3+3q^2+4q
        13: 2q^2+3q
        14: q^2+2q
        15: 2q^2+3q
        16: 4q^2+6q
        17: 4q^2+6q
        18: q^3+3q^2+2q
        19: q^2+4q
        20: q^2+4q
        21: 2q^2+2q
        22: 4q^2+6q
        23: 4q^2+6q
        24: 2q^3+5q^2+3q
        25: 4q^2+6q
        26: 4q^2+6q
        27: 2q^3+5q^2+3q
        28: 4q^2+6q
        29: q^2+4q
        30: 2q
        31: 4q^2+6q
        32: 2q^2+3q
        33: 4q^2+6q
        34: 4q^2+6q
        35: 2q^2+3q
        36: 4q^2+6q
        37: 2q^2+4q
        38: 2q^2+2q
        39: 2q^2+4q
        40: 2q^2+2q
        41: q^3+3q^2+2q
        42: q^3+2q^2+q
        43: 2q^2+3q
        44: q^2+2q
        45: 2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^2+2q
        49: q^2+4q
        50: q^2+4q
        51: 2q^2+2q
        52: q^2+4q
        53: q^2+4q
        54: 2q^2+2q
        55: q^2+4q
        56: q^2+4q
        57: 2q^2+2q
        58: 2q^2+3q
        59: 2q^2+3q
        60: 2q^2+3q
        61: 2q^2+3q
        62: 2q^2+4q
        63: 2q^2+2q
        64: q^2+2q
        65: q^2+q
        66: 2q^2+4q
        67: 2q^2+2q
        69: 2q
        70: 2q
        71: q^2+4q
        72: 2q
        73: 2q
        74: 2q
        76: 2q
        78: q^2+q
        80: 2q^2+3q
        81: 2q^2+3q
        82: q^2+4q
        83: 2q
        84: 2q^2+3q
        85: 2q^2+3q
        86: q^2+4q
        87: 2q
        88: 2q^2+3q
        89: 2q^2+3q
        90: q^2+2q
        91: 2q
        92: q^2+2q
        93: 2q
        94: q^2+4q
        95: q^2+4q
        96: 2q^2+2q
        97: q^2+4q
        98: q^2+4q
        99: 2q^2+2q
       100: q^2+4q
       101: q^2+4q
       102: 2q^2+2q
       103: q^2+2q
       104: q^2+q
       105: q^2+q
       106: q^2+2q
       107: q
       108: q
       109: q
       110: q
       113: 2q
       115: q
       121: q^2+2q
       122: q^2+q
       123: q^2+2q
       124: q^2+q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       134: 2q
       135: q
       136: q
       137: 2q^2+3q
       138: 2q
       139: q^2+4q
       140: 2q
       141: 2q
       142: 2q
       143: 2q^2+3q
       144: 2q
       145: q^2+4q
       146: 2q
       147: 2q
       148: 2q
       149: q^2+4q
       150: 2q
       151: 2q
       153: 2q
       155: q^2+q
       157: 2q
       158: q^2+2q
       159: 2q
       160: 2q
       161: q^2+2q
       162: 2q
       163: 2q
       164: q^2+2q
       165: 2q
       166: q^2+4q
       167: q^2+4q
       168: 2q^2+2q
       177: q
       179: 2q
       189: q
       193: q
       194: q
       195: q
       196: q
       201: q
       202: q
       203: q
       204: q
       207: q^2+2q
       208: q^2+q
       209: 2q
       211: q
       213: q
       215: q
       217: q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q
       228: 2q
       229: q
       230: q
       231: 2q
       233: 2q
       234: q
       235: q
       236: 2q
       237: 2q
       239: 2q
       241: q^2+q
       243: q^2+4q
       244: 2q
       245: 2q
       246: 2q
       247: 2
       248: 2
       250: 2q
       251: q^2+2q
       252: 2q
       253: 2q
       254: q^2+2q
       255: 2q
       256: 2q
       257: q^2+2q
       258: 2q
       281: q
       287: q
       315: q
       317: 2q
       319: q
       320: q
       321: q
       322: q
       325: q
       327: q
       329: q
       331: q
       334: q
       335: q
       337: 2
       338: 2
       340: 2
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: 2
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: 2
       360: q
       362: q
       364: q
       366: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: q^2+2q
       376: 2q
       411: q
       427: 2
       443: 1
       444: 1
       445: 2
       461: 1
       462: 1
       463: 2
       467: q
       469: q
       480: 2
       485: 1
       487: 1
       493: q
       494: q
       496: 1
       498: q
       499: q
       501: 1
       502: q
       504: q
       506: q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       547: 1
       561: 1
       563: 1
       574: 1
       576: 1
       580: 2
       617: 1
       633: 1
       637: q
       656: 1
       658: 1
       660: 1
       666: 1
       668: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: q
       688: q
       690: 1
       691: 1
       696: 1
       698: 1
       772: 1
       795: 1
       813: 1
       819: 1
       837: 1
       844: 1
       858: 1
       859: 1
       861: 1
       869: 1
       873: 1
       971: 1
       985: 1
      1014: 1
      1030: 1
      1047: 1
      1191: 1

1192:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: q^2+q+2
         5: 2q+2
         6: q^2+q+2
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 2q+2
        11: 2q+2
        12: q^2+q+2
        13: q+1
        14: 1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q+1
        19: q+2
        20: q+2
        21: q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: q+2
        30: 1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+2
        50: q+2
        51: q+1
        52: q+2
        53: q+2
        54: q+1
        55: q+2
        56: q+2
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: 1
        70: 1
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+1
        80: q+1
        81: q+1
        82: q+2
        83: 1
        84: q+1
        85: q+1
        86: q+2
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: 1
       122: q+1
       124: q+1
       126: 1
       128: q+2
       130: q+2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: 1
       139: q+2
       140: 2
       141: 1
       142: 2
       143: q+1
       144: 1
       145: q+2
       146: 1
       147: 2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: q+2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       214: 1
       216: q+1
       218: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: q+1
       332: 1
       334: 1
       335: 1
       337: 2
       339: 2
       341: 2
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: 1
       416: 1
       418: 1
       424: 1
       428: 2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       476: 1
       478: 2
       480: 2
       486: 1
       488: 1
       493: 1
       494: 1
       496: 1
       498: 1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       588: 1
       606: 1
       610: 1
       612: 1
       618: 1
       624: 1
       626: 1
       628: 1
       634: 1
       638: 1
       646: 1
       652: 1
       654: 1
       656: 1
       659: 1
       661: 1
       667: 1
       669: 1
       674: 1
       678: 1
       680: 1
       684: 1
       687: 1
       688: 1
       690: 1
       691: 1
       699: 1
       700: 1
       773: 1
       796: 1
       800: 1
       814: 1
       820: 1
       824: 1
       838: 1
       844: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: 1
       869: 1
       873: 1
       972: 1
       986: 1
      1015: 1
      1031: 1
      1047: 1
      1051: 1
      1192: 1

1193:    0: 2q^3+4q^2+2q
         1: 2q^3+4q^2+2q
         2: q^5+2q^4+2q^3+2q^2+q
         3: 2q^3+4q^2+2q
         4: 2q^4+3q^3+3q^2+2q
         5: 2q^3+4q^2+2q
         6: 2q^4+3q^3+3q^2+2q
         7: q^4+q^3+q^2+q
         8: q^3+2q^2+q
         9: q^4+q^3+q^2+q
        10: 2q^3+4q^2+2q
        11: 2q^3+4q^2+2q
        12: 2q^4+3q^3+3q^2+2q
        13: q^3+q^2+q
        14: q^3+q
        15: q^2+q
        16: 2q^3+4q^2+2q
        17: 2q^3+4q^2+2q
        18: q^4+q^3+q^2+q
        19: 2q^3+3q^2+2q
        20: 2q^3+3q^2+2q
        21: q^4+q^3+q^2+q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+2q^2+q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+2q^2+q
        28: 2q^3+4q^2+2q
        29: 2q^3+3q^2+2q
        30: q^3+q
        31: 4q^2+2q
        32: q^2+q
        33: 4q^2+2q
        34: 4q^2+2q
        35: q^2+q
        36: 4q^2+2q
        38: 4q^2+2q
        40: 4q^2+2q
        42: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^3+q
        45: q^2+q
        46: q^3+q^2+q
        47: q^2+q
        48: q^3+q
        49: 2q^3+3q^2+2q
        50: 2q^3+3q^2+2q
        51: q^4+q^3+q^2+q
        52: 3q^2+2q
        53: 3q^2+2q
        54: q^2+q
        55: 3q^2+2q
        56: 3q^2+2q
        57: q^2+q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        63: 4q^2+2q
        65: q^2+q
        67: 4q^2+2q
        69: q^3+q
        70: q^3+q
        71: 2q^3+3q^2+2q
        72: 2q^2+2q
        73: 2q^2+2q
        75: 3q^2+2q
        77: 3q^2+2q
        79: q^2+q
        80: q^2+q
        81: q^2+q
        82: 3q^2+2q
        83: q
        84: q^2+q
        85: q^2+q
        86: 3q^2+2q
        87: q
        88: q^3+q^2+q
        89: q^2+q
        90: q^3+q
        91: q
        92: q^2+q
        93: q
        94: 3q^2+2q
        95: 3q^2+2q
        96: q^2+q
        97: 3q^2+2q
        98: 3q^2+2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       104: 2q^2+q
       105: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       112: 2q^2+2q
       114: 3q^2+2q
       116: q
       122: q^2+q
       124: q^2+q
       126: q^3+q
       128: 3q^2+2q
       130: 3q^2+2q
       132: q^2+q
       134: q
       135: q
       136: q
       137: q^2+q
       138: q
       139: 3q^2+2q
       140: 2q
       141: q
       142: 2q^2+2q
       143: q^2+q
       144: q
       145: 3q^2+2q
       146: q
       147: 2q^2+2q
       148: 2q
       149: q^2+2q
       150: q
       152: q^2+2q
       154: q^2+2q
       156: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       170: q^2+q
       171: q^2+q
       178: q
       180: 3q^2+2q
       182: 2q^2+2q
       188: q
       190: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       198: 2q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       206: 2q
       208: q^2+q
       210: q^2+2q
       212: q
       214: q
       216: q^2+q
       218: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       260: q^2+q
       261: q^2+q
       268: q
       270: q
       272: q
       274: q
       282: q
       288: q
       290: q
       292: q
       298: q
       302: 2q
       306: q
       312: 2q
       314: q
       316: q
       318: q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: 2q
       326: q
       328: q
       330: q^2+q
       332: q
       334: q
       335: q
       346: q
       347: q
       348: q
       349: q
       350: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q
       390: q
       392: q
       398: q
       400: q
       407: q
       408: q
       412: q
       416: q
       418: q
       424: q
       434: q
       442: q
       452: q
       460: q
       470: q
       478: 2q
       493: q
       494: q
       498: q
       499: q
       571: q
       572: q
       588: q
       610: q
       626: q
       652: 1
       774: 1
       850: 1
       854: 1
       973: 1
       987: 1
      1051: 1
      1193: 1

1194:    0: 5q+1
         1: 5q+1
         2: 2q^2+3q+1
         3: 5q+1
         4: 2q^2+3q+1
         5: 5q+1
         6: 2q^2+3q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: 5q+1
        11: 5q+1
        12: 2q^2+3q+1
        13: 3q+1
        14: 2q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: 2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 5q+1
        23: 5q+1
        24: 2q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: 2q^2+3q+1
        28: 5q+1
        29: 3q+1
        30: 2q+1
        31: 5q+1
        32: 3q+1
        33: 5q+1
        34: 5q+1
        35: 3q+1
        36: 5q+1
        37: 3q+1
        38: 2q
        39: 3q+1
        40: 2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: 2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: 2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 3q+1
        59: 2q
        60: 3q+1
        61: 2q
        62: 3q+1
        63: 2q
        64: 2q+1
        65: q
        66: 3q+1
        67: 2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: 2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: 2q+1
       104: q
       105: q
       106: q
       107: q+1
       109: q+1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       128: q
       129: q+1
       130: q
       131: q+1
       132: q
       133: 1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       169: 1
       173: q+1
       177: q+1
       178: q
       179: q+1
       180: q
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       190: q
       191: q+1
       193: q+1
       195: q+1
       197: 1
       199: q+1
       201: q+1
       203: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       238: q
       239: q+1
       240: q
       241: q+1
       242: q
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: q+1
       288: q
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       316: q
       317: q+1
       318: q
       319: q+1
       321: q+1
       323: 1
       325: q+1
       326: q
       333: 1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 2
       445: 1
       446: 1
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 2
       463: 1
       464: 1
       469: q+1
       470: q
       471: 1
       473: 1
       475: 1
       477: 1
       479: 2
       484: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       529: 1
       533: 1
       541: 1
       545: 1
       546: 1
       549: 1
       557: 1
       561: 1
       562: 1
       565: 1
       569: 1
       573: 2
       577: 1
       578: 1
       603: 1
       607: 1
       609: 1
       615: 1
       619: 1
       621: 1
       625: 1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       657: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       694: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       793: 1
       815: 1
       817: 1
       839: 1
       843: 1
       845: 1
       847: 1
       851: 1
       857: 1
       865: 1
       869: 1
       873: 1
       964: 1
       974: 1
       988: 1
      1016: 1
      1032: 1
      1046: 1
      1194: 1

1195:    0: 5q+1
         1: 5q+1
         2: 2q^2+3q+1
         3: 5q+1
         4: 2q^2+3q+1
         5: 5q+1
         6: 2q^2+3q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: 5q+1
        11: 5q+1
        12: 2q^2+3q+1
        13: 3q+1
        14: 2q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: 2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 5q+1
        23: 5q+1
        24: 2q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: 2q^2+3q+1
        28: 5q+1
        29: 3q+1
        30: 2q+1
        31: 5q+1
        32: 3q+1
        33: 5q+1
        34: 5q+1
        35: 3q+1
        36: 5q+1
        37: 2q
        38: 3q+1
        39: 2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: 2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: 2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 2q
        59: 3q+1
        60: 3q+1
        61: 2q
        62: 2q
        63: 3q+1
        64: q
        65: 2q+1
        66: 2q
        67: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: 2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: 2q+1
       105: q
       106: q
       107: q+1
       110: q+1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       127: q
       128: q+1
       129: q
       130: q+1
       131: q
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       170: 1
       174: q+1
       177: q
       178: q+1
       179: q
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       189: q
       190: q+1
       192: q+1
       193: q+1
       196: q+1
       198: 1
       199: q+1
       201: q+1
       204: q+1
       206: 1
       207: q
       208: 2q+1
       209: q
       210: q+1
       211: q
       212: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q
       238: q+1
       239: q
       240: q+1
       241: q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       283: 1
       286: 1
       287: q
       288: q+1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       315: q
       316: q+1
       317: q
       318: q+1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: q+1
       333: 1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       427: 1
       428: 1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 2
       463: 1
       464: 1
       469: q
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 2
       484: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       530: 1
       534: 1
       542: 1
       545: 1
       546: 1
       551: 1
       560: 1
       563: 1
       564: 1
       566: 1
       571: 1
       574: 2
       580: 1
       581: 1
       603: 1
       608: 1
       610: 1
       615: 1
       619: 1
       622: 1
       626: 1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       657: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       696: 1
       699: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       793: 1
       815: 1
       818: 1
       840: 1
       844: 1
       845: 1
       848: 1
       852: 1
       858: 1
       865: 1
       869: 1
       873: 1
       965: 1
       976: 1
       989: 1
      1016: 1
      1033: 1
      1047: 1
      1195: 1

1196:    0: 5q+1
         1: 5q+1
         2: 2q^2+3q+1
         3: 5q+1
         4: 2q^2+3q+1
         5: 5q+1
         6: 2q^2+3q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: 5q+1
        11: 5q+1
        12: 2q^2+3q+1
        13: 3q+1
        14: 2q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: 2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 5q+1
        23: 5q+1
        24: 2q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: 2q^2+3q+1
        28: 5q+1
        29: 3q+1
        30: 2q+1
        31: 5q+1
        32: 3q+1
        33: 5q+1
        34: 5q+1
        35: 3q+1
        36: 5q+1
        37: 2q
        38: 3q+1
        39: 2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: 2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: 2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 3q+1
        59: 2q
        60: 2q
        61: 3q+1
        62: 2q
        63: 3q+1
        64: q
        65: 2q+1
        66: 2q
        67: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: 2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: q
       105: 2q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       127: q
       128: q+1
       129: q
       130: q+1
       131: q
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       171: 1
       175: q+1
       177: q
       178: q+1
       179: q
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       189: q
       190: q+1
       191: q+1
       194: q+1
       195: q+1
       198: 1
       200: q+1
       202: q+1
       203: q+1
       206: 1
       207: q
       208: 2q+1
       209: q
       210: q+1
       211: q
       212: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q
       238: q+1
       239: q
       240: q+1
       241: q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: q+1
       284: 1
       285: 1
       287: q
       288: q+1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       315: q
       316: q+1
       317: q
       318: q+1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: q+1
       333: 1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 2
       463: 1
       464: 1
       469: q
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 2
       484: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       531: 1
       535: 1
       544: 1
       547: 1
       548: 1
       550: 1
       558: 1
       561: 1
       562: 1
       567: 1
       572: 1
       576: 2
       580: 1
       581: 1
       604: 1
       607: 1
       610: 1
       616: 1
       620: 1
       621: 1
       626: 1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       657: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       698: 1
       700: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       794: 1
       816: 1
       817: 1
       839: 1
       844: 1
       846: 1
       847: 1
       852: 1
       858: 1
       865: 1
       869: 1
       873: 1
       966: 1
       977: 1
       990: 1
      1017: 1
      1032: 1
      1047: 1
      1196: 1

1197:    0: 5q+1
         1: 5q+1
         2: 2q^2+3q+1
         3: 5q+1
         4: 2q^2+3q+1
         5: 5q+1
         6: 2q^2+3q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: 5q+1
        11: 5q+1
        12: 2q^2+3q+1
        13: 3q+1
        14: 2q+1
        15: 3q+1
        16: 5q+1
        17: 5q+1
        18: 2q+1
        19: 3q+1
        20: 3q+1
        21: 2q+1
        22: 5q+1
        23: 5q+1
        24: 2q^2+3q+1
        25: 5q+1
        26: 5q+1
        27: 2q^2+3q+1
        28: 5q+1
        29: 3q+1
        30: 2q+1
        31: 5q+1
        32: 3q+1
        33: 5q+1
        34: 5q+1
        35: 3q+1
        36: 5q+1
        37: 3q+1
        38: 2q
        39: 3q+1
        40: 2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: 2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: 2q+1
        49: 3q+1
        50: 3q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 3q+1
        57: 2q+1
        58: 2q
        59: 3q+1
        60: 2q
        61: 3q+1
        62: 3q+1
        63: 2q
        64: 2q+1
        65: q
        66: 3q+1
        67: 2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: 2q+1
        91: 1
        92: q+1
        93: 1
        94: 3q+1
        95: 3q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: 2q+1
       100: 3q+1
       101: 3q+1
       102: 2q+1
       103: q
       104: q
       105: q
       106: 2q+1
       108: q+1
       110: q+1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       128: q
       129: q+1
       130: q
       131: q+1
       132: q
       133: 1
       134: 1
       135: 1
       136: 1
       137: 3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 3q+1
       167: 3q+1
       168: 2q+1
       172: 1
       176: q+1
       177: q+1
       178: q
       179: q+1
       180: q
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       190: q
       192: q+1
       194: q+1
       196: q+1
       197: 1
       200: q+1
       202: q+1
       204: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 2q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       238: q
       239: q+1
       240: q
       241: q+1
       242: q
       243: 3q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: q+1
       288: q
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       316: q
       317: q+1
       318: q
       320: q+1
       322: q+1
       323: 1
       325: q+1
       326: q
       333: 1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       427: 1
       428: 1
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 2
       445: 1
       446: 1
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 2
       463: 1
       464: 1
       469: q+1
       470: q
       472: 1
       474: 1
       475: 1
       477: 1
       479: 2
       484: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       532: 1
       536: 1
       543: 1
       547: 1
       548: 1
       552: 1
       559: 1
       563: 1
       564: 1
       568: 1
       570: 1
       575: 2
       577: 1
       578: 1
       604: 1
       608: 1
       609: 1
       616: 1
       620: 1
       622: 1
       625: 1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       657: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       697: 1
       701: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       794: 1
       816: 1
       818: 1
       840: 1
       843: 1
       846: 1
       848: 1
       851: 1
       857: 1
       865: 1
       869: 1
       873: 1
       967: 1
       975: 1
       991: 1
      1017: 1
      1033: 1
      1046: 1
      1197: 1

1198:    0: 3q^2+6q+1
         1: 3q^2+6q+1
         2: 3q^2+6q+1
         3: 3q^2+6q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+6q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+6q+1
         9: q^3+3q^2+3q+1
        10: q^2+6q+1
        11: q^2+6q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+6q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+6q+1
        16: 3q^2+6q+1
        17: 3q^2+6q+1
        18: q^3+3q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+6q+1
        23: 3q^2+6q+1
        24: 3q^2+6q+1
        25: 3q^2+6q+1
        26: 3q^2+6q+1
        27: 3q^2+6q+1
        28: q^2+6q+1
        29: 3q+1
        30: 3q+1
        31: q^2+6q+1
        32: 3q^2+6q+1
        33: 3q^2+6q+1
        34: q^2+6q+1
        35: 3q^2+6q+1
        36: 3q^2+6q+1
        37: 2q^2+4q+1
        38: q^2+2q
        39: 2q^2+4q+1
        40: q^2+2q
        41: 2q^2+4q+1
        42: q^2+2q
        43: q^2+6q+1
        44: q^3+3q^2+3q+1
        45: q^2+6q+1
        46: 3q^2+6q+1
        47: 3q^2+6q+1
        48: q^3+3q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: q^2+4q+1
        59: 2q
        60: q^2+4q+1
        61: 2q
        62: q^2+4q+1
        63: 2q
        64: 2q^2+4q+1
        65: q^2+2q
        66: 2q^2+4q+1
        67: q^2+2q
        68: q^2+6q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+6q+1
        81: 3q^2+6q+1
        82: 3q+1
        83: 3q+1
        84: q^2+6q+1
        85: 3q^2+6q+1
        86: 3q+1
        87: 3q+1
        88: q^2+6q+1
        89: q^2+6q+1
        90: q^3+3q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q^2+3q+1
       104: q
       105: q
       106: q
       107: q+1
       109: q+1
       111: 1
       113: q+1
       115: q+1
       117: q^2+4q+1
       118: 2q
       119: q^2+4q+1
       120: 2q
       121: q^2+4q+1
       122: 2q
       123: 2q^2+4q+1
       124: q^2+2q
       125: q^2+6q+1
       126: 3q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+6q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+6q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: 1
       173: q^2+3q+1
       174: q
       175: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q+1
       185: q+1
       187: 1
       189: q+1
       191: q^2+4q+1
       192: 2q
       193: q+1
       195: q+1
       197: 1
       199: q^2+4q+1
       200: 2q
       201: q+1
       203: q+1
       205: 1
       207: q^2+4q+1
       208: 2q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+3q+1
       276: q
       277: q
       278: q
       279: q+1
       281: q+1
       283: q+1
       285: q+1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: q+1
       301: 1
       303: q+1
       305: 1
       307: q+1
       309: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q+1
       321: q+1
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       417: 1
       419: 1
       421: 1
       423: 1
       429: q+1
       431: q+1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: q+1
       449: q+1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: q+1
       467: q+1
       469: q+1
       471: q+1
       473: q+1
       475: 1
       477: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       549: 1
       553: 1
       557: 1
       565: 1
       569: 1
       585: 1
       589: 1
       595: 1
       603: 1
       605: 1
       607: 1
       609: 1
       619: 1
       621: 1
       623: 1
       625: 1
       639: q+1
       641: q+1
       643: q+1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       709: 1
       721: 1
       725: 1
       737: 1
       741: 1
       753: 1
       757: 1
       761: 1
       797: 1
       801: 1
       807: 1
       821: 1
       825: 1
       831: 1
       845: 1
       847: 1
       849: 1
       851: 1
       877: 1
       878: 1
       920: 1
       944: 1
       960: 1
       974: 1
      1048: 1
      1052: 1
      1058: 1
      1198: 1

1199:    0: 3q^2+6q+1
         1: 3q^2+6q+1
         2: 3q^2+6q+1
         3: 3q^2+6q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+6q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+6q+1
         9: q^3+3q^2+3q+1
        10: q^2+6q+1
        11: q^2+6q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+6q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+6q+1
        16: 3q^2+6q+1
        17: 3q^2+6q+1
        18: q^3+3q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+6q+1
        23: 3q^2+6q+1
        24: 3q^2+6q+1
        25: 3q^2+6q+1
        26: 3q^2+6q+1
        27: 3q^2+6q+1
        28: q^2+6q+1
        29: 3q+1
        30: 3q+1
        31: q^2+6q+1
        32: 3q^2+6q+1
        33: 3q^2+6q+1
        34: q^2+6q+1
        35: 3q^2+6q+1
        36: 3q^2+6q+1
        37: 2q^2+4q+1
        38: q^2+2q
        39: 2q^2+4q+1
        40: q^2+2q
        41: 2q^2+4q+1
        42: q^2+2q
        43: q^2+6q+1
        44: q^3+3q^2+3q+1
        45: q^2+6q+1
        46: 3q^2+6q+1
        47: 3q^2+6q+1
        48: q^3+3q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: 2q
        59: q^2+4q+1
        60: 2q
        61: q^2+4q+1
        62: q^2+4q+1
        63: 2q
        64: 2q^2+4q+1
        65: q^2+2q
        66: 2q^2+4q+1
        67: q^2+2q
        68: q^2+6q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+6q+1
        81: 3q^2+6q+1
        82: 3q+1
        83: 3q+1
        84: q^2+6q+1
        85: 3q^2+6q+1
        86: 3q+1
        87: 3q+1
        88: q^2+6q+1
        89: q^2+6q+1
        90: q^3+3q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q
       106: q^2+3q+1
       108: q+1
       110: q+1
       111: 1
       113: q+1
       115: q+1
       117: 2q
       118: q^2+4q+1
       119: 2q
       120: q^2+4q+1
       121: q^2+4q+1
       122: 2q
       123: 2q^2+4q+1
       124: q^2+2q
       125: q^2+6q+1
       126: 3q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+6q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+6q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       172: 1
       173: q
       174: q
       175: q
       176: q^2+3q+1
       177: q+1
       179: q+1
       181: 1
       184: q+1
       186: q+1
       187: 1
       189: q+1
       191: 2q
       192: q^2+4q+1
       194: q+1
       196: q+1
       197: 1
       199: 2q
       200: q^2+4q+1
       202: q+1
       204: q+1
       205: 1
       207: q^2+4q+1
       208: 2q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q
       277: q
       278: q^2+3q+1
       279: q+1
       281: q+1
       284: q+1
       286: q+1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: q+1
       301: 1
       304: q+1
       305: 1
       308: q+1
       310: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: q+1
       322: q+1
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       417: 1
       420: 1
       422: 1
       423: 1
       430: q+1
       432: q+1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: q+1
       450: q+1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: q+1
       467: q+1
       469: q+1
       472: q+1
       474: q+1
       475: 1
       477: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       552: 1
       555: 1
       559: 1
       568: 1
       570: 1
       585: 1
       590: 1
       596: 1
       604: 1
       605: 1
       608: 1
       609: 1
       620: 1
       622: 1
       623: 1
       625: 1
       639: q+1
       642: q+1
       644: q+1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       712: 1
       723: 1
       727: 1
       739: 1
       743: 1
       756: 1
       758: 1
       762: 1
       797: 1
       802: 1
       808: 1
       821: 1
       826: 1
       832: 1
       846: 1
       848: 1
       849: 1
       851: 1
       877: 1
       878: 1
       922: 1
       946: 1
       961: 1
       975: 1
      1048: 1
      1053: 1
      1059: 1
      1199: 1

1200:    0: 3q^2+6q+1
         1: 3q^2+6q+1
         2: 3q^2+6q+1
         3: 3q^2+6q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+6q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+6q+1
         9: q^3+3q^2+3q+1
        10: q^2+6q+1
        11: q^2+6q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+6q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+6q+1
        16: 3q^2+6q+1
        17: 3q^2+6q+1
        18: q^3+3q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+6q+1
        23: 3q^2+6q+1
        24: 3q^2+6q+1
        25: 3q^2+6q+1
        26: 3q^2+6q+1
        27: 3q^2+6q+1
        28: q^2+6q+1
        29: 3q+1
        30: 3q+1
        31: q^2+6q+1
        32: 3q^2+6q+1
        33: 3q^2+6q+1
        34: q^2+6q+1
        35: 3q^2+6q+1
        36: 3q^2+6q+1
        37: q^2+2q
        38: 2q^2+4q+1
        39: q^2+2q
        40: 2q^2+4q+1
        41: q^2+2q
        42: 2q^2+4q+1
        43: q^2+6q+1
        44: q^3+3q^2+3q+1
        45: q^2+6q+1
        46: 3q^2+6q+1
        47: 3q^2+6q+1
        48: q^3+3q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: 2q
        59: q^2+4q+1
        60: q^2+4q+1
        61: 2q
        62: 2q
        63: q^2+4q+1
        64: q^2+2q
        65: 2q^2+4q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: q^2+6q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+6q+1
        81: 3q^2+6q+1
        82: 3q+1
        83: 3q+1
        84: q^2+6q+1
        85: 3q^2+6q+1
        86: 3q+1
        87: 3q+1
        88: q^2+6q+1
        89: q^2+6q+1
        90: q^3+3q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q^2+3q+1
       105: q
       106: q
       107: q+1
       110: q+1
       112: 1
       114: q+1
       116: q+1
       117: 2q
       118: q^2+4q+1
       119: q^2+4q+1
       120: 2q
       121: 2q
       122: q^2+4q+1
       123: q^2+2q
       124: 2q^2+4q+1
       125: q^2+6q+1
       126: 3q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+6q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+6q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       170: 1
       173: q
       174: q^2+3q+1
       175: q
       176: q
       178: q+1
       180: q+1
       182: 1
       183: q+1
       186: q+1
       188: 1
       190: q+1
       191: 2q
       192: q^2+4q+1
       193: q+1
       196: q+1
       198: 1
       199: q^2+4q+1
       200: 2q
       201: q+1
       204: q+1
       206: 1
       207: 2q
       208: q^2+4q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q
       276: q^2+3q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: q+1
       286: q+1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: q+1
       302: 1
       304: q+1
       306: 1
       307: q+1
       310: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q+1
       322: q+1
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: q+1
       418: 1
       419: 1
       422: 1
       424: 1
       429: q+1
       432: q+1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: q+1
       450: q+1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: q+1
       468: q+1
       470: q+1
       471: q+1
       474: q+1
       476: 1
       478: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       551: 1
       556: 1
       560: 1
       566: 1
       571: 1
       586: 1
       589: 1
       596: 1
       603: 1
       606: 1
       608: 1
       610: 1
       619: 1
       622: 1
       624: 1
       626: 1
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       710: 1
       722: 1
       726: 1
       740: 1
       744: 1
       754: 1
       759: 1
       763: 1
       798: 1
       801: 1
       808: 1
       822: 1
       825: 1
       832: 1
       845: 1
       848: 1
       850: 1
       852: 1
       877: 1
       878: 1
       921: 1
       947: 1
       962: 1
       976: 1
      1049: 1
      1052: 1
      1059: 1
      1200: 1

1201:    0: 3q^2+6q+1
         1: 3q^2+6q+1
         2: 3q^2+6q+1
         3: 3q^2+6q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+6q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+6q+1
         9: q^3+3q^2+3q+1
        10: q^2+6q+1
        11: q^2+6q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+6q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+6q+1
        16: 3q^2+6q+1
        17: 3q^2+6q+1
        18: q^3+3q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+6q+1
        23: 3q^2+6q+1
        24: 3q^2+6q+1
        25: 3q^2+6q+1
        26: 3q^2+6q+1
        27: 3q^2+6q+1
        28: q^2+6q+1
        29: 3q+1
        30: 3q+1
        31: q^2+6q+1
        32: 3q^2+6q+1
        33: 3q^2+6q+1
        34: q^2+6q+1
        35: 3q^2+6q+1
        36: 3q^2+6q+1
        37: q^2+2q
        38: 2q^2+4q+1
        39: q^2+2q
        40: 2q^2+4q+1
        41: q^2+2q
        42: 2q^2+4q+1
        43: q^2+6q+1
        44: q^3+3q^2+3q+1
        45: q^2+6q+1
        46: 3q^2+6q+1
        47: 3q^2+6q+1
        48: q^3+3q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: q^2+4q+1
        59: 2q
        60: 2q
        61: q^2+4q+1
        62: 2q
        63: q^2+4q+1
        64: q^2+2q
        65: 2q^2+4q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: q^2+6q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+6q+1
        81: 3q^2+6q+1
        82: 3q+1
        83: 3q+1
        84: q^2+6q+1
        85: 3q^2+6q+1
        86: 3q+1
        87: 3q+1
        88: q^2+6q+1
        89: q^2+6q+1
        90: q^3+3q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q^2+3q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       114: q+1
       116: q+1
       117: q^2+4q+1
       118: 2q
       119: 2q
       120: q^2+4q+1
       121: 2q
       122: q^2+4q+1
       123: q^2+2q
       124: 2q^2+4q+1
       125: q^2+6q+1
       126: 3q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+6q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+6q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       171: 1
       173: q
       174: q
       175: q^2+3q+1
       176: q
       178: q+1
       180: q+1
       182: 1
       184: q+1
       185: q+1
       188: 1
       190: q+1
       191: q^2+4q+1
       192: 2q
       194: q+1
       195: q+1
       198: 1
       199: 2q
       200: q^2+4q+1
       202: q+1
       203: q+1
       206: 1
       207: 2q
       208: q^2+4q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q
       276: q
       277: q^2+3q+1
       278: q
       280: q+1
       282: q+1
       284: q+1
       285: q+1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       303: q+1
       306: 1
       308: q+1
       309: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: q+1
       321: q+1
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: q+1
       418: 1
       420: 1
       421: 1
       424: 1
       430: q+1
       431: q+1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: q+1
       449: q+1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: q+1
       468: q+1
       470: q+1
       472: q+1
       473: q+1
       476: 1
       478: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       550: 1
       554: 1
       558: 1
       567: 1
       572: 1
       586: 1
       590: 1
       595: 1
       604: 1
       606: 1
       607: 1
       610: 1
       620: 1
       621: 1
       624: 1
       626: 1
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       711: 1
       724: 1
       728: 1
       738: 1
       742: 1
       755: 1
       760: 1
       764: 1
       798: 1
       802: 1
       807: 1
       822: 1
       826: 1
       831: 1
       846: 1
       847: 1
       850: 1
       852: 1
       877: 1
       878: 1
       923: 1
       945: 1
       963: 1
       977: 1
      1049: 1
      1053: 1
      1058: 1
      1201: 1

1202:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+3q+1
        38: q^2+2q
        39: q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+3q+1
        59: q^2+2q
        60: 2q^2+3q+1
        61: 2q
        62: q^2+3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+q
       105: q
       106: q
       107: q^2+q+1
       108: q
       109: q+1
       111: 1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: 1
       173: q+1
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       193: q^2+q+1
       194: q
       195: q+1
       197: 1
       199: q+1
       201: q^2+q+1
       202: q
       203: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q^2+q+1
       320: q
       321: q+1
       323: 1
       325: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 1
       444: 1
       445: 2
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 2
       463: 2
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       529: 1
       533: 1
       541: 1
       545: 1
       547: 1
       549: 1
       557: 1
       561: 2
       565: 1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       589: 1
       591: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: 1
       619: 1
       621: 1
       625: 1
       629: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       693: 1
       698: 1
       713: 1
       725: 1
       741: 1
       753: 1
       761: 1
       801: 1
       803: 1
       811: 1
       825: 1
       827: 1
       835: 1
       845: 1
       847: 1
       851: 1
       855: 1
       877: 1
       879: 1
       924: 1
       948: 1
       974: 1
      1052: 1
      1054: 1
      1062: 1
      1202: 1

1203:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: q^2+3q+1
        39: q^2+2q
        40: q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+3q+1
        59: q^2+2q
        60: 2q
        61: 2q^2+3q+1
        62: q^2+2q
        63: q^2+3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: q
       105: q^2+2q+1
       106: q^2+q
       107: q
       108: q^2+q+1
       109: q+1
       112: 1
       114: q+1
       116: q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       171: 1
       175: q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       193: q
       194: q^2+q+1
       195: q+1
       198: 1
       200: q+1
       201: q
       202: q^2+q+1
       203: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q
       320: q^2+q+1
       321: q+1
       324: 1
       326: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       443: 1
       444: 1
       446: 2
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 2
       464: 2
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       531: 1
       535: 1
       544: 1
       546: 1
       548: 1
       550: 1
       558: 1
       562: 2
       567: 1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       590: 1
       591: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: 1
       620: 1
       621: 1
       626: 1
       630: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       694: 1
       700: 1
       714: 1
       728: 1
       742: 1
       755: 1
       764: 1
       802: 1
       803: 1
       812: 1
       826: 1
       827: 1
       836: 1
       846: 1
       847: 1
       852: 1
       856: 1
       877: 1
       879: 1
       925: 1
       949: 1
       977: 1
      1053: 1
      1054: 1
      1063: 1
      1203: 1

1204:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+3q+1
        38: q^2+2q
        39: q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+2q
        59: q^2+3q+1
        60: 2q
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: q
       105: q^2+q
       106: q^2+2q+1
       107: q
       108: q^2+q+1
       110: q+1
       111: 1
       113: q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       172: 1
       176: q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       193: q
       194: q^2+q+1
       196: q+1
       197: 1
       200: q+1
       201: q
       202: q^2+q+1
       204: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q
       320: q^2+q+1
       322: q+1
       323: 1
       325: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 2
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 2
       463: 2
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       532: 1
       536: 1
       543: 1
       545: 1
       547: 1
       552: 1
       559: 1
       563: 2
       568: 1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       590: 1
       592: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: 1
       620: 1
       622: 1
       625: 1
       629: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       696: 1
       697: 1
       716: 1
       727: 1
       743: 1
       756: 1
       762: 1
       802: 1
       804: 1
       811: 1
       826: 1
       828: 1
       835: 1
       846: 1
       848: 1
       851: 1
       855: 1
       877: 1
       879: 1
       927: 1
       950: 1
       975: 1
      1053: 1
      1055: 1
      1062: 1
      1204: 1

1205:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: q^2+3q+1
        39: q^2+2q
        40: q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+2q
        59: q^2+3q+1
        60: 2q^2+3q+1
        61: 2q
        62: q^2+2q
        63: q^2+3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q^2+q
       104: q^2+2q+1
       105: q
       106: q
       107: q^2+q+1
       108: q
       110: q+1
       112: 1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: 1
       174: q+1
       178: q+1
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       193: q^2+q+1
       194: q
       196: q+1
       198: 1
       199: q+1
       201: q^2+q+1
       202: q
       204: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 2q+1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q^2+q+1
       320: q
       322: q+1
       324: 1
       326: q+1
       333: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 2
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 2
       464: 2
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       492: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       530: 1
       534: 1
       542: 1
       546: 1
       548: 1
       551: 1
       560: 1
       564: 2
       566: 1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       589: 1
       592: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: 1
       619: 1
       622: 1
       626: 1
       630: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       675: 1
       677: 1
       681: 1
       683: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       699: 1
       701: 1
       715: 1
       726: 1
       744: 1
       754: 1
       763: 1
       801: 1
       804: 1
       812: 1
       825: 1
       828: 1
       836: 1
       845: 1
       848: 1
       852: 1
       856: 1
       877: 1
       879: 1
       926: 1
       951: 1
       976: 1
      1052: 1
      1055: 1
      1063: 1
      1205: 1

1206:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+3q+1
        38: q^2+2q
        39: q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: 2q^2+3q+1
        59: 2q
        60: q^2+3q+1
        61: q^2+2q
        62: q^2+3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q+1
        73: q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q
       105: q^2+q
       106: q
       107: q+1
       109: q^2+q+1
       110: q
       111: 1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: 1
       173: q+1
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       193: q+1
       195: q^2+q+1
       196: q
       197: 1
       199: q+1
       201: q+1
       203: q^2+q+1
       204: q
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q+1
       321: q^2+q+1
       322: q
       323: 1
       325: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 2
       445: 2
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 1
       462: 1
       463: 2
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       529: 1
       533: 1
       541: 1
       545: 2
       549: 1
       557: 1
       561: 1
       563: 1
       565: 1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       593: 1
       595: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: 1
       619: 1
       621: 1
       625: 1
       629: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       693: 1
       696: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       805: 1
       807: 1
       811: 1
       829: 1
       831: 1
       835: 1
       845: 1
       847: 1
       851: 1
       855: 1
       878: 1
       879: 1
       928: 1
       952: 1
       974: 1
      1056: 1
      1058: 1
      1062: 1
      1206: 1

1207:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: q^2+3q+1
        39: q^2+2q
        40: q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: 2q
        59: 2q^2+3q+1
        60: q^2+3q+1
        61: q^2+2q
        62: q^2+2q
        63: q^2+3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q+1
        73: q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: q^2+2q+1
       105: q
       106: q^2+q
       107: q+1
       109: q
       110: q^2+q+1
       112: 1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: 1
       174: q+1
       178: q+1
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       193: q+1
       195: q
       196: q^2+q+1
       198: 1
       199: q+1
       201: q+1
       203: q
       204: q^2+q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q+1
       321: q
       322: q^2+q+1
       324: 1
       326: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 2
       446: 2
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       461: 1
       462: 1
       464: 2
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       530: 1
       534: 1
       542: 1
       546: 2
       551: 1
       560: 1
       562: 1
       564: 1
       566: 1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       593: 1
       596: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: 1
       619: 1
       622: 1
       626: 1
       630: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       694: 1
       699: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       805: 1
       808: 1
       812: 1
       829: 1
       832: 1
       836: 1
       845: 1
       848: 1
       852: 1
       856: 1
       878: 1
       879: 1
       929: 1
       953: 1
       976: 1
      1056: 1
      1059: 1
      1063: 1
      1207: 1

1208:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+3q+1
        38: q^2+2q
        39: q^2+3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: 2q
        59: 2q^2+3q+1
        60: q^2+2q
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q+1
        73: q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: q^2+q
       105: q
       106: q^2+2q+1
       108: q+1
       109: q
       110: q^2+q+1
       111: 1
       113: q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       172: 1
       176: q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       194: q+1
       195: q
       196: q^2+q+1
       197: 1
       200: q+1
       202: q+1
       203: q
       204: q^2+q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: q+1
       321: q
       322: q^2+q+1
       323: 1
       325: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 2
       445: 2
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 2
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       532: 1
       536: 1
       543: 1
       547: 2
       552: 1
       559: 1
       561: 1
       563: 1
       568: 1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       594: 1
       596: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: 1
       620: 1
       622: 1
       625: 1
       629: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       697: 1
       698: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       806: 1
       808: 1
       811: 1
       830: 1
       832: 1
       835: 1
       846: 1
       848: 1
       851: 1
       855: 1
       878: 1
       879: 1
       930: 1
       955: 1
       975: 1
      1057: 1
      1059: 1
      1062: 1
      1208: 1

1209:    0: 2q^2+5q+1
         1: 2q^2+5q+1
         2: 2q^2+3q+1
         3: 2q^2+5q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+5q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: q^3+3q^2+3q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 2q^2+5q+1
        17: 2q^2+5q+1
        18: q^3+2q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 2q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+3q+1
        25: 2q^2+5q+1
        26: 2q^2+5q+1
        27: 2q^2+3q+1
        28: 2q^2+5q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+5q+1
        32: 3q+1
        33: 2q^2+5q+1
        34: 2q^2+5q+1
        35: 3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: q^2+3q+1
        39: q^2+2q
        40: q^2+3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: 2q^2+3q+1
        59: 2q
        60: q^2+2q
        61: q^2+3q+1
        62: q^2+2q
        63: q^2+3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: q+1
        73: q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q^2+q
       104: q
       105: q^2+2q+1
       106: q
       108: q+1
       109: q^2+q+1
       110: q
       112: 1
       114: q+1
       116: q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       171: 1
       175: q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       194: q+1
       195: q^2+q+1
       196: q
       198: 1
       200: q+1
       202: q+1
       203: q^2+q+1
       204: q
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: q+1
       321: q^2+q+1
       322: q
       324: 1
       326: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       352: 1
       353: 1
       354: q+1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 2
       446: 2
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 1
       462: 1
       464: 2
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       531: 1
       535: 1
       544: 1
       548: 2
       550: 1
       558: 1
       562: 1
       564: 1
       567: 1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       594: 1
       595: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: 1
       620: 1
       621: 1
       626: 1
       630: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       676: 1
       677: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       700: 1
       701: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       806: 1
       807: 1
       812: 1
       830: 1
       831: 1
       836: 1
       846: 1
       847: 1
       852: 1
       856: 1
       878: 1
       879: 1
       931: 1
       954: 1
       977: 1
      1057: 1
      1058: 1
      1063: 1
      1209: 1

1210:    0: q^3+2q^2+3q+2
         1: q^3+2q^2+3q+2
         2: q^3+2q^2+3q+2
         3: q^3+2q^2+3q+2
         4: 2q^2+2q+2
         5: q^3+2q^2+3q+2
         6: 2q^2+2q+2
         7: 2q^2+2q+2
         8: q^3+2q^2+3q+2
         9: 2q^2+2q+2
        10: q^3+2q^2+3q+2
        11: q^3+2q^2+3q+2
        12: 2q^2+2q+2
        13: q^3+2q^2+3q+2
        14: 2q^2+2q+2
        15: q^3+2q^2+3q+2
        16: q^3+2q^2+3q+2
        17: q^3+2q^2+3q+2
        18: 2q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q^3+2q^2+3q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: q^3+2q^2+3q+2
        44: 2q^2+2q+2
        45: q^3+2q^2+3q+2
        46: q^3+2q^2+3q+2
        47: q^3+2q^2+3q+2
        48: 2q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: q^3+2q^2+3q+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: q^2+2q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: q^3+2q^2+3q+2
        89: q^3+2q^2+3q+2
        90: 2q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: 1
       101: 1
       102: 1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: 2q+2
       125: q^3+2q^2+3q+2
       126: q^2+2q+2
       127: q+2
       129: q+2
       131: q+2
       133: q^2+2q+2
       134: q^2+2q+2
       135: 2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       141: q+2
       142: 2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 1
       167: 1
       168: 1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: q+2
       179: q+2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: 1
       211: 1
       213: q+2
       215: q+2
       217: q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^2+2q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       230: 2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: q+1
       278: q+1
       279: q+2
       281: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       287: q+2
       289: 2
       291: 2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: 1
       327: q+2
       329: q+2
       331: q+2
       333: q^2+2q+2
       334: 2
       335: 2
       337: 1
       338: 1
       340: 1
       344: q+2
       345: q+2
       346: q+2
       349: 2
       350: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: q+2
       411: q+2
       413: q+2
       415: 2
       417: 2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       427: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: 1
       481: 2
       482: 2
       484: 1
       485: 1
       487: 1
       492: q+2
       494: 2
       497: q+2
       498: 2
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       583: q+2
       585: 2
       587: 2
       589: 1
       590: 1
       595: 1
       596: 1
       601: 1
       607: 1
       608: 1
       619: 1
       620: 1
       635: 1
       637: 1
       639: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       705: 1
       708: 1
       709: 1
       712: 1
       775: 1
       777: 2
       789: 1
       807: 1
       808: 1
       825: 1
       826: 1
       841: 1
       859: 1
       861: 1
       865: 1
       881: 1
       882: 1
       896: 1
       899: 1
       992: 1
      1066: 1
      1068: 1
      1072: 1
      1210: 1

1211:    0: q^3+2q^2+3q+2
         1: q^3+2q^2+3q+2
         2: q^3+2q^2+3q+2
         3: q^3+2q^2+3q+2
         4: 2q^2+2q+2
         5: q^3+2q^2+3q+2
         6: 2q^2+2q+2
         7: 2q^2+2q+2
         8: q^3+2q^2+3q+2
         9: 2q^2+2q+2
        10: q^3+2q^2+3q+2
        11: q^3+2q^2+3q+2
        12: 2q^2+2q+2
        13: q^3+2q^2+3q+2
        14: 2q^2+2q+2
        15: q^3+2q^2+3q+2
        16: q^3+2q^2+3q+2
        17: q^3+2q^2+3q+2
        18: 2q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q^3+2q^2+3q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: q^3+2q^2+3q+2
        44: 2q^2+2q+2
        45: q^3+2q^2+3q+2
        46: q^3+2q^2+3q+2
        47: q^3+2q^2+3q+2
        48: 2q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: q^3+2q^2+3q+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: q^2+2q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: q^3+2q^2+3q+2
        89: q^3+2q^2+3q+2
        90: 2q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: 1
       101: 1
       102: 1
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: 2q+2
       125: q^3+2q^2+3q+2
       126: q^2+2q+2
       128: q+2
       130: q+2
       132: q+2
       133: q^2+2q+2
       134: q^2+2q+2
       135: 2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       141: q+2
       142: 2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: q+2
       180: q+2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: 1
       212: 1
       214: q+2
       216: q+2
       218: q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^2+2q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       230: 2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: q+1
       277: q+1
       280: q+2
       282: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+2
       290: 2
       292: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: 1
       328: q+2
       330: q+2
       332: q+2
       333: q^2+2q+2
       334: 2
       335: 2
       337: 1
       339: 1
       341: 1
       344: q+2
       345: q+2
       346: q+2
       349: 2
       350: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: q+2
       412: q+2
       414: q+2
       416: 2
       418: 2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       428: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: 1
       481: 2
       482: 2
       484: 1
       486: 1
       488: 1
       492: q+2
       494: 2
       497: q+2
       498: 2
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       584: q+2
       586: 2
       588: 2
       589: 1
       590: 1
       595: 1
       596: 1
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       636: 1
       638: 1
       640: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       706: 1
       707: 1
       710: 1
       711: 1
       776: 1
       778: 2
       790: 1
       807: 1
       808: 1
       825: 1
       826: 1
       842: 1
       860: 1
       862: 1
       865: 1
       881: 1
       882: 1
       897: 1
       898: 1
       993: 1
      1067: 1
      1069: 1
      1072: 1
      1211: 1

1212:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: 2q+2
         4: q^2+2q+2
         5: 2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: 2q+2
         9: q^3+2q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: 2q+2
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q^2+2q+1
        49: q+2
        50: q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: q+2
        69: q+1
        70: q^2+2q+2
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: q+2
        89: q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: q+2
       134: q+1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+2
       158: q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: q+1
       211: q+1
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 1
       239: 1
       241: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: q+1
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 1
       362: 1
       364: q+1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: 1
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 1
       439: 1
       440: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: q+1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: q+1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       525: 1
       528: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 1
       635: 1
       637: 1
       639: 1
       658: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: q+1
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       690: 1
       692: 1
       777: 1
       779: 1
       781: 1
       783: 1
       789: 1
       841: 1
       859: 1
       863: 1
       867: 1
       868: 1
       881: 1
       883: 1
       996: 1
      1002: 1
      1066: 1
      1070: 1
      1073: 1
      1212: 1

1213:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: 2q+2
         4: q^2+2q+2
         5: 2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: 2q+2
         9: q^3+2q^2+2q+1
        10: q^2+2q+2
        11: 2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: 2q+2
        16: q+2
        17: q+2
        18: q^2+2q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: 2q+2
        46: q+2
        47: q+2
        48: q^2+2q+1
        49: q+2
        50: q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: q+2
        69: q+1
        70: q^2+2q+2
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: q+2
        89: q+2
        90: q^2+2q+1
        91: q+2
        92: q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: q+2
       134: q+1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: q+1
       212: q+1
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: q+2
       221: q+1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 1
       240: 1
       242: q+1
       243: 1
       246: q+1
       247: 1
       248: 1
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: q+1
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 1
       363: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: 1
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 1
       439: 1
       440: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: q+1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: q+1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       526: 1
       527: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 1
       636: 1
       638: 1
       640: 1
       659: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: q+1
       672: 1
       673: 1
       676: 1
       681: 1
       686: 1
       690: 1
       692: 1
       778: 1
       780: 1
       782: 1
       784: 1
       790: 1
       842: 1
       860: 1
       864: 1
       867: 1
       868: 1
       881: 1
       883: 1
       997: 1
      1003: 1
      1067: 1
      1071: 1
      1073: 1
      1213: 1

1214:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: q^3+3q^2+4q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^3+4q^2+4q+2
         9: q^3+3q^2+4q+2
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 2q^2+4q+2
        14: 2q^2+4q+2
        15: 3q^2+4q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: q^3+3q^2+4q+2
        22: 4q+2
        23: 4q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: q^2+3q+2
        28: 4q^2+5q+2
        29: 4q^2+5q+2
        30: 2q^2+4q+2
        31: 4q+2
        32: 3q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: 4q+2
        37: 4q+2
        39: 4q+2
        41: q^2+3q+2
        43: 2q^2+4q+2
        44: 2q^2+4q+2
        45: 3q^2+4q+2
        46: 2q^2+4q+2
        47: 3q^2+4q+2
        48: 2q^2+4q+2
        49: 4q^2+5q+2
        50: 4q^2+5q+2
        51: q^3+3q^2+4q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 4q+2
        64: 3q+2
        66: 4q+2
        68: q^2+3q+2
        69: 2q^2+4q+2
        70: 2q^2+4q+2
        71: 4q^2+5q+2
        72: 4q+2
        73: 4q+2
        74: 4q+2
        76: 4q+2
        78: q^2+3q+2
        80: 3q+2
        81: 3q+2
        82: 4q+2
        83: 3q+2
        84: 3q+2
        85: 3q+2
        86: 4q+2
        87: 3q+2
        88: 2q^2+4q+2
        89: 3q^2+4q+2
        90: 2q^2+4q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 4q+2
       113: 4q+2
       115: 3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 3q+2
       123: 3q+2
       125: q^2+3q+2
       126: 2q^2+4q+2
       127: 4q+2
       129: 4q+2
       131: q^2+3q+2
       133: q^2+3q+2
       134: 2q^2+4q+2
       135: 3q+2
       136: 3q+2
       137: 3q+2
       138: 3q+2
       139: 4q+2
       141: 3q+2
       142: 4q+2
       143: 3q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 4q+2
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q^2+4q+2
       158: 3q^2+4q+2
       159: 2q^2+4q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+1
       167: q+1
       168: q+1
       169: 2q+1
       172: 2q+1
       173: q+1
       176: q+1
       177: 3q+2
       179: 4q+2
       181: 4q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 3q+2
       189: 3q+2
       191: q+1
       192: q+1
       195: 2q+1
       196: 2q+1
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       207: 3q+2
       209: q+1
       211: q+1
       213: q+2
       215: q+2
       217: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: 2q^2+4q+2
       222: 3q+2
       223: 3q+2
       224: 3q+2
       225: 3q+2
       226: 3q+2
       227: 2
       228: q+2
       230: q+2
       231: 3q+2
       232: 2
       233: q+2
       234: q+2
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 2q+1
       262: 2q+1
       263: q+1
       266: q+1
       275: q+1
       278: q+1
       279: 2
       281: q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 3q+2
       289: q+2
       291: 3q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 3q+2
       303: 1
       304: 1
       307: 1
       308: 1
       315: q+1
       317: q+1
       325: q+1
       327: q+2
       329: q+2
       331: q+2
       333: q^2+3q+2
       334: 3q+2
       335: 3q+2
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 2
       345: 2
       346: q+2
       349: q+2
       350: q+2
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       360: 1
       362: 1
       364: 1
       366: q+1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: q+1
       380: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       409: 2
       411: q+2
       413: 2
       415: q+2
       417: q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 3q+2
       425: q+1
       427: q+1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       481: 2
       482: 2
       483: q+1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 2
       494: q+2
       497: 2
       498: q+2
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       524: 1
       525: 1
       528: 1
       529: q+1
       532: q+1
       583: 2
       585: 2
       587: q+2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       607: 1
       608: 1
       619: 1
       620: 1
       635: 1
       637: 1
       639: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       705: 1
       708: 1
       709: 1
       712: 1
       775: 1
       777: 2
       779: 1
       781: 1
       783: 1
       789: 1
       807: 1
       808: 1
       825: 1
       826: 1
       841: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       896: 1
       899: 1
       992: 1
       994: 1
       996: 1
      1002: 1
      1074: 1
      1214: 1

1215:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: q^3+3q^2+4q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: q^3+3q^2+4q+2
         8: 2q^3+4q^2+4q+2
         9: q^3+3q^2+4q+2
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 2q^2+4q+2
        14: 2q^2+4q+2
        15: 3q^2+4q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: q^3+3q^2+4q+2
        22: 4q+2
        23: 4q+2
        24: q^2+3q+2
        25: 4q+2
        26: 4q+2
        27: q^2+3q+2
        28: 4q^2+5q+2
        29: 4q^2+5q+2
        30: 2q^2+4q+2
        31: 4q+2
        32: 3q+2
        33: 4q+2
        34: 4q+2
        35: 3q+2
        36: 4q+2
        38: 4q+2
        40: 4q+2
        42: q^2+3q+2
        43: 2q^2+4q+2
        44: 2q^2+4q+2
        45: 3q^2+4q+2
        46: 2q^2+4q+2
        47: 3q^2+4q+2
        48: 2q^2+4q+2
        49: 4q^2+5q+2
        50: 4q^2+5q+2
        51: q^3+3q^2+4q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        63: 4q+2
        65: 3q+2
        67: 4q+2
        68: q^2+3q+2
        69: 2q^2+4q+2
        70: 2q^2+4q+2
        71: 4q^2+5q+2
        72: 4q+2
        73: 4q+2
        75: 4q+2
        77: 4q+2
        79: q^2+3q+2
        80: 3q+2
        81: 3q+2
        82: 4q+2
        83: 3q+2
        84: 3q+2
        85: 3q+2
        86: 4q+2
        87: 3q+2
        88: 2q^2+4q+2
        89: 3q^2+4q+2
        90: 2q^2+4q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: q+1
       101: q+1
       102: q+1
       104: 2q+1
       105: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       112: 4q+2
       114: 4q+2
       116: 3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 3q+2
       124: 3q+2
       125: q^2+3q+2
       126: 2q^2+4q+2
       128: 4q+2
       130: 4q+2
       132: q^2+3q+2
       133: q^2+3q+2
       134: 2q^2+4q+2
       135: 3q+2
       136: 3q+2
       137: 3q+2
       138: 3q+2
       139: 4q+2
       141: 3q+2
       142: 4q+2
       143: 3q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 4q+2
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q^2+4q+2
       158: 3q^2+4q+2
       159: 2q^2+4q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+1
       167: q+1
       168: q+1
       170: 2q+1
       171: 2q+1
       174: q+1
       175: q+1
       178: 3q+2
       180: 4q+2
       182: 4q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 3q+2
       190: 3q+2
       191: q+1
       192: q+1
       195: 2q+1
       196: 2q+1
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       208: 3q+2
       210: q+1
       212: q+1
       214: q+2
       216: q+2
       218: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: 2q^2+4q+2
       222: 3q+2
       223: 3q+2
       224: 3q+2
       225: 3q+2
       226: 3q+2
       227: 2
       228: q+2
       230: q+2
       231: 3q+2
       232: 2
       233: q+2
       234: q+2
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       260: 2q+1
       261: 2q+1
       264: q+1
       265: q+1
       276: q+1
       277: q+1
       280: 2
       282: q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: 3q+2
       290: q+2
       292: 3q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 3q+2
       303: 1
       304: 1
       307: 1
       308: 1
       316: q+1
       318: q+1
       326: q+1
       328: q+2
       330: q+2
       332: q+2
       333: q^2+3q+2
       334: 3q+2
       335: 3q+2
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 2
       345: 2
       346: q+2
       349: q+2
       350: q+2
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       361: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: q+1
       379: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       410: 2
       412: q+2
       414: 2
       416: q+2
       418: q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       424: 3q+2
       426: q+1
       428: q+1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       481: 2
       482: 2
       483: q+1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 2
       494: q+2
       497: 2
       498: q+2
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       530: q+1
       531: q+1
       584: 2
       586: 2
       588: q+2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       636: 1
       638: 1
       640: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       706: 1
       707: 1
       710: 1
       711: 1
       776: 1
       778: 2
       780: 1
       782: 1
       784: 1
       790: 1
       807: 1
       808: 1
       825: 1
       826: 1
       842: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       897: 1
       898: 1
       993: 1
       995: 1
       997: 1
      1003: 1
      1074: 1
      1215: 1

1216:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+4q^2+5q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+4q^2+5q+2
         8: q^4+4q^3+6q^2+5q+2
         9: q^3+4q^2+5q+2
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: 3q^2+5q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+4q^2+5q+2
        22: q^2+6q+2
        23: q^2+6q+2
        24: 2q^2+4q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: q^3+4q^2+5q+2
        28: q^3+7q^2+8q+2
        29: q^3+7q^2+8q+2
        30: q^2+5q+2
        31: q^2+6q+2
        32: 4q+2
        33: q^2+6q+2
        34: 4q^2+8q+2
        35: q^2+5q+2
        36: 4q^2+8q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+5q+2
        45: 3q^2+5q+2
        46: q^2+5q+2
        47: 3q^2+5q+2
        48: q^2+5q+2
        49: q^3+7q^2+8q+2
        50: q^3+7q^2+8q+2
        51: q^3+4q^2+5q+2
        52: q^2+6q+2
        53: q^2+6q+2
        54: 2q^2+4q+2
        55: 4q^2+8q+2
        56: 4q^2+8q+2
        57: q^3+4q^2+5q+2
        58: q^2+4q+2
        59: 2q
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^3+7q^2+8q+2
        72: 4q^2+8q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 4q+2
        81: 4q+2
        82: q^2+6q+2
        83: 4q+2
        84: q^2+5q+2
        85: q^2+5q+2
        86: 4q^2+8q+2
        87: q^2+5q+2
        88: q^2+5q+2
        89: 3q^2+5q+2
        90: q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: q^2+6q+2
        95: q^2+6q+2
        96: 2q^2+4q+2
        97: 4q^2+8q+2
        98: 4q^2+8q+2
        99: q^3+4q^2+5q+2
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: 2q^2+4q+1
       108: 2q^2+4q+1
       109: q^2+4q+2
       110: 2q
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+5q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q+2
       134: q^2+5q+2
       135: q^2+5q+2
       136: 4q+2
       137: 4q+2
       138: 4q+2
       139: q^2+6q+2
       141: 4q+2
       142: q^2+6q+2
       143: q^2+5q+2
       144: q^2+5q+2
       145: 4q^2+8q+2
       146: q^2+5q+2
       147: 4q^2+8q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q^2+5q+2
       158: 3q^2+5q+2
       159: q^2+5q+2
       160: q+1
       161: q+1
       162: q+1
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: 2q+2
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: q+1
       175: q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: q+1
       184: q+1
       185: 2q+2
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: 2q+2
       195: q^2+4q+2
       196: 2q
       199: q+1
       200: q+1
       201: 2q^2+4q+1
       202: 2q^2+4q+1
       203: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: 2q+2
       220: 2q+2
       221: q^2+5q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: 4q+2
       225: 4q+2
       226: 4q+2
       227: 1
       228: q+1
       230: q+1
       231: q^2+5q+2
       232: 2
       233: 2q+2
       234: 2q+2
       235: 2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 4q+2
       245: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q+2
       250: q+1
       251: q+1
       252: q+1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       260: q
       261: 2q+1
       262: q
       263: q+1
       265: q+1
       271: q+1
       272: q+1
       275: q+1
       277: q+1
       283: q+1
       284: q+1
       285: 2q+2
       287: 2q+1
       288: 2q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: 2q+2
       297: 2q+1
       298: 2q+1
       303: 1
       307: 1
       308: 1
       309: 2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       321: 2q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: q^2+5q+2
       335: 4q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: 2
       353: 2
       354: 2q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2q+2
       366: 2q+2
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       379: q+1
       385: q+1
       387: q+1
       397: q+1
       398: q+1
       401: 1
       402: 1
       419: q+1
       420: q+1
       421: 2q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       431: 1
       439: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       473: 1
       481: 2
       482: 1
       483: 2q+2
       484: 1
       491: 1
       492: 1
       494: q+1
       497: 2
       498: 2q+2
       499: 2
       500: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       529: q+1
       531: q+1
       549: 1
       550: 1
       557: 1
       558: 1
       561: q+1
       562: q+1
       589: 1
       590: 1
       591: 2
       595: 1
       599: q+1
       600: q+1
       607: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       643: 1
       649: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2
       683: 2
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       713: 1
       714: 1
       741: 1
       742: 1
       787: 1
       807: 1
       817: 1
       825: 1
       826: 1
       827: 2
       835: 1
       836: 1
       839: 1
       847: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       948: 1
       949: 1
       998: 1
      1006: 1
      1032: 1
      1074: 1
      1081: 1
      1216: 1

1217:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+4q^2+5q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+4q^2+5q+2
         8: q^4+4q^3+6q^2+5q+2
         9: q^3+4q^2+5q+2
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: 3q^2+5q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+4q^2+5q+2
        22: q^2+6q+2
        23: q^2+6q+2
        24: 2q^2+4q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: q^3+4q^2+5q+2
        28: q^3+7q^2+8q+2
        29: q^3+7q^2+8q+2
        30: q^2+5q+2
        31: q^2+6q+2
        32: 4q+2
        33: q^2+6q+2
        34: 4q^2+8q+2
        35: q^2+5q+2
        36: 4q^2+8q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+5q+2
        45: 3q^2+5q+2
        46: q^2+5q+2
        47: 3q^2+5q+2
        48: q^2+5q+2
        49: q^3+7q^2+8q+2
        50: q^3+7q^2+8q+2
        51: q^3+4q^2+5q+2
        52: q^2+6q+2
        53: q^2+6q+2
        54: 2q^2+4q+2
        55: 4q^2+8q+2
        56: 4q^2+8q+2
        57: q^3+4q^2+5q+2
        58: 2q
        59: q^2+4q+2
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^3+7q^2+8q+2
        72: 4q^2+8q+2
        73: q^2+6q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 4q+2
        81: 4q+2
        82: q^2+6q+2
        83: 4q+2
        84: q^2+5q+2
        85: q^2+5q+2
        86: 4q^2+8q+2
        87: q^2+5q+2
        88: q^2+5q+2
        89: 3q^2+5q+2
        90: q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: q^2+6q+2
        95: q^2+6q+2
        96: 2q^2+4q+2
        97: 4q^2+8q+2
        98: 4q^2+8q+2
        99: q^3+4q^2+5q+2
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: 2q^2+4q+1
       108: 2q^2+4q+1
       109: 2q
       110: q^2+4q+2
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+5q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q+2
       134: q^2+5q+2
       135: q^2+5q+2
       136: 4q+2
       137: 4q+2
       138: 4q+2
       139: q^2+6q+2
       141: 4q+2
       142: q^2+6q+2
       143: q^2+5q+2
       144: q^2+5q+2
       145: 4q^2+8q+2
       146: q^2+5q+2
       147: 4q^2+8q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q^2+5q+2
       158: 3q^2+5q+2
       159: q^2+5q+2
       160: q+1
       161: q+1
       162: q+1
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: 2q+2
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       174: q+1
       176: q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: q+1
       184: q+1
       186: 2q+2
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       192: 2q+2
       195: 2q
       196: q^2+4q+2
       199: q+1
       200: q+1
       201: 2q^2+4q+1
       202: 2q^2+4q+1
       204: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: 2q+2
       220: 2q+2
       221: q^2+5q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: 4q+2
       225: 4q+2
       226: 4q+2
       227: 1
       228: q+1
       230: q+1
       231: q^2+5q+2
       232: 2
       233: 2q+2
       234: 2q+2
       235: 2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 4q+2
       245: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q+2
       250: q+1
       251: q+1
       252: q+1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 1
       257: q+1
       258: 1
       259: q
       260: 2q+1
       261: q
       262: 2q+1
       264: q+1
       266: q+1
       273: q+1
       274: q+1
       276: q+1
       278: q+1
       283: q+1
       284: q+1
       286: 2q+2
       287: 2q+1
       288: 2q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       296: 2q+2
       297: 2q+1
       298: 2q+1
       304: 1
       307: 1
       308: 1
       310: 2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       322: 2q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: q^2+5q+2
       335: 4q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: 2
       353: 2
       354: 2q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2q+2
       366: 2q+2
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       380: q+1
       386: q+1
       388: q+1
       399: q+1
       400: q+1
       403: 1
       404: 1
       419: q+1
       420: q+1
       422: 2q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       432: 1
       440: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       474: 1
       481: 2
       482: 1
       483: 2q+2
       484: 1
       491: 1
       492: 1
       494: q+1
       497: 2
       498: 2q+2
       499: 2
       500: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       530: q+1
       532: q+1
       551: 1
       552: 1
       559: 1
       560: 1
       563: q+1
       564: q+1
       589: 1
       590: 1
       592: 2
       596: 1
       599: q+1
       600: q+1
       608: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 1
       644: 1
       650: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2
       683: 2
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       715: 1
       716: 1
       743: 1
       744: 1
       788: 1
       808: 1
       818: 1
       825: 1
       826: 1
       828: 2
       835: 1
       836: 1
       840: 1
       848: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       950: 1
       951: 1
       999: 1
      1007: 1
      1033: 1
      1074: 1
      1081: 1
      1217: 1

1218:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+4q^2+5q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+4q^2+5q+2
         8: q^4+4q^3+6q^2+5q+2
         9: q^3+4q^2+5q+2
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: 3q^2+5q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+4q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: q^3+4q^2+5q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: 2q^2+4q+2
        28: q^3+7q^2+8q+2
        29: q^3+7q^2+8q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: q^2+5q+2
        33: 4q^2+8q+2
        34: q^2+6q+2
        35: 4q+2
        36: q^2+6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+5q+2
        45: 3q^2+5q+2
        46: q^2+5q+2
        47: 3q^2+5q+2
        48: q^2+5q+2
        49: q^3+7q^2+8q+2
        50: q^3+7q^2+8q+2
        51: q^3+4q^2+5q+2
        52: 4q^2+8q+2
        53: 4q^2+8q+2
        54: q^3+4q^2+5q+2
        55: q^2+6q+2
        56: q^2+6q+2
        57: 2q^2+4q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: q^2+4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^3+7q^2+8q+2
        72: q^2+6q+2
        73: 4q^2+8q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: q^2+5q+2
        82: 4q^2+8q+2
        83: q^2+5q+2
        84: 4q+2
        85: 4q+2
        86: q^2+6q+2
        87: 4q+2
        88: q^2+5q+2
        89: 3q^2+5q+2
        90: q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: 4q^2+8q+2
        95: 4q^2+8q+2
        96: q^3+4q^2+5q+2
        97: q^2+6q+2
        98: q^2+6q+2
        99: 2q^2+4q+2
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q^2+4q+2
       108: 2q
       109: 2q^2+4q+1
       110: 2q^2+4q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+5q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q+2
       134: q^2+5q+2
       135: 4q+2
       136: q^2+5q+2
       137: q^2+5q+2
       138: q^2+5q+2
       139: 4q^2+8q+2
       140: 2q+2
       141: q^2+5q+2
       142: 4q^2+8q+2
       143: 4q+2
       144: 4q+2
       145: q^2+6q+2
       146: 4q+2
       147: q^2+6q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q^2+5q+2
       158: 3q^2+5q+2
       159: q^2+5q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q+1
       164: q+1
       165: q+1
       166: 4q+2
       167: 4q+2
       168: 2q+2
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: q+1
       174: q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 2q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: 2q^2+4q+1
       196: 2q^2+4q+1
       197: q+1
       198: q+1
       199: 2q+2
       201: q^2+4q+2
       202: 2q
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: 2q+2
       220: 2q+2
       221: q^2+5q+2
       222: 4q+2
       223: 4q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: q^2+5q+2
       227: 2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 4q+2
       232: 1
       233: q+1
       234: q+1
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       260: 2q+1
       261: q
       262: q
       263: q+1
       264: q+1
       267: q+1
       268: q+1
       275: q+1
       276: q+1
       283: 2q+2
       285: q+1
       286: q+1
       287: 2q+1
       288: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 4q+2
       335: q^2+5q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 2
       345: 2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2q+2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       366: 2q+2
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       385: q+1
       386: q+1
       389: q+1
       390: q+1
       393: 1
       394: 1
       419: 2q+2
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2q+2
       445: q+1
       446: q+1
       447: 1
       453: 1
       469: q+1
       470: q+1
       471: 1
       481: 1
       482: 2
       483: 2q+2
       484: 1
       491: 1
       492: 2
       493: 2
       494: 2q+2
       495: 2
       496: 1
       497: 1
       498: q+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       529: q+1
       530: q+1
       533: 1
       534: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       589: 1
       593: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       619: 1
       641: 1
       647: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 2
       677: 2
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       717: 1
       718: 1
       725: 1
       726: 1
       785: 1
       793: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 1
       825: 1
       845: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       928: 1
       929: 1
      1000: 1
      1004: 1
      1016: 1
      1074: 1
      1077: 1
      1218: 1

1219:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+4q^2+5q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+4q^2+5q+2
         8: q^4+4q^3+6q^2+5q+2
         9: q^3+4q^2+5q+2
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: q^2+5q+2
        14: q^2+5q+2
        15: 3q^2+5q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+4q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: q^3+4q^2+5q+2
        25: q^2+6q+2
        26: q^2+6q+2
        27: 2q^2+4q+2
        28: q^3+7q^2+8q+2
        29: q^3+7q^2+8q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: q^2+5q+2
        33: 4q^2+8q+2
        34: q^2+6q+2
        35: 4q+2
        36: q^2+6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+5q+2
        44: q^2+5q+2
        45: 3q^2+5q+2
        46: q^2+5q+2
        47: 3q^2+5q+2
        48: q^2+5q+2
        49: q^3+7q^2+8q+2
        50: q^3+7q^2+8q+2
        51: q^3+4q^2+5q+2
        52: 4q^2+8q+2
        53: 4q^2+8q+2
        54: q^3+4q^2+5q+2
        55: q^2+6q+2
        56: q^2+6q+2
        57: 2q^2+4q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q
        61: q^2+4q+2
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^3+7q^2+8q+2
        72: q^2+6q+2
        73: 4q^2+8q+2
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+5q+2
        81: q^2+5q+2
        82: 4q^2+8q+2
        83: q^2+5q+2
        84: 4q+2
        85: 4q+2
        86: q^2+6q+2
        87: 4q+2
        88: q^2+5q+2
        89: 3q^2+5q+2
        90: q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: 4q^2+8q+2
        95: 4q^2+8q+2
        96: q^3+4q^2+5q+2
        97: q^2+6q+2
        98: q^2+6q+2
        99: 2q^2+4q+2
       100: 4q+2
       101: 4q+2
       102: 2q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       107: 2q
       108: q^2+4q+2
       109: 2q^2+4q+1
       110: 2q^2+4q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q^2+5q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q+2
       134: q^2+5q+2
       135: 4q+2
       136: q^2+5q+2
       137: q^2+5q+2
       138: q^2+5q+2
       139: 4q^2+8q+2
       140: 2q+2
       141: q^2+5q+2
       142: 4q^2+8q+2
       143: 4q+2
       144: 4q+2
       145: q^2+6q+2
       146: 4q+2
       147: q^2+6q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q^2+5q+2
       158: 3q^2+5q+2
       159: q^2+5q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q+1
       164: q+1
       165: q+1
       166: 4q+2
       167: 4q+2
       168: 2q+2
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       175: q+1
       176: q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       184: 2q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: 2q^2+4q+1
       196: 2q^2+4q+1
       197: q+1
       198: q+1
       200: 2q+2
       201: 2q
       202: q^2+4q+2
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: 2q+2
       220: 2q+2
       221: q^2+5q+2
       222: 4q+2
       223: 4q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: q^2+5q+2
       227: 2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 4q+2
       232: 1
       233: q+1
       234: q+1
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       260: q
       261: 2q+1
       262: 2q+1
       265: q+1
       266: q+1
       269: q+1
       270: q+1
       277: q+1
       278: q+1
       284: 2q+2
       285: q+1
       286: q+1
       287: 2q+1
       288: 2q+1
       291: 2q+1
       292: 2q+1
       294: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       300: 2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       320: 2q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 4q+2
       335: q^2+5q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 2
       345: 2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2q+2
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       366: 2q+2
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       380: q+1
       387: q+1
       388: q+1
       391: q+1
       392: q+1
       395: 1
       396: 1
       420: 2q+2
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2q+2
       445: q+1
       446: q+1
       448: 1
       454: 1
       469: q+1
       470: q+1
       472: 1
       481: 1
       482: 2
       483: 2q+2
       484: 1
       491: 1
       492: 2
       493: 2
       494: 2q+2
       495: 2
       496: 1
       497: 1
       498: q+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       531: q+1
       532: q+1
       535: 1
       536: 1
       543: 1
       544: 1
       547: q+1
       548: q+1
       590: 1
       594: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 1
       620: 1
       642: 1
       648: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 2
       677: 2
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       719: 1
       720: 1
       727: 1
       728: 1
       786: 1
       794: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 1
       826: 1
       846: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       930: 1
       931: 1
      1001: 1
      1005: 1
      1017: 1
      1074: 1
      1077: 1
      1219: 1

1220:    0: 7q^3+19q^2+14q+2
         1: 2q^4+12q^3+22q^2+14q+2
         2: 7q^3+19q^2+14q+2
         3: 10q^3+22q^2+14q+2
         4: 7q^3+19q^2+14q+2
         5: q^4+8q^3+19q^2+14q+2
         6: 2q^4+12q^3+22q^2+14q+2
         7: 7q^3+19q^2+14q+2
         8: q^4+8q^3+19q^2+14q+2
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: 4q^3+14q^2+13q+2
        11: 3q^3+14q^2+13q+2
        12: 4q^3+14q^2+13q+2
        13: 7q^3+19q^2+14q+2
        14: 7q^3+19q^2+14q+2
        15: q^4+8q^3+19q^2+14q+2
        16: 9q^2+13q+2
        17: q^3+9q^2+13q+2
        18: 3q^3+6q^2+4q+1
        19: 7q^3+19q^2+14q+2
        20: 2q^4+12q^3+22q^2+14q+2
        21: 7q^3+19q^2+14q+2
        22: 3q^3+14q^2+14q+2
        23: 5q^3+17q^2+14q+2
        24: 3q^3+14q^2+14q+2
        25: 3q^3+14q^2+14q+2
        26: 5q^3+17q^2+14q+2
        27: 3q^3+14q^2+14q+2
        28: 5q^2+12q+2
        29: 4q^3+14q^2+13q+2
        30: 7q^3+19q^2+14q+2
        31: q^3+9q^2+13q+2
        32: 3q^3+14q^2+14q+2
        33: 6q^2+13q+2
        34: q^3+9q^2+13q+2
        35: 3q^3+14q^2+14q+2
        36: 6q^2+13q+2
        37: 7q^2+10q+2
        38: q^3+3q^2+4q
        39: q^3+9q^2+10q+2
        40: 4q^2+4q
        41: 7q^2+10q+2
        42: q^3+3q^2+4q
        43: 4q^3+14q^2+13q+2
        44: 4q^3+14q^2+13q+2
        45: 3q^3+14q^2+13q+2
        46: 9q^2+13q+2
        47: q^3+9q^2+13q+2
        48: 3q^3+6q^2+4q+1
        49: 9q^2+13q+2
        50: q^3+9q^2+13q+2
        51: 3q^3+6q^2+4q+1
        52: 3q^3+14q^2+14q+2
        53: 5q^3+17q^2+14q+2
        54: 3q^3+14q^2+14q+2
        55: 3q^3+14q^2+14q+2
        56: 5q^3+17q^2+14q+2
        57: 3q^3+14q^2+14q+2
        58: q^2+6q+1
        59: q^2+6q+1
        60: q^2+6q+1
        61: q^2+6q+1
        62: 4q^2+9q+2
        63: q^2+4q
        64: 7q^2+10q+2
        65: q^3+3q^2+4q
        66: 3q^2+9q+2
        67: q^2+4q
        68: 5q^2+12q+2
        69: 2q^2+3q+1
        70: 4q^3+14q^2+13q+2
        71: 5q^2+12q+2
        72: 6q^2+13q+2
        73: 6q^2+13q+2
        74: 7q^2+10q+2
        75: q^3+3q^2+4q
        76: q^3+9q^2+10q+2
        77: 4q^2+4q
        78: 7q^2+10q+2
        79: q^3+3q^2+4q
        80: q^3+9q^2+13q+2
        81: 6q^2+13q+2
        82: q^3+9q^2+13q+2
        83: 3q^3+14q^2+14q+2
        84: q^3+9q^2+13q+2
        85: 6q^2+13q+2
        86: q^3+9q^2+13q+2
        87: 3q^3+14q^2+14q+2
        88: q^2+8q+2
        89: q^2+8q+2
        90: q^3+3q^2+3q+1
        91: 9q^2+13q+2
        92: q^3+9q^2+13q+2
        93: 3q^3+6q^2+4q+1
        94: 4q^2+11q+2
        95: 4q^2+11q+2
        96: q^3+4q^2+4q+1
        97: 4q^2+11q+2
        98: 4q^2+11q+2
        99: q^3+4q^2+4q+1
       100: 7q^2+13q+2
       101: q^3+12q^2+13q+2
       102: 7q^2+13q+2
       103: 4q+1
       104: 2q
       105: 2q
       106: 4q+1
       107: q^2+6q+1
       108: q^2+6q+1
       109: q^2+6q+1
       110: q^2+6q+1
       111: 3q^2+9q+2
       112: q^2+4q
       113: 4q^2+9q+2
       114: q^2+4q
       115: 7q^2+10q+2
       116: q^3+3q^2+4q
       117: q^2+6q+1
       118: q^2+6q+1
       119: q^2+6q+1
       120: q^2+6q+1
       121: 4q^2+9q+2
       122: q^2+4q
       123: 3q^2+9q+2
       124: q^2+4q
       125: q^2+8q+2
       126: 2q+1
       127: 4q+2
       129: 4q+2
       131: q^2+2q+1
       133: 5q^2+12q+2
       134: 2q^2+3q+1
       135: 6q^2+13q+2
       136: 6q^2+13q+2
       137: 8q+2
       138: q^2+3q+1
       139: 2q^2+10q+2
       140: q^2+7q+2
       141: q^3+9q^2+13q+2
       142: 4q^2+11q+2
       143: 8q+2
       144: q^2+3q+1
       145: 2q^2+10q+2
       146: q^3+9q^2+13q+2
       147: 4q^2+11q+2
       148: q^2+7q+2
       149: 4q^2+12q+2
       150: 7q^2+13q+2
       151: 5q^2+9q+2
       152: 2q^2+4q
       153: q^3+8q^2+9q+2
       154: 4q^2+4q
       155: 5q^2+9q+2
       156: 2q^2+4q
       157: q^2+8q+2
       158: q^2+8q+2
       159: q^3+3q^2+3q+1
       160: 4q^2+11q+2
       161: 4q^2+11q+2
       162: q^3+4q^2+4q+1
       163: 4q^2+11q+2
       164: 4q^2+11q+2
       165: q^3+4q^2+4q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: 4q+1
       170: 2q
       171: 2q
       172: 4q+1
       173: 4q+1
       174: 2q
       175: 2q
       176: 4q+1
       177: q+1
       179: 4q+2
       181: 4q+2
       183: q^2+6q+1
       184: q^2+6q+1
       185: q^2+6q+1
       186: q^2+6q+1
       187: 3q^2+9q+2
       188: q^2+4q
       189: 4q^2+9q+2
       190: q^2+4q
       191: 4q+1
       192: 4q+1
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: q^2+5q+2
       198: 2q
       199: 4q+1
       200: 4q+1
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: q^2+5q+2
       206: 2q
       207: 6q+2
       208: 2q
       209: 3q^2+8q+2
       210: q^2+4q
       211: 5q^2+9q+2
       212: 2q^2+4q
       213: 4q+2
       215: 4q+2
       217: q^2+2q+1
       219: 2q+1
       220: q^2+8q+2
       221: 2q+1
       222: 8q+2
       223: q^2+3q+1
       224: 8q+2
       225: q^2+3q+1
       226: 2q+1
       227: 2q^2+10q+2
       228: q^2+3q+1
       229: q^2+7q+2
       230: 4q^2+11q+2
       231: 2q+1
       232: 2q^2+10q+2
       233: q^2+3q+1
       234: 4q^2+11q+2
       235: q^2+7q+2
       236: 2q+1
       237: q+2
       239: q+2
       241: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: 4q^2+12q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       259: 2q+1
       262: 2q+1
       263: 4q+1
       264: 2q
       265: 2q
       266: 4q+1
       267: 2q+1
       268: q
       269: 2q+1
       270: q
       271: 2q+1
       272: q
       273: 2q+1
       274: q
       275: 3q+1
       276: q
       277: q
       278: 3q+1
       279: 4q+2
       281: q+1
       287: q+1
       289: 4q+2
       291: q+1
       293: 4q+1
       294: 4q+1
       295: 4q+1
       296: 4q+1
       297: 6q+2
       298: 2q
       299: 3q+1
       300: 3q+1
       301: 2
       303: q^2+5q+1
       304: q^2+5q+1
       305: q^2+5q+2
       306: 2q
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       311: 2
       313: q^2+5q+2
       314: 2q
       315: 1
       317: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: 3q^2+8q+2
       326: q^2+4q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 5q+2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: q+1
       349: 4q+2
       350: q^2+3q+1
       351: 3q+2
       352: 2q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q^2+3q+1
       357: 2q+2
       358: q+1
       359: 3q+2
       360: q+2
       362: q+2
       364: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: q+2
       375: q+2
       376: q+1
       381: 2q+1
       384: 2q+1
       385: 3q+1
       386: q
       387: q
       388: 3q+1
       389: 1
       391: 1
       393: 2q+1
       394: q
       395: q
       396: 2q+1
       397: 1
       399: 1
       401: 2q+1
       402: q
       403: q
       404: 2q+1
       405: 1
       406: 1
       413: q+1
       417: q+1
       423: q+1
       425: 1
       427: q+2
       433: 1
       435: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 2q+2
       443: q+1
       444: q+1
       445: 2
       451: 1
       453: 2q+1
       454: 2q+1
       455: 2
       457: q+1
       458: q+1
       459: 2q+2
       461: q+1
       462: q+1
       463: 2
       465: q+2
       467: 1
       469: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: 4
       479: q+2
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 5q+2
       485: q+2
       487: q+2
       489: q+1
       491: 2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+2
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+2
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 1
       547: 1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 2
       570: 2
       573: 1
       575: 1
       577: 2
       579: 2
       585: q+1
       597: 1
       599: 1
       601: q+2
       605: 1
       609: 1
       613: 1
       615: q+1
       616: q+1
       617: 2
       623: 1
       625: 1
       629: 1
       631: q+1
       632: q+1
       633: 2
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 4
       653: 2
       655: q+2
       665: q+1
       672: q+2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       693: 1
       695: 1
       697: 1
       702: 1
       733: 1
       735: 1
       749: 1
       751: 1
       757: 2
       758: 2
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       771: 2
       781: 1
       791: 1
       797: 1
       809: 1
       811: 1
       815: 1
       816: 1
       821: 1
       833: 1
       835: 1
       839: 1
       840: 1
       849: 1
       851: 1
       857: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       889: 1
       893: 1
       988: 1
       991: 1
      1008: 1
      1010: 1
      1022: 1
      1038: 1
      1048: 1
      1078: 1
      1082: 1
      1220: 1

1221:    0: 7q^3+19q^2+14q+2
         1: 2q^4+12q^3+22q^2+14q+2
         2: 7q^3+19q^2+14q+2
         3: 10q^3+22q^2+14q+2
         4: 7q^3+19q^2+14q+2
         5: q^4+8q^3+19q^2+14q+2
         6: 2q^4+12q^3+22q^2+14q+2
         7: 7q^3+19q^2+14q+2
         8: q^4+8q^3+19q^2+14q+2
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: 4q^3+14q^2+13q+2
        11: 3q^3+14q^2+13q+2
        12: 4q^3+14q^2+13q+2
        13: 7q^3+19q^2+14q+2
        14: 7q^3+19q^2+14q+2
        15: q^4+8q^3+19q^2+14q+2
        16: 9q^2+13q+2
        17: q^3+9q^2+13q+2
        18: 3q^3+6q^2+4q+1
        19: 7q^3+19q^2+14q+2
        20: 2q^4+12q^3+22q^2+14q+2
        21: 7q^3+19q^2+14q+2
        22: 3q^3+14q^2+14q+2
        23: 5q^3+17q^2+14q+2
        24: 3q^3+14q^2+14q+2
        25: 3q^3+14q^2+14q+2
        26: 5q^3+17q^2+14q+2
        27: 3q^3+14q^2+14q+2
        28: 5q^2+12q+2
        29: 4q^3+14q^2+13q+2
        30: 7q^3+19q^2+14q+2
        31: q^3+9q^2+13q+2
        32: 3q^3+14q^2+14q+2
        33: 6q^2+13q+2
        34: q^3+9q^2+13q+2
        35: 3q^3+14q^2+14q+2
        36: 6q^2+13q+2
        37: q^3+3q^2+4q
        38: 7q^2+10q+2
        39: 4q^2+4q
        40: q^3+9q^2+10q+2
        41: q^3+3q^2+4q
        42: 7q^2+10q+2
        43: 4q^3+14q^2+13q+2
        44: 4q^3+14q^2+13q+2
        45: 3q^3+14q^2+13q+2
        46: 9q^2+13q+2
        47: q^3+9q^2+13q+2
        48: 3q^3+6q^2+4q+1
        49: 9q^2+13q+2
        50: q^3+9q^2+13q+2
        51: 3q^3+6q^2+4q+1
        52: 3q^3+14q^2+14q+2
        53: 5q^3+17q^2+14q+2
        54: 3q^3+14q^2+14q+2
        55: 3q^3+14q^2+14q+2
        56: 5q^3+17q^2+14q+2
        57: 3q^3+14q^2+14q+2
        58: q^2+6q+1
        59: q^2+6q+1
        60: q^2+6q+1
        61: q^2+6q+1
        62: q^2+4q
        63: 4q^2+9q+2
        64: q^3+3q^2+4q
        65: 7q^2+10q+2
        66: q^2+4q
        67: 3q^2+9q+2
        68: 5q^2+12q+2
        69: 2q^2+3q+1
        70: 4q^3+14q^2+13q+2
        71: 5q^2+12q+2
        72: 6q^2+13q+2
        73: 6q^2+13q+2
        74: q^3+3q^2+4q
        75: 7q^2+10q+2
        76: 4q^2+4q
        77: q^3+9q^2+10q+2
        78: q^3+3q^2+4q
        79: 7q^2+10q+2
        80: q^3+9q^2+13q+2
        81: 6q^2+13q+2
        82: q^3+9q^2+13q+2
        83: 3q^3+14q^2+14q+2
        84: q^3+9q^2+13q+2
        85: 6q^2+13q+2
        86: q^3+9q^2+13q+2
        87: 3q^3+14q^2+14q+2
        88: q^2+8q+2
        89: q^2+8q+2
        90: q^3+3q^2+3q+1
        91: 9q^2+13q+2
        92: q^3+9q^2+13q+2
        93: 3q^3+6q^2+4q+1
        94: 4q^2+11q+2
        95: 4q^2+11q+2
        96: q^3+4q^2+4q+1
        97: 4q^2+11q+2
        98: 4q^2+11q+2
        99: q^3+4q^2+4q+1
       100: 7q^2+13q+2
       101: q^3+12q^2+13q+2
       102: 7q^2+13q+2
       103: 2q
       104: 4q+1
       105: 4q+1
       106: 2q
       107: q^2+6q+1
       108: q^2+6q+1
       109: q^2+6q+1
       110: q^2+6q+1
       111: q^2+4q
       112: 3q^2+9q+2
       113: q^2+4q
       114: 4q^2+9q+2
       115: q^3+3q^2+4q
       116: 7q^2+10q+2
       117: q^2+6q+1
       118: q^2+6q+1
       119: q^2+6q+1
       120: q^2+6q+1
       121: q^2+4q
       122: 4q^2+9q+2
       123: q^2+4q
       124: 3q^2+9q+2
       125: q^2+8q+2
       126: 2q+1
       128: 4q+2
       130: 4q+2
       132: q^2+2q+1
       133: 5q^2+12q+2
       134: 2q^2+3q+1
       135: 6q^2+13q+2
       136: 6q^2+13q+2
       137: 8q+2
       138: q^2+3q+1
       139: 2q^2+10q+2
       140: q^2+7q+2
       141: q^3+9q^2+13q+2
       142: 4q^2+11q+2
       143: 8q+2
       144: q^2+3q+1
       145: 2q^2+10q+2
       146: q^3+9q^2+13q+2
       147: 4q^2+11q+2
       148: q^2+7q+2
       149: 4q^2+12q+2
       150: 7q^2+13q+2
       151: 2q^2+4q
       152: 5q^2+9q+2
       153: 4q^2+4q
       154: q^3+8q^2+9q+2
       155: 2q^2+4q
       156: 5q^2+9q+2
       157: q^2+8q+2
       158: q^2+8q+2
       159: q^3+3q^2+3q+1
       160: 4q^2+11q+2
       161: 4q^2+11q+2
       162: q^3+4q^2+4q+1
       163: 4q^2+11q+2
       164: 4q^2+11q+2
       165: q^3+4q^2+4q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: 2q
       170: 4q+1
       171: 4q+1
       172: 2q
       173: 2q
       174: 4q+1
       175: 4q+1
       176: 2q
       178: q+1
       180: 4q+2
       182: 4q+2
       183: q^2+6q+1
       184: q^2+6q+1
       185: q^2+6q+1
       186: q^2+6q+1
       187: q^2+4q
       188: 3q^2+9q+2
       189: q^2+4q
       190: 4q^2+9q+2
       191: 4q+1
       192: 4q+1
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: 2q
       198: q^2+5q+2
       199: 4q+1
       200: 4q+1
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 2q
       206: q^2+5q+2
       207: 2q
       208: 6q+2
       209: q^2+4q
       210: 3q^2+8q+2
       211: 2q^2+4q
       212: 5q^2+9q+2
       214: 4q+2
       216: 4q+2
       218: q^2+2q+1
       219: 2q+1
       220: q^2+8q+2
       221: 2q+1
       222: 8q+2
       223: q^2+3q+1
       224: 8q+2
       225: q^2+3q+1
       226: 2q+1
       227: 2q^2+10q+2
       228: q^2+3q+1
       229: q^2+7q+2
       230: 4q^2+11q+2
       231: 2q+1
       232: 2q^2+10q+2
       233: q^2+3q+1
       234: 4q^2+11q+2
       235: q^2+7q+2
       236: 2q+1
       238: q+2
       240: q+2
       242: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: 4q^2+12q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       260: 2q+1
       261: 2q+1
       263: 2q
       264: 4q+1
       265: 4q+1
       266: 2q
       267: q
       268: 2q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       273: q
       274: 2q+1
       275: q
       276: 3q+1
       277: 3q+1
       278: q
       280: 4q+2
       282: q+1
       288: q+1
       290: 4q+2
       292: q+1
       293: 4q+1
       294: 4q+1
       295: 4q+1
       296: 4q+1
       297: 2q
       298: 6q+2
       299: 3q+1
       300: 3q+1
       302: 2
       303: q^2+5q+1
       304: q^2+5q+1
       305: 2q
       306: q^2+5q+2
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       312: 2
       313: 2q
       314: q^2+5q+2
       316: 1
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       325: q^2+4q
       326: 3q^2+8q+2
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 5q+2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: q+1
       349: 4q+2
       350: q^2+3q+1
       351: 3q+2
       352: 2q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q^2+3q+1
       357: 2q+2
       358: q+1
       359: 3q+2
       361: q+2
       363: q+2
       365: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: q+2
       375: q+2
       376: q+1
       382: 2q+1
       383: 2q+1
       385: q
       386: 3q+1
       387: 3q+1
       388: q
       390: 1
       392: 1
       393: q
       394: 2q+1
       395: 2q+1
       396: q
       398: 1
       400: 1
       401: q
       402: 2q+1
       403: 2q+1
       404: q
       407: 1
       408: 1
       414: q+1
       418: q+1
       424: q+1
       426: 1
       428: q+2
       434: 1
       436: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 2q+2
       443: q+1
       444: q+1
       446: 2
       452: 1
       453: 2q+1
       454: 2q+1
       456: 2
       457: q+1
       458: q+1
       460: 2q+2
       461: q+1
       462: q+1
       464: 2
       466: q+2
       468: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: 4
       480: q+2
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 5q+2
       486: q+2
       488: q+2
       490: q+1
       491: 2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+2
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+2
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: 1
       548: 1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 2
       572: 2
       574: 1
       576: 1
       581: 2
       582: 2
       586: q+1
       598: 1
       600: 1
       602: q+2
       606: 1
       610: 1
       614: 1
       615: q+1
       616: q+1
       618: 2
       624: 1
       626: 1
       630: 1
       631: q+1
       632: q+1
       634: 2
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 4
       654: 2
       656: q+2
       665: q+1
       672: q+2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       699: 1
       700: 1
       703: 1
       704: 1
       734: 1
       736: 1
       750: 1
       752: 1
       759: 2
       760: 2
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       774: 2
       782: 1
       792: 1
       798: 1
       810: 1
       812: 1
       815: 1
       816: 1
       822: 1
       834: 1
       836: 1
       839: 1
       840: 1
       850: 1
       852: 1
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       891: 1
       894: 1
       895: 1
       989: 1
       990: 1
      1009: 1
      1011: 1
      1023: 1
      1039: 1
      1049: 1
      1078: 1
      1082: 1
      1221: 1

1222:    0: 2q^3+2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: q^4+q^3+2q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^3+2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^3+2q^2+4q+2
         7: q^4+q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^5+2q^4+q^3+q^2+2q+1
        10: 2q^3+2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^3+2q^2+4q+2
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: q^2+4q+2
        17: q^2+4q+2
        18: q^4+q^3+q^2+2q+1
        19: 2q^3+2q^2+4q+2
        20: 2q^3+2q^2+4q+2
        21: q^4+q^3+2q^2+3q+1
        22: q^2+4q+2
        23: q^2+4q+2
        24: 2q^2+3q+1
        25: q^2+4q+2
        26: q^2+4q+2
        27: 2q^2+3q+1
        28: q^2+4q+2
        29: 2q^3+2q^2+4q+2
        30: q^3+2q+1
        31: q^2+4q+2
        32: 2q+1
        33: 4q+2
        34: q^2+4q+2
        35: 2q+1
        36: 4q+2
        37: q^2+4q+2
        39: q^2+4q+2
        41: 2q^2+3q+1
        43: q^3+2q+1
        44: q^3+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^4+q^3+q^2+2q+1
        52: q^2+4q+2
        53: q^2+4q+2
        54: 2q^2+3q+1
        55: q^2+4q+2
        56: q^2+4q+2
        57: 2q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+4q+2
        64: 2q+1
        66: 4q+2
        69: q+1
        70: q^3+2q+1
        71: q^2+4q+2
        72: 4q+2
        73: 4q+2
        74: q^2+4q+2
        76: q^2+4q+2
        78: 2q^2+3q+1
        80: 2q+1
        81: 2q+1
        82: q^2+4q+2
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: q^2+4q+2
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^3+q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+2q+1
       103: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 4q+2
       113: q^2+4q+2
       115: 2q+1
       121: 2q+1
       123: 2q+1
       126: q+1
       127: 4q+2
       129: 4q+2
       131: q^2+2q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 2q+1
       142: 4q+2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: 2q+1
       147: 4q+2
       148: 2q+2
       149: q^2+3q+2
       150: q+1
       151: q^2+3q+2
       153: q^2+3q+2
       155: q^2+2q+1
       157: 2q+1
       158: q^2+2q+1
       159: q^3+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 2q+1
       172: 2q+1
       177: q+1
       179: 4q+2
       181: 4q+2
       187: 2q+1
       189: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 2q+2
       207: 2q+1
       209: q^2+3q+2
       211: q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: 2q+1
       267: q+1
       269: q+1
       271: q+1
       273: q+1
       281: q+1
       287: q+1
       289: 2q+1
       291: q+1
       297: 2q+1
       301: 2
       305: q+1
       311: 2
       313: q+1
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       338: q+2
       340: q+2
       342: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: q+1
       415: 2q+1
       417: q+1
       423: q+1
       425: 1
       427: q+2
       433: 1
       435: 1
       441: q+1
       443: 1
       444: 1
       445: 2
       451: 1
       455: 1
       459: q+1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       475: 1
       477: 4
       479: 2
       483: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 2
       570: 2
       573: 1
       575: 1
       577: 2
       579: 2
       587: q+1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       645: 1
       651: 2
       653: 1
       655: 1
       666: 1
       668: q+1
       670: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       693: 1
       695: 1
       697: 1
       702: 1
       769: 1
       771: 1
       783: 1
       791: 1
       799: 1
       809: 1
       811: 1
       813: 1
       823: 1
       833: 1
       835: 1
       837: 1
       849: 1
       851: 1
       853: 2
       857: 1
       872: 1
       876: 1
       982: 1
       984: 1
      1008: 1
      1010: 1
      1024: 1
      1042: 1
      1050: 1
      1222: 1

1223:    0: 2q^3+2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: q^4+q^3+2q^2+3q+1
         3: 2q^2+4q+2
         4: 2q^3+2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^3+2q^2+4q+2
         7: q^4+q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^5+2q^4+q^3+q^2+2q+1
        10: 2q^3+2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^3+2q^2+4q+2
        13: q^3+2q+1
        14: q^3+2q+1
        15: q^2+2q+1
        16: q^2+4q+2
        17: q^2+4q+2
        18: q^4+q^3+q^2+2q+1
        19: 2q^3+2q^2+4q+2
        20: 2q^3+2q^2+4q+2
        21: q^4+q^3+2q^2+3q+1
        22: q^2+4q+2
        23: q^2+4q+2
        24: 2q^2+3q+1
        25: q^2+4q+2
        26: q^2+4q+2
        27: 2q^2+3q+1
        28: q^2+4q+2
        29: 2q^3+2q^2+4q+2
        30: q^3+2q+1
        31: q^2+4q+2
        32: 2q+1
        33: 4q+2
        34: q^2+4q+2
        35: 2q+1
        36: 4q+2
        38: q^2+4q+2
        40: q^2+4q+2
        42: 2q^2+3q+1
        43: q^3+2q+1
        44: q^3+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+q+1
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^4+q^3+q^2+2q+1
        52: q^2+4q+2
        53: q^2+4q+2
        54: 2q^2+3q+1
        55: q^2+4q+2
        56: q^2+4q+2
        57: 2q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        63: q^2+4q+2
        65: 2q+1
        67: 4q+2
        69: q+1
        70: q^3+2q+1
        71: q^2+4q+2
        72: 4q+2
        73: 4q+2
        75: q^2+4q+2
        77: q^2+4q+2
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q+1
        82: q^2+4q+2
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: q^2+4q+2
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^3+q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^3+q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+2q+1
       104: 2q+1
       105: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       112: 4q+2
       114: q^2+4q+2
       116: 2q+1
       122: 2q+1
       124: 2q+1
       126: q+1
       128: 4q+2
       130: 4q+2
       132: q^2+2q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 2q+1
       142: 4q+2
       143: 2q+1
       144: q+1
       145: 4q+2
       146: 2q+1
       147: 4q+2
       148: 2q+2
       149: q^2+3q+2
       150: q+1
       152: q^2+3q+2
       154: q^2+3q+2
       156: q^2+2q+1
       157: 2q+1
       158: q^2+2q+1
       159: q^3+q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 2q+1
       171: 2q+1
       178: q+1
       180: 4q+2
       182: 4q+2
       188: 2q+1
       190: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       206: 2q+2
       208: 2q+1
       210: q^2+3q+2
       212: q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: q+1
       247: q+2
       248: q+2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: 2q+1
       268: q+1
       270: q+1
       272: q+1
       274: q+1
       282: q+1
       288: q+1
       290: 2q+1
       292: q+1
       298: 2q+1
       302: 2
       306: q+1
       312: 2
       314: q+1
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       339: q+2
       341: q+2
       343: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 2
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 2
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: q+1
       416: 2q+1
       418: q+1
       424: q+1
       426: 1
       428: q+2
       434: 1
       436: 1
       442: q+1
       443: 1
       444: 1
       446: 2
       452: 1
       456: 1
       460: q+1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       476: 1
       478: 4
       480: 2
       483: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 2
       572: 2
       574: 1
       576: 1
       581: 2
       582: 2
       588: q+1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       646: 1
       652: 2
       654: 1
       656: 1
       667: 1
       669: q+1
       671: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       699: 1
       700: 1
       703: 1
       704: 1
       773: 1
       774: 1
       784: 1
       792: 1
       800: 1
       810: 1
       812: 1
       814: 1
       824: 1
       834: 1
       836: 1
       838: 1
       850: 1
       852: 1
       854: 2
       858: 1
       872: 1
       876: 1
       986: 1
       987: 1
      1009: 1
      1011: 1
      1025: 1
      1043: 1
      1051: 1
      1223: 1

1224:    0: 5q^2+6q+2
         1: 5q^2+6q+2
         2: q^3+3q^2+3q+1
         3: 5q^2+6q+2
         4: 5q^2+6q+2
         5: 5q^2+6q+2
         6: 5q^2+6q+2
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 5q^2+6q+2
        11: 5q^2+6q+2
        12: 5q^2+6q+2
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 5q^2+6q+2
        17: 5q^2+6q+2
        18: q^3+3q^2+3q+1
        19: 5q^2+6q+2
        20: 5q^2+6q+2
        21: q^3+3q^2+3q+1
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: q^3+3q^2+3q+1
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: q^3+3q^2+3q+1
        28: 5q^2+6q+2
        29: 5q^2+6q+2
        30: 2q+1
        31: 2q^2+6q+2
        32: 2q+1
        33: 2q^2+6q+2
        34: 2q^2+6q+2
        35: 2q+1
        36: 2q^2+6q+2
        37: 2q+2
        38: 4q
        39: 2q+2
        40: 4q
        41: q^2+2q+1
        42: q^3+2q^2+q
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 5q^2+6q+2
        50: 5q^2+6q+2
        51: q^3+3q^2+3q+1
        52: 2q^2+6q+2
        53: 2q^2+6q+2
        54: q^3+3q^2+3q+1
        55: 2q^2+6q+2
        56: 2q^2+6q+2
        57: q^3+3q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 2q+2
        63: 4q
        64: q+1
        65: q
        66: 2q+2
        67: 4q
        69: 2q+1
        70: 2q+1
        71: 5q^2+6q+2
        72: 2q^2+6q+2
        73: 2q^2+6q+2
        74: 2q+2
        75: 4q
        76: 2q+2
        77: 4q
        78: q^2+2q+1
        79: q^3+2q^2+q
        80: 2q+1
        81: 2q+1
        82: 2q^2+6q+2
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 2q^2+6q+2
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+6q+2
        95: 2q^2+6q+2
        96: q^3+3q^2+3q+1
        97: 2q^2+6q+2
        98: 2q^2+6q+2
        99: q^3+3q^2+3q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: q+1
       104: 2q
       105: 2q
       106: q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 2q+2
       112: 4q
       113: 2q+2
       114: 4q
       115: q+1
       116: q
       121: q+1
       122: q
       123: q+1
       124: q
       126: 2q+1
       127: 2q+2
       128: 4q
       129: 2q+2
       130: 4q
       131: q^2+2q+1
       132: q^3+2q^2+q
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q^2+6q+2
       140: 2q+2
       141: 2q+1
       142: 2q^2+6q+2
       143: 2q+1
       144: 2q+1
       145: 2q^2+6q+2
       146: 2q+1
       147: 2q^2+6q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       151: q+2
       152: 4q
       153: q+2
       154: 4q
       155: q+1
       156: q^2+q
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: q+1
       170: 2q
       171: 2q
       172: q+1
       177: q+1
       178: q
       179: 2q+2
       180: 4q
       181: 2q+2
       182: 4q
       187: q+1
       188: q
       189: q+1
       190: q
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: 2
       198: 2q
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: 2
       206: 2q
       207: q+1
       208: q
       209: q+2
       210: 4q
       211: 1
       212: q
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+2
       238: 4q
       239: q+2
       240: 4q
       241: q+1
       242: q^2+q
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 5q+2
       248: 5q+2
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q+1
       260: 2q
       261: 2q
       262: q+1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       287: q+1
       288: q
       291: q+1
       292: q
       297: q+1
       298: q
       301: 2
       302: 2q
       305: 1
       311: 2
       312: 2q
       313: 1
       315: 1
       316: q
       317: q+2
       318: 4q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 1
       326: q
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 5q+2
       338: q+2
       339: 4q
       340: q+2
       341: 4q
       342: q+1
       343: q^2+q
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+2
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+2
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       390: q
       391: 1
       392: q
       397: 1
       398: q
       399: 1
       400: q
       405: 1
       406: 1
       423: q+1
       424: q
       425: 1
       426: q
       427: q+2
       428: 4q
       433: 1
       441: 1
       443: q+1
       444: q+1
       445: 2
       446: 2q
       451: 1
       459: 1
       461: q+1
       462: q+1
       463: 2
       464: 2q
       469: 1
       470: q
       475: 1
       477: 2
       479: 2
       483: q+1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       545: 1
       546: q
       547: 1
       548: q
       561: 1
       562: q
       563: 1
       564: q
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       599: 1
       600: q
       609: 1
       613: 1
       625: 1
       629: 1
       645: 1
       653: 1
       655: 1
       664: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: 1
       697: 1
       791: 1
       811: 1
       835: 1
       843: 1
       851: 1
       857: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
      1008: 1
      1012: 1
      1046: 1
      1077: 1
      1081: 1
      1224: 1

1225:    0: 5q^2+6q+2
         1: 5q^2+6q+2
         2: q^3+3q^2+3q+1
         3: 5q^2+6q+2
         4: 5q^2+6q+2
         5: 5q^2+6q+2
         6: 5q^2+6q+2
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 5q^2+6q+2
        11: 5q^2+6q+2
        12: 5q^2+6q+2
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 5q^2+6q+2
        17: 5q^2+6q+2
        18: q^3+3q^2+3q+1
        19: 5q^2+6q+2
        20: 5q^2+6q+2
        21: q^3+3q^2+3q+1
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: q^3+3q^2+3q+1
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: q^3+3q^2+3q+1
        28: 5q^2+6q+2
        29: 5q^2+6q+2
        30: 2q+1
        31: 2q^2+6q+2
        32: 2q+1
        33: 2q^2+6q+2
        34: 2q^2+6q+2
        35: 2q+1
        36: 2q^2+6q+2
        37: 4q
        38: 2q+2
        39: 4q
        40: 2q+2
        41: q^3+2q^2+q
        42: q^2+2q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: 5q^2+6q+2
        50: 5q^2+6q+2
        51: q^3+3q^2+3q+1
        52: 2q^2+6q+2
        53: 2q^2+6q+2
        54: q^3+3q^2+3q+1
        55: 2q^2+6q+2
        56: 2q^2+6q+2
        57: q^3+3q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 4q
        63: 2q+2
        64: q
        65: q+1
        66: 4q
        67: 2q+2
        69: 2q+1
        70: 2q+1
        71: 5q^2+6q+2
        72: 2q^2+6q+2
        73: 2q^2+6q+2
        74: 4q
        75: 2q+2
        76: 4q
        77: 2q+2
        78: q^3+2q^2+q
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 2q^2+6q+2
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 2q^2+6q+2
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+6q+2
        95: 2q^2+6q+2
        96: q^3+3q^2+3q+1
        97: 2q^2+6q+2
        98: 2q^2+6q+2
        99: q^3+3q^2+3q+1
       100: 5q+2
       101: 5q+2
       102: q^2+2q+1
       103: 2q
       104: q+1
       105: q+1
       106: 2q
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 4q
       112: 2q+2
       113: 4q
       114: 2q+2
       115: q
       116: q+1
       121: q
       122: q+1
       123: q
       124: q+1
       126: 2q+1
       127: 4q
       128: 2q+2
       129: 4q
       130: 2q+2
       131: q^3+2q^2+q
       132: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q^2+6q+2
       140: 2q+2
       141: 2q+1
       142: 2q^2+6q+2
       143: 2q+1
       144: 2q+1
       145: 2q^2+6q+2
       146: 2q+1
       147: 2q^2+6q+2
       148: 2q+2
       149: 5q+2
       150: q+1
       151: 4q
       152: q+2
       153: 4q
       154: q+2
       155: q^2+q
       156: q+1
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 5q+2
       167: 5q+2
       168: q^2+2q+1
       169: 2q
       170: q+1
       171: q+1
       172: 2q
       177: q
       178: q+1
       179: 4q
       180: 2q+2
       181: 4q
       182: 2q+2
       187: q
       188: q+1
       189: q
       190: q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: 2q
       198: 2
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: 2q
       206: 2
       207: q
       208: q+1
       209: 4q
       210: q+2
       211: q
       212: 1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 4q
       238: q+2
       239: 4q
       240: q+2
       241: q^2+q
       242: q+1
       243: 5q+2
       244: 2q+2
       245: 2q+2
       246: q+1
       247: 5q+2
       248: 5q+2
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q
       260: q+1
       261: q+1
       262: 2q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       287: q
       288: q+1
       291: q
       292: q+1
       297: q
       298: q+1
       301: 2q
       302: 2
       306: 1
       311: 2q
       312: 2
       314: 1
       315: q
       316: 1
       317: 4q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       325: q
       326: 1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 5q+2
       338: 4q
       339: q+2
       340: 4q
       341: q+2
       342: q^2+q
       343: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+2
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+2
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       389: q
       390: 1
       391: q
       392: 1
       397: q
       398: 1
       399: q
       400: 1
       407: 1
       408: 1
       423: q
       424: q+1
       425: q
       426: 1
       427: 4q
       428: q+2
       434: 1
       442: 1
       443: q+1
       444: q+1
       445: 2q
       446: 2
       452: 1
       460: 1
       461: q+1
       462: q+1
       463: 2q
       464: 2
       469: q
       470: 1
       476: 1
       478: 2
       480: 2
       483: q+1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       545: q
       546: 1
       547: q
       548: 1
       561: q
       562: 1
       563: q
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       599: q
       600: 1
       610: 1
       614: 1
       626: 1
       630: 1
       646: 1
       654: 1
       656: 1
       664: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: 1
       700: 1
       792: 1
       812: 1
       836: 1
       844: 1
       852: 1
       858: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
      1009: 1
      1013: 1
      1047: 1
      1077: 1
      1081: 1
      1225: 1

1226:    0: q^3+4q^2+5q+2
         1: q^3+4q^2+5q+2
         2: q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: q^3+4q^2+5q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: q^3+4q^2+5q+2
         9: q^3+2q^2+2q+1
        10: q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: q^3+3q^2+4q+2
        13: q^3+4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: q^3+4q^2+5q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: 2q^2+4q+2
        22: q^3+4q^2+5q+2
        23: q^3+4q^2+5q+2
        24: q^3+4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: 2q^2+4q+2
        31: q^3+4q^2+5q+2
        32: q^3+4q^2+5q+2
        33: 2q^2+4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: q^3+4q^2+5q+2
        44: q^3+3q^2+4q+2
        45: q^3+4q^2+5q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^2+2q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: 2q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 2q^2+4q+2
        69: q+1
        70: 2q^2+4q+2
        71: q^2+3q+2
        72: 2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^3+4q^2+5q+2
        81: 2q^2+4q+2
        82: 2q^2+4q+2
        83: 2q^2+4q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^2+2q+1
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+2q+1
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+2q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: 2q+2
       115: 2q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: 2q^2+4q+2
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       133: q^2+3q+2
       134: q+1
       135: 2
       136: 2q+2
       137: 2q^2+4q+2
       138: q+1
       139: q^2+3q+2
       140: 2
       141: 2q^2+4q+2
       142: 2q+2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+2q+1
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+2q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: q+2
       181: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: 2
       189: 2q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: 2q+2
       211: 2q+2
       213: q+2
       215: q+2
       217: q+1
       219: q+1
       220: q^2+3q+2
       221: q+1
       222: 2
       223: 1
       224: 2q+2
       225: q+1
       226: q+1
       227: q^2+3q+2
       228: q+1
       229: 2
       230: 2q+2
       231: 1
       232: q+2
       233: 1
       234: 2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       246: 2q+2
       247: 2
       248: 2
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+2q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: q+1
       278: q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: 2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: 1
       308: 1
       315: 1
       317: q+2
       319: 1
       320: 1
       325: 2q+2
       327: q+2
       329: q+2
       331: q+1
       333: q+1
       334: 1
       335: q+1
       337: 2
       338: 2
       340: 2
       344: q+1
       345: q^2+3q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       409: q+2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       453: 1
       454: 1
       465: q+2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       484: 2
       485: 2
       487: 2
       492: q+1
       493: 1
       494: q+1
       496: 2
       497: 1
       498: 1
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       515: 1
       516: 1
       518: 2
       519: 2
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       583: 1
       585: 1
       587: 1
       601: 2
       605: 1
       609: 1
       611: 2
       615: 1
       616: 1
       617: 2
       635: q+2
       637: 1
       639: 1
       647: 1
       648: 1
       658: 1
       660: 1
       666: 2
       668: 2
       672: 2
       674: 1
       675: 1
       676: q+1
       678: 2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       729: 1
       731: 1
       733: 1
       735: 1
       777: 1
       789: 2
       795: 1
       797: 1
       799: 1
       813: 2
       815: 1
       816: 1
       841: 1
       859: 1
       861: 1
       869: 1
       877: 1
       881: 1
       882: 1
       932: 1
       934: 1
      1014: 1
      1018: 1
      1066: 1
      1068: 1
      1075: 1
      1226: 1

1227:    0: q^3+4q^2+5q+2
         1: q^3+4q^2+5q+2
         2: q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: q^3+4q^2+5q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: q^3+4q^2+5q+2
         9: q^3+2q^2+2q+1
        10: q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: q^3+3q^2+4q+2
        13: q^3+4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: q^3+4q^2+5q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: 2q^2+4q+2
        22: q^3+4q^2+5q+2
        23: q^3+4q^2+5q+2
        24: q^3+4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: 2q^2+4q+2
        31: q^3+4q^2+5q+2
        32: q^3+4q^2+5q+2
        33: 2q^2+4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: q^3+4q^2+5q+2
        44: q^3+3q^2+4q+2
        45: q^3+4q^2+5q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^2+2q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: 2q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 2q^2+4q+2
        69: q+1
        70: 2q^2+4q+2
        71: q^2+3q+2
        72: 2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^3+4q^2+5q+2
        81: 2q^2+4q+2
        82: 2q^2+4q+2
        83: 2q^2+4q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^2+2q+1
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+2q+1
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+2q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: 2q+2
       116: 2q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: 2q^2+4q+2
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       133: q^2+3q+2
       134: q+1
       135: 2
       136: 2q+2
       137: 2q^2+4q+2
       138: q+1
       139: q^2+3q+2
       140: 2
       141: 2q^2+4q+2
       142: 2q+2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+2q+1
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+2q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: q+2
       182: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: 2
       190: 2q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: 2q+2
       212: 2q+2
       214: q+2
       216: q+2
       218: q+1
       219: q+1
       220: q^2+3q+2
       221: q+1
       222: 2
       223: 1
       224: 2q+2
       225: q+1
       226: q+1
       227: q^2+3q+2
       228: q+1
       229: 2
       230: 2q+2
       231: 1
       232: q+2
       233: 1
       234: 2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       246: 2q+2
       247: 2
       248: 2
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+2q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: q+1
       277: q+1
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       298: 2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: 1
       308: 1
       316: 1
       318: q+2
       319: 1
       320: 1
       326: 2q+2
       328: q+2
       330: q+2
       332: q+1
       333: q+1
       334: 1
       335: q+1
       337: 2
       339: 2
       341: 2
       344: q+1
       345: q^2+3q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       410: q+2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       453: 1
       454: 1
       466: q+2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       484: 2
       486: 2
       488: 2
       492: q+1
       493: 1
       494: q+1
       496: 2
       497: 1
       498: 1
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       515: 1
       516: 1
       518: 2
       519: 2
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       584: 1
       586: 1
       588: 1
       602: 2
       606: 1
       610: 1
       612: 2
       615: 1
       616: 1
       618: 2
       636: q+2
       638: 1
       640: 1
       647: 1
       648: 1
       659: 1
       661: 1
       667: 2
       669: 2
       672: 2
       674: 1
       675: 1
       676: q+1
       678: 2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       730: 1
       732: 1
       734: 1
       736: 1
       778: 1
       790: 2
       796: 1
       798: 1
       800: 1
       814: 2
       815: 1
       816: 1
       842: 1
       860: 1
       862: 1
       869: 1
       877: 1
       881: 1
       882: 1
       933: 1
       935: 1
      1015: 1
      1019: 1
      1067: 1
      1069: 1
      1075: 1
      1227: 1

1228:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+7q^2+8q+2
         3: q^3+7q^2+8q+2
         4: q^3+4q^2+5q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+6q^2+5q+2
         7: q^3+4q^2+5q+2
         8: q^3+7q^2+8q+2
         9: q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^3+7q^2+8q+2
        14: q^3+4q^2+5q+2
        15: q^3+7q^2+8q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^2+5q+2
        20: 3q^2+5q+2
        21: q^2+5q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+7q^2+8q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: 4q^2+6q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: q^3+7q^2+8q+2
        33: q^3+7q^2+8q+2
        34: 2q^2+6q+2
        35: 4q^2+6q+2
        36: 4q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+8q+2
        44: q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: q^3+7q^2+8q+2
        47: q^3+7q^2+8q+2
        48: q^3+4q^2+5q+2
        49: q^2+5q+2
        50: 3q^2+5q+2
        51: q^2+5q+2
        52: q^2+5q+2
        53: 3q^2+5q+2
        54: q^2+5q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q^2+4q+2
        61: 2q
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q^2+8q+2
        81: q^3+7q^2+8q+2
        82: q^2+5q+2
        83: q^2+5q+2
        84: 2q^2+6q+2
        85: 4q^2+6q+2
        86: 3q+2
        87: 3q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: q^3+4q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: q^2+5q+2
        95: 3q^2+5q+2
        96: q^2+5q+2
        97: 3q+2
        98: q^2+3q+2
        99: 3q+2
       100: 3q+2
       101: q^2+3q+2
       102: 3q+2
       103: q^2+2q+1
       104: q^2+2q+1
       105: q
       106: q
       107: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q^2+4q+1
       118: 2q^2+4q+1
       119: 2q^2+4q+2
       120: 2q
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 4q^2+8q+2
       126: q^2+5q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+5q+2
       134: q^2+5q+2
       135: q+2
       136: 2q+2
       137: 4q^2+8q+2
       138: q^2+5q+2
       139: q^2+5q+2
       140: q+2
       141: q^2+5q+2
       142: 2q+2
       143: 2q^2+6q+2
       144: 3q+2
       145: 3q+2
       146: 3q+2
       147: q+2
       149: 3q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: q^2+5q+2
       161: 3q^2+5q+2
       162: q^2+5q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: 3q+2
       167: q^2+3q+2
       168: 3q+2
       169: 1
       170: 1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q
       176: q
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       193: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q^2+4q+2
       200: 2q
       201: q+2
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+5q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: q+2
       224: 2
       225: 2q+2
       226: q^2+5q+2
       227: q^2+5q+2
       228: q^2+5q+2
       229: q+2
       230: 2q+2
       231: 3q+2
       232: 3q+2
       233: 3q+2
       234: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       244: q+2
       246: 3q+2
       247: 2
       248: 2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: q+1
       254: q+1
       255: q+1
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q
       278: q
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: q+2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       307: q+2
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: q^2+5q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: q+2
       349: 2
       350: 2q+2
       351: 2
       352: 3q+2
       353: q+1
       354: q+1
       355: 1
       356: q+2
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 3q+2
       368: 3q+2
       369: q+2
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: 1
       381: 1
       382: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       427: 1
       428: 1
       429: q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: q+2
       453: 1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+2
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: 2q+2
       493: 2
       494: 2
       496: 2
       497: q+1
       498: 1
       508: 3q+2
       509: q+1
       510: q+1
       511: 1
       512: q+2
       515: 2
       516: 2
       518: 1
       519: 1
       521: 1
       522: 1
       529: 1
       530: 1
       533: 1
       534: 1
       537: 1
       538: 1
       541: 1
       542: 1
       545: 1
       546: 1
       585: 1
       586: 1
       589: 2
       595: 1
       596: 1
       601: 1
       602: 1
       603: 2
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       615: 2
       617: 1
       618: 1
       619: 1
       639: q+1
       640: q+1
       641: q+2
       647: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 2
       676: 2
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       709: 1
       710: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: 1
       734: 1
       775: 1
       776: 1
       793: 2
       795: 1
       796: 1
       797: 1
       798: 1
       801: 2
       807: 1
       808: 1
       815: 1
       825: 1
       845: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       916: 1
       917: 1
       920: 1
       921: 1
      1016: 1
      1052: 1
      1072: 1
      1075: 1
      1228: 1

1229:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+7q^2+8q+2
         3: q^3+7q^2+8q+2
         4: q^3+4q^2+5q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+6q^2+5q+2
         7: q^3+4q^2+5q+2
         8: q^3+7q^2+8q+2
         9: q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^3+7q^2+8q+2
        14: q^3+4q^2+5q+2
        15: q^3+7q^2+8q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^2+5q+2
        20: 3q^2+5q+2
        21: q^2+5q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+7q^2+8q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: 4q^2+6q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: q^3+7q^2+8q+2
        33: q^3+7q^2+8q+2
        34: 2q^2+6q+2
        35: 4q^2+6q+2
        36: 4q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+8q+2
        44: q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: q^3+7q^2+8q+2
        47: q^3+7q^2+8q+2
        48: q^3+4q^2+5q+2
        49: q^2+5q+2
        50: 3q^2+5q+2
        51: q^2+5q+2
        52: q^2+5q+2
        53: 3q^2+5q+2
        54: q^2+5q+2
        55: 3q+2
        56: q^2+3q+2
        57: 3q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q
        61: 2q^2+4q+2
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q^2+8q+2
        81: q^3+7q^2+8q+2
        82: q^2+5q+2
        83: q^2+5q+2
        84: 2q^2+6q+2
        85: 4q^2+6q+2
        86: 3q+2
        87: 3q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: q^3+4q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: q^2+5q+2
        95: 3q^2+5q+2
        96: q^2+5q+2
        97: 3q+2
        98: q^2+3q+2
        99: 3q+2
       100: 3q+2
       101: q^2+3q+2
       102: 3q+2
       103: q
       104: q
       105: q^2+2q+1
       106: q^2+2q+1
       108: q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q^2+4q+1
       118: 2q^2+4q+1
       119: 2q
       120: 2q^2+4q+2
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 4q^2+8q+2
       126: q^2+5q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+5q+2
       134: q^2+5q+2
       135: q+2
       136: 2q+2
       137: 4q^2+8q+2
       138: q^2+5q+2
       139: q^2+5q+2
       140: q+2
       141: q^2+5q+2
       142: 2q+2
       143: 2q^2+6q+2
       144: 3q+2
       145: 3q+2
       146: 3q+2
       147: q+2
       149: 3q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: q^2+5q+2
       161: 3q^2+5q+2
       162: q^2+5q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: 3q+2
       167: q^2+3q+2
       168: 3q+2
       171: 1
       172: 1
       173: q
       174: q
       175: q^2+2q+1
       176: q^2+2q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       184: q+2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       194: q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q
       200: 2q^2+4q+2
       202: q+2
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+5q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: q+2
       224: 2
       225: 2q+2
       226: q^2+5q+2
       227: q^2+5q+2
       228: q^2+5q+2
       229: q+2
       230: 2q+2
       231: 3q+2
       232: 3q+2
       233: 3q+2
       234: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       244: q+2
       246: 3q+2
       247: 2
       248: 2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: q+1
       254: q+1
       255: q+1
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       275: q
       276: q
       277: q^2+2q+1
       278: q^2+2q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       284: q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: q+2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       308: q+2
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: q^2+5q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: q+2
       349: 2
       350: 2q+2
       351: 2
       352: 3q+2
       353: q+1
       354: q+1
       355: 1
       356: q+2
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 3q+2
       368: 3q+2
       369: q+2
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       379: 1
       380: 1
       383: 1
       384: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       427: 1
       428: 1
       430: q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: q+2
       454: 1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       472: q+2
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: 2q+2
       493: 2
       494: 2
       496: 2
       497: q+1
       498: 1
       508: 3q+2
       509: q+1
       510: q+1
       511: 1
       512: q+2
       515: 2
       516: 2
       518: 1
       519: 1
       523: 1
       524: 1
       531: 1
       532: 1
       535: 1
       536: 1
       539: 1
       540: 1
       543: 1
       544: 1
       547: 1
       548: 1
       585: 1
       586: 1
       590: 2
       595: 1
       596: 1
       601: 1
       602: 1
       604: 2
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       616: 2
       617: 1
       618: 1
       620: 1
       639: q+1
       640: q+1
       642: q+2
       648: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 2
       676: 2
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       711: 1
       712: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: 1
       736: 1
       775: 1
       776: 1
       794: 2
       795: 1
       796: 1
       797: 1
       798: 1
       802: 2
       807: 1
       808: 1
       816: 1
       826: 1
       846: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       918: 1
       919: 1
       922: 1
       923: 1
      1017: 1
      1053: 1
      1072: 1
      1075: 1
      1229: 1

1230:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: 4q^2+5q+2
         6: 2q^3+4q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 4q^2+5q+2
         9: q^3+3q^2+4q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: 4q^2+5q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 2q^2+4q+2
        20: 3q^2+4q+2
        21: 2q^2+4q+2
        22: 4q^2+5q+2
        23: 4q^2+5q+2
        24: 4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+4q+2
        31: 4q+2
        32: 4q^2+5q+2
        33: 4q^2+5q+2
        34: 2q+2
        35: q^2+3q+2
        36: q^2+3q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+5q+2
        47: 4q^2+5q+2
        48: q^3+3q^2+4q+2
        49: 2q^2+4q+2
        50: 3q^2+4q+2
        51: 2q^2+4q+2
        52: 2q^2+4q+2
        53: 3q^2+4q+2
        54: 2q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q^2+3q+2
        66: q^2+3q+2
        68: 4q+2
        69: 2q^2+4q+2
        70: 3q+2
        71: 3q+2
        72: q+2
        73: q^2+3q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 4q+2
        81: 4q^2+5q+2
        82: 3q+2
        83: 2q^2+4q+2
        84: 2q+2
        85: q^2+3q+2
        86: q+2
        87: 2q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 2q^2+4q+2
        95: 3q^2+4q+2
        96: 2q^2+4q+2
        97: 2q+2
        98: 2q+2
        99: 2q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: q+2
       113: q+2
       115: 2q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: q^2+3q+2
       125: 4q+2
       126: 3q+2
       127: 2q+2
       129: 2q+2
       131: 2q+2
       133: 3q+2
       134: 2q^2+4q+2
       135: q+2
       136: q^2+3q+2
       137: 4q+2
       138: 2q^2+4q+2
       139: 3q+2
       140: q+2
       141: 3q+2
       142: q^2+3q+2
       143: 2q+2
       144: 2q+2
       145: q+2
       146: q+2
       147: q+2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+4q+2
       161: 3q^2+4q+2
       162: 2q^2+4q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 2q+2
       179: q+2
       181: q+2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: q+2
       189: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+2
       211: 2q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q+2
       224: 2
       225: q^2+3q+2
       226: 3q+2
       227: 3q+2
       228: 2q^2+4q+2
       229: q+2
       230: q^2+3q+2
       231: q+2
       232: q+2
       233: 2q+2
       234: q+2
       236: 2q+2
       237: 2q+2
       239: 2q+2
       241: 2q+2
       243: q+2
       244: q+2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: q+1
       278: q+1
       279: q+2
       281: 2q+2
       283: 1
       284: 1
       285: q+1
       286: q+1
       287: q+2
       289: q+2
       291: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: q+2
       303: q+1
       304: q+1
       305: q+2
       307: 1
       308: 1
       315: 2q+2
       317: q+2
       319: 1
       320: 1
       325: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 3q+2
       345: q+2
       346: q+2
       347: 2
       348: q+2
       349: 2
       350: q^2+3q+2
       351: 2
       352: q+2
       356: q+2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: q+2
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       413: q+2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 2
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q+2
       435: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       447: 1
       448: 1
       465: q+2
       467: 2q+2
       469: q+2
       471: 1
       472: 1
       481: 2
       482: 2
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 2
       508: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       521: 1
       524: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 2
       603: 1
       604: 1
       605: q+2
       607: 1
       608: 1
       609: 2
       613: 1
       615: 1
       616: 1
       617: 2
       639: q+2
       641: 1
       642: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       674: 2
       675: 2
       676: 2
       677: 1
       679: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       733: 1
       735: 1
       775: 2
       779: 1
       781: 1
       793: 1
       794: 1
       795: 2
       797: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       811: 1
       866: 1
       870: 1
       871: 1
       916: 1
       918: 1
       920: 1
       922: 1
       994: 1
      1020: 1
      1022: 1
      1076: 1
      1230: 1

1231:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: 4q^2+5q+2
         6: 2q^3+4q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 4q^2+5q+2
         9: q^3+3q^2+4q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: 4q^2+5q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 2q^2+4q+2
        20: 3q^2+4q+2
        21: 2q^2+4q+2
        22: 4q^2+5q+2
        23: 4q^2+5q+2
        24: 4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+4q+2
        31: 4q+2
        32: 4q^2+5q+2
        33: 4q^2+5q+2
        34: 2q+2
        35: q^2+3q+2
        36: q^2+3q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+5q+2
        47: 4q^2+5q+2
        48: q^3+3q^2+4q+2
        49: 2q^2+4q+2
        50: 3q^2+4q+2
        51: 2q^2+4q+2
        52: 2q^2+4q+2
        53: 3q^2+4q+2
        54: 2q^2+4q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q^2+3q+2
        67: q^2+3q+2
        68: 4q+2
        69: 2q^2+4q+2
        70: 3q+2
        71: 3q+2
        72: q+2
        73: q^2+3q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 4q+2
        81: 4q^2+5q+2
        82: 3q+2
        83: 2q^2+4q+2
        84: 2q+2
        85: q^2+3q+2
        86: q+2
        87: 2q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 2q^2+4q+2
        95: 3q^2+4q+2
        96: 2q^2+4q+2
        97: 2q+2
        98: 2q+2
        99: 2q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: q+2
       114: q+2
       116: 2q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: q^2+3q+2
       125: 4q+2
       126: 3q+2
       128: 2q+2
       130: 2q+2
       132: 2q+2
       133: 3q+2
       134: 2q^2+4q+2
       135: q+2
       136: q^2+3q+2
       137: 4q+2
       138: 2q^2+4q+2
       139: 3q+2
       140: q+2
       141: 3q+2
       142: q^2+3q+2
       143: 2q+2
       144: 2q+2
       145: q+2
       146: q+2
       147: q+2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+4q+2
       161: 3q^2+4q+2
       162: 2q^2+4q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 2q+2
       180: q+2
       182: q+2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: q+2
       190: q+2
       191: 2q+1
       192: 2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+2
       212: 2q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q+2
       224: 2
       225: q^2+3q+2
       226: 3q+2
       227: 3q+2
       228: 2q^2+4q+2
       229: q+2
       230: q^2+3q+2
       231: q+2
       232: q+2
       233: 2q+2
       234: q+2
       236: 2q+2
       238: 2q+2
       240: 2q+2
       242: 2q+2
       243: q+2
       244: q+2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: q+1
       277: q+1
       280: q+2
       282: 2q+2
       283: 1
       284: 1
       285: q+1
       286: q+1
       288: q+2
       290: q+2
       292: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: q+2
       303: q+1
       304: q+1
       306: q+2
       307: 1
       308: 1
       316: 2q+2
       318: q+2
       319: 1
       320: 1
       326: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 3q+2
       345: q+2
       346: q+2
       347: 2
       348: q+2
       349: 2
       350: q^2+3q+2
       351: 2
       352: q+2
       356: q+2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: q+2
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       414: q+2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 2
       429: 1
       430: 1
       431: q+1
       432: q+1
       434: q+2
       436: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       447: 1
       448: 1
       466: q+2
       468: 2q+2
       470: q+2
       471: 1
       472: 1
       481: 2
       482: 2
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 2
       508: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       522: 1
       523: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       604: 1
       606: q+2
       607: 1
       608: 1
       610: 2
       614: 1
       615: 1
       616: 1
       618: 2
       640: q+2
       641: 1
       642: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       674: 2
       675: 2
       676: 2
       677: 1
       679: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       734: 1
       736: 1
       776: 2
       780: 1
       782: 1
       793: 1
       794: 1
       796: 2
       798: 2
       801: 1
       802: 1
       807: 1
       808: 1
       810: 1
       812: 1
       866: 1
       870: 1
       871: 1
       917: 1
       919: 1
       921: 1
       923: 1
       995: 1
      1021: 1
      1023: 1
      1076: 1
      1231: 1

1232:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+6q^2+6q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+8q^2+6q+2
         7: q^3+4q^2+5q+2
         8: q^3+6q^2+6q+2
         9: q^3+4q^2+5q+2
        10: q^2+6q+2
        11: q^2+6q+2
        12: 3q^2+4q+2
        13: 4q^2+6q+2
        14: 3q^2+5q+2
        15: 4q^2+6q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: 4q^2+6q+2
        20: q^3+6q^2+6q+2
        21: 3q^2+5q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+6q+2
        28: q^2+6q+2
        29: q^2+4q+2
        30: 2q^2+5q+2
        31: q^2+6q+2
        32: 4q^2+6q+2
        33: q^3+7q^2+8q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 4q^2+8q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: 3q^2+5q+2
        49: 4q^2+6q+2
        50: q^3+6q^2+6q+2
        51: 3q^2+5q+2
        52: 4q^2+6q+2
        53: q^3+6q^2+6q+2
        54: 3q^2+5q+2
        55: q^2+6q+2
        56: 3q^2+6q+2
        57: q^2+5q+2
        58: q^2+4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q+2
        69: 2q^2+5q+2
        70: 3q+2
        71: q^2+4q+2
        72: q^2+4q+2
        73: 3q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 4q+2
        81: 4q^2+6q+2
        82: q^2+4q+2
        83: 2q^2+5q+2
        84: 4q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: 5q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+4q+2
        92: 3q^2+4q+2
        93: q^2+4q+2
        94: 4q^2+6q+2
        95: q^3+6q^2+6q+2
        96: 3q^2+5q+2
        97: q^2+6q+2
        98: 3q^2+6q+2
        99: q^2+5q+2
       100: q^2+6q+2
       101: 3q^2+6q+2
       102: q^2+5q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q^2+2q+2
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: q+2
       134: q^2+4q+2
       135: 3q+2
       136: q^2+3q+2
       137: 4q+2
       138: 2q^2+5q+2
       139: q^2+4q+2
       140: q^2+4q+2
       141: 3q+2
       142: 3q^2+4q+2
       143: 4q+2
       144: 5q+2
       145: 4q+2
       146: 3q+2
       147: q^2+4q+2
       148: 2q+2
       149: 4q+2
       150: 5q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+4q+2
       161: 3q^2+4q+2
       162: q^2+4q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: q^2+6q+2
       167: 3q^2+6q+2
       168: q^2+5q+2
       169: 1
       171: 1
       173: q+1
       175: q+1
       177: 2q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: 1
       185: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+2
       193: q+1
       194: q+1
       195: q^2+2q+2
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: q+2
       220: 2
       221: q+2
       222: q+2
       223: 3q+2
       224: 2
       225: q^2+3q+2
       226: 3q+2
       227: q+2
       228: q^2+4q+2
       229: 3q+2
       230: q^2+3q+2
       231: 3q+2
       232: q+2
       233: 3q+2
       234: 2q+2
       235: q+2
       236: 5q+2
       237: 2q+1
       238: 2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 4q+2
       244: q^2+4q+2
       245: 2q+2
       246: 3q+2
       247: 2q+4
       248: 2q+4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 1
       261: 1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       283: 1
       284: 1
       285: q+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       309: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 4
       338: q+2
       339: q+2
       340: q+2
       341: q+2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: q+2
       348: 3q+2
       349: 2
       350: q^2+3q+2
       351: 2q+4
       352: q+2
       356: 2q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 3q+2
       369: 2q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       377: 1
       379: 1
       385: 1
       387: 1
       389: 1
       392: 1
       393: 1
       395: 1
       397: 1
       398: 1
       401: 1
       402: 1
       405: 1
       408: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       431: q+2
       433: q+1
       434: q+1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 2
       444: 2
       445: q+2
       446: q+2
       447: 1
       448: 1
       449: q+2
       451: 1
       452: 1
       461: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: 1
       483: 2
       484: 2
       491: 1
       492: 2
       493: q+2
       494: 2
       495: 2
       496: q+2
       500: 2
       501: 2
       508: q+2
       512: 2q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       529: 1
       531: 1
       533: 1
       535: 1
       541: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       561: 2
       562: 2
       565: 1
       567: 1
       569: 1
       572: 1
       573: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       591: 2
       595: 1
       599: 1
       600: 1
       603: 1
       604: 1
       607: 2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       629: 1
       630: 1
       631: 2
       641: 1
       642: 1
       643: q+2
       645: 1
       646: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: q+2
       675: 2
       676: 1
       677: 2
       679: 1
       680: 2
       685: 1
       689: 2
       693: 1
       694: 1
       698: 1
       700: 1
       713: 1
       714: 1
       725: 1
       728: 1
       753: 1
       755: 1
       765: 1
       767: 1
       787: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: 2
       807: 1
       811: 1
       812: 1
       817: 2
       843: 1
       844: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       924: 1
       925: 1
       964: 1
       966: 1
       998: 1
      1028: 1
      1076: 1
      1084: 1
      1232: 1

1233:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+6q^2+6q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+8q^2+6q+2
         7: q^3+4q^2+5q+2
         8: q^3+6q^2+6q+2
         9: q^3+4q^2+5q+2
        10: q^2+6q+2
        11: q^2+6q+2
        12: 3q^2+4q+2
        13: 4q^2+6q+2
        14: 3q^2+5q+2
        15: 4q^2+6q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: 4q^2+6q+2
        20: q^3+6q^2+6q+2
        21: 3q^2+5q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+6q+2
        28: q^2+6q+2
        29: q^2+4q+2
        30: 2q^2+5q+2
        31: q^2+6q+2
        32: 4q^2+6q+2
        33: q^3+7q^2+8q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 4q^2+8q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: 3q^2+5q+2
        49: 4q^2+6q+2
        50: q^3+6q^2+6q+2
        51: 3q^2+5q+2
        52: 4q^2+6q+2
        53: q^3+6q^2+6q+2
        54: 3q^2+5q+2
        55: q^2+6q+2
        56: 3q^2+6q+2
        57: q^2+5q+2
        58: 2q
        59: q^2+4q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q+2
        69: 2q^2+5q+2
        70: 3q+2
        71: q^2+4q+2
        72: q^2+4q+2
        73: 3q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 4q+2
        81: 4q^2+6q+2
        82: q^2+4q+2
        83: 2q^2+5q+2
        84: 4q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: 5q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+4q+2
        92: 3q^2+4q+2
        93: q^2+4q+2
        94: 4q^2+6q+2
        95: q^3+6q^2+6q+2
        96: 3q^2+5q+2
        97: q^2+6q+2
        98: 3q^2+6q+2
        99: q^2+5q+2
       100: q^2+6q+2
       101: 3q^2+6q+2
       102: q^2+5q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: q^2+2q+2
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: q+2
       134: q^2+4q+2
       135: 3q+2
       136: q^2+3q+2
       137: 4q+2
       138: 2q^2+5q+2
       139: q^2+4q+2
       140: q^2+4q+2
       141: 3q+2
       142: 3q^2+4q+2
       143: 4q+2
       144: 5q+2
       145: 4q+2
       146: 3q+2
       147: q^2+4q+2
       148: 2q+2
       149: 4q+2
       150: 5q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+4q+2
       161: 3q^2+4q+2
       162: q^2+4q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: q^2+6q+2
       167: 3q^2+6q+2
       168: q^2+5q+2
       170: 1
       172: 1
       174: q+1
       176: q+1
       177: 2q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: 1
       186: q+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       192: 2q+2
       193: q+1
       194: q+1
       196: q^2+2q+2
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: q+2
       220: 2
       221: q+2
       222: q+2
       223: 3q+2
       224: 2
       225: q^2+3q+2
       226: 3q+2
       227: q+2
       228: q^2+4q+2
       229: 3q+2
       230: q^2+3q+2
       231: 3q+2
       232: q+2
       233: 3q+2
       234: 2q+2
       235: q+2
       236: 5q+2
       237: 2q+1
       238: 2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 4q+2
       244: q^2+4q+2
       245: 2q+2
       246: 3q+2
       247: 2q+4
       248: 2q+4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       260: 1
       262: 1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       283: 1
       284: 1
       286: q+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       301: q+1
       302: q+1
       304: q+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       310: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       322: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 4
       338: q+2
       339: q+2
       340: q+2
       341: q+2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: q+2
       348: 3q+2
       349: 2
       350: q^2+3q+2
       351: 2q+4
       352: q+2
       356: 2q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 3q+2
       369: 2q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       378: 1
       380: 1
       386: 1
       388: 1
       390: 1
       391: 1
       394: 1
       396: 1
       399: 1
       400: 1
       403: 1
       404: 1
       406: 1
       407: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       432: q+2
       433: q+1
       434: q+1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 2
       444: 2
       445: q+2
       446: q+2
       447: 1
       448: 1
       450: q+2
       451: 1
       452: 1
       462: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: 1
       483: 2
       484: 2
       491: 1
       492: 2
       493: q+2
       494: 2
       495: 2
       496: q+2
       500: 2
       501: 2
       508: q+2
       512: 2q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       530: 1
       532: 1
       534: 1
       536: 1
       542: 1
       543: 1
       545: 1
       546: 1
       547: 1
       548: 1
       551: 1
       552: 1
       563: 2
       564: 2
       566: 1
       568: 1
       570: 1
       571: 1
       574: 2
       575: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       592: 2
       596: 1
       599: 1
       600: 1
       603: 1
       604: 1
       608: 2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       629: 1
       630: 1
       632: 2
       641: 1
       642: 1
       644: q+2
       645: 1
       646: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: q+2
       675: 2
       676: 1
       677: 2
       679: 1
       680: 2
       685: 1
       689: 2
       696: 1
       697: 1
       699: 1
       701: 1
       715: 1
       716: 1
       726: 1
       727: 1
       754: 1
       756: 1
       766: 1
       768: 1
       788: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: 2
       808: 1
       811: 1
       812: 1
       818: 2
       843: 1
       844: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       926: 1
       927: 1
       965: 1
       967: 1
       999: 1
      1029: 1
      1076: 1
      1084: 1
      1233: 1

1234:    0: q^3+q^2+2q+2
         1: q^3+q^2+2q+2
         2: 2q^2+q+2
         3: q^3+q^2+2q+2
         4: q^3+q^2+2q+2
         5: q^3+q^2+2q+2
         6: q^3+q^2+2q+2
         7: 2q^2+q+2
         8: 2q^2+q+2
         9: 2q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^3+q^2+2q+2
        17: q^3+q^2+2q+2
        18: 2q^2+q+2
        19: q^3+q^2+2q+2
        20: q^3+q^2+2q+2
        21: 2q^2+q+2
        22: q^3+q^2+2q+2
        23: q^3+q^2+2q+2
        24: 2q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q^2+q+2
        31: 2q+2
        32: q^2+q+2
        33: q^3+q^2+2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^3+q^2+2q+2
        50: q^3+q^2+2q+2
        51: 2q^2+q+2
        52: q^3+q^2+2q+2
        53: q^3+q^2+2q+2
        54: 2q^2+q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q^2+q+2
        70: q+2
        71: 2q+2
        72: 2
        73: q^3+q^2+2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q^2+q+2
        82: 2q+2
        83: q^2+q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: q^3+q^2+2q+2
        95: q^3+q^2+2q+2
        96: 2q^2+q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q^2+q+2
       135: 2
       136: q^2+q+2
       137: q+2
       138: q^2+q+2
       139: 2q+2
       140: 2
       141: q+2
       142: q^3+q^2+2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+q+2
       161: q^2+q+2
       162: q^2+q+2
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2
       224: q+2
       225: q^2+q+2
       226: q+2
       227: 2
       228: q^2+q+2
       229: 2
       230: q^2+q+2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: q+2
       251: q+2
       252: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q^2+q+2
       351: 2
       352: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: 1
       469: 1
       470: 1
       471: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 1
       546: 1
       589: 1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       641: 1
       657: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: 2
       677: 2
       679: 1
       717: 1
       718: 1
       725: 1
       726: 1
       785: 1
       793: 1
       801: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       866: 1
       870: 1
       871: 1
       928: 1
       929: 1
      1000: 1
      1026: 1
      1076: 1
      1234: 1

1235:    0: q^3+q^2+2q+2
         1: q^3+q^2+2q+2
         2: 2q^2+q+2
         3: q^3+q^2+2q+2
         4: q^3+q^2+2q+2
         5: q^3+q^2+2q+2
         6: q^3+q^2+2q+2
         7: 2q^2+q+2
         8: 2q^2+q+2
         9: 2q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^3+q^2+2q+2
        17: q^3+q^2+2q+2
        18: 2q^2+q+2
        19: q^3+q^2+2q+2
        20: q^3+q^2+2q+2
        21: 2q^2+q+2
        22: q^3+q^2+2q+2
        23: q^3+q^2+2q+2
        24: 2q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q^2+q+2
        31: 2q+2
        32: q^2+q+2
        33: q^3+q^2+2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^3+q^2+2q+2
        50: q^3+q^2+2q+2
        51: 2q^2+q+2
        52: q^3+q^2+2q+2
        53: q^3+q^2+2q+2
        54: 2q^2+q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q^2+q+2
        70: q+2
        71: 2q+2
        72: 2
        73: q^3+q^2+2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q^2+q+2
        82: 2q+2
        83: q^2+q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: q^3+q^2+2q+2
        95: q^3+q^2+2q+2
        96: 2q^2+q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q^2+q+2
       135: 2
       136: q^2+q+2
       137: q+2
       138: q^2+q+2
       139: 2q+2
       140: 2
       141: q+2
       142: q^3+q^2+2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+q+2
       161: q^2+q+2
       162: q^2+q+2
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2
       171: 1
       172: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2
       224: q+2
       225: q^2+q+2
       226: q+2
       227: 2
       228: q^2+q+2
       229: 2
       230: q^2+q+2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: q+2
       251: q+2
       252: q+2
       256: 1
       257: 1
       258: 1
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q^2+q+2
       351: 2
       352: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: 1
       469: 1
       470: 1
       472: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 1
       548: 1
       590: 1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 1
       642: 1
       657: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: 2
       677: 2
       679: 1
       719: 1
       720: 1
       727: 1
       728: 1
       786: 1
       794: 1
       802: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       866: 1
       870: 1
       871: 1
       930: 1
       931: 1
      1001: 1
      1027: 1
      1076: 1
      1235: 1

1236:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2q+2
        74: 2
        76: 2
        78: q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: 1
       202: 1
       207: 1
       209: 2
       211: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       233: 1
       234: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       467: 1
       469: 1
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: 1
       502: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       545: 1
       547: 1
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       637: 1
       658: 1
       660: 1
       662: 1
       664: 1
       666: 1
       668: 1
       670: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       687: 1
       690: 1
       691: 1
       692: 1
       779: 1
       783: 1
       795: 1
       799: 1
       809: 1
       811: 1
       813: 1
       859: 1
       861: 1
       863: 1
       867: 1
       869: 1
       870: 1
       872: 1
       996: 1
      1014: 1
      1020: 1
      1024: 1
      1077: 1
      1236: 1

1237:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2
        26: 2
        27: q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2
        56: 2
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2
        73: 2q+2
        75: 2
        77: 2
        79: q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: 1
        85: 1
        86: 2
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: 1
       202: 1
       208: 1
       210: 2
       212: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: 1
       233: 1
       234: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       468: 1
       470: 1
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: 1
       503: 1
       505: 1
       507: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       546: 1
       548: 1
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       638: 1
       659: 1
       661: 1
       663: 1
       664: 1
       667: 1
       669: 1
       671: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       687: 1
       690: 1
       691: 1
       692: 1
       780: 1
       784: 1
       796: 1
       800: 1
       810: 1
       812: 1
       814: 1
       860: 1
       862: 1
       864: 1
       867: 1
       869: 1
       870: 1
       872: 1
       997: 1
      1015: 1
      1021: 1
      1025: 1
      1077: 1
      1237: 1

1238:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: 4q^2+5q+2
         8: 4q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 4q^2+5q+2
        14: 4q^2+5q+2
        15: 4q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: 2q^2+2q+1
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: 4q^2+5q+2
        22: 4q^2+5q+2
        23: 4q^2+5q+2
        24: 4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: 4q^2+5q+2
        32: 4q^2+5q+2
        33: 4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 4q^2+5q+2
        44: 4q^2+5q+2
        45: 4q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: 2q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+2q+1
        52: 4q^2+5q+2
        53: 4q^2+5q+2
        54: 4q^2+5q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 4q+2
        69: q+1
        70: 4q^2+5q+2
        71: 4q+2
        72: 2q+2
        73: 4q+2
        74: q^2+3q+2
        76: q^2+3q+2
        78: q^2+3q+2
        80: 4q^2+5q+2
        81: 4q+2
        82: 4q^2+5q+2
        83: 4q^2+5q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: 2q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+3q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       111: 2q+2
       113: q^2+3q+2
       115: q^2+3q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 4q+2
       134: q+1
       135: 2q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 4q^2+5q+2
       142: 4q+2
       143: 2q+2
       144: 1
       145: 2
       146: q^2+3q+2
       147: 2
       149: q^2+3q+2
       150: q^2+3q+2
       151: q^2+3q+2
       153: q^2+3q+2
       155: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: 2q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: 2q+1
       186: 2q+1
       187: 2q+2
       189: q^2+3q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q^2+3q+2
       211: q^2+3q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 4q+2
       221: q+1
       222: 2q+2
       223: 1
       224: 4q+2
       225: q+1
       226: q+1
       227: 4q+2
       228: q+1
       229: 2q+2
       230: 4q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q^2+3q+2
       247: 2
       248: 2
       249: q+1
       250: 4q+2
       251: 4q+2
       252: 2q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: q+1
       266: q+1
       267: q+1
       269: q+1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+2
       299: q+1
       300: q+1
       301: 2
       303: 2q+1
       304: 2q+1
       305: 2q+2
       307: 1
       308: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q^2+3q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: 1
       349: 4q+2
       350: q+1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       389: 1
       391: 1
       393: q+1
       396: q+1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 2q+2
       443: 1
       444: 1
       445: 2
       453: 1
       454: 1
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: 1
       498: 1
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 1
       547: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       635: 2
       637: 1
       639: 1
       647: 1
       648: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: 1
       686: 1
       687: 1
       729: 1
       731: 1
       733: 1
       735: 1
       777: 1
       781: 1
       783: 1
       789: 2
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       841: 1
       868: 1
       871: 1
       872: 1
       877: 1
       932: 1
       934: 1
      1002: 1
      1018: 1
      1022: 1
      1024: 1
      1078: 1
      1238: 1

1239:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: 4q^2+5q+2
         8: 4q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 4q^2+5q+2
        14: 4q^2+5q+2
        15: 4q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: 2q^2+2q+1
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: 4q^2+5q+2
        22: 4q^2+5q+2
        23: 4q^2+5q+2
        24: 4q^2+5q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 4q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: 4q^2+5q+2
        32: 4q^2+5q+2
        33: 4q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 4q^2+5q+2
        44: 4q^2+5q+2
        45: 4q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: 2q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+2q+1
        52: 4q^2+5q+2
        53: 4q^2+5q+2
        54: 4q^2+5q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 4q+2
        69: q+1
        70: 4q^2+5q+2
        71: 4q+2
        72: 2q+2
        73: 4q+2
        75: q^2+3q+2
        77: q^2+3q+2
        79: q^2+3q+2
        80: 4q^2+5q+2
        81: 4q+2
        82: 4q^2+5q+2
        83: 4q^2+5q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: 2q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+3q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       112: 2q+2
       114: q^2+3q+2
       116: q^2+3q+2
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 4q+2
       134: q+1
       135: 2q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 4q^2+5q+2
       142: 4q+2
       143: 2q+2
       144: 1
       145: 2
       146: q^2+3q+2
       147: 2
       149: q^2+3q+2
       150: q^2+3q+2
       152: q^2+3q+2
       154: q^2+3q+2
       156: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: 2q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: 2q+1
       186: 2q+1
       188: 2q+2
       190: q^2+3q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q^2+3q+2
       212: q^2+3q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 4q+2
       221: q+1
       222: 2q+2
       223: 1
       224: 4q+2
       225: q+1
       226: q+1
       227: 4q+2
       228: q+1
       229: 2q+2
       230: 4q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q^2+3q+2
       247: 2
       248: 2
       249: q+1
       250: 4q+2
       251: 4q+2
       252: 2q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: q+1
       265: q+1
       268: q+1
       270: q+1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       298: 2q+2
       299: q+1
       300: q+1
       302: 2
       303: 2q+1
       304: 2q+1
       306: 2q+2
       307: 1
       308: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q^2+3q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: 1
       349: 4q+2
       350: q+1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       390: 1
       392: 1
       394: q+1
       395: q+1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 2q+2
       443: 1
       444: 1
       446: 2
       453: 1
       454: 1
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: 1
       498: 1
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: 1
       548: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       636: 2
       638: 1
       640: 1
       647: 1
       648: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: 1
       686: 1
       687: 1
       730: 1
       732: 1
       734: 1
       736: 1
       778: 1
       782: 1
       784: 1
       790: 2
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       842: 1
       868: 1
       871: 1
       872: 1
       877: 1
       933: 1
       935: 1
      1003: 1
      1019: 1
      1023: 1
      1025: 1
      1078: 1
      1239: 1

1240:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       319: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       385: 1
       386: 1
       393: 1
       394: 1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       447: 1
       453: 1
       471: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       541: 1
       542: 1
       589: 1
       593: 1
       603: 1
       615: 1
       619: 1
       641: 1
       647: 1
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       785: 1
       801: 1
       805: 1
       815: 1
       825: 1
       845: 1
       868: 1
       871: 1
       872: 1
       877: 1
      1004: 1
      1026: 1
      1052: 1
      1078: 1
      1240: 1

1241:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        25: 2
        26: 2
        27: 2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 1
       146: 2
       147: 1
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       243: 1
       244: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       320: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       387: 1
       388: 1
       395: 1
       396: 1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       448: 1
       454: 1
       472: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       543: 1
       544: 1
       590: 1
       594: 1
       604: 1
       616: 1
       620: 1
       642: 1
       648: 1
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       786: 1
       802: 1
       806: 1
       816: 1
       826: 1
       846: 1
       868: 1
       871: 1
       872: 1
       877: 1
      1005: 1
      1027: 1
      1053: 1
      1078: 1
      1241: 1

1242:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: 4q^2+6q+2
        14: 4q^2+6q+2
        15: 4q^2+6q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: 2q^2+2q+1
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+6q^2+6q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+6q+2
        28: q^2+6q+2
        29: q^3+7q^2+8q+2
        30: 4q^2+6q+2
        31: q^3+7q^2+8q+2
        32: 4q^2+6q+2
        33: q^2+6q+2
        34: 4q^2+8q+2
        35: 2q^2+6q+2
        36: 6q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: q^2+6q+2
        50: q^2+6q+2
        51: 2q^2+2q+1
        52: q^3+7q^2+8q+2
        53: q^3+7q^2+8q+2
        54: q^3+6q^2+6q+2
        55: 4q^2+8q+2
        56: 4q^2+8q+2
        57: 4q^2+6q+2
        58: q^2+4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q^2+6q+2
        71: q^2+6q+2
        72: 6q+2
        73: q^2+6q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 4q^2+6q+2
        81: 4q+2
        82: q^3+7q^2+8q+2
        83: 4q^2+6q+2
        84: 2q^2+6q+2
        85: 4q+2
        86: 4q^2+8q+2
        87: 2q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: q^2+2q+1
        94: q^2+6q+2
        95: q^2+6q+2
        96: 2q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q^2+8q+2
       101: 4q^2+8q+2
       102: 4q^2+6q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: 3q+1
       108: 3q+1
       109: q^2+4q+2
       110: 2q
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: q^2+6q+2
       140: 6q+2
       141: 4q^2+6q+2
       142: q^2+6q+2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 2q^2+6q+2
       147: 4q+2
       148: 2q+2
       149: 4q^2+8q+2
       150: 2q^2+6q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 4q+2
       158: 4q+2
       159: q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: q^2+2q+1
       163: q+2
       164: q+2
       165: q+1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: q+1
       175: q+1
       183: q+1
       184: q+1
       185: 2q+2
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 2q+2
       193: 3q+1
       194: 3q+1
       195: q^2+4q+2
       196: 2q
       197: 3q+1
       198: 3q+1
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 1
       220: 2q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 4q+2
       230: 4q+2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 4q+2
       244: 4q+2
       245: 2q+2
       246: 2q^2+6q+2
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       263: q+1
       265: q+1
       267: 2q+1
       268: q
       269: q
       270: 2q+1
       271: q+1
       272: q+1
       275: q+1
       277: q+1
       285: 1
       293: q+1
       294: q+1
       295: 2q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       303: 2q+2
       305: 2q+1
       306: 2q+1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       319: 2q+1
       320: 2q+1
       321: 2q+2
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 4q+2
       344: 1
       345: 2q+2
       346: q+1
       347: 4q+2
       348: q+1
       349: 4q+2
       350: q+1
       351: 4q+2
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 2q+2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       385: q+1
       387: q+1
       393: q+1
       395: q+1
       401: 1
       402: 1
       405: q+1
       408: q+1
       421: 1
       431: 1
       437: q+1
       438: q+1
       439: 2q+2
       441: 2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2q+2
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 2
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: q+2
       512: 1
       513: 2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       541: q+1
       544: q+1
       557: 1
       558: 1
       565: 1
       567: 1
       573: q+1
       576: q+1
       591: 1
       595: 1
       607: 1
       615: 1
       616: 1
       621: 1
       631: 2
       643: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: q+1
       678: q+2
       679: 1
       681: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       803: 1
       807: 1
       815: 1
       816: 1
       827: 1
       839: 2
       847: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: 1
       879: 1
       880: 1
       988: 1
       990: 1
      1006: 1
      1028: 1
      1054: 1
      1078: 1
      1085: 1
      1242: 1

1243:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: 4q^2+6q+2
        14: 4q^2+6q+2
        15: 4q^2+6q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: 2q^2+2q+1
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+6q^2+6q+2
        22: q^3+7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+6q+2
        28: q^2+6q+2
        29: q^3+7q^2+8q+2
        30: 4q^2+6q+2
        31: q^3+7q^2+8q+2
        32: 4q^2+6q+2
        33: q^2+6q+2
        34: 4q^2+8q+2
        35: 2q^2+6q+2
        36: 6q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: q^2+6q+2
        50: q^2+6q+2
        51: 2q^2+2q+1
        52: q^3+7q^2+8q+2
        53: q^3+7q^2+8q+2
        54: q^3+6q^2+6q+2
        55: 4q^2+8q+2
        56: 4q^2+8q+2
        57: 4q^2+6q+2
        58: 2q
        59: q^2+4q+2
        60: 3q+1
        61: 3q+1
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q^2+6q+2
        71: q^2+6q+2
        72: 6q+2
        73: q^2+6q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 4q^2+6q+2
        81: 4q+2
        82: q^3+7q^2+8q+2
        83: 4q^2+6q+2
        84: 2q^2+6q+2
        85: 4q+2
        86: 4q^2+8q+2
        87: 2q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: q^2+2q+1
        94: q^2+6q+2
        95: q^2+6q+2
        96: 2q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 4q^2+8q+2
       101: 4q^2+8q+2
       102: 4q^2+6q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: 3q+1
       108: 3q+1
       109: 2q
       110: q^2+4q+2
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: q^2+6q+2
       140: 6q+2
       141: 4q^2+6q+2
       142: q^2+6q+2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 2q^2+6q+2
       147: 4q+2
       148: 2q+2
       149: 4q^2+8q+2
       150: 2q^2+6q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 4q+2
       158: 4q+2
       159: q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: q^2+2q+1
       163: q+2
       164: q+2
       165: q+1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       174: q+1
       176: q+1
       183: q+1
       184: q+1
       186: 2q+2
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       192: 2q+2
       193: 3q+1
       194: 3q+1
       195: 2q
       196: q^2+4q+2
       197: 3q+1
       198: 3q+1
       199: q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       204: 2q+2
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 1
       220: 2q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 4q+2
       230: 4q+2
       231: q+1
       232: 2
       233: 1
       234: q+2
       235: 2
       236: q+1
       243: 4q+2
       244: 4q+2
       245: 2q+2
       246: 2q^2+6q+2
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       264: q+1
       266: q+1
       267: q
       268: 2q+1
       269: 2q+1
       270: q
       273: q+1
       274: q+1
       276: q+1
       278: q+1
       286: 1
       293: q+1
       294: q+1
       296: 2q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       304: 2q+2
       305: 2q+1
       306: 2q+1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       319: 2q+1
       320: 2q+1
       322: 2q+2
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 4q+2
       344: 1
       345: 2q+2
       346: q+1
       347: 4q+2
       348: q+1
       349: 4q+2
       350: q+1
       351: 4q+2
       352: 1
       353: 2
       354: 1
       355: q+2
       356: 1
       357: 2
       358: 1
       359: 2q+2
       366: q+1
       367: 2
       368: 1
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       386: q+1
       388: q+1
       394: q+1
       396: q+1
       403: 1
       404: 1
       406: q+1
       407: q+1
       422: 1
       432: 1
       437: q+1
       438: q+1
       440: 2q+2
       441: 2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2q+2
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 2
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: q+2
       512: 1
       513: 2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       542: q+1
       543: q+1
       559: 1
       560: 1
       566: 1
       568: 1
       574: q+1
       575: q+1
       592: 1
       596: 1
       608: 1
       615: 1
       616: 1
       622: 1
       632: 2
       644: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: q+1
       678: q+2
       679: 1
       681: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       804: 1
       808: 1
       815: 1
       816: 1
       828: 1
       840: 2
       848: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: 1
       879: 1
       880: 1
       989: 1
       991: 1
      1007: 1
      1029: 1
      1055: 1
      1078: 1
      1085: 1
      1243: 1

1244:    0: q^3+4q^2+5q+2
         1: q^3+4q^2+5q+2
         2: q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: q^3+4q^2+5q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: q^3+4q^2+5q+2
         9: q^3+2q^2+2q+1
        10: q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: q^3+3q^2+4q+2
        13: q^3+4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: q^3+4q^2+5q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: 2q^2+4q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^3+4q^2+5q+2
        26: q^3+4q^2+5q+2
        27: q^3+4q^2+5q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: 2q^2+4q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^3+4q^2+5q+2
        35: q^3+4q^2+5q+2
        36: 2q^2+4q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: q^3+4q^2+5q+2
        44: q^3+3q^2+4q+2
        45: q^3+4q^2+5q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^2+2q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: 2q^2+4q+2
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 2q^2+4q+2
        69: q+1
        70: 2q^2+4q+2
        71: q^2+3q+2
        72: 2q+2
        73: 2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^3+4q^2+5q+2
        85: 2q^2+4q+2
        86: 2q^2+4q+2
        87: 2q^2+4q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^2+2q+1
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+2q+1
        94: q+2
        95: q+2
        96: q+1
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: 2q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+3q+2
       123: 2q+2
       125: 2q^2+4q+2
       126: q+1
       127: q+2
       129: q+2
       131: q+1
       133: q^2+3q+2
       134: q+1
       135: 2q+2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       141: 2q+2
       142: 2
       143: 2q^2+4q+2
       144: q+1
       145: q^2+3q+2
       146: 2q^2+4q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: q+2
       181: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: 2q+2
       211: 2q+2
       213: q+2
       215: q+2
       217: q+1
       219: q+1
       220: q^2+3q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       230: 2
       231: q+1
       232: q^2+3q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       250: q+2
       251: q+2
       252: q+1
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: q+2
       321: 1
       322: 1
       325: 2q+2
       327: q+2
       329: q+2
       331: q+1
       333: q+1
       334: q+1
       335: 1
       337: 2
       338: 2
       340: 2
       344: 1
       345: q+2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: q^2+3q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       370: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       409: q+2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       427: 2
       439: 1
       440: 1
       451: 1
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: 1
       469: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       484: 2
       485: 2
       487: 2
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 2
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       513: 2
       514: 1
       515: 1
       516: 1
       518: 2
       519: 2
       525: 1
       528: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       583: 1
       585: 1
       587: 1
       601: 2
       623: 1
       625: 1
       627: 2
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 1
       639: 1
       649: 1
       650: 1
       658: 1
       660: 1
       666: 2
       668: 2
       672: 2
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 2
       686: 1
       688: 1
       690: 1
       691: 1
       745: 1
       747: 1
       749: 1
       751: 1
       777: 1
       789: 2
       819: 1
       821: 1
       823: 1
       837: 2
       839: 1
       840: 1
       841: 1
       859: 1
       861: 1
       873: 1
       878: 1
       881: 1
       882: 1
       956: 1
       958: 1
      1030: 1
      1034: 1
      1066: 1
      1068: 1
      1079: 1
      1244: 1

1245:    0: q^3+4q^2+5q+2
         1: q^3+4q^2+5q+2
         2: q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: q^3+4q^2+5q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: q^3+4q^2+5q+2
         9: q^3+2q^2+2q+1
        10: q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: q^3+3q^2+4q+2
        13: q^3+4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: q^3+4q^2+5q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^2+2q+1
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: 2q^2+4q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^3+4q^2+5q+2
        26: q^3+4q^2+5q+2
        27: q^3+4q^2+5q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: 2q^2+4q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^3+4q^2+5q+2
        35: q^3+4q^2+5q+2
        36: 2q^2+4q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: q^3+4q^2+5q+2
        44: q^3+3q^2+4q+2
        45: q^3+4q^2+5q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^2+2q+1
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: 2q^2+4q+2
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 2q^2+4q+2
        69: q+1
        70: 2q^2+4q+2
        71: q^2+3q+2
        72: 2q+2
        73: 2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^3+4q^2+5q+2
        85: 2q^2+4q+2
        86: 2q^2+4q+2
        87: 2q^2+4q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^2+2q+1
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+2q+1
        94: q+2
        95: q+2
        96: q+1
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: 2q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       122: q^2+3q+2
       124: 2q+2
       125: 2q^2+4q+2
       126: q+1
       128: q+2
       130: q+2
       132: q+1
       133: q^2+3q+2
       134: q+1
       135: 2q+2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       141: 2q+2
       142: 2
       143: 2q^2+4q+2
       144: q+1
       145: q^2+3q+2
       146: 2q^2+4q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: q+2
       182: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: 2q+2
       212: 2q+2
       214: q+2
       216: q+2
       218: q+1
       219: q+1
       220: q^2+3q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       230: 2
       231: q+1
       232: q^2+3q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       250: q+2
       251: q+2
       252: q+1
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: q+1
       294: q+1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: q+2
       321: 1
       322: 1
       326: 2q+2
       328: q+2
       330: q+2
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 2
       339: 2
       341: 2
       344: 1
       345: q+2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: q^2+3q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       370: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       410: q+2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       428: 2
       439: 1
       440: 1
       452: 1
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: 1
       470: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       484: 2
       486: 2
       488: 2
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       501: 2
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       513: 2
       514: 1
       515: 1
       516: 1
       518: 2
       519: 2
       526: 1
       527: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       584: 1
       586: 1
       588: 1
       602: 2
       624: 1
       626: 1
       628: 2
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 1
       640: 1
       649: 1
       650: 1
       659: 1
       661: 1
       667: 2
       669: 2
       672: 2
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 2
       686: 1
       688: 1
       690: 1
       691: 1
       746: 1
       748: 1
       750: 1
       752: 1
       778: 1
       790: 2
       820: 1
       822: 1
       824: 1
       838: 2
       839: 1
       840: 1
       842: 1
       860: 1
       862: 1
       873: 1
       878: 1
       881: 1
       882: 1
       957: 1
       959: 1
      1031: 1
      1035: 1
      1067: 1
      1069: 1
      1079: 1
      1245: 1

1246:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+7q^2+8q+2
         3: q^3+7q^2+8q+2
         4: q^3+4q^2+5q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+6q^2+5q+2
         7: q^3+4q^2+5q+2
         8: q^3+7q^2+8q+2
         9: q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^3+7q^2+8q+2
        14: q^3+4q^2+5q+2
        15: q^3+7q^2+8q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^2+5q+2
        20: 3q^2+5q+2
        21: q^2+5q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+7q^2+8q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 2q^2+6q+2
        32: 4q^2+6q+2
        33: 4q^2+6q+2
        34: 4q^2+8q+2
        35: q^3+7q^2+8q+2
        36: q^3+7q^2+8q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+8q+2
        44: q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: q^3+7q^2+8q+2
        47: q^3+7q^2+8q+2
        48: q^3+4q^2+5q+2
        49: q^2+5q+2
        50: 3q^2+5q+2
        51: q^2+5q+2
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: q^2+5q+2
        56: 3q^2+5q+2
        57: q^2+5q+2
        58: 2q^2+4q+2
        59: 2q
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q^2+6q+2
        81: 4q^2+6q+2
        82: 3q+2
        83: 3q+2
        84: 4q^2+8q+2
        85: q^3+7q^2+8q+2
        86: q^2+5q+2
        87: q^2+5q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: q^3+4q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: 3q+2
        95: q^2+3q+2
        96: 3q+2
        97: q^2+5q+2
        98: 3q^2+5q+2
        99: q^2+5q+2
       100: 3q+2
       101: q^2+3q+2
       102: 3q+2
       103: q^2+2q+1
       104: q
       105: q^2+2q+1
       106: q
       107: q+1
       108: q+1
       109: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q^2+4q+2
       118: 2q
       119: 2q^2+4q+1
       120: 2q^2+4q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 4q^2+8q+2
       126: q^2+5q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+5q+2
       134: q^2+5q+2
       135: 2q+2
       136: q+2
       137: 2q^2+6q+2
       138: 3q+2
       139: 3q+2
       141: 3q+2
       142: q+2
       143: 4q^2+8q+2
       144: q^2+5q+2
       145: q^2+5q+2
       146: q^2+5q+2
       147: 2q+2
       148: q+2
       149: 3q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: q^2+5q+2
       164: 3q^2+5q+2
       165: q^2+5q+2
       166: 3q+2
       167: q^2+3q+2
       168: 3q+2
       169: 1
       171: 1
       173: q^2+2q+1
       174: q
       175: q^2+2q+1
       176: q
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+1
       184: q+1
       185: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q^2+4q+2
       192: 2q
       195: q+2
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q+1
       202: q+1
       203: q+2
       205: 1
       206: 1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+5q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: 2q+2
       224: 2
       225: q+2
       226: 3q+2
       227: 3q+2
       228: 3q+2
       230: q+2
       231: q^2+5q+2
       232: q^2+5q+2
       233: q^2+5q+2
       234: 2q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       245: q+2
       246: 3q+2
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: q^2+2q+1
       276: q
       277: q^2+2q+1
       278: q
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+2
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: q+2
       307: q+1
       308: q+1
       309: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       321: q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+2
       345: q+1
       346: q+1
       349: 1
       350: q+2
       352: q^2+5q+2
       353: 2q+2
       354: 2q+2
       355: 2
       356: 2q+2
       357: 2
       358: q+2
       359: 2
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 3q+2
       368: 3q+2
       370: q+2
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       377: 1
       379: 1
       381: 1
       383: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       427: 1
       428: 1
       431: q+2
       439: 1
       447: q+1
       448: q+1
       449: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 2
       459: 1
       460: 1
       461: 2
       463: 1
       464: 1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       473: q+2
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       494: 1
       497: 2q+2
       498: 2
       499: 2
       501: 2
       508: 3q+2
       509: q+1
       510: q+1
       513: 1
       514: q+2
       515: 2
       516: 2
       518: 1
       519: 1
       521: 1
       523: 1
       529: 1
       531: 1
       549: 1
       550: 1
       553: 1
       554: 1
       557: 1
       558: 1
       561: 1
       562: 1
       585: 1
       586: 1
       589: 1
       590: 1
       595: 2
       601: 1
       602: 1
       607: 1
       619: 1
       620: 1
       621: 2
       623: 1
       624: 1
       625: 1
       626: 1
       631: 2
       633: 1
       634: 1
       639: q+1
       640: q+1
       643: q+2
       649: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       676: 1
       680: 2
       681: 2
       682: 2
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       709: 1
       711: 1
       737: 1
       738: 1
       741: 1
       742: 1
       749: 1
       750: 1
       775: 1
       776: 1
       807: 1
       817: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: 1
       826: 1
       831: 2
       839: 1
       847: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       940: 1
       941: 1
       944: 1
       945: 1
      1032: 1
      1058: 1
      1072: 1
      1079: 1
      1246: 1

1247:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+7q^2+8q+2
         3: q^3+7q^2+8q+2
         4: q^3+4q^2+5q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+6q^2+5q+2
         7: q^3+4q^2+5q+2
         8: q^3+7q^2+8q+2
         9: q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: q^3+4q^2+5q+2
        13: q^3+7q^2+8q+2
        14: q^3+4q^2+5q+2
        15: q^3+7q^2+8q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: q^2+5q+2
        20: 3q^2+5q+2
        21: q^2+5q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+7q^2+8q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 2q^2+6q+2
        32: 4q^2+6q+2
        33: 4q^2+6q+2
        34: 4q^2+8q+2
        35: q^3+7q^2+8q+2
        36: q^3+7q^2+8q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+8q+2
        44: q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: q^3+7q^2+8q+2
        47: q^3+7q^2+8q+2
        48: q^3+4q^2+5q+2
        49: q^2+5q+2
        50: 3q^2+5q+2
        51: q^2+5q+2
        52: 3q+2
        53: q^2+3q+2
        54: 3q+2
        55: q^2+5q+2
        56: 3q^2+5q+2
        57: q^2+5q+2
        58: 2q
        59: 2q^2+4q+2
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: 2q+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q^2+6q+2
        81: 4q^2+6q+2
        82: 3q+2
        83: 3q+2
        84: 4q^2+8q+2
        85: q^3+7q^2+8q+2
        86: q^2+5q+2
        87: q^2+5q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: q^3+4q^2+5q+2
        91: q^2+5q+2
        92: 3q^2+5q+2
        93: q^2+5q+2
        94: 3q+2
        95: q^2+3q+2
        96: 3q+2
        97: q^2+5q+2
        98: 3q^2+5q+2
        99: q^2+5q+2
       100: 3q+2
       101: q^2+3q+2
       102: 3q+2
       103: q
       104: q^2+2q+1
       105: q
       106: q^2+2q+1
       107: q+1
       108: q+1
       110: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q
       118: 2q^2+4q+2
       119: 2q^2+4q+1
       120: 2q^2+4q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 4q^2+8q+2
       126: q^2+5q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+5q+2
       134: q^2+5q+2
       135: 2q+2
       136: q+2
       137: 2q^2+6q+2
       138: 3q+2
       139: 3q+2
       141: 3q+2
       142: q+2
       143: 4q^2+8q+2
       144: q^2+5q+2
       145: q^2+5q+2
       146: q^2+5q+2
       147: 2q+2
       148: q+2
       149: 3q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: q^2+5q+2
       164: 3q^2+5q+2
       165: q^2+5q+2
       166: 3q+2
       167: q^2+3q+2
       168: 3q+2
       170: 1
       172: 1
       173: q
       174: q^2+2q+1
       175: q
       176: q^2+2q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+1
       184: q+1
       186: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q
       192: 2q^2+4q+2
       196: q+2
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q+1
       202: q+1
       204: q+2
       205: 1
       206: 1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+5q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: 2q+2
       224: 2
       225: q+2
       226: 3q+2
       227: 3q+2
       228: 3q+2
       230: q+2
       231: q^2+5q+2
       232: q^2+5q+2
       233: q^2+5q+2
       234: 2q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 3q+2
       245: q+2
       246: 3q+2
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       275: q
       276: q^2+2q+1
       277: q
       278: q^2+2q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       286: q+2
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: q+2
       307: q+1
       308: q+1
       310: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       322: q+2
       325: q+1
       326: q+1
       333: 2q+2
       334: 2
       335: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+2
       345: q+1
       346: q+1
       349: 1
       350: q+2
       352: q^2+5q+2
       353: 2q+2
       354: 2q+2
       355: 2
       356: 2q+2
       357: 2
       358: q+2
       359: 2
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 3q+2
       368: 3q+2
       370: q+2
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       378: 1
       380: 1
       382: 1
       384: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       427: 1
       428: 1
       432: q+2
       440: 1
       447: q+1
       448: q+1
       450: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 2
       459: 1
       460: 1
       462: 2
       463: 1
       464: 1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       474: q+2
       481: 2
       482: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       494: 1
       497: 2q+2
       498: 2
       499: 2
       501: 2
       508: 3q+2
       509: q+1
       510: q+1
       513: 1
       514: q+2
       515: 2
       516: 2
       518: 1
       519: 1
       522: 1
       524: 1
       530: 1
       532: 1
       551: 1
       552: 1
       555: 1
       556: 1
       559: 1
       560: 1
       563: 1
       564: 1
       585: 1
       586: 1
       589: 1
       590: 1
       596: 2
       601: 1
       602: 1
       608: 1
       619: 1
       620: 1
       622: 2
       623: 1
       624: 1
       625: 1
       626: 1
       632: 2
       633: 1
       634: 1
       639: q+1
       640: q+1
       644: q+2
       650: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       676: 1
       680: 2
       681: 2
       682: 2
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       710: 1
       712: 1
       739: 1
       740: 1
       743: 1
       744: 1
       751: 1
       752: 1
       775: 1
       776: 1
       808: 1
       818: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: 1
       826: 1
       832: 2
       840: 1
       848: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       942: 1
       943: 1
       946: 1
       947: 1
      1033: 1
      1059: 1
      1072: 1
      1079: 1
      1247: 1

1248:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: 4q^2+5q+2
         6: 2q^3+4q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 4q^2+5q+2
         9: q^3+3q^2+4q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: 4q^2+5q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 2q^2+4q+2
        20: 3q^2+4q+2
        21: 2q^2+4q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 4q^2+5q+2
        26: 4q^2+5q+2
        27: 4q^2+5q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+4q+2
        31: 2q+2
        32: q^2+3q+2
        33: q^2+3q+2
        34: 4q+2
        35: 4q^2+5q+2
        36: 4q^2+5q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+5q+2
        47: 4q^2+5q+2
        48: q^3+3q^2+4q+2
        49: 2q^2+4q+2
        50: 3q^2+4q+2
        51: 2q^2+4q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+4q+2
        56: 3q^2+4q+2
        57: 2q^2+4q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+2
        64: q^2+3q+2
        66: q^2+3q+2
        68: 4q+2
        69: 2q^2+4q+2
        70: 3q+2
        71: 3q+2
        72: q^2+3q+2
        73: q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 2q+2
        81: q^2+3q+2
        82: q+2
        83: 2q+2
        84: 4q+2
        85: 4q^2+5q+2
        86: 3q+2
        87: 2q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 2q+2
        95: 2q+2
        96: 2q+2
        97: 2q^2+4q+2
        98: 3q^2+4q+2
        99: 2q^2+4q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+2
       113: q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       121: 2q+2
       123: q^2+3q+2
       125: 4q+2
       126: 3q+2
       127: 2q+2
       129: 2q+2
       131: 2q+2
       133: 3q+2
       134: 2q^2+4q+2
       135: q^2+3q+2
       136: q+2
       137: 2q+2
       138: 2q+2
       139: q+2
       141: q+2
       142: q+2
       143: 4q+2
       144: 2q^2+4q+2
       145: 3q+2
       146: 3q+2
       147: q^2+3q+2
       148: q+2
       149: q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q^2+4q+2
       164: 3q^2+4q+2
       165: 2q^2+4q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 2q+2
       179: q+2
       181: q+2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: q+2
       189: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+2
       207: 2q+2
       209: q+2
       211: 2q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: 2
       225: q+2
       226: q+2
       227: q+2
       228: 2q+2
       230: q+2
       231: 3q+2
       232: 3q+2
       233: 2q^2+4q+2
       234: q^2+3q+2
       235: q+2
       236: 2q+2
       237: 2q+2
       239: 2q+2
       241: 2q+2
       243: q+2
       245: q+2
       246: q+2
       247: 2
       248: 2
       249: q+1
       253: q+2
       254: q+2
       255: q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: 2q+2
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: q+2
       289: q+2
       291: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+2
       313: q+2
       315: 2q+2
       317: q+2
       321: 1
       322: 1
       325: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q+2
       350: q+2
       352: 3q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: 2
       358: q+2
       359: 2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: q+2
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       413: q+2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 2
       431: 1
       432: 1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+2
       453: 1
       454: 1
       455: q+2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: 2q+2
       469: q+2
       473: 1
       474: 1
       481: 2
       482: 2
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 2
       508: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       521: 1
       524: 1
       529: 1
       532: 1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 2
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+2
       625: 2
       629: 1
       631: 1
       632: 1
       633: 2
       639: q+2
       643: 1
       644: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       680: 2
       681: 2
       682: 2
       683: 1
       685: 1
       709: 1
       712: 1
       737: 1
       739: 1
       741: 1
       743: 1
       749: 1
       751: 1
       775: 2
       779: 1
       781: 1
       817: 1
       818: 1
       819: 2
       821: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       835: 1
       866: 1
       874: 1
       875: 1
       940: 1
       942: 1
       944: 1
       946: 1
       994: 1
      1036: 1
      1038: 1
      1080: 1
      1248: 1

1249:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: q^3+3q^2+4q+2
         5: 4q^2+5q+2
         6: 2q^3+4q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 4q^2+5q+2
         9: q^3+3q^2+4q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+5q+2
        14: q^3+3q^2+4q+2
        15: 4q^2+5q+2
        16: 4q^2+5q+2
        17: 4q^2+5q+2
        18: q^3+3q^2+4q+2
        19: 2q^2+4q+2
        20: 3q^2+4q+2
        21: 2q^2+4q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 4q^2+5q+2
        26: 4q^2+5q+2
        27: 4q^2+5q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+4q+2
        31: 2q+2
        32: q^2+3q+2
        33: q^2+3q+2
        34: 4q+2
        35: 4q^2+5q+2
        36: 4q^2+5q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+5q+2
        47: 4q^2+5q+2
        48: q^3+3q^2+4q+2
        49: 2q^2+4q+2
        50: 3q^2+4q+2
        51: 2q^2+4q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q^2+4q+2
        56: 3q^2+4q+2
        57: 2q^2+4q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: 2q+2
        65: q^2+3q+2
        67: q^2+3q+2
        68: 4q+2
        69: 2q^2+4q+2
        70: 3q+2
        71: 3q+2
        72: q^2+3q+2
        73: q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 2q+2
        81: q^2+3q+2
        82: q+2
        83: 2q+2
        84: 4q+2
        85: 4q^2+5q+2
        86: 3q+2
        87: 2q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+4q+2
        92: 3q^2+4q+2
        93: 2q^2+4q+2
        94: 2q+2
        95: 2q+2
        96: 2q+2
        97: 2q^2+4q+2
        98: 3q^2+4q+2
        99: 2q^2+4q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: q+2
       114: q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       122: 2q+2
       124: q^2+3q+2
       125: 4q+2
       126: 3q+2
       128: 2q+2
       130: 2q+2
       132: 2q+2
       133: 3q+2
       134: 2q^2+4q+2
       135: q^2+3q+2
       136: q+2
       137: 2q+2
       138: 2q+2
       139: q+2
       141: q+2
       142: q+2
       143: 4q+2
       144: 2q^2+4q+2
       145: 3q+2
       146: 3q+2
       147: q^2+3q+2
       148: q+2
       149: q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q^2+4q+2
       164: 3q^2+4q+2
       165: 2q^2+4q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 2q+2
       180: q+2
       182: q+2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: q+2
       190: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: q+2
       208: 2q+2
       210: q+2
       212: 2q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: 2
       225: q+2
       226: q+2
       227: q+2
       228: 2q+2
       230: q+2
       231: 3q+2
       232: 3q+2
       233: 2q^2+4q+2
       234: q^2+3q+2
       235: q+2
       236: 2q+2
       238: 2q+2
       240: 2q+2
       242: 2q+2
       243: q+2
       245: q+2
       246: q+2
       247: 2
       248: 2
       249: q+1
       253: q+2
       254: q+2
       255: q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: 2q+2
       283: q+1
       284: q+1
       285: 1
       286: 1
       288: q+2
       290: q+2
       292: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: q+2
       314: q+2
       316: 2q+2
       318: q+2
       321: 1
       322: 1
       326: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q+2
       350: q+2
       352: 3q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: 2
       358: q+2
       359: 2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: q+2
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       414: q+2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 2
       431: 1
       432: 1
       447: q+1
       448: q+1
       449: 1
       450: 1
       452: q+2
       453: 1
       454: 1
       456: q+2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: 2q+2
       470: q+2
       473: 1
       474: 1
       481: 2
       482: 2
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 2
       508: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       522: 1
       523: 1
       530: 1
       531: 1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 2
       619: 1
       620: 1
       621: 1
       622: 1
       624: q+2
       626: 2
       630: 1
       631: 1
       632: 1
       634: 2
       640: q+2
       643: 1
       644: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       680: 2
       681: 2
       682: 2
       683: 1
       685: 1
       710: 1
       711: 1
       738: 1
       740: 1
       742: 1
       744: 1
       750: 1
       752: 1
       776: 2
       780: 1
       782: 1
       817: 1
       818: 1
       820: 2
       822: 2
       825: 1
       826: 1
       831: 1
       832: 1
       834: 1
       836: 1
       866: 1
       874: 1
       875: 1
       941: 1
       943: 1
       945: 1
       947: 1
       995: 1
      1037: 1
      1039: 1
      1080: 1
      1249: 1

1250:    0: q^3+q^2+2q+2
         1: q^3+q^2+2q+2
         2: 2q^2+q+2
         3: q^3+q^2+2q+2
         4: q^3+q^2+2q+2
         5: q^3+q^2+2q+2
         6: q^3+q^2+2q+2
         7: 2q^2+q+2
         8: 2q^2+q+2
         9: 2q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^3+q^2+2q+2
        17: q^3+q^2+2q+2
        18: 2q^2+q+2
        19: q^3+q^2+2q+2
        20: q^3+q^2+2q+2
        21: 2q^2+q+2
        22: 2
        23: 2
        24: 2
        25: q^3+q^2+2q+2
        26: q^3+q^2+2q+2
        27: 2q^2+q+2
        28: 2q+2
        29: 2q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q^2+q+2
        36: q^3+q^2+2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^3+q^2+2q+2
        50: q^3+q^2+2q+2
        51: 2q^2+q+2
        52: 2
        53: 2
        54: 2
        55: q^3+q^2+2q+2
        56: q^3+q^2+2q+2
        57: 2q^2+q+2
        58: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q^2+q+2
        70: q+2
        71: 2q+2
        72: q^3+q^2+2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q^2+q+2
        86: 2q+2
        87: q^2+q+2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: 2
        95: 2
        96: 2
        97: q^3+q^2+2q+2
        98: q^3+q^2+2q+2
        99: 2q^2+q+2
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: q+1
       108: q+1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q^2+q+2
       135: q^2+q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: q+2
       144: q^2+q+2
       145: 2q+2
       146: q+2
       147: q^3+q^2+2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: q^2+q+2
       164: q^2+q+2
       165: q^2+q+2
       166: 2
       167: 2
       168: 2
       169: 1
       171: 1
       173: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: q^2+q+2
       224: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: q^2+q+2
       234: q^2+q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       283: 1
       284: 1
       285: 2
       287: 1
       288: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       321: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       350: 1
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q^2+q+2
       357: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       377: 1
       379: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       431: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       463: 1
       464: 1
       469: 1
       470: 1
       473: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       529: 1
       531: 1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 1
       562: 1
       589: 1
       590: 1
       591: 2
       595: 1
       599: 1
       600: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       643: 1
       657: 1
       664: 1
       665: 1
       680: 1
       681: 2
       682: 1
       683: 2
       685: 1
       713: 1
       714: 1
       741: 1
       742: 1
       787: 1
       817: 1
       825: 1
       826: 1
       827: 2
       831: 1
       835: 1
       836: 1
       866: 1
       874: 1
       875: 1
       948: 1
       949: 1
       998: 1
      1044: 1
      1080: 1
      1250: 1

1251:    0: q^3+q^2+2q+2
         1: q^3+q^2+2q+2
         2: 2q^2+q+2
         3: q^3+q^2+2q+2
         4: q^3+q^2+2q+2
         5: q^3+q^2+2q+2
         6: q^3+q^2+2q+2
         7: 2q^2+q+2
         8: 2q^2+q+2
         9: 2q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^3+q^2+2q+2
        17: q^3+q^2+2q+2
        18: 2q^2+q+2
        19: q^3+q^2+2q+2
        20: q^3+q^2+2q+2
        21: 2q^2+q+2
        22: 2
        23: 2
        24: 2
        25: q^3+q^2+2q+2
        26: q^3+q^2+2q+2
        27: 2q^2+q+2
        28: 2q+2
        29: 2q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q^2+q+2
        36: q^3+q^2+2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^3+q^2+2q+2
        50: q^3+q^2+2q+2
        51: 2q^2+q+2
        52: 2
        53: 2
        54: 2
        55: q^3+q^2+2q+2
        56: q^3+q^2+2q+2
        57: 2q^2+q+2
        59: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q^2+q+2
        70: q+2
        71: 2q+2
        72: q^3+q^2+2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q^2+q+2
        86: 2q+2
        87: q^2+q+2
        88: q+2
        89: q+2
        90: q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: 2
        95: 2
        96: 2
        97: q^3+q^2+2q+2
        98: q^3+q^2+2q+2
        99: 2q^2+q+2
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: q+1
       108: q+1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q^2+q+2
       135: q^2+q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: q+2
       144: q^2+q+2
       145: 2q+2
       146: q+2
       147: q^3+q^2+2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: q^2+q+2
       164: q^2+q+2
       165: q^2+q+2
       166: 2
       167: 2
       168: 2
       170: 1
       172: 1
       174: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 2
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: q^2+q+2
       224: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: q^2+q+2
       234: q^2+q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       283: 1
       284: 1
       286: 2
       287: 1
       288: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       350: 1
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q^2+q+2
       357: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       378: 1
       380: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       432: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       463: 1
       464: 1
       469: 1
       470: 1
       474: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       530: 1
       532: 1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 1
       564: 1
       589: 1
       590: 1
       592: 2
       596: 1
       599: 1
       600: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 1
       644: 1
       657: 1
       664: 1
       665: 1
       680: 1
       681: 2
       682: 1
       683: 2
       685: 1
       715: 1
       716: 1
       743: 1
       744: 1
       788: 1
       818: 1
       825: 1
       826: 1
       828: 2
       832: 1
       835: 1
       836: 1
       866: 1
       874: 1
       875: 1
       950: 1
       951: 1
       999: 1
      1045: 1
      1080: 1
      1251: 1

1252:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2
        39: 2
        41: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 2
        64: 1
        66: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2q+2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: q+1
       127: 2
       129: 2
       131: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 1
       209: 2
       211: 1
       213: 1
       215: 1
       217: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       311: 2
       313: 1
       315: 1
       317: 2
       321: 1
       322: 1
       325: 1
       327: 1
       329: 1
       331: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       397: 1
       399: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       494: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       561: 1
       563: 1
       587: 1
       597: 1
       599: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       658: 1
       660: 1
       662: 1
       664: 1
       666: 1
       668: 1
       670: 1
       673: 1
       680: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       691: 1
       692: 1
       779: 1
       783: 1
       819: 1
       823: 1
       833: 1
       835: 1
       837: 1
       859: 1
       861: 1
       863: 1
       867: 1
       873: 1
       874: 1
       876: 1
       996: 1
      1030: 1
      1036: 1
      1042: 1
      1081: 1
      1252: 1

1253:    0: 2q+2
         1: 2q+2
         2: q^2+2q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+1
        14: q+1
        15: q+1
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: 2q+2
        20: 2q+2
        21: q^2+2q+1
        22: 2
        23: 2
        24: q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: 2q+2
        29: 2q+2
        30: q+1
        31: 2
        32: 1
        33: 2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2
        40: 2
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: 2
        53: 2
        54: q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        63: 2
        65: 1
        67: 2
        69: q+1
        70: q+1
        71: 2q+2
        72: 2q+2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: q+1
       128: 2
       130: 2
       132: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 2
       141: 1
       142: 2
       143: q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       195: 1
       196: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 1
       210: 2
       212: 1
       214: 1
       216: 1
       218: 1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       228: 1
       230: 1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       312: 2
       314: 1
       316: 1
       318: 2
       321: 1
       322: 1
       326: 1
       328: 1
       330: 1
       332: 1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: 1
       349: 1
       350: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       398: 1
       400: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       494: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       562: 1
       564: 1
       588: 1
       598: 1
       600: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       659: 1
       661: 1
       663: 1
       664: 1
       667: 1
       669: 1
       671: 1
       673: 1
       680: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       691: 1
       692: 1
       780: 1
       784: 1
       820: 1
       824: 1
       834: 1
       836: 1
       838: 1
       860: 1
       862: 1
       864: 1
       867: 1
       873: 1
       874: 1
       876: 1
       997: 1
      1031: 1
      1037: 1
      1043: 1
      1081: 1
      1253: 1

1254:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+6q^2+6q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+8q^2+6q+2
         7: q^3+4q^2+5q+2
         8: q^3+6q^2+6q+2
         9: q^3+4q^2+5q+2
        10: q^2+6q+2
        11: q^2+6q+2
        12: 3q^2+4q+2
        13: 4q^2+6q+2
        14: 3q^2+5q+2
        15: 4q^2+6q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: 4q^2+6q+2
        20: q^3+6q^2+6q+2
        21: 3q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+6q^2+6q+2
        28: q^2+6q+2
        29: q^2+4q+2
        30: 2q^2+5q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 4q^2+8q+2
        34: q^2+6q+2
        35: 4q^2+6q+2
        36: q^3+7q^2+8q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: 3q^2+5q+2
        49: 4q^2+6q+2
        50: q^3+6q^2+6q+2
        51: 3q^2+5q+2
        52: q^2+6q+2
        53: 3q^2+6q+2
        54: q^2+5q+2
        55: 4q^2+6q+2
        56: q^3+6q^2+6q+2
        57: 3q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: q^2+4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q+2
        69: 2q^2+5q+2
        70: 3q+2
        71: q^2+4q+2
        72: 3q^2+4q+2
        73: q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 4q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: 5q+2
        84: 4q+2
        85: 4q^2+6q+2
        86: q^2+4q+2
        87: 2q^2+5q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+4q+2
        92: 3q^2+4q+2
        93: q^2+4q+2
        94: q^2+6q+2
        95: 3q^2+6q+2
        96: q^2+5q+2
        97: 4q^2+6q+2
        98: q^3+6q^2+6q+2
        99: 3q^2+5q+2
       100: q^2+6q+2
       101: 3q^2+6q+2
       102: q^2+5q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q^2+2q+2
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: q+2
       134: q^2+4q+2
       135: q^2+3q+2
       136: 3q+2
       137: 4q+2
       138: 5q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: q^2+4q+2
       143: 4q+2
       144: 2q^2+5q+2
       145: q^2+4q+2
       146: 3q+2
       147: 3q^2+4q+2
       148: q^2+4q+2
       149: 4q+2
       150: 5q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: q^2+4q+2
       164: 3q^2+4q+2
       165: q^2+4q+2
       166: q^2+6q+2
       167: 3q^2+6q+2
       168: q^2+5q+2
       169: 1
       170: 1
       173: q+1
       174: q+1
       177: 2q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: q^2+2q+2
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: q+2
       220: 2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: q+2
       225: 3q+2
       226: 3q+2
       227: q+2
       228: 3q+2
       229: q+2
       230: 2q+2
       231: 3q+2
       232: q+2
       233: q^2+4q+2
       234: q^2+3q+2
       235: 3q+2
       236: 5q+2
       237: 2q+1
       238: 2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 4q+2
       244: 2q+2
       245: q^2+4q+2
       246: 3q+2
       247: 2q+4
       248: 2q+4
       249: 2q+2
       253: q+2
       254: q+2
       255: q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: q+1
       276: q+1
       283: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 4
       338: q+2
       339: q+2
       340: q+2
       341: q+2
       342: q+1
       343: q+1
       344: q+2
       348: q+2
       350: 2q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: q+2
       358: 3q+2
       359: 2q+4
       366: 3q+2
       367: q+2
       368: 3q+2
       369: q+2
       370: 2q+2
       371: q+2
       372: q+2
       373: q+1
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       397: 1
       400: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       443: 4
       445: 2
       446: 2
       447: q+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: q+2
       464: q+2
       469: q+1
       470: q+1
       471: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 1
       482: 2
       483: 2
       484: 2
       491: 1
       495: 2
       496: 2
       497: 2
       498: 2
       499: q+2
       500: 2
       501: q+2
       508: q+2
       512: q+2
       514: 2q+2
       515: q+2
       516: q+2
       517: q+1
       529: 1
       530: 1
       533: 1
       534: 1
       545: 2
       546: 2
       549: 1
       551: 1
       557: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       571: 1
       573: 2
       574: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       613: 1
       614: 1
       615: 2
       619: 2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       641: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: 2
       683: 2
       685: 1
       689: 2
       693: 1
       694: 1
       696: 1
       699: 1
       717: 1
       718: 1
       741: 1
       744: 1
       753: 1
       754: 1
       765: 1
       766: 1
       785: 1
       793: 2
       817: 1
       818: 1
       825: 1
       829: 2
       831: 1
       832: 1
       835: 1
       836: 1
       843: 1
       844: 1
       855: 1
       856: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       952: 1
       953: 1
       964: 1
       965: 1
      1000: 1
      1040: 1
      1080: 1
      1084: 1
      1254: 1

1255:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+6q^2+6q+2
         5: q^3+7q^2+8q+2
         6: q^4+4q^3+8q^2+6q+2
         7: q^3+4q^2+5q+2
         8: q^3+6q^2+6q+2
         9: q^3+4q^2+5q+2
        10: q^2+6q+2
        11: q^2+6q+2
        12: 3q^2+4q+2
        13: 4q^2+6q+2
        14: 3q^2+5q+2
        15: 4q^2+6q+2
        16: q^3+7q^2+8q+2
        17: q^3+7q^2+8q+2
        18: q^3+4q^2+5q+2
        19: 4q^2+6q+2
        20: q^3+6q^2+6q+2
        21: 3q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+6q^2+6q+2
        28: q^2+6q+2
        29: q^2+4q+2
        30: 2q^2+5q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 4q^2+8q+2
        34: q^2+6q+2
        35: 4q^2+6q+2
        36: q^3+7q^2+8q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: 3q^2+5q+2
        49: 4q^2+6q+2
        50: q^3+6q^2+6q+2
        51: 3q^2+5q+2
        52: q^2+6q+2
        53: 3q^2+6q+2
        54: q^2+5q+2
        55: 4q^2+6q+2
        56: q^3+6q^2+6q+2
        57: 3q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: q^2+4q+2
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q+2
        69: 2q^2+5q+2
        70: 3q+2
        71: q^2+4q+2
        72: 3q^2+4q+2
        73: q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q+1
        80: 4q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: 5q+2
        84: 4q+2
        85: 4q^2+6q+2
        86: q^2+4q+2
        87: 2q^2+5q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+4q+2
        92: 3q^2+4q+2
        93: q^2+4q+2
        94: q^2+6q+2
        95: 3q^2+6q+2
        96: q^2+5q+2
        97: 4q^2+6q+2
        98: q^3+6q^2+6q+2
        99: 3q^2+5q+2
       100: q^2+6q+2
       101: 3q^2+6q+2
       102: q^2+5q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: q^2+2q+2
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: q+2
       134: q^2+4q+2
       135: q^2+3q+2
       136: 3q+2
       137: 4q+2
       138: 5q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: q^2+4q+2
       143: 4q+2
       144: 2q^2+5q+2
       145: q^2+4q+2
       146: 3q+2
       147: 3q^2+4q+2
       148: q^2+4q+2
       149: 4q+2
       150: 5q+2
       151: 2q+1
       152: 2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+2
       158: q+2
       159: q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: q^2+4q+2
       164: 3q^2+4q+2
       165: q^2+4q+2
       166: q^2+6q+2
       167: 3q^2+6q+2
       168: q^2+5q+2
       171: 1
       172: 1
       175: q+1
       176: q+1
       177: 2q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       184: q+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: q^2+2q+2
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: 2q+1
       212: 2q+1
       219: q+2
       220: 2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: q+2
       225: 3q+2
       226: 3q+2
       227: q+2
       228: 3q+2
       229: q+2
       230: 2q+2
       231: 3q+2
       232: q+2
       233: q^2+4q+2
       234: q^2+3q+2
       235: 3q+2
       236: 5q+2
       237: 2q+1
       238: 2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 4q+2
       244: 2q+2
       245: q^2+4q+2
       246: 3q+2
       247: 2q+4
       248: 2q+4
       249: 2q+2
       253: q+2
       254: q+2
       255: q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: q+1
       278: q+1
       284: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       320: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 4
       338: q+2
       339: q+2
       340: q+2
       341: q+2
       342: q+1
       343: q+1
       344: q+2
       348: q+2
       350: 2q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: q+2
       358: 3q+2
       359: 2q+4
       366: 3q+2
       367: q+2
       368: 3q+2
       369: q+2
       370: 2q+2
       371: q+2
       372: q+2
       373: q+1
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       398: 1
       399: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       430: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       444: 4
       445: 2
       446: 2
       448: q+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: q+2
       464: q+2
       469: q+1
       470: q+1
       472: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 1
       482: 2
       483: 2
       484: 2
       491: 1
       495: 2
       496: 2
       497: 2
       498: 2
       499: q+2
       500: 2
       501: q+2
       508: q+2
       512: q+2
       514: 2q+2
       515: q+2
       516: q+2
       517: q+1
       531: 1
       532: 1
       535: 1
       536: 1
       547: 2
       548: 2
       550: 1
       552: 1
       558: 1
       559: 1
       561: 1
       562: 1
       563: 1
       564: 1
       567: 1
       568: 1
       570: 1
       572: 1
       575: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       590: 1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       613: 1
       614: 1
       616: 2
       620: 2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       642: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: 2
       683: 2
       685: 1
       689: 2
       697: 1
       698: 1
       700: 1
       701: 1
       719: 1
       720: 1
       742: 1
       743: 1
       755: 1
       756: 1
       767: 1
       768: 1
       786: 1
       794: 2
       817: 1
       818: 1
       826: 1
       830: 2
       831: 1
       832: 1
       835: 1
       836: 1
       843: 1
       844: 1
       855: 1
       856: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       954: 1
       955: 1
       966: 1
       967: 1
      1001: 1
      1041: 1
      1080: 1
      1084: 1
      1255: 1

1256:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: 4q^2+5q+2
         8: 4q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 4q^2+5q+2
        14: 4q^2+5q+2
        15: 4q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: 2q^2+2q+1
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: 4q^2+5q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 4q^2+5q+2
        26: 4q^2+5q+2
        27: 4q^2+5q+2
        28: 4q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: 4q^2+5q+2
        35: 4q^2+5q+2
        36: 4q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 4q^2+5q+2
        44: 4q^2+5q+2
        45: 4q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: 2q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: 4q^2+5q+2
        56: 4q^2+5q+2
        57: 4q^2+5q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 4q+2
        69: q+1
        70: 4q^2+5q+2
        71: 4q+2
        72: 4q+2
        73: 2q+2
        74: q^2+3q+2
        76: q^2+3q+2
        78: q^2+3q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 4q^2+5q+2
        85: 4q+2
        86: 4q^2+5q+2
        87: 4q^2+5q+2
        88: 4q+2
        89: 4q+2
        90: 2q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+2q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+3q+2
       103: q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: q^2+3q+2
       115: q^2+3q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       121: q^2+3q+2
       123: 2q+2
       125: 4q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 4q+2
       134: q+1
       135: 4q+2
       136: 2q+2
       137: 2q+2
       138: 1
       139: 2
       141: q^2+3q+2
       142: 2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 4q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: q^2+3q+2
       150: q^2+3q+2
       151: q^2+3q+2
       153: q^2+3q+2
       155: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 4q+2
       164: 4q+2
       165: 2q^2+2q+1
       166: 2
       167: 2
       168: q+1
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: 1
       179: 2
       181: 2
       183: 2q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 2q+2
       189: q^2+3q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 2q+2
       207: 2q+2
       209: q^2+3q+2
       211: q^2+3q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 4q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 2q+2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 4q+2
       233: q+1
       234: 4q+2
       235: 2q+2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q^2+3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 4q+2
       254: 4q+2
       255: 2q^2+2q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: q+1
       266: q+1
       271: q+1
       273: q+1
       275: q+1
       278: q+1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: 2q+2
       303: 1
       304: 1
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 2
       313: 2q+2
       315: 1
       317: 2
       321: 1
       322: 1
       325: q^2+3q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 2q+2
       358: 1
       359: 2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       397: 1
       399: 1
       401: q+1
       404: q+1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       439: 1
       440: 1
       451: 1
       453: 2q+1
       454: 2q+1
       455: 2
       457: q+1
       458: q+1
       459: 2q+2
       461: 1
       462: 1
       463: 2
       465: 2
       467: 1
       469: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 1
       563: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: 2
       637: 1
       639: 1
       649: 1
       650: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       688: 1
       745: 1
       747: 1
       749: 1
       751: 1
       777: 1
       781: 1
       783: 1
       789: 2
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       868: 1
       875: 1
       876: 1
       878: 1
       956: 1
       958: 1
      1002: 1
      1034: 1
      1038: 1
      1042: 1
      1082: 1
      1256: 1

1257:    0: 4q^2+5q+2
         1: 4q^2+5q+2
         2: 4q^2+5q+2
         3: 4q^2+5q+2
         4: 4q^2+5q+2
         5: 4q^2+5q+2
         6: 4q^2+5q+2
         7: 4q^2+5q+2
         8: 4q^2+5q+2
         9: q^4+2q^3+3q^2+2q+1
        10: 4q^2+5q+2
        11: 4q^2+5q+2
        12: 4q^2+5q+2
        13: 4q^2+5q+2
        14: 4q^2+5q+2
        15: 4q^2+5q+2
        16: 4q+2
        17: 4q+2
        18: 2q^2+2q+1
        19: 4q^2+5q+2
        20: 4q^2+5q+2
        21: 4q^2+5q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: 4q^2+5q+2
        26: 4q^2+5q+2
        27: 4q^2+5q+2
        28: 4q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: 4q^2+5q+2
        35: 4q^2+5q+2
        36: 4q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 4q^2+5q+2
        44: 4q^2+5q+2
        45: 4q^2+5q+2
        46: 4q+2
        47: 4q+2
        48: 2q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: 4q^2+5q+2
        56: 4q^2+5q+2
        57: 4q^2+5q+2
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 4q+2
        69: q+1
        70: 4q^2+5q+2
        71: 4q+2
        72: 4q+2
        73: 2q+2
        75: q^2+3q+2
        77: q^2+3q+2
        79: q^2+3q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 4q^2+5q+2
        85: 4q+2
        86: 4q^2+5q+2
        87: 4q^2+5q+2
        88: 4q+2
        89: 4q+2
        90: 2q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+2q+1
       100: q^2+3q+2
       101: q^2+3q+2
       102: q^2+3q+2
       104: q+1
       105: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: q^2+3q+2
       116: q^2+3q+2
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       122: q^2+3q+2
       124: 2q+2
       125: 4q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 4q+2
       134: q+1
       135: 4q+2
       136: 2q+2
       137: 2q+2
       138: 1
       139: 2
       141: q^2+3q+2
       142: 2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 4q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: q^2+3q+2
       150: q^2+3q+2
       152: q^2+3q+2
       154: q^2+3q+2
       156: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 4q+2
       164: 4q+2
       165: 2q^2+2q+1
       166: 2
       167: 2
       168: q+1
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: 1
       180: 2
       182: 2
       183: 2q+1
       184: 2q+1
       185: q+1
       186: q+1
       188: 2q+2
       190: q^2+3q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       206: 2q+2
       208: 2q+2
       210: q^2+3q+2
       212: q^2+3q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 4q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 2q+2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 4q+2
       233: q+1
       234: 4q+2
       235: 2q+2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q^2+3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 4q+2
       254: 4q+2
       255: 2q^2+2q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: q+1
       265: q+1
       272: q+1
       274: q+1
       276: q+1
       277: q+1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       298: 2q+2
       303: 1
       304: 1
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       312: 2
       314: 2q+2
       316: 1
       318: 2
       321: 1
       322: 1
       326: q^2+3q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 2q+2
       358: 1
       359: 2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       398: 1
       400: 1
       402: q+1
       403: q+1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       439: 1
       440: 1
       452: 1
       453: 2q+1
       454: 2q+1
       456: 2
       457: q+1
       458: q+1
       460: 2q+2
       461: 1
       462: 1
       464: 2
       466: 2
       468: 1
       470: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: 1
       564: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: 2
       638: 1
       640: 1
       649: 1
       650: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       688: 1
       746: 1
       748: 1
       750: 1
       752: 1
       778: 1
       782: 1
       784: 1
       790: 2
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       868: 1
       875: 1
       876: 1
       878: 1
       957: 1
       959: 1
      1003: 1
      1035: 1
      1039: 1
      1043: 1
      1082: 1
      1257: 1

1258:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: 4q^2+6q+2
        14: 4q^2+6q+2
        15: 4q^2+6q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: 2q^2+2q+1
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+6q^2+6q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+6q^2+6q+2
        28: q^2+6q+2
        29: q^3+7q^2+8q+2
        30: 4q^2+6q+2
        31: 4q^2+8q+2
        32: 2q^2+6q+2
        33: 6q+2
        34: q^3+7q^2+8q+2
        35: 4q^2+6q+2
        36: q^2+6q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: q^2+6q+2
        50: q^2+6q+2
        51: 2q^2+2q+1
        52: 4q^2+8q+2
        53: 4q^2+8q+2
        54: 4q^2+6q+2
        55: q^3+7q^2+8q+2
        56: q^3+7q^2+8q+2
        57: q^3+6q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: q^2+4q+2
        61: 2q
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q^2+6q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: 6q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+6q+2
        81: 4q+2
        82: 4q^2+8q+2
        83: 2q^2+6q+2
        84: 4q^2+6q+2
        85: 4q+2
        86: q^3+7q^2+8q+2
        87: 4q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: q^2+6q+2
        98: q^2+6q+2
        99: 2q^2+2q+1
       100: 4q^2+8q+2
       101: 4q^2+8q+2
       102: 4q^2+6q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: q^2+4q+2
       108: 2q
       109: 3q+1
       110: 3q+1
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 2q^2+6q+2
       142: 4q+2
       143: 4q+2
       144: q+1
       145: q^2+6q+2
       146: 4q^2+6q+2
       147: q^2+6q+2
       148: 6q+2
       149: 4q^2+8q+2
       150: 2q^2+6q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 4q+2
       158: 4q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: 4q+2
       164: 4q+2
       165: q^2+2q+1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: q+1
       174: q+1
       183: 2q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       199: 2q+2
       201: q^2+4q+2
       202: 2q
       203: 3q+1
       204: 3q+1
       205: 3q+1
       206: 3q+1
       207: 2q+1
       208: 2q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 1
       220: 2q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: 2q+2
       233: q+1
       234: 4q+2
       235: 4q+2
       236: q+1
       243: 4q+2
       244: 2q+2
       245: 4q+2
       246: 2q^2+6q+2
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q+2
       251: q+2
       252: q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       263: q+1
       264: q+1
       267: q+1
       268: q+1
       271: 2q+1
       272: q
       273: q
       274: 2q+1
       275: q+1
       276: q+1
       283: 1
       293: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 2q+2
       309: q+1
       310: q+1
       313: 2q+1
       314: 2q+1
       319: 2q+2
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 4q+2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 2q+2
       352: 1
       353: 2q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 4q+2
       358: q+1
       359: 4q+2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       385: q+1
       386: q+1
       393: 1
       394: 1
       401: q+1
       403: q+1
       405: q+1
       407: q+1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2q+2
       447: 1
       453: 2q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: 2q+1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: q+2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       541: 1
       542: 1
       557: q+1
       560: q+1
       565: 1
       566: 1
       573: q+1
       574: q+1
       589: 1
       593: 1
       603: 1
       615: 2
       619: 1
       631: 1
       632: 1
       641: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: q+1
       684: q+2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       805: 1
       815: 2
       825: 1
       829: 1
       839: 1
       840: 1
       845: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: 1
       879: 1
       880: 1
       988: 1
       989: 1
      1004: 1
      1040: 1
      1056: 1
      1082: 1
      1085: 1
      1258: 1

1259:    0: q^3+7q^2+8q+2
         1: q^3+7q^2+8q+2
         2: q^3+6q^2+6q+2
         3: q^3+7q^2+8q+2
         4: q^3+7q^2+8q+2
         5: q^3+7q^2+8q+2
         6: q^3+7q^2+8q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+7q^2+8q+2
        11: q^3+7q^2+8q+2
        12: q^3+7q^2+8q+2
        13: 4q^2+6q+2
        14: 4q^2+6q+2
        15: 4q^2+6q+2
        16: q^2+6q+2
        17: q^2+6q+2
        18: 2q^2+2q+1
        19: q^3+7q^2+8q+2
        20: q^3+7q^2+8q+2
        21: q^3+6q^2+6q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+6q+2
        25: q^3+7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: q^3+6q^2+6q+2
        28: q^2+6q+2
        29: q^3+7q^2+8q+2
        30: 4q^2+6q+2
        31: 4q^2+8q+2
        32: 2q^2+6q+2
        33: 6q+2
        34: q^3+7q^2+8q+2
        35: 4q^2+6q+2
        36: q^2+6q+2
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q+2
        47: 4q+2
        48: q^2+2q+1
        49: q^2+6q+2
        50: q^2+6q+2
        51: 2q^2+2q+1
        52: 4q^2+8q+2
        53: 4q^2+8q+2
        54: 4q^2+6q+2
        55: q^3+7q^2+8q+2
        56: q^3+7q^2+8q+2
        57: q^3+6q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: q^2+4q+2
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: q+1
        70: 4q^2+6q+2
        71: q^2+6q+2
        72: q^2+6q+2
        73: 6q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+6q+2
        81: 4q+2
        82: 4q^2+8q+2
        83: 2q^2+6q+2
        84: 4q^2+6q+2
        85: 4q+2
        86: q^3+7q^2+8q+2
        87: 4q^2+6q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 4q+2
        92: 4q+2
        93: q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: q^2+6q+2
        98: q^2+6q+2
        99: 2q^2+2q+1
       100: 4q^2+8q+2
       101: 4q^2+8q+2
       102: 4q^2+6q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       107: 2q
       108: q^2+4q+2
       109: 3q+1
       110: 3q+1
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: q+1
       133: 2q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 2q^2+6q+2
       142: 4q+2
       143: 4q+2
       144: q+1
       145: q^2+6q+2
       146: 4q^2+6q+2
       147: q^2+6q+2
       148: 6q+2
       149: 4q^2+8q+2
       150: 2q^2+6q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 4q+2
       158: 4q+2
       159: q^2+2q+1
       160: q+2
       161: q+2
       162: q+1
       163: 4q+2
       164: 4q+2
       165: q^2+2q+1
       166: 4q+2
       167: 4q+2
       168: q^2+2q+1
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       175: q+1
       176: q+1
       184: 2q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       200: 2q+2
       201: 2q
       202: q^2+4q+2
       203: 3q+1
       204: 3q+1
       205: 3q+1
       206: 3q+1
       207: 2q+1
       208: 2q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 1
       220: 2q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 2
       228: 1
       229: 2
       230: q+2
       231: q+1
       232: 2q+2
       233: q+1
       234: 4q+2
       235: 4q+2
       236: q+1
       243: 4q+2
       244: 2q+2
       245: 4q+2
       246: 2q^2+6q+2
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q+2
       251: q+2
       252: q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       265: q+1
       266: q+1
       269: q+1
       270: q+1
       271: q
       272: 2q+1
       273: 2q+1
       274: q
       277: q+1
       278: q+1
       284: 1
       294: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 2q+2
       309: q+1
       310: q+1
       313: 2q+1
       314: 2q+1
       320: 2q+2
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: 4q+2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: q+2
       350: 1
       351: 2q+2
       352: 1
       353: 2q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 4q+2
       358: q+1
       359: 4q+2
       366: q+1
       367: 2
       368: 1
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       387: q+1
       388: q+1
       395: 1
       396: 1
       402: q+1
       404: q+1
       406: q+1
       408: q+1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2q+2
       448: 1
       454: 2q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: 2q+1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: q+2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       543: 1
       544: 1
       558: q+1
       559: q+1
       567: 1
       568: 1
       575: q+1
       576: q+1
       590: 1
       594: 1
       604: 1
       616: 2
       620: 1
       631: 1
       632: 1
       642: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: q+1
       684: q+2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       806: 1
       816: 2
       826: 1
       830: 1
       839: 1
       840: 1
       846: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: 1
       879: 1
       880: 1
       990: 1
       991: 1
      1005: 1
      1041: 1
      1057: 1
      1082: 1
      1085: 1
      1259: 1

1260:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q+2
        56: q+2
        57: q+2
        58: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       321: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       385: 1
       387: 1
       401: 1
       402: 1
       421: 1
       431: 1
       439: 1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 1
       473: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       557: 1
       558: 1
       591: 1
       595: 1
       607: 1
       621: 1
       631: 1
       643: 1
       649: 1
       665: 1
       672: 1
       673: 1
       676: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       787: 1
       807: 1
       827: 1
       831: 1
       839: 1
       847: 1
       868: 1
       875: 1
       876: 1
       878: 1
      1006: 1
      1044: 1
      1058: 1
      1082: 1
      1260: 1

1261:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: 2
        23: 2
        24: 2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: 2
        55: q+2
        56: q+2
        57: q+2
        59: 2
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 1
       141: 2
       142: 1
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2
       158: 2
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 2
       164: 2
       165: q+1
       166: 1
       167: 1
       168: 1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 1
       245: 1
       246: 2
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2
       254: 2
       255: q+1
       256: 1
       257: 1
       258: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       322: 1
       325: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       386: 1
       388: 1
       403: 1
       404: 1
       422: 1
       432: 1
       440: 1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 1
       474: 1
       481: 1
       482: 1
       483: 1
       484: 1
       491: 1
       492: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       559: 1
       560: 1
       592: 1
       596: 1
       608: 1
       622: 1
       632: 1
       644: 1
       650: 1
       665: 1
       672: 1
       673: 1
       676: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       788: 1
       808: 1
       828: 1
       832: 1
       840: 1
       848: 1
       868: 1
       875: 1
       876: 1
       878: 1
      1007: 1
      1045: 1
      1059: 1
      1082: 1
      1261: 1

1262:    0: q^3+5q^2+10q+2
         1: 8q^2+10q+2
         2: q^3+5q^2+10q+2
         3: 8q^2+10q+2
         4: 5q^2+7q+2
         5: q^3+5q^2+10q+2
         6: 3q^3+8q^2+7q+2
         7: 5q^2+7q+2
         8: q^3+5q^2+10q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+9q+2
        11: 2q^2+9q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+10q+2
        14: 5q^2+7q+2
        15: q^3+5q^2+10q+2
        16: 2q^2+9q+2
        17: 2q^2+9q+2
        18: 2q^2+3q+1
        19: 2q^2+7q+2
        20: 5q^2+7q+2
        21: 2q^2+7q+2
        22: q^3+5q^2+10q+2
        23: 8q^2+10q+2
        24: q^3+5q^2+10q+2
        25: q^3+5q^2+10q+2
        26: 8q^2+10q+2
        27: q^3+5q^2+10q+2
        28: 8q+2
        29: q^2+6q+2
        30: 2q^2+7q+2
        31: 2q^2+9q+2
        32: q^3+5q^2+10q+2
        33: 2q^2+9q+2
        34: 2q^2+9q+2
        35: q^3+5q^2+10q+2
        36: 2q^2+9q+2
        37: 2q^2+6q+2
        38: q^3+3q^2+4q
        39: 4q^2+6q+2
        40: 4q^2+4q
        41: 2q^2+6q+2
        42: q^3+3q^2+4q
        43: 2q^2+9q+2
        44: 4q^2+6q+2
        45: 2q^2+9q+2
        46: 2q^2+9q+2
        47: 2q^2+9q+2
        48: 2q^2+3q+1
        49: 6q+2
        50: q^2+6q+2
        51: q^2+3q+1
        52: 2q^2+7q+2
        53: 5q^2+7q+2
        54: 2q^2+7q+2
        55: 2q^2+7q+2
        56: 5q^2+7q+2
        57: 2q^2+7q+2
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: q^2+5q+2
        63: q^2+4q
        64: 2q^2+6q+2
        65: q^3+3q^2+4q
        66: q^2+5q+2
        67: q^2+4q
        68: 8q+2
        69: 2q+1
        70: q^2+6q+2
        71: 5q+2
        72: 3q+2
        73: 3q+2
        74: 3q+2
        75: 2q^2+2q
        76: q^2+3q+2
        77: 2q^2+2q
        78: 3q+2
        79: 2q^2+2q
        80: 2q^2+9q+2
        81: 2q^2+9q+2
        82: q^2+6q+2
        83: 2q^2+7q+2
        84: 2q^2+9q+2
        85: 2q^2+9q+2
        86: q^2+6q+2
        87: 2q^2+7q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 6q+2
        92: q^2+6q+2
        93: q^2+3q+1
        94: 6q+2
        95: q^2+6q+2
        96: q^2+3q+1
        97: 6q+2
        98: q^2+6q+2
        99: q^2+3q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: 2q+1
       104: 2q
       105: 2q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       113: 2q+2
       114: q^2+2q
       115: 3q+2
       116: 2q^2+2q
       117: 4q+1
       118: 4q+1
       119: 4q+1
       120: 4q+1
       121: q^2+5q+2
       122: q^2+4q
       123: q^2+5q+2
       124: q^2+4q
       125: 4q+2
       126: q+1
       127: q+2
       128: 2q
       129: q+2
       130: 2q
       131: q+1
       132: q^2+q
       133: 5q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: 2q+1
       139: 5q+2
       140: 3q+2
       141: q^2+6q+2
       142: 3q+2
       143: 4q+2
       144: 2q+1
       145: 5q+2
       146: q^2+6q+2
       147: 3q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       151: 3q+2
       152: 2q^2+2q
       153: q^2+3q+2
       154: 2q^2+2q
       155: 3q+2
       156: 2q^2+2q
       157: q+2
       158: q+2
       159: q+1
       160: 6q+2
       161: q^2+6q+2
       162: q^2+3q+1
       163: 6q+2
       164: q^2+6q+2
       165: q^2+3q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: 1
       172: 1
       173: 2q+1
       174: 2q
       175: 2q
       176: 2q+1
       177: 1
       178: q
       179: q+2
       180: 2q
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       189: 2q+2
       190: q^2+2q
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       207: 2q+2
       208: 2q
       209: 2q+2
       210: q^2+2q
       211: 3q+2
       212: 2q^2+2q
       213: q+2
       214: 2q
       215: q+2
       216: 2q
       217: q+1
       218: q^2+q
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 5q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 5q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       237: q+2
       238: 2q
       239: q+2
       240: 2q
       241: q+1
       242: q^2+q
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       247: q+4
       248: q+4
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       276: q
       277: q
       278: q+1
       279: q+2
       280: 2q
       281: 1
       282: q
       287: 1
       288: q
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: q+2
       315: 1
       316: q
       317: q+2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: 2q+2
       326: q^2+2q
       333: 1
       334: 1
       335: 1
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: q+4
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: q+4
       360: q+2
       361: 2q
       362: q+2
       363: 2q
       364: q+1
       365: q^2+q
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: q+4
       372: q+4
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       413: 1
       414: q
       417: 1
       423: 1
       427: 2
       428: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 2
       444: 2
       445: 2
       446: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 2
       462: 2
       463: 2
       464: 2
       465: q+2
       466: 2q
       467: 1
       468: q
       469: 1
       470: q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: 2
       479: q+4
       481: 1
       482: 1
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       492: 1
       493: 1
       494: 1
       496: q+4
       497: 1
       498: 1
       499: 1
       501: q+4
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2
       518: 2
       519: 2
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       546: 1
       547: 1
       548: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 2
       575: 2
       577: 2
       578: 2
       585: 1
       601: 2
       602: 2
       605: 1
       609: 1
       615: 2
       616: 2
       617: 2
       618: 2
       623: 1
       625: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: 1
       640: q
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: q+4
       658: 1
       659: 1
       660: 1
       661: 1
       672: 2
       674: 2
       675: 1
       676: 1
       678: 2
       680: 2
       681: 1
       682: 1
       684: 2
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       694: 1
       697: 1
       701: 1
       733: 1
       734: 1
       735: 1
       736: 1
       749: 1
       750: 1
       751: 1
       752: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 2
       768: 2
       769: 2
       770: 2
       795: 1
       796: 1
       797: 1
       815: 1
       816: 1
       819: 1
       820: 1
       821: 1
       839: 1
       840: 1
       843: 2
       849: 1
       851: 1
       857: 2
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       884: 1
       885: 1
       889: 1
       892: 1
       968: 1
       969: 1
       988: 1
       991: 1
      1046: 1
      1048: 1
      1075: 1
      1079: 1
      1262: 1

1263:    0: q^3+5q^2+10q+2
         1: 8q^2+10q+2
         2: q^3+5q^2+10q+2
         3: 8q^2+10q+2
         4: 5q^2+7q+2
         5: q^3+5q^2+10q+2
         6: 3q^3+8q^2+7q+2
         7: 5q^2+7q+2
         8: q^3+5q^2+10q+2
         9: q^3+3q^2+3q+1
        10: 2q^2+9q+2
        11: 2q^2+9q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+10q+2
        14: 5q^2+7q+2
        15: q^3+5q^2+10q+2
        16: 2q^2+9q+2
        17: 2q^2+9q+2
        18: 2q^2+3q+1
        19: 2q^2+7q+2
        20: 5q^2+7q+2
        21: 2q^2+7q+2
        22: q^3+5q^2+10q+2
        23: 8q^2+10q+2
        24: q^3+5q^2+10q+2
        25: q^3+5q^2+10q+2
        26: 8q^2+10q+2
        27: q^3+5q^2+10q+2
        28: 8q+2
        29: q^2+6q+2
        30: 2q^2+7q+2
        31: 2q^2+9q+2
        32: q^3+5q^2+10q+2
        33: 2q^2+9q+2
        34: 2q^2+9q+2
        35: q^3+5q^2+10q+2
        36: 2q^2+9q+2
        37: q^3+3q^2+4q
        38: 2q^2+6q+2
        39: 4q^2+4q
        40: 4q^2+6q+2
        41: q^3+3q^2+4q
        42: 2q^2+6q+2
        43: 2q^2+9q+2
        44: 4q^2+6q+2
        45: 2q^2+9q+2
        46: 2q^2+9q+2
        47: 2q^2+9q+2
        48: 2q^2+3q+1
        49: 6q+2
        50: q^2+6q+2
        51: q^2+3q+1
        52: 2q^2+7q+2
        53: 5q^2+7q+2
        54: 2q^2+7q+2
        55: 2q^2+7q+2
        56: 5q^2+7q+2
        57: 2q^2+7q+2
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: q^2+4q
        63: q^2+5q+2
        64: q^3+3q^2+4q
        65: 2q^2+6q+2
        66: q^2+4q
        67: q^2+5q+2
        68: 8q+2
        69: 2q+1
        70: q^2+6q+2
        71: 5q+2
        72: 3q+2
        73: 3q+2
        74: 2q^2+2q
        75: 3q+2
        76: 2q^2+2q
        77: q^2+3q+2
        78: 2q^2+2q
        79: 3q+2
        80: 2q^2+9q+2
        81: 2q^2+9q+2
        82: q^2+6q+2
        83: 2q^2+7q+2
        84: 2q^2+9q+2
        85: 2q^2+9q+2
        86: q^2+6q+2
        87: 2q^2+7q+2
        88: 4q+2
        89: 4q+2
        90: q^2+2q+1
        91: 6q+2
        92: q^2+6q+2
        93: q^2+3q+1
        94: 6q+2
        95: q^2+6q+2
        96: q^2+3q+1
        97: 6q+2
        98: q^2+6q+2
        99: q^2+3q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: 2q
       104: 2q+1
       105: 2q+1
       106: 2q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+2
       113: q^2+2q
       114: 2q+2
       115: 2q^2+2q
       116: 3q+2
       117: 4q+1
       118: 4q+1
       119: 4q+1
       120: 4q+1
       121: q^2+4q
       122: q^2+5q+2
       123: q^2+4q
       124: q^2+5q+2
       125: 4q+2
       126: q+1
       127: 2q
       128: q+2
       129: 2q
       130: q+2
       131: q^2+q
       132: q+1
       133: 5q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 4q+2
       138: 2q+1
       139: 5q+2
       140: 3q+2
       141: q^2+6q+2
       142: 3q+2
       143: 4q+2
       144: 2q+1
       145: 5q+2
       146: q^2+6q+2
       147: 3q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       151: 2q^2+2q
       152: 3q+2
       153: 2q^2+2q
       154: q^2+3q+2
       155: 2q^2+2q
       156: 3q+2
       157: q+2
       158: q+2
       159: q+1
       160: 6q+2
       161: q^2+6q+2
       162: q^2+3q+1
       163: 6q+2
       164: q^2+6q+2
       165: q^2+3q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       170: 1
       171: 1
       173: 2q
       174: 2q+1
       175: 2q+1
       176: 2q
       177: q
       178: 1
       179: 2q
       180: q+2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: q+2
       189: q^2+2q
       190: 2q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+2
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: q+2
       207: 2q
       208: 2q+2
       209: q^2+2q
       210: 2q+2
       211: 2q^2+2q
       212: 3q+2
       213: 2q
       214: q+2
       215: 2q
       216: q+2
       217: q^2+q
       218: q+1
       219: q+1
       220: q+2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 5q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 5q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       237: 2q
       238: q+2
       239: 2q
       240: q+2
       241: q^2+q
       242: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       247: q+4
       248: q+4
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       275: q
       276: q+1
       277: q+1
       278: q
       279: 2q
       280: q+2
       281: q
       282: 1
       287: q
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       314: q+2
       315: q
       316: 1
       317: 2q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       325: q^2+2q
       326: 2q+2
       333: 1
       334: 1
       335: 1
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       344: q+1
       345: q+2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: q+4
       352: q+1
       353: q+2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: q+4
       360: 2q
       361: q+2
       362: 2q
       363: q+2
       364: q^2+q
       365: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: q+4
       372: q+4
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       413: q
       414: 1
       418: 1
       424: 1
       427: 2
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       465: 2q
       466: q+2
       467: q
       468: 1
       469: q
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: 2
       480: q+4
       481: 1
       482: 1
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       492: 1
       493: 1
       494: 1
       496: q+4
       497: 1
       498: 1
       499: 1
       501: q+4
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2
       518: 2
       519: 2
       538: 1
       540: 1
       542: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 2
       576: 2
       580: 2
       581: 2
       586: 1
       601: 2
       602: 2
       606: 1
       610: 1
       615: 2
       616: 2
       617: 2
       618: 2
       624: 1
       626: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: q
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: q+4
       658: 1
       659: 1
       660: 1
       661: 1
       672: 2
       674: 2
       675: 1
       676: 1
       678: 2
       680: 2
       681: 1
       682: 1
       684: 2
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       696: 1
       698: 1
       699: 1
       700: 1
       733: 1
       734: 1
       735: 1
       736: 1
       749: 1
       750: 1
       751: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 2
       767: 2
       772: 2
       773: 2
       795: 1
       796: 1
       798: 1
       815: 1
       816: 1
       819: 1
       820: 1
       822: 1
       839: 1
       840: 1
       844: 2
       850: 1
       852: 1
       858: 2
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       887: 1
       888: 1
       890: 1
       891: 1
       971: 1
       972: 1
       989: 1
       990: 1
      1047: 1
      1049: 1
      1075: 1
      1079: 1
      1263: 1

1264:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: 2q^3+q^2+2q+2
         5: q^2+3q+2
         6: 2q^3+q^2+2q+2
         7: 2q^3+q^2+2q+2
         8: q^2+3q+2
         9: q^5+q^3+q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: 2q^3+q^2+2q+2
        13: q^2+3q+2
        14: 2q^3+q^2+2q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^3+q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: 2q+2
        30: 2q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: q^2+3q+2
        44: 2q^3+q^2+2q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^3+q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 2q+2
        69: 1
        70: 2q+2
        71: q+2
        72: 2
        73: 2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q+2
        89: 2q+2
        90: q^3+q+1
        91: q+2
        92: q+2
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: 2q+2
       126: 1
       127: q+2
       129: q+2
       131: q+1
       133: q+2
       134: 1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       140: 2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: q+2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: 2q+2
       211: 2q+2
       213: q+2
       215: q+2
       217: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       229: 2
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       235: 2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 2q+2
       327: q+2
       329: q+2
       331: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: q+2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       465: q+2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       553: 1
       555: 1
       557: 1
       559: 1
       565: 1
       568: 1
       569: 1
       570: 1
       583: 1
       585: 1
       587: 1
       605: 1
       609: 1
       611: 2
       623: 1
       625: 1
       627: 2
       635: q+2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       675: 1
       676: 1
       681: 1
       682: 1
       686: 1
       687: 1
       688: 1
       729: 1
       731: 1
       745: 1
       747: 1
       757: 1
       758: 1
       761: 1
       762: 1
       777: 1
       797: 1
       799: 1
       821: 1
       823: 1
       841: 1
       849: 1
       851: 1
       853: 2
       877: 1
       878: 1
       978: 1
       979: 1
      1018: 1
      1034: 1
      1048: 1
      1050: 1
      1264: 1

1265:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: 2q^3+q^2+2q+2
         5: q^2+3q+2
         6: 2q^3+q^2+2q+2
         7: 2q^3+q^2+2q+2
         8: q^2+3q+2
         9: q^5+q^3+q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: 2q^3+q^2+2q+2
        13: q^2+3q+2
        14: 2q^3+q^2+2q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^3+q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: 2q+2
        30: 2q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: q^2+3q+2
        44: 2q^3+q^2+2q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^3+q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 2q+2
        69: 1
        70: 2q+2
        71: q+2
        72: 2
        73: 2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q+2
        89: 2q+2
        90: q^3+q+1
        91: q+2
        92: q+2
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: 2q+2
       126: 1
       128: q+2
       130: q+2
       132: q+1
       133: q+2
       134: 1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       140: 2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: q+2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: 2q+2
       212: 2q+2
       214: q+2
       216: q+2
       218: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       229: 2
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       235: 2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 2q+2
       328: q+2
       330: q+2
       332: q+1
       333: 1
       334: 1
       335: 1
       344: 1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: q+2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       466: q+2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       481: 1
       482: 1
       492: 1
       493: 1
       494: 1
       497: 1
       498: 1
       499: 1
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       554: 1
       556: 1
       558: 1
       560: 1
       566: 1
       567: 1
       571: 1
       572: 1
       584: 1
       586: 1
       588: 1
       606: 1
       610: 1
       612: 2
       624: 1
       626: 1
       628: 2
       636: q+2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       675: 1
       676: 1
       681: 1
       682: 1
       686: 1
       687: 1
       688: 1
       730: 1
       732: 1
       746: 1
       748: 1
       759: 1
       760: 1
       763: 1
       764: 1
       778: 1
       798: 1
       800: 1
       822: 1
       824: 1
       842: 1
       850: 1
       852: 1
       854: 2
       877: 1
       878: 1
       980: 1
       981: 1
      1019: 1
      1035: 1
      1049: 1
      1051: 1
      1265: 1

1266:    0: 3q^2+8q+2
         1: 6q^2+8q+2
         2: 3q^2+8q+2
         3: 6q^2+8q+2
         4: q^3+4q^2+6q+2
         5: 3q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: q^3+4q^2+6q+2
         8: 3q^2+8q+2
         9: q^4+2q^3+3q^2+3q+1
        10: q^2+7q+2
        11: q^2+7q+2
        12: 3q^2+5q+2
        13: 3q^2+8q+2
        14: q^3+4q^2+6q+2
        15: 3q^2+8q+2
        16: q^2+7q+2
        17: q^2+7q+2
        18: q^3+2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 3q^2+8q+2
        23: 6q^2+8q+2
        24: 3q^2+8q+2
        25: 3q^2+8q+2
        26: 6q^2+8q+2
        27: 3q^2+8q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: q^2+7q+2
        32: 3q^2+8q+2
        33: q^2+7q+2
        34: q^2+7q+2
        35: 3q^2+8q+2
        36: q^2+7q+2
        37: 2q^2+6q+2
        38: q^2+2q
        39: 4q^2+6q+2
        40: 2q^2+2q
        41: 2q^2+6q+2
        42: q^2+2q
        43: q^2+7q+2
        44: 3q^2+5q+2
        45: q^2+7q+2
        46: q^2+7q+2
        47: q^2+7q+2
        48: q^3+2q^2+3q+1
        49: 5q+2
        50: 5q+2
        51: q^2+3q+1
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: q^2+5q+2
        63: 2q
        64: 2q^2+6q+2
        65: q^2+2q
        66: q^2+5q+2
        67: 2q
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: 3q+2
        73: 3q+2
        74: q^2+4q+2
        76: 2q^2+4q+2
        78: q^2+4q+2
        80: q^2+7q+2
        81: q^2+7q+2
        82: q^2+5q+2
        83: 2q^2+6q+2
        84: q^2+7q+2
        85: q^2+7q+2
        86: q^2+5q+2
        87: 2q^2+6q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 5q+2
        92: 5q+2
        93: q^2+3q+1
        94: 5q+2
        95: 5q+2
        96: q^2+3q+1
        97: 5q+2
        98: 5q+2
        99: q^2+3q+1
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: 2q+1
       104: q
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       113: q^2+3q+2
       115: q^2+4q+2
       117: 3q+1
       118: 3q+1
       119: 3q+1
       120: 3q+1
       121: q^2+5q+2
       122: 2q
       123: q^2+5q+2
       124: 2q
       125: 2q+2
       126: q+1
       127: 2q+2
       129: 2q+2
       131: 2q+1
       133: 4q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 2q+2
       138: 2q+1
       139: 4q+2
       140: 3q+2
       141: q^2+5q+2
       142: 3q+2
       143: 2q+2
       144: 2q+1
       145: 4q+2
       146: q^2+5q+2
       147: 3q+2
       148: 3q+2
       149: q^2+5q+2
       150: 2q^2+6q+2
       151: q^2+4q+2
       153: 2q^2+4q+2
       155: q^2+4q+2
       157: 2
       158: 2
       159: q+1
       160: 5q+2
       161: 5q+2
       162: q^2+3q+1
       163: 5q+2
       164: 5q+2
       165: q^2+3q+1
       166: 5q+2
       167: 5q+2
       168: q^2+3q+1
       169: 1
       172: 1
       173: 2q+1
       174: q
       175: q
       176: 2q+1
       177: q+1
       179: 2q+2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       189: q^2+3q+2
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       207: 2q+2
       209: q^2+3q+2
       211: q^2+4q+2
       213: 2q+2
       215: 2q+2
       217: 2q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 4q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 4q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       237: 2q+2
       239: 2q+2
       241: 2q+1
       243: 4q+2
       244: 3q+2
       245: 3q+2
       246: q^2+5q+2
       247: 4
       248: 4
       249: 2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 5q+2
       257: 5q+2
       258: q^2+3q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: 2q+2
       281: q+1
       287: q+1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: q+2
       315: q+1
       317: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: q^2+3q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 4
       338: 4
       340: 4
       342: 2q+1
       344: q+1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 4
       352: q+1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 4
       360: 2q+2
       362: 2q+2
       364: 2q+1
       366: q+1
       367: 4q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 4
       372: 4
       373: 2q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       413: q+1
       417: 1
       423: 1
       425: 1
       427: 4
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 2
       444: 2
       445: 4
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 2
       462: 2
       463: 4
       465: 2q+2
       467: q+1
       469: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: 2
       479: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 4
       485: 4
       487: 4
       489: 2q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 4
       497: 1
       498: 1
       499: 1
       500: 1
       501: 4
       508: q+1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2
       547: 2
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2
       563: 2
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       585: 1
       597: 1
       599: 1
       601: 4
       605: 1
       609: 1
       613: 1
       615: 2
       616: 2
       617: 4
       623: 1
       625: 1
       629: 1
       631: 2
       632: 2
       633: 4
       639: q+1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       656: 2
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       693: 1
       696: 1
       697: 1
       698: 1
       733: 2
       735: 2
       749: 2
       751: 2
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       781: 1
       797: 1
       809: 1
       811: 1
       821: 1
       833: 1
       835: 1
       849: 1
       851: 1
       855: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
       884: 1
       887: 1
       888: 1
       889: 1
      1022: 1
      1038: 1
      1048: 1
      1060: 1
      1062: 1
      1083: 1
      1266: 1

1267:    0: 3q^2+8q+2
         1: 6q^2+8q+2
         2: 3q^2+8q+2
         3: 6q^2+8q+2
         4: q^3+4q^2+6q+2
         5: 3q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: q^3+4q^2+6q+2
         8: 3q^2+8q+2
         9: q^4+2q^3+3q^2+3q+1
        10: q^2+7q+2
        11: q^2+7q+2
        12: 3q^2+5q+2
        13: 3q^2+8q+2
        14: q^3+4q^2+6q+2
        15: 3q^2+8q+2
        16: q^2+7q+2
        17: q^2+7q+2
        18: q^3+2q^2+3q+1
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 3q^2+8q+2
        23: 6q^2+8q+2
        24: 3q^2+8q+2
        25: 3q^2+8q+2
        26: 6q^2+8q+2
        27: 3q^2+8q+2
        28: 6q+2
        29: q^2+5q+2
        30: 2q^2+6q+2
        31: q^2+7q+2
        32: 3q^2+8q+2
        33: q^2+7q+2
        34: q^2+7q+2
        35: 3q^2+8q+2
        36: q^2+7q+2
        37: q^2+2q
        38: 2q^2+6q+2
        39: 2q^2+2q
        40: 4q^2+6q+2
        41: q^2+2q
        42: 2q^2+6q+2
        43: q^2+7q+2
        44: 3q^2+5q+2
        45: q^2+7q+2
        46: q^2+7q+2
        47: q^2+7q+2
        48: q^3+2q^2+3q+1
        49: 5q+2
        50: 5q+2
        51: q^2+3q+1
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 2q
        63: q^2+5q+2
        64: q^2+2q
        65: 2q^2+6q+2
        66: 2q
        67: q^2+5q+2
        68: 6q+2
        69: 2q+1
        70: q^2+5q+2
        71: 4q+2
        72: 3q+2
        73: 3q+2
        75: q^2+4q+2
        77: 2q^2+4q+2
        79: q^2+4q+2
        80: q^2+7q+2
        81: q^2+7q+2
        82: q^2+5q+2
        83: 2q^2+6q+2
        84: q^2+7q+2
        85: q^2+7q+2
        86: q^2+5q+2
        87: 2q^2+6q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 5q+2
        92: 5q+2
        93: q^2+3q+1
        94: 5q+2
        95: 5q+2
        96: q^2+3q+1
        97: 5q+2
        98: 5q+2
        99: q^2+3q+1
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q
       104: 2q+1
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+2
       114: q^2+3q+2
       116: q^2+4q+2
       117: 3q+1
       118: 3q+1
       119: 3q+1
       120: 3q+1
       121: 2q
       122: q^2+5q+2
       123: 2q
       124: q^2+5q+2
       125: 2q+2
       126: q+1
       128: 2q+2
       130: 2q+2
       132: 2q+1
       133: 4q+2
       134: 2q+1
       135: 3q+2
       136: 3q+2
       137: 2q+2
       138: 2q+1
       139: 4q+2
       140: 3q+2
       141: q^2+5q+2
       142: 3q+2
       143: 2q+2
       144: 2q+1
       145: 4q+2
       146: q^2+5q+2
       147: 3q+2
       148: 3q+2
       149: q^2+5q+2
       150: 2q^2+6q+2
       152: q^2+4q+2
       154: 2q^2+4q+2
       156: q^2+4q+2
       157: 2
       158: 2
       159: q+1
       160: 5q+2
       161: 5q+2
       162: q^2+3q+1
       163: 5q+2
       164: 5q+2
       165: q^2+3q+1
       166: 5q+2
       167: 5q+2
       168: q^2+3q+1
       170: 1
       171: 1
       173: q
       174: 2q+1
       175: 2q+1
       176: q
       178: q+1
       180: 2q+2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: q+2
       190: q^2+3q+2
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: q+2
       208: 2q+2
       210: q^2+3q+2
       212: q^2+4q+2
       214: 2q+2
       216: 2q+2
       218: 2q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: q+1
       227: 4q+2
       228: 2q+1
       229: 3q+2
       230: 3q+2
       231: q+1
       232: 4q+2
       233: 2q+1
       234: 3q+2
       235: 3q+2
       236: 2q+1
       238: 2q+2
       240: 2q+2
       242: 2q+1
       243: 4q+2
       244: 3q+2
       245: 3q+2
       246: q^2+5q+2
       247: 4
       248: 4
       249: 2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 5q+2
       257: 5q+2
       258: q^2+3q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: 2q+2
       282: q+1
       288: q+1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       314: q+2
       316: q+1
       318: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       326: q^2+3q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 4
       339: 4
       341: 4
       343: 2q+1
       344: q+1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 4
       352: q+1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 4
       361: 2q+2
       363: 2q+2
       365: 2q+1
       366: q+1
       367: 4q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 4
       372: 4
       373: 2q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       414: q+1
       418: 1
       424: 1
       426: 1
       428: 4
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 2
       444: 2
       446: 4
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 2
       462: 2
       464: 4
       466: 2q+2
       468: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: 2
       479: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 4
       486: 4
       488: 4
       490: 2q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 4
       497: 1
       498: 1
       499: 1
       500: 1
       501: 4
       508: q+1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 2
       548: 2
       554: 1
       556: 1
       558: 1
       560: 1
       562: 2
       564: 2
       566: 1
       567: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       586: 1
       598: 1
       600: 1
       602: 4
       606: 1
       610: 1
       614: 1
       615: 2
       616: 2
       618: 4
       624: 1
       626: 1
       630: 1
       631: 2
       632: 2
       634: 4
       640: q+1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       655: 2
       656: 2
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       694: 1
       699: 1
       700: 1
       701: 1
       734: 2
       736: 2
       750: 2
       752: 2
       759: 1
       760: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       782: 1
       798: 1
       810: 1
       812: 1
       822: 1
       834: 1
       836: 1
       850: 1
       852: 1
       856: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       890: 1
       891: 1
       892: 1
      1023: 1
      1039: 1
      1049: 1
      1061: 1
      1063: 1
      1083: 1
      1267: 1

1268:    0: 2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^3+2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^4+2q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^3+q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^3+2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^3+2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+3q+2
        31: 4q+2
        32: 2q^2+4q+2
        33: 2q^2+2q+2
        34: 4q+2
        35: 2q^2+4q+2
        36: 2q^2+2q+2
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+q^2+2q+1
        40: q^3+q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+1
        49: q^2+q+2
        50: q^2+q+2
        51: 2q+1
        52: q^2+3q+2
        53: q^3+q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^3+q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: 2q+2
        62: 2q+1
        63: 2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+q+1
        67: q^2+q+1
        68: 2q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: q+2
        73: q^2+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+2q+2
        82: 3q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+2q+2
        86: 3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: q^2+q+2
        92: q^2+q+2
        93: 2q+1
        94: q^2+q+2
        95: q^2+q+2
        96: 2q+1
        97: q^2+q+2
        98: q^2+q+2
        99: 2q+1
       100: q^2+3q+2
       101: q^3+q^2+3q+2
       102: q^2+3q+2
       103: q+1
       104: q+1
       107: q+2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+q+1
       124: q^2+q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: q+2
       136: q^2+2
       137: 2q+2
       138: q+1
       139: q+2
       140: q+2
       141: 3q+2
       142: q^2+2
       143: 2q+2
       144: q+1
       145: q+2
       146: 3q+2
       147: q+2
       148: q^2+2
       149: 3q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: q^2+q+2
       161: q^2+q+2
       162: 2q+1
       163: q^2+q+2
       164: q^2+q+2
       165: 2q+1
       166: q^2+q+2
       167: q^2+q+2
       168: 2q+1
       169: 1
       170: 1
       173: q+1
       174: q+1
       183: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2q+2
       201: q+2
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: q+1
       227: q+2
       228: q+1
       229: q+2
       230: q^2+2
       231: q+1
       232: q+2
       233: q+1
       234: q+2
       235: q^2+2
       236: q+1
       243: q+2
       244: q+2
       245: q^2+2
       246: 3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: q^2+q+2
       257: q^2+q+2
       258: 2q+1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: q+1
       276: q+1
       283: q+1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: q+2
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       313: 1
       314: 1
       319: q+2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: q+1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: 1
       351: 2
       352: q+1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: 2
       366: q+1
       367: q+2
       368: q+1
       369: q+2
       370: q^2+2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       386: 1
       393: 1
       394: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 1
       429: q+1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       447: q+1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       471: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: q+1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: 1
       541: 1
       542: 1
       557: 1
       560: 1
       565: 1
       566: 1
       573: 1
       574: 1
       589: 1
       593: 1
       603: 1
       615: 2
       619: 1
       631: 1
       632: 1
       641: q+1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       801: 1
       805: 1
       825: 1
       829: 1
       845: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
      1026: 1
      1040: 1
      1052: 1
      1056: 1
      1083: 1
      1268: 1

1269:    0: 2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^3+2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^4+2q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^3+q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^3+2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^3+2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+3q+2
        31: 4q+2
        32: 2q^2+4q+2
        33: 2q^2+2q+2
        34: 4q+2
        35: 2q^2+4q+2
        36: 2q^2+2q+2
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+q^2+2q+1
        40: q^3+q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+1
        49: q^2+q+2
        50: q^2+q+2
        51: 2q+1
        52: q^2+3q+2
        53: q^3+q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^3+q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        61: 2q+2
        62: 2q+1
        63: 2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+q+1
        67: q^2+q+1
        68: 2q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: q+2
        73: q^2+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+2q+2
        82: 3q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+2q+2
        86: 3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: q^2+q+2
        92: q^2+q+2
        93: 2q+1
        94: q^2+q+2
        95: q^2+q+2
        96: 2q+1
        97: q^2+q+2
        98: q^2+q+2
        99: 2q+1
       100: q^2+3q+2
       101: q^3+q^2+3q+2
       102: q^2+3q+2
       105: q+1
       106: q+1
       108: q+2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+q+1
       124: q^2+q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: q+2
       136: q^2+2
       137: 2q+2
       138: q+1
       139: q+2
       140: q+2
       141: 3q+2
       142: q^2+2
       143: 2q+2
       144: q+1
       145: q+2
       146: 3q+2
       147: q+2
       148: q^2+2
       149: 3q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: q^2+q+2
       161: q^2+q+2
       162: 2q+1
       163: q^2+q+2
       164: q^2+q+2
       165: 2q+1
       166: q^2+q+2
       167: q^2+q+2
       168: 2q+1
       171: 1
       172: 1
       175: q+1
       176: q+1
       184: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: q+2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2q+2
       202: q+2
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: 1
       226: q+1
       227: q+2
       228: q+1
       229: q+2
       230: q^2+2
       231: q+1
       232: q+2
       233: q+1
       234: q+2
       235: q^2+2
       236: q+1
       243: q+2
       244: q+2
       245: q^2+2
       246: 3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: q^2+q+2
       257: q^2+q+2
       258: 2q+1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: q+1
       278: q+1
       284: q+1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: q+2
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       313: 1
       314: 1
       320: q+2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: q+1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: 1
       351: 2
       352: q+1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: 1
       359: 2
       366: q+1
       367: q+2
       368: q+1
       369: q+2
       370: q^2+2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       387: 1
       388: 1
       395: 1
       396: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 1
       430: q+1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       448: q+1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       472: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: q+1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: 1
       543: 1
       544: 1
       558: 1
       559: 1
       567: 1
       568: 1
       575: 1
       576: 1
       590: 1
       594: 1
       604: 1
       616: 2
       620: 1
       631: 1
       632: 1
       642: q+1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       802: 1
       806: 1
       826: 1
       830: 1
       846: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
      1027: 1
      1041: 1
      1053: 1
      1057: 1
      1083: 1
      1269: 1

1270:    0: 2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^3+2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^4+2q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^3+q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^3+2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^3+2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+3q+2
        31: 4q+2
        32: 2q^2+4q+2
        33: 2q^2+2q+2
        34: 4q+2
        35: 2q^2+4q+2
        36: 2q^2+2q+2
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+q^2+2q+1
        40: q^3+q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+1
        49: q^2+q+2
        50: q^2+q+2
        51: 2q+1
        52: q^2+3q+2
        53: q^3+q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^3+q^2+3q+2
        57: q^2+3q+2
        58: 2q+2
        60: q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+q+1
        67: q^2+q+1
        68: 2q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: q^2+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+2q+2
        82: 3q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+2q+2
        86: 3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: q^2+q+2
        92: q^2+q+2
        93: 2q+1
        94: q^2+q+2
        95: q^2+q+2
        96: 2q+1
        97: q^2+q+2
        98: q^2+q+2
        99: 2q+1
       100: q^2+3q+2
       101: q^3+q^2+3q+2
       102: q^2+3q+2
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+q+1
       124: q^2+q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: q^2+2
       136: q+2
       137: 2q+2
       138: q+1
       139: q+2
       140: q^2+2
       141: 3q+2
       142: q+2
       143: 2q+2
       144: q+1
       145: q+2
       146: 3q+2
       147: q^2+2
       148: q+2
       149: 3q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: q^2+q+2
       161: q^2+q+2
       162: 2q+1
       163: q^2+q+2
       164: q^2+q+2
       165: 2q+1
       166: q^2+q+2
       167: q^2+q+2
       168: 2q+1
       169: 1
       171: 1
       173: q+1
       175: q+1
       183: 1
       184: 1
       185: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q+2
       193: 1
       194: 1
       195: q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: q+2
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: q+2
       228: q+1
       229: q^2+2
       230: q+2
       231: q+1
       232: q+2
       233: q+1
       234: q^2+2
       235: q+2
       236: q+1
       243: q+2
       244: q^2+2
       245: q+2
       246: 3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: q^2+q+2
       257: q^2+q+2
       258: 2q+1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       285: q+1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       303: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+2
       313: 1
       314: 1
       319: 1
       320: 1
       321: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: q+1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: 2
       352: q+1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: q+1
       359: 2
       366: q+1
       367: q+2
       368: q+1
       369: q^2+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       387: 1
       393: 1
       395: 1
       401: 1
       402: 1
       405: 1
       408: 1
       421: 1
       431: q+1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 1
       444: 1
       449: q+1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       471: 1
       472: 1
       473: q+2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: q+1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: q+1
       541: 1
       544: 1
       557: 1
       558: 1
       565: 1
       567: 1
       573: 1
       576: 1
       591: 1
       595: 1
       607: 1
       615: 1
       616: 1
       621: 1
       631: 2
       643: q+1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       803: 1
       807: 1
       827: 1
       831: 1
       847: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
      1028: 1
      1044: 1
      1054: 1
      1058: 1
      1083: 1
      1270: 1

1271:    0: 2q^2+4q+2
         1: 2q^3+2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^3+2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^4+2q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+2q+2
        17: 2q^2+2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^3+q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^3+2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^3+2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+3q+2
        31: 4q+2
        32: 2q^2+4q+2
        33: 2q^2+2q+2
        34: 4q+2
        35: 2q^2+4q+2
        36: 2q^2+2q+2
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+q^2+2q+1
        40: q^3+q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+2q+2
        47: 2q^2+2q+2
        48: q^2+2q+1
        49: q^2+q+2
        50: q^2+q+2
        51: 2q+1
        52: q^2+3q+2
        53: q^3+q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^3+q^2+3q+2
        57: q^2+3q+2
        59: 2q+2
        60: q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+q+1
        67: q^2+q+1
        68: 2q+2
        69: q+1
        70: 3q+2
        71: q+2
        72: q^2+2
        73: q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+2q+2
        82: 3q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+2q+2
        86: 3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: q^2+q+2
        92: q^2+q+2
        93: 2q+1
        94: q^2+q+2
        95: q^2+q+2
        96: 2q+1
        97: q^2+q+2
        98: q^2+q+2
        99: 2q+1
       100: q^2+3q+2
       101: q^3+q^2+3q+2
       102: q^2+3q+2
       104: q+1
       106: q+1
       107: 1
       108: 1
       110: q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+q+1
       124: q^2+q+1
       125: 2q+2
       126: q+1
       133: q+2
       134: q+1
       135: q^2+2
       136: q+2
       137: 2q+2
       138: q+1
       139: q+2
       140: q^2+2
       141: 3q+2
       142: q+2
       143: 2q+2
       144: q+1
       145: q+2
       146: 3q+2
       147: q^2+2
       148: q+2
       149: 3q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: q^2+q+2
       161: q^2+q+2
       162: 2q+1
       163: q^2+q+2
       164: q^2+q+2
       165: 2q+1
       166: q^2+q+2
       167: q^2+q+2
       168: 2q+1
       170: 1
       172: 1
       174: q+1
       176: q+1
       183: 1
       184: 1
       186: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2q+2
       193: 1
       194: 1
       196: q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: 1
       202: 1
       204: q+2
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: q+1
       226: q+1
       227: q+2
       228: q+1
       229: q^2+2
       230: q+2
       231: q+1
       232: q+2
       233: q+1
       234: q^2+2
       235: q+2
       236: q+1
       243: q+2
       244: q^2+2
       245: q+2
       246: 3q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: q^2+q+2
       257: q^2+q+2
       258: 2q+1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       286: q+1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       304: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       310: q+2
       313: 1
       314: 1
       319: 1
       320: 1
       322: q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: q+1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: q+1
       351: 2
       352: q+1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: q+1
       359: 2
       366: q+1
       367: q+2
       368: q+1
       369: q^2+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       386: 1
       388: 1
       394: 1
       396: 1
       403: 1
       404: 1
       406: 1
       407: 1
       422: 1
       432: q+1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 1
       444: 1
       450: q+1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       471: 1
       472: 1
       474: q+2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: q+1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: q+1
       542: 1
       543: 1
       559: 1
       560: 1
       566: 1
       568: 1
       574: 1
       575: 1
       592: 1
       596: 1
       608: 1
       615: 1
       616: 1
       622: 1
       632: 2
       644: q+1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       804: 1
       808: 1
       828: 1
       832: 1
       848: 1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: 1
      1029: 1
      1045: 1
      1055: 1
      1059: 1
      1083: 1
      1271: 1

1272:    0: 6q^2+8q+2
         1: 6q^2+8q+2
         2: 3q^3+7q^2+5q+1
         3: 6q^2+8q+2
         4: 2q^3+6q^2+6q+2
         5: 6q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: q^4+4q^3+6q^2+4q+1
         8: 3q^3+7q^2+5q+1
         9: q^5+3q^4+4q^3+4q^2+3q+1
        10: 6q^2+8q+2
        11: 6q^2+8q+2
        12: 2q^3+6q^2+6q+2
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^4+3q^3+4q^2+3q+1
        19: 4q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^3+5q^2+4q+1
        22: 6q^2+8q+2
        23: 6q^2+8q+2
        24: 3q^3+7q^2+5q+1
        25: 6q^2+8q+2
        26: 6q^2+8q+2
        27: 3q^3+7q^2+5q+1
        28: 2q^2+8q+2
        29: 4q^2+6q+2
        30: 2q^2+3q+1
        31: 6q^2+8q+2
        32: 3q^2+4q+1
        33: 2q^2+8q+2
        34: 6q^2+8q+2
        35: 3q^2+4q+1
        36: 2q^2+8q+2
        37: 4q^2+6q+2
        38: 2q^2+2q
        39: 4q^2+6q+2
        40: 2q^2+2q
        41: 2q^3+5q^2+4q+1
        42: q^3+2q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 6q+2
        50: 6q+2
        51: q^3+3q^2+3q+1
        52: 4q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^3+5q^2+4q+1
        55: 4q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^3+5q^2+4q+1
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 4q^2+6q+2
        63: 2q^2+2q
        64: 2q^2+3q+1
        65: q^2+q
        66: 2q^2+6q+2
        67: 2q
        69: 2q+1
        70: 2q^2+3q+1
        71: 6q+2
        72: 4q+2
        73: 4q+2
        74: 2q^2+4q+2
        76: 2q^2+4q+2
        78: q^3+3q^2+3q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+6q+2
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+6q+2
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 6q+2
        95: 6q+2
        96: q^3+3q^2+3q+1
        97: 6q+2
        98: 6q+2
        99: q^3+3q^2+3q+1
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^3+5q^2+4q+1
       103: q^2+3q+1
       104: q
       105: q
       106: q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 2q+2
       113: 2q^2+4q+2
       115: q^2+2q+1
       121: 2q^2+3q+1
       122: q^2+q
       123: q^2+3q+1
       124: q
       126: 2q+1
       127: 2q+2
       129: 2q+2
       131: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 6q+2
       140: 4q+2
       141: 2q^2+3q+1
       142: 4q+2
       143: q^2+4q+1
       144: 2q+1
       145: 6q+2
       146: 2q^2+3q+1
       147: 4q+2
       148: 4q+2
       149: 4q^2+6q+2
       150: 2q^2+3q+1
       151: 2q^2+4q+2
       153: 2q^2+4q+2
       155: q^3+3q^2+3q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 6q+2
       167: 6q+2
       168: q^3+3q^2+3q+1
       169: q+1
       172: q+1
       177: q+1
       179: 2q+2
       181: 2
       187: q+1
       189: q^2+2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+2
       207: q^2+3q+1
       208: q
       209: 2q^2+4q+2
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: 2q+2
       239: 2q+2
       241: q^2+2q+1
       243: 6q+2
       244: 4q+2
       245: 4q+2
       246: 2q^2+3q+1
       247: 4
       248: 4
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: 1
       262: 1
       267: q+1
       269: q+1
       271: q+1
       273: q+1
       281: q+1
       287: q+1
       289: 1
       291: 1
       297: q+1
       301: 2
       305: q+1
       311: 2
       313: q+1
       315: q+1
       317: 2q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+2
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       338: 4
       340: 4
       342: q^2+2q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 4
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 4
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       389: 1
       391: 1
       397: 1
       399: 1
       405: q+1
       406: q+1
       411: q+1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 4
       433: 1
       435: 1
       441: q+1
       443: 2
       444: 2
       445: 4
       451: 1
       455: 1
       459: q+1
       461: 2
       462: 2
       463: 4
       467: q+1
       469: q+1
       475: q+1
       477: 2
       479: 2
       480: 2
       483: 1
       485: 2
       487: 2
       489: q+1
       491: 1
       493: q+1
       494: q+1
       495: 1
       496: 2
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       545: 2
       547: 2
       561: 2
       563: 2
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 2
       623: 1
       625: 1
       627: 1
       629: 1
       633: 2
       637: q+1
       645: 1
       651: 1
       653: q+1
       655: 1
       656: 1
       666: 2
       668: 2
       670: q+1
       673: 1
       677: 1
       678: 2
       679: 1
       683: 1
       684: 2
       685: 1
       687: q+1
       688: q+1
       689: 1
       693: 1
       696: 1
       697: 1
       698: 1
       769: 1
       772: 1
       783: 1
       799: 1
       809: 1
       811: 1
       813: 2
       823: 1
       833: 1
       835: 1
       837: 2
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       872: 1
       876: 1
       879: 1
       880: 1
       982: 1
       985: 1
      1024: 1
      1042: 1
      1050: 1
      1060: 1
      1062: 1
      1085: 1
      1272: 1

1273:    0: 6q^2+8q+2
         1: 6q^2+8q+2
         2: 3q^3+7q^2+5q+1
         3: 6q^2+8q+2
         4: 2q^3+6q^2+6q+2
         5: 6q^2+8q+2
         6: 2q^3+6q^2+6q+2
         7: q^4+4q^3+6q^2+4q+1
         8: 3q^3+7q^2+5q+1
         9: q^5+3q^4+4q^3+4q^2+3q+1
        10: 6q^2+8q+2
        11: 6q^2+8q+2
        12: 2q^3+6q^2+6q+2
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: q^4+3q^3+4q^2+3q+1
        19: 4q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^3+5q^2+4q+1
        22: 6q^2+8q+2
        23: 6q^2+8q+2
        24: 3q^3+7q^2+5q+1
        25: 6q^2+8q+2
        26: 6q^2+8q+2
        27: 3q^3+7q^2+5q+1
        28: 2q^2+8q+2
        29: 4q^2+6q+2
        30: 2q^2+3q+1
        31: 6q^2+8q+2
        32: 3q^2+4q+1
        33: 2q^2+8q+2
        34: 6q^2+8q+2
        35: 3q^2+4q+1
        36: 2q^2+8q+2
        37: 2q^2+2q
        38: 4q^2+6q+2
        39: 2q^2+2q
        40: 4q^2+6q+2
        41: q^3+2q^2+q
        42: 2q^3+5q^2+4q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 6q+2
        50: 6q+2
        51: q^3+3q^2+3q+1
        52: 4q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^3+5q^2+4q+1
        55: 4q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^3+5q^2+4q+1
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 2q^2+2q
        63: 4q^2+6q+2
        64: q^2+q
        65: 2q^2+3q+1
        66: 2q
        67: 2q^2+6q+2
        69: 2q+1
        70: 2q^2+3q+1
        71: 6q+2
        72: 4q+2
        73: 4q+2
        75: 2q^2+4q+2
        77: 2q^2+4q+2
        79: q^3+3q^2+3q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 4q^2+6q+2
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 4q^2+6q+2
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 6q+2
        95: 6q+2
        96: q^3+3q^2+3q+1
        97: 6q+2
        98: 6q+2
        99: q^3+3q^2+3q+1
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^3+5q^2+4q+1
       103: q
       104: q^2+3q+1
       105: q^2+3q+1
       106: q
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       112: 2q+2
       114: 2q^2+4q+2
       116: q^2+2q+1
       121: q^2+q
       122: 2q^2+3q+1
       123: q
       124: q^2+3q+1
       126: 2q+1
       128: 2q+2
       130: 2q+2
       132: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 6q+2
       140: 4q+2
       141: 2q^2+3q+1
       142: 4q+2
       143: q^2+4q+1
       144: 2q+1
       145: 6q+2
       146: 2q^2+3q+1
       147: 4q+2
       148: 4q+2
       149: 4q^2+6q+2
       150: 2q^2+3q+1
       152: 2q^2+4q+2
       154: 2q^2+4q+2
       156: q^3+3q^2+3q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 6q+2
       167: 6q+2
       168: q^3+3q^2+3q+1
       170: q+1
       171: q+1
       178: q+1
       180: 2q+2
       182: 2
       188: q+1
       190: q^2+2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       206: 2q+2
       207: q
       208: q^2+3q+1
       210: 2q^2+4q+2
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: 2q+2
       240: 2q+2
       242: q^2+2q+1
       243: 6q+2
       244: 4q+2
       245: 4q+2
       246: 2q^2+3q+1
       247: 4
       248: 4
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: 1
       261: 1
       268: q+1
       270: q+1
       272: q+1
       274: q+1
       282: q+1
       288: q+1
       290: 1
       292: 1
       298: q+1
       302: 2
       306: q+1
       312: 2
       314: q+1
       316: q+1
       318: 2q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       324: 2q+2
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       339: 4
       341: 4
       343: q^2+2q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 4
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 4
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       390: 1
       392: 1
       398: 1
       400: 1
       407: q+1
       408: q+1
       412: q+1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 4
       434: 1
       436: 1
       442: q+1
       443: 2
       444: 2
       446: 4
       452: 1
       456: 1
       460: q+1
       461: 2
       462: 2
       464: 4
       468: q+1
       470: q+1
       476: q+1
       478: 2
       479: 2
       480: 2
       483: 1
       486: 2
       488: 2
       490: q+1
       491: 1
       493: q+1
       494: q+1
       495: 1
       496: 2
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       546: 2
       548: 2
       562: 2
       564: 2
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 2
       624: 1
       626: 1
       628: 1
       630: 1
       634: 2
       638: q+1
       646: 1
       652: 1
       654: q+1
       655: 1
       656: 1
       667: 2
       669: 2
       671: q+1
       673: 1
       677: 1
       678: 2
       679: 1
       683: 1
       684: 2
       685: 1
       687: q+1
       688: q+1
       689: 1
       694: 1
       699: 1
       700: 1
       701: 1
       770: 1
       773: 1
       784: 1
       800: 1
       810: 1
       812: 1
       814: 2
       824: 1
       834: 1
       836: 1
       838: 2
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       872: 1
       876: 1
       879: 1
       880: 1
       983: 1
       986: 1
      1025: 1
      1043: 1
      1051: 1
      1061: 1
      1063: 1
      1085: 1
      1273: 1

1274:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
         9: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        30: 2q+1
        32: 3q+1
        33: 3q+1
        35: 3q+1
        36: 3q+1
        37: 2q+1
        38: q
        39: 2q+1
        40: q
        41: 2q+1
        42: q
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        64: 2q+1
        65: q
        66: 2q+1
        67: q
        69: 2q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        81: 3q+1
        83: 2q+1
        85: 3q+1
        87: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       111: 1
       115: q+1
       123: 2q+1
       124: q
       127: q+1
       129: q+1
       131: q+1
       134: 2q+1
       135: q+1
       136: q+1
       138: 2q+1
       140: q+1
       142: q+1
       144: 2q+1
       147: q+1
       148: q+1
       150: 2q+1
       151: q+1
       153: q+1
       155: q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       177: q+1
       181: 1
       187: 1
       197: 1
       205: 1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       223: q+1
       225: q+1
       228: 2q+1
       229: q+1
       230: q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       244: q+1
       245: q+1
       247: 2
       248: 2
       249: q+1
       256: 2q+1
       257: 2q+1
       258: 2q+1
       281: q+1
       289: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: q+1
       323: 1
       336: 1
       338: 2
       340: 2
       342: q+1
       348: q+1
       350: q+1
       351: 2
       356: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       368: 2q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 2
       451: 1
       455: 1
       463: 2
       467: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       485: 2
       487: 2
       489: q+1
       491: 1
       495: 1
       496: 2
       500: 1
       501: 2
       512: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       577: 1
       580: 1
       597: 1
       605: 1
       613: 1
       617: 2
       623: 1
       629: 1
       633: 2
       645: 1
       651: 1
       655: 1
       656: 1
       658: 2
       660: 2
       662: q+1
       664: 1
       674: 2
       679: 1
       680: 2
       685: 1
       689: 1
       769: 1
       772: 1
       779: 1
       795: 2
       809: 1
       819: 2
       833: 1
       843: 1
       844: 1
       849: 1
       855: 1
       870: 1
       874: 1
       880: 1
       968: 1
       971: 1
      1020: 1
      1036: 1
      1060: 1
      1084: 1
      1274: 1

1275:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q+1
         9: q^2+2q+1
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        30: 2q+1
        32: 3q+1
        33: 3q+1
        35: 3q+1
        36: 3q+1
        37: q
        38: 2q+1
        39: q
        40: 2q+1
        41: q
        42: 2q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        64: q
        65: 2q+1
        66: q
        67: 2q+1
        69: 2q+1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        81: 3q+1
        83: 2q+1
        85: 3q+1
        87: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       112: 1
       116: q+1
       123: q
       124: 2q+1
       128: q+1
       130: q+1
       132: q+1
       134: 2q+1
       135: q+1
       136: q+1
       138: 2q+1
       140: q+1
       142: q+1
       144: 2q+1
       147: q+1
       148: q+1
       150: 2q+1
       152: q+1
       154: q+1
       156: q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       178: q+1
       182: 1
       188: 1
       198: 1
       206: 1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       223: q+1
       225: q+1
       228: 2q+1
       229: q+1
       230: q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       244: q+1
       245: q+1
       247: 2
       248: 2
       249: q+1
       256: 2q+1
       257: 2q+1
       258: 2q+1
       282: q+1
       290: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: q+1
       324: 1
       336: 1
       339: 2
       341: 2
       343: q+1
       348: q+1
       350: q+1
       351: 2
       356: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       368: 2q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 2
       452: 1
       456: 1
       464: 2
       468: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       486: 2
       488: 2
       490: q+1
       491: 1
       495: 1
       496: 2
       500: 1
       501: 2
       512: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       578: 1
       581: 1
       598: 1
       606: 1
       614: 1
       618: 2
       624: 1
       630: 1
       634: 2
       646: 1
       652: 1
       655: 1
       656: 1
       659: 2
       661: 2
       663: q+1
       664: 1
       674: 2
       679: 1
       680: 2
       685: 1
       689: 1
       770: 1
       773: 1
       780: 1
       796: 2
       810: 1
       820: 2
       834: 1
       843: 1
       844: 1
       850: 1
       856: 1
       870: 1
       874: 1
       880: 1
       969: 1
       972: 1
      1021: 1
      1037: 1
      1061: 1
      1084: 1
      1275: 1

1276:    0: 2q^2+2q+2
         1: 2q^2+2q+2
         2: 2q^2+q+1
         3: 2q^2+2q+2
         4: 2q^2+2q+2
         5: 2q^2+2q+2
         6: 2q^2+2q+2
         7: 2q^2+q+1
         8: 2q^2+q+1
         9: q^4+q^2+q+1
        10: 2q^2+2q+2
        11: 2q^2+2q+2
        12: 2q^2+2q+2
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q^2+2q+2
        20: 2q^2+2q+2
        21: 2q^2+q+1
        22: 2q^2+2q+2
        23: 2q^2+2q+2
        24: 2q^2+q+1
        25: 2q^2+2q+2
        26: 2q^2+2q+2
        27: 2q^2+q+1
        28: 2q+2
        29: 2q^2+2q+2
        30: q^2+1
        31: 2q^2+2q+2
        32: q^2+1
        33: 2q+2
        34: 2q^2+2q+2
        35: q^2+1
        36: 2q+2
        37: 2q^2+2
        38: 2q
        39: 2q^2+2
        40: 2q
        41: q^2+q+1
        42: q^2
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q^2+2q+2
        53: 2q^2+2q+2
        54: 2q^2+q+1
        55: 2q^2+2q+2
        56: 2q^2+2q+2
        57: 2q^2+q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q^2+2
        63: 2q
        64: q^2+1
        66: 2
        67: 2q
        69: 1
        70: q^2+1
        71: 2q+2
        72: 2q+2
        73: 2q+2
        74: 2q^2+2
        75: 2q
        76: 2q^2+2
        77: 2q
        78: q^2+q+1
        79: q^2
        80: q^2+1
        81: 1
        82: 2q^2+2q+2
        83: q^2+1
        84: q^2+1
        85: 1
        86: 2q^2+2q+2
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2q^2+2q+2
       101: 2q^2+2q+2
       102: 2q^2+q+1
       103: 1
       104: q
       105: q
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       112: 2q
       113: 2q^2+2
       114: 2q
       115: q^2+1
       121: q^2+1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2q+2
       141: q^2+1
       142: 2q+2
       143: 1
       144: 1
       145: 2q+2
       146: q^2+1
       147: 2q+2
       148: 2q+2
       149: 2q^2+2q+2
       150: q^2+1
       151: 2q^2+2
       152: 2q
       153: 2q^2+2
       154: 2q
       155: q^2+q+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+2
       167: 2q+2
       168: q^2+q+1
       169: 1
       170: q
       171: q
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: q^2+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       198: 2q
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       206: 2q
       207: 1
       209: 2q^2+2
       210: 2q
       211: q^2+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2q+2
       244: 2q+2
       245: 2q+2
       246: q^2+1
       247: 2q+2
       248: 2q+2
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       287: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       324: 2q
       325: q^2+1
       334: 1
       335: 1
       336: 1
       337: 2q+2
       338: 2
       340: 2
       342: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2q+2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2q+2
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       407: q
       408: q
       423: 1
       425: 1
       427: 2
       433: 1
       441: 1
       443: q+1
       444: q+1
       445: 2
       451: 1
       459: 1
       461: q+1
       462: q+1
       463: 2
       469: 1
       475: 1
       477: 2
       479: 2
       480: 2q
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       599: 1
       609: 1
       613: 1
       625: 1
       629: 1
       645: 1
       653: 1
       655: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       693: 1
       697: 1
       791: 1
       811: 1
       835: 1
       851: 1
       855: 1
       857: 1
       872: 1
       876: 1
       879: 1
       880: 1
      1008: 1
      1062: 1
      1064: 1
      1085: 1
      1276: 1

1277:    0: 2q^2+2q+2
         1: 2q^2+2q+2
         2: 2q^2+q+1
         3: 2q^2+2q+2
         4: 2q^2+2q+2
         5: 2q^2+2q+2
         6: 2q^2+2q+2
         7: 2q^2+q+1
         8: 2q^2+q+1
         9: q^4+q^2+q+1
        10: 2q^2+2q+2
        11: 2q^2+2q+2
        12: 2q^2+2q+2
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q^2+2q+2
        20: 2q^2+2q+2
        21: 2q^2+q+1
        22: 2q^2+2q+2
        23: 2q^2+2q+2
        24: 2q^2+q+1
        25: 2q^2+2q+2
        26: 2q^2+2q+2
        27: 2q^2+q+1
        28: 2q+2
        29: 2q^2+2q+2
        30: q^2+1
        31: 2q^2+2q+2
        32: q^2+1
        33: 2q+2
        34: 2q^2+2q+2
        35: q^2+1
        36: 2q+2
        37: 2q
        38: 2q^2+2
        39: 2q
        40: 2q^2+2
        41: q^2
        42: q^2+q+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q^2+2q+2
        53: 2q^2+2q+2
        54: 2q^2+q+1
        55: 2q^2+2q+2
        56: 2q^2+2q+2
        57: 2q^2+q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q
        63: 2q^2+2
        65: q^2+1
        66: 2q
        67: 2
        69: 1
        70: q^2+1
        71: 2q+2
        72: 2q+2
        73: 2q+2
        74: 2q
        75: 2q^2+2
        76: 2q
        77: 2q^2+2
        78: q^2
        79: q^2+q+1
        80: q^2+1
        81: 1
        82: 2q^2+2q+2
        83: q^2+1
        84: q^2+1
        85: 1
        86: 2q^2+2q+2
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2q^2+2q+2
       101: 2q^2+2q+2
       102: 2q^2+q+1
       103: q
       104: 1
       105: 1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q
       112: 2
       113: 2q
       114: 2q^2+2
       116: q^2+1
       122: q^2+1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2q+2
       141: q^2+1
       142: 2q+2
       143: 1
       144: 1
       145: 2q+2
       146: q^2+1
       147: 2q+2
       148: 2q+2
       149: 2q^2+2q+2
       150: q^2+1
       151: 2q
       152: 2q^2+2
       153: 2q
       154: 2q^2+2
       155: q^2
       156: q^2+q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+2
       167: 2q+2
       168: q^2+q+1
       169: q
       170: 1
       171: 1
       172: q
       178: 1
       180: 2
       182: 2
       188: 1
       190: q^2+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q
       206: 2
       208: 1
       209: 2q
       210: 2q^2+2
       212: q^2+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2q+2
       244: 2q+2
       245: 2q+2
       246: q^2+1
       247: 2q+2
       248: 2q+2
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       288: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: 2
       326: q^2+1
       334: 1
       335: 1
       336: 1
       337: 2q+2
       339: 2
       341: 2
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2q+2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2q+2
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       405: q
       406: q
       407: 1
       408: 1
       424: 1
       426: 1
       428: 2
       434: 1
       442: 1
       443: q+1
       444: q+1
       446: 2
       452: 1
       460: 1
       461: q+1
       462: q+1
       464: 2
       470: 1
       476: 1
       478: 2
       479: 2q
       480: 2
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       581: 2
       600: 1
       610: 1
       614: 1
       626: 1
       630: 1
       646: 1
       654: 1
       656: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       699: 1
       700: 1
       792: 1
       812: 1
       836: 1
       852: 1
       856: 1
       858: 1
       872: 1
       876: 1
       879: 1
       880: 1
      1009: 1
      1063: 1
      1065: 1
      1085: 1
      1277: 1

1278:    0: 1
         1: q^3+1
         2: 1
         3: q^3+1
         4: 1
         5: 1
         6: q^3+1
         7: 1
         8: 1
         9: q^5+1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^3+1
        21: 1
        22: 1
        23: q^3+1
        24: 1
        25: 1
        26: q^3+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: q^3+1
        41: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q^3+1
        54: 1
        55: 1
        56: q^3+1
        57: 1
        64: 1
        66: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: q^3+1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: q^3+1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: q^3+1
       155: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 1
       451: 1
       455: 1
       463: 1
       467: 1
       475: 1
       477: 1
       479: 1
       485: 1
       487: 1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       577: 1
       597: 1
       605: 1
       613: 1
       617: 1
       623: 1
       629: 1
       633: 1
       645: 1
       651: 1
       655: 1
       679: 1
       685: 1
       689: 1
       769: 1
       791: 1
       809: 1
       833: 1
       849: 1
       855: 1
       880: 1
      1010: 1
      1060: 1
      1064: 1
      1278: 1

1279:    0: 1
         1: q^3+1
         2: 1
         3: q^3+1
         4: 1
         5: 1
         6: q^3+1
         7: 1
         8: 1
         9: q^5+1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^3+1
        21: 1
        22: 1
        23: q^3+1
        24: 1
        25: 1
        26: q^3+1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: q^3+1
        42: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q^3+1
        54: 1
        55: 1
        56: q^3+1
        57: 1
        65: 1
        67: 1
        69: 1
        72: 1
        73: 1
        75: 1
        77: q^3+1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: q^3+1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: q^3+1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 1
       452: 1
       456: 1
       464: 1
       468: 1
       476: 1
       478: 1
       480: 1
       486: 1
       488: 1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       581: 1
       598: 1
       606: 1
       614: 1
       618: 1
       624: 1
       630: 1
       634: 1
       646: 1
       652: 1
       656: 1
       679: 1
       685: 1
       689: 1
       773: 1
       792: 1
       810: 1
       834: 1
       850: 1
       856: 1
       880: 1
      1011: 1
      1061: 1
      1065: 1
      1279: 1

1280:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: q+1
        23: q+1
        24: q^2+1
        25: q+1
        26: q+1
        27: q^2+1
        30: 1
        32: 1
        33: q+1
        35: 1
        36: q+1
        37: 1
        38: q
        39: 1
        40: q
        41: 1
        42: q^2
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q+1
        53: q+1
        54: q^2+1
        55: q+1
        56: q+1
        57: q^2+1
        64: 1
        66: 1
        67: q
        69: 1
        72: q+1
        73: q+1
        74: 1
        75: q
        76: 1
        77: q
        78: 1
        79: q^2
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: q+1
        98: q+1
        99: q^2+1
       100: q+1
       101: q+1
       102: q^2+1
       111: 1
       112: q
       115: 1
       123: 1
       127: 1
       128: q
       129: 1
       130: q
       131: 1
       132: q^2
       134: 1
       135: 1
       136: 1
       138: 1
       140: q+1
       142: q+1
       144: 1
       147: q+1
       148: q+1
       150: 1
       151: 1
       152: q
       153: 1
       154: q
       155: 1
       156: q^2
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q^2+1
       177: 1
       181: 1
       182: q
       187: 1
       197: 1
       198: q
       205: 1
       206: q
       211: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q
       239: 1
       240: q
       241: 1
       242: q^2
       244: q+1
       245: q+1
       247: q+1
       248: q+1
       249: q^2+1
       256: 1
       257: 1
       258: 1
       291: 1
       301: 1
       302: q
       305: 1
       311: 1
       312: q
       313: 1
       315: 1
       323: 1
       324: q
       336: 1
       338: 1
       339: q
       340: 1
       341: q
       342: 1
       343: q^2
       348: 1
       350: 1
       351: q+1
       356: 1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       425: 1
       433: 1
       445: 1
       446: q
       451: 1
       463: 1
       464: q
       475: 1
       477: 1
       478: q
       479: 1
       480: q
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       517: 1
       577: 1
       581: q
       613: 1
       629: 1
       645: 1
       655: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       689: 1
       791: 1
       843: 1
       855: 1
       870: 1
       874: 1
       880: 1
      1012: 1
      1064: 1
      1084: 1
      1280: 1

1281:    0: q+1
         1: q+1
         2: q^2+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q^2+1
        19: q+1
        20: q+1
        21: q^2+1
        22: q+1
        23: q+1
        24: q^2+1
        25: q+1
        26: q+1
        27: q^2+1
        30: 1
        32: 1
        33: q+1
        35: 1
        36: q+1
        37: q
        38: 1
        39: q
        40: 1
        41: q^2
        42: 1
        46: 1
        47: 1
        48: 1
        49: q+1
        50: q+1
        51: q^2+1
        52: q+1
        53: q+1
        54: q^2+1
        55: q+1
        56: q+1
        57: q^2+1
        65: 1
        66: q
        67: 1
        69: 1
        72: q+1
        73: q+1
        74: q
        75: 1
        76: q
        77: 1
        78: q^2
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: q^2+1
        97: q+1
        98: q+1
        99: q^2+1
       100: q+1
       101: q+1
       102: q^2+1
       111: q
       112: 1
       116: 1
       124: 1
       127: q
       128: 1
       129: q
       130: 1
       131: q^2
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: q+1
       142: q+1
       144: 1
       147: q+1
       148: q+1
       150: 1
       151: q
       152: 1
       153: q
       154: 1
       155: q^2
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q^2+1
       178: 1
       181: q
       182: 1
       188: 1
       197: q
       198: 1
       205: q
       206: 1
       212: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q
       238: 1
       239: q
       240: 1
       241: q^2
       242: 1
       244: q+1
       245: q+1
       247: q+1
       248: q+1
       249: q^2+1
       256: 1
       257: 1
       258: 1
       292: 1
       301: q
       302: 1
       306: 1
       311: q
       312: 1
       314: 1
       316: 1
       323: q
       324: 1
       336: 1
       338: q
       339: 1
       340: q
       341: 1
       342: q^2
       343: 1
       348: 1
       350: 1
       351: q+1
       356: 1
       358: 1
       359: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       426: 1
       434: 1
       445: q
       446: 1
       452: 1
       463: q
       464: 1
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       517: 1
       577: q
       581: 1
       614: 1
       630: 1
       646: 1
       656: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       689: 1
       792: 1
       844: 1
       856: 1
       870: 1
       874: 1
       880: 1
      1013: 1
      1065: 1
      1084: 1
      1281: 1

1282:    0: q^3+3q^2+2q+4
         1: 4q^2+2q+4
         2: q^3+3q^2+2q+4
         3: q^3+3q^2+2q+4
         4: q^3+3q^2+2q+4
         5: 4q^2+2q+4
         6: 4q^2+2q+4
         7: q^3+3q^2+2q+4
         8: 4q^2+2q+4
         9: q^3+3q^2+2q+4
        10: q^2+2q+4
        11: q^2+2q+4
        12: q^2+2q+4
        13: q^3+3q^2+2q+4
        14: q^3+3q^2+2q+4
        15: 4q^2+2q+4
        16: q^3+3q^2+2q+4
        17: 4q^2+2q+4
        18: q^3+3q^2+2q+4
        19: q^3+3q^2+2q+4
        20: 4q^2+2q+4
        21: q^3+3q^2+2q+4
        22: q^2+4
        23: q^2+4
        24: q^2+4
        25: q^2+4
        26: q^2+4
        27: q^2+4
        28: q^2+2q+4
        29: q^2+2q+4
        30: q^3+3q^2+2q+4
        31: 4
        32: q^2+4
        33: q^2+4
        34: 4
        35: q^2+4
        36: q^2+4
        37: 2
        38: 2
        39: 2
        40: 2
        41: 2
        42: 2
        43: q^2+2q+4
        44: q^2+2q+4
        45: q^2+2q+4
        46: q^3+3q^2+2q+4
        47: 4q^2+2q+4
        48: q^3+3q^2+2q+4
        49: q^3+3q^2+2q+4
        50: 4q^2+2q+4
        51: q^3+3q^2+2q+4
        52: q^2+4
        53: q^2+4
        54: q^2+4
        55: q^2+4
        56: q^2+4
        57: q^2+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 2
        63: 2
        64: 2
        65: 2
        66: 2
        67: 2
        68: q^2+2q+4
        69: q^3+3q^2+2q+4
        70: q^2+2q+4
        71: q^2+2q+4
        72: q^2+4
        73: q^2+4
        74: 2
        75: 2
        76: 2
        77: 2
        78: 2
        79: 2
        80: 4
        81: q^2+4
        82: 4
        83: q^2+4
        84: 4
        85: q^2+4
        86: 4
        87: q^2+4
        88: q^2+2q+4
        89: q^2+2q+4
        90: q^2+2q+4
        91: q^3+3q^2+2q+4
        92: 4q^2+2q+4
        93: q^3+3q^2+2q+4
        94: q^2+4
        95: q^2+4
        96: q^2+4
        97: q^2+4
        98: q^2+4
        99: q^2+4
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 2
       114: 2
       115: 2
       116: 2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 2
       122: 2
       123: 2
       124: 2
       125: q^2+2q+4
       126: q^2+2q+4
       127: 2
       128: 2
       129: 2
       130: 2
       131: 2
       132: 2
       133: q^2+2q+4
       134: q^3+3q^2+2q+4
       135: q^2+4
       136: q^2+4
       137: 4
       138: q^2+4
       139: 4
       141: 4
       142: q^2+4
       143: 4
       144: q^2+4
       145: 4
       146: 4
       147: q^2+4
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q^2+2q+4
       158: q^2+2q+4
       159: q^2+2q+4
       160: q^2+4
       161: q^2+4
       162: q^2+4
       163: q^2+4
       164: q^2+4
       165: q^2+4
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 2
       178: 2
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 2
       190: 2
       191: 2
       192: 2
       195: 2
       196: 2
       199: 2
       200: 2
       201: 2
       202: 2
       207: 2
       208: 2
       209: 1
       210: 1
       211: 1
       212: 1
       213: 2
       214: 2
       215: 2
       216: 2
       217: 2
       218: 2
       219: q^2+2q+4
       220: q^2+2q+4
       221: q^2+2q+4
       222: 4
       223: q^2+4
       224: 4
       225: q^2+4
       226: 4
       227: 4
       228: q^2+4
       230: q^2+4
       231: 4
       232: 4
       233: q^2+4
       234: q^2+4
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 2
       251: 2
       252: 2
       253: 2
       254: 2
       255: 2
       256: 2
       257: 2
       258: 2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2
       280: 2
       281: 2
       282: 2
       283: 2
       284: 2
       285: 2
       286: 2
       287: 2
       288: 2
       289: 2
       290: 2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 2
       304: 2
       307: 2
       308: 2
       315: 1
       316: 1
       317: 1
       318: 1
       325: 1
       326: 1
       333: q^2+2q+4
       334: 4
       335: 4
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 4
       345: 2
       346: 2
       349: 2
       350: q^2+4
       352: 4
       353: 2
       354: 2
       355: 2
       356: q^2+4
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       371: 2
       372: 2
       373: 2
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       413: 2
       414: 2
       417: 2
       418: 2
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 1
       428: 1
       431: 2
       432: 2
       439: 1
       440: 1
       447: 2
       448: 2
       453: 1
       454: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       481: 4
       482: 4
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 2
       492: 2
       494: 2
       497: 2
       498: 2
       508: 2
       509: 1
       510: 1
       515: 2
       516: 2
       517: 2
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       585: 2
       586: 2
       589: 2
       590: 2
       595: 2
       596: 2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       639: 1
       640: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       709: 1
       710: 1
       711: 1
       712: 1
       775: 1
       776: 1
       779: 1
       780: 1
       781: 1
       782: 1
       807: 1
       808: 1
       825: 1
       826: 1
       865: 1
       866: 2
       867: 1
       868: 1
       881: 1
       882: 1
       883: 1
       994: 1
       995: 1
      1072: 1
      1073: 1
      1074: 1
      1282: 1

1283:    0: 2q^2+12q+4
         1: 2q^2+12q+4
         2: q^3+5q^2+8q+4
         3: 2q^2+12q+4
         4: q^3+5q^2+8q+4
         5: 2q^2+12q+4
         6: q^3+5q^2+8q+4
         7: q^4+3q^3+5q^2+5q+4
         8: q^3+5q^2+8q+4
         9: q^4+3q^3+5q^2+5q+4
        10: 2q^2+12q+4
        11: 2q^2+12q+4
        12: q^3+5q^2+8q+4
        13: q^2+8q+4
        14: q^3+3q^2+5q+4
        15: q^2+8q+4
        16: 2q^2+12q+4
        17: 2q^2+12q+4
        18: q^4+3q^3+5q^2+5q+4
        19: q^2+8q+4
        20: q^2+8q+4
        21: q^3+3q^2+5q+4
        22: 2q^2+12q+4
        23: 2q^2+12q+4
        24: q^3+5q^2+8q+4
        25: 8q+4
        26: 8q+4
        27: 2q^2+6q+4
        28: 2q^2+12q+4
        29: q^2+8q+4
        30: q^2+5q+4
        31: 2q^2+12q+4
        32: q^2+8q+4
        33: 2q^2+12q+4
        34: 8q+4
        35: 6q+4
        36: 8q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+3q+2
        42: q^2+3q+2
        43: q^2+8q+4
        44: q^3+3q^2+5q+4
        45: q^2+8q+4
        46: q^2+8q+4
        47: q^2+8q+4
        48: q^3+3q^2+5q+4
        49: q^2+8q+4
        50: q^2+8q+4
        51: q^3+3q^2+5q+4
        52: q^2+8q+4
        53: q^2+8q+4
        54: q^3+3q^2+5q+4
        55: 4q+4
        56: 4q+4
        57: q^2+3q+4
        58: q^2+6q+2
        59: q^2+6q+2
        60: 4q+2
        61: 4q+2
        62: 4q+2
        63: 4q+2
        64: 3q+2
        65: 3q+2
        66: 4q+2
        67: 4q+2
        68: 4q+4
        69: q^2+5q+4
        70: q^2+5q+4
        71: q^2+8q+4
        72: 2q+4
        73: 4q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: q^2+8q+4
        81: q^2+8q+4
        82: q^2+8q+4
        83: q^2+5q+4
        84: 6q+4
        85: 6q+4
        86: 4q+4
        87: 3q+4
        88: q^2+8q+4
        89: q^2+8q+4
        90: q^3+3q^2+5q+4
        91: q^2+3q+4
        92: 4q+4
        93: q^2+3q+4
        94: q^2+8q+4
        95: q^2+8q+4
        96: q^3+3q^2+5q+4
        97: 4q+4
        98: 4q+4
        99: q^2+3q+4
       100: 4q+4
       101: 4q+4
       102: q^2+3q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+2
       108: q+2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2q+2
       118: 2q+2
       119: 2q+2
       120: 2q+2
       121: 3q+2
       122: 3q+2
       123: 3q+2
       124: 3q+2
       125: 4q+4
       126: q^2+5q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q+4
       134: q^2+3q+4
       135: q+4
       136: q+4
       137: q^2+8q+4
       138: q^2+5q+4
       139: q^2+8q+4
       140: 2q+4
       141: q^2+5q+4
       142: 4q+4
       143: 6q+4
       144: 3q+4
       145: 4q+4
       146: 3q+4
       147: 2q+4
       149: 4q+4
       150: 3q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: q^2+3q+4
       158: 4q+4
       159: q^2+3q+4
       160: q^2+3q+4
       161: 4q+4
       162: q^2+3q+4
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+4
       167: 4q+4
       168: q^2+3q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2q+2
       192: 2q+2
       193: q+2
       194: q+2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       199: 2q+2
       200: 2q+2
       201: q+2
       202: q+2
       207: 3q+2
       208: 3q+2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       219: q+4
       220: q+4
       221: q^2+3q+4
       222: q+4
       223: q+4
       224: q+4
       225: q+4
       226: q^2+5q+4
       227: q+4
       228: q^2+3q+4
       229: q+4
       230: q+4
       231: 3q+4
       232: q+2
       233: 2q+2
       234: q+2
       236: 3q+4
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+2
       242: q+2
       243: 4q+4
       244: 2q+4
       246: 3q+4
       247: 4
       248: 4
       249: 2q+2
       250: q^2+3q+4
       251: 4q+4
       252: q^2+3q+4
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2
       284: 2
       285: 2
       286: 2
       287: q+2
       288: q+2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       301: 2
       302: 2
       303: 2
       304: 2
       305: 2
       306: 2
       307: 1
       308: 1
       315: q+2
       316: q+2
       317: q+2
       318: q+2
       319: q+2
       320: q+2
       325: q+2
       326: q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+4
       345: q+4
       346: q^2+3q+4
       347: q+4
       348: q+4
       349: q+4
       350: q+4
       351: 4
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       366: 3q+4
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       429: 2
       430: 2
       431: 2
       432: 2
       433: 2
       434: 2
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       453: 1
       454: 1
       469: q+2
       470: q+2
       471: 1
       472: 1
       481: 2
       482: 2
       483: 2
       484: 2
       491: 1
       492: q+4
       493: q+4
       494: q+4
       495: 2
       496: 2
       497: q+2
       498: q+2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       604: 2
       607: 2
       608: 2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 1
       616: 1
       619: 1
       620: 1
       641: 1
       642: 1
       647: 1
       648: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2
       677: 2
       678: 2
       679: 1
       681: 2
       686: q+2
       687: q+2
       690: 2
       691: 2
       692: q+1
       725: 1
       726: 1
       727: 1
       728: 1
       793: 1
       794: 1
       801: 1
       802: 1
       807: 1
       808: 1
       811: 1
       812: 1
       815: 1
       816: 1
       825: 1
       826: 1
       845: 1
       846: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       877: 2
      1016: 1
      1017: 1
      1052: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1283: 1

1284:    0: q^3+3q^2+8q+4
         1: 4q^2+8q+4
         2: q^3+3q^2+8q+4
         3: 4q^2+8q+4
         4: q^3+3q^2+8q+4
         5: q^3+3q^2+8q+4
         6: 4q^2+8q+4
         7: q^3+3q^2+8q+4
         8: q^3+3q^2+8q+4
         9: q^4+3q^3+5q^2+5q+2
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: q^3+3q^2+8q+4
        14: q^3+3q^2+8q+4
        15: q^3+3q^2+8q+4
        16: q^2+6q+4
        17: q^2+6q+4
        18: q^3+3q^2+5q+2
        19: q^3+3q^2+8q+4
        20: 4q^2+8q+4
        21: q^3+3q^2+8q+4
        22: q^3+3q^2+8q+4
        23: 4q^2+8q+4
        24: q^3+3q^2+8q+4
        25: 4q+4
        26: 4q+4
        27: 4q+4
        28: 4q+4
        29: q^2+6q+4
        30: q^3+3q^2+8q+4
        31: q^2+6q+4
        32: q^3+3q^2+8q+4
        33: q^2+6q+4
        34: 2q+4
        35: 4q+4
        36: 2q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+6q+4
        44: q^2+6q+4
        45: q^2+6q+4
        46: q^2+6q+4
        47: q^2+6q+4
        48: q^3+3q^2+5q+2
        49: q^2+6q+4
        50: q^2+6q+4
        51: q^3+3q^2+5q+2
        52: q^3+3q^2+8q+4
        53: 4q^2+8q+4
        54: q^3+3q^2+8q+4
        55: 4q+4
        56: 4q+4
        57: 4q+4
        58: 2q+2
        59: 2q+2
        60: 2
        61: 2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 4q+4
        69: q^2+3q+2
        70: q^2+6q+4
        71: 4q+4
        72: 2q+4
        73: q^2+6q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: q^2+6q+4
        81: q^2+6q+4
        82: q^2+6q+4
        83: q^3+3q^2+8q+4
        84: 2q+4
        85: 2q+4
        86: 2q+4
        87: 4q+4
        88: 2q+4
        89: 2q+4
        90: q^2+3q+2
        91: q^2+6q+4
        92: q^2+6q+4
        93: q^3+3q^2+5q+2
        94: q^2+6q+4
        95: q^2+6q+4
        96: q^3+3q^2+5q+2
        97: q+4
        98: q+4
        99: 3q+2
       100: 4q+4
       101: 4q+4
       102: 4q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2q+2
       110: 2q+2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 2q+2
       118: 2q+2
       119: 2
       120: 2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 2q+4
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       133: 4q+4
       134: q^2+3q+2
       135: 2q+4
       136: q^2+6q+4
       137: 2q+4
       138: q^2+3q+2
       139: 4q+4
       140: 2q+4
       141: q^2+6q+4
       142: q^2+6q+4
       143: 4
       144: q+2
       145: 4
       146: 2q+4
       147: q+4
       149: 2q+4
       150: 4q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 2q+4
       158: 2q+4
       159: q^2+3q+2
       160: q^2+6q+4
       161: q^2+6q+4
       162: q^3+3q^2+5q+2
       163: q+4
       164: q+4
       165: 3q+2
       166: q+4
       167: q+4
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2q+2
       186: 2q+2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: q+2
       192: q+2
       193: 2
       194: 2
       195: 2q+2
       196: 2q+2
       197: q+2
       198: q+2
       199: 2
       200: 2
       201: 2
       202: 2
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       213: 2
       214: 2
       215: 2
       216: 2
       217: q+1
       218: q+1
       219: q+2
       220: 2q+4
       221: q+2
       222: 4
       223: q+2
       224: 2q+4
       225: q^2+3q+2
       226: q+2
       227: 4q+4
       228: q^2+3q+2
       229: 2q+4
       230: q^2+6q+4
       231: 2
       232: 4
       233: q+2
       234: q+4
       236: q+2
       237: 2
       238: 2
       239: 2
       240: 2
       241: q+1
       242: q+1
       243: 4
       244: q+4
       246: 2q+4
       247: q+4
       248: q+4
       249: 3q+2
       250: 2q+4
       251: 2q+4
       252: q^2+3q+2
       253: 2
       254: 2
       255: q+1
       256: q+4
       257: q+4
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2
       280: 2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: 2
       294: 2
       295: q+2
       296: q+2
       297: 2
       298: 2
       299: 2
       300: 2
       301: 2
       302: 2
       303: 2q+2
       304: 2q+2
       305: q+2
       306: q+2
       307: 2
       308: 2
       315: 1
       316: 1
       317: 2
       318: 2
       319: 2
       320: 2
       325: q+2
       326: q+2
       333: q+2
       334: 2
       335: q+2
       336: q+2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: 2q+4
       346: q+2
       347: 4
       348: q+2
       349: 2q+4
       350: q^2+3q+2
       351: q+4
       352: 2
       353: 2
       354: 1
       355: 2
       356: q+2
       360: 2
       361: 2
       362: 2
       363: 2
       364: q+1
       365: q+1
       366: 2
       367: 4
       368: q+2
       369: q+4
       371: q+4
       372: q+4
       373: 3q+2
       374: 2
       375: 2
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       433: 1
       434: 1
       435: 2
       436: 2
       437: 2
       438: 2
       439: q+2
       440: q+2
       441: 2
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       453: 1
       454: 1
       465: 2
       466: 2
       467: 1
       468: 1
       469: 1
       470: 1
       471: 2
       472: 2
       481: 2
       482: q+2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: q+2
       492: q+2
       493: 2
       494: q+2
       495: q+2
       496: q+4
       497: 1
       498: 1
       508: 2
       509: 2
       510: 1
       511: 2
       512: q+2
       515: 2
       516: 2
       517: 2
       518: 2
       519: 2
       520: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       585: 1
       586: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       605: 1
       606: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       616: 2
       617: 2
       618: 2
       639: 1
       640: 1
       647: 1
       648: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 2
       675: 2
       676: q+2
       677: 2
       678: 2
       679: q+2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       733: 1
       734: 1
       735: 1
       736: 1
       779: 1
       780: 1
       781: 1
       782: 1
       795: 1
       796: 1
       797: 1
       798: 1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 1
       816: 1
       867: 1
       868: 1
       869: 1
       870: 2
       871: 2
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1284: 1

1285:    0: 2q^2+12q+4
         1: 2q^2+12q+4
         2: q^3+5q^2+8q+4
         3: 2q^2+12q+4
         4: q^3+5q^2+8q+4
         5: 2q^2+12q+4
         6: q^3+5q^2+8q+4
         7: q^4+3q^3+5q^2+5q+4
         8: q^3+5q^2+8q+4
         9: q^4+3q^3+5q^2+5q+4
        10: 2q^2+12q+4
        11: 2q^2+12q+4
        12: q^3+5q^2+8q+4
        13: q^2+8q+4
        14: q^3+3q^2+5q+4
        15: q^2+8q+4
        16: 2q^2+12q+4
        17: 2q^2+12q+4
        18: q^4+3q^3+5q^2+5q+4
        19: q^2+8q+4
        20: q^2+8q+4
        21: q^3+3q^2+5q+4
        22: 8q+4
        23: 8q+4
        24: 2q^2+6q+4
        25: 2q^2+12q+4
        26: 2q^2+12q+4
        27: q^3+5q^2+8q+4
        28: 2q^2+12q+4
        29: q^2+8q+4
        30: q^2+5q+4
        31: 8q+4
        32: 6q+4
        33: 8q+4
        34: 2q^2+12q+4
        35: q^2+8q+4
        36: 2q^2+12q+4
        37: 4q+2
        38: 4q+2
        39: 4q+2
        40: 4q+2
        41: q^2+3q+2
        42: q^2+3q+2
        43: q^2+8q+4
        44: q^3+3q^2+5q+4
        45: q^2+8q+4
        46: q^2+8q+4
        47: q^2+8q+4
        48: q^3+3q^2+5q+4
        49: q^2+8q+4
        50: q^2+8q+4
        51: q^3+3q^2+5q+4
        52: 4q+4
        53: 4q+4
        54: q^2+3q+4
        55: q^2+8q+4
        56: q^2+8q+4
        57: q^3+3q^2+5q+4
        58: 4q+2
        59: 4q+2
        60: q^2+6q+2
        61: q^2+6q+2
        62: 4q+2
        63: 4q+2
        64: 3q+2
        65: 3q+2
        66: 4q+2
        67: 4q+2
        68: 4q+4
        69: q^2+5q+4
        70: q^2+5q+4
        71: q^2+8q+4
        72: 4q+4
        73: 2q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 6q+4
        81: 6q+4
        82: 4q+4
        83: 3q+4
        84: q^2+8q+4
        85: q^2+8q+4
        86: q^2+8q+4
        87: q^2+5q+4
        88: q^2+8q+4
        89: q^2+8q+4
        90: q^3+3q^2+5q+4
        91: q^2+3q+4
        92: 4q+4
        93: q^2+3q+4
        94: 4q+4
        95: 4q+4
        96: q^2+3q+4
        97: q^2+8q+4
        98: q^2+8q+4
        99: q^3+3q^2+5q+4
       100: 4q+4
       101: 4q+4
       102: q^2+3q+4
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+2
       108: 2q+2
       109: q+2
       110: q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2q+2
       118: 2q+2
       119: 2q+2
       120: 2q+2
       121: 3q+2
       122: 3q+2
       123: 3q+2
       124: 3q+2
       125: 4q+4
       126: q^2+5q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q+4
       134: q^2+3q+4
       135: q+4
       136: q+4
       137: 6q+4
       138: 3q+4
       139: 4q+4
       141: 3q+4
       142: 2q+4
       143: q^2+8q+4
       144: q^2+5q+4
       145: q^2+8q+4
       146: q^2+5q+4
       147: 4q+4
       148: 2q+4
       149: 4q+4
       150: 3q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: q^2+3q+4
       158: 4q+4
       159: q^2+3q+4
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: q^2+3q+4
       164: 4q+4
       165: q^2+3q+4
       166: 4q+4
       167: 4q+4
       168: q^2+3q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2q+2
       192: 2q+2
       195: q+2
       196: q+2
       199: 2q+2
       200: 2q+2
       201: 2q+2
       202: 2q+2
       203: q+2
       204: q+2
       205: 2
       206: 2
       207: 3q+2
       208: 3q+2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       219: q+4
       220: q+4
       221: q^2+3q+4
       222: q+4
       223: q+4
       224: q+4
       225: q+4
       226: 3q+4
       227: q+2
       228: 2q+2
       230: q+2
       231: q^2+5q+4
       232: q+4
       233: q^2+3q+4
       234: q+4
       235: q+4
       236: 3q+4
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+2
       242: q+2
       243: 4q+4
       245: 2q+4
       246: 3q+4
       247: 4
       248: 4
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: q^2+3q+4
       254: 4q+4
       255: q^2+3q+4
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2
       284: 2
       285: 2
       286: 2
       287: q+2
       288: q+2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 1
       304: 1
       307: 2
       308: 2
       309: 2
       310: 2
       311: 2
       312: 2
       313: 2
       314: 2
       315: q+2
       316: q+2
       317: q+2
       318: q+2
       321: q+2
       322: q+2
       325: q+2
       326: q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: q+2
       346: 2q+2
       349: q+2
       350: q+2
       352: q+4
       353: q+4
       354: q^2+3q+4
       355: q+4
       356: q+4
       357: q+4
       358: q+4
       359: 4
       366: 3q+4
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       431: 1
       432: 1
       439: 1
       440: 1
       447: 2
       448: 2
       449: 2
       450: 2
       451: 2
       452: 2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+2
       470: q+2
       473: 1
       474: 1
       481: 2
       482: 2
       483: 2
       484: 2
       491: 1
       492: q+2
       494: q+2
       497: q+4
       498: q+4
       499: q+4
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 2q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       549: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       607: 1
       608: 1
       619: 2
       620: 2
       621: 2
       622: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 1
       632: 1
       643: 1
       644: 1
       649: 1
       650: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       676: 2
       680: 2
       681: 2
       682: 2
       683: 2
       684: 2
       685: 1
       686: q+2
       688: q+2
       690: 2
       691: 2
       692: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       807: 1
       808: 1
       817: 1
       818: 1
       825: 1
       826: 1
       831: 1
       832: 1
       835: 1
       836: 1
       839: 1
       840: 1
       847: 1
       848: 1
       865: 2
       866: 1
       867: 1
       868: 1
       873: 2
       874: 1
       875: 1
       876: 1
       878: 2
      1032: 1
      1033: 1
      1058: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1285: 1

1286:    0: q^3+3q^2+8q+4
         1: 4q^2+8q+4
         2: q^3+3q^2+8q+4
         3: 4q^2+8q+4
         4: q^3+3q^2+8q+4
         5: q^3+3q^2+8q+4
         6: 4q^2+8q+4
         7: q^3+3q^2+8q+4
         8: q^3+3q^2+8q+4
         9: q^4+3q^3+5q^2+5q+2
        10: q^2+6q+4
        11: q^2+6q+4
        12: q^2+6q+4
        13: q^3+3q^2+8q+4
        14: q^3+3q^2+8q+4
        15: q^3+3q^2+8q+4
        16: q^2+6q+4
        17: q^2+6q+4
        18: q^3+3q^2+5q+2
        19: q^3+3q^2+8q+4
        20: 4q^2+8q+4
        21: q^3+3q^2+8q+4
        22: 4q+4
        23: 4q+4
        24: 4q+4
        25: q^3+3q^2+8q+4
        26: 4q^2+8q+4
        27: q^3+3q^2+8q+4
        28: 4q+4
        29: q^2+6q+4
        30: q^3+3q^2+8q+4
        31: 2q+4
        32: 4q+4
        33: 2q+4
        34: q^2+6q+4
        35: q^3+3q^2+8q+4
        36: q^2+6q+4
        37: 2q+2
        38: 2q+2
        39: 2q+2
        40: 2q+2
        41: 2q+2
        42: 2q+2
        43: q^2+6q+4
        44: q^2+6q+4
        45: q^2+6q+4
        46: q^2+6q+4
        47: q^2+6q+4
        48: q^3+3q^2+5q+2
        49: q^2+6q+4
        50: q^2+6q+4
        51: q^3+3q^2+5q+2
        52: 4q+4
        53: 4q+4
        54: 4q+4
        55: q^3+3q^2+8q+4
        56: 4q^2+8q+4
        57: q^3+3q^2+8q+4
        58: 2
        59: 2
        60: 2q+2
        61: 2q+2
        62: q+2
        63: q+2
        64: 2q+2
        65: 2q+2
        66: q+2
        67: q+2
        68: 4q+4
        69: q^2+3q+2
        70: q^2+6q+4
        71: 4q+4
        72: q^2+6q+4
        73: 2q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: 2q+2
        79: 2q+2
        80: 2q+4
        81: 2q+4
        82: 2q+4
        83: 4q+4
        84: q^2+6q+4
        85: q^2+6q+4
        86: q^2+6q+4
        87: q^3+3q^2+8q+4
        88: 2q+4
        89: 2q+4
        90: q^2+3q+2
        91: q^2+6q+4
        92: q^2+6q+4
        93: q^3+3q^2+5q+2
        94: q+4
        95: q+4
        96: 3q+2
        97: q^2+6q+4
        98: q^2+6q+4
        99: q^3+3q^2+5q+2
       100: 4q+4
       101: 4q+4
       102: 4q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2q+2
       108: 2q+2
       109: 2
       110: 2
       111: q+2
       112: q+2
       113: q+2
       114: q+2
       115: 2q+2
       116: 2q+2
       117: 2
       118: 2
       119: 2q+2
       120: 2q+2
       121: q+2
       122: q+2
       123: q+2
       124: q+2
       125: 2q+4
       126: q+2
       127: 2
       128: 2
       129: 2
       130: 2
       131: q+1
       132: q+1
       133: 4q+4
       134: q^2+3q+2
       135: q^2+6q+4
       136: 2q+4
       137: 4
       138: q+2
       139: 4
       141: 2q+4
       142: q+4
       143: 2q+4
       144: q^2+3q+2
       145: 4q+4
       146: q^2+6q+4
       147: q^2+6q+4
       148: 2q+4
       149: 2q+4
       150: 4q+4
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: 2q+2
       156: 2q+2
       157: 2q+4
       158: 2q+4
       159: q^2+3q+2
       160: q+4
       161: q+4
       162: 3q+2
       163: q^2+6q+4
       164: q^2+6q+4
       165: q^3+3q^2+5q+2
       166: q+4
       167: q+4
       168: 3q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 2
       180: 2
       181: 2
       182: 2
       183: 2q+2
       184: 2q+2
       185: 2
       186: 2
       187: q+2
       188: q+2
       189: q+2
       190: q+2
       191: 2
       192: 2
       195: 2
       196: 2
       199: q+2
       200: q+2
       201: 2q+2
       202: 2q+2
       203: 2
       204: 2
       205: q+2
       206: q+2
       207: 2
       208: 2
       209: q+2
       210: q+2
       211: 2q+2
       212: 2q+2
       213: 2
       214: 2
       215: 2
       216: 2
       217: q+1
       218: q+1
       219: q+2
       220: 2q+4
       221: q+2
       222: 2q+4
       223: q^2+3q+2
       224: 4
       225: q+2
       226: 2
       227: 4
       228: q+2
       230: q+4
       231: q+2
       232: 4q+4
       233: q^2+3q+2
       234: q^2+6q+4
       235: 2q+4
       236: q+2
       237: 2
       238: 2
       239: 2
       240: 2
       241: q+1
       242: q+1
       243: 4
       245: q+4
       246: 2q+4
       247: q+4
       248: q+4
       249: 3q+2
       250: 2
       251: 2
       252: q+1
       253: 2q+4
       254: 2q+4
       255: q^2+3q+2
       256: q+4
       257: q+4
       258: 3q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2
       280: 2
       281: 1
       282: 1
       287: 1
       288: 1
       289: 2
       290: 2
       291: 1
       292: 1
       293: q+2
       294: q+2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 2
       304: 2
       307: 2q+2
       308: 2q+2
       309: 2
       310: 2
       311: 2
       312: 2
       313: q+2
       314: q+2
       315: 1
       316: 1
       317: 2
       318: 2
       321: 2
       322: 2
       325: q+2
       326: q+2
       333: q+2
       334: q+2
       335: 2
       336: q+2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 2
       345: 2
       346: 1
       349: 2
       350: q+2
       352: q+2
       353: 2q+4
       354: q+2
       355: 2q+4
       356: q^2+3q+2
       357: 4
       358: q+2
       359: q+4
       360: 2
       361: 2
       362: 2
       363: 2
       364: q+1
       365: q+1
       366: 2
       367: 4
       368: q+2
       370: q+4
       371: q+4
       372: q+4
       373: 3q+2
       374: 2
       375: 2
       376: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       413: 1
       414: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       439: 1
       440: 1
       451: 1
       452: 1
       453: q+2
       454: q+2
       455: 2
       456: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       465: 2
       466: 2
       467: 1
       468: 1
       469: 1
       470: 1
       473: 2
       474: 2
       481: q+2
       482: 2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: q+2
       492: 1
       494: 1
       497: q+2
       498: q+2
       499: 2
       500: q+2
       501: q+4
       508: 2
       509: 2
       510: 1
       513: 2
       514: q+2
       515: 2
       516: 2
       517: 2
       518: 2
       519: 2
       520: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       585: 1
       586: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: 1
       640: 1
       649: 1
       650: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 2
       673: 1
       676: 1
       680: 2
       681: q+2
       682: 2
       683: 2
       684: 2
       685: q+2
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       749: 1
       750: 1
       751: 1
       752: 1
       779: 1
       780: 1
       781: 1
       782: 1
       819: 1
       820: 1
       821: 1
       822: 1
       833: 1
       834: 1
       835: 1
       836: 1
       839: 1
       840: 1
       867: 1
       868: 1
       873: 1
       874: 2
       875: 2
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1073: 1
      1079: 1
      1081: 1
      1082: 1
      1286: 1

1287:    0: 2q^3+16q^2+26q+4
         1: 2q^3+16q^2+26q+4
         2: 4q^3+14q^2+20q+4
         3: 2q^3+16q^2+26q+4
         4: 3q^4+6q^3+16q^2+16q+4
         5: 2q^3+16q^2+26q+4
         6: 5q^4+11q^3+19q^2+16q+4
         7: 2q^4+5q^3+10q^2+13q+4
         8: 4q^3+14q^2+20q+4
         9: 2q^4+5q^3+10q^2+13q+4
        10: 8q^2+24q+4
        11: 8q^2+24q+4
        12: q^4+4q^3+14q^2+14q+4
        13: 8q^2+20q+4
        14: q^4+2q^3+8q^2+13q+4
        15: 8q^2+20q+4
        16: 2q^3+16q^2+26q+4
        17: 2q^3+16q^2+26q+4
        18: 2q^4+5q^3+10q^2+13q+4
        19: 6q^2+16q+4
        20: q^3+9q^2+16q+4
        21: q^3+4q^2+13q+4
        22: 2q^3+16q^2+26q+4
        23: 2q^3+16q^2+26q+4
        24: 4q^3+14q^2+20q+4
        25: 2q^3+16q^2+26q+4
        26: 2q^3+16q^2+26q+4
        27: 4q^3+14q^2+20q+4
        28: 8q^2+24q+4
        29: 4q^2+14q+4
        30: 2q^2+13q+4
        31: 8q^2+24q+4
        32: 8q^2+20q+4
        33: 2q^3+16q^2+26q+4
        34: 8q^2+24q+4
        35: 8q^2+20q+4
        36: 2q^3+16q^2+26q+4
        37: q^3+8q^2+13q+2
        38: q^3+8q^2+13q+2
        39: q^3+8q^2+13q+2
        40: q^3+8q^2+13q+2
        41: 2q^3+7q^2+10q+2
        42: 2q^3+7q^2+10q+2
        43: 2q^2+18q+4
        44: q^3+7q^2+11q+4
        45: 2q^2+18q+4
        46: 8q^2+20q+4
        47: 8q^2+20q+4
        48: q^4+2q^3+8q^2+13q+4
        49: 6q^2+16q+4
        50: q^3+9q^2+16q+4
        51: q^3+4q^2+13q+4
        52: 6q^2+16q+4
        53: q^3+9q^2+16q+4
        54: q^3+4q^2+13q+4
        55: 6q^2+16q+4
        56: q^3+9q^2+16q+4
        57: q^3+4q^2+13q+4
        58: 4q^2+12q+2
        59: 4q^2+12q+2
        60: 4q^2+12q+2
        61: 4q^2+12q+2
        62: 4q^2+12q+2
        63: 4q^2+12q+2
        64: 4q^2+10q+2
        65: 4q^2+10q+2
        66: q^3+8q^2+13q+2
        67: q^3+8q^2+13q+2
        68: 12q+4
        69: 2q^2+13q+4
        70: q^2+11q+4
        71: 4q^2+14q+4
        72: 3q^2+8q+4
        73: 3q^2+8q+4
        74: 4q+2
        75: 4q+2
        76: q^2+4q+2
        77: q^2+4q+2
        78: 4q+2
        79: 4q+2
        80: 2q^2+18q+4
        81: 8q^2+20q+4
        82: 4q^2+14q+4
        83: 2q^2+13q+4
        84: 2q^2+18q+4
        85: 8q^2+20q+4
        86: 4q^2+14q+4
        87: 2q^2+13q+4
        88: 2q^2+18q+4
        89: 2q^2+18q+4
        90: q^3+7q^2+11q+4
        91: 9q+4
        92: 3q^2+10q+4
        93: 9q+4
        94: 6q^2+16q+4
        95: q^3+9q^2+16q+4
        96: q^3+4q^2+13q+4
        97: 6q^2+16q+4
        98: q^3+9q^2+16q+4
        99: q^3+4q^2+13q+4
       100: 6q^2+16q+4
       101: q^3+9q^2+16q+4
       102: q^3+4q^2+13q+4
       103: 2q^2+6q+1
       104: 2q^2+6q+1
       105: 2q^2+6q+1
       106: 2q^2+6q+1
       107: q^2+3q+2
       108: q^2+3q+2
       109: q^2+3q+2
       110: q^2+3q+2
       111: q+2
       112: q+2
       113: 3q+2
       114: 3q+2
       115: 4q+2
       116: 4q+2
       117: 6q+2
       118: 6q+2
       119: 6q+2
       120: 6q+2
       121: q^2+9q+2
       122: q^2+9q+2
       123: 4q^2+10q+2
       124: 4q^2+10q+2
       125: 12q+4
       126: q^2+11q+4
       127: 4q+2
       128: 4q+2
       129: q^2+4q+2
       130: q^2+4q+2
       131: 4q+2
       132: 4q+2
       133: 5q+4
       134: 9q+4
       135: 5q+4
       136: 5q+4
       137: 2q^2+18q+4
       138: 2q^2+13q+4
       139: 4q^2+14q+4
       140: 3q^2+8q+4
       141: q^2+11q+4
       142: 3q^2+8q+4
       143: 2q^2+18q+4
       144: 2q^2+13q+4
       145: 4q^2+14q+4
       146: q^2+11q+4
       147: 3q^2+8q+4
       148: 3q^2+8q+4
       149: 4q^2+14q+4
       150: 2q^2+13q+4
       151: 4q+2
       152: 4q+2
       153: q^2+4q+2
       154: q^2+4q+2
       155: 4q+2
       156: 4q+2
       157: 3q+4
       158: 4q+4
       159: 3q+4
       160: 9q+4
       161: 3q^2+10q+4
       162: 9q+4
       163: 9q+4
       164: 3q^2+10q+4
       165: 9q+4
       166: 6q^2+16q+4
       167: q^3+9q^2+16q+4
       168: q^3+4q^2+13q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: 3q+1
       174: 3q+1
       175: 3q+1
       176: 3q+1
       177: 4q+2
       178: 4q+2
       179: 3q+2
       180: 3q+2
       181: q+2
       182: q+2
       183: q+2
       184: q+2
       185: q+2
       186: q+2
       187: q+2
       188: q+2
       189: 3q+2
       190: 3q+2
       191: 6q+2
       192: 6q+2
       193: q^2+3q+2
       194: q^2+3q+2
       195: q^2+3q+2
       196: q^2+3q+2
       197: q+2
       198: q+2
       199: 6q+2
       200: 6q+2
       201: q^2+3q+2
       202: q^2+3q+2
       203: q^2+3q+2
       204: q^2+3q+2
       205: q+2
       206: q+2
       207: q^2+9q+2
       208: q^2+9q+2
       209: 3q+2
       210: 3q+2
       211: 4q+2
       212: 4q+2
       219: 5q+4
       220: q+4
       221: 3q+4
       222: q+4
       223: 5q+4
       224: q+4
       225: 5q+4
       226: q^2+11q+4
       227: 5q+4
       228: 9q+4
       229: 5q+4
       230: 5q+4
       231: q^2+11q+4
       232: 5q+4
       233: 9q+4
       234: 5q+4
       235: 5q+4
       236: 2q^2+13q+4
       237: 4q+2
       238: 4q+2
       239: q^2+4q+2
       240: q^2+4q+2
       241: 4q+2
       242: 4q+2
       243: 4q^2+14q+4
       244: 3q^2+8q+4
       245: 3q^2+8q+4
       246: q^2+11q+4
       247: 8
       248: 8
       249: 4q+2
       250: 3q+4
       251: 4q+4
       252: 3q+4
       253: 3q+4
       254: 4q+4
       255: 3q+4
       256: 9q+4
       257: 3q^2+10q+4
       258: 9q+4
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 3q+1
       276: 3q+1
       277: 3q+1
       278: 3q+1
       283: q+2
       284: q+2
       285: q+2
       286: q+2
       287: 3q+2
       288: 3q+2
       291: q+2
       292: q+2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: q+2
       300: q+2
       301: q+2
       302: q+2
       303: q+2
       304: q+2
       305: q+2
       306: q+2
       307: q+2
       308: q+2
       309: q+2
       310: q+2
       311: q+2
       312: q+2
       313: q+2
       314: q+2
       315: 4q+2
       316: 4q+2
       317: 3q+2
       318: 3q+2
       319: q^2+3q+2
       320: q^2+3q+2
       321: q^2+3q+2
       322: q^2+3q+2
       323: q+2
       324: q+2
       325: 3q+2
       326: 3q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 8
       338: 4
       339: 4
       340: 4
       341: 4
       342: 2q+1
       343: 2q+1
       344: 5q+4
       345: q+4
       346: 3q+4
       347: q+4
       348: 5q+4
       349: q+4
       350: 5q+4
       351: 8
       352: 5q+4
       353: q+4
       354: 3q+4
       355: q+4
       356: 5q+4
       357: q+4
       358: 5q+4
       359: 8
       366: q^2+11q+4
       367: 5q+4
       368: 9q+4
       369: 5q+4
       370: 5q+4
       371: 4
       372: 4
       373: 2q+1
       374: 3q+4
       375: 4q+4
       376: 3q+4
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 4
       428: 4
       429: q+2
       430: q+2
       431: q+2
       432: q+2
       433: q+2
       434: q+2
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 4
       444: 4
       445: 4
       446: 4
       447: q+2
       448: q+2
       449: q+2
       450: q+2
       451: q+2
       452: q+2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 4
       462: 4
       463: 4
       464: 4
       469: 3q+2
       470: 3q+2
       471: q+2
       472: q+2
       473: q+2
       474: q+2
       475: q+2
       476: q+2
       477: q+2
       478: q+2
       479: 4
       480: 4
       481: 2
       482: 2
       483: 2
       484: 4
       491: 1
       492: q+4
       493: q+4
       494: q+4
       495: 2
       496: 4
       497: q+4
       498: q+4
       499: q+4
       500: 2
       501: 4
       508: 5q+4
       509: q+4
       510: 3q+4
       511: q+4
       512: 5q+4
       513: q+4
       514: 5q+4
       515: 4
       516: 4
       517: 2q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2
       546: 2
       547: 2
       548: 2
       549: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 2
       562: 2
       563: 2
       564: 2
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 2
       574: 2
       575: 2
       576: 2
       577: 2
       578: 2
       580: 2
       581: 2
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       604: 2
       607: 2
       608: 2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 2
       616: 2
       619: 2
       620: 2
       621: 2
       622: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 2
       632: 2
       641: q+2
       642: q+2
       643: q+2
       644: q+2
       645: q+2
       646: q+2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 2
       656: 2
       657: 4
       664: 1
       665: 1
       674: 4
       675: 2
       676: 2
       677: 2
       679: 1
       680: 4
       681: 2
       682: 2
       683: 2
       685: 1
       686: q+4
       687: q+4
       688: q+4
       689: 2
       693: 1
       694: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       725: 1
       726: 1
       727: 1
       728: 1
       741: 1
       742: 1
       743: 1
       744: 1
       753: 1
       754: 1
       755: 1
       756: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       793: 2
       794: 2
       801: 1
       802: 1
       807: 1
       808: 1
       811: 1
       812: 1
       817: 2
       818: 2
       825: 1
       826: 1
       831: 1
       832: 1
       835: 1
       836: 1
       843: 2
       844: 2
       845: 2
       846: 2
       847: 2
       848: 2
       851: 2
       852: 2
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 2
       878: 2
       879: 2
       880: 1
       964: 1
       965: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       977: 1
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1287: 1

1288:    0: 12q+4
         1: 12q+4
         2: 2q^3+6q^2+6q+2
         3: 12q+4
         4: 4q^2+8q+4
         5: 12q+4
         6: 4q^2+8q+4
         7: q^4+3q^3+5q^2+5q+2
         8: 2q^3+6q^2+6q+2
         9: q^4+3q^3+5q^2+5q+2
        10: 12q+4
        11: 12q+4
        12: 4q^2+8q+4
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 12q+4
        17: 12q+4
        18: q^4+3q^3+5q^2+5q+2
        19: 8q+4
        20: 8q+4
        21: q^3+4q^2+5q+2
        22: 12q+4
        23: 12q+4
        24: 2q^3+6q^2+6q+2
        25: 12q+4
        26: 12q+4
        27: 2q^3+6q^2+6q+2
        28: 12q+4
        29: 8q+4
        30: 3q+2
        31: 12q+4
        32: 4q+2
        33: 12q+4
        34: 12q+4
        35: 4q+2
        36: 12q+4
        37: 6q+2
        38: 6q+2
        39: 6q+2
        40: 6q+2
        41: q^3+3q^2+3q+1
        42: q^3+3q^2+3q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 8q+4
        50: 8q+4
        51: q^3+4q^2+5q+2
        52: 8q+4
        53: 8q+4
        54: q^3+4q^2+5q+2
        55: 8q+4
        56: 8q+4
        57: q^3+4q^2+5q+2
        58: 6q+2
        59: 6q+2
        60: 6q+2
        61: 6q+2
        62: 6q+2
        63: 6q+2
        64: 2q+1
        65: 2q+1
        66: 6q+2
        67: 6q+2
        69: 3q+2
        70: 3q+2
        71: 8q+4
        72: 4q+4
        73: 4q+4
        74: 2q+2
        75: 2q+2
        76: 2q+2
        77: 2q+2
        78: q^2+2q+1
        79: q^2+2q+1
        80: 4q+2
        81: 4q+2
        82: 8q+4
        83: 3q+2
        84: 4q+2
        85: 4q+2
        86: 8q+4
        87: 3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 8q+4
        95: 8q+4
        96: q^3+4q^2+5q+2
        97: 8q+4
        98: 8q+4
        99: q^3+4q^2+5q+2
       100: 8q+4
       101: 8q+4
       102: q^3+4q^2+5q+2
       103: 3q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: 2q+2
       108: 2q+2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: 2q+2
       114: 2q+2
       115: q+1
       116: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       126: 3q+2
       127: 2q+2
       128: 2q+2
       129: 2q+2
       130: 2q+2
       131: q^2+2q+1
       132: q^2+2q+1
       134: 2q+2
       135: q+2
       136: q+2
       137: 4q+2
       138: 3q+2
       139: 8q+4
       140: 4q+4
       141: 3q+2
       142: 4q+4
       143: 4q+2
       144: 3q+2
       145: 8q+4
       146: 3q+2
       147: 4q+4
       148: 4q+4
       149: 8q+4
       150: 3q+2
       151: 2q+2
       152: 2q+2
       153: 2q+2
       154: 2q+2
       155: q^2+2q+1
       156: q^2+2q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 8q+4
       167: 8q+4
       168: q^3+4q^2+5q+2
       169: 1
       170: 1
       171: 1
       172: 1
       177: q+1
       178: q+1
       179: 2q+2
       180: 2q+2
       181: 2
       182: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       193: 2q+2
       194: 2q+2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       201: 2q+2
       202: 2q+2
       203: 2q+2
       204: 2q+2
       205: 2
       206: 2
       207: 2q+1
       208: 2q+1
       209: 2q+2
       210: 2q+2
       211: q+1
       212: q+1
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: 3q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: 3q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: 2q+2
       238: 2q+2
       239: 2q+2
       240: 2q+2
       241: q^2+2q+1
       242: q^2+2q+1
       243: 8q+4
       244: 4q+4
       245: 4q+4
       246: 3q+2
       247: 8
       248: 8
       249: 2q^2+4q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       261: 1
       262: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       297: 1
       298: 1
       301: 2
       302: 2
       305: 1
       306: 1
       311: 2
       312: 2
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: 2q+2
       318: 2q+2
       319: 2q+2
       320: 2q+2
       321: 2q+2
       322: 2q+2
       323: 2
       324: 2
       325: q+1
       326: q+1
       334: q+2
       335: q+2
       336: 2
       337: 8
       338: 4
       339: 4
       340: 4
       341: 4
       342: q^2+2q+1
       343: q^2+2q+1
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 8
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 8
       366: 3q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       389: 1
       390: 1
       391: 1
       392: 1
       397: 1
       398: 1
       399: 1
       400: 1
       405: 1
       406: 1
       407: 1
       408: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 4
       428: 4
       433: 1
       434: 1
       441: 1
       442: 1
       443: 4
       444: 4
       445: 4
       446: 4
       451: 1
       452: 1
       459: 1
       460: 1
       461: 4
       462: 4
       463: 4
       464: 4
       469: q+1
       470: q+1
       475: 1
       476: 1
       477: 2
       478: 2
       479: 4
       480: 4
       483: 2
       491: 1
       493: q+2
       494: q+2
       495: 2
       496: 2
       498: q+2
       499: q+2
       500: 2
       501: 2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       545: 2
       546: 2
       547: 2
       548: 2
       561: 2
       562: 2
       563: 2
       564: 2
       569: 1
       570: 1
       571: 1
       572: 1
       573: 2
       574: 2
       575: 2
       576: 2
       577: 2
       578: 2
       580: 2
       581: 2
       599: 1
       600: 1
       609: 1
       610: 1
       613: 1
       614: 1
       625: 1
       626: 1
       629: 1
       630: 1
       645: 1
       646: 1
       653: 1
       654: 1
       655: 1
       656: 1
       664: 1
       673: 1
       674: 2
       677: 2
       678: 2
       679: 1
       680: 2
       683: 2
       684: 2
       685: 1
       687: q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       811: 1
       812: 1
       835: 1
       836: 1
       843: 1
       844: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       867: 1
       869: 2
       870: 1
       872: 1
       873: 2
       874: 1
       876: 1
       879: 2
       880: 1
      1046: 1
      1047: 1
      1062: 1
      1063: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1288: 1

1289:    0: 6q+4
         1: 6q+4
         2: 6q+4
         3: 6q+4
         4: 6q+4
         5: 6q+4
         6: 6q+4
         7: 6q+4
         8: 6q+4
         9: q^5+2q^3+2q^2+2q+1
        10: 6q+4
        11: 6q+4
        12: 6q+4
        13: 6q+4
        14: 6q+4
        15: 6q+4
        16: 4
        17: 4
        18: 2q+1
        19: 6q+4
        20: 6q+4
        21: 6q+4
        22: 6q+4
        23: 6q+4
        24: 6q+4
        25: 6q+4
        26: 6q+4
        27: 6q+4
        28: 4
        29: 6q+4
        30: 6q+4
        31: 6q+4
        32: 6q+4
        33: 4
        34: 6q+4
        35: 6q+4
        36: 4
        37: 3q+2
        38: 3q+2
        39: 3q+2
        40: 3q+2
        41: 3q+2
        42: 3q+2
        43: 6q+4
        44: 6q+4
        45: 6q+4
        46: 4
        47: 4
        48: 2q+1
        49: 4
        50: 4
        51: 2q+1
        52: 6q+4
        53: 6q+4
        54: 6q+4
        55: 6q+4
        56: 6q+4
        57: 6q+4
        58: 2
        59: 2
        60: 2
        61: 2
        62: 3q+2
        63: 3q+2
        64: 3q+2
        65: 3q+2
        66: 2
        67: 2
        68: 4
        69: 1
        70: 6q+4
        71: 4
        72: 4
        73: 4
        74: 3q+2
        75: 3q+2
        76: 3q+2
        77: 3q+2
        78: 3q+2
        79: 3q+2
        80: 6q+4
        81: 4
        82: 6q+4
        83: 6q+4
        84: 6q+4
        85: 4
        86: 6q+4
        87: 6q+4
        88: 4
        89: 4
        90: 2q+1
        91: 4
        92: 4
        93: 2q+1
        94: 4
        95: 4
        96: 2q+1
        97: 4
        98: 4
        99: 2q+1
       100: 6q+4
       101: 6q+4
       102: 6q+4
       103: 1
       104: 1
       105: 1
       106: 1
       107: 2
       108: 2
       109: 2
       110: 2
       111: 2
       112: 2
       113: 3q+2
       114: 3q+2
       115: 3q+2
       116: 3q+2
       117: 2
       118: 2
       119: 2
       120: 2
       121: 3q+2
       122: 3q+2
       123: 2
       124: 2
       125: 4
       126: 1
       133: 4
       134: 1
       135: 4
       136: 4
       137: 4
       138: 1
       139: 4
       140: 4
       141: 6q+4
       142: 4
       143: 4
       144: 1
       145: 4
       146: 6q+4
       147: 4
       148: 4
       149: 6q+4
       150: 6q+4
       151: 3q+2
       152: 3q+2
       153: 3q+2
       154: 3q+2
       155: 3q+2
       156: 3q+2
       157: 4
       158: 4
       159: 2q+1
       160: 4
       161: 4
       162: 2q+1
       163: 4
       164: 4
       165: 2q+1
       166: 4
       167: 4
       168: 2q+1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 3q+2
       190: 3q+2
       191: 2
       192: 2
       193: 2
       194: 2
       195: 2
       196: 2
       197: 2
       198: 2
       199: 2
       200: 2
       201: 2
       202: 2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 2
       208: 2
       209: 3q+2
       210: 3q+2
       211: 3q+2
       212: 3q+2
       219: 1
       220: 4
       221: 1
       222: 4
       223: 1
       224: 4
       225: 1
       226: 1
       227: 4
       228: 1
       229: 4
       230: 4
       231: 1
       232: 4
       233: 1
       234: 4
       235: 4
       236: 1
       243: 4
       244: 4
       245: 4
       246: 6q+4
       247: 4
       248: 4
       249: 2q+1
       250: 4
       251: 4
       252: 2q+1
       253: 4
       254: 4
       255: 2q+1
       256: 4
       257: 4
       258: 2q+1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       303: 2
       304: 2
       305: 2
       306: 2
       307: 2
       308: 2
       309: 2
       310: 2
       313: 2
       314: 2
       319: 2
       320: 2
       321: 2
       322: 2
       323: 2
       324: 2
       325: 3q+2
       326: 3q+2
       333: 1
       334: 1
       335: 1
       336: 1
       337: 4
       344: 1
       345: 4
       346: 1
       347: 4
       348: 1
       349: 4
       350: 1
       351: 4
       352: 1
       353: 4
       354: 1
       355: 4
       356: 1
       357: 4
       358: 1
       359: 4
       366: 1
       367: 4
       368: 1
       369: 4
       370: 4
       371: 4
       372: 4
       373: 2q+1
       374: 4
       375: 4
       376: 2q+1
       385: 1
       386: 1
       387: 1
       388: 1
       393: 1
       394: 1
       395: 1
       396: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 2
       444: 2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       471: 2
       472: 2
       473: 2
       474: 2
       475: 2
       476: 2
       479: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 4
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 4
       497: 1
       498: 1
       499: 1
       500: 1
       501: 4
       508: 1
       509: 4
       510: 1
       511: 4
       512: 1
       513: 4
       514: 1
       518: 4
       519: 4
       520: 2q+1
       541: 1
       542: 1
       543: 1
       544: 1
       557: 1
       558: 1
       559: 1
       560: 1
       565: 1
       566: 1
       567: 1
       568: 1
       573: 1
       574: 1
       575: 1
       576: 1
       615: 2
       616: 2
       631: 2
       632: 2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 2
       656: 2
       665: 1
       672: 4
       673: 1
       675: 1
       676: 1
       677: 1
       678: 4
       679: 1
       681: 1
       682: 1
       683: 1
       684: 4
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       815: 2
       816: 2
       839: 2
       840: 2
       857: 2
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       988: 1
       989: 1
       990: 1
       991: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1289: 1

1290:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       109: 1
       111: q+1
       113: 1
       115: q+1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: 1
       173: 1
       177: q+1
       179: 1
       181: q+1
       183: 1
       185: 1
       187: q+1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       549: 1
       553: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       733: 1
       737: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       775: 1
       779: 1
       781: 1
       785: 1
       787: 1
       791: 1
       793: 1
       795: 1
       809: 1
       817: 1
       819: 1
       833: 1
       843: 1
       849: 1
       866: 1
       870: 1
       874: 1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       940: 1
       960: 1
       964: 1
       968: 1
       994: 1
       998: 1
      1000: 1
      1010: 1
      1012: 1
      1020: 1
      1036: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1138: 1
      1290: 1

1291:    0: 6q^2+3q
         1: q^4+5q^3+6q^2+3q
         2: 6q^2+3q
         3: 3q^3+6q^2+3q
         4: 6q^2+3q
         5: 3q^3+6q^2+3q
         6: q^4+5q^3+6q^2+3q
         7: 6q^2+3q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 3q^2+3q
        11: 3q^2+3q
        12: 3q^2+3q
        13: 6q^2+3q
        14: 6q^2+3q
        15: 3q^3+6q^2+3q
        16: 5q^2+3q
        17: 2q^3+5q^2+3q
        18: 3q^2+2q
        19: 6q^2+3q
        20: q^4+5q^3+6q^2+3q
        21: 6q^2+3q
        22: 5q^2+3q
        23: 2q^3+5q^2+3q
        24: 5q^2+3q
        25: 5q^2+3q
        26: 2q^3+5q^2+3q
        27: 5q^2+3q
        28: 2q^2+3q
        29: 3q^2+3q
        30: 6q^2+3q
        31: 2q^2+3q
        32: 5q^2+3q
        33: 4q^2+3q
        34: 2q^2+3q
        35: 5q^2+3q
        36: 4q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 3q^2+3q
        44: 3q^2+3q
        45: 3q^2+3q
        46: 5q^2+3q
        47: 2q^3+5q^2+3q
        48: 3q^2+2q
        49: 5q^2+3q
        50: 2q^3+5q^2+3q
        51: 3q^2+2q
        52: 5q^2+3q
        53: 2q^3+5q^2+3q
        54: 5q^2+3q
        55: 5q^2+3q
        56: 2q^3+5q^2+3q
        57: 5q^2+3q
        58: q^2+2q
        59: q
        60: q^2+2q
        61: q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: 2q^2+3q
        69: 2q^2+2q
        70: 3q^2+3q
        71: 2q^2+3q
        72: 4q^2+3q
        73: 4q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: 2q^2+3q
        81: 4q^2+3q
        82: 2q^2+3q
        83: 5q^2+3q
        84: 2q^2+3q
        85: 4q^2+3q
        86: 2q^2+3q
        87: 5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 5q^2+3q
        92: 2q^3+5q^2+3q
        93: 3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: 2q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: q^3+4q^2+3q
       102: q^2+3q
       103: q
       104: q
       105: q
       107: q^2+2q
       108: q
       109: q^2+2q
       110: q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: q^2+2q
       118: q
       119: q^2+2q
       120: q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 2q^2+3q
       134: 2q^2+2q
       135: 4q^2+3q
       136: 4q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q
       141: 2q^2+3q
       142: 3q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 3q^2+3q
       148: 2q
       149: q^2+3q
       150: q^2+3q
       151: q
       152: q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q
       156: q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 3q
       167: 2q^2+3q
       168: 2q
       169: q
       170: q
       171: q
       173: q
       174: q
       175: q
       178: q
       180: 2q
       182: q^2+2q
       183: q^2+2q
       184: q
       185: q^2+2q
       186: q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: 2q
       192: q
       193: 2q
       195: q^2+2q
       196: q
       197: q
       198: q
       199: 2q
       200: q
       201: q^2+2q
       202: q
       203: 2q
       205: q
       206: q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q
       212: q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q
       238: 2q
       240: q^2+2q
       242: q
       243: 3q
       244: 2q
       245: 2q
       246: q^2+3q
       247: 3q
       248: 2q^2+3q
       249: 2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       260: q
       261: q
       263: q
       264: q
       265: q
       267: q
       268: q
       271: q
       272: q
       275: q
       276: q
       277: q
       280: 2q
       282: q
       283: q
       285: q
       288: q
       290: q^2+2q
       292: q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: 2q
       299: 2q
       302: q
       303: q^2+2q
       304: q
       305: q
       306: q
       307: q^2+2q
       308: q
       309: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       319: 2q
       321: 2q
       323: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       339: 2q
       341: q^2+2q
       343: q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       361: 2q
       363: q^2+2q
       365: q
       366: 2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q
       393: q
       394: q
       398: q
       401: q
       402: q
       405: q
       414: q
       418: q
       419: q
       421: q
       424: q
       426: q
       428: 2q
       429: q
       431: q
       436: q
       443: 2q
       446: q
       447: q
       449: q
       456: q
       461: 2q
       464: q
       466: 2q
       468: q
       470: q
       471: 2q
       473: 2q
       475: q
       479: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: 2q
       488: q^2+2q
       490: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       508: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       538: q
       546: q
       554: q
       562: q
       565: q
       573: q
       586: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: 2q
       615: 2q
       618: q
       631: 2q
       634: q
       640: q
       641: q
       643: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 2q
       674: 1
       679: q
       680: 1
       685: q
       734: q
       750: q
       765: q
       776: 1
       780: 1
       782: q
       785: q
       787: q
       793: 1
       796: 1
       817: 1
       820: 1
       843: 1
       866: 1
       870: 1
       874: 1
       917: 1
       941: 1
       964: 1
       969: 1
       995: 1
       998: 1
      1000: 1
      1012: 1
      1021: 1
      1037: 1
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1291: 1

1292:    0: q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^3+2q^2+q
         5: q^4+2q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^4+q^3+q^2+q
         8: q^3+q^2+q
         9: q^4+q^3+q^2+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^3+q^2+q
        16: q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+q^3+q^2+q
        19: q^3+2q^2+q
        20: q^4+2q^3+2q^2+q
        21: q^4+q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2+q
        39: 2q^2+q
        41: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^3+q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: q^2+q
        60: q^2+q
        62: q^2+q
        64: q^2+q
        66: 2q^2+q
        68: q
        69: q^3+q^2+q
        70: q^3+q
        71: q^3+q^2+q
        72: 2q^2+q
        73: 2q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: q
        81: q^2+q
        82: q^2+q
        83: q^2+q
        84: q
        85: q^2+q
        86: q^2+q
        87: q^2+q
        88: q^3+q
        89: q
        90: q^3+q
        91: q^3+q^2+q
        92: q^3+q^2+q
        93: q^3+q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q
       101: q^2+q
       102: q
       103: q^2+q
       107: q^2+q
       109: q^2+q
       111: 2q^2+q
       113: q^2+q
       115: q^2+q
       117: q
       119: q
       121: q
       123: q^2+q
       125: q
       126: q^3+q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: q
       134: q^3+q^2+q
       135: q^2+q
       136: q^2+q
       137: q
       138: q^2+q
       139: q^2+q
       140: q
       141: q
       142: 2q^2+q
       143: q
       144: q^2+q
       145: q^2+q
       146: q
       147: 2q^2+q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q
       167: q^2+q
       168: q
       169: q^2+q
       173: q
       177: q^2+q
       179: q^2+q
       181: 2q^2+q
       183: q
       185: q
       187: q^2+q
       189: q
       191: q
       193: q
       195: q^2+q
       197: q
       199: q
       201: q^2+q
       203: q
       205: q
       207: q
       209: q
       211: q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q^2+q
       249: q
       259: q^2+q
       263: q
       267: q
       271: q
       275: q
       279: q
       281: q^2+q
       283: q
       285: q
       287: q
       289: q^2+q
       291: q^2+q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q
       317: q
       319: q
       321: q
       323: q
       325: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q^2+q
       342: q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q
       356: q^2+q
       358: q
       359: q
       366: q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       413: q
       417: q^2+q
       419: q
       421: q
       423: q
       425: q
       427: q
       429: q
       431: q
       433: q
       443: q
       445: q
       447: q
       449: q
       451: q
       461: q
       463: q
       469: q
       477: q
       479: q
       481: q
       482: q
       483: q
       495: q
       500: q
       521: q
       529: q
       533: q
       545: q
       549: q
       561: q
       569: q
       573: q
       577: q
       585: q
       589: q
       591: q
       593: q
       595: q
       599: q
       613: q
       629: q
       651: 1
       693: q
       709: q
       713: q
       717: q
       757: 1
       771: 1
       849: 1
       886: 1
       960: 1
       970: 1
      1010: 1
      1088: 1
      1126: 1
      1140: 1
      1292: 1

1293:    0: 6q^2+3q
         1: q^4+5q^3+6q^2+3q
         2: 6q^2+3q
         3: 3q^3+6q^2+3q
         4: 6q^2+3q
         5: 3q^3+6q^2+3q
         6: q^4+5q^3+6q^2+3q
         7: 6q^2+3q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 3q^2+3q
        11: 3q^2+3q
        12: 3q^2+3q
        13: 6q^2+3q
        14: 6q^2+3q
        15: 3q^3+6q^2+3q
        16: 5q^2+3q
        17: 2q^3+5q^2+3q
        18: 3q^2+2q
        19: 6q^2+3q
        20: q^4+5q^3+6q^2+3q
        21: 6q^2+3q
        22: 5q^2+3q
        23: 2q^3+5q^2+3q
        24: 5q^2+3q
        25: 5q^2+3q
        26: 2q^3+5q^2+3q
        27: 5q^2+3q
        28: 2q^2+3q
        29: 3q^2+3q
        30: 6q^2+3q
        31: 2q^2+3q
        32: 5q^2+3q
        33: 4q^2+3q
        34: 2q^2+3q
        35: 5q^2+3q
        36: 4q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 3q^2+3q
        44: 3q^2+3q
        45: 3q^2+3q
        46: 5q^2+3q
        47: 2q^3+5q^2+3q
        48: 3q^2+2q
        49: 5q^2+3q
        50: 2q^3+5q^2+3q
        51: 3q^2+2q
        52: 5q^2+3q
        53: 2q^3+5q^2+3q
        54: 5q^2+3q
        55: 5q^2+3q
        56: 2q^3+5q^2+3q
        57: 5q^2+3q
        58: q
        59: q^2+2q
        60: q^2+2q
        61: q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: 2q^2+3q
        69: 2q^2+2q
        70: 3q^2+3q
        71: 2q^2+3q
        72: 4q^2+3q
        73: 4q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: 2q^2+3q
        81: 4q^2+3q
        82: 2q^2+3q
        83: 5q^2+3q
        84: 2q^2+3q
        85: 4q^2+3q
        86: 2q^2+3q
        87: 5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 5q^2+3q
        92: 2q^3+5q^2+3q
        93: 3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: 2q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: q^3+4q^2+3q
       102: q^2+3q
       103: q
       104: q
       106: q
       107: q^2+2q
       108: q
       109: q
       110: q^2+2q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: q
       118: q^2+2q
       119: q^2+2q
       120: q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 2q^2+3q
       134: 2q^2+2q
       135: 4q^2+3q
       136: 4q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q
       141: 2q^2+3q
       142: 3q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 3q^2+3q
       148: 2q
       149: q^2+3q
       150: q^2+3q
       151: q^2+2q
       152: q
       153: q^3+3q^2+2q
       154: q^2+q
       155: q^2+2q
       156: q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 3q
       167: 2q^2+3q
       168: 2q
       169: q
       170: q
       172: q
       173: q
       174: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: q^2+2q
       184: q
       185: q
       186: q^2+2q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: q
       192: 2q
       193: 2q
       195: q
       196: q^2+2q
       197: q
       198: q
       199: 2q
       200: q
       201: q^2+2q
       202: q
       204: 2q
       205: q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: q^2+2q
       212: q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q
       237: 2q
       239: q^2+2q
       241: q
       243: 3q
       244: 2q
       245: 2q
       246: q^2+3q
       247: 3q
       248: 2q^2+3q
       249: 2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       259: q
       262: q
       263: q
       264: q
       266: q
       267: q
       268: q
       273: q
       274: q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q
       289: q^2+2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: 2q
       301: q
       303: q
       304: q^2+2q
       305: q
       306: q
       307: q^2+2q
       308: q
       310: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       319: 2q
       322: 2q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       338: 2q
       340: q^2+2q
       342: q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       360: 2q
       362: q^2+2q
       364: q
       366: 2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       393: q
       394: q
       399: q
       403: q
       404: q
       407: q
       413: q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 2q
       429: q
       432: q
       435: q
       443: 2q
       445: q
       447: q
       450: q
       455: q
       462: 2q
       463: q
       465: 2q
       467: q
       469: q
       471: 2q
       474: 2q
       476: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: 2q
       487: q^2+2q
       489: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       508: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       537: q
       545: q
       555: q
       563: q
       566: q
       574: q
       585: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 2q
       615: 2q
       617: q
       632: 2q
       633: q
       639: q
       641: q
       644: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 2q
       674: 1
       679: q
       680: 1
       685: q
       733: q
       751: q
       766: q
       775: 1
       779: 1
       781: q
       785: q
       788: q
       793: 1
       795: 1
       818: 1
       819: 1
       844: 1
       866: 1
       870: 1
       874: 1
       916: 1
       942: 1
       965: 1
       971: 1
       994: 1
       999: 1
      1000: 1
      1013: 1
      1020: 1
      1036: 1
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1293: 1

1294:    0: 6q^2+3q
         1: q^4+5q^3+6q^2+3q
         2: 6q^2+3q
         3: 3q^3+6q^2+3q
         4: 6q^2+3q
         5: 3q^3+6q^2+3q
         6: q^4+5q^3+6q^2+3q
         7: 6q^2+3q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 3q^2+3q
        11: 3q^2+3q
        12: 3q^2+3q
        13: 6q^2+3q
        14: 6q^2+3q
        15: 3q^3+6q^2+3q
        16: 5q^2+3q
        17: 2q^3+5q^2+3q
        18: 3q^2+2q
        19: 6q^2+3q
        20: q^4+5q^3+6q^2+3q
        21: 6q^2+3q
        22: 5q^2+3q
        23: 2q^3+5q^2+3q
        24: 5q^2+3q
        25: 5q^2+3q
        26: 2q^3+5q^2+3q
        27: 5q^2+3q
        28: 2q^2+3q
        29: 3q^2+3q
        30: 6q^2+3q
        31: 2q^2+3q
        32: 5q^2+3q
        33: 4q^2+3q
        34: 2q^2+3q
        35: 5q^2+3q
        36: 4q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 3q^2+3q
        44: 3q^2+3q
        45: 3q^2+3q
        46: 5q^2+3q
        47: 2q^3+5q^2+3q
        48: 3q^2+2q
        49: 5q^2+3q
        50: 2q^3+5q^2+3q
        51: 3q^2+2q
        52: 5q^2+3q
        53: 2q^3+5q^2+3q
        54: 5q^2+3q
        55: 5q^2+3q
        56: 2q^3+5q^2+3q
        57: 5q^2+3q
        58: q^2+2q
        59: q
        60: q
        61: q^2+2q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: 2q^2+3q
        69: 2q^2+2q
        70: 3q^2+3q
        71: 2q^2+3q
        72: 4q^2+3q
        73: 4q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: 2q^2+3q
        81: 4q^2+3q
        82: 2q^2+3q
        83: 5q^2+3q
        84: 2q^2+3q
        85: 4q^2+3q
        86: 2q^2+3q
        87: 5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 5q^2+3q
        92: 2q^3+5q^2+3q
        93: 3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: 2q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: q^3+4q^2+3q
       102: q^2+3q
       103: q
       105: q
       106: q
       107: q
       108: q^2+2q
       109: q^2+2q
       110: q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: q^2+2q
       118: q
       119: q
       120: q^2+2q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 2q^2+3q
       134: 2q^2+2q
       135: 4q^2+3q
       136: 4q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q
       141: 2q^2+3q
       142: 3q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 3q^2+3q
       148: 2q
       149: q^2+3q
       150: q^2+3q
       151: q^2+2q
       152: q
       153: q^3+3q^2+2q
       154: q^2+q
       155: q^2+2q
       156: q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 3q
       167: 2q^2+3q
       168: 2q
       169: q
       171: q
       172: q
       173: q
       175: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: q
       184: q^2+2q
       185: q^2+2q
       186: q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: 2q
       192: q
       194: 2q
       195: q^2+2q
       196: q
       197: q
       198: q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       203: 2q
       205: q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: q^2+2q
       212: q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q
       237: 2q
       239: q^2+2q
       241: q
       243: 3q
       244: 2q
       245: 2q
       246: q^2+3q
       247: 3q
       248: 2q^2+3q
       249: 2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       259: q
       262: q
       263: q
       265: q
       266: q
       269: q
       270: q
       271: q
       272: q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q
       289: q^2+2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       300: 2q
       301: q
       303: q^2+2q
       304: q
       305: q
       306: q
       307: q
       308: q^2+2q
       309: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       320: 2q
       321: 2q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       338: 2q
       340: q^2+2q
       342: q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       360: 2q
       362: q^2+2q
       364: q
       366: 2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       381: q
       384: q
       385: q
       387: q
       388: q
       391: q
       395: q
       396: q
       397: q
       401: q
       402: q
       408: q
       413: q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 2q
       430: q
       431: q
       435: q
       444: 2q
       445: q
       448: q
       449: q
       455: q
       461: 2q
       463: q
       465: 2q
       467: q
       469: q
       472: 2q
       473: 2q
       476: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: 2q
       487: q^2+2q
       489: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       508: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       539: q
       547: q
       553: q
       561: q
       567: q
       576: q
       585: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 2q
       616: 2q
       617: q
       631: 2q
       633: q
       639: q
       642: q
       643: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 2q
       674: 1
       679: q
       680: 1
       685: q
       735: q
       749: q
       767: q
       775: 1
       779: 1
       781: q
       786: q
       787: q
       794: 1
       795: 1
       817: 1
       819: 1
       844: 1
       866: 1
       870: 1
       874: 1
       918: 1
       940: 1
       966: 1
       971: 1
       994: 1
       998: 1
      1001: 1
      1013: 1
      1020: 1
      1036: 1
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1294: 1

1295:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       106: 1
       108: 1
       110: 1
       111: q+1
       113: 1
       115: q+1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       172: 1
       176: 1
       177: q+1
       179: 1
       181: q+1
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       239: q+1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: q+1
       342: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: 1
       362: q+1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       552: 1
       555: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       735: 1
       739: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       775: 1
       779: 1
       781: 1
       786: 1
       788: 1
       791: 1
       794: 1
       795: 1
       809: 1
       818: 1
       819: 1
       833: 1
       843: 1
       849: 1
       866: 1
       870: 1
       874: 1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       942: 1
       961: 1
       967: 1
       968: 1
       994: 1
       999: 1
      1001: 1
      1010: 1
      1012: 1
      1020: 1
      1036: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1138: 1
      1295: 1

1296:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       104: 1
       107: 1
       110: 1
       112: q+1
       114: 1
       116: q+1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       170: 1
       174: 1
       178: q+1
       180: 1
       182: q+1
       183: 1
       186: 1
       188: q+1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       551: 1
       556: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       734: 1
       740: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       776: 1
       780: 1
       782: 1
       785: 1
       788: 1
       792: 1
       793: 1
       796: 1
       810: 1
       818: 1
       820: 1
       834: 1
       844: 1
       850: 1
       866: 1
       870: 1
       874: 1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       943: 1
       962: 1
       965: 1
       972: 1
       995: 1
       999: 1
      1000: 1
      1011: 1
      1013: 1
      1021: 1
      1037: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1142: 1
      1296: 1

1297:    0: q+1
         1: q^2+q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       105: 1
       108: 1
       109: 1
       112: q+1
       114: 1
       116: q+1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       171: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: 1
       240: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       256: 1
       257: q+1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: q+1
       343: 1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       508: 1
       512: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       550: 1
       554: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       674: 1
       679: 1
       680: 1
       685: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       736: 1
       738: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       776: 1
       780: 1
       782: 1
       786: 1
       787: 1
       792: 1
       794: 1
       796: 1
       810: 1
       817: 1
       820: 1
       834: 1
       844: 1
       850: 1
       866: 1
       870: 1
       874: 1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       941: 1
       963: 1
       966: 1
       972: 1
       995: 1
       998: 1
      1001: 1
      1011: 1
      1013: 1
      1021: 1
      1037: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1142: 1
      1297: 1

1298:    0: 6q^2+3q
         1: q^4+5q^3+6q^2+3q
         2: 6q^2+3q
         3: 3q^3+6q^2+3q
         4: 6q^2+3q
         5: 3q^3+6q^2+3q
         6: q^4+5q^3+6q^2+3q
         7: 6q^2+3q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 3q^2+3q
        11: 3q^2+3q
        12: 3q^2+3q
        13: 6q^2+3q
        14: 6q^2+3q
        15: 3q^3+6q^2+3q
        16: 5q^2+3q
        17: 2q^3+5q^2+3q
        18: 3q^2+2q
        19: 6q^2+3q
        20: q^4+5q^3+6q^2+3q
        21: 6q^2+3q
        22: 5q^2+3q
        23: 2q^3+5q^2+3q
        24: 5q^2+3q
        25: 5q^2+3q
        26: 2q^3+5q^2+3q
        27: 5q^2+3q
        28: 2q^2+3q
        29: 3q^2+3q
        30: 6q^2+3q
        31: 2q^2+3q
        32: 5q^2+3q
        33: 4q^2+3q
        34: 2q^2+3q
        35: 5q^2+3q
        36: 4q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 3q^2+3q
        44: 3q^2+3q
        45: 3q^2+3q
        46: 5q^2+3q
        47: 2q^3+5q^2+3q
        48: 3q^2+2q
        49: 5q^2+3q
        50: 2q^3+5q^2+3q
        51: 3q^2+2q
        52: 5q^2+3q
        53: 2q^3+5q^2+3q
        54: 5q^2+3q
        55: 5q^2+3q
        56: 2q^3+5q^2+3q
        57: 5q^2+3q
        58: q
        59: q^2+2q
        60: q
        61: q^2+2q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: 2q^2+3q
        69: 2q^2+2q
        70: 3q^2+3q
        71: 2q^2+3q
        72: 4q^2+3q
        73: 4q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: 2q^2+3q
        81: 4q^2+3q
        82: 2q^2+3q
        83: 5q^2+3q
        84: 2q^2+3q
        85: 4q^2+3q
        86: 2q^2+3q
        87: 5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 5q^2+3q
        92: 2q^3+5q^2+3q
        93: 3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: 2q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: 2q^2+2q
       100: q^2+3q
       101: q^3+4q^2+3q
       102: q^2+3q
       104: q
       105: q
       106: q
       107: q
       108: q^2+2q
       109: q
       110: q^2+2q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: q
       118: q^2+2q
       119: q
       120: q^2+2q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 2q^2+3q
       134: 2q^2+2q
       135: 4q^2+3q
       136: 4q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q
       141: 2q^2+3q
       142: 3q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 3q^2+3q
       148: 2q
       149: q^2+3q
       150: q^2+3q
       151: q
       152: q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q
       156: q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 3q
       167: 2q^2+3q
       168: 2q
       170: q
       171: q
       172: q
       174: q
       175: q
       176: q
       178: q
       180: 2q
       182: q^2+2q
       183: q
       184: q^2+2q
       185: q
       186: q^2+2q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: q
       192: 2q
       194: 2q
       195: q
       196: q^2+2q
       197: q
       198: q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       204: 2q
       205: q
       206: q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q
       212: q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q
       238: 2q
       240: q^2+2q
       242: q
       243: 3q
       244: 2q
       245: 2q
       246: q^2+3q
       247: 3q
       248: 2q^2+3q
       249: 2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       260: q
       261: q
       264: q
       265: q
       266: q
       269: q
       270: q
       273: q
       274: q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q
       290: q^2+2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       300: 2q
       302: q
       303: q
       304: q^2+2q
       305: q
       306: q
       307: q
       308: q^2+2q
       310: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       320: 2q
       322: 2q
       323: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       339: 2q
       341: q^2+2q
       343: q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       361: 2q
       363: q^2+2q
       365: q
       366: 2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       382: q
       383: q
       386: q
       387: q
       388: q
       392: q
       395: q
       396: q
       400: q
       403: q
       404: q
       406: q
       414: q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 2q
       430: q
       432: q
       436: q
       444: 2q
       446: q
       448: q
       450: q
       456: q
       462: 2q
       464: q
       466: 2q
       468: q
       470: q
       472: 2q
       474: 2q
       475: q
       479: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: 2q
       488: q^2+2q
       490: q
       491: 2q
       495: q
       496: 2q
       500: q
       501: 2q
       508: 2q
       512: q
       514: q
       515: 1
       516: q+1
       517: 1
       540: q
       548: q
       556: q
       564: q
       568: q
       575: q
       586: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 2q
       616: 2q
       618: q
       632: 2q
       634: q
       640: q
       642: q
       644: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 2q
       674: 1
       679: q
       680: 1
       685: q
       736: q
       752: q
       768: q
       776: 1
       780: 1
       782: q
       786: q
       788: q
       794: 1
       796: 1
       818: 1
       820: 1
       843: 1
       866: 1
       870: 1
       874: 1
       919: 1
       943: 1
       967: 1
       969: 1
       995: 1
       999: 1
      1001: 1
      1012: 1
      1021: 1
      1037: 1
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1298: 1

1299:    0: q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^3+2q^2+q
         5: q^4+2q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^4+q^3+q^2+q
         8: q^3+q^2+q
         9: q^4+q^3+q^2+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^3+q^2+q
        16: q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+q^3+q^2+q
        19: q^3+2q^2+q
        20: q^4+2q^3+2q^2+q
        21: q^4+q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2+q
        39: 2q^2+q
        41: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^3+q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        59: q^2+q
        61: q^2+q
        62: q^2+q
        64: q^2+q
        66: 2q^2+q
        68: q
        69: q^3+q^2+q
        70: q^3+q
        71: q^3+q^2+q
        72: 2q^2+q
        73: 2q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: q
        81: q^2+q
        82: q^2+q
        83: q^2+q
        84: q
        85: q^2+q
        86: q^2+q
        87: q^2+q
        88: q^3+q
        89: q
        90: q^3+q
        91: q^3+q^2+q
        92: q^3+q^2+q
        93: q^3+q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q
       101: q^2+q
       102: q
       106: q^2+q
       108: q^2+q
       110: q^2+q
       111: 2q^2+q
       113: q^2+q
       115: q^2+q
       118: q
       120: q
       121: q
       123: q^2+q
       125: q
       126: q^3+q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: q
       134: q^3+q^2+q
       135: q^2+q
       136: q^2+q
       137: q
       138: q^2+q
       139: q^2+q
       140: q
       141: q
       142: 2q^2+q
       143: q
       144: q^2+q
       145: q^2+q
       146: q
       147: 2q^2+q
       148: q
       149: q
       150: q
       151: q
       153: q^2+q
       155: q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q
       167: q^2+q
       168: q
       172: q^2+q
       176: q
       177: q^2+q
       179: q^2+q
       181: 2q^2+q
       184: q
       186: q
       187: q^2+q
       189: q
       192: q
       194: q
       196: q^2+q
       197: q
       200: q
       202: q^2+q
       204: q
       205: q
       207: q
       209: q
       211: q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q
       237: q
       239: q^2+q
       241: q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q^2+q
       249: q
       262: q^2+q
       266: q
       269: q
       273: q
       278: q
       279: q
       281: q^2+q
       284: q
       286: q
       287: q
       289: q^2+q
       291: q^2+q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q
       317: q
       320: q
       322: q
       323: q
       325: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q^2+q
       342: q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q
       356: q^2+q
       358: q
       359: q
       366: q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       413: q
       417: q^2+q
       420: q
       422: q
       423: q
       425: q
       427: q
       430: q
       432: q
       433: q
       444: q
       445: q
       448: q
       450: q
       451: q
       462: q
       463: q
       469: q
       477: q
       479: q
       481: q
       482: q
       483: q
       495: q
       500: q
       524: q
       532: q
       536: q
       547: q
       552: q
       563: q
       570: q
       575: q
       577: q
       585: q
       590: q
       592: q
       594: q
       596: q
       599: q
       613: q
       629: q
       651: 1
       697: q
       712: q
       716: q
       720: q
       758: 1
       771: 1
       849: 1
       893: 1
       961: 1
       970: 1
      1010: 1
      1095: 1
      1127: 1
      1140: 1
      1299: 1

1300:    0: q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^3+2q^2+q
         5: q^4+2q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^4+q^3+q^2+q
         8: q^3+q^2+q
         9: q^4+q^3+q^2+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^3+q^2+q
        16: q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+q^3+q^2+q
        19: q^3+2q^2+q
        20: q^4+2q^3+2q^2+q
        21: q^4+q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        38: 2q^2+q
        40: 2q^2+q
        42: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^3+q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        59: q^2+q
        60: q^2+q
        63: q^2+q
        65: q^2+q
        67: 2q^2+q
        68: q
        69: q^3+q^2+q
        70: q^3+q
        71: q^3+q^2+q
        72: 2q^2+q
        73: 2q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: q
        81: q^2+q
        82: q^2+q
        83: q^2+q
        84: q
        85: q^2+q
        86: q^2+q
        87: q^2+q
        88: q^3+q
        89: q
        90: q^3+q
        91: q^3+q^2+q
        92: q^3+q^2+q
        93: q^3+q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q
       101: q^2+q
       102: q
       104: q^2+q
       107: q^2+q
       110: q^2+q
       112: 2q^2+q
       114: q^2+q
       116: q^2+q
       118: q
       119: q
       122: q
       124: q^2+q
       125: q
       126: q^3+q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: q
       134: q^3+q^2+q
       135: q^2+q
       136: q^2+q
       137: q
       138: q^2+q
       139: q^2+q
       140: q
       141: q
       142: 2q^2+q
       143: q
       144: q^2+q
       145: q^2+q
       146: q
       147: 2q^2+q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q
       167: q^2+q
       168: q
       170: q^2+q
       174: q
       178: q^2+q
       180: q^2+q
       182: 2q^2+q
       183: q
       186: q
       188: q^2+q
       190: q
       192: q
       193: q
       196: q^2+q
       198: q
       199: q
       201: q^2+q
       204: q
       206: q
       208: q
       210: q
       212: q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q^2+q
       249: q
       260: q^2+q
       264: q
       268: q
       274: q
       276: q
       280: q
       282: q^2+q
       283: q
       286: q
       288: q
       290: q^2+q
       292: q^2+q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q
       318: q
       319: q
       322: q
       324: q
       326: q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q^2+q
       343: q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q
       356: q^2+q
       358: q
       359: q
       366: q
       378: q
       382: q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       414: q
       418: q^2+q
       419: q
       422: q
       424: q
       426: q
       428: q
       429: q
       432: q
       434: q
       443: q
       446: q
       447: q
       450: q
       452: q
       462: q
       464: q
       470: q
       478: q
       480: q
       481: q
       482: q
       483: q
       495: q
       500: q
       522: q
       530: q
       534: q
       546: q
       551: q
       564: q
       571: q
       574: q
       581: q
       586: q
       589: q
       592: q
       593: q
       596: q
       600: q
       614: q
       630: q
       652: 1
       699: q
       710: q
       715: q
       718: q
       759: 1
       774: 1
       850: 1
       894: 1
       962: 1
       973: 1
      1011: 1
      1096: 1
      1128: 1
      1143: 1
      1300: 1

1301:    0: q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+q^3+q^2+q
         3: q^3+2q^2+q
         4: q^3+2q^2+q
         5: q^4+2q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^4+q^3+q^2+q
         8: q^3+q^2+q
         9: q^4+q^3+q^2+q
        10: q^3+q^2+q
        11: q^3+q^2+q
        12: q^3+q^2+q
        13: q^3+q^2+q
        14: q^3+q^2+q
        15: q^3+q^2+q
        16: q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+q^3+q^2+q
        19: q^3+2q^2+q
        20: q^4+2q^3+2q^2+q
        21: q^4+q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^2+q
        28: q^3+q^2+q
        29: q^3+q^2+q
        30: q^3+q^2+q
        31: q^2+q
        32: q^2+q
        33: 2q^2+q
        34: q^2+q
        35: q^2+q
        36: 2q^2+q
        38: 2q^2+q
        40: 2q^2+q
        42: q^2+q
        43: q^3+q
        44: q^3+q
        45: q
        46: q^3+q^2+q
        47: q^3+q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: q^2+q
        61: q^2+q
        63: q^2+q
        65: q^2+q
        67: 2q^2+q
        68: q
        69: q^3+q^2+q
        70: q^3+q
        71: q^3+q^2+q
        72: 2q^2+q
        73: 2q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: q
        81: q^2+q
        82: q^2+q
        83: q^2+q
        84: q
        85: q^2+q
        86: q^2+q
        87: q^2+q
        88: q^3+q
        89: q
        90: q^3+q
        91: q^3+q^2+q
        92: q^3+q^2+q
        93: q^3+q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q
       101: q^2+q
       102: q
       105: q^2+q
       108: q^2+q
       109: q^2+q
       112: 2q^2+q
       114: q^2+q
       116: q^2+q
       117: q
       120: q
       122: q
       124: q^2+q
       125: q
       126: q^3+q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: q
       134: q^3+q^2+q
       135: q^2+q
       136: q^2+q
       137: q
       138: q^2+q
       139: q^2+q
       140: q
       141: q
       142: 2q^2+q
       143: q
       144: q^2+q
       145: q^2+q
       146: q
       147: 2q^2+q
       148: q
       149: q
       150: q
       152: q
       154: q^2+q
       156: q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q
       167: q^2+q
       168: q
       171: q^2+q
       175: q
       178: q^2+q
       180: q^2+q
       182: 2q^2+q
       184: q
       185: q
       188: q^2+q
       190: q
       191: q
       194: q
       195: q^2+q
       198: q
       200: q
       202: q^2+q
       203: q
       206: q
       208: q
       210: q
       212: q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q
       238: q
       240: q^2+q
       242: q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q^2+q
       249: q
       261: q^2+q
       265: q
       270: q
       272: q
       277: q
       280: q
       282: q^2+q
       284: q
       285: q
       288: q
       290: q^2+q
       292: q^2+q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q
       318: q
       320: q
       321: q
       324: q
       326: q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q^2+q
       343: q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q
       356: q^2+q
       358: q
       359: q
       366: q
       379: q
       383: q
       387: q
       392: q
       395: q
       398: q
       402: q
       408: q
       414: q
       418: q^2+q
       420: q
       421: q
       424: q
       426: q
       428: q
       430: q
       431: q
       434: q
       444: q
       446: q
       448: q
       449: q
       452: q
       461: q
       464: q
       470: q
       478: q
       480: q
       481: q
       482: q
       483: q
       495: q
       500: q
       523: q
       531: q
       535: q
       548: q
       550: q
       562: q
       572: q
       576: q
       581: q
       586: q
       590: q
       591: q
       594: q
       595: q
       600: q
       614: q
       630: q
       652: 1
       700: q
       711: q
       714: q
       719: q
       760: 1
       774: 1
       850: 1
       895: 1
       963: 1
       973: 1
      1011: 1
      1097: 1
      1129: 1
      1143: 1
      1301: 1

1302:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: q+1
       109: q+1
       111: q+1
       113: 2q+1
       115: q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: 2q+1
       181: q+1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q+1
       193: q+1
       195: q+1
       197: q+1
       199: q+1
       201: q+1
       203: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       259: q+1
       263: 1
       267: q+1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       338: q+1
       340: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       377: 1
       381: 1
       385: 1
       389: q+1
       393: 1
       397: q+1
       401: 1
       405: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       427: q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: q+1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       484: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: q+1
       549: 1
       553: 1
       557: 1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       587: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: q+1
       705: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       789: 1
       793: 1
       795: 1
       799: 1
       813: 1
       815: 1
       817: 1
       819: 1
       823: 1
       837: 1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       884: 1
       912: 1
       916: 1
       932: 1
       936: 1
       940: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
      1014: 1
      1016: 1
      1030: 1
      1032: 1
      1046: 1
      1050: 1
      1086: 1
      1098: 1
      1144: 1
      1164: 1
      1184: 1
      1188: 1
      1194: 1
      1302: 1

1303:    0: 9q^2+3q
         1: 9q^2+3q
         2: 3q^3+6q^2+3q
         3: 9q^2+3q
         4: q^4+4q^3+5q^2+2q
         5: 9q^2+3q
         6: q^4+4q^3+5q^2+2q
         7: q^3+3q^2+2q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 9q^2+3q
        11: 9q^2+3q
        12: q^4+4q^3+5q^2+2q
        13: 6q^2+3q
        14: q^3+3q^2+2q
        15: 6q^2+3q
        16: 9q^2+3q
        17: 9q^2+3q
        18: q^3+3q^2+2q
        19: 4q^2+2q
        20: 4q^2+2q
        21: 2q^2+2q
        22: 9q^2+3q
        23: 9q^2+3q
        24: 3q^3+6q^2+3q
        25: 9q^2+3q
        26: 9q^2+3q
        27: 3q^3+6q^2+3q
        28: 9q^2+3q
        29: 4q^2+2q
        30: 2q^2+2q
        31: 9q^2+3q
        32: 6q^2+3q
        33: 9q^2+3q
        34: 9q^2+3q
        35: 6q^2+3q
        36: 9q^2+3q
        37: 3q^2+q
        38: 6q^2+2q
        39: 3q^2+q
        40: 6q^2+2q
        41: q^3+2q^2+q
        42: 2q^3+4q^2+2q
        43: 6q^2+3q
        44: q^3+3q^2+2q
        45: 6q^2+3q
        46: 6q^2+3q
        47: 6q^2+3q
        48: q^3+3q^2+2q
        49: 4q^2+2q
        50: 4q^2+2q
        51: 2q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: 2q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: 2q^2+2q
        58: 5q^2+2q
        59: 4q^2+q
        60: 5q^2+2q
        61: 4q^2+q
        62: 3q^2+q
        63: 6q^2+2q
        64: 2q^2+q
        65: 4q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 3q^2+3q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 4q^2+2q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: 6q^2+3q
        81: 6q^2+3q
        82: 4q^2+2q
        83: 2q^2+2q
        84: 6q^2+3q
        85: 6q^2+3q
        86: 4q^2+2q
        87: 2q^2+2q
        88: 6q^2+3q
        89: 6q^2+3q
        90: q^3+3q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: 2q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: 2q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: 2q^2+2q
       103: 2q^2+q
       104: 3q^2+q
       105: 3q^2+q
       106: q^2
       107: q^2+q
       109: q^2+q
       114: 2q^2+q
       116: q^2+q
       117: 2q^2+2q
       118: q^2+q
       119: 2q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: 4q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 3q^2+3q
       126: 2q^2+2q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 6q^2+3q
       138: 2q^2+2q
       139: 4q^2+2q
       140: q^2+q
       141: 2q^2+2q
       142: q^2+q
       143: 6q^2+3q
       144: 2q^2+2q
       145: 4q^2+2q
       146: 2q^2+2q
       147: q^2+q
       148: q^2+q
       149: 4q^2+2q
       150: 2q^2+2q
       152: 2q^2+q
       154: 2q^2+q
       156: q^2+q
       157: 2q
       158: 2q^2+2q
       159: 2q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: 2q^2+2q
       173: q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: 2q^2+q
       183: q
       185: q
       190: q^2+q
       191: 2q^2+2q
       192: q^2+q
       193: q^2+q
       195: q^2+q
       199: 2q^2+2q
       200: q^2+q
       201: q^2+q
       203: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       210: 2q^2+q
       212: q^2+q
       214: q
       216: q^2+q
       218: q
       219: 2q
       220: 2q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q^2+2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q^2+2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q^2+2q
       238: 2q^2+q
       240: 2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: q^2+q
       245: q^2+q
       246: 2q^2+2q
       247: q+1
       248: q+1
       250: 2q
       251: 2q^2+2q
       252: 2q
       253: 2q
       254: 2q^2+2q
       255: 2q
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       280: q
       282: q
       283: q
       285: q
       288: q^2+q
       293: q
       295: q
       299: q
       303: q
       307: q
       309: q
       316: q^2+q
       318: 2q^2+q
       319: q^2+q
       321: q^2+q
       326: q^2+q
       328: q
       330: q^2+q
       332: q
       333: 2q
       334: q
       335: q
       337: q+1
       339: q+1
       341: q+1
       344: 2q
       345: 2q
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: q+1
       352: 2q
       353: 2q
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: q+1
       361: q
       363: q^2+q
       365: q
       366: 2q^2+2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q^2+2q
       376: 2q
       410: q
       412: q
       414: q
       419: q
       421: q
       428: q+1
       429: q
       431: q
       437: q
       439: q
       443: q+1
       446: q+1
       447: q
       449: q
       453: q
       457: q
       461: q+1
       464: q+1
       466: q
       468: q
       470: q^2+q
       471: q
       473: q
       479: q+1
       484: 1
       486: 1
       488: 1
       492: 2q
       493: q
       494: q
       496: 1
       497: 2q
       498: q
       499: q
       501: 1
       503: q
       505: q^2+q
       507: q
       508: 2q
       509: 2q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       546: q+1
       562: q+1
       573: q+1
       578: q+1
       584: q
       602: 1
       603: q
       607: q
       615: 1
       618: 1
       619: q
       621: q
       631: 1
       634: 1
       636: q
       638: q
       640: q
       641: q
       643: q
       647: q
       649: q
       655: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       694: q+1
       734: 1
       750: 1
       765: 1
       770: 1
       776: 1
       790: 1
       793: 1
       796: 1
       814: 1
       815: 1
       817: 1
       820: 1
       838: 1
       839: 1
       842: q
       843: 1
       845: q
       847: q
       857: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       885: 1
       917: 1
       933: 1
       941: 1
       957: 1
       964: 1
       969: 1
       983: 1
       988: 1
       993: 1
      1015: 1
      1016: 1
      1031: 1
      1032: 1
      1046: 1
      1087: 1
      1099: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1303: 1

1304:    0: q^3+3q^2+q
         1: q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: q^3+3q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q^2+q
         8: q^3+2q^2+q
         9: q^3+q^2+q
        10: q^3+3q^2+q
        11: q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^3+2q^2+q
        14: q^3+q^2+q
        15: 2q^2+q
        16: q^3+3q^2+q
        17: q^3+3q^2+q
        18: q^3+q^2+q
        19: q^3+2q^2+q
        20: q^3+2q^2+q
        21: q^3+q^2+q
        22: 3q^2+q
        23: 3q^2+q
        24: q^3+2q^2+q
        25: 3q^2+q
        26: 3q^2+q
        27: q^3+2q^2+q
        28: q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+q^2+q
        31: 3q^2+q
        32: 2q^2+q
        33: 3q^2+q
        34: 3q^2+q
        35: 2q^2+q
        36: 3q^2+q
        37: 3q^2+q
        39: 3q^2+q
        41: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+q^2+q
        45: 2q^2+q
        46: q^3+2q^2+q
        47: 2q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^3+2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: 2q^2+q
        59: q^2
        60: 2q^2+q
        61: q^2
        62: 3q^2+q
        64: 2q^2+q
        66: 3q^2+q
        68: q^2+q
        69: q^3+q^2+q
        70: q^3+q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: 2q^2+q
        83: q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^3+2q^2+q
        89: 2q^2+q
        90: q^3+q^2+q
        91: q
        92: q^2+q
        93: q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: 2q^2+q
       106: q^2
       107: q^2+q
       109: q^2+q
       111: q^2+q
       113: 2q^2+q
       115: q^2+q
       117: q^2+q
       119: q^2+q
       121: 2q^2+q
       123: 2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: q
       134: q
       135: q
       136: q
       137: 2q^2+q
       138: q^2+q
       139: 2q^2+q
       140: q
       141: q^2+q
       142: q^2+q
       143: 2q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^2+q
       173: q^2+q
       177: q^2+q
       179: 2q^2+q
       181: q^2+q
       183: q
       185: q
       187: q
       189: q^2+q
       191: q^2+q
       193: q
       195: q^2+q
       197: q
       199: q^2+q
       201: q^2+q
       203: q
       205: q
       207: 2q^2+q
       209: q^2+q
       211: q^2+q
       213: q
       215: q^2+q
       217: q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q^2+q
       227: q
       228: q
       229: q
       230: q
       231: q^2+q
       232: q
       233: q
       234: q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       259: q^2+q
       263: q
       267: q
       271: q
       275: q^2+q
       279: q
       281: q
       283: q
       285: q
       287: q^2+q
       289: q
       291: q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       319: q
       321: q
       323: q
       325: q^2+q
       327: q
       329: q^2+q
       331: q
       333: q
       334: q
       335: q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q^2+q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q
       413: q
       415: q
       417: q
       419: q
       421: q
       423: q
       429: q
       431: q
       433: q
       437: q
       439: q
       441: q
       447: q
       449: q
       451: q
       453: q
       457: q
       459: q
       469: q^2+q
       477: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       521: q
       525: q
       529: q
       533: q
       541: q
       549: q
       557: q
       569: q
       583: q
       587: q
       603: q
       607: q
       609: q
       619: q
       621: q
       625: q
       651: 1
       705: q
       725: q
       741: q
       757: 1
       771: 1
       849: 1
       853: 1
       886: 1
       960: 1
       970: 1
       978: 1
       984: 1
      1050: 1
      1088: 1
      1100: 1
      1184: 1
      1190: 1
      1304: 1

1305:    0: 9q^2+3q
         1: 9q^2+3q
         2: 3q^3+6q^2+3q
         3: 9q^2+3q
         4: q^4+4q^3+5q^2+2q
         5: 9q^2+3q
         6: q^4+4q^3+5q^2+2q
         7: q^3+3q^2+2q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 9q^2+3q
        11: 9q^2+3q
        12: q^4+4q^3+5q^2+2q
        13: 6q^2+3q
        14: q^3+3q^2+2q
        15: 6q^2+3q
        16: 9q^2+3q
        17: 9q^2+3q
        18: q^3+3q^2+2q
        19: 4q^2+2q
        20: 4q^2+2q
        21: 2q^2+2q
        22: 9q^2+3q
        23: 9q^2+3q
        24: 3q^3+6q^2+3q
        25: 9q^2+3q
        26: 9q^2+3q
        27: 3q^3+6q^2+3q
        28: 9q^2+3q
        29: 4q^2+2q
        30: 2q^2+2q
        31: 9q^2+3q
        32: 6q^2+3q
        33: 9q^2+3q
        34: 9q^2+3q
        35: 6q^2+3q
        36: 9q^2+3q
        37: 6q^2+2q
        38: 3q^2+q
        39: 6q^2+2q
        40: 3q^2+q
        41: 2q^3+4q^2+2q
        42: q^3+2q^2+q
        43: 6q^2+3q
        44: q^3+3q^2+2q
        45: 6q^2+3q
        46: 6q^2+3q
        47: 6q^2+3q
        48: q^3+3q^2+2q
        49: 4q^2+2q
        50: 4q^2+2q
        51: 2q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: 2q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: 2q^2+2q
        58: 4q^2+q
        59: 5q^2+2q
        60: 5q^2+2q
        61: 4q^2+q
        62: 6q^2+2q
        63: 3q^2+q
        64: 4q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 3q^2+3q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 4q^2+2q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: 6q^2+3q
        81: 6q^2+3q
        82: 4q^2+2q
        83: 2q^2+2q
        84: 6q^2+3q
        85: 6q^2+3q
        86: 4q^2+2q
        87: 2q^2+2q
        88: 6q^2+3q
        89: 6q^2+3q
        90: q^3+3q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: 2q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: 2q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: 2q^2+2q
       103: 3q^2+q
       104: 2q^2+q
       105: q^2
       106: 3q^2+q
       107: q^2+q
       110: q^2+q
       113: 2q^2+q
       115: q^2+q
       117: q^2+q
       118: 2q^2+2q
       119: 2q^2+2q
       120: q^2+q
       121: 4q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 3q^2+3q
       126: 2q^2+2q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 6q^2+3q
       138: 2q^2+2q
       139: 4q^2+2q
       140: q^2+q
       141: 2q^2+2q
       142: q^2+q
       143: 6q^2+3q
       144: 2q^2+2q
       145: 4q^2+2q
       146: 2q^2+2q
       147: q^2+q
       148: q^2+q
       149: 4q^2+2q
       150: 2q^2+2q
       151: 2q^2+q
       153: 2q^2+q
       155: q^2+q
       157: 2q
       158: 2q^2+2q
       159: 2q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: 2q^2+2q
       173: q^2+q
       174: q^2+q
       176: q^2+q
       177: q^2+q
       179: 2q^2+q
       183: q
       186: q
       189: q^2+q
       191: q^2+q
       192: 2q^2+2q
       193: q^2+q
       196: q^2+q
       199: 2q^2+2q
       200: q^2+q
       201: q^2+q
       204: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^2+q
       211: q^2+q
       213: q
       215: q^2+q
       217: q
       219: 2q
       220: 2q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q^2+2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q^2+2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q^2+2q
       237: 2q^2+q
       239: 2q^2+q
       241: q^2+q
       243: 4q^2+2q
       244: q^2+q
       245: q^2+q
       246: 2q^2+2q
       247: q+1
       248: q+1
       250: 2q
       251: 2q^2+2q
       252: 2q
       253: 2q
       254: 2q^2+2q
       255: 2q
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q^2+q
       276: q^2+q
       278: q^2+q
       279: q
       281: q
       283: q
       286: q
       287: q^2+q
       293: q
       296: q
       299: q
       304: q
       307: q
       310: q
       315: q^2+q
       317: 2q^2+q
       319: q^2+q
       322: q^2+q
       325: q^2+q
       327: q
       329: q^2+q
       331: q
       333: 2q
       334: q
       335: q
       337: q+1
       338: q+1
       340: q+1
       344: 2q
       345: 2q
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: q+1
       352: 2q
       353: 2q
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: q+1
       360: q
       362: q^2+q
       364: q
       366: 2q^2+2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q^2+2q
       376: 2q
       409: q
       411: q
       413: q
       419: q
       422: q
       427: q+1
       429: q
       432: q
       437: q
       440: q
       443: q+1
       445: q+1
       447: q
       450: q
       453: q
       458: q
       462: q+1
       463: q+1
       465: q
       467: q
       469: q^2+q
       471: q
       474: q
       480: q+1
       484: 1
       485: 1
       487: 1
       492: 2q
       493: q
       494: q
       496: 1
       497: 2q
       498: q
       499: q
       501: 1
       502: q
       504: q^2+q
       506: q
       508: 2q
       509: 2q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       545: q+1
       563: q+1
       574: q+1
       580: q+1
       583: q
       601: 1
       603: q
       608: q
       615: 1
       617: 1
       619: q
       622: q
       632: 1
       633: 1
       635: q
       637: q
       639: q
       641: q
       644: q
       647: q
       650: q
       656: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       696: q+1
       733: 1
       751: 1
       766: 1
       772: 1
       775: 1
       789: 1
       793: 1
       795: 1
       813: 1
       815: 1
       818: 1
       819: 1
       837: 1
       840: 1
       841: q
       844: 1
       845: q
       848: q
       858: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       887: 1
       916: 1
       932: 1
       942: 1
       958: 1
       965: 1
       971: 1
       985: 1
       989: 1
       992: 1
      1014: 1
      1016: 1
      1030: 1
      1033: 1
      1047: 1
      1089: 1
      1101: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1305: 1

1306:    0: 9q^2+3q
         1: 9q^2+3q
         2: 3q^3+6q^2+3q
         3: 9q^2+3q
         4: q^4+4q^3+5q^2+2q
         5: 9q^2+3q
         6: q^4+4q^3+5q^2+2q
         7: q^3+3q^2+2q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 9q^2+3q
        11: 9q^2+3q
        12: q^4+4q^3+5q^2+2q
        13: 6q^2+3q
        14: q^3+3q^2+2q
        15: 6q^2+3q
        16: 9q^2+3q
        17: 9q^2+3q
        18: q^3+3q^2+2q
        19: 4q^2+2q
        20: 4q^2+2q
        21: 2q^2+2q
        22: 9q^2+3q
        23: 9q^2+3q
        24: 3q^3+6q^2+3q
        25: 9q^2+3q
        26: 9q^2+3q
        27: 3q^3+6q^2+3q
        28: 9q^2+3q
        29: 4q^2+2q
        30: 2q^2+2q
        31: 9q^2+3q
        32: 6q^2+3q
        33: 9q^2+3q
        34: 9q^2+3q
        35: 6q^2+3q
        36: 9q^2+3q
        37: 6q^2+2q
        38: 3q^2+q
        39: 6q^2+2q
        40: 3q^2+q
        41: 2q^3+4q^2+2q
        42: q^3+2q^2+q
        43: 6q^2+3q
        44: q^3+3q^2+2q
        45: 6q^2+3q
        46: 6q^2+3q
        47: 6q^2+3q
        48: q^3+3q^2+2q
        49: 4q^2+2q
        50: 4q^2+2q
        51: 2q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: 2q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: 2q^2+2q
        58: 5q^2+2q
        59: 4q^2+q
        60: 4q^2+q
        61: 5q^2+2q
        62: 6q^2+2q
        63: 3q^2+q
        64: 4q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 3q^2+3q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 4q^2+2q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: 6q^2+3q
        81: 6q^2+3q
        82: 4q^2+2q
        83: 2q^2+2q
        84: 6q^2+3q
        85: 6q^2+3q
        86: 4q^2+2q
        87: 2q^2+2q
        88: 6q^2+3q
        89: 6q^2+3q
        90: q^3+3q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: 2q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: 2q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: 2q^2+2q
       103: 3q^2+q
       104: q^2
       105: 2q^2+q
       106: 3q^2+q
       108: q^2+q
       109: q^2+q
       113: 2q^2+q
       115: q^2+q
       117: 2q^2+2q
       118: q^2+q
       119: q^2+q
       120: 2q^2+2q
       121: 4q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 3q^2+3q
       126: 2q^2+2q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 6q^2+3q
       138: 2q^2+2q
       139: 4q^2+2q
       140: q^2+q
       141: 2q^2+2q
       142: q^2+q
       143: 6q^2+3q
       144: 2q^2+2q
       145: 4q^2+2q
       146: 2q^2+2q
       147: q^2+q
       148: q^2+q
       149: 4q^2+2q
       150: 2q^2+2q
       151: 2q^2+q
       153: 2q^2+q
       155: q^2+q
       157: 2q
       158: 2q^2+2q
       159: 2q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: 2q^2+2q
       173: q^2+q
       175: q^2+q
       176: q^2+q
       177: q^2+q
       179: 2q^2+q
       184: q
       185: q
       189: q^2+q
       191: 2q^2+2q
       192: q^2+q
       194: q^2+q
       195: q^2+q
       199: q^2+q
       200: 2q^2+2q
       202: q^2+q
       203: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^2+q
       211: q^2+q
       213: q
       215: q^2+q
       217: q
       219: 2q
       220: 2q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q^2+2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q^2+2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q^2+2q
       237: 2q^2+q
       239: 2q^2+q
       241: q^2+q
       243: 4q^2+2q
       244: q^2+q
       245: q^2+q
       246: 2q^2+2q
       247: q+1
       248: q+1
       250: 2q
       251: 2q^2+2q
       252: 2q
       253: 2q
       254: 2q^2+2q
       255: 2q
       256: 2q
       257: 2q^2+2q
       258: 2q
       275: q^2+q
       277: q^2+q
       278: q^2+q
       279: q
       281: q
       284: q
       285: q
       287: q^2+q
       294: q
       295: q
       300: q
       303: q
       308: q
       309: q
       315: q^2+q
       317: 2q^2+q
       320: q^2+q
       321: q^2+q
       325: q^2+q
       327: q
       329: q^2+q
       331: q
       333: 2q
       334: q
       335: q
       337: q+1
       338: q+1
       340: q+1
       344: 2q
       345: 2q
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: q+1
       352: 2q
       353: 2q
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: q+1
       360: q
       362: q^2+q
       364: q
       366: 2q^2+2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q^2+2q
       376: 2q
       409: q
       411: q
       413: q
       420: q
       421: q
       427: q+1
       430: q
       431: q
       438: q
       439: q
       444: q+1
       445: q+1
       448: q
       449: q
       454: q
       457: q
       461: q+1
       463: q+1
       465: q
       467: q
       469: q^2+q
       472: q
       473: q
       480: q+1
       484: 1
       485: 1
       487: 1
       492: 2q
       493: q
       494: q
       496: 1
       497: 2q
       498: q
       499: q
       501: 1
       502: q
       504: q^2+q
       506: q
       508: 2q
       509: 2q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       547: q+1
       561: q+1
       576: q+1
       580: q+1
       583: q
       601: 1
       604: q
       607: q
       616: 1
       617: 1
       620: q
       621: q
       631: 1
       633: 1
       635: q
       637: q
       639: q
       642: q
       643: q
       648: q
       649: q
       656: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       698: q+1
       735: 1
       749: 1
       767: 1
       772: 1
       775: 1
       789: 1
       794: 1
       795: 1
       813: 1
       816: 1
       817: 1
       819: 1
       837: 1
       839: 1
       841: q
       844: 1
       846: q
       847: q
       858: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       888: 1
       918: 1
       934: 1
       940: 1
       956: 1
       966: 1
       971: 1
       985: 1
       990: 1
       992: 1
      1014: 1
      1017: 1
      1030: 1
      1032: 1
      1047: 1
      1090: 1
      1103: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1306: 1

1307:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        76: 2q+1
        78: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       108: q+1
       110: q+1
       111: q+1
       113: 2q+1
       115: q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       129: 2q+1
       131: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: q+1
       184: 1
       186: 1
       187: 1
       189: q+1
       192: q+1
       194: q+1
       196: q+1
       197: q+1
       200: q+1
       202: q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: 1
       215: q+1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       262: q+1
       266: 1
       269: q+1
       273: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q+1
       327: 1
       329: q+1
       331: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       338: q+1
       340: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       380: 1
       384: 1
       388: 1
       391: q+1
       396: 1
       399: q+1
       404: 1
       406: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       427: q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       484: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: q+1
       552: 1
       555: 1
       559: 1
       563: q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       587: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       697: q+1
       708: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       789: 1
       794: 1
       795: 1
       799: 1
       813: 1
       816: 1
       818: 1
       819: 1
       823: 1
       837: 1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       889: 1
       914: 1
       918: 1
       934: 1
       938: 1
       942: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
      1014: 1
      1017: 1
      1030: 1
      1033: 1
      1046: 1
      1050: 1
      1091: 1
      1102: 1
      1146: 1
      1166: 1
      1185: 1
      1188: 1
      1197: 1
      1307: 1

1308:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q
        59: 2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: q+1
       110: q+1
       112: q+1
       114: 2q+1
       116: q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: 2q+1
       182: q+1
       183: 1
       186: 1
       188: 1
       190: q+1
       192: q+1
       193: q+1
       196: q+1
       198: q+1
       199: q+1
       201: q+1
       204: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       260: q+1
       264: 1
       268: q+1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: q+1
       341: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       378: 1
       382: 1
       386: 1
       390: q+1
       394: 1
       400: q+1
       403: 1
       407: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       428: q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       484: 1
       486: 1
       488: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: q+1
       551: 1
       556: 1
       560: 1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       588: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       699: q+1
       706: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       790: 1
       793: 1
       796: 1
       800: 1
       814: 1
       815: 1
       818: 1
       820: 1
       824: 1
       838: 1
       840: 1
       842: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       890: 1
       913: 1
       917: 1
       933: 1
       939: 1
       943: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
      1015: 1
      1016: 1
      1031: 1
      1033: 1
      1047: 1
      1051: 1
      1092: 1
      1104: 1
      1145: 1
      1167: 1
      1186: 1
      1192: 1
      1195: 1
      1308: 1

1309:    0: 3q+1
         1: 3q+1
         2: q^2+2q+1
         3: 3q+1
         4: q^2+2q+1
         5: 3q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 3q+1
        29: 2q+1
        30: q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: 2q+1
        77: 2q+1
        79: q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 1
        92: q+1
        93: 1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       108: q+1
       109: q+1
       112: q+1
       114: 2q+1
       116: q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       128: 2q+1
       130: 2q+1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: 2q+1
       182: q+1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q+1
       194: q+1
       195: q+1
       198: q+1
       200: q+1
       202: q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: 1
       216: q+1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       250: 1
       251: q+1
       252: 1
       253: 1
       254: q+1
       255: 1
       256: 1
       257: q+1
       258: 1
       261: q+1
       265: 1
       270: q+1
       272: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q+1
       328: 1
       330: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: q+1
       341: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: q+1
       376: 1
       379: 1
       383: 1
       387: 1
       392: q+1
       395: 1
       398: q+1
       402: 1
       408: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       428: q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: q+1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       484: 1
       486: 1
       488: 1
       492: 1
       493: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: q+1
       550: 1
       554: 1
       558: 1
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       588: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       700: q+1
       707: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       790: 1
       794: 1
       796: 1
       800: 1
       814: 1
       816: 1
       817: 1
       820: 1
       824: 1
       838: 1
       839: 1
       842: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       891: 1
       915: 1
       919: 1
       935: 1
       937: 1
       941: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
      1015: 1
      1017: 1
      1031: 1
      1032: 1
      1047: 1
      1051: 1
      1093: 1
      1105: 1
      1147: 1
      1165: 1
      1187: 1
      1192: 1
      1196: 1
      1309: 1

1310:    0: 9q^2+3q
         1: 9q^2+3q
         2: 3q^3+6q^2+3q
         3: 9q^2+3q
         4: q^4+4q^3+5q^2+2q
         5: 9q^2+3q
         6: q^4+4q^3+5q^2+2q
         7: q^3+3q^2+2q
         8: 3q^3+6q^2+3q
         9: q^3+3q^2+2q
        10: 9q^2+3q
        11: 9q^2+3q
        12: q^4+4q^3+5q^2+2q
        13: 6q^2+3q
        14: q^3+3q^2+2q
        15: 6q^2+3q
        16: 9q^2+3q
        17: 9q^2+3q
        18: q^3+3q^2+2q
        19: 4q^2+2q
        20: 4q^2+2q
        21: 2q^2+2q
        22: 9q^2+3q
        23: 9q^2+3q
        24: 3q^3+6q^2+3q
        25: 9q^2+3q
        26: 9q^2+3q
        27: 3q^3+6q^2+3q
        28: 9q^2+3q
        29: 4q^2+2q
        30: 2q^2+2q
        31: 9q^2+3q
        32: 6q^2+3q
        33: 9q^2+3q
        34: 9q^2+3q
        35: 6q^2+3q
        36: 9q^2+3q
        37: 3q^2+q
        38: 6q^2+2q
        39: 3q^2+q
        40: 6q^2+2q
        41: q^3+2q^2+q
        42: 2q^3+4q^2+2q
        43: 6q^2+3q
        44: q^3+3q^2+2q
        45: 6q^2+3q
        46: 6q^2+3q
        47: 6q^2+3q
        48: q^3+3q^2+2q
        49: 4q^2+2q
        50: 4q^2+2q
        51: 2q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: 2q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: 2q^2+2q
        58: 4q^2+q
        59: 5q^2+2q
        60: 4q^2+q
        61: 5q^2+2q
        62: 3q^2+q
        63: 6q^2+2q
        64: 2q^2+q
        65: 4q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 3q^2+3q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 4q^2+2q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: 6q^2+3q
        81: 6q^2+3q
        82: 4q^2+2q
        83: 2q^2+2q
        84: 6q^2+3q
        85: 6q^2+3q
        86: 4q^2+2q
        87: 2q^2+2q
        88: 6q^2+3q
        89: 6q^2+3q
        90: q^3+3q^2+2q
        91: 2q
        92: 2q^2+2q
        93: 2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: 2q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: 2q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: 2q^2+2q
       103: q^2
       104: 3q^2+q
       105: 3q^2+q
       106: 2q^2+q
       108: q^2+q
       110: q^2+q
       114: 2q^2+q
       116: q^2+q
       117: q^2+q
       118: 2q^2+2q
       119: q^2+q
       120: 2q^2+2q
       121: 2q^2+q
       122: 4q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 3q^2+3q
       126: 2q^2+2q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: 2q
       134: 2q
       135: q
       136: q
       137: 6q^2+3q
       138: 2q^2+2q
       139: 4q^2+2q
       140: q^2+q
       141: 2q^2+2q
       142: q^2+q
       143: 6q^2+3q
       144: 2q^2+2q
       145: 4q^2+2q
       146: 2q^2+2q
       147: q^2+q
       148: q^2+q
       149: 4q^2+2q
       150: 2q^2+2q
       152: 2q^2+q
       154: 2q^2+q
       156: q^2+q
       157: 2q
       158: 2q^2+2q
       159: 2q
       160: 2q
       161: 2q^2+2q
       162: 2q
       163: 2q
       164: 2q^2+2q
       165: 2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: 2q^2+2q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       178: q^2+q
       180: 2q^2+q
       184: q
       186: q
       190: q^2+q
       191: q^2+q
       192: 2q^2+2q
       194: q^2+q
       196: q^2+q
       199: q^2+q
       200: 2q^2+2q
       202: q^2+q
       204: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       210: 2q^2+q
       212: q^2+q
       214: q
       216: q^2+q
       218: q
       219: 2q
       220: 2q
       221: 2q
       222: q
       223: q
       224: q
       225: q
       226: 2q^2+2q
       227: 2q
       228: 2q
       229: q
       230: q
       231: 2q^2+2q
       232: 2q
       233: 2q
       234: q
       235: q
       236: 2q^2+2q
       238: 2q^2+q
       240: 2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: q^2+q
       245: q^2+q
       246: 2q^2+2q
       247: q+1
       248: q+1
       250: 2q
       251: 2q^2+2q
       252: 2q
       253: 2q
       254: 2q^2+2q
       255: 2q
       256: 2q
       257: 2q^2+2q
       258: 2q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: q
       282: q
       284: q
       286: q
       288: q^2+q
       294: q
       296: q
       300: q
       304: q
       308: q
       310: q
       316: q^2+q
       318: 2q^2+q
       320: q^2+q
       322: q^2+q
       326: q^2+q
       328: q
       330: q^2+q
       332: q
       333: 2q
       334: q
       335: q
       337: q+1
       339: q+1
       341: q+1
       344: 2q
       345: 2q
       346: 2q
       347: q
       348: q
       349: q
       350: q
       351: q+1
       352: 2q
       353: 2q
       354: 2q
       355: q
       356: q
       357: q
       358: q
       359: q+1
       361: q
       363: q^2+q
       365: q
       366: 2q^2+2q
       367: 2q
       368: 2q
       369: q
       370: q
       371: 1
       372: 1
       374: 2q
       375: 2q^2+2q
       376: 2q
       410: q
       412: q
       414: q
       420: q
       422: q
       428: q+1
       430: q
       432: q
       438: q
       440: q
       444: q+1
       446: q+1
       448: q
       450: q
       454: q
       458: q
       462: q+1
       464: q+1
       466: q
       468: q
       470: q^2+q
       472: q
       474: q
       479: q+1
       484: 1
       486: 1
       488: 1
       492: 2q
       493: q
       494: q
       496: 1
       497: 2q
       498: q
       499: q
       501: 1
       503: q
       505: q^2+q
       507: q
       508: 2q
       509: 2q
       510: 2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       548: q+1
       564: q+1
       575: q+1
       578: q+1
       584: q
       602: 1
       604: q
       608: q
       616: 1
       618: 1
       620: q
       622: q
       632: 1
       634: 1
       636: q
       638: q
       640: q
       642: q
       644: q
       648: q
       650: q
       655: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       678: 1
       680: 1
       684: 1
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       701: q+1
       736: 1
       752: 1
       768: 1
       770: 1
       776: 1
       790: 1
       794: 1
       796: 1
       814: 1
       816: 1
       818: 1
       820: 1
       838: 1
       840: 1
       842: q
       843: 1
       846: q
       848: q
       857: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       892: 1
       919: 1
       935: 1
       943: 1
       959: 1
       967: 1
       969: 1
       983: 1
       991: 1
       993: 1
      1015: 1
      1017: 1
      1031: 1
      1033: 1
      1046: 1
      1094: 1
      1106: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1310: 1

1311:    0: q^3+3q^2+q
         1: q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: q^3+3q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q^2+q
         8: q^3+2q^2+q
         9: q^3+q^2+q
        10: q^3+3q^2+q
        11: q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^3+2q^2+q
        14: q^3+q^2+q
        15: 2q^2+q
        16: q^3+3q^2+q
        17: q^3+3q^2+q
        18: q^3+q^2+q
        19: q^3+2q^2+q
        20: q^3+2q^2+q
        21: q^3+q^2+q
        22: 3q^2+q
        23: 3q^2+q
        24: q^3+2q^2+q
        25: 3q^2+q
        26: 3q^2+q
        27: q^3+2q^2+q
        28: q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+q^2+q
        31: 3q^2+q
        32: 2q^2+q
        33: 3q^2+q
        34: 3q^2+q
        35: 2q^2+q
        36: 3q^2+q
        37: 3q^2+q
        39: 3q^2+q
        41: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+q^2+q
        45: 2q^2+q
        46: q^3+2q^2+q
        47: 2q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^3+2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: q^2
        59: 2q^2+q
        60: q^2
        61: 2q^2+q
        62: 3q^2+q
        64: 2q^2+q
        66: 3q^2+q
        68: q^2+q
        69: q^3+q^2+q
        70: q^3+q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: 2q^2+q
        78: q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: 2q^2+q
        83: q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^3+2q^2+q
        89: 2q^2+q
        90: q^3+q^2+q
        91: q
        92: q^2+q
        93: q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^2
       106: 2q^2+q
       108: q^2+q
       110: q^2+q
       111: q^2+q
       113: 2q^2+q
       115: q^2+q
       118: q^2+q
       120: q^2+q
       121: 2q^2+q
       123: 2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: 2q^2+q
       131: q^2+q
       133: q
       134: q
       135: q
       136: q
       137: 2q^2+q
       138: q^2+q
       139: 2q^2+q
       140: q
       141: q^2+q
       142: q^2+q
       143: 2q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       172: q^2+q
       176: q^2+q
       177: q^2+q
       179: 2q^2+q
       181: q^2+q
       184: q
       186: q
       187: q
       189: q^2+q
       192: q^2+q
       194: q
       196: q^2+q
       197: q
       200: q^2+q
       202: q^2+q
       204: q
       205: q
       207: 2q^2+q
       209: q^2+q
       211: q^2+q
       213: q
       215: q^2+q
       217: q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q^2+q
       227: q
       228: q
       229: q
       230: q
       231: q^2+q
       232: q
       233: q
       234: q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       262: q^2+q
       266: q
       269: q
       273: q
       278: q^2+q
       279: q
       281: q
       284: q
       286: q
       287: q^2+q
       289: q
       291: q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       320: q
       322: q
       323: q
       325: q^2+q
       327: q
       329: q^2+q
       331: q
       333: q
       334: q
       335: q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q^2+q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q
       411: q
       413: q
       415: q
       417: q
       420: q
       422: q
       423: q
       430: q
       432: q
       433: q
       438: q
       440: q
       441: q
       448: q
       450: q
       451: q
       454: q
       458: q
       459: q
       469: q^2+q
       477: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       524: q
       528: q
       532: q
       536: q
       543: q
       552: q
       559: q
       570: q
       583: q
       587: q
       604: q
       608: q
       609: q
       620: q
       622: q
       625: q
       651: 1
       708: q
       727: q
       743: q
       758: 1
       771: 1
       849: 1
       853: 1
       893: 1
       961: 1
       970: 1
       979: 1
       984: 1
      1050: 1
      1095: 1
      1107: 1
      1185: 1
      1190: 1
      1311: 1

1312:    0: q^3+3q^2+q
         1: q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: q^3+3q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q^2+q
         8: q^3+2q^2+q
         9: q^3+q^2+q
        10: q^3+3q^2+q
        11: q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^3+2q^2+q
        14: q^3+q^2+q
        15: 2q^2+q
        16: q^3+3q^2+q
        17: q^3+3q^2+q
        18: q^3+q^2+q
        19: q^3+2q^2+q
        20: q^3+2q^2+q
        21: q^3+q^2+q
        22: 3q^2+q
        23: 3q^2+q
        24: q^3+2q^2+q
        25: 3q^2+q
        26: 3q^2+q
        27: q^3+2q^2+q
        28: q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+q^2+q
        31: 3q^2+q
        32: 2q^2+q
        33: 3q^2+q
        34: 3q^2+q
        35: 2q^2+q
        36: 3q^2+q
        38: 3q^2+q
        40: 3q^2+q
        42: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+q^2+q
        45: 2q^2+q
        46: q^3+2q^2+q
        47: 2q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^3+2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: q^2
        59: 2q^2+q
        60: 2q^2+q
        61: q^2
        63: 3q^2+q
        65: 2q^2+q
        67: 3q^2+q
        68: q^2+q
        69: q^3+q^2+q
        70: q^3+q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: 2q^2+q
        83: q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^3+2q^2+q
        89: 2q^2+q
        90: q^3+q^2+q
        91: q
        92: q^2+q
        93: q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: 2q^2+q
       105: q^2
       107: q^2+q
       110: q^2+q
       112: q^2+q
       114: 2q^2+q
       116: q^2+q
       118: q^2+q
       119: q^2+q
       122: 2q^2+q
       124: 2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: q
       134: q
       135: q
       136: q
       137: 2q^2+q
       138: q^2+q
       139: 2q^2+q
       140: q
       141: q^2+q
       142: q^2+q
       143: 2q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: q^2+q
       174: q^2+q
       178: q^2+q
       180: 2q^2+q
       182: q^2+q
       183: q
       186: q
       188: q
       190: q^2+q
       192: q^2+q
       193: q
       196: q^2+q
       198: q
       199: q^2+q
       201: q^2+q
       204: q
       206: q
       208: 2q^2+q
       210: q^2+q
       212: q^2+q
       214: q
       216: q^2+q
       218: q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q^2+q
       227: q
       228: q
       229: q
       230: q
       231: q^2+q
       232: q
       233: q
       234: q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       260: q^2+q
       264: q
       268: q
       274: q
       276: q^2+q
       280: q
       282: q
       283: q
       286: q
       288: q^2+q
       290: q
       292: q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       319: q
       322: q
       324: q
       326: q^2+q
       328: q
       330: q^2+q
       332: q
       333: q
       334: q
       335: q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q^2+q
       378: q
       382: q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q
       412: q
       414: q
       416: q
       418: q
       419: q
       422: q
       424: q
       429: q
       432: q
       434: q
       437: q
       440: q
       442: q
       447: q
       450: q
       452: q
       453: q
       458: q
       460: q
       470: q^2+q
       478: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       522: q
       526: q
       530: q
       534: q
       542: q
       551: q
       560: q
       571: q
       584: q
       588: q
       603: q
       608: q
       610: q
       619: q
       622: q
       626: q
       652: 1
       706: q
       726: q
       744: q
       759: 1
       774: 1
       850: 1
       854: 1
       894: 1
       962: 1
       973: 1
       980: 1
       987: 1
      1051: 1
      1096: 1
      1108: 1
      1186: 1
      1193: 1
      1312: 1

1313:    0: q^3+3q^2+q
         1: q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: q^3+3q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^3+q^2+q
         8: q^3+2q^2+q
         9: q^3+q^2+q
        10: q^3+3q^2+q
        11: q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^3+2q^2+q
        14: q^3+q^2+q
        15: 2q^2+q
        16: q^3+3q^2+q
        17: q^3+3q^2+q
        18: q^3+q^2+q
        19: q^3+2q^2+q
        20: q^3+2q^2+q
        21: q^3+q^2+q
        22: 3q^2+q
        23: 3q^2+q
        24: q^3+2q^2+q
        25: 3q^2+q
        26: 3q^2+q
        27: q^3+2q^2+q
        28: q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+q^2+q
        31: 3q^2+q
        32: 2q^2+q
        33: 3q^2+q
        34: 3q^2+q
        35: 2q^2+q
        36: 3q^2+q
        38: 3q^2+q
        40: 3q^2+q
        42: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+q^2+q
        45: 2q^2+q
        46: q^3+2q^2+q
        47: 2q^2+q
        48: q^3+q^2+q
        49: q^3+2q^2+q
        50: q^3+2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^2+q
        58: 2q^2+q
        59: q^2
        60: q^2
        61: 2q^2+q
        63: 3q^2+q
        65: 2q^2+q
        67: 3q^2+q
        68: q^2+q
        69: q^3+q^2+q
        70: q^3+q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: 2q^2+q
        79: q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: 2q^2+q
        83: q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^3+2q^2+q
        89: 2q^2+q
        90: q^3+q^2+q
        91: q
        92: q^2+q
        93: q
        94: 2q^2+q
        95: 2q^2+q
        96: q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q^2
       105: 2q^2+q
       108: q^2+q
       109: q^2+q
       112: q^2+q
       114: 2q^2+q
       116: q^2+q
       117: q^2+q
       120: q^2+q
       122: 2q^2+q
       124: 2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: 2q^2+q
       132: q^2+q
       133: q
       134: q
       135: q
       136: q
       137: 2q^2+q
       138: q^2+q
       139: 2q^2+q
       140: q
       141: q^2+q
       142: q^2+q
       143: 2q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q
       158: q^2+q
       159: q
       160: q
       161: q^2+q
       162: q
       163: q
       164: q^2+q
       165: q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       171: q^2+q
       175: q^2+q
       178: q^2+q
       180: 2q^2+q
       182: q^2+q
       184: q
       185: q
       188: q
       190: q^2+q
       191: q^2+q
       194: q
       195: q^2+q
       198: q
       200: q^2+q
       202: q^2+q
       203: q
       206: q
       208: 2q^2+q
       210: q^2+q
       212: q^2+q
       214: q
       216: q^2+q
       218: q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q^2+q
       227: q
       228: q
       229: q
       230: q
       231: q^2+q
       232: q
       233: q
       234: q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q
       251: q^2+q
       252: q
       253: q
       254: q^2+q
       255: q
       261: q^2+q
       265: q
       270: q
       272: q
       277: q^2+q
       280: q
       282: q
       284: q
       285: q
       288: q^2+q
       290: q
       292: q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       320: q
       321: q
       324: q
       326: q^2+q
       328: q
       330: q^2+q
       332: q
       333: q
       334: q
       335: q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       366: q^2+q
       379: q
       383: q
       387: q
       392: q
       395: q
       398: q
       402: q
       408: q
       410: q
       412: q
       414: q
       416: q
       418: q
       420: q
       421: q
       424: q
       430: q
       431: q
       434: q
       438: q
       439: q
       442: q
       448: q
       449: q
       452: q
       454: q
       457: q
       460: q
       470: q^2+q
       478: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       523: q
       527: q
       531: q
       535: q
       544: q
       550: q
       558: q
       572: q
       584: q
       588: q
       604: q
       607: q
       610: q
       620: q
       621: q
       626: q
       652: 1
       707: q
       728: q
       742: q
       760: 1
       774: 1
       850: 1
       854: 1
       895: 1
       963: 1
       973: 1
       981: 1
       987: 1
      1051: 1
      1097: 1
      1109: 1
      1187: 1
      1193: 1
      1313: 1

1314:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q^2+4q+1
        56: 3q^2+4q+1
        57: q^3+3q^2+3q+1
        58: 2q+1
        59: q
        60: q^2+2q+1
        61: 2q^2+2q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q^2+4q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: q^3+3q^2+3q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: q^2+2q+1
       108: 2q^2+2q
       109: 2q+1
       110: q
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q+1
       119: q+1
       120: q^2+q
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       141: 2q+1
       142: 3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       147: 3q^2+4q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       172: q
       173: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q+1
       184: q^2+q
       185: q+1
       187: 2q+1
       189: 2q+1
       191: q+1
       195: 2q+1
       196: q
       199: q+1
       200: q^2+q
       201: q^2+2q+1
       202: 2q^2+2q
       203: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       230: q+1
       231: 2q^2+3q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: q
       263: q+1
       271: q+1
       275: q+1
       279: 1
       281: q+1
       283: q+1
       284: q^2+q
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q+1
       294: q^2+q
       295: q+1
       297: 2q+1
       303: 1
       307: 1
       308: q
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       321: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 2q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: 1
       385: q+1
       397: q+1
       401: 1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       420: q^2+q
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       431: 1
       439: 1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       473: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: 1
       529: q+1
       549: 1
       553: 1
       557: 1
       561: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       590: q
       591: 1
       595: 1
       597: 1
       599: q+1
       601: 1
       607: 1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       705: 1
       709: 1
       713: 1
       737: 1
       741: 1
       745: 1
       749: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 1
       807: 1
       817: 1
       819: 1
       823: 1
       825: 1
       826: q
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       847: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       896: 1
       900: 1
       936: 1
       940: 1
       948: 1
       956: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1030: 1
      1032: 1
      1036: 1
      1042: 1
      1074: 1
      1081: 1
      1110: 1
      1114: 1
      1164: 1
      1214: 1
      1216: 1
      1252: 1
      1314: 1

1315:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q^2+4q+1
        56: 3q^2+4q+1
        57: q^3+3q^2+3q+1
        58: 2q+1
        59: q
        60: 2q^2+2q
        61: q^2+2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q^2+4q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: q^3+3q^2+3q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       107: 2q^2+2q
       108: q^2+2q+1
       109: 2q+1
       110: q
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q+1
       119: q^2+q
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       141: 2q+1
       142: 3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       147: 3q^2+4q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: 2q+1
       175: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+q
       184: q+1
       185: q+1
       188: 2q+1
       190: 2q+1
       191: q+1
       195: 2q+1
       196: q
       199: q^2+q
       200: q+1
       201: 2q^2+2q
       202: q^2+2q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       230: q+1
       231: 2q^2+3q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: 2q+1
       265: q+1
       272: q+1
       277: q+1
       280: 1
       282: q+1
       283: q^2+q
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q^2+q
       294: q+1
       295: q+1
       298: 2q+1
       303: 1
       307: q
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       321: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 2q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: 1
       387: q+1
       398: q+1
       402: 1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q^2+q
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       431: 1
       439: 1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       473: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: 1
       531: q+1
       550: 1
       554: 1
       558: 1
       562: q+1
       584: 1
       586: 1
       588: q+1
       589: q
       590: 1
       591: 1
       595: 1
       598: 1
       600: q+1
       602: 1
       607: 1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       707: 1
       711: 1
       714: 1
       738: 1
       742: 1
       746: 1
       750: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 1
       807: 1
       817: 1
       820: 1
       824: 1
       825: q
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       847: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       898: 1
       901: 1
       937: 1
       941: 1
       949: 1
       957: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1031: 1
      1032: 1
      1037: 1
      1043: 1
      1074: 1
      1081: 1
      1111: 1
      1115: 1
      1165: 1
      1215: 1
      1216: 1
      1253: 1
      1315: 1

1316:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q^2+4q+1
        56: 3q^2+4q+1
        57: q^3+3q^2+3q+1
        58: q
        59: 2q+1
        60: 2q^2+2q
        61: q^2+2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q^2+4q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: q^3+3q^2+3q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       107: 2q^2+2q
       108: q^2+2q+1
       109: q
       110: 2q+1
       111: 3q+1
       113: 3q+1
       115: 2q+1
       118: q+1
       119: q^2+q
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       141: 2q+1
       142: 3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       147: 3q^2+4q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: 2q+1
       176: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+q
       184: q+1
       186: q+1
       187: 2q+1
       189: 2q+1
       192: q+1
       195: q
       196: 2q+1
       199: q^2+q
       200: q+1
       201: 2q^2+2q
       202: q^2+2q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       230: q+1
       231: 2q^2+3q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: 2q+1
       266: q+1
       273: q+1
       278: q+1
       279: 1
       281: q+1
       283: q^2+q
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q^2+q
       294: q+1
       296: q+1
       297: 2q+1
       304: 1
       307: q
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       322: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 2q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: 1
       388: q+1
       399: q+1
       404: 1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q^2+q
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       432: 1
       440: 1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       474: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: 1
       532: q+1
       552: 1
       555: 1
       559: 1
       563: q+1
       583: 1
       585: 1
       587: q+1
       589: q
       590: 1
       592: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       608: 1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       708: 1
       712: 1
       716: 1
       739: 1
       743: 1
       747: 1
       751: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 1
       808: 1
       818: 1
       819: 1
       823: 1
       825: q
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       848: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       899: 1
       902: 1
       938: 1
       942: 1
       950: 1
       958: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1030: 1
      1033: 1
      1036: 1
      1042: 1
      1074: 1
      1081: 1
      1112: 1
      1116: 1
      1166: 1
      1214: 1
      1217: 1
      1252: 1
      1316: 1

1317:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+3q^2+3q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q^2+4q+1
        35: 2q^2+3q+1
        36: 3q^2+4q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q^2+4q+1
        56: 3q^2+4q+1
        57: q^3+3q^2+3q+1
        58: q
        59: 2q+1
        60: q^2+2q+1
        61: 2q^2+2q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q^2+4q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: q^3+3q^2+3q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: q^2+2q+1
       108: 2q^2+2q
       109: q
       110: 2q+1
       112: 3q+1
       114: 3q+1
       116: 2q+1
       118: q+1
       119: q+1
       120: q^2+q
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       141: 2q+1
       142: 3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       147: 3q^2+4q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: 2q+1
       171: q
       174: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q+1
       184: q^2+q
       186: q+1
       188: 2q+1
       190: 2q+1
       192: q+1
       195: q
       196: 2q+1
       199: q+1
       200: q^2+q
       201: q^2+2q+1
       202: 2q^2+2q
       204: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       230: q+1
       231: 2q^2+3q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: q
       264: q+1
       274: q+1
       276: q+1
       280: 1
       282: q+1
       283: q+1
       284: q^2+q
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q+1
       294: q^2+q
       296: q+1
       298: 2q+1
       304: 1
       307: 1
       308: q
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       322: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 2q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       349: q+1
       350: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: 1
       386: q+1
       400: q+1
       403: 1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       420: q^2+q
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       432: 1
       440: 1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       474: 1
       481: q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       494: q+1
       497: q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: 1
       530: q+1
       551: 1
       556: 1
       560: 1
       564: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       590: q
       592: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       608: 1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       706: 1
       710: 1
       715: 1
       740: 1
       744: 1
       748: 1
       752: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 1
       808: 1
       818: 1
       820: 1
       824: 1
       825: 1
       826: q
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       848: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       876: 1
       897: 1
       903: 1
       939: 1
       943: 1
       951: 1
       959: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1031: 1
      1033: 1
      1037: 1
      1043: 1
      1074: 1
      1081: 1
      1113: 1
      1117: 1
      1167: 1
      1215: 1
      1217: 1
      1253: 1
      1317: 1

1318:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q^2+4q+1
        53: 3q^2+4q+1
        54: q^3+3q^2+3q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q^2+2q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q+1
        73: 3q^2+4q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+4q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: q^3+3q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: 2q+1
       108: q
       109: q^2+2q+1
       110: 2q^2+2q
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q+1
       118: q^2+q
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+4q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       172: q
       173: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q+1
       185: q+1
       186: q^2+q
       187: 2q+1
       189: 2q+1
       191: q+1
       192: q^2+q
       193: q+1
       195: q^2+2q+1
       196: 2q^2+2q
       197: q+1
       199: q+1
       201: 2q+1
       202: q
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: q
       263: q+1
       267: q+1
       275: q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       286: q^2+q
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q+1
       295: q+1
       296: q^2+q
       297: 2q+1
       299: 1
       301: q+1
       303: 1
       304: q
       305: 1
       307: 1
       315: q+1
       317: 2q+1
       319: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: 1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       422: q^2+q
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: q+1
       445: q+1
       447: 1
       453: 1
       465: 1
       467: 1
       469: q+1
       471: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: 1
       529: q+1
       533: 1
       537: 1
       541: 1
       545: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       593: 1
       595: 1
       596: q
       597: 1
       599: q+1
       601: 1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 1
       793: 1
       795: 1
       799: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       813: 1
       815: 1
       825: 1
       841: 1
       845: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       896: 1
       904: 1
       912: 1
       916: 1
       928: 1
       932: 1
       992: 1
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 1
      1016: 1
      1020: 1
      1024: 1
      1074: 1
      1077: 1
      1118: 1
      1122: 1
      1144: 1
      1214: 1
      1218: 1
      1236: 1
      1318: 1

1319:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q^2+4q+1
        53: 3q^2+4q+1
        54: q^3+3q^2+3q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: 2q^2+2q
        59: q^2+2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q+1
        73: 3q^2+4q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+4q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: q^3+3q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: 2q+1
       108: q
       109: 2q^2+2q
       110: q^2+2q+1
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q^2+q
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+4q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: 2q+1
       171: q
       174: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q+1
       185: q^2+q
       186: q+1
       188: 2q+1
       190: 2q+1
       191: q^2+q
       192: q+1
       193: q+1
       195: 2q^2+2q
       196: q^2+2q+1
       198: q+1
       199: q+1
       201: 2q+1
       202: q
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: q
       264: q+1
       268: q+1
       276: q+1
       280: 1
       282: q+1
       283: q+1
       285: q^2+q
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q+1
       295: q^2+q
       296: q+1
       298: 2q+1
       299: 1
       302: q+1
       303: q
       304: 1
       306: 1
       307: 1
       316: q+1
       318: 2q+1
       319: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: 1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       421: q^2+q
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: 1
       453: 1
       466: 1
       468: 1
       470: q+1
       471: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: 1
       530: q+1
       534: 1
       538: 1
       542: 1
       546: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       593: 1
       595: q
       596: 1
       598: 1
       600: q+1
       602: 1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 1
       793: 1
       796: 1
       800: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       842: 1
       845: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       897: 1
       905: 1
       913: 1
       917: 1
       929: 1
       933: 1
       993: 1
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 1
      1016: 1
      1021: 1
      1025: 1
      1074: 1
      1077: 1
      1119: 1
      1123: 1
      1145: 1
      1215: 1
      1218: 1
      1237: 1
      1319: 1

1320:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q^2+4q+1
        53: 3q^2+4q+1
        54: q^3+3q^2+3q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: 2q^2+2q
        59: q^2+2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q+1
        73: 3q^2+4q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+4q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: q^3+3q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       107: q
       108: 2q+1
       109: 2q^2+2q
       110: q^2+2q+1
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q^2+q
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+4q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: 2q+1
       176: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q+1
       185: q^2+q
       186: q+1
       187: 2q+1
       189: 2q+1
       191: q^2+q
       192: q+1
       194: q+1
       195: 2q^2+2q
       196: q^2+2q+1
       197: q+1
       200: q+1
       201: q
       202: 2q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: 2q+1
       266: q+1
       269: q+1
       278: q+1
       279: 1
       281: q+1
       284: q+1
       285: q^2+q
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q+1
       295: q^2+q
       296: q+1
       297: 2q+1
       300: 1
       301: q+1
       303: q
       304: 1
       305: 1
       308: 1
       315: q+1
       317: 2q+1
       320: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: 1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       421: q^2+q
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       472: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: 1
       532: q+1
       536: 1
       539: 1
       543: 1
       547: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       594: 1
       595: q
       596: 1
       597: 1
       599: q+1
       601: 1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 1
       794: 1
       795: 1
       799: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       826: 1
       841: 1
       846: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       899: 1
       906: 1
       914: 1
       918: 1
       930: 1
       934: 1
       992: 1
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 1
      1017: 1
      1020: 1
      1024: 1
      1074: 1
      1077: 1
      1120: 1
      1124: 1
      1146: 1
      1214: 1
      1219: 1
      1236: 1
      1320: 1

1321:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+3q^2+3q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: q^3+4q^2+4q+1
         7: q^3+3q^2+3q+1
         8: q^4+3q^3+4q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: q^3+4q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+3q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: 2q^2+3q+1
        49: q^3+4q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+3q^2+3q+1
        52: 3q^2+4q+1
        53: 3q^2+4q+1
        54: q^3+3q^2+3q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q^2+2q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q^2+2q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: 3q+1
        73: 3q^2+4q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+4q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: q^3+3q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       107: q
       108: 2q+1
       109: q^2+2q+1
       110: 2q^2+2q
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q+1
       118: q^2+q
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+4q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+4q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q^2+3q+1
       158: q^3+3q^2+3q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: 2q+1
       175: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q+1
       185: q+1
       186: q^2+q
       188: 2q+1
       190: 2q+1
       191: q+1
       192: q^2+q
       194: q+1
       195: q^2+2q+1
       196: 2q^2+2q
       198: q+1
       200: q+1
       201: q
       202: 2q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: 2q+1
       265: q+1
       270: q+1
       277: q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       286: q^2+q
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q+1
       295: q+1
       296: q^2+q
       298: 2q+1
       300: 1
       302: q+1
       303: 1
       304: q
       306: 1
       308: 1
       316: q+1
       318: 2q+1
       320: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: 1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       422: q^2+q
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: q+1
       446: q+1
       448: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       472: 1
       481: 1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: 1
       531: q+1
       535: 1
       540: 1
       544: 1
       548: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       594: 1
       595: 1
       596: q
       598: 1
       600: q+1
       602: 1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: q+1
       692: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 1
       794: 1
       796: 1
       800: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       814: 1
       816: 1
       826: 1
       842: 1
       846: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       898: 1
       907: 1
       915: 1
       919: 1
       931: 1
       935: 1
       993: 1
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 1
      1017: 1
      1021: 1
      1025: 1
      1074: 1
      1077: 1
      1121: 1
      1125: 1
      1147: 1
      1215: 1
      1219: 1
      1237: 1
      1321: 1

1322:    0: q^4+q^3+3q^2+4q+1
         1: q^4+q^3+3q^2+4q+1
         2: q^3+2q^2+3q+1
         3: 3q^2+4q+1
         4: q^4+q^3+3q^2+4q+1
         5: 3q^2+4q+1
         6: q^4+q^3+3q^2+4q+1
         7: q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+q^3+q^2+2q+1
        10: q^4+q^3+3q^2+4q+1
        11: 3q^2+4q+1
        12: q^4+q^3+3q^2+4q+1
        13: q^3+q^2+3q+1
        14: q^3+q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+q^2+2q+1
        19: q^4+q^3+3q^2+4q+1
        20: q^4+q^3+3q^2+4q+1
        21: q^3+2q^2+3q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+3q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: 2q^2+3q+1
        28: 2q^2+4q+1
        29: q^4+q^3+3q^2+4q+1
        30: q^3+q^2+3q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: q^2+4q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: 2q^2+3q+1
        43: q^3+q^2+3q+1
        44: q^3+q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: q^3+2q+1
        49: 2q^2+4q+1
        50: 2q^2+4q+1
        51: q^3+q^2+2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+3q+1
        55: 2q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: q
        60: q^2+3q+1
        61: q
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: q^3+q^2+3q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: q^2+3q+1
        81: 3q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: q^2+3q+1
        90: q^3+2q+1
        91: 3q+1
        92: q^2+3q+1
        93: q^3+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: q^2+3q+1
       106: q
       107: q^2+3q+1
       108: q
       109: q^2+3q+1
       110: q
       111: q^2+4q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       117: 2q+1
       119: 2q+1
       121: q^2+3q+1
       123: 3q+1
       125: 2q+1
       126: 2q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: q^2+2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 3q+1
       158: q^2+3q+1
       159: q^3+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+3q+1
       172: q
       173: 2q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       183: 2q+1
       185: 2q+1
       187: 3q+1
       189: q^2+3q+1
       191: 2q+1
       193: q^2+2q+1
       195: q^2+3q+1
       196: q
       197: q^2+2q+1
       199: 2q+1
       201: q^2+3q+1
       202: q
       203: q^2+2q+1
       205: q^2+2q+1
       207: 3q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q^2+3q+1
       262: q
       263: 2q+1
       267: q^2+2q+1
       271: q^2+2q+1
       275: 2q+1
       279: q+1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       293: 2q+1
       295: 2q+1
       297: 3q+1
       299: q+1
       301: q+1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: q+1
       385: 2q+1
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: q+1
       439: q+1
       441: q+1
       443: q+1
       445: q+1
       447: 1
       449: 1
       451: 1
       453: q+1
       455: 1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 2q+2
       479: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: q+1
       529: q+1
       533: 1
       537: 1
       541: q+1
       545: q+1
       549: 1
       553: 1
       557: q+1
       561: q+1
       565: 1
       569: 2q+2
       573: q+1
       577: q+1
       579: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: q+1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 2
       653: 1
       655: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       693: q+1
       695: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 2
       761: 1
       765: 1
       769: 1
       771: 1
       777: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 2
       857: 1
       868: 1
       872: 1
       876: 1
       884: 1
       886: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       928: 1
       932: 1
       936: 1
       948: 1
       956: 1
       960: 1
       974: 1
       978: 2
       982: 1
       984: 1
       988: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1024: 1
      1042: 1
      1050: 1
      1098: 1
      1100: 1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1184: 1
      1222: 1
      1322: 1

1323:    0: q^4+q^3+3q^2+4q+1
         1: q^4+q^3+3q^2+4q+1
         2: q^3+2q^2+3q+1
         3: 3q^2+4q+1
         4: q^4+q^3+3q^2+4q+1
         5: 3q^2+4q+1
         6: q^4+q^3+3q^2+4q+1
         7: q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+q^3+q^2+2q+1
        10: q^4+q^3+3q^2+4q+1
        11: 3q^2+4q+1
        12: q^4+q^3+3q^2+4q+1
        13: q^3+q^2+3q+1
        14: q^3+q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+q^2+2q+1
        19: q^4+q^3+3q^2+4q+1
        20: q^4+q^3+3q^2+4q+1
        21: q^3+2q^2+3q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+3q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: 2q^2+3q+1
        28: 2q^2+4q+1
        29: q^4+q^3+3q^2+4q+1
        30: q^3+q^2+3q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: q^2+4q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        39: 2q^2+4q+1
        41: 2q^2+3q+1
        43: q^3+q^2+3q+1
        44: q^3+q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: q^3+2q+1
        49: 2q^2+4q+1
        50: 2q^2+4q+1
        51: q^3+q^2+2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+3q+1
        55: 2q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+3q+1
        60: q
        61: q^2+3q+1
        62: 2q^2+4q+1
        64: q^2+3q+1
        66: q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: q^3+q^2+3q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: q^2+3q+1
        81: 3q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: q^2+3q+1
        90: q^3+2q+1
        91: 3q+1
        92: q^2+3q+1
        93: q^3+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: q
       106: q^2+3q+1
       107: q
       108: q^2+3q+1
       109: q
       110: q^2+3q+1
       111: q^2+4q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       118: 2q+1
       120: 2q+1
       121: q^2+3q+1
       123: 3q+1
       125: 2q+1
       126: 2q+1
       127: q^2+4q+1
       129: q^2+4q+1
       131: q^2+2q+1
       133: 2q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: q^2+2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: q^2+2q+1
       157: 3q+1
       158: q^2+3q+1
       159: q^3+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: q^2+3q+1
       176: 2q+1
       177: 2q+1
       179: q^2+4q+1
       181: q^2+4q+1
       184: 2q+1
       186: 2q+1
       187: 3q+1
       189: q^2+3q+1
       192: 2q+1
       194: q^2+2q+1
       195: q
       196: q^2+3q+1
       197: q^2+2q+1
       200: 2q+1
       201: q
       202: q^2+3q+1
       204: q^2+2q+1
       205: q^2+2q+1
       207: 3q+1
       209: 2q^2+3q+1
       211: q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: q^2+3q+1
       266: 2q+1
       269: q^2+2q+1
       273: q^2+2q+1
       278: 2q+1
       279: q+1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: 2q+1
       291: 2q+1
       294: 2q+1
       296: 2q+1
       297: 3q+1
       300: q+1
       301: q+1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: q+1
       388: 2q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: q+1
       411: q+1
       413: 1
       415: 2q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: q+1
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       448: 1
       450: 1
       451: 1
       454: q+1
       455: 1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 2q+2
       479: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: q+1
       532: q+1
       536: 1
       539: 1
       543: q+1
       547: q+1
       552: 1
       555: 1
       559: q+1
       563: q+1
       568: 1
       570: 2q+2
       575: q+1
       577: q+1
       579: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 2
       653: 1
       655: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       697: q+1
       702: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 2
       762: 1
       768: 1
       769: 1
       771: 1
       777: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 2
       857: 1
       868: 1
       872: 1
       876: 1
       889: 1
       893: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       930: 1
       934: 1
       938: 1
       950: 1
       958: 1
       961: 1
       975: 1
       979: 2
       982: 1
       984: 1
       991: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1024: 1
      1042: 1
      1050: 1
      1102: 1
      1107: 1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1185: 1
      1222: 1
      1323: 1

1324:    0: q^4+q^3+3q^2+4q+1
         1: q^4+q^3+3q^2+4q+1
         2: q^3+2q^2+3q+1
         3: 3q^2+4q+1
         4: q^4+q^3+3q^2+4q+1
         5: 3q^2+4q+1
         6: q^4+q^3+3q^2+4q+1
         7: q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+q^3+q^2+2q+1
        10: q^4+q^3+3q^2+4q+1
        11: 3q^2+4q+1
        12: q^4+q^3+3q^2+4q+1
        13: q^3+q^2+3q+1
        14: q^3+q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+q^2+2q+1
        19: q^4+q^3+3q^2+4q+1
        20: q^4+q^3+3q^2+4q+1
        21: q^3+2q^2+3q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+3q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: 2q^2+3q+1
        28: 2q^2+4q+1
        29: q^4+q^3+3q^2+4q+1
        30: q^3+q^2+3q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: q^2+4q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: q^2+4q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: 2q^2+3q+1
        43: q^3+q^2+3q+1
        44: q^3+q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: q^3+2q+1
        49: 2q^2+4q+1
        50: 2q^2+4q+1
        51: q^3+q^2+2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+3q+1
        55: 2q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+3q+1
        60: q^2+3q+1
        61: q
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: q^3+q^2+3q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 3q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: q^2+3q+1
        90: q^3+2q+1
        91: 3q+1
        92: q^2+3q+1
        93: q^3+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: q^2+3q+1
       105: q
       107: q^2+3q+1
       108: q
       109: q
       110: q^2+3q+1
       112: q^2+4q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       118: 2q+1
       119: 2q+1
       122: q^2+3q+1
       124: 3q+1
       125: 2q+1
       126: 2q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: q^2+2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 3q+1
       158: q^2+3q+1
       159: q^3+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+3q+1
       171: q
       174: 2q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       183: 2q+1
       186: 2q+1
       188: 3q+1
       190: q^2+3q+1
       192: 2q+1
       193: q^2+2q+1
       195: q
       196: q^2+3q+1
       198: q^2+2q+1
       199: 2q+1
       201: q^2+3q+1
       202: q
       204: q^2+2q+1
       206: q^2+2q+1
       208: 3q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q^2+3q+1
       261: q
       264: 2q+1
       268: q^2+2q+1
       274: q^2+2q+1
       276: 2q+1
       280: q+1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       293: 2q+1
       296: 2q+1
       298: 3q+1
       299: q+1
       302: q+1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: q+1
       386: 2q+1
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: q+1
       440: q+1
       442: q+1
       443: q+1
       446: q+1
       447: 1
       450: 1
       452: 1
       453: q+1
       456: 1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 2q+2
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: q+1
       530: q+1
       534: 1
       538: 1
       542: q+1
       546: q+1
       551: 1
       556: 1
       560: q+1
       564: q+1
       566: 1
       571: 2q+2
       574: q+1
       581: q+1
       582: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 2
       654: 1
       656: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       699: q+1
       703: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 2
       763: 1
       766: 1
       773: 1
       774: 1
       778: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 2
       858: 1
       868: 1
       872: 1
       876: 1
       890: 1
       894: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       929: 1
       933: 1
       939: 1
       951: 1
       959: 1
       962: 1
       976: 1
       980: 2
       986: 1
       987: 1
       989: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1025: 1
      1043: 1
      1051: 1
      1104: 1
      1108: 1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1186: 1
      1223: 1
      1324: 1

1325:    0: q^4+q^3+3q^2+4q+1
         1: q^4+q^3+3q^2+4q+1
         2: q^3+2q^2+3q+1
         3: 3q^2+4q+1
         4: q^4+q^3+3q^2+4q+1
         5: 3q^2+4q+1
         6: q^4+q^3+3q^2+4q+1
         7: q^3+2q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+q^3+q^2+2q+1
        10: q^4+q^3+3q^2+4q+1
        11: 3q^2+4q+1
        12: q^4+q^3+3q^2+4q+1
        13: q^3+q^2+3q+1
        14: q^3+q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+q^2+2q+1
        19: q^4+q^3+3q^2+4q+1
        20: q^4+q^3+3q^2+4q+1
        21: q^3+2q^2+3q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+3q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: 2q^2+3q+1
        28: 2q^2+4q+1
        29: q^4+q^3+3q^2+4q+1
        30: q^3+q^2+3q+1
        31: 2q^2+4q+1
        32: q^2+3q+1
        33: q^2+4q+1
        34: 2q^2+4q+1
        35: q^2+3q+1
        36: q^2+4q+1
        38: 2q^2+4q+1
        40: 2q^2+4q+1
        42: 2q^2+3q+1
        43: q^3+q^2+3q+1
        44: q^3+q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: q^3+2q+1
        49: 2q^2+4q+1
        50: 2q^2+4q+1
        51: q^3+q^2+2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+3q+1
        55: 2q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: q
        60: q
        61: q^2+3q+1
        63: 2q^2+4q+1
        65: q^2+3q+1
        67: q^2+4q+1
        68: 2q+1
        69: 2q+1
        70: q^3+q^2+3q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 3q+1
        82: 2q^2+4q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 2q^2+4q+1
        87: q^2+3q+1
        88: 3q+1
        89: q^2+3q+1
        90: q^3+2q+1
        91: 3q+1
        92: q^2+3q+1
        93: q^3+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       104: q
       105: q^2+3q+1
       107: q
       108: q^2+3q+1
       109: q^2+3q+1
       110: q
       112: q^2+4q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       117: 2q+1
       120: 2q+1
       122: q^2+3q+1
       124: 3q+1
       125: 2q+1
       126: 2q+1
       128: q^2+4q+1
       130: q^2+4q+1
       132: q^2+2q+1
       133: 2q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: q^2+2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: q^2+2q+1
       157: 3q+1
       158: q^2+3q+1
       159: q^3+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: q^2+3q+1
       175: 2q+1
       178: 2q+1
       180: q^2+4q+1
       182: q^2+4q+1
       184: 2q+1
       185: 2q+1
       188: 3q+1
       190: q^2+3q+1
       191: 2q+1
       194: q^2+2q+1
       195: q^2+3q+1
       196: q
       198: q^2+2q+1
       200: 2q+1
       201: q
       202: q^2+3q+1
       203: q^2+2q+1
       206: q^2+2q+1
       208: 3q+1
       210: 2q^2+3q+1
       212: q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: q^2+3q+1
       265: 2q+1
       270: q^2+2q+1
       272: q^2+2q+1
       277: 2q+1
       280: q+1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: 2q+1
       292: 2q+1
       294: 2q+1
       295: 2q+1
       298: 3q+1
       300: q+1
       302: q+1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: q+1
       387: 2q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: q+1
       412: q+1
       414: 1
       416: 2q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: q+1
       439: q+1
       442: q+1
       444: q+1
       446: q+1
       448: 1
       449: 1
       452: 1
       454: q+1
       456: 1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 2q+2
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: q+1
       531: q+1
       535: 1
       540: 1
       544: q+1
       548: q+1
       550: 1
       554: 1
       558: q+1
       562: q+1
       567: 1
       572: 2q+2
       576: q+1
       581: q+1
       582: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: q+1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 2
       654: 1
       656: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       700: q+1
       704: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 2
       764: 1
       767: 1
       773: 1
       774: 1
       778: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 2
       858: 1
       868: 1
       872: 1
       876: 1
       891: 1
       895: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       931: 1
       935: 1
       937: 1
       949: 1
       957: 1
       963: 1
       977: 1
       981: 2
       986: 1
       987: 1
       990: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1025: 1
      1043: 1
      1051: 1
      1105: 1
      1109: 1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1187: 1
      1223: 1
      1325: 1

1326:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: 3q^2+5q+1
         5: 3q^2+5q+1
         6: 3q^2+5q+1
         7: 2q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+5q+1
        11: 3q^2+5q+1
        12: 3q^2+5q+1
        13: 3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q^2+5q+1
        20: 3q^2+5q+1
        21: 2q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: 3q^2+5q+1
        29: 3q^2+5q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 3q+1
        38: 2q
        39: 3q+1
        40: 2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: 3q+1
        45: q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: 3q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: 2q
        60: q^2+3q+1
        61: 2q
        62: 3q+1
        63: 2q
        64: 2q+1
        65: q
        66: 3q+1
        67: 2q
        68: q+1
        69: 3q+1
        70: 3q+1
        71: 3q^2+5q+1
        72: q^2+5q+1
        73: q^2+5q+1
        74: 3q+1
        75: 2q
        76: 3q+1
        77: 2q
        78: q^2+2q+1
        79: q^2+q
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: 3q+1
        89: q^2+3q+1
        90: 3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: 4q+1
       101: 4q+1
       102: 2q+1
       103: 2q+1
       104: q
       105: q
       106: q
       107: q^2+3q+1
       108: 2q
       109: q^2+3q+1
       110: 2q
       111: 3q+1
       112: 2q
       113: 3q+1
       114: 2q
       115: 2q+1
       116: q
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 3q+1
       127: 3q+1
       128: 2q
       129: 3q+1
       130: 2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: 4q+1
       150: 2q+1
       151: 2q+1
       152: 2q
       153: 2q+1
       154: 2q
       155: q+1
       156: q
       157: 3q+1
       158: q^2+3q+1
       159: 3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 4q+1
       167: 4q+1
       168: 2q+1
       169: 2q+1
       170: q
       171: q
       172: q
       173: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: 2q
       181: 3q+1
       182: 2q
       183: q+1
       185: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       191: q+1
       193: 2q+1
       195: q^2+3q+1
       196: 2q
       197: q+1
       198: q
       199: q+1
       201: q^2+3q+1
       202: 2q
       203: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 2q+1
       210: 2q
       211: q+1
       212: q
       219: q+1
       220: q+1
       221: 3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q+1
       238: 2q
       239: 2q+1
       240: 2q
       241: q+1
       242: q
       243: 4q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 4q+1
       248: 4q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       260: q
       261: q
       262: q
       263: q+1
       267: q+1
       268: q
       271: q+1
       272: q
       275: q+1
       283: q+1
       285: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       293: q+1
       295: q+1
       297: 2q+1
       298: q
       299: 1
       301: q+1
       302: q
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       312: q
       313: 1
       315: q+1
       316: q
       317: 2q+1
       318: 2q
       319: 2q+1
       321: 2q+1
       323: q+1
       325: q+1
       326: q
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       339: 2q
       340: 2q+1
       341: 2q
       342: q+1
       343: q
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       385: q+1
       389: q+1
       390: q
       393: 1
       397: q+1
       398: q
       401: 1
       405: q+1
       419: q+1
       421: q+1
       423: 2q+1
       424: q
       425: q+1
       426: q
       427: 2q+1
       428: 2q
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 2q+1
       445: q+1
       446: q
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 2q+1
       463: q+1
       464: q
       469: q+1
       470: q
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       529: q+1
       533: 1
       541: 1
       545: q+1
       546: q
       549: 1
       557: 1
       561: q+1
       562: q
       565: 1
       569: q+1
       573: q+1
       577: q+1
       589: 1
       591: 1
       593: 1
       595: 1
       599: q+1
       600: q
       603: 1
       607: 1
       609: 1
       613: 1
       615: 1
       619: 1
       621: 1
       625: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: q+1
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       805: 1
       807: 1
       811: 1
       815: 1
       817: 1
       825: 1
       827: 1
       835: 1
       839: 1
       843: 1
       845: 1
       847: 1
       851: 1
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       908: 1
       928: 1
       948: 1
       964: 1
       974: 1
       988: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1012: 1
      1016: 1
      1032: 1
      1046: 1
      1074: 1
      1077: 1
      1081: 1
      1130: 1
      1134: 1
      1194: 1
      1216: 1
      1218: 1
      1224: 1
      1326: 1

1327:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: 3q^2+5q+1
         5: 3q^2+5q+1
         6: 3q^2+5q+1
         7: 2q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+5q+1
        11: 3q^2+5q+1
        12: 3q^2+5q+1
        13: 3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q^2+5q+1
        20: 3q^2+5q+1
        21: 2q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: 3q^2+5q+1
        29: 3q^2+5q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 2q
        38: 3q+1
        39: 2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: 3q+1
        45: q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: 3q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q
        62: 2q
        63: 3q+1
        64: q
        65: 2q+1
        66: 2q
        67: 3q+1
        68: q+1
        69: 3q+1
        70: 3q+1
        71: 3q^2+5q+1
        72: q^2+5q+1
        73: q^2+5q+1
        74: 2q
        75: 3q+1
        76: 2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: 3q+1
        89: q^2+3q+1
        90: 3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: 4q+1
       101: 4q+1
       102: 2q+1
       103: q
       104: 2q+1
       105: q
       106: q
       107: q^2+3q+1
       108: 2q
       109: 2q
       110: q^2+3q+1
       111: 2q
       112: 3q+1
       113: 2q
       114: 3q+1
       115: q
       116: 2q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 3q+1
       127: 2q
       128: 3q+1
       129: 2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: 4q+1
       150: 2q+1
       151: 2q
       152: 2q+1
       153: 2q
       154: 2q+1
       155: q
       156: q+1
       157: 3q+1
       158: q^2+3q+1
       159: 3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 4q+1
       167: 4q+1
       168: 2q+1
       169: q
       170: 2q+1
       171: q
       172: q
       174: q+1
       177: q
       178: 2q+1
       179: 2q
       180: 3q+1
       181: 2q
       182: 3q+1
       183: q+1
       186: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       192: q+1
       193: 2q+1
       195: 2q
       196: q^2+3q+1
       197: q
       198: q+1
       199: q+1
       201: q^2+3q+1
       202: 2q
       204: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: 2q
       210: 2q+1
       211: q
       212: q+1
       219: q+1
       220: q+1
       221: 3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q
       238: 2q+1
       239: 2q
       240: 2q+1
       241: q
       242: q+1
       243: 4q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 4q+1
       248: 4q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       260: 2q+1
       261: q
       262: q
       264: q+1
       267: q
       268: q+1
       273: q
       274: q+1
       276: q+1
       283: q+1
       286: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       293: q+1
       296: q+1
       297: q
       298: 2q+1
       299: 1
       301: q
       302: q+1
       304: 1
       306: 1
       307: 1
       310: 1
       311: q
       312: q+1
       314: 1
       315: q
       316: q+1
       317: 2q
       318: 2q+1
       319: 2q+1
       322: 2q+1
       324: q+1
       325: q
       326: q+1
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 4q+1
       338: 2q
       339: 2q+1
       340: 2q
       341: 2q+1
       342: q
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       386: q+1
       389: q
       390: q+1
       394: 1
       399: q
       400: q+1
       403: 1
       407: q+1
       419: q+1
       422: q+1
       423: q
       424: 2q+1
       425: q
       426: q+1
       427: 2q
       428: 2q+1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 2q+1
       445: q
       446: q+1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 2q+1
       463: q
       464: q+1
       469: q
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       530: q+1
       534: 1
       542: 1
       545: q
       546: q+1
       551: 1
       560: 1
       563: q
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: q+1
       603: 1
       608: 1
       610: 1
       614: 1
       615: 1
       619: 1
       622: 1
       626: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: q+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       805: 1
       808: 1
       812: 1
       815: 1
       818: 1
       825: 1
       828: 1
       836: 1
       840: 1
       844: 1
       845: 1
       848: 1
       852: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       909: 1
       929: 1
       951: 1
       965: 1
       976: 1
       989: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1013: 1
      1016: 1
      1033: 1
      1047: 1
      1074: 1
      1077: 1
      1081: 1
      1131: 1
      1136: 1
      1195: 1
      1217: 1
      1218: 1
      1225: 1
      1327: 1

1328:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: 3q^2+5q+1
         5: 3q^2+5q+1
         6: 3q^2+5q+1
         7: 2q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+5q+1
        11: 3q^2+5q+1
        12: 3q^2+5q+1
        13: 3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q^2+5q+1
        20: 3q^2+5q+1
        21: 2q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: 3q^2+5q+1
        29: 3q^2+5q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 2q
        38: 3q+1
        39: 2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: 3q+1
        45: q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: 3q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: 2q
        60: 2q
        61: q^2+3q+1
        62: 2q
        63: 3q+1
        64: q
        65: 2q+1
        66: 2q
        67: 3q+1
        68: q+1
        69: 3q+1
        70: 3q+1
        71: 3q^2+5q+1
        72: q^2+5q+1
        73: q^2+5q+1
        74: 2q
        75: 3q+1
        76: 2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: 3q+1
        89: q^2+3q+1
        90: 3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: 4q+1
       101: 4q+1
       102: 2q+1
       103: q
       104: q
       105: 2q+1
       106: q
       107: 2q
       108: q^2+3q+1
       109: q^2+3q+1
       110: 2q
       111: 2q
       112: 3q+1
       113: 2q
       114: 3q+1
       115: q
       116: 2q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 3q+1
       127: 2q
       128: 3q+1
       129: 2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: 4q+1
       150: 2q+1
       151: 2q
       152: 2q+1
       153: 2q
       154: 2q+1
       155: q
       156: q+1
       157: 3q+1
       158: q^2+3q+1
       159: 3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 4q+1
       167: 4q+1
       168: 2q+1
       169: q
       170: q
       171: 2q+1
       172: q
       175: q+1
       177: q
       178: 2q+1
       179: 2q
       180: 3q+1
       181: 2q
       182: 3q+1
       184: q+1
       185: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       191: q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q
       197: q
       198: q+1
       200: q+1
       201: 2q
       202: q^2+3q+1
       203: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: 2q
       210: 2q+1
       211: q
       212: q+1
       219: q+1
       220: q+1
       221: 3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q
       238: 2q+1
       239: 2q
       240: 2q+1
       241: q
       242: q+1
       243: 4q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 4q+1
       248: 4q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       260: q
       261: 2q+1
       262: q
       265: q+1
       269: q
       270: q+1
       271: q
       272: q+1
       277: q+1
       284: q+1
       285: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       294: q+1
       295: q+1
       297: q
       298: 2q+1
       300: 1
       301: q
       302: q+1
       303: 1
       306: 1
       308: 1
       309: 1
       311: q
       312: q+1
       314: 1
       315: q
       316: q+1
       317: 2q
       318: 2q+1
       320: 2q+1
       321: 2q+1
       324: q+1
       325: q
       326: q+1
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 4q+1
       338: 2q
       339: 2q+1
       340: 2q
       341: 2q+1
       342: q
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       387: q+1
       391: q
       392: q+1
       395: 1
       397: q
       398: q+1
       402: 1
       408: q+1
       420: q+1
       421: q+1
       423: q
       424: 2q+1
       425: q
       426: q+1
       427: 2q
       428: 2q+1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 2q+1
       445: q
       446: q+1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 2q+1
       463: q
       464: q+1
       469: q
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       531: q+1
       535: 1
       544: 1
       547: q
       548: q+1
       550: 1
       558: 1
       561: q
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: q+1
       604: 1
       607: 1
       610: 1
       614: 1
       616: 1
       620: 1
       621: 1
       626: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       700: q+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       806: 1
       807: 1
       812: 1
       816: 1
       817: 1
       826: 1
       827: 1
       836: 1
       839: 1
       844: 1
       846: 1
       847: 1
       852: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       910: 1
       931: 1
       949: 1
       966: 1
       977: 1
       990: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1013: 1
      1017: 1
      1032: 1
      1047: 1
      1074: 1
      1077: 1
      1081: 1
      1132: 1
      1137: 1
      1196: 1
      1216: 1
      1219: 1
      1225: 1
      1328: 1

1329:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 2q^2+3q+1
         3: 3q^2+5q+1
         4: 3q^2+5q+1
         5: 3q^2+5q+1
         6: 3q^2+5q+1
         7: 2q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+5q+1
        11: 3q^2+5q+1
        12: 3q^2+5q+1
        13: 3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q^2+5q+1
        20: 3q^2+5q+1
        21: 2q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: 3q^2+5q+1
        29: 3q^2+5q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 3q+1
        38: 2q
        39: 3q+1
        40: 2q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: 3q+1
        45: q^2+3q+1
        46: 3q+1
        47: q^2+3q+1
        48: 3q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: 2q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+3q+1
        60: 2q
        61: q^2+3q+1
        62: 3q+1
        63: 2q
        64: 2q+1
        65: q
        66: 3q+1
        67: 2q
        68: q+1
        69: 3q+1
        70: 3q+1
        71: 3q^2+5q+1
        72: q^2+5q+1
        73: q^2+5q+1
        74: 3q+1
        75: 2q
        76: 3q+1
        77: 2q
        78: q^2+2q+1
        79: q^2+q
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: 3q+1
        89: q^2+3q+1
        90: 3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: 4q+1
       101: 4q+1
       102: 2q+1
       103: q
       104: q
       105: q
       106: 2q+1
       107: 2q
       108: q^2+3q+1
       109: 2q
       110: q^2+3q+1
       111: 3q+1
       112: 2q
       113: 3q+1
       114: 2q
       115: 2q+1
       116: q
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 3q+1
       127: 3q+1
       128: 2q
       129: 3q+1
       130: 2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: 4q+1
       150: 2q+1
       151: 2q+1
       152: 2q
       153: 2q+1
       154: 2q
       155: q+1
       156: q
       157: 3q+1
       158: q^2+3q+1
       159: 3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 4q+1
       167: 4q+1
       168: 2q+1
       169: q
       170: q
       171: q
       172: 2q+1
       176: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: 2q
       181: 3q+1
       182: 2q
       184: q+1
       186: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       192: q+1
       194: 2q+1
       195: 2q
       196: q^2+3q+1
       197: q+1
       198: q
       200: q+1
       201: 2q
       202: q^2+3q+1
       204: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 2q+1
       210: 2q
       211: q+1
       212: q
       219: q+1
       220: q+1
       221: 3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q+1
       238: 2q
       239: 2q+1
       240: 2q
       241: q+1
       242: q
       243: 4q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 4q+1
       248: 4q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       260: q
       261: q
       262: 2q+1
       266: q+1
       269: q+1
       270: q
       273: q+1
       274: q
       278: q+1
       284: q+1
       286: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       294: q+1
       296: q+1
       297: 2q+1
       298: q
       300: 1
       301: q+1
       302: q
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       312: q
       313: 1
       315: q+1
       316: q
       317: 2q+1
       318: 2q
       320: 2q+1
       322: 2q+1
       323: q+1
       325: q+1
       326: q
       333: q+1
       334: 3q+1
       335: 3q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       339: 2q
       340: 2q+1
       341: 2q
       342: q+1
       343: q
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       388: q+1
       391: q+1
       392: q
       396: 1
       399: q+1
       400: q
       404: 1
       406: q+1
       420: q+1
       422: q+1
       423: 2q+1
       424: q
       425: q+1
       426: q
       427: 2q+1
       428: 2q
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 2q+1
       445: q+1
       446: q
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 2q+1
       463: q+1
       464: q
       469: q+1
       470: q
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       532: q+1
       536: 1
       543: 1
       547: q+1
       548: q
       552: 1
       559: 1
       563: q+1
       564: q
       568: 1
       570: q+1
       575: q+1
       577: q+1
       590: 1
       592: 1
       594: 1
       596: 1
       599: q+1
       600: q
       604: 1
       608: 1
       609: 1
       613: 1
       616: 1
       620: 1
       622: 1
       625: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       697: q+1
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       806: 1
       808: 1
       811: 1
       816: 1
       818: 1
       826: 1
       828: 1
       835: 1
       840: 1
       843: 1
       846: 1
       848: 1
       851: 1
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       911: 1
       930: 1
       950: 1
       967: 1
       975: 1
       991: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1012: 1
      1017: 1
      1033: 1
      1046: 1
      1074: 1
      1077: 1
      1081: 1
      1133: 1
      1135: 1
      1197: 1
      1217: 1
      1219: 1
      1224: 1
      1329: 1

1330:    0: q^3+9q^2+7q+1
         1: q^4+4q^3+9q^2+7q+1
         2: q^3+9q^2+7q+1
         3: 3q^3+9q^2+7q+1
         4: q^3+9q^2+7q+1
         5: 3q^3+9q^2+7q+1
         6: q^4+4q^3+9q^2+7q+1
         7: q^3+9q^2+7q+1
         8: 3q^3+9q^2+7q+1
         9: q^4+4q^3+6q^2+4q+1
        10: q^3+7q^2+7q+1
        11: q^3+7q^2+7q+1
        12: q^3+7q^2+7q+1
        13: q^3+9q^2+7q+1
        14: q^3+9q^2+7q+1
        15: 3q^3+9q^2+7q+1
        16: 6q^2+7q+1
        17: q^3+6q^2+7q+1
        18: q^3+6q^2+4q+1
        19: q^3+9q^2+7q+1
        20: q^4+4q^3+9q^2+7q+1
        21: q^3+9q^2+7q+1
        22: 6q^2+7q+1
        23: q^3+6q^2+7q+1
        24: 6q^2+7q+1
        25: 6q^2+7q+1
        26: q^3+6q^2+7q+1
        27: 6q^2+7q+1
        28: 4q^2+7q+1
        29: q^3+7q^2+7q+1
        30: q^3+9q^2+7q+1
        31: 4q^2+7q+1
        32: 6q^2+7q+1
        33: 4q^2+7q+1
        34: 4q^2+7q+1
        35: 6q^2+7q+1
        36: 4q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 3q^2+5q+1
        42: q^2+2q
        43: q^3+7q^2+7q+1
        44: q^3+7q^2+7q+1
        45: q^3+7q^2+7q+1
        46: 6q^2+7q+1
        47: q^3+6q^2+7q+1
        48: q^3+6q^2+4q+1
        49: 6q^2+7q+1
        50: q^3+6q^2+7q+1
        51: q^3+6q^2+4q+1
        52: 6q^2+7q+1
        53: q^3+6q^2+7q+1
        54: 6q^2+7q+1
        55: 6q^2+7q+1
        56: q^3+6q^2+7q+1
        57: 6q^2+7q+1
        58: 2q^2+5q+1
        59: 2q
        60: 2q^2+5q+1
        61: 2q
        62: 2q^2+5q+1
        63: 2q
        64: 3q^2+5q+1
        65: q^2+2q
        66: 2q^2+5q+1
        67: q^2+2q
        68: 4q^2+7q+1
        69: 3q^2+4q+1
        70: q^3+7q^2+7q+1
        71: 4q^2+7q+1
        72: 4q^2+7q+1
        73: 4q^2+7q+1
        74: 3q^2+5q+1
        75: q^2+2q
        76: 3q^2+5q+1
        77: q^2+2q
        78: 3q^2+5q+1
        79: q^2+2q
        80: 4q^2+7q+1
        81: 4q^2+7q+1
        82: 4q^2+7q+1
        83: 6q^2+7q+1
        84: 4q^2+7q+1
        85: 4q^2+7q+1
        86: 4q^2+7q+1
        87: 6q^2+7q+1
        88: 2q^2+7q+1
        89: 2q^2+7q+1
        90: q^3+4q^2+4q+1
        91: 6q^2+7q+1
        92: q^3+6q^2+7q+1
        93: q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q^2+4q+1
       104: q
       105: q
       106: q
       107: 2q^2+5q+1
       108: 2q
       109: 2q^2+5q+1
       110: 2q
       111: 2q^2+5q+1
       112: q^2+2q
       113: 2q^2+5q+1
       114: 2q
       115: 3q^2+5q+1
       116: q^2+2q
       117: 2q^2+5q+1
       118: 2q
       119: 2q^2+5q+1
       120: 2q
       121: 2q^2+5q+1
       122: 2q
       123: 2q^2+5q+1
       124: q^2+2q
       125: 2q^2+7q+1
       126: q^2+4q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 4q^2+7q+1
       134: 3q^2+4q+1
       135: 4q^2+7q+1
       136: 4q^2+7q+1
       137: q^2+7q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+7q+1
       142: 2q^2+6q+1
       143: q^2+7q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+7q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: q^2+4q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: q^2+4q+1
       156: 2q
       157: 2q^2+7q+1
       158: 2q^2+7q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q^2+4q+1
       170: q
       171: q
       172: q
       173: q^2+4q+1
       174: q
       175: q
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: 2q^2+5q+1
       184: 2q
       185: 2q^2+5q+1
       186: 2q
       187: 2q^2+5q+1
       188: q^2+2q
       189: 2q^2+5q+1
       190: 2q
       191: q^2+5q+1
       192: 2q
       193: 3q+1
       195: q^2+4q+1
       196: 2q
       197: 2q+1
       198: q
       199: q^2+5q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       203: 3q+1
       205: 2q+1
       206: q
       207: q^2+5q+1
       208: 2q
       209: q^2+4q+1
       210: 2q
       211: q^2+4q+1
       212: 2q
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+7q+1
       221: q^2+4q+1
       222: q^2+7q+1
       223: q^2+4q+1
       224: q^2+7q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+6q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: 2q+1
       262: q
       263: q^2+4q+1
       264: q
       265: q
       266: q
       267: 2q+1
       268: q
       271: 2q+1
       272: q
       275: q^2+4q+1
       276: q
       277: q
       278: q
       279: 3q+1
       281: 2q+1
       283: 2q+1
       285: 2q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+5q+1
       294: 2q
       295: q^2+5q+1
       296: 2q
       297: q^2+5q+1
       298: 2q
       299: 3q+1
       301: 1
       303: q^2+4q+1
       304: 2q
       305: 2q+1
       306: q
       307: q^2+4q+1
       308: 2q
       309: 3q+1
       311: 1
       313: 2q+1
       314: q
       315: q+1
       317: q+1
       319: q+1
       321: q+1
       323: 1
       325: q^2+4q+1
       326: 2q
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 3q+1
       338: q+1
       340: q+1
       342: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+4q+1
       386: q
       387: q
       388: q
       389: 1
       393: 2q+1
       394: q
       397: 1
       401: 2q+1
       402: q
       405: 1
       413: 2q+1
       417: 2q+1
       419: 2q+1
       421: 2q+1
       423: 2q+1
       425: q+1
       427: q+1
       429: q+1
       431: 2q+1
       433: 1
       435: 1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: q+1
       445: 1
       447: 2q+1
       449: q+1
       451: 1
       453: 2q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: q+1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: q+1
       473: q+1
       475: 1
       477: 2
       479: 1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 3q+1
       485: q+1
       487: q+1
       489: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       529: q+1
       533: 1
       537: 1
       541: q+1
       545: 1
       549: 1
       553: 1
       557: q+1
       561: 1
       565: 1
       569: 2
       573: 1
       577: 1
       579: 1
       585: 2q+1
       589: 2q+1
       591: q+1
       593: q+1
       595: 2q+1
       597: q+1
       599: q+1
       601: q+1
       603: 1
       605: 1
       607: q+1
       609: 1
       613: 1
       615: q+1
       617: 1
       619: q+1
       621: 1
       623: 1
       625: 1
       629: 1
       631: q+1
       633: 1
       639: q+1
       641: q+1
       643: q+1
       645: 1
       647: 1
       649: 1
       651: 2
       653: 1
       655: 1
       665: 3q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: q+1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       693: 1
       695: 1
       709: q+1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 2
       761: 1
       765: 1
       769: 1
       771: 1
       781: q+1
       785: q+1
       787: q+1
       791: 1
       797: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       815: 1
       821: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       839: 1
       845: 1
       847: 1
       849: 1
       851: 1
       857: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       900: 1
       904: 1
       908: 1
       920: 1
       928: 1
       944: 1
       948: 1
       960: 1
       974: 1
       988: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1022: 1
      1026: 1
      1038: 1
      1044: 1
      1048: 1
      1052: 1
      1058: 1
      1078: 1
      1082: 1
      1126: 1
      1134: 1
      1156: 1
      1172: 1
      1198: 1
      1220: 1
      1240: 1
      1260: 1
      1330: 1

1331:    0: q^3+9q^2+7q+1
         1: q^4+4q^3+9q^2+7q+1
         2: q^3+9q^2+7q+1
         3: 3q^3+9q^2+7q+1
         4: q^3+9q^2+7q+1
         5: 3q^3+9q^2+7q+1
         6: q^4+4q^3+9q^2+7q+1
         7: q^3+9q^2+7q+1
         8: 3q^3+9q^2+7q+1
         9: q^4+4q^3+6q^2+4q+1
        10: q^3+7q^2+7q+1
        11: q^3+7q^2+7q+1
        12: q^3+7q^2+7q+1
        13: q^3+9q^2+7q+1
        14: q^3+9q^2+7q+1
        15: 3q^3+9q^2+7q+1
        16: 6q^2+7q+1
        17: q^3+6q^2+7q+1
        18: q^3+6q^2+4q+1
        19: q^3+9q^2+7q+1
        20: q^4+4q^3+9q^2+7q+1
        21: q^3+9q^2+7q+1
        22: 6q^2+7q+1
        23: q^3+6q^2+7q+1
        24: 6q^2+7q+1
        25: 6q^2+7q+1
        26: q^3+6q^2+7q+1
        27: 6q^2+7q+1
        28: 4q^2+7q+1
        29: q^3+7q^2+7q+1
        30: q^3+9q^2+7q+1
        31: 4q^2+7q+1
        32: 6q^2+7q+1
        33: 4q^2+7q+1
        34: 4q^2+7q+1
        35: 6q^2+7q+1
        36: 4q^2+7q+1
        37: 3q^2+5q+1
        38: q^2+2q
        39: 3q^2+5q+1
        40: q^2+2q
        41: 3q^2+5q+1
        42: q^2+2q
        43: q^3+7q^2+7q+1
        44: q^3+7q^2+7q+1
        45: q^3+7q^2+7q+1
        46: 6q^2+7q+1
        47: q^3+6q^2+7q+1
        48: q^3+6q^2+4q+1
        49: 6q^2+7q+1
        50: q^3+6q^2+7q+1
        51: q^3+6q^2+4q+1
        52: 6q^2+7q+1
        53: q^3+6q^2+7q+1
        54: 6q^2+7q+1
        55: 6q^2+7q+1
        56: q^3+6q^2+7q+1
        57: 6q^2+7q+1
        58: 2q
        59: 2q^2+5q+1
        60: 2q
        61: 2q^2+5q+1
        62: 2q^2+5q+1
        63: 2q
        64: 3q^2+5q+1
        65: q^2+2q
        66: 2q^2+5q+1
        67: q^2+2q
        68: 4q^2+7q+1
        69: 3q^2+4q+1
        70: q^3+7q^2+7q+1
        71: 4q^2+7q+1
        72: 4q^2+7q+1
        73: 4q^2+7q+1
        74: 3q^2+5q+1
        75: q^2+2q
        76: 3q^2+5q+1
        77: q^2+2q
        78: 3q^2+5q+1
        79: q^2+2q
        80: 4q^2+7q+1
        81: 4q^2+7q+1
        82: 4q^2+7q+1
        83: 6q^2+7q+1
        84: 4q^2+7q+1
        85: 4q^2+7q+1
        86: 4q^2+7q+1
        87: 6q^2+7q+1
        88: 2q^2+7q+1
        89: 2q^2+7q+1
        90: q^3+4q^2+4q+1
        91: 6q^2+7q+1
        92: q^3+6q^2+7q+1
        93: q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q
       104: q
       105: q
       106: q^2+4q+1
       107: 2q
       108: 2q^2+5q+1
       109: 2q
       110: 2q^2+5q+1
       111: 2q^2+5q+1
       112: q^2+2q
       113: 2q^2+5q+1
       114: 2q
       115: 3q^2+5q+1
       116: q^2+2q
       117: 2q
       118: 2q^2+5q+1
       119: 2q
       120: 2q^2+5q+1
       121: 2q^2+5q+1
       122: 2q
       123: 2q^2+5q+1
       124: q^2+2q
       125: 2q^2+7q+1
       126: q^2+4q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 4q^2+7q+1
       134: 3q^2+4q+1
       135: 4q^2+7q+1
       136: 4q^2+7q+1
       137: q^2+7q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+7q+1
       142: 2q^2+6q+1
       143: q^2+7q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+7q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: q^2+4q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: q^2+4q+1
       156: 2q
       157: 2q^2+7q+1
       158: 2q^2+7q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q
       171: q
       172: q^2+4q+1
       173: q
       174: q
       175: q
       176: q^2+4q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: 2q
       184: 2q^2+5q+1
       185: 2q
       186: 2q^2+5q+1
       187: 2q^2+5q+1
       188: q^2+2q
       189: 2q^2+5q+1
       190: 2q
       191: 2q
       192: q^2+5q+1
       194: 3q+1
       195: 2q
       196: q^2+4q+1
       197: 2q+1
       198: q
       199: 2q
       200: q^2+5q+1
       201: 2q
       202: q^2+4q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: q^2+5q+1
       208: 2q
       209: q^2+4q+1
       210: 2q
       211: q^2+4q+1
       212: 2q
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+7q+1
       221: q^2+4q+1
       222: q^2+7q+1
       223: q^2+4q+1
       224: q^2+7q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+6q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       262: 2q+1
       263: q
       264: q
       265: q
       266: q^2+4q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: q
       275: q
       276: q
       277: q
       278: q^2+4q+1
       279: 3q+1
       281: 2q+1
       284: 2q+1
       286: 2q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: 2q
       294: q^2+5q+1
       295: 2q
       296: q^2+5q+1
       297: q^2+5q+1
       298: 2q
       300: 3q+1
       301: 1
       303: 2q
       304: q^2+4q+1
       305: 2q+1
       306: q
       307: 2q
       308: q^2+4q+1
       310: 3q+1
       311: 1
       313: 2q+1
       314: q
       315: q+1
       317: q+1
       320: q+1
       322: q+1
       323: 1
       325: q^2+4q+1
       326: 2q
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 3q+1
       338: q+1
       340: q+1
       342: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       386: q
       387: q
       388: q^2+4q+1
       391: 1
       395: q
       396: 2q+1
       399: 1
       403: q
       404: 2q+1
       406: 1
       413: 2q+1
       417: 2q+1
       420: 2q+1
       422: 2q+1
       423: 2q+1
       425: q+1
       427: q+1
       430: q+1
       432: 2q+1
       433: 1
       435: 1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: q+1
       445: 1
       448: 2q+1
       450: q+1
       451: 1
       453: q
       454: 2q+1
       455: 1
       458: q+1
       459: q+1
       462: q+1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       472: q+1
       474: q+1
       475: 1
       477: 2
       479: 1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 3q+1
       485: q+1
       487: q+1
       489: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       524: q+1
       532: q+1
       536: 1
       539: 1
       543: q+1
       547: 1
       552: 1
       555: 1
       559: q+1
       563: 1
       568: 1
       570: 2
       575: 1
       577: 1
       579: 1
       585: 2q+1
       590: 2q+1
       592: q+1
       594: q+1
       596: 2q+1
       597: q+1
       599: q+1
       601: q+1
       604: 1
       605: 1
       608: q+1
       609: 1
       613: 1
       616: q+1
       617: 1
       620: q+1
       622: 1
       623: 1
       625: 1
       629: 1
       632: q+1
       633: 1
       639: q+1
       642: q+1
       644: q+1
       645: 1
       648: 1
       650: 1
       651: 2
       653: 1
       655: 1
       665: 3q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: q+1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       697: 1
       702: 1
       712: q+1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 2
       762: 1
       768: 1
       769: 1
       771: 1
       781: q+1
       786: q+1
       788: q+1
       791: 1
       797: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       816: 1
       821: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       840: 1
       846: 1
       848: 1
       849: 1
       851: 1
       857: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       889: 1
       893: 1
       902: 1
       906: 1
       911: 1
       922: 1
       930: 1
       946: 1
       950: 1
       961: 1
       975: 1
       991: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1022: 1
      1027: 1
      1038: 1
      1045: 1
      1048: 1
      1053: 1
      1059: 1
      1078: 1
      1082: 1
      1127: 1
      1135: 1
      1158: 1
      1174: 1
      1199: 1
      1220: 1
      1241: 1
      1261: 1
      1331: 1

1332:    0: q^3+9q^2+7q+1
         1: q^4+4q^3+9q^2+7q+1
         2: q^3+9q^2+7q+1
         3: 3q^3+9q^2+7q+1
         4: q^3+9q^2+7q+1
         5: 3q^3+9q^2+7q+1
         6: q^4+4q^3+9q^2+7q+1
         7: q^3+9q^2+7q+1
         8: 3q^3+9q^2+7q+1
         9: q^4+4q^3+6q^2+4q+1
        10: q^3+7q^2+7q+1
        11: q^3+7q^2+7q+1
        12: q^3+7q^2+7q+1
        13: q^3+9q^2+7q+1
        14: q^3+9q^2+7q+1
        15: 3q^3+9q^2+7q+1
        16: 6q^2+7q+1
        17: q^3+6q^2+7q+1
        18: q^3+6q^2+4q+1
        19: q^3+9q^2+7q+1
        20: q^4+4q^3+9q^2+7q+1
        21: q^3+9q^2+7q+1
        22: 6q^2+7q+1
        23: q^3+6q^2+7q+1
        24: 6q^2+7q+1
        25: 6q^2+7q+1
        26: q^3+6q^2+7q+1
        27: 6q^2+7q+1
        28: 4q^2+7q+1
        29: q^3+7q^2+7q+1
        30: q^3+9q^2+7q+1
        31: 4q^2+7q+1
        32: 6q^2+7q+1
        33: 4q^2+7q+1
        34: 4q^2+7q+1
        35: 6q^2+7q+1
        36: 4q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+2q
        42: 3q^2+5q+1
        43: q^3+7q^2+7q+1
        44: q^3+7q^2+7q+1
        45: q^3+7q^2+7q+1
        46: 6q^2+7q+1
        47: q^3+6q^2+7q+1
        48: q^3+6q^2+4q+1
        49: 6q^2+7q+1
        50: q^3+6q^2+7q+1
        51: q^3+6q^2+4q+1
        52: 6q^2+7q+1
        53: q^3+6q^2+7q+1
        54: 6q^2+7q+1
        55: 6q^2+7q+1
        56: q^3+6q^2+7q+1
        57: 6q^2+7q+1
        58: 2q
        59: 2q^2+5q+1
        60: 2q^2+5q+1
        61: 2q
        62: 2q
        63: 2q^2+5q+1
        64: q^2+2q
        65: 3q^2+5q+1
        66: q^2+2q
        67: 2q^2+5q+1
        68: 4q^2+7q+1
        69: 3q^2+4q+1
        70: q^3+7q^2+7q+1
        71: 4q^2+7q+1
        72: 4q^2+7q+1
        73: 4q^2+7q+1
        74: q^2+2q
        75: 3q^2+5q+1
        76: q^2+2q
        77: 3q^2+5q+1
        78: q^2+2q
        79: 3q^2+5q+1
        80: 4q^2+7q+1
        81: 4q^2+7q+1
        82: 4q^2+7q+1
        83: 6q^2+7q+1
        84: 4q^2+7q+1
        85: 4q^2+7q+1
        86: 4q^2+7q+1
        87: 6q^2+7q+1
        88: 2q^2+7q+1
        89: 2q^2+7q+1
        90: q^3+4q^2+4q+1
        91: 6q^2+7q+1
        92: q^3+6q^2+7q+1
        93: q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q
       104: q^2+4q+1
       105: q
       106: q
       107: 2q^2+5q+1
       108: 2q
       109: 2q
       110: 2q^2+5q+1
       111: q^2+2q
       112: 2q^2+5q+1
       113: 2q
       114: 2q^2+5q+1
       115: q^2+2q
       116: 3q^2+5q+1
       117: 2q
       118: 2q^2+5q+1
       119: 2q^2+5q+1
       120: 2q
       121: 2q
       122: 2q^2+5q+1
       123: q^2+2q
       124: 2q^2+5q+1
       125: 2q^2+7q+1
       126: q^2+4q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 4q^2+7q+1
       134: 3q^2+4q+1
       135: 4q^2+7q+1
       136: 4q^2+7q+1
       137: q^2+7q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+7q+1
       142: 2q^2+6q+1
       143: q^2+7q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+7q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: 2q
       152: q^2+4q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: 2q
       156: q^2+4q+1
       157: 2q^2+7q+1
       158: 2q^2+7q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q^2+4q+1
       171: q
       172: q
       173: q
       174: q^2+4q+1
       175: q
       176: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: 2q^2+5q+1
       184: 2q
       185: 2q
       186: 2q^2+5q+1
       187: q^2+2q
       188: 2q^2+5q+1
       189: 2q
       190: 2q^2+5q+1
       191: 2q
       192: q^2+5q+1
       193: 3q+1
       195: 2q
       196: q^2+4q+1
       197: q
       198: 2q+1
       199: q^2+5q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       204: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+5q+1
       209: 2q
       210: q^2+4q+1
       211: 2q
       212: q^2+4q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+7q+1
       221: q^2+4q+1
       222: q^2+7q+1
       223: q^2+4q+1
       224: q^2+7q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+6q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       260: 2q+1
       261: q
       263: q
       264: q^2+4q+1
       265: q
       266: q
       267: q
       268: 2q+1
       273: q
       274: 2q+1
       275: q
       276: q^2+4q+1
       277: q
       278: q
       280: 3q+1
       282: 2q+1
       283: 2q+1
       286: 2q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+5q+1
       294: 2q
       295: 2q
       296: q^2+5q+1
       297: 2q
       298: q^2+5q+1
       299: 3q+1
       302: 1
       303: 2q
       304: q^2+4q+1
       305: q
       306: 2q+1
       307: q^2+4q+1
       308: 2q
       310: 3q+1
       312: 1
       313: q
       314: 2q+1
       316: q+1
       318: q+1
       319: q+1
       322: q+1
       324: 1
       325: 2q
       326: q^2+4q+1
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 3q+1
       339: q+1
       341: q+1
       343: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 2q+1
       383: q
       385: q
       386: q^2+4q+1
       387: q
       388: q
       390: 1
       393: q
       394: 2q+1
       400: 1
       403: 2q+1
       404: q
       407: 1
       414: 2q+1
       418: 2q+1
       419: 2q+1
       422: 2q+1
       424: 2q+1
       426: q+1
       428: q+1
       429: q+1
       432: 2q+1
       434: 1
       436: 1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: q+1
       446: 1
       447: 2q+1
       450: q+1
       452: 1
       453: 2q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: q+1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: q+1
       474: q+1
       476: 1
       478: 2
       480: 1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 3q+1
       486: q+1
       488: q+1
       490: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q+1
       530: q+1
       534: 1
       538: 1
       542: q+1
       546: 1
       551: 1
       556: 1
       560: q+1
       564: 1
       566: 1
       571: 2
       574: 1
       581: 1
       582: 1
       586: 2q+1
       589: 2q+1
       592: q+1
       593: q+1
       596: 2q+1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       614: 1
       615: q+1
       618: 1
       619: q+1
       622: 1
       624: 1
       626: 1
       630: 1
       632: q+1
       634: 1
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: 1
       650: 1
       652: 2
       654: 1
       656: 1
       665: 3q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: q+1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       699: 1
       703: 1
       710: q+1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 2
       763: 1
       766: 1
       773: 1
       774: 1
       782: q+1
       785: q+1
       788: q+1
       792: 1
       798: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       815: 1
       822: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       840: 1
       845: 1
       848: 1
       850: 1
       852: 1
       858: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       894: 1
       903: 1
       905: 1
       909: 1
       921: 1
       929: 1
       947: 1
       951: 1
       962: 1
       976: 1
       989: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1023: 1
      1026: 1
      1039: 1
      1045: 1
      1049: 1
      1052: 1
      1059: 1
      1078: 1
      1082: 1
      1128: 1
      1136: 1
      1157: 1
      1175: 1
      1200: 1
      1221: 1
      1240: 1
      1261: 1
      1332: 1

1333:    0: q^3+9q^2+7q+1
         1: q^4+4q^3+9q^2+7q+1
         2: q^3+9q^2+7q+1
         3: 3q^3+9q^2+7q+1
         4: q^3+9q^2+7q+1
         5: 3q^3+9q^2+7q+1
         6: q^4+4q^3+9q^2+7q+1
         7: q^3+9q^2+7q+1
         8: 3q^3+9q^2+7q+1
         9: q^4+4q^3+6q^2+4q+1
        10: q^3+7q^2+7q+1
        11: q^3+7q^2+7q+1
        12: q^3+7q^2+7q+1
        13: q^3+9q^2+7q+1
        14: q^3+9q^2+7q+1
        15: 3q^3+9q^2+7q+1
        16: 6q^2+7q+1
        17: q^3+6q^2+7q+1
        18: q^3+6q^2+4q+1
        19: q^3+9q^2+7q+1
        20: q^4+4q^3+9q^2+7q+1
        21: q^3+9q^2+7q+1
        22: 6q^2+7q+1
        23: q^3+6q^2+7q+1
        24: 6q^2+7q+1
        25: 6q^2+7q+1
        26: q^3+6q^2+7q+1
        27: 6q^2+7q+1
        28: 4q^2+7q+1
        29: q^3+7q^2+7q+1
        30: q^3+9q^2+7q+1
        31: 4q^2+7q+1
        32: 6q^2+7q+1
        33: 4q^2+7q+1
        34: 4q^2+7q+1
        35: 6q^2+7q+1
        36: 4q^2+7q+1
        37: q^2+2q
        38: 3q^2+5q+1
        39: q^2+2q
        40: 3q^2+5q+1
        41: q^2+2q
        42: 3q^2+5q+1
        43: q^3+7q^2+7q+1
        44: q^3+7q^2+7q+1
        45: q^3+7q^2+7q+1
        46: 6q^2+7q+1
        47: q^3+6q^2+7q+1
        48: q^3+6q^2+4q+1
        49: 6q^2+7q+1
        50: q^3+6q^2+7q+1
        51: q^3+6q^2+4q+1
        52: 6q^2+7q+1
        53: q^3+6q^2+7q+1
        54: 6q^2+7q+1
        55: 6q^2+7q+1
        56: q^3+6q^2+7q+1
        57: 6q^2+7q+1
        58: 2q^2+5q+1
        59: 2q
        60: 2q
        61: 2q^2+5q+1
        62: 2q
        63: 2q^2+5q+1
        64: q^2+2q
        65: 3q^2+5q+1
        66: q^2+2q
        67: 2q^2+5q+1
        68: 4q^2+7q+1
        69: 3q^2+4q+1
        70: q^3+7q^2+7q+1
        71: 4q^2+7q+1
        72: 4q^2+7q+1
        73: 4q^2+7q+1
        74: q^2+2q
        75: 3q^2+5q+1
        76: q^2+2q
        77: 3q^2+5q+1
        78: q^2+2q
        79: 3q^2+5q+1
        80: 4q^2+7q+1
        81: 4q^2+7q+1
        82: 4q^2+7q+1
        83: 6q^2+7q+1
        84: 4q^2+7q+1
        85: 4q^2+7q+1
        86: 4q^2+7q+1
        87: 6q^2+7q+1
        88: 2q^2+7q+1
        89: 2q^2+7q+1
        90: q^3+4q^2+4q+1
        91: 6q^2+7q+1
        92: q^3+6q^2+7q+1
        93: q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q
       104: q
       105: q^2+4q+1
       106: q
       107: 2q
       108: 2q^2+5q+1
       109: 2q^2+5q+1
       110: 2q
       111: q^2+2q
       112: 2q^2+5q+1
       113: 2q
       114: 2q^2+5q+1
       115: q^2+2q
       116: 3q^2+5q+1
       117: 2q^2+5q+1
       118: 2q
       119: 2q
       120: 2q^2+5q+1
       121: 2q
       122: 2q^2+5q+1
       123: q^2+2q
       124: 2q^2+5q+1
       125: 2q^2+7q+1
       126: q^2+4q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 4q^2+7q+1
       134: 3q^2+4q+1
       135: 4q^2+7q+1
       136: 4q^2+7q+1
       137: q^2+7q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+7q+1
       142: 2q^2+6q+1
       143: q^2+7q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+7q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: 2q
       152: q^2+4q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: 2q
       156: q^2+4q+1
       157: 2q^2+7q+1
       158: 2q^2+7q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q
       171: q^2+4q+1
       172: q
       173: q
       174: q
       175: q^2+4q+1
       176: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: 2q
       184: 2q^2+5q+1
       185: 2q^2+5q+1
       186: 2q
       187: q^2+2q
       188: 2q^2+5q+1
       189: 2q
       190: 2q^2+5q+1
       191: q^2+5q+1
       192: 2q
       194: 3q+1
       195: q^2+4q+1
       196: 2q
       197: q
       198: 2q+1
       199: 2q
       200: q^2+5q+1
       201: 2q
       202: q^2+4q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+5q+1
       209: 2q
       210: q^2+4q+1
       211: 2q
       212: q^2+4q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+7q+1
       221: q^2+4q+1
       222: q^2+7q+1
       223: q^2+4q+1
       224: q^2+7q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: q^2+6q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       260: q
       261: 2q+1
       263: q
       264: q
       265: q^2+4q+1
       266: q
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       275: q
       276: q
       277: q^2+4q+1
       278: q
       280: 3q+1
       282: 2q+1
       284: 2q+1
       285: 2q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: 2q
       294: q^2+5q+1
       295: q^2+5q+1
       296: 2q
       297: 2q
       298: q^2+5q+1
       300: 3q+1
       302: 1
       303: q^2+4q+1
       304: 2q
       305: q
       306: 2q+1
       307: 2q
       308: q^2+4q+1
       309: 3q+1
       312: 1
       313: q
       314: 2q+1
       316: q+1
       318: q+1
       320: q+1
       321: q+1
       324: 1
       325: 2q
       326: q^2+4q+1
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 3q+1
       339: q+1
       341: q+1
       343: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       382: q
       383: 2q+1
       385: q
       386: q
       387: q^2+4q+1
       388: q
       392: 1
       395: 2q+1
       396: q
       398: 1
       401: q
       402: 2q+1
       408: 1
       414: 2q+1
       418: 2q+1
       420: 2q+1
       421: 2q+1
       424: 2q+1
       426: q+1
       428: q+1
       430: q+1
       431: 2q+1
       434: 1
       436: 1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: q+1
       446: 1
       448: 2q+1
       449: q+1
       452: 1
       453: q
       454: 2q+1
       456: 1
       457: q+1
       460: q+1
       461: q+1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       472: q+1
       473: q+1
       476: 1
       478: 2
       480: 1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 3q+1
       486: q+1
       488: q+1
       490: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       523: q+1
       531: q+1
       535: 1
       540: 1
       544: q+1
       548: 1
       550: 1
       554: 1
       558: q+1
       562: 1
       567: 1
       572: 2
       576: 1
       581: 1
       582: 1
       586: 2q+1
       590: 2q+1
       591: q+1
       594: q+1
       595: 2q+1
       598: q+1
       600: q+1
       602: q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       614: 1
       616: q+1
       618: 1
       620: q+1
       621: 1
       624: 1
       626: 1
       630: 1
       631: q+1
       634: 1
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: 1
       649: 1
       652: 2
       654: 1
       656: 1
       665: 3q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: q+1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       700: 1
       704: 1
       711: q+1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 2
       764: 1
       767: 1
       773: 1
       774: 1
       782: q+1
       786: q+1
       787: q+1
       792: 1
       798: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       816: 1
       822: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       839: 1
       846: 1
       847: 1
       850: 1
       852: 1
       858: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       891: 1
       895: 1
       901: 1
       907: 1
       910: 1
       923: 1
       931: 1
       945: 1
       949: 1
       963: 1
       977: 1
       990: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1023: 1
      1027: 1
      1039: 1
      1044: 1
      1049: 1
      1053: 1
      1058: 1
      1078: 1
      1082: 1
      1129: 1
      1137: 1
      1159: 1
      1173: 1
      1201: 1
      1221: 1
      1241: 1
      1260: 1
      1333: 1

1334:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+1
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: q^2+2q+2
        29: q^2+2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: q^2+2q+1
        43: q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: q+1
        66: 2q+2
        69: q+1
        70: q+1
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: q^2+2q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: q+1
        89: q^2+q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 2q+2
       115: q+1
       121: q+1
       123: q+1
       126: q+1
       127: 2q+2
       129: 2q+2
       131: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       151: q+2
       153: q+2
       155: q+1
       157: q+1
       158: q^2+q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: q+1
       172: q+1
       177: q+1
       179: 2q+2
       181: 2q+2
       187: q+1
       189: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: q+1
       209: q+2
       211: 1
       213: q+1
       215: q+1
       217: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q+1
       262: q+1
       267: 1
       269: 1
       271: 1
       273: 1
       281: q+1
       287: q+1
       289: q+1
       291: q+1
       297: q+1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: q+1
       329: q+1
       331: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       338: q+2
       340: q+2
       342: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       360: 1
       362: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: q+1
       415: q+1
       417: q+1
       423: q+1
       425: 1
       427: q+2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       475: 1
       477: 2
       479: 2
       483: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       587: q+1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       645: 1
       651: 1
       653: 1
       655: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       666: 1
       668: q+1
       670: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: 1
       697: 1
       769: 1
       779: 1
       783: 1
       791: 1
       795: 1
       799: 1
       809: 1
       811: 1
       813: 1
       819: 1
       823: 1
       833: 1
       835: 1
       837: 1
       843: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: q+1
       863: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       968: 1
       982: 1
       996: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1020: 1
      1024: 1
      1030: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1077: 1
      1081: 1
      1138: 1
      1188: 1
      1222: 1
      1224: 1
      1236: 1
      1252: 1
      1334: 1

1335:    0: 3q^3+10q^2+6q
         1: 3q^3+10q^2+6q
         2: 5q^3+8q^2+3q
         3: 4q^3+10q^2+6q
         4: 3q^3+10q^2+6q
         5: 4q^3+10q^2+6q
         6: 3q^3+10q^2+6q
         7: 5q^3+8q^2+3q
         8: 2q^4+7q^3+8q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: 3q^3+10q^2+6q
        11: 4q^3+10q^2+6q
        12: 3q^3+10q^2+6q
        13: 5q^2+3q
        14: 5q^2+3q
        15: 2q^3+5q^2+3q
        16: q^3+8q^2+6q
        17: q^3+8q^2+6q
        18: 3q^3+5q^2+2q
        19: 3q^3+10q^2+6q
        20: 3q^3+10q^2+6q
        21: 5q^3+8q^2+3q
        22: q^3+8q^2+6q
        23: q^3+8q^2+6q
        24: 4q^3+7q^2+3q
        25: q^3+8q^2+6q
        26: q^3+8q^2+6q
        27: 4q^3+7q^2+3q
        28: q^3+8q^2+6q
        29: 3q^3+10q^2+6q
        30: 5q^2+3q
        31: q^3+8q^2+6q
        32: 4q^2+3q
        33: 6q^2+6q
        34: q^3+8q^2+6q
        35: 4q^2+3q
        36: 6q^2+6q
        37: 2q^2+2q
        38: 4q^2+4q
        39: 2q^2+2q
        40: 4q^2+4q
        41: q^3+2q^2+q
        42: 2q^3+4q^2+2q
        43: 5q^2+3q
        44: 5q^2+3q
        45: 2q^3+5q^2+3q
        46: 4q^2+3q
        47: q^3+4q^2+3q
        48: 3q^2+2q
        49: q^3+8q^2+6q
        50: q^3+8q^2+6q
        51: 3q^3+5q^2+2q
        52: q^3+8q^2+6q
        53: q^3+8q^2+6q
        54: 4q^3+7q^2+3q
        55: q^3+8q^2+6q
        56: q^3+8q^2+6q
        57: 4q^3+7q^2+3q
        58: 3q^2+3q
        59: 3q^2+3q
        60: 3q^2+3q
        61: 3q^2+3q
        62: 2q^2+2q
        63: 4q^2+4q
        64: q^2+q
        65: 2q^2+2q
        66: 2q^2+2q
        67: 2q^2+4q
        69: 2q^2+2q
        70: 5q^2+3q
        71: q^3+8q^2+6q
        72: 6q^2+6q
        73: 6q^2+6q
        74: 2q^2+2q
        75: 4q^2+4q
        76: 2q^2+2q
        77: 4q^2+4q
        78: q^3+2q^2+q
        79: 2q^3+4q^2+2q
        80: 4q^2+3q
        81: 3q^2+3q
        82: q^3+8q^2+6q
        83: 4q^2+3q
        84: 4q^2+3q
        85: 3q^2+3q
        86: q^3+8q^2+6q
        87: 4q^2+3q
        88: 4q^2+3q
        89: q^3+4q^2+3q
        90: 3q^2+2q
        91: 4q^2+3q
        92: q^3+4q^2+3q
        93: 3q^2+2q
        94: 4q^2+6q
        95: 4q^2+6q
        96: 2q^3+4q^2+2q
        97: 4q^2+6q
        98: 4q^2+6q
        99: 2q^3+4q^2+2q
       100: 4q^2+6q
       101: 4q^2+6q
       102: q^3+4q^2+3q
       103: q^2+q
       104: q^2+2q
       105: q^2+2q
       106: q^2+q
       107: 3q^2+3q
       108: 3q^2+3q
       109: 3q^2+3q
       110: 3q^2+3q
       111: 2q^2+2q
       112: 2q^2+4q
       113: 2q^2+2q
       114: 4q^2+4q
       115: q^2+q
       116: 2q^2+2q
       121: q^2+q
       122: 2q^2+2q
       123: q^2+q
       124: q^2+2q
       126: 2q^2+2q
       128: 4q
       130: 4q
       132: q^3+2q^2+q
       134: 2q^2+2q
       135: 3q^2+3q
       136: 3q^2+3q
       137: 3q^2+3q
       138: q^2+2q
       139: 4q^2+6q
       140: 4q
       141: 4q^2+3q
       142: 4q^2+6q
       143: 3q^2+3q
       144: q^2+2q
       145: 4q^2+6q
       146: 4q^2+3q
       147: 4q^2+6q
       148: 4q
       149: 4q^2+6q
       150: q^2+3q
       151: q^2+2q
       152: 3q^2+4q
       153: q^2+2q
       154: 3q^2+4q
       155: q^2+q
       156: q^3+3q^2+2q
       157: 4q^2+3q
       158: q^3+4q^2+3q
       159: 3q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: q^2+6q
       167: q^2+6q
       168: 2q^2+2q
       169: q^2+q
       170: q^2+2q
       171: q^2+2q
       172: q^2+q
       178: q
       180: 4q
       182: 4q
       187: q^2+q
       188: q^2+2q
       189: q^2+q
       190: 2q^2+2q
       193: 2q
       194: 2q
       195: 2q^2+3q
       196: 2q^2+3q
       197: 2q
       198: 2q
       201: 2q^2+3q
       202: 2q^2+3q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: q^2+q
       208: q^2+2q
       209: q^2+2q
       210: 3q^2+4q
       211: q
       212: q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       221: 2q^2+2q
       222: 3q^2+3q
       223: q^2+2q
       224: 3q^2+3q
       225: q^2+2q
       226: q^2+2q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^2+2q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 2q
       238: 4q
       240: 4q
       242: q^2+q
       243: q^2+6q
       244: 4q
       245: 4q
       246: q^2+3q
       247: q^2+6q
       248: q^2+6q
       249: 2q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 3q
       257: q^2+3q
       258: 2q
       260: 2q
       261: 2q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       282: q
       288: q
       290: 2q
       292: q
       297: q^2+q
       298: q^2+2q
       302: 2q
       305: q
       306: q
       312: 2q
       313: q
       314: q
       316: q
       318: 4q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       325: q
       326: q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: q^2+6q
       339: 4q
       341: 4q
       343: q^2+q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 4q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 4q
       361: 2q
       363: 2q
       365: q
       366: 2q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: q^2+3q
       373: 2q
       374: 3q
       375: q^2+3q
       376: 2q
       390: q
       392: q
       398: q
       400: q
       405: q
       406: q
       412: q
       416: 2q
       418: q
       424: q
       426: q
       428: 4q
       436: q
       441: q
       442: q
       443: 2q
       444: 2q
       446: 2q
       456: q
       459: q
       460: q
       461: 2q
       462: 2q
       464: 2q
       468: q
       470: q
       475: q
       479: 2q
       483: 2q
       486: 2q
       488: 2q
       490: q
       491: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       503: 2q
       505: 2q
       507: q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: q^2+3q
       520: 2q
       546: q
       548: q
       562: q
       564: q
       573: q
       575: q
       588: q
       598: q
       600: q
       612: q
       618: q
       628: q
       634: q
       638: q
       653: q
       655: q
       659: 1
       661: q+1
       663: 1
       664: 1
       667: 2q
       669: 2q
       671: q
       673: 2q
       674: 1
       677: q
       678: 2q
       679: q
       680: 1
       683: q
       684: 2q
       685: q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       780: 1
       784: q
       796: 1
       814: q
       820: 1
       838: q
       843: 1
       857: q
       860: 1
       862: q+1
       864: 1
       867: 1
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       969: 1
       997: 1
      1012: 1
      1015: 1
      1021: 1
      1031: 1
      1037: 1
      1046: 1
      1077: 1
      1081: 1
      1139: 1
      1189: 1
      1224: 1
      1237: 1
      1253: 1
      1335: 1

1336:    0: q^3+2q^2+2q
         1: q^3+2q^2+2q
         2: q^4+q^2+q
         3: q^3+2q^2+2q
         4: q^3+2q^2+2q
         5: q^3+2q^2+2q
         6: q^3+2q^2+2q
         7: q^4+q^2+q
         8: q^2+q
         9: q^4+q^2+q
        10: q^3+2q^2+2q
        11: q^3+2q^2+2q
        12: q^3+2q^2+2q
        13: q
        14: q
        15: q
        16: q^3+2q^2+2q
        17: q^3+2q^2+2q
        18: q^4+q^2+q
        19: q^3+2q^2+2q
        20: q^3+2q^2+2q
        21: q^4+q^2+q
        22: 2q^2+2q
        23: 2q^2+2q
        24: q^2+q
        25: 2q^2+2q
        26: 2q^2+2q
        27: q^2+q
        28: q^3+2q^2+2q
        29: q^3+2q^2+2q
        30: q
        31: 2q^2+2q
        32: q
        33: 2q^2+2q
        34: 2q^2+2q
        35: q
        36: 2q^2+2q
        37: 2q^2+2q
        39: 2q^2+2q
        41: q^2+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q
        49: q^3+2q^2+2q
        50: q^3+2q^2+2q
        51: q^4+q^2+q
        52: 2q^2+2q
        53: 2q^2+2q
        54: q^2+q
        55: 2q^2+2q
        56: 2q^2+2q
        57: q^2+q
        58: q^2+q
        59: q^2+q
        60: q^2+q
        61: q^2+q
        62: 2q^2+2q
        64: q
        66: 2q^2+2q
        69: q
        70: q
        71: q^3+2q^2+2q
        72: 2q^2+2q
        73: 2q^2+2q
        74: 2q^2+2q
        76: 2q^2+2q
        78: q^2+q
        80: q
        81: q
        82: 2q^2+2q
        83: q
        84: q
        85: q
        86: 2q^2+2q
        87: q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q
        94: 2q^2+2q
        95: 2q^2+2q
        96: q^2+q
        97: 2q^2+2q
        98: 2q^2+2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       103: q^2+q
       106: q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       111: 2q^2+2q
       113: 2q^2+2q
       115: q
       121: q
       123: q
       126: q
       127: 2q^2+2q
       129: 2q^2+2q
       131: q^2+q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: 2q^2+2q
       140: 2q
       141: q
       142: 2q^2+2q
       143: q
       144: q
       145: 2q^2+2q
       146: q
       147: 2q^2+2q
       148: 2q
       149: q^2+2q
       150: q
       151: q^2+2q
       153: q^2+2q
       155: q^2+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       169: q^2+q
       172: q^2+q
       177: q
       179: 2q^2+2q
       181: 2q^2+2q
       187: q
       189: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       197: 2q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       205: 2q
       207: q
       209: q^2+2q
       211: q
       213: q
       215: q
       217: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       259: q^2+q
       262: q^2+q
       267: q
       269: q
       271: q
       273: q
       281: q
       287: q
       289: q
       291: q
       297: q
       301: 2q
       305: q
       311: 2q
       313: q
       315: q
       317: q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: 2q
       325: q
       327: q
       329: q
       331: q
       334: q
       335: q
       336: q
       337: q^2+2q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: 2q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: 2q
       366: q
       389: q
       391: q
       397: q
       399: q
       405: q
       406: q
       411: q
       415: q
       417: q
       423: q
       425: q
       427: q^2+2q
       433: q
       441: q
       443: q
       444: q
       445: 2q
       451: q
       459: q
       461: q
       462: q
       463: 2q
       469: q
       477: 2q
       479: 2q
       483: q
       493: q
       494: q
       495: q
       498: q
       499: q
       500: q
       545: q
       547: q
       561: q
       563: q
       569: q
       570: q
       573: q
       575: q
       577: 2q
       587: q
       599: q
       609: q
       613: q
       625: q
       629: q
       651: 1
       677: q
       683: q
       693: q
       697: q
       771: 1
       811: q
       835: q
       849: 1
       853: 1
       970: 1
       984: 1
      1010: 1
      1050: 1
      1140: 1
      1190: 1
      1222: 1
      1336: 1

1337:    0: 3q^3+10q^2+6q
         1: 3q^3+10q^2+6q
         2: 5q^3+8q^2+3q
         3: 4q^3+10q^2+6q
         4: 3q^3+10q^2+6q
         5: 4q^3+10q^2+6q
         6: 3q^3+10q^2+6q
         7: 5q^3+8q^2+3q
         8: 2q^4+7q^3+8q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: 3q^3+10q^2+6q
        11: 4q^3+10q^2+6q
        12: 3q^3+10q^2+6q
        13: 5q^2+3q
        14: 5q^2+3q
        15: 2q^3+5q^2+3q
        16: q^3+8q^2+6q
        17: q^3+8q^2+6q
        18: 3q^3+5q^2+2q
        19: 3q^3+10q^2+6q
        20: 3q^3+10q^2+6q
        21: 5q^3+8q^2+3q
        22: q^3+8q^2+6q
        23: q^3+8q^2+6q
        24: 4q^3+7q^2+3q
        25: q^3+8q^2+6q
        26: q^3+8q^2+6q
        27: 4q^3+7q^2+3q
        28: q^3+8q^2+6q
        29: 3q^3+10q^2+6q
        30: 5q^2+3q
        31: q^3+8q^2+6q
        32: 4q^2+3q
        33: 6q^2+6q
        34: q^3+8q^2+6q
        35: 4q^2+3q
        36: 6q^2+6q
        37: 4q^2+4q
        38: 2q^2+2q
        39: 4q^2+4q
        40: 2q^2+2q
        41: 2q^3+4q^2+2q
        42: q^3+2q^2+q
        43: 5q^2+3q
        44: 5q^2+3q
        45: 2q^3+5q^2+3q
        46: 4q^2+3q
        47: q^3+4q^2+3q
        48: 3q^2+2q
        49: q^3+8q^2+6q
        50: q^3+8q^2+6q
        51: 3q^3+5q^2+2q
        52: q^3+8q^2+6q
        53: q^3+8q^2+6q
        54: 4q^3+7q^2+3q
        55: q^3+8q^2+6q
        56: q^3+8q^2+6q
        57: 4q^3+7q^2+3q
        58: 3q^2+3q
        59: 3q^2+3q
        60: 3q^2+3q
        61: 3q^2+3q
        62: 4q^2+4q
        63: 2q^2+2q
        64: 2q^2+2q
        65: q^2+q
        66: 2q^2+4q
        67: 2q^2+2q
        69: 2q^2+2q
        70: 5q^2+3q
        71: q^3+8q^2+6q
        72: 6q^2+6q
        73: 6q^2+6q
        74: 4q^2+4q
        75: 2q^2+2q
        76: 4q^2+4q
        77: 2q^2+2q
        78: 2q^3+4q^2+2q
        79: q^3+2q^2+q
        80: 4q^2+3q
        81: 3q^2+3q
        82: q^3+8q^2+6q
        83: 4q^2+3q
        84: 4q^2+3q
        85: 3q^2+3q
        86: q^3+8q^2+6q
        87: 4q^2+3q
        88: 4q^2+3q
        89: q^3+4q^2+3q
        90: 3q^2+2q
        91: 4q^2+3q
        92: q^3+4q^2+3q
        93: 3q^2+2q
        94: 4q^2+6q
        95: 4q^2+6q
        96: 2q^3+4q^2+2q
        97: 4q^2+6q
        98: 4q^2+6q
        99: 2q^3+4q^2+2q
       100: 4q^2+6q
       101: 4q^2+6q
       102: q^3+4q^2+3q
       103: q^2+2q
       104: q^2+q
       105: q^2+q
       106: q^2+2q
       107: 3q^2+3q
       108: 3q^2+3q
       109: 3q^2+3q
       110: 3q^2+3q
       111: 2q^2+4q
       112: 2q^2+2q
       113: 4q^2+4q
       114: 2q^2+2q
       115: 2q^2+2q
       116: q^2+q
       121: 2q^2+2q
       122: q^2+q
       123: q^2+2q
       124: q^2+q
       126: 2q^2+2q
       127: 4q
       129: 4q
       131: q^3+2q^2+q
       134: 2q^2+2q
       135: 3q^2+3q
       136: 3q^2+3q
       137: 3q^2+3q
       138: q^2+2q
       139: 4q^2+6q
       140: 4q
       141: 4q^2+3q
       142: 4q^2+6q
       143: 3q^2+3q
       144: q^2+2q
       145: 4q^2+6q
       146: 4q^2+3q
       147: 4q^2+6q
       148: 4q
       149: 4q^2+6q
       150: q^2+3q
       151: 3q^2+4q
       152: q^2+2q
       153: 3q^2+4q
       154: q^2+2q
       155: q^3+3q^2+2q
       156: q^2+q
       157: 4q^2+3q
       158: q^3+4q^2+3q
       159: 3q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: q^2+6q
       167: q^2+6q
       168: 2q^2+2q
       169: q^2+2q
       170: q^2+q
       171: q^2+q
       172: q^2+2q
       177: q
       179: 4q
       181: 4q
       187: q^2+2q
       188: q^2+q
       189: 2q^2+2q
       190: q^2+q
       193: 2q
       194: 2q
       195: 2q^2+3q
       196: 2q^2+3q
       197: 2q
       198: 2q
       201: 2q^2+3q
       202: 2q^2+3q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: q^2+2q
       208: q^2+q
       209: 3q^2+4q
       210: q^2+2q
       211: q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       221: 2q^2+2q
       222: 3q^2+3q
       223: q^2+2q
       224: 3q^2+3q
       225: q^2+2q
       226: q^2+2q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^2+2q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 2q
       237: 4q
       239: 4q
       241: q^2+q
       243: q^2+6q
       244: 4q
       245: 4q
       246: q^2+3q
       247: q^2+6q
       248: q^2+6q
       249: 2q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 3q
       257: q^2+3q
       258: 2q
       259: 2q
       262: 2q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       281: q
       287: q
       289: 2q
       291: q
       297: q^2+2q
       298: q^2+q
       301: 2q
       305: q
       306: q
       311: 2q
       313: q
       314: q
       315: q
       317: 4q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       324: 2q
       325: q^2+2q
       326: q
       327: 2q
       329: 2q
       331: q^2+q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: q^2+6q
       338: 4q
       340: 4q
       342: q^2+q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 4q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 4q
       360: 2q
       362: 2q
       364: q
       366: 2q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: q^2+3q
       373: 2q
       374: 3q
       375: q^2+3q
       376: 2q
       389: q
       391: q
       397: q
       399: q
       407: q
       408: q
       411: q
       415: 2q
       417: q
       423: q
       425: q
       427: 4q
       435: q
       441: q
       442: q
       443: 2q
       444: 2q
       445: 2q
       455: q
       459: q
       460: q
       461: 2q
       462: 2q
       463: 2q
       467: q
       469: q
       476: q
       480: 2q
       483: 2q
       485: 2q
       487: 2q
       489: q
       491: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       502: 2q
       504: 2q
       506: q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: q^2+3q
       520: 2q
       545: q
       547: q
       561: q
       563: q
       574: q
       576: q
       587: q
       597: q
       599: q
       611: q
       617: q
       627: q
       633: q
       637: q
       654: q
       656: q
       658: 1
       660: q+1
       662: 1
       664: 1
       666: 2q
       668: 2q
       670: q
       673: 2q
       674: 1
       677: q
       678: 2q
       679: q
       680: 1
       683: q
       684: 2q
       685: q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       779: 1
       783: q
       795: 1
       813: q
       819: 1
       837: q
       844: 1
       858: q
       859: 1
       861: q+1
       863: 1
       867: 1
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       971: 1
       996: 1
      1013: 1
      1014: 1
      1020: 1
      1030: 1
      1036: 1
      1047: 1
      1077: 1
      1081: 1
      1141: 1
      1191: 1
      1225: 1
      1236: 1
      1252: 1
      1337: 1

1338:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+1
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: q+1
        14: q+1
        15: q^2+q+1
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+1
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+1
        22: 2q+2
        23: 2q+2
        24: q^2+2q+1
        25: 2q+2
        26: 2q+2
        27: q^2+2q+1
        28: q^2+2q+2
        29: q^2+2q+2
        30: q+1
        31: 2q+2
        32: q+1
        33: 2q+2
        34: 2q+2
        35: q+1
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q+1
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+1
        52: 2q+2
        53: 2q+2
        54: q^2+2q+1
        55: 2q+2
        56: 2q+2
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: q+1
        67: 2q+2
        69: q+1
        70: q+1
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 2q+2
        83: q+1
        84: q+1
        85: q+1
        86: 2q+2
        87: q+1
        88: q+1
        89: q^2+q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+1
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 2q+2
       116: q+1
       122: q+1
       124: q+1
       126: q+1
       128: 2q+2
       130: 2q+2
       132: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 2q+2
       140: 2
       141: q+1
       142: 2q+2
       143: q+1
       144: q+1
       145: 2q+2
       146: q+1
       147: 2q+2
       148: 2
       149: q+2
       150: 1
       152: q+2
       154: q+2
       156: q+1
       157: q+1
       158: q^2+q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: q+1
       171: q+1
       178: q+1
       180: 2q+2
       182: 2q+2
       188: q+1
       190: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: q+1
       210: q+2
       212: 1
       214: q+1
       216: q+1
       218: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q+1
       261: q+1
       268: 1
       270: 1
       272: 1
       274: 1
       282: q+1
       288: q+1
       290: q+1
       292: q+1
       298: q+1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: q+1
       330: q+1
       332: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       339: q+2
       341: q+2
       343: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2
       361: 1
       363: q+1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: q+1
       416: q+1
       418: q+1
       424: q+1
       426: 1
       428: q+2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       476: 1
       478: 2
       480: 2
       483: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       588: q+1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       646: 1
       652: 1
       654: 1
       656: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       667: 1
       669: q+1
       671: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: 1
       700: 1
       773: 1
       780: 1
       784: 1
       792: 1
       796: 1
       800: 1
       810: 1
       812: 1
       814: 1
       820: 1
       824: 1
       834: 1
       836: 1
       838: 1
       844: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: q+1
       864: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       972: 1
       986: 1
       997: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1021: 1
      1025: 1
      1031: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1077: 1
      1081: 1
      1142: 1
      1192: 1
      1223: 1
      1225: 1
      1237: 1
      1253: 1
      1338: 1

1339:    0: q^3+2q^2+2q
         1: q^3+2q^2+2q
         2: q^4+q^2+q
         3: q^3+2q^2+2q
         4: q^3+2q^2+2q
         5: q^3+2q^2+2q
         6: q^3+2q^2+2q
         7: q^4+q^2+q
         8: q^2+q
         9: q^4+q^2+q
        10: q^3+2q^2+2q
        11: q^3+2q^2+2q
        12: q^3+2q^2+2q
        13: q
        14: q
        15: q
        16: q^3+2q^2+2q
        17: q^3+2q^2+2q
        18: q^4+q^2+q
        19: q^3+2q^2+2q
        20: q^3+2q^2+2q
        21: q^4+q^2+q
        22: 2q^2+2q
        23: 2q^2+2q
        24: q^2+q
        25: 2q^2+2q
        26: 2q^2+2q
        27: q^2+q
        28: q^3+2q^2+2q
        29: q^3+2q^2+2q
        30: q
        31: 2q^2+2q
        32: q
        33: 2q^2+2q
        34: 2q^2+2q
        35: q
        36: 2q^2+2q
        38: 2q^2+2q
        40: 2q^2+2q
        42: q^2+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q
        49: q^3+2q^2+2q
        50: q^3+2q^2+2q
        51: q^4+q^2+q
        52: 2q^2+2q
        53: 2q^2+2q
        54: q^2+q
        55: 2q^2+2q
        56: 2q^2+2q
        57: q^2+q
        58: q^2+q
        59: q^2+q
        60: q^2+q
        61: q^2+q
        63: 2q^2+2q
        65: q
        67: 2q^2+2q
        69: q
        70: q
        71: q^3+2q^2+2q
        72: 2q^2+2q
        73: 2q^2+2q
        75: 2q^2+2q
        77: 2q^2+2q
        79: q^2+q
        80: q
        81: q
        82: 2q^2+2q
        83: q
        84: q
        85: q
        86: 2q^2+2q
        87: q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q
        94: 2q^2+2q
        95: 2q^2+2q
        96: q^2+q
        97: 2q^2+2q
        98: 2q^2+2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+q
       104: q^2+q
       105: q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       112: 2q^2+2q
       114: 2q^2+2q
       116: q
       122: q
       124: q
       126: q
       128: 2q^2+2q
       130: 2q^2+2q
       132: q^2+q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: 2q^2+2q
       140: 2q
       141: q
       142: 2q^2+2q
       143: q
       144: q
       145: 2q^2+2q
       146: q
       147: 2q^2+2q
       148: 2q
       149: q^2+2q
       150: q
       152: q^2+2q
       154: q^2+2q
       156: q^2+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       170: q^2+q
       171: q^2+q
       178: q
       180: 2q^2+2q
       182: 2q^2+2q
       188: q
       190: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       198: 2q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       206: 2q
       208: q
       210: q^2+2q
       212: q
       214: q
       216: q
       218: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       260: q^2+q
       261: q^2+q
       268: q
       270: q
       272: q
       274: q
       282: q
       288: q
       290: q
       292: q
       298: q
       302: 2q
       306: q
       312: 2q
       314: q
       316: q
       318: q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: 2q
       326: q
       328: q
       330: q
       332: q
       334: q
       335: q
       336: q
       337: q^2+2q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: 2q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: 2q
       366: q
       390: q
       392: q
       398: q
       400: q
       407: q
       408: q
       412: q
       416: q
       418: q
       424: q
       426: q
       428: q^2+2q
       434: q
       442: q
       443: q
       444: q
       446: 2q
       452: q
       460: q
       461: q
       462: q
       464: 2q
       470: q
       478: 2q
       480: 2q
       483: q
       493: q
       494: q
       495: q
       498: q
       499: q
       500: q
       546: q
       548: q
       562: q
       564: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       588: q
       600: q
       610: q
       614: q
       626: q
       630: q
       652: 1
       677: q
       683: q
       699: q
       700: q
       774: 1
       812: q
       836: q
       850: 1
       854: 1
       973: 1
       987: 1
      1011: 1
      1051: 1
      1143: 1
      1193: 1
      1223: 1
      1339: 1

1340:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^3+3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q^2+q+1
        59: q^3+q^2+2q
        60: q^2+q+1
        61: q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^3+3q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q^2+q+1
       106: q
       107: 1
       109: 1
       110: q
       111: 1
       113: q+1
       115: q+1
       117: 2q^2+q+1
       118: q^3+q^2+2q
       119: q^2+q+1
       120: q
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: 1
       136: q+1
       137: q^3+3q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: q^2+q+1
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       186: q
       187: 1
       189: q+1
       191: 2q^2+q+1
       192: q^3+q^2+2q
       193: 1
       195: 1
       196: q
       197: 1
       199: q^2+q+1
       200: q
       201: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       275: q^2+q+1
       278: q
       279: q+1
       281: q+1
       283: 1
       285: 1
       286: q
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       296: q
       297: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       315: q+1
       317: q+1
       319: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 1
       335: q+1
       337: 1
       338: 1
       340: 1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 1
       421: 1
       422: q
       423: 1
       427: 1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: 1
       445: 1
       447: 1
       453: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       481: 1
       482: q+1
       484: 1
       485: 1
       487: 1
       492: q^2+2q+1
       493: 1
       494: q+1
       496: 1
       497: q+1
       498: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       583: q+1
       585: 1
       587: 1
       589: 1
       595: 1
       596: q
       601: 1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       615: 1
       617: 1
       619: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       647: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: 1
       676: q+1
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       705: 1
       709: 1
       721: 1
       725: 1
       729: 1
       733: 1
       775: 1
       777: 1
       789: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       807: 1
       808: q
       813: 1
       815: 1
       825: 1
       841: q+1
       845: 1
       859: 1
       861: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       896: 1
       912: 1
       916: 1
       920: 1
       932: 1
       992: 1
      1014: 1
      1016: 1
      1018: 1
      1052: 1
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1144: 1
      1148: 1
      1210: 1
      1226: 1
      1228: 1
      1340: 1

1341:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^3+3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^3+q^2+2q
        59: 2q^2+q+1
        60: q^2+q+1
        61: q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^3+3q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q^2+q+1
       105: q
       107: 1
       109: q
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q^3+q^2+2q
       118: 2q^2+q+1
       119: q^2+q+1
       120: q
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: 1
       136: q+1
       137: q^3+3q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: q^2+q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: 1
       185: q
       186: 1
       188: 1
       190: q+1
       191: q^3+q^2+2q
       192: 2q^2+q+1
       193: 1
       195: q
       196: 1
       198: 1
       199: q^2+q+1
       200: q
       201: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       276: q^2+q+1
       277: q
       280: q+1
       282: q+1
       283: 1
       285: q
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       295: q
       296: 1
       298: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       316: q+1
       318: q+1
       319: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 1
       335: q+1
       337: 1
       339: 1
       341: 1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 1
       421: q
       422: 1
       424: 1
       428: 1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       453: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       481: 1
       482: q+1
       484: 1
       486: 1
       488: 1
       492: q^2+2q+1
       493: 1
       494: q+1
       496: 1
       497: q+1
       498: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       584: q+1
       586: 1
       588: 1
       589: 1
       595: q
       596: 1
       602: 1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       615: 1
       618: 1
       619: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       647: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: 1
       676: q+1
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       706: 1
       710: 1
       722: 1
       726: 1
       730: 1
       734: 1
       776: 1
       778: 1
       790: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       807: q
       808: 1
       814: 1
       815: 1
       825: 1
       842: q+1
       845: 1
       860: 1
       862: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       897: 1
       913: 1
       917: 1
       921: 1
       933: 1
       993: 1
      1015: 1
      1016: 1
      1019: 1
      1052: 1
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1145: 1
      1149: 1
      1211: 1
      1227: 1
      1228: 1
      1341: 1

1342:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^3+3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^3+q^2+2q
        59: 2q^2+q+1
        60: q
        61: q^2+q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^3+3q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: q^2+q+1
       108: 1
       109: q
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q^3+q^2+2q
       118: 2q^2+q+1
       119: q
       120: q^2+q+1
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: 1
       136: q+1
       137: q^3+3q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       173: q
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       185: q
       186: 1
       187: 1
       189: q+1
       191: q^3+q^2+2q
       192: 2q^2+q+1
       194: 1
       195: q
       196: 1
       197: 1
       199: q
       200: q^2+q+1
       202: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       275: q
       278: q^2+q+1
       279: q+1
       281: q+1
       284: 1
       285: q
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       295: q
       296: 1
       297: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       315: q+1
       317: q+1
       320: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: 1
       335: q+1
       337: 1
       338: 1
       340: 1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: 1
       421: q
       422: 1
       423: 1
       427: 1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       454: 1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       481: 1
       482: q+1
       484: 1
       485: 1
       487: 1
       492: q^2+2q+1
       493: 1
       494: q+1
       496: 1
       497: q+1
       498: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       583: q+1
       585: 1
       587: 1
       590: 1
       595: q
       596: 1
       601: 1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       616: 1
       617: 1
       620: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       648: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: 1
       676: q+1
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       708: 1
       712: 1
       723: 1
       727: 1
       731: 1
       735: 1
       775: 1
       777: 1
       789: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       807: q
       808: 1
       813: 1
       816: 1
       826: 1
       841: q+1
       846: 1
       859: 1
       861: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       899: 1
       914: 1
       918: 1
       922: 1
       934: 1
       992: 1
      1014: 1
      1017: 1
      1018: 1
      1053: 1
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1146: 1
      1150: 1
      1210: 1
      1226: 1
      1229: 1
      1342: 1

1343:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^3+3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q^2+q+1
        59: q^3+q^2+2q
        60: q
        61: q^2+q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^3+3q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: q^2+q+1
       108: 1
       109: 1
       110: q
       112: 1
       114: q+1
       116: q+1
       117: 2q^2+q+1
       118: q^3+q^2+2q
       119: q
       120: q^2+q+1
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: 1
       136: q+1
       137: q^3+3q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       174: q
       175: q^2+q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       186: q
       188: 1
       190: q+1
       191: 2q^2+q+1
       192: q^3+q^2+2q
       194: 1
       195: 1
       196: q
       198: 1
       199: q
       200: q^2+q+1
       202: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       246: q+1
       247: 1
       248: 1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       276: q
       277: q^2+q+1
       280: q+1
       282: q+1
       284: 1
       285: 1
       286: q
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       296: q
       298: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       316: q+1
       318: q+1
       320: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: 1
       335: q+1
       337: 1
       339: 1
       341: 1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: 1
       421: 1
       422: q
       424: 1
       428: 1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: 1
       446: 1
       448: 1
       454: 1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       481: 1
       482: q+1
       484: 1
       486: 1
       488: 1
       492: q^2+2q+1
       493: 1
       494: q+1
       496: 1
       497: q+1
       498: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       584: q+1
       586: 1
       588: 1
       590: 1
       595: 1
       596: q
       602: 1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       616: 1
       618: 1
       620: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       648: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: 1
       676: q+1
       678: 1
       681: 1
       686: q+1
       687: 1
       690: 1
       691: 1
       707: 1
       711: 1
       724: 1
       728: 1
       732: 1
       736: 1
       776: 1
       778: 1
       790: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       807: 1
       808: q
       814: 1
       816: 1
       826: 1
       842: q+1
       846: 1
       860: 1
       862: 1
       865: 1
       869: 1
       877: 1
       881: 1
       882: 1
       898: 1
       915: 1
       919: 1
       923: 1
       935: 1
       993: 1
      1015: 1
      1017: 1
      1019: 1
      1053: 1
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1147: 1
      1151: 1
      1211: 1
      1227: 1
      1229: 1
      1343: 1

1344:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: q^4+13q^3+21q^2+8q+1
        23: q^4+13q^3+21q^2+8q+1
        24: 3q^4+11q^3+16q^2+7q+1
        25: 7q^3+17q^2+8q+1
        26: 7q^3+17q^2+8q+1
        27: q^4+7q^3+13q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: q^4+13q^3+21q^2+8q+1
        32: 6q^3+15q^2+7q+1
        33: 7q^3+18q^2+8q+1
        34: 7q^3+17q^2+8q+1
        35: 3q^3+12q^2+7q+1
        36: 3q^3+14q^2+8q+1
        37: 5q^3+13q^2+7q+1
        38: 2q^3+4q^2+q
        39: 5q^3+13q^2+7q+1
        40: 2q^3+4q^2+q
        41: q^4+5q^3+10q^2+6q+1
        42: 2q^3+3q^2+q
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: q^4+8q^3+15q^2+7q+1
        53: q^4+8q^3+15q^2+7q+1
        54: q^4+6q^3+11q^2+6q+1
        55: 3q^3+11q^2+7q+1
        56: 3q^3+11q^2+7q+1
        57: 3q^3+8q^2+6q+1
        58: 4q^3+11q^2+6q+1
        59: 3q^3+7q^2+2q
        60: 2q^3+8q^2+5q+1
        61: q^3+6q^2+3q
        62: 5q^3+13q^2+7q+1
        63: 2q^3+4q^2+q
        64: 2q^3+9q^2+6q+1
        65: q^3+3q^2+q
        66: 3q^3+11q^2+7q+1
        67: 3q^2+q
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: 6q^2+6q+1
        73: q^3+7q^2+6q+1
        74: q^3+7q^2+6q+1
        76: q^3+7q^2+6q+1
        78: q^3+5q^2+5q+1
        80: 6q^3+15q^2+7q+1
        81: 2q^3+12q^2+7q+1
        82: q^4+8q^3+15q^2+7q+1
        83: 3q^3+10q^2+6q+1
        84: 3q^3+12q^2+7q+1
        85: q^3+9q^2+7q+1
        86: 3q^3+11q^2+7q+1
        87: q^3+7q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 3q^3+12q^2+7q+1
        95: 3q^3+12q^2+7q+1
        96: 3q^3+6q^2+4q+1
        97: 7q^2+7q+1
        98: 7q^2+7q+1
        99: q^3+4q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: 2q^3+7q^2+5q+1
       104: q^2
       105: 2q^2+q
       106: q^3+4q^2+2q
       107: 3q^2+4q+1
       108: 3q^2+2q
       109: q^3+5q^2+5q+1
       110: 2q^2+q
       111: 3q^2+5q+1
       113: q^3+7q^2+6q+1
       115: 4q^2+5q+1
       117: 5q^2+5q+1
       118: 2q^2+q
       119: 3q^2+4q+1
       120: 2q^2+2q
       121: 2q^3+9q^2+6q+1
       122: q^3+3q^2+q
       123: q^3+7q^2+6q+1
       124: 2q^2+q
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       127: 3q^2+5q+1
       129: 3q^2+5q+1
       131: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: 2q^3+12q^2+7q+1
       138: 4q^2+4q+1
       139: 3q^3+12q^2+7q+1
       140: 6q^2+6q+1
       141: 3q^3+10q^2+6q+1
       142: q^3+7q^2+6q+1
       143: q^3+9q^2+7q+1
       144: 2q^2+4q+1
       145: 7q^2+7q+1
       146: q^3+7q^2+6q+1
       147: 5q^2+6q+1
       148: 2q^2+3q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       151: q^3+7q^2+6q+1
       153: q^3+7q^2+6q+1
       155: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 6q^2+6q+1
       161: q^3+7q^2+6q+1
       162: q^3+4q^2+4q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       169: 2q^2+4q+1
       172: q^2+q
       173: 3q^2+4q+1
       175: q^2+q
       176: q^2+q
       177: q^2+3q+1
       179: 3q^2+5q+1
       181: q^2+4q+1
       183: 3q+1
       184: q^2+q
       185: q^2+4q+1
       187: q^2+4q+1
       189: 4q^2+5q+1
       191: 5q^2+5q+1
       192: 2q^2+q
       193: 3q^2+4q+1
       194: 3q^2+2q
       195: q^3+5q^2+5q+1
       196: 2q^2+q
       197: 3q^2+5q+1
       199: 3q^2+4q+1
       200: 2q^2+2q
       201: 3q^2+4q+1
       202: 2q^2+2q
       203: 2q^2+3q+1
       205: q^2+2q+1
       207: q^3+7q^2+6q+1
       208: 2q^2+q
       209: q^3+7q^2+6q+1
       211: 4q^2+5q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: 3q^2+5q+1
       228: 3q^2+4q+1
       229: 3q^2+5q+1
       230: 3q^2+5q+1
       231: 2q^2+4q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 2q^2+4q+1
       237: 3q^2+5q+1
       239: 3q^2+5q+1
       241: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 5q^2+6q+1
       245: 2q^2+3q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 6q^2+6q+1
       251: q^3+7q^2+6q+1
       252: q^3+4q^2+4q+1
       253: q^2+5q+1
       254: 2q^2+5q+1
       255: q^2+3q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q^2+3q+1
       262: q
       263: 3q+1
       267: 2q^2+4q+1
       269: q^2+q
       271: q^2+2q+1
       275: 3q^2+4q+1
       277: q^2+q
       278: q^2+q
       279: 2q+1
       281: 2q+1
       283: q+1
       285: 2q+1
       287: q^2+3q+1
       289: 2q+1
       291: 2q+1
       293: 3q+1
       294: q^2+q
       295: q^2+4q+1
       297: q^2+4q+1
       299: 3q+1
       300: q^2+q
       301: q^2+4q+1
       303: q^2+4q+1
       305: q^2+4q+1
       307: 2q+1
       308: q
       309: 2q+1
       311: q+1
       313: q+1
       315: q^2+3q+1
       317: 3q^2+5q+1
       319: 3q^2+4q+1
       320: 2q^2+2q
       321: 2q^2+3q+1
       323: q^2+2q+1
       325: 4q^2+5q+1
       327: 3q+1
       329: q^2+3q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^2+3q+1
       345: 3q^2+5q+1
       346: 3q^2+4q+1
       347: 3q^2+5q+1
       348: q^2+3q+1
       349: 3q^2+5q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 4q+1
       354: 3q+1
       355: q^2+4q+1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 2q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       377: q+1
       381: q+1
       385: 3q+1
       389: q^2+3q+1
       391: q
       393: 3q+1
       397: q+1
       401: q+1
       405: q^2+2q+1
       409: 2q+1
       411: 2q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q+1
       421: 2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       431: 2q+1
       433: 2q+1
       435: 2q+1
       437: 3q+1
       438: q^2+q
       439: q^2+4q+1
       441: q^2+4q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       447: 1
       449: q+1
       451: 1
       453: 2q+1
       454: q
       455: 1
       457: 2q+1
       459: q+1
       461: 2q+2
       463: 2q+2
       465: 2q+1
       467: 2q+1
       469: q^2+3q+1
       471: 2q+1
       472: q
       473: 2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+3q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: 2q+1
       499: q+1
       500: 1
       501: 2
       502: 3q+1
       504: q^2+3q+1
       506: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: q^2+4q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       521: 1
       525: q+1
       529: q+1
       533: q+1
       537: q+1
       541: 3q+1
       545: 2q+1
       547: 2q+1
       549: 1
       553: 1
       557: q+1
       561: 2q+2
       565: q+1
       569: q+1
       573: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       589: 1
       591: 1
       595: q+1
       597: 1
       599: q+1
       601: 2
       603: q+1
       605: q+1
       607: 2q+1
       609: 2q+1
       611: 2q+1
       613: q+1
       615: 1
       616: 1
       617: q+2
       619: 1
       621: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 2
       633: 2
       635: 2q+1
       637: 2q+1
       639: q+1
       641: 1
       643: q+1
       645: 1
       647: 2q+1
       648: q
       649: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: 2q+1
       688: q+1
       689: 1
       693: q+1
       698: q+1
       705: 1
       709: 1
       713: 1
       721: 1
       725: q+1
       729: q+1
       733: 1
       735: 1
       737: 1
       741: 1
       745: 1
       749: 2
       753: 1
       757: 1
       761: q+1
       765: 1
       767: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       787: 1
       789: 2
       797: 1
       799: q+1
       801: 1
       803: 1
       807: q+1
       809: 1
       811: q+1
       813: q+2
       815: 1
       816: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 2
       839: 2
       841: q+1
       845: 1
       847: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       884: 1
       888: 1
       896: 1
       900: 1
       912: 1
       920: 1
       924: 1
       932: 1
       934: 1
       936: 1
       948: 1
       956: 2
       960: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       990: 1
      1002: 1
      1006: 1
      1018: 1
      1022: 1
      1024: 1
      1028: 1
      1042: 1
      1050: 1
      1052: 1
      1054: 1
      1060: 1
      1062: 1
      1078: 1
      1085: 1
      1098: 1
      1103: 1
      1110: 1
      1148: 1
      1152: 1
      1184: 1
      1202: 1
      1238: 1
      1242: 1
      1272: 1
      1344: 1

1345:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: q^4+13q^3+21q^2+8q+1
        23: q^4+13q^3+21q^2+8q+1
        24: 3q^4+11q^3+16q^2+7q+1
        25: 7q^3+17q^2+8q+1
        26: 7q^3+17q^2+8q+1
        27: q^4+7q^3+13q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: q^4+13q^3+21q^2+8q+1
        32: 6q^3+15q^2+7q+1
        33: 7q^3+18q^2+8q+1
        34: 7q^3+17q^2+8q+1
        35: 3q^3+12q^2+7q+1
        36: 3q^3+14q^2+8q+1
        37: 2q^3+4q^2+q
        38: 5q^3+13q^2+7q+1
        39: 2q^3+4q^2+q
        40: 5q^3+13q^2+7q+1
        41: 2q^3+3q^2+q
        42: q^4+5q^3+10q^2+6q+1
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: q^4+8q^3+15q^2+7q+1
        53: q^4+8q^3+15q^2+7q+1
        54: q^4+6q^3+11q^2+6q+1
        55: 3q^3+11q^2+7q+1
        56: 3q^3+11q^2+7q+1
        57: 3q^3+8q^2+6q+1
        58: 4q^3+11q^2+6q+1
        59: 3q^3+7q^2+2q
        60: q^3+6q^2+3q
        61: 2q^3+8q^2+5q+1
        62: 2q^3+4q^2+q
        63: 5q^3+13q^2+7q+1
        64: q^3+3q^2+q
        65: 2q^3+9q^2+6q+1
        66: 3q^2+q
        67: 3q^3+11q^2+7q+1
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: 6q^2+6q+1
        73: q^3+7q^2+6q+1
        75: q^3+7q^2+6q+1
        77: q^3+7q^2+6q+1
        79: q^3+5q^2+5q+1
        80: 6q^3+15q^2+7q+1
        81: 2q^3+12q^2+7q+1
        82: q^4+8q^3+15q^2+7q+1
        83: 3q^3+10q^2+6q+1
        84: 3q^3+12q^2+7q+1
        85: q^3+9q^2+7q+1
        86: 3q^3+11q^2+7q+1
        87: q^3+7q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 3q^3+12q^2+7q+1
        95: 3q^3+12q^2+7q+1
        96: 3q^3+6q^2+4q+1
        97: 7q^2+7q+1
        98: 7q^2+7q+1
        99: q^3+4q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: 2q^2+q
       104: q^3+4q^2+2q
       105: 2q^3+7q^2+5q+1
       106: q^2
       107: 3q^2+2q
       108: 3q^2+4q+1
       109: q^3+5q^2+5q+1
       110: 2q^2+q
       112: 3q^2+5q+1
       114: q^3+7q^2+6q+1
       116: 4q^2+5q+1
       117: 5q^2+5q+1
       118: 2q^2+q
       119: 2q^2+2q
       120: 3q^2+4q+1
       121: q^3+3q^2+q
       122: 2q^3+9q^2+6q+1
       123: 2q^2+q
       124: q^3+7q^2+6q+1
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       128: 3q^2+5q+1
       130: 3q^2+5q+1
       132: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: 2q^3+12q^2+7q+1
       138: 4q^2+4q+1
       139: 3q^3+12q^2+7q+1
       140: 6q^2+6q+1
       141: 3q^3+10q^2+6q+1
       142: q^3+7q^2+6q+1
       143: q^3+9q^2+7q+1
       144: 2q^2+4q+1
       145: 7q^2+7q+1
       146: q^3+7q^2+6q+1
       147: 5q^2+6q+1
       148: 2q^2+3q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       152: q^3+7q^2+6q+1
       154: q^3+7q^2+6q+1
       156: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 6q^2+6q+1
       161: q^3+7q^2+6q+1
       162: q^3+4q^2+4q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       170: q^2+q
       171: 2q^2+4q+1
       173: q^2+q
       174: q^2+q
       175: 3q^2+4q+1
       178: q^2+3q+1
       180: 3q^2+5q+1
       182: q^2+4q+1
       183: q^2+q
       184: 3q+1
       185: q^2+4q+1
       188: q^2+4q+1
       190: 4q^2+5q+1
       191: 5q^2+5q+1
       192: 2q^2+q
       193: 3q^2+2q
       194: 3q^2+4q+1
       195: q^3+5q^2+5q+1
       196: 2q^2+q
       198: 3q^2+5q+1
       199: 2q^2+2q
       200: 3q^2+4q+1
       201: 2q^2+2q
       202: 3q^2+4q+1
       203: 2q^2+3q+1
       206: q^2+2q+1
       207: 2q^2+q
       208: q^3+7q^2+6q+1
       210: q^3+7q^2+6q+1
       212: 4q^2+5q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: 3q^2+5q+1
       228: 3q^2+4q+1
       229: 3q^2+5q+1
       230: 3q^2+5q+1
       231: 2q^2+4q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 2q^2+4q+1
       238: 3q^2+5q+1
       240: 3q^2+5q+1
       242: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 5q^2+6q+1
       245: 2q^2+3q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 6q^2+6q+1
       251: q^3+7q^2+6q+1
       252: q^3+4q^2+4q+1
       253: q^2+5q+1
       254: 2q^2+5q+1
       255: q^2+3q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q
       261: q^2+3q+1
       265: 3q+1
       268: q^2+q
       270: 2q^2+4q+1
       272: q^2+2q+1
       275: q^2+q
       276: q^2+q
       277: 3q^2+4q+1
       280: 2q+1
       282: 2q+1
       284: q+1
       285: 2q+1
       288: q^2+3q+1
       290: 2q+1
       292: 2q+1
       293: q^2+q
       294: 3q+1
       295: q^2+4q+1
       298: q^2+4q+1
       299: q^2+q
       300: 3q+1
       302: q^2+4q+1
       303: q^2+4q+1
       306: q^2+4q+1
       307: q
       308: 2q+1
       309: 2q+1
       312: q+1
       314: q+1
       316: q^2+3q+1
       318: 3q^2+5q+1
       319: 2q^2+2q
       320: 3q^2+4q+1
       321: 2q^2+3q+1
       324: q^2+2q+1
       326: 4q^2+5q+1
       328: 3q+1
       330: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^2+3q+1
       345: 3q^2+5q+1
       346: 3q^2+4q+1
       347: 3q^2+5q+1
       348: q^2+3q+1
       349: 3q^2+5q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 4q+1
       354: 3q+1
       355: q^2+4q+1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 2q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       379: q+1
       383: q+1
       387: 3q+1
       390: q
       392: q^2+3q+1
       395: 3q+1
       398: q+1
       402: q+1
       408: q^2+2q+1
       410: 2q+1
       412: 2q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: q+1
       421: 2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       430: q+1
       431: 2q+1
       434: 2q+1
       436: 2q+1
       437: q^2+q
       438: 3q+1
       439: q^2+4q+1
       442: q^2+4q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       448: 1
       449: q+1
       452: 1
       453: q
       454: 2q+1
       456: 1
       457: 2q+1
       460: q+1
       461: 2q+2
       464: 2q+2
       466: 2q+1
       468: 2q+1
       470: q^2+3q+1
       471: q
       472: 2q+1
       473: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+3q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: 2q+1
       499: q+1
       500: 1
       501: 2
       503: 3q+1
       505: q^2+3q+1
       507: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: q^2+4q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       523: 1
       527: q+1
       531: q+1
       535: q+1
       540: q+1
       544: 3q+1
       546: 2q+1
       548: 2q+1
       550: 1
       554: 1
       558: q+1
       562: 2q+2
       567: q+1
       572: q+1
       573: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       590: 1
       591: 1
       595: q+1
       598: 1
       600: q+1
       602: 2
       604: q+1
       606: q+1
       607: 2q+1
       610: 2q+1
       612: 2q+1
       614: q+1
       615: 1
       616: 1
       618: q+2
       620: 1
       621: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 2
       634: 2
       636: 2q+1
       638: 2q+1
       640: q+1
       642: 1
       643: q+1
       646: 1
       647: q
       648: 2q+1
       649: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: 2q+1
       688: q+1
       689: 1
       694: q+1
       700: q+1
       707: 1
       711: 1
       714: 1
       724: 1
       728: q+1
       732: q+1
       734: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 2
       755: 1
       760: 1
       764: q+1
       765: 1
       767: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       787: 1
       790: 2
       798: 1
       800: q+1
       802: 1
       803: 1
       807: q+1
       810: 1
       812: q+1
       814: q+2
       815: 1
       816: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 2
       839: 2
       842: q+1
       846: 1
       847: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       885: 1
       891: 1
       898: 1
       901: 1
       915: 1
       923: 1
       925: 1
       933: 1
       935: 1
       937: 1
       949: 1
       957: 2
       963: 1
       977: 1
       981: 1
       983: 1
       986: 1
       988: 1
       990: 1
      1003: 1
      1006: 1
      1019: 1
      1023: 1
      1025: 1
      1028: 1
      1043: 1
      1051: 1
      1053: 1
      1054: 1
      1061: 1
      1063: 1
      1078: 1
      1085: 1
      1099: 1
      1105: 1
      1111: 1
      1151: 1
      1153: 1
      1187: 1
      1203: 1
      1239: 1
      1242: 1
      1273: 1
      1345: 1

1346:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: q^4+13q^3+21q^2+8q+1
        23: q^4+13q^3+21q^2+8q+1
        24: 3q^4+11q^3+16q^2+7q+1
        25: 7q^3+17q^2+8q+1
        26: 7q^3+17q^2+8q+1
        27: q^4+7q^3+13q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: q^4+13q^3+21q^2+8q+1
        32: 6q^3+15q^2+7q+1
        33: 7q^3+18q^2+8q+1
        34: 7q^3+17q^2+8q+1
        35: 3q^3+12q^2+7q+1
        36: 3q^3+14q^2+8q+1
        37: 5q^3+13q^2+7q+1
        38: 2q^3+4q^2+q
        39: 5q^3+13q^2+7q+1
        40: 2q^3+4q^2+q
        41: q^4+5q^3+10q^2+6q+1
        42: 2q^3+3q^2+q
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: q^4+8q^3+15q^2+7q+1
        53: q^4+8q^3+15q^2+7q+1
        54: q^4+6q^3+11q^2+6q+1
        55: 3q^3+11q^2+7q+1
        56: 3q^3+11q^2+7q+1
        57: 3q^3+8q^2+6q+1
        58: 3q^3+7q^2+2q
        59: 4q^3+11q^2+6q+1
        60: q^3+6q^2+3q
        61: 2q^3+8q^2+5q+1
        62: 5q^3+13q^2+7q+1
        63: 2q^3+4q^2+q
        64: 2q^3+9q^2+6q+1
        65: q^3+3q^2+q
        66: 3q^3+11q^2+7q+1
        67: 3q^2+q
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: 6q^2+6q+1
        73: q^3+7q^2+6q+1
        74: q^3+7q^2+6q+1
        76: q^3+7q^2+6q+1
        78: q^3+5q^2+5q+1
        80: 6q^3+15q^2+7q+1
        81: 2q^3+12q^2+7q+1
        82: q^4+8q^3+15q^2+7q+1
        83: 3q^3+10q^2+6q+1
        84: 3q^3+12q^2+7q+1
        85: q^3+9q^2+7q+1
        86: 3q^3+11q^2+7q+1
        87: q^3+7q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 3q^3+12q^2+7q+1
        95: 3q^3+12q^2+7q+1
        96: 3q^3+6q^2+4q+1
        97: 7q^2+7q+1
        98: 7q^2+7q+1
        99: q^3+4q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: q^3+4q^2+2q
       104: 2q^2+q
       105: q^2
       106: 2q^3+7q^2+5q+1
       107: 3q^2+2q
       108: 3q^2+4q+1
       109: 2q^2+q
       110: q^3+5q^2+5q+1
       111: 3q^2+5q+1
       113: q^3+7q^2+6q+1
       115: 4q^2+5q+1
       117: 2q^2+q
       118: 5q^2+5q+1
       119: 2q^2+2q
       120: 3q^2+4q+1
       121: 2q^3+9q^2+6q+1
       122: q^3+3q^2+q
       123: q^3+7q^2+6q+1
       124: 2q^2+q
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       127: 3q^2+5q+1
       129: 3q^2+5q+1
       131: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: 2q^3+12q^2+7q+1
       138: 4q^2+4q+1
       139: 3q^3+12q^2+7q+1
       140: 6q^2+6q+1
       141: 3q^3+10q^2+6q+1
       142: q^3+7q^2+6q+1
       143: q^3+9q^2+7q+1
       144: 2q^2+4q+1
       145: 7q^2+7q+1
       146: q^3+7q^2+6q+1
       147: 5q^2+6q+1
       148: 2q^2+3q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       151: q^3+7q^2+6q+1
       153: q^3+7q^2+6q+1
       155: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 6q^2+6q+1
       161: q^3+7q^2+6q+1
       162: q^3+4q^2+4q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       169: q^2+q
       172: 2q^2+4q+1
       173: q^2+q
       174: q^2+q
       176: 3q^2+4q+1
       177: q^2+3q+1
       179: 3q^2+5q+1
       181: q^2+4q+1
       183: q^2+q
       184: 3q+1
       186: q^2+4q+1
       187: q^2+4q+1
       189: 4q^2+5q+1
       191: 2q^2+q
       192: 5q^2+5q+1
       193: 3q^2+2q
       194: 3q^2+4q+1
       195: 2q^2+q
       196: q^3+5q^2+5q+1
       197: 3q^2+5q+1
       199: 2q^2+2q
       200: 3q^2+4q+1
       201: 2q^2+2q
       202: 3q^2+4q+1
       204: 2q^2+3q+1
       205: q^2+2q+1
       207: q^3+7q^2+6q+1
       208: 2q^2+q
       209: q^3+7q^2+6q+1
       211: 4q^2+5q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: 3q^2+5q+1
       228: 3q^2+4q+1
       229: 3q^2+5q+1
       230: 3q^2+5q+1
       231: 2q^2+4q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 2q^2+4q+1
       237: 3q^2+5q+1
       239: 3q^2+5q+1
       241: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 5q^2+6q+1
       245: 2q^2+3q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 6q^2+6q+1
       251: q^3+7q^2+6q+1
       252: q^3+4q^2+4q+1
       253: q^2+5q+1
       254: 2q^2+5q+1
       255: q^2+3q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q
       262: q^2+3q+1
       266: 3q+1
       267: q^2+q
       269: 2q^2+4q+1
       273: q^2+2q+1
       275: q^2+q
       276: q^2+q
       278: 3q^2+4q+1
       279: 2q+1
       281: 2q+1
       284: q+1
       286: 2q+1
       287: q^2+3q+1
       289: 2q+1
       291: 2q+1
       293: q^2+q
       294: 3q+1
       296: q^2+4q+1
       297: q^2+4q+1
       299: q^2+q
       300: 3q+1
       301: q^2+4q+1
       304: q^2+4q+1
       305: q^2+4q+1
       307: q
       308: 2q+1
       310: 2q+1
       311: q+1
       313: q+1
       315: q^2+3q+1
       317: 3q^2+5q+1
       319: 2q^2+2q
       320: 3q^2+4q+1
       322: 2q^2+3q+1
       323: q^2+2q+1
       325: 4q^2+5q+1
       327: 3q+1
       329: q^2+3q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^2+3q+1
       345: 3q^2+5q+1
       346: 3q^2+4q+1
       347: 3q^2+5q+1
       348: q^2+3q+1
       349: 3q^2+5q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 4q+1
       354: 3q+1
       355: q^2+4q+1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 2q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       380: q+1
       384: q+1
       388: 3q+1
       389: q
       391: q^2+3q+1
       396: 3q+1
       399: q+1
       404: q+1
       406: q^2+2q+1
       409: 2q+1
       411: 2q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: q+1
       422: 2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       430: q+1
       432: 2q+1
       433: 2q+1
       435: 2q+1
       437: q^2+q
       438: 3q+1
       440: q^2+4q+1
       441: q^2+4q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       448: 1
       450: q+1
       451: 1
       453: q
       454: 2q+1
       455: 1
       458: 2q+1
       459: q+1
       462: 2q+2
       463: 2q+2
       465: 2q+1
       467: 2q+1
       469: q^2+3q+1
       471: q
       472: 2q+1
       474: 2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+3q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: 2q+1
       499: q+1
       500: 1
       501: 2
       502: 3q+1
       504: q^2+3q+1
       506: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: q^2+4q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       524: 1
       528: q+1
       532: q+1
       536: q+1
       539: q+1
       543: 3q+1
       545: 2q+1
       547: 2q+1
       552: 1
       555: 1
       559: q+1
       563: 2q+2
       568: q+1
       570: q+1
       574: q+1
       575: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       590: 1
       592: 1
       596: q+1
       597: 1
       599: q+1
       601: 2
       604: q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: 2q+1
       613: q+1
       615: 1
       616: 1
       617: q+2
       620: 1
       622: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 2
       633: 2
       635: 2q+1
       637: 2q+1
       639: q+1
       642: 1
       644: q+1
       645: 1
       647: q
       648: 2q+1
       650: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: 2q+1
       688: q+1
       689: 1
       696: q+1
       697: q+1
       708: 1
       712: 1
       716: 1
       723: 1
       727: q+1
       731: q+1
       733: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 2
       756: 1
       758: 1
       762: q+1
       766: 1
       768: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       788: 1
       789: 2
       797: 1
       799: q+1
       802: 1
       804: 1
       808: q+1
       809: 1
       811: q+1
       813: q+2
       815: 1
       816: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 2
       840: 2
       841: q+1
       846: 1
       848: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       887: 1
       889: 1
       899: 1
       902: 1
       914: 1
       922: 1
       927: 1
       932: 1
       934: 1
       938: 1
       950: 1
       958: 2
       961: 1
       975: 1
       979: 1
       982: 1
       985: 1
       989: 1
       991: 1
      1002: 1
      1007: 1
      1018: 1
      1022: 1
      1024: 1
      1029: 1
      1042: 1
      1050: 1
      1053: 1
      1055: 1
      1060: 1
      1062: 1
      1078: 1
      1085: 1
      1101: 1
      1102: 1
      1112: 1
      1150: 1
      1154: 1
      1185: 1
      1204: 1
      1238: 1
      1243: 1
      1272: 1
      1346: 1

1347:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: q^4+13q^3+21q^2+8q+1
        23: q^4+13q^3+21q^2+8q+1
        24: 3q^4+11q^3+16q^2+7q+1
        25: 7q^3+17q^2+8q+1
        26: 7q^3+17q^2+8q+1
        27: q^4+7q^3+13q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: q^4+13q^3+21q^2+8q+1
        32: 6q^3+15q^2+7q+1
        33: 7q^3+18q^2+8q+1
        34: 7q^3+17q^2+8q+1
        35: 3q^3+12q^2+7q+1
        36: 3q^3+14q^2+8q+1
        37: 2q^3+4q^2+q
        38: 5q^3+13q^2+7q+1
        39: 2q^3+4q^2+q
        40: 5q^3+13q^2+7q+1
        41: 2q^3+3q^2+q
        42: q^4+5q^3+10q^2+6q+1
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: q^4+8q^3+15q^2+7q+1
        53: q^4+8q^3+15q^2+7q+1
        54: q^4+6q^3+11q^2+6q+1
        55: 3q^3+11q^2+7q+1
        56: 3q^3+11q^2+7q+1
        57: 3q^3+8q^2+6q+1
        58: 3q^3+7q^2+2q
        59: 4q^3+11q^2+6q+1
        60: 2q^3+8q^2+5q+1
        61: q^3+6q^2+3q
        62: 2q^3+4q^2+q
        63: 5q^3+13q^2+7q+1
        64: q^3+3q^2+q
        65: 2q^3+9q^2+6q+1
        66: 3q^2+q
        67: 3q^3+11q^2+7q+1
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: 6q^2+6q+1
        73: q^3+7q^2+6q+1
        75: q^3+7q^2+6q+1
        77: q^3+7q^2+6q+1
        79: q^3+5q^2+5q+1
        80: 6q^3+15q^2+7q+1
        81: 2q^3+12q^2+7q+1
        82: q^4+8q^3+15q^2+7q+1
        83: 3q^3+10q^2+6q+1
        84: 3q^3+12q^2+7q+1
        85: q^3+9q^2+7q+1
        86: 3q^3+11q^2+7q+1
        87: q^3+7q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 3q^3+12q^2+7q+1
        95: 3q^3+12q^2+7q+1
        96: 3q^3+6q^2+4q+1
        97: 7q^2+7q+1
        98: 7q^2+7q+1
        99: q^3+4q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: q^2
       104: 2q^3+7q^2+5q+1
       105: q^3+4q^2+2q
       106: 2q^2+q
       107: 3q^2+4q+1
       108: 3q^2+2q
       109: 2q^2+q
       110: q^3+5q^2+5q+1
       112: 3q^2+5q+1
       114: q^3+7q^2+6q+1
       116: 4q^2+5q+1
       117: 2q^2+q
       118: 5q^2+5q+1
       119: 3q^2+4q+1
       120: 2q^2+2q
       121: q^3+3q^2+q
       122: 2q^3+9q^2+6q+1
       123: 2q^2+q
       124: q^3+7q^2+6q+1
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       128: 3q^2+5q+1
       130: 3q^2+5q+1
       132: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: 2q^3+12q^2+7q+1
       138: 4q^2+4q+1
       139: 3q^3+12q^2+7q+1
       140: 6q^2+6q+1
       141: 3q^3+10q^2+6q+1
       142: q^3+7q^2+6q+1
       143: q^3+9q^2+7q+1
       144: 2q^2+4q+1
       145: 7q^2+7q+1
       146: q^3+7q^2+6q+1
       147: 5q^2+6q+1
       148: 2q^2+3q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       152: q^3+7q^2+6q+1
       154: q^3+7q^2+6q+1
       156: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 6q^2+6q+1
       161: q^3+7q^2+6q+1
       162: q^3+4q^2+4q+1
       163: q^2+5q+1
       164: 2q^2+5q+1
       165: q^2+3q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       170: 2q^2+4q+1
       171: q^2+q
       174: 3q^2+4q+1
       175: q^2+q
       176: q^2+q
       178: q^2+3q+1
       180: 3q^2+5q+1
       182: q^2+4q+1
       183: 3q+1
       184: q^2+q
       186: q^2+4q+1
       188: q^2+4q+1
       190: 4q^2+5q+1
       191: 2q^2+q
       192: 5q^2+5q+1
       193: 3q^2+4q+1
       194: 3q^2+2q
       195: 2q^2+q
       196: q^3+5q^2+5q+1
       198: 3q^2+5q+1
       199: 3q^2+4q+1
       200: 2q^2+2q
       201: 3q^2+4q+1
       202: 2q^2+2q
       204: 2q^2+3q+1
       206: q^2+2q+1
       207: 2q^2+q
       208: q^3+7q^2+6q+1
       210: q^3+7q^2+6q+1
       212: 4q^2+5q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: 3q^2+5q+1
       228: 3q^2+4q+1
       229: 3q^2+5q+1
       230: 3q^2+5q+1
       231: 2q^2+4q+1
       232: 4q+1
       233: 3q+1
       234: q^2+4q+1
       235: 2q+1
       236: 2q^2+4q+1
       238: 3q^2+5q+1
       240: 3q^2+5q+1
       242: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 5q^2+6q+1
       245: 2q^2+3q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 6q^2+6q+1
       251: q^3+7q^2+6q+1
       252: q^3+4q^2+4q+1
       253: q^2+5q+1
       254: 2q^2+5q+1
       255: q^2+3q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q^2+3q+1
       261: q
       264: 3q+1
       268: 2q^2+4q+1
       270: q^2+q
       274: q^2+2q+1
       276: 3q^2+4q+1
       277: q^2+q
       278: q^2+q
       280: 2q+1
       282: 2q+1
       283: q+1
       286: 2q+1
       288: q^2+3q+1
       290: 2q+1
       292: 2q+1
       293: 3q+1
       294: q^2+q
       296: q^2+4q+1
       298: q^2+4q+1
       299: 3q+1
       300: q^2+q
       302: q^2+4q+1
       304: q^2+4q+1
       306: q^2+4q+1
       307: 2q+1
       308: q
       310: 2q+1
       312: q+1
       314: q+1
       316: q^2+3q+1
       318: 3q^2+5q+1
       319: 3q^2+4q+1
       320: 2q^2+2q
       322: 2q^2+3q+1
       324: q^2+2q+1
       326: 4q^2+5q+1
       328: 3q+1
       330: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^2+3q+1
       345: 3q^2+5q+1
       346: 3q^2+4q+1
       347: 3q^2+5q+1
       348: q^2+3q+1
       349: 3q^2+5q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 4q+1
       354: 3q+1
       355: q^2+4q+1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 2q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: q^2+4q+1
       370: 2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       378: q+1
       382: q+1
       386: 3q+1
       390: q^2+3q+1
       392: q
       394: 3q+1
       400: q+1
       403: q+1
       407: q^2+2q+1
       410: 2q+1
       412: 2q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q+1
       422: 2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       432: 2q+1
       434: 2q+1
       436: 2q+1
       437: 3q+1
       438: q^2+q
       440: q^2+4q+1
       442: q^2+4q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       447: 1
       450: q+1
       452: 1
       453: 2q+1
       454: q
       456: 1
       458: 2q+1
       460: q+1
       462: 2q+2
       464: 2q+2
       466: 2q+1
       468: 2q+1
       470: q^2+3q+1
       471: 2q+1
       472: q
       474: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+3q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: 2q+1
       499: q+1
       500: 1
       501: 2
       503: 3q+1
       505: q^2+3q+1
       507: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: q^2+4q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       518: q+2
       519: q+2
       520: q+1
       522: 1
       526: q+1
       530: q+1
       534: q+1
       538: q+1
       542: 3q+1
       546: 2q+1
       548: 2q+1
       551: 1
       556: 1
       560: q+1
       564: 2q+2
       566: q+1
       571: q+1
       574: q+1
       575: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       589: 1
       592: 1
       596: q+1
       598: 1
       600: q+1
       602: 2
       603: q+1
       606: q+1
       608: 2q+1
       610: 2q+1
       612: 2q+1
       614: q+1
       615: 1
       616: 1
       618: q+2
       619: 1
       622: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 2
       634: 2
       636: 2q+1
       638: 2q+1
       640: q+1
       641: 1
       644: q+1
       646: 1
       647: 2q+1
       648: q
       650: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: 2q+1
       688: q+1
       689: 1
       699: q+1
       701: q+1
       706: 1
       710: 1
       715: 1
       722: 1
       726: q+1
       730: q+1
       734: 1
       736: 1
       740: 1
       744: 1
       748: 1
       752: 2
       754: 1
       759: 1
       763: q+1
       766: 1
       768: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       788: 1
       790: 2
       798: 1
       800: q+1
       801: 1
       804: 1
       808: q+1
       810: 1
       812: q+1
       814: q+2
       815: 1
       816: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 2
       840: 2
       842: q+1
       845: 1
       848: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       890: 1
       892: 1
       897: 1
       903: 1
       913: 1
       921: 1
       926: 1
       933: 1
       935: 1
       939: 1
       951: 1
       959: 2
       962: 1
       976: 1
       980: 1
       983: 1
       986: 1
       989: 1
       991: 1
      1003: 1
      1007: 1
      1019: 1
      1023: 1
      1025: 1
      1029: 1
      1043: 1
      1051: 1
      1052: 1
      1055: 1
      1061: 1
      1063: 1
      1078: 1
      1085: 1
      1104: 1
      1106: 1
      1113: 1
      1149: 1
      1155: 1
      1186: 1
      1205: 1
      1239: 1
      1243: 1
      1273: 1
      1347: 1

1348:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: q^3+4q^2+4q+1
        33: q^3+4q^2+4q+1
        34: 3q+1
        35: 3q^2+4q+1
        36: 3q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^3+3q^2+3q+1
        54: 2q^2+3q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: 2q+1
        59: q
        60: q+1
        61: 2q
        62: 2q+1
        63: q
        64: 2q^2+3q+1
        65: q^2+q
        66: 2q^2+3q+1
        67: q^2+q
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: 3q+1
        81: q^3+4q^2+4q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: 2q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q+1
       105: q
       106: q
       107: 1
       108: q
       109: q+1
       111: q+1
       113: q+1
       115: 2q+1
       117: 2q+1
       118: q
       119: q+1
       120: 2q
       121: 2q+1
       122: q
       123: 2q^2+3q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: q^2+2q+1
       131: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: 2q^2+3q+1
       139: 2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+3q+1
       151: 2q+1
       153: q^2+2q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+3q+1
       161: q^3+3q^2+3q+1
       162: 2q^2+3q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       169: 1
       173: q+1
       175: q
       176: q
       177: 2q+1
       179: q+1
       181: q+1
       183: 1
       184: q
       185: q+1
       187: q+1
       189: q+1
       191: 2q+1
       192: q
       193: 1
       194: q
       195: q+1
       197: q+1
       199: q+1
       200: 2q
       201: 1
       202: q
       203: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: 2q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+3q+1
       237: 2q+1
       239: q^2+2q+1
       241: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       277: q
       278: q
       279: q+1
       281: 2q+1
       283: 1
       284: q
       285: q+1
       287: q+1
       289: q+1
       291: q+1
       293: 1
       294: q
       295: 1
       297: 1
       299: 1
       300: q
       301: q+1
       303: q+1
       305: q+1
       307: 1
       308: q
       309: q+1
       311: 1
       313: 1
       315: 2q+1
       317: q+1
       319: 1
       320: q
       321: q+1
       323: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: 1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: q^2+2q+1
       358: q+1
       359: 2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       417: q+1
       419: 1
       420: q
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       430: q
       431: q+1
       433: q+1
       435: q+1
       437: 1
       438: q
       439: 1
       441: 1
       443: 1
       444: 1
       445: q+2
       447: 1
       448: q
       449: q+1
       451: 1
       455: 1
       461: 2
       463: 2
       465: q+1
       467: 2q+1
       469: q+1
       471: 1
       472: q
       473: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       547: 1
       549: 1
       553: 1
       561: 2
       565: 1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       585: 1
       589: 1
       590: q
       591: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: 1
       604: q
       605: q+1
       607: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: q+2
       623: 1
       629: 1
       631: 2
       633: 2
       639: q+1
       641: 1
       642: q
       643: q+1
       645: 1
       651: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       674: q+2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       685: 1
       689: 1
       693: 1
       698: 1
       709: 1
       713: 1
       721: 1
       725: 1
       733: 1
       735: 1
       737: 1
       749: 2
       753: 1
       757: 1
       765: 1
       767: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       787: 1
       793: 1
       794: 1
       795: q+2
       797: 1
       801: 1
       802: q
       803: 1
       807: 1
       809: 1
       811: 1
       817: 2
       819: 2
       833: 1
       843: 1
       844: 1
       849: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       884: 1
       888: 1
       900: 1
       916: 1
       918: 1
       920: 1
       924: 1
       940: 2
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       994: 1
       998: 1
      1020: 1
      1022: 1
      1028: 1
      1036: 1
      1060: 1
      1076: 1
      1084: 1
      1086: 1
      1090: 1
      1114: 1
      1152: 1
      1230: 1
      1232: 1
      1274: 1
      1348: 1

1349:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: q^3+4q^2+4q+1
        33: q^3+4q^2+4q+1
        34: 3q+1
        35: 3q^2+4q+1
        36: 3q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^3+3q^2+3q+1
        54: 2q^2+3q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: 2q+1
        59: q
        60: 2q
        61: q+1
        62: q
        63: 2q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q^2+q
        67: 2q^2+3q+1
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: 3q+1
        81: q^3+4q^2+4q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: 2q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q
       104: q
       105: q+1
       107: q
       108: 1
       109: q+1
       112: q+1
       114: q+1
       116: 2q+1
       117: 2q+1
       118: q
       119: 2q
       120: q+1
       121: q
       122: 2q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: q^2+2q+1
       132: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: 2q^2+3q+1
       139: 2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+3q+1
       152: 2q+1
       154: q^2+2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+3q+1
       161: q^3+3q^2+3q+1
       162: 2q^2+3q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       171: 1
       173: q
       174: q
       175: q+1
       178: 2q+1
       180: q+1
       182: q+1
       183: q
       184: 1
       185: q+1
       188: q+1
       190: q+1
       191: 2q+1
       192: q
       193: q
       194: 1
       195: q+1
       198: q+1
       199: 2q
       200: q+1
       201: q
       202: 1
       203: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: 2q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+3q+1
       238: 2q+1
       240: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q
       276: q
       277: q+1
       280: q+1
       282: 2q+1
       283: q
       284: 1
       285: q+1
       288: q+1
       290: q+1
       292: q+1
       293: q
       294: 1
       295: 1
       298: 1
       299: q
       300: 1
       302: q+1
       303: q+1
       306: q+1
       307: q
       308: 1
       309: q+1
       312: 1
       314: 1
       316: 2q+1
       318: q+1
       319: q
       320: 1
       321: q+1
       324: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: 1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: q^2+2q+1
       358: q+1
       359: 2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: q+1
       418: q+1
       419: q
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       429: q
       430: 1
       431: q+1
       434: q+1
       436: q+1
       437: q
       438: 1
       439: 1
       442: 1
       443: 1
       444: 1
       446: q+2
       447: q
       448: 1
       449: q+1
       452: 1
       456: 1
       461: 2
       464: 2
       466: q+1
       468: 2q+1
       470: q+1
       471: q
       472: 1
       473: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       546: 1
       548: 1
       550: 1
       554: 1
       562: 2
       567: 1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       586: 1
       589: q
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 2
       603: q
       604: 1
       606: q+1
       607: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: q+2
       624: 1
       630: 1
       631: 2
       634: 2
       640: q+1
       641: q
       642: 1
       643: q+1
       646: 1
       652: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       674: q+2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       685: 1
       689: 1
       694: 1
       700: 1
       711: 1
       714: 1
       724: 1
       728: 1
       734: 1
       736: 1
       738: 1
       750: 2
       755: 1
       760: 1
       765: 1
       767: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       787: 1
       793: 1
       794: 1
       796: q+2
       798: 1
       801: q
       802: 1
       803: 1
       807: 1
       810: 1
       812: 1
       817: 2
       820: 2
       834: 1
       843: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       885: 1
       891: 1
       901: 1
       917: 1
       919: 1
       923: 1
       925: 1
       941: 2
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       995: 1
       998: 1
      1021: 1
      1023: 1
      1028: 1
      1037: 1
      1061: 1
      1076: 1
      1084: 1
      1087: 1
      1093: 1
      1115: 1
      1153: 1
      1231: 1
      1232: 1
      1275: 1
      1349: 1

1350:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: q^3+4q^2+4q+1
        33: q^3+4q^2+4q+1
        34: 3q+1
        35: 3q^2+4q+1
        36: 3q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^3+3q^2+3q+1
        54: 2q^2+3q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q
        59: 2q+1
        60: 2q
        61: q+1
        62: 2q+1
        63: q
        64: 2q^2+3q+1
        65: q^2+q
        66: 2q^2+3q+1
        67: q^2+q
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: 3q+1
        81: q^3+4q^2+4q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: 2q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q
       104: q
       106: q+1
       107: q
       108: 1
       110: q+1
       111: q+1
       113: q+1
       115: 2q+1
       117: q
       118: 2q+1
       119: 2q
       120: q+1
       121: 2q+1
       122: q
       123: 2q^2+3q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: q^2+2q+1
       131: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: 2q^2+3q+1
       139: 2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+3q+1
       151: 2q+1
       153: q^2+2q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+3q+1
       161: q^3+3q^2+3q+1
       162: 2q^2+3q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       172: 1
       173: q
       174: q
       176: q+1
       177: 2q+1
       179: q+1
       181: q+1
       183: q
       184: 1
       186: q+1
       187: q+1
       189: q+1
       191: q
       192: 2q+1
       193: q
       194: 1
       196: q+1
       197: q+1
       199: 2q
       200: q+1
       201: q
       202: 1
       204: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: 2q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+3q+1
       237: 2q+1
       239: q^2+2q+1
       241: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q
       278: q+1
       279: q+1
       281: 2q+1
       283: q
       284: 1
       286: q+1
       287: q+1
       289: q+1
       291: q+1
       293: q
       294: 1
       296: 1
       297: 1
       299: q
       300: 1
       301: q+1
       304: q+1
       305: q+1
       307: q
       308: 1
       310: q+1
       311: 1
       313: 1
       315: 2q+1
       317: q+1
       319: q
       320: 1
       322: q+1
       323: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: 1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: q^2+2q+1
       358: q+1
       359: 2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       417: q+1
       419: q
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       429: q
       430: 1
       432: q+1
       433: q+1
       435: q+1
       437: q
       438: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: q+2
       447: q
       448: 1
       450: q+1
       451: 1
       455: 1
       462: 2
       463: 2
       465: q+1
       467: 2q+1
       469: q+1
       471: q
       472: 1
       474: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       545: 1
       547: 1
       552: 1
       555: 1
       563: 2
       568: 1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       585: 1
       589: q
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 2
       603: q
       604: 1
       605: q+1
       608: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: q+2
       623: 1
       629: 1
       632: 2
       633: 2
       639: q+1
       641: q
       642: 1
       644: q+1
       645: 1
       651: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       674: q+2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       685: 1
       689: 1
       696: 1
       697: 1
       712: 1
       716: 1
       723: 1
       727: 1
       733: 1
       735: 1
       739: 1
       751: 2
       756: 1
       758: 1
       766: 1
       768: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       788: 1
       793: 1
       794: 1
       795: q+2
       797: 1
       801: q
       802: 1
       804: 1
       808: 1
       809: 1
       811: 1
       818: 2
       819: 2
       833: 1
       843: 1
       844: 1
       849: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       887: 1
       889: 1
       902: 1
       916: 1
       918: 1
       922: 1
       927: 1
       942: 2
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       994: 1
       999: 1
      1020: 1
      1022: 1
      1029: 1
      1036: 1
      1060: 1
      1076: 1
      1084: 1
      1089: 1
      1091: 1
      1116: 1
      1154: 1
      1230: 1
      1233: 1
      1274: 1
      1350: 1

1351:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: q^3+4q^2+4q+1
        33: q^3+4q^2+4q+1
        34: 3q+1
        35: 3q^2+4q+1
        36: 3q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^3+3q^2+3q+1
        54: 2q^2+3q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q
        59: 2q+1
        60: q+1
        61: 2q
        62: q
        63: 2q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q^2+q
        67: 2q^2+3q+1
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: 3q+1
        81: q^3+4q^2+4q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: 2q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       104: q+1
       105: q
       106: q
       107: 1
       108: q
       110: q+1
       112: q+1
       114: q+1
       116: 2q+1
       117: q
       118: 2q+1
       119: q+1
       120: 2q
       121: q
       122: 2q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: q^2+2q+1
       132: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: 2q^2+3q+1
       139: 2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+3q+1
       152: 2q+1
       154: q^2+2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+3q+1
       161: q^3+3q^2+3q+1
       162: 2q^2+3q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       170: 1
       174: q+1
       175: q
       176: q
       178: 2q+1
       180: q+1
       182: q+1
       183: 1
       184: q
       186: q+1
       188: q+1
       190: q+1
       191: q
       192: 2q+1
       193: 1
       194: q
       196: q+1
       198: q+1
       199: q+1
       200: 2q
       201: 1
       202: q
       204: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: 2q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+3q+1
       238: 2q+1
       240: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       277: q
       278: q
       280: q+1
       282: 2q+1
       283: 1
       284: q
       286: q+1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       294: q
       296: 1
       298: 1
       299: 1
       300: q
       302: q+1
       304: q+1
       306: q+1
       307: 1
       308: q
       310: q+1
       312: 1
       314: 1
       316: 2q+1
       318: q+1
       319: 1
       320: q
       322: q+1
       324: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: 1
       350: q^2+2q+1
       351: q+2
       352: 2q+1
       356: q^2+2q+1
       358: q+1
       359: 2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: q+1
       418: q+1
       419: 1
       420: q
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       430: q
       432: q+1
       434: q+1
       436: q+1
       437: 1
       438: q
       440: 1
       442: 1
       443: 1
       444: 1
       446: q+2
       447: 1
       448: q
       450: q+1
       452: 1
       456: 1
       462: 2
       464: 2
       466: q+1
       468: 2q+1
       470: q+1
       471: 1
       472: q
       474: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: q+2
       500: 1
       501: 2
       508: 2q+1
       512: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       548: 1
       551: 1
       556: 1
       564: 2
       566: 1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       586: 1
       589: 1
       590: q
       592: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       604: q
       606: q+1
       608: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: q+2
       624: 1
       630: 1
       632: 2
       634: 2
       640: q+1
       641: 1
       642: q
       644: q+1
       646: 1
       652: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       674: q+2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       685: 1
       689: 1
       699: 1
       701: 1
       710: 1
       715: 1
       722: 1
       726: 1
       734: 1
       736: 1
       740: 1
       752: 2
       754: 1
       759: 1
       766: 1
       768: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       788: 1
       793: 1
       794: 1
       796: q+2
       798: 1
       801: 1
       802: q
       804: 1
       808: 1
       810: 1
       812: 1
       818: 2
       820: 2
       834: 1
       843: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       880: 1
       890: 1
       892: 1
       903: 1
       917: 1
       919: 1
       921: 1
       926: 1
       943: 2
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       995: 1
       999: 1
      1021: 1
      1023: 1
      1029: 1
      1037: 1
      1061: 1
      1076: 1
      1084: 1
      1092: 1
      1094: 1
      1117: 1
      1155: 1
      1231: 1
      1233: 1
      1275: 1
      1351: 1

1352:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q+1
       109: q+1
       110: q
       111: q+1
       113: q+1
       115: q+1
       117: q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: q+1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q+1
       185: q+1
       186: q
       187: q+1
       189: q+1
       191: q+1
       192: q
       193: q+1
       195: q+1
       196: q
       197: q+1
       199: q+1
       201: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       263: q+1
       267: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: q+1
       301: 1
       303: q+1
       304: q
       305: q+1
       307: 1
       315: 1
       317: 1
       319: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: 1
       445: 1
       447: 1
       453: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 1
       583: 1
       585: 1
       587: 1
       589: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       777: 1
       781: 1
       783: 1
       785: 1
       789: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       825: 1
       841: 1
       845: 1
       868: 1
       871: 1
       872: 1
       877: 1
       896: 1
       904: 1
       912: 1
       920: 1
       928: 1
       932: 1
      1002: 1
      1004: 1
      1018: 1
      1022: 1
      1024: 1
      1026: 1
      1052: 1
      1078: 1
      1118: 1
      1148: 1
      1156: 1
      1238: 1
      1240: 1
      1352: 1

1353:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: 2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q+1
       109: q
       110: q+1
       112: q+1
       114: q+1
       116: q+1
       117: q
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: q+1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q+1
       185: q
       186: q+1
       188: q+1
       190: q+1
       191: q
       192: q+1
       193: q+1
       195: q
       196: q+1
       198: q+1
       199: q+1
       201: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       264: q+1
       268: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: q+1
       302: 1
       303: q
       304: q+1
       306: q+1
       307: 1
       316: 1
       318: 1
       319: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: 1
       446: 1
       447: 1
       453: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 1
       584: 1
       586: 1
       588: 1
       589: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       778: 1
       782: 1
       784: 1
       785: 1
       790: 1
       798: 1
       800: 1
       801: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       842: 1
       845: 1
       868: 1
       871: 1
       872: 1
       877: 1
       897: 1
       905: 1
       913: 1
       921: 1
       929: 1
       933: 1
      1003: 1
      1004: 1
      1019: 1
      1023: 1
      1025: 1
      1026: 1
      1052: 1
      1078: 1
      1119: 1
      1149: 1
      1157: 1
      1239: 1
      1240: 1
      1353: 1

1354:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       108: q+1
       109: q
       110: q+1
       111: q+1
       113: q+1
       115: q+1
       117: q
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: q+1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: q+1
       185: q
       186: q+1
       187: q+1
       189: q+1
       191: q
       192: q+1
       194: q+1
       195: q
       196: q+1
       197: q+1
       200: q+1
       202: 1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: 1
       266: q+1
       269: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: q+1
       301: 1
       303: q
       304: q+1
       305: q+1
       308: 1
       315: 1
       317: 1
       320: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: 1
       445: 1
       448: 1
       454: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       547: 1
       583: 1
       585: 1
       587: 1
       590: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       777: 1
       781: 1
       783: 1
       786: 1
       789: 1
       797: 1
       799: 1
       802: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       826: 1
       841: 1
       846: 1
       868: 1
       871: 1
       872: 1
       877: 1
       899: 1
       906: 1
       914: 1
       922: 1
       930: 1
       934: 1
      1002: 1
      1005: 1
      1018: 1
      1022: 1
      1024: 1
      1027: 1
      1053: 1
      1078: 1
      1120: 1
      1150: 1
      1158: 1
      1238: 1
      1241: 1
      1354: 1

1355:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: 2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       108: q+1
       109: q+1
       110: q
       112: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: q+1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: q+1
       175: q+1
       178: 1
       180: 1
       182: 1
       184: q+1
       185: q+1
       186: q
       188: q+1
       190: q+1
       191: q+1
       192: q
       194: q+1
       195: q+1
       196: q
       198: q+1
       200: q+1
       202: 1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: 1
       265: q+1
       270: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: q+1
       302: 1
       303: q+1
       304: q
       306: q+1
       308: 1
       316: 1
       318: 1
       320: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: 1
       446: 1
       448: 1
       454: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       548: 1
       584: 1
       586: 1
       588: 1
       590: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       778: 1
       782: 1
       784: 1
       786: 1
       790: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       826: 1
       842: 1
       846: 1
       868: 1
       871: 1
       872: 1
       877: 1
       898: 1
       907: 1
       915: 1
       923: 1
       931: 1
       935: 1
      1003: 1
      1005: 1
      1019: 1
      1023: 1
      1025: 1
      1027: 1
      1053: 1
      1078: 1
      1121: 1
      1151: 1
      1159: 1
      1239: 1
      1241: 1
      1355: 1

1356:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q
        60: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: 1
        73: q^2+q+1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: 1
       110: q
       111: 1
       113: 1
       115: 1
       117: 1
       118: q
       119: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       186: q
       187: 1
       189: 1
       191: 1
       192: q
       193: 1
       195: 1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       286: q
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       296: q
       297: 1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       413: 1
       417: 1
       419: 1
       421: 1
       422: q
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: 1
       445: 1
       447: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       585: 1
       589: 1
       593: 1
       595: 1
       596: q
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       613: 1
       615: 1
       617: 1
       639: 1
       641: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       709: 1
       717: 1
       721: 1
       725: 1
       733: 1
       775: 1
       779: 1
       781: 1
       785: 1
       793: 1
       795: 1
       797: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       866: 1
       870: 1
       871: 1
       904: 1
       916: 1
       920: 1
       928: 1
       994: 1
      1000: 1
      1020: 1
      1022: 1
      1026: 1
      1076: 1
      1122: 1
      1156: 1
      1230: 1
      1234: 1
      1356: 1

1357:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: 1
        73: q^2+q+1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       109: q
       110: 1
       112: 1
       114: 1
       116: 1
       117: q
       118: 1
       119: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       185: q
       186: 1
       188: 1
       190: 1
       191: q
       192: 1
       193: 1
       195: q
       196: 1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       276: 1
       280: 1
       282: 1
       283: 1
       285: q
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       295: q
       296: 1
       298: 1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       414: 1
       418: 1
       419: 1
       421: q
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       586: 1
       589: 1
       593: 1
       595: q
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       614: 1
       615: 1
       618: 1
       640: 1
       641: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       710: 1
       718: 1
       722: 1
       726: 1
       734: 1
       776: 1
       780: 1
       782: 1
       785: 1
       793: 1
       796: 1
       798: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       866: 1
       870: 1
       871: 1
       905: 1
       917: 1
       921: 1
       929: 1
       995: 1
      1000: 1
      1021: 1
      1023: 1
      1026: 1
      1076: 1
      1123: 1
      1157: 1
      1231: 1
      1234: 1
      1357: 1

1358:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: 1
        73: q^2+q+1
        74: 1
        76: 1
        78: 1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       109: q
       110: 1
       111: 1
       113: 1
       115: 1
       117: q
       118: 1
       120: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       185: q
       186: 1
       187: 1
       189: 1
       191: q
       192: 1
       194: 1
       195: q
       196: 1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       278: 1
       279: 1
       281: 1
       284: 1
       285: q
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       295: q
       296: 1
       297: 1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       413: 1
       417: 1
       420: 1
       421: q
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       585: 1
       590: 1
       594: 1
       595: q
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       613: 1
       616: 1
       617: 1
       639: 1
       642: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       712: 1
       720: 1
       723: 1
       727: 1
       735: 1
       775: 1
       779: 1
       781: 1
       786: 1
       794: 1
       795: 1
       797: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       866: 1
       870: 1
       871: 1
       906: 1
       918: 1
       922: 1
       930: 1
       994: 1
      1001: 1
      1020: 1
      1022: 1
      1027: 1
      1076: 1
      1124: 1
      1158: 1
      1230: 1
      1235: 1
      1358: 1

1359:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: 1
        73: q^2+q+1
        75: 1
        77: 1
        79: 1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       108: 1
       109: 1
       110: q
       112: 1
       114: 1
       116: 1
       117: 1
       118: q
       120: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: q+1
       140: 1
       141: q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       186: q
       188: 1
       190: 1
       191: 1
       192: q
       194: 1
       195: 1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       270: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: q
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       296: q
       298: 1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q^2+q+1
       351: 1
       352: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       414: 1
       418: 1
       420: 1
       421: 1
       422: q
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: 1
       446: 1
       448: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       508: 1
       512: 1
       515: 1
       516: 1
       517: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       586: 1
       590: 1
       594: 1
       595: 1
       596: q
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       614: 1
       616: 1
       618: 1
       640: 1
       642: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       711: 1
       719: 1
       724: 1
       728: 1
       736: 1
       776: 1
       780: 1
       782: 1
       786: 1
       794: 1
       796: 1
       798: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       866: 1
       870: 1
       871: 1
       907: 1
       919: 1
       923: 1
       931: 1
       995: 1
      1001: 1
      1021: 1
      1023: 1
      1027: 1
      1076: 1
      1125: 1
      1159: 1
      1231: 1
      1235: 1
      1359: 1

1360:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^3+2q^2+q+1
        23: q^4+2q^3+2q^2+q+1
        24: q^3+2q^2+q+1
        25: q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^3+q^2+1
        32: q^3+2q^2+q+1
        33: 2q^2+q+1
        34: q^2+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        39: q^3+q^2+q+1
        41: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^3+2q^2+q+1
        53: q^4+2q^3+2q^2+q+1
        54: q^3+2q^2+q+1
        55: q^2+q+1
        56: q^3+q^2+q+1
        57: q^2+q+1
        58: q^2+1
        60: q^2+1
        62: q^2+1
        64: q^2+q+1
        66: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: q^2+q+1
        73: 2q^2+q+1
        74: q^2+q+1
        76: q^3+q^2+q+1
        78: q^2+q+1
        80: q^3+q^2+1
        81: 2q^2+q+1
        82: q^3+q^2+1
        83: q^3+2q^2+q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+1
        87: q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       103: q^2+1
       107: q^2+1
       109: q^2+1
       111: q^2+q+1
       113: q^2+1
       115: q^2+q+1
       117: q^2+1
       119: q^2+1
       121: q^2+1
       123: q^2+q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+1
       134: q^2+q+1
       135: q^2+q+1
       136: 2q^2+q+1
       137: 1
       138: q^2+q+1
       139: q^2+1
       140: q^2+q+1
       141: q^3+q^2+1
       142: 2q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: q^2+1
       147: q+1
       148: 1
       149: q^2+1
       150: q^2+q+1
       151: q^2+q+1
       153: q^3+q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q^2+1
       173: q^2+1
       177: q+1
       179: 1
       181: q+1
       183: q^2+1
       185: q^2+1
       187: q^2+q+1
       189: q^2+1
       191: 1
       193: q^2+1
       195: q^2+1
       197: q^2+q+1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: q^2+1
       211: q^2+q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: q^2+1
       228: q^2+q+1
       229: q^2+q+1
       230: 2q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: q+1
       245: 1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: q^3+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: q^2+1
       267: q^2+1
       271: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: q^2+1
       301: q+1
       303: q^2+1
       305: q^2+q+1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: q^2+1
       397: 1
       401: 1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: q+1
       435: q+1
       437: 1
       439: 1
       441: 1
       443: 1
       445: q+1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: q+1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: 1
       603: 1
       605: q+1
       607: 1
       609: 1
       613: q+1
       615: 1
       617: q+1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       685: 1
       689: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       781: 1
       785: 1
       787: 1
       791: 1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: q+1
       811: 1
       833: 1
       849: 1
       855: 1
       871: 1
       880: 1
       884: 1
       900: 1
       904: 1
       908: 1
       920: 1
       924: 1
       928: 1
       960: 1
      1010: 1
      1022: 1
      1026: 1
      1028: 1
      1060: 1
      1064: 1
      1126: 1
      1152: 1
      1156: 1
      1160: 1
      1278: 1
      1360: 1

1361:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^3+2q^2+q+1
        23: q^4+2q^3+2q^2+q+1
        24: q^3+2q^2+q+1
        25: q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^3+q^2+1
        32: q^3+2q^2+q+1
        33: 2q^2+q+1
        34: q^2+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        39: q^3+q^2+q+1
        41: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^3+2q^2+q+1
        53: q^4+2q^3+2q^2+q+1
        54: q^3+2q^2+q+1
        55: q^2+q+1
        56: q^3+q^2+q+1
        57: q^2+q+1
        59: q^2+1
        61: q^2+1
        62: q^2+1
        64: q^2+q+1
        66: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: q^2+q+1
        73: 2q^2+q+1
        74: q^2+q+1
        76: q^3+q^2+q+1
        78: q^2+q+1
        80: q^3+q^2+1
        81: 2q^2+q+1
        82: q^3+q^2+1
        83: q^3+2q^2+q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+1
        87: q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       106: q^2+1
       108: q^2+1
       110: q^2+1
       111: q^2+q+1
       113: q^2+1
       115: q^2+q+1
       118: q^2+1
       120: q^2+1
       121: q^2+1
       123: q^2+q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+1
       134: q^2+q+1
       135: q^2+q+1
       136: 2q^2+q+1
       137: 1
       138: q^2+q+1
       139: q^2+1
       140: q^2+q+1
       141: q^3+q^2+1
       142: 2q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: q^2+1
       147: q+1
       148: 1
       149: q^2+1
       150: q^2+q+1
       151: q^2+q+1
       153: q^3+q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       172: q^2+1
       176: q^2+1
       177: q+1
       179: 1
       181: q+1
       184: q^2+1
       186: q^2+1
       187: q^2+q+1
       189: q^2+1
       192: 1
       194: q^2+1
       196: q^2+1
       197: q^2+q+1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: q^2+1
       211: q^2+q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: q^2+1
       228: q^2+q+1
       229: q^2+q+1
       230: 2q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: q+1
       245: 1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: q^3+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: q^2+1
       269: q^2+1
       273: 1
       278: 1
       279: 1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: q^2+1
       301: q+1
       304: q^2+1
       305: q^2+q+1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: q^2+1
       399: 1
       404: 1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: q+1
       435: q+1
       438: 1
       440: 1
       441: 1
       444: 1
       445: q+1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: q+1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: 1
       604: 1
       605: q+1
       608: 1
       609: 1
       613: q+1
       616: 1
       617: q+1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       685: 1
       689: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       781: 1
       786: 1
       788: 1
       791: 1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: q+1
       811: 1
       833: 1
       849: 1
       855: 1
       871: 1
       880: 1
       889: 1
       902: 1
       906: 1
       911: 1
       922: 1
       927: 1
       930: 1
       961: 1
      1010: 1
      1022: 1
      1027: 1
      1029: 1
      1060: 1
      1064: 1
      1127: 1
      1154: 1
      1158: 1
      1163: 1
      1278: 1
      1361: 1

1362:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^3+2q^2+q+1
        23: q^4+2q^3+2q^2+q+1
        24: q^3+2q^2+q+1
        25: q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^3+q^2+1
        32: q^3+2q^2+q+1
        33: 2q^2+q+1
        34: q^2+1
        35: q^2+q+1
        36: q^2+q+1
        38: q^2+q+1
        40: q^3+q^2+q+1
        42: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^3+2q^2+q+1
        53: q^4+2q^3+2q^2+q+1
        54: q^3+2q^2+q+1
        55: q^2+q+1
        56: q^3+q^2+q+1
        57: q^2+q+1
        58: q^2+1
        61: q^2+1
        63: q^2+1
        65: q^2+q+1
        67: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: q^2+q+1
        73: 2q^2+q+1
        75: q^2+q+1
        77: q^3+q^2+q+1
        79: q^2+q+1
        80: q^3+q^2+1
        81: 2q^2+q+1
        82: q^3+q^2+1
        83: q^3+2q^2+q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+1
        87: q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       105: q^2+1
       108: q^2+1
       109: q^2+1
       112: q^2+q+1
       114: q^2+1
       116: q^2+q+1
       117: q^2+1
       120: q^2+1
       122: q^2+1
       124: q^2+q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+1
       134: q^2+q+1
       135: q^2+q+1
       136: 2q^2+q+1
       137: 1
       138: q^2+q+1
       139: q^2+1
       140: q^2+q+1
       141: q^3+q^2+1
       142: 2q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: q^2+1
       147: q+1
       148: 1
       149: q^2+1
       150: q^2+q+1
       152: q^2+q+1
       154: q^3+q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       171: q^2+1
       175: q^2+1
       178: q+1
       180: 1
       182: q+1
       184: q^2+1
       185: q^2+1
       188: q^2+q+1
       190: q^2+1
       191: 1
       194: q^2+1
       195: q^2+1
       198: q^2+q+1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: q^2+1
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: q^2+1
       228: q^2+q+1
       229: q^2+q+1
       230: 2q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: q^3+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: q^2+1
       270: q^2+1
       272: 1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: q^2+1
       302: q+1
       303: q^2+1
       306: q^2+q+1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: q^2+1
       398: 1
       402: 1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: q+1
       436: q+1
       438: 1
       439: 1
       442: 1
       444: 1
       446: q+1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: q+1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: 1
       604: 1
       606: q+1
       607: 1
       610: 1
       614: q+1
       616: 1
       618: q+1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       685: 1
       689: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       782: 1
       786: 1
       787: 1
       792: 1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: q+1
       812: 1
       834: 1
       850: 1
       856: 1
       871: 1
       880: 1
       891: 1
       901: 1
       907: 1
       910: 1
       923: 1
       925: 1
       931: 1
       963: 1
      1011: 1
      1023: 1
      1027: 1
      1028: 1
      1061: 1
      1065: 1
      1129: 1
      1153: 1
      1159: 1
      1161: 1
      1279: 1
      1362: 1

1363:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^3+2q^2+q+1
        23: q^4+2q^3+2q^2+q+1
        24: q^3+2q^2+q+1
        25: q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^3+q^2+1
        32: q^3+2q^2+q+1
        33: 2q^2+q+1
        34: q^2+1
        35: q^2+q+1
        36: q^2+q+1
        38: q^2+q+1
        40: q^3+q^2+q+1
        42: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^3+2q^2+q+1
        53: q^4+2q^3+2q^2+q+1
        54: q^3+2q^2+q+1
        55: q^2+q+1
        56: q^3+q^2+q+1
        57: q^2+q+1
        59: q^2+1
        60: q^2+1
        63: q^2+1
        65: q^2+q+1
        67: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: q^2+q+1
        73: 2q^2+q+1
        75: q^2+q+1
        77: q^3+q^2+q+1
        79: q^2+q+1
        80: q^3+q^2+1
        81: 2q^2+q+1
        82: q^3+q^2+1
        83: q^3+2q^2+q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+1
        87: q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       104: q^2+1
       107: q^2+1
       110: q^2+1
       112: q^2+q+1
       114: q^2+1
       116: q^2+q+1
       118: q^2+1
       119: q^2+1
       122: q^2+1
       124: q^2+q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+1
       134: q^2+q+1
       135: q^2+q+1
       136: 2q^2+q+1
       137: 1
       138: q^2+q+1
       139: q^2+1
       140: q^2+q+1
       141: q^3+q^2+1
       142: 2q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: q^2+1
       147: q+1
       148: 1
       149: q^2+1
       150: q^2+q+1
       152: q^2+q+1
       154: q^3+q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: q^2+1
       174: q^2+1
       178: q+1
       180: 1
       182: q+1
       183: q^2+1
       186: q^2+1
       188: q^2+q+1
       190: q^2+1
       192: 1
       193: q^2+1
       196: q^2+1
       198: q^2+q+1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: q^2+1
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: q^2+1
       228: q^2+q+1
       229: q^2+q+1
       230: 2q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: q^3+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: q^2+1
       268: q^2+1
       274: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: q^2+1
       302: q+1
       304: q^2+1
       306: q^2+q+1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: q^2+1
       400: 1
       403: 1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: q+1
       436: q+1
       437: 1
       440: 1
       442: 1
       443: 1
       446: q+1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: q+1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: 1
       603: 1
       606: q+1
       608: 1
       610: 1
       614: q+1
       615: 1
       618: q+1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       685: 1
       689: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       782: 1
       785: 1
       788: 1
       792: 1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: q+1
       812: 1
       834: 1
       850: 1
       856: 1
       871: 1
       880: 1
       890: 1
       903: 1
       905: 1
       909: 1
       921: 1
       926: 1
       929: 1
       962: 1
      1011: 1
      1023: 1
      1026: 1
      1029: 1
      1061: 1
      1065: 1
      1128: 1
      1155: 1
      1157: 1
      1162: 1
      1279: 1
      1363: 1

1364:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q+1
        61: q
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+3q+1
        73: q^3+3q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+2q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: 1
       104: q
       105: q
       107: q+1
       108: q
       109: q^2+q+1
       110: q
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+3q+1
       141: q+1
       142: q^3+3q^2+3q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: q^2+3q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: 1
       170: q
       171: q
       173: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       183: 1
       185: 1
       187: q+1
       188: q
       189: 1
       190: q
       191: 1
       193: q+1
       194: q
       195: q^2+q+1
       196: q
       197: q+1
       198: q^2+2q
       199: 1
       201: q+1
       202: q
       203: q+1
       205: 1
       206: q
       207: 1
       208: q
       209: 1
       210: 2q
       211: q+1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       238: q^2+2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q
       261: q
       263: 1
       267: 1
       268: q
       270: q
       271: 1
       272: q
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: q+1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: 1
       301: q+1
       302: q^2+2q
       303: 1
       305: q+1
       306: q
       307: 1
       309: 1
       311: 1
       312: q
       313: 1
       315: q+1
       316: q
       317: 1
       318: 2q
       319: q+1
       320: q
       321: q+1
       323: 1
       324: q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       339: q^2+2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       385: 1
       389: 1
       390: q
       392: q
       393: 1
       397: 1
       398: q
       401: 1
       405: 1
       408: q
       419: 1
       421: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: 1
       428: 2q
       429: 1
       431: 1
       433: q+1
       434: q
       437: 1
       439: 1
       441: 1
       442: q
       443: q+1
       444: q
       445: q+1
       446: q^2+2q
       447: 1
       449: 1
       451: 1
       461: q+1
       463: 1
       464: q
       469: 1
       470: q
       471: 1
       473: 1
       475: 1
       477: 1
       478: q
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       529: 1
       533: 1
       541: 1
       545: 1
       546: q
       548: q
       549: 1
       561: 1
       562: q
       565: 1
       569: 1
       572: q
       573: 1
       576: q
       577: 1
       581: q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       603: 1
       607: 1
       609: 1
       610: q
       613: q+1
       614: q
       615: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 1
       685: 1
       689: 1
       693: 1
       700: q
       713: 1
       717: 1
       725: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       812: q
       817: 1
       843: 1
       855: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       908: 1
       924: 1
       928: 1
       964: 1
       998: 1
      1000: 1
      1012: 1
      1026: 1
      1028: 1
      1064: 1
      1076: 1
      1084: 1
      1130: 1
      1160: 1
      1232: 1
      1234: 1
      1280: 1
      1364: 1

1365:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q
        61: q+1
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+3q+1
        73: q^3+3q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+2q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       105: 1
       106: q
       107: q
       108: q+1
       109: q^2+q+1
       110: q
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       117: 1
       120: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+3q+1
       141: q+1
       142: q^3+3q^2+3q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: q^2+3q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q^2+2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: q^2+q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       171: 1
       172: q
       175: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       184: 1
       185: 1
       187: q
       188: q+1
       189: q
       190: 1
       191: 1
       193: q
       194: q+1
       195: q^2+q+1
       196: q
       197: q^2+2q
       198: q+1
       200: 1
       201: q
       202: q+1
       203: q+1
       205: q
       206: 1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q^2+2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       261: 1
       262: q
       265: 1
       267: q
       269: q
       270: 1
       271: q
       272: 1
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       291: q
       292: q+1
       294: 1
       295: 1
       297: q
       298: 1
       300: 1
       301: q^2+2q
       302: q+1
       303: 1
       305: q
       306: q+1
       308: 1
       309: 1
       311: q
       312: 1
       314: 1
       315: q
       316: q+1
       317: 2q
       318: 1
       319: q
       320: q+1
       321: q+1
       323: q
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: q^2+q
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       387: 1
       389: q
       391: q
       392: 1
       395: 1
       397: q
       398: 1
       402: 1
       405: q
       408: 1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 2q
       428: 1
       430: 1
       431: 1
       433: q
       434: q+1
       438: 1
       439: 1
       441: q
       442: 1
       443: q
       444: q+1
       445: q^2+2q
       446: q+1
       448: 1
       449: 1
       452: 1
       461: q+1
       463: q
       464: 1
       469: q
       470: 1
       472: 1
       473: 1
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       531: 1
       535: 1
       544: 1
       545: q
       547: q
       548: 1
       550: 1
       561: q
       562: 1
       567: 1
       569: q
       572: 1
       573: q
       576: 1
       577: q
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       604: 1
       607: 1
       609: q
       610: 1
       613: q
       614: q+1
       616: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 1
       685: 1
       689: 1
       693: q
       700: 1
       714: 1
       719: 1
       728: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       802: 1
       803: 1
       806: 1
       807: 1
       811: q
       812: 1
       817: 1
       844: 1
       856: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       910: 1
       925: 1
       931: 1
       966: 1
       998: 1
      1001: 1
      1013: 1
      1027: 1
      1028: 1
      1065: 1
      1076: 1
      1084: 1
      1132: 1
      1161: 1
      1232: 1
      1235: 1
      1281: 1
      1365: 1

1366:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q+1
        61: q
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+3q+1
        73: q^3+3q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+2q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: 1
       106: q
       107: q+1
       108: q
       109: q
       110: q^2+q+1
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       118: 1
       119: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+3q+1
       141: q+1
       142: q^3+3q^2+3q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: q^2+3q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q^2+2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: q^2+q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       170: 1
       172: q
       174: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       183: 1
       186: 1
       187: q
       188: q+1
       189: q
       190: 1
       192: 1
       193: q+1
       194: q
       195: q
       196: q^2+q+1
       197: q^2+2q
       198: q+1
       199: 1
       201: q+1
       202: q
       204: q+1
       205: q
       206: 1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q^2+2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: 1
       262: q
       264: 1
       267: q
       268: 1
       269: q
       273: q
       274: 1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       291: q
       292: q+1
       293: 1
       296: 1
       297: q
       298: 1
       299: 1
       301: q^2+2q
       302: q+1
       304: 1
       305: q
       306: q+1
       307: 1
       310: 1
       311: q
       312: 1
       314: 1
       315: q
       316: q+1
       317: 2q
       318: 1
       319: q+1
       320: q
       322: q+1
       323: q
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: q^2+q
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       386: 1
       389: q
       390: 1
       391: q
       394: 1
       399: q
       400: 1
       403: 1
       406: q
       407: 1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 2q
       428: 1
       429: 1
       432: 1
       433: q
       434: q+1
       437: 1
       440: 1
       441: q
       442: 1
       443: q+1
       444: q
       445: q^2+2q
       446: q+1
       447: 1
       450: 1
       452: 1
       462: q+1
       463: q
       464: 1
       469: q
       470: 1
       471: 1
       474: 1
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       530: 1
       534: 1
       542: 1
       545: q
       546: 1
       547: q
       551: 1
       563: q
       564: 1
       566: 1
       570: q
       571: 1
       574: 1
       575: q
       577: q
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       603: 1
       608: 1
       609: q
       610: 1
       613: q
       614: q+1
       615: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 1
       685: 1
       689: 1
       697: q
       699: 1
       715: 1
       718: 1
       726: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       801: 1
       804: 1
       805: 1
       808: 1
       811: q
       812: 1
       818: 1
       844: 1
       856: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       909: 1
       926: 1
       929: 1
       965: 1
       999: 1
      1000: 1
      1013: 1
      1026: 1
      1029: 1
      1065: 1
      1076: 1
      1084: 1
      1131: 1
      1162: 1
      1233: 1
      1234: 1
      1281: 1
      1366: 1

1367:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q
        61: q+1
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+3q+1
        73: q^3+3q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+2q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       104: q
       105: q
       106: 1
       107: q
       108: q+1
       109: q
       110: q^2+q+1
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+3q+1
       141: q+1
       142: q^3+3q^2+3q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: q^2+3q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: q
       171: q
       172: 1
       176: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       184: 1
       186: 1
       187: q+1
       188: q
       189: 1
       190: q
       192: 1
       193: q
       194: q+1
       195: q
       196: q^2+q+1
       197: q+1
       198: q^2+2q
       200: 1
       201: q
       202: q+1
       204: q+1
       205: 1
       206: q
       207: 1
       208: q
       209: 1
       210: 2q
       211: q+1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: q+1
       238: q^2+2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q
       262: 1
       266: 1
       268: q
       269: 1
       270: q
       273: 1
       274: q
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: q+1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: 1
       301: q+1
       302: q^2+2q
       304: 1
       305: q+1
       306: q
       308: 1
       310: 1
       311: 1
       312: q
       313: 1
       315: q+1
       316: q
       317: 1
       318: 2q
       319: q
       320: q+1
       322: q+1
       323: 1
       324: q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       339: q^2+2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+3q+1
       352: 1
       356: q+1
       358: 1
       359: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       388: 1
       390: q
       391: 1
       392: q
       396: 1
       399: 1
       400: q
       404: 1
       406: 1
       407: q
       420: 1
       422: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: 1
       428: 2q
       430: 1
       432: 1
       433: q+1
       434: q
       438: 1
       440: 1
       441: 1
       442: q
       443: q
       444: q+1
       445: q+1
       446: q^2+2q
       448: 1
       450: 1
       451: 1
       462: q+1
       463: 1
       464: q
       469: 1
       470: q
       472: 1
       474: 1
       475: 1
       477: 1
       478: q
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       532: 1
       536: 1
       543: 1
       546: q
       547: 1
       548: q
       552: 1
       563: 1
       564: q
       568: 1
       570: 1
       571: q
       574: q
       575: 1
       577: 1
       581: q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       604: 1
       608: 1
       609: 1
       610: q
       613: q+1
       614: q
       616: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 1
       685: 1
       689: 1
       697: 1
       699: q
       716: 1
       720: 1
       727: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       812: q
       818: 1
       843: 1
       855: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       911: 1
       927: 1
       930: 1
       967: 1
       999: 1
      1001: 1
      1012: 1
      1027: 1
      1029: 1
      1064: 1
      1076: 1
      1084: 1
      1133: 1
      1163: 1
      1233: 1
      1235: 1
      1280: 1
      1367: 1

1368:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: q^3+5q^2+5q+1
        23: q^3+5q^2+5q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: q^3+5q^2+5q+1
        32: 2q^2+3q+1
        33: 3q^2+5q+1
        34: 3q^2+5q+1
        35: q^2+3q+1
        36: 2q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: q^3+5q^2+5q+1
        53: q^3+5q^2+5q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+2q
        60: 2q^2+3q+1
        61: 2q
        62: 2q^2+3q+1
        63: q^2+2q
        64: q^2+2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 2q^2+5q+1
        73: 3q^2+5q+1
        74: 2q^2+3q+1
        75: q^2+2q
        76: 2q^2+3q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+3q+1
        81: 3q+1
        82: q^3+5q^2+5q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 3q^2+5q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q^2+5q+1
        95: 3q^2+5q+1
        96: q^3+3q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: 2q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q^2+2q+1
       104: q^2+q
       105: q
       106: q
       107: 2q^2+3q+1
       108: 2q
       109: 2q^2+3q+1
       110: q^2+2q
       111: q^2+3q+1
       112: q^2+2q
       113: 2q^2+3q+1
       114: q^2+2q
       115: q^2+2q+1
       116: q
       117: q+1
       119: q+1
       121: q^2+2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: 3q^2+5q+1
       140: 2q^2+5q+1
       141: 2q^2+3q+1
       142: 3q^2+5q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: 2q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: 2q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q^2+2q+1
       170: q^2+q
       171: q
       172: q
       173: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q+1
       185: q+1
       187: 2q+1
       188: q
       189: q^2+2q+1
       190: q
       191: q+1
       193: 2q^2+3q+1
       194: 2q
       195: 2q^2+3q+1
       196: q^2+2q
       197: q^2+3q+1
       198: q^2+2q
       199: q+1
       201: q^2+2q+1
       202: 2q
       203: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 2q^2+3q+1
       210: q^2+2q
       211: q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: 2q+1
       229: 3q+1
       230: 3q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       262: q
       263: q+1
       267: q^2+2q+1
       268: q^2+q
       269: q
       270: q
       271: q+1
       272: q
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: q+1
       293: q+1
       295: q+1
       297: 2q+1
       298: q
       299: q+1
       301: 2q+1
       303: q+1
       305: 2q+1
       306: q
       307: 1
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       319: q^2+2q+1
       320: 2q
       321: 2q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 1
       345: q+1
       346: 2q+1
       347: 3q+1
       348: 2q+1
       349: 3q+1
       350: 2q+1
       351: q^2+4q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: q+1
       389: q+1
       391: q
       393: q+1
       397: q+1
       401: 1
       405: q+1
       408: q
       419: 1
       421: 1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: q+1
       437: q+1
       439: q+1
       441: 2q+1
       442: q
       443: q^2+2q+1
       444: 2q
       445: 2q+1
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 2q+1
       463: q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       529: 1
       533: 1
       541: q+1
       545: q+1
       547: q
       549: 1
       557: 1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       576: q
       577: q+1
       589: 1
       591: 1
       593: 1
       595: 1
       599: q+1
       603: 1
       607: 1
       609: q+1
       613: q+1
       615: 1
       619: 1
       621: 1
       625: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: q+1
       675: 1
       676: 1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       693: q+1
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: q+1
       815: 1
       825: 1
       827: 1
       835: 1
       839: 1
       845: 1
       847: 1
       851: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       908: 1
       924: 1
       928: 1
       948: 1
       974: 1
       988: 1
      1004: 1
      1006: 1
      1008: 1
      1026: 1
      1028: 1
      1052: 1
      1054: 1
      1062: 1
      1064: 1
      1078: 1
      1085: 1
      1134: 1
      1160: 1
      1202: 1
      1240: 1
      1242: 1
      1276: 1
      1368: 1

1369:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: q^3+5q^2+5q+1
        23: q^3+5q^2+5q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: q^3+5q^2+5q+1
        32: 2q^2+3q+1
        33: 3q^2+5q+1
        34: 3q^2+5q+1
        35: q^2+3q+1
        36: 2q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: q^3+5q^2+5q+1
        53: q^3+5q^2+5q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+3q+1
        58: q^2+2q
        59: 2q^2+3q+1
        60: 2q
        61: 2q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+2q
        64: q^2+2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 2q^2+5q+1
        73: 3q^2+5q+1
        74: 2q^2+3q+1
        75: q^2+2q
        76: 2q^2+3q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+3q+1
        81: 3q+1
        82: q^3+5q^2+5q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 3q^2+5q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q^2+5q+1
        95: 3q^2+5q+1
        96: q^3+3q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: 2q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q
       104: q
       105: q^2+q
       106: q^2+2q+1
       107: 2q
       108: 2q^2+3q+1
       109: q^2+2q
       110: 2q^2+3q+1
       111: q^2+3q+1
       112: q^2+2q
       113: 2q^2+3q+1
       114: q^2+2q
       115: q^2+2q+1
       116: q
       118: q+1
       120: q+1
       121: q^2+2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: 3q^2+5q+1
       140: 2q^2+5q+1
       141: 2q^2+3q+1
       142: 3q^2+5q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: 2q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: 2q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q
       170: q
       171: q^2+q
       172: q^2+2q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       184: q+1
       186: q+1
       187: 2q+1
       188: q
       189: q^2+2q+1
       190: q
       192: q+1
       193: 2q
       194: 2q^2+3q+1
       195: q^2+2q
       196: 2q^2+3q+1
       197: q^2+3q+1
       198: q^2+2q
       200: q+1
       201: 2q
       202: q^2+2q+1
       204: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 2q^2+3q+1
       210: q^2+2q
       211: q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: 2q+1
       229: 3q+1
       230: 3q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: q+1
       266: q+1
       267: q
       268: q
       269: q^2+2q+1
       270: q^2+q
       273: q+1
       274: q
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: q+1
       294: q+1
       296: q+1
       297: 2q+1
       298: q
       300: q+1
       301: 2q+1
       304: q+1
       305: 2q+1
       306: q
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       319: 2q
       320: q^2+2q+1
       322: 2q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 1
       345: q+1
       346: 2q+1
       347: 3q+1
       348: 2q+1
       349: 3q+1
       350: 2q+1
       351: q^2+4q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: q+1
       389: q
       391: q+1
       396: q+1
       399: q+1
       404: 1
       406: q+1
       407: q
       420: 1
       422: 1
       423: q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: q+1
       438: q+1
       440: q+1
       441: 2q+1
       442: q
       443: 2q
       444: q^2+2q+1
       445: 2q+1
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 2q+1
       463: q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       532: 1
       536: 1
       543: q+1
       545: q
       547: q+1
       552: 1
       559: 1
       563: q+1
       568: 1
       570: q+1
       574: q
       575: q+1
       577: q+1
       590: 1
       592: 1
       594: 1
       596: 1
       599: q+1
       604: 1
       608: 1
       609: q+1
       613: q+1
       616: 1
       620: 1
       622: 1
       625: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: q+1
       675: 1
       676: 1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       697: q+1
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: q+1
       816: 1
       826: 1
       828: 1
       835: 1
       840: 1
       846: 1
       848: 1
       851: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       911: 1
       927: 1
       930: 1
       950: 1
       975: 1
       991: 1
      1005: 1
      1007: 1
      1008: 1
      1027: 1
      1029: 1
      1053: 1
      1055: 1
      1062: 1
      1064: 1
      1078: 1
      1085: 1
      1135: 1
      1163: 1
      1204: 1
      1241: 1
      1243: 1
      1276: 1
      1369: 1

1370:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: q^3+5q^2+5q+1
        23: q^3+5q^2+5q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: q^3+5q^2+5q+1
        32: 2q^2+3q+1
        33: 3q^2+5q+1
        34: 3q^2+5q+1
        35: q^2+3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: q^3+5q^2+5q+1
        53: q^3+5q^2+5q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+2q
        60: 2q
        61: 2q^2+3q+1
        62: q^2+2q
        63: 2q^2+3q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 2q^2+5q+1
        73: 3q^2+5q+1
        74: q^2+2q
        75: 2q^2+3q+1
        76: q^2+2q
        77: 2q^2+3q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+3q+1
        81: 3q+1
        82: q^3+5q^2+5q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 3q^2+5q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q^2+5q+1
        95: 3q^2+5q+1
        96: q^3+3q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: 2q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q
       104: q
       105: q^2+2q+1
       106: q^2+q
       107: 2q
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: q^2+2q
       111: q^2+2q
       112: q^2+3q+1
       113: q^2+2q
       114: 2q^2+3q+1
       115: q
       116: q^2+2q+1
       117: q+1
       120: q+1
       121: q
       122: q^2+2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: 3q^2+5q+1
       140: 2q^2+5q+1
       141: 2q^2+3q+1
       142: 3q^2+5q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: 2q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: q^2+2q
       152: 2q^2+3q+1
       153: q^2+2q
       154: 2q^2+3q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q
       170: q
       171: q^2+2q+1
       172: q^2+q
       175: q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       184: q+1
       185: q+1
       187: q
       188: 2q+1
       189: q
       190: q^2+2q+1
       191: q+1
       193: 2q
       194: 2q^2+3q+1
       195: 2q^2+3q+1
       196: q^2+2q
       197: q^2+2q
       198: q^2+3q+1
       200: q+1
       201: 2q
       202: q^2+2q+1
       203: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 2q^2+3q+1
       211: q
       212: q^2+2q+1
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: 2q+1
       229: 3q+1
       230: 3q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q+1
       265: q+1
       267: q
       268: q
       269: q^2+q
       270: q^2+2q+1
       271: q
       272: q+1
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: 2q+1
       300: q+1
       302: 2q+1
       303: q+1
       305: q
       306: 2q+1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       319: 2q
       320: q^2+2q+1
       321: 2q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 1
       345: q+1
       346: 2q+1
       347: 3q+1
       348: 2q+1
       349: 3q+1
       350: 2q+1
       351: q^2+4q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: q+1
       390: q
       392: q+1
       395: q+1
       398: q+1
       402: 1
       405: q
       408: q+1
       420: 1
       421: 1
       424: q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: q+1
       438: q+1
       439: q+1
       441: q
       442: 2q+1
       443: 2q
       444: q^2+2q+1
       446: 2q+1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 2q+1
       464: q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       531: 1
       535: 1
       544: q+1
       546: q
       548: q+1
       550: 1
       558: 1
       562: q+1
       567: 1
       572: q+1
       573: q
       576: q+1
       581: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       600: q+1
       604: 1
       607: 1
       610: q+1
       614: q+1
       616: 1
       620: 1
       621: 1
       626: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: q+1
       675: 1
       676: 1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       700: q+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       802: 1
       803: 1
       806: 1
       807: 1
       812: q+1
       816: 1
       826: 1
       827: 1
       836: 1
       839: 1
       846: 1
       847: 1
       852: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       910: 1
       925: 1
       931: 1
       949: 1
       977: 1
       990: 1
      1005: 1
      1006: 1
      1009: 1
      1027: 1
      1028: 1
      1053: 1
      1054: 1
      1063: 1
      1065: 1
      1078: 1
      1085: 1
      1137: 1
      1161: 1
      1203: 1
      1241: 1
      1242: 1
      1277: 1
      1370: 1

1371:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: q^3+5q^2+5q+1
        23: q^3+5q^2+5q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: q^3+5q^2+5q+1
        32: 2q^2+3q+1
        33: 3q^2+5q+1
        34: 3q^2+5q+1
        35: q^2+3q+1
        36: 2q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: q^3+5q^2+5q+1
        53: q^3+5q^2+5q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+3q+1
        58: q^2+2q
        59: 2q^2+3q+1
        60: 2q^2+3q+1
        61: 2q
        62: q^2+2q
        63: 2q^2+3q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 2q^2+5q+1
        73: 3q^2+5q+1
        74: q^2+2q
        75: 2q^2+3q+1
        76: q^2+2q
        77: 2q^2+3q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+3q+1
        81: 3q+1
        82: q^3+5q^2+5q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: 3q+1
        86: 3q^2+5q+1
        87: q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q^2+5q+1
        95: 3q^2+5q+1
        96: q^3+3q^2+2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: 2q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q^2+q
       104: q^2+2q+1
       105: q
       106: q
       107: 2q^2+3q+1
       108: 2q
       109: q^2+2q
       110: 2q^2+3q+1
       111: q^2+2q
       112: q^2+3q+1
       113: q^2+2q
       114: 2q^2+3q+1
       115: q
       116: q^2+2q+1
       118: q+1
       119: q+1
       121: q
       122: q^2+2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: 3q^2+5q+1
       140: 2q^2+5q+1
       141: 2q^2+3q+1
       142: 3q^2+5q+1
       143: 3q+1
       144: 2q+1
       145: q^2+4q+1
       146: q^2+3q+1
       147: q^2+4q+1
       148: 2q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: q^2+2q
       152: 2q^2+3q+1
       153: q^2+2q
       154: 2q^2+3q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q^2+q
       170: q^2+2q+1
       171: q
       172: q
       174: q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q+1
       186: q+1
       187: q
       188: 2q+1
       189: q
       190: q^2+2q+1
       192: q+1
       193: 2q^2+3q+1
       194: 2q
       195: q^2+2q
       196: 2q^2+3q+1
       197: q^2+2q
       198: q^2+3q+1
       199: q+1
       201: q^2+2q+1
       202: 2q
       204: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 2q^2+3q+1
       211: q
       212: q^2+2q+1
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: q+1
       228: 2q+1
       229: 3q+1
       230: 3q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q+1
       261: q
       264: q+1
       267: q^2+q
       268: q^2+2q+1
       269: q
       270: q
       273: q
       274: q+1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: 2q+1
       299: q+1
       302: 2q+1
       304: q+1
       305: q
       306: 2q+1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       319: q^2+2q+1
       320: 2q
       322: 2q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 1
       345: q+1
       346: 2q+1
       347: 3q+1
       348: 2q+1
       349: 3q+1
       350: 2q+1
       351: q^2+4q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: q+1
       390: q+1
       392: q
       394: q+1
       400: q+1
       403: 1
       406: q
       407: q+1
       419: 1
       422: 1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: q+1
       437: q+1
       440: q+1
       441: q
       442: 2q+1
       443: q^2+2q+1
       444: 2q
       446: 2q+1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 2q+1
       464: q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       530: 1
       534: 1
       542: q+1
       546: q+1
       548: q
       551: 1
       560: 1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       575: q
       581: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       600: q+1
       603: 1
       608: 1
       610: q+1
       614: q+1
       615: 1
       619: 1
       622: 1
       626: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: q+1
       675: 1
       676: 1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       699: q+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       801: 1
       804: 1
       805: 1
       808: 1
       812: q+1
       815: 1
       825: 1
       828: 1
       836: 1
       840: 1
       845: 1
       848: 1
       852: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       909: 1
       926: 1
       929: 1
       951: 1
       976: 1
       989: 1
      1004: 1
      1007: 1
      1009: 1
      1026: 1
      1029: 1
      1052: 1
      1055: 1
      1063: 1
      1065: 1
      1078: 1
      1085: 1
      1136: 1
      1162: 1
      1205: 1
      1240: 1
      1243: 1
      1277: 1
      1371: 1

1372:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: 2q^2+q+1
        61: q^3+q^2+2q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       103: q^2+q+1
       106: q
       107: 1
       108: q
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q^2+q+1
       118: q
       119: 2q^2+q+1
       120: q^3+q^2+2q
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       141: q+1
       142: 1
       143: q^3+3q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: q^2+q+1
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 1
       184: q
       185: 1
       187: 1
       189: q+1
       191: q^2+q+1
       192: q
       195: 1
       199: 2q^2+q+1
       200: q^3+q^2+2q
       201: 1
       202: q
       203: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       230: 1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       271: 1
       275: q^2+q+1
       278: q
       279: q+1
       281: q+1
       283: 1
       284: q
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       294: q
       295: 1
       297: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       321: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q+1
       335: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       345: q+1
       346: q+1
       349: 1
       350: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 1
       420: q
       421: 1
       423: 1
       427: 1
       431: 1
       439: 1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       473: 1
       481: q+1
       482: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       494: 1
       497: q^2+2q+1
       498: q+1
       499: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: 1
       561: 1
       583: q+1
       585: 1
       587: 1
       589: 1
       590: q
       595: 1
       601: 1
       607: 1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       643: 1
       649: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       705: 1
       709: 1
       737: 1
       741: 1
       745: 1
       749: 1
       775: 1
       777: 1
       789: 1
       807: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       826: q
       831: 1
       837: 1
       839: 1
       841: q+1
       847: 1
       859: 1
       861: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       896: 1
       936: 1
       940: 1
       944: 1
       956: 1
       992: 1
      1030: 1
      1032: 1
      1034: 1
      1058: 1
      1066: 1
      1068: 1
      1072: 1
      1079: 1
      1164: 1
      1168: 1
      1210: 1
      1244: 1
      1246: 1
      1372: 1

1373:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q^3+q^2+2q
        61: 2q^2+q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: q^2+q+1
       107: q
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q^2+q+1
       118: q
       119: q^3+q^2+2q
       120: 2q^2+q+1
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       141: q+1
       142: 1
       143: q^3+3q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       174: q
       175: q^2+q+1
       178: q+1
       180: q+1
       182: 1
       183: q
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q^2+q+1
       192: q
       195: 1
       199: q^3+q^2+2q
       200: 2q^2+q+1
       201: q
       202: 1
       203: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       230: 1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       272: 1
       276: q
       277: q^2+q+1
       280: q+1
       282: q+1
       283: q
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       293: q
       294: 1
       295: 1
       298: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       321: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       345: q+1
       346: q+1
       349: 1
       350: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q
       420: 1
       421: 1
       424: 1
       428: 1
       431: 1
       439: 1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       473: 1
       481: q+1
       482: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       494: 1
       497: q^2+2q+1
       498: q+1
       499: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: 1
       562: 1
       584: q+1
       586: 1
       588: 1
       589: q
       590: 1
       595: 1
       602: 1
       607: 1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       643: 1
       649: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       707: 1
       711: 1
       738: 1
       742: 1
       746: 1
       750: 1
       776: 1
       778: 1
       790: 1
       807: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: 1
       831: 1
       838: 1
       839: 1
       842: q+1
       847: 1
       860: 1
       862: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       898: 1
       937: 1
       941: 1
       945: 1
       957: 1
       993: 1
      1031: 1
      1032: 1
      1035: 1
      1058: 1
      1067: 1
      1069: 1
      1072: 1
      1079: 1
      1165: 1
      1169: 1
      1211: 1
      1245: 1
      1246: 1
      1373: 1

1374:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q^3+q^2+2q
        61: 2q^2+q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: q^2+q+1
       107: q
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: q^2+q+1
       119: q^3+q^2+2q
       120: 2q^2+q+1
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       141: q+1
       142: 1
       143: q^3+3q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       173: q
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       183: q
       184: 1
       186: 1
       187: 1
       189: q+1
       191: q
       192: q^2+q+1
       196: 1
       199: q^3+q^2+2q
       200: 2q^2+q+1
       201: q
       202: 1
       204: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       230: 1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       273: 1
       275: q
       278: q^2+q+1
       279: q+1
       281: q+1
       283: q
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       293: q
       294: 1
       296: 1
       297: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       322: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q+1
       335: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       345: q+1
       346: q+1
       349: 1
       350: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q
       420: 1
       422: 1
       423: 1
       427: 1
       432: 1
       440: 1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       474: 1
       481: q+1
       482: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       494: 1
       497: q^2+2q+1
       498: q+1
       499: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: 1
       563: 1
       583: q+1
       585: 1
       587: 1
       589: q
       590: 1
       596: 1
       601: 1
       608: 1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       644: 1
       650: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       708: 1
       712: 1
       739: 1
       743: 1
       747: 1
       751: 1
       775: 1
       777: 1
       789: 1
       808: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: 1
       832: 1
       837: 1
       840: 1
       841: q+1
       848: 1
       859: 1
       861: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       899: 1
       938: 1
       942: 1
       946: 1
       958: 1
       992: 1
      1030: 1
      1033: 1
      1034: 1
      1059: 1
      1066: 1
      1068: 1
      1072: 1
      1079: 1
      1166: 1
      1170: 1
      1210: 1
      1244: 1
      1247: 1
      1374: 1

1375:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+2q^2+2q+1
         5: q^3+3q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+2q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+2q^2+2q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+2q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: 2q^2+q+1
        61: q^3+q^2+2q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       104: q^2+q+1
       105: q
       107: 1
       108: q
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: q^2+q+1
       119: 2q^2+q+1
       120: q^3+q^2+2q
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+3q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       141: q+1
       142: 1
       143: q^3+3q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: q^2+q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: 1
       184: q
       186: 1
       188: 1
       190: q+1
       191: q
       192: q^2+q+1
       196: 1
       199: 2q^2+q+1
       200: q^3+q^2+2q
       201: 1
       202: q
       204: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       230: 1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       274: 1
       276: q^2+q+1
       277: q
       280: q+1
       282: q+1
       283: 1
       284: q
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       294: q
       296: 1
       298: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       322: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       345: q+1
       346: q+1
       349: 1
       350: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 1
       420: q
       422: 1
       424: 1
       428: 1
       432: 1
       440: 1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       474: 1
       481: q+1
       482: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       494: 1
       497: q^2+2q+1
       498: q+1
       499: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: 1
       564: 1
       584: q+1
       586: 1
       588: 1
       589: 1
       590: q
       596: 1
       602: 1
       608: 1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       644: 1
       650: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       684: 1
       686: q+1
       688: 1
       690: 1
       691: 1
       706: 1
       710: 1
       740: 1
       744: 1
       748: 1
       752: 1
       776: 1
       778: 1
       790: 1
       808: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: 1
       826: q
       832: 1
       838: 1
       840: 1
       842: q+1
       848: 1
       860: 1
       862: 1
       865: 1
       873: 1
       878: 1
       881: 1
       882: 1
       897: 1
       939: 1
       943: 1
       947: 1
       959: 1
       993: 1
      1031: 1
      1033: 1
      1035: 1
      1059: 1
      1067: 1
      1069: 1
      1072: 1
      1079: 1
      1167: 1
      1171: 1
      1211: 1
      1245: 1
      1247: 1
      1375: 1

1376:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        60: q+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q+1
       108: q
       109: q+1
       111: q+1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       120: q
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       169: q+1
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q+1
       184: q
       185: q+1
       187: q+1
       189: q+1
       191: q+1
       195: 1
       199: q+1
       200: q
       201: q+1
       202: q
       203: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: q+1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: q+1
       294: q
       295: q+1
       297: q+1
       303: 1
       307: q+1
       308: q
       309: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       321: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: q+1
       397: 1
       401: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       439: 1
       447: 1
       449: 1
       451: 1
       453: q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: q+1
       561: 1
       583: 1
       585: 1
       587: 1
       589: 1
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       607: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       705: 1
       709: 1
       713: 1
       737: 1
       741: 1
       745: 1
       749: 1
       777: 1
       781: 1
       783: 1
       787: 1
       789: 1
       807: 1
       821: 1
       823: 1
       825: 1
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       847: 1
       868: 1
       875: 1
       876: 1
       878: 1
       896: 1
       900: 1
       936: 1
       944: 1
       948: 1
       956: 1
      1002: 1
      1006: 1
      1034: 1
      1038: 1
      1042: 1
      1044: 1
      1058: 1
      1082: 1
      1110: 1
      1168: 1
      1172: 1
      1256: 1
      1260: 1
      1376: 1

1377:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        60: q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       107: q
       108: q+1
       109: q+1
       112: q+1
       114: q+1
       116: q+1
       117: q+1
       119: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       171: q+1
       175: q+1
       178: 1
       180: 1
       182: 1
       183: q
       184: q+1
       185: q+1
       188: q+1
       190: q+1
       191: q+1
       195: 1
       199: q
       200: q+1
       201: q
       202: q+1
       203: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: q+1
       272: q+1
       277: q+1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       293: q
       294: q+1
       295: q+1
       298: q+1
       303: 1
       307: q
       308: q+1
       309: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       321: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: q+1
       398: 1
       402: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       439: 1
       448: 1
       449: 1
       452: 1
       453: q
       454: q+1
       456: 1
       457: q+1
       460: q+1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: q+1
       562: 1
       584: 1
       586: 1
       588: 1
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       607: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       707: 1
       711: 1
       714: 1
       738: 1
       742: 1
       746: 1
       750: 1
       778: 1
       782: 1
       784: 1
       787: 1
       790: 1
       807: 1
       822: 1
       824: 1
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       847: 1
       868: 1
       875: 1
       876: 1
       878: 1
       898: 1
       901: 1
       937: 1
       945: 1
       949: 1
       957: 1
      1003: 1
      1006: 1
      1035: 1
      1039: 1
      1043: 1
      1044: 1
      1058: 1
      1082: 1
      1111: 1
      1169: 1
      1173: 1
      1257: 1
      1260: 1
      1377: 1

1378:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: q+1
        60: q
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       107: q
       108: q+1
       110: q+1
       111: q+1
       113: q+1
       115: q+1
       118: q+1
       119: q
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       172: q+1
       176: q+1
       177: 1
       179: 1
       181: 1
       183: q
       184: q+1
       186: q+1
       187: q+1
       189: q+1
       192: q+1
       196: 1
       199: q
       200: q+1
       201: q
       202: q+1
       204: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: q+1
       273: q+1
       278: q+1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       293: q
       294: q+1
       296: q+1
       297: q+1
       304: 1
       307: q
       308: q+1
       310: q+1
       311: 1
       313: q+1
       315: 1
       317: 1
       322: 1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: q+1
       399: 1
       404: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       440: 1
       448: 1
       450: 1
       451: 1
       453: q
       454: q+1
       455: 1
       458: q+1
       459: q+1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: q+1
       563: 1
       583: 1
       585: 1
       587: 1
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       608: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       708: 1
       712: 1
       716: 1
       739: 1
       743: 1
       747: 1
       751: 1
       777: 1
       781: 1
       783: 1
       788: 1
       789: 1
       808: 1
       821: 1
       823: 1
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       848: 1
       868: 1
       875: 1
       876: 1
       878: 1
       899: 1
       902: 1
       938: 1
       946: 1
       950: 1
       958: 1
      1002: 1
      1007: 1
      1034: 1
      1038: 1
      1042: 1
      1045: 1
      1059: 1
      1082: 1
      1112: 1
      1170: 1
      1174: 1
      1256: 1
      1261: 1
      1378: 1

1379:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: 2q+1
        50: 2q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        59: q+1
        60: q+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: 2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q+1
       108: q
       110: q+1
       112: q+1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       120: q
       122: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       141: q+1
       142: 1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       170: q+1
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q+1
       184: q
       186: q+1
       188: q+1
       190: q+1
       192: q+1
       196: 1
       199: q+1
       200: q
       201: q+1
       202: q
       204: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: q+1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: q+1
       294: q
       296: q+1
       298: q+1
       304: 1
       307: q+1
       308: q
       310: q+1
       312: 1
       314: q+1
       316: 1
       318: 1
       322: 1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: q+1
       400: 1
       403: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       440: 1
       447: 1
       450: 1
       452: 1
       453: q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: q+1
       564: 1
       584: 1
       586: 1
       588: 1
       589: 1
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       608: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       706: 1
       710: 1
       715: 1
       740: 1
       744: 1
       748: 1
       752: 1
       778: 1
       782: 1
       784: 1
       788: 1
       790: 1
       808: 1
       822: 1
       824: 1
       825: 1
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       848: 1
       868: 1
       875: 1
       876: 1
       878: 1
       897: 1
       903: 1
       939: 1
       947: 1
       951: 1
       959: 1
      1003: 1
      1007: 1
      1035: 1
      1039: 1
      1043: 1
      1045: 1
      1059: 1
      1082: 1
      1113: 1
      1171: 1
      1175: 1
      1257: 1
      1261: 1
      1379: 1

1380:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        60: 1
        61: q
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       108: q
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       120: q
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       184: q
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: 1
       200: q
       201: 1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       284: q
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       294: q
       295: 1
       297: 1
       303: 1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       413: 1
       417: 1
       419: 1
       420: q
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       521: 1
       529: 1
       549: 1
       553: 1
       557: 1
       561: 1
       585: 1
       589: 1
       590: q
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       629: 1
       631: 1
       633: 1
       639: 1
       643: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       709: 1
       713: 1
       737: 1
       741: 1
       749: 1
       775: 1
       779: 1
       781: 1
       787: 1
       817: 1
       819: 1
       821: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       866: 1
       874: 1
       875: 1
       900: 1
       940: 1
       944: 1
       948: 1
       994: 1
       998: 1
      1036: 1
      1038: 1
      1044: 1
      1080: 1
      1114: 1
      1172: 1
      1248: 1
      1250: 1
      1380: 1

1381:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        60: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       105: 1
       107: q
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       119: q
       120: 1
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: q
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       199: q
       200: 1
       201: q
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       272: 1
       277: 1
       280: 1
       282: 1
       283: q
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       293: q
       294: 1
       295: 1
       298: 1
       303: 1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       414: 1
       418: 1
       419: q
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       523: 1
       531: 1
       550: 1
       554: 1
       558: 1
       562: 1
       586: 1
       589: q
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 1
       634: 1
       640: 1
       643: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       711: 1
       714: 1
       738: 1
       742: 1
       750: 1
       776: 1
       780: 1
       782: 1
       787: 1
       817: 1
       820: 1
       822: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       866: 1
       874: 1
       875: 1
       901: 1
       941: 1
       945: 1
       949: 1
       995: 1
       998: 1
      1037: 1
      1039: 1
      1044: 1
      1080: 1
      1115: 1
      1173: 1
      1249: 1
      1250: 1
      1381: 1

1382:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: 1
        39: 1
        41: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        60: q
        61: 1
        62: 1
        64: 1
        66: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       106: 1
       107: q
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       119: q
       120: 1
       121: 1
       123: 1
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: 1
       133: q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       183: q
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       199: q
       200: 1
       201: q
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       273: 1
       278: 1
       279: 1
       281: 1
       283: q
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       293: q
       294: 1
       296: 1
       297: 1
       304: 1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       413: 1
       417: 1
       419: q
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       524: 1
       532: 1
       552: 1
       555: 1
       559: 1
       563: 1
       585: 1
       589: q
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 1
       633: 1
       639: 1
       644: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       712: 1
       716: 1
       739: 1
       743: 1
       751: 1
       775: 1
       779: 1
       781: 1
       788: 1
       818: 1
       819: 1
       821: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       866: 1
       874: 1
       875: 1
       902: 1
       942: 1
       946: 1
       950: 1
       994: 1
       999: 1
      1036: 1
      1038: 1
      1045: 1
      1080: 1
      1116: 1
      1174: 1
      1248: 1
      1251: 1
      1382: 1

1383:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        38: 1
        40: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        60: 1
        61: q
        63: 1
        65: 1
        67: 1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       108: q
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       120: q
       122: 1
       124: 1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: 1
       133: q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q+1
       144: q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       184: q
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: 1
       200: q
       201: 1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q+1
       232: q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       284: q
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: q
       296: 1
       298: 1
       304: 1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       414: 1
       418: 1
       419: 1
       420: q
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       514: 1
       515: 1
       516: 1
       517: 1
       522: 1
       530: 1
       551: 1
       556: 1
       560: 1
       564: 1
       586: 1
       589: 1
       590: q
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       630: 1
       632: 1
       634: 1
       640: 1
       644: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       710: 1
       715: 1
       740: 1
       744: 1
       752: 1
       776: 1
       780: 1
       782: 1
       788: 1
       818: 1
       820: 1
       822: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       866: 1
       874: 1
       875: 1
       903: 1
       943: 1
       947: 1
       951: 1
       995: 1
       999: 1
      1037: 1
      1039: 1
      1045: 1
      1080: 1
      1117: 1
      1175: 1
      1249: 1
      1251: 1
      1383: 1

1384:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: 7q^3+17q^2+8q+1
        23: 7q^3+17q^2+8q+1
        24: q^4+7q^3+13q^2+7q+1
        25: q^4+13q^3+21q^2+8q+1
        26: q^4+13q^3+21q^2+8q+1
        27: 3q^4+11q^3+16q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: 7q^3+17q^2+8q+1
        32: 3q^3+12q^2+7q+1
        33: 3q^3+14q^2+8q+1
        34: q^4+13q^3+21q^2+8q+1
        35: 6q^3+15q^2+7q+1
        36: 7q^3+18q^2+8q+1
        37: 5q^3+13q^2+7q+1
        38: 2q^3+4q^2+q
        39: 5q^3+13q^2+7q+1
        40: 2q^3+4q^2+q
        41: q^4+5q^3+10q^2+6q+1
        42: 2q^3+3q^2+q
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: 3q^3+11q^2+7q+1
        53: 3q^3+11q^2+7q+1
        54: 3q^3+8q^2+6q+1
        55: q^4+8q^3+15q^2+7q+1
        56: q^4+8q^3+15q^2+7q+1
        57: q^4+6q^3+11q^2+6q+1
        58: 2q^3+8q^2+5q+1
        59: q^3+6q^2+3q
        60: 4q^3+11q^2+6q+1
        61: 3q^3+7q^2+2q
        62: 5q^3+13q^2+7q+1
        63: 2q^3+4q^2+q
        64: 2q^3+9q^2+6q+1
        65: q^3+3q^2+q
        66: 3q^3+11q^2+7q+1
        67: 3q^2+q
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: q^3+7q^2+6q+1
        73: 6q^2+6q+1
        74: q^3+7q^2+6q+1
        76: q^3+7q^2+6q+1
        78: q^3+5q^2+5q+1
        80: 3q^3+12q^2+7q+1
        81: q^3+9q^2+7q+1
        82: 3q^3+11q^2+7q+1
        83: q^3+7q^2+6q+1
        84: 6q^3+15q^2+7q+1
        85: 2q^3+12q^2+7q+1
        86: q^4+8q^3+15q^2+7q+1
        87: 3q^3+10q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 7q^2+7q+1
        95: 7q^2+7q+1
        96: q^3+4q^2+4q+1
        97: 3q^3+12q^2+7q+1
        98: 3q^3+12q^2+7q+1
        99: 3q^3+6q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: 2q^3+7q^2+5q+1
       104: 2q^2+q
       105: q^2
       106: q^3+4q^2+2q
       107: q^3+5q^2+5q+1
       108: 2q^2+q
       109: 3q^2+4q+1
       110: 3q^2+2q
       111: 3q^2+5q+1
       113: q^3+7q^2+6q+1
       115: 4q^2+5q+1
       117: 3q^2+4q+1
       118: 2q^2+2q
       119: 5q^2+5q+1
       120: 2q^2+q
       121: 2q^3+9q^2+6q+1
       122: q^3+3q^2+q
       123: q^3+7q^2+6q+1
       124: 2q^2+q
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       127: 3q^2+5q+1
       129: 3q^2+5q+1
       131: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: q^3+9q^2+7q+1
       138: 2q^2+4q+1
       139: 7q^2+7q+1
       140: 2q^2+3q+1
       141: q^3+7q^2+6q+1
       142: 5q^2+6q+1
       143: 2q^3+12q^2+7q+1
       144: 4q^2+4q+1
       145: 3q^3+12q^2+7q+1
       146: 3q^3+10q^2+6q+1
       147: q^3+7q^2+6q+1
       148: 6q^2+6q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       151: q^3+7q^2+6q+1
       153: q^3+7q^2+6q+1
       155: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 6q^2+6q+1
       164: q^3+7q^2+6q+1
       165: q^3+4q^2+4q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       169: 2q^2+4q+1
       172: q^2+q
       173: 3q^2+4q+1
       174: q^2+q
       176: q^2+q
       177: q^2+3q+1
       179: 3q^2+5q+1
       181: q^2+4q+1
       183: q^2+4q+1
       185: 3q+1
       186: q^2+q
       187: q^2+4q+1
       189: 4q^2+5q+1
       191: 3q^2+4q+1
       192: 2q^2+2q
       193: 2q^2+3q+1
       195: 3q^2+4q+1
       196: 2q^2+2q
       197: q^2+2q+1
       199: 5q^2+5q+1
       200: 2q^2+q
       201: q^3+5q^2+5q+1
       202: 2q^2+q
       203: 3q^2+4q+1
       204: 3q^2+2q
       205: 3q^2+5q+1
       207: q^3+7q^2+6q+1
       208: 2q^2+q
       209: q^3+7q^2+6q+1
       211: 4q^2+5q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 4q^2+4q+1
       232: 3q^2+5q+1
       233: 3q^2+4q+1
       234: 3q^2+5q+1
       235: 3q^2+5q+1
       236: 2q^2+4q+1
       237: 3q^2+5q+1
       239: 3q^2+5q+1
       241: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 2q^2+3q+1
       245: 5q^2+6q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+5q+1
       251: 2q^2+5q+1
       252: q^2+3q+1
       253: 6q^2+6q+1
       254: q^3+7q^2+6q+1
       255: q^3+4q^2+4q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q^2+3q+1
       262: q
       263: 3q+1
       267: q^2+2q+1
       271: 2q^2+4q+1
       273: q^2+q
       275: 3q^2+4q+1
       276: q^2+q
       278: q^2+q
       279: 2q+1
       281: 2q+1
       283: 2q+1
       285: q+1
       287: q^2+3q+1
       289: 2q+1
       291: 2q+1
       293: q^2+4q+1
       295: 3q+1
       296: q^2+q
       297: q^2+4q+1
       299: 2q+1
       301: q+1
       303: 2q+1
       304: q
       305: q+1
       307: q^2+4q+1
       309: 3q+1
       310: q^2+q
       311: q^2+4q+1
       313: q^2+4q+1
       315: q^2+3q+1
       317: 3q^2+5q+1
       319: 2q^2+3q+1
       321: 3q^2+4q+1
       322: 2q^2+2q
       323: q^2+2q+1
       325: 4q^2+5q+1
       327: 3q+1
       329: q^2+3q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q+1
       345: 4q+1
       346: 3q+1
       347: 2q+1
       348: q+1
       349: q^2+4q+1
       350: 2q+1
       351: 2q+2
       352: q^2+3q+1
       353: 3q^2+5q+1
       354: 3q^2+4q+1
       355: 3q^2+5q+1
       356: q^2+3q+1
       357: 3q^2+5q+1
       358: q^2+3q+1
       359: 4q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       377: q+1
       381: q+1
       385: 3q+1
       389: q+1
       393: q+1
       397: q^2+3q+1
       399: q
       401: 3q+1
       405: q^2+2q+1
       409: 2q+1
       411: 2q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: 2q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       431: 1
       433: 1
       435: 1
       437: 2q+1
       439: 2q+1
       440: q
       441: q+1
       443: 2q+2
       445: 2q+2
       447: 2q+1
       449: q+1
       451: 2q+1
       453: q^2+4q+1
       455: 2q+1
       457: 3q+1
       458: q^2+q
       459: q^2+4q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: 2q+1
       467: 2q+1
       469: q^2+3q+1
       471: 2q+1
       473: 2q+1
       474: q
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: 2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: q+2
       502: 3q+1
       504: q^2+3q+1
       506: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: 2q+1
       512: q+1
       513: q^2+4q+1
       514: 2q+1
       518: q+2
       519: q+2
       520: q+1
       521: 1
       525: q+1
       529: q+1
       533: 1
       537: 1
       541: q+1
       545: 2q+2
       549: q+1
       553: q+1
       557: 3q+1
       561: 2q+1
       563: 2q+1
       565: q+1
       569: q+1
       573: q+1
       574: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       589: q+1
       593: 1
       595: 1
       597: 1
       599: q+1
       601: 2
       603: q+1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 2
       617: 2
       619: 2q+1
       621: q+1
       623: q+1
       625: 2q+1
       627: 2q+1
       629: q+1
       631: 1
       632: 1
       633: q+2
       635: 2q+1
       637: 2q+1
       639: q+1
       641: q+1
       643: 1
       645: 1
       647: 2q+1
       649: 2q+1
       650: q
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: 2q+1
       689: 1
       693: q+1
       696: q+1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 2
       737: 1
       741: q+1
       745: q+1
       749: 1
       751: 1
       753: 1
       757: 1
       761: q+1
       765: 1
       766: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       785: 1
       789: 2
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 2
       815: 2
       821: 1
       823: q+1
       825: q+1
       829: 1
       831: 1
       833: 1
       835: q+1
       837: q+2
       839: 1
       840: 1
       841: q+1
       845: q+1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       896: 1
       904: 1
       912: 1
       928: 1
       932: 2
       936: 1
       944: 1
       952: 1
       956: 1
       958: 1
       960: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       989: 1
      1002: 1
      1004: 1
      1024: 1
      1034: 1
      1038: 1
      1040: 1
      1042: 1
      1050: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1082: 1
      1085: 1
      1098: 1
      1101: 1
      1118: 1
      1168: 1
      1176: 1
      1184: 1
      1206: 1
      1256: 1
      1258: 1
      1272: 1
      1384: 1

1385:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: 7q^3+17q^2+8q+1
        23: 7q^3+17q^2+8q+1
        24: q^4+7q^3+13q^2+7q+1
        25: q^4+13q^3+21q^2+8q+1
        26: q^4+13q^3+21q^2+8q+1
        27: 3q^4+11q^3+16q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: 7q^3+17q^2+8q+1
        32: 3q^3+12q^2+7q+1
        33: 3q^3+14q^2+8q+1
        34: q^4+13q^3+21q^2+8q+1
        35: 6q^3+15q^2+7q+1
        36: 7q^3+18q^2+8q+1
        37: 2q^3+4q^2+q
        38: 5q^3+13q^2+7q+1
        39: 2q^3+4q^2+q
        40: 5q^3+13q^2+7q+1
        41: 2q^3+3q^2+q
        42: q^4+5q^3+10q^2+6q+1
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: 3q^3+11q^2+7q+1
        53: 3q^3+11q^2+7q+1
        54: 3q^3+8q^2+6q+1
        55: q^4+8q^3+15q^2+7q+1
        56: q^4+8q^3+15q^2+7q+1
        57: q^4+6q^3+11q^2+6q+1
        58: q^3+6q^2+3q
        59: 2q^3+8q^2+5q+1
        60: 4q^3+11q^2+6q+1
        61: 3q^3+7q^2+2q
        62: 2q^3+4q^2+q
        63: 5q^3+13q^2+7q+1
        64: q^3+3q^2+q
        65: 2q^3+9q^2+6q+1
        66: 3q^2+q
        67: 3q^3+11q^2+7q+1
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: q^3+7q^2+6q+1
        73: 6q^2+6q+1
        75: q^3+7q^2+6q+1
        77: q^3+7q^2+6q+1
        79: q^3+5q^2+5q+1
        80: 3q^3+12q^2+7q+1
        81: q^3+9q^2+7q+1
        82: 3q^3+11q^2+7q+1
        83: q^3+7q^2+6q+1
        84: 6q^3+15q^2+7q+1
        85: 2q^3+12q^2+7q+1
        86: q^4+8q^3+15q^2+7q+1
        87: 3q^3+10q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 7q^2+7q+1
        95: 7q^2+7q+1
        96: q^3+4q^2+4q+1
        97: 3q^3+12q^2+7q+1
        98: 3q^3+12q^2+7q+1
        99: 3q^3+6q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: 2q^2+q
       104: 2q^3+7q^2+5q+1
       105: q^3+4q^2+2q
       106: q^2
       107: q^3+5q^2+5q+1
       108: 2q^2+q
       109: 3q^2+2q
       110: 3q^2+4q+1
       112: 3q^2+5q+1
       114: q^3+7q^2+6q+1
       116: 4q^2+5q+1
       117: 2q^2+2q
       118: 3q^2+4q+1
       119: 5q^2+5q+1
       120: 2q^2+q
       121: q^3+3q^2+q
       122: 2q^3+9q^2+6q+1
       123: 2q^2+q
       124: q^3+7q^2+6q+1
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       128: 3q^2+5q+1
       130: 3q^2+5q+1
       132: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: q^3+9q^2+7q+1
       138: 2q^2+4q+1
       139: 7q^2+7q+1
       140: 2q^2+3q+1
       141: q^3+7q^2+6q+1
       142: 5q^2+6q+1
       143: 2q^3+12q^2+7q+1
       144: 4q^2+4q+1
       145: 3q^3+12q^2+7q+1
       146: 3q^3+10q^2+6q+1
       147: q^3+7q^2+6q+1
       148: 6q^2+6q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       152: q^3+7q^2+6q+1
       154: q^3+7q^2+6q+1
       156: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 6q^2+6q+1
       164: q^3+7q^2+6q+1
       165: q^3+4q^2+4q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       170: 2q^2+4q+1
       171: q^2+q
       173: q^2+q
       174: 3q^2+4q+1
       175: q^2+q
       178: q^2+3q+1
       180: 3q^2+5q+1
       182: q^2+4q+1
       183: q^2+4q+1
       185: q^2+q
       186: 3q+1
       188: q^2+4q+1
       190: 4q^2+5q+1
       191: 2q^2+2q
       192: 3q^2+4q+1
       193: 2q^2+3q+1
       195: 2q^2+2q
       196: 3q^2+4q+1
       198: q^2+2q+1
       199: 5q^2+5q+1
       200: 2q^2+q
       201: q^3+5q^2+5q+1
       202: 2q^2+q
       203: 3q^2+2q
       204: 3q^2+4q+1
       206: 3q^2+5q+1
       207: 2q^2+q
       208: q^3+7q^2+6q+1
       210: q^3+7q^2+6q+1
       212: 4q^2+5q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 4q^2+4q+1
       232: 3q^2+5q+1
       233: 3q^2+4q+1
       234: 3q^2+5q+1
       235: 3q^2+5q+1
       236: 2q^2+4q+1
       238: 3q^2+5q+1
       240: 3q^2+5q+1
       242: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 2q^2+3q+1
       245: 5q^2+6q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+5q+1
       251: 2q^2+5q+1
       252: q^2+3q+1
       253: 6q^2+6q+1
       254: q^3+7q^2+6q+1
       255: q^3+4q^2+4q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q^2+3q+1
       261: q
       264: 3q+1
       268: q^2+2q+1
       272: q^2+q
       274: 2q^2+4q+1
       275: q^2+q
       276: 3q^2+4q+1
       277: q^2+q
       280: 2q+1
       282: 2q+1
       283: 2q+1
       286: q+1
       288: q^2+3q+1
       290: 2q+1
       292: 2q+1
       293: q^2+4q+1
       295: q^2+q
       296: 3q+1
       298: q^2+4q+1
       299: 2q+1
       302: q+1
       303: q
       304: 2q+1
       306: q+1
       307: q^2+4q+1
       309: q^2+q
       310: 3q+1
       312: q^2+4q+1
       314: q^2+4q+1
       316: q^2+3q+1
       318: 3q^2+5q+1
       319: 2q^2+3q+1
       321: 2q^2+2q
       322: 3q^2+4q+1
       324: q^2+2q+1
       326: 4q^2+5q+1
       328: 3q+1
       330: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q+1
       345: 4q+1
       346: 3q+1
       347: 2q+1
       348: q+1
       349: q^2+4q+1
       350: 2q+1
       351: 2q+2
       352: q^2+3q+1
       353: 3q^2+5q+1
       354: 3q^2+4q+1
       355: 3q^2+5q+1
       356: q^2+3q+1
       357: 3q^2+5q+1
       358: q^2+3q+1
       359: 4q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       378: q+1
       382: q+1
       386: 3q+1
       390: q+1
       394: q+1
       398: q
       400: q^2+3q+1
       403: 3q+1
       407: q^2+2q+1
       410: 2q+1
       412: 2q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: 2q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       432: 1
       434: 1
       436: 1
       437: 2q+1
       439: q
       440: 2q+1
       442: q+1
       443: 2q+2
       446: 2q+2
       447: 2q+1
       450: q+1
       452: 2q+1
       453: q^2+4q+1
       456: 2q+1
       457: q^2+q
       458: 3q+1
       460: q^2+4q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: 2q+1
       468: 2q+1
       470: q^2+3q+1
       471: 2q+1
       473: q
       474: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: 2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: q+2
       503: 3q+1
       505: q^2+3q+1
       507: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: 2q+1
       512: q+1
       513: q^2+4q+1
       514: 2q+1
       518: q+2
       519: q+2
       520: q+1
       522: 1
       526: q+1
       530: q+1
       534: 1
       538: 1
       542: q+1
       546: 2q+2
       551: q+1
       556: q+1
       560: 3q+1
       562: 2q+1
       564: 2q+1
       566: q+1
       571: q+1
       573: q+1
       574: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       589: q+1
       593: 1
       596: 1
       598: 1
       600: q+1
       602: 2
       603: q+1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 2
       618: 2
       619: 2q+1
       622: q+1
       624: q+1
       626: 2q+1
       628: 2q+1
       630: q+1
       631: 1
       632: 1
       634: q+2
       636: 2q+1
       638: 2q+1
       640: q+1
       641: q+1
       644: 1
       646: 1
       647: 2q+1
       649: q
       650: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: 2q+1
       689: 1
       694: q+1
       699: q+1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 2
       740: 1
       744: q+1
       748: q+1
       750: 1
       752: 1
       754: 1
       759: 1
       763: q+1
       765: 1
       766: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       785: 1
       790: 2
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 2
       815: 2
       822: 1
       824: q+1
       825: q+1
       829: 1
       832: 1
       834: 1
       836: q+1
       838: q+2
       839: 1
       840: 1
       842: q+1
       845: q+1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       897: 1
       905: 1
       913: 1
       929: 1
       933: 2
       939: 1
       947: 1
       953: 1
       957: 1
       959: 1
       962: 1
       976: 1
       980: 1
       983: 1
       986: 1
       988: 1
       989: 1
      1003: 1
      1004: 1
      1025: 1
      1035: 1
      1039: 1
      1040: 1
      1043: 1
      1051: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1082: 1
      1085: 1
      1099: 1
      1104: 1
      1119: 1
      1171: 1
      1177: 1
      1186: 1
      1207: 1
      1257: 1
      1258: 1
      1273: 1
      1385: 1

1386:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: 7q^3+17q^2+8q+1
        23: 7q^3+17q^2+8q+1
        24: q^4+7q^3+13q^2+7q+1
        25: q^4+13q^3+21q^2+8q+1
        26: q^4+13q^3+21q^2+8q+1
        27: 3q^4+11q^3+16q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: 7q^3+17q^2+8q+1
        32: 3q^3+12q^2+7q+1
        33: 3q^3+14q^2+8q+1
        34: q^4+13q^3+21q^2+8q+1
        35: 6q^3+15q^2+7q+1
        36: 7q^3+18q^2+8q+1
        37: 5q^3+13q^2+7q+1
        38: 2q^3+4q^2+q
        39: 5q^3+13q^2+7q+1
        40: 2q^3+4q^2+q
        41: q^4+5q^3+10q^2+6q+1
        42: 2q^3+3q^2+q
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: 3q^3+11q^2+7q+1
        53: 3q^3+11q^2+7q+1
        54: 3q^3+8q^2+6q+1
        55: q^4+8q^3+15q^2+7q+1
        56: q^4+8q^3+15q^2+7q+1
        57: q^4+6q^3+11q^2+6q+1
        58: q^3+6q^2+3q
        59: 2q^3+8q^2+5q+1
        60: 3q^3+7q^2+2q
        61: 4q^3+11q^2+6q+1
        62: 5q^3+13q^2+7q+1
        63: 2q^3+4q^2+q
        64: 2q^3+9q^2+6q+1
        65: q^3+3q^2+q
        66: 3q^3+11q^2+7q+1
        67: 3q^2+q
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: q^3+7q^2+6q+1
        73: 6q^2+6q+1
        74: q^3+7q^2+6q+1
        76: q^3+7q^2+6q+1
        78: q^3+5q^2+5q+1
        80: 3q^3+12q^2+7q+1
        81: q^3+9q^2+7q+1
        82: 3q^3+11q^2+7q+1
        83: q^3+7q^2+6q+1
        84: 6q^3+15q^2+7q+1
        85: 2q^3+12q^2+7q+1
        86: q^4+8q^3+15q^2+7q+1
        87: 3q^3+10q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 7q^2+7q+1
        95: 7q^2+7q+1
        96: q^3+4q^2+4q+1
        97: 3q^3+12q^2+7q+1
        98: 3q^3+12q^2+7q+1
        99: 3q^3+6q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: q^3+4q^2+2q
       104: q^2
       105: 2q^2+q
       106: 2q^3+7q^2+5q+1
       107: 2q^2+q
       108: q^3+5q^2+5q+1
       109: 3q^2+2q
       110: 3q^2+4q+1
       111: 3q^2+5q+1
       113: q^3+7q^2+6q+1
       115: 4q^2+5q+1
       117: 2q^2+2q
       118: 3q^2+4q+1
       119: 2q^2+q
       120: 5q^2+5q+1
       121: 2q^3+9q^2+6q+1
       122: q^3+3q^2+q
       123: q^3+7q^2+6q+1
       124: 2q^2+q
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       127: 3q^2+5q+1
       129: 3q^2+5q+1
       131: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: q^3+9q^2+7q+1
       138: 2q^2+4q+1
       139: 7q^2+7q+1
       140: 2q^2+3q+1
       141: q^3+7q^2+6q+1
       142: 5q^2+6q+1
       143: 2q^3+12q^2+7q+1
       144: 4q^2+4q+1
       145: 3q^3+12q^2+7q+1
       146: 3q^3+10q^2+6q+1
       147: q^3+7q^2+6q+1
       148: 6q^2+6q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       151: q^3+7q^2+6q+1
       153: q^3+7q^2+6q+1
       155: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 6q^2+6q+1
       164: q^3+7q^2+6q+1
       165: q^3+4q^2+4q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       169: q^2+q
       172: 2q^2+4q+1
       173: q^2+q
       175: q^2+q
       176: 3q^2+4q+1
       177: q^2+3q+1
       179: 3q^2+5q+1
       181: q^2+4q+1
       184: q^2+4q+1
       185: q^2+q
       186: 3q+1
       187: q^2+4q+1
       189: 4q^2+5q+1
       191: 2q^2+2q
       192: 3q^2+4q+1
       194: 2q^2+3q+1
       195: 2q^2+2q
       196: 3q^2+4q+1
       197: q^2+2q+1
       199: 2q^2+q
       200: 5q^2+5q+1
       201: 2q^2+q
       202: q^3+5q^2+5q+1
       203: 3q^2+2q
       204: 3q^2+4q+1
       205: 3q^2+5q+1
       207: q^3+7q^2+6q+1
       208: 2q^2+q
       209: q^3+7q^2+6q+1
       211: 4q^2+5q+1
       213: 3q+1
       215: q^2+3q+1
       217: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 4q^2+4q+1
       232: 3q^2+5q+1
       233: 3q^2+4q+1
       234: 3q^2+5q+1
       235: 3q^2+5q+1
       236: 2q^2+4q+1
       237: 3q^2+5q+1
       239: 3q^2+5q+1
       241: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 2q^2+3q+1
       245: 5q^2+6q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+5q+1
       251: 2q^2+5q+1
       252: q^2+3q+1
       253: 6q^2+6q+1
       254: q^3+7q^2+6q+1
       255: q^3+4q^2+4q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       259: q
       262: q^2+3q+1
       266: 3q+1
       269: q^2+2q+1
       271: q^2+q
       273: 2q^2+4q+1
       275: q^2+q
       277: q^2+q
       278: 3q^2+4q+1
       279: 2q+1
       281: 2q+1
       284: 2q+1
       286: q+1
       287: q^2+3q+1
       289: 2q+1
       291: 2q+1
       294: q^2+4q+1
       295: q^2+q
       296: 3q+1
       297: q^2+4q+1
       300: 2q+1
       301: q+1
       303: q
       304: 2q+1
       305: q+1
       308: q^2+4q+1
       309: q^2+q
       310: 3q+1
       311: q^2+4q+1
       313: q^2+4q+1
       315: q^2+3q+1
       317: 3q^2+5q+1
       320: 2q^2+3q+1
       321: 2q^2+2q
       322: 3q^2+4q+1
       323: q^2+2q+1
       325: 4q^2+5q+1
       327: 3q+1
       329: q^2+3q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q+1
       345: 4q+1
       346: 3q+1
       347: 2q+1
       348: q+1
       349: q^2+4q+1
       350: 2q+1
       351: 2q+2
       352: q^2+3q+1
       353: 3q^2+5q+1
       354: 3q^2+4q+1
       355: 3q^2+5q+1
       356: q^2+3q+1
       357: 3q^2+5q+1
       358: q^2+3q+1
       359: 4q+2
       360: 3q+1
       362: q^2+3q+1
       364: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       380: q+1
       384: q+1
       388: 3q+1
       391: q+1
       396: q+1
       397: q
       399: q^2+3q+1
       404: 3q+1
       406: q^2+2q+1
       409: 2q+1
       411: 2q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: 2q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       430: q+1
       432: 1
       433: 1
       435: 1
       438: 2q+1
       439: q
       440: 2q+1
       441: q+1
       444: 2q+2
       445: 2q+2
       448: 2q+1
       450: q+1
       451: 2q+1
       454: q^2+4q+1
       455: 2q+1
       457: q^2+q
       458: 3q+1
       459: q^2+4q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: 2q+1
       467: 2q+1
       469: q^2+3q+1
       472: 2q+1
       473: q
       474: 2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: 2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: q+2
       502: 3q+1
       504: q^2+3q+1
       506: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: 2q+1
       512: q+1
       513: q^2+4q+1
       514: 2q+1
       518: q+2
       519: q+2
       520: q+1
       524: 1
       528: q+1
       532: q+1
       536: 1
       539: 1
       543: q+1
       547: 2q+2
       552: q+1
       555: q+1
       559: 3q+1
       561: 2q+1
       563: 2q+1
       568: q+1
       570: q+1
       575: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       590: q+1
       594: 1
       596: 1
       597: 1
       599: q+1
       601: 2
       604: q+1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 2
       617: 2
       620: 2q+1
       622: q+1
       623: q+1
       625: 2q+1
       627: 2q+1
       629: q+1
       631: 1
       632: 1
       633: q+2
       635: 2q+1
       637: 2q+1
       639: q+1
       642: q+1
       644: 1
       645: 1
       648: 2q+1
       649: q
       650: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: 2q+1
       689: 1
       697: q+1
       698: q+1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 2
       739: 1
       743: q+1
       747: q+1
       749: 1
       751: 1
       756: 1
       758: 1
       762: q+1
       767: 1
       768: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       786: 1
       789: 2
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 2
       816: 2
       821: 1
       823: q+1
       826: q+1
       830: 1
       832: 1
       833: 1
       835: q+1
       837: q+2
       839: 1
       840: 1
       841: q+1
       846: q+1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       888: 1
       889: 1
       899: 1
       906: 1
       914: 1
       930: 1
       934: 2
       938: 1
       946: 1
       955: 1
       956: 1
       958: 1
       961: 1
       975: 1
       979: 1
       982: 1
       985: 1
       990: 1
       991: 1
      1002: 1
      1005: 1
      1024: 1
      1034: 1
      1038: 1
      1041: 1
      1042: 1
      1050: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1082: 1
      1085: 1
      1102: 1
      1103: 1
      1120: 1
      1170: 1
      1178: 1
      1185: 1
      1208: 1
      1256: 1
      1259: 1
      1272: 1
      1386: 1

1387:    0: q^4+13q^3+21q^2+8q+1
         1: q^4+13q^3+21q^2+8q+1
         2: 3q^4+11q^3+16q^2+7q+1
         3: q^4+13q^3+21q^2+8q+1
         4: q^5+6q^4+14q^3+16q^2+7q+1
         5: q^4+13q^3+21q^2+8q+1
         6: q^5+6q^4+14q^3+16q^2+7q+1
         7: 4q^4+10q^3+12q^2+6q+1
         8: 3q^4+11q^3+16q^2+7q+1
         9: q^5+4q^4+7q^3+7q^2+4q+1
        10: q^4+13q^3+21q^2+8q+1
        11: q^4+13q^3+21q^2+8q+1
        12: q^5+6q^4+14q^3+16q^2+7q+1
        13: 6q^3+15q^2+7q+1
        14: 2q^4+7q^3+11q^2+6q+1
        15: 6q^3+15q^2+7q+1
        16: 7q^3+18q^2+8q+1
        17: 7q^3+18q^2+8q+1
        18: 2q^4+6q^3+7q^2+4q+1
        19: q^4+8q^3+15q^2+7q+1
        20: q^4+8q^3+15q^2+7q+1
        21: q^4+6q^3+11q^2+6q+1
        22: 7q^3+17q^2+8q+1
        23: 7q^3+17q^2+8q+1
        24: q^4+7q^3+13q^2+7q+1
        25: q^4+13q^3+21q^2+8q+1
        26: q^4+13q^3+21q^2+8q+1
        27: 3q^4+11q^3+16q^2+7q+1
        28: 7q^3+18q^2+8q+1
        29: q^4+8q^3+15q^2+7q+1
        30: 3q^3+10q^2+6q+1
        31: 7q^3+17q^2+8q+1
        32: 3q^3+12q^2+7q+1
        33: 3q^3+14q^2+8q+1
        34: q^4+13q^3+21q^2+8q+1
        35: 6q^3+15q^2+7q+1
        36: 7q^3+18q^2+8q+1
        37: 2q^3+4q^2+q
        38: 5q^3+13q^2+7q+1
        39: 2q^3+4q^2+q
        40: 5q^3+13q^2+7q+1
        41: 2q^3+3q^2+q
        42: q^4+5q^3+10q^2+6q+1
        43: 6q^3+15q^2+7q+1
        44: 2q^4+7q^3+11q^2+6q+1
        45: 6q^3+15q^2+7q+1
        46: 2q^3+12q^2+7q+1
        47: 2q^3+12q^2+7q+1
        48: q^4+4q^3+6q^2+4q+1
        49: 3q^3+12q^2+7q+1
        50: 3q^3+12q^2+7q+1
        51: 3q^3+6q^2+4q+1
        52: 3q^3+11q^2+7q+1
        53: 3q^3+11q^2+7q+1
        54: 3q^3+8q^2+6q+1
        55: q^4+8q^3+15q^2+7q+1
        56: q^4+8q^3+15q^2+7q+1
        57: q^4+6q^3+11q^2+6q+1
        58: 2q^3+8q^2+5q+1
        59: q^3+6q^2+3q
        60: 3q^3+7q^2+2q
        61: 4q^3+11q^2+6q+1
        62: 2q^3+4q^2+q
        63: 5q^3+13q^2+7q+1
        64: q^3+3q^2+q
        65: 2q^3+9q^2+6q+1
        66: 3q^2+q
        67: 3q^3+11q^2+7q+1
        68: 7q^2+6q+1
        69: 4q^2+4q+1
        70: 3q^3+10q^2+6q+1
        71: 3q^3+12q^2+7q+1
        72: q^3+7q^2+6q+1
        73: 6q^2+6q+1
        75: q^3+7q^2+6q+1
        77: q^3+7q^2+6q+1
        79: q^3+5q^2+5q+1
        80: 3q^3+12q^2+7q+1
        81: q^3+9q^2+7q+1
        82: 3q^3+11q^2+7q+1
        83: q^3+7q^2+6q+1
        84: 6q^3+15q^2+7q+1
        85: 2q^3+12q^2+7q+1
        86: q^4+8q^3+15q^2+7q+1
        87: 3q^3+10q^2+6q+1
        88: 2q^3+12q^2+7q+1
        89: 2q^3+12q^2+7q+1
        90: q^4+4q^3+6q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+7q^2+6q+1
        93: q^3+4q^2+4q+1
        94: 7q^2+7q+1
        95: 7q^2+7q+1
        96: q^3+4q^2+4q+1
        97: 3q^3+12q^2+7q+1
        98: 3q^3+12q^2+7q+1
        99: 3q^3+6q^2+4q+1
       100: 3q^3+11q^2+7q+1
       101: 3q^3+11q^2+7q+1
       102: 3q^3+8q^2+6q+1
       103: q^2
       104: q^3+4q^2+2q
       105: 2q^3+7q^2+5q+1
       106: 2q^2+q
       107: 2q^2+q
       108: q^3+5q^2+5q+1
       109: 3q^2+4q+1
       110: 3q^2+2q
       112: 3q^2+5q+1
       114: q^3+7q^2+6q+1
       116: 4q^2+5q+1
       117: 3q^2+4q+1
       118: 2q^2+2q
       119: 2q^2+q
       120: 5q^2+5q+1
       121: q^3+3q^2+q
       122: 2q^3+9q^2+6q+1
       123: 2q^2+q
       124: q^3+7q^2+6q+1
       125: 7q^2+6q+1
       126: 4q^2+4q+1
       128: 3q^2+5q+1
       130: 3q^2+5q+1
       132: 2q^2+3q+1
       133: 3q^2+5q+1
       134: 3q^2+4q+1
       135: 3q^2+5q+1
       136: 3q^2+5q+1
       137: q^3+9q^2+7q+1
       138: 2q^2+4q+1
       139: 7q^2+7q+1
       140: 2q^2+3q+1
       141: q^3+7q^2+6q+1
       142: 5q^2+6q+1
       143: 2q^3+12q^2+7q+1
       144: 4q^2+4q+1
       145: 3q^3+12q^2+7q+1
       146: 3q^3+10q^2+6q+1
       147: q^3+7q^2+6q+1
       148: 6q^2+6q+1
       149: 3q^3+11q^2+7q+1
       150: q^3+7q^2+6q+1
       152: q^3+7q^2+6q+1
       154: q^3+7q^2+6q+1
       156: q^3+5q^2+5q+1
       157: 6q^2+6q+1
       158: q^3+7q^2+6q+1
       159: q^3+4q^2+4q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: q^2+3q+1
       163: 6q^2+6q+1
       164: q^3+7q^2+6q+1
       165: q^3+4q^2+4q+1
       166: 7q^2+7q+1
       167: 7q^2+7q+1
       168: q^3+4q^2+4q+1
       170: q^2+q
       171: 2q^2+4q+1
       174: q^2+q
       175: 3q^2+4q+1
       176: q^2+q
       178: q^2+3q+1
       180: 3q^2+5q+1
       182: q^2+4q+1
       184: q^2+4q+1
       185: 3q+1
       186: q^2+q
       188: q^2+4q+1
       190: 4q^2+5q+1
       191: 3q^2+4q+1
       192: 2q^2+2q
       194: 2q^2+3q+1
       195: 3q^2+4q+1
       196: 2q^2+2q
       198: q^2+2q+1
       199: 2q^2+q
       200: 5q^2+5q+1
       201: 2q^2+q
       202: q^3+5q^2+5q+1
       203: 3q^2+4q+1
       204: 3q^2+2q
       206: 3q^2+5q+1
       207: 2q^2+q
       208: q^3+7q^2+6q+1
       210: q^3+7q^2+6q+1
       212: 4q^2+5q+1
       214: 3q+1
       216: q^2+3q+1
       218: 2q+1
       219: q^2+3q+1
       220: 3q^2+5q+1
       221: 3q^2+4q+1
       222: 3q^2+5q+1
       223: q^2+3q+1
       224: 3q^2+5q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q+1
       228: 3q+1
       229: 2q+1
       230: q^2+4q+1
       231: 4q^2+4q+1
       232: 3q^2+5q+1
       233: 3q^2+4q+1
       234: 3q^2+5q+1
       235: 3q^2+5q+1
       236: 2q^2+4q+1
       238: 3q^2+5q+1
       240: 3q^2+5q+1
       242: 2q^2+3q+1
       243: 7q^2+7q+1
       244: 2q^2+3q+1
       245: 5q^2+6q+1
       246: q^3+7q^2+6q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+5q+1
       251: 2q^2+5q+1
       252: q^2+3q+1
       253: 6q^2+6q+1
       254: q^3+7q^2+6q+1
       255: q^3+4q^2+4q+1
       256: q^2+5q+1
       257: 2q^2+5q+1
       258: q^2+3q+1
       260: q
       261: q^2+3q+1
       265: 3q+1
       270: q^2+2q+1
       272: 2q^2+4q+1
       274: q^2+q
       276: q^2+q
       277: 3q^2+4q+1
       278: q^2+q
       280: 2q+1
       282: 2q+1
       284: 2q+1
       285: q+1
       288: q^2+3q+1
       290: 2q+1
       292: 2q+1
       294: q^2+4q+1
       295: 3q+1
       296: q^2+q
       298: q^2+4q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       304: q
       306: q+1
       308: q^2+4q+1
       309: 3q+1
       310: q^2+q
       312: q^2+4q+1
       314: q^2+4q+1
       316: q^2+3q+1
       318: 3q^2+5q+1
       320: 2q^2+3q+1
       321: 3q^2+4q+1
       322: 2q^2+2q
       324: q^2+2q+1
       326: 4q^2+5q+1
       328: 3q+1
       330: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q+1
       345: 4q+1
       346: 3q+1
       347: 2q+1
       348: q+1
       349: q^2+4q+1
       350: 2q+1
       351: 2q+2
       352: q^2+3q+1
       353: 3q^2+5q+1
       354: 3q^2+4q+1
       355: 3q^2+5q+1
       356: q^2+3q+1
       357: 3q^2+5q+1
       358: q^2+3q+1
       359: 4q+2
       361: 3q+1
       363: q^2+3q+1
       365: 2q+1
       366: 2q^2+4q+1
       367: 4q+1
       368: 3q+1
       369: 2q+1
       370: q^2+4q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+5q+1
       375: 2q^2+5q+1
       376: q^2+3q+1
       379: q+1
       383: q+1
       387: 3q+1
       392: q+1
       395: q+1
       398: q^2+3q+1
       400: q
       402: 3q+1
       408: q^2+2q+1
       410: 2q+1
       412: 2q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: 2q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       430: q+1
       431: 1
       434: 1
       436: 1
       438: 2q+1
       439: 2q+1
       440: q
       442: q+1
       444: 2q+2
       446: 2q+2
       448: 2q+1
       449: q+1
       452: 2q+1
       454: q^2+4q+1
       456: 2q+1
       457: 3q+1
       458: q^2+q
       460: q^2+4q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: 2q+1
       468: 2q+1
       470: q^2+3q+1
       472: 2q+1
       473: 2q+1
       474: q
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: 2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: q+2
       503: 3q+1
       505: q^2+3q+1
       507: 2q+1
       508: 2q+1
       509: 4q+1
       510: 3q+1
       511: 2q+1
       512: q+1
       513: q^2+4q+1
       514: 2q+1
       518: q+2
       519: q+2
       520: q+1
       523: 1
       527: q+1
       531: q+1
       535: 1
       540: 1
       544: q+1
       548: 2q+2
       550: q+1
       554: q+1
       558: 3q+1
       562: 2q+1
       564: 2q+1
       567: q+1
       572: q+1
       575: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       590: q+1
       594: 1
       595: 1
       598: 1
       600: q+1
       602: 2
       604: q+1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 2
       618: 2
       620: 2q+1
       621: q+1
       624: q+1
       626: 2q+1
       628: 2q+1
       630: q+1
       631: 1
       632: 1
       634: q+2
       636: 2q+1
       638: 2q+1
       640: q+1
       642: q+1
       643: 1
       646: 1
       648: 2q+1
       649: 2q+1
       650: q
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: 2q+1
       689: 1
       700: q+1
       701: q+1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 2
       738: 1
       742: q+1
       746: q+1
       750: 1
       752: 1
       755: 1
       760: 1
       764: q+1
       767: 1
       768: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       786: 1
       790: 2
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 2
       816: 2
       822: 1
       824: q+1
       826: q+1
       830: 1
       831: 1
       834: 1
       836: q+1
       838: q+2
       839: 1
       840: 1
       842: q+1
       846: q+1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       891: 1
       892: 1
       898: 1
       907: 1
       915: 1
       931: 1
       935: 2
       937: 1
       945: 1
       954: 1
       957: 1
       959: 1
       963: 1
       977: 1
       981: 1
       983: 1
       986: 1
       990: 1
       991: 1
      1003: 1
      1005: 1
      1025: 1
      1035: 1
      1039: 1
      1041: 1
      1043: 1
      1051: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1082: 1
      1085: 1
      1105: 1
      1106: 1
      1121: 1
      1169: 1
      1179: 1
      1187: 1
      1209: 1
      1257: 1
      1259: 1
      1273: 1
      1387: 1

1388:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: q^3+4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 3q^2+4q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: q^3+4q^2+4q+1
        36: q^3+4q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 2q^2+3q+1
        56: q^3+3q^2+3q+1
        57: 2q^2+3q+1
        58: q+1
        59: 2q
        60: 2q+1
        61: q
        62: 2q+1
        63: q
        64: 2q^2+3q+1
        65: q^2+q
        66: 2q^2+3q+1
        67: q^2+q
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: 3q+1
        81: 3q^2+4q+1
        82: 2q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^3+4q^2+4q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q+1
       104: q
       106: q
       107: q+1
       109: 1
       110: q
       111: q+1
       113: q+1
       115: 2q+1
       117: q+1
       118: 2q
       119: 2q+1
       120: q
       121: 2q+1
       122: q
       123: 2q^2+3q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: q^2+2q+1
       131: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+3q+1
       151: 2q+1
       153: q^2+2q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       169: 1
       173: q+1
       174: q
       176: q
       177: 2q+1
       179: q+1
       181: q+1
       183: q+1
       185: 1
       186: q
       187: q+1
       189: q+1
       191: q+1
       192: 2q
       193: q+1
       195: 1
       196: q
       197: 1
       199: 2q+1
       200: q
       201: q+1
       203: 1
       204: q
       205: q+1
       207: 2q+1
       208: q
       209: q+1
       211: 2q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+3q+1
       237: 2q+1
       239: q^2+2q+1
       241: 2q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       276: q
       278: q
       279: q+1
       281: 2q+1
       283: q+1
       285: 1
       286: q
       287: q+1
       289: q+1
       291: q+1
       293: 1
       295: 1
       296: q
       297: 1
       299: q+1
       301: 1
       303: 1
       304: q
       305: 1
       307: q+1
       309: 1
       310: q
       311: q+1
       313: q+1
       315: 2q+1
       317: q+1
       319: q+1
       321: 1
       322: q
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       348: q+1
       350: q^2+2q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       417: q+1
       419: 1
       421: 1
       422: q
       423: 1
       425: 1
       427: 2
       429: q+1
       431: 1
       432: q
       433: 1
       435: 1
       443: 2
       445: 2
       447: q+1
       449: 1
       450: q
       451: q+1
       453: 1
       455: q+1
       457: 1
       458: q
       459: 1
       461: 1
       462: 1
       463: q+2
       465: q+1
       467: 2q+1
       469: q+1
       471: q+1
       473: 1
       474: q
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 2
       549: 1
       553: 1
       557: 1
       561: 1
       563: 1
       565: 1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       585: 1
       589: 1
       593: 1
       595: 1
       596: q
       597: 1
       599: 1
       601: 2
       605: 1
       613: 1
       615: 2
       617: 2
       619: 1
       621: 1
       622: q
       623: q+1
       625: 1
       629: 1
       631: 1
       632: 1
       633: q+2
       639: q+1
       641: q+1
       643: 1
       644: q
       645: 1
       651: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       693: 1
       696: 1
       709: 1
       717: 1
       721: 1
       733: 2
       737: 1
       741: 1
       749: 1
       751: 1
       753: 1
       757: 1
       765: 1
       766: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       785: 1
       793: 2
       795: 2
       809: 1
       817: 1
       818: 1
       819: q+2
       821: 1
       825: 1
       829: 1
       831: 1
       832: q
       833: 1
       835: 1
       843: 1
       844: 1
       849: 1
       855: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       884: 1
       887: 1
       904: 1
       916: 2
       940: 1
       942: 1
       944: 1
       952: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       994: 1
      1000: 1
      1020: 1
      1036: 1
      1038: 1
      1040: 1
      1060: 1
      1080: 1
      1084: 1
      1086: 1
      1089: 1
      1122: 1
      1176: 1
      1248: 1
      1254: 1
      1274: 1
      1388: 1

1389:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: q^3+4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 3q^2+4q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: q^3+4q^2+4q+1
        36: q^3+4q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 2q^2+3q+1
        56: q^3+3q^2+3q+1
        57: 2q^2+3q+1
        58: 2q
        59: q+1
        60: 2q+1
        61: q
        62: q
        63: 2q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q^2+q
        67: 2q^2+3q+1
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: 3q+1
        81: 3q^2+4q+1
        82: 2q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^3+4q^2+4q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q
       104: q+1
       105: q
       107: q+1
       109: q
       110: 1
       112: q+1
       114: q+1
       116: 2q+1
       117: 2q
       118: q+1
       119: 2q+1
       120: q
       121: q
       122: 2q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: q^2+2q+1
       132: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+3q+1
       152: 2q+1
       154: q^2+2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       170: 1
       173: q
       174: q+1
       175: q
       178: 2q+1
       180: q+1
       182: q+1
       183: q+1
       185: q
       186: 1
       188: q+1
       190: q+1
       191: 2q
       192: q+1
       193: q+1
       195: q
       196: 1
       198: 1
       199: 2q+1
       200: q
       201: q+1
       203: q
       204: 1
       206: q+1
       207: q
       208: 2q+1
       210: q+1
       212: 2q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+3q+1
       238: 2q+1
       240: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q
       276: q+1
       277: q
       280: q+1
       282: 2q+1
       283: q+1
       285: q
       286: 1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       295: q
       296: 1
       298: 1
       299: q+1
       302: 1
       303: q
       304: 1
       306: 1
       307: q+1
       309: q
       310: 1
       312: q+1
       314: q+1
       316: 2q+1
       318: q+1
       319: q+1
       321: q
       322: 1
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       348: q+1
       350: q^2+2q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: q+1
       418: q+1
       419: 1
       421: q
       422: 1
       424: 1
       426: 1
       428: 2
       429: q+1
       431: q
       432: 1
       434: 1
       436: 1
       443: 2
       446: 2
       447: q+1
       449: q
       450: 1
       452: q+1
       453: 1
       456: q+1
       457: q
       458: 1
       460: 1
       461: 1
       462: 1
       464: q+2
       466: q+1
       468: 2q+1
       470: q+1
       471: q+1
       473: q
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 2
       551: 1
       556: 1
       560: 1
       562: 1
       564: 1
       566: 1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       586: 1
       589: 1
       593: 1
       595: q
       596: 1
       598: 1
       600: 1
       602: 2
       606: 1
       614: 1
       615: 2
       618: 2
       619: 1
       621: q
       622: 1
       624: q+1
       626: 1
       630: 1
       631: 1
       632: 1
       634: q+2
       640: q+1
       641: q+1
       643: q
       644: 1
       646: 1
       652: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       694: 1
       699: 1
       710: 1
       718: 1
       722: 1
       734: 2
       740: 1
       744: 1
       750: 1
       752: 1
       754: 1
       759: 1
       765: 1
       766: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       785: 1
       793: 2
       796: 2
       810: 1
       817: 1
       818: 1
       820: q+2
       822: 1
       825: 1
       829: 1
       831: q
       832: 1
       834: 1
       836: 1
       843: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       885: 1
       890: 1
       905: 1
       917: 2
       941: 1
       943: 1
       947: 1
       953: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       995: 1
      1000: 1
      1021: 1
      1037: 1
      1039: 1
      1040: 1
      1061: 1
      1080: 1
      1084: 1
      1087: 1
      1092: 1
      1123: 1
      1177: 1
      1249: 1
      1254: 1
      1275: 1
      1389: 1

1390:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: q^3+4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 3q^2+4q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: q^3+4q^2+4q+1
        36: q^3+4q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 2q^2+3q+1
        56: q^3+3q^2+3q+1
        57: 2q^2+3q+1
        58: 2q
        59: q+1
        60: q
        61: 2q+1
        62: 2q+1
        63: q
        64: 2q^2+3q+1
        65: q^2+q
        66: 2q^2+3q+1
        67: q^2+q
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q+1
        76: q^2+2q+1
        78: 2q+1
        80: 3q+1
        81: 3q^2+4q+1
        82: 2q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^3+4q^2+4q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: q
       105: q
       106: q+1
       108: q+1
       109: q
       110: 1
       111: q+1
       113: q+1
       115: 2q+1
       117: 2q
       118: q+1
       119: q
       120: 2q+1
       121: 2q+1
       122: q
       123: 2q^2+3q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: q^2+2q+1
       131: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+3q+1
       151: 2q+1
       153: q^2+2q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       172: 1
       173: q
       175: q
       176: q+1
       177: 2q+1
       179: q+1
       181: q+1
       184: q+1
       185: q
       186: 1
       187: q+1
       189: q+1
       191: 2q
       192: q+1
       194: q+1
       195: q
       196: 1
       197: 1
       199: q
       200: 2q+1
       202: q+1
       203: q
       204: 1
       205: q+1
       207: 2q+1
       208: q
       209: q+1
       211: 2q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+3q+1
       237: 2q+1
       239: q^2+2q+1
       241: 2q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       277: q
       278: q+1
       279: q+1
       281: 2q+1
       284: q+1
       285: q
       286: 1
       287: q+1
       289: q+1
       291: q+1
       294: 1
       295: q
       296: 1
       297: 1
       300: q+1
       301: 1
       303: q
       304: 1
       305: 1
       308: q+1
       309: q
       310: 1
       311: q+1
       313: q+1
       315: 2q+1
       317: q+1
       320: q+1
       321: q
       322: 1
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: q+2
       340: q+2
       342: q+1
       344: 2q+1
       348: q+1
       350: q^2+2q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       417: q+1
       420: 1
       421: q
       422: 1
       423: 1
       425: 1
       427: 2
       430: q+1
       431: q
       432: 1
       433: 1
       435: 1
       444: 2
       445: 2
       448: q+1
       449: q
       450: 1
       451: q+1
       454: 1
       455: q+1
       457: q
       458: 1
       459: 1
       461: 1
       462: 1
       463: q+2
       465: q+1
       467: 2q+1
       469: q+1
       472: q+1
       473: q
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 2
       552: 1
       555: 1
       559: 1
       561: 1
       563: 1
       568: 1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       585: 1
       590: 1
       594: 1
       595: q
       596: 1
       597: 1
       599: 1
       601: 2
       605: 1
       613: 1
       616: 2
       617: 2
       620: 1
       621: q
       622: 1
       623: q+1
       625: 1
       629: 1
       631: 1
       632: 1
       633: q+2
       639: q+1
       642: q+1
       643: q
       644: 1
       645: 1
       651: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       697: 1
       698: 1
       712: 1
       720: 1
       723: 1
       735: 2
       739: 1
       743: 1
       749: 1
       751: 1
       756: 1
       758: 1
       767: 1
       768: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       786: 1
       794: 2
       795: 2
       809: 1
       817: 1
       818: 1
       819: q+2
       821: 1
       826: 1
       830: 1
       831: q
       832: 1
       833: 1
       835: 1
       843: 1
       844: 1
       849: 1
       855: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       888: 1
       889: 1
       906: 1
       918: 2
       940: 1
       942: 1
       946: 1
       955: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       994: 1
      1001: 1
      1020: 1
      1036: 1
      1038: 1
      1041: 1
      1060: 1
      1080: 1
      1084: 1
      1090: 1
      1091: 1
      1124: 1
      1178: 1
      1248: 1
      1255: 1
      1274: 1
      1390: 1

1391:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+3q^2+3q+1
         5: q^3+4q^2+4q+1
         6: q^4+3q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+4q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: q^3+4q^2+4q+1
        14: q^3+3q^2+3q+1
        15: q^3+4q^2+4q+1
        16: q^3+4q^2+4q+1
        17: q^3+4q^2+4q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: q^3+4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 3q^2+4q+1
        33: 3q^2+4q+1
        34: 3q+1
        35: q^3+4q^2+4q+1
        36: q^3+4q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: q^3+4q^2+4q+1
        47: q^3+4q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+3q+1
        55: 2q^2+3q+1
        56: q^3+3q^2+3q+1
        57: 2q^2+3q+1
        58: q+1
        59: 2q
        60: q
        61: 2q+1
        62: q
        63: 2q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q^2+q
        67: 2q^2+3q+1
        68: 3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: 2q+1
        77: q^2+2q+1
        79: 2q+1
        80: 3q+1
        81: 3q^2+4q+1
        82: 2q+1
        83: q^2+3q+1
        84: 3q+1
        85: q^3+4q^2+4q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       104: q
       105: q+1
       106: q
       108: q+1
       109: 1
       110: q
       112: q+1
       114: q+1
       116: 2q+1
       117: q+1
       118: 2q
       119: q
       120: 2q+1
       121: q
       122: 2q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: q^2+2q+1
       132: 2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 3q+1
       138: q^2+3q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 3q+1
       144: 2q^2+3q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+3q+1
       152: 2q+1
       154: q^2+2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+3q+1
       171: 1
       174: q
       175: q+1
       176: q
       178: 2q+1
       180: q+1
       182: q+1
       184: q+1
       185: 1
       186: q
       188: q+1
       190: q+1
       191: q+1
       192: 2q
       194: q+1
       195: 1
       196: q
       198: 1
       199: q
       200: 2q+1
       202: q+1
       203: 1
       204: q
       206: q+1
       207: q
       208: 2q+1
       210: q+1
       212: 2q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+3q+1
       238: 2q+1
       240: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q+2
       248: q+2
       249: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       261: 1
       265: 1
       270: 1
       272: 1
       276: q
       277: q+1
       278: q
       280: q+1
       282: 2q+1
       284: q+1
       285: 1
       286: q
       288: q+1
       290: q+1
       292: q+1
       294: 1
       295: 1
       296: q
       298: 1
       300: q+1
       302: 1
       303: 1
       304: q
       306: 1
       308: q+1
       309: 1
       310: q
       312: q+1
       314: q+1
       316: 2q+1
       318: q+1
       320: q+1
       321: 1
       322: q
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: q+2
       341: q+2
       343: q+1
       344: 2q+1
       348: q+1
       350: q^2+2q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: q+1
       418: q+1
       420: 1
       421: 1
       422: q
       424: 1
       426: 1
       428: 2
       430: q+1
       431: 1
       432: q
       434: 1
       436: 1
       444: 2
       446: 2
       448: q+1
       449: 1
       450: q
       452: q+1
       454: 1
       456: q+1
       457: 1
       458: q
       460: 1
       461: 1
       462: 1
       464: q+2
       466: q+1
       468: 2q+1
       470: q+1
       472: q+1
       473: 1
       474: q
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+2
       508: 2q+1
       512: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 2
       550: 1
       554: 1
       558: 1
       562: 1
       564: 1
       567: 1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       594: 1
       595: 1
       596: q
       598: 1
       600: 1
       602: 2
       606: 1
       614: 1
       616: 2
       618: 2
       620: 1
       621: 1
       622: q
       624: q+1
       626: 1
       630: 1
       631: 1
       632: 1
       634: q+2
       640: q+1
       642: q+1
       643: 1
       644: q
       646: 1
       652: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       674: 2
       679: 1
       680: q+2
       681: 1
       682: q+1
       683: 1
       685: 1
       689: 1
       700: 1
       701: 1
       711: 1
       719: 1
       724: 1
       736: 2
       738: 1
       742: 1
       750: 1
       752: 1
       755: 1
       760: 1
       767: 1
       768: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       786: 1
       794: 2
       796: 2
       810: 1
       817: 1
       818: 1
       820: q+2
       822: 1
       826: 1
       830: 1
       831: 1
       832: q
       834: 1
       836: 1
       843: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       874: 1
       875: 1
       880: 1
       891: 1
       892: 1
       907: 1
       919: 2
       941: 1
       943: 1
       945: 1
       954: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       995: 1
      1001: 1
      1021: 1
      1037: 1
      1039: 1
      1041: 1
      1061: 1
      1080: 1
      1084: 1
      1093: 1
      1094: 1
      1125: 1
      1179: 1
      1249: 1
      1255: 1
      1275: 1
      1391: 1

1392:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^2+q+1
        23: q^3+q^2+q+1
        24: q^2+q+1
        25: q^3+2q^2+q+1
        26: q^4+2q^3+2q^2+q+1
        27: q^3+2q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^2+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^3+q^2+1
        35: q^3+2q^2+q+1
        36: 2q^2+q+1
        37: q^2+q+1
        39: q^3+q^2+q+1
        41: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+q+1
        55: q^3+2q^2+q+1
        56: q^4+2q^3+2q^2+q+1
        57: q^3+2q^2+q+1
        58: q^2+1
        60: q^2+1
        62: q^2+1
        64: q^2+q+1
        66: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: 2q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        76: q^3+q^2+q+1
        78: q^2+q+1
        80: q^2+1
        81: q^2+q+1
        82: q^2+1
        83: q^2+q+1
        84: q^3+q^2+1
        85: 2q^2+q+1
        86: q^3+q^2+1
        87: q^3+2q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: q^3+q^2+q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       103: q^2+1
       107: q^2+1
       109: q^2+1
       111: q^2+q+1
       113: q^2+1
       115: q^2+q+1
       117: q^2+1
       119: q^2+1
       121: q^2+1
       123: q^2+q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: q^2+q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q^2+1
       142: q+1
       143: 1
       144: q^2+q+1
       145: q^2+1
       146: q^3+q^2+1
       147: 2q^2+q+1
       148: q^2+q+1
       149: q^2+1
       150: q^2+q+1
       151: q^2+q+1
       153: q^3+q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       169: q^2+1
       173: q^2+1
       177: q+1
       179: 1
       181: q+1
       183: q^2+1
       185: q^2+1
       187: q^2+q+1
       189: q^2+1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: q^2+1
       203: q^2+1
       205: q^2+q+1
       207: 1
       209: q^2+1
       211: q^2+q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: q^2+q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: 1
       245: q+1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: q^3+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: q^2+1
       267: 1
       271: q^2+1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: q^2+1
       309: q^2+1
       311: q+1
       313: q^2+q+1
       315: q+1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: q^2+1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: q+1
       453: 1
       455: q+1
       457: 1
       459: 1
       461: 1
       463: q+1
       465: 1
       467: q+1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: q+1
       625: 1
       629: q+1
       631: 1
       633: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       781: 1
       785: 1
       787: 1
       791: 1
       809: 1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: q+1
       835: 1
       849: 1
       855: 1
       875: 1
       880: 1
       884: 1
       900: 1
       904: 1
       908: 1
       944: 1
       948: 1
       952: 1
       960: 1
      1010: 1
      1038: 1
      1040: 1
      1044: 1
      1060: 1
      1064: 1
      1126: 1
      1172: 1
      1176: 1
      1180: 1
      1278: 1
      1392: 1

1393:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^2+q+1
        23: q^3+q^2+q+1
        24: q^2+q+1
        25: q^3+2q^2+q+1
        26: q^4+2q^3+2q^2+q+1
        27: q^3+2q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^2+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^3+q^2+1
        35: q^3+2q^2+q+1
        36: 2q^2+q+1
        37: q^2+q+1
        39: q^3+q^2+q+1
        41: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+q+1
        55: q^3+2q^2+q+1
        56: q^4+2q^3+2q^2+q+1
        57: q^3+2q^2+q+1
        59: q^2+1
        61: q^2+1
        62: q^2+1
        64: q^2+q+1
        66: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: 2q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        76: q^3+q^2+q+1
        78: q^2+q+1
        80: q^2+1
        81: q^2+q+1
        82: q^2+1
        83: q^2+q+1
        84: q^3+q^2+1
        85: 2q^2+q+1
        86: q^3+q^2+1
        87: q^3+2q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: q^3+q^2+q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       106: q^2+1
       108: q^2+1
       110: q^2+1
       111: q^2+q+1
       113: q^2+1
       115: q^2+q+1
       118: q^2+1
       120: q^2+1
       121: q^2+1
       123: q^2+q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: q^2+q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q^2+1
       142: q+1
       143: 1
       144: q^2+q+1
       145: q^2+1
       146: q^3+q^2+1
       147: 2q^2+q+1
       148: q^2+q+1
       149: q^2+1
       150: q^2+q+1
       151: q^2+q+1
       153: q^3+q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       172: q^2+1
       176: q^2+1
       177: q+1
       179: 1
       181: q+1
       184: q^2+1
       186: q^2+1
       187: q^2+q+1
       189: q^2+1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: q^2+1
       204: q^2+1
       205: q^2+q+1
       207: 1
       209: q^2+1
       211: q^2+q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: q^2+q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: 1
       245: q+1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: q^3+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: q^2+1
       269: 1
       273: q^2+1
       278: 1
       279: 1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: q^2+1
       310: q^2+1
       311: q+1
       313: q^2+q+1
       315: q+1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: q^2+1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: q+1
       454: 1
       455: q+1
       458: 1
       459: 1
       462: 1
       463: q+1
       465: 1
       467: q+1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: q+1
       625: 1
       629: q+1
       632: 1
       633: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       781: 1
       786: 1
       788: 1
       791: 1
       809: 1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: q+1
       835: 1
       849: 1
       855: 1
       875: 1
       880: 1
       889: 1
       902: 1
       906: 1
       911: 1
       946: 1
       950: 1
       955: 1
       961: 1
      1010: 1
      1038: 1
      1041: 1
      1045: 1
      1060: 1
      1064: 1
      1127: 1
      1174: 1
      1178: 1
      1183: 1
      1278: 1
      1393: 1

1394:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^2+q+1
        23: q^3+q^2+q+1
        24: q^2+q+1
        25: q^3+2q^2+q+1
        26: q^4+2q^3+2q^2+q+1
        27: q^3+2q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^2+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^3+q^2+1
        35: q^3+2q^2+q+1
        36: 2q^2+q+1
        38: q^2+q+1
        40: q^3+q^2+q+1
        42: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+q+1
        55: q^3+2q^2+q+1
        56: q^4+2q^3+2q^2+q+1
        57: q^3+2q^2+q+1
        59: q^2+1
        60: q^2+1
        63: q^2+1
        65: q^2+q+1
        67: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: 2q^2+q+1
        73: q^2+q+1
        75: q^2+q+1
        77: q^3+q^2+q+1
        79: q^2+q+1
        80: q^2+1
        81: q^2+q+1
        82: q^2+1
        83: q^2+q+1
        84: q^3+q^2+1
        85: 2q^2+q+1
        86: q^3+q^2+1
        87: q^3+2q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: q^3+q^2+q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       104: q^2+1
       107: q^2+1
       110: q^2+1
       112: q^2+q+1
       114: q^2+1
       116: q^2+q+1
       118: q^2+1
       119: q^2+1
       122: q^2+1
       124: q^2+q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: q^2+q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q^2+1
       142: q+1
       143: 1
       144: q^2+q+1
       145: q^2+1
       146: q^3+q^2+1
       147: 2q^2+q+1
       148: q^2+q+1
       149: q^2+1
       150: q^2+q+1
       152: q^2+q+1
       154: q^3+q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       170: q^2+1
       174: q^2+1
       178: q+1
       180: 1
       182: q+1
       183: q^2+1
       186: q^2+1
       188: q^2+q+1
       190: q^2+1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: q^2+1
       204: q^2+1
       206: q^2+q+1
       208: 1
       210: q^2+1
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: q^2+q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: q^3+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: q^2+1
       268: 1
       274: q^2+1
       276: 1
       280: 1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: q^2+1
       310: q^2+1
       312: q+1
       314: q^2+q+1
       316: q+1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: q^2+1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: q+1
       453: 1
       456: q+1
       458: 1
       460: 1
       462: 1
       464: q+1
       466: 1
       468: q+1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: q+1
       626: 1
       630: q+1
       632: 1
       634: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       782: 1
       785: 1
       788: 1
       792: 1
       810: 1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: q+1
       836: 1
       850: 1
       856: 1
       875: 1
       880: 1
       890: 1
       903: 1
       905: 1
       909: 1
       947: 1
       951: 1
       953: 1
       962: 1
      1011: 1
      1039: 1
      1040: 1
      1045: 1
      1061: 1
      1065: 1
      1128: 1
      1175: 1
      1177: 1
      1181: 1
      1279: 1
      1394: 1

1395:    0: q^3+2q^2+q+1
         1: q^4+2q^3+2q^2+q+1
         2: q^3+2q^2+q+1
         3: q^4+2q^3+2q^2+q+1
         4: q^3+2q^2+q+1
         5: q^3+2q^2+q+1
         6: q^4+2q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: q^3+2q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^3+q^2+1
        11: q^3+q^2+1
        12: q^3+q^2+1
        13: q^3+2q^2+q+1
        14: q^3+2q^2+q+1
        15: q^3+2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+2q^2+q+1
        20: q^4+2q^3+2q^2+q+1
        21: q^3+2q^2+q+1
        22: q^2+q+1
        23: q^3+q^2+q+1
        24: q^2+q+1
        25: q^3+2q^2+q+1
        26: q^4+2q^3+2q^2+q+1
        27: q^3+2q^2+q+1
        28: q^2+1
        29: q^3+q^2+1
        30: q^3+2q^2+q+1
        31: q^2+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^3+q^2+1
        35: q^3+2q^2+q+1
        36: 2q^2+q+1
        38: q^2+q+1
        40: q^3+q^2+q+1
        42: q^2+q+1
        43: q^3+q^2+1
        44: q^3+q^2+1
        45: q^3+q^2+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^3+q^2+q+1
        52: q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+q+1
        55: q^3+2q^2+q+1
        56: q^4+2q^3+2q^2+q+1
        57: q^3+2q^2+q+1
        58: q^2+1
        61: q^2+1
        63: q^2+1
        65: q^2+q+1
        67: q^2+q+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+1
        71: q^2+1
        72: 2q^2+q+1
        73: q^2+q+1
        75: q^2+q+1
        77: q^3+q^2+q+1
        79: q^2+q+1
        80: q^2+1
        81: q^2+q+1
        82: q^2+1
        83: q^2+q+1
        84: q^3+q^2+1
        85: 2q^2+q+1
        86: q^3+q^2+1
        87: q^3+2q^2+q+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: q^3+q^2+q+1
       100: q^2+q+1
       101: q^3+q^2+q+1
       102: q^2+q+1
       105: q^2+1
       108: q^2+1
       109: q^2+1
       112: q^2+q+1
       114: q^2+1
       116: q^2+q+1
       117: q^2+1
       120: q^2+1
       122: q^2+1
       124: q^2+q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: q^2+q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q^2+1
       142: q+1
       143: 1
       144: q^2+q+1
       145: q^2+1
       146: q^3+q^2+1
       147: 2q^2+q+1
       148: q^2+q+1
       149: q^2+1
       150: q^2+q+1
       152: q^2+q+1
       154: q^3+q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       171: q^2+1
       175: q^2+1
       178: q+1
       180: 1
       182: q+1
       184: q^2+1
       185: q^2+1
       188: q^2+q+1
       190: q^2+1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: q^2+1
       203: q^2+1
       206: q^2+q+1
       208: 1
       210: q^2+1
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: q^2+q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: q^2+1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: q^3+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: q^2+1
       270: 1
       272: q^2+1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: q^2+1
       309: q^2+1
       312: q+1
       314: q^2+q+1
       316: q+1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: q^2+1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       456: q+1
       457: 1
       460: 1
       461: 1
       464: q+1
       466: 1
       468: q+1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: q+1
       626: 1
       630: q+1
       631: 1
       634: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       665: 1
       679: 1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       782: 1
       786: 1
       787: 1
       792: 1
       810: 1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: q+1
       836: 1
       850: 1
       856: 1
       875: 1
       880: 1
       891: 1
       901: 1
       907: 1
       910: 1
       945: 1
       949: 1
       954: 1
       963: 1
      1011: 1
      1039: 1
      1041: 1
      1044: 1
      1061: 1
      1065: 1
      1129: 1
      1173: 1
      1179: 1
      1182: 1
      1279: 1
      1395: 1

1396:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q+1
        59: q
        60: q^2+q+1
        61: q
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: 1
       104: q
       105: q
       107: q^2+q+1
       108: q
       109: q+1
       110: q
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q^2+3q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: q^3+3q^2+3q+1
       148: q^2+3q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: 1
       170: q
       171: q
       173: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       183: 1
       185: 1
       187: q+1
       188: q
       189: 1
       190: q
       191: 1
       193: q+1
       195: q+1
       196: q
       197: 1
       198: q
       199: 1
       201: q^2+q+1
       202: q
       203: q+1
       204: q
       205: q+1
       206: q^2+2q
       207: 1
       208: q
       209: 1
       210: 2q
       211: q+1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       238: q^2+2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q
       261: q
       263: 1
       267: 1
       268: q
       271: 1
       272: q
       274: q
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: q+1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: 1
       301: 1
       302: q
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       312: q^2+2q
       313: q+1
       314: q
       315: q+1
       316: q
       317: 1
       318: 2q
       319: q+1
       321: q+1
       322: q
       323: 1
       324: q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       339: q^2+2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: q^2+q
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       385: 1
       389: 1
       390: q
       393: 1
       397: 1
       398: q
       400: q
       401: 1
       405: 1
       407: q
       419: 1
       421: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: 1
       428: 2q
       429: 1
       431: 1
       433: 1
       443: q+1
       445: 1
       446: q
       447: 1
       449: 1
       451: q+1
       452: q
       453: 1
       457: 1
       459: 1
       460: q
       461: q+1
       462: q
       463: q+1
       464: q^2+2q
       469: 1
       470: q
       471: 1
       473: 1
       475: 1
       477: 1
       478: q
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       529: 1
       533: 1
       545: 1
       546: q
       549: 1
       557: 1
       561: 1
       562: q
       564: q
       565: 1
       569: 1
       571: q
       573: 1
       574: q
       577: 1
       581: q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       613: 1
       615: 1
       619: 1
       621: 1
       625: 1
       626: q
       629: q+1
       630: q
       631: 1
       641: 1
       643: 1
       645: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       693: 1
       699: q
       713: 1
       717: 1
       741: 1
       753: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       817: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       836: q
       843: 1
       855: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       908: 1
       948: 1
       952: 1
       964: 1
       998: 1
      1000: 1
      1012: 1
      1040: 1
      1044: 1
      1064: 1
      1080: 1
      1084: 1
      1130: 1
      1180: 1
      1250: 1
      1254: 1
      1280: 1
      1396: 1

1397:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q
        59: q+1
        60: q^2+q+1
        61: q
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       104: 1
       106: q
       107: q^2+q+1
       108: q
       109: q
       110: q+1
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       118: 1
       119: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q^2+3q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: q^3+3q^2+3q+1
       148: q^2+3q+1
       149: 2q+1
       150: 2q+1
       151: q^2+2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: q^2+q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       170: 1
       172: q
       174: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       183: 1
       186: 1
       187: q
       188: q+1
       189: q
       190: 1
       192: 1
       193: q+1
       195: q
       196: q+1
       197: q
       198: 1
       199: 1
       201: q^2+q+1
       202: q
       203: q
       204: q+1
       205: q^2+2q
       206: q+1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: q^2+2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: 1
       262: q
       264: 1
       267: q
       268: 1
       271: q
       273: q
       274: 1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       291: q
       292: q+1
       293: 1
       296: 1
       297: q
       298: 1
       299: 1
       301: q
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       311: q^2+2q
       312: q+1
       313: q
       314: q+1
       315: q
       316: q+1
       317: 2q
       318: 1
       319: q+1
       321: q
       322: q+1
       323: q
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: q^2+q
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       386: 1
       389: q
       390: 1
       394: 1
       397: q
       399: q
       400: 1
       403: 1
       405: q
       407: 1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 2q
       428: 1
       429: 1
       432: 1
       434: 1
       443: q+1
       445: q
       446: 1
       447: 1
       450: 1
       451: q
       452: q+1
       453: 1
       458: 1
       459: q
       460: 1
       461: q
       462: q+1
       463: q^2+2q
       464: q+1
       469: q
       470: 1
       471: 1
       474: 1
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       530: 1
       534: 1
       545: q
       546: 1
       551: 1
       560: 1
       561: q
       563: q
       564: 1
       566: 1
       569: q
       571: 1
       573: q
       574: 1
       577: q
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       614: 1
       615: 1
       619: 1
       622: 1
       625: q
       626: 1
       629: q
       630: q+1
       632: 1
       641: 1
       644: 1
       646: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       693: q
       699: 1
       715: 1
       718: 1
       744: 1
       754: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       818: 1
       825: 1
       828: 1
       829: 1
       832: 1
       835: q
       836: 1
       844: 1
       856: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       909: 1
       951: 1
       953: 1
       965: 1
       999: 1
      1000: 1
      1013: 1
      1040: 1
      1045: 1
      1065: 1
      1080: 1
      1084: 1
      1131: 1
      1181: 1
      1251: 1
      1254: 1
      1281: 1
      1397: 1

1398:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q
        38: q+1
        39: q^2+2q
        40: q+1
        41: q^2+q
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q+1
        59: q
        60: q
        61: q^2+q+1
        62: 2q
        63: 1
        64: q
        65: q+1
        66: q^2+2q
        67: q+1
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+2q
        75: q+1
        76: q^2+2q
        77: q+1
        78: q^2+q
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       103: q
       105: 1
       106: q
       107: q
       108: q^2+q+1
       109: q+1
       110: q
       111: q^2+2q
       112: q+1
       113: 2q
       114: 1
       115: q
       116: q+1
       117: 1
       120: 1
       121: q
       122: 1
       123: q
       124: q+1
       125: 1
       126: q+1
       127: q^2+2q
       128: q+1
       129: q^2+2q
       130: q+1
       131: q^2+q
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q^2+3q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: q^3+3q^2+3q+1
       148: q^2+3q+1
       149: 2q+1
       150: 2q+1
       151: q^2+2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: q^2+q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       169: q
       171: 1
       172: q
       175: 1
       177: q
       178: q+1
       179: 2q
       180: 1
       181: q^2+2q
       182: q+1
       184: 1
       185: 1
       187: q
       188: q+1
       189: q
       190: 1
       191: 1
       194: q+1
       195: q+1
       196: q
       197: q
       198: 1
       200: 1
       201: q
       202: q^2+q+1
       203: q+1
       204: q
       205: q^2+2q
       206: q+1
       207: q
       208: 1
       209: 2q
       210: 1
       211: q
       212: q+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: q^2+2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       261: 1
       262: q
       265: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       291: q
       292: q+1
       294: 1
       295: 1
       297: q
       298: 1
       300: 1
       301: q
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       311: q^2+2q
       312: q+1
       313: q
       314: q+1
       315: q
       316: q+1
       317: 2q
       318: 1
       320: q+1
       321: q+1
       322: q
       323: q
       324: 1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: q^2+q
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       387: 1
       391: q
       392: 1
       395: 1
       397: q
       398: 1
       399: q
       402: 1
       406: q
       408: 1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 2q
       428: 1
       430: 1
       431: 1
       434: 1
       444: q+1
       445: q
       446: 1
       448: 1
       449: 1
       451: q
       452: q+1
       454: 1
       457: 1
       459: q
       460: 1
       461: q+1
       462: q
       463: q^2+2q
       464: q+1
       469: q
       470: 1
       472: 1
       473: 1
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       531: 1
       535: 1
       547: q
       548: 1
       550: 1
       558: 1
       561: q
       562: 1
       563: q
       567: 1
       570: q
       572: 1
       575: q
       576: 1
       577: q
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       614: 1
       616: 1
       620: 1
       621: 1
       625: q
       626: 1
       629: q
       630: q+1
       631: 1
       642: 1
       643: 1
       646: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       697: q
       700: 1
       714: 1
       719: 1
       742: 1
       755: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       817: 1
       826: 1
       827: 1
       830: 1
       831: 1
       835: q
       836: 1
       844: 1
       856: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       910: 1
       949: 1
       954: 1
       966: 1
       998: 1
      1001: 1
      1013: 1
      1041: 1
      1044: 1
      1065: 1
      1080: 1
      1084: 1
      1132: 1
      1182: 1
      1250: 1
      1255: 1
      1281: 1
      1398: 1

1399:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+2q^2+2q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+2q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+3q+1
        37: q+1
        38: q^2+2q
        39: q+1
        40: q^2+2q
        41: q+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+2q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q
        59: q+1
        60: q
        61: q^2+q+1
        62: 1
        63: 2q
        64: q+1
        65: q
        66: q+1
        67: q^2+2q
        68: 1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q^2+2q
        76: q+1
        77: q^2+2q
        78: q+1
        79: q^2+q
        80: q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+2q+1
       104: q
       105: q
       106: 1
       107: q
       108: q^2+q+1
       109: q
       110: q+1
       111: q+1
       112: q^2+2q
       113: 1
       114: 2q
       115: q+1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: q+1
       124: q
       125: 1
       126: q+1
       127: q+1
       128: q^2+2q
       129: q+1
       130: q^2+2q
       131: q+1
       132: q^2+q
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q^2+3q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: q^3+3q^2+3q+1
       148: q^2+3q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+2q+1
       170: q
       171: q
       172: 1
       176: 1
       177: q+1
       178: q
       179: 1
       180: 2q
       181: q+1
       182: q^2+2q
       184: 1
       186: 1
       187: q+1
       188: q
       189: 1
       190: q
       192: 1
       194: q+1
       195: q
       196: q+1
       197: 1
       198: q
       200: 1
       201: q
       202: q^2+q+1
       203: q
       204: q+1
       205: q+1
       206: q^2+2q
       207: 1
       208: q
       209: 1
       210: 2q
       211: q+1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: 2q+1
       226: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       238: q^2+2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q+1
       245: q^2+3q+1
       246: q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q
       262: 1
       266: 1
       269: 1
       270: q
       272: q
       273: 1
       274: q
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: q+1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: 1
       301: 1
       302: q
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       312: q^2+2q
       313: q+1
       314: q
       315: q+1
       316: q
       317: 1
       318: 2q
       320: q+1
       321: q
       322: q+1
       323: 1
       324: q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q+1
       339: q^2+2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: q^2+q
       344: 1
       348: 1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: 2q+1
       359: q^2+3q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       388: 1
       391: 1
       392: q
       396: 1
       398: q
       399: 1
       400: q
       404: 1
       406: 1
       408: q
       420: 1
       422: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: 1
       428: 2q
       430: 1
       432: 1
       433: 1
       444: q+1
       445: 1
       446: q
       448: 1
       450: 1
       451: q+1
       452: q
       454: 1
       458: 1
       459: 1
       460: q
       461: q
       462: q+1
       463: q+1
       464: q^2+2q
       469: 1
       470: q
       472: 1
       474: 1
       475: 1
       477: 1
       478: q
       479: 1
       480: q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       532: 1
       536: 1
       547: 1
       548: q
       552: 1
       559: 1
       562: q
       563: 1
       564: q
       568: 1
       570: 1
       572: q
       575: 1
       576: q
       577: 1
       581: q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       613: 1
       616: 1
       620: 1
       622: 1
       625: 1
       626: q
       629: q+1
       630: q
       632: 1
       642: 1
       644: 1
       645: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       689: 1
       697: 1
       700: q
       716: 1
       720: 1
       743: 1
       756: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       818: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       836: q
       843: 1
       855: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       911: 1
       950: 1
       955: 1
       967: 1
       999: 1
      1001: 1
      1012: 1
      1041: 1
      1045: 1
      1064: 1
      1080: 1
      1084: 1
      1133: 1
      1183: 1
      1251: 1
      1255: 1
      1280: 1
      1399: 1

1400:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+3q+1
        25: q^3+5q^2+5q+1
        26: q^3+5q^2+5q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: 3q^2+5q+1
        32: q^2+3q+1
        33: 2q^2+5q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+3q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+5q+1
        53: 3q^2+5q+1
        54: 3q^2+3q+1
        55: q^3+5q^2+5q+1
        56: q^3+5q^2+5q+1
        57: q^3+4q^2+3q+1
        58: 2q^2+3q+1
        59: 2q
        60: 2q^2+3q+1
        61: q^2+2q
        62: 2q^2+3q+1
        63: q^2+2q
        64: q^2+2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 3q^2+5q+1
        73: 2q^2+5q+1
        74: 2q^2+3q+1
        75: q^2+2q
        76: 2q^2+3q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: 3q+1
        82: 3q^2+5q+1
        83: q^2+3q+1
        84: 2q^2+3q+1
        85: 3q+1
        86: q^3+5q^2+5q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+2q+1
        97: 3q^2+5q+1
        98: 3q^2+5q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q^2+2q+1
       104: q
       105: q^2+q
       106: q
       107: 2q^2+3q+1
       108: q^2+2q
       109: 2q^2+3q+1
       110: 2q
       111: q^2+3q+1
       112: q^2+2q
       113: 2q^2+3q+1
       114: q^2+2q
       115: q^2+2q+1
       116: q
       117: q+1
       119: q+1
       121: q^2+2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: 3q^2+5q+1
       146: 2q^2+3q+1
       147: 3q^2+5q+1
       148: 2q^2+5q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: 2q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q^2+2q+1
       170: q
       171: q^2+q
       172: q
       173: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q+1
       185: q+1
       187: 2q+1
       188: q
       189: q^2+2q+1
       190: q
       191: q+1
       193: 2q+1
       195: q^2+2q+1
       196: 2q
       197: q+1
       198: q
       199: q+1
       201: 2q^2+3q+1
       202: q^2+2q
       203: 2q^2+3q+1
       204: 2q
       205: q^2+3q+1
       206: q^2+2q
       207: 2q+1
       208: q
       209: 2q^2+3q+1
       210: q^2+2q
       211: q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 3q+1
       235: 3q+1
       236: 2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 2q+1
       245: q^2+4q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       262: q
       263: q+1
       267: q+1
       268: q
       271: q^2+2q+1
       272: q^2+q
       273: q
       274: q
       275: q+1
       283: 1
       285: 1
       287: q+1
       291: q+1
       293: q+1
       295: q+1
       297: 2q+1
       298: q
       299: 1
       301: q+1
       303: 1
       305: 1
       307: q+1
       309: q+1
       311: 2q+1
       313: 2q+1
       314: q
       315: q+1
       317: 2q+1
       319: 2q+1
       321: q^2+2q+1
       322: 2q
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: 3q+1
       358: 2q+1
       359: q^2+4q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: q+1
       389: q+1
       393: 1
       397: q+1
       399: q
       401: q+1
       405: q+1
       407: q
       419: 1
       421: 1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 2q+1
       445: q+1
       447: 1
       449: 1
       451: q+1
       453: q+1
       457: q+1
       459: 2q+1
       460: q
       461: q^2+2q+1
       462: 2q
       463: 2q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       529: 1
       533: 1
       541: 1
       545: q+1
       549: 1
       557: q+1
       561: q+1
       563: q
       565: 1
       569: q+1
       573: q+1
       574: q
       577: q+1
       589: 1
       591: 1
       593: 1
       595: 1
       599: q+1
       603: 1
       607: 1
       609: 1
       613: 1
       615: 1
       619: 1
       621: 1
       625: q+1
       629: q+1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       693: q+1
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       805: 1
       807: 1
       811: 1
       815: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: q+1
       839: 1
       845: 1
       847: 1
       851: 1
       855: 1
       857: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       908: 1
       928: 1
       948: 1
       952: 1
       974: 1
       988: 1
      1004: 1
      1006: 1
      1008: 1
      1040: 1
      1044: 1
      1056: 1
      1058: 1
      1062: 1
      1064: 1
      1082: 1
      1085: 1
      1134: 1
      1180: 1
      1206: 1
      1258: 1
      1260: 1
      1276: 1
      1400: 1

1401:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+3q+1
        25: q^3+5q^2+5q+1
        26: q^3+5q^2+5q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: 3q^2+5q+1
        32: q^2+3q+1
        33: 2q^2+5q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+3q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+5q+1
        53: 3q^2+5q+1
        54: 3q^2+3q+1
        55: q^3+5q^2+5q+1
        56: q^3+5q^2+5q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: 2q^2+3q+1
        60: q^2+2q
        61: 2q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+2q
        64: q^2+2q+1
        65: q
        66: q^2+3q+1
        67: q^2+2q
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 3q^2+5q+1
        73: 2q^2+5q+1
        74: 2q^2+3q+1
        75: q^2+2q
        76: 2q^2+3q+1
        77: q^2+2q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: 3q+1
        82: 3q^2+5q+1
        83: q^2+3q+1
        84: 2q^2+3q+1
        85: 3q+1
        86: q^3+5q^2+5q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+2q+1
        97: 3q^2+5q+1
        98: 3q^2+5q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q
       104: q^2+q
       105: q
       106: q^2+2q+1
       107: q^2+2q
       108: 2q^2+3q+1
       109: 2q
       110: 2q^2+3q+1
       111: q^2+3q+1
       112: q^2+2q
       113: 2q^2+3q+1
       114: q^2+2q
       115: q^2+2q+1
       116: q
       118: q+1
       120: q+1
       121: q^2+2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: 3q^2+5q+1
       146: 2q^2+3q+1
       147: 3q^2+5q+1
       148: 2q^2+5q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: 2q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: q^2+2q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q
       170: q^2+q
       171: q
       172: q^2+2q+1
       176: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       184: q+1
       186: q+1
       187: 2q+1
       188: q
       189: q^2+2q+1
       190: q
       192: q+1
       194: 2q+1
       195: 2q
       196: q^2+2q+1
       197: q+1
       198: q
       200: q+1
       201: q^2+2q
       202: 2q^2+3q+1
       203: 2q
       204: 2q^2+3q+1
       205: q^2+3q+1
       206: q^2+2q
       207: 2q+1
       208: q
       209: 2q^2+3q+1
       210: q^2+2q
       211: q^2+2q+1
       212: q
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 3q+1
       235: 3q+1
       236: 2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 2q+1
       245: q^2+4q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: q+1
       266: q+1
       269: q+1
       270: q
       271: q
       272: q
       273: q^2+2q+1
       274: q^2+q
       278: q+1
       284: 1
       286: 1
       287: q+1
       291: q+1
       294: q+1
       296: q+1
       297: 2q+1
       298: q
       300: 1
       301: q+1
       304: 1
       305: 1
       308: q+1
       310: q+1
       311: 2q+1
       313: 2q+1
       314: q
       315: q+1
       317: 2q+1
       320: 2q+1
       321: 2q
       322: q^2+2q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: 3q+1
       358: 2q+1
       359: q^2+4q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: q+1
       391: q+1
       396: 1
       397: q
       399: q+1
       404: q+1
       406: q+1
       408: q
       420: 1
       422: 1
       423: q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 2q+1
       445: q+1
       448: 1
       450: 1
       451: q+1
       454: q+1
       458: q+1
       459: 2q+1
       460: q
       461: 2q
       462: q^2+2q+1
       463: 2q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       532: 1
       536: 1
       543: 1
       547: q+1
       552: 1
       559: q+1
       561: q
       563: q+1
       568: 1
       570: q+1
       575: q+1
       576: q
       577: q+1
       590: 1
       592: 1
       594: 1
       596: 1
       599: q+1
       604: 1
       608: 1
       609: 1
       613: 1
       616: 1
       620: 1
       622: 1
       625: q+1
       629: q+1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       665: 1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       697: q+1
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       806: 1
       808: 1
       811: 1
       816: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: q+1
       840: 1
       846: 1
       848: 1
       851: 1
       855: 1
       857: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       911: 1
       930: 1
       950: 1
       955: 1
       975: 1
       991: 1
      1005: 1
      1007: 1
      1008: 1
      1041: 1
      1045: 1
      1057: 1
      1059: 1
      1062: 1
      1064: 1
      1082: 1
      1085: 1
      1135: 1
      1183: 1
      1208: 1
      1259: 1
      1261: 1
      1276: 1
      1401: 1

1402:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+3q+1
        25: q^3+5q^2+5q+1
        26: q^3+5q^2+5q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: 3q^2+5q+1
        32: q^2+3q+1
        33: 2q^2+5q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+3q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+5q+1
        53: 3q^2+5q+1
        54: 3q^2+3q+1
        55: q^3+5q^2+5q+1
        56: q^3+5q^2+5q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: 2q^2+3q+1
        60: 2q^2+3q+1
        61: q^2+2q
        62: q^2+2q
        63: 2q^2+3q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 3q^2+5q+1
        73: 2q^2+5q+1
        74: q^2+2q
        75: 2q^2+3q+1
        76: q^2+2q
        77: 2q^2+3q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+3q+1
        81: 3q+1
        82: 3q^2+5q+1
        83: q^2+3q+1
        84: 2q^2+3q+1
        85: 3q+1
        86: q^3+5q^2+5q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+2q+1
        97: 3q^2+5q+1
        98: 3q^2+5q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q
       104: q^2+2q+1
       105: q
       106: q^2+q
       107: 2q^2+3q+1
       108: q^2+2q
       109: 2q
       110: 2q^2+3q+1
       111: q^2+2q
       112: q^2+3q+1
       113: q^2+2q
       114: 2q^2+3q+1
       115: q
       116: q^2+2q+1
       118: q+1
       119: q+1
       121: q
       122: q^2+2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: 3q^2+5q+1
       146: 2q^2+3q+1
       147: 3q^2+5q+1
       148: 2q^2+5q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: q^2+2q
       152: 2q^2+3q+1
       153: q^2+2q
       154: 2q^2+3q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q
       170: q^2+2q+1
       171: q
       172: q^2+q
       174: q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q+1
       186: q+1
       187: q
       188: 2q+1
       189: q
       190: q^2+2q+1
       192: q+1
       193: 2q+1
       195: 2q
       196: q^2+2q+1
       197: q
       198: q+1
       199: q+1
       201: 2q^2+3q+1
       202: q^2+2q
       203: 2q
       204: 2q^2+3q+1
       205: q^2+2q
       206: q^2+3q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 2q^2+3q+1
       211: q
       212: q^2+2q+1
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 3q+1
       235: 3q+1
       236: 2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 2q+1
       245: q^2+4q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q+1
       261: q
       264: q+1
       267: q
       268: q+1
       271: q
       272: q
       273: q^2+q
       274: q^2+2q+1
       276: q+1
       283: 1
       286: 1
       288: q+1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: 2q+1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: q+1
       310: q+1
       312: 2q+1
       313: q
       314: 2q+1
       316: q+1
       318: 2q+1
       319: 2q+1
       321: 2q
       322: q^2+2q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: 3q+1
       358: 2q+1
       359: q^2+4q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: q+1
       390: q+1
       394: 1
       398: q
       400: q+1
       403: q+1
       405: q
       407: q+1
       419: 1
       422: 1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 2q+1
       446: q+1
       447: 1
       450: 1
       452: q+1
       453: q+1
       458: q+1
       459: q
       460: 2q+1
       461: 2q
       462: q^2+2q+1
       464: 2q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       530: 1
       534: 1
       542: 1
       546: q+1
       551: 1
       560: q+1
       562: q
       564: q+1
       566: 1
       571: q+1
       573: q
       574: q+1
       581: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       600: q+1
       603: 1
       608: 1
       610: 1
       614: 1
       615: 1
       619: 1
       622: 1
       626: q+1
       630: q+1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       699: q+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       805: 1
       808: 1
       812: 1
       815: 1
       825: 1
       828: 1
       829: 1
       832: 1
       836: q+1
       840: 1
       845: 1
       848: 1
       852: 1
       856: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       909: 1
       929: 1
       951: 1
       953: 1
       976: 1
       989: 1
      1004: 1
      1007: 1
      1009: 1
      1040: 1
      1045: 1
      1056: 1
      1059: 1
      1063: 1
      1065: 1
      1082: 1
      1085: 1
      1136: 1
      1181: 1
      1207: 1
      1258: 1
      1261: 1
      1277: 1
      1402: 1

1403:    0: q^3+5q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^3+4q^2+3q+1
         3: q^3+5q^2+5q+1
         4: q^3+5q^2+5q+1
         5: q^3+5q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+5q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: q^3+3q^2+2q+1
        19: q^3+5q^2+5q+1
        20: q^3+5q^2+5q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+3q+1
        25: q^3+5q^2+5q+1
        26: q^3+5q^2+5q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^2+3q+1
        31: 3q^2+5q+1
        32: q^2+3q+1
        33: 2q^2+5q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+3q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 3q^2+5q+1
        50: 3q^2+5q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+5q+1
        53: 3q^2+5q+1
        54: 3q^2+3q+1
        55: q^3+5q^2+5q+1
        56: q^3+5q^2+5q+1
        57: q^3+4q^2+3q+1
        58: 2q^2+3q+1
        59: 2q
        60: q^2+2q
        61: 2q^2+3q+1
        62: q^2+2q
        63: 2q^2+3q+1
        64: q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+3q+1
        68: q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q^2+5q+1
        72: 3q^2+5q+1
        73: 2q^2+5q+1
        74: q^2+2q
        75: 2q^2+3q+1
        76: q^2+2q
        77: 2q^2+3q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+3q+1
        81: 3q+1
        82: 3q^2+5q+1
        83: q^2+3q+1
        84: 2q^2+3q+1
        85: 3q+1
        86: q^3+5q^2+5q+1
        87: 2q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+2q+1
        97: 3q^2+5q+1
        98: 3q^2+5q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+3q+1
       103: q^2+q
       104: q
       105: q^2+2q+1
       106: q
       107: q^2+2q
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q
       111: q^2+2q
       112: q^2+3q+1
       113: q^2+2q
       114: 2q^2+3q+1
       115: q
       116: q^2+2q+1
       117: q+1
       120: q+1
       121: q
       122: q^2+2q+1
       123: q
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q+1
       134: 2q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+4q+1
       143: 3q+1
       144: 2q+1
       145: 3q^2+5q+1
       146: 2q^2+3q+1
       147: 3q^2+5q+1
       148: 2q^2+5q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: q^2+2q
       152: 2q^2+3q+1
       153: q^2+2q
       154: 2q^2+3q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+2q+1
       169: q^2+q
       170: q
       171: q^2+2q+1
       172: q
       175: q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       184: q+1
       185: q+1
       187: q
       188: 2q+1
       189: q
       190: q^2+2q+1
       191: q+1
       194: 2q+1
       195: q^2+2q+1
       196: 2q
       197: q
       198: q+1
       200: q+1
       201: q^2+2q
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 2q
       205: q^2+2q
       206: q^2+3q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 2q^2+3q+1
       211: q
       212: q^2+2q+1
       219: 1
       220: q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 3q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 3q+1
       235: 3q+1
       236: 2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 2q+1
       245: q^2+4q+1
       246: q^2+3q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q+1
       265: q+1
       269: q
       270: q+1
       271: q^2+q
       272: q^2+2q+1
       273: q
       274: q
       277: q+1
       284: 1
       285: 1
       288: q+1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: 2q+1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: q+1
       309: q+1
       312: 2q+1
       313: q
       314: 2q+1
       316: q+1
       318: 2q+1
       320: 2q+1
       321: q^2+2q+1
       322: 2q
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: 1
       353: q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: 3q+1
       358: 2q+1
       359: q^2+4q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: q+1
       392: q+1
       395: 1
       398: q+1
       400: q
       402: q+1
       406: q
       408: q+1
       420: 1
       421: 1
       424: q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 2q+1
       446: q+1
       448: 1
       449: 1
       452: q+1
       454: q+1
       457: q+1
       459: q
       460: 2q+1
       461: q^2+2q+1
       462: 2q
       464: 2q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 2q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       531: 1
       535: 1
       544: 1
       548: q+1
       550: 1
       558: q+1
       562: q+1
       564: q
       567: 1
       572: q+1
       575: q
       576: q+1
       581: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       600: q+1
       604: 1
       607: 1
       610: 1
       614: 1
       616: 1
       620: 1
       621: 1
       626: q+1
       630: q+1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       665: 1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       700: q+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       806: 1
       807: 1
       812: 1
       816: 1
       826: 1
       827: 1
       830: 1
       831: 1
       836: q+1
       839: 1
       846: 1
       847: 1
       852: 1
       856: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       910: 1
       931: 1
       949: 1
       954: 1
       977: 1
       990: 1
      1005: 1
      1006: 1
      1009: 1
      1041: 1
      1044: 1
      1057: 1
      1058: 1
      1063: 1
      1065: 1
      1082: 1
      1085: 1
      1137: 1
      1182: 1
      1209: 1
      1259: 1
      1260: 1
      1277: 1
      1403: 1

1404:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+2q+2
         5: q^2+3q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+3q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+2q+2
        13: q^2+3q+2
        14: q^2+2q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: 2q+2
        30: 2q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: q^2+3q+2
        44: q^2+2q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: 2q+2
        69: 1
        70: 2q+2
        71: q+2
        72: 2
        73: 2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q+2
        89: 2q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: 2q+2
       126: 1
       127: q+2
       129: q+2
       131: q+1
       133: q+2
       134: 1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       140: 2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: 1
       179: q+2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: 2q+2
       211: 2q+2
       213: q+2
       215: q+2
       217: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       229: 2
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       235: 2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 2q+2
       327: q+2
       329: q+2
       331: q+1
       333: 1
       334: 1
       335: 1
       337: 2
       338: 2
       340: 2
       344: 1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: q+2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 1
       482: 1
       484: 2
       485: 2
       487: 2
       492: 1
       493: 1
       494: 1
       496: 2
       497: 1
       498: 1
       499: 1
       501: 2
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: 1
       518: 2
       519: 2
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: 1
       585: 1
       587: 1
       601: 2
       605: 1
       609: 1
       611: 2
       615: 1
       616: 1
       617: 2
       623: 1
       625: 1
       627: 2
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       658: 1
       660: 1
       666: 2
       668: 2
       672: 2
       674: 1
       675: 1
       676: 1
       678: 2
       680: 1
       681: 1
       682: 1
       684: 2
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       697: 1
       729: 1
       731: 1
       733: 1
       735: 1
       745: 1
       747: 1
       749: 1
       751: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       777: 1
       789: 2
       795: 1
       797: 1
       799: 1
       813: 2
       815: 1
       816: 1
       819: 1
       821: 1
       823: 1
       837: 2
       839: 1
       840: 1
       841: 1
       843: 1
       849: 1
       851: 1
       853: 2
       857: 2
       859: 1
       861: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       884: 1
       889: 1
       932: 1
       934: 1
       956: 1
       958: 1
       968: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
      1014: 1
      1018: 1
      1030: 1
      1034: 1
      1046: 1
      1048: 1
      1050: 1
      1066: 1
      1068: 1
      1075: 1
      1079: 1
      1098: 1
      1102: 1
      1188: 1
      1226: 1
      1244: 1
      1262: 1
      1264: 1
      1404: 1

1405:    0: 2q^3+7q^2+6q
         1: 2q^3+7q^2+6q
         2: 2q^3+7q^2+6q
         3: 2q^3+7q^2+6q
         4: 3q^3+5q^2+4q
         5: 2q^3+7q^2+6q
         6: 3q^3+5q^2+4q
         7: 3q^3+5q^2+4q
         8: 2q^3+7q^2+6q
         9: q^4+3q^3+3q^2+2q
        10: 2q^3+7q^2+6q
        11: 2q^3+7q^2+6q
        12: 3q^3+5q^2+4q
        13: 2q^3+7q^2+6q
        14: 3q^3+5q^2+4q
        15: 2q^3+7q^2+6q
        16: 4q^2+6q
        17: 4q^2+6q
        18: q^3+3q^2+2q
        19: 3q^2+4q
        20: 3q^2+4q
        21: 3q^2+4q
        22: 2q^3+7q^2+6q
        23: 2q^3+7q^2+6q
        24: 2q^3+7q^2+6q
        25: 2q^3+7q^2+6q
        26: 2q^3+7q^2+6q
        27: 2q^3+7q^2+6q
        28: 4q^2+6q
        29: 3q^2+4q
        30: 3q^2+4q
        31: 2q^3+7q^2+6q
        32: 2q^3+7q^2+6q
        33: 4q^2+6q
        34: 2q^3+7q^2+6q
        35: 2q^3+7q^2+6q
        36: 4q^2+6q
        37: q^3+3q^2+2q
        38: q^3+4q^2+4q
        39: q^3+3q^2+2q
        40: q^3+4q^2+4q
        41: q^3+3q^2+2q
        42: q^3+4q^2+4q
        43: 2q^3+7q^2+6q
        44: 3q^3+5q^2+4q
        45: 2q^3+7q^2+6q
        46: 4q^2+6q
        47: 4q^2+6q
        48: q^3+3q^2+2q
        49: q^2+4q
        50: q^2+4q
        51: 2q^2+2q
        52: 3q^2+4q
        53: 3q^2+4q
        54: 3q^2+4q
        55: 3q^2+4q
        56: 3q^2+4q
        57: 3q^2+4q
        58: 2q^2+3q
        59: 2q^2+3q
        60: 2q^2+3q
        61: 2q^2+3q
        62: q^3+3q^2+2q
        63: q^3+4q^2+4q
        64: q^3+3q^2+2q
        65: q^3+4q^2+4q
        66: 2q^2+2q
        67: 2q^2+4q
        68: 4q^2+6q
        69: 2q
        70: 3q^2+4q
        71: q^2+4q
        72: 2q
        73: 2q
        75: q^2+2q
        77: q^2+2q
        79: q^2+2q
        80: 2q^3+7q^2+6q
        81: 4q^2+6q
        82: 3q^2+4q
        83: 3q^2+4q
        84: 2q^3+7q^2+6q
        85: 4q^2+6q
        86: 3q^2+4q
        87: 3q^2+4q
        88: 4q^2+6q
        89: 4q^2+6q
        90: q^3+3q^2+2q
        91: q^2+4q
        92: q^2+4q
        93: 2q^2+2q
        94: q^2+4q
        95: q^2+4q
        96: 2q^2+2q
        97: q^2+4q
        98: q^2+4q
        99: 2q^2+2q
       100: 3q^2+4q
       101: 3q^2+4q
       102: 3q^2+4q
       103: q^2+q
       104: q^2+2q
       105: q^2+2q
       106: q^2+q
       107: q
       108: q
       109: q
       110: q
       114: q^2+2q
       116: q^2+2q
       117: 2q^2+3q
       118: 2q^2+3q
       119: 2q^2+3q
       120: 2q^2+3q
       121: q^3+3q^2+2q
       122: q^3+4q^2+4q
       123: 2q^2+2q
       124: 2q^2+4q
       125: 4q^2+6q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       133: q^2+4q
       134: 2q
       135: 2q
       136: 2q
       137: 4q^2+6q
       138: 2q
       139: q^2+4q
       140: 2q
       141: 3q^2+4q
       142: 2q
       143: 4q^2+6q
       144: 2q
       145: q^2+4q
       146: 3q^2+4q
       147: 2q
       148: 2q
       149: 3q^2+4q
       150: 3q^2+4q
       152: q^2+2q
       154: q^2+2q
       156: q^2+2q
       157: q^2+4q
       158: q^2+4q
       159: 2q^2+2q
       160: q^2+4q
       161: q^2+4q
       162: 2q^2+2q
       163: q^2+4q
       164: q^2+4q
       165: 2q^2+2q
       166: q^2+4q
       167: q^2+4q
       168: 2q^2+2q
       173: q^2+q
       174: q^2+2q
       175: q^2+2q
       176: q^2+q
       178: q
       180: 2q
       183: q
       184: q
       185: q
       186: q
       190: q^2+2q
       191: 2q^2+3q
       192: 2q^2+3q
       193: q
       194: q
       195: q
       196: q
       199: 2q^2+3q
       200: 2q^2+3q
       201: q
       202: q
       203: q
       204: q
       207: 2q^2+2q
       208: 2q^2+4q
       210: q^2+2q
       212: q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: q^2+4q
       221: 2q
       222: 2q
       223: q
       224: 2q
       225: q
       226: 2q
       227: q^2+4q
       228: 2q
       229: 2q
       230: 2q
       231: 2q
       232: q^2+4q
       233: 2q
       234: 2q
       235: 2q
       236: 2q
       238: 2q
       240: 2q
       242: q^2+q
       243: q^2+4q
       244: 2q
       245: 2q
       246: 3q^2+4q
       247: 2
       248: 2
       250: q^2+4q
       251: q^2+4q
       252: 2q^2+2q
       253: q^2+4q
       254: q^2+4q
       255: 2q^2+2q
       256: q^2+4q
       257: q^2+4q
       258: 2q^2+2q
       275: q^2+q
       276: q^2+2q
       277: q^2+2q
       278: q^2+q
       280: 2q
       282: q
       288: q
       293: q
       294: q
       295: q
       296: q
       299: q
       300: q
       303: q
       304: q
       307: q
       308: q
       309: q
       310: q
       316: q
       318: 2q
       319: q
       320: q
       321: q
       322: q
       326: q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: 2q
       334: q
       335: q
       337: 2
       339: 2
       341: 2
       344: 2q
       345: q^2+4q
       346: 2q
       347: 2q
       348: q
       349: 2q
       350: q
       351: 2
       352: 2q
       353: q^2+4q
       354: 2q
       355: 2q
       356: q
       357: 2q
       358: q
       359: 2
       361: 2q
       363: 2q
       365: q^2+q
       366: 2q
       367: q^2+4q
       368: 2q
       369: 2q
       370: 2q
       371: 2
       372: 2
       374: q^2+4q
       375: q^2+4q
       376: 2q^2+2q
       410: 2q
       412: q
       414: q
       428: 2
       437: q
       438: q
       439: q
       440: q
       443: 1
       444: 1
       446: 2
       453: q
       454: q
       457: q
       458: q
       461: 1
       462: 1
       464: 2
       466: 2q
       468: q
       470: q
       471: q
       472: q
       473: q
       474: q
       479: 2
       481: q
       482: q
       484: 2
       486: 2
       488: 2
       492: 2q
       493: q
       494: q
       496: 2
       497: 2q
       498: q
       499: q
       501: 2
       503: 2q
       505: 2q
       507: q^2+q
       508: 2q
       509: q^2+4q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: 1
       518: 2
       519: 2
       546: 1
       548: 1
       562: 1
       564: 1
       573: 1
       575: 1
       578: 2
       584: q
       602: 2
       615: 1
       616: 1
       618: 2
       631: 1
       632: 1
       634: 2
       636: 2q
       638: q
       640: q
       647: q
       648: q
       649: q
       650: q
       655: 2
       659: 1
       661: 1
       667: 2
       669: 2
       672: 2
       674: 1
       675: q
       676: q
       678: 2
       680: 1
       681: q
       682: q
       684: 2
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       694: 1
       701: 1
       734: 1
       736: 1
       750: 1
       752: 1
       765: 1
       768: 1
       770: 2
       790: 2
       796: 1
       814: 2
       815: 1
       816: 1
       820: 1
       838: 2
       839: 1
       840: 1
       842: q
       843: 1
       857: 2
       860: 1
       862: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       885: 1
       892: 1
       933: 1
       935: 1
       957: 1
       959: 1
       969: 1
       983: 2
       988: 1
       991: 1
      1015: 1
      1031: 1
      1046: 1
      1067: 1
      1069: 1
      1075: 1
      1079: 1
      1099: 1
      1106: 1
      1189: 1
      1227: 1
      1245: 1
      1262: 1
      1405: 1

1406:    0: q^5+3q^4+4q^3+6q^2+2q
         1: 2q^4+6q^3+6q^2+2q
         2: q^5+3q^4+4q^3+6q^2+2q
         3: 2q^4+6q^3+6q^2+2q
         4: 4q^4+3q^3+5q^2+2q
         5: 4q^3+6q^2+2q
         6: 2q^5+5q^4+6q^3+5q^2+2q
         7: 4q^4+3q^3+5q^2+2q
         8: 4q^3+6q^2+2q
         9: q^5+2q^4+2q^3+2q^2+q
        10: q^4+3q^3+5q^2+2q
        11: 3q^3+5q^2+2q
        12: 3q^4+3q^3+4q^2+2q
        13: q^5+3q^4+4q^3+6q^2+2q
        14: 4q^4+3q^3+5q^2+2q
        15: 4q^3+6q^2+2q
        16: q^4+3q^3+5q^2+2q
        17: 3q^3+5q^2+2q
        18: 2q^4+q^3+2q^2+q
        19: 2q^4+2q^3+5q^2+2q
        20: 2q^4+5q^3+5q^2+2q
        21: 2q^4+2q^3+5q^2+2q
        22: 2q^3+6q^2+2q
        23: 4q^3+6q^2+2q
        24: 2q^3+6q^2+2q
        25: 2q^3+6q^2+2q
        26: 4q^3+6q^2+2q
        27: 2q^3+6q^2+2q
        28: 2q^3+4q^2+2q
        29: q^4+2q^3+4q^2+2q
        30: 2q^4+2q^3+5q^2+2q
        31: q^3+5q^2+2q
        32: 2q^3+6q^2+2q
        33: q^3+5q^2+2q
        34: q^3+5q^2+2q
        35: 2q^3+6q^2+2q
        36: q^3+5q^2+2q
        37: 2q^3+6q^2+2q
        39: 4q^3+6q^2+2q
        41: 2q^3+6q^2+2q
        43: q^4+3q^3+5q^2+2q
        44: 3q^4+3q^3+4q^2+2q
        45: 3q^3+5q^2+2q
        46: q^4+3q^3+5q^2+2q
        47: 3q^3+5q^2+2q
        48: 2q^4+q^3+2q^2+q
        49: 2q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+q^3+2q^2+q
        52: 5q^2+2q
        53: 3q^3+5q^2+2q
        54: 5q^2+2q
        55: 5q^2+2q
        56: 3q^3+5q^2+2q
        57: 5q^2+2q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        62: q^3+5q^2+2q
        64: 2q^3+6q^2+2q
        66: q^3+5q^2+2q
        68: 2q^3+4q^2+2q
        69: q^3+q^2+q
        70: q^4+2q^3+4q^2+2q
        71: 2q^3+3q^2+2q
        72: 3q^2+2q
        73: 3q^2+2q
        74: 5q^2+2q
        76: 3q^3+5q^2+2q
        78: 5q^2+2q
        80: q^3+5q^2+2q
        81: q^3+5q^2+2q
        82: 4q^2+2q
        83: 5q^2+2q
        84: q^3+5q^2+2q
        85: q^3+5q^2+2q
        86: 4q^2+2q
        87: 5q^2+2q
        88: q^3+2q^2+2q
        89: q^3+2q^2+2q
        90: q^4+q^3+q^2+q
        91: 2q^3+4q^2+2q
        92: 3q^3+4q^2+2q
        93: q^4+q^3+2q^2+q
        94: 4q^2+2q
        95: q^3+4q^2+2q
        96: 2q^2+q
        97: 4q^2+2q
        98: q^3+4q^2+2q
        99: 2q^2+q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       103: 2q^2+q
       106: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       111: 3q^2+2q
       113: 4q^2+2q
       115: 5q^2+2q
       117: 2q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: 2q^2+q
       121: q^3+5q^2+2q
       123: q^3+5q^2+2q
       125: q^3+2q^2+2q
       126: q^3+q
       127: 4q^2+2q
       129: q^3+4q^2+2q
       131: 2q^2+q
       133: 2q^3+3q^2+2q
       134: q^3+q^2+q
       135: 3q^2+2q
       136: 3q^2+2q
       137: 2q^2+2q
       138: q^2+q
       139: 3q^2+2q
       140: q^2+2q
       141: 4q^2+2q
       142: 3q^2+2q
       143: 2q^2+2q
       144: q^2+q
       145: 3q^2+2q
       146: 4q^2+2q
       147: 3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       151: 3q^2+2q
       153: q^3+3q^2+2q
       155: 3q^2+2q
       157: q^2+2q
       158: q^2+2q
       159: q^2+q
       160: 4q^2+2q
       161: q^3+4q^2+2q
       162: 2q^2+q
       163: 4q^2+2q
       164: q^3+4q^2+2q
       165: 2q^2+q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       169: q^2+q
       172: q^2+q
       173: 2q^2+q
       176: 2q^2+q
       177: q^2+q
       179: 3q^2+2q
       181: 3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       187: 3q^2+2q
       189: 4q^2+2q
       191: q^2+q
       192: q^2+q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       197: q^2+2q
       199: q^2+q
       200: q^2+q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       205: q^2+2q
       207: 2q^2+2q
       209: 2q^2+2q
       211: 3q^2+2q
       213: 4q^2+2q
       215: q^3+4q^2+2q
       217: 2q^2+q
       219: q^3+q
       220: q^2+2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: 3q^2+2q
       228: q^2+q
       229: q^2+2q
       230: 3q^2+2q
       231: q
       232: 3q^2+2q
       233: q^2+q
       234: 3q^2+2q
       235: q^2+2q
       236: q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: 2q^2+2q
       250: q^2+2q
       251: q^2+2q
       252: q^2+q
       253: q^2+2q
       254: q^2+2q
       255: q^2+q
       256: q^2+2q
       257: q^2+2q
       258: q^2+q
       259: q^2+q
       262: q^2+q
       263: q^2+q
       266: q^2+q
       267: q
       269: q
       271: q
       273: q
       275: q^2+q
       278: q^2+q
       279: 3q^2+2q
       281: q^2+q
       287: q
       289: 3q^2+2q
       291: q^2+q
       293: q
       294: q
       295: q
       296: q
       297: 2q
       299: q
       300: q
       301: 2q
       303: q^2+q
       304: q^2+q
       305: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       311: 2q
       313: q^2+2q
       315: q
       317: q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: 2q
       325: 2q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: q
       334: q
       335: q
       344: q
       345: q^2+2q
       346: q
       347: 2q
       348: q
       349: 2q
       350: q^2+q
       352: q
       353: q^2+2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q
       367: q^2+2q
       368: q
       369: 2q
       370: 2q
       381: q^2+q
       384: q^2+q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: q^2+2q
       411: q
       413: q
       415: 2q
       417: q^2+q
       423: q
       433: q
       435: 2q
       437: q
       438: q
       439: q
       440: q
       441: 2q
       451: q
       453: q
       454: q
       455: 2q
       457: q
       458: q
       459: 2q
       465: q^2+2q
       467: q
       469: q
       471: q
       472: q
       473: q
       474: q
       475: 2q
       477: 3q
       481: q
       482: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       508: q
       512: q
       514: q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       553: q
       555: q
       557: q
       559: q
       565: q
       568: q
       569: q
       570: q
       579: q
       583: q
       585: q
       587: q
       605: q
       609: q
       623: q
       625: q
       639: q
       645: q
       651: 3q
       675: q
       676: q
       681: q
       682: q
       757: q
       758: q
       771: q
       777: q
       797: q
       821: q
       849: q
       853: 2
       978: 1
       979: 1
       984: 2
      1050: 1
      1100: 1
      1107: 1
      1190: 1
      1264: 1
      1406: 1

1407:    0: 2q^3+7q^2+6q
         1: 2q^3+7q^2+6q
         2: 2q^3+7q^2+6q
         3: 2q^3+7q^2+6q
         4: 3q^3+5q^2+4q
         5: 2q^3+7q^2+6q
         6: 3q^3+5q^2+4q
         7: 3q^3+5q^2+4q
         8: 2q^3+7q^2+6q
         9: q^4+3q^3+3q^2+2q
        10: 2q^3+7q^2+6q
        11: 2q^3+7q^2+6q
        12: 3q^3+5q^2+4q
        13: 2q^3+7q^2+6q
        14: 3q^3+5q^2+4q
        15: 2q^3+7q^2+6q
        16: 4q^2+6q
        17: 4q^2+6q
        18: q^3+3q^2+2q
        19: 3q^2+4q
        20: 3q^2+4q
        21: 3q^2+4q
        22: 2q^3+7q^2+6q
        23: 2q^3+7q^2+6q
        24: 2q^3+7q^2+6q
        25: 2q^3+7q^2+6q
        26: 2q^3+7q^2+6q
        27: 2q^3+7q^2+6q
        28: 4q^2+6q
        29: 3q^2+4q
        30: 3q^2+4q
        31: 2q^3+7q^2+6q
        32: 2q^3+7q^2+6q
        33: 4q^2+6q
        34: 2q^3+7q^2+6q
        35: 2q^3+7q^2+6q
        36: 4q^2+6q
        37: q^3+4q^2+4q
        38: q^3+3q^2+2q
        39: q^3+4q^2+4q
        40: q^3+3q^2+2q
        41: q^3+4q^2+4q
        42: q^3+3q^2+2q
        43: 2q^3+7q^2+6q
        44: 3q^3+5q^2+4q
        45: 2q^3+7q^2+6q
        46: 4q^2+6q
        47: 4q^2+6q
        48: q^3+3q^2+2q
        49: q^2+4q
        50: q^2+4q
        51: 2q^2+2q
        52: 3q^2+4q
        53: 3q^2+4q
        54: 3q^2+4q
        55: 3q^2+4q
        56: 3q^2+4q
        57: 3q^2+4q
        58: 2q^2+3q
        59: 2q^2+3q
        60: 2q^2+3q
        61: 2q^2+3q
        62: q^3+4q^2+4q
        63: q^3+3q^2+2q
        64: q^3+4q^2+4q
        65: q^3+3q^2+2q
        66: 2q^2+4q
        67: 2q^2+2q
        68: 4q^2+6q
        69: 2q
        70: 3q^2+4q
        71: q^2+4q
        72: 2q
        73: 2q
        74: q^2+2q
        76: q^2+2q
        78: q^2+2q
        80: 2q^3+7q^2+6q
        81: 4q^2+6q
        82: 3q^2+4q
        83: 3q^2+4q
        84: 2q^3+7q^2+6q
        85: 4q^2+6q
        86: 3q^2+4q
        87: 3q^2+4q
        88: 4q^2+6q
        89: 4q^2+6q
        90: q^3+3q^2+2q
        91: q^2+4q
        92: q^2+4q
        93: 2q^2+2q
        94: q^2+4q
        95: q^2+4q
        96: 2q^2+2q
        97: q^2+4q
        98: q^2+4q
        99: 2q^2+2q
       100: 3q^2+4q
       101: 3q^2+4q
       102: 3q^2+4q
       103: q^2+2q
       104: q^2+q
       105: q^2+q
       106: q^2+2q
       107: q
       108: q
       109: q
       110: q
       113: q^2+2q
       115: q^2+2q
       117: 2q^2+3q
       118: 2q^2+3q
       119: 2q^2+3q
       120: 2q^2+3q
       121: q^3+4q^2+4q
       122: q^3+3q^2+2q
       123: 2q^2+4q
       124: 2q^2+2q
       125: 4q^2+6q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       133: q^2+4q
       134: 2q
       135: 2q
       136: 2q
       137: 4q^2+6q
       138: 2q
       139: q^2+4q
       140: 2q
       141: 3q^2+4q
       142: 2q
       143: 4q^2+6q
       144: 2q
       145: q^2+4q
       146: 3q^2+4q
       147: 2q
       148: 2q
       149: 3q^2+4q
       150: 3q^2+4q
       151: q^2+2q
       153: q^2+2q
       155: q^2+2q
       157: q^2+4q
       158: q^2+4q
       159: 2q^2+2q
       160: q^2+4q
       161: q^2+4q
       162: 2q^2+2q
       163: q^2+4q
       164: q^2+4q
       165: 2q^2+2q
       166: q^2+4q
       167: q^2+4q
       168: 2q^2+2q
       173: q^2+2q
       174: q^2+q
       175: q^2+q
       176: q^2+2q
       177: q
       179: 2q
       183: q
       184: q
       185: q
       186: q
       189: q^2+2q
       191: 2q^2+3q
       192: 2q^2+3q
       193: q
       194: q
       195: q
       196: q
       199: 2q^2+3q
       200: 2q^2+3q
       201: q
       202: q
       203: q
       204: q
       207: 2q^2+4q
       208: 2q^2+2q
       209: q^2+2q
       211: q^2+2q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: q^2+4q
       221: 2q
       222: 2q
       223: q
       224: 2q
       225: q
       226: 2q
       227: q^2+4q
       228: 2q
       229: 2q
       230: 2q
       231: 2q
       232: q^2+4q
       233: 2q
       234: 2q
       235: 2q
       236: 2q
       237: 2q
       239: 2q
       241: q^2+q
       243: q^2+4q
       244: 2q
       245: 2q
       246: 3q^2+4q
       247: 2
       248: 2
       250: q^2+4q
       251: q^2+4q
       252: 2q^2+2q
       253: q^2+4q
       254: q^2+4q
       255: 2q^2+2q
       256: q^2+4q
       257: q^2+4q
       258: 2q^2+2q
       275: q^2+2q
       276: q^2+q
       277: q^2+q
       278: q^2+2q
       279: 2q
       281: q
       287: q
       293: q
       294: q
       295: q
       296: q
       299: q
       300: q
       303: q
       304: q
       307: q
       308: q
       309: q
       310: q
       315: q
       317: 2q
       319: q
       320: q
       321: q
       322: q
       325: q^2+2q
       327: 2q
       329: 2q
       331: q^2+q
       333: 2q
       334: q
       335: q
       337: 2
       338: 2
       340: 2
       344: 2q
       345: q^2+4q
       346: 2q
       347: 2q
       348: q
       349: 2q
       350: q
       351: 2
       352: 2q
       353: q^2+4q
       354: 2q
       355: 2q
       356: q
       357: 2q
       358: q
       359: 2
       360: 2q
       362: 2q
       364: q^2+q
       366: 2q
       367: q^2+4q
       368: 2q
       369: 2q
       370: 2q
       371: 2
       372: 2
       374: q^2+4q
       375: q^2+4q
       376: 2q^2+2q
       409: 2q
       411: q
       413: q
       427: 2
       437: q
       438: q
       439: q
       440: q
       443: 1
       444: 1
       445: 2
       453: q
       454: q
       457: q
       458: q
       461: 1
       462: 1
       463: 2
       465: 2q
       467: q
       469: q
       471: q
       472: q
       473: q
       474: q
       480: 2
       481: q
       482: q
       484: 2
       485: 2
       487: 2
       492: 2q
       493: q
       494: q
       496: 2
       497: 2q
       498: q
       499: q
       501: 2
       502: 2q
       504: 2q
       506: q^2+q
       508: 2q
       509: q^2+4q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: 1
       518: 2
       519: 2
       545: 1
       547: 1
       561: 1
       563: 1
       574: 1
       576: 1
       580: 2
       583: q
       601: 2
       615: 1
       616: 1
       617: 2
       631: 1
       632: 1
       633: 2
       635: 2q
       637: q
       639: q
       647: q
       648: q
       649: q
       650: q
       656: 2
       658: 1
       660: 1
       666: 2
       668: 2
       672: 2
       674: 1
       675: q
       676: q
       678: 2
       680: 1
       681: q
       682: q
       684: 2
       686: 2q
       687: q
       688: q
       690: 1
       691: 1
       696: 1
       698: 1
       733: 1
       735: 1
       749: 1
       751: 1
       766: 1
       767: 1
       772: 2
       789: 2
       795: 1
       813: 2
       815: 1
       816: 1
       819: 1
       837: 2
       839: 1
       840: 1
       841: q
       844: 1
       858: 2
       859: 1
       861: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       887: 1
       888: 1
       932: 1
       934: 1
       956: 1
       958: 1
       971: 1
       985: 2
       989: 1
       990: 1
      1014: 1
      1030: 1
      1047: 1
      1066: 1
      1068: 1
      1075: 1
      1079: 1
      1101: 1
      1103: 1
      1191: 1
      1226: 1
      1244: 1
      1263: 1
      1407: 1

1408:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+2q+2
         5: q^2+3q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+3q+2
         9: q^2+q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+2q+2
        13: q^2+3q+2
        14: q^2+2q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: 2q+2
        30: 2q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: q^2+3q+2
        44: q^2+2q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q+1
        49: q+2
        50: q+2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: 2q+2
        69: 1
        70: 2q+2
        71: q+2
        72: 2
        73: 2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: q^2+3q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: q^2+3q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: 2q+2
        89: 2q+2
        90: q+1
        91: q+2
        92: q+2
        93: q+1
        94: q+2
        95: q+2
        96: q+1
        97: q+2
        98: q+2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: 2q+2
       126: 1
       128: q+2
       130: q+2
       132: q+1
       133: q+2
       134: 1
       135: 2
       136: 2
       137: 2q+2
       138: 1
       139: q+2
       140: 2
       141: 2q+2
       142: 2
       143: 2q+2
       144: 1
       145: q+2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q+2
       158: q+2
       159: q+1
       160: q+2
       161: q+2
       162: q+1
       163: q+2
       164: q+2
       165: q+1
       166: q+2
       167: q+2
       168: q+1
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: 1
       180: q+2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: 2q+2
       212: 2q+2
       214: q+2
       216: q+2
       218: q+1
       219: 1
       220: q+2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: q+2
       228: 1
       229: 2
       230: 2
       231: 1
       232: q+2
       233: 1
       234: 2
       235: 2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       250: q+2
       251: q+2
       252: q+1
       253: q+2
       254: q+2
       255: q+1
       256: q+2
       257: q+2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 2q+2
       328: q+2
       330: q+2
       332: q+1
       333: 1
       334: 1
       335: 1
       337: 2
       339: 2
       341: 2
       344: 1
       345: q+2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: q+2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       374: q+2
       375: q+2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: q+2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 1
       482: 1
       484: 2
       486: 2
       488: 2
       492: 1
       493: 1
       494: 1
       496: 2
       497: 1
       498: 1
       499: 1
       501: 2
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: 1
       518: 2
       519: 2
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: 1
       586: 1
       588: 1
       602: 2
       606: 1
       610: 1
       612: 2
       615: 1
       616: 1
       618: 2
       624: 1
       626: 1
       628: 2
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       659: 1
       661: 1
       667: 2
       669: 2
       672: 2
       674: 1
       675: 1
       676: 1
       678: 2
       680: 1
       681: 1
       682: 1
       684: 2
       686: 1
       687: 1
       688: 1
       690: 1
       691: 1
       699: 1
       700: 1
       730: 1
       732: 1
       734: 1
       736: 1
       746: 1
       748: 1
       750: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       778: 1
       790: 2
       796: 1
       798: 1
       800: 1
       814: 2
       815: 1
       816: 1
       820: 1
       822: 1
       824: 1
       838: 2
       839: 1
       840: 1
       842: 1
       844: 1
       850: 1
       852: 1
       854: 2
       858: 2
       860: 1
       862: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       890: 1
       891: 1
       933: 1
       935: 1
       957: 1
       959: 1
       972: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
      1015: 1
      1019: 1
      1031: 1
      1035: 1
      1047: 1
      1049: 1
      1051: 1
      1067: 1
      1069: 1
      1075: 1
      1079: 1
      1104: 1
      1105: 1
      1192: 1
      1227: 1
      1245: 1
      1263: 1
      1265: 1
      1408: 1

1409:    0: q^5+3q^4+4q^3+6q^2+2q
         1: 2q^4+6q^3+6q^2+2q
         2: q^5+3q^4+4q^3+6q^2+2q
         3: 2q^4+6q^3+6q^2+2q
         4: 4q^4+3q^3+5q^2+2q
         5: 4q^3+6q^2+2q
         6: 2q^5+5q^4+6q^3+5q^2+2q
         7: 4q^4+3q^3+5q^2+2q
         8: 4q^3+6q^2+2q
         9: q^5+2q^4+2q^3+2q^2+q
        10: q^4+3q^3+5q^2+2q
        11: 3q^3+5q^2+2q
        12: 3q^4+3q^3+4q^2+2q
        13: q^5+3q^4+4q^3+6q^2+2q
        14: 4q^4+3q^3+5q^2+2q
        15: 4q^3+6q^2+2q
        16: q^4+3q^3+5q^2+2q
        17: 3q^3+5q^2+2q
        18: 2q^4+q^3+2q^2+q
        19: 2q^4+2q^3+5q^2+2q
        20: 2q^4+5q^3+5q^2+2q
        21: 2q^4+2q^3+5q^2+2q
        22: 2q^3+6q^2+2q
        23: 4q^3+6q^2+2q
        24: 2q^3+6q^2+2q
        25: 2q^3+6q^2+2q
        26: 4q^3+6q^2+2q
        27: 2q^3+6q^2+2q
        28: 2q^3+4q^2+2q
        29: q^4+2q^3+4q^2+2q
        30: 2q^4+2q^3+5q^2+2q
        31: q^3+5q^2+2q
        32: 2q^3+6q^2+2q
        33: q^3+5q^2+2q
        34: q^3+5q^2+2q
        35: 2q^3+6q^2+2q
        36: q^3+5q^2+2q
        38: 2q^3+6q^2+2q
        40: 4q^3+6q^2+2q
        42: 2q^3+6q^2+2q
        43: q^4+3q^3+5q^2+2q
        44: 3q^4+3q^3+4q^2+2q
        45: 3q^3+5q^2+2q
        46: q^4+3q^3+5q^2+2q
        47: 3q^3+5q^2+2q
        48: 2q^4+q^3+2q^2+q
        49: 2q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+q^3+2q^2+q
        52: 5q^2+2q
        53: 3q^3+5q^2+2q
        54: 5q^2+2q
        55: 5q^2+2q
        56: 3q^3+5q^2+2q
        57: 5q^2+2q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        63: q^3+5q^2+2q
        65: 2q^3+6q^2+2q
        67: q^3+5q^2+2q
        68: 2q^3+4q^2+2q
        69: q^3+q^2+q
        70: q^4+2q^3+4q^2+2q
        71: 2q^3+3q^2+2q
        72: 3q^2+2q
        73: 3q^2+2q
        75: 5q^2+2q
        77: 3q^3+5q^2+2q
        79: 5q^2+2q
        80: q^3+5q^2+2q
        81: q^3+5q^2+2q
        82: 4q^2+2q
        83: 5q^2+2q
        84: q^3+5q^2+2q
        85: q^3+5q^2+2q
        86: 4q^2+2q
        87: 5q^2+2q
        88: q^3+2q^2+2q
        89: q^3+2q^2+2q
        90: q^4+q^3+q^2+q
        91: 2q^3+4q^2+2q
        92: 3q^3+4q^2+2q
        93: q^4+q^3+2q^2+q
        94: 4q^2+2q
        95: q^3+4q^2+2q
        96: 2q^2+q
        97: 4q^2+2q
        98: q^3+4q^2+2q
        99: 2q^2+q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       104: 2q^2+q
       105: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       112: 3q^2+2q
       114: 4q^2+2q
       116: 5q^2+2q
       117: 2q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: 2q^2+q
       122: q^3+5q^2+2q
       124: q^3+5q^2+2q
       125: q^3+2q^2+2q
       126: q^3+q
       128: 4q^2+2q
       130: q^3+4q^2+2q
       132: 2q^2+q
       133: 2q^3+3q^2+2q
       134: q^3+q^2+q
       135: 3q^2+2q
       136: 3q^2+2q
       137: 2q^2+2q
       138: q^2+q
       139: 3q^2+2q
       140: q^2+2q
       141: 4q^2+2q
       142: 3q^2+2q
       143: 2q^2+2q
       144: q^2+q
       145: 3q^2+2q
       146: 4q^2+2q
       147: 3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       152: 3q^2+2q
       154: q^3+3q^2+2q
       156: 3q^2+2q
       157: q^2+2q
       158: q^2+2q
       159: q^2+q
       160: 4q^2+2q
       161: q^3+4q^2+2q
       162: 2q^2+q
       163: 4q^2+2q
       164: q^3+4q^2+2q
       165: 2q^2+q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       170: q^2+q
       171: q^2+q
       174: 2q^2+q
       175: 2q^2+q
       178: q^2+q
       180: 3q^2+2q
       182: 3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       188: 3q^2+2q
       190: 4q^2+2q
       191: q^2+q
       192: q^2+q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       198: q^2+2q
       199: q^2+q
       200: q^2+q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       206: q^2+2q
       208: 2q^2+2q
       210: 2q^2+2q
       212: 3q^2+2q
       214: 4q^2+2q
       216: q^3+4q^2+2q
       218: 2q^2+q
       219: q^3+q
       220: q^2+2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: 3q^2+2q
       228: q^2+q
       229: q^2+2q
       230: 3q^2+2q
       231: q
       232: 3q^2+2q
       233: q^2+q
       234: 3q^2+2q
       235: q^2+2q
       236: q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: 2q^2+2q
       250: q^2+2q
       251: q^2+2q
       252: q^2+q
       253: q^2+2q
       254: q^2+2q
       255: q^2+q
       256: q^2+2q
       257: q^2+2q
       258: q^2+q
       260: q^2+q
       261: q^2+q
       264: q^2+q
       265: q^2+q
       268: q
       270: q
       272: q
       274: q
       276: q^2+q
       277: q^2+q
       280: 3q^2+2q
       282: q^2+q
       288: q
       290: 3q^2+2q
       292: q^2+q
       293: q
       294: q
       295: q
       296: q
       298: 2q
       299: q
       300: q
       302: 2q
       303: q^2+q
       304: q^2+q
       306: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       312: 2q
       314: q^2+2q
       316: q
       318: q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: 2q
       326: 2q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: q
       334: q
       335: q
       344: q
       345: q^2+2q
       346: q
       347: 2q
       348: q
       349: 2q
       350: q^2+q
       352: q
       353: q^2+2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q
       367: q^2+2q
       368: q
       369: 2q
       370: 2q
       382: q^2+q
       383: q^2+q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: q^2+2q
       412: q
       414: q
       416: 2q
       418: q^2+q
       424: q
       434: q
       436: 2q
       437: q
       438: q
       439: q
       440: q
       442: 2q
       452: q
       453: q
       454: q
       456: 2q
       457: q
       458: q
       460: 2q
       466: q^2+2q
       468: q
       470: q
       471: q
       472: q
       473: q
       474: q
       476: 2q
       478: 3q
       481: q
       482: q
       492: q
       493: q
       494: q
       497: q
       498: q
       499: q
       508: q
       512: q
       514: q
       526: q
       527: q
       538: q
       540: q
       542: q
       544: q
       554: q
       556: q
       558: q
       560: q
       566: q
       567: q
       571: q
       572: q
       582: q
       584: q
       586: q
       588: q
       606: q
       610: q
       624: q
       626: q
       640: q
       646: q
       652: 3q
       675: q
       676: q
       681: q
       682: q
       759: q
       760: q
       774: q
       778: q
       798: q
       822: q
       850: q
       854: 2
       980: 1
       981: 1
       987: 2
      1051: 1
      1108: 1
      1109: 1
      1193: 1
      1265: 1
      1409: 1

1410:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 3q^2+5q+1
         3: 3q^2+5q+1
         4: 2q^2+3q+1
         5: 3q^2+5q+1
         6: 2q^3+3q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+5q+1
         9: 2q^2+3q+1
        10: q^2+5q+1
        11: q^2+5q+1
        12: 2q^2+3q+1
        13: 3q^2+5q+1
        14: 2q^2+3q+1
        15: 3q^2+5q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+5q+1
        28: q^2+5q+1
        29: 3q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q^2+5q+1
        33: 3q^2+5q+1
        34: q^2+5q+1
        35: 3q^2+5q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+2q
        43: q^2+5q+1
        44: 2q^2+3q+1
        45: q^2+5q+1
        46: 3q^2+5q+1
        47: 3q^2+5q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: q^2+3q+1
        59: 2q
        60: q^2+3q+1
        61: 2q
        62: q^2+3q+1
        63: 2q
        64: 2q^2+3q+1
        65: q^2+2q
        66: 2q^2+3q+1
        67: q^2+2q
        68: q^2+5q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: q^2+5q+1
        81: 3q^2+5q+1
        82: 3q+1
        83: 3q+1
        84: q^2+5q+1
        85: 3q^2+5q+1
        86: 3q+1
        87: 3q+1
        88: q^2+5q+1
        89: q^2+5q+1
        90: 2q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q^2+2q+1
       104: q
       105: q
       106: q
       107: q+1
       109: q+1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       117: q^2+3q+1
       118: 2q
       119: q^2+3q+1
       120: 2q
       121: q^2+3q+1
       122: 2q
       123: 2q^2+3q+1
       124: q^2+2q
       125: q^2+5q+1
       126: 3q+1
       127: q+1
       128: q
       129: q+1
       130: q
       131: q+1
       132: q
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+5q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+5q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: 1
       173: q^2+2q+1
       174: q
       175: q
       176: q
       177: q+1
       178: q
       179: q+1
       180: q
       181: 1
       183: q+1
       185: q+1
       187: 1
       189: q+1
       190: q
       191: q^2+3q+1
       192: 2q
       193: q+1
       195: q+1
       197: 1
       199: q^2+3q+1
       200: 2q
       201: q+1
       203: q+1
       205: 1
       207: q^2+3q+1
       208: 2q
       209: q+1
       210: q
       211: q+1
       212: q
       213: q+1
       214: q
       215: q+1
       216: q
       217: q+1
       218: q
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q+1
       238: q
       239: q+1
       240: q
       241: q+1
       242: q
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+2q+1
       276: q
       277: q
       278: q
       279: q+1
       280: q
       281: q+1
       282: q
       283: q+1
       285: q+1
       287: q+1
       288: q
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: q+1
       301: 1
       303: q+1
       305: 1
       307: q+1
       309: q+1
       311: 1
       313: 1
       315: q+1
       316: q
       317: q+1
       318: q
       319: q+1
       321: q+1
       323: 1
       325: q+1
       326: q
       333: q+1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       351: 2
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 2
       360: q+1
       361: q
       362: q+1
       363: q
       364: q+1
       365: q
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       414: q
       417: 1
       419: 1
       421: 1
       423: 1
       427: 1
       428: 1
       429: q+1
       431: q+1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 2
       445: 1
       446: 1
       447: q+1
       449: q+1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 2
       463: 1
       464: 1
       465: q+1
       466: q
       467: q+1
       468: q
       469: q+1
       470: q
       471: q+1
       473: q+1
       475: 1
       477: 1
       479: 2
       481: 1
       482: 1
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 2
       497: q+1
       498: 1
       499: 1
       501: 2
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       518: 1
       519: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       546: 1
       549: 1
       553: 1
       557: 1
       561: 1
       562: 1
       565: 1
       569: 1
       573: 2
       577: 1
       578: 1
       585: 1
       589: 1
       595: 1
       601: 1
       602: 1
       603: 1
       605: 1
       607: 1
       609: 1
       615: 2
       617: 1
       618: 1
       619: 1
       621: 1
       623: 1
       625: 1
       631: 2
       633: 1
       634: 1
       639: q+1
       640: q
       641: q+1
       643: q+1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 2
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 1
       676: 1
       678: 1
       680: 2
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       694: 1
       709: 1
       721: 1
       725: 1
       733: 1
       734: 1
       737: 1
       741: 1
       749: 1
       750: 1
       753: 1
       757: 1
       761: 1
       765: 2
       769: 1
       770: 1
       775: 1
       776: 1
       793: 2
       795: 1
       796: 1
       797: 1
       801: 1
       807: 1
       815: 1
       817: 2
       819: 1
       820: 1
       821: 1
       825: 1
       831: 1
       839: 1
       843: 2
       845: 1
       847: 1
       849: 1
       851: 1
       857: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       884: 1
       885: 1
       916: 1
       917: 1
       920: 1
       940: 1
       941: 1
       944: 1
       960: 1
       964: 2
       968: 1
       969: 1
       974: 1
       988: 1
      1016: 1
      1032: 1
      1046: 1
      1048: 1
      1052: 1
      1058: 1
      1072: 1
      1075: 1
      1079: 1
      1086: 1
      1087: 1
      1194: 1
      1198: 1
      1228: 1
      1246: 1
      1262: 1
      1410: 1

1411:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 3q^2+5q+1
         3: 3q^2+5q+1
         4: 2q^2+3q+1
         5: 3q^2+5q+1
         6: 2q^3+3q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+5q+1
         9: 2q^2+3q+1
        10: q^2+5q+1
        11: q^2+5q+1
        12: 2q^2+3q+1
        13: 3q^2+5q+1
        14: 2q^2+3q+1
        15: 3q^2+5q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+5q+1
        28: q^2+5q+1
        29: 3q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q^2+5q+1
        33: 3q^2+5q+1
        34: q^2+5q+1
        35: 3q^2+5q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+2q
        42: 2q^2+3q+1
        43: q^2+5q+1
        44: 2q^2+3q+1
        45: q^2+5q+1
        46: 3q^2+5q+1
        47: 3q^2+5q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: 2q
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q
        62: 2q
        63: q^2+3q+1
        64: q^2+2q
        65: 2q^2+3q+1
        66: q^2+2q
        67: 2q^2+3q+1
        68: q^2+5q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: q^2+5q+1
        81: 3q^2+5q+1
        82: 3q+1
        83: 3q+1
        84: q^2+5q+1
        85: 3q^2+5q+1
        86: 3q+1
        87: 3q+1
        88: q^2+5q+1
        89: q^2+5q+1
        90: 2q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q^2+2q+1
       105: q
       106: q
       107: q+1
       110: q+1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       117: 2q
       118: q^2+3q+1
       119: q^2+3q+1
       120: 2q
       121: 2q
       122: q^2+3q+1
       123: q^2+2q
       124: 2q^2+3q+1
       125: q^2+5q+1
       126: 3q+1
       127: q
       128: q+1
       129: q
       130: q+1
       131: q
       132: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+5q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+5q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       170: 1
       173: q
       174: q^2+2q+1
       175: q
       176: q
       177: q
       178: q+1
       179: q
       180: q+1
       182: 1
       183: q+1
       186: q+1
       188: 1
       189: q
       190: q+1
       191: 2q
       192: q^2+3q+1
       193: q+1
       196: q+1
       198: 1
       199: q^2+3q+1
       200: 2q
       201: q+1
       204: q+1
       206: 1
       207: 2q
       208: q^2+3q+1
       209: q
       210: q+1
       211: q
       212: q+1
       213: q
       214: q+1
       215: q
       216: q+1
       217: q
       218: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q
       238: q+1
       239: q
       240: q+1
       241: q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q
       276: q^2+2q+1
       277: q
       278: q
       279: q
       280: q+1
       281: q
       282: q+1
       283: q+1
       286: q+1
       287: q
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: q+1
       302: 1
       304: q+1
       306: 1
       307: q+1
       310: q+1
       312: 1
       314: 1
       315: q
       316: q+1
       317: q
       318: q+1
       319: q+1
       322: q+1
       324: 1
       325: q
       326: q+1
       333: q+1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       351: 2
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 2
       360: q
       361: q+1
       362: q
       363: q+1
       364: q
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       413: q
       414: q+1
       418: 1
       419: 1
       422: 1
       424: 1
       427: 1
       428: 1
       429: q+1
       432: q+1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: q+1
       450: q+1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 2
       463: 1
       464: 1
       465: q
       466: q+1
       467: q
       468: q+1
       469: q
       470: q+1
       471: q+1
       474: q+1
       476: 1
       478: 1
       480: 2
       481: 1
       482: 1
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 2
       497: q+1
       498: 1
       499: 1
       501: 2
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       518: 1
       519: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       545: 1
       546: 1
       551: 1
       556: 1
       560: 1
       563: 1
       564: 1
       566: 1
       571: 1
       574: 2
       580: 1
       581: 1
       586: 1
       589: 1
       596: 1
       601: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       615: 2
       617: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       632: 2
       633: 1
       634: 1
       639: q
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 2
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 1
       676: 1
       678: 1
       680: 2
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       696: 1
       699: 1
       710: 1
       722: 1
       726: 1
       733: 1
       734: 1
       740: 1
       744: 1
       751: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 2
       772: 1
       773: 1
       775: 1
       776: 1
       793: 2
       795: 1
       796: 1
       798: 1
       801: 1
       808: 1
       815: 1
       818: 2
       819: 1
       820: 1
       822: 1
       825: 1
       832: 1
       840: 1
       844: 2
       845: 1
       848: 1
       850: 1
       852: 1
       858: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       887: 1
       890: 1
       916: 1
       917: 1
       921: 1
       942: 1
       943: 1
       947: 1
       962: 1
       965: 2
       971: 1
       972: 1
       976: 1
       989: 1
      1016: 1
      1033: 1
      1047: 1
      1049: 1
      1052: 1
      1059: 1
      1072: 1
      1075: 1
      1079: 1
      1089: 1
      1092: 1
      1195: 1
      1200: 1
      1228: 1
      1247: 1
      1263: 1
      1411: 1

1412:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 3q^2+5q+1
         3: 3q^2+5q+1
         4: 2q^2+3q+1
         5: 3q^2+5q+1
         6: 2q^3+3q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+5q+1
         9: 2q^2+3q+1
        10: q^2+5q+1
        11: q^2+5q+1
        12: 2q^2+3q+1
        13: 3q^2+5q+1
        14: 2q^2+3q+1
        15: 3q^2+5q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+5q+1
        28: q^2+5q+1
        29: 3q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q^2+5q+1
        33: 3q^2+5q+1
        34: q^2+5q+1
        35: 3q^2+5q+1
        36: 3q^2+5q+1
        37: q^2+2q
        38: 2q^2+3q+1
        39: q^2+2q
        40: 2q^2+3q+1
        41: q^2+2q
        42: 2q^2+3q+1
        43: q^2+5q+1
        44: 2q^2+3q+1
        45: q^2+5q+1
        46: 3q^2+5q+1
        47: 3q^2+5q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: q^2+3q+1
        59: 2q
        60: 2q
        61: q^2+3q+1
        62: 2q
        63: q^2+3q+1
        64: q^2+2q
        65: 2q^2+3q+1
        66: q^2+2q
        67: 2q^2+3q+1
        68: q^2+5q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q
        75: q+1
        76: q
        77: q+1
        78: q
        79: q+1
        80: q^2+5q+1
        81: 3q^2+5q+1
        82: 3q+1
        83: 3q+1
        84: q^2+5q+1
        85: 3q^2+5q+1
        86: 3q+1
        87: 3q+1
        88: q^2+5q+1
        89: q^2+5q+1
        90: 2q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q^2+2q+1
       106: q
       108: q+1
       109: q+1
       112: 1
       113: q
       114: q+1
       115: q
       116: q+1
       117: q^2+3q+1
       118: 2q
       119: 2q
       120: q^2+3q+1
       121: 2q
       122: q^2+3q+1
       123: q^2+2q
       124: 2q^2+3q+1
       125: q^2+5q+1
       126: 3q+1
       127: q
       128: q+1
       129: q
       130: q+1
       131: q
       132: q+1
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+5q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+5q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q
       152: q+1
       153: q
       154: q+1
       155: q
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       171: 1
       173: q
       174: q
       175: q^2+2q+1
       176: q
       177: q
       178: q+1
       179: q
       180: q+1
       182: 1
       184: q+1
       185: q+1
       188: 1
       189: q
       190: q+1
       191: q^2+3q+1
       192: 2q
       194: q+1
       195: q+1
       198: 1
       199: 2q
       200: q^2+3q+1
       202: q+1
       203: q+1
       206: 1
       207: 2q
       208: q^2+3q+1
       209: q
       210: q+1
       211: q
       212: q+1
       213: q
       214: q+1
       215: q
       216: q+1
       217: q
       218: q+1
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q
       238: q+1
       239: q
       240: q+1
       241: q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q
       276: q
       277: q^2+2q+1
       278: q
       279: q
       280: q+1
       281: q
       282: q+1
       284: q+1
       285: q+1
       287: q
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       303: q+1
       306: 1
       308: q+1
       309: q+1
       312: 1
       314: 1
       315: q
       316: q+1
       317: q
       318: q+1
       320: q+1
       321: q+1
       324: 1
       325: q
       326: q+1
       333: q+1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       351: 2
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 2
       360: q
       361: q+1
       362: q
       363: q+1
       364: q
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       413: q
       414: q+1
       418: 1
       420: 1
       421: 1
       424: 1
       427: 1
       428: 1
       430: q+1
       431: q+1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: q+1
       449: q+1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: 2
       463: 1
       464: 1
       465: q
       466: q+1
       467: q
       468: q+1
       469: q
       470: q+1
       472: q+1
       473: q+1
       476: 1
       478: 1
       480: 2
       481: 1
       482: 1
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 2
       497: q+1
       498: 1
       499: 1
       501: 2
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       518: 1
       519: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       547: 1
       548: 1
       550: 1
       554: 1
       558: 1
       561: 1
       562: 1
       567: 1
       572: 1
       576: 2
       580: 1
       581: 1
       586: 1
       590: 1
       595: 1
       601: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       616: 2
       617: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       631: 2
       633: 1
       634: 1
       639: q
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 2
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 1
       676: 1
       678: 1
       680: 2
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       698: 1
       700: 1
       711: 1
       724: 1
       728: 1
       735: 1
       736: 1
       738: 1
       742: 1
       749: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 2
       772: 1
       773: 1
       775: 1
       776: 1
       794: 2
       795: 1
       796: 1
       798: 1
       802: 1
       807: 1
       816: 1
       817: 2
       819: 1
       820: 1
       822: 1
       826: 1
       831: 1
       839: 1
       844: 2
       846: 1
       847: 1
       850: 1
       852: 1
       858: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       888: 1
       891: 1
       918: 1
       919: 1
       923: 1
       940: 1
       941: 1
       945: 1
       963: 1
       966: 2
       971: 1
       972: 1
       977: 1
       990: 1
      1017: 1
      1032: 1
      1047: 1
      1049: 1
      1053: 1
      1058: 1
      1072: 1
      1075: 1
      1079: 1
      1090: 1
      1093: 1
      1196: 1
      1201: 1
      1229: 1
      1246: 1
      1263: 1
      1412: 1

1413:    0: 3q^2+5q+1
         1: 3q^2+5q+1
         2: 3q^2+5q+1
         3: 3q^2+5q+1
         4: 2q^2+3q+1
         5: 3q^2+5q+1
         6: 2q^3+3q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+5q+1
         9: 2q^2+3q+1
        10: q^2+5q+1
        11: q^2+5q+1
        12: 2q^2+3q+1
        13: 3q^2+5q+1
        14: 2q^2+3q+1
        15: 3q^2+5q+1
        16: 3q^2+5q+1
        17: 3q^2+5q+1
        18: 2q^2+3q+1
        19: 3q+1
        20: q^2+3q+1
        21: 3q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+5q+1
        27: 3q^2+5q+1
        28: q^2+5q+1
        29: 3q+1
        30: 3q+1
        31: q^2+5q+1
        32: 3q^2+5q+1
        33: 3q^2+5q+1
        34: q^2+5q+1
        35: 3q^2+5q+1
        36: 3q^2+5q+1
        37: 2q^2+3q+1
        38: q^2+2q
        39: 2q^2+3q+1
        40: q^2+2q
        41: 2q^2+3q+1
        42: q^2+2q
        43: q^2+5q+1
        44: 2q^2+3q+1
        45: q^2+5q+1
        46: 3q^2+5q+1
        47: 3q^2+5q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: q^2+3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: 3q+1
        58: 2q
        59: q^2+3q+1
        60: 2q
        61: q^2+3q+1
        62: q^2+3q+1
        63: 2q
        64: 2q^2+3q+1
        65: q^2+2q
        66: 2q^2+3q+1
        67: q^2+2q
        68: q^2+5q+1
        69: 3q+1
        70: 3q+1
        71: 3q+1
        72: q+1
        73: q+1
        74: q+1
        75: q
        76: q+1
        77: q
        78: q+1
        79: q
        80: q^2+5q+1
        81: 3q^2+5q+1
        82: 3q+1
        83: 3q+1
        84: q^2+5q+1
        85: 3q^2+5q+1
        86: 3q+1
        87: 3q+1
        88: q^2+5q+1
        89: q^2+5q+1
        90: 2q^2+3q+1
        91: 3q+1
        92: q^2+3q+1
        93: 3q+1
        94: 3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q+1
        98: q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q
       106: q^2+2q+1
       108: q+1
       110: q+1
       111: 1
       113: q+1
       114: q
       115: q+1
       116: q
       117: 2q
       118: q^2+3q+1
       119: 2q
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q
       123: 2q^2+3q+1
       124: q^2+2q
       125: q^2+5q+1
       126: 3q+1
       127: q+1
       128: q
       129: q+1
       130: q
       131: q+1
       132: q
       133: 3q+1
       134: 3q+1
       135: q+1
       136: q+1
       137: q^2+5q+1
       138: 3q+1
       139: 3q+1
       140: q+1
       141: 3q+1
       142: q+1
       143: q^2+5q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       152: q
       153: q+1
       154: q
       155: q+1
       156: q
       157: q+1
       158: q+1
       159: q+1
       160: 3q+1
       161: q^2+3q+1
       162: 3q+1
       163: 3q+1
       164: q^2+3q+1
       165: 3q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       172: 1
       173: q
       174: q
       175: q
       176: q^2+2q+1
       177: q+1
       178: q
       179: q+1
       180: q
       181: 1
       184: q+1
       186: q+1
       187: 1
       189: q+1
       190: q
       191: 2q
       192: q^2+3q+1
       194: q+1
       196: q+1
       197: 1
       199: 2q
       200: q^2+3q+1
       202: q+1
       204: q+1
       205: 1
       207: q^2+3q+1
       208: 2q
       209: q+1
       210: q
       211: q+1
       212: q
       213: q+1
       214: q
       215: q+1
       216: q
       217: q+1
       218: q
       219: 3q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       226: 3q+1
       227: 3q+1
       228: 3q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: q+1
       235: q+1
       236: 3q+1
       237: q+1
       238: q
       239: q+1
       240: q
       241: q+1
       242: q
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 2
       248: 2
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q
       277: q
       278: q^2+2q+1
       279: q+1
       280: q
       281: q+1
       282: q
       284: q+1
       286: q+1
       287: q+1
       288: q
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: q+1
       301: 1
       304: q+1
       305: 1
       308: q+1
       310: q+1
       311: 1
       313: 1
       315: q+1
       316: q
       317: q+1
       318: q
       320: q+1
       322: q+1
       323: 1
       325: q+1
       326: q
       333: q+1
       334: 1
       335: 1
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       344: 3q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: q+1
       351: 2
       352: 3q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 2
       360: q+1
       361: q
       362: q+1
       363: q
       364: q+1
       365: q
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       414: q
       417: 1
       420: 1
       422: 1
       423: 1
       427: 1
       428: 1
       430: q+1
       432: q+1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 2
       445: 1
       446: 1
       448: q+1
       450: q+1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 2
       463: 1
       464: 1
       465: q+1
       466: q
       467: q+1
       468: q
       469: q+1
       470: q
       472: q+1
       474: q+1
       475: 1
       477: 1
       479: 2
       481: 1
       482: 1
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 2
       497: q+1
       498: 1
       499: 1
       501: 2
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       518: 1
       519: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       548: 1
       552: 1
       555: 1
       559: 1
       563: 1
       564: 1
       568: 1
       570: 1
       575: 2
       577: 1
       578: 1
       585: 1
       590: 1
       596: 1
       601: 1
       602: 1
       604: 1
       605: 1
       608: 1
       609: 1
       616: 2
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       625: 1
       632: 2
       633: 1
       634: 1
       639: q+1
       640: q
       642: q+1
       644: q+1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 2
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       672: 1
       674: 2
       675: 1
       676: 1
       678: 1
       680: 2
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       697: 1
       701: 1
       712: 1
       723: 1
       727: 1
       735: 1
       736: 1
       739: 1
       743: 1
       751: 1
       752: 1
       756: 1
       758: 1
       762: 1
       768: 2
       769: 1
       770: 1
       775: 1
       776: 1
       794: 2
       795: 1
       796: 1
       797: 1
       802: 1
       808: 1
       816: 1
       818: 2
       819: 1
       820: 1
       821: 1
       826: 1
       832: 1
       840: 1
       843: 2
       846: 1
       848: 1
       849: 1
       851: 1
       857: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       889: 1
       892: 1
       918: 1
       919: 1
       922: 1
       942: 1
       943: 1
       946: 1
       961: 1
       967: 2
       968: 1
       969: 1
       975: 1
       991: 1
      1017: 1
      1033: 1
      1046: 1
      1048: 1
      1053: 1
      1059: 1
      1072: 1
      1075: 1
      1079: 1
      1091: 1
      1094: 1
      1197: 1
      1199: 1
      1229: 1
      1247: 1
      1262: 1
      1413: 1

1414:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^3+q^2+q+1
         5: q^2+2q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^3+q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^3+q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^3+q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^3+q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q^2+q+1
       106: q
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q^2+q+1
       118: q
       119: q^2+q+1
       120: q
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: q^2+q+1
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q^2+q+1
       192: q
       193: 1
       195: 1
       197: 1
       199: q^2+q+1
       200: q
       201: 1
       203: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+q+1
       278: q
       279: q+1
       281: q+1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: 1
       321: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       549: 1
       553: 1
       557: 1
       565: 1
       569: 1
       583: q+1
       585: 1
       587: 1
       589: 1
       595: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       705: 1
       709: 1
       721: 1
       725: 1
       729: 1
       737: 1
       741: 1
       745: 1
       753: 1
       757: 1
       761: 1
       777: 1
       797: 1
       799: 1
       801: 1
       807: 1
       821: 1
       823: 1
       825: 1
       831: 1
       841: q+1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       877: 1
       878: 1
       896: 1
       912: 1
       920: 1
       936: 1
       944: 1
       960: 1
       974: 1
       978: 1
      1018: 1
      1034: 1
      1048: 1
      1050: 1
      1052: 1
      1058: 1
      1148: 1
      1168: 1
      1184: 1
      1198: 1
      1264: 1
      1414: 1

1415:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^3+q^2+q+1
         5: q^2+2q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^3+q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^3+q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^3+q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        60: q
        61: q^2+q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^3+q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: q^2+q+1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: q^2+q+1
       119: q
       120: q^2+q+1
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       173: q
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       191: q
       192: q^2+q+1
       194: 1
       196: 1
       197: 1
       199: q
       200: q^2+q+1
       202: 1
       204: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       278: q^2+q+1
       279: q+1
       281: q+1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: 1
       322: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       552: 1
       555: 1
       559: 1
       568: 1
       570: 1
       583: q+1
       585: 1
       587: 1
       590: 1
       596: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       708: 1
       712: 1
       723: 1
       727: 1
       731: 1
       739: 1
       743: 1
       747: 1
       756: 1
       758: 1
       762: 1
       777: 1
       797: 1
       799: 1
       802: 1
       808: 1
       821: 1
       823: 1
       826: 1
       832: 1
       841: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       877: 1
       878: 1
       899: 1
       914: 1
       922: 1
       938: 1
       946: 1
       961: 1
       975: 1
       979: 1
      1018: 1
      1034: 1
      1048: 1
      1050: 1
      1053: 1
      1059: 1
      1150: 1
      1170: 1
      1185: 1
      1199: 1
      1264: 1
      1415: 1

1416:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^3+q^2+q+1
         5: q^2+2q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^3+q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^3+q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^3+q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        60: q^2+q+1
        61: q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^3+q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q^2+q+1
       105: q
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: q^2+q+1
       119: q^2+q+1
       120: q
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: q^2+q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       191: q
       192: q^2+q+1
       193: 1
       196: 1
       198: 1
       199: q^2+q+1
       200: q
       201: 1
       204: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q^2+q+1
       277: q
       280: q+1
       282: q+1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: 1
       322: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       551: 1
       556: 1
       560: 1
       566: 1
       571: 1
       584: q+1
       586: 1
       588: 1
       589: 1
       596: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       706: 1
       710: 1
       722: 1
       726: 1
       730: 1
       740: 1
       744: 1
       748: 1
       754: 1
       759: 1
       763: 1
       778: 1
       798: 1
       800: 1
       801: 1
       808: 1
       822: 1
       824: 1
       825: 1
       832: 1
       842: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       877: 1
       878: 1
       897: 1
       913: 1
       921: 1
       939: 1
       947: 1
       962: 1
       976: 1
       980: 1
      1019: 1
      1035: 1
      1049: 1
      1051: 1
      1052: 1
      1059: 1
      1149: 1
      1171: 1
      1186: 1
      1200: 1
      1265: 1
      1416: 1

1417:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^3+q^2+q+1
         5: q^2+2q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+2q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^3+q^2+q+1
        13: q^2+2q+1
        14: q^3+q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^3+q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^3+q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^3+q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: q^2+q+1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q^2+q+1
       118: q
       119: q
       120: q^2+q+1
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       174: q
       175: q^2+q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q^2+q+1
       192: q
       194: 1
       195: 1
       198: 1
       199: q
       200: q^2+q+1
       202: 1
       203: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       276: q
       277: q^2+q+1
       280: q+1
       282: q+1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: 1
       321: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 1
       335: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       481: 1
       482: 1
       492: q+1
       493: 1
       494: 1
       497: q+1
       498: 1
       499: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       550: 1
       554: 1
       558: 1
       567: 1
       572: 1
       584: q+1
       586: 1
       588: 1
       590: 1
       595: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       675: 1
       676: 1
       681: 1
       682: 1
       686: q+1
       687: 1
       688: 1
       707: 1
       711: 1
       724: 1
       728: 1
       732: 1
       738: 1
       742: 1
       746: 1
       755: 1
       760: 1
       764: 1
       778: 1
       798: 1
       800: 1
       802: 1
       807: 1
       822: 1
       824: 1
       826: 1
       831: 1
       842: q+1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       877: 1
       878: 1
       898: 1
       915: 1
       923: 1
       937: 1
       945: 1
       963: 1
       977: 1
       981: 1
      1019: 1
      1035: 1
      1049: 1
      1051: 1
      1053: 1
      1058: 1
      1151: 1
      1169: 1
      1187: 1
      1201: 1
      1265: 1
      1417: 1

1418:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 4q^2+3q+1
        38: 3q^2+q
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+q
        41: 4q^2+3q+1
        42: 3q^2+q
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+q
        60: 3q^2+2q+1
        61: 2q
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 4q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: 2q^2+2q+1
       104: q^2
       105: q
       106: q
       107: q^2+q+1
       108: q
       109: 2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: 2q^2+3q+1
       118: q^2+q
       119: 3q^2+2q+1
       120: 2q
       121: 3q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+2q+1
       141: 3q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q^2+2q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       169: q+1
       173: 2q^2+2q+1
       174: q^2
       175: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q^2+q+1
       184: q
       185: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q^2+q+1
       194: q
       195: 2q+1
       197: q+1
       199: q^2+2q+1
       200: 2q
       201: q^2+q+1
       202: q
       203: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: 2q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: 2q^2+2q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       259: 1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       277: q
       278: q
       279: q+1
       281: q+1
       283: 1
       285: q+1
       287: q+1
       289: 1
       291: 1
       293: q+1
       294: q
       295: q+1
       297: q+1
       299: q^2+q+1
       300: q
       301: 1
       303: 2q+1
       305: q+1
       307: q^2+q+1
       308: q
       309: 2q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: q^2+q+1
       320: q
       321: 2q+1
       323: q+1
       325: q^2+2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: q+1
       413: q+1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       431: q+1
       433: 1
       435: 1
       437: q+1
       438: q
       439: q+1
       441: q+1
       443: 1
       444: 1
       445: 2
       447: 1
       449: q+1
       451: 1
       453: q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q^2+q+1
       472: q
       473: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 1
       547: 1
       549: 1
       553: 1
       557: q+1
       561: 2
       565: q+1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       585: 1
       589: 1
       591: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 2
       633: 2
       639: q+1
       641: 1
       643: q+1
       645: 1
       647: q+1
       648: q
       649: q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       693: 1
       698: 1
       709: 1
       713: 1
       721: 1
       725: 1
       733: 1
       735: 1
       737: 1
       741: 1
       749: 2
       753: 1
       757: 1
       761: q+1
       765: 1
       767: 1
       769: 1
       772: 1
       781: 1
       787: 1
       797: 1
       801: 1
       803: 1
       807: 1
       809: 1
       811: 1
       821: 1
       825: 1
       827: 1
       831: 1
       833: 1
       835: 1
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       871: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       884: 1
       888: 1
       900: 1
       920: 1
       924: 1
       944: 1
       948: 1
       960: 1
       974: 1
      1022: 1
      1028: 1
      1038: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1083: 1
      1152: 1
      1172: 1
      1198: 1
      1202: 1
      1266: 1
      1270: 1
      1418: 1

1419:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: 4q^2+3q+1
        39: q^3+3q^2+q
        40: q^3+4q^2+3q+1
        41: 3q^2+q
        42: 4q^2+3q+1
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+q
        60: 2q
        61: 3q^2+2q+1
        62: 2q^2+q
        63: 3q^2+3q+1
        64: 3q^2+q
        65: 4q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q
       104: q
       105: 2q^2+2q+1
       106: q^2
       107: q
       108: q^2+q+1
       109: 2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: 2q^2+3q+1
       118: q^2+q
       119: 2q
       120: 3q^2+2q+1
       121: 2q^2+q
       122: 3q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+2q+1
       141: 3q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q^2+2q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       171: q+1
       173: q
       174: q
       175: 2q^2+2q+1
       176: q^2
       178: q+1
       180: q+1
       182: 1
       183: q
       184: q^2+q+1
       185: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q
       194: q^2+q+1
       195: 2q+1
       198: q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: q^2+q+1
       203: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: 2q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: 2q^2+2q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       261: 1
       265: q+1
       270: q+1
       272: q+1
       275: q
       276: q
       277: q^2+2q+1
       280: q+1
       282: q+1
       284: 1
       285: q+1
       288: q+1
       290: 1
       292: 1
       293: q
       294: q+1
       295: q+1
       298: q+1
       299: q
       300: q^2+q+1
       302: 1
       303: 2q+1
       306: q+1
       307: q
       308: q^2+q+1
       309: 2q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: q
       320: q^2+q+1
       321: 2q+1
       324: q+1
       326: q^2+2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: q+1
       414: q+1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: 1
       431: q+1
       434: 1
       436: 1
       437: q
       438: q+1
       439: q+1
       442: q+1
       443: 1
       444: 1
       446: 2
       448: 1
       449: q+1
       452: 1
       453: q
       454: q+1
       456: 1
       457: q+1
       460: q+1
       461: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q
       472: q^2+q+1
       473: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       546: 1
       548: 1
       550: 1
       554: 1
       558: q+1
       562: 2
       567: q+1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 2
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: 2
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 2
       634: 2
       640: q+1
       642: 1
       643: q+1
       646: 1
       647: q
       648: q+1
       649: q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       694: 1
       700: 1
       711: 1
       714: 1
       724: 1
       728: 1
       734: 1
       736: 1
       738: 1
       742: 1
       750: 2
       755: 1
       760: 1
       764: q+1
       765: 1
       767: 1
       770: 1
       773: 1
       782: 1
       787: 1
       798: 1
       802: 1
       803: 1
       807: 1
       810: 1
       812: 1
       822: 1
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       871: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       885: 1
       891: 1
       901: 1
       923: 1
       925: 1
       945: 1
       949: 1
       963: 1
       977: 1
      1023: 1
      1028: 1
      1039: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1083: 1
      1153: 1
      1173: 1
      1201: 1
      1203: 1
      1267: 1
      1270: 1
      1419: 1

1420:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 4q^2+3q+1
        38: 3q^2+q
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+q
        41: 4q^2+3q+1
        42: 3q^2+q
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: q^2+q
        59: 2q^2+3q+1
        60: 2q
        61: 3q^2+2q+1
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 4q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q
       104: q
       105: q^2
       106: 2q^2+2q+1
       107: q
       108: q^2+q+1
       110: 2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+q
       118: 2q^2+3q+1
       119: 2q
       120: 3q^2+2q+1
       121: 3q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+2q+1
       141: 3q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q^2+2q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       172: q+1
       173: q
       174: q
       175: q^2
       176: 2q^2+2q+1
       177: q+1
       179: q+1
       181: 1
       183: q
       184: q^2+q+1
       186: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q
       194: q^2+q+1
       196: 2q+1
       197: q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: q^2+q+1
       204: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: 2q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: 2q^2+2q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       262: 1
       266: q+1
       269: q+1
       273: q+1
       275: q
       276: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       284: 1
       286: q+1
       287: q+1
       289: 1
       291: 1
       293: q
       294: q+1
       296: q+1
       297: q+1
       299: q
       300: q^2+q+1
       301: 1
       304: 2q+1
       305: q+1
       307: q
       308: q^2+q+1
       310: 2q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: q
       320: q^2+q+1
       322: 2q+1
       323: q+1
       325: q^2+2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: q+1
       413: q+1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: 1
       432: q+1
       433: 1
       435: 1
       437: q
       438: q+1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 2
       448: 1
       450: q+1
       451: 1
       453: q
       454: q+1
       455: 1
       458: q+1
       459: q+1
       462: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q
       472: q^2+q+1
       474: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       545: 1
       547: 1
       552: 1
       555: 1
       559: q+1
       563: 2
       568: q+1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       585: 1
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 2
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: 2
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 2
       633: 2
       639: q+1
       642: 1
       644: q+1
       645: 1
       647: q
       648: q+1
       650: q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       696: 1
       697: 1
       712: 1
       716: 1
       723: 1
       727: 1
       733: 1
       735: 1
       739: 1
       743: 1
       751: 2
       756: 1
       758: 1
       762: q+1
       766: 1
       768: 1
       769: 1
       772: 1
       781: 1
       788: 1
       797: 1
       802: 1
       804: 1
       808: 1
       809: 1
       811: 1
       821: 1
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       871: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       887: 1
       889: 1
       902: 1
       922: 1
       927: 1
       946: 1
       950: 1
       961: 1
       975: 1
      1022: 1
      1029: 1
      1038: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1083: 1
      1154: 1
      1174: 1
      1199: 1
      1204: 1
      1266: 1
      1271: 1
      1420: 1

1421:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: 4q^2+3q+1
        39: q^3+3q^2+q
        40: q^3+4q^2+3q+1
        41: 3q^2+q
        42: 4q^2+3q+1
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: q^2+q
        59: 2q^2+3q+1
        60: 3q^2+2q+1
        61: 2q
        62: 2q^2+q
        63: 3q^2+3q+1
        64: 3q^2+q
        65: 4q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q^2
       104: 2q^2+2q+1
       105: q
       106: q
       107: q^2+q+1
       108: q
       110: 2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+q
       118: 2q^2+3q+1
       119: 3q^2+2q+1
       120: 2q
       121: 2q^2+q
       122: 3q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+2q+1
       141: 3q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q^2+2q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       170: q+1
       173: q^2
       174: 2q^2+2q+1
       175: q
       176: q
       178: q+1
       180: q+1
       182: 1
       183: q^2+q+1
       184: q
       186: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q^2+q+1
       194: q
       196: 2q+1
       198: q+1
       199: q^2+2q+1
       200: 2q
       201: q^2+q+1
       202: q
       204: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: 2q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: 2q^2+2q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       260: 1
       264: q+1
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: 1
       286: q+1
       288: q+1
       290: 1
       292: 1
       293: q+1
       294: q
       296: q+1
       298: q+1
       299: q^2+q+1
       300: q
       302: 1
       304: 2q+1
       306: q+1
       307: q^2+q+1
       308: q
       310: 2q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: q^2+q+1
       320: q
       322: 2q+1
       324: q+1
       326: q^2+2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: q+1
       414: q+1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       432: q+1
       434: 1
       436: 1
       437: q+1
       438: q
       440: q+1
       442: q+1
       443: 1
       444: 1
       446: 2
       447: 1
       450: q+1
       452: 1
       453: q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q^2+q+1
       472: q
       474: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 1
       548: 1
       551: 1
       556: 1
       560: q+1
       564: 2
       566: q+1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       586: 1
       589: 1
       592: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       632: 2
       634: 2
       640: q+1
       641: 1
       644: q+1
       646: 1
       647: q+1
       648: q
       650: q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       675: q+1
       676: 1
       677: 1
       679: 1
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       699: 1
       701: 1
       710: 1
       715: 1
       722: 1
       726: 1
       734: 1
       736: 1
       740: 1
       744: 1
       752: 2
       754: 1
       759: 1
       763: q+1
       766: 1
       768: 1
       770: 1
       773: 1
       782: 1
       788: 1
       798: 1
       801: 1
       804: 1
       808: 1
       810: 1
       812: 1
       822: 1
       825: 1
       828: 1
       832: 1
       834: 1
       836: 1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       871: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       890: 1
       892: 1
       903: 1
       921: 1
       926: 1
       947: 1
       951: 1
       962: 1
       976: 1
      1023: 1
      1029: 1
      1039: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1083: 1
      1155: 1
      1175: 1
      1200: 1
      1205: 1
      1267: 1
      1271: 1
      1421: 1

1422:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 4q^2+3q+1
        38: 3q^2+q
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+q
        41: 4q^2+3q+1
        42: 3q^2+q
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 3q^2+2q+1
        59: 2q
        60: 2q^2+3q+1
        61: q^2+q
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 4q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: 2q^2+2q+1
       104: q
       105: q^2
       106: q
       107: 2q+1
       109: q^2+q+1
       110: q
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: 3q^2+2q+1
       118: 2q
       119: 2q^2+3q+1
       120: q^2+q
       121: 3q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q+1
       136: 2q^2+2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: 2q^2+2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       169: q+1
       173: 2q^2+2q+1
       174: q
       175: q^2
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 2q+1
       185: q^2+q+1
       186: q
       187: q+1
       189: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       193: 2q+1
       195: q^2+q+1
       196: q
       197: q+1
       199: q^2+3q+1
       200: q
       201: 2q+1
       203: q^2+q+1
       204: q
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q^2+q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q+1
       235: 2q^2+2q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: 2q+1
       245: 2q^2+2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       259: 1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       276: q
       278: q
       279: q+1
       281: q+1
       283: q+1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: 2q+1
       301: 1
       303: q^2+q+1
       304: q
       305: q+1
       307: 2q+1
       309: q^2+q+1
       310: q
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: 2q+1
       321: q^2+q+1
       322: q
       323: q+1
       325: q^2+2q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q+1
       357: 2q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: q+1
       413: q+1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 2
       429: q+1
       431: 1
       433: 1
       435: 1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: 2
       445: 2
       447: q+1
       449: 1
       451: 1
       453: q+1
       455: 1
       457: q+1
       458: q
       459: q+1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: 2q+1
       473: q^2+q+1
       474: q
       475: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 2
       549: 1
       553: 1
       557: q+1
       561: 1
       563: 1
       565: q+1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       585: 1
       589: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: 2
       617: 2
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 1
       632: 1
       633: 2
       639: q+1
       641: q+1
       643: 1
       645: 1
       647: q+1
       649: q+1
       650: q
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       693: 1
       696: 1
       709: 1
       717: 1
       721: 1
       725: 1
       733: 2
       737: 1
       741: 1
       749: 1
       751: 1
       753: 1
       757: 1
       761: q+1
       765: 1
       766: 1
       769: 1
       772: 1
       781: 1
       785: 1
       797: 1
       801: 1
       805: 1
       807: 1
       809: 1
       811: 1
       821: 1
       825: 1
       829: 1
       831: 1
       833: 1
       835: 1
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       871: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       904: 1
       920: 1
       928: 1
       944: 1
       952: 1
       960: 1
       974: 1
      1022: 1
      1026: 1
      1038: 1
      1040: 1
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1083: 1
      1156: 1
      1176: 1
      1198: 1
      1206: 1
      1266: 1
      1268: 1
      1422: 1

1423:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: 4q^2+3q+1
        39: q^3+3q^2+q
        40: q^3+4q^2+3q+1
        41: 3q^2+q
        42: 4q^2+3q+1
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 2q
        59: 3q^2+2q+1
        60: 2q^2+3q+1
        61: q^2+q
        62: 2q^2+q
        63: 3q^2+3q+1
        64: 3q^2+q
        65: 4q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q+1
        73: 2q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q
       104: 2q^2+2q+1
       105: q
       106: q^2
       107: 2q+1
       109: q
       110: q^2+q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: 2q
       118: 3q^2+2q+1
       119: 2q^2+3q+1
       120: q^2+q
       121: 2q^2+q
       122: 3q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q+1
       136: 2q^2+2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: 2q^2+2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       170: q+1
       173: q
       174: 2q^2+2q+1
       175: q
       176: q^2
       178: q+1
       180: q+1
       182: 1
       183: 2q+1
       185: q
       186: q^2+q+1
       188: q+1
       190: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       193: 2q+1
       195: q
       196: q^2+q+1
       198: q+1
       199: q^2+3q+1
       200: q
       201: 2q+1
       203: q
       204: q^2+q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q^2+q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q+1
       235: 2q^2+2q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: 2q+1
       245: 2q^2+2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       260: 1
       264: q+1
       268: q+1
       274: q+1
       275: q
       276: q^2+2q+1
       277: q
       280: q+1
       282: q+1
       283: q+1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: 2q+1
       302: 1
       303: q
       304: q^2+q+1
       306: q+1
       307: 2q+1
       309: q
       310: q^2+q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: 2q+1
       321: q
       322: q^2+q+1
       324: q+1
       326: q^2+2q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q+1
       357: 2q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: q+1
       414: q+1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 2
       429: q+1
       432: 1
       434: 1
       436: 1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: 2
       446: 2
       447: q+1
       450: 1
       452: 1
       453: q+1
       456: 1
       457: q
       458: q+1
       460: q+1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: 2q+1
       473: q
       474: q^2+q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 2
       551: 1
       556: 1
       560: q+1
       562: 1
       564: 1
       566: q+1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       586: 1
       589: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: 2
       618: 2
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       631: 1
       632: 1
       634: 2
       640: q+1
       641: q+1
       644: 1
       646: 1
       647: q+1
       649: q
       650: q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       694: 1
       699: 1
       710: 1
       718: 1
       722: 1
       726: 1
       734: 2
       740: 1
       744: 1
       750: 1
       752: 1
       754: 1
       759: 1
       763: q+1
       765: 1
       766: 1
       770: 1
       773: 1
       782: 1
       785: 1
       798: 1
       801: 1
       805: 1
       808: 1
       810: 1
       812: 1
       822: 1
       825: 1
       829: 1
       832: 1
       834: 1
       836: 1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       871: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       905: 1
       921: 1
       929: 1
       947: 1
       953: 1
       962: 1
       976: 1
      1023: 1
      1026: 1
      1039: 1
      1040: 1
      1049: 1
      1052: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1083: 1
      1157: 1
      1177: 1
      1200: 1
      1207: 1
      1267: 1
      1268: 1
      1423: 1

1424:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 4q^2+3q+1
        38: 3q^2+q
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+q
        41: 4q^2+3q+1
        42: 3q^2+q
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 2q
        59: 3q^2+2q+1
        60: q^2+q
        61: 2q^2+3q+1
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 4q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q
       104: q^2
       105: q
       106: 2q^2+2q+1
       108: 2q+1
       109: q
       110: q^2+q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: 2q
       118: 3q^2+2q+1
       119: q^2+q
       120: 2q^2+3q+1
       121: 3q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q+1
       136: 2q^2+2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: 2q^2+2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       172: q+1
       173: q
       174: q^2
       175: q
       176: 2q^2+2q+1
       177: q+1
       179: q+1
       181: 1
       184: 2q+1
       185: q
       186: q^2+q+1
       187: q+1
       189: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       194: 2q+1
       195: q
       196: q^2+q+1
       197: q+1
       199: q
       200: q^2+3q+1
       202: 2q+1
       203: q
       204: q^2+q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q^2+q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q+1
       235: 2q^2+2q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+3q+1
       244: 2q+1
       245: 2q^2+2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       262: 1
       266: q+1
       269: q+1
       273: q+1
       275: q
       277: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       284: q+1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: 2q+1
       301: 1
       303: q
       304: q^2+q+1
       305: q+1
       308: 2q+1
       309: q
       310: q^2+q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       320: 2q+1
       321: q
       322: q^2+q+1
       323: q+1
       325: q^2+2q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q+1
       357: 2q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: q+1
       413: q+1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       430: q+1
       432: 1
       433: 1
       435: 1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: 2
       445: 2
       448: q+1
       450: 1
       451: 1
       454: q+1
       455: 1
       457: q
       458: q+1
       459: q+1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       472: 2q+1
       473: q
       474: q^2+q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       547: 2
       552: 1
       555: 1
       559: q+1
       561: 1
       563: 1
       568: q+1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       585: 1
       590: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 2
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       616: 2
       617: 2
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       631: 1
       632: 1
       633: 2
       639: q+1
       642: q+1
       644: 1
       645: 1
       648: q+1
       649: q
       650: q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       697: 1
       698: 1
       712: 1
       720: 1
       723: 1
       727: 1
       735: 2
       739: 1
       743: 1
       749: 1
       751: 1
       756: 1
       758: 1
       762: q+1
       767: 1
       768: 1
       769: 1
       772: 1
       781: 1
       786: 1
       797: 1
       802: 1
       806: 1
       808: 1
       809: 1
       811: 1
       821: 1
       826: 1
       830: 1
       832: 1
       833: 1
       835: 1
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       871: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       888: 1
       889: 1
       906: 1
       922: 1
       930: 1
       946: 1
       955: 1
       961: 1
       975: 1
      1022: 1
      1027: 1
      1038: 1
      1041: 1
      1048: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1083: 1
      1158: 1
      1178: 1
      1199: 1
      1208: 1
      1266: 1
      1269: 1
      1424: 1

1425:    0: 7q^2+4q+1
         1: 2q^3+7q^2+4q+1
         2: 7q^2+4q+1
         3: 2q^3+7q^2+4q+1
         4: 3q^3+5q^2+3q+1
         5: 7q^2+4q+1
         6: q^4+4q^3+5q^2+3q+1
         7: 3q^3+5q^2+3q+1
         8: 7q^2+4q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 7q^2+4q+1
        14: 3q^3+5q^2+3q+1
        15: 7q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 2q^3+3q^2+2q+1
        19: 4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: 4q^2+3q+1
        22: 7q^2+4q+1
        23: 2q^3+7q^2+4q+1
        24: 7q^2+4q+1
        25: 7q^2+4q+1
        26: 2q^3+7q^2+4q+1
        27: 7q^2+4q+1
        28: 3q^2+4q+1
        29: 3q^2+3q+1
        30: 4q^2+3q+1
        31: 5q^2+4q+1
        32: 7q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 7q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: 4q^2+3q+1
        39: q^3+3q^2+q
        40: q^3+4q^2+3q+1
        41: 3q^2+q
        42: 4q^2+3q+1
        43: 5q^2+4q+1
        44: 2q^3+4q^2+3q+1
        45: 5q^2+4q+1
        46: 5q^2+4q+1
        47: 5q^2+4q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 4q^2+3q+1
        55: 4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 4q^2+3q+1
        58: 3q^2+2q+1
        59: 2q
        60: q^2+q
        61: 2q^2+3q+1
        62: 2q^2+q
        63: 3q^2+3q+1
        64: 3q^2+q
        65: 4q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 3q^2+4q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: q^2+3q+1
        72: 2q+1
        73: 2q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 5q^2+4q+1
        81: 5q^2+4q+1
        82: 3q^2+3q+1
        83: 4q^2+3q+1
        84: 5q^2+4q+1
        85: 5q^2+4q+1
        86: 3q^2+3q+1
        87: 4q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+2q+1
       100: 4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 4q^2+3q+1
       103: q^2
       104: q
       105: 2q^2+2q+1
       106: q
       108: 2q+1
       109: q^2+q+1
       110: q
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: 3q^2+2q+1
       118: 2q
       119: q^2+q
       120: 2q^2+3q+1
       121: 2q^2+q
       122: 3q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q+1
       136: 2q^2+2q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: 2q^2+2q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: 2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 4q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+2q+1
       171: q+1
       173: q^2
       174: q
       175: 2q^2+2q+1
       176: q
       178: q+1
       180: q+1
       182: 1
       184: 2q+1
       185: q^2+q+1
       186: q
       188: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       194: 2q+1
       195: q^2+q+1
       196: q
       198: q+1
       199: q
       200: q^2+3q+1
       202: 2q+1
       203: q^2+q+1
       204: q
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q^2+q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q+1
       235: 2q^2+2q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+3q+1
       244: 2q+1
       245: 2q^2+2q+1
       246: 3q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+2q+1
       261: 1
       265: q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       278: q
       280: q+1
       282: q+1
       284: q+1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: 2q+1
       302: 1
       303: q^2+q+1
       304: q
       306: q+1
       308: 2q+1
       309: q^2+q+1
       310: q
       312: 1
       314: q+1
       316: q+1
       318: q+1
       320: 2q+1
       321: q^2+q+1
       322: q
       324: q+1
       326: q^2+2q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: 2q+1
       354: q+1
       355: q+1
       356: q+1
       357: 2q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: q+1
       414: q+1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       430: q+1
       431: 1
       434: 1
       436: 1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: 2
       446: 2
       448: q+1
       449: 1
       452: 1
       454: q+1
       456: 1
       457: q+1
       458: q
       460: q+1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       472: 2q+1
       473: q^2+q+1
       474: q
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       548: 2
       550: 1
       554: 1
       558: q+1
       562: 1
       564: 1
       567: q+1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 2
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       616: 2
       618: 2
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 1
       632: 1
       634: 2
       640: q+1
       642: q+1
       643: 1
       646: 1
       648: q+1
       649: q+1
       650: q
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       675: 1
       676: q+1
       677: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       700: 1
       701: 1
       711: 1
       719: 1
       724: 1
       728: 1
       736: 2
       738: 1
       742: 1
       750: 1
       752: 1
       755: 1
       760: 1
       764: q+1
       767: 1
       768: 1
       770: 1
       773: 1
       782: 1
       786: 1
       798: 1
       802: 1
       806: 1
       807: 1
       810: 1
       812: 1
       822: 1
       826: 1
       830: 1
       831: 1
       834: 1
       836: 1
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       871: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       891: 1
       892: 1
       907: 1
       923: 1
       931: 1
       945: 1
       954: 1
       963: 1
       977: 1
      1023: 1
      1027: 1
      1039: 1
      1041: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1083: 1
      1159: 1
      1179: 1
      1201: 1
      1209: 1
      1267: 1
      1269: 1
      1425: 1

1426:    0: 7q^3+12q^2+4q+1
         1: 2q^4+8q^3+12q^2+4q+1
         2: 4q^3+10q^2+3q+1
         3: 2q^4+8q^3+12q^2+4q+1
         4: 3q^4+7q^3+9q^2+4q+1
         5: 7q^3+12q^2+4q+1
         6: q^5+4q^4+8q^3+9q^2+4q+1
         7: 2q^4+4q^3+8q^2+3q+1
         8: 4q^3+10q^2+3q+1
         9: 3q^4+4q^3+5q^2+2q+1
        10: 2q^3+8q^2+4q+1
        11: 2q^3+8q^2+4q+1
        12: q^4+3q^3+6q^2+4q+1
        13: 2q^3+9q^2+3q+1
        14: q^4+3q^3+7q^2+3q+1
        15: 2q^3+9q^2+3q+1
        16: 5q^3+9q^2+4q+1
        17: 5q^3+9q^2+4q+1
        18: q^4+3q^3+5q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+5q^3+9q^2+4q+1
        21: 2q^3+8q^2+3q+1
        22: 7q^3+12q^2+4q+1
        23: 2q^4+8q^3+12q^2+4q+1
        24: 4q^3+10q^2+3q+1
        25: 7q^3+12q^2+4q+1
        26: 2q^4+8q^3+12q^2+4q+1
        27: 4q^3+10q^2+3q+1
        28: q^3+5q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+7q^2+3q+1
        31: 2q^3+8q^2+4q+1
        32: 2q^3+9q^2+3q+1
        33: 5q^3+9q^2+4q+1
        34: 2q^3+8q^2+4q+1
        35: 2q^3+9q^2+3q+1
        36: 5q^3+9q^2+4q+1
        37: 3q^3+8q^2+2q+1
        38: 4q^3+4q^2+2q
        39: q^4+4q^3+8q^2+2q+1
        40: q^4+4q^3+4q^2+2q
        41: 2q^3+6q^2+2q+1
        42: 2q^3+4q^2+q
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: q^3+6q^2+3q+1
        47: q^3+6q^2+3q+1
        48: 2q^3+4q^2+2q+1
        49: 2q^3+6q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: q^3+5q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+5q^3+9q^2+4q+1
        54: 2q^3+8q^2+3q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+5q^3+9q^2+4q+1
        57: 2q^3+8q^2+3q+1
        58: q^3+4q^2+3q+1
        59: q^2+q
        60: q^3+4q^2+3q+1
        61: q^2+q
        62: q^3+5q^2+2q+1
        63: q^3+3q^2+2q
        64: q^3+6q^2+2q+1
        65: q^3+3q^2+q
        66: 3q^3+6q^2+2q+1
        67: 2q^3+3q^2+2q
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 4q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: 5q^2+2q+1
        75: q^3+q^2+2q
        76: q^3+5q^2+2q+1
        77: q^3+q^2+2q
        78: 4q^2+2q+1
        79: 2q^2+q
        80: 5q^2+3q+1
        81: q^3+6q^2+3q+1
        82: q^3+6q^2+4q+1
        83: q^3+7q^2+3q+1
        84: 5q^2+3q+1
        85: q^3+6q^2+3q+1
        86: q^3+6q^2+4q+1
        87: q^3+7q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: 3q^2+2q+1
        94: 2q^3+6q^2+4q+1
        95: 2q^3+6q^2+4q+1
        96: q^3+5q^2+2q+1
        97: 2q^3+6q^2+4q+1
        98: 2q^3+6q^2+4q+1
        99: q^3+5q^2+2q+1
       100: 4q^3+9q^2+4q+1
       101: q^4+5q^3+9q^2+4q+1
       102: 2q^3+8q^2+3q+1
       103: q^3+3q^2+2q+1
       104: q^2+q
       105: q^2+q
       107: 2q^2+3q+1
       108: q
       109: 2q^2+3q+1
       110: q
       111: 2q^2+2q+1
       112: 2q
       113: 3q^2+2q+1
       114: q^2+2q
       115: 4q^2+2q+1
       116: q^2+q
       117: q^2+2q+1
       119: q^2+2q+1
       121: 3q^2+2q+1
       122: 2q^2+q
       123: q^3+4q^2+2q+1
       124: 2q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 3q^2+2q+1
       139: 3q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 2q^2+3q+1
       144: 3q^2+2q+1
       145: 3q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+7q^2+3q+1
       151: 5q^2+2q+1
       152: q^3+q^2+2q
       153: q^3+5q^2+2q+1
       154: q^3+q^2+2q
       155: 4q^2+2q+1
       156: 2q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+2q+1
       166: 2q^3+6q^2+4q+1
       167: 2q^3+6q^2+4q+1
       168: q^3+5q^2+2q+1
       169: q^2+2q+1
       170: q
       171: q
       173: q^2+2q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       183: 2q+1
       185: 2q+1
       187: q^2+2q+1
       188: q
       189: 2q^2+2q+1
       190: q^2+q
       191: q^2+2q+1
       193: 2q^2+3q+1
       194: q
       195: 2q^2+3q+1
       196: q
       197: 2q^2+2q+1
       198: 2q
       199: q^2+2q+1
       201: 2q^2+3q+1
       202: q
       203: 2q^2+3q+1
       204: q
       205: 2q^2+2q+1
       206: 2q
       207: q^2+2q+1
       208: q^2+q
       209: 3q^2+2q+1
       210: q^2+2q
       211: 4q^2+2q+1
       212: q^2+q
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+2q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: 3q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 3q^2+3q+1
       257: 3q^2+3q+1
       258: 3q^2+2q+1
       259: q+1
       263: 2q+1
       267: q^2+2q+1
       268: q
       270: q
       271: q^2+2q+1
       272: q
       274: q
       275: q^2+2q+1
       283: q+1
       285: q+1
       287: q+1
       291: q+1
       293: q+1
       295: q+1
       297: q+1
       298: q
       299: 2q+1
       301: q+1
       303: 2q+1
       305: q^2+2q+1
       306: q
       307: 2q+1
       309: 2q+1
       311: q+1
       313: q^2+2q+1
       314: q
       315: q^2+q+1
       317: q+1
       319: 2q^2+3q+1
       320: q
       321: 2q^2+3q+1
       322: q
       323: 2q^2+2q+1
       324: 2q
       325: 2q^2+2q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: q^2+2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: q+1
       385: q+1
       389: q+1
       393: 2q+1
       397: q+1
       401: 2q+1
       405: q^2+2q+1
       407: q
       408: q
       419: 1
       421: 1
       423: 1
       425: q+1
       427: q+1
       429: q+1
       431: q+1
       433: q+1
       437: q+1
       439: q+1
       441: q+1
       442: q
       443: 3q+1
       444: q
       445: 2q+1
       447: q+1
       449: q+1
       451: q+1
       453: q+1
       457: q+1
       459: q+1
       460: q
       461: 3q+1
       462: q
       463: 2q+1
       469: q+1
       471: 2q+1
       473: 2q+1
       475: q^2+2q+1
       476: q
       477: q+1
       479: q^2+2q+1
       480: 3q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: 2q+1
       514: q^2+2q+1
       529: 1
       533: q+1
       541: q+1
       545: q+1
       549: q+1
       557: q+1
       561: q+1
       565: 2q+1
       569: q+1
       573: 2q+1
       574: q
       576: q
       577: q+1
       580: q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: q+1
       615: q+1
       619: 1
       621: 1
       625: 1
       629: q+1
       631: q+1
       641: q+1
       643: q+1
       645: q+1
       647: q+1
       649: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       693: q+1
       713: 1
       717: 1
       725: 1
       741: 1
       753: q+1
       761: q+1
       765: q+1
       785: 1
       787: 1
       791: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       845: 1
       847: 1
       851: 1
       855: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       908: 1
       924: 1
       928: 1
       948: 1
       952: 1
       974: 1
      1026: 1
      1028: 1
      1040: 1
      1044: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1062: 1
      1064: 1
      1083: 1
      1160: 1
      1180: 1
      1202: 1
      1206: 1
      1268: 1
      1270: 1
      1426: 1

1427:    0: 7q^3+12q^2+4q+1
         1: 2q^4+8q^3+12q^2+4q+1
         2: 4q^3+10q^2+3q+1
         3: 2q^4+8q^3+12q^2+4q+1
         4: 3q^4+7q^3+9q^2+4q+1
         5: 7q^3+12q^2+4q+1
         6: q^5+4q^4+8q^3+9q^2+4q+1
         7: 2q^4+4q^3+8q^2+3q+1
         8: 4q^3+10q^2+3q+1
         9: 3q^4+4q^3+5q^2+2q+1
        10: 2q^3+8q^2+4q+1
        11: 2q^3+8q^2+4q+1
        12: q^4+3q^3+6q^2+4q+1
        13: 2q^3+9q^2+3q+1
        14: q^4+3q^3+7q^2+3q+1
        15: 2q^3+9q^2+3q+1
        16: 5q^3+9q^2+4q+1
        17: 5q^3+9q^2+4q+1
        18: q^4+3q^3+5q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+5q^3+9q^2+4q+1
        21: 2q^3+8q^2+3q+1
        22: 7q^3+12q^2+4q+1
        23: 2q^4+8q^3+12q^2+4q+1
        24: 4q^3+10q^2+3q+1
        25: 7q^3+12q^2+4q+1
        26: 2q^4+8q^3+12q^2+4q+1
        27: 4q^3+10q^2+3q+1
        28: q^3+5q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+7q^2+3q+1
        31: 2q^3+8q^2+4q+1
        32: 2q^3+9q^2+3q+1
        33: 5q^3+9q^2+4q+1
        34: 2q^3+8q^2+4q+1
        35: 2q^3+9q^2+3q+1
        36: 5q^3+9q^2+4q+1
        37: 4q^3+4q^2+2q
        38: 3q^3+8q^2+2q+1
        39: q^4+4q^3+4q^2+2q
        40: q^4+4q^3+8q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+6q^2+2q+1
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: q^3+6q^2+3q+1
        47: q^3+6q^2+3q+1
        48: 2q^3+4q^2+2q+1
        49: 2q^3+6q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: q^3+5q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+5q^3+9q^2+4q+1
        54: 2q^3+8q^2+3q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+5q^3+9q^2+4q+1
        57: 2q^3+8q^2+3q+1
        58: q^2+q
        59: q^3+4q^2+3q+1
        60: q^3+4q^2+3q+1
        61: q^2+q
        62: q^3+3q^2+2q
        63: q^3+5q^2+2q+1
        64: q^3+3q^2+q
        65: q^3+6q^2+2q+1
        66: 2q^3+3q^2+2q
        67: 3q^3+6q^2+2q+1
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 4q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: q^3+q^2+2q
        75: 5q^2+2q+1
        76: q^3+q^2+2q
        77: q^3+5q^2+2q+1
        78: 2q^2+q
        79: 4q^2+2q+1
        80: 5q^2+3q+1
        81: q^3+6q^2+3q+1
        82: q^3+6q^2+4q+1
        83: q^3+7q^2+3q+1
        84: 5q^2+3q+1
        85: q^3+6q^2+3q+1
        86: q^3+6q^2+4q+1
        87: q^3+7q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: 3q^2+2q+1
        94: 2q^3+6q^2+4q+1
        95: 2q^3+6q^2+4q+1
        96: q^3+5q^2+2q+1
        97: 2q^3+6q^2+4q+1
        98: 2q^3+6q^2+4q+1
        99: q^3+5q^2+2q+1
       100: 4q^3+9q^2+4q+1
       101: q^4+5q^3+9q^2+4q+1
       102: 2q^3+8q^2+3q+1
       103: q^2+q
       104: q^3+3q^2+2q+1
       106: q^2+q
       107: 2q^2+3q+1
       108: q
       109: q
       110: 2q^2+3q+1
       111: 2q
       112: 2q^2+2q+1
       113: q^2+2q
       114: 3q^2+2q+1
       115: q^2+q
       116: 4q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       121: 2q^2+q
       122: 3q^2+2q+1
       123: 2q^2+q
       124: q^3+4q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 3q^2+2q+1
       139: 3q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 2q^2+3q+1
       144: 3q^2+2q+1
       145: 3q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+7q^2+3q+1
       151: q^3+q^2+2q
       152: 5q^2+2q+1
       153: q^3+q^2+2q
       154: q^3+5q^2+2q+1
       155: 2q^2+q
       156: 4q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+2q+1
       166: 2q^3+6q^2+4q+1
       167: 2q^3+6q^2+4q+1
       168: q^3+5q^2+2q+1
       169: q
       170: q^2+2q+1
       172: q
       174: q^2+2q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       183: 2q+1
       186: 2q+1
       187: q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       192: q^2+2q+1
       193: 2q^2+3q+1
       194: q
       195: q
       196: 2q^2+3q+1
       197: 2q
       198: 2q^2+2q+1
       199: q^2+2q+1
       201: 2q^2+3q+1
       202: q
       203: q
       204: 2q^2+3q+1
       205: 2q
       206: 2q^2+2q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+2q
       210: 3q^2+2q+1
       211: q^2+q
       212: 4q^2+2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+2q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: 3q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 3q^2+3q+1
       257: 3q^2+3q+1
       258: 3q^2+2q+1
       260: q+1
       264: 2q+1
       267: q
       268: q^2+2q+1
       269: q
       271: q
       273: q
       274: q^2+2q+1
       276: q^2+2q+1
       283: q+1
       286: q+1
       288: q+1
       292: q+1
       293: q+1
       296: q+1
       297: q
       298: q+1
       299: 2q+1
       302: q+1
       304: 2q+1
       305: q
       306: q^2+2q+1
       307: 2q+1
       310: 2q+1
       312: q+1
       313: q
       314: q^2+2q+1
       316: q^2+q+1
       318: q+1
       319: 2q^2+3q+1
       320: q
       321: q
       322: 2q^2+3q+1
       323: 2q
       324: 2q^2+2q+1
       325: q^2+q
       326: 2q^2+2q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: q^2+2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: q+1
       386: q+1
       390: q+1
       394: 2q+1
       400: q+1
       403: 2q+1
       405: q
       406: q
       407: q^2+2q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: q+1
       429: q+1
       432: q+1
       434: q+1
       437: q+1
       440: q+1
       441: q
       442: q+1
       443: 3q+1
       444: q
       446: 2q+1
       447: q+1
       450: q+1
       452: q+1
       453: q+1
       458: q+1
       459: q
       460: q+1
       461: q
       462: 3q+1
       464: 2q+1
       470: q+1
       471: 2q+1
       474: 2q+1
       475: q
       476: q^2+2q+1
       478: q+1
       479: 3q
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: 2q+1
       514: q^2+2q+1
       530: 1
       534: q+1
       542: q+1
       546: q+1
       551: q+1
       560: q+1
       564: q+1
       566: 2q+1
       571: q+1
       573: q
       574: 2q+1
       575: q
       578: q
       581: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: q+1
       615: q+1
       619: 1
       622: 1
       626: 1
       630: q+1
       632: q+1
       641: q+1
       644: q+1
       646: q+1
       647: q+1
       650: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       699: q+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: q+1
       763: q+1
       766: q+1
       785: 1
       788: 1
       792: 1
       801: 1
       804: 1
       805: 1
       808: 1
       812: 1
       825: 1
       828: 1
       829: 1
       832: 1
       836: 1
       845: 1
       848: 1
       852: 1
       856: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       909: 1
       926: 1
       929: 1
       951: 1
       953: 1
       976: 1
      1026: 1
      1029: 1
      1040: 1
      1045: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1063: 1
      1065: 1
      1083: 1
      1162: 1
      1181: 1
      1205: 1
      1207: 1
      1268: 1
      1271: 1
      1427: 1

1428:    0: 7q^3+12q^2+4q+1
         1: 2q^4+8q^3+12q^2+4q+1
         2: 4q^3+10q^2+3q+1
         3: 2q^4+8q^3+12q^2+4q+1
         4: 3q^4+7q^3+9q^2+4q+1
         5: 7q^3+12q^2+4q+1
         6: q^5+4q^4+8q^3+9q^2+4q+1
         7: 2q^4+4q^3+8q^2+3q+1
         8: 4q^3+10q^2+3q+1
         9: 3q^4+4q^3+5q^2+2q+1
        10: 2q^3+8q^2+4q+1
        11: 2q^3+8q^2+4q+1
        12: q^4+3q^3+6q^2+4q+1
        13: 2q^3+9q^2+3q+1
        14: q^4+3q^3+7q^2+3q+1
        15: 2q^3+9q^2+3q+1
        16: 5q^3+9q^2+4q+1
        17: 5q^3+9q^2+4q+1
        18: q^4+3q^3+5q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+5q^3+9q^2+4q+1
        21: 2q^3+8q^2+3q+1
        22: 7q^3+12q^2+4q+1
        23: 2q^4+8q^3+12q^2+4q+1
        24: 4q^3+10q^2+3q+1
        25: 7q^3+12q^2+4q+1
        26: 2q^4+8q^3+12q^2+4q+1
        27: 4q^3+10q^2+3q+1
        28: q^3+5q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+7q^2+3q+1
        31: 2q^3+8q^2+4q+1
        32: 2q^3+9q^2+3q+1
        33: 5q^3+9q^2+4q+1
        34: 2q^3+8q^2+4q+1
        35: 2q^3+9q^2+3q+1
        36: 5q^3+9q^2+4q+1
        37: 4q^3+4q^2+2q
        38: 3q^3+8q^2+2q+1
        39: q^4+4q^3+4q^2+2q
        40: q^4+4q^3+8q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+6q^2+2q+1
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: q^3+6q^2+3q+1
        47: q^3+6q^2+3q+1
        48: 2q^3+4q^2+2q+1
        49: 2q^3+6q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: q^3+5q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+5q^3+9q^2+4q+1
        54: 2q^3+8q^2+3q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+5q^3+9q^2+4q+1
        57: 2q^3+8q^2+3q+1
        58: q^3+4q^2+3q+1
        59: q^2+q
        60: q^2+q
        61: q^3+4q^2+3q+1
        62: q^3+3q^2+2q
        63: q^3+5q^2+2q+1
        64: q^3+3q^2+q
        65: q^3+6q^2+2q+1
        66: 2q^3+3q^2+2q
        67: 3q^3+6q^2+2q+1
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 4q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: q^3+q^2+2q
        75: 5q^2+2q+1
        76: q^3+q^2+2q
        77: q^3+5q^2+2q+1
        78: 2q^2+q
        79: 4q^2+2q+1
        80: 5q^2+3q+1
        81: q^3+6q^2+3q+1
        82: q^3+6q^2+4q+1
        83: q^3+7q^2+3q+1
        84: 5q^2+3q+1
        85: q^3+6q^2+3q+1
        86: q^3+6q^2+4q+1
        87: q^3+7q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: 3q^2+2q+1
        94: 2q^3+6q^2+4q+1
        95: 2q^3+6q^2+4q+1
        96: q^3+5q^2+2q+1
        97: 2q^3+6q^2+4q+1
        98: 2q^3+6q^2+4q+1
        99: q^3+5q^2+2q+1
       100: 4q^3+9q^2+4q+1
       101: q^4+5q^3+9q^2+4q+1
       102: 2q^3+8q^2+3q+1
       103: q^2+q
       105: q^3+3q^2+2q+1
       106: q^2+q
       107: q
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: q
       111: 2q
       112: 2q^2+2q+1
       113: q^2+2q
       114: 3q^2+2q+1
       115: q^2+q
       116: 4q^2+2q+1
       117: q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+q
       122: 3q^2+2q+1
       123: 2q^2+q
       124: q^3+4q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 3q^2+2q+1
       139: 3q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 2q^2+3q+1
       144: 3q^2+2q+1
       145: 3q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+7q^2+3q+1
       151: q^3+q^2+2q
       152: 5q^2+2q+1
       153: q^3+q^2+2q
       154: q^3+5q^2+2q+1
       155: 2q^2+q
       156: 4q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+2q+1
       166: 2q^3+6q^2+4q+1
       167: 2q^3+6q^2+4q+1
       168: q^3+5q^2+2q+1
       169: q
       171: q^2+2q+1
       172: q
       175: q^2+2q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       184: 2q+1
       185: 2q+1
       187: q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: q^2+2q+1
       193: q
       194: 2q^2+3q+1
       195: 2q^2+3q+1
       196: q
       197: 2q
       198: 2q^2+2q+1
       200: q^2+2q+1
       201: q
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: q
       205: 2q
       206: 2q^2+2q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+2q
       210: 3q^2+2q+1
       211: q^2+q
       212: 4q^2+2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+2q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: 3q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 3q^2+3q+1
       257: 3q^2+3q+1
       258: 3q^2+2q+1
       261: q+1
       265: 2q+1
       267: q
       269: q
       270: q^2+2q+1
       271: q
       272: q^2+2q+1
       273: q
       277: q^2+2q+1
       284: q+1
       285: q+1
       288: q+1
       292: q+1
       294: q+1
       295: q+1
       297: q
       298: q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q
       306: q^2+2q+1
       308: 2q+1
       309: 2q+1
       312: q+1
       313: q
       314: q^2+2q+1
       316: q^2+q+1
       318: q+1
       319: q
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: q
       323: 2q
       324: 2q^2+2q+1
       325: q^2+q
       326: 2q^2+2q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: q^2+2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: q+1
       387: q+1
       392: q+1
       395: 2q+1
       398: q+1
       402: 2q+1
       405: q
       406: q
       408: q^2+2q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: q+1
       430: q+1
       431: q+1
       434: q+1
       438: q+1
       439: q+1
       441: q
       442: q+1
       443: q
       444: 3q+1
       446: 2q+1
       448: q+1
       449: q+1
       452: q+1
       454: q+1
       457: q+1
       459: q
       460: q+1
       461: 3q+1
       462: q
       464: 2q+1
       470: q+1
       472: 2q+1
       473: 2q+1
       475: q
       476: q^2+2q+1
       478: q+1
       479: 3q
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: 2q+1
       514: q^2+2q+1
       531: 1
       535: q+1
       544: q+1
       548: q+1
       550: q+1
       558: q+1
       562: q+1
       567: 2q+1
       572: q+1
       573: q
       575: q
       576: 2q+1
       578: q
       581: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: q+1
       616: q+1
       620: 1
       621: 1
       626: 1
       630: q+1
       631: q+1
       642: q+1
       643: q+1
       646: q+1
       648: q+1
       649: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       700: q+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: q+1
       764: q+1
       767: q+1
       786: 1
       787: 1
       792: 1
       802: 1
       803: 1
       806: 1
       807: 1
       812: 1
       826: 1
       827: 1
       830: 1
       831: 1
       836: 1
       846: 1
       847: 1
       852: 1
       856: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       910: 1
       925: 1
       931: 1
       949: 1
       954: 1
       977: 1
      1027: 1
      1028: 1
      1041: 1
      1044: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1063: 1
      1065: 1
      1083: 1
      1161: 1
      1182: 1
      1203: 1
      1209: 1
      1269: 1
      1270: 1
      1428: 1

1429:    0: 7q^3+12q^2+4q+1
         1: 2q^4+8q^3+12q^2+4q+1
         2: 4q^3+10q^2+3q+1
         3: 2q^4+8q^3+12q^2+4q+1
         4: 3q^4+7q^3+9q^2+4q+1
         5: 7q^3+12q^2+4q+1
         6: q^5+4q^4+8q^3+9q^2+4q+1
         7: 2q^4+4q^3+8q^2+3q+1
         8: 4q^3+10q^2+3q+1
         9: 3q^4+4q^3+5q^2+2q+1
        10: 2q^3+8q^2+4q+1
        11: 2q^3+8q^2+4q+1
        12: q^4+3q^3+6q^2+4q+1
        13: 2q^3+9q^2+3q+1
        14: q^4+3q^3+7q^2+3q+1
        15: 2q^3+9q^2+3q+1
        16: 5q^3+9q^2+4q+1
        17: 5q^3+9q^2+4q+1
        18: q^4+3q^3+5q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+5q^3+9q^2+4q+1
        21: 2q^3+8q^2+3q+1
        22: 7q^3+12q^2+4q+1
        23: 2q^4+8q^3+12q^2+4q+1
        24: 4q^3+10q^2+3q+1
        25: 7q^3+12q^2+4q+1
        26: 2q^4+8q^3+12q^2+4q+1
        27: 4q^3+10q^2+3q+1
        28: q^3+5q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+7q^2+3q+1
        31: 2q^3+8q^2+4q+1
        32: 2q^3+9q^2+3q+1
        33: 5q^3+9q^2+4q+1
        34: 2q^3+8q^2+4q+1
        35: 2q^3+9q^2+3q+1
        36: 5q^3+9q^2+4q+1
        37: 3q^3+8q^2+2q+1
        38: 4q^3+4q^2+2q
        39: q^4+4q^3+8q^2+2q+1
        40: q^4+4q^3+4q^2+2q
        41: 2q^3+6q^2+2q+1
        42: 2q^3+4q^2+q
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: q^3+6q^2+3q+1
        47: q^3+6q^2+3q+1
        48: 2q^3+4q^2+2q+1
        49: 2q^3+6q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: q^3+5q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+5q^3+9q^2+4q+1
        54: 2q^3+8q^2+3q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+5q^3+9q^2+4q+1
        57: 2q^3+8q^2+3q+1
        58: q^2+q
        59: q^3+4q^2+3q+1
        60: q^2+q
        61: q^3+4q^2+3q+1
        62: q^3+5q^2+2q+1
        63: q^3+3q^2+2q
        64: q^3+6q^2+2q+1
        65: q^3+3q^2+q
        66: 3q^3+6q^2+2q+1
        67: 2q^3+3q^2+2q
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 4q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: 5q^2+2q+1
        75: q^3+q^2+2q
        76: q^3+5q^2+2q+1
        77: q^3+q^2+2q
        78: 4q^2+2q+1
        79: 2q^2+q
        80: 5q^2+3q+1
        81: q^3+6q^2+3q+1
        82: q^3+6q^2+4q+1
        83: q^3+7q^2+3q+1
        84: 5q^2+3q+1
        85: q^3+6q^2+3q+1
        86: q^3+6q^2+4q+1
        87: q^3+7q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: 3q^2+2q+1
        94: 2q^3+6q^2+4q+1
        95: 2q^3+6q^2+4q+1
        96: q^3+5q^2+2q+1
        97: 2q^3+6q^2+4q+1
        98: 2q^3+6q^2+4q+1
        99: q^3+5q^2+2q+1
       100: 4q^3+9q^2+4q+1
       101: q^4+5q^3+9q^2+4q+1
       102: 2q^3+8q^2+3q+1
       104: q^2+q
       105: q^2+q
       106: q^3+3q^2+2q+1
       107: q
       108: 2q^2+3q+1
       109: q
       110: 2q^2+3q+1
       111: 2q^2+2q+1
       112: 2q
       113: 3q^2+2q+1
       114: q^2+2q
       115: 4q^2+2q+1
       116: q^2+q
       118: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+2q+1
       122: 2q^2+q
       123: q^3+4q^2+2q+1
       124: 2q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 3q^2+2q+1
       139: 3q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 2q^2+3q+1
       144: 3q^2+2q+1
       145: 3q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+7q^2+3q+1
       151: 5q^2+2q+1
       152: q^3+q^2+2q
       153: q^3+5q^2+2q+1
       154: q^3+q^2+2q
       155: 4q^2+2q+1
       156: 2q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+2q+1
       166: 2q^3+6q^2+4q+1
       167: 2q^3+6q^2+4q+1
       168: q^3+5q^2+2q+1
       170: q
       171: q
       172: q^2+2q+1
       176: q^2+2q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       184: 2q+1
       186: 2q+1
       187: q^2+2q+1
       188: q
       189: 2q^2+2q+1
       190: q^2+q
       192: q^2+2q+1
       193: q
       194: 2q^2+3q+1
       195: q
       196: 2q^2+3q+1
       197: 2q^2+2q+1
       198: 2q
       200: q^2+2q+1
       201: q
       202: 2q^2+3q+1
       203: q
       204: 2q^2+3q+1
       205: 2q^2+2q+1
       206: 2q
       207: q^2+2q+1
       208: q^2+q
       209: 3q^2+2q+1
       210: q^2+2q
       211: 4q^2+2q+1
       212: q^2+q
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+2q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: 3q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 3q^2+3q+1
       257: 3q^2+3q+1
       258: 3q^2+2q+1
       262: q+1
       266: 2q+1
       268: q
       269: q^2+2q+1
       270: q
       272: q
       273: q^2+2q+1
       274: q
       278: q^2+2q+1
       284: q+1
       286: q+1
       287: q+1
       291: q+1
       294: q+1
       296: q+1
       297: q+1
       298: q
       300: 2q+1
       301: q+1
       304: 2q+1
       305: q^2+2q+1
       306: q
       308: 2q+1
       310: 2q+1
       311: q+1
       313: q^2+2q+1
       314: q
       315: q^2+q+1
       317: q+1
       319: q
       320: 2q^2+3q+1
       321: q
       322: 2q^2+3q+1
       323: 2q^2+2q+1
       324: 2q
       325: 2q^2+2q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: q^2+2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: q+1
       388: q+1
       391: q+1
       396: 2q+1
       399: q+1
       404: 2q+1
       406: q^2+2q+1
       407: q
       408: q
       420: 1
       422: 1
       423: 1
       425: q+1
       427: q+1
       430: q+1
       432: q+1
       433: q+1
       438: q+1
       440: q+1
       441: q+1
       442: q
       443: q
       444: 3q+1
       445: 2q+1
       448: q+1
       450: q+1
       451: q+1
       454: q+1
       458: q+1
       459: q+1
       460: q
       461: q
       462: 3q+1
       463: 2q+1
       469: q+1
       472: 2q+1
       474: 2q+1
       475: q^2+2q+1
       476: q
       477: q+1
       479: q^2+2q+1
       480: 3q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: 2q+1
       514: q^2+2q+1
       532: 1
       536: q+1
       543: q+1
       547: q+1
       552: q+1
       559: q+1
       563: q+1
       568: 2q+1
       570: q+1
       574: q
       575: 2q+1
       576: q
       577: q+1
       580: q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: q+1
       616: q+1
       620: 1
       622: 1
       625: 1
       629: q+1
       632: q+1
       642: q+1
       644: q+1
       645: q+1
       648: q+1
       650: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       665: 1
       675: 1
       676: 1
       677: q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       697: q+1
       716: 1
       720: 1
       727: 1
       743: 1
       756: q+1
       762: q+1
       768: q+1
       786: 1
       788: 1
       791: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       846: 1
       848: 1
       851: 1
       855: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       911: 1
       927: 1
       930: 1
       950: 1
       955: 1
       975: 1
      1027: 1
      1029: 1
      1041: 1
      1045: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1062: 1
      1064: 1
      1083: 1
      1163: 1
      1183: 1
      1204: 1
      1208: 1
      1269: 1
      1271: 1
      1429: 1

1430:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        64: 1
        66: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       111: 1
       115: 1
       123: 1
       127: 1
       129: 1
       131: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       153: 1
       155: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       177: 1
       181: 1
       187: 1
       197: 1
       205: 1
       211: 1
       213: 1
       215: 1
       217: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       281: 1
       289: 1
       291: 1
       301: 1
       305: 1
       311: 1
       313: 1
       315: 1
       323: 1
       336: 1
       338: 1
       340: 1
       342: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       417: 1
       425: 1
       433: 1
       435: 1
       445: 1
       451: 1
       455: 1
       463: 1
       467: 1
       475: 1
       477: 1
       479: 1
       485: 1
       487: 1
       489: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       517: 1
       577: 1
       597: 1
       605: 1
       613: 1
       617: 1
       623: 1
       629: 1
       633: 1
       645: 1
       651: 1
       655: 1
       658: 1
       660: 1
       662: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       689: 1
       769: 1
       779: 1
       791: 1
       795: 1
       809: 1
       819: 1
       833: 1
       843: 1
       849: 1
       855: 1
       870: 1
       874: 1
       880: 1
       968: 1
      1010: 1
      1012: 1
      1020: 1
      1036: 1
      1060: 1
      1064: 1
      1084: 1
      1138: 1
      1274: 1
      1278: 1
      1280: 1
      1430: 1

1431:    0: q^2+2q
         1: q^2+2q
         2: q^2+2q
         3: q^2+2q
         4: q^2+2q
         5: q^2+2q
         6: q^2+2q
         7: q^2+2q
         8: q^2+2q
         9: q^3+q^2+q
        13: q^2+2q
        14: q^2+2q
        15: q^2+2q
        16: 2q
        17: 2q
        18: q^2+q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^2+2q
        23: q^2+2q
        24: q^2+2q
        25: q^2+2q
        26: q^2+2q
        27: q^2+2q
        30: q^2+2q
        32: q^2+2q
        33: 2q
        35: q^2+2q
        36: 2q
        37: q
        38: q^2+q
        39: q
        40: q^2+q
        41: q
        42: q^2+q
        46: 2q
        47: 2q
        48: q^2+q
        49: 2q
        50: 2q
        51: q^2+q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        64: q
        65: q^2+q
        66: q
        67: q
        69: q
        72: 2q
        73: 2q
        74: q
        75: q^2+q
        76: q
        77: q^2+q
        78: q
        79: q^2+q
        81: 2q
        83: q^2+2q
        85: 2q
        87: q^2+2q
        91: 2q
        92: 2q
        93: q^2+q
        94: 2q
        95: 2q
        96: q^2+q
        97: 2q
        98: 2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       111: q
       112: q
       115: q
       116: q^2+q
       123: q
       124: q
       128: q
       130: q
       132: q^2
       134: q
       135: 2q
       136: 2q
       138: q
       140: 2q
       142: 2q
       144: q
       147: 2q
       148: 2q
       150: q^2+2q
       151: q
       152: q^2+q
       153: q
       154: q^2+q
       155: q
       156: q^2+q
       160: 2q
       161: 2q
       162: q^2+q
       163: 2q
       164: 2q
       165: q^2+q
       166: 2q
       167: 2q
       168: q^2+q
       182: q
       187: q
       188: q
       197: q
       198: q
       205: q
       206: q
       211: q
       212: q^2+q
       214: q
       216: q
       218: q^2
       223: q
       225: q
       228: q
       229: 2q
       230: 2q
       233: q
       234: 2q
       235: 2q
       236: q
       238: q
       240: q
       242: q^2
       244: 2q
       245: 2q
       247: 2q
       248: 2q
       249: q^2+q
       256: 2q
       257: 2q
       258: q^2+q
       290: q
       302: q
       305: q
       306: q
       312: q
       313: q
       314: q
       323: q
       324: q
       336: q
       339: q
       341: q
       343: q^2
       348: q
       350: q
       351: 2q
       356: q
       358: q
       359: 2q
       361: q
       363: q
       365: q^2
       368: q
       369: 2q
       370: 2q
       371: 2q
       372: 2q
       373: q^2+q
       436: q
       446: q
       456: q
       464: q
       475: q
       476: q
       478: q
       479: q
       480: q
       486: q
       488: q
       490: q^2
       491: q
       495: q
       496: 2q
       500: q
       501: 2q
       512: q
       514: q
       515: 1
       516: 1
       517: 1
       581: q
       618: q
       634: q
       652: q
       655: q
       656: q
       659: 1
       661: 1
       663: 1
       664: 1
       674: 1
       679: q
       680: 1
       685: q
       689: q
       773: q
       780: 1
       796: 1
       820: 1
       843: 1
       870: 1
       874: 1
       880: q
       969: 1
      1012: 1
      1021: 1
      1037: 1
      1084: 1
      1139: 1
      1275: 1
      1280: 1
      1431: 1

1432:    0: q^3+q
         1: q^3+q
         2: q
         3: q^3+q
         4: q
         5: q^3+q
         6: q^4+q^3+q
         7: q^5+q
         8: q
         9: q^5+q
        13: q
        14: q
        15: q
        16: q^3+q
        17: q^3+q
        18: q^5+q
        19: q
        20: q^3+q
        21: q
        22: q^3+q
        23: q^3+q
        24: q
        25: q^3+q
        26: q^3+q
        27: q
        30: q
        32: q
        33: q^3+q
        35: q
        36: q^3+q
        37: q^3+q
        39: q^3+q
        41: q
        46: q
        47: q
        48: q
        49: q
        50: q^3+q
        51: q
        52: q
        53: q^3+q
        54: q
        55: q
        56: q^3+q
        57: q
        64: q
        66: q^3+q
        69: q
        72: q
        73: q
        74: q
        76: q^3+q
        78: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        93: q
        94: q
        95: q^3+q
        96: q
        97: q
        98: q^3+q
        99: q
       100: q
       101: q^3+q
       102: q
       111: q
       115: q
       123: q
       127: q
       129: q^3+q
       131: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q
       144: q
       147: q
       148: q
       150: q
       151: q
       153: q^3+q
       155: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q
       167: q^3+q
       168: q
       177: q
       181: q
       187: q
       197: q
       205: q
       211: q
       213: q
       215: q
       217: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q^3+q
       241: q
       244: q
       245: q
       247: q
       248: q
       249: q
       256: q
       257: q
       258: q
       281: q
       289: q
       291: q
       301: q
       305: q
       311: q
       313: q
       315: q
       323: q
       336: q
       338: q
       340: q
       342: q
       348: q
       350: q
       351: q
       356: q
       358: q
       359: q
       360: q
       362: q
       364: q
       368: q
       369: q
       370: q
       417: q
       425: q
       433: q
       435: q
       445: q
       451: q
       455: q
       463: q
       467: q
       475: q
       477: q
       479: q
       495: q
       500: q
       512: q
       514: q
       577: q
       605: q
       613: q
       623: q
       629: q
       645: q
       651: q
       689: q
       849: q
       855: q
      1010: 1
      1140: 1
      1278: 1
      1432: 1

1433:    0: q^2+2q
         1: q^2+2q
         2: q^2+2q
         3: q^2+2q
         4: q^2+2q
         5: q^2+2q
         6: q^2+2q
         7: q^2+2q
         8: q^2+2q
         9: q^3+q^2+q
        13: q^2+2q
        14: q^2+2q
        15: q^2+2q
        16: 2q
        17: 2q
        18: q^2+q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^2+2q
        23: q^2+2q
        24: q^2+2q
        25: q^2+2q
        26: q^2+2q
        27: q^2+2q
        30: q^2+2q
        32: q^2+2q
        33: 2q
        35: q^2+2q
        36: 2q
        37: q^2+q
        38: q
        39: q^2+q
        40: q
        41: q^2+q
        42: q
        46: 2q
        47: 2q
        48: q^2+q
        49: 2q
        50: 2q
        51: q^2+q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        64: q^2+q
        65: q
        66: q
        67: q
        69: q
        72: 2q
        73: 2q
        74: q^2+q
        75: q
        76: q^2+q
        77: q
        78: q^2+q
        79: q
        81: 2q
        83: q^2+2q
        85: 2q
        87: q^2+2q
        91: 2q
        92: 2q
        93: q^2+q
        94: 2q
        95: 2q
        96: q^2+q
        97: 2q
        98: 2q
        99: q^2+q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       111: q
       112: q
       115: q^2+q
       116: q
       123: q
       124: q
       127: q
       129: q
       131: q^2
       134: q
       135: 2q
       136: 2q
       138: q
       140: 2q
       142: 2q
       144: q
       147: 2q
       148: 2q
       150: q^2+2q
       151: q^2+q
       152: q
       153: q^2+q
       154: q
       155: q^2+q
       156: q
       160: 2q
       161: 2q
       162: q^2+q
       163: 2q
       164: 2q
       165: q^2+q
       166: 2q
       167: 2q
       168: q^2+q
       181: q
       187: q
       188: q
       197: q
       198: q
       205: q
       206: q
       211: q^2+q
       212: q
       213: q
       215: q
       217: q^2
       223: q
       225: q
       228: q
       229: 2q
       230: 2q
       233: q
       234: 2q
       235: 2q
       236: q
       237: q
       239: q
       241: q^2
       244: 2q
       245: 2q
       247: 2q
       248: 2q
       249: q^2+q
       256: 2q
       257: 2q
       258: q^2+q
       289: q
       301: q
       305: q
       306: q
       311: q
       313: q
       314: q
       323: q
       324: q
       336: q
       338: q
       340: q
       342: q^2
       348: q
       350: q
       351: 2q
       356: q
       358: q
       359: 2q
       360: q
       362: q
       364: q^2
       368: q
       369: 2q
       370: 2q
       371: 2q
       372: 2q
       373: q^2+q
       435: q
       445: q
       455: q
       463: q
       475: q
       476: q
       477: q
       479: q
       480: q
       485: q
       487: q
       489: q^2
       491: q
       495: q
       496: 2q
       500: q
       501: 2q
       512: q
       514: q
       515: 1
       516: 1
       517: 1
       577: q
       617: q
       633: q
       651: q
       655: q
       656: q
       658: 1
       660: 1
       662: 1
       664: 1
       674: 1
       679: q
       680: 1
       685: q
       689: q
       769: q
       779: 1
       795: 1
       819: 1
       844: 1
       870: 1
       874: 1
       880: q
       971: 1
      1013: 1
      1020: 1
      1036: 1
      1084: 1
      1141: 1
      1274: 1
      1281: 1
      1433: 1

1434:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        65: 1
        67: 1
        69: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        81: 1
        83: 1
        85: 1
        87: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       116: 1
       124: 1
       128: 1
       130: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       140: 1
       142: 1
       144: 1
       147: 1
       148: 1
       150: 1
       152: 1
       154: 1
       156: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       178: 1
       182: 1
       188: 1
       198: 1
       206: 1
       212: 1
       214: 1
       216: 1
       218: 1
       223: 1
       225: 1
       228: 1
       229: 1
       230: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       256: 1
       257: 1
       258: 1
       282: 1
       290: 1
       292: 1
       302: 1
       306: 1
       312: 1
       314: 1
       316: 1
       324: 1
       336: 1
       339: 1
       341: 1
       343: 1
       348: 1
       350: 1
       351: 1
       356: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       418: 1
       426: 1
       434: 1
       436: 1
       446: 1
       452: 1
       456: 1
       464: 1
       468: 1
       476: 1
       478: 1
       480: 1
       486: 1
       488: 1
       490: 1
       491: 1
       495: 1
       496: 1
       500: 1
       501: 1
       512: 1
       514: 1
       515: 1
       516: 1
       517: 1
       581: 1
       598: 1
       606: 1
       614: 1
       618: 1
       624: 1
       630: 1
       634: 1
       646: 1
       652: 1
       656: 1
       659: 1
       661: 1
       663: 1
       664: 1
       674: 1
       679: 1
       680: 1
       685: 1
       689: 1
       773: 1
       780: 1
       792: 1
       796: 1
       810: 1
       820: 1
       834: 1
       844: 1
       850: 1
       856: 1
       870: 1
       874: 1
       880: 1
       972: 1
      1011: 1
      1013: 1
      1021: 1
      1037: 1
      1061: 1
      1065: 1
      1084: 1
      1142: 1
      1275: 1
      1279: 1
      1281: 1
      1434: 1

1435:    0: q^3+q
         1: q^3+q
         2: q
         3: q^3+q
         4: q
         5: q^3+q
         6: q^4+q^3+q
         7: q^5+q
         8: q
         9: q^5+q
        13: q
        14: q
        15: q
        16: q^3+q
        17: q^3+q
        18: q^5+q
        19: q
        20: q^3+q
        21: q
        22: q^3+q
        23: q^3+q
        24: q
        25: q^3+q
        26: q^3+q
        27: q
        30: q
        32: q
        33: q^3+q
        35: q
        36: q^3+q
        38: q^3+q
        40: q^3+q
        42: q
        46: q
        47: q
        48: q
        49: q
        50: q^3+q
        51: q
        52: q
        53: q^3+q
        54: q
        55: q
        56: q^3+q
        57: q
        65: q
        67: q^3+q
        69: q
        72: q
        73: q
        75: q
        77: q^3+q
        79: q
        81: q
        83: q
        85: q
        87: q
        91: q
        92: q
        93: q
        94: q
        95: q^3+q
        96: q
        97: q
        98: q^3+q
        99: q
       100: q
       101: q^3+q
       102: q
       112: q
       116: q
       124: q
       128: q
       130: q^3+q
       132: q
       134: q
       135: q
       136: q
       138: q
       140: q
       142: q
       144: q
       147: q
       148: q
       150: q
       152: q
       154: q^3+q
       156: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q
       167: q^3+q
       168: q
       178: q
       182: q
       188: q
       198: q
       206: q
       212: q
       214: q
       216: q
       218: q
       223: q
       225: q
       228: q
       229: q
       230: q
       233: q
       234: q
       235: q
       236: q
       238: q
       240: q^3+q
       242: q
       244: q
       245: q
       247: q
       248: q
       249: q
       256: q
       257: q
       258: q
       282: q
       290: q
       292: q
       302: q
       306: q
       312: q
       314: q
       316: q
       324: q
       336: q
       339: q
       341: q
       343: q
       348: q
       350: q
       351: q
       356: q
       358: q
       359: q
       361: q
       363: q
       365: q
       368: q
       369: q
       370: q
       418: q
       426: q
       434: q
       436: q
       446: q
       452: q
       456: q
       464: q
       468: q
       476: q
       478: q
       480: q
       495: q
       500: q
       512: q
       514: q
       581: q
       606: q
       614: q
       624: q
       630: q
       646: q
       652: q
       689: q
       850: q
       856: q
      1011: 1
      1143: 1
      1279: 1
      1435: 1

1436:    0: 24q^3+45q^2+17q+2
         1: 4q^4+26q^3+45q^2+17q+2
         2: 7q^4+24q^3+33q^2+16q+2
         3: 24q^3+45q^2+17q+2
         4: 7q^4+24q^3+33q^2+16q+2
         5: 4q^4+26q^3+45q^2+17q+2
         6: 2q^5+14q^4+32q^3+36q^2+16q+2
         7: q^5+7q^4+15q^3+24q^2+15q+2
         8: q^5+9q^4+25q^3+33q^2+16q+2
         9: q^5+7q^4+15q^3+24q^2+15q+2
        10: 12q^3+35q^2+16q+2
        11: 12q^3+35q^2+16q+2
        12: 4q^4+18q^3+27q^2+15q+2
        13: 14q^3+32q^2+16q+2
        14: 3q^4+11q^3+23q^2+15q+2
        15: 2q^4+15q^3+32q^2+16q+2
        16: 24q^3+45q^2+17q+2
        17: 4q^4+26q^3+45q^2+17q+2
        18: q^5+7q^4+15q^3+24q^2+15q+2
        19: 14q^3+32q^2+16q+2
        20: 3q^4+19q^3+35q^2+16q+2
        21: 3q^4+11q^3+23q^2+15q+2
        22: 13q^3+38q^2+17q+2
        23: 13q^3+38q^2+17q+2
        24: 3q^4+16q^3+28q^2+16q+2
        25: 13q^3+38q^2+17q+2
        26: 13q^3+38q^2+17q+2
        27: 3q^4+16q^3+28q^2+16q+2
        28: 12q^3+35q^2+16q+2
        29: 9q^3+26q^2+15q+2
        30: 7q^3+22q^2+15q+2
        31: 4q^3+28q^2+16q+2
        32: 8q^3+27q^2+16q+2
        33: 13q^3+38q^2+17q+2
        34: 4q^3+28q^2+16q+2
        35: 8q^3+27q^2+16q+2
        36: 13q^3+38q^2+17q+2
        37: 4q^3+22q^2+13q+2
        38: 2q^3+10q^2+4q
        39: 4q^3+22q^2+13q+2
        40: 2q^3+10q^2+4q
        41: 7q^3+17q^2+12q+2
        42: q^4+4q^3+7q^2+4q
        43: 5q^3+22q^2+15q+2
        44: q^4+7q^3+17q^2+14q+2
        45: 4q^3+22q^2+15q+2
        46: 14q^3+32q^2+16q+2
        47: 2q^4+15q^3+32q^2+16q+2
        48: 3q^4+11q^3+23q^2+15q+2
        49: 14q^3+32q^2+16q+2
        50: 3q^4+19q^3+35q^2+16q+2
        51: 3q^4+11q^3+23q^2+15q+2
        52: 6q^3+25q^2+16q+2
        53: 8q^3+28q^2+16q+2
        54: q^4+6q^3+18q^2+15q+2
        55: 6q^3+25q^2+16q+2
        56: 8q^3+28q^2+16q+2
        57: q^4+6q^3+18q^2+15q+2
        58: 2q^3+14q^2+8q+1
        59: 2q^3+14q^2+8q+1
        60: 2q^3+14q^2+8q+1
        61: 2q^3+14q^2+8q+1
        62: 16q^2+12q+2
        63: 6q^2+4q
        64: 3q^3+16q^2+12q+2
        65: 2q^3+7q^2+4q
        66: 4q^3+22q^2+13q+2
        67: 2q^3+10q^2+4q
        68: q^3+13q^2+14q+2
        69: 7q^3+22q^2+15q+2
        70: 4q^3+16q^2+14q+2
        71: 9q^3+26q^2+15q+2
        72: 3q^3+17q^2+15q+2
        73: 3q^3+17q^2+15q+2
        74: 11q^2+12q+2
        75: q^3+3q^2+4q
        76: q^3+13q^2+12q+2
        77: 4q^2+4q
        78: q^3+9q^2+11q+2
        79: q^3+3q^2+4q
        80: q^3+17q^2+15q+2
        81: 8q^3+27q^2+16q+2
        82: 3q^3+19q^2+15q+2
        83: 3q^3+17q^2+15q+2
        84: q^3+17q^2+15q+2
        85: 8q^3+27q^2+16q+2
        86: 3q^3+19q^2+15q+2
        87: 3q^3+17q^2+15q+2
        88: 5q^3+22q^2+15q+2
        89: 4q^3+22q^2+15q+2
        90: q^4+7q^3+17q^2+14q+2
        91: 3q^3+16q^2+15q+2
        92: q^4+8q^3+22q^2+15q+2
        93: 3q^3+16q^2+15q+2
        94: 6q^3+25q^2+16q+2
        95: 8q^3+28q^2+16q+2
        96: q^4+6q^3+18q^2+15q+2
        97: 6q^3+25q^2+16q+2
        98: 8q^3+28q^2+16q+2
        99: q^4+6q^3+18q^2+15q+2
       100: 13q^2+15q+2
       101: 2q^3+18q^2+15q+2
       102: q^3+10q^2+14q+2
       103: 8q^2+6q+1
       104: 3q^2+2q
       105: 3q^2+2q
       106: 8q^2+6q+1
       107: q^3+6q^2+7q+1
       108: q^3+6q^2+7q+1
       109: q^3+6q^2+7q+1
       110: q^3+6q^2+7q+1
       111: 7q^2+11q+2
       112: q^2+4q
       113: 8q^2+11q+2
       114: q^2+4q
       115: 8q^2+11q+2
       116: q^3+3q^2+4q
       117: 5q^2+7q+1
       118: 5q^2+7q+1
       119: 5q^2+7q+1
       120: 5q^2+7q+1
       121: 10q^2+11q+2
       122: 3q^2+4q
       123: 3q^3+16q^2+12q+2
       124: 2q^3+7q^2+4q
       125: q^3+13q^2+14q+2
       126: 4q^3+16q^2+14q+2
       127: 11q^2+12q+2
       128: q^3+3q^2+4q
       129: q^3+13q^2+12q+2
       130: 4q^2+4q
       131: q^3+9q^2+11q+2
       132: q^3+3q^2+4q
       133: 7q^2+13q+2
       134: 3q^3+16q^2+15q+2
       135: 9q^2+14q+2
       136: 9q^2+14q+2
       137: q^3+17q^2+15q+2
       138: 3q^3+17q^2+15q+2
       139: 3q^3+19q^2+15q+2
       140: 4q^2+9q+2
       141: q^3+11q^2+14q+2
       142: 3q^3+17q^2+15q+2
       143: q^3+17q^2+15q+2
       144: 3q^3+17q^2+15q+2
       145: 3q^3+19q^2+15q+2
       146: q^3+11q^2+14q+2
       147: 3q^3+17q^2+15q+2
       148: 4q^2+9q+2
       149: 9q^2+14q+2
       150: 9q^2+14q+2
       151: 6q^2+11q+2
       152: 2q^2+4q
       153: q^3+9q^2+11q+2
       154: 4q^2+4q
       155: 6q^2+10q+2
       156: 2q^2+4q
       157: q^3+6q^2+10q+2
       158: q^3+9q^2+10q+2
       159: q^3+6q^2+10q+2
       160: q^3+10q^2+13q+2
       161: 3q^3+15q^2+13q+2
       162: q^3+10q^2+13q+2
       163: q^3+10q^2+13q+2
       164: 3q^3+15q^2+13q+2
       165: q^3+10q^2+13q+2
       166: 13q^2+15q+2
       167: 2q^3+18q^2+15q+2
       168: q^3+10q^2+14q+2
       169: 2q^2+5q+1
       170: 2q
       171: 2q
       172: 2q^2+5q+1
       173: 3q^2+5q+1
       174: q^2+2q
       175: q^2+2q
       176: 3q^2+5q+1
       177: 8q^2+11q+2
       178: q^3+3q^2+4q
       179: 8q^2+11q+2
       180: q^2+4q
       181: 7q^2+11q+2
       182: q^2+4q
       183: q^2+6q+1
       184: q^2+6q+1
       185: q^2+6q+1
       186: q^2+6q+1
       187: 4q^2+10q+2
       188: q^2+4q
       189: 5q^2+10q+2
       190: q^2+4q
       191: 5q^2+7q+1
       192: 5q^2+7q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^3+6q^2+7q+1
       196: q^3+6q^2+7q+1
       197: q^2+7q+2
       198: 2q
       199: 5q^2+7q+1
       200: 5q^2+7q+1
       201: q^3+6q^2+7q+1
       202: q^3+6q^2+7q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: q^2+7q+2
       206: 2q
       207: 10q^2+11q+2
       208: 3q^2+4q
       209: 4q^2+10q+2
       210: q^2+4q
       211: 5q^2+10q+2
       212: 2q^2+4q
       213: 2q^2+6q+2
       215: 4q^2+6q+2
       217: 2q^2+6q+2
       219: 7q^2+13q+2
       220: 3q^2+9q+2
       221: q^3+6q^2+10q+2
       222: 2q^2+9q+2
       223: 9q^2+14q+2
       224: 2q^2+9q+2
       225: 9q^2+14q+2
       226: q^3+11q^2+14q+2
       227: 4q^2+11q+2
       228: q^3+10q^2+13q+2
       229: 2q^2+8q+2
       230: 7q^2+12q+2
       231: q^3+11q^2+14q+2
       232: 4q^2+11q+2
       233: q^3+10q^2+13q+2
       234: 7q^2+12q+2
       235: 2q^2+8q+2
       236: 9q^2+14q+2
       237: 6q^2+11q+2
       238: 2q^2+4q
       239: q^3+9q^2+11q+2
       240: 4q^2+4q
       241: 6q^2+10q+2
       242: 2q^2+4q
       243: 9q^2+14q+2
       244: 4q^2+9q+2
       245: 4q^2+9q+2
       246: 5q^2+13q+2
       247: q^2+13q+2
       248: 3q^2+13q+2
       249: 3q^2+6q+1
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q^2+8q+2
       257: q^3+7q^2+8q+2
       258: 3q^2+8q+2
       259: 2q^2+5q+1
       260: 2q
       261: 2q
       262: 2q^2+5q+1
       263: 4q+1
       264: 2q
       265: 2q
       266: 4q+1
       267: 3q+1
       268: q
       269: 3q+1
       270: q
       271: 3q+1
       272: q
       273: 3q+1
       274: q
       275: 3q^2+5q+1
       276: q^2+2q
       277: q^2+2q
       278: 3q^2+5q+1
       279: q^2+5q+2
       281: 2q^2+6q+2
       283: q^2+6q+1
       284: q^2+6q+1
       285: q^2+6q+1
       286: q^2+6q+1
       287: 5q^2+10q+2
       288: q^2+4q
       289: q^2+5q+2
       291: 4q^2+10q+2
       292: q^2+4q
       293: 4q+1
       294: 4q+1
       295: 4q+1
       296: 4q+1
       297: q^2+7q+2
       298: 2q
       299: 3q+1
       300: 3q+1
       301: q^2+7q+2
       302: 2q
       303: q^2+5q+1
       304: q^2+5q+1
       305: q^2+6q+2
       306: 2q
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       311: q^2+7q+2
       312: 2q
       313: q^2+6q+2
       314: 2q
       315: 5q^2+10q+2
       316: 2q^2+4q
       317: 4q^2+10q+2
       318: q^2+4q
       319: q^2+4q+1
       320: q^2+4q+1
       321: q^2+4q+1
       322: q^2+4q+1
       323: 5q+2
       325: 3q^2+9q+2
       326: q^2+4q
       333: 3q^2+9q+2
       334: 2q^2+9q+2
       335: 2q^2+9q+2
       336: 5q+1
       337: q^2+11q+2
       338: q^2+8q+2
       339: 5q
       340: 2q^2+8q+2
       341: q^2+5q
       342: 2q^2+4q+1
       343: q^2+2q
       344: 4q^2+11q+2
       345: q^2+5q+2
       346: 2q^2+6q+2
       347: 3q+2
       348: 2q^2+8q+2
       349: q^2+5q+2
       350: 7q^2+12q+2
       351: 8q+2
       352: 4q^2+11q+2
       353: q^2+5q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: 7q^2+12q+2
       357: 3q+2
       358: 2q^2+8q+2
       359: 8q+2
       360: 3q+2
       362: q^2+3q+2
       364: 3q+2
       366: 5q^2+13q+2
       367: q^2+6q+2
       368: 3q^2+8q+2
       369: q^2+4q+2
       370: q^2+4q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       377: 4q+1
       378: 2q
       379: 2q
       380: 4q+1
       381: 2q+1
       384: 2q+1
       385: 3q+1
       386: q
       387: q
       388: 3q+1
       389: 3q+1
       390: q
       391: 3q+1
       392: q
       393: 2q+1
       394: q
       395: q
       396: 2q+1
       397: 3q+1
       398: q
       399: 3q+1
       400: q
       401: 2q+1
       402: q
       403: q
       404: 2q+1
       405: 2q+1
       406: 2q+1
       413: q^2+5q+2
       417: q^2+5q+2
       419: 4q+1
       420: 4q+1
       421: 4q+1
       422: 4q+1
       423: q^2+7q+2
       424: 2q
       425: 3q+1
       426: 2q
       427: q^2+7q+2
       428: 4q
       429: 3q+1
       430: 3q+1
       431: q^2+5q+1
       432: q^2+5q+1
       433: q^2+6q+2
       434: 2q
       435: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 3q+2
       443: 3q+1
       444: 3q+1
       445: 5q+2
       446: 3q
       447: q^2+5q+1
       448: q^2+5q+1
       449: 3q+1
       450: 3q+1
       451: q^2+6q+2
       452: 2q
       453: 2q+1
       454: 2q+1
       455: q+2
       457: q+1
       458: q+1
       459: 3q+2
       461: 3q+1
       462: 3q+1
       463: 5q+2
       464: 3q
       465: 2q+2
       467: 3q+2
       469: 3q^2+9q+2
       470: q^2+4q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q+2
       477: 5q+2
       479: 4q+2
       481: 4q+2
       482: 4q+2
       483: 3q+1
       484: 5q+2
       485: q+2
       487: q+2
       489: q+1
       491: 2q+1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: 3q+1
       496: 3q+2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: 3q+1
       501: 3q+2
       508: q^2+6q+2
       509: 2q+2
       510: 3q+2
       511: q+2
       512: q^2+4q+2
       513: q+2
       514: q^2+4q+2
       515: 6q+2
       516: q^2+6q+2
       517: q^2+3q+1
       518: q+2
       519: q+2
       520: q+1
       521: 2q+1
       524: 2q+1
       529: 3q+1
       530: q
       531: q
       532: 3q+1
       533: 2q+1
       534: q
       535: q
       536: 2q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 2q+1
       546: q
       547: 2q+1
       548: q
       549: 2q+1
       550: q
       551: q
       552: 2q+1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 2q+1
       562: q
       563: 2q+1
       564: q
       565: 1
       568: 1
       569: 2q+1
       570: 2q+1
       573: q+1
       575: q+1
       577: 3q+2
       578: q
       585: 2q+2
       589: 2q+1
       590: 2q+1
       595: 2q+1
       596: 2q+1
       597: 1
       599: 2q+1
       600: q
       601: q+2
       603: q+1
       604: q+1
       605: q+2
       607: 2q+1
       608: 2q+1
       609: 3q+2
       613: 2q+1
       614: q
       615: q+1
       616: q+1
       617: 2
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       623: q+2
       625: 3q+2
       629: 2q+1
       630: q
       631: q+1
       632: q+1
       633: 2
       639: 2q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q+2
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+4
       653: q+2
       655: q+2
       657: 5q+2
       658: q+2
       660: q+2
       662: q+1
       664: 2q+1
       665: q+1
       672: q+2
       673: 1
       674: 3q+2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: q+1
       680: 3q+2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: q+1
       686: 2q+2
       687: q+2
       688: q+2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       697: q+1
       709: q+1
       712: q+1
       721: 1
       723: 1
       725: q+1
       727: q+1
       733: 1
       735: 1
       737: 1
       739: 1
       741: q+1
       743: q+1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 2
       758: 2
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       771: 2
       775: q+2
       779: 1
       781: 1
       791: 1
       793: q+1
       794: q+1
       795: 2
       797: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       811: q+1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       821: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       835: q+1
       839: 1
       840: 1
       843: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+4
       851: q+2
       857: 2
       865: q+2
       866: q+1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       884: 1
       886: 1
       889: 1
       893: 1
       916: 1
       918: 1
       920: 1
       922: 1
       940: 1
       942: 1
       944: 1
       946: 1
       960: 2
       961: 2
       964: 1
       967: 1
       968: 2
       970: 2
       974: 1
       975: 1
       988: 1
       991: 1
       994: 1
      1008: 1
      1010: 2
      1012: 1
      1016: 1
      1017: 1
      1020: 1
      1022: 1
      1032: 1
      1033: 1
      1036: 1
      1038: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1088: 1
      1091: 1
      1095: 1
      1138: 1
      1140: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1220: 1
      1224: 1
      1230: 1
      1248: 1
      1283: 1
      1285: 1
      1436: 1

1437:    0: 24q^3+45q^2+17q+2
         1: 4q^4+26q^3+45q^2+17q+2
         2: 7q^4+24q^3+33q^2+16q+2
         3: 24q^3+45q^2+17q+2
         4: 7q^4+24q^3+33q^2+16q+2
         5: 4q^4+26q^3+45q^2+17q+2
         6: 2q^5+14q^4+32q^3+36q^2+16q+2
         7: q^5+7q^4+15q^3+24q^2+15q+2
         8: q^5+9q^4+25q^3+33q^2+16q+2
         9: q^5+7q^4+15q^3+24q^2+15q+2
        10: 12q^3+35q^2+16q+2
        11: 12q^3+35q^2+16q+2
        12: 4q^4+18q^3+27q^2+15q+2
        13: 14q^3+32q^2+16q+2
        14: 3q^4+11q^3+23q^2+15q+2
        15: 2q^4+15q^3+32q^2+16q+2
        16: 24q^3+45q^2+17q+2
        17: 4q^4+26q^3+45q^2+17q+2
        18: q^5+7q^4+15q^3+24q^2+15q+2
        19: 14q^3+32q^2+16q+2
        20: 3q^4+19q^3+35q^2+16q+2
        21: 3q^4+11q^3+23q^2+15q+2
        22: 13q^3+38q^2+17q+2
        23: 13q^3+38q^2+17q+2
        24: 3q^4+16q^3+28q^2+16q+2
        25: 13q^3+38q^2+17q+2
        26: 13q^3+38q^2+17q+2
        27: 3q^4+16q^3+28q^2+16q+2
        28: 12q^3+35q^2+16q+2
        29: 9q^3+26q^2+15q+2
        30: 7q^3+22q^2+15q+2
        31: 4q^3+28q^2+16q+2
        32: 8q^3+27q^2+16q+2
        33: 13q^3+38q^2+17q+2
        34: 4q^3+28q^2+16q+2
        35: 8q^3+27q^2+16q+2
        36: 13q^3+38q^2+17q+2
        37: 2q^3+10q^2+4q
        38: 4q^3+22q^2+13q+2
        39: 2q^3+10q^2+4q
        40: 4q^3+22q^2+13q+2
        41: q^4+4q^3+7q^2+4q
        42: 7q^3+17q^2+12q+2
        43: 5q^3+22q^2+15q+2
        44: q^4+7q^3+17q^2+14q+2
        45: 4q^3+22q^2+15q+2
        46: 14q^3+32q^2+16q+2
        47: 2q^4+15q^3+32q^2+16q+2
        48: 3q^4+11q^3+23q^2+15q+2
        49: 14q^3+32q^2+16q+2
        50: 3q^4+19q^3+35q^2+16q+2
        51: 3q^4+11q^3+23q^2+15q+2
        52: 6q^3+25q^2+16q+2
        53: 8q^3+28q^2+16q+2
        54: q^4+6q^3+18q^2+15q+2
        55: 6q^3+25q^2+16q+2
        56: 8q^3+28q^2+16q+2
        57: q^4+6q^3+18q^2+15q+2
        58: 2q^3+14q^2+8q+1
        59: 2q^3+14q^2+8q+1
        60: 2q^3+14q^2+8q+1
        61: 2q^3+14q^2+8q+1
        62: 6q^2+4q
        63: 16q^2+12q+2
        64: 2q^3+7q^2+4q
        65: 3q^3+16q^2+12q+2
        66: 2q^3+10q^2+4q
        67: 4q^3+22q^2+13q+2
        68: q^3+13q^2+14q+2
        69: 7q^3+22q^2+15q+2
        70: 4q^3+16q^2+14q+2
        71: 9q^3+26q^2+15q+2
        72: 3q^3+17q^2+15q+2
        73: 3q^3+17q^2+15q+2
        74: q^3+3q^2+4q
        75: 11q^2+12q+2
        76: 4q^2+4q
        77: q^3+13q^2+12q+2
        78: q^3+3q^2+4q
        79: q^3+9q^2+11q+2
        80: q^3+17q^2+15q+2
        81: 8q^3+27q^2+16q+2
        82: 3q^3+19q^2+15q+2
        83: 3q^3+17q^2+15q+2
        84: q^3+17q^2+15q+2
        85: 8q^3+27q^2+16q+2
        86: 3q^3+19q^2+15q+2
        87: 3q^3+17q^2+15q+2
        88: 5q^3+22q^2+15q+2
        89: 4q^3+22q^2+15q+2
        90: q^4+7q^3+17q^2+14q+2
        91: 3q^3+16q^2+15q+2
        92: q^4+8q^3+22q^2+15q+2
        93: 3q^3+16q^2+15q+2
        94: 6q^3+25q^2+16q+2
        95: 8q^3+28q^2+16q+2
        96: q^4+6q^3+18q^2+15q+2
        97: 6q^3+25q^2+16q+2
        98: 8q^3+28q^2+16q+2
        99: q^4+6q^3+18q^2+15q+2
       100: 13q^2+15q+2
       101: 2q^3+18q^2+15q+2
       102: q^3+10q^2+14q+2
       103: 3q^2+2q
       104: 8q^2+6q+1
       105: 8q^2+6q+1
       106: 3q^2+2q
       107: q^3+6q^2+7q+1
       108: q^3+6q^2+7q+1
       109: q^3+6q^2+7q+1
       110: q^3+6q^2+7q+1
       111: q^2+4q
       112: 7q^2+11q+2
       113: q^2+4q
       114: 8q^2+11q+2
       115: q^3+3q^2+4q
       116: 8q^2+11q+2
       117: 5q^2+7q+1
       118: 5q^2+7q+1
       119: 5q^2+7q+1
       120: 5q^2+7q+1
       121: 3q^2+4q
       122: 10q^2+11q+2
       123: 2q^3+7q^2+4q
       124: 3q^3+16q^2+12q+2
       125: q^3+13q^2+14q+2
       126: 4q^3+16q^2+14q+2
       127: q^3+3q^2+4q
       128: 11q^2+12q+2
       129: 4q^2+4q
       130: q^3+13q^2+12q+2
       131: q^3+3q^2+4q
       132: q^3+9q^2+11q+2
       133: 7q^2+13q+2
       134: 3q^3+16q^2+15q+2
       135: 9q^2+14q+2
       136: 9q^2+14q+2
       137: q^3+17q^2+15q+2
       138: 3q^3+17q^2+15q+2
       139: 3q^3+19q^2+15q+2
       140: 4q^2+9q+2
       141: q^3+11q^2+14q+2
       142: 3q^3+17q^2+15q+2
       143: q^3+17q^2+15q+2
       144: 3q^3+17q^2+15q+2
       145: 3q^3+19q^2+15q+2
       146: q^3+11q^2+14q+2
       147: 3q^3+17q^2+15q+2
       148: 4q^2+9q+2
       149: 9q^2+14q+2
       150: 9q^2+14q+2
       151: 2q^2+4q
       152: 6q^2+11q+2
       153: 4q^2+4q
       154: q^3+9q^2+11q+2
       155: 2q^2+4q
       156: 6q^2+10q+2
       157: q^3+6q^2+10q+2
       158: q^3+9q^2+10q+2
       159: q^3+6q^2+10q+2
       160: q^3+10q^2+13q+2
       161: 3q^3+15q^2+13q+2
       162: q^3+10q^2+13q+2
       163: q^3+10q^2+13q+2
       164: 3q^3+15q^2+13q+2
       165: q^3+10q^2+13q+2
       166: 13q^2+15q+2
       167: 2q^3+18q^2+15q+2
       168: q^3+10q^2+14q+2
       169: 2q
       170: 2q^2+5q+1
       171: 2q^2+5q+1
       172: 2q
       173: q^2+2q
       174: 3q^2+5q+1
       175: 3q^2+5q+1
       176: q^2+2q
       177: q^3+3q^2+4q
       178: 8q^2+11q+2
       179: q^2+4q
       180: 8q^2+11q+2
       181: q^2+4q
       182: 7q^2+11q+2
       183: q^2+6q+1
       184: q^2+6q+1
       185: q^2+6q+1
       186: q^2+6q+1
       187: q^2+4q
       188: 4q^2+10q+2
       189: q^2+4q
       190: 5q^2+10q+2
       191: 5q^2+7q+1
       192: 5q^2+7q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^3+6q^2+7q+1
       196: q^3+6q^2+7q+1
       197: 2q
       198: q^2+7q+2
       199: 5q^2+7q+1
       200: 5q^2+7q+1
       201: q^3+6q^2+7q+1
       202: q^3+6q^2+7q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: 2q
       206: q^2+7q+2
       207: 3q^2+4q
       208: 10q^2+11q+2
       209: q^2+4q
       210: 4q^2+10q+2
       211: 2q^2+4q
       212: 5q^2+10q+2
       214: 2q^2+6q+2
       216: 4q^2+6q+2
       218: 2q^2+6q+2
       219: 7q^2+13q+2
       220: 3q^2+9q+2
       221: q^3+6q^2+10q+2
       222: 2q^2+9q+2
       223: 9q^2+14q+2
       224: 2q^2+9q+2
       225: 9q^2+14q+2
       226: q^3+11q^2+14q+2
       227: 4q^2+11q+2
       228: q^3+10q^2+13q+2
       229: 2q^2+8q+2
       230: 7q^2+12q+2
       231: q^3+11q^2+14q+2
       232: 4q^2+11q+2
       233: q^3+10q^2+13q+2
       234: 7q^2+12q+2
       235: 2q^2+8q+2
       236: 9q^2+14q+2
       237: 2q^2+4q
       238: 6q^2+11q+2
       239: 4q^2+4q
       240: q^3+9q^2+11q+2
       241: 2q^2+4q
       242: 6q^2+10q+2
       243: 9q^2+14q+2
       244: 4q^2+9q+2
       245: 4q^2+9q+2
       246: 5q^2+13q+2
       247: q^2+13q+2
       248: 3q^2+13q+2
       249: 3q^2+6q+1
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q^2+8q+2
       257: q^3+7q^2+8q+2
       258: 3q^2+8q+2
       259: 2q
       260: 2q^2+5q+1
       261: 2q^2+5q+1
       262: 2q
       263: 2q
       264: 4q+1
       265: 4q+1
       266: 2q
       267: q
       268: 3q+1
       269: q
       270: 3q+1
       271: q
       272: 3q+1
       273: q
       274: 3q+1
       275: q^2+2q
       276: 3q^2+5q+1
       277: 3q^2+5q+1
       278: q^2+2q
       280: q^2+5q+2
       282: 2q^2+6q+2
       283: q^2+6q+1
       284: q^2+6q+1
       285: q^2+6q+1
       286: q^2+6q+1
       287: q^2+4q
       288: 5q^2+10q+2
       290: q^2+5q+2
       291: q^2+4q
       292: 4q^2+10q+2
       293: 4q+1
       294: 4q+1
       295: 4q+1
       296: 4q+1
       297: 2q
       298: q^2+7q+2
       299: 3q+1
       300: 3q+1
       301: 2q
       302: q^2+7q+2
       303: q^2+5q+1
       304: q^2+5q+1
       305: 2q
       306: q^2+6q+2
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       311: 2q
       312: q^2+7q+2
       313: 2q
       314: q^2+6q+2
       315: 2q^2+4q
       316: 5q^2+10q+2
       317: q^2+4q
       318: 4q^2+10q+2
       319: q^2+4q+1
       320: q^2+4q+1
       321: q^2+4q+1
       322: q^2+4q+1
       324: 5q+2
       325: q^2+4q
       326: 3q^2+9q+2
       333: 3q^2+9q+2
       334: 2q^2+9q+2
       335: 2q^2+9q+2
       336: 5q+1
       337: q^2+11q+2
       338: 5q
       339: q^2+8q+2
       340: q^2+5q
       341: 2q^2+8q+2
       342: q^2+2q
       343: 2q^2+4q+1
       344: 4q^2+11q+2
       345: q^2+5q+2
       346: 2q^2+6q+2
       347: 3q+2
       348: 2q^2+8q+2
       349: q^2+5q+2
       350: 7q^2+12q+2
       351: 8q+2
       352: 4q^2+11q+2
       353: q^2+5q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: 7q^2+12q+2
       357: 3q+2
       358: 2q^2+8q+2
       359: 8q+2
       361: 3q+2
       363: q^2+3q+2
       365: 3q+2
       366: 5q^2+13q+2
       367: q^2+6q+2
       368: 3q^2+8q+2
       369: q^2+4q+2
       370: q^2+4q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       377: 2q
       378: 4q+1
       379: 4q+1
       380: 2q
       382: 2q+1
       383: 2q+1
       385: q
       386: 3q+1
       387: 3q+1
       388: q
       389: q
       390: 3q+1
       391: q
       392: 3q+1
       393: q
       394: 2q+1
       395: 2q+1
       396: q
       397: q
       398: 3q+1
       399: q
       400: 3q+1
       401: q
       402: 2q+1
       403: 2q+1
       404: q
       407: 2q+1
       408: 2q+1
       414: q^2+5q+2
       418: q^2+5q+2
       419: 4q+1
       420: 4q+1
       421: 4q+1
       422: 4q+1
       423: 2q
       424: q^2+7q+2
       425: 2q
       426: 3q+1
       427: 4q
       428: q^2+7q+2
       429: 3q+1
       430: 3q+1
       431: q^2+5q+1
       432: q^2+5q+1
       433: 2q
       434: q^2+6q+2
       436: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 3q+2
       443: 3q+1
       444: 3q+1
       445: 3q
       446: 5q+2
       447: q^2+5q+1
       448: q^2+5q+1
       449: 3q+1
       450: 3q+1
       451: 2q
       452: q^2+6q+2
       453: 2q+1
       454: 2q+1
       456: q+2
       457: q+1
       458: q+1
       460: 3q+2
       461: 3q+1
       462: 3q+1
       463: 3q
       464: 5q+2
       466: 2q+2
       468: 3q+2
       469: q^2+4q
       470: 3q^2+9q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: 2q+2
       478: 5q+2
       480: 4q+2
       481: 4q+2
       482: 4q+2
       483: 3q+1
       484: 5q+2
       486: q+2
       488: q+2
       490: q+1
       491: 2q+1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: 3q+1
       496: 3q+2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: 3q+1
       501: 3q+2
       508: q^2+6q+2
       509: 2q+2
       510: 3q+2
       511: q+2
       512: q^2+4q+2
       513: q+2
       514: q^2+4q+2
       515: 6q+2
       516: q^2+6q+2
       517: q^2+3q+1
       518: q+2
       519: q+2
       520: q+1
       522: 2q+1
       523: 2q+1
       529: q
       530: 3q+1
       531: 3q+1
       532: q
       533: q
       534: 2q+1
       535: 2q+1
       536: q
       538: 1
       540: 1
       542: q+1
       544: q+1
       545: q
       546: 2q+1
       547: q
       548: 2q+1
       549: q
       550: 2q+1
       551: 2q+1
       552: q
       554: 1
       556: 1
       558: q+1
       560: q+1
       561: q
       562: 2q+1
       563: q
       564: 2q+1
       566: 1
       567: 1
       571: 2q+1
       572: 2q+1
       574: q+1
       576: q+1
       580: q
       581: 3q+2
       586: 2q+2
       589: 2q+1
       590: 2q+1
       595: 2q+1
       596: 2q+1
       598: 1
       599: q
       600: 2q+1
       602: q+2
       603: q+1
       604: q+1
       606: q+2
       607: 2q+1
       608: 2q+1
       610: 3q+2
       613: q
       614: 2q+1
       615: q+1
       616: q+1
       618: 2
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       624: q+2
       626: 3q+2
       629: q
       630: 2q+1
       631: q+1
       632: q+1
       634: 2
       640: 2q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: 2q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+4
       654: q+2
       656: q+2
       657: 5q+2
       659: q+2
       661: q+2
       663: q+1
       664: 2q+1
       665: q+1
       672: q+2
       673: 1
       674: 3q+2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: q+1
       680: 3q+2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: q+1
       686: 2q+2
       687: q+2
       688: q+2
       690: q+2
       691: q+2
       692: q+1
       699: q+1
       700: q+1
       710: q+1
       711: q+1
       722: 1
       724: 1
       726: q+1
       728: q+1
       734: 1
       736: 1
       738: 1
       740: 1
       742: q+1
       744: q+1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 2
       760: 2
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       774: 2
       776: q+2
       780: 1
       782: 1
       792: 1
       793: q+1
       794: q+1
       796: 2
       798: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       810: 1
       812: q+1
       815: 1
       816: 1
       817: q+1
       818: q+1
       820: 2
       822: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       834: 1
       836: q+1
       839: 1
       840: 1
       844: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+4
       852: q+2
       858: 2
       865: q+2
       866: q+1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       890: 1
       891: 1
       894: 1
       895: 1
       917: 1
       919: 1
       921: 1
       923: 1
       941: 1
       943: 1
       945: 1
       947: 1
       962: 2
       963: 2
       965: 1
       966: 1
       972: 2
       973: 2
       976: 1
       977: 1
       989: 1
       990: 1
       995: 1
      1009: 1
      1011: 2
      1013: 1
      1016: 1
      1017: 1
      1021: 1
      1023: 1
      1032: 1
      1033: 1
      1037: 1
      1039: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1142: 1
      1143: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1221: 1
      1225: 1
      1231: 1
      1249: 1
      1283: 1
      1285: 1
      1437: 1

1438:    0: q^2+q+2
         1: q^2+q+2
         2: q^2+q+2
         3: q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: q^2+q+2
        11: q^2+q+2
        12: q^2+q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+q+2
        17: q^2+q+2
        18: q^2+q+2
        19: q^2+q+2
        20: q^2+q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: q^2+q+2
        29: q^2+q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        37: 2
        39: 2
        41: 2
        43: q^2+q+2
        44: q^2+q+2
        45: q^2+q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^2+q+2
        50: q^2+q+2
        51: q^2+q+2
        52: 2
        53: 2
        54: 2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 2
        66: 2
        68: q^2+q+2
        69: q^2+q+2
        70: q^2+q+2
        71: q^2+q+2
        72: 2
        73: 2
        74: 2
        76: 2
        78: 2
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q^2+q+2
        89: q^2+q+2
        90: q^2+q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: 2
        95: 2
        96: 2
        97: 2
        98: 2
        99: 2
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 2
       117: 1
       118: 1
       119: 1
       120: 1
       121: 2
       123: 2
       125: q^2+q+2
       126: q^2+q+2
       127: 2
       129: 2
       131: 2
       133: q^2+q+2
       134: q^2+q+2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+2
       158: q^2+q+2
       159: q^2+q+2
       160: 2
       161: 2
       162: 2
       163: 2
       164: 2
       165: 2
       166: 1
       167: 1
       168: 1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 2
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: 1
       211: 1
       213: 2
       215: 2
       217: 2
       219: q^2+q+2
       220: q^2+q+2
       221: q^2+q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: 2
       253: 2
       254: 2
       255: 2
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       263: 1
       266: 1
       275: 1
       278: 1
       279: 2
       281: 2
       283: 1
       284: 1
       285: 1
       286: 1
       287: 2
       289: 2
       291: 2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: 1
       308: 1
       315: 1
       317: 1
       325: 1
       327: 2
       329: 2
       331: 2
       333: q^2+q+2
       334: 2
       335: 2
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 2
       345: 2
       346: 2
       349: 2
       350: 2
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       409: 2
       411: 2
       413: 2
       415: 2
       417: 2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       465: 1
       467: 1
       469: 1
       481: 2
       482: 2
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 2
       494: 2
       497: 2
       498: 2
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       583: 2
       585: 2
       587: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 1
       607: 1
       608: 1
       619: 1
       620: 1
       635: 1
       637: 1
       639: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       705: 1
       708: 1
       709: 1
       712: 1
       775: 1
       777: 2
       779: 1
       781: 1
       783: 1
       789: 1
       807: 1
       808: 1
       825: 1
       826: 1
       841: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       881: 1
       882: 1
       883: 1
       896: 1
       899: 1
       992: 1
       994: 1
       996: 1
      1002: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1210: 1
      1212: 1
      1214: 1
      1282: 1
      1438: 1

1439:    0: q^2+q+2
         1: q^2+q+2
         2: q^2+q+2
         3: q^2+q+2
         4: q^2+q+2
         5: q^2+q+2
         6: q^2+q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: q^2+q+2
        11: q^2+q+2
        12: q^2+q+2
        13: q^2+q+2
        14: q^2+q+2
        15: q^2+q+2
        16: q^2+q+2
        17: q^2+q+2
        18: q^2+q+2
        19: q^2+q+2
        20: q^2+q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: 2
        26: 2
        27: 2
        28: q^2+q+2
        29: q^2+q+2
        30: q^2+q+2
        31: 2
        32: 2
        33: 2
        34: 2
        35: 2
        36: 2
        38: 2
        40: 2
        42: 2
        43: q^2+q+2
        44: q^2+q+2
        45: q^2+q+2
        46: q^2+q+2
        47: q^2+q+2
        48: q^2+q+2
        49: q^2+q+2
        50: q^2+q+2
        51: q^2+q+2
        52: 2
        53: 2
        54: 2
        55: 2
        56: 2
        57: 2
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 2
        67: 2
        68: q^2+q+2
        69: q^2+q+2
        70: q^2+q+2
        71: q^2+q+2
        72: 2
        73: 2
        75: 2
        77: 2
        79: 2
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q^2+q+2
        89: q^2+q+2
        90: q^2+q+2
        91: q^2+q+2
        92: q^2+q+2
        93: q^2+q+2
        94: 2
        95: 2
        96: 2
        97: 2
        98: 2
        99: 2
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 2
       117: 1
       118: 1
       119: 1
       120: 1
       122: 2
       124: 2
       125: q^2+q+2
       126: q^2+q+2
       128: 2
       130: 2
       132: 2
       133: q^2+q+2
       134: q^2+q+2
       135: 2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+2
       158: q^2+q+2
       159: q^2+q+2
       160: 2
       161: 2
       162: 2
       163: 2
       164: 2
       165: 2
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 2
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: 2
       191: 1
       192: 1
       195: 1
       196: 1
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: 1
       212: 1
       214: 2
       216: 2
       218: 2
       219: q^2+q+2
       220: q^2+q+2
       221: q^2+q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 2
       251: 2
       252: 2
       253: 2
       254: 2
       255: 2
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       264: 1
       265: 1
       276: 1
       277: 1
       280: 2
       282: 2
       283: 1
       284: 1
       285: 1
       286: 1
       288: 2
       290: 2
       292: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: 1
       308: 1
       316: 1
       318: 1
       326: 1
       328: 2
       330: 2
       332: 2
       333: q^2+q+2
       334: 2
       335: 2
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 2
       345: 2
       346: 2
       349: 2
       350: 2
       352: 2
       353: 2
       354: 2
       355: 2
       356: 2
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       410: 2
       412: 2
       414: 2
       416: 2
       418: 2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 1
       431: 1
       432: 1
       439: 1
       440: 1
       447: 1
       448: 1
       453: 1
       454: 1
       466: 1
       468: 1
       470: 1
       481: 2
       482: 2
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 2
       494: 2
       497: 2
       498: 2
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       584: 2
       586: 2
       588: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 1
       607: 1
       608: 1
       619: 1
       620: 1
       636: 1
       638: 1
       640: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 2
       681: 2
       686: 1
       690: 1
       691: 1
       692: 1
       706: 1
       707: 1
       710: 1
       711: 1
       776: 1
       778: 2
       780: 1
       782: 1
       784: 1
       790: 1
       807: 1
       808: 1
       825: 1
       826: 1
       842: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       881: 1
       882: 1
       883: 1
       897: 1
       898: 1
       993: 1
       995: 1
       997: 1
      1003: 1
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1211: 1
      1213: 1
      1215: 1
      1282: 1
      1439: 1

1440:    0: 3q^3+15q^2+10q+2
         1: q^4+8q^3+15q^2+10q+2
         2: 3q^3+15q^2+10q+2
         3: q^4+8q^3+15q^2+10q+2
         4: 3q^3+15q^2+10q+2
         5: q^4+8q^3+15q^2+10q+2
         6: q^4+8q^3+15q^2+10q+2
         7: 3q^3+15q^2+10q+2
         8: q^4+8q^3+15q^2+10q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 2q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 2q^3+12q^2+10q+2
        13: 3q^3+15q^2+10q+2
        14: 3q^3+15q^2+10q+2
        15: q^4+8q^3+15q^2+10q+2
        16: 2q^3+12q^2+10q+2
        17: 4q^3+12q^2+10q+2
        18: 2q^3+9q^2+7q+2
        19: 3q^3+15q^2+10q+2
        20: q^4+8q^3+15q^2+10q+2
        21: 3q^3+15q^2+10q+2
        22: 7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: 7q^2+8q+2
        25: 2q^3+12q^2+10q+2
        26: 4q^3+12q^2+10q+2
        27: 2q^3+12q^2+10q+2
        28: q^3+9q^2+10q+2
        29: 2q^3+12q^2+10q+2
        30: 3q^3+15q^2+10q+2
        31: 5q^2+8q+2
        32: 7q^2+8q+2
        33: 5q^2+8q+2
        34: q^3+9q^2+10q+2
        35: 2q^3+12q^2+10q+2
        36: q^3+9q^2+10q+2
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+12q^2+10q+2
        44: 2q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: 2q^3+12q^2+10q+2
        47: 4q^3+12q^2+10q+2
        48: 2q^3+9q^2+7q+2
        49: 2q^3+12q^2+10q+2
        50: 4q^3+12q^2+10q+2
        51: 2q^3+9q^2+7q+2
        52: 7q^2+8q+2
        53: q^3+7q^2+8q+2
        54: 7q^2+8q+2
        55: 2q^3+12q^2+10q+2
        56: 4q^3+12q^2+10q+2
        57: 2q^3+12q^2+10q+2
        58: 3q^2+6q+2
        59: 2q
        60: 3q^2+5q+1
        61: 3q^2+5q+1
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 2q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: q^3+9q^2+10q+2
        73: 5q^2+8q+2
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: 3q^2+4q+1
        77: 3q^2+4q+1
        78: 3q^2+4q+1
        79: 3q^2+4q+1
        80: 5q^2+8q+2
        81: 5q^2+8q+2
        82: 5q^2+8q+2
        83: 7q^2+8q+2
        84: q^3+9q^2+10q+2
        85: q^3+9q^2+10q+2
        86: q^3+9q^2+10q+2
        87: 2q^3+12q^2+10q+2
        88: 6q^2+10q+2
        89: 6q^2+10q+2
        90: q^3+6q^2+7q+2
        91: 2q^3+12q^2+10q+2
        92: 4q^3+12q^2+10q+2
        93: 2q^3+9q^2+7q+2
        94: 2q^2+7q+2
        95: 2q^2+7q+2
        96: 3q^2+5q+2
        97: 6q^2+10q+2
        98: 6q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q^2+3q+1
       104: q
       105: q^2+3q+1
       106: q
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: 3q^2+6q+2
       110: 2q
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: 3q^2+4q+1
       116: 3q^2+4q+1
       117: 3q^2+6q+2
       118: 2q
       119: 3q^2+5q+1
       120: 3q^2+5q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: 6q^2+10q+2
       126: 3q^2+7q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: q^3+9q^2+10q+2
       136: 5q^2+8q+2
       137: 2q^2+8q+2
       138: q^2+5q+2
       139: q^2+7q+2
       141: 5q^2+8q+2
       142: 2q^2+7q+2
       143: 4q^2+10q+2
       144: 3q^2+7q+2
       145: 4q^2+10q+2
       146: q^3+9q^2+10q+2
       147: 6q^2+10q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 2q^2+6q+2
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 6q^2+10q+2
       158: 6q^2+10q+2
       159: q^3+6q^2+7q+2
       160: 2q^2+7q+2
       161: 2q^2+7q+2
       162: 3q^2+5q+2
       163: 6q^2+10q+2
       164: 6q^2+10q+2
       165: q^3+6q^2+7q+2
       166: 5q+2
       167: q^2+5q+2
       168: 3q+2
       169: q^2+3q+1
       170: q
       171: q^2+3q+1
       172: q
       173: q^2+3q+1
       174: q
       175: q^2+3q+1
       176: q
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: 3q^2+6q+2
       186: 2q
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: 2q^2+4q+1
       190: 2q^2+4q+1
       191: 2q^2+6q+2
       192: 2q
       195: q^2+5q+2
       196: 2q
       199: 2q^2+5q+1
       200: 2q^2+5q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       203: 4q+2
       205: 2q+1
       206: 2q+1
       207: q^2+4q+1
       208: q^2+4q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: 3q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: 3q^2+7q+2
       220: 6q^2+10q+2
       221: 3q^2+7q+2
       222: 4q^2+10q+2
       223: 3q^2+7q+2
       224: 2q^2+8q+2
       225: q^2+5q+2
       226: 5q+2
       227: q^2+7q+2
       228: q^2+5q+2
       230: 2q^2+7q+2
       231: q^2+7q+2
       232: 4q^2+10q+2
       233: 3q^2+7q+2
       234: 6q^2+10q+2
       235: 4q+2
       236: 3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 5q+2
       245: 3q+2
       246: 2q^2+6q+2
       247: 5q+2
       248: q^2+5q+2
       249: 3q+2
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 6q+2
       254: 6q+2
       255: 2q^2+4q+2
       256: 5q+2
       257: q^2+5q+2
       258: 3q+2
       259: 2q+1
       260: q
       261: 2q+1
       262: q
       263: q^2+3q+1
       264: q
       265: q^2+3q+1
       266: q
       271: 2q+1
       272: 2q+1
       275: q^2+3q+1
       276: q
       277: q^2+3q+1
       278: q
       279: 3q+1
       280: 3q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 3q+2
       287: 2q+1
       288: 2q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q^2+5q+1
       294: 2q^2+5q+1
       295: 2q^2+6q+2
       296: 2q
       297: q^2+4q+1
       298: q^2+4q+1
       303: q^2+5q+2
       304: 2q
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       309: 4q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       321: 3q+2
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q^2+7q+2
       334: q^2+7q+2
       335: 5q+2
       336: 3q+2
       337: 5q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 5q+2
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: q^2+5q+2
       352: q^2+7q+2
       353: 6q+2
       354: 4q+2
       355: 6q+2
       356: 3q^2+7q+2
       357: 2q+2
       358: q+2
       359: 3q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 5q+2
       368: 3q+2
       370: 3q+2
       371: 5q+2
       372: q^2+5q+2
       373: 3q+2
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       379: q+1
       381: 2q+1
       382: q
       383: 2q+1
       384: q
       385: q^2+3q+1
       386: q
       387: q^2+3q+1
       388: q
       397: q+1
       398: q+1
       401: 2q+1
       402: 2q+1
       413: 2q+1
       414: 2q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       421: 3q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       431: 3q+2
       439: 2q+1
       440: q
       447: 2q+1
       448: 2q+1
       449: q+2
       451: 1
       452: 1
       453: 3q+1
       454: 3q+1
       455: q+1
       456: q+1
       457: 2q+2
       459: q+1
       460: q+1
       461: 3q+2
       463: q+1
       464: q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       473: 3q+2
       481: q^2+7q+2
       482: 5q+2
       483: 3q+2
       484: 5q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q+1
       490: q+1
       491: 3q+2
       492: 2q+1
       494: 2q+1
       497: 4q+2
       498: 4q+2
       499: 2
       500: q+2
       501: 3q+2
       508: 3q+2
       509: 2q+1
       510: q+1
       513: q+1
       514: q+2
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       523: q+1
       529: q+1
       531: q+1
       549: 1
       550: 1
       553: q+1
       554: q+1
       557: q+1
       558: q+1
       561: q+1
       562: q+1
       585: 2q+1
       586: 2q+1
       589: 2q+1
       590: 2q+1
       591: q+2
       595: 3q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       607: q+1
       619: q+1
       620: q+1
       621: 2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 3q+2
       633: q+1
       634: q+1
       639: q+1
       640: q+1
       643: q+2
       649: q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+2
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 2
       681: 4q+2
       682: 2
       683: 2
       684: q+1
       685: q+2
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       709: q+1
       711: q+1
       713: 1
       714: 1
       737: 1
       738: 1
       741: 1
       742: 1
       749: q+1
       750: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       787: q+2
       807: q+1
       817: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: q+1
       826: q+1
       827: 2
       831: 2
       833: 1
       834: 1
       835: 1
       836: 1
       839: q+1
       847: 1
       865: 1
       866: 2
       867: 1
       868: q+1
       873: 1
       874: 2
       875: 2
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       900: 1
       901: 1
       940: 1
       941: 1
       944: 1
       945: 1
       948: 1
       949: 1
       994: 1
       995: 1
       998: 2
      1006: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1044: 2
      1058: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1114: 1
      1115: 1
      1172: 1
      1173: 1
      1216: 1
      1246: 1
      1260: 1
      1282: 1
      1286: 1
      1440: 1

1441:    0: 3q^3+15q^2+10q+2
         1: q^4+8q^3+15q^2+10q+2
         2: 3q^3+15q^2+10q+2
         3: q^4+8q^3+15q^2+10q+2
         4: 3q^3+15q^2+10q+2
         5: q^4+8q^3+15q^2+10q+2
         6: q^4+8q^3+15q^2+10q+2
         7: 3q^3+15q^2+10q+2
         8: q^4+8q^3+15q^2+10q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 2q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 2q^3+12q^2+10q+2
        13: 3q^3+15q^2+10q+2
        14: 3q^3+15q^2+10q+2
        15: q^4+8q^3+15q^2+10q+2
        16: 2q^3+12q^2+10q+2
        17: 4q^3+12q^2+10q+2
        18: 2q^3+9q^2+7q+2
        19: 3q^3+15q^2+10q+2
        20: q^4+8q^3+15q^2+10q+2
        21: 3q^3+15q^2+10q+2
        22: 7q^2+8q+2
        23: q^3+7q^2+8q+2
        24: 7q^2+8q+2
        25: 2q^3+12q^2+10q+2
        26: 4q^3+12q^2+10q+2
        27: 2q^3+12q^2+10q+2
        28: q^3+9q^2+10q+2
        29: 2q^3+12q^2+10q+2
        30: 3q^3+15q^2+10q+2
        31: 5q^2+8q+2
        32: 7q^2+8q+2
        33: 5q^2+8q+2
        34: q^3+9q^2+10q+2
        35: 2q^3+12q^2+10q+2
        36: q^3+9q^2+10q+2
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+12q^2+10q+2
        44: 2q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: 2q^3+12q^2+10q+2
        47: 4q^3+12q^2+10q+2
        48: 2q^3+9q^2+7q+2
        49: 2q^3+12q^2+10q+2
        50: 4q^3+12q^2+10q+2
        51: 2q^3+9q^2+7q+2
        52: 7q^2+8q+2
        53: q^3+7q^2+8q+2
        54: 7q^2+8q+2
        55: 2q^3+12q^2+10q+2
        56: 4q^3+12q^2+10q+2
        57: 2q^3+12q^2+10q+2
        58: 2q
        59: 3q^2+6q+2
        60: 3q^2+5q+1
        61: 3q^2+5q+1
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 2q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: q^3+9q^2+10q+2
        73: 5q^2+8q+2
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: 3q^2+4q+1
        77: 3q^2+4q+1
        78: 3q^2+4q+1
        79: 3q^2+4q+1
        80: 5q^2+8q+2
        81: 5q^2+8q+2
        82: 5q^2+8q+2
        83: 7q^2+8q+2
        84: q^3+9q^2+10q+2
        85: q^3+9q^2+10q+2
        86: q^3+9q^2+10q+2
        87: 2q^3+12q^2+10q+2
        88: 6q^2+10q+2
        89: 6q^2+10q+2
        90: q^3+6q^2+7q+2
        91: 2q^3+12q^2+10q+2
        92: 4q^3+12q^2+10q+2
        93: 2q^3+9q^2+7q+2
        94: 2q^2+7q+2
        95: 2q^2+7q+2
        96: 3q^2+5q+2
        97: 6q^2+10q+2
        98: 6q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q
       104: q^2+3q+1
       105: q
       106: q^2+3q+1
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: 2q
       110: 3q^2+6q+2
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: 3q^2+4q+1
       116: 3q^2+4q+1
       117: 2q
       118: 3q^2+6q+2
       119: 3q^2+5q+1
       120: 3q^2+5q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: 6q^2+10q+2
       126: 3q^2+7q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: q^3+9q^2+10q+2
       136: 5q^2+8q+2
       137: 2q^2+8q+2
       138: q^2+5q+2
       139: q^2+7q+2
       141: 5q^2+8q+2
       142: 2q^2+7q+2
       143: 4q^2+10q+2
       144: 3q^2+7q+2
       145: 4q^2+10q+2
       146: q^3+9q^2+10q+2
       147: 6q^2+10q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 2q^2+6q+2
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 6q^2+10q+2
       158: 6q^2+10q+2
       159: q^3+6q^2+7q+2
       160: 2q^2+7q+2
       161: 2q^2+7q+2
       162: 3q^2+5q+2
       163: 6q^2+10q+2
       164: 6q^2+10q+2
       165: q^3+6q^2+7q+2
       166: 5q+2
       167: q^2+5q+2
       168: 3q+2
       169: q
       170: q^2+3q+1
       171: q
       172: q^2+3q+1
       173: q
       174: q^2+3q+1
       175: q
       176: q^2+3q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: 2q
       186: 3q^2+6q+2
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: 2q^2+4q+1
       190: 2q^2+4q+1
       191: 2q
       192: 2q^2+6q+2
       195: 2q
       196: q^2+5q+2
       199: 2q^2+5q+1
       200: 2q^2+5q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       204: 4q+2
       205: 2q+1
       206: 2q+1
       207: q^2+4q+1
       208: q^2+4q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: 3q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: 3q^2+7q+2
       220: 6q^2+10q+2
       221: 3q^2+7q+2
       222: 4q^2+10q+2
       223: 3q^2+7q+2
       224: 2q^2+8q+2
       225: q^2+5q+2
       226: 5q+2
       227: q^2+7q+2
       228: q^2+5q+2
       230: 2q^2+7q+2
       231: q^2+7q+2
       232: 4q^2+10q+2
       233: 3q^2+7q+2
       234: 6q^2+10q+2
       235: 4q+2
       236: 3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 5q+2
       245: 3q+2
       246: 2q^2+6q+2
       247: 5q+2
       248: q^2+5q+2
       249: 3q+2
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 6q+2
       254: 6q+2
       255: 2q^2+4q+2
       256: 5q+2
       257: q^2+5q+2
       258: 3q+2
       259: q
       260: 2q+1
       261: q
       262: 2q+1
       263: q
       264: q^2+3q+1
       265: q
       266: q^2+3q+1
       273: 2q+1
       274: 2q+1
       275: q
       276: q^2+3q+1
       277: q
       278: q^2+3q+1
       279: 3q+1
       280: 3q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       286: 3q+2
       287: 2q+1
       288: 2q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q^2+5q+1
       294: 2q^2+5q+1
       295: 2q
       296: 2q^2+6q+2
       297: q^2+4q+1
       298: q^2+4q+1
       303: 2q
       304: q^2+5q+2
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       310: 4q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       322: 3q+2
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q^2+7q+2
       334: q^2+7q+2
       335: 5q+2
       336: 3q+2
       337: 5q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: 5q+2
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: q^2+5q+2
       352: q^2+7q+2
       353: 6q+2
       354: 4q+2
       355: 6q+2
       356: 3q^2+7q+2
       357: 2q+2
       358: q+2
       359: 3q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 5q+2
       368: 3q+2
       370: 3q+2
       371: 5q+2
       372: q^2+5q+2
       373: 3q+2
       374: 2q+1
       375: 2q+1
       376: q+1
       378: q+1
       380: q+1
       381: q
       382: 2q+1
       383: q
       384: 2q+1
       385: q
       386: q^2+3q+1
       387: q
       388: q^2+3q+1
       399: q+1
       400: q+1
       403: 2q+1
       404: 2q+1
       413: 2q+1
       414: 2q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       422: 3q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       432: 3q+2
       439: q
       440: 2q+1
       447: 2q+1
       448: 2q+1
       450: q+2
       451: 1
       452: 1
       453: 3q+1
       454: 3q+1
       455: q+1
       456: q+1
       458: 2q+2
       459: q+1
       460: q+1
       462: 3q+2
       463: q+1
       464: q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       474: 3q+2
       481: q^2+7q+2
       482: 5q+2
       483: 3q+2
       484: 5q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q+1
       490: q+1
       491: 3q+2
       492: 2q+1
       494: 2q+1
       497: 4q+2
       498: 4q+2
       499: 2
       500: q+2
       501: 3q+2
       508: 3q+2
       509: 2q+1
       510: q+1
       513: q+1
       514: q+2
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       522: q+1
       524: q+1
       530: q+1
       532: q+1
       551: 1
       552: 1
       555: q+1
       556: q+1
       559: q+1
       560: q+1
       563: q+1
       564: q+1
       585: 2q+1
       586: 2q+1
       589: 2q+1
       590: 2q+1
       592: q+2
       596: 3q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       608: q+1
       619: q+1
       620: q+1
       622: 2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       632: 3q+2
       633: q+1
       634: q+1
       639: q+1
       640: q+1
       644: q+2
       650: q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+2
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 2
       681: 4q+2
       682: 2
       683: 2
       684: q+1
       685: q+2
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       710: q+1
       712: q+1
       715: 1
       716: 1
       739: 1
       740: 1
       743: 1
       744: 1
       751: q+1
       752: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       788: q+2
       808: q+1
       818: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: q+1
       826: q+1
       828: 2
       832: 2
       833: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       848: 1
       865: 1
       866: 2
       867: 1
       868: q+1
       873: 1
       874: 2
       875: 2
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       902: 1
       903: 1
       942: 1
       943: 1
       946: 1
       947: 1
       950: 1
       951: 1
       994: 1
       995: 1
       999: 2
      1007: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1045: 2
      1059: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1116: 1
      1117: 1
      1174: 1
      1175: 1
      1217: 1
      1247: 1
      1261: 1
      1282: 1
      1286: 1
      1441: 1

1442:    0: 3q^3+15q^2+10q+2
         1: q^4+8q^3+15q^2+10q+2
         2: 3q^3+15q^2+10q+2
         3: q^4+8q^3+15q^2+10q+2
         4: 3q^3+15q^2+10q+2
         5: q^4+8q^3+15q^2+10q+2
         6: q^4+8q^3+15q^2+10q+2
         7: 3q^3+15q^2+10q+2
         8: q^4+8q^3+15q^2+10q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 2q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 2q^3+12q^2+10q+2
        13: 3q^3+15q^2+10q+2
        14: 3q^3+15q^2+10q+2
        15: q^4+8q^3+15q^2+10q+2
        16: 2q^3+12q^2+10q+2
        17: 4q^3+12q^2+10q+2
        18: 2q^3+9q^2+7q+2
        19: 3q^3+15q^2+10q+2
        20: q^4+8q^3+15q^2+10q+2
        21: 3q^3+15q^2+10q+2
        22: 2q^3+12q^2+10q+2
        23: 4q^3+12q^2+10q+2
        24: 2q^3+12q^2+10q+2
        25: 7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: 7q^2+8q+2
        28: q^3+9q^2+10q+2
        29: 2q^3+12q^2+10q+2
        30: 3q^3+15q^2+10q+2
        31: q^3+9q^2+10q+2
        32: 2q^3+12q^2+10q+2
        33: q^3+9q^2+10q+2
        34: 5q^2+8q+2
        35: 7q^2+8q+2
        36: 5q^2+8q+2
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+12q^2+10q+2
        44: 2q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: 2q^3+12q^2+10q+2
        47: 4q^3+12q^2+10q+2
        48: 2q^3+9q^2+7q+2
        49: 2q^3+12q^2+10q+2
        50: 4q^3+12q^2+10q+2
        51: 2q^3+9q^2+7q+2
        52: 2q^3+12q^2+10q+2
        53: 4q^3+12q^2+10q+2
        54: 2q^3+12q^2+10q+2
        55: 7q^2+8q+2
        56: q^3+7q^2+8q+2
        57: 7q^2+8q+2
        58: 3q^2+5q+1
        59: 3q^2+5q+1
        60: 3q^2+6q+2
        61: 2q
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 2q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: 5q^2+8q+2
        73: q^3+9q^2+10q+2
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: 3q^2+4q+1
        77: 3q^2+4q+1
        78: 3q^2+4q+1
        79: 3q^2+4q+1
        80: q^3+9q^2+10q+2
        81: q^3+9q^2+10q+2
        82: q^3+9q^2+10q+2
        83: 2q^3+12q^2+10q+2
        84: 5q^2+8q+2
        85: 5q^2+8q+2
        86: 5q^2+8q+2
        87: 7q^2+8q+2
        88: 6q^2+10q+2
        89: 6q^2+10q+2
        90: q^3+6q^2+7q+2
        91: 2q^3+12q^2+10q+2
        92: 4q^3+12q^2+10q+2
        93: 2q^3+9q^2+7q+2
        94: 6q^2+10q+2
        95: 6q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 2q^2+7q+2
        98: 2q^2+7q+2
        99: 3q^2+5q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q^2+3q+1
       104: q^2+3q+1
       105: q
       106: q
       107: 3q^2+6q+2
       108: 2q
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: 3q^2+4q+1
       116: 3q^2+4q+1
       117: 3q^2+5q+1
       118: 3q^2+5q+1
       119: 3q^2+6q+2
       120: 2q
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: 6q^2+10q+2
       126: 3q^2+7q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: 5q^2+8q+2
       136: q^3+9q^2+10q+2
       137: 4q^2+10q+2
       138: 3q^2+7q+2
       139: 4q^2+10q+2
       140: 4q+2
       141: q^3+9q^2+10q+2
       142: 6q^2+10q+2
       143: 2q^2+8q+2
       144: q^2+5q+2
       145: q^2+7q+2
       146: 5q^2+8q+2
       147: 2q^2+7q+2
       149: 2q^2+6q+2
       150: 2q^2+6q+2
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 6q^2+10q+2
       158: 6q^2+10q+2
       159: q^3+6q^2+7q+2
       160: 6q^2+10q+2
       161: 6q^2+10q+2
       162: q^3+6q^2+7q+2
       163: 2q^2+7q+2
       164: 2q^2+7q+2
       165: 3q^2+5q+2
       166: 5q+2
       167: q^2+5q+2
       168: 3q+2
       169: q^2+3q+1
       170: q^2+3q+1
       171: q
       172: q
       173: q^2+3q+1
       174: q^2+3q+1
       175: q
       176: q
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 3q^2+6q+2
       184: 2q
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: 2q^2+4q+1
       190: 2q^2+4q+1
       191: 2q^2+5q+1
       192: 2q^2+5q+1
       193: 4q+2
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 2q^2+6q+2
       200: 2q
       201: q^2+5q+2
       202: 2q
       207: q^2+4q+1
       208: q^2+4q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: 3q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: 3q^2+7q+2
       220: 6q^2+10q+2
       221: 3q^2+7q+2
       222: 2q^2+8q+2
       223: q^2+5q+2
       224: 4q^2+10q+2
       225: 3q^2+7q+2
       226: q^2+7q+2
       227: 4q^2+10q+2
       228: 3q^2+7q+2
       229: 4q+2
       230: 6q^2+10q+2
       231: 5q+2
       232: q^2+7q+2
       233: q^2+5q+2
       234: 2q^2+7q+2
       236: 3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 5q+2
       244: 3q+2
       246: 2q^2+6q+2
       247: 5q+2
       248: q^2+5q+2
       249: 3q+2
       250: 6q+2
       251: 6q+2
       252: 2q^2+4q+2
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+2
       257: q^2+5q+2
       258: 3q+2
       259: 2q+1
       260: 2q+1
       261: q
       262: q
       263: q^2+3q+1
       264: q^2+3q+1
       265: q
       266: q
       267: 2q+1
       268: 2q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q
       278: q
       279: 3q+1
       280: 3q+1
       281: 2q+1
       282: 2q+1
       283: 3q+2
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: 2q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q^2+6q+2
       294: 2q
       295: 2q^2+5q+1
       296: 2q^2+5q+1
       297: q^2+4q+1
       298: q^2+4q+1
       299: 4q+2
       301: q+1
       302: q+1
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 2q+1
       306: 2q+1
       307: q^2+5q+2
       308: 2q
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 3q+2
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q^2+7q+2
       334: 5q+2
       335: q^2+7q+2
       336: 3q+2
       337: 5q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: q^2+7q+2
       345: 6q+2
       346: 4q+2
       347: 2q+2
       348: q+2
       349: 6q+2
       350: 3q^2+7q+2
       351: 3q+2
       352: 5q+2
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+5q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 5q+2
       368: 3q+2
       369: 3q+2
       371: 5q+2
       372: q^2+5q+2
       373: 3q+2
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       378: q+1
       381: 2q+1
       382: 2q+1
       383: q
       384: q
       385: q^2+3q+1
       386: q^2+3q+1
       387: q
       388: q
       389: q+1
       390: q+1
       393: 2q+1
       394: 2q+1
       413: 2q+1
       414: 2q+1
       417: 2q+1
       418: 2q+1
       419: 3q+2
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: q+2
       431: 2q+1
       432: 2q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: 2q+2
       439: 3q+1
       440: 3q+1
       441: q+1
       442: q+1
       443: 3q+2
       445: q+1
       446: q+1
       447: 3q+2
       453: 2q+1
       454: q
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 3q+2
       481: 5q+2
       482: q^2+7q+2
       483: 3q+2
       484: 5q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q+1
       490: q+1
       491: 3q+2
       492: 4q+2
       493: 2
       494: 4q+2
       495: q+2
       496: 3q+2
       497: 2q+1
       498: 2q+1
       508: 3q+2
       509: 2q+1
       510: q+1
       511: q+1
       512: q+2
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       522: q+1
       529: q+1
       530: q+1
       533: 1
       534: 1
       537: q+1
       538: q+1
       541: q+1
       542: q+1
       545: q+1
       546: q+1
       585: 2q+1
       586: 2q+1
       589: 3q+2
       593: q+2
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: 2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 3q+2
       617: q+1
       618: q+1
       619: q+1
       639: q+1
       640: q+1
       641: q+2
       647: q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+2
       672: 2q+1
       673: q+1
       674: 2
       675: 2
       676: 4q+2
       677: 2
       678: q+1
       679: q+2
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       709: q+1
       710: q+1
       717: 1
       718: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: q+1
       734: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       785: q+2
       793: 2
       795: 1
       796: 1
       797: 1
       798: 1
       801: 2
       805: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       815: q+1
       825: q+1
       845: 1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 2
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       904: 1
       905: 1
       916: 1
       917: 1
       920: 1
       921: 1
       928: 1
       929: 1
       994: 1
       995: 1
      1000: 2
      1004: 1
      1016: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1026: 2
      1052: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1122: 1
      1123: 1
      1156: 1
      1157: 1
      1218: 1
      1228: 1
      1240: 1
      1282: 1
      1284: 1
      1442: 1

1443:    0: 3q^3+15q^2+10q+2
         1: q^4+8q^3+15q^2+10q+2
         2: 3q^3+15q^2+10q+2
         3: q^4+8q^3+15q^2+10q+2
         4: 3q^3+15q^2+10q+2
         5: q^4+8q^3+15q^2+10q+2
         6: q^4+8q^3+15q^2+10q+2
         7: 3q^3+15q^2+10q+2
         8: q^4+8q^3+15q^2+10q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 2q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 2q^3+12q^2+10q+2
        13: 3q^3+15q^2+10q+2
        14: 3q^3+15q^2+10q+2
        15: q^4+8q^3+15q^2+10q+2
        16: 2q^3+12q^2+10q+2
        17: 4q^3+12q^2+10q+2
        18: 2q^3+9q^2+7q+2
        19: 3q^3+15q^2+10q+2
        20: q^4+8q^3+15q^2+10q+2
        21: 3q^3+15q^2+10q+2
        22: 2q^3+12q^2+10q+2
        23: 4q^3+12q^2+10q+2
        24: 2q^3+12q^2+10q+2
        25: 7q^2+8q+2
        26: q^3+7q^2+8q+2
        27: 7q^2+8q+2
        28: q^3+9q^2+10q+2
        29: 2q^3+12q^2+10q+2
        30: 3q^3+15q^2+10q+2
        31: q^3+9q^2+10q+2
        32: 2q^3+12q^2+10q+2
        33: q^3+9q^2+10q+2
        34: 5q^2+8q+2
        35: 7q^2+8q+2
        36: 5q^2+8q+2
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+12q^2+10q+2
        44: 2q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: 2q^3+12q^2+10q+2
        47: 4q^3+12q^2+10q+2
        48: 2q^3+9q^2+7q+2
        49: 2q^3+12q^2+10q+2
        50: 4q^3+12q^2+10q+2
        51: 2q^3+9q^2+7q+2
        52: 2q^3+12q^2+10q+2
        53: 4q^3+12q^2+10q+2
        54: 2q^3+12q^2+10q+2
        55: 7q^2+8q+2
        56: q^3+7q^2+8q+2
        57: 7q^2+8q+2
        58: 3q^2+5q+1
        59: 3q^2+5q+1
        60: 2q
        61: 3q^2+6q+2
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 2q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: 5q^2+8q+2
        73: q^3+9q^2+10q+2
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: 3q^2+4q+1
        77: 3q^2+4q+1
        78: 3q^2+4q+1
        79: 3q^2+4q+1
        80: q^3+9q^2+10q+2
        81: q^3+9q^2+10q+2
        82: q^3+9q^2+10q+2
        83: 2q^3+12q^2+10q+2
        84: 5q^2+8q+2
        85: 5q^2+8q+2
        86: 5q^2+8q+2
        87: 7q^2+8q+2
        88: 6q^2+10q+2
        89: 6q^2+10q+2
        90: q^3+6q^2+7q+2
        91: 2q^3+12q^2+10q+2
        92: 4q^3+12q^2+10q+2
        93: 2q^3+9q^2+7q+2
        94: 6q^2+10q+2
        95: 6q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 2q^2+7q+2
        98: 2q^2+7q+2
        99: 3q^2+5q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q
       104: q
       105: q^2+3q+1
       106: q^2+3q+1
       107: 2q
       108: 3q^2+6q+2
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: 3q^2+4q+1
       116: 3q^2+4q+1
       117: 3q^2+5q+1
       118: 3q^2+5q+1
       119: 2q
       120: 3q^2+6q+2
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: 6q^2+10q+2
       126: 3q^2+7q+2
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: 5q^2+8q+2
       136: q^3+9q^2+10q+2
       137: 4q^2+10q+2
       138: 3q^2+7q+2
       139: 4q^2+10q+2
       140: 4q+2
       141: q^3+9q^2+10q+2
       142: 6q^2+10q+2
       143: 2q^2+8q+2
       144: q^2+5q+2
       145: q^2+7q+2
       146: 5q^2+8q+2
       147: 2q^2+7q+2
       149: 2q^2+6q+2
       150: 2q^2+6q+2
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 6q^2+10q+2
       158: 6q^2+10q+2
       159: q^3+6q^2+7q+2
       160: 6q^2+10q+2
       161: 6q^2+10q+2
       162: q^3+6q^2+7q+2
       163: 2q^2+7q+2
       164: 2q^2+7q+2
       165: 3q^2+5q+2
       166: 5q+2
       167: q^2+5q+2
       168: 3q+2
       169: q
       170: q
       171: q^2+3q+1
       172: q^2+3q+1
       173: q
       174: q
       175: q^2+3q+1
       176: q^2+3q+1
       177: 2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 2q
       184: 3q^2+6q+2
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: 2q^2+4q+1
       190: 2q^2+4q+1
       191: 2q^2+5q+1
       192: 2q^2+5q+1
       194: 4q+2
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 2q
       200: 2q^2+6q+2
       201: 2q
       202: q^2+5q+2
       207: q^2+4q+1
       208: q^2+4q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: 3q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: 3q^2+7q+2
       220: 6q^2+10q+2
       221: 3q^2+7q+2
       222: 2q^2+8q+2
       223: q^2+5q+2
       224: 4q^2+10q+2
       225: 3q^2+7q+2
       226: q^2+7q+2
       227: 4q^2+10q+2
       228: 3q^2+7q+2
       229: 4q+2
       230: 6q^2+10q+2
       231: 5q+2
       232: q^2+7q+2
       233: q^2+5q+2
       234: 2q^2+7q+2
       236: 3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 5q+2
       244: 3q+2
       246: 2q^2+6q+2
       247: 5q+2
       248: q^2+5q+2
       249: 3q+2
       250: 6q+2
       251: 6q+2
       252: 2q^2+4q+2
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+2
       257: q^2+5q+2
       258: 3q+2
       259: q
       260: q
       261: 2q+1
       262: 2q+1
       263: q
       264: q
       265: q^2+3q+1
       266: q^2+3q+1
       269: 2q+1
       270: 2q+1
       275: q
       276: q
       277: q^2+3q+1
       278: q^2+3q+1
       279: 3q+1
       280: 3q+1
       281: 2q+1
       282: 2q+1
       284: 3q+2
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: 2q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q
       294: 2q^2+6q+2
       295: 2q^2+5q+1
       296: 2q^2+5q+1
       297: q^2+4q+1
       298: q^2+4q+1
       300: 4q+2
       301: q+1
       302: q+1
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 2q+1
       306: 2q+1
       307: 2q
       308: q^2+5q+2
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       320: 3q+2
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q^2+7q+2
       334: 5q+2
       335: q^2+7q+2
       336: 3q+2
       337: 5q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: q^2+7q+2
       345: 6q+2
       346: 4q+2
       347: 2q+2
       348: q+2
       349: 6q+2
       350: 3q^2+7q+2
       351: 3q+2
       352: 5q+2
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+5q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q+1
       365: q+1
       366: 3q+2
       367: 5q+2
       368: 3q+2
       369: 3q+2
       371: 5q+2
       372: q^2+5q+2
       373: 3q+2
       374: 2q+1
       375: 2q+1
       376: q+1
       379: q+1
       380: q+1
       381: q
       382: q
       383: 2q+1
       384: 2q+1
       385: q
       386: q
       387: q^2+3q+1
       388: q^2+3q+1
       391: q+1
       392: q+1
       395: 2q+1
       396: 2q+1
       413: 2q+1
       414: 2q+1
       417: 2q+1
       418: 2q+1
       420: 3q+2
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       430: q+2
       431: 2q+1
       432: 2q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       438: 2q+2
       439: 3q+1
       440: 3q+1
       441: q+1
       442: q+1
       444: 3q+2
       445: q+1
       446: q+1
       448: 3q+2
       453: q
       454: 2q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       472: 3q+2
       481: 5q+2
       482: q^2+7q+2
       483: 3q+2
       484: 5q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q+1
       490: q+1
       491: 3q+2
       492: 4q+2
       493: 2
       494: 4q+2
       495: q+2
       496: 3q+2
       497: 2q+1
       498: 2q+1
       508: 3q+2
       509: 2q+1
       510: q+1
       511: q+1
       512: q+2
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       523: q+1
       524: q+1
       531: q+1
       532: q+1
       535: 1
       536: 1
       539: q+1
       540: q+1
       543: q+1
       544: q+1
       547: q+1
       548: q+1
       585: 2q+1
       586: 2q+1
       590: 3q+2
       594: q+2
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       604: 2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 3q+2
       617: q+1
       618: q+1
       620: q+1
       639: q+1
       640: q+1
       642: q+2
       648: q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+2
       672: 2q+1
       673: q+1
       674: 2
       675: 2
       676: 4q+2
       677: 2
       678: q+1
       679: q+2
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       711: q+1
       712: q+1
       719: 1
       720: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: q+1
       736: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       786: q+2
       794: 2
       795: 1
       796: 1
       797: 1
       798: 1
       802: 2
       806: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       816: q+1
       826: q+1
       846: 1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 2
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       906: 1
       907: 1
       918: 1
       919: 1
       922: 1
       923: 1
       930: 1
       931: 1
       994: 1
       995: 1
      1001: 2
      1005: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1027: 2
      1053: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1124: 1
      1125: 1
      1158: 1
      1159: 1
      1219: 1
      1229: 1
      1241: 1
      1282: 1
      1284: 1
      1443: 1

1444:    0: q^3+10q^2+8q+2
         1: 5q^3+11q^2+8q+2
         2: q^3+10q^2+8q+2
         3: 5q^3+11q^2+8q+2
         4: q^3+10q^2+8q+2
         5: q^4+4q^3+10q^2+8q+2
         6: 5q^3+11q^2+8q+2
         7: q^3+10q^2+8q+2
         8: q^4+4q^3+10q^2+8q+2
         9: q^4+4q^3+6q^2+4q+1
        10: 7q^2+7q+2
        11: q^3+7q^2+7q+2
        12: 7q^2+7q+2
        13: q^3+10q^2+8q+2
        14: q^3+10q^2+8q+2
        15: q^4+4q^3+10q^2+8q+2
        16: 7q^2+7q+2
        17: q^3+7q^2+7q+2
        18: q^3+5q^2+4q+1
        19: q^3+10q^2+8q+2
        20: 5q^3+11q^2+8q+2
        21: q^3+10q^2+8q+2
        22: q^3+7q^2+8q+2
        23: 2q^3+8q^2+8q+2
        24: q^3+7q^2+8q+2
        25: q^3+7q^2+8q+2
        26: 2q^3+8q^2+8q+2
        27: q^3+7q^2+8q+2
        28: 5q^2+6q+2
        29: 7q^2+7q+2
        30: q^3+10q^2+8q+2
        31: 4q^2+7q+2
        32: q^3+7q^2+8q+2
        33: 4q^2+7q+2
        34: 4q^2+7q+2
        35: q^3+7q^2+8q+2
        36: 4q^2+7q+2
        37: 2q^2+4q+2
        38: q^3+3q^2+4q
        39: 2q^2+4q+2
        40: 4q^2+4q
        41: 2q^2+4q+2
        42: q^3+3q^2+4q
        43: 7q^2+7q+2
        44: 7q^2+7q+2
        45: q^3+7q^2+7q+2
        46: 7q^2+7q+2
        47: q^3+7q^2+7q+2
        48: q^3+5q^2+4q+1
        49: 7q^2+7q+2
        50: q^3+7q^2+7q+2
        51: q^3+5q^2+4q+1
        52: q^3+7q^2+8q+2
        53: 2q^3+8q^2+8q+2
        54: q^3+7q^2+8q+2
        55: q^3+7q^2+8q+2
        56: 2q^3+8q^2+8q+2
        57: q^3+7q^2+8q+2
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+2
        63: q^2+4q
        64: 2q^2+4q+2
        65: q^3+3q^2+4q
        66: q^2+3q+2
        67: q^2+4q
        68: 5q^2+6q+2
        69: 2q^2+3q+1
        70: 7q^2+7q+2
        71: 5q^2+6q+2
        72: 4q^2+7q+2
        73: 4q^2+7q+2
        74: 2q^2+4q+2
        75: q^3+3q^2+4q
        76: 2q^2+4q+2
        77: 4q^2+4q
        78: 2q^2+4q+2
        79: q^3+3q^2+4q
        80: 4q^2+7q+2
        81: 4q^2+7q+2
        82: 4q^2+7q+2
        83: q^3+7q^2+8q+2
        84: 4q^2+7q+2
        85: 4q^2+7q+2
        86: 4q^2+7q+2
        87: q^3+7q^2+8q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: 2q^2+3q+1
        91: 7q^2+7q+2
        92: q^3+7q^2+7q+2
        93: q^3+5q^2+4q+1
        94: 3q^2+7q+2
        95: 3q^2+7q+2
        96: q^3+4q^2+4q+1
        97: 3q^2+7q+2
        98: 3q^2+7q+2
        99: q^3+4q^2+4q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: q+1
       104: 2q
       105: 2q
       106: q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q^2+3q+2
       112: q^2+4q
       113: q^2+3q+2
       114: q^2+4q
       115: 2q^2+4q+2
       116: q^3+3q^2+4q
       117: q^2+3q+1
       118: q^2+3q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+2
       122: q^2+4q
       123: q^2+3q+2
       124: q^2+4q
       125: q^2+4q+2
       126: 2q+1
       127: 2q+2
       128: 4q
       129: 2q+2
       130: 4q
       131: q^2+2q+1
       132: q^3+2q^2+q
       133: 5q^2+6q+2
       134: 2q^2+3q+1
       135: 4q^2+7q+2
       136: 4q^2+7q+2
       137: 4q+2
       138: q^2+3q+1
       139: 2q^2+6q+2
       140: 3q+2
       141: 4q^2+7q+2
       142: 3q^2+7q+2
       143: 4q+2
       144: q^2+3q+1
       145: 2q^2+6q+2
       146: 4q^2+7q+2
       147: 3q^2+7q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       151: 3q+2
       152: 2q^2+4q
       153: q^2+3q+2
       154: 4q^2+4q
       155: 3q+2
       156: 2q^2+4q
       157: q^2+4q+2
       158: q^2+4q+2
       159: 2q^2+3q+1
       160: 3q^2+7q+2
       161: 3q^2+7q+2
       162: q^3+4q^2+4q+1
       163: 3q^2+7q+2
       164: 3q^2+7q+2
       165: q^3+4q^2+4q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: q+1
       170: 2q
       171: 2q
       172: q+1
       173: q+1
       174: 2q
       175: 2q
       176: q+1
       177: q+1
       178: q
       179: 2q+2
       180: 4q
       181: 2q+2
       182: 4q
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+2
       188: q^2+4q
       189: q^2+3q+2
       190: q^2+4q
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: q+2
       198: 2q
       199: 2q+1
       200: 2q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: q+2
       206: 2q
       207: 2q+2
       208: 2q
       209: 2q+2
       210: q^2+4q
       211: 3q+2
       212: 2q^2+4q
       213: 2q+2
       214: 4q
       215: 2q+2
       216: 4q
       217: q^2+2q+1
       218: q^3+2q^2+q
       219: 2q+1
       220: q^2+4q+2
       221: 2q+1
       222: 4q+2
       223: q^2+3q+1
       224: 4q+2
       225: q^2+3q+1
       226: 2q+1
       227: 2q^2+6q+2
       228: q^2+3q+1
       229: 3q+2
       230: 3q^2+7q+2
       231: 2q+1
       232: 2q^2+6q+2
       233: q^2+3q+1
       234: 3q^2+7q+2
       235: 3q+2
       236: 2q+1
       237: q+2
       238: 4q
       239: q+2
       240: 4q
       241: q+1
       242: q^2+q
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       259: q+1
       260: 2q
       261: 2q
       262: q+1
       263: q+1
       264: 2q
       265: 2q
       266: q+1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: q+1
       276: q
       277: q
       278: q+1
       279: 2q+2
       280: 4q
       281: q+1
       282: q
       287: q+1
       288: q
       289: 2q+2
       290: 4q
       291: q+1
       292: q
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+2
       298: 2q
       299: q+1
       300: q+1
       301: 2
       302: 2q
       303: q^2+3q+1
       304: q^2+3q+1
       305: q+2
       306: 2q
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: 2
       312: 2q
       313: q+2
       314: 2q
       315: 1
       316: q
       317: q+2
       318: 4q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: 2q+2
       326: q^2+4q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 5q+2
       338: q+2
       339: 4q
       340: q+2
       341: 4q
       342: q+1
       343: q^2+q
       344: 2q+1
       345: 2q+2
       346: q+1
       347: 2
       348: q+1
       349: 2q+2
       350: q^2+3q+1
       351: 3q+2
       352: 2q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q^2+3q+1
       357: 2
       358: q+1
       359: 3q+2
       360: q+2
       361: 4q
       362: q+2
       363: 4q
       364: q+1
       365: q^2+q
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: q+2
       375: q+2
       376: q+1
       381: q+1
       382: 2q
       383: 2q
       384: q+1
       385: q+1
       386: q
       387: q
       388: q+1
       389: 1
       390: q
       391: 1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       398: q
       399: 1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       413: q+1
       414: q
       417: q+1
       418: q
       423: q+1
       424: q
       425: 1
       426: q
       427: q+2
       428: 4q
       433: 1
       435: 2
       436: 2q
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: q+1
       444: q+1
       445: 2
       446: 2q
       451: 1
       453: q+1
       454: q+1
       455: 2
       456: 2q
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       464: 2q
       465: q+2
       466: 4q
       467: 1
       468: q
       469: 1
       470: q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: 2
       479: q+2
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 5q+2
       485: q+2
       486: 4q
       487: q+2
       488: 4q
       489: q+1
       490: q^2+q
       491: 2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+2
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+2
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: q+2
       519: q+2
       520: q+1
       537: 1
       538: q
       539: 1
       540: q
       541: 1
       543: 1
       545: 1
       546: q
       547: 1
       548: q
       553: 1
       554: q
       555: 1
       556: q
       557: 1
       559: 1
       561: 1
       562: q
       563: 1
       564: q
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       585: q+1
       586: q
       597: 1
       598: q
       599: 1
       600: q
       601: q+2
       602: 4q
       605: 1
       609: 1
       613: 1
       615: q+1
       616: q+1
       617: 2
       618: 2q
       623: 1
       625: 1
       629: 1
       631: q+1
       632: q+1
       633: 2
       634: 2q
       639: 1
       640: q
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: q+2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: q+1
       672: q+2
       673: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 2
       679: q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: 1
       697: 1
       733: 1
       734: q
       735: 1
       736: q
       749: 1
       750: q
       751: 1
       752: q
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       779: 1
       780: 1
       781: 1
       782: q
       791: 1
       795: 1
       796: 1
       797: 1
       809: 1
       811: 1
       815: 1
       816: 1
       819: 1
       820: 1
       821: 1
       833: 1
       835: 1
       839: 1
       840: 1
       843: 2
       849: 1
       851: 1
       857: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       889: 1
       968: 1
       969: 1
       988: 1
       991: 1
      1008: 1
      1010: 1
      1012: 2
      1020: 1
      1021: 1
      1022: 1
      1036: 1
      1037: 1
      1038: 1
      1046: 1
      1048: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1138: 1
      1139: 1
      1220: 1
      1224: 1
      1262: 1
      1284: 1
      1286: 1
      1444: 1

1445:    0: q^3+10q^2+8q+2
         1: 5q^3+11q^2+8q+2
         2: q^3+10q^2+8q+2
         3: 5q^3+11q^2+8q+2
         4: q^3+10q^2+8q+2
         5: q^4+4q^3+10q^2+8q+2
         6: 5q^3+11q^2+8q+2
         7: q^3+10q^2+8q+2
         8: q^4+4q^3+10q^2+8q+2
         9: q^4+4q^3+6q^2+4q+1
        10: 7q^2+7q+2
        11: q^3+7q^2+7q+2
        12: 7q^2+7q+2
        13: q^3+10q^2+8q+2
        14: q^3+10q^2+8q+2
        15: q^4+4q^3+10q^2+8q+2
        16: 7q^2+7q+2
        17: q^3+7q^2+7q+2
        18: q^3+5q^2+4q+1
        19: q^3+10q^2+8q+2
        20: 5q^3+11q^2+8q+2
        21: q^3+10q^2+8q+2
        22: q^3+7q^2+8q+2
        23: 2q^3+8q^2+8q+2
        24: q^3+7q^2+8q+2
        25: q^3+7q^2+8q+2
        26: 2q^3+8q^2+8q+2
        27: q^3+7q^2+8q+2
        28: 5q^2+6q+2
        29: 7q^2+7q+2
        30: q^3+10q^2+8q+2
        31: 4q^2+7q+2
        32: q^3+7q^2+8q+2
        33: 4q^2+7q+2
        34: 4q^2+7q+2
        35: q^3+7q^2+8q+2
        36: 4q^2+7q+2
        37: q^3+3q^2+4q
        38: 2q^2+4q+2
        39: 4q^2+4q
        40: 2q^2+4q+2
        41: q^3+3q^2+4q
        42: 2q^2+4q+2
        43: 7q^2+7q+2
        44: 7q^2+7q+2
        45: q^3+7q^2+7q+2
        46: 7q^2+7q+2
        47: q^3+7q^2+7q+2
        48: q^3+5q^2+4q+1
        49: 7q^2+7q+2
        50: q^3+7q^2+7q+2
        51: q^3+5q^2+4q+1
        52: q^3+7q^2+8q+2
        53: 2q^3+8q^2+8q+2
        54: q^3+7q^2+8q+2
        55: q^3+7q^2+8q+2
        56: 2q^3+8q^2+8q+2
        57: q^3+7q^2+8q+2
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+4q
        63: q^2+3q+2
        64: q^3+3q^2+4q
        65: 2q^2+4q+2
        66: q^2+4q
        67: q^2+3q+2
        68: 5q^2+6q+2
        69: 2q^2+3q+1
        70: 7q^2+7q+2
        71: 5q^2+6q+2
        72: 4q^2+7q+2
        73: 4q^2+7q+2
        74: q^3+3q^2+4q
        75: 2q^2+4q+2
        76: 4q^2+4q
        77: 2q^2+4q+2
        78: q^3+3q^2+4q
        79: 2q^2+4q+2
        80: 4q^2+7q+2
        81: 4q^2+7q+2
        82: 4q^2+7q+2
        83: q^3+7q^2+8q+2
        84: 4q^2+7q+2
        85: 4q^2+7q+2
        86: 4q^2+7q+2
        87: q^3+7q^2+8q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: 2q^2+3q+1
        91: 7q^2+7q+2
        92: q^3+7q^2+7q+2
        93: q^3+5q^2+4q+1
        94: 3q^2+7q+2
        95: 3q^2+7q+2
        96: q^3+4q^2+4q+1
        97: 3q^2+7q+2
        98: 3q^2+7q+2
        99: q^3+4q^2+4q+1
       100: 2q^2+7q+2
       101: 5q^2+7q+2
       102: 2q^2+7q+2
       103: 2q
       104: q+1
       105: q+1
       106: 2q
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q^2+4q
       112: q^2+3q+2
       113: q^2+4q
       114: q^2+3q+2
       115: q^3+3q^2+4q
       116: 2q^2+4q+2
       117: q^2+3q+1
       118: q^2+3q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+4q
       122: q^2+3q+2
       123: q^2+4q
       124: q^2+3q+2
       125: q^2+4q+2
       126: 2q+1
       127: 4q
       128: 2q+2
       129: 4q
       130: 2q+2
       131: q^3+2q^2+q
       132: q^2+2q+1
       133: 5q^2+6q+2
       134: 2q^2+3q+1
       135: 4q^2+7q+2
       136: 4q^2+7q+2
       137: 4q+2
       138: q^2+3q+1
       139: 2q^2+6q+2
       140: 3q+2
       141: 4q^2+7q+2
       142: 3q^2+7q+2
       143: 4q+2
       144: q^2+3q+1
       145: 2q^2+6q+2
       146: 4q^2+7q+2
       147: 3q^2+7q+2
       148: 3q+2
       149: q^2+6q+2
       150: 2q^2+7q+2
       151: 2q^2+4q
       152: 3q+2
       153: 4q^2+4q
       154: q^2+3q+2
       155: 2q^2+4q
       156: 3q+2
       157: q^2+4q+2
       158: q^2+4q+2
       159: 2q^2+3q+1
       160: 3q^2+7q+2
       161: 3q^2+7q+2
       162: q^3+4q^2+4q+1
       163: 3q^2+7q+2
       164: 3q^2+7q+2
       165: q^3+4q^2+4q+1
       166: 6q+2
       167: q^2+6q+2
       168: q^2+3q+1
       169: 2q
       170: q+1
       171: q+1
       172: 2q
       173: 2q
       174: q+1
       175: q+1
       176: 2q
       177: q
       178: q+1
       179: 4q
       180: 2q+2
       181: 4q
       182: 2q+2
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+4q
       188: q^2+3q+2
       189: q^2+4q
       190: q^2+3q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: 2q
       198: q+2
       199: 2q+1
       200: 2q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: 2q
       206: q+2
       207: 2q
       208: 2q+2
       209: q^2+4q
       210: 2q+2
       211: 2q^2+4q
       212: 3q+2
       213: 4q
       214: 2q+2
       215: 4q
       216: 2q+2
       217: q^3+2q^2+q
       218: q^2+2q+1
       219: 2q+1
       220: q^2+4q+2
       221: 2q+1
       222: 4q+2
       223: q^2+3q+1
       224: 4q+2
       225: q^2+3q+1
       226: 2q+1
       227: 2q^2+6q+2
       228: q^2+3q+1
       229: 3q+2
       230: 3q^2+7q+2
       231: 2q+1
       232: 2q^2+6q+2
       233: q^2+3q+1
       234: 3q^2+7q+2
       235: 3q+2
       236: 2q+1
       237: 4q
       238: q+2
       239: 4q
       240: q+2
       241: q^2+q
       242: q+1
       243: 5q+2
       244: 3q+2
       245: 3q+2
       246: q^2+6q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 6q+2
       257: q^2+6q+2
       258: q^2+3q+1
       259: 2q
       260: q+1
       261: q+1
       262: 2q
       263: 2q
       264: q+1
       265: q+1
       266: 2q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       275: q
       276: q+1
       277: q+1
       278: q
       279: 4q
       280: 2q+2
       281: q
       282: q+1
       287: q
       288: q+1
       289: 4q
       290: 2q+2
       291: q
       292: q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q
       298: 2q+2
       299: q+1
       300: q+1
       301: 2q
       302: 2
       303: q^2+3q+1
       304: q^2+3q+1
       305: 2q
       306: q+2
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: 2q
       312: 2
       313: 2q
       314: q+2
       315: q
       316: 1
       317: 4q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       325: q^2+4q
       326: 2q+2
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 5q+2
       338: 4q
       339: q+2
       340: 4q
       341: q+2
       342: q^2+q
       343: q+1
       344: 2q+1
       345: 2q+2
       346: q+1
       347: 2
       348: q+1
       349: 2q+2
       350: q^2+3q+1
       351: 3q+2
       352: 2q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q^2+3q+1
       357: 2
       358: q+1
       359: 3q+2
       360: 4q
       361: q+2
       362: 4q
       363: q+2
       364: q^2+q
       365: q+1
       366: q+1
       367: 5q+2
       368: 2q+1
       369: 3q+2
       370: 3q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: q+2
       375: q+2
       376: q+1
       381: 2q
       382: q+1
       383: q+1
       384: 2q
       385: q
       386: q+1
       387: q+1
       388: q
       389: q
       390: 1
       391: q
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 1
       399: q
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       407: 1
       408: 1
       413: q
       414: q+1
       417: q
       418: q+1
       423: q
       424: q+1
       425: q
       426: 1
       427: 4q
       428: q+2
       434: 1
       435: 2q
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: q+1
       444: q+1
       445: 2q
       446: 2
       452: 1
       453: q+1
       454: q+1
       455: 2q
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       463: 2q
       464: 2
       465: 4q
       466: q+2
       467: q
       468: 1
       469: q
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: 2
       480: q+2
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 5q+2
       485: 4q
       486: q+2
       487: 4q
       488: q+2
       489: q^2+q
       490: q+1
       491: 2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+2
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+2
       508: q+1
       509: q+2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: q+2
       519: q+2
       520: q+1
       537: q
       538: 1
       539: q
       540: 1
       542: 1
       544: 1
       545: q
       546: 1
       547: q
       548: 1
       553: q
       554: 1
       555: q
       556: 1
       558: 1
       560: 1
       561: q
       562: 1
       563: q
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       585: q
       586: q+1
       597: q
       598: 1
       599: q
       600: 1
       601: 4q
       602: q+2
       606: 1
       610: 1
       614: 1
       615: q+1
       616: q+1
       617: 2q
       618: 2
       624: 1
       626: 1
       630: 1
       631: q+1
       632: q+1
       633: 2q
       634: 2
       639: q
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: q+2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: q+1
       672: q+2
       673: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 2
       679: q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: 1
       700: 1
       733: q
       734: 1
       735: q
       736: 1
       749: q
       750: 1
       751: q
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       779: 1
       780: 1
       781: q
       782: 1
       792: 1
       795: 1
       796: 1
       798: 1
       810: 1
       812: 1
       815: 1
       816: 1
       819: 1
       820: 1
       822: 1
       834: 1
       836: 1
       839: 1
       840: 1
       844: 2
       850: 1
       852: 1
       858: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       890: 1
       891: 1
       971: 1
       972: 1
       989: 1
       990: 1
      1009: 1
      1011: 1
      1013: 2
      1020: 1
      1021: 1
      1023: 1
      1036: 1
      1037: 1
      1039: 1
      1047: 1
      1049: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1141: 1
      1142: 1
      1221: 1
      1225: 1
      1263: 1
      1284: 1
      1286: 1
      1445: 1

1446:    0: 2q^3+4q^2+5q+2
         1: 2q^3+4q^2+5q+2
         2: 2q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: 2q^3+4q^2+5q+2
         5: q^3+4q^2+5q+2
         6: 2q^3+4q^2+5q+2
         7: 2q^3+4q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: 2q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: 2q^3+4q^2+5q+2
        13: 2q^3+4q^2+5q+2
        14: 2q^3+4q^2+5q+2
        15: q^3+4q^2+5q+2
        16: q^2+4q+2
        17: q^2+4q+2
        18: q^3+q^2+2q+1
        19: 2q^3+4q^2+5q+2
        20: 2q^3+4q^2+5q+2
        21: 2q^3+4q^2+5q+2
        22: 3q^2+5q+2
        23: 3q^2+5q+2
        24: 3q^2+5q+2
        25: 3q^2+5q+2
        26: 3q^2+5q+2
        27: 3q^2+5q+2
        28: q^2+4q+2
        29: 2q^3+4q^2+5q+2
        30: 2q^3+4q^2+5q+2
        31: 3q^2+5q+2
        32: 3q^2+5q+2
        33: 4q+2
        34: 3q^2+5q+2
        35: 3q^2+5q+2
        36: 4q+2
        37: 3q^2+5q+2
        39: 3q^2+5q+2
        41: 3q^2+5q+2
        43: 2q^3+4q^2+5q+2
        44: 2q^3+4q^2+5q+2
        45: q^3+4q^2+5q+2
        46: q^2+4q+2
        47: q^2+4q+2
        48: q^3+q^2+2q+1
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^3+q^2+2q+1
        52: 3q^2+5q+2
        53: 3q^2+5q+2
        54: 3q^2+5q+2
        55: 3q^2+5q+2
        56: 3q^2+5q+2
        57: 3q^2+5q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 3q^2+5q+2
        64: 3q^2+5q+2
        66: 4q+2
        68: q^2+4q+2
        69: q+1
        70: 2q^3+4q^2+5q+2
        71: q^2+4q+2
        72: 4q+2
        73: 4q+2
        74: 3q^2+5q+2
        76: 3q^2+5q+2
        78: 3q^2+5q+2
        80: 3q^2+5q+2
        81: 4q+2
        82: 3q^2+5q+2
        83: 3q^2+5q+2
        84: 3q^2+5q+2
        85: 4q+2
        86: 3q^2+5q+2
        87: 3q^2+5q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: q^3+q^2+2q+1
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^3+q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 2q^2+4q+2
       101: 2q^2+4q+2
       102: 2q^2+4q+2
       103: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 4q+2
       113: 3q^2+5q+2
       115: 3q^2+5q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 3q^2+5q+2
       123: 4q+2
       125: q^2+4q+2
       126: q+1
       127: 4q+2
       129: 4q+2
       131: q^2+2q+1
       133: q^2+4q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 3q^2+5q+2
       142: 4q+2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 3q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: 2q^2+4q+2
       150: 2q^2+4q+2
       151: 2q^2+4q+2
       153: 2q^2+4q+2
       155: 2q^2+4q+2
       157: q^2+4q+2
       158: q^2+4q+2
       159: q^3+q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: q^2+2q+1
       163: 4q+2
       164: 4q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       169: 2q+1
       172: 2q+1
       173: 2q+1
       176: 2q+1
       177: q+1
       179: 4q+2
       181: 4q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 4q+2
       189: 3q^2+5q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 2q+2
       207: 4q+2
       209: 2q^2+4q+2
       211: 2q^2+4q+2
       213: 4q+2
       215: 4q+2
       217: q^2+2q+1
       219: q+1
       220: q^2+4q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 4q+2
       228: q+1
       229: 2q+2
       230: 4q+2
       231: q+1
       232: 4q+2
       233: q+1
       234: 4q+2
       235: 2q+2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q^2+4q+2
       247: q+2
       248: q+2
       249: q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       259: 2q+1
       262: 2q+1
       263: 2q+1
       266: 2q+1
       267: q+1
       269: q+1
       271: q+1
       273: q+1
       275: 2q+1
       278: 2q+1
       279: 4q+2
       281: q+1
       287: q+1
       289: 4q+2
       291: q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 4q+2
       299: q+1
       300: q+1
       301: 2
       303: 2q+1
       304: 2q+1
       305: 2q+2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 2
       313: 2q+2
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 2q^2+4q+2
       327: 4q+2
       329: 4q+2
       331: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       338: q+2
       340: q+2
       342: q+1
       344: q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: 1
       349: 4q+2
       350: q+1
       351: 2
       352: q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 2q+2
       358: 1
       359: 2
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       381: 2q+1
       384: 2q+1
       385: 2q+1
       388: 2q+1
       389: 1
       391: 1
       393: q+1
       396: q+1
       397: 1
       399: 1
       401: q+1
       404: q+1
       405: 1
       406: 1
       409: 4q+2
       411: q+1
       413: q+1
       415: 4q+2
       417: q+1
       423: q+1
       425: 1
       427: q+2
       433: 1
       435: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 2q+2
       443: 1
       444: 1
       445: 2
       451: 1
       453: 2q+1
       454: 2q+1
       455: 2
       457: q+1
       458: q+1
       459: 2q+2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 4
       479: 2
       481: q+1
       482: q+1
       483: 1
       484: q+2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       525: 2q+1
       528: 2q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 1
       547: 1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 2
       570: 2
       573: 1
       575: 1
       577: 2
       579: 2
       583: q+1
       585: q+1
       587: q+1
       597: 1
       599: 1
       601: q+2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 4
       653: 2
       655: 2
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: q+2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       693: 1
       695: 1
       697: 1
       702: 1
       729: 1
       731: 1
       733: 1
       735: 1
       745: 1
       747: 1
       749: 1
       751: 1
       757: 2
       758: 2
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       771: 2
       777: q+1
       781: 1
       783: 1
       789: q+2
       791: 1
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       849: 1
       851: 1
       853: 4
       857: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       889: 1
       893: 1
       932: 1
       934: 1
       956: 1
       958: 1
       978: 2
       979: 2
       982: 2
       984: 2
       988: 1
       991: 1
      1002: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1034: 1
      1038: 1
      1042: 1
      1048: 1
      1050: 1
      1078: 1
      1082: 1
      1098: 1
      1100: 1
      1102: 1
      1107: 1
      1220: 1
      1222: 1
      1238: 1
      1256: 1
      1264: 1
      1446: 1

1447:    0: 2q^3+4q^2+5q+2
         1: 2q^3+4q^2+5q+2
         2: 2q^3+4q^2+5q+2
         3: q^3+4q^2+5q+2
         4: 2q^3+4q^2+5q+2
         5: q^3+4q^2+5q+2
         6: 2q^3+4q^2+5q+2
         7: 2q^3+4q^2+5q+2
         8: q^3+4q^2+5q+2
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: 2q^3+4q^2+5q+2
        11: q^3+4q^2+5q+2
        12: 2q^3+4q^2+5q+2
        13: 2q^3+4q^2+5q+2
        14: 2q^3+4q^2+5q+2
        15: q^3+4q^2+5q+2
        16: q^2+4q+2
        17: q^2+4q+2
        18: q^3+q^2+2q+1
        19: 2q^3+4q^2+5q+2
        20: 2q^3+4q^2+5q+2
        21: 2q^3+4q^2+5q+2
        22: 3q^2+5q+2
        23: 3q^2+5q+2
        24: 3q^2+5q+2
        25: 3q^2+5q+2
        26: 3q^2+5q+2
        27: 3q^2+5q+2
        28: q^2+4q+2
        29: 2q^3+4q^2+5q+2
        30: 2q^3+4q^2+5q+2
        31: 3q^2+5q+2
        32: 3q^2+5q+2
        33: 4q+2
        34: 3q^2+5q+2
        35: 3q^2+5q+2
        36: 4q+2
        38: 3q^2+5q+2
        40: 3q^2+5q+2
        42: 3q^2+5q+2
        43: 2q^3+4q^2+5q+2
        44: 2q^3+4q^2+5q+2
        45: q^3+4q^2+5q+2
        46: q^2+4q+2
        47: q^2+4q+2
        48: q^3+q^2+2q+1
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^3+q^2+2q+1
        52: 3q^2+5q+2
        53: 3q^2+5q+2
        54: 3q^2+5q+2
        55: 3q^2+5q+2
        56: 3q^2+5q+2
        57: 3q^2+5q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        63: 3q^2+5q+2
        65: 3q^2+5q+2
        67: 4q+2
        68: q^2+4q+2
        69: q+1
        70: 2q^3+4q^2+5q+2
        71: q^2+4q+2
        72: 4q+2
        73: 4q+2
        75: 3q^2+5q+2
        77: 3q^2+5q+2
        79: 3q^2+5q+2
        80: 3q^2+5q+2
        81: 4q+2
        82: 3q^2+5q+2
        83: 3q^2+5q+2
        84: 3q^2+5q+2
        85: 4q+2
        86: 3q^2+5q+2
        87: 3q^2+5q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: q^3+q^2+2q+1
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^3+q^2+2q+1
        94: 4q+2
        95: 4q+2
        96: q^2+2q+1
        97: 4q+2
        98: 4q+2
        99: q^2+2q+1
       100: 2q^2+4q+2
       101: 2q^2+4q+2
       102: 2q^2+4q+2
       104: 2q+1
       105: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       112: 4q+2
       114: 3q^2+5q+2
       116: 3q^2+5q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       122: 3q^2+5q+2
       124: 4q+2
       125: q^2+4q+2
       126: q+1
       128: 4q+2
       130: 4q+2
       132: q^2+2q+1
       133: q^2+4q+2
       134: q+1
       135: 4q+2
       136: 4q+2
       137: 4q+2
       138: q+1
       139: 4q+2
       140: 2q+2
       141: 3q^2+5q+2
       142: 4q+2
       143: 4q+2
       144: q+1
       145: 4q+2
       146: 3q^2+5q+2
       147: 4q+2
       148: 2q+2
       149: 2q^2+4q+2
       150: 2q^2+4q+2
       152: 2q^2+4q+2
       154: 2q^2+4q+2
       156: 2q^2+4q+2
       157: q^2+4q+2
       158: q^2+4q+2
       159: q^3+q^2+2q+1
       160: 4q+2
       161: 4q+2
       162: q^2+2q+1
       163: 4q+2
       164: 4q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       170: 2q+1
       171: 2q+1
       174: 2q+1
       175: 2q+1
       178: q+1
       180: 4q+2
       182: 4q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       188: 4q+2
       190: 3q^2+5q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       206: 2q+2
       208: 4q+2
       210: 2q^2+4q+2
       212: 2q^2+4q+2
       214: 4q+2
       216: 4q+2
       218: q^2+2q+1
       219: q+1
       220: q^2+4q+2
       221: q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: q+1
       227: 4q+2
       228: q+1
       229: 2q+2
       230: 4q+2
       231: q+1
       232: 4q+2
       233: q+1
       234: 4q+2
       235: 2q+2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q^2+4q+2
       247: q+2
       248: q+2
       249: q+1
       250: 4q+2
       251: 4q+2
       252: q^2+2q+1
       253: 4q+2
       254: 4q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       260: 2q+1
       261: 2q+1
       264: 2q+1
       265: 2q+1
       268: q+1
       270: q+1
       272: q+1
       274: q+1
       276: 2q+1
       277: 2q+1
       280: 4q+2
       282: q+1
       288: q+1
       290: 4q+2
       292: q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       298: 4q+2
       299: q+1
       300: q+1
       302: 2
       303: 2q+1
       304: 2q+1
       306: 2q+2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       312: 2
       314: 2q+2
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 2q^2+4q+2
       328: 4q+2
       330: 4q+2
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       339: q+2
       341: q+2
       343: q+1
       344: q+1
       345: 4q+2
       346: q+1
       347: 2q+2
       348: 1
       349: 4q+2
       350: q+1
       351: 2
       352: q+1
       353: 4q+2
       354: q+1
       355: 4q+2
       356: q+1
       357: 2q+2
       358: 1
       359: 2
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       382: 2q+1
       383: 2q+1
       386: 2q+1
       387: 2q+1
       390: 1
       392: 1
       394: q+1
       395: q+1
       398: 1
       400: 1
       402: q+1
       403: q+1
       407: 1
       408: 1
       410: 4q+2
       412: q+1
       414: q+1
       416: 4q+2
       418: q+1
       424: q+1
       426: 1
       428: q+2
       434: 1
       436: 2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 2q+2
       443: 1
       444: 1
       446: 2
       452: 1
       453: 2q+1
       454: 2q+1
       456: 2
       457: q+1
       458: q+1
       460: 2q+2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 4
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: q+2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: q+2
       519: q+2
       520: q+1
       526: 2q+1
       527: 2q+1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: 1
       548: 1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 2
       572: 2
       574: 1
       576: 1
       581: 2
       582: 2
       584: q+1
       586: q+1
       588: q+1
       598: 1
       600: 1
       602: q+2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 4
       654: 2
       656: 2
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: q+2
       673: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       699: 1
       700: 1
       703: 1
       704: 1
       730: 1
       732: 1
       734: 1
       736: 1
       746: 1
       748: 1
       750: 1
       752: 1
       759: 2
       760: 2
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       774: 2
       778: q+1
       782: 1
       784: 1
       790: q+2
       792: 1
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       850: 1
       852: 1
       854: 4
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       891: 1
       894: 1
       895: 1
       933: 1
       935: 1
       957: 1
       959: 1
       980: 2
       981: 2
       986: 2
       987: 2
       989: 1
       990: 1
      1003: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1035: 1
      1039: 1
      1043: 1
      1049: 1
      1051: 1
      1078: 1
      1082: 1
      1104: 1
      1105: 1
      1108: 1
      1109: 1
      1221: 1
      1223: 1
      1239: 1
      1257: 1
      1265: 1
      1447: 1

1448:    0: 12q^2+8q+2
         1: 12q^2+8q+2
         2: 4q^3+9q^2+7q+2
         3: 12q^2+8q+2
         4: 4q^3+9q^2+7q+2
         5: 12q^2+8q+2
         6: 4q^3+9q^2+7q+2
         7: q^4+4q^3+7q^2+6q+2
         8: 4q^3+9q^2+7q+2
         9: q^4+4q^3+7q^2+6q+2
        10: 12q^2+8q+2
        11: 12q^2+8q+2
        12: 4q^3+9q^2+7q+2
        13: 8q^2+7q+2
        14: 2q^3+6q^2+6q+2
        15: 8q^2+7q+2
        16: 12q^2+8q+2
        17: 12q^2+8q+2
        18: q^4+4q^3+7q^2+6q+2
        19: 8q^2+7q+2
        20: 8q^2+7q+2
        21: 2q^3+6q^2+6q+2
        22: 12q^2+8q+2
        23: 12q^2+8q+2
        24: 4q^3+9q^2+7q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: q^3+4q^2+5q+2
        28: 12q^2+8q+2
        29: 8q^2+7q+2
        30: 5q^2+6q+2
        31: 12q^2+8q+2
        32: 8q^2+7q+2
        33: 12q^2+8q+2
        34: 4q^2+6q+2
        35: 3q^2+5q+2
        36: 4q^2+6q+2
        37: 4q^2+6q+2
        39: 4q^2+6q+2
        41: q^3+4q^2+5q+2
        43: 8q^2+7q+2
        44: 2q^3+6q^2+6q+2
        45: 8q^2+7q+2
        46: 8q^2+7q+2
        47: 8q^2+7q+2
        48: 2q^3+6q^2+6q+2
        49: 8q^2+7q+2
        50: 8q^2+7q+2
        51: 2q^3+6q^2+6q+2
        52: 8q^2+7q+2
        53: 8q^2+7q+2
        54: 2q^3+6q^2+6q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: 2q^2+4q+2
        58: 6q^2+4q+1
        59: 6q^2+4q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: 4q^2+6q+2
        64: 3q^2+5q+2
        66: 4q^2+6q+2
        68: 4q^2+6q+2
        69: 5q^2+6q+2
        70: 5q^2+6q+2
        71: 8q^2+7q+2
        72: 4q+2
        73: 4q^2+6q+2
        74: q^2+5q+2
        76: q^2+5q+2
        78: 2q^2+4q+2
        80: 8q^2+7q+2
        81: 8q^2+7q+2
        82: 8q^2+7q+2
        83: 5q^2+6q+2
        84: 3q^2+5q+2
        85: 3q^2+5q+2
        86: q^2+5q+2
        87: q^2+4q+2
        88: 8q^2+7q+2
        89: 8q^2+7q+2
        90: 2q^3+6q^2+6q+2
        91: 3q^2+6q+2
        92: 4q^2+6q+2
        93: 3q^2+6q+2
        94: 8q^2+7q+2
        95: 8q^2+7q+2
        96: 2q^3+6q^2+6q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: 2q^2+4q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: 2q^2+4q+2
       103: 2q^2+3q+1
       106: 2q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 4q+2
       113: q^2+5q+2
       115: q^2+4q+2
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+5q+2
       123: 3q^2+5q+2
       125: 4q^2+6q+2
       126: 5q^2+6q+2
       127: q^2+5q+2
       129: q^2+5q+2
       131: 2q^2+4q+2
       133: q^2+5q+2
       134: 3q^2+6q+2
       135: 3q+2
       136: q^2+5q+2
       137: 8q^2+7q+2
       138: 5q^2+6q+2
       139: 8q^2+7q+2
       140: 4q+2
       141: 5q^2+6q+2
       142: 4q^2+6q+2
       143: 3q^2+5q+2
       144: q^2+4q+2
       145: q^2+5q+2
       146: q^2+4q+2
       147: 4q+2
       149: q^2+5q+2
       150: q^2+4q+2
       151: q^2+5q+2
       153: q^2+5q+2
       155: 2q^2+4q+2
       157: 3q^2+6q+2
       158: 4q^2+6q+2
       159: 3q^2+6q+2
       160: 3q^2+6q+2
       161: 4q^2+6q+2
       162: 3q^2+6q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: 2q^2+4q+2
       169: 2q+1
       172: 2q+1
       173: q^2+2q+1
       176: q^2+2q+1
       177: q^2+4q+2
       179: q^2+5q+2
       181: 4q+2
       183: q+1
       184: q+1
       185: 2q+1
       186: 2q+1
       187: 3q+2
       189: q^2+4q+2
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       197: 4q+2
       199: q^2+2q+1
       200: q^2+2q+1
       201: 2q+1
       202: 2q+1
       207: 3q^2+5q+2
       209: q^2+5q+2
       211: q^2+4q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: 3q^2+6q+2
       222: 3q+2
       223: 3q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 5q^2+6q+2
       227: q^2+5q+2
       228: 3q^2+6q+2
       229: 3q+2
       230: q^2+5q+2
       231: q^2+4q+2
       232: q+2
       233: 2q+2
       234: q+2
       236: q^2+4q+2
       237: q^2+5q+2
       239: q^2+5q+2
       241: 2q^2+4q+2
       243: q^2+5q+2
       244: 4q+2
       246: q^2+4q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 3q^2+6q+2
       251: 4q^2+6q+2
       252: 3q^2+6q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 2q+1
       262: 2q+1
       263: q+1
       266: q+1
       267: 2q+1
       269: 2q+1
       275: q^2+2q+1
       278: q^2+2q+1
       279: q+2
       281: 2q+2
       283: q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: q^2+4q+2
       289: q+2
       291: 3q+2
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 3q+2
       299: q+1
       300: q+1
       301: 4q+2
       303: 2q+1
       304: 2q+1
       305: 3q+2
       307: 1
       308: 1
       315: q^2+4q+2
       317: q^2+5q+2
       319: 2q+1
       320: 2q+1
       325: q^2+4q+2
       327: 2q+2
       329: 2q+2
       331: 2q+2
       333: q^2+5q+2
       334: 3q+2
       335: q^2+5q+2
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: 3q^2+6q+2
       347: 3q+2
       348: 3q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 2q+2
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: q^2+4q+2
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: q+1
       380: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       389: 2q+1
       391: 2q+1
       393: q+1
       396: q+1
       409: q+2
       411: 2q+2
       413: q+2
       415: q+2
       417: q+2
       419: q+1
       420: q+1
       421: 2q+1
       422: 2q+1
       423: 3q+2
       425: q+1
       427: 2q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 3q+2
       435: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 3q+2
       443: q+1
       444: q+1
       445: 2q+2
       447: 1
       448: 1
       453: 1
       454: 1
       465: q+2
       467: 2q+2
       469: q^2+4q+2
       471: 1
       472: 1
       481: 2
       482: 2q+2
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: q+1
       496: 2
       497: q+2
       498: q+2
       502: 2q+2
       504: 2q+2
       506: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: q+1
       532: q+1
       533: q+1
       536: q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: q+1
       547: q+1
       583: q+2
       585: 2
       587: q+2
       589: 1
       590: 1
       595: q+1
       596: q+1
       597: 1
       599: q+1
       601: 2
       603: q+1
       604: q+1
       605: q+2
       607: 2q+1
       608: 2q+1
       609: 3q+2
       611: q+2
       613: q+1
       615: 1
       616: 1
       617: 2
       619: 1
       620: 1
       635: q+2
       637: 2q+2
       639: q+2
       641: 1
       642: 1
       647: 1
       648: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: 1
       681: 2
       686: q+2
       687: q+2
       690: 2
       691: 2
       692: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: q+1
       727: q+1
       729: 1
       731: 1
       733: 1
       735: 1
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 2
       799: q+2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       811: q+1
       813: 2
       815: 1
       816: 1
       825: 1
       826: 1
       841: q+2
       845: 1
       846: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       877: 2
       896: 1
       899: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1052: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1214: 1
      1230: 1
      1236: 1
      1238: 1
      1283: 1
      1448: 1

1449:    0: 12q^2+8q+2
         1: 12q^2+8q+2
         2: 4q^3+9q^2+7q+2
         3: 12q^2+8q+2
         4: 4q^3+9q^2+7q+2
         5: 12q^2+8q+2
         6: 4q^3+9q^2+7q+2
         7: q^4+4q^3+7q^2+6q+2
         8: 4q^3+9q^2+7q+2
         9: q^4+4q^3+7q^2+6q+2
        10: 12q^2+8q+2
        11: 12q^2+8q+2
        12: 4q^3+9q^2+7q+2
        13: 8q^2+7q+2
        14: 2q^3+6q^2+6q+2
        15: 8q^2+7q+2
        16: 12q^2+8q+2
        17: 12q^2+8q+2
        18: q^4+4q^3+7q^2+6q+2
        19: 8q^2+7q+2
        20: 8q^2+7q+2
        21: 2q^3+6q^2+6q+2
        22: 12q^2+8q+2
        23: 12q^2+8q+2
        24: 4q^3+9q^2+7q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: q^3+4q^2+5q+2
        28: 12q^2+8q+2
        29: 8q^2+7q+2
        30: 5q^2+6q+2
        31: 12q^2+8q+2
        32: 8q^2+7q+2
        33: 12q^2+8q+2
        34: 4q^2+6q+2
        35: 3q^2+5q+2
        36: 4q^2+6q+2
        38: 4q^2+6q+2
        40: 4q^2+6q+2
        42: q^3+4q^2+5q+2
        43: 8q^2+7q+2
        44: 2q^3+6q^2+6q+2
        45: 8q^2+7q+2
        46: 8q^2+7q+2
        47: 8q^2+7q+2
        48: 2q^3+6q^2+6q+2
        49: 8q^2+7q+2
        50: 8q^2+7q+2
        51: 2q^3+6q^2+6q+2
        52: 8q^2+7q+2
        53: 8q^2+7q+2
        54: 2q^3+6q^2+6q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: 2q^2+4q+2
        58: 6q^2+4q+1
        59: 6q^2+4q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        63: 4q^2+6q+2
        65: 3q^2+5q+2
        67: 4q^2+6q+2
        68: 4q^2+6q+2
        69: 5q^2+6q+2
        70: 5q^2+6q+2
        71: 8q^2+7q+2
        72: 4q+2
        73: 4q^2+6q+2
        75: q^2+5q+2
        77: q^2+5q+2
        79: 2q^2+4q+2
        80: 8q^2+7q+2
        81: 8q^2+7q+2
        82: 8q^2+7q+2
        83: 5q^2+6q+2
        84: 3q^2+5q+2
        85: 3q^2+5q+2
        86: q^2+5q+2
        87: q^2+4q+2
        88: 8q^2+7q+2
        89: 8q^2+7q+2
        90: 2q^3+6q^2+6q+2
        91: 3q^2+6q+2
        92: 4q^2+6q+2
        93: 3q^2+6q+2
        94: 8q^2+7q+2
        95: 8q^2+7q+2
        96: 2q^3+6q^2+6q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: 2q^2+4q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: 2q^2+4q+2
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       112: 4q+2
       114: q^2+5q+2
       116: q^2+4q+2
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: q^2+2q+1
       120: q^2+2q+1
       122: 3q^2+5q+2
       124: 3q^2+5q+2
       125: 4q^2+6q+2
       126: 5q^2+6q+2
       128: q^2+5q+2
       130: q^2+5q+2
       132: 2q^2+4q+2
       133: q^2+5q+2
       134: 3q^2+6q+2
       135: 3q+2
       136: q^2+5q+2
       137: 8q^2+7q+2
       138: 5q^2+6q+2
       139: 8q^2+7q+2
       140: 4q+2
       141: 5q^2+6q+2
       142: 4q^2+6q+2
       143: 3q^2+5q+2
       144: q^2+4q+2
       145: q^2+5q+2
       146: q^2+4q+2
       147: 4q+2
       149: q^2+5q+2
       150: q^2+4q+2
       152: q^2+5q+2
       154: q^2+5q+2
       156: 2q^2+4q+2
       157: 3q^2+6q+2
       158: 4q^2+6q+2
       159: 3q^2+6q+2
       160: 3q^2+6q+2
       161: 4q^2+6q+2
       162: 3q^2+6q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: 2q^2+4q+2
       170: 2q+1
       171: 2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       178: q^2+4q+2
       180: q^2+5q+2
       182: 4q+2
       183: q+1
       184: q+1
       185: 2q+1
       186: 2q+1
       188: 3q+2
       190: q^2+4q+2
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       198: 4q+2
       199: q^2+2q+1
       200: q^2+2q+1
       201: 2q+1
       202: 2q+1
       208: 3q^2+5q+2
       210: q^2+5q+2
       212: q^2+4q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: 3q^2+6q+2
       222: 3q+2
       223: 3q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 5q^2+6q+2
       227: q^2+5q+2
       228: 3q^2+6q+2
       229: 3q+2
       230: q^2+5q+2
       231: q^2+4q+2
       232: q+2
       233: 2q+2
       234: q+2
       236: q^2+4q+2
       238: q^2+5q+2
       240: q^2+5q+2
       242: 2q^2+4q+2
       243: q^2+5q+2
       244: 4q+2
       246: q^2+4q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 3q^2+6q+2
       251: 4q^2+6q+2
       252: 3q^2+6q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: 2q+1
       261: 2q+1
       264: q+1
       265: q+1
       268: 2q+1
       270: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       280: q+2
       282: 2q+2
       283: q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       288: q^2+4q+2
       290: q+2
       292: 3q+2
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       298: 3q+2
       299: q+1
       300: q+1
       302: 4q+2
       303: 2q+1
       304: 2q+1
       306: 3q+2
       307: 1
       308: 1
       316: q^2+4q+2
       318: q^2+5q+2
       319: 2q+1
       320: 2q+1
       326: q^2+4q+2
       328: 2q+2
       330: 2q+2
       332: 2q+2
       333: q^2+5q+2
       334: 3q+2
       335: q^2+5q+2
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: 3q^2+6q+2
       347: 3q+2
       348: 3q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 2q+2
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: q^2+4q+2
       367: q+2
       368: 2q+2
       369: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       378: q+1
       379: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       390: 2q+1
       392: 2q+1
       394: q+1
       395: q+1
       410: q+2
       412: 2q+2
       414: q+2
       416: q+2
       418: q+2
       419: q+1
       420: q+1
       421: 2q+1
       422: 2q+1
       424: 3q+2
       426: q+1
       428: 2q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       434: 3q+2
       436: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 3q+2
       443: q+1
       444: q+1
       446: 2q+2
       447: 1
       448: 1
       453: 1
       454: 1
       466: q+2
       468: 2q+2
       470: q^2+4q+2
       471: 1
       472: 1
       481: 2
       482: 2q+2
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: q+1
       496: 2
       497: q+2
       498: q+2
       503: 2q+2
       505: 2q+2
       507: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: q+1
       531: q+1
       534: q+1
       535: q+1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: q+1
       548: q+1
       584: q+2
       586: 2
       588: q+2
       589: 1
       590: 1
       595: q+1
       596: q+1
       598: 1
       600: q+1
       602: 2
       603: q+1
       604: q+1
       606: q+2
       607: 2q+1
       608: 2q+1
       610: 3q+2
       612: q+2
       614: q+1
       615: 1
       616: 1
       618: 2
       619: 1
       620: 1
       636: q+2
       638: 2q+2
       640: q+2
       641: 1
       642: 1
       647: 1
       648: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: 1
       681: 2
       686: q+2
       687: q+2
       690: 2
       691: 2
       692: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: q+1
       728: q+1
       730: 1
       732: 1
       734: 1
       736: 1
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 2
       800: q+2
       801: 1
       802: 1
       807: q+1
       808: q+1
       810: 1
       812: q+1
       814: 2
       815: 1
       816: 1
       825: 1
       826: 1
       842: q+2
       845: 1
       846: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       877: 2
       897: 1
       898: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1052: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1215: 1
      1231: 1
      1237: 1
      1239: 1
      1283: 1
      1449: 1

1450:    0: 3q^3+19q^2+12q+2
         1: 3q^3+19q^2+12q+2
         2: q^4+7q^3+12q^2+8q+2
         3: 3q^3+19q^2+12q+2
         4: q^4+8q^3+15q^2+10q+2
         5: 3q^3+19q^2+12q+2
         6: q^4+8q^3+15q^2+10q+2
         7: q^4+5q^3+9q^2+7q+2
         8: q^4+7q^3+12q^2+8q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 3q^3+19q^2+12q+2
        11: 3q^3+19q^2+12q+2
        12: q^4+8q^3+15q^2+10q+2
        13: 8q^2+8q+2
        14: q^3+6q^2+7q+2
        15: 8q^2+8q+2
        16: 3q^3+19q^2+12q+2
        17: 3q^3+19q^2+12q+2
        18: q^4+5q^3+9q^2+7q+2
        19: 2q^3+13q^2+10q+2
        20: 2q^3+13q^2+10q+2
        21: 3q^3+8q^2+7q+2
        22: 3q^3+19q^2+12q+2
        23: 3q^3+19q^2+12q+2
        24: q^4+7q^3+12q^2+8q+2
        25: 14q^2+12q+2
        26: 14q^2+12q+2
        27: 4q^3+10q^2+8q+2
        28: 3q^3+19q^2+12q+2
        29: 2q^3+13q^2+10q+2
        30: 5q^2+7q+2
        31: 3q^3+19q^2+12q+2
        32: 8q^2+8q+2
        33: 3q^3+19q^2+12q+2
        34: 14q^2+12q+2
        35: 6q^2+8q+2
        36: 14q^2+12q+2
        37: 7q^2+6q+1
        38: 7q^2+6q+1
        39: 7q^2+6q+1
        40: 7q^2+6q+1
        41: 2q^3+5q^2+4q+1
        42: 2q^3+5q^2+4q+1
        43: 8q^2+8q+2
        44: q^3+6q^2+7q+2
        45: 8q^2+8q+2
        46: 8q^2+8q+2
        47: 8q^2+8q+2
        48: q^3+6q^2+7q+2
        49: 2q^3+13q^2+10q+2
        50: 2q^3+13q^2+10q+2
        51: 3q^3+8q^2+7q+2
        52: 2q^3+13q^2+10q+2
        53: 2q^3+13q^2+10q+2
        54: 3q^3+8q^2+7q+2
        55: 8q^2+10q+2
        56: 8q^2+10q+2
        57: q^3+6q^2+7q+2
        58: 2q^3+11q^2+8q+2
        59: q^3+8q^2+4q
        60: 7q^2+6q+1
        61: 7q^2+6q+1
        62: 7q^2+6q+1
        63: 7q^2+6q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 7q^2+6q+1
        67: 7q^2+6q+1
        68: 2q^2+4q+2
        69: 5q^2+7q+2
        70: 5q^2+7q+2
        71: 2q^3+13q^2+10q+2
        72: 4q^2+8q+2
        73: q^3+7q^2+8q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 8q^2+8q+2
        81: 8q^2+8q+2
        82: 2q^3+13q^2+10q+2
        83: 5q^2+7q+2
        84: 6q^2+8q+2
        85: 6q^2+8q+2
        86: 8q^2+10q+2
        87: 3q^2+7q+2
        88: 8q^2+8q+2
        89: 8q^2+8q+2
        90: q^3+6q^2+7q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 2q^3+13q^2+10q+2
        95: 2q^3+13q^2+10q+2
        96: 3q^3+8q^2+7q+2
        97: 8q^2+10q+2
        98: 8q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 8q^2+10q+2
       101: 8q^2+10q+2
       102: q^3+6q^2+7q+2
       103: 4q^2+4q+1
       104: 3q^2+2q
       105: 4q^2+4q+1
       106: 3q^2+2q
       107: 2q^2+4q+1
       108: 2q^2+4q+1
       109: q^3+5q^2+6q+2
       110: 2q^2+2q
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: 2q^2+4q+2
       119: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: 2q^2+4q+2
       126: 5q^2+7q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 3q+2
       134: 2q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 8q^2+8q+2
       138: 5q^2+7q+2
       139: 2q^3+13q^2+10q+2
       140: 4q^2+8q+2
       141: 5q^2+7q+2
       142: q^3+7q^2+8q+2
       143: 6q^2+8q+2
       144: 3q^2+7q+2
       145: 8q^2+10q+2
       146: 3q^2+7q+2
       147: 4q^2+8q+2
       148: 2q^2+4q+2
       149: 8q^2+10q+2
       150: 3q^2+7q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+6q+2
       158: 4q^2+6q+2
       159: 2q^2+6q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: 8q^2+10q+2
       167: 8q^2+10q+2
       168: q^3+6q^2+7q+2
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: q^2+2q+1
       175: q^2+2q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: q+1
       184: q+1
       185: 3q+2
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 2q^2+4q+2
       193: 2q^2+4q+1
       194: 2q^2+4q+1
       195: q^3+5q^2+6q+2
       196: 2q^2+2q
       197: 3q+1
       198: 3q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: 2q^2+4q+1
       202: 2q^2+4q+1
       203: 2q^2+4q+2
       205: q+1
       206: q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 3q+2
       220: 3q+2
       221: 2q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 5q^2+7q+2
       227: 3q+2
       228: 2q^2+6q+2
       229: q^2+5q+2
       230: q^2+5q+2
       231: 3q^2+7q+2
       232: q+2
       233: 3q+2
       234: 2q+2
       235: q+2
       236: 3q^2+7q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 8q^2+10q+2
       244: 4q^2+8q+2
       245: 2q^2+4q+2
       246: 3q^2+7q+2
       247: 8q+4
       248: 8q+4
       249: 2q^2+4q+2
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 3q+2
       254: q^2+3q+2
       255: 3q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 2q+1
       260: q
       261: 2q+1
       262: q
       263: q+1
       265: q+1
       267: 2q+1
       268: q
       269: q
       270: 2q+1
       271: q+1
       272: q+1
       275: q^2+2q+1
       277: q^2+2q+1
       283: q+1
       284: q+1
       285: 3q+2
       287: q^2+3q+1
       288: q^2+3q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: 3q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       301: 3q+1
       302: 3q+1
       303: 3q+2
       305: 2q+1
       306: 2q+1
       307: 1
       308: 1
       309: q+2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 2q^2+4q+1
       320: 2q^2+4q+1
       321: 2q^2+4q+2
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: 2q+2
       337: 8q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 3q+2
       345: 3q+2
       346: 2q^2+6q+2
       347: q^2+5q+2
       348: q^2+5q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 8q+4
       352: q+2
       353: q+2
       354: 3q+2
       355: 2q+2
       356: 2q+2
       357: q+2
       358: q+2
       359: 4q+4
       366: 3q^2+7q+2
       367: q+2
       368: 3q+2
       369: 2q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       377: q+1
       379: q+1
       385: q+1
       387: q+1
       389: 2q+1
       390: q
       391: q
       392: 2q+1
       393: q+1
       395: q+1
       397: q+1
       398: q+1
       401: 1
       402: 1
       405: q+1
       408: q+1
       419: q+1
       420: q+1
       421: 3q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: q+1
       430: q+1
       431: 3q+2
       433: 2q+1
       434: 2q+1
       437: q+1
       438: q+1
       439: 3q+2
       441: 2q+1
       442: 2q+1
       443: 4q+2
       444: 4q+2
       445: 4q+2
       446: 4q+2
       447: 1
       448: 1
       449: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       457: q+2
       459: 1
       460: 1
       461: 4q+4
       463: 2q+2
       464: 2q+2
       469: q^2+3q+1
       470: q^2+3q+1
       471: 1
       472: 1
       473: q+2
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: 2q+2
       480: 2q+2
       481: 2
       482: q+1
       483: 2q+2
       484: 2
       491: 1
       492: 3q+2
       493: q^2+5q+2
       494: q^2+5q+2
       495: 2q+2
       496: q+2
       497: q+2
       498: 2q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 3q+2
       511: 2q+2
       512: 2q+2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       529: q+1
       531: q+1
       533: q+1
       535: q+1
       541: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 2q+2
       562: 2q+2
       565: 1
       567: 1
       569: q+1
       572: q+1
       573: 2q+2
       576: 2q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       589: 1
       590: 1
       591: 2
       595: q+1
       599: q+1
       600: q+1
       603: q+1
       604: q+1
       607: 3q+2
       609: 2q+1
       610: 2q+1
       613: q+1
       614: q+1
       615: 1
       616: 1
       619: 1
       620: 1
       621: q+2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       641: 1
       642: 1
       643: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       649: q+2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: q+2
       675: 2
       676: q+1
       677: 2q+2
       678: q+2
       679: 1
       680: 2
       681: 2
       683: 2
       684: 2
       685: 1
       686: q+2
       687: 2q+2
       688: q+2
       689: 2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       694: q+1
       698: q+1
       700: q+1
       713: 1
       714: 1
       725: q+1
       728: q+1
       741: 1
       742: 1
       753: 1
       755: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: 2
       807: q+1
       811: q+1
       812: q+1
       815: 1
       816: 1
       817: 2
       825: 1
       826: 1
       827: 2
       835: 1
       836: 1
       839: 2
       843: 1
       844: 1
       845: 1
       846: 1
       847: q+2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: 2
       879: 2
       880: 1
       924: 1
       925: 1
       948: 1
       949: 1
       964: 1
       966: 1
       974: 1
       977: 1
       988: 1
       990: 1
       998: 1
      1006: 1
      1016: 1
      1017: 1
      1028: 1
      1032: 2
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1054: 2
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1194: 1
      1196: 1
      1202: 1
      1203: 1
      1216: 1
      1232: 1
      1242: 1
      1283: 1
      1288: 1
      1450: 1

1451:    0: 3q^3+19q^2+12q+2
         1: 3q^3+19q^2+12q+2
         2: q^4+7q^3+12q^2+8q+2
         3: 3q^3+19q^2+12q+2
         4: q^4+8q^3+15q^2+10q+2
         5: 3q^3+19q^2+12q+2
         6: q^4+8q^3+15q^2+10q+2
         7: q^4+5q^3+9q^2+7q+2
         8: q^4+7q^3+12q^2+8q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 3q^3+19q^2+12q+2
        11: 3q^3+19q^2+12q+2
        12: q^4+8q^3+15q^2+10q+2
        13: 8q^2+8q+2
        14: q^3+6q^2+7q+2
        15: 8q^2+8q+2
        16: 3q^3+19q^2+12q+2
        17: 3q^3+19q^2+12q+2
        18: q^4+5q^3+9q^2+7q+2
        19: 2q^3+13q^2+10q+2
        20: 2q^3+13q^2+10q+2
        21: 3q^3+8q^2+7q+2
        22: 3q^3+19q^2+12q+2
        23: 3q^3+19q^2+12q+2
        24: q^4+7q^3+12q^2+8q+2
        25: 14q^2+12q+2
        26: 14q^2+12q+2
        27: 4q^3+10q^2+8q+2
        28: 3q^3+19q^2+12q+2
        29: 2q^3+13q^2+10q+2
        30: 5q^2+7q+2
        31: 3q^3+19q^2+12q+2
        32: 8q^2+8q+2
        33: 3q^3+19q^2+12q+2
        34: 14q^2+12q+2
        35: 6q^2+8q+2
        36: 14q^2+12q+2
        37: 7q^2+6q+1
        38: 7q^2+6q+1
        39: 7q^2+6q+1
        40: 7q^2+6q+1
        41: 2q^3+5q^2+4q+1
        42: 2q^3+5q^2+4q+1
        43: 8q^2+8q+2
        44: q^3+6q^2+7q+2
        45: 8q^2+8q+2
        46: 8q^2+8q+2
        47: 8q^2+8q+2
        48: q^3+6q^2+7q+2
        49: 2q^3+13q^2+10q+2
        50: 2q^3+13q^2+10q+2
        51: 3q^3+8q^2+7q+2
        52: 2q^3+13q^2+10q+2
        53: 2q^3+13q^2+10q+2
        54: 3q^3+8q^2+7q+2
        55: 8q^2+10q+2
        56: 8q^2+10q+2
        57: q^3+6q^2+7q+2
        58: q^3+8q^2+4q
        59: 2q^3+11q^2+8q+2
        60: 7q^2+6q+1
        61: 7q^2+6q+1
        62: 7q^2+6q+1
        63: 7q^2+6q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 7q^2+6q+1
        67: 7q^2+6q+1
        68: 2q^2+4q+2
        69: 5q^2+7q+2
        70: 5q^2+7q+2
        71: 2q^3+13q^2+10q+2
        72: 4q^2+8q+2
        73: q^3+7q^2+8q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 8q^2+8q+2
        81: 8q^2+8q+2
        82: 2q^3+13q^2+10q+2
        83: 5q^2+7q+2
        84: 6q^2+8q+2
        85: 6q^2+8q+2
        86: 8q^2+10q+2
        87: 3q^2+7q+2
        88: 8q^2+8q+2
        89: 8q^2+8q+2
        90: q^3+6q^2+7q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 2q^3+13q^2+10q+2
        95: 2q^3+13q^2+10q+2
        96: 3q^3+8q^2+7q+2
        97: 8q^2+10q+2
        98: 8q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 8q^2+10q+2
       101: 8q^2+10q+2
       102: q^3+6q^2+7q+2
       103: 3q^2+2q
       104: 4q^2+4q+1
       105: 3q^2+2q
       106: 4q^2+4q+1
       107: 2q^2+4q+1
       108: 2q^2+4q+1
       109: 2q^2+2q
       110: q^3+5q^2+6q+2
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       118: 2q^2+4q+2
       119: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: 2q^2+4q+2
       126: 5q^2+7q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 3q+2
       134: 2q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 8q^2+8q+2
       138: 5q^2+7q+2
       139: 2q^3+13q^2+10q+2
       140: 4q^2+8q+2
       141: 5q^2+7q+2
       142: q^3+7q^2+8q+2
       143: 6q^2+8q+2
       144: 3q^2+7q+2
       145: 8q^2+10q+2
       146: 3q^2+7q+2
       147: 4q^2+8q+2
       148: 2q^2+4q+2
       149: 8q^2+10q+2
       150: 3q^2+7q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+6q+2
       158: 4q^2+6q+2
       159: 2q^2+6q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 3q+2
       164: q^2+3q+2
       165: 3q+2
       166: 8q^2+10q+2
       167: 8q^2+10q+2
       168: q^3+6q^2+7q+2
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       174: q^2+2q+1
       176: q^2+2q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: q+1
       184: q+1
       186: 3q+2
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       192: 2q^2+4q+2
       193: 2q^2+4q+1
       194: 2q^2+4q+1
       195: 2q^2+2q
       196: q^3+5q^2+6q+2
       197: 3q+1
       198: 3q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: 2q^2+4q+1
       202: 2q^2+4q+1
       204: 2q^2+4q+2
       205: q+1
       206: q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 3q+2
       220: 3q+2
       221: 2q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 5q^2+7q+2
       227: 3q+2
       228: 2q^2+6q+2
       229: q^2+5q+2
       230: q^2+5q+2
       231: 3q^2+7q+2
       232: q+2
       233: 3q+2
       234: 2q+2
       235: q+2
       236: 3q^2+7q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 8q^2+10q+2
       244: 4q^2+8q+2
       245: 2q^2+4q+2
       246: 3q^2+7q+2
       247: 8q+4
       248: 8q+4
       249: 2q^2+4q+2
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 3q+2
       254: q^2+3q+2
       255: 3q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: q
       260: 2q+1
       261: q
       262: 2q+1
       264: q+1
       266: q+1
       267: q
       268: 2q+1
       269: 2q+1
       270: q
       273: q+1
       274: q+1
       276: q^2+2q+1
       278: q^2+2q+1
       283: q+1
       284: q+1
       286: 3q+2
       287: q^2+3q+1
       288: q^2+3q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       296: 3q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       301: 3q+1
       302: 3q+1
       304: 3q+2
       305: 2q+1
       306: 2q+1
       307: 1
       308: 1
       310: q+2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 2q^2+4q+1
       320: 2q^2+4q+1
       322: 2q^2+4q+2
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: 2q+2
       337: 8q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 3q+2
       345: 3q+2
       346: 2q^2+6q+2
       347: q^2+5q+2
       348: q^2+5q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 8q+4
       352: q+2
       353: q+2
       354: 3q+2
       355: 2q+2
       356: 2q+2
       357: q+2
       358: q+2
       359: 4q+4
       366: 3q^2+7q+2
       367: q+2
       368: 3q+2
       369: 2q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       378: q+1
       380: q+1
       386: q+1
       388: q+1
       389: q
       390: 2q+1
       391: 2q+1
       392: q
       394: q+1
       396: q+1
       399: q+1
       400: q+1
       403: 1
       404: 1
       406: q+1
       407: q+1
       419: q+1
       420: q+1
       422: 3q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: q+1
       430: q+1
       432: 3q+2
       433: 2q+1
       434: 2q+1
       437: q+1
       438: q+1
       440: 3q+2
       441: 2q+1
       442: 2q+1
       443: 4q+2
       444: 4q+2
       445: 4q+2
       446: 4q+2
       447: 1
       448: 1
       450: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       458: q+2
       459: 1
       460: 1
       462: 4q+4
       463: 2q+2
       464: 2q+2
       469: q^2+3q+1
       470: q^2+3q+1
       471: 1
       472: 1
       474: q+2
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: 2q+2
       480: 2q+2
       481: 2
       482: q+1
       483: 2q+2
       484: 2
       491: 1
       492: 3q+2
       493: q^2+5q+2
       494: q^2+5q+2
       495: 2q+2
       496: q+2
       497: q+2
       498: 2q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 3q+2
       511: 2q+2
       512: 2q+2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       530: q+1
       532: q+1
       534: q+1
       536: q+1
       542: q+1
       543: q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 2q+2
       564: 2q+2
       566: 1
       568: 1
       570: q+1
       571: q+1
       574: 2q+2
       575: 2q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       589: 1
       590: 1
       592: 2
       596: q+1
       599: q+1
       600: q+1
       603: q+1
       604: q+1
       608: 3q+2
       609: 2q+1
       610: 2q+1
       613: q+1
       614: q+1
       615: 1
       616: 1
       619: 1
       620: 1
       622: q+2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2
       641: 1
       642: 1
       644: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       650: q+2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: q+2
       675: 2
       676: q+1
       677: 2q+2
       678: q+2
       679: 1
       680: 2
       681: 2
       683: 2
       684: 2
       685: 1
       686: q+2
       687: 2q+2
       688: q+2
       689: 2
       690: q+2
       691: q+2
       692: q+1
       696: q+1
       697: q+1
       699: q+1
       701: q+1
       715: 1
       716: 1
       726: q+1
       727: q+1
       743: 1
       744: 1
       754: 1
       756: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: 2
       808: q+1
       811: q+1
       812: q+1
       815: 1
       816: 1
       818: 2
       825: 1
       826: 1
       828: 2
       835: 1
       836: 1
       840: 2
       843: 1
       844: 1
       845: 1
       846: 1
       848: q+2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: 2
       879: 2
       880: 1
       926: 1
       927: 1
       950: 1
       951: 1
       965: 1
       967: 1
       975: 1
       976: 1
       989: 1
       991: 1
       999: 1
      1007: 1
      1016: 1
      1017: 1
      1029: 1
      1033: 2
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1055: 2
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1195: 1
      1197: 1
      1204: 1
      1205: 1
      1217: 1
      1233: 1
      1243: 1
      1283: 1
      1288: 1
      1451: 1

1452:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2q+2
        74: q+2
        76: q+2
        78: q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       103: 1
       106: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       115: q+2
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: 2q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2q+2
       137: 2q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: 2
       189: q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: 1
       200: 1
       201: 1
       202: 1
       207: 2
       209: q+2
       211: q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: 2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: 1
       308: 1
       315: 1
       317: 2
       319: 1
       320: 1
       325: q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       453: 1
       454: 1
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: 1
       498: 1
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       635: 2
       637: 1
       639: 1
       647: 1
       648: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       729: 1
       731: 1
       733: 1
       735: 1
       777: 1
       779: 1
       781: 1
       783: 1
       789: 2
       795: 1
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       841: 1
       859: 1
       861: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       932: 1
       934: 1
       996: 1
      1002: 1
      1014: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1066: 1
      1068: 1
      1070: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1212: 1
      1226: 1
      1236: 1
      1238: 1
      1284: 1
      1452: 1

1453:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2
        73: 2q+2
        75: q+2
        77: q+2
        79: q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       104: 1
       105: 1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: q+2
       116: q+2
       117: q+1
       118: q+1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: 2q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2
       136: 2q+2
       137: 2q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: 2
       190: q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: 1
       200: 1
       201: 1
       202: 1
       208: 2
       210: q+2
       212: q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2
       223: 1
       224: 2q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2q+2
       231: 1
       232: 2
       233: 1
       234: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       298: 2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: 1
       308: 1
       316: 1
       318: 2
       319: 1
       320: 1
       326: q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       453: 1
       454: 1
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: 1
       498: 1
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       636: 2
       638: 1
       640: 1
       647: 1
       648: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       730: 1
       732: 1
       734: 1
       736: 1
       778: 1
       780: 1
       782: 1
       784: 1
       790: 2
       796: 1
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       842: 1
       860: 1
       862: 1
       864: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       933: 1
       935: 1
       997: 1
      1003: 1
      1015: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1067: 1
      1069: 1
      1071: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1213: 1
      1227: 1
      1237: 1
      1239: 1
      1284: 1
      1453: 1

1454:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q+2
        31: 2q+2
        32: q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2q+2
        53: 2q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q+2
        70: q+2
        71: 2q+2
        72: 2
        73: 2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q+2
        82: 2q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 2q+2
        95: 2q+2
        96: q^2+q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q+2
       135: 2
       136: q+2
       137: q+2
       138: q+2
       139: 2q+2
       140: 2
       141: q+2
       142: 2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2
       224: q+2
       225: q+2
       226: q+2
       227: 2
       228: q+2
       229: 2
       230: q+2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: q+2
       251: q+2
       252: q+2
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       283: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q+2
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: 1
       453: 1
       469: 1
       470: 1
       471: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 1
       546: 1
       589: 1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       619: 1
       641: 1
       647: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2
       677: 2
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       717: 1
       718: 1
       725: 1
       726: 1
       785: 1
       793: 1
       801: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 1
       825: 1
       845: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       928: 1
       929: 1
      1000: 1
      1004: 1
      1016: 1
      1026: 1
      1052: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1218: 1
      1234: 1
      1240: 1
      1283: 1
      1454: 1

1455:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2q+2
        23: 2q+2
        24: q^2+q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q+2
        31: 2q+2
        32: q+2
        33: 2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2q+2
        53: 2q+2
        54: q^2+q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q+2
        70: q+2
        71: 2q+2
        72: 2
        73: 2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: q+2
        81: q+2
        82: 2q+2
        83: q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 2q+2
        95: 2q+2
        96: q^2+q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q+2
       135: 2
       136: q+2
       137: q+2
       138: q+2
       139: 2q+2
       140: 2
       141: q+2
       142: 2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: 2
       171: 1
       172: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: 2
       223: 2
       224: q+2
       225: q+2
       226: q+2
       227: 2
       228: q+2
       229: 2
       230: q+2
       231: 2
       232: 1
       233: 1
       234: 1
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: q+2
       251: q+2
       252: q+2
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       284: 2
       285: 1
       286: 1
       287: 1
       288: 1
       291: 1
       292: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 2
       325: 1
       326: 1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q+2
       351: 2
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       366: 2
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: 1
       454: 1
       469: 1
       470: 1
       472: 1
       481: 1
       482: 2
       483: 2
       484: 1
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 1
       497: 1
       498: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 1
       548: 1
       590: 1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 1
       620: 1
       642: 1
       648: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2
       677: 2
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       719: 1
       720: 1
       727: 1
       728: 1
       786: 1
       794: 1
       802: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 1
       826: 1
       846: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       930: 1
       931: 1
      1001: 1
      1005: 1
      1017: 1
      1027: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1219: 1
      1235: 1
      1241: 1
      1283: 1
      1455: 1

1456:    0: 12q^2+8q+2
         1: 12q^2+8q+2
         2: 4q^3+9q^2+7q+2
         3: 12q^2+8q+2
         4: 4q^3+9q^2+7q+2
         5: 12q^2+8q+2
         6: 4q^3+9q^2+7q+2
         7: q^4+4q^3+7q^2+6q+2
         8: 4q^3+9q^2+7q+2
         9: q^4+4q^3+7q^2+6q+2
        10: 12q^2+8q+2
        11: 12q^2+8q+2
        12: 4q^3+9q^2+7q+2
        13: 8q^2+7q+2
        14: 2q^3+6q^2+6q+2
        15: 8q^2+7q+2
        16: 12q^2+8q+2
        17: 12q^2+8q+2
        18: q^4+4q^3+7q^2+6q+2
        19: 8q^2+7q+2
        20: 8q^2+7q+2
        21: 2q^3+6q^2+6q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: q^3+4q^2+5q+2
        25: 12q^2+8q+2
        26: 12q^2+8q+2
        27: 4q^3+9q^2+7q+2
        28: 12q^2+8q+2
        29: 8q^2+7q+2
        30: 5q^2+6q+2
        31: 4q^2+6q+2
        32: 3q^2+5q+2
        33: 4q^2+6q+2
        34: 12q^2+8q+2
        35: 8q^2+7q+2
        36: 12q^2+8q+2
        37: 4q^2+6q+2
        39: 4q^2+6q+2
        41: q^3+4q^2+5q+2
        43: 8q^2+7q+2
        44: 2q^3+6q^2+6q+2
        45: 8q^2+7q+2
        46: 8q^2+7q+2
        47: 8q^2+7q+2
        48: 2q^3+6q^2+6q+2
        49: 8q^2+7q+2
        50: 8q^2+7q+2
        51: 2q^3+6q^2+6q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: 2q^2+4q+2
        55: 8q^2+7q+2
        56: 8q^2+7q+2
        57: 2q^3+6q^2+6q+2
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 6q^2+4q+1
        61: 6q^2+4q+1
        62: 4q^2+6q+2
        64: 3q^2+5q+2
        66: 4q^2+6q+2
        68: 4q^2+6q+2
        69: 5q^2+6q+2
        70: 5q^2+6q+2
        71: 8q^2+7q+2
        72: 4q^2+6q+2
        73: 4q+2
        74: q^2+5q+2
        76: q^2+5q+2
        78: 2q^2+4q+2
        80: 3q^2+5q+2
        81: 3q^2+5q+2
        82: q^2+5q+2
        83: q^2+4q+2
        84: 8q^2+7q+2
        85: 8q^2+7q+2
        86: 8q^2+7q+2
        87: 5q^2+6q+2
        88: 8q^2+7q+2
        89: 8q^2+7q+2
        90: 2q^3+6q^2+6q+2
        91: 3q^2+6q+2
        92: 4q^2+6q+2
        93: 3q^2+6q+2
        94: q^2+5q+2
        95: q^2+5q+2
        96: 2q^2+4q+2
        97: 8q^2+7q+2
        98: 8q^2+7q+2
        99: 2q^3+6q^2+6q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: 2q^2+4q+2
       103: 2q^2+3q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: 4q+2
       113: q^2+5q+2
       115: q^2+4q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 3q^2+5q+2
       123: 3q^2+5q+2
       125: 4q^2+6q+2
       126: 5q^2+6q+2
       127: q^2+5q+2
       129: q^2+5q+2
       131: 2q^2+4q+2
       133: q^2+5q+2
       134: 3q^2+6q+2
       135: q^2+5q+2
       136: 3q+2
       137: 3q^2+5q+2
       138: q^2+4q+2
       139: q^2+5q+2
       141: q^2+4q+2
       142: 4q+2
       143: 8q^2+7q+2
       144: 5q^2+6q+2
       145: 8q^2+7q+2
       146: 5q^2+6q+2
       147: 4q^2+6q+2
       148: 4q+2
       149: q^2+5q+2
       150: q^2+4q+2
       151: q^2+5q+2
       153: q^2+5q+2
       155: 2q^2+4q+2
       157: 3q^2+6q+2
       158: 4q^2+6q+2
       159: 3q^2+6q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 3q^2+6q+2
       164: 4q^2+6q+2
       165: 3q^2+6q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: 2q^2+4q+2
       169: 2q+1
       172: 2q+1
       173: q^2+2q+1
       176: q^2+2q+1
       177: q^2+4q+2
       179: q^2+5q+2
       181: 4q+2
       183: 2q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 3q+2
       189: q^2+4q+2
       191: q^2+2q+1
       192: q^2+2q+1
       195: 2q+1
       196: 2q+1
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q+1
       204: 2q+1
       205: 4q+2
       207: 3q^2+5q+2
       209: q^2+5q+2
       211: q^2+4q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: 3q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: 3q+2
       225: 3q+2
       226: q^2+4q+2
       227: q+2
       228: 2q+2
       230: q+2
       231: 5q^2+6q+2
       232: q^2+5q+2
       233: 3q^2+6q+2
       234: q^2+5q+2
       235: 3q+2
       236: q^2+4q+2
       237: q^2+5q+2
       239: q^2+5q+2
       241: 2q^2+4q+2
       243: q^2+5q+2
       245: 4q+2
       246: q^2+4q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 3q^2+6q+2
       254: 4q^2+6q+2
       255: 3q^2+6q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 2q+1
       262: 2q+1
       263: q+1
       266: q+1
       271: 2q+1
       273: 2q+1
       275: q^2+2q+1
       278: q^2+2q+1
       279: q+2
       281: 2q+2
       283: 2q+1
       284: 2q+1
       285: q+1
       286: q+1
       287: q^2+4q+2
       289: q+2
       291: 3q+2
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: 3q+2
       303: 1
       304: 1
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 4q+2
       313: 3q+2
       315: q^2+4q+2
       317: q^2+5q+2
       321: 2q+1
       322: 2q+1
       325: q^2+4q+2
       327: 2q+2
       329: 2q+2
       331: 2q+2
       333: q^2+5q+2
       334: q^2+5q+2
       335: 3q+2
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: q+2
       345: q+2
       346: 2q+2
       349: q+2
       350: q+2
       352: q^2+5q+2
       353: q^2+5q+2
       354: 3q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: 3q+2
       358: 3q+2
       359: 2q+2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: q^2+4q+2
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: q+1
       380: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       397: 2q+1
       399: 2q+1
       401: q+1
       404: q+1
       409: q+2
       411: 2q+2
       413: q+2
       415: q+2
       417: q+2
       419: 2q+1
       420: 2q+1
       421: q+1
       422: q+1
       423: 3q+2
       425: q+1
       427: 2q+2
       431: 1
       432: 1
       439: 1
       440: 1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 3q+2
       453: 2q+1
       454: 2q+1
       455: q+2
       457: q+1
       458: q+1
       459: 3q+2
       461: q+1
       462: q+1
       463: 2q+2
       465: q+2
       467: 2q+2
       469: q^2+4q+2
       473: 1
       474: 1
       481: 2q+2
       482: 2
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+2
       494: q+2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: q+1
       501: 2
       502: 2q+2
       504: 2q+2
       506: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: q+1
       532: q+1
       549: q+1
       552: q+1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: q+1
       563: q+1
       583: q+2
       585: 2
       587: q+2
       589: q+1
       590: q+1
       595: 1
       596: 1
       597: 1
       599: q+1
       601: 2
       607: 1
       608: 1
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       623: q+2
       625: 3q+2
       627: q+2
       629: q+1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 2q+2
       639: q+2
       643: 1
       644: 1
       649: 1
       650: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       676: 2
       680: 2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: q+2
       688: q+2
       690: 2
       691: 2
       692: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       737: 1
       739: 1
       741: q+1
       743: q+1
       745: 1
       747: 1
       749: 1
       751: 1
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       807: 1
       808: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: q+2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       835: q+1
       837: 2
       839: 1
       840: 1
       841: q+2
       847: 1
       848: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       873: 2
       874: 1
       875: 1
       876: 1
       878: 2
       896: 1
       899: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1058: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1214: 1
      1248: 1
      1252: 1
      1256: 1
      1285: 1
      1456: 1

1457:    0: 12q^2+8q+2
         1: 12q^2+8q+2
         2: 4q^3+9q^2+7q+2
         3: 12q^2+8q+2
         4: 4q^3+9q^2+7q+2
         5: 12q^2+8q+2
         6: 4q^3+9q^2+7q+2
         7: q^4+4q^3+7q^2+6q+2
         8: 4q^3+9q^2+7q+2
         9: q^4+4q^3+7q^2+6q+2
        10: 12q^2+8q+2
        11: 12q^2+8q+2
        12: 4q^3+9q^2+7q+2
        13: 8q^2+7q+2
        14: 2q^3+6q^2+6q+2
        15: 8q^2+7q+2
        16: 12q^2+8q+2
        17: 12q^2+8q+2
        18: q^4+4q^3+7q^2+6q+2
        19: 8q^2+7q+2
        20: 8q^2+7q+2
        21: 2q^3+6q^2+6q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: q^3+4q^2+5q+2
        25: 12q^2+8q+2
        26: 12q^2+8q+2
        27: 4q^3+9q^2+7q+2
        28: 12q^2+8q+2
        29: 8q^2+7q+2
        30: 5q^2+6q+2
        31: 4q^2+6q+2
        32: 3q^2+5q+2
        33: 4q^2+6q+2
        34: 12q^2+8q+2
        35: 8q^2+7q+2
        36: 12q^2+8q+2
        38: 4q^2+6q+2
        40: 4q^2+6q+2
        42: q^3+4q^2+5q+2
        43: 8q^2+7q+2
        44: 2q^3+6q^2+6q+2
        45: 8q^2+7q+2
        46: 8q^2+7q+2
        47: 8q^2+7q+2
        48: 2q^3+6q^2+6q+2
        49: 8q^2+7q+2
        50: 8q^2+7q+2
        51: 2q^3+6q^2+6q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: 2q^2+4q+2
        55: 8q^2+7q+2
        56: 8q^2+7q+2
        57: 2q^3+6q^2+6q+2
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 6q^2+4q+1
        61: 6q^2+4q+1
        63: 4q^2+6q+2
        65: 3q^2+5q+2
        67: 4q^2+6q+2
        68: 4q^2+6q+2
        69: 5q^2+6q+2
        70: 5q^2+6q+2
        71: 8q^2+7q+2
        72: 4q^2+6q+2
        73: 4q+2
        75: q^2+5q+2
        77: q^2+5q+2
        79: 2q^2+4q+2
        80: 3q^2+5q+2
        81: 3q^2+5q+2
        82: q^2+5q+2
        83: q^2+4q+2
        84: 8q^2+7q+2
        85: 8q^2+7q+2
        86: 8q^2+7q+2
        87: 5q^2+6q+2
        88: 8q^2+7q+2
        89: 8q^2+7q+2
        90: 2q^3+6q^2+6q+2
        91: 3q^2+6q+2
        92: 4q^2+6q+2
        93: 3q^2+6q+2
        94: q^2+5q+2
        95: q^2+5q+2
        96: 2q^2+4q+2
        97: 8q^2+7q+2
        98: 8q^2+7q+2
        99: 2q^3+6q^2+6q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: 2q^2+4q+2
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q+1
       110: 2q+1
       112: 4q+2
       114: q^2+5q+2
       116: q^2+4q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       122: 3q^2+5q+2
       124: 3q^2+5q+2
       125: 4q^2+6q+2
       126: 5q^2+6q+2
       128: q^2+5q+2
       130: q^2+5q+2
       132: 2q^2+4q+2
       133: q^2+5q+2
       134: 3q^2+6q+2
       135: q^2+5q+2
       136: 3q+2
       137: 3q^2+5q+2
       138: q^2+4q+2
       139: q^2+5q+2
       141: q^2+4q+2
       142: 4q+2
       143: 8q^2+7q+2
       144: 5q^2+6q+2
       145: 8q^2+7q+2
       146: 5q^2+6q+2
       147: 4q^2+6q+2
       148: 4q+2
       149: q^2+5q+2
       150: q^2+4q+2
       152: q^2+5q+2
       154: q^2+5q+2
       156: 2q^2+4q+2
       157: 3q^2+6q+2
       158: 4q^2+6q+2
       159: 3q^2+6q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 3q^2+6q+2
       164: 4q^2+6q+2
       165: 3q^2+6q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: 2q^2+4q+2
       170: 2q+1
       171: 2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       178: q^2+4q+2
       180: q^2+5q+2
       182: 4q+2
       183: 2q+1
       184: 2q+1
       185: q+1
       186: q+1
       188: 3q+2
       190: q^2+4q+2
       191: q^2+2q+1
       192: q^2+2q+1
       195: 2q+1
       196: 2q+1
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q+1
       204: 2q+1
       206: 4q+2
       208: 3q^2+5q+2
       210: q^2+5q+2
       212: q^2+4q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: 3q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: 3q+2
       225: 3q+2
       226: q^2+4q+2
       227: q+2
       228: 2q+2
       230: q+2
       231: 5q^2+6q+2
       232: q^2+5q+2
       233: 3q^2+6q+2
       234: q^2+5q+2
       235: 3q+2
       236: q^2+4q+2
       238: q^2+5q+2
       240: q^2+5q+2
       242: 2q^2+4q+2
       243: q^2+5q+2
       245: 4q+2
       246: q^2+4q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 3q^2+6q+2
       254: 4q^2+6q+2
       255: 3q^2+6q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: 2q+1
       261: 2q+1
       264: q+1
       265: q+1
       272: 2q+1
       274: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       280: q+2
       282: 2q+2
       283: 2q+1
       284: 2q+1
       285: q+1
       286: q+1
       288: q^2+4q+2
       290: q+2
       292: 3q+2
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       298: 3q+2
       303: 1
       304: 1
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       312: 4q+2
       314: 3q+2
       316: q^2+4q+2
       318: q^2+5q+2
       321: 2q+1
       322: 2q+1
       326: q^2+4q+2
       328: 2q+2
       330: 2q+2
       332: 2q+2
       333: q^2+5q+2
       334: q^2+5q+2
       335: 3q+2
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: q+2
       345: q+2
       346: 2q+2
       349: q+2
       350: q+2
       352: q^2+5q+2
       353: q^2+5q+2
       354: 3q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: 3q+2
       358: 3q+2
       359: 2q+2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: q^2+4q+2
       367: q+2
       368: 2q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       378: q+1
       379: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       398: 2q+1
       400: 2q+1
       402: q+1
       403: q+1
       410: q+2
       412: 2q+2
       414: q+2
       416: q+2
       418: q+2
       419: 2q+1
       420: 2q+1
       421: q+1
       422: q+1
       424: 3q+2
       426: q+1
       428: 2q+2
       431: 1
       432: 1
       439: 1
       440: 1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       452: 3q+2
       453: 2q+1
       454: 2q+1
       456: q+2
       457: q+1
       458: q+1
       460: 3q+2
       461: q+1
       462: q+1
       464: 2q+2
       466: q+2
       468: 2q+2
       470: q^2+4q+2
       473: 1
       474: 1
       481: 2q+2
       482: 2
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+2
       494: q+2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: q+1
       501: 2
       503: 2q+2
       505: 2q+2
       507: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: q+1
       531: q+1
       550: q+1
       551: q+1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: q+1
       564: q+1
       584: q+2
       586: 2
       588: q+2
       589: q+1
       590: q+1
       595: 1
       596: 1
       598: 1
       600: q+1
       602: 2
       607: 1
       608: 1
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       624: q+2
       626: 3q+2
       628: q+2
       630: q+1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 2q+2
       640: q+2
       643: 1
       644: 1
       649: 1
       650: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       676: 2
       680: 2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: q+2
       688: q+2
       690: 2
       691: 2
       692: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       738: 1
       740: 1
       742: q+1
       744: q+1
       746: 1
       748: 1
       750: 1
       752: 1
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       807: 1
       808: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: q+2
       825: q+1
       826: q+1
       831: 1
       832: 1
       834: 1
       836: q+1
       838: 2
       839: 1
       840: 1
       842: q+2
       847: 1
       848: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       873: 2
       874: 1
       875: 1
       876: 1
       878: 2
       897: 1
       898: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1058: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1215: 1
      1249: 1
      1253: 1
      1257: 1
      1285: 1
      1457: 1

1458:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q+2
        23: q+2
        24: q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q+2
        32: q+2
        33: 2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q+2
        39: q+2
        41: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: q+2
        64: q+2
        66: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2q+2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+2
       103: 1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+2
       123: 2
       125: 2q+2
       126: q+1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 2q+2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2
       209: q+2
       211: q+2
       213: 2
       215: 2
       217: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: 2
       321: 1
       322: 1
       325: q+2
       327: 2
       329: 2
       331: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       439: 1
       440: 1
       451: 1
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: 2
       467: 1
       469: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: 2
       637: 1
       639: 1
       649: 1
       650: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       745: 1
       747: 1
       749: 1
       751: 1
       777: 1
       779: 1
       781: 1
       783: 1
       789: 2
       819: 1
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       859: 1
       861: 1
       863: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       956: 1
       958: 1
       996: 1
      1002: 1
      1030: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1066: 1
      1068: 1
      1070: 1
      1073: 1
      1079: 1
      1081: 1
      1082: 1
      1212: 1
      1244: 1
      1252: 1
      1256: 1
      1286: 1
      1458: 1

1459:    0: q^2+3q+2
         1: q^2+3q+2
         2: q^2+3q+2
         3: q^2+3q+2
         4: q^2+3q+2
         5: q^2+3q+2
         6: q^2+3q+2
         7: q^2+3q+2
         8: q^2+3q+2
         9: q^3+2q^2+2q+1
        10: q^2+3q+2
        11: q^2+3q+2
        12: q^2+3q+2
        13: q^2+3q+2
        14: q^2+3q+2
        15: q^2+3q+2
        16: 2q+2
        17: 2q+2
        18: q^2+2q+1
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: q+2
        23: q+2
        24: q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: 2q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: q+2
        32: q+2
        33: 2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q+2
        40: q+2
        42: q+2
        43: q^2+3q+2
        44: q^2+3q+2
        45: q^2+3q+2
        46: 2q+2
        47: 2q+2
        48: q^2+2q+1
        49: 2q+2
        50: 2q+2
        51: q^2+2q+1
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: 1
        59: 1
        60: q+1
        61: q+1
        63: q+2
        65: q+2
        67: 2
        68: 2q+2
        69: q+1
        70: q^2+3q+2
        71: 2q+2
        72: 2q+2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2q+2
        89: 2q+2
        90: q^2+2q+1
        91: 2q+2
        92: 2q+2
        93: q^2+2q+1
        94: 2
        95: 2
        96: q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: q+2
       101: q+2
       102: q+2
       104: 1
       105: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 1
       118: 1
       119: q+1
       120: q+1
       122: q+2
       124: 2
       125: 2q+2
       126: q+1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 2q+2
       136: 2
       137: 2
       138: 1
       139: 2
       141: q+2
       142: 2
       143: 2q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: 2q+2
       158: 2q+2
       159: q^2+2q+1
       160: 2
       161: 2
       162: q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 1
       192: 1
       195: 1
       196: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2
       210: q+2
       212: q+2
       214: 2
       216: 2
       218: q+1
       219: q+1
       220: 2q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       230: 2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: q+1
       294: q+1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: 2
       321: 1
       322: 1
       326: q+2
       328: 2
       330: 2
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       349: 2
       350: 1
       352: q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       439: 1
       440: 1
       452: 1
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: 2
       468: 1
       470: 1
       473: 1
       474: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 1
       494: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       513: 2
       514: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: 2
       638: 1
       640: 1
       649: 1
       650: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       676: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       746: 1
       748: 1
       750: 1
       752: 1
       778: 1
       780: 1
       782: 1
       784: 1
       790: 2
       820: 1
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       860: 1
       862: 1
       864: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       957: 1
       959: 1
       997: 1
      1003: 1
      1031: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1067: 1
      1069: 1
      1071: 1
      1073: 1
      1079: 1
      1081: 1
      1082: 1
      1213: 1
      1245: 1
      1253: 1
      1257: 1
      1286: 1
      1459: 1

1460:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: 2q+2
        26: 2q+2
        27: q^2+q+2
        28: 2q+2
        29: 2q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2
        53: 2
        54: 2
        55: 2q+2
        56: 2q+2
        57: q^2+q+2
        58: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q+2
        70: q+2
        71: 2q+2
        72: 2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q+2
        86: 2q+2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 2
        95: 2
        96: 2
        97: 2q+2
        98: 2q+2
        99: q^2+q+2
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: q+1
       108: q+1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q+2
       135: q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: q+2
       144: q+2
       145: 2q+2
       146: q+2
       147: 2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: q+2
       164: q+2
       165: q+2
       166: 2
       167: 2
       168: 2
       169: 1
       171: 1
       173: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: q+2
       224: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: q+2
       234: q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 1
       251: 1
       252: 1
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       283: 1
       284: 1
       285: 2
       287: 1
       288: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       303: 1
       307: 1
       308: 1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       321: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       357: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       379: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       431: 1
       439: 1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       463: 1
       464: 1
       469: 1
       470: 1
       473: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       492: 1
       494: 1
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       529: 1
       531: 1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 1
       562: 1
       589: 1
       590: 1
       591: 2
       595: 1
       599: 1
       600: 1
       607: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       643: 1
       649: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2
       682: 1
       683: 2
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       713: 1
       714: 1
       741: 1
       742: 1
       787: 1
       807: 1
       817: 1
       825: 1
       826: 1
       827: 2
       831: 1
       835: 1
       836: 1
       839: 1
       847: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       948: 1
       949: 1
       998: 1
      1006: 1
      1032: 1
      1044: 1
      1058: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1216: 1
      1250: 1
      1260: 1
      1285: 1
      1460: 1

1461:    0: 2q+2
         1: 2q+2
         2: q^2+q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+2
         8: q^2+q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: 2q+2
        20: 2q+2
        21: q^2+q+2
        22: 2
        23: 2
        24: 2
        25: 2q+2
        26: 2q+2
        27: q^2+q+2
        28: 2q+2
        29: 2q+2
        30: q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q+2
        36: 2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+2
        44: q+2
        45: q+2
        46: q+2
        47: q+2
        48: q+2
        49: 2q+2
        50: 2q+2
        51: q^2+q+2
        52: 2
        53: 2
        54: 2
        55: 2q+2
        56: 2q+2
        57: q^2+q+2
        59: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2
        69: q+2
        70: q+2
        71: 2q+2
        72: 2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: q+2
        85: q+2
        86: 2q+2
        87: q+2
        88: q+2
        89: q+2
        90: q+2
        91: q+2
        92: q+2
        93: q+2
        94: 2
        95: 2
        96: 2
        97: 2q+2
        98: 2q+2
        99: q^2+q+2
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: q+1
       108: q+1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2
       126: q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2
       134: q+2
       135: q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: q+2
       144: q+2
       145: 2q+2
       146: q+2
       147: 2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+2
       158: q+2
       159: q+2
       160: 1
       161: 1
       162: 1
       163: q+2
       164: q+2
       165: q+2
       166: 2
       167: 2
       168: 2
       170: 1
       172: 1
       174: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 2
       199: 1
       200: 1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       219: 2
       220: 2
       221: q+2
       222: q+2
       223: q+2
       224: 2
       225: 2
       226: 2
       227: 1
       228: 1
       230: 1
       231: q+2
       232: 2
       233: q+2
       234: q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 1
       251: 1
       252: 1
       253: q+2
       254: q+2
       255: q+2
       256: 1
       257: 1
       258: 1
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       283: 1
       284: 1
       286: 2
       287: 1
       288: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       304: 1
       307: 1
       308: 1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 2
       325: 1
       326: 1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       357: 2
       358: 2
       359: 2
       366: 2
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       380: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       432: 1
       440: 1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       463: 1
       464: 1
       469: 1
       470: 1
       474: 1
       481: 2
       482: 1
       483: 2
       484: 1
       491: 1
       492: 1
       494: 1
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       530: 1
       532: 1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 1
       564: 1
       589: 1
       590: 1
       592: 2
       596: 1
       599: 1
       600: 1
       608: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 1
       644: 1
       650: 1
       657: 1
       664: 1
       665: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2
       682: 1
       683: 2
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       715: 1
       716: 1
       743: 1
       744: 1
       788: 1
       808: 1
       818: 1
       825: 1
       826: 1
       828: 2
       832: 1
       835: 1
       836: 1
       840: 1
       848: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       950: 1
       951: 1
       999: 1
      1007: 1
      1033: 1
      1045: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1217: 1
      1251: 1
      1261: 1
      1285: 1
      1461: 1

1462:    0: 3q^3+19q^2+12q+2
         1: 3q^3+19q^2+12q+2
         2: q^4+7q^3+12q^2+8q+2
         3: 3q^3+19q^2+12q+2
         4: q^4+8q^3+15q^2+10q+2
         5: 3q^3+19q^2+12q+2
         6: q^4+8q^3+15q^2+10q+2
         7: q^4+5q^3+9q^2+7q+2
         8: q^4+7q^3+12q^2+8q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 3q^3+19q^2+12q+2
        11: 3q^3+19q^2+12q+2
        12: q^4+8q^3+15q^2+10q+2
        13: 8q^2+8q+2
        14: q^3+6q^2+7q+2
        15: 8q^2+8q+2
        16: 3q^3+19q^2+12q+2
        17: 3q^3+19q^2+12q+2
        18: q^4+5q^3+9q^2+7q+2
        19: 2q^3+13q^2+10q+2
        20: 2q^3+13q^2+10q+2
        21: 3q^3+8q^2+7q+2
        22: 14q^2+12q+2
        23: 14q^2+12q+2
        24: 4q^3+10q^2+8q+2
        25: 3q^3+19q^2+12q+2
        26: 3q^3+19q^2+12q+2
        27: q^4+7q^3+12q^2+8q+2
        28: 3q^3+19q^2+12q+2
        29: 2q^3+13q^2+10q+2
        30: 5q^2+7q+2
        31: 14q^2+12q+2
        32: 6q^2+8q+2
        33: 14q^2+12q+2
        34: 3q^3+19q^2+12q+2
        35: 8q^2+8q+2
        36: 3q^3+19q^2+12q+2
        37: 7q^2+6q+1
        38: 7q^2+6q+1
        39: 7q^2+6q+1
        40: 7q^2+6q+1
        41: 2q^3+5q^2+4q+1
        42: 2q^3+5q^2+4q+1
        43: 8q^2+8q+2
        44: q^3+6q^2+7q+2
        45: 8q^2+8q+2
        46: 8q^2+8q+2
        47: 8q^2+8q+2
        48: q^3+6q^2+7q+2
        49: 2q^3+13q^2+10q+2
        50: 2q^3+13q^2+10q+2
        51: 3q^3+8q^2+7q+2
        52: 8q^2+10q+2
        53: 8q^2+10q+2
        54: q^3+6q^2+7q+2
        55: 2q^3+13q^2+10q+2
        56: 2q^3+13q^2+10q+2
        57: 3q^3+8q^2+7q+2
        58: 7q^2+6q+1
        59: 7q^2+6q+1
        60: 2q^3+11q^2+8q+2
        61: q^3+8q^2+4q
        62: 7q^2+6q+1
        63: 7q^2+6q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 7q^2+6q+1
        67: 7q^2+6q+1
        68: 2q^2+4q+2
        69: 5q^2+7q+2
        70: 5q^2+7q+2
        71: 2q^3+13q^2+10q+2
        72: q^3+7q^2+8q+2
        73: 4q^2+8q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 6q^2+8q+2
        81: 6q^2+8q+2
        82: 8q^2+10q+2
        83: 3q^2+7q+2
        84: 8q^2+8q+2
        85: 8q^2+8q+2
        86: 2q^3+13q^2+10q+2
        87: 5q^2+7q+2
        88: 8q^2+8q+2
        89: 8q^2+8q+2
        90: q^3+6q^2+7q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 8q^2+10q+2
        95: 8q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 2q^3+13q^2+10q+2
        98: 2q^3+13q^2+10q+2
        99: 3q^3+8q^2+7q+2
       100: 8q^2+10q+2
       101: 8q^2+10q+2
       102: q^3+6q^2+7q+2
       103: 4q^2+4q+1
       104: 4q^2+4q+1
       105: 3q^2+2q
       106: 3q^2+2q
       107: q^3+5q^2+6q+2
       108: 2q^2+2q
       109: 2q^2+4q+1
       110: 2q^2+4q+1
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q^2+4q+2
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: 2q^2+4q+2
       126: 5q^2+7q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 3q+2
       134: 2q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 6q^2+8q+2
       138: 3q^2+7q+2
       139: 8q^2+10q+2
       140: 2q^2+4q+2
       141: 3q^2+7q+2
       142: 4q^2+8q+2
       143: 8q^2+8q+2
       144: 5q^2+7q+2
       145: 2q^3+13q^2+10q+2
       146: 5q^2+7q+2
       147: q^3+7q^2+8q+2
       148: 4q^2+8q+2
       149: 8q^2+10q+2
       150: 3q^2+7q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+6q+2
       158: 4q^2+6q+2
       159: 2q^2+6q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 8q^2+10q+2
       167: 8q^2+10q+2
       168: q^3+6q^2+7q+2
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: q^2+2q+1
       174: q^2+2q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: 3q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: 2q^2+4q+2
       195: 2q^2+4q+1
       196: 2q^2+4q+1
       197: q+1
       198: q+1
       199: 2q^2+4q+2
       201: q^3+5q^2+6q+2
       202: 2q^2+2q
       203: 2q^2+4q+1
       204: 2q^2+4q+1
       205: 3q+1
       206: 3q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 3q+2
       220: 3q+2
       221: 2q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 3q^2+7q+2
       227: q+2
       228: 3q+2
       229: q+2
       230: 2q+2
       231: 5q^2+7q+2
       232: 3q+2
       233: 2q^2+6q+2
       234: q^2+5q+2
       235: q^2+5q+2
       236: 3q^2+7q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 8q^2+10q+2
       244: 2q^2+4q+2
       245: 4q^2+8q+2
       246: 3q^2+7q+2
       247: 8q+4
       248: 8q+4
       249: 2q^2+4q+2
       250: 3q+2
       251: q^2+3q+2
       252: 3q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 2q+1
       260: 2q+1
       261: q
       262: q
       263: q+1
       264: q+1
       267: q+1
       268: q+1
       271: 2q+1
       272: q
       273: q
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       283: 3q+2
       285: q+1
       286: q+1
       287: q^2+3q+1
       288: q^2+3q+1
       291: 2q+1
       292: 2q+1
       293: 3q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: q+2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 3q+2
       309: q+1
       310: q+1
       311: 3q+1
       312: 3q+1
       313: 2q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 2q^2+4q+2
       321: 2q^2+4q+1
       322: 2q^2+4q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: 2q+2
       337: 8q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+2
       345: q+2
       346: 3q+2
       347: q+2
       348: q+2
       349: 2q+2
       350: 2q+2
       351: 4q+4
       352: 3q+2
       353: 3q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: q^2+5q+2
       358: q^2+5q+2
       359: 8q+4
       366: 3q^2+7q+2
       367: q+2
       368: 3q+2
       369: q+2
       370: 2q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       377: q+1
       378: q+1
       385: q+1
       386: q+1
       389: q+1
       390: q+1
       393: 1
       394: 1
       397: 2q+1
       398: q
       399: q
       400: 2q+1
       401: q+1
       403: q+1
       405: q+1
       407: q+1
       419: 3q+2
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       437: q+2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 4q+4
       445: 2q+2
       446: 2q+2
       447: 3q+2
       449: q+1
       450: q+1
       451: 2q+1
       452: 2q+1
       453: 3q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 4q+2
       462: 4q+2
       463: 4q+2
       464: 4q+2
       469: q^2+3q+1
       470: q^2+3q+1
       471: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: 2q+2
       480: 2q+2
       481: q+1
       482: 2
       483: 2q+2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: 2q+2
       495: 2
       496: 2
       497: 3q+2
       498: q^2+5q+2
       499: q^2+5q+2
       500: 2q+2
       501: q+2
       508: q+2
       509: q+2
       510: 3q+2
       511: q+2
       512: q+2
       513: 2q+2
       514: 2q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       529: q+1
       530: q+1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 2q+2
       546: 2q+2
       549: q+1
       551: q+1
       557: q+1
       560: q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: 1
       566: 1
       569: q+1
       571: q+1
       573: 2q+2
       574: 2q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       589: q+1
       593: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       603: q+2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       619: 3q+2
       621: q+1
       622: q+1
       625: 2q+1
       626: 2q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       641: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       647: q+2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       676: 2
       677: 2
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: 2
       683: 2q+2
       684: q+2
       685: 1
       686: q+2
       687: q+2
       688: 2q+2
       689: 2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       694: q+1
       696: q+1
       699: q+1
       717: 1
       718: 1
       725: 1
       726: 1
       741: q+1
       744: q+1
       753: 1
       754: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       793: 2
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 2
       817: 1
       818: 1
       825: q+1
       829: 2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       845: q+2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: 2
       879: 2
       880: 1
       928: 1
       929: 1
       952: 1
       953: 1
       964: 1
       965: 1
       974: 1
       976: 1
       988: 1
       989: 1
      1000: 1
      1004: 1
      1016: 2
      1032: 1
      1033: 1
      1040: 1
      1046: 1
      1047: 1
      1056: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1194: 1
      1195: 1
      1206: 1
      1207: 1
      1218: 1
      1254: 1
      1258: 1
      1285: 1
      1288: 1
      1462: 1

1463:    0: 3q^3+19q^2+12q+2
         1: 3q^3+19q^2+12q+2
         2: q^4+7q^3+12q^2+8q+2
         3: 3q^3+19q^2+12q+2
         4: q^4+8q^3+15q^2+10q+2
         5: 3q^3+19q^2+12q+2
         6: q^4+8q^3+15q^2+10q+2
         7: q^4+5q^3+9q^2+7q+2
         8: q^4+7q^3+12q^2+8q+2
         9: q^4+5q^3+9q^2+7q+2
        10: 3q^3+19q^2+12q+2
        11: 3q^3+19q^2+12q+2
        12: q^4+8q^3+15q^2+10q+2
        13: 8q^2+8q+2
        14: q^3+6q^2+7q+2
        15: 8q^2+8q+2
        16: 3q^3+19q^2+12q+2
        17: 3q^3+19q^2+12q+2
        18: q^4+5q^3+9q^2+7q+2
        19: 2q^3+13q^2+10q+2
        20: 2q^3+13q^2+10q+2
        21: 3q^3+8q^2+7q+2
        22: 14q^2+12q+2
        23: 14q^2+12q+2
        24: 4q^3+10q^2+8q+2
        25: 3q^3+19q^2+12q+2
        26: 3q^3+19q^2+12q+2
        27: q^4+7q^3+12q^2+8q+2
        28: 3q^3+19q^2+12q+2
        29: 2q^3+13q^2+10q+2
        30: 5q^2+7q+2
        31: 14q^2+12q+2
        32: 6q^2+8q+2
        33: 14q^2+12q+2
        34: 3q^3+19q^2+12q+2
        35: 8q^2+8q+2
        36: 3q^3+19q^2+12q+2
        37: 7q^2+6q+1
        38: 7q^2+6q+1
        39: 7q^2+6q+1
        40: 7q^2+6q+1
        41: 2q^3+5q^2+4q+1
        42: 2q^3+5q^2+4q+1
        43: 8q^2+8q+2
        44: q^3+6q^2+7q+2
        45: 8q^2+8q+2
        46: 8q^2+8q+2
        47: 8q^2+8q+2
        48: q^3+6q^2+7q+2
        49: 2q^3+13q^2+10q+2
        50: 2q^3+13q^2+10q+2
        51: 3q^3+8q^2+7q+2
        52: 8q^2+10q+2
        53: 8q^2+10q+2
        54: q^3+6q^2+7q+2
        55: 2q^3+13q^2+10q+2
        56: 2q^3+13q^2+10q+2
        57: 3q^3+8q^2+7q+2
        58: 7q^2+6q+1
        59: 7q^2+6q+1
        60: q^3+8q^2+4q
        61: 2q^3+11q^2+8q+2
        62: 7q^2+6q+1
        63: 7q^2+6q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 7q^2+6q+1
        67: 7q^2+6q+1
        68: 2q^2+4q+2
        69: 5q^2+7q+2
        70: 5q^2+7q+2
        71: 2q^3+13q^2+10q+2
        72: q^3+7q^2+8q+2
        73: 4q^2+8q+2
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q^2+4q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 6q^2+8q+2
        81: 6q^2+8q+2
        82: 8q^2+10q+2
        83: 3q^2+7q+2
        84: 8q^2+8q+2
        85: 8q^2+8q+2
        86: 2q^3+13q^2+10q+2
        87: 5q^2+7q+2
        88: 8q^2+8q+2
        89: 8q^2+8q+2
        90: q^3+6q^2+7q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 8q^2+10q+2
        95: 8q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 2q^3+13q^2+10q+2
        98: 2q^3+13q^2+10q+2
        99: 3q^3+8q^2+7q+2
       100: 8q^2+10q+2
       101: 8q^2+10q+2
       102: q^3+6q^2+7q+2
       103: 3q^2+2q
       104: 3q^2+2q
       105: 4q^2+4q+1
       106: 4q^2+4q+1
       107: 2q^2+2q
       108: q^3+5q^2+6q+2
       109: 2q^2+4q+1
       110: 2q^2+4q+1
       111: 3q+1
       112: 3q+1
       113: 2q^2+4q+1
       114: 2q^2+4q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+2q+1
       118: q^2+2q+1
       120: 2q^2+4q+2
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: 2q^2+4q+2
       126: 5q^2+7q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 3q+2
       134: 2q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 6q^2+8q+2
       138: 3q^2+7q+2
       139: 8q^2+10q+2
       140: 2q^2+4q+2
       141: 3q^2+7q+2
       142: 4q^2+8q+2
       143: 8q^2+8q+2
       144: 5q^2+7q+2
       145: 2q^3+13q^2+10q+2
       146: 5q^2+7q+2
       147: q^3+7q^2+8q+2
       148: 4q^2+8q+2
       149: 8q^2+10q+2
       150: 3q^2+7q+2
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+6q+2
       158: 4q^2+6q+2
       159: 2q^2+6q+2
       160: 3q+2
       161: q^2+3q+2
       162: 3q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 8q^2+10q+2
       167: 8q^2+10q+2
       168: q^3+6q^2+7q+2
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       184: 3q+2
       185: q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: q^2+2q+1
       192: q^2+2q+1
       194: 2q^2+4q+2
       195: 2q^2+4q+1
       196: 2q^2+4q+1
       197: q+1
       198: q+1
       200: 2q^2+4q+2
       201: 2q^2+2q
       202: q^3+5q^2+6q+2
       203: 2q^2+4q+1
       204: 2q^2+4q+1
       205: 3q+1
       206: 3q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+3q+1
       212: q^2+3q+1
       219: 3q+2
       220: 3q+2
       221: 2q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 3q^2+7q+2
       227: q+2
       228: 3q+2
       229: q+2
       230: 2q+2
       231: 5q^2+7q+2
       232: 3q+2
       233: 2q^2+6q+2
       234: q^2+5q+2
       235: q^2+5q+2
       236: 3q^2+7q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 8q^2+10q+2
       244: 2q^2+4q+2
       245: 4q^2+8q+2
       246: 3q^2+7q+2
       247: 8q+4
       248: 8q+4
       249: 2q^2+4q+2
       250: 3q+2
       251: q^2+3q+2
       252: 3q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: q
       260: q
       261: 2q+1
       262: 2q+1
       265: q+1
       266: q+1
       269: q+1
       270: q+1
       271: q
       272: 2q+1
       273: 2q+1
       274: q
       277: q^2+2q+1
       278: q^2+2q+1
       284: 3q+2
       285: q+1
       286: q+1
       287: q^2+3q+1
       288: q^2+3q+1
       291: 2q+1
       292: 2q+1
       294: 3q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       300: q+2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       308: 3q+2
       309: q+1
       310: q+1
       311: 3q+1
       312: 3q+1
       313: 2q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       320: 2q^2+4q+2
       321: 2q^2+4q+1
       322: 2q^2+4q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: 3q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: 2q+2
       337: 8q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+2
       345: q+2
       346: 3q+2
       347: q+2
       348: q+2
       349: 2q+2
       350: 2q+2
       351: 4q+4
       352: 3q+2
       353: 3q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: q^2+5q+2
       358: q^2+5q+2
       359: 8q+4
       366: 3q^2+7q+2
       367: q+2
       368: 3q+2
       369: q+2
       370: 2q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       379: q+1
       380: q+1
       387: q+1
       388: q+1
       391: q+1
       392: q+1
       395: 1
       396: 1
       397: q
       398: 2q+1
       399: 2q+1
       400: q
       402: q+1
       404: q+1
       406: q+1
       408: q+1
       420: 3q+2
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       430: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       438: q+2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 4q+4
       445: 2q+2
       446: 2q+2
       448: 3q+2
       449: q+1
       450: q+1
       451: 2q+1
       452: 2q+1
       454: 3q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 4q+2
       462: 4q+2
       463: 4q+2
       464: 4q+2
       469: q^2+3q+1
       470: q^2+3q+1
       472: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: 2q+2
       480: 2q+2
       481: q+1
       482: 2
       483: 2q+2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: 2q+2
       495: 2
       496: 2
       497: 3q+2
       498: q^2+5q+2
       499: q^2+5q+2
       500: 2q+2
       501: q+2
       508: q+2
       509: q+2
       510: 3q+2
       511: q+2
       512: q+2
       513: 2q+2
       514: 2q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       531: q+1
       532: q+1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 2q+2
       548: 2q+2
       550: q+1
       552: q+1
       558: q+1
       559: q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       567: 1
       568: 1
       570: q+1
       572: q+1
       575: 2q+2
       576: 2q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       590: q+1
       594: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       604: q+2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2
       620: 3q+2
       621: q+1
       622: q+1
       625: 2q+1
       626: 2q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       642: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       648: q+2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       676: 2
       677: 2
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: 2
       683: 2q+2
       684: q+2
       685: 1
       686: q+2
       687: q+2
       688: 2q+2
       689: 2
       690: q+2
       691: q+2
       692: q+1
       697: q+1
       698: q+1
       700: q+1
       701: q+1
       719: 1
       720: 1
       727: 1
       728: 1
       742: q+1
       743: q+1
       755: 1
       756: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       794: 2
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 2
       817: 1
       818: 1
       826: q+1
       830: 2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       846: q+2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: 2
       879: 2
       880: 1
       930: 1
       931: 1
       954: 1
       955: 1
       966: 1
       967: 1
       975: 1
       977: 1
       990: 1
       991: 1
      1001: 1
      1005: 1
      1017: 2
      1032: 1
      1033: 1
      1041: 1
      1046: 1
      1047: 1
      1057: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1196: 1
      1197: 1
      1208: 1
      1209: 1
      1219: 1
      1255: 1
      1259: 1
      1285: 1
      1288: 1
      1463: 1

1464:    0: 7q^2+9q+2
         1: 7q^2+9q+2
         2: 7q^2+9q+2
         3: 7q^2+9q+2
         4: q^4+2q^3+5q^2+6q+2
         5: 7q^2+9q+2
         6: q^4+5q^3+7q^2+6q+2
         7: q^4+2q^3+5q^2+6q+2
         8: 7q^2+9q+2
         9: q^4+2q^3+5q^2+6q+2
        10: 8q+2
        11: 8q+2
        12: 3q^2+5q+2
        13: 7q^2+9q+2
        14: q^4+2q^3+5q^2+6q+2
        15: 7q^2+9q+2
        16: 7q^2+9q+2
        17: 7q^2+9q+2
        18: q^4+2q^3+5q^2+6q+2
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 7q^2+9q+2
        23: 7q^2+9q+2
        24: 7q^2+9q+2
        25: 7q^2+9q+2
        26: 7q^2+9q+2
        27: 7q^2+9q+2
        28: 8q+2
        29: 5q+2
        30: 2q^2+6q+2
        31: 8q+2
        32: 7q^2+9q+2
        33: 7q^2+9q+2
        34: 8q+2
        35: 7q^2+9q+2
        36: 7q^2+9q+2
        37: 4q^2+7q+2
        38: 3q^2+2q
        39: 4q^2+7q+2
        40: 3q^2+2q
        41: 4q^2+7q+2
        42: 3q^2+2q
        43: 8q+2
        44: 3q^2+5q+2
        45: 8q+2
        46: 7q^2+9q+2
        47: 7q^2+9q+2
        48: q^4+2q^3+5q^2+6q+2
        49: 2q^2+6q+2
        50: 4q^2+6q+2
        51: 2q^2+6q+2
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: 6q+2
        63: 2q
        64: 4q^2+7q+2
        65: 3q^2+2q
        66: 4q^2+7q+2
        67: 3q^2+2q
        68: 8q+2
        69: 2q^2+6q+2
        70: 5q+2
        71: 5q+2
        72: q^2+3q+2
        73: q^2+3q+2
        74: 4q+2
        76: q^2+4q+2
        78: 4q+2
        80: 8q+2
        81: 7q^2+9q+2
        82: 5q+2
        83: 2q^2+6q+2
        84: 8q+2
        85: 7q^2+9q+2
        86: 5q+2
        87: 2q^2+6q+2
        88: 8q+2
        89: 8q+2
        90: 3q^2+5q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 2q^2+6q+2
        95: 4q^2+6q+2
        96: 2q^2+6q+2
        97: 2q^2+6q+2
        98: 4q^2+6q+2
        99: 2q^2+6q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: 3q+1
       104: q
       105: q
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       113: 3q+2
       115: 4q+2
       117: 4q+1
       118: 4q+1
       119: 4q+1
       120: 4q+1
       121: 6q+2
       122: 2q
       123: 4q^2+7q+2
       124: 3q^2+2q
       125: 8q+2
       126: 5q+2
       127: 4q+2
       129: q^2+4q+2
       131: 4q+2
       133: 5q+2
       134: 2q^2+6q+2
       135: q^2+3q+2
       136: q^2+3q+2
       137: 8q+2
       138: 2q^2+6q+2
       139: 5q+2
       140: q^2+3q+2
       141: 5q+2
       142: q^2+3q+2
       143: 8q+2
       144: 2q^2+6q+2
       145: 5q+2
       146: 5q+2
       147: q^2+3q+2
       148: q^2+3q+2
       149: 5q+2
       150: 2q^2+6q+2
       151: 4q+2
       153: q^2+4q+2
       155: 4q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 2q^2+6q+2
       167: 4q^2+6q+2
       168: 2q^2+6q+2
       169: 1
       172: 1
       173: 3q+1
       174: q
       175: q
       176: 3q+1
       177: 4q+2
       179: 3q+2
       181: q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       189: 3q+2
       191: 4q+1
       192: 4q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       199: 4q+1
       200: 4q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       207: 6q+2
       208: 2q
       209: 3q+2
       211: 4q+2
       213: 4q+2
       215: q^2+4q+2
       217: 4q+2
       219: 5q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: 2
       225: q^2+3q+2
       226: 5q+2
       227: 5q+2
       228: 2q^2+6q+2
       229: q^2+3q+2
       230: q^2+3q+2
       231: 5q+2
       232: 5q+2
       233: 2q^2+6q+2
       234: q^2+3q+2
       235: q^2+3q+2
       236: 2q^2+6q+2
       237: 4q+2
       239: q^2+4q+2
       241: 4q+2
       243: 5q+2
       244: q^2+3q+2
       245: q^2+3q+2
       246: 5q+2
       247: 4
       248: 4
       249: 2q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 2q^2+6q+2
       257: 4q^2+6q+2
       258: 2q^2+6q+2
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: 3q+1
       276: q
       277: q
       278: 3q+1
       279: 3q+2
       281: 4q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 3q+2
       289: q+2
       291: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: q+2
       303: q+1
       304: q+1
       305: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+2
       313: q+2
       315: 4q+2
       317: 3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       325: 3q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 4
       338: 4
       340: 4
       342: 2q+1
       344: 5q+2
       345: q+2
       346: q+2
       347: 2
       348: q^2+3q+2
       349: 2
       350: q^2+3q+2
       351: 4
       352: 5q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: 2
       358: q^2+3q+2
       359: 4
       360: 4q+2
       362: q^2+4q+2
       364: 4q+2
       366: 5q+2
       367: 5q+2
       368: 2q^2+6q+2
       369: q^2+3q+2
       370: q^2+3q+2
       371: 4
       372: 4
       373: 2q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       413: 3q+2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 4
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+2
       435: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 2
       444: 2
       445: 4
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+2
       453: 1
       454: 1
       455: q+2
       457: 1
       458: 1
       459: 2
       461: 2
       462: 2
       463: 4
       465: 3q+2
       467: 4q+2
       469: 3q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       477: q+2
       479: 2
       480: 2
       481: 2
       482: 2
       483: 1
       484: 4
       485: 4
       487: 4
       489: 2q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 4
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 4
       508: 5q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+3q+2
       513: 2
       514: q^2+3q+2
       515: 4
       516: 4
       517: 2q+1
       521: 1
       524: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2
       547: 2
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2
       563: 2
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 4
       603: 1
       604: 1
       605: q+2
       607: 1
       608: 1
       609: 2
       613: 1
       615: 2
       616: 2
       617: 4
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+2
       625: 2
       629: 1
       631: 2
       632: 2
       633: 4
       639: 3q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+2
       653: 2
       655: 2
       656: 2
       657: 4
       658: 4
       660: 4
       662: 2q+1
       664: 1
       665: 1
       674: 4
       675: 2
       676: 2
       677: 1
       679: 1
       680: 4
       681: 2
       682: 2
       683: 1
       685: 1
       686: q+2
       687: 2
       688: 2
       689: 1
       693: 1
       696: 1
       697: 1
       698: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       733: 2
       735: 2
       737: 1
       739: 1
       741: 1
       743: 1
       749: 2
       751: 2
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       775: 4
       779: 1
       781: 1
       793: 2
       794: 2
       795: 4
       797: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       811: 1
       817: 2
       818: 2
       819: 4
       821: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       835: 1
       843: 2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: 2
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 2
       878: 2
       879: 1
       880: 1
       884: 1
       887: 1
       888: 1
       889: 1
       916: 2
       918: 2
       920: 1
       922: 1
       940: 2
       942: 2
       944: 1
       946: 1
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: 1
       975: 1
       994: 1
      1020: 1
      1022: 1
      1036: 1
      1038: 1
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1198: 1
      1199: 1
      1230: 1
      1248: 1
      1266: 1
      1274: 1
      1287: 1
      1464: 1

1465:    0: 7q^2+9q+2
         1: 7q^2+9q+2
         2: 7q^2+9q+2
         3: 7q^2+9q+2
         4: q^4+2q^3+5q^2+6q+2
         5: 7q^2+9q+2
         6: q^4+5q^3+7q^2+6q+2
         7: q^4+2q^3+5q^2+6q+2
         8: 7q^2+9q+2
         9: q^4+2q^3+5q^2+6q+2
        10: 8q+2
        11: 8q+2
        12: 3q^2+5q+2
        13: 7q^2+9q+2
        14: q^4+2q^3+5q^2+6q+2
        15: 7q^2+9q+2
        16: 7q^2+9q+2
        17: 7q^2+9q+2
        18: q^4+2q^3+5q^2+6q+2
        19: 2q^2+6q+2
        20: 4q^2+6q+2
        21: 2q^2+6q+2
        22: 7q^2+9q+2
        23: 7q^2+9q+2
        24: 7q^2+9q+2
        25: 7q^2+9q+2
        26: 7q^2+9q+2
        27: 7q^2+9q+2
        28: 8q+2
        29: 5q+2
        30: 2q^2+6q+2
        31: 8q+2
        32: 7q^2+9q+2
        33: 7q^2+9q+2
        34: 8q+2
        35: 7q^2+9q+2
        36: 7q^2+9q+2
        37: 3q^2+2q
        38: 4q^2+7q+2
        39: 3q^2+2q
        40: 4q^2+7q+2
        41: 3q^2+2q
        42: 4q^2+7q+2
        43: 8q+2
        44: 3q^2+5q+2
        45: 8q+2
        46: 7q^2+9q+2
        47: 7q^2+9q+2
        48: q^4+2q^3+5q^2+6q+2
        49: 2q^2+6q+2
        50: 4q^2+6q+2
        51: 2q^2+6q+2
        52: 2q^2+6q+2
        53: 4q^2+6q+2
        54: 2q^2+6q+2
        55: 2q^2+6q+2
        56: 4q^2+6q+2
        57: 2q^2+6q+2
        58: 4q+1
        59: 4q+1
        60: 4q+1
        61: 4q+1
        62: 2q
        63: 6q+2
        64: 3q^2+2q
        65: 4q^2+7q+2
        66: 3q^2+2q
        67: 4q^2+7q+2
        68: 8q+2
        69: 2q^2+6q+2
        70: 5q+2
        71: 5q+2
        72: q^2+3q+2
        73: q^2+3q+2
        75: 4q+2
        77: q^2+4q+2
        79: 4q+2
        80: 8q+2
        81: 7q^2+9q+2
        82: 5q+2
        83: 2q^2+6q+2
        84: 8q+2
        85: 7q^2+9q+2
        86: 5q+2
        87: 2q^2+6q+2
        88: 8q+2
        89: 8q+2
        90: 3q^2+5q+2
        91: 2q^2+6q+2
        92: 4q^2+6q+2
        93: 2q^2+6q+2
        94: 2q^2+6q+2
        95: 4q^2+6q+2
        96: 2q^2+6q+2
        97: 2q^2+6q+2
        98: 4q^2+6q+2
        99: 2q^2+6q+2
       100: 2q^2+6q+2
       101: 4q^2+6q+2
       102: 2q^2+6q+2
       103: q
       104: 3q+1
       105: 3q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+2
       114: 3q+2
       116: 4q+2
       117: 4q+1
       118: 4q+1
       119: 4q+1
       120: 4q+1
       121: 2q
       122: 6q+2
       123: 3q^2+2q
       124: 4q^2+7q+2
       125: 8q+2
       126: 5q+2
       128: 4q+2
       130: q^2+4q+2
       132: 4q+2
       133: 5q+2
       134: 2q^2+6q+2
       135: q^2+3q+2
       136: q^2+3q+2
       137: 8q+2
       138: 2q^2+6q+2
       139: 5q+2
       140: q^2+3q+2
       141: 5q+2
       142: q^2+3q+2
       143: 8q+2
       144: 2q^2+6q+2
       145: 5q+2
       146: 5q+2
       147: q^2+3q+2
       148: q^2+3q+2
       149: 5q+2
       150: 2q^2+6q+2
       152: 4q+2
       154: q^2+4q+2
       156: 4q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 2q^2+6q+2
       167: 4q^2+6q+2
       168: 2q^2+6q+2
       170: 1
       171: 1
       173: q
       174: 3q+1
       175: 3q+1
       176: q
       178: 4q+2
       180: 3q+2
       182: q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: q+2
       190: 3q+2
       191: 4q+1
       192: 4q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+2
       199: 4q+1
       200: 4q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: q+2
       207: 2q
       208: 6q+2
       210: 3q+2
       212: 4q+2
       214: 4q+2
       216: q^2+4q+2
       218: 4q+2
       219: 5q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+3q+2
       224: 2
       225: q^2+3q+2
       226: 5q+2
       227: 5q+2
       228: 2q^2+6q+2
       229: q^2+3q+2
       230: q^2+3q+2
       231: 5q+2
       232: 5q+2
       233: 2q^2+6q+2
       234: q^2+3q+2
       235: q^2+3q+2
       236: 2q^2+6q+2
       238: 4q+2
       240: q^2+4q+2
       242: 4q+2
       243: 5q+2
       244: q^2+3q+2
       245: q^2+3q+2
       246: 5q+2
       247: 4
       248: 4
       249: 2q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 2q^2+6q+2
       257: 4q^2+6q+2
       258: 2q^2+6q+2
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       275: q
       276: 3q+1
       277: 3q+1
       278: q
       280: 3q+2
       282: 4q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: 3q+2
       290: q+2
       292: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       302: q+2
       303: q+1
       304: q+1
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: q+2
       314: q+2
       316: 4q+2
       318: 3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: q+2
       326: 3q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 4
       339: 4
       341: 4
       343: 2q+1
       344: 5q+2
       345: q+2
       346: q+2
       347: 2
       348: q^2+3q+2
       349: 2
       350: q^2+3q+2
       351: 4
       352: 5q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+3q+2
       357: 2
       358: q^2+3q+2
       359: 4
       361: 4q+2
       363: q^2+4q+2
       365: 4q+2
       366: 5q+2
       367: 5q+2
       368: 2q^2+6q+2
       369: q^2+3q+2
       370: q^2+3q+2
       371: 4
       372: 4
       373: 2q+1
       374: q+2
       375: q+2
       376: q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       414: 3q+2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 4
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       434: q+2
       436: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 2
       444: 2
       446: 4
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       452: q+2
       453: 1
       454: 1
       456: q+2
       457: 1
       458: 1
       460: 2
       461: 2
       462: 2
       464: 4
       466: 3q+2
       468: 4q+2
       470: 3q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: q+2
       478: q+2
       479: 2
       480: 2
       481: 2
       482: 2
       483: 1
       484: 4
       486: 4
       488: 4
       490: 2q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 4
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 4
       508: 5q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+3q+2
       513: 2
       514: q^2+3q+2
       515: 4
       516: 4
       517: 2q+1
       522: 1
       523: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 2
       548: 2
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 2
       564: 2
       566: 1
       567: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 4
       603: 1
       604: 1
       606: q+2
       607: 1
       608: 1
       610: 2
       614: 1
       615: 2
       616: 2
       618: 4
       619: 1
       620: 1
       621: 1
       622: 1
       624: q+2
       626: 2
       630: 1
       631: 2
       632: 2
       634: 4
       640: 3q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+2
       654: 2
       655: 2
       656: 2
       657: 4
       659: 4
       661: 4
       663: 2q+1
       664: 1
       665: 1
       674: 4
       675: 2
       676: 2
       677: 1
       679: 1
       680: 4
       681: 2
       682: 2
       683: 1
       685: 1
       686: q+2
       687: 2
       688: 2
       689: 1
       694: 1
       699: 1
       700: 1
       701: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       734: 2
       736: 2
       738: 1
       740: 1
       742: 1
       744: 1
       750: 2
       752: 2
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       776: 4
       780: 1
       782: 1
       793: 2
       794: 2
       796: 4
       798: 2
       801: 1
       802: 1
       807: 1
       808: 1
       810: 1
       812: 1
       817: 2
       818: 2
       820: 4
       822: 2
       825: 1
       826: 1
       831: 1
       832: 1
       834: 1
       836: 1
       843: 2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: 2
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 2
       878: 2
       879: 1
       880: 1
       885: 1
       890: 1
       891: 1
       892: 1
       917: 2
       919: 2
       921: 1
       923: 1
       941: 2
       943: 2
       945: 1
       947: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: 1
       977: 1
       995: 1
      1021: 1
      1023: 1
      1037: 1
      1039: 1
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1200: 1
      1201: 1
      1231: 1
      1249: 1
      1267: 1
      1275: 1
      1287: 1
      1465: 1

1466:    0: 2q^3+2q^2+6q+2
         1: 2q^3+2q^2+6q+2
         2: 4q^2+4q+2
         3: 2q^3+2q^2+6q+2
         4: q^4+2q^3+3q^2+4q+2
         5: 2q^3+2q^2+6q+2
         6: q^4+2q^3+3q^2+4q+2
         7: 2q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: 2q^3+3q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^3+2q^2+6q+2
        17: 2q^3+2q^2+6q+2
        18: 2q^3+3q^2+3q+2
        19: q^3+q^2+4q+2
        20: q^3+q^2+4q+2
        21: 2q^2+3q+2
        22: 2q^3+2q^2+6q+2
        23: 2q^3+2q^2+6q+2
        24: 4q^2+4q+2
        25: 2q^3+2q^2+6q+2
        26: 2q^3+2q^2+6q+2
        27: 4q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: q^2+3q+2
        31: 6q+2
        32: 2q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 6q+2
        35: 2q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+q^2+3q+1
        38: q^3+q^2+3q+1
        39: q^3+q^2+3q+1
        40: q^3+q^2+3q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^3+q^2+4q+2
        50: q^3+q^2+4q+2
        51: 2q^2+3q+2
        52: q^3+q^2+4q+2
        53: q^3+q^2+4q+2
        54: 2q^2+3q+2
        55: q^3+q^2+4q+2
        56: q^3+q^2+4q+2
        57: 2q^2+3q+2
        58: 4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: 2q+2
        69: q^2+3q+2
        70: 3q+2
        71: 4q+2
        72: q^3+q^2+2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+4q+2
        82: 4q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+4q+2
        86: 4q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^3+q^2+4q+2
        95: q^3+q^2+4q+2
        96: 2q^2+3q+2
        97: q^3+q^2+4q+2
        98: q^3+q^2+4q+2
        99: 2q^2+3q+2
       100: q^3+q^2+4q+2
       101: q^3+q^2+4q+2
       102: 2q^2+3q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: q^2+2q+2
       135: q^2+q+2
       136: q+2
       137: 4q+2
       138: q^2+3q+2
       139: 4q+2
       140: q^3+q^2+2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: q^2+3q+2
       145: 4q+2
       146: 3q+2
       147: q^3+q^2+2q+2
       148: 2q+2
       149: 4q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+q^2+4q+2
       167: q^3+q^2+4q+2
       168: 2q^2+3q+2
       169: 1
       171: 1
       173: q+1
       175: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q+2
       193: q+1
       194: q+1
       195: 2q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: 2
       221: q+2
       222: q+2
       223: q^2+q+2
       224: 2
       225: q+2
       226: 3q+2
       227: q+2
       228: q^2+2q+2
       229: q^2+q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: q^2+2q+2
       234: q^2+q+2
       235: q+2
       236: q^2+3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: q^3+q^2+2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+2q+2
       257: q^2+2q+2
       258: q^2+2q+2
       259: 1
       261: 1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       283: 1
       284: 1
       285: q+2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: q+2
       348: q^2+q+2
       349: 2
       350: q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: q+2
       356: q^2+q+2
       357: 2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: q^2+2q+2
       369: q^2+q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       379: 1
       385: 1
       387: 1
       389: 1
       392: 1
       393: 1
       395: 1
       397: 1
       398: 1
       401: 1
       402: 1
       405: 1
       408: 1
       419: 1
       420: 1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       431: q+2
       433: 1
       434: 1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       449: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: 1
       483: 2
       484: 2
       491: 1
       492: 2
       493: q+2
       494: 2
       495: 2
       496: 2
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 2
       508: q+2
       509: 2
       510: q+2
       511: q+2
       512: q^2+q+2
       513: 2
       514: q+2
       515: 2
       516: 2
       517: q+1
       529: 1
       531: 1
       533: 1
       535: 1
       541: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 2
       562: 2
       565: 1
       567: 1
       569: 1
       572: 1
       573: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       591: 2
       595: 1
       599: 1
       600: 1
       603: 1
       604: 1
       607: 2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       641: 1
       642: 1
       643: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       675: 2
       676: 1
       677: 2
       679: 1
       680: 2
       681: 2
       682: 1
       683: 2
       685: 1
       686: 2
       687: q+2
       688: 2
       689: 2
       693: 1
       694: 1
       698: 1
       700: 1
       713: 1
       714: 1
       725: 1
       728: 1
       741: 1
       742: 1
       753: 1
       755: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: 2
       807: 1
       811: 1
       812: 1
       817: 2
       825: 1
       826: 1
       827: 2
       831: 1
       835: 1
       836: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 2
       851: 1
       852: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 2
       878: 1
       879: 2
       880: 1
       924: 1
       925: 1
       948: 1
       949: 1
       964: 1
       966: 1
       974: 1
       977: 1
       998: 1
      1028: 1
      1044: 1
      1052: 1
      1053: 1
      1054: 2
      1058: 1
      1062: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1202: 1
      1203: 1
      1232: 1
      1250: 1
      1270: 1
      1287: 1
      1466: 1

1467:    0: 2q^3+2q^2+6q+2
         1: 2q^3+2q^2+6q+2
         2: 4q^2+4q+2
         3: 2q^3+2q^2+6q+2
         4: q^4+2q^3+3q^2+4q+2
         5: 2q^3+2q^2+6q+2
         6: q^4+2q^3+3q^2+4q+2
         7: 2q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: 2q^3+3q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^3+2q^2+6q+2
        17: 2q^3+2q^2+6q+2
        18: 2q^3+3q^2+3q+2
        19: q^3+q^2+4q+2
        20: q^3+q^2+4q+2
        21: 2q^2+3q+2
        22: 2q^3+2q^2+6q+2
        23: 2q^3+2q^2+6q+2
        24: 4q^2+4q+2
        25: 2q^3+2q^2+6q+2
        26: 2q^3+2q^2+6q+2
        27: 4q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: q^2+3q+2
        31: 6q+2
        32: 2q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 6q+2
        35: 2q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+q^2+3q+1
        38: q^3+q^2+3q+1
        39: q^3+q^2+3q+1
        40: q^3+q^2+3q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^3+q^2+4q+2
        50: q^3+q^2+4q+2
        51: 2q^2+3q+2
        52: q^3+q^2+4q+2
        53: q^3+q^2+4q+2
        54: 2q^2+3q+2
        55: q^3+q^2+4q+2
        56: q^3+q^2+4q+2
        57: 2q^2+3q+2
        58: 2q
        59: 4q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: 2q+2
        69: q^2+3q+2
        70: 3q+2
        71: 4q+2
        72: q^3+q^2+2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+4q+2
        82: 4q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+4q+2
        86: 4q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^3+q^2+4q+2
        95: q^3+q^2+4q+2
        96: 2q^2+3q+2
        97: q^3+q^2+4q+2
        98: q^3+q^2+4q+2
        99: 2q^2+3q+2
       100: q^3+q^2+4q+2
       101: q^3+q^2+4q+2
       102: 2q^2+3q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: q^2+2q+2
       135: q^2+q+2
       136: q+2
       137: 4q+2
       138: q^2+3q+2
       139: 4q+2
       140: q^3+q^2+2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: q^2+3q+2
       145: 4q+2
       146: 3q+2
       147: q^3+q^2+2q+2
       148: 2q+2
       149: 4q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+q^2+4q+2
       167: q^3+q^2+4q+2
       168: 2q^2+3q+2
       170: 1
       172: 1
       174: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       186: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2q+2
       193: q+1
       194: q+1
       196: 2q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: 2
       221: q+2
       222: q+2
       223: q^2+q+2
       224: 2
       225: q+2
       226: 3q+2
       227: q+2
       228: q^2+2q+2
       229: q^2+q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: q^2+2q+2
       234: q^2+q+2
       235: q+2
       236: q^2+3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: q^3+q^2+2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+2q+2
       257: q^2+2q+2
       258: q^2+2q+2
       260: 1
       262: 1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       283: 1
       284: 1
       286: q+2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       304: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       310: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       322: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: q+2
       335: 2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: q+2
       348: q^2+q+2
       349: 2
       350: q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: q+2
       356: q^2+q+2
       357: 2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: q^2+2q+2
       369: q^2+q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       378: 1
       380: 1
       386: 1
       388: 1
       390: 1
       391: 1
       394: 1
       396: 1
       399: 1
       400: 1
       403: 1
       404: 1
       406: 1
       407: 1
       419: 1
       420: 1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       432: q+2
       433: 1
       434: 1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       450: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: 1
       483: 2
       484: 2
       491: 1
       492: 2
       493: q+2
       494: 2
       495: 2
       496: 2
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 2
       508: q+2
       509: 2
       510: q+2
       511: q+2
       512: q^2+q+2
       513: 2
       514: q+2
       515: 2
       516: 2
       517: q+1
       530: 1
       532: 1
       534: 1
       536: 1
       542: 1
       543: 1
       545: 1
       546: 1
       547: 1
       548: 1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 2
       564: 2
       566: 1
       568: 1
       570: 1
       571: 1
       574: 2
       575: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       592: 2
       596: 1
       599: 1
       600: 1
       603: 1
       604: 1
       608: 2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2
       641: 1
       642: 1
       644: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       675: 2
       676: 1
       677: 2
       679: 1
       680: 2
       681: 2
       682: 1
       683: 2
       685: 1
       686: 2
       687: q+2
       688: 2
       689: 2
       696: 1
       697: 1
       699: 1
       701: 1
       715: 1
       716: 1
       726: 1
       727: 1
       743: 1
       744: 1
       754: 1
       756: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: 2
       808: 1
       811: 1
       812: 1
       818: 2
       825: 1
       826: 1
       828: 2
       832: 1
       835: 1
       836: 1
       843: 1
       844: 1
       845: 1
       846: 1
       848: 2
       851: 1
       852: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 2
       878: 1
       879: 2
       880: 1
       926: 1
       927: 1
       950: 1
       951: 1
       965: 1
       967: 1
       975: 1
       976: 1
       999: 1
      1029: 1
      1045: 1
      1052: 1
      1053: 1
      1055: 2
      1059: 1
      1062: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1204: 1
      1205: 1
      1233: 1
      1251: 1
      1271: 1
      1287: 1
      1467: 1

1468:    0: 2q^3+2q^2+6q+2
         1: 2q^3+2q^2+6q+2
         2: 4q^2+4q+2
         3: 2q^3+2q^2+6q+2
         4: q^4+2q^3+3q^2+4q+2
         5: 2q^3+2q^2+6q+2
         6: q^4+2q^3+3q^2+4q+2
         7: 2q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: 2q^3+3q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^3+2q^2+6q+2
        17: 2q^3+2q^2+6q+2
        18: 2q^3+3q^2+3q+2
        19: q^3+q^2+4q+2
        20: q^3+q^2+4q+2
        21: 2q^2+3q+2
        22: 2q^3+2q^2+6q+2
        23: 2q^3+2q^2+6q+2
        24: 4q^2+4q+2
        25: 2q^3+2q^2+6q+2
        26: 2q^3+2q^2+6q+2
        27: 4q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: q^2+3q+2
        31: 6q+2
        32: 2q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 6q+2
        35: 2q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+q^2+3q+1
        38: q^3+q^2+3q+1
        39: q^3+q^2+3q+1
        40: q^3+q^2+3q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^3+q^2+4q+2
        50: q^3+q^2+4q+2
        51: 2q^2+3q+2
        52: q^3+q^2+4q+2
        53: q^3+q^2+4q+2
        54: 2q^2+3q+2
        55: q^3+q^2+4q+2
        56: q^3+q^2+4q+2
        57: 2q^2+3q+2
        58: 3q+1
        59: 3q+1
        60: 4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: 2q+2
        69: q^2+3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: q^3+q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+4q+2
        82: 4q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+4q+2
        86: 4q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^3+q^2+4q+2
        95: q^3+q^2+4q+2
        96: 2q^2+3q+2
        97: q^3+q^2+4q+2
        98: q^3+q^2+4q+2
        99: 2q^2+3q+2
       100: q^3+q^2+4q+2
       101: q^3+q^2+4q+2
       102: 2q^2+3q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: q^2+2q+2
       135: q+2
       136: q^2+q+2
       137: 4q+2
       138: q^2+3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: q^3+q^2+2q+2
       143: 4q+2
       144: q^2+3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: q^3+q^2+2q+2
       149: 4q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+q^2+4q+2
       167: q^3+q^2+4q+2
       168: 2q^2+3q+2
       169: 1
       170: 1
       173: q+1
       174: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: 2
       221: q+2
       222: 2
       223: q+2
       224: q+2
       225: q^2+q+2
       226: 3q+2
       227: q+2
       228: q^2+2q+2
       229: q+2
       230: q^2+q+2
       231: 3q+2
       232: q+2
       233: q^2+2q+2
       234: q+2
       235: q^2+q+2
       236: q^2+3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: q^3+q^2+2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+2q+2
       257: q^2+2q+2
       258: q^2+2q+2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: q+1
       276: q+1
       283: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: 2
       348: q+2
       349: q+2
       350: q^2+q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: 2
       356: q+2
       357: q+2
       358: q^2+q+2
       359: 4
       366: 3q+2
       367: q+2
       368: q^2+2q+2
       369: q+2
       370: q^2+q+2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       397: 1
       400: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 4
       445: 2
       446: 2
       447: q+2
       449: 1
       450: 1
       451: 1
       452: 1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 1
       482: 2
       483: 2
       484: 2
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 2
       497: 2
       498: 2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: 2
       510: q+2
       511: 2
       512: q+2
       513: q+2
       514: q^2+q+2
       515: 2
       516: 2
       517: q+1
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 2
       546: 2
       549: 1
       551: 1
       557: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       571: 1
       573: 2
       574: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       619: 2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       641: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       675: 1
       676: 2
       677: 2
       679: 1
       680: 2
       681: 1
       682: 2
       683: 2
       685: 1
       686: 2
       687: 2
       688: q+2
       689: 2
       693: 1
       694: 1
       696: 1
       699: 1
       717: 1
       718: 1
       725: 1
       726: 1
       741: 1
       744: 1
       753: 1
       754: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       793: 2
       801: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       817: 1
       818: 1
       825: 1
       829: 2
       831: 1
       832: 1
       835: 1
       836: 1
       843: 1
       844: 1
       845: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: 2
       879: 2
       880: 1
       928: 1
       929: 1
       952: 1
       953: 1
       964: 1
       965: 1
       974: 1
       976: 1
      1000: 1
      1026: 1
      1040: 1
      1052: 1
      1056: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1206: 1
      1207: 1
      1234: 1
      1254: 1
      1268: 1
      1287: 1
      1468: 1

1469:    0: 2q^3+2q^2+6q+2
         1: 2q^3+2q^2+6q+2
         2: 4q^2+4q+2
         3: 2q^3+2q^2+6q+2
         4: q^4+2q^3+3q^2+4q+2
         5: 2q^3+2q^2+6q+2
         6: q^4+2q^3+3q^2+4q+2
         7: 2q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: 2q^3+3q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^3+2q^2+6q+2
        17: 2q^3+2q^2+6q+2
        18: 2q^3+3q^2+3q+2
        19: q^3+q^2+4q+2
        20: q^3+q^2+4q+2
        21: 2q^2+3q+2
        22: 2q^3+2q^2+6q+2
        23: 2q^3+2q^2+6q+2
        24: 4q^2+4q+2
        25: 2q^3+2q^2+6q+2
        26: 2q^3+2q^2+6q+2
        27: 4q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: q^2+3q+2
        31: 6q+2
        32: 2q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 6q+2
        35: 2q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+q^2+3q+1
        38: q^3+q^2+3q+1
        39: q^3+q^2+3q+1
        40: q^3+q^2+3q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^3+q^2+4q+2
        50: q^3+q^2+4q+2
        51: 2q^2+3q+2
        52: q^3+q^2+4q+2
        53: q^3+q^2+4q+2
        54: 2q^2+3q+2
        55: q^3+q^2+4q+2
        56: q^3+q^2+4q+2
        57: 2q^2+3q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 4q+2
        62: 3q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: 2q+2
        69: q^2+3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: q^3+q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 2q^2+4q+2
        82: 4q+2
        83: q^2+3q+2
        84: 4q+2
        85: 2q^2+4q+2
        86: 4q+2
        87: q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^3+q^2+4q+2
        95: q^3+q^2+4q+2
        96: 2q^2+3q+2
        97: q^3+q^2+4q+2
        98: q^3+q^2+4q+2
        99: 2q^2+3q+2
       100: q^3+q^2+4q+2
       101: q^3+q^2+4q+2
       102: 2q^2+3q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: q^2+2q+2
       135: q+2
       136: q^2+q+2
       137: 4q+2
       138: q^2+3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: q^3+q^2+2q+2
       143: 4q+2
       144: q^2+3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: q^3+q^2+2q+2
       149: 4q+2
       150: q^2+3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+2
       158: q+2
       159: q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+q^2+4q+2
       167: q^3+q^2+4q+2
       168: 2q^2+3q+2
       171: 1
       172: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       184: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: 2
       221: q+2
       222: 2
       223: q+2
       224: q+2
       225: q^2+q+2
       226: 3q+2
       227: q+2
       228: q^2+2q+2
       229: q+2
       230: q^2+q+2
       231: 3q+2
       232: q+2
       233: q^2+2q+2
       234: q+2
       235: q^2+q+2
       236: q^2+3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: q^3+q^2+2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+2q+2
       257: q^2+2q+2
       258: q^2+2q+2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: q+1
       278: q+1
       284: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 2
       334: 2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: 2
       346: q+2
       347: 2
       348: q+2
       349: q+2
       350: q^2+q+2
       351: 4
       352: q+2
       353: 2
       354: q+2
       355: 2
       356: q+2
       357: q+2
       358: q^2+q+2
       359: 4
       366: 3q+2
       367: q+2
       368: q^2+2q+2
       369: q+2
       370: q^2+q+2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       398: 1
       399: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       430: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 4
       445: 2
       446: 2
       448: q+2
       449: 1
       450: 1
       451: 1
       452: 1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+1
       470: q+1
       472: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 1
       482: 2
       483: 2
       484: 2
       491: 1
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 2
       497: 2
       498: 2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: 2
       510: q+2
       511: 2
       512: q+2
       513: q+2
       514: q^2+q+2
       515: 2
       516: 2
       517: q+1
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 2
       548: 2
       550: 1
       552: 1
       558: 1
       559: 1
       561: 1
       562: 1
       563: 1
       564: 1
       567: 1
       568: 1
       570: 1
       572: 1
       575: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       590: 1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2
       620: 2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       642: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       674: 2
       675: 1
       676: 2
       677: 2
       679: 1
       680: 2
       681: 1
       682: 2
       683: 2
       685: 1
       686: 2
       687: 2
       688: q+2
       689: 2
       697: 1
       698: 1
       700: 1
       701: 1
       719: 1
       720: 1
       727: 1
       728: 1
       742: 1
       743: 1
       755: 1
       756: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       794: 2
       802: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       817: 1
       818: 1
       826: 1
       830: 2
       831: 1
       832: 1
       835: 1
       836: 1
       843: 1
       844: 1
       846: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: 2
       879: 2
       880: 1
       930: 1
       931: 1
       954: 1
       955: 1
       966: 1
       967: 1
       975: 1
       977: 1
      1001: 1
      1027: 1
      1041: 1
      1053: 1
      1057: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1208: 1
      1209: 1
      1235: 1
      1255: 1
      1269: 1
      1287: 1
      1469: 1

1470:    0: 9q^2+9q+2
         1: 9q^2+9q+2
         2: 9q^2+9q+2
         3: 9q^2+9q+2
         4: 3q^3+8q^2+7q+2
         5: 9q^2+9q+2
         6: 3q^3+8q^2+7q+2
         7: 3q^3+8q^2+7q+2
         8: 9q^2+9q+2
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 9q^2+9q+2
        11: 9q^2+9q+2
        12: 3q^3+8q^2+7q+2
        13: 9q^2+9q+2
        14: 3q^3+8q^2+7q+2
        15: 9q^2+9q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: 2q^3+3q^2+3q+1
        19: 6q^2+7q+2
        20: 6q^2+7q+2
        21: 6q^2+7q+2
        22: 9q^2+9q+2
        23: 9q^2+9q+2
        24: 9q^2+9q+2
        25: 9q^2+9q+2
        26: 9q^2+9q+2
        27: 9q^2+9q+2
        28: 2q^2+8q+2
        29: 6q^2+7q+2
        30: 6q^2+7q+2
        31: 9q^2+9q+2
        32: 9q^2+9q+2
        33: 2q^2+8q+2
        34: 9q^2+9q+2
        35: 9q^2+9q+2
        36: 2q^2+8q+2
        37: 6q^2+7q+2
        38: 3q^2+2q
        39: 6q^2+7q+2
        40: 3q^2+2q
        41: 6q^2+7q+2
        42: 3q^2+2q
        43: 9q^2+9q+2
        44: 3q^3+8q^2+7q+2
        45: 9q^2+9q+2
        46: 2q^2+8q+2
        47: 2q^2+8q+2
        48: 2q^3+3q^2+3q+1
        49: 6q+2
        50: 6q+2
        51: 2q^2+3q+1
        52: 6q^2+7q+2
        53: 6q^2+7q+2
        54: 6q^2+7q+2
        55: 6q^2+7q+2
        56: 6q^2+7q+2
        57: 6q^2+7q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 6q^2+7q+2
        63: 3q^2+2q
        64: 6q^2+7q+2
        65: 3q^2+2q
        66: 2q^2+6q+2
        67: 2q
        68: 2q^2+8q+2
        69: 2q+1
        70: 6q^2+7q+2
        71: 6q+2
        72: 4q+2
        73: 4q+2
        74: 3q^2+5q+2
        76: 3q^2+5q+2
        78: 3q^2+5q+2
        80: 9q^2+9q+2
        81: 2q^2+8q+2
        82: 6q^2+7q+2
        83: 6q^2+7q+2
        84: 9q^2+9q+2
        85: 2q^2+8q+2
        86: 6q^2+7q+2
        87: 6q^2+7q+2
        88: 2q^2+8q+2
        89: 2q^2+8q+2
        90: 2q^3+3q^2+3q+1
        91: 6q+2
        92: 6q+2
        93: 2q^2+3q+1
        94: 6q+2
        95: 6q+2
        96: 2q^2+3q+1
        97: 6q+2
        98: 6q+2
        99: 2q^2+3q+1
       100: 6q^2+7q+2
       101: 6q^2+7q+2
       102: 6q^2+7q+2
       103: q^2+3q+1
       104: q
       105: q
       106: q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 2q+2
       113: 3q^2+5q+2
       115: 3q^2+5q+2
       117: q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: 6q^2+7q+2
       122: 3q^2+2q
       123: 2q^2+6q+2
       124: 2q
       125: 2q^2+8q+2
       126: 2q+1
       127: 2q+2
       129: 2q+2
       131: 2q+1
       133: 6q+2
       134: 2q+1
       135: 4q+2
       136: 4q+2
       137: 2q^2+8q+2
       138: 2q+1
       139: 6q+2
       140: 4q+2
       141: 6q^2+7q+2
       142: 4q+2
       143: 2q^2+8q+2
       144: 2q+1
       145: 6q+2
       146: 6q^2+7q+2
       147: 4q+2
       148: 4q+2
       149: 6q^2+7q+2
       150: 6q^2+7q+2
       151: 3q^2+5q+2
       153: 3q^2+5q+2
       155: 3q^2+5q+2
       157: 6q+2
       158: 6q+2
       159: 2q^2+3q+1
       160: 6q+2
       161: 6q+2
       162: 2q^2+3q+1
       163: 6q+2
       164: 6q+2
       165: 2q^2+3q+1
       166: 6q+2
       167: 6q+2
       168: 2q^2+3q+1
       169: q+1
       172: q+1
       173: q^2+3q+1
       174: q
       175: q
       176: q^2+3q+1
       177: q+1
       179: 2q+2
       181: 2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+2
       189: 3q^2+5q+2
       191: q^2+4q+1
       192: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: 2q+1
       197: 2q+2
       199: q^2+4q+1
       200: q^2+4q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+2
       207: 2q^2+6q+2
       208: 2q
       209: 3q^2+5q+2
       211: 3q^2+5q+2
       213: 2q+2
       215: 2q+2
       217: 2q+1
       219: 2q+1
       220: 6q+2
       221: 2q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: 2q+1
       227: 6q+2
       228: 2q+1
       229: 4q+2
       230: 4q+2
       231: 2q+1
       232: 6q+2
       233: 2q+1
       234: 4q+2
       235: 4q+2
       236: 2q+1
       237: 2q+2
       239: 2q+2
       241: 2q+1
       243: 6q+2
       244: 4q+2
       245: 4q+2
       246: 6q^2+7q+2
       247: 4
       248: 4
       249: 2q+1
       250: 6q+2
       251: 6q+2
       252: 2q^2+3q+1
       253: 6q+2
       254: 6q+2
       255: 2q^2+3q+1
       256: 6q+2
       257: 6q+2
       258: 2q^2+3q+1
       259: 1
       262: 1
       263: q+1
       266: q+1
       267: q+1
       269: q+1
       271: q+1
       273: q+1
       275: q^2+3q+1
       276: q
       277: q
       278: q^2+3q+1
       279: 2q+2
       281: q+1
       287: q+1
       289: 2
       291: 1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+2
       299: 2q+1
       300: 2q+1
       301: 2
       303: 2q+1
       304: 2q+1
       305: 2q+2
       307: 2q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       311: 2
       313: 2q+2
       315: q+1
       317: 2q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+2
       325: 3q^2+5q+2
       327: 2q+2
       329: 2q+2
       331: 2q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       338: 4
       340: 4
       342: 2q+1
       344: 2q+1
       345: 6q+2
       346: 2q+1
       347: 4q+2
       348: q+1
       349: 4q+2
       350: q+1
       351: 4
       352: 2q+1
       353: 6q+2
       354: 2q+1
       355: 4q+2
       356: q+1
       357: 4q+2
       358: q+1
       359: 4
       360: 2q+2
       362: 2q+2
       364: 2q+1
       366: 2q+1
       367: 6q+2
       368: 2q+1
       369: 4q+2
       370: 4q+2
       371: 4
       372: 4
       373: 2q+1
       374: 6q+2
       375: 6q+2
       376: 2q^2+3q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       389: 1
       391: 1
       393: q+1
       396: q+1
       397: 1
       399: 1
       401: q+1
       404: q+1
       405: q+1
       406: q+1
       409: 2q+2
       411: q+1
       413: q+1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 4
       433: 1
       435: 2
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: 2q+2
       443: 2
       444: 2
       445: 4
       451: 1
       453: 2q+1
       454: 2q+1
       455: 2
       457: 2q+1
       458: 2q+1
       459: 2q+2
       461: 2
       462: 2
       463: 4
       465: 2q+2
       467: q+1
       469: q+1
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       475: 2q+2
       477: 2
       479: 2
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: 4
       485: 4
       487: 4
       489: 2q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 4
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 4
       502: 2q+2
       504: 2q+2
       506: 2q+1
       508: 2q+1
       509: 6q+2
       510: 2q+1
       511: 4q+2
       512: q+1
       513: 4q+2
       514: q+1
       518: 4
       519: 4
       520: 2q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 2
       547: 2
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 2
       563: 2
       565: q+1
       568: q+1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       583: q+1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 4
       605: 1
       609: 1
       611: 2
       613: 1
       615: 2
       616: 2
       617: 4
       623: 1
       625: 1
       627: 2
       629: 1
       631: 2
       632: 2
       633: 4
       635: 2q+2
       637: q+1
       639: q+1
       645: 1
       647: 2q+1
       648: 2q+1
       649: 2q+1
       650: 2q+1
       651: 2
       653: 2q+2
       655: 2
       656: 2
       665: 1
       666: 4
       668: 4
       670: 2q+1
       672: 4
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 4
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 4
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       693: 1
       696: 1
       697: 1
       698: 1
       729: 1
       731: 1
       733: 2
       735: 2
       745: 1
       747: 1
       749: 2
       751: 2
       757: 1
       758: 1
       761: q+1
       762: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       777: 1
       781: 1
       783: 1
       789: 4
       797: 1
       799: 1
       809: 1
       811: 1
       813: 4
       815: 2
       816: 2
       821: 1
       823: 1
       833: 1
       835: 1
       837: 4
       839: 2
       840: 2
       841: q+1
       849: 1
       851: 1
       853: 2
       855: 1
       857: 2
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       888: 1
       889: 1
       932: 2
       934: 2
       956: 2
       958: 2
       978: 1
       979: 1
       982: 2
       985: 2
       988: 1
       989: 1
       990: 1
       991: 1
      1002: 1
      1018: 1
      1022: 1
      1024: 1
      1034: 1
      1038: 1
      1042: 1
      1048: 1
      1050: 1
      1060: 1
      1062: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1098: 1
      1101: 1
      1102: 1
      1103: 1
      1238: 1
      1256: 1
      1264: 1
      1266: 1
      1272: 1
      1289: 1
      1470: 1

1471:    0: 9q^2+9q+2
         1: 9q^2+9q+2
         2: 9q^2+9q+2
         3: 9q^2+9q+2
         4: 3q^3+8q^2+7q+2
         5: 9q^2+9q+2
         6: 3q^3+8q^2+7q+2
         7: 3q^3+8q^2+7q+2
         8: 9q^2+9q+2
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 9q^2+9q+2
        11: 9q^2+9q+2
        12: 3q^3+8q^2+7q+2
        13: 9q^2+9q+2
        14: 3q^3+8q^2+7q+2
        15: 9q^2+9q+2
        16: 2q^2+8q+2
        17: 2q^2+8q+2
        18: 2q^3+3q^2+3q+1
        19: 6q^2+7q+2
        20: 6q^2+7q+2
        21: 6q^2+7q+2
        22: 9q^2+9q+2
        23: 9q^2+9q+2
        24: 9q^2+9q+2
        25: 9q^2+9q+2
        26: 9q^2+9q+2
        27: 9q^2+9q+2
        28: 2q^2+8q+2
        29: 6q^2+7q+2
        30: 6q^2+7q+2
        31: 9q^2+9q+2
        32: 9q^2+9q+2
        33: 2q^2+8q+2
        34: 9q^2+9q+2
        35: 9q^2+9q+2
        36: 2q^2+8q+2
        37: 3q^2+2q
        38: 6q^2+7q+2
        39: 3q^2+2q
        40: 6q^2+7q+2
        41: 3q^2+2q
        42: 6q^2+7q+2
        43: 9q^2+9q+2
        44: 3q^3+8q^2+7q+2
        45: 9q^2+9q+2
        46: 2q^2+8q+2
        47: 2q^2+8q+2
        48: 2q^3+3q^2+3q+1
        49: 6q+2
        50: 6q+2
        51: 2q^2+3q+1
        52: 6q^2+7q+2
        53: 6q^2+7q+2
        54: 6q^2+7q+2
        55: 6q^2+7q+2
        56: 6q^2+7q+2
        57: 6q^2+7q+2
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 3q^2+2q
        63: 6q^2+7q+2
        64: 3q^2+2q
        65: 6q^2+7q+2
        66: 2q
        67: 2q^2+6q+2
        68: 2q^2+8q+2
        69: 2q+1
        70: 6q^2+7q+2
        71: 6q+2
        72: 4q+2
        73: 4q+2
        75: 3q^2+5q+2
        77: 3q^2+5q+2
        79: 3q^2+5q+2
        80: 9q^2+9q+2
        81: 2q^2+8q+2
        82: 6q^2+7q+2
        83: 6q^2+7q+2
        84: 9q^2+9q+2
        85: 2q^2+8q+2
        86: 6q^2+7q+2
        87: 6q^2+7q+2
        88: 2q^2+8q+2
        89: 2q^2+8q+2
        90: 2q^3+3q^2+3q+1
        91: 6q+2
        92: 6q+2
        93: 2q^2+3q+1
        94: 6q+2
        95: 6q+2
        96: 2q^2+3q+1
        97: 6q+2
        98: 6q+2
        99: 2q^2+3q+1
       100: 6q^2+7q+2
       101: 6q^2+7q+2
       102: 6q^2+7q+2
       103: q
       104: q^2+3q+1
       105: q^2+3q+1
       106: q
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       112: 2q+2
       114: 3q^2+5q+2
       116: 3q^2+5q+2
       117: q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: 3q^2+2q
       122: 6q^2+7q+2
       123: 2q
       124: 2q^2+6q+2
       125: 2q^2+8q+2
       126: 2q+1
       128: 2q+2
       130: 2q+2
       132: 2q+1
       133: 6q+2
       134: 2q+1
       135: 4q+2
       136: 4q+2
       137: 2q^2+8q+2
       138: 2q+1
       139: 6q+2
       140: 4q+2
       141: 6q^2+7q+2
       142: 4q+2
       143: 2q^2+8q+2
       144: 2q+1
       145: 6q+2
       146: 6q^2+7q+2
       147: 4q+2
       148: 4q+2
       149: 6q^2+7q+2
       150: 6q^2+7q+2
       152: 3q^2+5q+2
       154: 3q^2+5q+2
       156: 3q^2+5q+2
       157: 6q+2
       158: 6q+2
       159: 2q^2+3q+1
       160: 6q+2
       161: 6q+2
       162: 2q^2+3q+1
       163: 6q+2
       164: 6q+2
       165: 2q^2+3q+1
       166: 6q+2
       167: 6q+2
       168: 2q^2+3q+1
       170: q+1
       171: q+1
       173: q
       174: q^2+3q+1
       175: q^2+3q+1
       176: q
       178: q+1
       180: 2q+2
       182: 2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       188: 2q+2
       190: 3q^2+5q+2
       191: q^2+4q+1
       192: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: 2q+1
       198: 2q+2
       199: q^2+4q+1
       200: q^2+4q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       206: 2q+2
       207: 2q
       208: 2q^2+6q+2
       210: 3q^2+5q+2
       212: 3q^2+5q+2
       214: 2q+2
       216: 2q+2
       218: 2q+1
       219: 2q+1
       220: 6q+2
       221: 2q+1
       222: 4q+2
       223: q+1
       224: 4q+2
       225: q+1
       226: 2q+1
       227: 6q+2
       228: 2q+1
       229: 4q+2
       230: 4q+2
       231: 2q+1
       232: 6q+2
       233: 2q+1
       234: 4q+2
       235: 4q+2
       236: 2q+1
       238: 2q+2
       240: 2q+2
       242: 2q+1
       243: 6q+2
       244: 4q+2
       245: 4q+2
       246: 6q^2+7q+2
       247: 4
       248: 4
       249: 2q+1
       250: 6q+2
       251: 6q+2
       252: 2q^2+3q+1
       253: 6q+2
       254: 6q+2
       255: 2q^2+3q+1
       256: 6q+2
       257: 6q+2
       258: 2q^2+3q+1
       260: 1
       261: 1
       264: q+1
       265: q+1
       268: q+1
       270: q+1
       272: q+1
       274: q+1
       275: q
       276: q^2+3q+1
       277: q^2+3q+1
       278: q
       280: 2q+2
       282: q+1
       288: q+1
       290: 2
       292: 1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       298: 2q+2
       299: 2q+1
       300: 2q+1
       302: 2
       303: 2q+1
       304: 2q+1
       306: 2q+2
       307: 2q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       312: 2
       314: 2q+2
       316: q+1
       318: 2q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       324: 2q+2
       326: 3q^2+5q+2
       328: 2q+2
       330: 2q+2
       332: 2q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       339: 4
       341: 4
       343: 2q+1
       344: 2q+1
       345: 6q+2
       346: 2q+1
       347: 4q+2
       348: q+1
       349: 4q+2
       350: q+1
       351: 4
       352: 2q+1
       353: 6q+2
       354: 2q+1
       355: 4q+2
       356: q+1
       357: 4q+2
       358: q+1
       359: 4
       361: 2q+2
       363: 2q+2
       365: 2q+1
       366: 2q+1
       367: 6q+2
       368: 2q+1
       369: 4q+2
       370: 4q+2
       371: 4
       372: 4
       373: 2q+1
       374: 6q+2
       375: 6q+2
       376: 2q^2+3q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       390: 1
       392: 1
       394: q+1
       395: q+1
       398: 1
       400: 1
       402: q+1
       403: q+1
       407: q+1
       408: q+1
       410: 2q+2
       412: q+1
       414: q+1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 4
       434: 1
       436: 2
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       442: 2q+2
       443: 2
       444: 2
       446: 4
       452: 1
       453: 2q+1
       454: 2q+1
       456: 2
       457: 2q+1
       458: 2q+1
       460: 2q+2
       461: 2
       462: 2
       464: 4
       466: 2q+2
       468: q+1
       470: q+1
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       476: 2q+2
       478: 2
       479: 2
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: 4
       486: 4
       488: 4
       490: 2q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 4
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 4
       503: 2q+2
       505: 2q+2
       507: 2q+1
       508: 2q+1
       509: 6q+2
       510: 2q+1
       511: 4q+2
       512: q+1
       513: 4q+2
       514: q+1
       518: 4
       519: 4
       520: 2q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: 2
       548: 2
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: 2
       564: 2
       566: q+1
       567: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       584: q+1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 4
       606: 1
       610: 1
       612: 2
       614: 1
       615: 2
       616: 2
       618: 4
       624: 1
       626: 1
       628: 2
       630: 1
       631: 2
       632: 2
       634: 4
       636: 2q+2
       638: q+1
       640: q+1
       646: 1
       647: 2q+1
       648: 2q+1
       649: 2q+1
       650: 2q+1
       652: 2
       654: 2q+2
       655: 2
       656: 2
       665: 1
       667: 4
       669: 4
       671: 2q+1
       672: 4
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 4
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 4
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       694: 1
       699: 1
       700: 1
       701: 1
       730: 1
       732: 1
       734: 2
       736: 2
       746: 1
       748: 1
       750: 2
       752: 2
       759: 1
       760: 1
       763: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       778: 1
       782: 1
       784: 1
       790: 4
       798: 1
       800: 1
       810: 1
       812: 1
       814: 4
       815: 2
       816: 2
       822: 1
       824: 1
       834: 1
       836: 1
       838: 4
       839: 2
       840: 2
       842: q+1
       850: 1
       852: 1
       854: 2
       856: 1
       857: 2
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       891: 1
       892: 1
       933: 2
       935: 2
       957: 2
       959: 2
       980: 1
       981: 1
       983: 2
       986: 2
       988: 1
       989: 1
       990: 1
       991: 1
      1003: 1
      1019: 1
      1023: 1
      1025: 1
      1035: 1
      1039: 1
      1043: 1
      1049: 1
      1051: 1
      1061: 1
      1063: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1239: 1
      1257: 1
      1265: 1
      1267: 1
      1273: 1
      1289: 1
      1471: 1

1472:    0: 6q+2
         1: 6q+2
         2: 3q^2+4q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 6q+2
        17: 6q+2
        18: q^3+3q^2+3q+1
        19: 4q+2
        20: 4q+2
        21: 2q^2+3q+1
        22: 6q+2
        23: 6q+2
        24: 3q^2+4q+1
        25: 6q+2
        26: 6q+2
        27: 3q^2+4q+1
        28: 6q+2
        29: 4q+2
        30: 2q+1
        31: 6q+2
        32: 3q+1
        33: 6q+2
        34: 6q+2
        35: 3q+1
        36: 6q+2
        37: 4q+2
        38: 2q
        39: 4q+2
        40: 2q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+3q+1
        52: 4q+2
        53: 4q+2
        54: 2q^2+3q+1
        55: 4q+2
        56: 4q+2
        57: 2q^2+3q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 4q+2
        63: 2q
        64: 2q+1
        65: q
        66: 4q+2
        67: 2q
        69: 2q+1
        70: 2q+1
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: 4q+2
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 4q+2
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+3q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+3q+1
       100: 4q+2
       101: 4q+2
       102: 2q^2+3q+1
       103: 2q+1
       104: q
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: 2q+2
       115: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       126: 2q+1
       127: 2q+2
       129: 2q+2
       131: q^2+2q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 4q+2
       140: 2q+2
       141: 2q+1
       142: 2q+2
       143: 3q+1
       144: 2q+1
       145: 4q+2
       146: 2q+1
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 2q+1
       151: 2q+2
       153: 2q+2
       155: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 4q+2
       167: 4q+2
       168: 2q^2+3q+1
       169: 1
       172: 1
       177: q+1
       179: 2q+2
       181: 2
       187: 1
       189: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: 2q+1
       208: q
       209: 2q+2
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       221: 2q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: 2q+1
       228: 2q+1
       229: q+1
       230: q+1
       231: 2q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: 2q+1
       237: 2q+2
       239: 2q+2
       241: q^2+2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 2q+1
       247: 4
       248: 4
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 2q+1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       281: q+1
       287: q+1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: q+1
       317: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       338: 4
       340: 4
       342: q^2+2q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 4
       354: 2q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 4
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       368: 2q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: q+1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 4
       433: 1
       435: 1
       441: 1
       443: 2
       444: 2
       445: 4
       451: 1
       455: 1
       459: 1
       461: 2
       462: 2
       463: 4
       467: q+1
       469: q+1
       475: 1
       477: 2
       479: 2
       480: 2
       483: 1
       485: 2
       487: 2
       489: q+1
       491: 1
       493: q+1
       494: q+1
       495: 1
       496: 2
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       545: 2
       547: 2
       561: 2
       563: 2
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 2
       623: 1
       625: 1
       627: 1
       629: 1
       633: 2
       637: q+1
       645: 1
       651: 1
       653: 1
       655: 1
       656: 1
       658: 2
       660: 2
       662: q+1
       664: 1
       666: 2
       668: 2
       670: q+1
       673: 1
       674: 2
       677: 1
       678: 2
       679: 1
       680: 2
       683: 1
       684: 2
       685: 1
       687: q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       693: 1
       696: 1
       697: 1
       698: 1
       769: 1
       772: 1
       779: 1
       783: 1
       795: 2
       799: 1
       809: 1
       811: 1
       813: 2
       819: 2
       823: 1
       833: 1
       835: 1
       837: 2
       843: 1
       844: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       867: 1
       869: 2
       870: 1
       872: 1
       873: 2
       874: 1
       876: 1
       879: 1
       880: 1
       968: 1
       971: 1
       982: 1
       985: 1
       996: 1
      1014: 2
      1020: 1
      1024: 1
      1030: 2
      1036: 1
      1042: 1
      1046: 1
      1047: 1
      1050: 1
      1060: 1
      1062: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1188: 1
      1191: 1
      1236: 1
      1252: 1
      1272: 1
      1274: 1
      1288: 1
      1472: 1

1473:    0: 6q+2
         1: 6q+2
         2: 3q^2+4q+1
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^3+3q^2+3q+1
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 3q+1
        14: q^2+2q+1
        15: 3q+1
        16: 6q+2
        17: 6q+2
        18: q^3+3q^2+3q+1
        19: 4q+2
        20: 4q+2
        21: 2q^2+3q+1
        22: 6q+2
        23: 6q+2
        24: 3q^2+4q+1
        25: 6q+2
        26: 6q+2
        27: 3q^2+4q+1
        28: 6q+2
        29: 4q+2
        30: 2q+1
        31: 6q+2
        32: 3q+1
        33: 6q+2
        34: 6q+2
        35: 3q+1
        36: 6q+2
        37: 2q
        38: 4q+2
        39: 2q
        40: 4q+2
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 3q+1
        47: 3q+1
        48: q^2+2q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+3q+1
        52: 4q+2
        53: 4q+2
        54: 2q^2+3q+1
        55: 4q+2
        56: 4q+2
        57: 2q^2+3q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 2q
        63: 4q+2
        64: q
        65: 2q+1
        66: 2q
        67: 4q+2
        69: 2q+1
        70: 2q+1
        71: 4q+2
        72: 2q+2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: 4q+2
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 4q+2
        87: 2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+3q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+3q+1
       100: 4q+2
       101: 4q+2
       102: 2q^2+3q+1
       103: q
       104: 2q+1
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       114: 2q+2
       116: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       126: 2q+1
       128: 2q+2
       130: 2q+2
       132: q^2+2q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: 3q+1
       138: 2q+1
       139: 4q+2
       140: 2q+2
       141: 2q+1
       142: 2q+2
       143: 3q+1
       144: 2q+1
       145: 4q+2
       146: 2q+1
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 2q+1
       152: 2q+2
       154: 2q+2
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 4q+2
       167: 4q+2
       168: 2q^2+3q+1
       170: 1
       171: 1
       178: q+1
       180: 2q+2
       182: 2
       188: 1
       190: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       207: q
       208: 2q+1
       210: 2q+2
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       221: 2q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: 2q+1
       228: 2q+1
       229: q+1
       230: q+1
       231: 2q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: 2q+1
       238: 2q+2
       240: 2q+2
       242: q^2+2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 2q+1
       247: 4
       248: 4
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 2q+1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       282: q+1
       288: q+1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: q+1
       318: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       339: 4
       341: 4
       343: q^2+2q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 4
       354: 2q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 4
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       368: 2q+1
       369: q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: q+1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 4
       434: 1
       436: 1
       442: 1
       443: 2
       444: 2
       446: 4
       452: 1
       456: 1
       460: 1
       461: 2
       462: 2
       464: 4
       468: q+1
       470: q+1
       476: 1
       478: 2
       479: 2
       480: 2
       483: 1
       486: 2
       488: 2
       490: q+1
       491: 1
       493: q+1
       494: q+1
       495: 1
       496: 2
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       546: 2
       548: 2
       562: 2
       564: 2
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 2
       624: 1
       626: 1
       628: 1
       630: 1
       634: 2
       638: q+1
       646: 1
       652: 1
       654: 1
       655: 1
       656: 1
       659: 2
       661: 2
       663: q+1
       664: 1
       667: 2
       669: 2
       671: q+1
       673: 1
       674: 2
       677: 1
       678: 2
       679: 1
       680: 2
       683: 1
       684: 2
       685: 1
       687: q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       694: 1
       699: 1
       700: 1
       701: 1
       770: 1
       773: 1
       780: 1
       784: 1
       796: 2
       800: 1
       810: 1
       812: 1
       814: 2
       820: 2
       824: 1
       834: 1
       836: 1
       838: 2
       843: 1
       844: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       867: 1
       869: 2
       870: 1
       872: 1
       873: 2
       874: 1
       876: 1
       879: 1
       880: 1
       969: 1
       972: 1
       983: 1
       986: 1
       997: 1
      1015: 2
      1021: 1
      1025: 1
      1031: 2
      1037: 1
      1043: 1
      1046: 1
      1047: 1
      1051: 1
      1061: 1
      1063: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1189: 1
      1192: 1
      1237: 1
      1253: 1
      1273: 1
      1275: 1
      1288: 1
      1473: 1

1474:    0: 3q^2+4q+2
         1: q^3+4q^2+4q+2
         2: 3q^2+4q+2
         3: q^3+4q^2+4q+2
         4: 3q^2+4q+2
         5: 3q^2+4q+2
         6: q^3+4q^2+4q+2
         7: 3q^2+4q+2
         8: 3q^2+4q+2
         9: q^5+q^4+q^3+2q^2+2q+1
        10: 2q^2+3q+2
        11: 2q^2+3q+2
        12: 2q^2+3q+2
        13: 3q^2+4q+2
        14: 3q^2+4q+2
        15: 3q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: 3q^2+4q+2
        20: q^3+4q^2+4q+2
        21: 3q^2+4q+2
        22: 3q^2+4q+2
        23: q^3+4q^2+4q+2
        24: 3q^2+4q+2
        25: 3q^2+4q+2
        26: q^3+4q^2+4q+2
        27: 3q^2+4q+2
        28: 2q+2
        29: 2q^2+3q+2
        30: 3q^2+4q+2
        31: 2q^2+3q+2
        32: 3q^2+4q+2
        33: 3q+2
        34: 2q^2+3q+2
        35: 3q^2+4q+2
        36: 3q+2
        37: 2q^2+2q+2
        38: q^2+2q
        39: q^3+2q^2+2q+2
        40: 2q^2+2q
        41: 2q^2+2q+2
        42: q^2+2q
        43: 2q^2+3q+2
        44: 2q^2+3q+2
        45: 2q^2+3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 3q^2+4q+2
        53: q^3+4q^2+4q+2
        54: 3q^2+4q+2
        55: 3q^2+4q+2
        56: q^3+4q^2+4q+2
        57: 3q^2+4q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q^2+q+2
        63: 2q
        64: 2q^2+2q+2
        65: q^2+2q
        66: q+2
        67: 2q
        68: 2q+2
        69: q+1
        70: 2q^2+3q+2
        71: 2q+2
        72: 3q+2
        73: 3q+2
        74: 2q^2+2q+2
        75: q^2+2q
        76: q^3+2q^2+2q+2
        77: 2q^2+2q
        78: 2q^2+2q+2
        79: q^2+2q
        80: 2q^2+3q+2
        81: 3q+2
        82: 2q^2+3q+2
        83: 3q^2+4q+2
        84: 2q^2+3q+2
        85: 3q+2
        86: 2q^2+3q+2
        87: 3q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: 3q^2+4q+2
       101: q^3+4q^2+4q+2
       102: 3q^2+4q+2
       103: 1
       104: q
       105: q
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       112: 2q
       113: 2q^2+q+2
       114: 2q
       115: 2q^2+2q+2
       116: q^2+2q
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q^2+q+2
       122: 2q
       123: q+2
       124: 2q
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: 3q+2
       141: 2q^2+3q+2
       142: 3q+2
       143: 2
       144: q+1
       145: 2q+2
       146: 2q^2+3q+2
       147: 3q+2
       148: 3q+2
       149: 2q^2+3q+2
       150: 3q^2+4q+2
       151: 2q^2+2q+2
       152: q^2+2q
       153: q^3+2q^2+2q+2
       154: 2q^2+2q
       155: 2q^2+2q+2
       156: q^2+2q
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 3q+2
       167: 3q+2
       168: q^2+2q+1
       169: 1
       170: q
       171: q
       172: 1
       173: 1
       174: q
       175: q
       176: 1
       177: 1
       179: 2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       188: 2q
       189: 2q^2+q+2
       190: 2q
       191: 1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       198: 2q
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       206: 2q
       207: 2
       209: 2q^2+q+2
       210: 2q
       211: 2q^2+2q+2
       212: q^2+2q
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       237: 2
       239: 2
       241: q+1
       243: 2q+2
       244: 3q+2
       245: 3q+2
       246: 2q^2+3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 3q+2
       257: 3q+2
       258: q^2+2q+1
       259: 1
       262: 1
       263: 1
       264: q
       265: q
       266: 1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: q+2
       306: 2q
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: q+2
       314: 2q
       315: 1
       317: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       324: 2q
       325: 2q^2+q+2
       326: 2q
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 2q+2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 3q+2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 3q+2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2q+2
       368: q+1
       369: 3q+2
       370: 3q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       399: 1
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       407: q
       408: q
       413: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: q+1
       444: q+1
       445: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       465: 2
       467: 1
       469: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       476: 2q
       477: 2
       479: q+2
       480: 2q
       481: 1
       482: 1
       483: 1
       484: 2q+2
       485: 2
       487: 2
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 3q+2
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 3q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       518: 2
       519: 2
       520: q+1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       566: q
       567: q
       568: 1
       569: 1
       570: 1
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       585: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       613: 1
       615: q+1
       616: q+1
       617: 2
       623: 1
       625: 1
       629: 1
       631: q+1
       632: q+1
       633: 2
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: q+2
       656: 2q
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       693: 1
       697: 1
       733: 1
       735: 1
       749: 1
       751: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       781: 1
       791: 1
       797: 1
       809: 1
       811: 1
       815: 1
       816: 1
       821: 1
       833: 1
       835: 1
       839: 1
       840: 1
       849: 1
       851: 1
       855: 1
       857: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       884: 1
       889: 1
       988: 1
       991: 1
      1008: 1
      1010: 1
      1022: 1
      1038: 1
      1048: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1220: 1
      1266: 1
      1276: 1
      1278: 1
      1289: 1
      1474: 1

1475:    0: 3q^2+4q+2
         1: q^3+4q^2+4q+2
         2: 3q^2+4q+2
         3: q^3+4q^2+4q+2
         4: 3q^2+4q+2
         5: 3q^2+4q+2
         6: q^3+4q^2+4q+2
         7: 3q^2+4q+2
         8: 3q^2+4q+2
         9: q^5+q^4+q^3+2q^2+2q+1
        10: 2q^2+3q+2
        11: 2q^2+3q+2
        12: 2q^2+3q+2
        13: 3q^2+4q+2
        14: 3q^2+4q+2
        15: 3q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: 3q^2+4q+2
        20: q^3+4q^2+4q+2
        21: 3q^2+4q+2
        22: 3q^2+4q+2
        23: q^3+4q^2+4q+2
        24: 3q^2+4q+2
        25: 3q^2+4q+2
        26: q^3+4q^2+4q+2
        27: 3q^2+4q+2
        28: 2q+2
        29: 2q^2+3q+2
        30: 3q^2+4q+2
        31: 2q^2+3q+2
        32: 3q^2+4q+2
        33: 3q+2
        34: 2q^2+3q+2
        35: 3q^2+4q+2
        36: 3q+2
        37: q^2+2q
        38: 2q^2+2q+2
        39: 2q^2+2q
        40: q^3+2q^2+2q+2
        41: q^2+2q
        42: 2q^2+2q+2
        43: 2q^2+3q+2
        44: 2q^2+3q+2
        45: 2q^2+3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: 3q^2+4q+2
        53: q^3+4q^2+4q+2
        54: 3q^2+4q+2
        55: 3q^2+4q+2
        56: q^3+4q^2+4q+2
        57: 3q^2+4q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q
        63: 2q^2+q+2
        64: q^2+2q
        65: 2q^2+2q+2
        66: 2q
        67: q+2
        68: 2q+2
        69: q+1
        70: 2q^2+3q+2
        71: 2q+2
        72: 3q+2
        73: 3q+2
        74: q^2+2q
        75: 2q^2+2q+2
        76: 2q^2+2q
        77: q^3+2q^2+2q+2
        78: q^2+2q
        79: 2q^2+2q+2
        80: 2q^2+3q+2
        81: 3q+2
        82: 2q^2+3q+2
        83: 3q^2+4q+2
        84: 2q^2+3q+2
        85: 3q+2
        86: 2q^2+3q+2
        87: 3q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: 3q^2+4q+2
       101: q^3+4q^2+4q+2
       102: 3q^2+4q+2
       103: q
       104: 1
       105: 1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q
       112: q+2
       113: 2q
       114: 2q^2+q+2
       115: q^2+2q
       116: 2q^2+2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q
       122: 2q^2+q+2
       123: 2q
       124: q+2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: 3q+2
       141: 2q^2+3q+2
       142: 3q+2
       143: 2
       144: q+1
       145: 2q+2
       146: 2q^2+3q+2
       147: 3q+2
       148: 3q+2
       149: 2q^2+3q+2
       150: 3q^2+4q+2
       151: q^2+2q
       152: 2q^2+2q+2
       153: 2q^2+2q
       154: q^3+2q^2+2q+2
       155: q^2+2q
       156: 2q^2+2q+2
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 3q+2
       167: 3q+2
       168: q^2+2q+1
       169: q
       170: 1
       171: 1
       172: q
       173: q
       174: 1
       175: 1
       176: q
       178: 1
       180: 2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q
       188: q+2
       189: 2q
       190: 2q^2+q+2
       191: 1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q
       198: q+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q
       206: q+2
       208: 2
       209: 2q
       210: 2q^2+q+2
       211: q^2+2q
       212: 2q^2+2q+2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       238: 2
       240: 2
       242: q+1
       243: 2q+2
       244: 3q+2
       245: 3q+2
       246: 2q^2+3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 3q+2
       257: 3q+2
       258: q^2+2q+1
       260: 1
       261: 1
       263: q
       264: 1
       265: 1
       266: q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       305: 2q
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       313: 2q
       314: q+2
       316: 1
       318: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: q+2
       325: 2q
       326: 2q^2+q+2
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 2q+2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 3q+2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 3q+2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2q+2
       368: q+1
       369: 3q+2
       370: 3q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       398: 1
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: 1
       408: 1
       414: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: q+1
       444: q+1
       446: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       464: 2
       466: 2
       468: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: q+2
       478: 2
       479: 2q
       480: q+2
       481: 1
       482: 1
       483: 1
       484: 2q+2
       486: 2
       488: 2
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 3q+2
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 3q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       518: 2
       519: 2
       520: q+1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       565: q
       566: 1
       567: 1
       568: q
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       581: 2
       586: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       614: 1
       615: q+1
       616: q+1
       618: 2
       624: 1
       626: 1
       630: 1
       631: q+1
       632: q+1
       634: 2
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       655: 2q
       656: q+2
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       699: 1
       700: 1
       734: 1
       736: 1
       750: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       773: 2
       782: 1
       792: 1
       798: 1
       810: 1
       812: 1
       815: 1
       816: 1
       822: 1
       834: 1
       836: 1
       839: 1
       840: 1
       850: 1
       852: 1
       856: 1
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       890: 1
       891: 1
       989: 1
       990: 1
      1009: 1
      1011: 1
      1023: 1
      1039: 1
      1049: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1221: 1
      1267: 1
      1277: 1
      1279: 1
      1289: 1
      1475: 1

1476:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: 2q+2
         8: 2q+2
         9: q^3+q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2
        17: 2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 2q+2
        30: 2q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        60: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       104: 1
       107: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       170: 1
       173: 1
       174: 1
       183: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 2
       195: 1
       196: 1
       197: 1
       198: 1
       199: 2
       201: 2
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: 1
       276: 1
       283: 1
       293: 2
       295: 1
       296: 1
       297: 1
       298: 1
       299: 2
       303: 1
       304: 1
       305: 1
       306: 1
       307: 2
       309: 1
       310: 1
       313: 1
       314: 1
       319: 2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       386: 1
       393: 1
       394: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: 1
       429: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2
       447: 1
       453: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       541: 1
       542: 1
       557: 1
       560: 1
       565: 1
       566: 1
       573: 1
       574: 1
       589: 1
       593: 1
       603: 1
       615: 2
       619: 1
       631: 1
       632: 1
       641: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       801: 1
       805: 1
       815: 2
       825: 1
       829: 1
       839: 1
       840: 1
       845: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       988: 1
       989: 1
      1004: 1
      1026: 1
      1040: 1
      1052: 1
      1056: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1240: 1
      1258: 1
      1268: 1
      1289: 1
      1476: 1

1477:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: 2q+2
         8: 2q+2
         9: q^3+q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2
        17: 2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 2q+2
        30: 2q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 1
        59: 1
        61: 2
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       105: 1
       106: 1
       108: 2
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: 2
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       171: 1
       172: 1
       175: 1
       176: 1
       184: 2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       194: 2
       195: 1
       196: 1
       197: 1
       198: 1
       200: 2
       202: 2
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: 1
       278: 1
       284: 1
       294: 2
       295: 1
       296: 1
       297: 1
       298: 1
       300: 2
       303: 1
       304: 1
       305: 1
       306: 1
       308: 2
       309: 1
       310: 1
       313: 1
       314: 1
       320: 2
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       387: 1
       388: 1
       395: 1
       396: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: 1
       430: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2
       448: 1
       454: 2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       543: 1
       544: 1
       558: 1
       559: 1
       567: 1
       568: 1
       575: 1
       576: 1
       590: 1
       594: 1
       604: 1
       616: 2
       620: 1
       631: 1
       632: 1
       642: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       802: 1
       806: 1
       816: 2
       826: 1
       830: 1
       839: 1
       840: 1
       846: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       990: 1
       991: 1
      1005: 1
      1027: 1
      1041: 1
      1053: 1
      1057: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1241: 1
      1259: 1
      1269: 1
      1289: 1
      1477: 1

1478:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: 2q+2
         8: 2q+2
         9: q^3+q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2
        17: 2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 2q+2
        30: 2q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: 1
       105: 1
       107: 1
       108: 1
       109: 2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       171: 1
       173: 1
       175: 1
       183: 1
       184: 1
       185: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2
       193: 1
       194: 1
       195: 2
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: 1
       277: 1
       285: 1
       293: 1
       294: 1
       295: 2
       297: 1
       298: 1
       299: 1
       300: 1
       303: 2
       305: 1
       306: 1
       307: 1
       308: 1
       309: 2
       313: 1
       314: 1
       319: 1
       320: 1
       321: 2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       385: 1
       387: 1
       393: 1
       395: 1
       401: 1
       402: 1
       405: 1
       408: 1
       421: 1
       431: 1
       437: 1
       438: 1
       439: 2
       441: 1
       442: 1
       443: 1
       444: 1
       449: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       541: 1
       544: 1
       557: 1
       558: 1
       565: 1
       567: 1
       573: 1
       576: 1
       591: 1
       595: 1
       607: 1
       615: 1
       616: 1
       621: 1
       631: 2
       643: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       803: 1
       807: 1
       815: 1
       816: 1
       827: 1
       831: 1
       839: 2
       847: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       988: 1
       990: 1
      1006: 1
      1028: 1
      1044: 1
      1054: 1
      1058: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1242: 1
      1260: 1
      1270: 1
      1289: 1
      1478: 1

1479:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: 2q+2
         8: 2q+2
         9: q^3+q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 2q+2
        14: 2q+2
        15: 2q+2
        16: 2
        17: 2
        18: q+1
        19: 2q+2
        20: 2q+2
        21: 2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2
        29: 2q+2
        30: 2q+2
        31: 2q+2
        32: 2q+2
        33: 2
        34: 2q+2
        35: 2q+2
        36: 2
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        59: 2
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: 1
        67: 1
        68: 2
        69: 1
        70: 2q+2
        71: 2
        72: 2
        73: 2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 2q+2
        81: 2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2
        86: 2q+2
        87: 2q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: 1
       106: 1
       107: 1
       108: 1
       110: 2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 2
       126: 1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: 2q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: 2q+2
       147: 2
       148: 2
       149: 2q+2
       150: 2q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       172: 1
       174: 1
       176: 1
       183: 1
       184: 1
       186: 2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2
       193: 1
       194: 1
       196: 2
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       243: 2
       244: 2
       245: 2
       246: 2q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: 1
       278: 1
       286: 1
       293: 1
       294: 1
       296: 2
       297: 1
       298: 1
       299: 1
       300: 1
       304: 2
       305: 1
       306: 1
       307: 1
       308: 1
       310: 2
       313: 1
       314: 1
       319: 1
       320: 1
       322: 2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       386: 1
       388: 1
       394: 1
       396: 1
       403: 1
       404: 1
       406: 1
       407: 1
       422: 1
       432: 1
       437: 1
       438: 1
       440: 2
       441: 1
       442: 1
       443: 1
       444: 1
       450: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 2
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       542: 1
       543: 1
       559: 1
       560: 1
       566: 1
       568: 1
       574: 1
       575: 1
       592: 1
       596: 1
       608: 1
       615: 1
       616: 1
       622: 1
       632: 2
       644: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: 1
       656: 1
       665: 1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       804: 1
       808: 1
       815: 1
       816: 1
       828: 1
       832: 1
       840: 2
       848: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       989: 1
       991: 1
      1007: 1
      1029: 1
      1045: 1
      1055: 1
      1059: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1243: 1
      1261: 1
      1271: 1
      1289: 1
      1479: 1

1480:    0: q^3+2
         1: q^3+2
         2: q+1
         3: q^3+2
         4: q^3+2
         5: q^3+2
         6: q^3+2
         7: q+1
         8: q+1
         9: q^5+q+1
        10: q^3+2
        11: q^3+2
        12: q^3+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: q^3+2
        20: q^3+2
        21: q+1
        22: q^3+2
        23: q^3+2
        24: q+1
        25: q^3+2
        26: q^3+2
        27: q+1
        28: 2
        29: q^3+2
        30: 1
        31: q^3+2
        32: 1
        33: 2
        34: q^3+2
        35: 1
        36: 2
        37: q^3+2
        39: q^3+2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        52: q^3+2
        53: q^3+2
        54: q+1
        55: q^3+2
        56: q^3+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: q^3+2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 2
        72: 2
        73: 2
        74: q^3+2
        76: q^3+2
        78: q+1
        80: 1
        81: 1
        82: q^3+2
        83: 1
        84: 1
        85: 1
        86: q^3+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q^3+2
       101: q^3+2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q^3+2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q^3+2
       150: 1
       151: q^3+2
       153: q^3+2
       155: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: q^3+2
       211: 1
       213: 1
       215: 1
       217: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       475: 1
       477: 2
       479: 2
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       645: 1
       651: 1
       653: 1
       655: 1
       666: 1
       668: 1
       670: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       693: 1
       697: 1
       769: 1
       783: 1
       791: 1
       799: 1
       809: 1
       811: 1
       813: 1
       823: 1
       833: 1
       835: 1
       837: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       872: 1
       876: 1
       879: 1
       880: 1
       982: 1
      1008: 1
      1010: 1
      1024: 1
      1042: 1
      1050: 1
      1060: 1
      1062: 1
      1064: 1
      1085: 1
      1222: 1
      1272: 1
      1276: 1
      1278: 1
      1480: 1

1481:    0: q^3+2
         1: q^3+2
         2: q+1
         3: q^3+2
         4: q^3+2
         5: q^3+2
         6: q^3+2
         7: q+1
         8: q+1
         9: q^5+q+1
        10: q^3+2
        11: q^3+2
        12: q^3+2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: q^3+2
        20: q^3+2
        21: q+1
        22: q^3+2
        23: q^3+2
        24: q+1
        25: q^3+2
        26: q^3+2
        27: q+1
        28: 2
        29: q^3+2
        30: 1
        31: q^3+2
        32: 1
        33: 2
        34: q^3+2
        35: 1
        36: 2
        38: q^3+2
        40: q^3+2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        52: q^3+2
        53: q^3+2
        54: q+1
        55: q^3+2
        56: q^3+2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: q^3+2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 2
        72: 2
        73: 2
        75: q^3+2
        77: q^3+2
        79: q+1
        80: 1
        81: 1
        82: q^3+2
        83: 1
        84: 1
        85: 1
        86: q^3+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q^3+2
       101: q^3+2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q^3+2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: q^3+2
       150: 1
       152: q^3+2
       154: q^3+2
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       210: q^3+2
       212: 1
       214: 1
       216: 1
       218: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       476: 1
       478: 2
       480: 2
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       646: 1
       652: 1
       654: 1
       656: 1
       667: 1
       669: 1
       671: 1
       673: 1
       677: 1
       678: 1
       679: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       699: 1
       700: 1
       773: 1
       784: 1
       792: 1
       800: 1
       810: 1
       812: 1
       814: 1
       824: 1
       834: 1
       836: 1
       838: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       872: 1
       876: 1
       879: 1
       880: 1
       986: 1
      1009: 1
      1011: 1
      1025: 1
      1043: 1
      1051: 1
      1061: 1
      1063: 1
      1065: 1
      1085: 1
      1223: 1
      1273: 1
      1277: 1
      1279: 1
      1481: 1

1482:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2q+2
        23: 2q+2
        24: q^2+q+1
        25: 2q+2
        26: 2q+2
        27: q^2+q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2q+2
        32: 1
        33: 2q+2
        34: 2q+2
        35: 1
        36: 2q+2
        37: 2
        38: 2q
        39: 2
        40: 2q
        41: q+1
        42: q^2
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q+2
        53: 2q+2
        54: q^2+q+1
        55: 2q+2
        56: 2q+2
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2
        63: 2q
        64: 1
        66: 2
        67: 2q
        69: 1
        70: 1
        71: 2q+2
        72: 2q+2
        73: 2q+2
        74: 2
        75: 2q
        76: 2
        77: 2q
        78: q+1
        79: q^2
        80: 1
        81: 1
        82: 2q+2
        83: 1
        84: 1
        85: 1
        86: 2q+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2q+2
       101: 2q+2
       102: q^2+q+1
       103: 1
       104: q
       105: q
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       112: 2q
       113: 2
       114: 2q
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       128: 2q
       129: 2
       130: 2q
       131: q+1
       132: q^2
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2q+2
       141: 1
       142: 2q+2
       143: 1
       144: 1
       145: 2q+2
       146: 1
       147: 2q+2
       148: 2q+2
       149: 2q+2
       150: 1
       151: 2
       152: 2q
       153: 2
       154: 2q
       155: q+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+2
       167: 2q+2
       168: q^2+q+1
       169: 1
       170: q
       171: q
       172: 1
       177: 1
       179: 2
       180: 2q
       181: 2
       182: 2q
       187: 1
       189: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       198: 2q
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       206: 2q
       207: 1
       209: 2
       210: 2q
       211: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       238: 2q
       239: 2
       240: 2q
       241: q+1
       242: q^2
       243: 2q+2
       244: 2q+2
       245: 2q+2
       246: 1
       247: 2q+2
       248: 2q+2
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q
       261: q
       262: 1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       287: 1
       291: 1
       297: 1
       301: 2
       302: 2q
       305: 1
       311: 2
       312: 2q
       313: 1
       315: 1
       317: 2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       324: 2q
       325: 1
       334: 1
       335: 1
       336: 1
       337: 2q+2
       338: 2
       339: 2q
       340: 2
       341: 2q
       342: q+1
       343: q^2
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2q+2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2q+2
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       390: q
       391: 1
       392: q
       397: 1
       398: q
       399: 1
       400: q
       405: 1
       406: 1
       407: q
       408: q
       423: 1
       425: 1
       427: 2
       428: 2q
       433: 1
       441: 1
       443: q+1
       444: q+1
       445: 2
       446: 2q
       451: 1
       459: 1
       461: q+1
       462: q+1
       463: 2
       464: 2q
       469: 1
       475: 1
       477: 2
       478: 2q
       479: 2
       480: 2q
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       545: 1
       546: q
       547: 1
       548: q
       561: 1
       562: q
       563: 1
       564: q
       569: 1
       570: 1
       571: q
       572: q
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       581: 2q
       599: 1
       609: 1
       613: 1
       625: 1
       629: 1
       645: 1
       653: 1
       655: 1
       664: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       697: 1
       699: q
       700: q
       791: 1
       811: 1
       835: 1
       843: 1
       851: 1
       855: 1
       857: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
      1008: 1
      1012: 1
      1046: 1
      1062: 1
      1064: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1224: 1
      1276: 1
      1280: 1
      1288: 1
      1482: 1

1483:    0: 2q+2
         1: 2q+2
         2: q^2+q+1
         3: 2q+2
         4: 2q+2
         5: 2q+2
         6: 2q+2
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: 1
        14: 1
        15: 1
        16: 2q+2
        17: 2q+2
        18: q^2+q+1
        19: 2q+2
        20: 2q+2
        21: q^2+q+1
        22: 2q+2
        23: 2q+2
        24: q^2+q+1
        25: 2q+2
        26: 2q+2
        27: q^2+q+1
        28: 2q+2
        29: 2q+2
        30: 1
        31: 2q+2
        32: 1
        33: 2q+2
        34: 2q+2
        35: 1
        36: 2q+2
        37: 2q
        38: 2
        39: 2q
        40: 2
        41: q^2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2q+2
        50: 2q+2
        51: q^2+q+1
        52: 2q+2
        53: 2q+2
        54: q^2+q+1
        55: 2q+2
        56: 2q+2
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q
        63: 2
        65: 1
        66: 2q
        67: 2
        69: 1
        70: 1
        71: 2q+2
        72: 2q+2
        73: 2q+2
        74: 2q
        75: 2
        76: 2q
        77: 2
        78: q^2
        79: q+1
        80: 1
        81: 1
        82: 2q+2
        83: 1
        84: 1
        85: 1
        86: 2q+2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2q+2
        95: 2q+2
        96: q^2+q+1
        97: 2q+2
        98: 2q+2
        99: q^2+q+1
       100: 2q+2
       101: 2q+2
       102: q^2+q+1
       103: q
       104: 1
       105: 1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q
       112: 2
       113: 2q
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       127: 2q
       128: 2
       129: 2q
       130: 2
       131: q^2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2q+2
       140: 2q+2
       141: 1
       142: 2q+2
       143: 1
       144: 1
       145: 2q+2
       146: 1
       147: 2q+2
       148: 2q+2
       149: 2q+2
       150: 1
       151: 2q
       152: 2
       153: 2q
       154: 2
       155: q^2
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2q+2
       167: 2q+2
       168: q^2+q+1
       169: q
       170: 1
       171: 1
       172: q
       178: 1
       179: 2q
       180: 2
       181: 2q
       182: 2
       188: 1
       190: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q
       198: 2
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q
       206: 2
       208: 1
       209: 2q
       210: 2
       212: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2q
       238: 2
       239: 2q
       240: 2
       241: q^2
       242: q+1
       243: 2q+2
       244: 2q+2
       245: 2q+2
       246: 1
       247: 2q+2
       248: 2q+2
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q
       260: 1
       261: 1
       262: q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       288: 1
       292: 1
       298: 1
       301: 2q
       302: 2
       306: 1
       311: 2q
       312: 2
       314: 1
       316: 1
       317: 2q
       318: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: 2
       326: 1
       334: 1
       335: 1
       336: 1
       337: 2q+2
       338: 2q
       339: 2
       340: 2q
       341: 2
       342: q^2
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2q+2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2q+2
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: q
       390: 1
       391: q
       392: 1
       397: q
       398: 1
       399: q
       400: 1
       405: q
       406: q
       407: 1
       408: 1
       424: 1
       426: 1
       427: 2q
       428: 2
       434: 1
       442: 1
       443: q+1
       444: q+1
       445: 2q
       446: 2
       452: 1
       460: 1
       461: q+1
       462: q+1
       463: 2q
       464: 2
       470: 1
       476: 1
       477: 2q
       478: 2
       479: 2q
       480: 2
       483: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       545: q
       546: 1
       547: q
       548: 1
       561: q
       562: 1
       563: q
       564: 1
       569: q
       570: q
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       577: 2q
       581: 2
       600: 1
       610: 1
       614: 1
       626: 1
       630: 1
       646: 1
       654: 1
       656: 1
       664: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q
       697: q
       699: 1
       700: 1
       792: 1
       812: 1
       836: 1
       844: 1
       852: 1
       856: 1
       858: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
      1009: 1
      1013: 1
      1047: 1
      1063: 1
      1065: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1225: 1
      1277: 1
      1281: 1
      1288: 1
      1483: 1

1484:    0: 3q^4+14q^3+42q^2+30q+4
         1: 6q^4+21q^3+42q^2+30q+4
         2: 3q^4+12q^3+33q^2+24q+4
         3: 2q^4+18q^3+42q^2+30q+4
         4: 3q^4+14q^3+42q^2+30q+4
         5: 2q^4+18q^3+42q^2+30q+4
         6: 6q^4+21q^3+42q^2+30q+4
         7: 3q^4+12q^3+33q^2+24q+4
         8: 4q^4+18q^3+34q^2+24q+4
         9: 2q^5+7q^4+15q^3+23q^2+17q+4
        10: q^4+8q^3+32q^2+28q+4
        11: 8q^3+32q^2+28q+4
        12: q^4+8q^3+32q^2+28q+4
        13: q^4+4q^3+27q^2+24q+4
        14: q^4+4q^3+27q^2+24q+4
        15: 8q^3+28q^2+24q+4
        16: 8q^3+32q^2+30q+4
        17: q^4+11q^3+32q^2+30q+4
        18: 3q^4+9q^3+23q^2+17q+4
        19: 3q^4+14q^3+42q^2+30q+4
        20: 6q^4+21q^3+42q^2+30q+4
        21: 3q^4+12q^3+33q^2+24q+4
        22: 8q^3+32q^2+30q+4
        23: q^4+11q^3+32q^2+30q+4
        24: q^4+8q^3+27q^2+24q+4
        25: 8q^3+32q^2+30q+4
        26: q^4+11q^3+32q^2+30q+4
        27: q^4+8q^3+27q^2+24q+4
        28: 4q^3+22q^2+28q+4
        29: q^4+8q^3+32q^2+28q+4
        30: q^4+4q^3+27q^2+24q+4
        31: 4q^3+22q^2+28q+4
        32: 2q^3+21q^2+24q+4
        33: 5q^3+24q^2+30q+4
        34: 4q^3+22q^2+28q+4
        35: 2q^3+21q^2+24q+4
        36: 5q^3+24q^2+30q+4
        37: q^3+12q^2+15q+2
        38: q^3+12q^2+15q+2
        39: 2q^3+12q^2+15q+2
        40: 2q^3+12q^2+15q+2
        41: 2q^3+11q^2+12q+2
        42: 2q^3+11q^2+12q+2
        43: 2q^3+19q^2+22q+4
        44: 2q^3+19q^2+22q+4
        45: 2q^3+20q^2+22q+4
        46: 17q^2+24q+4
        47: 3q^3+18q^2+24q+4
        48: q^4+2q^3+17q^2+17q+4
        49: 8q^3+32q^2+30q+4
        50: q^4+11q^3+32q^2+30q+4
        51: 3q^4+9q^3+23q^2+17q+4
        52: 8q^3+32q^2+30q+4
        53: q^4+11q^3+32q^2+30q+4
        54: q^4+8q^3+27q^2+24q+4
        55: 8q^3+32q^2+30q+4
        56: q^4+11q^3+32q^2+30q+4
        57: q^4+8q^3+27q^2+24q+4
        58: q^3+7q^2+14q+2
        59: q^3+7q^2+14q+2
        60: q^3+7q^2+14q+2
        61: q^3+7q^2+14q+2
        62: 7q^2+14q+2
        63: 7q^2+14q+2
        64: 8q^2+12q+2
        65: 8q^2+12q+2
        66: q^3+9q^2+15q+2
        67: q^3+9q^2+15q+2
        68: 5q^2+16q+4
        69: 11q^2+17q+4
        70: 2q^3+19q^2+22q+4
        71: 4q^3+22q^2+28q+4
        72: 5q^3+24q^2+30q+4
        73: 5q^3+24q^2+30q+4
        74: q^3+12q^2+15q+2
        75: q^3+12q^2+15q+2
        76: 2q^3+12q^2+15q+2
        77: 2q^3+12q^2+15q+2
        78: 2q^3+11q^2+12q+2
        79: 2q^3+11q^2+12q+2
        80: q^3+13q^2+22q+4
        81: 13q^2+24q+4
        82: 4q^3+22q^2+28q+4
        83: 2q^3+21q^2+24q+4
        84: q^3+13q^2+22q+4
        85: 13q^2+24q+4
        86: 4q^3+22q^2+28q+4
        87: 2q^3+21q^2+24q+4
        88: 5q^2+22q+4
        89: 6q^2+22q+4
        90: q^3+10q^2+15q+4
        91: 17q^2+24q+4
        92: 3q^3+18q^2+24q+4
        93: q^4+2q^3+17q^2+17q+4
        94: 4q^3+20q^2+28q+4
        95: 4q^3+20q^2+28q+4
        96: q^4+5q^3+17q^2+17q+4
        97: 4q^3+20q^2+28q+4
        98: 4q^3+20q^2+28q+4
        99: q^4+5q^3+17q^2+17q+4
       100: 20q^2+28q+4
       101: 4q^3+24q^2+28q+4
       102: 2q^3+16q^2+22q+4
       103: 2q^2+7q+1
       104: 2q^2+7q+1
       105: 2q^2+7q+1
       106: 2q^2+7q+1
       107: q^3+7q^2+14q+2
       108: q^3+7q^2+14q+2
       109: q^3+7q^2+14q+2
       110: q^3+7q^2+14q+2
       111: q^3+9q^2+15q+2
       112: q^3+9q^2+15q+2
       113: 7q^2+14q+2
       114: 7q^2+14q+2
       115: 8q^2+12q+2
       116: 8q^2+12q+2
       117: q^2+8q+2
       118: q^2+8q+2
       119: q^2+8q+2
       120: q^2+8q+2
       121: 4q^2+11q+2
       122: 4q^2+11q+2
       123: 5q^2+12q+2
       124: 5q^2+12q+2
       125: q^2+16q+4
       126: 4q^2+15q+4
       127: 2q^2+9q+2
       128: 2q^2+9q+2
       129: 2q^2+9q+2
       130: 2q^2+9q+2
       131: 4q^2+6q+2
       132: 4q^2+6q+2
       133: 5q^2+16q+4
       134: 11q^2+17q+4
       135: 13q^2+24q+4
       136: 13q^2+24q+4
       137: 3q^2+22q+4
       138: 7q^2+17q+4
       139: 2q^3+12q^2+26q+4
       140: 8q^2+18q+4
       141: q^3+13q^2+22q+4
       142: 4q^3+20q^2+28q+4
       143: 3q^2+22q+4
       144: 7q^2+17q+4
       145: 2q^3+12q^2+26q+4
       146: q^3+13q^2+22q+4
       147: 4q^3+20q^2+28q+4
       148: 8q^2+18q+4
       149: 14q^2+26q+4
       150: 12q^2+22q+4
       151: 10q^2+14q+2
       152: 10q^2+14q+2
       153: 2q^3+12q^2+14q+2
       154: 2q^3+12q^2+14q+2
       155: q^3+8q^2+11q+2
       156: q^3+8q^2+11q+2
       157: 5q^2+22q+4
       158: 6q^2+22q+4
       159: q^3+10q^2+15q+4
       160: 8q^2+18q+4
       161: 8q^2+18q+4
       162: 9q^2+13q+4
       163: 8q^2+18q+4
       164: 8q^2+18q+4
       165: 9q^2+13q+4
       166: 6q^2+24q+4
       167: q^3+9q^2+24q+4
       168: q^3+8q^2+15q+4
       169: 2q^2+7q+1
       170: 2q^2+7q+1
       171: 2q^2+7q+1
       172: 2q^2+7q+1
       173: 4q+1
       174: 4q+1
       175: 4q+1
       176: 4q+1
       177: q^2+6q+2
       178: q^2+6q+2
       179: 8q+2
       180: 8q+2
       181: 2q^2+9q+2
       182: 2q^2+9q+2
       183: q^2+8q+2
       184: q^2+8q+2
       185: q^2+8q+2
       186: q^2+8q+2
       187: 5q^2+12q+2
       188: 5q^2+12q+2
       189: 4q^2+11q+2
       190: 4q^2+11q+2
       191: 8q+2
       192: 8q+2
       193: 2q^2+8q+2
       194: 2q^2+8q+2
       195: q^3+6q^2+13q+2
       196: q^3+6q^2+13q+2
       197: 4q^2+9q+2
       198: 4q^2+9q+2
       199: 8q+2
       200: 8q+2
       201: q^3+6q^2+13q+2
       202: q^3+6q^2+13q+2
       203: 2q^2+8q+2
       204: 2q^2+8q+2
       205: 4q^2+9q+2
       206: 4q^2+9q+2
       207: q^2+11q+2
       208: q^2+11q+2
       209: 7q^2+13q+2
       210: 7q^2+13q+2
       211: 6q^2+11q+2
       212: 6q^2+11q+2
       219: q^2+9q+4
       220: q^2+16q+4
       221: 4q^2+15q+4
       222: 3q^2+22q+4
       223: 7q^2+17q+4
       224: 3q^2+22q+4
       225: 7q^2+17q+4
       226: 2q^2+15q+4
       227: 2q^2+12q+4
       228: 5q^2+13q+4
       229: 2q^2+12q+4
       230: 8q^2+18q+4
       231: 2q^2+15q+4
       232: 2q^2+12q+4
       233: 5q^2+13q+4
       234: 8q^2+18q+4
       235: 2q^2+12q+4
       236: 2q^2+15q+4
       237: 8q+2
       238: 8q+2
       239: q^2+8q+2
       240: q^2+8q+2
       241: 2q^2+5q+2
       242: 2q^2+5q+2
       243: 4q^2+22q+4
       244: 3q^2+16q+4
       245: 3q^2+16q+4
       246: 8q^2+20q+4
       247: 6q^2+24q+4
       248: q^3+9q^2+24q+4
       249: q^3+8q^2+15q+4
       250: q^2+10q+4
       251: q^2+10q+4
       252: 3q^2+7q+4
       253: q^2+10q+4
       254: q^2+10q+4
       255: 3q^2+7q+4
       256: 13q+4
       257: 3q^2+14q+4
       258: 2q^2+10q+4
       259: 4q+1
       260: 4q+1
       261: 4q+1
       262: 4q+1
       263: 4q+1
       264: 4q+1
       265: 4q+1
       266: 4q+1
       267: q^2+4q+1
       268: q^2+4q+1
       269: q^2+4q+1
       270: q^2+4q+1
       271: q^2+4q+1
       272: q^2+4q+1
       273: q^2+4q+1
       274: q^2+4q+1
       275: 4q+1
       276: 4q+1
       277: 4q+1
       278: 4q+1
       283: 3q+2
       284: 3q+2
       285: 3q+2
       286: 3q+2
       287: 5q+2
       288: 5q+2
       291: q^2+6q+2
       292: q^2+6q+2
       293: 8q+2
       294: 8q+2
       295: 8q+2
       296: 8q+2
       297: q^2+11q+2
       298: q^2+11q+2
       299: 4q+2
       300: 4q+2
       301: 5q+2
       302: 5q+2
       303: q^2+6q+2
       304: q^2+6q+2
       305: q^2+6q+2
       306: q^2+6q+2
       307: q^2+6q+2
       308: q^2+6q+2
       309: 4q+2
       310: 4q+2
       311: 5q+2
       312: 5q+2
       313: q^2+6q+2
       314: q^2+6q+2
       315: 5q+2
       316: 5q+2
       317: 7q+2
       318: 7q+2
       319: q^2+7q+2
       320: q^2+7q+2
       321: q^2+7q+2
       322: q^2+7q+2
       323: 5q+2
       324: 5q+2
       325: 4q^2+10q+2
       326: 4q^2+10q+2
       333: q^2+9q+4
       334: 2q^2+15q+4
       335: 2q^2+15q+4
       336: 2q^2+15q+4
       337: 4q^2+22q+4
       338: 8q+2
       339: 8q+2
       340: q^2+8q+2
       341: q^2+8q+2
       342: 2q^2+5q+2
       343: 2q^2+5q+2
       344: 7q+4
       345: 6q+4
       346: q^2+7q+4
       347: 6q+4
       348: 7q+4
       349: q^2+10q+4
       350: 5q^2+13q+4
       351: 3q^2+16q+4
       352: 7q+4
       353: 6q+4
       354: q^2+7q+4
       355: q^2+10q+4
       356: 5q^2+13q+4
       357: 6q+4
       358: 7q+4
       359: 3q^2+16q+4
       366: q^2+13q+4
       367: 9q+4
       368: 10q+4
       369: 9q+4
       370: 9q+4
       371: 13q+4
       372: 3q^2+14q+4
       373: 2q^2+10q+4
       374: 3q+4
       375: 4q+4
       376: 3q+4
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       385: 4q+1
       386: 4q+1
       387: 4q+1
       388: 4q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: 2q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: 2q+1
       403: 2q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       419: 3q+2
       420: 3q+2
       421: 3q+2
       422: 3q+2
       423: 5q+2
       424: 5q+2
       425: 5q+2
       426: 5q+2
       427: 7q+2
       428: 7q+2
       429: q+2
       430: q+2
       431: 2q+2
       432: 2q+2
       433: 2q+2
       434: 2q+2
       437: 2q+2
       438: 2q+2
       439: 3q+2
       440: 3q+2
       441: 3q+2
       442: 3q+2
       443: q^2+7q+2
       444: q^2+7q+2
       445: 5q+2
       446: 5q+2
       447: 2q+2
       448: 2q+2
       449: q+2
       450: q+2
       451: 2q+2
       452: 2q+2
       453: 3q+2
       454: 3q+2
       457: 2q+2
       458: 2q+2
       459: 3q+2
       460: 3q+2
       461: q^2+7q+2
       462: q^2+7q+2
       463: 5q+2
       464: 5q+2
       469: 4q+2
       470: 4q+2
       471: 3q+2
       472: 3q+2
       473: 3q+2
       474: 3q+2
       475: 3q+2
       476: 3q+2
       477: 4q+2
       478: 4q+2
       479: 5q+2
       480: 5q+2
       481: 7q+4
       482: 7q+4
       483: q^2+13q+4
       484: 9q+4
       491: 10q+4
       492: 3q+4
       493: 3q+4
       494: q^2+7q+4
       495: 7q+4
       496: 9q+4
       497: 3q+4
       498: q^2+7q+4
       499: 3q+4
       500: 7q+4
       501: 9q+4
       508: 6q+4
       509: q+4
       510: 3q+4
       511: q+4
       512: 6q+4
       513: q+4
       514: 6q+4
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: 3q+4
       519: 4q+4
       520: 3q+4
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 1
       550: 1
       551: 1
       552: 1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 3q+2
       579: q
       581: 3q+2
       582: q
       589: 2q+2
       590: 2q+2
       591: q+2
       592: q+2
       593: q+2
       594: q+2
       595: 2q+2
       596: 2q+2
       599: 4q+2
       600: 4q+2
       603: 2
       604: 2
       607: q+2
       608: q+2
       609: q+2
       610: q+2
       613: 2q+2
       614: 2q+2
       615: 3q+2
       616: 3q+2
       619: q+2
       620: q+2
       621: 2
       622: 2
       625: q+2
       626: q+2
       629: 2q+2
       630: 2q+2
       631: 3q+2
       632: 3q+2
       641: q+2
       642: q+2
       643: q+2
       644: q+2
       645: q+2
       646: q+2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 3q+2
       656: 3q+2
       657: q+4
       664: 3q+4
       665: 6q+4
       672: q+4
       673: 3q+4
       674: q+4
       675: q+2
       676: 3q+4
       677: 3q+4
       678: q+4
       679: 6q+4
       680: q+4
       681: 3q+4
       682: q+2
       683: 3q+4
       684: q+4
       685: 6q+4
       686: q+4
       687: q+4
       688: q+4
       689: q+2
       693: q+1
       697: q+1
       699: q+1
       700: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       741: 1
       742: 1
       743: 1
       744: 1
       753: 1
       754: 1
       755: 1
       756: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: q+1
       766: q+1
       767: q+1
       768: q+1
       785: q+2
       786: q+2
       787: q+2
       788: q+2
       791: q+2
       792: q+2
       793: 2
       794: 2
       801: 1
       802: 1
       805: 2
       806: 2
       807: q+2
       808: q+2
       811: q+2
       812: q+2
       815: 2
       816: 2
       817: 2
       818: 2
       825: q+2
       826: q+2
       827: 2
       828: 2
       831: 1
       832: 1
       835: q+2
       836: q+2
       839: 2
       840: 2
       843: 2
       844: 2
       845: 2
       846: 2
       847: 2
       848: 2
       851: 2
       852: 2
       855: 1
       856: 1
       857: 2
       858: 2
       866: q+4
       868: q+4
       870: q+4
       871: q+2
       872: q+4
       874: q+4
       875: q+2
       876: q+4
       877: 2
       878: 2
       879: 2
       880: q+2
       908: 1
       909: 1
       910: 1
       911: 1
       928: 1
       929: 1
       930: 1
       931: 1
       948: 1
       949: 1
       950: 1
       951: 1
       964: 1
       965: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       977: 1
       988: 1
       989: 1
       990: 1
       991: 1
       998: 2
       999: 2
      1000: 2
      1001: 2
      1004: 2
      1005: 2
      1006: 2
      1007: 2
      1008: 2
      1009: 2
      1012: 2
      1013: 2
      1026: 1
      1027: 1
      1044: 1
      1045: 1
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 2
      1078: 2
      1080: 2
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1484: 1

1485:    0: q^3+6q^2+8q+4
         1: q^3+6q^2+8q+4
         2: q^3+6q^2+8q+4
         3: q^3+6q^2+8q+4
         4: q^4+3q^3+5q^2+6q+4
         5: q^3+6q^2+8q+4
         6: 3q^3+6q^2+6q+4
         7: q^4+3q^3+5q^2+6q+4
         8: q^3+6q^2+8q+4
         9: q^4+3q^3+5q^2+6q+4
        10: 2q^2+8q+4
        11: 2q^2+8q+4
        12: q^3+3q^2+6q+4
        13: q^3+6q^2+8q+4
        14: q^4+3q^3+5q^2+6q+4
        15: q^3+6q^2+8q+4
        16: q^3+6q^2+8q+4
        17: q^3+6q^2+8q+4
        18: q^4+3q^3+5q^2+6q+4
        19: q^3+3q^2+6q+4
        20: 4q^2+6q+4
        21: q^3+3q^2+6q+4
        22: q^3+6q^2+8q+4
        23: q^3+6q^2+8q+4
        24: q^3+6q^2+8q+4
        25: 2q^2+4q+4
        26: 2q^2+4q+4
        27: 2q^2+4q+4
        28: 2q^2+8q+4
        29: q^2+6q+4
        30: q^3+3q^2+6q+4
        31: 2q^2+8q+4
        32: q^3+6q^2+8q+4
        33: q^3+6q^2+8q+4
        34: 4q+4
        35: 2q^2+4q+4
        36: 2q^2+4q+4
        37: q^2+2q+2
        38: q^2+2q+2
        39: q^2+2q+2
        40: q^2+2q+2
        41: q^2+2q+2
        42: q^2+2q+2
        43: 2q^2+8q+4
        44: q^3+3q^2+6q+4
        45: 2q^2+8q+4
        46: q^3+6q^2+8q+4
        47: q^3+6q^2+8q+4
        48: q^4+3q^3+5q^2+6q+4
        49: q^3+3q^2+6q+4
        50: 4q^2+6q+4
        51: q^3+3q^2+6q+4
        52: q^3+3q^2+6q+4
        53: 4q^2+6q+4
        54: q^3+3q^2+6q+4
        55: q^2+2q+4
        56: q^2+2q+4
        57: q^2+2q+4
        58: q^2+4q+2
        59: q^2+4q+2
        60: 2q+2
        61: 2q+2
        62: 2q+2
        63: 2q+2
        64: q^2+2q+2
        65: q^2+2q+2
        66: q^2+2q+2
        67: q^2+2q+2
        68: 2q^2+8q+4
        69: q^3+3q^2+6q+4
        70: q^2+6q+4
        71: q^2+6q+4
        72: q^2+4
        73: q^2+4q+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 2q^2+8q+4
        81: q^3+6q^2+8q+4
        82: q^2+6q+4
        83: q^3+3q^2+6q+4
        84: 4q+4
        85: 2q^2+4q+4
        86: 2q+4
        87: q^2+2q+4
        88: 2q^2+8q+4
        89: 2q^2+8q+4
        90: q^3+3q^2+6q+4
        91: q^3+3q^2+6q+4
        92: 4q^2+6q+4
        93: q^3+3q^2+6q+4
        94: q^3+3q^2+6q+4
        95: 4q^2+6q+4
        96: q^3+3q^2+6q+4
        97: q^2+2q+4
        98: q^2+2q+4
        99: q^2+2q+4
       100: q^2+2q+4
       101: q^2+2q+4
       102: q^2+2q+4
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 2
       108: 2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: q^2+4q+2
       118: q^2+4q+2
       119: 2q+2
       120: 2q+2
       121: 2q+2
       122: 2q+2
       123: q^2+2q+2
       124: q^2+2q+2
       125: 2q^2+8q+4
       126: q^2+6q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q^2+6q+4
       134: q^3+3q^2+6q+4
       135: q^2+4
       136: q^2+4q+4
       137: 2q^2+8q+4
       138: q^3+3q^2+6q+4
       139: q^2+6q+4
       140: q^2+4
       141: q^2+6q+4
       142: q^2+4q+4
       143: 4q+4
       144: q^2+2q+4
       145: 2q+4
       146: 2q+4
       147: q^2+4
       149: 2q+4
       150: q^2+2q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: q^2+4q+4
       158: q^2+4q+4
       159: q^2+4q+4
       160: q^3+3q^2+6q+4
       161: 4q^2+6q+4
       162: q^3+3q^2+6q+4
       163: q^2+2q+4
       164: q^2+2q+4
       165: q^2+2q+4
       166: q^2+2q+4
       167: q^2+2q+4
       168: q^2+2q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2q+2
       186: 2q+2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: q^2+4q+2
       192: q^2+4q+2
       193: 2
       194: 2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       199: 2q+2
       200: 2q+2
       201: 2
       202: 2
       207: 2q+2
       208: 2q+2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+2
       218: q+2
       219: q^2+6q+4
       220: q^2+4q+4
       221: q^2+4q+4
       222: 4
       223: q^2+4
       224: 2q+4
       225: q^2+4q+4
       226: q^2+6q+4
       227: q^2+6q+4
       228: q^3+3q^2+6q+4
       229: q^2+4
       230: q^2+4q+4
       231: 2q+4
       232: 2q+4
       233: q^2+2q+4
       234: q^2+4
       236: q^2+2q+4
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+2
       242: q+2
       243: 2q+4
       244: q^2+4
       246: 2q+4
       247: 4
       248: 4
       249: 2q+2
       250: q^2+4q+4
       251: q^2+4q+4
       252: q^2+4q+4
       253: q+2
       254: q+2
       255: q+2
       256: q^2+2q+4
       257: q^2+2q+4
       258: q^2+2q+4
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: q+2
       282: q+2
       283: 2
       284: 2
       285: 2q+2
       286: 2q+2
       287: q+2
       288: q+2
       289: 2
       290: 2
       291: 2
       292: 2
       293: 2
       294: 2
       295: q+2
       296: q+2
       297: 2
       298: 2
       299: 2
       300: 2
       301: 2
       302: 2
       303: 2q+2
       304: 2q+2
       305: 2
       306: 2
       307: 2
       308: 2
       315: q+2
       316: q+2
       317: q+2
       318: q+2
       319: 2
       320: 2
       325: q+2
       326: q+2
       333: q^2+4q+4
       334: 4
       335: 2q+4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q^2+6q+4
       345: q^2+4q+4
       346: q^2+4q+4
       347: 4
       348: q^2+4
       349: 2q+4
       350: q^2+4q+4
       351: 4
       352: 2q+4
       353: q+2
       354: q+2
       355: 2
       356: q^2+4
       360: q+2
       361: q+2
       362: q+2
       363: q+2
       364: q+2
       365: q+2
       366: 2q+4
       367: 2q+4
       368: q^2+2q+4
       369: q^2+4
       371: 4
       372: 4
       373: 2q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       413: q+2
       414: q+2
       417: 2
       418: 2
       419: 2
       420: 2
       421: q+2
       422: q+2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       429: 2
       430: 2
       431: 2q+2
       432: 2q+2
       433: 2
       434: 2
       435: 2
       436: 2
       437: 2
       438: 2
       439: q+2
       440: q+2
       441: 2
       442: 2
       443: 2
       444: 2
       445: 2
       446: 2
       447: 2
       448: 2
       453: 1
       454: 1
       465: q+2
       466: q+2
       467: q+2
       468: q+2
       469: q+2
       470: q+2
       471: 2
       472: 2
       481: 4
       482: 2q+4
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: q^2+4q+4
       493: 4
       494: 2q+4
       495: 2
       496: 4
       497: q+2
       498: 2
       508: 2q+4
       509: q+2
       510: q+2
       511: 2
       512: q^2+4
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       585: 2
       586: 2
       589: 2
       590: 2
       595: q+2
       596: q+2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       603: 2
       604: 2
       605: 2
       606: 2
       607: q+2
       608: q+2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 2
       616: 2
       617: 2
       618: 2
       619: 1
       620: 1
       639: q+2
       640: q+2
       641: 2
       642: 2
       647: 1
       648: 1
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 4
       675: 4
       676: 2q+4
       677: 2
       678: 2
       679: 2
       681: 2
       686: q+2
       687: 2
       690: 2
       691: 2
       692: q+1
       709: 1
       710: 1
       711: 1
       712: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       733: 1
       734: 1
       735: 1
       736: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       793: 2
       794: 2
       795: 2
       796: 2
       797: 2
       798: 2
       801: 2
       802: 2
       807: q+2
       808: q+2
       809: 1
       810: 1
       811: 1
       812: 1
       815: 1
       816: 1
       825: 1
       826: 1
       845: 1
       846: 1
       865: 2
       866: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       877: 2
       881: 2
       882: 2
       883: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       994: 1
       995: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1052: 1
      1053: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 2
      1077: 1
      1078: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1282: 1
      1283: 1
      1284: 1
      1485: 1

1486:    0: q^3+6q^2+8q+4
         1: q^3+6q^2+8q+4
         2: q^3+6q^2+8q+4
         3: q^3+6q^2+8q+4
         4: q^4+3q^3+5q^2+6q+4
         5: q^3+6q^2+8q+4
         6: 3q^3+6q^2+6q+4
         7: q^4+3q^3+5q^2+6q+4
         8: q^3+6q^2+8q+4
         9: q^4+3q^3+5q^2+6q+4
        10: 2q^2+8q+4
        11: 2q^2+8q+4
        12: q^3+3q^2+6q+4
        13: q^3+6q^2+8q+4
        14: q^4+3q^3+5q^2+6q+4
        15: q^3+6q^2+8q+4
        16: q^3+6q^2+8q+4
        17: q^3+6q^2+8q+4
        18: q^4+3q^3+5q^2+6q+4
        19: q^3+3q^2+6q+4
        20: 4q^2+6q+4
        21: q^3+3q^2+6q+4
        22: 2q^2+4q+4
        23: 2q^2+4q+4
        24: 2q^2+4q+4
        25: q^3+6q^2+8q+4
        26: q^3+6q^2+8q+4
        27: q^3+6q^2+8q+4
        28: 2q^2+8q+4
        29: q^2+6q+4
        30: q^3+3q^2+6q+4
        31: 4q+4
        32: 2q^2+4q+4
        33: 2q^2+4q+4
        34: 2q^2+8q+4
        35: q^3+6q^2+8q+4
        36: q^3+6q^2+8q+4
        37: q^2+2q+2
        38: q^2+2q+2
        39: q^2+2q+2
        40: q^2+2q+2
        41: q^2+2q+2
        42: q^2+2q+2
        43: 2q^2+8q+4
        44: q^3+3q^2+6q+4
        45: 2q^2+8q+4
        46: q^3+6q^2+8q+4
        47: q^3+6q^2+8q+4
        48: q^4+3q^3+5q^2+6q+4
        49: q^3+3q^2+6q+4
        50: 4q^2+6q+4
        51: q^3+3q^2+6q+4
        52: q^2+2q+4
        53: q^2+2q+4
        54: q^2+2q+4
        55: q^3+3q^2+6q+4
        56: 4q^2+6q+4
        57: q^3+3q^2+6q+4
        58: 2q+2
        59: 2q+2
        60: q^2+4q+2
        61: q^2+4q+2
        62: 2q+2
        63: 2q+2
        64: q^2+2q+2
        65: q^2+2q+2
        66: q^2+2q+2
        67: q^2+2q+2
        68: 2q^2+8q+4
        69: q^3+3q^2+6q+4
        70: q^2+6q+4
        71: q^2+6q+4
        72: q^2+4q+4
        73: q^2+4
        74: q+2
        75: q+2
        76: q+2
        77: q+2
        78: q+2
        79: q+2
        80: 4q+4
        81: 2q^2+4q+4
        82: 2q+4
        83: q^2+2q+4
        84: 2q^2+8q+4
        85: q^3+6q^2+8q+4
        86: q^2+6q+4
        87: q^3+3q^2+6q+4
        88: 2q^2+8q+4
        89: 2q^2+8q+4
        90: q^3+3q^2+6q+4
        91: q^3+3q^2+6q+4
        92: 4q^2+6q+4
        93: q^3+3q^2+6q+4
        94: q^2+2q+4
        95: q^2+2q+4
        96: q^2+2q+4
        97: q^3+3q^2+6q+4
        98: 4q^2+6q+4
        99: q^3+3q^2+6q+4
       100: q^2+2q+4
       101: q^2+2q+4
       102: q^2+2q+4
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 2q+2
       108: 2q+2
       109: 2
       110: 2
       111: 2
       112: 2
       113: q+2
       114: q+2
       115: q+2
       116: q+2
       117: 2q+2
       118: 2q+2
       119: q^2+4q+2
       120: q^2+4q+2
       121: 2q+2
       122: 2q+2
       123: q^2+2q+2
       124: q^2+2q+2
       125: 2q^2+8q+4
       126: q^2+6q+4
       127: q+2
       128: q+2
       129: q+2
       130: q+2
       131: q+2
       132: q+2
       133: q^2+6q+4
       134: q^3+3q^2+6q+4
       135: q^2+4q+4
       136: q^2+4
       137: 4q+4
       138: q^2+2q+4
       139: 2q+4
       141: 2q+4
       142: q^2+4
       143: 2q^2+8q+4
       144: q^3+3q^2+6q+4
       145: q^2+6q+4
       146: q^2+6q+4
       147: q^2+4q+4
       148: q^2+4
       149: 2q+4
       150: q^2+2q+4
       151: q+2
       152: q+2
       153: q+2
       154: q+2
       155: q+2
       156: q+2
       157: q^2+4q+4
       158: q^2+4q+4
       159: q^2+4q+4
       160: q^2+2q+4
       161: q^2+2q+4
       162: q^2+2q+4
       163: q^3+3q^2+6q+4
       164: 4q^2+6q+4
       165: q^3+3q^2+6q+4
       166: q^2+2q+4
       167: q^2+2q+4
       168: q^2+2q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+2
       178: q+2
       179: q+2
       180: q+2
       181: 2
       182: 2
       183: 2q+2
       184: 2q+2
       185: 2
       186: 2
       187: 2
       188: 2
       189: q+2
       190: q+2
       191: 2q+2
       192: 2q+2
       195: 2
       196: 2
       199: q^2+4q+2
       200: q^2+4q+2
       201: 2q+2
       202: 2q+2
       203: 2
       204: 2
       205: 2
       206: 2
       207: 2q+2
       208: 2q+2
       209: q+2
       210: q+2
       211: q+2
       212: q+2
       213: q+2
       214: q+2
       215: q+2
       216: q+2
       217: q+2
       218: q+2
       219: q^2+6q+4
       220: q^2+4q+4
       221: q^2+4q+4
       222: 2q+4
       223: q^2+4q+4
       224: 4
       225: q^2+4
       226: 2q+4
       227: 2q+4
       228: q^2+2q+4
       230: q^2+4
       231: q^2+6q+4
       232: q^2+6q+4
       233: q^3+3q^2+6q+4
       234: q^2+4q+4
       235: q^2+4
       236: q^2+2q+4
       237: q+2
       238: q+2
       239: q+2
       240: q+2
       241: q+2
       242: q+2
       243: 2q+4
       245: q^2+4
       246: 2q+4
       247: 4
       248: 4
       249: 2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q^2+4q+4
       254: q^2+4q+4
       255: q^2+4q+4
       256: q^2+2q+4
       257: q^2+2q+4
       258: q^2+2q+4
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+2
       280: q+2
       281: q+2
       282: q+2
       283: 2q+2
       284: 2q+2
       285: 2
       286: 2
       287: q+2
       288: q+2
       289: 2
       290: 2
       291: 2
       292: 2
       293: q+2
       294: q+2
       295: 2
       296: 2
       297: 2
       298: 2
       303: 2
       304: 2
       307: 2q+2
       308: 2q+2
       309: 2
       310: 2
       311: 2
       312: 2
       313: 2
       314: 2
       315: q+2
       316: q+2
       317: q+2
       318: q+2
       321: 2
       322: 2
       325: q+2
       326: q+2
       333: q^2+4q+4
       334: 2q+4
       335: 4
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 2q+4
       345: q+2
       346: q+2
       349: 2
       350: q^2+4
       352: q^2+6q+4
       353: q^2+4q+4
       354: q^2+4q+4
       355: 2q+4
       356: q^2+4q+4
       357: 4
       358: q^2+4
       359: 4
       360: q+2
       361: q+2
       362: q+2
       363: q+2
       364: q+2
       365: q+2
       366: 2q+4
       367: 2q+4
       368: q^2+2q+4
       370: q^2+4
       371: 4
       372: 4
       373: 2q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       413: q+2
       414: q+2
       417: 2
       418: 2
       419: q+2
       420: q+2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 2
       428: 2
       431: 2
       432: 2
       439: 1
       440: 1
       447: 2q+2
       448: 2q+2
       449: 2
       450: 2
       451: 2
       452: 2
       453: q+2
       454: q+2
       455: 2
       456: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 2
       462: 2
       463: 2
       464: 2
       465: q+2
       466: q+2
       467: q+2
       468: q+2
       469: q+2
       470: q+2
       473: 2
       474: 2
       481: 2q+4
       482: 4
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: q+2
       494: 2
       497: q^2+4q+4
       498: 2q+4
       499: 4
       500: 2
       501: 4
       508: 2q+4
       509: q+2
       510: q+2
       513: 2
       514: q^2+4
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       585: 2
       586: 2
       589: q+2
       590: q+2
       595: 2
       596: 2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       607: 1
       608: 1
       619: q+2
       620: q+2
       621: 2
       622: 2
       623: 2
       624: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: q+2
       640: q+2
       643: 2
       644: 2
       649: 1
       650: 1
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       676: 2
       680: 4
       681: 2q+4
       682: 4
       683: 2
       684: 2
       685: 2
       686: q+2
       688: 2
       690: 2
       691: 2
       692: q+1
       709: 1
       710: 1
       711: 1
       712: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       749: 1
       750: 1
       751: 1
       752: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       807: 1
       808: 1
       817: 2
       818: 2
       819: 2
       820: 2
       821: 2
       822: 2
       825: q+2
       826: q+2
       831: 2
       832: 2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 1
       840: 1
       847: 1
       848: 1
       865: 2
       866: 2
       867: 1
       868: 1
       873: 2
       874: 2
       875: 2
       876: 1
       878: 2
       881: 2
       882: 2
       883: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       994: 1
       995: 1
      1032: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1058: 1
      1059: 1
      1072: 2
      1073: 1
      1074: 1
      1079: 2
      1080: 2
      1081: 1
      1082: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1282: 1
      1285: 1
      1286: 1
      1486: 1

1487:    0: 16q+4
         1: 16q+4
         2: 6q^2+10q+4
         3: 16q+4
         4: 6q^2+10q+4
         5: 16q+4
         6: 6q^2+10q+4
         7: q^5+2q^3+4q^2+7q+4
         8: 6q^2+10q+4
         9: q^5+2q^3+4q^2+7q+4
        10: 16q+4
        11: 16q+4
        12: 6q^2+10q+4
        13: 10q+4
        14: 2q^2+7q+4
        15: 10q+4
        16: 16q+4
        17: 16q+4
        18: q^5+2q^3+4q^2+7q+4
        19: 10q+4
        20: 10q+4
        21: 2q^2+7q+4
        22: 16q+4
        23: 16q+4
        24: 6q^2+10q+4
        25: 16q+4
        26: 16q+4
        27: 6q^2+10q+4
        28: 16q+4
        29: 10q+4
        30: 7q+4
        31: 16q+4
        32: 10q+4
        33: 16q+4
        34: 16q+4
        35: 10q+4
        36: 16q+4
        37: 8q+2
        38: 8q+2
        39: 8q+2
        40: 8q+2
        41: 3q^2+5q+2
        42: 3q^2+5q+2
        43: 10q+4
        44: 2q^2+7q+4
        45: 10q+4
        46: 10q+4
        47: 10q+4
        48: 2q^2+7q+4
        49: 10q+4
        50: 10q+4
        51: 2q^2+7q+4
        52: 10q+4
        53: 10q+4
        54: 2q^2+7q+4
        55: 10q+4
        56: 10q+4
        57: 2q^2+7q+4
        58: 8q+2
        59: 8q+2
        60: 8q+2
        61: 8q+2
        62: 8q+2
        63: 8q+2
        64: 5q+2
        65: 5q+2
        66: 8q+2
        67: 8q+2
        68: 4q+4
        69: 7q+4
        70: 7q+4
        71: 10q+4
        72: 4q+4
        73: 4q+4
        74: 3q+2
        75: 3q+2
        76: 3q+2
        77: 3q+2
        78: 3q+2
        79: 3q+2
        80: 10q+4
        81: 10q+4
        82: 10q+4
        83: 7q+4
        84: 10q+4
        85: 10q+4
        86: 10q+4
        87: 7q+4
        88: 10q+4
        89: 10q+4
        90: 2q^2+7q+4
        91: 3q+4
        92: 4q+4
        93: 3q+4
        94: 10q+4
        95: 10q+4
        96: 2q^2+7q+4
        97: 10q+4
        98: 10q+4
        99: 2q^2+7q+4
       100: 10q+4
       101: 10q+4
       102: 2q^2+7q+4
       103: 4q+1
       104: 4q+1
       105: 4q+1
       106: 4q+1
       107: 2q+2
       108: 2q+2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: 3q+2
       114: 3q+2
       115: 3q+2
       116: 3q+2
       117: 2q+2
       118: 2q+2
       119: 2q+2
       120: 2q+2
       121: 5q+2
       122: 5q+2
       123: 5q+2
       124: 5q+2
       125: 4q+4
       126: 7q+4
       127: 3q+2
       128: 3q+2
       129: 3q+2
       130: 3q+2
       131: 3q+2
       132: 3q+2
       133: q+4
       134: 3q+4
       135: q+4
       136: q+4
       137: 10q+4
       138: 7q+4
       139: 10q+4
       140: 4q+4
       141: 7q+4
       142: 4q+4
       143: 10q+4
       144: 7q+4
       145: 10q+4
       146: 7q+4
       147: 4q+4
       148: 4q+4
       149: 10q+4
       150: 7q+4
       151: 3q+2
       152: 3q+2
       153: 3q+2
       154: 3q+2
       155: 3q+2
       156: 3q+2
       157: 3q+4
       158: 4q+4
       159: 3q+4
       160: 3q+4
       161: 4q+4
       162: 3q+4
       163: 3q+4
       164: 4q+4
       165: 3q+4
       166: 10q+4
       167: 10q+4
       168: 2q^2+7q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: 3q+2
       178: 3q+2
       179: 3q+2
       180: 3q+2
       181: 2
       182: 2
       183: 2
       184: 2
       185: 2
       186: 2
       187: 2
       188: 2
       189: 3q+2
       190: 3q+2
       191: 2q+2
       192: 2q+2
       193: 2q+2
       194: 2q+2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       199: 2q+2
       200: 2q+2
       201: 2q+2
       202: 2q+2
       203: 2q+2
       204: 2q+2
       205: 2
       206: 2
       207: 5q+2
       208: 5q+2
       209: 3q+2
       210: 3q+2
       211: 3q+2
       212: 3q+2
       219: q+4
       220: q+4
       221: 3q+4
       222: q+4
       223: q+4
       224: q+4
       225: q+4
       226: 7q+4
       227: q+4
       228: 3q+4
       229: q+4
       230: q+4
       231: 7q+4
       232: q+4
       233: 3q+4
       234: q+4
       235: q+4
       236: 7q+4
       237: 3q+2
       238: 3q+2
       239: 3q+2
       240: 3q+2
       241: 3q+2
       242: 3q+2
       243: 10q+4
       244: 4q+4
       245: 4q+4
       246: 7q+4
       247: 8
       248: 8
       249: 4q+2
       250: 3q+4
       251: 4q+4
       252: 3q+4
       253: 3q+4
       254: 4q+4
       255: 3q+4
       256: 3q+4
       257: 4q+4
       258: 3q+4
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2
       284: 2
       285: 2
       286: 2
       287: 3q+2
       288: 3q+2
       291: 2
       292: 2
       293: 2
       294: 2
       295: 2
       296: 2
       297: 2
       298: 2
       299: 2
       300: 2
       301: 2
       302: 2
       303: 2
       304: 2
       305: 2
       306: 2
       307: 2
       308: 2
       309: 2
       310: 2
       311: 2
       312: 2
       313: 2
       314: 2
       315: 3q+2
       316: 3q+2
       317: 3q+2
       318: 3q+2
       319: 2q+2
       320: 2q+2
       321: 2q+2
       322: 2q+2
       323: 2
       324: 2
       325: 3q+2
       326: 3q+2
       333: q+4
       334: q+4
       335: q+4
       336: 2
       337: 8
       338: 4
       339: 4
       340: 4
       341: 4
       342: 2q+1
       343: 2q+1
       344: q+4
       345: q+4
       346: 3q+4
       347: q+4
       348: q+4
       349: q+4
       350: q+4
       351: 8
       352: q+4
       353: q+4
       354: 3q+4
       355: q+4
       356: q+4
       357: q+4
       358: q+4
       359: 8
       366: 7q+4
       367: q+4
       368: 3q+4
       369: q+4
       370: q+4
       371: 4
       372: 4
       373: 2q+1
       374: 3q+4
       375: 4q+4
       376: 3q+4
       377: 1
       378: 1
       379: 1
       380: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       419: 2
       420: 2
       421: 2
       422: 2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 4
       428: 4
       429: 2
       430: 2
       431: 2
       432: 2
       433: 2
       434: 2
       437: 2
       438: 2
       439: 2
       440: 2
       441: 2
       442: 2
       443: 4
       444: 4
       445: 4
       446: 4
       447: 2
       448: 2
       449: 2
       450: 2
       451: 2
       452: 2
       453: 2
       454: 2
       457: 2
       458: 2
       459: 2
       460: 2
       461: 4
       462: 4
       463: 4
       464: 4
       469: 3q+2
       470: 3q+2
       471: 2
       472: 2
       473: 2
       474: 2
       475: 2
       476: 2
       477: 2
       478: 2
       479: 4
       480: 4
       481: 2
       482: 2
       483: 2
       484: 4
       491: 1
       492: q+4
       493: q+4
       494: q+4
       495: 2
       496: 4
       497: q+4
       498: q+4
       499: q+4
       500: 2
       501: 4
       508: q+4
       509: q+4
       510: 3q+4
       511: q+4
       512: q+4
       513: q+4
       514: q+4
       515: 4
       516: 4
       517: 2q+1
       518: 4
       519: 4
       520: 2q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2
       546: 2
       547: 2
       548: 2
       549: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 2
       562: 2
       563: 2
       564: 2
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 2
       574: 2
       575: 2
       576: 2
       577: 2
       578: 2
       580: 2
       581: 2
       589: 1
       590: 1
       595: 1
       596: 1
       599: 1
       600: 1
       603: 2
       604: 2
       607: 2
       608: 2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 2
       616: 2
       619: 2
       620: 2
       621: 2
       622: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 2
       632: 2
       641: 2
       642: 2
       643: 2
       644: 2
       645: 2
       646: 2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 2
       656: 2
       657: 4
       664: 1
       665: 1
       672: 4
       673: 1
       674: 4
       675: 2
       676: 2
       677: 2
       678: 4
       679: 1
       680: 4
       681: 2
       682: 2
       683: 2
       684: 4
       685: 1
       686: q+4
       687: q+4
       688: q+4
       689: 2
       690: 4
       691: 4
       692: 2q+1
       693: 1
       694: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       725: 1
       726: 1
       727: 1
       728: 1
       741: 1
       742: 1
       743: 1
       744: 1
       753: 1
       754: 1
       755: 1
       756: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       793: 2
       794: 2
       801: 1
       802: 1
       807: 1
       808: 1
       811: 1
       812: 1
       815: 2
       816: 2
       817: 2
       818: 2
       825: 1
       826: 1
       831: 1
       832: 1
       835: 1
       836: 1
       839: 2
       840: 2
       843: 2
       844: 2
       845: 2
       846: 2
       847: 2
       848: 2
       851: 2
       852: 2
       855: 1
       856: 1
       857: 2
       858: 2
       865: 4
       866: 1
       867: 1
       868: 1
       869: 4
       870: 1
       871: 1
       872: 1
       873: 4
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       879: 2
       880: 1
       964: 1
       965: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       977: 1
       988: 1
       989: 1
       990: 1
       991: 1
      1016: 2
      1017: 2
      1032: 2
      1033: 2
      1046: 2
      1047: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1487: 1

1488:    0: 2q^3+10q^2+16q+4
         1: 12q^2+16q+4
         2: 2q^3+10q^2+16q+4
         3: 12q^2+16q+4
         4: q^4+4q^3+11q^2+12q+4
         5: 2q^3+10q^2+16q+4
         6: 4q^3+12q^2+12q+4
         7: q^4+4q^3+11q^2+12q+4
         8: 2q^3+10q^2+16q+4
         9: q^5+4q^4+8q^3+10q^2+7q+2
        10: 4q^2+14q+4
        11: 4q^2+14q+4
        12: q^3+7q^2+10q+4
        13: 2q^3+10q^2+16q+4
        14: q^4+4q^3+11q^2+12q+4
        15: 2q^3+10q^2+16q+4
        16: 4q^2+14q+4
        17: 4q^2+14q+4
        18: q^4+4q^3+8q^2+7q+2
        19: q^3+7q^2+12q+4
        20: 8q^2+12q+4
        21: q^3+7q^2+12q+4
        22: 2q^3+10q^2+16q+4
        23: 12q^2+16q+4
        24: 2q^3+10q^2+16q+4
        25: 2q^3+10q^2+16q+4
        26: 12q^2+16q+4
        27: 2q^3+10q^2+16q+4
        28: 12q+4
        29: 3q^2+10q+4
        30: q^3+7q^2+12q+4
        31: 4q^2+14q+4
        32: 2q^3+10q^2+16q+4
        33: 4q^2+14q+4
        34: 4q^2+14q+4
        35: 2q^3+10q^2+16q+4
        36: 4q^2+14q+4
        37: q^3+5q^2+8q+2
        38: q^3+5q^2+8q+2
        39: 6q^2+8q+2
        40: 6q^2+8q+2
        41: q^3+5q^2+8q+2
        42: q^3+5q^2+8q+2
        43: 4q^2+14q+4
        44: q^3+7q^2+10q+4
        45: 4q^2+14q+4
        46: 4q^2+14q+4
        47: 4q^2+14q+4
        48: q^4+4q^3+8q^2+7q+2
        49: 2q^2+10q+4
        50: 2q^2+10q+4
        51: q^3+6q^2+7q+2
        52: q^3+7q^2+12q+4
        53: 8q^2+12q+4
        54: q^3+7q^2+12q+4
        55: q^3+7q^2+12q+4
        56: 8q^2+12q+4
        57: q^3+7q^2+12q+4
        58: 6q+2
        59: 6q+2
        60: 6q+2
        61: 6q+2
        62: 2q^2+7q+2
        63: 2q^2+7q+2
        64: q^3+5q^2+8q+2
        65: q^3+5q^2+8q+2
        66: 2q^2+7q+2
        67: 2q^2+7q+2
        68: 12q+4
        69: 2q^2+5q+2
        70: 3q^2+10q+4
        71: 8q+4
        72: q^2+6q+4
        73: q^2+6q+4
        74: 2q^2+4q+2
        75: 2q^2+4q+2
        76: 2q^2+4q+2
        77: 2q^2+4q+2
        78: 2q^2+4q+2
        79: 2q^2+4q+2
        80: 4q^2+14q+4
        81: 4q^2+14q+4
        82: 3q^2+10q+4
        83: q^3+7q^2+12q+4
        84: 4q^2+14q+4
        85: 4q^2+14q+4
        86: 3q^2+10q+4
        87: q^3+7q^2+12q+4
        88: 8q+4
        89: 8q+4
        90: q^3+4q^2+5q+2
        91: 2q^2+10q+4
        92: 2q^2+10q+4
        93: q^3+6q^2+7q+2
        94: 2q^2+10q+4
        95: 2q^2+10q+4
        96: q^3+6q^2+7q+2
        97: 2q^2+10q+4
        98: 2q^2+10q+4
        99: q^3+6q^2+7q+2
       100: q^3+7q^2+12q+4
       101: 8q^2+12q+4
       102: q^3+7q^2+12q+4
       103: 3q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: 2q+2
       108: 2q+2
       109: 2q+2
       110: 2q+2
       111: q+2
       112: q+2
       113: q^2+3q+2
       114: q^2+3q+2
       115: 2q^2+4q+2
       116: 2q^2+4q+2
       117: 6q+2
       118: 6q+2
       119: 6q+2
       120: 6q+2
       121: 2q^2+7q+2
       122: 2q^2+7q+2
       123: 2q^2+7q+2
       124: 2q^2+7q+2
       125: 8q+4
       126: 3q+2
       127: 2q+2
       128: 2q+2
       129: 2q+2
       130: 2q+2
       131: q^2+2q+1
       132: q^2+2q+1
       133: 8q+4
       134: 2q^2+5q+2
       135: q^2+6q+4
       136: q^2+6q+4
       137: 8q+4
       138: 2q^2+5q+2
       139: 8q+4
       140: q^2+6q+4
       141: 3q^2+10q+4
       142: q^2+6q+4
       143: 8q+4
       144: 2q^2+5q+2
       145: 8q+4
       146: 3q^2+10q+4
       147: q^2+6q+4
       148: q^2+6q+4
       149: 3q^2+10q+4
       150: q^3+7q^2+12q+4
       151: 2q^2+4q+2
       152: 2q^2+4q+2
       153: 2q^2+4q+2
       154: 2q^2+4q+2
       155: 2q^2+4q+2
       156: 2q^2+4q+2
       157: 4q+4
       158: 4q+4
       159: 2q^2+4q+2
       160: 2q^2+10q+4
       161: 2q^2+10q+4
       162: q^3+6q^2+7q+2
       163: 2q^2+10q+4
       164: 2q^2+10q+4
       165: q^3+6q^2+7q+2
       166: 2q^2+10q+4
       167: 2q^2+10q+4
       168: q^3+6q^2+7q+2
       169: 1
       170: 1
       171: 1
       172: 1
       173: 3q+1
       174: 3q+1
       175: 3q+1
       176: 3q+1
       177: q+1
       178: q+1
       179: 2q+2
       180: 2q+2
       181: 2
       182: 2
       183: 2q+2
       184: 2q+2
       185: 2q+2
       186: 2q+2
       187: q+2
       188: q+2
       189: q^2+3q+2
       190: q^2+3q+2
       191: 4q+2
       192: 4q+2
       193: 2q+2
       194: 2q+2
       195: 2q+2
       196: 2q+2
       197: q+2
       198: q+2
       199: 4q+2
       200: 4q+2
       201: 2q+2
       202: 2q+2
       203: 2q+2
       204: 2q+2
       205: q+2
       206: q+2
       207: 4q+2
       208: 4q+2
       209: q^2+3q+2
       210: q^2+3q+2
       211: 2q^2+4q+2
       212: 2q^2+4q+2
       213: 2q+2
       214: 2q+2
       215: 2q+2
       216: 2q+2
       217: q^2+2q+1
       218: q^2+2q+1
       219: 3q+2
       220: 4q+4
       221: 2q+2
       222: 2q+4
       223: q^2+3q+2
       224: 2q+4
       225: q^2+3q+2
       226: 3q+2
       227: 8q+4
       228: 2q^2+5q+2
       229: q^2+6q+4
       230: q^2+6q+4
       231: 3q+2
       232: 8q+4
       233: 2q^2+5q+2
       234: q^2+6q+4
       235: q^2+6q+4
       236: 2q^2+5q+2
       237: 2q+2
       238: 2q+2
       239: 2q+2
       240: 2q+2
       241: q^2+2q+1
       242: q^2+2q+1
       243: 8q+4
       244: q^2+6q+4
       245: q^2+6q+4
       246: 3q^2+10q+4
       247: 2q+8
       248: 2q+8
       249: 3q^2+5q+2
       250: 4q+4
       251: 4q+4
       252: 2q^2+4q+2
       253: 4q+4
       254: 4q+4
       255: 2q^2+4q+2
       256: 2q^2+10q+4
       257: 2q^2+10q+4
       258: q^3+6q^2+7q+2
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: 2q+2
       280: 2q+2
       281: q+1
       282: q+1
       287: q+1
       288: q+1
       289: 2
       290: 2
       291: 1
       292: 1
       293: q+2
       294: q+2
       295: q+2
       296: q+2
       297: 2
       298: 2
       299: 2q+2
       300: 2q+2
       301: 2
       302: 2
       303: 2q+2
       304: 2q+2
       305: q+2
       306: q+2
       307: 2q+2
       308: 2q+2
       309: 2q+2
       310: 2q+2
       311: 2
       312: 2
       313: q+2
       314: q+2
       315: q+1
       316: q+1
       317: 2q+2
       318: 2q+2
       319: 2q+2
       320: 2q+2
       321: 2q+2
       322: 2q+2
       323: q+2
       324: q+2
       325: q^2+3q+2
       326: q^2+3q+2
       333: 2q+2
       334: q+2
       335: q+2
       336: q+2
       337: 8
       338: 4
       339: 4
       340: 4
       341: 4
       342: q^2+2q+1
       343: q^2+2q+1
       344: 3q+2
       345: 4q+4
       346: 2q+2
       347: 2q+4
       348: q^2+3q+2
       349: 2q+4
       350: q^2+3q+2
       351: 2q+8
       352: 3q+2
       353: 4q+4
       354: 2q+2
       355: 2q+4
       356: q^2+3q+2
       357: 2q+4
       358: q^2+3q+2
       359: 2q+8
       360: 2q+2
       361: 2q+2
       362: 2q+2
       363: 2q+2
       364: q^2+2q+1
       365: q^2+2q+1
       366: 3q+2
       367: 8q+4
       368: 2q^2+5q+2
       369: q^2+6q+4
       370: q^2+6q+4
       371: 2q+8
       372: 2q+8
       373: 3q^2+5q+2
       374: 4q+4
       375: 4q+4
       376: 2q^2+4q+2
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 4
       428: 4
       433: 1
       434: 1
       435: 2
       436: 2
       437: q+2
       438: q+2
       439: q+2
       440: q+2
       441: 2
       442: 2
       443: 4
       444: 4
       445: 4
       446: 4
       451: 1
       452: 1
       453: q+2
       454: q+2
       455: 2
       456: 2
       457: q+2
       458: q+2
       459: 2
       460: 2
       461: 4
       462: 4
       463: 4
       464: 4
       465: 2q+2
       466: 2q+2
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 2q+2
       472: 2q+2
       473: 2q+2
       474: 2q+2
       475: q+2
       476: q+2
       477: 2
       478: 2
       479: q+4
       480: q+4
       481: q+2
       482: q+2
       483: 2
       484: 8
       485: 4
       486: 4
       487: 4
       488: 4
       489: q^2+2q+1
       490: q^2+2q+1
       491: q+2
       492: 2q+2
       493: q+2
       494: q+2
       495: q+2
       496: 2q+8
       497: 2q+2
       498: q+2
       499: q+2
       500: q+2
       501: 2q+8
       508: 3q+2
       509: 4q+4
       510: 2q+2
       511: 2q+4
       512: q^2+3q+2
       513: 2q+4
       514: q^2+3q+2
       515: 4
       516: 4
       517: 2q+2
       518: 4
       519: 4
       520: q^2+2q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2
       546: 2
       547: 2
       548: 2
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 2
       562: 2
       563: 2
       564: 2
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 2
       574: 2
       575: 2
       576: 2
       577: 2
       578: 2
       580: 2
       581: 2
       585: 1
       586: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 4
       602: 4
       605: 1
       606: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 4
       616: 4
       617: 4
       618: 4
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 4
       632: 4
       633: 4
       634: 4
       639: q+1
       640: q+1
       645: 1
       646: 1
       647: q+2
       648: q+2
       649: q+2
       650: q+2
       651: 2
       652: 2
       653: 2
       654: 2
       655: q+4
       656: q+4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 4
       673: 1
       674: 4
       675: q+2
       676: q+2
       677: 2
       678: 4
       679: q+2
       680: 4
       681: q+2
       682: q+2
       683: 2
       684: 4
       685: q+2
       686: 2q+2
       687: q+2
       688: q+2
       689: q+2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       733: 2
       734: 2
       735: 2
       736: 2
       749: 2
       750: 2
       751: 2
       752: 2
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 2
       766: 2
       767: 2
       768: 2
       769: 2
       770: 2
       772: 2
       773: 2
       779: 1
       780: 1
       781: 1
       782: 1
       795: 2
       796: 2
       797: 1
       798: 1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 2
       816: 2
       819: 2
       820: 2
       821: 1
       822: 1
       833: 1
       834: 1
       835: 1
       836: 1
       839: 2
       840: 2
       843: 2
       844: 2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 2
       858: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       873: 2
       874: 2
       875: 2
       876: 1
       877: q+2
       878: q+2
       879: 2
       880: q+2
       881: 2
       882: 2
       883: q+1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       968: 1
       969: 1
       971: 1
       972: 1
       988: 1
       989: 1
       990: 1
       991: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1073: 1
      1075: 2
      1077: 1
      1078: 1
      1079: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1274: 1
      1275: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1488: 1

1489:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+2q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: 3q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q
       107: 2q+1
       108: q
       109: 2q+1
       110: q
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: 2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       172: q
       173: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q+1
       185: q+1
       187: 2q+1
       189: 2q+1
       191: q+1
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q+1
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: 2q+1
       262: q
       263: q+1
       267: q+1
       271: q+1
       275: q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q+1
       295: q+1
       297: 2q+1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: 1
       397: q+1
       401: 1
       405: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: q+1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       521: 1
       525: 1
       529: q+1
       533: 1
       537: 1
       541: 1
       545: q+1
       549: 1
       553: 1
       557: 1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: q+1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       928: 1
       932: 1
       936: 1
       940: 1
       948: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1020: 1
      1024: 1
      1030: 1
      1032: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1074: 1
      1077: 1
      1081: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1164: 1
      1184: 1
      1188: 1
      1194: 1
      1214: 1
      1216: 1
      1218: 1
      1222: 1
      1224: 1
      1236: 1
      1252: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1334: 1
      1489: 1

1490:    0: q^4+8q^3+12q^2+3q
         1: q^4+8q^3+12q^2+3q
         2: 6q^3+9q^2+3q
         3: 9q^3+12q^2+3q
         4: q^4+8q^3+12q^2+3q
         5: 9q^3+12q^2+3q
         6: q^4+8q^3+12q^2+3q
         7: 6q^3+9q^2+3q
         8: 3q^4+9q^3+9q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: q^4+8q^3+12q^2+3q
        11: 9q^3+12q^2+3q
        12: q^4+8q^3+12q^2+3q
        13: 3q^3+9q^2+3q
        14: 3q^3+9q^2+3q
        15: 6q^3+9q^2+3q
        16: 4q^3+11q^2+3q
        17: 4q^3+11q^2+3q
        18: 3q^3+5q^2+2q
        19: q^4+8q^3+12q^2+3q
        20: q^4+8q^3+12q^2+3q
        21: 6q^3+9q^2+3q
        22: 4q^3+11q^2+3q
        23: 4q^3+11q^2+3q
        24: 5q^3+8q^2+3q
        25: 4q^3+11q^2+3q
        26: 4q^3+11q^2+3q
        27: 5q^3+8q^2+3q
        28: 4q^3+11q^2+3q
        29: q^4+8q^3+12q^2+3q
        30: 3q^3+9q^2+3q
        31: 4q^3+11q^2+3q
        32: 2q^3+8q^2+3q
        33: q^3+10q^2+3q
        34: 4q^3+11q^2+3q
        35: 2q^3+8q^2+3q
        36: q^3+10q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 3q^3+9q^2+3q
        44: 3q^3+9q^2+3q
        45: 6q^3+9q^2+3q
        46: 8q^2+3q
        47: 2q^3+8q^2+3q
        48: q^3+5q^2+2q
        49: 4q^3+11q^2+3q
        50: 4q^3+11q^2+3q
        51: 3q^3+5q^2+2q
        52: 4q^3+11q^2+3q
        53: 4q^3+11q^2+3q
        54: 5q^3+8q^2+3q
        55: 4q^3+11q^2+3q
        56: 4q^3+11q^2+3q
        57: 5q^3+8q^2+3q
        58: q^3+6q^2+2q
        59: 4q^2+q
        60: q^3+6q^2+2q
        61: 4q^2+q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 5q^2+3q
        69: 4q^2+2q
        70: 3q^3+9q^2+3q
        71: 4q^3+11q^2+3q
        72: q^3+10q^2+3q
        73: q^3+10q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: 2q^3+8q^2+3q
        81: 7q^2+3q
        82: 4q^3+11q^2+3q
        83: 2q^3+8q^2+3q
        84: 2q^3+8q^2+3q
        85: 7q^2+3q
        86: 4q^3+11q^2+3q
        87: 2q^3+8q^2+3q
        88: 8q^2+3q
        89: 2q^3+8q^2+3q
        90: q^3+5q^2+2q
        91: 8q^2+3q
        92: 2q^3+8q^2+3q
        93: q^3+5q^2+2q
        94: q^3+8q^2+3q
        95: q^3+8q^2+3q
        96: 2q^3+4q^2+2q
        97: q^3+8q^2+3q
        98: q^3+8q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+7q^2+3q
       101: 2q^3+7q^2+3q
       102: q^3+4q^2+3q
       103: 2q^2+q
       104: 3q^2+q
       105: 3q^2+q
       106: q^2
       107: q^3+6q^2+2q
       108: 4q^2+q
       109: q^3+6q^2+2q
       110: 4q^2+q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: 3q^2+2q
       118: q^2+q
       119: 3q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 5q^2+3q
       126: 4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 5q^2+3q
       134: 4q^2+2q
       135: 7q^2+3q
       136: 7q^2+3q
       137: 7q^2+3q
       138: 3q^2+2q
       139: q^3+8q^2+3q
       140: 2q^2+2q
       141: 2q^3+8q^2+3q
       142: q^3+8q^2+3q
       143: 7q^2+3q
       144: 3q^2+2q
       145: q^3+8q^2+3q
       146: 2q^3+8q^2+3q
       147: q^3+8q^2+3q
       148: 2q^2+2q
       149: 2q^3+7q^2+3q
       150: q^3+4q^2+3q
       151: 2q^2+q
       152: 2q^3+5q^2+2q
       153: 2q^2+q
       154: 2q^3+5q^2+2q
       155: q^2+q
       156: q^3+3q^2+2q
       157: 8q^2+3q
       158: 2q^3+8q^2+3q
       159: q^3+5q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 5q^2+3q
       167: 5q^2+3q
       168: 2q^2+2q
       169: 2q^2+q
       170: 3q^2+q
       171: 3q^2+q
       172: q^2
       173: q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: 3q^2+2q
       184: q^2+q
       185: 3q^2+2q
       186: q^2+q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: 3q^2+2q
       192: q^2+q
       193: 2q^2+2q
       195: q^3+5q^2+2q
       196: 3q^2+q
       197: q^2+q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: q^3+5q^2+2q
       202: 3q^2+q
       203: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       209: 2q^2+q
       210: 2q^3+5q^2+2q
       211: q^2+q
       212: q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 5q^2+3q
       221: 4q^2+2q
       222: 7q^2+3q
       223: 3q^2+2q
       224: 7q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 3q^2+2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q^2+2q
       238: 3q^2+2q
       240: 3q^2+2q
       242: q^2+q
       243: 5q^2+3q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^3+4q^2+3q
       247: 5q^2+3q
       248: 5q^2+3q
       249: 2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 2q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 2q^2+2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       260: 2q^2+q
       261: 2q^2+q
       263: q^2+q
       264: q^2+q
       265: q^2+q
       267: q^2+q
       268: q^2+q
       271: q^2+q
       272: q^2+q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       280: 2q
       282: q
       283: q^2+q
       285: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: 3q^2+2q
       294: q^2+q
       295: 3q^2+2q
       296: q^2+q
       297: 2q^2+q
       298: 4q^2+2q
       299: 2q
       302: q^2+q
       303: q^2+2q
       304: q
       305: q
       306: q
       307: q^2+2q
       308: q
       309: 2q
       312: q^2+q
       313: q
       314: q
       316: q^2+q
       318: 3q^2+2q
       319: 2q^2+2q
       321: 2q^2+2q
       323: q^2+q
       325: q^2+q
       326: q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: 3q^2+2q
       336: 2q^2+2q
       337: 5q^2+3q
       339: 3q^2+2q
       341: 3q^2+2q
       343: q^2+q
       344: 2q
       345: q^2+3q
       346: q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q
       353: q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       361: 2q
       363: q^2+2q
       365: q
       366: 2q^2+2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       374: 3q
       375: 2q^2+3q
       376: 2q
       382: q
       383: q
       385: q^2+q
       386: q^2+q
       387: q^2+q
       390: q^2+q
       393: q
       394: q
       398: q^2+q
       401: q
       402: q
       405: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       419: q^2+q
       421: q^2+q
       424: q^2+q
       426: q^2+q
       428: 3q^2+2q
       429: q
       431: q
       436: q
       437: 2q
       439: q^2+2q
       440: q
       441: q
       442: q
       443: 2q^2+2q
       446: q^2+q
       447: q
       449: q
       453: q^2+2q
       454: q
       456: q
       457: 2q
       459: q
       460: q
       461: 2q^2+2q
       464: q^2+q
       466: 2q
       468: q
       470: q^2+q
       471: 2q
       473: 2q
       475: q
       479: q^2+q
       481: 2q
       482: 2q
       483: 2q^2+2q
       484: 3q
       486: 2q
       488: q^2+2q
       490: q
       491: 2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       503: 2q
       505: q^2+2q
       507: q
       508: 2q
       509: 3q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: 2q^2+3q
       520: 2q
       526: q
       527: q
       538: q
       541: q
       542: q
       546: q^2+q
       554: q
       557: q
       558: q
       562: q^2+q
       565: q
       573: q^2+q
       584: q
       586: q
       588: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q^2+q
       602: 2q
       603: q
       607: q
       612: q
       615: 2q
       618: q
       619: q
       621: q
       628: q
       631: 2q
       634: q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       647: 2q
       649: 2q
       653: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 2q
       667: 2q
       669: q^2+2q
       671: q
       672: 3q
       673: 2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       730: q
       734: q
       746: q
       750: q
       761: q
       765: q
       776: 1
       778: q
       780: 1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       793: 1
       796: 1
       805: q
       807: q
       814: q
       815: 2q
       817: 1
       820: 1
       825: q
       827: q
       838: q
       839: 2q
       842: q
       843: 1
       845: q
       847: q
       857: q
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       917: 1
       933: q
       941: 1
       957: q
       964: 1
       969: 1
       988: q
       993: 1
       995: 1
       997: 1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 1
      1016: 1
      1021: 1
      1031: 1
      1032: 1
      1037: 1
      1046: 1
      1074: 1
      1077: 1
      1081: 1
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1237: 1
      1253: 1
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1490: 1

1491:    0: q^4+3q^3+3q^2+q
         1: q^4+3q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+3q^3+3q^2+q
         5: q^4+3q^3+3q^2+q
         6: q^4+3q^3+3q^2+q
         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^4+3q^3+3q^2+q
        11: q^4+3q^3+3q^2+q
        12: q^4+3q^3+3q^2+q
        13: q^3+2q^2+q
        14: q^3+2q^2+q
        15: q^3+2q^2+q
        16: q^4+3q^3+3q^2+q
        17: q^4+3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^4+3q^3+3q^2+q
        20: q^4+3q^3+3q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^3+3q^2+q
        23: q^3+3q^2+q
        24: q^3+2q^2+q
        25: q^3+3q^2+q
        26: q^3+3q^2+q
        27: q^3+2q^2+q
        28: q^4+3q^3+3q^2+q
        29: q^4+3q^3+3q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^2+q
        33: q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^2+q
        36: q^3+3q^2+q
        37: q^3+3q^2+q
        39: q^3+3q^2+q
        41: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^3+2q^2+q
        47: q^3+2q^2+q
        48: q^3+2q^2+q
        49: q^4+3q^3+3q^2+q
        50: q^4+3q^3+3q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+3q^2+q
        53: q^3+3q^2+q
        54: q^3+2q^2+q
        55: q^3+3q^2+q
        56: q^3+3q^2+q
        57: q^3+2q^2+q
        58: q^3+2q^2+q
        59: q^2
        60: q^3+2q^2+q
        61: q^2
        62: q^3+3q^2+q
        64: 2q^2+q
        66: q^3+3q^2+q
        68: q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^4+3q^3+3q^2+q
        72: q^3+3q^2+q
        73: q^3+3q^2+q
        74: q^3+3q^2+q
        76: q^3+3q^2+q
        78: q^3+2q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: q^3+3q^2+q
        83: 2q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: q^3+3q^2+q
        87: 2q^2+q
        88: q^3+2q^2+q
        89: q^3+2q^2+q
        90: q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^3+3q^2+q
        95: q^3+3q^2+q
        96: q^3+2q^2+q
        97: q^3+3q^2+q
        98: q^3+3q^2+q
        99: q^3+2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^3+2q^2+q
       106: q^2
       107: q^3+2q^2+q
       108: q^2
       109: q^3+2q^2+q
       110: q^2
       111: q^3+3q^2+q
       113: q^3+3q^2+q
       115: 2q^2+q
       117: q^2+q
       119: q^2+q
       121: 2q^2+q
       123: 2q^2+q
       125: q^2+q
       126: q^3+2q^2+q
       127: q^3+3q^2+q
       129: q^3+3q^2+q
       131: q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^2+q
       138: 2q^2+q
       139: q^3+3q^2+q
       140: q
       141: 2q^2+q
       142: q^3+3q^2+q
       143: 2q^2+q
       144: 2q^2+q
       145: q^3+3q^2+q
       146: 2q^2+q
       147: q^3+3q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^3+2q^2+q
       172: q^2
       173: q^2+q
       177: 2q^2+q
       179: q^3+3q^2+q
       181: q^3+3q^2+q
       183: q^2+q
       185: q^2+q
       187: 2q^2+q
       189: 2q^2+q
       191: q^2+q
       193: q
       195: q^3+2q^2+q
       196: q^2
       197: q
       199: q^2+q
       201: q^3+2q^2+q
       202: q^2
       203: q
       205: q
       207: 2q^2+q
       209: q^2+q
       211: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: q^2+q
       267: q
       271: q
       275: q^2+q
       279: q
       281: q^2+q
       283: q^2+q
       285: q^2+q
       287: 2q^2+q
       289: q^2+q
       291: 2q^2+q
       293: q^2+q
       295: q^2+q
       297: 2q^2+q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       319: q
       321: q
       323: q
       325: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q
       366: q^2+q
       377: q^2+q
       381: q
       385: q^2+q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: q^2+q
       429: q
       431: q
       433: q
       437: q
       439: q
       441: q
       443: q
       445: q
       447: q
       449: q
       451: q
       453: q
       457: q
       459: q
       461: q
       463: q
       469: q^2+q
       477: q
       479: q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q
       498: q^2+q
       499: q
       500: q
       521: q
       525: q
       529: q^2+q
       533: q
       541: q
       545: q
       549: q
       557: q
       561: q
       569: q
       573: q
       577: q
       583: q
       585: q
       587: q^2+q
       589: q
       591: q
       593: q
       595: q
       599: q^2+q
       603: q
       607: q
       609: q
       613: q
       619: q
       621: q
       625: q
       629: q
       651: 1
       676: q
       677: q
       681: q
       683: q
       693: q
       705: q
       709: q
       713: q
       717: q
       725: q
       741: q
       757: 1
       771: 1
       777: q
       805: q
       807: q
       811: q
       825: q
       827: q
       835: q
       849: 1
       853: 1
       886: 1
       896: q
       928: q
       948: q
       960: 1
       970: 1
       978: 1
       984: 1
      1010: 1
      1050: 1
      1088: 1
      1100: 1
      1126: 1
      1140: 1
      1184: 1
      1190: 1
      1222: 1
      1292: 1
      1304: 1
      1322: 1
      1336: 1
      1491: 1

1492:    0: q^4+8q^3+12q^2+3q
         1: q^4+8q^3+12q^2+3q
         2: 6q^3+9q^2+3q
         3: 9q^3+12q^2+3q
         4: q^4+8q^3+12q^2+3q
         5: 9q^3+12q^2+3q
         6: q^4+8q^3+12q^2+3q
         7: 6q^3+9q^2+3q
         8: 3q^4+9q^3+9q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: q^4+8q^3+12q^2+3q
        11: 9q^3+12q^2+3q
        12: q^4+8q^3+12q^2+3q
        13: 3q^3+9q^2+3q
        14: 3q^3+9q^2+3q
        15: 6q^3+9q^2+3q
        16: 4q^3+11q^2+3q
        17: 4q^3+11q^2+3q
        18: 3q^3+5q^2+2q
        19: q^4+8q^3+12q^2+3q
        20: q^4+8q^3+12q^2+3q
        21: 6q^3+9q^2+3q
        22: 4q^3+11q^2+3q
        23: 4q^3+11q^2+3q
        24: 5q^3+8q^2+3q
        25: 4q^3+11q^2+3q
        26: 4q^3+11q^2+3q
        27: 5q^3+8q^2+3q
        28: 4q^3+11q^2+3q
        29: q^4+8q^3+12q^2+3q
        30: 3q^3+9q^2+3q
        31: 4q^3+11q^2+3q
        32: 2q^3+8q^2+3q
        33: q^3+10q^2+3q
        34: 4q^3+11q^2+3q
        35: 2q^3+8q^2+3q
        36: q^3+10q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 3q^3+9q^2+3q
        44: 3q^3+9q^2+3q
        45: 6q^3+9q^2+3q
        46: 8q^2+3q
        47: 2q^3+8q^2+3q
        48: q^3+5q^2+2q
        49: 4q^3+11q^2+3q
        50: 4q^3+11q^2+3q
        51: 3q^3+5q^2+2q
        52: 4q^3+11q^2+3q
        53: 4q^3+11q^2+3q
        54: 5q^3+8q^2+3q
        55: 4q^3+11q^2+3q
        56: 4q^3+11q^2+3q
        57: 5q^3+8q^2+3q
        58: 4q^2+q
        59: q^3+6q^2+2q
        60: q^3+6q^2+2q
        61: 4q^2+q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 5q^2+3q
        69: 4q^2+2q
        70: 3q^3+9q^2+3q
        71: 4q^3+11q^2+3q
        72: q^3+10q^2+3q
        73: q^3+10q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+8q^2+3q
        81: 7q^2+3q
        82: 4q^3+11q^2+3q
        83: 2q^3+8q^2+3q
        84: 2q^3+8q^2+3q
        85: 7q^2+3q
        86: 4q^3+11q^2+3q
        87: 2q^3+8q^2+3q
        88: 8q^2+3q
        89: 2q^3+8q^2+3q
        90: q^3+5q^2+2q
        91: 8q^2+3q
        92: 2q^3+8q^2+3q
        93: q^3+5q^2+2q
        94: q^3+8q^2+3q
        95: q^3+8q^2+3q
        96: 2q^3+4q^2+2q
        97: q^3+8q^2+3q
        98: q^3+8q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+7q^2+3q
       101: 2q^3+7q^2+3q
       102: q^3+4q^2+3q
       103: 3q^2+q
       104: 2q^2+q
       105: q^2
       106: 3q^2+q
       107: q^3+6q^2+2q
       108: 4q^2+q
       109: 4q^2+q
       110: q^3+6q^2+2q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: q^2+q
       118: 3q^2+2q
       119: 3q^2+2q
       120: q^2+q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 5q^2+3q
       126: 4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 5q^2+3q
       134: 4q^2+2q
       135: 7q^2+3q
       136: 7q^2+3q
       137: 7q^2+3q
       138: 3q^2+2q
       139: q^3+8q^2+3q
       140: 2q^2+2q
       141: 2q^3+8q^2+3q
       142: q^3+8q^2+3q
       143: 7q^2+3q
       144: 3q^2+2q
       145: q^3+8q^2+3q
       146: 2q^3+8q^2+3q
       147: q^3+8q^2+3q
       148: 2q^2+2q
       149: 2q^3+7q^2+3q
       150: q^3+4q^2+3q
       151: 2q^3+5q^2+2q
       152: 2q^2+q
       153: 2q^3+5q^2+2q
       154: 2q^2+q
       155: q^3+3q^2+2q
       156: q^2+q
       157: 8q^2+3q
       158: 2q^3+8q^2+3q
       159: q^3+5q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 5q^2+3q
       167: 5q^2+3q
       168: 2q^2+2q
       169: 3q^2+q
       170: 2q^2+q
       171: q^2
       172: 3q^2+q
       173: q^2+q
       174: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: 3q^2+2q
       184: q^2+q
       185: q^2+q
       186: 3q^2+2q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: q^2+q
       192: 3q^2+2q
       193: 2q^2+2q
       195: 3q^2+q
       196: q^3+5q^2+2q
       197: q^2+q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: q^3+5q^2+2q
       202: 3q^2+q
       204: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+5q^2+2q
       210: 2q^2+q
       211: q^3+3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 5q^2+3q
       221: 4q^2+2q
       222: 7q^2+3q
       223: 3q^2+2q
       224: 7q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 3q^2+2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q^2+2q
       237: 3q^2+2q
       239: 3q^2+2q
       241: q^2+q
       243: 5q^2+3q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^3+4q^2+3q
       247: 5q^2+3q
       248: 5q^2+3q
       249: 2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 2q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 2q^2+2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       264: q^2+q
       266: q^2+q
       267: q^2+q
       268: q^2+q
       273: q^2+q
       274: q^2+q
       275: q^2+q
       276: q^2+q
       278: q^2+q
       279: 2q
       281: q
       283: q^2+q
       286: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: 3q^2+2q
       294: q^2+q
       295: q^2+q
       296: 3q^2+2q
       297: 4q^2+2q
       298: 2q^2+q
       299: 2q
       301: q^2+q
       303: q
       304: q^2+2q
       305: q
       306: q
       307: q^2+2q
       308: q
       310: 2q
       311: q^2+q
       313: q
       314: q
       315: q^2+q
       317: 3q^2+2q
       319: 2q^2+2q
       322: 2q^2+2q
       324: q^2+q
       325: q^3+3q^2+2q
       326: q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: 3q^2+2q
       336: 2q^2+2q
       337: 5q^2+3q
       338: 3q^2+2q
       340: 3q^2+2q
       342: q^2+q
       344: 2q
       345: q^2+3q
       346: q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q
       353: q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       360: 2q
       362: q^2+2q
       364: q
       366: 2q^2+2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       374: 3q
       375: 2q^2+3q
       376: 2q
       381: q
       384: q
       385: q^2+q
       386: q^2+q
       388: q^2+q
       389: q^2+q
       393: q
       394: q
       399: q^2+q
       403: q
       404: q
       407: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       419: q^2+q
       422: q^2+q
       423: q^2+q
       425: q^2+q
       427: 3q^2+2q
       429: q
       432: q
       435: q
       437: 2q
       439: q
       440: q^2+2q
       441: q
       442: q
       443: 2q^2+2q
       445: q^2+q
       447: q
       450: q
       453: q^2+2q
       454: q
       455: q
       458: 2q
       459: q
       460: q
       462: 2q^2+2q
       463: q^2+q
       465: 2q
       467: q
       469: q^2+q
       471: 2q
       474: 2q
       476: q
       480: q^2+q
       481: 2q
       482: 2q
       483: 2q^2+2q
       484: 3q
       485: 2q
       487: q^2+2q
       489: q
       491: 2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       502: 2q
       504: q^2+2q
       506: q
       508: 2q
       509: 3q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: 2q^2+3q
       520: 2q
       525: q
       528: q
       537: q
       541: q
       542: q
       545: q^2+q
       555: q
       559: q
       560: q
       563: q^2+q
       566: q
       574: q^2+q
       583: q
       585: q
       587: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q^2+q
       601: 2q
       603: q
       608: q
       611: q
       615: 2q
       617: q
       619: q
       622: q
       627: q
       632: 2q
       633: q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       647: 2q
       650: 2q
       654: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 2q
       666: 2q
       668: q^2+2q
       670: q
       672: 3q
       673: 2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       729: q
       733: q
       747: q
       751: q
       763: q
       766: q
       775: 1
       777: q
       779: 1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       793: 1
       795: 1
       805: q
       808: q
       813: q
       815: 2q
       818: 1
       819: 1
       825: q
       828: q
       837: q
       840: 2q
       841: q
       844: 1
       845: q
       848: q
       858: q
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       916: 1
       932: q
       942: 1
       958: q
       965: 1
       971: 1
       989: q
       992: 1
       994: 1
       996: 1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 1
      1016: 1
      1020: 1
      1030: 1
      1033: 1
      1036: 1
      1047: 1
      1074: 1
      1077: 1
      1081: 1
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1236: 1
      1252: 1
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1492: 1

1493:    0: q^4+8q^3+12q^2+3q
         1: q^4+8q^3+12q^2+3q
         2: 6q^3+9q^2+3q
         3: 9q^3+12q^2+3q
         4: q^4+8q^3+12q^2+3q
         5: 9q^3+12q^2+3q
         6: q^4+8q^3+12q^2+3q
         7: 6q^3+9q^2+3q
         8: 3q^4+9q^3+9q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: q^4+8q^3+12q^2+3q
        11: 9q^3+12q^2+3q
        12: q^4+8q^3+12q^2+3q
        13: 3q^3+9q^2+3q
        14: 3q^3+9q^2+3q
        15: 6q^3+9q^2+3q
        16: 4q^3+11q^2+3q
        17: 4q^3+11q^2+3q
        18: 3q^3+5q^2+2q
        19: q^4+8q^3+12q^2+3q
        20: q^4+8q^3+12q^2+3q
        21: 6q^3+9q^2+3q
        22: 4q^3+11q^2+3q
        23: 4q^3+11q^2+3q
        24: 5q^3+8q^2+3q
        25: 4q^3+11q^2+3q
        26: 4q^3+11q^2+3q
        27: 5q^3+8q^2+3q
        28: 4q^3+11q^2+3q
        29: q^4+8q^3+12q^2+3q
        30: 3q^3+9q^2+3q
        31: 4q^3+11q^2+3q
        32: 2q^3+8q^2+3q
        33: q^3+10q^2+3q
        34: 4q^3+11q^2+3q
        35: 2q^3+8q^2+3q
        36: q^3+10q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 3q^3+9q^2+3q
        44: 3q^3+9q^2+3q
        45: 6q^3+9q^2+3q
        46: 8q^2+3q
        47: 2q^3+8q^2+3q
        48: q^3+5q^2+2q
        49: 4q^3+11q^2+3q
        50: 4q^3+11q^2+3q
        51: 3q^3+5q^2+2q
        52: 4q^3+11q^2+3q
        53: 4q^3+11q^2+3q
        54: 5q^3+8q^2+3q
        55: 4q^3+11q^2+3q
        56: 4q^3+11q^2+3q
        57: 5q^3+8q^2+3q
        58: q^3+6q^2+2q
        59: 4q^2+q
        60: 4q^2+q
        61: q^3+6q^2+2q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 5q^2+3q
        69: 4q^2+2q
        70: 3q^3+9q^2+3q
        71: 4q^3+11q^2+3q
        72: q^3+10q^2+3q
        73: q^3+10q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+8q^2+3q
        81: 7q^2+3q
        82: 4q^3+11q^2+3q
        83: 2q^3+8q^2+3q
        84: 2q^3+8q^2+3q
        85: 7q^2+3q
        86: 4q^3+11q^2+3q
        87: 2q^3+8q^2+3q
        88: 8q^2+3q
        89: 2q^3+8q^2+3q
        90: q^3+5q^2+2q
        91: 8q^2+3q
        92: 2q^3+8q^2+3q
        93: q^3+5q^2+2q
        94: q^3+8q^2+3q
        95: q^3+8q^2+3q
        96: 2q^3+4q^2+2q
        97: q^3+8q^2+3q
        98: q^3+8q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+7q^2+3q
       101: 2q^3+7q^2+3q
       102: q^3+4q^2+3q
       103: 3q^2+q
       104: q^2
       105: 2q^2+q
       106: 3q^2+q
       107: 4q^2+q
       108: q^3+6q^2+2q
       109: q^3+6q^2+2q
       110: 4q^2+q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: 3q^2+2q
       118: q^2+q
       119: q^2+q
       120: 3q^2+2q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 5q^2+3q
       126: 4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 5q^2+3q
       134: 4q^2+2q
       135: 7q^2+3q
       136: 7q^2+3q
       137: 7q^2+3q
       138: 3q^2+2q
       139: q^3+8q^2+3q
       140: 2q^2+2q
       141: 2q^3+8q^2+3q
       142: q^3+8q^2+3q
       143: 7q^2+3q
       144: 3q^2+2q
       145: q^3+8q^2+3q
       146: 2q^3+8q^2+3q
       147: q^3+8q^2+3q
       148: 2q^2+2q
       149: 2q^3+7q^2+3q
       150: q^3+4q^2+3q
       151: 2q^3+5q^2+2q
       152: 2q^2+q
       153: 2q^3+5q^2+2q
       154: 2q^2+q
       155: q^3+3q^2+2q
       156: q^2+q
       157: 8q^2+3q
       158: 2q^3+8q^2+3q
       159: q^3+5q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 5q^2+3q
       167: 5q^2+3q
       168: 2q^2+2q
       169: 3q^2+q
       170: q^2
       171: 2q^2+q
       172: 3q^2+q
       173: q^2+q
       175: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: q^2+q
       184: 3q^2+2q
       185: 3q^2+2q
       186: q^2+q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: 3q^2+2q
       192: q^2+q
       194: 2q^2+2q
       195: q^3+5q^2+2q
       196: 3q^2+q
       197: q^2+q
       198: q^2+q
       199: q^2+q
       200: 3q^2+2q
       201: 3q^2+q
       202: q^3+5q^2+2q
       203: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+5q^2+2q
       210: 2q^2+q
       211: q^3+3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 5q^2+3q
       221: 4q^2+2q
       222: 7q^2+3q
       223: 3q^2+2q
       224: 7q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 3q^2+2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q^2+2q
       237: 3q^2+2q
       239: 3q^2+2q
       241: q^2+q
       243: 5q^2+3q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^3+4q^2+3q
       247: 5q^2+3q
       248: 5q^2+3q
       249: 2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 2q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 2q^2+2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       265: q^2+q
       266: q^2+q
       269: q^2+q
       270: q^2+q
       271: q^2+q
       272: q^2+q
       275: q^2+q
       277: q^2+q
       278: q^2+q
       279: 2q
       281: q
       284: q^2+q
       285: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: q^2+q
       294: 3q^2+2q
       295: 3q^2+2q
       296: q^2+q
       297: 4q^2+2q
       298: 2q^2+q
       300: 2q
       301: q^2+q
       303: q^2+2q
       304: q
       305: q
       306: q
       307: q
       308: q^2+2q
       309: 2q
       311: q^2+q
       313: q
       314: q
       315: q^2+q
       317: 3q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       324: q^2+q
       325: q^3+3q^2+2q
       326: q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: 3q^2+2q
       336: 2q^2+2q
       337: 5q^2+3q
       338: 3q^2+2q
       340: 3q^2+2q
       342: q^2+q
       344: 2q
       345: q^2+3q
       346: q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q
       353: q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       360: 2q
       362: q^2+2q
       364: q
       366: 2q^2+2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       374: 3q
       375: 2q^2+3q
       376: 2q
       381: q
       384: q
       385: q^2+q
       387: q^2+q
       388: q^2+q
       391: q^2+q
       395: q
       396: q
       397: q^2+q
       401: q
       402: q
       408: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       420: q^2+q
       421: q^2+q
       423: q^2+q
       425: q^2+q
       427: 3q^2+2q
       430: q
       431: q
       435: q
       438: 2q
       439: q^2+2q
       440: q
       441: q
       442: q
       444: 2q^2+2q
       445: q^2+q
       448: q
       449: q
       453: q
       454: q^2+2q
       455: q
       457: 2q
       459: q
       460: q
       461: 2q^2+2q
       463: q^2+q
       465: 2q
       467: q
       469: q^2+q
       472: 2q
       473: 2q
       476: q
       480: q^2+q
       481: 2q
       482: 2q
       483: 2q^2+2q
       484: 3q
       485: 2q
       487: q^2+2q
       489: q
       491: 2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       502: 2q
       504: q^2+2q
       506: q
       508: 2q
       509: 3q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: 2q^2+3q
       520: 2q
       525: q
       528: q
       539: q
       543: q
       544: q
       547: q^2+q
       553: q
       557: q
       558: q
       561: q^2+q
       567: q
       576: q^2+q
       583: q
       585: q
       587: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q^2+q
       601: 2q
       604: q
       607: q
       611: q
       616: 2q
       617: q
       620: q
       621: q
       627: q
       631: 2q
       633: q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       648: 2q
       649: 2q
       654: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 2q
       666: 2q
       668: q^2+2q
       670: q
       672: 3q
       673: 2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       731: q
       735: q
       745: q
       749: q
       764: q
       767: q
       775: 1
       777: q
       779: 1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       794: 1
       795: 1
       806: q
       807: q
       813: q
       816: 2q
       817: 1
       819: 1
       826: q
       827: q
       837: q
       839: 2q
       841: q
       844: 1
       846: q
       847: q
       858: q
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       918: 1
       934: q
       940: 1
       956: q
       966: 1
       971: 1
       990: q
       992: 1
       994: 1
       996: 1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 1
      1017: 1
      1020: 1
      1030: 1
      1032: 1
      1036: 1
      1047: 1
      1074: 1
      1077: 1
      1081: 1
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1236: 1
      1252: 1
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1493: 1

1494:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+2q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: 3q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q
       106: 2q+1
       107: q
       108: 2q+1
       109: q
       110: 2q+1
       111: 3q+1
       113: 3q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: 2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       153: 2q+1
       155: q+1
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: 2q+1
       176: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q+1
       186: q+1
       187: 2q+1
       189: 2q+1
       192: q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       200: q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 2q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       259: q
       262: 2q+1
       266: q+1
       269: q+1
       273: q+1
       278: q+1
       279: 1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q+1
       296: q+1
       297: 2q+1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: q+1
       317: 2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       362: q+1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: 1
       399: q+1
       404: 1
       406: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: q+1
       489: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: q+1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       524: 1
       528: 1
       532: q+1
       536: 1
       539: 1
       543: 1
       547: q+1
       552: 1
       555: 1
       559: 1
       563: q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: q+1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       668: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       697: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       930: 1
       934: 1
       938: 1
       942: 1
       950: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1020: 1
      1024: 1
      1030: 1
      1033: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1074: 1
      1077: 1
      1081: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1166: 1
      1185: 1
      1188: 1
      1197: 1
      1214: 1
      1217: 1
      1219: 1
      1222: 1
      1224: 1
      1236: 1
      1252: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1334: 1
      1494: 1

1495:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+2q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: 3q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: 2q+1
       105: q
       107: 2q+1
       108: q
       109: q
       110: 2q+1
       112: 3q+1
       114: 3q+1
       116: 2q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: 2q+1
       171: q
       174: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q+1
       186: q+1
       188: 2q+1
       190: 2q+1
       192: q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q+1
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: 2q+1
       261: q
       264: q+1
       268: q+1
       274: q+1
       276: q+1
       280: 1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q+1
       296: q+1
       298: 2q+1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: 1
       400: q+1
       403: 1
       407: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       522: 1
       526: 1
       530: q+1
       534: 1
       538: 1
       542: 1
       546: q+1
       551: 1
       556: 1
       560: 1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: q+1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: 1
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       818: 1
       820: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       929: 1
       933: 1
       939: 1
       943: 1
       951: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1021: 1
      1025: 1
      1031: 1
      1033: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1074: 1
      1077: 1
      1081: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1167: 1
      1186: 1
      1192: 1
      1195: 1
      1215: 1
      1217: 1
      1218: 1
      1223: 1
      1225: 1
      1237: 1
      1253: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1338: 1
      1495: 1

1496:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+2q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q^2+3q+1
        72: 3q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q
       105: 2q+1
       107: q
       108: 2q+1
       109: 2q+1
       110: q
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: 2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 2q+1
       150: q+1
       152: 2q+1
       154: 2q+1
       156: q+1
       157: 2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: 2q+1
       175: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q+1
       185: q+1
       188: 2q+1
       190: 2q+1
       191: q+1
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       200: q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 2q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 1
       257: q+1
       258: 1
       260: q
       261: 2q+1
       265: q+1
       270: q+1
       272: q+1
       277: q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q+1
       295: q+1
       298: 2q+1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       374: 1
       375: q+1
       376: 1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: 1
       398: q+1
       402: 1
       408: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: q+1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       520: 1
       523: 1
       527: 1
       531: q+1
       535: 1
       540: 1
       544: 1
       548: q+1
       550: 1
       554: 1
       558: 1
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: q+1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       700: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: 1
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       820: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       931: 1
       935: 1
       937: 1
       941: 1
       949: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1021: 1
      1025: 1
      1031: 1
      1032: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1074: 1
      1077: 1
      1081: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1165: 1
      1187: 1
      1192: 1
      1196: 1
      1215: 1
      1216: 1
      1219: 1
      1223: 1
      1225: 1
      1237: 1
      1253: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1338: 1
      1496: 1

1497:    0: q^4+8q^3+12q^2+3q
         1: q^4+8q^3+12q^2+3q
         2: 6q^3+9q^2+3q
         3: 9q^3+12q^2+3q
         4: q^4+8q^3+12q^2+3q
         5: 9q^3+12q^2+3q
         6: q^4+8q^3+12q^2+3q
         7: 6q^3+9q^2+3q
         8: 3q^4+9q^3+9q^2+3q
         9: q^4+4q^3+5q^2+2q
        10: q^4+8q^3+12q^2+3q
        11: 9q^3+12q^2+3q
        12: q^4+8q^3+12q^2+3q
        13: 3q^3+9q^2+3q
        14: 3q^3+9q^2+3q
        15: 6q^3+9q^2+3q
        16: 4q^3+11q^2+3q
        17: 4q^3+11q^2+3q
        18: 3q^3+5q^2+2q
        19: q^4+8q^3+12q^2+3q
        20: q^4+8q^3+12q^2+3q
        21: 6q^3+9q^2+3q
        22: 4q^3+11q^2+3q
        23: 4q^3+11q^2+3q
        24: 5q^3+8q^2+3q
        25: 4q^3+11q^2+3q
        26: 4q^3+11q^2+3q
        27: 5q^3+8q^2+3q
        28: 4q^3+11q^2+3q
        29: q^4+8q^3+12q^2+3q
        30: 3q^3+9q^2+3q
        31: 4q^3+11q^2+3q
        32: 2q^3+8q^2+3q
        33: q^3+10q^2+3q
        34: 4q^3+11q^2+3q
        35: 2q^3+8q^2+3q
        36: q^3+10q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 3q^3+9q^2+3q
        44: 3q^3+9q^2+3q
        45: 6q^3+9q^2+3q
        46: 8q^2+3q
        47: 2q^3+8q^2+3q
        48: q^3+5q^2+2q
        49: 4q^3+11q^2+3q
        50: 4q^3+11q^2+3q
        51: 3q^3+5q^2+2q
        52: 4q^3+11q^2+3q
        53: 4q^3+11q^2+3q
        54: 5q^3+8q^2+3q
        55: 4q^3+11q^2+3q
        56: 4q^3+11q^2+3q
        57: 5q^3+8q^2+3q
        58: 4q^2+q
        59: q^3+6q^2+2q
        60: 4q^2+q
        61: q^3+6q^2+2q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 5q^2+3q
        69: 4q^2+2q
        70: 3q^3+9q^2+3q
        71: 4q^3+11q^2+3q
        72: q^3+10q^2+3q
        73: q^3+10q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: 2q^3+8q^2+3q
        81: 7q^2+3q
        82: 4q^3+11q^2+3q
        83: 2q^3+8q^2+3q
        84: 2q^3+8q^2+3q
        85: 7q^2+3q
        86: 4q^3+11q^2+3q
        87: 2q^3+8q^2+3q
        88: 8q^2+3q
        89: 2q^3+8q^2+3q
        90: q^3+5q^2+2q
        91: 8q^2+3q
        92: 2q^3+8q^2+3q
        93: q^3+5q^2+2q
        94: q^3+8q^2+3q
        95: q^3+8q^2+3q
        96: 2q^3+4q^2+2q
        97: q^3+8q^2+3q
        98: q^3+8q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+7q^2+3q
       101: 2q^3+7q^2+3q
       102: q^3+4q^2+3q
       103: q^2
       104: 3q^2+q
       105: 3q^2+q
       106: 2q^2+q
       107: 4q^2+q
       108: q^3+6q^2+2q
       109: 4q^2+q
       110: q^3+6q^2+2q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: q^2+q
       118: 3q^2+2q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 5q^2+3q
       126: 4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 5q^2+3q
       134: 4q^2+2q
       135: 7q^2+3q
       136: 7q^2+3q
       137: 7q^2+3q
       138: 3q^2+2q
       139: q^3+8q^2+3q
       140: 2q^2+2q
       141: 2q^3+8q^2+3q
       142: q^3+8q^2+3q
       143: 7q^2+3q
       144: 3q^2+2q
       145: q^3+8q^2+3q
       146: 2q^3+8q^2+3q
       147: q^3+8q^2+3q
       148: 2q^2+2q
       149: 2q^3+7q^2+3q
       150: q^3+4q^2+3q
       151: 2q^2+q
       152: 2q^3+5q^2+2q
       153: 2q^2+q
       154: 2q^3+5q^2+2q
       155: q^2+q
       156: q^3+3q^2+2q
       157: 8q^2+3q
       158: 2q^3+8q^2+3q
       159: q^3+5q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: 2q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: 2q^2+2q
       166: 5q^2+3q
       167: 5q^2+3q
       168: 2q^2+2q
       169: q^2
       170: 3q^2+q
       171: 3q^2+q
       172: 2q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: q^2+q
       184: 3q^2+2q
       185: q^2+q
       186: 3q^2+2q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: q^2+q
       192: 3q^2+2q
       194: 2q^2+2q
       195: 3q^2+q
       196: q^3+5q^2+2q
       197: q^2+q
       198: q^2+q
       199: q^2+q
       200: 3q^2+2q
       201: 3q^2+q
       202: q^3+5q^2+2q
       204: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       209: 2q^2+q
       210: 2q^3+5q^2+2q
       211: q^2+q
       212: q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 5q^2+3q
       221: 4q^2+2q
       222: 7q^2+3q
       223: 3q^2+2q
       224: 7q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+3q
       228: q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 3q^2+2q
       232: q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: 2q
       236: 2q^2+2q
       238: 3q^2+2q
       240: 3q^2+2q
       242: q^2+q
       243: 5q^2+3q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^3+4q^2+3q
       247: 5q^2+3q
       248: 5q^2+3q
       249: 2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 2q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 2q^2+2q
       256: 3q
       257: 2q^2+3q
       258: 2q
       260: 2q^2+q
       261: 2q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2+q
       269: q^2+q
       270: q^2+q
       273: q^2+q
       274: q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: 2q
       282: q
       284: q^2+q
       286: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: q^2+q
       294: 3q^2+2q
       295: q^2+q
       296: 3q^2+2q
       297: 2q^2+q
       298: 4q^2+2q
       300: 2q
       302: q^2+q
       303: q
       304: q^2+2q
       305: q
       306: q
       307: q
       308: q^2+2q
       310: 2q
       312: q^2+q
       313: q
       314: q
       316: q^2+q
       318: 3q^2+2q
       320: 2q^2+2q
       322: 2q^2+2q
       323: q^2+q
       325: q^2+q
       326: q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: 3q^2+2q
       336: 2q^2+2q
       337: 5q^2+3q
       339: 3q^2+2q
       341: 3q^2+2q
       343: q^2+q
       344: 2q
       345: q^2+3q
       346: q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q
       353: q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       361: 2q
       363: q^2+2q
       365: q
       366: 2q^2+2q
       367: 3q
       368: 2q
       369: 2q
       370: 2q
       371: 3q
       372: 2q^2+3q
       373: 2q
       374: 3q
       375: 2q^2+3q
       376: 2q
       382: q
       383: q
       386: q^2+q
       387: q^2+q
       388: q^2+q
       392: q^2+q
       395: q
       396: q
       400: q^2+q
       403: q
       404: q
       406: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       420: q^2+q
       422: q^2+q
       424: q^2+q
       426: q^2+q
       428: 3q^2+2q
       430: q
       432: q
       436: q
       438: 2q
       439: q
       440: q^2+2q
       441: q
       442: q
       444: 2q^2+2q
       446: q^2+q
       448: q
       450: q
       453: q
       454: q^2+2q
       456: q
       458: 2q
       459: q
       460: q
       462: 2q^2+2q
       464: q^2+q
       466: 2q
       468: q
       470: q^2+q
       472: 2q
       474: 2q
       475: q
       479: q^2+q
       481: 2q
       482: 2q
       483: 2q^2+2q
       484: 3q
       486: 2q
       488: q^2+2q
       490: q
       491: 2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       503: 2q
       505: q^2+2q
       507: q
       508: 2q
       509: 3q
       510: 2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: 3q
       519: 2q^2+3q
       520: 2q
       526: q
       527: q
       540: q
       543: q
       544: q
       548: q^2+q
       556: q
       559: q
       560: q
       564: q^2+q
       568: q
       575: q^2+q
       584: q
       586: q
       588: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q^2+q
       602: 2q
       604: q
       608: q
       612: q
       616: 2q
       618: q
       620: q
       622: q
       628: q
       632: 2q
       634: q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       648: 2q
       650: 2q
       653: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 2q
       667: 2q
       669: q^2+2q
       671: q
       672: 3q
       673: 2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       732: q
       736: q
       748: q
       752: q
       762: q
       768: q
       776: 1
       778: q
       780: 1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       794: 1
       796: 1
       806: q
       808: q
       814: q
       816: 2q
       818: 1
       820: 1
       826: q
       828: q
       838: q
       840: 2q
       842: q
       843: 1
       846: q
       848: q
       857: q
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       919: 1
       935: q
       943: 1
       959: q
       967: 1
       969: 1
       991: q
       993: 1
       995: 1
       997: 1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 1
      1017: 1
      1021: 1
      1031: 1
      1033: 1
      1037: 1
      1046: 1
      1074: 1
      1077: 1
      1081: 1
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1237: 1
      1253: 1
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1497: 1

1498:    0: q^4+3q^3+3q^2+q
         1: q^4+3q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+3q^3+3q^2+q
         5: q^4+3q^3+3q^2+q
         6: q^4+3q^3+3q^2+q
         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^4+3q^3+3q^2+q
        11: q^4+3q^3+3q^2+q
        12: q^4+3q^3+3q^2+q
        13: q^3+2q^2+q
        14: q^3+2q^2+q
        15: q^3+2q^2+q
        16: q^4+3q^3+3q^2+q
        17: q^4+3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^4+3q^3+3q^2+q
        20: q^4+3q^3+3q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^3+3q^2+q
        23: q^3+3q^2+q
        24: q^3+2q^2+q
        25: q^3+3q^2+q
        26: q^3+3q^2+q
        27: q^3+2q^2+q
        28: q^4+3q^3+3q^2+q
        29: q^4+3q^3+3q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^2+q
        33: q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^2+q
        36: q^3+3q^2+q
        37: q^3+3q^2+q
        39: q^3+3q^2+q
        41: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^3+2q^2+q
        47: q^3+2q^2+q
        48: q^3+2q^2+q
        49: q^4+3q^3+3q^2+q
        50: q^4+3q^3+3q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+3q^2+q
        53: q^3+3q^2+q
        54: q^3+2q^2+q
        55: q^3+3q^2+q
        56: q^3+3q^2+q
        57: q^3+2q^2+q
        58: q^2
        59: q^3+2q^2+q
        60: q^2
        61: q^3+2q^2+q
        62: q^3+3q^2+q
        64: 2q^2+q
        66: q^3+3q^2+q
        68: q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^4+3q^3+3q^2+q
        72: q^3+3q^2+q
        73: q^3+3q^2+q
        74: q^3+3q^2+q
        76: q^3+3q^2+q
        78: q^3+2q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: q^3+3q^2+q
        83: 2q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: q^3+3q^2+q
        87: 2q^2+q
        88: q^3+2q^2+q
        89: q^3+2q^2+q
        90: q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^3+3q^2+q
        95: q^3+3q^2+q
        96: q^3+2q^2+q
        97: q^3+3q^2+q
        98: q^3+3q^2+q
        99: q^3+2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^2
       106: q^3+2q^2+q
       107: q^2
       108: q^3+2q^2+q
       109: q^2
       110: q^3+2q^2+q
       111: q^3+3q^2+q
       113: q^3+3q^2+q
       115: 2q^2+q
       118: q^2+q
       120: q^2+q
       121: 2q^2+q
       123: 2q^2+q
       125: q^2+q
       126: q^3+2q^2+q
       127: q^3+3q^2+q
       129: q^3+3q^2+q
       131: q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^2+q
       138: 2q^2+q
       139: q^3+3q^2+q
       140: q
       141: 2q^2+q
       142: q^3+3q^2+q
       143: 2q^2+q
       144: 2q^2+q
       145: q^3+3q^2+q
       146: 2q^2+q
       147: q^3+3q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^2
       172: q^3+2q^2+q
       176: q^2+q
       177: 2q^2+q
       179: q^3+3q^2+q
       181: q^3+3q^2+q
       184: q^2+q
       186: q^2+q
       187: 2q^2+q
       189: 2q^2+q
       192: q^2+q
       194: q
       195: q^2
       196: q^3+2q^2+q
       197: q
       200: q^2+q
       201: q^2
       202: q^3+2q^2+q
       204: q
       205: q
       207: 2q^2+q
       209: q^2+q
       211: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
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       248: q^2+q
       249: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       259: q^2
       262: q^3+2q^2+q
       266: q^2+q
       269: q
       273: q
       278: q^2+q
       279: q
       281: q^2+q
       284: q^2+q
       286: q^2+q
       287: 2q^2+q
       289: q^2+q
       291: 2q^2+q
       294: q^2+q
       296: q^2+q
       297: 2q^2+q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       320: q
       322: q
       323: q
       325: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q
       366: q^2+q
       380: q^2+q
       384: q
       388: q^2+q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: q^2+q
       430: q
       432: q
       433: q
       438: q
       440: q
       441: q
       444: q
       445: q
       448: q
       450: q
       451: q
       454: q
       458: q
       459: q
       462: q
       463: q
       469: q^2+q
       477: q
       479: q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q
       498: q^2+q
       499: q
       500: q
       524: q
       528: q
       532: q^2+q
       536: q
       543: q
       547: q
       552: q
       559: q
       563: q
       570: q
       575: q
       577: q
       583: q
       585: q
       587: q^2+q
       590: q
       592: q
       594: q
       596: q
       599: q^2+q
       604: q
       608: q
       609: q
       613: q
       620: q
       622: q
       625: q
       629: q
       651: 1
       676: q
       677: q
       681: q
       683: q
       697: q
       708: q
       712: q
       716: q
       720: q
       727: q
       743: q
       758: 1
       771: 1
       777: q
       806: q
       808: q
       811: q
       826: q
       828: q
       835: q
       849: 1
       853: 1
       893: 1
       899: q
       930: q
       950: q
       961: 1
       970: 1
       979: 1
       984: 1
      1010: 1
      1050: 1
      1095: 1
      1107: 1
      1127: 1
      1140: 1
      1185: 1
      1190: 1
      1222: 1
      1299: 1
      1311: 1
      1323: 1
      1336: 1
      1498: 1

1499:    0: q^4+3q^3+3q^2+q
         1: q^4+3q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+3q^3+3q^2+q
         5: q^4+3q^3+3q^2+q
         6: q^4+3q^3+3q^2+q
         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^4+3q^3+3q^2+q
        11: q^4+3q^3+3q^2+q
        12: q^4+3q^3+3q^2+q
        13: q^3+2q^2+q
        14: q^3+2q^2+q
        15: q^3+2q^2+q
        16: q^4+3q^3+3q^2+q
        17: q^4+3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^4+3q^3+3q^2+q
        20: q^4+3q^3+3q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^3+3q^2+q
        23: q^3+3q^2+q
        24: q^3+2q^2+q
        25: q^3+3q^2+q
        26: q^3+3q^2+q
        27: q^3+2q^2+q
        28: q^4+3q^3+3q^2+q
        29: q^4+3q^3+3q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^2+q
        33: q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^2+q
        36: q^3+3q^2+q
        38: q^3+3q^2+q
        40: q^3+3q^2+q
        42: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^3+2q^2+q
        47: q^3+2q^2+q
        48: q^3+2q^2+q
        49: q^4+3q^3+3q^2+q
        50: q^4+3q^3+3q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+3q^2+q
        53: q^3+3q^2+q
        54: q^3+2q^2+q
        55: q^3+3q^2+q
        56: q^3+3q^2+q
        57: q^3+2q^2+q
        58: q^2
        59: q^3+2q^2+q
        60: q^3+2q^2+q
        61: q^2
        63: q^3+3q^2+q
        65: 2q^2+q
        67: q^3+3q^2+q
        68: q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^4+3q^3+3q^2+q
        72: q^3+3q^2+q
        73: q^3+3q^2+q
        75: q^3+3q^2+q
        77: q^3+3q^2+q
        79: q^3+2q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: q^3+3q^2+q
        83: 2q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: q^3+3q^2+q
        87: 2q^2+q
        88: q^3+2q^2+q
        89: q^3+2q^2+q
        90: q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^3+3q^2+q
        95: q^3+3q^2+q
        96: q^3+2q^2+q
        97: q^3+3q^2+q
        98: q^3+3q^2+q
        99: q^3+2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q^3+2q^2+q
       105: q^2
       107: q^3+2q^2+q
       108: q^2
       109: q^2
       110: q^3+2q^2+q
       112: q^3+3q^2+q
       114: q^3+3q^2+q
       116: 2q^2+q
       118: q^2+q
       119: q^2+q
       122: 2q^2+q
       124: 2q^2+q
       125: q^2+q
       126: q^3+2q^2+q
       128: q^3+3q^2+q
       130: q^3+3q^2+q
       132: q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^2+q
       138: 2q^2+q
       139: q^3+3q^2+q
       140: q
       141: 2q^2+q
       142: q^3+3q^2+q
       143: 2q^2+q
       144: 2q^2+q
       145: q^3+3q^2+q
       146: 2q^2+q
       147: q^3+3q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: q^3+2q^2+q
       171: q^2
       174: q^2+q
       178: 2q^2+q
       180: q^3+3q^2+q
       182: q^3+3q^2+q
       183: q^2+q
       186: q^2+q
       188: 2q^2+q
       190: 2q^2+q
       192: q^2+q
       193: q
       195: q^2
       196: q^3+2q^2+q
       198: q
       199: q^2+q
       201: q^3+2q^2+q
       202: q^2
       204: q
       206: q
       208: 2q^2+q
       210: q^2+q
       212: q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: q^2+q
       268: q
       274: q
       276: q^2+q
       280: q
       282: q^2+q
       283: q^2+q
       286: q^2+q
       288: 2q^2+q
       290: q^2+q
       292: 2q^2+q
       293: q^2+q
       296: q^2+q
       298: 2q^2+q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       319: q
       322: q
       324: q
       326: q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q
       366: q^2+q
       378: q^2+q
       382: q
       386: q^2+q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: q^2+q
       429: q
       432: q
       434: q
       437: q
       440: q
       442: q
       443: q
       446: q
       447: q
       450: q
       452: q
       453: q
       458: q
       460: q
       462: q
       464: q
       470: q^2+q
       478: q
       480: q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q
       498: q^2+q
       499: q
       500: q
       522: q
       526: q
       530: q^2+q
       534: q
       542: q
       546: q
       551: q
       560: q
       564: q
       571: q
       574: q
       581: q
       584: q
       586: q
       588: q^2+q
       589: q
       592: q
       593: q
       596: q
       600: q^2+q
       603: q
       608: q
       610: q
       614: q
       619: q
       622: q
       626: q
       630: q
       652: 1
       676: q
       677: q
       681: q
       683: q
       699: q
       706: q
       710: q
       715: q
       718: q
       726: q
       744: q
       759: 1
       774: 1
       778: q
       805: q
       808: q
       812: q
       825: q
       828: q
       836: q
       850: 1
       854: 1
       894: 1
       897: q
       929: q
       951: q
       962: 1
       973: 1
       980: 1
       987: 1
      1011: 1
      1051: 1
      1096: 1
      1108: 1
      1128: 1
      1143: 1
      1186: 1
      1193: 1
      1223: 1
      1300: 1
      1312: 1
      1324: 1
      1339: 1
      1499: 1

1500:    0: q^4+3q^3+3q^2+q
         1: q^4+3q^3+3q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+3q^3+3q^2+q
         5: q^4+3q^3+3q^2+q
         6: q^4+3q^3+3q^2+q
         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^4+3q^3+3q^2+q
        11: q^4+3q^3+3q^2+q
        12: q^4+3q^3+3q^2+q
        13: q^3+2q^2+q
        14: q^3+2q^2+q
        15: q^3+2q^2+q
        16: q^4+3q^3+3q^2+q
        17: q^4+3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^4+3q^3+3q^2+q
        20: q^4+3q^3+3q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^3+3q^2+q
        23: q^3+3q^2+q
        24: q^3+2q^2+q
        25: q^3+3q^2+q
        26: q^3+3q^2+q
        27: q^3+2q^2+q
        28: q^4+3q^3+3q^2+q
        29: q^4+3q^3+3q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^2+q
        33: q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^2+q
        36: q^3+3q^2+q
        38: q^3+3q^2+q
        40: q^3+3q^2+q
        42: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^3+2q^2+q
        47: q^3+2q^2+q
        48: q^3+2q^2+q
        49: q^4+3q^3+3q^2+q
        50: q^4+3q^3+3q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+3q^2+q
        53: q^3+3q^2+q
        54: q^3+2q^2+q
        55: q^3+3q^2+q
        56: q^3+3q^2+q
        57: q^3+2q^2+q
        58: q^3+2q^2+q
        59: q^2
        60: q^2
        61: q^3+2q^2+q
        63: q^3+3q^2+q
        65: 2q^2+q
        67: q^3+3q^2+q
        68: q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^4+3q^3+3q^2+q
        72: q^3+3q^2+q
        73: q^3+3q^2+q
        75: q^3+3q^2+q
        77: q^3+3q^2+q
        79: q^3+2q^2+q
        80: 2q^2+q
        81: 2q^2+q
        82: q^3+3q^2+q
        83: 2q^2+q
        84: 2q^2+q
        85: 2q^2+q
        86: q^3+3q^2+q
        87: 2q^2+q
        88: q^3+2q^2+q
        89: q^3+2q^2+q
        90: q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^3+3q^2+q
        95: q^3+3q^2+q
        96: q^3+2q^2+q
        97: q^3+3q^2+q
        98: q^3+3q^2+q
        99: q^3+2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q^2
       105: q^3+2q^2+q
       107: q^2
       108: q^3+2q^2+q
       109: q^3+2q^2+q
       110: q^2
       112: q^3+3q^2+q
       114: q^3+3q^2+q
       116: 2q^2+q
       117: q^2+q
       120: q^2+q
       122: 2q^2+q
       124: 2q^2+q
       125: q^2+q
       126: q^3+2q^2+q
       128: q^3+3q^2+q
       130: q^3+3q^2+q
       132: q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^2+q
       138: 2q^2+q
       139: q^3+3q^2+q
       140: q
       141: 2q^2+q
       142: q^3+3q^2+q
       143: 2q^2+q
       144: 2q^2+q
       145: q^3+3q^2+q
       146: 2q^2+q
       147: q^3+3q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: q^2
       171: q^3+2q^2+q
       175: q^2+q
       178: 2q^2+q
       180: q^3+3q^2+q
       182: q^3+3q^2+q
       184: q^2+q
       185: q^2+q
       188: 2q^2+q
       190: 2q^2+q
       191: q^2+q
       194: q
       195: q^3+2q^2+q
       196: q^2
       198: q
       200: q^2+q
       201: q^2
       202: q^3+2q^2+q
       203: q
       206: q
       208: 2q^2+q
       210: q^2+q
       212: q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       260: q^2
       261: q^3+2q^2+q
       265: q^2+q
       270: q
       272: q
       277: q^2+q
       280: q
       282: q^2+q
       284: q^2+q
       285: q^2+q
       288: 2q^2+q
       290: q^2+q
       292: 2q^2+q
       294: q^2+q
       295: q^2+q
       298: 2q^2+q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       320: q
       321: q
       324: q
       326: q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q
       366: q^2+q
       379: q^2+q
       383: q
       387: q^2+q
       392: q
       395: q
       398: q
       402: q
       408: q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: q^2+q
       430: q
       431: q
       434: q
       438: q
       439: q
       442: q
       444: q
       446: q
       448: q
       449: q
       452: q
       454: q
       457: q
       460: q
       461: q
       464: q
       470: q^2+q
       478: q
       480: q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q
       498: q^2+q
       499: q
       500: q
       523: q
       527: q
       531: q^2+q
       535: q
       544: q
       548: q
       550: q
       558: q
       562: q
       572: q
       576: q
       581: q
       584: q
       586: q
       588: q^2+q
       590: q
       591: q
       594: q
       595: q
       600: q^2+q
       604: q
       607: q
       610: q
       614: q
       620: q
       621: q
       626: q
       630: q
       652: 1
       676: q
       677: q
       681: q
       683: q
       700: q
       707: q
       711: q
       714: q
       719: q
       728: q
       742: q
       760: 1
       774: 1
       778: q
       806: q
       807: q
       812: q
       826: q
       827: q
       836: q
       850: 1
       854: 1
       895: 1
       898: q
       931: q
       949: q
       963: 1
       973: 1
       981: 1
       987: 1
      1011: 1
      1051: 1
      1097: 1
      1109: 1
      1129: 1
      1143: 1
      1187: 1
      1193: 1
      1223: 1
      1301: 1
      1313: 1
      1325: 1
      1339: 1
      1500: 1

1501:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       111: q+1
       113: 1
       115: q+1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: 1
       138: q^2+q+1
       139: 1
       140: q+1
       141: 1
       142: q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       159: 1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: 1
       177: q+1
       179: 1
       181: q+1
       183: 1
       185: 1
       187: q+1
       189: 1
       191: 1
       193: 1
       195: 1
       197: q+1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: 1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: q+1
       303: 1
       305: q+1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: q+1
       435: q+1
       437: 1
       439: 1
       441: 1
       443: 1
       445: q+1
       447: 1
       449: 1
       451: 1
       455: 1
       461: 1
       463: 1
       465: 1
       467: q+1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: 1
       603: 1
       605: q+1
       607: 1
       609: 1
       613: q+1
       615: 1
       617: q+1
       623: 1
       629: 1
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 1
       685: 1
       689: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       775: 1
       779: q+1
       781: 1
       785: 1
       787: 1
       791: 1
       793: 1
       795: q+1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: q+1
       811: 1
       817: 1
       819: 1
       833: 1
       843: 1
       849: 1
       855: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       920: 1
       924: 1
       928: 1
       940: 1
       960: 1
       964: 1
       968: 1
       994: 1
       998: 1
      1000: 1
      1010: 1
      1012: 1
      1020: q+1
      1022: 1
      1026: 1
      1028: 1
      1036: 1
      1060: 1
      1064: 1
      1076: 1
      1084: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1138: 1
      1152: 1
      1156: 1
      1160: 1
      1230: 1
      1232: 1
      1234: 1
      1274: 1
      1278: 1
      1280: 1
      1290: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1430: 1
      1501: 1

1502:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 3q^3+5q^2+3q
        23: q^4+4q^3+5q^2+3q
        24: 3q^3+5q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: 2q^2+3q
        32: 3q^3+5q^2+3q
        33: 2q^3+4q^2+3q
        34: q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 3q^3+5q^2+3q
        53: q^4+4q^3+5q^2+3q
        54: 3q^3+5q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        58: q^2+2q
        59: q
        60: 2q
        61: q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 3q^2+3q
        73: 2q^3+4q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: 2q^2+3q
        81: 2q^3+4q^2+3q
        82: 2q^2+3q
        83: 3q^3+5q^2+3q
        84: q^2+3q
        85: 3q^2+3q
        86: q^2+3q
        87: 4q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^3+4q^2+3q
        95: 2q^3+4q^2+3q
        96: 2q^3+3q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       104: q
       105: q
       107: 2q
       108: q
       109: q^2+2q
       110: q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: q^2+2q
       118: q
       119: 2q
       120: q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 3q^2+3q
       136: 2q^3+4q^2+3q
       137: 3q
       138: q^3+2q^2+2q
       139: q^2+3q
       140: 3q^2+3q
       141: 2q^2+3q
       142: 2q^3+4q^2+3q
       143: 3q
       144: q^2+2q
       145: 3q
       146: q^2+3q
       147: 2q^2+3q
       148: 2q
       149: q^2+3q
       150: 4q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q^2+q
       156: 3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+3q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       170: q
       171: q
       173: q
       174: q
       175: q
       178: q
       180: 2q
       182: q^2+2q
       183: 2q
       184: q
       185: q^2+2q
       186: q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: 2q
       192: q
       193: 2q
       194: q
       195: q^2+2q
       196: q
       197: q^2+q
       198: 2q^2+2q
       199: 2q
       200: q
       201: 2q
       202: q
       203: 2q
       205: q
       206: q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q^2+q
       212: 3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q
       227: q^2+3q
       228: q^3+2q^2+2q
       229: 3q^2+3q
       230: 2q^3+4q^2+3q
       231: 2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q
       244: 2q^2+3q
       245: 2q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: q
       261: q
       263: q
       264: q
       265: q
       267: q
       268: q
       270: q
       271: q
       272: q
       275: q
       276: q
       277: q
       280: 2q
       282: q
       283: q
       285: q
       288: q
       290: q^2+2q
       292: q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: 2q
       299: 2q
       300: q
       302: q^2+2q
       303: q^2+2q
       304: q
       305: q^2+q
       306: 2q^2+2q
       307: 2q
       308: q
       309: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       319: 2q
       320: q
       321: 2q
       323: q
       324: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 2q^2+3q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q
       392: q
       393: q
       394: q
       395: q
       398: q
       401: q
       402: q
       405: q
       408: q
       414: q
       418: q
       419: q
       421: q
       424: q
       426: q
       428: 2q
       429: q
       431: q
       434: q
       436: q^2+2q
       437: 2q
       438: q
       439: 2q
       440: q
       441: q
       442: 2q
       443: 2q
       444: q
       446: q^2+2q
       447: q
       449: q
       456: q
       461: 2q
       464: q
       466: 2q
       468: q
       470: q
       471: 2q
       472: q
       473: 2q
       475: q
       476: q
       478: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       500: q
       501: 2q
       508: 2q
       512: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       538: q
       540: q
       541: q
       542: q
       544: q
       546: q
       548: q
       554: q
       562: q
       565: q
       567: q
       572: q
       573: q
       576: q
       581: q
       586: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: 2q
       603: q
       606: q
       607: q
       610: q
       614: q
       615: 2q
       616: q
       618: q^2+2q
       631: 2q
       634: q
       640: q
       641: q
       643: q
       652: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 1
       685: q
       689: q
       700: q
       734: q
       736: q
       750: q
       760: q
       765: q
       767: q
       773: q
       776: 1
       780: q+1
       782: q
       785: q
       787: q
       793: 1
       796: q+1
       798: q
       801: q
       803: q
       805: q
       807: q
       810: q
       812: q
       817: 1
       820: 1
       843: 1
       866: 1
       870: q+1
       871: 2q
       874: 1
       880: q
       891: q
       917: 1
       941: 1
       964: 1
       969: 1
       995: 1
       998: 1
      1000: 1
      1012: 1
      1021: q+1
      1023: q
      1026: q
      1028: q
      1037: 1
      1076: 1
      1084: 1
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1231: 1
      1232: 1
      1234: 1
      1275: 1
      1280: 1
      1291: 1
      1349: 1
      1357: 1
      1364: 1
      1431: 1
      1502: 1

1503:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^4+5q^3+2q^2+q
        23: q^4+5q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^3+2q^2+q
        26: 2q^3+2q^2+q
        27: q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: 3q^3+q^2+q
        32: 3q^3+2q^2+q
        33: q^4+5q^3+2q^2+q
        34: q^3+q^2+q
        35: q^3+2q^2+q
        36: 2q^3+2q^2+q
        37: 2q^3+2q^2+q
        39: 2q^3+2q^2+q
        41: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 3q^3+2q^2+q
        53: q^4+4q^3+2q^2+q
        54: q^4+2q^3+2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: 2q^3+q^2+q
        59: q^3
        60: q^3+q^2+q
        62: q^3+q^2+q
        64: q^3+2q^2+q
        66: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^2+q
        73: 2q^3+2q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^3+q^2+q
        81: 3q^3+2q^2+q
        82: 2q^3+q^2+q
        83: 2q^3+2q^2+q
        84: q^2+q
        85: q^3+2q^2+q
        86: q^2+q
        87: 2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 3q^3+2q^2+q
        95: q^4+4q^3+2q^2+q
        96: q^4+2q^3+2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       103: q^3+q^2+q
       107: q^2+q
       109: q^3+q^2+q
       111: 2q^2+q
       113: q^2+q
       115: 2q^2+q
       117: q^2+q
       119: q^2+q
       121: q^2+q
       123: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: 2q^2+q
       136: q^3+2q^2+q
       137: q^3+q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+q^2+q
       140: 2q^2+q
       141: q^3+q^2+q
       142: 2q^3+2q^2+q
       143: q^2+q
       144: 2q^2+q
       145: q^2+q
       146: q^2+q
       147: 2q^2+q
       148: q
       149: q^2+q
       150: 2q^2+q
       151: 2q^2+q
       153: q^3+2q^2+q
       155: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       169: q^2+q
       173: q^2+q
       177: 2q^2+q
       179: q^2+q
       181: 2q^2+q
       183: q^2+q
       185: q^2+q
       187: 2q^2+q
       189: q^2+q
       191: q^2+q
       193: q^2+q
       195: q^3+q^2+q
       197: 2q^2+q
       199: q^2+q
       201: q^2+q
       203: q
       205: q
       207: q^2+q
       209: q^2+q
       211: 2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: 2q^2+q
       224: q
       225: q^3+2q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: q^3+2q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: 2q^2+q
       237: 2q^2+q
       239: q^3+2q^2+q
       241: 2q^2+q
       243: q^2+q
       244: 2q^2+q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2+q
       263: q^2+q
       267: q^2+q
       271: q
       275: q^2+q
       279: q
       281: q^2+q
       283: q^2+q
       285: q^2+q
       287: q^2+q
       289: q^2+q
       291: 2q^2+q
       293: q
       295: q
       297: q
       299: q^2+q
       301: 2q^2+q
       303: q^2+q
       305: 2q^2+q
       307: q
       309: q
       311: q
       313: q
       315: 2q^2+q
       317: q^2+q
       319: q^2+q
       321: q
       323: q
       325: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: 2q^2+q
       349: q
       350: q^3+2q^2+q
       351: q^2+q
       352: q
       356: q^2+q
       358: q
       359: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       377: q^2+q
       381: q
       385: q
       389: q^2+q
       393: q^2+q
       397: q
       401: q
       405: q
       413: q
       417: q^2+q
       419: q
       421: q
       423: q
       425: q^2+q
       427: q
       429: q^2+q
       431: q^2+q
       433: 2q^2+q
       435: q^2+q
       437: q
       439: q
       441: q
       443: q
       445: q^2+q
       447: q
       449: q
       451: q
       455: q
       461: q
       463: q
       465: q
       467: q^2+q
       469: q^2+q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       500: q
       508: q
       512: q^2+q
       514: q
       521: q
       529: q
       533: q^2+q
       537: q
       541: q
       545: q
       549: q
       553: q
       561: q
       565: q
       569: q
       573: q
       577: q
       585: q
       589: q
       591: q
       593: q
       595: q
       599: q
       603: q
       605: q^2+q
       607: q
       609: q
       613: q^2+q
       623: q
       629: q
       639: q
       641: q
       643: q
       645: q
       651: q
       675: q
       676: q
       677: q
       689: q
       693: q
       709: q
       713: q
       717: q
       721: q
       725: q
       737: q
       753: q
       757: q
       797: q
       801: q
       803: q
       805: q
       807: q
       811: q
       849: q
       855: q
       920: q
       924: q
       928: q
       960: q
      1010: 1
      1126: 1
      1140: 1
      1278: 1
      1292: 1
      1360: 1
      1432: 1
      1503: 1

1504:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 3q^3+5q^2+3q
        23: q^4+4q^3+5q^2+3q
        24: 3q^3+5q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: 2q^2+3q
        32: 3q^3+5q^2+3q
        33: 2q^3+4q^2+3q
        34: q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 3q^3+5q^2+3q
        53: q^4+4q^3+5q^2+3q
        54: 3q^3+5q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        58: q^2+2q
        59: q
        60: q
        61: 2q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 3q^2+3q
        73: 2q^3+4q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: 2q^2+3q
        81: 2q^3+4q^2+3q
        82: 2q^2+3q
        83: 3q^3+5q^2+3q
        84: q^2+3q
        85: 3q^2+3q
        86: q^2+3q
        87: 4q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^3+4q^2+3q
        95: 2q^3+4q^2+3q
        96: 2q^3+3q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       105: q
       106: q
       107: q
       108: 2q
       109: q^2+2q
       110: q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: q^2+2q
       118: q
       119: q
       120: 2q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 3q^2+3q
       136: 2q^3+4q^2+3q
       137: 3q
       138: q^3+2q^2+2q
       139: q^2+3q
       140: 3q^2+3q
       141: 2q^2+3q
       142: 2q^3+4q^2+3q
       143: 3q
       144: q^2+2q
       145: 3q
       146: q^2+3q
       147: 2q^2+3q
       148: 2q
       149: q^2+3q
       150: 4q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: q^3+3q^2+2q
       154: q^2+q
       155: 3q^2+2q
       156: q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+3q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       171: q
       172: q
       173: q
       175: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: q
       184: 2q
       185: q^2+2q
       186: q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: 2q
       192: q
       193: q
       194: 2q
       195: q^2+2q
       196: q
       197: 2q^2+2q
       198: q^2+q
       199: q
       200: 2q
       201: q
       202: 2q
       203: 2q
       205: q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: 3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q
       227: q^2+3q
       228: q^3+2q^2+2q
       229: 3q^2+3q
       230: 2q^3+4q^2+3q
       231: 2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q
       244: 2q^2+3q
       245: 2q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       265: q
       266: q
       267: q
       269: q
       270: q
       271: q
       272: q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q
       289: q^2+2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       299: q
       300: 2q
       301: q^2+2q
       303: q^2+2q
       304: q
       305: 2q^2+2q
       306: q^2+q
       307: q
       308: 2q
       309: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       319: q
       320: 2q
       321: 2q
       323: q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 2q^2+3q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       389: q
       391: q
       393: q
       395: q
       396: q
       397: q
       401: q
       402: q
       405: q
       408: q
       413: q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 2q
       430: q
       431: q
       433: q
       435: q^2+2q
       437: q
       438: 2q
       439: 2q
       440: q
       441: 2q
       442: q
       443: q
       444: 2q
       445: q^2+2q
       448: q
       449: q
       455: q
       461: 2q
       463: q
       465: 2q
       467: q
       469: q
       471: q
       472: 2q
       473: 2q
       475: q
       476: q
       477: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       500: q
       501: 2q
       508: 2q
       512: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       537: q
       539: q
       541: q
       543: q
       544: q
       545: q
       547: q
       553: q
       561: q
       565: q
       567: q
       569: q
       573: q
       576: q
       577: q
       585: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 2q
       604: q
       605: q
       607: q
       609: q
       613: q
       615: q
       616: 2q
       617: q^2+2q
       631: 2q
       633: q
       639: q
       642: q
       643: q
       651: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 1
       685: q
       689: q
       693: q
       733: q
       735: q
       749: q
       757: q
       765: q
       767: q
       769: q
       775: 1
       779: q+1
       781: q
       786: q
       787: q
       794: 1
       795: q+1
       797: q
       802: q
       803: q
       806: q
       807: q
       809: q
       811: q
       817: 1
       819: 1
       844: 1
       866: 1
       870: q+1
       871: 2q
       874: 1
       880: q
       884: q
       918: 1
       940: 1
       966: 1
       971: 1
       994: 1
       998: 1
      1001: 1
      1013: 1
      1020: q+1
      1022: q
      1027: q
      1028: q
      1036: 1
      1076: 1
      1084: 1
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1230: 1
      1232: 1
      1235: 1
      1274: 1
      1281: 1
      1294: 1
      1348: 1
      1358: 1
      1365: 1
      1433: 1
      1504: 1

1505:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 3q^3+5q^2+3q
        23: q^4+4q^3+5q^2+3q
        24: 3q^3+5q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: 2q^2+3q
        32: 3q^3+5q^2+3q
        33: 2q^3+4q^2+3q
        34: q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 3q^3+5q^2+3q
        53: q^4+4q^3+5q^2+3q
        54: 3q^3+5q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        58: q
        59: q^2+2q
        60: 2q
        61: q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 3q^2+3q
        73: 2q^3+4q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: 2q^2+3q
        81: 2q^3+4q^2+3q
        82: 2q^2+3q
        83: 3q^3+5q^2+3q
        84: q^2+3q
        85: 3q^2+3q
        86: q^2+3q
        87: 4q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^3+4q^2+3q
        95: 2q^3+4q^2+3q
        96: 2q^3+3q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       104: q
       106: q
       107: 2q
       108: q
       109: q
       110: q^2+2q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: q
       118: q^2+2q
       119: 2q
       120: q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 3q^2+3q
       136: 2q^3+4q^2+3q
       137: 3q
       138: q^3+2q^2+2q
       139: q^2+3q
       140: 3q^2+3q
       141: 2q^2+3q
       142: 2q^3+4q^2+3q
       143: 3q
       144: q^2+2q
       145: 3q
       146: q^2+3q
       147: 2q^2+3q
       148: 2q
       149: q^2+3q
       150: 4q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: q^3+3q^2+2q
       154: q^2+q
       155: 3q^2+2q
       156: q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+3q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       170: q
       172: q
       173: q
       174: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: 2q
       184: q
       185: q
       186: q^2+2q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: q
       192: 2q
       193: 2q
       194: q
       195: q
       196: q^2+2q
       197: 2q^2+2q
       198: q^2+q
       199: 2q
       200: q
       201: 2q
       202: q
       204: 2q
       205: q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: 3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q
       227: q^2+3q
       228: q^3+2q^2+2q
       229: 3q^2+3q
       230: 2q^3+4q^2+3q
       231: 2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q
       244: 2q^2+3q
       245: 2q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       264: q
       266: q
       267: q
       268: q
       269: q
       273: q
       274: q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q
       289: q^2+2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: 2q
       300: q
       301: q^2+2q
       303: q
       304: q^2+2q
       305: 2q^2+2q
       306: q^2+q
       307: 2q
       308: q
       310: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       319: 2q
       320: q
       322: 2q
       323: q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 2q^2+3q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       391: q
       393: q
       394: q
       396: q
       399: q
       403: q
       404: q
       406: q
       407: q
       413: q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 2q
       429: q
       432: q
       433: q
       435: q^2+2q
       437: 2q
       438: q
       439: q
       440: 2q
       441: 2q
       442: q
       443: 2q
       444: q
       445: q^2+2q
       447: q
       450: q
       455: q
       462: 2q
       463: q
       465: 2q
       467: q
       469: q
       471: 2q
       472: q
       474: 2q
       475: q
       476: q
       477: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       500: q
       501: 2q
       508: 2q
       512: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       537: q
       539: q
       541: q
       542: q
       543: q
       545: q
       547: q
       555: q
       563: q
       566: q
       568: q
       570: q
       574: q
       575: q
       577: q
       585: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 2q
       603: q
       605: q
       608: q
       609: q
       613: q
       615: 2q
       616: q
       617: q^2+2q
       632: 2q
       633: q
       639: q
       641: q
       644: q
       651: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 1
       685: q
       689: q
       697: q
       733: q
       735: q
       751: q
       758: q
       766: q
       768: q
       769: q
       775: 1
       779: q+1
       781: q
       785: q
       788: q
       793: 1
       795: q+1
       797: q
       801: q
       804: q
       805: q
       808: q
       809: q
       811: q
       818: 1
       819: 1
       844: 1
       866: 1
       870: q+1
       871: 2q
       874: 1
       880: q
       889: q
       916: 1
       942: 1
       965: 1
       971: 1
       994: 1
       999: 1
      1000: 1
      1013: 1
      1020: q+1
      1022: q
      1026: q
      1029: q
      1036: 1
      1076: 1
      1084: 1
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1230: 1
      1233: 1
      1234: 1
      1274: 1
      1281: 1
      1293: 1
      1350: 1
      1356: 1
      1366: 1
      1433: 1
      1505: 1

1506:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       108: 1
       110: 1
       111: q+1
       113: 1
       115: q+1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: 1
       138: q^2+q+1
       139: 1
       140: q+1
       141: 1
       142: q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       159: 1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       176: 1
       177: q+1
       179: 1
       181: q+1
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       194: 1
       196: 1
       197: q+1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: 1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: q+1
       304: 1
       305: q+1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: q+1
       435: q+1
       438: 1
       440: 1
       441: 1
       444: 1
       445: q+1
       448: 1
       450: 1
       451: 1
       455: 1
       462: 1
       463: 1
       465: 1
       467: q+1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: 1
       604: 1
       605: q+1
       608: 1
       609: 1
       613: q+1
       616: 1
       617: q+1
       623: 1
       629: 1
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 1
       685: 1
       689: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       775: 1
       779: q+1
       781: 1
       786: 1
       788: 1
       791: 1
       794: 1
       795: q+1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: q+1
       811: 1
       818: 1
       819: 1
       833: 1
       843: 1
       849: 1
       855: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       922: 1
       927: 1
       930: 1
       942: 1
       961: 1
       967: 1
       968: 1
       994: 1
       999: 1
      1001: 1
      1010: 1
      1012: 1
      1020: q+1
      1022: 1
      1027: 1
      1029: 1
      1036: 1
      1060: 1
      1064: 1
      1076: 1
      1084: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1138: 1
      1154: 1
      1158: 1
      1163: 1
      1230: 1
      1233: 1
      1235: 1
      1274: 1
      1278: 1
      1280: 1
      1295: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1430: 1
      1506: 1

1507:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       112: q+1
       114: 1
       116: q+1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: 1
       138: q^2+q+1
       139: 1
       140: q+1
       141: 1
       142: q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       194: 1
       195: 1
       198: q+1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: 1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: q+1
       303: 1
       306: q+1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: q+1
       436: q+1
       438: 1
       439: 1
       442: 1
       444: 1
       446: q+1
       448: 1
       449: 1
       452: 1
       456: 1
       461: 1
       464: 1
       466: 1
       468: q+1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: 1
       604: 1
       606: q+1
       607: 1
       610: 1
       614: q+1
       616: 1
       618: q+1
       624: 1
       630: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 1
       685: 1
       689: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       776: 1
       780: q+1
       782: 1
       786: 1
       787: 1
       792: 1
       794: 1
       796: q+1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: q+1
       812: 1
       817: 1
       820: 1
       834: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       923: 1
       925: 1
       931: 1
       941: 1
       963: 1
       966: 1
       972: 1
       995: 1
       998: 1
      1001: 1
      1011: 1
      1013: 1
      1021: q+1
      1023: 1
      1027: 1
      1028: 1
      1037: 1
      1061: 1
      1065: 1
      1076: 1
      1084: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1231: 1
      1232: 1
      1235: 1
      1275: 1
      1279: 1
      1281: 1
      1297: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1434: 1
      1507: 1

1508:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       110: 1
       112: q+1
       114: 1
       116: q+1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: 1
       138: q^2+q+1
       139: 1
       140: q+1
       141: 1
       142: q^2+q+1
       143: 1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: 1
       149: 1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: 1
       178: q+1
       180: 1
       182: q+1
       183: 1
       186: 1
       188: q+1
       190: 1
       192: 1
       193: 1
       196: 1
       198: q+1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q^2+q+1
       226: 1
       227: 1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: 1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: q+1
       304: 1
       306: q+1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q+1
       349: 1
       350: q^2+q+1
       351: q+1
       352: 1
       356: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: q+1
       436: q+1
       437: 1
       440: 1
       442: 1
       443: 1
       446: q+1
       447: 1
       450: 1
       452: 1
       456: 1
       462: 1
       464: 1
       466: 1
       468: q+1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       500: 1
       501: 1
       508: 1
       512: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: 1
       603: 1
       606: q+1
       608: 1
       610: 1
       614: q+1
       615: 1
       618: q+1
       624: 1
       630: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 1
       685: 1
       689: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       776: 1
       780: q+1
       782: 1
       785: 1
       788: 1
       792: 1
       793: 1
       796: q+1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: q+1
       812: 1
       818: 1
       820: 1
       834: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: q+1
       871: 1
       874: 1
       880: 1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       921: 1
       926: 1
       929: 1
       943: 1
       962: 1
       965: 1
       972: 1
       995: 1
       999: 1
      1000: 1
      1011: 1
      1013: 1
      1021: q+1
      1023: 1
      1026: 1
      1029: 1
      1037: 1
      1061: 1
      1065: 1
      1076: 1
      1084: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1231: 1
      1233: 1
      1234: 1
      1275: 1
      1279: 1
      1281: 1
      1296: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1434: 1
      1508: 1

1509:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 3q^3+5q^2+3q
        23: q^4+4q^3+5q^2+3q
        24: 3q^3+5q^2+3q
        25: 4q^2+3q
        26: q^3+4q^2+3q
        27: 4q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: 2q^2+3q
        32: 3q^3+5q^2+3q
        33: 2q^3+4q^2+3q
        34: q^2+3q
        35: 4q^2+3q
        36: 3q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 3q^3+5q^2+3q
        53: q^4+4q^3+5q^2+3q
        54: 3q^3+5q^2+3q
        55: 4q^2+3q
        56: q^3+4q^2+3q
        57: 4q^2+3q
        58: q
        59: q^2+2q
        60: q
        61: 2q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 3q^2+3q
        73: 2q^3+4q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: 2q^2+3q
        81: 2q^3+4q^2+3q
        82: 2q^2+3q
        83: 3q^3+5q^2+3q
        84: q^2+3q
        85: 3q^2+3q
        86: q^2+3q
        87: 4q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^3+4q^2+3q
        95: 2q^3+4q^2+3q
        96: 2q^3+3q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: 2q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       104: q
       105: q
       106: q
       107: q
       108: 2q
       109: q
       110: q^2+2q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: q
       118: q^2+2q
       119: q
       120: 2q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 3q^2+3q
       136: 2q^3+4q^2+3q
       137: 3q
       138: q^3+2q^2+2q
       139: q^2+3q
       140: 3q^2+3q
       141: 2q^2+3q
       142: 2q^3+4q^2+3q
       143: 3q
       144: q^2+2q
       145: 3q
       146: q^2+3q
       147: 2q^2+3q
       148: 2q
       149: q^2+3q
       150: 4q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q^2+q
       156: 3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+3q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       170: q
       171: q
       172: q
       174: q
       175: q
       176: q
       178: q
       180: 2q
       182: q^2+2q
       183: q
       184: 2q
       185: q
       186: q^2+2q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: q
       192: 2q
       193: q
       194: 2q
       195: q
       196: q^2+2q
       197: q^2+q
       198: 2q^2+2q
       199: q
       200: 2q
       201: q
       202: 2q
       204: 2q
       205: q
       206: q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q^2+q
       212: 3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q
       227: q^2+3q
       228: q^3+2q^2+2q
       229: 3q^2+3q
       230: 2q^3+4q^2+3q
       231: 2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q
       244: 2q^2+3q
       245: 2q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q
       268: q
       269: q
       270: q
       273: q
       274: q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q
       290: q^2+2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       299: q
       300: 2q
       302: q^2+2q
       303: q
       304: q^2+2q
       305: q^2+q
       306: 2q^2+2q
       307: q
       308: 2q
       310: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       319: q
       320: 2q
       322: 2q
       323: q
       324: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 2q^2+3q
       352: 2q
       356: q^2+2q
       358: q
       359: 2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q
       392: q
       394: q
       395: q
       396: q
       400: q
       403: q
       404: q
       406: q
       407: q
       414: q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 2q
       430: q
       432: q
       434: q
       436: q^2+2q
       437: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: 2q
       443: q
       444: 2q
       446: q^2+2q
       448: q
       450: q
       456: q
       462: 2q
       464: q
       466: 2q
       468: q
       470: q
       471: q
       472: 2q
       474: 2q
       475: q
       476: q
       478: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       500: q
       501: 2q
       508: 2q
       512: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q
       548: q
       556: q
       564: q
       566: q
       568: q
       571: q
       574: q
       575: q
       581: q
       586: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 2q
       604: q
       606: q
       608: q
       610: q
       614: q
       615: q
       616: 2q
       618: q^2+2q
       632: 2q
       634: q
       640: q
       642: q
       644: q
       652: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 1
       685: q
       689: q
       699: q
       734: q
       736: q
       752: q
       759: q
       766: q
       768: q
       773: q
       776: 1
       780: q+1
       782: q
       786: q
       788: q
       794: 1
       796: q+1
       798: q
       802: q
       804: q
       806: q
       808: q
       810: q
       812: q
       818: 1
       820: 1
       843: 1
       866: 1
       870: q+1
       871: 2q
       874: 1
       880: q
       890: q
       919: 1
       943: 1
       967: 1
       969: 1
       995: 1
       999: 1
      1001: 1
      1012: 1
      1021: q+1
      1023: q
      1027: q
      1029: q
      1037: 1
      1076: 1
      1084: 1
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1231: 1
      1233: 1
      1235: 1
      1275: 1
      1280: 1
      1298: 1
      1351: 1
      1359: 1
      1367: 1
      1431: 1
      1509: 1

1510:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^4+5q^3+2q^2+q
        23: q^4+5q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^3+2q^2+q
        26: 2q^3+2q^2+q
        27: q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: 3q^3+q^2+q
        32: 3q^3+2q^2+q
        33: q^4+5q^3+2q^2+q
        34: q^3+q^2+q
        35: q^3+2q^2+q
        36: 2q^3+2q^2+q
        37: 2q^3+2q^2+q
        39: 2q^3+2q^2+q
        41: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 3q^3+2q^2+q
        53: q^4+4q^3+2q^2+q
        54: q^4+2q^3+2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^3
        59: 2q^3+q^2+q
        61: q^3+q^2+q
        62: q^3+q^2+q
        64: q^3+2q^2+q
        66: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^2+q
        73: 2q^3+2q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^3+q^2+q
        81: 3q^3+2q^2+q
        82: 2q^3+q^2+q
        83: 2q^3+2q^2+q
        84: q^2+q
        85: q^3+2q^2+q
        86: q^2+q
        87: 2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 3q^3+2q^2+q
        95: q^4+4q^3+2q^2+q
        96: q^4+2q^3+2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       106: q^3+q^2+q
       108: q^2+q
       110: q^3+q^2+q
       111: 2q^2+q
       113: q^2+q
       115: 2q^2+q
       118: q^2+q
       120: q^2+q
       121: q^2+q
       123: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: 2q^2+q
       136: q^3+2q^2+q
       137: q^3+q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+q^2+q
       140: 2q^2+q
       141: q^3+q^2+q
       142: 2q^3+2q^2+q
       143: q^2+q
       144: 2q^2+q
       145: q^2+q
       146: q^2+q
       147: 2q^2+q
       148: q
       149: q^2+q
       150: 2q^2+q
       151: 2q^2+q
       153: q^3+2q^2+q
       155: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       172: q^2+q
       176: q^2+q
       177: 2q^2+q
       179: q^2+q
       181: 2q^2+q
       184: q^2+q
       186: q^2+q
       187: 2q^2+q
       189: q^2+q
       192: q^2+q
       194: q^2+q
       196: q^3+q^2+q
       197: 2q^2+q
       200: q^2+q
       202: q^2+q
       204: q
       205: q
       207: q^2+q
       209: q^2+q
       211: 2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: 2q^2+q
       224: q
       225: q^3+2q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: q^3+2q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: 2q^2+q
       237: 2q^2+q
       239: q^3+2q^2+q
       241: 2q^2+q
       243: q^2+q
       244: 2q^2+q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       262: q^2+q
       266: q^2+q
       269: q^2+q
       273: q
       278: q^2+q
       279: q
       281: q^2+q
       284: q^2+q
       286: q^2+q
       287: q^2+q
       289: q^2+q
       291: 2q^2+q
       294: q
       296: q
       297: q
       300: q^2+q
       301: 2q^2+q
       304: q^2+q
       305: 2q^2+q
       308: q
       310: q
       311: q
       313: q
       315: 2q^2+q
       317: q^2+q
       320: q^2+q
       322: q
       323: q
       325: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: 2q^2+q
       349: q
       350: q^3+2q^2+q
       351: q^2+q
       352: q
       356: q^2+q
       358: q
       359: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       380: q^2+q
       384: q
       388: q
       391: q^2+q
       396: q^2+q
       399: q
       404: q
       406: q
       413: q
       417: q^2+q
       420: q
       422: q
       423: q
       425: q^2+q
       427: q
       430: q^2+q
       432: q^2+q
       433: 2q^2+q
       435: q^2+q
       438: q
       440: q
       441: q
       444: q
       445: q^2+q
       448: q
       450: q
       451: q
       455: q
       462: q
       463: q
       465: q
       467: q^2+q
       469: q^2+q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       500: q
       508: q
       512: q^2+q
       514: q
       524: q
       532: q
       536: q^2+q
       539: q
       543: q
       547: q
       552: q
       555: q
       563: q
       568: q
       570: q
       575: q
       577: q
       585: q
       590: q
       592: q
       594: q
       596: q
       599: q
       604: q
       605: q^2+q
       608: q
       609: q
       613: q^2+q
       623: q
       629: q
       639: q
       642: q
       644: q
       645: q
       651: q
       675: q
       676: q
       677: q
       689: q
       697: q
       712: q
       716: q
       720: q
       723: q
       727: q
       739: q
       756: q
       758: q
       797: q
       802: q
       804: q
       806: q
       808: q
       811: q
       849: q
       855: q
       922: q
       927: q
       930: q
       961: q
      1010: 1
      1127: 1
      1140: 1
      1278: 1
      1299: 1
      1361: 1
      1432: 1
      1510: 1

1511:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^4+5q^3+2q^2+q
        23: q^4+5q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^3+2q^2+q
        26: 2q^3+2q^2+q
        27: q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: 3q^3+q^2+q
        32: 3q^3+2q^2+q
        33: q^4+5q^3+2q^2+q
        34: q^3+q^2+q
        35: q^3+2q^2+q
        36: 2q^3+2q^2+q
        38: 2q^3+2q^2+q
        40: 2q^3+2q^2+q
        42: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 3q^3+2q^2+q
        53: q^4+4q^3+2q^2+q
        54: q^4+2q^3+2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: 2q^3+q^2+q
        59: q^3
        61: q^3+q^2+q
        63: q^3+q^2+q
        65: q^3+2q^2+q
        67: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^2+q
        73: 2q^3+2q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^3+q^2+q
        81: 3q^3+2q^2+q
        82: 2q^3+q^2+q
        83: 2q^3+2q^2+q
        84: q^2+q
        85: q^3+2q^2+q
        86: q^2+q
        87: 2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 3q^3+2q^2+q
        95: q^4+4q^3+2q^2+q
        96: q^4+2q^3+2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       105: q^3+q^2+q
       108: q^2+q
       109: q^3+q^2+q
       112: 2q^2+q
       114: q^2+q
       116: 2q^2+q
       117: q^2+q
       120: q^2+q
       122: q^2+q
       124: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: 2q^2+q
       136: q^3+2q^2+q
       137: q^3+q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+q^2+q
       140: 2q^2+q
       141: q^3+q^2+q
       142: 2q^3+2q^2+q
       143: q^2+q
       144: 2q^2+q
       145: q^2+q
       146: q^2+q
       147: 2q^2+q
       148: q
       149: q^2+q
       150: 2q^2+q
       152: 2q^2+q
       154: q^3+2q^2+q
       156: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       171: q^2+q
       175: q^2+q
       178: 2q^2+q
       180: q^2+q
       182: 2q^2+q
       184: q^2+q
       185: q^2+q
       188: 2q^2+q
       190: q^2+q
       191: q^2+q
       194: q^2+q
       195: q^3+q^2+q
       198: 2q^2+q
       200: q^2+q
       202: q^2+q
       203: q
       206: q
       208: q^2+q
       210: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: 2q^2+q
       224: q
       225: q^3+2q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: q^3+2q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: 2q^2+q
       238: 2q^2+q
       240: q^3+2q^2+q
       242: 2q^2+q
       243: q^2+q
       244: 2q^2+q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       261: q^2+q
       265: q^2+q
       270: q^2+q
       272: q
       277: q^2+q
       280: q
       282: q^2+q
       284: q^2+q
       285: q^2+q
       288: q^2+q
       290: q^2+q
       292: 2q^2+q
       294: q
       295: q
       298: q
       300: q^2+q
       302: 2q^2+q
       303: q^2+q
       306: 2q^2+q
       308: q
       309: q
       312: q
       314: q
       316: 2q^2+q
       318: q^2+q
       320: q^2+q
       321: q
       324: q
       326: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: 2q^2+q
       349: q
       350: q^3+2q^2+q
       351: q^2+q
       352: q
       356: q^2+q
       358: q
       359: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       379: q^2+q
       383: q
       387: q
       392: q^2+q
       395: q^2+q
       398: q
       402: q
       408: q
       414: q
       418: q^2+q
       420: q
       421: q
       424: q
       426: q^2+q
       428: q
       430: q^2+q
       431: q^2+q
       434: 2q^2+q
       436: q^2+q
       438: q
       439: q
       442: q
       444: q
       446: q^2+q
       448: q
       449: q
       452: q
       456: q
       461: q
       464: q
       466: q
       468: q^2+q
       470: q^2+q
       472: q
       473: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       500: q
       508: q
       512: q^2+q
       514: q
       523: q
       531: q
       535: q^2+q
       540: q
       544: q
       548: q
       550: q
       554: q
       562: q
       567: q
       572: q
       576: q
       581: q
       586: q
       590: q
       591: q
       594: q
       595: q
       600: q
       604: q
       606: q^2+q
       607: q
       610: q
       614: q^2+q
       624: q
       630: q
       640: q
       642: q
       643: q
       646: q
       652: q
       675: q
       676: q
       677: q
       689: q
       700: q
       711: q
       714: q
       719: q
       724: q
       728: q
       738: q
       755: q
       760: q
       798: q
       802: q
       803: q
       806: q
       807: q
       812: q
       850: q
       856: q
       923: q
       925: q
       931: q
       963: q
      1011: 1
      1129: 1
      1143: 1
      1279: 1
      1301: 1
      1362: 1
      1435: 1
      1511: 1

1512:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^4+5q^3+2q^2+q
        23: q^4+5q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^3+2q^2+q
        26: 2q^3+2q^2+q
        27: q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: 3q^3+q^2+q
        32: 3q^3+2q^2+q
        33: q^4+5q^3+2q^2+q
        34: q^3+q^2+q
        35: q^3+2q^2+q
        36: 2q^3+2q^2+q
        38: 2q^3+2q^2+q
        40: 2q^3+2q^2+q
        42: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 3q^3+2q^2+q
        53: q^4+4q^3+2q^2+q
        54: q^4+2q^3+2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^3
        59: 2q^3+q^2+q
        60: q^3+q^2+q
        63: q^3+q^2+q
        65: q^3+2q^2+q
        67: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^2+q
        73: 2q^3+2q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^3+q^2+q
        81: 3q^3+2q^2+q
        82: 2q^3+q^2+q
        83: 2q^3+2q^2+q
        84: q^2+q
        85: q^3+2q^2+q
        86: q^2+q
        87: 2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 3q^3+2q^2+q
        95: q^4+4q^3+2q^2+q
        96: q^4+2q^3+2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       104: q^3+q^2+q
       107: q^2+q
       110: q^3+q^2+q
       112: 2q^2+q
       114: q^2+q
       116: 2q^2+q
       118: q^2+q
       119: q^2+q
       122: q^2+q
       124: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: 2q^2+q
       136: q^3+2q^2+q
       137: q^3+q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+q^2+q
       140: 2q^2+q
       141: q^3+q^2+q
       142: 2q^3+2q^2+q
       143: q^2+q
       144: 2q^2+q
       145: q^2+q
       146: q^2+q
       147: 2q^2+q
       148: q
       149: q^2+q
       150: 2q^2+q
       152: 2q^2+q
       154: q^3+2q^2+q
       156: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       170: q^2+q
       174: q^2+q
       178: 2q^2+q
       180: q^2+q
       182: 2q^2+q
       183: q^2+q
       186: q^2+q
       188: 2q^2+q
       190: q^2+q
       192: q^2+q
       193: q^2+q
       196: q^3+q^2+q
       198: 2q^2+q
       199: q^2+q
       201: q^2+q
       204: q
       206: q
       208: q^2+q
       210: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: 2q^2+q
       224: q
       225: q^3+2q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: q^3+2q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: 2q^2+q
       238: 2q^2+q
       240: q^3+2q^2+q
       242: 2q^2+q
       243: q^2+q
       244: 2q^2+q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2+q
       264: q^2+q
       268: q^2+q
       274: q
       276: q^2+q
       280: q
       282: q^2+q
       283: q^2+q
       286: q^2+q
       288: q^2+q
       290: q^2+q
       292: 2q^2+q
       293: q
       296: q
       298: q
       299: q^2+q
       302: 2q^2+q
       304: q^2+q
       306: 2q^2+q
       307: q
       310: q
       312: q
       314: q
       316: 2q^2+q
       318: q^2+q
       319: q^2+q
       322: q
       324: q
       326: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: 2q^2+q
       349: q
       350: q^3+2q^2+q
       351: q^2+q
       352: q
       356: q^2+q
       358: q
       359: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       378: q^2+q
       382: q
       386: q
       390: q^2+q
       394: q^2+q
       400: q
       403: q
       407: q
       414: q
       418: q^2+q
       419: q
       422: q
       424: q
       426: q^2+q
       428: q
       429: q^2+q
       432: q^2+q
       434: 2q^2+q
       436: q^2+q
       437: q
       440: q
       442: q
       443: q
       446: q^2+q
       447: q
       450: q
       452: q
       456: q
       462: q
       464: q
       466: q
       468: q^2+q
       470: q^2+q
       471: q
       474: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       500: q
       508: q
       512: q^2+q
       514: q
       522: q
       530: q
       534: q^2+q
       538: q
       542: q
       546: q
       551: q
       556: q
       564: q
       566: q
       571: q
       574: q
       581: q
       586: q
       589: q
       592: q
       593: q
       596: q
       600: q
       603: q
       606: q^2+q
       608: q
       610: q
       614: q^2+q
       624: q
       630: q
       640: q
       641: q
       644: q
       646: q
       652: q
       675: q
       676: q
       677: q
       689: q
       699: q
       710: q
       715: q
       718: q
       722: q
       726: q
       740: q
       754: q
       759: q
       798: q
       801: q
       804: q
       805: q
       808: q
       812: q
       850: q
       856: q
       921: q
       926: q
       929: q
       962: q
      1011: 1
      1128: 1
      1143: 1
      1279: 1
      1300: 1
      1363: 1
      1435: 1
      1512: 1

1513:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q^2+q+1
        36: q^2+q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        60: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q^2+q+1
        86: 1
        87: q^2+q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       111: q+1
       113: 1
       115: q+1
       117: 1
       119: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q^2+q+1
       145: 1
       146: 1
       147: q^2+q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: 1
       177: q+1
       179: 1
       181: q+1
       183: 1
       185: 1
       187: q+1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: q+1
       207: 1
       209: 1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: 1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: q+1
       283: 1
       285: 1
       287: 1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: q+1
       313: q+1
       315: q+1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: q+1
       453: 1
       455: q+1
       457: 1
       459: 1
       461: 1
       463: q+1
       465: 1
       467: q+1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: 1
       605: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: q+1
       625: 1
       629: q+1
       631: 1
       633: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 1
       765: 1
       769: 1
       775: 1
       779: q+1
       781: 1
       785: 1
       787: 1
       791: 1
       793: 1
       795: 1
       809: 1
       817: 1
       819: q+1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: q+1
       835: 1
       843: 1
       849: 1
       855: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       940: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 1
       968: 1
       994: 1
       998: 1
      1000: 1
      1010: 1
      1012: 1
      1020: 1
      1036: q+1
      1038: 1
      1040: 1
      1044: 1
      1060: 1
      1064: 1
      1080: 1
      1084: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1138: 1
      1172: 1
      1176: 1
      1180: 1
      1248: 1
      1250: 1
      1254: 1
      1274: 1
      1278: 1
      1280: 1
      1290: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1430: 1
      1513: 1

1514:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 3q^3+5q^2+3q
        26: q^4+4q^3+5q^2+3q
        27: 3q^3+5q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        34: 2q^2+3q
        35: 3q^3+5q^2+3q
        36: 2q^3+4q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 3q^3+5q^2+3q
        56: q^4+4q^3+5q^2+3q
        57: 3q^3+5q^2+3q
        58: 2q
        59: q
        60: q^2+2q
        61: q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 2q^3+4q^2+3q
        73: 3q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: q^2+3q
        81: 3q^2+3q
        82: q^2+3q
        83: 4q^2+3q
        84: 2q^2+3q
        85: 2q^3+4q^2+3q
        86: 2q^2+3q
        87: 3q^3+5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^3+4q^2+3q
        98: 2q^3+4q^2+3q
        99: 2q^3+3q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       104: q
       105: q
       107: q^2+2q
       108: q
       109: 2q
       110: q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: 2q
       118: q
       119: q^2+2q
       120: q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 2q^3+4q^2+3q
       136: 3q^2+3q
       137: 3q
       138: q^2+2q
       139: 3q
       140: 2q
       141: q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^3+2q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 2q^3+4q^2+3q
       148: 3q^2+3q
       149: q^2+3q
       150: 4q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q^2+q
       156: 3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+3q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       170: q
       171: q
       173: q
       174: q
       175: q
       178: q
       180: 2q
       182: q^2+2q
       183: q^2+2q
       184: q
       185: 2q
       186: q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: 2q
       192: q
       193: 2q
       195: 2q
       196: q
       197: q
       198: q
       199: 2q
       200: q
       201: q^2+2q
       202: q
       203: 2q
       204: q
       205: q^2+q
       206: 2q^2+2q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q^2+q
       212: 3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^3+2q^2+2q
       234: 2q^3+4q^2+3q
       235: 3q^2+3q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q
       244: 2q
       245: 2q^2+3q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: q
       261: q
       263: q
       264: q
       265: q
       267: q
       268: q
       271: q
       272: q
       274: q
       275: q
       276: q
       277: q
       280: 2q
       282: q
       283: q
       285: q
       288: q
       290: q^2+2q
       292: q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: 2q
       299: 2q
       302: q
       303: 2q
       304: q
       305: q
       306: q
       307: q^2+2q
       308: q
       309: 2q
       310: q
       312: q^2+2q
       313: q^2+q
       314: 2q^2+2q
       316: q
       318: 2q
       319: 2q
       321: 2q
       322: q
       323: q
       324: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q
       393: q
       394: q
       398: q
       400: q
       401: q
       402: q
       403: q
       405: q
       407: q
       414: q
       418: q
       419: q
       421: q
       424: q
       426: q
       428: 2q
       429: q
       431: q
       436: q
       443: 2q
       446: q
       447: q
       449: q
       452: q
       453: 2q
       454: q
       456: q^2+2q
       457: 2q
       458: q
       459: q
       460: 2q
       461: 2q
       462: q
       464: q^2+2q
       466: 2q
       468: q
       470: q
       471: 2q
       473: 2q
       474: q
       475: q
       476: q
       478: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       512: q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       538: q
       546: q
       554: q
       556: q
       557: q
       558: q
       560: q
       562: q
       564: q
       565: q
       566: q
       571: q
       573: q
       574: q
       581: q
       586: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: 2q
       615: 2q
       618: q
       619: q
       621: q
       624: q
       626: q
       630: q
       631: 2q
       632: q
       634: q^2+2q
       640: q
       641: q
       643: q
       652: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       674: 1
       679: q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       689: q
       699: q
       734: q
       750: q
       752: q
       759: q
       765: q
       766: q
       773: q
       776: 1
       780: q+1
       782: q
       785: q
       787: q
       793: 1
       796: 1
       817: 1
       820: q+1
       822: q
       825: q
       827: q
       829: q
       831: q
       834: q
       836: q
       843: 1
       866: 1
       870: 1
       874: q+1
       875: 2q
       880: q
       890: q
       917: 1
       941: 1
       964: 1
       969: 1
       995: 1
       998: 1
      1000: 1
      1012: 1
      1021: 1
      1037: q+1
      1039: q
      1040: q
      1044: q
      1080: 1
      1084: 1
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1249: 1
      1250: 1
      1254: 1
      1275: 1
      1280: 1
      1291: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1514: 1

1515:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: 2q^3+2q^2+q
        23: 2q^3+2q^2+q
        24: q^3+2q^2+q
        25: q^4+5q^3+2q^2+q
        26: q^4+5q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: q^3+q^2+q
        32: q^3+2q^2+q
        33: 2q^3+2q^2+q
        34: 3q^3+q^2+q
        35: 3q^3+2q^2+q
        36: q^4+5q^3+2q^2+q
        37: 2q^3+2q^2+q
        39: 2q^3+2q^2+q
        41: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 3q^3+2q^2+q
        56: q^4+4q^3+2q^2+q
        57: q^4+2q^3+2q^2+q
        58: q^3+q^2+q
        60: 2q^3+q^2+q
        61: q^3
        62: q^3+q^2+q
        64: q^3+2q^2+q
        66: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^3+2q^2+q
        73: 2q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^2+q
        81: q^3+2q^2+q
        82: q^2+q
        83: 2q^2+q
        84: q^3+q^2+q
        85: 3q^3+2q^2+q
        86: 2q^3+q^2+q
        87: 2q^3+2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 3q^3+2q^2+q
        98: q^4+4q^3+2q^2+q
        99: q^4+2q^3+2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       103: q^3+q^2+q
       107: q^3+q^2+q
       109: q^2+q
       111: 2q^2+q
       113: q^2+q
       115: 2q^2+q
       117: q^2+q
       119: q^2+q
       121: q^2+q
       123: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^2+q
       137: q^2+q
       138: 2q^2+q
       139: q^2+q
       140: q
       141: q^2+q
       142: 2q^2+q
       143: q^3+q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+2q^2+q
       148: 2q^2+q
       149: q^2+q
       150: 2q^2+q
       151: 2q^2+q
       153: q^3+2q^2+q
       155: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       169: q^2+q
       173: q^2+q
       177: 2q^2+q
       179: q^2+q
       181: 2q^2+q
       183: q^2+q
       185: q^2+q
       187: 2q^2+q
       189: q^2+q
       191: q^2+q
       193: q
       195: q^2+q
       197: q
       199: q^2+q
       201: q^3+q^2+q
       203: q^2+q
       205: 2q^2+q
       207: q^2+q
       209: q^2+q
       211: 2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+2q^2+q
       224: q
       225: 2q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: 2q^2+q
       236: 2q^2+q
       237: 2q^2+q
       239: q^3+2q^2+q
       241: 2q^2+q
       243: q^2+q
       244: q
       245: 2q^2+q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2+q
       263: q^2+q
       267: q
       271: q^2+q
       275: q^2+q
       279: q
       281: q^2+q
       283: q^2+q
       285: q^2+q
       287: q^2+q
       289: q^2+q
       291: 2q^2+q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q^2+q
       309: q^2+q
       311: 2q^2+q
       313: 2q^2+q
       315: 2q^2+q
       317: q^2+q
       319: q
       321: q^2+q
       323: q
       325: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+2q^2+q
       357: q
       358: 2q^2+q
       359: q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       377: q^2+q
       381: q
       385: q
       389: q
       393: q
       397: q^2+q
       401: q^2+q
       405: q
       413: q
       417: q^2+q
       419: q
       421: q
       423: q
       425: q^2+q
       427: q
       429: q
       431: q
       433: q
       435: q
       443: q
       445: q
       447: q^2+q
       449: q^2+q
       451: 2q^2+q
       453: q
       455: q^2+q
       457: q
       459: q
       461: q
       463: q^2+q
       465: q
       467: q^2+q
       469: q^2+q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       495: q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q
       512: q
       514: q^2+q
       521: q
       529: q
       533: q
       537: q
       545: q
       549: q^2+q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       585: q
       589: q
       591: q
       593: q
       595: q
       599: q
       605: q
       613: q
       619: q
       621: q
       623: q^2+q
       625: q
       629: q^2+q
       639: q
       641: q
       643: q
       645: q
       651: q
       681: q
       682: q
       683: q
       689: q
       693: q
       709: q
       713: q
       717: q
       721: q
       737: q
       741: q
       753: q
       757: q
       821: q
       825: q
       827: q
       829: q
       831: q
       835: q
       849: q
       855: q
       944: q
       948: q
       952: q
       960: q
      1010: 1
      1126: 1
      1140: 1
      1278: 1
      1292: 1
      1392: 1
      1432: 1
      1515: 1

1516:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 3q^3+5q^2+3q
        26: q^4+4q^3+5q^2+3q
        27: 3q^3+5q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        34: 2q^2+3q
        35: 3q^3+5q^2+3q
        36: 2q^3+4q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 3q^3+5q^2+3q
        56: q^4+4q^3+5q^2+3q
        57: 3q^3+5q^2+3q
        58: q
        59: 2q
        60: q^2+2q
        61: q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 2q^3+4q^2+3q
        73: 3q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: q^2+3q
        81: 3q^2+3q
        82: q^2+3q
        83: 4q^2+3q
        84: 2q^2+3q
        85: 2q^3+4q^2+3q
        86: 2q^2+3q
        87: 3q^3+5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^3+4q^2+3q
        98: 2q^3+4q^2+3q
        99: 2q^3+3q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       104: q
       106: q
       107: q^2+2q
       108: q
       109: q
       110: 2q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: q
       118: 2q
       119: q^2+2q
       120: q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 2q^3+4q^2+3q
       136: 3q^2+3q
       137: 3q
       138: q^2+2q
       139: 3q
       140: 2q
       141: q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^3+2q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 2q^3+4q^2+3q
       148: 3q^2+3q
       149: q^2+3q
       150: 4q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: q^3+3q^2+2q
       154: q^2+q
       155: 3q^2+2q
       156: q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+3q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       170: q
       172: q
       173: q
       174: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: q^2+2q
       184: q
       185: q
       186: 2q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: q
       192: 2q
       193: 2q
       195: q
       196: 2q
       197: q
       198: q
       199: 2q
       200: q
       201: q^2+2q
       202: q
       203: q
       204: 2q
       205: 2q^2+2q
       206: q^2+q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: 3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^3+2q^2+2q
       234: 2q^3+4q^2+3q
       235: 3q^2+3q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q
       244: 2q
       245: 2q^2+3q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       264: q
       266: q
       267: q
       268: q
       271: q
       273: q
       274: q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q
       289: q^2+2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: 2q
       301: q
       303: q
       304: 2q
       305: q
       306: q
       307: q^2+2q
       308: q
       309: q
       310: 2q
       311: q^2+2q
       313: 2q^2+2q
       314: q^2+q
       315: q
       317: 2q
       319: 2q
       321: q
       322: 2q
       323: q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       393: q
       394: q
       397: q
       399: q
       401: q
       403: q
       404: q
       405: q
       407: q
       413: q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 2q
       429: q
       432: q
       435: q
       443: 2q
       445: q
       447: q
       450: q
       451: q
       453: 2q
       454: q
       455: q^2+2q
       457: q
       458: 2q
       459: 2q
       460: q
       461: q
       462: 2q
       463: q^2+2q
       465: 2q
       467: q
       469: q
       471: 2q
       473: q
       474: 2q
       475: q
       476: q
       477: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       512: q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       537: q
       545: q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q
       563: q
       565: q
       566: q
       569: q
       573: q
       574: q
       577: q
       585: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 2q
       615: 2q
       617: q
       619: q
       622: q
       623: q
       625: q
       629: q
       631: q
       632: 2q
       633: q^2+2q
       639: q
       641: q
       644: q
       651: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       674: 1
       679: q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       689: q
       693: q
       733: q
       749: q
       751: q
       757: q
       765: q
       766: q
       769: q
       775: 1
       779: q+1
       781: q
       785: q
       788: q
       793: 1
       795: 1
       818: 1
       819: q+1
       821: q
       825: q
       828: q
       829: q
       832: q
       833: q
       835: q
       844: 1
       866: 1
       870: 1
       874: q+1
       875: 2q
       880: q
       884: q
       916: 1
       942: 1
       965: 1
       971: 1
       994: 1
       999: 1
      1000: 1
      1013: 1
      1020: 1
      1036: q+1
      1038: q
      1040: q
      1045: q
      1080: 1
      1084: 1
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1248: 1
      1251: 1
      1254: 1
      1274: 1
      1281: 1
      1293: 1
      1382: 1
      1388: 1
      1397: 1
      1433: 1
      1516: 1

1517:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 3q^3+5q^2+3q
        26: q^4+4q^3+5q^2+3q
        27: 3q^3+5q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        34: 2q^2+3q
        35: 3q^3+5q^2+3q
        36: 2q^3+4q^2+3q
        37: 3q^2+2q
        38: q^2+q
        39: q^3+3q^2+2q
        40: q^2+q
        41: 3q^2+2q
        42: q^2+q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 3q^3+5q^2+3q
        56: q^4+4q^3+5q^2+3q
        57: 3q^3+5q^2+3q
        58: 2q
        59: q
        60: q
        61: q^2+2q
        62: q^2+2q
        63: q
        64: 3q^2+2q
        65: q^2+q
        66: 2q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 2q^3+4q^2+3q
        73: 3q^2+3q
        74: 3q^2+2q
        75: q^2+q
        76: q^3+3q^2+2q
        77: q^2+q
        78: 3q^2+2q
        79: q^2+q
        80: q^2+3q
        81: 3q^2+3q
        82: q^2+3q
        83: 4q^2+3q
        84: 2q^2+3q
        85: 2q^3+4q^2+3q
        86: 2q^2+3q
        87: 3q^3+5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^3+4q^2+3q
        98: 2q^3+4q^2+3q
        99: 2q^3+3q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       103: q
       105: q
       106: q
       107: q
       108: q^2+2q
       109: 2q
       110: q
       111: 2q^2+2q
       112: q^2+q
       113: q^2+2q
       114: q
       115: 3q^2+2q
       116: q^2+q
       117: 2q
       118: q
       119: q
       120: q^2+2q
       121: q^2+2q
       122: q
       123: 2q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 2q^3+4q^2+3q
       136: 3q^2+3q
       137: 3q
       138: q^2+2q
       139: 3q
       140: 2q
       141: q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^3+2q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 2q^3+4q^2+3q
       148: 3q^2+3q
       149: q^2+3q
       150: 4q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: q^3+3q^2+2q
       154: q^2+q
       155: 3q^2+2q
       156: q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+3q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       169: q
       171: q
       172: q
       173: q
       175: q
       176: q
       177: q
       179: 2q
       181: q^2+2q
       183: q
       184: q^2+2q
       185: 2q
       186: q
       187: 2q^2+2q
       188: q^2+q
       189: q^2+2q
       190: q
       191: 2q
       192: q
       194: 2q
       195: 2q
       196: q
       197: q
       198: q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       203: 2q
       204: q
       205: 2q^2+2q
       206: q^2+q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: 3q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^3+2q^2+2q
       234: 2q^3+4q^2+3q
       235: 3q^2+3q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q
       244: 2q
       245: 2q^2+3q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       265: q
       266: q
       269: q
       270: q
       271: q
       272: q
       273: q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q
       289: q^2+2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       300: 2q
       301: q
       303: 2q
       304: q
       305: q
       306: q
       307: q
       308: q^2+2q
       309: 2q
       310: q
       311: q^2+2q
       313: 2q^2+2q
       314: q^2+q
       315: q
       317: 2q
       320: 2q
       321: 2q
       322: q
       323: q
       324: q
       325: q^2+2q
       326: q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       391: q
       395: q
       396: q
       397: q
       399: q
       401: q
       402: q
       404: q
       406: q
       408: q
       413: q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 2q
       430: q
       431: q
       435: q
       444: 2q
       445: q
       448: q
       449: q
       451: q
       453: q
       454: 2q
       455: q^2+2q
       457: 2q
       458: q
       459: 2q
       460: q
       461: 2q
       462: q
       463: q^2+2q
       465: 2q
       467: q
       469: q
       472: 2q
       473: 2q
       474: q
       475: q
       476: q
       477: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       512: q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       539: q
       547: q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: q
       563: q
       567: q
       568: q
       570: q
       575: q
       576: q
       577: q
       585: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 2q
       616: 2q
       617: q
       620: q
       621: q
       623: q
       625: q
       629: q
       631: 2q
       632: q
       633: q^2+2q
       639: q
       642: q
       643: q
       651: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       674: 1
       679: q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       689: q
       697: q
       735: q
       749: q
       751: q
       758: q
       767: q
       768: q
       769: q
       775: 1
       779: q+1
       781: q
       786: q
       787: q
       794: 1
       795: 1
       817: 1
       819: q+1
       821: q
       826: q
       827: q
       830: q
       831: q
       833: q
       835: q
       844: 1
       866: 1
       870: 1
       874: q+1
       875: 2q
       880: q
       889: q
       918: 1
       940: 1
       966: 1
       971: 1
       994: 1
       998: 1
      1001: 1
      1013: 1
      1020: 1
      1036: q+1
      1038: q
      1041: q
      1044: q
      1080: 1
      1084: 1
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1248: 1
      1250: 1
      1255: 1
      1274: 1
      1281: 1
      1294: 1
      1380: 1
      1390: 1
      1398: 1
      1433: 1
      1517: 1

1518:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q^2+q+1
        36: q^2+q+1
        37: q+1
        39: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        61: 1
        62: 1
        64: q+1
        66: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q^2+q+1
        86: 1
        87: q^2+q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       106: 1
       108: 1
       110: 1
       111: q+1
       113: 1
       115: q+1
       118: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       127: q+1
       129: q+1
       131: q+1
       133: 1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q^2+q+1
       145: 1
       146: 1
       147: q^2+q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       176: 1
       177: q+1
       179: 1
       181: q+1
       184: 1
       186: 1
       187: q+1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: q+1
       207: 1
       209: 1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: 1
       244: 1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: q+1
       284: 1
       286: 1
       287: 1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: q+1
       313: q+1
       315: q+1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: q+1
       454: 1
       455: q+1
       458: 1
       459: 1
       462: 1
       463: q+1
       465: 1
       467: q+1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: 1
       605: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: q+1
       625: 1
       629: q+1
       632: 1
       633: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       651: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 1
       768: 1
       769: 1
       775: 1
       779: q+1
       781: 1
       786: 1
       788: 1
       791: 1
       794: 1
       795: 1
       809: 1
       818: 1
       819: q+1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: q+1
       835: 1
       843: 1
       849: 1
       855: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       942: 1
       946: 1
       950: 1
       955: 1
       961: 1
       967: 1
       968: 1
       994: 1
       999: 1
      1001: 1
      1010: 1
      1012: 1
      1020: 1
      1036: q+1
      1038: 1
      1041: 1
      1045: 1
      1060: 1
      1064: 1
      1080: 1
      1084: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1138: 1
      1174: 1
      1178: 1
      1183: 1
      1248: 1
      1251: 1
      1255: 1
      1274: 1
      1278: 1
      1280: 1
      1295: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1430: 1
      1518: 1

1519:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q^2+q+1
        36: q^2+q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        60: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q^2+q+1
        86: 1
        87: q^2+q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       107: 1
       110: 1
       112: q+1
       114: 1
       116: q+1
       118: 1
       119: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q^2+q+1
       145: 1
       146: 1
       147: q^2+q+1
       148: q+1
       149: 1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: 1
       178: q+1
       180: 1
       182: q+1
       183: 1
       186: 1
       188: q+1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: q+1
       208: 1
       210: 1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: q+1
       283: 1
       286: 1
       288: 1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: q+1
       314: q+1
       316: q+1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: q+1
       453: 1
       456: q+1
       458: 1
       460: 1
       462: 1
       464: q+1
       466: 1
       468: q+1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: 1
       606: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: q+1
       626: 1
       630: q+1
       632: 1
       634: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 1
       766: 1
       773: 1
       776: 1
       780: q+1
       782: 1
       785: 1
       788: 1
       792: 1
       793: 1
       796: 1
       810: 1
       818: 1
       820: q+1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: q+1
       836: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       965: 1
       972: 1
       995: 1
       999: 1
      1000: 1
      1011: 1
      1013: 1
      1021: 1
      1037: q+1
      1039: 1
      1040: 1
      1045: 1
      1061: 1
      1065: 1
      1080: 1
      1084: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1142: 1
      1175: 1
      1177: 1
      1181: 1
      1249: 1
      1251: 1
      1254: 1
      1275: 1
      1279: 1
      1281: 1
      1296: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1434: 1
      1519: 1

1520:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: q+1
        33: q+1
        34: 1
        35: q^2+q+1
        36: q^2+q+1
        38: q+1
        40: q+1
        42: q+1
        43: 1
        44: 1
        45: 1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        61: 1
        63: 1
        65: q+1
        67: q+1
        68: 1
        69: q^2+q+1
        70: 1
        71: 1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q^2+q+1
        86: 1
        87: q^2+q+1
        88: 1
        89: 1
        90: 1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       108: 1
       109: 1
       112: q+1
       114: 1
       116: q+1
       117: 1
       120: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       130: q+1
       132: q+1
       133: 1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: q^2+q+1
       145: 1
       146: 1
       147: q^2+q+1
       148: q+1
       149: 1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       184: 1
       185: 1
       188: q+1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: q+1
       208: 1
       210: 1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: q+1
       284: 1
       285: 1
       288: 1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: q+1
       314: q+1
       316: q+1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       348: 1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       456: q+1
       457: 1
       460: 1
       461: 1
       464: q+1
       466: 1
       468: q+1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       508: 1
       512: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: 1
       606: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: q+1
       626: 1
       630: q+1
       631: 1
       634: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       652: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       674: 1
       679: 1
       680: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       689: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 1
       767: 1
       773: 1
       776: 1
       780: q+1
       782: 1
       786: 1
       787: 1
       792: 1
       794: 1
       796: 1
       810: 1
       817: 1
       820: q+1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: q+1
       836: 1
       844: 1
       850: 1
       856: 1
       866: 1
       870: 1
       874: q+1
       875: 1
       880: 1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       941: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 1
       972: 1
       995: 1
       998: 1
      1001: 1
      1011: 1
      1013: 1
      1021: 1
      1037: q+1
      1039: 1
      1041: 1
      1044: 1
      1061: 1
      1065: 1
      1080: 1
      1084: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1142: 1
      1173: 1
      1179: 1
      1182: 1
      1249: 1
      1250: 1
      1255: 1
      1275: 1
      1279: 1
      1281: 1
      1297: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1434: 1
      1520: 1

1521:    0: 3q^3+5q^2+3q
         1: q^4+4q^3+5q^2+3q
         2: 3q^3+5q^2+3q
         3: q^4+4q^3+5q^2+3q
         4: 3q^3+5q^2+3q
         5: 3q^3+5q^2+3q
         6: q^4+4q^3+5q^2+3q
         7: 3q^3+5q^2+3q
         8: 3q^3+5q^2+3q
         9: q^4+3q^3+3q^2+2q
        10: 2q^2+3q
        11: 2q^2+3q
        12: 2q^2+3q
        13: 3q^3+5q^2+3q
        14: 3q^3+5q^2+3q
        15: 3q^3+5q^2+3q
        16: 2q^3+4q^2+3q
        17: 2q^3+4q^2+3q
        18: 2q^3+3q^2+2q
        19: 3q^3+5q^2+3q
        20: q^4+4q^3+5q^2+3q
        21: 3q^3+5q^2+3q
        22: 4q^2+3q
        23: q^3+4q^2+3q
        24: 4q^2+3q
        25: 3q^3+5q^2+3q
        26: q^4+4q^3+5q^2+3q
        27: 3q^3+5q^2+3q
        28: q^2+3q
        29: 2q^2+3q
        30: 3q^3+5q^2+3q
        31: q^2+3q
        32: 4q^2+3q
        33: 3q^2+3q
        34: 2q^2+3q
        35: 3q^3+5q^2+3q
        36: 2q^3+4q^2+3q
        37: q^2+q
        38: 3q^2+2q
        39: q^2+q
        40: q^3+3q^2+2q
        41: q^2+q
        42: 3q^2+2q
        43: 2q^2+3q
        44: 2q^2+3q
        45: 2q^2+3q
        46: 2q^3+4q^2+3q
        47: 2q^3+4q^2+3q
        48: 2q^3+3q^2+2q
        49: 2q^3+4q^2+3q
        50: 2q^3+4q^2+3q
        51: 2q^3+3q^2+2q
        52: 4q^2+3q
        53: q^3+4q^2+3q
        54: 4q^2+3q
        55: 3q^3+5q^2+3q
        56: q^4+4q^3+5q^2+3q
        57: 3q^3+5q^2+3q
        58: q
        59: 2q
        60: q
        61: q^2+2q
        62: q
        63: q^2+2q
        64: q^2+q
        65: 3q^2+2q
        66: q^2+q
        67: 2q^2+2q
        68: q^2+3q
        69: q^3+2q^2+2q
        70: 2q^2+3q
        71: q^2+3q
        72: 2q^3+4q^2+3q
        73: 3q^2+3q
        74: q^2+q
        75: 3q^2+2q
        76: q^2+q
        77: q^3+3q^2+2q
        78: q^2+q
        79: 3q^2+2q
        80: q^2+3q
        81: 3q^2+3q
        82: q^2+3q
        83: 4q^2+3q
        84: 2q^2+3q
        85: 2q^3+4q^2+3q
        86: 2q^2+3q
        87: 3q^3+5q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+3q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: 2q^2+2q
        97: 2q^3+4q^2+3q
        98: 2q^3+4q^2+3q
        99: 2q^3+3q^2+2q
       100: 4q^2+3q
       101: q^3+4q^2+3q
       102: 4q^2+3q
       104: q
       105: q
       106: q
       107: q
       108: q^2+2q
       109: q
       110: 2q
       111: q^2+q
       112: 2q^2+2q
       113: q
       114: q^2+2q
       115: q^2+q
       116: 3q^2+2q
       117: q
       118: 2q
       119: q
       120: q^2+2q
       121: q
       122: q^2+2q
       123: q^2+q
       124: 2q^2+2q
       125: 3q
       126: 2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: q^2+3q
       134: q^3+2q^2+2q
       135: 2q^3+4q^2+3q
       136: 3q^2+3q
       137: 3q
       138: q^2+2q
       139: 3q
       140: 2q
       141: q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^3+2q^2+2q
       145: q^2+3q
       146: 2q^2+3q
       147: 2q^3+4q^2+3q
       148: 3q^2+3q
       149: q^2+3q
       150: 4q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: q^3+3q^2+2q
       155: q^2+q
       156: 3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+3q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: 2q^2+2q
       170: q
       171: q
       172: q
       174: q
       175: q
       176: q
       178: q
       180: 2q
       182: q^2+2q
       183: q
       184: q^2+2q
       185: q
       186: 2q
       187: q^2+q
       188: 2q^2+2q
       189: q
       190: q^2+2q
       191: q
       192: 2q
       194: 2q
       195: q
       196: 2q
       197: q
       198: q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       203: q
       204: 2q
       205: q^2+q
       206: 2q^2+2q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q^2+q
       212: 3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^3+2q^2+2q
       234: 2q^3+4q^2+3q
       235: 3q^2+3q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q
       244: 2q
       245: 2q^2+3q
       246: q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: 2q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q
       269: q
       270: q
       272: q
       273: q
       274: q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q
       290: q^2+2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       300: 2q
       302: q
       303: q
       304: 2q
       305: q
       306: q
       307: q
       308: q^2+2q
       309: q
       310: 2q
       312: q^2+2q
       313: q^2+q
       314: 2q^2+2q
       316: q
       318: 2q
       320: 2q
       321: q
       322: 2q
       323: q
       324: q
       325: q
       326: q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: 3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: 2q
       348: q
       350: q^2+2q
       351: 2q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       392: q
       395: q
       396: q
       398: q
       400: q
       402: q
       403: q
       404: q
       406: q
       408: q
       414: q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 2q
       430: q
       432: q
       436: q
       444: 2q
       446: q
       448: q
       450: q
       452: q
       453: q
       454: 2q
       456: q^2+2q
       457: q
       458: 2q
       459: q
       460: 2q
       461: q
       462: 2q
       464: q^2+2q
       466: 2q
       468: q
       470: q
       472: 2q
       473: q
       474: 2q
       475: q
       476: q
       478: q
       479: q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       495: q
       496: 2q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       512: q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       540: q
       548: q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q
       564: q
       567: q
       568: q
       572: q
       575: q
       576: q
       581: q
       586: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 2q
       616: 2q
       618: q
       620: q
       622: q
       624: q
       626: q
       630: q
       631: q
       632: 2q
       634: q^2+2q
       640: q
       642: q
       644: q
       652: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       674: 1
       679: q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       689: q
       700: q
       736: q
       750: q
       752: q
       760: q
       767: q
       768: q
       773: q
       776: 1
       780: q+1
       782: q
       786: q
       788: q
       794: 1
       796: 1
       818: 1
       820: q+1
       822: q
       826: q
       828: q
       830: q
       832: q
       834: q
       836: q
       843: 1
       866: 1
       870: 1
       874: q+1
       875: 2q
       880: q
       891: q
       919: 1
       943: 1
       967: 1
       969: 1
       995: 1
       999: 1
      1001: 1
      1012: 1
      1021: 1
      1037: q+1
      1039: q
      1041: q
      1045: q
      1080: 1
      1084: 1
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1249: 1
      1251: 1
      1255: 1
      1275: 1
      1280: 1
      1298: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1521: 1

1522:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: 2q^3+2q^2+q
        23: 2q^3+2q^2+q
        24: q^3+2q^2+q
        25: q^4+5q^3+2q^2+q
        26: q^4+5q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: q^3+q^2+q
        32: q^3+2q^2+q
        33: 2q^3+2q^2+q
        34: 3q^3+q^2+q
        35: 3q^3+2q^2+q
        36: q^4+5q^3+2q^2+q
        37: 2q^3+2q^2+q
        39: 2q^3+2q^2+q
        41: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 3q^3+2q^2+q
        56: q^4+4q^3+2q^2+q
        57: q^4+2q^3+2q^2+q
        59: q^3+q^2+q
        60: q^3
        61: 2q^3+q^2+q
        62: q^3+q^2+q
        64: q^3+2q^2+q
        66: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^3+2q^2+q
        73: 2q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^2+q
        81: q^3+2q^2+q
        82: q^2+q
        83: 2q^2+q
        84: q^3+q^2+q
        85: 3q^3+2q^2+q
        86: 2q^3+q^2+q
        87: 2q^3+2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 3q^3+2q^2+q
        98: q^4+4q^3+2q^2+q
        99: q^4+2q^3+2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       106: q^3+q^2+q
       108: q^3+q^2+q
       110: q^2+q
       111: 2q^2+q
       113: q^2+q
       115: 2q^2+q
       118: q^2+q
       120: q^2+q
       121: q^2+q
       123: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^2+q
       137: q^2+q
       138: 2q^2+q
       139: q^2+q
       140: q
       141: q^2+q
       142: 2q^2+q
       143: q^3+q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+2q^2+q
       148: 2q^2+q
       149: q^2+q
       150: 2q^2+q
       151: 2q^2+q
       153: q^3+2q^2+q
       155: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       172: q^2+q
       176: q^2+q
       177: 2q^2+q
       179: q^2+q
       181: 2q^2+q
       184: q^2+q
       186: q^2+q
       187: 2q^2+q
       189: q^2+q
       192: q^2+q
       194: q
       196: q^2+q
       197: q
       200: q^2+q
       202: q^3+q^2+q
       204: q^2+q
       205: 2q^2+q
       207: q^2+q
       209: q^2+q
       211: 2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+2q^2+q
       224: q
       225: 2q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: 2q^2+q
       236: 2q^2+q
       237: 2q^2+q
       239: q^3+2q^2+q
       241: 2q^2+q
       243: q^2+q
       244: q
       245: 2q^2+q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       262: q^2+q
       266: q^2+q
       269: q
       273: q^2+q
       278: q^2+q
       279: q
       281: q^2+q
       284: q^2+q
       286: q^2+q
       287: q^2+q
       289: q^2+q
       291: 2q^2+q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q^2+q
       310: q^2+q
       311: 2q^2+q
       313: 2q^2+q
       315: 2q^2+q
       317: q^2+q
       320: q
       322: q^2+q
       323: q
       325: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+2q^2+q
       357: q
       358: 2q^2+q
       359: q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       380: q^2+q
       384: q
       388: q
       391: q
       396: q
       399: q^2+q
       404: q^2+q
       406: q
       413: q
       417: q^2+q
       420: q
       422: q
       423: q
       425: q^2+q
       427: q
       430: q
       432: q
       433: q
       435: q
       444: q
       445: q
       448: q^2+q
       450: q^2+q
       451: 2q^2+q
       454: q
       455: q^2+q
       458: q
       459: q
       462: q
       463: q^2+q
       465: q
       467: q^2+q
       469: q^2+q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       495: q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q
       512: q
       514: q^2+q
       524: q
       532: q
       536: q
       539: q
       547: q
       552: q^2+q
       555: q
       559: q
       563: q
       568: q
       570: q
       575: q
       577: q
       585: q
       590: q
       592: q
       594: q
       596: q
       599: q
       605: q
       613: q
       620: q
       622: q
       623: q^2+q
       625: q
       629: q^2+q
       639: q
       642: q
       644: q
       645: q
       651: q
       681: q
       682: q
       683: q
       689: q
       697: q
       712: q
       716: q
       720: q
       723: q
       739: q
       743: q
       756: q
       758: q
       821: q
       826: q
       828: q
       830: q
       832: q
       835: q
       849: q
       855: q
       946: q
       950: q
       955: q
       961: q
      1010: 1
      1127: 1
      1140: 1
      1278: 1
      1299: 1
      1393: 1
      1432: 1
      1522: 1

1523:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: 2q^3+2q^2+q
        23: 2q^3+2q^2+q
        24: q^3+2q^2+q
        25: q^4+5q^3+2q^2+q
        26: q^4+5q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: q^3+q^2+q
        32: q^3+2q^2+q
        33: 2q^3+2q^2+q
        34: 3q^3+q^2+q
        35: 3q^3+2q^2+q
        36: q^4+5q^3+2q^2+q
        38: 2q^3+2q^2+q
        40: 2q^3+2q^2+q
        42: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 3q^3+2q^2+q
        56: q^4+4q^3+2q^2+q
        57: q^4+2q^3+2q^2+q
        59: q^3+q^2+q
        60: 2q^3+q^2+q
        61: q^3
        63: q^3+q^2+q
        65: q^3+2q^2+q
        67: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^3+2q^2+q
        73: 2q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^2+q
        81: q^3+2q^2+q
        82: q^2+q
        83: 2q^2+q
        84: q^3+q^2+q
        85: 3q^3+2q^2+q
        86: 2q^3+q^2+q
        87: 2q^3+2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 3q^3+2q^2+q
        98: q^4+4q^3+2q^2+q
        99: q^4+2q^3+2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       104: q^3+q^2+q
       107: q^3+q^2+q
       110: q^2+q
       112: 2q^2+q
       114: q^2+q
       116: 2q^2+q
       118: q^2+q
       119: q^2+q
       122: q^2+q
       124: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^2+q
       137: q^2+q
       138: 2q^2+q
       139: q^2+q
       140: q
       141: q^2+q
       142: 2q^2+q
       143: q^3+q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+2q^2+q
       148: 2q^2+q
       149: q^2+q
       150: 2q^2+q
       152: 2q^2+q
       154: q^3+2q^2+q
       156: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       170: q^2+q
       174: q^2+q
       178: 2q^2+q
       180: q^2+q
       182: 2q^2+q
       183: q^2+q
       186: q^2+q
       188: 2q^2+q
       190: q^2+q
       192: q^2+q
       193: q
       196: q^2+q
       198: q
       199: q^2+q
       201: q^3+q^2+q
       204: q^2+q
       206: 2q^2+q
       208: q^2+q
       210: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+2q^2+q
       224: q
       225: 2q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: 2q^2+q
       236: 2q^2+q
       238: 2q^2+q
       240: q^3+2q^2+q
       242: 2q^2+q
       243: q^2+q
       244: q
       245: 2q^2+q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2+q
       264: q^2+q
       268: q
       274: q^2+q
       276: q^2+q
       280: q
       282: q^2+q
       283: q^2+q
       286: q^2+q
       288: q^2+q
       290: q^2+q
       292: 2q^2+q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q
       306: q
       307: q^2+q
       310: q^2+q
       312: 2q^2+q
       314: 2q^2+q
       316: 2q^2+q
       318: q^2+q
       319: q
       322: q^2+q
       324: q
       326: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+2q^2+q
       357: q
       358: 2q^2+q
       359: q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       378: q^2+q
       382: q
       386: q
       390: q
       394: q
       400: q^2+q
       403: q^2+q
       407: q
       414: q
       418: q^2+q
       419: q
       422: q
       424: q
       426: q^2+q
       428: q
       429: q
       432: q
       434: q
       436: q
       443: q
       446: q
       447: q^2+q
       450: q^2+q
       452: 2q^2+q
       453: q
       456: q^2+q
       458: q
       460: q
       462: q
       464: q^2+q
       466: q
       468: q^2+q
       470: q^2+q
       471: q
       474: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       495: q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q
       512: q
       514: q^2+q
       522: q
       530: q
       534: q
       538: q
       546: q
       551: q^2+q
       556: q
       560: q
       564: q
       566: q
       571: q
       574: q
       581: q
       586: q
       589: q
       592: q
       593: q
       596: q
       600: q
       606: q
       614: q
       619: q
       622: q
       624: q^2+q
       626: q
       630: q^2+q
       640: q
       641: q
       644: q
       646: q
       652: q
       681: q
       682: q
       683: q
       689: q
       699: q
       710: q
       715: q
       718: q
       722: q
       740: q
       744: q
       754: q
       759: q
       822: q
       825: q
       828: q
       829: q
       832: q
       836: q
       850: q
       856: q
       947: q
       951: q
       953: q
       962: q
      1011: 1
      1128: 1
      1143: 1
      1279: 1
      1300: 1
      1394: 1
      1435: 1
      1523: 1

1524:    0: q^4+5q^3+2q^2+q
         1: q^4+5q^3+2q^2+q
         2: q^4+3q^3+2q^2+q
         3: q^4+5q^3+2q^2+q
         4: q^4+3q^3+2q^2+q
         5: q^4+5q^3+2q^2+q
         6: q^5+3q^4+4q^3+2q^2+q
         7: q^5+2q^4+2q^3+2q^2+q
         8: q^4+3q^3+2q^2+q
         9: q^5+2q^4+2q^3+2q^2+q
        10: 3q^3+q^2+q
        11: 3q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: q^4+5q^3+2q^2+q
        17: q^4+5q^3+2q^2+q
        18: q^5+2q^4+2q^3+2q^2+q
        19: 3q^3+2q^2+q
        20: q^4+4q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: 2q^3+2q^2+q
        23: 2q^3+2q^2+q
        24: q^3+2q^2+q
        25: q^4+5q^3+2q^2+q
        26: q^4+5q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+q^2+q
        29: 2q^3+q^2+q
        30: 2q^3+2q^2+q
        31: q^3+q^2+q
        32: q^3+2q^2+q
        33: 2q^3+2q^2+q
        34: 3q^3+q^2+q
        35: 3q^3+2q^2+q
        36: q^4+5q^3+2q^2+q
        38: 2q^3+2q^2+q
        40: 2q^3+2q^2+q
        42: q^3+2q^2+q
        43: q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: 3q^3+2q^2+q
        50: q^4+4q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 3q^3+2q^2+q
        56: q^4+4q^3+2q^2+q
        57: q^4+2q^3+2q^2+q
        58: q^3+q^2+q
        60: q^3
        61: 2q^3+q^2+q
        63: q^3+q^2+q
        65: q^3+2q^2+q
        67: 2q^3+2q^2+q
        68: q^2+q
        69: 2q^3+2q^2+q
        70: q^3+q^2+q
        71: 2q^3+q^2+q
        72: 2q^3+2q^2+q
        73: 2q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^2+q
        81: q^3+2q^2+q
        82: q^2+q
        83: 2q^2+q
        84: q^3+q^2+q
        85: 3q^3+2q^2+q
        86: 2q^3+q^2+q
        87: 2q^3+2q^2+q
        88: q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: 2q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: 2q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 3q^3+2q^2+q
        98: q^4+4q^3+2q^2+q
        99: q^4+2q^3+2q^2+q
       100: 2q^2+q
       101: q^3+2q^2+q
       102: 2q^2+q
       105: q^3+q^2+q
       108: q^3+q^2+q
       109: q^2+q
       112: 2q^2+q
       114: q^2+q
       116: 2q^2+q
       117: q^2+q
       120: q^2+q
       122: q^2+q
       124: q^3+2q^2+q
       125: q^2+q
       126: q^3+q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^2+q
       134: 2q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^2+q
       137: q^2+q
       138: 2q^2+q
       139: q^2+q
       140: q
       141: q^2+q
       142: 2q^2+q
       143: q^3+q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+2q^2+q
       148: 2q^2+q
       149: q^2+q
       150: 2q^2+q
       152: 2q^2+q
       154: q^3+2q^2+q
       156: 2q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^2+q
       167: q^3+2q^2+q
       168: 2q^2+q
       171: q^2+q
       175: q^2+q
       178: 2q^2+q
       180: q^2+q
       182: 2q^2+q
       184: q^2+q
       185: q^2+q
       188: 2q^2+q
       190: q^2+q
       191: q^2+q
       194: q
       195: q^2+q
       198: q
       200: q^2+q
       202: q^3+q^2+q
       203: q^2+q
       206: 2q^2+q
       208: q^2+q
       210: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+2q^2+q
       224: q
       225: 2q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: 2q^2+q
       236: 2q^2+q
       238: 2q^2+q
       240: q^3+2q^2+q
       242: 2q^2+q
       243: q^2+q
       244: q
       245: 2q^2+q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       261: q^2+q
       265: q^2+q
       270: q
       272: q^2+q
       277: q^2+q
       280: q
       282: q^2+q
       284: q^2+q
       285: q^2+q
       288: q^2+q
       290: q^2+q
       292: 2q^2+q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q
       306: q
       308: q^2+q
       309: q^2+q
       312: 2q^2+q
       314: 2q^2+q
       316: 2q^2+q
       318: q^2+q
       320: q
       321: q^2+q
       324: q
       326: q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: q
       348: q
       350: q^2+q
       351: q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+2q^2+q
       357: q
       358: 2q^2+q
       359: q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       379: q^2+q
       383: q
       387: q
       392: q
       395: q
       398: q^2+q
       402: q^2+q
       408: q
       414: q
       418: q^2+q
       420: q
       421: q
       424: q
       426: q^2+q
       428: q
       430: q
       431: q
       434: q
       436: q
       444: q
       446: q
       448: q^2+q
       449: q^2+q
       452: 2q^2+q
       454: q
       456: q^2+q
       457: q
       460: q
       461: q
       464: q^2+q
       466: q
       468: q^2+q
       470: q^2+q
       472: q
       473: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       495: q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q
       512: q
       514: q^2+q
       523: q
       531: q
       535: q
       540: q
       548: q
       550: q^2+q
       554: q
       558: q
       562: q
       567: q
       572: q
       576: q
       581: q
       586: q
       590: q
       591: q
       594: q
       595: q
       600: q
       606: q
       614: q
       620: q
       621: q
       624: q^2+q
       626: q
       630: q^2+q
       640: q
       642: q
       643: q
       646: q
       652: q
       681: q
       682: q
       683: q
       689: q
       700: q
       711: q
       714: q
       719: q
       724: q
       738: q
       742: q
       755: q
       760: q
       822: q
       826: q
       827: q
       830: q
       831: q
       836: q
       850: q
       856: q
       945: q
       949: q
       954: q
       963: q
      1011: 1
      1129: 1
      1143: 1
      1279: 1
      1301: 1
      1395: 1
      1435: 1
      1524: 1

1525:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+q+1
        13: q^2+2q+1
        14: q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q^2+q+1
       106: q
       107: 1
       109: 1
       111: 1
       113: q+1
       115: q+1
       117: q^2+q+1
       118: q
       119: q^2+q+1
       120: q
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       173: q^2+q+1
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q+1
       191: q^2+q+1
       192: q
       193: 1
       195: 1
       197: 1
       199: q^2+q+1
       200: q
       201: 1
       203: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+q+1
       278: q
       279: q+1
       281: q+1
       283: 1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: 1
       321: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       493: 1
       494: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: q+1
       585: 1
       587: 1
       589: 1
       595: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: 1
       676: 1
       678: 1
       680: 1
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       693: 1
       705: 1
       709: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       789: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       807: 1
       813: 1
       815: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       831: 1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       884: 1
       896: 1
       912: 1
       916: 1
       920: 1
       932: 1
       936: 1
       940: 1
       944: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
      1014: 1
      1016: 1
      1018: 1
      1030: 1
      1032: 1
      1034: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1058: 1
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1079: 1
      1086: 1
      1098: 1
      1144: 1
      1148: 1
      1164: 1
      1168: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1210: 1
      1226: 1
      1228: 1
      1244: 1
      1246: 1
      1262: 1
      1264: 1
      1302: 1
      1340: 1
      1372: 1
      1404: 1
      1410: 1
      1414: 1
      1525: 1

1526:    0: q^3+4q^2+3q
         1: q^3+4q^2+3q
         2: q^3+4q^2+3q
         3: q^3+4q^2+3q
         4: 2q^3+2q^2+2q
         5: q^3+4q^2+3q
         6: 2q^3+2q^2+2q
         7: 2q^3+2q^2+2q
         8: q^3+4q^2+3q
         9: 2q^3+2q^2+2q
        10: q^3+4q^2+3q
        11: q^3+4q^2+3q
        12: 2q^3+2q^2+2q
        13: q^3+4q^2+3q
        14: 2q^3+2q^2+2q
        15: q^3+4q^2+3q
        16: q^3+4q^2+3q
        17: q^3+4q^2+3q
        18: 2q^3+2q^2+2q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^3+4q^2+3q
        23: q^3+4q^2+3q
        24: q^3+4q^2+3q
        25: q^3+4q^2+3q
        26: q^3+4q^2+3q
        27: q^3+4q^2+3q
        28: q^3+4q^2+3q
        29: q^2+2q
        30: q^2+2q
        31: q^3+4q^2+3q
        32: q^3+4q^2+3q
        33: q^3+4q^2+3q
        34: q^3+4q^2+3q
        35: q^3+4q^2+3q
        36: q^3+4q^2+3q
        37: q^3+2q^2+q
        38: 2q^2+2q
        39: q^3+2q^2+q
        40: 2q^2+2q
        41: q^3+2q^2+q
        42: 2q^2+2q
        43: q^3+4q^2+3q
        44: 2q^3+2q^2+2q
        45: q^3+4q^2+3q
        46: q^3+4q^2+3q
        47: q^3+4q^2+3q
        48: 2q^3+2q^2+2q
        49: q^2+2q
        50: q^2+2q
        51: q^2+2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        58: q^3+2q^2+2q
        59: 2q^2+q
        60: q^3+2q^2+2q
        61: 2q^2+q
        62: q^3+2q^2+q
        63: 2q^2+2q
        64: q^3+2q^2+q
        65: 2q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: q^3+4q^2+3q
        69: q^2+2q
        70: q^2+2q
        71: q^2+2q
        72: q
        73: q
        75: q
        77: q
        79: q
        80: q^3+4q^2+3q
        81: q^3+4q^2+3q
        82: q^2+2q
        83: q^2+2q
        84: q^3+4q^2+3q
        85: q^3+4q^2+3q
        86: q^2+2q
        87: q^2+2q
        88: q^3+4q^2+3q
        89: q^3+4q^2+3q
        90: 2q^3+2q^2+2q
        91: q^2+2q
        92: q^2+2q
        93: q^2+2q
        94: q^2+2q
        95: q^2+2q
        96: q^2+2q
        97: q^2+2q
        98: q^2+2q
        99: q^2+2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       103: q^3+q^2+q
       104: q^2+q
       105: q^2+q
       106: q^2
       107: q
       109: q
       114: q
       116: q
       117: q^3+2q^2+2q
       118: 2q^2+q
       119: q^3+2q^2+2q
       120: 2q^2+q
       121: q^3+2q^2+q
       122: 2q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: q^3+4q^2+3q
       126: q^2+2q
       128: q
       130: q
       132: q
       133: q^2+2q
       134: q^2+2q
       135: q
       136: q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: q^2+2q
       140: q
       141: q^2+2q
       142: q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: q^2+2q
       146: q^2+2q
       147: q
       148: q
       149: q^2+2q
       150: q^2+2q
       152: q
       154: q
       156: q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^2+2q
       161: q^2+2q
       162: q^2+2q
       163: q^2+2q
       164: q^2+2q
       165: q^2+2q
       166: q^2+2q
       167: q^2+2q
       168: q^2+2q
       173: q^3+q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q
       180: q
       183: q
       185: q
       190: q
       191: q^3+2q^2+2q
       192: 2q^2+q
       193: q
       195: q
       199: q^3+2q^2+2q
       200: 2q^2+q
       201: q
       203: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       210: q
       212: q
       214: q
       216: q
       218: q
       219: q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: q
       223: q
       224: q
       225: q
       226: q^2+2q
       227: q^2+2q
       228: q^2+2q
       229: q
       230: q
       231: q^2+2q
       232: q^2+2q
       233: q^2+2q
       234: q
       235: q
       236: q^2+2q
       238: q
       240: q
       242: q
       243: q^2+2q
       244: q
       245: q
       246: q^2+2q
       247: 1
       248: 1
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: q^2+2q
       257: q^2+2q
       258: q^2+2q
       275: q^3+q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: q
       282: q
       283: q
       285: q
       288: q
       293: q
       295: q
       299: q
       303: q
       307: q
       309: q
       316: q
       318: q
       319: q
       321: q
       326: q
       328: q
       330: q
       332: q
       333: q^2+2q
       334: q
       335: q
       337: 1
       339: 1
       341: 1
       344: q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: q
       348: q
       349: q
       350: q
       351: 1
       352: q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: q
       356: q
       357: q
       358: q
       359: 1
       361: q
       363: q
       365: q
       366: q^2+2q
       367: q^2+2q
       368: q^2+2q
       369: q
       370: q
       371: 1
       372: 1
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       410: q
       412: q
       414: q
       419: q
       421: q
       428: 1
       429: q
       431: q
       437: q
       439: q
       443: 1
       446: 1
       447: q
       449: q
       453: q
       457: q
       461: 1
       464: 1
       466: q
       468: q
       470: q
       471: q
       473: q
       479: 1
       481: q
       482: q
       484: 1
       486: 1
       488: 1
       492: q^2+2q
       493: q
       494: q
       496: 1
       497: q^2+2q
       498: q
       499: q
       501: 1
       503: q
       505: q
       507: q
       508: q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       546: 1
       562: 1
       573: 1
       578: 1
       584: q
       589: q
       595: q
       602: 1
       603: q
       607: q
       615: 1
       618: 1
       619: q
       621: q
       631: 1
       634: 1
       636: q
       638: q
       640: q
       641: q
       643: q
       647: q
       649: q
       655: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: q
       676: q
       678: 1
       680: 1
       681: q
       682: q
       684: 1
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: 1
       694: 1
       734: 1
       750: 1
       765: 1
       770: 1
       776: 1
       790: 1
       793: 1
       796: 1
       801: q
       807: q
       814: 1
       815: 1
       817: 1
       820: 1
       825: q
       831: q
       838: 1
       839: 1
       842: q
       843: 1
       845: q
       847: q
       857: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       885: 1
       917: 1
       933: 1
       941: 1
       957: 1
       964: 1
       969: 1
       983: 1
       988: 1
       993: 1
      1015: 1
      1016: 1
      1031: 1
      1032: 1
      1046: 1
      1052: q
      1058: q
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1079: 1
      1087: 1
      1099: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1211: 1
      1227: 1
      1228: 1
      1245: 1
      1246: 1
      1262: 1
      1303: 1
      1341: 1
      1373: 1
      1405: 1
      1410: 1
      1526: 1

1527:    0: q^4+3q^3+3q^2+q
         1: 3q^3+3q^2+q
         2: q^4+3q^3+3q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: 3q^3+3q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^4+2q^3+2q^2+q
         8: 3q^3+3q^2+q
         9: q^4+2q^3+2q^2+q
        10: 2q^3+3q^2+q
        11: 2q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^4+3q^3+3q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+3q^2+q
        16: q^4+3q^3+3q^2+q
        17: 3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^3+2q^2+q
        20: 2q^3+2q^2+q
        21: q^3+2q^2+q
        22: 2q^3+3q^2+q
        23: 2q^3+3q^2+q
        24: 2q^3+3q^2+q
        25: 2q^3+3q^2+q
        26: 2q^3+3q^2+q
        27: 2q^3+3q^2+q
        28: 2q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^3+3q^2+q
        33: 2q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^3+3q^2+q
        36: 2q^3+3q^2+q
        37: 2q^3+3q^2+q
        39: 2q^3+3q^2+q
        41: 2q^3+3q^2+q
        43: 2q^3+3q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+3q^2+q
        46: q^4+3q^3+3q^2+q
        47: 3q^3+3q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^3+2q^2+q
        50: 2q^3+2q^2+q
        51: q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^3+2q^2+q
        59: q^2
        60: q^3+2q^2+q
        61: q^2
        62: q^3+3q^2+q
        64: 2q^3+3q^2+q
        66: 2q^3+3q^2+q
        68: 2q^3+3q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^3+3q^2+q
        81: 2q^3+3q^2+q
        82: 2q^2+q
        83: 2q^2+q
        84: q^3+3q^2+q
        85: 2q^3+3q^2+q
        86: 2q^2+q
        87: 2q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^3+2q^2+q
       106: q^2
       107: q^2+q
       109: q^2+q
       111: q^2+q
       113: 2q^2+q
       115: 2q^2+q
       117: q^3+2q^2+q
       118: q^2
       119: q^3+2q^2+q
       120: q^2
       121: q^3+3q^2+q
       123: 2q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^3+2q^2+q
       134: q^3+2q^2+q
       135: q^2+q
       136: q^2+q
       137: q^3+3q^2+q
       138: 2q^2+q
       139: 2q^2+q
       140: q
       141: 2q^2+q
       142: q^2+q
       143: q^3+3q^2+q
       144: 2q^2+q
       145: 2q^2+q
       146: 2q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: 2q^2+q
       161: q^3+2q^2+q
       162: 2q^2+q
       163: 2q^2+q
       164: q^3+2q^2+q
       165: 2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^2+q
       173: q^3+2q^2+q
       176: q^2
       177: 2q^2+q
       179: 2q^2+q
       181: q^2+q
       183: q^2+q
       185: q^2+q
       187: q^2+q
       189: 2q^2+q
       191: q^3+2q^2+q
       192: q^2
       193: q
       195: q^2+q
       197: q
       199: q^3+2q^2+q
       200: q^2
       201: q^2+q
       203: q
       205: q
       207: q^3+3q^2+q
       209: q^2+q
       211: q^2+q
       213: 2q^2+q
       215: q^3+2q^2+q
       217: 2q^2+q
       219: q^3+2q^2+q
       220: q^2+q
       221: q^2+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: 2q^2+q
       227: 2q^2+q
       228: 2q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: 2q^2+q
       233: 2q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2+q
       263: q^2+q
       267: q
       271: q
       275: q^3+2q^2+q
       278: q^2
       279: 2q^2+q
       281: 2q^2+q
       283: q^2+q
       285: q^2+q
       287: 2q^2+q
       289: q^2+q
       291: q^2+q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q^2+q
       305: q
       307: q^2+q
       309: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       319: q
       321: q
       323: q
       325: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: q
       335: q
       344: 2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q
       350: q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^2+q
       355: q
       356: q^2+q
       357: q
       358: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       377: q^2+q
       381: q^2+q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q^2+q
       411: q^2+q
       413: 2q^2+q
       415: q
       417: q^2+q
       419: q
       421: q
       423: q
       429: q
       431: q^2+q
       433: q
       435: q
       437: q
       439: q
       441: q
       447: q^2+q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       465: q^2+q
       467: q^2+q
       469: q^2+q
       471: q
       473: q
       475: q
       477: q
       481: q
       482: q
       492: q^2+q
       493: q
       494: q
       497: q^2+q
       498: q
       499: q
       508: q^2+q
       512: q
       514: q
       521: q^2+q
       525: q
       529: q
       533: q
       537: q
       541: q
       549: q
       553: q
       557: q
       565: q
       569: q
       583: q^2+q
       585: q
       587: q
       589: q
       595: q
       603: q
       605: q
       607: q
       609: q
       619: q
       621: q
       623: q
       625: q
       639: q^2+q
       641: q
       643: q
       645: q
       651: q
       675: q
       676: q
       681: q
       682: q
       705: q
       709: q
       721: q
       725: q
       737: q
       741: q
       753: q
       757: q
       777: q
       797: q
       801: q
       807: q
       821: q
       825: q
       831: q
       849: q
       853: 1
       896: q
       920: q
       944: q
       960: q
       978: 1
       984: 1
      1050: 1
      1100: 1
      1184: 1
      1190: 1
      1264: 1
      1304: 1
      1406: 1
      1414: 1
      1527: 1

1528:    0: q^3+4q^2+3q
         1: q^3+4q^2+3q
         2: q^3+4q^2+3q
         3: q^3+4q^2+3q
         4: 2q^3+2q^2+2q
         5: q^3+4q^2+3q
         6: 2q^3+2q^2+2q
         7: 2q^3+2q^2+2q
         8: q^3+4q^2+3q
         9: 2q^3+2q^2+2q
        10: q^3+4q^2+3q
        11: q^3+4q^2+3q
        12: 2q^3+2q^2+2q
        13: q^3+4q^2+3q
        14: 2q^3+2q^2+2q
        15: q^3+4q^2+3q
        16: q^3+4q^2+3q
        17: q^3+4q^2+3q
        18: 2q^3+2q^2+2q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^3+4q^2+3q
        23: q^3+4q^2+3q
        24: q^3+4q^2+3q
        25: q^3+4q^2+3q
        26: q^3+4q^2+3q
        27: q^3+4q^2+3q
        28: q^3+4q^2+3q
        29: q^2+2q
        30: q^2+2q
        31: q^3+4q^2+3q
        32: q^3+4q^2+3q
        33: q^3+4q^2+3q
        34: q^3+4q^2+3q
        35: q^3+4q^2+3q
        36: q^3+4q^2+3q
        37: 2q^2+2q
        38: q^3+2q^2+q
        39: 2q^2+2q
        40: q^3+2q^2+q
        41: 2q^2+2q
        42: q^3+2q^2+q
        43: q^3+4q^2+3q
        44: 2q^3+2q^2+2q
        45: q^3+4q^2+3q
        46: q^3+4q^2+3q
        47: q^3+4q^2+3q
        48: 2q^3+2q^2+2q
        49: q^2+2q
        50: q^2+2q
        51: q^2+2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        58: 2q^2+q
        59: q^3+2q^2+2q
        60: q^3+2q^2+2q
        61: 2q^2+q
        62: 2q^2+2q
        63: q^3+2q^2+q
        64: 2q^2+2q
        65: q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: q^3+4q^2+3q
        69: q^2+2q
        70: q^2+2q
        71: q^2+2q
        72: q
        73: q
        74: q
        76: q
        78: q
        80: q^3+4q^2+3q
        81: q^3+4q^2+3q
        82: q^2+2q
        83: q^2+2q
        84: q^3+4q^2+3q
        85: q^3+4q^2+3q
        86: q^2+2q
        87: q^2+2q
        88: q^3+4q^2+3q
        89: q^3+4q^2+3q
        90: 2q^3+2q^2+2q
        91: q^2+2q
        92: q^2+2q
        93: q^2+2q
        94: q^2+2q
        95: q^2+2q
        96: q^2+2q
        97: q^2+2q
        98: q^2+2q
        99: q^2+2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       103: q^2+q
       104: q^3+q^2+q
       105: q^2
       106: q^2+q
       107: q
       110: q
       113: q
       115: q
       117: 2q^2+q
       118: q^3+2q^2+2q
       119: q^3+2q^2+2q
       120: 2q^2+q
       121: 2q^2+2q
       122: q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: q^3+4q^2+3q
       126: q^2+2q
       127: q
       129: q
       131: q
       133: q^2+2q
       134: q^2+2q
       135: q
       136: q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: q^2+2q
       140: q
       141: q^2+2q
       142: q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: q^2+2q
       146: q^2+2q
       147: q
       148: q
       149: q^2+2q
       150: q^2+2q
       151: q
       153: q
       155: q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^2+2q
       161: q^2+2q
       162: q^2+2q
       163: q^2+2q
       164: q^2+2q
       165: q^2+2q
       166: q^2+2q
       167: q^2+2q
       168: q^2+2q
       173: q^2+q
       174: q^3+q^2+q
       175: q^2
       176: q^2+q
       177: q
       179: q
       183: q
       186: q
       189: q
       191: 2q^2+q
       192: q^3+2q^2+2q
       193: q
       196: q
       199: q^3+2q^2+2q
       200: 2q^2+q
       201: q
       204: q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: q
       211: q
       213: q
       215: q
       217: q
       219: q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: q
       223: q
       224: q
       225: q
       226: q^2+2q
       227: q^2+2q
       228: q^2+2q
       229: q
       230: q
       231: q^2+2q
       232: q^2+2q
       233: q^2+2q
       234: q
       235: q
       236: q^2+2q
       237: q
       239: q
       241: q
       243: q^2+2q
       244: q
       245: q
       246: q^2+2q
       247: 1
       248: 1
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: q^2+2q
       257: q^2+2q
       258: q^2+2q
       275: q^2+q
       276: q^3+q^2+q
       277: q^2
       278: q^2+q
       279: q
       281: q
       283: q
       286: q
       287: q
       293: q
       296: q
       299: q
       304: q
       307: q
       310: q
       315: q
       317: q
       319: q
       322: q
       325: q
       327: q
       329: q
       331: q
       333: q^2+2q
       334: q
       335: q
       337: 1
       338: 1
       340: 1
       344: q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: q
       348: q
       349: q
       350: q
       351: 1
       352: q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: q
       356: q
       357: q
       358: q
       359: 1
       360: q
       362: q
       364: q
       366: q^2+2q
       367: q^2+2q
       368: q^2+2q
       369: q
       370: q
       371: 1
       372: 1
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       409: q
       411: q
       413: q
       419: q
       422: q
       427: 1
       429: q
       432: q
       437: q
       440: q
       443: 1
       445: 1
       447: q
       450: q
       453: q
       458: q
       462: 1
       463: 1
       465: q
       467: q
       469: q
       471: q
       474: q
       480: 1
       481: q
       482: q
       484: 1
       485: 1
       487: 1
       492: q^2+2q
       493: q
       494: q
       496: 1
       497: q^2+2q
       498: q
       499: q
       501: 1
       502: q
       504: q
       506: q
       508: q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       545: 1
       563: 1
       574: 1
       580: 1
       583: q
       589: q
       596: q
       601: 1
       603: q
       608: q
       615: 1
       617: 1
       619: q
       622: q
       632: 1
       633: 1
       635: q
       637: q
       639: q
       641: q
       644: q
       647: q
       650: q
       656: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: q
       676: q
       678: 1
       680: 1
       681: q
       682: q
       684: 1
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: 1
       696: 1
       733: 1
       751: 1
       766: 1
       772: 1
       775: 1
       789: 1
       793: 1
       795: 1
       801: q
       808: q
       813: 1
       815: 1
       818: 1
       819: 1
       825: q
       832: q
       837: 1
       840: 1
       841: q
       844: 1
       845: q
       848: q
       858: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       887: 1
       916: 1
       932: 1
       942: 1
       958: 1
       965: 1
       971: 1
       985: 1
       989: 1
       992: 1
      1014: 1
      1016: 1
      1030: 1
      1033: 1
      1047: 1
      1052: q
      1059: q
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1079: 1
      1089: 1
      1101: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1210: 1
      1226: 1
      1228: 1
      1244: 1
      1247: 1
      1263: 1
      1305: 1
      1340: 1
      1374: 1
      1407: 1
      1411: 1
      1528: 1

1529:    0: q^3+4q^2+3q
         1: q^3+4q^2+3q
         2: q^3+4q^2+3q
         3: q^3+4q^2+3q
         4: 2q^3+2q^2+2q
         5: q^3+4q^2+3q
         6: 2q^3+2q^2+2q
         7: 2q^3+2q^2+2q
         8: q^3+4q^2+3q
         9: 2q^3+2q^2+2q
        10: q^3+4q^2+3q
        11: q^3+4q^2+3q
        12: 2q^3+2q^2+2q
        13: q^3+4q^2+3q
        14: 2q^3+2q^2+2q
        15: q^3+4q^2+3q
        16: q^3+4q^2+3q
        17: q^3+4q^2+3q
        18: 2q^3+2q^2+2q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^3+4q^2+3q
        23: q^3+4q^2+3q
        24: q^3+4q^2+3q
        25: q^3+4q^2+3q
        26: q^3+4q^2+3q
        27: q^3+4q^2+3q
        28: q^3+4q^2+3q
        29: q^2+2q
        30: q^2+2q
        31: q^3+4q^2+3q
        32: q^3+4q^2+3q
        33: q^3+4q^2+3q
        34: q^3+4q^2+3q
        35: q^3+4q^2+3q
        36: q^3+4q^2+3q
        37: 2q^2+2q
        38: q^3+2q^2+q
        39: 2q^2+2q
        40: q^3+2q^2+q
        41: 2q^2+2q
        42: q^3+2q^2+q
        43: q^3+4q^2+3q
        44: 2q^3+2q^2+2q
        45: q^3+4q^2+3q
        46: q^3+4q^2+3q
        47: q^3+4q^2+3q
        48: 2q^3+2q^2+2q
        49: q^2+2q
        50: q^2+2q
        51: q^2+2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        58: q^3+2q^2+2q
        59: 2q^2+q
        60: 2q^2+q
        61: q^3+2q^2+2q
        62: 2q^2+2q
        63: q^3+2q^2+q
        64: 2q^2+2q
        65: q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: q^3+4q^2+3q
        69: q^2+2q
        70: q^2+2q
        71: q^2+2q
        72: q
        73: q
        74: q
        76: q
        78: q
        80: q^3+4q^2+3q
        81: q^3+4q^2+3q
        82: q^2+2q
        83: q^2+2q
        84: q^3+4q^2+3q
        85: q^3+4q^2+3q
        86: q^2+2q
        87: q^2+2q
        88: q^3+4q^2+3q
        89: q^3+4q^2+3q
        90: 2q^3+2q^2+2q
        91: q^2+2q
        92: q^2+2q
        93: q^2+2q
        94: q^2+2q
        95: q^2+2q
        96: q^2+2q
        97: q^2+2q
        98: q^2+2q
        99: q^2+2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       103: q^2+q
       104: q^2
       105: q^3+q^2+q
       106: q^2+q
       108: q
       109: q
       113: q
       115: q
       117: q^3+2q^2+2q
       118: 2q^2+q
       119: 2q^2+q
       120: q^3+2q^2+2q
       121: 2q^2+2q
       122: q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: q^3+4q^2+3q
       126: q^2+2q
       127: q
       129: q
       131: q
       133: q^2+2q
       134: q^2+2q
       135: q
       136: q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: q^2+2q
       140: q
       141: q^2+2q
       142: q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: q^2+2q
       146: q^2+2q
       147: q
       148: q
       149: q^2+2q
       150: q^2+2q
       151: q
       153: q
       155: q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^2+2q
       161: q^2+2q
       162: q^2+2q
       163: q^2+2q
       164: q^2+2q
       165: q^2+2q
       166: q^2+2q
       167: q^2+2q
       168: q^2+2q
       173: q^2+q
       174: q^2
       175: q^3+q^2+q
       176: q^2+q
       177: q
       179: q
       184: q
       185: q
       189: q
       191: q^3+2q^2+2q
       192: 2q^2+q
       194: q
       195: q
       199: 2q^2+q
       200: q^3+2q^2+2q
       202: q
       203: q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: q
       211: q
       213: q
       215: q
       217: q
       219: q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: q
       223: q
       224: q
       225: q
       226: q^2+2q
       227: q^2+2q
       228: q^2+2q
       229: q
       230: q
       231: q^2+2q
       232: q^2+2q
       233: q^2+2q
       234: q
       235: q
       236: q^2+2q
       237: q
       239: q
       241: q
       243: q^2+2q
       244: q
       245: q
       246: q^2+2q
       247: 1
       248: 1
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: q^2+2q
       257: q^2+2q
       258: q^2+2q
       275: q^2+q
       276: q^2
       277: q^3+q^2+q
       278: q^2+q
       279: q
       281: q
       284: q
       285: q
       287: q
       294: q
       295: q
       300: q
       303: q
       308: q
       309: q
       315: q
       317: q
       320: q
       321: q
       325: q
       327: q
       329: q
       331: q
       333: q^2+2q
       334: q
       335: q
       337: 1
       338: 1
       340: 1
       344: q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: q
       348: q
       349: q
       350: q
       351: 1
       352: q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: q
       356: q
       357: q
       358: q
       359: 1
       360: q
       362: q
       364: q
       366: q^2+2q
       367: q^2+2q
       368: q^2+2q
       369: q
       370: q
       371: 1
       372: 1
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       409: q
       411: q
       413: q
       420: q
       421: q
       427: 1
       430: q
       431: q
       438: q
       439: q
       444: 1
       445: 1
       448: q
       449: q
       454: q
       457: q
       461: 1
       463: 1
       465: q
       467: q
       469: q
       472: q
       473: q
       480: 1
       481: q
       482: q
       484: 1
       485: 1
       487: 1
       492: q^2+2q
       493: q
       494: q
       496: 1
       497: q^2+2q
       498: q
       499: q
       501: 1
       502: q
       504: q
       506: q
       508: q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       547: 1
       561: 1
       576: 1
       580: 1
       583: q
       590: q
       595: q
       601: 1
       604: q
       607: q
       616: 1
       617: 1
       620: q
       621: q
       631: 1
       633: 1
       635: q
       637: q
       639: q
       642: q
       643: q
       648: q
       649: q
       656: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: q
       676: q
       678: 1
       680: 1
       681: q
       682: q
       684: 1
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: 1
       698: 1
       735: 1
       749: 1
       767: 1
       772: 1
       775: 1
       789: 1
       794: 1
       795: 1
       802: q
       807: q
       813: 1
       816: 1
       817: 1
       819: 1
       826: q
       831: q
       837: 1
       839: 1
       841: q
       844: 1
       846: q
       847: q
       858: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       888: 1
       918: 1
       934: 1
       940: 1
       956: 1
       966: 1
       971: 1
       985: 1
       990: 1
       992: 1
      1014: 1
      1017: 1
      1030: 1
      1032: 1
      1047: 1
      1053: q
      1058: q
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1079: 1
      1090: 1
      1103: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1210: 1
      1226: 1
      1229: 1
      1244: 1
      1246: 1
      1263: 1
      1306: 1
      1342: 1
      1372: 1
      1407: 1
      1412: 1
      1529: 1

1530:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+q+1
        13: q^2+2q+1
        14: q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        60: q
        61: q^2+q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: q^2+q+1
       108: 1
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: q^2+q+1
       119: q
       120: q^2+q+1
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       129: q+1
       131: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       172: 1
       173: q
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q+1
       191: q
       192: q^2+q+1
       194: 1
       196: 1
       197: 1
       199: q
       200: q^2+q+1
       202: 1
       204: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       278: q^2+q+1
       279: q+1
       281: q+1
       284: 1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: 1
       322: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       338: 1
       340: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       484: 1
       485: 1
       487: 1
       492: q+1
       493: 1
       494: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: q+1
       585: 1
       587: 1
       590: 1
       596: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       666: 1
       668: 1
       672: 1
       674: 1
       675: 1
       676: 1
       678: 1
       680: 1
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       697: 1
       708: 1
       712: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       789: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       808: 1
       813: 1
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       826: 1
       832: 1
       837: 1
       840: 1
       841: q+1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: 1
       861: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       889: 1
       899: 1
       914: 1
       918: 1
       922: 1
       934: 1
       938: 1
       942: 1
       946: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
      1014: 1
      1017: 1
      1018: 1
      1030: 1
      1033: 1
      1034: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1059: 1
      1066: 1
      1068: 1
      1072: 1
      1075: 1
      1079: 1
      1091: 1
      1102: 1
      1146: 1
      1150: 1
      1166: 1
      1170: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1210: 1
      1226: 1
      1229: 1
      1244: 1
      1247: 1
      1262: 1
      1264: 1
      1307: 1
      1342: 1
      1374: 1
      1404: 1
      1413: 1
      1415: 1
      1530: 1

1531:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+q+1
        13: q^2+2q+1
        14: q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+q+1
        60: q^2+q+1
        61: q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q^2+q+1
       105: q
       107: 1
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: q^2+q+1
       119: q^2+q+1
       120: q
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       174: q^2+q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q+1
       191: q
       192: q^2+q+1
       193: 1
       196: 1
       198: 1
       199: q^2+q+1
       200: q
       201: 1
       204: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q^2+q+1
       277: q
       280: q+1
       282: q+1
       283: 1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: 1
       322: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: 1
       596: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: 1
       676: 1
       678: 1
       680: 1
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       699: 1
       706: 1
       710: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       778: 1
       790: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       808: 1
       814: 1
       815: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: 1
       832: 1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       890: 1
       897: 1
       913: 1
       917: 1
       921: 1
       933: 1
       939: 1
       943: 1
       947: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
      1015: 1
      1016: 1
      1019: 1
      1031: 1
      1033: 1
      1035: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1059: 1
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1079: 1
      1092: 1
      1104: 1
      1145: 1
      1149: 1
      1167: 1
      1171: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1211: 1
      1227: 1
      1228: 1
      1245: 1
      1247: 1
      1263: 1
      1265: 1
      1308: 1
      1341: 1
      1375: 1
      1408: 1
      1411: 1
      1416: 1
      1531: 1

1532:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+q+1
        13: q^2+2q+1
        14: q^2+q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: q^2+q+1
       108: 1
       109: 1
       112: 1
       114: q+1
       116: q+1
       117: q^2+q+1
       118: q
       119: q
       120: q^2+q+1
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       130: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: 1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       171: 1
       174: q
       175: q^2+q+1
       178: q+1
       180: q+1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q+1
       191: q^2+q+1
       192: q
       194: 1
       195: 1
       198: 1
       199: q
       200: q^2+q+1
       202: 1
       203: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       261: 1
       265: 1
       270: 1
       272: 1
       276: q
       277: q^2+q+1
       280: q+1
       282: q+1
       284: 1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: 1
       321: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 1
       335: 1
       337: 1
       339: 1
       341: 1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       484: 1
       486: 1
       488: 1
       492: q+1
       493: 1
       494: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       518: 1
       519: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       590: 1
       595: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: 1
       676: 1
       678: 1
       680: 1
       681: 1
       682: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: 1
       700: 1
       707: 1
       711: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       778: 1
       790: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       807: 1
       814: 1
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       826: 1
       831: 1
       838: 1
       839: 1
       842: q+1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       877: 1
       878: 1
       881: 1
       882: 1
       891: 1
       898: 1
       915: 1
       919: 1
       923: 1
       935: 1
       937: 1
       941: 1
       945: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
      1015: 1
      1017: 1
      1019: 1
      1031: 1
      1032: 1
      1035: 1
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1058: 1
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1079: 1
      1093: 1
      1105: 1
      1147: 1
      1151: 1
      1165: 1
      1169: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1211: 1
      1227: 1
      1229: 1
      1245: 1
      1246: 1
      1263: 1
      1265: 1
      1309: 1
      1343: 1
      1373: 1
      1408: 1
      1412: 1
      1417: 1
      1532: 1

1533:    0: q^3+4q^2+3q
         1: q^3+4q^2+3q
         2: q^3+4q^2+3q
         3: q^3+4q^2+3q
         4: 2q^3+2q^2+2q
         5: q^3+4q^2+3q
         6: 2q^3+2q^2+2q
         7: 2q^3+2q^2+2q
         8: q^3+4q^2+3q
         9: 2q^3+2q^2+2q
        10: q^3+4q^2+3q
        11: q^3+4q^2+3q
        12: 2q^3+2q^2+2q
        13: q^3+4q^2+3q
        14: 2q^3+2q^2+2q
        15: q^3+4q^2+3q
        16: q^3+4q^2+3q
        17: q^3+4q^2+3q
        18: 2q^3+2q^2+2q
        19: q^2+2q
        20: q^2+2q
        21: q^2+2q
        22: q^3+4q^2+3q
        23: q^3+4q^2+3q
        24: q^3+4q^2+3q
        25: q^3+4q^2+3q
        26: q^3+4q^2+3q
        27: q^3+4q^2+3q
        28: q^3+4q^2+3q
        29: q^2+2q
        30: q^2+2q
        31: q^3+4q^2+3q
        32: q^3+4q^2+3q
        33: q^3+4q^2+3q
        34: q^3+4q^2+3q
        35: q^3+4q^2+3q
        36: q^3+4q^2+3q
        37: q^3+2q^2+q
        38: 2q^2+2q
        39: q^3+2q^2+q
        40: 2q^2+2q
        41: q^3+2q^2+q
        42: 2q^2+2q
        43: q^3+4q^2+3q
        44: 2q^3+2q^2+2q
        45: q^3+4q^2+3q
        46: q^3+4q^2+3q
        47: q^3+4q^2+3q
        48: 2q^3+2q^2+2q
        49: q^2+2q
        50: q^2+2q
        51: q^2+2q
        52: q^2+2q
        53: q^2+2q
        54: q^2+2q
        55: q^2+2q
        56: q^2+2q
        57: q^2+2q
        58: 2q^2+q
        59: q^3+2q^2+2q
        60: 2q^2+q
        61: q^3+2q^2+2q
        62: q^3+2q^2+q
        63: 2q^2+2q
        64: q^3+2q^2+q
        65: 2q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: q^3+4q^2+3q
        69: q^2+2q
        70: q^2+2q
        71: q^2+2q
        72: q
        73: q
        75: q
        77: q
        79: q
        80: q^3+4q^2+3q
        81: q^3+4q^2+3q
        82: q^2+2q
        83: q^2+2q
        84: q^3+4q^2+3q
        85: q^3+4q^2+3q
        86: q^2+2q
        87: q^2+2q
        88: q^3+4q^2+3q
        89: q^3+4q^2+3q
        90: 2q^3+2q^2+2q
        91: q^2+2q
        92: q^2+2q
        93: q^2+2q
        94: q^2+2q
        95: q^2+2q
        96: q^2+2q
        97: q^2+2q
        98: q^2+2q
        99: q^2+2q
       100: q^2+2q
       101: q^2+2q
       102: q^2+2q
       103: q^2
       104: q^2+q
       105: q^2+q
       106: q^3+q^2+q
       108: q
       110: q
       114: q
       116: q
       117: 2q^2+q
       118: q^3+2q^2+2q
       119: 2q^2+q
       120: q^3+2q^2+2q
       121: q^3+2q^2+q
       122: 2q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: q^3+4q^2+3q
       126: q^2+2q
       128: q
       130: q
       132: q
       133: q^2+2q
       134: q^2+2q
       135: q
       136: q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: q^2+2q
       140: q
       141: q^2+2q
       142: q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: q^2+2q
       146: q^2+2q
       147: q
       148: q
       149: q^2+2q
       150: q^2+2q
       152: q
       154: q
       156: q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^2+2q
       161: q^2+2q
       162: q^2+2q
       163: q^2+2q
       164: q^2+2q
       165: q^2+2q
       166: q^2+2q
       167: q^2+2q
       168: q^2+2q
       173: q^2
       174: q^2+q
       175: q^2+q
       176: q^3+q^2+q
       178: q
       180: q
       184: q
       186: q
       190: q
       191: 2q^2+q
       192: q^3+2q^2+2q
       194: q
       196: q
       199: 2q^2+q
       200: q^3+2q^2+2q
       202: q
       204: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       210: q
       212: q
       214: q
       216: q
       218: q
       219: q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: q
       223: q
       224: q
       225: q
       226: q^2+2q
       227: q^2+2q
       228: q^2+2q
       229: q
       230: q
       231: q^2+2q
       232: q^2+2q
       233: q^2+2q
       234: q
       235: q
       236: q^2+2q
       238: q
       240: q
       242: q
       243: q^2+2q
       244: q
       245: q
       246: q^2+2q
       247: 1
       248: 1
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: q^2+2q
       257: q^2+2q
       258: q^2+2q
       275: q^2
       276: q^2+q
       277: q^2+q
       278: q^3+q^2+q
       280: q
       282: q
       284: q
       286: q
       288: q
       294: q
       296: q
       300: q
       304: q
       308: q
       310: q
       316: q
       318: q
       320: q
       322: q
       326: q
       328: q
       330: q
       332: q
       333: q^2+2q
       334: q
       335: q
       337: 1
       339: 1
       341: 1
       344: q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: q
       348: q
       349: q
       350: q
       351: 1
       352: q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: q
       356: q
       357: q
       358: q
       359: 1
       361: q
       363: q
       365: q
       366: q^2+2q
       367: q^2+2q
       368: q^2+2q
       369: q
       370: q
       371: 1
       372: 1
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       410: q
       412: q
       414: q
       420: q
       422: q
       428: 1
       430: q
       432: q
       438: q
       440: q
       444: 1
       446: 1
       448: q
       450: q
       454: q
       458: q
       462: 1
       464: 1
       466: q
       468: q
       470: q
       472: q
       474: q
       479: 1
       481: q
       482: q
       484: 1
       486: 1
       488: 1
       492: q^2+2q
       493: q
       494: q
       496: 1
       497: q^2+2q
       498: q
       499: q
       501: 1
       503: q
       505: q
       507: q
       508: q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: q
       512: q
       513: q
       514: q
       515: 1
       516: 1
       518: 1
       519: 1
       548: 1
       564: 1
       575: 1
       578: 1
       584: q
       590: q
       596: q
       602: 1
       604: q
       608: q
       616: 1
       618: 1
       620: q
       622: q
       632: 1
       634: 1
       636: q
       638: q
       640: q
       642: q
       644: q
       648: q
       650: q
       655: 1
       657: 1
       659: 1
       661: 1
       667: 1
       669: 1
       672: 1
       674: 1
       675: q
       676: q
       678: 1
       680: 1
       681: q
       682: q
       684: 1
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: 1
       701: 1
       736: 1
       752: 1
       768: 1
       770: 1
       776: 1
       790: 1
       794: 1
       796: 1
       802: q
       808: q
       814: 1
       816: 1
       818: 1
       820: 1
       826: q
       832: q
       838: 1
       840: 1
       842: q
       843: 1
       846: q
       848: q
       857: 1
       860: 1
       862: 1
       865: 1
       869: 1
       873: 1
       877: q
       878: q
       881: 1
       882: 1
       892: 1
       919: 1
       935: 1
       943: 1
       959: 1
       967: 1
       969: 1
       983: 1
       991: 1
       993: 1
      1015: 1
      1017: 1
      1031: 1
      1033: 1
      1046: 1
      1053: q
      1059: q
      1067: 1
      1069: 1
      1072: 1
      1075: 1
      1079: 1
      1094: 1
      1106: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1211: 1
      1227: 1
      1229: 1
      1245: 1
      1247: 1
      1262: 1
      1310: 1
      1343: 1
      1375: 1
      1405: 1
      1413: 1
      1533: 1

1534:    0: q^4+3q^3+3q^2+q
         1: 3q^3+3q^2+q
         2: q^4+3q^3+3q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: 3q^3+3q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^4+2q^3+2q^2+q
         8: 3q^3+3q^2+q
         9: q^4+2q^3+2q^2+q
        10: 2q^3+3q^2+q
        11: 2q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^4+3q^3+3q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+3q^2+q
        16: q^4+3q^3+3q^2+q
        17: 3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^3+2q^2+q
        20: 2q^3+2q^2+q
        21: q^3+2q^2+q
        22: 2q^3+3q^2+q
        23: 2q^3+3q^2+q
        24: 2q^3+3q^2+q
        25: 2q^3+3q^2+q
        26: 2q^3+3q^2+q
        27: 2q^3+3q^2+q
        28: 2q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^3+3q^2+q
        33: 2q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^3+3q^2+q
        36: 2q^3+3q^2+q
        37: 2q^3+3q^2+q
        39: 2q^3+3q^2+q
        41: 2q^3+3q^2+q
        43: 2q^3+3q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+3q^2+q
        46: q^4+3q^3+3q^2+q
        47: 3q^3+3q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^3+2q^2+q
        50: 2q^3+2q^2+q
        51: q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^2
        59: q^3+2q^2+q
        60: q^2
        61: q^3+2q^2+q
        62: q^3+3q^2+q
        64: 2q^3+3q^2+q
        66: 2q^3+3q^2+q
        68: 2q^3+3q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        74: 2q^2+q
        76: q^3+2q^2+q
        78: 2q^2+q
        80: q^3+3q^2+q
        81: 2q^3+3q^2+q
        82: 2q^2+q
        83: 2q^2+q
        84: q^3+3q^2+q
        85: 2q^3+3q^2+q
        86: 2q^2+q
        87: 2q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^2
       106: q^3+2q^2+q
       108: q^2+q
       110: q^2+q
       111: q^2+q
       113: 2q^2+q
       115: 2q^2+q
       117: q^2
       118: q^3+2q^2+q
       119: q^2
       120: q^3+2q^2+q
       121: q^3+3q^2+q
       123: 2q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       127: 2q^2+q
       129: q^3+2q^2+q
       131: 2q^2+q
       133: q^3+2q^2+q
       134: q^3+2q^2+q
       135: q^2+q
       136: q^2+q
       137: q^3+3q^2+q
       138: 2q^2+q
       139: 2q^2+q
       140: q
       141: 2q^2+q
       142: q^2+q
       143: q^3+3q^2+q
       144: 2q^2+q
       145: 2q^2+q
       146: 2q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: 2q^2+q
       161: q^3+2q^2+q
       162: 2q^2+q
       163: 2q^2+q
       164: q^3+2q^2+q
       165: 2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       172: q^2+q
       173: q^2
       176: q^3+2q^2+q
       177: 2q^2+q
       179: 2q^2+q
       181: q^2+q
       184: q^2+q
       186: q^2+q
       187: q^2+q
       189: 2q^2+q
       191: q^2
       192: q^3+2q^2+q
       194: q
       196: q^2+q
       197: q
       199: q^2
       200: q^3+2q^2+q
       202: q^2+q
       204: q
       205: q
       207: q^3+3q^2+q
       209: q^2+q
       211: q^2+q
       213: 2q^2+q
       215: q^3+2q^2+q
       217: 2q^2+q
       219: q^3+2q^2+q
       220: q^2+q
       221: q^2+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: 2q^2+q
       227: 2q^2+q
       228: 2q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: 2q^2+q
       233: 2q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       262: q^2+q
       266: q^2+q
       269: q
       273: q
       275: q^2
       278: q^3+2q^2+q
       279: 2q^2+q
       281: 2q^2+q
       284: q^2+q
       286: q^2+q
       287: 2q^2+q
       289: q^2+q
       291: q^2+q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q^2+q
       305: q
       308: q^2+q
       310: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       320: q
       322: q
       323: q
       325: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: q
       335: q
       344: 2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q
       350: q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^2+q
       355: q
       356: q^2+q
       357: q
       358: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       380: q^2+q
       384: q^2+q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q^2+q
       411: q^2+q
       413: 2q^2+q
       415: q
       417: q^2+q
       420: q
       422: q
       423: q
       430: q
       432: q^2+q
       433: q
       435: q
       438: q
       440: q
       441: q
       448: q^2+q
       450: q
       451: q
       454: q
       455: q
       458: q
       459: q
       465: q^2+q
       467: q^2+q
       469: q^2+q
       472: q
       474: q
       475: q
       477: q
       481: q
       482: q
       492: q^2+q
       493: q
       494: q
       497: q^2+q
       498: q
       499: q
       508: q^2+q
       512: q
       514: q
       524: q^2+q
       528: q
       532: q
       536: q
       539: q
       543: q
       552: q
       555: q
       559: q
       568: q
       570: q
       583: q^2+q
       585: q
       587: q
       590: q
       596: q
       604: q
       605: q
       608: q
       609: q
       620: q
       622: q
       623: q
       625: q
       639: q^2+q
       642: q
       644: q
       645: q
       651: q
       675: q
       676: q
       681: q
       682: q
       708: q
       712: q
       723: q
       727: q
       739: q
       743: q
       756: q
       758: q
       777: q
       797: q
       802: q
       808: q
       821: q
       826: q
       832: q
       849: q
       853: 1
       899: q
       922: q
       946: q
       961: q
       979: 1
       984: 1
      1050: 1
      1107: 1
      1185: 1
      1190: 1
      1264: 1
      1311: 1
      1406: 1
      1415: 1
      1534: 1

1535:    0: q^4+3q^3+3q^2+q
         1: 3q^3+3q^2+q
         2: q^4+3q^3+3q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: 3q^3+3q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^4+2q^3+2q^2+q
         8: 3q^3+3q^2+q
         9: q^4+2q^3+2q^2+q
        10: 2q^3+3q^2+q
        11: 2q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^4+3q^3+3q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+3q^2+q
        16: q^4+3q^3+3q^2+q
        17: 3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^3+2q^2+q
        20: 2q^3+2q^2+q
        21: q^3+2q^2+q
        22: 2q^3+3q^2+q
        23: 2q^3+3q^2+q
        24: 2q^3+3q^2+q
        25: 2q^3+3q^2+q
        26: 2q^3+3q^2+q
        27: 2q^3+3q^2+q
        28: 2q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^3+3q^2+q
        33: 2q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^3+3q^2+q
        36: 2q^3+3q^2+q
        38: 2q^3+3q^2+q
        40: 2q^3+3q^2+q
        42: 2q^3+3q^2+q
        43: 2q^3+3q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+3q^2+q
        46: q^4+3q^3+3q^2+q
        47: 3q^3+3q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^3+2q^2+q
        50: 2q^3+2q^2+q
        51: q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^2
        59: q^3+2q^2+q
        60: q^3+2q^2+q
        61: q^2
        63: q^3+3q^2+q
        65: 2q^3+3q^2+q
        67: 2q^3+3q^2+q
        68: 2q^3+3q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^3+3q^2+q
        81: 2q^3+3q^2+q
        82: 2q^2+q
        83: 2q^2+q
        84: q^3+3q^2+q
        85: 2q^3+3q^2+q
        86: 2q^2+q
        87: 2q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q^3+2q^2+q
       105: q^2
       107: q^2+q
       110: q^2+q
       112: q^2+q
       114: 2q^2+q
       116: 2q^2+q
       117: q^2
       118: q^3+2q^2+q
       119: q^3+2q^2+q
       120: q^2
       122: q^3+3q^2+q
       124: 2q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^3+2q^2+q
       134: q^3+2q^2+q
       135: q^2+q
       136: q^2+q
       137: q^3+3q^2+q
       138: 2q^2+q
       139: 2q^2+q
       140: q
       141: 2q^2+q
       142: q^2+q
       143: q^3+3q^2+q
       144: 2q^2+q
       145: 2q^2+q
       146: 2q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: 2q^2+q
       161: q^3+2q^2+q
       162: 2q^2+q
       163: 2q^2+q
       164: q^3+2q^2+q
       165: 2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: q^2+q
       174: q^3+2q^2+q
       175: q^2
       178: 2q^2+q
       180: 2q^2+q
       182: q^2+q
       183: q^2+q
       186: q^2+q
       188: q^2+q
       190: 2q^2+q
       191: q^2
       192: q^3+2q^2+q
       193: q
       196: q^2+q
       198: q
       199: q^3+2q^2+q
       200: q^2
       201: q^2+q
       204: q
       206: q
       208: q^3+3q^2+q
       210: q^2+q
       212: q^2+q
       214: 2q^2+q
       216: q^3+2q^2+q
       218: 2q^2+q
       219: q^3+2q^2+q
       220: q^2+q
       221: q^2+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: 2q^2+q
       227: 2q^2+q
       228: 2q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: 2q^2+q
       233: 2q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2+q
       264: q^2+q
       268: q
       274: q
       276: q^3+2q^2+q
       277: q^2
       280: 2q^2+q
       282: 2q^2+q
       283: q^2+q
       286: q^2+q
       288: 2q^2+q
       290: q^2+q
       292: q^2+q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q^2+q
       306: q
       307: q^2+q
       310: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       319: q
       322: q
       324: q
       326: q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: q
       335: q
       344: 2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q
       350: q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^2+q
       355: q
       356: q^2+q
       357: q
       358: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       378: q^2+q
       382: q^2+q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q^2+q
       412: q^2+q
       414: 2q^2+q
       416: q
       418: q^2+q
       419: q
       422: q
       424: q
       429: q
       432: q^2+q
       434: q
       436: q
       437: q
       440: q
       442: q
       447: q^2+q
       450: q
       452: q
       453: q
       456: q
       458: q
       460: q
       466: q^2+q
       468: q^2+q
       470: q^2+q
       471: q
       474: q
       476: q
       478: q
       481: q
       482: q
       492: q^2+q
       493: q
       494: q
       497: q^2+q
       498: q
       499: q
       508: q^2+q
       512: q
       514: q
       522: q^2+q
       526: q
       530: q
       534: q
       538: q
       542: q
       551: q
       556: q
       560: q
       566: q
       571: q
       584: q^2+q
       586: q
       588: q
       589: q
       596: q
       603: q
       606: q
       608: q
       610: q
       619: q
       622: q
       624: q
       626: q
       640: q^2+q
       641: q
       644: q
       646: q
       652: q
       675: q
       676: q
       681: q
       682: q
       706: q
       710: q
       722: q
       726: q
       740: q
       744: q
       754: q
       759: q
       778: q
       798: q
       801: q
       808: q
       822: q
       825: q
       832: q
       850: q
       854: 1
       897: q
       921: q
       947: q
       962: q
       980: 1
       987: 1
      1051: 1
      1108: 1
      1186: 1
      1193: 1
      1265: 1
      1312: 1
      1409: 1
      1416: 1
      1535: 1

1536:    0: q^4+3q^3+3q^2+q
         1: 3q^3+3q^2+q
         2: q^4+3q^3+3q^2+q
         3: q^4+3q^3+3q^2+q
         4: q^4+2q^3+2q^2+q
         5: 3q^3+3q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^4+2q^3+2q^2+q
         8: 3q^3+3q^2+q
         9: q^4+2q^3+2q^2+q
        10: 2q^3+3q^2+q
        11: 2q^3+3q^2+q
        12: q^4+2q^3+2q^2+q
        13: q^4+3q^3+3q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+3q^2+q
        16: q^4+3q^3+3q^2+q
        17: 3q^3+3q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^3+2q^2+q
        20: 2q^3+2q^2+q
        21: q^3+2q^2+q
        22: 2q^3+3q^2+q
        23: 2q^3+3q^2+q
        24: 2q^3+3q^2+q
        25: 2q^3+3q^2+q
        26: 2q^3+3q^2+q
        27: 2q^3+3q^2+q
        28: 2q^3+3q^2+q
        29: q^3+2q^2+q
        30: q^3+2q^2+q
        31: q^3+3q^2+q
        32: 2q^3+3q^2+q
        33: 2q^3+3q^2+q
        34: q^3+3q^2+q
        35: 2q^3+3q^2+q
        36: 2q^3+3q^2+q
        38: 2q^3+3q^2+q
        40: 2q^3+3q^2+q
        42: 2q^3+3q^2+q
        43: 2q^3+3q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+3q^2+q
        46: q^4+3q^3+3q^2+q
        47: 3q^3+3q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^3+2q^2+q
        50: 2q^3+2q^2+q
        51: q^3+2q^2+q
        52: 2q^2+q
        53: q^3+2q^2+q
        54: 2q^2+q
        55: 2q^2+q
        56: q^3+2q^2+q
        57: 2q^2+q
        58: q^3+2q^2+q
        59: q^2
        60: q^2
        61: q^3+2q^2+q
        63: q^3+3q^2+q
        65: 2q^3+3q^2+q
        67: 2q^3+3q^2+q
        68: 2q^3+3q^2+q
        69: q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^3+2q^2+q
        72: q^2+q
        73: q^2+q
        75: 2q^2+q
        77: q^3+2q^2+q
        79: 2q^2+q
        80: q^3+3q^2+q
        81: 2q^3+3q^2+q
        82: 2q^2+q
        83: 2q^2+q
        84: q^3+3q^2+q
        85: 2q^3+3q^2+q
        86: 2q^2+q
        87: 2q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: 2q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^2+q
        95: q^3+2q^2+q
        96: 2q^2+q
        97: 2q^2+q
        98: q^3+2q^2+q
        99: 2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       104: q^2
       105: q^3+2q^2+q
       108: q^2+q
       109: q^2+q
       112: q^2+q
       114: 2q^2+q
       116: 2q^2+q
       117: q^3+2q^2+q
       118: q^2
       119: q^2
       120: q^3+2q^2+q
       122: q^3+3q^2+q
       124: 2q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       128: 2q^2+q
       130: q^3+2q^2+q
       132: 2q^2+q
       133: q^3+2q^2+q
       134: q^3+2q^2+q
       135: q^2+q
       136: q^2+q
       137: q^3+3q^2+q
       138: 2q^2+q
       139: 2q^2+q
       140: q
       141: 2q^2+q
       142: q^2+q
       143: q^3+3q^2+q
       144: 2q^2+q
       145: 2q^2+q
       146: 2q^2+q
       147: q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       152: q^2+q
       154: q^2+q
       156: q^2+q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: 2q^2+q
       161: q^3+2q^2+q
       162: 2q^2+q
       163: 2q^2+q
       164: q^3+2q^2+q
       165: 2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       171: q^2+q
       174: q^2
       175: q^3+2q^2+q
       178: 2q^2+q
       180: 2q^2+q
       182: q^2+q
       184: q^2+q
       185: q^2+q
       188: q^2+q
       190: 2q^2+q
       191: q^3+2q^2+q
       192: q^2
       194: q
       195: q^2+q
       198: q
       199: q^2
       200: q^3+2q^2+q
       202: q^2+q
       203: q
       206: q
       208: q^3+3q^2+q
       210: q^2+q
       212: q^2+q
       214: 2q^2+q
       216: q^3+2q^2+q
       218: 2q^2+q
       219: q^3+2q^2+q
       220: q^2+q
       221: q^2+q
       222: q
       223: q^2+q
       224: q
       225: q^2+q
       226: 2q^2+q
       227: 2q^2+q
       228: 2q^2+q
       229: q
       230: q^2+q
       231: 2q^2+q
       232: 2q^2+q
       233: 2q^2+q
       234: q^2+q
       235: q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       261: q^2+q
       265: q^2+q
       270: q
       272: q
       276: q^2
       277: q^3+2q^2+q
       280: 2q^2+q
       282: 2q^2+q
       284: q^2+q
       285: q^2+q
       288: 2q^2+q
       290: q^2+q
       292: q^2+q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q^2+q
       306: q
       308: q^2+q
       309: q
       312: q
       314: q
       316: q^2+q
       318: q^2+q
       320: q
       321: q
       324: q
       326: q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: q
       335: q
       344: 2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q
       350: q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^2+q
       355: q
       356: q^2+q
       357: q
       358: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       379: q^2+q
       383: q^2+q
       387: q
       392: q
       395: q
       398: q
       402: q
       408: q
       410: q^2+q
       412: q^2+q
       414: 2q^2+q
       416: q
       418: q^2+q
       420: q
       421: q
       424: q
       430: q
       431: q^2+q
       434: q
       436: q
       438: q
       439: q
       442: q
       448: q^2+q
       449: q
       452: q
       454: q
       456: q
       457: q
       460: q
       466: q^2+q
       468: q^2+q
       470: q^2+q
       472: q
       473: q
       476: q
       478: q
       481: q
       482: q
       492: q^2+q
       493: q
       494: q
       497: q^2+q
       498: q
       499: q
       508: q^2+q
       512: q
       514: q
       523: q^2+q
       527: q
       531: q
       535: q
       540: q
       544: q
       550: q
       554: q
       558: q
       567: q
       572: q
       584: q^2+q
       586: q
       588: q
       590: q
       595: q
       604: q
       606: q
       607: q
       610: q
       620: q
       621: q
       624: q
       626: q
       640: q^2+q
       642: q
       643: q
       646: q
       652: q
       675: q
       676: q
       681: q
       682: q
       707: q
       711: q
       724: q
       728: q
       738: q
       742: q
       755: q
       760: q
       778: q
       798: q
       802: q
       807: q
       822: q
       826: q
       831: q
       850: q
       854: 1
       898: q
       923: q
       945: q
       963: q
       981: 1
       987: 1
      1051: 1
      1109: 1
      1187: 1
      1193: 1
      1265: 1
      1313: 1
      1409: 1
      1417: 1
      1536: 1

1537:    0: 6q^3+10q^2+7q+1
         1: q^4+8q^3+10q^2+7q+1
         2: q^4+6q^3+7q^2+7q+1
         3: 6q^3+10q^2+7q+1
         4: 6q^3+10q^2+7q+1
         5: q^4+8q^3+10q^2+7q+1
         6: q^4+8q^3+10q^2+7q+1
         7: q^4+6q^3+7q^2+7q+1
         8: 2q^4+8q^3+7q^2+7q+1
         9: q^4+6q^3+7q^2+7q+1
        10: 4q^3+8q^2+7q+1
        11: 4q^3+8q^2+7q+1
        12: 4q^3+8q^2+7q+1
        13: 3q^3+7q^2+7q+1
        14: 3q^3+7q^2+7q+1
        15: 5q^3+7q^2+7q+1
        16: 6q^3+10q^2+7q+1
        17: q^4+8q^3+10q^2+7q+1
        18: q^4+6q^3+7q^2+7q+1
        19: 6q^3+10q^2+7q+1
        20: q^4+8q^3+10q^2+7q+1
        21: q^4+6q^3+7q^2+7q+1
        22: 2q^3+7q^2+7q+1
        23: 2q^3+7q^2+7q+1
        24: 3q^3+5q^2+7q+1
        25: 2q^3+7q^2+7q+1
        26: 2q^3+7q^2+7q+1
        27: 3q^3+5q^2+7q+1
        28: 4q^3+8q^2+7q+1
        29: 4q^3+8q^2+7q+1
        30: 3q^3+7q^2+7q+1
        31: q^3+5q^2+7q+1
        32: q^3+5q^2+7q+1
        33: 2q^3+7q^2+7q+1
        34: q^3+5q^2+7q+1
        35: q^3+5q^2+7q+1
        36: 2q^3+7q^2+7q+1
        37: 4q^2+5q+1
        38: q^2+2q
        39: 4q^2+5q+1
        40: q^2+2q
        41: q^3+3q^2+5q+1
        42: q^2+2q
        43: q^3+5q^2+7q+1
        44: q^3+5q^2+7q+1
        45: q^3+5q^2+7q+1
        46: 3q^3+7q^2+7q+1
        47: 5q^3+7q^2+7q+1
        48: 3q^3+7q^2+7q+1
        49: 6q^3+10q^2+7q+1
        50: q^4+8q^3+10q^2+7q+1
        51: q^4+6q^3+7q^2+7q+1
        52: 2q^3+7q^2+7q+1
        53: 2q^3+7q^2+7q+1
        54: 3q^3+5q^2+7q+1
        55: 2q^3+7q^2+7q+1
        56: 2q^3+7q^2+7q+1
        57: 3q^3+5q^2+7q+1
        58: q^3+3q^2+5q+1
        59: 2q^2+2q
        60: q^3+3q^2+5q+1
        61: 2q^2+2q
        62: 3q^2+5q+1
        63: 2q
        64: 3q^2+5q+1
        65: q^2+2q
        66: 4q^2+5q+1
        67: q^2+2q
        68: 2q^2+7q+1
        69: 3q^3+7q^2+7q+1
        70: q^3+5q^2+7q+1
        71: 4q^3+8q^2+7q+1
        72: 2q^3+7q^2+7q+1
        73: 2q^3+7q^2+7q+1
        74: 4q^2+5q+1
        75: q^2+2q
        76: 4q^2+5q+1
        77: q^2+2q
        78: q^3+3q^2+5q+1
        79: q^2+2q
        80: 3q^2+7q+1
        81: q^3+5q^2+7q+1
        82: q^3+5q^2+7q+1
        83: q^3+5q^2+7q+1
        84: 3q^2+7q+1
        85: q^3+5q^2+7q+1
        86: q^3+5q^2+7q+1
        87: q^3+5q^2+7q+1
        88: q^3+5q^2+7q+1
        89: q^3+5q^2+7q+1
        90: q^3+5q^2+7q+1
        91: 3q^3+7q^2+7q+1
        92: 5q^3+7q^2+7q+1
        93: 3q^3+7q^2+7q+1
        94: 2q^3+7q^2+7q+1
        95: 2q^3+7q^2+7q+1
        96: 3q^3+5q^2+7q+1
        97: 2q^3+7q^2+7q+1
        98: 2q^3+7q^2+7q+1
        99: 3q^3+5q^2+7q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: 2q^2+4q+1
       104: q
       105: q
       106: q^2+q
       107: q^3+3q^2+5q+1
       108: 2q^2+2q
       109: q^3+3q^2+5q+1
       110: 2q^2+2q
       111: 4q^2+5q+1
       112: q^2+2q
       113: 3q^2+5q+1
       114: 2q
       115: 3q^2+5q+1
       116: q^2+2q
       117: q^2+5q+1
       118: 2q
       119: q^2+5q+1
       120: 2q
       121: 2q^2+5q+1
       122: 2q
       123: 3q^2+5q+1
       124: q^2+2q
       125: 2q^2+7q+1
       126: q^3+5q^2+7q+1
       127: 4q^2+5q+1
       128: q^2+2q
       129: 4q^2+5q+1
       130: q^2+2q
       131: q^3+3q^2+5q+1
       132: q^2+2q
       133: 2q^2+7q+1
       134: 3q^3+7q^2+7q+1
       135: q^3+5q^2+7q+1
       136: q^3+5q^2+7q+1
       137: 3q^2+7q+1
       138: q^3+5q^2+7q+1
       139: q^3+5q^2+7q+1
       140: 3q+1
       141: 3q^2+7q+1
       142: 2q^3+7q^2+7q+1
       143: 3q^2+7q+1
       144: q^3+5q^2+7q+1
       145: q^3+5q^2+7q+1
       146: 3q^2+7q+1
       147: 2q^3+7q^2+7q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: q^2+4q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: q^2+4q+1
       156: 2q
       157: q^3+5q^2+7q+1
       158: q^3+5q^2+7q+1
       159: q^3+5q^2+7q+1
       160: q^3+3q^2+6q+1
       161: q^3+3q^2+6q+1
       162: q^3+3q^2+6q+1
       163: q^3+3q^2+6q+1
       164: q^3+3q^2+6q+1
       165: q^3+3q^2+6q+1
       166: q^2+6q+1
       167: 3q^2+6q+1
       168: q^2+6q+1
       169: 2q^2+4q+1
       170: q
       171: q
       172: q^2+q
       173: q^2+4q+1
       174: q
       175: q
       176: q
       177: 3q^2+5q+1
       178: q^2+2q
       179: 3q^2+5q+1
       180: 2q
       181: 4q^2+5q+1
       182: q^2+2q
       183: q^2+5q+1
       184: 2q
       185: q^2+5q+1
       186: 2q
       187: 3q^2+5q+1
       188: q^2+2q
       189: 2q^2+5q+1
       190: 2q
       191: q^2+5q+1
       192: 2q
       193: 3q+1
       195: q^3+3q^2+5q+1
       196: 2q^2+2q
       197: 2q+1
       198: q
       199: q^2+5q+1
       200: 2q
       201: q^3+3q^2+5q+1
       202: 2q^2+2q
       203: 3q+1
       205: 2q+1
       206: q
       207: 2q^2+5q+1
       208: 2q
       209: q^2+4q+1
       210: 2q
       211: q^2+4q+1
       212: 2q
       213: q^2+3q+1
       215: q^2+3q+1
       217: q^2+3q+1
       219: 2q^2+7q+1
       220: 2q^2+7q+1
       221: q^3+5q^2+7q+1
       222: 3q^2+7q+1
       223: q^3+5q^2+7q+1
       224: 3q^2+7q+1
       225: q^3+5q^2+7q+1
       226: 3q^2+7q+1
       227: 6q+1
       228: q^3+3q^2+6q+1
       229: 3q+1
       230: q^3+3q^2+6q+1
       231: 3q^2+7q+1
       232: 6q+1
       233: q^3+3q^2+6q+1
       234: q^3+3q^2+6q+1
       235: 3q+1
       236: q^2+6q+1
       237: q^2+4q+1
       238: 2q
       239: 2q^2+4q+1
       240: q^2+2q
       241: q^2+4q+1
       242: 2q
       243: q^2+6q+1
       244: 3q+1
       245: 3q+1
       246: q^2+6q+1
       247: q^2+6q+1
       248: 3q^2+6q+1
       249: q^2+6q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: 2q^2+4q+1
       260: q
       261: q
       262: q^2+q
       263: q^2+4q+1
       264: q
       265: q
       266: q
       267: 2q+1
       268: q
       271: 2q+1
       272: q
       275: q^2+4q+1
       276: q
       277: q
       278: q
       279: 3q+1
       281: q^2+3q+1
       283: q^2+5q+1
       284: 2q
       285: q^2+5q+1
       286: 2q
       287: 2q^2+5q+1
       288: 2q
       289: q^2+3q+1
       291: 3q^2+5q+1
       292: q^2+2q
       293: q^2+5q+1
       294: 2q
       295: q^2+5q+1
       296: 2q
       297: 2q^2+5q+1
       298: 2q
       299: 3q+1
       301: 2q+1
       302: q
       303: 4q+1
       304: 2q
       305: 2q+1
       306: q
       307: 4q+1
       308: 2q
       309: 3q+1
       311: 2q+1
       312: q
       313: 2q+1
       314: q
       315: q^2+4q+1
       316: 2q
       317: q^2+4q+1
       318: 2q
       319: 3q+1
       321: 3q+1
       323: q+1
       325: q^2+4q+1
       326: 2q
       333: 2q^2+7q+1
       334: 3q^2+7q+1
       335: 3q^2+7q+1
       336: q^2+6q+1
       337: q^2+6q+1
       338: q^2+4q+1
       339: 2q
       340: 2q^2+4q+1
       341: q^2+2q
       342: q^2+4q+1
       343: 2q
       344: 6q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^3+3q^2+6q+1
       351: 3q+1
       352: 6q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^3+3q^2+6q+1
       357: q+1
       358: 3q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+6q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+4q+1
       378: q
       379: q
       380: q
       381: 2q+1
       384: q
       385: q^2+4q+1
       386: q
       387: q
       388: q
       389: 2q+1
       390: q
       393: 2q+1
       394: q
       397: 2q+1
       398: q
       401: 2q+1
       402: q
       405: q+1
       413: 3q+1
       417: q^2+3q+1
       419: q^2+5q+1
       420: 2q
       421: q^2+5q+1
       422: 2q
       423: 2q^2+5q+1
       424: 2q
       425: q^2+4q+1
       426: 2q
       427: q^2+4q+1
       428: 2q
       429: 3q+1
       431: 4q+1
       432: 2q
       433: 2q+1
       434: q
       435: 1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: 3q+1
       445: 2q+1
       446: q
       447: 4q+1
       448: 2q
       449: 3q+1
       451: 2q+1
       452: q
       453: 2q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: 3q+1
       463: 2q+1
       464: q
       465: q+1
       467: q+1
       469: q^2+4q+1
       470: 2q
       471: q+1
       473: q+1
       475: 1
       477: q+1
       479: q+1
       481: 6q+1
       482: 6q+1
       483: q^2+6q+1
       484: 3q+1
       485: q+1
       487: q+1
       489: q+1
       491: 3q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: 3q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: 2q+1
       524: q
       529: q^2+4q+1
       530: q
       531: q
       532: q
       533: 2q+1
       534: q
       537: 1
       541: q+1
       545: 2q+1
       546: q
       549: 2q+1
       550: q
       553: 1
       557: q+1
       561: 2q+1
       562: q
       565: 1
       569: q+1
       573: q+1
       577: q+1
       585: 3q+1
       589: 4q+1
       590: 2q
       591: 3q+1
       593: 3q+1
       595: 4q+1
       596: 2q
       597: q+1
       599: q^2+4q+1
       600: 2q
       601: q+1
       603: q+1
       605: 1
       607: 2q+1
       608: q
       609: q+1
       613: 2q+1
       614: q
       615: q+1
       617: 1
       619: 2q+1
       620: q
       621: q+1
       623: 1
       625: q+1
       629: 2q+1
       630: q
       631: q+1
       633: 1
       639: q+1
       641: q+1
       643: q+1
       645: 1
       647: 1
       649: 1
       651: 2
       653: 1
       655: 1
       657: 3q+1
       658: q+1
       660: q+1
       662: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: q+1
       680: q+1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       709: 2q+1
       712: q
       713: 2q+1
       714: q
       717: 2q+1
       718: q
       721: 1
       725: q+1
       733: 1
       737: 1
       741: q+1
       749: 1
       753: 1
       757: 2
       761: 1
       765: 1
       769: 1
       771: 1
       775: q+1
       779: q+1
       781: q+1
       785: q+1
       787: q+1
       791: 1
       793: q+1
       795: 1
       797: 1
       801: 1
       805: q+1
       807: 2q+1
       808: q
       809: 1
       811: q+1
       815: 1
       817: q+1
       819: 1
       821: 1
       825: 2q+1
       826: q
       827: q+1
       831: 1
       833: 1
       835: q+1
       839: 1
       843: 1
       845: 1
       847: 1
       849: 2
       851: 1
       857: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       900: 1
       904: 1
       908: 1
       916: 1
       920: 1
       928: q+1
       940: 1
       944: 1
       948: q+1
       960: 2
       964: 1
       968: 1
       970: 1
       974: 1
       988: 1
       994: q+1
       998: q+1
      1000: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1016: 1
      1020: 1
      1022: 1
      1026: 1
      1032: 1
      1036: 1
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1058: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1088: 1
      1114: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1156: 1
      1172: 1
      1194: 1
      1198: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1230: 1
      1234: 1
      1240: 1
      1248: 1
      1250: 1
      1260: 1
      1283: 1
      1285: 1
      1290: 1
      1292: 1
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1436: 1
      1454: 1
      1460: 1
      1537: 1

1538:    0: 6q^3+10q^2+7q+1
         1: q^4+8q^3+10q^2+7q+1
         2: q^4+6q^3+7q^2+7q+1
         3: 6q^3+10q^2+7q+1
         4: 6q^3+10q^2+7q+1
         5: q^4+8q^3+10q^2+7q+1
         6: q^4+8q^3+10q^2+7q+1
         7: q^4+6q^3+7q^2+7q+1
         8: 2q^4+8q^3+7q^2+7q+1
         9: q^4+6q^3+7q^2+7q+1
        10: 4q^3+8q^2+7q+1
        11: 4q^3+8q^2+7q+1
        12: 4q^3+8q^2+7q+1
        13: 3q^3+7q^2+7q+1
        14: 3q^3+7q^2+7q+1
        15: 5q^3+7q^2+7q+1
        16: 6q^3+10q^2+7q+1
        17: q^4+8q^3+10q^2+7q+1
        18: q^4+6q^3+7q^2+7q+1
        19: 6q^3+10q^2+7q+1
        20: q^4+8q^3+10q^2+7q+1
        21: q^4+6q^3+7q^2+7q+1
        22: 2q^3+7q^2+7q+1
        23: 2q^3+7q^2+7q+1
        24: 3q^3+5q^2+7q+1
        25: 2q^3+7q^2+7q+1
        26: 2q^3+7q^2+7q+1
        27: 3q^3+5q^2+7q+1
        28: 4q^3+8q^2+7q+1
        29: 4q^3+8q^2+7q+1
        30: 3q^3+7q^2+7q+1
        31: q^3+5q^2+7q+1
        32: q^3+5q^2+7q+1
        33: 2q^3+7q^2+7q+1
        34: q^3+5q^2+7q+1
        35: q^3+5q^2+7q+1
        36: 2q^3+7q^2+7q+1
        37: 4q^2+5q+1
        38: q^2+2q
        39: 4q^2+5q+1
        40: q^2+2q
        41: q^3+3q^2+5q+1
        42: q^2+2q
        43: q^3+5q^2+7q+1
        44: q^3+5q^2+7q+1
        45: q^3+5q^2+7q+1
        46: 3q^3+7q^2+7q+1
        47: 5q^3+7q^2+7q+1
        48: 3q^3+7q^2+7q+1
        49: 6q^3+10q^2+7q+1
        50: q^4+8q^3+10q^2+7q+1
        51: q^4+6q^3+7q^2+7q+1
        52: 2q^3+7q^2+7q+1
        53: 2q^3+7q^2+7q+1
        54: 3q^3+5q^2+7q+1
        55: 2q^3+7q^2+7q+1
        56: 2q^3+7q^2+7q+1
        57: 3q^3+5q^2+7q+1
        58: 2q^2+2q
        59: q^3+3q^2+5q+1
        60: 2q^2+2q
        61: q^3+3q^2+5q+1
        62: 3q^2+5q+1
        63: 2q
        64: 3q^2+5q+1
        65: q^2+2q
        66: 4q^2+5q+1
        67: q^2+2q
        68: 2q^2+7q+1
        69: 3q^3+7q^2+7q+1
        70: q^3+5q^2+7q+1
        71: 4q^3+8q^2+7q+1
        72: 2q^3+7q^2+7q+1
        73: 2q^3+7q^2+7q+1
        74: 4q^2+5q+1
        75: q^2+2q
        76: 4q^2+5q+1
        77: q^2+2q
        78: q^3+3q^2+5q+1
        79: q^2+2q
        80: 3q^2+7q+1
        81: q^3+5q^2+7q+1
        82: q^3+5q^2+7q+1
        83: q^3+5q^2+7q+1
        84: 3q^2+7q+1
        85: q^3+5q^2+7q+1
        86: q^3+5q^2+7q+1
        87: q^3+5q^2+7q+1
        88: q^3+5q^2+7q+1
        89: q^3+5q^2+7q+1
        90: q^3+5q^2+7q+1
        91: 3q^3+7q^2+7q+1
        92: 5q^3+7q^2+7q+1
        93: 3q^3+7q^2+7q+1
        94: 2q^3+7q^2+7q+1
        95: 2q^3+7q^2+7q+1
        96: 3q^3+5q^2+7q+1
        97: 2q^3+7q^2+7q+1
        98: 2q^3+7q^2+7q+1
        99: 3q^3+5q^2+7q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q^2+q
       104: q
       105: q
       106: 2q^2+4q+1
       107: 2q^2+2q
       108: q^3+3q^2+5q+1
       109: 2q^2+2q
       110: q^3+3q^2+5q+1
       111: 4q^2+5q+1
       112: q^2+2q
       113: 3q^2+5q+1
       114: 2q
       115: 3q^2+5q+1
       116: q^2+2q
       117: 2q
       118: q^2+5q+1
       119: 2q
       120: q^2+5q+1
       121: 2q^2+5q+1
       122: 2q
       123: 3q^2+5q+1
       124: q^2+2q
       125: 2q^2+7q+1
       126: q^3+5q^2+7q+1
       127: 4q^2+5q+1
       128: q^2+2q
       129: 4q^2+5q+1
       130: q^2+2q
       131: q^3+3q^2+5q+1
       132: q^2+2q
       133: 2q^2+7q+1
       134: 3q^3+7q^2+7q+1
       135: q^3+5q^2+7q+1
       136: q^3+5q^2+7q+1
       137: 3q^2+7q+1
       138: q^3+5q^2+7q+1
       139: q^3+5q^2+7q+1
       140: 3q+1
       141: 3q^2+7q+1
       142: 2q^3+7q^2+7q+1
       143: 3q^2+7q+1
       144: q^3+5q^2+7q+1
       145: q^3+5q^2+7q+1
       146: 3q^2+7q+1
       147: 2q^3+7q^2+7q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: q^2+4q+1
       152: 2q
       153: 2q^2+4q+1
       154: q^2+2q
       155: q^2+4q+1
       156: 2q
       157: q^3+5q^2+7q+1
       158: q^3+5q^2+7q+1
       159: q^3+5q^2+7q+1
       160: q^3+3q^2+6q+1
       161: q^3+3q^2+6q+1
       162: q^3+3q^2+6q+1
       163: q^3+3q^2+6q+1
       164: q^3+3q^2+6q+1
       165: q^3+3q^2+6q+1
       166: q^2+6q+1
       167: 3q^2+6q+1
       168: q^2+6q+1
       169: q^2+q
       170: q
       171: q
       172: 2q^2+4q+1
       173: q
       174: q
       175: q
       176: q^2+4q+1
       177: 3q^2+5q+1
       178: q^2+2q
       179: 3q^2+5q+1
       180: 2q
       181: 4q^2+5q+1
       182: q^2+2q
       183: 2q
       184: q^2+5q+1
       185: 2q
       186: q^2+5q+1
       187: 3q^2+5q+1
       188: q^2+2q
       189: 2q^2+5q+1
       190: 2q
       191: 2q
       192: q^2+5q+1
       194: 3q+1
       195: 2q^2+2q
       196: q^3+3q^2+5q+1
       197: 2q+1
       198: q
       199: 2q
       200: q^2+5q+1
       201: 2q^2+2q
       202: q^3+3q^2+5q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: 2q^2+5q+1
       208: 2q
       209: q^2+4q+1
       210: 2q
       211: q^2+4q+1
       212: 2q
       213: q^2+3q+1
       215: q^2+3q+1
       217: q^2+3q+1
       219: 2q^2+7q+1
       220: 2q^2+7q+1
       221: q^3+5q^2+7q+1
       222: 3q^2+7q+1
       223: q^3+5q^2+7q+1
       224: 3q^2+7q+1
       225: q^3+5q^2+7q+1
       226: 3q^2+7q+1
       227: 6q+1
       228: q^3+3q^2+6q+1
       229: 3q+1
       230: q^3+3q^2+6q+1
       231: 3q^2+7q+1
       232: 6q+1
       233: q^3+3q^2+6q+1
       234: q^3+3q^2+6q+1
       235: 3q+1
       236: q^2+6q+1
       237: q^2+4q+1
       238: 2q
       239: 2q^2+4q+1
       240: q^2+2q
       241: q^2+4q+1
       242: 2q
       243: q^2+6q+1
       244: 3q+1
       245: 3q+1
       246: q^2+6q+1
       247: q^2+6q+1
       248: 3q^2+6q+1
       249: q^2+6q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q^2+q
       260: q
       261: q
       262: 2q^2+4q+1
       263: q
       264: q
       265: q
       266: q^2+4q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: q
       275: q
       276: q
       277: q
       278: q^2+4q+1
       279: 3q+1
       281: q^2+3q+1
       283: 2q
       284: q^2+5q+1
       285: 2q
       286: q^2+5q+1
       287: 2q^2+5q+1
       288: 2q
       289: q^2+3q+1
       291: 3q^2+5q+1
       292: q^2+2q
       293: 2q
       294: q^2+5q+1
       295: 2q
       296: q^2+5q+1
       297: 2q^2+5q+1
       298: 2q
       300: 3q+1
       301: 2q+1
       302: q
       303: 2q
       304: 4q+1
       305: 2q+1
       306: q
       307: 2q
       308: 4q+1
       310: 3q+1
       311: 2q+1
       312: q
       313: 2q+1
       314: q
       315: q^2+4q+1
       316: 2q
       317: q^2+4q+1
       318: 2q
       320: 3q+1
       322: 3q+1
       323: q+1
       325: q^2+4q+1
       326: 2q
       333: 2q^2+7q+1
       334: 3q^2+7q+1
       335: 3q^2+7q+1
       336: q^2+6q+1
       337: q^2+6q+1
       338: q^2+4q+1
       339: 2q
       340: 2q^2+4q+1
       341: q^2+2q
       342: q^2+4q+1
       343: 2q
       344: 6q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^3+3q^2+6q+1
       351: 3q+1
       352: 6q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^3+3q^2+6q+1
       357: q+1
       358: 3q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+6q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: q
       380: q^2+4q+1
       381: q
       384: 2q+1
       385: q
       386: q
       387: q
       388: q^2+4q+1
       391: 2q+1
       392: q
       395: q
       396: 2q+1
       399: 2q+1
       400: q
       403: q
       404: 2q+1
       406: q+1
       413: 3q+1
       417: q^2+3q+1
       419: 2q
       420: q^2+5q+1
       421: 2q
       422: q^2+5q+1
       423: 2q^2+5q+1
       424: 2q
       425: q^2+4q+1
       426: 2q
       427: q^2+4q+1
       428: 2q
       430: 3q+1
       431: 2q
       432: 4q+1
       433: 2q+1
       434: q
       435: 1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: 3q+1
       445: 2q+1
       446: q
       447: 2q
       448: 4q+1
       450: 3q+1
       451: 2q+1
       452: q
       453: q
       454: 2q+1
       455: 1
       458: q+1
       459: q+1
       462: 3q+1
       463: 2q+1
       464: q
       465: q+1
       467: q+1
       469: q^2+4q+1
       470: 2q
       472: q+1
       474: q+1
       475: 1
       477: q+1
       479: q+1
       481: 6q+1
       482: 6q+1
       483: q^2+6q+1
       484: 3q+1
       485: q+1
       487: q+1
       489: q+1
       491: 3q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: 3q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 2q+1
       529: q
       530: q
       531: q
       532: q^2+4q+1
       535: q
       536: 2q+1
       539: 1
       543: q+1
       547: 2q+1
       548: q
       551: q
       552: 2q+1
       555: 1
       559: q+1
       563: 2q+1
       564: q
       568: 1
       570: q+1
       575: q+1
       577: q+1
       585: 3q+1
       589: 2q
       590: 4q+1
       592: 3q+1
       594: 3q+1
       595: 2q
       596: 4q+1
       597: q+1
       599: q^2+4q+1
       600: 2q
       601: q+1
       604: q+1
       605: 1
       607: q
       608: 2q+1
       609: q+1
       613: 2q+1
       614: q
       616: q+1
       617: 1
       619: q
       620: 2q+1
       622: q+1
       623: 1
       625: q+1
       629: 2q+1
       630: q
       632: q+1
       633: 1
       639: q+1
       642: q+1
       644: q+1
       645: 1
       648: 1
       650: 1
       651: 2
       653: 1
       655: 1
       657: 3q+1
       658: q+1
       660: q+1
       662: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: q+1
       680: q+1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       709: q
       712: 2q+1
       715: q
       716: 2q+1
       719: q
       720: 2q+1
       723: 1
       727: q+1
       735: 1
       739: 1
       743: q+1
       751: 1
       756: 1
       758: 2
       762: 1
       768: 1
       769: 1
       771: 1
       775: q+1
       779: q+1
       781: q+1
       786: q+1
       788: q+1
       791: 1
       794: q+1
       795: 1
       797: 1
       802: 1
       806: q+1
       807: q
       808: 2q+1
       809: 1
       811: q+1
       816: 1
       818: q+1
       819: 1
       821: 1
       825: q
       826: 2q+1
       828: q+1
       832: 1
       833: 1
       835: q+1
       840: 1
       843: 1
       846: 1
       848: 1
       849: 2
       851: 1
       857: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       889: 1
       893: 1
       902: 1
       906: 1
       911: 1
       918: 1
       922: 1
       930: q+1
       942: 1
       946: 1
       950: q+1
       961: 2
       967: 1
       968: 1
       970: 1
       975: 1
       991: 1
       994: q+1
       999: q+1
      1001: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1017: 1
      1020: 1
      1022: 1
      1027: 1
      1033: 1
      1036: 1
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1059: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1091: 1
      1095: 1
      1116: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1158: 1
      1174: 1
      1197: 1
      1199: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: 1
      1235: 1
      1241: 1
      1248: 1
      1251: 1
      1261: 1
      1283: 1
      1285: 1
      1295: 1
      1299: 1
      1329: 1
      1331: 1
      1358: 1
      1382: 1
      1436: 1
      1455: 1
      1461: 1
      1538: 1

1539:    0: 6q^3+10q^2+7q+1
         1: q^4+8q^3+10q^2+7q+1
         2: q^4+6q^3+7q^2+7q+1
         3: 6q^3+10q^2+7q+1
         4: 6q^3+10q^2+7q+1
         5: q^4+8q^3+10q^2+7q+1
         6: q^4+8q^3+10q^2+7q+1
         7: q^4+6q^3+7q^2+7q+1
         8: 2q^4+8q^3+7q^2+7q+1
         9: q^4+6q^3+7q^2+7q+1
        10: 4q^3+8q^2+7q+1
        11: 4q^3+8q^2+7q+1
        12: 4q^3+8q^2+7q+1
        13: 3q^3+7q^2+7q+1
        14: 3q^3+7q^2+7q+1
        15: 5q^3+7q^2+7q+1
        16: 6q^3+10q^2+7q+1
        17: q^4+8q^3+10q^2+7q+1
        18: q^4+6q^3+7q^2+7q+1
        19: 6q^3+10q^2+7q+1
        20: q^4+8q^3+10q^2+7q+1
        21: q^4+6q^3+7q^2+7q+1
        22: 2q^3+7q^2+7q+1
        23: 2q^3+7q^2+7q+1
        24: 3q^3+5q^2+7q+1
        25: 2q^3+7q^2+7q+1
        26: 2q^3+7q^2+7q+1
        27: 3q^3+5q^2+7q+1
        28: 4q^3+8q^2+7q+1
        29: 4q^3+8q^2+7q+1
        30: 3q^3+7q^2+7q+1
        31: q^3+5q^2+7q+1
        32: q^3+5q^2+7q+1
        33: 2q^3+7q^2+7q+1
        34: q^3+5q^2+7q+1
        35: q^3+5q^2+7q+1
        36: 2q^3+7q^2+7q+1
        37: q^2+2q
        38: 4q^2+5q+1
        39: q^2+2q
        40: 4q^2+5q+1
        41: q^2+2q
        42: q^3+3q^2+5q+1
        43: q^3+5q^2+7q+1
        44: q^3+5q^2+7q+1
        45: q^3+5q^2+7q+1
        46: 3q^3+7q^2+7q+1
        47: 5q^3+7q^2+7q+1
        48: 3q^3+7q^2+7q+1
        49: 6q^3+10q^2+7q+1
        50: q^4+8q^3+10q^2+7q+1
        51: q^4+6q^3+7q^2+7q+1
        52: 2q^3+7q^2+7q+1
        53: 2q^3+7q^2+7q+1
        54: 3q^3+5q^2+7q+1
        55: 2q^3+7q^2+7q+1
        56: 2q^3+7q^2+7q+1
        57: 3q^3+5q^2+7q+1
        58: 2q^2+2q
        59: q^3+3q^2+5q+1
        60: q^3+3q^2+5q+1
        61: 2q^2+2q
        62: 2q
        63: 3q^2+5q+1
        64: q^2+2q
        65: 3q^2+5q+1
        66: q^2+2q
        67: 4q^2+5q+1
        68: 2q^2+7q+1
        69: 3q^3+7q^2+7q+1
        70: q^3+5q^2+7q+1
        71: 4q^3+8q^2+7q+1
        72: 2q^3+7q^2+7q+1
        73: 2q^3+7q^2+7q+1
        74: q^2+2q
        75: 4q^2+5q+1
        76: q^2+2q
        77: 4q^2+5q+1
        78: q^2+2q
        79: q^3+3q^2+5q+1
        80: 3q^2+7q+1
        81: q^3+5q^2+7q+1
        82: q^3+5q^2+7q+1
        83: q^3+5q^2+7q+1
        84: 3q^2+7q+1
        85: q^3+5q^2+7q+1
        86: q^3+5q^2+7q+1
        87: q^3+5q^2+7q+1
        88: q^3+5q^2+7q+1
        89: q^3+5q^2+7q+1
        90: q^3+5q^2+7q+1
        91: 3q^3+7q^2+7q+1
        92: 5q^3+7q^2+7q+1
        93: 3q^3+7q^2+7q+1
        94: 2q^3+7q^2+7q+1
        95: 2q^3+7q^2+7q+1
        96: 3q^3+5q^2+7q+1
        97: 2q^3+7q^2+7q+1
        98: 2q^3+7q^2+7q+1
        99: 3q^3+5q^2+7q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q
       104: 2q^2+4q+1
       105: q^2+q
       106: q
       107: q^3+3q^2+5q+1
       108: 2q^2+2q
       109: 2q^2+2q
       110: q^3+3q^2+5q+1
       111: q^2+2q
       112: 4q^2+5q+1
       113: 2q
       114: 3q^2+5q+1
       115: q^2+2q
       116: 3q^2+5q+1
       117: 2q
       118: q^2+5q+1
       119: q^2+5q+1
       120: 2q
       121: 2q
       122: 2q^2+5q+1
       123: q^2+2q
       124: 3q^2+5q+1
       125: 2q^2+7q+1
       126: q^3+5q^2+7q+1
       127: q^2+2q
       128: 4q^2+5q+1
       129: q^2+2q
       130: 4q^2+5q+1
       131: q^2+2q
       132: q^3+3q^2+5q+1
       133: 2q^2+7q+1
       134: 3q^3+7q^2+7q+1
       135: q^3+5q^2+7q+1
       136: q^3+5q^2+7q+1
       137: 3q^2+7q+1
       138: q^3+5q^2+7q+1
       139: q^3+5q^2+7q+1
       140: 3q+1
       141: 3q^2+7q+1
       142: 2q^3+7q^2+7q+1
       143: 3q^2+7q+1
       144: q^3+5q^2+7q+1
       145: q^3+5q^2+7q+1
       146: 3q^2+7q+1
       147: 2q^3+7q^2+7q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: 2q
       152: q^2+4q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: 2q
       156: q^2+4q+1
       157: q^3+5q^2+7q+1
       158: q^3+5q^2+7q+1
       159: q^3+5q^2+7q+1
       160: q^3+3q^2+6q+1
       161: q^3+3q^2+6q+1
       162: q^3+3q^2+6q+1
       163: q^3+3q^2+6q+1
       164: q^3+3q^2+6q+1
       165: q^3+3q^2+6q+1
       166: q^2+6q+1
       167: 3q^2+6q+1
       168: q^2+6q+1
       169: q
       170: 2q^2+4q+1
       171: q^2+q
       172: q
       173: q
       174: q^2+4q+1
       175: q
       176: q
       177: q^2+2q
       178: 3q^2+5q+1
       179: 2q
       180: 3q^2+5q+1
       181: q^2+2q
       182: 4q^2+5q+1
       183: q^2+5q+1
       184: 2q
       185: 2q
       186: q^2+5q+1
       187: q^2+2q
       188: 3q^2+5q+1
       189: 2q
       190: 2q^2+5q+1
       191: 2q
       192: q^2+5q+1
       193: 3q+1
       195: 2q^2+2q
       196: q^3+3q^2+5q+1
       197: q
       198: 2q+1
       199: q^2+5q+1
       200: 2q
       201: q^3+3q^2+5q+1
       202: 2q^2+2q
       204: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: 2q^2+5q+1
       209: 2q
       210: q^2+4q+1
       211: 2q
       212: q^2+4q+1
       214: q^2+3q+1
       216: q^2+3q+1
       218: q^2+3q+1
       219: 2q^2+7q+1
       220: 2q^2+7q+1
       221: q^3+5q^2+7q+1
       222: 3q^2+7q+1
       223: q^3+5q^2+7q+1
       224: 3q^2+7q+1
       225: q^3+5q^2+7q+1
       226: 3q^2+7q+1
       227: 6q+1
       228: q^3+3q^2+6q+1
       229: 3q+1
       230: q^3+3q^2+6q+1
       231: 3q^2+7q+1
       232: 6q+1
       233: q^3+3q^2+6q+1
       234: q^3+3q^2+6q+1
       235: 3q+1
       236: q^2+6q+1
       237: 2q
       238: q^2+4q+1
       239: q^2+2q
       240: 2q^2+4q+1
       241: 2q
       242: q^2+4q+1
       243: q^2+6q+1
       244: 3q+1
       245: 3q+1
       246: q^2+6q+1
       247: q^2+6q+1
       248: 3q^2+6q+1
       249: q^2+6q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       260: 2q^2+4q+1
       261: q^2+q
       262: q
       263: q
       264: q^2+4q+1
       265: q
       266: q
       267: q
       268: 2q+1
       273: q
       274: 2q+1
       275: q
       276: q^2+4q+1
       277: q
       278: q
       280: 3q+1
       282: q^2+3q+1
       283: q^2+5q+1
       284: 2q
       285: 2q
       286: q^2+5q+1
       287: 2q
       288: 2q^2+5q+1
       290: q^2+3q+1
       291: q^2+2q
       292: 3q^2+5q+1
       293: q^2+5q+1
       294: 2q
       295: 2q
       296: q^2+5q+1
       297: 2q
       298: 2q^2+5q+1
       299: 3q+1
       301: q
       302: 2q+1
       303: 2q
       304: 4q+1
       305: q
       306: 2q+1
       307: 4q+1
       308: 2q
       310: 3q+1
       311: q
       312: 2q+1
       313: q
       314: 2q+1
       315: 2q
       316: q^2+4q+1
       317: 2q
       318: q^2+4q+1
       319: 3q+1
       322: 3q+1
       324: q+1
       325: 2q
       326: q^2+4q+1
       333: 2q^2+7q+1
       334: 3q^2+7q+1
       335: 3q^2+7q+1
       336: q^2+6q+1
       337: q^2+6q+1
       338: 2q
       339: q^2+4q+1
       340: q^2+2q
       341: 2q^2+4q+1
       342: 2q
       343: q^2+4q+1
       344: 6q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^3+3q^2+6q+1
       351: 3q+1
       352: 6q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^3+3q^2+6q+1
       357: q+1
       358: 3q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+6q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q^2+4q+1
       379: q
       380: q
       382: 2q+1
       383: q
       385: q
       386: q^2+4q+1
       387: q
       388: q
       389: q
       390: 2q+1
       393: q
       394: 2q+1
       399: q
       400: 2q+1
       403: 2q+1
       404: q
       407: q+1
       414: 3q+1
       418: q^2+3q+1
       419: q^2+5q+1
       420: 2q
       421: 2q
       422: q^2+5q+1
       423: 2q
       424: 2q^2+5q+1
       425: 2q
       426: q^2+4q+1
       427: 2q
       428: q^2+4q+1
       429: 3q+1
       431: 2q
       432: 4q+1
       433: q
       434: 2q+1
       436: 1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: 3q+1
       445: q
       446: 2q+1
       447: 4q+1
       448: 2q
       450: 3q+1
       451: q
       452: 2q+1
       453: 2q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: 3q+1
       463: q
       464: 2q+1
       466: q+1
       468: q+1
       469: 2q
       470: q^2+4q+1
       471: q+1
       474: q+1
       476: 1
       478: q+1
       480: q+1
       481: 6q+1
       482: 6q+1
       483: q^2+6q+1
       484: 3q+1
       486: q+1
       488: q+1
       490: q+1
       491: 3q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: 3q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       522: 2q+1
       523: q
       529: q
       530: q^2+4q+1
       531: q
       532: q
       533: q
       534: 2q+1
       538: 1
       542: q+1
       545: q
       546: 2q+1
       551: 2q+1
       552: q
       556: 1
       560: q+1
       563: q
       564: 2q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       586: 3q+1
       589: 4q+1
       590: 2q
       592: 3q+1
       593: 3q+1
       595: 2q
       596: 4q+1
       598: q+1
       599: 2q
       600: q^2+4q+1
       602: q+1
       603: q+1
       606: 1
       607: q
       608: 2q+1
       610: q+1
       613: q
       614: 2q+1
       615: q+1
       618: 1
       619: 2q+1
       620: q
       622: q+1
       624: 1
       626: q+1
       629: q
       630: 2q+1
       632: q+1
       634: 1
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: 1
       650: 1
       652: 2
       654: 1
       656: 1
       657: 3q+1
       659: q+1
       661: q+1
       663: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: q+1
       680: q+1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       710: 2q+1
       711: q
       715: 2q+1
       716: q
       717: q
       718: 2q+1
       722: 1
       726: q+1
       734: 1
       740: 1
       744: q+1
       752: 1
       754: 1
       759: 2
       763: 1
       766: 1
       773: 1
       774: 1
       776: q+1
       780: q+1
       782: q+1
       785: q+1
       788: q+1
       792: 1
       793: q+1
       796: 1
       798: 1
       801: 1
       805: q+1
       807: q
       808: 2q+1
       810: 1
       812: q+1
       815: 1
       818: q+1
       820: 1
       822: 1
       825: 2q+1
       826: q
       828: q+1
       832: 1
       834: 1
       836: q+1
       840: 1
       844: 1
       845: 1
       848: 1
       850: 2
       852: 1
       858: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       894: 1
       903: 1
       905: 1
       909: 1
       917: 1
       921: 1
       929: q+1
       943: 1
       947: 1
       951: q+1
       962: 2
       965: 1
       972: 1
       973: 1
       976: 1
       989: 1
       995: q+1
       999: q+1
      1000: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1016: 1
      1021: 1
      1023: 1
      1026: 1
      1033: 1
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1059: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1096: 1
      1117: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1157: 1
      1175: 1
      1195: 1
      1200: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: 1
      1234: 1
      1240: 1
      1249: 1
      1251: 1
      1261: 1
      1283: 1
      1285: 1
      1296: 1
      1300: 1
      1327: 1
      1332: 1
      1357: 1
      1383: 1
      1437: 1
      1454: 1
      1461: 1
      1539: 1

1540:    0: 6q^3+10q^2+7q+1
         1: q^4+8q^3+10q^2+7q+1
         2: q^4+6q^3+7q^2+7q+1
         3: 6q^3+10q^2+7q+1
         4: 6q^3+10q^2+7q+1
         5: q^4+8q^3+10q^2+7q+1
         6: q^4+8q^3+10q^2+7q+1
         7: q^4+6q^3+7q^2+7q+1
         8: 2q^4+8q^3+7q^2+7q+1
         9: q^4+6q^3+7q^2+7q+1
        10: 4q^3+8q^2+7q+1
        11: 4q^3+8q^2+7q+1
        12: 4q^3+8q^2+7q+1
        13: 3q^3+7q^2+7q+1
        14: 3q^3+7q^2+7q+1
        15: 5q^3+7q^2+7q+1
        16: 6q^3+10q^2+7q+1
        17: q^4+8q^3+10q^2+7q+1
        18: q^4+6q^3+7q^2+7q+1
        19: 6q^3+10q^2+7q+1
        20: q^4+8q^3+10q^2+7q+1
        21: q^4+6q^3+7q^2+7q+1
        22: 2q^3+7q^2+7q+1
        23: 2q^3+7q^2+7q+1
        24: 3q^3+5q^2+7q+1
        25: 2q^3+7q^2+7q+1
        26: 2q^3+7q^2+7q+1
        27: 3q^3+5q^2+7q+1
        28: 4q^3+8q^2+7q+1
        29: 4q^3+8q^2+7q+1
        30: 3q^3+7q^2+7q+1
        31: q^3+5q^2+7q+1
        32: q^3+5q^2+7q+1
        33: 2q^3+7q^2+7q+1
        34: q^3+5q^2+7q+1
        35: q^3+5q^2+7q+1
        36: 2q^3+7q^2+7q+1
        37: q^2+2q
        38: 4q^2+5q+1
        39: q^2+2q
        40: 4q^2+5q+1
        41: q^2+2q
        42: q^3+3q^2+5q+1
        43: q^3+5q^2+7q+1
        44: q^3+5q^2+7q+1
        45: q^3+5q^2+7q+1
        46: 3q^3+7q^2+7q+1
        47: 5q^3+7q^2+7q+1
        48: 3q^3+7q^2+7q+1
        49: 6q^3+10q^2+7q+1
        50: q^4+8q^3+10q^2+7q+1
        51: q^4+6q^3+7q^2+7q+1
        52: 2q^3+7q^2+7q+1
        53: 2q^3+7q^2+7q+1
        54: 3q^3+5q^2+7q+1
        55: 2q^3+7q^2+7q+1
        56: 2q^3+7q^2+7q+1
        57: 3q^3+5q^2+7q+1
        58: q^3+3q^2+5q+1
        59: 2q^2+2q
        60: 2q^2+2q
        61: q^3+3q^2+5q+1
        62: 2q
        63: 3q^2+5q+1
        64: q^2+2q
        65: 3q^2+5q+1
        66: q^2+2q
        67: 4q^2+5q+1
        68: 2q^2+7q+1
        69: 3q^3+7q^2+7q+1
        70: q^3+5q^2+7q+1
        71: 4q^3+8q^2+7q+1
        72: 2q^3+7q^2+7q+1
        73: 2q^3+7q^2+7q+1
        74: q^2+2q
        75: 4q^2+5q+1
        76: q^2+2q
        77: 4q^2+5q+1
        78: q^2+2q
        79: q^3+3q^2+5q+1
        80: 3q^2+7q+1
        81: q^3+5q^2+7q+1
        82: q^3+5q^2+7q+1
        83: q^3+5q^2+7q+1
        84: 3q^2+7q+1
        85: q^3+5q^2+7q+1
        86: q^3+5q^2+7q+1
        87: q^3+5q^2+7q+1
        88: q^3+5q^2+7q+1
        89: q^3+5q^2+7q+1
        90: q^3+5q^2+7q+1
        91: 3q^3+7q^2+7q+1
        92: 5q^3+7q^2+7q+1
        93: 3q^3+7q^2+7q+1
        94: 2q^3+7q^2+7q+1
        95: 2q^3+7q^2+7q+1
        96: 3q^3+5q^2+7q+1
        97: 2q^3+7q^2+7q+1
        98: 2q^3+7q^2+7q+1
        99: 3q^3+5q^2+7q+1
       100: q^2+6q+1
       101: 3q^2+6q+1
       102: q^2+6q+1
       103: q
       104: q^2+q
       105: 2q^2+4q+1
       106: q
       107: 2q^2+2q
       108: q^3+3q^2+5q+1
       109: q^3+3q^2+5q+1
       110: 2q^2+2q
       111: q^2+2q
       112: 4q^2+5q+1
       113: 2q
       114: 3q^2+5q+1
       115: q^2+2q
       116: 3q^2+5q+1
       117: q^2+5q+1
       118: 2q
       119: 2q
       120: q^2+5q+1
       121: 2q
       122: 2q^2+5q+1
       123: q^2+2q
       124: 3q^2+5q+1
       125: 2q^2+7q+1
       126: q^3+5q^2+7q+1
       127: q^2+2q
       128: 4q^2+5q+1
       129: q^2+2q
       130: 4q^2+5q+1
       131: q^2+2q
       132: q^3+3q^2+5q+1
       133: 2q^2+7q+1
       134: 3q^3+7q^2+7q+1
       135: q^3+5q^2+7q+1
       136: q^3+5q^2+7q+1
       137: 3q^2+7q+1
       138: q^3+5q^2+7q+1
       139: q^3+5q^2+7q+1
       140: 3q+1
       141: 3q^2+7q+1
       142: 2q^3+7q^2+7q+1
       143: 3q^2+7q+1
       144: q^3+5q^2+7q+1
       145: q^3+5q^2+7q+1
       146: 3q^2+7q+1
       147: 2q^3+7q^2+7q+1
       148: 3q+1
       149: q^2+6q+1
       150: q^2+6q+1
       151: 2q
       152: q^2+4q+1
       153: q^2+2q
       154: 2q^2+4q+1
       155: 2q
       156: q^2+4q+1
       157: q^3+5q^2+7q+1
       158: q^3+5q^2+7q+1
       159: q^3+5q^2+7q+1
       160: q^3+3q^2+6q+1
       161: q^3+3q^2+6q+1
       162: q^3+3q^2+6q+1
       163: q^3+3q^2+6q+1
       164: q^3+3q^2+6q+1
       165: q^3+3q^2+6q+1
       166: q^2+6q+1
       167: 3q^2+6q+1
       168: q^2+6q+1
       169: q
       170: q^2+q
       171: 2q^2+4q+1
       172: q
       173: q
       174: q
       175: q^2+4q+1
       176: q
       177: q^2+2q
       178: 3q^2+5q+1
       179: 2q
       180: 3q^2+5q+1
       181: q^2+2q
       182: 4q^2+5q+1
       183: 2q
       184: q^2+5q+1
       185: q^2+5q+1
       186: 2q
       187: q^2+2q
       188: 3q^2+5q+1
       189: 2q
       190: 2q^2+5q+1
       191: q^2+5q+1
       192: 2q
       194: 3q+1
       195: q^3+3q^2+5q+1
       196: 2q^2+2q
       197: q
       198: 2q+1
       199: 2q
       200: q^2+5q+1
       201: 2q^2+2q
       202: q^3+3q^2+5q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: 2q^2+5q+1
       209: 2q
       210: q^2+4q+1
       211: 2q
       212: q^2+4q+1
       214: q^2+3q+1
       216: q^2+3q+1
       218: q^2+3q+1
       219: 2q^2+7q+1
       220: 2q^2+7q+1
       221: q^3+5q^2+7q+1
       222: 3q^2+7q+1
       223: q^3+5q^2+7q+1
       224: 3q^2+7q+1
       225: q^3+5q^2+7q+1
       226: 3q^2+7q+1
       227: 6q+1
       228: q^3+3q^2+6q+1
       229: 3q+1
       230: q^3+3q^2+6q+1
       231: 3q^2+7q+1
       232: 6q+1
       233: q^3+3q^2+6q+1
       234: q^3+3q^2+6q+1
       235: 3q+1
       236: q^2+6q+1
       237: 2q
       238: q^2+4q+1
       239: q^2+2q
       240: 2q^2+4q+1
       241: 2q
       242: q^2+4q+1
       243: q^2+6q+1
       244: 3q+1
       245: 3q+1
       246: q^2+6q+1
       247: q^2+6q+1
       248: 3q^2+6q+1
       249: q^2+6q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       260: q^2+q
       261: 2q^2+4q+1
       262: q
       263: q
       264: q
       265: q^2+4q+1
       266: q
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       275: q
       276: q
       277: q^2+4q+1
       278: q
       280: 3q+1
       282: q^2+3q+1
       283: 2q
       284: q^2+5q+1
       285: q^2+5q+1
       286: 2q
       287: 2q
       288: 2q^2+5q+1
       290: q^2+3q+1
       291: q^2+2q
       292: 3q^2+5q+1
       293: 2q
       294: q^2+5q+1
       295: q^2+5q+1
       296: 2q
       297: 2q
       298: 2q^2+5q+1
       300: 3q+1
       301: q
       302: 2q+1
       303: 4q+1
       304: 2q
       305: q
       306: 2q+1
       307: 2q
       308: 4q+1
       309: 3q+1
       311: q
       312: 2q+1
       313: q
       314: 2q+1
       315: 2q
       316: q^2+4q+1
       317: 2q
       318: q^2+4q+1
       320: 3q+1
       321: 3q+1
       324: q+1
       325: 2q
       326: q^2+4q+1
       333: 2q^2+7q+1
       334: 3q^2+7q+1
       335: 3q^2+7q+1
       336: q^2+6q+1
       337: q^2+6q+1
       338: 2q
       339: q^2+4q+1
       340: q^2+2q
       341: 2q^2+4q+1
       342: 2q
       343: q^2+4q+1
       344: 6q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^3+3q^2+6q+1
       351: 3q+1
       352: 6q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^3+3q^2+6q+1
       357: q+1
       358: 3q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+6q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: q^2+4q+1
       380: q
       382: q
       383: 2q+1
       385: q
       386: q
       387: q^2+4q+1
       388: q
       391: q
       392: 2q+1
       395: 2q+1
       396: q
       397: q
       398: 2q+1
       401: q
       402: 2q+1
       408: q+1
       414: 3q+1
       418: q^2+3q+1
       419: 2q
       420: q^2+5q+1
       421: q^2+5q+1
       422: 2q
       423: 2q
       424: 2q^2+5q+1
       425: 2q
       426: q^2+4q+1
       427: 2q
       428: q^2+4q+1
       430: 3q+1
       431: 4q+1
       432: 2q
       433: q
       434: 2q+1
       436: 1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: 3q+1
       445: q
       446: 2q+1
       447: 2q
       448: 4q+1
       449: 3q+1
       451: q
       452: 2q+1
       453: q
       454: 2q+1
       456: 1
       457: q+1
       460: q+1
       461: 3q+1
       463: q
       464: 2q+1
       466: q+1
       468: q+1
       469: 2q
       470: q^2+4q+1
       472: q+1
       473: q+1
       476: 1
       478: q+1
       480: q+1
       481: 6q+1
       482: 6q+1
       483: q^2+6q+1
       484: 3q+1
       486: q+1
       488: q+1
       490: q+1
       491: 3q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: 3q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 2q+1
       529: q
       530: q
       531: q^2+4q+1
       532: q
       535: 2q+1
       536: q
       540: 1
       544: q+1
       547: q
       548: 2q+1
       549: q
       550: 2q+1
       554: 1
       558: q+1
       561: q
       562: 2q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       586: 3q+1
       589: 2q
       590: 4q+1
       591: 3q+1
       594: 3q+1
       595: 4q+1
       596: 2q
       598: q+1
       599: 2q
       600: q^2+4q+1
       602: q+1
       604: q+1
       606: 1
       607: 2q+1
       608: q
       610: q+1
       613: q
       614: 2q+1
       616: q+1
       618: 1
       619: q
       620: 2q+1
       621: q+1
       624: 1
       626: q+1
       629: q
       630: 2q+1
       631: q+1
       634: 1
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: 1
       649: 1
       652: 2
       654: 1
       656: 1
       657: 3q+1
       659: q+1
       661: q+1
       663: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: q+1
       680: q+1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       710: q
       711: 2q+1
       713: q
       714: 2q+1
       719: 2q+1
       720: q
       724: 1
       728: q+1
       736: 1
       738: 1
       742: q+1
       750: 1
       755: 1
       760: 2
       764: 1
       767: 1
       773: 1
       774: 1
       776: q+1
       780: q+1
       782: q+1
       786: q+1
       787: q+1
       792: 1
       794: q+1
       796: 1
       798: 1
       802: 1
       806: q+1
       807: 2q+1
       808: q
       810: 1
       812: q+1
       816: 1
       817: q+1
       820: 1
       822: 1
       825: q
       826: 2q+1
       827: q+1
       831: 1
       834: 1
       836: q+1
       839: 1
       844: 1
       846: 1
       847: 1
       850: 2
       852: 1
       858: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       891: 1
       895: 1
       901: 1
       907: 1
       910: 1
       919: 1
       923: 1
       931: q+1
       941: 1
       945: 1
       949: q+1
       963: 2
       966: 1
       972: 1
       973: 1
       977: 1
       990: 1
       995: q+1
       998: q+1
      1001: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1017: 1
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1053: 1
      1058: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1093: 1
      1097: 1
      1115: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1159: 1
      1173: 1
      1196: 1
      1201: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1231: 1
      1235: 1
      1241: 1
      1249: 1
      1250: 1
      1260: 1
      1283: 1
      1285: 1
      1297: 1
      1301: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1437: 1
      1455: 1
      1460: 1
      1540: 1

1541:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^3+4q^2+4q+1
        26: 2q^3+4q^2+4q+1
        27: 2q^3+4q^2+4q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^3+4q^2+4q+1
        35: 2q^3+4q^2+4q+1
        36: q^3+3q^2+4q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^3+4q^2+4q+1
        56: 2q^3+4q^2+4q+1
        57: 2q^3+4q^2+4q+1
        58: q^2+2q+1
        59: q
        60: 2q^2+2q+1
        61: q^3+q^2+2q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^3+4q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^3+4q^2+4q+1
        87: 2q^3+4q^2+4q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       106: q
       107: 2q^2+2q+1
       108: q^3+q^2+2q
       109: q^2+2q+1
       110: q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: 2q^2+2q+1
       120: q^3+q^2+2q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^3+3q^2+4q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^3+3q^2+4q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q^3+4q^2+4q+1
       147: 2q^2+4q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: q^3+2q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: 2q^2+2q+1
       184: q^3+q^2+2q
       185: q^2+2q+1
       186: q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       195: 2q+1
       196: q
       199: 2q^2+2q+1
       200: q^3+q^2+2q
       201: q^2+2q+1
       202: q^2+2q
       203: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       230: 3q+1
       231: q^2+3q+1
       232: 2q^2+4q+1
       233: q^2+3q+1
       234: 2q^2+4q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 2q^2+4q+1
       254: 2q^2+4q+1
       255: q^3+2q^2+3q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       271: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q+1
       284: q
       285: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: 2q^2+2q+1
       294: q^3+q^2+2q
       295: q^2+2q+1
       296: q
       297: q^2+3q+1
       303: 2q+1
       304: q
       307: q^2+2q+1
       308: q^2+2q
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       321: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: 2q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: q^2+3q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       397: q+1
       401: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       420: q
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       431: q+1
       439: 2q+1
       440: q
       447: q+1
       448: q
       449: 1
       451: 1
       453: q^2+2q+1
       454: q^2+2q
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       473: q+1
       481: q^2+3q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: 2q+1
       494: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       549: 1
       553: q+1
       557: q+1
       561: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       590: q
       591: 1
       595: q+1
       597: q+1
       599: q+1
       601: 2q+1
       607: q+1
       619: q+1
       620: q
       621: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       643: 1
       649: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 1
       681: q^2+3q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       705: q+1
       709: q+1
       713: 1
       737: 1
       741: 1
       745: q+1
       749: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       787: 1
       789: 2q+1
       807: q+1
       817: 1
       819: 1
       821: 1
       823: 1
       825: q+1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       837: q+1
       839: q+1
       841: q+1
       847: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       896: q+1
       900: 1
       936: 1
       940: 1
       944: 1
       948: 1
       956: q+1
       992: 1
       994: 1
       996: 1
       998: 1
      1002: q+1
      1006: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1058: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1110: 1
      1114: 1
      1164: 1
      1168: 1
      1172: 1
      1210: 1
      1212: 1
      1214: 1
      1216: 1
      1244: 1
      1246: 1
      1252: 1
      1256: 1
      1260: 1
      1282: 1
      1286: 1
      1314: 1
      1372: 1
      1376: 1
      1438: 1
      1440: 1
      1458: 1
      1541: 1

1542:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^3+4q^2+4q+1
        26: 2q^3+4q^2+4q+1
        27: 2q^3+4q^2+4q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^3+4q^2+4q+1
        35: 2q^3+4q^2+4q+1
        36: q^3+3q^2+4q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^3+4q^2+4q+1
        56: 2q^3+4q^2+4q+1
        57: 2q^3+4q^2+4q+1
        58: q^2+2q+1
        59: q
        60: q^3+q^2+2q
        61: 2q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^3+4q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^3+4q^2+4q+1
        87: 2q^3+4q^2+4q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: q^2+2q+1
       107: q^3+q^2+2q
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q^3+q^2+2q
       120: 2q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^3+3q^2+4q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^3+3q^2+4q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q^3+4q^2+4q+1
       147: 2q^2+4q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: q^3+2q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^3+q^2+2q
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       195: 2q+1
       196: q
       199: q^3+q^2+2q
       200: 2q^2+2q+1
       201: q^2+2q
       202: q^2+2q+1
       203: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       230: 3q+1
       231: q^2+3q+1
       232: 2q^2+4q+1
       233: q^2+3q+1
       234: 2q^2+4q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 2q^2+4q+1
       254: 2q^2+4q+1
       255: q^3+2q^2+3q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       272: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       283: q
       284: q+1
       285: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^3+q^2+2q
       294: 2q^2+2q+1
       295: q^2+2q+1
       296: q
       298: q^2+3q+1
       303: 2q+1
       304: q
       307: q^2+2q
       308: q^2+2q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       321: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: 2q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: q^2+3q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       398: q+1
       402: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       431: q+1
       439: 2q+1
       440: q
       447: q
       448: q+1
       449: 1
       452: 1
       453: q^2+2q
       454: q^2+2q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       473: q+1
       481: q^2+3q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: 2q+1
       494: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       550: 1
       554: q+1
       558: q+1
       562: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q
       590: q+1
       591: 1
       595: q+1
       598: q+1
       600: q+1
       602: 2q+1
       607: q+1
       619: q
       620: q+1
       621: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       643: 1
       649: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 1
       681: q^2+3q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       707: q+1
       711: q+1
       714: 1
       738: 1
       742: 1
       746: q+1
       750: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       787: 1
       790: 2q+1
       807: q+1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: q+1
       839: q+1
       842: q+1
       847: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       898: q+1
       901: 1
       937: 1
       941: 1
       945: 1
       949: 1
       957: q+1
       993: 1
       995: 1
       997: 1
       998: 1
      1003: q+1
      1006: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1058: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1111: 1
      1115: 1
      1165: 1
      1169: 1
      1173: 1
      1211: 1
      1213: 1
      1215: 1
      1216: 1
      1245: 1
      1246: 1
      1253: 1
      1257: 1
      1260: 1
      1282: 1
      1286: 1
      1315: 1
      1373: 1
      1377: 1
      1439: 1
      1440: 1
      1459: 1
      1542: 1

1543:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^3+4q^2+4q+1
        26: 2q^3+4q^2+4q+1
        27: 2q^3+4q^2+4q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^3+4q^2+4q+1
        35: 2q^3+4q^2+4q+1
        36: q^3+3q^2+4q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^3+4q^2+4q+1
        56: 2q^3+4q^2+4q+1
        57: 2q^3+4q^2+4q+1
        58: q
        59: q^2+2q+1
        60: q^3+q^2+2q
        61: 2q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^3+4q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^3+4q^2+4q+1
        87: 2q^3+4q^2+4q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       106: q^2+2q+1
       107: q^3+q^2+2q
       108: 2q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q^3+q^2+2q
       120: 2q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^3+3q^2+4q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^3+3q^2+4q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q^3+4q^2+4q+1
       147: 2q^2+4q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: q^3+2q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^3+q^2+2q
       184: 2q^2+2q+1
       185: q
       186: q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       195: q
       196: 2q+1
       199: q^3+q^2+2q
       200: 2q^2+2q+1
       201: q^2+2q
       202: q^2+2q+1
       204: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       230: 3q+1
       231: q^2+3q+1
       232: 2q^2+4q+1
       233: q^2+3q+1
       234: 2q^2+4q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 2q^2+4q+1
       254: 2q^2+4q+1
       255: q^3+2q^2+3q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       273: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       283: q
       284: q+1
       286: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^3+q^2+2q
       294: 2q^2+2q+1
       295: q
       296: q^2+2q+1
       297: q^2+3q+1
       303: q
       304: 2q+1
       307: q^2+2q
       308: q^2+2q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       322: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: 2q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: q^2+3q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       399: q+1
       404: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       432: q+1
       439: q
       440: 2q+1
       447: q
       448: q+1
       450: 1
       451: 1
       453: q^2+2q
       454: q^2+2q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       474: q+1
       481: q^2+3q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: 2q+1
       494: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       552: 1
       555: q+1
       559: q+1
       563: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q
       590: q+1
       592: 1
       596: q+1
       597: q+1
       599: q+1
       601: 2q+1
       608: q+1
       619: q
       620: q+1
       622: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       644: 1
       650: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 1
       681: q^2+3q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       708: q+1
       712: q+1
       716: 1
       739: 1
       743: 1
       747: q+1
       751: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       788: 1
       789: 2q+1
       808: q+1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: q+1
       840: q+1
       841: q+1
       848: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       899: q+1
       902: 1
       938: 1
       942: 1
       946: 1
       950: 1
       958: q+1
       992: 1
       994: 1
       996: 1
       999: 1
      1002: q+1
      1007: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1059: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1112: 1
      1116: 1
      1166: 1
      1170: 1
      1174: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1244: 1
      1247: 1
      1252: 1
      1256: 1
      1261: 1
      1282: 1
      1286: 1
      1316: 1
      1374: 1
      1378: 1
      1438: 1
      1441: 1
      1458: 1
      1543: 1

1544:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^3+4q^2+4q+1
        26: 2q^3+4q^2+4q+1
        27: 2q^3+4q^2+4q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^3+4q^2+4q+1
        35: 2q^3+4q^2+4q+1
        36: q^3+3q^2+4q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^3+4q^2+4q+1
        56: 2q^3+4q^2+4q+1
        57: 2q^3+4q^2+4q+1
        58: q
        59: q^2+2q+1
        60: 2q^2+2q+1
        61: q^3+q^2+2q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^3+4q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^3+4q^2+4q+1
        87: 2q^3+4q^2+4q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q^2+2q+1
       105: q
       107: 2q^2+2q+1
       108: q^3+q^2+2q
       109: q
       110: q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: 2q^2+2q+1
       120: q^3+q^2+2q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^3+3q^2+4q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^3+3q^2+4q+1
       144: q^2+3q+1
       145: 2q^2+4q+1
       146: 2q^3+4q^2+4q+1
       147: 2q^2+4q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: q^3+2q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: 2q^2+2q+1
       184: q^3+q^2+2q
       185: q
       186: q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       195: q
       196: 2q+1
       199: 2q^2+2q+1
       200: q^3+q^2+2q
       201: q^2+2q+1
       202: q^2+2q
       204: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       230: 3q+1
       231: q^2+3q+1
       232: 2q^2+4q+1
       233: q^2+3q+1
       234: 2q^2+4q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 2q^2+4q+1
       254: 2q^2+4q+1
       255: q^3+2q^2+3q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       274: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q+1
       284: q
       286: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: 2q^2+2q+1
       294: q^3+q^2+2q
       295: q
       296: q^2+2q+1
       298: q^2+3q+1
       303: q
       304: 2q+1
       307: q^2+2q+1
       308: q^2+2q
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       322: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: q^2+3q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       349: 3q+1
       350: 2q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: q^2+3q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       400: q+1
       403: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       420: q
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       432: q+1
       439: q
       440: 2q+1
       447: q+1
       448: q
       450: 1
       452: 1
       453: q^2+2q+1
       454: q^2+2q
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       474: q+1
       481: q^2+3q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: 2q+1
       494: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       551: 1
       556: q+1
       560: q+1
       564: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       590: q
       592: 1
       596: q+1
       598: q+1
       600: q+1
       602: 2q+1
       608: q+1
       619: q+1
       620: q
       622: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       644: 1
       650: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       676: 2q+1
       680: 1
       681: q^2+3q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       688: 1
       690: 1
       691: q+1
       692: 1
       706: q+1
       710: q+1
       715: 1
       740: 1
       744: 1
       748: q+1
       752: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       788: 1
       790: 2q+1
       808: q+1
       818: 1
       820: 1
       822: 1
       824: 1
       825: q+1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       838: q+1
       840: q+1
       842: q+1
       848: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       897: q+1
       903: 1
       939: 1
       943: 1
       947: 1
       951: 1
       959: q+1
       993: 1
       995: 1
       997: 1
       999: 1
      1003: q+1
      1007: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1059: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1081: 1
      1082: 1
      1113: 1
      1117: 1
      1167: 1
      1171: 1
      1175: 1
      1211: 1
      1213: 1
      1215: 1
      1217: 1
      1245: 1
      1247: 1
      1253: 1
      1257: 1
      1261: 1
      1282: 1
      1286: 1
      1317: 1
      1375: 1
      1379: 1
      1439: 1
      1441: 1
      1459: 1
      1544: 1

1545:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^3+4q^2+4q+1
        23: 2q^3+4q^2+4q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^3+4q^2+4q+1
        32: 2q^3+4q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^3+4q^2+4q+1
        53: 2q^3+4q^2+4q+1
        54: 2q^3+4q^2+4q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q^2+2q+1
        59: q^3+q^2+2q
        60: q^2+2q+1
        61: q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^2+3q+1
        73: q^3+3q^2+4q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^3+4q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^3+4q^2+4q+1
        83: 2q^3+4q^2+4q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: q^3+2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       106: q
       107: q^2+2q+1
       108: q
       109: 2q^2+2q+1
       110: q^3+q^2+2q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: 2q^2+2q+1
       118: q^3+q^2+2q
       119: q^2+2q+1
       120: q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^2+3q+1
       136: q^3+3q^2+4q+1
       137: q^3+3q^2+4q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^3+4q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: q^3+2q^2+3q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+2q+1
       184: q
       185: 2q^2+2q+1
       186: q^3+q^2+2q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: 2q^2+2q+1
       192: q^3+q^2+2q
       193: q+1
       195: q^2+2q+1
       196: q^2+2q
       197: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 2q^2+4q+1
       228: q^2+3q+1
       229: q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q^2+4q+1
       251: 2q^2+4q+1
       252: q^3+2q^2+3q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q+1
       285: q+1
       286: q
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+2q+1
       294: q
       295: 2q^2+2q+1
       296: q^3+q^2+2q
       297: q^2+3q+1
       299: q+1
       301: q+1
       303: q^2+2q+1
       304: q^2+2q
       305: q+1
       307: 2q+1
       308: q
       315: q+1
       317: 2q+1
       319: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: q^2+3q+1
       347: q+1
       348: 1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q+1
       393: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       421: q+1
       422: q
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: q+1
       432: q
       433: 1
       435: q+1
       437: q+1
       439: q^2+2q+1
       440: q^2+2q
       441: q+1
       443: q+1
       445: q+1
       447: q+1
       453: 2q+1
       454: q
       465: 2q+1
       467: q+1
       469: q+1
       471: q+1
       481: 2q+1
       482: q^2+3q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: q^2+3q+1
       493: 1
       494: q^2+3q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: 1
       537: q+1
       541: q+1
       545: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       593: 1
       595: q+1
       596: q
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: 1
       607: q+1
       608: q
       609: 1
       611: q+1
       613: 1
       615: q+1
       617: q+1
       619: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: 1
       647: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+3q+1
       677: 1
       678: q+1
       679: 1
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       705: q+1
       709: q+1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       785: 1
       789: 2q+1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q+1
       808: q
       809: 1
       811: 1
       813: q+1
       815: q+1
       825: q+1
       841: q+1
       845: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       896: q+1
       904: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: q+1
       992: 1
       994: 1
       996: 1
      1000: 1
      1002: q+1
      1004: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1052: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1118: 1
      1122: 1
      1144: 1
      1148: 1
      1156: 1
      1210: 1
      1212: 1
      1214: 1
      1218: 1
      1226: 1
      1228: 1
      1236: 1
      1238: 1
      1240: 1
      1282: 1
      1284: 1
      1318: 1
      1340: 1
      1352: 1
      1438: 1
      1442: 1
      1452: 1
      1545: 1

1546:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^3+4q^2+4q+1
        23: 2q^3+4q^2+4q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^3+4q^2+4q+1
        32: 2q^3+4q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^3+4q^2+4q+1
        53: 2q^3+4q^2+4q+1
        54: 2q^3+4q^2+4q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^3+q^2+2q
        59: 2q^2+2q+1
        60: q^2+2q+1
        61: q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^2+3q+1
        73: q^3+3q^2+4q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^3+4q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^3+4q^2+4q+1
        83: 2q^3+4q^2+4q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: q^3+2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q^2+2q+1
       105: q
       107: q^2+2q+1
       108: q
       109: q^3+q^2+2q
       110: 2q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^3+q^2+2q
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^2+3q+1
       136: q^3+3q^2+4q+1
       137: q^3+3q^2+4q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^3+4q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: q^3+2q^2+3q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+2q+1
       184: q
       185: q^3+q^2+2q
       186: 2q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^3+q^2+2q
       192: 2q^2+2q+1
       193: q+1
       195: q^2+2q
       196: q^2+2q+1
       198: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 2q^2+4q+1
       228: q^2+3q+1
       229: q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q^2+4q+1
       251: 2q^2+4q+1
       252: q^3+2q^2+3q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q+1
       285: q
       286: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+2q+1
       294: q
       295: q^3+q^2+2q
       296: 2q^2+2q+1
       298: q^2+3q+1
       299: q+1
       302: q+1
       303: q^2+2q
       304: q^2+2q+1
       306: q+1
       307: 2q+1
       308: q
       316: q+1
       318: 2q+1
       319: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: q^2+3q+1
       347: q+1
       348: 1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q+1
       394: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       421: q
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       431: q
       432: q+1
       434: 1
       436: q+1
       437: q+1
       439: q^2+2q
       440: q^2+2q+1
       442: q+1
       443: q+1
       446: q+1
       447: q+1
       453: 2q+1
       454: q
       466: 2q+1
       468: q+1
       470: q+1
       471: q+1
       481: 2q+1
       482: q^2+3q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: q^2+3q+1
       493: 1
       494: q^2+3q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: 1
       538: q+1
       542: q+1
       546: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       593: 1
       595: q
       596: q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: 1
       607: q
       608: q+1
       610: 1
       612: q+1
       614: 1
       615: q+1
       618: q+1
       619: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: 1
       647: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+3q+1
       677: 1
       678: q+1
       679: 1
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       706: q+1
       710: q+1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       785: 1
       790: 2q+1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       807: q
       808: q+1
       810: 1
       812: 1
       814: q+1
       815: q+1
       825: q+1
       842: q+1
       845: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       897: q+1
       905: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: q+1
       993: 1
       995: 1
       997: 1
      1000: 1
      1003: q+1
      1004: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1052: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1119: 1
      1123: 1
      1145: 1
      1149: 1
      1157: 1
      1211: 1
      1213: 1
      1215: 1
      1218: 1
      1227: 1
      1228: 1
      1237: 1
      1239: 1
      1240: 1
      1282: 1
      1284: 1
      1319: 1
      1341: 1
      1353: 1
      1439: 1
      1442: 1
      1453: 1
      1546: 1

1547:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^3+4q^2+4q+1
        23: 2q^3+4q^2+4q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^3+4q^2+4q+1
        32: 2q^3+4q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^3+4q^2+4q+1
        53: 2q^3+4q^2+4q+1
        54: 2q^3+4q^2+4q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^3+q^2+2q
        59: 2q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^2+3q+1
        73: q^3+3q^2+4q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^3+4q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^3+4q^2+4q+1
        83: 2q^3+4q^2+4q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: q^3+2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       106: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q^3+q^2+2q
       110: 2q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^3+q^2+2q
       118: 2q^2+2q+1
       119: q
       120: q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^2+3q+1
       136: q^3+3q^2+4q+1
       137: q^3+3q^2+4q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^3+4q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: q^3+2q^2+3q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q
       184: q^2+2q+1
       185: q^3+q^2+2q
       186: 2q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^3+q^2+2q
       192: 2q^2+2q+1
       194: q+1
       195: q^2+2q
       196: q^2+2q+1
       197: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 2q^2+4q+1
       228: q^2+3q+1
       229: q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q^2+4q+1
       251: 2q^2+4q+1
       252: q^3+2q^2+3q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       284: q+1
       285: q
       286: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q
       294: q^2+2q+1
       295: q^3+q^2+2q
       296: 2q^2+2q+1
       297: q^2+3q+1
       300: q+1
       301: q+1
       303: q^2+2q
       304: q^2+2q+1
       305: q+1
       307: q
       308: 2q+1
       315: q+1
       317: 2q+1
       320: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: q^2+3q+1
       347: q+1
       348: 1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q+1
       396: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       420: q+1
       421: q
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       431: q
       432: q+1
       433: 1
       435: q+1
       438: q+1
       439: q^2+2q
       440: q^2+2q+1
       441: q+1
       444: q+1
       445: q+1
       448: q+1
       453: q
       454: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: q+1
       481: 2q+1
       482: q^2+3q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: q^2+3q+1
       493: 1
       494: q^2+3q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: 1
       539: q+1
       543: q+1
       547: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       590: q+1
       594: 1
       595: q
       596: q+1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: 1
       607: q
       608: q+1
       609: 1
       611: q+1
       613: 1
       616: q+1
       617: q+1
       620: q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: 1
       648: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+3q+1
       677: 1
       678: q+1
       679: 1
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       708: q+1
       712: q+1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       786: 1
       789: 2q+1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       807: q
       808: q+1
       809: 1
       811: 1
       813: q+1
       816: q+1
       826: q+1
       841: q+1
       846: 1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       899: q+1
       906: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: q+1
       992: 1
       994: 1
       996: 1
      1001: 1
      1002: q+1
      1005: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1053: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1120: 1
      1124: 1
      1146: 1
      1150: 1
      1158: 1
      1210: 1
      1212: 1
      1214: 1
      1219: 1
      1226: 1
      1229: 1
      1236: 1
      1238: 1
      1241: 1
      1282: 1
      1284: 1
      1320: 1
      1342: 1
      1354: 1
      1438: 1
      1443: 1
      1452: 1
      1547: 1

1548:    0: 3q^3+5q^2+4q+1
         1: 3q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: q^4+4q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: 3q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^4+3q^3+3q^2+3q+1
        10: 3q^3+5q^2+4q+1
        11: q^4+4q^3+5q^2+4q+1
        12: 3q^3+5q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 2q^3+4q^2+4q+1
        17: 2q^3+4q^2+4q+1
        18: 2q^3+3q^2+3q+1
        19: 3q^3+5q^2+4q+1
        20: 3q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: 2q^3+4q^2+4q+1
        23: 2q^3+4q^2+4q+1
        24: 2q^3+4q^2+4q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^3+4q^2+4q+1
        29: 3q^3+5q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^3+4q^2+4q+1
        32: 2q^3+4q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^3+5q^2+4q+1
        44: 3q^3+5q^2+4q+1
        45: q^4+4q^3+5q^2+4q+1
        46: 2q^3+4q^2+4q+1
        47: 2q^3+4q^2+4q+1
        48: 2q^3+3q^2+3q+1
        49: 2q^3+4q^2+4q+1
        50: 2q^3+4q^2+4q+1
        51: 2q^3+3q^2+3q+1
        52: 2q^3+4q^2+4q+1
        53: 2q^3+4q^2+4q+1
        54: 2q^3+4q^2+4q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q^2+2q+1
        59: q^3+q^2+2q
        60: q
        61: q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^3+4q^2+4q+1
        69: q^3+2q^2+3q+1
        70: 3q^3+5q^2+4q+1
        71: 2q^3+4q^2+4q+1
        72: q^2+3q+1
        73: q^3+3q^2+4q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^3+4q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^3+4q^2+4q+1
        83: 2q^3+4q^2+4q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^3+4q^2+4q+1
        89: 2q^3+4q^2+4q+1
        90: 2q^3+3q^2+3q+1
        91: 2q^3+4q^2+4q+1
        92: 2q^3+4q^2+4q+1
        93: 2q^3+3q^2+3q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: q^3+2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: q^3+q^2+2q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 2q^2+2q+1
       118: q^3+q^2+2q
       119: q
       120: q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^3+4q^2+4q+1
       126: q^3+2q^2+3q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^3+4q^2+4q+1
       134: q^3+2q^2+3q+1
       135: q^2+3q+1
       136: q^3+3q^2+4q+1
       137: q^3+3q^2+4q+1
       138: q^2+3q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^3+4q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^3+4q^2+4q+1
       158: 2q^3+4q^2+4q+1
       159: 2q^3+3q^2+3q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: q^3+2q^2+3q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q
       184: q^2+2q+1
       185: 2q^2+2q+1
       186: q^3+q^2+2q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: 2q^2+2q+1
       192: q^3+q^2+2q
       194: q+1
       195: q^2+2q+1
       196: q^2+2q
       198: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^3+2q^2+3q+1
       220: 2q^3+4q^2+4q+1
       221: q^3+2q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 2q^2+4q+1
       228: q^2+3q+1
       229: q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q^2+4q+1
       251: 2q^2+4q+1
       252: q^3+2q^2+3q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       284: q+1
       285: q+1
       286: q
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: q^3+q^2+2q
       298: q^2+3q+1
       300: q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q
       306: q+1
       307: q
       308: 2q+1
       316: q+1
       318: 2q+1
       320: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^3+2q^2+3q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: q^2+3q+1
       347: q+1
       348: 1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q+1
       395: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       420: q+1
       421: q+1
       422: q
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: q+1
       432: q
       434: 1
       436: q+1
       438: q+1
       439: q^2+2q+1
       440: q^2+2q
       442: q+1
       444: q+1
       446: q+1
       448: q+1
       453: q
       454: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: q+1
       481: 2q+1
       482: q^2+3q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: q^2+3q+1
       493: 1
       494: q^2+3q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: 1
       540: q+1
       544: q+1
       548: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       590: q+1
       594: 1
       595: q+1
       596: q
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: 1
       607: q+1
       608: q
       610: 1
       612: q+1
       614: 1
       616: q+1
       618: q+1
       620: q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: 1
       648: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+3q+1
       677: 1
       678: q+1
       679: 1
       681: 2q+1
       686: q+1
       687: 1
       690: 1
       691: q+1
       692: 1
       707: q+1
       711: q+1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       786: 1
       790: 2q+1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q+1
       808: q
       810: 1
       812: 1
       814: q+1
       816: q+1
       826: q+1
       842: q+1
       846: 1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: q+1
       883: 1
       898: q+1
       907: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: q+1
       993: 1
       995: 1
       997: 1
      1001: 1
      1003: q+1
      1005: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1053: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1121: 1
      1125: 1
      1147: 1
      1151: 1
      1159: 1
      1211: 1
      1213: 1
      1215: 1
      1219: 1
      1227: 1
      1229: 1
      1237: 1
      1239: 1
      1241: 1
      1282: 1
      1284: 1
      1321: 1
      1343: 1
      1355: 1
      1439: 1
      1443: 1
      1453: 1
      1548: 1

1549:    0: 8q^2+6q+1
         1: 3q^3+8q^2+6q+1
         2: 8q^2+6q+1
         3: 3q^3+8q^2+6q+1
         4: 8q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: 3q^3+8q^2+6q+1
         7: 8q^2+6q+1
         8: 3q^3+8q^2+6q+1
         9: 2q^3+5q^2+4q+1
        10: 6q^2+6q+1
        11: q^3+6q^2+6q+1
        12: 6q^2+6q+1
        13: 8q^2+6q+1
        14: 8q^2+6q+1
        15: 3q^3+8q^2+6q+1
        16: 6q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 5q^2+4q+1
        19: 8q^2+6q+1
        20: 3q^3+8q^2+6q+1
        21: 8q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: 4q^2+6q+1
        29: 6q^2+6q+1
        30: 8q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+4q+1
        38: 2q^2+2q
        39: 3q^2+4q+1
        40: 2q^2+2q
        41: 3q^2+4q+1
        42: 2q^2+2q
        43: 6q^2+6q+1
        44: 6q^2+6q+1
        45: q^3+6q^2+6q+1
        46: 6q^2+6q+1
        47: q^3+6q^2+6q+1
        48: 5q^2+4q+1
        49: 6q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 5q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q^2+4q+1
        59: 2q
        60: 2q^2+4q+1
        61: 2q
        62: 2q^2+4q+1
        63: q^2+2q
        64: 3q^2+4q+1
        65: 2q^2+2q
        66: 2q^2+4q+1
        67: q^2+2q
        68: 4q^2+6q+1
        69: 3q^2+4q+1
        70: 6q^2+6q+1
        71: 4q^2+6q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+4q+1
        75: 2q^2+2q
        76: 3q^2+4q+1
        77: 2q^2+2q
        78: 3q^2+4q+1
        79: 2q^2+2q
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 2q^2+6q+1
        89: 2q^2+6q+1
        90: 3q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+6q^2+6q+1
        93: 5q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 2q^2+5q+1
       101: 4q^2+5q+1
       102: 2q^2+5q+1
       103: q^2+3q+1
       104: q
       105: q
       106: q
       107: 2q^2+4q+1
       108: 2q
       109: 2q^2+4q+1
       110: 2q
       111: 2q^2+4q+1
       112: q^2+2q
       113: 2q^2+4q+1
       114: q^2+2q
       115: 3q^2+4q+1
       116: 2q^2+2q
       117: 2q^2+4q+1
       118: 2q
       119: 2q^2+4q+1
       120: 2q
       121: 2q^2+4q+1
       122: q^2+2q
       123: 2q^2+4q+1
       124: q^2+2q
       125: 2q^2+6q+1
       126: q^2+4q+1
       127: 3q+1
       128: 2q
       129: 3q+1
       130: 2q
       131: q^2+2q+1
       132: q^2+q
       133: 4q^2+6q+1
       134: 3q^2+4q+1
       135: 4q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 2q^2+5q+1
       150: 2q^2+5q+1
       151: q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: 2q^2+2q
       155: q^2+3q+1
       156: q^2+2q
       157: 2q^2+6q+1
       158: 2q^2+6q+1
       159: 3q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 5q+1
       167: q^2+5q+1
       168: 3q+1
       169: q^2+3q+1
       170: q
       171: q
       172: q
       173: q^2+3q+1
       174: q
       175: q
       176: q
       177: 2q+1
       178: q
       179: 3q+1
       180: 2q
       181: 3q+1
       182: 2q
       183: 2q^2+4q+1
       184: 2q
       185: 2q^2+4q+1
       186: 2q
       187: 2q^2+4q+1
       188: q^2+2q
       189: 2q^2+4q+1
       190: q^2+2q
       191: q^2+4q+1
       192: 2q
       193: 3q+1
       195: q^2+4q+1
       196: 2q
       197: 2q+1
       198: q
       199: q^2+4q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       203: 3q+1
       205: 2q+1
       206: q
       207: q^2+4q+1
       208: 2q
       209: q^2+3q+1
       210: q^2+2q
       211: q^2+3q+1
       212: q^2+2q
       213: 3q+1
       214: 2q
       215: 3q+1
       216: 2q
       217: q^2+2q+1
       218: q^2+q
       219: q^2+4q+1
       220: 2q^2+6q+1
       221: q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: 2q+1
       238: 2q
       239: 2q+1
       240: 2q
       241: q+1
       242: q
       243: 5q+1
       244: 3q+1
       245: 3q+1
       246: 2q^2+5q+1
       247: 5q+1
       248: q^2+5q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+1
       257: q^2+5q+1
       258: 3q+1
       259: 2q+1
       260: q
       261: q
       262: q
       263: q^2+3q+1
       264: q
       265: q
       266: q
       267: 2q+1
       268: q
       271: 2q+1
       272: q
       275: q^2+3q+1
       276: q
       277: q
       278: q
       279: 3q+1
       280: 2q
       281: 2q+1
       282: q
       283: 2q+1
       285: 2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: 2q
       291: 2q+1
       292: q
       293: q^2+4q+1
       294: 2q
       295: q^2+4q+1
       296: 2q
       297: q^2+4q+1
       298: 2q
       299: 3q+1
       301: q+1
       302: q
       303: q^2+4q+1
       304: 2q
       305: 2q+1
       306: q
       307: q^2+4q+1
       308: 2q
       309: 3q+1
       311: q+1
       312: q
       313: 2q+1
       314: q
       315: q+1
       316: q
       317: 2q+1
       318: 2q
       319: 3q+1
       321: 3q+1
       323: 2q+1
       325: q^2+3q+1
       326: q^2+2q
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 5q+1
       338: 2q+1
       339: 2q
       340: 2q+1
       341: 2q
       342: q+1
       343: q
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q+1
       361: 2q
       362: 2q+1
       363: 2q
       364: q+1
       365: q
       366: 3q+1
       367: 5q+1
       368: 3q+1
       369: 3q+1
       370: 3q+1
       371: 5q+1
       372: q^2+5q+1
       373: 3q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       381: 2q+1
       382: q
       383: q
       384: q
       385: q^2+3q+1
       386: q
       387: q
       388: q
       389: q+1
       390: q
       393: 2q+1
       394: q
       397: q+1
       398: q
       401: 2q+1
       402: q
       405: 2q+1
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       419: 2q+1
       421: 2q+1
       423: 2q+1
       424: q
       425: q+1
       426: q
       427: 2q+1
       428: 2q
       429: q+1
       431: 2q+1
       433: 1
       435: q+1
       436: q
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: 3q+1
       445: q+1
       446: q
       447: 2q+1
       449: q+1
       451: 1
       453: 2q+1
       454: q
       455: q+1
       456: q
       457: q+1
       459: q+1
       461: 3q+1
       463: q+1
       464: q
       465: 2q+1
       466: 2q
       467: q+1
       468: q
       469: q+1
       470: q
       471: 3q+1
       473: 3q+1
       475: 2q+1
       477: q+1
       479: 2q+1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 5q+1
       485: 2q+1
       486: 2q
       487: 2q+1
       488: 2q
       489: q+1
       490: q
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 3q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       529: q+1
       533: 1
       537: q+1
       538: q
       541: q+1
       545: q+1
       546: q
       549: 1
       553: q+1
       554: q
       557: q+1
       561: q+1
       562: q
       565: 2q+1
       569: q+1
       573: 2q+1
       577: q+1
       585: 2q+1
       586: q
       589: 2q+1
       591: q+1
       593: q+1
       595: 2q+1
       597: q+1
       598: q
       599: q+1
       600: q
       601: 2q+1
       602: 2q
       603: 1
       605: 1
       607: q+1
       609: 1
       613: 1
       615: 3q+1
       617: q+1
       618: q
       619: q+1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 3q+1
       633: q+1
       634: q
       639: q+1
       640: q
       641: q+1
       643: q+1
       645: 1
       647: q+1
       649: q+1
       651: q+1
       653: q+1
       655: 2q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+1
       672: 2q+1
       673: q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: q+1
       709: q+1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q+1
       734: q
       737: 1
       741: 1
       749: q+1
       750: q
       753: 1
       757: q+1
       761: q+1
       765: 2q+1
       769: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q
       785: q+1
       787: q+1
       791: 1
       793: 2
       795: 1
       796: 1
       797: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       815: q+1
       817: 2
       819: 1
       820: 1
       821: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       839: q+1
       843: 2
       845: 1
       847: 1
       849: 1
       851: 1
       857: q+1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       928: 1
       940: 1
       941: 1
       944: 1
       948: 1
       960: 1
       964: 2
       968: 1
       969: 1
       974: 1
       988: q+1
       994: 1
       995: 1
       998: 2
      1000: 2
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 2
      1016: 1
      1020: 1
      1021: 1
      1022: 1
      1026: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1058: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1086: 1
      1087: 1
      1114: 1
      1115: 1
      1122: 1
      1123: 1
      1126: 1
      1130: 2
      1134: 1
      1138: 1
      1139: 1
      1156: 1
      1172: 1
      1194: 1
      1198: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1240: 1
      1246: 1
      1260: 1
      1262: 1
      1282: 1
      1284: 1
      1286: 1
      1290: 1
      1291: 1
      1326: 1
      1330: 1
      1410: 1
      1440: 1
      1442: 1
      1444: 1
      1549: 1

1550:    0: 8q^2+6q+1
         1: 3q^3+8q^2+6q+1
         2: 8q^2+6q+1
         3: 3q^3+8q^2+6q+1
         4: 8q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: 3q^3+8q^2+6q+1
         7: 8q^2+6q+1
         8: 3q^3+8q^2+6q+1
         9: 2q^3+5q^2+4q+1
        10: 6q^2+6q+1
        11: q^3+6q^2+6q+1
        12: 6q^2+6q+1
        13: 8q^2+6q+1
        14: 8q^2+6q+1
        15: 3q^3+8q^2+6q+1
        16: 6q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 5q^2+4q+1
        19: 8q^2+6q+1
        20: 3q^3+8q^2+6q+1
        21: 8q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: 4q^2+6q+1
        29: 6q^2+6q+1
        30: 8q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 2q^2+2q
        38: 3q^2+4q+1
        39: 2q^2+2q
        40: 3q^2+4q+1
        41: 2q^2+2q
        42: 3q^2+4q+1
        43: 6q^2+6q+1
        44: 6q^2+6q+1
        45: q^3+6q^2+6q+1
        46: 6q^2+6q+1
        47: q^3+6q^2+6q+1
        48: 5q^2+4q+1
        49: 6q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 5q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q
        59: 2q^2+4q+1
        60: 2q^2+4q+1
        61: 2q
        62: q^2+2q
        63: 2q^2+4q+1
        64: 2q^2+2q
        65: 3q^2+4q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: 4q^2+6q+1
        69: 3q^2+4q+1
        70: 6q^2+6q+1
        71: 4q^2+6q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 2q^2+2q
        75: 3q^2+4q+1
        76: 2q^2+2q
        77: 3q^2+4q+1
        78: 2q^2+2q
        79: 3q^2+4q+1
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 2q^2+6q+1
        89: 2q^2+6q+1
        90: 3q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+6q^2+6q+1
        93: 5q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 2q^2+5q+1
       101: 4q^2+5q+1
       102: 2q^2+5q+1
       103: q
       104: q^2+3q+1
       105: q
       106: q
       107: 2q^2+4q+1
       108: 2q
       109: 2q
       110: 2q^2+4q+1
       111: q^2+2q
       112: 2q^2+4q+1
       113: q^2+2q
       114: 2q^2+4q+1
       115: 2q^2+2q
       116: 3q^2+4q+1
       117: 2q
       118: 2q^2+4q+1
       119: 2q^2+4q+1
       120: 2q
       121: q^2+2q
       122: 2q^2+4q+1
       123: q^2+2q
       124: 2q^2+4q+1
       125: 2q^2+6q+1
       126: q^2+4q+1
       127: 2q
       128: 3q+1
       129: 2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: 4q^2+6q+1
       134: 3q^2+4q+1
       135: 4q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 2q^2+5q+1
       150: 2q^2+5q+1
       151: q^2+2q
       152: q^2+3q+1
       153: 2q^2+2q
       154: 2q^2+3q+1
       155: q^2+2q
       156: q^2+3q+1
       157: 2q^2+6q+1
       158: 2q^2+6q+1
       159: 3q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 5q+1
       167: q^2+5q+1
       168: 3q+1
       169: q
       170: q^2+3q+1
       171: q
       172: q
       173: q
       174: q^2+3q+1
       175: q
       176: q
       177: q
       178: 2q+1
       179: 2q
       180: 3q+1
       181: 2q
       182: 3q+1
       183: 2q^2+4q+1
       184: 2q
       185: 2q
       186: 2q^2+4q+1
       187: q^2+2q
       188: 2q^2+4q+1
       189: q^2+2q
       190: 2q^2+4q+1
       191: 2q
       192: q^2+4q+1
       193: 3q+1
       195: 2q
       196: q^2+4q+1
       197: q
       198: 2q+1
       199: q^2+4q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       204: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+4q+1
       209: q^2+2q
       210: q^2+3q+1
       211: q^2+2q
       212: q^2+3q+1
       213: 2q
       214: 3q+1
       215: 2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+6q+1
       221: q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: 2q
       238: 2q+1
       239: 2q
       240: 2q+1
       241: q
       242: q+1
       243: 5q+1
       244: 3q+1
       245: 3q+1
       246: 2q^2+5q+1
       247: 5q+1
       248: q^2+5q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+1
       257: q^2+5q+1
       258: 3q+1
       259: q
       260: 2q+1
       261: q
       262: q
       263: q
       264: q^2+3q+1
       265: q
       266: q
       267: q
       268: 2q+1
       273: q
       274: 2q+1
       275: q
       276: q^2+3q+1
       277: q
       278: q
       279: 2q
       280: 3q+1
       281: q
       282: 2q+1
       283: 2q+1
       286: 2q+1
       287: q
       288: 2q+1
       289: 2q
       290: 3q+1
       291: q
       292: 2q+1
       293: q^2+4q+1
       294: 2q
       295: 2q
       296: q^2+4q+1
       297: 2q
       298: q^2+4q+1
       299: 3q+1
       301: q
       302: q+1
       303: 2q
       304: q^2+4q+1
       305: q
       306: 2q+1
       307: q^2+4q+1
       308: 2q
       310: 3q+1
       311: q
       312: q+1
       313: q
       314: 2q+1
       315: q
       316: q+1
       317: 2q
       318: 2q+1
       319: 3q+1
       322: 3q+1
       324: 2q+1
       325: q^2+2q
       326: q^2+3q+1
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 5q+1
       338: 2q
       339: 2q+1
       340: 2q
       341: 2q+1
       342: q
       343: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q
       361: 2q+1
       362: 2q
       363: 2q+1
       364: q
       365: q+1
       366: 3q+1
       367: 5q+1
       368: 3q+1
       369: 3q+1
       370: 3q+1
       371: 5q+1
       372: q^2+5q+1
       373: 3q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       378: q+1
       381: q
       382: 2q+1
       383: q
       384: q
       385: q
       386: q^2+3q+1
       387: q
       388: q
       389: q
       390: q+1
       393: q
       394: 2q+1
       399: q
       400: q+1
       403: 2q+1
       404: q
       407: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       419: 2q+1
       422: 2q+1
       423: q
       424: 2q+1
       425: q
       426: q+1
       427: 2q
       428: 2q+1
       429: q+1
       432: 2q+1
       434: 1
       435: q
       436: q+1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: 3q+1
       445: q
       446: q+1
       447: 2q+1
       450: q+1
       452: 1
       453: 2q+1
       454: q
       455: q
       456: q+1
       458: q+1
       460: q+1
       462: 3q+1
       463: q
       464: q+1
       465: 2q
       466: 2q+1
       467: q
       468: q+1
       469: q
       470: q+1
       471: 3q+1
       474: 3q+1
       476: 2q+1
       478: q+1
       480: 2q+1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 5q+1
       485: 2q
       486: 2q+1
       487: 2q
       488: 2q+1
       489: q
       490: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 3q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       522: q+1
       530: q+1
       534: 1
       537: q
       538: q+1
       542: q+1
       545: q
       546: q+1
       551: 1
       555: q
       556: q+1
       560: q+1
       563: q
       564: q+1
       566: 2q+1
       571: q+1
       574: 2q+1
       581: q+1
       585: q
       586: 2q+1
       589: 2q+1
       592: q+1
       593: q+1
       596: 2q+1
       597: q
       598: q+1
       599: q
       600: q+1
       601: 2q
       602: 2q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       614: 1
       615: 3q+1
       617: q
       618: q+1
       619: q+1
       622: 1
       624: 1
       626: 1
       630: 1
       632: 3q+1
       633: q
       634: q+1
       639: q
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: q+1
       650: q+1
       652: q+1
       654: q+1
       656: 2q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+1
       672: 2q+1
       673: q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: q+1
       710: q+1
       715: 1
       718: 1
       722: 1
       726: 1
       733: q
       734: q+1
       740: 1
       744: 1
       751: q
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: 2q+1
       773: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q
       782: q+1
       785: q+1
       788: q+1
       792: 1
       793: 2
       795: 1
       796: 1
       798: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       815: q+1
       818: 2
       819: 1
       820: 1
       822: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       840: q+1
       844: 2
       845: 1
       848: 1
       850: 1
       852: 1
       858: q+1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       890: q+1
       903: 1
       905: 1
       909: 1
       916: 1
       917: 1
       921: 1
       929: 1
       942: 1
       943: 1
       947: 1
       951: 1
       962: 1
       965: 2
       971: 1
       972: 1
       976: 1
       989: q+1
       994: 1
       995: 1
       999: 2
      1000: 2
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 2
      1016: 1
      1020: 1
      1021: 1
      1023: 1
      1026: 1
      1033: 1
      1036: 1
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1059: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1089: 1
      1092: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1128: 1
      1131: 2
      1136: 1
      1141: 1
      1142: 1
      1157: 1
      1175: 1
      1195: 1
      1200: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1240: 1
      1247: 1
      1261: 1
      1263: 1
      1282: 1
      1284: 1
      1286: 1
      1293: 1
      1296: 1
      1327: 1
      1332: 1
      1411: 1
      1441: 1
      1442: 1
      1445: 1
      1550: 1

1551:    0: 8q^2+6q+1
         1: 3q^3+8q^2+6q+1
         2: 8q^2+6q+1
         3: 3q^3+8q^2+6q+1
         4: 8q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: 3q^3+8q^2+6q+1
         7: 8q^2+6q+1
         8: 3q^3+8q^2+6q+1
         9: 2q^3+5q^2+4q+1
        10: 6q^2+6q+1
        11: q^3+6q^2+6q+1
        12: 6q^2+6q+1
        13: 8q^2+6q+1
        14: 8q^2+6q+1
        15: 3q^3+8q^2+6q+1
        16: 6q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 5q^2+4q+1
        19: 8q^2+6q+1
        20: 3q^3+8q^2+6q+1
        21: 8q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: 4q^2+6q+1
        29: 6q^2+6q+1
        30: 8q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 2q^2+2q
        38: 3q^2+4q+1
        39: 2q^2+2q
        40: 3q^2+4q+1
        41: 2q^2+2q
        42: 3q^2+4q+1
        43: 6q^2+6q+1
        44: 6q^2+6q+1
        45: q^3+6q^2+6q+1
        46: 6q^2+6q+1
        47: q^3+6q^2+6q+1
        48: 5q^2+4q+1
        49: 6q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 5q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q^2+4q+1
        59: 2q
        60: 2q
        61: 2q^2+4q+1
        62: q^2+2q
        63: 2q^2+4q+1
        64: 2q^2+2q
        65: 3q^2+4q+1
        66: q^2+2q
        67: 2q^2+4q+1
        68: 4q^2+6q+1
        69: 3q^2+4q+1
        70: 6q^2+6q+1
        71: 4q^2+6q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 2q^2+2q
        75: 3q^2+4q+1
        76: 2q^2+2q
        77: 3q^2+4q+1
        78: 2q^2+2q
        79: 3q^2+4q+1
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 2q^2+6q+1
        89: 2q^2+6q+1
        90: 3q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+6q^2+6q+1
        93: 5q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 2q^2+5q+1
       101: 4q^2+5q+1
       102: 2q^2+5q+1
       103: q
       104: q
       105: q^2+3q+1
       106: q
       107: 2q
       108: 2q^2+4q+1
       109: 2q^2+4q+1
       110: 2q
       111: q^2+2q
       112: 2q^2+4q+1
       113: q^2+2q
       114: 2q^2+4q+1
       115: 2q^2+2q
       116: 3q^2+4q+1
       117: 2q^2+4q+1
       118: 2q
       119: 2q
       120: 2q^2+4q+1
       121: q^2+2q
       122: 2q^2+4q+1
       123: q^2+2q
       124: 2q^2+4q+1
       125: 2q^2+6q+1
       126: q^2+4q+1
       127: 2q
       128: 3q+1
       129: 2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: 4q^2+6q+1
       134: 3q^2+4q+1
       135: 4q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 2q^2+5q+1
       150: 2q^2+5q+1
       151: q^2+2q
       152: q^2+3q+1
       153: 2q^2+2q
       154: 2q^2+3q+1
       155: q^2+2q
       156: q^2+3q+1
       157: 2q^2+6q+1
       158: 2q^2+6q+1
       159: 3q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 5q+1
       167: q^2+5q+1
       168: 3q+1
       169: q
       170: q
       171: q^2+3q+1
       172: q
       173: q
       174: q
       175: q^2+3q+1
       176: q
       177: q
       178: 2q+1
       179: 2q
       180: 3q+1
       181: 2q
       182: 3q+1
       183: 2q
       184: 2q^2+4q+1
       185: 2q^2+4q+1
       186: 2q
       187: q^2+2q
       188: 2q^2+4q+1
       189: q^2+2q
       190: 2q^2+4q+1
       191: q^2+4q+1
       192: 2q
       194: 3q+1
       195: q^2+4q+1
       196: 2q
       197: q
       198: 2q+1
       199: 2q
       200: q^2+4q+1
       201: 2q
       202: q^2+4q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+4q+1
       209: q^2+2q
       210: q^2+3q+1
       211: q^2+2q
       212: q^2+3q+1
       213: 2q
       214: 3q+1
       215: 2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: q^2+4q+1
       220: 2q^2+6q+1
       221: q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: 2q
       238: 2q+1
       239: 2q
       240: 2q+1
       241: q
       242: q+1
       243: 5q+1
       244: 3q+1
       245: 3q+1
       246: 2q^2+5q+1
       247: 5q+1
       248: q^2+5q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+1
       257: q^2+5q+1
       258: 3q+1
       259: q
       260: q
       261: 2q+1
       262: q
       263: q
       264: q
       265: q^2+3q+1
       266: q
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       275: q
       276: q
       277: q^2+3q+1
       278: q
       279: 2q
       280: 3q+1
       281: q
       282: 2q+1
       284: 2q+1
       285: 2q+1
       287: q
       288: 2q+1
       289: 2q
       290: 3q+1
       291: q
       292: 2q+1
       293: 2q
       294: q^2+4q+1
       295: q^2+4q+1
       296: 2q
       297: 2q
       298: q^2+4q+1
       300: 3q+1
       301: q
       302: q+1
       303: q^2+4q+1
       304: 2q
       305: q
       306: 2q+1
       307: 2q
       308: q^2+4q+1
       309: 3q+1
       311: q
       312: q+1
       313: q
       314: 2q+1
       315: q
       316: q+1
       317: 2q
       318: 2q+1
       320: 3q+1
       321: 3q+1
       324: 2q+1
       325: q^2+2q
       326: q^2+3q+1
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 5q+1
       338: 2q
       339: 2q+1
       340: 2q
       341: 2q+1
       342: q
       343: q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q
       361: 2q+1
       362: 2q
       363: 2q+1
       364: q
       365: q+1
       366: 3q+1
       367: 5q+1
       368: 3q+1
       369: 3q+1
       370: 3q+1
       371: 5q+1
       372: q^2+5q+1
       373: 3q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       379: q+1
       381: q
       382: q
       383: 2q+1
       384: q
       385: q
       386: q
       387: q^2+3q+1
       388: q
       391: q
       392: q+1
       395: 2q+1
       396: q
       397: q
       398: q+1
       401: q
       402: 2q+1
       408: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       420: 2q+1
       421: 2q+1
       423: q
       424: 2q+1
       425: q
       426: q+1
       427: 2q
       428: 2q+1
       430: q+1
       431: 2q+1
       434: 1
       435: q
       436: q+1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: 3q+1
       445: q
       446: q+1
       448: 2q+1
       449: q+1
       452: 1
       453: q
       454: 2q+1
       455: q
       456: q+1
       457: q+1
       460: q+1
       461: 3q+1
       463: q
       464: q+1
       465: 2q
       466: 2q+1
       467: q
       468: q+1
       469: q
       470: q+1
       472: 3q+1
       473: 3q+1
       476: 2q+1
       478: q+1
       480: 2q+1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 5q+1
       485: 2q
       486: 2q+1
       487: 2q
       488: 2q+1
       489: q
       490: q+1
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 3q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       523: q+1
       531: q+1
       535: 1
       539: q
       540: q+1
       544: q+1
       547: q
       548: q+1
       550: 1
       553: q
       554: q+1
       558: q+1
       561: q
       562: q+1
       567: 2q+1
       572: q+1
       576: 2q+1
       581: q+1
       585: q
       586: 2q+1
       590: 2q+1
       591: q+1
       594: q+1
       595: 2q+1
       597: q
       598: q+1
       599: q
       600: q+1
       601: 2q
       602: 2q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       614: 1
       616: 3q+1
       617: q
       618: q+1
       620: q+1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 3q+1
       633: q
       634: q+1
       639: q
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       656: 2q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+1
       672: 2q+1
       673: q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       700: q+1
       711: q+1
       714: 1
       719: 1
       724: 1
       728: 1
       735: q
       736: q+1
       738: 1
       742: 1
       749: q
       750: q+1
       755: 1
       760: q+1
       764: q+1
       767: 2q+1
       773: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q
       782: q+1
       786: q+1
       787: q+1
       792: 1
       794: 2
       795: 1
       796: 1
       798: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       816: q+1
       817: 2
       819: 1
       820: 1
       822: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       839: q+1
       844: 2
       846: 1
       847: 1
       850: 1
       852: 1
       858: q+1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       891: q+1
       901: 1
       907: 1
       910: 1
       918: 1
       919: 1
       923: 1
       931: 1
       940: 1
       941: 1
       945: 1
       949: 1
       963: 1
       966: 2
       971: 1
       972: 1
       977: 1
       990: q+1
       994: 1
       995: 1
       998: 2
      1001: 2
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 2
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1036: 1
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1053: 1
      1058: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1124: 1
      1125: 1
      1129: 1
      1132: 2
      1137: 1
      1141: 1
      1142: 1
      1159: 1
      1173: 1
      1196: 1
      1201: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1241: 1
      1246: 1
      1260: 1
      1263: 1
      1282: 1
      1284: 1
      1286: 1
      1294: 1
      1297: 1
      1328: 1
      1333: 1
      1412: 1
      1440: 1
      1443: 1
      1445: 1
      1551: 1

1552:    0: 8q^2+6q+1
         1: 3q^3+8q^2+6q+1
         2: 8q^2+6q+1
         3: 3q^3+8q^2+6q+1
         4: 8q^2+6q+1
         5: 3q^3+8q^2+6q+1
         6: 3q^3+8q^2+6q+1
         7: 8q^2+6q+1
         8: 3q^3+8q^2+6q+1
         9: 2q^3+5q^2+4q+1
        10: 6q^2+6q+1
        11: q^3+6q^2+6q+1
        12: 6q^2+6q+1
        13: 8q^2+6q+1
        14: 8q^2+6q+1
        15: 3q^3+8q^2+6q+1
        16: 6q^2+6q+1
        17: q^3+6q^2+6q+1
        18: 5q^2+4q+1
        19: 8q^2+6q+1
        20: 3q^3+8q^2+6q+1
        21: 8q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: 4q^2+6q+1
        29: 6q^2+6q+1
        30: 8q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+4q+1
        38: 2q^2+2q
        39: 3q^2+4q+1
        40: 2q^2+2q
        41: 3q^2+4q+1
        42: 2q^2+2q
        43: 6q^2+6q+1
        44: 6q^2+6q+1
        45: q^3+6q^2+6q+1
        46: 6q^2+6q+1
        47: q^3+6q^2+6q+1
        48: 5q^2+4q+1
        49: 6q^2+6q+1
        50: q^3+6q^2+6q+1
        51: 5q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q
        59: 2q^2+4q+1
        60: 2q
        61: 2q^2+4q+1
        62: 2q^2+4q+1
        63: q^2+2q
        64: 3q^2+4q+1
        65: 2q^2+2q
        66: 2q^2+4q+1
        67: q^2+2q
        68: 4q^2+6q+1
        69: 3q^2+4q+1
        70: 6q^2+6q+1
        71: 4q^2+6q+1
        72: 4q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+4q+1
        75: 2q^2+2q
        76: 3q^2+4q+1
        77: 2q^2+2q
        78: 3q^2+4q+1
        79: 2q^2+2q
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 2q^2+6q+1
        89: 2q^2+6q+1
        90: 3q^2+4q+1
        91: 6q^2+6q+1
        92: q^3+6q^2+6q+1
        93: 5q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 2q^2+5q+1
       101: 4q^2+5q+1
       102: 2q^2+5q+1
       103: q
       104: q
       105: q
       106: q^2+3q+1
       107: 2q
       108: 2q^2+4q+1
       109: 2q
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: q^2+2q
       113: 2q^2+4q+1
       114: q^2+2q
       115: 3q^2+4q+1
       116: 2q^2+2q
       117: 2q
       118: 2q^2+4q+1
       119: 2q
       120: 2q^2+4q+1
       121: 2q^2+4q+1
       122: q^2+2q
       123: 2q^2+4q+1
       124: q^2+2q
       125: 2q^2+6q+1
       126: q^2+4q+1
       127: 3q+1
       128: 2q
       129: 3q+1
       130: 2q
       131: q^2+2q+1
       132: q^2+q
       133: 4q^2+6q+1
       134: 3q^2+4q+1
       135: 4q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 2q^2+5q+1
       150: 2q^2+5q+1
       151: q^2+3q+1
       152: q^2+2q
       153: 2q^2+3q+1
       154: 2q^2+2q
       155: q^2+3q+1
       156: q^2+2q
       157: 2q^2+6q+1
       158: 2q^2+6q+1
       159: 3q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 5q+1
       167: q^2+5q+1
       168: 3q+1
       169: q
       170: q
       171: q
       172: q^2+3q+1
       173: q
       174: q
       175: q
       176: q^2+3q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: 2q
       181: 3q+1
       182: 2q
       183: 2q
       184: 2q^2+4q+1
       185: 2q
       186: 2q^2+4q+1
       187: 2q^2+4q+1
       188: q^2+2q
       189: 2q^2+4q+1
       190: q^2+2q
       191: 2q
       192: q^2+4q+1
       194: 3q+1
       195: 2q
       196: q^2+4q+1
       197: 2q+1
       198: q
       199: 2q
       200: q^2+4q+1
       201: 2q
       202: q^2+4q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: q^2+4q+1
       208: 2q
       209: q^2+3q+1
       210: q^2+2q
       211: q^2+3q+1
       212: q^2+2q
       213: 3q+1
       214: 2q
       215: 3q+1
       216: 2q
       217: q^2+2q+1
       218: q^2+q
       219: q^2+4q+1
       220: 2q^2+6q+1
       221: q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: 3q+1
       237: 2q+1
       238: 2q
       239: 2q+1
       240: 2q
       241: q+1
       242: q
       243: 5q+1
       244: 3q+1
       245: 3q+1
       246: 2q^2+5q+1
       247: 5q+1
       248: q^2+5q+1
       249: 3q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 5q+1
       257: q^2+5q+1
       258: 3q+1
       259: q
       260: q
       261: q
       262: 2q+1
       263: q
       264: q
       265: q
       266: q^2+3q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: q
       275: q
       276: q
       277: q
       278: q^2+3q+1
       279: 3q+1
       280: 2q
       281: 2q+1
       282: q
       284: 2q+1
       286: 2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: 2q
       291: 2q+1
       292: q
       293: 2q
       294: q^2+4q+1
       295: 2q
       296: q^2+4q+1
       297: q^2+4q+1
       298: 2q
       300: 3q+1
       301: q+1
       302: q
       303: 2q
       304: q^2+4q+1
       305: 2q+1
       306: q
       307: 2q
       308: q^2+4q+1
       310: 3q+1
       311: q+1
       312: q
       313: 2q+1
       314: q
       315: q+1
       316: q
       317: 2q+1
       318: 2q
       320: 3q+1
       322: 3q+1
       323: 2q+1
       325: q^2+3q+1
       326: q^2+2q
       333: q^2+4q+1
       334: 4q+1
       335: 4q+1
       336: 3q+1
       337: 5q+1
       338: 2q+1
       339: 2q
       340: 2q+1
       341: 2q
       342: q+1
       343: q
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q+1
       361: 2q
       362: 2q+1
       363: 2q
       364: q+1
       365: q
       366: 3q+1
       367: 5q+1
       368: 3q+1
       369: 3q+1
       370: 3q+1
       371: 5q+1
       372: q^2+5q+1
       373: 3q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       380: q+1
       381: q
       382: q
       383: q
       384: 2q+1
       385: q
       386: q
       387: q
       388: q^2+3q+1
       391: q+1
       392: q
       395: q
       396: 2q+1
       399: q+1
       400: q
       403: q
       404: 2q+1
       406: 2q+1
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       420: 2q+1
       422: 2q+1
       423: 2q+1
       424: q
       425: q+1
       426: q
       427: 2q+1
       428: 2q
       430: q+1
       432: 2q+1
       433: 1
       435: q+1
       436: q
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: 3q+1
       445: q+1
       446: q
       448: 2q+1
       450: q+1
       451: 1
       453: q
       454: 2q+1
       455: q+1
       456: q
       458: q+1
       459: q+1
       462: 3q+1
       463: q+1
       464: q
       465: 2q+1
       466: 2q
       467: q+1
       468: q
       469: q+1
       470: q
       472: 3q+1
       474: 3q+1
       475: 2q+1
       477: q+1
       479: 2q+1
       481: 4q+1
       482: 4q+1
       483: 3q+1
       484: 5q+1
       485: 2q+1
       486: 2q
       487: 2q+1
       488: 2q
       489: q+1
       490: q
       491: 3q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 3q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2
       516: 2q+2
       517: 2
       518: 2q+1
       519: 2q+1
       520: q+1
       524: q+1
       532: q+1
       536: 1
       539: q+1
       540: q
       543: q+1
       547: q+1
       548: q
       552: 1
       555: q+1
       556: q
       559: q+1
       563: q+1
       564: q
       568: 2q+1
       570: q+1
       575: 2q+1
       577: q+1
       585: 2q+1
       586: q
       590: 2q+1
       592: q+1
       594: q+1
       596: 2q+1
       597: q+1
       598: q
       599: q+1
       600: q
       601: 2q+1
       602: 2q
       604: 1
       605: 1
       608: q+1
       609: 1
       613: 1
       616: 3q+1
       617: q+1
       618: q
       620: q+1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 3q+1
       633: q+1
       634: q
       639: q+1
       640: q
       642: q+1
       644: q+1
       645: 1
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: 2q+1
       657: 2
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 2
       665: 3q+1
       672: 2q+1
       673: q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       697: q+1
       712: q+1
       716: 1
       720: 1
       723: 1
       727: 1
       735: q+1
       736: q
       739: 1
       743: 1
       751: q+1
       752: q
       756: 1
       758: q+1
       762: q+1
       768: 2q+1
       769: q+1
       775: 1
       776: 1
       779: 1
       780: 1
       781: q+1
       782: q
       786: q+1
       788: q+1
       791: 1
       794: 2
       795: 1
       796: 1
       797: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       816: q+1
       818: 2
       819: 1
       820: 1
       821: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       840: q+1
       843: 2
       846: 1
       848: 1
       849: 1
       851: 1
       857: q+1
       865: 1
       866: 2
       867: 1
       868: q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       889: q+1
       902: 1
       906: 1
       911: 1
       918: 1
       919: 1
       922: 1
       930: 1
       942: 1
       943: 1
       946: 1
       950: 1
       961: 1
       967: 2
       968: 1
       969: 1
       975: 1
       991: q+1
       994: 1
       995: 1
       999: 2
      1001: 2
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 2
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1059: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1091: 1
      1094: 1
      1116: 1
      1117: 1
      1124: 1
      1125: 1
      1127: 1
      1133: 2
      1135: 1
      1138: 1
      1139: 1
      1158: 1
      1174: 1
      1197: 1
      1199: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1241: 1
      1247: 1
      1261: 1
      1262: 1
      1282: 1
      1284: 1
      1286: 1
      1295: 1
      1298: 1
      1329: 1
      1331: 1
      1413: 1
      1441: 1
      1443: 1
      1444: 1
      1552: 1

1553:    0: 2q^2+3q+2
         1: 2q^2+3q+2
         2: 2q^2+3q+2
         3: q^3+2q^2+3q+2
         4: 2q^2+3q+2
         5: q^3+2q^2+3q+2
         6: 2q^2+3q+2
         7: 2q^2+3q+2
         8: q^3+2q^2+3q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+2
        11: q^3+2q^2+3q+2
        12: 2q^2+3q+2
        13: 2q^2+3q+2
        14: 2q^2+3q+2
        15: q^3+2q^2+3q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+1
        19: 2q^2+3q+2
        20: 2q^2+3q+2
        21: 2q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: q^2+2q+2
        29: 2q^2+3q+2
        30: 2q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        37: q^2+3q+2
        39: q^2+3q+2
        41: q^2+3q+2
        43: 2q^2+3q+2
        44: 2q^2+3q+2
        45: q^3+2q^2+3q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+1
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+3q+2
        64: q^2+3q+2
        66: 2q+2
        68: q^2+2q+2
        69: q+1
        70: 2q^2+3q+2
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        74: q^2+3q+2
        76: q^2+3q+2
        78: q^2+3q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+1
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: q^2+3q+2
       115: q^2+3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+3q+2
       123: 2q+2
       125: q^2+2q+2
       126: q+1
       127: 2q+2
       129: 2q+2
       131: q^2+2q+1
       133: q^2+2q+2
       134: q+1
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: q+1
       179: 2q+2
       181: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q+2
       189: q^2+3q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: 2q+2
       211: 2q+2
       213: 2q+2
       215: 2q+2
       217: q^2+2q+1
       219: q+1
       220: q^2+2q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2q+2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       237: q+2
       239: q+2
       241: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       259: q+1
       262: q+1
       263: q+1
       266: q+1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: 2q+2
       281: q+1
       287: q+1
       289: 2q+2
       291: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2q+2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 2q+2
       327: 2q+2
       329: 2q+2
       331: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       338: q+2
       340: q+2
       342: q+1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       360: q+2
       362: q+2
       364: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       381: q+1
       384: q+1
       385: q+1
       388: q+1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 2q+2
       411: q+1
       413: q+1
       415: 2q+2
       417: q+1
       423: q+1
       425: 1
       427: q+2
       433: 1
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       451: 1
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: q+1
       482: q+1
       483: 1
       484: q+2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       502: q+2
       504: q+2
       506: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: q+1
       517: 1
       518: q+2
       519: q+2
       520: q+1
       525: q+1
       528: q+1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: q+1
       585: q+1
       587: q+1
       597: 1
       599: 1
       601: q+2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: q+2
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: 1
       697: 1
       729: 1
       731: 1
       733: 1
       735: 1
       745: 1
       747: 1
       749: 1
       751: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       777: q+1
       779: 1
       781: 1
       783: 1
       789: q+2
       791: 1
       795: 1
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       819: 1
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       843: 1
       849: 1
       851: 1
       853: 2
       857: 2
       859: 1
       861: q+1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       889: 1
       932: 1
       934: 1
       956: 1
       958: 1
       968: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       996: 1
      1002: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1030: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1046: 1
      1048: 1
      1050: 1
      1066: 1
      1068: q+1
      1070: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1098: 1
      1102: 1
      1138: 1
      1188: 1
      1212: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1236: 1
      1238: 1
      1244: 1
      1252: 1
      1256: 1
      1262: 1
      1264: 1
      1284: 1
      1286: 1
      1334: 1
      1404: 1
      1444: 1
      1446: 1
      1452: 1
      1458: 1
      1553: 1

1554:    0: 8q^3+13q^2+6q
         1: 8q^3+13q^2+6q
         2: 8q^3+13q^2+6q
         3: 2q^4+9q^3+13q^2+6q
         4: 8q^3+13q^2+6q
         5: 2q^4+9q^3+13q^2+6q
         6: 8q^3+13q^2+6q
         7: 8q^3+13q^2+6q
         8: 2q^4+9q^3+13q^2+6q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: 8q^3+13q^2+6q
        11: 2q^4+9q^3+13q^2+6q
        12: 8q^3+13q^2+6q
        13: 8q^3+13q^2+6q
        14: 8q^3+13q^2+6q
        15: 2q^4+9q^3+13q^2+6q
        16: q^3+8q^2+6q
        17: q^3+8q^2+6q
        18: 3q^3+5q^2+2q
        19: 8q^3+13q^2+6q
        20: 8q^3+13q^2+6q
        21: 8q^3+13q^2+6q
        22: 5q^3+11q^2+6q
        23: 5q^3+11q^2+6q
        24: 5q^3+11q^2+6q
        25: 5q^3+11q^2+6q
        26: 5q^3+11q^2+6q
        27: 5q^3+11q^2+6q
        28: q^3+8q^2+6q
        29: 8q^3+13q^2+6q
        30: 8q^3+13q^2+6q
        31: 5q^3+11q^2+6q
        32: 5q^3+11q^2+6q
        33: 6q^2+6q
        34: 5q^3+11q^2+6q
        35: 5q^3+11q^2+6q
        36: 6q^2+6q
        37: q^3+3q^2+2q
        38: 2q^3+6q^2+4q
        39: q^3+3q^2+2q
        40: 2q^3+6q^2+4q
        41: q^3+3q^2+2q
        42: 2q^3+6q^2+4q
        43: 8q^3+13q^2+6q
        44: 8q^3+13q^2+6q
        45: 2q^4+9q^3+13q^2+6q
        46: q^3+8q^2+6q
        47: q^3+8q^2+6q
        48: 3q^3+5q^2+2q
        49: q^3+8q^2+6q
        50: q^3+8q^2+6q
        51: 3q^3+5q^2+2q
        52: 5q^3+11q^2+6q
        53: 5q^3+11q^2+6q
        54: 5q^3+11q^2+6q
        55: 5q^3+11q^2+6q
        56: 5q^3+11q^2+6q
        57: 5q^3+11q^2+6q
        58: 3q^2+3q
        59: 3q^2+3q
        60: 3q^2+3q
        61: 3q^2+3q
        62: q^3+3q^2+2q
        63: 2q^3+6q^2+4q
        64: q^3+3q^2+2q
        65: 2q^3+6q^2+4q
        66: 2q^2+2q
        67: 2q^2+4q
        68: q^3+8q^2+6q
        69: 2q^2+2q
        70: 8q^3+13q^2+6q
        71: q^3+8q^2+6q
        72: 6q^2+6q
        73: 6q^2+6q
        74: q^3+3q^2+2q
        75: 2q^3+6q^2+4q
        76: q^3+3q^2+2q
        77: 2q^3+6q^2+4q
        78: q^3+3q^2+2q
        79: 2q^3+6q^2+4q
        80: 5q^3+11q^2+6q
        81: 6q^2+6q
        82: 5q^3+11q^2+6q
        83: 5q^3+11q^2+6q
        84: 5q^3+11q^2+6q
        85: 6q^2+6q
        86: 5q^3+11q^2+6q
        87: 5q^3+11q^2+6q
        88: q^3+8q^2+6q
        89: q^3+8q^2+6q
        90: 3q^3+5q^2+2q
        91: q^3+8q^2+6q
        92: q^3+8q^2+6q
        93: 3q^3+5q^2+2q
        94: 4q^2+6q
        95: 4q^2+6q
        96: 2q^3+4q^2+2q
        97: 4q^2+6q
        98: 4q^2+6q
        99: 2q^3+4q^2+2q
       100: q^3+7q^2+6q
       101: q^3+7q^2+6q
       102: q^3+7q^2+6q
       103: q^2+q
       104: q^2+2q
       105: q^2+2q
       106: q^2+q
       107: 3q^2+3q
       108: 3q^2+3q
       109: 3q^2+3q
       110: 3q^2+3q
       111: 2q^2+2q
       112: 2q^2+4q
       113: q^3+3q^2+2q
       114: 2q^3+6q^2+4q
       115: q^3+3q^2+2q
       116: 2q^3+6q^2+4q
       117: 3q^2+3q
       118: 3q^2+3q
       119: 3q^2+3q
       120: 3q^2+3q
       121: q^3+3q^2+2q
       122: 2q^3+6q^2+4q
       123: 2q^2+2q
       124: 2q^2+4q
       125: q^3+8q^2+6q
       126: 2q^2+2q
       128: 4q
       130: 4q
       132: q^3+2q^2+q
       133: q^3+8q^2+6q
       134: 2q^2+2q
       135: 6q^2+6q
       136: 6q^2+6q
       137: 6q^2+6q
       138: q^2+2q
       139: 4q^2+6q
       140: 4q
       141: 5q^3+11q^2+6q
       142: 4q^2+6q
       143: 6q^2+6q
       144: q^2+2q
       145: 4q^2+6q
       146: 5q^3+11q^2+6q
       147: 4q^2+6q
       148: 4q
       149: q^3+7q^2+6q
       150: q^3+7q^2+6q
       151: 2q^2+2q
       152: q^3+5q^2+4q
       153: 2q^2+2q
       154: q^3+5q^2+4q
       155: 2q^2+2q
       156: q^3+5q^2+4q
       157: q^3+8q^2+6q
       158: q^3+8q^2+6q
       159: 3q^3+5q^2+2q
       160: 4q^2+6q
       161: 4q^2+6q
       162: 2q^3+4q^2+2q
       163: 4q^2+6q
       164: 4q^2+6q
       165: 2q^3+4q^2+2q
       166: q^2+6q
       167: q^2+6q
       168: 2q^2+2q
       169: q^2+q
       170: q^2+2q
       171: q^2+2q
       172: q^2+q
       173: q^2+q
       174: q^2+2q
       175: q^2+2q
       176: q^2+q
       178: q
       180: 4q
       182: 4q
       183: 3q^2+3q
       184: 3q^2+3q
       185: 3q^2+3q
       186: 3q^2+3q
       187: 2q^2+2q
       188: 2q^2+4q
       189: q^3+3q^2+2q
       190: 2q^3+6q^2+4q
       191: 3q^2+3q
       192: 3q^2+3q
       193: 2q
       194: 2q
       195: 2q^2+3q
       196: 2q^2+3q
       197: 2q
       198: 2q
       199: 3q^2+3q
       200: 3q^2+3q
       201: 2q^2+3q
       202: 2q^2+3q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: 2q^2+2q
       208: 2q^2+4q
       209: 2q^2+2q
       210: q^3+5q^2+4q
       211: 2q^2+2q
       212: q^3+5q^2+4q
       214: 4q
       216: 4q
       218: q^3+2q^2+q
       219: 2q^2+2q
       220: q^3+8q^2+6q
       221: 2q^2+2q
       222: 6q^2+6q
       223: q^2+2q
       224: 6q^2+6q
       225: q^2+2q
       226: q^2+2q
       227: 4q^2+6q
       228: q^2+2q
       229: 4q
       230: 4q^2+6q
       231: q^2+2q
       232: 4q^2+6q
       233: q^2+2q
       234: 4q^2+6q
       235: 4q
       236: 2q
       238: 4q
       240: 4q
       242: q^2+q
       243: q^2+6q
       244: 4q
       245: 4q
       246: q^3+7q^2+6q
       247: q^2+6q
       248: q^2+6q
       249: 2q^2+2q
       250: 4q^2+6q
       251: 4q^2+6q
       252: 2q^3+4q^2+2q
       253: 4q^2+6q
       254: 4q^2+6q
       255: 2q^3+4q^2+2q
       256: q^2+6q
       257: q^2+6q
       258: 2q^2+2q
       260: 2q
       261: 2q
       263: q^2+q
       264: q^2+2q
       265: q^2+2q
       266: q^2+q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       275: q^2+q
       276: q^2+2q
       277: q^2+2q
       278: q^2+q
       280: 4q
       282: q
       288: q
       290: 4q
       292: q
       293: 3q^2+3q
       294: 3q^2+3q
       295: 3q^2+3q
       296: 3q^2+3q
       297: 2q^2+2q
       298: 2q^2+4q
       299: 2q
       300: 2q
       302: 2q
       303: 2q^2+3q
       304: 2q^2+3q
       305: 2q
       306: 2q
       307: 2q^2+3q
       308: 2q^2+3q
       309: 2q
       310: 2q
       312: 2q
       313: 2q
       314: 2q
       316: q
       318: 4q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       325: 2q^2+2q
       326: q^3+5q^2+4q
       328: 4q
       330: 4q
       332: q^3+2q^2+q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: q^2+6q
       339: 4q
       341: 4q
       343: q^2+q
       344: q^2+2q
       345: 4q^2+6q
       346: q^2+2q
       347: 4q
       348: q
       349: 4q^2+6q
       350: q^2+2q
       351: 4q
       352: q^2+2q
       353: 4q^2+6q
       354: q^2+2q
       355: 4q^2+6q
       356: q^2+2q
       357: 4q
       358: q
       359: 4q
       361: 4q
       363: 4q
       365: q^2+q
       366: 2q
       367: q^2+6q
       368: 2q
       369: 4q
       370: 4q
       371: q^2+6q
       372: q^2+6q
       373: 2q^2+2q
       374: q^2+6q
       375: q^2+6q
       376: 2q^2+2q
       382: 2q
       383: 2q
       385: q^2+q
       386: q^2+2q
       387: q^2+2q
       388: q^2+q
       390: q
       392: q
       393: q
       394: q
       395: q
       396: q
       398: q
       400: q
       401: q
       402: q
       403: q
       404: q
       405: q
       406: q
       410: 4q
       412: q
       414: q
       416: 4q
       418: q
       424: q
       426: q
       428: 4q
       436: 2q
       437: 2q
       438: 2q
       439: 2q^2+3q
       440: 2q^2+3q
       441: 2q
       442: 2q
       443: 2q
       444: 2q
       446: 2q
       453: 2q^2+3q
       454: 2q^2+3q
       456: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: 2q
       462: 2q
       464: 2q
       466: 4q
       468: q
       470: q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       479: 2q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: q^2+6q
       486: 4q
       488: 4q
       490: q^2+q
       491: 2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: 4q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: 4q
       503: 4q
       505: 4q
       507: q^2+q
       508: 2q
       509: q^2+6q
       510: 2q
       511: 4q
       512: q
       513: 4q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+6q
       519: q^2+6q
       520: 2q^2+2q
       526: 2q
       527: 2q
       538: q
       540: q
       541: q
       542: q
       543: q
       544: q
       546: q
       548: q
       554: q
       556: q
       557: q
       558: q
       559: q
       560: q
       562: q
       564: q
       565: q
       568: q
       573: q
       575: q
       584: q
       586: q
       588: q
       598: q
       600: q
       602: 4q
       612: 2q
       615: 2q
       616: 2q
       618: 2q
       628: 2q
       631: 2q
       632: 2q
       634: 2q
       636: 4q
       638: q
       640: q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       653: 2q
       655: 2q
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 2q
       667: 4q
       669: 4q
       671: q^2+q
       672: q^2+6q
       673: 2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: 4q
       679: q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: 4q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       761: q
       762: q
       765: q
       768: q
       778: q
       780: 1
       782: q
       784: q
       790: 4q
       796: 1
       814: 2q
       815: 2q
       816: 2q
       820: 1
       838: 2q
       839: 2q
       840: 2q
       842: q
       843: 1
       857: 2q
       860: 1
       862: q+1
       864: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       933: q
       935: q
       957: q
       959: q
       969: 1
       988: q
       991: q
       997: 1
      1003: q
      1012: 1
      1015: 1
      1021: 1
      1031: 1
      1037: 1
      1046: 1
      1067: 1
      1069: q+1
      1071: 1
      1073: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1139: 1
      1189: 1
      1213: 1
      1224: 1
      1227: 1
      1237: 1
      1245: 1
      1253: 1
      1262: 1
      1284: 1
      1286: 1
      1335: 1
      1405: 1
      1444: 1
      1453: 1
      1459: 1
      1554: 1

1555:    0: q^4+q^3+4q^2+2q
         1: q^4+3q^3+4q^2+2q
         2: q^4+q^3+4q^2+2q
         3: q^4+3q^3+4q^2+2q
         4: q^4+q^3+4q^2+2q
         5: q^3+4q^2+2q
         6: q^4+3q^3+4q^2+2q
         7: q^4+q^3+4q^2+2q
         8: q^3+4q^2+2q
         9: q^5+q^4+q^3+2q^2+q
        10: q^3+3q^2+2q
        11: q^3+3q^2+2q
        12: q^3+3q^2+2q
        13: q^4+q^3+4q^2+2q
        14: q^4+q^3+4q^2+2q
        15: q^3+4q^2+2q
        16: q^3+3q^2+2q
        17: q^3+3q^2+2q
        18: q^4+2q^2+q
        19: q^4+q^3+4q^2+2q
        20: q^4+3q^3+4q^2+2q
        21: q^4+q^3+4q^2+2q
        22: 4q^2+2q
        23: 2q^3+4q^2+2q
        24: 4q^2+2q
        25: 4q^2+2q
        26: 2q^3+4q^2+2q
        27: 4q^2+2q
        28: q^3+2q^2+2q
        29: q^3+3q^2+2q
        30: q^4+q^3+4q^2+2q
        31: 3q^2+2q
        32: 4q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 4q^2+2q
        36: 3q^2+2q
        37: 4q^2+2q
        39: 2q^3+4q^2+2q
        41: 4q^2+2q
        43: q^3+3q^2+2q
        44: q^3+3q^2+2q
        45: q^3+3q^2+2q
        46: q^3+3q^2+2q
        47: q^3+3q^2+2q
        48: q^4+2q^2+q
        49: q^3+3q^2+2q
        50: q^3+3q^2+2q
        51: q^4+2q^2+q
        52: 4q^2+2q
        53: 2q^3+4q^2+2q
        54: 4q^2+2q
        55: 4q^2+2q
        56: 2q^3+4q^2+2q
        57: 4q^2+2q
        58: q^2+q
        59: q^2+q
        60: q^2+q
        61: q^2+q
        62: 3q^2+2q
        64: 4q^2+2q
        66: 3q^2+2q
        68: q^3+2q^2+2q
        69: q^2+q
        70: q^3+3q^2+2q
        71: q^3+2q^2+2q
        72: 3q^2+2q
        73: 3q^2+2q
        74: 4q^2+2q
        76: 2q^3+4q^2+2q
        78: 4q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 3q^2+2q
        83: 4q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 3q^2+2q
        87: 4q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: q^3+3q^2+2q
        92: q^3+3q^2+2q
        93: q^4+2q^2+q
        94: 3q^2+2q
        95: 3q^2+2q
        96: 2q^2+q
        97: 3q^2+2q
        98: 3q^2+2q
        99: 2q^2+q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       103: q^2+q
       106: q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       111: 3q^2+2q
       113: 3q^2+2q
       115: 4q^2+2q
       117: q^2+q
       118: q^2+q
       119: q^2+q
       120: q^2+q
       121: 3q^2+2q
       123: 3q^2+2q
       125: 2q
       126: q
       127: 3q^2+2q
       129: 3q^2+2q
       131: 2q^2+q
       133: q^3+2q^2+2q
       134: q^2+q
       135: 3q^2+2q
       136: 3q^2+2q
       137: 2q
       138: q^2+q
       139: 2q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 3q^2+2q
       143: 2q
       144: q^2+q
       145: 2q^2+2q
       146: 3q^2+2q
       147: 3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       151: 3q^2+2q
       153: q^3+3q^2+2q
       155: 3q^2+2q
       157: 2q
       158: 2q
       159: q^2+q
       160: 3q^2+2q
       161: 3q^2+2q
       162: 2q^2+q
       163: 3q^2+2q
       164: 3q^2+2q
       165: 2q^2+q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       169: q^2+q
       172: q^2+q
       173: q^2+q
       176: q^2+q
       177: q^2+q
       179: 2q^2+2q
       181: 3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       187: 3q^2+2q
       189: 3q^2+2q
       191: q
       192: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       197: q^2+2q
       199: q
       200: q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       205: q^2+2q
       207: 2q
       209: 2q^2+2q
       211: 3q^2+2q
       213: 3q^2+2q
       215: 3q^2+2q
       217: 2q^2+q
       219: q
       220: 2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: 2q^2+2q
       228: q^2+q
       229: q^2+2q
       230: 3q^2+2q
       231: q
       232: 2q^2+2q
       233: q^2+q
       234: 3q^2+2q
       235: q^2+2q
       236: q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: 2q^2+2q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: q^2+2q
       257: q^2+2q
       258: q^2+q
       259: q^2+q
       262: q^2+q
       263: q^2+q
       266: q^2+q
       267: q
       269: q
       271: q
       273: q
       275: q
       278: q
       279: 2q^2+2q
       281: q^2+q
       287: q
       289: 3q^2+2q
       291: q^2+q
       293: q
       294: q
       295: q
       296: q
       297: 2q
       299: q
       300: q
       301: 2q
       303: q^2+q
       304: q^2+q
       305: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       311: 2q
       313: q^2+2q
       315: q
       317: q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: 2q
       325: 2q^2+2q
       327: 2q
       329: 2q
       331: q^2+q
       333: q
       334: q
       335: q
       336: q
       337: q^2+2q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: q
       345: 2q
       346: q
       347: 2q
       348: q
       349: 2q
       350: q^2+q
       351: 2q
       352: q
       353: 2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q
       359: 2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q
       367: q^2+2q
       368: q
       369: 2q
       370: 2q
       371: q^2+2q
       372: q^2+2q
       373: q^2+q
       381: q^2+q
       384: q^2+q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q^2+q
       423: q
       425: q
       427: q^2+2q
       433: q
       435: 2q
       437: q
       438: q
       439: q
       440: q
       441: 2q
       443: q
       444: q
       445: 2q
       451: q
       453: q
       454: q
       455: 2q
       457: q
       458: q
       459: 2q
       461: q
       462: q
       463: 2q
       465: q^2+2q
       467: q
       469: q
       471: q
       472: q
       473: q
       474: q
       475: 2q
       477: 3q
       479: 2q
       481: q
       482: q
       483: q
       484: q^2+2q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 2q
       497: q
       498: q
       499: q
       500: q
       501: 2q
       508: q
       512: q
       514: q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       545: q
       547: q
       553: q
       555: q
       557: q
       559: q
       561: q
       563: q
       565: q
       568: q
       569: q
       570: q
       573: q
       575: q
       577: 2q
       579: q
       583: q
       585: q
       587: q
       597: q
       599: q
       601: q^2+2q
       605: q
       609: q
       613: q
       615: q
       616: q
       617: 2q
       623: q
       625: q
       629: q
       631: q
       632: q
       633: 2q
       639: q
       645: q
       651: 3q
       655: 2q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       693: q
       697: q
       733: q
       735: q
       749: q
       751: q
       757: q
       758: q
       765: q
       768: q
       769: 2q
       771: q
       777: q
       781: q
       791: q
       797: q
       809: q
       811: q
       821: q
       833: q
       835: q
       849: q
       853: 2
       871: q
       875: q
       884: q
       889: q
       978: 1
       979: 1
       984: 2
      1010: q
      1022: q
      1038: q
      1050: 1
      1100: 1
      1107: 1
      1190: 1
      1222: 1
      1264: 1
      1336: 1
      1406: 1
      1446: 1
      1555: 1

1556:    0: 8q^3+13q^2+6q
         1: 8q^3+13q^2+6q
         2: 8q^3+13q^2+6q
         3: 2q^4+9q^3+13q^2+6q
         4: 8q^3+13q^2+6q
         5: 2q^4+9q^3+13q^2+6q
         6: 8q^3+13q^2+6q
         7: 8q^3+13q^2+6q
         8: 2q^4+9q^3+13q^2+6q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: 8q^3+13q^2+6q
        11: 2q^4+9q^3+13q^2+6q
        12: 8q^3+13q^2+6q
        13: 8q^3+13q^2+6q
        14: 8q^3+13q^2+6q
        15: 2q^4+9q^3+13q^2+6q
        16: q^3+8q^2+6q
        17: q^3+8q^2+6q
        18: 3q^3+5q^2+2q
        19: 8q^3+13q^2+6q
        20: 8q^3+13q^2+6q
        21: 8q^3+13q^2+6q
        22: 5q^3+11q^2+6q
        23: 5q^3+11q^2+6q
        24: 5q^3+11q^2+6q
        25: 5q^3+11q^2+6q
        26: 5q^3+11q^2+6q
        27: 5q^3+11q^2+6q
        28: q^3+8q^2+6q
        29: 8q^3+13q^2+6q
        30: 8q^3+13q^2+6q
        31: 5q^3+11q^2+6q
        32: 5q^3+11q^2+6q
        33: 6q^2+6q
        34: 5q^3+11q^2+6q
        35: 5q^3+11q^2+6q
        36: 6q^2+6q
        37: 2q^3+6q^2+4q
        38: q^3+3q^2+2q
        39: 2q^3+6q^2+4q
        40: q^3+3q^2+2q
        41: 2q^3+6q^2+4q
        42: q^3+3q^2+2q
        43: 8q^3+13q^2+6q
        44: 8q^3+13q^2+6q
        45: 2q^4+9q^3+13q^2+6q
        46: q^3+8q^2+6q
        47: q^3+8q^2+6q
        48: 3q^3+5q^2+2q
        49: q^3+8q^2+6q
        50: q^3+8q^2+6q
        51: 3q^3+5q^2+2q
        52: 5q^3+11q^2+6q
        53: 5q^3+11q^2+6q
        54: 5q^3+11q^2+6q
        55: 5q^3+11q^2+6q
        56: 5q^3+11q^2+6q
        57: 5q^3+11q^2+6q
        58: 3q^2+3q
        59: 3q^2+3q
        60: 3q^2+3q
        61: 3q^2+3q
        62: 2q^3+6q^2+4q
        63: q^3+3q^2+2q
        64: 2q^3+6q^2+4q
        65: q^3+3q^2+2q
        66: 2q^2+4q
        67: 2q^2+2q
        68: q^3+8q^2+6q
        69: 2q^2+2q
        70: 8q^3+13q^2+6q
        71: q^3+8q^2+6q
        72: 6q^2+6q
        73: 6q^2+6q
        74: 2q^3+6q^2+4q
        75: q^3+3q^2+2q
        76: 2q^3+6q^2+4q
        77: q^3+3q^2+2q
        78: 2q^3+6q^2+4q
        79: q^3+3q^2+2q
        80: 5q^3+11q^2+6q
        81: 6q^2+6q
        82: 5q^3+11q^2+6q
        83: 5q^3+11q^2+6q
        84: 5q^3+11q^2+6q
        85: 6q^2+6q
        86: 5q^3+11q^2+6q
        87: 5q^3+11q^2+6q
        88: q^3+8q^2+6q
        89: q^3+8q^2+6q
        90: 3q^3+5q^2+2q
        91: q^3+8q^2+6q
        92: q^3+8q^2+6q
        93: 3q^3+5q^2+2q
        94: 4q^2+6q
        95: 4q^2+6q
        96: 2q^3+4q^2+2q
        97: 4q^2+6q
        98: 4q^2+6q
        99: 2q^3+4q^2+2q
       100: q^3+7q^2+6q
       101: q^3+7q^2+6q
       102: q^3+7q^2+6q
       103: q^2+2q
       104: q^2+q
       105: q^2+q
       106: q^2+2q
       107: 3q^2+3q
       108: 3q^2+3q
       109: 3q^2+3q
       110: 3q^2+3q
       111: 2q^2+4q
       112: 2q^2+2q
       113: 2q^3+6q^2+4q
       114: q^3+3q^2+2q
       115: 2q^3+6q^2+4q
       116: q^3+3q^2+2q
       117: 3q^2+3q
       118: 3q^2+3q
       119: 3q^2+3q
       120: 3q^2+3q
       121: 2q^3+6q^2+4q
       122: q^3+3q^2+2q
       123: 2q^2+4q
       124: 2q^2+2q
       125: q^3+8q^2+6q
       126: 2q^2+2q
       127: 4q
       129: 4q
       131: q^3+2q^2+q
       133: q^3+8q^2+6q
       134: 2q^2+2q
       135: 6q^2+6q
       136: 6q^2+6q
       137: 6q^2+6q
       138: q^2+2q
       139: 4q^2+6q
       140: 4q
       141: 5q^3+11q^2+6q
       142: 4q^2+6q
       143: 6q^2+6q
       144: q^2+2q
       145: 4q^2+6q
       146: 5q^3+11q^2+6q
       147: 4q^2+6q
       148: 4q
       149: q^3+7q^2+6q
       150: q^3+7q^2+6q
       151: q^3+5q^2+4q
       152: 2q^2+2q
       153: q^3+5q^2+4q
       154: 2q^2+2q
       155: q^3+5q^2+4q
       156: 2q^2+2q
       157: q^3+8q^2+6q
       158: q^3+8q^2+6q
       159: 3q^3+5q^2+2q
       160: 4q^2+6q
       161: 4q^2+6q
       162: 2q^3+4q^2+2q
       163: 4q^2+6q
       164: 4q^2+6q
       165: 2q^3+4q^2+2q
       166: q^2+6q
       167: q^2+6q
       168: 2q^2+2q
       169: q^2+2q
       170: q^2+q
       171: q^2+q
       172: q^2+2q
       173: q^2+2q
       174: q^2+q
       175: q^2+q
       176: q^2+2q
       177: q
       179: 4q
       181: 4q
       183: 3q^2+3q
       184: 3q^2+3q
       185: 3q^2+3q
       186: 3q^2+3q
       187: 2q^2+4q
       188: 2q^2+2q
       189: 2q^3+6q^2+4q
       190: q^3+3q^2+2q
       191: 3q^2+3q
       192: 3q^2+3q
       193: 2q
       194: 2q
       195: 2q^2+3q
       196: 2q^2+3q
       197: 2q
       198: 2q
       199: 3q^2+3q
       200: 3q^2+3q
       201: 2q^2+3q
       202: 2q^2+3q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: 2q^2+4q
       208: 2q^2+2q
       209: q^3+5q^2+4q
       210: 2q^2+2q
       211: q^3+5q^2+4q
       212: 2q^2+2q
       213: 4q
       215: 4q
       217: q^3+2q^2+q
       219: 2q^2+2q
       220: q^3+8q^2+6q
       221: 2q^2+2q
       222: 6q^2+6q
       223: q^2+2q
       224: 6q^2+6q
       225: q^2+2q
       226: q^2+2q
       227: 4q^2+6q
       228: q^2+2q
       229: 4q
       230: 4q^2+6q
       231: q^2+2q
       232: 4q^2+6q
       233: q^2+2q
       234: 4q^2+6q
       235: 4q
       236: 2q
       237: 4q
       239: 4q
       241: q^2+q
       243: q^2+6q
       244: 4q
       245: 4q
       246: q^3+7q^2+6q
       247: q^2+6q
       248: q^2+6q
       249: 2q^2+2q
       250: 4q^2+6q
       251: 4q^2+6q
       252: 2q^3+4q^2+2q
       253: 4q^2+6q
       254: 4q^2+6q
       255: 2q^3+4q^2+2q
       256: q^2+6q
       257: q^2+6q
       258: 2q^2+2q
       259: 2q
       262: 2q
       263: q^2+2q
       264: q^2+q
       265: q^2+q
       266: q^2+2q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       275: q^2+2q
       276: q^2+q
       277: q^2+q
       278: q^2+2q
       279: 4q
       281: q
       287: q
       289: 4q
       291: q
       293: 3q^2+3q
       294: 3q^2+3q
       295: 3q^2+3q
       296: 3q^2+3q
       297: 2q^2+4q
       298: 2q^2+2q
       299: 2q
       300: 2q
       301: 2q
       303: 2q^2+3q
       304: 2q^2+3q
       305: 2q
       306: 2q
       307: 2q^2+3q
       308: 2q^2+3q
       309: 2q
       310: 2q
       311: 2q
       313: 2q
       314: 2q
       315: q
       317: 4q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       324: 2q
       325: q^3+5q^2+4q
       326: 2q^2+2q
       327: 4q
       329: 4q
       331: q^3+2q^2+q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: q^2+6q
       338: 4q
       340: 4q
       342: q^2+q
       344: q^2+2q
       345: 4q^2+6q
       346: q^2+2q
       347: 4q
       348: q
       349: 4q^2+6q
       350: q^2+2q
       351: 4q
       352: q^2+2q
       353: 4q^2+6q
       354: q^2+2q
       355: 4q^2+6q
       356: q^2+2q
       357: 4q
       358: q
       359: 4q
       360: 4q
       362: 4q
       364: q^2+q
       366: 2q
       367: q^2+6q
       368: 2q
       369: 4q
       370: 4q
       371: q^2+6q
       372: q^2+6q
       373: 2q^2+2q
       374: q^2+6q
       375: q^2+6q
       376: 2q^2+2q
       381: 2q
       384: 2q
       385: q^2+2q
       386: q^2+q
       387: q^2+q
       388: q^2+2q
       389: q
       391: q
       393: q
       394: q
       395: q
       396: q
       397: q
       399: q
       401: q
       402: q
       403: q
       404: q
       407: q
       408: q
       409: 4q
       411: q
       413: q
       415: 4q
       417: q
       423: q
       425: q
       427: 4q
       435: 2q
       437: 2q
       438: 2q
       439: 2q^2+3q
       440: 2q^2+3q
       441: 2q
       442: 2q
       443: 2q
       444: 2q
       445: 2q
       453: 2q^2+3q
       454: 2q^2+3q
       455: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: 2q
       462: 2q
       463: 2q
       465: 4q
       467: q
       469: q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       476: 2q
       480: 2q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: q^2+6q
       485: 4q
       487: 4q
       489: q^2+q
       491: 2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: 4q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: 4q
       502: 4q
       504: 4q
       506: q^2+q
       508: 2q
       509: q^2+6q
       510: 2q
       511: 4q
       512: q
       513: 4q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+6q
       519: q^2+6q
       520: 2q^2+2q
       525: 2q
       528: 2q
       537: q
       539: q
       541: q
       542: q
       543: q
       544: q
       545: q
       547: q
       553: q
       555: q
       557: q
       558: q
       559: q
       560: q
       561: q
       563: q
       566: q
       567: q
       574: q
       576: q
       583: q
       585: q
       587: q
       597: q
       599: q
       601: 4q
       611: 2q
       615: 2q
       616: 2q
       617: 2q
       627: 2q
       631: 2q
       632: 2q
       633: 2q
       635: 4q
       637: q
       639: q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       654: 2q
       656: 2q
       658: 1
       660: q+1
       662: 1
       664: 1
       665: 2q
       666: 4q
       668: 4q
       670: q^2+q
       672: q^2+6q
       673: 2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: 4q
       679: q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: 4q
       685: q
       686: 2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       763: q
       764: q
       766: q
       767: q
       777: q
       779: 1
       781: q
       783: q
       789: 4q
       795: 1
       813: 2q
       815: 2q
       816: 2q
       819: 1
       837: 2q
       839: 2q
       840: 2q
       841: q
       844: 1
       858: 2q
       859: 1
       861: q+1
       863: 1
       867: 1
       868: 2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       932: q
       934: q
       956: q
       958: q
       971: 1
       989: q
       990: q
       996: 1
      1002: q
      1013: 1
      1014: 1
      1020: 1
      1030: 1
      1036: 1
      1047: 1
      1066: 1
      1068: q+1
      1070: 1
      1073: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1141: 1
      1191: 1
      1212: 1
      1225: 1
      1226: 1
      1236: 1
      1244: 1
      1252: 1
      1263: 1
      1284: 1
      1286: 1
      1337: 1
      1407: 1
      1445: 1
      1452: 1
      1458: 1
      1556: 1

1557:    0: 2q^2+3q+2
         1: 2q^2+3q+2
         2: 2q^2+3q+2
         3: q^3+2q^2+3q+2
         4: 2q^2+3q+2
         5: q^3+2q^2+3q+2
         6: 2q^2+3q+2
         7: 2q^2+3q+2
         8: q^3+2q^2+3q+2
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+2
        11: q^3+2q^2+3q+2
        12: 2q^2+3q+2
        13: 2q^2+3q+2
        14: 2q^2+3q+2
        15: q^3+2q^2+3q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+1
        19: 2q^2+3q+2
        20: 2q^2+3q+2
        21: 2q^2+3q+2
        22: q^2+3q+2
        23: q^2+3q+2
        24: q^2+3q+2
        25: q^2+3q+2
        26: q^2+3q+2
        27: q^2+3q+2
        28: q^2+2q+2
        29: 2q^2+3q+2
        30: 2q^2+3q+2
        31: q^2+3q+2
        32: q^2+3q+2
        33: 2q+2
        34: q^2+3q+2
        35: q^2+3q+2
        36: 2q+2
        38: q^2+3q+2
        40: q^2+3q+2
        42: q^2+3q+2
        43: 2q^2+3q+2
        44: 2q^2+3q+2
        45: q^3+2q^2+3q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+1
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+1
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q^2+3q+2
        65: q^2+3q+2
        67: 2q+2
        68: q^2+2q+2
        69: q+1
        70: 2q^2+3q+2
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        75: q^2+3q+2
        77: q^2+3q+2
        79: q^2+3q+2
        80: q^2+3q+2
        81: 2q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: q^2+3q+2
        85: 2q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+1
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+1
        94: 2q+2
        95: 2q+2
        96: q^2+2q+1
        97: 2q+2
        98: 2q+2
        99: q^2+2q+1
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: q^2+3q+2
       116: q^2+3q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^2+3q+2
       124: 2q+2
       125: q^2+2q+2
       126: q+1
       128: 2q+2
       130: 2q+2
       132: q^2+2q+1
       133: q^2+2q+2
       134: q+1
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: q+1
       139: 2q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q+2
       144: q+1
       145: 2q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+1
       160: 2q+2
       161: 2q+2
       162: q^2+2q+1
       163: 2q+2
       164: 2q+2
       165: q^2+2q+1
       166: q+2
       167: q+2
       168: q+1
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: q+1
       180: 2q+2
       182: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2q+2
       190: q^2+3q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: 2q+2
       212: 2q+2
       214: 2q+2
       216: 2q+2
       218: q^2+2q+1
       219: q+1
       220: q^2+2q+2
       221: q+1
       222: 2q+2
       223: q+1
       224: 2q+2
       225: q+1
       226: q+1
       227: 2q+2
       228: q+1
       229: 2
       230: 2q+2
       231: q+1
       232: 2q+2
       233: q+1
       234: 2q+2
       235: 2
       236: 1
       238: q+2
       240: q+2
       242: q+1
       243: q+2
       244: 2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: 2q+2
       251: 2q+2
       252: q^2+2q+1
       253: 2q+2
       254: 2q+2
       255: q^2+2q+1
       256: q+2
       257: q+2
       258: q+1
       260: q+1
       261: q+1
       264: q+1
       265: q+1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: 2q+2
       282: q+1
       288: q+1
       290: 2q+2
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2q+2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 2q+2
       328: 2q+2
       330: 2q+2
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+2
       339: q+2
       341: q+2
       343: q+1
       344: q+1
       345: 2q+2
       346: q+1
       347: 2
       348: 1
       349: 2q+2
       350: q+1
       351: 2
       352: q+1
       353: 2q+2
       354: q+1
       355: 2q+2
       356: q+1
       357: 2
       358: 1
       359: 2
       361: q+2
       363: q+2
       365: q+1
       366: 1
       367: q+2
       368: 1
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: q+2
       375: q+2
       376: q+1
       382: q+1
       383: q+1
       386: q+1
       387: q+1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 2q+2
       412: q+1
       414: q+1
       416: 2q+2
       418: q+1
       424: q+1
       426: 1
       428: q+2
       434: 1
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       452: 1
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: q+2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       503: q+2
       505: q+2
       507: q+1
       508: 1
       509: q+2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: q+1
       517: 1
       518: q+2
       519: q+2
       520: q+1
       526: q+1
       527: q+1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: q+1
       586: q+1
       588: q+1
       598: 1
       600: 1
       602: q+2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       659: 1
       661: q+1
       663: 1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: q+2
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: 1
       700: 1
       730: 1
       732: 1
       734: 1
       736: 1
       746: 1
       748: 1
       750: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       778: q+1
       780: 1
       782: 1
       784: 1
       790: q+2
       792: 1
       796: 1
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       820: 1
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       844: 1
       850: 1
       852: 1
       854: 2
       858: 2
       860: 1
       862: q+1
       864: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       890: 1
       891: 1
       933: 1
       935: 1
       957: 1
       959: 1
       972: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       997: 1
      1003: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1031: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1047: 1
      1049: 1
      1051: 1
      1067: 1
      1069: q+1
      1071: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1104: 1
      1105: 1
      1142: 1
      1192: 1
      1213: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1237: 1
      1239: 1
      1245: 1
      1253: 1
      1257: 1
      1263: 1
      1265: 1
      1284: 1
      1286: 1
      1338: 1
      1408: 1
      1445: 1
      1447: 1
      1453: 1
      1459: 1
      1557: 1

1558:    0: q^4+q^3+4q^2+2q
         1: q^4+3q^3+4q^2+2q
         2: q^4+q^3+4q^2+2q
         3: q^4+3q^3+4q^2+2q
         4: q^4+q^3+4q^2+2q
         5: q^3+4q^2+2q
         6: q^4+3q^3+4q^2+2q
         7: q^4+q^3+4q^2+2q
         8: q^3+4q^2+2q
         9: q^5+q^4+q^3+2q^2+q
        10: q^3+3q^2+2q
        11: q^3+3q^2+2q
        12: q^3+3q^2+2q
        13: q^4+q^3+4q^2+2q
        14: q^4+q^3+4q^2+2q
        15: q^3+4q^2+2q
        16: q^3+3q^2+2q
        17: q^3+3q^2+2q
        18: q^4+2q^2+q
        19: q^4+q^3+4q^2+2q
        20: q^4+3q^3+4q^2+2q
        21: q^4+q^3+4q^2+2q
        22: 4q^2+2q
        23: 2q^3+4q^2+2q
        24: 4q^2+2q
        25: 4q^2+2q
        26: 2q^3+4q^2+2q
        27: 4q^2+2q
        28: q^3+2q^2+2q
        29: q^3+3q^2+2q
        30: q^4+q^3+4q^2+2q
        31: 3q^2+2q
        32: 4q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 4q^2+2q
        36: 3q^2+2q
        38: 4q^2+2q
        40: 2q^3+4q^2+2q
        42: 4q^2+2q
        43: q^3+3q^2+2q
        44: q^3+3q^2+2q
        45: q^3+3q^2+2q
        46: q^3+3q^2+2q
        47: q^3+3q^2+2q
        48: q^4+2q^2+q
        49: q^3+3q^2+2q
        50: q^3+3q^2+2q
        51: q^4+2q^2+q
        52: 4q^2+2q
        53: 2q^3+4q^2+2q
        54: 4q^2+2q
        55: 4q^2+2q
        56: 2q^3+4q^2+2q
        57: 4q^2+2q
        58: q^2+q
        59: q^2+q
        60: q^2+q
        61: q^2+q
        63: 3q^2+2q
        65: 4q^2+2q
        67: 3q^2+2q
        68: q^3+2q^2+2q
        69: q^2+q
        70: q^3+3q^2+2q
        71: q^3+2q^2+2q
        72: 3q^2+2q
        73: 3q^2+2q
        75: 4q^2+2q
        77: 2q^3+4q^2+2q
        79: 4q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 3q^2+2q
        83: 4q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 3q^2+2q
        87: 4q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: q^3+3q^2+2q
        92: q^3+3q^2+2q
        93: q^4+2q^2+q
        94: 3q^2+2q
        95: 3q^2+2q
        96: 2q^2+q
        97: 3q^2+2q
        98: 3q^2+2q
        99: 2q^2+q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       104: q^2+q
       105: q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       112: 3q^2+2q
       114: 3q^2+2q
       116: 4q^2+2q
       117: q^2+q
       118: q^2+q
       119: q^2+q
       120: q^2+q
       122: 3q^2+2q
       124: 3q^2+2q
       125: 2q
       126: q
       128: 3q^2+2q
       130: 3q^2+2q
       132: 2q^2+q
       133: q^3+2q^2+2q
       134: q^2+q
       135: 3q^2+2q
       136: 3q^2+2q
       137: 2q
       138: q^2+q
       139: 2q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 3q^2+2q
       143: 2q
       144: q^2+q
       145: 2q^2+2q
       146: 3q^2+2q
       147: 3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       152: 3q^2+2q
       154: q^3+3q^2+2q
       156: 3q^2+2q
       157: 2q
       158: 2q
       159: q^2+q
       160: 3q^2+2q
       161: 3q^2+2q
       162: 2q^2+q
       163: 3q^2+2q
       164: 3q^2+2q
       165: 2q^2+q
       166: q^2+2q
       167: q^2+2q
       168: q^2+q
       170: q^2+q
       171: q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: 2q^2+2q
       182: 3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       188: 3q^2+2q
       190: 3q^2+2q
       191: q
       192: q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       198: q^2+2q
       199: q
       200: q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       206: q^2+2q
       208: 2q
       210: 2q^2+2q
       212: 3q^2+2q
       214: 3q^2+2q
       216: 3q^2+2q
       218: 2q^2+q
       219: q
       220: 2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: 2q^2+2q
       228: q^2+q
       229: q^2+2q
       230: 3q^2+2q
       231: q
       232: 2q^2+2q
       233: q^2+q
       234: 3q^2+2q
       235: q^2+2q
       236: q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: q^2+2q
       244: 2q
       245: 2q
       246: 2q^2+2q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: q^2+2q
       257: q^2+2q
       258: q^2+q
       260: q^2+q
       261: q^2+q
       264: q^2+q
       265: q^2+q
       268: q
       270: q
       272: q
       274: q
       276: q
       277: q
       280: 2q^2+2q
       282: q^2+q
       288: q
       290: 3q^2+2q
       292: q^2+q
       293: q
       294: q
       295: q
       296: q
       298: 2q
       299: q
       300: q
       302: 2q
       303: q^2+q
       304: q^2+q
       306: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       312: 2q
       314: q^2+2q
       316: q
       318: q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: 2q
       326: 2q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: q
       334: q
       335: q
       336: q
       337: q^2+2q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: q
       345: 2q
       346: q
       347: 2q
       348: q
       349: 2q
       350: q^2+q
       351: 2q
       352: q
       353: 2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q
       359: 2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q
       367: q^2+2q
       368: q
       369: 2q
       370: 2q
       371: q^2+2q
       372: q^2+2q
       373: q^2+q
       382: q^2+q
       383: q^2+q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q^2+q
       424: q
       426: q
       428: q^2+2q
       434: q
       436: 2q
       437: q
       438: q
       439: q
       440: q
       442: 2q
       443: q
       444: q
       446: 2q
       452: q
       453: q
       454: q
       456: 2q
       457: q
       458: q
       460: 2q
       461: q
       462: q
       464: 2q
       466: q^2+2q
       468: q
       470: q
       471: q
       472: q
       473: q
       474: q
       476: 2q
       478: 3q
       480: 2q
       481: q
       482: q
       483: q
       484: q^2+2q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 2q
       497: q
       498: q
       499: q
       500: q
       501: 2q
       508: q
       512: q
       514: q
       526: q
       527: q
       538: q
       540: q
       542: q
       544: q
       546: q
       548: q
       554: q
       556: q
       558: q
       560: q
       562: q
       564: q
       566: q
       567: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       582: q
       584: q
       586: q
       588: q
       598: q
       600: q
       602: q^2+2q
       606: q
       610: q
       614: q
       615: q
       616: q
       618: 2q
       624: q
       626: q
       630: q
       631: q
       632: q
       634: 2q
       640: q
       646: q
       652: 3q
       656: 2q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       699: q
       700: q
       734: q
       736: q
       750: q
       752: q
       759: q
       760: q
       766: q
       767: q
       773: 2q
       774: q
       778: q
       782: q
       792: q
       798: q
       810: q
       812: q
       822: q
       834: q
       836: q
       850: q
       854: 2
       871: q
       875: q
       890: q
       891: q
       980: 1
       981: 1
       987: 2
      1011: q
      1023: q
      1039: q
      1051: 1
      1108: 1
      1109: 1
      1193: 1
      1223: 1
      1265: 1
      1339: 1
      1409: 1
      1447: 1
      1558: 1

1559:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+3q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q^2+2q+1
        61: q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^3+3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       106: q
       107: q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q^2+2q+1
       120: q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: q^3+2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+2q+1
       184: q
       185: q^2+2q+1
       186: q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q+1
       271: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+2q+1
       294: q
       295: q^2+2q+1
       296: q
       297: q^2+3q+1
       299: q+1
       301: 1
       303: 2q+1
       304: q
       305: q+1
       307: 2q+1
       308: q
       309: q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: 1
       321: 1
       323: 1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: 1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: 1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: q+1
       429: 1
       431: q+1
       433: 1
       435: 1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: 1
       445: 1
       447: q+1
       449: 1
       451: 1
       453: 2q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 2
       479: 1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: 1
       537: 1
       541: q+1
       545: 1
       549: 1
       553: 1
       557: q+1
       561: 1
       565: 1
       569: 2
       573: 1
       577: 1
       579: 1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       591: 1
       593: 1
       595: q+1
       597: q+1
       599: q+1
       601: q+1
       603: 1
       605: 1
       607: q+1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q+1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 2
       653: 1
       655: 1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: 1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       693: 1
       695: 1
       705: q+1
       709: q+1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 2
       761: 1
       765: 1
       769: 1
       771: 1
       777: 2q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: q+1
       791: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       813: 1
       815: 1
       821: 1
       823: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: q+1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 2
       857: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       896: q+1
       900: 1
       904: 1
       908: 1
       912: 1
       920: 1
       928: 1
       932: 1
       936: 1
       944: 1
       948: 1
       956: 1
       960: 1
       974: 1
       978: 2
       982: 1
       984: 1
       988: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1026: 1
      1034: 1
      1038: 1
      1042: 1
      1044: 1
      1048: 1
      1050: 1
      1052: 1
      1058: 1
      1078: 1
      1082: 1
      1098: 1
      1100: 1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1156: 1
      1168: 1
      1172: 1
      1184: 1
      1198: 1
      1220: 1
      1222: 1
      1238: 1
      1240: 1
      1256: 1
      1260: 1
      1264: 1
      1322: 1
      1330: 1
      1352: 1
      1376: 1
      1414: 1
      1446: 1
      1559: 1

1560:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+3q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^3+3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       106: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q
       120: q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: q^3+2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q
       184: q^2+2q+1
       185: q
       186: q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       273: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q
       294: q^2+2q+1
       295: q
       296: q^2+2q+1
       297: q^2+3q+1
       300: q+1
       301: 1
       303: q
       304: 2q+1
       305: q+1
       307: q
       308: 2q+1
       310: q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       320: 1
       322: 1
       323: 1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: 1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: 1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: q+1
       430: 1
       432: q+1
       433: 1
       435: 1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: 1
       445: 1
       448: q+1
       450: 1
       451: 1
       453: q
       454: 2q+1
       455: 1
       458: q+1
       459: q+1
       462: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 2
       479: 1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: 1
       539: 1
       543: q+1
       547: 1
       552: 1
       555: 1
       559: q+1
       563: 1
       568: 1
       570: 2
       575: 1
       577: 1
       579: 1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       590: q+1
       592: 1
       594: 1
       596: q+1
       597: q+1
       599: q+1
       601: q+1
       604: 1
       605: 1
       608: q+1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: q+1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 2
       653: 1
       655: 1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: 1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       697: 1
       702: 1
       708: q+1
       712: q+1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 2
       762: 1
       768: 1
       769: 1
       771: 1
       777: 2q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: q+1
       791: 1
       797: 1
       799: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       813: 1
       816: 1
       821: 1
       823: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 2
       857: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       889: 1
       893: 1
       899: q+1
       902: 1
       906: 1
       911: 1
       914: 1
       922: 1
       930: 1
       934: 1
       938: 1
       946: 1
       950: 1
       958: 1
       961: 1
       975: 1
       979: 2
       982: 1
       984: 1
       991: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1027: 1
      1034: 1
      1038: 1
      1042: 1
      1045: 1
      1048: 1
      1050: 1
      1053: 1
      1059: 1
      1078: 1
      1082: 1
      1102: 1
      1107: 1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1158: 1
      1170: 1
      1174: 1
      1185: 1
      1199: 1
      1220: 1
      1222: 1
      1238: 1
      1241: 1
      1256: 1
      1261: 1
      1264: 1
      1323: 1
      1331: 1
      1354: 1
      1378: 1
      1415: 1
      1446: 1
      1560: 1

1561:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+3q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q^2+2q+1
        61: q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^3+3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q^2+2q+1
       105: q
       107: q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q^2+2q+1
       120: q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: q^3+2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+2q+1
       184: q
       185: q
       186: q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+2q+1
       294: q
       295: q
       296: q^2+2q+1
       298: q^2+3q+1
       299: q+1
       302: 1
       303: q
       304: 2q+1
       306: q+1
       307: 2q+1
       308: q
       310: q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: 1
       322: 1
       324: 1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: 1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: 1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: q+1
       429: 1
       432: q+1
       434: 1
       436: 1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: 1
       446: 1
       447: q+1
       450: 1
       452: 1
       453: 2q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 2
       480: 1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: 1
       538: 1
       542: q+1
       546: 1
       551: 1
       556: 1
       560: q+1
       564: 1
       566: 1
       571: 2
       574: 1
       581: 1
       582: 1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       592: 1
       593: 1
       596: q+1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q+1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 2
       654: 1
       656: 1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: 1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       699: 1
       703: 1
       706: q+1
       710: q+1
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 2
       763: 1
       766: 1
       773: 1
       774: 1
       778: 2q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: q+1
       792: 1
       798: 1
       800: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       814: 1
       815: 1
       822: 1
       824: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 2
       858: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       894: 1
       897: q+1
       903: 1
       905: 1
       909: 1
       913: 1
       921: 1
       929: 1
       933: 1
       939: 1
       947: 1
       951: 1
       959: 1
       962: 1
       976: 1
       980: 2
       986: 1
       987: 1
       989: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1026: 1
      1035: 1
      1039: 1
      1043: 1
      1045: 1
      1049: 1
      1051: 1
      1052: 1
      1059: 1
      1078: 1
      1082: 1
      1104: 1
      1108: 1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1157: 1
      1171: 1
      1175: 1
      1186: 1
      1200: 1
      1221: 1
      1223: 1
      1239: 1
      1240: 1
      1257: 1
      1261: 1
      1265: 1
      1324: 1
      1332: 1
      1353: 1
      1379: 1
      1416: 1
      1447: 1
      1561: 1

1562:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+3q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q
        61: q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^3+3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q^2+2q+1
       110: q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q
       120: q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: q^3+2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q
       184: q^2+2q+1
       185: q^2+2q+1
       186: q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q
       294: q^2+2q+1
       295: q^2+2q+1
       296: q
       298: q^2+3q+1
       300: q+1
       302: 1
       303: 2q+1
       304: q
       306: q+1
       307: q
       308: 2q+1
       309: q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       320: 1
       321: 1
       324: 1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: 1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: 1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: q+1
       430: 1
       431: q+1
       434: 1
       436: 1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: 1
       446: 1
       448: q+1
       449: 1
       452: 1
       453: q
       454: 2q+1
       456: 1
       457: q+1
       460: q+1
       461: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 2
       480: 1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: 1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: 1
       540: 1
       544: q+1
       548: 1
       550: 1
       554: 1
       558: q+1
       562: 1
       567: 1
       572: 2
       576: 1
       581: 1
       582: 1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       590: q+1
       591: 1
       594: 1
       595: q+1
       598: q+1
       600: q+1
       602: q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: q+1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 2
       654: 1
       656: 1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       675: 1
       676: 2q+1
       677: 1
       678: 1
       679: 1
       681: 2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       700: 1
       704: 1
       707: q+1
       711: q+1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 2
       764: 1
       767: 1
       773: 1
       774: 1
       778: 2q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: q+1
       792: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       814: 1
       816: 1
       822: 1
       824: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: q+1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 2
       858: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       891: 1
       895: 1
       898: q+1
       901: 1
       907: 1
       910: 1
       915: 1
       923: 1
       931: 1
       935: 1
       937: 1
       945: 1
       949: 1
       957: 1
       963: 1
       977: 1
       981: 2
       986: 1
       987: 1
       990: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1027: 1
      1035: 1
      1039: 1
      1043: 1
      1044: 1
      1049: 1
      1051: 1
      1053: 1
      1058: 1
      1078: 1
      1082: 1
      1105: 1
      1109: 1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1159: 1
      1169: 1
      1173: 1
      1187: 1
      1201: 1
      1221: 1
      1223: 1
      1239: 1
      1241: 1
      1257: 1
      1260: 1
      1265: 1
      1325: 1
      1333: 1
      1355: 1
      1377: 1
      1417: 1
      1447: 1
      1562: 1

1563:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 2q^3+11q^2+6q+1
        23: 2q^3+11q^2+6q+1
        24: q^4+5q^3+8q^2+5q+1
        25: 9q^2+6q+1
        26: 9q^2+6q+1
        27: 3q^3+7q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 2q^3+11q^2+6q+1
        32: q^3+7q^2+5q+1
        33: 2q^3+11q^2+6q+1
        34: 9q^2+6q+1
        35: 6q^2+5q+1
        36: 9q^2+6q+1
        37: 6q^2+5q+1
        38: 3q^2+q
        39: 6q^2+5q+1
        40: 3q^2+q
        41: 2q^3+5q^2+4q+1
        42: q^3+2q^2+q
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: q^3+7q^2+5q+1
        53: q^3+7q^2+5q+1
        54: 2q^3+5q^2+4q+1
        55: 5q^2+5q+1
        56: 5q^2+5q+1
        57: q^3+4q^2+4q+1
        58: q^3+6q^2+4q+1
        59: q^3+5q^2+2q
        60: 4q^2+3q+1
        61: 5q^2+3q
        62: 6q^2+5q+1
        63: 3q^2+q
        64: 4q^2+4q+1
        65: 2q^2+q
        66: 6q^2+5q+1
        67: 3q^2+q
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: q^3+7q^2+5q+1
        81: q^3+7q^2+5q+1
        82: q^3+7q^2+5q+1
        83: 4q^2+4q+1
        84: 6q^2+5q+1
        85: 6q^2+5q+1
        86: 5q^2+5q+1
        87: 3q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: q^3+7q^2+5q+1
        95: q^3+7q^2+5q+1
        96: 2q^3+5q^2+4q+1
        97: 5q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+4q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 3q^2+3q+1
       104: q^2
       105: 2q^2+q
       106: 3q^2+2q
       107: q^2+2q+1
       108: 2q^2+2q
       109: 2q^2+3q+1
       110: q^2+q
       111: 3q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       117: 2q^2+3q+1
       118: q^2+q
       119: q^2+2q+1
       120: 2q^2+2q
       121: 4q^2+4q+1
       122: 2q^2+q
       123: 4q^2+4q+1
       124: 2q^2+q
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^3+7q^2+5q+1
       138: 4q^2+4q+1
       139: q^3+7q^2+5q+1
       140: 3q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: 6q^2+5q+1
       144: 3q^2+4q+1
       145: 5q^2+5q+1
       146: 3q^2+4q+1
       147: 3q^2+4q+1
       148: q^2+2q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       151: 2q^2+4q+1
       153: 2q^2+4q+1
       155: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: q^3+4q^2+4q+1
       162: 3q^2+4q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       169: 2q+1
       172: q
       173: q^2+2q+1
       175: q^2+q
       176: q^2+q
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: q+1
       184: q^2+q
       185: 2q+1
       187: 2q+1
       189: q^2+3q+1
       191: 2q^2+3q+1
       192: q^2+q
       193: q^2+2q+1
       194: 2q^2+2q
       195: 2q^2+3q+1
       196: q^2+q
       197: 3q+1
       199: q^2+2q+1
       200: 2q^2+2q
       201: q^2+2q+1
       202: 2q^2+2q
       203: q^2+2q+1
       205: q+1
       207: 4q^2+4q+1
       208: 2q^2+q
       209: 2q^2+4q+1
       211: q^2+3q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: q^2+3q+1
       228: 3q^2+4q+1
       229: 2q^2+3q+1
       230: q^2+3q+1
       231: 3q^2+4q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: 3q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 5q^2+5q+1
       244: 3q^2+4q+1
       245: q^2+2q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 3q^2+4q+1
       251: q^3+4q^2+4q+1
       252: 3q^2+4q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: 2q+1
       262: q
       263: q+1
       267: 2q+1
       269: q
       271: q+1
       275: q^2+2q+1
       277: q^2+q
       278: q^2+q
       279: q+1
       281: 2q+1
       283: q+1
       284: q^2+q
       285: 2q+1
       287: q^2+3q+1
       289: q+1
       291: 2q+1
       293: q+1
       294: q^2+q
       295: 2q+1
       297: 2q+1
       299: q+1
       300: q^2+q
       301: 3q+1
       303: 2q+1
       305: 2q+1
       307: 1
       308: q
       309: q+1
       311: q+1
       313: 1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: q^2+2q+1
       320: 2q^2+2q
       321: q^2+2q+1
       323: q+1
       325: q^2+3q+1
       327: 2q+1
       329: q^2+2q+1
       331: 2q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 3q^2+4q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 2q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 2q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       377: q+1
       381: 1
       385: q+1
       389: 2q+1
       391: q
       393: q+1
       397: q+1
       401: 1
       405: q+1
       409: q+1
       411: 2q+1
       413: q+1
       415: q+1
       417: q+1
       419: q+1
       420: q^2+q
       421: 2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       430: q^2+q
       431: 2q+1
       433: 2q+1
       435: q+1
       437: q+1
       438: q^2+q
       439: 2q+1
       441: 2q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       447: 1
       448: q
       449: q+1
       451: 1
       453: 1
       454: q
       455: 1
       457: q+1
       459: 1
       461: 2q+2
       463: 2q+2
       465: q+1
       467: 2q+1
       469: q^2+3q+1
       471: 1
       472: q
       473: q+1
       475: 1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: 2
       502: 2q+1
       504: q^2+2q+1
       506: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q+1
       545: 2q+1
       547: 2q+1
       549: 1
       553: 1
       557: 1
       561: 2q+2
       565: 1
       569: q+1
       573: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       589: 1
       590: q
       591: 1
       595: q+1
       597: 1
       599: q+1
       601: 2
       603: q+1
       604: q^2+q
       605: q+1
       607: 2q+1
       609: 2q+1
       611: q+1
       613: q+1
       615: 1
       616: 1
       617: q+2
       619: 1
       620: q
       621: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 2
       633: 2
       635: q+1
       637: 2q+1
       639: q+1
       641: 1
       642: q
       643: q+1
       645: 1
       647: 1
       648: q
       649: q+1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       674: q+2
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       680: 2
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       698: q+1
       705: 1
       709: 1
       713: 1
       721: 1
       725: q+1
       729: 1
       733: 1
       735: 1
       737: 1
       741: 1
       745: 1
       749: 2
       753: 1
       757: 1
       761: 1
       765: 1
       767: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 2
       793: 1
       794: 1
       795: q+2
       797: 1
       799: q+1
       801: 1
       802: q
       803: 1
       807: q+1
       809: 1
       811: q+1
       813: q+2
       815: 1
       816: 1
       817: 2
       819: 2
       823: 1
       825: 1
       826: q
       827: 1
       833: 1
       835: 1
       837: 2
       839: 2
       841: q+1
       843: 1
       844: 1
       845: 1
       846: q
       847: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       884: 1
       888: 1
       896: 1
       900: 1
       912: 1
       916: 1
       918: 1
       920: 1
       924: 1
       932: 1
       934: 1
       936: 1
       940: 2
       948: 1
       956: 2
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       990: 1
       992: 2
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1028: 1
      1030: 2
      1032: 2
      1036: 1
      1042: 1
      1046: 1
      1047: 1
      1050: 1
      1052: 1
      1053: q
      1054: 1
      1060: 1
      1062: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1086: 1
      1090: 1
      1098: 1
      1103: 1
      1110: 1
      1114: 1
      1144: 1
      1146: 1
      1148: 1
      1152: 1
      1164: 2
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1202: 1
      1214: 1
      1216: 1
      1230: 1
      1232: 1
      1236: 1
      1238: 1
      1242: 1
      1252: 1
      1272: 1
      1274: 1
      1283: 1
      1288: 1
      1302: 1
      1306: 1
      1314: 1
      1344: 1
      1348: 1
      1448: 1
      1450: 1
      1472: 1
      1563: 1

1564:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 2q^3+11q^2+6q+1
        23: 2q^3+11q^2+6q+1
        24: q^4+5q^3+8q^2+5q+1
        25: 9q^2+6q+1
        26: 9q^2+6q+1
        27: 3q^3+7q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 2q^3+11q^2+6q+1
        32: q^3+7q^2+5q+1
        33: 2q^3+11q^2+6q+1
        34: 9q^2+6q+1
        35: 6q^2+5q+1
        36: 9q^2+6q+1
        37: 3q^2+q
        38: 6q^2+5q+1
        39: 3q^2+q
        40: 6q^2+5q+1
        41: q^3+2q^2+q
        42: 2q^3+5q^2+4q+1
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: q^3+7q^2+5q+1
        53: q^3+7q^2+5q+1
        54: 2q^3+5q^2+4q+1
        55: 5q^2+5q+1
        56: 5q^2+5q+1
        57: q^3+4q^2+4q+1
        58: q^3+6q^2+4q+1
        59: q^3+5q^2+2q
        60: 5q^2+3q
        61: 4q^2+3q+1
        62: 3q^2+q
        63: 6q^2+5q+1
        64: 2q^2+q
        65: 4q^2+4q+1
        66: 3q^2+q
        67: 6q^2+5q+1
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: q^3+7q^2+5q+1
        81: q^3+7q^2+5q+1
        82: q^3+7q^2+5q+1
        83: 4q^2+4q+1
        84: 6q^2+5q+1
        85: 6q^2+5q+1
        86: 5q^2+5q+1
        87: 3q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: q^3+7q^2+5q+1
        95: q^3+7q^2+5q+1
        96: 2q^3+5q^2+4q+1
        97: 5q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+4q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 2q^2+q
       104: 3q^2+2q
       105: 3q^2+3q+1
       106: q^2
       107: 2q^2+2q
       108: q^2+2q+1
       109: 2q^2+3q+1
       110: q^2+q
       112: 3q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       117: 2q^2+3q+1
       118: q^2+q
       119: 2q^2+2q
       120: q^2+2q+1
       121: 2q^2+q
       122: 4q^2+4q+1
       123: 2q^2+q
       124: 4q^2+4q+1
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^3+7q^2+5q+1
       138: 4q^2+4q+1
       139: q^3+7q^2+5q+1
       140: 3q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: 6q^2+5q+1
       144: 3q^2+4q+1
       145: 5q^2+5q+1
       146: 3q^2+4q+1
       147: 3q^2+4q+1
       148: q^2+2q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       152: 2q^2+4q+1
       154: 2q^2+4q+1
       156: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: q^3+4q^2+4q+1
       162: 3q^2+4q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       170: q
       171: 2q+1
       173: q^2+q
       174: q^2+q
       175: q^2+2q+1
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: q^2+q
       184: q+1
       185: 2q+1
       188: 2q+1
       190: q^2+3q+1
       191: 2q^2+3q+1
       192: q^2+q
       193: 2q^2+2q
       194: q^2+2q+1
       195: 2q^2+3q+1
       196: q^2+q
       198: 3q+1
       199: 2q^2+2q
       200: q^2+2q+1
       201: 2q^2+2q
       202: q^2+2q+1
       203: q^2+2q+1
       206: q+1
       207: 2q^2+q
       208: 4q^2+4q+1
       210: 2q^2+4q+1
       212: q^2+3q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: q^2+3q+1
       228: 3q^2+4q+1
       229: 2q^2+3q+1
       230: q^2+3q+1
       231: 3q^2+4q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: 3q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 5q^2+5q+1
       244: 3q^2+4q+1
       245: q^2+2q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 3q^2+4q+1
       251: q^3+4q^2+4q+1
       252: 3q^2+4q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: q
       261: 2q+1
       265: q+1
       268: q
       270: 2q+1
       272: q+1
       275: q^2+q
       276: q^2+q
       277: q^2+2q+1
       280: q+1
       282: 2q+1
       283: q^2+q
       284: q+1
       285: 2q+1
       288: q^2+3q+1
       290: q+1
       292: 2q+1
       293: q^2+q
       294: q+1
       295: 2q+1
       298: 2q+1
       299: q^2+q
       300: q+1
       302: 3q+1
       303: 2q+1
       306: 2q+1
       307: q
       308: 1
       309: q+1
       312: q+1
       314: 1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: 2q^2+2q
       320: q^2+2q+1
       321: q^2+2q+1
       324: q+1
       326: q^2+3q+1
       328: 2q+1
       330: q^2+2q+1
       332: 2q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 3q^2+4q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 2q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 2q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       379: q+1
       383: 1
       387: q+1
       390: q
       392: 2q+1
       395: q+1
       398: q+1
       402: 1
       408: q+1
       410: q+1
       412: 2q+1
       414: q+1
       416: q+1
       418: q+1
       419: q^2+q
       420: q+1
       421: 2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q^2+q
       430: q+1
       431: 2q+1
       434: 2q+1
       436: q+1
       437: q^2+q
       438: q+1
       439: 2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       447: q
       448: 1
       449: q+1
       452: 1
       453: q
       454: 1
       456: 1
       457: q+1
       460: 1
       461: 2q+2
       464: 2q+2
       466: q+1
       468: 2q+1
       470: q^2+3q+1
       471: q
       472: 1
       473: q+1
       476: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: 2
       503: 2q+1
       505: q^2+2q+1
       507: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q+1
       546: 2q+1
       548: 2q+1
       550: 1
       554: 1
       558: 1
       562: 2q+2
       567: 1
       572: q+1
       573: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       589: q
       590: 1
       591: 1
       595: q+1
       598: 1
       600: q+1
       602: 2
       603: q^2+q
       604: q+1
       606: q+1
       607: 2q+1
       610: 2q+1
       612: q+1
       614: q+1
       615: 1
       616: 1
       618: q+2
       619: q
       620: 1
       621: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 2
       634: 2
       636: q+1
       638: 2q+1
       640: q+1
       641: q
       642: 1
       643: q+1
       646: 1
       647: q
       648: 1
       649: q+1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       674: q+2
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       680: 2
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       694: q+1
       700: q+1
       707: 1
       711: 1
       714: 1
       724: 1
       728: q+1
       732: 1
       734: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 2
       755: 1
       760: 1
       764: 1
       765: 1
       767: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 2
       793: 1
       794: 1
       796: q+2
       798: 1
       800: q+1
       801: q
       802: 1
       803: 1
       807: q+1
       810: 1
       812: q+1
       814: q+2
       815: 1
       816: 1
       817: 2
       820: 2
       824: 1
       825: q
       826: 1
       827: 1
       834: 1
       836: 1
       838: 2
       839: 2
       842: q+1
       843: 1
       844: 1
       845: q
       846: 1
       847: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       885: 1
       891: 1
       898: 1
       901: 1
       915: 1
       917: 1
       919: 1
       923: 1
       925: 1
       933: 1
       935: 1
       937: 1
       941: 2
       949: 1
       957: 2
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       981: 1
       983: 1
       986: 1
       988: 1
       990: 1
       993: 2
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1028: 1
      1031: 2
      1032: 2
      1037: 1
      1043: 1
      1046: 1
      1047: 1
      1051: 1
      1052: q
      1053: 1
      1054: 1
      1061: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1087: 1
      1093: 1
      1099: 1
      1105: 1
      1111: 1
      1115: 1
      1145: 1
      1147: 1
      1151: 1
      1153: 1
      1165: 2
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1203: 1
      1215: 1
      1216: 1
      1231: 1
      1232: 1
      1237: 1
      1239: 1
      1242: 1
      1253: 1
      1273: 1
      1275: 1
      1283: 1
      1288: 1
      1303: 1
      1309: 1
      1315: 1
      1345: 1
      1349: 1
      1449: 1
      1450: 1
      1473: 1
      1564: 1

1565:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 2q^3+11q^2+6q+1
        23: 2q^3+11q^2+6q+1
        24: q^4+5q^3+8q^2+5q+1
        25: 9q^2+6q+1
        26: 9q^2+6q+1
        27: 3q^3+7q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 2q^3+11q^2+6q+1
        32: q^3+7q^2+5q+1
        33: 2q^3+11q^2+6q+1
        34: 9q^2+6q+1
        35: 6q^2+5q+1
        36: 9q^2+6q+1
        37: 6q^2+5q+1
        38: 3q^2+q
        39: 6q^2+5q+1
        40: 3q^2+q
        41: 2q^3+5q^2+4q+1
        42: q^3+2q^2+q
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: q^3+7q^2+5q+1
        53: q^3+7q^2+5q+1
        54: 2q^3+5q^2+4q+1
        55: 5q^2+5q+1
        56: 5q^2+5q+1
        57: q^3+4q^2+4q+1
        58: q^3+5q^2+2q
        59: q^3+6q^2+4q+1
        60: 5q^2+3q
        61: 4q^2+3q+1
        62: 6q^2+5q+1
        63: 3q^2+q
        64: 4q^2+4q+1
        65: 2q^2+q
        66: 6q^2+5q+1
        67: 3q^2+q
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: q^3+7q^2+5q+1
        81: q^3+7q^2+5q+1
        82: q^3+7q^2+5q+1
        83: 4q^2+4q+1
        84: 6q^2+5q+1
        85: 6q^2+5q+1
        86: 5q^2+5q+1
        87: 3q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: q^3+7q^2+5q+1
        95: q^3+7q^2+5q+1
        96: 2q^3+5q^2+4q+1
        97: 5q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+4q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 3q^2+2q
       104: 2q^2+q
       105: q^2
       106: 3q^2+3q+1
       107: 2q^2+2q
       108: q^2+2q+1
       109: q^2+q
       110: 2q^2+3q+1
       111: 3q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       117: q^2+q
       118: 2q^2+3q+1
       119: 2q^2+2q
       120: q^2+2q+1
       121: 4q^2+4q+1
       122: 2q^2+q
       123: 4q^2+4q+1
       124: 2q^2+q
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^3+7q^2+5q+1
       138: 4q^2+4q+1
       139: q^3+7q^2+5q+1
       140: 3q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: 6q^2+5q+1
       144: 3q^2+4q+1
       145: 5q^2+5q+1
       146: 3q^2+4q+1
       147: 3q^2+4q+1
       148: q^2+2q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       151: 2q^2+4q+1
       153: 2q^2+4q+1
       155: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: q^3+4q^2+4q+1
       162: 3q^2+4q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       169: q
       172: 2q+1
       173: q^2+q
       174: q^2+q
       176: q^2+2q+1
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: q^2+q
       184: q+1
       186: 2q+1
       187: 2q+1
       189: q^2+3q+1
       191: q^2+q
       192: 2q^2+3q+1
       193: 2q^2+2q
       194: q^2+2q+1
       195: q^2+q
       196: 2q^2+3q+1
       197: 3q+1
       199: 2q^2+2q
       200: q^2+2q+1
       201: 2q^2+2q
       202: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       207: 4q^2+4q+1
       208: 2q^2+q
       209: 2q^2+4q+1
       211: q^2+3q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: q^2+3q+1
       228: 3q^2+4q+1
       229: 2q^2+3q+1
       230: q^2+3q+1
       231: 3q^2+4q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: 3q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 5q^2+5q+1
       244: 3q^2+4q+1
       245: q^2+2q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 3q^2+4q+1
       251: q^3+4q^2+4q+1
       252: 3q^2+4q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: q
       262: 2q+1
       266: q+1
       267: q
       269: 2q+1
       273: q+1
       275: q^2+q
       276: q^2+q
       278: q^2+2q+1
       279: q+1
       281: 2q+1
       283: q^2+q
       284: q+1
       286: 2q+1
       287: q^2+3q+1
       289: q+1
       291: 2q+1
       293: q^2+q
       294: q+1
       296: 2q+1
       297: 2q+1
       299: q^2+q
       300: q+1
       301: 3q+1
       304: 2q+1
       305: 2q+1
       307: q
       308: 1
       310: q+1
       311: q+1
       313: 1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: 2q^2+2q
       320: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       325: q^2+3q+1
       327: 2q+1
       329: q^2+2q+1
       331: 2q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 3q^2+4q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 2q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 2q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       380: q+1
       384: 1
       388: q+1
       389: q
       391: 2q+1
       396: q+1
       399: q+1
       404: 1
       406: q+1
       409: q+1
       411: 2q+1
       413: q+1
       415: q+1
       417: q+1
       419: q^2+q
       420: q+1
       422: 2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q^2+q
       430: q+1
       432: 2q+1
       433: 2q+1
       435: q+1
       437: q^2+q
       438: q+1
       440: 2q+1
       441: 2q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       447: q
       448: 1
       450: q+1
       451: 1
       453: q
       454: 1
       455: 1
       458: q+1
       459: 1
       462: 2q+2
       463: 2q+2
       465: q+1
       467: 2q+1
       469: q^2+3q+1
       471: q
       472: 1
       474: q+1
       475: 1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: 2
       502: 2q+1
       504: q^2+2q+1
       506: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q+1
       545: 2q+1
       547: 2q+1
       552: 1
       555: 1
       559: 1
       563: 2q+2
       568: 1
       570: q+1
       574: q+1
       575: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       589: q
       590: 1
       592: 1
       596: q+1
       597: 1
       599: q+1
       601: 2
       603: q^2+q
       604: q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       613: q+1
       615: 1
       616: 1
       617: q+2
       619: q
       620: 1
       622: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 2
       633: 2
       635: q+1
       637: 2q+1
       639: q+1
       641: q
       642: 1
       644: q+1
       645: 1
       647: q
       648: 1
       650: q+1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       674: q+2
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       680: 2
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       696: q+1
       697: q+1
       708: 1
       712: 1
       716: 1
       723: 1
       727: q+1
       731: 1
       733: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 2
       756: 1
       758: 1
       762: 1
       766: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 2
       793: 1
       794: 1
       795: q+2
       797: 1
       799: q+1
       801: q
       802: 1
       804: 1
       808: q+1
       809: 1
       811: q+1
       813: q+2
       815: 1
       816: 1
       818: 2
       819: 2
       823: 1
       825: q
       826: 1
       828: 1
       833: 1
       835: 1
       837: 2
       840: 2
       841: q+1
       843: 1
       844: 1
       845: q
       846: 1
       848: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       887: 1
       889: 1
       899: 1
       902: 1
       914: 1
       916: 1
       918: 1
       922: 1
       927: 1
       932: 1
       934: 1
       938: 1
       942: 2
       950: 1
       958: 2
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: 1
       982: 1
       985: 1
       989: 1
       991: 1
       992: 2
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1029: 1
      1030: 2
      1033: 2
      1036: 1
      1042: 1
      1046: 1
      1047: 1
      1050: 1
      1052: q
      1053: 1
      1055: 1
      1060: 1
      1062: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1101: 1
      1102: 1
      1112: 1
      1116: 1
      1144: 1
      1146: 1
      1150: 1
      1154: 1
      1166: 2
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1204: 1
      1214: 1
      1217: 1
      1230: 1
      1233: 1
      1236: 1
      1238: 1
      1243: 1
      1252: 1
      1272: 1
      1274: 1
      1283: 1
      1288: 1
      1305: 1
      1307: 1
      1316: 1
      1346: 1
      1350: 1
      1448: 1
      1451: 1
      1472: 1
      1565: 1

1566:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 2q^3+11q^2+6q+1
        23: 2q^3+11q^2+6q+1
        24: q^4+5q^3+8q^2+5q+1
        25: 9q^2+6q+1
        26: 9q^2+6q+1
        27: 3q^3+7q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 2q^3+11q^2+6q+1
        32: q^3+7q^2+5q+1
        33: 2q^3+11q^2+6q+1
        34: 9q^2+6q+1
        35: 6q^2+5q+1
        36: 9q^2+6q+1
        37: 3q^2+q
        38: 6q^2+5q+1
        39: 3q^2+q
        40: 6q^2+5q+1
        41: q^3+2q^2+q
        42: 2q^3+5q^2+4q+1
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: q^3+7q^2+5q+1
        53: q^3+7q^2+5q+1
        54: 2q^3+5q^2+4q+1
        55: 5q^2+5q+1
        56: 5q^2+5q+1
        57: q^3+4q^2+4q+1
        58: q^3+5q^2+2q
        59: q^3+6q^2+4q+1
        60: 4q^2+3q+1
        61: 5q^2+3q
        62: 3q^2+q
        63: 6q^2+5q+1
        64: 2q^2+q
        65: 4q^2+4q+1
        66: 3q^2+q
        67: 6q^2+5q+1
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: q^3+7q^2+5q+1
        81: q^3+7q^2+5q+1
        82: q^3+7q^2+5q+1
        83: 4q^2+4q+1
        84: 6q^2+5q+1
        85: 6q^2+5q+1
        86: 5q^2+5q+1
        87: 3q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: q^3+7q^2+5q+1
        95: q^3+7q^2+5q+1
        96: 2q^3+5q^2+4q+1
        97: 5q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+4q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: q^2
       104: 3q^2+3q+1
       105: 3q^2+2q
       106: 2q^2+q
       107: q^2+2q+1
       108: 2q^2+2q
       109: q^2+q
       110: 2q^2+3q+1
       112: 3q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       117: q^2+q
       118: 2q^2+3q+1
       119: q^2+2q+1
       120: 2q^2+2q
       121: 2q^2+q
       122: 4q^2+4q+1
       123: 2q^2+q
       124: 4q^2+4q+1
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^3+7q^2+5q+1
       138: 4q^2+4q+1
       139: q^3+7q^2+5q+1
       140: 3q^2+4q+1
       141: 4q^2+4q+1
       142: 3q^2+4q+1
       143: 6q^2+5q+1
       144: 3q^2+4q+1
       145: 5q^2+5q+1
       146: 3q^2+4q+1
       147: 3q^2+4q+1
       148: q^2+2q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       152: 2q^2+4q+1
       154: 2q^2+4q+1
       156: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: q^3+4q^2+4q+1
       162: 3q^2+4q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       170: 2q+1
       171: q
       174: q^2+2q+1
       175: q^2+q
       176: q^2+q
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: q+1
       184: q^2+q
       186: 2q+1
       188: 2q+1
       190: q^2+3q+1
       191: q^2+q
       192: 2q^2+3q+1
       193: q^2+2q+1
       194: 2q^2+2q
       195: q^2+q
       196: 2q^2+3q+1
       198: 3q+1
       199: q^2+2q+1
       200: 2q^2+2q
       201: q^2+2q+1
       202: 2q^2+2q
       204: q^2+2q+1
       206: q+1
       207: 2q^2+q
       208: 4q^2+4q+1
       210: 2q^2+4q+1
       212: q^2+3q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+4q+1
       227: q^2+3q+1
       228: 3q^2+4q+1
       229: 2q^2+3q+1
       230: q^2+3q+1
       231: 3q^2+4q+1
       232: 2q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: q+1
       236: 3q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 5q^2+5q+1
       244: 3q^2+4q+1
       245: q^2+2q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 3q^2+4q+1
       251: q^3+4q^2+4q+1
       252: 3q^2+4q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: 2q+1
       261: q
       264: q+1
       268: 2q+1
       270: q
       274: q+1
       276: q^2+2q+1
       277: q^2+q
       278: q^2+q
       280: q+1
       282: 2q+1
       283: q+1
       284: q^2+q
       286: 2q+1
       288: q^2+3q+1
       290: q+1
       292: 2q+1
       293: q+1
       294: q^2+q
       296: 2q+1
       298: 2q+1
       299: q+1
       300: q^2+q
       302: 3q+1
       304: 2q+1
       306: 2q+1
       307: 1
       308: q
       310: q+1
       312: q+1
       314: 1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: q^2+2q+1
       320: 2q^2+2q
       322: q^2+2q+1
       324: q+1
       326: q^2+3q+1
       328: 2q+1
       330: q^2+2q+1
       332: 2q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 3q^2+4q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 4q+2
       352: 2q+1
       353: 2q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 2q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       378: q+1
       382: 1
       386: q+1
       390: 2q+1
       392: q
       394: q+1
       400: q+1
       403: 1
       407: q+1
       410: q+1
       412: 2q+1
       414: q+1
       416: q+1
       418: q+1
       419: q+1
       420: q^2+q
       422: 2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       430: q^2+q
       432: 2q+1
       434: 2q+1
       436: q+1
       437: q+1
       438: q^2+q
       440: 2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       447: 1
       448: q
       450: q+1
       452: 1
       453: 1
       454: q
       456: 1
       458: q+1
       460: 1
       462: 2q+2
       464: 2q+2
       466: q+1
       468: 2q+1
       470: q^2+3q+1
       471: 1
       472: q
       474: q+1
       476: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: q^2+3q+1
       495: q+1
       496: q+2
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: 2
       503: 2q+1
       505: q^2+2q+1
       507: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q+1
       546: 2q+1
       548: 2q+1
       551: 1
       556: 1
       560: 1
       564: 2q+2
       566: 1
       571: q+1
       574: q+1
       575: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       589: 1
       590: q
       592: 1
       596: q+1
       598: 1
       600: q+1
       602: 2
       603: q+1
       604: q^2+q
       606: q+1
       608: 2q+1
       610: 2q+1
       612: q+1
       614: q+1
       615: 1
       616: 1
       618: q+2
       619: 1
       620: q
       622: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 2
       634: 2
       636: q+1
       638: 2q+1
       640: q+1
       641: 1
       642: q
       644: q+1
       646: 1
       647: 1
       648: q
       650: q+1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       674: q+2
       675: q+1
       676: q+1
       677: q+1
       678: q+2
       679: 1
       680: 2
       681: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       699: q+1
       701: q+1
       706: 1
       710: 1
       715: 1
       722: 1
       726: q+1
       730: 1
       734: 1
       736: 1
       740: 1
       744: 1
       748: 1
       752: 2
       754: 1
       759: 1
       763: 1
       766: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 2
       793: 1
       794: 1
       796: q+2
       798: 1
       800: q+1
       801: 1
       802: q
       804: 1
       808: q+1
       810: 1
       812: q+1
       814: q+2
       815: 1
       816: 1
       818: 2
       820: 2
       824: 1
       825: 1
       826: q
       828: 1
       834: 1
       836: 1
       838: 2
       840: 2
       842: q+1
       843: 1
       844: 1
       845: 1
       846: q
       848: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: q+2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       876: 1
       877: q+1
       879: 1
       880: 1
       890: 1
       892: 1
       897: 1
       903: 1
       913: 1
       917: 1
       919: 1
       921: 1
       926: 1
       933: 1
       935: 1
       939: 1
       943: 2
       951: 1
       959: 2
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       980: 1
       983: 1
       986: 1
       989: 1
       991: 1
       993: 2
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1029: 1
      1031: 2
      1033: 2
      1037: 1
      1043: 1
      1046: 1
      1047: 1
      1051: 1
      1052: 1
      1053: q
      1055: 1
      1061: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1092: 1
      1094: 1
      1104: 1
      1106: 1
      1113: 1
      1117: 1
      1145: 1
      1147: 1
      1149: 1
      1155: 1
      1167: 2
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1205: 1
      1215: 1
      1217: 1
      1231: 1
      1233: 1
      1237: 1
      1239: 1
      1243: 1
      1253: 1
      1273: 1
      1275: 1
      1283: 1
      1288: 1
      1308: 1
      1310: 1
      1317: 1
      1347: 1
      1351: 1
      1449: 1
      1451: 1
      1473: 1
      1566: 1

1567:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^3+q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q^2+q
        60: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q+1
       109: q^2+q+1
       110: q^2+q
       111: q+1
       113: q+1
       115: q+1
       117: q+1
       118: q
       119: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: q+1
       181: q+1
       183: q+1
       185: q+1
       186: q
       187: q+1
       189: q+1
       191: q+1
       192: q
       193: q+1
       195: q^2+q+1
       196: q^2+q
       197: q+1
       199: q+1
       201: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       263: q+1
       267: q+1
       275: q+1
       279: 1
       281: 1
       283: q+1
       285: q+1
       286: q
       287: q+1
       289: 1
       291: q+1
       293: q+1
       295: q+1
       296: q
       297: q+1
       299: q+1
       301: q+1
       303: q+1
       304: q
       305: q+1
       307: 1
       315: q+1
       317: q+1
       319: q+1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: 2q+1
       334: q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q+1
       421: q+1
       422: q
       423: q+1
       425: q+1
       427: q+1
       429: q+1
       431: q+1
       432: q
       433: q+1
       435: 1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: 1
       453: 1
       465: 1
       467: 1
       469: q+1
       471: 1
       481: 1
       482: 2q+1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q+1
       545: q+1
       583: 1
       585: 1
       587: 1
       589: 1
       593: q+1
       595: q+1
       596: q
       597: 1
       599: q+1
       601: 1
       603: q+1
       605: 1
       607: q+1
       608: q
       609: q+1
       611: 1
       613: q+1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2q+1
       677: q+1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       705: 1
       709: 1
       717: q+1
       721: 1
       725: q+1
       729: 1
       733: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: q+1
       807: q+1
       808: q
       809: 1
       811: q+1
       813: 1
       815: 1
       825: 1
       841: 1
       845: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       896: 1
       904: 1
       912: 1
       916: 1
       920: 1
       928: q+1
       932: 1
       992: 1
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1052: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1118: 1
      1122: 1
      1144: 1
      1148: 1
      1156: 1
      1214: 1
      1218: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1283: 1
      1318: 1
      1352: 1
      1356: 1
      1448: 1
      1454: 1
      1567: 1

1568:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^3+q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q
        59: q^2+q+1
        60: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q+1
       109: q^2+q
       110: q^2+q+1
       112: q+1
       114: q+1
       116: q+1
       117: q
       118: q+1
       119: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: q+1
       182: q+1
       183: q+1
       185: q
       186: q+1
       188: q+1
       190: q+1
       191: q
       192: q+1
       193: q+1
       195: q^2+q
       196: q^2+q+1
       198: q+1
       199: q+1
       201: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: q+1
       264: q+1
       268: q+1
       276: q+1
       280: 1
       282: 1
       283: q+1
       285: q
       286: q+1
       288: q+1
       290: 1
       292: q+1
       293: q+1
       295: q
       296: q+1
       298: q+1
       299: q+1
       302: q+1
       303: q
       304: q+1
       306: q+1
       307: 1
       316: q+1
       318: q+1
       319: q+1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: 2q+1
       334: q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q+1
       421: q
       422: q+1
       424: q+1
       426: q+1
       428: q+1
       429: q+1
       431: q
       432: q+1
       434: q+1
       436: 1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: q+1
       446: q+1
       447: 1
       453: 1
       466: 1
       468: 1
       470: q+1
       471: 1
       481: 1
       482: 2q+1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q+1
       546: q+1
       584: 1
       586: 1
       588: 1
       589: 1
       593: q+1
       595: q
       596: q+1
       598: 1
       600: q+1
       602: 1
       603: q+1
       606: 1
       607: q
       608: q+1
       610: q+1
       612: 1
       614: q+1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2q+1
       677: q+1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       706: 1
       710: 1
       718: q+1
       722: 1
       726: q+1
       730: 1
       734: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: q+1
       807: q
       808: q+1
       810: 1
       812: q+1
       814: 1
       815: 1
       825: 1
       842: 1
       845: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       897: 1
       905: 1
       913: 1
       917: 1
       921: 1
       929: q+1
       933: 1
       993: 1
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1052: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1119: 1
      1123: 1
      1145: 1
      1149: 1
      1157: 1
      1215: 1
      1218: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1283: 1
      1319: 1
      1353: 1
      1357: 1
      1449: 1
      1454: 1
      1568: 1

1569:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^3+q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q
        59: q^2+q+1
        61: q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       108: q+1
       109: q^2+q
       110: q^2+q+1
       111: q+1
       113: q+1
       115: q+1
       117: q
       118: q+1
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: q+1
       181: q+1
       184: q+1
       185: q
       186: q+1
       187: q+1
       189: q+1
       191: q
       192: q+1
       194: q+1
       195: q^2+q
       196: q^2+q+1
       197: q+1
       200: q+1
       202: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: q+1
       266: q+1
       269: q+1
       278: q+1
       279: 1
       281: 1
       284: q+1
       285: q
       286: q+1
       287: q+1
       289: 1
       291: q+1
       294: q+1
       295: q
       296: q+1
       297: q+1
       300: q+1
       301: q+1
       303: q
       304: q+1
       305: q+1
       308: 1
       315: q+1
       317: q+1
       320: q+1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: 2q+1
       334: q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 2q+1
       345: 2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: q+1
       421: q
       422: q+1
       423: q+1
       425: q+1
       427: q+1
       430: q+1
       431: q
       432: q+1
       433: q+1
       435: 1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       448: 1
       454: 1
       465: 1
       467: 1
       469: q+1
       472: 1
       481: 1
       482: 2q+1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q+1
       547: q+1
       583: 1
       585: 1
       587: 1
       590: 1
       594: q+1
       595: q
       596: q+1
       597: 1
       599: q+1
       601: 1
       604: q+1
       605: 1
       607: q
       608: q+1
       609: q+1
       611: 1
       613: q+1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2q+1
       677: q+1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       708: 1
       712: 1
       720: q+1
       723: 1
       727: q+1
       731: 1
       735: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: q+1
       807: q
       808: q+1
       809: 1
       811: q+1
       813: 1
       816: 1
       826: 1
       841: 1
       846: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       899: 1
       906: 1
       914: 1
       918: 1
       922: 1
       930: q+1
       934: 1
       992: 1
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1120: 1
      1124: 1
      1146: 1
      1150: 1
      1158: 1
      1214: 1
      1219: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1283: 1
      1320: 1
      1354: 1
      1358: 1
      1448: 1
      1455: 1
      1569: 1

1570:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^3+q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+q+1
        59: q^2+q
        61: q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q+1
        73: 2q^2+2q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       108: q+1
       109: q^2+q+1
       110: q^2+q
       112: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: q+1
       182: q+1
       184: q+1
       185: q+1
       186: q
       188: q+1
       190: q+1
       191: q+1
       192: q
       194: q+1
       195: q^2+q+1
       196: q^2+q
       198: q+1
       200: q+1
       202: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: q+1
       265: q+1
       270: q+1
       277: q+1
       280: 1
       282: 1
       284: q+1
       285: q+1
       286: q
       288: q+1
       290: 1
       292: q+1
       294: q+1
       295: q+1
       296: q
       298: q+1
       300: q+1
       302: q+1
       303: q+1
       304: q
       306: q+1
       308: 1
       316: q+1
       318: q+1
       320: q+1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: 2q+1
       334: q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: q+1
       421: q+1
       422: q
       424: q+1
       426: q+1
       428: q+1
       430: q+1
       431: q+1
       432: q
       434: q+1
       436: 1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       448: 1
       454: 1
       466: 1
       468: 1
       470: q+1
       472: 1
       481: 1
       482: 2q+1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q+1
       548: q+1
       584: 1
       586: 1
       588: 1
       590: 1
       594: q+1
       595: q+1
       596: q
       598: 1
       600: q+1
       602: 1
       604: q+1
       606: 1
       607: q+1
       608: q
       610: q+1
       612: 1
       614: q+1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 2q+1
       677: q+1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       707: 1
       711: 1
       719: q+1
       724: 1
       728: q+1
       732: 1
       736: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: q+1
       807: q+1
       808: q
       810: 1
       812: q+1
       814: 1
       816: 1
       826: 1
       842: 1
       846: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       898: 1
       907: 1
       915: 1
       919: 1
       923: 1
       931: q+1
       935: 1
       993: 1
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1053: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1121: 1
      1125: 1
      1147: 1
      1151: 1
      1159: 1
      1215: 1
      1219: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1283: 1
      1321: 1
      1355: 1
      1359: 1
      1449: 1
      1455: 1
      1570: 1

1571:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: q^4+3q^3+3q^2+3q+1
        23: q^4+3q^3+3q^2+3q+1
        24: 3q^3+3q^2+2q+1
        25: 2q^3+q^2+3q+1
        26: 2q^3+q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: q^4+3q^3+3q^2+3q+1
        32: 2q^3+2q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+q^2+3q+1
        35: q^3+q^2+2q+1
        36: q^3+q^2+3q+1
        37: 2q^3+q^2+3q+1
        39: 2q^3+q^2+3q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: q^4+3q^3+3q^2+3q+1
        53: q^4+3q^3+3q^2+3q+1
        54: 3q^3+3q^2+2q+1
        55: 2q^3+q^2+3q+1
        56: 2q^3+q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^2+q
        60: q^3+q^2+2q+1
        61: q
        62: 2q^3+q^2+3q+1
        64: q^3+q^2+2q+1
        66: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+q^2+3q+1
        73: q^3+3q^2+3q+1
        74: 2q^3+q^2+3q+1
        76: 2q^3+q^2+3q+1
        78: q^3+2q^2+2q+1
        80: 2q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^4+3q^3+3q^2+3q+1
        83: 2q^3+2q^2+2q+1
        84: q^3+q^2+2q+1
        85: q^2+2q+1
        86: 2q^3+q^2+3q+1
        87: q^3+q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       103: q^3+q^2+2q+1
       106: q
       107: q^3+q^2+2q+1
       108: q
       109: q^3+2q^2+2q+1
       110: q^2+q
       111: q^3+q^2+3q+1
       113: 2q^3+q^2+3q+1
       115: q^3+q^2+2q+1
       117: q^2+q+1
       119: q^2+q+1
       121: q^3+q^2+2q+1
       123: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: q^3+3q^2+3q+1
       140: q^3+q^2+3q+1
       141: 2q^3+2q^2+2q+1
       142: q^3+3q^2+3q+1
       143: q^2+2q+1
       144: 2q+1
       145: 3q+1
       146: q^3+q^2+2q+1
       147: 3q+1
       148: q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       151: 2q^3+q^2+3q+1
       153: 2q^3+q^2+3q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q^3+q^2+2q+1
       172: q
       173: q^2+q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+q+1
       185: q^2+q+1
       187: q^2+2q+1
       189: q^3+q^2+2q+1
       191: q^2+q+1
       193: q^3+q^2+2q+1
       194: q
       195: q^3+2q^2+2q+1
       196: q^2+q
       197: q^3+q^2+3q+1
       199: q^2+q+1
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: q^2+2q+1
       209: 2q^3+q^2+3q+1
       211: q^3+q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: 2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+q+1
       267: q^3+q^2+2q+1
       269: q
       271: q+1
       275: q^2+q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q^2+q+1
       295: q^2+q+1
       297: q^2+2q+1
       299: q^2+q+1
       301: 3q+1
       303: q^2+q+1
       305: q^2+2q+1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: 2q+1
       317: 3q+1
       319: 2q+1
       320: q
       321: q+1
       323: q+1
       325: q^3+q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: q+1
       345: q^2+q+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 1
       385: q^2+q+1
       389: 2q+1
       391: q
       393: q^2+q+1
       397: q+1
       401: 1
       405: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: q+1
       431: q+1
       433: 2q+1
       435: q+1
       437: q^2+q+1
       439: q^2+q+1
       441: q^2+2q+1
       443: 2q+1
       444: q
       445: 3q+1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: q+1
       469: 2q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q^2+q+1
       545: 2q+1
       547: q
       549: 1
       553: 1
       557: 1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       591: 1
       593: q+1
       595: q+1
       597: q+1
       599: 2q+1
       601: 1
       603: q+1
       605: q+1
       607: q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       615: 1
       617: q+1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       693: q+1
       705: 1
       709: 1
       713: 1
       717: q+1
       721: 1
       725: q+1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       777: 1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: 1
       791: 1
       797: 1
       799: q+1
       801: 1
       803: 1
       805: q+1
       807: q+1
       809: q+1
       811: 2q+1
       813: q+1
       815: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       920: 1
       924: 1
       928: q+1
       932: 1
       936: 1
       948: 1
       956: 1
       960: 1
       974: 1
       978: 1
       982: 1
       988: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: q+1
      1026: 1
      1028: 1
      1042: 1
      1050: 1
      1052: 1
      1054: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1085: 1
      1098: 1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1184: 1
      1202: 1
      1222: 1
      1238: 1
      1240: 1
      1242: 1
      1272: 1
      1276: 1
      1278: 1
      1322: 1
      1344: 1
      1352: 1
      1360: 1
      1368: 1
      1480: 1
      1571: 1

1572:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: q^4+3q^3+3q^2+3q+1
        23: q^4+3q^3+3q^2+3q+1
        24: 3q^3+3q^2+2q+1
        25: 2q^3+q^2+3q+1
        26: 2q^3+q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: q^4+3q^3+3q^2+3q+1
        32: 2q^3+2q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+q^2+3q+1
        35: q^3+q^2+2q+1
        36: q^3+q^2+3q+1
        37: 2q^3+q^2+3q+1
        39: 2q^3+q^2+3q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: q^4+3q^3+3q^2+3q+1
        53: q^4+3q^3+3q^2+3q+1
        54: 3q^3+3q^2+2q+1
        55: 2q^3+q^2+3q+1
        56: 2q^3+q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+2q+1
        60: q
        61: q^3+q^2+2q+1
        62: 2q^3+q^2+3q+1
        64: q^3+q^2+2q+1
        66: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+q^2+3q+1
        73: q^3+3q^2+3q+1
        74: 2q^3+q^2+3q+1
        76: 2q^3+q^2+3q+1
        78: q^3+2q^2+2q+1
        80: 2q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^4+3q^3+3q^2+3q+1
        83: 2q^3+2q^2+2q+1
        84: q^3+q^2+2q+1
        85: q^2+2q+1
        86: 2q^3+q^2+3q+1
        87: q^3+q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       103: q
       106: q^3+q^2+2q+1
       107: q
       108: q^3+q^2+2q+1
       109: q^2+q
       110: q^3+2q^2+2q+1
       111: q^3+q^2+3q+1
       113: 2q^3+q^2+3q+1
       115: q^3+q^2+2q+1
       118: q^2+q+1
       120: q^2+q+1
       121: q^3+q^2+2q+1
       123: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: q^3+3q^2+3q+1
       140: q^3+q^2+3q+1
       141: 2q^3+2q^2+2q+1
       142: q^3+3q^2+3q+1
       143: q^2+2q+1
       144: 2q+1
       145: 3q+1
       146: q^3+q^2+2q+1
       147: 3q+1
       148: q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       151: 2q^3+q^2+3q+1
       153: 2q^3+q^2+3q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: q^3+q^2+2q+1
       176: q^2+q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q^2+q+1
       186: q^2+q+1
       187: q^2+2q+1
       189: q^3+q^2+2q+1
       192: q^2+q+1
       193: q
       194: q^3+q^2+2q+1
       195: q^2+q
       196: q^3+2q^2+2q+1
       197: q^3+q^2+3q+1
       200: q^2+q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: q^2+2q+1
       209: 2q^3+q^2+3q+1
       211: q^3+q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: 2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 2q+1
       266: q^2+q+1
       267: q
       269: q^3+q^2+2q+1
       273: q+1
       278: q^2+q+1
       279: 1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q^2+q+1
       296: q^2+q+1
       297: q^2+2q+1
       300: q^2+q+1
       301: 3q+1
       304: q^2+q+1
       305: q^2+2q+1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: 2q+1
       317: 3q+1
       319: q
       320: 2q+1
       322: q+1
       323: q+1
       325: q^3+q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: q+1
       345: q^2+q+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       384: 1
       388: q^2+q+1
       389: q
       391: 2q+1
       396: q^2+q+1
       399: q+1
       404: 1
       406: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: q+1
       432: q+1
       433: 2q+1
       435: q+1
       438: q^2+q+1
       440: q^2+q+1
       441: q^2+2q+1
       443: q
       444: 2q+1
       445: 3q+1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: q+1
       469: 2q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q^2+q+1
       545: q
       547: 2q+1
       552: 1
       555: 1
       559: 1
       563: q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       592: 1
       594: q+1
       596: q+1
       597: q+1
       599: 2q+1
       601: 1
       604: q+1
       605: q+1
       608: q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       697: q+1
       708: 1
       712: 1
       716: 1
       720: q+1
       723: 1
       727: q+1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       777: 1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: 1
       791: 1
       797: 1
       799: q+1
       802: 1
       804: 1
       806: q+1
       808: q+1
       809: q+1
       811: 2q+1
       813: q+1
       816: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       922: 1
       927: 1
       930: q+1
       934: 1
       938: 1
       950: 1
       958: 1
       961: 1
       975: 1
       979: 1
       982: 1
       991: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: q+1
      1027: 1
      1029: 1
      1042: 1
      1050: 1
      1053: 1
      1055: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1085: 1
      1102: 1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1185: 1
      1204: 1
      1222: 1
      1238: 1
      1241: 1
      1243: 1
      1272: 1
      1276: 1
      1278: 1
      1323: 1
      1346: 1
      1354: 1
      1361: 1
      1369: 1
      1480: 1
      1572: 1

1573:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: q^4+3q^3+3q^2+3q+1
        23: q^4+3q^3+3q^2+3q+1
        24: 3q^3+3q^2+2q+1
        25: 2q^3+q^2+3q+1
        26: 2q^3+q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: q^4+3q^3+3q^2+3q+1
        32: 2q^3+2q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+q^2+3q+1
        35: q^3+q^2+2q+1
        36: q^3+q^2+3q+1
        38: 2q^3+q^2+3q+1
        40: 2q^3+q^2+3q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: q^4+3q^3+3q^2+3q+1
        53: q^4+3q^3+3q^2+3q+1
        54: 3q^3+3q^2+2q+1
        55: 2q^3+q^2+3q+1
        56: 2q^3+q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^2+q
        60: q
        61: q^3+q^2+2q+1
        63: 2q^3+q^2+3q+1
        65: q^3+q^2+2q+1
        67: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+q^2+3q+1
        73: q^3+3q^2+3q+1
        75: 2q^3+q^2+3q+1
        77: 2q^3+q^2+3q+1
        79: q^3+2q^2+2q+1
        80: 2q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^4+3q^3+3q^2+3q+1
        83: 2q^3+2q^2+2q+1
        84: q^3+q^2+2q+1
        85: q^2+2q+1
        86: 2q^3+q^2+3q+1
        87: q^3+q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       104: q
       105: q^3+q^2+2q+1
       107: q
       108: q^3+q^2+2q+1
       109: q^3+2q^2+2q+1
       110: q^2+q
       112: q^3+q^2+3q+1
       114: 2q^3+q^2+3q+1
       116: q^3+q^2+2q+1
       117: q^2+q+1
       120: q^2+q+1
       122: q^3+q^2+2q+1
       124: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: q^3+3q^2+3q+1
       140: q^3+q^2+3q+1
       141: 2q^3+2q^2+2q+1
       142: q^3+3q^2+3q+1
       143: q^2+2q+1
       144: 2q+1
       145: 3q+1
       146: q^3+q^2+2q+1
       147: 3q+1
       148: q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       152: 2q^3+q^2+3q+1
       154: 2q^3+q^2+3q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: q^3+q^2+2q+1
       175: q^2+q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q^2+q+1
       185: q^2+q+1
       188: q^2+2q+1
       190: q^3+q^2+2q+1
       191: q^2+q+1
       193: q
       194: q^3+q^2+2q+1
       195: q^3+2q^2+2q+1
       196: q^2+q
       198: q^3+q^2+3q+1
       200: q^2+q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: q^2+2q+1
       210: 2q^3+q^2+3q+1
       212: q^3+q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: 2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 2q+1
       265: q^2+q+1
       268: q
       270: q^3+q^2+2q+1
       272: q+1
       277: q^2+q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q^2+q+1
       295: q^2+q+1
       298: q^2+2q+1
       300: q^2+q+1
       302: 3q+1
       303: q^2+q+1
       306: q^2+2q+1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: 2q+1
       318: 3q+1
       319: q
       320: 2q+1
       321: q+1
       324: q+1
       326: q^3+q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: q+1
       345: q^2+q+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       383: 1
       387: q^2+q+1
       390: q
       392: 2q+1
       395: q^2+q+1
       398: q+1
       402: 1
       408: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: q+1
       431: q+1
       434: 2q+1
       436: q+1
       438: q^2+q+1
       439: q^2+q+1
       442: q^2+2q+1
       443: q
       444: 2q+1
       446: 3q+1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: q+1
       470: 2q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q^2+q+1
       546: q
       548: 2q+1
       550: 1
       554: 1
       558: 1
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       591: 1
       594: q+1
       595: q+1
       598: q+1
       600: 2q+1
       602: 1
       604: q+1
       606: q+1
       607: q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       616: 1
       618: q+1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       700: q+1
       707: 1
       711: 1
       714: 1
       719: q+1
       724: 1
       728: q+1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       778: 1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: 1
       792: 1
       798: 1
       800: q+1
       802: 1
       803: 1
       806: q+1
       807: q+1
       810: q+1
       812: 2q+1
       814: q+1
       816: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       923: 1
       925: 1
       931: q+1
       935: 1
       937: 1
       949: 1
       957: 1
       963: 1
       977: 1
       981: 1
       986: 1
       990: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: q+1
      1027: 1
      1028: 1
      1043: 1
      1051: 1
      1053: 1
      1054: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1085: 1
      1105: 1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1187: 1
      1203: 1
      1223: 1
      1239: 1
      1241: 1
      1242: 1
      1273: 1
      1277: 1
      1279: 1
      1325: 1
      1345: 1
      1355: 1
      1362: 1
      1370: 1
      1481: 1
      1573: 1

1574:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: q^4+3q^3+3q^2+3q+1
        23: q^4+3q^3+3q^2+3q+1
        24: 3q^3+3q^2+2q+1
        25: 2q^3+q^2+3q+1
        26: 2q^3+q^2+3q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: q^4+3q^3+3q^2+3q+1
        32: 2q^3+2q^2+2q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+q^2+3q+1
        35: q^3+q^2+2q+1
        36: q^3+q^2+3q+1
        38: 2q^3+q^2+3q+1
        40: 2q^3+q^2+3q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: q^4+3q^3+3q^2+3q+1
        53: q^4+3q^3+3q^2+3q+1
        54: 3q^3+3q^2+2q+1
        55: 2q^3+q^2+3q+1
        56: 2q^3+q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+2q+1
        60: q^3+q^2+2q+1
        61: q
        63: 2q^3+q^2+3q+1
        65: q^3+q^2+2q+1
        67: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+q^2+3q+1
        73: q^3+3q^2+3q+1
        75: 2q^3+q^2+3q+1
        77: 2q^3+q^2+3q+1
        79: q^3+2q^2+2q+1
        80: 2q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^4+3q^3+3q^2+3q+1
        83: 2q^3+2q^2+2q+1
        84: q^3+q^2+2q+1
        85: q^2+2q+1
        86: 2q^3+q^2+3q+1
        87: q^3+q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: 2q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       104: q^3+q^2+2q+1
       105: q
       107: q^3+q^2+2q+1
       108: q
       109: q^2+q
       110: q^3+2q^2+2q+1
       112: q^3+q^2+3q+1
       114: 2q^3+q^2+3q+1
       116: q^3+q^2+2q+1
       118: q^2+q+1
       119: q^2+q+1
       122: q^3+q^2+2q+1
       124: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: q^3+3q^2+3q+1
       140: q^3+q^2+3q+1
       141: 2q^3+2q^2+2q+1
       142: q^3+3q^2+3q+1
       143: q^2+2q+1
       144: 2q+1
       145: 3q+1
       146: q^3+q^2+2q+1
       147: 3q+1
       148: q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       152: 2q^3+q^2+3q+1
       154: 2q^3+q^2+3q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q^3+q^2+2q+1
       171: q
       174: q^2+q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+q+1
       186: q^2+q+1
       188: q^2+2q+1
       190: q^3+q^2+2q+1
       192: q^2+q+1
       193: q^3+q^2+2q+1
       194: q
       195: q^2+q
       196: q^3+2q^2+2q+1
       198: q^3+q^2+3q+1
       199: q^2+q+1
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: q^2+2q+1
       210: 2q^3+q^2+3q+1
       212: q^3+q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: 2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+q+1
       268: q^3+q^2+2q+1
       270: q
       274: q+1
       276: q^2+q+1
       280: 1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q^2+q+1
       296: q^2+q+1
       298: q^2+2q+1
       299: q^2+q+1
       302: 3q+1
       304: q^2+q+1
       306: q^2+2q+1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: 2q+1
       318: 3q+1
       319: 2q+1
       320: q
       322: q+1
       324: q+1
       326: q^3+q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: q+1
       345: q^2+q+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 1
       386: q^2+q+1
       390: 2q+1
       392: q
       394: q^2+q+1
       400: q+1
       403: 1
       407: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: q+1
       432: q+1
       434: 2q+1
       436: q+1
       437: q^2+q+1
       440: q^2+q+1
       442: q^2+2q+1
       443: 2q+1
       444: q
       446: 3q+1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: q+1
       470: 2q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q^2+q+1
       546: 2q+1
       548: q
       551: 1
       556: 1
       560: 1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       592: 1
       593: q+1
       596: q+1
       598: q+1
       600: 2q+1
       602: 1
       603: q+1
       606: q+1
       608: q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       615: 1
       618: q+1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       699: q+1
       706: 1
       710: 1
       715: 1
       718: q+1
       722: 1
       726: q+1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       778: 1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: 1
       792: 1
       798: 1
       800: q+1
       801: 1
       804: 1
       805: q+1
       808: q+1
       810: q+1
       812: 2q+1
       814: q+1
       815: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: q+1
       876: 1
       877: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       921: 1
       926: 1
       929: q+1
       933: 1
       939: 1
       951: 1
       959: 1
       962: 1
       976: 1
       980: 1
       986: 1
       989: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: q+1
      1026: 1
      1029: 1
      1043: 1
      1051: 1
      1052: 1
      1055: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1085: 1
      1104: 1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1186: 1
      1205: 1
      1223: 1
      1239: 1
      1240: 1
      1243: 1
      1273: 1
      1277: 1
      1279: 1
      1324: 1
      1347: 1
      1353: 1
      1363: 1
      1371: 1
      1481: 1
      1574: 1

1575:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^3+4q^2+5q+1
        23: q^3+4q^2+5q+1
        24: 2q^3+3q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^3+4q^2+5q+1
        32: q^2+3q+1
        33: q^3+4q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 3q+1
        38: q^2+2q
        39: 3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^3+4q^2+5q+1
        53: q^3+4q^2+5q+1
        54: 2q^3+3q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: q^3+2q^2+3q+1
        59: 2q^2+2q
        60: q^2+3q+1
        61: 2q
        62: 3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: 3q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^2+5q+1
        73: q^3+4q^2+5q+1
        74: 3q+1
        75: q^2+2q
        76: 3q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^3+4q^2+5q+1
        83: q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^3+4q^2+5q+1
        95: q^3+4q^2+5q+1
        96: 2q^3+3q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: 2q+1
       104: q^2+q
       105: q
       106: q
       107: q^2+3q+1
       108: 2q
       109: q^3+2q^2+3q+1
       110: 2q^2+2q
       111: 3q+1
       112: q^2+2q
       113: 3q+1
       114: q^2+2q
       115: 2q+1
       116: q
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: q^2+3q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: q^2+3q+1
       135: 3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^3+4q^2+5q+1
       140: q^2+5q+1
       141: q^2+3q+1
       142: q^3+4q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: q^2+5q+1
       150: 3q+1
       151: 3q+1
       152: q^2+2q
       153: 3q+1
       154: q^2+2q
       155: q^2+2q+1
       156: q^2+q
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: 2q+1
       170: q^2+q
       171: q
       172: q
       173: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: q+1
       185: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       191: q+1
       193: q^2+3q+1
       194: 2q
       195: q^3+2q^2+3q+1
       196: 2q^2+2q
       197: 3q+1
       198: q^2+2q
       199: q+1
       201: q^2+3q+1
       202: 2q
       203: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 3q+1
       210: q^2+2q
       211: 2q+1
       212: q
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: 3q+1
       223: 3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+3q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+5q+1
       244: q^2+5q+1
       245: 2q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q^2+q
       261: q
       262: q
       263: q+1
       267: 2q+1
       268: q^2+q
       269: q
       270: q
       271: q+1
       272: q
       275: q+1
       283: q+1
       285: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       293: q+1
       295: q+1
       297: 2q+1
       298: q
       299: q+1
       301: 3q+1
       302: q^2+2q
       303: q+1
       305: 2q+1
       306: q
       307: 1
       309: 1
       311: q+1
       312: q
       313: 1
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: q^2+3q+1
       320: 2q
       321: 2q+1
       323: q+1
       324: q
       325: 2q+1
       326: q
       333: q+1
       334: 3q+1
       335: q^2+3q+1
       336: 3q+1
       337: q^2+5q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: 3q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+5q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 3q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       385: q+1
       389: 2q+1
       390: q^2+q
       391: q
       392: q
       393: q+1
       397: q+1
       398: q
       401: 1
       405: q+1
       408: q
       419: q+1
       421: q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       429: q+1
       431: q+1
       433: 2q+1
       434: q
       437: q+1
       439: q+1
       441: 2q+1
       442: q
       443: q^2+3q+1
       444: 2q
       445: 3q+1
       446: q^2+2q
       447: 1
       449: 1
       451: 1
       453: 1
       457: 1
       459: 1
       461: 2q+1
       463: q+1
       464: q
       469: 2q+1
       470: q
       471: 1
       473: 1
       475: 1
       477: q+1
       478: q
       479: q+1
       480: q
       481: 1
       482: q+1
       483: 3q+1
       484: 1
       491: q+1
       492: q+1
       493: 3q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       529: q+1
       533: q+1
       541: q+1
       545: 2q+1
       546: q^2+q
       547: q
       548: q
       549: 1
       557: 1
       561: q+1
       562: q
       565: 1
       569: q+1
       572: q
       573: q+1
       576: q
       577: q+1
       581: q
       589: 1
       591: 1
       593: q+1
       595: q+1
       599: 2q+1
       600: q
       603: q+1
       607: q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: 1
       619: 1
       621: 1
       625: 1
       629: 1
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 3q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       700: q
       713: 1
       717: q+1
       725: q+1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       801: 1
       803: 1
       805: q+1
       807: q+1
       811: 2q+1
       812: q
       815: 1
       817: 1
       825: 1
       827: 1
       835: 1
       839: 1
       843: 1
       845: 1
       847: 1
       851: 1
       855: 1
       857: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       908: 1
       924: 1
       928: q+1
       948: 1
       964: 1
       974: 1
       988: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1012: 1
      1016: 1
      1026: 1
      1028: 1
      1032: 1
      1046: 1
      1052: 1
      1054: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1130: 1
      1134: 1
      1160: 1
      1194: 1
      1202: 1
      1216: 1
      1218: 1
      1224: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1276: 1
      1280: 1
      1283: 1
      1288: 1
      1326: 1
      1364: 1
      1368: 1
      1450: 1
      1454: 1
      1482: 1
      1575: 1

1576:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^3+4q^2+5q+1
        23: q^3+4q^2+5q+1
        24: 2q^3+3q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^3+4q^2+5q+1
        32: q^2+3q+1
        33: q^3+4q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: q^2+2q
        38: 3q+1
        39: q^2+2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^3+4q^2+5q+1
        53: q^3+4q^2+5q+1
        54: 2q^3+3q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: q^3+2q^2+3q+1
        59: 2q^2+2q
        60: 2q
        61: q^2+3q+1
        62: q^2+2q
        63: 3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: 3q+1
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^2+5q+1
        73: q^3+4q^2+5q+1
        74: q^2+2q
        75: 3q+1
        76: q^2+2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^3+4q^2+5q+1
        83: q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^3+4q^2+5q+1
        95: q^3+4q^2+5q+1
        96: 2q^3+3q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q
       104: q
       105: 2q+1
       106: q^2+q
       107: 2q
       108: q^2+3q+1
       109: q^3+2q^2+3q+1
       110: 2q^2+2q
       111: q^2+2q
       112: 3q+1
       113: q^2+2q
       114: 3q+1
       115: q
       116: 2q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: q^2+3q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: q^2+3q+1
       135: 3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^3+4q^2+5q+1
       140: q^2+5q+1
       141: q^2+3q+1
       142: q^3+4q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: q^2+5q+1
       150: 3q+1
       151: q^2+2q
       152: 3q+1
       153: q^2+2q
       154: 3q+1
       155: q^2+q
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q
       170: q
       171: 2q+1
       172: q^2+q
       175: q+1
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       184: q+1
       185: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       191: q+1
       193: 2q
       194: q^2+3q+1
       195: q^3+2q^2+3q+1
       196: 2q^2+2q
       197: q^2+2q
       198: 3q+1
       200: q+1
       201: 2q
       202: q^2+3q+1
       203: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 3q+1
       211: q
       212: 2q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: 3q+1
       223: 3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+3q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+5q+1
       244: q^2+5q+1
       245: 2q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: q
       261: 2q+1
       262: q^2+q
       265: q+1
       267: q
       268: q
       269: q^2+q
       270: 2q+1
       271: q
       272: q+1
       277: q+1
       284: q+1
       285: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       294: q+1
       295: q+1
       297: q
       298: 2q+1
       300: q+1
       301: q^2+2q
       302: 3q+1
       303: q+1
       305: q
       306: 2q+1
       308: 1
       309: 1
       311: q
       312: q+1
       314: 1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: 2q
       320: q^2+3q+1
       321: 2q+1
       323: q
       324: q+1
       325: q
       326: 2q+1
       333: q+1
       334: 3q+1
       335: q^2+3q+1
       336: 3q+1
       337: q^2+5q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: 3q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+5q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 3q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       387: q+1
       389: q
       390: q
       391: q^2+q
       392: 2q+1
       395: q+1
       397: q
       398: q+1
       402: 1
       405: q
       408: q+1
       420: q+1
       421: q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       430: q+1
       431: q+1
       433: q
       434: 2q+1
       438: q+1
       439: q+1
       441: q
       442: 2q+1
       443: 2q
       444: q^2+3q+1
       445: q^2+2q
       446: 3q+1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       460: 1
       461: 2q+1
       463: q
       464: q+1
       469: q
       470: 2q+1
       472: 1
       473: 1
       476: 1
       477: q
       478: q+1
       479: q
       480: q+1
       481: 1
       482: q+1
       483: 3q+1
       484: 1
       491: q+1
       492: q+1
       493: 3q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       531: q+1
       535: q+1
       544: q+1
       545: q
       546: q
       547: q^2+q
       548: 2q+1
       550: 1
       558: 1
       561: q
       562: q+1
       567: 1
       569: q
       572: q+1
       573: q
       576: q+1
       577: q
       581: q+1
       590: 1
       591: 1
       594: q+1
       595: q+1
       599: q
       600: 2q+1
       604: q+1
       607: q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       616: 1
       620: 1
       621: 1
       626: 1
       630: 1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 3q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q
       700: q+1
       714: 1
       719: q+1
       728: q+1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       802: 1
       803: 1
       806: q+1
       807: q+1
       811: q
       812: 2q+1
       816: 1
       817: 1
       826: 1
       827: 1
       836: 1
       839: 1
       844: 1
       846: 1
       847: 1
       852: 1
       856: 1
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       910: 1
       925: 1
       931: q+1
       949: 1
       966: 1
       977: 1
       990: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1013: 1
      1017: 1
      1027: 1
      1028: 1
      1032: 1
      1047: 1
      1053: 1
      1054: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1132: 1
      1137: 1
      1161: 1
      1196: 1
      1203: 1
      1216: 1
      1219: 1
      1225: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1277: 1
      1281: 1
      1283: 1
      1288: 1
      1328: 1
      1365: 1
      1370: 1
      1450: 1
      1455: 1
      1483: 1
      1576: 1

1577:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^3+4q^2+5q+1
        23: q^3+4q^2+5q+1
        24: 2q^3+3q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^3+4q^2+5q+1
        32: q^2+3q+1
        33: q^3+4q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: q^2+2q
        38: 3q+1
        39: q^2+2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^3+4q^2+5q+1
        53: q^3+4q^2+5q+1
        54: 2q^3+3q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: 2q^2+2q
        59: q^3+2q^2+3q+1
        60: q^2+3q+1
        61: 2q
        62: q^2+2q
        63: 3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: 3q+1
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^2+5q+1
        73: q^3+4q^2+5q+1
        74: q^2+2q
        75: 3q+1
        76: q^2+2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^3+4q^2+5q+1
        83: q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^3+4q^2+5q+1
        95: q^3+4q^2+5q+1
        96: 2q^3+3q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q^2+q
       104: 2q+1
       105: q
       106: q
       107: q^2+3q+1
       108: 2q
       109: 2q^2+2q
       110: q^3+2q^2+3q+1
       111: q^2+2q
       112: 3q+1
       113: q^2+2q
       114: 3q+1
       115: q
       116: 2q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: q^2+3q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: q^2+3q+1
       135: 3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^3+4q^2+5q+1
       140: q^2+5q+1
       141: q^2+3q+1
       142: q^3+4q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: q^2+5q+1
       150: 3q+1
       151: q^2+2q
       152: 3q+1
       153: q^2+2q
       154: 3q+1
       155: q^2+q
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q^2+q
       170: 2q+1
       171: q
       172: q
       174: q+1
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: q+1
       186: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       192: q+1
       193: q^2+3q+1
       194: 2q
       195: 2q^2+2q
       196: q^3+2q^2+3q+1
       197: q^2+2q
       198: 3q+1
       199: q+1
       201: q^2+3q+1
       202: 2q
       204: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 3q+1
       211: q
       212: 2q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: 3q+1
       223: 3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+3q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+5q+1
       244: q^2+5q+1
       245: 2q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q
       260: 2q+1
       261: q
       262: q
       264: q+1
       267: q^2+q
       268: 2q+1
       269: q
       270: q
       273: q
       274: q+1
       276: q+1
       283: q+1
       286: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       293: q+1
       296: q+1
       297: q
       298: 2q+1
       299: q+1
       301: q^2+2q
       302: 3q+1
       304: q+1
       305: q
       306: 2q+1
       307: 1
       310: 1
       311: q
       312: q+1
       314: 1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: q^2+3q+1
       320: 2q
       322: 2q+1
       323: q
       324: q+1
       325: q
       326: 2q+1
       333: q+1
       334: 3q+1
       335: q^2+3q+1
       336: 3q+1
       337: q^2+5q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: 3q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+5q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 3q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       386: q+1
       389: q^2+q
       390: 2q+1
       391: q
       392: q
       394: q+1
       399: q
       400: q+1
       403: 1
       406: q
       407: q+1
       419: q+1
       422: q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       429: q+1
       432: q+1
       433: q
       434: 2q+1
       437: q+1
       440: q+1
       441: q
       442: 2q+1
       443: q^2+3q+1
       444: 2q
       445: q^2+2q
       446: 3q+1
       447: 1
       450: 1
       452: 1
       453: 1
       458: 1
       460: 1
       462: 2q+1
       463: q
       464: q+1
       469: q
       470: 2q+1
       471: 1
       474: 1
       476: 1
       477: q
       478: q+1
       479: q
       480: q+1
       481: 1
       482: q+1
       483: 3q+1
       484: 1
       491: q+1
       492: q+1
       493: 3q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       530: q+1
       534: q+1
       542: q+1
       545: q^2+q
       546: 2q+1
       547: q
       548: q
       551: 1
       560: 1
       563: q
       564: q+1
       566: 1
       570: q
       571: q+1
       574: q+1
       575: q
       577: q
       581: q+1
       589: 1
       592: 1
       593: q+1
       596: q+1
       599: q
       600: 2q+1
       603: q+1
       608: q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: 1
       619: 1
       622: 1
       626: 1
       630: 1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 3q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q
       699: q+1
       715: 1
       718: q+1
       726: q+1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       801: 1
       804: 1
       805: q+1
       808: q+1
       811: q
       812: 2q+1
       815: 1
       818: 1
       825: 1
       828: 1
       836: 1
       840: 1
       844: 1
       845: 1
       848: 1
       852: 1
       856: 1
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       909: 1
       926: 1
       929: q+1
       951: 1
       965: 1
       976: 1
       989: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1013: 1
      1016: 1
      1026: 1
      1029: 1
      1033: 1
      1047: 1
      1052: 1
      1055: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1131: 1
      1136: 1
      1162: 1
      1195: 1
      1205: 1
      1217: 1
      1218: 1
      1225: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1277: 1
      1281: 1
      1283: 1
      1288: 1
      1327: 1
      1366: 1
      1371: 1
      1451: 1
      1454: 1
      1483: 1
      1577: 1

1578:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^3+4q^2+5q+1
        23: q^3+4q^2+5q+1
        24: 2q^3+3q^2+3q+1
        25: q^2+5q+1
        26: q^2+5q+1
        27: 2q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^3+4q^2+5q+1
        32: q^2+3q+1
        33: q^3+4q^2+5q+1
        34: q^2+5q+1
        35: 3q+1
        36: q^2+5q+1
        37: 3q+1
        38: q^2+2q
        39: 3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^3+4q^2+5q+1
        53: q^3+4q^2+5q+1
        54: 2q^3+3q^2+3q+1
        55: q^2+5q+1
        56: q^2+5q+1
        57: 2q^2+3q+1
        58: 2q^2+2q
        59: q^3+2q^2+3q+1
        60: 2q
        61: q^2+3q+1
        62: 3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: 3q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^2+5q+1
        73: q^3+4q^2+5q+1
        74: 3q+1
        75: q^2+2q
        76: 3q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^3+4q^2+5q+1
        83: q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: q^2+5q+1
        87: 3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^3+4q^2+5q+1
        95: q^3+4q^2+5q+1
        96: 2q^3+3q^2+3q+1
        97: q^2+5q+1
        98: q^2+5q+1
        99: 2q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q
       104: q
       105: q^2+q
       106: 2q+1
       107: 2q
       108: q^2+3q+1
       109: 2q^2+2q
       110: q^3+2q^2+3q+1
       111: 3q+1
       112: q^2+2q
       113: 3q+1
       114: q^2+2q
       115: 2q+1
       116: q
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: q^2+3q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: q^2+3q+1
       135: 3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^3+4q^2+5q+1
       140: q^2+5q+1
       141: q^2+3q+1
       142: q^3+4q^2+5q+1
       143: 3q+1
       144: 3q+1
       145: q^2+5q+1
       146: 3q+1
       147: q^2+5q+1
       148: 2q+1
       149: q^2+5q+1
       150: 3q+1
       151: 3q+1
       152: q^2+2q
       153: 3q+1
       154: q^2+2q
       155: q^2+2q+1
       156: q^2+q
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q
       170: q
       171: q^2+q
       172: 2q+1
       176: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       184: q+1
       186: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       192: q+1
       193: 2q
       194: q^2+3q+1
       195: 2q^2+2q
       196: q^3+2q^2+3q+1
       197: 3q+1
       198: q^2+2q
       200: q+1
       201: 2q
       202: q^2+3q+1
       204: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: 3q+1
       210: q^2+2q
       211: 2q+1
       212: q
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: 3q+1
       223: 3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+3q+1
       231: 3q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 3q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+5q+1
       244: q^2+5q+1
       245: 2q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: q
       261: q^2+q
       262: 2q+1
       266: q+1
       267: q
       268: q
       269: 2q+1
       270: q^2+q
       273: q+1
       274: q
       278: q+1
       284: q+1
       286: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       294: q+1
       296: q+1
       297: 2q+1
       298: q
       300: q+1
       301: 3q+1
       302: q^2+2q
       304: q+1
       305: 2q+1
       306: q
       308: 1
       310: 1
       311: q+1
       312: q
       313: 1
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: 2q
       320: q^2+3q+1
       322: 2q+1
       323: q+1
       324: q
       325: 2q+1
       326: q
       333: q+1
       334: 3q+1
       335: q^2+3q+1
       336: 3q+1
       337: q^2+5q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: 3q+1
       348: 3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+5q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 2q+1
       366: 3q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       388: q+1
       389: q
       390: q
       391: 2q+1
       392: q^2+q
       396: q+1
       399: q+1
       400: q
       404: 1
       406: q+1
       407: q
       420: q+1
       422: q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       430: q+1
       432: q+1
       433: 2q+1
       434: q
       438: q+1
       440: q+1
       441: 2q+1
       442: q
       443: 2q
       444: q^2+3q+1
       445: 3q+1
       446: q^2+2q
       448: 1
       450: 1
       451: 1
       454: 1
       458: 1
       459: 1
       462: 2q+1
       463: q+1
       464: q
       469: 2q+1
       470: q
       472: 1
       474: 1
       475: 1
       477: q+1
       478: q
       479: q+1
       480: q
       481: 1
       482: q+1
       483: 3q+1
       484: 1
       491: q+1
       492: q+1
       493: 3q+1
       494: q^2+3q+1
       495: 3q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       532: q+1
       536: q+1
       543: q+1
       545: q
       546: q
       547: 2q+1
       548: q^2+q
       552: 1
       559: 1
       563: q+1
       564: q
       568: 1
       570: q+1
       571: q
       574: q
       575: q+1
       577: q+1
       581: q
       590: 1
       592: 1
       594: q+1
       596: q+1
       599: 2q+1
       600: q
       604: q+1
       608: q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       616: 1
       620: 1
       622: 1
       625: 1
       629: 1
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 3q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       699: q
       716: 1
       720: q+1
       727: q+1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       802: 1
       804: 1
       806: q+1
       808: q+1
       811: 2q+1
       812: q
       816: 1
       818: 1
       826: 1
       828: 1
       835: 1
       840: 1
       843: 1
       846: 1
       848: 1
       851: 1
       855: 1
       857: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       911: 1
       927: 1
       930: q+1
       950: 1
       967: 1
       975: 1
       991: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1012: 1
      1017: 1
      1027: 1
      1029: 1
      1033: 1
      1046: 1
      1053: 1
      1055: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1133: 1
      1135: 1
      1163: 1
      1197: 1
      1204: 1
      1217: 1
      1219: 1
      1224: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1276: 1
      1280: 1
      1283: 1
      1288: 1
      1329: 1
      1367: 1
      1369: 1
      1451: 1
      1455: 1
      1482: 1
      1578: 1

1579:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: 4q^3+9q^2+4q+1
        23: q^4+6q^3+9q^2+4q+1
        24: 4q^3+9q^2+4q+1
        25: q^3+8q^2+4q+1
        26: 3q^3+8q^2+4q+1
        27: q^3+8q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 4q^3+9q^2+4q+1
        33: 6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+8q^2+4q+1
        36: 5q^2+4q+1
        37: q^3+5q^2+3q+1
        38: 3q^2+q
        39: 2q^3+5q^2+3q+1
        40: q^3+3q^2+q
        41: q^3+5q^2+3q+1
        42: 3q^2+q
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+6q^3+9q^2+4q+1
        54: 4q^3+9q^2+4q+1
        55: q^3+8q^2+4q+1
        56: 3q^3+8q^2+4q+1
        57: q^3+8q^2+4q+1
        58: 3q^2+3q+1
        59: q^2+q
        60: 3q^2+2q+1
        61: 2q
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+5q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 5q^2+4q+1
        73: 6q^2+4q+1
        74: q^3+5q^2+3q+1
        75: 3q^2+q
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+q
        78: q^3+5q^2+3q+1
        79: 3q^2+q
        80: 3q^3+7q^2+4q+1
        81: 6q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 4q^3+9q^2+4q+1
        84: q^3+6q^2+4q+1
        85: 5q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+8q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+4q+1
        95: 6q^2+4q+1
        96: 2q^3+4q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: 3q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: 2q^2+2q+1
       104: q^2
       105: q
       106: q
       107: 3q^2+2q+1
       108: 2q
       109: 3q^2+3q+1
       110: q^2+q
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+5q^2+3q+1
       116: 3q^2+q
       117: 3q^2+3q+1
       118: q^2+q
       119: 3q^2+2q+1
       120: 2q
       121: q^3+4q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 5q^2+4q+1
       136: 6q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+2q+1
       139: 4q^2+4q+1
       140: 5q^2+4q+1
       141: 3q^3+7q^2+4q+1
       142: 6q^2+4q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+4q+1
       146: q^3+6q^2+4q+1
       147: 2q^2+4q+1
       148: 3q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: q^3+5q^2+3q+1
       152: 3q^2+q
       153: 2q^3+5q^2+3q+1
       154: q^3+3q^2+q
       155: q^3+5q^2+3q+1
       156: 3q^2+q
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 6q^2+4q+1
       161: 6q^2+4q+1
       162: 2q^3+4q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: 3q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: 2q^2+2q+1
       170: q^2
       171: q
       172: q
       173: 2q^2+2q+1
       174: q^2
       175: q
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 3q^2+2q+1
       184: 2q
       185: 3q^2+3q+1
       186: q^2+q
       187: 3q^2+3q+1
       188: 2q^2+q
       189: q^3+4q^2+3q+1
       190: 2q^2+q
       191: q^2+3q+1
       192: q
       193: 3q^2+2q+1
       194: 2q
       195: 3q^2+3q+1
       196: q^2+q
       197: 3q^2+3q+1
       198: 2q^2+q
       199: q^2+2q+1
       200: 2q
       201: q^2+2q+1
       202: 2q
       203: 3q+1
       205: 2q+1
       206: q
       207: q^2+3q+1
       208: q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+5q^2+3q+1
       212: 3q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: q^2+2q+1
       224: q^2+4q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: 4q^2+4q+1
       228: 2q^2+2q+1
       229: 5q^2+4q+1
       230: 6q^2+4q+1
       231: 2q+1
       232: q^2+4q+1
       233: q^2+2q+1
       234: 2q^2+4q+1
       235: 3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 2q^2+4q+1
       245: 3q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^3+2q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       259: q+1
       262: q
       263: 2q^2+2q+1
       264: q^2
       265: q
       266: q
       267: 2q^2+2q+1
       268: q^2
       269: q
       270: q
       271: 2q+1
       272: q
       275: q^2+2q+1
       277: q
       278: q
       279: 2q+1
       281: q+1
       283: 1
       285: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q^2+2q+1
       294: 2q
       295: q^2+3q+1
       296: q
       297: q^2+3q+1
       298: q
       299: 3q^2+2q+1
       300: 2q
       301: 2q+1
       303: 3q^2+3q+1
       304: q^2+q
       305: 3q^2+3q+1
       306: 2q^2+q
       307: q^2+2q+1
       308: 2q
       309: 3q+1
       311: q+1
       313: 2q+1
       314: q
       315: q+1
       317: 2q+1
       319: q^2+2q+1
       320: 2q
       321: 3q+1
       323: 2q+1
       324: q
       325: q^3+4q^2+3q+1
       326: 2q^2+q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: q^2+4q+1
       346: 2q+1
       347: q^2+4q+1
       348: q^2+2q+1
       349: q^2+4q+1
       350: 2q^2+2q+1
       351: 2q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 2q^2+4q+1
       370: 3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: q+1
       384: q
       385: q^2+2q+1
       387: q
       388: q
       389: q+1
       391: q
       393: 2q^2+2q+1
       394: q^2
       395: q
       396: q
       397: q+1
       401: 2q+1
       402: q
       405: 2q+1
       408: q
       413: q+1
       417: q+1
       419: 1
       421: q+1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       431: q+1
       433: q+1
       435: 2q+1
       437: q^2+2q+1
       438: 2q
       439: q^2+3q+1
       440: q
       441: q^2+3q+1
       442: q
       443: q^2+2q+1
       444: 2q
       445: 2q+1
       447: 1
       449: q+1
       451: 1
       453: q+1
       454: q
       455: q+1
       457: q+1
       459: q+1
       461: 3q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q^2+2q+1
       472: 2q
       473: 3q+1
       475: 2q+1
       476: q
       477: q+1
       479: 2q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 1
       529: 1
       533: 1
       537: q+1
       539: q
       541: q^2+2q+1
       543: q
       544: q
       545: q+1
       547: q
       549: 1
       553: q+1
       557: q+1
       561: q+1
       565: 2q+1
       567: q
       569: q+1
       573: 2q+1
       576: q
       577: q+1
       585: q+1
       589: 1
       591: q+1
       593: 1
       595: q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: q+1
       607: q+1
       609: q+1
       613: q+1
       615: q^2+2q+1
       616: 2q
       617: 2q+1
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 3q+1
       633: q+1
       639: q+1
       641: 1
       643: q+1
       645: 1
       647: q+1
       648: q
       649: q+1
       651: q+1
       653: q+1
       655: 2q+1
       656: q
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q+1
       735: q
       737: 1
       741: 1
       749: q+1
       753: 1
       757: q+1
       761: q+1
       765: 2q+1
       767: q
       769: q+1
       781: q+1
       785: 1
       787: q+1
       791: 1
       797: q+1
       801: 1
       803: q+1
       805: 1
       807: q+1
       809: q+1
       811: q+1
       815: q+1
       816: q
       821: 1
       825: 1
       827: 1
       831: 1
       833: 1
       835: 1
       839: q+1
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       868: q+1
       871: 2q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       920: 1
       924: 1
       928: 1
       944: 1
       948: 1
       960: 1
       974: 1
       988: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1022: q+1
      1026: 1
      1028: q+1
      1038: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1126: 1
      1134: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1198: 1
      1202: 1
      1220: 1
      1240: 1
      1242: 1
      1260: 1
      1266: 1
      1270: 1
      1276: 1
      1278: 1
      1289: 1
      1330: 1
      1360: 1
      1368: 1
      1418: 1
      1474: 1
      1478: 1
      1579: 1

1580:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: 4q^3+9q^2+4q+1
        23: q^4+6q^3+9q^2+4q+1
        24: 4q^3+9q^2+4q+1
        25: q^3+8q^2+4q+1
        26: 3q^3+8q^2+4q+1
        27: q^3+8q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 4q^3+9q^2+4q+1
        33: 6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+8q^2+4q+1
        36: 5q^2+4q+1
        37: q^3+5q^2+3q+1
        38: 3q^2+q
        39: 2q^3+5q^2+3q+1
        40: q^3+3q^2+q
        41: q^3+5q^2+3q+1
        42: 3q^2+q
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+6q^3+9q^2+4q+1
        54: 4q^3+9q^2+4q+1
        55: q^3+8q^2+4q+1
        56: 3q^3+8q^2+4q+1
        57: q^3+8q^2+4q+1
        58: q^2+q
        59: 3q^2+3q+1
        60: 2q
        61: 3q^2+2q+1
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+5q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 5q^2+4q+1
        73: 6q^2+4q+1
        74: q^3+5q^2+3q+1
        75: 3q^2+q
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+q
        78: q^3+5q^2+3q+1
        79: 3q^2+q
        80: 3q^3+7q^2+4q+1
        81: 6q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 4q^3+9q^2+4q+1
        84: q^3+6q^2+4q+1
        85: 5q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+8q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+4q+1
        95: 6q^2+4q+1
        96: 2q^3+4q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: 3q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q
       104: q
       105: q^2
       106: 2q^2+2q+1
       107: 2q
       108: 3q^2+2q+1
       109: q^2+q
       110: 3q^2+3q+1
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+5q^2+3q+1
       116: 3q^2+q
       117: q^2+q
       118: 3q^2+3q+1
       119: 2q
       120: 3q^2+2q+1
       121: q^3+4q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 5q^2+4q+1
       136: 6q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+2q+1
       139: 4q^2+4q+1
       140: 5q^2+4q+1
       141: 3q^3+7q^2+4q+1
       142: 6q^2+4q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+4q+1
       146: q^3+6q^2+4q+1
       147: 2q^2+4q+1
       148: 3q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: q^3+5q^2+3q+1
       152: 3q^2+q
       153: 2q^3+5q^2+3q+1
       154: q^3+3q^2+q
       155: q^3+5q^2+3q+1
       156: 3q^2+q
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 6q^2+4q+1
       161: 6q^2+4q+1
       162: 2q^3+4q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: 3q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q
       170: q
       171: q^2
       172: 2q^2+2q+1
       173: q
       174: q
       175: q^2
       176: 2q^2+2q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q
       184: 3q^2+2q+1
       185: q^2+q
       186: 3q^2+3q+1
       187: 3q^2+3q+1
       188: 2q^2+q
       189: q^3+4q^2+3q+1
       190: 2q^2+q
       191: q
       192: q^2+3q+1
       193: 2q
       194: 3q^2+2q+1
       195: q^2+q
       196: 3q^2+3q+1
       197: 3q^2+3q+1
       198: 2q^2+q
       199: 2q
       200: q^2+2q+1
       201: 2q
       202: q^2+2q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: q^2+3q+1
       208: q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+5q^2+3q+1
       212: 3q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: q^2+2q+1
       224: q^2+4q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: 4q^2+4q+1
       228: 2q^2+2q+1
       229: 5q^2+4q+1
       230: 6q^2+4q+1
       231: 2q+1
       232: q^2+4q+1
       233: q^2+2q+1
       234: 2q^2+4q+1
       235: 3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 2q^2+4q+1
       245: 3q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^3+2q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       259: q
       262: q+1
       263: q
       264: q
       265: q^2
       266: 2q^2+2q+1
       267: q
       268: q
       269: 2q^2+2q+1
       270: q^2
       273: 2q+1
       274: q
       275: q
       276: q
       278: q^2+2q+1
       279: 2q+1
       281: q+1
       284: 1
       286: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q
       294: q^2+2q+1
       295: q
       296: q^2+3q+1
       297: q^2+3q+1
       298: q
       299: 2q
       300: 3q^2+2q+1
       301: 2q+1
       303: q^2+q
       304: 3q^2+3q+1
       305: 3q^2+3q+1
       306: 2q^2+q
       307: 2q
       308: q^2+2q+1
       310: 3q+1
       311: q+1
       313: 2q+1
       314: q
       315: q+1
       317: 2q+1
       319: 2q
       320: q^2+2q+1
       322: 3q+1
       323: 2q+1
       324: q
       325: q^3+4q^2+3q+1
       326: 2q^2+q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: q^2+4q+1
       346: 2q+1
       347: q^2+4q+1
       348: q^2+2q+1
       349: q^2+4q+1
       350: 2q^2+2q+1
       351: 2q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 2q^2+4q+1
       370: 3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       381: q
       384: q+1
       385: q
       386: q
       388: q^2+2q+1
       389: q
       391: q+1
       393: q
       394: q
       395: q^2
       396: 2q^2+2q+1
       399: q+1
       403: q
       404: 2q+1
       406: 2q+1
       407: q
       413: q+1
       417: q+1
       420: 1
       422: q+1
       423: q+1
       425: q+1
       427: 2q+1
       430: 1
       432: q+1
       433: q+1
       435: 2q+1
       437: 2q
       438: q^2+2q+1
       439: q
       440: q^2+3q+1
       441: q^2+3q+1
       442: q
       443: 2q
       444: q^2+2q+1
       445: 2q+1
       448: 1
       450: q+1
       451: 1
       453: q
       454: q+1
       455: q+1
       458: q+1
       459: q+1
       462: 3q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 2q
       472: q^2+2q+1
       474: 3q+1
       475: 2q+1
       476: q
       477: q+1
       479: 2q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: 1
       532: 1
       536: 1
       537: q
       539: q+1
       541: q
       542: q
       543: q^2+2q+1
       545: q
       547: q+1
       552: 1
       555: q+1
       559: q+1
       563: q+1
       566: q
       568: 2q+1
       570: q+1
       574: q
       575: 2q+1
       577: q+1
       585: q+1
       590: 1
       592: q+1
       594: 1
       596: q+1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: q+1
       608: q+1
       609: q+1
       613: q+1
       615: 2q
       616: q^2+2q+1
       617: 2q+1
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 3q+1
       633: q+1
       639: q+1
       642: 1
       644: q+1
       645: 1
       647: q
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: 2q+1
       656: q
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       733: q
       735: q+1
       739: 1
       743: 1
       751: q+1
       756: 1
       758: q+1
       762: q+1
       766: q
       768: 2q+1
       769: q+1
       781: q+1
       786: 1
       788: q+1
       791: 1
       797: q+1
       802: 1
       804: q+1
       806: 1
       808: q+1
       809: q+1
       811: q+1
       815: q
       816: q+1
       821: 1
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       840: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       868: q+1
       871: 2q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       922: 1
       927: 1
       930: 1
       946: 1
       950: 1
       961: 1
       975: 1
       991: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1022: q+1
      1027: 1
      1029: q+1
      1038: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1127: 1
      1135: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1199: 1
      1204: 1
      1220: 1
      1241: 1
      1243: 1
      1261: 1
      1266: 1
      1271: 1
      1276: 1
      1278: 1
      1289: 1
      1331: 1
      1361: 1
      1369: 1
      1420: 1
      1474: 1
      1479: 1
      1580: 1

1581:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: 4q^3+9q^2+4q+1
        23: q^4+6q^3+9q^2+4q+1
        24: 4q^3+9q^2+4q+1
        25: q^3+8q^2+4q+1
        26: 3q^3+8q^2+4q+1
        27: q^3+8q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 4q^3+9q^2+4q+1
        33: 6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+8q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: q^3+5q^2+3q+1
        39: q^3+3q^2+q
        40: 2q^3+5q^2+3q+1
        41: 3q^2+q
        42: q^3+5q^2+3q+1
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+6q^3+9q^2+4q+1
        54: 4q^3+9q^2+4q+1
        55: q^3+8q^2+4q+1
        56: 3q^3+8q^2+4q+1
        57: q^3+8q^2+4q+1
        58: 3q^2+3q+1
        59: q^2+q
        60: 2q
        61: 3q^2+2q+1
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: 3q^2+q
        65: q^3+5q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 5q^2+4q+1
        73: 6q^2+4q+1
        74: 3q^2+q
        75: q^3+5q^2+3q+1
        76: q^3+3q^2+q
        77: 2q^3+5q^2+3q+1
        78: 3q^2+q
        79: q^3+5q^2+3q+1
        80: 3q^3+7q^2+4q+1
        81: 6q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 4q^3+9q^2+4q+1
        84: q^3+6q^2+4q+1
        85: 5q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+8q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+4q+1
        95: 6q^2+4q+1
        96: 2q^3+4q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: 3q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q
       104: q
       105: 2q^2+2q+1
       106: q^2
       107: 2q
       108: 3q^2+2q+1
       109: 3q^2+3q+1
       110: q^2+q
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: 3q^2+q
       116: q^3+5q^2+3q+1
       117: 3q^2+3q+1
       118: q^2+q
       119: 2q
       120: 3q^2+2q+1
       121: 2q^2+q
       122: q^3+4q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 5q^2+4q+1
       136: 6q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+2q+1
       139: 4q^2+4q+1
       140: 5q^2+4q+1
       141: 3q^3+7q^2+4q+1
       142: 6q^2+4q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+4q+1
       146: q^3+6q^2+4q+1
       147: 2q^2+4q+1
       148: 3q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: 3q^2+q
       152: q^3+5q^2+3q+1
       153: q^3+3q^2+q
       154: 2q^3+5q^2+3q+1
       155: 3q^2+q
       156: q^3+5q^2+3q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 6q^2+4q+1
       161: 6q^2+4q+1
       162: 2q^3+4q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: 3q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q
       170: q
       171: 2q^2+2q+1
       172: q^2
       173: q
       174: q
       175: 2q^2+2q+1
       176: q^2
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q
       184: 3q^2+2q+1
       185: 3q^2+3q+1
       186: q^2+q
       187: 2q^2+q
       188: 3q^2+3q+1
       189: 2q^2+q
       190: q^3+4q^2+3q+1
       191: q^2+3q+1
       192: q
       193: 2q
       194: 3q^2+2q+1
       195: 3q^2+3q+1
       196: q^2+q
       197: 2q^2+q
       198: 3q^2+3q+1
       199: 2q
       200: q^2+2q+1
       201: 2q
       202: q^2+2q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: q
       208: q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: 3q^2+q
       212: q^3+5q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: q^2+2q+1
       224: q^2+4q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: 4q^2+4q+1
       228: 2q^2+2q+1
       229: 5q^2+4q+1
       230: 6q^2+4q+1
       231: 2q+1
       232: q^2+4q+1
       233: q^2+2q+1
       234: 2q^2+4q+1
       235: 3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 2q^2+4q+1
       245: 3q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^3+2q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       260: q
       261: q+1
       263: q
       264: q
       265: 2q^2+2q+1
       266: q^2
       267: q
       268: q
       269: q^2
       270: 2q^2+2q+1
       271: q
       272: 2q+1
       275: q
       276: q
       277: q^2+2q+1
       280: 2q+1
       282: q+1
       284: 1
       285: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q
       294: q^2+2q+1
       295: q^2+3q+1
       296: q
       297: q
       298: q^2+3q+1
       299: 2q
       300: 3q^2+2q+1
       302: 2q+1
       303: 3q^2+3q+1
       304: q^2+q
       305: 2q^2+q
       306: 3q^2+3q+1
       307: 2q
       308: q^2+2q+1
       309: 3q+1
       312: q+1
       313: q
       314: 2q+1
       316: q+1
       318: 2q+1
       319: 2q
       320: q^2+2q+1
       321: 3q+1
       323: q
       324: 2q+1
       325: 2q^2+q
       326: q^3+4q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: q^2+4q+1
       346: 2q+1
       347: q^2+4q+1
       348: q^2+2q+1
       349: q^2+4q+1
       350: 2q^2+2q+1
       351: 2q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 2q^2+4q+1
       370: 3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       382: q
       383: q+1
       385: q
       386: q
       387: q^2+2q+1
       390: q
       392: q+1
       393: q
       394: q
       395: 2q^2+2q+1
       396: q^2
       398: q+1
       401: q
       402: 2q+1
       405: q
       408: 2q+1
       414: q+1
       418: q+1
       420: 1
       421: q+1
       424: q+1
       426: q+1
       428: 2q+1
       430: 1
       431: q+1
       434: q+1
       436: 2q+1
       437: 2q
       438: q^2+2q+1
       439: q^2+3q+1
       440: q
       441: q
       442: q^2+3q+1
       443: 2q
       444: q^2+2q+1
       446: 2q+1
       448: 1
       449: q+1
       452: 1
       453: q
       454: q+1
       456: q+1
       457: q+1
       460: q+1
       461: 3q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 2q
       472: q^2+2q+1
       473: 3q+1
       475: q
       476: 2q+1
       478: q+1
       479: q
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: 1
       531: 1
       535: 1
       538: q
       540: q+1
       541: q
       542: q
       544: q^2+2q+1
       546: q
       548: q+1
       550: 1
       554: q+1
       558: q+1
       562: q+1
       565: q
       567: 2q+1
       572: q+1
       573: q
       576: 2q+1
       581: q+1
       586: q+1
       590: 1
       591: q+1
       594: 1
       595: q+1
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: q+1
       607: q+1
       610: q+1
       614: q+1
       615: 2q
       616: q^2+2q+1
       618: 2q+1
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 3q+1
       634: q+1
       640: q+1
       642: 1
       643: q+1
       646: 1
       647: q
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       734: q
       736: q+1
       738: 1
       742: 1
       750: q+1
       755: 1
       760: q+1
       764: q+1
       765: q
       767: 2q+1
       773: q+1
       782: q+1
       786: 1
       787: q+1
       792: 1
       798: q+1
       802: 1
       803: q+1
       806: 1
       807: q+1
       810: q+1
       812: q+1
       815: q
       816: q+1
       822: 1
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       839: q+1
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       868: q+1
       871: 2q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       923: 1
       925: 1
       931: 1
       945: 1
       949: 1
       963: 1
       977: 1
       990: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1023: q+1
      1027: 1
      1028: q+1
      1039: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1129: 1
      1137: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1201: 1
      1203: 1
      1221: 1
      1241: 1
      1242: 1
      1260: 1
      1267: 1
      1270: 1
      1277: 1
      1279: 1
      1289: 1
      1333: 1
      1362: 1
      1370: 1
      1419: 1
      1475: 1
      1478: 1
      1581: 1

1582:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: 4q^3+9q^2+4q+1
        23: q^4+6q^3+9q^2+4q+1
        24: 4q^3+9q^2+4q+1
        25: q^3+8q^2+4q+1
        26: 3q^3+8q^2+4q+1
        27: q^3+8q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 4q^3+9q^2+4q+1
        33: 6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+8q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+q
        38: q^3+5q^2+3q+1
        39: q^3+3q^2+q
        40: 2q^3+5q^2+3q+1
        41: 3q^2+q
        42: q^3+5q^2+3q+1
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: 4q^3+9q^2+4q+1
        53: q^4+6q^3+9q^2+4q+1
        54: 4q^3+9q^2+4q+1
        55: q^3+8q^2+4q+1
        56: 3q^3+8q^2+4q+1
        57: q^3+8q^2+4q+1
        58: q^2+q
        59: 3q^2+3q+1
        60: 3q^2+2q+1
        61: 2q
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: 3q^2+q
        65: q^3+5q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 5q^2+4q+1
        73: 6q^2+4q+1
        74: 3q^2+q
        75: q^3+5q^2+3q+1
        76: q^3+3q^2+q
        77: 2q^3+5q^2+3q+1
        78: 3q^2+q
        79: q^3+5q^2+3q+1
        80: 3q^3+7q^2+4q+1
        81: 6q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 4q^3+9q^2+4q+1
        84: q^3+6q^2+4q+1
        85: 5q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+8q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+4q+1
        95: 6q^2+4q+1
        96: 2q^3+4q^2+2q+1
        97: 2q^2+4q+1
        98: 2q^2+4q+1
        99: 3q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q^2
       104: 2q^2+2q+1
       105: q
       106: q
       107: 3q^2+2q+1
       108: 2q
       109: q^2+q
       110: 3q^2+3q+1
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: 3q^2+q
       116: q^3+5q^2+3q+1
       117: q^2+q
       118: 3q^2+3q+1
       119: 3q^2+2q+1
       120: 2q
       121: 2q^2+q
       122: q^3+4q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 5q^2+4q+1
       136: 6q^2+4q+1
       137: q^2+4q+1
       138: 2q^2+2q+1
       139: 4q^2+4q+1
       140: 5q^2+4q+1
       141: 3q^3+7q^2+4q+1
       142: 6q^2+4q+1
       143: q^2+4q+1
       144: q^2+2q+1
       145: q^2+4q+1
       146: q^3+6q^2+4q+1
       147: 2q^2+4q+1
       148: 3q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: 3q^2+q
       152: q^3+5q^2+3q+1
       153: q^3+3q^2+q
       154: 2q^3+5q^2+3q+1
       155: 3q^2+q
       156: q^3+5q^2+3q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 6q^2+4q+1
       161: 6q^2+4q+1
       162: 2q^3+4q^2+2q+1
       163: 2q^2+4q+1
       164: 2q^2+4q+1
       165: 3q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q^2
       170: 2q^2+2q+1
       171: q
       172: q
       173: q^2
       174: 2q^2+2q+1
       175: q
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 3q^2+2q+1
       184: 2q
       185: q^2+q
       186: 3q^2+3q+1
       187: 2q^2+q
       188: 3q^2+3q+1
       189: 2q^2+q
       190: q^3+4q^2+3q+1
       191: q
       192: q^2+3q+1
       193: 3q^2+2q+1
       194: 2q
       195: q^2+q
       196: 3q^2+3q+1
       197: 2q^2+q
       198: 3q^2+3q+1
       199: q^2+2q+1
       200: 2q
       201: q^2+2q+1
       202: 2q
       204: 3q+1
       205: q
       206: 2q+1
       207: q
       208: q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: 3q^2+q
       212: q^3+5q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: q^2+2q+1
       224: q^2+4q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: 4q^2+4q+1
       228: 2q^2+2q+1
       229: 5q^2+4q+1
       230: 6q^2+4q+1
       231: 2q+1
       232: q^2+4q+1
       233: q^2+2q+1
       234: 2q^2+4q+1
       235: 3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 2q^2+4q+1
       245: 3q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: q^3+2q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       260: q+1
       261: q
       263: q^2
       264: 2q^2+2q+1
       265: q
       266: q
       267: q^2
       268: 2q^2+2q+1
       269: q
       270: q
       273: q
       274: 2q+1
       276: q^2+2q+1
       277: q
       278: q
       280: 2q+1
       282: q+1
       283: 1
       286: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q^2+2q+1
       294: 2q
       295: q
       296: q^2+3q+1
       297: q
       298: q^2+3q+1
       299: 3q^2+2q+1
       300: 2q
       302: 2q+1
       303: q^2+q
       304: 3q^2+3q+1
       305: 2q^2+q
       306: 3q^2+3q+1
       307: q^2+2q+1
       308: 2q
       310: 3q+1
       312: q+1
       313: q
       314: 2q+1
       316: q+1
       318: 2q+1
       319: q^2+2q+1
       320: 2q
       322: 3q+1
       323: q
       324: 2q+1
       325: 2q^2+q
       326: q^3+4q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: q^2+4q+1
       346: 2q+1
       347: q^2+4q+1
       348: q^2+2q+1
       349: q^2+4q+1
       350: 2q^2+2q+1
       351: 2q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: 3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 2q^2+4q+1
       370: 3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: q+1
       383: q
       386: q^2+2q+1
       387: q
       388: q
       390: q+1
       392: q
       393: q^2
       394: 2q^2+2q+1
       395: q
       396: q
       400: q+1
       403: 2q+1
       404: q
       406: q
       407: 2q+1
       414: q+1
       418: q+1
       419: 1
       422: q+1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       432: q+1
       434: q+1
       436: 2q+1
       437: q^2+2q+1
       438: 2q
       439: q
       440: q^2+3q+1
       441: q
       442: q^2+3q+1
       443: q^2+2q+1
       444: 2q
       446: 2q+1
       447: 1
       450: q+1
       452: 1
       453: q+1
       454: q
       456: q+1
       458: q+1
       460: q+1
       462: 3q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q^2+2q+1
       472: 2q
       474: 3q+1
       475: q
       476: 2q+1
       478: q+1
       479: q
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 1
       530: 1
       534: 1
       538: q+1
       540: q
       542: q^2+2q+1
       543: q
       544: q
       546: q+1
       548: q
       551: 1
       556: q+1
       560: q+1
       564: q+1
       566: 2q+1
       568: q
       571: q+1
       574: 2q+1
       575: q
       581: q+1
       586: q+1
       589: 1
       592: q+1
       593: 1
       596: q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: q+1
       608: q+1
       610: q+1
       614: q+1
       615: q^2+2q+1
       616: 2q
       618: 2q+1
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       632: 3q+1
       634: q+1
       640: q+1
       641: 1
       644: q+1
       646: 1
       647: q+1
       648: q
       650: q+1
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: q+1
       736: q
       740: 1
       744: 1
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: 2q+1
       768: q
       773: q+1
       782: q+1
       785: 1
       788: q+1
       792: 1
       798: q+1
       801: 1
       804: q+1
       805: 1
       808: q+1
       810: q+1
       812: q+1
       815: q+1
       816: q
       822: 1
       825: 1
       828: 1
       832: 1
       834: 1
       836: 1
       840: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       868: q+1
       871: 2q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       921: 1
       926: 1
       929: 1
       947: 1
       951: 1
       962: 1
       976: 1
       989: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1023: q+1
      1026: 1
      1029: q+1
      1039: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1128: 1
      1136: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1200: 1
      1205: 1
      1221: 1
      1240: 1
      1243: 1
      1261: 1
      1267: 1
      1271: 1
      1277: 1
      1279: 1
      1289: 1
      1332: 1
      1363: 1
      1371: 1
      1421: 1
      1475: 1
      1479: 1
      1582: 1

1583:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^3+q^2+2q+1
        58: q+1
        60: q^2+q+1
        61: q^2+q
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       107: q^2+q+1
       108: q^2+q
       109: q+1
       111: q+1
       113: q+1
       115: q+1
       117: q+1
       119: q+1
       120: q
       121: q+1
       123: q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       173: q+1
       177: q+1
       179: q+1
       181: q+1
       183: q+1
       184: q
       185: q+1
       187: q+1
       189: q+1
       191: q+1
       195: q+1
       199: q+1
       200: q
       201: q^2+q+1
       202: q^2+q
       203: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: 1
       258: 1
       259: q+1
       263: q+1
       271: q+1
       275: q+1
       279: 1
       281: 1
       283: q+1
       284: q
       285: q+1
       287: q+1
       289: 1
       291: q+1
       293: q+1
       294: q
       295: q+1
       297: q+1
       303: 1
       307: q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: q+1
       321: q+1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: 2q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2q+1
       353: 2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       362: 1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: q+1
       381: 1
       385: q+1
       397: q+1
       401: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q+1
       420: q
       421: q+1
       423: q+1
       425: q+1
       427: q+1
       431: 1
       439: 1
       447: q+1
       448: q
       449: q+1
       451: q+1
       453: q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       473: 1
       481: 2q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: q+1
       549: q+1
       553: 1
       557: q+1
       561: q+1
       583: 1
       585: 1
       587: 1
       589: q+1
       590: q
       591: q+1
       595: 1
       597: 1
       599: q+1
       601: 1
       607: 1
       619: q+1
       620: q
       621: q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       705: 1
       709: 1
       713: q+1
       737: 1
       741: q+1
       745: 1
       749: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 1
       807: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: q+1
       826: q
       827: q+1
       831: 1
       833: 1
       835: q+1
       837: 1
       839: 1
       841: 1
       847: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       896: 1
       900: 1
       936: 1
       940: 1
       944: 1
       948: q+1
       956: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1058: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1110: 1
      1114: 1
      1164: 1
      1168: 1
      1172: 1
      1214: 1
      1216: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1285: 1
      1314: 1
      1376: 1
      1380: 1
      1456: 1
      1460: 1
      1583: 1

1584:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^3+q^2+2q+1
        58: q+1
        60: q^2+q
        61: q^2+q+1
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       105: q+1
       107: q^2+q
       108: q^2+q+1
       109: q+1
       112: q+1
       114: q+1
       116: q+1
       117: q+1
       119: q
       120: q+1
       122: q+1
       124: q+1
       125: 2q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       171: q+1
       175: q+1
       178: q+1
       180: q+1
       182: q+1
       183: q
       184: q+1
       185: q+1
       188: q+1
       190: q+1
       191: q+1
       195: q+1
       199: q
       200: q+1
       201: q^2+q
       202: q^2+q+1
       203: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: 1
       258: 1
       261: q+1
       265: q+1
       272: q+1
       277: q+1
       280: 1
       282: 1
       283: q
       284: q+1
       285: q+1
       288: q+1
       290: 1
       292: q+1
       293: q
       294: q+1
       295: q+1
       298: q+1
       303: 1
       307: q
       308: q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: q+1
       321: q+1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: 2q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2q+1
       353: 2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: q+1
       383: 1
       387: q+1
       398: q+1
       402: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       428: q+1
       431: 1
       439: 1
       447: q
       448: q+1
       449: q+1
       452: q+1
       453: q
       454: q+1
       456: 1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       473: 1
       481: 2q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: q+1
       550: q+1
       554: 1
       558: q+1
       562: q+1
       584: 1
       586: 1
       588: 1
       589: q
       590: q+1
       591: q+1
       595: 1
       598: 1
       600: q+1
       602: 1
       607: 1
       619: q
       620: q+1
       621: q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       707: 1
       711: 1
       714: q+1
       738: 1
       742: q+1
       746: 1
       750: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 1
       807: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: q+1
       827: q+1
       831: 1
       834: 1
       836: q+1
       838: 1
       839: 1
       842: 1
       847: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       898: 1
       901: 1
       937: 1
       941: 1
       945: 1
       949: q+1
       957: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1058: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1111: 1
      1115: 1
      1165: 1
      1169: 1
      1173: 1
      1215: 1
      1216: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1285: 1
      1315: 1
      1377: 1
      1381: 1
      1457: 1
      1460: 1
      1584: 1

1585:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^3+q^2+2q+1
        59: q+1
        60: q^2+q
        61: q^2+q+1
        62: q+1
        64: q+1
        66: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       106: q+1
       107: q^2+q
       108: q^2+q+1
       110: q+1
       111: q+1
       113: q+1
       115: q+1
       118: q+1
       119: q
       120: q+1
       121: q+1
       123: q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       172: q+1
       176: q+1
       177: q+1
       179: q+1
       181: q+1
       183: q
       184: q+1
       186: q+1
       187: q+1
       189: q+1
       192: q+1
       196: q+1
       199: q
       200: q+1
       201: q^2+q
       202: q^2+q+1
       204: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: 1
       215: 1
       217: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: 1
       258: 1
       262: q+1
       266: q+1
       273: q+1
       278: q+1
       279: 1
       281: 1
       283: q
       284: q+1
       286: q+1
       287: q+1
       289: 1
       291: q+1
       293: q
       294: q+1
       296: q+1
       297: q+1
       304: 1
       307: q
       308: q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: q+1
       322: q+1
       325: q+1
       327: 1
       329: 1
       331: 1
       333: 2q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2q+1
       353: 2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       362: 1
       364: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: q+1
       384: 1
       388: q+1
       399: q+1
       404: q+1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q
       420: q+1
       422: q+1
       423: q+1
       425: q+1
       427: q+1
       432: 1
       440: 1
       447: q
       448: q+1
       450: q+1
       451: q+1
       453: q
       454: q+1
       455: 1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       467: 1
       469: q+1
       474: 1
       481: 2q+1
       482: 1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: q+1
       552: q+1
       555: 1
       559: q+1
       563: q+1
       583: 1
       585: 1
       587: 1
       589: q
       590: q+1
       592: q+1
       596: 1
       597: 1
       599: q+1
       601: 1
       608: 1
       619: q
       620: q+1
       622: q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       708: 1
       712: 1
       716: q+1
       739: 1
       743: q+1
       747: 1
       751: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 1
       808: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: q+1
       828: q+1
       832: 1
       833: 1
       835: q+1
       837: 1
       840: 1
       841: 1
       848: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       899: 1
       902: 1
       938: 1
       942: 1
       946: 1
       950: q+1
       958: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1112: 1
      1116: 1
      1166: 1
      1170: 1
      1174: 1
      1214: 1
      1217: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1285: 1
      1316: 1
      1378: 1
      1382: 1
      1456: 1
      1461: 1
      1585: 1

1586:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^3+q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^3+q^2+2q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q
        63: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       107: q^2+q+1
       108: q^2+q
       110: q+1
       112: q+1
       114: q+1
       116: q+1
       118: q+1
       119: q+1
       120: q
       122: q+1
       124: q+1
       125: 2q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 2q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 1
       161: 1
       162: 1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: q+1
       174: q+1
       178: q+1
       180: q+1
       182: q+1
       183: q+1
       184: q
       186: q+1
       188: q+1
       190: q+1
       192: q+1
       196: q+1
       199: q+1
       200: q
       201: q^2+q+1
       202: q^2+q
       204: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: 1
       216: 1
       218: 1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 1
       230: 1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 1
       257: 1
       258: 1
       260: q+1
       264: q+1
       274: q+1
       276: q+1
       280: 1
       282: 1
       283: q+1
       284: q
       286: q+1
       288: q+1
       290: 1
       292: q+1
       293: q+1
       294: q
       296: q+1
       298: q+1
       304: 1
       307: q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: q+1
       322: q+1
       326: q+1
       328: 1
       330: 1
       332: 1
       333: 2q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: 2q+1
       353: 2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: q+1
       382: 1
       386: q+1
       400: q+1
       403: q+1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q+1
       420: q
       422: q+1
       424: q+1
       426: q+1
       428: q+1
       432: 1
       440: 1
       447: q+1
       448: q
       450: q+1
       452: q+1
       453: q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 1
       468: 1
       470: q+1
       474: 1
       481: 2q+1
       482: 1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: 2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: q+1
       551: q+1
       556: 1
       560: q+1
       564: q+1
       584: 1
       586: 1
       588: 1
       589: q+1
       590: q
       592: q+1
       596: 1
       598: 1
       600: q+1
       602: 1
       608: 1
       619: q+1
       620: q
       622: q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: 2q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       706: 1
       710: 1
       715: q+1
       740: 1
       744: q+1
       748: 1
       752: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 1
       808: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: q+1
       826: q
       828: q+1
       832: 1
       834: 1
       836: q+1
       838: 1
       840: 1
       842: 1
       848: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       897: 1
       903: 1
       939: 1
       943: 1
       947: 1
       951: q+1
       959: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1059: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1113: 1
      1117: 1
      1167: 1
      1171: 1
      1175: 1
      1215: 1
      1217: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1285: 1
      1317: 1
      1379: 1
      1383: 1
      1457: 1
      1461: 1
      1586: 1

1587:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 9q^2+6q+1
        23: 9q^2+6q+1
        24: 3q^3+7q^2+5q+1
        25: 2q^3+11q^2+6q+1
        26: 2q^3+11q^2+6q+1
        27: q^4+5q^3+8q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 9q^2+6q+1
        32: 6q^2+5q+1
        33: 9q^2+6q+1
        34: 2q^3+11q^2+6q+1
        35: q^3+7q^2+5q+1
        36: 2q^3+11q^2+6q+1
        37: 6q^2+5q+1
        38: 3q^2+q
        39: 6q^2+5q+1
        40: 3q^2+q
        41: 2q^3+5q^2+4q+1
        42: q^3+2q^2+q
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: 5q^2+5q+1
        53: 5q^2+5q+1
        54: q^3+4q^2+4q+1
        55: q^3+7q^2+5q+1
        56: q^3+7q^2+5q+1
        57: 2q^3+5q^2+4q+1
        58: 4q^2+3q+1
        59: 5q^2+3q
        60: q^3+6q^2+4q+1
        61: q^3+5q^2+2q
        62: 6q^2+5q+1
        63: 3q^2+q
        64: 4q^2+4q+1
        65: 2q^2+q
        66: 6q^2+5q+1
        67: 3q^2+q
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: 6q^2+5q+1
        81: 6q^2+5q+1
        82: 5q^2+5q+1
        83: 3q^2+4q+1
        84: q^3+7q^2+5q+1
        85: q^3+7q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 4q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: 5q^2+5q+1
        95: 5q^2+5q+1
        96: q^3+4q^2+4q+1
        97: q^3+7q^2+5q+1
        98: q^3+7q^2+5q+1
        99: 2q^3+5q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 3q^2+3q+1
       104: 2q^2+q
       105: q^2
       106: 3q^2+2q
       107: 2q^2+3q+1
       108: q^2+q
       109: q^2+2q+1
       110: 2q^2+2q
       111: 3q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       117: q^2+2q+1
       118: 2q^2+2q
       119: 2q^2+3q+1
       120: q^2+q
       121: 4q^2+4q+1
       122: 2q^2+q
       123: 4q^2+4q+1
       124: 2q^2+q
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 6q^2+5q+1
       138: 3q^2+4q+1
       139: 5q^2+5q+1
       140: q^2+2q+1
       141: 3q^2+4q+1
       142: 3q^2+4q+1
       143: q^3+7q^2+5q+1
       144: 4q^2+4q+1
       145: q^3+7q^2+5q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 3q^2+4q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       151: 2q^2+4q+1
       153: 2q^2+4q+1
       155: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 3q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 3q^2+4q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       169: 2q+1
       172: q
       173: q^2+2q+1
       174: q^2+q
       176: q^2+q
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: 2q+1
       185: q+1
       186: q^2+q
       187: 2q+1
       189: q^2+3q+1
       191: q^2+2q+1
       192: 2q^2+2q
       193: q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q
       197: q+1
       199: 2q^2+3q+1
       200: q^2+q
       201: 2q^2+3q+1
       202: q^2+q
       203: q^2+2q+1
       204: 2q^2+2q
       205: 3q+1
       207: 4q^2+4q+1
       208: 2q^2+q
       209: 2q^2+4q+1
       211: q^2+3q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 3q^2+4q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 4q^2+4q+1
       232: q^2+3q+1
       233: 3q^2+4q+1
       234: q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 5q^2+5q+1
       244: q^2+2q+1
       245: 3q^2+4q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: 2q^2+3q+1
       252: q^2+3q+1
       253: 3q^2+4q+1
       254: q^3+4q^2+4q+1
       255: 3q^2+4q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: 2q+1
       262: q
       263: q+1
       267: q+1
       271: 2q+1
       273: q
       275: q^2+2q+1
       276: q^2+q
       278: q^2+q
       279: q+1
       281: 2q+1
       283: 2q+1
       285: q+1
       286: q^2+q
       287: q^2+3q+1
       289: q+1
       291: 2q+1
       293: 2q+1
       295: q+1
       296: q^2+q
       297: 2q+1
       299: q+1
       301: q+1
       303: 1
       304: q
       305: 1
       307: 2q+1
       309: q+1
       310: q^2+q
       311: 3q+1
       313: 2q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: q^2+2q+1
       321: q^2+2q+1
       322: 2q^2+2q
       323: q+1
       325: q^2+3q+1
       327: 2q+1
       329: q^2+2q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: q^2+3q+1
       353: q^2+3q+1
       354: 3q^2+4q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 4q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: 1
       397: 2q+1
       399: q
       401: q+1
       405: q+1
       409: q+1
       411: 2q+1
       413: q+1
       415: q+1
       417: q+1
       419: 2q+1
       421: q+1
       422: q^2+q
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       431: 1
       432: q
       433: 1
       435: 1
       437: q+1
       439: 1
       440: q
       441: 1
       443: 2q+2
       445: 2q+2
       447: 2q+1
       449: q+1
       450: q^2+q
       451: 2q+1
       453: 2q+1
       455: q+1
       457: q+1
       458: q^2+q
       459: 2q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: q+1
       467: 2q+1
       469: q^2+3q+1
       471: q+1
       473: 1
       474: q
       475: 1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q^2+3q+1
       500: q+1
       501: q+2
       502: 2q+1
       504: q^2+2q+1
       506: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: 1
       537: 1
       541: 1
       545: 2q+2
       549: q+1
       553: 1
       557: q+1
       561: 2q+1
       563: 2q+1
       565: 1
       569: q+1
       573: q+1
       574: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       589: q+1
       593: 1
       595: 1
       596: q
       597: 1
       599: q+1
       601: 2
       603: q+1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       613: 1
       615: 2
       617: 2
       619: 2q+1
       621: q+1
       622: q^2+q
       623: q+1
       625: 2q+1
       627: q+1
       629: q+1
       631: 1
       632: 1
       633: q+2
       635: q+1
       637: 2q+1
       639: q+1
       641: q+1
       643: 1
       644: q
       645: 1
       647: q+1
       649: 1
       650: q
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       674: 2
       676: q+1
       677: 1
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       696: q+1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 2
       737: 1
       741: q+1
       745: 1
       749: 1
       751: 1
       753: 1
       757: 1
       761: 1
       765: 1
       766: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 2
       793: 2
       795: 2
       799: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       813: 2
       815: 2
       817: 1
       818: 1
       819: q+2
       821: 1
       823: q+1
       825: q+1
       829: 1
       831: 1
       832: q
       833: 1
       835: q+1
       837: q+2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       845: q+1
       847: 1
       848: q
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       896: 1
       904: 1
       912: 1
       916: 2
       928: 1
       932: 2
       936: 1
       940: 1
       942: 1
       944: 1
       952: 1
       956: 1
       958: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       989: 1
       992: 2
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 2
      1016: 2
      1020: 1
      1024: 1
      1030: q+2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1046: 1
      1047: 1
      1050: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1098: 1
      1101: 1
      1118: 1
      1122: 1
      1144: 2
      1164: 1
      1166: 1
      1168: 1
      1176: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1206: 1
      1214: 1
      1218: 1
      1236: 1
      1248: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1272: 1
      1274: 1
      1285: 1
      1288: 1
      1302: 1
      1305: 1
      1318: 1
      1384: 1
      1388: 1
      1456: 1
      1462: 1
      1472: 1
      1587: 1

1588:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 9q^2+6q+1
        23: 9q^2+6q+1
        24: 3q^3+7q^2+5q+1
        25: 2q^3+11q^2+6q+1
        26: 2q^3+11q^2+6q+1
        27: q^4+5q^3+8q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 9q^2+6q+1
        32: 6q^2+5q+1
        33: 9q^2+6q+1
        34: 2q^3+11q^2+6q+1
        35: q^3+7q^2+5q+1
        36: 2q^3+11q^2+6q+1
        37: 3q^2+q
        38: 6q^2+5q+1
        39: 3q^2+q
        40: 6q^2+5q+1
        41: q^3+2q^2+q
        42: 2q^3+5q^2+4q+1
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: 5q^2+5q+1
        53: 5q^2+5q+1
        54: q^3+4q^2+4q+1
        55: q^3+7q^2+5q+1
        56: q^3+7q^2+5q+1
        57: 2q^3+5q^2+4q+1
        58: 5q^2+3q
        59: 4q^2+3q+1
        60: q^3+6q^2+4q+1
        61: q^3+5q^2+2q
        62: 3q^2+q
        63: 6q^2+5q+1
        64: 2q^2+q
        65: 4q^2+4q+1
        66: 3q^2+q
        67: 6q^2+5q+1
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: 6q^2+5q+1
        81: 6q^2+5q+1
        82: 5q^2+5q+1
        83: 3q^2+4q+1
        84: q^3+7q^2+5q+1
        85: q^3+7q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 4q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: 5q^2+5q+1
        95: 5q^2+5q+1
        96: q^3+4q^2+4q+1
        97: q^3+7q^2+5q+1
        98: q^3+7q^2+5q+1
        99: 2q^3+5q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 2q^2+q
       104: 3q^2+3q+1
       105: 3q^2+2q
       106: q^2
       107: 2q^2+3q+1
       108: q^2+q
       109: 2q^2+2q
       110: q^2+2q+1
       112: 3q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       117: 2q^2+2q
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: q^2+q
       121: 2q^2+q
       122: 4q^2+4q+1
       123: 2q^2+q
       124: 4q^2+4q+1
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 6q^2+5q+1
       138: 3q^2+4q+1
       139: 5q^2+5q+1
       140: q^2+2q+1
       141: 3q^2+4q+1
       142: 3q^2+4q+1
       143: q^3+7q^2+5q+1
       144: 4q^2+4q+1
       145: q^3+7q^2+5q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 3q^2+4q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       152: 2q^2+4q+1
       154: 2q^2+4q+1
       156: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 3q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 3q^2+4q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       170: 2q+1
       171: q
       173: q^2+q
       174: q^2+2q+1
       175: q^2+q
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: 2q+1
       185: q^2+q
       186: q+1
       188: 2q+1
       190: q^2+3q+1
       191: 2q^2+2q
       192: q^2+2q+1
       193: q^2+2q+1
       195: 2q^2+2q
       196: q^2+2q+1
       198: q+1
       199: 2q^2+3q+1
       200: q^2+q
       201: 2q^2+3q+1
       202: q^2+q
       203: 2q^2+2q
       204: q^2+2q+1
       206: 3q+1
       207: 2q^2+q
       208: 4q^2+4q+1
       210: 2q^2+4q+1
       212: q^2+3q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 3q^2+4q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 4q^2+4q+1
       232: q^2+3q+1
       233: 3q^2+4q+1
       234: q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 5q^2+5q+1
       244: q^2+2q+1
       245: 3q^2+4q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: 2q^2+3q+1
       252: q^2+3q+1
       253: 3q^2+4q+1
       254: q^3+4q^2+4q+1
       255: 3q^2+4q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: 2q+1
       261: q
       264: q+1
       268: q+1
       272: q
       274: 2q+1
       275: q^2+q
       276: q^2+2q+1
       277: q^2+q
       280: q+1
       282: 2q+1
       283: 2q+1
       285: q^2+q
       286: q+1
       288: q^2+3q+1
       290: q+1
       292: 2q+1
       293: 2q+1
       295: q^2+q
       296: q+1
       298: 2q+1
       299: q+1
       302: q+1
       303: q
       304: 1
       306: 1
       307: 2q+1
       309: q^2+q
       310: q+1
       312: 3q+1
       314: 2q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: q^2+2q+1
       321: 2q^2+2q
       322: q^2+2q+1
       324: q+1
       326: q^2+3q+1
       328: 2q+1
       330: q^2+2q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: q^2+3q+1
       353: q^2+3q+1
       354: 3q^2+4q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 4q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: 1
       398: q
       400: 2q+1
       403: q+1
       407: q+1
       410: q+1
       412: 2q+1
       414: q+1
       416: q+1
       418: q+1
       419: 2q+1
       421: q^2+q
       422: q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       431: q
       432: 1
       434: 1
       436: 1
       437: q+1
       439: q
       440: 1
       442: 1
       443: 2q+2
       446: 2q+2
       447: 2q+1
       449: q^2+q
       450: q+1
       452: 2q+1
       453: 2q+1
       456: q+1
       457: q^2+q
       458: q+1
       460: 2q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: q+1
       468: 2q+1
       470: q^2+3q+1
       471: q+1
       473: q
       474: 1
       476: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q^2+3q+1
       500: q+1
       501: q+2
       503: 2q+1
       505: q^2+2q+1
       507: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: 1
       538: 1
       542: 1
       546: 2q+2
       551: q+1
       556: 1
       560: q+1
       562: 2q+1
       564: 2q+1
       566: 1
       571: q+1
       573: q+1
       574: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       589: q+1
       593: 1
       595: q
       596: 1
       598: 1
       600: q+1
       602: 2
       603: q+1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       614: 1
       615: 2
       618: 2
       619: 2q+1
       621: q^2+q
       622: q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: q+1
       631: 1
       632: 1
       634: q+2
       636: q+1
       638: 2q+1
       640: q+1
       641: q+1
       643: q
       644: 1
       646: 1
       647: q+1
       649: q
       650: 1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       674: 2
       676: q+1
       677: 1
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       694: q+1
       699: q+1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 2
       740: 1
       744: q+1
       748: 1
       750: 1
       752: 1
       754: 1
       759: 1
       763: 1
       765: 1
       766: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 2
       793: 2
       796: 2
       800: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       814: 2
       815: 2
       817: 1
       818: 1
       820: q+2
       822: 1
       824: q+1
       825: q+1
       829: 1
       831: q
       832: 1
       834: 1
       836: q+1
       838: q+2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       845: q+1
       847: q
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       897: 1
       905: 1
       913: 1
       917: 2
       929: 1
       933: 2
       939: 1
       941: 1
       943: 1
       947: 1
       953: 1
       957: 1
       959: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       980: 1
       983: 1
       986: 1
       988: 1
       989: 1
       993: 2
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 2
      1016: 2
      1021: 1
      1025: 1
      1031: q+2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1046: 1
      1047: 1
      1051: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1099: 1
      1104: 1
      1119: 1
      1123: 1
      1145: 2
      1165: 1
      1167: 1
      1171: 1
      1177: 1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1207: 1
      1215: 1
      1218: 1
      1237: 1
      1249: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1273: 1
      1275: 1
      1285: 1
      1288: 1
      1303: 1
      1308: 1
      1319: 1
      1385: 1
      1389: 1
      1457: 1
      1462: 1
      1473: 1
      1588: 1

1589:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 9q^2+6q+1
        23: 9q^2+6q+1
        24: 3q^3+7q^2+5q+1
        25: 2q^3+11q^2+6q+1
        26: 2q^3+11q^2+6q+1
        27: q^4+5q^3+8q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 9q^2+6q+1
        32: 6q^2+5q+1
        33: 9q^2+6q+1
        34: 2q^3+11q^2+6q+1
        35: q^3+7q^2+5q+1
        36: 2q^3+11q^2+6q+1
        37: 6q^2+5q+1
        38: 3q^2+q
        39: 6q^2+5q+1
        40: 3q^2+q
        41: 2q^3+5q^2+4q+1
        42: q^3+2q^2+q
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: 5q^2+5q+1
        53: 5q^2+5q+1
        54: q^3+4q^2+4q+1
        55: q^3+7q^2+5q+1
        56: q^3+7q^2+5q+1
        57: 2q^3+5q^2+4q+1
        58: 5q^2+3q
        59: 4q^2+3q+1
        60: q^3+5q^2+2q
        61: q^3+6q^2+4q+1
        62: 6q^2+5q+1
        63: 3q^2+q
        64: 4q^2+4q+1
        65: 2q^2+q
        66: 6q^2+5q+1
        67: 3q^2+q
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+4q+1
        76: 2q^2+4q+1
        78: 2q^2+3q+1
        80: 6q^2+5q+1
        81: 6q^2+5q+1
        82: 5q^2+5q+1
        83: 3q^2+4q+1
        84: q^3+7q^2+5q+1
        85: q^3+7q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 4q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: 5q^2+5q+1
        95: 5q^2+5q+1
        96: q^3+4q^2+4q+1
        97: q^3+7q^2+5q+1
        98: q^3+7q^2+5q+1
        99: 2q^3+5q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: 3q^2+2q
       104: q^2
       105: 2q^2+q
       106: 3q^2+3q+1
       107: q^2+q
       108: 2q^2+3q+1
       109: 2q^2+2q
       110: q^2+2q+1
       111: 3q+1
       113: 2q^2+4q+1
       115: q^2+3q+1
       117: 2q^2+2q
       118: q^2+2q+1
       119: q^2+q
       120: 2q^2+3q+1
       121: 4q^2+4q+1
       122: 2q^2+q
       123: 4q^2+4q+1
       124: 2q^2+q
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 6q^2+5q+1
       138: 3q^2+4q+1
       139: 5q^2+5q+1
       140: q^2+2q+1
       141: 3q^2+4q+1
       142: 3q^2+4q+1
       143: q^3+7q^2+5q+1
       144: 4q^2+4q+1
       145: q^3+7q^2+5q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 3q^2+4q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       151: 2q^2+4q+1
       153: 2q^2+4q+1
       155: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 3q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 3q^2+4q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       169: q
       172: 2q+1
       173: q^2+q
       175: q^2+q
       176: q^2+2q+1
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       184: 2q+1
       185: q^2+q
       186: q+1
       187: 2q+1
       189: q^2+3q+1
       191: 2q^2+2q
       192: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+2q
       196: q^2+2q+1
       197: q+1
       199: q^2+q
       200: 2q^2+3q+1
       201: q^2+q
       202: 2q^2+3q+1
       203: 2q^2+2q
       204: q^2+2q+1
       205: 3q+1
       207: 4q^2+4q+1
       208: 2q^2+q
       209: 2q^2+4q+1
       211: q^2+3q+1
       213: 2q+1
       215: q^2+2q+1
       217: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 3q^2+4q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 4q^2+4q+1
       232: q^2+3q+1
       233: 3q^2+4q+1
       234: q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 5q^2+5q+1
       244: q^2+2q+1
       245: 3q^2+4q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: 2q^2+3q+1
       252: q^2+3q+1
       253: 3q^2+4q+1
       254: q^3+4q^2+4q+1
       255: 3q^2+4q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       259: q
       262: 2q+1
       266: q+1
       269: q+1
       271: q
       273: 2q+1
       275: q^2+q
       277: q^2+q
       278: q^2+2q+1
       279: q+1
       281: 2q+1
       284: 2q+1
       285: q^2+q
       286: q+1
       287: q^2+3q+1
       289: q+1
       291: 2q+1
       294: 2q+1
       295: q^2+q
       296: q+1
       297: 2q+1
       300: q+1
       301: q+1
       303: q
       304: 1
       305: 1
       308: 2q+1
       309: q^2+q
       310: q+1
       311: 3q+1
       313: 2q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       320: q^2+2q+1
       321: 2q^2+2q
       322: q^2+2q+1
       323: q+1
       325: q^2+3q+1
       327: 2q+1
       329: q^2+2q+1
       331: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: q^2+3q+1
       353: q^2+3q+1
       354: 3q^2+4q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 4q+2
       360: 2q+1
       362: q^2+2q+1
       364: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: 1
       397: q
       399: 2q+1
       404: q+1
       406: q+1
       409: q+1
       411: 2q+1
       413: q+1
       415: q+1
       417: q+1
       420: 2q+1
       421: q^2+q
       422: q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       430: q+1
       431: q
       432: 1
       433: 1
       435: 1
       438: q+1
       439: q
       440: 1
       441: 1
       444: 2q+2
       445: 2q+2
       448: 2q+1
       449: q^2+q
       450: q+1
       451: 2q+1
       454: 2q+1
       455: q+1
       457: q^2+q
       458: q+1
       459: 2q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: q+1
       467: 2q+1
       469: q^2+3q+1
       472: q+1
       473: q
       474: 1
       475: 1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q^2+3q+1
       500: q+1
       501: q+2
       502: 2q+1
       504: q^2+2q+1
       506: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: 1
       539: 1
       543: 1
       547: 2q+2
       552: q+1
       555: 1
       559: q+1
       561: 2q+1
       563: 2q+1
       568: 1
       570: q+1
       575: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: q+1
       590: q+1
       594: 1
       595: q
       596: 1
       597: 1
       599: q+1
       601: 2
       604: q+1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       613: 1
       616: 2
       617: 2
       620: 2q+1
       621: q^2+q
       622: q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: q+1
       631: 1
       632: 1
       633: q+2
       635: q+1
       637: 2q+1
       639: q+1
       642: q+1
       643: q
       644: 1
       645: 1
       648: q+1
       649: q
       650: 1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: 2
       673: 1
       674: 2
       676: q+1
       677: 1
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       697: q+1
       698: q+1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 2
       739: 1
       743: q+1
       747: 1
       749: 1
       751: 1
       756: 1
       758: 1
       762: 1
       767: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 2
       794: 2
       795: 2
       799: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       813: 2
       816: 2
       817: 1
       818: 1
       819: q+2
       821: 1
       823: q+1
       826: q+1
       830: 1
       831: q
       832: 1
       833: 1
       835: q+1
       837: q+2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       846: q+1
       847: q
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       888: 1
       889: 1
       899: 1
       906: 1
       914: 1
       918: 2
       930: 1
       934: 2
       938: 1
       940: 1
       942: 1
       946: 1
       955: 1
       956: 1
       958: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: 1
       982: 1
       985: 1
       990: 1
       991: 1
       992: 2
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 2
      1017: 2
      1020: 1
      1024: 1
      1030: q+2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1046: 1
      1047: 1
      1050: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1102: 1
      1103: 1
      1120: 1
      1124: 1
      1146: 2
      1164: 1
      1166: 1
      1170: 1
      1178: 1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1208: 1
      1214: 1
      1219: 1
      1236: 1
      1248: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1272: 1
      1274: 1
      1285: 1
      1288: 1
      1306: 1
      1307: 1
      1320: 1
      1386: 1
      1390: 1
      1456: 1
      1463: 1
      1472: 1
      1589: 1

1590:    0: 2q^3+11q^2+6q+1
         1: 2q^3+11q^2+6q+1
         2: q^4+5q^3+8q^2+5q+1
         3: 2q^3+11q^2+6q+1
         4: q^4+5q^3+8q^2+5q+1
         5: 2q^3+11q^2+6q+1
         6: q^4+5q^3+8q^2+5q+1
         7: q^4+4q^3+6q^2+4q+1
         8: q^4+5q^3+8q^2+5q+1
         9: q^4+4q^3+6q^2+4q+1
        10: 2q^3+11q^2+6q+1
        11: 2q^3+11q^2+6q+1
        12: q^4+5q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 2q^3+5q^2+4q+1
        15: q^3+7q^2+5q+1
        16: 2q^3+11q^2+6q+1
        17: 2q^3+11q^2+6q+1
        18: q^4+4q^3+6q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^3+7q^2+5q+1
        21: 2q^3+5q^2+4q+1
        22: 9q^2+6q+1
        23: 9q^2+6q+1
        24: 3q^3+7q^2+5q+1
        25: 2q^3+11q^2+6q+1
        26: 2q^3+11q^2+6q+1
        27: q^4+5q^3+8q^2+5q+1
        28: 2q^3+11q^2+6q+1
        29: q^3+7q^2+5q+1
        30: 4q^2+4q+1
        31: 9q^2+6q+1
        32: 6q^2+5q+1
        33: 9q^2+6q+1
        34: 2q^3+11q^2+6q+1
        35: q^3+7q^2+5q+1
        36: 2q^3+11q^2+6q+1
        37: 3q^2+q
        38: 6q^2+5q+1
        39: 3q^2+q
        40: 6q^2+5q+1
        41: q^3+2q^2+q
        42: 2q^3+5q^2+4q+1
        43: q^3+7q^2+5q+1
        44: 2q^3+5q^2+4q+1
        45: q^3+7q^2+5q+1
        46: q^3+7q^2+5q+1
        47: q^3+7q^2+5q+1
        48: 2q^3+5q^2+4q+1
        49: q^3+7q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 2q^3+5q^2+4q+1
        52: 5q^2+5q+1
        53: 5q^2+5q+1
        54: q^3+4q^2+4q+1
        55: q^3+7q^2+5q+1
        56: q^3+7q^2+5q+1
        57: 2q^3+5q^2+4q+1
        58: 4q^2+3q+1
        59: 5q^2+3q
        60: q^3+5q^2+2q
        61: q^3+6q^2+4q+1
        62: 3q^2+q
        63: 6q^2+5q+1
        64: 2q^2+q
        65: 4q^2+4q+1
        66: 3q^2+q
        67: 6q^2+5q+1
        68: 3q^2+4q+1
        69: 4q^2+4q+1
        70: 4q^2+4q+1
        71: q^3+7q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        75: 2q^2+4q+1
        77: 2q^2+4q+1
        79: 2q^2+3q+1
        80: 6q^2+5q+1
        81: 6q^2+5q+1
        82: 5q^2+5q+1
        83: 3q^2+4q+1
        84: q^3+7q^2+5q+1
        85: q^3+7q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 4q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: 2q^3+5q^2+4q+1
        91: 3q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 3q^2+4q+1
        94: 5q^2+5q+1
        95: 5q^2+5q+1
        96: q^3+4q^2+4q+1
        97: q^3+7q^2+5q+1
        98: q^3+7q^2+5q+1
        99: 2q^3+5q^2+4q+1
       100: 5q^2+5q+1
       101: 5q^2+5q+1
       102: q^3+4q^2+4q+1
       103: q^2
       104: 3q^2+2q
       105: 3q^2+3q+1
       106: 2q^2+q
       107: q^2+q
       108: 2q^2+3q+1
       109: q^2+2q+1
       110: 2q^2+2q
       112: 3q+1
       114: 2q^2+4q+1
       116: q^2+3q+1
       117: q^2+2q+1
       118: 2q^2+2q
       119: q^2+q
       120: 2q^2+3q+1
       121: 2q^2+q
       122: 4q^2+4q+1
       123: 2q^2+q
       124: 4q^2+4q+1
       125: 3q^2+4q+1
       126: 4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: q^2+3q+1
       136: 2q^2+3q+1
       137: 6q^2+5q+1
       138: 3q^2+4q+1
       139: 5q^2+5q+1
       140: q^2+2q+1
       141: 3q^2+4q+1
       142: 3q^2+4q+1
       143: q^3+7q^2+5q+1
       144: 4q^2+4q+1
       145: q^3+7q^2+5q+1
       146: 4q^2+4q+1
       147: 3q^2+4q+1
       148: 3q^2+4q+1
       149: 5q^2+5q+1
       150: 3q^2+4q+1
       152: 2q^2+4q+1
       154: 2q^2+4q+1
       156: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^3+4q^2+4q+1
       159: 3q^2+4q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: 3q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 3q^2+4q+1
       166: 5q^2+5q+1
       167: 5q^2+5q+1
       168: q^3+4q^2+4q+1
       170: q
       171: 2q+1
       174: q^2+q
       175: q^2+2q+1
       176: q^2+q
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       184: 2q+1
       185: q+1
       186: q^2+q
       188: 2q+1
       190: q^2+3q+1
       191: q^2+2q+1
       192: 2q^2+2q
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q
       198: q+1
       199: q^2+q
       200: 2q^2+3q+1
       201: q^2+q
       202: 2q^2+3q+1
       203: q^2+2q+1
       204: 2q^2+2q
       206: 3q+1
       207: 2q^2+q
       208: 4q^2+4q+1
       210: 2q^2+4q+1
       212: q^2+3q+1
       214: 2q+1
       216: q^2+2q+1
       218: 2q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+4q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 3q^2+4q+1
       227: 2q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+2q+1
       231: 4q^2+4q+1
       232: q^2+3q+1
       233: 3q^2+4q+1
       234: q^2+3q+1
       235: 2q^2+3q+1
       236: 3q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 5q^2+5q+1
       244: q^2+2q+1
       245: 3q^2+4q+1
       246: 3q^2+4q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: 2q^2+3q+1
       252: q^2+3q+1
       253: 3q^2+4q+1
       254: q^3+4q^2+4q+1
       255: 3q^2+4q+1
       256: q^2+3q+1
       257: 2q^2+3q+1
       258: q^2+3q+1
       260: q
       261: 2q+1
       265: q+1
       270: q+1
       272: 2q+1
       274: q
       276: q^2+q
       277: q^2+2q+1
       278: q^2+q
       280: q+1
       282: 2q+1
       284: 2q+1
       285: q+1
       286: q^2+q
       288: q^2+3q+1
       290: q+1
       292: 2q+1
       294: 2q+1
       295: q+1
       296: q^2+q
       298: 2q+1
       300: q+1
       302: q+1
       303: 1
       304: q
       306: 1
       308: 2q+1
       309: q+1
       310: q^2+q
       312: 3q+1
       314: 2q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: 2q^2+2q
       324: q+1
       326: q^2+3q+1
       328: 2q+1
       330: q^2+2q+1
       332: 2q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: q^2+3q+1
       353: q^2+3q+1
       354: 3q^2+4q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 4q+2
       361: 2q+1
       363: q^2+2q+1
       365: 2q+1
       366: 3q^2+4q+1
       367: 2q+1
       368: q^2+3q+1
       369: q+1
       370: q^2+2q+1
       371: q+2
       372: q+2
       373: q+1
       374: q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+3q+1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: 1
       398: 2q+1
       400: q
       402: q+1
       408: q+1
       410: q+1
       412: 2q+1
       414: q+1
       416: q+1
       418: q+1
       420: 2q+1
       421: q+1
       422: q^2+q
       424: 2q+1
       426: q+1
       428: 4q+2
       430: q+1
       431: 1
       432: q
       434: 1
       436: 1
       438: q+1
       439: 1
       440: q
       442: 1
       444: 2q+2
       446: 2q+2
       448: 2q+1
       449: q+1
       450: q^2+q
       452: 2q+1
       454: 2q+1
       456: q+1
       457: q+1
       458: q^2+q
       460: 2q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: q+1
       468: 2q+1
       470: q^2+3q+1
       472: q+1
       473: 1
       474: q
       476: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: 2
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q^2+3q+1
       500: q+1
       501: q+2
       503: 2q+1
       505: q^2+2q+1
       507: 2q+1
       508: 2q+1
       509: 2q+1
       510: q^2+3q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: 1
       540: 1
       544: 1
       548: 2q+2
       550: q+1
       554: 1
       558: q+1
       562: 2q+1
       564: 2q+1
       567: 1
       572: q+1
       575: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: q+1
       590: q+1
       594: 1
       595: 1
       596: q
       598: 1
       600: q+1
       602: 2
       604: q+1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       614: 1
       616: 2
       618: 2
       620: 2q+1
       621: q+1
       622: q^2+q
       624: q+1
       626: 2q+1
       628: q+1
       630: q+1
       631: 1
       632: 1
       634: q+2
       636: q+1
       638: 2q+1
       640: q+1
       642: q+1
       643: 1
       644: q
       646: 1
       648: q+1
       649: 1
       650: q
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: 2
       673: 1
       674: 2
       676: q+1
       677: 1
       678: 2
       679: 1
       680: q+2
       681: q+1
       682: q+1
       683: q+1
       684: q+2
       685: 1
       686: 2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       700: q+1
       701: q+1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 2
       738: 1
       742: q+1
       746: 1
       750: 1
       752: 1
       755: 1
       760: 1
       764: 1
       767: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 2
       794: 2
       796: 2
       800: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       814: 2
       816: 2
       817: 1
       818: 1
       820: q+2
       822: 1
       824: q+1
       826: q+1
       830: 1
       831: 1
       832: q
       834: 1
       836: q+1
       838: q+2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       846: q+1
       847: 1
       848: q
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       872: 1
       873: q+2
       874: 1
       875: 1
       876: 1
       878: q+1
       879: 1
       880: 1
       891: 1
       892: 1
       898: 1
       907: 1
       915: 1
       919: 2
       931: 1
       935: 2
       937: 1
       941: 1
       943: 1
       945: 1
       954: 1
       957: 1
       959: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       981: 1
       983: 1
       986: 1
       990: 1
       991: 1
       993: 2
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 2
      1017: 2
      1021: 1
      1025: 1
      1031: q+2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1046: 1
      1047: 1
      1051: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1074: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1084: 1
      1085: 1
      1093: 1
      1094: 1
      1105: 1
      1106: 1
      1121: 1
      1125: 1
      1147: 2
      1165: 1
      1167: 1
      1169: 1
      1179: 1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1209: 1
      1215: 1
      1219: 1
      1237: 1
      1249: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1273: 1
      1275: 1
      1285: 1
      1288: 1
      1309: 1
      1310: 1
      1321: 1
      1387: 1
      1391: 1
      1457: 1
      1463: 1
      1473: 1
      1590: 1

1591:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: 2q^3+q^2+3q+1
        23: 2q^3+q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^4+3q^3+3q^2+3q+1
        26: q^4+3q^3+3q^2+3q+1
        27: 3q^3+3q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: 2q^3+q^2+3q+1
        32: q^3+q^2+2q+1
        33: q^3+q^2+3q+1
        34: q^4+3q^3+3q^2+3q+1
        35: 2q^3+2q^2+2q+1
        36: q^3+3q^2+3q+1
        37: 2q^3+q^2+3q+1
        39: 2q^3+q^2+3q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: 2q^3+q^2+3q+1
        53: 2q^3+q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^4+3q^3+3q^2+3q+1
        56: q^4+3q^3+3q^2+3q+1
        57: 3q^3+3q^2+2q+1
        58: q^3+q^2+2q+1
        59: q
        60: q^3+2q^2+2q+1
        61: q^2+q
        62: 2q^3+q^2+3q+1
        64: q^3+q^2+2q+1
        66: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^3+q^2+3q+1
        74: 2q^3+q^2+3q+1
        76: 2q^3+q^2+3q+1
        78: q^3+2q^2+2q+1
        80: q^3+q^2+2q+1
        81: q^2+2q+1
        82: 2q^3+q^2+3q+1
        83: q^3+q^2+2q+1
        84: 2q^3+2q^2+2q+1
        85: 2q^2+2q+1
        86: q^4+3q^3+3q^2+3q+1
        87: 2q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^3+2q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       103: q^3+q^2+2q+1
       106: q
       107: q^3+2q^2+2q+1
       108: q^2+q
       109: q^3+q^2+2q+1
       110: q
       111: q^3+q^2+3q+1
       113: 2q^3+q^2+3q+1
       115: q^3+q^2+2q+1
       117: q^2+q+1
       119: q^2+q+1
       121: q^3+q^2+2q+1
       123: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^3+q^2+2q+1
       142: 3q+1
       143: 2q^2+2q+1
       144: q^2+2q+1
       145: q^3+3q^2+3q+1
       146: 2q^3+2q^2+2q+1
       147: q^3+3q^2+3q+1
       148: q^3+q^2+3q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       151: 2q^3+q^2+3q+1
       153: 2q^3+q^2+3q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q^3+q^2+2q+1
       172: q
       173: q^2+q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+q+1
       185: q^2+q+1
       187: q^2+2q+1
       189: q^3+q^2+2q+1
       191: q^2+q+1
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q^2+q+1
       201: q^3+2q^2+2q+1
       202: q^2+q
       203: q^3+q^2+2q+1
       204: q
       205: q^3+q^2+3q+1
       207: q^2+2q+1
       209: 2q^3+q^2+3q+1
       211: q^3+q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q^2+q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+q+1
       267: q+1
       271: q^3+q^2+2q+1
       273: q
       275: q^2+q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q^2+q+1
       295: q^2+q+1
       297: q^2+2q+1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: q^2+q+1
       309: q^2+q+1
       311: 3q+1
       313: q^2+2q+1
       315: 2q+1
       317: 3q+1
       319: q+1
       321: 2q+1
       322: q
       323: q+1
       325: q^3+q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 1
       385: q^2+q+1
       389: q+1
       393: 1
       397: 2q+1
       399: q
       401: q^2+q+1
       405: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: q+1
       447: q+1
       449: q+1
       451: 2q+1
       453: q^2+q+1
       455: q+1
       457: q^2+q+1
       459: q^2+2q+1
       461: 2q+1
       462: q
       463: 3q+1
       465: 1
       467: q+1
       469: 2q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: 1
       537: 1
       541: 1
       545: q+1
       549: q+1
       553: 1
       557: q^2+q+1
       561: 2q+1
       563: q
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       589: q+1
       591: q+1
       593: 1
       595: 1
       597: q+1
       599: 2q+1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q+1
       621: q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       631: 1
       633: q+1
       635: 1
       637: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       693: q+1
       705: 1
       709: 1
       713: q+1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: q+1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       777: 1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: 1
       791: 1
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       821: 1
       823: q+1
       825: q+1
       827: q+1
       829: 1
       831: 1
       833: q+1
       835: 2q+1
       837: q+1
       839: 1
       841: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       928: 1
       932: 1
       936: 1
       944: 1
       948: q+1
       952: 1
       956: 1
       960: 1
       974: 1
       978: 1
       982: 1
       988: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1024: 1
      1034: 1
      1038: 1
      1040: 1
      1042: q+1
      1044: 1
      1050: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1082: 1
      1085: 1
      1098: 1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1206: 1
      1222: 1
      1256: 1
      1258: 1
      1260: 1
      1272: 1
      1276: 1
      1278: 1
      1322: 1
      1376: 1
      1384: 1
      1392: 1
      1400: 1
      1480: 1
      1591: 1

1592:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: 2q^3+q^2+3q+1
        23: 2q^3+q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^4+3q^3+3q^2+3q+1
        26: q^4+3q^3+3q^2+3q+1
        27: 3q^3+3q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: 2q^3+q^2+3q+1
        32: q^3+q^2+2q+1
        33: q^3+q^2+3q+1
        34: q^4+3q^3+3q^2+3q+1
        35: 2q^3+2q^2+2q+1
        36: q^3+3q^2+3q+1
        37: 2q^3+q^2+3q+1
        39: 2q^3+q^2+3q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: 2q^3+q^2+3q+1
        53: 2q^3+q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^4+3q^3+3q^2+3q+1
        56: q^4+3q^3+3q^2+3q+1
        57: 3q^3+3q^2+2q+1
        58: q
        59: q^3+q^2+2q+1
        60: q^2+q
        61: q^3+2q^2+2q+1
        62: 2q^3+q^2+3q+1
        64: q^3+q^2+2q+1
        66: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^3+q^2+3q+1
        74: 2q^3+q^2+3q+1
        76: 2q^3+q^2+3q+1
        78: q^3+2q^2+2q+1
        80: q^3+q^2+2q+1
        81: q^2+2q+1
        82: 2q^3+q^2+3q+1
        83: q^3+q^2+2q+1
        84: 2q^3+2q^2+2q+1
        85: 2q^2+2q+1
        86: q^4+3q^3+3q^2+3q+1
        87: 2q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^3+2q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       103: q
       106: q^3+q^2+2q+1
       107: q^2+q
       108: q^3+2q^2+2q+1
       109: q
       110: q^3+q^2+2q+1
       111: q^3+q^2+3q+1
       113: 2q^3+q^2+3q+1
       115: q^3+q^2+2q+1
       118: q^2+q+1
       120: q^2+q+1
       121: q^3+q^2+2q+1
       123: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^3+q^2+2q+1
       142: 3q+1
       143: 2q^2+2q+1
       144: q^2+2q+1
       145: q^3+3q^2+3q+1
       146: 2q^3+2q^2+2q+1
       147: q^3+3q^2+3q+1
       148: q^3+q^2+3q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       151: 2q^3+q^2+3q+1
       153: 2q^3+q^2+3q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: q^3+q^2+2q+1
       176: q^2+q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q^2+q+1
       186: q^2+q+1
       187: q^2+2q+1
       189: q^3+q^2+2q+1
       192: q^2+q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       200: q^2+q+1
       201: q^2+q
       202: q^3+2q^2+2q+1
       203: q
       204: q^3+q^2+2q+1
       205: q^3+q^2+3q+1
       207: q^2+2q+1
       209: 2q^3+q^2+3q+1
       211: q^3+q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q^2+q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 2q+1
       266: q^2+q+1
       269: q+1
       271: q
       273: q^3+q^2+2q+1
       278: q^2+q+1
       279: 1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q^2+q+1
       296: q^2+q+1
       297: q^2+2q+1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: q^2+q+1
       310: q^2+q+1
       311: 3q+1
       313: q^2+2q+1
       315: 2q+1
       317: 3q+1
       320: q+1
       321: q
       322: 2q+1
       323: q+1
       325: q^3+q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       384: 1
       388: q^2+q+1
       391: q+1
       396: 1
       397: q
       399: 2q+1
       404: q^2+q+1
       406: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: q+1
       450: q+1
       451: 2q+1
       454: q^2+q+1
       455: q+1
       458: q^2+q+1
       459: q^2+2q+1
       461: q
       462: 2q+1
       463: 3q+1
       465: 1
       467: q+1
       469: 2q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: 1
       539: 1
       543: 1
       547: q+1
       552: q+1
       555: 1
       559: q^2+q+1
       561: q
       563: 2q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       590: q+1
       592: q+1
       594: 1
       596: 1
       597: q+1
       599: 2q+1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: q+1
       622: q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       632: 1
       633: q+1
       635: 1
       637: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       697: q+1
       708: 1
       712: 1
       716: q+1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: q+1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       777: 1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: 1
       791: 1
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       821: 1
       823: q+1
       826: q+1
       828: q+1
       830: 1
       832: 1
       833: q+1
       835: 2q+1
       837: q+1
       840: 1
       841: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       930: 1
       934: 1
       938: 1
       946: 1
       950: q+1
       955: 1
       958: 1
       961: 1
       975: 1
       979: 1
       982: 1
       991: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1024: 1
      1034: 1
      1038: 1
      1041: 1
      1042: q+1
      1045: 1
      1050: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1082: 1
      1085: 1
      1102: 1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1208: 1
      1222: 1
      1256: 1
      1259: 1
      1261: 1
      1272: 1
      1276: 1
      1278: 1
      1323: 1
      1378: 1
      1386: 1
      1393: 1
      1401: 1
      1480: 1
      1592: 1

1593:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: 2q^3+q^2+3q+1
        23: 2q^3+q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^4+3q^3+3q^2+3q+1
        26: q^4+3q^3+3q^2+3q+1
        27: 3q^3+3q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: 2q^3+q^2+3q+1
        32: q^3+q^2+2q+1
        33: q^3+q^2+3q+1
        34: q^4+3q^3+3q^2+3q+1
        35: 2q^3+2q^2+2q+1
        36: q^3+3q^2+3q+1
        38: 2q^3+q^2+3q+1
        40: 2q^3+q^2+3q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: 2q^3+q^2+3q+1
        53: 2q^3+q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^4+3q^3+3q^2+3q+1
        56: q^4+3q^3+3q^2+3q+1
        57: 3q^3+3q^2+2q+1
        58: q
        59: q^3+q^2+2q+1
        60: q^3+2q^2+2q+1
        61: q^2+q
        63: 2q^3+q^2+3q+1
        65: q^3+q^2+2q+1
        67: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^3+q^2+3q+1
        75: 2q^3+q^2+3q+1
        77: 2q^3+q^2+3q+1
        79: q^3+2q^2+2q+1
        80: q^3+q^2+2q+1
        81: q^2+2q+1
        82: 2q^3+q^2+3q+1
        83: q^3+q^2+2q+1
        84: 2q^3+2q^2+2q+1
        85: 2q^2+2q+1
        86: q^4+3q^3+3q^2+3q+1
        87: 2q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^3+2q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       104: q^3+q^2+2q+1
       105: q
       107: q^3+2q^2+2q+1
       108: q^2+q
       109: q
       110: q^3+q^2+2q+1
       112: q^3+q^2+3q+1
       114: 2q^3+q^2+3q+1
       116: q^3+q^2+2q+1
       118: q^2+q+1
       119: q^2+q+1
       122: q^3+q^2+2q+1
       124: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^3+q^2+2q+1
       142: 3q+1
       143: 2q^2+2q+1
       144: q^2+2q+1
       145: q^3+3q^2+3q+1
       146: 2q^3+2q^2+2q+1
       147: q^3+3q^2+3q+1
       148: q^3+q^2+3q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       152: 2q^3+q^2+3q+1
       154: 2q^3+q^2+3q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q^3+q^2+2q+1
       171: q
       174: q^2+q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+q+1
       186: q^2+q+1
       188: q^2+2q+1
       190: q^3+q^2+2q+1
       192: q^2+q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q^2+q+1
       201: q^3+2q^2+2q+1
       202: q^2+q
       203: q
       204: q^3+q^2+2q+1
       206: q^3+q^2+3q+1
       208: q^2+2q+1
       210: 2q^3+q^2+3q+1
       212: q^3+q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q^2+q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+q+1
       268: q+1
       272: q
       274: q^3+q^2+2q+1
       276: q^2+q+1
       280: 1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q^2+q+1
       296: q^2+q+1
       298: q^2+2q+1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: q^2+q+1
       310: q^2+q+1
       312: 3q+1
       314: q^2+2q+1
       316: 2q+1
       318: 3q+1
       319: q+1
       321: q
       322: 2q+1
       324: q+1
       326: q^3+q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 1
       386: q^2+q+1
       390: q+1
       394: 1
       398: q
       400: 2q+1
       403: q^2+q+1
       407: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: q+1
       450: q+1
       452: 2q+1
       453: q^2+q+1
       456: q+1
       458: q^2+q+1
       460: q^2+2q+1
       461: q
       462: 2q+1
       464: 3q+1
       466: 1
       468: q+1
       470: 2q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: 1
       538: 1
       542: 1
       546: q+1
       551: q+1
       556: 1
       560: q^2+q+1
       562: q
       564: 2q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       589: q+1
       592: q+1
       593: 1
       596: 1
       598: q+1
       600: 2q+1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q+1
       622: q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       632: 1
       634: q+1
       636: 1
       638: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       699: q+1
       706: 1
       710: 1
       715: q+1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: q+1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       778: 1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: 1
       792: 1
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       822: 1
       824: q+1
       825: q+1
       828: q+1
       829: 1
       832: 1
       834: q+1
       836: 2q+1
       838: q+1
       840: 1
       842: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       929: 1
       933: 1
       939: 1
       947: 1
       951: q+1
       953: 1
       959: 1
       962: 1
       976: 1
       980: 1
       986: 1
       989: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1025: 1
      1035: 1
      1039: 1
      1040: 1
      1043: q+1
      1045: 1
      1051: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1082: 1
      1085: 1
      1104: 1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1207: 1
      1223: 1
      1257: 1
      1258: 1
      1261: 1
      1273: 1
      1277: 1
      1279: 1
      1324: 1
      1379: 1
      1385: 1
      1394: 1
      1402: 1
      1481: 1
      1593: 1

1594:    0: q^4+3q^3+3q^2+3q+1
         1: q^4+3q^3+3q^2+3q+1
         2: 3q^3+3q^2+2q+1
         3: q^4+3q^3+3q^2+3q+1
         4: q^4+3q^3+3q^2+3q+1
         5: q^4+3q^3+3q^2+3q+1
         6: q^4+3q^3+3q^2+3q+1
         7: 3q^3+3q^2+2q+1
         8: 3q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+2q+1
        10: q^4+3q^3+3q^2+3q+1
        11: q^4+3q^3+3q^2+3q+1
        12: q^4+3q^3+3q^2+3q+1
        13: 2q^3+2q^2+2q+1
        14: 2q^3+2q^2+2q+1
        15: 2q^3+2q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^3+2q^2+2q+1
        19: q^4+3q^3+3q^2+3q+1
        20: q^4+3q^3+3q^2+3q+1
        21: 3q^3+3q^2+2q+1
        22: 2q^3+q^2+3q+1
        23: 2q^3+q^2+3q+1
        24: q^3+2q^2+2q+1
        25: q^4+3q^3+3q^2+3q+1
        26: q^4+3q^3+3q^2+3q+1
        27: 3q^3+3q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^4+3q^3+3q^2+3q+1
        30: 2q^3+2q^2+2q+1
        31: 2q^3+q^2+3q+1
        32: q^3+q^2+2q+1
        33: q^3+q^2+3q+1
        34: q^4+3q^3+3q^2+3q+1
        35: 2q^3+2q^2+2q+1
        36: q^3+3q^2+3q+1
        38: 2q^3+q^2+3q+1
        40: 2q^3+q^2+3q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+2q^2+2q+1
        44: 2q^3+2q^2+2q+1
        45: 2q^3+2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+q^2+2q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^3+2q^2+2q+1
        52: 2q^3+q^2+3q+1
        53: 2q^3+q^2+3q+1
        54: q^3+2q^2+2q+1
        55: q^4+3q^3+3q^2+3q+1
        56: q^4+3q^3+3q^2+3q+1
        57: 3q^3+3q^2+2q+1
        58: q^3+q^2+2q+1
        59: q
        60: q^2+q
        61: q^3+2q^2+2q+1
        63: 2q^3+q^2+3q+1
        65: q^3+q^2+2q+1
        67: q^3+q^2+3q+1
        68: q^2+q+1
        69: q^2+2q+1
        70: 2q^3+2q^2+2q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^3+q^2+3q+1
        75: 2q^3+q^2+3q+1
        77: 2q^3+q^2+3q+1
        79: q^3+2q^2+2q+1
        80: q^3+q^2+2q+1
        81: q^2+2q+1
        82: 2q^3+q^2+3q+1
        83: q^3+q^2+2q+1
        84: 2q^3+2q^2+2q+1
        85: 2q^2+2q+1
        86: q^4+3q^3+3q^2+3q+1
        87: 2q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^3+2q^2+2q+1
       100: 2q^3+q^2+3q+1
       101: 2q^3+q^2+3q+1
       102: q^3+2q^2+2q+1
       104: q
       105: q^3+q^2+2q+1
       107: q^2+q
       108: q^3+2q^2+2q+1
       109: q^3+q^2+2q+1
       110: q
       112: q^3+q^2+3q+1
       114: 2q^3+q^2+3q+1
       116: q^3+q^2+2q+1
       117: q^2+q+1
       120: q^2+q+1
       122: q^3+q^2+2q+1
       124: q^2+2q+1
       125: q^2+q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q^2+q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: q^3+q^2+2q+1
       142: 3q+1
       143: 2q^2+2q+1
       144: q^2+2q+1
       145: q^3+3q^2+3q+1
       146: 2q^3+2q^2+2q+1
       147: q^3+3q^2+3q+1
       148: q^3+q^2+3q+1
       149: 2q^3+q^2+3q+1
       150: q^3+q^2+2q+1
       152: 2q^3+q^2+3q+1
       154: 2q^3+q^2+3q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: q^3+q^2+2q+1
       175: q^2+q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q^2+q+1
       185: q^2+q+1
       188: q^2+2q+1
       190: q^3+q^2+2q+1
       191: q^2+q+1
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       200: q^2+q+1
       201: q^2+q
       202: q^3+2q^2+2q+1
       203: q^3+q^2+2q+1
       204: q
       206: q^3+q^2+3q+1
       208: q^2+2q+1
       210: 2q^3+q^2+3q+1
       212: q^3+q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q^2+q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q^2+q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: q^3+q^2+2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 2q+1
       265: q^2+q+1
       270: q+1
       272: q^3+q^2+2q+1
       274: q
       277: q^2+q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q^2+q+1
       295: q^2+q+1
       298: q^2+2q+1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: q^2+q+1
       309: q^2+q+1
       312: 3q+1
       314: q^2+2q+1
       316: 2q+1
       318: 3q+1
       320: q+1
       321: 2q+1
       322: q
       324: q+1
       326: q^3+q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       383: 1
       387: q^2+q+1
       392: q+1
       395: 1
       398: 2q+1
       400: q
       402: q^2+q+1
       408: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: q+1
       448: q+1
       449: q+1
       452: 2q+1
       454: q^2+q+1
       456: q+1
       457: q^2+q+1
       460: q^2+2q+1
       461: 2q+1
       462: q
       464: 3q+1
       466: 1
       468: q+1
       470: 2q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       518: q+1
       519: q+1
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: 1
       540: 1
       544: 1
       548: q+1
       550: q+1
       554: 1
       558: q^2+q+1
       562: 2q+1
       564: q
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       590: q+1
       591: q+1
       594: 1
       595: 1
       598: q+1
       600: 2q+1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: q+1
       621: q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       631: 1
       634: q+1
       636: 1
       638: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       700: q+1
       707: 1
       711: 1
       714: q+1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: q+1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       778: 1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: 1
       792: 1
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       822: 1
       824: q+1
       826: q+1
       827: q+1
       830: 1
       831: 1
       834: q+1
       836: 2q+1
       838: q+1
       839: 1
       842: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       872: 1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       931: 1
       935: 1
       937: 1
       945: 1
       949: q+1
       954: 1
       957: 1
       963: 1
       977: 1
       981: 1
       986: 1
       990: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1025: 1
      1035: 1
      1039: 1
      1041: 1
      1043: q+1
      1044: 1
      1051: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1082: 1
      1085: 1
      1105: 1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1209: 1
      1223: 1
      1257: 1
      1259: 1
      1260: 1
      1273: 1
      1277: 1
      1279: 1
      1325: 1
      1377: 1
      1387: 1
      1395: 1
      1403: 1
      1481: 1
      1594: 1

1595:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+5q+1
        26: q^3+4q^2+5q+1
        27: 2q^3+3q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^3+4q^2+5q+1
        35: q^2+3q+1
        36: q^3+4q^2+5q+1
        37: 3q+1
        38: q^2+2q
        39: 3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+5q+1
        56: q^3+4q^2+5q+1
        57: 2q^3+3q^2+3q+1
        58: q^2+3q+1
        59: 2q
        60: q^3+2q^2+3q+1
        61: 2q^2+2q
        62: 3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: 3q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^3+4q^2+5q+1
        73: q^2+5q+1
        74: 3q+1
        75: q^2+2q
        76: 3q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+q
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^3+4q^2+5q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+5q+1
        98: q^3+4q^2+5q+1
        99: 2q^3+3q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: 2q+1
       104: q
       105: q^2+q
       106: q
       107: q^3+2q^2+3q+1
       108: 2q^2+2q
       109: q^2+3q+1
       110: 2q
       111: 3q+1
       112: q^2+2q
       113: 3q+1
       114: q^2+2q
       115: 2q+1
       116: q
       117: q+1
       119: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: q^2+3q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^3+4q^2+5q+1
       146: q^2+3q+1
       147: q^3+4q^2+5q+1
       148: q^2+5q+1
       149: q^2+5q+1
       150: 3q+1
       151: 3q+1
       152: q^2+2q
       153: 3q+1
       154: q^2+2q
       155: q^2+2q+1
       156: q^2+q
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: 2q+1
       170: q
       171: q^2+q
       172: q
       173: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: q+1
       185: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       191: q+1
       193: 2q+1
       195: q^2+3q+1
       196: 2q
       197: q+1
       198: q
       199: q+1
       201: q^3+2q^2+3q+1
       202: 2q^2+2q
       203: q^2+3q+1
       204: 2q
       205: 3q+1
       206: q^2+2q
       207: 2q+1
       208: q
       209: 3q+1
       210: q^2+2q
       211: 2q+1
       212: q
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+3q+1
       232: q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 3q+1
       236: 3q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+5q+1
       244: 2q+1
       245: q^2+5q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q
       261: q^2+q
       262: q
       263: q+1
       267: q+1
       268: q
       271: 2q+1
       272: q^2+q
       273: q
       274: q
       275: q+1
       283: q+1
       285: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       293: q+1
       295: q+1
       297: 2q+1
       298: q
       299: 1
       301: q+1
       302: q
       303: 1
       305: 1
       307: q+1
       309: q+1
       311: 3q+1
       312: q^2+2q
       313: 2q+1
       314: q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: 2q+1
       321: q^2+3q+1
       322: 2q
       323: q+1
       324: q
       325: 2q+1
       326: q
       333: q+1
       334: q^2+3q+1
       335: 3q+1
       336: 3q+1
       337: q^2+5q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 3q+1
       358: 3q+1
       359: q^2+5q+1
       366: 3q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       385: q+1
       389: q+1
       390: q
       393: 1
       397: 2q+1
       398: q^2+q
       399: q
       400: q
       401: q+1
       405: q+1
       407: q
       419: q+1
       421: q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       429: 1
       431: 1
       433: 1
       437: 1
       439: 1
       441: 1
       443: 2q+1
       445: q+1
       446: q
       447: q+1
       449: q+1
       451: 2q+1
       452: q
       453: q+1
       457: q+1
       459: 2q+1
       460: q
       461: q^2+3q+1
       462: 2q
       463: 3q+1
       464: q^2+2q
       469: 2q+1
       470: q
       471: 1
       473: 1
       475: 1
       477: q+1
       478: q
       479: q+1
       480: q
       481: q+1
       482: 1
       483: 3q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+3q+1
       499: 3q+1
       500: 3q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       529: q+1
       533: 1
       541: 1
       545: q+1
       546: q
       549: q+1
       557: q+1
       561: 2q+1
       562: q^2+q
       563: q
       564: q
       565: 1
       569: q+1
       571: q
       573: q+1
       574: q
       577: q+1
       581: q
       589: q+1
       591: q+1
       593: 1
       595: 1
       599: 2q+1
       600: q
       603: 1
       607: 1
       609: 1
       613: 1
       615: 1
       619: q+1
       621: q+1
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       653: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 3q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       699: q
       713: q+1
       717: 1
       725: 1
       741: q+1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       793: 1
       805: 1
       807: 1
       811: 1
       815: 1
       817: 1
       825: q+1
       827: q+1
       829: 1
       831: 1
       835: 2q+1
       836: q
       839: 1
       843: 1
       845: 1
       847: 1
       851: 1
       855: 1
       857: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       908: 1
       928: 1
       948: q+1
       952: 1
       964: 1
       974: 1
       988: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1012: 1
      1016: 1
      1032: 1
      1040: 1
      1044: 1
      1046: 1
      1056: 1
      1058: 1
      1062: 1
      1064: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1130: 1
      1134: 1
      1180: 1
      1194: 1
      1206: 1
      1216: 1
      1218: 1
      1224: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1276: 1
      1280: 1
      1285: 1
      1288: 1
      1326: 1
      1396: 1
      1400: 1
      1460: 1
      1462: 1
      1482: 1
      1595: 1

1596:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+5q+1
        26: q^3+4q^2+5q+1
        27: 2q^3+3q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^3+4q^2+5q+1
        35: q^2+3q+1
        36: q^3+4q^2+5q+1
        37: q^2+2q
        38: 3q+1
        39: q^2+2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+5q+1
        56: q^3+4q^2+5q+1
        57: 2q^3+3q^2+3q+1
        58: 2q
        59: q^2+3q+1
        60: q^3+2q^2+3q+1
        61: 2q^2+2q
        62: q^2+2q
        63: 3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: 3q+1
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^3+4q^2+5q+1
        73: q^2+5q+1
        74: q^2+2q
        75: 3q+1
        76: q^2+2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^3+4q^2+5q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+5q+1
        98: q^3+4q^2+5q+1
        99: 2q^3+3q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q
       104: 2q+1
       105: q
       106: q^2+q
       107: q^3+2q^2+3q+1
       108: 2q^2+2q
       109: 2q
       110: q^2+3q+1
       111: q^2+2q
       112: 3q+1
       113: q^2+2q
       114: 3q+1
       115: q
       116: 2q+1
       118: q+1
       119: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: q^2+3q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^3+4q^2+5q+1
       146: q^2+3q+1
       147: q^3+4q^2+5q+1
       148: q^2+5q+1
       149: q^2+5q+1
       150: 3q+1
       151: q^2+2q
       152: 3q+1
       153: q^2+2q
       154: 3q+1
       155: q^2+q
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q
       170: 2q+1
       171: q
       172: q^2+q
       174: q+1
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: q+1
       186: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       192: q+1
       193: 2q+1
       195: 2q
       196: q^2+3q+1
       197: q
       198: q+1
       199: q+1
       201: q^3+2q^2+3q+1
       202: 2q^2+2q
       203: 2q
       204: q^2+3q+1
       205: q^2+2q
       206: 3q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 3q+1
       211: q
       212: 2q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+3q+1
       232: q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 3q+1
       236: 3q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+5q+1
       244: 2q+1
       245: q^2+5q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: 2q+1
       261: q
       262: q^2+q
       264: q+1
       267: q
       268: q+1
       271: q
       272: q
       273: q^2+q
       274: 2q+1
       276: q+1
       283: q+1
       286: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       293: q+1
       296: q+1
       297: q
       298: 2q+1
       299: 1
       301: q
       302: q+1
       304: 1
       306: 1
       307: q+1
       310: q+1
       311: q^2+2q
       312: 3q+1
       313: q
       314: 2q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: 2q+1
       321: 2q
       322: q^2+3q+1
       323: q
       324: q+1
       325: q
       326: 2q+1
       333: q+1
       334: q^2+3q+1
       335: 3q+1
       336: 3q+1
       337: q^2+5q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 3q+1
       358: 3q+1
       359: q^2+5q+1
       366: 3q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       386: q+1
       389: q
       390: q+1
       394: 1
       397: q
       398: q
       399: q^2+q
       400: 2q+1
       403: q+1
       405: q
       407: q+1
       419: q+1
       422: q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       429: 1
       432: 1
       434: 1
       437: 1
       440: 1
       442: 1
       443: 2q+1
       445: q
       446: q+1
       447: q+1
       450: q+1
       451: q
       452: 2q+1
       453: q+1
       458: q+1
       459: q
       460: 2q+1
       461: 2q
       462: q^2+3q+1
       463: q^2+2q
       464: 3q+1
       469: q
       470: 2q+1
       471: 1
       474: 1
       476: 1
       477: q
       478: q+1
       479: q
       480: q+1
       481: q+1
       482: 1
       483: 3q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+3q+1
       499: 3q+1
       500: 3q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       530: q+1
       534: 1
       542: 1
       545: q
       546: q+1
       551: q+1
       560: q+1
       561: q
       562: q
       563: q^2+q
       564: 2q+1
       566: 1
       569: q
       571: q+1
       573: q
       574: q+1
       577: q
       581: q+1
       589: q+1
       592: q+1
       593: 1
       596: 1
       599: q
       600: 2q+1
       603: 1
       608: 1
       610: 1
       614: 1
       615: 1
       619: q+1
       622: q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       632: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       654: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 3q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q
       699: q+1
       715: q+1
       718: 1
       726: 1
       744: q+1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       792: 1
       793: 1
       805: 1
       808: 1
       812: 1
       815: 1
       818: 1
       825: q+1
       828: q+1
       829: 1
       832: 1
       835: q
       836: 2q+1
       840: 1
       844: 1
       845: 1
       848: 1
       852: 1
       856: 1
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       909: 1
       929: 1
       951: q+1
       953: 1
       965: 1
       976: 1
       989: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1013: 1
      1016: 1
      1033: 1
      1040: 1
      1045: 1
      1047: 1
      1056: 1
      1059: 1
      1063: 1
      1065: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1131: 1
      1136: 1
      1181: 1
      1195: 1
      1207: 1
      1217: 1
      1218: 1
      1225: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1277: 1
      1281: 1
      1285: 1
      1288: 1
      1327: 1
      1397: 1
      1402: 1
      1461: 1
      1462: 1
      1483: 1
      1596: 1

1597:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+5q+1
        26: q^3+4q^2+5q+1
        27: 2q^3+3q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^3+4q^2+5q+1
        35: q^2+3q+1
        36: q^3+4q^2+5q+1
        37: q^2+2q
        38: 3q+1
        39: q^2+2q
        40: 3q+1
        41: q^2+q
        42: q^2+2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+5q+1
        56: q^3+4q^2+5q+1
        57: 2q^3+3q^2+3q+1
        58: q^2+3q+1
        59: 2q
        60: 2q^2+2q
        61: q^3+2q^2+3q+1
        62: q^2+2q
        63: 3q+1
        64: q
        65: 2q+1
        66: q^2+2q
        67: 3q+1
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^3+4q^2+5q+1
        73: q^2+5q+1
        74: q^2+2q
        75: 3q+1
        76: q^2+2q
        77: 3q+1
        78: q^2+q
        79: q^2+2q+1
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^3+4q^2+5q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+5q+1
        98: q^3+4q^2+5q+1
        99: 2q^3+3q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q^2+q
       104: q
       105: 2q+1
       106: q
       107: 2q^2+2q
       108: q^3+2q^2+3q+1
       109: q^2+3q+1
       110: 2q
       111: q^2+2q
       112: 3q+1
       113: q^2+2q
       114: 3q+1
       115: q
       116: 2q+1
       117: q+1
       120: q+1
       121: q
       122: 2q+1
       123: q
       124: 2q+1
       125: q+1
       126: q^2+3q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^3+4q^2+5q+1
       146: q^2+3q+1
       147: q^3+4q^2+5q+1
       148: q^2+5q+1
       149: q^2+5q+1
       150: 3q+1
       151: q^2+2q
       152: 3q+1
       153: q^2+2q
       154: 3q+1
       155: q^2+q
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q^2+q
       170: q
       171: 2q+1
       172: q
       175: q+1
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       184: q+1
       185: q+1
       187: q
       188: 2q+1
       189: q
       190: 2q+1
       191: q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q
       197: q
       198: q+1
       200: q+1
       201: 2q^2+2q
       202: q^3+2q^2+3q+1
       203: q^2+3q+1
       204: 2q
       205: q^2+2q
       206: 3q+1
       207: q
       208: 2q+1
       209: q^2+2q
       210: 3q+1
       211: q
       212: 2q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+3q+1
       232: q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 3q+1
       236: 3q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+5q+1
       244: 2q+1
       245: q^2+5q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q
       260: q
       261: 2q+1
       262: q
       265: q+1
       269: q
       270: q+1
       271: q^2+q
       272: 2q+1
       273: q
       274: q
       277: q+1
       284: q+1
       285: q+1
       287: q
       288: 2q+1
       291: q
       292: 2q+1
       294: q+1
       295: q+1
       297: q
       298: 2q+1
       300: 1
       301: q
       302: q+1
       303: 1
       306: 1
       308: q+1
       309: q+1
       311: q^2+2q
       312: 3q+1
       313: q
       314: 2q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       320: 2q+1
       321: q^2+3q+1
       322: 2q
       323: q
       324: q+1
       325: q
       326: 2q+1
       333: q+1
       334: q^2+3q+1
       335: 3q+1
       336: 3q+1
       337: q^2+5q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 3q+1
       358: 3q+1
       359: q^2+5q+1
       366: 3q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       387: q+1
       391: q
       392: q+1
       395: 1
       397: q^2+q
       398: 2q+1
       399: q
       400: q
       402: q+1
       406: q
       408: q+1
       420: q+1
       421: q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       430: 1
       431: 1
       434: 1
       438: 1
       439: 1
       442: 1
       444: 2q+1
       445: q
       446: q+1
       448: q+1
       449: q+1
       451: q
       452: 2q+1
       454: q+1
       457: q+1
       459: q
       460: 2q+1
       461: q^2+3q+1
       462: 2q
       463: q^2+2q
       464: 3q+1
       469: q
       470: 2q+1
       472: 1
       473: 1
       476: 1
       477: q
       478: q+1
       479: q
       480: q+1
       481: q+1
       482: 1
       483: 3q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+3q+1
       499: 3q+1
       500: 3q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       531: q+1
       535: 1
       544: 1
       547: q
       548: q+1
       550: q+1
       558: q+1
       561: q^2+q
       562: 2q+1
       563: q
       564: q
       567: 1
       570: q
       572: q+1
       575: q
       576: q+1
       577: q
       581: q+1
       590: q+1
       591: q+1
       594: 1
       595: 1
       599: q
       600: 2q+1
       604: 1
       607: 1
       610: 1
       614: 1
       616: 1
       620: q+1
       621: q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       654: 1
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 3q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q
       700: q+1
       714: q+1
       719: 1
       728: 1
       742: q+1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       792: 1
       794: 1
       806: 1
       807: 1
       812: 1
       816: 1
       817: 1
       826: q+1
       827: q+1
       830: 1
       831: 1
       835: q
       836: 2q+1
       839: 1
       844: 1
       846: 1
       847: 1
       852: 1
       856: 1
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       910: 1
       931: 1
       949: q+1
       954: 1
       966: 1
       977: 1
       990: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1013: 1
      1017: 1
      1032: 1
      1041: 1
      1044: 1
      1047: 1
      1057: 1
      1058: 1
      1063: 1
      1065: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1132: 1
      1137: 1
      1182: 1
      1196: 1
      1209: 1
      1216: 1
      1219: 1
      1225: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1277: 1
      1281: 1
      1285: 1
      1288: 1
      1328: 1
      1398: 1
      1403: 1
      1460: 1
      1463: 1
      1483: 1
      1597: 1

1598:    0: q^3+4q^2+5q+1
         1: q^3+4q^2+5q+1
         2: 2q^3+3q^2+3q+1
         3: q^3+4q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^3+4q^2+5q+1
         7: 2q^3+3q^2+3q+1
         8: 2q^3+3q^2+3q+1
         9: 2q^3+3q^2+3q+1
        10: q^3+4q^2+5q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^3+4q^2+5q+1
        17: q^3+4q^2+5q+1
        18: 2q^3+3q^2+3q+1
        19: q^3+4q^2+5q+1
        20: q^3+4q^2+5q+1
        21: 2q^3+3q^2+3q+1
        22: q^2+5q+1
        23: q^2+5q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+5q+1
        26: q^3+4q^2+5q+1
        27: 2q^3+3q^2+3q+1
        28: q^3+4q^2+5q+1
        29: q^3+4q^2+5q+1
        30: q^2+3q+1
        31: q^2+5q+1
        32: 3q+1
        33: q^2+5q+1
        34: q^3+4q^2+5q+1
        35: q^2+3q+1
        36: q^3+4q^2+5q+1
        37: 3q+1
        38: q^2+2q
        39: 3q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+q
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^3+4q^2+5q+1
        50: q^3+4q^2+5q+1
        51: 2q^3+3q^2+3q+1
        52: q^2+5q+1
        53: q^2+5q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+5q+1
        56: q^3+4q^2+5q+1
        57: 2q^3+3q^2+3q+1
        58: 2q
        59: q^2+3q+1
        60: 2q^2+2q
        61: q^3+2q^2+3q+1
        62: 3q+1
        63: q^2+2q
        64: 2q+1
        65: q
        66: 3q+1
        67: q^2+2q
        68: q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q^3+4q^2+5q+1
        72: q^3+4q^2+5q+1
        73: q^2+5q+1
        74: 3q+1
        75: q^2+2q
        76: 3q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+q
        80: 3q+1
        81: 3q+1
        82: q^2+5q+1
        83: 3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^3+4q^2+5q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+5q+1
        95: q^2+5q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+5q+1
        98: q^3+4q^2+5q+1
        99: 2q^3+3q^2+3q+1
       100: q^2+5q+1
       101: q^2+5q+1
       102: 2q^2+3q+1
       103: q
       104: q^2+q
       105: q
       106: 2q+1
       107: 2q^2+2q
       108: q^3+2q^2+3q+1
       109: 2q
       110: q^2+3q+1
       111: 3q+1
       112: q^2+2q
       113: 3q+1
       114: q^2+2q
       115: 2q+1
       116: q
       118: q+1
       120: q+1
       121: 2q+1
       122: q
       123: 2q+1
       124: q
       125: q+1
       126: q^2+3q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: q^2+5q+1
       140: 2q+1
       141: 3q+1
       142: q^2+5q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^3+4q^2+5q+1
       146: q^2+3q+1
       147: q^3+4q^2+5q+1
       148: q^2+5q+1
       149: q^2+5q+1
       150: 3q+1
       151: 3q+1
       152: q^2+2q
       153: 3q+1
       154: q^2+2q
       155: q^2+2q+1
       156: q^2+q
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+5q+1
       167: q^2+5q+1
       168: 2q^2+3q+1
       169: q
       170: q^2+q
       171: q
       172: 2q+1
       176: q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       184: q+1
       186: q+1
       187: 2q+1
       188: q
       189: 2q+1
       190: q
       192: q+1
       194: 2q+1
       195: 2q
       196: q^2+3q+1
       197: q+1
       198: q
       200: q+1
       201: 2q^2+2q
       202: q^3+2q^2+3q+1
       203: 2q
       204: q^2+3q+1
       205: 3q+1
       206: q^2+2q
       207: 2q+1
       208: q
       209: 3q+1
       210: q^2+2q
       211: 2q+1
       212: q
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+3q+1
       232: q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 3q+1
       236: 3q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+5q+1
       244: 2q+1
       245: q^2+5q+1
       246: 3q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 2q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: q^2+q
       261: q
       262: 2q+1
       266: q+1
       269: q+1
       270: q
       271: q
       272: q
       273: 2q+1
       274: q^2+q
       278: q+1
       284: q+1
       286: q+1
       287: 2q+1
       288: q
       291: 2q+1
       292: q
       294: q+1
       296: q+1
       297: 2q+1
       298: q
       300: 1
       301: q+1
       302: q
       304: 1
       305: 1
       308: q+1
       310: q+1
       311: 3q+1
       312: q^2+2q
       313: 2q+1
       314: q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       320: 2q+1
       321: 2q
       322: q^2+3q+1
       323: q+1
       324: q
       325: 2q+1
       326: q
       333: q+1
       334: q^2+3q+1
       335: 3q+1
       336: 3q+1
       337: q^2+5q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 3q+1
       358: 3q+1
       359: q^2+5q+1
       366: 3q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       388: q+1
       391: q+1
       392: q
       396: 1
       397: q
       398: q
       399: 2q+1
       400: q^2+q
       404: q+1
       406: q+1
       408: q
       420: q+1
       422: q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       430: 1
       432: 1
       433: 1
       438: 1
       440: 1
       441: 1
       444: 2q+1
       445: q+1
       446: q
       448: q+1
       450: q+1
       451: 2q+1
       452: q
       454: q+1
       458: q+1
       459: 2q+1
       460: q
       461: 2q
       462: q^2+3q+1
       463: 3q+1
       464: q^2+2q
       469: 2q+1
       470: q
       472: 1
       474: 1
       475: 1
       477: q+1
       478: q
       479: q+1
       480: q
       481: q+1
       482: 1
       483: 3q+1
       484: 1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+3q+1
       499: 3q+1
       500: 3q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       532: q+1
       536: 1
       543: 1
       547: q+1
       548: q
       552: q+1
       559: q+1
       561: q
       562: q
       563: 2q+1
       564: q^2+q
       568: 1
       570: q+1
       572: q
       575: q+1
       576: q
       577: q+1
       581: q
       590: q+1
       592: q+1
       594: 1
       596: 1
       599: 2q+1
       600: q
       604: 1
       608: 1
       609: 1
       613: 1
       616: 1
       620: q+1
       622: q+1
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       632: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       653: 1
       655: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 3q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       700: q
       716: q+1
       720: 1
       727: 1
       743: q+1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       794: 1
       806: 1
       808: 1
       811: 1
       816: 1
       818: 1
       826: q+1
       828: q+1
       830: 1
       832: 1
       835: 2q+1
       836: q
       840: 1
       843: 1
       846: 1
       848: 1
       851: 1
       855: 1
       857: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       911: 1
       930: 1
       950: q+1
       955: 1
       967: 1
       975: 1
       991: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1012: 1
      1017: 1
      1033: 1
      1041: 1
      1045: 1
      1046: 1
      1057: 1
      1059: 1
      1062: 1
      1064: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1133: 1
      1135: 1
      1183: 1
      1197: 1
      1208: 1
      1217: 1
      1219: 1
      1224: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1276: 1
      1280: 1
      1285: 1
      1288: 1
      1329: 1
      1399: 1
      1401: 1
      1461: 1
      1463: 1
      1482: 1
      1598: 1

1599:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: q^3+8q^2+4q+1
        23: 3q^3+8q^2+4q+1
        24: q^3+8q^2+4q+1
        25: 4q^3+9q^2+4q+1
        26: q^4+6q^3+9q^2+4q+1
        27: 4q^3+9q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+8q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 4q^3+9q^2+4q+1
        36: 6q^2+4q+1
        37: q^3+5q^2+3q+1
        38: 3q^2+q
        39: 2q^3+5q^2+3q+1
        40: q^3+3q^2+q
        41: q^3+5q^2+3q+1
        42: 3q^2+q
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: q^3+8q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: q^3+8q^2+4q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+6q^3+9q^2+4q+1
        57: 4q^3+9q^2+4q+1
        58: 3q^2+2q+1
        59: 2q
        60: 3q^2+3q+1
        61: q^2+q
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+5q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 6q^2+4q+1
        73: 5q^2+4q+1
        74: q^3+5q^2+3q+1
        75: 3q^2+q
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+q
        78: q^3+5q^2+3q+1
        79: 3q^2+q
        80: q^3+6q^2+4q+1
        81: 5q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+8q^2+4q+1
        84: 3q^3+7q^2+4q+1
        85: 6q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 4q^3+9q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: 3q^2+2q+1
        97: 6q^2+4q+1
        98: 6q^2+4q+1
        99: 2q^3+4q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: 2q^2+2q+1
       104: q
       105: q^2
       106: q
       107: 3q^2+3q+1
       108: q^2+q
       109: 3q^2+2q+1
       110: 2q
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+5q^2+3q+1
       116: 3q^2+q
       117: 3q^2+2q+1
       118: 2q
       119: 3q^2+3q+1
       120: q^2+q
       121: q^3+4q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 6q^2+4q+1
       136: 5q^2+4q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^3+6q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+2q+1
       145: 4q^2+4q+1
       146: 3q^3+7q^2+4q+1
       147: 6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: q^3+5q^2+3q+1
       152: 3q^2+q
       153: 2q^3+5q^2+3q+1
       154: q^3+3q^2+q
       155: q^3+5q^2+3q+1
       156: 3q^2+q
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: 3q^2+2q+1
       163: 6q^2+4q+1
       164: 6q^2+4q+1
       165: 2q^3+4q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: 2q^2+2q+1
       170: q
       171: q^2
       172: q
       173: 2q^2+2q+1
       174: q
       175: q^2
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 3q^2+3q+1
       184: q^2+q
       185: 3q^2+2q+1
       186: 2q
       187: 3q^2+3q+1
       188: 2q^2+q
       189: q^3+4q^2+3q+1
       190: 2q^2+q
       191: q^2+2q+1
       192: 2q
       193: 3q+1
       195: q^2+2q+1
       196: 2q
       197: 2q+1
       198: q
       199: q^2+3q+1
       200: q
       201: 3q^2+3q+1
       202: q^2+q
       203: 3q^2+2q+1
       204: 2q
       205: 3q^2+3q+1
       206: 2q^2+q
       207: q^2+3q+1
       208: q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+5q^2+3q+1
       212: 3q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: 2q^2+2q+1
       224: q^2+4q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+4q+1
       228: q^2+2q+1
       229: 3q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 4q^2+4q+1
       233: 2q^2+2q+1
       234: 6q^2+4q+1
       235: 5q^2+4q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 3q+1
       245: 2q^2+4q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^3+2q^2+2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       259: q+1
       262: q
       263: 2q^2+2q+1
       264: q
       265: q^2
       266: q
       267: 2q+1
       268: q
       271: 2q^2+2q+1
       272: q^2
       273: q
       274: q
       275: q^2+2q+1
       276: q
       278: q
       279: 2q+1
       281: q+1
       283: q+1
       285: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: q^2+3q+1
       294: q
       295: q^2+2q+1
       296: 2q
       297: q^2+3q+1
       298: q
       299: 3q+1
       301: q+1
       303: q^2+2q+1
       304: 2q
       305: 2q+1
       306: q
       307: 3q^2+3q+1
       308: q^2+q
       309: 3q^2+2q+1
       310: 2q
       311: 2q+1
       313: 3q^2+3q+1
       314: 2q^2+q
       315: q+1
       317: 2q+1
       319: 3q+1
       321: q^2+2q+1
       322: 2q
       323: 2q+1
       324: q
       325: q^3+4q^2+3q+1
       326: 2q^2+q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: q^2+4q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q^2+2q+1
       357: q^2+4q+1
       358: q^2+2q+1
       359: 2q^2+4q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 3q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: q+1
       384: q
       385: q^2+2q+1
       386: q
       388: q
       389: q+1
       393: 2q+1
       394: q
       397: q+1
       399: q
       401: 2q^2+2q+1
       402: q^2
       403: q
       404: q
       405: 2q+1
       407: q
       413: q+1
       417: q+1
       419: q+1
       421: 1
       423: q+1
       425: q+1
       427: 2q+1
       429: q+1
       431: 1
       433: 1
       435: q+1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: 3q+1
       445: q+1
       447: q+1
       449: 1
       451: q+1
       453: q^2+3q+1
       454: q
       455: 2q+1
       457: q^2+2q+1
       458: 2q
       459: q^2+3q+1
       460: q
       461: q^2+2q+1
       462: 2q
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 3q+1
       473: q^2+2q+1
       474: 2q
       475: 2q+1
       476: q
       477: q+1
       479: 2q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 1
       529: 1
       533: 1
       537: q+1
       541: q+1
       545: q+1
       549: 1
       553: q+1
       555: q
       557: q^2+2q+1
       559: q
       560: q
       561: q+1
       563: q
       565: 2q+1
       566: q
       569: q+1
       573: 2q+1
       574: q
       577: q+1
       585: q+1
       589: q+1
       591: 1
       593: q+1
       595: 1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: 3q+1
       617: q+1
       619: q+1
       621: 1
       623: q+1
       625: q+1
       629: q+1
       631: q^2+2q+1
       632: 2q
       633: 2q+1
       639: q+1
       641: q+1
       643: 1
       645: 1
       647: q+1
       649: q+1
       650: q
       651: q+1
       653: q+1
       655: 2q+1
       656: q
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: q+1
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q+1
       737: 1
       741: 1
       749: q+1
       751: q
       753: 1
       757: q+1
       761: q+1
       765: 2q+1
       766: q
       769: q+1
       781: q+1
       785: q+1
       787: 1
       791: 1
       797: 1
       801: 1
       805: 1
       807: 1
       809: 1
       811: 1
       815: q+1
       821: q+1
       825: q+1
       827: 1
       829: q+1
       831: 1
       833: q+1
       835: q+1
       839: q+1
       840: q
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       868: q+1
       871: 1
       872: 1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       920: 1
       928: 1
       944: 1
       948: 1
       952: 1
       960: 1
       974: 1
       988: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1022: 1
      1026: 1
      1038: q+1
      1040: q+1
      1044: 1
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1126: 1
      1134: 1
      1156: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1206: 1
      1220: 1
      1240: 1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1276: 1
      1278: 1
      1289: 1
      1330: 1
      1392: 1
      1400: 1
      1422: 1
      1474: 1
      1476: 1
      1599: 1

1600:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: q^3+8q^2+4q+1
        23: 3q^3+8q^2+4q+1
        24: q^3+8q^2+4q+1
        25: 4q^3+9q^2+4q+1
        26: q^4+6q^3+9q^2+4q+1
        27: 4q^3+9q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+8q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 4q^3+9q^2+4q+1
        36: 6q^2+4q+1
        37: q^3+5q^2+3q+1
        38: 3q^2+q
        39: 2q^3+5q^2+3q+1
        40: q^3+3q^2+q
        41: q^3+5q^2+3q+1
        42: 3q^2+q
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: q^3+8q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: q^3+8q^2+4q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+6q^3+9q^2+4q+1
        57: 4q^3+9q^2+4q+1
        58: 2q
        59: 3q^2+2q+1
        60: q^2+q
        61: 3q^2+3q+1
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+5q^2+3q+1
        65: 3q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 6q^2+4q+1
        73: 5q^2+4q+1
        74: q^3+5q^2+3q+1
        75: 3q^2+q
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+q
        78: q^3+5q^2+3q+1
        79: 3q^2+q
        80: q^3+6q^2+4q+1
        81: 5q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+8q^2+4q+1
        84: 3q^3+7q^2+4q+1
        85: 6q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 4q^3+9q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: 3q^2+2q+1
        97: 6q^2+4q+1
        98: 6q^2+4q+1
        99: 2q^3+4q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q
       104: q^2
       105: q
       106: 2q^2+2q+1
       107: q^2+q
       108: 3q^2+3q+1
       109: 2q
       110: 3q^2+2q+1
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+5q^2+3q+1
       116: 3q^2+q
       117: 2q
       118: 3q^2+2q+1
       119: q^2+q
       120: 3q^2+3q+1
       121: q^3+4q^2+3q+1
       122: 2q^2+q
       123: 3q^2+3q+1
       124: 2q^2+q
       125: q^2+4q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 6q^2+4q+1
       136: 5q^2+4q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^3+6q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+2q+1
       145: 4q^2+4q+1
       146: 3q^3+7q^2+4q+1
       147: 6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: q^3+5q^2+3q+1
       152: 3q^2+q
       153: 2q^3+5q^2+3q+1
       154: q^3+3q^2+q
       155: q^3+5q^2+3q+1
       156: 3q^2+q
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: 3q^2+2q+1
       163: 6q^2+4q+1
       164: 6q^2+4q+1
       165: 2q^3+4q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q
       170: q^2
       171: q
       172: 2q^2+2q+1
       173: q
       174: q^2
       175: q
       176: 2q^2+2q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q^2+q
       184: 3q^2+3q+1
       185: 2q
       186: 3q^2+2q+1
       187: 3q^2+3q+1
       188: 2q^2+q
       189: q^3+4q^2+3q+1
       190: 2q^2+q
       191: 2q
       192: q^2+2q+1
       194: 3q+1
       195: 2q
       196: q^2+2q+1
       197: 2q+1
       198: q
       199: q
       200: q^2+3q+1
       201: q^2+q
       202: 3q^2+3q+1
       203: 2q
       204: 3q^2+2q+1
       205: 3q^2+3q+1
       206: 2q^2+q
       207: q^2+3q+1
       208: q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+5q^2+3q+1
       212: 3q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: 2q^2+2q+1
       224: q^2+4q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+4q+1
       228: q^2+2q+1
       229: 3q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 4q^2+4q+1
       233: 2q^2+2q+1
       234: 6q^2+4q+1
       235: 5q^2+4q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+4q+1
       244: 3q+1
       245: 2q^2+4q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^3+2q^2+2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       259: q
       262: q+1
       263: q
       264: q^2
       265: q
       266: 2q^2+2q+1
       269: 2q+1
       270: q
       271: q
       272: q
       273: 2q^2+2q+1
       274: q^2
       275: q
       277: q
       278: q^2+2q+1
       279: 2q+1
       281: q+1
       284: q+1
       286: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: q
       294: q^2+3q+1
       295: 2q
       296: q^2+2q+1
       297: q^2+3q+1
       298: q
       300: 3q+1
       301: q+1
       303: 2q
       304: q^2+2q+1
       305: 2q+1
       306: q
       307: q^2+q
       308: 3q^2+3q+1
       309: 2q
       310: 3q^2+2q+1
       311: 2q+1
       313: 3q^2+3q+1
       314: 2q^2+q
       315: q+1
       317: 2q+1
       320: 3q+1
       321: 2q
       322: q^2+2q+1
       323: 2q+1
       324: q
       325: q^3+4q^2+3q+1
       326: 2q^2+q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: q^2+4q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q^2+2q+1
       357: q^2+4q+1
       358: q^2+2q+1
       359: 2q^2+4q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 3q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       381: q
       384: q+1
       385: q
       387: q
       388: q^2+2q+1
       391: q+1
       395: q
       396: 2q+1
       397: q
       399: q+1
       401: q
       402: q
       403: q^2
       404: 2q^2+2q+1
       406: 2q+1
       408: q
       413: q+1
       417: q+1
       420: q+1
       422: 1
       423: q+1
       425: q+1
       427: 2q+1
       430: q+1
       432: 1
       433: 1
       435: q+1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: 3q+1
       445: q+1
       448: q+1
       450: 1
       451: q+1
       453: q
       454: q^2+3q+1
       455: 2q+1
       457: 2q
       458: q^2+2q+1
       459: q^2+3q+1
       460: q
       461: 2q
       462: q^2+2q+1
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: 3q+1
       473: 2q
       474: q^2+2q+1
       475: 2q+1
       476: q
       477: q+1
       479: 2q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: 1
       532: 1
       536: 1
       539: q+1
       543: q+1
       547: q+1
       552: 1
       553: q
       555: q+1
       557: q
       558: q
       559: q^2+2q+1
       561: q
       563: q+1
       567: q
       568: 2q+1
       570: q+1
       575: 2q+1
       576: q
       577: q+1
       585: q+1
       590: q+1
       592: 1
       594: q+1
       596: 1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       616: 3q+1
       617: q+1
       620: q+1
       622: 1
       623: q+1
       625: q+1
       629: q+1
       631: 2q
       632: q^2+2q+1
       633: 2q+1
       639: q+1
       642: q+1
       644: 1
       645: 1
       648: q+1
       649: q
       650: q+1
       651: q+1
       653: q+1
       655: 2q+1
       656: q
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: q+1
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: q+1
       739: 1
       743: 1
       749: q
       751: q+1
       756: 1
       758: q+1
       762: q+1
       767: q
       768: 2q+1
       769: q+1
       781: q+1
       786: q+1
       788: 1
       791: 1
       797: 1
       802: 1
       806: 1
       808: 1
       809: 1
       811: 1
       816: q+1
       821: q+1
       826: q+1
       828: 1
       830: q+1
       832: 1
       833: q+1
       835: q+1
       839: q
       840: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       868: q+1
       871: 1
       872: 1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       922: 1
       930: 1
       946: 1
       950: 1
       955: 1
       961: 1
       975: 1
       991: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1022: 1
      1027: 1
      1038: q+1
      1041: q+1
      1045: 1
      1048: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1127: 1
      1135: 1
      1158: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1208: 1
      1220: 1
      1241: 1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1276: 1
      1278: 1
      1289: 1
      1331: 1
      1393: 1
      1401: 1
      1424: 1
      1474: 1
      1477: 1
      1600: 1

1601:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: q^3+8q^2+4q+1
        23: 3q^3+8q^2+4q+1
        24: q^3+8q^2+4q+1
        25: 4q^3+9q^2+4q+1
        26: q^4+6q^3+9q^2+4q+1
        27: 4q^3+9q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+8q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 4q^3+9q^2+4q+1
        36: 6q^2+4q+1
        37: 3q^2+q
        38: q^3+5q^2+3q+1
        39: q^3+3q^2+q
        40: 2q^3+5q^2+3q+1
        41: 3q^2+q
        42: q^3+5q^2+3q+1
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: q^3+8q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: q^3+8q^2+4q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+6q^3+9q^2+4q+1
        57: 4q^3+9q^2+4q+1
        58: 2q
        59: 3q^2+2q+1
        60: 3q^2+3q+1
        61: q^2+q
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: 3q^2+q
        65: q^3+5q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 6q^2+4q+1
        73: 5q^2+4q+1
        74: 3q^2+q
        75: q^3+5q^2+3q+1
        76: q^3+3q^2+q
        77: 2q^3+5q^2+3q+1
        78: 3q^2+q
        79: q^3+5q^2+3q+1
        80: q^3+6q^2+4q+1
        81: 5q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+8q^2+4q+1
        84: 3q^3+7q^2+4q+1
        85: 6q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 4q^3+9q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: 3q^2+2q+1
        97: 6q^2+4q+1
        98: 6q^2+4q+1
        99: 2q^3+4q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q
       104: 2q^2+2q+1
       105: q
       106: q^2
       107: 3q^2+3q+1
       108: q^2+q
       109: 2q
       110: 3q^2+2q+1
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: 3q^2+q
       116: q^3+5q^2+3q+1
       117: 2q
       118: 3q^2+2q+1
       119: 3q^2+3q+1
       120: q^2+q
       121: 2q^2+q
       122: q^3+4q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 6q^2+4q+1
       136: 5q^2+4q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^3+6q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+2q+1
       145: 4q^2+4q+1
       146: 3q^3+7q^2+4q+1
       147: 6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: 3q^2+q
       152: q^3+5q^2+3q+1
       153: q^3+3q^2+q
       154: 2q^3+5q^2+3q+1
       155: 3q^2+q
       156: q^3+5q^2+3q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: 3q^2+2q+1
       163: 6q^2+4q+1
       164: 6q^2+4q+1
       165: 2q^3+4q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q
       170: 2q^2+2q+1
       171: q
       172: q^2
       173: q
       174: 2q^2+2q+1
       175: q
       176: q^2
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 3q^2+3q+1
       184: q^2+q
       185: 2q
       186: 3q^2+2q+1
       187: 2q^2+q
       188: 3q^2+3q+1
       189: 2q^2+q
       190: q^3+4q^2+3q+1
       191: 2q
       192: q^2+2q+1
       193: 3q+1
       195: 2q
       196: q^2+2q+1
       197: q
       198: 2q+1
       199: q^2+3q+1
       200: q
       201: 3q^2+3q+1
       202: q^2+q
       203: 2q
       204: 3q^2+2q+1
       205: 2q^2+q
       206: 3q^2+3q+1
       207: q
       208: q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: 3q^2+q
       212: q^3+5q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: 2q^2+2q+1
       224: q^2+4q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+4q+1
       228: q^2+2q+1
       229: 3q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 4q^2+4q+1
       233: 2q^2+2q+1
       234: 6q^2+4q+1
       235: 5q^2+4q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 3q+1
       245: 2q^2+4q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^3+2q^2+2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       260: q+1
       261: q
       263: q
       264: 2q^2+2q+1
       265: q
       266: q^2
       267: q
       268: 2q+1
       271: q
       272: q
       273: q^2
       274: 2q^2+2q+1
       275: q
       276: q^2+2q+1
       277: q
       280: 2q+1
       282: q+1
       283: q+1
       286: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: q^2+3q+1
       294: q
       295: 2q
       296: q^2+2q+1
       297: q
       298: q^2+3q+1
       299: 3q+1
       302: q+1
       303: 2q
       304: q^2+2q+1
       305: q
       306: 2q+1
       307: 3q^2+3q+1
       308: q^2+q
       309: 2q
       310: 3q^2+2q+1
       312: 2q+1
       313: 2q^2+q
       314: 3q^2+3q+1
       316: q+1
       318: 2q+1
       319: 3q+1
       321: 2q
       322: q^2+2q+1
       323: q
       324: 2q+1
       325: 2q^2+q
       326: q^3+4q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: q^2+4q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q^2+2q+1
       357: q^2+4q+1
       358: q^2+2q+1
       359: 2q^2+4q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 3q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: q+1
       383: q
       385: q
       386: q^2+2q+1
       387: q
       390: q+1
       393: q
       394: 2q+1
       398: q
       400: q+1
       401: q
       402: q
       403: 2q^2+2q+1
       404: q^2
       405: q
       407: 2q+1
       414: q+1
       418: q+1
       419: q+1
       422: 1
       424: q+1
       426: q+1
       428: 2q+1
       429: q+1
       432: 1
       434: 1
       436: q+1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: 3q+1
       446: q+1
       447: q+1
       450: 1
       452: q+1
       453: q^2+3q+1
       454: q
       456: 2q+1
       457: 2q
       458: q^2+2q+1
       459: q
       460: q^2+3q+1
       461: 2q
       462: q^2+2q+1
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 3q+1
       473: 2q
       474: q^2+2q+1
       475: q
       476: 2q+1
       478: q+1
       479: q
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 1
       530: 1
       534: 1
       538: q+1
       542: q+1
       546: q+1
       551: 1
       554: q
       556: q+1
       557: q
       558: q
       560: q^2+2q+1
       562: q
       564: q+1
       565: q
       566: 2q+1
       571: q+1
       573: q
       574: 2q+1
       581: q+1
       586: q+1
       589: q+1
       592: 1
       593: q+1
       596: 1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: 3q+1
       618: q+1
       619: q+1
       622: 1
       624: q+1
       626: q+1
       630: q+1
       631: 2q
       632: q^2+2q+1
       634: 2q+1
       640: q+1
       641: q+1
       644: 1
       646: 1
       647: q+1
       649: q
       650: q+1
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: q+1
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: q+1
       740: 1
       744: 1
       750: q
       752: q+1
       754: 1
       759: q+1
       763: q+1
       765: q
       766: 2q+1
       773: q+1
       782: q+1
       785: q+1
       788: 1
       792: 1
       798: 1
       801: 1
       805: 1
       808: 1
       810: 1
       812: 1
       815: q+1
       822: q+1
       825: q+1
       828: 1
       829: q+1
       832: 1
       834: q+1
       836: q+1
       839: q
       840: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       868: q+1
       871: 1
       872: 1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       921: 1
       929: 1
       947: 1
       951: 1
       953: 1
       962: 1
       976: 1
       989: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1023: 1
      1026: 1
      1039: q+1
      1040: q+1
      1045: 1
      1049: 1
      1052: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1128: 1
      1136: 1
      1157: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1207: 1
      1221: 1
      1240: 1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1277: 1
      1279: 1
      1289: 1
      1332: 1
      1394: 1
      1402: 1
      1423: 1
      1475: 1
      1476: 1
      1601: 1

1602:    0: 4q^3+9q^2+4q+1
         1: q^4+6q^3+9q^2+4q+1
         2: 4q^3+9q^2+4q+1
         3: q^4+6q^3+9q^2+4q+1
         4: 4q^3+9q^2+4q+1
         5: 4q^3+9q^2+4q+1
         6: q^4+6q^3+9q^2+4q+1
         7: 4q^3+9q^2+4q+1
         8: 4q^3+9q^2+4q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 4q^3+9q^2+4q+1
        14: 4q^3+9q^2+4q+1
        15: 4q^3+9q^2+4q+1
        16: 6q^2+4q+1
        17: 6q^2+4q+1
        18: 2q^3+4q^2+2q+1
        19: 4q^3+9q^2+4q+1
        20: q^4+6q^3+9q^2+4q+1
        21: 4q^3+9q^2+4q+1
        22: q^3+8q^2+4q+1
        23: 3q^3+8q^2+4q+1
        24: q^3+8q^2+4q+1
        25: 4q^3+9q^2+4q+1
        26: q^4+6q^3+9q^2+4q+1
        27: 4q^3+9q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 4q^3+9q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+8q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 4q^3+9q^2+4q+1
        36: 6q^2+4q+1
        37: 3q^2+q
        38: q^3+5q^2+3q+1
        39: q^3+3q^2+q
        40: 2q^3+5q^2+3q+1
        41: 3q^2+q
        42: q^3+5q^2+3q+1
        43: 3q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: 6q^2+4q+1
        47: 6q^2+4q+1
        48: 2q^3+4q^2+2q+1
        49: 6q^2+4q+1
        50: 6q^2+4q+1
        51: 2q^3+4q^2+2q+1
        52: q^3+8q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: q^3+8q^2+4q+1
        55: 4q^3+9q^2+4q+1
        56: q^4+6q^3+9q^2+4q+1
        57: 4q^3+9q^2+4q+1
        58: 3q^2+2q+1
        59: 2q
        60: q^2+q
        61: 3q^2+3q+1
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: 3q^2+q
        65: q^3+5q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 4q^2+4q+1
        69: 2q^2+2q+1
        70: 3q^3+7q^2+4q+1
        71: 4q^2+4q+1
        72: 6q^2+4q+1
        73: 5q^2+4q+1
        74: 3q^2+q
        75: q^3+5q^2+3q+1
        76: q^3+3q^2+q
        77: 2q^3+5q^2+3q+1
        78: 3q^2+q
        79: q^3+5q^2+3q+1
        80: q^3+6q^2+4q+1
        81: 5q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+8q^2+4q+1
        84: 3q^3+7q^2+4q+1
        85: 6q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 4q^3+9q^2+4q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 6q^2+4q+1
        92: 6q^2+4q+1
        93: 2q^3+4q^2+2q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: 3q^2+2q+1
        97: 6q^2+4q+1
        98: 6q^2+4q+1
        99: 2q^3+4q^2+2q+1
       100: q^3+8q^2+4q+1
       101: 3q^3+8q^2+4q+1
       102: q^3+8q^2+4q+1
       103: q^2
       104: q
       105: 2q^2+2q+1
       106: q
       107: q^2+q
       108: 3q^2+3q+1
       109: 3q^2+2q+1
       110: 2q
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: 3q^2+q
       116: q^3+5q^2+3q+1
       117: 3q^2+2q+1
       118: 2q
       119: q^2+q
       120: 3q^2+3q+1
       121: 2q^2+q
       122: q^3+4q^2+3q+1
       123: 2q^2+q
       124: 3q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 4q^2+4q+1
       134: 2q^2+2q+1
       135: 6q^2+4q+1
       136: 5q^2+4q+1
       137: q^2+4q+1
       138: q^2+2q+1
       139: q^2+4q+1
       140: 3q+1
       141: q^3+6q^2+4q+1
       142: 2q^2+4q+1
       143: q^2+4q+1
       144: 2q^2+2q+1
       145: 4q^2+4q+1
       146: 3q^3+7q^2+4q+1
       147: 6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+8q^2+4q+1
       151: 3q^2+q
       152: q^3+5q^2+3q+1
       153: q^3+3q^2+q
       154: 2q^3+5q^2+3q+1
       155: 3q^2+q
       156: q^3+5q^2+3q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^3+2q^2+2q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: 3q^2+2q+1
       163: 6q^2+4q+1
       164: 6q^2+4q+1
       165: 2q^3+4q^2+2q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 3q^2+2q+1
       169: q^2
       170: q
       171: 2q^2+2q+1
       172: q
       173: q^2
       174: q
       175: 2q^2+2q+1
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q^2+q
       184: 3q^2+3q+1
       185: 3q^2+2q+1
       186: 2q
       187: 2q^2+q
       188: 3q^2+3q+1
       189: 2q^2+q
       190: q^3+4q^2+3q+1
       191: q^2+2q+1
       192: 2q
       194: 3q+1
       195: q^2+2q+1
       196: 2q
       197: q
       198: 2q+1
       199: q
       200: q^2+3q+1
       201: q^2+q
       202: 3q^2+3q+1
       203: 3q^2+2q+1
       204: 2q
       205: 2q^2+q
       206: 3q^2+3q+1
       207: q
       208: q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: 3q^2+q
       212: q^3+5q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+4q+1
       221: 2q+1
       222: q^2+4q+1
       223: 2q^2+2q+1
       224: q^2+4q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+4q+1
       228: q^2+2q+1
       229: 3q+1
       230: 2q^2+4q+1
       231: 2q+1
       232: 4q^2+4q+1
       233: 2q^2+2q+1
       234: 6q^2+4q+1
       235: 5q^2+4q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+4q+1
       244: 3q+1
       245: 2q^2+4q+1
       246: q^3+6q^2+4q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^3+2q^2+2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 3q^2+2q+1
       260: q
       261: q+1
       263: q^2
       264: q
       265: 2q^2+2q+1
       266: q
       269: q
       270: 2q+1
       271: q^2
       272: 2q^2+2q+1
       273: q
       274: q
       276: q
       277: q^2+2q+1
       278: q
       280: 2q+1
       282: q+1
       284: q+1
       285: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: q
       294: q^2+3q+1
       295: q^2+2q+1
       296: 2q
       297: q
       298: q^2+3q+1
       300: 3q+1
       302: q+1
       303: q^2+2q+1
       304: 2q
       305: q
       306: 2q+1
       307: q^2+q
       308: 3q^2+3q+1
       309: 3q^2+2q+1
       310: 2q
       312: 2q+1
       313: 2q^2+q
       314: 3q^2+3q+1
       316: q+1
       318: 2q+1
       320: 3q+1
       321: q^2+2q+1
       322: 2q
       323: q
       324: 2q+1
       325: 2q^2+q
       326: q^3+4q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+4q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: q^2+4q+1
       354: 2q+1
       355: q^2+4q+1
       356: 2q^2+2q+1
       357: q^2+4q+1
       358: q^2+2q+1
       359: 2q^2+4q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: q^2+4q+1
       368: q^2+2q+1
       369: 3q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       382: q
       383: q+1
       386: q
       387: q^2+2q+1
       388: q
       392: q+1
       395: 2q+1
       396: q
       398: q+1
       400: q
       401: q^2
       402: 2q^2+2q+1
       403: q
       404: q
       406: q
       408: 2q+1
       414: q+1
       418: q+1
       420: q+1
       421: 1
       424: q+1
       426: q+1
       428: 2q+1
       430: q+1
       431: 1
       434: 1
       436: q+1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: 3q+1
       446: q+1
       448: q+1
       449: 1
       452: q+1
       453: q
       454: q^2+3q+1
       456: 2q+1
       457: q^2+2q+1
       458: 2q
       459: q
       460: q^2+3q+1
       461: q^2+2q+1
       462: 2q
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: 3q+1
       473: q^2+2q+1
       474: 2q
       475: q
       476: 2q+1
       478: q+1
       479: q
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: 1
       531: 1
       535: 1
       540: q+1
       544: q+1
       548: q+1
       550: 1
       554: q+1
       556: q
       558: q^2+2q+1
       559: q
       560: q
       562: q+1
       564: q
       567: 2q+1
       568: q
       572: q+1
       575: q
       576: 2q+1
       581: q+1
       586: q+1
       590: q+1
       591: 1
       594: q+1
       595: 1
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       616: 3q+1
       618: q+1
       620: q+1
       621: 1
       624: q+1
       626: q+1
       630: q+1
       631: q^2+2q+1
       632: 2q
       634: 2q+1
       640: q+1
       642: q+1
       643: 1
       646: 1
       648: q+1
       649: q+1
       650: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: q+1
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: q+1
       738: 1
       742: 1
       750: q+1
       752: q
       755: 1
       760: q+1
       764: q+1
       767: 2q+1
       768: q
       773: q+1
       782: q+1
       786: q+1
       787: 1
       792: 1
       798: 1
       802: 1
       806: 1
       807: 1
       810: 1
       812: 1
       816: q+1
       822: q+1
       826: q+1
       827: 1
       830: q+1
       831: 1
       834: q+1
       836: q+1
       839: q+1
       840: q
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       868: q+1
       871: 1
       872: 1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       923: 1
       931: 1
       945: 1
       949: 1
       954: 1
       963: 1
       977: 1
       990: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1023: 1
      1027: 1
      1039: q+1
      1041: q+1
      1044: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1129: 1
      1137: 1
      1159: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1209: 1
      1221: 1
      1241: 1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1277: 1
      1279: 1
      1289: 1
      1333: 1
      1395: 1
      1403: 1
      1425: 1
      1475: 1
      1477: 1
      1602: 1

1603:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: q
        60: q^2+2q+1
        61: 2q
        62: 2q^2+3q+1
        63: q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: q^2+3q+1
        67: q
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       105: q
       106: q
       107: q+1
       108: q
       109: 2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+3q+1
       118: q
       119: q^2+2q+1
       120: 2q
       121: 2q^2+3q+1
       122: q^2+q
       123: q^2+3q+1
       124: q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q+1
       173: q^2+2q+1
       175: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q+1
       184: q
       185: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q+1
       194: q
       195: 2q+1
       197: q+1
       199: q^2+2q+1
       200: 2q
       201: q+1
       202: q
       203: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: 1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       277: q
       278: q
       279: q+1
       281: q+1
       283: 1
       285: q+1
       287: q+1
       289: 1
       291: 1
       293: q+1
       294: q
       295: 2q+1
       297: q+1
       299: q+1
       300: q
       301: 1
       303: 2q+1
       305: q+1
       307: q+1
       308: q
       309: 2q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: q+1
       320: q
       321: 2q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 1
       421: q+1
       423: 1
       425: 1
       427: 2
       429: 1
       431: q+1
       433: 1
       435: 1
       437: q+1
       438: q
       439: 2q+1
       441: q+1
       443: 1
       444: 1
       445: 2
       447: 1
       449: q+1
       451: 1
       453: q+1
       454: q
       455: 1
       457: 2q+1
       459: q+1
       461: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q+1
       472: q
       473: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 1
       547: 1
       549: 1
       553: 1
       557: q+1
       561: 2
       565: q+1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       589: 1
       591: 1
       595: q+1
       597: 1
       599: 1
       601: 2
       603: 1
       605: 1
       607: q+1
       609: 1
       611: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: 1
       621: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: q+1
       645: 1
       647: q+1
       648: q
       649: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       693: 1
       698: 1
       705: 1
       709: 1
       713: 1
       721: 1
       725: 1
       729: 1
       733: 1
       735: 1
       737: 1
       741: 1
       745: 1
       749: 2
       753: 1
       757: 1
       761: q+1
       765: 1
       767: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       787: 1
       789: 2
       797: 1
       799: 1
       801: 1
       803: 1
       807: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       821: 1
       823: 1
       825: 1
       827: 1
       831: q+1
       833: 1
       835: 1
       837: 2
       839: 2
       841: q+1
       845: 1
       847: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       884: 1
       888: 1
       896: 1
       900: 1
       912: 1
       920: 1
       924: 1
       932: 1
       934: 1
       936: 1
       944: 1
       948: 1
       956: 2
       960: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       990: 1
      1002: 1
      1006: 1
      1018: 1
      1022: 1
      1024: 1
      1028: 1
      1034: 1
      1038: 1
      1042: 1
      1044: 1
      1048: 1
      1050: 1
      1052: 1
      1054: 1
      1058: q+1
      1060: 1
      1062: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1098: 1
      1103: 1
      1110: 1
      1148: 1
      1152: 1
      1168: 1
      1172: 1
      1184: 1
      1198: 1
      1202: 1
      1238: 1
      1242: 1
      1256: 1
      1260: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1289: 1
      1344: 1
      1376: 1
      1414: 1
      1418: 1
      1470: 1
      1478: 1
      1603: 1

1604:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+3q+1
        59: q
        60: 2q
        61: q^2+2q+1
        62: q^2+q
        63: 2q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q
        67: q^2+3q+1
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       104: q
       105: q^2+2q+1
       107: q
       108: q+1
       109: 2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+3q+1
       118: q
       119: 2q
       120: q^2+2q+1
       121: q^2+q
       122: 2q^2+3q+1
       123: q
       124: q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       171: q+1
       173: q
       174: q
       175: q^2+2q+1
       178: q+1
       180: q+1
       182: 1
       183: q
       184: q+1
       185: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q
       194: q+1
       195: 2q+1
       198: q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: q+1
       203: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       261: 1
       265: q+1
       270: q+1
       272: q+1
       275: q
       276: q
       277: q^2+2q+1
       280: q+1
       282: q+1
       284: 1
       285: q+1
       288: q+1
       290: 1
       292: 1
       293: q
       294: q+1
       295: 2q+1
       298: q+1
       299: q
       300: q+1
       302: 1
       303: 2q+1
       306: q+1
       307: q
       308: q+1
       309: 2q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: q
       320: q+1
       321: 2q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: 1
       428: 2
       430: 1
       431: q+1
       434: 1
       436: 1
       437: q
       438: q+1
       439: 2q+1
       442: q+1
       443: 1
       444: 1
       446: 2
       448: 1
       449: q+1
       452: 1
       453: q
       454: q+1
       456: 1
       457: 2q+1
       460: q+1
       461: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q
       472: q+1
       473: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       546: 1
       548: 1
       550: 1
       554: 1
       558: q+1
       562: 2
       567: q+1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       590: 1
       591: 1
       595: q+1
       598: 1
       600: 1
       602: 2
       604: 1
       606: 1
       607: q+1
       610: 1
       612: 1
       614: 1
       615: 1
       616: 1
       618: 2
       620: 1
       621: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: q+1
       646: 1
       647: q
       648: q+1
       649: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       694: 1
       700: 1
       707: 1
       711: 1
       714: 1
       724: 1
       728: 1
       732: 1
       734: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 2
       755: 1
       760: 1
       764: q+1
       765: 1
       767: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       787: 1
       790: 2
       798: 1
       800: 1
       802: 1
       803: 1
       807: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       822: 1
       824: 1
       826: 1
       827: 1
       831: q+1
       834: 1
       836: 1
       838: 2
       839: 2
       842: q+1
       846: 1
       847: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       885: 1
       891: 1
       898: 1
       901: 1
       915: 1
       923: 1
       925: 1
       933: 1
       935: 1
       937: 1
       945: 1
       949: 1
       957: 2
       963: 1
       977: 1
       981: 1
       983: 1
       986: 1
       988: 1
       990: 1
      1003: 1
      1006: 1
      1019: 1
      1023: 1
      1025: 1
      1028: 1
      1035: 1
      1039: 1
      1043: 1
      1044: 1
      1049: 1
      1051: 1
      1053: 1
      1054: 1
      1058: q+1
      1061: 1
      1063: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1099: 1
      1105: 1
      1111: 1
      1151: 1
      1153: 1
      1169: 1
      1173: 1
      1187: 1
      1201: 1
      1203: 1
      1239: 1
      1242: 1
      1257: 1
      1260: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1289: 1
      1345: 1
      1377: 1
      1417: 1
      1419: 1
      1471: 1
      1478: 1
      1604: 1

1605:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+3q+1
        60: 2q
        61: q^2+2q+1
        62: 2q^2+3q+1
        63: q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: q^2+3q+1
        67: q
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       104: q
       106: q^2+2q+1
       107: q
       108: q+1
       110: 2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q
       118: q^2+3q+1
       119: 2q
       120: q^2+2q+1
       121: 2q^2+3q+1
       122: q^2+q
       123: q^2+3q+1
       124: q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       172: q+1
       173: q
       174: q
       176: q^2+2q+1
       177: q+1
       179: q+1
       181: 1
       183: q
       184: q+1
       186: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q
       194: q+1
       196: 2q+1
       197: q+1
       199: 2q
       200: q^2+2q+1
       201: q
       202: q+1
       204: 2q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       262: 1
       266: q+1
       269: q+1
       273: q+1
       275: q
       276: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       284: 1
       286: q+1
       287: q+1
       289: 1
       291: 1
       293: q
       294: q+1
       296: 2q+1
       297: q+1
       299: q
       300: q+1
       301: 1
       304: 2q+1
       305: q+1
       307: q
       308: q+1
       310: 2q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: q
       320: q+1
       322: 2q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: 1
       422: q+1
       423: 1
       425: 1
       427: 2
       430: 1
       432: q+1
       433: 1
       435: 1
       437: q
       438: q+1
       440: 2q+1
       441: q+1
       443: 1
       444: 1
       445: 2
       448: 1
       450: q+1
       451: 1
       453: q
       454: q+1
       455: 1
       458: 2q+1
       459: q+1
       462: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q
       472: q+1
       474: 2q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       545: 1
       547: 1
       552: 1
       555: 1
       559: q+1
       563: 2
       568: q+1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       590: 1
       592: 1
       596: q+1
       597: 1
       599: 1
       601: 2
       604: 1
       605: 1
       608: q+1
       609: 1
       611: 1
       613: 1
       615: 1
       616: 1
       617: 2
       620: 1
       622: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: q+1
       645: 1
       647: q
       648: q+1
       650: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       696: 1
       697: 1
       708: 1
       712: 1
       716: 1
       723: 1
       727: 1
       731: 1
       733: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 2
       756: 1
       758: 1
       762: q+1
       766: 1
       768: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       788: 1
       789: 2
       797: 1
       799: 1
       802: 1
       804: 1
       808: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       821: 1
       823: 1
       826: 1
       828: 1
       832: q+1
       833: 1
       835: 1
       837: 2
       840: 2
       841: q+1
       846: 1
       848: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       887: 1
       889: 1
       899: 1
       902: 1
       914: 1
       922: 1
       927: 1
       932: 1
       934: 1
       938: 1
       946: 1
       950: 1
       958: 2
       961: 1
       975: 1
       979: 1
       982: 1
       985: 1
       989: 1
       991: 1
      1002: 1
      1007: 1
      1018: 1
      1022: 1
      1024: 1
      1029: 1
      1034: 1
      1038: 1
      1042: 1
      1045: 1
      1048: 1
      1050: 1
      1053: 1
      1055: 1
      1059: q+1
      1060: 1
      1062: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1101: 1
      1102: 1
      1112: 1
      1150: 1
      1154: 1
      1170: 1
      1174: 1
      1185: 1
      1199: 1
      1204: 1
      1238: 1
      1243: 1
      1256: 1
      1261: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1289: 1
      1346: 1
      1378: 1
      1415: 1
      1420: 1
      1470: 1
      1479: 1
      1605: 1

1606:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+3q+1
        60: q^2+2q+1
        61: 2q
        62: q^2+q
        63: 2q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q
        67: q^2+3q+1
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q^2+2q+1
       105: q
       106: q
       107: q+1
       108: q
       110: 2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q
       118: q^2+3q+1
       119: q^2+2q+1
       120: 2q
       121: q^2+q
       122: 2q^2+3q+1
       123: q
       124: q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q+1
       174: q^2+2q+1
       175: q
       176: q
       178: q+1
       180: q+1
       182: 1
       183: q+1
       184: q
       186: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q+1
       194: q
       196: 2q+1
       198: q+1
       199: q^2+2q+1
       200: 2q
       201: q+1
       202: q
       204: 2q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: 1
       264: q+1
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: 1
       286: q+1
       288: q+1
       290: 1
       292: 1
       293: q+1
       294: q
       296: 2q+1
       298: q+1
       299: q+1
       300: q
       302: 1
       304: 2q+1
       306: q+1
       307: q+1
       308: q
       310: 2q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: q+1
       320: q
       322: 2q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 1
       422: q+1
       424: 1
       426: 1
       428: 2
       429: 1
       432: q+1
       434: 1
       436: 1
       437: q+1
       438: q
       440: 2q+1
       442: q+1
       443: 1
       444: 1
       446: 2
       447: 1
       450: q+1
       452: 1
       453: q+1
       454: q
       456: 1
       458: 2q+1
       460: q+1
       462: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q+1
       472: q
       474: 2q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 1
       548: 1
       551: 1
       556: 1
       560: q+1
       564: 2
       566: q+1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: 1
       592: 1
       596: q+1
       598: 1
       600: 1
       602: 2
       603: 1
       606: 1
       608: q+1
       610: 1
       612: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: 1
       622: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: q+1
       646: 1
       647: q+1
       648: q
       650: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       699: 1
       701: 1
       706: 1
       710: 1
       715: 1
       722: 1
       726: 1
       730: 1
       734: 1
       736: 1
       740: 1
       744: 1
       748: 1
       752: 2
       754: 1
       759: 1
       763: q+1
       766: 1
       768: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       788: 1
       790: 2
       798: 1
       800: 1
       801: 1
       804: 1
       808: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       822: 1
       824: 1
       825: 1
       828: 1
       832: q+1
       834: 1
       836: 1
       838: 2
       840: 2
       842: q+1
       845: 1
       848: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       890: 1
       892: 1
       897: 1
       903: 1
       913: 1
       921: 1
       926: 1
       933: 1
       935: 1
       939: 1
       947: 1
       951: 1
       959: 2
       962: 1
       976: 1
       980: 1
       983: 1
       986: 1
       989: 1
       991: 1
      1003: 1
      1007: 1
      1019: 1
      1023: 1
      1025: 1
      1029: 1
      1035: 1
      1039: 1
      1043: 1
      1045: 1
      1049: 1
      1051: 1
      1052: 1
      1055: 1
      1059: q+1
      1061: 1
      1063: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1104: 1
      1106: 1
      1113: 1
      1149: 1
      1155: 1
      1171: 1
      1175: 1
      1186: 1
      1200: 1
      1205: 1
      1239: 1
      1243: 1
      1257: 1
      1261: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1289: 1
      1347: 1
      1379: 1
      1416: 1
      1421: 1
      1471: 1
      1479: 1
      1606: 1

1607:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: q+1
        61: 2q
        62: 2q+1
        63: q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       105: q
       106: q
       107: 1
       108: q
       109: q+1
       111: 1
       113: q+1
       115: q+1
       117: 2q+1
       118: q
       119: q+1
       120: 2q
       121: 2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q^2+q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       173: q+1
       175: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 1
       184: q
       185: q+1
       187: 1
       189: q+1
       191: 2q+1
       192: q
       193: 1
       194: q
       195: q+1
       197: 1
       199: q+1
       200: 2q
       201: 1
       202: q
       203: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q^2+q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       277: q
       278: q
       279: q+1
       281: q+1
       283: 1
       284: q
       285: q+1
       287: q+1
       289: 1
       291: 1
       293: 1
       294: q
       295: 1
       297: 1
       299: 1
       300: q
       301: 1
       303: q+1
       305: 1
       307: 1
       308: q
       309: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: 1
       320: q
       321: q+1
       323: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: 1
       350: q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       417: 1
       419: 1
       420: q
       421: 1
       423: 1
       425: 1
       427: 2
       429: 1
       430: q
       431: q+1
       433: 1
       435: 1
       437: 1
       438: q
       439: 1
       441: 1
       443: 1
       444: 1
       445: 2
       447: 1
       448: q
       449: q+1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: 1
       472: q
       473: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       547: 1
       549: 1
       553: 1
       557: 1
       561: 2
       565: 1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       585: 1
       589: 1
       590: q
       591: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: 1
       604: q
       605: 1
       607: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       629: 1
       631: 2
       633: 2
       639: q+1
       641: 1
       642: q
       643: q+1
       645: 1
       647: 1
       648: q
       649: 1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       674: 2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       693: 1
       698: 1
       709: 1
       713: 1
       721: 1
       725: 1
       733: 1
       735: 1
       737: 1
       741: 1
       749: 2
       753: 1
       757: 1
       761: 1
       765: 1
       767: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       787: 1
       793: 1
       794: 1
       795: 2
       797: 1
       801: 1
       802: q
       803: 1
       807: 1
       809: 1
       811: 1
       817: 2
       819: 2
       821: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       843: 1
       844: 1
       845: 1
       846: q
       847: 1
       849: 1
       851: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       884: 1
       888: 1
       900: 1
       916: 1
       918: 1
       920: 1
       924: 1
       940: 2
       944: 1
       948: 1
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       994: 1
       998: 1
      1020: 1
      1022: 1
      1028: 1
      1036: 1
      1038: 1
      1044: 1
      1048: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1086: 1
      1090: 1
      1114: 1
      1152: 1
      1172: 1
      1198: 1
      1202: 1
      1230: 1
      1232: 1
      1248: 1
      1250: 1
      1266: 1
      1270: 1
      1274: 1
      1287: 1
      1348: 1
      1380: 1
      1418: 1
      1464: 1
      1466: 1
      1607: 1

1608:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q+1
        59: q
        60: 2q
        61: q+1
        62: q
        63: 2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       105: q+1
       107: q
       108: 1
       109: q+1
       112: 1
       114: q+1
       116: q+1
       117: 2q+1
       118: q
       119: 2q
       120: q+1
       121: q
       122: 2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q^2+q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       171: 1
       173: q
       174: q
       175: q+1
       178: q+1
       180: q+1
       182: 1
       183: q
       184: 1
       185: q+1
       188: 1
       190: q+1
       191: 2q+1
       192: q
       193: q
       194: 1
       195: q+1
       198: 1
       199: 2q
       200: q+1
       201: q
       202: 1
       203: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q^2+q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q
       276: q
       277: q+1
       280: q+1
       282: q+1
       283: q
       284: 1
       285: q+1
       288: q+1
       290: 1
       292: 1
       293: q
       294: 1
       295: 1
       298: 1
       299: q
       300: 1
       302: 1
       303: q+1
       306: 1
       307: q
       308: 1
       309: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q
       320: 1
       321: q+1
       324: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: 1
       350: q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: q+1
       418: 1
       419: q
       420: 1
       421: 1
       424: 1
       426: 1
       428: 2
       429: q
       430: 1
       431: q+1
       434: 1
       436: 1
       437: q
       438: 1
       439: 1
       442: 1
       443: 1
       444: 1
       446: 2
       447: q
       448: 1
       449: q+1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q
       472: 1
       473: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       546: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 2
       567: 1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       586: 1
       589: q
       590: 1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 2
       603: q
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 2
       634: 2
       640: q+1
       641: q
       642: 1
       643: q+1
       646: 1
       647: q
       648: 1
       649: 1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       674: 2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       694: 1
       700: 1
       711: 1
       714: 1
       724: 1
       728: 1
       734: 1
       736: 1
       738: 1
       742: 1
       750: 2
       755: 1
       760: 1
       764: 1
       765: 1
       767: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       787: 1
       793: 1
       794: 1
       796: 2
       798: 1
       801: q
       802: 1
       803: 1
       807: 1
       810: 1
       812: 1
       817: 2
       820: 2
       822: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       843: 1
       844: 1
       845: q
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       885: 1
       891: 1
       901: 1
       917: 1
       919: 1
       923: 1
       925: 1
       941: 2
       945: 1
       949: 1
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       995: 1
       998: 1
      1021: 1
      1023: 1
      1028: 1
      1037: 1
      1039: 1
      1044: 1
      1049: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1087: 1
      1093: 1
      1115: 1
      1153: 1
      1173: 1
      1201: 1
      1203: 1
      1231: 1
      1232: 1
      1249: 1
      1250: 1
      1267: 1
      1270: 1
      1275: 1
      1287: 1
      1349: 1
      1381: 1
      1419: 1
      1465: 1
      1466: 1
      1608: 1

1609:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: 2q
        61: q+1
        62: 2q+1
        63: q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       106: q+1
       107: q
       108: 1
       110: q+1
       111: 1
       113: q+1
       115: q+1
       117: q
       118: 2q+1
       119: 2q
       120: q+1
       121: 2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q^2+q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       172: 1
       173: q
       174: q
       176: q+1
       177: q+1
       179: q+1
       181: 1
       183: q
       184: 1
       186: q+1
       187: 1
       189: q+1
       191: q
       192: 2q+1
       193: q
       194: 1
       196: q+1
       197: 1
       199: 2q
       200: q+1
       201: q
       202: 1
       204: q+1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q^2+q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q
       278: q+1
       279: q+1
       281: q+1
       283: q
       284: 1
       286: q+1
       287: q+1
       289: 1
       291: 1
       293: q
       294: 1
       296: 1
       297: 1
       299: q
       300: 1
       301: 1
       304: q+1
       305: 1
       307: q
       308: 1
       310: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q
       320: 1
       322: q+1
       323: 1
       325: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: 1
       350: q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       417: 1
       419: q
       420: 1
       422: 1
       423: 1
       425: 1
       427: 2
       429: q
       430: 1
       432: q+1
       433: 1
       435: 1
       437: q
       438: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 2
       447: q
       448: 1
       450: q+1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q
       472: 1
       474: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       545: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 2
       568: 1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       585: 1
       589: q
       590: 1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 2
       603: q
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 2
       633: 2
       639: q+1
       641: q
       642: 1
       644: q+1
       645: 1
       647: q
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       674: 2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       696: 1
       697: 1
       712: 1
       716: 1
       723: 1
       727: 1
       733: 1
       735: 1
       739: 1
       743: 1
       751: 2
       756: 1
       758: 1
       762: 1
       766: 1
       768: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       788: 1
       793: 1
       794: 1
       795: 2
       797: 1
       801: q
       802: 1
       804: 1
       808: 1
       809: 1
       811: 1
       818: 2
       819: 2
       821: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       843: 1
       844: 1
       845: q
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       887: 1
       889: 1
       902: 1
       916: 1
       918: 1
       922: 1
       927: 1
       942: 2
       946: 1
       950: 1
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       994: 1
       999: 1
      1020: 1
      1022: 1
      1029: 1
      1036: 1
      1038: 1
      1045: 1
      1048: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1089: 1
      1091: 1
      1116: 1
      1154: 1
      1174: 1
      1199: 1
      1204: 1
      1230: 1
      1233: 1
      1248: 1
      1251: 1
      1266: 1
      1271: 1
      1274: 1
      1287: 1
      1350: 1
      1382: 1
      1420: 1
      1464: 1
      1467: 1
      1609: 1

1610:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: 2q+1
        60: q+1
        61: 2q
        62: q
        63: 2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q+1
       105: q
       106: q
       107: 1
       108: q
       110: q+1
       112: 1
       114: q+1
       116: q+1
       117: q
       118: 2q+1
       119: q+1
       120: 2q
       121: q
       122: 2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q^2+q+1
       141: 2q+1
       142: q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 1
       174: q+1
       175: q
       176: q
       178: q+1
       180: q+1
       182: 1
       183: 1
       184: q
       186: q+1
       188: 1
       190: q+1
       191: q
       192: 2q+1
       193: 1
       194: q
       196: q+1
       198: 1
       199: q+1
       200: 2q
       201: 1
       202: q
       204: q+1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q^2+q+1
       245: q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: 1
       284: q
       286: q+1
       288: q+1
       290: 1
       292: 1
       293: 1
       294: q
       296: 1
       298: 1
       299: 1
       300: q
       302: 1
       304: q+1
       306: 1
       307: 1
       308: q
       310: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: 1
       320: q
       322: q+1
       324: 1
       326: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: 1
       350: q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: 1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: q+1
       418: 1
       419: 1
       420: q
       422: 1
       424: 1
       426: 1
       428: 2
       429: 1
       430: q
       432: q+1
       434: 1
       436: 1
       437: 1
       438: q
       440: 1
       442: 1
       443: 1
       444: 1
       446: 2
       447: 1
       448: q
       450: q+1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: 1
       472: q
       474: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 2
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: 1
       514: q+1
       515: 2
       516: 2
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       548: 1
       551: 1
       556: 1
       560: 1
       564: 2
       566: 1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       586: 1
       589: 1
       590: q
       592: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       604: q
       606: 1
       608: 1
       610: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       630: 1
       632: 2
       634: 2
       640: q+1
       641: 1
       642: q
       644: q+1
       646: 1
       647: 1
       648: q
       650: 1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       674: 2
       675: q+1
       676: 1
       677: 1
       679: 1
       680: 2
       681: q+1
       682: 1
       683: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       699: 1
       701: 1
       710: 1
       715: 1
       722: 1
       726: 1
       734: 1
       736: 1
       740: 1
       744: 1
       752: 2
       754: 1
       759: 1
       763: 1
       766: 1
       768: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       788: 1
       793: 1
       794: 1
       796: 2
       798: 1
       801: 1
       802: q
       804: 1
       808: 1
       810: 1
       812: 1
       818: 2
       820: 2
       822: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       843: 1
       844: 1
       845: 1
       846: q
       848: 1
       850: 1
       852: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       890: 1
       892: 1
       903: 1
       917: 1
       919: 1
       921: 1
       926: 1
       943: 2
       947: 1
       951: 1
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       995: 1
       999: 1
      1021: 1
      1023: 1
      1029: 1
      1037: 1
      1039: 1
      1045: 1
      1049: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1092: 1
      1094: 1
      1117: 1
      1155: 1
      1175: 1
      1200: 1
      1205: 1
      1231: 1
      1233: 1
      1249: 1
      1251: 1
      1267: 1
      1271: 1
      1275: 1
      1287: 1
      1351: 1
      1383: 1
      1421: 1
      1465: 1
      1467: 1
      1610: 1

1611:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q
        60: q^2+3q+1
        61: q
        62: 2q^2+3q+1
        63: q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: q^2+3q+1
        67: q
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: q
       106: q
       107: 2q+1
       109: q+1
       110: q
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+2q+1
       118: 2q
       119: q^2+3q+1
       120: q
       121: 2q^2+3q+1
       122: q^2+q
       123: q^2+3q+1
       124: q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q+1
       173: q^2+2q+1
       174: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: 2q+1
       185: q+1
       186: q
       187: q+1
       189: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       193: 2q+1
       195: q+1
       196: q
       197: q+1
       199: q^2+3q+1
       200: q
       201: 2q+1
       203: q+1
       204: q
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: 1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       276: q
       278: q
       279: q+1
       281: q+1
       283: q+1
       285: 1
       287: q+1
       289: 1
       291: 1
       293: 2q+1
       295: q+1
       296: q
       297: q+1
       299: 2q+1
       301: 1
       303: q+1
       304: q
       305: q+1
       307: 2q+1
       309: q+1
       310: q
       311: 1
       313: q+1
       315: q+1
       317: q+1
       319: 2q+1
       321: q+1
       322: q
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: 1
       381: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q+1
       421: 1
       423: 1
       425: 1
       427: 2
       429: q+1
       431: 1
       433: 1
       435: 1
       437: 2q+1
       439: q+1
       440: q
       441: q+1
       443: 2
       445: 2
       447: q+1
       449: 1
       451: 1
       453: 2q+1
       455: 1
       457: q+1
       458: q
       459: q+1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: 2q+1
       473: q+1
       474: q
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: q+1
       545: 2
       549: 1
       553: 1
       557: q+1
       561: 1
       563: 1
       565: q+1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       589: q+1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 2
       603: q+1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 2
       617: 2
       619: q+1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q+1
       643: 1
       645: 1
       647: 2q+1
       649: q+1
       650: q
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       693: 1
       696: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 2
       737: 1
       741: 1
       745: 1
       749: 1
       751: 1
       753: 1
       757: 1
       761: q+1
       765: 1
       766: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       785: 1
       789: 2
       797: 1
       799: 1
       801: q+1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 2
       815: 2
       821: 1
       823: 1
       825: q+1
       829: 1
       831: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+1
       845: q+1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       896: 1
       904: 1
       912: 1
       920: 1
       928: 1
       932: 2
       936: 1
       944: 1
       952: 1
       956: 1
       958: 1
       960: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       989: 1
      1002: 1
      1004: 1
      1018: 1
      1022: 1
      1024: 1
      1026: 1
      1034: 1
      1038: 1
      1040: 1
      1042: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1098: 1
      1101: 1
      1118: 1
      1148: 1
      1156: 1
      1168: 1
      1176: 1
      1184: 1
      1198: 1
      1206: 1
      1238: 1
      1240: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1289: 1
      1352: 1
      1384: 1
      1414: 1
      1422: 1
      1470: 1
      1476: 1
      1611: 1

1612:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+2q+1
        60: q^2+3q+1
        61: q
        62: q^2+q
        63: 2q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q
        67: q^2+3q+1
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       104: q^2+2q+1
       105: q
       107: 2q+1
       109: q
       110: q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: 2q
       118: q^2+2q+1
       119: q^2+3q+1
       120: q
       121: q^2+q
       122: 2q^2+3q+1
       123: q
       124: q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q+1
       173: q
       174: q^2+2q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: 2q+1
       185: q
       186: q+1
       188: q+1
       190: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       193: 2q+1
       195: q
       196: q+1
       198: q+1
       199: q^2+3q+1
       200: q
       201: 2q+1
       203: q
       204: q+1
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: 1
       264: q+1
       268: q+1
       274: q+1
       275: q
       276: q^2+2q+1
       277: q
       280: q+1
       282: q+1
       283: q+1
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 2q+1
       295: q
       296: q+1
       298: q+1
       299: 2q+1
       302: 1
       303: q
       304: q+1
       306: q+1
       307: 2q+1
       309: q
       310: q+1
       312: 1
       314: q+1
       316: q+1
       318: q+1
       319: 2q+1
       321: q
       322: q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: 1
       382: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       407: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q+1
       422: 1
       424: 1
       426: 1
       428: 2
       429: q+1
       432: 1
       434: 1
       436: 1
       437: 2q+1
       439: q
       440: q+1
       442: q+1
       443: 2
       446: 2
       447: q+1
       450: 1
       452: 1
       453: 2q+1
       456: 1
       457: q
       458: q+1
       460: q+1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: 2q+1
       473: q
       474: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: q+1
       546: 2
       551: 1
       556: 1
       560: q+1
       562: 1
       564: 1
       566: q+1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: q+1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: q+1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 2
       618: 2
       619: q+1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q+1
       644: 1
       646: 1
       647: 2q+1
       649: q
       650: q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       694: 1
       699: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 2
       740: 1
       744: 1
       748: 1
       750: 1
       752: 1
       754: 1
       759: 1
       763: q+1
       765: 1
       766: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       785: 1
       790: 2
       798: 1
       800: 1
       801: q+1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 2
       815: 2
       822: 1
       824: 1
       825: q+1
       829: 1
       832: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+1
       845: q+1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       897: 1
       905: 1
       913: 1
       921: 1
       929: 1
       933: 2
       939: 1
       947: 1
       953: 1
       957: 1
       959: 1
       962: 1
       976: 1
       980: 1
       983: 1
       986: 1
       988: 1
       989: 1
      1003: 1
      1004: 1
      1019: 1
      1023: 1
      1025: 1
      1026: 1
      1035: 1
      1039: 1
      1040: 1
      1043: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1099: 1
      1104: 1
      1119: 1
      1149: 1
      1157: 1
      1171: 1
      1177: 1
      1186: 1
      1200: 1
      1207: 1
      1239: 1
      1240: 1
      1257: 1
      1258: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1289: 1
      1353: 1
      1385: 1
      1416: 1
      1423: 1
      1471: 1
      1476: 1
      1612: 1

1613:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+q
        39: 2q^2+3q+1
        40: q^2+q
        41: 2q^2+3q+1
        42: q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q
        59: q^2+2q+1
        60: q
        61: q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: q^2+3q+1
        67: q
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       105: q
       106: q^2+2q+1
       108: 2q+1
       109: q
       110: q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: 2q
       118: q^2+2q+1
       119: q
       120: q^2+3q+1
       121: 2q^2+3q+1
       122: q^2+q
       123: q^2+3q+1
       124: q
       125: q^2+4q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       172: q+1
       173: q
       175: q
       176: q^2+2q+1
       177: q+1
       179: q+1
       181: 1
       184: 2q+1
       185: q
       186: q+1
       187: q+1
       189: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       194: 2q+1
       195: q
       196: q+1
       197: q+1
       199: q
       200: q^2+3q+1
       202: 2q+1
       203: q
       204: q+1
       205: q+1
       207: q^2+3q+1
       208: q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       262: 1
       266: q+1
       269: q+1
       273: q+1
       275: q
       277: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       284: q+1
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 2q+1
       295: q
       296: q+1
       297: q+1
       300: 2q+1
       301: 1
       303: q
       304: q+1
       305: q+1
       308: 2q+1
       309: q
       310: q+1
       311: 1
       313: q+1
       315: q+1
       317: q+1
       320: 2q+1
       321: q
       322: q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: 1
       384: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: q+1
       422: 1
       423: 1
       425: 1
       427: 2
       430: q+1
       432: 1
       433: 1
       435: 1
       438: 2q+1
       439: q
       440: q+1
       441: q+1
       444: 2
       445: 2
       448: q+1
       450: 1
       451: 1
       454: 2q+1
       455: 1
       457: q
       458: q+1
       459: q+1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       472: 2q+1
       473: q
       474: q+1
       475: q+1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: q+1
       547: 2
       552: 1
       555: 1
       559: q+1
       561: 1
       563: 1
       568: q+1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       590: q+1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 2
       604: q+1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 2
       617: 2
       620: q+1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       642: q+1
       644: 1
       645: 1
       648: 2q+1
       649: q
       650: q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       697: 1
       698: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 2
       739: 1
       743: 1
       747: 1
       749: 1
       751: 1
       756: 1
       758: 1
       762: q+1
       767: 1
       768: 1
       769: 1
       772: 1
       777: 1
       781: 1
       783: 1
       786: 1
       789: 2
       797: 1
       799: 1
       802: q+1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 2
       816: 2
       821: 1
       823: 1
       826: q+1
       830: 1
       832: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+1
       846: q+1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       888: 1
       889: 1
       899: 1
       906: 1
       914: 1
       922: 1
       930: 1
       934: 2
       938: 1
       946: 1
       955: 1
       956: 1
       958: 1
       961: 1
       975: 1
       979: 1
       982: 1
       985: 1
       990: 1
       991: 1
      1002: 1
      1005: 1
      1018: 1
      1022: 1
      1024: 1
      1027: 1
      1034: 1
      1038: 1
      1041: 1
      1042: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1102: 1
      1103: 1
      1120: 1
      1150: 1
      1158: 1
      1170: 1
      1178: 1
      1185: 1
      1199: 1
      1208: 1
      1238: 1
      1241: 1
      1256: 1
      1259: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1289: 1
      1354: 1
      1386: 1
      1415: 1
      1424: 1
      1470: 1
      1477: 1
      1613: 1

1614:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q^2+4q+1
         3: 3q^2+4q+1
         4: q^3+3q^2+3q+1
         5: 3q^2+4q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+4q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+3q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: q^2+4q+1
        17: q^2+4q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 3q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+4q+1
        34: 3q^2+4q+1
        35: 3q^2+4q+1
        36: q^2+4q+1
        37: q^2+q
        38: 2q^2+3q+1
        39: q^2+q
        40: 2q^2+3q+1
        41: q^2+q
        42: 2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: q^2+4q+1
        47: q^2+4q+1
        48: q^3+2q^2+2q+1
        49: 3q+1
        50: 3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q
        60: q
        61: q^2+3q+1
        62: q^2+q
        63: 2q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: q
        67: q^2+3q+1
        68: q^2+4q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+4q+1
        89: q^2+4q+1
        90: q^3+2q^2+2q+1
        91: 3q+1
        92: 3q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q
       105: q^2+2q+1
       106: q
       108: 2q+1
       109: q+1
       110: q
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: 2q
       119: q
       120: q^2+3q+1
       121: q^2+q
       122: 2q^2+3q+1
       123: q
       124: q^2+3q+1
       125: q^2+4q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: 2q+1
       139: 3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q+1
       143: q^2+4q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       171: q+1
       174: q
       175: q^2+2q+1
       176: q
       178: q+1
       180: q+1
       182: 1
       184: 2q+1
       185: q+1
       186: q
       188: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       194: 2q+1
       195: q+1
       196: q
       198: q+1
       199: q
       200: q^2+3q+1
       202: 2q+1
       203: q+1
       204: q
       206: q+1
       207: q
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2
       248: 2
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       261: 1
       265: q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       278: q
       280: q+1
       282: q+1
       284: q+1
       285: 1
       288: q+1
       290: 1
       292: 1
       294: 2q+1
       295: q+1
       296: q
       298: q+1
       300: 2q+1
       302: 1
       303: q+1
       304: q
       306: q+1
       308: 2q+1
       309: q+1
       310: q
       312: 1
       314: q+1
       316: q+1
       318: q+1
       320: 2q+1
       321: q+1
       322: q
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: 1
       383: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       408: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: q+1
       421: 1
       424: 1
       426: 1
       428: 2
       430: q+1
       431: 1
       434: 1
       436: 1
       438: 2q+1
       439: q+1
       440: q
       442: q+1
       444: 2
       446: 2
       448: q+1
       449: 1
       452: 1
       454: 2q+1
       456: 1
       457: q+1
       458: q
       460: q+1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       472: 2q+1
       473: q+1
       474: q
       476: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 2
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: q+1
       548: 2
       550: 1
       554: 1
       558: q+1
       562: 1
       564: 1
       567: q+1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       590: q+1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 2
       604: q+1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 2
       618: 2
       620: q+1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       642: q+1
       643: 1
       646: 1
       648: 2q+1
       649: q+1
       650: q
       652: 1
       654: q+1
       655: 1
       656: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       700: 1
       701: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 2
       738: 1
       742: 1
       746: 1
       750: 1
       752: 1
       755: 1
       760: 1
       764: q+1
       767: 1
       768: 1
       770: 1
       773: 1
       778: 1
       782: 1
       784: 1
       786: 1
       790: 2
       798: 1
       800: 1
       802: q+1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 2
       816: 2
       822: 1
       824: 1
       826: q+1
       830: 1
       831: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+1
       846: q+1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       891: 1
       892: 1
       898: 1
       907: 1
       915: 1
       923: 1
       931: 1
       935: 2
       937: 1
       945: 1
       954: 1
       957: 1
       959: 1
       963: 1
       977: 1
       981: 1
       983: 1
       986: 1
       990: 1
       991: 1
      1003: 1
      1005: 1
      1019: 1
      1023: 1
      1025: 1
      1027: 1
      1035: 1
      1039: 1
      1041: 1
      1043: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1105: 1
      1106: 1
      1121: 1
      1151: 1
      1159: 1
      1169: 1
      1179: 1
      1187: 1
      1201: 1
      1209: 1
      1239: 1
      1241: 1
      1257: 1
      1259: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1289: 1
      1355: 1
      1387: 1
      1417: 1
      1425: 1
      1471: 1
      1477: 1
      1614: 1

1615:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        59: 2q
        60: 2q+1
        61: q
        62: 2q+1
        63: q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: q
       106: q
       107: q+1
       109: 1
       110: q
       111: 1
       113: q+1
       115: q+1
       117: q+1
       118: 2q
       119: 2q+1
       120: q
       121: 2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q^2+q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       173: q+1
       174: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q+1
       185: 1
       186: q
       187: 1
       189: q+1
       191: q+1
       192: 2q
       193: q+1
       195: 1
       196: q
       197: 1
       199: 2q+1
       200: q
       201: q+1
       203: 1
       204: q
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q+1
       276: q
       278: q
       279: q+1
       281: q+1
       283: q+1
       285: 1
       286: q
       287: q+1
       289: 1
       291: 1
       293: 1
       295: 1
       296: q
       297: 1
       299: q+1
       301: 1
       303: 1
       304: q
       305: 1
       307: q+1
       309: 1
       310: q
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q+1
       321: 1
       322: q
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: q+1
       417: 1
       419: 1
       421: 1
       422: q
       423: 1
       425: 1
       427: 2
       429: q+1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: 2
       445: 2
       447: q+1
       449: 1
       450: q
       451: 1
       453: 1
       455: 1
       457: 1
       458: q
       459: 1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q+1
       473: 1
       474: q
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 2
       549: 1
       553: 1
       557: 1
       561: 1
       563: 1
       565: 1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       585: 1
       589: 1
       593: 1
       595: 1
       596: q
       597: 1
       599: 1
       601: 2
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       613: 1
       615: 2
       617: 2
       619: 1
       621: 1
       622: q
       623: 1
       625: 1
       629: 1
       631: 1
       632: 1
       633: 2
       639: q+1
       641: q+1
       643: 1
       644: q
       645: 1
       647: 1
       649: 1
       650: q
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       679: 1
       680: 2
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       693: 1
       696: 1
       709: 1
       717: 1
       721: 1
       725: 1
       733: 2
       737: 1
       741: 1
       749: 1
       751: 1
       753: 1
       757: 1
       761: 1
       765: 1
       766: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       785: 1
       793: 2
       795: 2
       797: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       817: 1
       818: 1
       819: 2
       821: 1
       825: 1
       829: 1
       831: 1
       832: q
       833: 1
       835: 1
       843: 1
       844: 1
       845: 1
       847: 1
       848: q
       849: 1
       851: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       884: 1
       887: 1
       904: 1
       916: 2
       920: 1
       928: 1
       940: 1
       942: 1
       944: 1
       952: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       994: 1
      1000: 1
      1020: 1
      1022: 1
      1026: 1
      1036: 1
      1038: 1
      1040: 1
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1086: 1
      1089: 1
      1122: 1
      1156: 1
      1176: 1
      1198: 1
      1206: 1
      1230: 1
      1234: 1
      1248: 1
      1254: 1
      1266: 1
      1268: 1
      1274: 1
      1287: 1
      1356: 1
      1388: 1
      1422: 1
      1464: 1
      1468: 1
      1615: 1

1616:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q
        59: q+1
        60: 2q+1
        61: q
        62: q
        63: 2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q+1
       105: q
       107: q+1
       109: q
       110: 1
       112: 1
       114: q+1
       116: q+1
       117: 2q
       118: q+1
       119: 2q+1
       120: q
       121: q
       122: 2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q^2+q+1
       149: 2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 1
       173: q
       174: q+1
       175: q
       178: q+1
       180: q+1
       182: 1
       183: q+1
       185: q
       186: 1
       188: 1
       190: q+1
       191: 2q
       192: q+1
       193: q+1
       195: q
       196: 1
       198: 1
       199: 2q+1
       200: q
       201: q+1
       203: q
       204: 1
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q
       276: q+1
       277: q
       280: q+1
       282: q+1
       283: q+1
       285: q
       286: 1
       288: q+1
       290: 1
       292: 1
       293: 1
       295: q
       296: 1
       298: 1
       299: q+1
       302: 1
       303: q
       304: 1
       306: 1
       307: q+1
       309: q
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q+1
       321: q
       322: 1
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: q+1
       418: 1
       419: 1
       421: q
       422: 1
       424: 1
       426: 1
       428: 2
       429: q+1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: 2
       446: 2
       447: q+1
       449: q
       450: 1
       452: 1
       453: 1
       456: 1
       457: q
       458: 1
       460: 1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q+1
       473: q
       474: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 2
       551: 1
       556: 1
       560: 1
       562: 1
       564: 1
       566: 1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       586: 1
       589: 1
       593: 1
       595: q
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       614: 1
       615: 2
       618: 2
       619: 1
       621: q
       622: 1
       624: 1
       626: 1
       630: 1
       631: 1
       632: 1
       634: 2
       640: q+1
       641: q+1
       643: q
       644: 1
       646: 1
       647: 1
       649: q
       650: 1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       679: 1
       680: 2
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       694: 1
       699: 1
       710: 1
       718: 1
       722: 1
       726: 1
       734: 2
       740: 1
       744: 1
       750: 1
       752: 1
       754: 1
       759: 1
       763: 1
       765: 1
       766: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       785: 1
       793: 2
       796: 2
       798: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       817: 1
       818: 1
       820: 2
       822: 1
       825: 1
       829: 1
       831: q
       832: 1
       834: 1
       836: 1
       843: 1
       844: 1
       845: 1
       847: q
       848: 1
       850: 1
       852: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       885: 1
       890: 1
       905: 1
       917: 2
       921: 1
       929: 1
       941: 1
       943: 1
       947: 1
       953: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       995: 1
      1000: 1
      1021: 1
      1023: 1
      1026: 1
      1037: 1
      1039: 1
      1040: 1
      1049: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1087: 1
      1092: 1
      1123: 1
      1157: 1
      1177: 1
      1200: 1
      1207: 1
      1231: 1
      1234: 1
      1249: 1
      1254: 1
      1267: 1
      1268: 1
      1275: 1
      1287: 1
      1357: 1
      1389: 1
      1423: 1
      1465: 1
      1468: 1
      1616: 1

1617:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q
        59: q+1
        60: q
        61: 2q+1
        62: 2q+1
        63: q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       105: q
       106: q+1
       108: q+1
       109: q
       110: 1
       111: 1
       113: q+1
       115: q+1
       117: 2q
       118: q+1
       119: q
       120: 2q+1
       121: 2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: q+1
       129: q+1
       131: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q^2+q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       172: 1
       173: q
       175: q
       176: q+1
       177: q+1
       179: q+1
       181: 1
       184: q+1
       185: q
       186: 1
       187: 1
       189: q+1
       191: 2q
       192: q+1
       194: q+1
       195: q
       196: 1
       197: 1
       199: q
       200: 2q+1
       202: q+1
       203: q
       204: 1
       205: 1
       207: 2q+1
       208: q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       277: q
       278: q+1
       279: q+1
       281: q+1
       284: q+1
       285: q
       286: 1
       287: q+1
       289: 1
       291: 1
       294: 1
       295: q
       296: 1
       297: 1
       300: q+1
       301: 1
       303: q
       304: 1
       305: 1
       308: q+1
       309: q
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: q+1
       321: q
       322: 1
       323: 1
       325: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: q+1
       417: 1
       420: 1
       421: q
       422: 1
       423: 1
       425: 1
       427: 2
       430: q+1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: 2
       445: 2
       448: q+1
       449: q
       450: 1
       451: 1
       454: 1
       455: 1
       457: q
       458: 1
       459: 1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       472: q+1
       473: q
       474: 1
       475: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 2
       552: 1
       555: 1
       559: 1
       561: 1
       563: 1
       568: 1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       585: 1
       590: 1
       594: 1
       595: q
       596: 1
       597: 1
       599: 1
       601: 2
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       613: 1
       616: 2
       617: 2
       620: 1
       621: q
       622: 1
       623: 1
       625: 1
       629: 1
       631: 1
       632: 1
       633: 2
       639: q+1
       642: q+1
       643: q
       644: 1
       645: 1
       648: 1
       649: q
       650: 1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       679: 1
       680: 2
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       697: 1
       698: 1
       712: 1
       720: 1
       723: 1
       727: 1
       735: 2
       739: 1
       743: 1
       749: 1
       751: 1
       756: 1
       758: 1
       762: 1
       767: 1
       768: 1
       769: 1
       772: 1
       775: 2
       779: 1
       781: 1
       786: 1
       794: 2
       795: 2
       797: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       817: 1
       818: 1
       819: 2
       821: 1
       826: 1
       830: 1
       831: q
       832: 1
       833: 1
       835: 1
       843: 1
       844: 1
       846: 1
       847: q
       848: 1
       849: 1
       851: 1
       855: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       888: 1
       889: 1
       906: 1
       918: 2
       922: 1
       930: 1
       940: 1
       942: 1
       946: 1
       955: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       994: 1
      1001: 1
      1020: 1
      1022: 1
      1027: 1
      1036: 1
      1038: 1
      1041: 1
      1048: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1124: 1
      1158: 1
      1178: 1
      1199: 1
      1208: 1
      1230: 1
      1235: 1
      1248: 1
      1255: 1
      1266: 1
      1269: 1
      1274: 1
      1287: 1
      1358: 1
      1390: 1
      1424: 1
      1464: 1
      1469: 1
      1617: 1

1618:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q+1
        11: 3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q+1
        29: 2q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 3q+1
        44: q^2+2q+1
        45: 3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q+1
        59: 2q
        60: q
        61: 2q+1
        62: q
        63: 2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q+1
        69: q^2+2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: q+1
       106: q
       108: q+1
       109: 1
       110: q
       112: 1
       114: q+1
       116: q+1
       117: q+1
       118: 2q
       119: q
       120: 2q+1
       121: q
       122: 2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: q+1
       130: q+1
       132: q+1
       133: 2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 3q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+q+1
       143: 3q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q^2+q+1
       149: 2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       171: 1
       174: q
       175: q+1
       176: q
       178: q+1
       180: q+1
       182: 1
       184: q+1
       185: 1
       186: q
       188: 1
       190: q+1
       191: q+1
       192: 2q
       194: q+1
       195: 1
       196: q
       198: 1
       199: q
       200: 2q+1
       202: q+1
       203: 1
       204: q
       206: 1
       207: q
       208: 2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: 2q+1
       247: 2
       248: 2
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       261: 1
       265: 1
       270: 1
       272: 1
       276: q
       277: q+1
       278: q
       280: q+1
       282: q+1
       284: q+1
       285: 1
       286: q
       288: q+1
       290: 1
       292: 1
       294: 1
       295: 1
       296: q
       298: 1
       300: q+1
       302: 1
       303: 1
       304: q
       306: 1
       308: q+1
       309: 1
       310: q
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: q+1
       321: 1
       322: q
       324: 1
       326: q+1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+q+1
       351: 2
       352: 2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: q+1
       418: 1
       420: 1
       421: 1
       422: q
       424: 1
       426: 1
       428: 2
       430: q+1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: 2
       446: 2
       448: q+1
       449: 1
       450: q
       452: 1
       454: 1
       456: 1
       457: 1
       458: q
       460: 1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       472: q+1
       473: 1
       474: q
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 2
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: 2
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 2
       550: 1
       554: 1
       558: 1
       562: 1
       564: 1
       567: 1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       586: 1
       590: 1
       594: 1
       595: 1
       596: q
       598: 1
       600: 1
       602: 2
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       614: 1
       616: 2
       618: 2
       620: 1
       621: 1
       622: q
       624: 1
       626: 1
       630: 1
       631: 1
       632: 1
       634: 2
       640: q+1
       642: q+1
       643: 1
       644: q
       646: 1
       648: 1
       649: 1
       650: q
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       674: 2
       675: 1
       676: q+1
       677: 1
       679: 1
       680: 2
       681: 1
       682: q+1
       683: 1
       685: 1
       686: q+1
       687: 1
       688: q+1
       689: 1
       700: 1
       701: 1
       711: 1
       719: 1
       724: 1
       728: 1
       736: 2
       738: 1
       742: 1
       750: 1
       752: 1
       755: 1
       760: 1
       764: 1
       767: 1
       768: 1
       770: 1
       773: 1
       776: 2
       780: 1
       782: 1
       786: 1
       794: 2
       796: 2
       798: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       817: 1
       818: 1
       820: 2
       822: 1
       826: 1
       830: 1
       831: 1
       832: q
       834: 1
       836: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: q
       850: 1
       852: 1
       856: 1
       866: 1
       870: 1
       871: 1
       874: 1
       875: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       891: 1
       892: 1
       907: 1
       919: 2
       923: 1
       931: 1
       941: 1
       943: 1
       945: 1
       954: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       995: 1
      1001: 1
      1021: 1
      1023: 1
      1027: 1
      1037: 1
      1039: 1
      1041: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1076: 1
      1080: 1
      1083: 1
      1084: 1
      1093: 1
      1094: 1
      1125: 1
      1159: 1
      1179: 1
      1201: 1
      1209: 1
      1231: 1
      1235: 1
      1249: 1
      1255: 1
      1267: 1
      1269: 1
      1275: 1
      1287: 1
      1359: 1
      1391: 1
      1425: 1
      1465: 1
      1469: 1
      1618: 1

1619:    0: 3q^3+4q^2+q+1
         1: 2q^4+4q^3+4q^2+q+1
         2: 3q^3+4q^2+q+1
         3: 2q^4+4q^3+4q^2+q+1
         4: q^4+3q^3+3q^2+q+1
         5: 3q^3+4q^2+q+1
         6: q^5+2q^4+4q^3+3q^2+q+1
         7: q^4+3q^3+3q^2+q+1
         8: 3q^3+4q^2+q+1
         9: 2q^5+2q^4+2q^3+2q^2+q+1
        10: 3q^3+q^2+q+1
        11: 3q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: 3q^3+4q^2+q+1
        14: q^4+3q^3+3q^2+q+1
        15: 3q^3+4q^2+q+1
        16: q^3+4q^2+q+1
        17: q^3+4q^2+q+1
        18: q^4+2q^3+2q^2+q+1
        19: 2q^3+3q^2+q+1
        20: q^4+3q^3+3q^2+q+1
        21: 2q^3+3q^2+q+1
        22: 3q^3+4q^2+q+1
        23: 2q^4+4q^3+4q^2+q+1
        24: 3q^3+4q^2+q+1
        25: 3q^3+4q^2+q+1
        26: 2q^4+4q^3+4q^2+q+1
        27: 3q^3+4q^2+q+1
        28: q^3+q^2+q+1
        29: 2q^3+q^2+q+1
        30: 2q^3+3q^2+q+1
        31: 3q^3+q^2+q+1
        32: 3q^3+4q^2+q+1
        33: q^3+4q^2+q+1
        34: 3q^3+q^2+q+1
        35: 3q^3+4q^2+q+1
        36: q^3+4q^2+q+1
        37: 2q^3+3q^2+q+1
        38: q^3+q^2
        39: q^4+3q^3+3q^2+q+1
        40: q^4+q^3+q^2
        41: 2q^3+3q^2+q+1
        42: q^3+q^2
        43: 3q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 3q^3+q^2+q+1
        46: q^3+4q^2+q+1
        47: q^3+4q^2+q+1
        48: q^4+2q^3+2q^2+q+1
        49: 3q^2+q+1
        50: 3q^2+q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+q+1
        53: q^4+3q^3+3q^2+q+1
        54: 2q^3+3q^2+q+1
        55: 2q^3+3q^2+q+1
        56: q^4+3q^3+3q^2+q+1
        57: 2q^3+3q^2+q+1
        58: q^3+q^2+q+1
        60: q^3+q^2+q+1
        62: 2q^3+q^2+q+1
        63: q^3
        64: 2q^3+3q^2+q+1
        65: q^3+q^2
        66: q^3+3q^2+q+1
        67: q^2
        68: q^3+q^2+q+1
        69: 2q^2+q+1
        70: 2q^3+q^2+q+1
        71: q^2+q+1
        72: 2q^2+q+1
        73: 2q^2+q+1
        74: q^3+2q^2+q+1
        76: 2q^3+2q^2+q+1
        78: q^3+2q^2+q+1
        80: 3q^3+q^2+q+1
        81: q^3+4q^2+q+1
        82: 2q^3+q^2+q+1
        83: 2q^3+3q^2+q+1
        84: 3q^3+q^2+q+1
        85: q^3+4q^2+q+1
        86: 2q^3+q^2+q+1
        87: 2q^3+3q^2+q+1
        88: q+1
        89: q+1
        90: q^4+q^3+q+1
        91: 3q^2+q+1
        92: 3q^2+q+1
        93: q^3+2q^2+q+1
        94: 3q^2+q+1
        95: 3q^2+q+1
        96: q^3+2q^2+q+1
        97: 3q^2+q+1
        98: 3q^2+q+1
        99: q^3+2q^2+q+1
       100: 2q^3+3q^2+q+1
       101: q^4+3q^3+3q^2+q+1
       102: 2q^3+3q^2+q+1
       103: q^3+q^2+q+1
       107: q^2+q+1
       109: q^2+q+1
       111: q^2+q+1
       113: q^3+q^2+q+1
       115: q^3+2q^2+q+1
       117: q^3+q^2+q+1
       119: q^3+q^2+q+1
       121: 2q^3+q^2+q+1
       122: q^3
       123: q^3+3q^2+q+1
       124: q^2
       125: q+1
       126: q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: q^2+q+1
       134: 2q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q^2+q+1
       140: 2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^2+q+1
       148: 2q^2+q+1
       149: 2q^3+q^2+q+1
       150: 2q^3+3q^2+q+1
       151: q^3+2q^2+q+1
       153: 2q^3+2q^2+q+1
       155: q^3+2q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 3q^2+q+1
       161: 3q^2+q+1
       162: q^3+2q^2+q+1
       163: 3q^2+q+1
       164: 3q^2+q+1
       165: q^3+2q^2+q+1
       166: 3q^2+q+1
       167: 3q^2+q+1
       168: q^3+2q^2+q+1
       169: q^2+q+1
       173: q^3+q^2+q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       183: q^2+q+1
       185: q^2+q+1
       187: q^2+q+1
       189: q^3+q^2+q+1
       191: q+1
       193: q^2+q+1
       195: q^2+q+1
       197: q^2+q+1
       199: q+1
       201: q^2+q+1
       203: q^2+q+1
       205: q^2+q+1
       207: q+1
       209: q^3+q^2+q+1
       211: q^3+2q^2+q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 2q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+q+1
       233: 2q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: 2q^2+q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: q^2+q+1
       244: 2q^2+q+1
       245: 2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 3q^2+q+1
       257: 3q^2+q+1
       258: q^3+2q^2+q+1
       259: q+1
       263: q^2+q+1
       267: q^2+q+1
       271: q^2+q+1
       275: q+1
       279: q+1
       281: q^2+q+1
       283: q+1
       285: q+1
       287: q+1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: q^2+q+1
       301: q+1
       303: q^2+q+1
       305: q^2+q+1
       307: q^2+q+1
       309: q^2+q+1
       311: q+1
       313: q^2+q+1
       315: q^2+q+1
       317: q+1
       319: q^2+q+1
       321: q^2+q+1
       323: q^2+q+1
       325: q^3+q^2+q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: q+1
       367: q^2+q+1
       368: 2q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: q^3+1
       377: q+1
       381: q+1
       385: 1
       389: q+1
       393: q^2+q+1
       397: q+1
       401: q^2+q+1
       405: q^2+q+1
       413: q+1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: q+1
       429: q+1
       431: q+1
       433: q+1
       435: q+1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: 2q+1
       447: q+1
       449: q+1
       451: q+1
       453: 1
       455: q+1
       457: 1
       459: 1
       461: q+1
       463: 2q+1
       465: q+1
       467: q^2+q+1
       469: q+1
       471: q^2+q+1
       473: q^2+q+1
       475: q^2+q+1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       521: q+1
       529: 1
       533: q+1
       537: q+1
       541: 1
       545: q+1
       549: q+1
       553: q+1
       557: 1
       561: q+1
       565: q^2+q+1
       569: q+1
       573: q+1
       577: q+1
       580: q
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: q+1
       603: 1
       605: q+1
       607: 1
       609: 1
       613: q+1
       615: q+1
       617: 2q+1
       619: 1
       621: 1
       623: q+1
       625: 1
       629: q+1
       631: q+1
       633: 2q+1
       639: q+1
       641: q+1
       643: q+1
       645: q+1
       647: 1
       649: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: q+1
       725: 1
       733: q+1
       737: q+1
       741: 1
       749: q+1
       753: q+1
       757: q+1
       761: 1
       765: q+1
       769: q+1
       772: q
       781: 1
       785: 1
       787: 1
       791: 1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: q+1
       811: 1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: q+1
       835: 1
       845: 1
       847: 1
       849: q+1
       851: 1
       855: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       920: 1
       924: 1
       928: 1
       944: 1
       948: 1
       952: 1
       960: q+1
       974: 1
      1010: 1
      1022: 1
      1026: 1
      1028: 1
      1038: 1
      1040: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: q+1
      1062: 1
      1064: 1
      1083: 1
      1126: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1202: 1
      1206: 1
      1266: 1
      1268: 1
      1270: 1
      1278: 1
      1360: 1
      1392: 1
      1418: 1
      1422: 1
      1426: 1
      1619: 1

1620:    0: 3q^3+4q^2+q+1
         1: 2q^4+4q^3+4q^2+q+1
         2: 3q^3+4q^2+q+1
         3: 2q^4+4q^3+4q^2+q+1
         4: q^4+3q^3+3q^2+q+1
         5: 3q^3+4q^2+q+1
         6: q^5+2q^4+4q^3+3q^2+q+1
         7: q^4+3q^3+3q^2+q+1
         8: 3q^3+4q^2+q+1
         9: 2q^5+2q^4+2q^3+2q^2+q+1
        10: 3q^3+q^2+q+1
        11: 3q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: 3q^3+4q^2+q+1
        14: q^4+3q^3+3q^2+q+1
        15: 3q^3+4q^2+q+1
        16: q^3+4q^2+q+1
        17: q^3+4q^2+q+1
        18: q^4+2q^3+2q^2+q+1
        19: 2q^3+3q^2+q+1
        20: q^4+3q^3+3q^2+q+1
        21: 2q^3+3q^2+q+1
        22: 3q^3+4q^2+q+1
        23: 2q^4+4q^3+4q^2+q+1
        24: 3q^3+4q^2+q+1
        25: 3q^3+4q^2+q+1
        26: 2q^4+4q^3+4q^2+q+1
        27: 3q^3+4q^2+q+1
        28: q^3+q^2+q+1
        29: 2q^3+q^2+q+1
        30: 2q^3+3q^2+q+1
        31: 3q^3+q^2+q+1
        32: 3q^3+4q^2+q+1
        33: q^3+4q^2+q+1
        34: 3q^3+q^2+q+1
        35: 3q^3+4q^2+q+1
        36: q^3+4q^2+q+1
        37: q^3+q^2
        38: 2q^3+3q^2+q+1
        39: q^4+q^3+q^2
        40: q^4+3q^3+3q^2+q+1
        41: q^3+q^2
        42: 2q^3+3q^2+q+1
        43: 3q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 3q^3+q^2+q+1
        46: q^3+4q^2+q+1
        47: q^3+4q^2+q+1
        48: q^4+2q^3+2q^2+q+1
        49: 3q^2+q+1
        50: 3q^2+q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+q+1
        53: q^4+3q^3+3q^2+q+1
        54: 2q^3+3q^2+q+1
        55: 2q^3+3q^2+q+1
        56: q^4+3q^3+3q^2+q+1
        57: 2q^3+3q^2+q+1
        59: q^3+q^2+q+1
        60: q^3+q^2+q+1
        62: q^3
        63: 2q^3+q^2+q+1
        64: q^3+q^2
        65: 2q^3+3q^2+q+1
        66: q^2
        67: q^3+3q^2+q+1
        68: q^3+q^2+q+1
        69: 2q^2+q+1
        70: 2q^3+q^2+q+1
        71: q^2+q+1
        72: 2q^2+q+1
        73: 2q^2+q+1
        75: q^3+2q^2+q+1
        77: 2q^3+2q^2+q+1
        79: q^3+2q^2+q+1
        80: 3q^3+q^2+q+1
        81: q^3+4q^2+q+1
        82: 2q^3+q^2+q+1
        83: 2q^3+3q^2+q+1
        84: 3q^3+q^2+q+1
        85: q^3+4q^2+q+1
        86: 2q^3+q^2+q+1
        87: 2q^3+3q^2+q+1
        88: q+1
        89: q+1
        90: q^4+q^3+q+1
        91: 3q^2+q+1
        92: 3q^2+q+1
        93: q^3+2q^2+q+1
        94: 3q^2+q+1
        95: 3q^2+q+1
        96: q^3+2q^2+q+1
        97: 3q^2+q+1
        98: 3q^2+q+1
        99: q^3+2q^2+q+1
       100: 2q^3+3q^2+q+1
       101: q^4+3q^3+3q^2+q+1
       102: 2q^3+3q^2+q+1
       104: q^3+q^2+q+1
       107: q^2+q+1
       110: q^2+q+1
       112: q^2+q+1
       114: q^3+q^2+q+1
       116: q^3+2q^2+q+1
       118: q^3+q^2+q+1
       119: q^3+q^2+q+1
       121: q^3
       122: 2q^3+q^2+q+1
       123: q^2
       124: q^3+3q^2+q+1
       125: q+1
       126: q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: q^2+q+1
       134: 2q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q^2+q+1
       140: 2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^2+q+1
       148: 2q^2+q+1
       149: 2q^3+q^2+q+1
       150: 2q^3+3q^2+q+1
       152: q^3+2q^2+q+1
       154: 2q^3+2q^2+q+1
       156: q^3+2q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 3q^2+q+1
       161: 3q^2+q+1
       162: q^3+2q^2+q+1
       163: 3q^2+q+1
       164: 3q^2+q+1
       165: q^3+2q^2+q+1
       166: 3q^2+q+1
       167: 3q^2+q+1
       168: q^3+2q^2+q+1
       170: q^2+q+1
       174: q^3+q^2+q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       183: q^2+q+1
       186: q^2+q+1
       188: q^2+q+1
       190: q^3+q^2+q+1
       192: q+1
       193: q^2+q+1
       196: q^2+q+1
       198: q^2+q+1
       199: q+1
       201: q^2+q+1
       204: q^2+q+1
       206: q^2+q+1
       208: q+1
       210: q^3+q^2+q+1
       212: q^3+2q^2+q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 2q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+q+1
       233: 2q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: 2q^2+q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: q^2+q+1
       244: 2q^2+q+1
       245: 2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 3q^2+q+1
       257: 3q^2+q+1
       258: q^3+2q^2+q+1
       260: q+1
       264: q^2+q+1
       268: q^2+q+1
       274: q^2+q+1
       276: q+1
       280: q+1
       282: q^2+q+1
       283: q+1
       286: q+1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: q^2+q+1
       302: q+1
       304: q^2+q+1
       306: q^2+q+1
       307: q^2+q+1
       310: q^2+q+1
       312: q+1
       314: q^2+q+1
       316: q^2+q+1
       318: q+1
       319: q^2+q+1
       322: q^2+q+1
       324: q^2+q+1
       326: q^3+q^2+q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: q+1
       367: q^2+q+1
       368: 2q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: q^3+1
       378: q+1
       382: q+1
       386: 1
       390: q+1
       394: q^2+q+1
       400: q+1
       403: q^2+q+1
       407: q^2+q+1
       414: q+1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: q+1
       429: q+1
       432: q+1
       434: q+1
       436: q+1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: 2q+1
       447: q+1
       450: q+1
       452: q+1
       453: 1
       456: q+1
       458: 1
       460: 1
       462: q+1
       464: 2q+1
       466: q+1
       468: q^2+q+1
       470: q+1
       471: q^2+q+1
       474: q^2+q+1
       476: q^2+q+1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       522: q+1
       530: 1
       534: q+1
       538: q+1
       542: 1
       546: q+1
       551: q+1
       556: q+1
       560: 1
       564: q+1
       566: q^2+q+1
       571: q+1
       574: q+1
       578: q
       581: q+1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: q+1
       603: 1
       606: q+1
       608: 1
       610: 1
       614: q+1
       615: q+1
       618: 2q+1
       619: 1
       622: 1
       624: q+1
       626: 1
       630: q+1
       632: q+1
       634: 2q+1
       640: q+1
       641: q+1
       644: q+1
       646: q+1
       647: 1
       650: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: q+1
       726: 1
       734: q+1
       740: q+1
       744: 1
       752: q+1
       754: q+1
       759: q+1
       763: 1
       766: q+1
       770: q
       773: q+1
       782: 1
       785: 1
       788: 1
       792: 1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: q+1
       812: 1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: q+1
       836: 1
       845: 1
       848: 1
       850: q+1
       852: 1
       856: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       921: 1
       926: 1
       929: 1
       947: 1
       951: 1
       953: 1
       962: q+1
       976: 1
      1011: 1
      1023: 1
      1026: 1
      1029: 1
      1039: 1
      1040: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: q+1
      1063: 1
      1065: 1
      1083: 1
      1128: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1205: 1
      1207: 1
      1267: 1
      1268: 1
      1271: 1
      1279: 1
      1363: 1
      1394: 1
      1421: 1
      1423: 1
      1427: 1
      1620: 1

1621:    0: 3q^3+4q^2+q+1
         1: 2q^4+4q^3+4q^2+q+1
         2: 3q^3+4q^2+q+1
         3: 2q^4+4q^3+4q^2+q+1
         4: q^4+3q^3+3q^2+q+1
         5: 3q^3+4q^2+q+1
         6: q^5+2q^4+4q^3+3q^2+q+1
         7: q^4+3q^3+3q^2+q+1
         8: 3q^3+4q^2+q+1
         9: 2q^5+2q^4+2q^3+2q^2+q+1
        10: 3q^3+q^2+q+1
        11: 3q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: 3q^3+4q^2+q+1
        14: q^4+3q^3+3q^2+q+1
        15: 3q^3+4q^2+q+1
        16: q^3+4q^2+q+1
        17: q^3+4q^2+q+1
        18: q^4+2q^3+2q^2+q+1
        19: 2q^3+3q^2+q+1
        20: q^4+3q^3+3q^2+q+1
        21: 2q^3+3q^2+q+1
        22: 3q^3+4q^2+q+1
        23: 2q^4+4q^3+4q^2+q+1
        24: 3q^3+4q^2+q+1
        25: 3q^3+4q^2+q+1
        26: 2q^4+4q^3+4q^2+q+1
        27: 3q^3+4q^2+q+1
        28: q^3+q^2+q+1
        29: 2q^3+q^2+q+1
        30: 2q^3+3q^2+q+1
        31: 3q^3+q^2+q+1
        32: 3q^3+4q^2+q+1
        33: q^3+4q^2+q+1
        34: 3q^3+q^2+q+1
        35: 3q^3+4q^2+q+1
        36: q^3+4q^2+q+1
        37: q^3+q^2
        38: 2q^3+3q^2+q+1
        39: q^4+q^3+q^2
        40: q^4+3q^3+3q^2+q+1
        41: q^3+q^2
        42: 2q^3+3q^2+q+1
        43: 3q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 3q^3+q^2+q+1
        46: q^3+4q^2+q+1
        47: q^3+4q^2+q+1
        48: q^4+2q^3+2q^2+q+1
        49: 3q^2+q+1
        50: 3q^2+q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+q+1
        53: q^4+3q^3+3q^2+q+1
        54: 2q^3+3q^2+q+1
        55: 2q^3+3q^2+q+1
        56: q^4+3q^3+3q^2+q+1
        57: 2q^3+3q^2+q+1
        58: q^3+q^2+q+1
        61: q^3+q^2+q+1
        62: q^3
        63: 2q^3+q^2+q+1
        64: q^3+q^2
        65: 2q^3+3q^2+q+1
        66: q^2
        67: q^3+3q^2+q+1
        68: q^3+q^2+q+1
        69: 2q^2+q+1
        70: 2q^3+q^2+q+1
        71: q^2+q+1
        72: 2q^2+q+1
        73: 2q^2+q+1
        75: q^3+2q^2+q+1
        77: 2q^3+2q^2+q+1
        79: q^3+2q^2+q+1
        80: 3q^3+q^2+q+1
        81: q^3+4q^2+q+1
        82: 2q^3+q^2+q+1
        83: 2q^3+3q^2+q+1
        84: 3q^3+q^2+q+1
        85: q^3+4q^2+q+1
        86: 2q^3+q^2+q+1
        87: 2q^3+3q^2+q+1
        88: q+1
        89: q+1
        90: q^4+q^3+q+1
        91: 3q^2+q+1
        92: 3q^2+q+1
        93: q^3+2q^2+q+1
        94: 3q^2+q+1
        95: 3q^2+q+1
        96: q^3+2q^2+q+1
        97: 3q^2+q+1
        98: 3q^2+q+1
        99: q^3+2q^2+q+1
       100: 2q^3+3q^2+q+1
       101: q^4+3q^3+3q^2+q+1
       102: 2q^3+3q^2+q+1
       105: q^3+q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       112: q^2+q+1
       114: q^3+q^2+q+1
       116: q^3+2q^2+q+1
       117: q^3+q^2+q+1
       120: q^3+q^2+q+1
       121: q^3
       122: 2q^3+q^2+q+1
       123: q^2
       124: q^3+3q^2+q+1
       125: q+1
       126: q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: q^2+q+1
       134: 2q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q^2+q+1
       140: 2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^2+q+1
       148: 2q^2+q+1
       149: 2q^3+q^2+q+1
       150: 2q^3+3q^2+q+1
       152: q^3+2q^2+q+1
       154: 2q^3+2q^2+q+1
       156: q^3+2q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 3q^2+q+1
       161: 3q^2+q+1
       162: q^3+2q^2+q+1
       163: 3q^2+q+1
       164: 3q^2+q+1
       165: q^3+2q^2+q+1
       166: 3q^2+q+1
       167: 3q^2+q+1
       168: q^3+2q^2+q+1
       171: q^2+q+1
       175: q^3+q^2+q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       184: q^2+q+1
       185: q^2+q+1
       188: q^2+q+1
       190: q^3+q^2+q+1
       191: q+1
       194: q^2+q+1
       195: q^2+q+1
       198: q^2+q+1
       200: q+1
       202: q^2+q+1
       203: q^2+q+1
       206: q^2+q+1
       208: q+1
       210: q^3+q^2+q+1
       212: q^3+2q^2+q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 2q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+q+1
       233: 2q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: 2q^2+q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: q^2+q+1
       244: 2q^2+q+1
       245: 2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 3q^2+q+1
       257: 3q^2+q+1
       258: q^3+2q^2+q+1
       261: q+1
       265: q^2+q+1
       270: q^2+q+1
       272: q^2+q+1
       277: q+1
       280: q+1
       282: q^2+q+1
       284: q+1
       285: q+1
       288: q+1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: q^2+q+1
       302: q+1
       303: q^2+q+1
       306: q^2+q+1
       308: q^2+q+1
       309: q^2+q+1
       312: q+1
       314: q^2+q+1
       316: q^2+q+1
       318: q+1
       320: q^2+q+1
       321: q^2+q+1
       324: q^2+q+1
       326: q^3+q^2+q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: q+1
       367: q^2+q+1
       368: 2q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: q^3+1
       379: q+1
       383: q+1
       387: 1
       392: q+1
       395: q^2+q+1
       398: q+1
       402: q^2+q+1
       408: q^2+q+1
       414: q+1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: q+1
       430: q+1
       431: q+1
       434: q+1
       436: q+1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: 2q+1
       448: q+1
       449: q+1
       452: q+1
       454: 1
       456: q+1
       457: 1
       460: 1
       461: q+1
       464: 2q+1
       466: q+1
       468: q^2+q+1
       470: q+1
       472: q^2+q+1
       473: q^2+q+1
       476: q^2+q+1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       523: q+1
       531: 1
       535: q+1
       540: q+1
       544: 1
       548: q+1
       550: q+1
       554: q+1
       558: 1
       562: q+1
       567: q^2+q+1
       572: q+1
       576: q+1
       578: q
       581: q+1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: q+1
       604: 1
       606: q+1
       607: 1
       610: 1
       614: q+1
       616: q+1
       618: 2q+1
       620: 1
       621: 1
       624: q+1
       626: 1
       630: q+1
       631: q+1
       634: 2q+1
       640: q+1
       642: q+1
       643: q+1
       646: q+1
       648: 1
       649: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: q+1
       728: 1
       736: q+1
       738: q+1
       742: 1
       750: q+1
       755: q+1
       760: q+1
       764: 1
       767: q+1
       770: q
       773: q+1
       782: 1
       786: 1
       787: 1
       792: 1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: q+1
       812: 1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: q+1
       836: 1
       846: 1
       847: 1
       850: q+1
       852: 1
       856: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       923: 1
       925: 1
       931: 1
       945: 1
       949: 1
       954: 1
       963: q+1
       977: 1
      1011: 1
      1023: 1
      1027: 1
      1028: 1
      1039: 1
      1041: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: q+1
      1063: 1
      1065: 1
      1083: 1
      1129: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1203: 1
      1209: 1
      1267: 1
      1269: 1
      1270: 1
      1279: 1
      1362: 1
      1395: 1
      1419: 1
      1425: 1
      1428: 1
      1621: 1

1622:    0: 3q^3+4q^2+q+1
         1: 2q^4+4q^3+4q^2+q+1
         2: 3q^3+4q^2+q+1
         3: 2q^4+4q^3+4q^2+q+1
         4: q^4+3q^3+3q^2+q+1
         5: 3q^3+4q^2+q+1
         6: q^5+2q^4+4q^3+3q^2+q+1
         7: q^4+3q^3+3q^2+q+1
         8: 3q^3+4q^2+q+1
         9: 2q^5+2q^4+2q^3+2q^2+q+1
        10: 3q^3+q^2+q+1
        11: 3q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: 3q^3+4q^2+q+1
        14: q^4+3q^3+3q^2+q+1
        15: 3q^3+4q^2+q+1
        16: q^3+4q^2+q+1
        17: q^3+4q^2+q+1
        18: q^4+2q^3+2q^2+q+1
        19: 2q^3+3q^2+q+1
        20: q^4+3q^3+3q^2+q+1
        21: 2q^3+3q^2+q+1
        22: 3q^3+4q^2+q+1
        23: 2q^4+4q^3+4q^2+q+1
        24: 3q^3+4q^2+q+1
        25: 3q^3+4q^2+q+1
        26: 2q^4+4q^3+4q^2+q+1
        27: 3q^3+4q^2+q+1
        28: q^3+q^2+q+1
        29: 2q^3+q^2+q+1
        30: 2q^3+3q^2+q+1
        31: 3q^3+q^2+q+1
        32: 3q^3+4q^2+q+1
        33: q^3+4q^2+q+1
        34: 3q^3+q^2+q+1
        35: 3q^3+4q^2+q+1
        36: q^3+4q^2+q+1
        37: 2q^3+3q^2+q+1
        38: q^3+q^2
        39: q^4+3q^3+3q^2+q+1
        40: q^4+q^3+q^2
        41: 2q^3+3q^2+q+1
        42: q^3+q^2
        43: 3q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 3q^3+q^2+q+1
        46: q^3+4q^2+q+1
        47: q^3+4q^2+q+1
        48: q^4+2q^3+2q^2+q+1
        49: 3q^2+q+1
        50: 3q^2+q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+q+1
        53: q^4+3q^3+3q^2+q+1
        54: 2q^3+3q^2+q+1
        55: 2q^3+3q^2+q+1
        56: q^4+3q^3+3q^2+q+1
        57: 2q^3+3q^2+q+1
        59: q^3+q^2+q+1
        61: q^3+q^2+q+1
        62: 2q^3+q^2+q+1
        63: q^3
        64: 2q^3+3q^2+q+1
        65: q^3+q^2
        66: q^3+3q^2+q+1
        67: q^2
        68: q^3+q^2+q+1
        69: 2q^2+q+1
        70: 2q^3+q^2+q+1
        71: q^2+q+1
        72: 2q^2+q+1
        73: 2q^2+q+1
        74: q^3+2q^2+q+1
        76: 2q^3+2q^2+q+1
        78: q^3+2q^2+q+1
        80: 3q^3+q^2+q+1
        81: q^3+4q^2+q+1
        82: 2q^3+q^2+q+1
        83: 2q^3+3q^2+q+1
        84: 3q^3+q^2+q+1
        85: q^3+4q^2+q+1
        86: 2q^3+q^2+q+1
        87: 2q^3+3q^2+q+1
        88: q+1
        89: q+1
        90: q^4+q^3+q+1
        91: 3q^2+q+1
        92: 3q^2+q+1
        93: q^3+2q^2+q+1
        94: 3q^2+q+1
        95: 3q^2+q+1
        96: q^3+2q^2+q+1
        97: 3q^2+q+1
        98: 3q^2+q+1
        99: q^3+2q^2+q+1
       100: 2q^3+3q^2+q+1
       101: q^4+3q^3+3q^2+q+1
       102: 2q^3+3q^2+q+1
       106: q^3+q^2+q+1
       108: q^2+q+1
       110: q^2+q+1
       111: q^2+q+1
       113: q^3+q^2+q+1
       115: q^3+2q^2+q+1
       118: q^3+q^2+q+1
       120: q^3+q^2+q+1
       121: 2q^3+q^2+q+1
       122: q^3
       123: q^3+3q^2+q+1
       124: q^2
       125: q+1
       126: q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: q^2+q+1
       134: 2q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q^2+q+1
       140: 2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^2+q+1
       148: 2q^2+q+1
       149: 2q^3+q^2+q+1
       150: 2q^3+3q^2+q+1
       151: q^3+2q^2+q+1
       153: 2q^3+2q^2+q+1
       155: q^3+2q^2+q+1
       157: 1
       158: 1
       159: q^3+1
       160: 3q^2+q+1
       161: 3q^2+q+1
       162: q^3+2q^2+q+1
       163: 3q^2+q+1
       164: 3q^2+q+1
       165: q^3+2q^2+q+1
       166: 3q^2+q+1
       167: 3q^2+q+1
       168: q^3+2q^2+q+1
       172: q^2+q+1
       176: q^3+q^2+q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       184: q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       189: q^3+q^2+q+1
       192: q+1
       194: q^2+q+1
       196: q^2+q+1
       197: q^2+q+1
       200: q+1
       202: q^2+q+1
       204: q^2+q+1
       205: q^2+q+1
       207: q+1
       209: q^3+q^2+q+1
       211: q^3+2q^2+q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 2q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+q+1
       233: 2q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: 2q^2+q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: q^2+q+1
       244: 2q^2+q+1
       245: 2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 3q^2+q+1
       257: 3q^2+q+1
       258: q^3+2q^2+q+1
       262: q+1
       266: q^2+q+1
       269: q^2+q+1
       273: q^2+q+1
       278: q+1
       279: q+1
       281: q^2+q+1
       284: q+1
       286: q+1
       287: q+1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: q^2+q+1
       301: q+1
       304: q^2+q+1
       305: q^2+q+1
       308: q^2+q+1
       310: q^2+q+1
       311: q+1
       313: q^2+q+1
       315: q^2+q+1
       317: q+1
       320: q^2+q+1
       322: q^2+q+1
       323: q^2+q+1
       325: q^3+q^2+q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: q+1
       367: q^2+q+1
       368: 2q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: q^3+1
       380: q+1
       384: q+1
       388: 1
       391: q+1
       396: q^2+q+1
       399: q+1
       404: q^2+q+1
       406: q^2+q+1
       413: q+1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: q+1
       430: q+1
       432: q+1
       433: q+1
       435: q+1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: 2q+1
       448: q+1
       450: q+1
       451: q+1
       454: 1
       455: q+1
       458: 1
       459: 1
       462: q+1
       463: 2q+1
       465: q+1
       467: q^2+q+1
       469: q+1
       472: q^2+q+1
       474: q^2+q+1
       475: q^2+q+1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       524: q+1
       532: 1
       536: q+1
       539: q+1
       543: 1
       547: q+1
       552: q+1
       555: q+1
       559: 1
       563: q+1
       568: q^2+q+1
       570: q+1
       575: q+1
       577: q+1
       580: q
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: q+1
       604: 1
       605: q+1
       608: 1
       609: 1
       613: q+1
       616: q+1
       617: 2q+1
       620: 1
       622: 1
       623: q+1
       625: 1
       629: q+1
       632: q+1
       633: 2q+1
       639: q+1
       642: q+1
       644: q+1
       645: q+1
       648: 1
       650: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       665: 1
       675: 1
       676: 1
       677: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: q+1
       727: 1
       735: q+1
       739: q+1
       743: 1
       751: q+1
       756: q+1
       758: q+1
       762: 1
       768: q+1
       769: q+1
       772: q
       781: 1
       786: 1
       788: 1
       791: 1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: q+1
       811: 1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: q+1
       835: 1
       846: 1
       848: 1
       849: q+1
       851: 1
       855: q+1
       871: 1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       922: 1
       927: 1
       930: 1
       946: 1
       950: 1
       955: 1
       961: q+1
       975: 1
      1010: 1
      1022: 1
      1027: 1
      1029: 1
      1038: 1
      1041: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: q+1
      1062: 1
      1064: 1
      1083: 1
      1127: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1204: 1
      1208: 1
      1266: 1
      1269: 1
      1271: 1
      1278: 1
      1361: 1
      1393: 1
      1420: 1
      1424: 1
      1429: 1
      1622: 1

1623:    0: 3q^3+6q^2+3q+1
         1: 3q^3+6q^2+3q+1
         2: 2q^3+5q^2+2q+1
         3: 3q^3+6q^2+3q+1
         4: q^4+4q^3+4q^2+3q+1
         5: 3q^3+6q^2+3q+1
         6: q^4+4q^3+4q^2+3q+1
         7: q^4+2q^3+4q^2+2q+1
         8: 2q^3+5q^2+2q+1
         9: q^4+2q^3+4q^2+2q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: q^3+2q^2+3q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 3q^3+6q^2+3q+1
        17: 3q^3+6q^2+3q+1
        18: q^4+2q^3+4q^2+2q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: 3q^3+6q^2+3q+1
        23: 3q^3+6q^2+3q+1
        24: 2q^3+5q^2+2q+1
        25: 3q^3+6q^2+3q+1
        26: 3q^3+6q^2+3q+1
        27: 2q^3+5q^2+2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+2q+1
        31: 3q^2+3q+1
        32: 4q^2+2q+1
        33: 3q^3+6q^2+3q+1
        34: 3q^2+3q+1
        35: 4q^2+2q+1
        36: 3q^3+6q^2+3q+1
        37: q^3+3q^2+q+1
        38: 2q^3+3q^2+2q
        39: q^3+3q^2+q+1
        40: 2q^3+3q^2+2q
        41: q^3+2q^2+q+1
        42: q^3+3q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^3+4q^2+2q+1
        52: 2q^3+4q^2+3q+1
        53: 2q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: 2q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: 2q^2+2q+1
        61: q^2+q
        62: q^2+q+1
        63: 2q^2+2q
        64: 2q^2+q+1
        65: 2q^2+q
        66: q^3+3q^2+q+1
        67: 2q^3+3q^2+2q
        68: q+1
        69: 3q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+2q^2+3q+1
        73: q^3+2q^2+3q+1
        74: q^2+q+1
        75: q^3+q^2+2q
        76: q^2+q+1
        77: q^3+q^2+2q
        78: q^2+q+1
        79: 2q^2+q
        80: q^2+2q+1
        81: 4q^2+2q+1
        82: 2q^2+3q+1
        83: 3q^2+2q+1
        84: q^2+2q+1
        85: 4q^2+2q+1
        86: 2q^2+3q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^3+4q^2+3q+1
        95: 2q^3+4q^2+3q+1
        96: q^3+4q^2+2q+1
        97: 2q^3+4q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: q^3+4q^2+2q+1
       100: 2q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q^2+q+1
       104: q^2+q
       105: q^2+q
       107: q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: q+1
       112: 2q
       113: q+1
       114: q^2+2q
       115: q^2+q+1
       116: q^2+q
       117: q+1
       119: q+1
       121: q+1
       122: q^2+q
       123: 2q^2+q+1
       124: 2q^2+q
       125: q+1
       126: q^2+2q+1
       127: q^2+q+1
       128: q^3+q^2+2q
       129: q^2+q+1
       130: q^3+q^2+2q
       131: q^2+q+1
       132: 2q^2+q
       133: q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 3q^2+2q+1
       139: 2q^2+3q+1
       140: q^3+2q^2+3q+1
       141: q^2+2q+1
       142: q^3+2q^2+3q+1
       143: q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^3+2q^2+3q+1
       148: q^3+2q^2+3q+1
       149: 2q^2+3q+1
       150: 3q^2+2q+1
       151: q^2+q+1
       152: q^3+q^2+2q
       153: q^2+q+1
       154: q^3+q^2+2q
       155: q^2+q+1
       156: 2q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^3+4q^2+3q+1
       167: 2q^3+4q^2+3q+1
       168: q^3+4q^2+2q+1
       169: q+1
       170: q
       171: q
       173: q+1
       177: q^2+q+1
       178: q^2+q
       179: q+1
       180: q^2+2q
       181: q+1
       182: 2q
       183: q+1
       185: q+1
       187: q+1
       188: q
       189: q+1
       190: q^2+q
       191: q+1
       193: q^2+2q+1
       194: q
       195: q^2+2q+1
       196: q
       197: q+1
       198: 2q
       199: q+1
       201: q^2+2q+1
       202: q
       203: q^2+2q+1
       204: q
       205: q+1
       206: 2q
       207: q+1
       208: q^2+q
       209: q+1
       210: q^2+2q
       211: q^2+q+1
       212: q^2+q
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: q^2+q+1
       238: q^3+q^2+2q
       239: q^2+q+1
       240: q^3+q^2+2q
       241: q^2+q+1
       242: 2q^2+q
       243: 2q^2+3q+1
       244: q^3+2q^2+3q+1
       245: q^3+2q^2+3q+1
       246: q^2+2q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q+1
       260: q
       261: q
       263: q+1
       267: q+1
       268: q
       270: q
       271: q+1
       272: q
       274: q
       275: q+1
       283: q+1
       285: q+1
       287: q+1
       288: q^2+q
       291: q+1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: q+1
       301: q+1
       302: 2q
       303: q+1
       305: q+1
       306: q
       307: q+1
       309: q+1
       311: q+1
       312: 2q
       313: q+1
       314: q
       315: q^2+q+1
       316: q^2+q
       317: q+1
       318: q^2+2q
       319: q^2+2q+1
       320: q
       321: q^2+2q+1
       322: q
       323: q+1
       324: 2q
       325: q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       339: q^2+3q
       340: 2q+1
       341: q^2+3q
       342: q^2+q+1
       343: 2q^2+q
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       385: 1
       389: q+1
       390: q
       392: q
       393: q+1
       397: q+1
       398: q
       400: q
       401: q+1
       405: q+1
       407: q
       408: q
       419: 1
       421: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: q+1
       428: 3q
       429: q+1
       431: q+1
       433: q+1
       434: q
       437: 1
       439: 1
       441: 1
       442: q
       443: 3q+1
       444: q
       445: 2q+1
       446: q^2+3q
       447: q+1
       449: q+1
       451: q+1
       452: q
       453: 1
       457: 1
       459: 1
       460: q
       461: 3q+1
       462: q
       463: 2q+1
       464: q^2+3q
       469: q+1
       470: q^2+q
       471: q+1
       473: q+1
       475: q+1
       476: q
       477: q+1
       478: 2q
       479: q^2+2q+1
       480: 3q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       529: 1
       533: q+1
       541: 1
       545: q+1
       546: 2q
       548: q
       549: q+1
       557: 1
       561: q+1
       562: 2q
       564: q
       565: q+1
       569: q+1
       571: q
       572: q
       573: 2q+1
       574: q
       576: q
       577: q+1
       578: q^2+q
       580: q
       581: 2q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       603: 1
       607: 1
       609: 1
       610: q
       613: q+1
       614: q
       615: q+1
       619: 1
       621: 1
       625: 1
       626: q
       629: q+1
       630: q
       631: q+1
       641: q+1
       643: q+1
       645: q+1
       646: q
       647: 1
       649: 1
       653: 1
       654: q
       655: q+1
       656: q
       657: q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       693: q+1
       694: q
       699: q
       700: q
       713: 1
       717: 1
       725: 1
       741: 1
       753: q+1
       761: 1
       765: q+1
       785: 1
       787: 1
       791: 1
       793: q+1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       812: q
       817: q+1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       836: q
       843: q+1
       844: q
       845: 1
       847: 1
       851: 1
       852: q
       855: q+1
       856: q
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       908: 1
       924: 1
       928: 1
       948: 1
       952: 1
       964: q+1
       974: 1
       998: 1
      1000: 1
      1012: 1
      1026: 1
      1028: 1
      1040: 1
      1044: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1062: 1
      1063: q
      1064: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1130: 1
      1160: 1
      1180: 1
      1202: 1
      1206: 1
      1232: 1
      1234: 1
      1250: 1
      1254: 1
      1268: 1
      1270: 1
      1280: 1
      1287: 1
      1364: 1
      1396: 1
      1426: 1
      1466: 1
      1468: 1
      1623: 1

1624:    0: 3q^3+6q^2+3q+1
         1: 3q^3+6q^2+3q+1
         2: 2q^3+5q^2+2q+1
         3: 3q^3+6q^2+3q+1
         4: q^4+4q^3+4q^2+3q+1
         5: 3q^3+6q^2+3q+1
         6: q^4+4q^3+4q^2+3q+1
         7: q^4+2q^3+4q^2+2q+1
         8: 2q^3+5q^2+2q+1
         9: q^4+2q^3+4q^2+2q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: q^3+2q^2+3q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 3q^3+6q^2+3q+1
        17: 3q^3+6q^2+3q+1
        18: q^4+2q^3+4q^2+2q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: 3q^3+6q^2+3q+1
        23: 3q^3+6q^2+3q+1
        24: 2q^3+5q^2+2q+1
        25: 3q^3+6q^2+3q+1
        26: 3q^3+6q^2+3q+1
        27: 2q^3+5q^2+2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+2q+1
        31: 3q^2+3q+1
        32: 4q^2+2q+1
        33: 3q^3+6q^2+3q+1
        34: 3q^2+3q+1
        35: 4q^2+2q+1
        36: 3q^3+6q^2+3q+1
        37: 2q^3+3q^2+2q
        38: q^3+3q^2+q+1
        39: 2q^3+3q^2+2q
        40: q^3+3q^2+q+1
        41: q^3+3q^2+q
        42: q^3+2q^2+q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^3+4q^2+2q+1
        52: 2q^3+4q^2+3q+1
        53: 2q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: 2q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: q^2+q
        62: 2q^2+2q
        63: q^2+q+1
        64: 2q^2+q
        65: 2q^2+q+1
        66: 2q^3+3q^2+2q
        67: q^3+3q^2+q+1
        68: q+1
        69: 3q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+2q^2+3q+1
        73: q^3+2q^2+3q+1
        74: q^3+q^2+2q
        75: q^2+q+1
        76: q^3+q^2+2q
        77: q^2+q+1
        78: 2q^2+q
        79: q^2+q+1
        80: q^2+2q+1
        81: 4q^2+2q+1
        82: 2q^2+3q+1
        83: 3q^2+2q+1
        84: q^2+2q+1
        85: 4q^2+2q+1
        86: 2q^2+3q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^3+4q^2+3q+1
        95: 2q^3+4q^2+3q+1
        96: q^3+4q^2+2q+1
        97: 2q^3+4q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: q^3+4q^2+2q+1
       100: 2q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q^2+q
       104: q^2+q+1
       106: q^2+q
       107: q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       111: 2q
       112: q+1
       113: q^2+2q
       114: q+1
       115: q^2+q
       116: q^2+q+1
       118: q+1
       119: q+1
       121: q^2+q
       122: q+1
       123: 2q^2+q
       124: 2q^2+q+1
       125: q+1
       126: q^2+2q+1
       127: q^3+q^2+2q
       128: q^2+q+1
       129: q^3+q^2+2q
       130: q^2+q+1
       131: 2q^2+q
       132: q^2+q+1
       133: q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 3q^2+2q+1
       139: 2q^2+3q+1
       140: q^3+2q^2+3q+1
       141: q^2+2q+1
       142: q^3+2q^2+3q+1
       143: q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^3+2q^2+3q+1
       148: q^3+2q^2+3q+1
       149: 2q^2+3q+1
       150: 3q^2+2q+1
       151: q^3+q^2+2q
       152: q^2+q+1
       153: q^3+q^2+2q
       154: q^2+q+1
       155: 2q^2+q
       156: q^2+q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^3+4q^2+3q+1
       167: 2q^3+4q^2+3q+1
       168: q^3+4q^2+2q+1
       169: q
       170: q+1
       172: q
       174: q+1
       177: q^2+q
       178: q^2+q+1
       179: q^2+2q
       180: q+1
       181: 2q
       182: q+1
       183: q+1
       186: q+1
       187: q
       188: q+1
       189: q^2+q
       190: q+1
       192: q+1
       193: q^2+2q+1
       194: q
       195: q
       196: q^2+2q+1
       197: 2q
       198: q+1
       199: q+1
       201: q^2+2q+1
       202: q
       203: q
       204: q^2+2q+1
       205: 2q
       206: q+1
       207: q^2+q
       208: q+1
       209: q^2+2q
       210: q+1
       211: q^2+q
       212: q^2+q+1
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: q^3+q^2+2q
       238: q^2+q+1
       239: q^3+q^2+2q
       240: q^2+q+1
       241: 2q^2+q
       242: q^2+q+1
       243: 2q^2+3q+1
       244: q^3+2q^2+3q+1
       245: q^3+2q^2+3q+1
       246: q^2+2q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q
       260: q+1
       262: q
       264: q+1
       267: q
       268: q+1
       269: q
       271: q
       273: q
       274: q+1
       276: q+1
       283: q+1
       286: q+1
       287: q^2+q
       288: q+1
       291: q
       292: q+1
       293: 1
       296: 1
       297: q
       298: 1
       299: q+1
       301: 2q
       302: q+1
       304: q+1
       305: q
       306: q+1
       307: q+1
       310: q+1
       311: 2q
       312: q+1
       313: q
       314: q+1
       315: q^2+q
       316: q^2+q+1
       317: q^2+2q
       318: q+1
       319: q^2+2q+1
       320: q
       321: q
       322: q^2+2q+1
       323: 2q
       324: q+1
       325: q^2+q
       326: q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: q^2+3q
       339: 2q+1
       340: q^2+3q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       386: 1
       389: q
       390: q+1
       391: q
       394: q+1
       397: q
       399: q
       400: q+1
       403: q+1
       405: q
       406: q
       407: q+1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 3q
       428: q+1
       429: q+1
       432: q+1
       433: q
       434: q+1
       437: 1
       440: 1
       441: q
       442: 1
       443: 3q+1
       444: q
       445: q^2+3q
       446: 2q+1
       447: q+1
       450: q+1
       451: q
       452: q+1
       453: 1
       458: 1
       459: q
       460: 1
       461: q
       462: 3q+1
       463: q^2+3q
       464: 2q+1
       469: q^2+q
       470: q+1
       471: q+1
       474: q+1
       475: q
       476: q+1
       477: 2q
       478: q+1
       479: 3q
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       530: 1
       534: q+1
       542: 1
       545: 2q
       546: q+1
       547: q
       551: q+1
       560: 1
       561: q
       563: 2q
       564: q+1
       566: q+1
       569: q
       570: q
       571: q+1
       573: q
       574: 2q+1
       575: q
       577: 2q
       578: q
       580: q^2+q
       581: q+1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       603: 1
       608: 1
       609: q
       610: 1
       613: q
       614: q+1
       615: q+1
       619: 1
       622: 1
       625: q
       626: 1
       629: q
       630: q+1
       632: q+1
       641: q+1
       644: q+1
       645: q
       646: q+1
       647: 1
       650: 1
       653: q
       654: 1
       655: q
       656: q+1
       657: q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       693: q
       696: q
       697: q
       699: q+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: q+1
       763: 1
       766: q+1
       785: 1
       788: 1
       792: 1
       793: q+1
       801: 1
       804: 1
       805: 1
       808: 1
       811: q
       812: 1
       818: q+1
       825: 1
       828: 1
       829: 1
       832: 1
       835: q
       836: 1
       843: q
       844: q+1
       845: 1
       848: 1
       851: q
       852: 1
       855: q
       856: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       909: 1
       926: 1
       929: 1
       951: 1
       953: 1
       965: q+1
       976: 1
       999: 1
      1000: 1
      1013: 1
      1026: 1
      1029: 1
      1040: 1
      1045: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1062: q
      1063: 1
      1065: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1131: 1
      1162: 1
      1181: 1
      1205: 1
      1207: 1
      1233: 1
      1234: 1
      1251: 1
      1254: 1
      1268: 1
      1271: 1
      1281: 1
      1287: 1
      1366: 1
      1397: 1
      1427: 1
      1467: 1
      1468: 1
      1624: 1

1625:    0: 3q^3+6q^2+3q+1
         1: 3q^3+6q^2+3q+1
         2: 2q^3+5q^2+2q+1
         3: 3q^3+6q^2+3q+1
         4: q^4+4q^3+4q^2+3q+1
         5: 3q^3+6q^2+3q+1
         6: q^4+4q^3+4q^2+3q+1
         7: q^4+2q^3+4q^2+2q+1
         8: 2q^3+5q^2+2q+1
         9: q^4+2q^3+4q^2+2q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: q^3+2q^2+3q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 3q^3+6q^2+3q+1
        17: 3q^3+6q^2+3q+1
        18: q^4+2q^3+4q^2+2q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: 3q^3+6q^2+3q+1
        23: 3q^3+6q^2+3q+1
        24: 2q^3+5q^2+2q+1
        25: 3q^3+6q^2+3q+1
        26: 3q^3+6q^2+3q+1
        27: 2q^3+5q^2+2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+2q+1
        31: 3q^2+3q+1
        32: 4q^2+2q+1
        33: 3q^3+6q^2+3q+1
        34: 3q^2+3q+1
        35: 4q^2+2q+1
        36: 3q^3+6q^2+3q+1
        37: 2q^3+3q^2+2q
        38: q^3+3q^2+q+1
        39: 2q^3+3q^2+2q
        40: q^3+3q^2+q+1
        41: q^3+3q^2+q
        42: q^3+2q^2+q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^3+4q^2+2q+1
        52: 2q^3+4q^2+3q+1
        53: 2q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: 2q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: q^2+q
        61: 2q^2+2q+1
        62: 2q^2+2q
        63: q^2+q+1
        64: 2q^2+q
        65: 2q^2+q+1
        66: 2q^3+3q^2+2q
        67: q^3+3q^2+q+1
        68: q+1
        69: 3q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+2q^2+3q+1
        73: q^3+2q^2+3q+1
        74: q^3+q^2+2q
        75: q^2+q+1
        76: q^3+q^2+2q
        77: q^2+q+1
        78: 2q^2+q
        79: q^2+q+1
        80: q^2+2q+1
        81: 4q^2+2q+1
        82: 2q^2+3q+1
        83: 3q^2+2q+1
        84: q^2+2q+1
        85: 4q^2+2q+1
        86: 2q^2+3q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^3+4q^2+3q+1
        95: 2q^3+4q^2+3q+1
        96: q^3+4q^2+2q+1
        97: 2q^3+4q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: q^3+4q^2+2q+1
       100: 2q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q^2+q
       105: q^2+q+1
       106: q^2+q
       107: q
       108: q^2+2q+1
       109: q^2+2q+1
       110: q
       111: 2q
       112: q+1
       113: q^2+2q
       114: q+1
       115: q^2+q
       116: q^2+q+1
       117: q+1
       120: q+1
       121: q^2+q
       122: q+1
       123: 2q^2+q
       124: 2q^2+q+1
       125: q+1
       126: q^2+2q+1
       127: q^3+q^2+2q
       128: q^2+q+1
       129: q^3+q^2+2q
       130: q^2+q+1
       131: 2q^2+q
       132: q^2+q+1
       133: q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 3q^2+2q+1
       139: 2q^2+3q+1
       140: q^3+2q^2+3q+1
       141: q^2+2q+1
       142: q^3+2q^2+3q+1
       143: q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^3+2q^2+3q+1
       148: q^3+2q^2+3q+1
       149: 2q^2+3q+1
       150: 3q^2+2q+1
       151: q^3+q^2+2q
       152: q^2+q+1
       153: q^3+q^2+2q
       154: q^2+q+1
       155: 2q^2+q
       156: q^2+q+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^3+4q^2+3q+1
       167: 2q^3+4q^2+3q+1
       168: q^3+4q^2+2q+1
       169: q
       171: q+1
       172: q
       175: q+1
       177: q^2+q
       178: q^2+q+1
       179: q^2+2q
       180: q+1
       181: 2q
       182: q+1
       184: q+1
       185: q+1
       187: q
       188: q+1
       189: q^2+q
       190: q+1
       191: q+1
       193: q
       194: q^2+2q+1
       195: q^2+2q+1
       196: q
       197: 2q
       198: q+1
       200: q+1
       201: q
       202: q^2+2q+1
       203: q^2+2q+1
       204: q
       205: 2q
       206: q+1
       207: q^2+q
       208: q+1
       209: q^2+2q
       210: q+1
       211: q^2+q
       212: q^2+q+1
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: q^3+q^2+2q
       238: q^2+q+1
       239: q^3+q^2+2q
       240: q^2+q+1
       241: 2q^2+q
       242: q^2+q+1
       243: 2q^2+3q+1
       244: q^3+2q^2+3q+1
       245: q^3+2q^2+3q+1
       246: q^2+2q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q
       261: q+1
       262: q
       265: q+1
       267: q
       269: q
       270: q+1
       271: q
       272: q+1
       273: q
       277: q+1
       284: q+1
       285: q+1
       287: q^2+q
       288: q+1
       291: q
       292: q+1
       294: 1
       295: 1
       297: q
       298: 1
       300: q+1
       301: 2q
       302: q+1
       303: q+1
       305: q
       306: q+1
       308: q+1
       309: q+1
       311: 2q
       312: q+1
       313: q
       314: q+1
       315: q^2+q
       316: q^2+q+1
       317: q^2+2q
       318: q+1
       319: q
       320: q^2+2q+1
       321: q^2+2q+1
       322: q
       323: 2q
       324: q+1
       325: q^2+q
       326: q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: q^2+3q
       339: 2q+1
       340: q^2+3q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       387: 1
       389: q
       391: q
       392: q+1
       395: q+1
       397: q
       398: q+1
       399: q
       402: q+1
       405: q
       406: q
       408: q+1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: q+1
       427: 3q
       428: q+1
       430: q+1
       431: q+1
       433: q
       434: q+1
       438: 1
       439: 1
       441: q
       442: 1
       443: q
       444: 3q+1
       445: q^2+3q
       446: 2q+1
       448: q+1
       449: q+1
       451: q
       452: q+1
       454: 1
       457: 1
       459: q
       460: 1
       461: 3q+1
       462: q
       463: q^2+3q
       464: 2q+1
       469: q^2+q
       470: q+1
       472: q+1
       473: q+1
       475: q
       476: q+1
       477: 2q
       478: q+1
       479: 3q
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       531: 1
       535: q+1
       544: 1
       545: q
       547: 2q
       548: q+1
       550: q+1
       558: 1
       561: 2q
       562: q+1
       563: q
       567: q+1
       569: q
       570: q
       572: q+1
       573: q
       575: q
       576: 2q+1
       577: 2q
       578: q
       580: q^2+q
       581: q+1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       604: 1
       607: 1
       609: q
       610: 1
       613: q
       614: q+1
       616: q+1
       620: 1
       621: 1
       625: q
       626: 1
       629: q
       630: q+1
       631: q+1
       642: q+1
       643: q+1
       645: q
       646: q+1
       648: 1
       649: 1
       653: q
       654: 1
       655: q
       656: q+1
       657: q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       693: q
       697: q
       698: q
       700: q+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: q+1
       764: 1
       767: q+1
       786: 1
       787: 1
       792: 1
       794: q+1
       802: 1
       803: 1
       806: 1
       807: 1
       811: q
       812: 1
       817: q+1
       826: 1
       827: 1
       830: 1
       831: 1
       835: q
       836: 1
       843: q
       844: q+1
       846: 1
       847: 1
       851: q
       852: 1
       855: q
       856: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       910: 1
       925: 1
       931: 1
       949: 1
       954: 1
       966: q+1
       977: 1
       998: 1
      1001: 1
      1013: 1
      1027: 1
      1028: 1
      1041: 1
      1044: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1062: q
      1063: 1
      1065: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1132: 1
      1161: 1
      1182: 1
      1203: 1
      1209: 1
      1232: 1
      1235: 1
      1250: 1
      1255: 1
      1269: 1
      1270: 1
      1281: 1
      1287: 1
      1365: 1
      1398: 1
      1428: 1
      1466: 1
      1469: 1
      1625: 1

1626:    0: 3q^3+6q^2+3q+1
         1: 3q^3+6q^2+3q+1
         2: 2q^3+5q^2+2q+1
         3: 3q^3+6q^2+3q+1
         4: q^4+4q^3+4q^2+3q+1
         5: 3q^3+6q^2+3q+1
         6: q^4+4q^3+4q^2+3q+1
         7: q^4+2q^3+4q^2+2q+1
         8: 2q^3+5q^2+2q+1
         9: q^4+2q^3+4q^2+2q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: q^3+2q^2+3q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 3q^3+6q^2+3q+1
        17: 3q^3+6q^2+3q+1
        18: q^4+2q^3+4q^2+2q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: 3q^3+6q^2+3q+1
        23: 3q^3+6q^2+3q+1
        24: 2q^3+5q^2+2q+1
        25: 3q^3+6q^2+3q+1
        26: 3q^3+6q^2+3q+1
        27: 2q^3+5q^2+2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+2q+1
        31: 3q^2+3q+1
        32: 4q^2+2q+1
        33: 3q^3+6q^2+3q+1
        34: 3q^2+3q+1
        35: 4q^2+2q+1
        36: 3q^3+6q^2+3q+1
        37: q^3+3q^2+q+1
        38: 2q^3+3q^2+2q
        39: q^3+3q^2+q+1
        40: 2q^3+3q^2+2q
        41: q^3+2q^2+q+1
        42: q^3+3q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^3+4q^2+2q+1
        52: 2q^3+4q^2+3q+1
        53: 2q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: 2q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: q^2+q
        61: 2q^2+2q+1
        62: q^2+q+1
        63: 2q^2+2q
        64: 2q^2+q+1
        65: 2q^2+q
        66: q^3+3q^2+q+1
        67: 2q^3+3q^2+2q
        68: q+1
        69: 3q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+2q^2+3q+1
        73: q^3+2q^2+3q+1
        74: q^2+q+1
        75: q^3+q^2+2q
        76: q^2+q+1
        77: q^3+q^2+2q
        78: q^2+q+1
        79: 2q^2+q
        80: q^2+2q+1
        81: 4q^2+2q+1
        82: 2q^2+3q+1
        83: 3q^2+2q+1
        84: q^2+2q+1
        85: 4q^2+2q+1
        86: 2q^2+3q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^3+4q^2+3q+1
        95: 2q^3+4q^2+3q+1
        96: q^3+4q^2+2q+1
        97: 2q^3+4q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: q^3+4q^2+2q+1
       100: 2q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       104: q^2+q
       105: q^2+q
       106: q^2+q+1
       107: q
       108: q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q+1
       112: 2q
       113: q+1
       114: q^2+2q
       115: q^2+q+1
       116: q^2+q
       118: q+1
       120: q+1
       121: q+1
       122: q^2+q
       123: 2q^2+q+1
       124: 2q^2+q
       125: q+1
       126: q^2+2q+1
       127: q^2+q+1
       128: q^3+q^2+2q
       129: q^2+q+1
       130: q^3+q^2+2q
       131: q^2+q+1
       132: 2q^2+q
       133: q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 3q^2+2q+1
       139: 2q^2+3q+1
       140: q^3+2q^2+3q+1
       141: q^2+2q+1
       142: q^3+2q^2+3q+1
       143: q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^3+2q^2+3q+1
       148: q^3+2q^2+3q+1
       149: 2q^2+3q+1
       150: 3q^2+2q+1
       151: q^2+q+1
       152: q^3+q^2+2q
       153: q^2+q+1
       154: q^3+q^2+2q
       155: q^2+q+1
       156: 2q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^3+4q^2+3q+1
       167: 2q^3+4q^2+3q+1
       168: q^3+4q^2+2q+1
       170: q
       171: q
       172: q+1
       176: q+1
       177: q^2+q+1
       178: q^2+q
       179: q+1
       180: q^2+2q
       181: q+1
       182: 2q
       184: q+1
       186: q+1
       187: q+1
       188: q
       189: q+1
       190: q^2+q
       192: q+1
       193: q
       194: q^2+2q+1
       195: q
       196: q^2+2q+1
       197: q+1
       198: 2q
       200: q+1
       201: q
       202: q^2+2q+1
       203: q
       204: q^2+2q+1
       205: q+1
       206: 2q
       207: q+1
       208: q^2+q
       209: q+1
       210: q^2+2q
       211: q^2+q+1
       212: q^2+q
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: q^2+q+1
       238: q^3+q^2+2q
       239: q^2+q+1
       240: q^3+q^2+2q
       241: q^2+q+1
       242: 2q^2+q
       243: 2q^2+3q+1
       244: q^3+2q^2+3q+1
       245: q^3+2q^2+3q+1
       246: q^2+2q+1
       247: q^2+5q+1
       248: q^2+5q+1
       249: 3q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q
       261: q
       262: q+1
       266: q+1
       268: q
       269: q+1
       270: q
       272: q
       273: q+1
       274: q
       278: q+1
       284: q+1
       286: q+1
       287: q+1
       288: q^2+q
       291: q+1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: q+1
       301: q+1
       302: 2q
       304: q+1
       305: q+1
       306: q
       308: q+1
       310: q+1
       311: q+1
       312: 2q
       313: q+1
       314: q
       315: q^2+q+1
       316: q^2+q
       317: q+1
       318: q^2+2q
       319: q
       320: q^2+2q+1
       321: q
       322: q^2+2q+1
       323: q+1
       324: 2q
       325: q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 4q+1
       338: 2q+1
       339: q^2+3q
       340: 2q+1
       341: q^2+3q
       342: q^2+q+1
       343: 2q^2+q
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+5q+1
       352: q+1
       353: 1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q+1
       358: q^2+2q+1
       359: q^2+5q+1
       366: q^2+2q+1
       367: q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       388: 1
       390: q
       391: q+1
       392: q
       396: q+1
       398: q
       399: q+1
       400: q
       404: q+1
       406: q+1
       407: q
       408: q
       420: 1
       422: 1
       423: 1
       424: q
       425: q+1
       426: q
       427: q+1
       428: 3q
       430: q+1
       432: q+1
       433: q+1
       434: q
       438: 1
       440: 1
       441: 1
       442: q
       443: q
       444: 3q+1
       445: 2q+1
       446: q^2+3q
       448: q+1
       450: q+1
       451: q+1
       452: q
       454: 1
       458: 1
       459: 1
       460: q
       461: q
       462: 3q+1
       463: 2q+1
       464: q^2+3q
       469: q+1
       470: q^2+q
       472: q+1
       474: q+1
       475: q+1
       476: q
       477: q+1
       478: 2q
       479: q^2+2q+1
       480: 3q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 2q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       532: 1
       536: q+1
       543: 1
       546: q
       547: q+1
       548: 2q
       552: q+1
       559: 1
       562: q
       563: q+1
       564: 2q
       568: q+1
       570: q+1
       571: q
       572: q
       574: q
       575: 2q+1
       576: q
       577: q+1
       578: q^2+q
       580: q
       581: 2q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       604: 1
       608: 1
       609: 1
       610: q
       613: q+1
       614: q
       616: q+1
       620: 1
       622: 1
       625: 1
       626: q
       629: q+1
       630: q
       632: q+1
       642: q+1
       644: q+1
       645: q+1
       646: q
       648: 1
       650: 1
       653: 1
       654: q
       655: q+1
       656: q
       657: q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: q+1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: 2q+1
       697: q+1
       699: q
       700: q
       701: q
       716: 1
       720: 1
       727: 1
       743: 1
       756: q+1
       762: 1
       768: q+1
       786: 1
       788: 1
       791: 1
       794: q+1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       812: q
       818: q+1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       836: q
       843: q+1
       844: q
       846: 1
       848: 1
       851: 1
       852: q
       855: q+1
       856: q
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: q+1
       880: q+1
       911: 1
       927: 1
       930: 1
       950: 1
       955: 1
       967: q+1
       975: 1
       999: 1
      1001: 1
      1012: 1
      1027: 1
      1029: 1
      1041: 1
      1045: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1062: 1
      1063: q
      1064: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1133: 1
      1163: 1
      1183: 1
      1204: 1
      1208: 1
      1233: 1
      1235: 1
      1251: 1
      1255: 1
      1269: 1
      1271: 1
      1280: 1
      1287: 1
      1367: 1
      1399: 1
      1429: 1
      1467: 1
      1469: 1
      1626: 1

1627:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+2q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+2q+1
         8: q^3+4q^2+2q+1
         9: 2q^4+2q^3+2q^2+q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^3+2q^2+q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+2q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+2q+1
        28: q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 3q^2+2q+1
        31: q^3+4q^2+3q+1
        32: 3q^2+2q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+2q+1
        36: q^2+3q+1
        37: 3q^2+q+1
        38: q^3+q^2+2q
        39: 3q^2+q+1
        40: q^3+q^2+2q
        41: q^3+2q^2+q+1
        42: 2q^2+q
        43: 3q^2+2q+1
        44: 3q^2+2q+1
        45: 3q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^3+2q^2+q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q^2+2q+1
        59: q
        60: q^2+2q+1
        61: q
        62: 3q^2+q+1
        63: q^3+q^2+2q
        64: 2q^2+q+1
        65: q^2+q
        66: q^2+q+1
        67: 2q
        68: q+1
        69: q+1
        70: 3q^2+2q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 3q^2+q+1
        75: q^3+q^2+2q
        76: 3q^2+q+1
        77: q^3+q^2+2q
        78: q^3+2q^2+q+1
        79: 2q^2+q
        80: 3q^2+2q+1
        81: 2q+1
        82: q^3+4q^2+3q+1
        83: 3q^2+2q+1
        84: 3q^2+2q+1
        85: 2q+1
        86: q^3+4q^2+3q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^3+2q^2+q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^3+2q^2+q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q^2+q+1
       104: q
       105: q
       107: q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: q^2+q+1
       112: 2q
       113: 3q^2+q+1
       114: q^3+q^2+2q
       115: 2q^2+q+1
       116: q^2+q
       117: q+1
       119: q+1
       121: 2q^2+q+1
       122: q^2+q
       123: q+1
       124: q
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: q^3+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 3q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q+1
       145: q^2+3q+1
       146: 3q^2+2q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 3q^2+2q+1
       151: 3q^2+q+1
       152: q^3+q^2+2q
       153: 3q^2+q+1
       154: q^3+q^2+2q
       155: q^3+2q^2+q+1
       156: 2q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^3+2q^2+q+1
       169: q^2+q+1
       170: q
       171: q
       173: q+1
       177: 1
       179: 1
       181: 1
       183: q+1
       185: q+1
       187: q+1
       188: q
       189: 2q^2+q+1
       190: q^2+q
       191: q+1
       193: q^2+2q+1
       194: q
       195: q^2+2q+1
       196: q
       197: q^2+q+1
       198: 2q
       199: q+1
       201: q^2+2q+1
       202: q
       203: q^2+2q+1
       204: q
       205: q^2+q+1
       206: 2q
       207: q+1
       208: q
       209: 3q^2+q+1
       210: q^3+q^2+2q
       211: 2q^2+q+1
       212: q^2+q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 2q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       237: 1
       239: 1
       241: q^3+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 3q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^3+2q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       259: 1
       263: q+1
       267: q^2+q+1
       268: q
       270: q
       271: q^2+q+1
       272: q
       274: q
       275: q+1
       283: 1
       285: 1
       287: 1
       291: 1
       293: q+1
       295: q+1
       297: q+1
       298: q
       299: q+1
       301: 1
       303: q+1
       305: q+1
       306: q
       307: q+1
       309: q+1
       311: 1
       313: q+1
       314: q
       315: 1
       317: 1
       319: q^2+2q+1
       320: q
       321: q^2+2q+1
       322: q
       323: q^2+q+1
       324: 2q
       325: 2q^2+q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+3q+1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q^2+3q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: q^2+3q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       385: q+1
       389: 1
       393: q+1
       397: 1
       401: q+1
       405: q^2+q+1
       407: q
       408: q
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       437: q+1
       439: q+1
       441: q+1
       442: q
       443: q^2+2q+1
       444: q
       445: 1
       447: 1
       449: 1
       451: 1
       453: q+1
       457: q+1
       459: q+1
       460: q
       461: q^2+2q+1
       462: q
       463: 1
       469: 1
       471: q+1
       473: q+1
       475: q+1
       476: q
       477: 1
       479: q^2+q+1
       480: 2q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 2q+1
       508: 1
       509: q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       529: 1
       533: 1
       541: q+1
       545: 1
       549: 1
       557: q+1
       561: 1
       565: q+1
       569: 1
       573: q^2+q+1
       574: q
       576: q
       577: 1
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       603: 1
       607: 1
       609: 1
       613: 1
       615: q+1
       619: 1
       621: 1
       625: 1
       629: 1
       631: q+1
       641: 1
       643: 1
       645: 1
       647: q+1
       649: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       665: 1
       672: q+1
       673: q+1
       675: 1
       676: 1
       677: q+1
       678: 2q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       684: 2q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       693: 1
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: q+1
       765: q+1
       785: 1
       787: 1
       791: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       815: q+1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       839: q+1
       845: 1
       847: 1
       851: 1
       855: 1
       857: q+1
       858: q
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       908: 1
       924: 1
       928: 1
       948: 1
       952: 1
       974: 1
       988: q+1
      1004: 1
      1006: 1
      1008: 1
      1026: 1
      1028: 1
      1040: 1
      1044: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1134: 1
      1160: 1
      1180: 1
      1202: 1
      1206: 1
      1240: 1
      1242: 1
      1258: 1
      1260: 1
      1268: 1
      1270: 1
      1276: 1
      1289: 1
      1368: 1
      1400: 1
      1426: 1
      1476: 1
      1478: 1
      1627: 1

1628:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+2q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+2q+1
         8: q^3+4q^2+2q+1
         9: 2q^4+2q^3+2q^2+q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^3+2q^2+q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+2q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+2q+1
        28: q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 3q^2+2q+1
        31: q^3+4q^2+3q+1
        32: 3q^2+2q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+2q+1
        36: q^2+3q+1
        37: q^3+q^2+2q
        38: 3q^2+q+1
        39: q^3+q^2+2q
        40: 3q^2+q+1
        41: 2q^2+q
        42: q^3+2q^2+q+1
        43: 3q^2+2q+1
        44: 3q^2+2q+1
        45: 3q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^3+2q^2+q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q
        59: q^2+2q+1
        60: q^2+2q+1
        61: q
        62: q^3+q^2+2q
        63: 3q^2+q+1
        64: q^2+q
        65: 2q^2+q+1
        66: 2q
        67: q^2+q+1
        68: q+1
        69: q+1
        70: 3q^2+2q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q^3+q^2+2q
        75: 3q^2+q+1
        76: q^3+q^2+2q
        77: 3q^2+q+1
        78: 2q^2+q
        79: q^3+2q^2+q+1
        80: 3q^2+2q+1
        81: 2q+1
        82: q^3+4q^2+3q+1
        83: 3q^2+2q+1
        84: 3q^2+2q+1
        85: 2q+1
        86: q^3+4q^2+3q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^3+2q^2+q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^3+2q^2+q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q
       104: q^2+q+1
       106: q
       107: q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       111: 2q
       112: q^2+q+1
       113: q^3+q^2+2q
       114: 3q^2+q+1
       115: q^2+q
       116: 2q^2+q+1
       118: q+1
       119: q+1
       121: q^2+q
       122: 2q^2+q+1
       123: q
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: q^3+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 3q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q+1
       145: q^2+3q+1
       146: 3q^2+2q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 3q^2+2q+1
       151: q^3+q^2+2q
       152: 3q^2+q+1
       153: q^3+q^2+2q
       154: 3q^2+q+1
       155: 2q^2+q
       156: q^3+2q^2+q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^3+2q^2+q+1
       169: q
       170: q^2+q+1
       172: q
       174: q+1
       178: 1
       180: 1
       182: 1
       183: q+1
       186: q+1
       187: q
       188: q+1
       189: q^2+q
       190: 2q^2+q+1
       192: q+1
       193: q^2+2q+1
       194: q
       195: q
       196: q^2+2q+1
       197: 2q
       198: q^2+q+1
       199: q+1
       201: q^2+2q+1
       202: q
       203: q
       204: q^2+2q+1
       205: 2q
       206: q^2+q+1
       207: q
       208: q+1
       209: q^3+q^2+2q
       210: 3q^2+q+1
       211: q^2+q
       212: 2q^2+q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 2q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       238: 1
       240: 1
       242: q^3+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 3q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^3+2q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       260: 1
       264: q+1
       267: q
       268: q^2+q+1
       269: q
       271: q
       273: q
       274: q^2+q+1
       276: q+1
       283: 1
       286: 1
       288: 1
       292: 1
       293: q+1
       296: q+1
       297: q
       298: q+1
       299: q+1
       302: 1
       304: q+1
       305: q
       306: q+1
       307: q+1
       310: q+1
       312: 1
       313: q
       314: q+1
       316: 1
       318: 1
       319: q^2+2q+1
       320: q
       321: q
       322: q^2+2q+1
       323: 2q
       324: q^2+q+1
       325: q^2+q
       326: 2q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+3q+1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q^2+3q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: q^2+3q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       386: q+1
       390: 1
       394: q+1
       400: 1
       403: q+1
       405: q
       406: q
       407: q^2+q+1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       437: q+1
       440: q+1
       441: q
       442: q+1
       443: q^2+2q+1
       444: q
       446: 1
       447: 1
       450: 1
       452: 1
       453: q+1
       458: q+1
       459: q
       460: q+1
       461: q
       462: q^2+2q+1
       464: 1
       470: 1
       471: q+1
       474: q+1
       475: q
       476: q+1
       478: 1
       479: 2q
       480: q^2+q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 2q+1
       508: 1
       509: q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       530: 1
       534: 1
       542: q+1
       546: 1
       551: 1
       560: q+1
       564: 1
       566: q+1
       571: 1
       573: q
       574: q^2+q+1
       575: q
       581: 1
       589: 1
       592: 1
       593: 1
       596: 1
       600: 1
       603: 1
       608: 1
       610: 1
       614: 1
       615: q+1
       619: 1
       622: 1
       626: 1
       630: 1
       632: q+1
       641: 1
       644: 1
       646: 1
       647: q+1
       650: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       665: 1
       672: q+1
       673: q+1
       675: 1
       676: 1
       677: q+1
       678: 2q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       684: 2q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       699: 1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: q+1
       766: q+1
       785: 1
       788: 1
       792: 1
       801: 1
       804: 1
       805: 1
       808: 1
       812: 1
       815: q+1
       825: 1
       828: 1
       829: 1
       832: 1
       836: 1
       840: q+1
       845: 1
       848: 1
       852: 1
       856: 1
       857: q
       858: q+1
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       909: 1
       926: 1
       929: 1
       951: 1
       953: 1
       976: 1
       989: q+1
      1004: 1
      1007: 1
      1009: 1
      1026: 1
      1029: 1
      1040: 1
      1045: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1136: 1
      1162: 1
      1181: 1
      1205: 1
      1207: 1
      1240: 1
      1243: 1
      1258: 1
      1261: 1
      1268: 1
      1271: 1
      1277: 1
      1289: 1
      1371: 1
      1402: 1
      1427: 1
      1476: 1
      1479: 1
      1628: 1

1629:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+2q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+2q+1
         8: q^3+4q^2+2q+1
         9: 2q^4+2q^3+2q^2+q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^3+2q^2+q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+2q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+2q+1
        28: q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 3q^2+2q+1
        31: q^3+4q^2+3q+1
        32: 3q^2+2q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+2q+1
        36: q^2+3q+1
        37: q^3+q^2+2q
        38: 3q^2+q+1
        39: q^3+q^2+2q
        40: 3q^2+q+1
        41: 2q^2+q
        42: q^3+2q^2+q+1
        43: 3q^2+2q+1
        44: 3q^2+2q+1
        45: 3q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^3+2q^2+q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q^2+2q+1
        59: q
        60: q
        61: q^2+2q+1
        62: q^3+q^2+2q
        63: 3q^2+q+1
        64: q^2+q
        65: 2q^2+q+1
        66: 2q
        67: q^2+q+1
        68: q+1
        69: q+1
        70: 3q^2+2q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q^3+q^2+2q
        75: 3q^2+q+1
        76: q^3+q^2+2q
        77: 3q^2+q+1
        78: 2q^2+q
        79: q^3+2q^2+q+1
        80: 3q^2+2q+1
        81: 2q+1
        82: q^3+4q^2+3q+1
        83: 3q^2+2q+1
        84: 3q^2+2q+1
        85: 2q+1
        86: q^3+4q^2+3q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^3+2q^2+q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^3+2q^2+q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       103: q
       105: q^2+q+1
       106: q
       107: q
       108: q^2+2q+1
       109: q^2+2q+1
       110: q
       111: 2q
       112: q^2+q+1
       113: q^3+q^2+2q
       114: 3q^2+q+1
       115: q^2+q
       116: 2q^2+q+1
       117: q+1
       120: q+1
       121: q^2+q
       122: 2q^2+q+1
       123: q
       124: q+1
       125: q+1
       126: q+1
       128: 1
       130: 1
       132: q^3+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 3q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q+1
       145: q^2+3q+1
       146: 3q^2+2q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 3q^2+2q+1
       151: q^3+q^2+2q
       152: 3q^2+q+1
       153: q^3+q^2+2q
       154: 3q^2+q+1
       155: 2q^2+q
       156: q^3+2q^2+q+1
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^3+2q^2+q+1
       169: q
       171: q^2+q+1
       172: q
       175: q+1
       178: 1
       180: 1
       182: 1
       184: q+1
       185: q+1
       187: q
       188: q+1
       189: q^2+q
       190: 2q^2+q+1
       191: q+1
       193: q
       194: q^2+2q+1
       195: q^2+2q+1
       196: q
       197: 2q
       198: q^2+q+1
       200: q+1
       201: q
       202: q^2+2q+1
       203: q^2+2q+1
       204: q
       205: 2q
       206: q^2+q+1
       207: q
       208: q+1
       209: q^3+q^2+2q
       210: 3q^2+q+1
       211: q^2+q
       212: 2q^2+q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 2q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       238: 1
       240: 1
       242: q^3+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 3q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^3+2q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       261: 1
       265: q+1
       267: q
       269: q
       270: q^2+q+1
       271: q
       272: q^2+q+1
       273: q
       277: q+1
       284: 1
       285: 1
       288: 1
       292: 1
       294: q+1
       295: q+1
       297: q
       298: q+1
       300: q+1
       302: 1
       303: q+1
       305: q
       306: q+1
       308: q+1
       309: q+1
       312: 1
       313: q
       314: q+1
       316: 1
       318: 1
       319: q
       320: q^2+2q+1
       321: q^2+2q+1
       322: q
       323: 2q
       324: q^2+q+1
       325: q^2+q
       326: 2q^2+q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+3q+1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q^2+3q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: q^2+3q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       387: q+1
       392: 1
       395: q+1
       398: 1
       402: q+1
       405: q
       406: q
       408: q^2+q+1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       438: q+1
       439: q+1
       441: q
       442: q+1
       443: q
       444: q^2+2q+1
       446: 1
       448: 1
       449: 1
       452: 1
       454: q+1
       457: q+1
       459: q
       460: q+1
       461: q^2+2q+1
       462: q
       464: 1
       470: 1
       472: q+1
       473: q+1
       475: q
       476: q+1
       478: 1
       479: 2q
       480: q^2+q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 2q+1
       508: 1
       509: q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       531: 1
       535: 1
       544: q+1
       548: 1
       550: 1
       558: q+1
       562: 1
       567: q+1
       572: 1
       573: q
       575: q
       576: q^2+q+1
       581: 1
       590: 1
       591: 1
       594: 1
       595: 1
       600: 1
       604: 1
       607: 1
       610: 1
       614: 1
       616: q+1
       620: 1
       621: 1
       626: 1
       630: 1
       631: q+1
       642: 1
       643: 1
       646: 1
       648: q+1
       649: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       665: 1
       672: q+1
       673: q+1
       675: 1
       676: 1
       677: q+1
       678: 2q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       684: 2q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       700: 1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: q+1
       767: q+1
       786: 1
       787: 1
       792: 1
       802: 1
       803: 1
       806: 1
       807: 1
       812: 1
       816: q+1
       826: 1
       827: 1
       830: 1
       831: 1
       836: 1
       839: q+1
       846: 1
       847: 1
       852: 1
       856: 1
       857: q
       858: q+1
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       910: 1
       925: 1
       931: 1
       949: 1
       954: 1
       977: 1
       990: q+1
      1005: 1
      1006: 1
      1009: 1
      1027: 1
      1028: 1
      1041: 1
      1044: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1137: 1
      1161: 1
      1182: 1
      1203: 1
      1209: 1
      1241: 1
      1242: 1
      1259: 1
      1260: 1
      1269: 1
      1270: 1
      1277: 1
      1289: 1
      1370: 1
      1403: 1
      1428: 1
      1477: 1
      1478: 1
      1629: 1

1630:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+2q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+2q+1
         8: q^3+4q^2+2q+1
         9: 2q^4+2q^3+2q^2+q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 3q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^3+2q^2+q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+2q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+2q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+2q+1
        28: q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 3q^2+2q+1
        31: q^3+4q^2+3q+1
        32: 3q^2+2q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+2q+1
        36: q^2+3q+1
        37: 3q^2+q+1
        38: q^3+q^2+2q
        39: 3q^2+q+1
        40: q^3+q^2+2q
        41: q^3+2q^2+q+1
        42: 2q^2+q
        43: 3q^2+2q+1
        44: 3q^2+2q+1
        45: 3q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^3+2q^2+q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+2q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+2q+1
        58: q
        59: q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 3q^2+q+1
        63: q^3+q^2+2q
        64: 2q^2+q+1
        65: q^2+q
        66: q^2+q+1
        67: 2q
        68: q+1
        69: q+1
        70: 3q^2+2q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 3q^2+q+1
        75: q^3+q^2+2q
        76: 3q^2+q+1
        77: q^3+q^2+2q
        78: q^3+2q^2+q+1
        79: 2q^2+q
        80: 3q^2+2q+1
        81: 2q+1
        82: q^3+4q^2+3q+1
        83: 3q^2+2q+1
        84: 3q^2+2q+1
        85: 2q+1
        86: q^3+4q^2+3q+1
        87: 3q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q+1
        92: 2q+1
        93: q^2+q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^3+2q^2+q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^3+2q^2+q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+2q+1
       104: q
       105: q
       106: q^2+q+1
       107: q
       108: q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+q+1
       112: 2q
       113: 3q^2+q+1
       114: q^3+q^2+2q
       115: 2q^2+q+1
       116: q^2+q
       118: q+1
       120: q+1
       121: 2q^2+q+1
       122: q^2+q
       123: q+1
       124: q
       125: q+1
       126: q+1
       127: 1
       129: 1
       131: q^3+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 3q^2+2q+1
       142: q^2+3q+1
       143: 2q+1
       144: q+1
       145: q^2+3q+1
       146: 3q^2+2q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 3q^2+2q+1
       151: 3q^2+q+1
       152: q^3+q^2+2q
       153: 3q^2+q+1
       154: q^3+q^2+2q
       155: q^3+2q^2+q+1
       156: 2q^2+q
       157: 2q+1
       158: 2q+1
       159: q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^3+2q^2+q+1
       170: q
       171: q
       172: q^2+q+1
       176: q+1
       177: 1
       179: 1
       181: 1
       184: q+1
       186: q+1
       187: q+1
       188: q
       189: 2q^2+q+1
       190: q^2+q
       192: q+1
       193: q
       194: q^2+2q+1
       195: q
       196: q^2+2q+1
       197: q^2+q+1
       198: 2q
       200: q+1
       201: q
       202: q^2+2q+1
       203: q
       204: q^2+2q+1
       205: q^2+q+1
       206: 2q
       207: q+1
       208: q
       209: 3q^2+q+1
       210: q^3+q^2+2q
       211: 2q^2+q+1
       212: q^2+q
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 2q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       237: 1
       239: 1
       241: q^3+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 3q^2+2q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: q^3+2q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       262: 1
       266: q+1
       268: q
       269: q^2+q+1
       270: q
       272: q
       273: q^2+q+1
       274: q
       278: q+1
       284: 1
       286: 1
       287: 1
       291: 1
       294: q+1
       296: q+1
       297: q+1
       298: q
       300: q+1
       301: 1
       304: q+1
       305: q+1
       306: q
       308: q+1
       310: q+1
       311: 1
       313: q+1
       314: q
       315: 1
       317: 1
       319: q
       320: q^2+2q+1
       321: q
       322: q^2+2q+1
       323: q^2+q+1
       324: 2q
       325: 2q^2+q+1
       326: q^2+q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+3q+1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q^2+3q+1
       352: 1
       353: q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q+1
       359: q^2+3q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       388: q+1
       391: 1
       396: q+1
       399: 1
       404: q+1
       406: q^2+q+1
       407: q
       408: q
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       438: q+1
       440: q+1
       441: q+1
       442: q
       443: q
       444: q^2+2q+1
       445: 1
       448: 1
       450: 1
       451: 1
       454: q+1
       458: q+1
       459: q+1
       460: q
       461: q
       462: q^2+2q+1
       463: 1
       469: 1
       472: q+1
       474: q+1
       475: q+1
       476: q
       477: 1
       479: q^2+q+1
       480: 2q
       481: 1
       482: 1
       483: q+1
       484: q+1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 2q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 2q+1
       508: 1
       509: q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       532: 1
       536: 1
       543: q+1
       547: 1
       552: 1
       559: q+1
       563: 1
       568: q+1
       570: 1
       574: q
       575: q^2+q+1
       576: q
       577: 1
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       604: 1
       608: 1
       609: 1
       613: 1
       616: q+1
       620: 1
       622: 1
       625: 1
       629: 1
       632: q+1
       642: 1
       644: 1
       645: 1
       648: q+1
       650: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       665: 1
       672: q+1
       673: q+1
       675: 1
       676: 1
       677: q+1
       678: 2q+1
       679: q+1
       681: 1
       682: 1
       683: q+1
       684: 2q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       697: 1
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: q+1
       768: q+1
       786: 1
       788: 1
       791: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       816: q+1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       840: q+1
       846: 1
       848: 1
       851: 1
       855: 1
       857: q+1
       858: q
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       911: 1
       927: 1
       930: 1
       950: 1
       955: 1
       975: 1
       991: q+1
      1005: 1
      1007: 1
      1008: 1
      1027: 1
      1029: 1
      1041: 1
      1045: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1135: 1
      1163: 1
      1183: 1
      1204: 1
      1208: 1
      1241: 1
      1243: 1
      1259: 1
      1261: 1
      1269: 1
      1271: 1
      1276: 1
      1289: 1
      1369: 1
      1401: 1
      1429: 1
      1477: 1
      1479: 1
      1630: 1

1631:    0: 2
         1: 2
         2: q+1
         3: 2
         4: 2
         5: 2
         6: 2
         7: q+1
         8: q+1
         9: q+1
        10: 2
        11: 2
        12: 2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        37: 2
        39: 2
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 2
        64: 1
        66: 2
        69: 1
        70: 1
        71: 2
        72: 2
        73: 2
        74: 2
        76: 2
        78: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: 2
       115: 1
       121: 1
       123: 1
       126: 1
       127: 2
       129: 2
       131: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: 2
       150: 1
       151: 2
       153: 2
       155: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       177: 1
       179: 2
       181: 2
       187: 1
       189: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 1
       209: 2
       211: 1
       213: 1
       215: 1
       217: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       262: 1
       267: 1
       269: 1
       271: 1
       273: 1
       281: 1
       287: 1
       289: 1
       291: 1
       297: 1
       301: 2
       305: 1
       311: 2
       313: 1
       315: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 1
       327: 1
       329: 1
       331: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       360: 1
       362: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       389: 1
       391: 1
       397: 1
       399: 1
       405: 1
       406: 1
       411: 1
       415: 1
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 1
       441: 1
       443: 1
       444: 1
       445: 2
       451: 1
       455: 1
       459: 1
       461: 1
       462: 1
       463: 2
       467: 1
       469: 1
       475: 1
       477: 2
       479: 2
       483: 1
       485: 1
       487: 1
       489: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       545: 1
       547: 1
       561: 1
       563: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       587: 1
       597: 1
       599: 1
       605: 1
       609: 1
       611: 1
       613: 1
       617: 1
       623: 1
       625: 1
       627: 1
       629: 1
       633: 1
       637: 1
       645: 1
       651: 1
       653: 1
       655: 1
       658: 1
       660: 1
       662: 1
       664: 1
       666: 1
       668: 1
       670: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       697: 1
       769: 1
       779: 1
       783: 1
       791: 1
       795: 1
       799: 1
       809: 1
       811: 1
       813: 1
       819: 1
       823: 1
       833: 1
       835: 1
       837: 1
       843: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: 1
       861: 1
       863: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       968: 1
       982: 1
       996: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1020: 1
      1024: 1
      1030: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1060: 1
      1062: 1
      1064: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1138: 1
      1188: 1
      1222: 1
      1224: 1
      1236: 1
      1252: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1288: 1
      1334: 1
      1430: 1
      1472: 1
      1480: 1
      1482: 1
      1631: 1

1632:    0: 2q^2+4q
         1: 2q^2+4q
         2: q^3+3q^2+2q
         3: 2q^2+4q
         4: 2q^2+4q
         5: 2q^2+4q
         6: 2q^2+4q
         7: q^3+3q^2+2q
         8: q^3+3q^2+2q
         9: q^4+2q^3+2q^2+q
        10: 2q^2+4q
        11: 2q^2+4q
        12: 2q^2+4q
        13: q^2+2q
        14: q^2+2q
        15: q^2+2q
        16: 4q
        17: 4q
        18: q^3+2q^2+q
        19: 2q^2+4q
        20: 2q^2+4q
        21: q^3+3q^2+2q
        22: 2q^2+4q
        23: 2q^2+4q
        24: q^3+3q^2+2q
        25: 2q^2+4q
        26: 2q^2+4q
        27: q^3+3q^2+2q
        28: 4q
        29: 2q^2+4q
        30: q^2+2q
        31: 2q^2+4q
        32: q^2+2q
        33: 4q
        34: 2q^2+4q
        35: q^2+2q
        36: 4q
        37: 2q
        38: 2q^2+2q
        39: 2q
        40: 2q^2+2q
        41: q^2+q
        42: q^3+2q^2+q
        43: q^2+2q
        44: q^2+2q
        45: q^2+2q
        46: 2q
        47: 2q
        48: q^2+q
        49: 4q
        50: 4q
        51: q^3+2q^2+q
        52: 2q^2+4q
        53: 2q^2+4q
        54: q^3+3q^2+2q
        55: 2q^2+4q
        56: 2q^2+4q
        57: q^3+3q^2+2q
        58: 2q
        59: 2q
        60: 2q
        61: 2q
        62: 2q
        63: 2q^2+2q
        64: q
        65: q^2+q
        66: 2q
        67: 2q
        69: q
        70: q^2+2q
        71: 4q
        72: 4q
        73: 4q
        74: 2q
        75: 2q^2+2q
        76: 2q
        77: 2q^2+2q
        78: q^2+q
        79: q^3+2q^2+q
        80: q^2+2q
        81: 2q
        82: 2q^2+4q
        83: q^2+2q
        84: q^2+2q
        85: 2q
        86: 2q^2+4q
        87: q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: 2q
        92: 2q
        93: q^2+q
        94: 4q
        95: 4q
        96: q^3+2q^2+q
        97: 4q
        98: 4q
        99: q^3+2q^2+q
       100: 2q^2+4q
       101: 2q^2+4q
       102: q^3+3q^2+2q
       103: q
       104: q
       105: q
       106: q
       107: 2q
       108: 2q
       109: 2q
       110: 2q
       111: 2q
       112: 2q
       113: 2q
       114: 2q^2+2q
       115: q
       116: q^2+q
       121: q
       122: q^2+q
       123: q
       124: q
       126: q
       128: 2q
       130: 2q
       132: q^3+q^2
       134: q
       135: 2q
       136: 2q
       137: 2q
       138: q
       139: 4q
       140: 4q
       141: q^2+2q
       142: 4q
       143: 2q
       144: q
       145: 4q
       146: q^2+2q
       147: 4q
       148: 4q
       149: 2q^2+4q
       150: q^2+2q
       151: 2q
       152: 2q^2+2q
       153: 2q
       154: 2q^2+2q
       155: q^2+q
       156: q^3+2q^2+q
       157: 2q
       158: 2q
       159: q^2+q
       160: 2q
       161: 2q
       162: q^2+q
       163: 2q
       164: 2q
       165: q^2+q
       166: 4q
       167: 4q
       168: q^3+2q^2+q
       169: q
       170: q
       171: q
       172: q
       180: 2q
       182: 2q
       187: q
       188: q
       189: q
       190: q^2+q
       193: 2q
       194: 2q
       195: 2q
       196: 2q
       197: 2q
       198: 2q
       201: 2q
       202: 2q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: q
       208: q
       209: 2q
       210: 2q^2+2q
       211: q
       212: q^2+q
       214: q
       216: q
       218: q^2
       221: q
       222: 2q
       223: q
       224: 2q
       225: q
       226: q
       228: q
       229: 2q
       230: 2q
       231: q
       233: q
       234: 2q
       235: 2q
       236: q
       238: 2q
       240: 2q
       242: q^3+q^2
       243: 4q
       244: 4q
       245: 4q
       246: q^2+2q
       247: 4q
       248: 4q
       249: q^3+2q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: 2q
       257: 2q
       258: q^2+q
       260: q
       261: q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       290: q
       297: q
       298: q
       302: 2q
       305: q
       306: q
       312: 2q
       313: q
       314: q
       318: 2q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       324: 2q
       325: q
       326: q^2+q
       328: q
       330: q
       332: q^2
       334: q
       335: q
       336: q
       337: 4q
       339: 2q
       341: 2q
       343: q^3+q^2
       346: q
       347: 2q
       348: q
       349: 2q
       350: q
       351: 4q
       354: q
       355: 2q
       356: q
       357: 2q
       358: q
       359: 4q
       361: q
       363: q
       365: q^2
       366: q
       368: q
       369: 2q
       370: 2q
       371: 2q
       372: 2q
       373: q^2+q
       374: 2q
       375: 2q
       376: q^2+q
       390: q
       392: q
       398: q
       400: q
       405: q
       406: q
       407: q
       408: q
       416: q
       428: 2q
       436: q
       441: q
       442: q
       443: 2q
       444: 2q
       446: 2q
       456: q
       459: q
       460: q
       461: 2q
       462: 2q
       464: 2q
       475: q
       476: q
       478: 2q
       479: 2q
       480: 2q
       483: q
       486: q
       488: q
       490: q^2
       491: q
       493: q
       494: q
       495: q
       496: 2q
       498: q
       499: q
       500: q
       501: 2q
       503: q
       505: q
       507: q^2
       510: q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: 1
       517: 1
       518: 2q
       519: 2q
       520: q^2+q
       546: q
       548: q
       562: q
       564: q
       571: q
       572: q
       573: q
       574: q
       575: q
       576: q
       581: 2q
       612: q
       618: q
       628: q
       634: q
       652: q
       653: q
       654: q
       655: q
       656: q
       659: 1
       661: 1
       663: 1
       664: 1
       667: q
       669: q
       671: q^2
       673: q
       674: 1
       677: q
       678: 2q
       679: q
       680: 1
       683: q
       684: 2q
       685: q
       687: q
       688: q
       689: q
       690: 1
       691: 1
       692: 1
       699: q
       700: q
       773: q
       780: 1
       796: 1
       814: q
       820: 1
       838: q
       843: 1
       854: q
       857: q
       858: q
       860: 1
       862: 1
       864: 1
       867: 1
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       879: q
       880: q
       969: 1
       986: q
       997: 1
      1012: 1
      1015: 1
      1021: 1
      1031: 1
      1037: 1
      1046: 1
      1077: 1
      1081: 1
      1084: 1
      1085: q
      1139: 1
      1189: 1
      1224: 1
      1237: 1
      1253: 1
      1275: 1
      1280: 1
      1288: 1
      1335: 1
      1431: 1
      1473: 1
      1482: 1
      1632: 1

1633:    0: 2q^3+2q
         1: 2q^3+2q
         2: q^2+q
         3: 2q^3+2q
         4: q^4+q^3+2q
         5: 2q^3+2q
         6: q^4+q^3+2q
         7: q^5+q^2+q
         8: q^2+q
         9: q^5+q^2+q
        10: 2q^3+2q
        11: 2q^3+2q
        12: q^4+q^3+2q
        13: q
        14: q
        15: q
        16: 2q^3+2q
        17: 2q^3+2q
        18: q^5+q^2+q
        19: q^3+2q
        20: q^3+2q
        21: q^2+q
        22: 2q^3+2q
        23: 2q^3+2q
        24: q^2+q
        25: 2q^3+2q
        26: 2q^3+2q
        27: q^2+q
        28: 2q^3+2q
        29: q^3+2q
        30: q
        31: 2q^3+2q
        32: q
        33: 2q^3+2q
        34: 2q^3+2q
        35: q
        36: 2q^3+2q
        37: 2q^3+2q
        39: 2q^3+2q
        41: q^2+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q
        49: q^3+2q
        50: q^3+2q
        51: q^2+q
        52: q^3+2q
        53: q^3+2q
        54: q^2+q
        55: q^3+2q
        56: q^3+2q
        57: q^2+q
        58: q^3+q
        59: q^3+q
        60: q^3+q
        61: q^3+q
        62: 2q^3+2q
        64: q
        66: 2q^3+2q
        69: q
        70: q
        71: q^3+2q
        72: 2q
        73: 2q
        74: q^3+2q
        76: q^3+2q
        78: q^2+q
        80: q
        81: q
        82: q^3+2q
        83: q
        84: q
        85: q
        86: q^3+2q
        87: q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q
        94: q^3+2q
        95: q^3+2q
        96: q^2+q
        97: q^3+2q
        98: q^3+2q
        99: q^2+q
       100: q^3+2q
       101: q^3+2q
       102: q^2+q
       103: q^3+q
       106: q^3+q
       107: q
       108: q
       109: q
       110: q
       111: 2q
       113: q^3+2q
       115: q
       121: q
       123: q
       126: q
       127: q^3+2q
       129: q^3+2q
       131: q^2+q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^3+2q
       140: 2q
       141: q
       142: 2q
       143: q
       144: q
       145: q^3+2q
       146: q
       147: 2q
       148: 2q
       149: q^3+2q
       150: q
       151: q^3+2q
       153: q^3+2q
       155: q^2+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q^3+2q
       167: q^3+2q
       168: q^2+q
       169: q
       172: q
       177: q
       179: q^3+2q
       181: 2q
       187: q
       189: q
       193: q
       194: q
       195: q
       196: q
       197: 2q
       201: q
       202: q
       203: q
       204: q
       205: 2q
       207: q
       209: q^3+2q
       211: q
       213: q
       215: q
       217: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       237: q^3+2q
       239: q^3+2q
       241: q^2+q
       243: q^3+2q
       244: 2q
       245: 2q
       246: q
       247: 2q
       248: 2q
       249: q^2+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q
       257: q
       258: q
       259: q
       262: q
       267: q
       269: q
       271: q
       273: q
       281: q
       287: q
       289: q
       291: q
       297: q
       301: 2q
       305: q
       311: 2q
       313: q
       315: q
       317: q^3+2q
       319: q
       320: q
       321: q
       322: q
       323: 2q
       325: q
       327: q
       329: q
       331: q
       334: q
       335: q
       336: q
       337: 2q
       338: 2q
       340: 2q
       342: q^2+q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: 2q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: 2q
       360: q
       362: q
       364: q
       366: q
       368: q
       369: q
       370: q
       374: q
       375: q
       376: q
       389: q
       391: q
       397: q
       399: q
       405: q
       406: q
       411: q
       415: q
       417: q
       423: q
       425: q
       427: 2q
       433: q
       435: q
       441: q
       443: q
       444: q
       445: 2q
       451: q
       455: q
       459: q
       461: q
       462: q
       463: 2q
       467: q
       469: q
       475: q
       477: 2q
       479: 2q
       483: q
       493: q
       494: q
       495: q
       498: q
       499: q
       500: q
       502: q
       504: q
       506: q
       510: q
       511: q
       512: q
       513: q
       514: q
       545: q
       547: q
       561: q
       563: q
       569: q
       570: q
       573: q
       575: q
       577: 2q
       587: q
       599: q
       605: q
       609: q
       611: q
       613: q
       623: q
       625: q
       627: q
       629: q
       637: q
       645: q
       651: q
       653: q
       677: q
       683: q
       687: q
       688: q
       689: q
       693: q
       697: q
       799: q
       811: q
       823: q
       835: q
       849: q
       851: q
       853: q
       855: q
       879: q
      1010: 1
      1050: q
      1062: q
      1140: 1
      1222: 1
      1278: 1
      1336: 1
      1432: 1
      1480: 1
      1633: 1

1634:    0: 2q^2+4q
         1: 2q^2+4q
         2: q^3+3q^2+2q
         3: 2q^2+4q
         4: 2q^2+4q
         5: 2q^2+4q
         6: 2q^2+4q
         7: q^3+3q^2+2q
         8: q^3+3q^2+2q
         9: q^4+2q^3+2q^2+q
        10: 2q^2+4q
        11: 2q^2+4q
        12: 2q^2+4q
        13: q^2+2q
        14: q^2+2q
        15: q^2+2q
        16: 4q
        17: 4q
        18: q^3+2q^2+q
        19: 2q^2+4q
        20: 2q^2+4q
        21: q^3+3q^2+2q
        22: 2q^2+4q
        23: 2q^2+4q
        24: q^3+3q^2+2q
        25: 2q^2+4q
        26: 2q^2+4q
        27: q^3+3q^2+2q
        28: 4q
        29: 2q^2+4q
        30: q^2+2q
        31: 2q^2+4q
        32: q^2+2q
        33: 4q
        34: 2q^2+4q
        35: q^2+2q
        36: 4q
        37: 2q^2+2q
        38: 2q
        39: 2q^2+2q
        40: 2q
        41: q^3+2q^2+q
        42: q^2+q
        43: q^2+2q
        44: q^2+2q
        45: q^2+2q
        46: 2q
        47: 2q
        48: q^2+q
        49: 4q
        50: 4q
        51: q^3+2q^2+q
        52: 2q^2+4q
        53: 2q^2+4q
        54: q^3+3q^2+2q
        55: 2q^2+4q
        56: 2q^2+4q
        57: q^3+3q^2+2q
        58: 2q
        59: 2q
        60: 2q
        61: 2q
        62: 2q^2+2q
        63: 2q
        64: q^2+q
        65: q
        66: 2q
        67: 2q
        69: q
        70: q^2+2q
        71: 4q
        72: 4q
        73: 4q
        74: 2q^2+2q
        75: 2q
        76: 2q^2+2q
        77: 2q
        78: q^3+2q^2+q
        79: q^2+q
        80: q^2+2q
        81: 2q
        82: 2q^2+4q
        83: q^2+2q
        84: q^2+2q
        85: 2q
        86: 2q^2+4q
        87: q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: 2q
        92: 2q
        93: q^2+q
        94: 4q
        95: 4q
        96: q^3+2q^2+q
        97: 4q
        98: 4q
        99: q^3+2q^2+q
       100: 2q^2+4q
       101: 2q^2+4q
       102: q^3+3q^2+2q
       103: q
       104: q
       105: q
       106: q
       107: 2q
       108: 2q
       109: 2q
       110: 2q
       111: 2q
       112: 2q
       113: 2q^2+2q
       114: 2q
       115: q^2+q
       116: q
       121: q^2+q
       122: q
       123: q
       124: q
       126: q
       127: 2q
       129: 2q
       131: q^3+q^2
       134: q
       135: 2q
       136: 2q
       137: 2q
       138: q
       139: 4q
       140: 4q
       141: q^2+2q
       142: 4q
       143: 2q
       144: q
       145: 4q
       146: q^2+2q
       147: 4q
       148: 4q
       149: 2q^2+4q
       150: q^2+2q
       151: 2q^2+2q
       152: 2q
       153: 2q^2+2q
       154: 2q
       155: q^3+2q^2+q
       156: q^2+q
       157: 2q
       158: 2q
       159: q^2+q
       160: 2q
       161: 2q
       162: q^2+q
       163: 2q
       164: 2q
       165: q^2+q
       166: 4q
       167: 4q
       168: q^3+2q^2+q
       169: q
       170: q
       171: q
       172: q
       179: 2q
       181: 2q
       187: q
       188: q
       189: q^2+q
       190: q
       193: 2q
       194: 2q
       195: 2q
       196: 2q
       197: 2q
       198: 2q
       201: 2q
       202: 2q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: q
       208: q
       209: 2q^2+2q
       210: 2q
       211: q^2+q
       212: q
       213: q
       215: q
       217: q^2
       221: q
       222: 2q
       223: q
       224: 2q
       225: q
       226: q
       228: q
       229: 2q
       230: 2q
       231: q
       233: q
       234: 2q
       235: 2q
       236: q
       237: 2q
       239: 2q
       241: q^3+q^2
       243: 4q
       244: 4q
       245: 4q
       246: q^2+2q
       247: 4q
       248: 4q
       249: q^3+2q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: 2q
       257: 2q
       258: q^2+q
       259: q
       262: q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       289: q
       297: q
       298: q
       301: 2q
       305: q
       306: q
       311: 2q
       313: q
       314: q
       317: 2q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       324: 2q
       325: q^2+q
       326: q
       327: q
       329: q
       331: q^2
       334: q
       335: q
       336: q
       337: 4q
       338: 2q
       340: 2q
       342: q^3+q^2
       346: q
       347: 2q
       348: q
       349: 2q
       350: q
       351: 4q
       354: q
       355: 2q
       356: q
       357: 2q
       358: q
       359: 4q
       360: q
       362: q
       364: q^2
       366: q
       368: q
       369: 2q
       370: 2q
       371: 2q
       372: 2q
       373: q^2+q
       374: 2q
       375: 2q
       376: q^2+q
       389: q
       391: q
       397: q
       399: q
       405: q
       406: q
       407: q
       408: q
       415: q
       427: 2q
       435: q
       441: q
       442: q
       443: 2q
       444: 2q
       445: 2q
       455: q
       459: q
       460: q
       461: 2q
       462: 2q
       463: 2q
       475: q
       476: q
       477: 2q
       479: 2q
       480: 2q
       483: q
       485: q
       487: q
       489: q^2
       491: q
       493: q
       494: q
       495: q
       496: 2q
       498: q
       499: q
       500: q
       501: 2q
       502: q
       504: q
       506: q^2
       510: q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: 1
       517: 1
       518: 2q
       519: 2q
       520: q^2+q
       545: q
       547: q
       561: q
       563: q
       569: q
       570: q
       573: q
       574: q
       575: q
       576: q
       577: 2q
       611: q
       617: q
       627: q
       633: q
       651: q
       653: q
       654: q
       655: q
       656: q
       658: 1
       660: 1
       662: 1
       664: 1
       666: q
       668: q
       670: q^2
       673: q
       674: 1
       677: q
       678: 2q
       679: q
       680: 1
       683: q
       684: 2q
       685: q
       687: q
       688: q
       689: q
       690: 1
       691: 1
       692: 1
       693: q
       697: q
       769: q
       779: 1
       795: 1
       813: q
       819: 1
       837: q
       844: 1
       853: q
       857: q
       858: q
       859: 1
       861: 1
       863: 1
       867: 1
       869: 1
       870: 1
       872: q
       873: 1
       874: 1
       876: q
       879: q
       880: q
       971: 1
       982: q
       996: 1
      1013: 1
      1014: 1
      1020: 1
      1030: 1
      1036: 1
      1047: 1
      1077: 1
      1081: 1
      1084: 1
      1085: q
      1141: 1
      1191: 1
      1225: 1
      1236: 1
      1252: 1
      1274: 1
      1281: 1
      1288: 1
      1337: 1
      1433: 1
      1472: 1
      1483: 1
      1634: 1

1635:    0: 2
         1: 2
         2: q+1
         3: 2
         4: 2
         5: 2
         6: 2
         7: q+1
         8: q+1
         9: q+1
        10: 2
        11: 2
        12: 2
        13: 1
        14: 1
        15: 1
        16: 2
        17: 2
        18: q+1
        19: 2
        20: 2
        21: q+1
        22: 2
        23: 2
        24: q+1
        25: 2
        26: 2
        27: q+1
        28: 2
        29: 2
        30: 1
        31: 2
        32: 1
        33: 2
        34: 2
        35: 1
        36: 2
        38: 2
        40: 2
        42: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 2
        50: 2
        51: q+1
        52: 2
        53: 2
        54: q+1
        55: 2
        56: 2
        57: q+1
        58: 1
        59: 1
        60: 1
        61: 1
        63: 2
        65: 1
        67: 2
        69: 1
        70: 1
        71: 2
        72: 2
        73: 2
        75: 2
        77: 2
        79: q+1
        80: 1
        81: 1
        82: 2
        83: 1
        84: 1
        85: 1
        86: 2
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: 2
       101: 2
       102: q+1
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: 2
       116: 1
       122: 1
       124: 1
       126: 1
       128: 2
       130: 2
       132: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 2
       140: 2
       141: 1
       142: 2
       143: 1
       144: 1
       145: 2
       146: 1
       147: 2
       148: 2
       149: 2
       150: 1
       152: 2
       154: 2
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       178: 1
       180: 2
       182: 2
       188: 1
       190: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 1
       210: 2
       212: 1
       214: 1
       216: 1
       218: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       245: 2
       246: 1
       247: 2
       248: 2
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       261: 1
       268: 1
       270: 1
       272: 1
       274: 1
       282: 1
       288: 1
       290: 1
       292: 1
       298: 1
       302: 2
       306: 1
       312: 2
       314: 1
       316: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 1
       328: 1
       330: 1
       332: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 2
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 2
       361: 1
       363: 1
       365: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       390: 1
       392: 1
       398: 1
       400: 1
       407: 1
       408: 1
       412: 1
       416: 1
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 1
       442: 1
       443: 1
       444: 1
       446: 2
       452: 1
       456: 1
       460: 1
       461: 1
       462: 1
       464: 2
       468: 1
       470: 1
       476: 1
       478: 2
       480: 2
       483: 1
       486: 1
       488: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       546: 1
       548: 1
       562: 1
       564: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       588: 1
       598: 1
       600: 1
       606: 1
       610: 1
       612: 1
       614: 1
       618: 1
       624: 1
       626: 1
       628: 1
       630: 1
       634: 1
       638: 1
       646: 1
       652: 1
       654: 1
       656: 1
       659: 1
       661: 1
       663: 1
       664: 1
       667: 1
       669: 1
       671: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       699: 1
       700: 1
       773: 1
       780: 1
       784: 1
       792: 1
       796: 1
       800: 1
       810: 1
       812: 1
       814: 1
       820: 1
       824: 1
       834: 1
       836: 1
       838: 1
       844: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: 1
       862: 1
       864: 1
       867: 1
       869: 1
       870: 1
       872: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       972: 1
       986: 1
       997: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1021: 1
      1025: 1
      1031: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1061: 1
      1063: 1
      1065: 1
      1077: 1
      1081: 1
      1084: 1
      1085: 1
      1142: 1
      1192: 1
      1223: 1
      1225: 1
      1237: 1
      1253: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1288: 1
      1338: 1
      1434: 1
      1473: 1
      1481: 1
      1483: 1
      1635: 1

1636:    0: 2q^3+2q
         1: 2q^3+2q
         2: q^2+q
         3: 2q^3+2q
         4: q^4+q^3+2q
         5: 2q^3+2q
         6: q^4+q^3+2q
         7: q^5+q^2+q
         8: q^2+q
         9: q^5+q^2+q
        10: 2q^3+2q
        11: 2q^3+2q
        12: q^4+q^3+2q
        13: q
        14: q
        15: q
        16: 2q^3+2q
        17: 2q^3+2q
        18: q^5+q^2+q
        19: q^3+2q
        20: q^3+2q
        21: q^2+q
        22: 2q^3+2q
        23: 2q^3+2q
        24: q^2+q
        25: 2q^3+2q
        26: 2q^3+2q
        27: q^2+q
        28: 2q^3+2q
        29: q^3+2q
        30: q
        31: 2q^3+2q
        32: q
        33: 2q^3+2q
        34: 2q^3+2q
        35: q
        36: 2q^3+2q
        38: 2q^3+2q
        40: 2q^3+2q
        42: q^2+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q
        49: q^3+2q
        50: q^3+2q
        51: q^2+q
        52: q^3+2q
        53: q^3+2q
        54: q^2+q
        55: q^3+2q
        56: q^3+2q
        57: q^2+q
        58: q^3+q
        59: q^3+q
        60: q^3+q
        61: q^3+q
        63: 2q^3+2q
        65: q
        67: 2q^3+2q
        69: q
        70: q
        71: q^3+2q
        72: 2q
        73: 2q
        75: q^3+2q
        77: q^3+2q
        79: q^2+q
        80: q
        81: q
        82: q^3+2q
        83: q
        84: q
        85: q
        86: q^3+2q
        87: q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q
        94: q^3+2q
        95: q^3+2q
        96: q^2+q
        97: q^3+2q
        98: q^3+2q
        99: q^2+q
       100: q^3+2q
       101: q^3+2q
       102: q^2+q
       104: q^3+q
       105: q^3+q
       107: q
       108: q
       109: q
       110: q
       112: 2q
       114: q^3+2q
       116: q
       122: q
       124: q
       126: q
       128: q^3+2q
       130: q^3+2q
       132: q^2+q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q^3+2q
       140: 2q
       141: q
       142: 2q
       143: q
       144: q
       145: q^3+2q
       146: q
       147: 2q
       148: 2q
       149: q^3+2q
       150: q
       152: q^3+2q
       154: q^3+2q
       156: q^2+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q
       163: q
       164: q
       165: q
       166: q^3+2q
       167: q^3+2q
       168: q^2+q
       170: q
       171: q
       178: q
       180: q^3+2q
       182: 2q
       188: q
       190: q
       193: q
       194: q
       195: q
       196: q
       198: 2q
       201: q
       202: q
       203: q
       204: q
       206: 2q
       208: q
       210: q^3+2q
       212: q
       214: q
       216: q
       218: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       228: q
       229: q
       230: q
       231: q
       233: q
       234: q
       235: q
       236: q
       238: q^3+2q
       240: q^3+2q
       242: q^2+q
       243: q^3+2q
       244: 2q
       245: 2q
       246: q
       247: 2q
       248: 2q
       249: q^2+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q
       257: q
       258: q
       260: q
       261: q
       268: q
       270: q
       272: q
       274: q
       282: q
       288: q
       290: q
       292: q
       298: q
       302: 2q
       306: q
       312: 2q
       314: q
       316: q
       318: q^3+2q
       319: q
       320: q
       321: q
       322: q
       324: 2q
       326: q
       328: q
       330: q
       332: q
       334: q
       335: q
       336: q
       337: 2q
       339: 2q
       341: 2q
       343: q^2+q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: 2q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: 2q
       361: q
       363: q
       365: q
       366: q
       368: q
       369: q
       370: q
       374: q
       375: q
       376: q
       390: q
       392: q
       398: q
       400: q
       407: q
       408: q
       412: q
       416: q
       418: q
       424: q
       426: q
       428: 2q
       434: q
       436: q
       442: q
       443: q
       444: q
       446: 2q
       452: q
       456: q
       460: q
       461: q
       462: q
       464: 2q
       468: q
       470: q
       476: q
       478: 2q
       480: 2q
       483: q
       493: q
       494: q
       495: q
       498: q
       499: q
       500: q
       503: q
       505: q
       507: q
       510: q
       511: q
       512: q
       513: q
       514: q
       546: q
       548: q
       562: q
       564: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       588: q
       600: q
       606: q
       610: q
       612: q
       614: q
       624: q
       626: q
       628: q
       630: q
       638: q
       646: q
       652: q
       654: q
       677: q
       683: q
       687: q
       688: q
       689: q
       699: q
       700: q
       800: q
       812: q
       824: q
       836: q
       850: q
       852: q
       854: q
       856: q
       879: q
      1011: 1
      1051: q
      1063: q
      1143: 1
      1223: 1
      1279: 1
      1339: 1
      1435: 1
      1481: 1
      1636: 1

1637:    0: 4q^3+11q^2+8q+2
         1: 4q^3+11q^2+8q+2
         2: 2q^4+6q^3+9q^2+7q+2
         3: 4q^3+11q^2+8q+2
         4: 2q^4+6q^3+9q^2+7q+2
         5: 4q^3+11q^2+8q+2
         6: 2q^4+6q^3+9q^2+7q+2
         7: q^5+2q^4+4q^3+7q^2+6q+2
         8: q^4+5q^3+9q^2+7q+2
         9: q^5+2q^4+4q^3+7q^2+6q+2
        10: 4q^3+11q^2+8q+2
        11: 4q^3+11q^2+8q+2
        12: 2q^4+6q^3+9q^2+7q+2
        13: 3q^3+8q^2+7q+2
        14: q^4+3q^3+6q^2+6q+2
        15: 2q^3+8q^2+7q+2
        16: 4q^3+11q^2+8q+2
        17: 4q^3+11q^2+8q+2
        18: q^5+2q^4+4q^3+7q^2+6q+2
        19: 3q^3+8q^2+7q+2
        20: 3q^3+8q^2+7q+2
        21: q^4+3q^3+6q^2+6q+2
        22: 10q^2+8q+2
        23: 10q^2+8q+2
        24: 3q^3+8q^2+7q+2
        25: 10q^2+8q+2
        26: 10q^2+8q+2
        27: 3q^3+8q^2+7q+2
        28: 4q^3+11q^2+8q+2
        29: 3q^3+8q^2+7q+2
        30: 2q^3+5q^2+6q+2
        31: 10q^2+8q+2
        32: 7q^2+7q+2
        33: 10q^2+8q+2
        34: 10q^2+8q+2
        35: 7q^2+7q+2
        36: 10q^2+8q+2
        37: 10q^2+8q+2
        39: 10q^2+8q+2
        41: 3q^3+8q^2+7q+2
        43: 3q^3+8q^2+7q+2
        44: q^4+3q^3+6q^2+6q+2
        45: 2q^3+8q^2+7q+2
        46: 3q^3+8q^2+7q+2
        47: 2q^3+8q^2+7q+2
        48: q^4+3q^3+6q^2+6q+2
        49: 3q^3+8q^2+7q+2
        50: 3q^3+8q^2+7q+2
        51: q^4+3q^3+6q^2+6q+2
        52: 7q^2+7q+2
        53: 7q^2+7q+2
        54: q^3+5q^2+6q+2
        55: 7q^2+7q+2
        56: 7q^2+7q+2
        57: q^3+5q^2+6q+2
        58: 5q^2+4q+1
        59: 5q^2+4q+1
        60: 5q^2+4q+1
        61: 5q^2+4q+1
        62: 10q^2+8q+2
        64: 7q^2+7q+2
        66: 10q^2+8q+2
        68: q^3+5q^2+6q+2
        69: 2q^3+5q^2+6q+2
        70: 2q^3+5q^2+6q+2
        71: 3q^3+8q^2+7q+2
        72: 4q^2+6q+2
        73: 4q^2+6q+2
        74: 7q^2+7q+2
        76: 7q^2+7q+2
        78: q^3+5q^2+6q+2
        80: 7q^2+7q+2
        81: 7q^2+7q+2
        82: 7q^2+7q+2
        83: 4q^2+6q+2
        84: 7q^2+7q+2
        85: 7q^2+7q+2
        86: 7q^2+7q+2
        87: 4q^2+6q+2
        88: 3q^3+8q^2+7q+2
        89: 2q^3+8q^2+7q+2
        90: q^4+3q^3+6q^2+6q+2
        91: q^3+3q^2+6q+2
        92: q^3+5q^2+6q+2
        93: q^3+3q^2+6q+2
        94: 7q^2+7q+2
        95: 7q^2+7q+2
        96: q^3+5q^2+6q+2
        97: 7q^2+7q+2
        98: 7q^2+7q+2
        99: q^3+5q^2+6q+2
       100: 3q^2+6q+2
       101: 3q^2+6q+2
       102: 3q^2+5q+2
       103: 5q^2+4q+1
       106: 5q^2+4q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 4q^2+6q+2
       113: 7q^2+7q+2
       115: 4q^2+6q+2
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 7q^2+7q+2
       123: 7q^2+7q+2
       125: q^3+5q^2+6q+2
       126: 2q^3+5q^2+6q+2
       127: 7q^2+7q+2
       129: 7q^2+7q+2
       131: q^3+5q^2+6q+2
       133: 2q^2+5q+2
       134: q^3+3q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 7q^2+7q+2
       138: 4q^2+6q+2
       139: 7q^2+7q+2
       140: 4q+2
       141: 4q^2+6q+2
       142: 4q^2+6q+2
       143: 7q^2+7q+2
       144: 4q^2+6q+2
       145: 7q^2+7q+2
       146: 4q^2+6q+2
       147: 4q^2+6q+2
       148: 4q+2
       149: 3q^2+6q+2
       150: 2q^2+5q+2
       151: 3q^2+6q+2
       153: 3q^2+6q+2
       155: 3q^2+5q+2
       157: q^3+3q^2+6q+2
       158: q^3+5q^2+6q+2
       159: q^3+3q^2+6q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 3q^2+6q+2
       167: 3q^2+6q+2
       168: 3q^2+5q+2
       169: 2q^2+3q+1
       172: 2q^2+3q+1
       173: 2q^2+3q+1
       176: 2q^2+3q+1
       177: 4q^2+6q+2
       179: 7q^2+7q+2
       181: 4q^2+6q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: q^2+5q+2
       189: 4q^2+6q+2
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       197: 4q+2
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q+1
       204: 2q+1
       205: 4q+2
       207: 7q^2+7q+2
       209: 3q^2+6q+2
       211: 2q^2+5q+2
       213: 2q^2+6q+2
       215: 4q^2+6q+2
       217: 2q^2+6q+2
       219: 2q^2+5q+2
       220: 2q^2+5q+2
       221: q^3+3q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 4q^2+6q+2
       227: q^2+5q+2
       228: 2q^2+6q+2
       229: 3q+2
       230: q^2+5q+2
       231: 4q^2+6q+2
       232: q^2+5q+2
       233: 2q^2+6q+2
       234: q^2+5q+2
       235: 3q+2
       236: 2q^2+5q+2
       237: 3q^2+6q+2
       239: 3q^2+6q+2
       241: 3q^2+5q+2
       243: 3q^2+6q+2
       244: 4q+2
       245: 4q+2
       246: 2q^2+5q+2
       247: q^2+3q+2
       248: q^2+3q+2
       249: q^2+2q+1
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       259: 2q^2+3q+1
       262: 2q^2+3q+1
       263: 2q+1
       266: 2q+1
       267: 2q+1
       269: 2q+1
       271: 2q+1
       273: 2q+1
       275: 2q^2+3q+1
       278: 2q^2+3q+1
       279: q^2+5q+2
       281: 2q^2+6q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 4q^2+6q+2
       289: q^2+5q+2
       291: q^2+5q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+5q+2
       299: q+1
       300: q+1
       301: 4q+2
       303: 2q+1
       304: 2q+1
       305: 3q+2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 4q+2
       313: 3q+2
       315: 2q^2+5q+2
       317: 3q^2+6q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 4q+2
       325: 2q^2+5q+2
       327: 2q^2+6q+2
       329: 4q^2+6q+2
       331: 2q^2+6q+2
       333: 2q^2+5q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: q+1
       337: q^2+3q+2
       338: q^2+3q+2
       340: q^2+3q+2
       342: q^2+2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: 2q^2+6q+2
       347: 3q+2
       348: 3q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 2q+2
       352: q^2+5q+2
       353: q^2+5q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: 3q+2
       358: 3q+2
       359: 2q+2
       360: 3q+2
       362: q^2+3q+2
       364: 3q+2
       366: 2q^2+5q+2
       367: 2q+2
       368: 3q+2
       369: q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       377: 2q+1
       380: 2q+1
       381: 2q+1
       384: 2q+1
       385: 2q+1
       388: 2q+1
       389: 2q+1
       391: 2q+1
       393: q+1
       396: q+1
       397: 2q+1
       399: 2q+1
       401: q+1
       404: q+1
       405: 2q+1
       406: 2q+1
       409: q^2+5q+2
       411: 2q^2+6q+2
       413: q^2+5q+2
       415: q^2+5q+2
       417: q^2+5q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: q^2+5q+2
       425: q+1
       427: q^2+3q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 3q+2
       435: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 3q+2
       443: q+1
       444: q+1
       445: 2q+2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 3q+2
       453: 2q+1
       454: 2q+1
       455: q+2
       457: q+1
       458: q+1
       459: 3q+2
       461: q+1
       462: q+1
       463: 2q+2
       465: 2q+2
       467: 3q+2
       469: 2q^2+5q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+2
       477: 4q+2
       479: 2q+2
       481: 2q+2
       482: 2q+2
       483: q+1
       484: q+2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: q+1
       496: 2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: q+1
       501: 2
       502: 3q+2
       504: q^2+3q+2
       506: 3q+2
       508: 2q+2
       509: 2q+2
       510: 3q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       521: 2q+1
       524: 2q+1
       525: 2q+1
       528: 2q+1
       529: 2q+1
       532: 2q+1
       533: q+1
       536: q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: q+1
       547: q+1
       549: q+1
       552: q+1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: q+1
       563: q+1
       565: 1
       568: 1
       569: 2q+1
       570: 2q+1
       573: q+1
       575: q+1
       577: 2q+2
       583: q^2+5q+2
       585: 2q+2
       587: q^2+5q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       597: 1
       599: q+1
       601: q+2
       603: q+1
       604: q+1
       605: q+2
       607: 2q+1
       608: 2q+1
       609: 3q+2
       611: q+2
       613: q+1
       615: 1
       616: 1
       617: 2
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       623: q+2
       625: 3q+2
       627: q+2
       629: q+1
       631: 1
       632: 1
       633: 2
       635: 2q+2
       637: 3q+2
       639: 2q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+4
       653: q+2
       655: 2
       657: q+2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: q+2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: 2q+2
       687: q+2
       688: q+2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       697: q+1
       705: 2q+1
       708: 2q+1
       709: q+1
       712: q+1
       721: 1
       723: 1
       725: q+1
       727: q+1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: q+1
       743: q+1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 2
       758: 2
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       771: 2
       775: q+2
       777: 2q+2
       779: 1
       781: 1
       783: 1
       789: q+2
       791: 1
       793: 1
       794: 1
       795: 2
       797: 2
       799: q+2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       811: q+1
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: q+2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       835: q+1
       837: 2
       839: 1
       840: 1
       841: 2q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+4
       851: q+2
       853: q+4
       857: 2
       859: q+2
       861: q+2
       863: q+1
       865: q+2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       884: 1
       886: 1
       889: 1
       893: 1
       896: q+1
       899: q+1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       960: 2
       961: 2
       964: 1
       967: 1
       968: 2
       970: 2
       974: 1
       975: 1
       978: 2
       979: 2
       982: 2
       984: 2
       988: 1
       991: 1
       992: q+2
       994: 1
       996: 1
      1002: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1048: 2
      1050: q+4
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1088: 1
      1091: 1
      1095: 1
      1098: 1
      1100: 1
      1102: 1
      1107: 1
      1138: 1
      1140: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1184: 2
      1185: 2
      1188: 2
      1190: 2
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1214: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1236: 1
      1238: 1
      1248: 1
      1252: 1
      1256: 1
      1264: 2
      1283: 1
      1285: 1
      1302: 1
      1304: 1
      1307: 1
      1311: 1
      1334: 1
      1336: 1
      1414: 1
      1415: 1
      1436: 1
      1446: 1
      1448: 1
      1456: 1
      1637: 1

1638:    0: 4q^3+11q^2+8q+2
         1: 4q^3+11q^2+8q+2
         2: 2q^4+6q^3+9q^2+7q+2
         3: 4q^3+11q^2+8q+2
         4: 2q^4+6q^3+9q^2+7q+2
         5: 4q^3+11q^2+8q+2
         6: 2q^4+6q^3+9q^2+7q+2
         7: q^5+2q^4+4q^3+7q^2+6q+2
         8: q^4+5q^3+9q^2+7q+2
         9: q^5+2q^4+4q^3+7q^2+6q+2
        10: 4q^3+11q^2+8q+2
        11: 4q^3+11q^2+8q+2
        12: 2q^4+6q^3+9q^2+7q+2
        13: 3q^3+8q^2+7q+2
        14: q^4+3q^3+6q^2+6q+2
        15: 2q^3+8q^2+7q+2
        16: 4q^3+11q^2+8q+2
        17: 4q^3+11q^2+8q+2
        18: q^5+2q^4+4q^3+7q^2+6q+2
        19: 3q^3+8q^2+7q+2
        20: 3q^3+8q^2+7q+2
        21: q^4+3q^3+6q^2+6q+2
        22: 10q^2+8q+2
        23: 10q^2+8q+2
        24: 3q^3+8q^2+7q+2
        25: 10q^2+8q+2
        26: 10q^2+8q+2
        27: 3q^3+8q^2+7q+2
        28: 4q^3+11q^2+8q+2
        29: 3q^3+8q^2+7q+2
        30: 2q^3+5q^2+6q+2
        31: 10q^2+8q+2
        32: 7q^2+7q+2
        33: 10q^2+8q+2
        34: 10q^2+8q+2
        35: 7q^2+7q+2
        36: 10q^2+8q+2
        38: 10q^2+8q+2
        40: 10q^2+8q+2
        42: 3q^3+8q^2+7q+2
        43: 3q^3+8q^2+7q+2
        44: q^4+3q^3+6q^2+6q+2
        45: 2q^3+8q^2+7q+2
        46: 3q^3+8q^2+7q+2
        47: 2q^3+8q^2+7q+2
        48: q^4+3q^3+6q^2+6q+2
        49: 3q^3+8q^2+7q+2
        50: 3q^3+8q^2+7q+2
        51: q^4+3q^3+6q^2+6q+2
        52: 7q^2+7q+2
        53: 7q^2+7q+2
        54: q^3+5q^2+6q+2
        55: 7q^2+7q+2
        56: 7q^2+7q+2
        57: q^3+5q^2+6q+2
        58: 5q^2+4q+1
        59: 5q^2+4q+1
        60: 5q^2+4q+1
        61: 5q^2+4q+1
        63: 10q^2+8q+2
        65: 7q^2+7q+2
        67: 10q^2+8q+2
        68: q^3+5q^2+6q+2
        69: 2q^3+5q^2+6q+2
        70: 2q^3+5q^2+6q+2
        71: 3q^3+8q^2+7q+2
        72: 4q^2+6q+2
        73: 4q^2+6q+2
        75: 7q^2+7q+2
        77: 7q^2+7q+2
        79: q^3+5q^2+6q+2
        80: 7q^2+7q+2
        81: 7q^2+7q+2
        82: 7q^2+7q+2
        83: 4q^2+6q+2
        84: 7q^2+7q+2
        85: 7q^2+7q+2
        86: 7q^2+7q+2
        87: 4q^2+6q+2
        88: 3q^3+8q^2+7q+2
        89: 2q^3+8q^2+7q+2
        90: q^4+3q^3+6q^2+6q+2
        91: q^3+3q^2+6q+2
        92: q^3+5q^2+6q+2
        93: q^3+3q^2+6q+2
        94: 7q^2+7q+2
        95: 7q^2+7q+2
        96: q^3+5q^2+6q+2
        97: 7q^2+7q+2
        98: 7q^2+7q+2
        99: q^3+5q^2+6q+2
       100: 3q^2+6q+2
       101: 3q^2+6q+2
       102: 3q^2+5q+2
       104: 5q^2+4q+1
       105: 5q^2+4q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       112: 4q^2+6q+2
       114: 7q^2+7q+2
       116: 4q^2+6q+2
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       122: 7q^2+7q+2
       124: 7q^2+7q+2
       125: q^3+5q^2+6q+2
       126: 2q^3+5q^2+6q+2
       128: 7q^2+7q+2
       130: 7q^2+7q+2
       132: q^3+5q^2+6q+2
       133: 2q^2+5q+2
       134: q^3+3q^2+6q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 7q^2+7q+2
       138: 4q^2+6q+2
       139: 7q^2+7q+2
       140: 4q+2
       141: 4q^2+6q+2
       142: 4q^2+6q+2
       143: 7q^2+7q+2
       144: 4q^2+6q+2
       145: 7q^2+7q+2
       146: 4q^2+6q+2
       147: 4q^2+6q+2
       148: 4q+2
       149: 3q^2+6q+2
       150: 2q^2+5q+2
       152: 3q^2+6q+2
       154: 3q^2+6q+2
       156: 3q^2+5q+2
       157: q^3+3q^2+6q+2
       158: q^3+5q^2+6q+2
       159: q^3+3q^2+6q+2
       160: 2q^2+6q+2
       161: 4q^2+6q+2
       162: 2q^2+6q+2
       163: 2q^2+6q+2
       164: 4q^2+6q+2
       165: 2q^2+6q+2
       166: 3q^2+6q+2
       167: 3q^2+6q+2
       168: 3q^2+5q+2
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       174: 2q^2+3q+1
       175: 2q^2+3q+1
       178: 4q^2+6q+2
       180: 7q^2+7q+2
       182: 4q^2+6q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       188: q^2+5q+2
       190: 4q^2+6q+2
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       198: 4q+2
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q+1
       204: 2q+1
       206: 4q+2
       208: 7q^2+7q+2
       210: 3q^2+6q+2
       212: 2q^2+5q+2
       214: 2q^2+6q+2
       216: 4q^2+6q+2
       218: 2q^2+6q+2
       219: 2q^2+5q+2
       220: 2q^2+5q+2
       221: q^3+3q^2+6q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 4q^2+6q+2
       227: q^2+5q+2
       228: 2q^2+6q+2
       229: 3q+2
       230: q^2+5q+2
       231: 4q^2+6q+2
       232: q^2+5q+2
       233: 2q^2+6q+2
       234: q^2+5q+2
       235: 3q+2
       236: 2q^2+5q+2
       238: 3q^2+6q+2
       240: 3q^2+6q+2
       242: 3q^2+5q+2
       243: 3q^2+6q+2
       244: 4q+2
       245: 4q+2
       246: 2q^2+5q+2
       247: q^2+3q+2
       248: q^2+3q+2
       249: q^2+2q+1
       250: 2q^2+6q+2
       251: 4q^2+6q+2
       252: 2q^2+6q+2
       253: 2q^2+6q+2
       254: 4q^2+6q+2
       255: 2q^2+6q+2
       256: 3q+2
       257: q^2+3q+2
       258: 3q+2
       260: 2q^2+3q+1
       261: 2q^2+3q+1
       264: 2q+1
       265: 2q+1
       268: 2q+1
       270: 2q+1
       272: 2q+1
       274: 2q+1
       276: 2q^2+3q+1
       277: 2q^2+3q+1
       280: q^2+5q+2
       282: 2q^2+6q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       288: 4q^2+6q+2
       290: q^2+5q+2
       292: q^2+5q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       298: q^2+5q+2
       299: q+1
       300: q+1
       302: 4q+2
       303: 2q+1
       304: 2q+1
       306: 3q+2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       312: 4q+2
       314: 3q+2
       316: 2q^2+5q+2
       318: 3q^2+6q+2
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       324: 4q+2
       326: 2q^2+5q+2
       328: 2q^2+6q+2
       330: 4q^2+6q+2
       332: 2q^2+6q+2
       333: 2q^2+5q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: q+1
       337: q^2+3q+2
       339: q^2+3q+2
       341: q^2+3q+2
       343: q^2+2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: 2q^2+6q+2
       347: 3q+2
       348: 3q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 2q+2
       352: q^2+5q+2
       353: q^2+5q+2
       354: 2q^2+6q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: 3q+2
       358: 3q+2
       359: 2q+2
       361: 3q+2
       363: q^2+3q+2
       365: 3q+2
       366: 2q^2+5q+2
       367: 2q+2
       368: 3q+2
       369: q+2
       370: q+2
       371: q+2
       372: q+2
       373: q+1
       374: 3q+2
       375: q^2+3q+2
       376: 3q+2
       378: 2q+1
       379: 2q+1
       382: 2q+1
       383: 2q+1
       386: 2q+1
       387: 2q+1
       390: 2q+1
       392: 2q+1
       394: q+1
       395: q+1
       398: 2q+1
       400: 2q+1
       402: q+1
       403: q+1
       407: 2q+1
       408: 2q+1
       410: q^2+5q+2
       412: 2q^2+6q+2
       414: q^2+5q+2
       416: q^2+5q+2
       418: q^2+5q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       424: q^2+5q+2
       426: q+1
       428: q^2+3q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       434: 3q+2
       436: q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 3q+2
       443: q+1
       444: q+1
       446: 2q+2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       452: 3q+2
       453: 2q+1
       454: 2q+1
       456: q+2
       457: q+1
       458: q+1
       460: 3q+2
       461: q+1
       462: q+1
       464: 2q+2
       466: 2q+2
       468: 3q+2
       470: 2q^2+5q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: q+2
       478: 4q+2
       480: 2q+2
       481: 2q+2
       482: 2q+2
       483: q+1
       484: q+2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+5q+2
       493: 3q+2
       494: q^2+5q+2
       495: q+1
       496: 2
       497: q^2+5q+2
       498: q^2+5q+2
       499: 3q+2
       500: q+1
       501: 2
       503: 3q+2
       505: q^2+3q+2
       507: 3q+2
       508: 2q+2
       509: 2q+2
       510: 3q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       522: 2q+1
       523: 2q+1
       526: 2q+1
       527: 2q+1
       530: 2q+1
       531: 2q+1
       534: q+1
       535: q+1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: q+1
       548: q+1
       550: q+1
       551: q+1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: q+1
       564: q+1
       566: 1
       567: 1
       571: 2q+1
       572: 2q+1
       574: q+1
       576: q+1
       581: 2q+2
       584: q^2+5q+2
       586: 2q+2
       588: q^2+5q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       598: 1
       600: q+1
       602: q+2
       603: q+1
       604: q+1
       606: q+2
       607: 2q+1
       608: 2q+1
       610: 3q+2
       612: q+2
       614: q+1
       615: 1
       616: 1
       618: 2
       619: 2q+1
       620: 2q+1
       621: q+1
       622: q+1
       624: q+2
       626: 3q+2
       628: q+2
       630: q+1
       631: 1
       632: 1
       634: 2
       636: 2q+2
       638: 3q+2
       640: 2q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+4
       654: q+2
       656: 2
       657: q+2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: q+2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: 2q+2
       687: q+2
       688: q+2
       690: q+2
       691: q+2
       692: q+1
       699: q+1
       700: q+1
       706: 2q+1
       707: 2q+1
       710: q+1
       711: q+1
       722: 1
       724: 1
       726: q+1
       728: q+1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: q+1
       744: q+1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 2
       760: 2
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       774: 2
       776: q+2
       778: 2q+2
       780: 1
       782: 1
       784: 1
       790: q+2
       792: 1
       793: 1
       794: 1
       796: 2
       798: 2
       800: q+2
       801: 1
       802: 1
       807: q+1
       808: q+1
       810: 1
       812: q+1
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: q+2
       825: q+1
       826: q+1
       831: 1
       832: 1
       834: 1
       836: q+1
       838: 2
       839: 1
       840: 1
       842: 2q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+4
       852: q+2
       854: q+4
       858: 2
       860: q+2
       862: q+2
       864: q+1
       865: q+2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       890: 1
       891: 1
       894: 1
       895: 1
       897: q+1
       898: q+1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       962: 2
       963: 2
       965: 1
       966: 1
       972: 2
       973: 2
       976: 1
       977: 1
       980: 2
       981: 2
       986: 2
       987: 2
       989: 1
       990: 1
       993: q+2
       995: 1
       997: 1
      1003: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1047: 2
      1049: 2
      1051: q+4
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1104: 1
      1105: 1
      1108: 1
      1109: 1
      1142: 1
      1143: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1186: 2
      1187: 2
      1192: 2
      1193: 2
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1215: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1237: 1
      1239: 1
      1249: 1
      1253: 1
      1257: 1
      1265: 2
      1283: 1
      1285: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1338: 1
      1339: 1
      1416: 1
      1417: 1
      1437: 1
      1447: 1
      1449: 1
      1457: 1
      1638: 1

1639:    0: 8q^3+14q^2+8q+2
         1: 2q^4+9q^3+14q^2+8q+2
         2: 8q^3+14q^2+8q+2
         3: 8q^3+14q^2+8q+2
         4: q^4+6q^3+11q^2+7q+2
         5: 2q^4+9q^3+14q^2+8q+2
         6: 5q^4+10q^3+12q^2+7q+2
         7: q^4+6q^3+11q^2+7q+2
         8: 2q^4+9q^3+14q^2+8q+2
         9: q^4+6q^3+11q^2+7q+2
        10: q^3+9q^2+8q+2
        11: q^3+9q^2+8q+2
        12: 2q^3+8q^2+7q+2
        13: 8q^3+14q^2+8q+2
        14: q^4+6q^3+11q^2+7q+2
        15: 2q^4+9q^3+14q^2+8q+2
        16: 8q^3+14q^2+8q+2
        17: 2q^4+9q^3+14q^2+8q+2
        18: q^4+6q^3+11q^2+7q+2
        19: 3q^3+10q^2+7q+2
        20: q^4+6q^3+11q^2+7q+2
        21: 3q^3+10q^2+7q+2
        22: 5q^3+11q^2+8q+2
        23: 5q^3+11q^2+8q+2
        24: 5q^3+11q^2+8q+2
        25: 5q^3+11q^2+8q+2
        26: 5q^3+11q^2+8q+2
        27: 5q^3+11q^2+8q+2
        28: q^3+9q^2+8q+2
        29: 7q^2+7q+2
        30: 3q^3+10q^2+7q+2
        31: 6q^2+8q+2
        32: 5q^3+11q^2+8q+2
        33: 5q^3+11q^2+8q+2
        34: 6q^2+8q+2
        35: 5q^3+11q^2+8q+2
        36: 5q^3+11q^2+8q+2
        37: q^3+3q^2+4q+2
        38: 2q^3+6q^2+4q
        39: q^3+3q^2+4q+2
        40: 2q^3+6q^2+4q
        41: q^3+3q^2+4q+2
        42: 2q^3+6q^2+4q
        43: q^3+9q^2+8q+2
        44: 2q^3+8q^2+7q+2
        45: q^3+9q^2+8q+2
        46: 8q^3+14q^2+8q+2
        47: 2q^4+9q^3+14q^2+8q+2
        48: q^4+6q^3+11q^2+7q+2
        49: 3q^3+10q^2+7q+2
        50: q^4+6q^3+11q^2+7q+2
        51: 3q^3+10q^2+7q+2
        52: 2q^3+7q^2+7q+2
        53: 3q^3+8q^2+7q+2
        54: 2q^3+7q^2+7q+2
        55: 2q^3+7q^2+7q+2
        56: 3q^3+8q^2+7q+2
        57: 2q^3+7q^2+7q+2
        58: 3q^2+4q+1
        59: 3q^2+4q+1
        60: 3q^2+4q+1
        61: 3q^2+4q+1
        62: 2q^2+4q+2
        63: 2q^2+4q
        64: q^3+3q^2+4q+2
        65: 2q^3+6q^2+4q
        66: q^3+3q^2+4q+2
        67: 2q^3+6q^2+4q
        68: q^3+9q^2+8q+2
        69: 3q^3+10q^2+7q+2
        70: 7q^2+7q+2
        71: 7q^2+7q+2
        72: q^3+4q^2+6q+2
        73: q^3+4q^2+6q+2
        74: q^2+3q+2
        75: q^3+3q^2+4q
        76: q^2+3q+2
        77: 4q^2+4q
        78: q^2+3q+2
        79: q^3+3q^2+4q
        80: 6q^2+8q+2
        81: 5q^3+11q^2+8q+2
        82: 4q^2+7q+2
        83: 2q^3+7q^2+7q+2
        84: 6q^2+8q+2
        85: 5q^3+11q^2+8q+2
        86: 4q^2+7q+2
        87: 2q^3+7q^2+7q+2
        88: q^3+9q^2+8q+2
        89: q^3+9q^2+8q+2
        90: 2q^3+8q^2+7q+2
        91: 3q^3+10q^2+7q+2
        92: q^4+6q^3+11q^2+7q+2
        93: 3q^3+10q^2+7q+2
        94: 2q^3+7q^2+7q+2
        95: 3q^3+8q^2+7q+2
        96: 2q^3+7q^2+7q+2
        97: 2q^3+7q^2+7q+2
        98: 3q^3+8q^2+7q+2
        99: 2q^3+7q^2+7q+2
       100: 3q^2+6q+2
       101: q^3+5q^2+6q+2
       102: 3q^2+6q+2
       103: q^2+2q+1
       104: q^2+2q
       105: q^2+2q
       106: q^2+2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 2q+2
       112: q^2+4q
       113: q^2+3q+2
       114: q^2+4q
       115: q^2+3q+2
       116: q^3+3q^2+4q
       117: 3q^2+4q+1
       118: 3q^2+4q+1
       119: 3q^2+4q+1
       120: 3q^2+4q+1
       121: 2q^2+4q+2
       122: 2q^2+4q
       123: q^3+3q^2+4q+2
       124: 2q^3+6q^2+4q
       125: q^3+9q^2+8q+2
       126: 7q^2+7q+2
       127: q^2+3q+2
       128: q^3+3q^2+4q
       129: q^2+3q+2
       130: 4q^2+4q
       131: q^2+3q+2
       132: q^3+3q^2+4q
       133: 7q^2+7q+2
       134: 3q^3+10q^2+7q+2
       135: q^3+4q^2+6q+2
       136: q^3+4q^2+6q+2
       137: 6q^2+8q+2
       138: 2q^3+7q^2+7q+2
       139: 4q^2+7q+2
       140: q^2+2q+2
       141: 4q^2+7q+2
       142: q^3+4q^2+6q+2
       143: 6q^2+8q+2
       144: 2q^3+7q^2+7q+2
       145: 4q^2+7q+2
       146: 4q^2+7q+2
       147: q^3+4q^2+6q+2
       148: q^2+2q+2
       149: q^2+6q+2
       150: 3q^2+6q+2
       151: 2q+2
       152: 2q^2+4q
       153: 2q+2
       154: 4q^2+4q
       155: 2q+2
       156: 2q^2+4q
       157: 3q^2+5q+2
       158: 3q^2+5q+2
       159: 3q^2+5q+2
       160: 2q^3+7q^2+7q+2
       161: 3q^3+8q^2+7q+2
       162: 2q^3+7q^2+7q+2
       163: 2q^3+7q^2+7q+2
       164: 3q^3+8q^2+7q+2
       165: 2q^3+7q^2+7q+2
       166: 3q^2+6q+2
       167: q^3+5q^2+6q+2
       168: 3q^2+6q+2
       169: q+1
       170: 2q
       171: 2q
       172: q+1
       173: q^2+2q+1
       174: q^2+2q
       175: q^2+2q
       176: q^2+2q+1
       177: q^2+3q+2
       178: q^3+3q^2+4q
       179: q^2+3q+2
       180: q^2+4q
       181: 2q+2
       182: q^2+4q
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: 2q+2
       188: q^2+4q
       189: q^2+3q+2
       190: q^2+4q
       191: 3q^2+4q+1
       192: 3q^2+4q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: 2
       198: 2q
       199: 3q^2+4q+1
       200: 3q^2+4q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: 2
       206: 2q
       207: 2q^2+4q+2
       208: 2q^2+4q
       209: 2q+2
       210: q^2+4q
       211: 2q+2
       212: 2q^2+4q
       213: q^2+3q+2
       214: q^3+3q^2+4q
       215: q^2+3q+2
       216: 4q^2+4q
       217: q^2+3q+2
       218: q^3+3q^2+4q
       219: 7q^2+7q+2
       220: 3q^2+5q+2
       221: 3q^2+5q+2
       222: 4q+2
       223: q^3+4q^2+6q+2
       224: 4q+2
       225: q^3+4q^2+6q+2
       226: 4q^2+7q+2
       227: 4q^2+7q+2
       228: 2q^3+7q^2+7q+2
       229: q^2+2q+2
       230: q^3+4q^2+6q+2
       231: 4q^2+7q+2
       232: 4q^2+7q+2
       233: 2q^3+7q^2+7q+2
       234: q^3+4q^2+6q+2
       235: q^2+2q+2
       236: 3q^2+6q+2
       237: 2q+2
       238: 2q^2+4q
       239: 2q+2
       240: 4q^2+4q
       241: 2q+2
       242: 2q^2+4q
       243: q^2+6q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: q^2+6q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: 3q^2+6q+2
       257: q^3+5q^2+6q+2
       258: 3q^2+6q+2
       259: q+1
       260: 2q
       261: 2q
       262: q+1
       263: q+1
       264: 2q
       265: 2q
       266: q+1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: q^2+2q+1
       276: q^2+2q
       277: q^2+2q
       278: q^2+2q+1
       279: q^2+3q+2
       280: q^2+4q
       281: q^2+3q+2
       282: q^3+3q^2+4q
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: q^2+3q+1
       287: q^2+3q+2
       288: q^2+4q
       289: 2q+2
       290: q^2+4q
       291: 2q+2
       292: q^2+4q
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+2
       298: 2q
       299: q+1
       300: q+1
       301: 2
       302: 2q
       303: q^2+3q+1
       304: q^2+3q+1
       305: 2
       306: 2q
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: 2
       312: 2q
       313: 2
       314: 2q
       315: 2q+2
       316: 2q^2+4q
       317: 2q+2
       318: q^2+4q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 2q+2
       326: q^2+4q
       333: 3q^2+5q+2
       334: 4q+2
       335: 4q+2
       336: 2q+1
       337: 5q+2
       338: q+2
       339: 5q
       340: q+2
       341: q^2+5q
       342: q+1
       343: q^2+2q
       344: 4q^2+7q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: q^2+2q+2
       349: 2q+2
       350: q^3+4q^2+6q+2
       351: 3q+2
       352: 4q^2+7q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: q^3+4q^2+6q+2
       357: 2
       358: q^2+2q+2
       359: 3q+2
       360: 2q+2
       361: 2q^2+4q
       362: 2q+2
       363: 4q^2+4q
       364: 2q+2
       365: 2q^2+4q
       366: q^2+6q+2
       367: q^2+6q+2
       368: 3q^2+6q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: q+1
       378: 2q
       379: 2q
       380: q+1
       381: q+1
       382: 2q
       383: 2q
       384: q+1
       385: q+1
       386: q
       387: q
       388: q+1
       389: 1
       390: q
       391: 1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       398: q
       399: 1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       413: q^2+3q+2
       414: q^2+4q
       417: 2q+2
       418: q^2+4q
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+2
       424: 2q
       425: 1
       426: 2q
       427: q+2
       428: 4q
       429: q+1
       430: q+1
       431: q^2+3q+1
       432: q^2+3q+1
       433: 2
       434: 2q
       435: 2
       436: 2q
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: q+1
       444: q+1
       445: 2
       446: 3q
       447: q^2+3q+1
       448: q^2+3q+1
       449: q+1
       450: q+1
       451: 2
       452: 2q
       453: q+1
       454: q+1
       455: 2
       456: 2q
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       464: 3q
       465: 2q+2
       466: q^2+4q
       467: 2q+2
       468: 2q^2+4q
       469: 2q+2
       470: q^2+4q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       477: 2
       479: q+2
       481: 4q+2
       482: 4q+2
       483: q+1
       484: 5q+2
       485: q+2
       486: 5q
       487: q+2
       488: q^2+5q
       489: q+1
       490: q^2+2q
       491: 2q+1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: q+1
       496: 3q+2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: q+1
       501: 3q+2
       508: q^2+6q+2
       509: 2q+2
       510: 2q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 6q+2
       516: q^2+6q+2
       517: q^2+3q+1
       518: q+2
       519: q+2
       520: q+1
       521: q+1
       522: 2q
       523: 2q
       524: q+1
       529: q+1
       530: q
       531: q
       532: q+1
       533: 1
       534: q
       535: q
       536: 1
       537: 1
       538: q
       539: 1
       540: q
       541: 1
       543: 1
       545: 1
       546: q
       547: 1
       548: q
       549: 1
       550: q
       551: q
       552: 1
       553: 1
       554: q
       555: 1
       556: q
       557: 1
       559: 1
       561: 1
       562: q
       563: 1
       564: q
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       578: q
       585: 2q+2
       586: 2q
       589: 2q+1
       590: 2q+1
       595: 2q+1
       596: 2q+1
       597: 1
       598: 2q
       599: 1
       600: q
       601: q+2
       602: 4q
       603: 1
       604: 1
       605: 2
       606: 2q
       607: q+1
       608: q+1
       609: 2
       613: 1
       614: q
       615: q+1
       616: q+1
       617: 2
       618: 3q
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       624: 2q
       625: 2
       629: 1
       630: q
       631: q+1
       632: q+1
       633: 2
       634: 3q
       639: 2q+2
       640: q^2+4q
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: q+2
       657: 5q+2
       658: q+2
       659: 5q
       660: q+2
       661: q^2+5q
       662: q+1
       663: q^2+2q
       664: 2q+1
       665: q+1
       672: q+2
       673: 1
       674: 3q+2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: q+1
       680: 3q+2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: q+1
       686: 2q+2
       687: 2
       688: 2
       690: q+2
       691: q+2
       692: q+1
       693: 1
       697: 1
       709: q+1
       710: q
       711: q
       712: q+1
       721: 1
       722: q
       723: 1
       724: q
       725: 1
       727: 1
       733: 1
       734: q
       735: 1
       736: q
       737: 1
       738: q
       739: 1
       740: q
       741: 1
       743: 1
       749: 1
       750: q
       751: 1
       752: q
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       770: q
       775: q+2
       776: 4q
       779: 1
       780: 2q
       781: 1
       782: q
       791: 1
       793: q+1
       794: q+1
       795: 2
       796: 3q
       797: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       810: q
       811: 1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       820: 3q
       821: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       834: q
       835: 1
       839: 1
       840: 1
       843: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       851: 2
       857: 2
       865: q+2
       866: q+1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       881: q+2
       882: q+2
       883: q+1
       884: 1
       889: 1
       916: 1
       917: q
       918: 1
       919: q
       920: 1
       922: 1
       940: 1
       941: q
       942: 1
       943: q
       944: 1
       946: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       969: q
       974: 1
       975: 1
       988: 1
       991: 1
       994: 1
       995: q
      1008: 1
      1010: 1
      1012: 1
      1016: 1
      1017: 1
      1020: 1
      1021: q
      1022: 1
      1032: 1
      1033: 1
      1036: 1
      1037: q
      1038: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1072: q+2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1091: 1
      1138: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1220: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1246: 1
      1247: 1
      1248: 1
      1262: 2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1410: 1
      1413: 1
      1436: 1
      1444: 1
      1485: 1
      1486: 1
      1639: 1

1640:    0: 8q^3+14q^2+8q+2
         1: 2q^4+9q^3+14q^2+8q+2
         2: 8q^3+14q^2+8q+2
         3: 8q^3+14q^2+8q+2
         4: q^4+6q^3+11q^2+7q+2
         5: 2q^4+9q^3+14q^2+8q+2
         6: 5q^4+10q^3+12q^2+7q+2
         7: q^4+6q^3+11q^2+7q+2
         8: 2q^4+9q^3+14q^2+8q+2
         9: q^4+6q^3+11q^2+7q+2
        10: q^3+9q^2+8q+2
        11: q^3+9q^2+8q+2
        12: 2q^3+8q^2+7q+2
        13: 8q^3+14q^2+8q+2
        14: q^4+6q^3+11q^2+7q+2
        15: 2q^4+9q^3+14q^2+8q+2
        16: 8q^3+14q^2+8q+2
        17: 2q^4+9q^3+14q^2+8q+2
        18: q^4+6q^3+11q^2+7q+2
        19: 3q^3+10q^2+7q+2
        20: q^4+6q^3+11q^2+7q+2
        21: 3q^3+10q^2+7q+2
        22: 5q^3+11q^2+8q+2
        23: 5q^3+11q^2+8q+2
        24: 5q^3+11q^2+8q+2
        25: 5q^3+11q^2+8q+2
        26: 5q^3+11q^2+8q+2
        27: 5q^3+11q^2+8q+2
        28: q^3+9q^2+8q+2
        29: 7q^2+7q+2
        30: 3q^3+10q^2+7q+2
        31: 6q^2+8q+2
        32: 5q^3+11q^2+8q+2
        33: 5q^3+11q^2+8q+2
        34: 6q^2+8q+2
        35: 5q^3+11q^2+8q+2
        36: 5q^3+11q^2+8q+2
        37: 2q^3+6q^2+4q
        38: q^3+3q^2+4q+2
        39: 2q^3+6q^2+4q
        40: q^3+3q^2+4q+2
        41: 2q^3+6q^2+4q
        42: q^3+3q^2+4q+2
        43: q^3+9q^2+8q+2
        44: 2q^3+8q^2+7q+2
        45: q^3+9q^2+8q+2
        46: 8q^3+14q^2+8q+2
        47: 2q^4+9q^3+14q^2+8q+2
        48: q^4+6q^3+11q^2+7q+2
        49: 3q^3+10q^2+7q+2
        50: q^4+6q^3+11q^2+7q+2
        51: 3q^3+10q^2+7q+2
        52: 2q^3+7q^2+7q+2
        53: 3q^3+8q^2+7q+2
        54: 2q^3+7q^2+7q+2
        55: 2q^3+7q^2+7q+2
        56: 3q^3+8q^2+7q+2
        57: 2q^3+7q^2+7q+2
        58: 3q^2+4q+1
        59: 3q^2+4q+1
        60: 3q^2+4q+1
        61: 3q^2+4q+1
        62: 2q^2+4q
        63: 2q^2+4q+2
        64: 2q^3+6q^2+4q
        65: q^3+3q^2+4q+2
        66: 2q^3+6q^2+4q
        67: q^3+3q^2+4q+2
        68: q^3+9q^2+8q+2
        69: 3q^3+10q^2+7q+2
        70: 7q^2+7q+2
        71: 7q^2+7q+2
        72: q^3+4q^2+6q+2
        73: q^3+4q^2+6q+2
        74: q^3+3q^2+4q
        75: q^2+3q+2
        76: 4q^2+4q
        77: q^2+3q+2
        78: q^3+3q^2+4q
        79: q^2+3q+2
        80: 6q^2+8q+2
        81: 5q^3+11q^2+8q+2
        82: 4q^2+7q+2
        83: 2q^3+7q^2+7q+2
        84: 6q^2+8q+2
        85: 5q^3+11q^2+8q+2
        86: 4q^2+7q+2
        87: 2q^3+7q^2+7q+2
        88: q^3+9q^2+8q+2
        89: q^3+9q^2+8q+2
        90: 2q^3+8q^2+7q+2
        91: 3q^3+10q^2+7q+2
        92: q^4+6q^3+11q^2+7q+2
        93: 3q^3+10q^2+7q+2
        94: 2q^3+7q^2+7q+2
        95: 3q^3+8q^2+7q+2
        96: 2q^3+7q^2+7q+2
        97: 2q^3+7q^2+7q+2
        98: 3q^3+8q^2+7q+2
        99: 2q^3+7q^2+7q+2
       100: 3q^2+6q+2
       101: q^3+5q^2+6q+2
       102: 3q^2+6q+2
       103: q^2+2q
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q^2+4q
       112: 2q+2
       113: q^2+4q
       114: q^2+3q+2
       115: q^3+3q^2+4q
       116: q^2+3q+2
       117: 3q^2+4q+1
       118: 3q^2+4q+1
       119: 3q^2+4q+1
       120: 3q^2+4q+1
       121: 2q^2+4q
       122: 2q^2+4q+2
       123: 2q^3+6q^2+4q
       124: q^3+3q^2+4q+2
       125: q^3+9q^2+8q+2
       126: 7q^2+7q+2
       127: q^3+3q^2+4q
       128: q^2+3q+2
       129: 4q^2+4q
       130: q^2+3q+2
       131: q^3+3q^2+4q
       132: q^2+3q+2
       133: 7q^2+7q+2
       134: 3q^3+10q^2+7q+2
       135: q^3+4q^2+6q+2
       136: q^3+4q^2+6q+2
       137: 6q^2+8q+2
       138: 2q^3+7q^2+7q+2
       139: 4q^2+7q+2
       140: q^2+2q+2
       141: 4q^2+7q+2
       142: q^3+4q^2+6q+2
       143: 6q^2+8q+2
       144: 2q^3+7q^2+7q+2
       145: 4q^2+7q+2
       146: 4q^2+7q+2
       147: q^3+4q^2+6q+2
       148: q^2+2q+2
       149: q^2+6q+2
       150: 3q^2+6q+2
       151: 2q^2+4q
       152: 2q+2
       153: 4q^2+4q
       154: 2q+2
       155: 2q^2+4q
       156: 2q+2
       157: 3q^2+5q+2
       158: 3q^2+5q+2
       159: 3q^2+5q+2
       160: 2q^3+7q^2+7q+2
       161: 3q^3+8q^2+7q+2
       162: 2q^3+7q^2+7q+2
       163: 2q^3+7q^2+7q+2
       164: 3q^3+8q^2+7q+2
       165: 2q^3+7q^2+7q+2
       166: 3q^2+6q+2
       167: q^3+5q^2+6q+2
       168: 3q^2+6q+2
       169: 2q
       170: q+1
       171: q+1
       172: 2q
       173: q^2+2q
       174: q^2+2q+1
       175: q^2+2q+1
       176: q^2+2q
       177: q^3+3q^2+4q
       178: q^2+3q+2
       179: q^2+4q
       180: q^2+3q+2
       181: q^2+4q
       182: 2q+2
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+4q
       188: 2q+2
       189: q^2+4q
       190: q^2+3q+2
       191: 3q^2+4q+1
       192: 3q^2+4q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: 2q
       198: 2
       199: 3q^2+4q+1
       200: 3q^2+4q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q+1
       204: q+1
       205: 2q
       206: 2
       207: 2q^2+4q
       208: 2q^2+4q+2
       209: q^2+4q
       210: 2q+2
       211: 2q^2+4q
       212: 2q+2
       213: q^3+3q^2+4q
       214: q^2+3q+2
       215: 4q^2+4q
       216: q^2+3q+2
       217: q^3+3q^2+4q
       218: q^2+3q+2
       219: 7q^2+7q+2
       220: 3q^2+5q+2
       221: 3q^2+5q+2
       222: 4q+2
       223: q^3+4q^2+6q+2
       224: 4q+2
       225: q^3+4q^2+6q+2
       226: 4q^2+7q+2
       227: 4q^2+7q+2
       228: 2q^3+7q^2+7q+2
       229: q^2+2q+2
       230: q^3+4q^2+6q+2
       231: 4q^2+7q+2
       232: 4q^2+7q+2
       233: 2q^3+7q^2+7q+2
       234: q^3+4q^2+6q+2
       235: q^2+2q+2
       236: 3q^2+6q+2
       237: 2q^2+4q
       238: 2q+2
       239: 4q^2+4q
       240: 2q+2
       241: 2q^2+4q
       242: 2q+2
       243: q^2+6q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: q^2+6q+2
       247: 6q+2
       248: q^2+6q+2
       249: q^2+3q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: 3q^2+6q+2
       257: q^3+5q^2+6q+2
       258: 3q^2+6q+2
       259: 2q
       260: q+1
       261: q+1
       262: 2q
       263: 2q
       264: q+1
       265: q+1
       266: 2q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       275: q^2+2q
       276: q^2+2q+1
       277: q^2+2q+1
       278: q^2+2q
       279: q^2+4q
       280: q^2+3q+2
       281: q^3+3q^2+4q
       282: q^2+3q+2
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: q^2+3q+1
       287: q^2+4q
       288: q^2+3q+2
       289: q^2+4q
       290: 2q+2
       291: q^2+4q
       292: 2q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q
       298: 2q+2
       299: q+1
       300: q+1
       301: 2q
       302: 2
       303: q^2+3q+1
       304: q^2+3q+1
       305: 2q
       306: 2
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: 2q
       312: 2
       313: 2q
       314: 2
       315: 2q^2+4q
       316: 2q+2
       317: q^2+4q
       318: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       325: q^2+4q
       326: 2q+2
       333: 3q^2+5q+2
       334: 4q+2
       335: 4q+2
       336: 2q+1
       337: 5q+2
       338: 5q
       339: q+2
       340: q^2+5q
       341: q+2
       342: q^2+2q
       343: q+1
       344: 4q^2+7q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: q^2+2q+2
       349: 2q+2
       350: q^3+4q^2+6q+2
       351: 3q+2
       352: 4q^2+7q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: q^3+4q^2+6q+2
       357: 2
       358: q^2+2q+2
       359: 3q+2
       360: 2q^2+4q
       361: 2q+2
       362: 4q^2+4q
       363: 2q+2
       364: 2q^2+4q
       365: 2q+2
       366: q^2+6q+2
       367: q^2+6q+2
       368: 3q^2+6q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 6q+2
       372: q^2+6q+2
       373: q^2+3q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 2q
       378: q+1
       379: q+1
       380: 2q
       381: 2q
       382: q+1
       383: q+1
       384: 2q
       385: q
       386: q+1
       387: q+1
       388: q
       389: q
       390: 1
       391: q
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 1
       399: q
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       407: 1
       408: 1
       413: q^2+4q
       414: q^2+3q+2
       417: q^2+4q
       418: 2q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q
       424: 2q+2
       425: 2q
       426: 1
       427: 4q
       428: q+2
       429: q+1
       430: q+1
       431: q^2+3q+1
       432: q^2+3q+1
       433: 2q
       434: 2
       435: 2q
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: q+1
       444: q+1
       445: 3q
       446: 2
       447: q^2+3q+1
       448: q^2+3q+1
       449: q+1
       450: q+1
       451: 2q
       452: 2
       453: q+1
       454: q+1
       455: 2q
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       463: 3q
       464: 2
       465: q^2+4q
       466: 2q+2
       467: 2q^2+4q
       468: 2q+2
       469: q^2+4q
       470: 2q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: 2
       478: 2
       480: q+2
       481: 4q+2
       482: 4q+2
       483: q+1
       484: 5q+2
       485: 5q
       486: q+2
       487: q^2+5q
       488: q+2
       489: q^2+2q
       490: q+1
       491: 2q+1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: q+1
       496: 3q+2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: q+1
       501: 3q+2
       508: q^2+6q+2
       509: 2q+2
       510: 2q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 6q+2
       516: q^2+6q+2
       517: q^2+3q+1
       518: q+2
       519: q+2
       520: q+1
       521: 2q
       522: q+1
       523: q+1
       524: 2q
       529: q
       530: q+1
       531: q+1
       532: q
       533: q
       534: 1
       535: 1
       536: q
       537: q
       538: 1
       539: q
       540: 1
       542: 1
       544: 1
       545: q
       546: 1
       547: q
       548: 1
       549: q
       550: 1
       551: 1
       552: q
       553: q
       554: 1
       555: q
       556: 1
       558: 1
       560: 1
       561: q
       562: 1
       563: q
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       580: q
       581: 2
       585: 2q
       586: 2q+2
       589: 2q+1
       590: 2q+1
       595: 2q+1
       596: 2q+1
       597: 2q
       598: 1
       599: q
       600: 1
       601: 4q
       602: q+2
       603: 1
       604: 1
       605: 2q
       606: 2
       607: q+1
       608: q+1
       610: 2
       613: q
       614: 1
       615: q+1
       616: q+1
       617: 3q
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2q
       624: 2
       626: 2
       629: q
       630: 1
       631: q+1
       632: q+1
       633: 3q
       634: 2
       639: q^2+4q
       640: 2q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: q+2
       657: 5q+2
       658: 5q
       659: q+2
       660: q^2+5q
       661: q+2
       662: q^2+2q
       663: q+1
       664: 2q+1
       665: q+1
       672: q+2
       673: 1
       674: 3q+2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: q+1
       680: 3q+2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: q+1
       686: 2q+2
       687: 2
       688: 2
       690: q+2
       691: q+2
       692: q+1
       699: 1
       700: 1
       709: q
       710: q+1
       711: q+1
       712: q
       721: q
       722: 1
       723: q
       724: 1
       726: 1
       728: 1
       733: q
       734: 1
       735: q
       736: 1
       737: q
       738: 1
       739: q
       740: 1
       742: 1
       744: 1
       749: q
       750: 1
       751: q
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       772: q
       773: 2
       775: 4q
       776: q+2
       779: 2q
       780: 1
       781: q
       782: 1
       792: 1
       793: q+1
       794: q+1
       795: 3q
       796: 2
       798: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: q
       810: 1
       812: 1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 3q
       820: 2
       822: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: q
       834: 1
       836: 1
       839: 1
       840: 1
       844: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       850: 2
       852: 2
       858: 2
       865: q+2
       866: q+1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       881: q+2
       882: q+2
       883: q+1
       890: 1
       891: 1
       916: q
       917: 1
       918: q
       919: 1
       921: 1
       923: 1
       940: q
       941: 1
       942: q
       943: 1
       945: 1
       947: 1
       962: 1
       963: 1
       965: 1
       966: 1
       971: q
       972: 2
       976: 1
       977: 1
       989: 1
       990: 1
       994: q
       995: 1
      1009: 1
      1011: 1
      1013: 1
      1016: 1
      1017: 1
      1020: q
      1021: 1
      1023: 1
      1032: 1
      1033: 1
      1036: q
      1037: 1
      1039: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1072: q+2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1093: 1
      1142: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1221: 1
      1225: 1
      1228: 1
      1229: 1
      1231: 1
      1246: 1
      1247: 1
      1249: 1
      1263: 2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1411: 1
      1412: 1
      1437: 1
      1445: 1
      1485: 1
      1486: 1
      1640: 1

1641:    0: q^4+4q^3+16q^2+11q+2
         1: q^4+9q^3+16q^2+11q+2
         2: q^4+4q^3+16q^2+11q+2
         3: 7q^3+16q^2+11q+2
         4: q^4+4q^3+16q^2+11q+2
         5: 7q^3+16q^2+11q+2
         6: q^4+9q^3+16q^2+11q+2
         7: q^4+4q^3+16q^2+11q+2
         8: 7q^3+16q^2+11q+2
         9: q^5+3q^4+7q^3+11q^2+8q+2
        10: 8q^2+10q+2
        11: 8q^2+10q+2
        12: 8q^2+10q+2
        13: q^4+4q^3+16q^2+11q+2
        14: q^4+4q^3+16q^2+11q+2
        15: 7q^3+16q^2+11q+2
        16: 2q^3+13q^2+11q+2
        17: 4q^3+13q^2+11q+2
        18: q^4+4q^3+11q^2+8q+2
        19: q^4+4q^3+16q^2+11q+2
        20: q^4+9q^3+16q^2+11q+2
        21: q^4+4q^3+16q^2+11q+2
        22: 2q^3+13q^2+11q+2
        23: 4q^3+13q^2+11q+2
        24: 2q^3+13q^2+11q+2
        25: 2q^3+13q^2+11q+2
        26: 4q^3+13q^2+11q+2
        27: 2q^3+13q^2+11q+2
        28: 5q^2+10q+2
        29: 8q^2+10q+2
        30: q^4+4q^3+16q^2+11q+2
        31: 5q^2+10q+2
        32: 2q^3+13q^2+11q+2
        33: q^3+10q^2+11q+2
        34: 5q^2+10q+2
        35: 2q^3+13q^2+11q+2
        36: q^3+10q^2+11q+2
        37: 8q^2+9q+2
        38: 3q^2+2q
        39: q^3+8q^2+9q+2
        40: 3q^2+2q
        41: 8q^2+9q+2
        42: 3q^2+2q
        43: 8q^2+10q+2
        44: 8q^2+10q+2
        45: 8q^2+10q+2
        46: 2q^3+13q^2+11q+2
        47: 4q^3+13q^2+11q+2
        48: q^4+4q^3+11q^2+8q+2
        49: 2q^3+13q^2+11q+2
        50: 4q^3+13q^2+11q+2
        51: q^4+4q^3+11q^2+8q+2
        52: 2q^3+13q^2+11q+2
        53: 4q^3+13q^2+11q+2
        54: 2q^3+13q^2+11q+2
        55: 2q^3+13q^2+11q+2
        56: 4q^3+13q^2+11q+2
        57: 2q^3+13q^2+11q+2
        58: q^2+5q+1
        59: q^2+5q+1
        60: q^2+5q+1
        61: q^2+5q+1
        62: 3q^2+8q+2
        63: 2q
        64: 8q^2+9q+2
        65: 3q^2+2q
        66: 5q^2+9q+2
        67: 3q^2+2q
        68: 5q^2+10q+2
        69: 2q^3+8q^2+8q+2
        70: 8q^2+10q+2
        71: 5q^2+10q+2
        72: q^3+10q^2+11q+2
        73: q^3+10q^2+11q+2
        74: 8q^2+9q+2
        75: 3q^2+2q
        76: q^3+8q^2+9q+2
        77: 3q^2+2q
        78: 8q^2+9q+2
        79: 3q^2+2q
        80: 5q^2+10q+2
        81: q^3+10q^2+11q+2
        82: 5q^2+10q+2
        83: 2q^3+13q^2+11q+2
        84: 5q^2+10q+2
        85: q^3+10q^2+11q+2
        86: 5q^2+10q+2
        87: 2q^3+13q^2+11q+2
        88: q^2+10q+2
        89: q^2+10q+2
        90: 4q^2+7q+2
        91: 2q^3+13q^2+11q+2
        92: 4q^3+13q^2+11q+2
        93: q^4+4q^3+11q^2+8q+2
        94: q^3+8q^2+11q+2
        95: q^3+8q^2+11q+2
        96: 2q^3+8q^2+8q+2
        97: q^3+8q^2+11q+2
        98: q^3+8q^2+11q+2
        99: 2q^3+8q^2+8q+2
       100: 8q^2+10q+2
       101: q^3+11q^2+10q+2
       102: 8q^2+10q+2
       103: 4q+1
       104: q
       105: q
       106: 4q+1
       107: q^2+5q+1
       108: q^2+5q+1
       109: q^2+5q+1
       110: q^2+5q+1
       111: 5q^2+9q+2
       112: 3q^2+2q
       113: 3q^2+8q+2
       114: 2q
       115: 8q^2+9q+2
       116: 3q^2+2q
       117: q^2+5q+1
       118: q^2+5q+1
       119: q^2+5q+1
       120: q^2+5q+1
       121: 3q^2+8q+2
       122: 2q
       123: 5q^2+9q+2
       124: 3q^2+2q
       125: q^2+10q+2
       126: q^2+7q+2
       127: 2q^2+9q+2
       129: 2q^2+9q+2
       131: 4q^2+6q+2
       133: 5q^2+10q+2
       134: 2q^3+8q^2+8q+2
       135: q^3+10q^2+11q+2
       136: q^3+10q^2+11q+2
       137: 10q+2
       138: q^3+5q^2+8q+2
       139: 2q^2+10q+2
       140: 3q^2+7q+2
       141: 5q^2+10q+2
       142: q^3+8q^2+11q+2
       143: 10q+2
       144: q^3+5q^2+8q+2
       145: 2q^2+10q+2
       146: 5q^2+10q+2
       147: q^3+8q^2+11q+2
       148: 3q^2+7q+2
       149: 3q^2+9q+2
       150: 8q^2+10q+2
       151: 6q^2+8q+2
       152: 2q^2+2q
       153: q^3+8q^2+8q+2
       154: 3q^2+2q
       155: 6q^2+8q+2
       156: 2q^2+2q
       157: q^2+10q+2
       158: q^2+10q+2
       159: 4q^2+7q+2
       160: q^3+8q^2+11q+2
       161: q^3+8q^2+11q+2
       162: 2q^3+8q^2+8q+2
       163: q^3+8q^2+11q+2
       164: q^3+8q^2+11q+2
       165: 2q^3+8q^2+8q+2
       166: 2q^2+10q+2
       167: 4q^2+10q+2
       168: 4q^2+7q+2
       169: 4q+1
       170: q
       171: q
       172: 4q+1
       173: 4q+1
       174: q
       175: q
       176: 4q+1
       177: q^2+6q+2
       179: 8q+2
       181: 2q^2+9q+2
       183: q^2+5q+1
       184: q^2+5q+1
       185: q^2+5q+1
       186: q^2+5q+1
       187: 5q^2+9q+2
       188: 3q^2+2q
       189: 3q^2+8q+2
       190: 2q
       191: 5q+1
       192: 5q+1
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: 2q^2+5q+2
       198: q^2+2q
       199: 5q+1
       200: 5q+1
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 2q^2+5q+2
       206: q^2+2q
       207: 8q+2
       208: 2q
       209: 3q^2+7q+2
       210: 2q
       211: 6q^2+8q+2
       212: 2q^2+2q
       213: 2q^2+9q+2
       215: 2q^2+9q+2
       217: 4q^2+6q+2
       219: q^2+7q+2
       220: q^2+10q+2
       221: q^2+7q+2
       222: 10q+2
       223: q^3+5q^2+8q+2
       224: 10q+2
       225: q^3+5q^2+8q+2
       226: 7q+2
       227: 2q^2+10q+2
       228: q^3+5q^2+8q+2
       229: 3q^2+7q+2
       230: q^3+8q^2+11q+2
       231: 7q+2
       232: 2q^2+10q+2
       233: q^3+5q^2+8q+2
       234: q^3+8q^2+11q+2
       235: 3q^2+7q+2
       236: 2q^2+7q+2
       237: 8q+2
       239: q^2+8q+2
       241: 2q^2+5q+2
       243: 9q+2
       244: q^2+7q+2
       245: q^2+7q+2
       246: 3q^2+9q+2
       247: 2q^2+10q+2
       248: 4q^2+10q+2
       249: 4q^2+7q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: 2q^2+10q+2
       257: 4q^2+10q+2
       258: 4q^2+7q+2
       259: 4q+1
       262: 4q+1
       263: 4q+1
       264: q
       265: q
       266: 4q+1
       267: 2q+1
       268: q
       269: 2q+1
       270: q
       271: 2q+1
       272: q
       273: 2q+1
       274: q
       275: 4q+1
       276: q
       277: q
       278: 4q+1
       279: 8q+2
       281: q^2+6q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 5q+2
       289: 2q^2+9q+2
       291: q^2+6q+2
       293: 5q+1
       294: 5q+1
       295: 5q+1
       296: 5q+1
       297: 8q+2
       298: 2q
       299: 3q+1
       300: 3q+1
       301: 5q+2
       303: q^2+5q+1
       304: q^2+5q+1
       305: 2q^2+5q+2
       306: q^2+2q
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       311: 5q+2
       313: 2q^2+5q+2
       314: q^2+2q
       315: 5q+2
       317: 7q+2
       319: 3q+1
       320: 3q+1
       321: 3q+1
       322: 3q+1
       323: 3q+2
       324: 2q
       325: 3q^2+7q+2
       326: 2q
       333: q^2+7q+2
       334: 7q+2
       335: 7q+2
       336: 2q^2+7q+2
       337: 9q+2
       338: 8q+2
       340: q^2+8q+2
       342: 2q^2+5q+2
       344: 7q+2
       345: 4q+2
       346: 3q+2
       347: 2q+2
       348: q^2+4q+2
       349: 4q+2
       350: q^3+5q^2+8q+2
       351: q^2+7q+2
       352: 7q+2
       353: 4q+2
       354: 3q+2
       355: 4q+2
       356: q^3+5q^2+8q+2
       357: 2q+2
       358: q^2+4q+2
       359: q^2+7q+2
       360: 8q+2
       362: q^2+8q+2
       364: 2q^2+5q+2
       366: 6q+2
       367: 9q+2
       368: 2q^2+7q+2
       369: q^2+7q+2
       370: q^2+7q+2
       371: 2q^2+10q+2
       372: 4q^2+10q+2
       373: 4q^2+7q+2
       374: q+2
       375: q+2
       376: q+2
       377: q+1
       380: q+1
       381: 4q+1
       384: 4q+1
       385: 4q+1
       386: q
       387: q
       388: 4q+1
       389: 2q+1
       391: 2q+1
       393: 2q+1
       394: q
       395: q
       396: 2q+1
       397: 2q+1
       399: 2q+1
       401: 2q+1
       402: q
       403: q
       404: 2q+1
       405: q+1
       406: q+1
       407: q
       408: q
       413: 5q+2
       417: q^2+6q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 5q+2
       425: 5q+2
       427: 7q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 2q+2
       435: 5q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       441: 2q+2
       443: 3q+1
       444: 3q+1
       445: 5q+2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 2q+2
       453: 2q+1
       454: 2q+1
       455: 5q+2
       457: q+1
       458: q+1
       459: 2q+2
       461: 3q+1
       462: 3q+1
       463: 5q+2
       465: 7q+2
       467: 5q+2
       469: 4q+2
       471: 3q+1
       472: 3q+1
       473: 3q+1
       474: 3q+1
       475: 3q+2
       476: 2q
       477: 4q+2
       479: 3q+2
       480: 2q
       481: 7q+2
       482: 7q+2
       483: 6q+2
       484: 9q+2
       485: 8q+2
       487: q^2+8q+2
       489: 2q^2+5q+2
       491: 2q^2+7q+2
       492: 3q+2
       493: q+2
       494: 3q+2
       495: q^2+4q+2
       496: q^2+7q+2
       497: 3q+2
       498: 3q+2
       499: q+2
       500: q^2+4q+2
       501: q^2+7q+2
       508: 6q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+4q+2
       513: 2
       514: q^2+4q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: q+2
       519: q+2
       520: q+2
       521: q+1
       524: q+1
       529: q+1
       532: q+1
       533: 1
       536: 1
       537: 2q+1
       539: 2q+1
       541: q+1
       543: q+1
       545: 2q+1
       547: 2q+1
       549: 1
       552: 1
       553: 2q+1
       555: 2q+1
       557: q+1
       559: q+1
       561: 2q+1
       563: 2q+1
       565: q+1
       566: q
       567: q
       568: q+1
       569: q+1
       570: q+1
       573: q+1
       574: q
       575: q+1
       576: q
       577: 3q+2
       579: q
       585: 5q+2
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: 5q+2
       599: 4q+2
       601: 7q+2
       603: 1
       604: 1
       605: 2q+2
       607: q+1
       608: q+1
       609: q+2
       613: 2q+2
       615: 3q+1
       616: 3q+1
       617: 5q+2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2q+2
       625: q+2
       629: 2q+2
       631: 3q+1
       632: 3q+1
       633: 5q+2
       639: 4q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 4q+2
       653: 2
       655: 3q+2
       656: 2q
       657: q+4
       658: 3q+4
       660: 4q+4
       662: 3q+4
       664: 3q+4
       665: 6q+2
       672: q+2
       673: q+2
       674: q+4
       675: q+2
       676: 3q+2
       677: q+2
       678: 2
       679: q^2+4q+2
       680: q+4
       681: 3q+2
       682: q+2
       683: q+2
       684: 2
       685: q^2+4q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       693: q+1
       697: q+1
       709: q+1
       712: q+1
       713: 1
       716: 1
       717: 1
       720: 1
       721: 1
       723: 1
       725: 1
       727: 1
       733: 2q+1
       735: 2q+1
       737: 1
       739: 1
       741: 1
       743: 1
       749: 2q+1
       751: 2q+1
       753: 1
       756: 1
       757: q+1
       758: q+1
       761: 1
       762: 1
       765: q+1
       766: q
       767: q
       768: q+1
       769: 3q+2
       771: q
       775: q+4
       779: 3q+4
       781: 4q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       791: q+2
       793: 2
       794: 2
       795: q+4
       797: q+2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+2
       811: q+2
       815: 1
       816: 1
       817: 2
       818: 2
       819: q+4
       821: q+2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: 2q+2
       835: q+2
       839: 1
       840: 1
       843: 2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: 2
       855: 1
       857: 2
       866: q+4
       868: q+2
       870: q+4
       871: q+2
       872: 2
       874: q+4
       875: q+2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       884: q+1
       889: q+1
       900: 1
       902: 1
       904: 1
       906: 1
       908: 1
       911: 1
       916: 2
       918: 2
       920: 1
       922: 1
       928: 1
       930: 1
       940: 2
       942: 2
       944: 1
       946: 1
       948: 1
       950: 1
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: 1
       975: 1
       988: 1
       991: 1
       994: q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 2
      1010: q+2
      1012: 2
      1013: 2
      1020: q+4
      1022: q+2
      1026: 1
      1027: 1
      1036: q+4
      1038: q+2
      1044: 1
      1045: 1
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 2
      1078: 2
      1080: 2
      1082: 2
      1083: 1
      1084: 2
      1085: 1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1114: 2
      1116: 2
      1122: 2
      1124: 2
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1141: 2
      1156: 1
      1158: 1
      1172: 1
      1174: 1
      1198: 1
      1199: 1
      1220: 2
      1230: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1248: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1266: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1290: 1
      1293: 1
      1294: 1
      1295: 1
      1330: 1
      1331: 1
      1356: 1
      1358: 1
      1380: 1
      1382: 1
      1430: 1
      1433: 1
      1464: 1
      1474: 1
      1484: 1
      1641: 1

1642:    0: q^4+4q^3+16q^2+11q+2
         1: q^4+9q^3+16q^2+11q+2
         2: q^4+4q^3+16q^2+11q+2
         3: 7q^3+16q^2+11q+2
         4: q^4+4q^3+16q^2+11q+2
         5: 7q^3+16q^2+11q+2
         6: q^4+9q^3+16q^2+11q+2
         7: q^4+4q^3+16q^2+11q+2
         8: 7q^3+16q^2+11q+2
         9: q^5+3q^4+7q^3+11q^2+8q+2
        10: 8q^2+10q+2
        11: 8q^2+10q+2
        12: 8q^2+10q+2
        13: q^4+4q^3+16q^2+11q+2
        14: q^4+4q^3+16q^2+11q+2
        15: 7q^3+16q^2+11q+2
        16: 2q^3+13q^2+11q+2
        17: 4q^3+13q^2+11q+2
        18: q^4+4q^3+11q^2+8q+2
        19: q^4+4q^3+16q^2+11q+2
        20: q^4+9q^3+16q^2+11q+2
        21: q^4+4q^3+16q^2+11q+2
        22: 2q^3+13q^2+11q+2
        23: 4q^3+13q^2+11q+2
        24: 2q^3+13q^2+11q+2
        25: 2q^3+13q^2+11q+2
        26: 4q^3+13q^2+11q+2
        27: 2q^3+13q^2+11q+2
        28: 5q^2+10q+2
        29: 8q^2+10q+2
        30: q^4+4q^3+16q^2+11q+2
        31: 5q^2+10q+2
        32: 2q^3+13q^2+11q+2
        33: q^3+10q^2+11q+2
        34: 5q^2+10q+2
        35: 2q^3+13q^2+11q+2
        36: q^3+10q^2+11q+2
        37: 3q^2+2q
        38: 8q^2+9q+2
        39: 3q^2+2q
        40: q^3+8q^2+9q+2
        41: 3q^2+2q
        42: 8q^2+9q+2
        43: 8q^2+10q+2
        44: 8q^2+10q+2
        45: 8q^2+10q+2
        46: 2q^3+13q^2+11q+2
        47: 4q^3+13q^2+11q+2
        48: q^4+4q^3+11q^2+8q+2
        49: 2q^3+13q^2+11q+2
        50: 4q^3+13q^2+11q+2
        51: q^4+4q^3+11q^2+8q+2
        52: 2q^3+13q^2+11q+2
        53: 4q^3+13q^2+11q+2
        54: 2q^3+13q^2+11q+2
        55: 2q^3+13q^2+11q+2
        56: 4q^3+13q^2+11q+2
        57: 2q^3+13q^2+11q+2
        58: q^2+5q+1
        59: q^2+5q+1
        60: q^2+5q+1
        61: q^2+5q+1
        62: 2q
        63: 3q^2+8q+2
        64: 3q^2+2q
        65: 8q^2+9q+2
        66: 3q^2+2q
        67: 5q^2+9q+2
        68: 5q^2+10q+2
        69: 2q^3+8q^2+8q+2
        70: 8q^2+10q+2
        71: 5q^2+10q+2
        72: q^3+10q^2+11q+2
        73: q^3+10q^2+11q+2
        74: 3q^2+2q
        75: 8q^2+9q+2
        76: 3q^2+2q
        77: q^3+8q^2+9q+2
        78: 3q^2+2q
        79: 8q^2+9q+2
        80: 5q^2+10q+2
        81: q^3+10q^2+11q+2
        82: 5q^2+10q+2
        83: 2q^3+13q^2+11q+2
        84: 5q^2+10q+2
        85: q^3+10q^2+11q+2
        86: 5q^2+10q+2
        87: 2q^3+13q^2+11q+2
        88: q^2+10q+2
        89: q^2+10q+2
        90: 4q^2+7q+2
        91: 2q^3+13q^2+11q+2
        92: 4q^3+13q^2+11q+2
        93: q^4+4q^3+11q^2+8q+2
        94: q^3+8q^2+11q+2
        95: q^3+8q^2+11q+2
        96: 2q^3+8q^2+8q+2
        97: q^3+8q^2+11q+2
        98: q^3+8q^2+11q+2
        99: 2q^3+8q^2+8q+2
       100: 8q^2+10q+2
       101: q^3+11q^2+10q+2
       102: 8q^2+10q+2
       103: q
       104: 4q+1
       105: 4q+1
       106: q
       107: q^2+5q+1
       108: q^2+5q+1
       109: q^2+5q+1
       110: q^2+5q+1
       111: 3q^2+2q
       112: 5q^2+9q+2
       113: 2q
       114: 3q^2+8q+2
       115: 3q^2+2q
       116: 8q^2+9q+2
       117: q^2+5q+1
       118: q^2+5q+1
       119: q^2+5q+1
       120: q^2+5q+1
       121: 2q
       122: 3q^2+8q+2
       123: 3q^2+2q
       124: 5q^2+9q+2
       125: q^2+10q+2
       126: q^2+7q+2
       128: 2q^2+9q+2
       130: 2q^2+9q+2
       132: 4q^2+6q+2
       133: 5q^2+10q+2
       134: 2q^3+8q^2+8q+2
       135: q^3+10q^2+11q+2
       136: q^3+10q^2+11q+2
       137: 10q+2
       138: q^3+5q^2+8q+2
       139: 2q^2+10q+2
       140: 3q^2+7q+2
       141: 5q^2+10q+2
       142: q^3+8q^2+11q+2
       143: 10q+2
       144: q^3+5q^2+8q+2
       145: 2q^2+10q+2
       146: 5q^2+10q+2
       147: q^3+8q^2+11q+2
       148: 3q^2+7q+2
       149: 3q^2+9q+2
       150: 8q^2+10q+2
       151: 2q^2+2q
       152: 6q^2+8q+2
       153: 3q^2+2q
       154: q^3+8q^2+8q+2
       155: 2q^2+2q
       156: 6q^2+8q+2
       157: q^2+10q+2
       158: q^2+10q+2
       159: 4q^2+7q+2
       160: q^3+8q^2+11q+2
       161: q^3+8q^2+11q+2
       162: 2q^3+8q^2+8q+2
       163: q^3+8q^2+11q+2
       164: q^3+8q^2+11q+2
       165: 2q^3+8q^2+8q+2
       166: 2q^2+10q+2
       167: 4q^2+10q+2
       168: 4q^2+7q+2
       169: q
       170: 4q+1
       171: 4q+1
       172: q
       173: q
       174: 4q+1
       175: 4q+1
       176: q
       178: q^2+6q+2
       180: 8q+2
       182: 2q^2+9q+2
       183: q^2+5q+1
       184: q^2+5q+1
       185: q^2+5q+1
       186: q^2+5q+1
       187: 3q^2+2q
       188: 5q^2+9q+2
       189: 2q
       190: 3q^2+8q+2
       191: 5q+1
       192: 5q+1
       193: 3q+1
       194: 3q+1
       195: q^2+5q+1
       196: q^2+5q+1
       197: q^2+2q
       198: 2q^2+5q+2
       199: 5q+1
       200: 5q+1
       201: q^2+5q+1
       202: q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: q^2+2q
       206: 2q^2+5q+2
       207: 2q
       208: 8q+2
       209: 2q
       210: 3q^2+7q+2
       211: 2q^2+2q
       212: 6q^2+8q+2
       214: 2q^2+9q+2
       216: 2q^2+9q+2
       218: 4q^2+6q+2
       219: q^2+7q+2
       220: q^2+10q+2
       221: q^2+7q+2
       222: 10q+2
       223: q^3+5q^2+8q+2
       224: 10q+2
       225: q^3+5q^2+8q+2
       226: 7q+2
       227: 2q^2+10q+2
       228: q^3+5q^2+8q+2
       229: 3q^2+7q+2
       230: q^3+8q^2+11q+2
       231: 7q+2
       232: 2q^2+10q+2
       233: q^3+5q^2+8q+2
       234: q^3+8q^2+11q+2
       235: 3q^2+7q+2
       236: 2q^2+7q+2
       238: 8q+2
       240: q^2+8q+2
       242: 2q^2+5q+2
       243: 9q+2
       244: q^2+7q+2
       245: q^2+7q+2
       246: 3q^2+9q+2
       247: 2q^2+10q+2
       248: 4q^2+10q+2
       249: 4q^2+7q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: 2q^2+10q+2
       257: 4q^2+10q+2
       258: 4q^2+7q+2
       260: 4q+1
       261: 4q+1
       263: q
       264: 4q+1
       265: 4q+1
       266: q
       267: q
       268: 2q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       273: q
       274: 2q+1
       275: q
       276: 4q+1
       277: 4q+1
       278: q
       280: 8q+2
       282: q^2+6q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       288: 5q+2
       290: 2q^2+9q+2
       292: q^2+6q+2
       293: 5q+1
       294: 5q+1
       295: 5q+1
       296: 5q+1
       297: 2q
       298: 8q+2
       299: 3q+1
       300: 3q+1
       302: 5q+2
       303: q^2+5q+1
       304: q^2+5q+1
       305: q^2+2q
       306: 2q^2+5q+2
       307: q^2+5q+1
       308: q^2+5q+1
       309: 3q+1
       310: 3q+1
       312: 5q+2
       313: q^2+2q
       314: 2q^2+5q+2
       316: 5q+2
       318: 7q+2
       319: 3q+1
       320: 3q+1
       321: 3q+1
       322: 3q+1
       323: 2q
       324: 3q+2
       325: 2q
       326: 3q^2+7q+2
       333: q^2+7q+2
       334: 7q+2
       335: 7q+2
       336: 2q^2+7q+2
       337: 9q+2
       339: 8q+2
       341: q^2+8q+2
       343: 2q^2+5q+2
       344: 7q+2
       345: 4q+2
       346: 3q+2
       347: 2q+2
       348: q^2+4q+2
       349: 4q+2
       350: q^3+5q^2+8q+2
       351: q^2+7q+2
       352: 7q+2
       353: 4q+2
       354: 3q+2
       355: 4q+2
       356: q^3+5q^2+8q+2
       357: 2q+2
       358: q^2+4q+2
       359: q^2+7q+2
       361: 8q+2
       363: q^2+8q+2
       365: 2q^2+5q+2
       366: 6q+2
       367: 9q+2
       368: 2q^2+7q+2
       369: q^2+7q+2
       370: q^2+7q+2
       371: 2q^2+10q+2
       372: 4q^2+10q+2
       373: 4q^2+7q+2
       374: q+2
       375: q+2
       376: q+2
       378: q+1
       379: q+1
       382: 4q+1
       383: 4q+1
       385: q
       386: 4q+1
       387: 4q+1
       388: q
       390: 2q+1
       392: 2q+1
       393: q
       394: 2q+1
       395: 2q+1
       396: q
       398: 2q+1
       400: 2q+1
       401: q
       402: 2q+1
       403: 2q+1
       404: q
       405: q
       406: q
       407: q+1
       408: q+1
       414: 5q+2
       418: q^2+6q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       424: 5q+2
       426: 5q+2
       428: 7q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       434: 2q+2
       436: 5q+2
       437: q+1
       438: q+1
       439: 2q+1
       440: 2q+1
       442: 2q+2
       443: 3q+1
       444: 3q+1
       446: 5q+2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       452: 2q+2
       453: 2q+1
       454: 2q+1
       456: 5q+2
       457: q+1
       458: q+1
       460: 2q+2
       461: 3q+1
       462: 3q+1
       464: 5q+2
       466: 7q+2
       468: 5q+2
       470: 4q+2
       471: 3q+1
       472: 3q+1
       473: 3q+1
       474: 3q+1
       475: 2q
       476: 3q+2
       478: 4q+2
       479: 2q
       480: 3q+2
       481: 7q+2
       482: 7q+2
       483: 6q+2
       484: 9q+2
       486: 8q+2
       488: q^2+8q+2
       490: 2q^2+5q+2
       491: 2q^2+7q+2
       492: 3q+2
       493: q+2
       494: 3q+2
       495: q^2+4q+2
       496: q^2+7q+2
       497: 3q+2
       498: 3q+2
       499: q+2
       500: q^2+4q+2
       501: q^2+7q+2
       508: 6q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+4q+2
       513: 2
       514: q^2+4q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: q+2
       519: q+2
       520: q+2
       522: q+1
       523: q+1
       530: q+1
       531: q+1
       534: 1
       535: 1
       538: 2q+1
       540: 2q+1
       542: q+1
       544: q+1
       546: 2q+1
       548: 2q+1
       550: 1
       551: 1
       554: 2q+1
       556: 2q+1
       558: q+1
       560: q+1
       562: 2q+1
       564: 2q+1
       565: q
       566: q+1
       567: q+1
       568: q
       571: q+1
       572: q+1
       573: q
       574: q+1
       575: q
       576: q+1
       581: 3q+2
       582: q
       586: 5q+2
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       598: 5q+2
       600: 4q+2
       602: 7q+2
       603: 1
       604: 1
       606: 2q+2
       607: q+1
       608: q+1
       610: q+2
       614: 2q+2
       615: 3q+1
       616: 3q+1
       618: 5q+2
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2q+2
       626: q+2
       630: 2q+2
       631: 3q+1
       632: 3q+1
       634: 5q+2
       640: 4q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: 4q+2
       654: 2
       655: 2q
       656: 3q+2
       657: q+4
       659: 3q+4
       661: 4q+4
       663: 3q+4
       664: 3q+4
       665: 6q+2
       672: q+2
       673: q+2
       674: q+4
       675: q+2
       676: 3q+2
       677: q+2
       678: 2
       679: q^2+4q+2
       680: q+4
       681: 3q+2
       682: q+2
       683: q+2
       684: 2
       685: q^2+4q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       699: q+1
       700: q+1
       710: q+1
       711: q+1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       724: 1
       726: 1
       728: 1
       734: 2q+1
       736: 2q+1
       738: 1
       740: 1
       742: 1
       744: 1
       750: 2q+1
       752: 2q+1
       754: 1
       755: 1
       759: q+1
       760: q+1
       763: 1
       764: 1
       765: q
       766: q+1
       767: q+1
       768: q
       773: 3q+2
       774: q
       776: q+4
       780: 3q+4
       782: 4q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       792: q+2
       793: 2
       794: 2
       796: q+4
       798: q+2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       810: 2q+2
       812: q+2
       815: 1
       816: 1
       817: 2
       818: 2
       820: q+4
       822: q+2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       834: 2q+2
       836: q+2
       839: 1
       840: 1
       843: 2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: 2
       856: 1
       858: 2
       866: q+4
       868: q+2
       870: q+4
       871: q+2
       872: 2
       874: q+4
       875: q+2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       890: q+1
       891: q+1
       901: 1
       903: 1
       905: 1
       907: 1
       909: 1
       910: 1
       917: 2
       919: 2
       921: 1
       923: 1
       929: 1
       931: 1
       941: 2
       943: 2
       945: 1
       947: 1
       949: 1
       951: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: 1
       977: 1
       989: 1
       990: 1
       995: q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1009: 2
      1011: q+2
      1012: 2
      1013: 2
      1021: q+4
      1023: q+2
      1026: 1
      1027: 1
      1037: q+4
      1039: q+2
      1044: 1
      1045: 1
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 2
      1078: 2
      1080: 2
      1082: 2
      1083: 1
      1084: 2
      1085: 1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1115: 2
      1117: 2
      1123: 2
      1125: 2
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1136: 1
      1137: 1
      1139: 2
      1142: 2
      1157: 1
      1159: 1
      1173: 1
      1175: 1
      1200: 1
      1201: 1
      1221: 2
      1231: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1249: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1267: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1291: 1
      1296: 1
      1297: 1
      1298: 1
      1332: 1
      1333: 1
      1357: 1
      1359: 1
      1381: 1
      1383: 1
      1431: 1
      1434: 1
      1465: 1
      1475: 1
      1484: 1
      1642: 1

1643:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+2q^2+3q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q^2+4q+2
        32: 2q^2+4q+2
        33: 2q^2+4q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 2q^2+4q+2
        44: q^3+2q^2+3q+2
        45: 2q^2+4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+3q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: 2q^2+4q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+3q+2
        72: 2
        73: 2q+2
        74: q+2
        76: q+2
        78: q+2
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^3+2q^2+3q+2
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+3q+2
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+3q+2
        97: q+2
        98: q+2
        99: q+2
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       111: 2
       113: q+2
       115: q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: 2q+2
       125: 2q^2+4q+2
       126: q^2+3q+2
       127: q+2
       129: q+2
       131: q+2
       133: q^2+3q+2
       134: q^2+3q+2
       135: 2
       136: 2q+2
       137: 2q^2+4q+2
       138: q^2+3q+2
       139: q^2+3q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+3q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+2
       167: q+2
       168: q+2
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: q+2
       179: q+2
       181: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       187: 2
       189: q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       207: 2q+2
       209: q+2
       211: q+2
       213: q+2
       215: q+2
       217: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: q^2+3q+2
       222: 2
       223: 2
       224: 2q+2
       225: 2q+2
       226: q^2+3q+2
       227: q^2+3q+2
       228: q^2+3q+2
       229: 2
       230: 2q+2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       236: q+2
       237: q+2
       239: q+2
       241: q+2
       243: q+2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       275: q+1
       278: q+1
       279: q+2
       281: q+2
       283: 1
       284: 1
       285: q+1
       286: q+1
       287: q+2
       289: 2
       291: 2
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: 2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: 1
       308: 1
       315: q+2
       317: q+2
       319: 1
       320: 1
       325: q+2
       327: q+2
       329: q+2
       331: q+2
       333: q^2+3q+2
       334: 2
       335: 2q+2
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q^2+3q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       360: q+2
       362: q+2
       364: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       409: q+2
       411: q+2
       413: q+2
       415: 2
       417: 2
       419: 1
       420: 1
       421: q+1
       422: q+1
       423: 2
       425: 1
       427: 2
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 2
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       447: 1
       448: 1
       453: 1
       454: 1
       465: q+2
       467: q+2
       469: q+2
       471: 1
       472: 1
       481: 2
       482: 2q+2
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: 1
       496: 2
       497: q+2
       498: 2
       502: q+2
       504: q+2
       506: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       583: q+2
       585: 2
       587: 2
       589: 1
       590: 1
       595: q+1
       596: q+1
       597: 1
       599: 1
       601: 2
       603: 1
       604: 1
       605: 2
       607: q+1
       608: q+1
       609: 2
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       619: 1
       620: 1
       635: q+2
       637: q+2
       639: q+2
       641: 1
       642: 1
       647: 1
       648: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: 1
       681: 2
       686: q+2
       687: 2
       690: 2
       691: 2
       692: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 2
       799: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       825: 1
       826: 1
       841: q+2
       845: 1
       846: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       877: 2
       881: 2
       882: 2
       883: q+1
       896: 1
       899: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1052: 1
      1053: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1210: 2
      1212: 1
      1214: 1
      1226: 2
      1228: 1
      1229: 1
      1230: 1
      1236: 1
      1238: 1
      1282: 1
      1283: 1
      1284: 1
      1340: 1
      1342: 1
      1438: 1
      1448: 1
      1452: 1
      1485: 1
      1643: 1

1644:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+2q^2+3q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q^2+4q+2
        32: 2q^2+4q+2
        33: 2q^2+4q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 2q^2+4q+2
        44: q^3+2q^2+3q+2
        45: 2q^2+4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+3q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q+2
        56: q+2
        57: q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: 2q^2+4q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+3q+2
        72: 2
        73: 2q+2
        75: q+2
        77: q+2
        79: q+2
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^3+2q^2+3q+2
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+3q+2
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+3q+2
        97: q+2
        98: q+2
        99: q+2
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: q+1
       110: q+1
       112: 2
       114: q+2
       116: q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: 2q+2
       125: 2q^2+4q+2
       126: q^2+3q+2
       128: q+2
       130: q+2
       132: q+2
       133: q^2+3q+2
       134: q^2+3q+2
       135: 2
       136: 2q+2
       137: 2q^2+4q+2
       138: q^2+3q+2
       139: q^2+3q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+3q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+2
       167: q+2
       168: q+2
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: q+2
       180: q+2
       182: 2
       183: 1
       184: 1
       185: q+1
       186: q+1
       188: 2
       190: q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       208: 2q+2
       210: q+2
       212: q+2
       214: q+2
       216: q+2
       218: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: q^2+3q+2
       222: 2
       223: 2
       224: 2q+2
       225: 2q+2
       226: q^2+3q+2
       227: q^2+3q+2
       228: q^2+3q+2
       229: 2
       230: 2q+2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       236: q+2
       238: q+2
       240: q+2
       242: q+2
       243: q+2
       244: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       276: q+1
       277: q+1
       280: q+2
       282: q+2
       283: 1
       284: 1
       285: q+1
       286: q+1
       288: q+2
       290: 2
       292: 2
       293: 1
       294: 1
       295: q+1
       296: q+1
       298: 2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: 1
       308: 1
       316: q+2
       318: q+2
       319: 1
       320: 1
       326: q+2
       328: q+2
       330: q+2
       332: q+2
       333: q^2+3q+2
       334: 2
       335: 2q+2
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q^2+3q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       361: q+2
       363: q+2
       365: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       410: q+2
       412: q+2
       414: q+2
       416: 2
       418: 2
       419: 1
       420: 1
       421: q+1
       422: q+1
       424: 2
       426: 1
       428: 2
       429: 1
       430: 1
       431: q+1
       432: q+1
       434: 2
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       447: 1
       448: 1
       453: 1
       454: 1
       466: q+2
       468: q+2
       470: q+2
       471: 1
       472: 1
       481: 2
       482: 2q+2
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: 1
       496: 2
       497: q+2
       498: 2
       503: q+2
       505: q+2
       507: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       584: q+2
       586: 2
       588: 2
       589: 1
       590: 1
       595: q+1
       596: q+1
       598: 1
       600: 1
       602: 2
       603: 1
       604: 1
       606: 2
       607: q+1
       608: q+1
       610: 2
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       619: 1
       620: 1
       636: q+2
       638: q+2
       640: q+2
       641: 1
       642: 1
       647: 1
       648: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: 1
       681: 2
       686: q+2
       687: 2
       690: 2
       691: 2
       692: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 2
       800: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       825: 1
       826: 1
       842: q+2
       845: 1
       846: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       877: 2
       881: 2
       882: 2
       883: q+1
       897: 1
       898: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1052: 1
      1053: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1211: 2
      1213: 1
      1215: 1
      1227: 2
      1228: 1
      1229: 1
      1231: 1
      1237: 1
      1239: 1
      1282: 1
      1283: 1
      1284: 1
      1341: 1
      1343: 1
      1439: 1
      1449: 1
      1453: 1
      1485: 1
      1644: 1

1645:    0: q^4+18q^3+30q^2+14q+2
         1: 3q^4+22q^3+30q^2+14q+2
         2: q^4+18q^3+30q^2+14q+2
         3: 3q^4+22q^3+30q^2+14q+2
         4: 3q^4+18q^3+24q^2+12q+2
         5: q^4+18q^3+30q^2+14q+2
         6: q^5+9q^4+23q^3+24q^2+12q+2
         7: 3q^4+18q^3+24q^2+12q+2
         8: q^4+18q^3+30q^2+14q+2
         9: q^5+6q^4+14q^3+15q^2+9q+2
        10: 11q^3+26q^2+14q+2
        11: 11q^3+26q^2+14q+2
        12: 2q^4+14q^3+21q^2+12q+2
        13: q^4+18q^3+30q^2+14q+2
        14: 3q^4+18q^3+24q^2+12q+2
        15: q^4+18q^3+30q^2+14q+2
        16: 11q^3+26q^2+14q+2
        17: 11q^3+26q^2+14q+2
        18: 2q^4+11q^3+15q^2+9q+2
        19: 10q^3+22q^2+12q+2
        20: 2q^4+15q^3+22q^2+12q+2
        21: 10q^3+22q^2+12q+2
        22: q^4+18q^3+30q^2+14q+2
        23: 3q^4+22q^3+30q^2+14q+2
        24: q^4+18q^3+30q^2+14q+2
        25: 10q^3+26q^2+14q+2
        26: 14q^3+26q^2+14q+2
        27: 10q^3+26q^2+14q+2
        28: 5q^3+22q^2+14q+2
        29: 7q^3+19q^2+12q+2
        30: 10q^3+22q^2+12q+2
        31: 11q^3+26q^2+14q+2
        32: q^4+18q^3+30q^2+14q+2
        33: 11q^3+26q^2+14q+2
        34: 6q^3+22q^2+14q+2
        35: 10q^3+26q^2+14q+2
        36: 6q^3+22q^2+14q+2
        37: 5q^3+13q^2+7q+1
        38: 5q^3+13q^2+7q+1
        39: 7q^3+13q^2+7q+1
        40: 7q^3+13q^2+7q+1
        41: 5q^3+13q^2+7q+1
        42: 5q^3+13q^2+7q+1
        43: 11q^3+26q^2+14q+2
        44: 2q^4+14q^3+21q^2+12q+2
        45: 11q^3+26q^2+14q+2
        46: 11q^3+26q^2+14q+2
        47: 11q^3+26q^2+14q+2
        48: 2q^4+11q^3+15q^2+9q+2
        49: 4q^3+18q^2+12q+2
        50: 6q^3+18q^2+12q+2
        51: 5q^3+13q^2+9q+2
        52: 10q^3+22q^2+12q+2
        53: 2q^4+15q^3+22q^2+12q+2
        54: 10q^3+22q^2+12q+2
        55: 4q^3+18q^2+12q+2
        56: 8q^3+18q^2+12q+2
        57: 4q^3+18q^2+12q+2
        58: 4q^3+14q^2+10q+2
        59: q^3+8q^2+4q
        60: q^3+9q^2+7q+1
        61: q^3+9q^2+7q+1
        62: 3q^3+11q^2+7q+1
        63: 3q^3+11q^2+7q+1
        64: 5q^3+13q^2+7q+1
        65: 5q^3+13q^2+7q+1
        66: 3q^3+11q^2+7q+1
        67: 3q^3+11q^2+7q+1
        68: 5q^3+22q^2+14q+2
        69: 2q^3+10q^2+9q+2
        70: 7q^3+19q^2+12q+2
        71: 2q^3+15q^2+12q+2
        72: q^3+9q^2+10q+2
        73: 2q^3+11q^2+10q+2
        74: q^3+6q^2+5q+1
        75: q^3+6q^2+5q+1
        76: 2q^3+6q^2+5q+1
        77: 2q^3+6q^2+5q+1
        78: q^3+6q^2+5q+1
        79: q^3+6q^2+5q+1
        80: 11q^3+26q^2+14q+2
        81: 11q^3+26q^2+14q+2
        82: 7q^3+19q^2+12q+2
        83: 10q^3+22q^2+12q+2
        84: 6q^3+22q^2+14q+2
        85: 6q^3+22q^2+14q+2
        86: 3q^3+15q^2+12q+2
        87: 4q^3+18q^2+12q+2
        88: 2q^3+17q^2+14q+2
        89: 2q^3+17q^2+14q+2
        90: q^4+7q^3+12q^2+9q+2
        91: 4q^3+18q^2+12q+2
        92: 6q^3+18q^2+12q+2
        93: 5q^3+13q^2+9q+2
        94: 4q^3+18q^2+12q+2
        95: 6q^3+18q^2+12q+2
        96: 5q^3+13q^2+9q+2
        97: 11q^2+12q+2
        98: q^3+11q^2+12q+2
        99: q^3+9q^2+9q+2
       100: 4q^3+18q^2+12q+2
       101: 8q^3+18q^2+12q+2
       102: 4q^3+18q^2+12q+2
       103: q^3+6q^2+5q+1
       104: 3q^2+2q
       105: q^3+6q^2+5q+1
       106: 3q^2+2q
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: q^3+7q^2+8q+2
       110: 2q^2+2q
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: q^3+5q^2+5q+1
       114: q^3+5q^2+5q+1
       115: q^3+6q^2+5q+1
       116: q^3+6q^2+5q+1
       117: 4q^3+14q^2+10q+2
       118: q^3+8q^2+4q
       119: q^3+9q^2+7q+1
       120: q^3+9q^2+7q+1
       121: 3q^3+11q^2+7q+1
       122: 3q^3+11q^2+7q+1
       123: 3q^3+11q^2+7q+1
       124: 3q^3+11q^2+7q+1
       125: 2q^3+17q^2+14q+2
       126: 7q^2+9q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^3+15q^2+12q+2
       134: 2q^3+10q^2+9q+2
       135: q^3+9q^2+10q+2
       136: 2q^3+11q^2+10q+2
       137: 2q^3+17q^2+14q+2
       138: 2q^3+10q^2+9q+2
       139: 2q^3+15q^2+12q+2
       140: q^3+9q^2+10q+2
       141: 7q^3+19q^2+12q+2
       142: 2q^3+11q^2+10q+2
       143: 2q^3+14q^2+14q+2
       144: 6q^2+9q+2
       145: 9q^2+12q+2
       146: 3q^3+15q^2+12q+2
       147: 6q^2+10q+2
       148: 3q^2+6q+2
       149: 3q^3+15q^2+12q+2
       150: 4q^3+18q^2+12q+2
       151: q^3+6q^2+5q+1
       152: q^3+6q^2+5q+1
       153: 2q^3+6q^2+5q+1
       154: 2q^3+6q^2+5q+1
       155: q^3+6q^2+5q+1
       156: q^3+6q^2+5q+1
       157: 8q^2+11q+2
       158: 8q^2+11q+2
       159: 2q^3+7q^2+8q+2
       160: 4q^3+18q^2+12q+2
       161: 6q^3+18q^2+12q+2
       162: 5q^3+13q^2+9q+2
       163: 11q^2+12q+2
       164: q^3+11q^2+12q+2
       165: q^3+9q^2+9q+2
       166: 11q^2+12q+2
       167: q^3+11q^2+12q+2
       168: q^3+9q^2+9q+2
       169: q^2+3q+1
       170: q
       171: q^2+3q+1
       172: q
       173: q^3+6q^2+5q+1
       174: 3q^2+2q
       175: q^3+6q^2+5q+1
       176: 3q^2+2q
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: q^3+7q^2+8q+2
       186: 2q^2+2q
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: q^3+5q^2+5q+1
       190: q^3+5q^2+5q+1
       191: 2q^3+11q^2+10q+2
       192: 6q^2+4q
       193: 3q^2+5q+1
       194: 3q^2+5q+1
       195: q^3+7q^2+8q+2
       196: 2q^2+2q
       197: 2q^2+4q+1
       198: 2q^2+4q+1
       199: q^3+7q^2+7q+1
       200: q^3+7q^2+7q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       203: 3q^2+6q+2
       205: 2q+1
       206: 2q+1
       207: q^3+7q^2+7q+1
       208: q^3+7q^2+7q+1
       209: q^3+5q^2+5q+1
       210: q^3+5q^2+5q+1
       211: q^3+6q^2+5q+1
       212: q^3+6q^2+5q+1
       213: 2q^2+4q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: 2q^2+4q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 7q^2+9q+2
       220: 8q^2+11q+2
       221: 4q^2+8q+2
       222: 4q^2+10q+2
       223: 3q^2+7q+2
       224: 4q^2+9q+2
       225: q^3+5q^2+7q+2
       226: 7q^2+9q+2
       227: 2q^3+15q^2+12q+2
       228: 2q^3+10q^2+9q+2
       229: q^3+9q^2+10q+2
       230: 2q^3+11q^2+10q+2
       231: 4q^2+9q+2
       232: 9q^2+12q+2
       233: 6q^2+9q+2
       234: 6q^2+10q+2
       235: 3q^2+6q+2
       236: 6q^2+9q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 9q^2+12q+2
       244: 6q^2+10q+2
       245: 3q^2+6q+2
       246: 3q^3+15q^2+12q+2
       247: q^2+10q+4
       248: q^2+10q+4
       249: 3q^2+5q+2
       250: 8q^2+11q+2
       251: 8q^2+11q+2
       252: 2q^3+7q^2+8q+2
       253: 2q^2+7q+2
       254: 2q^2+7q+2
       255: 3q^2+5q+2
       256: 11q^2+12q+2
       257: q^3+11q^2+12q+2
       258: q^3+9q^2+9q+2
       259: 2q+1
       260: q
       261: 2q+1
       262: q
       263: q^2+3q+1
       264: q
       265: q^2+3q+1
       266: q
       267: q^2+3q+1
       268: q
       269: q
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       275: q^3+5q^2+5q+1
       276: 2q^2+2q
       277: q^3+5q^2+5q+1
       278: 2q^2+2q
       279: 2q^2+4q+1
       280: 2q^2+4q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: 2q+1
       284: 2q+1
       285: 2q^2+5q+2
       287: q^2+3q+1
       288: q^2+3q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q^2+5q+1
       294: 2q^2+5q+1
       295: 3q^2+7q+2
       296: q^2+2q
       297: q^2+4q+1
       298: q^2+4q+1
       299: 3q^2+5q+1
       300: 3q^2+5q+1
       301: 3q+1
       302: 3q+1
       303: q^3+7q^2+8q+2
       304: 2q^2+2q
       305: 2q^2+4q+1
       306: 2q^2+4q+1
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       309: 3q^2+6q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 2q^2+5q+1
       320: 2q^2+5q+1
       321: 3q^2+6q+2
       323: 2q+1
       324: 2q+1
       325: q^3+5q^2+5q+1
       326: q^3+5q^2+5q+1
       333: 4q^2+8q+2
       334: q^2+7q+2
       335: q^2+6q+2
       336: 3q+2
       337: 10q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 7q^2+9q+2
       345: 8q^2+11q+2
       346: 4q^2+8q+2
       347: 4q^2+10q+2
       348: 3q^2+7q+2
       349: 4q^2+9q+2
       350: q^3+5q^2+7q+2
       351: q^2+10q+4
       352: 4q^2+9q+2
       353: 2q^2+7q+2
       354: q^2+5q+2
       355: 6q+2
       356: 3q^2+7q+2
       357: q^2+3q+2
       358: q^2+3q+2
       359: 6q+4
       360: 2q^2+4q+1
       361: 2q^2+4q+1
       362: 2q^2+4q+1
       363: 2q^2+4q+1
       364: 2q^2+3q+1
       365: 2q^2+3q+1
       366: 4q^2+9q+2
       367: 9q^2+12q+2
       368: 6q^2+9q+2
       369: 6q^2+10q+2
       370: 3q^2+6q+2
       371: q^2+10q+4
       372: q^2+10q+4
       373: 3q^2+5q+2
       374: 2q^2+7q+2
       375: 2q^2+7q+2
       376: 3q^2+5q+2
       377: q+1
       379: q+1
       381: 2q+1
       382: q
       383: 2q+1
       384: q
       385: q^2+3q+1
       386: q
       387: q^2+3q+1
       388: q
       389: 2q+1
       390: q
       391: q
       392: 2q+1
       393: q^2+3q+1
       394: q
       395: q^2+3q+1
       396: q
       397: q+1
       398: q+1
       401: 2q+1
       402: 2q+1
       405: 2q+1
       408: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       421: 4q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: 2q+1
       430: 2q+1
       431: 2q^2+5q+2
       433: 2q+1
       434: 2q+1
       435: 3q+1
       436: 3q+1
       437: 2q^2+5q+1
       438: 2q^2+5q+1
       439: 3q^2+7q+2
       440: q^2+2q
       441: q^2+4q+1
       442: q^2+4q+1
       443: 5q+2
       444: 5q+2
       445: 4q+2
       446: 4q+2
       447: 2q+1
       448: 2q+1
       449: q^2+3q+2
       451: 1
       452: 1
       453: 3q+1
       454: 3q+1
       455: q+1
       456: q+1
       457: q^2+3q+2
       459: q+1
       460: q+1
       461: 6q+4
       463: 2q+2
       464: 2q+2
       465: 2q^2+4q+1
       466: 2q^2+4q+1
       467: q^2+3q+1
       468: q^2+3q+1
       469: q^2+3q+1
       470: q^2+3q+1
       471: 2q^2+5q+1
       472: 2q^2+5q+1
       473: 3q^2+6q+2
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 3q+2
       480: 3q+2
       481: q^2+7q+2
       482: q^2+6q+2
       483: 3q+2
       484: 10q+4
       485: 4q+2
       486: 4q+2
       487: 4q+2
       488: 4q+2
       489: q^2+2q+1
       490: q^2+2q+1
       491: 3q+2
       492: 4q^2+8q+2
       493: q^2+7q+2
       494: q^2+6q+2
       495: 3q+2
       496: q^2+10q+4
       497: q^2+5q+2
       498: 4q+2
       499: q+2
       500: q+2
       501: 6q+4
       508: 4q^2+9q+2
       509: 2q^2+7q+2
       510: q^2+5q+2
       511: 6q+2
       512: 3q^2+7q+2
       513: q^2+3q+2
       514: q^2+3q+2
       515: 2q+4
       516: 2q+4
       517: 2q+2
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       521: q+1
       523: q+1
       529: q+1
       531: q+1
       533: q+1
       535: q+1
       537: 2q+1
       538: q
       539: q
       540: 2q+1
       541: q^2+3q+1
       542: q
       543: q
       544: q^2+3q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 1
       550: 1
       553: q+1
       554: q+1
       557: q+1
       558: q+1
       561: 2q+2
       562: 2q+2
       565: 2q+1
       567: 2q+1
       569: q+1
       572: q+1
       573: 3q+2
       576: 3q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       585: 2q+1
       586: 2q+1
       589: 2q+1
       590: 2q+1
       591: q+2
       595: 4q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 4q+2
       602: 4q+2
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: 2q+1
       607: 4q+2
       609: 2q+1
       610: 2q+1
       613: q+1
       614: q+1
       615: 5q+2
       616: 5q+2
       617: 4q+2
       618: 4q+2
       619: q+1
       620: q+1
       621: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 6q+4
       633: 2q+2
       634: 2q+2
       639: q^2+3q+1
       640: q^2+3q+1
       641: 2q+1
       642: 2q+1
       643: q^2+3q+2
       645: 1
       646: 1
       647: 3q+1
       648: 3q+1
       649: q^2+3q+2
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 3q+2
       656: 3q+2
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+1
       663: q+1
       664: 2
       665: 3q+2
       672: 4q+2
       673: q+1
       674: 2q+4
       675: q^2+7q+2
       676: q^2+6q+2
       677: 3q+2
       678: 4q+2
       679: 3q+2
       680: 4
       681: 4q+2
       682: q+2
       683: 2
       684: 2q+2
       685: q+2
       686: q^2+5q+2
       687: 4q+2
       688: q+2
       689: q+2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       694: q+1
       698: q+1
       700: q+1
       709: q+1
       711: q+1
       713: 1
       714: 1
       721: q+1
       724: q+1
       725: q+1
       728: q+1
       733: 2q+1
       734: 2q+1
       735: 2q+1
       736: 2q+1
       737: 1
       738: 1
       741: 1
       742: 1
       749: 2q+2
       750: 2q+2
       753: 1
       755: 1
       757: q+1
       760: q+1
       761: q+1
       764: q+1
       765: 3q+2
       767: 3q+2
       769: q+1
       770: q+1
       772: q+1
       773: q+1
       775: 2
       776: 2
       779: 1
       780: 1
       781: q+1
       782: q+1
       787: q+2
       793: 2
       794: 2
       795: q+2
       796: q+2
       797: 2q+1
       798: 2q+1
       801: 2q+1
       802: 2q+1
       803: q+2
       807: 4q+2
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       815: 2q+1
       816: 2q+1
       817: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       827: 2
       831: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 2q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 2
       867: 1
       868: q+1
       869: q+2
       870: 2
       871: 3q+2
       872: q+1
       873: 2
       874: 2
       875: 2
       876: 1
       877: 4q+2
       878: q+2
       879: 2
       880: q+2
       881: q+2
       882: q+2
       883: q+1
       884: q+1
       885: q+1
       888: q+1
       891: q+1
       900: 1
       901: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       923: q+1
       924: 1
       925: 1
       940: 2
       941: 2
       944: 1
       945: 1
       948: 1
       949: 1
       960: 1
       963: 1
       964: 2
       966: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       977: 1
       988: q+1
       990: q+1
       994: 1
       995: 1
       998: 2
      1006: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: q+1
      1028: q+2
      1032: 2
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1044: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1054: 2
      1058: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 2
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1152: 1
      1153: 1
      1172: 1
      1173: 1
      1194: 1
      1196: 1
      1198: 1
      1201: 1
      1202: 1
      1203: 1
      1216: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 2
      1242: 1
      1246: 2
      1260: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1270: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1348: 1
      1349: 1
      1410: 1
      1412: 1
      1418: 1
      1419: 1
      1440: 1
      1450: 1
      1478: 1
      1485: 1
      1488: 1
      1645: 1

1646:    0: q^4+18q^3+30q^2+14q+2
         1: 3q^4+22q^3+30q^2+14q+2
         2: q^4+18q^3+30q^2+14q+2
         3: 3q^4+22q^3+30q^2+14q+2
         4: 3q^4+18q^3+24q^2+12q+2
         5: q^4+18q^3+30q^2+14q+2
         6: q^5+9q^4+23q^3+24q^2+12q+2
         7: 3q^4+18q^3+24q^2+12q+2
         8: q^4+18q^3+30q^2+14q+2
         9: q^5+6q^4+14q^3+15q^2+9q+2
        10: 11q^3+26q^2+14q+2
        11: 11q^3+26q^2+14q+2
        12: 2q^4+14q^3+21q^2+12q+2
        13: q^4+18q^3+30q^2+14q+2
        14: 3q^4+18q^3+24q^2+12q+2
        15: q^4+18q^3+30q^2+14q+2
        16: 11q^3+26q^2+14q+2
        17: 11q^3+26q^2+14q+2
        18: 2q^4+11q^3+15q^2+9q+2
        19: 10q^3+22q^2+12q+2
        20: 2q^4+15q^3+22q^2+12q+2
        21: 10q^3+22q^2+12q+2
        22: q^4+18q^3+30q^2+14q+2
        23: 3q^4+22q^3+30q^2+14q+2
        24: q^4+18q^3+30q^2+14q+2
        25: 10q^3+26q^2+14q+2
        26: 14q^3+26q^2+14q+2
        27: 10q^3+26q^2+14q+2
        28: 5q^3+22q^2+14q+2
        29: 7q^3+19q^2+12q+2
        30: 10q^3+22q^2+12q+2
        31: 11q^3+26q^2+14q+2
        32: q^4+18q^3+30q^2+14q+2
        33: 11q^3+26q^2+14q+2
        34: 6q^3+22q^2+14q+2
        35: 10q^3+26q^2+14q+2
        36: 6q^3+22q^2+14q+2
        37: 5q^3+13q^2+7q+1
        38: 5q^3+13q^2+7q+1
        39: 7q^3+13q^2+7q+1
        40: 7q^3+13q^2+7q+1
        41: 5q^3+13q^2+7q+1
        42: 5q^3+13q^2+7q+1
        43: 11q^3+26q^2+14q+2
        44: 2q^4+14q^3+21q^2+12q+2
        45: 11q^3+26q^2+14q+2
        46: 11q^3+26q^2+14q+2
        47: 11q^3+26q^2+14q+2
        48: 2q^4+11q^3+15q^2+9q+2
        49: 4q^3+18q^2+12q+2
        50: 6q^3+18q^2+12q+2
        51: 5q^3+13q^2+9q+2
        52: 10q^3+22q^2+12q+2
        53: 2q^4+15q^3+22q^2+12q+2
        54: 10q^3+22q^2+12q+2
        55: 4q^3+18q^2+12q+2
        56: 8q^3+18q^2+12q+2
        57: 4q^3+18q^2+12q+2
        58: q^3+8q^2+4q
        59: 4q^3+14q^2+10q+2
        60: q^3+9q^2+7q+1
        61: q^3+9q^2+7q+1
        62: 3q^3+11q^2+7q+1
        63: 3q^3+11q^2+7q+1
        64: 5q^3+13q^2+7q+1
        65: 5q^3+13q^2+7q+1
        66: 3q^3+11q^2+7q+1
        67: 3q^3+11q^2+7q+1
        68: 5q^3+22q^2+14q+2
        69: 2q^3+10q^2+9q+2
        70: 7q^3+19q^2+12q+2
        71: 2q^3+15q^2+12q+2
        72: q^3+9q^2+10q+2
        73: 2q^3+11q^2+10q+2
        74: q^3+6q^2+5q+1
        75: q^3+6q^2+5q+1
        76: 2q^3+6q^2+5q+1
        77: 2q^3+6q^2+5q+1
        78: q^3+6q^2+5q+1
        79: q^3+6q^2+5q+1
        80: 11q^3+26q^2+14q+2
        81: 11q^3+26q^2+14q+2
        82: 7q^3+19q^2+12q+2
        83: 10q^3+22q^2+12q+2
        84: 6q^3+22q^2+14q+2
        85: 6q^3+22q^2+14q+2
        86: 3q^3+15q^2+12q+2
        87: 4q^3+18q^2+12q+2
        88: 2q^3+17q^2+14q+2
        89: 2q^3+17q^2+14q+2
        90: q^4+7q^3+12q^2+9q+2
        91: 4q^3+18q^2+12q+2
        92: 6q^3+18q^2+12q+2
        93: 5q^3+13q^2+9q+2
        94: 4q^3+18q^2+12q+2
        95: 6q^3+18q^2+12q+2
        96: 5q^3+13q^2+9q+2
        97: 11q^2+12q+2
        98: q^3+11q^2+12q+2
        99: q^3+9q^2+9q+2
       100: 4q^3+18q^2+12q+2
       101: 8q^3+18q^2+12q+2
       102: 4q^3+18q^2+12q+2
       103: 3q^2+2q
       104: q^3+6q^2+5q+1
       105: 3q^2+2q
       106: q^3+6q^2+5q+1
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: 2q^2+2q
       110: q^3+7q^2+8q+2
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: q^3+5q^2+5q+1
       114: q^3+5q^2+5q+1
       115: q^3+6q^2+5q+1
       116: q^3+6q^2+5q+1
       117: q^3+8q^2+4q
       118: 4q^3+14q^2+10q+2
       119: q^3+9q^2+7q+1
       120: q^3+9q^2+7q+1
       121: 3q^3+11q^2+7q+1
       122: 3q^3+11q^2+7q+1
       123: 3q^3+11q^2+7q+1
       124: 3q^3+11q^2+7q+1
       125: 2q^3+17q^2+14q+2
       126: 7q^2+9q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^3+15q^2+12q+2
       134: 2q^3+10q^2+9q+2
       135: q^3+9q^2+10q+2
       136: 2q^3+11q^2+10q+2
       137: 2q^3+17q^2+14q+2
       138: 2q^3+10q^2+9q+2
       139: 2q^3+15q^2+12q+2
       140: q^3+9q^2+10q+2
       141: 7q^3+19q^2+12q+2
       142: 2q^3+11q^2+10q+2
       143: 2q^3+14q^2+14q+2
       144: 6q^2+9q+2
       145: 9q^2+12q+2
       146: 3q^3+15q^2+12q+2
       147: 6q^2+10q+2
       148: 3q^2+6q+2
       149: 3q^3+15q^2+12q+2
       150: 4q^3+18q^2+12q+2
       151: q^3+6q^2+5q+1
       152: q^3+6q^2+5q+1
       153: 2q^3+6q^2+5q+1
       154: 2q^3+6q^2+5q+1
       155: q^3+6q^2+5q+1
       156: q^3+6q^2+5q+1
       157: 8q^2+11q+2
       158: 8q^2+11q+2
       159: 2q^3+7q^2+8q+2
       160: 4q^3+18q^2+12q+2
       161: 6q^3+18q^2+12q+2
       162: 5q^3+13q^2+9q+2
       163: 11q^2+12q+2
       164: q^3+11q^2+12q+2
       165: q^3+9q^2+9q+2
       166: 11q^2+12q+2
       167: q^3+11q^2+12q+2
       168: q^3+9q^2+9q+2
       169: q
       170: q^2+3q+1
       171: q
       172: q^2+3q+1
       173: 3q^2+2q
       174: q^3+6q^2+5q+1
       175: 3q^2+2q
       176: q^3+6q^2+5q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: 2q^2+2q
       186: q^3+7q^2+8q+2
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: q^3+5q^2+5q+1
       190: q^3+5q^2+5q+1
       191: 6q^2+4q
       192: 2q^3+11q^2+10q+2
       193: 3q^2+5q+1
       194: 3q^2+5q+1
       195: 2q^2+2q
       196: q^3+7q^2+8q+2
       197: 2q^2+4q+1
       198: 2q^2+4q+1
       199: q^3+7q^2+7q+1
       200: q^3+7q^2+7q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       204: 3q^2+6q+2
       205: 2q+1
       206: 2q+1
       207: q^3+7q^2+7q+1
       208: q^3+7q^2+7q+1
       209: q^3+5q^2+5q+1
       210: q^3+5q^2+5q+1
       211: q^3+6q^2+5q+1
       212: q^3+6q^2+5q+1
       213: 2q^2+4q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: 2q^2+4q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 7q^2+9q+2
       220: 8q^2+11q+2
       221: 4q^2+8q+2
       222: 4q^2+10q+2
       223: 3q^2+7q+2
       224: 4q^2+9q+2
       225: q^3+5q^2+7q+2
       226: 7q^2+9q+2
       227: 2q^3+15q^2+12q+2
       228: 2q^3+10q^2+9q+2
       229: q^3+9q^2+10q+2
       230: 2q^3+11q^2+10q+2
       231: 4q^2+9q+2
       232: 9q^2+12q+2
       233: 6q^2+9q+2
       234: 6q^2+10q+2
       235: 3q^2+6q+2
       236: 6q^2+9q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 9q^2+12q+2
       244: 6q^2+10q+2
       245: 3q^2+6q+2
       246: 3q^3+15q^2+12q+2
       247: q^2+10q+4
       248: q^2+10q+4
       249: 3q^2+5q+2
       250: 8q^2+11q+2
       251: 8q^2+11q+2
       252: 2q^3+7q^2+8q+2
       253: 2q^2+7q+2
       254: 2q^2+7q+2
       255: 3q^2+5q+2
       256: 11q^2+12q+2
       257: q^3+11q^2+12q+2
       258: q^3+9q^2+9q+2
       259: q
       260: 2q+1
       261: q
       262: 2q+1
       263: q
       264: q^2+3q+1
       265: q
       266: q^2+3q+1
       267: q
       268: q^2+3q+1
       269: q^2+3q+1
       270: q
       273: 2q+1
       274: 2q+1
       275: 2q^2+2q
       276: q^3+5q^2+5q+1
       277: 2q^2+2q
       278: q^3+5q^2+5q+1
       279: 2q^2+4q+1
       280: 2q^2+4q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: 2q+1
       284: 2q+1
       286: 2q^2+5q+2
       287: q^2+3q+1
       288: q^2+3q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 2q^2+5q+1
       294: 2q^2+5q+1
       295: q^2+2q
       296: 3q^2+7q+2
       297: q^2+4q+1
       298: q^2+4q+1
       299: 3q^2+5q+1
       300: 3q^2+5q+1
       301: 3q+1
       302: 3q+1
       303: 2q^2+2q
       304: q^3+7q^2+8q+2
       305: 2q^2+4q+1
       306: 2q^2+4q+1
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       310: 3q^2+6q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 2q^2+5q+1
       320: 2q^2+5q+1
       322: 3q^2+6q+2
       323: 2q+1
       324: 2q+1
       325: q^3+5q^2+5q+1
       326: q^3+5q^2+5q+1
       333: 4q^2+8q+2
       334: q^2+7q+2
       335: q^2+6q+2
       336: 3q+2
       337: 10q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 7q^2+9q+2
       345: 8q^2+11q+2
       346: 4q^2+8q+2
       347: 4q^2+10q+2
       348: 3q^2+7q+2
       349: 4q^2+9q+2
       350: q^3+5q^2+7q+2
       351: q^2+10q+4
       352: 4q^2+9q+2
       353: 2q^2+7q+2
       354: q^2+5q+2
       355: 6q+2
       356: 3q^2+7q+2
       357: q^2+3q+2
       358: q^2+3q+2
       359: 6q+4
       360: 2q^2+4q+1
       361: 2q^2+4q+1
       362: 2q^2+4q+1
       363: 2q^2+4q+1
       364: 2q^2+3q+1
       365: 2q^2+3q+1
       366: 4q^2+9q+2
       367: 9q^2+12q+2
       368: 6q^2+9q+2
       369: 6q^2+10q+2
       370: 3q^2+6q+2
       371: q^2+10q+4
       372: q^2+10q+4
       373: 3q^2+5q+2
       374: 2q^2+7q+2
       375: 2q^2+7q+2
       376: 3q^2+5q+2
       378: q+1
       380: q+1
       381: q
       382: 2q+1
       383: q
       384: 2q+1
       385: q
       386: q^2+3q+1
       387: q
       388: q^2+3q+1
       389: q
       390: 2q+1
       391: 2q+1
       392: q
       393: q
       394: q^2+3q+1
       395: q
       396: q^2+3q+1
       399: q+1
       400: q+1
       403: 2q+1
       404: 2q+1
       406: 2q+1
       407: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       422: 4q+2
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: 2q+1
       430: 2q+1
       432: 2q^2+5q+2
       433: 2q+1
       434: 2q+1
       435: 3q+1
       436: 3q+1
       437: 2q^2+5q+1
       438: 2q^2+5q+1
       439: q^2+2q
       440: 3q^2+7q+2
       441: q^2+4q+1
       442: q^2+4q+1
       443: 5q+2
       444: 5q+2
       445: 4q+2
       446: 4q+2
       447: 2q+1
       448: 2q+1
       450: q^2+3q+2
       451: 1
       452: 1
       453: 3q+1
       454: 3q+1
       455: q+1
       456: q+1
       458: q^2+3q+2
       459: q+1
       460: q+1
       462: 6q+4
       463: 2q+2
       464: 2q+2
       465: 2q^2+4q+1
       466: 2q^2+4q+1
       467: q^2+3q+1
       468: q^2+3q+1
       469: q^2+3q+1
       470: q^2+3q+1
       471: 2q^2+5q+1
       472: 2q^2+5q+1
       474: 3q^2+6q+2
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 3q+2
       480: 3q+2
       481: q^2+7q+2
       482: q^2+6q+2
       483: 3q+2
       484: 10q+4
       485: 4q+2
       486: 4q+2
       487: 4q+2
       488: 4q+2
       489: q^2+2q+1
       490: q^2+2q+1
       491: 3q+2
       492: 4q^2+8q+2
       493: q^2+7q+2
       494: q^2+6q+2
       495: 3q+2
       496: q^2+10q+4
       497: q^2+5q+2
       498: 4q+2
       499: q+2
       500: q+2
       501: 6q+4
       508: 4q^2+9q+2
       509: 2q^2+7q+2
       510: q^2+5q+2
       511: 6q+2
       512: 3q^2+7q+2
       513: q^2+3q+2
       514: q^2+3q+2
       515: 2q+4
       516: 2q+4
       517: 2q+2
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       522: q+1
       524: q+1
       530: q+1
       532: q+1
       534: q+1
       536: q+1
       537: q
       538: 2q+1
       539: 2q+1
       540: q
       541: q
       542: q^2+3q+1
       543: q^2+3q+1
       544: q
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       551: 1
       552: 1
       555: q+1
       556: q+1
       559: q+1
       560: q+1
       563: 2q+2
       564: 2q+2
       566: 2q+1
       568: 2q+1
       570: q+1
       571: q+1
       574: 3q+2
       575: 3q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       585: 2q+1
       586: 2q+1
       589: 2q+1
       590: 2q+1
       592: q+2
       596: 4q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 4q+2
       602: 4q+2
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: 2q+1
       608: 4q+2
       609: 2q+1
       610: 2q+1
       613: q+1
       614: q+1
       615: 5q+2
       616: 5q+2
       617: 4q+2
       618: 4q+2
       619: q+1
       620: q+1
       622: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       632: 6q+4
       633: 2q+2
       634: 2q+2
       639: q^2+3q+1
       640: q^2+3q+1
       641: 2q+1
       642: 2q+1
       644: q^2+3q+2
       645: 1
       646: 1
       647: 3q+1
       648: 3q+1
       650: q^2+3q+2
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 3q+2
       656: 3q+2
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+1
       663: q+1
       664: 2
       665: 3q+2
       672: 4q+2
       673: q+1
       674: 2q+4
       675: q^2+7q+2
       676: q^2+6q+2
       677: 3q+2
       678: 4q+2
       679: 3q+2
       680: 4
       681: 4q+2
       682: q+2
       683: 2
       684: 2q+2
       685: q+2
       686: q^2+5q+2
       687: 4q+2
       688: q+2
       689: q+2
       690: q+2
       691: q+2
       692: q+1
       696: q+1
       697: q+1
       699: q+1
       701: q+1
       710: q+1
       712: q+1
       715: 1
       716: 1
       722: q+1
       723: q+1
       726: q+1
       727: q+1
       733: 2q+1
       734: 2q+1
       735: 2q+1
       736: 2q+1
       739: 1
       740: 1
       743: 1
       744: 1
       751: 2q+2
       752: 2q+2
       754: 1
       756: 1
       758: q+1
       759: q+1
       762: q+1
       763: q+1
       766: 3q+2
       768: 3q+2
       769: q+1
       770: q+1
       772: q+1
       773: q+1
       775: 2
       776: 2
       779: 1
       780: 1
       781: q+1
       782: q+1
       788: q+2
       793: 2
       794: 2
       795: q+2
       796: q+2
       797: 2q+1
       798: 2q+1
       801: 2q+1
       802: 2q+1
       804: q+2
       808: 4q+2
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       815: 2q+1
       816: 2q+1
       818: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       828: 2
       832: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       840: 2q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       848: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 2
       867: 1
       868: q+1
       869: q+2
       870: 2
       871: 3q+2
       872: q+1
       873: 2
       874: 2
       875: 2
       876: 1
       877: 4q+2
       878: q+2
       879: 2
       880: q+2
       881: q+2
       882: q+2
       883: q+1
       887: q+1
       889: q+1
       890: q+1
       892: q+1
       902: 1
       903: 1
       916: 1
       917: 1
       918: 1
       919: 1
       921: q+1
       922: q+1
       926: 1
       927: 1
       942: 2
       943: 2
       946: 1
       947: 1
       950: 1
       951: 1
       961: 1
       962: 1
       965: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       976: 1
       989: q+1
       991: q+1
       994: 1
       995: 1
       999: 2
      1007: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: q+1
      1029: q+2
      1033: 2
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1045: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1055: 2
      1059: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 2
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1089: 1
      1091: 1
      1092: 1
      1094: 1
      1116: 1
      1117: 1
      1154: 1
      1155: 1
      1174: 1
      1175: 1
      1195: 1
      1197: 1
      1199: 1
      1200: 1
      1204: 1
      1205: 1
      1217: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1233: 2
      1243: 1
      1247: 2
      1261: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1271: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1350: 1
      1351: 1
      1411: 1
      1413: 1
      1420: 1
      1421: 1
      1441: 1
      1451: 1
      1479: 1
      1485: 1
      1488: 1
      1646: 1

1647:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q^2+2q+2
        23: q^2+2q+2
        24: q^2+2q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q^2+2q+2
        31: 2q+2
        32: q^2+2q+2
        33: q^2+2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: q^2+2q+2
        53: q^2+2q+2
        54: q^2+2q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        60: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2q+2
        69: q^2+2q+2
        70: 2q+2
        71: 2q+2
        72: 2
        73: q^2+2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2q+2
        81: q^2+2q+2
        82: 2q+2
        83: q^2+2q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2q+2
        89: 2q+2
        90: 2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^2+2q+2
        95: q^2+2q+2
        96: q^2+2q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       103: 1
       104: 1
       107: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+2
       126: 2q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2q+2
       134: q^2+2q+2
       135: 2
       136: q^2+2q+2
       137: 2q+2
       138: q^2+2q+2
       139: 2q+2
       140: 2
       141: 2q+2
       142: q^2+2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: 2
       164: 2
       165: 2
       166: 2
       167: 2
       168: 2
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: q+1
       193: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2
       201: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 2q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: 2
       224: 2q+2
       225: q^2+2q+2
       226: 2q+2
       227: 2q+2
       228: q^2+2q+2
       229: 2
       230: q^2+2q+2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 1
       254: 1
       255: 1
       256: 2
       257: 2
       258: 2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       275: 1
       276: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 2
       285: q+1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 2
       295: q+1
       296: q+1
       297: 1
       298: 1
       299: 2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       307: 2
       315: 1
       316: 1
       317: 1
       318: 1
       319: 2
       325: 1
       326: 1
       333: 2q+2
       334: 2
       335: 2q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: q^2+2q+2
       351: 2
       352: 2
       353: 1
       354: 1
       355: 1
       356: 2
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       369: 2
       371: 2
       372: 2
       373: 2
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       381: 1
       382: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       413: 1
       414: 1
       417: 1
       418: 1
       419: 2
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 2
       439: q+1
       440: q+1
       441: 1
       442: 1
       443: 2
       445: 1
       446: 1
       447: 2
       453: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 2
       481: 2
       482: 2q+2
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 2
       492: 2q+2
       493: 2
       494: 2q+2
       495: 2
       496: 2
       497: 1
       498: 1
       508: 2
       509: 1
       510: 1
       511: 1
       512: 2
       515: 2
       516: 2
       517: 2
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       529: 1
       530: 1
       533: 1
       534: 1
       537: 1
       538: 1
       541: 1
       542: 1
       545: 1
       546: 1
       585: 1
       586: 1
       589: 2
       593: 2
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       617: 1
       618: 1
       619: 1
       639: 1
       640: 1
       641: 2
       647: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 2
       678: 1
       679: 2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       709: 1
       710: 1
       717: 1
       718: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: 1
       734: 1
       775: 1
       776: 1
       779: 1
       780: 1
       781: 1
       782: 1
       785: 2
       793: 2
       795: 1
       796: 1
       797: 1
       798: 1
       801: 2
       805: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 1
       825: 1
       845: 1
       865: 1
       866: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 2
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       904: 1
       905: 1
       916: 1
       917: 1
       920: 1
       921: 1
       928: 1
       929: 1
       994: 1
       995: 1
      1000: 2
      1004: 1
      1016: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1026: 2
      1052: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 2
      1077: 1
      1078: 1
      1122: 1
      1123: 1
      1156: 1
      1157: 1
      1218: 1
      1228: 1
      1230: 1
      1231: 1
      1234: 2
      1240: 1
      1282: 1
      1283: 1
      1284: 1
      1356: 1
      1357: 1
      1442: 1
      1454: 1
      1485: 1
      1647: 1

1648:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: q^2+2q+2
        23: q^2+2q+2
        24: q^2+2q+2
        25: 2
        26: 2
        27: 2
        28: 2q+2
        29: 2q+2
        30: q^2+2q+2
        31: 2q+2
        32: q^2+2q+2
        33: q^2+2q+2
        34: 2
        35: 2
        36: 2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: q^2+2q+2
        53: q^2+2q+2
        54: q^2+2q+2
        55: 2
        56: 2
        57: 2
        58: q+1
        59: q+1
        61: 2
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2q+2
        69: q^2+2q+2
        70: 2q+2
        71: 2q+2
        72: 2
        73: q^2+2q+2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2q+2
        81: q^2+2q+2
        82: 2q+2
        83: q^2+2q+2
        84: 2
        85: 2
        86: 2
        87: 2
        88: 2q+2
        89: 2q+2
        90: 2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: q^2+2q+2
        95: q^2+2q+2
        96: q^2+2q+2
        97: 2
        98: 2
        99: 2
       100: 2
       101: 2
       102: 2
       105: 1
       106: 1
       108: 2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       120: 2
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+2
       126: 2q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2q+2
       134: q^2+2q+2
       135: 2
       136: q^2+2q+2
       137: 2q+2
       138: q^2+2q+2
       139: 2q+2
       140: 2
       141: 2q+2
       142: q^2+2q+2
       143: 2
       144: 2
       145: 2
       146: 2
       147: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: 2
       164: 2
       165: 2
       166: 2
       167: 2
       168: 2
       171: 1
       172: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       184: 2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: q+1
       194: 2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2
       202: 2
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 2q+2
       220: 2q+2
       221: 2q+2
       222: 2
       223: 2
       224: 2q+2
       225: q^2+2q+2
       226: 2q+2
       227: 2q+2
       228: q^2+2q+2
       229: 2
       230: q^2+2q+2
       231: 2
       232: 2
       233: 2
       234: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       244: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 1
       254: 1
       255: 1
       256: 2
       257: 2
       258: 2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       284: 2
       285: q+1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       294: 2
       295: q+1
       296: q+1
       297: 1
       298: 1
       300: 2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       308: 2
       315: 1
       316: 1
       317: 1
       318: 1
       320: 2
       325: 1
       326: 1
       333: 2q+2
       334: 2
       335: 2q+2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: q^2+2q+2
       351: 2
       352: 2
       353: 1
       354: 1
       355: 1
       356: 2
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       369: 2
       371: 2
       372: 2
       373: 2
       374: 1
       375: 1
       376: 1
       379: 1
       380: 1
       383: 1
       384: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       413: 1
       414: 1
       417: 1
       418: 1
       420: 2
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       430: 2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       438: 2
       439: q+1
       440: q+1
       441: 1
       442: 1
       444: 2
       445: 1
       446: 1
       448: 2
       454: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       472: 2
       481: 2
       482: 2q+2
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 2
       492: 2q+2
       493: 2
       494: 2q+2
       495: 2
       496: 2
       497: 1
       498: 1
       508: 2
       509: 1
       510: 1
       511: 1
       512: 2
       515: 2
       516: 2
       517: 2
       518: 1
       519: 1
       520: 1
       523: 1
       524: 1
       531: 1
       532: 1
       535: 1
       536: 1
       539: 1
       540: 1
       543: 1
       544: 1
       547: 1
       548: 1
       585: 1
       586: 1
       590: 2
       594: 2
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       604: 2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2
       617: 1
       618: 1
       620: 1
       639: 1
       640: 1
       642: 2
       648: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 2
       678: 1
       679: 2
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       711: 1
       712: 1
       719: 1
       720: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: 1
       736: 1
       775: 1
       776: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 2
       794: 2
       795: 1
       796: 1
       797: 1
       798: 1
       802: 2
       806: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       816: 1
       826: 1
       846: 1
       865: 1
       866: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 2
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       906: 1
       907: 1
       918: 1
       919: 1
       922: 1
       923: 1
       930: 1
       931: 1
       994: 1
       995: 1
      1001: 2
      1005: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1027: 2
      1053: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 2
      1077: 1
      1078: 1
      1124: 1
      1125: 1
      1158: 1
      1159: 1
      1219: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 2
      1241: 1
      1282: 1
      1283: 1
      1284: 1
      1358: 1
      1359: 1
      1443: 1
      1455: 1
      1485: 1
      1648: 1

1649:    0: q^4+3q^3+6q^2+6q+2
         1: q^4+3q^3+6q^2+6q+2
         2: 2q^3+7q^2+4q+2
         3: q^4+3q^3+6q^2+6q+2
         4: q^4+3q^3+6q^2+6q+2
         5: q^4+3q^3+6q^2+6q+2
         6: q^4+3q^3+6q^2+6q+2
         7: 2q^3+7q^2+4q+2
         8: 2q^3+7q^2+4q+2
         9: 2q^4+3q^3+5q^2+3q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+4q+2
        14: q^3+5q^2+4q+2
        15: q^3+5q^2+4q+2
        16: 2q^3+4q^2+6q+2
        17: 2q^3+4q^2+6q+2
        18: 2q^3+5q^2+3q+2
        19: q^4+3q^3+6q^2+6q+2
        20: q^4+3q^3+6q^2+6q+2
        21: 2q^3+7q^2+4q+2
        22: q^4+3q^3+6q^2+6q+2
        23: q^4+3q^3+6q^2+6q+2
        24: 2q^3+7q^2+4q+2
        25: 2q^3+4q^2+6q+2
        26: 2q^3+4q^2+6q+2
        27: 6q^2+4q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+5q^2+4q+2
        31: 4q^2+6q+2
        32: q^3+5q^2+4q+2
        33: 2q^3+4q^2+6q+2
        34: 2q^2+6q+2
        35: 4q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+2q^2+3q+1
        38: q^3+2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: q^3+2q^2+3q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: 3q^2+4q+2
        44: 3q^2+4q+2
        45: 3q^2+4q+2
        46: 3q^2+4q+2
        47: 3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^3+4q^2+6q+2
        50: 2q^3+4q^2+6q+2
        51: 2q^3+5q^2+3q+2
        52: q^4+3q^3+6q^2+6q+2
        53: q^4+3q^3+6q^2+6q+2
        54: 2q^3+7q^2+4q+2
        55: 2q^3+4q^2+6q+2
        56: 2q^3+4q^2+6q+2
        57: 6q^2+4q+2
        58: 2q^2+4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+2q+1
        65: 2q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: q^2+2q+2
        69: 2q^2+3q+2
        70: 3q^2+4q+2
        71: 2q^2+6q+2
        72: 2q^3+2q^2+6q+2
        73: 2q^3+4q^2+6q+2
        74: q^3+2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: q^3+2q^2+3q+1
        77: q^3+2q^2+3q+1
        78: 3q^2+2q+1
        79: 3q^2+2q+1
        80: 3q^2+4q+2
        81: 3q^2+4q+2
        82: 4q^2+6q+2
        83: q^3+5q^2+4q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: 2q^2+6q+2
        87: 4q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 3q^2+4q+2
        92: 3q^2+4q+2
        93: q^3+3q^2+3q+2
        94: 2q^3+4q^2+6q+2
        95: 2q^3+4q^2+6q+2
        96: 2q^3+5q^2+3q+2
        97: q^3+q^2+6q+2
        98: q^3+q^2+6q+2
        99: 4q^2+3q+2
       100: 2q^3+4q^2+6q+2
       101: 2q^3+4q^2+6q+2
       102: 6q^2+4q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: 3q+1
       108: 3q+1
       109: 2q^2+4q+2
       110: 2q
       111: q^3+q^2+3q+1
       112: q^3+q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^2+2q+2
       119: q+1
       120: q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2q+2
       134: 2q^2+3q+2
       135: 2q^2+4q+2
       136: 3q^2+4q+2
       137: 4q+2
       138: 2q^2+3q+2
       139: 2q^2+6q+2
       140: 2q^3+2q^2+6q+2
       141: 3q^2+4q+2
       142: 2q^3+4q^2+6q+2
       143: 4q+2
       144: q^2+3q+2
       145: 6q+2
       146: 2q^2+4q+2
       147: q^3+q^2+6q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 4q^2+4q+2
       151: q^3+2q^2+3q+1
       152: q^3+2q^2+3q+1
       153: q^3+2q^2+3q+1
       154: q^3+2q^2+3q+1
       155: 3q^2+2q+1
       156: 3q^2+2q+1
       157: 4q+2
       158: 4q+2
       159: q^2+3q+2
       160: 3q^2+4q+2
       161: 3q^2+4q+2
       162: q^3+3q^2+3q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: 2q^2+2q+2
       166: q^3+q^2+6q+2
       167: q^3+q^2+6q+2
       168: 4q^2+3q+2
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: q+1
       175: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: q+1
       184: q+1
       185: q^2+2q+2
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+2
       193: 3q+1
       194: 3q+1
       195: 2q^2+4q+2
       196: 2q
       197: q^3+q^2+3q+1
       198: q^3+q^2+3q+1
       199: q+1
       200: q+1
       201: 3q+1
       202: 3q+1
       203: 4q+2
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       219: q+2
       220: 2q+2
       221: 3q+2
       222: 4q+2
       223: q^2+3q+2
       224: 4q+2
       225: 2q^2+3q+2
       226: 3q+2
       227: q^2+2q+2
       228: 2q^2+3q+2
       229: 2q^2+4q+2
       230: 3q^2+4q+2
       231: 3q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+3q+2
       235: 2q+2
       236: q^2+3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: q^3+q^2+6q+2
       245: 4q+2
       246: 2q^2+4q+2
       247: q^3+q^2+6q+2
       248: q^3+q^2+6q+2
       249: 4q^2+3q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+3q+2
       257: q^2+3q+2
       258: 2q^2+2q+2
       259: q+1
       260: q
       261: q+1
       262: q
       263: q+1
       265: q+1
       267: 2q+1
       268: q
       269: q
       270: 2q+1
       271: 2q+1
       272: 2q+1
       275: q+1
       277: q+1
       283: 1
       284: 1
       285: q+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 2q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       301: 2q+1
       302: 2q+1
       303: q^2+2q+2
       305: q^2+2q+1
       306: q^2+2q+1
       307: q+1
       308: q+1
       309: 2q+2
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 3q+1
       320: 3q+1
       321: 4q+2
       323: 2q+1
       324: 2q+1
       325: q^2+2q+1
       326: q^2+2q+1
       333: q+2
       334: 3q+2
       335: 3q+2
       336: q^2+3q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q+2
       345: 2q+2
       346: 3q+2
       347: 4q+2
       348: q^2+3q+2
       349: 4q+2
       350: 2q^2+3q+2
       351: q^3+q^2+6q+2
       352: q+2
       353: 2
       354: q+2
       355: q+2
       356: q^2+2q+2
       357: 2
       358: q+2
       359: 4q+2
       366: 3q+2
       367: 2q+2
       368: q^2+2q+2
       369: q^2+3q+2
       370: 2q+2
       371: q^2+3q+2
       372: q^2+3q+2
       373: 2q^2+2q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       379: 1
       385: q+1
       387: q+1
       389: q+1
       390: q
       391: q
       392: q+1
       393: q+1
       395: q+1
       397: q+1
       398: q+1
       401: q+1
       402: q+1
       405: 2q+1
       408: 2q+1
       419: 1
       420: 1
       421: q+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 1
       430: 1
       431: q+2
       433: q+1
       434: q+1
       437: q+1
       438: q+1
       439: 2q+2
       441: 2q+1
       442: 2q+1
       443: 3q+1
       444: 3q+1
       445: 2q+1
       446: 2q+1
       447: 1
       448: 1
       449: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 4q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: 2q+2
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q+2
       482: q+2
       483: 3q+2
       484: 2q+2
       491: q^2+2q+2
       492: q+2
       493: 3q+2
       494: 3q+2
       495: q^2+3q+2
       496: q^2+3q+2
       497: 2
       498: q+2
       499: 2
       500: q+2
       501: 2q+2
       508: q+2
       509: 2
       510: q+2
       511: q+2
       512: q^2+2q+2
       513: 2
       514: q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       529: 1
       531: 1
       533: 1
       535: 1
       541: q+1
       544: q+1
       545: q+1
       546: q
       547: q
       548: q+1
       549: 1
       550: 1
       557: 1
       558: 1
       561: q+1
       562: q+1
       565: q+1
       567: q+1
       569: q+1
       572: q+1
       573: 2q+1
       576: 2q+1
       577: q+1
       581: q+1
       589: 1
       590: 1
       591: q+2
       593: 1
       594: 1
       595: q+2
       599: q+1
       600: q+1
       603: 1
       604: 1
       607: q+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2q+2
       641: 1
       642: 1
       643: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: q+1
       656: q+1
       657: 2
       664: q+2
       665: q+2
       672: 2
       673: q+2
       674: q+2
       675: q+2
       676: q+2
       677: 3q+2
       678: q+2
       679: q^2+2q+2
       680: 2
       681: 2
       682: 1
       683: 2
       684: 2
       685: q+2
       686: 2
       687: q+2
       688: 2
       689: q+2
       693: q+1
       700: q+1
       713: 1
       714: 1
       717: 1
       719: 1
       725: 1
       728: 1
       741: 1
       742: 1
       753: 1
       755: 1
       761: 1
       764: 1
       765: q+1
       767: q+1
       785: 1
       786: 1
       787: q+2
       791: 1
       792: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: q+2
       805: 1
       806: 1
       807: q+2
       811: q+1
       812: q+1
       815: 1
       816: 1
       817: 2
       825: 1
       826: 1
       827: 2
       831: 1
       835: 1
       836: 1
       839: 2
       843: 1
       844: 1
       845: 1
       846: 1
       847: 2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       866: 2
       868: 2
       870: q+2
       871: q+2
       872: q+2
       874: 2
       875: 1
       876: 2
       877: 2
       878: 1
       879: 2
       880: q+2
       908: 1
       910: 1
       924: 1
       925: 1
       928: 1
       931: 1
       948: 1
       949: 1
       964: 1
       966: 1
       974: 1
       977: 1
       988: 1
       990: 1
       998: 2
      1000: 1
      1001: 1
      1004: 1
      1005: 1
      1006: 2
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1026: 1
      1027: 1
      1028: q+2
      1044: 1
      1052: 1
      1053: 1
      1054: 2
      1058: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 2
      1078: 2
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1132: 1
      1134: 1
      1137: 1
      1160: 1
      1161: 1
      1202: 1
      1203: 1
      1232: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1242: 2
      1250: 1
      1260: 1
      1270: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1364: 1
      1365: 1
      1368: 1
      1370: 1
      1466: 1
      1478: 1
      1484: 1
      1649: 1

1650:    0: q^4+3q^3+6q^2+6q+2
         1: q^4+3q^3+6q^2+6q+2
         2: 2q^3+7q^2+4q+2
         3: q^4+3q^3+6q^2+6q+2
         4: q^4+3q^3+6q^2+6q+2
         5: q^4+3q^3+6q^2+6q+2
         6: q^4+3q^3+6q^2+6q+2
         7: 2q^3+7q^2+4q+2
         8: 2q^3+7q^2+4q+2
         9: 2q^4+3q^3+5q^2+3q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+4q+2
        14: q^3+5q^2+4q+2
        15: q^3+5q^2+4q+2
        16: 2q^3+4q^2+6q+2
        17: 2q^3+4q^2+6q+2
        18: 2q^3+5q^2+3q+2
        19: q^4+3q^3+6q^2+6q+2
        20: q^4+3q^3+6q^2+6q+2
        21: 2q^3+7q^2+4q+2
        22: q^4+3q^3+6q^2+6q+2
        23: q^4+3q^3+6q^2+6q+2
        24: 2q^3+7q^2+4q+2
        25: 2q^3+4q^2+6q+2
        26: 2q^3+4q^2+6q+2
        27: 6q^2+4q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+5q^2+4q+2
        31: 4q^2+6q+2
        32: q^3+5q^2+4q+2
        33: 2q^3+4q^2+6q+2
        34: 2q^2+6q+2
        35: 4q^2+4q+2
        36: 2q^3+2q^2+6q+2
        37: q^3+2q^2+3q+1
        38: q^3+2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: q^3+2q^2+3q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: 3q^2+4q+2
        44: 3q^2+4q+2
        45: 3q^2+4q+2
        46: 3q^2+4q+2
        47: 3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^3+4q^2+6q+2
        50: 2q^3+4q^2+6q+2
        51: 2q^3+5q^2+3q+2
        52: q^4+3q^3+6q^2+6q+2
        53: q^4+3q^3+6q^2+6q+2
        54: 2q^3+7q^2+4q+2
        55: 2q^3+4q^2+6q+2
        56: 2q^3+4q^2+6q+2
        57: 6q^2+4q+2
        58: 2q
        59: 2q^2+4q+2
        60: 3q+1
        61: 3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+2q+1
        65: 2q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: q^2+2q+2
        69: 2q^2+3q+2
        70: 3q^2+4q+2
        71: 2q^2+6q+2
        72: 2q^3+2q^2+6q+2
        73: 2q^3+4q^2+6q+2
        74: q^3+2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: q^3+2q^2+3q+1
        77: q^3+2q^2+3q+1
        78: 3q^2+2q+1
        79: 3q^2+2q+1
        80: 3q^2+4q+2
        81: 3q^2+4q+2
        82: 4q^2+6q+2
        83: q^3+5q^2+4q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: 2q^2+6q+2
        87: 4q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 3q^2+4q+2
        92: 3q^2+4q+2
        93: q^3+3q^2+3q+2
        94: 2q^3+4q^2+6q+2
        95: 2q^3+4q^2+6q+2
        96: 2q^3+5q^2+3q+2
        97: q^3+q^2+6q+2
        98: q^3+q^2+6q+2
        99: 4q^2+3q+2
       100: 2q^3+4q^2+6q+2
       101: 2q^3+4q^2+6q+2
       102: 6q^2+4q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: 3q+1
       108: 3q+1
       109: 2q
       110: 2q^2+4q+2
       111: q^3+q^2+3q+1
       112: q^3+q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       118: q^2+2q+2
       119: q+1
       120: q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2q+2
       134: 2q^2+3q+2
       135: 2q^2+4q+2
       136: 3q^2+4q+2
       137: 4q+2
       138: 2q^2+3q+2
       139: 2q^2+6q+2
       140: 2q^3+2q^2+6q+2
       141: 3q^2+4q+2
       142: 2q^3+4q^2+6q+2
       143: 4q+2
       144: q^2+3q+2
       145: 6q+2
       146: 2q^2+4q+2
       147: q^3+q^2+6q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 4q^2+4q+2
       151: q^3+2q^2+3q+1
       152: q^3+2q^2+3q+1
       153: q^3+2q^2+3q+1
       154: q^3+2q^2+3q+1
       155: 3q^2+2q+1
       156: 3q^2+2q+1
       157: 4q+2
       158: 4q+2
       159: q^2+3q+2
       160: 3q^2+4q+2
       161: 3q^2+4q+2
       162: q^3+3q^2+3q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: 2q^2+2q+2
       166: q^3+q^2+6q+2
       167: q^3+q^2+6q+2
       168: 4q^2+3q+2
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       174: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: q+1
       184: q+1
       186: q^2+2q+2
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       192: 2q+2
       193: 3q+1
       194: 3q+1
       195: 2q
       196: 2q^2+4q+2
       197: q^3+q^2+3q+1
       198: q^3+q^2+3q+1
       199: q+1
       200: q+1
       201: 3q+1
       202: 3q+1
       204: 4q+2
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       219: q+2
       220: 2q+2
       221: 3q+2
       222: 4q+2
       223: q^2+3q+2
       224: 4q+2
       225: 2q^2+3q+2
       226: 3q+2
       227: q^2+2q+2
       228: 2q^2+3q+2
       229: 2q^2+4q+2
       230: 3q^2+4q+2
       231: 3q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+3q+2
       235: 2q+2
       236: q^2+3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: q^3+q^2+6q+2
       245: 4q+2
       246: 2q^2+4q+2
       247: q^3+q^2+6q+2
       248: q^3+q^2+6q+2
       249: 4q^2+3q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: q+2
       254: q+2
       255: q+2
       256: q^2+3q+2
       257: q^2+3q+2
       258: 2q^2+2q+2
       259: q
       260: q+1
       261: q
       262: q+1
       264: q+1
       266: q+1
       267: q
       268: 2q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: 2q+1
       276: q+1
       278: q+1
       283: 1
       284: 1
       286: q+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       296: 2q+2
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q+1
       301: 2q+1
       302: 2q+1
       304: q^2+2q+2
       305: q^2+2q+1
       306: q^2+2q+1
       307: q+1
       308: q+1
       310: 2q+2
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 3q+1
       320: 3q+1
       322: 4q+2
       323: 2q+1
       324: 2q+1
       325: q^2+2q+1
       326: q^2+2q+1
       333: q+2
       334: 3q+2
       335: 3q+2
       336: q^2+3q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q+2
       345: 2q+2
       346: 3q+2
       347: 4q+2
       348: q^2+3q+2
       349: 4q+2
       350: 2q^2+3q+2
       351: q^3+q^2+6q+2
       352: q+2
       353: 2
       354: q+2
       355: q+2
       356: q^2+2q+2
       357: 2
       358: q+2
       359: 4q+2
       366: 3q+2
       367: 2q+2
       368: q^2+2q+2
       369: q^2+3q+2
       370: 2q+2
       371: q^2+3q+2
       372: q^2+3q+2
       373: 2q^2+2q+2
       374: q+2
       375: q+2
       376: q+2
       378: 1
       380: 1
       386: q+1
       388: q+1
       389: q
       390: q+1
       391: q+1
       392: q
       394: q+1
       396: q+1
       399: q+1
       400: q+1
       403: q+1
       404: q+1
       406: 2q+1
       407: 2q+1
       419: 1
       420: 1
       422: q+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 1
       430: 1
       432: q+2
       433: q+1
       434: q+1
       437: q+1
       438: q+1
       440: 2q+2
       441: 2q+1
       442: 2q+1
       443: 3q+1
       444: 3q+1
       445: 2q+1
       446: 2q+1
       447: 1
       448: 1
       450: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 4q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       474: 2q+2
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q+2
       482: q+2
       483: 3q+2
       484: 2q+2
       491: q^2+2q+2
       492: q+2
       493: 3q+2
       494: 3q+2
       495: q^2+3q+2
       496: q^2+3q+2
       497: 2
       498: q+2
       499: 2
       500: q+2
       501: 2q+2
       508: q+2
       509: 2
       510: q+2
       511: q+2
       512: q^2+2q+2
       513: 2
       514: q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       530: 1
       532: 1
       534: 1
       536: 1
       542: q+1
       543: q+1
       545: q
       546: q+1
       547: q+1
       548: q
       551: 1
       552: 1
       559: 1
       560: 1
       563: q+1
       564: q+1
       566: q+1
       568: q+1
       570: q+1
       571: q+1
       574: 2q+1
       575: 2q+1
       577: q+1
       581: q+1
       589: 1
       590: 1
       592: q+2
       593: 1
       594: 1
       596: q+2
       599: q+1
       600: q+1
       603: 1
       604: 1
       608: q+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2q+2
       641: 1
       642: 1
       644: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: q+1
       656: q+1
       657: 2
       664: q+2
       665: q+2
       672: 2
       673: q+2
       674: q+2
       675: q+2
       676: q+2
       677: 3q+2
       678: q+2
       679: q^2+2q+2
       680: 2
       681: 2
       682: 1
       683: 2
       684: 2
       685: q+2
       686: 2
       687: q+2
       688: 2
       689: q+2
       697: q+1
       699: q+1
       715: 1
       716: 1
       718: 1
       720: 1
       726: 1
       727: 1
       743: 1
       744: 1
       754: 1
       756: 1
       762: 1
       763: 1
       766: q+1
       768: q+1
       785: 1
       786: 1
       788: q+2
       791: 1
       792: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: q+2
       805: 1
       806: 1
       808: q+2
       811: q+1
       812: q+1
       815: 1
       816: 1
       818: 2
       825: 1
       826: 1
       828: 2
       832: 1
       835: 1
       836: 1
       840: 2
       843: 1
       844: 1
       845: 1
       846: 1
       848: 2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       866: 2
       868: 2
       870: q+2
       871: q+2
       872: q+2
       874: 2
       875: 1
       876: 2
       877: 2
       878: 1
       879: 2
       880: q+2
       909: 1
       911: 1
       926: 1
       927: 1
       929: 1
       930: 1
       950: 1
       951: 1
       965: 1
       967: 1
       975: 1
       976: 1
       989: 1
       991: 1
       999: 2
      1000: 1
      1001: 1
      1004: 1
      1005: 1
      1007: 2
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1026: 1
      1027: 1
      1029: q+2
      1045: 1
      1052: 1
      1053: 1
      1055: 2
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 2
      1078: 2
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 2
      1131: 1
      1133: 1
      1135: 1
      1136: 1
      1162: 1
      1163: 1
      1204: 1
      1205: 1
      1233: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1243: 2
      1251: 1
      1261: 1
      1271: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1366: 1
      1367: 1
      1369: 1
      1371: 1
      1467: 1
      1479: 1
      1484: 1
      1650: 1

1651:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+2q^2+3q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q^2+4q+2
        35: 2q^2+4q+2
        36: 2q^2+4q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 2q^2+4q+2
        44: q^3+2q^2+3q+2
        45: 2q^2+4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+3q+2
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: 2q^2+4q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+3q+2
        72: 2q+2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^3+2q^2+3q+2
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+3q+2
        94: q+2
        95: q+2
        96: q+2
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+3q+2
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+2
       123: 2q+2
       125: 2q^2+4q+2
       126: q^2+3q+2
       127: q+2
       129: q+2
       131: q+2
       133: q^2+3q+2
       134: q^2+3q+2
       135: 2q+2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       141: q+2
       142: 2
       143: 2q^2+4q+2
       144: q^2+3q+2
       145: q^2+3q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+3q+2
       160: q+2
       161: q+2
       162: q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+3q+2
       166: q+2
       167: q+2
       168: q+2
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: q+2
       179: q+2
       181: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: q+2
       211: q+2
       213: q+2
       215: q+2
       217: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: q^2+3q+2
       222: 2q+2
       223: 2q+2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       230: 2
       231: q^2+3q+2
       232: q^2+3q+2
       233: q^2+3q+2
       234: 2q+2
       235: 2
       236: q+2
       237: q+2
       239: q+2
       241: q+2
       243: q+2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: q+2
       257: q+2
       258: q+2
       259: 1
       262: 1
       263: 1
       266: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: q+2
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: q+2
       289: 2
       291: 2
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: q+2
       317: q+2
       321: 1
       322: 1
       325: q+2
       327: q+2
       329: q+2
       331: q+2
       333: q^2+3q+2
       334: 2q+2
       335: 2
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q+2
       345: q+2
       346: q+2
       349: 2
       350: 2
       352: q^2+3q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       360: q+2
       362: q+2
       364: q+2
       366: q+2
       367: q+2
       368: q+2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       397: 1
       399: 1
       401: 1
       404: 1
       409: q+2
       411: q+2
       413: q+2
       415: 2
       417: 2
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 2
       431: 1
       432: 1
       439: 1
       440: 1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: 2
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: q+2
       469: q+2
       473: 1
       474: 1
       481: 2q+2
       482: 2
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+2
       494: 2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: 1
       501: 2
       502: q+2
       504: q+2
       506: q+2
       508: q+2
       509: q+2
       510: q+2
       513: 2
       514: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       583: q+2
       585: 2
       587: 2
       589: q+1
       590: q+1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 2
       607: 1
       608: 1
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       625: 2
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: q+2
       639: q+2
       643: 1
       644: 1
       649: 1
       650: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       676: 2
       680: 2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: 1
       686: q+2
       688: 2
       690: 2
       691: 2
       692: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       807: 1
       808: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+2
       847: 1
       848: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       873: 2
       874: 1
       875: 1
       876: 1
       878: 2
       881: 2
       882: 2
       883: q+1
       896: 1
       899: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1058: 1
      1059: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1210: 2
      1212: 1
      1214: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1256: 1
      1282: 1
      1285: 1
      1286: 1
      1372: 1
      1374: 1
      1438: 1
      1456: 1
      1458: 1
      1486: 1
      1651: 1

1652:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: 2q^2+4q+2
         3: 2q^2+4q+2
         4: q^3+2q^2+3q+2
         5: 2q^2+4q+2
         6: q^3+2q^2+3q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: q^3+2q^2+3q+2
        13: 2q^2+4q+2
        14: q^3+2q^2+3q+2
        15: 2q^2+4q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+2q^2+3q+2
        19: q^2+3q+2
        20: q^2+3q+2
        21: q^2+3q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: 2q^2+4q+2
        29: q^2+3q+2
        30: q^2+3q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q^2+4q+2
        35: 2q^2+4q+2
        36: 2q^2+4q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 2q^2+4q+2
        44: q^3+2q^2+3q+2
        45: 2q^2+4q+2
        46: 2q^2+4q+2
        47: 2q^2+4q+2
        48: q^3+2q^2+3q+2
        49: q^2+3q+2
        50: q^2+3q+2
        51: q^2+3q+2
        52: q+2
        53: q+2
        54: q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: 2q^2+4q+2
        69: q^2+3q+2
        70: q^2+3q+2
        71: q^2+3q+2
        72: 2q+2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: 2q^2+4q+2
        89: 2q^2+4q+2
        90: q^3+2q^2+3q+2
        91: q^2+3q+2
        92: q^2+3q+2
        93: q^2+3q+2
        94: q+2
        95: q+2
        96: q+2
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+3q+2
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       122: 2q+2
       124: 2q+2
       125: 2q^2+4q+2
       126: q^2+3q+2
       128: q+2
       130: q+2
       132: q+2
       133: q^2+3q+2
       134: q^2+3q+2
       135: 2q+2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       141: q+2
       142: 2
       143: 2q^2+4q+2
       144: q^2+3q+2
       145: q^2+3q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: q^2+3q+2
       158: q^2+3q+2
       159: q^2+3q+2
       160: q+2
       161: q+2
       162: q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+3q+2
       166: q+2
       167: q+2
       168: q+2
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: q+2
       180: q+2
       182: 2
       183: q+1
       184: q+1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: q+1
       192: q+1
       195: 1
       196: 1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: q+2
       212: q+2
       214: q+2
       216: q+2
       218: q+2
       219: q^2+3q+2
       220: q^2+3q+2
       221: q^2+3q+2
       222: 2q+2
       223: 2q+2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       230: 2
       231: q^2+3q+2
       232: q^2+3q+2
       233: q^2+3q+2
       234: 2q+2
       235: 2
       236: q+2
       238: q+2
       240: q+2
       242: q+2
       243: q+2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: q+2
       257: q+2
       258: q+2
       260: 1
       261: 1
       264: 1
       265: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: q+2
       283: q+1
       284: q+1
       285: 1
       286: 1
       288: q+2
       290: 2
       292: 2
       293: q+1
       294: q+1
       295: 1
       296: 1
       298: 2
       303: 1
       304: 1
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: q+2
       318: q+2
       321: 1
       322: 1
       326: q+2
       328: q+2
       330: q+2
       332: q+2
       333: q^2+3q+2
       334: 2q+2
       335: 2
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q+2
       345: q+2
       346: q+2
       349: 2
       350: 2
       352: q^2+3q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       361: q+2
       363: q+2
       365: q+2
       366: q+2
       367: q+2
       368: q+2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       398: 1
       400: 1
       402: 1
       403: 1
       410: q+2
       412: q+2
       414: q+2
       416: 2
       418: 2
       419: q+1
       420: q+1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 2
       431: 1
       432: 1
       439: 1
       440: 1
       447: q+1
       448: q+1
       449: 1
       450: 1
       452: 2
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: q+2
       470: q+2
       473: 1
       474: 1
       481: 2q+2
       482: 2
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+2
       494: 2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: 1
       501: 2
       503: q+2
       505: q+2
       507: q+2
       508: q+2
       509: q+2
       510: q+2
       513: 2
       514: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       584: q+2
       586: 2
       588: 2
       589: q+1
       590: q+1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 2
       607: 1
       608: 1
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2
       626: 2
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: q+2
       640: q+2
       643: 1
       644: 1
       649: 1
       650: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       676: 2
       680: 2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: 1
       686: q+2
       688: 2
       690: 2
       691: 2
       692: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       807: 1
       808: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+2
       847: 1
       848: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       873: 2
       874: 1
       875: 1
       876: 1
       878: 2
       881: 2
       882: 2
       883: q+1
       897: 1
       898: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1058: 1
      1059: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1211: 2
      1213: 1
      1215: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1257: 1
      1282: 1
      1285: 1
      1286: 1
      1373: 1
      1375: 1
      1439: 1
      1457: 1
      1459: 1
      1486: 1
      1652: 1

1653:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2
        23: 2
        24: 2
        25: q^2+2q+2
        26: q^2+2q+2
        27: q^2+2q+2
        28: 2q+2
        29: 2q+2
        30: q^2+2q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q^2+2q+2
        36: q^2+2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: 2
        53: 2
        54: 2
        55: q^2+2q+2
        56: q^2+2q+2
        57: q^2+2q+2
        58: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2q+2
        69: q^2+2q+2
        70: 2q+2
        71: 2q+2
        72: q^2+2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2q+2
        85: q^2+2q+2
        86: 2q+2
        87: q^2+2q+2
        88: 2q+2
        89: 2q+2
        90: 2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2
        95: 2
        96: 2
        97: q^2+2q+2
        98: q^2+2q+2
        99: q^2+2q+2
       100: 2
       101: 2
       102: 2
       103: 1
       105: 1
       107: q+1
       108: q+1
       109: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 2
       119: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+2
       126: 2q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2q+2
       134: q^2+2q+2
       135: q^2+2q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2q+2
       144: q^2+2q+2
       145: 2q+2
       146: 2q+2
       147: q^2+2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2
       161: 2
       162: 2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: 2
       167: 2
       168: 2
       169: 1
       171: 1
       173: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: q+1
       184: q+1
       185: 2
       187: 1
       188: 1
       189: 1
       190: 1
       191: 2
       195: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 2q+2
       220: 2q+2
       221: 2q+2
       222: 2q+2
       223: q^2+2q+2
       224: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 1
       251: 1
       252: 1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2
       257: 2
       258: 2
       259: 1
       261: 1
       263: 1
       265: 1
       271: 1
       272: 1
       275: 1
       277: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 2
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: q+1
       294: q+1
       295: 2
       297: 1
       298: 1
       303: 2
       307: q+1
       308: q+1
       309: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       321: 2
       325: 1
       326: 1
       333: 2q+2
       334: 2q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 1
       346: 1
       349: 1
       350: 2
       352: 2q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: q^2+2q+2
       357: 2
       358: 2
       359: 2
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       370: 2
       371: 2
       372: 2
       373: 2
       374: 1
       375: 1
       376: 1
       377: 1
       379: 1
       381: 1
       383: 1
       385: 1
       387: 1
       397: 1
       398: 1
       401: 1
       402: 1
       413: 1
       414: 1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       431: 2
       439: 1
       447: q+1
       448: q+1
       449: 2
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       457: 2
       459: 1
       460: 1
       461: 2
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       473: 2
       481: 2q+2
       482: 2
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 2
       492: 1
       494: 1
       497: 2q+2
       498: 2q+2
       499: 2
       500: 2
       501: 2
       508: 2
       509: 1
       510: 1
       513: 1
       514: 2
       515: 2
       516: 2
       517: 2
       518: 1
       519: 1
       520: 1
       521: 1
       523: 1
       529: 1
       531: 1
       549: 1
       550: 1
       553: 1
       554: 1
       557: 1
       558: 1
       561: 1
       562: 1
       585: 1
       586: 1
       589: q+1
       590: q+1
       591: 2
       595: 2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       607: 1
       619: q+1
       620: q+1
       621: 2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       633: 1
       634: 1
       639: 1
       640: 1
       643: 2
       649: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       676: 1
       680: 2
       681: 2q+2
       682: 2
       683: 2
       684: 1
       685: 2
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       709: 1
       711: 1
       713: 1
       714: 1
       737: 1
       738: 1
       741: 1
       742: 1
       749: 1
       750: 1
       775: 1
       776: 1
       779: 1
       780: 1
       781: 1
       782: 1
       787: 2
       807: 1
       817: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: q+1
       826: q+1
       827: 2
       831: 2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 1
       847: 1
       865: 1
       866: 2
       867: 1
       868: 1
       873: 1
       874: 2
       875: 2
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       900: 1
       901: 1
       940: 1
       941: 1
       944: 1
       945: 1
       948: 1
       949: 1
       994: 1
       995: 1
       998: 2
      1006: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1044: 2
      1058: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 2
      1081: 1
      1082: 1
      1114: 1
      1115: 1
      1172: 1
      1173: 1
      1216: 1
      1246: 1
      1248: 1
      1249: 1
      1250: 2
      1260: 1
      1282: 1
      1285: 1
      1286: 1
      1380: 1
      1381: 1
      1440: 1
      1460: 1
      1486: 1
      1653: 1

1654:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: 2q+2
        11: 2q+2
        12: 2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2
        23: 2
        24: 2
        25: q^2+2q+2
        26: q^2+2q+2
        27: q^2+2q+2
        28: 2q+2
        29: 2q+2
        30: q^2+2q+2
        31: 2
        32: 2
        33: 2
        34: 2q+2
        35: q^2+2q+2
        36: q^2+2q+2
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 2q+2
        44: 2q+2
        45: 2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: 2
        53: 2
        54: 2
        55: q^2+2q+2
        56: q^2+2q+2
        57: q^2+2q+2
        59: 2
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2q+2
        69: q^2+2q+2
        70: 2q+2
        71: 2q+2
        72: q^2+2q+2
        73: 2
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 2
        81: 2
        82: 2
        83: 2
        84: 2q+2
        85: q^2+2q+2
        86: 2q+2
        87: q^2+2q+2
        88: 2q+2
        89: 2q+2
        90: 2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2
        95: 2
        96: 2
        97: q^2+2q+2
        98: q^2+2q+2
        99: q^2+2q+2
       100: 2
       101: 2
       102: 2
       104: 1
       106: 1
       107: q+1
       108: q+1
       110: 2
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       118: 2
       119: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+2
       126: 2q+2
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 2q+2
       134: q^2+2q+2
       135: q^2+2q+2
       136: 2
       137: 2
       138: 2
       139: 2
       141: 2
       142: 2
       143: 2q+2
       144: q^2+2q+2
       145: 2q+2
       146: 2q+2
       147: q^2+2q+2
       148: 2
       149: 2
       150: 2
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2
       161: 2
       162: 2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: 2
       167: 2
       168: 2
       170: 1
       172: 1
       174: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: q+1
       184: q+1
       186: 2
       187: 1
       188: 1
       189: 1
       190: 1
       192: 2
       196: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: 2
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 2q+2
       220: 2q+2
       221: 2q+2
       222: 2q+2
       223: q^2+2q+2
       224: 2
       225: 2
       226: 2
       227: 2
       228: 2
       230: 2
       231: 2q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: 2
       236: 2
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 2
       245: 2
       246: 2
       247: 2
       248: 2
       249: 2
       250: 1
       251: 1
       252: 1
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2
       257: 2
       258: 2
       260: 1
       262: 1
       264: 1
       266: 1
       273: 1
       274: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       286: 2
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: q+1
       294: q+1
       296: 2
       297: 1
       298: 1
       304: 2
       307: q+1
       308: q+1
       310: 2
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 2
       325: 1
       326: 1
       333: 2q+2
       334: 2q+2
       335: 2
       336: 2
       337: 2
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 2
       345: 1
       346: 1
       349: 1
       350: 2
       352: 2q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: q^2+2q+2
       357: 2
       358: 2
       359: 2
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 2
       367: 2
       368: 2
       370: 2
       371: 2
       372: 2
       373: 2
       374: 1
       375: 1
       376: 1
       378: 1
       380: 1
       382: 1
       384: 1
       386: 1
       388: 1
       399: 1
       400: 1
       403: 1
       404: 1
       413: 1
       414: 1
       417: 1
       418: 1
       419: q+1
       420: q+1
       422: 2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       432: 2
       440: 1
       447: q+1
       448: q+1
       450: 2
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: 2
       459: 1
       460: 1
       462: 2
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 2
       481: 2q+2
       482: 2
       483: 2
       484: 2
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 2
       492: 1
       494: 1
       497: 2q+2
       498: 2q+2
       499: 2
       500: 2
       501: 2
       508: 2
       509: 1
       510: 1
       513: 1
       514: 2
       515: 2
       516: 2
       517: 2
       518: 1
       519: 1
       520: 1
       522: 1
       524: 1
       530: 1
       532: 1
       551: 1
       552: 1
       555: 1
       556: 1
       559: 1
       560: 1
       563: 1
       564: 1
       585: 1
       586: 1
       589: q+1
       590: q+1
       592: 2
       596: 2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       608: 1
       619: q+1
       620: q+1
       622: 2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2
       633: 1
       634: 1
       639: 1
       640: 1
       644: 2
       650: 1
       657: 2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 2
       672: 1
       673: 1
       676: 1
       680: 2
       681: 2q+2
       682: 2
       683: 2
       684: 1
       685: 2
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       710: 1
       712: 1
       715: 1
       716: 1
       739: 1
       740: 1
       743: 1
       744: 1
       751: 1
       752: 1
       775: 1
       776: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 2
       808: 1
       818: 2
       819: 1
       820: 1
       821: 1
       822: 1
       825: q+1
       826: q+1
       828: 2
       832: 2
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       848: 1
       865: 1
       866: 2
       867: 1
       868: 1
       873: 1
       874: 2
       875: 2
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       902: 1
       903: 1
       942: 1
       943: 1
       946: 1
       947: 1
       950: 1
       951: 1
       994: 1
       995: 1
       999: 2
      1007: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1045: 2
      1059: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 2
      1081: 1
      1082: 1
      1116: 1
      1117: 1
      1174: 1
      1175: 1
      1217: 1
      1247: 1
      1248: 1
      1249: 1
      1251: 2
      1261: 1
      1282: 1
      1285: 1
      1286: 1
      1382: 1
      1383: 1
      1441: 1
      1461: 1
      1486: 1
      1654: 1

1655:    0: q^4+18q^3+30q^2+14q+2
         1: 3q^4+22q^3+30q^2+14q+2
         2: q^4+18q^3+30q^2+14q+2
         3: 3q^4+22q^3+30q^2+14q+2
         4: 3q^4+18q^3+24q^2+12q+2
         5: q^4+18q^3+30q^2+14q+2
         6: q^5+9q^4+23q^3+24q^2+12q+2
         7: 3q^4+18q^3+24q^2+12q+2
         8: q^4+18q^3+30q^2+14q+2
         9: q^5+6q^4+14q^3+15q^2+9q+2
        10: 11q^3+26q^2+14q+2
        11: 11q^3+26q^2+14q+2
        12: 2q^4+14q^3+21q^2+12q+2
        13: q^4+18q^3+30q^2+14q+2
        14: 3q^4+18q^3+24q^2+12q+2
        15: q^4+18q^3+30q^2+14q+2
        16: 11q^3+26q^2+14q+2
        17: 11q^3+26q^2+14q+2
        18: 2q^4+11q^3+15q^2+9q+2
        19: 10q^3+22q^2+12q+2
        20: 2q^4+15q^3+22q^2+12q+2
        21: 10q^3+22q^2+12q+2
        22: 10q^3+26q^2+14q+2
        23: 14q^3+26q^2+14q+2
        24: 10q^3+26q^2+14q+2
        25: q^4+18q^3+30q^2+14q+2
        26: 3q^4+22q^3+30q^2+14q+2
        27: q^4+18q^3+30q^2+14q+2
        28: 5q^3+22q^2+14q+2
        29: 7q^3+19q^2+12q+2
        30: 10q^3+22q^2+12q+2
        31: 6q^3+22q^2+14q+2
        32: 10q^3+26q^2+14q+2
        33: 6q^3+22q^2+14q+2
        34: 11q^3+26q^2+14q+2
        35: q^4+18q^3+30q^2+14q+2
        36: 11q^3+26q^2+14q+2
        37: 5q^3+13q^2+7q+1
        38: 5q^3+13q^2+7q+1
        39: 7q^3+13q^2+7q+1
        40: 7q^3+13q^2+7q+1
        41: 5q^3+13q^2+7q+1
        42: 5q^3+13q^2+7q+1
        43: 11q^3+26q^2+14q+2
        44: 2q^4+14q^3+21q^2+12q+2
        45: 11q^3+26q^2+14q+2
        46: 11q^3+26q^2+14q+2
        47: 11q^3+26q^2+14q+2
        48: 2q^4+11q^3+15q^2+9q+2
        49: 4q^3+18q^2+12q+2
        50: 6q^3+18q^2+12q+2
        51: 5q^3+13q^2+9q+2
        52: 4q^3+18q^2+12q+2
        53: 8q^3+18q^2+12q+2
        54: 4q^3+18q^2+12q+2
        55: 10q^3+22q^2+12q+2
        56: 2q^4+15q^3+22q^2+12q+2
        57: 10q^3+22q^2+12q+2
        58: q^3+9q^2+7q+1
        59: q^3+9q^2+7q+1
        60: 4q^3+14q^2+10q+2
        61: q^3+8q^2+4q
        62: 3q^3+11q^2+7q+1
        63: 3q^3+11q^2+7q+1
        64: 5q^3+13q^2+7q+1
        65: 5q^3+13q^2+7q+1
        66: 3q^3+11q^2+7q+1
        67: 3q^3+11q^2+7q+1
        68: 5q^3+22q^2+14q+2
        69: 2q^3+10q^2+9q+2
        70: 7q^3+19q^2+12q+2
        71: 2q^3+15q^2+12q+2
        72: 2q^3+11q^2+10q+2
        73: q^3+9q^2+10q+2
        74: q^3+6q^2+5q+1
        75: q^3+6q^2+5q+1
        76: 2q^3+6q^2+5q+1
        77: 2q^3+6q^2+5q+1
        78: q^3+6q^2+5q+1
        79: q^3+6q^2+5q+1
        80: 6q^3+22q^2+14q+2
        81: 6q^3+22q^2+14q+2
        82: 3q^3+15q^2+12q+2
        83: 4q^3+18q^2+12q+2
        84: 11q^3+26q^2+14q+2
        85: 11q^3+26q^2+14q+2
        86: 7q^3+19q^2+12q+2
        87: 10q^3+22q^2+12q+2
        88: 2q^3+17q^2+14q+2
        89: 2q^3+17q^2+14q+2
        90: q^4+7q^3+12q^2+9q+2
        91: 4q^3+18q^2+12q+2
        92: 6q^3+18q^2+12q+2
        93: 5q^3+13q^2+9q+2
        94: 11q^2+12q+2
        95: q^3+11q^2+12q+2
        96: q^3+9q^2+9q+2
        97: 4q^3+18q^2+12q+2
        98: 6q^3+18q^2+12q+2
        99: 5q^3+13q^2+9q+2
       100: 4q^3+18q^2+12q+2
       101: 8q^3+18q^2+12q+2
       102: 4q^3+18q^2+12q+2
       103: q^3+6q^2+5q+1
       104: q^3+6q^2+5q+1
       105: 3q^2+2q
       106: 3q^2+2q
       107: q^3+7q^2+8q+2
       108: 2q^2+2q
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: q^3+5q^2+5q+1
       114: q^3+5q^2+5q+1
       115: q^3+6q^2+5q+1
       116: q^3+6q^2+5q+1
       117: q^3+9q^2+7q+1
       118: q^3+9q^2+7q+1
       119: 4q^3+14q^2+10q+2
       120: q^3+8q^2+4q
       121: 3q^3+11q^2+7q+1
       122: 3q^3+11q^2+7q+1
       123: 3q^3+11q^2+7q+1
       124: 3q^3+11q^2+7q+1
       125: 2q^3+17q^2+14q+2
       126: 7q^2+9q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^3+15q^2+12q+2
       134: 2q^3+10q^2+9q+2
       135: 2q^3+11q^2+10q+2
       136: q^3+9q^2+10q+2
       137: 2q^3+14q^2+14q+2
       138: 6q^2+9q+2
       139: 9q^2+12q+2
       140: 3q^2+6q+2
       141: 3q^3+15q^2+12q+2
       142: 6q^2+10q+2
       143: 2q^3+17q^2+14q+2
       144: 2q^3+10q^2+9q+2
       145: 2q^3+15q^2+12q+2
       146: 7q^3+19q^2+12q+2
       147: 2q^3+11q^2+10q+2
       148: q^3+9q^2+10q+2
       149: 3q^3+15q^2+12q+2
       150: 4q^3+18q^2+12q+2
       151: q^3+6q^2+5q+1
       152: q^3+6q^2+5q+1
       153: 2q^3+6q^2+5q+1
       154: 2q^3+6q^2+5q+1
       155: q^3+6q^2+5q+1
       156: q^3+6q^2+5q+1
       157: 8q^2+11q+2
       158: 8q^2+11q+2
       159: 2q^3+7q^2+8q+2
       160: 11q^2+12q+2
       161: q^3+11q^2+12q+2
       162: q^3+9q^2+9q+2
       163: 4q^3+18q^2+12q+2
       164: 6q^3+18q^2+12q+2
       165: 5q^3+13q^2+9q+2
       166: 11q^2+12q+2
       167: q^3+11q^2+12q+2
       168: q^3+9q^2+9q+2
       169: q^2+3q+1
       170: q^2+3q+1
       171: q
       172: q
       173: q^3+6q^2+5q+1
       174: q^3+6q^2+5q+1
       175: 3q^2+2q
       176: 3q^2+2q
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: q^3+7q^2+8q+2
       184: 2q^2+2q
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: q^3+5q^2+5q+1
       190: q^3+5q^2+5q+1
       191: q^3+7q^2+7q+1
       192: q^3+7q^2+7q+1
       193: 3q^2+6q+2
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 2q^3+11q^2+10q+2
       200: 6q^2+4q
       201: q^3+7q^2+8q+2
       202: 2q^2+2q
       203: 3q^2+5q+1
       204: 3q^2+5q+1
       205: 2q^2+4q+1
       206: 2q^2+4q+1
       207: q^3+7q^2+7q+1
       208: q^3+7q^2+7q+1
       209: q^3+5q^2+5q+1
       210: q^3+5q^2+5q+1
       211: q^3+6q^2+5q+1
       212: q^3+6q^2+5q+1
       213: 2q^2+4q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: 2q^2+4q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 7q^2+9q+2
       220: 8q^2+11q+2
       221: 4q^2+8q+2
       222: 4q^2+9q+2
       223: q^3+5q^2+7q+2
       224: 4q^2+10q+2
       225: 3q^2+7q+2
       226: 4q^2+9q+2
       227: 9q^2+12q+2
       228: 6q^2+9q+2
       229: 3q^2+6q+2
       230: 6q^2+10q+2
       231: 7q^2+9q+2
       232: 2q^3+15q^2+12q+2
       233: 2q^3+10q^2+9q+2
       234: 2q^3+11q^2+10q+2
       235: q^3+9q^2+10q+2
       236: 6q^2+9q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 9q^2+12q+2
       244: 3q^2+6q+2
       245: 6q^2+10q+2
       246: 3q^3+15q^2+12q+2
       247: q^2+10q+4
       248: q^2+10q+4
       249: 3q^2+5q+2
       250: 2q^2+7q+2
       251: 2q^2+7q+2
       252: 3q^2+5q+2
       253: 8q^2+11q+2
       254: 8q^2+11q+2
       255: 2q^3+7q^2+8q+2
       256: 11q^2+12q+2
       257: q^3+11q^2+12q+2
       258: q^3+9q^2+9q+2
       259: 2q+1
       260: 2q+1
       261: q
       262: q
       263: q^2+3q+1
       264: q^2+3q+1
       265: q
       266: q
       267: 2q+1
       268: 2q+1
       271: q^2+3q+1
       272: q
       273: q
       274: q^2+3q+1
       275: q^3+5q^2+5q+1
       276: q^3+5q^2+5q+1
       277: 2q^2+2q
       278: 2q^2+2q
       279: 2q^2+4q+1
       280: 2q^2+4q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: 2q^2+5q+2
       285: 2q+1
       286: 2q+1
       287: q^2+3q+1
       288: q^2+3q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: 3q^2+7q+2
       294: q^2+2q
       295: 2q^2+5q+1
       296: 2q^2+5q+1
       297: q^2+4q+1
       298: q^2+4q+1
       299: 3q^2+6q+2
       301: q+1
       302: q+1
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 2q+1
       306: 2q+1
       307: q^3+7q^2+8q+2
       308: 2q^2+2q
       309: 3q^2+5q+1
       310: 3q^2+5q+1
       311: 3q+1
       312: 3q+1
       313: 2q^2+4q+1
       314: 2q^2+4q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       319: 3q^2+6q+2
       321: 2q^2+5q+1
       322: 2q^2+5q+1
       323: 2q+1
       324: 2q+1
       325: q^3+5q^2+5q+1
       326: q^3+5q^2+5q+1
       333: 4q^2+8q+2
       334: q^2+6q+2
       335: q^2+7q+2
       336: 3q+2
       337: 10q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 4q^2+9q+2
       345: 2q^2+7q+2
       346: q^2+5q+2
       347: q^2+3q+2
       348: q^2+3q+2
       349: 6q+2
       350: 3q^2+7q+2
       351: 6q+4
       352: 7q^2+9q+2
       353: 8q^2+11q+2
       354: 4q^2+8q+2
       355: 4q^2+9q+2
       356: q^3+5q^2+7q+2
       357: 4q^2+10q+2
       358: 3q^2+7q+2
       359: q^2+10q+4
       360: 2q^2+4q+1
       361: 2q^2+4q+1
       362: 2q^2+4q+1
       363: 2q^2+4q+1
       364: 2q^2+3q+1
       365: 2q^2+3q+1
       366: 4q^2+9q+2
       367: 9q^2+12q+2
       368: 6q^2+9q+2
       369: 3q^2+6q+2
       370: 6q^2+10q+2
       371: q^2+10q+4
       372: q^2+10q+4
       373: 3q^2+5q+2
       374: 2q^2+7q+2
       375: 2q^2+7q+2
       376: 3q^2+5q+2
       377: q+1
       378: q+1
       381: 2q+1
       382: 2q+1
       383: q
       384: q
       385: q^2+3q+1
       386: q^2+3q+1
       387: q
       388: q
       389: q+1
       390: q+1
       393: 2q+1
       394: 2q+1
       397: 2q+1
       398: q
       399: q
       400: 2q+1
       401: q^2+3q+1
       402: q
       403: q^2+3q+1
       404: q
       405: 2q+1
       407: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       417: 2q+1
       418: 2q+1
       419: 4q+2
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       429: q^2+3q+2
       431: 2q+1
       432: 2q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q^2+3q+2
       439: 3q+1
       440: 3q+1
       441: q+1
       442: q+1
       443: 6q+4
       445: 2q+2
       446: 2q+2
       447: 2q^2+5q+2
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 3q^2+7q+2
       454: q^2+2q
       455: 3q+1
       456: 3q+1
       457: 2q^2+5q+1
       458: 2q^2+5q+1
       459: q^2+4q+1
       460: q^2+4q+1
       461: 5q+2
       462: 5q+2
       463: 4q+2
       464: 4q+2
       465: 2q^2+4q+1
       466: 2q^2+4q+1
       467: q^2+3q+1
       468: q^2+3q+1
       469: q^2+3q+1
       470: q^2+3q+1
       471: 3q^2+6q+2
       473: 2q^2+5q+1
       474: 2q^2+5q+1
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 3q+2
       480: 3q+2
       481: q^2+6q+2
       482: q^2+7q+2
       483: 3q+2
       484: 10q+4
       485: 4q+2
       486: 4q+2
       487: 4q+2
       488: 4q+2
       489: q^2+2q+1
       490: q^2+2q+1
       491: 3q+2
       492: q^2+5q+2
       493: q+2
       494: 4q+2
       495: q+2
       496: 6q+4
       497: 4q^2+8q+2
       498: q^2+6q+2
       499: q^2+7q+2
       500: 3q+2
       501: q^2+10q+4
       508: 4q^2+9q+2
       509: 2q^2+7q+2
       510: q^2+5q+2
       511: q^2+3q+2
       512: q^2+3q+2
       513: 6q+2
       514: 3q^2+7q+2
       515: 2q+4
       516: 2q+4
       517: 2q+2
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       521: q+1
       522: q+1
       529: q+1
       530: q+1
       533: 1
       534: 1
       537: q+1
       538: q+1
       541: q+1
       542: q+1
       545: 2q+2
       546: 2q+2
       549: q+1
       551: q+1
       553: 2q+1
       554: q
       555: q
       556: 2q+1
       557: q^2+3q+1
       558: q
       559: q
       560: q^2+3q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: 2q+1
       566: 2q+1
       569: q+1
       571: q+1
       573: 3q+2
       574: 3q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       585: 2q+1
       586: 2q+1
       589: 4q+2
       593: q+2
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 4q+2
       602: 4q+2
       603: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 6q+4
       617: 2q+2
       618: 2q+2
       619: 4q+2
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       629: q+1
       630: q+1
       631: 5q+2
       632: 5q+2
       633: 4q+2
       634: 4q+2
       639: q^2+3q+1
       640: q^2+3q+1
       641: q^2+3q+2
       643: 2q+1
       644: 2q+1
       645: 1
       646: 1
       647: q^2+3q+2
       649: 3q+1
       650: 3q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 3q+2
       656: 3q+2
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+1
       663: q+1
       664: 2
       665: 3q+2
       672: 4q+2
       673: q+1
       674: 4
       675: q+2
       676: 4q+2
       677: 2
       678: 2q+2
       679: q+2
       680: 2q+4
       681: q^2+6q+2
       682: q^2+7q+2
       683: 3q+2
       684: 4q+2
       685: 3q+2
       686: q^2+5q+2
       687: q+2
       688: 4q+2
       689: q+2
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       694: q+1
       696: q+1
       699: q+1
       709: q+1
       710: q+1
       717: 1
       718: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: 2q+2
       734: 2q+2
       737: q+1
       740: q+1
       741: q+1
       744: q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 1
       754: 1
       757: q+1
       759: q+1
       761: q+1
       763: q+1
       765: 3q+2
       766: 3q+2
       769: q+1
       770: q+1
       772: q+1
       773: q+1
       775: 2
       776: 2
       779: 1
       780: 1
       781: q+1
       782: q+1
       785: q+2
       793: 4
       795: 2
       796: 2
       797: 1
       798: 1
       801: q+2
       805: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 2q+2
       817: 2
       818: 2
       819: q+2
       820: q+2
       821: 2q+1
       822: 2q+1
       825: 4q+2
       829: q+2
       831: 2q+1
       832: 2q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       839: 2q+1
       840: 2q+1
       843: 2
       844: 2
       845: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 2
       867: 1
       868: q+1
       869: 2
       870: 2
       871: 2
       872: 1
       873: q+2
       874: 2
       875: 3q+2
       876: q+1
       877: q+2
       878: 4q+2
       879: 2
       880: q+2
       881: q+2
       882: q+2
       883: q+1
       884: q+1
       885: q+1
       887: q+1
       890: q+1
       904: 1
       905: 1
       916: 2
       917: 2
       920: 1
       921: 1
       928: 1
       929: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: q+1
       947: q+1
       952: 1
       953: 1
       960: 1
       962: 1
       964: 2
       965: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       976: 1
       988: q+1
       989: q+1
       994: 1
       995: 1
      1000: 2
      1004: 1
      1016: 2
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1026: 2
      1032: 1
      1033: 1
      1036: 1
      1037: 1
      1038: q+1
      1039: q+1
      1040: q+2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+2
      1056: 2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 2
      1081: 1
      1082: q+1
      1083: 2
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1092: 1
      1122: 1
      1123: 1
      1156: 1
      1157: 1
      1176: 1
      1177: 1
      1194: 1
      1195: 1
      1198: 1
      1200: 1
      1206: 1
      1207: 1
      1218: 1
      1228: 2
      1240: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1254: 2
      1258: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1268: 2
      1274: 1
      1275: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1388: 1
      1389: 1
      1410: 1
      1411: 1
      1422: 1
      1423: 1
      1442: 1
      1462: 1
      1476: 1
      1486: 1
      1488: 1
      1655: 1

1656:    0: q^4+18q^3+30q^2+14q+2
         1: 3q^4+22q^3+30q^2+14q+2
         2: q^4+18q^3+30q^2+14q+2
         3: 3q^4+22q^3+30q^2+14q+2
         4: 3q^4+18q^3+24q^2+12q+2
         5: q^4+18q^3+30q^2+14q+2
         6: q^5+9q^4+23q^3+24q^2+12q+2
         7: 3q^4+18q^3+24q^2+12q+2
         8: q^4+18q^3+30q^2+14q+2
         9: q^5+6q^4+14q^3+15q^2+9q+2
        10: 11q^3+26q^2+14q+2
        11: 11q^3+26q^2+14q+2
        12: 2q^4+14q^3+21q^2+12q+2
        13: q^4+18q^3+30q^2+14q+2
        14: 3q^4+18q^3+24q^2+12q+2
        15: q^4+18q^3+30q^2+14q+2
        16: 11q^3+26q^2+14q+2
        17: 11q^3+26q^2+14q+2
        18: 2q^4+11q^3+15q^2+9q+2
        19: 10q^3+22q^2+12q+2
        20: 2q^4+15q^3+22q^2+12q+2
        21: 10q^3+22q^2+12q+2
        22: 10q^3+26q^2+14q+2
        23: 14q^3+26q^2+14q+2
        24: 10q^3+26q^2+14q+2
        25: q^4+18q^3+30q^2+14q+2
        26: 3q^4+22q^3+30q^2+14q+2
        27: q^4+18q^3+30q^2+14q+2
        28: 5q^3+22q^2+14q+2
        29: 7q^3+19q^2+12q+2
        30: 10q^3+22q^2+12q+2
        31: 6q^3+22q^2+14q+2
        32: 10q^3+26q^2+14q+2
        33: 6q^3+22q^2+14q+2
        34: 11q^3+26q^2+14q+2
        35: q^4+18q^3+30q^2+14q+2
        36: 11q^3+26q^2+14q+2
        37: 5q^3+13q^2+7q+1
        38: 5q^3+13q^2+7q+1
        39: 7q^3+13q^2+7q+1
        40: 7q^3+13q^2+7q+1
        41: 5q^3+13q^2+7q+1
        42: 5q^3+13q^2+7q+1
        43: 11q^3+26q^2+14q+2
        44: 2q^4+14q^3+21q^2+12q+2
        45: 11q^3+26q^2+14q+2
        46: 11q^3+26q^2+14q+2
        47: 11q^3+26q^2+14q+2
        48: 2q^4+11q^3+15q^2+9q+2
        49: 4q^3+18q^2+12q+2
        50: 6q^3+18q^2+12q+2
        51: 5q^3+13q^2+9q+2
        52: 4q^3+18q^2+12q+2
        53: 8q^3+18q^2+12q+2
        54: 4q^3+18q^2+12q+2
        55: 10q^3+22q^2+12q+2
        56: 2q^4+15q^3+22q^2+12q+2
        57: 10q^3+22q^2+12q+2
        58: q^3+9q^2+7q+1
        59: q^3+9q^2+7q+1
        60: q^3+8q^2+4q
        61: 4q^3+14q^2+10q+2
        62: 3q^3+11q^2+7q+1
        63: 3q^3+11q^2+7q+1
        64: 5q^3+13q^2+7q+1
        65: 5q^3+13q^2+7q+1
        66: 3q^3+11q^2+7q+1
        67: 3q^3+11q^2+7q+1
        68: 5q^3+22q^2+14q+2
        69: 2q^3+10q^2+9q+2
        70: 7q^3+19q^2+12q+2
        71: 2q^3+15q^2+12q+2
        72: 2q^3+11q^2+10q+2
        73: q^3+9q^2+10q+2
        74: q^3+6q^2+5q+1
        75: q^3+6q^2+5q+1
        76: 2q^3+6q^2+5q+1
        77: 2q^3+6q^2+5q+1
        78: q^3+6q^2+5q+1
        79: q^3+6q^2+5q+1
        80: 6q^3+22q^2+14q+2
        81: 6q^3+22q^2+14q+2
        82: 3q^3+15q^2+12q+2
        83: 4q^3+18q^2+12q+2
        84: 11q^3+26q^2+14q+2
        85: 11q^3+26q^2+14q+2
        86: 7q^3+19q^2+12q+2
        87: 10q^3+22q^2+12q+2
        88: 2q^3+17q^2+14q+2
        89: 2q^3+17q^2+14q+2
        90: q^4+7q^3+12q^2+9q+2
        91: 4q^3+18q^2+12q+2
        92: 6q^3+18q^2+12q+2
        93: 5q^3+13q^2+9q+2
        94: 11q^2+12q+2
        95: q^3+11q^2+12q+2
        96: q^3+9q^2+9q+2
        97: 4q^3+18q^2+12q+2
        98: 6q^3+18q^2+12q+2
        99: 5q^3+13q^2+9q+2
       100: 4q^3+18q^2+12q+2
       101: 8q^3+18q^2+12q+2
       102: 4q^3+18q^2+12q+2
       103: 3q^2+2q
       104: 3q^2+2q
       105: q^3+6q^2+5q+1
       106: q^3+6q^2+5q+1
       107: 2q^2+2q
       108: q^3+7q^2+8q+2
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+4q+1
       112: 2q^2+4q+1
       113: q^3+5q^2+5q+1
       114: q^3+5q^2+5q+1
       115: q^3+6q^2+5q+1
       116: q^3+6q^2+5q+1
       117: q^3+9q^2+7q+1
       118: q^3+9q^2+7q+1
       119: q^3+8q^2+4q
       120: 4q^3+14q^2+10q+2
       121: 3q^3+11q^2+7q+1
       122: 3q^3+11q^2+7q+1
       123: 3q^3+11q^2+7q+1
       124: 3q^3+11q^2+7q+1
       125: 2q^3+17q^2+14q+2
       126: 7q^2+9q+2
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^3+15q^2+12q+2
       134: 2q^3+10q^2+9q+2
       135: 2q^3+11q^2+10q+2
       136: q^3+9q^2+10q+2
       137: 2q^3+14q^2+14q+2
       138: 6q^2+9q+2
       139: 9q^2+12q+2
       140: 3q^2+6q+2
       141: 3q^3+15q^2+12q+2
       142: 6q^2+10q+2
       143: 2q^3+17q^2+14q+2
       144: 2q^3+10q^2+9q+2
       145: 2q^3+15q^2+12q+2
       146: 7q^3+19q^2+12q+2
       147: 2q^3+11q^2+10q+2
       148: q^3+9q^2+10q+2
       149: 3q^3+15q^2+12q+2
       150: 4q^3+18q^2+12q+2
       151: q^3+6q^2+5q+1
       152: q^3+6q^2+5q+1
       153: 2q^3+6q^2+5q+1
       154: 2q^3+6q^2+5q+1
       155: q^3+6q^2+5q+1
       156: q^3+6q^2+5q+1
       157: 8q^2+11q+2
       158: 8q^2+11q+2
       159: 2q^3+7q^2+8q+2
       160: 11q^2+12q+2
       161: q^3+11q^2+12q+2
       162: q^3+9q^2+9q+2
       163: 4q^3+18q^2+12q+2
       164: 6q^3+18q^2+12q+2
       165: 5q^3+13q^2+9q+2
       166: 11q^2+12q+2
       167: q^3+11q^2+12q+2
       168: q^3+9q^2+9q+2
       169: q
       170: q
       171: q^2+3q+1
       172: q^2+3q+1
       173: 3q^2+2q
       174: 3q^2+2q
       175: q^3+6q^2+5q+1
       176: q^3+6q^2+5q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 3q+1
       182: 3q+1
       183: 2q^2+2q
       184: q^3+7q^2+8q+2
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: q^3+5q^2+5q+1
       190: q^3+5q^2+5q+1
       191: q^3+7q^2+7q+1
       192: q^3+7q^2+7q+1
       194: 3q^2+6q+2
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 6q^2+4q
       200: 2q^3+11q^2+10q+2
       201: 2q^2+2q
       202: q^3+7q^2+8q+2
       203: 3q^2+5q+1
       204: 3q^2+5q+1
       205: 2q^2+4q+1
       206: 2q^2+4q+1
       207: q^3+7q^2+7q+1
       208: q^3+7q^2+7q+1
       209: q^3+5q^2+5q+1
       210: q^3+5q^2+5q+1
       211: q^3+6q^2+5q+1
       212: q^3+6q^2+5q+1
       213: 2q^2+4q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: 2q^2+4q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 7q^2+9q+2
       220: 8q^2+11q+2
       221: 4q^2+8q+2
       222: 4q^2+9q+2
       223: q^3+5q^2+7q+2
       224: 4q^2+10q+2
       225: 3q^2+7q+2
       226: 4q^2+9q+2
       227: 9q^2+12q+2
       228: 6q^2+9q+2
       229: 3q^2+6q+2
       230: 6q^2+10q+2
       231: 7q^2+9q+2
       232: 2q^3+15q^2+12q+2
       233: 2q^3+10q^2+9q+2
       234: 2q^3+11q^2+10q+2
       235: q^3+9q^2+10q+2
       236: 6q^2+9q+2
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 9q^2+12q+2
       244: 3q^2+6q+2
       245: 6q^2+10q+2
       246: 3q^3+15q^2+12q+2
       247: q^2+10q+4
       248: q^2+10q+4
       249: 3q^2+5q+2
       250: 2q^2+7q+2
       251: 2q^2+7q+2
       252: 3q^2+5q+2
       253: 8q^2+11q+2
       254: 8q^2+11q+2
       255: 2q^3+7q^2+8q+2
       256: 11q^2+12q+2
       257: q^3+11q^2+12q+2
       258: q^3+9q^2+9q+2
       259: q
       260: q
       261: 2q+1
       262: 2q+1
       263: q
       264: q
       265: q^2+3q+1
       266: q^2+3q+1
       269: 2q+1
       270: 2q+1
       271: q
       272: q^2+3q+1
       273: q^2+3q+1
       274: q
       275: 2q^2+2q
       276: 2q^2+2q
       277: q^3+5q^2+5q+1
       278: q^3+5q^2+5q+1
       279: 2q^2+4q+1
       280: 2q^2+4q+1
       281: q^2+3q+1
       282: q^2+3q+1
       284: 2q^2+5q+2
       285: 2q+1
       286: 2q+1
       287: q^2+3q+1
       288: q^2+3q+1
       289: 3q+1
       290: 3q+1
       291: 2q+1
       292: 2q+1
       293: q^2+2q
       294: 3q^2+7q+2
       295: 2q^2+5q+1
       296: 2q^2+5q+1
       297: q^2+4q+1
       298: q^2+4q+1
       300: 3q^2+6q+2
       301: q+1
       302: q+1
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 2q+1
       306: 2q+1
       307: 2q^2+2q
       308: q^3+7q^2+8q+2
       309: 3q^2+5q+1
       310: 3q^2+5q+1
       311: 3q+1
       312: 3q+1
       313: 2q^2+4q+1
       314: 2q^2+4q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+4q+1
       318: 2q^2+4q+1
       320: 3q^2+6q+2
       321: 2q^2+5q+1
       322: 2q^2+5q+1
       323: 2q+1
       324: 2q+1
       325: q^3+5q^2+5q+1
       326: q^3+5q^2+5q+1
       333: 4q^2+8q+2
       334: q^2+6q+2
       335: q^2+7q+2
       336: 3q+2
       337: 10q+4
       338: 4q+2
       339: 4q+2
       340: 4q+2
       341: 4q+2
       342: q^2+2q+1
       343: q^2+2q+1
       344: 4q^2+9q+2
       345: 2q^2+7q+2
       346: q^2+5q+2
       347: q^2+3q+2
       348: q^2+3q+2
       349: 6q+2
       350: 3q^2+7q+2
       351: 6q+4
       352: 7q^2+9q+2
       353: 8q^2+11q+2
       354: 4q^2+8q+2
       355: 4q^2+9q+2
       356: q^3+5q^2+7q+2
       357: 4q^2+10q+2
       358: 3q^2+7q+2
       359: q^2+10q+4
       360: 2q^2+4q+1
       361: 2q^2+4q+1
       362: 2q^2+4q+1
       363: 2q^2+4q+1
       364: 2q^2+3q+1
       365: 2q^2+3q+1
       366: 4q^2+9q+2
       367: 9q^2+12q+2
       368: 6q^2+9q+2
       369: 3q^2+6q+2
       370: 6q^2+10q+2
       371: q^2+10q+4
       372: q^2+10q+4
       373: 3q^2+5q+2
       374: 2q^2+7q+2
       375: 2q^2+7q+2
       376: 3q^2+5q+2
       379: q+1
       380: q+1
       381: q
       382: q
       383: 2q+1
       384: 2q+1
       385: q
       386: q
       387: q^2+3q+1
       388: q^2+3q+1
       391: q+1
       392: q+1
       395: 2q+1
       396: 2q+1
       397: q
       398: 2q+1
       399: 2q+1
       400: q
       401: q
       402: q^2+3q+1
       403: q
       404: q^2+3q+1
       406: 2q+1
       408: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       417: 2q+1
       418: 2q+1
       420: 4q+2
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 4q+2
       428: 4q+2
       430: q^2+3q+2
       431: 2q+1
       432: 2q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       438: q^2+3q+2
       439: 3q+1
       440: 3q+1
       441: q+1
       442: q+1
       444: 6q+4
       445: 2q+2
       446: 2q+2
       448: 2q^2+5q+2
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: q^2+2q
       454: 3q^2+7q+2
       455: 3q+1
       456: 3q+1
       457: 2q^2+5q+1
       458: 2q^2+5q+1
       459: q^2+4q+1
       460: q^2+4q+1
       461: 5q+2
       462: 5q+2
       463: 4q+2
       464: 4q+2
       465: 2q^2+4q+1
       466: 2q^2+4q+1
       467: q^2+3q+1
       468: q^2+3q+1
       469: q^2+3q+1
       470: q^2+3q+1
       472: 3q^2+6q+2
       473: 2q^2+5q+1
       474: 2q^2+5q+1
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 3q+2
       480: 3q+2
       481: q^2+6q+2
       482: q^2+7q+2
       483: 3q+2
       484: 10q+4
       485: 4q+2
       486: 4q+2
       487: 4q+2
       488: 4q+2
       489: q^2+2q+1
       490: q^2+2q+1
       491: 3q+2
       492: q^2+5q+2
       493: q+2
       494: 4q+2
       495: q+2
       496: 6q+4
       497: 4q^2+8q+2
       498: q^2+6q+2
       499: q^2+7q+2
       500: 3q+2
       501: q^2+10q+4
       508: 4q^2+9q+2
       509: 2q^2+7q+2
       510: q^2+5q+2
       511: q^2+3q+2
       512: q^2+3q+2
       513: 6q+2
       514: 3q^2+7q+2
       515: 2q+4
       516: 2q+4
       517: 2q+2
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       523: q+1
       524: q+1
       531: q+1
       532: q+1
       535: 1
       536: 1
       539: q+1
       540: q+1
       543: q+1
       544: q+1
       547: 2q+2
       548: 2q+2
       550: q+1
       552: q+1
       553: q
       554: 2q+1
       555: 2q+1
       556: q
       557: q
       558: q^2+3q+1
       559: q^2+3q+1
       560: q
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       567: 2q+1
       568: 2q+1
       570: q+1
       572: q+1
       575: 3q+2
       576: 3q+2
       577: q+1
       578: q+1
       580: q+1
       581: q+1
       585: 2q+1
       586: 2q+1
       590: 4q+2
       594: q+2
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 4q+2
       602: 4q+2
       604: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 6q+4
       617: 2q+2
       618: 2q+2
       620: 4q+2
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       629: q+1
       630: q+1
       631: 5q+2
       632: 5q+2
       633: 4q+2
       634: 4q+2
       639: q^2+3q+1
       640: q^2+3q+1
       642: q^2+3q+2
       643: 2q+1
       644: 2q+1
       645: 1
       646: 1
       648: q^2+3q+2
       649: 3q+1
       650: 3q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 3q+2
       656: 3q+2
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+1
       663: q+1
       664: 2
       665: 3q+2
       672: 4q+2
       673: q+1
       674: 4
       675: q+2
       676: 4q+2
       677: 2
       678: 2q+2
       679: q+2
       680: 2q+4
       681: q^2+6q+2
       682: q^2+7q+2
       683: 3q+2
       684: 4q+2
       685: 3q+2
       686: q^2+5q+2
       687: q+2
       688: 4q+2
       689: q+2
       690: q+2
       691: q+2
       692: q+1
       697: q+1
       698: q+1
       700: q+1
       701: q+1
       711: q+1
       712: q+1
       719: 1
       720: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: 2q+2
       736: 2q+2
       738: q+1
       739: q+1
       742: q+1
       743: q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       755: 1
       756: 1
       758: q+1
       760: q+1
       762: q+1
       764: q+1
       767: 3q+2
       768: 3q+2
       769: q+1
       770: q+1
       772: q+1
       773: q+1
       775: 2
       776: 2
       779: 1
       780: 1
       781: q+1
       782: q+1
       786: q+2
       794: 4
       795: 2
       796: 2
       797: 1
       798: 1
       802: q+2
       806: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       816: 2q+2
       817: 2
       818: 2
       819: q+2
       820: q+2
       821: 2q+1
       822: 2q+1
       826: 4q+2
       830: q+2
       831: 2q+1
       832: 2q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       839: 2q+1
       840: 2q+1
       843: 2
       844: 2
       846: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 2
       867: 1
       868: q+1
       869: 2
       870: 2
       871: 2
       872: 1
       873: q+2
       874: 2
       875: 3q+2
       876: q+1
       877: q+2
       878: 4q+2
       879: 2
       880: q+2
       881: q+2
       882: q+2
       883: q+1
       888: q+1
       889: q+1
       891: q+1
       892: q+1
       906: 1
       907: 1
       918: 2
       919: 2
       922: 1
       923: 1
       930: 1
       931: 1
       940: 1
       941: 1
       942: 1
       943: 1
       945: q+1
       946: q+1
       954: 1
       955: 1
       961: 1
       963: 1
       966: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       977: 1
       990: q+1
       991: q+1
       994: 1
       995: 1
      1001: 2
      1005: 1
      1017: 2
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1027: 2
      1032: 1
      1033: 1
      1036: 1
      1037: 1
      1038: q+1
      1039: q+1
      1041: q+2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: q+2
      1057: 2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 2
      1081: 1
      1082: q+1
      1083: 2
      1084: 2
      1085: 1
      1090: 1
      1091: 1
      1093: 1
      1094: 1
      1124: 1
      1125: 1
      1158: 1
      1159: 1
      1178: 1
      1179: 1
      1196: 1
      1197: 1
      1199: 1
      1201: 1
      1208: 1
      1209: 1
      1219: 1
      1229: 2
      1241: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1255: 2
      1259: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1269: 2
      1274: 1
      1275: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1390: 1
      1391: 1
      1412: 1
      1413: 1
      1424: 1
      1425: 1
      1443: 1
      1463: 1
      1477: 1
      1486: 1
      1488: 1
      1656: 1

1657:    0: q^4+3q^3+6q^2+6q+2
         1: q^4+3q^3+6q^2+6q+2
         2: 2q^3+7q^2+4q+2
         3: q^4+3q^3+6q^2+6q+2
         4: q^4+3q^3+6q^2+6q+2
         5: q^4+3q^3+6q^2+6q+2
         6: q^4+3q^3+6q^2+6q+2
         7: 2q^3+7q^2+4q+2
         8: 2q^3+7q^2+4q+2
         9: 2q^4+3q^3+5q^2+3q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+4q+2
        14: q^3+5q^2+4q+2
        15: q^3+5q^2+4q+2
        16: 2q^3+4q^2+6q+2
        17: 2q^3+4q^2+6q+2
        18: 2q^3+5q^2+3q+2
        19: q^4+3q^3+6q^2+6q+2
        20: q^4+3q^3+6q^2+6q+2
        21: 2q^3+7q^2+4q+2
        22: 2q^3+4q^2+6q+2
        23: 2q^3+4q^2+6q+2
        24: 6q^2+4q+2
        25: q^4+3q^3+6q^2+6q+2
        26: q^4+3q^3+6q^2+6q+2
        27: 2q^3+7q^2+4q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+5q^2+4q+2
        31: 2q^2+6q+2
        32: 4q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 4q^2+6q+2
        35: q^3+5q^2+4q+2
        36: 2q^3+4q^2+6q+2
        37: q^3+2q^2+3q+1
        38: q^3+2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: q^3+2q^2+3q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: 3q^2+4q+2
        44: 3q^2+4q+2
        45: 3q^2+4q+2
        46: 3q^2+4q+2
        47: 3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^3+4q^2+6q+2
        50: 2q^3+4q^2+6q+2
        51: 2q^3+5q^2+3q+2
        52: 2q^3+4q^2+6q+2
        53: 2q^3+4q^2+6q+2
        54: 6q^2+4q+2
        55: q^4+3q^3+6q^2+6q+2
        56: q^4+3q^3+6q^2+6q+2
        57: 2q^3+7q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 2q^2+4q+2
        61: 2q
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+2q+1
        65: 2q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: q^2+2q+2
        69: 2q^2+3q+2
        70: 3q^2+4q+2
        71: 2q^2+6q+2
        72: 2q^3+4q^2+6q+2
        73: 2q^3+2q^2+6q+2
        74: q^3+2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: q^3+2q^2+3q+1
        77: q^3+2q^2+3q+1
        78: 3q^2+2q+1
        79: 3q^2+2q+1
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: 2q^2+6q+2
        83: 4q^2+4q+2
        84: 3q^2+4q+2
        85: 3q^2+4q+2
        86: 4q^2+6q+2
        87: q^3+5q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 3q^2+4q+2
        92: 3q^2+4q+2
        93: q^3+3q^2+3q+2
        94: q^3+q^2+6q+2
        95: q^3+q^2+6q+2
        96: 4q^2+3q+2
        97: 2q^3+4q^2+6q+2
        98: 2q^3+4q^2+6q+2
        99: 2q^3+5q^2+3q+2
       100: 2q^3+4q^2+6q+2
       101: 2q^3+4q^2+6q+2
       102: 6q^2+4q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: 2q^2+4q+2
       108: 2q
       109: 3q+1
       110: 3q+1
       111: q^3+q^2+3q+1
       112: q^3+q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q+1
       118: q+1
       119: q^2+2q+2
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2q+2
       134: 2q^2+3q+2
       135: 3q^2+4q+2
       136: 2q^2+4q+2
       137: 4q+2
       138: q^2+3q+2
       139: 6q+2
       140: 4q+2
       141: 2q^2+4q+2
       142: q^3+q^2+6q+2
       143: 4q+2
       144: 2q^2+3q+2
       145: 2q^2+6q+2
       146: 3q^2+4q+2
       147: 2q^3+4q^2+6q+2
       148: 2q^3+2q^2+6q+2
       149: 2q^2+6q+2
       150: 4q^2+4q+2
       151: q^3+2q^2+3q+1
       152: q^3+2q^2+3q+1
       153: q^3+2q^2+3q+1
       154: q^3+2q^2+3q+1
       155: 3q^2+2q+1
       156: 3q^2+2q+1
       157: 4q+2
       158: 4q+2
       159: q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: 2q^2+2q+2
       163: 3q^2+4q+2
       164: 3q^2+4q+2
       165: q^3+3q^2+3q+2
       166: q^3+q^2+6q+2
       167: q^3+q^2+6q+2
       168: 4q^2+3q+2
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: q+1
       174: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: q^2+2q+2
       185: q+1
       186: q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 4q+2
       195: 3q+1
       196: 3q+1
       197: 2q+1
       198: 2q+1
       199: 2q+2
       201: 2q^2+4q+2
       202: 2q
       203: 3q+1
       204: 3q+1
       205: q^3+q^2+3q+1
       206: q^3+q^2+3q+1
       207: 2q+1
       208: 2q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       219: q+2
       220: 2q+2
       221: 3q+2
       222: 4q+2
       223: 2q^2+3q+2
       224: 4q+2
       225: q^2+3q+2
       226: 3q+2
       227: 2q+2
       228: q^2+2q+2
       229: 2q+2
       230: q^2+3q+2
       231: 3q+2
       232: q^2+2q+2
       233: 2q^2+3q+2
       234: 3q^2+4q+2
       235: 2q^2+4q+2
       236: q^2+3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: 4q+2
       245: q^3+q^2+6q+2
       246: 2q^2+4q+2
       247: q^3+q^2+6q+2
       248: q^3+q^2+6q+2
       249: 4q^2+3q+2
       250: q+2
       251: q+2
       252: q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: q^2+3q+2
       257: q^2+3q+2
       258: 2q^2+2q+2
       259: q+1
       260: q+1
       261: q
       262: q
       263: q+1
       264: q+1
       267: 2q+1
       268: 2q+1
       271: 2q+1
       272: q
       273: q
       274: 2q+1
       275: q+1
       276: q+1
       283: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2q+2
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q^2+2q+2
       309: q+1
       310: q+1
       311: 2q+1
       312: 2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 4q+2
       321: 3q+1
       322: 3q+1
       323: 2q+1
       324: 2q+1
       325: q^2+2q+1
       326: q^2+2q+1
       333: q+2
       334: 3q+2
       335: 3q+2
       336: q^2+3q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q+2
       345: 2
       346: q+2
       347: 2
       348: q+2
       349: q+2
       350: q^2+2q+2
       351: 4q+2
       352: q+2
       353: 2q+2
       354: 3q+2
       355: 4q+2
       356: 2q^2+3q+2
       357: 4q+2
       358: q^2+3q+2
       359: q^3+q^2+6q+2
       366: 3q+2
       367: 2q+2
       368: q^2+2q+2
       369: 2q+2
       370: q^2+3q+2
       371: q^2+3q+2
       372: q^2+3q+2
       373: 2q^2+2q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: 1
       385: q+1
       386: q+1
       389: q+1
       390: q+1
       393: q+1
       394: q+1
       397: q+1
       398: q
       399: q
       400: q+1
       401: q+1
       403: q+1
       405: 2q+1
       407: 2q+1
       419: q+2
       421: 1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 4q+2
       445: q+1
       446: q+1
       447: q+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 2q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 3q+1
       462: 3q+1
       463: 2q+1
       464: 2q+1
       469: q+1
       470: q+1
       471: 2q+2
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q+2
       482: q+2
       483: 3q+2
       484: 2q+2
       491: q^2+2q+2
       492: 2
       493: 2
       494: q+2
       495: q+2
       496: 2q+2
       497: q+2
       498: 3q+2
       499: 3q+2
       500: q^2+3q+2
       501: q^2+3q+2
       508: q+2
       509: 2
       510: q+2
       511: 2
       512: q+2
       513: q+2
       514: q^2+2q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       549: 1
       551: 1
       557: q+1
       560: q+1
       561: q+1
       562: q
       563: q
       564: q+1
       565: q+1
       566: q+1
       569: q+1
       571: q+1
       573: 2q+1
       574: 2q+1
       577: q+1
       581: q+1
       589: q+2
       591: 1
       592: 1
       593: q+2
       595: 1
       596: 1
       599: q+1
       600: q+1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2q+2
       619: q+2
       621: 1
       622: 1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       641: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: q+1
       656: q+1
       657: 2
       664: q+2
       665: q+2
       672: 2
       673: q+2
       674: 2
       675: 1
       676: 2
       677: 2
       678: 2
       679: q+2
       680: q+2
       681: q+2
       682: q+2
       683: 3q+2
       684: q+2
       685: q^2+2q+2
       686: 2
       687: 2
       688: q+2
       689: q+2
       693: q+1
       699: q+1
       713: 1
       715: 1
       717: 1
       718: 1
       725: 1
       726: 1
       741: 1
       744: 1
       753: 1
       754: 1
       761: 1
       763: 1
       765: q+1
       766: q+1
       785: q+2
       787: 1
       788: 1
       791: 1
       792: 1
       793: 2
       801: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 2
       817: 1
       818: 1
       825: q+2
       827: 1
       828: 1
       829: q+2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       845: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       866: 2
       868: 2
       870: 2
       871: 1
       872: 2
       874: q+2
       875: q+2
       876: q+2
       877: 1
       878: 2
       879: 2
       880: q+2
       908: 1
       909: 1
       928: 1
       929: 1
       948: 1
       951: 1
       952: 1
       953: 1
       964: 1
       965: 1
       974: 1
       976: 1
       988: 1
       989: 1
       998: 1
       999: 1
      1000: 2
      1004: 2
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1026: 1
      1040: q+2
      1044: 1
      1045: 1
      1052: 1
      1056: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 2
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1131: 1
      1134: 1
      1136: 1
      1180: 1
      1181: 1
      1206: 1
      1207: 1
      1234: 1
      1240: 1
      1250: 1
      1251: 1
      1254: 2
      1258: 2
      1260: 1
      1261: 1
      1268: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1396: 1
      1397: 1
      1400: 1
      1402: 1
      1468: 1
      1476: 1
      1484: 1
      1657: 1

1658:    0: q^4+3q^3+6q^2+6q+2
         1: q^4+3q^3+6q^2+6q+2
         2: 2q^3+7q^2+4q+2
         3: q^4+3q^3+6q^2+6q+2
         4: q^4+3q^3+6q^2+6q+2
         5: q^4+3q^3+6q^2+6q+2
         6: q^4+3q^3+6q^2+6q+2
         7: 2q^3+7q^2+4q+2
         8: 2q^3+7q^2+4q+2
         9: 2q^4+3q^3+5q^2+3q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+5q^2+4q+2
        14: q^3+5q^2+4q+2
        15: q^3+5q^2+4q+2
        16: 2q^3+4q^2+6q+2
        17: 2q^3+4q^2+6q+2
        18: 2q^3+5q^2+3q+2
        19: q^4+3q^3+6q^2+6q+2
        20: q^4+3q^3+6q^2+6q+2
        21: 2q^3+7q^2+4q+2
        22: 2q^3+4q^2+6q+2
        23: 2q^3+4q^2+6q+2
        24: 6q^2+4q+2
        25: q^4+3q^3+6q^2+6q+2
        26: q^4+3q^3+6q^2+6q+2
        27: 2q^3+7q^2+4q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+5q^2+4q+2
        31: 2q^2+6q+2
        32: 4q^2+4q+2
        33: 2q^3+2q^2+6q+2
        34: 4q^2+6q+2
        35: q^3+5q^2+4q+2
        36: 2q^3+4q^2+6q+2
        37: q^3+2q^2+3q+1
        38: q^3+2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: q^3+2q^2+3q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: 3q^2+4q+2
        44: 3q^2+4q+2
        45: 3q^2+4q+2
        46: 3q^2+4q+2
        47: 3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^3+4q^2+6q+2
        50: 2q^3+4q^2+6q+2
        51: 2q^3+5q^2+3q+2
        52: 2q^3+4q^2+6q+2
        53: 2q^3+4q^2+6q+2
        54: 6q^2+4q+2
        55: q^4+3q^3+6q^2+6q+2
        56: q^4+3q^3+6q^2+6q+2
        57: 2q^3+7q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 2q^2+4q+2
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+2q+1
        65: 2q^2+2q+1
        66: q^3+q^2+3q+1
        67: q^3+q^2+3q+1
        68: q^2+2q+2
        69: 2q^2+3q+2
        70: 3q^2+4q+2
        71: 2q^2+6q+2
        72: 2q^3+4q^2+6q+2
        73: 2q^3+2q^2+6q+2
        74: q^3+2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: q^3+2q^2+3q+1
        77: q^3+2q^2+3q+1
        78: 3q^2+2q+1
        79: 3q^2+2q+1
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: 2q^2+6q+2
        83: 4q^2+4q+2
        84: 3q^2+4q+2
        85: 3q^2+4q+2
        86: 4q^2+6q+2
        87: q^3+5q^2+4q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 3q^2+4q+2
        92: 3q^2+4q+2
        93: q^3+3q^2+3q+2
        94: q^3+q^2+6q+2
        95: q^3+q^2+6q+2
        96: 4q^2+3q+2
        97: 2q^3+4q^2+6q+2
        98: 2q^3+4q^2+6q+2
        99: 2q^3+5q^2+3q+2
       100: 2q^3+4q^2+6q+2
       101: 2q^3+4q^2+6q+2
       102: 6q^2+4q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       107: 2q
       108: 2q^2+4q+2
       109: 3q+1
       110: 3q+1
       111: q^3+q^2+3q+1
       112: q^3+q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q+1
       118: q+1
       120: q^2+2q+2
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q+2
       126: 3q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2q+2
       134: 2q^2+3q+2
       135: 3q^2+4q+2
       136: 2q^2+4q+2
       137: 4q+2
       138: q^2+3q+2
       139: 6q+2
       140: 4q+2
       141: 2q^2+4q+2
       142: q^3+q^2+6q+2
       143: 4q+2
       144: 2q^2+3q+2
       145: 2q^2+6q+2
       146: 3q^2+4q+2
       147: 2q^3+4q^2+6q+2
       148: 2q^3+2q^2+6q+2
       149: 2q^2+6q+2
       150: 4q^2+4q+2
       151: q^3+2q^2+3q+1
       152: q^3+2q^2+3q+1
       153: q^3+2q^2+3q+1
       154: q^3+2q^2+3q+1
       155: 3q^2+2q+1
       156: 3q^2+2q+1
       157: 4q+2
       158: 4q+2
       159: q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: 2q^2+2q+2
       163: 3q^2+4q+2
       164: 3q^2+4q+2
       165: q^3+3q^2+3q+2
       166: q^3+q^2+6q+2
       167: q^3+q^2+6q+2
       168: 4q^2+3q+2
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       184: q^2+2q+2
       185: q+1
       186: q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       194: 4q+2
       195: 3q+1
       196: 3q+1
       197: 2q+1
       198: 2q+1
       200: 2q+2
       201: 2q
       202: 2q^2+4q+2
       203: 3q+1
       204: 3q+1
       205: q^3+q^2+3q+1
       206: q^3+q^2+3q+1
       207: 2q+1
       208: 2q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       219: q+2
       220: 2q+2
       221: 3q+2
       222: 4q+2
       223: 2q^2+3q+2
       224: 4q+2
       225: q^2+3q+2
       226: 3q+2
       227: 2q+2
       228: q^2+2q+2
       229: 2q+2
       230: q^2+3q+2
       231: 3q+2
       232: q^2+2q+2
       233: 2q^2+3q+2
       234: 3q^2+4q+2
       235: 2q^2+4q+2
       236: q^2+3q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: 4q+2
       245: q^3+q^2+6q+2
       246: 2q^2+4q+2
       247: q^3+q^2+6q+2
       248: q^3+q^2+6q+2
       249: 4q^2+3q+2
       250: q+2
       251: q+2
       252: q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: q^2+3q+2
       257: q^2+3q+2
       258: 2q^2+2q+2
       259: q
       260: q
       261: q+1
       262: q+1
       265: q+1
       266: q+1
       269: 2q+1
       270: 2q+1
       271: q
       272: 2q+1
       273: 2q+1
       274: q
       277: q+1
       278: q+1
       284: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       294: 2q+2
       295: q+1
       296: q+1
       297: 2q+1
       298: 2q+1
       300: 2q+2
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       308: q^2+2q+2
       309: q+1
       310: q+1
       311: 2q+1
       312: 2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       320: 4q+2
       321: 3q+1
       322: 3q+1
       323: 2q+1
       324: 2q+1
       325: q^2+2q+1
       326: q^2+2q+1
       333: q+2
       334: 3q+2
       335: 3q+2
       336: q^2+3q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q+2
       345: 2
       346: q+2
       347: 2
       348: q+2
       349: q+2
       350: q^2+2q+2
       351: 4q+2
       352: q+2
       353: 2q+2
       354: 3q+2
       355: 4q+2
       356: 2q^2+3q+2
       357: 4q+2
       358: q^2+3q+2
       359: q^3+q^2+6q+2
       366: 3q+2
       367: 2q+2
       368: q^2+2q+2
       369: 2q+2
       370: q^2+3q+2
       371: q^2+3q+2
       372: q^2+3q+2
       373: 2q^2+2q+2
       374: q+2
       375: q+2
       376: q+2
       379: 1
       380: 1
       387: q+1
       388: q+1
       391: q+1
       392: q+1
       395: q+1
       396: q+1
       397: q
       398: q+1
       399: q+1
       400: q
       402: q+1
       404: q+1
       406: 2q+1
       408: 2q+1
       420: q+2
       421: 1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       430: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 4q+2
       445: q+1
       446: q+1
       448: q+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 2q+2
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 3q+1
       462: 3q+1
       463: 2q+1
       464: 2q+1
       469: q+1
       470: q+1
       472: 2q+2
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q+2
       482: q+2
       483: 3q+2
       484: 2q+2
       491: q^2+2q+2
       492: 2
       493: 2
       494: q+2
       495: q+2
       496: 2q+2
       497: q+2
       498: 3q+2
       499: 3q+2
       500: q^2+3q+2
       501: q^2+3q+2
       508: q+2
       509: 2
       510: q+2
       511: 2
       512: q+2
       513: q+2
       514: q^2+2q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: q+1
       548: q+1
       550: 1
       552: 1
       558: q+1
       559: q+1
       561: q
       562: q+1
       563: q+1
       564: q
       567: q+1
       568: q+1
       570: q+1
       572: q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       581: q+1
       590: q+2
       591: 1
       592: 1
       594: q+2
       595: 1
       596: 1
       599: q+1
       600: q+1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2q+2
       620: q+2
       621: 1
       622: 1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       642: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: q+1
       656: q+1
       657: 2
       664: q+2
       665: q+2
       672: 2
       673: q+2
       674: 2
       675: 1
       676: 2
       677: 2
       678: 2
       679: q+2
       680: q+2
       681: q+2
       682: q+2
       683: 3q+2
       684: q+2
       685: q^2+2q+2
       686: 2
       687: 2
       688: q+2
       689: q+2
       697: q+1
       700: q+1
       714: 1
       716: 1
       719: 1
       720: 1
       727: 1
       728: 1
       742: 1
       743: 1
       755: 1
       756: 1
       762: 1
       764: 1
       767: q+1
       768: q+1
       786: q+2
       787: 1
       788: 1
       791: 1
       792: 1
       794: 2
       802: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 2
       817: 1
       818: 1
       826: q+2
       827: 1
       828: 1
       830: q+2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       846: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       866: 2
       868: 2
       870: 2
       871: 1
       872: 2
       874: q+2
       875: q+2
       876: q+2
       877: 1
       878: 2
       879: 2
       880: q+2
       910: 1
       911: 1
       930: 1
       931: 1
       949: 1
       950: 1
       954: 1
       955: 1
       966: 1
       967: 1
       975: 1
       977: 1
       990: 1
       991: 1
       998: 1
       999: 1
      1001: 2
      1005: 2
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1027: 1
      1041: q+2
      1044: 1
      1045: 1
      1053: 1
      1057: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 2
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1132: 1
      1133: 1
      1135: 1
      1137: 1
      1182: 1
      1183: 1
      1208: 1
      1209: 1
      1235: 1
      1241: 1
      1250: 1
      1251: 1
      1255: 2
      1259: 2
      1260: 1
      1261: 1
      1269: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1398: 1
      1399: 1
      1401: 1
      1403: 1
      1469: 1
      1477: 1
      1484: 1
      1658: 1

1659:    0: q^3+10q^2+7q+2
         1: q^3+10q^2+7q+2
         2: 3q^3+7q^2+6q+2
         3: q^3+10q^2+7q+2
         4: 3q^3+7q^2+6q+2
         5: q^3+10q^2+7q+2
         6: q^4+5q^3+8q^2+6q+2
         7: q^5+q^4+2q^3+6q^2+5q+2
         8: 3q^3+7q^2+6q+2
         9: q^5+q^4+2q^3+6q^2+5q+2
        10: 6q^2+6q+2
        11: 6q^2+6q+2
        12: 2q^3+5q^2+5q+2
        13: 6q^2+6q+2
        14: q^3+5q^2+5q+2
        15: 6q^2+6q+2
        16: q^3+10q^2+7q+2
        17: q^3+10q^2+7q+2
        18: q^5+q^4+2q^3+6q^2+5q+2
        19: 6q^2+6q+2
        20: q^3+7q^2+6q+2
        21: q^3+5q^2+5q+2
        22: q^3+10q^2+7q+2
        23: q^3+10q^2+7q+2
        24: 3q^3+7q^2+6q+2
        25: q^3+10q^2+7q+2
        26: q^3+10q^2+7q+2
        27: 3q^3+7q^2+6q+2
        28: 6q^2+6q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: 6q^2+6q+2
        32: 6q^2+6q+2
        33: q^3+10q^2+7q+2
        34: 6q^2+6q+2
        35: 6q^2+6q+2
        36: q^3+10q^2+7q+2
        37: q^3+5q^2+5q+2
        38: 5q^2+2q
        39: q^3+5q^2+5q+2
        40: 5q^2+2q
        41: 2q^3+4q^2+4q+2
        42: q^3+3q^2+2q
        43: 2q^2+5q+2
        44: 3q^2+4q+2
        45: 2q^2+5q+2
        46: 6q^2+6q+2
        47: 6q^2+6q+2
        48: q^3+5q^2+5q+2
        49: 6q^2+6q+2
        50: q^3+7q^2+6q+2
        51: q^3+5q^2+5q+2
        52: 6q^2+6q+2
        53: q^3+7q^2+6q+2
        54: q^3+5q^2+5q+2
        55: 6q^2+6q+2
        56: q^3+7q^2+6q+2
        57: q^3+5q^2+5q+2
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: 4q^2+4q+2
        63: 2q^2+2q
        64: 3q^2+4q+2
        65: 3q^2+2q
        66: q^3+5q^2+5q+2
        67: 5q^2+2q
        68: 4q+2
        69: 4q^2+5q+2
        70: 2q^2+4q+2
        71: 4q^2+5q+2
        72: 3q^2+5q+2
        73: 3q^2+5q+2
        74: 2q^2+4q+2
        75: q^2+2q
        76: q^3+2q^2+4q+2
        77: 2q^2+2q
        78: 3q^2+3q+2
        79: q^2+2q
        80: 2q^2+5q+2
        81: 6q^2+6q+2
        82: 4q^2+5q+2
        83: 4q^2+5q+2
        84: 2q^2+5q+2
        85: 6q^2+6q+2
        86: 4q^2+5q+2
        87: 4q^2+5q+2
        88: 2q^2+5q+2
        89: 2q^2+5q+2
        90: 3q^2+4q+2
        91: 2q^2+5q+2
        92: 3q^2+5q+2
        93: 2q^2+5q+2
        94: 6q^2+6q+2
        95: q^3+7q^2+6q+2
        96: q^3+5q^2+5q+2
        97: 6q^2+6q+2
        98: q^3+7q^2+6q+2
        99: q^3+5q^2+5q+2
       100: 6q^2+6q+2
       101: q^3+7q^2+6q+2
       102: q^3+5q^2+5q+2
       103: 2q^2+2q+1
       104: q^2+q
       105: q^2+q
       106: 2q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: 3q+2
       112: 2q
       113: 2q^2+3q+2
       114: 2q
       115: 2q^2+3q+2
       116: q^2+2q
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q^2+3q+2
       122: 2q
       123: 3q^2+4q+2
       124: 3q^2+2q
       125: 4q+2
       126: 2q^2+4q+2
       127: 2q^2+4q+2
       128: q^2+2q
       129: q^3+2q^2+4q+2
       130: 2q^2+2q
       131: 3q^2+3q+2
       132: q^2+2q
       133: 3q+2
       134: 2q^2+5q+2
       135: q^2+4q+2
       136: q^2+4q+2
       137: 2q^2+5q+2
       138: 4q^2+5q+2
       139: 4q^2+5q+2
       140: 3q^2+5q+2
       141: 2q^2+4q+2
       142: 3q^2+5q+2
       143: 2q^2+5q+2
       144: 4q^2+5q+2
       145: 4q^2+5q+2
       146: 2q^2+4q+2
       147: 3q^2+5q+2
       148: 3q^2+5q+2
       149: 4q^2+5q+2
       150: 4q^2+5q+2
       151: 2q^2+4q+2
       152: q^2+2q
       153: q^3+2q^2+4q+2
       154: 2q^2+2q
       155: 3q^2+3q+2
       156: q^2+2q
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q^2+5q+2
       161: 3q^2+5q+2
       162: 2q^2+5q+2
       163: 2q^2+5q+2
       164: 3q^2+5q+2
       165: 2q^2+5q+2
       166: 6q^2+6q+2
       167: q^3+7q^2+6q+2
       168: q^3+5q^2+5q+2
       169: q+1
       170: q
       171: q
       172: q+1
       173: q+1
       174: q
       175: q
       176: q+1
       177: 2q^2+3q+2
       178: q^2+2q
       179: 2q^2+3q+2
       180: 2q
       181: 3q+2
       182: 2q
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q+2
       188: 2q
       189: 2q^2+2q+2
       190: 2q
       191: 2q+1
       192: 2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: 3q+2
       198: 2q
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 3q+2
       206: 2q
       207: 2q^2+3q+2
       208: 2q
       209: 2q^2+3q+2
       210: 2q
       211: 2q^2+3q+2
       212: q^2+2q
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: 3q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q^2+4q+2
       224: q+2
       225: q^2+4q+2
       226: 2q^2+4q+2
       227: 3q+2
       228: 2q^2+5q+2
       229: q^2+4q+2
       230: q^2+4q+2
       231: 2q^2+4q+2
       232: 3q+2
       233: 2q^2+5q+2
       234: q^2+4q+2
       235: q^2+4q+2
       236: 4q^2+5q+2
       237: 2q^2+4q+2
       238: q^2+2q
       239: q^3+2q^2+4q+2
       240: 2q^2+2q
       241: 3q^2+3q+2
       242: q^2+2q
       243: 4q^2+5q+2
       244: 3q^2+5q+2
       245: 3q^2+5q+2
       246: 2q^2+4q+2
       247: 8q+2
       248: 8q+2
       249: 3q^2+4q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q^2+5q+2
       257: 3q^2+5q+2
       258: 2q^2+5q+2
       259: q+1
       260: q
       261: q
       262: q+1
       263: 1
       264: q
       265: q
       266: 1
       267: q+1
       268: q
       269: q+1
       270: q
       271: q+1
       272: q
       273: q+1
       274: q
       275: q+1
       276: q
       277: q
       278: q+1
       279: q+2
       281: 2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 2q^2+2q+2
       288: 2q
       289: q+2
       291: 2q+2
       292: 2q
       293: 1
       294: 1
       295: 1
       296: 1
       297: q+2
       299: q+1
       300: q+1
       301: 3q+2
       302: 2q
       303: q+1
       304: q+1
       305: 2q+2
       306: 2q
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 3q+2
       312: 2q
       313: 2q+2
       314: 2q
       315: 2q^2+3q+2
       316: q^2+2q
       317: 2q^2+3q+2
       318: 2q
       319: q^2+2q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: 3q+2
       324: 2q
       325: 2q^2+2q+2
       326: 2q
       333: q+2
       334: q+2
       335: q+2
       336: 3q+1
       337: 6q+2
       338: 5q+2
       339: 3q
       340: 5q+2
       341: 3q
       342: 2q^2+3q+1
       343: q^2+q
       344: 3q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q^2+4q+2
       349: q+2
       350: q^2+4q+2
       351: 8q+2
       352: 3q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q^2+4q+2
       357: q+2
       358: q^2+4q+2
       359: 8q+2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: 2q^2+4q+2
       367: 3q+2
       368: 2q^2+5q+2
       369: q^2+4q+2
       370: q^2+4q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       378: q
       379: q
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: q+1
       390: q
       391: q+1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: q+1
       398: q
       399: q+1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: q+1
       406: q+1
       407: q
       408: q
       413: q+2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: q+2
       425: 2q+1
       426: q
       427: 4q+2
       428: 2q
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 2q+2
       434: 2q
       435: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       441: q+2
       443: 3q+1
       444: 3q+1
       445: 5q+2
       446: 3q
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: 2q+2
       452: 2q
       453: 1
       454: 1
       455: q+2
       457: 1
       458: 1
       459: q+2
       461: 3q+1
       462: 3q+1
       463: 5q+2
       464: 3q
       465: q+2
       467: 2q+2
       469: 2q^2+2q+2
       470: 2q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q+2
       476: 2q
       477: 3q+2
       478: 2q
       479: 4q+2
       480: 4q
       481: 2
       482: 2
       483: q+1
       484: 2q+2
       485: 2
       487: 2
       489: q+1
       491: q+1
       492: q+2
       493: q+2
       494: q+2
       495: 3q+1
       496: 3q+2
       497: q+2
       498: q+2
       499: q+2
       500: 3q+1
       501: 3q+2
       508: 3q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q^2+4q+2
       513: q+2
       514: q^2+4q+2
       515: 3q+2
       516: 3q+2
       517: q^2+2q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       529: 1
       532: 1
       533: 1
       534: q
       535: q
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2q+1
       546: q
       547: 2q+1
       548: q
       549: 1
       550: q
       551: q
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2q+1
       562: q
       563: 2q+1
       564: q
       565: 1
       566: q
       567: q
       568: 1
       569: q+1
       570: q+1
       571: q
       572: q
       573: q+1
       574: 2q
       575: q+1
       576: 2q
       577: 3q+2
       578: q
       580: 2q
       581: 2q
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       601: 2
       603: 1
       604: 1
       605: q+2
       607: 1
       608: 1
       609: q+2
       613: 2q+1
       614: q
       615: q+1
       616: q+1
       617: 2
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+2
       625: q+2
       629: 2q+1
       630: q
       631: q+1
       632: q+1
       633: 2
       639: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q+2
       646: 2q
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+2
       653: q+2
       655: q+2
       656: 2q
       657: 2q+2
       658: 2
       660: 2
       662: q+1
       664: q+1
       665: 1
       672: 2
       673: 1
       674: 3q+2
       675: 2
       676: 2
       677: q+1
       678: 2
       679: q+1
       680: 3q+2
       681: 2
       682: 2
       683: q+1
       684: 2
       685: q+1
       686: q+2
       687: q+2
       688: q+2
       689: 3q+1
       690: 2
       691: 2
       692: q+1
       693: q+1
       696: q
       697: q+1
       698: q
       699: q
       700: q
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       749: 1
       751: 1
       753: 1
       754: q
       755: q
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       775: 2
       779: 1
       781: 1
       791: 1
       793: q+1
       794: q+1
       795: 2
       797: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       811: q+1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       821: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       835: q+1
       839: 1
       840: 1
       843: q+2
       844: 2q
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: q+2
       855: 2q+1
       856: q
       857: 2
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       879: q+1
       880: q+1
       884: 1
       889: 1
       916: 1
       918: 1
       920: 1
       922: 1
       940: 1
       942: 1
       944: 1
       946: 1
       960: 1
       961: 1
       964: 1
       965: q
       966: q
       967: 1
       968: 2
       974: 1
       975: 1
       988: 1
       991: 1
       994: 1
      1008: 1
      1010: 2
      1012: 1
      1016: 1
      1017: 1
      1020: 1
      1022: 1
      1032: 1
      1033: 1
      1036: 1
      1038: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1091: 1
      1138: 1
      1140: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1220: 1
      1224: 1
      1230: 1
      1248: 1
      1266: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1430: 1
      1432: 1
      1436: 1
      1464: 1
      1474: 1
      1482: 1
      1487: 1
      1659: 1

1660:    0: q^3+10q^2+7q+2
         1: q^3+10q^2+7q+2
         2: 3q^3+7q^2+6q+2
         3: q^3+10q^2+7q+2
         4: 3q^3+7q^2+6q+2
         5: q^3+10q^2+7q+2
         6: q^4+5q^3+8q^2+6q+2
         7: q^5+q^4+2q^3+6q^2+5q+2
         8: 3q^3+7q^2+6q+2
         9: q^5+q^4+2q^3+6q^2+5q+2
        10: 6q^2+6q+2
        11: 6q^2+6q+2
        12: 2q^3+5q^2+5q+2
        13: 6q^2+6q+2
        14: q^3+5q^2+5q+2
        15: 6q^2+6q+2
        16: q^3+10q^2+7q+2
        17: q^3+10q^2+7q+2
        18: q^5+q^4+2q^3+6q^2+5q+2
        19: 6q^2+6q+2
        20: q^3+7q^2+6q+2
        21: q^3+5q^2+5q+2
        22: q^3+10q^2+7q+2
        23: q^3+10q^2+7q+2
        24: 3q^3+7q^2+6q+2
        25: q^3+10q^2+7q+2
        26: q^3+10q^2+7q+2
        27: 3q^3+7q^2+6q+2
        28: 6q^2+6q+2
        29: 4q^2+5q+2
        30: 4q^2+5q+2
        31: 6q^2+6q+2
        32: 6q^2+6q+2
        33: q^3+10q^2+7q+2
        34: 6q^2+6q+2
        35: 6q^2+6q+2
        36: q^3+10q^2+7q+2
        37: 5q^2+2q
        38: q^3+5q^2+5q+2
        39: 5q^2+2q
        40: q^3+5q^2+5q+2
        41: q^3+3q^2+2q
        42: 2q^3+4q^2+4q+2
        43: 2q^2+5q+2
        44: 3q^2+4q+2
        45: 2q^2+5q+2
        46: 6q^2+6q+2
        47: 6q^2+6q+2
        48: q^3+5q^2+5q+2
        49: 6q^2+6q+2
        50: q^3+7q^2+6q+2
        51: q^3+5q^2+5q+2
        52: 6q^2+6q+2
        53: q^3+7q^2+6q+2
        54: q^3+5q^2+5q+2
        55: 6q^2+6q+2
        56: q^3+7q^2+6q+2
        57: q^3+5q^2+5q+2
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: 2q^2+2q
        63: 4q^2+4q+2
        64: 3q^2+2q
        65: 3q^2+4q+2
        66: 5q^2+2q
        67: q^3+5q^2+5q+2
        68: 4q+2
        69: 4q^2+5q+2
        70: 2q^2+4q+2
        71: 4q^2+5q+2
        72: 3q^2+5q+2
        73: 3q^2+5q+2
        74: q^2+2q
        75: 2q^2+4q+2
        76: 2q^2+2q
        77: q^3+2q^2+4q+2
        78: q^2+2q
        79: 3q^2+3q+2
        80: 2q^2+5q+2
        81: 6q^2+6q+2
        82: 4q^2+5q+2
        83: 4q^2+5q+2
        84: 2q^2+5q+2
        85: 6q^2+6q+2
        86: 4q^2+5q+2
        87: 4q^2+5q+2
        88: 2q^2+5q+2
        89: 2q^2+5q+2
        90: 3q^2+4q+2
        91: 2q^2+5q+2
        92: 3q^2+5q+2
        93: 2q^2+5q+2
        94: 6q^2+6q+2
        95: q^3+7q^2+6q+2
        96: q^3+5q^2+5q+2
        97: 6q^2+6q+2
        98: q^3+7q^2+6q+2
        99: q^3+5q^2+5q+2
       100: 6q^2+6q+2
       101: q^3+7q^2+6q+2
       102: q^3+5q^2+5q+2
       103: q^2+q
       104: 2q^2+2q+1
       105: 2q^2+2q+1
       106: q^2+q
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: 2q
       112: 3q+2
       113: 2q
       114: 2q^2+3q+2
       115: q^2+2q
       116: 2q^2+3q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q
       122: 2q^2+3q+2
       123: 3q^2+2q
       124: 3q^2+4q+2
       125: 4q+2
       126: 2q^2+4q+2
       127: q^2+2q
       128: 2q^2+4q+2
       129: 2q^2+2q
       130: q^3+2q^2+4q+2
       131: q^2+2q
       132: 3q^2+3q+2
       133: 3q+2
       134: 2q^2+5q+2
       135: q^2+4q+2
       136: q^2+4q+2
       137: 2q^2+5q+2
       138: 4q^2+5q+2
       139: 4q^2+5q+2
       140: 3q^2+5q+2
       141: 2q^2+4q+2
       142: 3q^2+5q+2
       143: 2q^2+5q+2
       144: 4q^2+5q+2
       145: 4q^2+5q+2
       146: 2q^2+4q+2
       147: 3q^2+5q+2
       148: 3q^2+5q+2
       149: 4q^2+5q+2
       150: 4q^2+5q+2
       151: q^2+2q
       152: 2q^2+4q+2
       153: 2q^2+2q
       154: q^3+2q^2+4q+2
       155: q^2+2q
       156: 3q^2+3q+2
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q^2+5q+2
       161: 3q^2+5q+2
       162: 2q^2+5q+2
       163: 2q^2+5q+2
       164: 3q^2+5q+2
       165: 2q^2+5q+2
       166: 6q^2+6q+2
       167: q^3+7q^2+6q+2
       168: q^3+5q^2+5q+2
       169: q
       170: q+1
       171: q+1
       172: q
       173: q
       174: q+1
       175: q+1
       176: q
       177: q^2+2q
       178: 2q^2+3q+2
       179: 2q
       180: 2q^2+3q+2
       181: 2q
       182: 3q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q
       188: 2q+2
       189: 2q
       190: 2q^2+2q+2
       191: 2q+1
       192: 2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: 2q
       198: 3q+2
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 2q
       206: 3q+2
       207: 2q
       208: 2q^2+3q+2
       209: 2q
       210: 2q^2+3q+2
       211: q^2+2q
       212: 2q^2+3q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: 3q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q^2+4q+2
       224: q+2
       225: q^2+4q+2
       226: 2q^2+4q+2
       227: 3q+2
       228: 2q^2+5q+2
       229: q^2+4q+2
       230: q^2+4q+2
       231: 2q^2+4q+2
       232: 3q+2
       233: 2q^2+5q+2
       234: q^2+4q+2
       235: q^2+4q+2
       236: 4q^2+5q+2
       237: q^2+2q
       238: 2q^2+4q+2
       239: 2q^2+2q
       240: q^3+2q^2+4q+2
       241: q^2+2q
       242: 3q^2+3q+2
       243: 4q^2+5q+2
       244: 3q^2+5q+2
       245: 3q^2+5q+2
       246: 2q^2+4q+2
       247: 8q+2
       248: 8q+2
       249: 3q^2+4q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q^2+5q+2
       257: 3q^2+5q+2
       258: 2q^2+5q+2
       259: q
       260: q+1
       261: q+1
       262: q
       263: q
       264: 1
       265: 1
       266: q
       267: q
       268: q+1
       269: q
       270: q+1
       271: q
       272: q+1
       273: q
       274: q+1
       275: q
       276: q+1
       277: q+1
       278: q
       280: q+2
       282: 2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 2q
       288: 2q^2+2q+2
       290: q+2
       291: 2q
       292: 2q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: q+2
       299: q+1
       300: q+1
       301: 2q
       302: 3q+2
       303: q+1
       304: q+1
       305: 2q
       306: 2q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q
       312: 3q+2
       313: 2q
       314: 2q+2
       315: q^2+2q
       316: 2q^2+3q+2
       317: 2q
       318: 2q^2+3q+2
       319: q^2+2q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: 2q
       324: 3q+2
       325: 2q
       326: 2q^2+2q+2
       333: q+2
       334: q+2
       335: q+2
       336: 3q+1
       337: 6q+2
       338: 3q
       339: 5q+2
       340: 3q
       341: 5q+2
       342: q^2+q
       343: 2q^2+3q+1
       344: 3q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q^2+4q+2
       349: q+2
       350: q^2+4q+2
       351: 8q+2
       352: 3q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q^2+4q+2
       357: q+2
       358: q^2+4q+2
       359: 8q+2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: 2q^2+4q+2
       367: 3q+2
       368: 2q^2+5q+2
       369: q^2+4q+2
       370: q^2+4q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: q
       378: 1
       379: 1
       380: q
       382: 1
       383: 1
       386: 1
       387: 1
       389: q
       390: q+1
       391: q
       392: q+1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: q+1
       399: q
       400: q+1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: q+1
       408: q+1
       414: q+2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: q+2
       425: q
       426: 2q+1
       427: 2q
       428: 4q+2
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 2q
       434: 2q+2
       436: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       442: q+2
       443: 3q+1
       444: 3q+1
       445: 3q
       446: 5q+2
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: 2q
       452: 2q+2
       453: 1
       454: 1
       456: q+2
       457: 1
       458: 1
       460: q+2
       461: 3q+1
       462: 3q+1
       463: 3q
       464: 5q+2
       466: q+2
       468: 2q+2
       469: 2q
       470: 2q^2+2q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: 2q+2
       477: 2q
       478: 3q+2
       479: 4q
       480: 4q+2
       481: 2
       482: 2
       483: q+1
       484: 2q+2
       486: 2
       488: 2
       490: q+1
       491: q+1
       492: q+2
       493: q+2
       494: q+2
       495: 3q+1
       496: 3q+2
       497: q+2
       498: q+2
       499: q+2
       500: 3q+1
       501: 3q+2
       508: 3q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q^2+4q+2
       513: q+2
       514: q^2+4q+2
       515: 3q+2
       516: 3q+2
       517: q^2+2q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       530: 1
       531: 1
       533: q
       534: 1
       535: 1
       536: q
       538: 1
       540: 1
       542: 1
       544: 1
       545: q
       546: 2q+1
       547: q
       548: 2q+1
       549: q
       550: 1
       551: 1
       552: q
       554: 1
       556: 1
       558: 1
       560: 1
       561: q
       562: 2q+1
       563: q
       564: 2q+1
       565: q
       566: 1
       567: 1
       568: q
       569: q
       570: q
       571: q+1
       572: q+1
       573: 2q
       574: q+1
       575: 2q
       576: q+1
       577: 2q
       578: 2q
       580: q
       581: 3q+2
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: q+1
       602: 2
       603: 1
       604: 1
       606: q+2
       607: 1
       608: 1
       610: q+2
       613: q
       614: 2q+1
       615: q+1
       616: q+1
       618: 2
       619: 1
       620: 1
       621: 1
       622: 1
       624: q+2
       626: q+2
       629: q
       630: 2q+1
       631: q+1
       632: q+1
       634: 2
       640: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q
       646: 2q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+2
       654: q+2
       655: 2q
       656: q+2
       657: 2q+2
       659: 2
       661: 2
       663: q+1
       664: q+1
       665: 1
       672: 2
       673: 1
       674: 3q+2
       675: 2
       676: 2
       677: q+1
       678: 2
       679: q+1
       680: 3q+2
       681: 2
       682: 2
       683: q+1
       684: 2
       685: q+1
       686: q+2
       687: q+2
       688: q+2
       689: 3q+1
       690: 2
       691: 2
       692: q+1
       693: q
       694: q
       697: q
       699: q+1
       700: q+1
       701: q
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       750: 1
       752: 1
       753: q
       754: 1
       755: 1
       756: q
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       773: 2
       776: 2
       780: 1
       782: 1
       792: 1
       793: q+1
       794: q+1
       796: 2
       798: 2
       801: 1
       802: 1
       807: 1
       808: 1
       810: 1
       812: q+1
       815: 1
       816: 1
       817: q+1
       818: q+1
       820: 2
       822: 2
       825: 1
       826: 1
       831: 1
       832: 1
       834: 1
       836: q+1
       839: 1
       840: 1
       843: 2q
       844: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: q+2
       855: q
       856: 2q+1
       858: 2
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       879: q+1
       880: q+1
       890: 1
       891: 1
       917: 1
       919: 1
       921: 1
       923: 1
       941: 1
       943: 1
       945: 1
       947: 1
       962: 1
       963: 1
       964: q
       965: 1
       966: 1
       967: q
       972: 2
       976: 1
       977: 1
       989: 1
       990: 1
       995: 1
      1009: 1
      1011: 2
      1013: 1
      1016: 1
      1017: 1
      1021: 1
      1023: 1
      1032: 1
      1033: 1
      1037: 1
      1039: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1092: 1
      1093: 1
      1142: 1
      1143: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1221: 1
      1225: 1
      1231: 1
      1249: 1
      1267: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1434: 1
      1435: 1
      1437: 1
      1465: 1
      1475: 1
      1483: 1
      1487: 1
      1660: 1

1661:    0: 22q^2+12q+2
         1: 22q^2+12q+2
         2: 7q^3+16q^2+11q+2
         3: 22q^2+12q+2
         4: 2q^4+10q^3+14q^2+9q+2
         5: 22q^2+12q+2
         6: 2q^4+10q^3+14q^2+9q+2
         7: q^5+3q^4+7q^3+11q^2+8q+2
         8: 7q^3+16q^2+11q+2
         9: q^5+3q^4+7q^3+11q^2+8q+2
        10: 22q^2+12q+2
        11: 22q^2+12q+2
        12: 2q^4+10q^3+14q^2+9q+2
        13: 15q^2+11q+2
        14: q^4+5q^3+10q^2+8q+2
        15: 15q^2+11q+2
        16: 22q^2+12q+2
        17: 22q^2+12q+2
        18: q^5+3q^4+7q^3+11q^2+8q+2
        19: 11q^2+9q+2
        20: 11q^2+9q+2
        21: 2q^3+8q^2+8q+2
        22: 22q^2+12q+2
        23: 22q^2+12q+2
        24: 7q^3+16q^2+11q+2
        25: 22q^2+12q+2
        26: 22q^2+12q+2
        27: 7q^3+16q^2+11q+2
        28: 22q^2+12q+2
        29: 11q^2+9q+2
        30: 7q^2+8q+2
        31: 22q^2+12q+2
        32: 15q^2+11q+2
        33: 22q^2+12q+2
        34: 22q^2+12q+2
        35: 15q^2+11q+2
        36: 22q^2+12q+2
        37: 14q^2+10q+2
        38: 8q^2+2q
        39: 14q^2+10q+2
        40: 8q^2+2q
        41: 4q^3+11q^2+9q+2
        42: 3q^3+5q^2+2q
        43: 15q^2+11q+2
        44: q^4+5q^3+10q^2+8q+2
        45: 15q^2+11q+2
        46: 15q^2+11q+2
        47: 15q^2+11q+2
        48: q^4+5q^3+10q^2+8q+2
        49: 11q^2+9q+2
        50: 11q^2+9q+2
        51: 2q^3+8q^2+8q+2
        52: 11q^2+9q+2
        53: 11q^2+9q+2
        54: 2q^3+8q^2+8q+2
        55: 11q^2+9q+2
        56: 11q^2+9q+2
        57: 2q^3+8q^2+8q+2
        58: 11q^2+6q+1
        59: 11q^2+6q+1
        60: 11q^2+6q+1
        61: 11q^2+6q+1
        62: 14q^2+10q+2
        63: 8q^2+2q
        64: 10q^2+9q+2
        65: 5q^2+2q
        66: 14q^2+10q+2
        67: 8q^2+2q
        68: 8q^2+10q+2
        69: 7q^2+8q+2
        70: 7q^2+8q+2
        71: 11q^2+9q+2
        72: 4q^2+6q+2
        73: 4q^2+6q+2
        74: 4q^2+7q+2
        76: 4q^2+7q+2
        78: 4q^2+6q+2
        80: 15q^2+11q+2
        81: 15q^2+11q+2
        82: 11q^2+9q+2
        83: 7q^2+8q+2
        84: 15q^2+11q+2
        85: 15q^2+11q+2
        86: 11q^2+9q+2
        87: 7q^2+8q+2
        88: 15q^2+11q+2
        89: 15q^2+11q+2
        90: q^4+5q^3+10q^2+8q+2
        91: 3q^2+8q+2
        92: 5q^2+8q+2
        93: 3q^2+8q+2
        94: 11q^2+9q+2
        95: 11q^2+9q+2
        96: 2q^3+8q^2+8q+2
        97: 11q^2+9q+2
        98: 11q^2+9q+2
        99: 2q^3+8q^2+8q+2
       100: 11q^2+9q+2
       101: 11q^2+9q+2
       102: 2q^3+8q^2+8q+2
       103: 7q^2+5q+1
       104: 4q^2+q
       105: 4q^2+q
       106: 7q^2+5q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 4q+2
       113: 4q^2+7q+2
       115: 3q^2+6q+2
       117: 4q^2+5q+1
       118: 4q^2+5q+1
       119: 4q^2+5q+1
       120: 4q^2+5q+1
       121: 10q^2+9q+2
       122: 5q^2+2q
       123: 10q^2+9q+2
       124: 5q^2+2q
       125: 8q^2+10q+2
       126: 7q^2+8q+2
       127: 4q^2+7q+2
       129: 4q^2+7q+2
       131: 4q^2+6q+2
       133: q^2+7q+2
       134: 3q^2+8q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 15q^2+11q+2
       138: 7q^2+8q+2
       139: 11q^2+9q+2
       140: 4q^2+6q+2
       141: 7q^2+8q+2
       142: 4q^2+6q+2
       143: 15q^2+11q+2
       144: 7q^2+8q+2
       145: 11q^2+9q+2
       146: 7q^2+8q+2
       147: 4q^2+6q+2
       148: 4q^2+6q+2
       149: 11q^2+9q+2
       150: 7q^2+8q+2
       151: 4q^2+7q+2
       153: 4q^2+7q+2
       155: 4q^2+6q+2
       157: 3q^2+8q+2
       158: 5q^2+8q+2
       159: 3q^2+8q+2
       160: 3q^2+8q+2
       161: 5q^2+8q+2
       162: 3q^2+8q+2
       163: 3q^2+8q+2
       164: 5q^2+8q+2
       165: 3q^2+8q+2
       166: 11q^2+9q+2
       167: 11q^2+9q+2
       168: 2q^3+8q^2+8q+2
       169: 2q+1
       172: 2q+1
       173: 3q^2+4q+1
       174: q^2+q
       175: q^2+q
       176: 3q^2+4q+1
       177: 3q^2+6q+2
       179: 4q^2+7q+2
       181: 4q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 3q+2
       189: 3q^2+6q+2
       191: 4q^2+5q+1
       192: 4q^2+5q+1
       193: 2q^2+3q+1
       194: 2q^2+3q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       197: 4q+2
       199: 4q^2+5q+1
       200: 4q^2+5q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 2q^2+3q+1
       205: 4q+2
       207: 10q^2+9q+2
       208: 5q^2+2q
       209: 4q^2+7q+2
       211: 3q^2+6q+2
       213: 4q+2
       215: q^2+4q+2
       217: 4q+2
       219: q^2+7q+2
       220: q^2+7q+2
       221: 3q^2+8q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 7q^2+8q+2
       227: q^2+7q+2
       228: 3q^2+8q+2
       229: q^2+5q+2
       230: q^2+5q+2
       231: 7q^2+8q+2
       232: q^2+7q+2
       233: 3q^2+8q+2
       234: q^2+5q+2
       235: q^2+5q+2
       236: 7q^2+8q+2
       237: 4q^2+7q+2
       239: 4q^2+7q+2
       241: 4q^2+6q+2
       243: 11q^2+9q+2
       244: 4q^2+6q+2
       245: 4q^2+6q+2
       246: 7q^2+8q+2
       247: 4q+4
       248: 4q+4
       249: 2q^2+3q+1
       250: 3q^2+8q+2
       251: 5q^2+8q+2
       252: 3q^2+8q+2
       253: 3q^2+8q+2
       254: 5q^2+8q+2
       255: 3q^2+8q+2
       256: 3q^2+8q+2
       257: 5q^2+8q+2
       258: 3q^2+8q+2
       259: 2q+1
       262: 2q+1
       263: q+1
       266: q+1
       267: 2q+1
       269: 2q+1
       271: 2q+1
       273: 2q+1
       275: 3q^2+4q+1
       276: q^2+q
       277: q^2+q
       278: 3q^2+4q+1
       279: 3q+2
       281: 4q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 3q^2+6q+2
       289: q+2
       291: 3q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 3q+2
       299: 2q+1
       300: 2q+1
       301: 4q+2
       303: 2q+1
       304: 2q+1
       305: 3q+2
       307: 2q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       311: 4q+2
       313: 3q+2
       315: 3q^2+6q+2
       317: 4q^2+7q+2
       319: 2q^2+3q+1
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: 4q+2
       325: 3q^2+6q+2
       327: 4q+2
       329: q^2+4q+2
       331: 4q+2
       333: q^2+7q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: q+1
       337: 4q+4
       338: 4q+4
       340: 4q+4
       342: 2q^2+3q+1
       344: q^2+7q+2
       345: q^2+7q+2
       346: 3q^2+8q+2
       347: q^2+5q+2
       348: q^2+5q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 4q+4
       352: q^2+7q+2
       353: q^2+7q+2
       354: 3q^2+8q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: q^2+5q+2
       358: q^2+5q+2
       359: 4q+4
       360: 4q+2
       362: q^2+4q+2
       364: 4q+2
       366: 7q^2+8q+2
       367: q^2+7q+2
       368: 3q^2+8q+2
       369: q^2+5q+2
       370: q^2+5q+2
       371: 4
       372: 4
       373: 2q+1
       374: 3q^2+8q+2
       375: 5q^2+8q+2
       376: 3q^2+8q+2
       377: q+1
       380: q+1
       381: 1
       384: 1
       385: q+1
       388: q+1
       389: 2q+1
       391: 2q+1
       393: q+1
       396: q+1
       397: 2q+1
       399: 2q+1
       401: q+1
       404: q+1
       405: 2q+1
       406: 2q+1
       409: 3q+2
       411: 4q+2
       413: 3q+2
       415: q+2
       417: q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 3q+2
       425: q+1
       427: 4q+4
       429: 2q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       433: 3q+2
       435: q+2
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: 3q+2
       443: 2q+2
       444: 2q+2
       445: 4q+4
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 3q+2
       453: 2q+1
       454: 2q+1
       455: q+2
       457: 2q+1
       458: 2q+1
       459: 3q+2
       461: 2q+2
       462: 2q+2
       463: 4q+4
       465: 3q+2
       467: 4q+2
       469: 3q^2+6q+2
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       475: 3q+2
       477: 4q+2
       479: 2q+2
       480: 2q+2
       481: 2q+2
       482: 2q+2
       483: q+1
       484: 4
       485: 4
       487: 4
       489: 2q+1
       491: 1
       492: q^2+7q+2
       493: q^2+5q+2
       494: q^2+5q+2
       495: q+1
       496: 4
       497: q^2+7q+2
       498: q^2+5q+2
       499: q^2+5q+2
       500: q+1
       501: 4
       502: 4q+2
       504: q^2+4q+2
       506: 4q+2
       508: q^2+7q+2
       509: q^2+7q+2
       510: 3q^2+8q+2
       511: q^2+5q+2
       512: q^2+5q+2
       513: q^2+5q+2
       514: q^2+5q+2
       515: 4
       516: 4
       517: 2q+1
       518: 4
       519: 4
       520: 2q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: q+1
       532: q+1
       533: q+1
       536: q+1
       537: 1
       539: 1
       541: q+1
       543: q+1
       545: 2q+2
       547: 2q+2
       549: q+1
       552: q+1
       553: 1
       555: 1
       557: q+1
       559: q+1
       561: 2q+2
       563: 2q+2
       565: q+1
       568: q+1
       569: 2q+1
       570: 2q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 2q+2
       580: 2q+2
       583: 3q+2
       585: 2
       587: q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       597: 1
       599: q+1
       601: 4
       603: 2q+1
       604: 2q+1
       605: q+2
       607: 2q+1
       608: 2q+1
       609: 3q+2
       611: q+2
       613: q+1
       615: 2
       616: 2
       617: 4
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: q+2
       625: 3q+2
       627: q+2
       629: q+1
       631: 2
       632: 2
       633: 4
       635: 3q+2
       637: 4q+2
       639: 3q+2
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: 3q+2
       647: 2q+1
       648: 2q+1
       649: 2q+1
       650: 2q+1
       651: q+2
       653: 3q+2
       655: 2
       656: 2
       657: 4
       658: 4
       660: 4
       662: 2q+1
       664: 1
       665: 1
       666: 4
       668: 4
       670: 2q+1
       672: 4
       673: 1
       674: 4
       675: 2q+2
       676: 2q+2
       677: q+1
       678: 4
       679: 1
       680: 4
       681: 2q+2
       682: 2q+2
       683: q+1
       684: 4
       685: 1
       686: q^2+7q+2
       687: q^2+5q+2
       688: q^2+5q+2
       689: q+1
       690: 4
       691: 4
       692: 2q+1
       693: q+1
       696: q+1
       697: q+1
       698: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: q+1
       727: q+1
       729: 1
       731: 1
       733: 2
       735: 2
       737: 1
       739: 1
       741: q+1
       743: q+1
       745: 1
       747: 1
       749: 2
       751: 2
       753: q+1
       756: q+1
       757: 1
       758: 1
       761: q+1
       762: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       775: 4
       777: 2
       779: 1
       781: 1
       783: 1
       789: 4
       793: 2
       794: 2
       795: 4
       797: 2
       799: q+2
       801: q+1
       802: q+1
       807: q+1
       808: q+1
       809: 1
       811: q+1
       813: 4
       815: 2
       816: 2
       817: 2
       818: 2
       819: 4
       821: 2
       823: q+2
       825: q+1
       826: q+1
       831: q+1
       832: q+1
       833: 1
       835: q+1
       837: 4
       839: 2
       840: 2
       841: 3q+2
       843: 2
       844: 2
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: q+2
       851: 3q+2
       853: q+2
       855: q+1
       857: 2
       858: 2
       859: 4
       861: 4
       863: 2q+1
       865: 4
       866: 1
       867: 1
       868: 1
       869: 4
       870: 1
       871: 1
       872: 1
       873: 4
       874: 1
       875: 1
       876: 1
       877: 2q+2
       878: 2q+2
       879: q+1
       880: 1
       884: 1
       887: 1
       888: 1
       889: 1
       896: 1
       899: 1
       912: 1
       914: 1
       916: 2
       918: 2
       920: 1
       922: 1
       932: 2
       934: 2
       936: 1
       938: 1
       940: 2
       942: 2
       944: 1
       946: 1
       956: 2
       958: 2
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: q+1
       975: q+1
       978: 1
       979: 1
       982: 2
       985: 2
       988: 1
       989: 1
       990: 1
       991: 1
       992: 4
       994: 1
       996: 1
      1002: 1
      1014: 4
      1016: 2
      1017: 2
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 4
      1032: 2
      1033: 2
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1047: 2
      1048: 2
      1050: q+2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1098: 1
      1101: 1
      1102: 1
      1103: 1
      1144: 2
      1146: 2
      1148: 1
      1150: 1
      1164: 2
      1166: 2
      1168: 1
      1170: 1
      1184: 1
      1185: 1
      1188: 2
      1191: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1214: 1
      1230: 1
      1236: 1
      1238: 1
      1248: 1
      1252: 1
      1256: 1
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1305: 1
      1306: 1
      1307: 1
      1414: 1
      1415: 1
      1448: 1
      1456: 1
      1464: 1
      1470: 1
      1472: 1
      1487: 1
      1661: 1

1662:    0: 22q^2+12q+2
         1: 22q^2+12q+2
         2: 7q^3+16q^2+11q+2
         3: 22q^2+12q+2
         4: 2q^4+10q^3+14q^2+9q+2
         5: 22q^2+12q+2
         6: 2q^4+10q^3+14q^2+9q+2
         7: q^5+3q^4+7q^3+11q^2+8q+2
         8: 7q^3+16q^2+11q+2
         9: q^5+3q^4+7q^3+11q^2+8q+2
        10: 22q^2+12q+2
        11: 22q^2+12q+2
        12: 2q^4+10q^3+14q^2+9q+2
        13: 15q^2+11q+2
        14: q^4+5q^3+10q^2+8q+2
        15: 15q^2+11q+2
        16: 22q^2+12q+2
        17: 22q^2+12q+2
        18: q^5+3q^4+7q^3+11q^2+8q+2
        19: 11q^2+9q+2
        20: 11q^2+9q+2
        21: 2q^3+8q^2+8q+2
        22: 22q^2+12q+2
        23: 22q^2+12q+2
        24: 7q^3+16q^2+11q+2
        25: 22q^2+12q+2
        26: 22q^2+12q+2
        27: 7q^3+16q^2+11q+2
        28: 22q^2+12q+2
        29: 11q^2+9q+2
        30: 7q^2+8q+2
        31: 22q^2+12q+2
        32: 15q^2+11q+2
        33: 22q^2+12q+2
        34: 22q^2+12q+2
        35: 15q^2+11q+2
        36: 22q^2+12q+2
        37: 8q^2+2q
        38: 14q^2+10q+2
        39: 8q^2+2q
        40: 14q^2+10q+2
        41: 3q^3+5q^2+2q
        42: 4q^3+11q^2+9q+2
        43: 15q^2+11q+2
        44: q^4+5q^3+10q^2+8q+2
        45: 15q^2+11q+2
        46: 15q^2+11q+2
        47: 15q^2+11q+2
        48: q^4+5q^3+10q^2+8q+2
        49: 11q^2+9q+2
        50: 11q^2+9q+2
        51: 2q^3+8q^2+8q+2
        52: 11q^2+9q+2
        53: 11q^2+9q+2
        54: 2q^3+8q^2+8q+2
        55: 11q^2+9q+2
        56: 11q^2+9q+2
        57: 2q^3+8q^2+8q+2
        58: 11q^2+6q+1
        59: 11q^2+6q+1
        60: 11q^2+6q+1
        61: 11q^2+6q+1
        62: 8q^2+2q
        63: 14q^2+10q+2
        64: 5q^2+2q
        65: 10q^2+9q+2
        66: 8q^2+2q
        67: 14q^2+10q+2
        68: 8q^2+10q+2
        69: 7q^2+8q+2
        70: 7q^2+8q+2
        71: 11q^2+9q+2
        72: 4q^2+6q+2
        73: 4q^2+6q+2
        75: 4q^2+7q+2
        77: 4q^2+7q+2
        79: 4q^2+6q+2
        80: 15q^2+11q+2
        81: 15q^2+11q+2
        82: 11q^2+9q+2
        83: 7q^2+8q+2
        84: 15q^2+11q+2
        85: 15q^2+11q+2
        86: 11q^2+9q+2
        87: 7q^2+8q+2
        88: 15q^2+11q+2
        89: 15q^2+11q+2
        90: q^4+5q^3+10q^2+8q+2
        91: 3q^2+8q+2
        92: 5q^2+8q+2
        93: 3q^2+8q+2
        94: 11q^2+9q+2
        95: 11q^2+9q+2
        96: 2q^3+8q^2+8q+2
        97: 11q^2+9q+2
        98: 11q^2+9q+2
        99: 2q^3+8q^2+8q+2
       100: 11q^2+9q+2
       101: 11q^2+9q+2
       102: 2q^3+8q^2+8q+2
       103: 4q^2+q
       104: 7q^2+5q+1
       105: 7q^2+5q+1
       106: 4q^2+q
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       112: 4q+2
       114: 4q^2+7q+2
       116: 3q^2+6q+2
       117: 4q^2+5q+1
       118: 4q^2+5q+1
       119: 4q^2+5q+1
       120: 4q^2+5q+1
       121: 5q^2+2q
       122: 10q^2+9q+2
       123: 5q^2+2q
       124: 10q^2+9q+2
       125: 8q^2+10q+2
       126: 7q^2+8q+2
       128: 4q^2+7q+2
       130: 4q^2+7q+2
       132: 4q^2+6q+2
       133: q^2+7q+2
       134: 3q^2+8q+2
       135: q^2+5q+2
       136: q^2+5q+2
       137: 15q^2+11q+2
       138: 7q^2+8q+2
       139: 11q^2+9q+2
       140: 4q^2+6q+2
       141: 7q^2+8q+2
       142: 4q^2+6q+2
       143: 15q^2+11q+2
       144: 7q^2+8q+2
       145: 11q^2+9q+2
       146: 7q^2+8q+2
       147: 4q^2+6q+2
       148: 4q^2+6q+2
       149: 11q^2+9q+2
       150: 7q^2+8q+2
       152: 4q^2+7q+2
       154: 4q^2+7q+2
       156: 4q^2+6q+2
       157: 3q^2+8q+2
       158: 5q^2+8q+2
       159: 3q^2+8q+2
       160: 3q^2+8q+2
       161: 5q^2+8q+2
       162: 3q^2+8q+2
       163: 3q^2+8q+2
       164: 5q^2+8q+2
       165: 3q^2+8q+2
       166: 11q^2+9q+2
       167: 11q^2+9q+2
       168: 2q^3+8q^2+8q+2
       170: 2q+1
       171: 2q+1
       173: q^2+q
       174: 3q^2+4q+1
       175: 3q^2+4q+1
       176: q^2+q
       178: 3q^2+6q+2
       180: 4q^2+7q+2
       182: 4q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       188: 3q+2
       190: 3q^2+6q+2
       191: 4q^2+5q+1
       192: 4q^2+5q+1
       193: 2q^2+3q+1
       194: 2q^2+3q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       198: 4q+2
       199: 4q^2+5q+1
       200: 4q^2+5q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 2q^2+3q+1
       206: 4q+2
       207: 5q^2+2q
       208: 10q^2+9q+2
       210: 4q^2+7q+2
       212: 3q^2+6q+2
       214: 4q+2
       216: q^2+4q+2
       218: 4q+2
       219: q^2+7q+2
       220: q^2+7q+2
       221: 3q^2+8q+2
       222: q^2+5q+2
       223: q^2+5q+2
       224: q^2+5q+2
       225: q^2+5q+2
       226: 7q^2+8q+2
       227: q^2+7q+2
       228: 3q^2+8q+2
       229: q^2+5q+2
       230: q^2+5q+2
       231: 7q^2+8q+2
       232: q^2+7q+2
       233: 3q^2+8q+2
       234: q^2+5q+2
       235: q^2+5q+2
       236: 7q^2+8q+2
       238: 4q^2+7q+2
       240: 4q^2+7q+2
       242: 4q^2+6q+2
       243: 11q^2+9q+2
       244: 4q^2+6q+2
       245: 4q^2+6q+2
       246: 7q^2+8q+2
       247: 4q+4
       248: 4q+4
       249: 2q^2+3q+1
       250: 3q^2+8q+2
       251: 5q^2+8q+2
       252: 3q^2+8q+2
       253: 3q^2+8q+2
       254: 5q^2+8q+2
       255: 3q^2+8q+2
       256: 3q^2+8q+2
       257: 5q^2+8q+2
       258: 3q^2+8q+2
       260: 2q+1
       261: 2q+1
       264: q+1
       265: q+1
       268: 2q+1
       270: 2q+1
       272: 2q+1
       274: 2q+1
       275: q^2+q
       276: 3q^2+4q+1
       277: 3q^2+4q+1
       278: q^2+q
       280: 3q+2
       282: 4q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       288: 3q^2+6q+2
       290: q+2
       292: 3q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       298: 3q+2
       299: 2q+1
       300: 2q+1
       302: 4q+2
       303: 2q+1
       304: 2q+1
       306: 3q+2
       307: 2q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       312: 4q+2
       314: 3q+2
       316: 3q^2+6q+2
       318: 4q^2+7q+2
       319: 2q^2+3q+1
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       324: 4q+2
       326: 3q^2+6q+2
       328: 4q+2
       330: q^2+4q+2
       332: 4q+2
       333: q^2+7q+2
       334: q^2+5q+2
       335: q^2+5q+2
       336: q+1
       337: 4q+4
       339: 4q+4
       341: 4q+4
       343: 2q^2+3q+1
       344: q^2+7q+2
       345: q^2+7q+2
       346: 3q^2+8q+2
       347: q^2+5q+2
       348: q^2+5q+2
       349: q^2+5q+2
       350: q^2+5q+2
       351: 4q+4
       352: q^2+7q+2
       353: q^2+7q+2
       354: 3q^2+8q+2
       355: q^2+5q+2
       356: q^2+5q+2
       357: q^2+5q+2
       358: q^2+5q+2
       359: 4q+4
       361: 4q+2
       363: q^2+4q+2
       365: 4q+2
       366: 7q^2+8q+2
       367: q^2+7q+2
       368: 3q^2+8q+2
       369: q^2+5q+2
       370: q^2+5q+2
       371: 4
       372: 4
       373: 2q+1
       374: 3q^2+8q+2
       375: 5q^2+8q+2
       376: 3q^2+8q+2
       378: q+1
       379: q+1
       382: 1
       383: 1
       386: q+1
       387: q+1
       390: 2q+1
       392: 2q+1
       394: q+1
       395: q+1
       398: 2q+1
       400: 2q+1
       402: q+1
       403: q+1
       407: 2q+1
       408: 2q+1
       410: 3q+2
       412: 4q+2
       414: 3q+2
       416: q+2
       418: q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       424: 3q+2
       426: q+1
       428: 4q+4
       429: 2q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       434: 3q+2
       436: q+2
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       442: 3q+2
       443: 2q+2
       444: 2q+2
       446: 4q+4
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       452: 3q+2
       453: 2q+1
       454: 2q+1
       456: q+2
       457: 2q+1
       458: 2q+1
       460: 3q+2
       461: 2q+2
       462: 2q+2
       464: 4q+4
       466: 3q+2
       468: 4q+2
       470: 3q^2+6q+2
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       476: 3q+2
       478: 4q+2
       479: 2q+2
       480: 2q+2
       481: 2q+2
       482: 2q+2
       483: q+1
       484: 4
       486: 4
       488: 4
       490: 2q+1
       491: 1
       492: q^2+7q+2
       493: q^2+5q+2
       494: q^2+5q+2
       495: q+1
       496: 4
       497: q^2+7q+2
       498: q^2+5q+2
       499: q^2+5q+2
       500: q+1
       501: 4
       503: 4q+2
       505: q^2+4q+2
       507: 4q+2
       508: q^2+7q+2
       509: q^2+7q+2
       510: 3q^2+8q+2
       511: q^2+5q+2
       512: q^2+5q+2
       513: q^2+5q+2
       514: q^2+5q+2
       515: 4
       516: 4
       517: 2q+1
       518: 4
       519: 4
       520: 2q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: q+1
       531: q+1
       534: q+1
       535: q+1
       538: 1
       540: 1
       542: q+1
       544: q+1
       546: 2q+2
       548: 2q+2
       550: q+1
       551: q+1
       554: 1
       556: 1
       558: q+1
       560: q+1
       562: 2q+2
       564: 2q+2
       566: q+1
       567: q+1
       571: 2q+1
       572: 2q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       578: 2q+2
       581: 2q+2
       584: 3q+2
       586: 2
       588: q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       598: 1
       600: q+1
       602: 4
       603: 2q+1
       604: 2q+1
       606: q+2
       607: 2q+1
       608: 2q+1
       610: 3q+2
       612: q+2
       614: q+1
       615: 2
       616: 2
       618: 4
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       624: q+2
       626: 3q+2
       628: q+2
       630: q+1
       631: 2
       632: 2
       634: 4
       636: 3q+2
       638: 4q+2
       640: 3q+2
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       646: 3q+2
       647: 2q+1
       648: 2q+1
       649: 2q+1
       650: 2q+1
       652: q+2
       654: 3q+2
       655: 2
       656: 2
       657: 4
       659: 4
       661: 4
       663: 2q+1
       664: 1
       665: 1
       667: 4
       669: 4
       671: 2q+1
       672: 4
       673: 1
       674: 4
       675: 2q+2
       676: 2q+2
       677: q+1
       678: 4
       679: 1
       680: 4
       681: 2q+2
       682: 2q+2
       683: q+1
       684: 4
       685: 1
       686: q^2+7q+2
       687: q^2+5q+2
       688: q^2+5q+2
       689: q+1
       690: 4
       691: 4
       692: 2q+1
       694: q+1
       699: q+1
       700: q+1
       701: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: q+1
       728: q+1
       730: 1
       732: 1
       734: 2
       736: 2
       738: 1
       740: 1
       742: q+1
       744: q+1
       746: 1
       748: 1
       750: 2
       752: 2
       754: q+1
       755: q+1
       759: 1
       760: 1
       763: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       776: 4
       778: 2
       780: 1
       782: 1
       784: 1
       790: 4
       793: 2
       794: 2
       796: 4
       798: 2
       800: q+2
       801: q+1
       802: q+1
       807: q+1
       808: q+1
       810: 1
       812: q+1
       814: 4
       815: 2
       816: 2
       817: 2
       818: 2
       820: 4
       822: 2
       824: q+2
       825: q+1
       826: q+1
       831: q+1
       832: q+1
       834: 1
       836: q+1
       838: 4
       839: 2
       840: 2
       842: 3q+2
       843: 2
       844: 2
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       850: q+2
       852: 3q+2
       854: q+2
       856: q+1
       857: 2
       858: 2
       860: 4
       862: 4
       864: 2q+1
       865: 4
       866: 1
       867: 1
       868: 1
       869: 4
       870: 1
       871: 1
       872: 1
       873: 4
       874: 1
       875: 1
       876: 1
       877: 2q+2
       878: 2q+2
       879: q+1
       880: 1
       885: 1
       890: 1
       891: 1
       892: 1
       897: 1
       898: 1
       913: 1
       915: 1
       917: 2
       919: 2
       921: 1
       923: 1
       933: 2
       935: 2
       937: 1
       939: 1
       941: 2
       943: 2
       945: 1
       947: 1
       957: 2
       959: 2
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: q+1
       977: q+1
       980: 1
       981: 1
       983: 2
       986: 2
       988: 1
       989: 1
       990: 1
       991: 1
       993: 4
       995: 1
       997: 1
      1003: 1
      1015: 4
      1016: 2
      1017: 2
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 4
      1032: 2
      1033: 2
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1046: 2
      1047: 2
      1049: 2
      1051: q+2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1145: 2
      1147: 2
      1149: 1
      1151: 1
      1165: 2
      1167: 2
      1169: 1
      1171: 1
      1186: 1
      1187: 1
      1189: 2
      1192: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1215: 1
      1231: 1
      1237: 1
      1239: 1
      1249: 1
      1253: 1
      1257: 1
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1416: 1
      1417: 1
      1449: 1
      1457: 1
      1465: 1
      1471: 1
      1473: 1
      1487: 1
      1662: 1

1663:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^3+2q^2+3q+2
        19: 4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: 3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 4q+2
        50: 4q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: 3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 3q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: 4q+2
       101: 4q+2
       102: q^2+3q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: 4q+2
       138: 3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: q^2+3q+2
       169: 1
       171: 1
       173: q+1
       175: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q+2
       193: q+1
       194: q+1
       195: 2q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: 3q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       261: 1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: q+1
       277: q+1
       283: 1
       284: 1
       285: q+2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       295: q+2
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: q+2
       334: q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 4
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       379: 1
       385: 1
       387: 1
       389: 1
       392: 1
       393: 1
       395: 1
       397: 1
       398: 1
       401: 1
       402: 1
       405: 1
       408: 1
       419: 1
       420: 1
       421: q+2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       431: q+2
       433: 1
       434: 1
       437: 1
       438: 1
       439: q+2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       449: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       457: q+2
       459: 1
       460: 1
       461: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: q+1
       483: 2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: 2
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       529: 1
       531: 1
       533: 1
       535: 1
       541: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       557: 1
       558: 1
       561: 2
       562: 2
       565: 1
       567: 1
       569: 1
       572: 1
       573: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       591: 2
       595: q+1
       599: 1
       600: 1
       603: 1
       604: 1
       607: q+2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: q+2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       641: 1
       642: 1
       643: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       649: q+2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       675: 2
       676: q+1
       677: 2
       678: 2
       679: 1
       680: 2
       681: 2
       682: q+1
       683: 2
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       698: 1
       700: 1
       713: 1
       714: 1
       725: 1
       728: 1
       741: 1
       742: 1
       753: 1
       755: 1
       761: 1
       764: 1
       765: 1
       767: 1
       787: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: 2
       807: q+1
       811: 1
       812: 1
       815: 1
       816: 1
       817: 2
       825: 1
       826: 1
       827: 2
       831: q+1
       835: 1
       836: 1
       839: 2
       843: 1
       844: 1
       845: 1
       846: 1
       847: q+2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: q+1
       879: 2
       880: 1
       924: 1
       925: 1
       948: 1
       949: 1
       964: 1
       966: 1
       974: 1
       977: 1
       988: 1
       990: 1
       998: 1
      1006: 1
      1016: 1
      1017: 1
      1028: 1
      1032: 2
      1044: 1
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1054: 2
      1058: q+1
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1194: 1
      1196: 1
      1202: 1
      1203: 1
      1216: 1
      1232: 1
      1242: 1
      1250: 1
      1260: 1
      1270: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1450: 1
      1460: 1
      1466: 1
      1478: 1
      1487: 1
      1663: 1

1664:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^3+2q^2+3q+2
        19: 4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: 3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 4q+2
        50: 4q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 2q
        59: 4q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: 3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 3q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: 4q+2
       101: 4q+2
       102: q^2+3q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       118: 2q+2
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: 4q+2
       138: 3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: q^2+3q+2
       170: 1
       172: 1
       174: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       186: q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       192: 2q+2
       193: q+1
       194: q+1
       196: 2q+2
       197: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       204: 2q+2
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: 3q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: 1
       262: 1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       276: q+1
       278: q+1
       283: 1
       284: 1
       286: q+2
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       296: q+2
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       304: q+2
       305: 1
       306: 1
       307: 1
       308: 1
       310: q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       322: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: q+2
       334: q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 4
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       378: 1
       380: 1
       386: 1
       388: 1
       390: 1
       391: 1
       394: 1
       396: 1
       399: 1
       400: 1
       403: 1
       404: 1
       406: 1
       407: 1
       419: 1
       420: 1
       422: q+2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 1
       430: 1
       432: q+2
       433: 1
       434: 1
       437: 1
       438: 1
       440: q+2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: 1
       448: 1
       450: q+2
       451: 1
       452: 1
       453: 1
       454: 1
       458: q+2
       459: 1
       460: 1
       462: 4
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2
       482: q+1
       483: 2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: 2
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       530: 1
       532: 1
       534: 1
       536: 1
       542: 1
       543: 1
       545: 1
       546: 1
       547: 1
       548: 1
       551: 1
       552: 1
       559: 1
       560: 1
       563: 2
       564: 2
       566: 1
       568: 1
       570: 1
       571: 1
       574: 2
       575: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: 1
       590: 1
       592: 2
       596: q+1
       599: 1
       600: 1
       603: 1
       604: 1
       608: q+2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 1
       616: 1
       619: 1
       620: 1
       622: q+2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2
       641: 1
       642: 1
       644: q+2
       645: 1
       646: 1
       647: 1
       648: 1
       650: q+2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       675: 2
       676: q+1
       677: 2
       678: 2
       679: 1
       680: 2
       681: 2
       682: q+1
       683: 2
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       696: 1
       697: 1
       699: 1
       701: 1
       715: 1
       716: 1
       726: 1
       727: 1
       743: 1
       744: 1
       754: 1
       756: 1
       762: 1
       763: 1
       766: 1
       768: 1
       788: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: 2
       808: q+1
       811: 1
       812: 1
       815: 1
       816: 1
       818: 2
       825: 1
       826: 1
       828: 2
       832: q+1
       835: 1
       836: 1
       840: 2
       843: 1
       844: 1
       845: 1
       846: 1
       848: q+2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: q+1
       879: 2
       880: 1
       926: 1
       927: 1
       950: 1
       951: 1
       965: 1
       967: 1
       975: 1
       976: 1
       989: 1
       991: 1
       999: 1
      1007: 1
      1016: 1
      1017: 1
      1029: 1
      1033: 2
      1045: 1
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1055: 2
      1059: q+1
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1195: 1
      1197: 1
      1204: 1
      1205: 1
      1217: 1
      1233: 1
      1243: 1
      1251: 1
      1261: 1
      1271: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1451: 1
      1461: 1
      1467: 1
      1479: 1
      1487: 1
      1664: 1

1665:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^3+2q^2+3q+2
        19: 4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: 3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 4q+2
        50: 4q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 3q+1
        59: 3q+1
        60: 4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: 3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 3q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: 4q+2
       101: 4q+2
       102: q^2+3q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: 4q+2
       138: 3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: q^2+3q+2
       169: 1
       170: 1
       173: q+1
       174: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q+2
       201: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: 3q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: q+1
       276: q+1
       283: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       293: q+2
       295: 1
       296: 1
       297: 1
       298: 1
       299: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: q+2
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: q+2
       334: q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 4
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       378: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       397: 1
       400: 1
       401: 1
       403: 1
       405: 1
       407: 1
       419: q+2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       437: q+2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 4
       445: 2
       446: 2
       447: q+2
       449: 1
       450: 1
       451: 1
       452: 1
       453: q+2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+1
       470: q+1
       471: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: q+1
       482: 2
       483: 2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: 2
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: 2
       546: 2
       549: 1
       551: 1
       557: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       571: 1
       573: 2
       574: 2
       577: 1
       578: 1
       580: 1
       581: 1
       589: q+1
       593: 2
       595: 1
       596: 1
       599: 1
       600: 1
       603: q+2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       619: q+2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       641: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       647: q+2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2
       677: 2
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2
       683: 2
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       696: 1
       699: 1
       717: 1
       718: 1
       725: 1
       726: 1
       741: 1
       744: 1
       753: 1
       754: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 1
       793: 2
       801: q+1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 2
       817: 1
       818: 1
       825: q+1
       829: 2
       831: 1
       832: 1
       835: 1
       836: 1
       839: 1
       840: 1
       843: 1
       844: 1
       845: q+2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2
       879: 2
       880: 1
       928: 1
       929: 1
       952: 1
       953: 1
       964: 1
       965: 1
       974: 1
       976: 1
       988: 1
       989: 1
      1000: 1
      1004: 1
      1016: 2
      1026: 1
      1032: 1
      1033: 1
      1040: 1
      1046: 1
      1047: 1
      1052: q+1
      1056: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1194: 1
      1195: 1
      1206: 1
      1207: 1
      1218: 1
      1234: 1
      1240: 1
      1254: 1
      1258: 1
      1268: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1454: 1
      1462: 1
      1468: 1
      1476: 1
      1487: 1
      1665: 1

1666:    0: 6q+2
         1: 6q+2
         2: 2q^2+4q+2
         3: 6q+2
         4: 2q^2+4q+2
         5: 6q+2
         6: 2q^2+4q+2
         7: q^3+2q^2+3q+2
         8: 2q^2+4q+2
         9: q^3+2q^2+3q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 4q+2
        14: q^2+3q+2
        15: 4q+2
        16: 6q+2
        17: 6q+2
        18: q^3+2q^2+3q+2
        19: 4q+2
        20: 4q+2
        21: q^2+3q+2
        22: 6q+2
        23: 6q+2
        24: 2q^2+4q+2
        25: 6q+2
        26: 6q+2
        27: 2q^2+4q+2
        28: 6q+2
        29: 4q+2
        30: 3q+2
        31: 6q+2
        32: 4q+2
        33: 6q+2
        34: 6q+2
        35: 4q+2
        36: 6q+2
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q+2
        47: 4q+2
        48: q^2+3q+2
        49: 4q+2
        50: 4q+2
        51: q^2+3q+2
        52: 4q+2
        53: 4q+2
        54: q^2+3q+2
        55: 4q+2
        56: 4q+2
        57: q^2+3q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 4q+2
        62: 3q+1
        63: 3q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+2
        69: 3q+2
        70: 3q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 4q+2
        81: 4q+2
        82: 4q+2
        83: 3q+2
        84: 4q+2
        85: 4q+2
        86: 4q+2
        87: 3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: 4q+2
        95: 4q+2
        96: q^2+3q+2
        97: 4q+2
        98: 4q+2
        99: q^2+3q+2
       100: 4q+2
       101: 4q+2
       102: q^2+3q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 2q+2
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+2
       126: 3q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: 4q+2
       138: 3q+2
       139: 4q+2
       140: 2q+2
       141: 3q+2
       142: 2q+2
       143: 4q+2
       144: 3q+2
       145: 4q+2
       146: 3q+2
       147: 2q+2
       148: 2q+2
       149: 4q+2
       150: 3q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: 4q+2
       167: 4q+2
       168: q^2+3q+2
       171: 1
       172: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       184: q+2
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       194: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       200: 2q+2
       202: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: 3q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: 3q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: 3q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 3q+2
       247: 4
       248: 4
       249: 2q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       277: q+1
       278: q+1
       284: q+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: 1
       292: 1
       294: q+2
       295: 1
       296: 1
       297: 1
       298: 1
       300: q+2
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       308: q+2
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: q+2
       334: q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 4
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 4
       366: 3q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       379: 1
       380: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       398: 1
       399: 1
       402: 1
       404: 1
       406: 1
       408: 1
       420: q+2
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       430: q+2
       431: 1
       432: 1
       433: 1
       434: 1
       438: q+2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 4
       445: 2
       446: 2
       448: q+2
       449: 1
       450: 1
       451: 1
       452: 1
       454: q+2
       457: 1
       458: 1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       469: q+1
       470: q+1
       472: q+2
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: q+1
       482: 2
       483: 2
       484: 2
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: 2
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: 2
       501: 2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: 2
       548: 2
       550: 1
       552: 1
       558: 1
       559: 1
       561: 1
       562: 1
       563: 1
       564: 1
       567: 1
       568: 1
       570: 1
       572: 1
       575: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       590: q+1
       594: 2
       595: 1
       596: 1
       599: 1
       600: 1
       604: q+2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2
       620: q+2
       621: 1
       622: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       642: q+2
       643: 1
       644: 1
       645: 1
       646: 1
       648: q+2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: 1
       665: 1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2
       677: 2
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2
       683: 2
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       697: 1
       698: 1
       700: 1
       701: 1
       719: 1
       720: 1
       727: 1
       728: 1
       742: 1
       743: 1
       755: 1
       756: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 1
       794: 2
       802: q+1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 2
       817: 1
       818: 1
       826: q+1
       830: 2
       831: 1
       832: 1
       835: 1
       836: 1
       839: 1
       840: 1
       843: 1
       844: 1
       846: q+2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2
       879: 2
       880: 1
       930: 1
       931: 1
       954: 1
       955: 1
       966: 1
       967: 1
       975: 1
       977: 1
       990: 1
       991: 1
      1001: 1
      1005: 1
      1017: 2
      1027: 1
      1032: 1
      1033: 1
      1041: 1
      1046: 1
      1047: 1
      1053: q+1
      1057: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1196: 1
      1197: 1
      1208: 1
      1209: 1
      1219: 1
      1235: 1
      1241: 1
      1255: 1
      1259: 1
      1269: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1455: 1
      1463: 1
      1469: 1
      1477: 1
      1487: 1
      1666: 1

1667:    0: 3q^2+7q+2
         1: 3q^2+7q+2
         2: 3q^2+7q+2
         3: 3q^2+7q+2
         4: q^3+4q^2+5q+2
         5: 3q^2+7q+2
         6: q^3+4q^2+5q+2
         7: q^3+4q^2+5q+2
         8: 3q^2+7q+2
         9: q^4+3q^3+4q^2+3q+1
        10: 3q^2+7q+2
        11: 3q^2+7q+2
        12: q^3+4q^2+5q+2
        13: 3q^2+7q+2
        14: q^3+4q^2+5q+2
        15: 3q^2+7q+2
        16: 6q+2
        17: 6q+2
        18: q^3+3q^2+3q+1
        19: 2q^2+5q+2
        20: 2q^2+5q+2
        21: 2q^2+5q+2
        22: 3q^2+7q+2
        23: 3q^2+7q+2
        24: 3q^2+7q+2
        25: 3q^2+7q+2
        26: 3q^2+7q+2
        27: 3q^2+7q+2
        28: 6q+2
        29: 2q^2+5q+2
        30: 2q^2+5q+2
        31: 3q^2+7q+2
        32: 3q^2+7q+2
        33: 6q+2
        34: 3q^2+7q+2
        35: 3q^2+7q+2
        36: 6q+2
        37: 2q^2+5q+2
        38: q^2+2q
        39: 2q^2+5q+2
        40: q^2+2q
        41: 2q^2+5q+2
        42: q^2+2q
        43: 3q^2+7q+2
        44: q^3+4q^2+5q+2
        45: 3q^2+7q+2
        46: 6q+2
        47: 6q+2
        48: q^3+3q^2+3q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+3q+1
        52: 2q^2+5q+2
        53: 2q^2+5q+2
        54: 2q^2+5q+2
        55: 2q^2+5q+2
        56: 2q^2+5q+2
        57: 2q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 2q^2+5q+2
        63: q^2+2q
        64: 2q^2+5q+2
        65: q^2+2q
        66: 4q+2
        67: 2q
        68: 6q+2
        69: 2q+1
        70: 2q^2+5q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        74: q^2+3q+2
        76: q^2+3q+2
        78: q^2+3q+2
        80: 3q^2+7q+2
        81: 6q+2
        82: 2q^2+5q+2
        83: 2q^2+5q+2
        84: 3q^2+7q+2
        85: 6q+2
        86: 2q^2+5q+2
        87: 2q^2+5q+2
        88: 6q+2
        89: 6q+2
        90: q^3+3q^2+3q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+3q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+3q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+3q+1
       100: 2q^2+5q+2
       101: 2q^2+5q+2
       102: 2q^2+5q+2
       103: 2q+1
       104: q
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: q^2+3q+2
       115: q^2+3q+2
       117: 3q+1
       118: 3q+1
       119: 3q+1
       120: 3q+1
       121: 2q^2+5q+2
       122: q^2+2q
       123: 4q+2
       124: 2q
       125: 6q+2
       126: 2q+1
       127: 2q+2
       129: 2q+2
       131: q^2+2q+1
       133: 4q+2
       134: 2q+1
       135: 2q+2
       136: 2q+2
       137: 6q+2
       138: 2q+1
       139: 4q+2
       140: 2q+2
       141: 2q^2+5q+2
       142: 2q+2
       143: 6q+2
       144: 2q+1
       145: 4q+2
       146: 2q^2+5q+2
       147: 2q+2
       148: 2q+2
       149: 2q^2+5q+2
       150: 2q^2+5q+2
       151: q^2+3q+2
       153: q^2+3q+2
       155: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+3q+1
       160: 4q+2
       161: 4q+2
       162: 2q^2+3q+1
       163: 4q+2
       164: 4q+2
       165: 2q^2+3q+1
       166: 4q+2
       167: 4q+2
       168: 2q^2+3q+1
       169: 1
       172: 1
       173: 2q+1
       174: q
       175: q
       176: 2q+1
       177: q+1
       179: 2q+2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2
       189: q^2+3q+2
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: 4q+2
       208: 2q
       209: q^2+3q+2
       211: q^2+3q+2
       213: 2q+2
       215: 2q+2
       217: q^2+2q+1
       219: 2q+1
       220: 4q+2
       221: 2q+1
       222: 2q+2
       223: q+1
       224: 2q+2
       225: q+1
       226: 2q+1
       227: 4q+2
       228: 2q+1
       229: 2q+2
       230: 2q+2
       231: 2q+1
       232: 4q+2
       233: 2q+1
       234: 2q+2
       235: 2q+2
       236: 2q+1
       237: 2q+2
       239: 2q+2
       241: q^2+2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 2q^2+5q+2
       247: 4
       248: 4
       249: q^2+2q+1
       250: 4q+2
       251: 4q+2
       252: 2q^2+3q+1
       253: 4q+2
       254: 4q+2
       255: 2q^2+3q+1
       256: 4q+2
       257: 4q+2
       258: 2q^2+3q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: 2q+1
       276: q
       277: q
       278: 2q+1
       279: 2q+2
       281: q+1
       287: q+1
       289: 2
       291: 1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: 2
       315: q+1
       317: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: q^2+3q+2
       327: 2q+2
       329: 2q+2
       331: q^2+2q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       338: 4
       340: 4
       342: q^2+2q+1
       344: 2q+1
       345: 4q+2
       346: 2q+1
       347: 2q+2
       348: q+1
       349: 2q+2
       350: q+1
       351: 4
       352: 2q+1
       353: 4q+2
       354: 2q+1
       355: 2q+2
       356: q+1
       357: 2q+2
       358: q+1
       359: 4
       360: 2q+2
       362: 2q+2
       364: q^2+2q+1
       366: 2q+1
       367: 4q+2
       368: 2q+1
       369: 2q+2
       370: 2q+2
       371: 4
       372: 4
       373: q^2+2q+1
       374: 4q+2
       375: 4q+2
       376: 2q^2+3q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 2q+2
       411: q+1
       413: q+1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 4
       433: 1
       435: 2
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2
       443: 2
       444: 2
       445: 4
       451: 1
       453: q+1
       454: q+1
       455: 2
       457: q+1
       458: q+1
       459: 2
       461: 2
       462: 2
       463: 4
       465: 2q+2
       467: q+1
       469: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       477: 2
       479: 2
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: 4
       485: 4
       487: 4
       489: q^2+2q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 4
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 4
       502: 2q+2
       504: 2q+2
       506: q^2+2q+1
       508: 2q+1
       509: 4q+2
       510: 2q+1
       511: 2q+2
       512: q+1
       513: 2q+2
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 4
       519: 4
       520: q^2+2q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2
       547: 2
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2
       563: 2
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       583: q+1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 4
       605: 1
       609: 1
       611: 2
       613: 1
       615: 2
       616: 2
       617: 4
       623: 1
       625: 1
       627: 2
       629: 1
       631: 2
       632: 2
       633: 4
       635: 2q+2
       637: q+1
       639: q+1
       645: 1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 2
       653: 2
       655: 2
       656: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 4
       668: 4
       670: q^2+2q+1
       672: 4
       673: 1
       674: 2
       675: q+1
       676: q+1
       677: 1
       678: 4
       679: 1
       680: 2
       681: q+1
       682: q+1
       683: 1
       684: 4
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       693: 1
       696: 1
       697: 1
       698: 1
       729: 1
       731: 1
       733: 2
       735: 2
       745: 1
       747: 1
       749: 2
       751: 2
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       777: 1
       779: 1
       781: 1
       783: 1
       789: 4
       795: 2
       797: 1
       799: 1
       809: 1
       811: 1
       813: 4
       815: 2
       816: 2
       819: 2
       821: 1
       823: 1
       833: 1
       835: 1
       837: 4
       839: 2
       840: 2
       841: q+1
       843: 1
       844: 1
       849: 1
       851: 1
       853: 2
       855: 1
       857: 2
       858: 2
       859: 2
       861: 2
       863: q+1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       884: 1
       887: 1
       888: 1
       889: 1
       932: 2
       934: 2
       956: 2
       958: 2
       968: 1
       971: 1
       978: 1
       979: 1
       982: 2
       985: 2
       988: 1
       989: 1
       990: 1
       991: 1
       996: 1
      1002: 1
      1014: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1030: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1060: 1
      1062: 1
      1066: 2
      1068: 2
      1070: q+1
      1073: 1
      1075: 2
      1077: 1
      1078: 1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1101: 1
      1102: 1
      1103: 1
      1188: 1
      1191: 1
      1212: 1
      1226: 2
      1236: 1
      1238: 1
      1244: 2
      1252: 1
      1256: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1272: 1
      1274: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1404: 1
      1407: 1
      1452: 1
      1458: 1
      1470: 1
      1472: 1
      1488: 1
      1667: 1

1668:    0: 3q^2+7q+2
         1: 3q^2+7q+2
         2: 3q^2+7q+2
         3: 3q^2+7q+2
         4: q^3+4q^2+5q+2
         5: 3q^2+7q+2
         6: q^3+4q^2+5q+2
         7: q^3+4q^2+5q+2
         8: 3q^2+7q+2
         9: q^4+3q^3+4q^2+3q+1
        10: 3q^2+7q+2
        11: 3q^2+7q+2
        12: q^3+4q^2+5q+2
        13: 3q^2+7q+2
        14: q^3+4q^2+5q+2
        15: 3q^2+7q+2
        16: 6q+2
        17: 6q+2
        18: q^3+3q^2+3q+1
        19: 2q^2+5q+2
        20: 2q^2+5q+2
        21: 2q^2+5q+2
        22: 3q^2+7q+2
        23: 3q^2+7q+2
        24: 3q^2+7q+2
        25: 3q^2+7q+2
        26: 3q^2+7q+2
        27: 3q^2+7q+2
        28: 6q+2
        29: 2q^2+5q+2
        30: 2q^2+5q+2
        31: 3q^2+7q+2
        32: 3q^2+7q+2
        33: 6q+2
        34: 3q^2+7q+2
        35: 3q^2+7q+2
        36: 6q+2
        37: q^2+2q
        38: 2q^2+5q+2
        39: q^2+2q
        40: 2q^2+5q+2
        41: q^2+2q
        42: 2q^2+5q+2
        43: 3q^2+7q+2
        44: q^3+4q^2+5q+2
        45: 3q^2+7q+2
        46: 6q+2
        47: 6q+2
        48: q^3+3q^2+3q+1
        49: 4q+2
        50: 4q+2
        51: 2q^2+3q+1
        52: 2q^2+5q+2
        53: 2q^2+5q+2
        54: 2q^2+5q+2
        55: 2q^2+5q+2
        56: 2q^2+5q+2
        57: 2q^2+5q+2
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: q^2+2q
        63: 2q^2+5q+2
        64: q^2+2q
        65: 2q^2+5q+2
        66: 2q
        67: 4q+2
        68: 6q+2
        69: 2q+1
        70: 2q^2+5q+2
        71: 4q+2
        72: 2q+2
        73: 2q+2
        75: q^2+3q+2
        77: q^2+3q+2
        79: q^2+3q+2
        80: 3q^2+7q+2
        81: 6q+2
        82: 2q^2+5q+2
        83: 2q^2+5q+2
        84: 3q^2+7q+2
        85: 6q+2
        86: 2q^2+5q+2
        87: 2q^2+5q+2
        88: 6q+2
        89: 6q+2
        90: q^3+3q^2+3q+1
        91: 4q+2
        92: 4q+2
        93: 2q^2+3q+1
        94: 4q+2
        95: 4q+2
        96: 2q^2+3q+1
        97: 4q+2
        98: 4q+2
        99: 2q^2+3q+1
       100: 2q^2+5q+2
       101: 2q^2+5q+2
       102: 2q^2+5q+2
       103: q
       104: 2q+1
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       114: q^2+3q+2
       116: q^2+3q+2
       117: 3q+1
       118: 3q+1
       119: 3q+1
       120: 3q+1
       121: q^2+2q
       122: 2q^2+5q+2
       123: 2q
       124: 4q+2
       125: 6q+2
       126: 2q+1
       128: 2q+2
       130: 2q+2
       132: q^2+2q+1
       133: 4q+2
       134: 2q+1
       135: 2q+2
       136: 2q+2
       137: 6q+2
       138: 2q+1
       139: 4q+2
       140: 2q+2
       141: 2q^2+5q+2
       142: 2q+2
       143: 6q+2
       144: 2q+1
       145: 4q+2
       146: 2q^2+5q+2
       147: 2q+2
       148: 2q+2
       149: 2q^2+5q+2
       150: 2q^2+5q+2
       152: q^2+3q+2
       154: q^2+3q+2
       156: q^2+3q+2
       157: 4q+2
       158: 4q+2
       159: 2q^2+3q+1
       160: 4q+2
       161: 4q+2
       162: 2q^2+3q+1
       163: 4q+2
       164: 4q+2
       165: 2q^2+3q+1
       166: 4q+2
       167: 4q+2
       168: 2q^2+3q+1
       170: 1
       171: 1
       173: q
       174: 2q+1
       175: 2q+1
       176: q
       178: q+1
       180: 2q+2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2
       190: q^2+3q+2
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       207: 2q
       208: 4q+2
       210: q^2+3q+2
       212: q^2+3q+2
       214: 2q+2
       216: 2q+2
       218: q^2+2q+1
       219: 2q+1
       220: 4q+2
       221: 2q+1
       222: 2q+2
       223: q+1
       224: 2q+2
       225: q+1
       226: 2q+1
       227: 4q+2
       228: 2q+1
       229: 2q+2
       230: 2q+2
       231: 2q+1
       232: 4q+2
       233: 2q+1
       234: 2q+2
       235: 2q+2
       236: 2q+1
       238: 2q+2
       240: 2q+2
       242: q^2+2q+1
       243: 4q+2
       244: 2q+2
       245: 2q+2
       246: 2q^2+5q+2
       247: 4
       248: 4
       249: q^2+2q+1
       250: 4q+2
       251: 4q+2
       252: 2q^2+3q+1
       253: 4q+2
       254: 4q+2
       255: 2q^2+3q+1
       256: 4q+2
       257: 4q+2
       258: 2q^2+3q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       275: q
       276: 2q+1
       277: 2q+1
       278: q
       280: 2q+2
       282: q+1
       288: q+1
       290: 2
       292: 1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       314: 2
       316: q+1
       318: 2q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       326: q^2+3q+2
       328: 2q+2
       330: 2q+2
       332: q^2+2q+1
       333: 2q+1
       334: q+1
       335: q+1
       336: 1
       337: 4
       339: 4
       341: 4
       343: q^2+2q+1
       344: 2q+1
       345: 4q+2
       346: 2q+1
       347: 2q+2
       348: q+1
       349: 2q+2
       350: q+1
       351: 4
       352: 2q+1
       353: 4q+2
       354: 2q+1
       355: 2q+2
       356: q+1
       357: 2q+2
       358: q+1
       359: 4
       361: 2q+2
       363: 2q+2
       365: q^2+2q+1
       366: 2q+1
       367: 4q+2
       368: 2q+1
       369: 2q+2
       370: 2q+2
       371: 4
       372: 4
       373: q^2+2q+1
       374: 4q+2
       375: 4q+2
       376: 2q^2+3q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 2q+2
       412: q+1
       414: q+1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 4
       434: 1
       436: 2
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: 2
       443: 2
       444: 2
       446: 4
       452: 1
       453: q+1
       454: q+1
       456: 2
       457: q+1
       458: q+1
       460: 2
       461: 2
       462: 2
       464: 4
       466: 2q+2
       468: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: 2
       478: 2
       479: 2
       480: 2
       481: q+1
       482: q+1
       483: 1
       484: 4
       486: 4
       488: 4
       490: q^2+2q+1
       491: 1
       492: 2q+1
       493: q+1
       494: q+1
       495: 1
       496: 4
       497: 2q+1
       498: q+1
       499: q+1
       500: 1
       501: 4
       503: 2q+2
       505: 2q+2
       507: q^2+2q+1
       508: 2q+1
       509: 4q+2
       510: 2q+1
       511: 2q+2
       512: q+1
       513: 2q+2
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 4
       519: 4
       520: q^2+2q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 2
       548: 2
       554: 1
       556: 1
       558: 1
       560: 1
       562: 2
       564: 2
       566: 1
       567: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       584: q+1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 4
       606: 1
       610: 1
       612: 2
       614: 1
       615: 2
       616: 2
       618: 4
       624: 1
       626: 1
       628: 2
       630: 1
       631: 2
       632: 2
       634: 4
       636: 2q+2
       638: q+1
       640: q+1
       646: 1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       652: 2
       654: 2
       655: 2
       656: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 4
       669: 4
       671: q^2+2q+1
       672: 4
       673: 1
       674: 2
       675: q+1
       676: q+1
       677: 1
       678: 4
       679: 1
       680: 2
       681: q+1
       682: q+1
       683: 1
       684: 4
       685: 1
       686: 2q+1
       687: q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       694: 1
       699: 1
       700: 1
       701: 1
       730: 1
       732: 1
       734: 2
       736: 2
       746: 1
       748: 1
       750: 2
       752: 2
       759: 1
       760: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       778: 1
       780: 1
       782: 1
       784: 1
       790: 4
       796: 2
       798: 1
       800: 1
       810: 1
       812: 1
       814: 4
       815: 2
       816: 2
       820: 2
       822: 1
       824: 1
       834: 1
       836: 1
       838: 4
       839: 2
       840: 2
       842: q+1
       843: 1
       844: 1
       850: 1
       852: 1
       854: 2
       856: 1
       857: 2
       858: 2
       860: 2
       862: 2
       864: q+1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       885: 1
       890: 1
       891: 1
       892: 1
       933: 2
       935: 2
       957: 2
       959: 2
       969: 1
       972: 1
       980: 1
       981: 1
       983: 2
       986: 2
       988: 1
       989: 1
       990: 1
       991: 1
       997: 1
      1003: 1
      1015: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1031: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1061: 1
      1063: 1
      1067: 2
      1069: 2
      1071: q+1
      1073: 1
      1075: 2
      1077: 1
      1078: 1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1189: 1
      1192: 1
      1213: 1
      1227: 2
      1237: 1
      1239: 1
      1245: 2
      1253: 1
      1257: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1273: 1
      1275: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1405: 1
      1408: 1
      1453: 1
      1459: 1
      1471: 1
      1473: 1
      1488: 1
      1668: 1

1669:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: q^2+4q+2
        23: 2q^2+4q+2
        24: q^2+4q+2
        25: q^2+4q+2
        26: 2q^2+4q+2
        27: q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: 3q+2
        32: q^2+4q+2
        33: 3q+2
        34: 3q+2
        35: q^2+4q+2
        36: 3q+2
        37: 2q+2
        38: q^2+2q
        39: 2q+2
        40: 2q^2+2q
        41: 2q+2
        42: q^2+2q
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: q^2+4q+2
        53: 2q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: 2q^2+4q+2
        57: q^2+4q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+2
        63: 2q
        64: 2q+2
        65: q^2+2q
        66: q+2
        67: 2q
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: 3q+2
        73: 3q+2
        74: 2q+2
        75: q^2+2q
        76: 2q+2
        77: 2q^2+2q
        78: 2q+2
        79: q^2+2q
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+4q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: q^2+4q+2
       101: 2q^2+4q+2
       102: q^2+4q+2
       103: 1
       104: q
       105: q
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+2
       112: 2q
       113: q+2
       114: 2q
       115: 2q+2
       116: q^2+2q
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+2
       122: 2q
       123: q+2
       124: 2q
       125: 2
       126: 1
       127: 2
       128: 2q
       129: 2
       130: 2q
       131: q+1
       132: q^2
       133: 2q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: 3q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: q+1
       145: 2q+2
       146: 3q+2
       147: 3q+2
       148: 3q+2
       149: 3q+2
       150: q^2+4q+2
       151: 2q+2
       152: q^2+2q
       153: 2q+2
       154: 2q^2+2q
       155: 2q+2
       156: q^2+2q
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 3q+2
       167: 3q+2
       168: q^2+2q+1
       169: 1
       170: q
       171: q
       172: 1
       173: 1
       174: q
       175: q
       176: 1
       177: 1
       179: 2
       180: 2q
       181: 2
       182: 2q
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+2
       188: 2q
       189: q+2
       190: 2q
       191: 1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+2
       198: 2q
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+2
       206: 2q
       207: 2
       209: q+2
       210: 2q
       211: 2q+2
       212: q^2+2q
       213: 2
       214: 2q
       215: 2
       216: 2q
       217: q+1
       218: q^2
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       237: 2
       238: 2q
       239: 2
       240: 2q
       241: q+1
       242: q^2
       243: 2q+2
       244: 3q+2
       245: 3q+2
       246: 3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 3q+2
       257: 3q+2
       258: q^2+2q+1
       259: 1
       260: q
       261: q
       262: 1
       263: 1
       264: q
       265: q
       266: 1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: 1
       278: 1
       279: 2
       280: 2q
       281: 1
       287: 1
       289: 2
       290: 2q
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       302: 2q
       303: q+1
       304: q+1
       305: q+2
       306: 2q
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       312: 2q
       313: q+2
       314: 2q
       315: 1
       317: 2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+2
       324: 2q
       325: q+2
       326: 2q
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 2q+2
       338: 2
       339: 2q
       340: 2
       341: 2q
       342: q+1
       343: q^2
       344: 1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 3q+2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 3q+2
       360: 2
       361: 2q
       362: 2
       363: 2q
       364: q+1
       365: q^2
       366: 1
       367: 2q+2
       368: q+1
       369: 3q+2
       370: 3q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       382: q
       383: q
       384: 1
       385: 1
       388: 1
       389: 1
       390: q
       391: 1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       398: q
       399: 1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       407: q
       408: q
       413: 1
       417: 1
       423: 1
       425: 1
       427: 2
       428: 2q
       433: 1
       435: 2
       436: 2q
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: q+1
       444: q+1
       445: 2
       446: 2q
       451: 1
       453: 1
       454: 1
       455: 2
       456: 2q
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       464: 2q
       465: 2
       466: 2q
       467: 1
       469: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+2
       476: 2q
       477: 2
       478: 2q
       479: q+2
       480: 2q
       481: 1
       482: 1
       483: 1
       484: 2q+2
       485: 2
       486: 2q
       487: 2
       488: 2q
       489: q+1
       490: q^2
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 3q+2
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 3q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2
       517: 2
       518: 2
       519: 2
       520: q+1
       537: 1
       538: q
       539: 1
       540: q
       541: 1
       543: 1
       545: 1
       546: q
       547: 1
       548: q
       553: 1
       554: q
       555: 1
       556: q
       557: 1
       559: 1
       561: 1
       562: q
       563: 1
       564: q
       565: 1
       566: q
       567: q
       568: 1
       569: 1
       570: 1
       571: q
       572: q
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       581: 2q
       585: 1
       597: 1
       599: 1
       601: 2
       602: 2q
       605: 1
       609: 1
       613: 1
       615: q+1
       616: q+1
       617: 2
       618: 2q
       623: 1
       625: 1
       629: 1
       631: q+1
       632: q+1
       633: 2
       634: 2q
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       652: 2q
       653: 2
       655: q+2
       656: 2q
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 1
       672: 2
       673: 1
       674: 2
       675: 1
       676: 1
       677: 1
       678: 2
       679: q+1
       680: 2
       681: 1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: 1
       692: 1
       693: 1
       697: 1
       699: q
       700: q
       733: 1
       734: q
       735: 1
       736: q
       749: 1
       750: q
       751: 1
       752: q
       757: 1
       758: 1
       759: q
       760: q
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       773: 2q
       779: 1
       780: 1
       781: 1
       791: 1
       795: 1
       796: 1
       797: 1
       809: 1
       811: 1
       815: 1
       816: 1
       819: 1
       820: 1
       821: 1
       833: 1
       835: 1
       839: 1
       840: 1
       843: 2
       849: 1
       851: 1
       855: 1
       857: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: q
       891: q
       968: 1
       969: 1
       988: 1
       991: 1
      1008: 1
      1010: 1
      1012: 2
      1020: 1
      1021: 1
      1022: 1
      1036: 1
      1037: 1
      1038: 1
      1046: 1
      1048: 1
      1060: 1
      1062: 1
      1064: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1138: 1
      1139: 1
      1220: 1
      1224: 1
      1262: 1
      1266: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1280: 2
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1430: 1
      1431: 1
      1444: 1
      1474: 1
      1482: 1
      1488: 1
      1669: 1

1670:    0: q^2+4q+2
         1: 2q^2+4q+2
         2: q^2+4q+2
         3: 2q^2+4q+2
         4: q^2+4q+2
         5: q^2+4q+2
         6: 2q^2+4q+2
         7: q^2+4q+2
         8: q^2+4q+2
         9: q^3+2q^2+2q+1
        10: 3q+2
        11: 3q+2
        12: 3q+2
        13: q^2+4q+2
        14: q^2+4q+2
        15: q^2+4q+2
        16: 3q+2
        17: 3q+2
        18: q^2+2q+1
        19: q^2+4q+2
        20: 2q^2+4q+2
        21: q^2+4q+2
        22: q^2+4q+2
        23: 2q^2+4q+2
        24: q^2+4q+2
        25: q^2+4q+2
        26: 2q^2+4q+2
        27: q^2+4q+2
        28: 2q+2
        29: 3q+2
        30: q^2+4q+2
        31: 3q+2
        32: q^2+4q+2
        33: 3q+2
        34: 3q+2
        35: q^2+4q+2
        36: 3q+2
        37: q^2+2q
        38: 2q+2
        39: 2q^2+2q
        40: 2q+2
        41: q^2+2q
        42: 2q+2
        43: 3q+2
        44: 3q+2
        45: 3q+2
        46: 3q+2
        47: 3q+2
        48: q^2+2q+1
        49: 3q+2
        50: 3q+2
        51: q^2+2q+1
        52: q^2+4q+2
        53: 2q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: 2q^2+4q+2
        57: q^2+4q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q
        63: q+2
        64: q^2+2q
        65: 2q+2
        66: 2q
        67: q+2
        68: 2q+2
        69: q+1
        70: 3q+2
        71: 2q+2
        72: 3q+2
        73: 3q+2
        74: q^2+2q
        75: 2q+2
        76: 2q^2+2q
        77: 2q+2
        78: q^2+2q
        79: 2q+2
        80: 3q+2
        81: 3q+2
        82: 3q+2
        83: q^2+4q+2
        84: 3q+2
        85: 3q+2
        86: 3q+2
        87: q^2+4q+2
        88: 2
        89: 2
        90: q+1
        91: 3q+2
        92: 3q+2
        93: q^2+2q+1
        94: 3q+2
        95: 3q+2
        96: q^2+2q+1
        97: 3q+2
        98: 3q+2
        99: q^2+2q+1
       100: q^2+4q+2
       101: 2q^2+4q+2
       102: q^2+4q+2
       103: q
       104: 1
       105: 1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q
       112: q+2
       113: 2q
       114: q+2
       115: q^2+2q
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q
       122: q+2
       123: 2q
       124: q+2
       125: 2
       126: 1
       127: 2q
       128: 2
       129: 2q
       130: 2
       131: q^2
       132: q+1
       133: 2q+2
       134: q+1
       135: 3q+2
       136: 3q+2
       137: 2
       138: q+1
       139: 2q+2
       140: 3q+2
       141: 3q+2
       142: 3q+2
       143: 2
       144: q+1
       145: 2q+2
       146: 3q+2
       147: 3q+2
       148: 3q+2
       149: 3q+2
       150: q^2+4q+2
       151: q^2+2q
       152: 2q+2
       153: 2q^2+2q
       154: 2q+2
       155: q^2+2q
       156: 2q+2
       157: 2
       158: 2
       159: q+1
       160: 3q+2
       161: 3q+2
       162: q^2+2q+1
       163: 3q+2
       164: 3q+2
       165: q^2+2q+1
       166: 3q+2
       167: 3q+2
       168: q^2+2q+1
       169: q
       170: 1
       171: 1
       172: q
       173: q
       174: 1
       175: 1
       176: q
       178: 1
       179: 2q
       180: 2
       181: 2q
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q
       188: q+2
       189: 2q
       190: q+2
       191: 1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q
       198: q+2
       199: 1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q
       206: q+2
       208: 2
       209: 2q
       210: q+2
       211: q^2+2q
       212: 2q+2
       213: 2q
       214: 2
       215: 2q
       216: 2
       217: q^2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: q+1
       224: 2
       225: q+1
       226: 1
       227: 2q+2
       228: q+1
       229: 3q+2
       230: 3q+2
       231: 1
       232: 2q+2
       233: q+1
       234: 3q+2
       235: 3q+2
       236: q+1
       237: 2q
       238: 2
       239: 2q
       240: 2
       241: q^2
       242: q+1
       243: 2q+2
       244: 3q+2
       245: 3q+2
       246: 3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 3q+2
       257: 3q+2
       258: q^2+2q+1
       259: q
       260: 1
       261: 1
       262: q
       263: q
       264: 1
       265: 1
       266: q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       276: 1
       277: 1
       279: 2q
       280: 2
       282: 1
       288: 1
       289: 2q
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       301: 2q
       302: 2
       303: q+1
       304: q+1
       305: 2q
       306: q+2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q
       312: 2
       313: 2q
       314: q+2
       316: 1
       317: 2q
       318: 2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: q+2
       325: 2q
       326: q+2
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 2q+2
       338: 2q
       339: 2
       340: 2q
       341: 2
       342: q^2
       343: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: q+1
       349: 2
       350: q+1
       351: 3q+2
       352: 1
       353: 2
       354: 1
       355: 2
       356: q+1
       357: 2
       358: q+1
       359: 3q+2
       360: 2q
       361: 2
       362: 2q
       363: 2
       364: q^2
       365: q+1
       366: 1
       367: 2q+2
       368: q+1
       369: 3q+2
       370: 3q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: 2
       375: 2
       376: q+1
       381: q
       382: 1
       383: 1
       384: q
       386: 1
       387: 1
       389: q
       390: 1
       391: q
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 1
       399: q
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: 1
       408: 1
       414: 1
       418: 1
       424: 1
       426: 1
       427: 2q
       428: 2
       434: 1
       435: 2q
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: q+1
       444: q+1
       445: 2q
       446: 2
       452: 1
       453: 1
       454: 1
       455: 2q
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       463: 2q
       464: 2
       465: 2q
       466: 2
       468: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: q+2
       477: 2q
       478: 2
       479: 2q
       480: q+2
       481: 1
       482: 1
       483: 1
       484: 2q+2
       485: 2q
       486: 2
       487: 2q
       488: 2
       489: q^2
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 3q+2
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 3q+2
       508: 1
       509: 2
       510: 1
       511: 2
       512: q+1
       513: 2
       514: q+1
       515: 2
       516: 2
       517: 2
       518: 2
       519: 2
       520: q+1
       537: q
       538: 1
       539: q
       540: 1
       542: 1
       544: 1
       545: q
       546: 1
       547: q
       548: 1
       553: q
       554: 1
       555: q
       556: 1
       558: 1
       560: 1
       561: q
       562: 1
       563: q
       564: 1
       565: q
       566: 1
       567: 1
       568: q
       569: q
       570: q
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       577: 2q
       581: 2
       586: 1
       598: 1
       600: 1
       601: 2q
       602: 2
       606: 1
       610: 1
       614: 1
       615: q+1
       616: q+1
       617: 2q
       618: 2
       624: 1
       626: 1
       630: 1
       631: q+1
       632: q+1
       633: 2q
       634: 2
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2q
       652: 2
       654: 2
       655: 2q
       656: q+2
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2
       665: 1
       672: 2
       673: 1
       674: 2
       675: 1
       676: 1
       677: 1
       678: 2
       679: q+1
       680: 2
       681: 1
       682: 1
       683: 1
       684: 2
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: 1
       692: 1
       693: q
       697: q
       699: 1
       700: 1
       733: q
       734: 1
       735: q
       736: 1
       749: q
       750: 1
       751: q
       752: 1
       757: q
       758: q
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       769: 2q
       773: 2
       779: 1
       780: 1
       782: 1
       792: 1
       795: 1
       796: 1
       798: 1
       810: 1
       812: 1
       815: 1
       816: 1
       819: 1
       820: 1
       822: 1
       834: 1
       836: 1
       839: 1
       840: 1
       844: 2
       850: 1
       852: 1
       856: 1
       858: 2
       867: 1
       868: 1
       869: 1
       870: 2
       871: 1
       872: 1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: 1
       882: 1
       883: 1
       884: q
       889: q
       890: 1
       891: 1
       971: 1
       972: 1
       989: 1
       990: 1
      1009: 1
      1011: 1
      1013: 2
      1020: 1
      1021: 1
      1023: 1
      1036: 1
      1037: 1
      1039: 1
      1047: 1
      1049: 1
      1061: 1
      1063: 1
      1065: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1141: 1
      1142: 1
      1221: 1
      1225: 1
      1263: 1
      1267: 1
      1274: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 2
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1433: 1
      1434: 1
      1445: 1
      1475: 1
      1483: 1
      1488: 1
      1670: 1

1671:    0: q^3+q+2
         1: q^3+q+2
         2: q^3+q+2
         3: q^3+q+2
         4: q^3+q+2
         5: q^3+q+2
         6: q^3+q+2
         7: q^3+q+2
         8: q^3+q+2
         9: q^5+q^2+q+1
        10: q^3+q+2
        11: q^3+q+2
        12: q^3+q+2
        13: q^3+q+2
        14: q^3+q+2
        15: q^3+q+2
        16: 2
        17: 2
        18: q+1
        19: q^3+q+2
        20: q^3+q+2
        21: q^3+q+2
        22: q^3+q+2
        23: q^3+q+2
        24: q^3+q+2
        25: q^3+q+2
        26: q^3+q+2
        27: q^3+q+2
        28: 2
        29: q^3+q+2
        30: q^3+q+2
        31: q^3+q+2
        32: q^3+q+2
        33: 2
        34: q^3+q+2
        35: q^3+q+2
        36: 2
        37: q^3+q+2
        39: q^3+q+2
        41: q^3+q+2
        43: q^3+q+2
        44: q^3+q+2
        45: q^3+q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q^3+q+2
        53: q^3+q+2
        54: q^3+q+2
        55: q^3+q+2
        56: q^3+q+2
        57: q^3+q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q^3+q+2
        64: q^3+q+2
        66: 2
        68: 2
        69: 1
        70: q^3+q+2
        71: 2
        72: 2
        73: 2
        74: q^3+q+2
        76: q^3+q+2
        78: q^3+q+2
        80: q^3+q+2
        81: 2
        82: q^3+q+2
        83: q^3+q+2
        84: q^3+q+2
        85: 2
        86: q^3+q+2
        87: q^3+q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q^3+q+2
       101: q^3+q+2
       102: q^3+q+2
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q^3+q+2
       115: q^3+q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q^3+q+2
       123: 2
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q^3+q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q^3+q+2
       147: 2
       148: 2
       149: q^3+q+2
       150: q^3+q+2
       151: q^3+q+2
       153: q^3+q+2
       155: q^3+q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q^3+q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2
       209: q^3+q+2
       211: q^3+q+2
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       245: 2
       246: q^3+q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: q^3+q+2
       327: 2
       329: 2
       331: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: 2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       693: 1
       697: 1
       729: 1
       731: 1
       733: 1
       735: 1
       745: 1
       747: 1
       749: 1
       751: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       777: 1
       781: 1
       783: 1
       789: 2
       791: 1
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       849: 1
       851: 1
       853: 2
       855: 1
       857: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       884: 1
       889: 1
       932: 1
       934: 1
       956: 1
       958: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
      1002: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1034: 1
      1038: 1
      1042: 1
      1048: 1
      1050: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1098: 1
      1102: 1
      1220: 1
      1222: 1
      1238: 1
      1256: 1
      1264: 1
      1266: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1446: 1
      1470: 1
      1474: 1
      1480: 1
      1671: 1

1672:    0: q^3+q+2
         1: q^3+q+2
         2: q^3+q+2
         3: q^3+q+2
         4: q^3+q+2
         5: q^3+q+2
         6: q^3+q+2
         7: q^3+q+2
         8: q^3+q+2
         9: q^5+q^2+q+1
        10: q^3+q+2
        11: q^3+q+2
        12: q^3+q+2
        13: q^3+q+2
        14: q^3+q+2
        15: q^3+q+2
        16: 2
        17: 2
        18: q+1
        19: q^3+q+2
        20: q^3+q+2
        21: q^3+q+2
        22: q^3+q+2
        23: q^3+q+2
        24: q^3+q+2
        25: q^3+q+2
        26: q^3+q+2
        27: q^3+q+2
        28: 2
        29: q^3+q+2
        30: q^3+q+2
        31: q^3+q+2
        32: q^3+q+2
        33: 2
        34: q^3+q+2
        35: q^3+q+2
        36: 2
        38: q^3+q+2
        40: q^3+q+2
        42: q^3+q+2
        43: q^3+q+2
        44: q^3+q+2
        45: q^3+q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q^3+q+2
        53: q^3+q+2
        54: q^3+q+2
        55: q^3+q+2
        56: q^3+q+2
        57: q^3+q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q^3+q+2
        65: q^3+q+2
        67: 2
        68: 2
        69: 1
        70: q^3+q+2
        71: 2
        72: 2
        73: 2
        75: q^3+q+2
        77: q^3+q+2
        79: q^3+q+2
        80: q^3+q+2
        81: 2
        82: q^3+q+2
        83: q^3+q+2
        84: q^3+q+2
        85: 2
        86: q^3+q+2
        87: q^3+q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q^3+q+2
       101: q^3+q+2
       102: q^3+q+2
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q^3+q+2
       116: q^3+q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q^3+q+2
       124: 2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q^3+q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q^3+q+2
       147: 2
       148: 2
       149: q^3+q+2
       150: q^3+q+2
       152: q^3+q+2
       154: q^3+q+2
       156: q^3+q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q^3+q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2
       210: q^3+q+2
       212: q^3+q+2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       245: 2
       246: q^3+q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: q^3+q+2
       328: 2
       330: 2
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: 2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       699: 1
       700: 1
       730: 1
       732: 1
       734: 1
       736: 1
       746: 1
       748: 1
       750: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       778: 1
       782: 1
       784: 1
       790: 2
       792: 1
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       850: 1
       852: 1
       854: 2
       856: 1
       858: 2
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       890: 1
       891: 1
       933: 1
       935: 1
       957: 1
       959: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
      1003: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1035: 1
      1039: 1
      1043: 1
      1049: 1
      1051: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1104: 1
      1105: 1
      1221: 1
      1223: 1
      1239: 1
      1257: 1
      1265: 1
      1267: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1447: 1
      1471: 1
      1475: 1
      1481: 1
      1672: 1

1673:    0: 10q^2+16q+4
         1: 10q^2+16q+4
         2: q^5+4q^3+9q^2+10q+4
         3: 10q^2+16q+4
         4: 10q^2+16q+4
         5: 10q^2+16q+4
         6: 10q^2+16q+4
         7: q^5+4q^3+9q^2+10q+4
         8: 6q^3+10q^2+10q+4
         9: q^5+4q^3+9q^2+10q+4
        10: 10q^2+16q+4
        11: 10q^2+16q+4
        12: 10q^2+16q+4
        13: 3q^2+10q+4
        14: 3q^2+10q+4
        15: 4q^2+10q+4
        16: 10q^2+16q+4
        17: 10q^2+16q+4
        18: q^5+4q^3+9q^2+10q+4
        19: 10q^2+16q+4
        20: 10q^2+16q+4
        21: q^5+4q^3+9q^2+10q+4
        22: 4q^2+16q+4
        23: 4q^2+16q+4
        24: 2q^3+7q^2+10q+4
        25: 4q^2+16q+4
        26: 4q^2+16q+4
        27: 2q^3+7q^2+10q+4
        28: 10q^2+16q+4
        29: 10q^2+16q+4
        30: 3q^2+10q+4
        31: 4q^2+16q+4
        32: q^2+10q+4
        33: 4q^2+16q+4
        34: 4q^2+16q+4
        35: q^2+10q+4
        36: 4q^2+16q+4
        37: 8q+2
        38: 8q+2
        39: 8q+2
        40: 8q+2
        41: 3q^2+5q+2
        42: 3q^2+5q+2
        43: 3q^2+10q+4
        44: 3q^2+10q+4
        45: 4q^2+10q+4
        46: 3q^2+10q+4
        47: 4q^2+10q+4
        48: 3q^2+10q+4
        49: 10q^2+16q+4
        50: 10q^2+16q+4
        51: q^5+4q^3+9q^2+10q+4
        52: 4q^2+16q+4
        53: 4q^2+16q+4
        54: 2q^3+7q^2+10q+4
        55: 4q^2+16q+4
        56: 4q^2+16q+4
        57: 2q^3+7q^2+10q+4
        58: 2q^2+8q+2
        59: 2q^2+8q+2
        60: 2q^2+8q+2
        61: 2q^2+8q+2
        62: 8q+2
        63: 8q+2
        64: 5q+2
        65: 5q+2
        66: 8q+2
        67: 8q+2
        68: q^2+4q+4
        69: 3q^2+10q+4
        70: 3q^2+10q+4
        71: 10q^2+16q+4
        72: 4q^2+16q+4
        73: 4q^2+16q+4
        74: 8q+2
        75: 8q+2
        76: 8q+2
        77: 8q+2
        78: 3q^2+5q+2
        79: 3q^2+5q+2
        80: q^2+10q+4
        81: q^2+10q+4
        82: 4q^2+16q+4
        83: q^2+10q+4
        84: q^2+10q+4
        85: q^2+10q+4
        86: 4q^2+16q+4
        87: q^2+10q+4
        88: 3q^2+10q+4
        89: 4q^2+10q+4
        90: 3q^2+10q+4
        91: 3q^2+10q+4
        92: 4q^2+10q+4
        93: 3q^2+10q+4
        94: 4q^2+16q+4
        95: 4q^2+16q+4
        96: 2q^3+7q^2+10q+4
        97: 4q^2+16q+4
        98: 4q^2+16q+4
        99: 2q^3+7q^2+10q+4
       100: 14q+4
       101: 14q+4
       102: 4q^2+8q+4
       103: 4q+1
       104: 4q+1
       105: 4q+1
       106: 4q+1
       107: 2q^2+8q+2
       108: 2q^2+8q+2
       109: 2q^2+8q+2
       110: 2q^2+8q+2
       111: 8q+2
       112: 8q+2
       113: 8q+2
       114: 8q+2
       115: 5q+2
       116: 5q+2
       117: 2q+2
       118: 2q+2
       119: 2q+2
       120: 2q+2
       121: 5q+2
       122: 5q+2
       123: 5q+2
       124: 5q+2
       125: q^2+4q+4
       126: 3q^2+10q+4
       127: 8q+2
       128: 8q+2
       129: 8q+2
       130: 8q+2
       131: 3q^2+5q+2
       132: 3q^2+5q+2
       133: q^2+4q+4
       134: 3q^2+10q+4
       135: q^2+10q+4
       136: q^2+10q+4
       137: q^2+10q+4
       138: q^2+10q+4
       139: 4q^2+16q+4
       140: 8q+4
       141: q^2+10q+4
       142: 4q^2+16q+4
       143: q^2+10q+4
       144: q^2+10q+4
       145: 4q^2+16q+4
       146: q^2+10q+4
       147: 4q^2+16q+4
       148: 8q+4
       149: 14q+4
       150: 8q+4
       151: 7q+2
       152: 7q+2
       153: 7q+2
       154: 7q+2
       155: 2q^2+4q+2
       156: 2q^2+4q+2
       157: 3q^2+10q+4
       158: 4q^2+10q+4
       159: 3q^2+10q+4
       160: q^2+6q+4
       161: q^2+6q+4
       162: q^2+6q+4
       163: q^2+6q+4
       164: q^2+6q+4
       165: q^2+6q+4
       166: 14q+4
       167: 14q+4
       168: 4q^2+8q+4
       169: 4q+1
       170: 4q+1
       171: 4q+1
       172: 4q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: 5q+2
       178: 5q+2
       179: 8q+2
       180: 8q+2
       181: 8q+2
       182: 8q+2
       183: 2q+2
       184: 2q+2
       185: 2q+2
       186: 2q+2
       187: 5q+2
       188: 5q+2
       189: 5q+2
       190: 5q+2
       191: 2q+2
       192: 2q+2
       193: 4q+2
       194: 4q+2
       195: 2q^2+8q+2
       196: 2q^2+8q+2
       197: 4q+2
       198: 4q+2
       199: 2q+2
       200: 2q+2
       201: 2q^2+8q+2
       202: 2q^2+8q+2
       203: 4q+2
       204: 4q+2
       205: 4q+2
       206: 4q+2
       207: 5q+2
       208: 5q+2
       209: 7q+2
       210: 7q+2
       211: 4q+2
       212: 4q+2
       219: q^2+4q+4
       220: q^2+4q+4
       221: 3q^2+10q+4
       222: q^2+10q+4
       223: q^2+10q+4
       224: q^2+10q+4
       225: q^2+10q+4
       226: q^2+10q+4
       227: 2q+4
       228: q^2+6q+4
       229: 2q+4
       230: q^2+6q+4
       231: q^2+10q+4
       232: 2q+4
       233: q^2+6q+4
       234: q^2+6q+4
       235: 2q+4
       236: 8q+4
       237: 7q+2
       238: 7q+2
       239: 7q+2
       240: 7q+2
       241: 2q^2+4q+2
       242: 2q^2+4q+2
       243: 14q+4
       244: 8q+4
       245: 8q+4
       246: 8q+4
       247: 14q+4
       248: 14q+4
       249: 4q^2+8q+4
       250: q^2+6q+4
       251: q^2+6q+4
       252: q^2+6q+4
       253: q^2+6q+4
       254: q^2+6q+4
       255: q^2+6q+4
       256: 3q+4
       257: 4q+4
       258: 3q+4
       259: 4q+1
       260: 4q+1
       261: 4q+1
       262: 4q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       283: 2q+2
       284: 2q+2
       285: 2q+2
       286: 2q+2
       287: 5q+2
       288: 5q+2
       291: 5q+2
       292: 5q+2
       293: 2q+2
       294: 2q+2
       295: 2q+2
       296: 2q+2
       297: 5q+2
       298: 5q+2
       299: 2
       300: 2
       301: 4q+2
       302: 4q+2
       303: q+2
       304: q+2
       305: q+2
       306: q+2
       307: q+2
       308: q+2
       309: 2
       310: 2
       311: 4q+2
       312: 4q+2
       313: q+2
       314: q+2
       315: 4q+2
       316: 4q+2
       317: 7q+2
       318: 7q+2
       319: 4q+2
       320: 4q+2
       321: 4q+2
       322: 4q+2
       323: 2q+2
       324: 2q+2
       325: 4q+2
       326: 4q+2
       333: q^2+4q+4
       334: q^2+10q+4
       335: q^2+10q+4
       336: 8q+4
       337: 14q+4
       338: 7q+2
       339: 7q+2
       340: 7q+2
       341: 7q+2
       342: 2q^2+4q+2
       343: 2q^2+4q+2
       344: 2q+4
       345: 2q+4
       346: q^2+6q+4
       347: 2q+4
       348: 2q+4
       349: q^2+6q+4
       350: q^2+6q+4
       351: 8q+4
       352: 2q+4
       353: 2q+4
       354: q^2+6q+4
       355: q^2+6q+4
       356: q^2+6q+4
       357: 2q+4
       358: 2q+4
       359: 8q+4
       366: 8q+4
       367: q+4
       368: 3q+4
       369: q+4
       370: q+4
       371: 3q+4
       372: 4q+4
       373: 3q+4
       374: 3q+4
       375: 4q+4
       376: 3q+4
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: 2q+1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       419: 2q+2
       420: 2q+2
       421: 2q+2
       422: 2q+2
       423: 5q+2
       424: 5q+2
       425: 4q+2
       426: 4q+2
       427: 7q+2
       428: 7q+2
       429: 2
       430: 2
       431: q+2
       432: q+2
       433: q+2
       434: q+2
       437: 2
       438: 2
       439: q+2
       440: q+2
       441: q+2
       442: q+2
       443: 4q+2
       444: 4q+2
       445: 4q+2
       446: 4q+2
       447: q+2
       448: q+2
       449: 2
       450: 2
       451: q+2
       452: q+2
       453: q+2
       454: q+2
       457: 2
       458: 2
       459: q+2
       460: q+2
       461: 4q+2
       462: 4q+2
       463: 4q+2
       464: 4q+2
       469: 4q+2
       470: 4q+2
       471: 2
       472: 2
       473: 2
       474: 2
       475: 2
       476: 2
       477: 2q+2
       478: 2q+2
       479: 2q+2
       480: 2q+2
       481: 2q+4
       482: 2q+4
       483: 8q+4
       484: q+4
       491: 3q+4
       492: 2q+4
       493: 2q+4
       494: q^2+6q+4
       495: 2q+4
       496: q+4
       497: 2q+4
       498: q^2+6q+4
       499: 2q+4
       500: 2q+4
       501: q+4
       508: q+4
       509: q+4
       510: 3q+4
       511: q+4
       512: q+4
       513: q+4
       514: q+4
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: 3q+4
       519: 4q+4
       520: 3q+4
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 2q+2
       581: 2q+2
       589: q+2
       590: q+2
       591: 2
       592: 2
       593: 2
       594: 2
       595: q+2
       596: q+2
       599: 4q+2
       600: 4q+2
       603: 2
       604: 2
       607: q+2
       608: q+2
       609: q+2
       610: q+2
       613: q+2
       614: q+2
       615: 2
       616: 2
       619: q+2
       620: q+2
       621: 2
       622: 2
       625: q+2
       626: q+2
       629: q+2
       630: q+2
       631: 2
       632: 2
       641: 2
       642: 2
       643: 2
       644: 2
       645: 2
       646: 2
       647: 2
       648: 2
       649: 2
       650: 2
       653: 2
       654: 2
       655: 2
       656: 2
       657: q+4
       664: 3q+4
       665: q+4
       672: q+4
       673: 3q+4
       674: q+4
       675: 2
       676: 2q+4
       677: 2q+4
       678: q+4
       679: q+4
       680: q+4
       681: 2q+4
       682: 2
       683: 2q+4
       684: q+4
       685: q+4
       686: q+4
       687: q+4
       688: q+4
       689: 2
       690: 3q+4
       691: 4q+4
       692: 3q+4
       693: q+1
       697: q+1
       699: q+1
       700: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       741: 1
       742: 1
       743: 1
       744: 1
       753: 1
       754: 1
       755: 1
       756: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       785: 2
       786: 2
       787: 2
       788: 2
       791: 2
       792: 2
       793: 2
       794: 2
       801: 1
       802: 1
       805: 2
       806: 2
       807: q+2
       808: q+2
       811: q+2
       812: q+2
       815: 2
       816: 2
       817: 2
       818: 2
       825: q+2
       826: q+2
       827: 2
       828: 2
       831: 1
       832: 1
       835: q+2
       836: q+2
       839: 2
       840: 2
       843: 2
       844: 2
       845: 2
       846: 2
       847: 2
       848: 2
       851: 2
       852: 2
       855: 1
       856: 1
       857: 2
       858: 2
       865: q+4
       866: q+4
       867: 3q+4
       868: q+4
       869: q+4
       870: q+4
       871: 2
       872: q+4
       873: q+4
       874: q+4
       875: 2
       876: q+4
       877: 2
       878: 2
       879: 2
       880: 2
       908: 1
       909: 1
       910: 1
       911: 1
       928: 1
       929: 1
       930: 1
       931: 1
       948: 1
       949: 1
       950: 1
       951: 1
       964: 1
       965: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       977: 1
       988: 1
       989: 1
       990: 1
       991: 1
       998: 2
       999: 2
      1000: 2
      1001: 2
      1004: 2
      1005: 2
      1006: 2
      1007: 2
      1008: 2
      1009: 2
      1012: 2
      1013: 2
      1016: 2
      1017: 2
      1026: 1
      1027: 1
      1032: 2
      1033: 2
      1044: 1
      1045: 1
      1046: 2
      1047: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1074: q+4
      1076: 2
      1077: q+4
      1078: 2
      1080: 2
      1081: q+4
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1224: 2
      1225: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 2
      1289: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1673: 1

1674:    0: 10q^2+16q+4
         1: 10q^2+16q+4
         2: 10q^2+16q+4
         3: 10q^2+16q+4
         4: q^5+4q^3+9q^2+10q+4
         5: 10q^2+16q+4
         6: 6q^3+10q^2+10q+4
         7: q^5+4q^3+9q^2+10q+4
         8: 10q^2+16q+4
         9: q^5+4q^3+9q^2+10q+4
        10: 4q^2+16q+4
        11: 4q^2+16q+4
        12: 2q^3+7q^2+10q+4
        13: 10q^2+16q+4
        14: q^5+4q^3+9q^2+10q+4
        15: 10q^2+16q+4
        16: 10q^2+16q+4
        17: 10q^2+16q+4
        18: q^5+4q^3+9q^2+10q+4
        19: 3q^2+10q+4
        20: 4q^2+10q+4
        21: 3q^2+10q+4
        22: 10q^2+16q+4
        23: 10q^2+16q+4
        24: 10q^2+16q+4
        25: 10q^2+16q+4
        26: 10q^2+16q+4
        27: 10q^2+16q+4
        28: 4q^2+16q+4
        29: q^2+10q+4
        30: 3q^2+10q+4
        31: 4q^2+16q+4
        32: 10q^2+16q+4
        33: 10q^2+16q+4
        34: 4q^2+16q+4
        35: 10q^2+16q+4
        36: 10q^2+16q+4
        37: 5q^2+8q+2
        38: 5q^2+8q+2
        39: 5q^2+8q+2
        40: 5q^2+8q+2
        41: 5q^2+8q+2
        42: 5q^2+8q+2
        43: 4q^2+16q+4
        44: 2q^3+7q^2+10q+4
        45: 4q^2+16q+4
        46: 10q^2+16q+4
        47: 10q^2+16q+4
        48: q^5+4q^3+9q^2+10q+4
        49: 3q^2+10q+4
        50: 4q^2+10q+4
        51: 3q^2+10q+4
        52: 3q^2+10q+4
        53: 4q^2+10q+4
        54: 3q^2+10q+4
        55: 3q^2+10q+4
        56: 4q^2+10q+4
        57: 3q^2+10q+4
        58: 2q^2+8q+2
        59: 2q^2+8q+2
        60: 2q^2+8q+2
        61: 2q^2+8q+2
        62: 2q^2+8q+2
        63: 2q^2+8q+2
        64: 5q^2+8q+2
        65: 5q^2+8q+2
        66: 5q^2+8q+2
        67: 5q^2+8q+2
        68: 4q^2+16q+4
        69: 3q^2+10q+4
        70: q^2+10q+4
        71: q^2+10q+4
        72: q^2+4q+4
        73: q^2+4q+4
        74: 3q+2
        75: 3q+2
        76: 3q+2
        77: 3q+2
        78: 3q+2
        79: 3q+2
        80: 4q^2+16q+4
        81: 10q^2+16q+4
        82: q^2+10q+4
        83: 3q^2+10q+4
        84: 4q^2+16q+4
        85: 10q^2+16q+4
        86: q^2+10q+4
        87: 3q^2+10q+4
        88: 4q^2+16q+4
        89: 4q^2+16q+4
        90: 2q^3+7q^2+10q+4
        91: 3q^2+10q+4
        92: 4q^2+10q+4
        93: 3q^2+10q+4
        94: 3q^2+10q+4
        95: 4q^2+10q+4
        96: 3q^2+10q+4
        97: 3q^2+10q+4
        98: 4q^2+10q+4
        99: 3q^2+10q+4
       100: 3q^2+10q+4
       101: 4q^2+10q+4
       102: 3q^2+10q+4
       103: q^2+4q+1
       104: q^2+4q+1
       105: q^2+4q+1
       106: q^2+4q+1
       107: 2q+2
       108: 2q+2
       109: 2q+2
       110: 2q+2
       111: 2
       112: 2
       113: 3q+2
       114: 3q+2
       115: 3q+2
       116: 3q+2
       117: 2q^2+8q+2
       118: 2q^2+8q+2
       119: 2q^2+8q+2
       120: 2q^2+8q+2
       121: 2q^2+8q+2
       122: 2q^2+8q+2
       123: 5q^2+8q+2
       124: 5q^2+8q+2
       125: 4q^2+16q+4
       126: q^2+10q+4
       127: 3q+2
       128: 3q+2
       129: 3q+2
       130: 3q+2
       131: 3q+2
       132: 3q+2
       133: q^2+10q+4
       134: 3q^2+10q+4
       135: q^2+4q+4
       136: q^2+4q+4
       137: 4q^2+16q+4
       138: 3q^2+10q+4
       139: q^2+10q+4
       140: q^2+4q+4
       141: q^2+10q+4
       142: q^2+4q+4
       143: 4q^2+16q+4
       144: 3q^2+10q+4
       145: q^2+10q+4
       146: q^2+10q+4
       147: q^2+4q+4
       148: q^2+4q+4
       149: q^2+10q+4
       150: 3q^2+10q+4
       151: 3q+2
       152: 3q+2
       153: 3q+2
       154: 3q+2
       155: 3q+2
       156: 3q+2
       157: q^2+6q+4
       158: q^2+6q+4
       159: q^2+6q+4
       160: 3q^2+10q+4
       161: 4q^2+10q+4
       162: 3q^2+10q+4
       163: 3q^2+10q+4
       164: 4q^2+10q+4
       165: 3q^2+10q+4
       166: 3q^2+10q+4
       167: 4q^2+10q+4
       168: 3q^2+10q+4
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+4q+1
       174: q^2+4q+1
       175: q^2+4q+1
       176: q^2+4q+1
       177: 3q+2
       178: 3q+2
       179: 3q+2
       180: 3q+2
       181: 2
       182: 2
       183: 2q+2
       184: 2q+2
       185: 2q+2
       186: 2q+2
       187: 2
       188: 2
       189: 3q+2
       190: 3q+2
       191: 2q^2+8q+2
       192: 2q^2+8q+2
       193: 2q+2
       194: 2q+2
       195: 2q+2
       196: 2q+2
       197: 2
       198: 2
       199: 2q^2+8q+2
       200: 2q^2+8q+2
       201: 2q+2
       202: 2q+2
       203: 2q+2
       204: 2q+2
       205: 2
       206: 2
       207: 2q^2+8q+2
       208: 2q^2+8q+2
       209: 3q+2
       210: 3q+2
       211: 3q+2
       212: 3q+2
       213: 3q+2
       214: 3q+2
       215: 3q+2
       216: 3q+2
       217: 3q+2
       218: 3q+2
       219: q^2+10q+4
       220: q^2+6q+4
       221: q^2+6q+4
       222: 2q+4
       223: q^2+4q+4
       224: 2q+4
       225: q^2+4q+4
       226: q^2+10q+4
       227: q^2+10q+4
       228: 3q^2+10q+4
       229: q^2+4q+4
       230: q^2+4q+4
       231: q^2+10q+4
       232: q^2+10q+4
       233: 3q^2+10q+4
       234: q^2+4q+4
       235: q^2+4q+4
       236: 3q^2+10q+4
       237: 3q+2
       238: 3q+2
       239: 3q+2
       240: 3q+2
       241: 3q+2
       242: 3q+2
       243: q^2+10q+4
       244: q^2+4q+4
       245: q^2+4q+4
       246: q^2+10q+4
       247: 8
       248: 8
       249: 4q+2
       250: q^2+6q+4
       251: q^2+6q+4
       252: q^2+6q+4
       253: q^2+6q+4
       254: q^2+6q+4
       255: q^2+6q+4
       256: 3q^2+10q+4
       257: 4q^2+10q+4
       258: 3q^2+10q+4
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q^2+4q+1
       276: q^2+4q+1
       277: q^2+4q+1
       278: q^2+4q+1
       279: 3q+2
       280: 3q+2
       281: 3q+2
       282: 3q+2
       283: 2q+2
       284: 2q+2
       285: 2q+2
       286: 2q+2
       287: 3q+2
       288: 3q+2
       289: 2
       290: 2
       291: 2
       292: 2
       293: q+2
       294: q+2
       295: q+2
       296: q+2
       297: 2
       298: 2
       299: 2q+2
       300: 2q+2
       301: 2
       302: 2
       303: 2q+2
       304: 2q+2
       305: 2
       306: 2
       307: 2q+2
       308: 2q+2
       309: 2q+2
       310: 2q+2
       311: 2
       312: 2
       313: 2
       314: 2
       315: 3q+2
       316: 3q+2
       317: 3q+2
       318: 3q+2
       319: 2q+2
       320: 2q+2
       321: 2q+2
       322: 2q+2
       323: 2
       324: 2
       325: 3q+2
       326: 3q+2
       333: q^2+6q+4
       334: 2q+4
       335: 2q+4
       336: 2
       337: 8
       338: 4
       339: 4
       340: 4
       341: 4
       342: 2q+1
       343: 2q+1
       344: q^2+10q+4
       345: q^2+6q+4
       346: q^2+6q+4
       347: 2q+4
       348: q^2+4q+4
       349: 2q+4
       350: q^2+4q+4
       351: 8
       352: q^2+10q+4
       353: q^2+6q+4
       354: q^2+6q+4
       355: 2q+4
       356: q^2+4q+4
       357: 2q+4
       358: q^2+4q+4
       359: 8
       360: 3q+2
       361: 3q+2
       362: 3q+2
       363: 3q+2
       364: 3q+2
       365: 3q+2
       366: q^2+10q+4
       367: q^2+10q+4
       368: 3q^2+10q+4
       369: q^2+4q+4
       370: q^2+4q+4
       371: 8
       372: 8
       373: 4q+2
       374: q^2+6q+4
       375: q^2+6q+4
       376: q^2+6q+4
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       413: 3q+2
       414: 3q+2
       417: 2
       418: 2
       419: q+2
       420: q+2
       421: q+2
       422: q+2
       423: 2
       424: 2
       425: 1
       426: 1
       427: 4
       428: 4
       429: 2q+2
       430: 2q+2
       431: 2q+2
       432: 2q+2
       433: 2
       434: 2
       435: 2
       436: 2
       437: q+2
       438: q+2
       439: q+2
       440: q+2
       441: 2
       442: 2
       443: 4
       444: 4
       445: 4
       446: 4
       447: 2q+2
       448: 2q+2
       449: 2q+2
       450: 2q+2
       451: 2
       452: 2
       453: q+2
       454: q+2
       455: 2
       456: 2
       457: q+2
       458: q+2
       459: 2
       460: 2
       461: 4
       462: 4
       463: 4
       464: 4
       465: 3q+2
       466: 3q+2
       467: 3q+2
       468: 3q+2
       469: 3q+2
       470: 3q+2
       471: 2q+2
       472: 2q+2
       473: 2q+2
       474: 2q+2
       475: 2
       476: 2
       477: 2
       478: 2
       479: 4
       480: 4
       481: 2q+4
       482: 2q+4
       483: 2
       484: 8
       485: 4
       486: 4
       487: 4
       488: 4
       489: 2q+1
       490: 2q+1
       491: 2
       492: q^2+6q+4
       493: 2q+4
       494: 2q+4
       495: 2
       496: 8
       497: q^2+6q+4
       498: 2q+4
       499: 2q+4
       500: 2
       501: 8
       508: q^2+10q+4
       509: q^2+6q+4
       510: q^2+6q+4
       511: 2q+4
       512: q^2+4q+4
       513: 2q+4
       514: q^2+4q+4
       515: 8
       516: 8
       517: 4q+2
       518: 4
       519: 4
       520: 2q+1
       521: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2
       546: 2
       547: 2
       548: 2
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 2
       562: 2
       563: 2
       564: 2
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 2
       574: 2
       575: 2
       576: 2
       577: 2
       578: 2
       580: 2
       581: 2
       585: 2
       586: 2
       589: q+2
       590: q+2
       595: q+2
       596: q+2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 4
       602: 4
       603: q+2
       604: q+2
       605: 2
       606: 2
       607: q+2
       608: q+2
       609: 2
       610: 2
       613: 1
       614: 1
       615: 4
       616: 4
       617: 4
       618: 4
       619: q+2
       620: q+2
       621: q+2
       622: q+2
       623: 2
       624: 2
       625: 2
       626: 2
       629: 1
       630: 1
       631: 4
       632: 4
       633: 4
       634: 4
       639: 3q+2
       640: 3q+2
       641: 2q+2
       642: 2q+2
       643: 2q+2
       644: 2q+2
       645: 2
       646: 2
       647: q+2
       648: q+2
       649: q+2
       650: q+2
       651: 2
       652: 2
       653: 2
       654: 2
       655: 4
       656: 4
       657: 8
       658: 4
       659: 4
       660: 4
       661: 4
       662: 2q+1
       663: 2q+1
       664: 2
       665: 2
       672: 4
       673: 1
       674: 8
       675: 2q+4
       676: 2q+4
       677: 2
       678: 4
       679: 2
       680: 8
       681: 2q+4
       682: 2q+4
       683: 2
       684: 4
       685: 2
       686: q^2+6q+4
       687: 2q+4
       688: 2q+4
       689: 2
       690: 4
       691: 4
       692: 2q+1
       693: 1
       694: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       709: 1
       710: 1
       711: 1
       712: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       733: 2
       734: 2
       735: 2
       736: 2
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       749: 2
       750: 2
       751: 2
       752: 2
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 2
       766: 2
       767: 2
       768: 2
       769: 2
       770: 2
       772: 2
       773: 2
       775: 4
       776: 4
       779: 1
       780: 1
       781: 1
       782: 1
       793: 4
       794: 4
       795: 4
       796: 4
       797: 2
       798: 2
       801: q+2
       802: q+2
       807: q+2
       808: q+2
       809: 1
       810: 1
       811: 1
       812: 1
       815: 2
       816: 2
       817: 4
       818: 4
       819: 4
       820: 4
       821: 2
       822: 2
       825: q+2
       826: q+2
       831: q+2
       832: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 2
       840: 2
       843: 4
       844: 4
       845: q+2
       846: q+2
       847: q+2
       848: q+2
       849: 2
       850: 2
       851: 2
       852: 2
       855: 1
       856: 1
       857: 2
       858: 2
       865: 4
       866: 2
       867: 1
       868: 1
       869: 4
       870: 2
       871: 2
       872: 1
       873: 4
       874: 2
       875: 2
       876: 1
       877: 2q+4
       878: 2q+4
       879: 2
       880: 2
       881: 4
       882: 4
       883: 2q+1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       916: 2
       917: 2
       918: 2
       919: 2
       920: 1
       921: 1
       922: 1
       923: 1
       940: 2
       941: 2
       942: 2
       943: 2
       944: 1
       945: 1
       946: 1
       947: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 2
       965: 2
       966: 2
       967: 2
       968: 2
       969: 2
       971: 2
       972: 2
       974: 1
       975: 1
       976: 1
       977: 1
       988: 1
       989: 1
       990: 1
       991: 1
       994: 1
       995: 1
      1016: 2
      1017: 2
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1032: 2
      1033: 2
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1046: 2
      1047: 2
      1048: 2
      1049: 2
      1052: q+2
      1053: q+2
      1058: q+2
      1059: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 4
      1073: 1
      1074: 1
      1075: 4
      1076: 2
      1077: 1
      1078: 1
      1079: 4
      1080: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1228: 2
      1229: 2
      1230: 1
      1231: 1
      1246: 2
      1247: 2
      1248: 1
      1249: 1
      1262: 2
      1263: 2
      1266: 1
      1267: 1
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 2
      1288: 1
      1289: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1464: 1
      1465: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1674: 1

1675:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+2q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: 3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q^2+2q+1
        61: q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       106: q
       107: q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q^2+2q+1
       120: q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+2q+1
       184: q
       185: q^2+2q+1
       186: q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q+1
       271: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+2q+1
       294: q
       295: q^2+2q+1
       296: q
       297: q^2+3q+1
       299: q+1
       301: q+1
       303: 2q+1
       304: q
       305: q+1
       307: 2q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       429: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: q+1
       449: 1
       451: 1
       453: 2q+1
       454: q
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q+1
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: 1
       537: q+1
       541: q+1
       545: q+1
       549: 1
       553: q+1
       557: q+1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       591: 1
       593: 1
       595: q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: 1
       607: q+1
       609: 1
       611: q+1
       613: 1
       615: q+1
       617: q+1
       619: q+1
       621: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: q+1
       649: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       693: q+1
       705: q+1
       709: q+1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: q+1
       737: 1
       741: 1
       745: q+1
       749: q+1
       753: 1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       813: q+1
       815: q+1
       817: 1
       819: 1
       821: 1
       823: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       837: q+1
       839: q+1
       841: q+1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: q+1
       857: q+1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       884: q+1
       896: q+1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: q+1
       936: 1
       940: 1
       944: 1
       948: 1
       956: q+1
       960: 1
       964: 1
       968: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
       992: 1
       994: 1
       996: 1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1058: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1086: 1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1210: 1
      1212: 1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1228: 1
      1236: 1
      1238: 1
      1240: 1
      1244: 1
      1246: 1
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1264: 1
      1282: 1
      1284: 1
      1286: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1352: 1
      1372: 1
      1376: 1
      1404: 1
      1410: 1
      1414: 1
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1452: 1
      1458: 1
      1489: 1
      1525: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1675: 1

1676:    0: 4q^3+7q^2+3q
         1: 4q^3+7q^2+3q
         2: 4q^3+7q^2+3q
         3: q^4+5q^3+7q^2+3q
         4: 4q^3+7q^2+3q
         5: q^4+5q^3+7q^2+3q
         6: 4q^3+7q^2+3q
         7: 4q^3+7q^2+3q
         8: q^4+5q^3+7q^2+3q
         9: 2q^4+4q^3+4q^2+2q
        10: 4q^3+7q^2+3q
        11: q^4+5q^3+7q^2+3q
        12: 4q^3+7q^2+3q
        13: 4q^3+7q^2+3q
        14: 4q^3+7q^2+3q
        15: q^4+5q^3+7q^2+3q
        16: 2q^3+6q^2+3q
        17: 2q^3+6q^2+3q
        18: 3q^3+4q^2+2q
        19: 4q^3+7q^2+3q
        20: 4q^3+7q^2+3q
        21: 4q^3+7q^2+3q
        22: 2q^3+6q^2+3q
        23: 2q^3+6q^2+3q
        24: 2q^3+6q^2+3q
        25: 2q^3+6q^2+3q
        26: 2q^3+6q^2+3q
        27: 2q^3+6q^2+3q
        28: 2q^3+6q^2+3q
        29: 4q^3+7q^2+3q
        30: 4q^3+7q^2+3q
        31: 2q^3+6q^2+3q
        32: 2q^3+6q^2+3q
        33: q^3+5q^2+3q
        34: 2q^3+6q^2+3q
        35: 2q^3+6q^2+3q
        36: q^3+5q^2+3q
        37: q^3+2q^2+q
        38: 3q^2+2q
        39: q^3+2q^2+q
        40: 3q^2+2q
        41: q^3+2q^2+q
        42: 3q^2+2q
        43: 4q^3+7q^2+3q
        44: 4q^3+7q^2+3q
        45: q^4+5q^3+7q^2+3q
        46: 2q^3+6q^2+3q
        47: 2q^3+6q^2+3q
        48: 3q^3+4q^2+2q
        49: 2q^3+6q^2+3q
        50: 2q^3+6q^2+3q
        51: 3q^3+4q^2+2q
        52: 2q^3+6q^2+3q
        53: 2q^3+6q^2+3q
        54: 2q^3+6q^2+3q
        55: 2q^3+6q^2+3q
        56: 2q^3+6q^2+3q
        57: 2q^3+6q^2+3q
        58: q^3+3q^2+2q
        59: 2q^2+q
        60: q^3+3q^2+2q
        61: 2q^2+q
        62: q^3+2q^2+q
        63: 3q^2+2q
        64: q^3+2q^2+q
        65: 3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 2q^3+6q^2+3q
        69: q^3+3q^2+2q
        70: 4q^3+7q^2+3q
        71: 2q^3+6q^2+3q
        72: q^3+5q^2+3q
        73: q^3+5q^2+3q
        74: q^3+2q^2+q
        75: 3q^2+2q
        76: q^3+2q^2+q
        77: 3q^2+2q
        78: q^3+2q^2+q
        79: 3q^2+2q
        80: 2q^3+6q^2+3q
        81: q^3+5q^2+3q
        82: 2q^3+6q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: q^3+5q^2+3q
        86: 2q^3+6q^2+3q
        87: 2q^3+6q^2+3q
        88: 2q^3+6q^2+3q
        89: 2q^3+6q^2+3q
        90: 3q^3+4q^2+2q
        91: 2q^3+6q^2+3q
        92: 2q^3+6q^2+3q
        93: 3q^3+4q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+3q^2+2q
       100: 3q^2+3q
       101: 3q^2+3q
       102: 3q^2+3q
       103: q^3+q^2+q
       104: q^2+q
       105: q^2+q
       106: q^2
       107: q^3+3q^2+2q
       108: 2q^2+q
       109: q^3+3q^2+2q
       110: 2q^2+q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: q^3+2q^2+q
       114: 3q^2+2q
       115: q^3+2q^2+q
       116: 3q^2+2q
       117: q^3+3q^2+2q
       118: 2q^2+q
       119: q^3+3q^2+2q
       120: 2q^2+q
       121: q^3+2q^2+q
       122: 3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 2q^3+6q^2+3q
       126: q^3+3q^2+2q
       128: 2q
       130: 2q
       132: q^2+q
       133: 2q^3+6q^2+3q
       134: q^3+3q^2+2q
       135: q^3+5q^2+3q
       136: q^3+5q^2+3q
       137: q^3+5q^2+3q
       138: 2q^2+2q
       139: 3q^2+3q
       140: 2q
       141: 2q^3+6q^2+3q
       142: 3q^2+3q
       143: q^3+5q^2+3q
       144: 2q^2+2q
       145: 3q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^2+3q
       148: 2q
       149: 3q^2+3q
       150: 3q^2+3q
       151: q^2+q
       152: 2q^2+2q
       153: q^2+q
       154: 2q^2+2q
       155: q^2+q
       156: 2q^2+2q
       157: 2q^3+6q^2+3q
       158: 2q^3+6q^2+3q
       159: 3q^3+4q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+3q^2+2q
       166: q^2+3q
       167: q^2+3q
       168: q^2+2q
       169: q^3+q^2+q
       170: q^2+q
       171: q^2+q
       172: q^2
       173: q^3+q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q
       180: 2q
       182: 2q
       183: q^3+3q^2+2q
       184: 2q^2+q
       185: q^3+3q^2+2q
       186: 2q^2+q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: q^3+2q^2+q
       190: 3q^2+2q
       191: q^3+3q^2+2q
       192: 2q^2+q
       193: 2q
       195: 2q^2+2q
       196: q^2+q
       197: q
       198: q
       199: q^3+3q^2+2q
       200: 2q^2+q
       201: 2q^2+2q
       202: q^2+q
       203: 2q
       205: q
       206: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: 2q^2+2q
       211: q^2+q
       212: 2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: q^3+3q^2+2q
       220: 2q^3+6q^2+3q
       221: q^3+3q^2+2q
       222: q^3+5q^2+3q
       223: 2q^2+2q
       224: q^3+5q^2+3q
       225: 2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^2+2q
       234: 3q^2+3q
       235: 2q
       236: q^2+2q
       238: 2q
       240: 2q
       242: q
       243: q^2+3q
       244: 2q
       245: 2q
       246: 3q^2+3q
       247: q^2+3q
       248: q^2+3q
       249: q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+3q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: q^2+2q
       260: q
       261: q
       263: q^3+q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2
       267: q
       268: q
       271: q
       272: q
       275: q^3+q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: 2q
       282: q
       283: q^2+q
       285: q^2+q
       288: q
       290: 2q
       292: q
       293: q^3+3q^2+2q
       294: 2q^2+q
       295: q^3+3q^2+2q
       296: 2q^2+q
       297: q^3+2q^2+q
       298: 2q^2+2q
       299: 2q
       302: q
       303: 2q^2+2q
       304: q^2+q
       305: q
       306: q
       307: 2q^2+2q
       308: q^2+q
       309: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       319: 2q
       321: 2q
       323: q
       325: q^2+q
       326: 2q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: q^3+3q^2+2q
       334: 2q^2+2q
       335: 2q^2+2q
       336: q^2+2q
       337: q^2+3q
       339: 2q
       341: 2q
       343: q
       344: 2q^2+2q
       345: 3q^2+3q
       346: 2q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: 2q^2+2q
       351: 2q
       352: 2q^2+2q
       353: 3q^2+3q
       354: 2q^2+2q
       355: 3q^2+3q
       356: 2q^2+2q
       357: 2q
       358: q
       359: 2q
       361: 2q
       363: 2q
       365: q
       366: q^2+2q
       367: q^2+3q
       368: q^2+2q
       369: 2q
       370: 2q
       371: q^2+3q
       372: q^2+3q
       373: q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: q^2+2q
       382: q
       383: q
       385: q^3+q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2
       390: q
       393: q
       394: q
       398: q
       401: q
       402: q
       405: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       419: q^2+q
       421: q^2+q
       424: q
       426: q
       428: 2q
       429: q
       431: q^2+q
       436: q
       437: 2q
       439: 2q^2+2q
       440: q^2+q
       441: q
       442: q
       443: 2q
       446: q
       447: q^2+q
       449: q
       453: 2q^2+2q
       454: q^2+q
       456: q
       457: 2q
       459: q
       460: q
       461: 2q
       464: q
       466: 2q
       468: q
       470: q
       471: 2q
       473: 2q
       475: q
       479: q
       481: 2q^2+2q
       482: 2q^2+2q
       483: q^2+2q
       484: q^2+3q
       486: 2q
       488: 2q
       490: q
       491: q^2+2q
       492: 2q^2+2q
       493: q
       494: 2q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: 2q^2+2q
       499: q
       500: q
       501: 2q
       503: 2q
       505: 2q
       507: q
       508: q^2+2q
       509: q^2+3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+3q
       519: q^2+3q
       520: q^2+2q
       526: q
       527: q
       538: q
       541: q
       542: q
       546: q
       554: q
       557: q
       558: q
       562: q
       565: q
       573: q
       584: q
       586: q
       588: q
       589: q^2+q
       591: q
       593: q
       595: q^2+q
       598: q
       600: q
       602: 2q
       603: q
       607: q^2+q
       612: q
       615: 2q
       618: q
       619: q^2+q
       621: q
       628: q
       631: 2q
       634: q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       647: 2q
       649: 2q
       653: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q^2+2q
       667: 2q
       669: 2q
       671: q
       672: q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: 2q^2+2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q^2+2q
       682: q
       683: q
       684: 2q
       685: q
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       730: q
       734: q
       746: q
       750: q
       761: q
       765: q
       776: 1
       778: q
       780: 1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       793: 1
       796: 1
       801: q
       805: q
       807: q^2+q
       814: q
       815: 2q
       817: 1
       820: 1
       825: q^2+q
       827: q
       831: q
       838: q
       839: 2q
       842: q
       843: 1
       845: q
       847: q
       857: q
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       917: 1
       933: q
       941: 1
       957: q
       964: 1
       969: 1
       988: q
       993: 1
       995: 1
       997: 1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 1
      1016: 1
      1021: 1
      1026: q
      1031: 1
      1032: 1
      1037: 1
      1044: q
      1046: 1
      1052: q
      1058: q
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1211: 1
      1213: 1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1227: 1
      1228: 1
      1237: 1
      1240: q
      1245: 1
      1246: 1
      1253: 1
      1260: q
      1262: 1
      1282: 1
      1284: 1
      1286: 1
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1341: 1
      1373: 1
      1405: 1
      1410: 1
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1453: 1
      1459: 1
      1490: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1676: 1

1677:    0: 3q^4+5q^3+3q^2+q
         1: q^5+4q^4+5q^3+3q^2+q
         2: 3q^4+5q^3+3q^2+q
         3: q^5+4q^4+5q^3+3q^2+q
         4: 3q^4+5q^3+3q^2+q
         5: 3q^4+5q^3+3q^2+q
         6: q^5+4q^4+5q^3+3q^2+q
         7: 3q^4+5q^3+3q^2+q
         8: 3q^4+5q^3+3q^2+q
         9: q^5+3q^4+3q^3+2q^2+q
        10: 2q^4+4q^3+3q^2+q
        11: 2q^4+4q^3+3q^2+q
        12: 2q^4+4q^3+3q^2+q
        13: 3q^4+5q^3+3q^2+q
        14: 3q^4+5q^3+3q^2+q
        15: 3q^4+5q^3+3q^2+q
        16: 2q^4+4q^3+3q^2+q
        17: 2q^4+4q^3+3q^2+q
        18: 2q^4+3q^3+2q^2+q
        19: 3q^4+5q^3+3q^2+q
        20: q^5+4q^4+5q^3+3q^2+q
        21: 3q^4+5q^3+3q^2+q
        22: 4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: 4q^3+3q^2+q
        25: 4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: 4q^3+3q^2+q
        28: q^4+3q^3+3q^2+q
        29: 2q^4+4q^3+3q^2+q
        30: 3q^4+5q^3+3q^2+q
        31: 3q^3+3q^2+q
        32: 4q^3+3q^2+q
        33: 3q^3+3q^2+q
        34: 3q^3+3q^2+q
        35: 4q^3+3q^2+q
        36: 3q^3+3q^2+q
        37: 4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: 4q^3+3q^2+q
        43: 2q^4+4q^3+3q^2+q
        44: 2q^4+4q^3+3q^2+q
        45: 2q^4+4q^3+3q^2+q
        46: 2q^4+4q^3+3q^2+q
        47: 2q^4+4q^3+3q^2+q
        48: 2q^4+3q^3+2q^2+q
        49: 2q^4+4q^3+3q^2+q
        50: 2q^4+4q^3+3q^2+q
        51: 2q^4+3q^3+2q^2+q
        52: 4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: 4q^3+3q^2+q
        55: 4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: 4q^3+3q^2+q
        58: 2q^3+2q^2+q
        59: q^2
        60: 2q^3+2q^2+q
        61: q^2
        62: 3q^3+3q^2+q
        64: 4q^3+3q^2+q
        66: 3q^3+3q^2+q
        68: q^4+3q^3+3q^2+q
        69: q^4+2q^3+2q^2+q
        70: 2q^4+4q^3+3q^2+q
        71: q^4+3q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 3q^3+3q^2+q
        74: 4q^3+3q^2+q
        76: q^4+4q^3+3q^2+q
        78: 4q^3+3q^2+q
        80: 3q^3+3q^2+q
        81: 3q^3+3q^2+q
        82: 3q^3+3q^2+q
        83: 4q^3+3q^2+q
        84: 3q^3+3q^2+q
        85: 3q^3+3q^2+q
        86: 3q^3+3q^2+q
        87: 4q^3+3q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: 2q^4+4q^3+3q^2+q
        92: 2q^4+4q^3+3q^2+q
        93: 2q^4+3q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: q^3+2q^2+q
       101: q^3+2q^2+q
       102: q^3+2q^2+q
       103: 2q^3+2q^2+q
       106: q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: 2q^3+2q^2+q
       110: q^2
       111: 3q^3+3q^2+q
       113: 3q^3+3q^2+q
       115: 4q^3+3q^2+q
       117: 2q^3+2q^2+q
       118: q^2
       119: 2q^3+2q^2+q
       120: q^2
       121: 3q^3+3q^2+q
       123: 3q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^4+3q^3+3q^2+q
       134: q^4+2q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^3+3q^2+q
       138: q^3+2q^2+q
       139: q^3+3q^2+q
       140: q^2+q
       141: 3q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^3+3q^2+q
       144: q^3+2q^2+q
       145: q^3+3q^2+q
       146: 3q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: q^3+2q^2+q
       151: q^3+2q^2+q
       153: q^3+2q^2+q
       155: q^3+2q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^3+3q^2+q
       161: 2q^3+3q^2+q
       162: 2q^3+2q^2+q
       163: 2q^3+3q^2+q
       164: 2q^3+3q^2+q
       165: 2q^3+2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: 2q^3+2q^2+q
       172: q^2
       173: 2q^3+2q^2+q
       176: q^2
       177: q^3+2q^2+q
       179: q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: 2q^3+2q^2+q
       184: q^2
       185: 2q^3+2q^2+q
       186: q^2
       187: 3q^3+3q^2+q
       189: 3q^3+3q^2+q
       191: q^3+2q^2+q
       192: q^2
       193: q^2+q
       195: q^3+2q^2+q
       196: q^2
       197: q^2+q
       199: q^3+2q^2+q
       200: q^2
       201: q^3+2q^2+q
       202: q^2
       203: q^2+q
       205: q^2+q
       207: q^3+3q^2+q
       209: q^3+2q^2+q
       211: q^3+2q^2+q
       213: 2q^3+3q^2+q
       215: 2q^3+3q^2+q
       217: 2q^3+2q^2+q
       219: q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: 2q^2+q
       227: q^3+3q^2+q
       228: q^3+2q^2+q
       229: q^2+q
       230: 2q^3+3q^2+q
       231: 2q^2+q
       232: q^3+3q^2+q
       233: q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: q^2+q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^3+2q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: 2q^3+2q^2+q
       266: q^2
       267: q^2+q
       271: q^2+q
       275: q^3+2q^2+q
       278: q^2
       279: q^3+3q^2+q
       281: q^3+2q^2+q
       283: q^2+q
       285: q^2+q
       287: 2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^3+2q^2+q
       296: q^2
       297: q^3+3q^2+q
       299: q^2+q
       301: q
       303: q^3+2q^2+q
       304: q^2
       305: q^2+q
       307: q^3+2q^2+q
       308: q^2
       309: q^2+q
       311: q
       313: q^2+q
       315: q^2+q
       317: q^2+q
       319: q
       321: q
       323: q
       325: q^3+2q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: 2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q
       352: 2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q
       359: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       377: q^2+q
       381: q^3+2q^2+q
       384: q^2
       385: q^3+2q^2+q
       388: q^2
       389: q
       393: q^2+q
       397: q
       401: q^2+q
       405: q
       409: 2q^2+q
       411: q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: q^2+q
       429: q
       431: q^2+q
       433: q
       435: q
       437: q^2+q
       439: q^2+q
       440: q^2
       441: q^2+q
       443: q
       445: q
       447: q^2+q
       449: q
       451: q
       453: q^2+q
       454: q^2
       455: q
       457: q^2+q
       459: q^2+q
       461: q
       463: q
       465: q^2+q
       467: q^2+q
       469: q^2+q
       471: q
       473: q
       475: q
       477: 2q
       479: q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: q^2+q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q
       508: q^2+q
       512: q
       514: q
       521: q^2+q
       525: q^2+q
       528: q^2
       529: q^2+q
       533: q
       537: q
       541: q^2+q
       545: q
       549: q
       553: q
       557: q^2+q
       561: q
       565: q
       569: 2q
       573: q
       577: q
       579: q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       591: q
       593: q
       595: q^2+q
       597: q^2+q
       599: q^2+q
       601: q^2+q
       603: q
       605: q
       607: q
       609: q
       613: q
       615: q
       617: q
       619: q
       621: q
       623: q
       625: q
       629: q
       631: q
       633: q
       639: q^2+q
       641: q
       643: q
       645: q
       651: 2q
       655: q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: q^2+q
       682: q
       683: q
       685: q
       693: q
       695: q
       705: q
       709: q^2+q
       713: q
       717: q
       721: q
       725: q
       733: q
       737: q
       741: q
       749: q
       753: q
       757: 2q
       765: q
       769: q
       771: q
       777: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       797: q
       801: q
       805: q
       807: q
       809: q
       811: q
       821: q
       825: q
       827: q
       831: q
       833: q
       835: q
       849: q
       853: q+1
       871: q
       875: q
       884: q
       886: q
       896: q
       900: q
       904: q
       908: q
       920: q
       928: q
       944: q
       948: q
       960: q
       978: q+1
       984: q+1
      1010: q
      1022: q
      1026: q
      1038: q
      1044: q
      1050: 1
      1100: q+1
      1126: q
      1156: q
      1172: q
      1184: 1
      1190: 1
      1222: 1
      1264: 1
      1304: 1
      1322: 1
      1336: 1
      1406: 1
      1414: 1
      1446: 1
      1491: 1
      1527: 1
      1555: 1
      1559: 1
      1677: 1

1678:    0: 4q^3+7q^2+3q
         1: 4q^3+7q^2+3q
         2: 4q^3+7q^2+3q
         3: q^4+5q^3+7q^2+3q
         4: 4q^3+7q^2+3q
         5: q^4+5q^3+7q^2+3q
         6: 4q^3+7q^2+3q
         7: 4q^3+7q^2+3q
         8: q^4+5q^3+7q^2+3q
         9: 2q^4+4q^3+4q^2+2q
        10: 4q^3+7q^2+3q
        11: q^4+5q^3+7q^2+3q
        12: 4q^3+7q^2+3q
        13: 4q^3+7q^2+3q
        14: 4q^3+7q^2+3q
        15: q^4+5q^3+7q^2+3q
        16: 2q^3+6q^2+3q
        17: 2q^3+6q^2+3q
        18: 3q^3+4q^2+2q
        19: 4q^3+7q^2+3q
        20: 4q^3+7q^2+3q
        21: 4q^3+7q^2+3q
        22: 2q^3+6q^2+3q
        23: 2q^3+6q^2+3q
        24: 2q^3+6q^2+3q
        25: 2q^3+6q^2+3q
        26: 2q^3+6q^2+3q
        27: 2q^3+6q^2+3q
        28: 2q^3+6q^2+3q
        29: 4q^3+7q^2+3q
        30: 4q^3+7q^2+3q
        31: 2q^3+6q^2+3q
        32: 2q^3+6q^2+3q
        33: q^3+5q^2+3q
        34: 2q^3+6q^2+3q
        35: 2q^3+6q^2+3q
        36: q^3+5q^2+3q
        37: 3q^2+2q
        38: q^3+2q^2+q
        39: 3q^2+2q
        40: q^3+2q^2+q
        41: 3q^2+2q
        42: q^3+2q^2+q
        43: 4q^3+7q^2+3q
        44: 4q^3+7q^2+3q
        45: q^4+5q^3+7q^2+3q
        46: 2q^3+6q^2+3q
        47: 2q^3+6q^2+3q
        48: 3q^3+4q^2+2q
        49: 2q^3+6q^2+3q
        50: 2q^3+6q^2+3q
        51: 3q^3+4q^2+2q
        52: 2q^3+6q^2+3q
        53: 2q^3+6q^2+3q
        54: 2q^3+6q^2+3q
        55: 2q^3+6q^2+3q
        56: 2q^3+6q^2+3q
        57: 2q^3+6q^2+3q
        58: 2q^2+q
        59: q^3+3q^2+2q
        60: q^3+3q^2+2q
        61: 2q^2+q
        62: 3q^2+2q
        63: q^3+2q^2+q
        64: 3q^2+2q
        65: q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 2q^3+6q^2+3q
        69: q^3+3q^2+2q
        70: 4q^3+7q^2+3q
        71: 2q^3+6q^2+3q
        72: q^3+5q^2+3q
        73: q^3+5q^2+3q
        74: 3q^2+2q
        75: q^3+2q^2+q
        76: 3q^2+2q
        77: q^3+2q^2+q
        78: 3q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+6q^2+3q
        81: q^3+5q^2+3q
        82: 2q^3+6q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: q^3+5q^2+3q
        86: 2q^3+6q^2+3q
        87: 2q^3+6q^2+3q
        88: 2q^3+6q^2+3q
        89: 2q^3+6q^2+3q
        90: 3q^3+4q^2+2q
        91: 2q^3+6q^2+3q
        92: 2q^3+6q^2+3q
        93: 3q^3+4q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+3q^2+2q
       100: 3q^2+3q
       101: 3q^2+3q
       102: 3q^2+3q
       103: q^2+q
       104: q^3+q^2+q
       105: q^2
       106: q^2+q
       107: q^3+3q^2+2q
       108: 2q^2+q
       109: 2q^2+q
       110: q^3+3q^2+2q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 3q^2+2q
       114: q^3+2q^2+q
       115: 3q^2+2q
       116: q^3+2q^2+q
       117: 2q^2+q
       118: q^3+3q^2+2q
       119: q^3+3q^2+2q
       120: 2q^2+q
       121: 3q^2+2q
       122: q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 2q^3+6q^2+3q
       126: q^3+3q^2+2q
       127: 2q
       129: 2q
       131: q^2+q
       133: 2q^3+6q^2+3q
       134: q^3+3q^2+2q
       135: q^3+5q^2+3q
       136: q^3+5q^2+3q
       137: q^3+5q^2+3q
       138: 2q^2+2q
       139: 3q^2+3q
       140: 2q
       141: 2q^3+6q^2+3q
       142: 3q^2+3q
       143: q^3+5q^2+3q
       144: 2q^2+2q
       145: 3q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^2+3q
       148: 2q
       149: 3q^2+3q
       150: 3q^2+3q
       151: 2q^2+2q
       152: q^2+q
       153: 2q^2+2q
       154: q^2+q
       155: 2q^2+2q
       156: q^2+q
       157: 2q^3+6q^2+3q
       158: 2q^3+6q^2+3q
       159: 3q^3+4q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+3q^2+2q
       166: q^2+3q
       167: q^2+3q
       168: q^2+2q
       169: q^2+q
       170: q^3+q^2+q
       171: q^2
       172: q^2+q
       173: q^2+q
       174: q^3+q^2+q
       175: q^2
       176: q^2+q
       177: q
       179: 2q
       181: 2q
       183: q^3+3q^2+2q
       184: 2q^2+q
       185: 2q^2+q
       186: q^3+3q^2+2q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 3q^2+2q
       190: q^3+2q^2+q
       191: 2q^2+q
       192: q^3+3q^2+2q
       193: 2q
       195: q^2+q
       196: 2q^2+2q
       197: q
       198: q
       199: q^3+3q^2+2q
       200: 2q^2+q
       201: 2q^2+2q
       202: q^2+q
       204: 2q
       205: q
       206: q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^2+2q
       210: q^2+q
       211: 2q^2+2q
       212: q^2+q
       213: 2q
       215: 2q
       217: q^2+q
       219: q^3+3q^2+2q
       220: 2q^3+6q^2+3q
       221: q^3+3q^2+2q
       222: q^3+5q^2+3q
       223: 2q^2+2q
       224: q^3+5q^2+3q
       225: 2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^2+2q
       234: 3q^2+3q
       235: 2q
       236: q^2+2q
       237: 2q
       239: 2q
       241: q
       243: q^2+3q
       244: 2q
       245: 2q
       246: 3q^2+3q
       247: q^2+3q
       248: q^2+3q
       249: q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+3q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: q^2+2q
       259: q
       262: q
       263: q^2+q
       264: q^3+q^2+q
       265: q^2
       266: q^2+q
       267: q
       268: q
       273: q
       274: q
       275: q^2+q
       276: q^3+q^2+q
       277: q^2
       278: q^2+q
       279: 2q
       281: q
       283: q^2+q
       286: q^2+q
       287: q
       289: 2q
       291: q
       293: q^3+3q^2+2q
       294: 2q^2+q
       295: 2q^2+q
       296: q^3+3q^2+2q
       297: 2q^2+2q
       298: q^3+2q^2+q
       299: 2q
       301: q
       303: q^2+q
       304: 2q^2+2q
       305: q
       306: q
       307: 2q^2+2q
       308: q^2+q
       310: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       319: 2q
       322: 2q
       324: q
       325: 2q^2+2q
       326: q^2+q
       327: 2q
       329: 2q
       331: q^2+q
       333: q^3+3q^2+2q
       334: 2q^2+2q
       335: 2q^2+2q
       336: q^2+2q
       337: q^2+3q
       338: 2q
       340: 2q
       342: q
       344: 2q^2+2q
       345: 3q^2+3q
       346: 2q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: 2q^2+2q
       351: 2q
       352: 2q^2+2q
       353: 3q^2+3q
       354: 2q^2+2q
       355: 3q^2+3q
       356: 2q^2+2q
       357: 2q
       358: q
       359: 2q
       360: 2q
       362: 2q
       364: q
       366: q^2+2q
       367: q^2+3q
       368: q^2+2q
       369: 2q
       370: 2q
       371: q^2+3q
       372: q^2+3q
       373: q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: q^2+2q
       381: q
       384: q
       385: q^2+q
       386: q^3+q^2+q
       387: q^2
       388: q^2+q
       389: q
       393: q
       394: q
       399: q
       403: q
       404: q
       407: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       419: q^2+q
       422: q^2+q
       423: q
       425: q
       427: 2q
       429: q
       432: q^2+q
       435: q
       437: 2q
       439: q^2+q
       440: 2q^2+2q
       441: q
       442: q
       443: 2q
       445: q
       447: q^2+q
       450: q
       453: 2q^2+2q
       454: q^2+q
       455: q
       458: 2q
       459: q
       460: q
       462: 2q
       463: q
       465: 2q
       467: q
       469: q
       471: 2q
       474: 2q
       476: q
       480: q
       481: 2q^2+2q
       482: 2q^2+2q
       483: q^2+2q
       484: q^2+3q
       485: 2q
       487: 2q
       489: q
       491: q^2+2q
       492: 2q^2+2q
       493: q
       494: 2q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: 2q^2+2q
       499: q
       500: q
       501: 2q
       502: 2q
       504: 2q
       506: q
       508: q^2+2q
       509: q^2+3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+3q
       519: q^2+3q
       520: q^2+2q
       525: q
       528: q
       537: q
       541: q
       542: q
       545: q
       555: q
       559: q
       560: q
       563: q
       566: q
       574: q
       583: q
       585: q
       587: q
       589: q^2+q
       592: q
       593: q
       596: q^2+q
       597: q
       599: q
       601: 2q
       603: q
       608: q^2+q
       611: q
       615: 2q
       617: q
       619: q^2+q
       622: q
       627: q
       632: 2q
       633: q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       647: 2q
       650: 2q
       654: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q^2+2q
       666: 2q
       668: 2q
       670: q
       672: q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: 2q^2+2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q^2+2q
       682: q
       683: q
       684: 2q
       685: q
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       729: q
       733: q
       747: q
       751: q
       763: q
       766: q
       775: 1
       777: q
       779: 1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       793: 1
       795: 1
       801: q
       805: q
       808: q^2+q
       813: q
       815: 2q
       818: 1
       819: 1
       825: q^2+q
       828: q
       832: q
       837: q
       840: 2q
       841: q
       844: 1
       845: q
       848: q
       858: q
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       916: 1
       932: q
       942: 1
       958: q
       965: 1
       971: 1
       989: q
       992: 1
       994: 1
       996: 1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 1
      1016: 1
      1020: 1
      1026: q
      1030: 1
      1033: 1
      1036: 1
      1045: q
      1047: 1
      1052: q
      1059: q
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1226: 1
      1228: 1
      1236: 1
      1240: q
      1244: 1
      1247: 1
      1252: 1
      1261: q
      1263: 1
      1282: 1
      1284: 1
      1286: 1
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1340: 1
      1374: 1
      1407: 1
      1411: 1
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1452: 1
      1458: 1
      1492: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1678: 1

1679:    0: 4q^3+7q^2+3q
         1: 4q^3+7q^2+3q
         2: 4q^3+7q^2+3q
         3: q^4+5q^3+7q^2+3q
         4: 4q^3+7q^2+3q
         5: q^4+5q^3+7q^2+3q
         6: 4q^3+7q^2+3q
         7: 4q^3+7q^2+3q
         8: q^4+5q^3+7q^2+3q
         9: 2q^4+4q^3+4q^2+2q
        10: 4q^3+7q^2+3q
        11: q^4+5q^3+7q^2+3q
        12: 4q^3+7q^2+3q
        13: 4q^3+7q^2+3q
        14: 4q^3+7q^2+3q
        15: q^4+5q^3+7q^2+3q
        16: 2q^3+6q^2+3q
        17: 2q^3+6q^2+3q
        18: 3q^3+4q^2+2q
        19: 4q^3+7q^2+3q
        20: 4q^3+7q^2+3q
        21: 4q^3+7q^2+3q
        22: 2q^3+6q^2+3q
        23: 2q^3+6q^2+3q
        24: 2q^3+6q^2+3q
        25: 2q^3+6q^2+3q
        26: 2q^3+6q^2+3q
        27: 2q^3+6q^2+3q
        28: 2q^3+6q^2+3q
        29: 4q^3+7q^2+3q
        30: 4q^3+7q^2+3q
        31: 2q^3+6q^2+3q
        32: 2q^3+6q^2+3q
        33: q^3+5q^2+3q
        34: 2q^3+6q^2+3q
        35: 2q^3+6q^2+3q
        36: q^3+5q^2+3q
        37: 3q^2+2q
        38: q^3+2q^2+q
        39: 3q^2+2q
        40: q^3+2q^2+q
        41: 3q^2+2q
        42: q^3+2q^2+q
        43: 4q^3+7q^2+3q
        44: 4q^3+7q^2+3q
        45: q^4+5q^3+7q^2+3q
        46: 2q^3+6q^2+3q
        47: 2q^3+6q^2+3q
        48: 3q^3+4q^2+2q
        49: 2q^3+6q^2+3q
        50: 2q^3+6q^2+3q
        51: 3q^3+4q^2+2q
        52: 2q^3+6q^2+3q
        53: 2q^3+6q^2+3q
        54: 2q^3+6q^2+3q
        55: 2q^3+6q^2+3q
        56: 2q^3+6q^2+3q
        57: 2q^3+6q^2+3q
        58: q^3+3q^2+2q
        59: 2q^2+q
        60: 2q^2+q
        61: q^3+3q^2+2q
        62: 3q^2+2q
        63: q^3+2q^2+q
        64: 3q^2+2q
        65: q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 2q^3+6q^2+3q
        69: q^3+3q^2+2q
        70: 4q^3+7q^2+3q
        71: 2q^3+6q^2+3q
        72: q^3+5q^2+3q
        73: q^3+5q^2+3q
        74: 3q^2+2q
        75: q^3+2q^2+q
        76: 3q^2+2q
        77: q^3+2q^2+q
        78: 3q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+6q^2+3q
        81: q^3+5q^2+3q
        82: 2q^3+6q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: q^3+5q^2+3q
        86: 2q^3+6q^2+3q
        87: 2q^3+6q^2+3q
        88: 2q^3+6q^2+3q
        89: 2q^3+6q^2+3q
        90: 3q^3+4q^2+2q
        91: 2q^3+6q^2+3q
        92: 2q^3+6q^2+3q
        93: 3q^3+4q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+3q^2+2q
       100: 3q^2+3q
       101: 3q^2+3q
       102: 3q^2+3q
       103: q^2+q
       104: q^2
       105: q^3+q^2+q
       106: q^2+q
       107: 2q^2+q
       108: q^3+3q^2+2q
       109: q^3+3q^2+2q
       110: 2q^2+q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 3q^2+2q
       114: q^3+2q^2+q
       115: 3q^2+2q
       116: q^3+2q^2+q
       117: q^3+3q^2+2q
       118: 2q^2+q
       119: 2q^2+q
       120: q^3+3q^2+2q
       121: 3q^2+2q
       122: q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 2q^3+6q^2+3q
       126: q^3+3q^2+2q
       127: 2q
       129: 2q
       131: q^2+q
       133: 2q^3+6q^2+3q
       134: q^3+3q^2+2q
       135: q^3+5q^2+3q
       136: q^3+5q^2+3q
       137: q^3+5q^2+3q
       138: 2q^2+2q
       139: 3q^2+3q
       140: 2q
       141: 2q^3+6q^2+3q
       142: 3q^2+3q
       143: q^3+5q^2+3q
       144: 2q^2+2q
       145: 3q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^2+3q
       148: 2q
       149: 3q^2+3q
       150: 3q^2+3q
       151: 2q^2+2q
       152: q^2+q
       153: 2q^2+2q
       154: q^2+q
       155: 2q^2+2q
       156: q^2+q
       157: 2q^3+6q^2+3q
       158: 2q^3+6q^2+3q
       159: 3q^3+4q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+3q^2+2q
       166: q^2+3q
       167: q^2+3q
       168: q^2+2q
       169: q^2+q
       170: q^2
       171: q^3+q^2+q
       172: q^2+q
       173: q^2+q
       174: q^2
       175: q^3+q^2+q
       176: q^2+q
       177: q
       179: 2q
       181: 2q
       183: 2q^2+q
       184: q^3+3q^2+2q
       185: q^3+3q^2+2q
       186: 2q^2+q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 3q^2+2q
       190: q^3+2q^2+q
       191: q^3+3q^2+2q
       192: 2q^2+q
       194: 2q
       195: 2q^2+2q
       196: q^2+q
       197: q
       198: q
       199: 2q^2+q
       200: q^3+3q^2+2q
       201: q^2+q
       202: 2q^2+2q
       203: 2q
       205: q
       206: q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^2+2q
       210: q^2+q
       211: 2q^2+2q
       212: q^2+q
       213: 2q
       215: 2q
       217: q^2+q
       219: q^3+3q^2+2q
       220: 2q^3+6q^2+3q
       221: q^3+3q^2+2q
       222: q^3+5q^2+3q
       223: 2q^2+2q
       224: q^3+5q^2+3q
       225: 2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^2+2q
       234: 3q^2+3q
       235: 2q
       236: q^2+2q
       237: 2q
       239: 2q
       241: q
       243: q^2+3q
       244: 2q
       245: 2q
       246: 3q^2+3q
       247: q^2+3q
       248: q^2+3q
       249: q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+3q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: q^2+2q
       259: q
       262: q
       263: q^2+q
       264: q^2
       265: q^3+q^2+q
       266: q^2+q
       269: q
       270: q
       271: q
       272: q
       275: q^2+q
       276: q^2
       277: q^3+q^2+q
       278: q^2+q
       279: 2q
       281: q
       284: q^2+q
       285: q^2+q
       287: q
       289: 2q
       291: q
       293: 2q^2+q
       294: q^3+3q^2+2q
       295: q^3+3q^2+2q
       296: 2q^2+q
       297: 2q^2+2q
       298: q^3+2q^2+q
       300: 2q
       301: q
       303: 2q^2+2q
       304: q^2+q
       305: q
       306: q
       307: q^2+q
       308: 2q^2+2q
       309: 2q
       311: q
       313: q
       314: q
       315: q
       317: 2q
       320: 2q
       321: 2q
       324: q
       325: 2q^2+2q
       326: q^2+q
       327: 2q
       329: 2q
       331: q^2+q
       333: q^3+3q^2+2q
       334: 2q^2+2q
       335: 2q^2+2q
       336: q^2+2q
       337: q^2+3q
       338: 2q
       340: 2q
       342: q
       344: 2q^2+2q
       345: 3q^2+3q
       346: 2q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: 2q^2+2q
       351: 2q
       352: 2q^2+2q
       353: 3q^2+3q
       354: 2q^2+2q
       355: 3q^2+3q
       356: 2q^2+2q
       357: 2q
       358: q
       359: 2q
       360: 2q
       362: 2q
       364: q
       366: q^2+2q
       367: q^2+3q
       368: q^2+2q
       369: 2q
       370: 2q
       371: q^2+3q
       372: q^2+3q
       373: q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: q^2+2q
       381: q
       384: q
       385: q^2+q
       386: q^2
       387: q^3+q^2+q
       388: q^2+q
       391: q
       395: q
       396: q
       397: q
       401: q
       402: q
       408: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       420: q^2+q
       421: q^2+q
       423: q
       425: q
       427: 2q
       430: q
       431: q^2+q
       435: q
       438: 2q
       439: 2q^2+2q
       440: q^2+q
       441: q
       442: q
       444: 2q
       445: q
       448: q^2+q
       449: q
       453: q^2+q
       454: 2q^2+2q
       455: q
       457: 2q
       459: q
       460: q
       461: 2q
       463: q
       465: 2q
       467: q
       469: q
       472: 2q
       473: 2q
       476: q
       480: q
       481: 2q^2+2q
       482: 2q^2+2q
       483: q^2+2q
       484: q^2+3q
       485: 2q
       487: 2q
       489: q
       491: q^2+2q
       492: 2q^2+2q
       493: q
       494: 2q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: 2q^2+2q
       499: q
       500: q
       501: 2q
       502: 2q
       504: 2q
       506: q
       508: q^2+2q
       509: q^2+3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+3q
       519: q^2+3q
       520: q^2+2q
       525: q
       528: q
       539: q
       543: q
       544: q
       547: q
       553: q
       557: q
       558: q
       561: q
       567: q
       576: q
       583: q
       585: q
       587: q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       597: q
       599: q
       601: 2q
       604: q
       607: q^2+q
       611: q
       616: 2q
       617: q
       620: q^2+q
       621: q
       627: q
       631: 2q
       633: q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       648: 2q
       649: 2q
       654: q
       656: q
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q^2+2q
       666: 2q
       668: 2q
       670: q
       672: q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: 2q^2+2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q^2+2q
       682: q
       683: q
       684: 2q
       685: q
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       731: q
       735: q
       745: q
       749: q
       764: q
       767: q
       775: 1
       777: q
       779: 1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       794: 1
       795: 1
       802: q
       806: q
       807: q^2+q
       813: q
       816: 2q
       817: 1
       819: 1
       826: q^2+q
       827: q
       831: q
       837: q
       839: 2q
       841: q
       844: 1
       846: q
       847: q
       858: q
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       918: 1
       934: q
       940: 1
       956: q
       966: 1
       971: 1
       990: q
       992: 1
       994: 1
       996: 1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 1
      1017: 1
      1020: 1
      1027: q
      1030: 1
      1032: 1
      1036: 1
      1044: q
      1047: 1
      1053: q
      1058: q
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1210: 1
      1212: 1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1226: 1
      1229: 1
      1236: 1
      1241: q
      1244: 1
      1246: 1
      1252: 1
      1260: q
      1263: 1
      1282: 1
      1284: 1
      1286: 1
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1342: 1
      1372: 1
      1407: 1
      1412: 1
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1452: 1
      1458: 1
      1493: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1679: 1

1680:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+2q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: 3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       106: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q
       120: q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q
       184: q^2+2q+1
       185: q
       186: q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       273: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q
       294: q^2+2q+1
       295: q
       296: q^2+2q+1
       297: q^2+3q+1
       300: q+1
       301: q+1
       303: q
       304: 2q+1
       305: q+1
       307: q
       308: 2q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q^2+2q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: q+1
       427: 2q+1
       430: 1
       432: q+1
       433: 1
       435: q+1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: q+1
       445: q+1
       448: q+1
       450: 1
       451: 1
       453: q
       454: 2q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: 1
       539: q+1
       543: q+1
       547: q+1
       552: 1
       555: q+1
       559: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       590: q+1
       592: 1
       594: 1
       596: q+1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: 1
       608: q+1
       609: 1
       611: q+1
       613: 1
       616: q+1
       617: q+1
       620: q+1
       622: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: 1
       660: q+1
       662: 1
       664: 1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       697: q+1
       708: q+1
       712: q+1
       716: 1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: q+1
       739: 1
       743: 1
       747: q+1
       751: q+1
       756: 1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       813: q+1
       816: q+1
       818: 1
       819: 1
       821: 1
       823: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: q+1
       840: q+1
       841: q+1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: q+1
       857: q+1
       859: 1
       861: q+1
       863: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       889: q+1
       899: q+1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: q+1
       938: 1
       942: 1
       946: 1
       950: 1
       958: q+1
       961: 1
       967: 1
       968: 1
       975: 1
       979: q+1
       982: q+1
       991: q+1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1059: 1
      1066: 1
      1068: q+1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1091: 1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1158: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1236: 1
      1238: 1
      1241: 1
      1244: 1
      1247: 1
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1264: 1
      1282: 1
      1284: 1
      1286: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1354: 1
      1374: 1
      1378: 1
      1404: 1
      1413: 1
      1415: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1452: 1
      1458: 1
      1494: 1
      1530: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1680: 1

1681:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+2q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: 3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q^2+2q+1
        61: q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q^2+2q+1
       105: q
       107: q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q^2+2q+1
       120: q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+2q+1
       184: q
       185: q
       186: q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+2q+1
       294: q
       295: q
       296: q^2+2q+1
       298: q^2+3q+1
       299: q+1
       302: q+1
       303: q
       304: 2q+1
       306: q+1
       307: 2q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       429: 1
       432: q+1
       434: 1
       436: q+1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: q+1
       446: q+1
       447: q+1
       450: 1
       452: 1
       453: 2q+1
       454: q
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q+1
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: 1
       538: q+1
       542: q+1
       546: q+1
       551: 1
       556: q+1
       560: q+1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       592: 1
       593: 1
       596: q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       612: q+1
       614: 1
       615: q+1
       618: q+1
       619: q+1
       622: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: q+1
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       699: q+1
       706: q+1
       710: q+1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: q+1
       740: 1
       744: 1
       748: q+1
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       814: q+1
       815: q+1
       818: 1
       820: 1
       822: 1
       824: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       838: q+1
       840: q+1
       842: q+1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: q+1
       858: q+1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       890: q+1
       897: q+1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: q+1
       939: 1
       943: 1
       947: 1
       951: 1
       959: q+1
       962: 1
       965: 1
       972: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
       993: 1
       995: 1
       997: 1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1059: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1092: 1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1157: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1211: 1
      1213: 1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1228: 1
      1237: 1
      1239: 1
      1240: 1
      1245: 1
      1247: 1
      1253: 1
      1257: 1
      1261: 1
      1263: 1
      1265: 1
      1282: 1
      1284: 1
      1286: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1353: 1
      1375: 1
      1379: 1
      1408: 1
      1411: 1
      1416: 1
      1439: 1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1453: 1
      1459: 1
      1495: 1
      1531: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1681: 1

1682:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+2q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: 3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q
        61: q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: 3q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q^2+2q+1
       110: q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q
       120: q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q
       184: q^2+2q+1
       185: q^2+2q+1
       186: q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q
       294: q^2+2q+1
       295: q^2+2q+1
       296: q
       298: q^2+3q+1
       300: q+1
       302: q+1
       303: 2q+1
       304: q
       306: q+1
       307: q
       308: 2q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q^2+2q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       428: 2q+1
       430: 1
       431: q+1
       434: 1
       436: q+1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       448: q+1
       449: 1
       452: 1
       453: q
       454: 2q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: q+1
       473: q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 1
       518: 2q+1
       519: 2q+1
       520: q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: 1
       540: q+1
       544: q+1
       548: q+1
       550: 1
       554: q+1
       558: q+1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       590: q+1
       591: 1
       594: 1
       595: q+1
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       612: q+1
       614: 1
       616: q+1
       618: q+1
       620: q+1
       621: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q+1
       672: 2q+1
       673: q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: 1
       691: q+1
       692: 1
       700: q+1
       707: q+1
       711: q+1
       714: 1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: q+1
       738: 1
       742: 1
       746: q+1
       750: q+1
       755: 1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       814: q+1
       816: q+1
       817: 1
       820: 1
       822: 1
       824: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: q+1
       839: q+1
       842: q+1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: q+1
       858: q+1
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: 1
       882: q+1
       883: 1
       891: q+1
       898: q+1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: q+1
       937: 1
       941: 1
       945: 1
       949: 1
       957: q+1
       963: 1
       966: 1
       972: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
       993: 1
       995: 1
       997: 1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1058: 1
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1093: 1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1211: 1
      1213: 1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1229: 1
      1237: 1
      1239: 1
      1241: 1
      1245: 1
      1246: 1
      1253: 1
      1257: 1
      1260: 1
      1263: 1
      1265: 1
      1282: 1
      1284: 1
      1286: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1355: 1
      1373: 1
      1377: 1
      1408: 1
      1412: 1
      1417: 1
      1439: 1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1453: 1
      1459: 1
      1496: 1
      1532: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1682: 1

1683:    0: 4q^3+7q^2+3q
         1: 4q^3+7q^2+3q
         2: 4q^3+7q^2+3q
         3: q^4+5q^3+7q^2+3q
         4: 4q^3+7q^2+3q
         5: q^4+5q^3+7q^2+3q
         6: 4q^3+7q^2+3q
         7: 4q^3+7q^2+3q
         8: q^4+5q^3+7q^2+3q
         9: 2q^4+4q^3+4q^2+2q
        10: 4q^3+7q^2+3q
        11: q^4+5q^3+7q^2+3q
        12: 4q^3+7q^2+3q
        13: 4q^3+7q^2+3q
        14: 4q^3+7q^2+3q
        15: q^4+5q^3+7q^2+3q
        16: 2q^3+6q^2+3q
        17: 2q^3+6q^2+3q
        18: 3q^3+4q^2+2q
        19: 4q^3+7q^2+3q
        20: 4q^3+7q^2+3q
        21: 4q^3+7q^2+3q
        22: 2q^3+6q^2+3q
        23: 2q^3+6q^2+3q
        24: 2q^3+6q^2+3q
        25: 2q^3+6q^2+3q
        26: 2q^3+6q^2+3q
        27: 2q^3+6q^2+3q
        28: 2q^3+6q^2+3q
        29: 4q^3+7q^2+3q
        30: 4q^3+7q^2+3q
        31: 2q^3+6q^2+3q
        32: 2q^3+6q^2+3q
        33: q^3+5q^2+3q
        34: 2q^3+6q^2+3q
        35: 2q^3+6q^2+3q
        36: q^3+5q^2+3q
        37: q^3+2q^2+q
        38: 3q^2+2q
        39: q^3+2q^2+q
        40: 3q^2+2q
        41: q^3+2q^2+q
        42: 3q^2+2q
        43: 4q^3+7q^2+3q
        44: 4q^3+7q^2+3q
        45: q^4+5q^3+7q^2+3q
        46: 2q^3+6q^2+3q
        47: 2q^3+6q^2+3q
        48: 3q^3+4q^2+2q
        49: 2q^3+6q^2+3q
        50: 2q^3+6q^2+3q
        51: 3q^3+4q^2+2q
        52: 2q^3+6q^2+3q
        53: 2q^3+6q^2+3q
        54: 2q^3+6q^2+3q
        55: 2q^3+6q^2+3q
        56: 2q^3+6q^2+3q
        57: 2q^3+6q^2+3q
        58: 2q^2+q
        59: q^3+3q^2+2q
        60: 2q^2+q
        61: q^3+3q^2+2q
        62: q^3+2q^2+q
        63: 3q^2+2q
        64: q^3+2q^2+q
        65: 3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 2q^3+6q^2+3q
        69: q^3+3q^2+2q
        70: 4q^3+7q^2+3q
        71: 2q^3+6q^2+3q
        72: q^3+5q^2+3q
        73: q^3+5q^2+3q
        74: q^3+2q^2+q
        75: 3q^2+2q
        76: q^3+2q^2+q
        77: 3q^2+2q
        78: q^3+2q^2+q
        79: 3q^2+2q
        80: 2q^3+6q^2+3q
        81: q^3+5q^2+3q
        82: 2q^3+6q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: q^3+5q^2+3q
        86: 2q^3+6q^2+3q
        87: 2q^3+6q^2+3q
        88: 2q^3+6q^2+3q
        89: 2q^3+6q^2+3q
        90: 3q^3+4q^2+2q
        91: 2q^3+6q^2+3q
        92: 2q^3+6q^2+3q
        93: 3q^3+4q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+3q^2+2q
       100: 3q^2+3q
       101: 3q^2+3q
       102: 3q^2+3q
       103: q^2
       104: q^2+q
       105: q^2+q
       106: q^3+q^2+q
       107: 2q^2+q
       108: q^3+3q^2+2q
       109: 2q^2+q
       110: q^3+3q^2+2q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: q^3+2q^2+q
       114: 3q^2+2q
       115: q^3+2q^2+q
       116: 3q^2+2q
       117: 2q^2+q
       118: q^3+3q^2+2q
       119: 2q^2+q
       120: q^3+3q^2+2q
       121: q^3+2q^2+q
       122: 3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 2q^3+6q^2+3q
       126: q^3+3q^2+2q
       128: 2q
       130: 2q
       132: q^2+q
       133: 2q^3+6q^2+3q
       134: q^3+3q^2+2q
       135: q^3+5q^2+3q
       136: q^3+5q^2+3q
       137: q^3+5q^2+3q
       138: 2q^2+2q
       139: 3q^2+3q
       140: 2q
       141: 2q^3+6q^2+3q
       142: 3q^2+3q
       143: q^3+5q^2+3q
       144: 2q^2+2q
       145: 3q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^2+3q
       148: 2q
       149: 3q^2+3q
       150: 3q^2+3q
       151: q^2+q
       152: 2q^2+2q
       153: q^2+q
       154: 2q^2+2q
       155: q^2+q
       156: 2q^2+2q
       157: 2q^3+6q^2+3q
       158: 2q^3+6q^2+3q
       159: 3q^3+4q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+3q^2+2q
       166: q^2+3q
       167: q^2+3q
       168: q^2+2q
       169: q^2
       170: q^2+q
       171: q^2+q
       172: q^3+q^2+q
       173: q^2
       174: q^2+q
       175: q^2+q
       176: q^3+q^2+q
       178: q
       180: 2q
       182: 2q
       183: 2q^2+q
       184: q^3+3q^2+2q
       185: 2q^2+q
       186: q^3+3q^2+2q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: q^3+2q^2+q
       190: 3q^2+2q
       191: 2q^2+q
       192: q^3+3q^2+2q
       194: 2q
       195: q^2+q
       196: 2q^2+2q
       197: q
       198: q
       199: 2q^2+q
       200: q^3+3q^2+2q
       201: q^2+q
       202: 2q^2+2q
       204: 2q
       205: q
       206: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: 2q^2+2q
       211: q^2+q
       212: 2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: q^3+3q^2+2q
       220: 2q^3+6q^2+3q
       221: q^3+3q^2+2q
       222: q^3+5q^2+3q
       223: 2q^2+2q
       224: q^3+5q^2+3q
       225: 2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^2+2q
       229: 2q
       230: 3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^2+2q
       234: 3q^2+3q
       235: 2q
       236: q^2+2q
       238: 2q
       240: 2q
       242: q
       243: q^2+3q
       244: 2q
       245: 2q
       246: 3q^2+3q
       247: q^2+3q
       248: q^2+3q
       249: q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+3q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: q^2+2q
       260: q
       261: q
       263: q^2
       264: q^2+q
       265: q^2+q
       266: q^3+q^2+q
       269: q
       270: q
       273: q
       274: q
       275: q^2
       276: q^2+q
       277: q^2+q
       278: q^3+q^2+q
       280: 2q
       282: q
       284: q^2+q
       286: q^2+q
       288: q
       290: 2q
       292: q
       293: 2q^2+q
       294: q^3+3q^2+2q
       295: 2q^2+q
       296: q^3+3q^2+2q
       297: q^3+2q^2+q
       298: 2q^2+2q
       300: 2q
       302: q
       303: q^2+q
       304: 2q^2+2q
       305: q
       306: q
       307: q^2+q
       308: 2q^2+2q
       310: 2q
       312: q
       313: q
       314: q
       316: q
       318: 2q
       320: 2q
       322: 2q
       323: q
       325: q^2+q
       326: 2q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: q^3+3q^2+2q
       334: 2q^2+2q
       335: 2q^2+2q
       336: q^2+2q
       337: q^2+3q
       339: 2q
       341: 2q
       343: q
       344: 2q^2+2q
       345: 3q^2+3q
       346: 2q^2+2q
       347: 2q
       348: q
       349: 3q^2+3q
       350: 2q^2+2q
       351: 2q
       352: 2q^2+2q
       353: 3q^2+3q
       354: 2q^2+2q
       355: 3q^2+3q
       356: 2q^2+2q
       357: 2q
       358: q
       359: 2q
       361: 2q
       363: 2q
       365: q
       366: q^2+2q
       367: q^2+3q
       368: q^2+2q
       369: 2q
       370: 2q
       371: q^2+3q
       372: q^2+3q
       373: q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: q^2+2q
       382: q
       383: q
       385: q^2
       386: q^2+q
       387: q^2+q
       388: q^3+q^2+q
       392: q
       395: q
       396: q
       400: q
       403: q
       404: q
       406: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       420: q^2+q
       422: q^2+q
       424: q
       426: q
       428: 2q
       430: q
       432: q^2+q
       436: q
       438: 2q
       439: q^2+q
       440: 2q^2+2q
       441: q
       442: q
       444: 2q
       446: q
       448: q^2+q
       450: q
       453: q^2+q
       454: 2q^2+2q
       456: q
       458: 2q
       459: q
       460: q
       462: 2q
       464: q
       466: 2q
       468: q
       470: q
       472: 2q
       474: 2q
       475: q
       479: q
       481: 2q^2+2q
       482: 2q^2+2q
       483: q^2+2q
       484: q^2+3q
       486: 2q
       488: 2q
       490: q
       491: q^2+2q
       492: 2q^2+2q
       493: q
       494: 2q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: 2q^2+2q
       499: q
       500: q
       501: 2q
       503: 2q
       505: 2q
       507: q
       508: q^2+2q
       509: q^2+3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q
       514: q
       515: 1
       516: q+1
       517: 1
       518: q^2+3q
       519: q^2+3q
       520: q^2+2q
       526: q
       527: q
       540: q
       543: q
       544: q
       548: q
       556: q
       559: q
       560: q
       564: q
       568: q
       575: q
       584: q
       586: q
       588: q
       590: q^2+q
       592: q
       594: q
       596: q^2+q
       598: q
       600: q
       602: 2q
       604: q
       608: q^2+q
       612: q
       616: 2q
       618: q
       620: q^2+q
       622: q
       628: q
       632: 2q
       634: q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       648: 2q
       650: 2q
       653: q
       655: q
       657: 1
       659: 1
       661: q+1
       663: 1
       664: 1
       665: q^2+2q
       667: 2q
       669: 2q
       671: q
       672: q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: 2q^2+2q
       677: q
       678: 2q
       679: q
       680: 1
       681: 2q^2+2q
       682: q
       683: q
       684: 2q
       685: q
       686: q^2+2q
       687: q
       688: q
       690: 1
       691: q+1
       692: 1
       732: q
       736: q
       748: q
       752: q
       762: q
       768: q
       776: 1
       778: q
       780: 1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       794: 1
       796: 1
       802: q
       806: q
       808: q^2+q
       814: q
       816: 2q
       818: 1
       820: 1
       826: q^2+q
       828: q
       832: q
       838: q
       840: 2q
       842: q
       843: 1
       846: q
       848: q
       857: q
       860: 1
       862: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       881: 1
       882: q+1
       883: 1
       919: 1
       935: q
       943: 1
       959: q
       967: 1
       969: 1
       991: q
       993: 1
       995: 1
       997: 1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 1
      1017: 1
      1021: 1
      1027: q
      1031: 1
      1033: 1
      1037: 1
      1045: q
      1046: 1
      1053: q
      1059: q
      1067: 1
      1069: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1211: 1
      1213: 1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1227: 1
      1229: 1
      1237: 1
      1241: q
      1245: 1
      1247: 1
      1253: 1
      1261: q
      1262: 1
      1282: 1
      1284: 1
      1286: 1
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1343: 1
      1375: 1
      1405: 1
      1413: 1
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1453: 1
      1459: 1
      1497: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1683: 1

1684:    0: 3q^4+5q^3+3q^2+q
         1: q^5+4q^4+5q^3+3q^2+q
         2: 3q^4+5q^3+3q^2+q
         3: q^5+4q^4+5q^3+3q^2+q
         4: 3q^4+5q^3+3q^2+q
         5: 3q^4+5q^3+3q^2+q
         6: q^5+4q^4+5q^3+3q^2+q
         7: 3q^4+5q^3+3q^2+q
         8: 3q^4+5q^3+3q^2+q
         9: q^5+3q^4+3q^3+2q^2+q
        10: 2q^4+4q^3+3q^2+q
        11: 2q^4+4q^3+3q^2+q
        12: 2q^4+4q^3+3q^2+q
        13: 3q^4+5q^3+3q^2+q
        14: 3q^4+5q^3+3q^2+q
        15: 3q^4+5q^3+3q^2+q
        16: 2q^4+4q^3+3q^2+q
        17: 2q^4+4q^3+3q^2+q
        18: 2q^4+3q^3+2q^2+q
        19: 3q^4+5q^3+3q^2+q
        20: q^5+4q^4+5q^3+3q^2+q
        21: 3q^4+5q^3+3q^2+q
        22: 4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: 4q^3+3q^2+q
        25: 4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: 4q^3+3q^2+q
        28: q^4+3q^3+3q^2+q
        29: 2q^4+4q^3+3q^2+q
        30: 3q^4+5q^3+3q^2+q
        31: 3q^3+3q^2+q
        32: 4q^3+3q^2+q
        33: 3q^3+3q^2+q
        34: 3q^3+3q^2+q
        35: 4q^3+3q^2+q
        36: 3q^3+3q^2+q
        37: 4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: 4q^3+3q^2+q
        43: 2q^4+4q^3+3q^2+q
        44: 2q^4+4q^3+3q^2+q
        45: 2q^4+4q^3+3q^2+q
        46: 2q^4+4q^3+3q^2+q
        47: 2q^4+4q^3+3q^2+q
        48: 2q^4+3q^3+2q^2+q
        49: 2q^4+4q^3+3q^2+q
        50: 2q^4+4q^3+3q^2+q
        51: 2q^4+3q^3+2q^2+q
        52: 4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: 4q^3+3q^2+q
        55: 4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: 4q^3+3q^2+q
        58: q^2
        59: 2q^3+2q^2+q
        60: q^2
        61: 2q^3+2q^2+q
        62: 3q^3+3q^2+q
        64: 4q^3+3q^2+q
        66: 3q^3+3q^2+q
        68: q^4+3q^3+3q^2+q
        69: q^4+2q^3+2q^2+q
        70: 2q^4+4q^3+3q^2+q
        71: q^4+3q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 3q^3+3q^2+q
        74: 4q^3+3q^2+q
        76: q^4+4q^3+3q^2+q
        78: 4q^3+3q^2+q
        80: 3q^3+3q^2+q
        81: 3q^3+3q^2+q
        82: 3q^3+3q^2+q
        83: 4q^3+3q^2+q
        84: 3q^3+3q^2+q
        85: 3q^3+3q^2+q
        86: 3q^3+3q^2+q
        87: 4q^3+3q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: 2q^4+4q^3+3q^2+q
        92: 2q^4+4q^3+3q^2+q
        93: 2q^4+3q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: q^3+2q^2+q
       101: q^3+2q^2+q
       102: q^3+2q^2+q
       103: q^2
       106: 2q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: q^2
       110: 2q^3+2q^2+q
       111: 3q^3+3q^2+q
       113: 3q^3+3q^2+q
       115: 4q^3+3q^2+q
       117: q^2
       118: 2q^3+2q^2+q
       119: q^2
       120: 2q^3+2q^2+q
       121: 3q^3+3q^2+q
       123: 3q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^4+3q^3+3q^2+q
       134: q^4+2q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^3+3q^2+q
       138: q^3+2q^2+q
       139: q^3+3q^2+q
       140: q^2+q
       141: 3q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^3+3q^2+q
       144: q^3+2q^2+q
       145: q^3+3q^2+q
       146: 3q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: q^3+2q^2+q
       151: q^3+2q^2+q
       153: q^3+2q^2+q
       155: q^3+2q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^3+3q^2+q
       161: 2q^3+3q^2+q
       162: 2q^3+2q^2+q
       163: 2q^3+3q^2+q
       164: 2q^3+3q^2+q
       165: 2q^3+2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^2
       172: 2q^3+2q^2+q
       173: q^2
       176: 2q^3+2q^2+q
       177: q^3+2q^2+q
       179: q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: q^2
       184: 2q^3+2q^2+q
       185: q^2
       186: 2q^3+2q^2+q
       187: 3q^3+3q^2+q
       189: 3q^3+3q^2+q
       191: q^2
       192: q^3+2q^2+q
       194: q^2+q
       195: q^2
       196: q^3+2q^2+q
       197: q^2+q
       199: q^2
       200: q^3+2q^2+q
       201: q^2
       202: q^3+2q^2+q
       204: q^2+q
       205: q^2+q
       207: q^3+3q^2+q
       209: q^3+2q^2+q
       211: q^3+2q^2+q
       213: 2q^3+3q^2+q
       215: 2q^3+3q^2+q
       217: 2q^3+2q^2+q
       219: q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: 2q^2+q
       227: q^3+3q^2+q
       228: q^3+2q^2+q
       229: q^2+q
       230: 2q^3+3q^2+q
       231: 2q^2+q
       232: q^3+3q^2+q
       233: q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: q^2+q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^3+2q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2
       262: q^3+2q^2+q
       263: q^2
       266: 2q^3+2q^2+q
       269: q^2+q
       273: q^2+q
       275: q^2
       278: q^3+2q^2+q
       279: q^3+3q^2+q
       281: q^3+2q^2+q
       284: q^2+q
       286: q^2+q
       287: 2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^2
       296: q^3+2q^2+q
       297: q^3+3q^2+q
       300: q^2+q
       301: q
       303: q^2
       304: q^3+2q^2+q
       305: q^2+q
       307: q^2
       308: q^3+2q^2+q
       310: q^2+q
       311: q
       313: q^2+q
       315: q^2+q
       317: q^2+q
       320: q
       322: q
       323: q
       325: q^3+2q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: 2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q
       352: 2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q
       359: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       380: q^2+q
       381: q^2
       384: q^3+2q^2+q
       385: q^2
       388: q^3+2q^2+q
       391: q
       396: q^2+q
       399: q
       404: q^2+q
       406: q
       409: 2q^2+q
       411: q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: q^2+q
       430: q
       432: q^2+q
       433: q
       435: q
       438: q^2+q
       439: q^2
       440: q^2+q
       441: q^2+q
       444: q
       445: q
       448: q^2+q
       450: q
       451: q
       453: q^2
       454: q^2+q
       455: q
       458: q^2+q
       459: q^2+q
       462: q
       463: q
       465: q^2+q
       467: q^2+q
       469: q^2+q
       472: q
       474: q
       475: q
       477: 2q
       479: q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: q^2+q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q
       508: q^2+q
       512: q
       514: q
       524: q^2+q
       525: q^2
       528: q^2+q
       532: q^2+q
       536: q
       539: q
       543: q^2+q
       547: q
       552: q
       555: q
       559: q^2+q
       563: q
       568: q
       570: 2q
       575: q
       577: q
       579: q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       590: q^2+q
       592: q
       594: q
       596: q^2+q
       597: q^2+q
       599: q^2+q
       601: q^2+q
       604: q
       605: q
       608: q
       609: q
       613: q
       616: q
       617: q
       620: q
       622: q
       623: q
       625: q
       629: q
       632: q
       633: q
       639: q^2+q
       642: q
       644: q
       645: q
       651: 2q
       655: q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: q^2+q
       682: q
       683: q
       685: q
       697: q
       702: q
       708: q
       712: q^2+q
       716: q
       720: q
       723: q
       727: q
       735: q
       739: q
       743: q
       751: q
       756: q
       758: 2q
       768: q
       769: q
       771: q
       777: q^2+q
       781: q^2+q
       786: q
       788: q
       791: q
       797: q
       802: q
       806: q
       808: q
       809: q
       811: q
       821: q
       826: q
       828: q
       832: q
       833: q
       835: q
       849: q
       853: q+1
       871: q
       875: q
       889: q
       893: q
       899: q
       902: q
       906: q
       911: q
       922: q
       930: q
       946: q
       950: q
       961: q
       979: q+1
       984: q+1
      1010: q
      1022: q
      1027: q
      1038: q
      1045: q
      1050: 1
      1107: q+1
      1127: q
      1158: q
      1174: q
      1185: 1
      1190: 1
      1222: 1
      1264: 1
      1311: 1
      1323: 1
      1336: 1
      1406: 1
      1415: 1
      1446: 1
      1498: 1
      1534: 1
      1555: 1
      1560: 1
      1684: 1

1685:    0: 3q^4+5q^3+3q^2+q
         1: q^5+4q^4+5q^3+3q^2+q
         2: 3q^4+5q^3+3q^2+q
         3: q^5+4q^4+5q^3+3q^2+q
         4: 3q^4+5q^3+3q^2+q
         5: 3q^4+5q^3+3q^2+q
         6: q^5+4q^4+5q^3+3q^2+q
         7: 3q^4+5q^3+3q^2+q
         8: 3q^4+5q^3+3q^2+q
         9: q^5+3q^4+3q^3+2q^2+q
        10: 2q^4+4q^3+3q^2+q
        11: 2q^4+4q^3+3q^2+q
        12: 2q^4+4q^3+3q^2+q
        13: 3q^4+5q^3+3q^2+q
        14: 3q^4+5q^3+3q^2+q
        15: 3q^4+5q^3+3q^2+q
        16: 2q^4+4q^3+3q^2+q
        17: 2q^4+4q^3+3q^2+q
        18: 2q^4+3q^3+2q^2+q
        19: 3q^4+5q^3+3q^2+q
        20: q^5+4q^4+5q^3+3q^2+q
        21: 3q^4+5q^3+3q^2+q
        22: 4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: 4q^3+3q^2+q
        25: 4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: 4q^3+3q^2+q
        28: q^4+3q^3+3q^2+q
        29: 2q^4+4q^3+3q^2+q
        30: 3q^4+5q^3+3q^2+q
        31: 3q^3+3q^2+q
        32: 4q^3+3q^2+q
        33: 3q^3+3q^2+q
        34: 3q^3+3q^2+q
        35: 4q^3+3q^2+q
        36: 3q^3+3q^2+q
        38: 4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: 4q^3+3q^2+q
        43: 2q^4+4q^3+3q^2+q
        44: 2q^4+4q^3+3q^2+q
        45: 2q^4+4q^3+3q^2+q
        46: 2q^4+4q^3+3q^2+q
        47: 2q^4+4q^3+3q^2+q
        48: 2q^4+3q^3+2q^2+q
        49: 2q^4+4q^3+3q^2+q
        50: 2q^4+4q^3+3q^2+q
        51: 2q^4+3q^3+2q^2+q
        52: 4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: 4q^3+3q^2+q
        55: 4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: 4q^3+3q^2+q
        58: q^2
        59: 2q^3+2q^2+q
        60: 2q^3+2q^2+q
        61: q^2
        63: 3q^3+3q^2+q
        65: 4q^3+3q^2+q
        67: 3q^3+3q^2+q
        68: q^4+3q^3+3q^2+q
        69: q^4+2q^3+2q^2+q
        70: 2q^4+4q^3+3q^2+q
        71: q^4+3q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 3q^3+3q^2+q
        75: 4q^3+3q^2+q
        77: q^4+4q^3+3q^2+q
        79: 4q^3+3q^2+q
        80: 3q^3+3q^2+q
        81: 3q^3+3q^2+q
        82: 3q^3+3q^2+q
        83: 4q^3+3q^2+q
        84: 3q^3+3q^2+q
        85: 3q^3+3q^2+q
        86: 3q^3+3q^2+q
        87: 4q^3+3q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: 2q^4+4q^3+3q^2+q
        92: 2q^4+4q^3+3q^2+q
        93: 2q^4+3q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: q^3+2q^2+q
       101: q^3+2q^2+q
       102: q^3+2q^2+q
       104: 2q^3+2q^2+q
       105: q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: q^2
       110: 2q^3+2q^2+q
       112: 3q^3+3q^2+q
       114: 3q^3+3q^2+q
       116: 4q^3+3q^2+q
       117: q^2
       118: 2q^3+2q^2+q
       119: 2q^3+2q^2+q
       120: q^2
       122: 3q^3+3q^2+q
       124: 3q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^4+3q^3+3q^2+q
       134: q^4+2q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^3+3q^2+q
       138: q^3+2q^2+q
       139: q^3+3q^2+q
       140: q^2+q
       141: 3q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^3+3q^2+q
       144: q^3+2q^2+q
       145: q^3+3q^2+q
       146: 3q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: q^3+2q^2+q
       152: q^3+2q^2+q
       154: q^3+2q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^3+3q^2+q
       161: 2q^3+3q^2+q
       162: 2q^3+2q^2+q
       163: 2q^3+3q^2+q
       164: 2q^3+3q^2+q
       165: 2q^3+2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: 2q^3+2q^2+q
       171: q^2
       174: 2q^3+2q^2+q
       175: q^2
       178: q^3+2q^2+q
       180: q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: 2q^3+2q^2+q
       184: q^2
       185: q^2
       186: 2q^3+2q^2+q
       188: 3q^3+3q^2+q
       190: 3q^3+3q^2+q
       191: q^2
       192: q^3+2q^2+q
       193: q^2+q
       195: q^2
       196: q^3+2q^2+q
       198: q^2+q
       199: q^3+2q^2+q
       200: q^2
       201: q^3+2q^2+q
       202: q^2
       204: q^2+q
       206: q^2+q
       208: q^3+3q^2+q
       210: q^3+2q^2+q
       212: q^3+2q^2+q
       214: 2q^3+3q^2+q
       216: 2q^3+3q^2+q
       218: 2q^3+2q^2+q
       219: q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: 2q^2+q
       227: q^3+3q^2+q
       228: q^3+2q^2+q
       229: q^2+q
       230: 2q^3+3q^2+q
       231: 2q^2+q
       232: q^3+3q^2+q
       233: q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: q^2+q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^3+2q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: 2q^3+2q^2+q
       265: q^2
       268: q^2+q
       274: q^2+q
       276: q^3+2q^2+q
       277: q^2
       280: q^3+3q^2+q
       282: q^3+2q^2+q
       283: q^2+q
       286: q^2+q
       288: 2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^2
       296: q^3+2q^2+q
       298: q^3+3q^2+q
       299: q^2+q
       302: q
       303: q^2
       304: q^3+2q^2+q
       306: q^2+q
       307: q^3+2q^2+q
       308: q^2
       310: q^2+q
       312: q
       314: q^2+q
       316: q^2+q
       318: q^2+q
       319: q
       322: q
       324: q
       326: q^3+2q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: 2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q
       352: 2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q
       359: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       378: q^2+q
       382: q^3+2q^2+q
       383: q^2
       386: q^3+2q^2+q
       387: q^2
       390: q
       394: q^2+q
       400: q
       403: q^2+q
       407: q
       410: 2q^2+q
       412: q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: q^2+q
       429: q
       432: q^2+q
       434: q
       436: q
       437: q^2+q
       439: q^2
       440: q^2+q
       442: q^2+q
       443: q
       446: q
       447: q^2+q
       450: q
       452: q
       453: q^2+q
       454: q^2
       456: q
       458: q^2+q
       460: q^2+q
       462: q
       464: q
       466: q^2+q
       468: q^2+q
       470: q^2+q
       471: q
       474: q
       476: q
       478: 2q
       480: q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: q^2+q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q
       508: q^2+q
       512: q
       514: q
       522: q^2+q
       526: q^2+q
       527: q^2
       530: q^2+q
       534: q
       538: q
       542: q^2+q
       546: q
       551: q
       556: q
       560: q^2+q
       564: q
       566: q
       571: 2q
       574: q
       581: q
       582: q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2+q
       592: q
       593: q
       596: q^2+q
       598: q^2+q
       600: q^2+q
       602: q^2+q
       603: q
       606: q
       608: q
       610: q
       614: q
       615: q
       618: q
       619: q
       622: q
       624: q
       626: q
       630: q
       632: q
       634: q
       640: q^2+q
       641: q
       644: q
       646: q
       652: 2q
       656: q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: q^2+q
       682: q
       683: q
       685: q
       699: q
       703: q
       706: q
       710: q^2+q
       715: q
       718: q
       722: q
       726: q
       734: q
       740: q
       744: q
       752: q
       754: q
       759: 2q
       766: q
       773: q
       774: q
       778: q^2+q
       782: q^2+q
       785: q
       788: q
       792: q
       798: q
       801: q
       805: q
       808: q
       810: q
       812: q
       822: q
       825: q
       828: q
       832: q
       834: q
       836: q
       850: q
       854: q+1
       871: q
       875: q
       890: q
       894: q
       897: q
       903: q
       905: q
       909: q
       921: q
       929: q
       947: q
       951: q
       962: q
       980: q+1
       987: q+1
      1011: q
      1023: q
      1026: q
      1039: q
      1045: q
      1051: 1
      1108: q+1
      1128: q
      1157: q
      1175: q
      1186: 1
      1193: 1
      1223: 1
      1265: 1
      1312: 1
      1324: 1
      1339: 1
      1409: 1
      1416: 1
      1447: 1
      1499: 1
      1535: 1
      1558: 1
      1561: 1
      1685: 1

1686:    0: 3q^4+5q^3+3q^2+q
         1: q^5+4q^4+5q^3+3q^2+q
         2: 3q^4+5q^3+3q^2+q
         3: q^5+4q^4+5q^3+3q^2+q
         4: 3q^4+5q^3+3q^2+q
         5: 3q^4+5q^3+3q^2+q
         6: q^5+4q^4+5q^3+3q^2+q
         7: 3q^4+5q^3+3q^2+q
         8: 3q^4+5q^3+3q^2+q
         9: q^5+3q^4+3q^3+2q^2+q
        10: 2q^4+4q^3+3q^2+q
        11: 2q^4+4q^3+3q^2+q
        12: 2q^4+4q^3+3q^2+q
        13: 3q^4+5q^3+3q^2+q
        14: 3q^4+5q^3+3q^2+q
        15: 3q^4+5q^3+3q^2+q
        16: 2q^4+4q^3+3q^2+q
        17: 2q^4+4q^3+3q^2+q
        18: 2q^4+3q^3+2q^2+q
        19: 3q^4+5q^3+3q^2+q
        20: q^5+4q^4+5q^3+3q^2+q
        21: 3q^4+5q^3+3q^2+q
        22: 4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: 4q^3+3q^2+q
        25: 4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: 4q^3+3q^2+q
        28: q^4+3q^3+3q^2+q
        29: 2q^4+4q^3+3q^2+q
        30: 3q^4+5q^3+3q^2+q
        31: 3q^3+3q^2+q
        32: 4q^3+3q^2+q
        33: 3q^3+3q^2+q
        34: 3q^3+3q^2+q
        35: 4q^3+3q^2+q
        36: 3q^3+3q^2+q
        38: 4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: 4q^3+3q^2+q
        43: 2q^4+4q^3+3q^2+q
        44: 2q^4+4q^3+3q^2+q
        45: 2q^4+4q^3+3q^2+q
        46: 2q^4+4q^3+3q^2+q
        47: 2q^4+4q^3+3q^2+q
        48: 2q^4+3q^3+2q^2+q
        49: 2q^4+4q^3+3q^2+q
        50: 2q^4+4q^3+3q^2+q
        51: 2q^4+3q^3+2q^2+q
        52: 4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: 4q^3+3q^2+q
        55: 4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: 4q^3+3q^2+q
        58: 2q^3+2q^2+q
        59: q^2
        60: q^2
        61: 2q^3+2q^2+q
        63: 3q^3+3q^2+q
        65: 4q^3+3q^2+q
        67: 3q^3+3q^2+q
        68: q^4+3q^3+3q^2+q
        69: q^4+2q^3+2q^2+q
        70: 2q^4+4q^3+3q^2+q
        71: q^4+3q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 3q^3+3q^2+q
        75: 4q^3+3q^2+q
        77: q^4+4q^3+3q^2+q
        79: 4q^3+3q^2+q
        80: 3q^3+3q^2+q
        81: 3q^3+3q^2+q
        82: 3q^3+3q^2+q
        83: 4q^3+3q^2+q
        84: 3q^3+3q^2+q
        85: 3q^3+3q^2+q
        86: 3q^3+3q^2+q
        87: 4q^3+3q^2+q
        88: 2q^3+3q^2+q
        89: 2q^3+3q^2+q
        90: q^4+2q^3+2q^2+q
        91: 2q^4+4q^3+3q^2+q
        92: 2q^4+4q^3+3q^2+q
        93: 2q^4+3q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: q^3+2q^2+q
       101: q^3+2q^2+q
       102: q^3+2q^2+q
       104: q^2
       105: 2q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: 2q^3+2q^2+q
       110: q^2
       112: 3q^3+3q^2+q
       114: 3q^3+3q^2+q
       116: 4q^3+3q^2+q
       117: 2q^3+2q^2+q
       118: q^2
       119: q^2
       120: 2q^3+2q^2+q
       122: 3q^3+3q^2+q
       124: 3q^3+3q^2+q
       125: 2q^3+3q^2+q
       126: q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^4+3q^3+3q^2+q
       134: q^4+2q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^3+3q^2+q
       138: q^3+2q^2+q
       139: q^3+3q^2+q
       140: q^2+q
       141: 3q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^3+3q^2+q
       144: q^3+2q^2+q
       145: q^3+3q^2+q
       146: 3q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: q^3+2q^2+q
       152: q^3+2q^2+q
       154: q^3+2q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^3+3q^2+q
       161: 2q^3+3q^2+q
       162: 2q^3+2q^2+q
       163: 2q^3+3q^2+q
       164: 2q^3+3q^2+q
       165: 2q^3+2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       170: q^2
       171: 2q^3+2q^2+q
       174: q^2
       175: 2q^3+2q^2+q
       178: q^3+2q^2+q
       180: q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: q^2
       184: 2q^3+2q^2+q
       185: 2q^3+2q^2+q
       186: q^2
       188: 3q^3+3q^2+q
       190: 3q^3+3q^2+q
       191: q^3+2q^2+q
       192: q^2
       194: q^2+q
       195: q^3+2q^2+q
       196: q^2
       198: q^2+q
       199: q^2
       200: q^3+2q^2+q
       201: q^2
       202: q^3+2q^2+q
       203: q^2+q
       206: q^2+q
       208: q^3+3q^2+q
       210: q^3+2q^2+q
       212: q^3+2q^2+q
       214: 2q^3+3q^2+q
       216: 2q^3+3q^2+q
       218: 2q^3+2q^2+q
       219: q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: 2q^2+q
       227: q^3+3q^2+q
       228: q^3+2q^2+q
       229: q^2+q
       230: 2q^3+3q^2+q
       231: 2q^2+q
       232: q^3+3q^2+q
       233: q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: q^2+q
       236: q^2+q
       238: q^2+q
       240: q^2+q
       242: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^3+2q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2
       261: q^3+2q^2+q
       264: q^2
       265: 2q^3+2q^2+q
       270: q^2+q
       272: q^2+q
       276: q^2
       277: q^3+2q^2+q
       280: q^3+3q^2+q
       282: q^3+2q^2+q
       284: q^2+q
       285: q^2+q
       288: 2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       296: q^2
       298: q^3+3q^2+q
       300: q^2+q
       302: q
       303: q^3+2q^2+q
       304: q^2
       306: q^2+q
       307: q^2
       308: q^3+2q^2+q
       309: q^2+q
       312: q
       314: q^2+q
       316: q^2+q
       318: q^2+q
       320: q
       321: q
       324: q
       326: q^3+2q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       339: q^2+q
       341: q^2+q
       343: q^2+q
       344: 2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q
       352: 2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q
       359: q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       379: q^2+q
       382: q^2
       383: q^3+2q^2+q
       386: q^2
       387: q^3+2q^2+q
       392: q
       395: q^2+q
       398: q
       402: q^2+q
       408: q
       410: 2q^2+q
       412: q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: q^2+q
       430: q
       431: q^2+q
       434: q
       436: q
       438: q^2+q
       439: q^2+q
       440: q^2
       442: q^2+q
       444: q
       446: q
       448: q^2+q
       449: q
       452: q
       453: q^2
       454: q^2+q
       456: q
       457: q^2+q
       460: q^2+q
       461: q
       464: q
       466: q^2+q
       468: q^2+q
       470: q^2+q
       472: q
       473: q
       476: q
       478: 2q
       480: q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: q^2+q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q
       508: q^2+q
       512: q
       514: q
       523: q^2+q
       526: q^2
       527: q^2+q
       531: q^2+q
       535: q
       540: q
       544: q^2+q
       548: q
       550: q
       554: q
       558: q^2+q
       562: q
       567: q
       572: 2q
       576: q
       581: q
       582: q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       598: q^2+q
       600: q^2+q
       602: q^2+q
       604: q
       606: q
       607: q
       610: q
       614: q
       616: q
       618: q
       620: q
       621: q
       624: q
       626: q
       630: q
       631: q
       634: q
       640: q^2+q
       642: q
       643: q
       646: q
       652: 2q
       656: q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: q^2+q
       682: q
       683: q
       685: q
       700: q
       704: q
       707: q
       711: q^2+q
       714: q
       719: q
       724: q
       728: q
       736: q
       738: q
       742: q
       750: q
       755: q
       760: 2q
       767: q
       773: q
       774: q
       778: q^2+q
       782: q^2+q
       786: q
       787: q
       792: q
       798: q
       802: q
       806: q
       807: q
       810: q
       812: q
       822: q
       826: q
       827: q
       831: q
       834: q
       836: q
       850: q
       854: q+1
       871: q
       875: q
       891: q
       895: q
       898: q
       901: q
       907: q
       910: q
       923: q
       931: q
       945: q
       949: q
       963: q
       981: q+1
       987: q+1
      1011: q
      1023: q
      1027: q
      1039: q
      1044: q
      1051: 1
      1109: q+1
      1129: q
      1159: q
      1173: q
      1187: 1
      1193: 1
      1223: 1
      1265: 1
      1313: 1
      1325: 1
      1339: 1
      1409: 1
      1417: 1
      1447: 1
      1500: 1
      1536: 1
      1558: 1
      1562: 1
      1686: 1

1687:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^3+2q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+2q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^3+2q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+q
        60: 2q+1
        61: q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 3q+1
        73: 2q^2+3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       103: 2q+1
       106: q
       107: 2q+1
       108: q
       109: q^2+2q+1
       110: q^2+q
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q+1
       141: q^2+2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: 3q+1
       153: 3q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: 2q+1
       172: q
       173: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q+1
       185: q+1
       187: 2q+1
       189: 2q+1
       191: q+1
       193: 2q+1
       194: q
       195: q^2+2q+1
       196: q^2+q
       197: 3q+1
       199: q+1
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: 2q+1
       209: 3q+1
       211: 2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       262: q
       263: q+1
       267: 2q+1
       269: q
       271: q+1
       275: q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q+1
       295: q+1
       297: 2q+1
       299: q+1
       301: 3q+1
       303: q+1
       305: 2q+1
       307: 1
       309: 1
       311: q+1
       313: 1
       315: 2q+1
       317: 3q+1
       319: 2q+1
       320: q
       321: q+1
       323: q+1
       325: 2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 1
       385: q+1
       389: 2q+1
       391: q
       393: q+1
       397: q+1
       401: 1
       405: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: q+1
       431: q+1
       433: 2q+1
       435: q+1
       437: q+1
       439: q+1
       441: 2q+1
       443: 2q+1
       444: q
       445: 3q+1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: q+1
       463: q+1
       465: 1
       467: q+1
       469: 2q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q+1
       545: 2q+1
       547: q
       549: 1
       553: 1
       557: 1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       589: 1
       591: 1
       593: q+1
       595: q+1
       597: q+1
       599: 2q+1
       601: 1
       603: q+1
       605: q+1
       607: q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       615: 1
       617: q+1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       705: 1
       709: 1
       713: 1
       717: q+1
       721: 1
       725: q+1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: q+1
       797: 1
       799: q+1
       801: 1
       803: 1
       805: q+1
       807: q+1
       809: q+1
       811: 2q+1
       813: q+1
       815: 1
       817: 1
       819: 1
       823: 1
       825: 1
       827: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       924: 1
       928: q+1
       932: 1
       936: 1
       940: 1
       948: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: q+1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1052: 1
      1054: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1164: 1
      1184: 1
      1188: 1
      1194: 1
      1202: 1
      1214: 1
      1216: 1
      1218: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 1
      1240: 1
      1242: 1
      1252: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1288: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1334: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1430: 1
      1448: 1
      1450: 1
      1454: 1
      1472: 1
      1480: 1
      1482: 1
      1489: 1
      1501: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1631: 1
      1687: 1

1688:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: q^4+9q^3+11q^2+3q
        23: q^4+9q^3+11q^2+3q
        24: 3q^4+8q^3+8q^2+3q
        25: 2q^3+10q^2+3q
        26: 2q^3+10q^2+3q
        27: 4q^3+7q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: q^4+9q^3+11q^2+3q
        32: 5q^3+8q^2+3q
        33: 5q^3+10q^2+3q
        34: 2q^3+10q^2+3q
        35: q^3+7q^2+3q
        36: 9q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: q^4+9q^3+11q^2+3q
        53: q^4+9q^3+11q^2+3q
        54: 3q^4+8q^3+8q^2+3q
        55: 2q^3+10q^2+3q
        56: 2q^3+10q^2+3q
        57: 4q^3+7q^2+3q
        58: 3q^3+6q^2+2q
        59: 2q^3+4q^2+q
        60: 5q^2+2q
        61: 4q^2+q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 9q^2+3q
        73: 5q^3+10q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: 5q^3+8q^2+3q
        81: 2q^3+7q^2+3q
        82: q^4+9q^3+11q^2+3q
        83: 5q^3+8q^2+3q
        84: q^3+7q^2+3q
        85: 6q^2+3q
        86: 2q^3+10q^2+3q
        87: q^3+7q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 5q^3+10q^2+3q
        95: 5q^3+10q^2+3q
        96: 2q^4+5q^3+5q^2+2q
        97: 7q^2+3q
        98: 7q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 2q^2+q
       104: 3q^2+q
       105: 3q^2+q
       106: q^2
       107: 5q^2+2q
       108: 4q^2+q
       109: 3q^3+6q^2+2q
       110: 2q^3+4q^2+q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: 3q^2+2q
       118: q^2+q
       119: 2q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 6q^2+3q
       136: 2q^3+7q^2+3q
       137: 2q^3+7q^2+3q
       138: q^3+4q^2+2q
       139: 5q^3+10q^2+3q
       140: 9q^2+3q
       141: 5q^3+8q^2+3q
       142: 5q^3+10q^2+3q
       143: 6q^2+3q
       144: 3q^2+2q
       145: 7q^2+3q
       146: q^3+7q^2+3q
       147: 7q^2+3q
       148: 2q^2+2q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 3q^2+q
       152: 2q^3+7q^2+2q
       153: 3q^2+q
       154: 2q^3+7q^2+2q
       155: q^3+2q^2+q
       156: 3q^3+5q^2+2q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^3+7q^2+3q
       161: 2q^3+7q^2+3q
       162: 3q^3+5q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 2q^2+q
       170: 3q^2+q
       171: 3q^2+q
       172: q^2
       173: q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: 2q^2+2q
       184: q^2+q
       185: 3q^2+2q
       186: q^2+q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: 3q^2+2q
       192: q^2+q
       193: 5q^2+2q
       194: 4q^2+q
       195: 3q^3+6q^2+2q
       196: 2q^3+4q^2+q
       197: 3q^2+q
       198: 6q^2+2q
       199: 2q^2+2q
       200: q^2+q
       201: 4q^2+2q
       202: 3q^2+q
       203: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       209: 3q^2+q
       210: 2q^3+7q^2+2q
       211: 2q^2+q
       212: q^3+5q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 6q^2+3q
       223: 3q^2+2q
       224: 2q^3+7q^2+3q
       225: q^3+4q^2+2q
       226: q^3+4q^2+2q
       227: 4q^2+3q
       228: q^3+4q^2+2q
       229: 6q^2+3q
       230: 2q^3+7q^2+3q
       231: 3q^2+2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 3q^2+2q
       238: 4q^2+2q
       240: 4q^2+2q
       242: q^3+2q^2+q
       243: 7q^2+3q
       244: 7q^2+3q
       245: 2q^2+2q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^3+7q^2+3q
       251: 2q^3+7q^2+3q
       252: 3q^3+5q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: 2q^2+q
       261: 2q^2+q
       263: q^2+q
       264: q^2+q
       265: q^2+q
       267: 2q^2+q
       268: 3q^2+q
       269: q^2
       270: 3q^2+q
       271: q^2+q
       272: q^2+q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       280: 2q
       282: q
       283: q^2+q
       285: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: 2q^2+2q
       294: q^2+q
       295: 3q^2+2q
       296: q^2+q
       297: 2q^2+q
       298: 4q^2+2q
       299: 2q^2+2q
       300: q^2+q
       302: 4q^2+2q
       303: 3q^2+2q
       304: q^2+q
       305: 2q^2+q
       306: 4q^2+2q
       307: 2q
       308: q
       309: 2q
       312: q^2+q
       313: q
       314: q
       316: q^2+q
       318: 4q^2+2q
       319: 4q^2+2q
       320: 3q^2+q
       321: 2q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^2+q
       326: q^3+5q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       339: 4q^2+2q
       341: 4q^2+2q
       343: q^3+2q^2+q
       344: 2q^2+2q
       345: 4q^2+3q
       346: q^3+4q^2+2q
       347: 6q^2+3q
       348: 3q^2+2q
       349: 2q^3+7q^2+3q
       350: q^3+4q^2+2q
       351: 7q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       385: q^2+q
       386: q^2+q
       387: q^2+q
       390: 2q^2+q
       392: 2q^2+q
       393: q^2+q
       394: q^2+q
       395: q^2+q
       398: q^2+q
       401: q
       402: q
       405: q^2+q
       408: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       419: q^2+q
       421: q^2+q
       424: q^2+q
       426: q^2+q
       428: 4q^2+2q
       429: q^2+q
       431: q^2+q
       434: q^2+q
       436: q^2+2q
       437: 2q^2+2q
       438: q^2+q
       439: 3q^2+2q
       440: q^2+q
       441: 2q^2+q
       442: 4q^2+2q
       443: 4q^2+2q
       444: 3q^2+q
       446: 4q^2+2q
       447: q
       449: q
       453: 2q
       454: q
       456: q
       457: 2q
       459: q
       460: q
       461: 2q^2+2q
       464: q^2+q
       466: 2q
       468: q
       470: q^2+q
       471: 2q
       472: q
       473: 2q
       475: q
       476: q
       478: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q^2+2q
       493: 3q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 2q^2+3q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q^2+3q
       512: q^2+2q
       513: 2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       538: q
       540: q
       541: q^2+q
       542: q^2+q
       544: q^2+q
       546: 2q^2+q
       548: 2q^2+q
       554: q
       557: q
       558: q
       562: q^2+q
       565: q
       567: q
       572: q^2+q
       573: q^2+q
       576: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q
       589: q
       591: q
       593: q^2+q
       595: q^2+q
       598: q
       600: q^2+q
       602: 2q
       603: q^2+q
       606: q
       607: q^2+q
       610: q^2+q
       612: q^2+2q
       614: q^2+q
       615: 2q
       616: q
       618: q^2+2q
       619: q
       621: q
       628: q
       631: 2q
       634: q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       647: 2q
       648: q
       649: 2q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 2q^2+3q
       679: q^2+2q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       700: q^2+q
       730: q
       732: q
       734: q
       736: q
       746: q
       750: q
       760: q
       761: q
       764: q
       765: q
       767: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       793: 1
       796: q+1
       798: q
       800: q
       801: q
       803: q
       805: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       814: q^2+2q
       815: 2q
       816: q
       817: 1
       820: 1
       825: q
       827: q
       838: q
       839: 2q
       842: q
       843: 1
       845: q
       847: q
       854: q
       857: q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 1
       874: 1
       876: q
       877: 2q
       879: q
       880: q
       891: q
       917: 1
       933: q
       935: q
       941: 1
       957: q
       964: 1
       969: 1
       981: q
       986: q
       988: q
       990: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: q+1
      1016: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: 1
      1032: 1
      1037: 1
      1046: 1
      1052: q
      1054: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1081: 1
      1084: 1
      1085: q
      1087: 1
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1253: 1
      1275: 1
      1280: 1
      1283: 1
      1288: 1
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1349: 1
      1357: 1
      1364: 1
      1431: 1
      1449: 1
      1450: 1
      1454: 1
      1473: 1
      1482: 1
      1490: 1
      1502: 1
      1564: 1
      1568: 1
      1575: 1
      1632: 1
      1688: 1

1689:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+6q^3+3q^2+q
        23: 2q^4+6q^3+3q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: q^4+3q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: 2q^4+6q^3+3q^2+q
        32: 3q^3+2q^2+q
        33: 2q^4+6q^3+3q^2+q
        34: q^4+4q^3+3q^2+q
        35: 2q^3+2q^2+q
        36: q^4+4q^3+3q^2+q
        37: q^4+4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+3q^2+q
        56: 2q^3+3q^2+q
        57: 2q^3+2q^2+q
        58: q^4+4q^3+2q^2+q
        59: q^4+2q^3+q^2
        60: q^4+3q^3+2q^2+q
        61: q^3+q^2
        62: q^4+4q^3+3q^2+q
        64: 2q^3+2q^2+q
        66: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: q^3+3q^2+q
        73: 2q^3+3q^2+q
        74: 2q^3+3q^2+q
        76: 2q^3+3q^2+q
        78: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 3q^3+2q^2+q
        82: q^4+4q^3+3q^2+q
        83: 2q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: 2q^3+2q^2+q
        86: 2q^3+3q^2+q
        87: q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^4+4q^3+3q^2+q
        95: q^4+4q^3+3q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       103: q^4+3q^3+2q^2+q
       106: q^3+q^2
       107: q^3+2q^2+q
       108: q^2
       109: 2q^3+2q^2+q
       110: q^2
       111: q^3+3q^2+q
       113: 2q^3+3q^2+q
       115: q^3+2q^2+q
       117: q^3+q^2+q
       119: q^3+q^2+q
       121: 2q^3+2q^2+q
       123: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 3q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: q^3+3q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+3q^2+q
       143: 2q^3+2q^2+q
       144: q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^3+2q^2+q
       147: q^3+3q^2+q
       148: q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       151: 2q^3+3q^2+q
       153: 2q^3+3q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^3+2q^2+q
       161: q^3+2q^2+q
       162: q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       169: q^3+2q^2+q
       172: q^2
       173: q^3+q^2+q
       177: q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: q^3+3q^2+q
       183: q^2+q
       185: q^2+q
       187: 2q^2+q
       189: q^3+2q^2+q
       191: q^3+q^2+q
       193: q^3+2q^2+q
       194: q^2
       195: 2q^3+2q^2+q
       196: q^2
       197: q^3+3q^2+q
       199: q^3+q^2+q
       201: q^3+2q^2+q
       202: q^2
       203: q^2+q
       205: q^2+q
       207: 2q^3+2q^2+q
       209: 2q^3+3q^2+q
       211: q^3+2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^3+2q^2+q
       227: q^2+q
       228: q^3+2q^2+q
       229: 2q^2+q
       230: 2q^2+q
       231: q^3+2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^3+2q^2+q
       237: 2q^3+3q^2+q
       239: 2q^3+3q^2+q
       241: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^3+3q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: q^2+q
       267: q^3+2q^2+q
       269: q^2
       271: q^2+q
       275: q^3+q^2+q
       279: q
       281: q^2+q
       283: q^2+q
       285: q^2+q
       287: q^3+2q^2+q
       289: q^2+q
       291: 2q^2+q
       293: q^2+q
       295: q^2+q
       297: 2q^2+q
       299: q^2+q
       301: q^3+3q^2+q
       303: q^2+q
       305: 2q^2+q
       307: q
       309: q
       311: q^2+q
       313: q
       315: q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: q^3+2q^2+q
       320: q^2
       321: q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: 2q^2+q
       349: 2q^2+q
       350: 2q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2+q
       381: q
       385: q^2+q
       389: q^3+2q^2+q
       391: q^2
       393: q^2+q
       397: q^2+q
       401: q
       405: q^2+q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2+q
       431: q^2+q
       433: 2q^2+q
       435: q^2+q
       437: q^2+q
       439: q^2+q
       441: 2q^2+q
       443: q^2+q
       444: q^2
       445: 2q^2+q
       447: q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       461: q^2+q
       463: q^2+q
       465: q
       467: q^2+q
       469: q^3+2q^2+q
       471: q
       473: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       497: q
       498: q^2+q
       499: q
       500: q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q
       514: q
       521: q
       525: q
       529: q^2+q
       533: q^2+q
       537: q
       541: q^2+q
       545: q^2+q
       547: q^2
       549: q
       553: q
       557: q
       561: q^2+q
       565: q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q^2+q
       589: q
       591: q
       593: q
       595: q
       599: q^2+q
       603: q^2+q
       605: q^2+q
       607: q^2+q
       609: 2q^2+q
       611: q^2+q
       613: q^2+q
       619: q
       621: q
       623: q
       625: q
       627: q
       629: q
       635: q
       637: q^2+q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       675: q
       676: q
       677: q^2+q
       681: q
       683: q
       686: q
       687: q^2+q
       688: q
       689: q
       693: q^2+q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q^2+q
       729: q
       737: q
       741: q
       745: q
       753: q
       757: q
       761: q
       777: q
       797: q
       799: q^2+q
       801: q
       803: q
       805: q
       807: q
       811: q^2+q
       823: q
       825: q
       827: q
       835: q
       841: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       877: q
       879: q
       896: q
       912: q
       920: q
       924: q
       928: q
       936: q
       948: q
       960: q
       974: q
       978: q
      1010: 1
      1018: q
      1050: q
      1052: q
      1054: q
      1062: q
      1126: 1
      1140: 1
      1148: q
      1184: q
      1202: q
      1222: 1
      1278: 1
      1292: 1
      1322: 1
      1336: 1
      1360: 1
      1432: 1
      1480: 1
      1491: 1
      1503: 1
      1571: 1
      1633: 1
      1689: 1

1690:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: q^4+9q^3+11q^2+3q
        23: q^4+9q^3+11q^2+3q
        24: 3q^4+8q^3+8q^2+3q
        25: 2q^3+10q^2+3q
        26: 2q^3+10q^2+3q
        27: 4q^3+7q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: q^4+9q^3+11q^2+3q
        32: 5q^3+8q^2+3q
        33: 5q^3+10q^2+3q
        34: 2q^3+10q^2+3q
        35: q^3+7q^2+3q
        36: 9q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: q^4+9q^3+11q^2+3q
        53: q^4+9q^3+11q^2+3q
        54: 3q^4+8q^3+8q^2+3q
        55: 2q^3+10q^2+3q
        56: 2q^3+10q^2+3q
        57: 4q^3+7q^2+3q
        58: 3q^3+6q^2+2q
        59: 2q^3+4q^2+q
        60: 4q^2+q
        61: 5q^2+2q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 9q^2+3q
        73: 5q^3+10q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: 5q^3+8q^2+3q
        81: 2q^3+7q^2+3q
        82: q^4+9q^3+11q^2+3q
        83: 5q^3+8q^2+3q
        84: q^3+7q^2+3q
        85: 6q^2+3q
        86: 2q^3+10q^2+3q
        87: q^3+7q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 5q^3+10q^2+3q
        95: 5q^3+10q^2+3q
        96: 2q^4+5q^3+5q^2+2q
        97: 7q^2+3q
        98: 7q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 3q^2+q
       104: q^2
       105: 2q^2+q
       106: 3q^2+q
       107: 4q^2+q
       108: 5q^2+2q
       109: 3q^3+6q^2+2q
       110: 2q^3+4q^2+q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: 3q^2+2q
       118: q^2+q
       119: q^2+q
       120: 2q^2+2q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 6q^2+3q
       136: 2q^3+7q^2+3q
       137: 2q^3+7q^2+3q
       138: q^3+4q^2+2q
       139: 5q^3+10q^2+3q
       140: 9q^2+3q
       141: 5q^3+8q^2+3q
       142: 5q^3+10q^2+3q
       143: 6q^2+3q
       144: 3q^2+2q
       145: 7q^2+3q
       146: q^3+7q^2+3q
       147: 7q^2+3q
       148: 2q^2+2q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 2q^3+7q^2+2q
       152: 3q^2+q
       153: 2q^3+7q^2+2q
       154: 3q^2+q
       155: 3q^3+5q^2+2q
       156: q^3+2q^2+q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^3+7q^2+3q
       161: 2q^3+7q^2+3q
       162: 3q^3+5q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 3q^2+q
       170: q^2
       171: 2q^2+q
       172: 3q^2+q
       173: q^2+q
       175: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: q^2+q
       184: 2q^2+2q
       185: 3q^2+2q
       186: q^2+q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: 3q^2+2q
       192: q^2+q
       193: 4q^2+q
       194: 5q^2+2q
       195: 3q^3+6q^2+2q
       196: 2q^3+4q^2+q
       197: 6q^2+2q
       198: 3q^2+q
       199: q^2+q
       200: 2q^2+2q
       201: 3q^2+q
       202: 4q^2+2q
       203: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+7q^2+2q
       210: 3q^2+q
       211: q^3+5q^2+2q
       212: 2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 6q^2+3q
       223: 3q^2+2q
       224: 2q^3+7q^2+3q
       225: q^3+4q^2+2q
       226: q^3+4q^2+2q
       227: 4q^2+3q
       228: q^3+4q^2+2q
       229: 6q^2+3q
       230: 2q^3+7q^2+3q
       231: 3q^2+2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 3q^2+2q
       237: 4q^2+2q
       239: 4q^2+2q
       241: q^3+2q^2+q
       243: 7q^2+3q
       244: 7q^2+3q
       245: 2q^2+2q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^3+7q^2+3q
       251: 2q^3+7q^2+3q
       252: 3q^3+5q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       265: q^2+q
       266: q^2+q
       267: 3q^2+q
       268: q^2
       269: 3q^2+q
       270: 2q^2+q
       271: q^2+q
       272: q^2+q
       275: q^2+q
       277: q^2+q
       278: q^2+q
       279: 2q
       281: q
       284: q^2+q
       285: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: q^2+q
       294: 2q^2+2q
       295: 3q^2+2q
       296: q^2+q
       297: 4q^2+2q
       298: 2q^2+q
       299: q^2+q
       300: 2q^2+2q
       301: 4q^2+2q
       303: 3q^2+2q
       304: q^2+q
       305: 4q^2+2q
       306: 2q^2+q
       307: q
       308: 2q
       309: 2q
       311: q^2+q
       313: q
       314: q
       315: q^2+q
       317: 4q^2+2q
       319: 3q^2+q
       320: 4q^2+2q
       321: 2q^2+2q
       323: q^2+q
       324: q^2+q
       325: q^3+5q^2+2q
       326: 2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       338: 4q^2+2q
       340: 4q^2+2q
       342: q^3+2q^2+q
       344: 2q^2+2q
       345: 4q^2+3q
       346: q^3+4q^2+2q
       347: 6q^2+3q
       348: 3q^2+2q
       349: 2q^3+7q^2+3q
       350: q^3+4q^2+2q
       351: 7q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q^2+q
       387: q^2+q
       388: q^2+q
       389: 2q^2+q
       391: 2q^2+q
       393: q^2+q
       395: q^2+q
       396: q^2+q
       397: q^2+q
       401: q
       402: q
       405: q^2+q
       408: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       420: q^2+q
       421: q^2+q
       423: q^2+q
       425: q^2+q
       427: 4q^2+2q
       430: q^2+q
       431: q^2+q
       433: q^2+q
       435: q^2+2q
       437: q^2+q
       438: 2q^2+2q
       439: 3q^2+2q
       440: q^2+q
       441: 4q^2+2q
       442: 2q^2+q
       443: 3q^2+q
       444: 4q^2+2q
       445: 4q^2+2q
       448: q
       449: q
       453: q
       454: 2q
       455: q
       457: 2q
       459: q
       460: q
       461: 2q^2+2q
       463: q^2+q
       465: 2q
       467: q
       469: q^2+q
       471: q
       472: 2q
       473: 2q
       475: q
       476: q
       477: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q^2+2q
       493: 3q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 2q^2+3q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q^2+3q
       512: q^2+2q
       513: 2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q^2+q
       543: q^2+q
       544: q^2+q
       545: 2q^2+q
       547: 2q^2+q
       553: q
       557: q
       558: q
       561: q^2+q
       565: q
       567: q
       569: q^2+q
       573: q^2+q
       576: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q
       590: q
       591: q
       594: q^2+q
       595: q^2+q
       597: q
       599: q^2+q
       601: 2q
       604: q^2+q
       605: q
       607: q^2+q
       609: q^2+q
       611: q^2+2q
       613: q^2+q
       615: q
       616: 2q
       617: q^2+2q
       620: q
       621: q
       627: q
       631: 2q
       633: q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       647: q
       648: 2q
       649: 2q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 2q^2+3q
       679: q^2+2q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q
       729: q
       731: q
       733: q
       735: q
       745: q
       749: q
       757: q
       761: q
       764: q
       765: q
       767: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       794: 1
       795: q+1
       797: q
       799: q
       802: q
       803: q
       806: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       813: q^2+2q
       815: q
       816: 2q
       817: 1
       819: 1
       826: q
       827: q
       837: q
       839: 2q
       841: q
       844: 1
       846: q
       847: q
       853: q
       857: q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 1
       874: 1
       876: q
       877: 2q
       879: q
       880: q
       884: q
       918: 1
       932: q
       934: q
       940: 1
       956: q
       966: 1
       971: 1
       978: q
       982: q
       988: q
       990: q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: q+1
      1017: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: 1
      1032: 1
      1036: 1
      1047: 1
      1053: q
      1054: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1081: 1
      1084: 1
      1085: q
      1090: 1
      1098: q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1252: 1
      1274: 1
      1281: 1
      1283: 1
      1288: 1
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1348: 1
      1358: 1
      1365: 1
      1433: 1
      1448: 1
      1450: 1
      1455: 1
      1472: 1
      1483: 1
      1493: 1
      1504: 1
      1563: 1
      1569: 1
      1576: 1
      1634: 1
      1690: 1

1691:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: q^4+9q^3+11q^2+3q
        23: q^4+9q^3+11q^2+3q
        24: 3q^4+8q^3+8q^2+3q
        25: 2q^3+10q^2+3q
        26: 2q^3+10q^2+3q
        27: 4q^3+7q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: q^4+9q^3+11q^2+3q
        32: 5q^3+8q^2+3q
        33: 5q^3+10q^2+3q
        34: 2q^3+10q^2+3q
        35: q^3+7q^2+3q
        36: 9q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: q^4+9q^3+11q^2+3q
        53: q^4+9q^3+11q^2+3q
        54: 3q^4+8q^3+8q^2+3q
        55: 2q^3+10q^2+3q
        56: 2q^3+10q^2+3q
        57: 4q^3+7q^2+3q
        58: 2q^3+4q^2+q
        59: 3q^3+6q^2+2q
        60: 5q^2+2q
        61: 4q^2+q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 9q^2+3q
        73: 5q^3+10q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: 5q^3+8q^2+3q
        81: 2q^3+7q^2+3q
        82: q^4+9q^3+11q^2+3q
        83: 5q^3+8q^2+3q
        84: q^3+7q^2+3q
        85: 6q^2+3q
        86: 2q^3+10q^2+3q
        87: q^3+7q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 5q^3+10q^2+3q
        95: 5q^3+10q^2+3q
        96: 2q^4+5q^3+5q^2+2q
        97: 7q^2+3q
        98: 7q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 3q^2+q
       104: 2q^2+q
       105: q^2
       106: 3q^2+q
       107: 5q^2+2q
       108: 4q^2+q
       109: 2q^3+4q^2+q
       110: 3q^3+6q^2+2q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: q^2+q
       118: 3q^2+2q
       119: 2q^2+2q
       120: q^2+q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 6q^2+3q
       136: 2q^3+7q^2+3q
       137: 2q^3+7q^2+3q
       138: q^3+4q^2+2q
       139: 5q^3+10q^2+3q
       140: 9q^2+3q
       141: 5q^3+8q^2+3q
       142: 5q^3+10q^2+3q
       143: 6q^2+3q
       144: 3q^2+2q
       145: 7q^2+3q
       146: q^3+7q^2+3q
       147: 7q^2+3q
       148: 2q^2+2q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 2q^3+7q^2+2q
       152: 3q^2+q
       153: 2q^3+7q^2+2q
       154: 3q^2+q
       155: 3q^3+5q^2+2q
       156: q^3+2q^2+q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^3+7q^2+3q
       161: 2q^3+7q^2+3q
       162: 3q^3+5q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 3q^2+q
       170: 2q^2+q
       171: q^2
       172: 3q^2+q
       173: q^2+q
       174: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: 2q^2+2q
       184: q^2+q
       185: q^2+q
       186: 3q^2+2q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: q^2+q
       192: 3q^2+2q
       193: 5q^2+2q
       194: 4q^2+q
       195: 2q^3+4q^2+q
       196: 3q^3+6q^2+2q
       197: 6q^2+2q
       198: 3q^2+q
       199: 2q^2+2q
       200: q^2+q
       201: 4q^2+2q
       202: 3q^2+q
       204: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+7q^2+2q
       210: 3q^2+q
       211: q^3+5q^2+2q
       212: 2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 6q^2+3q
       223: 3q^2+2q
       224: 2q^3+7q^2+3q
       225: q^3+4q^2+2q
       226: q^3+4q^2+2q
       227: 4q^2+3q
       228: q^3+4q^2+2q
       229: 6q^2+3q
       230: 2q^3+7q^2+3q
       231: 3q^2+2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 3q^2+2q
       237: 4q^2+2q
       239: 4q^2+2q
       241: q^3+2q^2+q
       243: 7q^2+3q
       244: 7q^2+3q
       245: 2q^2+2q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^3+7q^2+3q
       251: 2q^3+7q^2+3q
       252: 3q^3+5q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       264: q^2+q
       266: q^2+q
       267: 3q^2+q
       268: 2q^2+q
       269: 3q^2+q
       270: q^2
       273: q^2+q
       274: q^2+q
       275: q^2+q
       276: q^2+q
       278: q^2+q
       279: 2q
       281: q
       283: q^2+q
       286: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: 2q^2+2q
       294: q^2+q
       295: q^2+q
       296: 3q^2+2q
       297: 4q^2+2q
       298: 2q^2+q
       299: 2q^2+2q
       300: q^2+q
       301: 4q^2+2q
       303: q^2+q
       304: 3q^2+2q
       305: 4q^2+2q
       306: 2q^2+q
       307: 2q
       308: q
       310: 2q
       311: q^2+q
       313: q
       314: q
       315: q^2+q
       317: 4q^2+2q
       319: 4q^2+2q
       320: 3q^2+q
       322: 2q^2+2q
       323: q^2+q
       324: q^2+q
       325: q^3+5q^2+2q
       326: 2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       338: 4q^2+2q
       340: 4q^2+2q
       342: q^3+2q^2+q
       344: 2q^2+2q
       345: 4q^2+3q
       346: q^3+4q^2+2q
       347: 6q^2+3q
       348: 3q^2+2q
       349: 2q^3+7q^2+3q
       350: q^3+4q^2+2q
       351: 7q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q^2+q
       386: q^2+q
       388: q^2+q
       389: 2q^2+q
       391: 2q^2+q
       393: q^2+q
       394: q^2+q
       396: q^2+q
       399: q^2+q
       403: q
       404: q
       406: q^2+q
       407: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       419: q^2+q
       422: q^2+q
       423: q^2+q
       425: q^2+q
       427: 4q^2+2q
       429: q^2+q
       432: q^2+q
       433: q^2+q
       435: q^2+2q
       437: 2q^2+2q
       438: q^2+q
       439: q^2+q
       440: 3q^2+2q
       441: 4q^2+2q
       442: 2q^2+q
       443: 4q^2+2q
       444: 3q^2+q
       445: 4q^2+2q
       447: q
       450: q
       453: 2q
       454: q
       455: q
       458: 2q
       459: q
       460: q
       462: 2q^2+2q
       463: q^2+q
       465: 2q
       467: q
       469: q^2+q
       471: 2q
       472: q
       474: 2q
       475: q
       476: q
       477: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q^2+2q
       493: 3q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 2q^2+3q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q^2+3q
       512: q^2+2q
       513: 2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q^2+q
       542: q^2+q
       543: q^2+q
       545: 2q^2+q
       547: 2q^2+q
       555: q
       559: q
       560: q
       563: q^2+q
       566: q
       568: q
       570: q^2+q
       574: q^2+q
       575: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q
       589: q
       592: q
       593: q^2+q
       596: q^2+q
       597: q
       599: q^2+q
       601: 2q
       603: q^2+q
       605: q
       608: q^2+q
       609: q^2+q
       611: q^2+2q
       613: q^2+q
       615: 2q
       616: q
       617: q^2+2q
       619: q
       622: q
       627: q
       632: 2q
       633: q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       647: 2q
       648: q
       650: 2q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 2q^2+3q
       679: q^2+2q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       697: q^2+q
       729: q
       731: q
       733: q
       735: q
       747: q
       751: q
       758: q
       762: q
       763: q
       766: q
       768: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       793: 1
       795: q+1
       797: q
       799: q
       801: q
       804: q
       805: q^2+q
       808: q^2+q
       809: q
       811: q^2+q
       813: q^2+2q
       815: 2q
       816: q
       818: 1
       819: 1
       825: q
       828: q
       837: q
       840: 2q
       841: q
       844: 1
       845: q
       848: q
       853: q
       857: q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 1
       874: 1
       876: q
       877: 2q
       879: q
       880: q
       889: q
       916: 1
       932: q
       934: q
       942: 1
       958: q
       965: 1
       971: 1
       979: q
       982: q
       989: q
       991: q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: q+1
      1016: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: 1
      1033: 1
      1036: 1
      1047: 1
      1052: q
      1055: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1081: 1
      1084: 1
      1085: q
      1089: 1
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1252: 1
      1274: 1
      1281: 1
      1283: 1
      1288: 1
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1350: 1
      1356: 1
      1366: 1
      1433: 1
      1448: 1
      1451: 1
      1454: 1
      1472: 1
      1483: 1
      1492: 1
      1505: 1
      1565: 1
      1567: 1
      1577: 1
      1634: 1
      1691: 1

1692:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^3+2q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+2q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^3+2q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+2q+1
        60: q
        61: 2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 3q+1
        73: 2q^2+3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       103: q
       106: 2q+1
       107: q
       108: 2q+1
       109: q^2+q
       110: q^2+2q+1
       111: 3q+1
       113: 3q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q+1
       141: q^2+2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       151: 3q+1
       153: 3q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: 2q+1
       176: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q+1
       186: q+1
       187: 2q+1
       189: 2q+1
       192: q+1
       193: q
       194: 2q+1
       195: q^2+q
       196: q^2+2q+1
       197: 3q+1
       200: q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: 2q+1
       209: 3q+1
       211: 2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 2q+1
       266: q+1
       267: q
       269: 2q+1
       273: q+1
       278: q+1
       279: 1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q+1
       296: q+1
       297: 2q+1
       300: q+1
       301: 3q+1
       304: q+1
       305: 2q+1
       308: 1
       310: 1
       311: q+1
       313: 1
       315: 2q+1
       317: 3q+1
       319: q
       320: 2q+1
       322: q+1
       323: q+1
       325: 2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       384: 1
       388: q+1
       389: q
       391: 2q+1
       396: q+1
       399: q+1
       404: 1
       406: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: q+1
       432: q+1
       433: 2q+1
       435: q+1
       438: q+1
       440: q+1
       441: 2q+1
       443: q
       444: 2q+1
       445: 3q+1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: q+1
       463: q+1
       465: 1
       467: q+1
       469: 2q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q+1
       545: q
       547: 2q+1
       552: 1
       555: 1
       559: 1
       563: q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       590: 1
       592: 1
       594: q+1
       596: q+1
       597: q+1
       599: 2q+1
       601: 1
       604: q+1
       605: q+1
       608: q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       708: 1
       712: 1
       716: 1
       720: q+1
       723: 1
       727: q+1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: q+1
       797: 1
       799: q+1
       802: 1
       804: 1
       806: q+1
       808: q+1
       809: q+1
       811: 2q+1
       813: q+1
       816: 1
       818: 1
       819: 1
       823: 1
       826: 1
       828: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       927: 1
       930: q+1
       934: 1
       938: 1
       942: 1
       950: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1017: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: q+1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1036: 1
      1042: 1
      1046: 1
      1050: 1
      1053: 1
      1055: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1185: 1
      1188: 1
      1197: 1
      1204: 1
      1214: 1
      1217: 1
      1219: 1
      1222: 1
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 1
      1241: 1
      1243: 1
      1252: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1288: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1334: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1430: 1
      1448: 1
      1451: 1
      1455: 1
      1472: 1
      1480: 1
      1482: 1
      1494: 1
      1506: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1631: 1
      1692: 1

1693:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^3+2q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+2q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^3+2q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+q
        60: q
        61: 2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 3q+1
        73: 2q^2+3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       104: q
       105: 2q+1
       107: q
       108: 2q+1
       109: q^2+2q+1
       110: q^2+q
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q+1
       141: q^2+2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       152: 3q+1
       154: 3q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: 2q+1
       175: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q+1
       185: q+1
       188: 2q+1
       190: 2q+1
       191: q+1
       193: q
       194: 2q+1
       195: q^2+2q+1
       196: q^2+q
       198: 3q+1
       200: q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: 2q+1
       210: 3q+1
       212: 2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 2q+1
       265: q+1
       268: q
       270: 2q+1
       272: q+1
       277: q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q+1
       295: q+1
       298: 2q+1
       300: q+1
       302: 3q+1
       303: q+1
       306: 2q+1
       308: 1
       309: 1
       312: q+1
       314: 1
       316: 2q+1
       318: 3q+1
       319: q
       320: 2q+1
       321: q+1
       324: q+1
       326: 2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       383: 1
       387: q+1
       390: q
       392: 2q+1
       395: q+1
       398: q+1
       402: 1
       408: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: q+1
       431: q+1
       434: 2q+1
       436: q+1
       438: q+1
       439: q+1
       442: 2q+1
       443: q
       444: 2q+1
       446: 3q+1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q+1
       464: q+1
       466: 1
       468: q+1
       470: 2q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q+1
       546: q
       548: 2q+1
       550: 1
       554: 1
       558: 1
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       590: 1
       591: 1
       594: q+1
       595: q+1
       598: q+1
       600: 2q+1
       602: 1
       604: q+1
       606: q+1
       607: q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       616: 1
       618: q+1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       707: 1
       711: 1
       714: 1
       719: q+1
       724: 1
       728: q+1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: q+1
       798: 1
       800: q+1
       802: 1
       803: 1
       806: q+1
       807: q+1
       810: q+1
       812: 2q+1
       814: q+1
       816: 1
       817: 1
       820: 1
       824: 1
       826: 1
       827: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       925: 1
       931: q+1
       935: 1
       937: 1
       941: 1
       949: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1017: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: q+1
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1053: 1
      1054: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1165: 1
      1187: 1
      1192: 1
      1196: 1
      1203: 1
      1215: 1
      1216: 1
      1219: 1
      1223: 1
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 1
      1241: 1
      1242: 1
      1253: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1288: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1338: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1434: 1
      1449: 1
      1450: 1
      1455: 1
      1473: 1
      1481: 1
      1483: 1
      1496: 1
      1507: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1635: 1
      1693: 1

1694:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^3+2q^2+2q+1
        25: 3q+1
        26: 3q+1
        27: q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+2q+1
        33: 2q^2+3q+1
        34: 3q+1
        35: 2q+1
        36: 3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: q^3+2q^2+2q+1
        55: 3q+1
        56: 3q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+2q+1
        60: 2q+1
        61: q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 3q+1
        73: 2q^2+3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       104: 2q+1
       105: q
       107: 2q+1
       108: q
       109: q^2+q
       110: q^2+2q+1
       112: 3q+1
       114: 3q+1
       116: 2q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: 2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: 3q+1
       141: q^2+2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: 3q+1
       146: 2q+1
       147: 3q+1
       148: q+1
       149: 3q+1
       150: 2q+1
       152: 3q+1
       154: 3q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: 2q+1
       171: q
       174: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q+1
       186: q+1
       188: 2q+1
       190: 2q+1
       192: q+1
       193: 2q+1
       194: q
       195: q^2+q
       196: q^2+2q+1
       198: 3q+1
       199: q+1
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: 2q+1
       210: 3q+1
       212: 2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 1
       233: q+1
       234: q+1
       235: 1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q+1
       261: q
       264: q+1
       268: 2q+1
       270: q
       274: q+1
       276: q+1
       280: 1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q+1
       296: q+1
       298: 2q+1
       299: q+1
       302: 3q+1
       304: q+1
       306: 2q+1
       307: 1
       310: 1
       312: q+1
       314: 1
       316: 2q+1
       318: 3q+1
       319: 2q+1
       320: q
       322: q+1
       324: q+1
       326: 2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 3q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 1
       386: q+1
       390: 2q+1
       392: q
       394: q+1
       400: q+1
       403: 1
       407: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: q+1
       432: q+1
       434: 2q+1
       436: q+1
       437: q+1
       440: q+1
       442: 2q+1
       443: 2q+1
       444: q
       446: 3q+1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q+1
       464: q+1
       466: 1
       468: q+1
       470: 2q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+2q+1
       495: 2q+1
       496: q+1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q+1
       546: 2q+1
       548: q
       551: 1
       556: 1
       560: 1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       589: 1
       592: 1
       593: q+1
       596: q+1
       598: q+1
       600: 2q+1
       602: 1
       603: q+1
       606: q+1
       608: q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       615: 1
       618: q+1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: 1
       681: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       706: 1
       710: 1
       715: 1
       718: q+1
       722: 1
       726: q+1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: q+1
       798: 1
       800: q+1
       801: 1
       804: 1
       805: q+1
       808: q+1
       810: q+1
       812: 2q+1
       814: q+1
       815: 1
       818: 1
       820: 1
       824: 1
       825: 1
       828: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       876: 1
       877: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       926: 1
       929: q+1
       933: 1
       939: 1
       943: 1
       951: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: q+1
      1026: 1
      1029: 1
      1031: 1
      1033: 1
      1037: 1
      1043: 1
      1047: 1
      1051: 1
      1052: 1
      1055: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1081: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1167: 1
      1186: 1
      1192: 1
      1195: 1
      1205: 1
      1215: 1
      1217: 1
      1218: 1
      1223: 1
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 1
      1240: 1
      1243: 1
      1253: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1288: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1338: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1434: 1
      1449: 1
      1451: 1
      1454: 1
      1473: 1
      1481: 1
      1483: 1
      1495: 1
      1508: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1635: 1
      1694: 1

1695:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: q^4+9q^3+11q^2+3q
        23: q^4+9q^3+11q^2+3q
        24: 3q^4+8q^3+8q^2+3q
        25: 2q^3+10q^2+3q
        26: 2q^3+10q^2+3q
        27: 4q^3+7q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: q^4+9q^3+11q^2+3q
        32: 5q^3+8q^2+3q
        33: 5q^3+10q^2+3q
        34: 2q^3+10q^2+3q
        35: q^3+7q^2+3q
        36: 9q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: q^4+9q^3+11q^2+3q
        53: q^4+9q^3+11q^2+3q
        54: 3q^4+8q^3+8q^2+3q
        55: 2q^3+10q^2+3q
        56: 2q^3+10q^2+3q
        57: 4q^3+7q^2+3q
        58: 2q^3+4q^2+q
        59: 3q^3+6q^2+2q
        60: 4q^2+q
        61: 5q^2+2q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 9q^2+3q
        73: 5q^3+10q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: 5q^3+8q^2+3q
        81: 2q^3+7q^2+3q
        82: q^4+9q^3+11q^2+3q
        83: 5q^3+8q^2+3q
        84: q^3+7q^2+3q
        85: 6q^2+3q
        86: 2q^3+10q^2+3q
        87: q^3+7q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 5q^3+10q^2+3q
        95: 5q^3+10q^2+3q
        96: 2q^4+5q^3+5q^2+2q
        97: 7q^2+3q
        98: 7q^2+3q
        99: 2q^3+4q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: q^2
       104: 3q^2+q
       105: 3q^2+q
       106: 2q^2+q
       107: 4q^2+q
       108: 5q^2+2q
       109: 2q^3+4q^2+q
       110: 3q^3+6q^2+2q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: q^2+q
       118: 3q^2+2q
       119: q^2+q
       120: 2q^2+2q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 6q^2+3q
       136: 2q^3+7q^2+3q
       137: 2q^3+7q^2+3q
       138: q^3+4q^2+2q
       139: 5q^3+10q^2+3q
       140: 9q^2+3q
       141: 5q^3+8q^2+3q
       142: 5q^3+10q^2+3q
       143: 6q^2+3q
       144: 3q^2+2q
       145: 7q^2+3q
       146: q^3+7q^2+3q
       147: 7q^2+3q
       148: 2q^2+2q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 3q^2+q
       152: 2q^3+7q^2+2q
       153: 3q^2+q
       154: 2q^3+7q^2+2q
       155: q^3+2q^2+q
       156: 3q^3+5q^2+2q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^3+7q^2+3q
       161: 2q^3+7q^2+3q
       162: 3q^3+5q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: 2q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: q^2
       170: 3q^2+q
       171: 3q^2+q
       172: 2q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: q^2+q
       184: 2q^2+2q
       185: q^2+q
       186: 3q^2+2q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: q^2+q
       192: 3q^2+2q
       193: 4q^2+q
       194: 5q^2+2q
       195: 2q^3+4q^2+q
       196: 3q^3+6q^2+2q
       197: 3q^2+q
       198: 6q^2+2q
       199: q^2+q
       200: 2q^2+2q
       201: 3q^2+q
       202: 4q^2+2q
       204: 2q^2+2q
       205: q^2+q
       206: q^2+q
       207: 2q^2+q
       208: 4q^2+2q
       209: 3q^2+q
       210: 2q^3+7q^2+2q
       211: 2q^2+q
       212: q^3+5q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 6q^2+3q
       223: 3q^2+2q
       224: 2q^3+7q^2+3q
       225: q^3+4q^2+2q
       226: q^3+4q^2+2q
       227: 4q^2+3q
       228: q^3+4q^2+2q
       229: 6q^2+3q
       230: 2q^3+7q^2+3q
       231: 3q^2+2q
       232: 3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q
       236: 3q^2+2q
       238: 4q^2+2q
       240: 4q^2+2q
       242: q^3+2q^2+q
       243: 7q^2+3q
       244: 7q^2+3q
       245: 2q^2+2q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^3+7q^2+3q
       251: 2q^3+7q^2+3q
       252: 3q^3+5q^2+2q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: 2q^2+q
       261: 2q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2+q
       267: q^2
       268: 3q^2+q
       269: 2q^2+q
       270: 3q^2+q
       273: q^2+q
       274: q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: 2q
       282: q
       284: q^2+q
       286: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: q^2+q
       294: 2q^2+2q
       295: q^2+q
       296: 3q^2+2q
       297: 2q^2+q
       298: 4q^2+2q
       299: q^2+q
       300: 2q^2+2q
       302: 4q^2+2q
       303: q^2+q
       304: 3q^2+2q
       305: 2q^2+q
       306: 4q^2+2q
       307: q
       308: 2q
       310: 2q
       312: q^2+q
       313: q
       314: q
       316: q^2+q
       318: 4q^2+2q
       319: 3q^2+q
       320: 4q^2+2q
       322: 2q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^2+q
       326: q^3+5q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: 3q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       339: 4q^2+2q
       341: 4q^2+2q
       343: q^3+2q^2+q
       344: 2q^2+2q
       345: 4q^2+3q
       346: q^3+4q^2+2q
       347: 6q^2+3q
       348: 3q^2+2q
       349: 2q^3+7q^2+3q
       350: q^3+4q^2+2q
       351: 7q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: 2q^2+3q
       356: q^2+2q
       357: 2q
       358: q
       359: 2q^2+2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       386: q^2+q
       387: q^2+q
       388: q^2+q
       390: 2q^2+q
       392: 2q^2+q
       394: q^2+q
       395: q^2+q
       396: q^2+q
       400: q^2+q
       403: q
       404: q
       406: q^2+q
       407: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       420: q^2+q
       422: q^2+q
       424: q^2+q
       426: q^2+q
       428: 4q^2+2q
       430: q^2+q
       432: q^2+q
       434: q^2+q
       436: q^2+2q
       437: q^2+q
       438: 2q^2+2q
       439: q^2+q
       440: 3q^2+2q
       441: 2q^2+q
       442: 4q^2+2q
       443: 3q^2+q
       444: 4q^2+2q
       446: 4q^2+2q
       448: q
       450: q
       453: q
       454: 2q
       456: q
       458: 2q
       459: q
       460: q
       462: 2q^2+2q
       464: q^2+q
       466: 2q
       468: q
       470: q^2+q
       471: q
       472: 2q
       474: 2q
       475: q
       476: q
       478: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q^2+2q
       493: 3q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 2q^2+3q
       497: 2q
       498: q^2+2q
       499: q
       500: q
       501: 2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q^2+3q
       512: q^2+2q
       513: 2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       538: q
       540: q
       542: q^2+q
       543: q^2+q
       544: q^2+q
       546: 2q^2+q
       548: 2q^2+q
       556: q
       559: q
       560: q
       564: q^2+q
       566: q
       568: q
       571: q^2+q
       574: q^2+q
       575: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q
       590: q
       592: q
       594: q^2+q
       596: q^2+q
       598: q
       600: q^2+q
       602: 2q
       604: q^2+q
       606: q
       608: q^2+q
       610: q^2+q
       612: q^2+2q
       614: q^2+q
       615: q
       616: 2q
       618: q^2+2q
       620: q
       622: q
       628: q
       632: 2q
       634: q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       647: q
       648: 2q
       650: 2q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 2q^2+3q
       679: q^2+2q
       680: 1
       681: 2q
       683: q
       684: 2q
       685: q
       686: 2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       699: q^2+q
       730: q
       732: q
       734: q
       736: q
       748: q
       752: q
       759: q
       762: q
       763: q
       766: q
       768: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       794: 1
       796: q+1
       798: q
       800: q
       802: q
       804: q
       806: q^2+q
       808: q^2+q
       810: q
       812: q^2+q
       814: q^2+2q
       815: q
       816: 2q
       818: 1
       820: 1
       826: q
       828: q
       838: q
       840: 2q
       842: q
       843: 1
       846: q
       848: q
       854: q
       857: q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 1
       874: 1
       876: q
       877: 2q
       879: q
       880: q
       890: q
       919: 1
       933: q
       935: q
       943: 1
       959: q
       967: 1
       969: 1
       980: q
       986: q
       989: q
       991: q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: q+1
      1017: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: 1
      1033: 1
      1037: 1
      1046: 1
      1053: q
      1055: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1081: 1
      1084: 1
      1085: q
      1094: 1
      1104: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1253: 1
      1275: 1
      1280: 1
      1283: 1
      1288: 1
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1351: 1
      1359: 1
      1367: 1
      1431: 1
      1449: 1
      1451: 1
      1455: 1
      1473: 1
      1482: 1
      1497: 1
      1509: 1
      1566: 1
      1570: 1
      1578: 1
      1632: 1
      1695: 1

1696:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+6q^3+3q^2+q
        23: 2q^4+6q^3+3q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: q^4+3q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: 2q^4+6q^3+3q^2+q
        32: 3q^3+2q^2+q
        33: 2q^4+6q^3+3q^2+q
        34: q^4+4q^3+3q^2+q
        35: 2q^3+2q^2+q
        36: q^4+4q^3+3q^2+q
        37: q^4+4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+3q^2+q
        56: 2q^3+3q^2+q
        57: 2q^3+2q^2+q
        58: q^4+2q^3+q^2
        59: q^4+4q^3+2q^2+q
        60: q^3+q^2
        61: q^4+3q^3+2q^2+q
        62: q^4+4q^3+3q^2+q
        64: 2q^3+2q^2+q
        66: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: q^3+3q^2+q
        73: 2q^3+3q^2+q
        74: 2q^3+3q^2+q
        76: 2q^3+3q^2+q
        78: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 3q^3+2q^2+q
        82: q^4+4q^3+3q^2+q
        83: 2q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: 2q^3+2q^2+q
        86: 2q^3+3q^2+q
        87: q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^4+4q^3+3q^2+q
        95: q^4+4q^3+3q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2
       106: q^4+3q^3+2q^2+q
       107: q^2
       108: q^3+2q^2+q
       109: q^2
       110: 2q^3+2q^2+q
       111: q^3+3q^2+q
       113: 2q^3+3q^2+q
       115: q^3+2q^2+q
       118: q^3+q^2+q
       120: q^3+q^2+q
       121: 2q^3+2q^2+q
       123: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 3q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: q^3+3q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+3q^2+q
       143: 2q^3+2q^2+q
       144: q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^3+2q^2+q
       147: q^3+3q^2+q
       148: q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       151: 2q^3+3q^2+q
       153: 2q^3+3q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^3+2q^2+q
       161: q^3+2q^2+q
       162: q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       169: q^2
       172: q^3+2q^2+q
       176: q^3+q^2+q
       177: q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: q^3+3q^2+q
       184: q^2+q
       186: q^2+q
       187: 2q^2+q
       189: q^3+2q^2+q
       192: q^3+q^2+q
       193: q^2
       194: q^3+2q^2+q
       195: q^2
       196: 2q^3+2q^2+q
       197: q^3+3q^2+q
       200: q^3+q^2+q
       201: q^2
       202: q^3+2q^2+q
       204: q^2+q
       205: q^2+q
       207: 2q^3+2q^2+q
       209: 2q^3+3q^2+q
       211: q^3+2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^3+2q^2+q
       227: q^2+q
       228: q^3+2q^2+q
       229: 2q^2+q
       230: 2q^2+q
       231: q^3+2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^3+2q^2+q
       237: 2q^3+3q^2+q
       239: 2q^3+3q^2+q
       241: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^3+3q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2
       262: q^3+2q^2+q
       266: q^2+q
       267: q^2
       269: q^3+2q^2+q
       273: q^2+q
       278: q^3+q^2+q
       279: q
       281: q^2+q
       284: q^2+q
       286: q^2+q
       287: q^3+2q^2+q
       289: q^2+q
       291: 2q^2+q
       294: q^2+q
       296: q^2+q
       297: 2q^2+q
       300: q^2+q
       301: q^3+3q^2+q
       304: q^2+q
       305: 2q^2+q
       308: q
       310: q
       311: q^2+q
       313: q
       315: q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: q^2
       320: q^3+2q^2+q
       322: q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: 2q^2+q
       349: 2q^2+q
       350: 2q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       380: q^2+q
       384: q
       388: q^2+q
       389: q^2
       391: q^3+2q^2+q
       396: q^2+q
       399: q^2+q
       404: q
       406: q^2+q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       430: q^2+q
       432: q^2+q
       433: 2q^2+q
       435: q^2+q
       438: q^2+q
       440: q^2+q
       441: 2q^2+q
       443: q^2
       444: q^2+q
       445: 2q^2+q
       448: q
       450: q
       451: q
       454: q
       455: q
       458: q
       459: q
       462: q^2+q
       463: q^2+q
       465: q
       467: q^2+q
       469: q^3+2q^2+q
       472: q
       474: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       497: q
       498: q^2+q
       499: q
       500: q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q
       514: q
       524: q
       528: q
       532: q^2+q
       536: q^2+q
       539: q
       543: q^2+q
       545: q^2
       547: q^2+q
       552: q
       555: q
       559: q
       563: q^2+q
       568: q
       570: q^2+q
       575: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q^2+q
       590: q
       592: q
       594: q
       596: q
       599: q^2+q
       604: q^2+q
       605: q^2+q
       608: q^2+q
       609: 2q^2+q
       611: q^2+q
       613: q^2+q
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       635: q
       637: q^2+q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: q
       653: q
       675: q
       676: q
       677: q^2+q
       681: q
       683: q
       686: q
       687: q^2+q
       688: q
       689: q
       697: q^2+q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q^2+q
       731: q
       739: q
       743: q
       747: q
       756: q
       758: q
       762: q
       777: q
       797: q
       799: q^2+q
       802: q
       804: q
       806: q
       808: q
       811: q^2+q
       823: q
       826: q
       828: q
       835: q
       841: q
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       877: q
       879: q
       899: q
       914: q
       922: q
       927: q
       930: q
       938: q
       950: q
       961: q
       975: q
       979: q
      1010: 1
      1018: q
      1050: q
      1053: q
      1055: q
      1062: q
      1127: 1
      1140: 1
      1150: q
      1185: q
      1204: q
      1222: 1
      1278: 1
      1299: 1
      1323: 1
      1336: 1
      1361: 1
      1432: 1
      1480: 1
      1498: 1
      1510: 1
      1572: 1
      1633: 1
      1696: 1

1697:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+6q^3+3q^2+q
        23: 2q^4+6q^3+3q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: q^4+3q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: 2q^4+6q^3+3q^2+q
        32: 3q^3+2q^2+q
        33: 2q^4+6q^3+3q^2+q
        34: q^4+4q^3+3q^2+q
        35: 2q^3+2q^2+q
        36: q^4+4q^3+3q^2+q
        38: q^4+4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+3q^2+q
        56: 2q^3+3q^2+q
        57: 2q^3+2q^2+q
        58: q^4+4q^3+2q^2+q
        59: q^4+2q^3+q^2
        60: q^3+q^2
        61: q^4+3q^3+2q^2+q
        63: q^4+4q^3+3q^2+q
        65: 2q^3+2q^2+q
        67: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: q^3+3q^2+q
        73: 2q^3+3q^2+q
        75: 2q^3+3q^2+q
        77: 2q^3+3q^2+q
        79: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 3q^3+2q^2+q
        82: q^4+4q^3+3q^2+q
        83: 2q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: 2q^3+2q^2+q
        86: 2q^3+3q^2+q
        87: q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^4+4q^3+3q^2+q
        95: q^4+4q^3+3q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2
       105: q^4+3q^3+2q^2+q
       107: q^2
       108: q^3+2q^2+q
       109: 2q^3+2q^2+q
       110: q^2
       112: q^3+3q^2+q
       114: 2q^3+3q^2+q
       116: q^3+2q^2+q
       117: q^3+q^2+q
       120: q^3+q^2+q
       122: 2q^3+2q^2+q
       124: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 3q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: q^3+3q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+3q^2+q
       143: 2q^3+2q^2+q
       144: q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^3+2q^2+q
       147: q^3+3q^2+q
       148: q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       152: 2q^3+3q^2+q
       154: 2q^3+3q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^3+2q^2+q
       161: q^3+2q^2+q
       162: q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       170: q^2
       171: q^3+2q^2+q
       175: q^3+q^2+q
       178: q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: q^3+3q^2+q
       184: q^2+q
       185: q^2+q
       188: 2q^2+q
       190: q^3+2q^2+q
       191: q^3+q^2+q
       193: q^2
       194: q^3+2q^2+q
       195: 2q^3+2q^2+q
       196: q^2
       198: q^3+3q^2+q
       200: q^3+q^2+q
       201: q^2
       202: q^3+2q^2+q
       203: q^2+q
       206: q^2+q
       208: 2q^3+2q^2+q
       210: 2q^3+3q^2+q
       212: q^3+2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^3+2q^2+q
       227: q^2+q
       228: q^3+2q^2+q
       229: 2q^2+q
       230: 2q^2+q
       231: q^3+2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^3+2q^2+q
       238: 2q^3+3q^2+q
       240: 2q^3+3q^2+q
       242: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^3+3q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2
       261: q^3+2q^2+q
       265: q^2+q
       268: q^2
       270: q^3+2q^2+q
       272: q^2+q
       277: q^3+q^2+q
       280: q
       282: q^2+q
       284: q^2+q
       285: q^2+q
       288: q^3+2q^2+q
       290: q^2+q
       292: 2q^2+q
       294: q^2+q
       295: q^2+q
       298: 2q^2+q
       300: q^2+q
       302: q^3+3q^2+q
       303: q^2+q
       306: 2q^2+q
       308: q
       309: q
       312: q^2+q
       314: q
       316: q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: q^2
       320: q^3+2q^2+q
       321: q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: 2q^2+q
       349: 2q^2+q
       350: 2q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       379: q^2+q
       383: q
       387: q^2+q
       390: q^2
       392: q^3+2q^2+q
       395: q^2+q
       398: q^2+q
       402: q
       408: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       430: q^2+q
       431: q^2+q
       434: 2q^2+q
       436: q^2+q
       438: q^2+q
       439: q^2+q
       442: 2q^2+q
       443: q^2
       444: q^2+q
       446: 2q^2+q
       448: q
       449: q
       452: q
       454: q
       456: q
       457: q
       460: q
       461: q^2+q
       464: q^2+q
       466: q
       468: q^2+q
       470: q^3+2q^2+q
       472: q
       473: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       497: q
       498: q^2+q
       499: q
       500: q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q
       514: q
       523: q
       527: q
       531: q^2+q
       535: q^2+q
       540: q
       544: q^2+q
       546: q^2
       548: q^2+q
       550: q
       554: q
       558: q
       562: q^2+q
       567: q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       590: q
       591: q
       594: q
       595: q
       600: q^2+q
       604: q^2+q
       606: q^2+q
       607: q^2+q
       610: 2q^2+q
       612: q^2+q
       614: q^2+q
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       636: q
       638: q^2+q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       675: q
       676: q
       677: q^2+q
       681: q
       683: q
       686: q
       687: q^2+q
       688: q
       689: q
       700: q^2+q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q^2+q
       732: q
       738: q
       742: q
       746: q
       755: q
       760: q
       764: q
       778: q
       798: q
       800: q^2+q
       802: q
       803: q
       806: q
       807: q
       812: q^2+q
       824: q
       826: q
       827: q
       836: q
       842: q
       846: q
       847: q
       850: q
       852: q
       854: q
       856: q
       877: q
       879: q
       898: q
       915: q
       923: q
       925: q
       931: q
       937: q
       949: q
       963: q
       977: q
       981: q
      1011: 1
      1019: q
      1051: q
      1053: q
      1054: q
      1063: q
      1129: 1
      1143: 1
      1151: q
      1187: q
      1203: q
      1223: 1
      1279: 1
      1301: 1
      1325: 1
      1339: 1
      1362: 1
      1435: 1
      1481: 1
      1500: 1
      1511: 1
      1573: 1
      1636: 1
      1697: 1

1698:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+6q^3+3q^2+q
        23: 2q^4+6q^3+3q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+4q^3+3q^2+q
        26: q^4+4q^3+3q^2+q
        27: q^4+3q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: 2q^4+6q^3+3q^2+q
        32: 3q^3+2q^2+q
        33: 2q^4+6q^3+3q^2+q
        34: q^4+4q^3+3q^2+q
        35: 2q^3+2q^2+q
        36: q^4+4q^3+3q^2+q
        38: q^4+4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+4q^3+3q^2+q
        53: q^4+4q^3+3q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+3q^2+q
        56: 2q^3+3q^2+q
        57: 2q^3+2q^2+q
        58: q^4+2q^3+q^2
        59: q^4+4q^3+2q^2+q
        60: q^4+3q^3+2q^2+q
        61: q^3+q^2
        63: q^4+4q^3+3q^2+q
        65: 2q^3+2q^2+q
        67: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: q^3+3q^2+q
        73: 2q^3+3q^2+q
        75: 2q^3+3q^2+q
        77: 2q^3+3q^2+q
        79: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 3q^3+2q^2+q
        82: q^4+4q^3+3q^2+q
        83: 2q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: 2q^3+2q^2+q
        86: 2q^3+3q^2+q
        87: q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: q^4+4q^3+3q^2+q
        95: q^4+4q^3+3q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+3q^2+q
        98: 2q^3+3q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       104: q^4+3q^3+2q^2+q
       105: q^3+q^2
       107: q^3+2q^2+q
       108: q^2
       109: q^2
       110: 2q^3+2q^2+q
       112: q^3+3q^2+q
       114: 2q^3+3q^2+q
       116: q^3+2q^2+q
       118: q^3+q^2+q
       119: q^3+q^2+q
       122: 2q^3+2q^2+q
       124: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 3q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: q^3+3q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+3q^2+q
       143: 2q^3+2q^2+q
       144: q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^3+2q^2+q
       147: q^3+3q^2+q
       148: q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       152: 2q^3+3q^2+q
       154: 2q^3+3q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^3+2q^2+q
       161: q^3+2q^2+q
       162: q^3+2q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       170: q^3+2q^2+q
       171: q^2
       174: q^3+q^2+q
       178: q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: q^3+3q^2+q
       183: q^2+q
       186: q^2+q
       188: 2q^2+q
       190: q^3+2q^2+q
       192: q^3+q^2+q
       193: q^3+2q^2+q
       194: q^2
       195: q^2
       196: 2q^3+2q^2+q
       198: q^3+3q^2+q
       199: q^3+q^2+q
       201: q^3+2q^2+q
       202: q^2
       204: q^2+q
       206: q^2+q
       208: 2q^3+2q^2+q
       210: 2q^3+3q^2+q
       212: q^3+2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: 2q^3+2q^2+q
       227: q^2+q
       228: q^3+2q^2+q
       229: 2q^2+q
       230: 2q^2+q
       231: q^3+2q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q
       236: q^3+2q^2+q
       238: 2q^3+3q^2+q
       240: 2q^3+3q^2+q
       242: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^3+3q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: q^2+q
       268: q^3+2q^2+q
       270: q^2
       274: q^2+q
       276: q^3+q^2+q
       280: q
       282: q^2+q
       283: q^2+q
       286: q^2+q
       288: q^3+2q^2+q
       290: q^2+q
       292: 2q^2+q
       293: q^2+q
       296: q^2+q
       298: 2q^2+q
       299: q^2+q
       302: q^3+3q^2+q
       304: q^2+q
       306: 2q^2+q
       307: q
       310: q
       312: q^2+q
       314: q
       316: q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: q^3+2q^2+q
       320: q^2
       322: q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: 2q^2+q
       349: 2q^2+q
       350: 2q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q
       358: q
       359: q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2+q
       382: q
       386: q^2+q
       390: q^3+2q^2+q
       392: q^2
       394: q^2+q
       400: q^2+q
       403: q
       407: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2+q
       432: q^2+q
       434: 2q^2+q
       436: q^2+q
       437: q^2+q
       440: q^2+q
       442: 2q^2+q
       443: q^2+q
       444: q^2
       446: 2q^2+q
       447: q
       450: q
       452: q
       453: q
       456: q
       458: q
       460: q
       462: q^2+q
       464: q^2+q
       466: q
       468: q^2+q
       470: q^3+2q^2+q
       471: q
       474: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       497: q
       498: q^2+q
       499: q
       500: q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q
       514: q
       522: q
       526: q
       530: q^2+q
       534: q^2+q
       538: q
       542: q^2+q
       546: q^2+q
       548: q^2
       551: q
       556: q
       560: q
       564: q^2+q
       566: q
       571: q^2+q
       574: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q
       592: q
       593: q
       596: q
       600: q^2+q
       603: q^2+q
       606: q^2+q
       608: q^2+q
       610: 2q^2+q
       612: q^2+q
       614: q^2+q
       619: q
       622: q
       624: q
       626: q
       628: q
       630: q
       636: q
       638: q^2+q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: q
       654: q
       675: q
       676: q
       677: q^2+q
       681: q
       683: q
       686: q
       687: q^2+q
       688: q
       689: q
       699: q^2+q
       706: q
       710: q
       715: q
       718: q
       722: q
       726: q^2+q
       730: q
       740: q
       744: q
       748: q
       754: q
       759: q
       763: q
       778: q
       798: q
       800: q^2+q
       801: q
       804: q
       805: q
       808: q
       812: q^2+q
       824: q
       825: q
       828: q
       836: q
       842: q
       845: q
       848: q
       850: q
       852: q
       854: q
       856: q
       877: q
       879: q
       897: q
       913: q
       921: q
       926: q
       929: q
       939: q
       951: q
       962: q
       976: q
       980: q
      1011: 1
      1019: q
      1051: q
      1052: q
      1055: q
      1063: q
      1128: 1
      1143: 1
      1149: q
      1186: q
      1205: q
      1223: 1
      1279: 1
      1300: 1
      1324: 1
      1339: 1
      1363: 1
      1435: 1
      1481: 1
      1499: 1
      1512: 1
      1574: 1
      1636: 1
      1698: 1

1699:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 2q^2+3q+1
        35: q^2+2q+1
        36: 2q^2+3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+2q^2+2q+1
        58: 2q+1
        59: q
        60: q^2+2q+1
        61: q^2+q
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       103: 2q+1
       106: q
       107: q^2+2q+1
       108: q^2+q
       109: 2q+1
       110: q
       111: 3q+1
       113: 3q+1
       115: 2q+1
       117: q+1
       119: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 3q+1
       149: 3q+1
       150: 2q+1
       151: 3q+1
       153: 3q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: 2q+1
       172: q
       173: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q+1
       185: q+1
       187: 2q+1
       189: 2q+1
       191: q+1
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: q+1
       201: q^2+2q+1
       202: q^2+q
       203: 2q+1
       204: q
       205: 3q+1
       207: 2q+1
       209: 3q+1
       211: 2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       262: q
       263: q+1
       267: q+1
       271: 2q+1
       273: q
       275: q+1
       279: 1
       281: q+1
       283: q+1
       285: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       293: q+1
       295: q+1
       297: 2q+1
       299: 1
       301: q+1
       303: 1
       305: 1
       307: q+1
       309: q+1
       311: 3q+1
       313: 2q+1
       315: 2q+1
       317: 3q+1
       319: q+1
       321: 2q+1
       322: q
       323: q+1
       325: 2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: 1
       397: 2q+1
       399: q
       401: q+1
       405: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: q+1
       447: q+1
       449: q+1
       451: 2q+1
       453: q+1
       455: q+1
       457: q+1
       459: 2q+1
       461: 2q+1
       462: q
       463: 3q+1
       465: 1
       467: q+1
       469: 2q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: 1
       537: 1
       541: 1
       545: q+1
       549: q+1
       553: 1
       557: q+1
       561: 2q+1
       563: q
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       589: q+1
       591: q+1
       593: 1
       595: 1
       597: q+1
       599: 2q+1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q+1
       621: q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       631: 1
       633: q+1
       635: 1
       637: q+1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       705: 1
       709: 1
       713: q+1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: q+1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       799: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: q+1
       821: 1
       823: q+1
       825: q+1
       827: q+1
       829: 1
       831: 1
       833: q+1
       835: 2q+1
       837: q+1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       928: 1
       932: 1
       936: 1
       940: 1
       944: 1
       948: q+1
       952: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1020: 1
      1024: 1
      1030: q+1
      1032: 1
      1034: 1
      1036: q+1
      1038: 1
      1040: 1
      1042: q+1
      1044: 1
      1046: 1
      1050: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1164: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1194: 1
      1206: 1
      1214: 1
      1216: 1
      1218: 1
      1222: 1
      1224: 1
      1236: 1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 1
      1258: 1
      1260: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1334: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1430: 1
      1456: 1
      1460: 1
      1462: 1
      1472: 1
      1480: 1
      1482: 1
      1489: 1
      1513: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1631: 1
      1699: 1

1700:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: 2q^3+10q^2+3q
        23: 2q^3+10q^2+3q
        24: 4q^3+7q^2+3q
        25: q^4+9q^3+11q^2+3q
        26: q^4+9q^3+11q^2+3q
        27: 3q^4+8q^3+8q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: 2q^3+10q^2+3q
        32: q^3+7q^2+3q
        33: 9q^2+3q
        34: q^4+9q^3+11q^2+3q
        35: 5q^3+8q^2+3q
        36: 5q^3+10q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: 2q^3+10q^2+3q
        53: 2q^3+10q^2+3q
        54: 4q^3+7q^2+3q
        55: q^4+9q^3+11q^2+3q
        56: q^4+9q^3+11q^2+3q
        57: 3q^4+8q^3+8q^2+3q
        58: 5q^2+2q
        59: 4q^2+q
        60: 3q^3+6q^2+2q
        61: 2q^3+4q^2+q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 5q^3+10q^2+3q
        73: 9q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: q^3+7q^2+3q
        81: 6q^2+3q
        82: 2q^3+10q^2+3q
        83: q^3+7q^2+3q
        84: 5q^3+8q^2+3q
        85: 2q^3+7q^2+3q
        86: q^4+9q^3+11q^2+3q
        87: 5q^3+8q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 7q^2+3q
        95: 7q^2+3q
        96: 2q^3+4q^2+2q
        97: 5q^3+10q^2+3q
        98: 5q^3+10q^2+3q
        99: 2q^4+5q^3+5q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 2q^2+q
       104: 3q^2+q
       105: 3q^2+q
       106: q^2
       107: 3q^3+6q^2+2q
       108: 2q^3+4q^2+q
       109: 5q^2+2q
       110: 4q^2+q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: 2q^2+2q
       118: q^2+q
       119: 3q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 2q^3+7q^2+3q
       136: 6q^2+3q
       137: 6q^2+3q
       138: 3q^2+2q
       139: 7q^2+3q
       140: 2q^2+2q
       141: q^3+7q^2+3q
       142: 7q^2+3q
       143: 2q^3+7q^2+3q
       144: q^3+4q^2+2q
       145: 5q^3+10q^2+3q
       146: 5q^3+8q^2+3q
       147: 5q^3+10q^2+3q
       148: 9q^2+3q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 3q^2+q
       152: 2q^3+7q^2+2q
       153: 3q^2+q
       154: 2q^3+7q^2+2q
       155: q^3+2q^2+q
       156: 3q^3+5q^2+2q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+7q^2+3q
       164: 2q^3+7q^2+3q
       165: 3q^3+5q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 2q^2+q
       170: 3q^2+q
       171: 3q^2+q
       172: q^2
       173: q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: 3q^2+2q
       184: q^2+q
       185: 2q^2+2q
       186: q^2+q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: 2q^2+2q
       192: q^2+q
       193: 2q^2+2q
       195: 4q^2+2q
       196: 3q^2+q
       197: q^2+q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: 3q^3+6q^2+2q
       202: 2q^3+4q^2+q
       203: 5q^2+2q
       204: 4q^2+q
       205: 3q^2+q
       206: 6q^2+2q
       207: 2q^2+q
       208: 4q^2+2q
       209: 3q^2+q
       210: 2q^3+7q^2+2q
       211: 2q^2+q
       212: q^3+5q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 2q^3+7q^2+3q
       223: q^3+4q^2+2q
       224: 6q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^3+4q^2+2q
       232: 4q^2+3q
       233: q^3+4q^2+2q
       234: 2q^3+7q^2+3q
       235: 6q^2+3q
       236: 3q^2+2q
       238: 4q^2+2q
       240: 4q^2+2q
       242: q^3+2q^2+q
       243: 7q^2+3q
       244: 2q^2+2q
       245: 7q^2+3q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^3+7q^2+3q
       254: 2q^3+7q^2+3q
       255: 3q^3+5q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: 2q^2+q
       261: 2q^2+q
       263: q^2+q
       264: q^2+q
       265: q^2+q
       267: q^2+q
       268: q^2+q
       271: 2q^2+q
       272: 3q^2+q
       273: q^2
       274: 3q^2+q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       280: 2q
       282: q
       283: q^2+q
       285: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: 3q^2+2q
       294: q^2+q
       295: 2q^2+2q
       296: q^2+q
       297: 2q^2+q
       298: 4q^2+2q
       299: 2q
       302: q^2+q
       303: 2q
       304: q
       305: q
       306: q
       307: 3q^2+2q
       308: q^2+q
       309: 2q^2+2q
       310: q^2+q
       312: 4q^2+2q
       313: 2q^2+q
       314: 4q^2+2q
       316: q^2+q
       318: 4q^2+2q
       319: 2q^2+2q
       321: 4q^2+2q
       322: 3q^2+q
       323: q^2+q
       324: q^2+q
       325: 2q^2+q
       326: q^3+5q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: q^3+4q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       339: 4q^2+2q
       341: 4q^2+2q
       343: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q^2+2q
       353: 4q^2+3q
       354: q^3+4q^2+2q
       355: 2q^3+7q^2+3q
       356: q^3+4q^2+2q
       357: 6q^2+3q
       358: 3q^2+2q
       359: 7q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       385: q^2+q
       386: q^2+q
       387: q^2+q
       390: q^2+q
       393: q
       394: q
       398: 2q^2+q
       400: 2q^2+q
       401: q^2+q
       402: q^2+q
       403: q^2+q
       405: q^2+q
       407: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       419: q^2+q
       421: q^2+q
       424: q^2+q
       426: q^2+q
       428: 4q^2+2q
       429: q
       431: q
       436: q
       437: 2q
       439: 2q
       440: q
       441: q
       442: q
       443: 2q^2+2q
       446: q^2+q
       447: q^2+q
       449: q^2+q
       452: q^2+q
       453: 3q^2+2q
       454: q^2+q
       456: q^2+2q
       457: 2q^2+2q
       458: q^2+q
       459: 2q^2+q
       460: 4q^2+2q
       461: 4q^2+2q
       462: 3q^2+q
       464: 4q^2+2q
       466: 2q
       468: q
       470: q^2+q
       471: 2q
       473: 2q
       474: q
       475: q
       476: q
       478: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q^2+2q
       482: 2q
       483: 3q^2+2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: q^3+4q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       538: q
       541: q
       542: q
       546: q^2+q
       554: q
       556: q
       557: q^2+q
       558: q^2+q
       560: q^2+q
       562: 2q^2+q
       564: 2q^2+q
       565: q
       566: q
       571: q^2+q
       573: q^2+q
       574: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q
       589: q^2+q
       591: q^2+q
       593: q
       595: q
       598: q
       600: q^2+q
       602: 2q
       603: q
       607: q
       612: q
       615: 2q
       618: q
       619: q^2+q
       621: q^2+q
       624: q
       626: q^2+q
       628: q^2+2q
       630: q^2+q
       631: 2q
       632: q
       634: q^2+2q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       647: 2q
       649: 2q
       650: q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: q+1
       681: 2q^2+2q
       682: 2q
       683: 3q^2+2q
       684: 2q^2+3q
       685: q^2+2q
       686: 2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       699: q^2+q
       730: q
       734: q
       746: q
       748: q
       750: q
       752: q
       759: q
       761: q
       763: q
       765: q
       766: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       793: 1
       796: 1
       805: q
       807: q
       814: q
       815: 2q
       817: 1
       820: q+1
       822: q
       824: q
       825: q^2+q
       827: q^2+q
       829: q
       831: q
       834: q
       836: q^2+q
       838: q^2+2q
       839: 2q
       840: q
       842: q
       843: 1
       845: q
       847: q
       854: q
       857: q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: 1
       870: 1
       872: q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       878: 2q
       879: q
       880: q
       890: q
       917: 1
       933: q
       941: 1
       957: q
       959: q
       964: 1
       969: 1
       980: q
       986: q
       988: q
       989: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 1
      1016: 1
      1021: 1
      1031: q+1
      1032: 1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: 1
      1056: q
      1058: q
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 2q
      1084: 1
      1085: q
      1087: 1
      1104: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1237: 1
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1275: 1
      1280: 1
      1285: 1
      1288: 1
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1457: 1
      1460: 1
      1462: 1
      1473: 1
      1482: 1
      1490: 1
      1514: 1
      1584: 1
      1588: 1
      1595: 1
      1632: 1
      1700: 1

1701:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+6q^3+3q^2+q
        26: 2q^4+6q^3+3q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: q^4+4q^3+3q^2+q
        32: 2q^3+2q^2+q
        33: q^4+4q^3+3q^2+q
        34: 2q^4+6q^3+3q^2+q
        35: 3q^3+2q^2+q
        36: 2q^4+6q^3+3q^2+q
        37: q^4+4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+3q^2+q
        53: 2q^3+3q^2+q
        54: 2q^3+2q^2+q
        55: q^4+4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^4+3q^3+2q^2+q
        59: q^3+q^2
        60: q^4+4q^3+2q^2+q
        61: q^4+2q^3+q^2
        62: q^4+4q^3+3q^2+q
        64: 2q^3+2q^2+q
        66: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: 2q^3+3q^2+q
        73: q^3+3q^2+q
        74: 2q^3+3q^2+q
        76: 2q^3+3q^2+q
        78: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: 2q^3+2q^2+q
        82: 2q^3+3q^2+q
        83: q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 3q^3+2q^2+q
        86: q^4+4q^3+3q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: q^4+4q^3+3q^2+q
        98: q^4+4q^3+3q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       103: q^4+3q^3+2q^2+q
       106: q^3+q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: q^3+2q^2+q
       110: q^2
       111: q^3+3q^2+q
       113: 2q^3+3q^2+q
       115: q^3+2q^2+q
       117: q^3+q^2+q
       119: q^3+q^2+q
       121: 2q^3+2q^2+q
       123: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^3+2q^2+q
       138: q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+3q^2+q
       143: 3q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+3q^2+q
       148: q^3+3q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       151: 2q^3+3q^2+q
       153: 2q^3+3q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^3+2q^2+q
       164: q^3+2q^2+q
       165: q^3+2q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       169: q^3+2q^2+q
       172: q^2
       173: q^3+q^2+q
       177: q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: q^3+3q^2+q
       183: q^2+q
       185: q^2+q
       187: 2q^2+q
       189: q^3+2q^2+q
       191: q^3+q^2+q
       193: q^2+q
       195: q^3+2q^2+q
       196: q^2
       197: q^2+q
       199: q^3+q^2+q
       201: 2q^3+2q^2+q
       202: q^2
       203: q^3+2q^2+q
       204: q^2
       205: q^3+3q^2+q
       207: 2q^3+2q^2+q
       209: 2q^3+3q^2+q
       211: q^3+2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: q^3+2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^3+2q^2+q
       232: q^2+q
       233: q^3+2q^2+q
       234: 2q^2+q
       235: 2q^2+q
       236: q^3+2q^2+q
       237: 2q^3+3q^2+q
       239: 2q^3+3q^2+q
       241: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^2+q
       245: q^3+3q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: q^2+q
       267: q^2+q
       271: q^3+2q^2+q
       273: q^2
       275: q^3+q^2+q
       279: q
       281: q^2+q
       283: q^2+q
       285: q^2+q
       287: q^3+2q^2+q
       289: q^2+q
       291: 2q^2+q
       293: q^2+q
       295: q^2+q
       297: 2q^2+q
       299: q
       301: q^2+q
       303: q
       305: q
       307: q^2+q
       309: q^2+q
       311: q^3+3q^2+q
       313: 2q^2+q
       315: q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: q^2+q
       321: q^3+2q^2+q
       322: q^2
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^2+q
       357: 2q^2+q
       358: 2q^2+q
       359: 2q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2+q
       381: q
       385: q^2+q
       389: q^2+q
       393: q
       397: q^3+2q^2+q
       399: q^2
       401: q^2+q
       405: q^2+q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q
       431: q
       433: q
       435: q
       437: q
       439: q
       441: q
       443: q^2+q
       445: q^2+q
       447: q^2+q
       449: q^2+q
       451: 2q^2+q
       453: q^2+q
       455: q^2+q
       457: q^2+q
       459: 2q^2+q
       461: q^2+q
       462: q^2
       463: 2q^2+q
       465: q
       467: q^2+q
       469: q^3+2q^2+q
       471: q
       473: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^2+q
       521: q
       525: q
       529: q^2+q
       533: q
       537: q
       541: q
       545: q^2+q
       549: q^2+q
       553: q
       557: q^2+q
       561: q^2+q
       563: q^2
       565: q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q^2+q
       589: q
       591: q
       593: q
       595: q
       599: q^2+q
       603: q
       605: q
       607: q
       609: q
       611: q
       613: q
       619: q^2+q
       621: q^2+q
       623: q^2+q
       625: 2q^2+q
       627: q^2+q
       629: q^2+q
       635: q
       637: q^2+q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       676: q
       677: q
       681: q
       682: q
       683: q^2+q
       686: q
       687: q
       688: q^2+q
       689: q
       693: q^2+q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q
       729: q
       737: q
       741: q^2+q
       745: q
       753: q
       757: q
       761: q
       777: q
       799: q
       805: q
       807: q
       811: q
       821: q
       823: q^2+q
       825: q
       827: q
       829: q
       831: q
       835: q^2+q
       841: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       878: q
       879: q
       896: q
       912: q
       928: q
       936: q
       944: q
       948: q
       952: q
       960: q
       974: q
       978: q
      1010: 1
      1034: q
      1050: q
      1056: q
      1058: q
      1062: q
      1126: 1
      1140: 1
      1168: q
      1184: q
      1206: q
      1222: 1
      1278: 1
      1292: 1
      1322: 1
      1336: 1
      1392: 1
      1432: 1
      1480: 1
      1491: 1
      1515: 1
      1591: 1
      1633: 1
      1701: 1

1702:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: 2q^3+10q^2+3q
        23: 2q^3+10q^2+3q
        24: 4q^3+7q^2+3q
        25: q^4+9q^3+11q^2+3q
        26: q^4+9q^3+11q^2+3q
        27: 3q^4+8q^3+8q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: 2q^3+10q^2+3q
        32: q^3+7q^2+3q
        33: 9q^2+3q
        34: q^4+9q^3+11q^2+3q
        35: 5q^3+8q^2+3q
        36: 5q^3+10q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: 2q^3+10q^2+3q
        53: 2q^3+10q^2+3q
        54: 4q^3+7q^2+3q
        55: q^4+9q^3+11q^2+3q
        56: q^4+9q^3+11q^2+3q
        57: 3q^4+8q^3+8q^2+3q
        58: 4q^2+q
        59: 5q^2+2q
        60: 3q^3+6q^2+2q
        61: 2q^3+4q^2+q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 5q^3+10q^2+3q
        73: 9q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: q^3+7q^2+3q
        81: 6q^2+3q
        82: 2q^3+10q^2+3q
        83: q^3+7q^2+3q
        84: 5q^3+8q^2+3q
        85: 2q^3+7q^2+3q
        86: q^4+9q^3+11q^2+3q
        87: 5q^3+8q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 7q^2+3q
        95: 7q^2+3q
        96: 2q^3+4q^2+2q
        97: 5q^3+10q^2+3q
        98: 5q^3+10q^2+3q
        99: 2q^4+5q^3+5q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 3q^2+q
       104: 2q^2+q
       105: q^2
       106: 3q^2+q
       107: 3q^3+6q^2+2q
       108: 2q^3+4q^2+q
       109: 4q^2+q
       110: 5q^2+2q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: q^2+q
       118: 2q^2+2q
       119: 3q^2+2q
       120: q^2+q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 2q^3+7q^2+3q
       136: 6q^2+3q
       137: 6q^2+3q
       138: 3q^2+2q
       139: 7q^2+3q
       140: 2q^2+2q
       141: q^3+7q^2+3q
       142: 7q^2+3q
       143: 2q^3+7q^2+3q
       144: q^3+4q^2+2q
       145: 5q^3+10q^2+3q
       146: 5q^3+8q^2+3q
       147: 5q^3+10q^2+3q
       148: 9q^2+3q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 2q^3+7q^2+2q
       152: 3q^2+q
       153: 2q^3+7q^2+2q
       154: 3q^2+q
       155: 3q^3+5q^2+2q
       156: q^3+2q^2+q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+7q^2+3q
       164: 2q^3+7q^2+3q
       165: 3q^3+5q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 3q^2+q
       170: 2q^2+q
       171: q^2
       172: 3q^2+q
       173: q^2+q
       174: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: 3q^2+2q
       184: q^2+q
       185: q^2+q
       186: 2q^2+2q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: q^2+q
       192: 2q^2+2q
       193: 2q^2+2q
       195: 3q^2+q
       196: 4q^2+2q
       197: q^2+q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: 3q^3+6q^2+2q
       202: 2q^3+4q^2+q
       203: 4q^2+q
       204: 5q^2+2q
       205: 6q^2+2q
       206: 3q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+7q^2+2q
       210: 3q^2+q
       211: q^3+5q^2+2q
       212: 2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 2q^3+7q^2+3q
       223: q^3+4q^2+2q
       224: 6q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^3+4q^2+2q
       232: 4q^2+3q
       233: q^3+4q^2+2q
       234: 2q^3+7q^2+3q
       235: 6q^2+3q
       236: 3q^2+2q
       237: 4q^2+2q
       239: 4q^2+2q
       241: q^3+2q^2+q
       243: 7q^2+3q
       244: 2q^2+2q
       245: 7q^2+3q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^3+7q^2+3q
       254: 2q^3+7q^2+3q
       255: 3q^3+5q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       264: q^2+q
       266: q^2+q
       267: q^2+q
       268: q^2+q
       271: 3q^2+q
       272: q^2
       273: 3q^2+q
       274: 2q^2+q
       275: q^2+q
       276: q^2+q
       278: q^2+q
       279: 2q
       281: q
       283: q^2+q
       286: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: 3q^2+2q
       294: q^2+q
       295: q^2+q
       296: 2q^2+2q
       297: 4q^2+2q
       298: 2q^2+q
       299: 2q
       301: q^2+q
       303: q
       304: 2q
       305: q
       306: q
       307: 3q^2+2q
       308: q^2+q
       309: q^2+q
       310: 2q^2+2q
       311: 4q^2+2q
       313: 4q^2+2q
       314: 2q^2+q
       315: q^2+q
       317: 4q^2+2q
       319: 2q^2+2q
       321: 3q^2+q
       322: 4q^2+2q
       323: q^2+q
       324: q^2+q
       325: q^3+5q^2+2q
       326: 2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: q^3+4q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       338: 4q^2+2q
       340: 4q^2+2q
       342: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q^2+2q
       353: 4q^2+3q
       354: q^3+4q^2+2q
       355: 2q^3+7q^2+3q
       356: q^3+4q^2+2q
       357: 6q^2+3q
       358: 3q^2+2q
       359: 7q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q^2+q
       386: q^2+q
       388: q^2+q
       389: q^2+q
       393: q
       394: q
       397: 2q^2+q
       399: 2q^2+q
       401: q^2+q
       403: q^2+q
       404: q^2+q
       405: q^2+q
       407: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       419: q^2+q
       422: q^2+q
       423: q^2+q
       425: q^2+q
       427: 4q^2+2q
       429: q
       432: q
       435: q
       437: 2q
       439: q
       440: 2q
       441: q
       442: q
       443: 2q^2+2q
       445: q^2+q
       447: q^2+q
       450: q^2+q
       451: q^2+q
       453: 3q^2+2q
       454: q^2+q
       455: q^2+2q
       457: q^2+q
       458: 2q^2+2q
       459: 4q^2+2q
       460: 2q^2+q
       461: 3q^2+q
       462: 4q^2+2q
       463: 4q^2+2q
       465: 2q
       467: q
       469: q^2+q
       471: 2q
       473: q
       474: 2q
       475: q
       476: q
       477: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q^2+2q
       482: 2q
       483: 3q^2+2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: q^3+4q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       537: q
       541: q
       542: q
       545: q^2+q
       553: q
       555: q
       557: q^2+q
       559: q^2+q
       560: q^2+q
       561: 2q^2+q
       563: 2q^2+q
       565: q
       566: q
       569: q^2+q
       573: q^2+q
       574: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q
       589: q^2+q
       592: q^2+q
       593: q
       596: q
       597: q
       599: q^2+q
       601: 2q
       603: q
       608: q
       611: q
       615: 2q
       617: q
       619: q^2+q
       622: q^2+q
       623: q
       625: q^2+q
       627: q^2+2q
       629: q^2+q
       631: q
       632: 2q
       633: q^2+2q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       647: 2q
       649: q
       650: 2q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: q+1
       681: 2q^2+2q
       682: 2q
       683: 3q^2+2q
       684: 2q^2+3q
       685: q^2+2q
       686: 2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q
       729: q
       733: q
       745: q
       747: q
       749: q
       751: q
       757: q
       761: q
       763: q
       765: q
       766: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       793: 1
       795: 1
       805: q
       808: q
       813: q
       815: 2q
       818: 1
       819: q+1
       821: q
       823: q
       825: q^2+q
       828: q^2+q
       829: q
       832: q
       833: q
       835: q^2+q
       837: q^2+2q
       839: q
       840: 2q
       841: q
       844: 1
       845: q
       848: q
       853: q
       857: q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: 1
       870: 1
       872: q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       878: 2q
       879: q
       880: q
       884: q
       916: 1
       932: q
       942: 1
       956: q
       958: q
       965: 1
       971: 1
       978: q
       982: q
       988: q
       989: q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 1
      1016: 1
      1020: 1
      1030: q+1
      1033: 1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1047: 1
      1056: q
      1059: q
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 2q
      1084: 1
      1085: q
      1089: 1
      1098: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1236: 1
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1274: 1
      1281: 1
      1285: 1
      1288: 1
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1382: 1
      1388: 1
      1397: 1
      1433: 1
      1456: 1
      1461: 1
      1462: 1
      1472: 1
      1483: 1
      1492: 1
      1516: 1
      1585: 1
      1587: 1
      1596: 1
      1634: 1
      1702: 1

1703:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: 2q^3+10q^2+3q
        23: 2q^3+10q^2+3q
        24: 4q^3+7q^2+3q
        25: q^4+9q^3+11q^2+3q
        26: q^4+9q^3+11q^2+3q
        27: 3q^4+8q^3+8q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: 2q^3+10q^2+3q
        32: q^3+7q^2+3q
        33: 9q^2+3q
        34: q^4+9q^3+11q^2+3q
        35: 5q^3+8q^2+3q
        36: 5q^3+10q^2+3q
        37: 2q^3+7q^2+2q
        38: 3q^2+q
        39: 2q^3+7q^2+2q
        40: 3q^2+q
        41: 3q^3+5q^2+2q
        42: q^3+2q^2+q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: 2q^3+10q^2+3q
        53: 2q^3+10q^2+3q
        54: 4q^3+7q^2+3q
        55: q^4+9q^3+11q^2+3q
        56: q^4+9q^3+11q^2+3q
        57: 3q^4+8q^3+8q^2+3q
        58: 5q^2+2q
        59: 4q^2+q
        60: 2q^3+4q^2+q
        61: 3q^3+6q^2+2q
        62: 2q^3+7q^2+2q
        63: 3q^2+q
        64: q^3+5q^2+2q
        65: 2q^2+q
        66: 6q^2+2q
        67: 3q^2+q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 5q^3+10q^2+3q
        73: 9q^2+3q
        74: 2q^3+7q^2+2q
        75: 3q^2+q
        76: 2q^3+7q^2+2q
        77: 3q^2+q
        78: 3q^3+5q^2+2q
        79: q^3+2q^2+q
        80: q^3+7q^2+3q
        81: 6q^2+3q
        82: 2q^3+10q^2+3q
        83: q^3+7q^2+3q
        84: 5q^3+8q^2+3q
        85: 2q^3+7q^2+3q
        86: q^4+9q^3+11q^2+3q
        87: 5q^3+8q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 7q^2+3q
        95: 7q^2+3q
        96: 2q^3+4q^2+2q
        97: 5q^3+10q^2+3q
        98: 5q^3+10q^2+3q
        99: 2q^4+5q^3+5q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: 3q^2+q
       104: q^2
       105: 2q^2+q
       106: 3q^2+q
       107: 2q^3+4q^2+q
       108: 3q^3+6q^2+2q
       109: 5q^2+2q
       110: 4q^2+q
       111: 6q^2+2q
       112: 3q^2+q
       113: 2q^3+7q^2+2q
       114: 3q^2+q
       115: q^3+5q^2+2q
       116: 2q^2+q
       117: 2q^2+2q
       118: q^2+q
       119: q^2+q
       120: 3q^2+2q
       121: q^3+5q^2+2q
       122: 2q^2+q
       123: 4q^2+2q
       124: 2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       127: 4q^2+2q
       129: 4q^2+2q
       131: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 2q^3+7q^2+3q
       136: 6q^2+3q
       137: 6q^2+3q
       138: 3q^2+2q
       139: 7q^2+3q
       140: 2q^2+2q
       141: q^3+7q^2+3q
       142: 7q^2+3q
       143: 2q^3+7q^2+3q
       144: q^3+4q^2+2q
       145: 5q^3+10q^2+3q
       146: 5q^3+8q^2+3q
       147: 5q^3+10q^2+3q
       148: 9q^2+3q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 2q^3+7q^2+2q
       152: 3q^2+q
       153: 2q^3+7q^2+2q
       154: 3q^2+q
       155: 3q^3+5q^2+2q
       156: q^3+2q^2+q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+7q^2+3q
       164: 2q^3+7q^2+3q
       165: 3q^3+5q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: 3q^2+q
       170: q^2
       171: 2q^2+q
       172: 3q^2+q
       173: q^2+q
       175: q^2+q
       176: q^2+q
       177: q^2+q
       179: 4q^2+2q
       181: 4q^2+2q
       183: q^2+q
       184: 3q^2+2q
       185: 2q^2+2q
       186: q^2+q
       187: 4q^2+2q
       188: 2q^2+q
       189: q^3+5q^2+2q
       190: 2q^2+q
       191: 2q^2+2q
       192: q^2+q
       194: 2q^2+2q
       195: 4q^2+2q
       196: 3q^2+q
       197: q^2+q
       198: q^2+q
       199: q^2+q
       200: 3q^2+2q
       201: 2q^3+4q^2+q
       202: 3q^3+6q^2+2q
       203: 5q^2+2q
       204: 4q^2+q
       205: 6q^2+2q
       206: 3q^2+q
       207: 4q^2+2q
       208: 2q^2+q
       209: 2q^3+7q^2+2q
       210: 3q^2+q
       211: q^3+5q^2+2q
       212: 2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 2q^3+7q^2+3q
       223: q^3+4q^2+2q
       224: 6q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^3+4q^2+2q
       232: 4q^2+3q
       233: q^3+4q^2+2q
       234: 2q^3+7q^2+3q
       235: 6q^2+3q
       236: 3q^2+2q
       237: 4q^2+2q
       239: 4q^2+2q
       241: q^3+2q^2+q
       243: 7q^2+3q
       244: 2q^2+2q
       245: 7q^2+3q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^3+7q^2+3q
       254: 2q^3+7q^2+3q
       255: 3q^3+5q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       259: 2q^2+q
       262: 2q^2+q
       263: q^2+q
       265: q^2+q
       266: q^2+q
       269: q^2+q
       270: q^2+q
       271: 3q^2+q
       272: 2q^2+q
       273: 3q^2+q
       274: q^2
       275: q^2+q
       277: q^2+q
       278: q^2+q
       279: 2q
       281: q
       284: q^2+q
       285: q^2+q
       287: q^2+q
       289: q^2+2q
       291: q^2+q
       293: q^2+q
       294: 3q^2+2q
       295: 2q^2+2q
       296: q^2+q
       297: 4q^2+2q
       298: 2q^2+q
       300: 2q
       301: q^2+q
       303: 2q
       304: q
       305: q
       306: q
       307: q^2+q
       308: 3q^2+2q
       309: 2q^2+2q
       310: q^2+q
       311: 4q^2+2q
       313: 4q^2+2q
       314: 2q^2+q
       315: q^2+q
       317: 4q^2+2q
       320: 2q^2+2q
       321: 4q^2+2q
       322: 3q^2+q
       323: q^2+q
       324: q^2+q
       325: q^3+5q^2+2q
       326: 2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: 2q^2+2q
       334: q^3+4q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       338: 4q^2+2q
       340: 4q^2+2q
       342: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q^2+2q
       353: 4q^2+3q
       354: q^3+4q^2+2q
       355: 2q^3+7q^2+3q
       356: q^3+4q^2+2q
       357: 6q^2+3q
       358: 3q^2+2q
       359: 7q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q^2+q
       387: q^2+q
       388: q^2+q
       391: q^2+q
       395: q
       396: q
       397: 2q^2+q
       399: 2q^2+q
       401: q^2+q
       402: q^2+q
       404: q^2+q
       406: q^2+q
       408: q^2+q
       409: 2q
       411: q
       413: q
       415: q^2+2q
       417: q
       420: q^2+q
       421: q^2+q
       423: q^2+q
       425: q^2+q
       427: 4q^2+2q
       430: q
       431: q
       435: q
       438: 2q
       439: 2q
       440: q
       441: q
       442: q
       444: 2q^2+2q
       445: q^2+q
       448: q^2+q
       449: q^2+q
       451: q^2+q
       453: q^2+q
       454: 3q^2+2q
       455: q^2+2q
       457: 2q^2+2q
       458: q^2+q
       459: 4q^2+2q
       460: 2q^2+q
       461: 4q^2+2q
       462: 3q^2+q
       463: 4q^2+2q
       465: 2q
       467: q
       469: q^2+q
       472: 2q
       473: 2q
       474: q
       475: q
       476: q
       477: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q^2+2q
       482: 2q
       483: 3q^2+2q
       484: 3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: q^3+4q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       539: q
       543: q
       544: q
       547: q^2+q
       553: q
       555: q
       557: q^2+q
       558: q^2+q
       559: q^2+q
       561: 2q^2+q
       563: 2q^2+q
       567: q
       568: q
       570: q^2+q
       575: q^2+q
       576: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q
       590: q^2+q
       591: q^2+q
       594: q
       595: q
       597: q
       599: q^2+q
       601: 2q
       604: q
       607: q
       611: q
       616: 2q
       617: q
       620: q^2+q
       621: q^2+q
       623: q
       625: q^2+q
       627: q^2+2q
       629: q^2+q
       631: 2q
       632: q
       633: q^2+2q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       648: 2q
       649: 2q
       650: q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: q+1
       681: 2q^2+2q
       682: 2q
       683: 3q^2+2q
       684: 2q^2+3q
       685: q^2+2q
       686: 2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       697: q^2+q
       731: q
       735: q
       745: q
       747: q
       749: q
       751: q
       758: q
       762: q
       764: q
       767: q
       768: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       794: 1
       795: 1
       806: q
       807: q
       813: q
       816: 2q
       817: 1
       819: q+1
       821: q
       823: q
       826: q^2+q
       827: q^2+q
       830: q
       831: q
       833: q
       835: q^2+q
       837: q^2+2q
       839: 2q
       840: q
       841: q
       844: 1
       846: q
       847: q
       853: q
       857: q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: 1
       870: 1
       872: q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       878: 2q
       879: q
       880: q
       889: q
       918: 1
       934: q
       940: 1
       956: q
       958: q
       966: 1
       971: 1
       979: q
       982: q
       990: q
       991: q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 1
      1017: 1
      1020: 1
      1030: q+1
      1032: 1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1047: 1
      1057: q
      1058: q
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 2q
      1084: 1
      1085: q
      1090: 1
      1102: q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1236: 1
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1274: 1
      1281: 1
      1285: 1
      1288: 1
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1380: 1
      1390: 1
      1398: 1
      1433: 1
      1456: 1
      1460: 1
      1463: 1
      1472: 1
      1483: 1
      1493: 1
      1517: 1
      1583: 1
      1589: 1
      1597: 1
      1634: 1
      1703: 1

1704:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 2q^2+3q+1
        35: q^2+2q+1
        36: 2q^2+3q+1
        37: 3q+1
        39: 3q+1
        41: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q
        59: 2q+1
        60: q^2+q
        61: q^2+2q+1
        62: 3q+1
        64: 2q+1
        66: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 3q+1
        74: 3q+1
        76: 3q+1
        78: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       103: q
       106: 2q+1
       107: q^2+q
       108: q^2+2q+1
       109: q
       110: 2q+1
       111: 3q+1
       113: 3q+1
       115: 2q+1
       118: q+1
       120: q+1
       121: 2q+1
       123: 2q+1
       125: q+1
       126: q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 3q+1
       149: 3q+1
       150: 2q+1
       151: 3q+1
       153: 3q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: 2q+1
       176: q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       184: q+1
       186: q+1
       187: 2q+1
       189: 2q+1
       192: q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       200: q+1
       201: q^2+q
       202: q^2+2q+1
       203: q
       204: 2q+1
       205: 3q+1
       207: 2q+1
       209: 3q+1
       211: 2q+1
       213: q+1
       215: q+1
       217: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 2q+1
       266: q+1
       269: q+1
       271: q
       273: 2q+1
       278: q+1
       279: 1
       281: q+1
       284: q+1
       286: q+1
       287: 2q+1
       289: q+1
       291: 2q+1
       294: q+1
       296: q+1
       297: 2q+1
       300: 1
       301: q+1
       304: 1
       305: 1
       308: q+1
       310: q+1
       311: 3q+1
       313: 2q+1
       315: 2q+1
       317: 3q+1
       320: q+1
       321: q
       322: 2q+1
       323: q+1
       325: 2q+1
       327: q+1
       329: q+1
       331: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 3q+1
       360: q+1
       362: q+1
       364: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: 1
       397: q
       399: 2q+1
       404: q+1
       406: q+1
       409: 1
       411: q+1
       413: 1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       448: q+1
       450: q+1
       451: 2q+1
       454: q+1
       455: q+1
       458: q+1
       459: 2q+1
       461: q
       462: 2q+1
       463: 3q+1
       465: 1
       467: q+1
       469: 2q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: 1
       539: 1
       543: 1
       547: q+1
       552: q+1
       555: 1
       559: q+1
       561: q
       563: 2q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 1
       585: 1
       587: q+1
       590: q+1
       592: q+1
       594: 1
       596: 1
       597: q+1
       599: 2q+1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: q+1
       622: q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       632: 1
       633: q+1
       635: 1
       637: q+1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       666: q+1
       668: q+1
       670: q+1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       708: 1
       712: 1
       716: q+1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: q+1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       799: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: q+1
       821: 1
       823: q+1
       826: q+1
       828: q+1
       830: 1
       832: 1
       833: q+1
       835: 2q+1
       837: q+1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       930: 1
       934: 1
       938: 1
       942: 1
       946: 1
       950: q+1
       955: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1020: 1
      1024: 1
      1030: q+1
      1033: 1
      1034: 1
      1036: q+1
      1038: 1
      1041: 1
      1042: q+1
      1045: 1
      1046: 1
      1050: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1208: 1
      1214: 1
      1217: 1
      1219: 1
      1222: 1
      1224: 1
      1236: 1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1334: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1430: 1
      1456: 1
      1461: 1
      1463: 1
      1472: 1
      1480: 1
      1482: 1
      1494: 1
      1518: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1631: 1
      1704: 1

1705:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 2q^2+3q+1
        35: q^2+2q+1
        36: 2q^2+3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+2q^2+2q+1
        58: q
        59: 2q+1
        60: q^2+2q+1
        61: q^2+q
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       104: 2q+1
       105: q
       107: q^2+2q+1
       108: q^2+q
       109: q
       110: 2q+1
       112: 3q+1
       114: 3q+1
       116: 2q+1
       118: q+1
       119: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 3q+1
       149: 3q+1
       150: 2q+1
       152: 3q+1
       154: 3q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: 2q+1
       171: q
       174: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q+1
       186: q+1
       188: 2q+1
       190: 2q+1
       192: q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: q+1
       201: q^2+2q+1
       202: q^2+q
       203: q
       204: 2q+1
       206: 3q+1
       208: 2q+1
       210: 3q+1
       212: 2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q+1
       261: q
       264: q+1
       268: q+1
       272: q
       274: 2q+1
       276: q+1
       280: 1
       282: q+1
       283: q+1
       286: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       293: q+1
       296: q+1
       298: 2q+1
       299: 1
       302: q+1
       304: 1
       306: 1
       307: q+1
       310: q+1
       312: 3q+1
       314: 2q+1
       316: 2q+1
       318: 3q+1
       319: q+1
       321: q
       322: 2q+1
       324: q+1
       326: 2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: 1
       398: q
       400: 2q+1
       403: q+1
       407: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: q+1
       447: q+1
       450: q+1
       452: 2q+1
       453: q+1
       456: q+1
       458: q+1
       460: 2q+1
       461: q
       462: 2q+1
       464: 3q+1
       466: 1
       468: q+1
       470: 2q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: 1
       538: 1
       542: 1
       546: q+1
       551: q+1
       556: 1
       560: q+1
       562: q
       564: 2q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       589: q+1
       592: q+1
       593: 1
       596: 1
       598: q+1
       600: 2q+1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q+1
       622: q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       632: 1
       634: q+1
       636: 1
       638: q+1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       706: 1
       710: 1
       715: q+1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: q+1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: 1
       800: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       818: 1
       820: q+1
       822: 1
       824: q+1
       825: q+1
       828: q+1
       829: 1
       832: 1
       834: q+1
       836: 2q+1
       838: q+1
       840: 1
       842: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       929: 1
       933: 1
       939: 1
       943: 1
       947: 1
       951: q+1
       953: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1021: 1
      1025: 1
      1031: q+1
      1033: 1
      1035: 1
      1037: q+1
      1039: 1
      1040: 1
      1043: q+1
      1045: 1
      1047: 1
      1051: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1192: 1
      1195: 1
      1207: 1
      1215: 1
      1217: 1
      1218: 1
      1223: 1
      1225: 1
      1237: 1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 1
      1258: 1
      1261: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1285: 1
      1288: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1338: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1434: 1
      1457: 1
      1461: 1
      1462: 1
      1473: 1
      1481: 1
      1483: 1
      1495: 1
      1519: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1635: 1
      1705: 1

1706:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+2q^2+2q+1
        22: 3q+1
        23: 3q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 2q^2+3q+1
        35: q^2+2q+1
        36: 2q^2+3q+1
        38: 3q+1
        40: 3q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: 3q+1
        53: 3q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+2q^2+2q+1
        58: 2q+1
        59: q
        60: q^2+q
        61: q^2+2q+1
        63: 3q+1
        65: 2q+1
        67: 3q+1
        68: q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 3q+1
        75: 3q+1
        77: 3q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q+1
        82: 3q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: 3q+1
       101: 3q+1
       102: q^2+2q+1
       104: q
       105: 2q+1
       107: q^2+q
       108: q^2+2q+1
       109: 2q+1
       110: q
       112: 3q+1
       114: 3q+1
       116: 2q+1
       117: q+1
       120: q+1
       122: 2q+1
       124: 2q+1
       125: q+1
       126: q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q+1
       142: 3q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 3q+1
       149: 3q+1
       150: 2q+1
       152: 3q+1
       154: 3q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: 2q+1
       175: q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       184: q+1
       185: q+1
       188: 2q+1
       190: 2q+1
       191: q+1
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       200: q+1
       201: q^2+q
       202: q^2+2q+1
       203: 2q+1
       204: q
       206: 3q+1
       208: 2q+1
       210: 3q+1
       212: 2q+1
       214: q+1
       216: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 2q+1
       265: q+1
       270: q+1
       272: 2q+1
       274: q
       277: q+1
       280: 1
       282: q+1
       284: q+1
       285: q+1
       288: 2q+1
       290: q+1
       292: 2q+1
       294: q+1
       295: q+1
       298: 2q+1
       300: 1
       302: q+1
       303: 1
       306: 1
       308: q+1
       309: q+1
       312: 3q+1
       314: 2q+1
       316: 2q+1
       318: 3q+1
       320: q+1
       321: 2q+1
       322: q
       324: q+1
       326: 2q+1
       328: q+1
       330: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 1
       345: 1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 3q+1
       361: q+1
       363: q+1
       365: q+1
       366: 2q+1
       367: 1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: 1
       398: 2q+1
       400: q
       402: q+1
       408: q+1
       410: 1
       412: q+1
       414: 1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: q+1
       448: q+1
       449: q+1
       452: 2q+1
       454: q+1
       456: q+1
       457: q+1
       460: 2q+1
       461: 2q+1
       462: q
       464: 3q+1
       466: 1
       468: q+1
       470: 2q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: q+1
       482: 1
       483: 2q+1
       484: 1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: 1
       540: 1
       544: 1
       548: q+1
       550: q+1
       554: 1
       558: q+1
       562: 2q+1
       564: q
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 1
       586: 1
       588: q+1
       590: q+1
       591: q+1
       594: 1
       595: 1
       598: q+1
       600: 2q+1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: q+1
       621: q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       631: 1
       634: q+1
       636: 1
       638: q+1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       667: q+1
       669: q+1
       671: q+1
       672: 1
       673: q+1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q+1
       682: 1
       683: 2q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       707: 1
       711: 1
       714: q+1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: q+1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: 1
       800: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       820: q+1
       822: 1
       824: q+1
       826: q+1
       827: q+1
       830: 1
       831: 1
       834: q+1
       836: 2q+1
       838: q+1
       839: 1
       842: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: 1
       870: 1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       878: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       931: 1
       935: 1
       937: 1
       941: 1
       945: 1
       949: q+1
       954: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1021: 1
      1025: 1
      1031: q+1
      1032: 1
      1035: 1
      1037: q+1
      1039: 1
      1041: 1
      1043: q+1
      1044: 1
      1047: 1
      1051: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1165: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1192: 1
      1196: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1223: 1
      1225: 1
      1237: 1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 1
      1259: 1
      1260: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1285: 1
      1288: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1338: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1434: 1
      1457: 1
      1460: 1
      1463: 1
      1473: 1
      1481: 1
      1483: 1
      1496: 1
      1520: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1635: 1
      1706: 1

1707:    0: q^4+9q^3+11q^2+3q
         1: q^4+9q^3+11q^2+3q
         2: 3q^4+8q^3+8q^2+3q
         3: q^4+9q^3+11q^2+3q
         4: q^4+9q^3+11q^2+3q
         5: q^4+9q^3+11q^2+3q
         6: q^4+9q^3+11q^2+3q
         7: 3q^4+8q^3+8q^2+3q
         8: 3q^4+8q^3+8q^2+3q
         9: q^5+4q^4+6q^3+5q^2+2q
        10: q^4+9q^3+11q^2+3q
        11: q^4+9q^3+11q^2+3q
        12: q^4+9q^3+11q^2+3q
        13: 5q^3+8q^2+3q
        14: 5q^3+8q^2+3q
        15: 5q^3+8q^2+3q
        16: 5q^3+10q^2+3q
        17: 5q^3+10q^2+3q
        18: 2q^4+5q^3+5q^2+2q
        19: q^4+9q^3+11q^2+3q
        20: q^4+9q^3+11q^2+3q
        21: 3q^4+8q^3+8q^2+3q
        22: 2q^3+10q^2+3q
        23: 2q^3+10q^2+3q
        24: 4q^3+7q^2+3q
        25: q^4+9q^3+11q^2+3q
        26: q^4+9q^3+11q^2+3q
        27: 3q^4+8q^3+8q^2+3q
        28: 5q^3+10q^2+3q
        29: q^4+9q^3+11q^2+3q
        30: 5q^3+8q^2+3q
        31: 2q^3+10q^2+3q
        32: q^3+7q^2+3q
        33: 9q^2+3q
        34: q^4+9q^3+11q^2+3q
        35: 5q^3+8q^2+3q
        36: 5q^3+10q^2+3q
        37: 3q^2+q
        38: 2q^3+7q^2+2q
        39: 3q^2+q
        40: 2q^3+7q^2+2q
        41: q^3+2q^2+q
        42: 3q^3+5q^2+2q
        43: 5q^3+8q^2+3q
        44: 5q^3+8q^2+3q
        45: 5q^3+8q^2+3q
        46: 2q^3+7q^2+3q
        47: 2q^3+7q^2+3q
        48: 3q^3+5q^2+2q
        49: 5q^3+10q^2+3q
        50: 5q^3+10q^2+3q
        51: 2q^4+5q^3+5q^2+2q
        52: 2q^3+10q^2+3q
        53: 2q^3+10q^2+3q
        54: 4q^3+7q^2+3q
        55: q^4+9q^3+11q^2+3q
        56: q^4+9q^3+11q^2+3q
        57: 3q^4+8q^3+8q^2+3q
        58: 4q^2+q
        59: 5q^2+2q
        60: 2q^3+4q^2+q
        61: 3q^3+6q^2+2q
        62: 3q^2+q
        63: 2q^3+7q^2+2q
        64: 2q^2+q
        65: q^3+5q^2+2q
        66: 3q^2+q
        67: 6q^2+2q
        68: 4q^2+3q
        69: q^3+4q^2+2q
        70: 5q^3+8q^2+3q
        71: 5q^3+10q^2+3q
        72: 5q^3+10q^2+3q
        73: 9q^2+3q
        74: 3q^2+q
        75: 2q^3+7q^2+2q
        76: 3q^2+q
        77: 2q^3+7q^2+2q
        78: q^3+2q^2+q
        79: 3q^3+5q^2+2q
        80: q^3+7q^2+3q
        81: 6q^2+3q
        82: 2q^3+10q^2+3q
        83: q^3+7q^2+3q
        84: 5q^3+8q^2+3q
        85: 2q^3+7q^2+3q
        86: q^4+9q^3+11q^2+3q
        87: 5q^3+8q^2+3q
        88: 2q^3+7q^2+3q
        89: 2q^3+7q^2+3q
        90: 3q^3+5q^2+2q
        91: 2q^3+7q^2+3q
        92: 2q^3+7q^2+3q
        93: 3q^3+5q^2+2q
        94: 7q^2+3q
        95: 7q^2+3q
        96: 2q^3+4q^2+2q
        97: 5q^3+10q^2+3q
        98: 5q^3+10q^2+3q
        99: 2q^4+5q^3+5q^2+2q
       100: 2q^3+10q^2+3q
       101: 2q^3+10q^2+3q
       102: 4q^3+7q^2+3q
       103: q^2
       104: 3q^2+q
       105: 3q^2+q
       106: 2q^2+q
       107: 2q^3+4q^2+q
       108: 3q^3+6q^2+2q
       109: 4q^2+q
       110: 5q^2+2q
       111: 3q^2+q
       112: 6q^2+2q
       113: 3q^2+q
       114: 2q^3+7q^2+2q
       115: 2q^2+q
       116: q^3+5q^2+2q
       117: q^2+q
       118: 2q^2+2q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+q
       122: q^3+5q^2+2q
       123: 2q^2+q
       124: 4q^2+2q
       125: 4q^2+3q
       126: q^3+4q^2+2q
       128: 4q^2+2q
       130: 4q^2+2q
       132: q^3+2q^2+q
       133: 4q^2+3q
       134: q^3+4q^2+2q
       135: 2q^3+7q^2+3q
       136: 6q^2+3q
       137: 6q^2+3q
       138: 3q^2+2q
       139: 7q^2+3q
       140: 2q^2+2q
       141: q^3+7q^2+3q
       142: 7q^2+3q
       143: 2q^3+7q^2+3q
       144: q^3+4q^2+2q
       145: 5q^3+10q^2+3q
       146: 5q^3+8q^2+3q
       147: 5q^3+10q^2+3q
       148: 9q^2+3q
       149: 2q^3+10q^2+3q
       150: q^3+7q^2+3q
       151: 3q^2+q
       152: 2q^3+7q^2+2q
       153: 3q^2+q
       154: 2q^3+7q^2+2q
       155: q^3+2q^2+q
       156: 3q^3+5q^2+2q
       157: 2q^3+7q^2+3q
       158: 2q^3+7q^2+3q
       159: 3q^3+5q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: 2q^2+2q
       163: 2q^3+7q^2+3q
       164: 2q^3+7q^2+3q
       165: 3q^3+5q^2+2q
       166: 7q^2+3q
       167: 7q^2+3q
       168: 2q^3+4q^2+2q
       169: q^2
       170: 3q^2+q
       171: 3q^2+q
       172: 2q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       178: q^2+q
       180: 4q^2+2q
       182: 4q^2+2q
       183: q^2+q
       184: 3q^2+2q
       185: q^2+q
       186: 2q^2+2q
       187: 2q^2+q
       188: 4q^2+2q
       189: 2q^2+q
       190: q^3+5q^2+2q
       191: q^2+q
       192: 2q^2+2q
       194: 2q^2+2q
       195: 3q^2+q
       196: 4q^2+2q
       197: q^2+q
       198: q^2+q
       199: q^2+q
       200: 3q^2+2q
       201: 2q^3+4q^2+q
       202: 3q^3+6q^2+2q
       203: 4q^2+q
       204: 5q^2+2q
       205: 3q^2+q
       206: 6q^2+2q
       207: 2q^2+q
       208: 4q^2+2q
       209: 3q^2+q
       210: 2q^3+7q^2+2q
       211: 2q^2+q
       212: q^3+5q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: 2q^2+2q
       220: 4q^2+3q
       221: q^3+4q^2+2q
       222: 2q^3+7q^2+3q
       223: q^3+4q^2+2q
       224: 6q^2+3q
       225: 3q^2+2q
       226: 3q^2+2q
       227: 3q
       228: q^2+2q
       229: 2q
       230: 2q^2+3q
       231: q^3+4q^2+2q
       232: 4q^2+3q
       233: q^3+4q^2+2q
       234: 2q^3+7q^2+3q
       235: 6q^2+3q
       236: 3q^2+2q
       238: 4q^2+2q
       240: 4q^2+2q
       242: q^3+2q^2+q
       243: 7q^2+3q
       244: 2q^2+2q
       245: 7q^2+3q
       246: q^3+7q^2+3q
       247: 7q^2+3q
       248: 7q^2+3q
       249: 2q^3+4q^2+2q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+2q
       253: 2q^3+7q^2+3q
       254: 2q^3+7q^2+3q
       255: 3q^3+5q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: 2q^2+2q
       260: 2q^2+q
       261: 2q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2+q
       269: q^2+q
       270: q^2+q
       271: q^2
       272: 3q^2+q
       273: 2q^2+q
       274: 3q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: 2q
       282: q
       284: q^2+q
       286: q^2+q
       288: q^2+q
       290: q^2+2q
       292: q^2+q
       293: q^2+q
       294: 3q^2+2q
       295: q^2+q
       296: 2q^2+2q
       297: 2q^2+q
       298: 4q^2+2q
       300: 2q
       302: q^2+q
       303: q
       304: 2q
       305: q
       306: q
       307: q^2+q
       308: 3q^2+2q
       309: q^2+q
       310: 2q^2+2q
       312: 4q^2+2q
       313: 2q^2+q
       314: 4q^2+2q
       316: q^2+q
       318: 4q^2+2q
       320: 2q^2+2q
       321: 3q^2+q
       322: 4q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^2+q
       326: q^3+5q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: 2q^2+2q
       334: q^3+4q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 7q^2+3q
       339: 4q^2+2q
       341: 4q^2+2q
       343: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: 2q
       348: q
       349: 2q^2+3q
       350: q^2+2q
       351: 2q^2+2q
       352: 2q^2+2q
       353: 4q^2+3q
       354: q^3+4q^2+2q
       355: 2q^3+7q^2+3q
       356: q^3+4q^2+2q
       357: 6q^2+3q
       358: 3q^2+2q
       359: 7q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: 3q^2+2q
       367: 3q
       368: q^2+2q
       369: 2q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: 2q^2+2q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       386: q^2+q
       387: q^2+q
       388: q^2+q
       392: q^2+q
       395: q
       396: q
       398: 2q^2+q
       400: 2q^2+q
       402: q^2+q
       403: q^2+q
       404: q^2+q
       406: q^2+q
       408: q^2+q
       410: 2q
       412: q
       414: q
       416: q^2+2q
       418: q
       420: q^2+q
       422: q^2+q
       424: q^2+q
       426: q^2+q
       428: 4q^2+2q
       430: q
       432: q
       436: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: q
       444: 2q^2+2q
       446: q^2+q
       448: q^2+q
       450: q^2+q
       452: q^2+q
       453: q^2+q
       454: 3q^2+2q
       456: q^2+2q
       457: q^2+q
       458: 2q^2+2q
       459: 2q^2+q
       460: 4q^2+2q
       461: 3q^2+q
       462: 4q^2+2q
       464: 4q^2+2q
       466: 2q
       468: q
       470: q^2+q
       472: 2q
       473: q
       474: 2q
       475: q
       476: q
       478: q^2+q
       479: q^2+q
       480: q^2+q
       481: 2q^2+2q
       482: 2q
       483: 3q^2+2q
       484: 3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: q
       494: q^2+2q
       495: q
       496: 2q
       497: 2q^2+2q
       498: q^3+4q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: 2q
       512: q
       513: 2q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+3q
       519: 2q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       540: q
       543: q
       544: q
       548: q^2+q
       554: q
       556: q
       558: q^2+q
       559: q^2+q
       560: q^2+q
       562: 2q^2+q
       564: 2q^2+q
       567: q
       568: q
       572: q^2+q
       575: q^2+q
       576: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q
       590: q^2+q
       592: q^2+q
       594: q
       596: q
       598: q
       600: q^2+q
       602: 2q
       604: q
       608: q
       612: q
       616: 2q
       618: q
       620: q^2+q
       622: q^2+q
       624: q
       626: q^2+q
       628: q^2+2q
       630: q^2+q
       631: q
       632: 2q
       634: q^2+2q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       648: 2q
       649: q
       650: 2q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: 1
       676: 2q
       677: q
       678: 2q
       679: q
       680: q+1
       681: 2q^2+2q
       682: 2q
       683: 3q^2+2q
       684: 2q^2+3q
       685: q^2+2q
       686: 2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       700: q^2+q
       732: q
       736: q
       746: q
       748: q
       750: q
       752: q
       760: q
       762: q
       764: q
       767: q
       768: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       794: 1
       796: 1
       806: q
       808: q
       814: q
       816: 2q
       818: 1
       820: q+1
       822: q
       824: q
       826: q^2+q
       828: q^2+q
       830: q
       832: q
       834: q
       836: q^2+q
       838: q^2+2q
       839: q
       840: 2q
       842: q
       843: 1
       846: q
       848: q
       854: q
       857: q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: 1
       870: 1
       872: q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       878: 2q
       879: q
       880: q
       891: q
       919: 1
       935: q
       943: 1
       957: q
       959: q
       967: 1
       969: 1
       981: q
       986: q
       990: q
       991: q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 1
      1017: 1
      1021: 1
      1031: q+1
      1033: 1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: 1
      1057: q
      1059: q
      1074: 1
      1077: 1
      1080: 1
      1081: q+1
      1082: 2q
      1084: 1
      1085: q
      1094: 1
      1105: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1237: 1
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1275: 1
      1280: 1
      1285: 1
      1288: 1
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1457: 1
      1461: 1
      1463: 1
      1473: 1
      1482: 1
      1497: 1
      1521: 1
      1586: 1
      1590: 1
      1598: 1
      1632: 1
      1707: 1

1708:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+6q^3+3q^2+q
        26: 2q^4+6q^3+3q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: q^4+4q^3+3q^2+q
        32: 2q^3+2q^2+q
        33: q^4+4q^3+3q^2+q
        34: 2q^4+6q^3+3q^2+q
        35: 3q^3+2q^2+q
        36: 2q^4+6q^3+3q^2+q
        37: q^4+4q^3+3q^2+q
        39: q^4+4q^3+3q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+3q^2+q
        53: 2q^3+3q^2+q
        54: 2q^3+2q^2+q
        55: q^4+4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2
        59: q^4+3q^3+2q^2+q
        60: q^4+2q^3+q^2
        61: q^4+4q^3+2q^2+q
        62: q^4+4q^3+3q^2+q
        64: 2q^3+2q^2+q
        66: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: 2q^3+3q^2+q
        73: q^3+3q^2+q
        74: 2q^3+3q^2+q
        76: 2q^3+3q^2+q
        78: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: 2q^3+2q^2+q
        82: 2q^3+3q^2+q
        83: q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 3q^3+2q^2+q
        86: q^4+4q^3+3q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: q^4+4q^3+3q^2+q
        98: q^4+4q^3+3q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2
       106: q^4+3q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: q^2
       110: q^3+2q^2+q
       111: q^3+3q^2+q
       113: 2q^3+3q^2+q
       115: q^3+2q^2+q
       118: q^3+q^2+q
       120: q^3+q^2+q
       121: 2q^3+2q^2+q
       123: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+3q^2+q
       129: 2q^3+3q^2+q
       131: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^3+2q^2+q
       138: q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+3q^2+q
       143: 3q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+3q^2+q
       148: q^3+3q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       151: 2q^3+3q^2+q
       153: 2q^3+3q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^3+2q^2+q
       164: q^3+2q^2+q
       165: q^3+2q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       169: q^2
       172: q^3+2q^2+q
       176: q^3+q^2+q
       177: q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: q^3+3q^2+q
       184: q^2+q
       186: q^2+q
       187: 2q^2+q
       189: q^3+2q^2+q
       192: q^3+q^2+q
       194: q^2+q
       195: q^2
       196: q^3+2q^2+q
       197: q^2+q
       200: q^3+q^2+q
       201: q^2
       202: 2q^3+2q^2+q
       203: q^2
       204: q^3+2q^2+q
       205: q^3+3q^2+q
       207: 2q^3+2q^2+q
       209: 2q^3+3q^2+q
       211: q^3+2q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: q^3+2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^3+2q^2+q
       232: q^2+q
       233: q^3+2q^2+q
       234: 2q^2+q
       235: 2q^2+q
       236: q^3+2q^2+q
       237: 2q^3+3q^2+q
       239: 2q^3+3q^2+q
       241: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^2+q
       245: q^3+3q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2
       262: q^3+2q^2+q
       266: q^2+q
       269: q^2+q
       271: q^2
       273: q^3+2q^2+q
       278: q^3+q^2+q
       279: q
       281: q^2+q
       284: q^2+q
       286: q^2+q
       287: q^3+2q^2+q
       289: q^2+q
       291: 2q^2+q
       294: q^2+q
       296: q^2+q
       297: 2q^2+q
       300: q
       301: q^2+q
       304: q
       305: q
       308: q^2+q
       310: q^2+q
       311: q^3+3q^2+q
       313: 2q^2+q
       315: q^3+2q^2+q
       317: 2q^3+3q^2+q
       320: q^2+q
       321: q^2
       322: q^3+2q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^2+q
       357: 2q^2+q
       358: 2q^2+q
       359: 2q^2+q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       380: q^2+q
       384: q
       388: q^2+q
       391: q^2+q
       396: q
       397: q^2
       399: q^3+2q^2+q
       404: q^2+q
       406: q^2+q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       430: q
       432: q
       433: q
       435: q
       438: q
       440: q
       441: q
       444: q^2+q
       445: q^2+q
       448: q^2+q
       450: q^2+q
       451: 2q^2+q
       454: q^2+q
       455: q^2+q
       458: q^2+q
       459: 2q^2+q
       461: q^2
       462: q^2+q
       463: 2q^2+q
       465: q
       467: q^2+q
       469: q^3+2q^2+q
       472: q
       474: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^2+q
       524: q
       528: q
       532: q^2+q
       536: q
       539: q
       543: q
       547: q^2+q
       552: q^2+q
       555: q
       559: q^2+q
       561: q^2
       563: q^2+q
       568: q
       570: q^2+q
       575: q^2+q
       577: q^2+q
       583: q
       585: q
       587: q^2+q
       590: q
       592: q
       594: q
       596: q
       599: q^2+q
       604: q
       605: q
       608: q
       609: q
       611: q
       613: q
       620: q^2+q
       622: q^2+q
       623: q^2+q
       625: 2q^2+q
       627: q^2+q
       629: q^2+q
       635: q
       637: q^2+q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: q
       653: q
       676: q
       677: q
       681: q
       682: q
       683: q^2+q
       686: q
       687: q
       688: q^2+q
       689: q
       697: q^2+q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q
       731: q
       739: q
       743: q^2+q
       747: q
       756: q
       758: q
       762: q
       777: q
       799: q
       806: q
       808: q
       811: q
       821: q
       823: q^2+q
       826: q
       828: q
       830: q
       832: q
       835: q^2+q
       841: q
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       878: q
       879: q
       899: q
       914: q
       930: q
       938: q
       946: q
       950: q
       955: q
       961: q
       975: q
       979: q
      1010: 1
      1034: q
      1050: q
      1057: q
      1059: q
      1062: q
      1127: 1
      1140: 1
      1170: q
      1185: q
      1208: q
      1222: 1
      1278: 1
      1299: 1
      1323: 1
      1336: 1
      1393: 1
      1432: 1
      1480: 1
      1498: 1
      1522: 1
      1592: 1
      1633: 1
      1708: 1

1709:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+6q^3+3q^2+q
        26: 2q^4+6q^3+3q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: q^4+4q^3+3q^2+q
        32: 2q^3+2q^2+q
        33: q^4+4q^3+3q^2+q
        34: 2q^4+6q^3+3q^2+q
        35: 3q^3+2q^2+q
        36: 2q^4+6q^3+3q^2+q
        38: q^4+4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+3q^2+q
        53: 2q^3+3q^2+q
        54: 2q^3+2q^2+q
        55: q^4+4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2
        59: q^4+3q^3+2q^2+q
        60: q^4+4q^3+2q^2+q
        61: q^4+2q^3+q^2
        63: q^4+4q^3+3q^2+q
        65: 2q^3+2q^2+q
        67: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: 2q^3+3q^2+q
        73: q^3+3q^2+q
        75: 2q^3+3q^2+q
        77: 2q^3+3q^2+q
        79: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: 2q^3+2q^2+q
        82: 2q^3+3q^2+q
        83: q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 3q^3+2q^2+q
        86: q^4+4q^3+3q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: q^4+4q^3+3q^2+q
        98: q^4+4q^3+3q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       104: q^4+3q^3+2q^2+q
       105: q^3+q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: q^2
       110: q^3+2q^2+q
       112: q^3+3q^2+q
       114: 2q^3+3q^2+q
       116: q^3+2q^2+q
       118: q^3+q^2+q
       119: q^3+q^2+q
       122: 2q^3+2q^2+q
       124: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^3+2q^2+q
       138: q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+3q^2+q
       143: 3q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+3q^2+q
       148: q^3+3q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       152: 2q^3+3q^2+q
       154: 2q^3+3q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^3+2q^2+q
       164: q^3+2q^2+q
       165: q^3+2q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       170: q^3+2q^2+q
       171: q^2
       174: q^3+q^2+q
       178: q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: q^3+3q^2+q
       183: q^2+q
       186: q^2+q
       188: 2q^2+q
       190: q^3+2q^2+q
       192: q^3+q^2+q
       193: q^2+q
       195: q^2
       196: q^3+2q^2+q
       198: q^2+q
       199: q^3+q^2+q
       201: 2q^3+2q^2+q
       202: q^2
       203: q^2
       204: q^3+2q^2+q
       206: q^3+3q^2+q
       208: 2q^3+2q^2+q
       210: 2q^3+3q^2+q
       212: q^3+2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: q^3+2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^3+2q^2+q
       232: q^2+q
       233: q^3+2q^2+q
       234: 2q^2+q
       235: 2q^2+q
       236: q^3+2q^2+q
       238: 2q^3+3q^2+q
       240: 2q^3+3q^2+q
       242: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^2+q
       245: q^3+3q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: q^2+q
       268: q^2+q
       272: q^2
       274: q^3+2q^2+q
       276: q^3+q^2+q
       280: q
       282: q^2+q
       283: q^2+q
       286: q^2+q
       288: q^3+2q^2+q
       290: q^2+q
       292: 2q^2+q
       293: q^2+q
       296: q^2+q
       298: 2q^2+q
       299: q
       302: q^2+q
       304: q
       306: q
       307: q^2+q
       310: q^2+q
       312: q^3+3q^2+q
       314: 2q^2+q
       316: q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: q^2+q
       321: q^2
       322: q^3+2q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^2+q
       357: 2q^2+q
       358: 2q^2+q
       359: 2q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2+q
       382: q
       386: q^2+q
       390: q^2+q
       394: q
       398: q^2
       400: q^3+2q^2+q
       403: q^2+q
       407: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q
       432: q
       434: q
       436: q
       437: q
       440: q
       442: q
       443: q^2+q
       446: q^2+q
       447: q^2+q
       450: q^2+q
       452: 2q^2+q
       453: q^2+q
       456: q^2+q
       458: q^2+q
       460: 2q^2+q
       461: q^2
       462: q^2+q
       464: 2q^2+q
       466: q
       468: q^2+q
       470: q^3+2q^2+q
       471: q
       474: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^2+q
       522: q
       526: q
       530: q^2+q
       534: q
       538: q
       542: q
       546: q^2+q
       551: q^2+q
       556: q
       560: q^2+q
       562: q^2
       564: q^2+q
       566: q
       571: q^2+q
       574: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q
       592: q
       593: q
       596: q
       600: q^2+q
       603: q
       606: q
       608: q
       610: q
       612: q
       614: q
       619: q^2+q
       622: q^2+q
       624: q^2+q
       626: 2q^2+q
       628: q^2+q
       630: q^2+q
       636: q
       638: q^2+q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: q
       654: q
       676: q
       677: q
       681: q
       682: q
       683: q^2+q
       686: q
       687: q
       688: q^2+q
       689: q
       699: q^2+q
       706: q
       710: q
       715: q
       718: q
       722: q
       726: q
       730: q
       740: q
       744: q^2+q
       748: q
       754: q
       759: q
       763: q
       778: q
       800: q
       805: q
       808: q
       812: q
       822: q
       824: q^2+q
       825: q
       828: q
       829: q
       832: q
       836: q^2+q
       842: q
       845: q
       848: q
       850: q
       852: q
       854: q
       856: q
       878: q
       879: q
       897: q
       913: q
       929: q
       939: q
       947: q
       951: q
       953: q
       962: q
       976: q
       980: q
      1011: 1
      1035: q
      1051: q
      1056: q
      1059: q
      1063: q
      1128: 1
      1143: 1
      1171: q
      1186: q
      1207: q
      1223: 1
      1279: 1
      1300: 1
      1324: 1
      1339: 1
      1394: 1
      1435: 1
      1481: 1
      1499: 1
      1523: 1
      1593: 1
      1636: 1
      1709: 1

1710:    0: 2q^4+6q^3+3q^2+q
         1: 2q^4+6q^3+3q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+6q^3+3q^2+q
         4: q^5+3q^4+4q^3+3q^2+q
         5: 2q^4+6q^3+3q^2+q
         6: q^5+3q^4+4q^3+3q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 2q^4+6q^3+3q^2+q
        11: 2q^4+6q^3+3q^2+q
        12: q^5+3q^4+4q^3+3q^2+q
        13: 3q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: 3q^3+2q^2+q
        16: 2q^4+6q^3+3q^2+q
        17: 2q^4+6q^3+3q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+4q^3+3q^2+q
        20: q^4+4q^3+3q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+4q^3+3q^2+q
        23: q^4+4q^3+3q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+6q^3+3q^2+q
        26: 2q^4+6q^3+3q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 2q^4+6q^3+3q^2+q
        29: q^4+4q^3+3q^2+q
        30: 2q^3+2q^2+q
        31: q^4+4q^3+3q^2+q
        32: 2q^3+2q^2+q
        33: q^4+4q^3+3q^2+q
        34: 2q^4+6q^3+3q^2+q
        35: 3q^3+2q^2+q
        36: 2q^4+6q^3+3q^2+q
        38: q^4+4q^3+3q^2+q
        40: q^4+4q^3+3q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 3q^3+2q^2+q
        47: 3q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+4q^3+3q^2+q
        50: q^4+4q^3+3q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+3q^2+q
        53: 2q^3+3q^2+q
        54: 2q^3+2q^2+q
        55: q^4+4q^3+3q^2+q
        56: q^4+4q^3+3q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^4+3q^3+2q^2+q
        59: q^3+q^2
        60: q^4+2q^3+q^2
        61: q^4+4q^3+2q^2+q
        63: q^4+4q^3+3q^2+q
        65: 2q^3+2q^2+q
        67: q^4+4q^3+3q^2+q
        68: q^3+q^2+q
        69: 2q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: q^4+4q^3+3q^2+q
        72: 2q^3+3q^2+q
        73: q^3+3q^2+q
        75: 2q^3+3q^2+q
        77: 2q^3+3q^2+q
        79: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: 2q^3+2q^2+q
        82: 2q^3+3q^2+q
        83: q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 3q^3+2q^2+q
        86: q^4+4q^3+3q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^3+2q^2+q
        92: q^3+2q^2+q
        93: q^3+2q^2+q
        94: 2q^3+3q^2+q
        95: 2q^3+3q^2+q
        96: 2q^3+2q^2+q
        97: q^4+4q^3+3q^2+q
        98: q^4+4q^3+3q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+3q^2+q
       101: 2q^3+3q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2
       105: q^4+3q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: q^3+2q^2+q
       110: q^2
       112: q^3+3q^2+q
       114: 2q^3+3q^2+q
       116: q^3+2q^2+q
       117: q^3+q^2+q
       120: q^3+q^2+q
       122: 2q^3+2q^2+q
       124: 2q^3+2q^2+q
       125: q^3+q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+3q^2+q
       130: 2q^3+3q^2+q
       132: 2q^3+2q^2+q
       133: q^2+q
       134: q^3+2q^2+q
       135: 2q^2+q
       136: 2q^2+q
       137: 2q^3+2q^2+q
       138: q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+3q^2+q
       143: 3q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+3q^2+q
       148: q^3+3q^2+q
       149: 2q^3+3q^2+q
       150: q^3+2q^2+q
       152: 2q^3+3q^2+q
       154: 2q^3+3q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^3+2q^2+q
       164: q^3+2q^2+q
       165: q^3+2q^2+q
       166: 2q^3+3q^2+q
       167: 2q^3+3q^2+q
       168: 2q^3+2q^2+q
       170: q^2
       171: q^3+2q^2+q
       175: q^3+q^2+q
       178: q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: q^3+3q^2+q
       184: q^2+q
       185: q^2+q
       188: 2q^2+q
       190: q^3+2q^2+q
       191: q^3+q^2+q
       194: q^2+q
       195: q^3+2q^2+q
       196: q^2
       198: q^2+q
       200: q^3+q^2+q
       201: q^2
       202: 2q^3+2q^2+q
       203: q^3+2q^2+q
       204: q^2
       206: q^3+3q^2+q
       208: 2q^3+2q^2+q
       210: 2q^3+3q^2+q
       212: q^3+2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^2+q
       220: q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^2+q
       224: 2q^2+q
       225: 2q^2+q
       226: q^3+2q^2+q
       227: q
       228: q^2+q
       229: q
       230: q^2+q
       231: 2q^3+2q^2+q
       232: q^2+q
       233: q^3+2q^2+q
       234: 2q^2+q
       235: 2q^2+q
       236: q^3+2q^2+q
       238: 2q^3+3q^2+q
       240: 2q^3+3q^2+q
       242: 2q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: q^2+q
       245: q^3+3q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2
       261: q^3+2q^2+q
       265: q^2+q
       270: q^2+q
       272: q^3+2q^2+q
       274: q^2
       277: q^3+q^2+q
       280: q
       282: q^2+q
       284: q^2+q
       285: q^2+q
       288: q^3+2q^2+q
       290: q^2+q
       292: 2q^2+q
       294: q^2+q
       295: q^2+q
       298: 2q^2+q
       300: q
       302: q^2+q
       303: q
       306: q
       308: q^2+q
       309: q^2+q
       312: q^3+3q^2+q
       314: 2q^2+q
       316: q^3+2q^2+q
       318: 2q^3+3q^2+q
       320: q^2+q
       321: q^3+2q^2+q
       322: q^2
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q
       345: q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^2+q
       357: 2q^2+q
       358: 2q^2+q
       359: 2q^2+q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: q^3+2q^2+q
       367: q
       368: q^2+q
       369: q
       370: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       379: q^2+q
       383: q
       387: q^2+q
       392: q^2+q
       395: q
       398: q^3+2q^2+q
       400: q^2
       402: q^2+q
       408: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       430: q
       431: q
       434: q
       436: q
       438: q
       439: q
       442: q
       444: q^2+q
       446: q^2+q
       448: q^2+q
       449: q^2+q
       452: 2q^2+q
       454: q^2+q
       456: q^2+q
       457: q^2+q
       460: 2q^2+q
       461: q^2+q
       462: q^2
       464: 2q^2+q
       466: q
       468: q^2+q
       470: q^3+2q^2+q
       472: q
       473: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q
       482: q
       483: q^2+q
       492: q
       493: q
       494: q^2+q
       495: q
       497: q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q
       509: q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^2+q
       523: q
       527: q
       531: q^2+q
       535: q
       540: q
       544: q
       548: q^2+q
       550: q^2+q
       554: q
       558: q^2+q
       562: q^2+q
       564: q^2
       567: q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       590: q
       591: q
       594: q
       595: q
       600: q^2+q
       604: q
       606: q
       607: q
       610: q
       612: q
       614: q
       620: q^2+q
       621: q^2+q
       624: q^2+q
       626: 2q^2+q
       628: q^2+q
       630: q^2+q
       636: q
       638: q^2+q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       676: q
       677: q
       681: q
       682: q
       683: q^2+q
       686: q
       687: q
       688: q^2+q
       689: q
       700: q^2+q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q
       732: q
       738: q
       742: q^2+q
       746: q
       755: q
       760: q
       764: q
       778: q
       800: q
       806: q
       807: q
       812: q
       822: q
       824: q^2+q
       826: q
       827: q
       830: q
       831: q
       836: q^2+q
       842: q
       846: q
       847: q
       850: q
       852: q
       854: q
       856: q
       878: q
       879: q
       898: q
       915: q
       931: q
       937: q
       945: q
       949: q
       954: q
       963: q
       977: q
       981: q
      1011: 1
      1035: q
      1051: q
      1057: q
      1058: q
      1063: q
      1129: 1
      1143: 1
      1169: q
      1187: q
      1209: q
      1223: 1
      1279: 1
      1301: 1
      1325: 1
      1339: 1
      1395: 1
      1435: 1
      1481: 1
      1500: 1
      1524: 1
      1594: 1
      1636: 1
      1710: 1

1711:    0: 3q^2+q+1
         1: 3q^2+q+1
         2: 3q^2+q+1
         3: 3q^2+q+1
         4: q^3+2q^2+q+1
         5: 3q^2+q+1
         6: q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: 3q^2+q+1
         9: q^3+2q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q^2+q+1
        14: q^3+2q^2+q+1
        15: 3q^2+q+1
        16: 3q^2+q+1
        17: 3q^2+q+1
        18: q^3+2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: 2q^2+q+1
        22: 3q^2+q+1
        23: 3q^2+q+1
        24: 3q^2+q+1
        25: 3q^2+q+1
        26: 3q^2+q+1
        27: 3q^2+q+1
        28: q+1
        29: q+1
        30: 2q^2+q+1
        31: q+1
        32: 3q^2+q+1
        33: 3q^2+q+1
        34: q+1
        35: 3q^2+q+1
        36: 3q^2+q+1
        37: 2q^2+q+1
        38: q^2
        39: 2q^2+q+1
        40: q^2
        41: 2q^2+q+1
        42: q^2
        43: q+1
        44: q+1
        45: q+1
        46: 3q^2+q+1
        47: 3q^2+q+1
        48: q^3+2q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: 2q^2+q+1
        52: 2q^2+q+1
        53: 2q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: 2q^2+q+1
        58: q+1
        60: q+1
        62: q+1
        64: 2q^2+q+1
        65: q^2
        66: 2q^2+q+1
        67: q^2
        68: q+1
        69: 2q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        76: q^2+q+1
        78: q^2+q+1
        80: q+1
        81: 3q^2+q+1
        82: q+1
        83: 2q^2+q+1
        84: q+1
        85: 3q^2+q+1
        86: q+1
        87: 2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       103: q+1
       107: q+1
       109: q+1
       111: q+1
       113: q+1
       115: q^2+q+1
       117: q+1
       119: q+1
       121: q+1
       123: 2q^2+q+1
       124: q^2
       125: q+1
       126: q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: q+1
       134: 2q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q+1
       140: q^2+q+1
       141: q+1
       142: q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: 2q^2+q+1
       151: q^2+q+1
       153: q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: 2q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: 2q^2+q+1
       166: 2q^2+q+1
       167: 2q^2+q+1
       168: 2q^2+q+1
       169: q+1
       173: q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       183: q+1
       185: q+1
       187: q+1
       189: q+1
       191: q+1
       193: q+1
       195: q+1
       197: q+1
       199: q+1
       201: q+1
       203: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q^2+q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: 2q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: 2q^2+q+1
       234: q^2+q+1
       235: q^2+q+1
       236: 2q^2+q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: 2q^2+q+1
       259: q+1
       263: q+1
       267: q+1
       271: q+1
       275: q+1
       279: q+1
       281: q^2+q+1
       283: q+1
       285: q+1
       287: q+1
       289: q+1
       291: q+1
       293: 1
       295: 1
       297: 1
       299: q+1
       301: q+1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: q+1
       313: q+1
       315: q^2+q+1
       317: q+1
       319: q+1
       321: q+1
       323: q+1
       325: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: q+1
       367: q+1
       368: 2q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: 1
       377: q+1
       381: q+1
       385: 1
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       413: q+1
       417: q+1
       419: 1
       421: 1
       423: 1
       425: q+1
       427: q+1
       429: q+1
       431: q+1
       433: q+1
       435: q+1
       437: 1
       439: 1
       441: 1
       443: q+1
       445: 2q+1
       447: q+1
       449: q+1
       451: q+1
       453: 1
       455: q+1
       457: 1
       459: 1
       461: q+1
       463: 2q+1
       465: q+1
       467: q^2+q+1
       469: q+1
       471: q+1
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       521: q+1
       529: 1
       533: q+1
       537: q+1
       541: 1
       545: q+1
       549: q+1
       553: q+1
       557: 1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       580: q
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: 1
       601: q+1
       603: 1
       605: q+1
       607: 1
       609: 1
       613: q+1
       615: q+1
       617: 2q+1
       619: 1
       621: 1
       623: q+1
       625: 1
       629: q+1
       631: q+1
       633: 2q+1
       639: q+1
       641: q+1
       643: q+1
       645: q+1
       647: 1
       649: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: q+1
       725: 1
       733: q+1
       737: q+1
       741: 1
       749: q+1
       753: q+1
       757: q+1
       761: 1
       765: q+1
       769: q+1
       772: q
       775: q+1
       779: q+1
       781: 1
       785: 1
       787: 1
       791: 1
       793: q+1
       795: 2q+1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: q+1
       811: 1
       817: q+1
       819: 2q+1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: q+1
       835: 1
       843: q+1
       844: q
       845: 1
       847: 1
       849: q+1
       851: 1
       855: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: q+1
       920: 1
       924: 1
       928: 1
       940: q+1
       944: 1
       948: 1
       952: 1
       960: q+1
       964: q+1
       968: q+1
       971: q
       974: 1
       994: 1
       998: 1
      1000: 1
      1010: 1
      1012: 1
      1020: q+1
      1022: 1
      1026: 1
      1028: 1
      1036: q+1
      1038: 1
      1040: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: q+1
      1062: 1
      1064: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1086: q+1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1138: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1202: 1
      1206: 1
      1230: 1
      1232: 1
      1234: 1
      1248: 1
      1250: 1
      1254: 1
      1266: 1
      1268: 1
      1270: 1
      1274: q+1
      1278: 1
      1280: 1
      1287: 1
      1290: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1464: 1
      1466: 1
      1468: 1
      1501: 1
      1513: 1
      1607: 1
      1615: 1
      1619: 1
      1623: 1
      1711: 1

1712:    0: 9q^3+6q^2+3q
         1: 3q^4+9q^3+6q^2+3q
         2: 9q^3+6q^2+3q
         3: 3q^4+9q^3+6q^2+3q
         4: 3q^4+7q^3+5q^2+3q
         5: 9q^3+6q^2+3q
         6: q^5+5q^4+7q^3+5q^2+3q
         7: 3q^4+7q^3+5q^2+3q
         8: 9q^3+6q^2+3q
         9: q^5+3q^4+5q^3+4q^2+2q
        10: q^3+5q^2+3q
        11: q^3+5q^2+3q
        12: 2q^3+4q^2+3q
        13: 9q^3+6q^2+3q
        14: 3q^4+7q^3+5q^2+3q
        15: 9q^3+6q^2+3q
        16: 7q^3+5q^2+3q
        17: 7q^3+5q^2+3q
        18: 2q^4+4q^3+4q^2+2q
        19: 6q^3+5q^2+3q
        20: 2q^4+6q^3+5q^2+3q
        21: 6q^3+5q^2+3q
        22: 9q^3+6q^2+3q
        23: 3q^4+9q^3+6q^2+3q
        24: 9q^3+6q^2+3q
        25: 9q^3+6q^2+3q
        26: 3q^4+9q^3+6q^2+3q
        27: 9q^3+6q^2+3q
        28: 4q^2+3q
        29: q^3+4q^2+3q
        30: 6q^3+5q^2+3q
        31: q^3+5q^2+3q
        32: 9q^3+6q^2+3q
        33: 7q^3+5q^2+3q
        34: q^3+5q^2+3q
        35: 9q^3+6q^2+3q
        36: 7q^3+5q^2+3q
        37: 4q^3+2q^2+q
        38: 5q^3+4q^2+2q
        39: q^4+4q^3+2q^2+q
        40: 2q^4+5q^3+4q^2+2q
        41: 4q^3+2q^2+q
        42: 5q^3+4q^2+2q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 7q^3+5q^2+3q
        47: 7q^3+5q^2+3q
        48: 2q^4+4q^3+4q^2+2q
        49: 4q^3+4q^2+3q
        50: 4q^3+4q^2+3q
        51: 3q^3+4q^2+2q
        52: 6q^3+5q^2+3q
        53: 2q^4+6q^3+5q^2+3q
        54: 6q^3+5q^2+3q
        55: 6q^3+5q^2+3q
        56: 2q^4+6q^3+5q^2+3q
        57: 6q^3+5q^2+3q
        58: 3q^2+2q
        59: q^2+q
        60: 3q^2+2q
        61: q^2+q
        62: 2q^2+q
        63: q^3+3q^2+2q
        64: 4q^3+2q^2+q
        65: 5q^3+4q^2+2q
        66: 3q^3+2q^2+q
        67: 4q^3+3q^2+2q
        68: 4q^2+3q
        69: 2q^3+3q^2+2q
        70: q^3+4q^2+3q
        71: 3q^2+3q
        72: 2q^3+3q^2+3q
        73: 2q^3+3q^2+3q
        74: q^3+q^2+q
        75: 2q^3+3q^2+2q
        76: q^3+q^2+q
        77: q^4+2q^3+3q^2+2q
        78: q^3+q^2+q
        79: 2q^3+3q^2+2q
        80: q^3+5q^2+3q
        81: 7q^3+5q^2+3q
        82: q^3+4q^2+3q
        83: 6q^3+5q^2+3q
        84: q^3+5q^2+3q
        85: 7q^3+5q^2+3q
        86: q^3+4q^2+3q
        87: 6q^3+5q^2+3q
        88: 3q^2+3q
        89: 3q^2+3q
        90: q^3+3q^2+2q
        91: 4q^3+4q^2+3q
        92: 4q^3+4q^2+3q
        93: 3q^3+4q^2+2q
        94: 4q^3+4q^2+3q
        95: 4q^3+4q^2+3q
        96: 3q^3+4q^2+2q
        97: 4q^3+4q^2+3q
        98: 4q^3+4q^2+3q
        99: 3q^3+4q^2+2q
       100: 6q^3+5q^2+3q
       101: 2q^4+6q^3+5q^2+3q
       102: 6q^3+5q^2+3q
       103: 2q^2+q
       104: q^2+q
       105: q^2+q
       107: 2q^2+2q
       108: q
       109: 2q^2+2q
       110: q
       111: q^2+q
       112: q^2+2q
       113: q^2+q
       114: q^3+2q^2+2q
       115: q^3+q^2+q
       116: 2q^3+3q^2+2q
       117: 3q^2+2q
       118: q^2+q
       119: 3q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: q^3+3q^2+2q
       123: 3q^3+2q^2+q
       124: 4q^3+3q^2+2q
       125: 3q^2+3q
       126: 2q^2+2q
       128: q^3+q^2+2q
       130: q^3+q^2+2q
       132: 2q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+3q
       136: 2q^3+3q^2+3q
       137: 3q^2+3q
       138: 2q^3+3q^2+2q
       139: 3q^2+3q
       140: 2q^3+3q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+3q^2+3q
       143: 3q^2+3q
       144: 2q^3+3q^2+2q
       145: 3q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+3q^2+3q
       148: 2q^3+3q^2+3q
       149: q^3+4q^2+3q
       150: 6q^3+5q^2+3q
       151: q^3+q^2+q
       152: 2q^3+3q^2+2q
       153: q^3+q^2+q
       154: q^4+2q^3+3q^2+2q
       155: q^3+q^2+q
       156: 2q^3+3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 4q^3+4q^2+3q
       161: 4q^3+4q^2+3q
       162: 3q^3+4q^2+2q
       163: 4q^3+4q^2+3q
       164: 4q^3+4q^2+3q
       165: 3q^3+4q^2+2q
       166: 4q^3+4q^2+3q
       167: 4q^3+4q^2+3q
       168: 3q^3+4q^2+2q
       169: q^2+q
       170: q
       171: q
       173: 2q^2+q
       174: q^2+q
       175: q^2+q
       178: q^2+q
       180: q^2+2q
       182: 2q
       183: 2q^2+2q
       184: q
       185: 2q^2+2q
       186: q
       187: q^2+q
       188: q^2+2q
       189: q^2+q
       190: q^3+2q^2+2q
       191: 2q^2+2q
       192: q^2+q
       193: 2q^2+2q
       194: q
       195: 2q^2+2q
       196: q
       197: q^2+q
       198: q^2+2q
       199: 2q^2+2q
       200: q^2+q
       201: 2q^2+2q
       202: q
       203: 2q^2+2q
       204: q
       205: q^2+q
       206: q^2+2q
       207: q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: q^3+2q^2+2q
       211: q^3+q^2+q
       212: 2q^3+3q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 2q^2+2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^3+3q^2+2q
       229: 2q^3+3q^2+3q
       230: 2q^3+3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+3q
       235: 2q^3+3q^2+3q
       236: 2q^3+3q^2+2q
       238: q^3+q^2+2q
       240: q^3+q^2+2q
       242: 2q^2+q
       243: 3q^2+3q
       244: 2q^3+3q^2+3q
       245: 2q^3+3q^2+3q
       246: q^3+4q^2+3q
       247: 3q^2+4q
       248: 3q^2+4q
       249: q^3+3q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 4q^3+4q^2+3q
       257: 4q^3+4q^2+3q
       258: 3q^3+4q^2+2q
       260: q
       261: q
       263: q^2+q
       264: q
       265: q
       267: q^2+q
       268: q
       270: q
       271: q^2+q
       272: q
       274: q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       280: q^2+2q
       282: q^2+q
       283: q^2+q
       285: q^2+q
       288: q^2+q
       290: 2q
       292: q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: 2q
       299: 2q^2+2q
       300: q
       302: 2q
       303: 2q^2+2q
       304: q
       305: q^2+q
       306: q^2+2q
       307: 2q^2+2q
       308: q
       309: 2q^2+2q
       310: q
       312: 2q
       313: q^2+q
       314: q^2+2q
       316: q^2+q
       318: q^2+2q
       319: 2q^2+2q
       320: q
       321: 2q^2+2q
       322: q
       323: q^2+q
       324: q^2+2q
       325: q^2+q
       326: q^3+2q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+4q
       339: q^2+3q
       341: q^2+3q
       343: 2q^2+q
       344: 2q^2+2q
       345: 3q
       346: 2q
       347: 3q
       348: q^3+2q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 3q^2+4q
       352: 2q^2+2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^3+2q^2+2q
       359: 3q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 2q^2+2q
       367: 3q^2+3q
       368: 2q^3+3q^2+2q
       369: 2q^3+3q^2+3q
       370: 2q^3+3q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q
       392: q
       393: q^2+q
       394: q
       395: q
       398: q
       400: q
       401: q^2+q
       402: q
       403: q
       405: q^2+q
       407: q
       408: q
       414: q^2+q
       418: q
       419: q
       421: q
       424: q
       426: q
       428: 3q
       429: q^2+q
       431: q^2+q
       434: q
       436: 2q
       437: 2q
       438: q
       439: 2q
       440: q
       441: q
       442: 2q
       443: q^2+3q
       444: q
       446: q^2+3q
       447: q^2+q
       449: q^2+q
       452: q
       453: 2q
       454: q
       456: 2q
       457: 2q
       458: q
       459: q
       460: 2q
       461: q^2+3q
       462: q
       464: q^2+3q
       466: q^2+2q
       468: q^2+q
       470: q^2+q
       471: 2q^2+2q
       472: q
       473: 2q^2+2q
       474: q
       475: q^2+q
       476: q^2+2q
       478: 2q
       479: 2q^2+2q
       480: q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 3q^2+4q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 3q^2+4q
       508: 2q^2+2q
       509: 3q
       510: 2q
       511: 3q
       512: q^3+2q^2+2q
       513: 3q
       514: q^3+2q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       538: q
       540: q
       541: q
       542: q
       544: q
       546: 2q
       548: q
       554: q
       556: q
       557: q
       558: q
       560: q
       562: 2q
       564: q
       565: q^2+q
       566: q
       567: q
       571: q
       572: q
       573: q^2+2q
       574: q
       576: q
       578: q^2+q
       581: 2q
       586: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: 3q
       603: q
       606: q
       607: q
       610: q
       614: q
       615: q^2+3q
       616: q
       618: q^2+3q
       619: q
       621: q
       624: q
       626: q
       630: q
       631: q^2+3q
       632: q
       634: q^2+3q
       640: q^2+q
       641: q^2+q
       643: q^2+q
       646: q
       647: 2q
       648: q
       649: 2q
       650: q
       652: 2q
       653: q
       654: 2q
       655: 2q^2+2q
       656: q^2+2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       674: 2q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 2q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       694: q
       699: q
       700: q
       734: 2q
       736: q
       750: 2q
       752: q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q^2+2q
       766: q
       767: q
       770: q^2+q
       773: 2q
       776: q+1
       780: q+1
       782: q
       785: q
       787: q
       793: q+1
       796: 2q+1
       798: q
       801: q
       803: q
       805: q
       807: q
       810: q
       812: q
       817: q+1
       820: 2q+1
       822: q
       825: q
       827: q
       829: q
       831: q
       834: q
       836: q
       843: q+1
       844: q
       845: q
       847: q
       850: q
       852: q
       856: q
       866: 1
       870: q+1
       871: 2q
       874: q+1
       875: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       885: q
       890: q
       891: q
       917: q+1
       941: q+1
       964: q+1
       969: q+1
       972: q
       995: 1
       998: 1
      1000: 1
      1012: 1
      1021: q+1
      1023: q
      1026: q
      1028: q
      1037: q+1
      1039: q
      1040: q
      1044: q
      1049: q
      1052: q
      1054: q
      1056: q
      1058: q
      1061: q
      1063: q
      1076: 1
      1080: 1
      1083: 2q
      1084: q+1
      1087: q+1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1231: 1
      1232: 1
      1234: 1
      1249: 1
      1250: 1
      1254: 1
      1267: q
      1268: q
      1270: q
      1275: q+1
      1280: 1
      1287: 1
      1291: 1
      1349: 1
      1357: 1
      1364: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1465: 1
      1466: 1
      1468: 1
      1502: 1
      1514: 1
      1608: 1
      1616: 1
      1623: 1
      1712: 1

1713:    0: 3q^4+9q^3+q^2+q
         1: 3q^4+9q^3+q^2+q
         2: 3q^4+6q^3+q^2+q
         3: 3q^4+9q^3+q^2+q
         4: 4q^4+5q^3+q^2+q
         5: 3q^4+9q^3+q^2+q
         6: 2q^5+5q^4+5q^3+q^2+q
         7: 2q^5+4q^4+4q^3+q^2+q
         8: 3q^4+6q^3+q^2+q
         9: 2q^5+4q^4+4q^3+q^2+q
        10: q^4+6q^3+q^2+q
        11: q^4+6q^3+q^2+q
        12: 3q^4+3q^3+q^2+q
        13: q^4+6q^3+q^2+q
        14: 3q^4+4q^3+q^2+q
        15: q^4+6q^3+q^2+q
        16: 3q^4+9q^3+q^2+q
        17: 3q^4+9q^3+q^2+q
        18: 2q^5+4q^4+4q^3+q^2+q
        19: 5q^3+q^2+q
        20: q^4+5q^3+q^2+q
        21: q^4+4q^3+q^2+q
        22: 3q^4+9q^3+q^2+q
        23: 3q^4+9q^3+q^2+q
        24: 3q^4+6q^3+q^2+q
        25: 3q^4+9q^3+q^2+q
        26: 3q^4+9q^3+q^2+q
        27: 3q^4+6q^3+q^2+q
        28: q^4+6q^3+q^2+q
        29: 3q^3+q^2+q
        30: 4q^3+q^2+q
        31: q^4+6q^3+q^2+q
        32: q^4+6q^3+q^2+q
        33: 3q^4+9q^3+q^2+q
        34: q^4+6q^3+q^2+q
        35: q^4+6q^3+q^2+q
        36: 3q^4+9q^3+q^2+q
        37: 2q^4+6q^3+q^2+q
        38: q^4+3q^3
        39: 2q^4+6q^3+q^2+q
        40: q^4+3q^3
        41: 2q^4+4q^3+q^2+q
        42: q^4+2q^3
        43: 3q^3+q^2+q
        44: 2q^4+2q^3+q^2+q
        45: 3q^3+q^2+q
        46: q^4+6q^3+q^2+q
        47: q^4+6q^3+q^2+q
        48: 3q^4+4q^3+q^2+q
        49: 5q^3+q^2+q
        50: q^4+5q^3+q^2+q
        51: q^4+4q^3+q^2+q
        52: 5q^3+q^2+q
        53: q^4+5q^3+q^2+q
        54: q^4+4q^3+q^2+q
        55: 5q^3+q^2+q
        56: q^4+5q^3+q^2+q
        57: q^4+4q^3+q^2+q
        58: q^4+4q^3+q^2+q
        59: 2q^3
        60: q^4+4q^3+q^2+q
        61: 2q^3
        62: q^4+4q^3+q^2+q
        63: 2q^3
        64: q^4+4q^3+q^2+q
        65: 2q^3
        66: 2q^4+6q^3+q^2+q
        67: q^4+3q^3
        68: q^3+q^2+q
        69: 4q^3+q^2+q
        70: 2q^3+q^2+q
        71: 3q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        74: 2q^3+q^2+q
        76: 2q^3+q^2+q
        78: 2q^3+q^2+q
        80: 3q^3+q^2+q
        81: q^4+6q^3+q^2+q
        82: 3q^3+q^2+q
        83: 4q^3+q^2+q
        84: 3q^3+q^2+q
        85: q^4+6q^3+q^2+q
        86: 3q^3+q^2+q
        87: 4q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: 2q^4+2q^3+q^2+q
        91: 3q^3+q^2+q
        92: 2q^3+q^2+q
        93: 3q^3+q^2+q
        94: 5q^3+q^2+q
        95: q^4+5q^3+q^2+q
        96: q^4+4q^3+q^2+q
        97: 5q^3+q^2+q
        98: q^4+5q^3+q^2+q
        99: q^4+4q^3+q^2+q
       100: 5q^3+q^2+q
       101: q^4+5q^3+q^2+q
       102: q^4+4q^3+q^2+q
       103: q^4+3q^3+q^2+q
       104: q^3
       105: q^3
       106: q^3
       107: q^3+q^2+q
       109: q^3+q^2+q
       111: q^2+q
       113: q^3+q^2+q
       115: 2q^3+q^2+q
       117: q^3+q^2+q
       119: q^3+q^2+q
       121: 2q^3+q^2+q
       122: q^3
       123: q^4+4q^3+q^2+q
       124: 2q^3
       125: q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: 2q^3+q^2+q
       133: q^2+q
       134: 3q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: 3q^3+q^2+q
       138: 4q^3+q^2+q
       139: 3q^3+q^2+q
       140: 2q^3+q^2+q
       141: 2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: 4q^3+q^2+q
       145: 3q^3+q^2+q
       146: 2q^3+q^2+q
       147: 2q^3+q^2+q
       148: 2q^3+q^2+q
       149: 3q^3+q^2+q
       150: 4q^3+q^2+q
       151: 2q^3+q^2+q
       153: 2q^3+q^2+q
       155: 2q^3+q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 3q^3+q^2+q
       161: 2q^3+q^2+q
       162: 3q^3+q^2+q
       163: 3q^3+q^2+q
       164: 2q^3+q^2+q
       165: 3q^3+q^2+q
       166: 5q^3+q^2+q
       167: q^4+5q^3+q^2+q
       168: q^4+4q^3+q^2+q
       169: q^2+q
       173: q^3+q^2+q
       177: 2q^3+q^2+q
       179: q^3+q^2+q
       181: q^2+q
       183: q^2+q
       185: q^2+q
       187: q^2+q
       189: q^3+q^2+q
       191: q^3+q^2+q
       193: q^3+q^2+q
       195: q^3+q^2+q
       197: q^2+q
       199: q^3+q^2+q
       201: q^3+q^2+q
       203: q^3+q^2+q
       205: q^2+q
       207: 2q^3+q^2+q
       208: q^3
       209: q^3+q^2+q
       211: 2q^3+q^2+q
       213: q^3+q
       215: q
       217: q^3+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+q^2+q
       224: q
       225: q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^2+q
       228: 3q^3+q^2+q
       229: q^3+q^2+q
       230: q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^2+q
       233: 3q^3+q^2+q
       234: q^3+q^2+q
       235: q^3+q^2+q
       236: 4q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: 2q^3+q^2+q
       243: 3q^3+q^2+q
       244: 2q^3+q^2+q
       245: 2q^3+q^2+q
       246: 2q^3+q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^2+q
       263: q^2+q
       267: q^2+q
       271: q^2+q
       275: q^3+q^2+q
       279: q
       281: q^3+q
       283: q^2+q
       285: q^2+q
       287: q^3+q^2+q
       289: q
       291: q^2+q
       293: q
       295: q
       297: q
       299: q^2+q
       301: q^2+q
       303: q^2+q
       305: q^2+q
       307: q^2+q
       309: q^2+q
       311: q^2+q
       313: q^2+q
       315: 2q^3+q^2+q
       317: q^3+q^2+q
       319: q^3+q^2+q
       321: q^3+q^2+q
       323: q^2+q
       325: q^3+q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: q^3+q^2+q
       349: q
       350: q^3+q^2+q
       351: 2q^2+q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+q^2+q
       357: q
       358: q^3+q^2+q
       359: 2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       377: q^2+q
       381: q
       385: q
       389: q^2+q
       393: q^2+q
       397: q^2+q
       401: q^2+q
       405: q^2+q
       413: q
       417: q
       419: q
       421: q
       423: q
       425: q^2+q
       427: q^2+q
       429: q^2+q
       431: q^2+q
       433: q^2+q
       435: q
       437: q
       439: q
       441: q
       443: q^2+q
       445: 2q^2+q
       447: q^2+q
       449: q^2+q
       451: q^2+q
       453: q
       455: q
       457: q
       459: q
       461: q^2+q
       463: 2q^2+q
       465: q
       467: q^3+q
       469: q^3+q^2+q
       471: q^2+q
       473: q^2+q
       475: q^2+q
       477: q^2+q
       479: q^2+q
       480: q^2
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       521: q
       529: q
       533: q^2+q
       537: q
       541: q
       545: q^2+q
       549: q^2+q
       553: q
       557: q
       561: q^2+q
       565: q^2+q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       580: q^2
       585: q
       589: q
       591: q
       593: q
       595: q
       599: q
       603: q
       605: q
       607: q
       609: q
       613: q^2+q
       619: q
       621: q
       623: q
       625: q
       629: q^2+q
       639: q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q
       649: q
       651: q
       653: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q^2+q
       693: q^2+q
       709: q
       713: q
       717: q
       721: q
       725: q
       737: q
       741: q
       753: q^2+q
       757: q
       761: q
       797: q
       801: q
       803: q
       805: q
       807: q
       811: q
       821: q
       825: q
       827: q
       829: q
       831: q
       835: q
       845: q
       847: q
       849: q
       851: q
       855: q^2+q
       877: q
       878: q
       879: q
       920: q
       924: q
       928: q
       944: q
       948: q
       952: q
       960: q
       974: q
      1010: 1
      1048: q
      1052: q
      1054: q
      1056: q
      1058: q
      1062: q
      1126: 1
      1140: 1
      1198: q
      1202: q
      1206: q
      1278: 1
      1292: 1
      1360: 1
      1392: 1
      1432: 1
      1503: 1
      1515: 1
      1619: 1
      1713: 1

1714:    0: 9q^3+6q^2+3q
         1: 3q^4+9q^3+6q^2+3q
         2: 9q^3+6q^2+3q
         3: 3q^4+9q^3+6q^2+3q
         4: 3q^4+7q^3+5q^2+3q
         5: 9q^3+6q^2+3q
         6: q^5+5q^4+7q^3+5q^2+3q
         7: 3q^4+7q^3+5q^2+3q
         8: 9q^3+6q^2+3q
         9: q^5+3q^4+5q^3+4q^2+2q
        10: q^3+5q^2+3q
        11: q^3+5q^2+3q
        12: 2q^3+4q^2+3q
        13: 9q^3+6q^2+3q
        14: 3q^4+7q^3+5q^2+3q
        15: 9q^3+6q^2+3q
        16: 7q^3+5q^2+3q
        17: 7q^3+5q^2+3q
        18: 2q^4+4q^3+4q^2+2q
        19: 6q^3+5q^2+3q
        20: 2q^4+6q^3+5q^2+3q
        21: 6q^3+5q^2+3q
        22: 9q^3+6q^2+3q
        23: 3q^4+9q^3+6q^2+3q
        24: 9q^3+6q^2+3q
        25: 9q^3+6q^2+3q
        26: 3q^4+9q^3+6q^2+3q
        27: 9q^3+6q^2+3q
        28: 4q^2+3q
        29: q^3+4q^2+3q
        30: 6q^3+5q^2+3q
        31: q^3+5q^2+3q
        32: 9q^3+6q^2+3q
        33: 7q^3+5q^2+3q
        34: q^3+5q^2+3q
        35: 9q^3+6q^2+3q
        36: 7q^3+5q^2+3q
        37: 5q^3+4q^2+2q
        38: 4q^3+2q^2+q
        39: 2q^4+5q^3+4q^2+2q
        40: q^4+4q^3+2q^2+q
        41: 5q^3+4q^2+2q
        42: 4q^3+2q^2+q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 7q^3+5q^2+3q
        47: 7q^3+5q^2+3q
        48: 2q^4+4q^3+4q^2+2q
        49: 4q^3+4q^2+3q
        50: 4q^3+4q^2+3q
        51: 3q^3+4q^2+2q
        52: 6q^3+5q^2+3q
        53: 2q^4+6q^3+5q^2+3q
        54: 6q^3+5q^2+3q
        55: 6q^3+5q^2+3q
        56: 2q^4+6q^3+5q^2+3q
        57: 6q^3+5q^2+3q
        58: q^2+q
        59: 3q^2+2q
        60: 3q^2+2q
        61: q^2+q
        62: q^3+3q^2+2q
        63: 2q^2+q
        64: 5q^3+4q^2+2q
        65: 4q^3+2q^2+q
        66: 4q^3+3q^2+2q
        67: 3q^3+2q^2+q
        68: 4q^2+3q
        69: 2q^3+3q^2+2q
        70: q^3+4q^2+3q
        71: 3q^2+3q
        72: 2q^3+3q^2+3q
        73: 2q^3+3q^2+3q
        74: 2q^3+3q^2+2q
        75: q^3+q^2+q
        76: q^4+2q^3+3q^2+2q
        77: q^3+q^2+q
        78: 2q^3+3q^2+2q
        79: q^3+q^2+q
        80: q^3+5q^2+3q
        81: 7q^3+5q^2+3q
        82: q^3+4q^2+3q
        83: 6q^3+5q^2+3q
        84: q^3+5q^2+3q
        85: 7q^3+5q^2+3q
        86: q^3+4q^2+3q
        87: 6q^3+5q^2+3q
        88: 3q^2+3q
        89: 3q^2+3q
        90: q^3+3q^2+2q
        91: 4q^3+4q^2+3q
        92: 4q^3+4q^2+3q
        93: 3q^3+4q^2+2q
        94: 4q^3+4q^2+3q
        95: 4q^3+4q^2+3q
        96: 3q^3+4q^2+2q
        97: 4q^3+4q^2+3q
        98: 4q^3+4q^2+3q
        99: 3q^3+4q^2+2q
       100: 6q^3+5q^2+3q
       101: 2q^4+6q^3+5q^2+3q
       102: 6q^3+5q^2+3q
       103: q^2+q
       104: 2q^2+q
       106: q^2+q
       107: 2q^2+2q
       108: q
       109: q
       110: 2q^2+2q
       111: q^2+2q
       112: q^2+q
       113: q^3+2q^2+2q
       114: q^2+q
       115: 2q^3+3q^2+2q
       116: q^3+q^2+q
       117: q^2+q
       118: 3q^2+2q
       119: 3q^2+2q
       120: q^2+q
       121: q^3+3q^2+2q
       122: 2q^2+q
       123: 4q^3+3q^2+2q
       124: 3q^3+2q^2+q
       125: 3q^2+3q
       126: 2q^2+2q
       127: q^3+q^2+2q
       129: q^3+q^2+2q
       131: 2q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+3q
       136: 2q^3+3q^2+3q
       137: 3q^2+3q
       138: 2q^3+3q^2+2q
       139: 3q^2+3q
       140: 2q^3+3q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+3q^2+3q
       143: 3q^2+3q
       144: 2q^3+3q^2+2q
       145: 3q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+3q^2+3q
       148: 2q^3+3q^2+3q
       149: q^3+4q^2+3q
       150: 6q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: q^3+q^2+q
       153: q^4+2q^3+3q^2+2q
       154: q^3+q^2+q
       155: 2q^3+3q^2+2q
       156: q^3+q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 4q^3+4q^2+3q
       161: 4q^3+4q^2+3q
       162: 3q^3+4q^2+2q
       163: 4q^3+4q^2+3q
       164: 4q^3+4q^2+3q
       165: 3q^3+4q^2+2q
       166: 4q^3+4q^2+3q
       167: 4q^3+4q^2+3q
       168: 3q^3+4q^2+2q
       169: q
       170: q^2+q
       172: q
       173: q^2+q
       174: 2q^2+q
       176: q^2+q
       177: q^2+q
       179: q^2+2q
       181: 2q
       183: 2q^2+2q
       184: q
       185: q
       186: 2q^2+2q
       187: q^2+2q
       188: q^2+q
       189: q^3+2q^2+2q
       190: q^2+q
       191: q^2+q
       192: 2q^2+2q
       193: 2q^2+2q
       194: q
       195: q
       196: 2q^2+2q
       197: q^2+2q
       198: q^2+q
       199: 2q^2+2q
       200: q^2+q
       201: 2q^2+2q
       202: q
       203: q
       204: 2q^2+2q
       205: q^2+2q
       206: q^2+q
       207: 2q^2+2q
       208: q^2+q
       209: q^3+2q^2+2q
       210: q^2+q
       211: 2q^3+3q^2+2q
       212: q^3+q^2+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 2q^2+2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^3+3q^2+2q
       229: 2q^3+3q^2+3q
       230: 2q^3+3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+3q
       235: 2q^3+3q^2+3q
       236: 2q^3+3q^2+2q
       237: q^3+q^2+2q
       239: q^3+q^2+2q
       241: 2q^2+q
       243: 3q^2+3q
       244: 2q^3+3q^2+3q
       245: 2q^3+3q^2+3q
       246: q^3+4q^2+3q
       247: 3q^2+4q
       248: 3q^2+4q
       249: q^3+3q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 4q^3+4q^2+3q
       257: 4q^3+4q^2+3q
       258: 3q^3+4q^2+2q
       259: q
       262: q
       263: q
       264: q^2+q
       266: q
       267: q
       268: q^2+q
       269: q
       271: q
       273: q
       274: q^2+q
       275: q^2+q
       276: q^2+q
       278: q^2+q
       279: q^2+2q
       281: q^2+q
       283: q^2+q
       286: q^2+q
       287: q^2+q
       289: 2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: 2q^2+2q
       300: q
       301: 2q
       303: q
       304: 2q^2+2q
       305: q^2+2q
       306: q^2+q
       307: 2q^2+2q
       308: q
       309: q
       310: 2q^2+2q
       311: 2q
       313: q^2+2q
       314: q^2+q
       315: q^2+q
       317: q^2+2q
       319: 2q^2+2q
       320: q
       321: q
       322: 2q^2+2q
       323: q^2+2q
       324: q^2+q
       325: q^3+2q^2+2q
       326: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+4q
       338: q^2+3q
       340: q^2+3q
       342: 2q^2+q
       344: 2q^2+2q
       345: 3q
       346: 2q
       347: 3q
       348: q^3+2q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 3q^2+4q
       352: 2q^2+2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^3+2q^2+2q
       359: 3q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 2q^2+2q
       367: 3q^2+3q
       368: 2q^3+3q^2+2q
       369: 2q^3+3q^2+3q
       370: 2q^3+3q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       391: q
       393: q
       394: q^2+q
       396: q
       397: q
       399: q
       401: q
       403: q^2+q
       404: q
       405: q
       406: q
       407: q^2+q
       413: q^2+q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 3q
       429: q^2+q
       432: q^2+q
       433: q
       435: 2q
       437: 2q
       438: q
       439: q
       440: 2q
       441: 2q
       442: q
       443: q^2+3q
       444: q
       445: q^2+3q
       447: q^2+q
       450: q^2+q
       451: q
       453: 2q
       454: q
       455: 2q
       457: q
       458: 2q
       459: 2q
       460: q
       461: q
       462: q^2+3q
       463: q^2+3q
       465: q^2+2q
       467: q^2+q
       469: q^2+q
       471: 2q^2+2q
       472: q
       473: q
       474: 2q^2+2q
       475: q^2+2q
       476: q^2+q
       477: 2q
       479: q^2+2q
       480: 2q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 3q^2+4q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 3q^2+4q
       508: 2q^2+2q
       509: 3q
       510: 2q
       511: 3q
       512: q^3+2q^2+2q
       513: 3q
       514: q^3+2q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       537: q
       539: q
       541: q
       542: q
       543: q
       545: 2q
       547: q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q
       563: 2q
       565: q
       566: q^2+q
       568: q
       569: q
       570: q
       573: q
       574: q^2+2q
       575: q
       577: 2q
       580: q^2+q
       585: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 3q
       603: q
       605: q
       608: q
       609: q
       613: q
       615: q^2+3q
       616: q
       617: q^2+3q
       619: q
       622: q
       623: q
       625: q
       629: q
       631: q
       632: q^2+3q
       633: q^2+3q
       639: q^2+q
       641: q^2+q
       644: q^2+q
       645: q
       647: 2q
       648: q
       649: q
       650: 2q
       651: 2q
       653: 2q
       654: q
       655: q^2+2q
       656: 2q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       674: 2q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 2q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       693: q
       696: q
       697: q
       733: 2q
       735: q
       749: q
       751: 2q
       757: q
       758: q
       761: q
       762: q
       763: q
       765: q
       766: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       779: q+1
       781: q
       785: q
       788: q
       793: q+1
       795: 2q+1
       797: q
       801: q
       804: q
       805: q
       808: q
       809: q
       811: q
       818: q+1
       819: 2q+1
       821: q
       825: q
       828: q
       829: q
       832: q
       833: q
       835: q
       843: q
       844: q+1
       845: q
       848: q
       849: q
       851: q
       855: q
       866: 1
       870: q+1
       871: 2q
       874: q+1
       875: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       884: q
       887: q
       889: q
       916: q+1
       942: q+1
       965: q+1
       968: q
       971: q+1
       994: 1
       999: 1
      1000: 1
      1013: 1
      1020: q+1
      1022: q
      1026: q
      1029: q
      1036: q+1
      1038: q
      1040: q
      1045: q
      1048: q
      1052: q
      1055: q
      1056: q
      1059: q
      1060: q
      1062: q
      1076: 1
      1080: 1
      1083: 2q
      1084: q+1
      1089: q+1
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1230: 1
      1233: 1
      1234: 1
      1248: 1
      1251: 1
      1254: 1
      1266: q
      1268: q
      1271: q
      1274: q+1
      1281: 1
      1287: 1
      1293: 1
      1350: 1
      1356: 1
      1366: 1
      1382: 1
      1388: 1
      1397: 1
      1433: 1
      1464: 1
      1467: 1
      1468: 1
      1505: 1
      1516: 1
      1609: 1
      1615: 1
      1624: 1
      1714: 1

1715:    0: 9q^3+6q^2+3q
         1: 3q^4+9q^3+6q^2+3q
         2: 9q^3+6q^2+3q
         3: 3q^4+9q^3+6q^2+3q
         4: 3q^4+7q^3+5q^2+3q
         5: 9q^3+6q^2+3q
         6: q^5+5q^4+7q^3+5q^2+3q
         7: 3q^4+7q^3+5q^2+3q
         8: 9q^3+6q^2+3q
         9: q^5+3q^4+5q^3+4q^2+2q
        10: q^3+5q^2+3q
        11: q^3+5q^2+3q
        12: 2q^3+4q^2+3q
        13: 9q^3+6q^2+3q
        14: 3q^4+7q^3+5q^2+3q
        15: 9q^3+6q^2+3q
        16: 7q^3+5q^2+3q
        17: 7q^3+5q^2+3q
        18: 2q^4+4q^3+4q^2+2q
        19: 6q^3+5q^2+3q
        20: 2q^4+6q^3+5q^2+3q
        21: 6q^3+5q^2+3q
        22: 9q^3+6q^2+3q
        23: 3q^4+9q^3+6q^2+3q
        24: 9q^3+6q^2+3q
        25: 9q^3+6q^2+3q
        26: 3q^4+9q^3+6q^2+3q
        27: 9q^3+6q^2+3q
        28: 4q^2+3q
        29: q^3+4q^2+3q
        30: 6q^3+5q^2+3q
        31: q^3+5q^2+3q
        32: 9q^3+6q^2+3q
        33: 7q^3+5q^2+3q
        34: q^3+5q^2+3q
        35: 9q^3+6q^2+3q
        36: 7q^3+5q^2+3q
        37: 5q^3+4q^2+2q
        38: 4q^3+2q^2+q
        39: 2q^4+5q^3+4q^2+2q
        40: q^4+4q^3+2q^2+q
        41: 5q^3+4q^2+2q
        42: 4q^3+2q^2+q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 7q^3+5q^2+3q
        47: 7q^3+5q^2+3q
        48: 2q^4+4q^3+4q^2+2q
        49: 4q^3+4q^2+3q
        50: 4q^3+4q^2+3q
        51: 3q^3+4q^2+2q
        52: 6q^3+5q^2+3q
        53: 2q^4+6q^3+5q^2+3q
        54: 6q^3+5q^2+3q
        55: 6q^3+5q^2+3q
        56: 2q^4+6q^3+5q^2+3q
        57: 6q^3+5q^2+3q
        58: 3q^2+2q
        59: q^2+q
        60: q^2+q
        61: 3q^2+2q
        62: q^3+3q^2+2q
        63: 2q^2+q
        64: 5q^3+4q^2+2q
        65: 4q^3+2q^2+q
        66: 4q^3+3q^2+2q
        67: 3q^3+2q^2+q
        68: 4q^2+3q
        69: 2q^3+3q^2+2q
        70: q^3+4q^2+3q
        71: 3q^2+3q
        72: 2q^3+3q^2+3q
        73: 2q^3+3q^2+3q
        74: 2q^3+3q^2+2q
        75: q^3+q^2+q
        76: q^4+2q^3+3q^2+2q
        77: q^3+q^2+q
        78: 2q^3+3q^2+2q
        79: q^3+q^2+q
        80: q^3+5q^2+3q
        81: 7q^3+5q^2+3q
        82: q^3+4q^2+3q
        83: 6q^3+5q^2+3q
        84: q^3+5q^2+3q
        85: 7q^3+5q^2+3q
        86: q^3+4q^2+3q
        87: 6q^3+5q^2+3q
        88: 3q^2+3q
        89: 3q^2+3q
        90: q^3+3q^2+2q
        91: 4q^3+4q^2+3q
        92: 4q^3+4q^2+3q
        93: 3q^3+4q^2+2q
        94: 4q^3+4q^2+3q
        95: 4q^3+4q^2+3q
        96: 3q^3+4q^2+2q
        97: 4q^3+4q^2+3q
        98: 4q^3+4q^2+3q
        99: 3q^3+4q^2+2q
       100: 6q^3+5q^2+3q
       101: 2q^4+6q^3+5q^2+3q
       102: 6q^3+5q^2+3q
       103: q^2+q
       105: 2q^2+q
       106: q^2+q
       107: q
       108: 2q^2+2q
       109: 2q^2+2q
       110: q
       111: q^2+2q
       112: q^2+q
       113: q^3+2q^2+2q
       114: q^2+q
       115: 2q^3+3q^2+2q
       116: q^3+q^2+q
       117: 3q^2+2q
       118: q^2+q
       119: q^2+q
       120: 3q^2+2q
       121: q^3+3q^2+2q
       122: 2q^2+q
       123: 4q^3+3q^2+2q
       124: 3q^3+2q^2+q
       125: 3q^2+3q
       126: 2q^2+2q
       127: q^3+q^2+2q
       129: q^3+q^2+2q
       131: 2q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+3q
       136: 2q^3+3q^2+3q
       137: 3q^2+3q
       138: 2q^3+3q^2+2q
       139: 3q^2+3q
       140: 2q^3+3q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+3q^2+3q
       143: 3q^2+3q
       144: 2q^3+3q^2+2q
       145: 3q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+3q^2+3q
       148: 2q^3+3q^2+3q
       149: q^3+4q^2+3q
       150: 6q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: q^3+q^2+q
       153: q^4+2q^3+3q^2+2q
       154: q^3+q^2+q
       155: 2q^3+3q^2+2q
       156: q^3+q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 4q^3+4q^2+3q
       161: 4q^3+4q^2+3q
       162: 3q^3+4q^2+2q
       163: 4q^3+4q^2+3q
       164: 4q^3+4q^2+3q
       165: 3q^3+4q^2+2q
       166: 4q^3+4q^2+3q
       167: 4q^3+4q^2+3q
       168: 3q^3+4q^2+2q
       169: q
       171: q^2+q
       172: q
       173: q^2+q
       175: 2q^2+q
       176: q^2+q
       177: q^2+q
       179: q^2+2q
       181: 2q
       183: q
       184: 2q^2+2q
       185: 2q^2+2q
       186: q
       187: q^2+2q
       188: q^2+q
       189: q^3+2q^2+2q
       190: q^2+q
       191: 2q^2+2q
       192: q^2+q
       193: q
       194: 2q^2+2q
       195: 2q^2+2q
       196: q
       197: q^2+2q
       198: q^2+q
       199: q^2+q
       200: 2q^2+2q
       201: q
       202: 2q^2+2q
       203: 2q^2+2q
       204: q
       205: q^2+2q
       206: q^2+q
       207: 2q^2+2q
       208: q^2+q
       209: q^3+2q^2+2q
       210: q^2+q
       211: 2q^3+3q^2+2q
       212: q^3+q^2+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 2q^2+2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^3+3q^2+2q
       229: 2q^3+3q^2+3q
       230: 2q^3+3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+3q
       235: 2q^3+3q^2+3q
       236: 2q^3+3q^2+2q
       237: q^3+q^2+2q
       239: q^3+q^2+2q
       241: 2q^2+q
       243: 3q^2+3q
       244: 2q^3+3q^2+3q
       245: 2q^3+3q^2+3q
       246: q^3+4q^2+3q
       247: 3q^2+4q
       248: 3q^2+4q
       249: q^3+3q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 4q^3+4q^2+3q
       257: 4q^3+4q^2+3q
       258: 3q^3+4q^2+2q
       259: q
       262: q
       263: q
       265: q^2+q
       266: q
       267: q
       269: q
       270: q^2+q
       271: q
       272: q^2+q
       273: q
       275: q^2+q
       277: q^2+q
       278: q^2+q
       279: q^2+2q
       281: q^2+q
       284: q^2+q
       285: q^2+q
       287: q^2+q
       289: 2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       299: q
       300: 2q^2+2q
       301: 2q
       303: 2q^2+2q
       304: q
       305: q^2+2q
       306: q^2+q
       307: q
       308: 2q^2+2q
       309: 2q^2+2q
       310: q
       311: 2q
       313: q^2+2q
       314: q^2+q
       315: q^2+q
       317: q^2+2q
       319: q
       320: 2q^2+2q
       321: 2q^2+2q
       322: q
       323: q^2+2q
       324: q^2+q
       325: q^3+2q^2+2q
       326: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+4q
       338: q^2+3q
       340: q^2+3q
       342: 2q^2+q
       344: 2q^2+2q
       345: 3q
       346: 2q
       347: 3q
       348: q^3+2q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 3q^2+4q
       352: 2q^2+2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^3+2q^2+2q
       359: 3q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 2q^2+2q
       367: 3q^2+3q
       368: 2q^3+3q^2+2q
       369: 2q^3+3q^2+3q
       370: 2q^3+3q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       389: q
       391: q
       393: q
       395: q^2+q
       396: q
       397: q
       399: q
       401: q
       402: q^2+q
       404: q
       405: q
       406: q
       408: q^2+q
       413: q^2+q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 3q
       430: q^2+q
       431: q^2+q
       433: q
       435: 2q
       437: q
       438: 2q
       439: 2q
       440: q
       441: 2q
       442: q
       443: q
       444: q^2+3q
       445: q^2+3q
       448: q^2+q
       449: q^2+q
       451: q
       453: q
       454: 2q
       455: 2q
       457: 2q
       458: q
       459: 2q
       460: q
       461: q^2+3q
       462: q
       463: q^2+3q
       465: q^2+2q
       467: q^2+q
       469: q^2+q
       471: q
       472: 2q^2+2q
       473: 2q^2+2q
       474: q
       475: q^2+2q
       476: q^2+q
       477: 2q
       479: q^2+2q
       480: 2q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 3q^2+4q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 3q^2+4q
       508: 2q^2+2q
       509: 3q
       510: 2q
       511: 3q
       512: q^3+2q^2+2q
       513: 3q
       514: q^3+2q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       537: q
       539: q
       541: q
       543: q
       544: q
       545: q
       547: 2q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: 2q
       563: q
       565: q
       567: q^2+q
       568: q
       569: q
       570: q
       573: q
       575: q
       576: q^2+2q
       577: 2q
       580: q^2+q
       585: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 3q
       604: q
       605: q
       607: q
       609: q
       613: q
       615: q
       616: q^2+3q
       617: q^2+3q
       620: q
       621: q
       623: q
       625: q
       629: q
       631: q^2+3q
       632: q
       633: q^2+3q
       639: q^2+q
       642: q^2+q
       643: q^2+q
       645: q
       647: q
       648: 2q
       649: 2q
       650: q
       651: 2q
       653: 2q
       654: q
       655: q^2+2q
       656: 2q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       674: 2q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 2q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       693: q
       697: q
       698: q
       733: q
       735: 2q
       749: 2q
       751: q
       757: q
       758: q
       761: q
       762: q
       764: q
       765: q
       767: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       779: q+1
       781: q
       786: q
       787: q
       794: q+1
       795: 2q+1
       797: q
       802: q
       803: q
       806: q
       807: q
       809: q
       811: q
       817: q+1
       819: 2q+1
       821: q
       826: q
       827: q
       830: q
       831: q
       833: q
       835: q
       843: q
       844: q+1
       846: q
       847: q
       849: q
       851: q
       855: q
       866: 1
       870: q+1
       871: 2q
       874: q+1
       875: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       884: q
       888: q
       889: q
       918: q+1
       940: q+1
       966: q+1
       968: q
       971: q+1
       994: 1
       998: 1
      1001: 1
      1013: 1
      1020: q+1
      1022: q
      1027: q
      1028: q
      1036: q+1
      1038: q
      1041: q
      1044: q
      1048: q
      1053: q
      1054: q
      1057: q
      1058: q
      1060: q
      1062: q
      1076: 1
      1080: 1
      1083: 2q
      1084: q+1
      1090: q+1
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1230: 1
      1232: 1
      1235: 1
      1248: 1
      1250: 1
      1255: 1
      1266: q
      1269: q
      1270: q
      1274: q+1
      1281: 1
      1287: 1
      1294: 1
      1348: 1
      1358: 1
      1365: 1
      1380: 1
      1390: 1
      1398: 1
      1433: 1
      1464: 1
      1466: 1
      1469: 1
      1504: 1
      1517: 1
      1607: 1
      1617: 1
      1625: 1
      1715: 1

1716:    0: 3q^2+q+1
         1: 3q^2+q+1
         2: 3q^2+q+1
         3: 3q^2+q+1
         4: q^3+2q^2+q+1
         5: 3q^2+q+1
         6: q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: 3q^2+q+1
         9: q^3+2q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q^2+q+1
        14: q^3+2q^2+q+1
        15: 3q^2+q+1
        16: 3q^2+q+1
        17: 3q^2+q+1
        18: q^3+2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: 2q^2+q+1
        22: 3q^2+q+1
        23: 3q^2+q+1
        24: 3q^2+q+1
        25: 3q^2+q+1
        26: 3q^2+q+1
        27: 3q^2+q+1
        28: q+1
        29: q+1
        30: 2q^2+q+1
        31: q+1
        32: 3q^2+q+1
        33: 3q^2+q+1
        34: q+1
        35: 3q^2+q+1
        36: 3q^2+q+1
        37: q^2
        38: 2q^2+q+1
        39: q^2
        40: 2q^2+q+1
        41: q^2
        42: 2q^2+q+1
        43: q+1
        44: q+1
        45: q+1
        46: 3q^2+q+1
        47: 3q^2+q+1
        48: q^3+2q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: 2q^2+q+1
        52: 2q^2+q+1
        53: 2q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: 2q^2+q+1
        59: q+1
        60: q+1
        63: q+1
        64: q^2
        65: 2q^2+q+1
        66: q^2
        67: 2q^2+q+1
        68: q+1
        69: 2q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q^2+q+1
        75: q^2+q+1
        77: q^2+q+1
        79: q^2+q+1
        80: q+1
        81: 3q^2+q+1
        82: q+1
        83: 2q^2+q+1
        84: q+1
        85: 3q^2+q+1
        86: q+1
        87: 2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       104: q+1
       107: q+1
       110: q+1
       112: q+1
       114: q+1
       116: q^2+q+1
       118: q+1
       119: q+1
       122: q+1
       123: q^2
       124: 2q^2+q+1
       125: q+1
       126: q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: q+1
       134: 2q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q+1
       140: q^2+q+1
       141: q+1
       142: q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: 2q^2+q+1
       152: q^2+q+1
       154: q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: 2q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: 2q^2+q+1
       166: 2q^2+q+1
       167: 2q^2+q+1
       168: 2q^2+q+1
       170: q+1
       174: q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       183: q+1
       186: q+1
       188: q+1
       190: q+1
       192: q+1
       193: q+1
       196: q+1
       198: q+1
       199: q+1
       201: q+1
       204: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q^2+q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: 2q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: 2q^2+q+1
       234: q^2+q+1
       235: q^2+q+1
       236: 2q^2+q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: 2q^2+q+1
       260: q+1
       264: q+1
       268: q+1
       274: q+1
       276: q+1
       280: q+1
       282: q^2+q+1
       283: q+1
       286: q+1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       296: 1
       298: 1
       299: q+1
       302: q+1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: q+1
       314: q+1
       316: q^2+q+1
       318: q+1
       319: q+1
       322: q+1
       324: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: q+1
       367: q+1
       368: 2q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: 1
       378: q+1
       382: q+1
       386: 1
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       414: q+1
       418: q+1
       419: 1
       422: 1
       424: 1
       426: q+1
       428: q+1
       429: q+1
       432: q+1
       434: q+1
       436: q+1
       437: 1
       440: 1
       442: 1
       443: q+1
       446: 2q+1
       447: q+1
       450: q+1
       452: q+1
       453: 1
       456: q+1
       458: 1
       460: 1
       462: q+1
       464: 2q+1
       466: q+1
       468: q^2+q+1
       470: q+1
       471: q+1
       474: q+1
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       522: q+1
       530: 1
       534: q+1
       538: q+1
       542: 1
       546: q+1
       551: q+1
       556: q+1
       560: 1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       578: q
       581: q+1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: 1
       602: q+1
       603: 1
       606: q+1
       608: 1
       610: 1
       614: q+1
       615: q+1
       618: 2q+1
       619: 1
       622: 1
       624: q+1
       626: 1
       630: q+1
       632: q+1
       634: 2q+1
       640: q+1
       641: q+1
       644: q+1
       646: q+1
       647: 1
       650: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: q+1
       726: 1
       734: q+1
       740: q+1
       744: 1
       752: q+1
       754: q+1
       759: q+1
       763: 1
       766: q+1
       770: q
       773: q+1
       776: q+1
       780: q+1
       782: 1
       785: 1
       788: 1
       792: 1
       793: q+1
       796: 2q+1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: q+1
       812: 1
       818: q+1
       820: 2q+1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: q+1
       836: 1
       843: q
       844: q+1
       845: 1
       848: 1
       850: q+1
       852: 1
       856: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       917: q+1
       921: 1
       926: 1
       929: 1
       943: q+1
       947: 1
       951: 1
       953: 1
       962: q+1
       965: q+1
       969: q
       972: q+1
       976: 1
       995: 1
       999: 1
      1000: 1
      1011: 1
      1013: 1
      1021: q+1
      1023: 1
      1026: 1
      1029: 1
      1037: q+1
      1039: 1
      1040: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: q+1
      1063: 1
      1065: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1092: q+1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1205: 1
      1207: 1
      1231: 1
      1233: 1
      1234: 1
      1249: 1
      1251: 1
      1254: 1
      1267: 1
      1268: 1
      1271: 1
      1275: q+1
      1279: 1
      1281: 1
      1287: 1
      1296: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1465: 1
      1467: 1
      1468: 1
      1508: 1
      1519: 1
      1610: 1
      1616: 1
      1620: 1
      1624: 1
      1716: 1

1717:    0: 3q^2+q+1
         1: 3q^2+q+1
         2: 3q^2+q+1
         3: 3q^2+q+1
         4: q^3+2q^2+q+1
         5: 3q^2+q+1
         6: q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: 3q^2+q+1
         9: q^3+2q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q^2+q+1
        14: q^3+2q^2+q+1
        15: 3q^2+q+1
        16: 3q^2+q+1
        17: 3q^2+q+1
        18: q^3+2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: 2q^2+q+1
        22: 3q^2+q+1
        23: 3q^2+q+1
        24: 3q^2+q+1
        25: 3q^2+q+1
        26: 3q^2+q+1
        27: 3q^2+q+1
        28: q+1
        29: q+1
        30: 2q^2+q+1
        31: q+1
        32: 3q^2+q+1
        33: 3q^2+q+1
        34: q+1
        35: 3q^2+q+1
        36: 3q^2+q+1
        37: q^2
        38: 2q^2+q+1
        39: q^2
        40: 2q^2+q+1
        41: q^2
        42: 2q^2+q+1
        43: q+1
        44: q+1
        45: q+1
        46: 3q^2+q+1
        47: 3q^2+q+1
        48: q^3+2q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: 2q^2+q+1
        52: 2q^2+q+1
        53: 2q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: 2q^2+q+1
        58: q+1
        61: q+1
        63: q+1
        64: q^2
        65: 2q^2+q+1
        66: q^2
        67: 2q^2+q+1
        68: q+1
        69: 2q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q^2+q+1
        75: q^2+q+1
        77: q^2+q+1
        79: q^2+q+1
        80: q+1
        81: 3q^2+q+1
        82: q+1
        83: 2q^2+q+1
        84: q+1
        85: 3q^2+q+1
        86: q+1
        87: 2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       105: q+1
       108: q+1
       109: q+1
       112: q+1
       114: q+1
       116: q^2+q+1
       117: q+1
       120: q+1
       122: q+1
       123: q^2
       124: 2q^2+q+1
       125: q+1
       126: q+1
       128: q^2+q+1
       130: q^2+q+1
       132: q^2+q+1
       133: q+1
       134: 2q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q+1
       140: q^2+q+1
       141: q+1
       142: q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: 2q^2+q+1
       152: q^2+q+1
       154: q^2+q+1
       156: q^2+q+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: 2q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: 2q^2+q+1
       166: 2q^2+q+1
       167: 2q^2+q+1
       168: 2q^2+q+1
       171: q+1
       175: q+1
       178: q^2+q+1
       180: q+1
       182: q+1
       184: q+1
       185: q+1
       188: q+1
       190: q+1
       191: q+1
       194: q+1
       195: q+1
       198: q+1
       200: q+1
       202: q+1
       203: q+1
       206: q+1
       208: q+1
       210: q+1
       212: q^2+q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: 2q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: 2q^2+q+1
       234: q^2+q+1
       235: q^2+q+1
       236: 2q^2+q+1
       238: q^2+q+1
       240: q^2+q+1
       242: q^2+q+1
       243: q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: 2q^2+q+1
       261: q+1
       265: q+1
       270: q+1
       272: q+1
       277: q+1
       280: q+1
       282: q^2+q+1
       284: q+1
       285: q+1
       288: q+1
       290: q+1
       292: q+1
       294: 1
       295: 1
       298: 1
       300: q+1
       302: q+1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: q+1
       314: q+1
       316: q^2+q+1
       318: q+1
       320: q+1
       321: q+1
       324: q+1
       326: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: q+1
       367: q+1
       368: 2q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: 1
       379: q+1
       383: q+1
       387: 1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       414: q+1
       418: q+1
       420: 1
       421: 1
       424: 1
       426: q+1
       428: q+1
       430: q+1
       431: q+1
       434: q+1
       436: q+1
       438: 1
       439: 1
       442: 1
       444: q+1
       446: 2q+1
       448: q+1
       449: q+1
       452: q+1
       454: 1
       456: q+1
       457: 1
       460: 1
       461: q+1
       464: 2q+1
       466: q+1
       468: q^2+q+1
       470: q+1
       472: q+1
       473: q+1
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       523: q+1
       531: 1
       535: q+1
       540: q+1
       544: 1
       548: q+1
       550: q+1
       554: q+1
       558: 1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       578: q
       581: q+1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: 1
       602: q+1
       604: 1
       606: q+1
       607: 1
       610: 1
       614: q+1
       616: q+1
       618: 2q+1
       620: 1
       621: 1
       624: q+1
       626: 1
       630: q+1
       631: q+1
       634: 2q+1
       640: q+1
       642: q+1
       643: q+1
       646: q+1
       648: 1
       649: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: q+1
       728: 1
       736: q+1
       738: q+1
       742: 1
       750: q+1
       755: q+1
       760: q+1
       764: 1
       767: q+1
       770: q
       773: q+1
       776: q+1
       780: q+1
       782: 1
       786: 1
       787: 1
       792: 1
       794: q+1
       796: 2q+1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: q+1
       812: 1
       817: q+1
       820: 2q+1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: q+1
       836: 1
       843: q
       844: q+1
       846: 1
       847: 1
       850: q+1
       852: 1
       856: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       919: q+1
       923: 1
       925: 1
       931: 1
       941: q+1
       945: 1
       949: 1
       954: 1
       963: q+1
       966: q+1
       969: q
       972: q+1
       977: 1
       995: 1
       998: 1
      1001: 1
      1011: 1
      1013: 1
      1021: q+1
      1023: 1
      1027: 1
      1028: 1
      1037: q+1
      1039: 1
      1041: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: q+1
      1063: 1
      1065: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1093: q+1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1203: 1
      1209: 1
      1231: 1
      1232: 1
      1235: 1
      1249: 1
      1250: 1
      1255: 1
      1267: 1
      1269: 1
      1270: 1
      1275: q+1
      1279: 1
      1281: 1
      1287: 1
      1297: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1465: 1
      1466: 1
      1469: 1
      1507: 1
      1520: 1
      1608: 1
      1618: 1
      1621: 1
      1625: 1
      1717: 1

1718:    0: 3q^2+q+1
         1: 3q^2+q+1
         2: 3q^2+q+1
         3: 3q^2+q+1
         4: q^3+2q^2+q+1
         5: 3q^2+q+1
         6: q^3+2q^2+q+1
         7: q^3+2q^2+q+1
         8: 3q^2+q+1
         9: q^3+2q^2+q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q^2+q+1
        14: q^3+2q^2+q+1
        15: 3q^2+q+1
        16: 3q^2+q+1
        17: 3q^2+q+1
        18: q^3+2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: 2q^2+q+1
        22: 3q^2+q+1
        23: 3q^2+q+1
        24: 3q^2+q+1
        25: 3q^2+q+1
        26: 3q^2+q+1
        27: 3q^2+q+1
        28: q+1
        29: q+1
        30: 2q^2+q+1
        31: q+1
        32: 3q^2+q+1
        33: 3q^2+q+1
        34: q+1
        35: 3q^2+q+1
        36: 3q^2+q+1
        37: 2q^2+q+1
        38: q^2
        39: 2q^2+q+1
        40: q^2
        41: 2q^2+q+1
        42: q^2
        43: q+1
        44: q+1
        45: q+1
        46: 3q^2+q+1
        47: 3q^2+q+1
        48: q^3+2q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: 2q^2+q+1
        52: 2q^2+q+1
        53: 2q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: 2q^2+q+1
        59: q+1
        61: q+1
        62: q+1
        64: 2q^2+q+1
        65: q^2
        66: 2q^2+q+1
        67: q^2
        68: q+1
        69: 2q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        76: q^2+q+1
        78: q^2+q+1
        80: q+1
        81: 3q^2+q+1
        82: q+1
        83: 2q^2+q+1
        84: q+1
        85: 3q^2+q+1
        86: q+1
        87: 2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       106: q+1
       108: q+1
       110: q+1
       111: q+1
       113: q+1
       115: q^2+q+1
       118: q+1
       120: q+1
       121: q+1
       123: 2q^2+q+1
       124: q^2
       125: q+1
       126: q+1
       127: q^2+q+1
       129: q^2+q+1
       131: q^2+q+1
       133: q+1
       134: 2q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: 2q^2+q+1
       139: q+1
       140: q^2+q+1
       141: q+1
       142: q^2+q+1
       143: q+1
       144: 2q^2+q+1
       145: q+1
       146: q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: 2q^2+q+1
       151: q^2+q+1
       153: q^2+q+1
       155: q^2+q+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: 2q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: 2q^2+q+1
       166: 2q^2+q+1
       167: 2q^2+q+1
       168: 2q^2+q+1
       172: q+1
       176: q+1
       177: q^2+q+1
       179: q+1
       181: q+1
       184: q+1
       186: q+1
       187: q+1
       189: q+1
       192: q+1
       194: q+1
       196: q+1
       197: q+1
       200: q+1
       202: q+1
       204: q+1
       205: q+1
       207: q+1
       209: q+1
       211: q^2+q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q+1
       228: 2q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: 2q^2+q+1
       234: q^2+q+1
       235: q^2+q+1
       236: 2q^2+q+1
       237: q^2+q+1
       239: q^2+q+1
       241: q^2+q+1
       243: q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: 2q^2+q+1
       262: q+1
       266: q+1
       269: q+1
       273: q+1
       278: q+1
       279: q+1
       281: q^2+q+1
       284: q+1
       286: q+1
       287: q+1
       289: q+1
       291: q+1
       294: 1
       296: 1
       297: 1
       300: q+1
       301: q+1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: q+1
       313: q+1
       315: q^2+q+1
       317: q+1
       320: q+1
       322: q+1
       323: q+1
       325: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: q^2+q+1
       349: 1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+q+1
       357: 1
       358: q^2+q+1
       359: 2q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: q+1
       367: q+1
       368: 2q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 1
       375: 1
       376: 1
       380: q+1
       384: q+1
       388: 1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       413: q+1
       417: q+1
       420: 1
       422: 1
       423: 1
       425: q+1
       427: q+1
       430: q+1
       432: q+1
       433: q+1
       435: q+1
       438: 1
       440: 1
       441: 1
       444: q+1
       445: 2q+1
       448: q+1
       450: q+1
       451: q+1
       454: 1
       455: q+1
       458: 1
       459: 1
       462: q+1
       463: 2q+1
       465: q+1
       467: q^2+q+1
       469: q+1
       472: q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       480: q
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 2q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q^2+q+1
       513: 1
       514: q^2+q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       524: q+1
       532: 1
       536: q+1
       539: q+1
       543: 1
       547: q+1
       552: q+1
       555: q+1
       559: 1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       580: q
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: 1
       601: q+1
       604: 1
       605: q+1
       608: 1
       609: 1
       613: q+1
       616: q+1
       617: 2q+1
       620: 1
       622: 1
       623: q+1
       625: 1
       629: q+1
       632: q+1
       633: 2q+1
       639: q+1
       642: q+1
       644: q+1
       645: q+1
       648: 1
       650: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       679: q+1
       680: 2q+1
       681: 1
       682: 1
       683: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: q+1
       727: 1
       735: q+1
       739: q+1
       743: 1
       751: q+1
       756: q+1
       758: q+1
       762: 1
       768: q+1
       769: q+1
       772: q
       775: q+1
       779: q+1
       781: 1
       786: 1
       788: 1
       791: 1
       794: q+1
       795: 2q+1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: q+1
       811: 1
       818: q+1
       819: 2q+1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: q+1
       835: 1
       843: q+1
       844: q
       846: 1
       848: 1
       849: q+1
       851: 1
       855: q+1
       866: 1
       870: q+1
       871: 1
       874: q+1
       875: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       918: q+1
       922: 1
       927: 1
       930: 1
       942: q+1
       946: 1
       950: 1
       955: 1
       961: q+1
       967: q+1
       968: q+1
       971: q
       975: 1
       994: 1
       999: 1
      1001: 1
      1010: 1
      1012: 1
      1020: q+1
      1022: 1
      1027: 1
      1029: 1
      1036: q+1
      1038: 1
      1041: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: q+1
      1062: 1
      1064: 1
      1076: 1
      1080: 1
      1083: 1
      1084: q+1
      1091: q+1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1138: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1204: 1
      1208: 1
      1230: 1
      1233: 1
      1235: 1
      1248: 1
      1251: 1
      1255: 1
      1266: 1
      1269: 1
      1271: 1
      1274: q+1
      1278: 1
      1280: 1
      1287: 1
      1295: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1464: 1
      1467: 1
      1469: 1
      1506: 1
      1518: 1
      1609: 1
      1617: 1
      1622: 1
      1626: 1
      1718: 1

1719:    0: 3q^4+9q^3+q^2+q
         1: 3q^4+9q^3+q^2+q
         2: 3q^4+6q^3+q^2+q
         3: 3q^4+9q^3+q^2+q
         4: 4q^4+5q^3+q^2+q
         5: 3q^4+9q^3+q^2+q
         6: 2q^5+5q^4+5q^3+q^2+q
         7: 2q^5+4q^4+4q^3+q^2+q
         8: 3q^4+6q^3+q^2+q
         9: 2q^5+4q^4+4q^3+q^2+q
        10: q^4+6q^3+q^2+q
        11: q^4+6q^3+q^2+q
        12: 3q^4+3q^3+q^2+q
        13: q^4+6q^3+q^2+q
        14: 3q^4+4q^3+q^2+q
        15: q^4+6q^3+q^2+q
        16: 3q^4+9q^3+q^2+q
        17: 3q^4+9q^3+q^2+q
        18: 2q^5+4q^4+4q^3+q^2+q
        19: 5q^3+q^2+q
        20: q^4+5q^3+q^2+q
        21: q^4+4q^3+q^2+q
        22: 3q^4+9q^3+q^2+q
        23: 3q^4+9q^3+q^2+q
        24: 3q^4+6q^3+q^2+q
        25: 3q^4+9q^3+q^2+q
        26: 3q^4+9q^3+q^2+q
        27: 3q^4+6q^3+q^2+q
        28: q^4+6q^3+q^2+q
        29: 3q^3+q^2+q
        30: 4q^3+q^2+q
        31: q^4+6q^3+q^2+q
        32: q^4+6q^3+q^2+q
        33: 3q^4+9q^3+q^2+q
        34: q^4+6q^3+q^2+q
        35: q^4+6q^3+q^2+q
        36: 3q^4+9q^3+q^2+q
        37: q^4+3q^3
        38: 2q^4+6q^3+q^2+q
        39: q^4+3q^3
        40: 2q^4+6q^3+q^2+q
        41: q^4+2q^3
        42: 2q^4+4q^3+q^2+q
        43: 3q^3+q^2+q
        44: 2q^4+2q^3+q^2+q
        45: 3q^3+q^2+q
        46: q^4+6q^3+q^2+q
        47: q^4+6q^3+q^2+q
        48: 3q^4+4q^3+q^2+q
        49: 5q^3+q^2+q
        50: q^4+5q^3+q^2+q
        51: q^4+4q^3+q^2+q
        52: 5q^3+q^2+q
        53: q^4+5q^3+q^2+q
        54: q^4+4q^3+q^2+q
        55: 5q^3+q^2+q
        56: q^4+5q^3+q^2+q
        57: q^4+4q^3+q^2+q
        58: 2q^3
        59: q^4+4q^3+q^2+q
        60: q^4+4q^3+q^2+q
        61: 2q^3
        62: 2q^3
        63: q^4+4q^3+q^2+q
        64: 2q^3
        65: q^4+4q^3+q^2+q
        66: q^4+3q^3
        67: 2q^4+6q^3+q^2+q
        68: q^3+q^2+q
        69: 4q^3+q^2+q
        70: 2q^3+q^2+q
        71: 3q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        75: 2q^3+q^2+q
        77: 2q^3+q^2+q
        79: 2q^3+q^2+q
        80: 3q^3+q^2+q
        81: q^4+6q^3+q^2+q
        82: 3q^3+q^2+q
        83: 4q^3+q^2+q
        84: 3q^3+q^2+q
        85: q^4+6q^3+q^2+q
        86: 3q^3+q^2+q
        87: 4q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: 2q^4+2q^3+q^2+q
        91: 3q^3+q^2+q
        92: 2q^3+q^2+q
        93: 3q^3+q^2+q
        94: 5q^3+q^2+q
        95: q^4+5q^3+q^2+q
        96: q^4+4q^3+q^2+q
        97: 5q^3+q^2+q
        98: q^4+5q^3+q^2+q
        99: q^4+4q^3+q^2+q
       100: 5q^3+q^2+q
       101: q^4+5q^3+q^2+q
       102: q^4+4q^3+q^2+q
       103: q^3
       104: q^4+3q^3+q^2+q
       105: q^3
       106: q^3
       107: q^3+q^2+q
       110: q^3+q^2+q
       112: q^2+q
       114: q^3+q^2+q
       116: 2q^3+q^2+q
       118: q^3+q^2+q
       119: q^3+q^2+q
       121: q^3
       122: 2q^3+q^2+q
       123: 2q^3
       124: q^4+4q^3+q^2+q
       125: q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: 2q^3+q^2+q
       133: q^2+q
       134: 3q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: 3q^3+q^2+q
       138: 4q^3+q^2+q
       139: 3q^3+q^2+q
       140: 2q^3+q^2+q
       141: 2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: 4q^3+q^2+q
       145: 3q^3+q^2+q
       146: 2q^3+q^2+q
       147: 2q^3+q^2+q
       148: 2q^3+q^2+q
       149: 3q^3+q^2+q
       150: 4q^3+q^2+q
       152: 2q^3+q^2+q
       154: 2q^3+q^2+q
       156: 2q^3+q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 3q^3+q^2+q
       161: 2q^3+q^2+q
       162: 3q^3+q^2+q
       163: 3q^3+q^2+q
       164: 2q^3+q^2+q
       165: 3q^3+q^2+q
       166: 5q^3+q^2+q
       167: q^4+5q^3+q^2+q
       168: q^4+4q^3+q^2+q
       170: q^2+q
       174: q^3+q^2+q
       178: 2q^3+q^2+q
       180: q^3+q^2+q
       182: q^2+q
       183: q^2+q
       186: q^2+q
       188: q^2+q
       190: q^3+q^2+q
       192: q^3+q^2+q
       193: q^3+q^2+q
       196: q^3+q^2+q
       198: q^2+q
       199: q^3+q^2+q
       201: q^3+q^2+q
       204: q^3+q^2+q
       206: q^2+q
       207: q^3
       208: 2q^3+q^2+q
       210: q^3+q^2+q
       212: 2q^3+q^2+q
       214: q^3+q
       216: q
       218: q^3+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+q^2+q
       224: q
       225: q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^2+q
       228: 3q^3+q^2+q
       229: q^3+q^2+q
       230: q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^2+q
       233: 3q^3+q^2+q
       234: q^3+q^2+q
       235: q^3+q^2+q
       236: 4q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: 2q^3+q^2+q
       243: 3q^3+q^2+q
       244: 2q^3+q^2+q
       245: 2q^3+q^2+q
       246: 2q^3+q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       260: q^2+q
       264: q^2+q
       268: q^2+q
       274: q^2+q
       276: q^3+q^2+q
       280: q
       282: q^3+q
       283: q^2+q
       286: q^2+q
       288: q^3+q^2+q
       290: q
       292: q^2+q
       293: q
       296: q
       298: q
       299: q^2+q
       302: q^2+q
       304: q^2+q
       306: q^2+q
       307: q^2+q
       310: q^2+q
       312: q^2+q
       314: q^2+q
       316: 2q^3+q^2+q
       318: q^3+q^2+q
       319: q^3+q^2+q
       322: q^3+q^2+q
       324: q^2+q
       326: q^3+q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: q^3+q^2+q
       349: q
       350: q^3+q^2+q
       351: 2q^2+q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+q^2+q
       357: q
       358: q^3+q^2+q
       359: 2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       378: q^2+q
       382: q
       386: q
       390: q^2+q
       394: q^2+q
       400: q^2+q
       403: q^2+q
       407: q^2+q
       414: q
       418: q
       419: q
       422: q
       424: q
       426: q^2+q
       428: q^2+q
       429: q^2+q
       432: q^2+q
       434: q^2+q
       436: q
       437: q
       440: q
       442: q
       443: q^2+q
       446: 2q^2+q
       447: q^2+q
       450: q^2+q
       452: q^2+q
       453: q
       456: q
       458: q
       460: q
       462: q^2+q
       464: 2q^2+q
       466: q
       468: q^3+q
       470: q^3+q^2+q
       471: q^2+q
       474: q^2+q
       476: q^2+q
       478: q^2+q
       479: q^2
       480: q^2+q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       522: q
       530: q
       534: q^2+q
       538: q
       542: q
       546: q^2+q
       551: q^2+q
       556: q
       560: q
       564: q^2+q
       566: q^2+q
       571: q^2+q
       574: q^2+q
       578: q^2
       581: q^2+q
       586: q
       589: q
       592: q
       593: q
       596: q
       600: q
       603: q
       606: q
       608: q
       610: q
       614: q^2+q
       619: q
       622: q
       624: q
       626: q
       630: q^2+q
       640: q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q
       650: q
       652: q
       654: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q^2+q
       699: q^2+q
       710: q
       715: q
       718: q
       722: q
       726: q
       740: q
       744: q
       754: q^2+q
       759: q
       763: q
       798: q
       801: q
       804: q
       805: q
       808: q
       812: q
       822: q
       825: q
       828: q
       829: q
       832: q
       836: q
       845: q
       848: q
       850: q
       852: q
       856: q^2+q
       877: q
       878: q
       879: q
       921: q
       926: q
       929: q
       947: q
       951: q
       953: q
       962: q
       976: q
      1011: 1
      1049: q
      1052: q
      1055: q
      1056: q
      1059: q
      1063: q
      1128: 1
      1143: 1
      1200: q
      1205: q
      1207: q
      1279: 1
      1300: 1
      1363: 1
      1394: 1
      1435: 1
      1512: 1
      1523: 1
      1620: 1
      1719: 1

1720:    0: 9q^3+6q^2+3q
         1: 3q^4+9q^3+6q^2+3q
         2: 9q^3+6q^2+3q
         3: 3q^4+9q^3+6q^2+3q
         4: 3q^4+7q^3+5q^2+3q
         5: 9q^3+6q^2+3q
         6: q^5+5q^4+7q^3+5q^2+3q
         7: 3q^4+7q^3+5q^2+3q
         8: 9q^3+6q^2+3q
         9: q^5+3q^4+5q^3+4q^2+2q
        10: q^3+5q^2+3q
        11: q^3+5q^2+3q
        12: 2q^3+4q^2+3q
        13: 9q^3+6q^2+3q
        14: 3q^4+7q^3+5q^2+3q
        15: 9q^3+6q^2+3q
        16: 7q^3+5q^2+3q
        17: 7q^3+5q^2+3q
        18: 2q^4+4q^3+4q^2+2q
        19: 6q^3+5q^2+3q
        20: 2q^4+6q^3+5q^2+3q
        21: 6q^3+5q^2+3q
        22: 9q^3+6q^2+3q
        23: 3q^4+9q^3+6q^2+3q
        24: 9q^3+6q^2+3q
        25: 9q^3+6q^2+3q
        26: 3q^4+9q^3+6q^2+3q
        27: 9q^3+6q^2+3q
        28: 4q^2+3q
        29: q^3+4q^2+3q
        30: 6q^3+5q^2+3q
        31: q^3+5q^2+3q
        32: 9q^3+6q^2+3q
        33: 7q^3+5q^2+3q
        34: q^3+5q^2+3q
        35: 9q^3+6q^2+3q
        36: 7q^3+5q^2+3q
        37: 4q^3+2q^2+q
        38: 5q^3+4q^2+2q
        39: q^4+4q^3+2q^2+q
        40: 2q^4+5q^3+4q^2+2q
        41: 4q^3+2q^2+q
        42: 5q^3+4q^2+2q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 7q^3+5q^2+3q
        47: 7q^3+5q^2+3q
        48: 2q^4+4q^3+4q^2+2q
        49: 4q^3+4q^2+3q
        50: 4q^3+4q^2+3q
        51: 3q^3+4q^2+2q
        52: 6q^3+5q^2+3q
        53: 2q^4+6q^3+5q^2+3q
        54: 6q^3+5q^2+3q
        55: 6q^3+5q^2+3q
        56: 2q^4+6q^3+5q^2+3q
        57: 6q^3+5q^2+3q
        58: q^2+q
        59: 3q^2+2q
        60: q^2+q
        61: 3q^2+2q
        62: 2q^2+q
        63: q^3+3q^2+2q
        64: 4q^3+2q^2+q
        65: 5q^3+4q^2+2q
        66: 3q^3+2q^2+q
        67: 4q^3+3q^2+2q
        68: 4q^2+3q
        69: 2q^3+3q^2+2q
        70: q^3+4q^2+3q
        71: 3q^2+3q
        72: 2q^3+3q^2+3q
        73: 2q^3+3q^2+3q
        74: q^3+q^2+q
        75: 2q^3+3q^2+2q
        76: q^3+q^2+q
        77: q^4+2q^3+3q^2+2q
        78: q^3+q^2+q
        79: 2q^3+3q^2+2q
        80: q^3+5q^2+3q
        81: 7q^3+5q^2+3q
        82: q^3+4q^2+3q
        83: 6q^3+5q^2+3q
        84: q^3+5q^2+3q
        85: 7q^3+5q^2+3q
        86: q^3+4q^2+3q
        87: 6q^3+5q^2+3q
        88: 3q^2+3q
        89: 3q^2+3q
        90: q^3+3q^2+2q
        91: 4q^3+4q^2+3q
        92: 4q^3+4q^2+3q
        93: 3q^3+4q^2+2q
        94: 4q^3+4q^2+3q
        95: 4q^3+4q^2+3q
        96: 3q^3+4q^2+2q
        97: 4q^3+4q^2+3q
        98: 4q^3+4q^2+3q
        99: 3q^3+4q^2+2q
       100: 6q^3+5q^2+3q
       101: 2q^4+6q^3+5q^2+3q
       102: 6q^3+5q^2+3q
       104: q^2+q
       105: q^2+q
       106: 2q^2+q
       107: q
       108: 2q^2+2q
       109: q
       110: 2q^2+2q
       111: q^2+q
       112: q^2+2q
       113: q^2+q
       114: q^3+2q^2+2q
       115: q^3+q^2+q
       116: 2q^3+3q^2+2q
       117: q^2+q
       118: 3q^2+2q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+q
       122: q^3+3q^2+2q
       123: 3q^3+2q^2+q
       124: 4q^3+3q^2+2q
       125: 3q^2+3q
       126: 2q^2+2q
       128: q^3+q^2+2q
       130: q^3+q^2+2q
       132: 2q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+3q
       136: 2q^3+3q^2+3q
       137: 3q^2+3q
       138: 2q^3+3q^2+2q
       139: 3q^2+3q
       140: 2q^3+3q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+3q^2+3q
       143: 3q^2+3q
       144: 2q^3+3q^2+2q
       145: 3q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+3q^2+3q
       148: 2q^3+3q^2+3q
       149: q^3+4q^2+3q
       150: 6q^3+5q^2+3q
       151: q^3+q^2+q
       152: 2q^3+3q^2+2q
       153: q^3+q^2+q
       154: q^4+2q^3+3q^2+2q
       155: q^3+q^2+q
       156: 2q^3+3q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 4q^3+4q^2+3q
       161: 4q^3+4q^2+3q
       162: 3q^3+4q^2+2q
       163: 4q^3+4q^2+3q
       164: 4q^3+4q^2+3q
       165: 3q^3+4q^2+2q
       166: 4q^3+4q^2+3q
       167: 4q^3+4q^2+3q
       168: 3q^3+4q^2+2q
       170: q
       171: q
       172: q^2+q
       174: q^2+q
       175: q^2+q
       176: 2q^2+q
       178: q^2+q
       180: q^2+2q
       182: 2q
       183: q
       184: 2q^2+2q
       185: q
       186: 2q^2+2q
       187: q^2+q
       188: q^2+2q
       189: q^2+q
       190: q^3+2q^2+2q
       191: q^2+q
       192: 2q^2+2q
       193: q
       194: 2q^2+2q
       195: q
       196: 2q^2+2q
       197: q^2+q
       198: q^2+2q
       199: q^2+q
       200: 2q^2+2q
       201: q
       202: 2q^2+2q
       203: q
       204: 2q^2+2q
       205: q^2+q
       206: q^2+2q
       207: q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: q^3+2q^2+2q
       211: q^3+q^2+q
       212: 2q^3+3q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 2q^2+2q
       220: 3q
       221: 2q
       222: 3q
       223: q^3+2q^2+2q
       224: 3q
       225: q^3+2q^2+2q
       226: 2q^2+2q
       227: 3q^2+3q
       228: 2q^3+3q^2+2q
       229: 2q^3+3q^2+3q
       230: 2q^3+3q^2+3q
       231: 2q^2+2q
       232: 3q^2+3q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+3q
       235: 2q^3+3q^2+3q
       236: 2q^3+3q^2+2q
       238: q^3+q^2+2q
       240: q^3+q^2+2q
       242: 2q^2+q
       243: 3q^2+3q
       244: 2q^3+3q^2+3q
       245: 2q^3+3q^2+3q
       246: q^3+4q^2+3q
       247: 3q^2+4q
       248: 3q^2+4q
       249: q^3+3q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 4q^3+4q^2+3q
       257: 4q^3+4q^2+3q
       258: 3q^3+4q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q^2+q
       268: q
       269: q^2+q
       270: q
       272: q
       273: q^2+q
       274: q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: q^2+2q
       282: q^2+q
       284: q^2+q
       286: q^2+q
       288: q^2+q
       290: 2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       299: q
       300: 2q^2+2q
       302: 2q
       303: q
       304: 2q^2+2q
       305: q^2+q
       306: q^2+2q
       307: q
       308: 2q^2+2q
       309: q
       310: 2q^2+2q
       312: 2q
       313: q^2+q
       314: q^2+2q
       316: q^2+q
       318: q^2+2q
       319: q
       320: 2q^2+2q
       321: q
       322: 2q^2+2q
       323: q^2+q
       324: q^2+2q
       325: q^2+q
       326: q^3+2q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+4q
       339: q^2+3q
       341: q^2+3q
       343: 2q^2+q
       344: 2q^2+2q
       345: 3q
       346: 2q
       347: 3q
       348: q^3+2q^2+2q
       349: 3q
       350: q^3+2q^2+2q
       351: 3q^2+4q
       352: 2q^2+2q
       353: 3q
       354: 2q
       355: 3q
       356: q^3+2q^2+2q
       357: 3q
       358: q^3+2q^2+2q
       359: 3q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 2q^2+2q
       367: 3q^2+3q
       368: 2q^3+3q^2+2q
       369: 2q^3+3q^2+3q
       370: 2q^3+3q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q
       392: q
       394: q
       395: q
       396: q^2+q
       398: q
       400: q
       402: q
       403: q
       404: q^2+q
       406: q^2+q
       407: q
       408: q
       414: q^2+q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 3q
       430: q^2+q
       432: q^2+q
       434: q
       436: 2q
       437: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: 2q
       443: q
       444: q^2+3q
       446: q^2+3q
       448: q^2+q
       450: q^2+q
       452: q
       453: q
       454: 2q
       456: 2q
       457: q
       458: 2q
       459: q
       460: 2q
       461: q
       462: q^2+3q
       464: q^2+3q
       466: q^2+2q
       468: q^2+q
       470: q^2+q
       471: q
       472: 2q^2+2q
       473: q
       474: 2q^2+2q
       475: q^2+q
       476: q^2+2q
       478: 2q
       479: 2q^2+2q
       480: q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 3q^2+4q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 3q^2+4q
       508: 2q^2+2q
       509: 3q
       510: 2q
       511: 3q
       512: q^3+2q^2+2q
       513: 3q
       514: q^3+2q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q
       548: 2q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q
       564: 2q
       566: q
       567: q
       568: q^2+q
       571: q
       572: q
       574: q
       575: q^2+2q
       576: q
       578: q^2+q
       581: 2q
       586: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 3q
       604: q
       606: q
       608: q
       610: q
       614: q
       615: q
       616: q^2+3q
       618: q^2+3q
       620: q
       622: q
       624: q
       626: q
       630: q
       631: q
       632: q^2+3q
       634: q^2+3q
       640: q^2+q
       642: q^2+q
       644: q^2+q
       646: q
       647: q
       648: 2q
       649: q
       650: 2q
       652: 2q
       653: q
       654: 2q
       655: 2q^2+2q
       656: q^2+2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       674: 2q+1
       675: 2q
       676: 2q
       677: 2q
       679: q^2+2q
       680: 2q+1
       681: 2q
       682: 2q
       683: 2q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       699: q
       700: q
       701: q
       734: q
       736: 2q
       750: q
       752: 2q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q^2+2q
       770: q^2+q
       773: 2q
       776: q+1
       780: q+1
       782: q
       786: q
       788: q
       794: q+1
       796: 2q+1
       798: q
       802: q
       804: q
       806: q
       808: q
       810: q
       812: q
       818: q+1
       820: 2q+1
       822: q
       826: q
       828: q
       830: q
       832: q
       834: q
       836: q
       843: q+1
       844: q
       846: q
       848: q
       850: q
       852: q
       856: q
       866: 1
       870: q+1
       871: 2q
       874: q+1
       875: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       890: q
       891: q
       892: q
       919: q+1
       943: q+1
       967: q+1
       969: q+1
       972: q
       995: 1
       999: 1
      1001: 1
      1012: 1
      1021: q+1
      1023: q
      1027: q
      1029: q
      1037: q+1
      1039: q
      1041: q
      1045: q
      1049: q
      1053: q
      1055: q
      1057: q
      1059: q
      1061: q
      1063: q
      1076: 1
      1080: 1
      1083: 2q
      1084: q+1
      1094: q+1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1231: 1
      1233: 1
      1235: 1
      1249: 1
      1251: 1
      1255: 1
      1267: q
      1269: q
      1271: q
      1275: q+1
      1280: 1
      1287: 1
      1298: 1
      1351: 1
      1359: 1
      1367: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1465: 1
      1467: 1
      1469: 1
      1509: 1
      1521: 1
      1610: 1
      1618: 1
      1626: 1
      1720: 1

1721:    0: 3q^4+9q^3+q^2+q
         1: 3q^4+9q^3+q^2+q
         2: 3q^4+6q^3+q^2+q
         3: 3q^4+9q^3+q^2+q
         4: 4q^4+5q^3+q^2+q
         5: 3q^4+9q^3+q^2+q
         6: 2q^5+5q^4+5q^3+q^2+q
         7: 2q^5+4q^4+4q^3+q^2+q
         8: 3q^4+6q^3+q^2+q
         9: 2q^5+4q^4+4q^3+q^2+q
        10: q^4+6q^3+q^2+q
        11: q^4+6q^3+q^2+q
        12: 3q^4+3q^3+q^2+q
        13: q^4+6q^3+q^2+q
        14: 3q^4+4q^3+q^2+q
        15: q^4+6q^3+q^2+q
        16: 3q^4+9q^3+q^2+q
        17: 3q^4+9q^3+q^2+q
        18: 2q^5+4q^4+4q^3+q^2+q
        19: 5q^3+q^2+q
        20: q^4+5q^3+q^2+q
        21: q^4+4q^3+q^2+q
        22: 3q^4+9q^3+q^2+q
        23: 3q^4+9q^3+q^2+q
        24: 3q^4+6q^3+q^2+q
        25: 3q^4+9q^3+q^2+q
        26: 3q^4+9q^3+q^2+q
        27: 3q^4+6q^3+q^2+q
        28: q^4+6q^3+q^2+q
        29: 3q^3+q^2+q
        30: 4q^3+q^2+q
        31: q^4+6q^3+q^2+q
        32: q^4+6q^3+q^2+q
        33: 3q^4+9q^3+q^2+q
        34: q^4+6q^3+q^2+q
        35: q^4+6q^3+q^2+q
        36: 3q^4+9q^3+q^2+q
        37: q^4+3q^3
        38: 2q^4+6q^3+q^2+q
        39: q^4+3q^3
        40: 2q^4+6q^3+q^2+q
        41: q^4+2q^3
        42: 2q^4+4q^3+q^2+q
        43: 3q^3+q^2+q
        44: 2q^4+2q^3+q^2+q
        45: 3q^3+q^2+q
        46: q^4+6q^3+q^2+q
        47: q^4+6q^3+q^2+q
        48: 3q^4+4q^3+q^2+q
        49: 5q^3+q^2+q
        50: q^4+5q^3+q^2+q
        51: q^4+4q^3+q^2+q
        52: 5q^3+q^2+q
        53: q^4+5q^3+q^2+q
        54: q^4+4q^3+q^2+q
        55: 5q^3+q^2+q
        56: q^4+5q^3+q^2+q
        57: q^4+4q^3+q^2+q
        58: q^4+4q^3+q^2+q
        59: 2q^3
        60: 2q^3
        61: q^4+4q^3+q^2+q
        62: 2q^3
        63: q^4+4q^3+q^2+q
        64: 2q^3
        65: q^4+4q^3+q^2+q
        66: q^4+3q^3
        67: 2q^4+6q^3+q^2+q
        68: q^3+q^2+q
        69: 4q^3+q^2+q
        70: 2q^3+q^2+q
        71: 3q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        75: 2q^3+q^2+q
        77: 2q^3+q^2+q
        79: 2q^3+q^2+q
        80: 3q^3+q^2+q
        81: q^4+6q^3+q^2+q
        82: 3q^3+q^2+q
        83: 4q^3+q^2+q
        84: 3q^3+q^2+q
        85: q^4+6q^3+q^2+q
        86: 3q^3+q^2+q
        87: 4q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: 2q^4+2q^3+q^2+q
        91: 3q^3+q^2+q
        92: 2q^3+q^2+q
        93: 3q^3+q^2+q
        94: 5q^3+q^2+q
        95: q^4+5q^3+q^2+q
        96: q^4+4q^3+q^2+q
        97: 5q^3+q^2+q
        98: q^4+5q^3+q^2+q
        99: q^4+4q^3+q^2+q
       100: 5q^3+q^2+q
       101: q^4+5q^3+q^2+q
       102: q^4+4q^3+q^2+q
       103: q^3
       104: q^3
       105: q^4+3q^3+q^2+q
       106: q^3
       108: q^3+q^2+q
       109: q^3+q^2+q
       112: q^2+q
       114: q^3+q^2+q
       116: 2q^3+q^2+q
       117: q^3+q^2+q
       120: q^3+q^2+q
       121: q^3
       122: 2q^3+q^2+q
       123: 2q^3
       124: q^4+4q^3+q^2+q
       125: q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: 2q^3+q^2+q
       133: q^2+q
       134: 3q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: 3q^3+q^2+q
       138: 4q^3+q^2+q
       139: 3q^3+q^2+q
       140: 2q^3+q^2+q
       141: 2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: 4q^3+q^2+q
       145: 3q^3+q^2+q
       146: 2q^3+q^2+q
       147: 2q^3+q^2+q
       148: 2q^3+q^2+q
       149: 3q^3+q^2+q
       150: 4q^3+q^2+q
       152: 2q^3+q^2+q
       154: 2q^3+q^2+q
       156: 2q^3+q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 3q^3+q^2+q
       161: 2q^3+q^2+q
       162: 3q^3+q^2+q
       163: 3q^3+q^2+q
       164: 2q^3+q^2+q
       165: 3q^3+q^2+q
       166: 5q^3+q^2+q
       167: q^4+5q^3+q^2+q
       168: q^4+4q^3+q^2+q
       171: q^2+q
       175: q^3+q^2+q
       178: 2q^3+q^2+q
       180: q^3+q^2+q
       182: q^2+q
       184: q^2+q
       185: q^2+q
       188: q^2+q
       190: q^3+q^2+q
       191: q^3+q^2+q
       194: q^3+q^2+q
       195: q^3+q^2+q
       198: q^2+q
       200: q^3+q^2+q
       202: q^3+q^2+q
       203: q^3+q^2+q
       206: q^2+q
       207: q^3
       208: 2q^3+q^2+q
       210: q^3+q^2+q
       212: 2q^3+q^2+q
       214: q^3+q
       216: q
       218: q^3+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+q^2+q
       224: q
       225: q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^2+q
       228: 3q^3+q^2+q
       229: q^3+q^2+q
       230: q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^2+q
       233: 3q^3+q^2+q
       234: q^3+q^2+q
       235: q^3+q^2+q
       236: 4q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: 2q^3+q^2+q
       243: 3q^3+q^2+q
       244: 2q^3+q^2+q
       245: 2q^3+q^2+q
       246: 2q^3+q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       261: q^2+q
       265: q^2+q
       270: q^2+q
       272: q^2+q
       277: q^3+q^2+q
       280: q
       282: q^3+q
       284: q^2+q
       285: q^2+q
       288: q^3+q^2+q
       290: q
       292: q^2+q
       294: q
       295: q
       298: q
       300: q^2+q
       302: q^2+q
       303: q^2+q
       306: q^2+q
       308: q^2+q
       309: q^2+q
       312: q^2+q
       314: q^2+q
       316: 2q^3+q^2+q
       318: q^3+q^2+q
       320: q^3+q^2+q
       321: q^3+q^2+q
       324: q^2+q
       326: q^3+q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: q^3+q^2+q
       349: q
       350: q^3+q^2+q
       351: 2q^2+q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+q^2+q
       357: q
       358: q^3+q^2+q
       359: 2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       379: q^2+q
       383: q
       387: q
       392: q^2+q
       395: q^2+q
       398: q^2+q
       402: q^2+q
       408: q^2+q
       414: q
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       424: q
       426: q^2+q
       428: q^2+q
       430: q^2+q
       431: q^2+q
       434: q^2+q
       436: q
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       439: q
       442: q
       444: q^2+q
       446: 2q^2+q
       448: q^2+q
       449: q^2+q
       452: q^2+q
       454: q
       456: q
       457: q
       460: q
       461: q^2+q
       464: 2q^2+q
       466: q
       468: q^3+q
       470: q^3+q^2+q
       472: q^2+q
       473: q^2+q
       476: q^2+q
       478: q^2+q
       479: q^2
       480: q^2+q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       523: q
       531: q
       535: q^2+q
       540: q
       544: q
       548: q^2+q
       550: q^2+q
       554: q
       558: q
       562: q^2+q
       567: q^2+q
       572: q^2+q
       576: q^2+q
       578: q^2
       581: q^2+q
       586: q
       590: q
       591: q
       594: q
       595: q
       600: q
       604: q
       606: q
       607: q
       610: q
       614: q^2+q
       620: q
       621: q
       624: q
       626: q
       630: q^2+q
       640: q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       648: q
       649: q
       652: q
       654: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q^2+q
       700: q^2+q
       711: q
       714: q
       719: q
       724: q
       728: q
       738: q
       742: q
       755: q^2+q
       760: q
       764: q
       798: q
       802: q
       803: q
       806: q
       807: q
       812: q
       822: q
       826: q
       827: q
       830: q
       831: q
       836: q
       846: q
       847: q
       850: q
       852: q
       856: q^2+q
       877: q
       878: q
       879: q
       923: q
       925: q
       931: q
       945: q
       949: q
       954: q
       963: q
       977: q
      1011: 1
      1049: q
      1053: q
      1054: q
      1057: q
      1058: q
      1063: q
      1129: 1
      1143: 1
      1201: q
      1203: q
      1209: q
      1279: 1
      1301: 1
      1362: 1
      1395: 1
      1435: 1
      1511: 1
      1524: 1
      1621: 1
      1721: 1

1722:    0: 3q^4+9q^3+q^2+q
         1: 3q^4+9q^3+q^2+q
         2: 3q^4+6q^3+q^2+q
         3: 3q^4+9q^3+q^2+q
         4: 4q^4+5q^3+q^2+q
         5: 3q^4+9q^3+q^2+q
         6: 2q^5+5q^4+5q^3+q^2+q
         7: 2q^5+4q^4+4q^3+q^2+q
         8: 3q^4+6q^3+q^2+q
         9: 2q^5+4q^4+4q^3+q^2+q
        10: q^4+6q^3+q^2+q
        11: q^4+6q^3+q^2+q
        12: 3q^4+3q^3+q^2+q
        13: q^4+6q^3+q^2+q
        14: 3q^4+4q^3+q^2+q
        15: q^4+6q^3+q^2+q
        16: 3q^4+9q^3+q^2+q
        17: 3q^4+9q^3+q^2+q
        18: 2q^5+4q^4+4q^3+q^2+q
        19: 5q^3+q^2+q
        20: q^4+5q^3+q^2+q
        21: q^4+4q^3+q^2+q
        22: 3q^4+9q^3+q^2+q
        23: 3q^4+9q^3+q^2+q
        24: 3q^4+6q^3+q^2+q
        25: 3q^4+9q^3+q^2+q
        26: 3q^4+9q^3+q^2+q
        27: 3q^4+6q^3+q^2+q
        28: q^4+6q^3+q^2+q
        29: 3q^3+q^2+q
        30: 4q^3+q^2+q
        31: q^4+6q^3+q^2+q
        32: q^4+6q^3+q^2+q
        33: 3q^4+9q^3+q^2+q
        34: q^4+6q^3+q^2+q
        35: q^4+6q^3+q^2+q
        36: 3q^4+9q^3+q^2+q
        37: 2q^4+6q^3+q^2+q
        38: q^4+3q^3
        39: 2q^4+6q^3+q^2+q
        40: q^4+3q^3
        41: 2q^4+4q^3+q^2+q
        42: q^4+2q^3
        43: 3q^3+q^2+q
        44: 2q^4+2q^3+q^2+q
        45: 3q^3+q^2+q
        46: q^4+6q^3+q^2+q
        47: q^4+6q^3+q^2+q
        48: 3q^4+4q^3+q^2+q
        49: 5q^3+q^2+q
        50: q^4+5q^3+q^2+q
        51: q^4+4q^3+q^2+q
        52: 5q^3+q^2+q
        53: q^4+5q^3+q^2+q
        54: q^4+4q^3+q^2+q
        55: 5q^3+q^2+q
        56: q^4+5q^3+q^2+q
        57: q^4+4q^3+q^2+q
        58: 2q^3
        59: q^4+4q^3+q^2+q
        60: 2q^3
        61: q^4+4q^3+q^2+q
        62: q^4+4q^3+q^2+q
        63: 2q^3
        64: q^4+4q^3+q^2+q
        65: 2q^3
        66: 2q^4+6q^3+q^2+q
        67: q^4+3q^3
        68: q^3+q^2+q
        69: 4q^3+q^2+q
        70: 2q^3+q^2+q
        71: 3q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        74: 2q^3+q^2+q
        76: 2q^3+q^2+q
        78: 2q^3+q^2+q
        80: 3q^3+q^2+q
        81: q^4+6q^3+q^2+q
        82: 3q^3+q^2+q
        83: 4q^3+q^2+q
        84: 3q^3+q^2+q
        85: q^4+6q^3+q^2+q
        86: 3q^3+q^2+q
        87: 4q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: 2q^4+2q^3+q^2+q
        91: 3q^3+q^2+q
        92: 2q^3+q^2+q
        93: 3q^3+q^2+q
        94: 5q^3+q^2+q
        95: q^4+5q^3+q^2+q
        96: q^4+4q^3+q^2+q
        97: 5q^3+q^2+q
        98: q^4+5q^3+q^2+q
        99: q^4+4q^3+q^2+q
       100: 5q^3+q^2+q
       101: q^4+5q^3+q^2+q
       102: q^4+4q^3+q^2+q
       103: q^3
       104: q^3
       105: q^3
       106: q^4+3q^3+q^2+q
       108: q^3+q^2+q
       110: q^3+q^2+q
       111: q^2+q
       113: q^3+q^2+q
       115: 2q^3+q^2+q
       118: q^3+q^2+q
       120: q^3+q^2+q
       121: 2q^3+q^2+q
       122: q^3
       123: q^4+4q^3+q^2+q
       124: 2q^3
       125: q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: 2q^3+q^2+q
       133: q^2+q
       134: 3q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: 3q^3+q^2+q
       138: 4q^3+q^2+q
       139: 3q^3+q^2+q
       140: 2q^3+q^2+q
       141: 2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: 4q^3+q^2+q
       145: 3q^3+q^2+q
       146: 2q^3+q^2+q
       147: 2q^3+q^2+q
       148: 2q^3+q^2+q
       149: 3q^3+q^2+q
       150: 4q^3+q^2+q
       151: 2q^3+q^2+q
       153: 2q^3+q^2+q
       155: 2q^3+q^2+q
       157: q^3+q
       158: q
       159: q^3+q
       160: 3q^3+q^2+q
       161: 2q^3+q^2+q
       162: 3q^3+q^2+q
       163: 3q^3+q^2+q
       164: 2q^3+q^2+q
       165: 3q^3+q^2+q
       166: 5q^3+q^2+q
       167: q^4+5q^3+q^2+q
       168: q^4+4q^3+q^2+q
       172: q^2+q
       176: q^3+q^2+q
       177: 2q^3+q^2+q
       179: q^3+q^2+q
       181: q^2+q
       184: q^2+q
       186: q^2+q
       187: q^2+q
       189: q^3+q^2+q
       192: q^3+q^2+q
       194: q^3+q^2+q
       196: q^3+q^2+q
       197: q^2+q
       200: q^3+q^2+q
       202: q^3+q^2+q
       204: q^3+q^2+q
       205: q^2+q
       207: 2q^3+q^2+q
       208: q^3
       209: q^3+q^2+q
       211: 2q^3+q^2+q
       213: q^3+q
       215: q
       217: q^3+q
       219: q^2+q
       220: q
       221: q^3+q
       222: q
       223: q^3+q^2+q
       224: q
       225: q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^2+q
       228: 3q^3+q^2+q
       229: q^3+q^2+q
       230: q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^2+q
       233: 3q^3+q^2+q
       234: q^3+q^2+q
       235: q^3+q^2+q
       236: 4q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: 2q^3+q^2+q
       243: 3q^3+q^2+q
       244: 2q^3+q^2+q
       245: 2q^3+q^2+q
       246: 2q^3+q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       262: q^2+q
       266: q^2+q
       269: q^2+q
       273: q^2+q
       278: q^3+q^2+q
       279: q
       281: q^3+q
       284: q^2+q
       286: q^2+q
       287: q^3+q^2+q
       289: q
       291: q^2+q
       294: q
       296: q
       297: q
       300: q^2+q
       301: q^2+q
       304: q^2+q
       305: q^2+q
       308: q^2+q
       310: q^2+q
       311: q^2+q
       313: q^2+q
       315: 2q^3+q^2+q
       317: q^3+q^2+q
       320: q^3+q^2+q
       322: q^3+q^2+q
       323: q^2+q
       325: q^3+q^2+q
       333: q
       334: q
       335: q
       336: q^2+q
       337: q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^2+q
       345: q
       346: q^3+q
       347: q
       348: q^3+q^2+q
       349: q
       350: q^3+q^2+q
       351: 2q^2+q
       352: q^2+q
       353: q
       354: q^3+q
       355: q
       356: q^3+q^2+q
       357: q
       358: q^3+q^2+q
       359: 2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       380: q^2+q
       384: q
       388: q
       391: q^2+q
       396: q^2+q
       399: q^2+q
       404: q^2+q
       406: q^2+q
       413: q
       417: q
       420: q
       422: q
       423: q
       425: q^2+q
       427: q^2+q
       430: q^2+q
       432: q^2+q
       433: q^2+q
       435: q
       438: q
       440: q
       441: q
       444: q^2+q
       445: 2q^2+q
       448: q^2+q
       450: q^2+q
       451: q^2+q
       454: q
       455: q
       458: q
       459: q
       462: q^2+q
       463: 2q^2+q
       465: q
       467: q^3+q
       469: q^3+q^2+q
       472: q^2+q
       474: q^2+q
       475: q^2+q
       477: q^2+q
       479: q^2+q
       480: q^2
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q^2+q
       497: q
       498: q
       499: q
       500: q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       524: q
       532: q
       536: q^2+q
       539: q
       543: q
       547: q^2+q
       552: q^2+q
       555: q
       559: q
       563: q^2+q
       568: q^2+q
       570: q^2+q
       575: q^2+q
       577: q^2+q
       580: q^2
       585: q
       590: q
       592: q
       594: q
       596: q
       599: q
       604: q
       605: q
       608: q
       609: q
       613: q^2+q
       620: q
       622: q
       623: q
       625: q
       629: q^2+q
       639: q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       648: q
       650: q
       651: q
       653: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q^2+q
       697: q^2+q
       712: q
       716: q
       720: q
       723: q
       727: q
       739: q
       743: q
       756: q^2+q
       758: q
       762: q
       797: q
       802: q
       804: q
       806: q
       808: q
       811: q
       821: q
       826: q
       828: q
       830: q
       832: q
       835: q
       846: q
       848: q
       849: q
       851: q
       855: q^2+q
       877: q
       878: q
       879: q
       922: q
       927: q
       930: q
       946: q
       950: q
       955: q
       961: q
       975: q
      1010: 1
      1048: q
      1053: q
      1055: q
      1057: q
      1059: q
      1062: q
      1127: 1
      1140: 1
      1199: q
      1204: q
      1208: q
      1278: 1
      1299: 1
      1361: 1
      1393: 1
      1432: 1
      1510: 1
      1522: 1
      1622: 1
      1722: 1

1723:    0: q^3+3q^2+4q+2
         1: q^3+3q^2+4q+2
         2: q^3+3q^2+4q+2
         3: q^3+3q^2+4q+2
         4: q^3+3q^2+3q+2
         5: q^3+3q^2+4q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: q^3+3q^2+4q+2
         9: q^3+3q^2+3q+2
        10: q^3+3q^2+4q+2
        11: q^3+3q^2+4q+2
        12: q^3+3q^2+3q+2
        13: q^3+3q^2+4q+2
        14: q^3+3q^2+3q+2
        15: q^3+3q^2+4q+2
        16: q^3+3q^2+4q+2
        17: q^3+3q^2+4q+2
        18: q^3+3q^2+3q+2
        19: 2q^2+3q+2
        20: 2q^2+3q+2
        21: 2q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: q^3+3q^2+4q+2
        29: 2q^2+3q+2
        30: 2q^2+3q+2
        31: 2q^2+4q+2
        32: 2q^2+4q+2
        33: 2q^2+4q+2
        34: 2q^2+4q+2
        35: 2q^2+4q+2
        36: 2q^2+4q+2
        37: 2q^2+4q+2
        39: 2q^2+4q+2
        41: 2q^2+4q+2
        43: q^3+3q^2+4q+2
        44: q^3+3q^2+3q+2
        45: q^3+3q^2+4q+2
        46: q^3+3q^2+4q+2
        47: q^3+3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^2+3q+2
        50: 2q^2+3q+2
        51: 2q^2+3q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+4q+2
        64: 2q^2+4q+2
        66: 2q^2+4q+2
        68: q^3+3q^2+4q+2
        69: 2q^2+3q+2
        70: 2q^2+3q+2
        71: 2q^2+3q+2
        72: 2q+2
        73: 2q+2
        74: q^2+3q+2
        76: q^2+3q+2
        78: q^2+3q+2
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: q^3+3q^2+4q+2
        89: q^3+3q^2+4q+2
        90: q^3+3q^2+3q+2
        91: 2q^2+3q+2
        92: 2q^2+3q+2
        93: 2q^2+3q+2
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+3q+2
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+3q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       103: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: q^2+3q+2
       115: q^2+3q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+4q+2
       123: 2q^2+4q+2
       125: q^3+3q^2+4q+2
       126: 2q^2+3q+2
       127: q^2+3q+2
       129: q^2+3q+2
       131: q^2+3q+2
       133: 2q^2+3q+2
       134: 2q^2+3q+2
       135: 2q+2
       136: 2q+2
       137: 2q^2+4q+2
       138: q^2+3q+2
       139: q^2+3q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q^2+4q+2
       144: q^2+3q+2
       145: q^2+3q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       151: 2q+2
       153: 2q+2
       155: 2q+2
       157: 2q^2+3q+2
       158: 2q^2+3q+2
       159: 2q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+3q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+3q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       169: q+1
       172: q+1
       173: q^2+2q+1
       176: q^2+2q+1
       177: q^2+3q+2
       179: q^2+3q+2
       181: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q+2
       189: q^2+3q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2q^2+4q+2
       209: 2q+2
       211: 2q+2
       213: q^2+3q+2
       215: q^2+3q+2
       217: q^2+3q+2
       219: 2q^2+3q+2
       220: 2q^2+3q+2
       221: 2q^2+3q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: q^2+3q+2
       227: q^2+3q+2
       228: q^2+3q+2
       229: 2
       230: 2q+2
       231: q^2+3q+2
       232: q^2+3q+2
       233: q^2+3q+2
       234: 2q+2
       235: 2
       236: 2q+2
       237: 2q+2
       239: 2q+2
       241: 2q+2
       243: 2q+2
       244: 2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: q+1
       262: q+1
       263: q+1
       266: q+1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q^2+2q+1
       278: q^2+2q+1
       279: q^2+3q+2
       281: q^2+3q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q^2+3q+2
       289: 2q+2
       291: 2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2q+2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 2q+2
       317: 2q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: 2q+2
       327: q^2+3q+2
       329: q^2+3q+2
       331: q^2+3q+2
       333: 2q^2+3q+2
       334: 2q+2
       335: 2q+2
       336: 1
       337: q+2
       338: q+2
       340: q+2
       342: q+1
       344: q^2+3q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: q^2+3q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: 2q+2
       367: 2q+2
       368: 2q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: q+1
       380: q+1
       381: q+1
       384: q+1
       385: q+1
       388: q+1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: q^2+3q+2
       411: q^2+3q+2
       413: q^2+3q+2
       415: 2q+2
       417: 2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2q+2
       425: 1
       427: q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 2
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: 2
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: 2q+2
       467: 2q+2
       469: 2q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 2q+2
       482: 2q+2
       483: 1
       484: q+2
       485: q+2
       487: q+2
       489: q+1
       491: 1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: 1
       496: 2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: 1
       501: 2
       502: 2q+2
       504: 2q+2
       506: 2q+2
       508: 2q+2
       509: 2q+2
       510: 2q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       521: q+1
       524: q+1
       525: q+1
       528: q+1
       529: q+1
       532: q+1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: q^2+3q+2
       585: 2q+2
       587: 2q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       597: 1
       599: 1
       601: q+2
       603: 1
       604: 1
       605: 2
       607: q+1
       608: q+1
       609: 2
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       625: 2
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: 2q+2
       637: 2q+2
       639: 2q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       657: q+2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: 1
       666: q+2
       668: q+2
       670: q+1
       672: q+2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: 1
       680: 2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: 1
       686: 2q+2
       687: 2
       688: 2
       690: q+2
       691: q+2
       692: q+1
       693: 1
       697: 1
       705: q+1
       708: q+1
       709: q+1
       712: q+1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       775: q+2
       777: 2q+2
       779: 1
       781: 1
       783: 1
       789: q+2
       791: 1
       793: 1
       794: 1
       795: 2
       797: 2
       799: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 2q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       851: 2
       853: 2
       857: 2
       859: q+2
       861: q+2
       863: q+1
       865: q+2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       881: q+2
       882: q+2
       883: q+1
       884: 1
       889: 1
       896: q+1
       899: q+1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       992: q+2
       994: 1
       996: 1
      1002: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1048: 2
      1050: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1066: q+2
      1068: q+2
      1070: q+1
      1072: q+2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1091: 1
      1098: 1
      1102: 1
      1138: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1184: 1
      1185: 1
      1188: 2
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1210: q+2
      1212: 1
      1214: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2
      1228: 1
      1229: 1
      1230: 1
      1236: 1
      1238: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1256: 1
      1262: 2
      1264: 2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1302: 1
      1307: 1
      1334: 1
      1340: 1
      1342: 1
      1372: 1
      1374: 1
      1404: 2
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1436: 1
      1438: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1456: 1
      1458: 1
      1485: 1
      1486: 1
      1525: 1
      1530: 1
      1553: 1
      1637: 1
      1639: 1
      1643: 1
      1651: 1
      1723: 1

1724:    0: 3q^4+24q^3+24q^2+6q
         1: 3q^4+24q^3+24q^2+6q
         2: 8q^4+21q^3+19q^2+6q
         3: 3q^4+24q^3+24q^2+6q
         4: 8q^4+21q^3+19q^2+6q
         5: 3q^4+24q^3+24q^2+6q
         6: 8q^4+21q^3+19q^2+6q
         7: q^5+7q^4+16q^3+15q^2+6q
         8: 2q^5+11q^4+22q^3+19q^2+6q
         9: q^5+7q^4+16q^3+15q^2+6q
        10: 3q^4+24q^3+24q^2+6q
        11: 3q^4+24q^3+24q^2+6q
        12: 8q^4+21q^3+19q^2+6q
        13: q^4+16q^3+19q^2+6q
        14: 3q^4+13q^3+15q^2+6q
        15: 3q^4+17q^3+19q^2+6q
        16: 3q^4+24q^3+24q^2+6q
        17: 3q^4+24q^3+24q^2+6q
        18: q^5+7q^4+16q^3+15q^2+6q
        19: q^4+16q^3+19q^2+6q
        20: q^4+16q^3+19q^2+6q
        21: 3q^4+13q^3+15q^2+6q
        22: 16q^3+22q^2+6q
        23: 16q^3+22q^2+6q
        24: 5q^4+16q^3+17q^2+6q
        25: 16q^3+22q^2+6q
        26: 16q^3+22q^2+6q
        27: 5q^4+16q^3+17q^2+6q
        28: 3q^4+24q^3+24q^2+6q
        29: q^4+16q^3+19q^2+6q
        30: 10q^3+15q^2+6q
        31: 16q^3+22q^2+6q
        32: 11q^3+17q^2+6q
        33: 16q^3+22q^2+6q
        34: 16q^3+22q^2+6q
        35: 11q^3+17q^2+6q
        36: 16q^3+22q^2+6q
        37: 4q^3+6q^2+2q
        38: 6q^3+14q^2+4q
        39: 4q^3+6q^2+2q
        40: 6q^3+14q^2+4q
        41: q^4+4q^3+5q^2+2q
        42: 2q^4+8q^3+10q^2+4q
        43: q^4+16q^3+19q^2+6q
        44: 3q^4+13q^3+15q^2+6q
        45: 3q^4+17q^3+19q^2+6q
        46: q^4+16q^3+19q^2+6q
        47: 3q^4+17q^3+19q^2+6q
        48: 3q^4+13q^3+15q^2+6q
        49: q^4+16q^3+19q^2+6q
        50: q^4+16q^3+19q^2+6q
        51: 3q^4+13q^3+15q^2+6q
        52: 9q^3+17q^2+6q
        53: 9q^3+17q^2+6q
        54: 2q^4+9q^3+13q^2+6q
        55: 9q^3+17q^2+6q
        56: 9q^3+17q^2+6q
        57: 2q^4+9q^3+13q^2+6q
        58: 8q^3+11q^2+3q
        59: 8q^3+11q^2+3q
        60: 8q^3+11q^2+3q
        61: 8q^3+11q^2+3q
        62: 4q^3+6q^2+2q
        63: 6q^3+14q^2+4q
        64: 3q^3+5q^2+2q
        65: 4q^3+10q^2+4q
        66: 4q^3+6q^2+2q
        67: 6q^3+14q^2+4q
        68: q^4+9q^3+14q^2+6q
        69: 10q^3+15q^2+6q
        70: 10q^3+15q^2+6q
        71: q^4+16q^3+19q^2+6q
        72: 4q^3+12q^2+6q
        73: 4q^3+12q^2+6q
        74: q^3+3q^2+2q
        75: 2q^3+10q^2+4q
        76: q^3+3q^2+2q
        77: 2q^3+10q^2+4q
        78: q^3+3q^2+2q
        79: q^4+4q^3+7q^2+4q
        80: 11q^3+17q^2+6q
        81: 11q^3+17q^2+6q
        82: 9q^3+17q^2+6q
        83: 6q^3+13q^2+6q
        84: 11q^3+17q^2+6q
        85: 11q^3+17q^2+6q
        86: 9q^3+17q^2+6q
        87: 6q^3+13q^2+6q
        88: q^4+16q^3+19q^2+6q
        89: 3q^4+17q^3+19q^2+6q
        90: 3q^4+13q^3+15q^2+6q
        91: 6q^3+13q^2+6q
        92: q^4+9q^3+14q^2+6q
        93: 6q^3+13q^2+6q
        94: 9q^3+17q^2+6q
        95: 9q^3+17q^2+6q
        96: 2q^4+9q^3+13q^2+6q
        97: 9q^3+17q^2+6q
        98: 9q^3+17q^2+6q
        99: 2q^4+9q^3+13q^2+6q
       100: 2q^3+13q^2+6q
       101: 2q^3+13q^2+6q
       102: 3q^3+9q^2+6q
       103: 2q^3+3q^2+q
       104: 3q^3+7q^2+2q
       105: 3q^3+7q^2+2q
       106: 2q^3+3q^2+q
       107: 2q^3+6q^2+3q
       108: 2q^3+6q^2+3q
       109: 2q^3+6q^2+3q
       110: 2q^3+6q^2+3q
       111: 2q^2+2q
       112: 6q^2+4q
       113: q^3+3q^2+2q
       114: 2q^3+10q^2+4q
       115: q^3+3q^2+2q
       116: 2q^3+7q^2+4q
       117: 3q^3+6q^2+3q
       118: 3q^3+6q^2+3q
       119: 3q^3+6q^2+3q
       120: 3q^3+6q^2+3q
       121: 3q^3+5q^2+2q
       122: 4q^3+10q^2+4q
       123: 3q^3+5q^2+2q
       124: 4q^3+10q^2+4q
       125: q^4+9q^3+14q^2+6q
       126: 10q^3+15q^2+6q
       127: q^3+3q^2+2q
       128: 2q^3+10q^2+4q
       129: q^3+3q^2+2q
       130: 2q^3+10q^2+4q
       131: q^3+3q^2+2q
       132: q^4+4q^3+7q^2+4q
       133: 3q^3+10q^2+6q
       134: 6q^3+13q^2+6q
       135: q^3+8q^2+6q
       136: q^3+8q^2+6q
       137: 11q^3+17q^2+6q
       138: 6q^3+13q^2+6q
       139: 9q^3+17q^2+6q
       140: 4q^2+4q
       141: 6q^3+13q^2+6q
       142: 4q^3+12q^2+6q
       143: 11q^3+17q^2+6q
       144: 6q^3+13q^2+6q
       145: 9q^3+17q^2+6q
       146: 6q^3+13q^2+6q
       147: 4q^3+12q^2+6q
       148: 4q^2+4q
       149: 2q^3+13q^2+6q
       150: q^3+9q^2+6q
       151: 2q^2+2q
       152: q^3+9q^2+4q
       153: 2q^2+2q
       154: q^3+9q^2+4q
       155: 2q^2+2q
       156: 2q^3+6q^2+4q
       157: 6q^3+13q^2+6q
       158: q^4+9q^3+14q^2+6q
       159: 6q^3+13q^2+6q
       160: 3q^3+9q^2+6q
       161: 4q^3+10q^2+6q
       162: 3q^3+9q^2+6q
       163: 3q^3+9q^2+6q
       164: 4q^3+10q^2+6q
       165: 3q^3+9q^2+6q
       166: 2q^3+13q^2+6q
       167: 2q^3+13q^2+6q
       168: 3q^3+9q^2+6q
       169: q^2+q
       170: 3q^2+2q
       171: 3q^2+2q
       172: q^2+q
       173: q^3+2q^2+q
       174: q^3+3q^2+2q
       175: q^3+3q^2+2q
       176: q^3+2q^2+q
       177: q^3+3q^2+2q
       178: 2q^3+7q^2+4q
       179: q^3+3q^2+2q
       180: 2q^3+10q^2+4q
       181: 2q^2+2q
       182: 6q^2+4q
       183: 3q^2+3q
       184: 3q^2+3q
       185: 3q^2+3q
       186: 3q^2+3q
       187: 2q^2+2q
       188: 3q^2+4q
       189: q^3+3q^2+2q
       190: 2q^3+7q^2+4q
       191: 3q^3+6q^2+3q
       192: 3q^3+6q^2+3q
       193: 2q^2+2q
       194: 2q^2+2q
       195: 2q^3+6q^2+3q
       196: 2q^3+6q^2+3q
       197: 2q
       198: 2q^2+2q
       199: 3q^3+6q^2+3q
       200: 3q^3+6q^2+3q
       201: 2q^3+6q^2+3q
       202: 2q^3+6q^2+3q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 2q
       206: 2q^2+2q
       207: 3q^3+5q^2+2q
       208: 4q^3+10q^2+4q
       209: 2q^2+2q
       210: q^3+9q^2+4q
       211: 2q^2+2q
       212: q^3+6q^2+4q
       214: q^3+3q^2+4q
       216: 4q^2+4q
       218: q^3+3q^2+4q
       219: 3q^3+10q^2+6q
       220: 3q^3+10q^2+6q
       221: 6q^3+13q^2+6q
       222: q^3+8q^2+6q
       223: q^3+8q^2+6q
       224: q^3+8q^2+6q
       225: q^3+8q^2+6q
       226: 6q^3+13q^2+6q
       227: q^3+6q^2+6q
       228: 3q^3+9q^2+6q
       229: q^2+4q
       230: q^3+6q^2+6q
       231: 6q^3+13q^2+6q
       232: q^3+6q^2+6q
       233: 3q^3+9q^2+6q
       234: q^3+6q^2+6q
       235: q^2+4q
       236: q^3+9q^2+6q
       237: 2q^2+2q
       238: q^3+9q^2+4q
       239: 2q^2+2q
       240: q^3+9q^2+4q
       241: 2q^2+2q
       242: 2q^3+6q^2+4q
       243: 2q^3+13q^2+6q
       244: 4q^2+4q
       245: 4q^2+4q
       246: q^3+9q^2+6q
       247: 6q^2+8q
       248: 6q^2+8q
       249: q^3+4q^2+3q
       250: 3q^3+9q^2+6q
       251: 4q^3+10q^2+6q
       252: 3q^3+9q^2+6q
       253: 3q^3+9q^2+6q
       254: 4q^3+10q^2+6q
       255: 3q^3+9q^2+6q
       256: 5q^2+6q
       257: q^3+7q^2+6q
       258: 5q^2+6q
       259: q^2+q
       260: 3q^2+2q
       261: 3q^2+2q
       262: q^2+q
       263: q^2+q
       264: q^2+2q
       265: q^2+2q
       266: q^2+q
       267: q
       268: q^2+q
       269: q
       270: q^2+q
       271: q
       272: q^2+q
       273: q
       274: q^2+q
       275: q^3+2q^2+q
       276: q^3+3q^2+2q
       277: q^3+3q^2+2q
       278: q^3+2q^2+q
       280: q^2+4q
       282: q^3+3q^2+4q
       283: 3q^2+3q
       284: 3q^2+3q
       285: 3q^2+3q
       286: 3q^2+3q
       287: q^3+3q^2+2q
       288: 2q^3+7q^2+4q
       290: q^2+4q
       291: 2q^2+2q
       292: 3q^2+4q
       293: 3q^2+3q
       294: 3q^2+3q
       295: 3q^2+3q
       296: 3q^2+3q
       297: 2q^2+2q
       298: 3q^2+4q
       299: 2q
       300: 2q
       301: 2q
       302: 2q^2+2q
       303: 2q^2+3q
       304: 2q^2+3q
       305: 2q
       306: 2q
       307: 2q^2+3q
       308: 2q^2+3q
       309: 2q
       310: 2q
       311: 2q
       312: 2q^2+2q
       313: 2q
       314: 2q
       315: 2q^2+2q
       316: q^3+6q^2+4q
       317: 2q^2+2q
       318: q^3+9q^2+4q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       323: 2q
       325: 2q^2+2q
       326: q^3+6q^2+4q
       328: q^3+3q^2+4q
       330: 4q^2+4q
       332: q^3+3q^2+4q
       333: 3q^3+10q^2+6q
       334: q^3+8q^2+6q
       335: q^3+8q^2+6q
       336: q^2+3q
       337: 6q^2+8q
       338: q^2+2q
       339: 5q^2+6q
       340: q^2+2q
       341: 5q^2+6q
       342: q^2+q
       343: q^3+3q^2+2q
       344: q^3+6q^2+6q
       345: q^3+6q^2+6q
       346: 3q^3+9q^2+6q
       347: q^2+4q
       348: q^2+4q
       349: q^3+6q^2+6q
       350: q^3+6q^2+6q
       351: 2q^2+6q
       352: q^3+6q^2+6q
       353: q^3+6q^2+6q
       354: 3q^3+9q^2+6q
       355: q^3+6q^2+6q
       356: q^3+6q^2+6q
       357: q^2+4q
       358: q^2+4q
       359: 2q^2+6q
       361: 2q^2+4q
       363: 4q^2+4q
       365: 2q^2+4q
       366: q^3+9q^2+6q
       367: 3q^2+6q
       368: 5q^2+6q
       369: q^2+4q
       370: q^2+4q
       371: q^2+7q
       372: 2q^2+7q
       373: 2q^2+3q
       374: 5q^2+6q
       375: q^3+7q^2+6q
       376: 5q^2+6q
       377: q^2+q
       378: q^2+2q
       379: q^2+2q
       380: q^2+q
       382: 2q
       383: 2q
       385: q^2+q
       386: q^2+2q
       387: q^2+2q
       388: q^2+q
       389: q
       390: q^2+q
       391: q
       392: q^2+q
       393: q
       394: q
       395: q
       396: q
       397: q
       398: q^2+q
       399: q
       400: q^2+q
       401: q
       402: q
       403: q
       404: q
       405: q
       406: q
       410: q^2+4q
       412: q^3+3q^2+4q
       414: q^2+4q
       416: q^2+4q
       418: q^2+4q
       419: 3q^2+3q
       420: 3q^2+3q
       421: 3q^2+3q
       422: 3q^2+3q
       423: 2q^2+2q
       424: 3q^2+4q
       425: q
       426: q^2+2q
       427: q^2+2q
       428: 5q^2+6q
       429: 2q
       430: 2q
       431: 2q^2+3q
       432: 2q^2+3q
       433: 2q
       434: 2q
       436: 2q
       437: 2q
       438: 2q
       439: 2q^2+3q
       440: 2q^2+3q
       441: 2q
       442: 2q
       443: q^2+3q
       444: q^2+3q
       445: 2q
       446: 2q^2+4q
       447: 2q^2+3q
       448: 2q^2+3q
       449: 2q
       450: 2q
       451: 2q
       452: 2q
       453: 2q^2+3q
       454: 2q^2+3q
       456: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: q^2+3q
       462: q^2+3q
       463: 2q
       464: 2q^2+4q
       466: q^2+4q
       468: 2q^2+4q
       469: 2q^2+2q
       470: q^3+6q^2+4q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       477: 2q
       479: 4q
       481: 2q^2+4q
       482: 2q^2+4q
       483: q^2+3q
       484: q^2+6q
       486: 5q
       488: q^2+5q
       490: q^2+2q
       491: 3q
       492: q^3+6q^2+6q
       493: q^2+4q
       494: q^3+6q^2+6q
       495: 2q
       496: 5q
       497: q^3+6q^2+6q
       498: q^3+6q^2+6q
       499: q^2+4q
       500: 2q
       501: 5q
       503: 2q^2+4q
       505: 4q^2+4q
       507: 2q^2+4q
       508: 3q^2+6q
       509: 3q^2+6q
       510: 5q^2+6q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: q^2+7q
       516: 2q^2+7q
       517: 2q^2+3q
       518: q^2+7q
       519: 2q^2+7q
       520: 2q^2+3q
       522: 2q
       523: 2q
       526: 2q
       527: 2q
       529: q^2+q
       530: q^2+2q
       531: q^2+2q
       532: q^2+q
       533: q
       534: q
       535: q
       536: q
       538: q
       540: q
       541: q
       542: q
       543: q
       544: q
       545: q
       546: q^2+2q
       547: q
       548: q^2+2q
       549: q
       550: q
       551: q
       552: q
       554: q
       556: q
       557: q
       558: q
       559: q
       560: q
       561: q
       562: q^2+2q
       563: q
       564: q^2+2q
       565: q
       568: q
       569: q
       570: q
       573: 2q
       575: 2q
       577: 2q
       578: 2q
       584: q^2+4q
       586: 2q
       588: q^2+4q
       589: q^2+2q
       590: q^2+2q
       595: q^2+2q
       596: q^2+2q
       598: 2q
       599: q
       600: q^2+2q
       602: 4q
       603: 2q
       604: 2q
       606: 2q
       607: 2q^2+3q
       608: 2q^2+3q
       609: 2q
       610: 2q
       612: 2q
       613: q
       614: q
       615: 2q
       616: 2q
       618: 3q
       619: 2q^2+3q
       620: 2q^2+3q
       621: 2q
       622: 2q
       624: 2q
       625: 2q
       626: 2q
       628: 2q
       629: q
       630: q
       631: 2q
       632: 2q
       634: 3q
       636: q^2+4q
       638: 2q^2+4q
       640: q^2+4q
       641: 2q
       642: 2q
       643: 2q
       644: 2q
       645: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       653: 2q
       655: 3q
       657: q^2+6q
       659: 5q
       661: q^2+5q
       663: q^2+2q
       664: 3q
       665: 2q
       667: 5q
       669: q^2+5q
       671: q^2+2q
       672: q^2+6q
       673: 3q
       674: 5q
       675: 2q
       676: 2q^2+4q
       677: 2q
       678: 5q
       679: 2q
       680: 5q
       681: 2q^2+4q
       682: 2q
       683: 2q
       684: 5q
       685: 2q
       686: 3q^2+6q
       687: q^2+4q
       688: q^2+4q
       690: q^2+7q
       691: 2q^2+7q
       692: 2q^2+3q
       693: q
       694: q
       697: q
       701: q
       706: 2q
       707: 2q
       710: q
       711: q
       722: q
       724: q
       725: q
       726: q
       727: q
       728: q
       730: q
       732: q
       734: q
       736: q
       738: q
       740: q
       741: q
       742: q
       743: q
       744: q
       746: q
       748: q
       750: q
       752: q
       753: q
       756: q
       761: q
       762: q
       765: q
       768: q
       770: q
       776: 4q
       778: 2q
       780: 2q
       782: q
       784: 2q
       790: 4q
       791: q
       793: 2q
       794: 2q
       796: 3q
       800: 2q
       801: q
       802: q
       807: q^2+2q
       808: q^2+2q
       810: q
       811: q
       812: q
       814: 3q
       815: 2q
       816: 2q
       817: 2q
       818: 2q
       820: 3q
       824: 2q
       825: q^2+2q
       826: q^2+2q
       831: q
       832: q
       834: q
       835: q
       836: q
       838: 3q
       839: 2q
       840: 2q
       842: q^2+4q
       843: 3q
       845: 2q
       846: 2q
       847: 2q
       848: 2q
       851: 2q
       857: 3q
       860: 5q
       862: q^2+5q
       864: q^2+2q
       865: q^2+6q
       866: 2q
       867: 3q
       868: 2q
       869: 5q
       870: 2q
       871: q
       872: 2q
       873: 5q
       874: 2q
       875: q
       876: 2q
       877: 2q
       878: 2q
       881: q+2
       882: q+2
       883: q+1
       897: q
       898: q
       913: q
       915: q
       917: q
       919: q
       933: q
       935: q
       937: q
       939: q
       941: q
       943: q
       957: q
       959: q
       964: q
       967: q
       969: q
       974: q
       975: q
       983: q
       988: q
       991: q
       993: 4q
       995: q
       997: 2q
      1003: q
      1008: q
      1012: q
      1015: 3q
      1016: 2q
      1017: 2q
      1021: q
      1025: q
      1031: 3q
      1032: 2q
      1033: 2q
      1037: q
      1043: q
      1046: 3q
      1052: q
      1053: q
      1058: q
      1059: q
      1067: q+2
      1069: q+2
      1071: q+1
      1072: q+2
      1073: 1
      1074: 2q
      1075: 2
      1076: q
      1077: 2q
      1078: q
      1079: 2
      1080: q
      1081: 2q
      1082: q
      1145: q
      1147: q
      1165: q
      1167: q
      1189: q
      1194: q
      1197: q
      1211: q+2
      1213: 1
      1215: q
      1224: q
      1227: 2
      1228: 1
      1229: 1
      1237: q
      1245: 2
      1246: 1
      1247: 1
      1253: q
      1262: 2
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1341: 1
      1343: 1
      1373: 1
      1375: 1
      1405: 2
      1410: 1
      1413: 1
      1439: 1
      1444: 1
      1453: 1
      1459: 1
      1485: 1
      1486: 1
      1526: 1
      1533: 1
      1554: 1
      1639: 1
      1644: 1
      1652: 1
      1724: 1

1725:    0: 2q^4+4q^3+5q^2+2q
         1: q^4+4q^3+5q^2+2q
         2: 2q^4+4q^3+5q^2+2q
         3: 2q^4+4q^3+5q^2+2q
         4: q^5+q^4+3q^3+4q^2+2q
         5: q^4+4q^3+5q^2+2q
         6: q^5+3q^4+5q^3+4q^2+2q
         7: q^5+q^4+3q^3+4q^2+2q
         8: q^4+4q^3+5q^2+2q
         9: q^5+q^4+3q^3+4q^2+2q
        10: q^3+4q^2+2q
        11: q^3+4q^2+2q
        12: 2q^3+3q^2+2q
        13: 2q^4+4q^3+5q^2+2q
        14: q^5+q^4+3q^3+4q^2+2q
        15: q^4+4q^3+5q^2+2q
        16: 2q^4+4q^3+5q^2+2q
        17: q^4+4q^3+5q^2+2q
        18: q^5+q^4+3q^3+4q^2+2q
        19: q^4+2q^3+4q^2+2q
        20: q^4+4q^3+4q^2+2q
        21: q^4+2q^3+4q^2+2q
        22: 3q^3+5q^2+2q
        23: 3q^3+5q^2+2q
        24: 3q^3+5q^2+2q
        25: 3q^3+5q^2+2q
        26: 3q^3+5q^2+2q
        27: 3q^3+5q^2+2q
        28: q^3+4q^2+2q
        29: q^3+3q^2+2q
        30: q^4+2q^3+4q^2+2q
        31: 4q^2+2q
        32: 3q^3+5q^2+2q
        33: 3q^3+5q^2+2q
        34: 4q^2+2q
        35: 3q^3+5q^2+2q
        36: 3q^3+5q^2+2q
        37: 3q^3+5q^2+2q
        39: 3q^3+5q^2+2q
        41: 3q^3+5q^2+2q
        43: q^3+4q^2+2q
        44: 2q^3+3q^2+2q
        45: q^3+4q^2+2q
        46: 2q^4+4q^3+5q^2+2q
        47: q^4+4q^3+5q^2+2q
        48: q^5+q^4+3q^3+4q^2+2q
        49: q^4+2q^3+4q^2+2q
        50: q^4+4q^3+4q^2+2q
        51: q^4+2q^3+4q^2+2q
        52: q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^3+4q^2+2q
        55: q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^3+4q^2+2q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        62: 4q^2+2q
        64: 3q^3+5q^2+2q
        66: 3q^3+5q^2+2q
        68: q^3+4q^2+2q
        69: q^4+2q^3+4q^2+2q
        70: q^3+3q^2+2q
        71: q^3+3q^2+2q
        72: q^3+3q^2+2q
        73: q^3+3q^2+2q
        74: q^3+4q^2+2q
        76: 3q^3+4q^2+2q
        78: q^3+4q^2+2q
        80: 4q^2+2q
        81: 3q^3+5q^2+2q
        82: 3q^2+2q
        83: q^3+4q^2+2q
        84: 4q^2+2q
        85: 3q^3+5q^2+2q
        86: 3q^2+2q
        87: q^3+4q^2+2q
        88: q^3+4q^2+2q
        89: q^3+4q^2+2q
        90: 2q^3+3q^2+2q
        91: q^4+2q^3+4q^2+2q
        92: q^4+4q^3+4q^2+2q
        93: q^4+2q^3+4q^2+2q
        94: q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^3+4q^2+2q
        97: q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^3+4q^2+2q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       103: 2q^2+q
       106: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       111: q^3+3q^2+2q
       113: 3q^2+2q
       115: q^3+4q^2+2q
       117: 2q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: 2q^2+q
       121: 4q^2+2q
       123: 3q^3+5q^2+2q
       125: q^3+4q^2+2q
       126: q^3+3q^2+2q
       127: q^3+4q^2+2q
       129: 3q^3+4q^2+2q
       131: q^3+4q^2+2q
       133: q^3+3q^2+2q
       134: q^4+2q^3+4q^2+2q
       135: q^3+3q^2+2q
       136: q^3+3q^2+2q
       137: 4q^2+2q
       138: q^3+4q^2+2q
       139: 3q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: q^3+3q^2+2q
       143: 4q^2+2q
       144: q^3+4q^2+2q
       145: 3q^2+2q
       146: 3q^2+2q
       147: q^3+3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       151: 3q^2+2q
       153: q^3+3q^2+2q
       155: 3q^2+2q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^3+4q^2+2q
       161: 3q^3+4q^2+2q
       162: q^3+4q^2+2q
       163: q^3+4q^2+2q
       164: 3q^3+4q^2+2q
       165: q^3+4q^2+2q
       166: 3q^2+2q
       167: q^3+3q^2+2q
       168: 3q^2+2q
       169: q^2+q
       172: q^2+q
       173: 2q^2+q
       176: 2q^2+q
       177: q^3+4q^2+2q
       179: 3q^2+2q
       181: q^3+3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       187: q^3+3q^2+2q
       189: 3q^2+2q
       191: 2q^2+q
       192: 2q^2+q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       197: q^2+2q
       199: 2q^2+q
       200: 2q^2+q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       205: q^2+2q
       207: 4q^2+2q
       209: 2q^2+2q
       211: 3q^2+2q
       213: q^3+4q^2+2q
       215: 3q^3+4q^2+2q
       217: q^3+4q^2+2q
       219: q^3+3q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: 2q
       223: q^3+3q^2+2q
       224: 2q
       225: q^3+3q^2+2q
       226: 3q^2+2q
       227: 3q^2+2q
       228: q^3+4q^2+2q
       229: q^2+2q
       230: q^3+3q^2+2q
       231: 3q^2+2q
       232: 3q^2+2q
       233: q^3+4q^2+2q
       234: q^3+3q^2+2q
       235: q^2+2q
       236: 3q^2+2q
       237: 3q^2+2q
       239: q^3+3q^2+2q
       241: 3q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: 3q^2+2q
       257: q^3+3q^2+2q
       258: 3q^2+2q
       259: q^2+q
       262: q^2+q
       263: q^2+q
       266: q^2+q
       267: q
       269: q
       271: q
       273: q
       275: 2q^2+q
       278: 2q^2+q
       279: 3q^2+2q
       281: q^3+4q^2+2q
       283: q^2+q
       284: q^2+q
       285: q^2+q
       286: q^2+q
       287: 3q^2+2q
       289: q^3+3q^2+2q
       291: q^3+3q^2+2q
       293: q
       294: q
       295: q
       296: q
       297: 2q
       299: q
       300: q
       301: q^2+2q
       303: q^2+q
       304: q^2+q
       305: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       311: q^2+2q
       313: q^2+2q
       315: 3q^2+2q
       317: 2q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: q^2+2q
       325: 2q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: q^2+2q
       334: 2q
       335: 2q
       336: q
       337: q^2+2q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: 3q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: 2q
       348: q^2+2q
       349: 2q
       350: q^3+3q^2+2q
       351: 2q
       352: 3q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: 2q
       356: q^3+3q^2+2q
       357: 2q
       358: q^2+2q
       359: 2q
       360: 3q^2+2q
       362: q^3+3q^2+2q
       364: 3q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 3q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: q^2+2q
       372: q^2+2q
       373: q^2+q
       377: q^2+q
       380: q^2+q
       381: q^2+q
       384: q^2+q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: q^2+2q
       411: q^2+2q
       413: 3q^2+2q
       415: 2q
       417: q^3+3q^2+2q
       419: q
       420: q
       421: q
       422: q
       423: 2q
       425: q
       427: q^2+2q
       429: q
       430: q
       431: q^2+q
       432: q^2+q
       433: q^2+2q
       435: q^2+2q
       437: q
       438: q
       439: q
       440: q
       441: 2q
       443: q
       444: q
       445: 2q
       447: q^2+q
       448: q^2+q
       449: q
       450: q
       451: q^2+2q
       453: q
       454: q
       455: q^2+2q
       457: q
       458: q
       459: 2q
       461: q
       462: q
       463: 2q
       465: 2q^2+2q
       467: 3q^2+2q
       469: 2q^2+2q
       471: q
       472: q
       473: q
       474: q
       475: q^2+2q
       477: q^2+2q
       479: 2q
       481: 2q
       482: 2q
       483: q
       484: q^2+2q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q
       492: q^2+2q
       493: 2q
       494: 2q
       495: q
       496: 2q
       497: q^2+2q
       498: 2q
       499: 2q
       500: q
       501: 2q
       508: 2q^2+2q
       512: q^2+2q
       514: q^2+2q
       515: q^2+2q
       516: q^2+2q
       517: q^2+q
       521: q^2+q
       524: q^2+q
       525: q
       528: q
       529: q
       532: q
       533: q
       536: q
       537: q
       539: q
       541: q
       543: q
       545: q
       547: q
       549: q
       552: q
       553: q
       555: q
       557: q
       559: q
       561: q
       563: q
       565: q
       568: q
       569: q
       570: q
       573: q
       575: q
       577: 2q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q
       590: q
       595: q
       596: q
       597: q
       599: q
       601: q^2+2q
       603: q
       604: q
       605: q^2+2q
       607: q
       608: q
       609: 2q
       613: q
       615: q
       616: q
       617: 2q
       619: q
       620: q
       621: q
       622: q
       623: q^2+2q
       625: 2q
       629: q
       631: q
       632: q
       633: 2q
       639: 2q^2+2q
       641: q
       642: q
       643: q
       644: q
       645: q^2+2q
       651: q^2+2q
       655: 2q
       657: q^2+2q
       658: q^2+2q
       660: q^2+2q
       662: q^2+q
       664: q
       665: q
       674: 2q
       675: 2q
       676: 2q
       677: q
       679: q
       680: 2q
       681: 2q
       682: 2q
       683: q
       685: q
       693: q
       697: q
       705: q
       708: q
       709: q
       712: q
       721: q
       723: q
       725: q
       727: q
       733: q
       735: q
       737: q
       739: q
       741: q
       743: q
       749: q
       751: q
       753: q
       756: q
       757: q
       758: q
       765: q
       768: q
       769: 2q
       775: q^2+2q
       777: 2q
       779: q
       781: q
       791: q
       793: q
       794: q
       795: 2q
       797: 2q
       801: q
       802: q
       807: q
       808: q
       809: q
       811: q
       817: q
       818: q
       819: 2q
       821: 2q
       825: q
       826: q
       831: q
       832: q
       833: q
       835: q
       843: 2q
       849: q^2+2q
       853: 2
       866: q
       870: q
       871: q
       874: q
       875: q
       884: q
       889: q
       896: q
       899: q
       916: q
       918: q
       920: q
       922: q
       940: q
       942: q
       944: q
       946: q
       960: q
       961: q
       964: q
       967: q
       968: 2q
       978: 1
       979: 1
       984: 2
       994: q
      1010: q
      1012: q
      1020: q
      1022: q
      1036: q
      1038: q
      1050: 2
      1076: q
      1080: q
      1086: q
      1091: q
      1100: 1
      1107: 1
      1138: q
      1184: 1
      1185: 1
      1190: 2
      1222: 1
      1230: q
      1248: q
      1264: 2
      1304: 1
      1311: 1
      1336: 1
      1406: 2
      1414: 1
      1415: 1
      1446: 1
      1527: 1
      1534: 1
      1555: 1
      1637: 1
      1725: 1

1726:    0: 3q^4+24q^3+24q^2+6q
         1: 3q^4+24q^3+24q^2+6q
         2: 8q^4+21q^3+19q^2+6q
         3: 3q^4+24q^3+24q^2+6q
         4: 8q^4+21q^3+19q^2+6q
         5: 3q^4+24q^3+24q^2+6q
         6: 8q^4+21q^3+19q^2+6q
         7: q^5+7q^4+16q^3+15q^2+6q
         8: 2q^5+11q^4+22q^3+19q^2+6q
         9: q^5+7q^4+16q^3+15q^2+6q
        10: 3q^4+24q^3+24q^2+6q
        11: 3q^4+24q^3+24q^2+6q
        12: 8q^4+21q^3+19q^2+6q
        13: q^4+16q^3+19q^2+6q
        14: 3q^4+13q^3+15q^2+6q
        15: 3q^4+17q^3+19q^2+6q
        16: 3q^4+24q^3+24q^2+6q
        17: 3q^4+24q^3+24q^2+6q
        18: q^5+7q^4+16q^3+15q^2+6q
        19: q^4+16q^3+19q^2+6q
        20: q^4+16q^3+19q^2+6q
        21: 3q^4+13q^3+15q^2+6q
        22: 16q^3+22q^2+6q
        23: 16q^3+22q^2+6q
        24: 5q^4+16q^3+17q^2+6q
        25: 16q^3+22q^2+6q
        26: 16q^3+22q^2+6q
        27: 5q^4+16q^3+17q^2+6q
        28: 3q^4+24q^3+24q^2+6q
        29: q^4+16q^3+19q^2+6q
        30: 10q^3+15q^2+6q
        31: 16q^3+22q^2+6q
        32: 11q^3+17q^2+6q
        33: 16q^3+22q^2+6q
        34: 16q^3+22q^2+6q
        35: 11q^3+17q^2+6q
        36: 16q^3+22q^2+6q
        37: 6q^3+14q^2+4q
        38: 4q^3+6q^2+2q
        39: 6q^3+14q^2+4q
        40: 4q^3+6q^2+2q
        41: 2q^4+8q^3+10q^2+4q
        42: q^4+4q^3+5q^2+2q
        43: q^4+16q^3+19q^2+6q
        44: 3q^4+13q^3+15q^2+6q
        45: 3q^4+17q^3+19q^2+6q
        46: q^4+16q^3+19q^2+6q
        47: 3q^4+17q^3+19q^2+6q
        48: 3q^4+13q^3+15q^2+6q
        49: q^4+16q^3+19q^2+6q
        50: q^4+16q^3+19q^2+6q
        51: 3q^4+13q^3+15q^2+6q
        52: 9q^3+17q^2+6q
        53: 9q^3+17q^2+6q
        54: 2q^4+9q^3+13q^2+6q
        55: 9q^3+17q^2+6q
        56: 9q^3+17q^2+6q
        57: 2q^4+9q^3+13q^2+6q
        58: 8q^3+11q^2+3q
        59: 8q^3+11q^2+3q
        60: 8q^3+11q^2+3q
        61: 8q^3+11q^2+3q
        62: 6q^3+14q^2+4q
        63: 4q^3+6q^2+2q
        64: 4q^3+10q^2+4q
        65: 3q^3+5q^2+2q
        66: 6q^3+14q^2+4q
        67: 4q^3+6q^2+2q
        68: q^4+9q^3+14q^2+6q
        69: 10q^3+15q^2+6q
        70: 10q^3+15q^2+6q
        71: q^4+16q^3+19q^2+6q
        72: 4q^3+12q^2+6q
        73: 4q^3+12q^2+6q
        74: 2q^3+10q^2+4q
        75: q^3+3q^2+2q
        76: 2q^3+10q^2+4q
        77: q^3+3q^2+2q
        78: q^4+4q^3+7q^2+4q
        79: q^3+3q^2+2q
        80: 11q^3+17q^2+6q
        81: 11q^3+17q^2+6q
        82: 9q^3+17q^2+6q
        83: 6q^3+13q^2+6q
        84: 11q^3+17q^2+6q
        85: 11q^3+17q^2+6q
        86: 9q^3+17q^2+6q
        87: 6q^3+13q^2+6q
        88: q^4+16q^3+19q^2+6q
        89: 3q^4+17q^3+19q^2+6q
        90: 3q^4+13q^3+15q^2+6q
        91: 6q^3+13q^2+6q
        92: q^4+9q^3+14q^2+6q
        93: 6q^3+13q^2+6q
        94: 9q^3+17q^2+6q
        95: 9q^3+17q^2+6q
        96: 2q^4+9q^3+13q^2+6q
        97: 9q^3+17q^2+6q
        98: 9q^3+17q^2+6q
        99: 2q^4+9q^3+13q^2+6q
       100: 2q^3+13q^2+6q
       101: 2q^3+13q^2+6q
       102: 3q^3+9q^2+6q
       103: 3q^3+7q^2+2q
       104: 2q^3+3q^2+q
       105: 2q^3+3q^2+q
       106: 3q^3+7q^2+2q
       107: 2q^3+6q^2+3q
       108: 2q^3+6q^2+3q
       109: 2q^3+6q^2+3q
       110: 2q^3+6q^2+3q
       111: 6q^2+4q
       112: 2q^2+2q
       113: 2q^3+10q^2+4q
       114: q^3+3q^2+2q
       115: 2q^3+7q^2+4q
       116: q^3+3q^2+2q
       117: 3q^3+6q^2+3q
       118: 3q^3+6q^2+3q
       119: 3q^3+6q^2+3q
       120: 3q^3+6q^2+3q
       121: 4q^3+10q^2+4q
       122: 3q^3+5q^2+2q
       123: 4q^3+10q^2+4q
       124: 3q^3+5q^2+2q
       125: q^4+9q^3+14q^2+6q
       126: 10q^3+15q^2+6q
       127: 2q^3+10q^2+4q
       128: q^3+3q^2+2q
       129: 2q^3+10q^2+4q
       130: q^3+3q^2+2q
       131: q^4+4q^3+7q^2+4q
       132: q^3+3q^2+2q
       133: 3q^3+10q^2+6q
       134: 6q^3+13q^2+6q
       135: q^3+8q^2+6q
       136: q^3+8q^2+6q
       137: 11q^3+17q^2+6q
       138: 6q^3+13q^2+6q
       139: 9q^3+17q^2+6q
       140: 4q^2+4q
       141: 6q^3+13q^2+6q
       142: 4q^3+12q^2+6q
       143: 11q^3+17q^2+6q
       144: 6q^3+13q^2+6q
       145: 9q^3+17q^2+6q
       146: 6q^3+13q^2+6q
       147: 4q^3+12q^2+6q
       148: 4q^2+4q
       149: 2q^3+13q^2+6q
       150: q^3+9q^2+6q
       151: q^3+9q^2+4q
       152: 2q^2+2q
       153: q^3+9q^2+4q
       154: 2q^2+2q
       155: 2q^3+6q^2+4q
       156: 2q^2+2q
       157: 6q^3+13q^2+6q
       158: q^4+9q^3+14q^2+6q
       159: 6q^3+13q^2+6q
       160: 3q^3+9q^2+6q
       161: 4q^3+10q^2+6q
       162: 3q^3+9q^2+6q
       163: 3q^3+9q^2+6q
       164: 4q^3+10q^2+6q
       165: 3q^3+9q^2+6q
       166: 2q^3+13q^2+6q
       167: 2q^3+13q^2+6q
       168: 3q^3+9q^2+6q
       169: 3q^2+2q
       170: q^2+q
       171: q^2+q
       172: 3q^2+2q
       173: q^3+3q^2+2q
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       176: q^3+3q^2+2q
       177: 2q^3+7q^2+4q
       178: q^3+3q^2+2q
       179: 2q^3+10q^2+4q
       180: q^3+3q^2+2q
       181: 6q^2+4q
       182: 2q^2+2q
       183: 3q^2+3q
       184: 3q^2+3q
       185: 3q^2+3q
       186: 3q^2+3q
       187: 3q^2+4q
       188: 2q^2+2q
       189: 2q^3+7q^2+4q
       190: q^3+3q^2+2q
       191: 3q^3+6q^2+3q
       192: 3q^3+6q^2+3q
       193: 2q^2+2q
       194: 2q^2+2q
       195: 2q^3+6q^2+3q
       196: 2q^3+6q^2+3q
       197: 2q^2+2q
       198: 2q
       199: 3q^3+6q^2+3q
       200: 3q^3+6q^2+3q
       201: 2q^3+6q^2+3q
       202: 2q^3+6q^2+3q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 2q^2+2q
       206: 2q
       207: 4q^3+10q^2+4q
       208: 3q^3+5q^2+2q
       209: q^3+9q^2+4q
       210: 2q^2+2q
       211: q^3+6q^2+4q
       212: 2q^2+2q
       213: q^3+3q^2+4q
       215: 4q^2+4q
       217: q^3+3q^2+4q
       219: 3q^3+10q^2+6q
       220: 3q^3+10q^2+6q
       221: 6q^3+13q^2+6q
       222: q^3+8q^2+6q
       223: q^3+8q^2+6q
       224: q^3+8q^2+6q
       225: q^3+8q^2+6q
       226: 6q^3+13q^2+6q
       227: q^3+6q^2+6q
       228: 3q^3+9q^2+6q
       229: q^2+4q
       230: q^3+6q^2+6q
       231: 6q^3+13q^2+6q
       232: q^3+6q^2+6q
       233: 3q^3+9q^2+6q
       234: q^3+6q^2+6q
       235: q^2+4q
       236: q^3+9q^2+6q
       237: q^3+9q^2+4q
       238: 2q^2+2q
       239: q^3+9q^2+4q
       240: 2q^2+2q
       241: 2q^3+6q^2+4q
       242: 2q^2+2q
       243: 2q^3+13q^2+6q
       244: 4q^2+4q
       245: 4q^2+4q
       246: q^3+9q^2+6q
       247: 6q^2+8q
       248: 6q^2+8q
       249: q^3+4q^2+3q
       250: 3q^3+9q^2+6q
       251: 4q^3+10q^2+6q
       252: 3q^3+9q^2+6q
       253: 3q^3+9q^2+6q
       254: 4q^3+10q^2+6q
       255: 3q^3+9q^2+6q
       256: 5q^2+6q
       257: q^3+7q^2+6q
       258: 5q^2+6q
       259: 3q^2+2q
       260: q^2+q
       261: q^2+q
       262: 3q^2+2q
       263: q^2+2q
       264: q^2+q
       265: q^2+q
       266: q^2+2q
       267: q^2+q
       268: q
       269: q^2+q
       270: q
       271: q^2+q
       272: q
       273: q^2+q
       274: q
       275: q^3+3q^2+2q
       276: q^3+2q^2+q
       277: q^3+2q^2+q
       278: q^3+3q^2+2q
       279: q^2+4q
       281: q^3+3q^2+4q
       283: 3q^2+3q
       284: 3q^2+3q
       285: 3q^2+3q
       286: 3q^2+3q
       287: 2q^3+7q^2+4q
       288: q^3+3q^2+2q
       289: q^2+4q
       291: 3q^2+4q
       292: 2q^2+2q
       293: 3q^2+3q
       294: 3q^2+3q
       295: 3q^2+3q
       296: 3q^2+3q
       297: 3q^2+4q
       298: 2q^2+2q
       299: 2q
       300: 2q
       301: 2q^2+2q
       302: 2q
       303: 2q^2+3q
       304: 2q^2+3q
       305: 2q
       306: 2q
       307: 2q^2+3q
       308: 2q^2+3q
       309: 2q
       310: 2q
       311: 2q^2+2q
       312: 2q
       313: 2q
       314: 2q
       315: q^3+6q^2+4q
       316: 2q^2+2q
       317: q^3+9q^2+4q
       318: 2q^2+2q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       324: 2q
       325: q^3+6q^2+4q
       326: 2q^2+2q
       327: q^3+3q^2+4q
       329: 4q^2+4q
       331: q^3+3q^2+4q
       333: 3q^3+10q^2+6q
       334: q^3+8q^2+6q
       335: q^3+8q^2+6q
       336: q^2+3q
       337: 6q^2+8q
       338: 5q^2+6q
       339: q^2+2q
       340: 5q^2+6q
       341: q^2+2q
       342: q^3+3q^2+2q
       343: q^2+q
       344: q^3+6q^2+6q
       345: q^3+6q^2+6q
       346: 3q^3+9q^2+6q
       347: q^2+4q
       348: q^2+4q
       349: q^3+6q^2+6q
       350: q^3+6q^2+6q
       351: 2q^2+6q
       352: q^3+6q^2+6q
       353: q^3+6q^2+6q
       354: 3q^3+9q^2+6q
       355: q^3+6q^2+6q
       356: q^3+6q^2+6q
       357: q^2+4q
       358: q^2+4q
       359: 2q^2+6q
       360: 2q^2+4q
       362: 4q^2+4q
       364: 2q^2+4q
       366: q^3+9q^2+6q
       367: 3q^2+6q
       368: 5q^2+6q
       369: q^2+4q
       370: q^2+4q
       371: q^2+7q
       372: 2q^2+7q
       373: 2q^2+3q
       374: 5q^2+6q
       375: q^3+7q^2+6q
       376: 5q^2+6q
       377: q^2+2q
       378: q^2+q
       379: q^2+q
       380: q^2+2q
       381: 2q
       384: 2q
       385: q^2+2q
       386: q^2+q
       387: q^2+q
       388: q^2+2q
       389: q^2+q
       390: q
       391: q^2+q
       392: q
       393: q
       394: q
       395: q
       396: q
       397: q^2+q
       398: q
       399: q^2+q
       400: q
       401: q
       402: q
       403: q
       404: q
       407: q
       408: q
       409: q^2+4q
       411: q^3+3q^2+4q
       413: q^2+4q
       415: q^2+4q
       417: q^2+4q
       419: 3q^2+3q
       420: 3q^2+3q
       421: 3q^2+3q
       422: 3q^2+3q
       423: 3q^2+4q
       424: 2q^2+2q
       425: q^2+2q
       426: q
       427: 5q^2+6q
       428: q^2+2q
       429: 2q
       430: 2q
       431: 2q^2+3q
       432: 2q^2+3q
       433: 2q
       434: 2q
       435: 2q
       437: 2q
       438: 2q
       439: 2q^2+3q
       440: 2q^2+3q
       441: 2q
       442: 2q
       443: q^2+3q
       444: q^2+3q
       445: 2q^2+4q
       446: 2q
       447: 2q^2+3q
       448: 2q^2+3q
       449: 2q
       450: 2q
       451: 2q
       452: 2q
       453: 2q^2+3q
       454: 2q^2+3q
       455: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: q^2+3q
       462: q^2+3q
       463: 2q^2+4q
       464: 2q
       465: q^2+4q
       467: 2q^2+4q
       469: q^3+6q^2+4q
       470: 2q^2+2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       476: 2q
       478: 2q
       480: 4q
       481: 2q^2+4q
       482: 2q^2+4q
       483: q^2+3q
       484: q^2+6q
       485: 5q
       487: q^2+5q
       489: q^2+2q
       491: 3q
       492: q^3+6q^2+6q
       493: q^2+4q
       494: q^3+6q^2+6q
       495: 2q
       496: 5q
       497: q^3+6q^2+6q
       498: q^3+6q^2+6q
       499: q^2+4q
       500: 2q
       501: 5q
       502: 2q^2+4q
       504: 4q^2+4q
       506: 2q^2+4q
       508: 3q^2+6q
       509: 3q^2+6q
       510: 5q^2+6q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: q^2+7q
       516: 2q^2+7q
       517: 2q^2+3q
       518: q^2+7q
       519: 2q^2+7q
       520: 2q^2+3q
       521: 2q
       524: 2q
       525: 2q
       528: 2q
       529: q^2+2q
       530: q^2+q
       531: q^2+q
       532: q^2+2q
       533: q
       534: q
       535: q
       536: q
       537: q
       539: q
       541: q
       542: q
       543: q
       544: q
       545: q^2+2q
       546: q
       547: q^2+2q
       548: q
       549: q
       550: q
       551: q
       552: q
       553: q
       555: q
       557: q
       558: q
       559: q
       560: q
       561: q^2+2q
       562: q
       563: q^2+2q
       564: q
       566: q
       567: q
       571: q
       572: q
       574: 2q
       576: 2q
       580: 2q
       581: 2q
       583: q^2+4q
       585: 2q
       587: q^2+4q
       589: q^2+2q
       590: q^2+2q
       595: q^2+2q
       596: q^2+2q
       597: 2q
       599: q^2+2q
       600: q
       601: 4q
       603: 2q
       604: 2q
       605: 2q
       607: 2q^2+3q
       608: 2q^2+3q
       609: 2q
       610: 2q
       611: 2q
       613: q
       614: q
       615: 2q
       616: 2q
       617: 3q
       619: 2q^2+3q
       620: 2q^2+3q
       621: 2q
       622: 2q
       623: 2q
       625: 2q
       626: 2q
       627: 2q
       629: q
       630: q
       631: 2q
       632: 2q
       633: 3q
       635: q^2+4q
       637: 2q^2+4q
       639: q^2+4q
       641: 2q
       642: 2q
       643: 2q
       644: 2q
       646: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       654: 2q
       656: 3q
       657: q^2+6q
       658: 5q
       660: q^2+5q
       662: q^2+2q
       664: 3q
       665: 2q
       666: 5q
       668: q^2+5q
       670: q^2+2q
       672: q^2+6q
       673: 3q
       674: 5q
       675: 2q
       676: 2q^2+4q
       677: 2q
       678: 5q
       679: 2q
       680: 5q
       681: 2q^2+4q
       682: 2q
       683: 2q
       684: 5q
       685: 2q
       686: 3q^2+6q
       687: q^2+4q
       688: q^2+4q
       690: q^2+7q
       691: 2q^2+7q
       692: 2q^2+3q
       696: q
       698: q
       699: q
       700: q
       705: 2q
       708: 2q
       709: q
       712: q
       721: q
       723: q
       725: q
       726: q
       727: q
       728: q
       729: q
       731: q
       733: q
       735: q
       737: q
       739: q
       741: q
       742: q
       743: q
       744: q
       745: q
       747: q
       749: q
       751: q
       754: q
       755: q
       763: q
       764: q
       766: q
       767: q
       772: q
       775: 4q
       777: 2q
       779: 2q
       781: q
       783: 2q
       789: 4q
       792: q
       793: 2q
       794: 2q
       795: 3q
       799: 2q
       801: q
       802: q
       807: q^2+2q
       808: q^2+2q
       809: q
       811: q
       812: q
       813: 3q
       815: 2q
       816: 2q
       817: 2q
       818: 2q
       819: 3q
       823: 2q
       825: q^2+2q
       826: q^2+2q
       831: q
       832: q
       833: q
       835: q
       836: q
       837: 3q
       839: 2q
       840: 2q
       841: q^2+4q
       844: 3q
       845: 2q
       846: 2q
       847: 2q
       848: 2q
       852: 2q
       858: 3q
       859: 5q
       861: q^2+5q
       863: q^2+2q
       865: q^2+6q
       866: 2q
       867: 3q
       868: 2q
       869: 5q
       870: 2q
       871: q
       872: 2q
       873: 5q
       874: 2q
       875: q
       876: 2q
       877: 2q
       878: 2q
       881: q+2
       882: q+2
       883: q+1
       896: q
       899: q
       912: q
       914: q
       916: q
       918: q
       932: q
       934: q
       936: q
       938: q
       940: q
       942: q
       956: q
       958: q
       965: q
       966: q
       971: q
       976: q
       977: q
       985: q
       989: q
       990: q
       992: 4q
       994: q
       996: 2q
      1002: q
      1009: q
      1013: q
      1014: 3q
      1016: 2q
      1017: 2q
      1020: q
      1024: q
      1030: 3q
      1032: 2q
      1033: 2q
      1036: q
      1042: q
      1047: 3q
      1052: q
      1053: q
      1058: q
      1059: q
      1066: q+2
      1068: q+2
      1070: q+1
      1072: q+2
      1073: 1
      1074: 2q
      1075: 2
      1076: q
      1077: 2q
      1078: q
      1079: 2
      1080: q
      1081: 2q
      1082: q
      1144: q
      1146: q
      1164: q
      1166: q
      1191: q
      1195: q
      1196: q
      1210: q+2
      1212: 1
      1214: q
      1225: q
      1226: 2
      1228: 1
      1229: 1
      1236: q
      1244: 2
      1246: 1
      1247: 1
      1252: q
      1263: 2
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1340: 1
      1342: 1
      1372: 1
      1374: 1
      1407: 2
      1411: 1
      1412: 1
      1438: 1
      1445: 1
      1452: 1
      1458: 1
      1485: 1
      1486: 1
      1528: 1
      1529: 1
      1556: 1
      1640: 1
      1643: 1
      1651: 1
      1726: 1

1727:    0: q^3+3q^2+4q+2
         1: q^3+3q^2+4q+2
         2: q^3+3q^2+4q+2
         3: q^3+3q^2+4q+2
         4: q^3+3q^2+3q+2
         5: q^3+3q^2+4q+2
         6: q^3+3q^2+3q+2
         7: q^3+3q^2+3q+2
         8: q^3+3q^2+4q+2
         9: q^3+3q^2+3q+2
        10: q^3+3q^2+4q+2
        11: q^3+3q^2+4q+2
        12: q^3+3q^2+3q+2
        13: q^3+3q^2+4q+2
        14: q^3+3q^2+3q+2
        15: q^3+3q^2+4q+2
        16: q^3+3q^2+4q+2
        17: q^3+3q^2+4q+2
        18: q^3+3q^2+3q+2
        19: 2q^2+3q+2
        20: 2q^2+3q+2
        21: 2q^2+3q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: 2q^2+4q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: 2q^2+4q+2
        28: q^3+3q^2+4q+2
        29: 2q^2+3q+2
        30: 2q^2+3q+2
        31: 2q^2+4q+2
        32: 2q^2+4q+2
        33: 2q^2+4q+2
        34: 2q^2+4q+2
        35: 2q^2+4q+2
        36: 2q^2+4q+2
        38: 2q^2+4q+2
        40: 2q^2+4q+2
        42: 2q^2+4q+2
        43: q^3+3q^2+4q+2
        44: q^3+3q^2+3q+2
        45: q^3+3q^2+4q+2
        46: q^3+3q^2+4q+2
        47: q^3+3q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^2+3q+2
        50: 2q^2+3q+2
        51: 2q^2+3q+2
        52: q^2+3q+2
        53: q^2+3q+2
        54: q^2+3q+2
        55: q^2+3q+2
        56: q^2+3q+2
        57: q^2+3q+2
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        63: 2q^2+4q+2
        65: 2q^2+4q+2
        67: 2q^2+4q+2
        68: q^3+3q^2+4q+2
        69: 2q^2+3q+2
        70: 2q^2+3q+2
        71: 2q^2+3q+2
        72: 2q+2
        73: 2q+2
        75: q^2+3q+2
        77: q^2+3q+2
        79: q^2+3q+2
        80: 2q^2+4q+2
        81: 2q^2+4q+2
        82: q^2+3q+2
        83: q^2+3q+2
        84: 2q^2+4q+2
        85: 2q^2+4q+2
        86: q^2+3q+2
        87: q^2+3q+2
        88: q^3+3q^2+4q+2
        89: q^3+3q^2+4q+2
        90: q^3+3q^2+3q+2
        91: 2q^2+3q+2
        92: 2q^2+3q+2
        93: 2q^2+3q+2
        94: q^2+3q+2
        95: q^2+3q+2
        96: q^2+3q+2
        97: q^2+3q+2
        98: q^2+3q+2
        99: q^2+3q+2
       100: 2q+2
       101: 2q+2
       102: 2q+2
       104: q^2+2q+1
       105: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: q^2+3q+2
       116: q^2+3q+2
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       122: 2q^2+4q+2
       124: 2q^2+4q+2
       125: q^3+3q^2+4q+2
       126: 2q^2+3q+2
       128: q^2+3q+2
       130: q^2+3q+2
       132: q^2+3q+2
       133: 2q^2+3q+2
       134: 2q^2+3q+2
       135: 2q+2
       136: 2q+2
       137: 2q^2+4q+2
       138: q^2+3q+2
       139: q^2+3q+2
       140: 2
       141: q^2+3q+2
       142: 2q+2
       143: 2q^2+4q+2
       144: q^2+3q+2
       145: q^2+3q+2
       146: q^2+3q+2
       147: 2q+2
       148: 2
       149: 2q+2
       150: 2q+2
       152: 2q+2
       154: 2q+2
       156: 2q+2
       157: 2q^2+3q+2
       158: 2q^2+3q+2
       159: 2q^2+3q+2
       160: q^2+3q+2
       161: q^2+3q+2
       162: q^2+3q+2
       163: q^2+3q+2
       164: q^2+3q+2
       165: q^2+3q+2
       166: 2q+2
       167: 2q+2
       168: 2q+2
       170: q+1
       171: q+1
       174: q^2+2q+1
       175: q^2+2q+1
       178: q^2+3q+2
       180: q^2+3q+2
       182: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2q+2
       190: q^2+3q+2
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: q^2+2q+1
       200: q^2+2q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2q^2+4q+2
       210: 2q+2
       212: 2q+2
       214: q^2+3q+2
       216: q^2+3q+2
       218: q^2+3q+2
       219: 2q^2+3q+2
       220: 2q^2+3q+2
       221: 2q^2+3q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: q^2+3q+2
       227: q^2+3q+2
       228: q^2+3q+2
       229: 2
       230: 2q+2
       231: q^2+3q+2
       232: q^2+3q+2
       233: q^2+3q+2
       234: 2q+2
       235: 2
       236: 2q+2
       238: 2q+2
       240: 2q+2
       242: 2q+2
       243: 2q+2
       244: 2
       245: 2
       246: 2q+2
       247: q+2
       248: q+2
       249: q+1
       250: q^2+3q+2
       251: q^2+3q+2
       252: q^2+3q+2
       253: q^2+3q+2
       254: q^2+3q+2
       255: q^2+3q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: q+1
       261: q+1
       264: q+1
       265: q+1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q^2+2q+1
       277: q^2+2q+1
       280: q^2+3q+2
       282: q^2+3q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: q^2+3q+2
       290: 2q+2
       292: 2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2q+2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 2q+2
       318: 2q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: 2q+2
       328: q^2+3q+2
       330: q^2+3q+2
       332: q^2+3q+2
       333: 2q^2+3q+2
       334: 2q+2
       335: 2q+2
       336: 1
       337: q+2
       339: q+2
       341: q+2
       343: q+1
       344: q^2+3q+2
       345: q^2+3q+2
       346: q^2+3q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: q^2+3q+2
       353: q^2+3q+2
       354: q^2+3q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: 2q+2
       367: 2q+2
       368: 2q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       378: q+1
       379: q+1
       382: q+1
       383: q+1
       386: q+1
       387: q+1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: q^2+3q+2
       412: q^2+3q+2
       414: q^2+3q+2
       416: 2q+2
       418: 2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       424: 2q+2
       426: 1
       428: q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       434: 2
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       447: q+1
       448: q+1
       449: 1
       450: 1
       452: 2
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: 2q+2
       468: 2q+2
       470: 2q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 2q+2
       482: 2q+2
       483: 1
       484: q+2
       486: q+2
       488: q+2
       490: q+1
       491: 1
       492: q^2+3q+2
       493: 2
       494: 2q+2
       495: 1
       496: 2
       497: q^2+3q+2
       498: 2q+2
       499: 2
       500: 1
       501: 2
       503: 2q+2
       505: 2q+2
       507: 2q+2
       508: 2q+2
       509: 2q+2
       510: 2q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+1
       518: q+2
       519: q+2
       520: q+1
       522: q+1
       523: q+1
       526: q+1
       527: q+1
       530: q+1
       531: q+1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: q^2+3q+2
       586: 2q+2
       588: 2q+2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       598: 1
       600: 1
       602: q+2
       603: 1
       604: 1
       606: 2
       607: q+1
       608: q+1
       610: 2
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2
       626: 2
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: 2q+2
       638: 2q+2
       640: 2q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       657: q+2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: 1
       667: q+2
       669: q+2
       671: q+1
       672: q+2
       673: 1
       674: 2
       675: 2
       676: 2q+2
       677: 1
       678: 2
       679: 1
       680: 2
       681: 2q+2
       682: 2
       683: 1
       684: 2
       685: 1
       686: 2q+2
       687: 2
       688: 2
       690: q+2
       691: q+2
       692: q+1
       699: 1
       700: 1
       706: q+1
       707: q+1
       710: q+1
       711: q+1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       776: q+2
       778: 2q+2
       780: 1
       782: 1
       784: 1
       790: q+2
       792: 1
       793: 1
       794: 1
       796: 2
       798: 2
       800: 2
       801: 1
       802: 1
       807: q+1
       808: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: 2
       825: q+1
       826: q+1
       831: 1
       832: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 2q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: 2
       852: 2
       854: 2
       858: 2
       860: q+2
       862: q+2
       864: q+1
       865: q+2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       881: q+2
       882: q+2
       883: q+1
       890: 1
       891: 1
       897: q+1
       898: q+1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       962: 1
       963: 1
       965: 1
       966: 1
       972: 2
       976: 1
       977: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       993: q+2
       995: 1
       997: 1
      1003: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1047: 2
      1049: 2
      1051: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1067: q+2
      1069: q+2
      1071: q+1
      1072: q+2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1093: 1
      1104: 1
      1105: 1
      1142: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1186: 1
      1187: 1
      1192: 2
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1211: q+2
      1213: 1
      1215: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2
      1228: 1
      1229: 1
      1231: 1
      1237: 1
      1239: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1257: 1
      1263: 2
      1265: 2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1308: 1
      1309: 1
      1338: 1
      1341: 1
      1343: 1
      1373: 1
      1375: 1
      1408: 2
      1411: 1
      1412: 1
      1416: 1
      1417: 1
      1437: 1
      1439: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1457: 1
      1459: 1
      1485: 1
      1486: 1
      1531: 1
      1532: 1
      1557: 1
      1638: 1
      1640: 1
      1644: 1
      1652: 1
      1727: 1

1728:    0: 2q^4+4q^3+5q^2+2q
         1: q^4+4q^3+5q^2+2q
         2: 2q^4+4q^3+5q^2+2q
         3: 2q^4+4q^3+5q^2+2q
         4: q^5+q^4+3q^3+4q^2+2q
         5: q^4+4q^3+5q^2+2q
         6: q^5+3q^4+5q^3+4q^2+2q
         7: q^5+q^4+3q^3+4q^2+2q
         8: q^4+4q^3+5q^2+2q
         9: q^5+q^4+3q^3+4q^2+2q
        10: q^3+4q^2+2q
        11: q^3+4q^2+2q
        12: 2q^3+3q^2+2q
        13: 2q^4+4q^3+5q^2+2q
        14: q^5+q^4+3q^3+4q^2+2q
        15: q^4+4q^3+5q^2+2q
        16: 2q^4+4q^3+5q^2+2q
        17: q^4+4q^3+5q^2+2q
        18: q^5+q^4+3q^3+4q^2+2q
        19: q^4+2q^3+4q^2+2q
        20: q^4+4q^3+4q^2+2q
        21: q^4+2q^3+4q^2+2q
        22: 3q^3+5q^2+2q
        23: 3q^3+5q^2+2q
        24: 3q^3+5q^2+2q
        25: 3q^3+5q^2+2q
        26: 3q^3+5q^2+2q
        27: 3q^3+5q^2+2q
        28: q^3+4q^2+2q
        29: q^3+3q^2+2q
        30: q^4+2q^3+4q^2+2q
        31: 4q^2+2q
        32: 3q^3+5q^2+2q
        33: 3q^3+5q^2+2q
        34: 4q^2+2q
        35: 3q^3+5q^2+2q
        36: 3q^3+5q^2+2q
        38: 3q^3+5q^2+2q
        40: 3q^3+5q^2+2q
        42: 3q^3+5q^2+2q
        43: q^3+4q^2+2q
        44: 2q^3+3q^2+2q
        45: q^3+4q^2+2q
        46: 2q^4+4q^3+5q^2+2q
        47: q^4+4q^3+5q^2+2q
        48: q^5+q^4+3q^3+4q^2+2q
        49: q^4+2q^3+4q^2+2q
        50: q^4+4q^3+4q^2+2q
        51: q^4+2q^3+4q^2+2q
        52: q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^3+4q^2+2q
        55: q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^3+4q^2+2q
        58: 2q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: 2q^2+q
        63: 4q^2+2q
        65: 3q^3+5q^2+2q
        67: 3q^3+5q^2+2q
        68: q^3+4q^2+2q
        69: q^4+2q^3+4q^2+2q
        70: q^3+3q^2+2q
        71: q^3+3q^2+2q
        72: q^3+3q^2+2q
        73: q^3+3q^2+2q
        75: q^3+4q^2+2q
        77: 3q^3+4q^2+2q
        79: q^3+4q^2+2q
        80: 4q^2+2q
        81: 3q^3+5q^2+2q
        82: 3q^2+2q
        83: q^3+4q^2+2q
        84: 4q^2+2q
        85: 3q^3+5q^2+2q
        86: 3q^2+2q
        87: q^3+4q^2+2q
        88: q^3+4q^2+2q
        89: q^3+4q^2+2q
        90: 2q^3+3q^2+2q
        91: q^4+2q^3+4q^2+2q
        92: q^4+4q^3+4q^2+2q
        93: q^4+2q^3+4q^2+2q
        94: q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^3+4q^2+2q
        97: q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^3+4q^2+2q
       100: 3q^2+2q
       101: q^3+3q^2+2q
       102: 3q^2+2q
       104: 2q^2+q
       105: 2q^2+q
       107: q^2+q
       108: q^2+q
       109: q^2+q
       110: q^2+q
       112: q^3+3q^2+2q
       114: 3q^2+2q
       116: q^3+4q^2+2q
       117: 2q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: 2q^2+q
       122: 4q^2+2q
       124: 3q^3+5q^2+2q
       125: q^3+4q^2+2q
       126: q^3+3q^2+2q
       128: q^3+4q^2+2q
       130: 3q^3+4q^2+2q
       132: q^3+4q^2+2q
       133: q^3+3q^2+2q
       134: q^4+2q^3+4q^2+2q
       135: q^3+3q^2+2q
       136: q^3+3q^2+2q
       137: 4q^2+2q
       138: q^3+4q^2+2q
       139: 3q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: q^3+3q^2+2q
       143: 4q^2+2q
       144: q^3+4q^2+2q
       145: 3q^2+2q
       146: 3q^2+2q
       147: q^3+3q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 3q^2+2q
       152: 3q^2+2q
       154: q^3+3q^2+2q
       156: 3q^2+2q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^3+4q^2+2q
       161: 3q^3+4q^2+2q
       162: q^3+4q^2+2q
       163: q^3+4q^2+2q
       164: 3q^3+4q^2+2q
       165: q^3+4q^2+2q
       166: 3q^2+2q
       167: q^3+3q^2+2q
       168: 3q^2+2q
       170: q^2+q
       171: q^2+q
       174: 2q^2+q
       175: 2q^2+q
       178: q^3+4q^2+2q
       180: 3q^2+2q
       182: q^3+3q^2+2q
       183: q^2+q
       184: q^2+q
       185: q^2+q
       186: q^2+q
       188: q^3+3q^2+2q
       190: 3q^2+2q
       191: 2q^2+q
       192: 2q^2+q
       193: q
       194: q
       195: q^2+q
       196: q^2+q
       198: q^2+2q
       199: 2q^2+q
       200: 2q^2+q
       201: q^2+q
       202: q^2+q
       203: q
       204: q
       206: q^2+2q
       208: 4q^2+2q
       210: 2q^2+2q
       212: 3q^2+2q
       214: q^3+4q^2+2q
       216: 3q^3+4q^2+2q
       218: q^3+4q^2+2q
       219: q^3+3q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: 2q
       223: q^3+3q^2+2q
       224: 2q
       225: q^3+3q^2+2q
       226: 3q^2+2q
       227: 3q^2+2q
       228: q^3+4q^2+2q
       229: q^2+2q
       230: q^3+3q^2+2q
       231: 3q^2+2q
       232: 3q^2+2q
       233: q^3+4q^2+2q
       234: q^3+3q^2+2q
       235: q^2+2q
       236: 3q^2+2q
       238: 3q^2+2q
       240: q^3+3q^2+2q
       242: 3q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: q^2+2q
       248: q^2+2q
       249: q^2+q
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: 3q^2+2q
       257: q^3+3q^2+2q
       258: 3q^2+2q
       260: q^2+q
       261: q^2+q
       264: q^2+q
       265: q^2+q
       268: q
       270: q
       272: q
       274: q
       276: 2q^2+q
       277: 2q^2+q
       280: 3q^2+2q
       282: q^3+4q^2+2q
       283: q^2+q
       284: q^2+q
       285: q^2+q
       286: q^2+q
       288: 3q^2+2q
       290: q^3+3q^2+2q
       292: q^3+3q^2+2q
       293: q
       294: q
       295: q
       296: q
       298: 2q
       299: q
       300: q
       302: q^2+2q
       303: q^2+q
       304: q^2+q
       306: q^2+2q
       307: q^2+q
       308: q^2+q
       309: q
       310: q
       312: q^2+2q
       314: q^2+2q
       316: 3q^2+2q
       318: 2q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: q^2+2q
       326: 2q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: q^2+2q
       334: 2q
       335: 2q
       336: q
       337: q^2+2q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: 3q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: 2q
       348: q^2+2q
       349: 2q
       350: q^3+3q^2+2q
       351: 2q
       352: 3q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: 2q
       356: q^3+3q^2+2q
       357: 2q
       358: q^2+2q
       359: 2q
       361: 3q^2+2q
       363: q^3+3q^2+2q
       365: 3q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 3q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: q^2+2q
       372: q^2+2q
       373: q^2+q
       378: q^2+q
       379: q^2+q
       382: q^2+q
       383: q^2+q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: q^2+2q
       412: q^2+2q
       414: 3q^2+2q
       416: 2q
       418: q^3+3q^2+2q
       419: q
       420: q
       421: q
       422: q
       424: 2q
       426: q
       428: q^2+2q
       429: q
       430: q
       431: q^2+q
       432: q^2+q
       434: q^2+2q
       436: q^2+2q
       437: q
       438: q
       439: q
       440: q
       442: 2q
       443: q
       444: q
       446: 2q
       447: q^2+q
       448: q^2+q
       449: q
       450: q
       452: q^2+2q
       453: q
       454: q
       456: q^2+2q
       457: q
       458: q
       460: 2q
       461: q
       462: q
       464: 2q
       466: 2q^2+2q
       468: 3q^2+2q
       470: 2q^2+2q
       471: q
       472: q
       473: q
       474: q
       476: q^2+2q
       478: q^2+2q
       480: 2q
       481: 2q
       482: 2q
       483: q
       484: q^2+2q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q
       492: q^2+2q
       493: 2q
       494: 2q
       495: q
       496: 2q
       497: q^2+2q
       498: 2q
       499: 2q
       500: q
       501: 2q
       508: 2q^2+2q
       512: q^2+2q
       514: q^2+2q
       515: q^2+2q
       516: q^2+2q
       517: q^2+q
       522: q^2+q
       523: q^2+q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: q
       548: q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: q
       564: q
       566: q
       567: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q
       590: q
       595: q
       596: q
       598: q
       600: q
       602: q^2+2q
       603: q
       604: q
       606: q^2+2q
       607: q
       608: q
       610: 2q
       614: q
       615: q
       616: q
       618: 2q
       619: q
       620: q
       621: q
       622: q
       624: q^2+2q
       626: 2q
       630: q
       631: q
       632: q
       634: 2q
       640: 2q^2+2q
       641: q
       642: q
       643: q
       644: q
       646: q^2+2q
       652: q^2+2q
       656: 2q
       657: q^2+2q
       659: q^2+2q
       661: q^2+2q
       663: q^2+q
       664: q
       665: q
       674: 2q
       675: 2q
       676: 2q
       677: q
       679: q
       680: 2q
       681: 2q
       682: 2q
       683: q
       685: q
       699: q
       700: q
       706: q
       707: q
       710: q
       711: q
       722: q
       724: q
       726: q
       728: q
       734: q
       736: q
       738: q
       740: q
       742: q
       744: q
       750: q
       752: q
       754: q
       755: q
       759: q
       760: q
       766: q
       767: q
       773: 2q
       776: q^2+2q
       778: 2q
       780: q
       782: q
       792: q
       793: q
       794: q
       796: 2q
       798: 2q
       801: q
       802: q
       807: q
       808: q
       810: q
       812: q
       817: q
       818: q
       820: 2q
       822: 2q
       825: q
       826: q
       831: q
       832: q
       834: q
       836: q
       844: 2q
       850: q^2+2q
       854: 2
       866: q
       870: q
       871: q
       874: q
       875: q
       890: q
       891: q
       897: q
       898: q
       917: q
       919: q
       921: q
       923: q
       941: q
       943: q
       945: q
       947: q
       962: q
       963: q
       965: q
       966: q
       972: 2q
       980: 1
       981: 1
       987: 2
       995: q
      1011: q
      1013: q
      1021: q
      1023: q
      1037: q
      1039: q
      1051: 2
      1076: q
      1080: q
      1092: q
      1093: q
      1108: 1
      1109: 1
      1142: q
      1186: 1
      1187: 1
      1193: 2
      1223: 1
      1231: q
      1249: q
      1265: 2
      1312: 1
      1313: 1
      1339: 1
      1409: 2
      1416: 1
      1417: 1
      1447: 1
      1535: 1
      1536: 1
      1558: 1
      1638: 1
      1728: 1

1729:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^4+2q^3+3q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: q^4+2q^3+3q^2+3q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^4+2q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: q^3+2q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: q^3+2q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        39: 3q^2+3q+1
        41: q^3+2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^4+2q^3+3q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: 2q^2+2q+1
        61: q^2+q
        62: 3q^2+3q+1
        64: 2q^2+3q+1
        66: 3q^2+3q+1
        68: 2q^2+3q+1
        69: q^3+3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 2q^3+4q^2+3q+1
        72: 3q^2+3q+1
        73: 3q^2+3q+1
        74: 3q^2+3q+1
        76: 3q^2+3q+1
        78: q^3+2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       106: q^2+q
       107: 2q^2+2q+1
       108: q^2+q
       109: 2q^2+2q+1
       110: q^2+q
       111: 3q^2+3q+1
       113: 3q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q^2+2q+1
       120: q
       121: 2q^2+3q+1
       123: 2q^2+3q+1
       125: 2q^2+3q+1
       126: q^3+3q^2+3q+1
       127: 3q^2+3q+1
       129: 3q^2+3q+1
       131: q^3+2q^2+3q+1
       133: 2q^2+3q+1
       134: q^3+3q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: q^3+3q^2+3q+1
       159: q^3+3q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q^2+2q+1
       172: q^2+q
       173: q^2+2q+1
       176: q
       177: 2q^2+3q+1
       179: 3q^2+3q+1
       181: 3q^2+3q+1
       183: q^2+2q+1
       184: q
       185: q^2+2q+1
       186: q
       187: 2q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       193: q+1
       195: 2q^2+2q+1
       196: q^2+q
       197: q+1
       199: q^2+2q+1
       200: q
       201: 2q^2+2q+1
       202: q^2+q
       203: q+1
       205: q+1
       207: 2q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: q^2+3q+1
       215: q^2+3q+1
       217: q^2+3q+1
       219: 2q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+3q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q^2+2q+1
       262: q^2+q
       263: q^2+2q+1
       266: q
       267: q+1
       271: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: q^2+3q+1
       283: q^2+2q+1
       284: q
       285: q^2+2q+1
       286: q
       287: 2q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: q^2+2q+1
       294: q
       295: q^2+2q+1
       296: q
       297: 2q^2+3q+1
       299: q+1
       301: q+1
       303: 2q+1
       304: q
       305: q+1
       307: 2q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       319: q+1
       321: q+1
       323: q+1
       325: q^2+2q+1
       327: q^2+3q+1
       329: q^2+3q+1
       331: q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       340: q^2+2q+1
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q+1
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+2q+1
       380: q
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: 3q+1
       411: q^2+3q+1
       413: 3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: q^2+2q+1
       420: q
       421: q^2+2q+1
       422: q
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: q^2+2q+1
       429: q+1
       431: 2q+1
       432: q
       433: q+1
       435: 1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: 2q+1
       448: q
       449: q+1
       451: q+1
       453: 2q+1
       454: q
       455: 1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: q+1
       467: q+1
       469: q^2+2q+1
       471: 1
       473: 1
       475: 1
       477: q+1
       479: q+1
       481: 3q+1
       482: 3q+1
       483: q^2+2q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: q+1
       496: 1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 2q+1
       524: q
       525: 2q+1
       528: q
       529: q^2+2q+1
       532: q
       533: q+1
       537: 1
       541: q+1
       545: q+1
       549: q+1
       553: 1
       557: q+1
       561: q+1
       565: 1
       569: q+1
       573: q+1
       577: q+1
       583: 3q+1
       585: 3q+1
       587: q^2+3q+1
       589: 2q+1
       590: q
       591: q+1
       593: q+1
       595: 2q+1
       596: q
       597: q+1
       599: q^2+2q+1
       601: q+1
       603: q+1
       605: 1
       607: 2q+1
       608: q
       609: q+1
       611: 1
       613: q+1
       615: 1
       617: 1
       619: 2q+1
       620: q
       621: q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 2
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       705: 2q+1
       708: q
       709: 2q+1
       712: q
       713: q+1
       717: q+1
       721: 1
       725: q+1
       729: 1
       733: 1
       737: 1
       741: q+1
       745: 1
       749: 1
       753: 1
       757: 2
       761: 1
       765: 1
       769: 1
       771: 1
       775: q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: q+1
       807: 2q+1
       808: q
       809: 1
       811: q+1
       813: 1
       815: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: 2q+1
       826: q
       827: q+1
       831: 1
       833: 1
       835: q+1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: 1
       847: 1
       849: 2
       851: 1
       853: 2
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       884: 1
       886: 1
       896: 2q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: q+1
       932: 1
       936: 1
       940: 1
       944: 1
       948: q+1
       956: 1
       960: 2
       964: 1
       968: 1
       970: 1
       974: 1
       978: 2
       982: 1
       984: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 2
      1052: 1
      1058: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1088: 1
      1098: 1
      1100: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 2
      1188: 1
      1190: 1
      1194: 1
      1198: 1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1264: 1
      1283: 1
      1285: 1
      1290: 1
      1292: 1
      1302: 1
      1304: 1
      1314: 1
      1318: 1
      1322: 2
      1326: 1
      1330: 1
      1334: 1
      1336: 1
      1352: 1
      1356: 1
      1376: 1
      1380: 1
      1414: 1
      1436: 1
      1446: 1
      1448: 1
      1454: 1
      1456: 1
      1460: 1
      1489: 1
      1491: 1
      1537: 1
      1559: 1
      1567: 1
      1583: 1
      1637: 1
      1729: 1

1730:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^4+2q^3+3q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: q^4+2q^3+3q^2+3q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^4+2q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: q^3+2q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: q^3+2q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        39: 3q^2+3q+1
        41: q^3+2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^4+2q^3+3q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: q^2+q
        61: 2q^2+2q+1
        62: 3q^2+3q+1
        64: 2q^2+3q+1
        66: 3q^2+3q+1
        68: 2q^2+3q+1
        69: q^3+3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 2q^3+4q^2+3q+1
        72: 3q^2+3q+1
        73: 3q^2+3q+1
        74: 3q^2+3q+1
        76: 3q^2+3q+1
        78: q^3+2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+q
       106: 2q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: q^2+q
       110: 2q^2+2q+1
       111: 3q^2+3q+1
       113: 3q^2+3q+1
       115: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q
       120: q^2+2q+1
       121: 2q^2+3q+1
       123: 2q^2+3q+1
       125: 2q^2+3q+1
       126: q^3+3q^2+3q+1
       127: 3q^2+3q+1
       129: 3q^2+3q+1
       131: q^3+2q^2+3q+1
       133: 2q^2+3q+1
       134: q^3+3q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: q^3+3q^2+3q+1
       159: q^3+3q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+q
       172: 2q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q^2+3q+1
       179: 3q^2+3q+1
       181: 3q^2+3q+1
       183: q
       184: q^2+2q+1
       185: q
       186: q^2+2q+1
       187: 2q^2+3q+1
       189: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       194: q+1
       195: q^2+q
       196: 2q^2+2q+1
       197: q+1
       199: q
       200: q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       204: q+1
       205: q+1
       207: 2q^2+3q+1
       209: q^2+2q+1
       211: q^2+2q+1
       213: q^2+3q+1
       215: q^2+3q+1
       217: q^2+3q+1
       219: 2q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+3q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q
       262: 2q^2+2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       273: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: q^2+3q+1
       283: q
       284: q^2+2q+1
       285: q
       286: q^2+2q+1
       287: 2q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: q
       294: q^2+2q+1
       295: q
       296: q^2+2q+1
       297: 2q^2+3q+1
       300: q+1
       301: q+1
       303: q
       304: 2q+1
       305: q+1
       307: q
       308: 2q+1
       310: q+1
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       320: q+1
       322: q+1
       323: q+1
       325: q^2+2q+1
       327: q^2+3q+1
       329: q^2+3q+1
       331: q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       340: q^2+2q+1
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q+1
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: q^2+2q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: 3q+1
       411: q^2+3q+1
       413: 3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: q
       420: q^2+2q+1
       421: q
       422: q^2+2q+1
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: q^2+2q+1
       430: q+1
       431: q
       432: 2q+1
       433: q+1
       435: 1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: q+1
       445: q+1
       447: q
       448: 2q+1
       450: q+1
       451: q+1
       453: q
       454: 2q+1
       455: 1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: q+1
       467: q+1
       469: q^2+2q+1
       472: 1
       474: 1
       475: 1
       477: q+1
       479: q+1
       481: 3q+1
       482: 3q+1
       483: q^2+2q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: q+1
       496: 1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 2q+1
       525: q
       528: 2q+1
       529: q
       532: q^2+2q+1
       536: q+1
       539: 1
       543: q+1
       547: q+1
       552: q+1
       555: 1
       559: q+1
       563: q+1
       568: 1
       570: q+1
       575: q+1
       577: q+1
       583: 3q+1
       585: 3q+1
       587: q^2+3q+1
       589: q
       590: 2q+1
       592: q+1
       594: q+1
       595: q
       596: 2q+1
       597: q+1
       599: q^2+2q+1
       601: q+1
       604: q+1
       605: 1
       607: q
       608: 2q+1
       609: q+1
       611: 1
       613: q+1
       616: 1
       617: 1
       619: q
       620: 2q+1
       622: q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 2
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       705: q
       708: 2q+1
       709: q
       712: 2q+1
       716: q+1
       720: q+1
       723: 1
       727: q+1
       731: 1
       735: 1
       739: 1
       743: q+1
       747: 1
       751: 1
       756: 1
       758: 2
       762: 1
       768: 1
       769: 1
       771: 1
       775: q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: q+1
       807: q
       808: 2q+1
       809: 1
       811: q+1
       813: 1
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: 2q+1
       828: q+1
       832: 1
       833: 1
       835: q+1
       837: 1
       840: 1
       841: q+1
       843: 1
       846: 1
       848: 1
       849: 2
       851: 1
       853: 2
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       889: 1
       893: 1
       896: q
       899: 2q+1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: q+1
       934: 1
       938: 1
       942: 1
       946: 1
       950: q+1
       958: 1
       961: 2
       967: 1
       968: 1
       970: 1
       975: 1
       979: 2
       982: 1
       984: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 2
      1053: 1
      1059: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1091: 1
      1095: 1
      1102: 1
      1107: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1146: 1
      1150: 1
      1158: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 2
      1188: 1
      1190: 1
      1197: 1
      1199: 1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1264: 1
      1283: 1
      1285: 1
      1295: 1
      1299: 1
      1307: 1
      1311: 1
      1316: 1
      1320: 1
      1323: 2
      1329: 1
      1331: 1
      1334: 1
      1336: 1
      1354: 1
      1358: 1
      1378: 1
      1382: 1
      1415: 1
      1436: 1
      1446: 1
      1448: 1
      1455: 1
      1456: 1
      1461: 1
      1494: 1
      1498: 1
      1538: 1
      1560: 1
      1569: 1
      1585: 1
      1637: 1
      1730: 1

1731:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^4+2q^3+3q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: q^4+2q^3+3q^2+3q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^4+2q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: q^3+2q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: q^3+2q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        38: 3q^2+3q+1
        40: 3q^2+3q+1
        42: q^3+2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^4+2q^3+3q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: q^2+q
        63: 3q^2+3q+1
        65: 2q^2+3q+1
        67: 3q^2+3q+1
        68: 2q^2+3q+1
        69: q^3+3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 2q^3+4q^2+3q+1
        72: 3q^2+3q+1
        73: 3q^2+3q+1
        75: 3q^2+3q+1
        77: 3q^2+3q+1
        79: q^3+2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: 2q^2+2q+1
       105: q^2+q
       107: 2q^2+2q+1
       108: q^2+q
       109: q^2+q
       110: 2q^2+2q+1
       112: 3q^2+3q+1
       114: 3q^2+3q+1
       116: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q^2+2q+1
       120: q
       122: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: q^3+3q^2+3q+1
       128: 3q^2+3q+1
       130: 3q^2+3q+1
       132: q^3+2q^2+3q+1
       133: 2q^2+3q+1
       134: q^3+3q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: q^3+3q^2+3q+1
       159: q^3+3q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+q
       174: q^2+2q+1
       175: q
       178: 2q^2+3q+1
       180: 3q^2+3q+1
       182: 3q^2+3q+1
       183: q^2+2q+1
       184: q
       185: q
       186: q^2+2q+1
       188: 2q^2+3q+1
       190: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       193: q+1
       195: q^2+q
       196: 2q^2+2q+1
       198: q+1
       199: q^2+2q+1
       200: q
       201: 2q^2+2q+1
       202: q^2+q
       204: q+1
       206: q+1
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q^2+3q+1
       216: q^2+3q+1
       218: q^2+3q+1
       219: 2q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+3q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q+1
       236: q^2+2q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       260: 2q^2+2q+1
       261: q^2+q
       264: q^2+2q+1
       265: q
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: q^2+3q+1
       283: q^2+2q+1
       284: q
       285: q
       286: q^2+2q+1
       288: 2q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: q^2+2q+1
       294: q
       295: q
       296: q^2+2q+1
       298: 2q^2+3q+1
       299: q+1
       302: q+1
       303: q
       304: 2q+1
       306: q+1
       307: 2q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       319: q+1
       322: q+1
       324: q+1
       326: q^2+2q+1
       328: q^2+3q+1
       330: q^2+3q+1
       332: q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+2q+1
       339: q^2+2q+1
       341: q^2+2q+1
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q+1
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q^2+2q+1
       379: q
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: 3q+1
       412: q^2+3q+1
       414: 3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: q^2+2q+1
       420: q
       421: q
       422: q^2+2q+1
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: q^2+2q+1
       429: q+1
       431: q
       432: 2q+1
       434: q+1
       436: 1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: q+1
       446: q+1
       447: 2q+1
       448: q
       450: q+1
       452: q+1
       453: 2q+1
       454: q
       456: 1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: q+1
       468: q+1
       470: q^2+2q+1
       471: 1
       474: 1
       476: 1
       478: q+1
       480: q+1
       481: 3q+1
       482: 3q+1
       483: q^2+2q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: q+1
       496: 1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: q+1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 2q+1
       523: q
       526: 2q+1
       527: q
       530: q^2+2q+1
       531: q
       534: q+1
       538: 1
       542: q+1
       546: q+1
       551: q+1
       556: 1
       560: q+1
       564: q+1
       566: 1
       571: q+1
       574: q+1
       581: q+1
       584: 3q+1
       586: 3q+1
       588: q^2+3q+1
       589: 2q+1
       590: q
       592: q+1
       593: q+1
       595: q
       596: 2q+1
       598: q+1
       600: q^2+2q+1
       602: q+1
       603: q+1
       606: 1
       607: q
       608: 2q+1
       610: q+1
       612: 1
       614: q+1
       615: 1
       618: 1
       619: 2q+1
       620: q
       622: q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 2
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       706: 2q+1
       707: q
       710: 2q+1
       711: q
       715: q+1
       718: q+1
       722: 1
       726: q+1
       730: 1
       734: 1
       740: 1
       744: q+1
       748: 1
       752: 1
       754: 1
       759: 2
       763: 1
       766: 1
       773: 1
       774: 1
       776: q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: q+1
       807: q
       808: 2q+1
       810: 1
       812: q+1
       814: 1
       815: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: 2q+1
       826: q
       828: q+1
       832: 1
       834: 1
       836: q+1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: 1
       848: 1
       850: 2
       852: 1
       854: 2
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       890: 1
       894: 1
       897: 2q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: q+1
       933: 1
       939: 1
       943: 1
       947: 1
       951: q+1
       959: 1
       962: 2
       965: 1
       972: 1
       973: 1
       976: 1
       980: 2
       986: 1
       987: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 2
      1052: 1
      1059: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1096: 1
      1104: 1
      1108: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1145: 1
      1149: 1
      1157: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 2
      1192: 1
      1193: 1
      1195: 1
      1200: 1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1265: 1
      1283: 1
      1285: 1
      1296: 1
      1300: 1
      1308: 1
      1312: 1
      1317: 1
      1319: 1
      1324: 2
      1327: 1
      1332: 1
      1338: 1
      1339: 1
      1353: 1
      1357: 1
      1379: 1
      1383: 1
      1416: 1
      1437: 1
      1447: 1
      1449: 1
      1454: 1
      1457: 1
      1461: 1
      1495: 1
      1499: 1
      1539: 1
      1561: 1
      1568: 1
      1586: 1
      1638: 1
      1731: 1

1732:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^4+2q^3+3q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: q^4+2q^3+3q^2+3q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: q^4+2q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: q^3+2q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: q^3+2q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        38: 3q^2+3q+1
        40: 3q^2+3q+1
        42: q^3+2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^3+4q^2+3q+1
        51: q^4+2q^3+3q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: q^2+q
        61: 2q^2+2q+1
        63: 3q^2+3q+1
        65: 2q^2+3q+1
        67: 3q^2+3q+1
        68: 2q^2+3q+1
        69: q^3+3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 2q^3+4q^2+3q+1
        72: 3q^2+3q+1
        73: 3q^2+3q+1
        75: 3q^2+3q+1
        77: 3q^2+3q+1
        79: q^3+2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: q^3+3q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q^2+q
       105: 2q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: q^2+q
       112: 3q^2+3q+1
       114: 3q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q
       120: q^2+2q+1
       122: 2q^2+3q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: q^3+3q^2+3q+1
       128: 3q^2+3q+1
       130: 3q^2+3q+1
       132: q^3+2q^2+3q+1
       133: 2q^2+3q+1
       134: q^3+3q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: q^3+3q^2+3q+1
       159: q^3+3q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: q^2+q
       171: 2q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q^2+3q+1
       180: 3q^2+3q+1
       182: 3q^2+3q+1
       183: q
       184: q^2+2q+1
       185: q^2+2q+1
       186: q
       188: 2q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       194: q+1
       195: 2q^2+2q+1
       196: q^2+q
       198: q+1
       199: q
       200: q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: q+1
       206: q+1
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q^2+3q+1
       216: q^2+3q+1
       218: q^2+3q+1
       219: 2q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q+1
       230: q^2+3q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q+1
       236: q^2+2q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^2+q
       261: 2q^2+2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: q^2+3q+1
       283: q
       284: q^2+2q+1
       285: q^2+2q+1
       286: q
       288: 2q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: q
       294: q^2+2q+1
       295: q^2+2q+1
       296: q
       298: 2q^2+3q+1
       300: q+1
       302: q+1
       303: 2q+1
       304: q
       306: q+1
       307: q
       308: 2q+1
       309: q+1
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       320: q+1
       321: q+1
       324: q+1
       326: q^2+2q+1
       328: q^2+3q+1
       330: q^2+3q+1
       332: q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+2q+1
       339: q^2+2q+1
       341: q^2+2q+1
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q+1
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: q^2+2q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: 3q+1
       412: q^2+3q+1
       414: 3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: q
       420: q^2+2q+1
       421: q^2+2q+1
       422: q
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: q^2+2q+1
       430: q+1
       431: 2q+1
       432: q
       434: q+1
       436: 1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       447: q
       448: 2q+1
       449: q+1
       452: q+1
       453: q
       454: 2q+1
       456: 1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: q+1
       468: q+1
       470: q^2+2q+1
       472: 1
       473: 1
       476: 1
       478: q+1
       480: q+1
       481: 3q+1
       482: 3q+1
       483: q^2+2q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: 3q+1
       493: q+1
       494: q^2+3q+1
       495: q+1
       496: 1
       497: 3q+1
       498: q^2+3q+1
       499: q+1
       500: q+1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 2q+1
       526: q
       527: 2q+1
       530: q
       531: q^2+2q+1
       535: q+1
       540: 1
       544: q+1
       548: q+1
       550: q+1
       554: 1
       558: q+1
       562: q+1
       567: 1
       572: q+1
       576: q+1
       581: q+1
       584: 3q+1
       586: 3q+1
       588: q^2+3q+1
       589: q
       590: 2q+1
       591: q+1
       594: q+1
       595: 2q+1
       596: q
       598: q+1
       600: q^2+2q+1
       602: q+1
       604: q+1
       606: 1
       607: 2q+1
       608: q
       610: q+1
       612: 1
       614: q+1
       616: 1
       618: 1
       619: q
       620: 2q+1
       621: q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 2
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 3q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 3q+1
       682: 1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       706: q
       707: 2q+1
       710: q
       711: 2q+1
       714: q+1
       719: q+1
       724: 1
       728: q+1
       732: 1
       736: 1
       738: 1
       742: q+1
       746: 1
       750: 1
       755: 1
       760: 2
       764: 1
       767: 1
       773: 1
       774: 1
       776: q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: q+1
       807: 2q+1
       808: q
       810: 1
       812: q+1
       814: 1
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: 2q+1
       827: q+1
       831: 1
       834: 1
       836: q+1
       838: 1
       839: 1
       842: q+1
       844: 1
       846: 1
       847: 1
       850: 2
       852: 1
       854: 2
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       891: 1
       895: 1
       897: q
       898: 2q+1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: q+1
       935: 1
       937: 1
       941: 1
       945: 1
       949: q+1
       957: 1
       963: 2
       966: 1
       972: 1
       973: 1
       977: 1
       981: 2
       986: 1
       987: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 2
      1053: 1
      1058: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1093: 1
      1097: 1
      1105: 1
      1109: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 2
      1192: 1
      1193: 1
      1196: 1
      1201: 1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1265: 1
      1283: 1
      1285: 1
      1297: 1
      1301: 1
      1309: 1
      1313: 1
      1315: 1
      1321: 1
      1325: 2
      1328: 1
      1333: 1
      1338: 1
      1339: 1
      1355: 1
      1359: 1
      1377: 1
      1381: 1
      1417: 1
      1437: 1
      1447: 1
      1449: 1
      1455: 1
      1457: 1
      1460: 1
      1496: 1
      1500: 1
      1540: 1
      1562: 1
      1570: 1
      1584: 1
      1638: 1
      1732: 1

1733:    0: 3q^3+5q^2+4q+1
         1: q^4+4q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: 3q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: q^4+4q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: 3q^3+5q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 3q^3+5q^2+4q+1
        17: q^4+4q^3+5q^2+4q+1
        18: 3q^3+5q^2+4q+1
        19: 3q^3+5q^2+4q+1
        20: q^4+4q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: q^3+3q^2+4q+1
        23: q^3+3q^2+4q+1
        24: q^3+3q^2+4q+1
        25: q^3+3q^2+4q+1
        26: q^3+3q^2+4q+1
        27: q^3+3q^2+4q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+4q+1
        32: q^3+3q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+4q+1
        35: q^3+3q^2+4q+1
        36: q^3+3q^2+4q+1
        37: q^2+2q+1
        38: q^2+2q
        39: q^2+2q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+2q
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 3q^3+5q^2+4q+1
        47: q^4+4q^3+5q^2+4q+1
        48: 3q^3+5q^2+4q+1
        49: 3q^3+5q^2+4q+1
        50: q^4+4q^3+5q^2+4q+1
        51: 3q^3+5q^2+4q+1
        52: q^3+3q^2+4q+1
        53: q^3+3q^2+4q+1
        54: q^3+3q^2+4q+1
        55: q^3+3q^2+4q+1
        56: q^3+3q^2+4q+1
        57: q^3+3q^2+4q+1
        58: 2q^2+2q+1
        59: 2q
        60: 2q^2+2q+1
        61: 2q
        62: q^2+2q+1
        63: 2q
        64: q^2+2q+1
        65: q^2+2q
        66: q^2+2q+1
        67: q^2+2q
        68: q^3+4q^2+4q+1
        69: 3q^3+5q^2+4q+1
        70: q^3+4q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^2+2q+1
        75: q^2+2q
        76: q^2+2q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+2q
        80: 2q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^2+4q+1
        83: q^3+3q^2+4q+1
        84: 2q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^2+4q+1
        87: q^3+3q^2+4q+1
        88: q^3+4q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: 3q^3+5q^2+4q+1
        92: q^4+4q^3+5q^2+4q+1
        93: 3q^3+5q^2+4q+1
        94: q^3+3q^2+4q+1
        95: q^3+3q^2+4q+1
        96: q^3+3q^2+4q+1
        97: q^3+3q^2+4q+1
        98: q^3+3q^2+4q+1
        99: q^3+3q^2+4q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q^2+q+1
       104: q
       105: q
       106: q
       107: 2q^2+2q+1
       108: 2q
       109: 2q^2+2q+1
       110: 2q
       111: q^2+2q+1
       112: q^2+2q
       113: q^2+2q+1
       114: 2q
       115: q^2+2q+1
       116: q^2+2q
       117: 2q^2+2q+1
       118: 2q
       119: 2q^2+2q+1
       120: 2q
       121: q^2+2q+1
       122: 2q
       123: q^2+2q+1
       124: q^2+2q
       125: q^3+4q^2+4q+1
       126: q^3+4q^2+4q+1
       127: q^2+2q+1
       128: q^2+2q
       129: q^2+2q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+2q
       133: q^3+4q^2+4q+1
       134: 3q^3+5q^2+4q+1
       135: q^3+3q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 2q^2+4q+1
       138: q^3+3q^2+4q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^2+4q+1
       142: q^3+3q^2+4q+1
       143: 2q^2+4q+1
       144: q^3+3q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: q^3+3q^2+4q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       152: 2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: 2q
       157: q^3+4q^2+4q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: q^3+3q^2+4q+1
       161: q^3+3q^2+4q+1
       162: q^3+3q^2+4q+1
       163: q^3+3q^2+4q+1
       164: q^3+3q^2+4q+1
       165: q^3+3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q^2+q+1
       170: q
       171: q
       172: q
       173: q^2+q+1
       174: q
       175: q
       176: q
       177: q^2+2q+1
       178: q^2+2q
       179: q^2+2q+1
       180: 2q
       181: q^2+2q+1
       182: q^2+2q
       183: 2q^2+2q+1
       184: 2q
       185: 2q^2+2q+1
       186: 2q
       187: q^2+2q+1
       188: q^2+2q
       189: q^2+2q+1
       190: 2q
       191: 2q^2+2q+1
       192: 2q
       193: q+1
       195: 2q^2+2q+1
       196: 2q
       197: 1
       198: q
       199: 2q^2+2q+1
       200: 2q
       201: 2q^2+2q+1
       202: 2q
       203: q+1
       205: 1
       206: q
       207: q^2+2q+1
       208: 2q
       209: q+1
       210: 2q
       211: q+1
       212: 2q
       213: q^2+2q+1
       214: q^2+2q
       215: q^2+2q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+2q
       219: q^3+4q^2+4q+1
       220: q^3+4q^2+4q+1
       221: q^3+4q^2+4q+1
       222: 2q^2+4q+1
       223: q^3+3q^2+4q+1
       224: 2q^2+4q+1
       225: q^3+3q^2+4q+1
       226: 2q^2+4q+1
       227: 2q^2+4q+1
       228: q^3+3q^2+4q+1
       229: q+1
       230: q^3+3q^2+4q+1
       231: 2q^2+4q+1
       232: 2q^2+4q+1
       233: q^3+3q^2+4q+1
       234: q^3+3q^2+4q+1
       235: q+1
       236: 3q+1
       237: q+1
       238: 2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: 2q
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q^2+q+1
       260: q
       261: q
       262: q
       263: q^2+q+1
       264: q
       265: q
       266: q
       267: 1
       268: q
       271: 1
       272: q
       275: q^2+q+1
       276: q
       277: q
       278: q
       279: q^2+2q+1
       280: 2q
       281: q^2+2q+1
       282: q^2+2q
       283: 2q^2+2q+1
       284: 2q
       285: 2q^2+2q+1
       286: 2q
       287: q^2+2q+1
       288: 2q
       289: q^2+2q+1
       290: q^2+2q
       291: q^2+2q+1
       292: q^2+2q
       293: 2q^2+2q+1
       294: 2q
       295: 2q^2+2q+1
       296: 2q
       297: q^2+2q+1
       298: 2q
       299: q+1
       301: 1
       302: q
       303: 2q^2+2q+1
       304: 2q
       305: 1
       306: q
       307: 2q^2+2q+1
       308: 2q
       309: q+1
       311: 1
       312: q
       313: 1
       314: q
       315: q+1
       316: 2q
       317: q+1
       318: 2q
       319: q+1
       321: q+1
       323: 1
       325: q+1
       326: 2q
       333: q^3+4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: 3q+1
       337: 3q+1
       338: q+1
       339: 2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: 2q
       344: 2q^2+4q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q+1
       349: q^2+2q+1
       350: q^3+3q^2+4q+1
       351: q+1
       352: 2q^2+4q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+3q^2+4q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       361: 2q
       362: q+1
       363: q^2+2q
       364: q+1
       365: 2q
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+q+1
       378: q
       379: q
       380: q
       381: q^2+q+1
       382: q
       383: q
       384: q
       385: q^2+q+1
       386: q
       387: q
       388: q
       389: 1
       390: q
       393: 1
       394: q
       397: 1
       398: q
       401: 1
       402: q
       405: 1
       413: q^2+2q+1
       414: 2q
       417: q^2+2q+1
       418: q^2+2q
       419: 2q^2+2q+1
       420: 2q
       421: 2q^2+2q+1
       422: 2q
       423: q^2+2q+1
       424: 2q
       425: q+1
       426: 2q
       427: q+1
       428: 2q
       429: q+1
       431: 2q^2+2q+1
       432: 2q
       433: 1
       434: q
       435: 1
       436: q
       437: 1
       439: q^2+q+1
       440: q
       441: 1
       443: q+1
       445: 1
       446: q
       447: 2q^2+2q+1
       448: 2q
       449: q+1
       451: 1
       452: q
       453: q^2+q+1
       454: q
       455: 1
       456: q
       457: 1
       459: 1
       461: q+1
       463: 1
       464: q
       465: q+1
       466: 2q
       467: q+1
       468: 2q
       469: q+1
       470: 2q
       471: q+1
       473: q+1
       475: 1
       477: 1
       479: 1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 3q+1
       484: 3q+1
       485: q+1
       486: 2q
       487: q+1
       488: q^2+2q
       489: q+1
       490: 2q
       491: 3q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: q^2+q+1
       522: q
       523: q
       524: q
       529: q^2+q+1
       530: q
       531: q
       532: q
       533: 1
       534: q
       537: 1
       538: q
       541: 1
       545: 1
       546: q
       549: 1
       550: q
       553: 1
       554: q
       557: 1
       561: 1
       562: q
       565: 1
       569: 1
       573: 1
       577: 1
       585: q^2+2q+1
       586: 2q
       589: 2q^2+2q+1
       590: 2q
       591: q+1
       593: q+1
       595: 2q^2+2q+1
       596: 2q
       597: q+1
       598: 2q
       599: q+1
       600: 2q
       601: q+1
       602: 2q
       603: 1
       605: 1
       606: q
       607: q^2+q+1
       608: q
       609: 1
       613: 1
       614: q
       615: q+1
       617: 1
       618: q
       619: q^2+q+1
       620: q
       621: 1
       623: 1
       624: q
       625: 1
       629: 1
       630: q
       631: q+1
       633: 1
       634: q
       639: q+1
       640: 2q
       641: q+1
       643: q+1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 3q+1
       658: q+1
       659: 2q
       660: q+1
       661: q^2+2q
       662: q+1
       663: 2q
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       709: q^2+q+1
       710: q
       711: q
       712: q
       713: 1
       714: q
       717: 1
       718: q
       721: 1
       722: q
       725: 1
       733: 1
       734: q
       737: 1
       738: q
       741: 1
       749: 1
       750: q
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       776: 2q
       779: q+1
       780: 2q
       781: q+1
       782: 2q
       785: q+1
       787: q+1
       791: 1
       793: q+1
       795: 1
       796: q
       797: 1
       801: 1
       805: 1
       807: q^2+q+1
       808: q
       809: 1
       810: q
       811: 1
       815: 1
       817: q+1
       819: 1
       820: q
       821: 1
       825: q^2+q+1
       826: q
       827: 1
       831: 1
       833: 1
       834: q
       835: 1
       839: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       857: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       900: 1
       901: q
       904: 1
       905: q
       908: 1
       916: 1
       917: q
       920: 1
       928: 1
       940: 1
       941: q
       944: 1
       948: 1
       960: 1
       964: 1
       968: 1
       974: 1
       988: 1
       994: q+1
       995: 2q
       998: q+1
      1000: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1016: 1
      1020: 1
      1021: q
      1022: 1
      1026: 1
      1032: 1
      1036: 1
      1037: q
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1058: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1114: 1
      1115: q
      1122: 1
      1123: q
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1156: 1
      1172: 1
      1194: 1
      1198: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1230: 1
      1234: 1
      1240: 1
      1246: 1
      1248: 1
      1250: 1
      1260: 1
      1262: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1290: 1
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1410: 1
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1454: 1
      1460: 1
      1485: 1
      1486: 1
      1537: 1
      1549: 1
      1639: 1
      1647: 1
      1653: 1
      1733: 1

1734:    0: 3q^3+5q^2+4q+1
         1: q^4+4q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: 3q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: q^4+4q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: 3q^3+5q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 3q^3+5q^2+4q+1
        17: q^4+4q^3+5q^2+4q+1
        18: 3q^3+5q^2+4q+1
        19: 3q^3+5q^2+4q+1
        20: q^4+4q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: q^3+3q^2+4q+1
        23: q^3+3q^2+4q+1
        24: q^3+3q^2+4q+1
        25: q^3+3q^2+4q+1
        26: q^3+3q^2+4q+1
        27: q^3+3q^2+4q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+4q+1
        32: q^3+3q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+4q+1
        35: q^3+3q^2+4q+1
        36: q^3+3q^2+4q+1
        37: q^2+2q
        38: q^2+2q+1
        39: q^2+2q
        40: q^2+2q+1
        41: q^2+2q
        42: q^2+2q+1
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 3q^3+5q^2+4q+1
        47: q^4+4q^3+5q^2+4q+1
        48: 3q^3+5q^2+4q+1
        49: 3q^3+5q^2+4q+1
        50: q^4+4q^3+5q^2+4q+1
        51: 3q^3+5q^2+4q+1
        52: q^3+3q^2+4q+1
        53: q^3+3q^2+4q+1
        54: q^3+3q^2+4q+1
        55: q^3+3q^2+4q+1
        56: q^3+3q^2+4q+1
        57: q^3+3q^2+4q+1
        58: 2q
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q
        62: 2q
        63: q^2+2q+1
        64: q^2+2q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+2q+1
        68: q^3+4q^2+4q+1
        69: 3q^3+5q^2+4q+1
        70: q^3+4q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^2+2q
        75: q^2+2q+1
        76: q^2+2q
        77: q^2+2q+1
        78: q^2+2q
        79: q^2+2q+1
        80: 2q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^2+4q+1
        83: q^3+3q^2+4q+1
        84: 2q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^2+4q+1
        87: q^3+3q^2+4q+1
        88: q^3+4q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: 3q^3+5q^2+4q+1
        92: q^4+4q^3+5q^2+4q+1
        93: 3q^3+5q^2+4q+1
        94: q^3+3q^2+4q+1
        95: q^3+3q^2+4q+1
        96: q^3+3q^2+4q+1
        97: q^3+3q^2+4q+1
        98: q^3+3q^2+4q+1
        99: q^3+3q^2+4q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q^2+q+1
       105: q
       106: q
       107: 2q^2+2q+1
       108: 2q
       109: 2q
       110: 2q^2+2q+1
       111: q^2+2q
       112: q^2+2q+1
       113: 2q
       114: q^2+2q+1
       115: q^2+2q
       116: q^2+2q+1
       117: 2q
       118: 2q^2+2q+1
       119: 2q^2+2q+1
       120: 2q
       121: 2q
       122: q^2+2q+1
       123: q^2+2q
       124: q^2+2q+1
       125: q^3+4q^2+4q+1
       126: q^3+4q^2+4q+1
       127: q^2+2q
       128: q^2+2q+1
       129: q^2+2q
       130: q^2+2q+1
       131: q^2+2q
       132: q^2+2q+1
       133: q^3+4q^2+4q+1
       134: 3q^3+5q^2+4q+1
       135: q^3+3q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 2q^2+4q+1
       138: q^3+3q^2+4q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^2+4q+1
       142: q^3+3q^2+4q+1
       143: 2q^2+4q+1
       144: q^3+3q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: q^3+3q^2+4q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: 2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: 2q
       156: q+1
       157: q^3+4q^2+4q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: q^3+3q^2+4q+1
       161: q^3+3q^2+4q+1
       162: q^3+3q^2+4q+1
       163: q^3+3q^2+4q+1
       164: q^3+3q^2+4q+1
       165: q^3+3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q^2+q+1
       171: q
       172: q
       173: q
       174: q^2+q+1
       175: q
       176: q
       177: q^2+2q
       178: q^2+2q+1
       179: 2q
       180: q^2+2q+1
       181: q^2+2q
       182: q^2+2q+1
       183: 2q^2+2q+1
       184: 2q
       185: 2q
       186: 2q^2+2q+1
       187: q^2+2q
       188: q^2+2q+1
       189: 2q
       190: q^2+2q+1
       191: 2q
       192: 2q^2+2q+1
       193: q+1
       195: 2q
       196: 2q^2+2q+1
       197: q
       198: 1
       199: 2q^2+2q+1
       200: 2q
       201: 2q^2+2q+1
       202: 2q
       204: q+1
       205: q
       206: 1
       207: 2q
       208: q^2+2q+1
       209: 2q
       210: q+1
       211: 2q
       212: q+1
       213: q^2+2q
       214: q^2+2q+1
       215: q^2+2q
       216: q^2+2q+1
       217: q^2+2q
       218: q^2+2q+1
       219: q^3+4q^2+4q+1
       220: q^3+4q^2+4q+1
       221: q^3+4q^2+4q+1
       222: 2q^2+4q+1
       223: q^3+3q^2+4q+1
       224: 2q^2+4q+1
       225: q^3+3q^2+4q+1
       226: 2q^2+4q+1
       227: 2q^2+4q+1
       228: q^3+3q^2+4q+1
       229: q+1
       230: q^3+3q^2+4q+1
       231: 2q^2+4q+1
       232: 2q^2+4q+1
       233: q^3+3q^2+4q+1
       234: q^3+3q^2+4q+1
       235: q+1
       236: 3q+1
       237: 2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: 2q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       260: q^2+q+1
       261: q
       262: q
       263: q
       264: q^2+q+1
       265: q
       266: q
       267: q
       268: 1
       273: q
       274: 1
       275: q
       276: q^2+q+1
       277: q
       278: q
       279: 2q
       280: q^2+2q+1
       281: q^2+2q
       282: q^2+2q+1
       283: 2q^2+2q+1
       284: 2q
       285: 2q
       286: 2q^2+2q+1
       287: 2q
       288: q^2+2q+1
       289: q^2+2q
       290: q^2+2q+1
       291: q^2+2q
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: 2q
       295: 2q
       296: 2q^2+2q+1
       297: 2q
       298: q^2+2q+1
       299: q+1
       301: q
       302: 1
       303: 2q
       304: 2q^2+2q+1
       305: q
       306: 1
       307: 2q^2+2q+1
       308: 2q
       310: q+1
       311: q
       312: 1
       313: q
       314: 1
       315: 2q
       316: q+1
       317: 2q
       318: q+1
       319: q+1
       322: q+1
       324: 1
       325: 2q
       326: q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: 3q+1
       337: 3q+1
       338: 2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: 2q
       343: q+1
       344: 2q^2+4q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q+1
       349: q^2+2q+1
       350: q^3+3q^2+4q+1
       351: q+1
       352: 2q^2+4q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+3q^2+4q+1
       357: 1
       358: q+1
       359: q+1
       360: 2q
       361: q+1
       362: q^2+2q
       363: q+1
       364: 2q
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q^2+q+1
       379: q
       380: q
       381: q
       382: q^2+q+1
       383: q
       384: q
       385: q
       386: q^2+q+1
       387: q
       388: q
       389: q
       390: 1
       393: q
       394: 1
       399: q
       400: 1
       403: 1
       404: q
       407: 1
       413: 2q
       414: q^2+2q+1
       417: q^2+2q
       418: q^2+2q+1
       419: 2q^2+2q+1
       420: 2q
       421: 2q
       422: 2q^2+2q+1
       423: 2q
       424: q^2+2q+1
       425: 2q
       426: q+1
       427: 2q
       428: q+1
       429: q+1
       431: 2q
       432: 2q^2+2q+1
       433: q
       434: 1
       435: q
       436: 1
       437: 1
       439: q
       440: q^2+q+1
       442: 1
       443: q+1
       445: q
       446: 1
       447: 2q^2+2q+1
       448: 2q
       450: q+1
       451: q
       452: 1
       453: q^2+q+1
       454: q
       455: q
       456: 1
       458: 1
       460: 1
       462: q+1
       463: q
       464: 1
       465: 2q
       466: q+1
       467: 2q
       468: q+1
       469: 2q
       470: q+1
       471: q+1
       474: q+1
       476: 1
       478: 1
       480: 1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 3q+1
       484: 3q+1
       485: 2q
       486: q+1
       487: q^2+2q
       488: q+1
       489: 2q
       490: q+1
       491: 3q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: q^2+q+1
       523: q
       524: q
       529: q
       530: q^2+q+1
       531: q
       532: q
       533: q
       534: 1
       537: q
       538: 1
       542: 1
       545: q
       546: 1
       551: 1
       552: q
       555: q
       556: 1
       560: 1
       563: q
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       585: 2q
       586: q^2+2q+1
       589: 2q^2+2q+1
       590: 2q
       592: q+1
       593: q+1
       595: 2q
       596: 2q^2+2q+1
       597: 2q
       598: q+1
       599: 2q
       600: q+1
       601: 2q
       602: q+1
       603: 1
       605: q
       606: 1
       607: q
       608: q^2+q+1
       610: 1
       613: q
       614: 1
       615: q+1
       617: q
       618: 1
       619: q^2+q+1
       620: q
       622: 1
       623: q
       624: 1
       626: 1
       629: q
       630: 1
       632: q+1
       633: q
       634: 1
       639: 2q
       640: q+1
       641: q+1
       644: q+1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 3q+1
       658: 2q
       659: q+1
       660: q^2+2q
       661: q+1
       662: 2q
       663: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       699: 1
       709: q
       710: q^2+q+1
       711: q
       712: q
       715: 1
       716: q
       717: q
       718: 1
       721: q
       722: 1
       726: 1
       733: q
       734: 1
       739: q
       740: 1
       744: 1
       751: q
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       775: 2q
       776: q+1
       779: 2q
       780: q+1
       781: 2q
       782: q+1
       785: q+1
       788: q+1
       792: 1
       793: q+1
       795: q
       796: 1
       798: 1
       801: 1
       805: 1
       807: q
       808: q^2+q+1
       809: q
       810: 1
       812: 1
       815: 1
       818: q+1
       819: q
       820: 1
       822: 1
       825: q^2+q+1
       826: q
       828: 1
       832: 1
       833: q
       834: 1
       836: 1
       840: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       858: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       890: 1
       902: q
       903: 1
       904: q
       905: 1
       909: 1
       916: q
       917: 1
       921: 1
       929: 1
       942: q
       943: 1
       947: 1
       951: 1
       962: 1
       965: 1
       972: 1
       976: 1
       989: 1
       994: 2q
       995: q+1
       999: q+1
      1000: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1016: 1
      1020: q
      1021: 1
      1023: 1
      1026: 1
      1033: 1
      1036: q
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1059: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1116: q
      1117: 1
      1122: q
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1157: 1
      1175: 1
      1195: 1
      1200: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1231: 1
      1234: 1
      1240: 1
      1247: 1
      1249: 1
      1251: 1
      1261: 1
      1263: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1296: 1
      1327: 1
      1332: 1
      1357: 1
      1383: 1
      1411: 1
      1437: 1
      1441: 1
      1442: 1
      1445: 1
      1454: 1
      1461: 1
      1485: 1
      1486: 1
      1539: 1
      1550: 1
      1640: 1
      1647: 1
      1654: 1
      1734: 1

1735:    0: 3q^3+5q^2+4q+1
         1: q^4+4q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: 3q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: q^4+4q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: 3q^3+5q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 3q^3+5q^2+4q+1
        17: q^4+4q^3+5q^2+4q+1
        18: 3q^3+5q^2+4q+1
        19: 3q^3+5q^2+4q+1
        20: q^4+4q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: q^3+3q^2+4q+1
        23: q^3+3q^2+4q+1
        24: q^3+3q^2+4q+1
        25: q^3+3q^2+4q+1
        26: q^3+3q^2+4q+1
        27: q^3+3q^2+4q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+4q+1
        32: q^3+3q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+4q+1
        35: q^3+3q^2+4q+1
        36: q^3+3q^2+4q+1
        37: q^2+2q
        38: q^2+2q+1
        39: q^2+2q
        40: q^2+2q+1
        41: q^2+2q
        42: q^2+2q+1
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 3q^3+5q^2+4q+1
        47: q^4+4q^3+5q^2+4q+1
        48: 3q^3+5q^2+4q+1
        49: 3q^3+5q^2+4q+1
        50: q^4+4q^3+5q^2+4q+1
        51: 3q^3+5q^2+4q+1
        52: q^3+3q^2+4q+1
        53: q^3+3q^2+4q+1
        54: q^3+3q^2+4q+1
        55: q^3+3q^2+4q+1
        56: q^3+3q^2+4q+1
        57: q^3+3q^2+4q+1
        58: 2q^2+2q+1
        59: 2q
        60: 2q
        61: 2q^2+2q+1
        62: 2q
        63: q^2+2q+1
        64: q^2+2q
        65: q^2+2q+1
        66: q^2+2q
        67: q^2+2q+1
        68: q^3+4q^2+4q+1
        69: 3q^3+5q^2+4q+1
        70: q^3+4q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^2+2q
        75: q^2+2q+1
        76: q^2+2q
        77: q^2+2q+1
        78: q^2+2q
        79: q^2+2q+1
        80: 2q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^2+4q+1
        83: q^3+3q^2+4q+1
        84: 2q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^2+4q+1
        87: q^3+3q^2+4q+1
        88: q^3+4q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: 3q^3+5q^2+4q+1
        92: q^4+4q^3+5q^2+4q+1
        93: 3q^3+5q^2+4q+1
        94: q^3+3q^2+4q+1
        95: q^3+3q^2+4q+1
        96: q^3+3q^2+4q+1
        97: q^3+3q^2+4q+1
        98: q^3+3q^2+4q+1
        99: q^3+3q^2+4q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q^2+q+1
       106: q
       107: 2q
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: 2q
       111: q^2+2q
       112: q^2+2q+1
       113: 2q
       114: q^2+2q+1
       115: q^2+2q
       116: q^2+2q+1
       117: 2q^2+2q+1
       118: 2q
       119: 2q
       120: 2q^2+2q+1
       121: 2q
       122: q^2+2q+1
       123: q^2+2q
       124: q^2+2q+1
       125: q^3+4q^2+4q+1
       126: q^3+4q^2+4q+1
       127: q^2+2q
       128: q^2+2q+1
       129: q^2+2q
       130: q^2+2q+1
       131: q^2+2q
       132: q^2+2q+1
       133: q^3+4q^2+4q+1
       134: 3q^3+5q^2+4q+1
       135: q^3+3q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 2q^2+4q+1
       138: q^3+3q^2+4q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^2+4q+1
       142: q^3+3q^2+4q+1
       143: 2q^2+4q+1
       144: q^3+3q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: q^3+3q^2+4q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: 2q
       152: q+1
       153: q^2+2q
       154: q+1
       155: 2q
       156: q+1
       157: q^3+4q^2+4q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: q^3+3q^2+4q+1
       161: q^3+3q^2+4q+1
       162: q^3+3q^2+4q+1
       163: q^3+3q^2+4q+1
       164: q^3+3q^2+4q+1
       165: q^3+3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q
       171: q^2+q+1
       172: q
       173: q
       174: q
       175: q^2+q+1
       176: q
       177: q^2+2q
       178: q^2+2q+1
       179: 2q
       180: q^2+2q+1
       181: q^2+2q
       182: q^2+2q+1
       183: 2q
       184: 2q^2+2q+1
       185: 2q^2+2q+1
       186: 2q
       187: q^2+2q
       188: q^2+2q+1
       189: 2q
       190: q^2+2q+1
       191: 2q^2+2q+1
       192: 2q
       194: q+1
       195: 2q^2+2q+1
       196: 2q
       197: q
       198: 1
       199: 2q
       200: 2q^2+2q+1
       201: 2q
       202: 2q^2+2q+1
       203: q+1
       205: q
       206: 1
       207: 2q
       208: q^2+2q+1
       209: 2q
       210: q+1
       211: 2q
       212: q+1
       213: q^2+2q
       214: q^2+2q+1
       215: q^2+2q
       216: q^2+2q+1
       217: q^2+2q
       218: q^2+2q+1
       219: q^3+4q^2+4q+1
       220: q^3+4q^2+4q+1
       221: q^3+4q^2+4q+1
       222: 2q^2+4q+1
       223: q^3+3q^2+4q+1
       224: 2q^2+4q+1
       225: q^3+3q^2+4q+1
       226: 2q^2+4q+1
       227: 2q^2+4q+1
       228: q^3+3q^2+4q+1
       229: q+1
       230: q^3+3q^2+4q+1
       231: 2q^2+4q+1
       232: 2q^2+4q+1
       233: q^3+3q^2+4q+1
       234: q^3+3q^2+4q+1
       235: q+1
       236: 3q+1
       237: 2q
       238: q+1
       239: q^2+2q
       240: q+1
       241: 2q
       242: q+1
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       260: q
       261: q^2+q+1
       262: q
       263: q
       264: q
       265: q^2+q+1
       266: q
       269: q
       270: 1
       271: q
       272: 1
       275: q
       276: q
       277: q^2+q+1
       278: q
       279: 2q
       280: q^2+2q+1
       281: q^2+2q
       282: q^2+2q+1
       283: 2q
       284: 2q^2+2q+1
       285: 2q^2+2q+1
       286: 2q
       287: 2q
       288: q^2+2q+1
       289: q^2+2q
       290: q^2+2q+1
       291: q^2+2q
       292: q^2+2q+1
       293: 2q
       294: 2q^2+2q+1
       295: 2q^2+2q+1
       296: 2q
       297: 2q
       298: q^2+2q+1
       300: q+1
       301: q
       302: 1
       303: 2q^2+2q+1
       304: 2q
       305: q
       306: 1
       307: 2q
       308: 2q^2+2q+1
       309: q+1
       311: q
       312: 1
       313: q
       314: 1
       315: 2q
       316: q+1
       317: 2q
       318: q+1
       320: q+1
       321: q+1
       324: 1
       325: 2q
       326: q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: 3q+1
       337: 3q+1
       338: 2q
       339: q+1
       340: q^2+2q
       341: q+1
       342: 2q
       343: q+1
       344: 2q^2+4q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q+1
       349: q^2+2q+1
       350: q^3+3q^2+4q+1
       351: q+1
       352: 2q^2+4q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+3q^2+4q+1
       357: 1
       358: q+1
       359: q+1
       360: 2q
       361: q+1
       362: q^2+2q
       363: q+1
       364: 2q
       365: q+1
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: q^2+q+1
       380: q
       381: q
       382: q
       383: q^2+q+1
       384: q
       385: q
       386: q
       387: q^2+q+1
       388: q
       391: q
       392: 1
       395: 1
       396: q
       397: q
       398: 1
       401: q
       402: 1
       408: 1
       413: 2q
       414: q^2+2q+1
       417: q^2+2q
       418: q^2+2q+1
       419: 2q
       420: 2q^2+2q+1
       421: 2q^2+2q+1
       422: 2q
       423: 2q
       424: q^2+2q+1
       425: 2q
       426: q+1
       427: 2q
       428: q+1
       430: q+1
       431: 2q^2+2q+1
       432: 2q
       433: q
       434: 1
       435: q
       436: 1
       438: 1
       439: q^2+q+1
       440: q
       442: 1
       444: q+1
       445: q
       446: 1
       447: 2q
       448: 2q^2+2q+1
       449: q+1
       451: q
       452: 1
       453: q
       454: q^2+q+1
       455: q
       456: 1
       457: 1
       460: 1
       461: q+1
       463: q
       464: 1
       465: 2q
       466: q+1
       467: 2q
       468: q+1
       469: 2q
       470: q+1
       472: q+1
       473: q+1
       476: 1
       478: 1
       480: 1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 3q+1
       484: 3q+1
       485: 2q
       486: q+1
       487: q^2+2q
       488: q+1
       489: 2q
       490: q+1
       491: 3q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: q
       523: q^2+q+1
       524: q
       529: q
       530: q
       531: q^2+q+1
       532: q
       535: 1
       536: q
       539: q
       540: 1
       544: 1
       547: q
       548: 1
       549: q
       550: 1
       553: q
       554: 1
       558: 1
       561: q
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       585: 2q
       586: q^2+2q+1
       589: 2q
       590: 2q^2+2q+1
       591: q+1
       594: q+1
       595: 2q^2+2q+1
       596: 2q
       597: 2q
       598: q+1
       599: 2q
       600: q+1
       601: 2q
       602: q+1
       604: 1
       605: q
       606: 1
       607: q^2+q+1
       608: q
       610: 1
       613: q
       614: 1
       616: q+1
       617: q
       618: 1
       619: q
       620: q^2+q+1
       621: 1
       623: q
       624: 1
       626: 1
       629: q
       630: 1
       631: q+1
       633: q
       634: 1
       639: 2q
       640: q+1
       642: q+1
       643: q+1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 3q+1
       658: 2q
       659: q+1
       660: q^2+2q
       661: q+1
       662: 2q
       663: q+1
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       700: 1
       709: q
       710: q
       711: q^2+q+1
       712: q
       713: q
       714: 1
       719: 1
       720: q
       723: q
       724: 1
       728: 1
       735: q
       736: 1
       737: q
       738: 1
       742: 1
       749: q
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       775: 2q
       776: q+1
       779: 2q
       780: q+1
       781: 2q
       782: q+1
       786: q+1
       787: q+1
       792: 1
       794: q+1
       795: q
       796: 1
       798: 1
       802: 1
       806: 1
       807: q^2+q+1
       808: q
       809: q
       810: 1
       812: 1
       816: 1
       817: q+1
       819: q
       820: 1
       822: 1
       825: q
       826: q^2+q+1
       827: 1
       831: 1
       833: q
       834: 1
       836: 1
       839: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       858: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       891: 1
       900: q
       901: 1
       906: q
       907: 1
       910: 1
       918: q
       919: 1
       923: 1
       931: 1
       940: q
       941: 1
       945: 1
       949: 1
       963: 1
       966: 1
       972: 1
       977: 1
       990: 1
       994: 2q
       995: q+1
       998: q+1
      1001: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1017: 1
      1020: q
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1036: q
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1053: 1
      1058: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1093: 1
      1114: q
      1115: 1
      1124: q
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1159: 1
      1173: 1
      1196: 1
      1201: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1231: 1
      1235: 1
      1241: 1
      1246: 1
      1249: 1
      1250: 1
      1260: 1
      1263: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1297: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1412: 1
      1437: 1
      1440: 1
      1443: 1
      1445: 1
      1455: 1
      1460: 1
      1485: 1
      1486: 1
      1540: 1
      1551: 1
      1640: 1
      1648: 1
      1653: 1
      1735: 1

1736:    0: 3q^3+5q^2+4q+1
         1: q^4+4q^3+5q^2+4q+1
         2: 3q^3+5q^2+4q+1
         3: 3q^3+5q^2+4q+1
         4: 3q^3+5q^2+4q+1
         5: q^4+4q^3+5q^2+4q+1
         6: q^4+4q^3+5q^2+4q+1
         7: 3q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: 3q^3+5q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^3+5q^2+4q+1
        14: 3q^3+5q^2+4q+1
        15: q^4+4q^3+5q^2+4q+1
        16: 3q^3+5q^2+4q+1
        17: q^4+4q^3+5q^2+4q+1
        18: 3q^3+5q^2+4q+1
        19: 3q^3+5q^2+4q+1
        20: q^4+4q^3+5q^2+4q+1
        21: 3q^3+5q^2+4q+1
        22: q^3+3q^2+4q+1
        23: q^3+3q^2+4q+1
        24: q^3+3q^2+4q+1
        25: q^3+3q^2+4q+1
        26: q^3+3q^2+4q+1
        27: q^3+3q^2+4q+1
        28: q^3+4q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 3q^3+5q^2+4q+1
        31: 2q^2+4q+1
        32: q^3+3q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+4q+1
        35: q^3+3q^2+4q+1
        36: q^3+3q^2+4q+1
        37: q^2+2q+1
        38: q^2+2q
        39: q^2+2q+1
        40: q^2+2q
        41: q^2+2q+1
        42: q^2+2q
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 3q^3+5q^2+4q+1
        47: q^4+4q^3+5q^2+4q+1
        48: 3q^3+5q^2+4q+1
        49: 3q^3+5q^2+4q+1
        50: q^4+4q^3+5q^2+4q+1
        51: 3q^3+5q^2+4q+1
        52: q^3+3q^2+4q+1
        53: q^3+3q^2+4q+1
        54: q^3+3q^2+4q+1
        55: q^3+3q^2+4q+1
        56: q^3+3q^2+4q+1
        57: q^3+3q^2+4q+1
        58: 2q
        59: 2q^2+2q+1
        60: 2q
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: 2q
        64: q^2+2q+1
        65: q^2+2q
        66: q^2+2q+1
        67: q^2+2q
        68: q^3+4q^2+4q+1
        69: 3q^3+5q^2+4q+1
        70: q^3+4q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+3q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^2+2q+1
        75: q^2+2q
        76: q^2+2q+1
        77: q^2+2q
        78: q^2+2q+1
        79: q^2+2q
        80: 2q^2+4q+1
        81: q^3+3q^2+4q+1
        82: 2q^2+4q+1
        83: q^3+3q^2+4q+1
        84: 2q^2+4q+1
        85: q^3+3q^2+4q+1
        86: 2q^2+4q+1
        87: q^3+3q^2+4q+1
        88: q^3+4q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: 3q^3+5q^2+4q+1
        92: q^4+4q^3+5q^2+4q+1
        93: 3q^3+5q^2+4q+1
        94: q^3+3q^2+4q+1
        95: q^3+3q^2+4q+1
        96: q^3+3q^2+4q+1
        97: q^3+3q^2+4q+1
        98: q^3+3q^2+4q+1
        99: q^3+3q^2+4q+1
       100: 3q+1
       101: q^2+3q+1
       102: 3q+1
       103: q
       104: q
       105: q
       106: q^2+q+1
       107: 2q
       108: 2q^2+2q+1
       109: 2q
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q
       113: q^2+2q+1
       114: 2q
       115: q^2+2q+1
       116: q^2+2q
       117: 2q
       118: 2q^2+2q+1
       119: 2q
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: 2q
       123: q^2+2q+1
       124: q^2+2q
       125: q^3+4q^2+4q+1
       126: q^3+4q^2+4q+1
       127: q^2+2q+1
       128: q^2+2q
       129: q^2+2q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+2q
       133: q^3+4q^2+4q+1
       134: 3q^3+5q^2+4q+1
       135: q^3+3q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 2q^2+4q+1
       138: q^3+3q^2+4q+1
       139: 2q^2+4q+1
       140: q+1
       141: 2q^2+4q+1
       142: q^3+3q^2+4q+1
       143: 2q^2+4q+1
       144: q^3+3q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: q^3+3q^2+4q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       152: 2q
       153: q+1
       154: q^2+2q
       155: q+1
       156: 2q
       157: q^3+4q^2+4q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: q^3+3q^2+4q+1
       161: q^3+3q^2+4q+1
       162: q^3+3q^2+4q+1
       163: q^3+3q^2+4q+1
       164: q^3+3q^2+4q+1
       165: q^3+3q^2+4q+1
       166: 3q+1
       167: q^2+3q+1
       168: 3q+1
       169: q
       170: q
       171: q
       172: q^2+q+1
       173: q
       174: q
       175: q
       176: q^2+q+1
       177: q^2+2q+1
       178: q^2+2q
       179: q^2+2q+1
       180: 2q
       181: q^2+2q+1
       182: q^2+2q
       183: 2q
       184: 2q^2+2q+1
       185: 2q
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q
       189: q^2+2q+1
       190: 2q
       191: 2q
       192: 2q^2+2q+1
       194: q+1
       195: 2q
       196: 2q^2+2q+1
       197: 1
       198: q
       199: 2q
       200: 2q^2+2q+1
       201: 2q
       202: 2q^2+2q+1
       204: q+1
       205: 1
       206: q
       207: q^2+2q+1
       208: 2q
       209: q+1
       210: 2q
       211: q+1
       212: 2q
       213: q^2+2q+1
       214: q^2+2q
       215: q^2+2q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+2q
       219: q^3+4q^2+4q+1
       220: q^3+4q^2+4q+1
       221: q^3+4q^2+4q+1
       222: 2q^2+4q+1
       223: q^3+3q^2+4q+1
       224: 2q^2+4q+1
       225: q^3+3q^2+4q+1
       226: 2q^2+4q+1
       227: 2q^2+4q+1
       228: q^3+3q^2+4q+1
       229: q+1
       230: q^3+3q^2+4q+1
       231: 2q^2+4q+1
       232: 2q^2+4q+1
       233: q^3+3q^2+4q+1
       234: q^3+3q^2+4q+1
       235: q+1
       236: 3q+1
       237: q+1
       238: 2q
       239: q+1
       240: q^2+2q
       241: q+1
       242: 2q
       243: 3q+1
       244: q+1
       245: q+1
       246: 3q+1
       247: 3q+1
       248: q^2+3q+1
       249: 3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: 3q+1
       257: q^2+3q+1
       258: 3q+1
       259: q
       260: q
       261: q
       262: q^2+q+1
       263: q
       264: q
       265: q
       266: q^2+q+1
       269: 1
       270: q
       273: 1
       274: q
       275: q
       276: q
       277: q
       278: q^2+q+1
       279: q^2+2q+1
       280: 2q
       281: q^2+2q+1
       282: q^2+2q
       283: 2q
       284: 2q^2+2q+1
       285: 2q
       286: 2q^2+2q+1
       287: q^2+2q+1
       288: 2q
       289: q^2+2q+1
       290: q^2+2q
       291: q^2+2q+1
       292: q^2+2q
       293: 2q
       294: 2q^2+2q+1
       295: 2q
       296: 2q^2+2q+1
       297: q^2+2q+1
       298: 2q
       300: q+1
       301: 1
       302: q
       303: 2q
       304: 2q^2+2q+1
       305: 1
       306: q
       307: 2q
       308: 2q^2+2q+1
       310: q+1
       311: 1
       312: q
       313: 1
       314: q
       315: q+1
       316: 2q
       317: q+1
       318: 2q
       320: q+1
       322: q+1
       323: 1
       325: q+1
       326: 2q
       333: q^3+4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: 3q+1
       337: 3q+1
       338: q+1
       339: 2q
       340: q+1
       341: q^2+2q
       342: q+1
       343: 2q
       344: 2q^2+4q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q+1
       349: q^2+2q+1
       350: q^3+3q^2+4q+1
       351: q+1
       352: 2q^2+4q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+3q^2+4q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       361: 2q
       362: q+1
       363: q^2+2q
       364: q+1
       365: 2q
       366: 3q+1
       367: 3q+1
       368: 3q+1
       369: q+1
       370: q+1
       371: 3q+1
       372: q^2+3q+1
       373: 3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: q
       380: q^2+q+1
       381: q
       382: q
       383: q
       384: q^2+q+1
       385: q
       386: q
       387: q
       388: q^2+q+1
       391: 1
       392: q
       395: q
       396: 1
       399: 1
       400: q
       403: q
       404: 1
       406: 1
       413: q^2+2q+1
       414: 2q
       417: q^2+2q+1
       418: q^2+2q
       419: 2q
       420: 2q^2+2q+1
       421: 2q
       422: 2q^2+2q+1
       423: q^2+2q+1
       424: 2q
       425: q+1
       426: 2q
       427: q+1
       428: 2q
       430: q+1
       431: 2q
       432: 2q^2+2q+1
       433: 1
       434: q
       435: 1
       436: q
       438: 1
       439: q
       440: q^2+q+1
       441: 1
       444: q+1
       445: 1
       446: q
       447: 2q
       448: 2q^2+2q+1
       450: q+1
       451: 1
       452: q
       453: q
       454: q^2+q+1
       455: 1
       456: q
       458: 1
       459: 1
       462: q+1
       463: 1
       464: q
       465: q+1
       466: 2q
       467: q+1
       468: 2q
       469: q+1
       470: 2q
       472: q+1
       474: q+1
       475: 1
       477: 1
       479: 1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 3q+1
       484: 3q+1
       485: q+1
       486: 2q
       487: q+1
       488: q^2+2q
       489: q+1
       490: 2q
       491: 3q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: q+1
       501: q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: 1
       514: q+1
       515: 3q+1
       516: q^2+3q+1
       517: 3q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: q
       523: q
       524: q^2+q+1
       529: q
       530: q
       531: q
       532: q^2+q+1
       535: q
       536: 1
       539: 1
       540: q
       543: 1
       547: 1
       548: q
       551: q
       552: 1
       555: 1
       556: q
       559: 1
       563: 1
       564: q
       568: 1
       570: 1
       575: 1
       577: 1
       585: q^2+2q+1
       586: 2q
       589: 2q
       590: 2q^2+2q+1
       592: q+1
       594: q+1
       595: 2q
       596: 2q^2+2q+1
       597: q+1
       598: 2q
       599: q+1
       600: 2q
       601: q+1
       602: 2q
       604: 1
       605: 1
       606: q
       607: q
       608: q^2+q+1
       609: 1
       613: 1
       614: q
       616: q+1
       617: 1
       618: q
       619: q
       620: q^2+q+1
       622: 1
       623: 1
       624: q
       625: 1
       629: 1
       630: q
       632: q+1
       633: 1
       634: q
       639: q+1
       640: 2q
       642: q+1
       644: q+1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 3q+1
       658: q+1
       659: 2q
       660: q+1
       661: q^2+2q
       662: q+1
       663: 2q
       664: 3q+1
       665: 3q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       709: q
       710: q
       711: q
       712: q^2+q+1
       715: q
       716: 1
       719: q
       720: 1
       723: 1
       724: q
       727: 1
       735: 1
       736: q
       739: 1
       740: q
       743: 1
       751: 1
       752: q
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       776: 2q
       779: q+1
       780: 2q
       781: q+1
       782: 2q
       786: q+1
       788: q+1
       791: 1
       794: q+1
       795: 1
       796: q
       797: 1
       802: 1
       806: 1
       807: q
       808: q^2+q+1
       809: 1
       810: q
       811: 1
       816: 1
       818: q+1
       819: 1
       820: q
       821: 1
       825: q
       826: q^2+q+1
       828: 1
       832: 1
       833: 1
       834: q
       835: 1
       840: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       857: 1
       865: q+1
       866: 3q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       902: 1
       903: q
       906: 1
       907: q
       911: 1
       918: 1
       919: q
       922: 1
       930: 1
       942: 1
       943: q
       946: 1
       950: 1
       961: 1
       967: 1
       968: 1
       975: 1
       991: 1
       994: q+1
       995: 2q
       999: q+1
      1001: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1017: 1
      1020: 1
      1021: q
      1022: 1
      1027: 1
      1033: 1
      1036: 1
      1037: q
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1059: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1091: 1
      1116: 1
      1117: q
      1124: 1
      1125: q
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1158: 1
      1174: 1
      1197: 1
      1199: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1230: 1
      1235: 1
      1241: 1
      1247: 1
      1248: 1
      1251: 1
      1261: 1
      1262: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1295: 1
      1329: 1
      1331: 1
      1358: 1
      1382: 1
      1413: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1455: 1
      1461: 1
      1485: 1
      1486: 1
      1538: 1
      1552: 1
      1639: 1
      1648: 1
      1654: 1
      1736: 1

1737:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: q^4+9q^3+11q^2+6q+1
        23: q^4+9q^3+11q^2+6q+1
        24: q^4+9q^3+11q^2+6q+1
        25: 6q^3+9q^2+6q+1
        26: 6q^3+9q^2+6q+1
        27: 6q^3+9q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: q^4+9q^3+11q^2+6q+1
        32: q^4+9q^3+11q^2+6q+1
        33: 5q^3+10q^2+6q+1
        34: 6q^3+9q^2+6q+1
        35: 6q^3+9q^2+6q+1
        36: 3q^3+8q^2+6q+1
        37: 4q^3+7q^2+5q+1
        38: 2q^3+2q^2+q
        39: 4q^3+7q^2+5q+1
        40: 2q^3+2q^2+q
        41: 4q^3+7q^2+5q+1
        42: 2q^3+2q^2+q
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 5q^3+8q^2+5q+1
        53: 5q^3+8q^2+5q+1
        54: 5q^3+8q^2+5q+1
        55: 3q^3+6q^2+5q+1
        56: 3q^3+6q^2+5q+1
        57: 3q^3+6q^2+5q+1
        58: 3q^3+6q^2+4q+1
        59: 2q^3+4q^2+2q
        60: q^3+5q^2+3q+1
        61: 2q^3+3q^2+3q
        62: 4q^3+7q^2+5q+1
        63: 2q^3+2q^2+q
        64: 4q^3+7q^2+5q+1
        65: 2q^3+2q^2+q
        66: 2q^3+6q^2+5q+1
        67: q^3+2q^2+q
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: q^3+3q^2+4q+1
        73: 4q^2+4q+1
        74: q^3+4q^2+4q+1
        76: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        80: q^4+9q^3+11q^2+6q+1
        81: 5q^3+10q^2+6q+1
        82: 5q^3+8q^2+5q+1
        83: 5q^3+8q^2+5q+1
        84: 6q^3+9q^2+6q+1
        85: 3q^3+8q^2+6q+1
        86: 3q^3+6q^2+5q+1
        87: 3q^3+6q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 2q^3+7q^2+5q+1
        95: 2q^3+7q^2+5q+1
        96: 3q^3+5q^2+4q+1
        97: 4q^2+5q+1
        98: 4q^2+5q+1
        99: q^3+3q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+4q^2+3q+1
       104: q^2
       105: q^3+q^2+q
       106: q^3+2q^2+2q
       107: 2q^2+2q+1
       108: q^3+q^2+2q
       109: 3q^2+3q+1
       110: q^2+q
       111: q^2+3q+1
       113: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       117: 3q^3+6q^2+4q+1
       118: 2q^3+4q^2+2q
       119: q^3+5q^2+3q+1
       120: 2q^3+3q^2+3q
       121: 4q^3+7q^2+5q+1
       122: 2q^3+2q^2+q
       123: 2q^3+6q^2+5q+1
       124: q^3+2q^2+q
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: q^3+3q^2+4q+1
       136: 4q^2+4q+1
       137: 5q^3+10q^2+6q+1
       138: q^3+4q^2+4q+1
       139: 2q^3+7q^2+5q+1
       140: q^3+3q^2+4q+1
       141: 5q^3+8q^2+5q+1
       142: 4q^2+4q+1
       143: 3q^3+8q^2+6q+1
       144: 2q^2+4q+1
       145: 4q^2+5q+1
       146: 3q^3+6q^2+5q+1
       147: 2q^2+4q+1
       148: q^2+2q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       151: q^3+4q^2+4q+1
       153: q^3+4q^2+4q+1
       155: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 2q^3+7q^2+5q+1
       161: 2q^3+7q^2+5q+1
       162: 3q^3+5q^2+4q+1
       163: 4q^2+5q+1
       164: 4q^2+5q+1
       165: q^3+3q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       169: q^2+2q+1
       172: q
       173: q^3+4q^2+3q+1
       174: q^2
       175: q^3+q^2+q
       176: q^3+2q^2+2q
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: 2q^2+2q+1
       184: q^3+q^2+2q
       185: 3q^2+3q+1
       186: q^2+q
       187: q^2+3q+1
       189: q^3+4q^2+4q+1
       191: 3q^3+6q^2+4q+1
       192: 2q^3+4q^2+2q
       193: 2q^2+2q+1
       194: q^3+q^2+2q
       195: 3q^2+3q+1
       196: q^2+q
       197: q^2+3q+1
       199: q^3+5q^2+3q+1
       200: 2q^3+3q^2+3q
       201: q^2+2q+1
       202: q^2+2q
       203: q^2+2q+1
       205: q+1
       207: 2q^3+6q^2+5q+1
       208: q^3+2q^2+q
       209: q^3+4q^2+4q+1
       211: q^3+4q^2+4q+1
       213: 2q^2+4q+1
       215: 2q^2+4q+1
       217: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: 4q^2+4q+1
       225: 2q^2+3q+1
       226: q^3+4q^2+4q+1
       227: 2q^3+7q^2+5q+1
       228: q^3+4q^2+4q+1
       229: q^3+3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+4q+1
       232: 4q^2+5q+1
       233: 2q^2+4q+1
       234: 2q^2+4q+1
       235: q^2+2q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 4q^2+5q+1
       244: 2q^2+4q+1
       245: q^2+2q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 2q^3+7q^2+5q+1
       251: 2q^3+7q^2+5q+1
       252: 3q^3+5q^2+4q+1
       253: 4q^2+5q+1
       254: 4q^2+5q+1
       255: q^3+3q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q^2+2q+1
       269: q
       271: q+1
       275: q^3+4q^2+3q+1
       276: q^2
       277: q^3+q^2+q
       278: q^3+2q^2+2q
       279: 2q^2+4q+1
       281: q^2+3q+1
       283: q+1
       284: q
       285: q^2+2q+1
       287: q^2+3q+1
       289: 3q+1
       291: 2q+1
       293: 2q^2+2q+1
       294: q^3+q^2+2q
       295: 3q^2+3q+1
       296: q^2+q
       297: q^2+3q+1
       299: 2q^2+2q+1
       300: q^3+q^2+2q
       301: 3q+1
       303: 3q^2+3q+1
       304: q^2+q
       305: q^2+3q+1
       307: q^2+2q+1
       308: q^2+2q
       309: q^2+2q+1
       311: q+1
       313: q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: q^2+2q+1
       320: q^2+2q
       321: q^2+2q+1
       323: q+1
       325: q^3+4q^2+4q+1
       327: 2q^2+4q+1
       329: 2q^2+4q+1
       331: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^3+4q^2+4q+1
       345: 2q^3+7q^2+5q+1
       346: q^3+4q^2+4q+1
       347: q^3+3q^2+4q+1
       348: q^2+3q+1
       349: 4q^2+4q+1
       350: 2q^2+3q+1
       351: 4q+2
       352: 2q^2+4q+1
       353: 4q^2+5q+1
       354: 2q^2+4q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+2
       360: 2q^2+4q+1
       362: 2q^2+4q+1
       364: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: 2q^2+4q+1
       370: q^2+2q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: 2q+1
       391: q
       393: q^2+2q+1
       396: q
       397: q+1
       401: q+1
       405: q+1
       409: 2q^2+4q+1
       411: q^2+3q+1
       413: q^2+3q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       420: q
       421: q^2+2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       430: q
       431: q^2+2q+1
       433: 2q+1
       435: 3q+1
       437: 2q^2+2q+1
       438: q^3+q^2+2q
       439: 3q^2+3q+1
       440: q^2+q
       441: q^2+3q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       447: q+1
       448: q
       449: q+1
       451: 1
       453: q^2+2q+1
       454: q^2+2q
       455: q+1
       457: q^2+2q+1
       459: q+1
       461: 2q+2
       463: 2q+2
       465: 2q^2+4q+1
       467: q^2+3q+1
       469: q^2+3q+1
       471: q^2+2q+1
       472: q^2+2q
       473: q^2+2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q^2+3q+1
       482: 2q^2+3q+1
       483: q+1
       484: 4q+2
       485: 4q+2
       487: 4q+2
       489: q^2+2q+1
       491: q+1
       492: q^3+4q^2+4q+1
       493: q^2+3q+1
       494: 2q^2+3q+1
       495: q+1
       496: 4q+2
       497: 2q^2+4q+1
       498: q^2+3q+1
       499: q+1
       500: 1
       501: 2q+2
       502: 2q^2+4q+1
       504: 2q^2+4q+1
       506: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: 2q^2+4q+1
       512: q^2+3q+1
       513: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: q+1
       537: 2q+1
       539: q
       541: q^2+2q+1
       543: q
       545: 2q+1
       547: 2q+1
       549: 1
       553: q+1
       557: q+1
       561: 2q+2
       565: q+1
       569: q+1
       573: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q^2+3q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       590: q
       591: 1
       595: q^2+2q+1
       597: q+1
       599: q+1
       601: 4q+2
       603: q+1
       604: q
       605: 2q+1
       607: q^2+2q+1
       609: 2q+1
       611: 3q+1
       613: q+1
       615: 2q+1
       616: 2q+1
       617: 4q+2
       619: q+1
       620: q
       621: q+1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: 2q+2
       633: 2q+2
       635: 2q^2+4q+1
       637: q^2+3q+1
       639: q^2+3q+1
       641: q+1
       642: q
       643: q+1
       645: 1
       647: q^2+2q+1
       648: q^2+2q
       649: q^2+2q+1
       651: q+1
       653: q+1
       655: q+1
       656: q+1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: q+1
       666: 4q+2
       668: 4q+2
       670: q^2+2q+1
       672: 4q+2
       673: q+1
       674: q+2
       675: q^2+3q+1
       676: 2q^2+3q+1
       677: q+1
       678: 4q+2
       679: q+1
       680: 2
       681: q^2+3q+1
       682: q+1
       683: 1
       684: 2q+2
       685: 1
       686: 2q^2+4q+1
       687: q^2+3q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       698: q+1
       705: q+1
       709: q+1
       713: 1
       721: q+1
       725: q+1
       729: 2q+1
       731: q
       733: 2q+1
       735: 2q+1
       737: 1
       741: 1
       745: q+1
       749: 2q+2
       753: 1
       757: q+1
       761: q+1
       765: q+1
       767: q+1
       769: q+1
       772: q+1
       775: 2
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       787: 1
       789: 4q+2
       793: 1
       794: 1
       795: q+2
       797: 2q+1
       799: 2q+1
       801: q+1
       802: q
       803: 1
       807: q^2+2q+1
       809: q+1
       811: q+1
       813: 4q+2
       815: 2q+1
       816: 2q+1
       817: 2
       819: 2
       821: 1
       823: 1
       825: q+1
       826: q
       827: 1
       831: q+1
       833: 1
       835: 1
       837: 2q+2
       839: 2q+2
       841: q^2+3q+1
       843: 1
       844: 1
       845: q+1
       846: q
       847: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q+1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: q+2
       870: 1
       871: q+1
       872: q+1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+3q+1
       878: q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       884: q+1
       888: q+1
       896: q+1
       900: 1
       912: q+1
       916: 1
       918: 1
       920: q+1
       924: 1
       932: 2q+1
       934: 2q+1
       936: 1
       940: 2
       944: 1
       948: 1
       956: 2q+2
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       978: q+1
       982: q+1
       985: q+1
       988: q+1
       990: q+1
       992: 2
       994: 1
       996: 1
       998: 1
      1002: q+1
      1006: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: 2q+1
      1020: 1
      1022: q+1
      1024: q+1
      1028: 1
      1030: 2
      1032: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1053: q
      1054: 1
      1058: q+1
      1060: 1
      1062: 1
      1066: q+2
      1068: q+2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 1
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1090: 1
      1098: q+1
      1103: q+1
      1110: 1
      1114: 1
      1144: 1
      1146: 1
      1148: q+1
      1152: 1
      1164: 2
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1198: 1
      1202: 1
      1210: 2
      1212: 1
      1214: 1
      1216: 1
      1226: q+2
      1228: 1
      1229: 1
      1230: 1
      1232: 1
      1236: 1
      1238: q+1
      1242: 1
      1244: 2
      1246: 2
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1302: 1
      1306: 1
      1314: 1
      1340: 1
      1342: 1
      1344: 1
      1348: 1
      1372: 2
      1376: 1
      1404: 1
      1407: 1
      1410: 1
      1412: 1
      1414: 1
      1418: 1
      1438: 1
      1440: 1
      1448: 1
      1450: 1
      1452: 1
      1458: 1
      1470: 1
      1472: 1
      1478: 1
      1485: 1
      1488: 1
      1525: 1
      1529: 1
      1541: 1
      1563: 1
      1603: 1
      1643: 1
      1645: 1
      1667: 1
      1737: 1

1738:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: q^4+9q^3+11q^2+6q+1
        23: q^4+9q^3+11q^2+6q+1
        24: q^4+9q^3+11q^2+6q+1
        25: 6q^3+9q^2+6q+1
        26: 6q^3+9q^2+6q+1
        27: 6q^3+9q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: q^4+9q^3+11q^2+6q+1
        32: q^4+9q^3+11q^2+6q+1
        33: 5q^3+10q^2+6q+1
        34: 6q^3+9q^2+6q+1
        35: 6q^3+9q^2+6q+1
        36: 3q^3+8q^2+6q+1
        37: 2q^3+2q^2+q
        38: 4q^3+7q^2+5q+1
        39: 2q^3+2q^2+q
        40: 4q^3+7q^2+5q+1
        41: 2q^3+2q^2+q
        42: 4q^3+7q^2+5q+1
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 5q^3+8q^2+5q+1
        53: 5q^3+8q^2+5q+1
        54: 5q^3+8q^2+5q+1
        55: 3q^3+6q^2+5q+1
        56: 3q^3+6q^2+5q+1
        57: 3q^3+6q^2+5q+1
        58: 3q^3+6q^2+4q+1
        59: 2q^3+4q^2+2q
        60: 2q^3+3q^2+3q
        61: q^3+5q^2+3q+1
        62: 2q^3+2q^2+q
        63: 4q^3+7q^2+5q+1
        64: 2q^3+2q^2+q
        65: 4q^3+7q^2+5q+1
        66: q^3+2q^2+q
        67: 2q^3+6q^2+5q+1
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: q^3+3q^2+4q+1
        73: 4q^2+4q+1
        75: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        79: q^3+4q^2+4q+1
        80: q^4+9q^3+11q^2+6q+1
        81: 5q^3+10q^2+6q+1
        82: 5q^3+8q^2+5q+1
        83: 5q^3+8q^2+5q+1
        84: 6q^3+9q^2+6q+1
        85: 3q^3+8q^2+6q+1
        86: 3q^3+6q^2+5q+1
        87: 3q^3+6q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 2q^3+7q^2+5q+1
        95: 2q^3+7q^2+5q+1
        96: 3q^3+5q^2+4q+1
        97: 4q^2+5q+1
        98: 4q^2+5q+1
        99: q^3+3q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+q^2+q
       104: q^3+2q^2+2q
       105: q^3+4q^2+3q+1
       106: q^2
       107: q^3+q^2+2q
       108: 2q^2+2q+1
       109: 3q^2+3q+1
       110: q^2+q
       112: q^2+3q+1
       114: q^3+4q^2+4q+1
       116: q^3+4q^2+4q+1
       117: 3q^3+6q^2+4q+1
       118: 2q^3+4q^2+2q
       119: 2q^3+3q^2+3q
       120: q^3+5q^2+3q+1
       121: 2q^3+2q^2+q
       122: 4q^3+7q^2+5q+1
       123: q^3+2q^2+q
       124: 2q^3+6q^2+5q+1
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: q^3+3q^2+4q+1
       136: 4q^2+4q+1
       137: 5q^3+10q^2+6q+1
       138: q^3+4q^2+4q+1
       139: 2q^3+7q^2+5q+1
       140: q^3+3q^2+4q+1
       141: 5q^3+8q^2+5q+1
       142: 4q^2+4q+1
       143: 3q^3+8q^2+6q+1
       144: 2q^2+4q+1
       145: 4q^2+5q+1
       146: 3q^3+6q^2+5q+1
       147: 2q^2+4q+1
       148: q^2+2q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       152: q^3+4q^2+4q+1
       154: q^3+4q^2+4q+1
       156: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 2q^3+7q^2+5q+1
       161: 2q^3+7q^2+5q+1
       162: 3q^3+5q^2+4q+1
       163: 4q^2+5q+1
       164: 4q^2+5q+1
       165: q^3+3q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       170: q
       171: q^2+2q+1
       173: q^3+q^2+q
       174: q^3+2q^2+2q
       175: q^3+4q^2+3q+1
       176: q^2
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: q^3+q^2+2q
       184: 2q^2+2q+1
       185: 3q^2+3q+1
       186: q^2+q
       188: q^2+3q+1
       190: q^3+4q^2+4q+1
       191: 3q^3+6q^2+4q+1
       192: 2q^3+4q^2+2q
       193: q^3+q^2+2q
       194: 2q^2+2q+1
       195: 3q^2+3q+1
       196: q^2+q
       198: q^2+3q+1
       199: 2q^3+3q^2+3q
       200: q^3+5q^2+3q+1
       201: q^2+2q
       202: q^2+2q+1
       203: q^2+2q+1
       206: q+1
       207: q^3+2q^2+q
       208: 2q^3+6q^2+5q+1
       210: q^3+4q^2+4q+1
       212: q^3+4q^2+4q+1
       214: 2q^2+4q+1
       216: 2q^2+4q+1
       218: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: 4q^2+4q+1
       225: 2q^2+3q+1
       226: q^3+4q^2+4q+1
       227: 2q^3+7q^2+5q+1
       228: q^3+4q^2+4q+1
       229: q^3+3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+4q+1
       232: 4q^2+5q+1
       233: 2q^2+4q+1
       234: 2q^2+4q+1
       235: q^2+2q+1
       236: 2q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 4q^2+5q+1
       244: 2q^2+4q+1
       245: q^2+2q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 2q^3+7q^2+5q+1
       251: 2q^3+7q^2+5q+1
       252: 3q^3+5q^2+4q+1
       253: 4q^2+5q+1
       254: 4q^2+5q+1
       255: q^3+3q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       268: q
       270: q^2+2q+1
       272: q+1
       275: q^3+q^2+q
       276: q^3+2q^2+2q
       277: q^3+4q^2+3q+1
       278: q^2
       280: 2q^2+4q+1
       282: q^2+3q+1
       283: q
       284: q+1
       285: q^2+2q+1
       288: q^2+3q+1
       290: 3q+1
       292: 2q+1
       293: q^3+q^2+2q
       294: 2q^2+2q+1
       295: 3q^2+3q+1
       296: q^2+q
       298: q^2+3q+1
       299: q^3+q^2+2q
       300: 2q^2+2q+1
       302: 3q+1
       303: 3q^2+3q+1
       304: q^2+q
       306: q^2+3q+1
       307: q^2+2q
       308: q^2+2q+1
       309: q^2+2q+1
       312: q+1
       314: q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: q^2+2q
       320: q^2+2q+1
       321: q^2+2q+1
       324: q+1
       326: q^3+4q^2+4q+1
       328: 2q^2+4q+1
       330: 2q^2+4q+1
       332: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^3+4q^2+4q+1
       345: 2q^3+7q^2+5q+1
       346: q^3+4q^2+4q+1
       347: q^3+3q^2+4q+1
       348: q^2+3q+1
       349: 4q^2+4q+1
       350: 2q^2+3q+1
       351: 4q+2
       352: 2q^2+4q+1
       353: 4q^2+5q+1
       354: 2q^2+4q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+2
       361: 2q^2+4q+1
       363: 2q^2+4q+1
       365: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: 2q^2+4q+1
       370: q^2+2q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       390: q
       392: 2q+1
       394: q
       395: q^2+2q+1
       398: q+1
       402: q+1
       408: q+1
       410: 2q^2+4q+1
       412: q^2+3q+1
       414: q^2+3q+1
       416: 3q+1
       418: 2q+1
       419: q
       420: q+1
       421: q^2+2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q
       430: q+1
       431: q^2+2q+1
       434: 2q+1
       436: 3q+1
       437: q^3+q^2+2q
       438: 2q^2+2q+1
       439: 3q^2+3q+1
       440: q^2+q
       442: q^2+3q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       447: q
       448: q+1
       449: q+1
       452: 1
       453: q^2+2q
       454: q^2+2q+1
       456: q+1
       457: q^2+2q+1
       460: q+1
       461: 2q+2
       464: 2q+2
       466: 2q^2+4q+1
       468: q^2+3q+1
       470: q^2+3q+1
       471: q^2+2q
       472: q^2+2q+1
       473: q^2+2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q^2+3q+1
       482: 2q^2+3q+1
       483: q+1
       484: 4q+2
       486: 4q+2
       488: 4q+2
       490: q^2+2q+1
       491: q+1
       492: q^3+4q^2+4q+1
       493: q^2+3q+1
       494: 2q^2+3q+1
       495: q+1
       496: 4q+2
       497: 2q^2+4q+1
       498: q^2+3q+1
       499: q+1
       500: 1
       501: 2q+2
       503: 2q^2+4q+1
       505: 2q^2+4q+1
       507: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: 2q^2+4q+1
       512: q^2+3q+1
       513: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: q+1
       538: q
       540: 2q+1
       542: q
       544: q^2+2q+1
       546: 2q+1
       548: 2q+1
       550: 1
       554: q+1
       558: q+1
       562: 2q+2
       567: q+1
       572: q+1
       573: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q^2+3q+1
       586: 2q+1
       588: 2q+1
       589: q
       590: q+1
       591: 1
       595: q^2+2q+1
       598: q+1
       600: q+1
       602: 4q+2
       603: q
       604: q+1
       606: 2q+1
       607: q^2+2q+1
       610: 2q+1
       612: 3q+1
       614: q+1
       615: 2q+1
       616: 2q+1
       618: 4q+2
       619: q
       620: q+1
       621: q+1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: 2q+2
       634: 2q+2
       636: 2q^2+4q+1
       638: q^2+3q+1
       640: q^2+3q+1
       641: q
       642: q+1
       643: q+1
       646: 1
       647: q^2+2q
       648: q^2+2q+1
       649: q^2+2q+1
       652: q+1
       654: q+1
       655: q+1
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: q+1
       667: 4q+2
       669: 4q+2
       671: q^2+2q+1
       672: 4q+2
       673: q+1
       674: q+2
       675: q^2+3q+1
       676: 2q^2+3q+1
       677: q+1
       678: 4q+2
       679: q+1
       680: 2
       681: q^2+3q+1
       682: q+1
       683: 1
       684: 2q+2
       685: 1
       686: 2q^2+4q+1
       687: q^2+3q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       694: q+1
       700: q+1
       707: q+1
       711: q+1
       714: 1
       724: q+1
       728: q+1
       730: q
       732: 2q+1
       734: 2q+1
       736: 2q+1
       738: 1
       742: 1
       746: q+1
       750: 2q+2
       755: 1
       760: q+1
       764: q+1
       765: q+1
       767: q+1
       770: q+1
       773: q+1
       776: 2
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       787: 1
       790: 4q+2
       793: 1
       794: 1
       796: q+2
       798: 2q+1
       800: 2q+1
       801: q
       802: q+1
       803: 1
       807: q^2+2q+1
       810: q+1
       812: q+1
       814: 4q+2
       815: 2q+1
       816: 2q+1
       817: 2
       820: 2
       822: 1
       824: 1
       825: q
       826: q+1
       827: 1
       831: q+1
       834: 1
       836: 1
       838: 2q+2
       839: 2q+2
       842: q^2+3q+1
       843: 1
       844: 1
       845: q
       846: q+1
       847: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q+1
       858: q+1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: q+2
       870: 1
       871: q+1
       872: q+1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+3q+1
       878: q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       885: q+1
       891: q+1
       898: q+1
       901: 1
       915: q+1
       917: 1
       919: 1
       923: q+1
       925: 1
       933: 2q+1
       935: 2q+1
       937: 1
       941: 2
       945: 1
       949: 1
       957: 2q+2
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       981: q+1
       983: q+1
       986: q+1
       988: q+1
       990: q+1
       993: 2
       995: 1
       997: 1
       998: 1
      1003: q+1
      1006: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: 2q+1
      1021: 1
      1023: q+1
      1025: q+1
      1028: 1
      1031: 2
      1032: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: q+1
      1054: 1
      1058: q+1
      1061: 1
      1063: 1
      1067: q+2
      1069: q+2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 1
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1093: 1
      1099: q+1
      1105: q+1
      1111: 1
      1115: 1
      1145: 1
      1147: 1
      1151: q+1
      1153: 1
      1165: 2
      1169: 1
      1173: 1
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1211: 2
      1213: 1
      1215: 1
      1216: 1
      1227: q+2
      1228: 1
      1229: 1
      1231: 1
      1232: 1
      1237: 1
      1239: q+1
      1242: 1
      1245: 2
      1246: 2
      1253: 1
      1257: 1
      1260: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1303: 1
      1309: 1
      1315: 1
      1341: 1
      1343: 1
      1345: 1
      1349: 1
      1373: 2
      1377: 1
      1405: 1
      1408: 1
      1410: 1
      1412: 1
      1417: 1
      1419: 1
      1439: 1
      1440: 1
      1449: 1
      1450: 1
      1453: 1
      1459: 1
      1471: 1
      1473: 1
      1478: 1
      1485: 1
      1488: 1
      1526: 1
      1532: 1
      1542: 1
      1564: 1
      1604: 1
      1644: 1
      1645: 1
      1668: 1
      1738: 1

1739:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: q^4+9q^3+11q^2+6q+1
        23: q^4+9q^3+11q^2+6q+1
        24: q^4+9q^3+11q^2+6q+1
        25: 6q^3+9q^2+6q+1
        26: 6q^3+9q^2+6q+1
        27: 6q^3+9q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: q^4+9q^3+11q^2+6q+1
        32: q^4+9q^3+11q^2+6q+1
        33: 5q^3+10q^2+6q+1
        34: 6q^3+9q^2+6q+1
        35: 6q^3+9q^2+6q+1
        36: 3q^3+8q^2+6q+1
        37: 4q^3+7q^2+5q+1
        38: 2q^3+2q^2+q
        39: 4q^3+7q^2+5q+1
        40: 2q^3+2q^2+q
        41: 4q^3+7q^2+5q+1
        42: 2q^3+2q^2+q
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 5q^3+8q^2+5q+1
        53: 5q^3+8q^2+5q+1
        54: 5q^3+8q^2+5q+1
        55: 3q^3+6q^2+5q+1
        56: 3q^3+6q^2+5q+1
        57: 3q^3+6q^2+5q+1
        58: 2q^3+4q^2+2q
        59: 3q^3+6q^2+4q+1
        60: 2q^3+3q^2+3q
        61: q^3+5q^2+3q+1
        62: 4q^3+7q^2+5q+1
        63: 2q^3+2q^2+q
        64: 4q^3+7q^2+5q+1
        65: 2q^3+2q^2+q
        66: 2q^3+6q^2+5q+1
        67: q^3+2q^2+q
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: q^3+3q^2+4q+1
        73: 4q^2+4q+1
        74: q^3+4q^2+4q+1
        76: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        80: q^4+9q^3+11q^2+6q+1
        81: 5q^3+10q^2+6q+1
        82: 5q^3+8q^2+5q+1
        83: 5q^3+8q^2+5q+1
        84: 6q^3+9q^2+6q+1
        85: 3q^3+8q^2+6q+1
        86: 3q^3+6q^2+5q+1
        87: 3q^3+6q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 2q^3+7q^2+5q+1
        95: 2q^3+7q^2+5q+1
        96: 3q^3+5q^2+4q+1
        97: 4q^2+5q+1
        98: 4q^2+5q+1
        99: q^3+3q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+2q^2+2q
       104: q^3+q^2+q
       105: q^2
       106: q^3+4q^2+3q+1
       107: q^3+q^2+2q
       108: 2q^2+2q+1
       109: q^2+q
       110: 3q^2+3q+1
       111: q^2+3q+1
       113: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       117: 2q^3+4q^2+2q
       118: 3q^3+6q^2+4q+1
       119: 2q^3+3q^2+3q
       120: q^3+5q^2+3q+1
       121: 4q^3+7q^2+5q+1
       122: 2q^3+2q^2+q
       123: 2q^3+6q^2+5q+1
       124: q^3+2q^2+q
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: q^3+3q^2+4q+1
       136: 4q^2+4q+1
       137: 5q^3+10q^2+6q+1
       138: q^3+4q^2+4q+1
       139: 2q^3+7q^2+5q+1
       140: q^3+3q^2+4q+1
       141: 5q^3+8q^2+5q+1
       142: 4q^2+4q+1
       143: 3q^3+8q^2+6q+1
       144: 2q^2+4q+1
       145: 4q^2+5q+1
       146: 3q^3+6q^2+5q+1
       147: 2q^2+4q+1
       148: q^2+2q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       151: q^3+4q^2+4q+1
       153: q^3+4q^2+4q+1
       155: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 2q^3+7q^2+5q+1
       161: 2q^3+7q^2+5q+1
       162: 3q^3+5q^2+4q+1
       163: 4q^2+5q+1
       164: 4q^2+5q+1
       165: q^3+3q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       169: q
       172: q^2+2q+1
       173: q^3+2q^2+2q
       174: q^3+q^2+q
       175: q^2
       176: q^3+4q^2+3q+1
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: q^3+q^2+2q
       184: 2q^2+2q+1
       185: q^2+q
       186: 3q^2+3q+1
       187: q^2+3q+1
       189: q^3+4q^2+4q+1
       191: 2q^3+4q^2+2q
       192: 3q^3+6q^2+4q+1
       193: q^3+q^2+2q
       194: 2q^2+2q+1
       195: q^2+q
       196: 3q^2+3q+1
       197: q^2+3q+1
       199: 2q^3+3q^2+3q
       200: q^3+5q^2+3q+1
       201: q^2+2q
       202: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       207: 2q^3+6q^2+5q+1
       208: q^3+2q^2+q
       209: q^3+4q^2+4q+1
       211: q^3+4q^2+4q+1
       213: 2q^2+4q+1
       215: 2q^2+4q+1
       217: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: 4q^2+4q+1
       225: 2q^2+3q+1
       226: q^3+4q^2+4q+1
       227: 2q^3+7q^2+5q+1
       228: q^3+4q^2+4q+1
       229: q^3+3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+4q+1
       232: 4q^2+5q+1
       233: 2q^2+4q+1
       234: 2q^2+4q+1
       235: q^2+2q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 4q^2+5q+1
       244: 2q^2+4q+1
       245: q^2+2q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 2q^3+7q^2+5q+1
       251: 2q^3+7q^2+5q+1
       252: 3q^3+5q^2+4q+1
       253: 4q^2+5q+1
       254: 4q^2+5q+1
       255: q^3+3q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       267: q
       269: q^2+2q+1
       273: q+1
       275: q^3+2q^2+2q
       276: q^3+q^2+q
       277: q^2
       278: q^3+4q^2+3q+1
       279: 2q^2+4q+1
       281: q^2+3q+1
       283: q
       284: q+1
       286: q^2+2q+1
       287: q^2+3q+1
       289: 3q+1
       291: 2q+1
       293: q^3+q^2+2q
       294: 2q^2+2q+1
       295: q^2+q
       296: 3q^2+3q+1
       297: q^2+3q+1
       299: q^3+q^2+2q
       300: 2q^2+2q+1
       301: 3q+1
       303: q^2+q
       304: 3q^2+3q+1
       305: q^2+3q+1
       307: q^2+2q
       308: q^2+2q+1
       310: q^2+2q+1
       311: q+1
       313: q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: q^2+2q
       320: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       325: q^3+4q^2+4q+1
       327: 2q^2+4q+1
       329: 2q^2+4q+1
       331: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: q^3+4q^2+4q+1
       345: 2q^3+7q^2+5q+1
       346: q^3+4q^2+4q+1
       347: q^3+3q^2+4q+1
       348: q^2+3q+1
       349: 4q^2+4q+1
       350: 2q^2+3q+1
       351: 4q+2
       352: 2q^2+4q+1
       353: 4q^2+5q+1
       354: 2q^2+4q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+2
       360: 2q^2+4q+1
       362: 2q^2+4q+1
       364: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: 2q^2+4q+1
       370: q^2+2q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       389: q
       391: 2q+1
       393: q
       396: q^2+2q+1
       399: q+1
       404: q+1
       406: q+1
       409: 2q^2+4q+1
       411: q^2+3q+1
       413: q^2+3q+1
       415: 3q+1
       417: 2q+1
       419: q
       420: q+1
       422: q^2+2q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q
       430: q+1
       432: q^2+2q+1
       433: 2q+1
       435: 3q+1
       437: q^3+q^2+2q
       438: 2q^2+2q+1
       439: q^2+q
       440: 3q^2+3q+1
       441: q^2+3q+1
       443: 2q+1
       444: 2q+1
       445: 4q+2
       447: q
       448: q+1
       450: q+1
       451: 1
       453: q^2+2q
       454: q^2+2q+1
       455: q+1
       458: q^2+2q+1
       459: q+1
       462: 2q+2
       463: 2q+2
       465: 2q^2+4q+1
       467: q^2+3q+1
       469: q^2+3q+1
       471: q^2+2q
       472: q^2+2q+1
       474: q^2+2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q^2+3q+1
       482: 2q^2+3q+1
       483: q+1
       484: 4q+2
       485: 4q+2
       487: 4q+2
       489: q^2+2q+1
       491: q+1
       492: q^3+4q^2+4q+1
       493: q^2+3q+1
       494: 2q^2+3q+1
       495: q+1
       496: 4q+2
       497: 2q^2+4q+1
       498: q^2+3q+1
       499: q+1
       500: 1
       501: 2q+2
       502: 2q^2+4q+1
       504: 2q^2+4q+1
       506: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: 2q^2+4q+1
       512: q^2+3q+1
       513: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: q+1
       537: q
       539: 2q+1
       541: q
       543: q^2+2q+1
       545: 2q+1
       547: 2q+1
       552: 1
       555: q+1
       559: q+1
       563: 2q+2
       568: q+1
       570: q+1
       574: q+1
       575: q+1
       577: q+1
       580: q+1
       583: q^2+3q+1
       585: 2q+1
       587: 2q+1
       589: q
       590: q+1
       592: 1
       596: q^2+2q+1
       597: q+1
       599: q+1
       601: 4q+2
       603: q
       604: q+1
       605: 2q+1
       608: q^2+2q+1
       609: 2q+1
       611: 3q+1
       613: q+1
       615: 2q+1
       616: 2q+1
       617: 4q+2
       619: q
       620: q+1
       622: q+1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: 2q+2
       633: 2q+2
       635: 2q^2+4q+1
       637: q^2+3q+1
       639: q^2+3q+1
       641: q
       642: q+1
       644: q+1
       645: 1
       647: q^2+2q
       648: q^2+2q+1
       650: q^2+2q+1
       651: q+1
       653: q+1
       655: q+1
       656: q+1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: q+1
       666: 4q+2
       668: 4q+2
       670: q^2+2q+1
       672: 4q+2
       673: q+1
       674: q+2
       675: q^2+3q+1
       676: 2q^2+3q+1
       677: q+1
       678: 4q+2
       679: q+1
       680: 2
       681: q^2+3q+1
       682: q+1
       683: 1
       684: 2q+2
       685: 1
       686: 2q^2+4q+1
       687: q^2+3q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       696: q+1
       697: q+1
       708: q+1
       712: q+1
       716: 1
       723: q+1
       727: q+1
       729: q
       731: 2q+1
       733: 2q+1
       735: 2q+1
       739: 1
       743: 1
       747: q+1
       751: 2q+2
       756: 1
       758: q+1
       762: q+1
       766: q+1
       768: q+1
       769: q+1
       772: q+1
       775: 2
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       788: 1
       789: 4q+2
       793: 1
       794: 1
       795: q+2
       797: 2q+1
       799: 2q+1
       801: q
       802: q+1
       804: 1
       808: q^2+2q+1
       809: q+1
       811: q+1
       813: 4q+2
       815: 2q+1
       816: 2q+1
       818: 2
       819: 2
       821: 1
       823: 1
       825: q
       826: q+1
       828: 1
       832: q+1
       833: 1
       835: 1
       837: 2q+2
       840: 2q+2
       841: q^2+3q+1
       843: 1
       844: 1
       845: q
       846: q+1
       848: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q+1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: q+2
       870: 1
       871: q+1
       872: q+1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+3q+1
       878: q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       887: q+1
       889: q+1
       899: q+1
       902: 1
       914: q+1
       916: 1
       918: 1
       922: q+1
       927: 1
       932: 2q+1
       934: 2q+1
       938: 1
       942: 2
       946: 1
       950: 1
       958: 2q+2
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: q+1
       982: q+1
       985: q+1
       989: q+1
       991: q+1
       992: 2
       994: 1
       996: 1
       999: 1
      1002: q+1
      1007: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: 2q+1
      1020: 1
      1022: q+1
      1024: q+1
      1029: 1
      1030: 2
      1033: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q
      1053: q+1
      1055: 1
      1059: q+1
      1060: 1
      1062: 1
      1066: q+2
      1068: q+2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 1
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1101: q+1
      1102: q+1
      1112: 1
      1116: 1
      1144: 1
      1146: 1
      1150: q+1
      1154: 1
      1166: 2
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1199: 1
      1204: 1
      1210: 2
      1212: 1
      1214: 1
      1217: 1
      1226: q+2
      1228: 1
      1229: 1
      1230: 1
      1233: 1
      1236: 1
      1238: q+1
      1243: 1
      1244: 2
      1247: 2
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1305: 1
      1307: 1
      1316: 1
      1340: 1
      1342: 1
      1346: 1
      1350: 1
      1374: 2
      1378: 1
      1404: 1
      1407: 1
      1411: 1
      1413: 1
      1415: 1
      1420: 1
      1438: 1
      1441: 1
      1448: 1
      1451: 1
      1452: 1
      1458: 1
      1470: 1
      1472: 1
      1479: 1
      1485: 1
      1488: 1
      1528: 1
      1530: 1
      1543: 1
      1565: 1
      1605: 1
      1643: 1
      1646: 1
      1667: 1
      1739: 1

1740:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: q^4+9q^3+11q^2+6q+1
        23: q^4+9q^3+11q^2+6q+1
        24: q^4+9q^3+11q^2+6q+1
        25: 6q^3+9q^2+6q+1
        26: 6q^3+9q^2+6q+1
        27: 6q^3+9q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: q^4+9q^3+11q^2+6q+1
        32: q^4+9q^3+11q^2+6q+1
        33: 5q^3+10q^2+6q+1
        34: 6q^3+9q^2+6q+1
        35: 6q^3+9q^2+6q+1
        36: 3q^3+8q^2+6q+1
        37: 2q^3+2q^2+q
        38: 4q^3+7q^2+5q+1
        39: 2q^3+2q^2+q
        40: 4q^3+7q^2+5q+1
        41: 2q^3+2q^2+q
        42: 4q^3+7q^2+5q+1
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 5q^3+8q^2+5q+1
        53: 5q^3+8q^2+5q+1
        54: 5q^3+8q^2+5q+1
        55: 3q^3+6q^2+5q+1
        56: 3q^3+6q^2+5q+1
        57: 3q^3+6q^2+5q+1
        58: 2q^3+4q^2+2q
        59: 3q^3+6q^2+4q+1
        60: q^3+5q^2+3q+1
        61: 2q^3+3q^2+3q
        62: 2q^3+2q^2+q
        63: 4q^3+7q^2+5q+1
        64: 2q^3+2q^2+q
        65: 4q^3+7q^2+5q+1
        66: q^3+2q^2+q
        67: 2q^3+6q^2+5q+1
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: q^3+3q^2+4q+1
        73: 4q^2+4q+1
        75: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        79: q^3+4q^2+4q+1
        80: q^4+9q^3+11q^2+6q+1
        81: 5q^3+10q^2+6q+1
        82: 5q^3+8q^2+5q+1
        83: 5q^3+8q^2+5q+1
        84: 6q^3+9q^2+6q+1
        85: 3q^3+8q^2+6q+1
        86: 3q^3+6q^2+5q+1
        87: 3q^3+6q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 2q^3+7q^2+5q+1
        95: 2q^3+7q^2+5q+1
        96: 3q^3+5q^2+4q+1
        97: 4q^2+5q+1
        98: 4q^2+5q+1
        99: q^3+3q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^2
       104: q^3+4q^2+3q+1
       105: q^3+2q^2+2q
       106: q^3+q^2+q
       107: 2q^2+2q+1
       108: q^3+q^2+2q
       109: q^2+q
       110: 3q^2+3q+1
       112: q^2+3q+1
       114: q^3+4q^2+4q+1
       116: q^3+4q^2+4q+1
       117: 2q^3+4q^2+2q
       118: 3q^3+6q^2+4q+1
       119: q^3+5q^2+3q+1
       120: 2q^3+3q^2+3q
       121: 2q^3+2q^2+q
       122: 4q^3+7q^2+5q+1
       123: q^3+2q^2+q
       124: 2q^3+6q^2+5q+1
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: q^3+3q^2+4q+1
       136: 4q^2+4q+1
       137: 5q^3+10q^2+6q+1
       138: q^3+4q^2+4q+1
       139: 2q^3+7q^2+5q+1
       140: q^3+3q^2+4q+1
       141: 5q^3+8q^2+5q+1
       142: 4q^2+4q+1
       143: 3q^3+8q^2+6q+1
       144: 2q^2+4q+1
       145: 4q^2+5q+1
       146: 3q^3+6q^2+5q+1
       147: 2q^2+4q+1
       148: q^2+2q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       152: q^3+4q^2+4q+1
       154: q^3+4q^2+4q+1
       156: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 2q^3+7q^2+5q+1
       161: 2q^3+7q^2+5q+1
       162: 3q^3+5q^2+4q+1
       163: 4q^2+5q+1
       164: 4q^2+5q+1
       165: q^3+3q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       170: q^2+2q+1
       171: q
       173: q^2
       174: q^3+4q^2+3q+1
       175: q^3+2q^2+2q
       176: q^3+q^2+q
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: 2q^2+2q+1
       184: q^3+q^2+2q
       185: q^2+q
       186: 3q^2+3q+1
       188: q^2+3q+1
       190: q^3+4q^2+4q+1
       191: 2q^3+4q^2+2q
       192: 3q^3+6q^2+4q+1
       193: 2q^2+2q+1
       194: q^3+q^2+2q
       195: q^2+q
       196: 3q^2+3q+1
       198: q^2+3q+1
       199: q^3+5q^2+3q+1
       200: 2q^3+3q^2+3q
       201: q^2+2q+1
       202: q^2+2q
       204: q^2+2q+1
       206: q+1
       207: q^3+2q^2+q
       208: 2q^3+6q^2+5q+1
       210: q^3+4q^2+4q+1
       212: q^3+4q^2+4q+1
       214: 2q^2+4q+1
       216: 2q^2+4q+1
       218: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: q^3+3q^2+4q+1
       223: q^2+3q+1
       224: 4q^2+4q+1
       225: 2q^2+3q+1
       226: q^3+4q^2+4q+1
       227: 2q^3+7q^2+5q+1
       228: q^3+4q^2+4q+1
       229: q^3+3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+4q+1
       232: 4q^2+5q+1
       233: 2q^2+4q+1
       234: 2q^2+4q+1
       235: q^2+2q+1
       236: 2q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 4q^2+5q+1
       244: 2q^2+4q+1
       245: q^2+2q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 2q^3+7q^2+5q+1
       251: 2q^3+7q^2+5q+1
       252: 3q^3+5q^2+4q+1
       253: 4q^2+5q+1
       254: 4q^2+5q+1
       255: q^3+3q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q^2+2q+1
       270: q
       274: q+1
       275: q^2
       276: q^3+4q^2+3q+1
       277: q^3+2q^2+2q
       278: q^3+q^2+q
       280: 2q^2+4q+1
       282: q^2+3q+1
       283: q+1
       284: q
       286: q^2+2q+1
       288: q^2+3q+1
       290: 3q+1
       292: 2q+1
       293: 2q^2+2q+1
       294: q^3+q^2+2q
       295: q^2+q
       296: 3q^2+3q+1
       298: q^2+3q+1
       299: 2q^2+2q+1
       300: q^3+q^2+2q
       302: 3q+1
       303: q^2+q
       304: 3q^2+3q+1
       306: q^2+3q+1
       307: q^2+2q+1
       308: q^2+2q
       310: q^2+2q+1
       312: q+1
       314: q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: q^2+2q+1
       320: q^2+2q
       322: q^2+2q+1
       324: q+1
       326: q^3+4q^2+4q+1
       328: 2q^2+4q+1
       330: 2q^2+4q+1
       332: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: q^3+4q^2+4q+1
       345: 2q^3+7q^2+5q+1
       346: q^3+4q^2+4q+1
       347: q^3+3q^2+4q+1
       348: q^2+3q+1
       349: 4q^2+4q+1
       350: 2q^2+3q+1
       351: 4q+2
       352: 2q^2+4q+1
       353: 4q^2+5q+1
       354: 2q^2+4q+1
       355: 2q^2+4q+1
       356: q^2+3q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+2
       361: 2q^2+4q+1
       363: 2q^2+4q+1
       365: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: 2q^2+4q+1
       370: q^2+2q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: 2q+1
       392: q
       394: q^2+2q+1
       395: q
       400: q+1
       403: q+1
       407: q+1
       410: 2q^2+4q+1
       412: q^2+3q+1
       414: q^2+3q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       420: q
       422: q^2+2q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       430: q
       432: q^2+2q+1
       434: 2q+1
       436: 3q+1
       437: 2q^2+2q+1
       438: q^3+q^2+2q
       439: q^2+q
       440: 3q^2+3q+1
       442: q^2+3q+1
       443: 2q+1
       444: 2q+1
       446: 4q+2
       447: q+1
       448: q
       450: q+1
       452: 1
       453: q^2+2q+1
       454: q^2+2q
       456: q+1
       458: q^2+2q+1
       460: q+1
       462: 2q+2
       464: 2q+2
       466: 2q^2+4q+1
       468: q^2+3q+1
       470: q^2+3q+1
       471: q^2+2q+1
       472: q^2+2q
       474: q^2+2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q^2+3q+1
       482: 2q^2+3q+1
       483: q+1
       484: 4q+2
       486: 4q+2
       488: 4q+2
       490: q^2+2q+1
       491: q+1
       492: q^3+4q^2+4q+1
       493: q^2+3q+1
       494: 2q^2+3q+1
       495: q+1
       496: 4q+2
       497: 2q^2+4q+1
       498: q^2+3q+1
       499: q+1
       500: 1
       501: 2q+2
       503: 2q^2+4q+1
       505: 2q^2+4q+1
       507: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: 2q^2+4q+1
       512: q^2+3q+1
       513: q^2+2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: q+1
       538: 2q+1
       540: q
       542: q^2+2q+1
       544: q
       546: 2q+1
       548: 2q+1
       551: 1
       556: q+1
       560: q+1
       564: 2q+2
       566: q+1
       571: q+1
       574: q+1
       575: q+1
       578: q+1
       581: q+1
       584: q^2+3q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       590: q
       592: 1
       596: q^2+2q+1
       598: q+1
       600: q+1
       602: 4q+2
       603: q+1
       604: q
       606: 2q+1
       608: q^2+2q+1
       610: 2q+1
       612: 3q+1
       614: q+1
       615: 2q+1
       616: 2q+1
       618: 4q+2
       619: q+1
       620: q
       622: q+1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: 2q+2
       634: 2q+2
       636: 2q^2+4q+1
       638: q^2+3q+1
       640: q^2+3q+1
       641: q+1
       642: q
       644: q+1
       646: 1
       647: q^2+2q+1
       648: q^2+2q
       650: q^2+2q+1
       652: q+1
       654: q+1
       655: q+1
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: q+1
       667: 4q+2
       669: 4q+2
       671: q^2+2q+1
       672: 4q+2
       673: q+1
       674: q+2
       675: q^2+3q+1
       676: 2q^2+3q+1
       677: q+1
       678: 4q+2
       679: q+1
       680: 2
       681: q^2+3q+1
       682: q+1
       683: 1
       684: 2q+2
       685: 1
       686: 2q^2+4q+1
       687: q^2+3q+1
       688: q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       699: q+1
       701: q+1
       706: q+1
       710: q+1
       715: 1
       722: q+1
       726: q+1
       730: 2q+1
       732: q
       734: 2q+1
       736: 2q+1
       740: 1
       744: 1
       748: q+1
       752: 2q+2
       754: 1
       759: q+1
       763: q+1
       766: q+1
       768: q+1
       770: q+1
       773: q+1
       776: 2
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       788: 1
       790: 4q+2
       793: 1
       794: 1
       796: q+2
       798: 2q+1
       800: 2q+1
       801: q+1
       802: q
       804: 1
       808: q^2+2q+1
       810: q+1
       812: q+1
       814: 4q+2
       815: 2q+1
       816: 2q+1
       818: 2
       820: 2
       822: 1
       824: 1
       825: q+1
       826: q
       828: 1
       832: q+1
       834: 1
       836: 1
       838: 2q+2
       840: 2q+2
       842: q^2+3q+1
       843: 1
       844: 1
       845: q+1
       846: q
       848: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q+1
       858: q+1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: q+2
       870: 1
       871: q+1
       872: q+1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+3q+1
       878: q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       890: q+1
       892: q+1
       897: q+1
       903: 1
       913: q+1
       917: 1
       919: 1
       921: q+1
       926: 1
       933: 2q+1
       935: 2q+1
       939: 1
       943: 2
       947: 1
       951: 1
       959: 2q+2
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       980: q+1
       983: q+1
       986: q+1
       989: q+1
       991: q+1
       993: 2
       995: 1
       997: 1
       999: 1
      1003: q+1
      1007: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: 2q+1
      1021: 1
      1023: q+1
      1025: q+1
      1029: 1
      1031: 2
      1033: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: q
      1055: 1
      1059: q+1
      1061: 1
      1063: 1
      1067: q+2
      1069: q+2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: q+2
      1076: 1
      1077: 1
      1078: q+1
      1079: 2
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1094: 1
      1104: q+1
      1106: q+1
      1113: 1
      1117: 1
      1145: 1
      1147: 1
      1149: q+1
      1155: 1
      1167: 2
      1171: 1
      1175: 1
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1200: 1
      1205: 1
      1211: 2
      1213: 1
      1215: 1
      1217: 1
      1227: q+2
      1228: 1
      1229: 1
      1231: 1
      1233: 1
      1237: 1
      1239: q+1
      1243: 1
      1245: 2
      1247: 2
      1253: 1
      1257: 1
      1261: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1308: 1
      1310: 1
      1317: 1
      1341: 1
      1343: 1
      1347: 1
      1351: 1
      1375: 2
      1379: 1
      1405: 1
      1408: 1
      1411: 1
      1413: 1
      1416: 1
      1421: 1
      1439: 1
      1441: 1
      1449: 1
      1451: 1
      1453: 1
      1459: 1
      1471: 1
      1473: 1
      1479: 1
      1485: 1
      1488: 1
      1531: 1
      1533: 1
      1544: 1
      1566: 1
      1606: 1
      1644: 1
      1646: 1
      1668: 1
      1740: 1

1741:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: q^4+16q^3+16q^2+5q+1
        23: q^4+16q^3+16q^2+5q+1
        24: 4q^4+13q^3+13q^2+5q+1
        25: 9q^3+15q^2+5q+1
        26: 9q^3+15q^2+5q+1
        27: q^4+9q^3+12q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 10q^3+14q^2+5q+1
        32: 10q^3+13q^2+5q+1
        33: q^4+16q^3+16q^2+5q+1
        34: 5q^3+13q^2+5q+1
        35: 6q^3+12q^2+5q+1
        36: 9q^3+15q^2+5q+1
        37: 6q^3+10q^2+4q+1
        38: 3q^3+5q^2+q
        39: 6q^3+10q^2+4q+1
        40: 3q^3+5q^2+q
        41: q^4+6q^3+8q^2+4q+1
        42: 3q^3+4q^2+q
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 10q^3+13q^2+5q+1
        53: q^4+12q^3+13q^2+5q+1
        54: 2q^4+8q^3+11q^2+5q+1
        55: 3q^3+12q^2+5q+1
        56: 5q^3+12q^2+5q+1
        57: 4q^3+10q^2+5q+1
        58: 6q^3+9q^2+4q+1
        59: 4q^3+5q^2+q
        60: 4q^3+8q^2+3q+1
        61: q^3+5q^2+2q
        62: 4q^3+9q^2+4q+1
        63: q^3+4q^2+q
        64: 4q^3+8q^2+4q+1
        65: 2q^3+4q^2+q
        66: 6q^3+10q^2+4q+1
        67: 3q^3+5q^2+q
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 2q^3+9q^2+5q+1
        73: 6q^3+10q^2+5q+1
        74: q^3+7q^2+4q+1
        75: 3q^2+q
        76: 2q^3+7q^2+4q+1
        77: q^3+3q^2+q
        78: 2q^3+6q^2+4q+1
        79: 3q^2+q
        80: 4q^3+11q^2+5q+1
        81: 10q^3+13q^2+5q+1
        82: 7q^3+11q^2+5q+1
        83: 6q^3+11q^2+5q+1
        84: 2q^3+10q^2+5q+1
        85: 6q^3+12q^2+5q+1
        86: 2q^3+10q^2+5q+1
        87: 2q^3+10q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 10q^3+13q^2+5q+1
        95: q^4+12q^3+13q^2+5q+1
        96: 2q^4+8q^3+11q^2+5q+1
        97: 3q^3+12q^2+5q+1
        98: 5q^3+12q^2+5q+1
        99: 4q^3+10q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: 3q^3+6q^2+3q+1
       104: q^3+2q^2
       105: 2q^2+q
       106: q^3+3q^2+q
       107: q^3+5q^2+3q+1
       108: 2q^2+2q
       109: 3q^3+6q^2+4q+1
       110: q^3+2q^2+q
       111: 5q^2+4q+1
       112: 2q^2+q
       113: q^3+6q^2+4q+1
       114: 2q^2+q
       115: q^3+6q^2+4q+1
       116: 3q^2+q
       117: q^3+6q^2+4q+1
       118: 2q^2+q
       119: q^3+5q^2+3q+1
       120: 2q^2+2q
       121: 2q^3+7q^2+4q+1
       122: 3q^2+q
       123: 4q^3+8q^2+4q+1
       124: 2q^3+4q^2+q
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: q^3+7q^2+4q+1
       128: 3q^2+q
       129: 2q^3+7q^2+4q+1
       130: q^3+3q^2+q
       131: 2q^3+6q^2+4q+1
       132: 3q^2+q
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: q^3+7q^2+5q+1
       136: 2q^3+8q^2+5q+1
       137: 4q^3+11q^2+5q+1
       138: 6q^3+11q^2+5q+1
       139: 7q^3+11q^2+5q+1
       140: 2q^3+9q^2+5q+1
       141: 3q^3+9q^2+5q+1
       142: 6q^3+10q^2+5q+1
       143: 2q^3+10q^2+5q+1
       144: 2q^3+10q^2+5q+1
       145: 2q^3+10q^2+5q+1
       146: q^3+8q^2+5q+1
       147: 2q^3+9q^2+5q+1
       148: 3q^2+4q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: q^3+7q^2+4q+1
       152: 3q^2+q
       153: 2q^3+7q^2+4q+1
       154: q^3+3q^2+q
       155: 2q^3+6q^2+4q+1
       156: 3q^2+q
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: 4q^3+10q^2+5q+1
       161: 6q^3+10q^2+5q+1
       162: 4q^3+10q^2+5q+1
       163: q^3+6q^2+5q+1
       164: 2q^3+6q^2+5q+1
       165: q^3+6q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: 3q^2+3q+1
       170: q^2
       171: q
       172: q^2+q
       173: q^3+4q^2+3q+1
       174: q^2
       175: q^2+q
       176: q^2+q
       177: q^3+6q^2+4q+1
       178: 3q^2+q
       179: q^3+6q^2+4q+1
       180: 2q^2+q
       181: 5q^2+4q+1
       182: 2q^2+q
       183: 3q^2+3q+1
       184: 2q
       185: 4q^2+4q+1
       186: q^2+q
       187: 4q^2+4q+1
       188: 2q^2+q
       189: q^3+5q^2+4q+1
       190: 2q^2+q
       191: q^3+6q^2+4q+1
       192: 2q^2+q
       193: q^3+5q^2+3q+1
       194: 2q^2+2q
       195: 3q^3+6q^2+4q+1
       196: q^3+2q^2+q
       197: 5q^2+4q+1
       198: 2q^2+q
       199: q^3+5q^2+3q+1
       200: 2q^2+2q
       201: q^3+5q^2+3q+1
       202: 2q^2+2q
       203: 3q^2+4q+1
       205: q^2+3q+1
       206: q
       207: 2q^3+7q^2+4q+1
       208: 3q^2+q
       209: q^3+6q^2+4q+1
       210: 2q^2+q
       211: q^3+6q^2+4q+1
       212: 3q^2+q
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: q^3+7q^2+5q+1
       224: 3q^2+5q+1
       225: 2q^3+8q^2+5q+1
       226: 3q^3+9q^2+5q+1
       227: 6q^2+5q+1
       228: 4q^3+10q^2+5q+1
       229: q^3+7q^2+5q+1
       230: 2q^3+8q^2+5q+1
       231: q^3+8q^2+5q+1
       232: 3q^2+5q+1
       233: q^3+6q^2+5q+1
       234: q^3+4q^2+5q+1
       235: q^2+4q+1
       236: 2q^3+10q^2+5q+1
       237: q^3+7q^2+4q+1
       238: 3q^2+q
       239: 2q^3+7q^2+4q+1
       240: q^3+3q^2+q
       241: 2q^3+6q^2+4q+1
       242: 3q^2+q
       243: 2q^3+10q^2+5q+1
       244: 2q^3+9q^2+5q+1
       245: 3q^2+4q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: q^3+5q^2+5q+1
       251: q^3+5q^2+5q+1
       252: q^3+5q^2+5q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: 3q^2+3q+1
       260: q^2
       261: q
       262: q^2+q
       263: 2q^2+3q+1
       264: q^2
       265: q
       266: q
       267: 3q^2+3q+1
       268: q^2
       269: q^2+q
       270: q
       271: q^2+3q+1
       272: q
       275: q^3+4q^2+3q+1
       276: q^2
       277: q^2+q
       278: q^2+q
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: 3q^2+3q+1
       284: 2q
       285: 4q^2+4q+1
       286: q^2+q
       287: q^3+5q^2+4q+1
       288: 2q^2+q
       289: q^2+3q+1
       291: 4q^2+4q+1
       292: 2q^2+q
       293: q^2+3q+1
       294: 2q
       295: 2q^2+4q+1
       296: q
       297: 2q^2+4q+1
       298: q
       299: 3q^2+3q+1
       300: 2q
       301: 5q^2+4q+1
       302: 2q^2+q
       303: 4q^2+4q+1
       304: q^2+q
       305: 4q^2+4q+1
       306: 2q^2+q
       307: q^2+3q+1
       308: 2q
       309: q^2+4q+1
       311: q^2+3q+1
       312: q
       313: 3q+1
       314: q
       315: q^3+6q^2+4q+1
       316: 3q^2+q
       317: q^3+6q^2+4q+1
       318: 2q^2+q
       319: q^3+5q^2+3q+1
       320: 2q^2+2q
       321: 3q^2+4q+1
       323: q^2+3q+1
       324: q
       325: q^3+5q^2+4q+1
       326: 2q^2+q
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 4q^2+5q+1
       339: 2q^2+2q
       340: 4q^2+5q+1
       341: 2q^2+2q
       342: q^3+4q^2+3q+1
       343: 2q^2+q
       344: 6q^2+5q+1
       345: 3q^2+5q+1
       346: q^3+5q^2+5q+1
       347: 3q^2+5q+1
       348: q^3+7q^2+5q+1
       349: 3q^2+5q+1
       350: 2q^3+8q^2+5q+1
       351: 6q^2+7q+1
       352: 3q^2+5q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^3+4q^2+5q+1
       357: 2q+1
       358: q^2+4q+1
       359: q^2+6q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^3+4q^2+5q+1
       370: q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: 2q^2+3q+1
       378: q^2
       379: q
       380: q
       381: 2q+1
       384: q
       385: q^2+3q+1
       387: q
       388: q
       389: 3q^2+3q+1
       390: q^2
       391: q^2+q
       392: q
       393: 2q^2+3q+1
       394: q^2
       395: q
       396: q
       397: q^2+3q+1
       398: q
       401: 3q+1
       402: q
       405: q^2+3q+1
       408: q
       413: q^2+3q+1
       417: q^2+3q+1
       419: q^2+3q+1
       420: 2q
       421: 2q^2+4q+1
       422: q
       423: 2q^2+4q+1
       424: q
       425: 2q^2+3q+1
       426: q^2+q
       427: 3q^2+5q+1
       428: q^2+2q
       429: 3q^2+3q+1
       430: 2q
       431: 4q^2+4q+1
       432: q^2+q
       433: 4q^2+4q+1
       434: 2q^2+q
       435: q^2+3q+1
       437: q^2+3q+1
       438: 2q
       439: 2q^2+4q+1
       440: q
       441: 2q^2+4q+1
       442: q
       443: 3q^2+4q+1
       444: q^2+3q
       445: 4q^2+5q+1
       446: 2q^2+2q
       447: q^2+3q+1
       448: 2q
       449: q^2+4q+1
       451: 3q+1
       452: q
       453: 2q+1
       454: q
       455: 2q+1
       457: 2q+1
       459: 2q+1
       461: q^2+6q+1
       463: q^2+4q+1
       464: 2q
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+5q^2+4q+1
       470: 2q^2+q
       471: q^2+3q+1
       472: 2q
       473: q^2+4q+1
       475: 3q+1
       476: q
       477: q^2+3q+1
       478: q
       479: q^2+4q+1
       480: 2q
       481: 5q+1
       482: q^2+4q+1
       483: q^2+4q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 3q^2+5q+1
       493: 3q^2+5q+1
       494: 3q^2+5q+1
       495: 3q^2+4q+1
       496: 2q^2+4q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 3q+1
       501: 3q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^3+4q^2+5q+1
       513: 2q+1
       514: q^2+4q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 2q+1
       524: q
       529: q^2+3q+1
       531: q
       532: q
       533: 2q^2+3q+1
       534: q^2
       535: q
       536: q
       537: 2q+1
       539: q
       541: q^2+3q+1
       543: q
       544: q
       545: 2q^2+3q+1
       546: q^2+q
       547: q^2+2q
       548: q
       549: 3q+1
       550: q
       553: 2q+1
       557: 2q+1
       561: q^2+4q+1
       562: 2q
       565: 3q+1
       567: q
       569: q^2+3q+1
       572: q
       573: q^2+4q+1
       576: 2q
       577: q^2+3q+1
       578: q
       580: q
       581: q
       585: 3q+1
       589: 3q+1
       590: 2q
       591: 3q+1
       593: q+1
       595: q^2+3q+1
       596: q
       597: q+1
       599: q^2+3q+1
       600: q
       601: 2q+1
       603: q^2+3q+1
       604: 2q
       605: q^2+3q+1
       607: 2q^2+4q+1
       608: q
       609: 2q^2+4q+1
       610: q
       613: 2q^2+3q+1
       614: q^2+q
       615: q^2+2q+1
       616: 2q
       617: 2q+1
       619: 2q+1
       620: q
       621: 2q+1
       623: 2q+1
       625: 2q+1
       629: 2q+1
       630: q
       631: 3q+1
       633: q+1
       639: q^2+3q+1
       641: q^2+3q+1
       642: 2q
       643: q^2+4q+1
       645: 3q+1
       646: q
       647: 2q+1
       648: q
       649: 2q+1
       651: 2q+1
       653: 2q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 5q+1
       676: q^2+4q+1
       677: q^2+4q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+3q+1
       694: q
       698: q
       700: q
       709: 2q+1
       712: q
       713: 2q+1
       714: q
       717: q+1
       721: 2q+1
       723: q
       725: q^2+3q+1
       727: q
       728: q
       733: q+1
       735: q
       737: 2q+1
       741: 2q+1
       749: q+1
       753: 3q+1
       755: q
       757: 2q+1
       761: 2q+1
       765: 2q+1
       767: q
       769: q+1
       775: 2q+1
       779: q+1
       781: q+1
       785: 1
       787: q+1
       791: 1
       793: q^2+2q+1
       794: 2q
       795: 2q+1
       797: 3q+1
       801: 3q+1
       802: 2q
       803: 3q+1
       805: q+1
       807: q^2+3q+1
       808: q
       809: q+1
       811: q^2+3q+1
       812: q
       815: q+1
       816: q
       817: 3q+1
       819: q+1
       821: q+1
       825: 2q+1
       826: q
       827: q+1
       831: q+1
       833: 1
       835: q+1
       839: q+1
       843: 2q+1
       844: q
       845: 2q+1
       846: q
       847: 2q+1
       849: 2q+1
       851: 2q+1
       855: 2q+1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: q+1
       918: q
       920: 2q+1
       922: q
       924: 2q+1
       925: q
       928: q+1
       940: q+1
       944: q+1
       948: q+1
       960: 2q+1
       964: 2q+1
       966: q
       968: q+1
       974: 2q+1
       988: q+1
       994: q+1
       998: q+1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1016: q+1
      1017: q
      1020: q+1
      1022: q+1
      1026: 1
      1028: q+1
      1032: q+1
      1036: 1
      1038: 1
      1044: 1
      1046: q+1
      1048: q+1
      1052: 2q+1
      1053: q
      1054: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: q+1
      1114: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1194: q+1
      1198: q+1
      1202: q+1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1230: q+1
      1232: q+1
      1234: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1260: 1
      1266: 1
      1270: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 2
      1364: 1
      1368: 1
      1380: 1
      1418: 1
      1430: 1
      1432: 1
      1436: 1
      1450: 1
      1454: 1
      1460: 1
      1464: 1
      1466: 1
      1474: 1
      1478: 1
      1482: 1
      1487: 1
      1501: 1
      1503: 1
      1537: 1
      1575: 1
      1579: 1
      1607: 1
      1659: 1
      1663: 1
      1741: 1

1742:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: q^4+16q^3+16q^2+5q+1
        23: q^4+16q^3+16q^2+5q+1
        24: 4q^4+13q^3+13q^2+5q+1
        25: 9q^3+15q^2+5q+1
        26: 9q^3+15q^2+5q+1
        27: q^4+9q^3+12q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 10q^3+14q^2+5q+1
        32: 10q^3+13q^2+5q+1
        33: q^4+16q^3+16q^2+5q+1
        34: 5q^3+13q^2+5q+1
        35: 6q^3+12q^2+5q+1
        36: 9q^3+15q^2+5q+1
        37: 6q^3+10q^2+4q+1
        38: 3q^3+5q^2+q
        39: 6q^3+10q^2+4q+1
        40: 3q^3+5q^2+q
        41: q^4+6q^3+8q^2+4q+1
        42: 3q^3+4q^2+q
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 10q^3+13q^2+5q+1
        53: q^4+12q^3+13q^2+5q+1
        54: 2q^4+8q^3+11q^2+5q+1
        55: 3q^3+12q^2+5q+1
        56: 5q^3+12q^2+5q+1
        57: 4q^3+10q^2+5q+1
        58: 4q^3+5q^2+q
        59: 6q^3+9q^2+4q+1
        60: q^3+5q^2+2q
        61: 4q^3+8q^2+3q+1
        62: 4q^3+9q^2+4q+1
        63: q^3+4q^2+q
        64: 4q^3+8q^2+4q+1
        65: 2q^3+4q^2+q
        66: 6q^3+10q^2+4q+1
        67: 3q^3+5q^2+q
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 2q^3+9q^2+5q+1
        73: 6q^3+10q^2+5q+1
        74: q^3+7q^2+4q+1
        75: 3q^2+q
        76: 2q^3+7q^2+4q+1
        77: q^3+3q^2+q
        78: 2q^3+6q^2+4q+1
        79: 3q^2+q
        80: 4q^3+11q^2+5q+1
        81: 10q^3+13q^2+5q+1
        82: 7q^3+11q^2+5q+1
        83: 6q^3+11q^2+5q+1
        84: 2q^3+10q^2+5q+1
        85: 6q^3+12q^2+5q+1
        86: 2q^3+10q^2+5q+1
        87: 2q^3+10q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 10q^3+13q^2+5q+1
        95: q^4+12q^3+13q^2+5q+1
        96: 2q^4+8q^3+11q^2+5q+1
        97: 3q^3+12q^2+5q+1
        98: 5q^3+12q^2+5q+1
        99: 4q^3+10q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: q^3+3q^2+q
       104: 2q^2+q
       105: q^3+2q^2
       106: 3q^3+6q^2+3q+1
       107: 2q^2+2q
       108: q^3+5q^2+3q+1
       109: q^3+2q^2+q
       110: 3q^3+6q^2+4q+1
       111: 5q^2+4q+1
       112: 2q^2+q
       113: q^3+6q^2+4q+1
       114: 2q^2+q
       115: q^3+6q^2+4q+1
       116: 3q^2+q
       117: 2q^2+q
       118: q^3+6q^2+4q+1
       119: 2q^2+2q
       120: q^3+5q^2+3q+1
       121: 2q^3+7q^2+4q+1
       122: 3q^2+q
       123: 4q^3+8q^2+4q+1
       124: 2q^3+4q^2+q
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: q^3+7q^2+4q+1
       128: 3q^2+q
       129: 2q^3+7q^2+4q+1
       130: q^3+3q^2+q
       131: 2q^3+6q^2+4q+1
       132: 3q^2+q
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: q^3+7q^2+5q+1
       136: 2q^3+8q^2+5q+1
       137: 4q^3+11q^2+5q+1
       138: 6q^3+11q^2+5q+1
       139: 7q^3+11q^2+5q+1
       140: 2q^3+9q^2+5q+1
       141: 3q^3+9q^2+5q+1
       142: 6q^3+10q^2+5q+1
       143: 2q^3+10q^2+5q+1
       144: 2q^3+10q^2+5q+1
       145: 2q^3+10q^2+5q+1
       146: q^3+8q^2+5q+1
       147: 2q^3+9q^2+5q+1
       148: 3q^2+4q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: q^3+7q^2+4q+1
       152: 3q^2+q
       153: 2q^3+7q^2+4q+1
       154: q^3+3q^2+q
       155: 2q^3+6q^2+4q+1
       156: 3q^2+q
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: 4q^3+10q^2+5q+1
       161: 6q^3+10q^2+5q+1
       162: 4q^3+10q^2+5q+1
       163: q^3+6q^2+5q+1
       164: 2q^3+6q^2+5q+1
       165: q^3+6q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q^2+q
       170: q
       171: q^2
       172: 3q^2+3q+1
       173: q^2+q
       174: q^2+q
       175: q^2
       176: q^3+4q^2+3q+1
       177: q^3+6q^2+4q+1
       178: 3q^2+q
       179: q^3+6q^2+4q+1
       180: 2q^2+q
       181: 5q^2+4q+1
       182: 2q^2+q
       183: 2q
       184: 3q^2+3q+1
       185: q^2+q
       186: 4q^2+4q+1
       187: 4q^2+4q+1
       188: 2q^2+q
       189: q^3+5q^2+4q+1
       190: 2q^2+q
       191: 2q^2+q
       192: q^3+6q^2+4q+1
       193: 2q^2+2q
       194: q^3+5q^2+3q+1
       195: q^3+2q^2+q
       196: 3q^3+6q^2+4q+1
       197: 5q^2+4q+1
       198: 2q^2+q
       199: 2q^2+2q
       200: q^3+5q^2+3q+1
       201: 2q^2+2q
       202: q^3+5q^2+3q+1
       204: 3q^2+4q+1
       205: q^2+3q+1
       206: q
       207: 2q^3+7q^2+4q+1
       208: 3q^2+q
       209: q^3+6q^2+4q+1
       210: 2q^2+q
       211: q^3+6q^2+4q+1
       212: 3q^2+q
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: q^3+7q^2+5q+1
       224: 3q^2+5q+1
       225: 2q^3+8q^2+5q+1
       226: 3q^3+9q^2+5q+1
       227: 6q^2+5q+1
       228: 4q^3+10q^2+5q+1
       229: q^3+7q^2+5q+1
       230: 2q^3+8q^2+5q+1
       231: q^3+8q^2+5q+1
       232: 3q^2+5q+1
       233: q^3+6q^2+5q+1
       234: q^3+4q^2+5q+1
       235: q^2+4q+1
       236: 2q^3+10q^2+5q+1
       237: q^3+7q^2+4q+1
       238: 3q^2+q
       239: 2q^3+7q^2+4q+1
       240: q^3+3q^2+q
       241: 2q^3+6q^2+4q+1
       242: 3q^2+q
       243: 2q^3+10q^2+5q+1
       244: 2q^3+9q^2+5q+1
       245: 3q^2+4q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: q^3+5q^2+5q+1
       251: q^3+5q^2+5q+1
       252: q^3+5q^2+5q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q^2+q
       260: q
       261: q^2
       262: 3q^2+3q+1
       263: q
       264: q
       265: q^2
       266: 2q^2+3q+1
       267: q^2+q
       268: q
       269: 3q^2+3q+1
       270: q^2
       273: q^2+3q+1
       274: q
       275: q^2+q
       276: q^2+q
       277: q^2
       278: q^3+4q^2+3q+1
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: 2q
       284: 3q^2+3q+1
       285: q^2+q
       286: 4q^2+4q+1
       287: q^3+5q^2+4q+1
       288: 2q^2+q
       289: q^2+3q+1
       291: 4q^2+4q+1
       292: 2q^2+q
       293: 2q
       294: q^2+3q+1
       295: q
       296: 2q^2+4q+1
       297: 2q^2+4q+1
       298: q
       299: 2q
       300: 3q^2+3q+1
       301: 5q^2+4q+1
       302: 2q^2+q
       303: q^2+q
       304: 4q^2+4q+1
       305: 4q^2+4q+1
       306: 2q^2+q
       307: 2q
       308: q^2+3q+1
       310: q^2+4q+1
       311: q^2+3q+1
       312: q
       313: 3q+1
       314: q
       315: q^3+6q^2+4q+1
       316: 3q^2+q
       317: q^3+6q^2+4q+1
       318: 2q^2+q
       319: 2q^2+2q
       320: q^3+5q^2+3q+1
       322: 3q^2+4q+1
       323: q^2+3q+1
       324: q
       325: q^3+5q^2+4q+1
       326: 2q^2+q
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 4q^2+5q+1
       339: 2q^2+2q
       340: 4q^2+5q+1
       341: 2q^2+2q
       342: q^3+4q^2+3q+1
       343: 2q^2+q
       344: 6q^2+5q+1
       345: 3q^2+5q+1
       346: q^3+5q^2+5q+1
       347: 3q^2+5q+1
       348: q^3+7q^2+5q+1
       349: 3q^2+5q+1
       350: 2q^3+8q^2+5q+1
       351: 6q^2+7q+1
       352: 3q^2+5q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^3+4q^2+5q+1
       357: 2q+1
       358: q^2+4q+1
       359: q^2+6q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^3+4q^2+5q+1
       370: q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       378: q
       379: q^2
       380: 2q^2+3q+1
       381: q
       384: 2q+1
       385: q
       386: q
       388: q^2+3q+1
       389: q^2+q
       390: q
       391: 3q^2+3q+1
       392: q^2
       393: q
       394: q
       395: q^2
       396: 2q^2+3q+1
       399: q^2+3q+1
       400: q
       403: q
       404: 3q+1
       406: q^2+3q+1
       407: q
       413: q^2+3q+1
       417: q^2+3q+1
       419: 2q
       420: q^2+3q+1
       421: q
       422: 2q^2+4q+1
       423: 2q^2+4q+1
       424: q
       425: 2q^2+3q+1
       426: q^2+q
       427: 3q^2+5q+1
       428: q^2+2q
       429: 2q
       430: 3q^2+3q+1
       431: q^2+q
       432: 4q^2+4q+1
       433: 4q^2+4q+1
       434: 2q^2+q
       435: q^2+3q+1
       437: 2q
       438: q^2+3q+1
       439: q
       440: 2q^2+4q+1
       441: 2q^2+4q+1
       442: q
       443: q^2+3q
       444: 3q^2+4q+1
       445: 4q^2+5q+1
       446: 2q^2+2q
       447: 2q
       448: q^2+3q+1
       450: q^2+4q+1
       451: 3q+1
       452: q
       453: q
       454: 2q+1
       455: 2q+1
       458: 2q+1
       459: 2q+1
       462: q^2+6q+1
       463: q^2+4q+1
       464: 2q
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+5q^2+4q+1
       470: 2q^2+q
       471: 2q
       472: q^2+3q+1
       474: q^2+4q+1
       475: 3q+1
       476: q
       477: q^2+3q+1
       478: q
       479: q^2+4q+1
       480: 2q
       481: 5q+1
       482: q^2+4q+1
       483: q^2+4q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 3q^2+5q+1
       493: 3q^2+5q+1
       494: 3q^2+5q+1
       495: 3q^2+4q+1
       496: 2q^2+4q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 3q+1
       501: 3q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^3+4q^2+5q+1
       513: 2q+1
       514: q^2+4q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: 2q+1
       529: q
       530: q
       532: q^2+3q+1
       533: q
       534: q
       535: q^2
       536: 2q^2+3q+1
       537: q
       539: 2q+1
       541: q
       542: q
       543: q^2+3q+1
       545: q^2+2q
       546: q
       547: 2q^2+3q+1
       548: q^2+q
       551: q
       552: 3q+1
       555: 2q+1
       559: 2q+1
       563: q^2+4q+1
       564: 2q
       566: q
       568: 3q+1
       570: q^2+3q+1
       571: q
       574: 2q
       575: q^2+4q+1
       577: q^2+3q+1
       578: q
       580: q
       581: q
       585: 3q+1
       589: 2q
       590: 3q+1
       592: 3q+1
       594: q+1
       595: q
       596: q^2+3q+1
       597: q+1
       599: q^2+3q+1
       600: q
       601: 2q+1
       603: 2q
       604: q^2+3q+1
       605: q^2+3q+1
       607: q
       608: 2q^2+4q+1
       609: 2q^2+4q+1
       610: q
       613: 2q^2+3q+1
       614: q^2+q
       615: 2q
       616: q^2+2q+1
       617: 2q+1
       619: q
       620: 2q+1
       622: 2q+1
       623: 2q+1
       625: 2q+1
       629: 2q+1
       630: q
       632: 3q+1
       633: q+1
       639: q^2+3q+1
       641: 2q
       642: q^2+3q+1
       644: q^2+4q+1
       645: 3q+1
       646: q
       647: q
       648: 2q+1
       650: 2q+1
       651: 2q+1
       653: 2q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 5q+1
       676: q^2+4q+1
       677: q^2+4q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q^2+3q+1
       699: q
       701: q
       709: q
       712: 2q+1
       715: q
       716: 2q+1
       720: q+1
       721: q
       723: 2q+1
       725: q
       726: q
       727: q^2+3q+1
       733: q
       735: q+1
       739: 2q+1
       743: 2q+1
       751: q+1
       754: q
       756: 3q+1
       758: 2q+1
       762: 2q+1
       766: q
       768: 2q+1
       769: q+1
       775: 2q+1
       779: q+1
       781: q+1
       786: 1
       788: q+1
       791: 1
       793: 2q
       794: q^2+2q+1
       795: 2q+1
       797: 3q+1
       801: 2q
       802: 3q+1
       804: 3q+1
       806: q+1
       807: q
       808: q^2+3q+1
       809: q+1
       811: q^2+3q+1
       812: q
       815: q
       816: q+1
       818: 3q+1
       819: q+1
       821: q+1
       825: q
       826: 2q+1
       828: q+1
       832: q+1
       833: 1
       835: q+1
       840: q+1
       843: 2q+1
       844: q
       845: q
       846: 2q+1
       848: 2q+1
       849: 2q+1
       851: 2q+1
       855: 2q+1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       916: q
       918: q+1
       920: q
       922: 2q+1
       926: q
       927: 2q+1
       930: q+1
       942: q+1
       946: q+1
       950: q+1
       961: 2q+1
       965: q
       967: 2q+1
       968: q+1
       975: 2q+1
       991: q+1
       994: q+1
       999: q+1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1016: q
      1017: q+1
      1020: q+1
      1022: q+1
      1027: 1
      1029: q+1
      1033: q+1
      1036: 1
      1038: 1
      1045: 1
      1046: q+1
      1048: q+1
      1052: q
      1053: 2q+1
      1055: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: q+1
      1116: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1197: q+1
      1199: q+1
      1204: q+1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: q+1
      1233: q+1
      1235: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1261: 1
      1266: 1
      1271: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1329: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 2
      1367: 1
      1369: 1
      1382: 1
      1420: 1
      1430: 1
      1432: 1
      1436: 1
      1451: 1
      1455: 1
      1461: 1
      1464: 1
      1467: 1
      1474: 1
      1479: 1
      1482: 1
      1487: 1
      1506: 1
      1510: 1
      1538: 1
      1578: 1
      1580: 1
      1609: 1
      1659: 1
      1664: 1
      1742: 1

1743:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: q^4+16q^3+16q^2+5q+1
        23: q^4+16q^3+16q^2+5q+1
        24: 4q^4+13q^3+13q^2+5q+1
        25: 9q^3+15q^2+5q+1
        26: 9q^3+15q^2+5q+1
        27: q^4+9q^3+12q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 10q^3+14q^2+5q+1
        32: 10q^3+13q^2+5q+1
        33: q^4+16q^3+16q^2+5q+1
        34: 5q^3+13q^2+5q+1
        35: 6q^3+12q^2+5q+1
        36: 9q^3+15q^2+5q+1
        37: 3q^3+5q^2+q
        38: 6q^3+10q^2+4q+1
        39: 3q^3+5q^2+q
        40: 6q^3+10q^2+4q+1
        41: 3q^3+4q^2+q
        42: q^4+6q^3+8q^2+4q+1
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 10q^3+13q^2+5q+1
        53: q^4+12q^3+13q^2+5q+1
        54: 2q^4+8q^3+11q^2+5q+1
        55: 3q^3+12q^2+5q+1
        56: 5q^3+12q^2+5q+1
        57: 4q^3+10q^2+5q+1
        58: 6q^3+9q^2+4q+1
        59: 4q^3+5q^2+q
        60: q^3+5q^2+2q
        61: 4q^3+8q^2+3q+1
        62: q^3+4q^2+q
        63: 4q^3+9q^2+4q+1
        64: 2q^3+4q^2+q
        65: 4q^3+8q^2+4q+1
        66: 3q^3+5q^2+q
        67: 6q^3+10q^2+4q+1
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 2q^3+9q^2+5q+1
        73: 6q^3+10q^2+5q+1
        74: 3q^2+q
        75: q^3+7q^2+4q+1
        76: q^3+3q^2+q
        77: 2q^3+7q^2+4q+1
        78: 3q^2+q
        79: 2q^3+6q^2+4q+1
        80: 4q^3+11q^2+5q+1
        81: 10q^3+13q^2+5q+1
        82: 7q^3+11q^2+5q+1
        83: 6q^3+11q^2+5q+1
        84: 2q^3+10q^2+5q+1
        85: 6q^3+12q^2+5q+1
        86: 2q^3+10q^2+5q+1
        87: 2q^3+10q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 10q^3+13q^2+5q+1
        95: q^4+12q^3+13q^2+5q+1
        96: 2q^4+8q^3+11q^2+5q+1
        97: 3q^3+12q^2+5q+1
        98: 5q^3+12q^2+5q+1
        99: 4q^3+10q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: 2q^2+q
       104: q^3+3q^2+q
       105: 3q^3+6q^2+3q+1
       106: q^3+2q^2
       107: 2q^2+2q
       108: q^3+5q^2+3q+1
       109: 3q^3+6q^2+4q+1
       110: q^3+2q^2+q
       111: 2q^2+q
       112: 5q^2+4q+1
       113: 2q^2+q
       114: q^3+6q^2+4q+1
       115: 3q^2+q
       116: q^3+6q^2+4q+1
       117: q^3+6q^2+4q+1
       118: 2q^2+q
       119: 2q^2+2q
       120: q^3+5q^2+3q+1
       121: 3q^2+q
       122: 2q^3+7q^2+4q+1
       123: 2q^3+4q^2+q
       124: 4q^3+8q^2+4q+1
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: 3q^2+q
       128: q^3+7q^2+4q+1
       129: q^3+3q^2+q
       130: 2q^3+7q^2+4q+1
       131: 3q^2+q
       132: 2q^3+6q^2+4q+1
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: q^3+7q^2+5q+1
       136: 2q^3+8q^2+5q+1
       137: 4q^3+11q^2+5q+1
       138: 6q^3+11q^2+5q+1
       139: 7q^3+11q^2+5q+1
       140: 2q^3+9q^2+5q+1
       141: 3q^3+9q^2+5q+1
       142: 6q^3+10q^2+5q+1
       143: 2q^3+10q^2+5q+1
       144: 2q^3+10q^2+5q+1
       145: 2q^3+10q^2+5q+1
       146: q^3+8q^2+5q+1
       147: 2q^3+9q^2+5q+1
       148: 3q^2+4q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: 3q^2+q
       152: q^3+7q^2+4q+1
       153: q^3+3q^2+q
       154: 2q^3+7q^2+4q+1
       155: 3q^2+q
       156: 2q^3+6q^2+4q+1
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: 4q^3+10q^2+5q+1
       161: 6q^3+10q^2+5q+1
       162: 4q^3+10q^2+5q+1
       163: q^3+6q^2+5q+1
       164: 2q^3+6q^2+5q+1
       165: q^3+6q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q
       170: q^2+q
       171: 3q^2+3q+1
       172: q^2
       173: q^2+q
       174: q^2+q
       175: q^3+4q^2+3q+1
       176: q^2
       177: 3q^2+q
       178: q^3+6q^2+4q+1
       179: 2q^2+q
       180: q^3+6q^2+4q+1
       181: 2q^2+q
       182: 5q^2+4q+1
       183: 2q
       184: 3q^2+3q+1
       185: 4q^2+4q+1
       186: q^2+q
       187: 2q^2+q
       188: 4q^2+4q+1
       189: 2q^2+q
       190: q^3+5q^2+4q+1
       191: q^3+6q^2+4q+1
       192: 2q^2+q
       193: 2q^2+2q
       194: q^3+5q^2+3q+1
       195: 3q^3+6q^2+4q+1
       196: q^3+2q^2+q
       197: 2q^2+q
       198: 5q^2+4q+1
       199: 2q^2+2q
       200: q^3+5q^2+3q+1
       201: 2q^2+2q
       202: q^3+5q^2+3q+1
       203: 3q^2+4q+1
       205: q
       206: q^2+3q+1
       207: 3q^2+q
       208: 2q^3+7q^2+4q+1
       209: 2q^2+q
       210: q^3+6q^2+4q+1
       211: 3q^2+q
       212: q^3+6q^2+4q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: q^3+7q^2+5q+1
       224: 3q^2+5q+1
       225: 2q^3+8q^2+5q+1
       226: 3q^3+9q^2+5q+1
       227: 6q^2+5q+1
       228: 4q^3+10q^2+5q+1
       229: q^3+7q^2+5q+1
       230: 2q^3+8q^2+5q+1
       231: q^3+8q^2+5q+1
       232: 3q^2+5q+1
       233: q^3+6q^2+5q+1
       234: q^3+4q^2+5q+1
       235: q^2+4q+1
       236: 2q^3+10q^2+5q+1
       237: 3q^2+q
       238: q^3+7q^2+4q+1
       239: q^3+3q^2+q
       240: 2q^3+7q^2+4q+1
       241: 3q^2+q
       242: 2q^3+6q^2+4q+1
       243: 2q^3+10q^2+5q+1
       244: 2q^3+9q^2+5q+1
       245: 3q^2+4q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: q^3+5q^2+5q+1
       251: q^3+5q^2+5q+1
       252: q^3+5q^2+5q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q
       260: q^2+q
       261: 3q^2+3q+1
       262: q^2
       263: q
       264: q
       265: 2q^2+3q+1
       266: q^2
       267: q
       268: q^2+q
       269: q^2
       270: 3q^2+3q+1
       271: q
       272: q^2+3q+1
       275: q^2+q
       276: q^2+q
       277: q^3+4q^2+3q+1
       278: q^2
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: 2q
       284: 3q^2+3q+1
       285: 4q^2+4q+1
       286: q^2+q
       287: 2q^2+q
       288: q^3+5q^2+4q+1
       290: q^2+3q+1
       291: 2q^2+q
       292: 4q^2+4q+1
       293: 2q
       294: q^2+3q+1
       295: 2q^2+4q+1
       296: q
       297: q
       298: 2q^2+4q+1
       299: 2q
       300: 3q^2+3q+1
       301: 2q^2+q
       302: 5q^2+4q+1
       303: 4q^2+4q+1
       304: q^2+q
       305: 2q^2+q
       306: 4q^2+4q+1
       307: 2q
       308: q^2+3q+1
       309: q^2+4q+1
       311: q
       312: q^2+3q+1
       313: q
       314: 3q+1
       315: 3q^2+q
       316: q^3+6q^2+4q+1
       317: 2q^2+q
       318: q^3+6q^2+4q+1
       319: 2q^2+2q
       320: q^3+5q^2+3q+1
       321: 3q^2+4q+1
       323: q
       324: q^2+3q+1
       325: 2q^2+q
       326: q^3+5q^2+4q+1
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 2q^2+2q
       339: 4q^2+5q+1
       340: 2q^2+2q
       341: 4q^2+5q+1
       342: 2q^2+q
       343: q^3+4q^2+3q+1
       344: 6q^2+5q+1
       345: 3q^2+5q+1
       346: q^3+5q^2+5q+1
       347: 3q^2+5q+1
       348: q^3+7q^2+5q+1
       349: 3q^2+5q+1
       350: 2q^3+8q^2+5q+1
       351: 6q^2+7q+1
       352: 3q^2+5q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^3+4q^2+5q+1
       357: 2q+1
       358: q^2+4q+1
       359: q^2+6q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^3+4q^2+5q+1
       370: q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       378: q
       379: 2q^2+3q+1
       380: q^2
       382: q
       383: 2q+1
       385: q
       386: q
       387: q^2+3q+1
       389: q
       390: q^2+q
       391: q^2
       392: 3q^2+3q+1
       393: q
       394: q
       395: 2q^2+3q+1
       396: q^2
       397: q
       398: q^2+3q+1
       401: q
       402: 3q+1
       405: q
       408: q^2+3q+1
       414: q^2+3q+1
       418: q^2+3q+1
       419: 2q
       420: q^2+3q+1
       421: 2q^2+4q+1
       422: q
       423: q
       424: 2q^2+4q+1
       425: q^2+q
       426: 2q^2+3q+1
       427: q^2+2q
       428: 3q^2+5q+1
       429: 2q
       430: 3q^2+3q+1
       431: 4q^2+4q+1
       432: q^2+q
       433: 2q^2+q
       434: 4q^2+4q+1
       436: q^2+3q+1
       437: 2q
       438: q^2+3q+1
       439: 2q^2+4q+1
       440: q
       441: q
       442: 2q^2+4q+1
       443: q^2+3q
       444: 3q^2+4q+1
       445: 2q^2+2q
       446: 4q^2+5q+1
       447: 2q
       448: q^2+3q+1
       449: q^2+4q+1
       451: q
       452: 3q+1
       453: q
       454: 2q+1
       456: 2q+1
       457: 2q+1
       460: 2q+1
       461: q^2+6q+1
       463: 2q
       464: q^2+4q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       469: 2q^2+q
       470: q^3+5q^2+4q+1
       471: 2q
       472: q^2+3q+1
       473: q^2+4q+1
       475: q
       476: 3q+1
       477: q
       478: q^2+3q+1
       479: 2q
       480: q^2+4q+1
       481: 5q+1
       482: q^2+4q+1
       483: q^2+4q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 3q^2+5q+1
       493: 3q^2+5q+1
       494: 3q^2+5q+1
       495: 3q^2+4q+1
       496: 2q^2+4q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 3q+1
       501: 3q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^3+4q^2+5q+1
       513: 2q+1
       514: q^2+4q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: 2q+1
       529: q
       530: q
       531: q^2+3q+1
       533: q
       534: q
       535: 2q^2+3q+1
       536: q^2
       538: q
       540: 2q+1
       541: q
       542: q
       544: q^2+3q+1
       545: q
       546: q^2+2q
       547: q^2+q
       548: 2q^2+3q+1
       549: q
       550: 3q+1
       554: 2q+1
       558: 2q+1
       561: 2q
       562: q^2+4q+1
       565: q
       567: 3q+1
       569: q
       572: q^2+3q+1
       573: 2q
       576: q^2+4q+1
       577: q
       578: q
       580: q
       581: q^2+3q+1
       586: 3q+1
       589: 2q
       590: 3q+1
       591: 3q+1
       594: q+1
       595: q^2+3q+1
       596: q
       598: q+1
       599: q
       600: q^2+3q+1
       602: 2q+1
       603: 2q
       604: q^2+3q+1
       606: q^2+3q+1
       607: 2q^2+4q+1
       608: q
       609: q
       610: 2q^2+4q+1
       613: q^2+q
       614: 2q^2+3q+1
       615: 2q
       616: q^2+2q+1
       618: 2q+1
       619: q
       620: 2q+1
       621: 2q+1
       624: 2q+1
       626: 2q+1
       629: q
       630: 2q+1
       631: 3q+1
       634: q+1
       640: q^2+3q+1
       641: 2q
       642: q^2+3q+1
       643: q^2+4q+1
       645: q
       646: 3q+1
       647: q
       648: 2q+1
       649: 2q+1
       652: 2q+1
       654: 2q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 5q+1
       676: q^2+4q+1
       677: q^2+4q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       698: q
       700: q^2+3q+1
       710: q
       711: 2q+1
       713: q
       714: 2q+1
       719: q+1
       722: q
       724: 2q+1
       725: q
       726: q
       728: q^2+3q+1
       734: q
       736: q+1
       738: 2q+1
       742: 2q+1
       750: q+1
       753: q
       755: 3q+1
       760: 2q+1
       764: 2q+1
       765: q
       767: 2q+1
       773: q+1
       776: 2q+1
       780: q+1
       782: q+1
       786: 1
       787: q+1
       792: 1
       793: 2q
       794: q^2+2q+1
       796: 2q+1
       798: 3q+1
       801: 2q
       802: 3q+1
       803: 3q+1
       806: q+1
       807: q^2+3q+1
       808: q
       810: q+1
       811: q
       812: q^2+3q+1
       815: q
       816: q+1
       817: 3q+1
       820: q+1
       822: q+1
       825: q
       826: 2q+1
       827: q+1
       831: q+1
       834: 1
       836: q+1
       839: q+1
       843: q
       844: 2q+1
       845: q
       846: 2q+1
       847: 2q+1
       850: 2q+1
       852: 2q+1
       855: q
       856: 2q+1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       917: q
       919: q+1
       921: q
       923: 2q+1
       924: q
       925: 2q+1
       931: q+1
       941: q+1
       945: q+1
       949: q+1
       963: 2q+1
       964: q
       966: 2q+1
       972: q+1
       977: 2q+1
       990: q+1
       995: q+1
       998: q+1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1016: q
      1017: q+1
      1021: q+1
      1023: q+1
      1027: 1
      1028: q+1
      1032: q+1
      1037: 1
      1039: 1
      1044: 1
      1047: q+1
      1049: q+1
      1052: q
      1053: 2q+1
      1054: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1093: q+1
      1115: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1196: q+1
      1201: q+1
      1203: q+1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1231: q+1
      1232: q+1
      1235: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1260: 1
      1267: 1
      1270: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1328: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 2
      1365: 1
      1370: 1
      1381: 1
      1419: 1
      1434: 1
      1435: 1
      1437: 1
      1450: 1
      1455: 1
      1460: 1
      1465: 1
      1466: 1
      1475: 1
      1478: 1
      1483: 1
      1487: 1
      1507: 1
      1511: 1
      1540: 1
      1576: 1
      1581: 1
      1608: 1
      1660: 1
      1663: 1
      1743: 1

1744:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: q^4+16q^3+16q^2+5q+1
        23: q^4+16q^3+16q^2+5q+1
        24: 4q^4+13q^3+13q^2+5q+1
        25: 9q^3+15q^2+5q+1
        26: 9q^3+15q^2+5q+1
        27: q^4+9q^3+12q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 10q^3+14q^2+5q+1
        32: 10q^3+13q^2+5q+1
        33: q^4+16q^3+16q^2+5q+1
        34: 5q^3+13q^2+5q+1
        35: 6q^3+12q^2+5q+1
        36: 9q^3+15q^2+5q+1
        37: 3q^3+5q^2+q
        38: 6q^3+10q^2+4q+1
        39: 3q^3+5q^2+q
        40: 6q^3+10q^2+4q+1
        41: 3q^3+4q^2+q
        42: q^4+6q^3+8q^2+4q+1
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 10q^3+13q^2+5q+1
        53: q^4+12q^3+13q^2+5q+1
        54: 2q^4+8q^3+11q^2+5q+1
        55: 3q^3+12q^2+5q+1
        56: 5q^3+12q^2+5q+1
        57: 4q^3+10q^2+5q+1
        58: 4q^3+5q^2+q
        59: 6q^3+9q^2+4q+1
        60: 4q^3+8q^2+3q+1
        61: q^3+5q^2+2q
        62: q^3+4q^2+q
        63: 4q^3+9q^2+4q+1
        64: 2q^3+4q^2+q
        65: 4q^3+8q^2+4q+1
        66: 3q^3+5q^2+q
        67: 6q^3+10q^2+4q+1
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 2q^3+9q^2+5q+1
        73: 6q^3+10q^2+5q+1
        74: 3q^2+q
        75: q^3+7q^2+4q+1
        76: q^3+3q^2+q
        77: 2q^3+7q^2+4q+1
        78: 3q^2+q
        79: 2q^3+6q^2+4q+1
        80: 4q^3+11q^2+5q+1
        81: 10q^3+13q^2+5q+1
        82: 7q^3+11q^2+5q+1
        83: 6q^3+11q^2+5q+1
        84: 2q^3+10q^2+5q+1
        85: 6q^3+12q^2+5q+1
        86: 2q^3+10q^2+5q+1
        87: 2q^3+10q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 10q^3+13q^2+5q+1
        95: q^4+12q^3+13q^2+5q+1
        96: 2q^4+8q^3+11q^2+5q+1
        97: 3q^3+12q^2+5q+1
        98: 5q^3+12q^2+5q+1
        99: 4q^3+10q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: q^3+2q^2
       104: 3q^3+6q^2+3q+1
       105: q^3+3q^2+q
       106: 2q^2+q
       107: q^3+5q^2+3q+1
       108: 2q^2+2q
       109: q^3+2q^2+q
       110: 3q^3+6q^2+4q+1
       111: 2q^2+q
       112: 5q^2+4q+1
       113: 2q^2+q
       114: q^3+6q^2+4q+1
       115: 3q^2+q
       116: q^3+6q^2+4q+1
       117: 2q^2+q
       118: q^3+6q^2+4q+1
       119: q^3+5q^2+3q+1
       120: 2q^2+2q
       121: 3q^2+q
       122: 2q^3+7q^2+4q+1
       123: 2q^3+4q^2+q
       124: 4q^3+8q^2+4q+1
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: 3q^2+q
       128: q^3+7q^2+4q+1
       129: q^3+3q^2+q
       130: 2q^3+7q^2+4q+1
       131: 3q^2+q
       132: 2q^3+6q^2+4q+1
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: q^3+7q^2+5q+1
       136: 2q^3+8q^2+5q+1
       137: 4q^3+11q^2+5q+1
       138: 6q^3+11q^2+5q+1
       139: 7q^3+11q^2+5q+1
       140: 2q^3+9q^2+5q+1
       141: 3q^3+9q^2+5q+1
       142: 6q^3+10q^2+5q+1
       143: 2q^3+10q^2+5q+1
       144: 2q^3+10q^2+5q+1
       145: 2q^3+10q^2+5q+1
       146: q^3+8q^2+5q+1
       147: 2q^3+9q^2+5q+1
       148: 3q^2+4q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: 3q^2+q
       152: q^3+7q^2+4q+1
       153: q^3+3q^2+q
       154: 2q^3+7q^2+4q+1
       155: 3q^2+q
       156: 2q^3+6q^2+4q+1
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: 4q^3+10q^2+5q+1
       161: 6q^3+10q^2+5q+1
       162: 4q^3+10q^2+5q+1
       163: q^3+6q^2+5q+1
       164: 2q^3+6q^2+5q+1
       165: q^3+6q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q^2
       170: 3q^2+3q+1
       171: q^2+q
       172: q
       173: q^2
       174: q^3+4q^2+3q+1
       175: q^2+q
       176: q^2+q
       177: 3q^2+q
       178: q^3+6q^2+4q+1
       179: 2q^2+q
       180: q^3+6q^2+4q+1
       181: 2q^2+q
       182: 5q^2+4q+1
       183: 3q^2+3q+1
       184: 2q
       185: q^2+q
       186: 4q^2+4q+1
       187: 2q^2+q
       188: 4q^2+4q+1
       189: 2q^2+q
       190: q^3+5q^2+4q+1
       191: 2q^2+q
       192: q^3+6q^2+4q+1
       193: q^3+5q^2+3q+1
       194: 2q^2+2q
       195: q^3+2q^2+q
       196: 3q^3+6q^2+4q+1
       197: 2q^2+q
       198: 5q^2+4q+1
       199: q^3+5q^2+3q+1
       200: 2q^2+2q
       201: q^3+5q^2+3q+1
       202: 2q^2+2q
       204: 3q^2+4q+1
       205: q
       206: q^2+3q+1
       207: 3q^2+q
       208: 2q^3+7q^2+4q+1
       209: 2q^2+q
       210: q^3+6q^2+4q+1
       211: 3q^2+q
       212: q^3+6q^2+4q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: q^3+7q^2+5q+1
       224: 3q^2+5q+1
       225: 2q^3+8q^2+5q+1
       226: 3q^3+9q^2+5q+1
       227: 6q^2+5q+1
       228: 4q^3+10q^2+5q+1
       229: q^3+7q^2+5q+1
       230: 2q^3+8q^2+5q+1
       231: q^3+8q^2+5q+1
       232: 3q^2+5q+1
       233: q^3+6q^2+5q+1
       234: q^3+4q^2+5q+1
       235: q^2+4q+1
       236: 2q^3+10q^2+5q+1
       237: 3q^2+q
       238: q^3+7q^2+4q+1
       239: q^3+3q^2+q
       240: 2q^3+7q^2+4q+1
       241: 3q^2+q
       242: 2q^3+6q^2+4q+1
       243: 2q^3+10q^2+5q+1
       244: 2q^3+9q^2+5q+1
       245: 3q^2+4q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: q^3+5q^2+5q+1
       251: q^3+5q^2+5q+1
       252: q^3+5q^2+5q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q^2
       260: 3q^2+3q+1
       261: q^2+q
       262: q
       263: q^2
       264: 2q^2+3q+1
       265: q
       266: q
       267: q^2
       268: 3q^2+3q+1
       269: q
       270: q^2+q
       273: q
       274: q^2+3q+1
       275: q^2
       276: q^3+4q^2+3q+1
       277: q^2+q
       278: q^2+q
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: 3q^2+3q+1
       284: 2q
       285: q^2+q
       286: 4q^2+4q+1
       287: 2q^2+q
       288: q^3+5q^2+4q+1
       290: q^2+3q+1
       291: 2q^2+q
       292: 4q^2+4q+1
       293: q^2+3q+1
       294: 2q
       295: q
       296: 2q^2+4q+1
       297: q
       298: 2q^2+4q+1
       299: 3q^2+3q+1
       300: 2q
       301: 2q^2+q
       302: 5q^2+4q+1
       303: q^2+q
       304: 4q^2+4q+1
       305: 2q^2+q
       306: 4q^2+4q+1
       307: q^2+3q+1
       308: 2q
       310: q^2+4q+1
       311: q
       312: q^2+3q+1
       313: q
       314: 3q+1
       315: 3q^2+q
       316: q^3+6q^2+4q+1
       317: 2q^2+q
       318: q^3+6q^2+4q+1
       319: q^3+5q^2+3q+1
       320: 2q^2+2q
       322: 3q^2+4q+1
       323: q
       324: q^2+3q+1
       325: 2q^2+q
       326: q^3+5q^2+4q+1
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 2q^2+2q
       339: 4q^2+5q+1
       340: 2q^2+2q
       341: 4q^2+5q+1
       342: 2q^2+q
       343: q^3+4q^2+3q+1
       344: 6q^2+5q+1
       345: 3q^2+5q+1
       346: q^3+5q^2+5q+1
       347: 3q^2+5q+1
       348: q^3+7q^2+5q+1
       349: 3q^2+5q+1
       350: 2q^3+8q^2+5q+1
       351: 6q^2+7q+1
       352: 3q^2+5q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^3+4q^2+5q+1
       357: 2q+1
       358: q^2+4q+1
       359: q^2+6q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^3+4q^2+5q+1
       370: q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q^2
       378: 2q^2+3q+1
       379: q
       380: q
       382: 2q+1
       383: q
       386: q^2+3q+1
       387: q
       388: q
       389: q^2
       390: 3q^2+3q+1
       391: q
       392: q^2+q
       393: q^2
       394: 2q^2+3q+1
       395: q
       396: q
       399: q
       400: q^2+3q+1
       403: 3q+1
       404: q
       406: q
       407: q^2+3q+1
       414: q^2+3q+1
       418: q^2+3q+1
       419: q^2+3q+1
       420: 2q
       421: q
       422: 2q^2+4q+1
       423: q
       424: 2q^2+4q+1
       425: q^2+q
       426: 2q^2+3q+1
       427: q^2+2q
       428: 3q^2+5q+1
       429: 3q^2+3q+1
       430: 2q
       431: q^2+q
       432: 4q^2+4q+1
       433: 2q^2+q
       434: 4q^2+4q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q
       439: q
       440: 2q^2+4q+1
       441: q
       442: 2q^2+4q+1
       443: 3q^2+4q+1
       444: q^2+3q
       445: 2q^2+2q
       446: 4q^2+5q+1
       447: q^2+3q+1
       448: 2q
       450: q^2+4q+1
       451: q
       452: 3q+1
       453: 2q+1
       454: q
       456: 2q+1
       458: 2q+1
       460: 2q+1
       462: q^2+6q+1
       463: 2q
       464: q^2+4q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       469: 2q^2+q
       470: q^3+5q^2+4q+1
       471: q^2+3q+1
       472: 2q
       474: q^2+4q+1
       475: q
       476: 3q+1
       477: q
       478: q^2+3q+1
       479: 2q
       480: q^2+4q+1
       481: 5q+1
       482: q^2+4q+1
       483: q^2+4q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 3q^2+5q+1
       493: 3q^2+5q+1
       494: 3q^2+5q+1
       495: 3q^2+4q+1
       496: 2q^2+4q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 3q+1
       501: 3q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^3+4q^2+5q+1
       513: 2q+1
       514: q^2+4q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 2q+1
       523: q
       530: q^2+3q+1
       531: q
       532: q
       533: q^2
       534: 2q^2+3q+1
       535: q
       536: q
       538: 2q+1
       540: q
       542: q^2+3q+1
       543: q
       544: q
       545: q^2+q
       546: 2q^2+3q+1
       547: q
       548: q^2+2q
       551: 3q+1
       552: q
       556: 2q+1
       560: 2q+1
       563: 2q
       564: q^2+4q+1
       566: 3q+1
       568: q
       570: q
       571: q^2+3q+1
       574: q^2+4q+1
       575: 2q
       577: q
       578: q
       580: q
       581: q^2+3q+1
       586: 3q+1
       589: 3q+1
       590: 2q
       592: 3q+1
       593: q+1
       595: q
       596: q^2+3q+1
       598: q+1
       599: q
       600: q^2+3q+1
       602: 2q+1
       603: q^2+3q+1
       604: 2q
       606: q^2+3q+1
       607: q
       608: 2q^2+4q+1
       609: q
       610: 2q^2+4q+1
       613: q^2+q
       614: 2q^2+3q+1
       615: q^2+2q+1
       616: 2q
       618: 2q+1
       619: 2q+1
       620: q
       622: 2q+1
       624: 2q+1
       626: 2q+1
       629: q
       630: 2q+1
       632: 3q+1
       634: q+1
       640: q^2+3q+1
       641: q^2+3q+1
       642: 2q
       644: q^2+4q+1
       645: q
       646: 3q+1
       647: 2q+1
       648: q
       650: 2q+1
       652: 2q+1
       654: 2q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 5q+1
       676: q^2+4q+1
       677: q^2+4q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q
       699: q^2+3q+1
       701: q
       710: 2q+1
       711: q
       715: 2q+1
       716: q
       718: q+1
       722: 2q+1
       724: q
       726: q^2+3q+1
       727: q
       728: q
       734: q+1
       736: q
       740: 2q+1
       744: 2q+1
       752: q+1
       754: 3q+1
       756: q
       759: 2q+1
       763: 2q+1
       766: 2q+1
       768: q
       773: q+1
       776: 2q+1
       780: q+1
       782: q+1
       785: 1
       788: q+1
       792: 1
       793: q^2+2q+1
       794: 2q
       796: 2q+1
       798: 3q+1
       801: 3q+1
       802: 2q
       804: 3q+1
       805: q+1
       807: q
       808: q^2+3q+1
       810: q+1
       811: q
       812: q^2+3q+1
       815: q+1
       816: q
       818: 3q+1
       820: q+1
       822: q+1
       825: 2q+1
       826: q
       828: q+1
       832: q+1
       834: 1
       836: q+1
       840: q+1
       843: q
       844: 2q+1
       845: 2q+1
       846: q
       848: 2q+1
       850: 2q+1
       852: 2q+1
       855: q
       856: 2q+1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       917: q+1
       919: q
       921: 2q+1
       923: q
       926: 2q+1
       927: q
       929: q+1
       943: q+1
       947: q+1
       951: q+1
       962: 2q+1
       965: 2q+1
       967: q
       972: q+1
       976: 2q+1
       989: q+1
       995: q+1
       999: q+1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1016: q+1
      1017: q
      1021: q+1
      1023: q+1
      1026: 1
      1029: q+1
      1033: q+1
      1037: 1
      1039: 1
      1045: 1
      1047: q+1
      1049: q+1
      1052: 2q+1
      1053: q
      1055: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1092: q+1
      1117: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1195: q+1
      1200: q+1
      1205: q+1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: q+1
      1233: q+1
      1234: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1261: 1
      1267: 1
      1271: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 2
      1366: 1
      1371: 1
      1383: 1
      1421: 1
      1434: 1
      1435: 1
      1437: 1
      1451: 1
      1454: 1
      1461: 1
      1465: 1
      1467: 1
      1475: 1
      1479: 1
      1483: 1
      1487: 1
      1508: 1
      1512: 1
      1539: 1
      1577: 1
      1582: 1
      1610: 1
      1660: 1
      1664: 1
      1744: 1

1745:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q^2+1
        59: q
        60: 1
        62: 1
        64: 1
        66: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: 1
        73: q^2+q+1
        74: 1
        76: 1
        78: 1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: q^2+1
       110: q
       111: 1
       113: 1
       115: 1
       117: q^2+1
       118: q
       119: 1
       121: 1
       123: 1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       129: 1
       131: 1
       133: q^2+q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: q^2+1
       186: q
       187: 1
       189: 1
       191: q^2+1
       192: q
       193: 1
       195: q^2+1
       196: q
       197: 1
       199: 1
       201: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 1
       223: 1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: q^2+1
       286: q
       287: 1
       289: 1
       291: 1
       293: 1
       295: q^2+1
       296: q
       297: 1
       299: 1
       301: 1
       303: q^2+1
       304: q
       305: 1
       307: 1
       315: 1
       317: 1
       319: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q^2+q+1
       334: 1
       335: q^2+q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 1
       348: 1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: q^2+1
       422: q
       423: 1
       425: 1
       427: 1
       429: 1
       431: q^2+1
       432: q
       433: 1
       435: 1
       437: 1
       439: q^2+1
       440: q
       441: 1
       443: 1
       445: 1
       447: 1
       453: 1
       465: 1
       467: 1
       469: 1
       471: 1
       481: 1
       482: q^2+q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q^2+q+1
       493: 1
       494: q^2+q+1
       495: 1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       583: 1
       585: 1
       587: 1
       589: 1
       593: 1
       595: q^2+1
       596: q
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: q^2+1
       608: q
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       635: 1
       637: 1
       639: 1
       641: 1
       647: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q^2+q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q^2+1
       808: q
       809: 1
       811: 1
       813: 1
       815: 1
       825: 1
       841: 1
       845: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       896: 1
       904: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: 1
       992: 1
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1052: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1118: 1
      1122: 1
      1144: 1
      1148: 1
      1156: 1
      1210: 1
      1212: 1
      1214: 1
      1218: 1
      1226: 1
      1228: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1282: 1
      1283: 1
      1284: 1
      1318: 1
      1340: 1
      1352: 1
      1356: 1
      1438: 1
      1442: 1
      1448: 1
      1452: 1
      1454: 1
      1485: 1
      1545: 1
      1567: 1
      1643: 1
      1647: 1
      1745: 1

1746:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q^2+1
        60: 1
        63: 1
        65: 1
        67: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: 1
        73: q^2+q+1
        75: 1
        77: 1
        79: 1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       109: q
       110: q^2+1
       112: 1
       114: 1
       116: 1
       117: q
       118: q^2+1
       119: 1
       122: 1
       124: 1
       125: q^2+q+1
       126: q^2+q+1
       128: 1
       130: 1
       132: 1
       133: q^2+q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       185: q
       186: q^2+1
       188: 1
       190: 1
       191: q
       192: q^2+1
       193: 1
       195: q
       196: q^2+1
       198: 1
       199: 1
       201: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 1
       223: 1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       276: 1
       280: 1
       282: 1
       283: 1
       285: q
       286: q^2+1
       288: 1
       290: 1
       292: 1
       293: 1
       295: q
       296: q^2+1
       298: 1
       299: 1
       302: 1
       303: q
       304: q^2+1
       306: 1
       307: 1
       316: 1
       318: 1
       319: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q^2+q+1
       334: 1
       335: q^2+q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 1
       348: 1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       421: q
       422: q^2+1
       424: 1
       426: 1
       428: 1
       429: 1
       431: q
       432: q^2+1
       434: 1
       436: 1
       437: 1
       439: q
       440: q^2+1
       442: 1
       443: 1
       446: 1
       447: 1
       453: 1
       466: 1
       468: 1
       470: 1
       471: 1
       481: 1
       482: q^2+q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q^2+q+1
       493: 1
       494: q^2+q+1
       495: 1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       584: 1
       586: 1
       588: 1
       589: 1
       593: 1
       595: q
       596: q^2+1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       607: q
       608: q^2+1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       636: 1
       638: 1
       640: 1
       641: 1
       647: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q^2+q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       807: q
       808: q^2+1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       842: 1
       845: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       897: 1
       905: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: 1
       993: 1
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1052: 1
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1119: 1
      1123: 1
      1145: 1
      1149: 1
      1157: 1
      1211: 1
      1213: 1
      1215: 1
      1218: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1282: 1
      1283: 1
      1284: 1
      1319: 1
      1341: 1
      1353: 1
      1357: 1
      1439: 1
      1442: 1
      1449: 1
      1453: 1
      1454: 1
      1485: 1
      1546: 1
      1568: 1
      1644: 1
      1647: 1
      1746: 1

1747:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q
        59: q^2+1
        61: 1
        62: 1
        64: 1
        66: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: 1
        73: q^2+q+1
        74: 1
        76: 1
        78: 1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       109: q
       110: q^2+1
       111: 1
       113: 1
       115: 1
       117: q
       118: q^2+1
       120: 1
       121: 1
       123: 1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       129: 1
       131: 1
       133: q^2+q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       185: q
       186: q^2+1
       187: 1
       189: 1
       191: q
       192: q^2+1
       194: 1
       195: q
       196: q^2+1
       197: 1
       200: 1
       202: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 1
       223: 1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       278: 1
       279: 1
       281: 1
       284: 1
       285: q
       286: q^2+1
       287: 1
       289: 1
       291: 1
       294: 1
       295: q
       296: q^2+1
       297: 1
       300: 1
       301: 1
       303: q
       304: q^2+1
       305: 1
       308: 1
       315: 1
       317: 1
       320: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q^2+q+1
       334: 1
       335: q^2+q+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 1
       348: 1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       421: q
       422: q^2+1
       423: 1
       425: 1
       427: 1
       430: 1
       431: q
       432: q^2+1
       433: 1
       435: 1
       438: 1
       439: q
       440: q^2+1
       441: 1
       444: 1
       445: 1
       448: 1
       454: 1
       465: 1
       467: 1
       469: 1
       472: 1
       481: 1
       482: q^2+q+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: q^2+q+1
       493: 1
       494: q^2+q+1
       495: 1
       496: 1
       497: 1
       498: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       583: 1
       585: 1
       587: 1
       590: 1
       594: 1
       595: q
       596: q^2+1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       607: q
       608: q^2+1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       635: 1
       637: 1
       639: 1
       642: 1
       648: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q^2+q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       807: q
       808: q^2+1
       809: 1
       811: 1
       813: 1
       816: 1
       826: 1
       841: 1
       846: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       899: 1
       906: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: 1
       992: 1
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1053: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1120: 1
      1124: 1
      1146: 1
      1150: 1
      1158: 1
      1210: 1
      1212: 1
      1214: 1
      1219: 1
      1226: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1282: 1
      1283: 1
      1284: 1
      1320: 1
      1342: 1
      1354: 1
      1358: 1
      1438: 1
      1443: 1
      1448: 1
      1452: 1
      1455: 1
      1485: 1
      1547: 1
      1569: 1
      1643: 1
      1648: 1
      1747: 1

1748:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: 1
        58: q^2+1
        59: q
        61: 1
        63: 1
        65: 1
        67: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: 1
        73: q^2+q+1
        75: 1
        77: 1
        79: 1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       108: 1
       109: q^2+1
       110: q
       112: 1
       114: 1
       116: 1
       117: q^2+1
       118: q
       120: 1
       122: 1
       124: 1
       125: q^2+q+1
       126: q^2+q+1
       128: 1
       130: 1
       132: 1
       133: q^2+q+1
       134: q^2+q+1
       135: 1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: q^2+1
       186: q
       188: 1
       190: 1
       191: q^2+1
       192: q
       194: 1
       195: q^2+1
       196: q
       198: 1
       200: 1
       202: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 1
       223: 1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 1
       230: q^2+q+1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       270: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: q^2+1
       286: q
       288: 1
       290: 1
       292: 1
       294: 1
       295: q^2+1
       296: q
       298: 1
       300: 1
       302: 1
       303: q^2+1
       304: q
       306: 1
       308: 1
       316: 1
       318: 1
       320: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q^2+q+1
       334: 1
       335: q^2+q+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 1
       348: 1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: q^2+1
       422: q
       424: 1
       426: 1
       428: 1
       430: 1
       431: q^2+1
       432: q
       434: 1
       436: 1
       438: 1
       439: q^2+1
       440: q
       442: 1
       444: 1
       446: 1
       448: 1
       454: 1
       466: 1
       468: 1
       470: 1
       472: 1
       481: 1
       482: q^2+q+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: q^2+q+1
       493: 1
       494: q^2+q+1
       495: 1
       496: 1
       497: 1
       498: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       584: 1
       586: 1
       588: 1
       590: 1
       594: 1
       595: q^2+1
       596: q
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: q^2+1
       608: q
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       636: 1
       638: 1
       640: 1
       642: 1
       648: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q^2+q+1
       677: 1
       678: 1
       679: 1
       681: 1
       686: 1
       687: 1
       690: 1
       691: 1
       692: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q^2+1
       808: q
       810: 1
       812: 1
       814: 1
       816: 1
       826: 1
       842: 1
       846: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       898: 1
       907: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: 1
       993: 1
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1053: 1
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1121: 1
      1125: 1
      1147: 1
      1151: 1
      1159: 1
      1211: 1
      1213: 1
      1215: 1
      1219: 1
      1227: 1
      1229: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1282: 1
      1283: 1
      1284: 1
      1321: 1
      1343: 1
      1355: 1
      1359: 1
      1439: 1
      1443: 1
      1449: 1
      1453: 1
      1455: 1
      1485: 1
      1548: 1
      1570: 1
      1644: 1
      1648: 1
      1748: 1

1749:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 4q^3+9q^2+6q+1
        23: q^4+5q^3+9q^2+6q+1
        24: 4q^3+9q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 2q^3+7q^2+6q+1
        32: 4q^3+9q^2+6q+1
        33: 2q^3+7q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+4q+1
        38: 3q^2+2q
        39: 3q^2+4q+1
        40: q^3+3q^2+2q
        41: 3q^2+4q+1
        42: 3q^2+2q
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 4q^3+9q^2+6q+1
        53: q^4+5q^3+9q^2+6q+1
        54: 4q^3+9q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: q^3+3q^2+4q+1
        59: 2q^2+2q
        60: 2q^2+4q+1
        61: 2q
        62: 2q^2+4q+1
        63: 2q^2+2q
        64: 3q^2+4q+1
        65: 3q^2+2q
        66: 2q^2+4q+1
        67: 2q^2+2q
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 4q^2+6q+1
        73: 2q^3+7q^2+6q+1
        74: 3q^2+4q+1
        75: 3q^2+2q
        76: 3q^2+4q+1
        77: q^3+3q^2+2q
        78: 3q^2+4q+1
        79: 3q^2+2q
        80: 2q^3+7q^2+6q+1
        81: 2q^3+7q^2+6q+1
        82: 2q^3+7q^2+6q+1
        83: 4q^3+9q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^3+7q^2+6q+1
        95: 2q^3+7q^2+6q+1
        96: 3q^3+6q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q^2+3q+1
       104: q^2+q
       105: q
       106: q
       107: 2q^2+4q+1
       108: 2q
       109: q^3+3q^2+4q+1
       110: 2q^2+2q
       111: 2q^2+4q+1
       112: 2q^2+2q
       113: 2q^2+4q+1
       114: 2q^2+2q
       115: 3q^2+4q+1
       116: 3q^2+2q
       117: q^3+3q^2+4q+1
       118: 2q^2+2q
       119: 2q^2+4q+1
       120: 2q
       121: 2q^2+4q+1
       122: 2q^2+2q
       123: 2q^2+4q+1
       124: 2q^2+2q
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+6q+1
       136: 2q^3+7q^2+6q+1
       137: 3q^2+6q+1
       138: q^3+4q^2+4q+1
       139: q^3+5q^2+6q+1
       140: 4q^2+6q+1
       141: 2q^3+7q^2+6q+1
       142: 2q^3+7q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+4q+1
       152: 3q^2+2q
       153: 3q^2+4q+1
       154: q^3+3q^2+2q
       155: 3q^2+4q+1
       156: 3q^2+2q
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^3+7q^2+6q+1
       161: 2q^3+7q^2+6q+1
       162: 3q^3+6q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q^2+3q+1
       170: q^2+q
       171: q
       172: q
       173: q^2+3q+1
       174: q^2+q
       175: q
       176: q
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: 2q^2+4q+1
       184: 2q
       185: q^3+3q^2+4q+1
       186: 2q^2+2q
       187: 2q^2+4q+1
       188: 2q^2+2q
       189: 2q^2+4q+1
       190: 2q^2+2q
       191: 2q^2+4q+1
       192: q^2+2q
       193: 2q^2+4q+1
       194: 2q
       195: q^3+3q^2+4q+1
       196: 2q^2+2q
       197: 2q^2+4q+1
       198: 2q^2+2q
       199: q^2+4q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       203: 3q+1
       205: 2q+1
       206: q
       207: q^2+4q+1
       208: 2q
       209: 2q^2+4q+1
       210: 2q^2+2q
       211: 3q^2+4q+1
       212: 3q^2+2q
       213: 3q+1
       214: q^2+2q
       215: 3q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+q
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: 3q^2+6q+1
       225: q^3+4q^2+4q+1
       226: 2q^2+4q+1
       227: q^3+5q^2+6q+1
       228: q^3+4q^2+4q+1
       229: 4q^2+6q+1
       230: 2q^3+7q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: q^2+4q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+6q+1
       244: 2q^2+6q+1
       245: 3q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q^2+6q+1
       251: 3q^2+6q+1
       252: q^3+4q^2+4q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: 2q+1
       260: q^2+q
       261: q
       262: q
       263: q^2+3q+1
       264: q^2+q
       265: q
       266: q
       267: q^2+3q+1
       268: q^2+q
       269: q
       270: q
       271: 2q+1
       272: q
       275: q^2+3q+1
       276: q
       277: q
       278: q
       279: 3q+1
       280: q^2+2q
       281: 2q+1
       282: q
       283: 2q+1
       285: q^2+2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: q^2+2q
       291: 2q+1
       292: q
       293: q^2+4q+1
       294: 2q
       295: 2q^2+4q+1
       296: q^2+2q
       297: q^2+4q+1
       298: 2q
       299: 2q^2+4q+1
       300: 2q
       301: 3q+1
       302: q^2+2q
       303: q^3+3q^2+4q+1
       304: 2q^2+2q
       305: 2q^2+4q+1
       306: 2q^2+2q
       307: q^2+4q+1
       308: 2q
       309: 3q+1
       311: q+1
       312: q
       313: 2q+1
       314: q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: q^2+4q+1
       320: 2q
       321: 3q+1
       323: 2q+1
       324: q
       325: 2q^2+4q+1
       326: 2q^2+2q
       333: 2q^2+4q+1
       334: 4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 2q^2+4q+1
       345: 3q^2+6q+1
       346: 2q^2+4q+1
       347: q^2+6q+1
       348: q^2+4q+1
       349: 3q^2+6q+1
       350: q^3+4q^2+4q+1
       351: 2q^2+6q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 3q+1
       361: q^2+2q
       362: 3q+1
       363: q^2+2q
       364: q^2+2q+1
       365: q^2+q
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 2q^2+6q+1
       370: 3q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: q+1
       381: 2q+1
       382: q^2+q
       383: q
       384: q
       385: q^2+3q+1
       386: q
       387: q
       388: q
       389: 2q+1
       390: q^2+q
       391: q
       392: q
       393: q^2+3q+1
       394: q^2+q
       395: q
       396: q
       397: q+1
       398: q
       401: 2q+1
       402: q
       405: 2q+1
       408: q
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       419: 2q+1
       421: q^2+2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       429: 2q+1
       431: q^2+2q+1
       433: 2q+1
       434: q
       435: 3q+1
       436: q^2+2q
       437: q^2+4q+1
       438: 2q
       439: 2q^2+4q+1
       440: q^2+2q
       441: q^2+4q+1
       442: 2q
       443: q^2+4q+1
       444: 2q
       445: 3q+1
       446: q^2+2q
       447: 2q+1
       449: q+1
       451: 1
       453: 2q+1
       454: q
       455: q+1
       456: q
       457: q+1
       459: q+1
       461: 3q+1
       463: q+1
       464: q
       465: 3q+1
       466: q^2+2q
       467: 2q+1
       468: q
       469: 2q+1
       470: q
       471: q^2+4q+1
       472: 2q
       473: 3q+1
       475: 2q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: q^2+6q+1
       485: 3q+1
       486: q^2+2q
       487: 3q+1
       488: q^2+2q
       489: q^2+2q+1
       490: q^2+q
       491: q^2+4q+1
       492: 2q^2+4q+1
       493: 4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 2q^2+6q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+4q+1
       513: q+1
       514: q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       521: q+1
       529: q+1
       533: q+1
       537: 2q+1
       538: q^2+q
       539: q
       540: q
       541: q^2+3q+1
       542: q
       543: q
       544: q
       545: 2q+1
       546: q^2+q
       547: q
       548: q
       549: 1
       553: q+1
       554: q
       557: q+1
       561: q+1
       562: q
       565: 2q+1
       567: q
       569: q+1
       572: q
       573: 2q+1
       576: q
       577: q+1
       581: q
       585: 2q+1
       586: q
       589: 2q+1
       591: q+1
       593: 2q+1
       595: q^2+2q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: 3q+1
       602: q^2+2q
       603: 2q+1
       605: 2q+1
       606: q
       607: q^2+2q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: q^2+4q+1
       616: 2q
       617: 3q+1
       618: q^2+2q
       619: q+1
       621: 1
       623: 1
       625: 1
       629: 1
       631: 3q+1
       633: q+1
       634: q
       639: 2q+1
       640: q
       641: 2q+1
       643: q+1
       645: 1
       647: 2q+1
       648: q
       649: q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: 3q+1
       679: q^2+4q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       700: q
       709: q+1
       713: 1
       717: q+1
       721: q+1
       725: q+1
       733: 2q+1
       734: q^2+q
       735: q
       736: q
       737: 1
       741: 1
       749: q+1
       750: q
       753: 1
       757: q+1
       760: q
       761: q+1
       765: 2q+1
       767: q
       769: q+1
       773: q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       785: 2q+1
       787: q+1
       791: 1
       793: 2
       795: q+1
       796: q+1
       797: 2q+1
       798: q
       801: 2q+1
       803: q+1
       805: 2q+1
       807: q^2+2q+1
       809: 2q+1
       810: q
       811: 2q+1
       812: q
       815: 2q+1
       816: q
       817: 2
       819: 1
       820: 1
       821: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       839: q+1
       843: 2
       845: q+1
       847: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       891: q
       900: 1
       904: q+1
       908: 1
       916: 1
       917: 1
       920: q+1
       924: 1
       928: q+1
       940: 1
       941: 1
       944: 1
       948: 1
       960: 1
       964: 2
       968: 1
       969: 1
       974: 1
       988: q+1
       994: 1
       995: 1
       998: 2
      1000: 2
      1004: q+1
      1006: 1
      1008: 1
      1010: 1
      1012: 2
      1016: 1
      1020: q+1
      1021: q+1
      1022: 2q+1
      1023: q
      1026: 2q+1
      1028: q+1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: q+1
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1114: 1
      1115: 1
      1122: 1
      1123: 1
      1126: 1
      1130: 2
      1134: 1
      1138: 1
      1139: 1
      1152: 1
      1156: q+1
      1160: 1
      1172: 1
      1194: 1
      1198: 1
      1202: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1230: 1
      1231: 1
      1232: 2
      1234: 2
      1240: q+1
      1242: 1
      1246: 1
      1260: 1
      1262: 1
      1266: 1
      1270: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1326: 1
      1330: 1
      1348: 1
      1349: 1
      1356: 1
      1357: 1
      1360: 1
      1364: 2
      1368: 1
      1410: 1
      1418: 1
      1430: 1
      1431: 1
      1440: 1
      1442: 1
      1444: 1
      1450: 1
      1454: 1
      1474: 1
      1478: 1
      1482: 1
      1485: 1
      1488: 1
      1501: 1
      1502: 1
      1549: 1
      1575: 1
      1579: 1
      1645: 1
      1647: 1
      1669: 1
      1749: 1

1750:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 4q^3+9q^2+6q+1
        23: q^4+5q^3+9q^2+6q+1
        24: 4q^3+9q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 2q^3+7q^2+6q+1
        32: 4q^3+9q^2+6q+1
        33: 2q^3+7q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+2q
        38: 3q^2+4q+1
        39: q^3+3q^2+2q
        40: 3q^2+4q+1
        41: 3q^2+2q
        42: 3q^2+4q+1
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 4q^3+9q^2+6q+1
        53: q^4+5q^3+9q^2+6q+1
        54: 4q^3+9q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: q^3+3q^2+4q+1
        59: 2q^2+2q
        60: 2q
        61: 2q^2+4q+1
        62: 2q^2+2q
        63: 2q^2+4q+1
        64: 3q^2+2q
        65: 3q^2+4q+1
        66: 2q^2+2q
        67: 2q^2+4q+1
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 4q^2+6q+1
        73: 2q^3+7q^2+6q+1
        74: 3q^2+2q
        75: 3q^2+4q+1
        76: q^3+3q^2+2q
        77: 3q^2+4q+1
        78: 3q^2+2q
        79: 3q^2+4q+1
        80: 2q^3+7q^2+6q+1
        81: 2q^3+7q^2+6q+1
        82: 2q^3+7q^2+6q+1
        83: 4q^3+9q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^3+7q^2+6q+1
        95: 2q^3+7q^2+6q+1
        96: 3q^3+6q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q
       104: q
       105: q^2+3q+1
       106: q^2+q
       107: 2q
       108: 2q^2+4q+1
       109: q^3+3q^2+4q+1
       110: 2q^2+2q
       111: 2q^2+2q
       112: 2q^2+4q+1
       113: 2q^2+2q
       114: 2q^2+4q+1
       115: 3q^2+2q
       116: 3q^2+4q+1
       117: q^3+3q^2+4q+1
       118: 2q^2+2q
       119: 2q
       120: 2q^2+4q+1
       121: 2q^2+2q
       122: 2q^2+4q+1
       123: 2q^2+2q
       124: 2q^2+4q+1
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+6q+1
       136: 2q^3+7q^2+6q+1
       137: 3q^2+6q+1
       138: q^3+4q^2+4q+1
       139: q^3+5q^2+6q+1
       140: 4q^2+6q+1
       141: 2q^3+7q^2+6q+1
       142: 2q^3+7q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+2q
       152: 3q^2+4q+1
       153: q^3+3q^2+2q
       154: 3q^2+4q+1
       155: 3q^2+2q
       156: 3q^2+4q+1
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^3+7q^2+6q+1
       161: 2q^3+7q^2+6q+1
       162: 3q^3+6q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q
       170: q
       171: q^2+3q+1
       172: q^2+q
       173: q
       174: q
       175: q^2+3q+1
       176: q^2+q
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: 2q
       184: 2q^2+4q+1
       185: q^3+3q^2+4q+1
       186: 2q^2+2q
       187: 2q^2+2q
       188: 2q^2+4q+1
       189: 2q^2+2q
       190: 2q^2+4q+1
       191: 2q^2+4q+1
       192: q^2+2q
       193: 2q
       194: 2q^2+4q+1
       195: q^3+3q^2+4q+1
       196: 2q^2+2q
       197: 2q^2+2q
       198: 2q^2+4q+1
       199: 2q
       200: q^2+4q+1
       201: 2q
       202: q^2+4q+1
       203: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+4q+1
       209: 2q^2+2q
       210: 2q^2+4q+1
       211: 3q^2+2q
       212: 3q^2+4q+1
       213: q^2+2q
       214: 3q+1
       215: q^2+2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: 3q^2+6q+1
       225: q^3+4q^2+4q+1
       226: 2q^2+4q+1
       227: q^3+5q^2+6q+1
       228: q^3+4q^2+4q+1
       229: 4q^2+6q+1
       230: 2q^3+7q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: q^2+4q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+6q+1
       244: 2q^2+6q+1
       245: 3q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q^2+6q+1
       251: 3q^2+6q+1
       252: q^3+4q^2+4q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q
       260: q
       261: 2q+1
       262: q^2+q
       263: q
       264: q
       265: q^2+3q+1
       266: q^2+q
       267: q
       268: q
       269: q^2+q
       270: q^2+3q+1
       271: q
       272: 2q+1
       275: q
       276: q
       277: q^2+3q+1
       278: q
       279: q^2+2q
       280: 3q+1
       281: q
       282: 2q+1
       284: 2q+1
       285: q^2+2q+1
       287: q
       288: 2q+1
       289: q^2+2q
       290: 3q+1
       291: q
       292: 2q+1
       293: 2q
       294: q^2+4q+1
       295: 2q^2+4q+1
       296: q^2+2q
       297: 2q
       298: q^2+4q+1
       299: 2q
       300: 2q^2+4q+1
       301: q^2+2q
       302: 3q+1
       303: q^3+3q^2+4q+1
       304: 2q^2+2q
       305: 2q^2+2q
       306: 2q^2+4q+1
       307: 2q
       308: q^2+4q+1
       309: 3q+1
       311: q
       312: q+1
       313: q
       314: 2q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: 2q
       320: q^2+4q+1
       321: 3q+1
       323: q
       324: 2q+1
       325: 2q^2+2q
       326: 2q^2+4q+1
       333: 2q^2+4q+1
       334: 4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 2q^2+4q+1
       345: 3q^2+6q+1
       346: 2q^2+4q+1
       347: q^2+6q+1
       348: q^2+4q+1
       349: 3q^2+6q+1
       350: q^3+4q^2+4q+1
       351: 2q^2+6q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: q^2+2q
       361: 3q+1
       362: q^2+2q
       363: 3q+1
       364: q^2+q
       365: q^2+2q+1
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 2q^2+6q+1
       370: 3q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: q+1
       381: q
       382: q
       383: 2q+1
       384: q^2+q
       385: q
       386: q
       387: q^2+3q+1
       388: q
       389: q
       390: q
       391: q^2+q
       392: 2q+1
       393: q
       394: q
       395: q^2+3q+1
       396: q^2+q
       397: q
       398: q+1
       401: q
       402: 2q+1
       405: q
       408: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       420: 2q+1
       421: q^2+2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       430: 2q+1
       431: q^2+2q+1
       433: q
       434: 2q+1
       435: q^2+2q
       436: 3q+1
       437: 2q
       438: q^2+4q+1
       439: 2q^2+4q+1
       440: q^2+2q
       441: 2q
       442: q^2+4q+1
       443: 2q
       444: q^2+4q+1
       445: q^2+2q
       446: 3q+1
       448: 2q+1
       449: q+1
       452: 1
       453: q
       454: 2q+1
       455: q
       456: q+1
       457: q+1
       460: q+1
       461: 3q+1
       463: q
       464: q+1
       465: q^2+2q
       466: 3q+1
       467: q
       468: 2q+1
       469: q
       470: 2q+1
       471: 2q
       472: q^2+4q+1
       473: 3q+1
       475: q
       476: 2q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: q^2+6q+1
       485: q^2+2q
       486: 3q+1
       487: q^2+2q
       488: 3q+1
       489: q^2+q
       490: q^2+2q+1
       491: q^2+4q+1
       492: 2q^2+4q+1
       493: 4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 2q^2+6q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+4q+1
       513: q+1
       514: q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       523: q+1
       531: q+1
       535: q+1
       537: q
       538: q
       539: q^2+q
       540: 2q+1
       541: q
       542: q
       543: q
       544: q^2+3q+1
       545: q
       546: q
       547: q^2+q
       548: 2q+1
       550: 1
       553: q
       554: q+1
       558: q+1
       561: q
       562: q+1
       565: q
       567: 2q+1
       569: q
       572: q+1
       573: q
       576: 2q+1
       577: q
       581: q+1
       585: q
       586: 2q+1
       590: 2q+1
       591: q+1
       594: 2q+1
       595: q^2+2q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+2q
       602: 3q+1
       604: 2q+1
       605: q
       606: 2q+1
       607: q^2+2q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: 2q
       616: q^2+4q+1
       617: q^2+2q
       618: 3q+1
       620: q+1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 3q+1
       633: q
       634: q+1
       639: q
       640: 2q+1
       642: 2q+1
       643: q+1
       646: 1
       647: q
       648: 2q+1
       649: q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: 3q+1
       679: q^2+4q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       700: q+1
       711: q+1
       714: 1
       719: q+1
       724: q+1
       728: q+1
       733: q
       734: q
       735: q^2+q
       736: 2q+1
       738: 1
       742: 1
       749: q
       750: q+1
       755: 1
       757: q
       760: q+1
       764: q+1
       765: q
       767: 2q+1
       769: q
       773: q+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       786: 2q+1
       787: q+1
       792: 1
       794: 2
       795: q+1
       796: q+1
       797: q
       798: 2q+1
       802: 2q+1
       803: q+1
       806: 2q+1
       807: q^2+2q+1
       809: q
       810: 2q+1
       811: q
       812: 2q+1
       815: q
       816: 2q+1
       817: 2
       819: 1
       820: 1
       822: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       839: q+1
       844: 2
       846: q+1
       847: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       891: q+1
       901: 1
       907: q+1
       910: 1
       918: 1
       919: 1
       923: q+1
       925: 1
       931: q+1
       940: 1
       941: 1
       945: 1
       949: 1
       963: 1
       966: 2
       971: 1
       972: 1
       977: 1
       990: q+1
       994: 1
       995: 1
       998: 2
      1001: 2
      1005: q+1
      1006: 1
      1009: 1
      1011: 1
      1013: 2
      1017: 1
      1020: q+1
      1021: q+1
      1022: q
      1023: 2q+1
      1027: 2q+1
      1028: q+1
      1032: 1
      1036: 1
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1053: q+1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1124: 1
      1125: 1
      1129: 1
      1132: 2
      1137: 1
      1141: 1
      1142: 1
      1153: 1
      1159: q+1
      1161: 1
      1173: 1
      1196: 1
      1201: 1
      1203: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 2
      1235: 2
      1241: q+1
      1242: 1
      1246: 1
      1260: 1
      1263: 1
      1267: 1
      1270: 1
      1274: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1294: 1
      1297: 1
      1328: 1
      1333: 1
      1348: 1
      1349: 1
      1358: 1
      1359: 1
      1362: 1
      1365: 2
      1370: 1
      1412: 1
      1419: 1
      1433: 1
      1434: 1
      1440: 1
      1443: 1
      1445: 1
      1450: 1
      1455: 1
      1475: 1
      1478: 1
      1483: 1
      1485: 1
      1488: 1
      1504: 1
      1507: 1
      1551: 1
      1576: 1
      1581: 1
      1645: 1
      1648: 1
      1670: 1
      1750: 1

1751:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 4q^3+9q^2+6q+1
        23: q^4+5q^3+9q^2+6q+1
        24: 4q^3+9q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 2q^3+7q^2+6q+1
        32: 4q^3+9q^2+6q+1
        33: 2q^3+7q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+2q
        38: 3q^2+4q+1
        39: q^3+3q^2+2q
        40: 3q^2+4q+1
        41: 3q^2+2q
        42: 3q^2+4q+1
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 4q^3+9q^2+6q+1
        53: q^4+5q^3+9q^2+6q+1
        54: 4q^3+9q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q^2+2q
        59: q^3+3q^2+4q+1
        60: 2q^2+4q+1
        61: 2q
        62: 2q^2+2q
        63: 2q^2+4q+1
        64: 3q^2+2q
        65: 3q^2+4q+1
        66: 2q^2+2q
        67: 2q^2+4q+1
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 4q^2+6q+1
        73: 2q^3+7q^2+6q+1
        74: 3q^2+2q
        75: 3q^2+4q+1
        76: q^3+3q^2+2q
        77: 3q^2+4q+1
        78: 3q^2+2q
        79: 3q^2+4q+1
        80: 2q^3+7q^2+6q+1
        81: 2q^3+7q^2+6q+1
        82: 2q^3+7q^2+6q+1
        83: 4q^3+9q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^3+7q^2+6q+1
        95: 2q^3+7q^2+6q+1
        96: 3q^3+6q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q^2+q
       104: q^2+3q+1
       105: q
       106: q
       107: 2q^2+4q+1
       108: 2q
       109: 2q^2+2q
       110: q^3+3q^2+4q+1
       111: 2q^2+2q
       112: 2q^2+4q+1
       113: 2q^2+2q
       114: 2q^2+4q+1
       115: 3q^2+2q
       116: 3q^2+4q+1
       117: 2q^2+2q
       118: q^3+3q^2+4q+1
       119: 2q^2+4q+1
       120: 2q
       121: 2q^2+2q
       122: 2q^2+4q+1
       123: 2q^2+2q
       124: 2q^2+4q+1
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+6q+1
       136: 2q^3+7q^2+6q+1
       137: 3q^2+6q+1
       138: q^3+4q^2+4q+1
       139: q^3+5q^2+6q+1
       140: 4q^2+6q+1
       141: 2q^3+7q^2+6q+1
       142: 2q^3+7q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+2q
       152: 3q^2+4q+1
       153: q^3+3q^2+2q
       154: 3q^2+4q+1
       155: 3q^2+2q
       156: 3q^2+4q+1
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^3+7q^2+6q+1
       161: 2q^3+7q^2+6q+1
       162: 3q^3+6q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q^2+q
       170: q^2+3q+1
       171: q
       172: q
       173: q^2+q
       174: q^2+3q+1
       175: q
       176: q
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: 2q^2+4q+1
       184: 2q
       185: 2q^2+2q
       186: q^3+3q^2+4q+1
       187: 2q^2+2q
       188: 2q^2+4q+1
       189: 2q^2+2q
       190: 2q^2+4q+1
       191: q^2+2q
       192: 2q^2+4q+1
       193: 2q^2+4q+1
       194: 2q
       195: 2q^2+2q
       196: q^3+3q^2+4q+1
       197: 2q^2+2q
       198: 2q^2+4q+1
       199: q^2+4q+1
       200: 2q
       201: q^2+4q+1
       202: 2q
       204: 3q+1
       205: q
       206: 2q+1
       207: 2q
       208: q^2+4q+1
       209: 2q^2+2q
       210: 2q^2+4q+1
       211: 3q^2+2q
       212: 3q^2+4q+1
       213: q^2+2q
       214: 3q+1
       215: q^2+2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: 3q^2+6q+1
       225: q^3+4q^2+4q+1
       226: 2q^2+4q+1
       227: q^3+5q^2+6q+1
       228: q^3+4q^2+4q+1
       229: 4q^2+6q+1
       230: 2q^3+7q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: q^2+4q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+6q+1
       244: 2q^2+6q+1
       245: 3q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q^2+6q+1
       251: 3q^2+6q+1
       252: q^3+4q^2+4q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q^2+q
       260: 2q+1
       261: q
       262: q
       263: q^2+q
       264: q^2+3q+1
       265: q
       266: q
       267: q^2+q
       268: q^2+3q+1
       269: q
       270: q
       273: q
       274: 2q+1
       275: q
       276: q^2+3q+1
       277: q
       278: q
       279: q^2+2q
       280: 3q+1
       281: q
       282: 2q+1
       283: 2q+1
       286: q^2+2q+1
       287: q
       288: 2q+1
       289: q^2+2q
       290: 3q+1
       291: q
       292: 2q+1
       293: q^2+4q+1
       294: 2q
       295: q^2+2q
       296: 2q^2+4q+1
       297: 2q
       298: q^2+4q+1
       299: 2q^2+4q+1
       300: 2q
       301: q^2+2q
       302: 3q+1
       303: 2q^2+2q
       304: q^3+3q^2+4q+1
       305: 2q^2+2q
       306: 2q^2+4q+1
       307: q^2+4q+1
       308: 2q
       310: 3q+1
       311: q
       312: q+1
       313: q
       314: 2q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: q^2+4q+1
       320: 2q
       322: 3q+1
       323: q
       324: 2q+1
       325: 2q^2+2q
       326: 2q^2+4q+1
       333: 2q^2+4q+1
       334: 4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 2q^2+4q+1
       345: 3q^2+6q+1
       346: 2q^2+4q+1
       347: q^2+6q+1
       348: q^2+4q+1
       349: 3q^2+6q+1
       350: q^3+4q^2+4q+1
       351: 2q^2+6q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: q^2+2q
       361: 3q+1
       362: q^2+2q
       363: 3q+1
       364: q^2+q
       365: q^2+2q+1
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 2q^2+6q+1
       370: 3q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: q+1
       381: q^2+q
       382: 2q+1
       383: q
       384: q
       385: q
       386: q^2+3q+1
       387: q
       388: q
       389: q^2+q
       390: 2q+1
       391: q
       392: q
       393: q^2+q
       394: q^2+3q+1
       395: q
       396: q
       399: q
       400: q+1
       403: 2q+1
       404: q
       406: q
       407: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       419: 2q+1
       422: q^2+2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       429: 2q+1
       432: q^2+2q+1
       433: q
       434: 2q+1
       435: q^2+2q
       436: 3q+1
       437: q^2+4q+1
       438: 2q
       439: q^2+2q
       440: 2q^2+4q+1
       441: 2q
       442: q^2+4q+1
       443: q^2+4q+1
       444: 2q
       445: q^2+2q
       446: 3q+1
       447: 2q+1
       450: q+1
       452: 1
       453: 2q+1
       454: q
       455: q
       456: q+1
       458: q+1
       460: q+1
       462: 3q+1
       463: q
       464: q+1
       465: q^2+2q
       466: 3q+1
       467: q
       468: 2q+1
       469: q
       470: 2q+1
       471: q^2+4q+1
       472: 2q
       474: 3q+1
       475: q
       476: 2q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: q^2+6q+1
       485: q^2+2q
       486: 3q+1
       487: q^2+2q
       488: 3q+1
       489: q^2+q
       490: q^2+2q+1
       491: q^2+4q+1
       492: 2q^2+4q+1
       493: 4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 2q^2+6q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+4q+1
       513: q+1
       514: q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       522: q+1
       530: q+1
       534: q+1
       537: q^2+q
       538: 2q+1
       539: q
       540: q
       541: q
       542: q^2+3q+1
       543: q
       544: q
       545: q^2+q
       546: 2q+1
       547: q
       548: q
       551: 1
       555: q
       556: q+1
       560: q+1
       563: q
       564: q+1
       566: 2q+1
       568: q
       570: q
       571: q+1
       574: 2q+1
       575: q
       577: q
       581: q+1
       585: q
       586: 2q+1
       589: 2q+1
       592: q+1
       593: 2q+1
       596: q^2+2q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+2q
       602: 3q+1
       603: 2q+1
       605: q
       606: 2q+1
       608: q^2+2q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: q^2+4q+1
       616: 2q
       617: q^2+2q
       618: 3q+1
       619: q+1
       622: 1
       624: 1
       626: 1
       630: 1
       632: 3q+1
       633: q
       634: q+1
       639: q
       640: 2q+1
       641: 2q+1
       644: q+1
       646: 1
       647: 2q+1
       648: q
       650: q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: 3q+1
       679: q^2+4q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       699: q+1
       710: q+1
       715: 1
       718: q+1
       722: q+1
       726: q+1
       733: q^2+q
       734: 2q+1
       735: q
       736: q
       740: 1
       744: 1
       751: q
       752: q+1
       754: 1
       758: q
       759: q+1
       763: q+1
       766: 2q+1
       768: q
       769: q
       773: q+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       785: 2q+1
       788: q+1
       792: 1
       793: 2
       795: q+1
       796: q+1
       797: q
       798: 2q+1
       801: 2q+1
       804: q+1
       805: 2q+1
       808: q^2+2q+1
       809: q
       810: 2q+1
       811: q
       812: 2q+1
       815: 2q+1
       816: q
       818: 2
       819: 1
       820: 1
       822: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       840: q+1
       844: 2
       845: q+1
       848: 1
       850: 1
       852: 1
       856: 1
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q
       890: q+1
       903: 1
       905: q+1
       909: 1
       916: 1
       917: 1
       921: q+1
       926: 1
       929: q+1
       942: 1
       943: 1
       947: 1
       951: 1
       962: 1
       965: 2
       971: 1
       972: 1
       976: 1
       989: q+1
       994: 1
       995: 1
       999: 2
      1000: 2
      1004: q+1
      1007: 1
      1009: 1
      1011: 1
      1013: 2
      1016: 1
      1020: q+1
      1021: q+1
      1022: q
      1023: 2q+1
      1026: 2q+1
      1029: q+1
      1033: 1
      1036: 1
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: q+1
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1089: 1
      1092: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1128: 1
      1131: 2
      1136: 1
      1141: 1
      1142: 1
      1155: 1
      1157: q+1
      1162: 1
      1175: 1
      1195: 1
      1200: 1
      1205: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1230: 1
      1231: 1
      1233: 2
      1234: 2
      1240: q+1
      1243: 1
      1247: 1
      1261: 1
      1263: 1
      1267: 1
      1271: 1
      1274: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1293: 1
      1296: 1
      1327: 1
      1332: 1
      1350: 1
      1351: 1
      1356: 1
      1357: 1
      1363: 1
      1366: 2
      1371: 1
      1411: 1
      1421: 1
      1433: 1
      1434: 1
      1441: 1
      1442: 1
      1445: 1
      1451: 1
      1454: 1
      1475: 1
      1479: 1
      1483: 1
      1485: 1
      1488: 1
      1505: 1
      1508: 1
      1550: 1
      1577: 1
      1582: 1
      1646: 1
      1647: 1
      1670: 1
      1751: 1

1752:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 4q^3+9q^2+6q+1
        23: q^4+5q^3+9q^2+6q+1
        24: 4q^3+9q^2+6q+1
        25: 6q^2+6q+1
        26: q^3+6q^2+6q+1
        27: 6q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 2q^3+7q^2+6q+1
        32: 4q^3+9q^2+6q+1
        33: 2q^3+7q^2+6q+1
        34: 4q^2+6q+1
        35: 6q^2+6q+1
        36: 4q^2+6q+1
        37: 3q^2+4q+1
        38: 3q^2+2q
        39: 3q^2+4q+1
        40: q^3+3q^2+2q
        41: 3q^2+4q+1
        42: 3q^2+2q
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 4q^3+9q^2+6q+1
        53: q^4+5q^3+9q^2+6q+1
        54: 4q^3+9q^2+6q+1
        55: 6q^2+6q+1
        56: q^3+6q^2+6q+1
        57: 6q^2+6q+1
        58: 2q^2+2q
        59: q^3+3q^2+4q+1
        60: 2q
        61: 2q^2+4q+1
        62: 2q^2+4q+1
        63: 2q^2+2q
        64: 3q^2+4q+1
        65: 3q^2+2q
        66: 2q^2+4q+1
        67: 2q^2+2q
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 4q^2+6q+1
        73: 2q^3+7q^2+6q+1
        74: 3q^2+4q+1
        75: 3q^2+2q
        76: 3q^2+4q+1
        77: q^3+3q^2+2q
        78: 3q^2+4q+1
        79: 3q^2+2q
        80: 2q^3+7q^2+6q+1
        81: 2q^3+7q^2+6q+1
        82: 2q^3+7q^2+6q+1
        83: 4q^3+9q^2+6q+1
        84: 4q^2+6q+1
        85: 4q^2+6q+1
        86: 4q^2+6q+1
        87: 6q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^3+7q^2+6q+1
        95: 2q^3+7q^2+6q+1
        96: 3q^3+6q^2+4q+1
        97: 2q^2+6q+1
        98: 2q^2+6q+1
        99: 3q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q
       104: q
       105: q^2+q
       106: q^2+3q+1
       107: 2q
       108: 2q^2+4q+1
       109: 2q^2+2q
       110: q^3+3q^2+4q+1
       111: 2q^2+4q+1
       112: 2q^2+2q
       113: 2q^2+4q+1
       114: 2q^2+2q
       115: 3q^2+4q+1
       116: 3q^2+2q
       117: 2q^2+2q
       118: q^3+3q^2+4q+1
       119: 2q
       120: 2q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+2q
       123: 2q^2+4q+1
       124: 2q^2+2q
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+6q+1
       136: 2q^3+7q^2+6q+1
       137: 3q^2+6q+1
       138: q^3+4q^2+4q+1
       139: q^3+5q^2+6q+1
       140: 4q^2+6q+1
       141: 2q^3+7q^2+6q+1
       142: 2q^3+7q^2+6q+1
       143: q^2+6q+1
       144: q^2+4q+1
       145: q^2+6q+1
       146: 4q^2+6q+1
       147: 2q^2+6q+1
       148: 3q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+4q+1
       152: 3q^2+2q
       153: 3q^2+4q+1
       154: q^3+3q^2+2q
       155: 3q^2+4q+1
       156: 3q^2+2q
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^3+7q^2+6q+1
       161: 2q^3+7q^2+6q+1
       162: 3q^3+6q^2+4q+1
       163: 2q^2+6q+1
       164: 2q^2+6q+1
       165: 3q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q
       170: q
       171: q^2+q
       172: q^2+3q+1
       173: q
       174: q
       175: q^2+q
       176: q^2+3q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: 2q
       184: 2q^2+4q+1
       185: 2q^2+2q
       186: q^3+3q^2+4q+1
       187: 2q^2+4q+1
       188: 2q^2+2q
       189: 2q^2+4q+1
       190: 2q^2+2q
       191: q^2+2q
       192: 2q^2+4q+1
       193: 2q
       194: 2q^2+4q+1
       195: 2q^2+2q
       196: q^3+3q^2+4q+1
       197: 2q^2+4q+1
       198: 2q^2+2q
       199: 2q
       200: q^2+4q+1
       201: 2q
       202: q^2+4q+1
       204: 3q+1
       205: 2q+1
       206: q
       207: q^2+4q+1
       208: 2q
       209: 2q^2+4q+1
       210: 2q^2+2q
       211: 3q^2+4q+1
       212: 3q^2+2q
       213: 3q+1
       214: q^2+2q
       215: 3q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+q
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: q^2+6q+1
       223: q^2+4q+1
       224: 3q^2+6q+1
       225: q^3+4q^2+4q+1
       226: 2q^2+4q+1
       227: q^3+5q^2+6q+1
       228: q^3+4q^2+4q+1
       229: 4q^2+6q+1
       230: 2q^3+7q^2+6q+1
       231: 4q+1
       232: q^2+6q+1
       233: q^2+4q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: q^2+4q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+6q+1
       244: 2q^2+6q+1
       245: 3q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q^2+6q+1
       251: 3q^2+6q+1
       252: q^3+4q^2+4q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q
       260: q
       261: q^2+q
       262: 2q+1
       263: q
       264: q
       265: q^2+q
       266: q^2+3q+1
       267: q
       268: q
       269: q^2+3q+1
       270: q^2+q
       273: 2q+1
       274: q
       275: q
       276: q
       277: q
       278: q^2+3q+1
       279: 3q+1
       280: q^2+2q
       281: 2q+1
       282: q
       284: 2q+1
       286: q^2+2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: q^2+2q
       291: 2q+1
       292: q
       293: 2q
       294: q^2+4q+1
       295: q^2+2q
       296: 2q^2+4q+1
       297: q^2+4q+1
       298: 2q
       299: 2q
       300: 2q^2+4q+1
       301: 3q+1
       302: q^2+2q
       303: 2q^2+2q
       304: q^3+3q^2+4q+1
       305: 2q^2+4q+1
       306: 2q^2+2q
       307: 2q
       308: q^2+4q+1
       310: 3q+1
       311: q+1
       312: q
       313: 2q+1
       314: q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: 2q
       320: q^2+4q+1
       322: 3q+1
       323: 2q+1
       324: q
       325: 2q^2+4q+1
       326: 2q^2+2q
       333: 2q^2+4q+1
       334: 4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 2q^2+4q+1
       345: 3q^2+6q+1
       346: 2q^2+4q+1
       347: q^2+6q+1
       348: q^2+4q+1
       349: 3q^2+6q+1
       350: q^3+4q^2+4q+1
       351: 2q^2+6q+1
       352: 4q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+4q+1
       357: q+1
       358: q+1
       359: 3q+1
       360: 3q+1
       361: q^2+2q
       362: 3q+1
       363: q^2+2q
       364: q^2+2q+1
       365: q^2+q
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 2q^2+6q+1
       370: 3q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: q+1
       381: q
       382: q
       383: q^2+q
       384: 2q+1
       385: q
       386: q
       387: q
       388: q^2+3q+1
       389: q
       390: q
       391: 2q+1
       392: q^2+q
       393: q
       394: q
       395: q^2+q
       396: q^2+3q+1
       399: q+1
       400: q
       403: q
       404: 2q+1
       406: 2q+1
       407: q
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       420: 2q+1
       422: q^2+2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       430: 2q+1
       432: q^2+2q+1
       433: 2q+1
       434: q
       435: 3q+1
       436: q^2+2q
       437: 2q
       438: q^2+4q+1
       439: q^2+2q
       440: 2q^2+4q+1
       441: q^2+4q+1
       442: 2q
       443: 2q
       444: q^2+4q+1
       445: 3q+1
       446: q^2+2q
       448: 2q+1
       450: q+1
       451: 1
       453: q
       454: 2q+1
       455: q+1
       456: q
       458: q+1
       459: q+1
       462: 3q+1
       463: q+1
       464: q
       465: 3q+1
       466: q^2+2q
       467: 2q+1
       468: q
       469: 2q+1
       470: q
       471: 2q
       472: q^2+4q+1
       474: 3q+1
       475: 2q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: q^2+6q+1
       485: 3q+1
       486: q^2+2q
       487: 3q+1
       488: q^2+2q
       489: q^2+2q+1
       490: q^2+q
       491: q^2+4q+1
       492: 2q^2+4q+1
       493: 4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 2q^2+6q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: q+1
       501: 3q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+4q+1
       513: q+1
       514: q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       524: q+1
       532: q+1
       536: q+1
       537: q
       538: q
       539: 2q+1
       540: q^2+q
       541: q
       542: q
       543: q^2+3q+1
       544: q
       545: q
       546: q
       547: 2q+1
       548: q^2+q
       552: 1
       555: q+1
       556: q
       559: q+1
       563: q+1
       564: q
       566: q
       568: 2q+1
       570: q+1
       571: q
       574: q
       575: 2q+1
       577: q+1
       581: q
       585: 2q+1
       586: q
       590: 2q+1
       592: q+1
       594: 2q+1
       596: q^2+2q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: 3q+1
       602: q^2+2q
       604: 2q+1
       605: 2q+1
       606: q
       608: q^2+2q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: 2q
       616: q^2+4q+1
       617: 3q+1
       618: q^2+2q
       620: q+1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 3q+1
       633: q+1
       634: q
       639: 2q+1
       640: q
       642: 2q+1
       644: q+1
       645: 1
       647: q
       648: 2q+1
       650: q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: 3q+1
       679: q^2+4q+1
       680: 2
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       699: q
       712: q+1
       716: 1
       720: q+1
       723: q+1
       727: q+1
       733: q
       734: q
       735: 2q+1
       736: q^2+q
       739: 1
       743: 1
       751: q+1
       752: q
       756: 1
       758: q+1
       759: q
       762: q+1
       766: q
       768: 2q+1
       769: q+1
       773: q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       786: 2q+1
       788: q+1
       791: 1
       794: 2
       795: q+1
       796: q+1
       797: 2q+1
       798: q
       802: 2q+1
       804: q+1
       806: 2q+1
       808: q^2+2q+1
       809: 2q+1
       810: q
       811: 2q+1
       812: q
       815: q
       816: 2q+1
       818: 2
       819: 1
       820: 1
       821: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       840: q+1
       843: 2
       846: q+1
       848: 1
       849: 1
       851: 1
       855: 1
       857: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 1
       874: 2
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q+1
       890: q
       902: 1
       906: q+1
       911: 1
       918: 1
       919: 1
       922: q+1
       927: 1
       930: q+1
       942: 1
       943: 1
       946: 1
       950: 1
       961: 1
       967: 2
       968: 1
       969: 1
       975: 1
       991: q+1
       994: 1
       995: 1
       999: 2
      1001: 2
      1005: q+1
      1007: 1
      1008: 1
      1010: 1
      1012: 2
      1017: 1
      1020: q+1
      1021: q+1
      1022: 2q+1
      1023: q
      1027: 2q+1
      1029: q+1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1053: q+1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1091: 1
      1094: 1
      1116: 1
      1117: 1
      1124: 1
      1125: 1
      1127: 1
      1133: 2
      1135: 1
      1138: 1
      1139: 1
      1154: 1
      1158: q+1
      1163: 1
      1174: 1
      1197: 1
      1199: 1
      1204: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1230: 1
      1231: 1
      1233: 2
      1235: 2
      1241: q+1
      1243: 1
      1247: 1
      1261: 1
      1262: 1
      1266: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1295: 1
      1298: 1
      1329: 1
      1331: 1
      1350: 1
      1351: 1
      1358: 1
      1359: 1
      1361: 1
      1367: 2
      1369: 1
      1413: 1
      1420: 1
      1430: 1
      1431: 1
      1441: 1
      1443: 1
      1444: 1
      1451: 1
      1455: 1
      1474: 1
      1479: 1
      1482: 1
      1485: 1
      1488: 1
      1506: 1
      1509: 1
      1552: 1
      1578: 1
      1580: 1
      1646: 1
      1648: 1
      1669: 1
      1752: 1

1753:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 2q^3+3q^2+2q+1
        23: 2q^3+3q^2+2q+1
        24: 2q^3+3q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: 2q^3+3q^2+2q+1
        32: 2q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^2+2q+1
        37: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+2q+1
        53: 2q^3+3q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 2q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: q^3+2q^2+2q+1
        64: q^3+2q^2+2q+1
        66: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^3+2q^2+2q+1
        76: q^3+2q^2+2q+1
        78: q^3+2q^2+2q+1
        80: 2q^3+3q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^3+3q^2+2q+1
        83: 2q^3+3q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+2q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+q+1
       106: q
       107: q^2+q+1
       108: q
       109: 2q^2+q+1
       110: q
       111: q^2+2q+1
       113: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       117: 2q^2+q+1
       118: q
       119: q^2+q+1
       120: q
       121: q^3+2q^2+2q+1
       123: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q^3+2q^2+2q+1
       147: 2q+1
       148: q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       151: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+2q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       169: q^2+q+1
       172: q
       173: q^2+q+1
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q^2+q+1
       184: q
       185: 2q^2+q+1
       186: q
       187: q^2+2q+1
       189: q^3+2q^2+2q+1
       191: 2q^2+q+1
       192: q
       193: q^2+q+1
       194: q
       195: 2q^2+q+1
       196: q
       197: q^2+2q+1
       199: q^2+q+1
       200: q
       201: q+1
       202: q
       203: q+1
       205: q+1
       207: q^2+2q+1
       209: q^3+2q^2+2q+1
       211: q^3+2q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: q^2+2q+1
       223: q+1
       224: 2q^2+2q+1
       225: q^2+q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q^2+q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 2q+1
       244: 2q+1
       245: q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+2q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       259: q+1
       262: q
       263: q^2+q+1
       266: q
       267: q^2+q+1
       269: q
       271: q+1
       275: q^2+q+1
       278: q
       279: 2q+1
       281: q+1
       283: 1
       285: q^2+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q^2+q+1
       294: q
       295: 2q^2+q+1
       296: q
       297: q^2+2q+1
       299: q^2+q+1
       300: q
       301: 2q+1
       303: 2q^2+q+1
       304: q
       305: q^2+2q+1
       307: q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       319: q+1
       320: q
       321: q+1
       323: q+1
       325: q^3+2q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^2+q+1
       345: 2q^2+2q+1
       346: q^2+q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+2q+1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: q+1
       384: q
       385: q^2+q+1
       388: q
       389: q+1
       391: q
       393: q^2+q+1
       396: q
       397: q+1
       401: q+1
       405: q+1
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: 1
       421: q^2+1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       431: q^2+1
       433: q+1
       435: 2q+1
       437: q^2+q+1
       438: q
       439: 2q^2+q+1
       440: q
       441: q^2+2q+1
       443: q+1
       444: q
       445: 2q+1
       447: 1
       449: 1
       451: 1
       453: q+1
       454: q
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q+1
       472: q
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: 2q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 1
       525: q+1
       528: q
       529: 1
       533: 1
       537: q+1
       539: q
       541: q^2+q+1
       543: q
       545: q+1
       547: q
       549: 1
       553: q+1
       557: q+1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: 1
       591: 1
       593: 1
       595: q^2+1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: q+1
       607: q^2+1
       609: q+1
       611: 2q+1
       613: q+1
       615: q+1
       616: q
       617: 2q+1
       619: 1
       621: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: q+1
       648: q
       649: q+1
       651: q+1
       653: q+1
       655: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       693: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q+1
       731: q
       733: q+1
       735: q
       737: 1
       741: 1
       745: q+1
       749: q+1
       753: 1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       777: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       797: q+1
       799: q+1
       801: 1
       803: 1
       805: 1
       807: q^2+1
       809: q+1
       811: q+1
       813: 2q+1
       815: q+1
       816: q
       821: 1
       823: 1
       825: 1
       827: 1
       831: 1
       833: 1
       835: 1
       837: q+1
       839: q+1
       841: q+1
       845: 1
       847: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       868: q+1
       871: q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       920: 1
       924: 1
       928: 1
       932: q+1
       934: q
       936: 1
       944: 1
       948: 1
       956: q+1
       960: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: q+1
      1022: q+1
      1024: q+1
      1026: 1
      1028: 1
      1034: 1
      1038: 1
      1042: 1
      1044: 1
      1048: 1
      1050: 1
      1052: 1
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1098: q+1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1168: 1
      1172: 1
      1184: 1
      1198: 1
      1202: 1
      1220: 1
      1222: 1
      1238: q+1
      1240: 1
      1242: 1
      1256: 1
      1260: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1322: 1
      1330: 1
      1344: 1
      1352: 1
      1360: 1
      1368: 1
      1376: 1
      1414: 1
      1418: 1
      1446: 1
      1470: 1
      1474: 1
      1478: 1
      1480: 1
      1559: 1
      1571: 1
      1579: 1
      1603: 1
      1671: 1
      1753: 1

1754:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 2q^3+3q^2+2q+1
        23: 2q^3+3q^2+2q+1
        24: 2q^3+3q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: 2q^3+3q^2+2q+1
        32: 2q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^2+2q+1
        37: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+2q+1
        53: 2q^3+3q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q
        59: 2q^2+q+1
        60: q
        61: q^2+q+1
        62: q^3+2q^2+2q+1
        64: q^3+2q^2+2q+1
        66: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^3+2q^2+2q+1
        76: q^3+2q^2+2q+1
        78: q^3+2q^2+2q+1
        80: 2q^3+3q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^3+3q^2+2q+1
        83: 2q^3+3q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+2q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q
       106: q^2+q+1
       107: q
       108: q^2+q+1
       109: q
       110: 2q^2+q+1
       111: q^2+2q+1
       113: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       117: q
       118: 2q^2+q+1
       119: q
       120: q^2+q+1
       121: q^3+2q^2+2q+1
       123: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q^3+2q^2+2q+1
       147: 2q+1
       148: q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       151: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+2q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       169: q
       172: q^2+q+1
       173: q
       176: q^2+q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q
       184: q^2+q+1
       185: q
       186: 2q^2+q+1
       187: q^2+2q+1
       189: q^3+2q^2+2q+1
       191: q
       192: 2q^2+q+1
       193: q
       194: q^2+q+1
       195: q
       196: 2q^2+q+1
       197: q^2+2q+1
       199: q
       200: q^2+q+1
       201: q
       202: q+1
       204: q+1
       205: q+1
       207: q^2+2q+1
       209: q^3+2q^2+2q+1
       211: q^3+2q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: q^2+2q+1
       223: q+1
       224: 2q^2+2q+1
       225: q^2+q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q^2+q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 2q+1
       244: 2q+1
       245: q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+2q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       259: q
       262: q+1
       263: q
       266: q^2+q+1
       267: q
       269: q^2+q+1
       273: q+1
       275: q
       278: q^2+q+1
       279: 2q+1
       281: q+1
       284: 1
       286: q^2+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q
       294: q^2+q+1
       295: q
       296: 2q^2+q+1
       297: q^2+2q+1
       299: q
       300: q^2+q+1
       301: 2q+1
       303: q
       304: 2q^2+q+1
       305: q^2+2q+1
       307: q
       308: q+1
       310: q+1
       311: q+1
       313: q+1
       315: q+1
       317: 2q+1
       319: q
       320: q+1
       322: q+1
       323: q+1
       325: q^3+2q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^2+q+1
       345: 2q^2+2q+1
       346: q^2+q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+2q+1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       381: q
       384: q+1
       385: q
       388: q^2+q+1
       389: q
       391: q+1
       393: q
       396: q^2+q+1
       399: q+1
       404: q+1
       406: q+1
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: 1
       422: q^2+1
       423: q+1
       425: q+1
       427: 2q+1
       430: 1
       432: q^2+1
       433: q+1
       435: 2q+1
       437: q
       438: q^2+q+1
       439: q
       440: 2q^2+q+1
       441: q^2+2q+1
       443: q
       444: q+1
       445: 2q+1
       448: 1
       450: 1
       451: 1
       453: q
       454: q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q
       472: q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: 2q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: 1
       525: q
       528: q+1
       532: 1
       536: 1
       537: q
       539: q+1
       541: q
       543: q^2+q+1
       545: q
       547: q+1
       552: 1
       555: q+1
       559: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       590: 1
       592: 1
       594: 1
       596: q^2+1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: q+1
       608: q^2+1
       609: q+1
       611: 2q+1
       613: q+1
       615: q
       616: q+1
       617: 2q+1
       620: 1
       622: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       647: q
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       697: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       729: q
       731: q+1
       733: q
       735: q+1
       739: 1
       743: 1
       747: q+1
       751: q+1
       756: 1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       777: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       797: q+1
       799: q+1
       802: 1
       804: 1
       806: 1
       808: q^2+1
       809: q+1
       811: q+1
       813: 2q+1
       815: q
       816: q+1
       821: 1
       823: 1
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       837: q+1
       840: q+1
       841: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       868: q+1
       871: q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       922: 1
       927: 1
       930: 1
       932: q
       934: q+1
       938: 1
       946: 1
       950: 1
       958: q+1
       961: 1
       975: 1
       979: q+1
       982: q+1
       991: q+1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: q+1
      1022: q+1
      1024: q+1
      1027: 1
      1029: 1
      1034: 1
      1038: 1
      1042: 1
      1045: 1
      1048: 1
      1050: 1
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1102: q+1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1170: 1
      1174: 1
      1185: 1
      1199: 1
      1204: 1
      1220: 1
      1222: 1
      1238: q+1
      1241: 1
      1243: 1
      1256: 1
      1261: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1323: 1
      1331: 1
      1346: 1
      1354: 1
      1361: 1
      1369: 1
      1378: 1
      1415: 1
      1420: 1
      1446: 1
      1470: 1
      1474: 1
      1479: 1
      1480: 1
      1560: 1
      1572: 1
      1580: 1
      1605: 1
      1671: 1
      1754: 1

1755:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 2q^3+3q^2+2q+1
        23: 2q^3+3q^2+2q+1
        24: 2q^3+3q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: 2q^3+3q^2+2q+1
        32: 2q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^2+2q+1
        38: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+2q+1
        53: 2q^3+3q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 2q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        63: q^3+2q^2+2q+1
        65: q^3+2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: q^3+2q^2+2q+1
        77: q^3+2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: 2q^3+3q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^3+3q^2+2q+1
        83: 2q^3+3q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+2q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q
       105: q^2+q+1
       107: q
       108: q^2+q+1
       109: 2q^2+q+1
       110: q
       112: q^2+2q+1
       114: q^3+2q^2+2q+1
       116: q^3+2q^2+2q+1
       117: 2q^2+q+1
       118: q
       119: q
       120: q^2+q+1
       122: q^3+2q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q^3+2q^2+2q+1
       147: 2q+1
       148: q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       152: q^3+2q^2+2q+1
       154: q^3+2q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+2q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       170: q
       171: q^2+q+1
       174: q
       175: q^2+q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q
       184: q^2+q+1
       185: 2q^2+q+1
       186: q
       188: q^2+2q+1
       190: q^3+2q^2+2q+1
       191: 2q^2+q+1
       192: q
       193: q
       194: q^2+q+1
       195: 2q^2+q+1
       196: q
       198: q^2+2q+1
       199: q
       200: q^2+q+1
       201: q
       202: q+1
       203: q+1
       206: q+1
       208: q^2+2q+1
       210: q^3+2q^2+2q+1
       212: q^3+2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: q^2+2q+1
       223: q+1
       224: 2q^2+2q+1
       225: q^2+q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q^2+q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 2q+1
       244: 2q+1
       245: q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+2q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       260: q
       261: q+1
       264: q
       265: q^2+q+1
       268: q
       270: q^2+q+1
       272: q+1
       276: q
       277: q^2+q+1
       280: 2q+1
       282: q+1
       284: 1
       285: q^2+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q
       294: q^2+q+1
       295: 2q^2+q+1
       296: q
       298: q^2+2q+1
       299: q
       300: q^2+q+1
       302: 2q+1
       303: 2q^2+q+1
       304: q
       306: q^2+2q+1
       307: q
       308: q+1
       309: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       319: q
       320: q+1
       321: q+1
       324: q+1
       326: q^3+2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^2+q+1
       345: 2q^2+2q+1
       346: q^2+q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+2q+1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       382: q
       383: q+1
       386: q
       387: q^2+q+1
       390: q
       392: q+1
       394: q
       395: q^2+q+1
       398: q+1
       402: q+1
       408: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: 1
       421: q^2+1
       424: q+1
       426: q+1
       428: 2q+1
       430: 1
       431: q^2+1
       434: q+1
       436: 2q+1
       437: q
       438: q^2+q+1
       439: 2q^2+q+1
       440: q
       442: q^2+2q+1
       443: q
       444: q+1
       446: 2q+1
       448: 1
       449: 1
       452: 1
       453: q
       454: q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q
       472: q+1
       473: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: 2q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: 1
       526: q
       527: q+1
       531: 1
       535: 1
       538: q
       540: q+1
       542: q
       544: q^2+q+1
       546: q
       548: q+1
       550: 1
       554: q+1
       558: q+1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       590: 1
       591: 1
       594: 1
       595: q^2+1
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: q+1
       607: q^2+1
       610: q+1
       612: 2q+1
       614: q+1
       615: q
       616: q+1
       618: 2q+1
       620: 1
       621: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       647: q
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       656: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       700: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       730: q
       732: q+1
       734: q
       736: q+1
       738: 1
       742: 1
       746: q+1
       750: q+1
       755: 1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       778: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       798: q+1
       800: q+1
       802: 1
       803: 1
       806: 1
       807: q^2+1
       810: q+1
       812: q+1
       814: 2q+1
       815: q
       816: q+1
       822: 1
       824: 1
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       838: q+1
       839: q+1
       842: q+1
       846: 1
       847: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       868: q+1
       871: q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       923: 1
       925: 1
       931: 1
       933: q
       935: q+1
       937: 1
       945: 1
       949: 1
       957: q+1
       963: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: q+1
      1023: q+1
      1025: q+1
      1027: 1
      1028: 1
      1035: 1
      1039: 1
      1043: 1
      1044: 1
      1049: 1
      1051: 1
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1105: q+1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1169: 1
      1173: 1
      1187: 1
      1201: 1
      1203: 1
      1221: 1
      1223: 1
      1239: q+1
      1241: 1
      1242: 1
      1257: 1
      1260: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1325: 1
      1333: 1
      1345: 1
      1355: 1
      1362: 1
      1370: 1
      1377: 1
      1417: 1
      1419: 1
      1447: 1
      1471: 1
      1475: 1
      1478: 1
      1481: 1
      1562: 1
      1573: 1
      1581: 1
      1604: 1
      1672: 1
      1755: 1

1756:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 2q^3+3q^2+2q+1
        23: 2q^3+3q^2+2q+1
        24: 2q^3+3q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: 2q^3+3q^2+2q+1
        32: 2q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^2+2q+1
        38: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: 2q^3+3q^2+2q+1
        53: 2q^3+3q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q
        59: 2q^2+q+1
        60: q^2+q+1
        61: q
        63: q^3+2q^2+2q+1
        65: q^3+2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: q^3+2q^2+2q+1
        77: q^3+2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: 2q^3+3q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^3+3q^2+2q+1
        83: 2q^3+3q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^3+2q^2+q+1
        97: 2q+1
        98: 2q+1
        99: q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q^2+q+1
       105: q
       107: q^2+q+1
       108: q
       109: q
       110: 2q^2+q+1
       112: q^2+2q+1
       114: q^3+2q^2+2q+1
       116: q^3+2q^2+2q+1
       117: q
       118: 2q^2+q+1
       119: q^2+q+1
       120: q
       122: q^3+2q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q^3+2q^2+2q+1
       147: 2q+1
       148: q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       152: q^3+2q^2+2q+1
       154: q^3+2q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q^3+2q^2+q+1
       163: 2q+1
       164: 2q+1
       165: q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       170: q^2+q+1
       171: q
       174: q^2+q+1
       175: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q^2+q+1
       184: q
       185: q
       186: 2q^2+q+1
       188: q^2+2q+1
       190: q^3+2q^2+2q+1
       191: q
       192: 2q^2+q+1
       193: q^2+q+1
       194: q
       195: q
       196: 2q^2+q+1
       198: q^2+2q+1
       199: q^2+q+1
       200: q
       201: q+1
       202: q
       204: q+1
       206: q+1
       208: q^2+2q+1
       210: q^3+2q^2+2q+1
       212: q^3+2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: q^2+2q+1
       223: q+1
       224: 2q^2+2q+1
       225: q^2+q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q^2+q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 2q+1
       244: 2q+1
       245: q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: q^3+2q^2+q+1
       253: 2q+1
       254: 2q+1
       255: q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       260: q+1
       261: q
       264: q^2+q+1
       265: q
       268: q^2+q+1
       270: q
       274: q+1
       276: q^2+q+1
       277: q
       280: 2q+1
       282: q+1
       283: 1
       286: q^2+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q^2+q+1
       294: q
       295: q
       296: 2q^2+q+1
       298: q^2+2q+1
       299: q^2+q+1
       300: q
       302: 2q+1
       303: q
       304: 2q^2+q+1
       306: q^2+2q+1
       307: q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: q+1
       318: 2q+1
       319: q+1
       320: q
       322: q+1
       324: q+1
       326: q^3+2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^2+q+1
       345: 2q^2+2q+1
       346: q^2+q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+2q+1
       350: q^2+q+1
       351: 2q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: q+1
       383: q
       386: q^2+q+1
       387: q
       390: q+1
       392: q
       394: q^2+q+1
       395: q
       400: q+1
       403: q+1
       407: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: 1
       422: q^2+1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       432: q^2+1
       434: q+1
       436: 2q+1
       437: q^2+q+1
       438: q
       439: q
       440: 2q^2+q+1
       442: q^2+2q+1
       443: q+1
       444: q
       446: 2q+1
       447: 1
       450: 1
       452: 1
       453: q+1
       454: q
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q+1
       472: q
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: 2q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 1
       526: q+1
       527: q
       530: 1
       534: 1
       538: q+1
       540: q
       542: q^2+q+1
       544: q
       546: q+1
       548: q
       551: 1
       556: q+1
       560: q+1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: 1
       592: 1
       593: 1
       596: q^2+1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: q+1
       608: q^2+1
       610: q+1
       612: 2q+1
       614: q+1
       615: q+1
       616: q
       618: 2q+1
       619: 1
       622: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: q+1
       648: q
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       699: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q+1
       732: q
       734: q+1
       736: q
       740: 1
       744: 1
       748: q+1
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       778: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       798: q+1
       800: q+1
       801: 1
       804: 1
       805: 1
       808: q^2+1
       810: q+1
       812: q+1
       814: 2q+1
       815: q+1
       816: q
       822: 1
       824: 1
       825: 1
       828: 1
       832: 1
       834: 1
       836: 1
       838: q+1
       840: q+1
       842: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       868: q+1
       871: q+1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       921: 1
       926: 1
       929: 1
       933: q+1
       935: q
       939: 1
       947: 1
       951: 1
       959: q+1
       962: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: q+1
      1023: q+1
      1025: q+1
      1026: 1
      1029: 1
      1035: 1
      1039: 1
      1043: 1
      1045: 1
      1049: 1
      1051: 1
      1052: 1
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: q+1
      1082: 1
      1083: 1
      1085: 1
      1104: q+1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1171: 1
      1175: 1
      1186: 1
      1200: 1
      1205: 1
      1221: 1
      1223: 1
      1239: q+1
      1240: 1
      1243: 1
      1257: 1
      1261: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1324: 1
      1332: 1
      1347: 1
      1353: 1
      1363: 1
      1371: 1
      1379: 1
      1416: 1
      1421: 1
      1447: 1
      1471: 1
      1475: 1
      1479: 1
      1481: 1
      1561: 1
      1574: 1
      1582: 1
      1606: 1
      1672: 1
      1756: 1

1757:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q+1
        61: 2q
        62: q^2+2q+1
        63: q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q+1
       105: q
       106: q
       107: q+1
       108: 2q
       109: q^2+2q+1
       110: q
       111: q^2+2q+1
       112: q^2+q
       113: q^2+2q+1
       114: q
       115: 2q^2+2q+1
       116: q^2+q
       117: q^2+2q+1
       118: q
       119: q+1
       120: 2q
       121: q^2+2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q+1
       138: 2q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q+1
       171: q
       172: q
       173: q+1
       175: q
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q+1
       184: 2q
       185: q^2+2q+1
       186: q
       187: q^2+2q+1
       188: q^2+q
       189: q^2+2q+1
       190: q
       191: 2q+1
       192: q
       193: q+1
       194: 2q
       195: q^2+2q+1
       196: q
       197: q^2+2q+1
       198: q^2+q
       199: q+1
       200: 2q
       201: q+1
       202: 2q
       203: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: q^2+2q+1
       210: q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 3q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q+1
       262: q
       263: q+1
       265: q
       266: q
       267: q+1
       269: q
       270: q
       271: q+1
       272: q
       275: q+1
       277: q
       278: q
       279: 2q+1
       281: q+1
       283: 1
       284: q
       285: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q+1
       294: 2q
       295: 2q+1
       296: q
       297: 2q+1
       298: q
       299: q+1
       300: 2q
       301: 2q+1
       303: q^2+2q+1
       304: q
       305: q^2+2q+1
       306: q^2+q
       307: q+1
       308: 2q
       309: 2q+1
       311: q+1
       313: q+1
       314: q
       315: q+1
       317: 2q+1
       319: q+1
       320: 2q
       321: 2q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: q+1
       384: q
       385: q+1
       387: q
       388: q
       389: q+1
       391: q
       393: q+1
       395: q
       396: q
       397: q+1
       401: q+1
       402: q
       405: q+1
       408: q
       413: q+1
       417: q+1
       419: 1
       420: q
       421: q+1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       430: q
       431: q+1
       433: q+1
       435: 2q+1
       437: q+1
       438: 2q
       439: 2q+1
       440: q
       441: 2q+1
       442: q
       443: q+1
       444: 2q
       445: 2q+1
       447: 1
       448: q
       449: q+1
       451: 1
       453: 1
       454: q
       455: q+1
       457: 1
       459: 1
       461: 2q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q+1
       472: 2q
       473: 2q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       521: 1
       529: 1
       533: 1
       537: q+1
       539: q
       541: q+1
       543: q
       544: q
       545: q+1
       547: q
       549: 1
       553: q+1
       557: 1
       561: q+1
       565: q+1
       567: q
       569: q+1
       573: q+1
       576: q
       577: q+1
       585: q+1
       589: 1
       590: q
       591: q+1
       593: 1
       594: q
       595: q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       604: q
       605: q+1
       607: q+1
       609: q+1
       613: q+1
       615: q+1
       616: 2q
       617: 2q+1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       629: 1
       631: 2q+1
       633: q+1
       639: q+1
       641: 1
       642: q
       643: q+1
       645: 1
       647: 1
       648: q
       649: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q+1
       735: q
       737: 1
       741: 1
       749: q+1
       753: 1
       757: q+1
       761: 1
       765: q+1
       767: q
       769: q+1
       775: 2
       779: q+2
       781: q+1
       785: 1
       786: q
       787: q+1
       791: 1
       793: 1
       794: 1
       795: q+2
       797: q+1
       801: 1
       802: q
       803: q+1
       805: 1
       806: q
       807: q+1
       809: q+1
       811: q+1
       815: 1
       816: q
       817: 2
       819: 2
       821: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       839: 1
       843: 1
       844: 1
       845: 1
       846: q
       847: 1
       849: 1
       851: 1
       855: 1
       857: 1
       866: 2
       868: q+1
       870: q+2
       871: 2q+1
       872: q+1
       874: 2
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: 1
       918: 1
       920: 1
       924: 1
       928: 1
       940: 2
       944: 1
       948: 1
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       988: 1
       994: 2
       998: 2
      1000: 1
      1001: 1
      1004: 1
      1005: q
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1020: q+2
      1022: q+1
      1026: 1
      1027: q
      1028: q+1
      1036: 2
      1038: 1
      1044: 1
      1048: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 2
      1078: q+1
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1086: 1
      1090: 1
      1114: 2
      1122: 1
      1124: 1
      1126: 1
      1130: 1
      1132: 1
      1134: 1
      1138: 1
      1141: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1198: 1
      1202: 1
      1220: 1
      1230: 2
      1232: 2
      1234: 1
      1235: 1
      1240: 1
      1241: q
      1242: 1
      1248: 1
      1250: 1
      1260: 1
      1266: 1
      1270: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1290: 1
      1294: 1
      1330: 1
      1348: 2
      1356: 1
      1358: 1
      1360: 1
      1364: 1
      1365: 1
      1368: 1
      1380: 1
      1418: 1
      1430: 1
      1433: 1
      1464: 1
      1466: 1
      1474: 1
      1478: 1
      1484: 1
      1501: 1
      1504: 1
      1579: 1
      1607: 1
      1641: 1
      1649: 1
      1757: 1

1758:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^2+2q+1
        59: q
        60: 2q
        61: q+1
        62: q
        63: q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q
       105: q+1
       107: 2q
       108: q+1
       109: q^2+2q+1
       110: q
       111: q^2+q
       112: q^2+2q+1
       113: q
       114: q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: q^2+2q+1
       118: q
       119: 2q
       120: q+1
       121: q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q+1
       138: 2q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q
       171: q+1
       173: q
       174: q
       175: q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q
       184: q+1
       185: q^2+2q+1
       186: q
       187: q^2+q
       188: q^2+2q+1
       189: q
       190: q^2+2q+1
       191: 2q+1
       192: q
       193: 2q
       194: q+1
       195: q^2+2q+1
       196: q
       197: q^2+q
       198: q^2+2q+1
       199: 2q
       200: q+1
       201: 2q
       202: q+1
       203: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q
       210: q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 3q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q
       261: q+1
       263: q
       264: q
       265: q+1
       267: q
       268: q
       270: q+1
       271: q
       272: q+1
       275: q
       276: q
       277: q+1
       280: 2q+1
       282: q+1
       283: q
       284: 1
       285: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q
       294: q+1
       295: 2q+1
       296: q
       297: q
       298: 2q+1
       299: 2q
       300: q+1
       302: 2q+1
       303: q^2+2q+1
       304: q
       305: q^2+q
       306: q^2+2q+1
       307: 2q
       308: q+1
       309: 2q+1
       312: q+1
       313: q
       314: q+1
       316: q+1
       318: 2q+1
       319: 2q
       320: q+1
       321: 2q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       382: q
       383: q+1
       385: q
       386: q
       387: q+1
       390: q
       392: q+1
       393: q
       394: q
       395: q+1
       398: q+1
       401: q
       402: q+1
       405: q
       408: q+1
       414: q+1
       418: q+1
       419: q
       420: 1
       421: q+1
       424: q+1
       426: q+1
       428: 2q+1
       429: q
       430: 1
       431: q+1
       434: q+1
       436: 2q+1
       437: 2q
       438: q+1
       439: 2q+1
       440: q
       441: q
       442: 2q+1
       443: 2q
       444: q+1
       446: 2q+1
       447: q
       448: 1
       449: q+1
       452: 1
       453: q
       454: 1
       456: q+1
       457: 1
       460: 1
       461: 2q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 2q
       472: q+1
       473: 2q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       523: 1
       531: 1
       535: 1
       538: q
       540: q+1
       541: q
       542: q
       544: q+1
       546: q
       548: q+1
       550: 1
       554: q+1
       558: 1
       562: q+1
       565: q
       567: q+1
       572: q+1
       573: q
       576: q+1
       581: q+1
       586: q+1
       589: q
       590: 1
       591: q+1
       593: q
       594: 1
       595: q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q
       604: 1
       606: q+1
       607: q+1
       610: q+1
       614: q+1
       615: 2q
       616: q+1
       618: 2q+1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: 2q+1
       634: q+1
       640: q+1
       641: q
       642: 1
       643: q+1
       646: 1
       647: q
       648: 1
       649: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       734: q
       736: q+1
       738: 1
       742: 1
       750: q+1
       755: 1
       760: q+1
       764: 1
       765: q
       767: q+1
       773: q+1
       776: 2
       780: q+2
       782: q+1
       785: q
       786: 1
       787: q+1
       792: 1
       793: 1
       794: 1
       796: q+2
       798: q+1
       801: q
       802: 1
       803: q+1
       805: q
       806: 1
       807: q+1
       810: q+1
       812: q+1
       815: q
       816: 1
       817: 2
       820: 2
       822: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       839: 1
       843: 1
       844: 1
       845: q
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       858: 1
       866: 2
       868: q+1
       870: q+2
       871: 2q+1
       872: q+1
       874: 2
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       917: 1
       919: 1
       923: 1
       925: 1
       931: 1
       941: 2
       945: 1
       949: 1
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       990: 1
       995: 2
       998: 2
      1000: 1
      1001: 1
      1004: q
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1021: q+2
      1023: q+1
      1026: q
      1027: 1
      1028: q+1
      1037: 2
      1039: 1
      1044: 1
      1049: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 2
      1078: q+1
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1087: 1
      1093: 1
      1115: 2
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1137: 1
      1139: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1201: 1
      1203: 1
      1221: 1
      1231: 2
      1232: 2
      1234: 1
      1235: 1
      1240: q
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1260: 1
      1267: 1
      1270: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1291: 1
      1297: 1
      1333: 1
      1349: 2
      1357: 1
      1359: 1
      1362: 1
      1364: 1
      1365: 1
      1370: 1
      1381: 1
      1419: 1
      1431: 1
      1434: 1
      1465: 1
      1466: 1
      1475: 1
      1478: 1
      1484: 1
      1502: 1
      1507: 1
      1581: 1
      1608: 1
      1642: 1
      1649: 1
      1758: 1

1759:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q
        59: q^2+2q+1
        60: 2q
        61: q+1
        62: q^2+2q+1
        63: q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q
       106: q+1
       107: 2q
       108: q+1
       109: q
       110: q^2+2q+1
       111: q^2+2q+1
       112: q^2+q
       113: q^2+2q+1
       114: q
       115: 2q^2+2q+1
       116: q^2+q
       117: q
       118: q^2+2q+1
       119: 2q
       120: q+1
       121: q^2+2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q+1
       138: 2q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q
       172: q+1
       173: q
       174: q
       176: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q
       184: q+1
       185: q
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+q
       189: q^2+2q+1
       190: q
       191: q
       192: 2q+1
       193: 2q
       194: q+1
       195: q
       196: q^2+2q+1
       197: q^2+2q+1
       198: q^2+q
       199: 2q
       200: q+1
       201: 2q
       202: q+1
       204: 2q+1
       205: q+1
       206: q
       207: 2q+1
       208: q
       209: q^2+2q+1
       210: q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 3q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q
       262: q+1
       263: q
       264: q
       266: q+1
       267: q
       268: q
       269: q+1
       273: q+1
       274: q
       275: q
       276: q
       278: q+1
       279: 2q+1
       281: q+1
       283: q
       284: 1
       286: q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q
       294: q+1
       295: q
       296: 2q+1
       297: 2q+1
       298: q
       299: 2q
       300: q+1
       301: 2q+1
       303: q
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^2+q
       307: 2q
       308: q+1
       310: 2q+1
       311: q+1
       313: q+1
       314: q
       315: q+1
       317: 2q+1
       319: 2q
       320: q+1
       322: 2q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       381: q
       384: q+1
       385: q
       386: q
       388: q+1
       389: q
       391: q+1
       393: q
       394: q
       396: q+1
       399: q+1
       403: q
       404: q+1
       406: q+1
       407: q
       413: q+1
       417: q+1
       419: q
       420: 1
       422: q+1
       423: q+1
       425: q+1
       427: 2q+1
       429: q
       430: 1
       432: q+1
       433: q+1
       435: 2q+1
       437: 2q
       438: q+1
       439: q
       440: 2q+1
       441: 2q+1
       442: q
       443: 2q
       444: q+1
       445: 2q+1
       447: q
       448: 1
       450: q+1
       451: 1
       453: q
       454: 1
       455: q+1
       458: 1
       459: 1
       462: 2q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 2q
       472: q+1
       474: 2q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       524: 1
       532: 1
       536: 1
       537: q
       539: q+1
       541: q
       542: q
       543: q+1
       545: q
       547: q+1
       552: 1
       555: q+1
       559: 1
       563: q+1
       566: q
       568: q+1
       570: q+1
       574: q
       575: q+1
       577: q+1
       585: q+1
       589: q
       590: 1
       592: q+1
       593: q
       594: 1
       596: q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: q
       604: 1
       605: q+1
       608: q+1
       609: q+1
       613: q+1
       615: 2q
       616: q+1
       617: 2q+1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: 2q+1
       633: q+1
       639: q+1
       641: q
       642: 1
       644: q+1
       645: 1
       647: q
       648: 1
       650: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       733: q
       735: q+1
       739: 1
       743: 1
       751: q+1
       756: 1
       758: q+1
       762: 1
       766: q
       768: q+1
       769: q+1
       775: 2
       779: q+2
       781: q+1
       785: q
       786: 1
       788: q+1
       791: 1
       793: 1
       794: 1
       795: q+2
       797: q+1
       801: q
       802: 1
       804: q+1
       805: q
       806: 1
       808: q+1
       809: q+1
       811: q+1
       815: q
       816: 1
       818: 2
       819: 2
       821: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       840: 1
       843: 1
       844: 1
       845: q
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       857: 1
       866: 2
       868: q+1
       870: q+2
       871: 2q+1
       872: q+1
       874: 2
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       916: 1
       918: 1
       922: 1
       927: 1
       930: 1
       942: 2
       946: 1
       950: 1
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       991: 1
       994: 2
       999: 2
      1000: 1
      1001: 1
      1004: q
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1020: q+2
      1022: q+1
      1026: q
      1027: 1
      1029: q+1
      1036: 2
      1038: 1
      1045: 1
      1048: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 2
      1078: q+1
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1089: 1
      1091: 1
      1116: 2
      1122: 1
      1124: 1
      1127: 1
      1131: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1199: 1
      1204: 1
      1220: 1
      1230: 2
      1233: 2
      1234: 1
      1235: 1
      1240: q
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1261: 1
      1266: 1
      1271: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1293: 1
      1295: 1
      1331: 1
      1350: 2
      1356: 1
      1358: 1
      1361: 1
      1366: 1
      1367: 1
      1369: 1
      1382: 1
      1420: 1
      1430: 1
      1433: 1
      1464: 1
      1467: 1
      1474: 1
      1479: 1
      1484: 1
      1505: 1
      1506: 1
      1580: 1
      1609: 1
      1641: 1
      1650: 1
      1759: 1

1760:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q+1
        61: 2q
        62: q
        63: q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       104: q+1
       105: q
       106: q
       107: q+1
       108: 2q
       109: q
       110: q^2+2q+1
       111: q^2+q
       112: q^2+2q+1
       113: q
       114: q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: q
       118: q^2+2q+1
       119: q+1
       120: 2q
       121: q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q+1
       138: 2q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 3q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: 3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       170: q+1
       171: q
       172: q
       174: q+1
       175: q
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q+1
       184: 2q
       185: q
       186: q^2+2q+1
       187: q^2+q
       188: q^2+2q+1
       189: q
       190: q^2+2q+1
       191: q
       192: 2q+1
       193: q+1
       194: 2q
       195: q
       196: q^2+2q+1
       197: q^2+q
       198: q^2+2q+1
       199: q+1
       200: 2q
       201: q+1
       202: 2q
       204: 2q+1
       205: q
       206: q+1
       207: q
       208: 2q+1
       209: q
       210: q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: 2q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 3q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q+1
       261: q
       264: q+1
       265: q
       266: q
       268: q+1
       269: q
       270: q
       273: q
       274: q+1
       276: q+1
       277: q
       278: q
       280: 2q+1
       282: q+1
       283: 1
       284: q
       286: q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: q+1
       294: 2q
       295: q
       296: 2q+1
       297: q
       298: 2q+1
       299: q+1
       300: 2q
       302: 2q+1
       303: q
       304: q^2+2q+1
       305: q^2+q
       306: q^2+2q+1
       307: q+1
       308: 2q
       310: 2q+1
       312: q+1
       313: q
       314: q+1
       316: q+1
       318: 2q+1
       319: q+1
       320: 2q
       322: 2q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: q+1
       383: q
       386: q+1
       387: q
       388: q
       390: q+1
       392: q
       394: q+1
       395: q
       396: q
       400: q+1
       403: q+1
       404: q
       406: q
       407: q+1
       414: q+1
       418: q+1
       419: 1
       420: q
       422: q+1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       430: q
       432: q+1
       434: q+1
       436: 2q+1
       437: q+1
       438: 2q
       439: q
       440: 2q+1
       441: q
       442: 2q+1
       443: q+1
       444: 2q
       446: 2q+1
       447: 1
       448: q
       450: q+1
       452: 1
       453: 1
       454: q
       456: q+1
       458: 1
       460: 1
       462: 2q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q+1
       472: 2q
       474: 2q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       522: 1
       530: 1
       534: 1
       538: q+1
       540: q
       542: q+1
       543: q
       544: q
       546: q+1
       548: q
       551: 1
       556: q+1
       560: 1
       564: q+1
       566: q+1
       568: q
       571: q+1
       574: q+1
       575: q
       581: q+1
       586: q+1
       589: 1
       590: q
       592: q+1
       593: 1
       594: q
       596: q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       604: q
       606: q+1
       608: q+1
       610: q+1
       614: q+1
       615: q+1
       616: 2q
       618: 2q+1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       630: 1
       632: 2q+1
       634: q+1
       640: q+1
       641: 1
       642: q
       644: q+1
       646: 1
       647: 1
       648: q
       650: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: 2
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: q+1
       736: q
       740: 1
       744: 1
       752: q+1
       754: 1
       759: q+1
       763: 1
       766: q+1
       768: q
       773: q+1
       776: 2
       780: q+2
       782: q+1
       785: 1
       786: q
       788: q+1
       792: 1
       793: 1
       794: 1
       796: q+2
       798: q+1
       801: 1
       802: q
       804: q+1
       805: 1
       806: q
       808: q+1
       810: q+1
       812: q+1
       815: 1
       816: q
       818: 2
       820: 2
       822: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       840: 1
       843: 1
       844: 1
       845: 1
       846: q
       848: 1
       850: 1
       852: 1
       856: 1
       858: 1
       866: 2
       868: q+1
       870: q+2
       871: 2q+1
       872: q+1
       874: 2
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       917: 1
       919: 1
       921: 1
       926: 1
       929: 1
       943: 2
       947: 1
       951: 1
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       989: 1
       995: 2
       999: 2
      1000: 1
      1001: 1
      1004: 1
      1005: q
      1007: 1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1021: q+2
      1023: q+1
      1026: 1
      1027: q
      1029: q+1
      1037: 2
      1039: 1
      1045: 1
      1049: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 2
      1078: q+1
      1080: 1
      1082: 1
      1083: 1
      1084: 2
      1085: 1
      1092: 1
      1094: 1
      1117: 2
      1123: 1
      1125: 1
      1128: 1
      1131: 1
      1133: 1
      1136: 1
      1139: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1200: 1
      1205: 1
      1221: 1
      1231: 2
      1233: 2
      1234: 1
      1235: 1
      1240: 1
      1241: q
      1243: 1
      1249: 1
      1251: 1
      1261: 1
      1267: 1
      1271: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1296: 1
      1298: 1
      1332: 1
      1351: 2
      1357: 1
      1359: 1
      1363: 1
      1366: 1
      1367: 1
      1371: 1
      1383: 1
      1421: 1
      1431: 1
      1434: 1
      1465: 1
      1467: 1
      1475: 1
      1479: 1
      1484: 1
      1508: 1
      1509: 1
      1582: 1
      1610: 1
      1642: 1
      1650: 1
      1760: 1

1761:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: 1
        39: 1
        41: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        60: q^2+1
        61: q
        62: 1
        64: 1
        66: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       103: 1
       107: q^2+1
       108: q
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: q^2+1
       120: q
       121: 1
       123: 1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       129: 1
       131: 1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: q^2+1
       184: q
       185: 1
       187: 1
       189: 1
       191: 1
       195: 1
       199: q^2+1
       200: q
       201: q^2+1
       202: q
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: q^2+1
       284: q
       285: 1
       287: 1
       289: 1
       291: 1
       293: q^2+1
       294: q
       295: 1
       297: 1
       303: 1
       307: q^2+1
       308: q
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       321: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q^2+q+1
       334: q^2+q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       397: 1
       401: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q^2+1
       420: q
       421: 1
       423: 1
       425: 1
       427: 1
       431: 1
       439: 1
       447: q^2+1
       448: q
       449: 1
       451: 1
       453: q^2+1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       473: 1
       481: q^2+q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: q^2+q+1
       498: q^2+q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       549: 1
       553: 1
       557: 1
       561: 1
       583: 1
       585: 1
       587: 1
       589: q^2+1
       590: q
       591: 1
       595: 1
       597: 1
       599: 1
       601: 1
       607: 1
       619: q^2+1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       643: 1
       649: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q^2+q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       705: 1
       709: 1
       713: 1
       737: 1
       741: 1
       745: 1
       749: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 1
       807: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: q^2+1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       847: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       896: 1
       900: 1
       936: 1
       940: 1
       944: 1
       948: 1
       956: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1058: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1110: 1
      1114: 1
      1164: 1
      1168: 1
      1172: 1
      1210: 1
      1212: 1
      1214: 1
      1216: 1
      1244: 1
      1246: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1282: 1
      1285: 1
      1286: 1
      1314: 1
      1372: 1
      1376: 1
      1380: 1
      1438: 1
      1440: 1
      1456: 1
      1458: 1
      1460: 1
      1486: 1
      1541: 1
      1583: 1
      1651: 1
      1653: 1
      1761: 1

1762:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        38: 1
        40: 1
        42: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        60: q
        61: q^2+1
        63: 1
        65: 1
        67: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       105: 1
       107: q
       108: q^2+1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       119: q
       120: q^2+1
       122: 1
       124: 1
       125: q^2+q+1
       126: q^2+q+1
       128: 1
       130: 1
       132: 1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: q
       184: q^2+1
       185: 1
       188: 1
       190: 1
       191: 1
       195: 1
       199: q
       200: q^2+1
       201: q
       202: q^2+1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       272: 1
       277: 1
       280: 1
       282: 1
       283: q
       284: q^2+1
       285: 1
       288: 1
       290: 1
       292: 1
       293: q
       294: q^2+1
       295: 1
       298: 1
       303: 1
       307: q
       308: q^2+1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       321: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q^2+q+1
       334: q^2+q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       398: 1
       402: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q
       420: q^2+1
       421: 1
       424: 1
       426: 1
       428: 1
       431: 1
       439: 1
       447: q
       448: q^2+1
       449: 1
       452: 1
       453: q
       454: q^2+1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       473: 1
       481: q^2+q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: q^2+q+1
       498: q^2+q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: 1
       550: 1
       554: 1
       558: 1
       562: 1
       584: 1
       586: 1
       588: 1
       589: q
       590: q^2+1
       591: 1
       595: 1
       598: 1
       600: 1
       602: 1
       607: 1
       619: q
       620: q^2+1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       643: 1
       649: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q^2+q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       707: 1
       711: 1
       714: 1
       738: 1
       742: 1
       746: 1
       750: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 1
       807: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: q^2+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       847: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       898: 1
       901: 1
       937: 1
       941: 1
       945: 1
       949: 1
       957: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1058: 1
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1111: 1
      1115: 1
      1165: 1
      1169: 1
      1173: 1
      1211: 1
      1213: 1
      1215: 1
      1216: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1282: 1
      1285: 1
      1286: 1
      1315: 1
      1373: 1
      1377: 1
      1381: 1
      1439: 1
      1440: 1
      1457: 1
      1459: 1
      1460: 1
      1486: 1
      1542: 1
      1584: 1
      1652: 1
      1653: 1
      1762: 1

1763:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: 1
        39: 1
        41: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        60: q
        61: q^2+1
        62: 1
        64: 1
        66: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       106: 1
       107: q
       108: q^2+1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       119: q
       120: q^2+1
       121: 1
       123: 1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       129: 1
       131: 1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       183: q
       184: q^2+1
       186: 1
       187: 1
       189: 1
       192: 1
       196: 1
       199: q
       200: q^2+1
       201: q
       202: q^2+1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       273: 1
       278: 1
       279: 1
       281: 1
       283: q
       284: q^2+1
       286: 1
       287: 1
       289: 1
       291: 1
       293: q
       294: q^2+1
       296: 1
       297: 1
       304: 1
       307: q
       308: q^2+1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       322: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: q^2+q+1
       334: q^2+q+1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       399: 1
       404: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: q
       420: q^2+1
       422: 1
       423: 1
       425: 1
       427: 1
       432: 1
       440: 1
       447: q
       448: q^2+1
       450: 1
       451: 1
       453: q
       454: q^2+1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       474: 1
       481: q^2+q+1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       494: 1
       497: q^2+q+1
       498: q^2+q+1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       552: 1
       555: 1
       559: 1
       563: 1
       583: 1
       585: 1
       587: 1
       589: q
       590: q^2+1
       592: 1
       596: 1
       597: 1
       599: 1
       601: 1
       608: 1
       619: q
       620: q^2+1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       644: 1
       650: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q^2+q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       708: 1
       712: 1
       716: 1
       739: 1
       743: 1
       747: 1
       751: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 1
       808: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: q^2+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       848: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       899: 1
       902: 1
       938: 1
       942: 1
       946: 1
       950: 1
       958: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1059: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1112: 1
      1116: 1
      1166: 1
      1170: 1
      1174: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1244: 1
      1247: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1282: 1
      1285: 1
      1286: 1
      1316: 1
      1374: 1
      1378: 1
      1382: 1
      1438: 1
      1441: 1
      1456: 1
      1458: 1
      1461: 1
      1486: 1
      1543: 1
      1585: 1
      1651: 1
      1654: 1
      1763: 1

1764:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        38: 1
        40: 1
        42: 1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 1
        53: 1
        54: 1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        59: 1
        60: q^2+1
        61: q
        63: 1
        65: 1
        67: 1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: 1
       101: 1
       102: 1
       104: 1
       107: q^2+1
       108: q
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: q^2+1
       120: q
       122: 1
       124: 1
       125: q^2+q+1
       126: q^2+q+1
       128: 1
       130: 1
       132: 1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 1
       137: 1
       138: 1
       139: 1
       141: 1
       142: 1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: 1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: q^2+1
       184: q
       186: 1
       188: 1
       190: 1
       192: 1
       196: 1
       199: q^2+1
       200: q
       201: q^2+1
       202: q
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       230: 1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: q^2+1
       284: q
       286: 1
       288: 1
       290: 1
       292: 1
       293: q^2+1
       294: q
       296: 1
       298: 1
       304: 1
       307: q^2+1
       308: q
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       322: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: q^2+q+1
       334: q^2+q+1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: 1
       349: 1
       350: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       400: 1
       403: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: q^2+1
       420: q
       422: 1
       424: 1
       426: 1
       428: 1
       432: 1
       440: 1
       447: q^2+1
       448: q
       450: 1
       452: 1
       453: q^2+1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       474: 1
       481: q^2+q+1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       494: 1
       497: q^2+q+1
       498: q^2+q+1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       551: 1
       556: 1
       560: 1
       564: 1
       584: 1
       586: 1
       588: 1
       589: q^2+1
       590: q
       592: 1
       596: 1
       598: 1
       600: 1
       602: 1
       608: 1
       619: q^2+1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       644: 1
       650: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       676: 1
       680: 1
       681: q^2+q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       688: 1
       690: 1
       691: 1
       692: 1
       706: 1
       710: 1
       715: 1
       740: 1
       744: 1
       748: 1
       752: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 1
       808: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: q^2+1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       848: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       873: 1
       874: 1
       875: 1
       876: 1
       878: 1
       881: 1
       882: 1
       883: 1
       897: 1
       903: 1
       939: 1
       943: 1
       947: 1
       951: 1
       959: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1059: 1
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1113: 1
      1117: 1
      1167: 1
      1171: 1
      1175: 1
      1211: 1
      1213: 1
      1215: 1
      1217: 1
      1245: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1282: 1
      1285: 1
      1286: 1
      1317: 1
      1375: 1
      1379: 1
      1383: 1
      1439: 1
      1441: 1
      1457: 1
      1459: 1
      1461: 1
      1486: 1
      1544: 1
      1586: 1
      1652: 1
      1654: 1
      1764: 1

1765:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: 6q^3+9q^2+6q+1
        23: 6q^3+9q^2+6q+1
        24: 6q^3+9q^2+6q+1
        25: q^4+9q^3+11q^2+6q+1
        26: q^4+9q^3+11q^2+6q+1
        27: q^4+9q^3+11q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: 6q^3+9q^2+6q+1
        32: 6q^3+9q^2+6q+1
        33: 3q^3+8q^2+6q+1
        34: q^4+9q^3+11q^2+6q+1
        35: q^4+9q^3+11q^2+6q+1
        36: 5q^3+10q^2+6q+1
        37: 4q^3+7q^2+5q+1
        38: 2q^3+2q^2+q
        39: 4q^3+7q^2+5q+1
        40: 2q^3+2q^2+q
        41: 4q^3+7q^2+5q+1
        42: 2q^3+2q^2+q
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 3q^3+6q^2+5q+1
        53: 3q^3+6q^2+5q+1
        54: 3q^3+6q^2+5q+1
        55: 5q^3+8q^2+5q+1
        56: 5q^3+8q^2+5q+1
        57: 5q^3+8q^2+5q+1
        58: q^3+5q^2+3q+1
        59: 2q^3+3q^2+3q
        60: 3q^3+6q^2+4q+1
        61: 2q^3+4q^2+2q
        62: 4q^3+7q^2+5q+1
        63: 2q^3+2q^2+q
        64: 4q^3+7q^2+5q+1
        65: 2q^3+2q^2+q
        66: 2q^3+6q^2+5q+1
        67: q^3+2q^2+q
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: 4q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^3+4q^2+4q+1
        76: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        80: 6q^3+9q^2+6q+1
        81: 3q^3+8q^2+6q+1
        82: 3q^3+6q^2+5q+1
        83: 3q^3+6q^2+5q+1
        84: q^4+9q^3+11q^2+6q+1
        85: 5q^3+10q^2+6q+1
        86: 5q^3+8q^2+5q+1
        87: 5q^3+8q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 4q^2+5q+1
        95: 4q^2+5q+1
        96: q^3+3q^2+4q+1
        97: 2q^3+7q^2+5q+1
        98: 2q^3+7q^2+5q+1
        99: 3q^3+5q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+4q^2+3q+1
       104: q^3+q^2+q
       105: q^2
       106: q^3+2q^2+2q
       107: 3q^2+3q+1
       108: q^2+q
       109: 2q^2+2q+1
       110: q^3+q^2+2q
       111: q^2+3q+1
       113: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       117: q^3+5q^2+3q+1
       118: 2q^3+3q^2+3q
       119: 3q^3+6q^2+4q+1
       120: 2q^3+4q^2+2q
       121: 4q^3+7q^2+5q+1
       122: 2q^3+2q^2+q
       123: 2q^3+6q^2+5q+1
       124: q^3+2q^2+q
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 3q^3+8q^2+6q+1
       138: 2q^2+4q+1
       139: 4q^2+5q+1
       140: q^2+2q+1
       141: 3q^3+6q^2+5q+1
       142: 2q^2+4q+1
       143: 5q^3+10q^2+6q+1
       144: q^3+4q^2+4q+1
       145: 2q^3+7q^2+5q+1
       146: 5q^3+8q^2+5q+1
       147: 4q^2+4q+1
       148: q^3+3q^2+4q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       151: q^3+4q^2+4q+1
       153: q^3+4q^2+4q+1
       155: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 4q^2+5q+1
       161: 4q^2+5q+1
       162: q^3+3q^2+4q+1
       163: 2q^3+7q^2+5q+1
       164: 2q^3+7q^2+5q+1
       165: 3q^3+5q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       169: q^2+2q+1
       172: q
       173: q^3+4q^2+3q+1
       174: q^3+q^2+q
       175: q^2
       176: q^3+2q^2+2q
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: 3q^2+3q+1
       184: q^2+q
       185: 2q^2+2q+1
       186: q^3+q^2+2q
       187: q^2+3q+1
       189: q^3+4q^2+4q+1
       191: q^3+5q^2+3q+1
       192: 2q^3+3q^2+3q
       193: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q
       197: q+1
       199: 3q^3+6q^2+4q+1
       200: 2q^3+4q^2+2q
       201: 3q^2+3q+1
       202: q^2+q
       203: 2q^2+2q+1
       204: q^3+q^2+2q
       205: q^2+3q+1
       207: 2q^3+6q^2+5q+1
       208: q^3+2q^2+q
       209: q^3+4q^2+4q+1
       211: q^3+4q^2+4q+1
       213: 2q^2+4q+1
       215: 2q^2+4q+1
       217: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: 4q^2+4q+1
       223: 2q^2+3q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q^2+5q+1
       228: 2q^2+4q+1
       229: q^2+2q+1
       230: 2q^2+4q+1
       231: q^3+4q^2+4q+1
       232: 2q^3+7q^2+5q+1
       233: q^3+4q^2+4q+1
       234: 4q^2+4q+1
       235: q^3+3q^2+4q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 4q^2+5q+1
       244: q^2+2q+1
       245: 2q^2+4q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q^2+5q+1
       251: 4q^2+5q+1
       252: q^3+3q^2+4q+1
       253: 2q^3+7q^2+5q+1
       254: 2q^3+7q^2+5q+1
       255: 3q^3+5q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q+1
       271: q^2+2q+1
       273: q
       275: q^3+4q^2+3q+1
       276: q^3+q^2+q
       277: q^2
       278: q^3+2q^2+2q
       279: 2q^2+4q+1
       281: q^2+3q+1
       283: q^2+2q+1
       285: q+1
       286: q
       287: q^2+3q+1
       289: 3q+1
       291: 2q+1
       293: 3q^2+3q+1
       294: q^2+q
       295: 2q^2+2q+1
       296: q^3+q^2+2q
       297: q^2+3q+1
       299: q^2+2q+1
       301: q+1
       303: q^2+2q+1
       304: q^2+2q
       305: q+1
       307: 3q^2+3q+1
       308: q^2+q
       309: 2q^2+2q+1
       310: q^3+q^2+2q
       311: 3q+1
       313: q^2+3q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       319: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q
       323: q+1
       325: q^3+4q^2+4q+1
       327: 2q^2+4q+1
       329: 2q^2+4q+1
       331: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q^2+4q+1
       345: 4q^2+5q+1
       346: 2q^2+4q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: 2q+2
       352: q^3+4q^2+4q+1
       353: 2q^3+7q^2+5q+1
       354: q^3+4q^2+4q+1
       355: 4q^2+4q+1
       356: 2q^2+3q+1
       357: q^3+3q^2+4q+1
       358: q^2+3q+1
       359: 4q+2
       360: 2q^2+4q+1
       362: 2q^2+4q+1
       364: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: q^2+2q+1
       370: 2q^2+4q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q+1
       393: q+1
       397: 2q+1
       399: q
       401: q^2+2q+1
       404: q
       405: q+1
       409: 2q^2+4q+1
       411: q^2+3q+1
       413: q^2+3q+1
       415: 3q+1
       417: 2q+1
       419: q^2+2q+1
       421: q+1
       422: q
       423: 2q+1
       425: q+1
       427: 4q+2
       429: q+1
       431: q+1
       432: q
       433: 1
       435: q+1
       437: q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q
       441: q+1
       443: 2q+2
       445: 2q+2
       447: q^2+2q+1
       449: q+1
       450: q
       451: 2q+1
       453: 3q^2+3q+1
       454: q^2+q
       455: 3q+1
       457: 2q^2+2q+1
       458: q^3+q^2+2q
       459: q^2+3q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: 2q^2+4q+1
       467: q^2+3q+1
       469: q^2+3q+1
       471: q^2+2q+1
       473: q^2+2q+1
       474: q^2+2q
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: 2q^2+3q+1
       482: q^2+3q+1
       483: q+1
       484: 4q+2
       485: 4q+2
       487: 4q+2
       489: q^2+2q+1
       491: q+1
       492: 2q^2+4q+1
       493: q+1
       494: q^2+3q+1
       495: 1
       496: 2q+2
       497: q^3+4q^2+4q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: 4q+2
       502: 2q^2+4q+1
       504: 2q^2+4q+1
       506: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: q^2+2q+1
       512: q+1
       513: 2q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: 1
       537: q+1
       541: q+1
       545: 2q+2
       549: q+1
       553: 2q+1
       555: q
       557: q^2+2q+1
       559: q
       561: 2q+1
       563: 2q+1
       565: q+1
       569: q+1
       573: q+1
       574: q+1
       577: q+1
       580: q+1
       583: q^2+3q+1
       585: 2q+1
       587: 2q+1
       589: q^2+2q+1
       593: 1
       595: q+1
       596: q
       597: q+1
       599: q+1
       601: 4q+2
       603: q+1
       605: 1
       607: q+1
       608: q
       609: 1
       611: q+1
       613: 1
       615: 2q+2
       617: 2q+2
       619: q^2+2q+1
       621: q+1
       622: q
       623: 2q+1
       625: 2q+1
       627: 3q+1
       629: q+1
       631: 2q+1
       632: 2q+1
       633: 4q+2
       635: 2q^2+4q+1
       637: q^2+3q+1
       639: q^2+3q+1
       641: q+1
       643: q+1
       644: q
       645: 1
       647: q^2+2q+1
       649: q^2+2q+1
       650: q^2+2q
       651: q+1
       653: q+1
       655: q+1
       656: q+1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: q+1
       666: 4q+2
       668: 4q+2
       670: q^2+2q+1
       672: 4q+2
       673: q+1
       674: 2
       675: q+1
       676: q^2+3q+1
       677: 1
       678: 2q+2
       679: 1
       680: q+2
       681: 2q^2+3q+1
       682: q^2+3q+1
       683: q+1
       684: 4q+2
       685: q+1
       686: 2q^2+4q+1
       687: q+1
       688: q^2+3q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       693: q+1
       696: q+1
       705: q+1
       709: q+1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: 2q+2
       737: q+1
       741: q+1
       745: 2q+1
       747: q
       749: 2q+1
       751: 2q+1
       753: 1
       757: q+1
       761: q+1
       765: q+1
       766: q+1
       769: q+1
       772: q+1
       775: 2
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       785: 1
       789: 4q+2
       793: 2
       795: 2
       797: 1
       799: 1
       801: q+1
       805: 1
       807: q+1
       808: q
       809: 1
       811: 1
       813: 2q+2
       815: 2q+2
       817: 1
       818: 1
       819: q+2
       821: 2q+1
       823: 2q+1
       825: q^2+2q+1
       829: 1
       831: q+1
       832: q
       833: q+1
       835: q+1
       837: 4q+2
       839: 2q+1
       840: 2q+1
       841: q^2+3q+1
       843: 1
       844: 1
       845: q+1
       847: q+1
       848: q
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q+1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: 2
       870: 1
       871: 1
       872: 1
       873: q+2
       874: 1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+3q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       884: q+1
       887: q+1
       896: q+1
       904: 1
       912: 1
       916: 2
       920: 1
       928: 1
       932: 2q+2
       936: q+1
       940: 1
       942: 1
       944: q+1
       952: 1
       956: 2q+1
       958: 2q+1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       978: q+1
       982: q+1
       985: q+1
       988: q+1
       989: q+1
       992: 2
       994: 1
       996: 1
      1000: 1
      1002: q+1
      1004: 1
      1014: 2
      1016: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: q+2
      1032: 1
      1033: 1
      1034: 2q+1
      1036: 1
      1038: q+1
      1040: 1
      1042: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: 1
      1058: q+1
      1059: q
      1060: 1
      1062: 1
      1066: q+2
      1068: q+2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 1
      1081: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1098: q+1
      1101: q+1
      1118: 1
      1122: 1
      1144: 2
      1148: 1
      1156: 1
      1164: 1
      1166: 1
      1168: q+1
      1176: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1198: 1
      1206: 1
      1210: 2
      1212: 1
      1214: 1
      1218: 1
      1226: 2
      1228: 2
      1236: 1
      1238: 1
      1240: 1
      1244: q+2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1254: 1
      1256: q+1
      1258: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1302: 1
      1305: 1
      1318: 1
      1340: 2
      1352: 1
      1372: 1
      1374: 1
      1384: 1
      1388: 1
      1404: 1
      1407: 1
      1410: 1
      1411: 1
      1414: 1
      1422: 1
      1438: 1
      1442: 1
      1452: 1
      1456: 1
      1458: 1
      1462: 1
      1470: 1
      1472: 1
      1476: 1
      1486: 1
      1488: 1
      1525: 1
      1528: 1
      1545: 1
      1587: 1
      1611: 1
      1651: 1
      1655: 1
      1667: 1
      1765: 1

1766:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: 6q^3+9q^2+6q+1
        23: 6q^3+9q^2+6q+1
        24: 6q^3+9q^2+6q+1
        25: q^4+9q^3+11q^2+6q+1
        26: q^4+9q^3+11q^2+6q+1
        27: q^4+9q^3+11q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: 6q^3+9q^2+6q+1
        32: 6q^3+9q^2+6q+1
        33: 3q^3+8q^2+6q+1
        34: q^4+9q^3+11q^2+6q+1
        35: q^4+9q^3+11q^2+6q+1
        36: 5q^3+10q^2+6q+1
        37: 2q^3+2q^2+q
        38: 4q^3+7q^2+5q+1
        39: 2q^3+2q^2+q
        40: 4q^3+7q^2+5q+1
        41: 2q^3+2q^2+q
        42: 4q^3+7q^2+5q+1
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 3q^3+6q^2+5q+1
        53: 3q^3+6q^2+5q+1
        54: 3q^3+6q^2+5q+1
        55: 5q^3+8q^2+5q+1
        56: 5q^3+8q^2+5q+1
        57: 5q^3+8q^2+5q+1
        58: 2q^3+3q^2+3q
        59: q^3+5q^2+3q+1
        60: 3q^3+6q^2+4q+1
        61: 2q^3+4q^2+2q
        62: 2q^3+2q^2+q
        63: 4q^3+7q^2+5q+1
        64: 2q^3+2q^2+q
        65: 4q^3+7q^2+5q+1
        66: q^3+2q^2+q
        67: 2q^3+6q^2+5q+1
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: 4q^2+4q+1
        73: q^3+3q^2+4q+1
        75: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        79: q^3+4q^2+4q+1
        80: 6q^3+9q^2+6q+1
        81: 3q^3+8q^2+6q+1
        82: 3q^3+6q^2+5q+1
        83: 3q^3+6q^2+5q+1
        84: q^4+9q^3+11q^2+6q+1
        85: 5q^3+10q^2+6q+1
        86: 5q^3+8q^2+5q+1
        87: 5q^3+8q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 4q^2+5q+1
        95: 4q^2+5q+1
        96: q^3+3q^2+4q+1
        97: 2q^3+7q^2+5q+1
        98: 2q^3+7q^2+5q+1
        99: 3q^3+5q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+q^2+q
       104: q^3+4q^2+3q+1
       105: q^3+2q^2+2q
       106: q^2
       107: 3q^2+3q+1
       108: q^2+q
       109: q^3+q^2+2q
       110: 2q^2+2q+1
       112: q^2+3q+1
       114: q^3+4q^2+4q+1
       116: q^3+4q^2+4q+1
       117: 2q^3+3q^2+3q
       118: q^3+5q^2+3q+1
       119: 3q^3+6q^2+4q+1
       120: 2q^3+4q^2+2q
       121: 2q^3+2q^2+q
       122: 4q^3+7q^2+5q+1
       123: q^3+2q^2+q
       124: 2q^3+6q^2+5q+1
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 3q^3+8q^2+6q+1
       138: 2q^2+4q+1
       139: 4q^2+5q+1
       140: q^2+2q+1
       141: 3q^3+6q^2+5q+1
       142: 2q^2+4q+1
       143: 5q^3+10q^2+6q+1
       144: q^3+4q^2+4q+1
       145: 2q^3+7q^2+5q+1
       146: 5q^3+8q^2+5q+1
       147: 4q^2+4q+1
       148: q^3+3q^2+4q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       152: q^3+4q^2+4q+1
       154: q^3+4q^2+4q+1
       156: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 4q^2+5q+1
       161: 4q^2+5q+1
       162: q^3+3q^2+4q+1
       163: 2q^3+7q^2+5q+1
       164: 2q^3+7q^2+5q+1
       165: 3q^3+5q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       170: q^2+2q+1
       171: q
       173: q^3+q^2+q
       174: q^3+4q^2+3q+1
       175: q^3+2q^2+2q
       176: q^2
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: 3q^2+3q+1
       184: q^2+q
       185: q^3+q^2+2q
       186: 2q^2+2q+1
       188: q^2+3q+1
       190: q^3+4q^2+4q+1
       191: 2q^3+3q^2+3q
       192: q^3+5q^2+3q+1
       193: q^2+2q+1
       195: q^2+2q
       196: q^2+2q+1
       198: q+1
       199: 3q^3+6q^2+4q+1
       200: 2q^3+4q^2+2q
       201: 3q^2+3q+1
       202: q^2+q
       203: q^3+q^2+2q
       204: 2q^2+2q+1
       206: q^2+3q+1
       207: q^3+2q^2+q
       208: 2q^3+6q^2+5q+1
       210: q^3+4q^2+4q+1
       212: q^3+4q^2+4q+1
       214: 2q^2+4q+1
       216: 2q^2+4q+1
       218: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: 4q^2+4q+1
       223: 2q^2+3q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q^2+5q+1
       228: 2q^2+4q+1
       229: q^2+2q+1
       230: 2q^2+4q+1
       231: q^3+4q^2+4q+1
       232: 2q^3+7q^2+5q+1
       233: q^3+4q^2+4q+1
       234: 4q^2+4q+1
       235: q^3+3q^2+4q+1
       236: 2q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 4q^2+5q+1
       244: q^2+2q+1
       245: 2q^2+4q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q^2+5q+1
       251: 4q^2+5q+1
       252: q^3+3q^2+4q+1
       253: 2q^3+7q^2+5q+1
       254: 2q^3+7q^2+5q+1
       255: 3q^3+5q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q+1
       272: q
       274: q^2+2q+1
       275: q^3+q^2+q
       276: q^3+4q^2+3q+1
       277: q^3+2q^2+2q
       278: q^2
       280: 2q^2+4q+1
       282: q^2+3q+1
       283: q^2+2q+1
       285: q
       286: q+1
       288: q^2+3q+1
       290: 3q+1
       292: 2q+1
       293: 3q^2+3q+1
       294: q^2+q
       295: q^3+q^2+2q
       296: 2q^2+2q+1
       298: q^2+3q+1
       299: q^2+2q+1
       302: q+1
       303: q^2+2q
       304: q^2+2q+1
       306: q+1
       307: 3q^2+3q+1
       308: q^2+q
       309: q^3+q^2+2q
       310: 2q^2+2q+1
       312: 3q+1
       314: q^2+3q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       319: q^2+2q+1
       321: q^2+2q
       322: q^2+2q+1
       324: q+1
       326: q^3+4q^2+4q+1
       328: 2q^2+4q+1
       330: 2q^2+4q+1
       332: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q^2+4q+1
       345: 4q^2+5q+1
       346: 2q^2+4q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: 2q+2
       352: q^3+4q^2+4q+1
       353: 2q^3+7q^2+5q+1
       354: q^3+4q^2+4q+1
       355: 4q^2+4q+1
       356: 2q^2+3q+1
       357: q^3+3q^2+4q+1
       358: q^2+3q+1
       359: 4q+2
       361: 2q^2+4q+1
       363: 2q^2+4q+1
       365: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: q^2+2q+1
       370: 2q^2+4q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q+1
       394: q+1
       398: q
       400: 2q+1
       402: q
       403: q^2+2q+1
       407: q+1
       410: 2q^2+4q+1
       412: q^2+3q+1
       414: q^2+3q+1
       416: 3q+1
       418: 2q+1
       419: q^2+2q+1
       421: q
       422: q+1
       424: 2q+1
       426: q+1
       428: 4q+2
       429: q+1
       431: q
       432: q+1
       434: 1
       436: q+1
       437: q^2+2q+1
       439: q^2+2q
       440: q^2+2q+1
       442: q+1
       443: 2q+2
       446: 2q+2
       447: q^2+2q+1
       449: q
       450: q+1
       452: 2q+1
       453: 3q^2+3q+1
       454: q^2+q
       456: 3q+1
       457: q^3+q^2+2q
       458: 2q^2+2q+1
       460: q^2+3q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: 2q^2+4q+1
       468: q^2+3q+1
       470: q^2+3q+1
       471: q^2+2q+1
       473: q^2+2q
       474: q^2+2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2q^2+3q+1
       482: q^2+3q+1
       483: q+1
       484: 4q+2
       486: 4q+2
       488: 4q+2
       490: q^2+2q+1
       491: q+1
       492: 2q^2+4q+1
       493: q+1
       494: q^2+3q+1
       495: 1
       496: 2q+2
       497: q^3+4q^2+4q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: 4q+2
       503: 2q^2+4q+1
       505: 2q^2+4q+1
       507: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: q^2+2q+1
       512: q+1
       513: 2q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: 1
       538: q+1
       542: q+1
       546: 2q+2
       551: q+1
       554: q
       556: 2q+1
       558: q
       560: q^2+2q+1
       562: 2q+1
       564: 2q+1
       566: q+1
       571: q+1
       573: q+1
       574: q+1
       578: q+1
       581: q+1
       584: q^2+3q+1
       586: 2q+1
       588: 2q+1
       589: q^2+2q+1
       593: 1
       595: q
       596: q+1
       598: q+1
       600: q+1
       602: 4q+2
       603: q+1
       606: 1
       607: q
       608: q+1
       610: 1
       612: q+1
       614: 1
       615: 2q+2
       618: 2q+2
       619: q^2+2q+1
       621: q
       622: q+1
       624: 2q+1
       626: 2q+1
       628: 3q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       634: 4q+2
       636: 2q^2+4q+1
       638: q^2+3q+1
       640: q^2+3q+1
       641: q+1
       643: q
       644: q+1
       646: 1
       647: q^2+2q+1
       649: q^2+2q
       650: q^2+2q+1
       652: q+1
       654: q+1
       655: q+1
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: q+1
       667: 4q+2
       669: 4q+2
       671: q^2+2q+1
       672: 4q+2
       673: q+1
       674: 2
       675: q+1
       676: q^2+3q+1
       677: 1
       678: 2q+2
       679: 1
       680: q+2
       681: 2q^2+3q+1
       682: q^2+3q+1
       683: q+1
       684: 4q+2
       685: q+1
       686: 2q^2+4q+1
       687: q+1
       688: q^2+3q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       694: q+1
       699: q+1
       706: q+1
       710: q+1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: 2q+2
       740: q+1
       744: q+1
       746: q
       748: 2q+1
       750: 2q+1
       752: 2q+1
       754: 1
       759: q+1
       763: q+1
       765: q+1
       766: q+1
       770: q+1
       773: q+1
       776: 2
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       785: 1
       790: 4q+2
       793: 2
       796: 2
       798: 1
       800: 1
       801: q+1
       805: 1
       807: q
       808: q+1
       810: 1
       812: 1
       814: 2q+2
       815: 2q+2
       817: 1
       818: 1
       820: q+2
       822: 2q+1
       824: 2q+1
       825: q^2+2q+1
       829: 1
       831: q
       832: q+1
       834: q+1
       836: q+1
       838: 4q+2
       839: 2q+1
       840: 2q+1
       842: q^2+3q+1
       843: 1
       844: 1
       845: q+1
       847: q
       848: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q+1
       858: q+1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: 2
       870: 1
       871: 1
       872: 1
       873: q+2
       874: 1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+3q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       885: q+1
       890: q+1
       897: q+1
       905: 1
       913: 1
       917: 2
       921: 1
       929: 1
       933: 2q+2
       939: q+1
       941: 1
       943: 1
       947: q+1
       953: 1
       957: 2q+1
       959: 2q+1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       980: q+1
       983: q+1
       986: q+1
       988: q+1
       989: q+1
       993: 2
       995: 1
       997: 1
      1000: 1
      1003: q+1
      1004: 1
      1015: 2
      1016: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: q+2
      1032: 1
      1033: 1
      1035: 2q+1
      1037: 1
      1039: q+1
      1040: 1
      1043: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: 1
      1058: q
      1059: q+1
      1061: 1
      1063: 1
      1067: q+2
      1069: q+2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 1
      1081: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1099: q+1
      1104: q+1
      1119: 1
      1123: 1
      1145: 2
      1149: 1
      1157: 1
      1165: 1
      1167: 1
      1171: q+1
      1177: 1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1200: 1
      1207: 1
      1211: 2
      1213: 1
      1215: 1
      1218: 1
      1227: 2
      1228: 2
      1237: 1
      1239: 1
      1240: 1
      1245: q+2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1254: 1
      1257: q+1
      1258: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1303: 1
      1308: 1
      1319: 1
      1341: 2
      1353: 1
      1373: 1
      1375: 1
      1385: 1
      1389: 1
      1405: 1
      1408: 1
      1410: 1
      1411: 1
      1416: 1
      1423: 1
      1439: 1
      1442: 1
      1453: 1
      1457: 1
      1459: 1
      1462: 1
      1471: 1
      1473: 1
      1476: 1
      1486: 1
      1488: 1
      1526: 1
      1531: 1
      1546: 1
      1588: 1
      1612: 1
      1652: 1
      1655: 1
      1668: 1
      1766: 1

1767:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: 6q^3+9q^2+6q+1
        23: 6q^3+9q^2+6q+1
        24: 6q^3+9q^2+6q+1
        25: q^4+9q^3+11q^2+6q+1
        26: q^4+9q^3+11q^2+6q+1
        27: q^4+9q^3+11q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: 6q^3+9q^2+6q+1
        32: 6q^3+9q^2+6q+1
        33: 3q^3+8q^2+6q+1
        34: q^4+9q^3+11q^2+6q+1
        35: q^4+9q^3+11q^2+6q+1
        36: 5q^3+10q^2+6q+1
        37: 4q^3+7q^2+5q+1
        38: 2q^3+2q^2+q
        39: 4q^3+7q^2+5q+1
        40: 2q^3+2q^2+q
        41: 4q^3+7q^2+5q+1
        42: 2q^3+2q^2+q
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 3q^3+6q^2+5q+1
        53: 3q^3+6q^2+5q+1
        54: 3q^3+6q^2+5q+1
        55: 5q^3+8q^2+5q+1
        56: 5q^3+8q^2+5q+1
        57: 5q^3+8q^2+5q+1
        58: 2q^3+3q^2+3q
        59: q^3+5q^2+3q+1
        60: 2q^3+4q^2+2q
        61: 3q^3+6q^2+4q+1
        62: 4q^3+7q^2+5q+1
        63: 2q^3+2q^2+q
        64: 4q^3+7q^2+5q+1
        65: 2q^3+2q^2+q
        66: 2q^3+6q^2+5q+1
        67: q^3+2q^2+q
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: 4q^2+4q+1
        73: q^3+3q^2+4q+1
        74: q^3+4q^2+4q+1
        76: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        80: 6q^3+9q^2+6q+1
        81: 3q^3+8q^2+6q+1
        82: 3q^3+6q^2+5q+1
        83: 3q^3+6q^2+5q+1
        84: q^4+9q^3+11q^2+6q+1
        85: 5q^3+10q^2+6q+1
        86: 5q^3+8q^2+5q+1
        87: 5q^3+8q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 4q^2+5q+1
        95: 4q^2+5q+1
        96: q^3+3q^2+4q+1
        97: 2q^3+7q^2+5q+1
        98: 2q^3+7q^2+5q+1
        99: 3q^3+5q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^3+2q^2+2q
       104: q^2
       105: q^3+q^2+q
       106: q^3+4q^2+3q+1
       107: q^2+q
       108: 3q^2+3q+1
       109: q^3+q^2+2q
       110: 2q^2+2q+1
       111: q^2+3q+1
       113: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       117: 2q^3+3q^2+3q
       118: q^3+5q^2+3q+1
       119: 2q^3+4q^2+2q
       120: 3q^3+6q^2+4q+1
       121: 4q^3+7q^2+5q+1
       122: 2q^3+2q^2+q
       123: 2q^3+6q^2+5q+1
       124: q^3+2q^2+q
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       127: 2q^2+4q+1
       129: 2q^2+4q+1
       131: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 3q^3+8q^2+6q+1
       138: 2q^2+4q+1
       139: 4q^2+5q+1
       140: q^2+2q+1
       141: 3q^3+6q^2+5q+1
       142: 2q^2+4q+1
       143: 5q^3+10q^2+6q+1
       144: q^3+4q^2+4q+1
       145: 2q^3+7q^2+5q+1
       146: 5q^3+8q^2+5q+1
       147: 4q^2+4q+1
       148: q^3+3q^2+4q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       151: q^3+4q^2+4q+1
       153: q^3+4q^2+4q+1
       155: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 4q^2+5q+1
       161: 4q^2+5q+1
       162: q^3+3q^2+4q+1
       163: 2q^3+7q^2+5q+1
       164: 2q^3+7q^2+5q+1
       165: 3q^3+5q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       169: q
       172: q^2+2q+1
       173: q^3+2q^2+2q
       174: q^2
       175: q^3+q^2+q
       176: q^3+4q^2+3q+1
       177: q^2+3q+1
       179: 2q^2+4q+1
       181: 3q+1
       183: q^2+q
       184: 3q^2+3q+1
       185: q^3+q^2+2q
       186: 2q^2+2q+1
       187: q^2+3q+1
       189: q^3+4q^2+4q+1
       191: 2q^3+3q^2+3q
       192: q^3+5q^2+3q+1
       194: q^2+2q+1
       195: q^2+2q
       196: q^2+2q+1
       197: q+1
       199: 2q^3+4q^2+2q
       200: 3q^3+6q^2+4q+1
       201: q^2+q
       202: 3q^2+3q+1
       203: q^3+q^2+2q
       204: 2q^2+2q+1
       205: q^2+3q+1
       207: 2q^3+6q^2+5q+1
       208: q^3+2q^2+q
       209: q^3+4q^2+4q+1
       211: q^3+4q^2+4q+1
       213: 2q^2+4q+1
       215: 2q^2+4q+1
       217: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: 4q^2+4q+1
       223: 2q^2+3q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q^2+5q+1
       228: 2q^2+4q+1
       229: q^2+2q+1
       230: 2q^2+4q+1
       231: q^3+4q^2+4q+1
       232: 2q^3+7q^2+5q+1
       233: q^3+4q^2+4q+1
       234: 4q^2+4q+1
       235: q^3+3q^2+4q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       239: 2q^2+4q+1
       241: 2q^2+3q+1
       243: 4q^2+5q+1
       244: q^2+2q+1
       245: 2q^2+4q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q^2+5q+1
       251: 4q^2+5q+1
       252: q^3+3q^2+4q+1
       253: 2q^3+7q^2+5q+1
       254: 2q^3+7q^2+5q+1
       255: 3q^3+5q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       271: q
       273: q^2+2q+1
       275: q^3+2q^2+2q
       276: q^2
       277: q^3+q^2+q
       278: q^3+4q^2+3q+1
       279: 2q^2+4q+1
       281: q^2+3q+1
       284: q^2+2q+1
       285: q
       286: q+1
       287: q^2+3q+1
       289: 3q+1
       291: 2q+1
       293: q^2+q
       294: 3q^2+3q+1
       295: q^3+q^2+2q
       296: 2q^2+2q+1
       297: q^2+3q+1
       300: q^2+2q+1
       301: q+1
       303: q^2+2q
       304: q^2+2q+1
       305: q+1
       307: q^2+q
       308: 3q^2+3q+1
       309: q^3+q^2+2q
       310: 2q^2+2q+1
       311: 3q+1
       313: q^2+3q+1
       315: q^2+3q+1
       317: 2q^2+4q+1
       320: q^2+2q+1
       321: q^2+2q
       322: q^2+2q+1
       323: q+1
       325: q^3+4q^2+4q+1
       327: 2q^2+4q+1
       329: 2q^2+4q+1
       331: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       338: 4q+2
       340: 4q+2
       342: q^2+2q+1
       344: 2q^2+4q+1
       345: 4q^2+5q+1
       346: 2q^2+4q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: 2q+2
       352: q^3+4q^2+4q+1
       353: 2q^3+7q^2+5q+1
       354: q^3+4q^2+4q+1
       355: 4q^2+4q+1
       356: 2q^2+3q+1
       357: q^3+3q^2+4q+1
       358: q^2+3q+1
       359: 4q+2
       360: 2q^2+4q+1
       362: 2q^2+4q+1
       364: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: q^2+2q+1
       370: 2q^2+4q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q+1
       396: q+1
       397: q
       399: 2q+1
       401: q
       404: q^2+2q+1
       406: q+1
       409: 2q^2+4q+1
       411: q^2+3q+1
       413: q^2+3q+1
       415: 3q+1
       417: 2q+1
       420: q^2+2q+1
       421: q
       422: q+1
       423: 2q+1
       425: q+1
       427: 4q+2
       430: q+1
       431: q
       432: q+1
       433: 1
       435: q+1
       438: q^2+2q+1
       439: q^2+2q
       440: q^2+2q+1
       441: q+1
       444: 2q+2
       445: 2q+2
       448: q^2+2q+1
       449: q
       450: q+1
       451: 2q+1
       453: q^2+q
       454: 3q^2+3q+1
       455: 3q+1
       457: q^3+q^2+2q
       458: 2q^2+2q+1
       459: q^2+3q+1
       461: 2q+1
       462: 2q+1
       463: 4q+2
       465: 2q^2+4q+1
       467: q^2+3q+1
       469: q^2+3q+1
       472: q^2+2q+1
       473: q^2+2q
       474: q^2+2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: 2q^2+3q+1
       482: q^2+3q+1
       483: q+1
       484: 4q+2
       485: 4q+2
       487: 4q+2
       489: q^2+2q+1
       491: q+1
       492: 2q^2+4q+1
       493: q+1
       494: q^2+3q+1
       495: 1
       496: 2q+2
       497: q^3+4q^2+4q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: 4q+2
       502: 2q^2+4q+1
       504: 2q^2+4q+1
       506: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: q^2+2q+1
       512: q+1
       513: 2q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: 1
       539: q+1
       543: q+1
       547: 2q+2
       552: q+1
       553: q
       555: 2q+1
       557: q
       559: q^2+2q+1
       561: 2q+1
       563: 2q+1
       568: q+1
       570: q+1
       575: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q^2+3q+1
       585: 2q+1
       587: 2q+1
       590: q^2+2q+1
       594: 1
       595: q
       596: q+1
       597: q+1
       599: q+1
       601: 4q+2
       604: q+1
       605: 1
       607: q
       608: q+1
       609: 1
       611: q+1
       613: 1
       616: 2q+2
       617: 2q+2
       620: q^2+2q+1
       621: q
       622: q+1
       623: 2q+1
       625: 2q+1
       627: 3q+1
       629: q+1
       631: 2q+1
       632: 2q+1
       633: 4q+2
       635: 2q^2+4q+1
       637: q^2+3q+1
       639: q^2+3q+1
       642: q+1
       643: q
       644: q+1
       645: 1
       648: q^2+2q+1
       649: q^2+2q
       650: q^2+2q+1
       651: q+1
       653: q+1
       655: q+1
       656: q+1
       657: 2
       658: q+2
       660: q+2
       662: q+1
       664: 1
       665: q+1
       666: 4q+2
       668: 4q+2
       670: q^2+2q+1
       672: 4q+2
       673: q+1
       674: 2
       675: q+1
       676: q^2+3q+1
       677: 1
       678: 2q+2
       679: 1
       680: q+2
       681: 2q^2+3q+1
       682: q^2+3q+1
       683: q+1
       684: 4q+2
       685: q+1
       686: 2q^2+4q+1
       687: q+1
       688: q^2+3q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       697: q+1
       698: q+1
       708: q+1
       712: q+1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: 2q+2
       739: q+1
       743: q+1
       745: q
       747: 2q+1
       749: 2q+1
       751: 2q+1
       756: 1
       758: q+1
       762: q+1
       767: q+1
       768: q+1
       769: q+1
       772: q+1
       775: 2
       777: 2q+1
       779: 1
       781: q+1
       783: q+1
       786: 1
       789: 4q+2
       794: 2
       795: 2
       797: 1
       799: 1
       802: q+1
       806: 1
       807: q
       808: q+1
       809: 1
       811: 1
       813: 2q+2
       816: 2q+2
       817: 1
       818: 1
       819: q+2
       821: 2q+1
       823: 2q+1
       826: q^2+2q+1
       830: 1
       831: q
       832: q+1
       833: q+1
       835: q+1
       837: 4q+2
       839: 2q+1
       840: 2q+1
       841: q^2+3q+1
       843: 1
       844: 1
       846: q+1
       847: q
       848: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q+1
       859: q+2
       861: q+2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: 2
       870: 1
       871: 1
       872: 1
       873: q+2
       874: 1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+3q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       888: q+1
       889: q+1
       899: q+1
       906: 1
       914: 1
       918: 2
       922: 1
       930: 1
       934: 2q+2
       938: q+1
       940: 1
       942: 1
       946: q+1
       955: 1
       956: 2q+1
       958: 2q+1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: q+1
       982: q+1
       985: q+1
       990: q+1
       991: q+1
       992: 2
       994: 1
       996: 1
      1001: 1
      1002: q+1
      1005: 1
      1014: 2
      1017: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: q+2
      1032: 1
      1033: 1
      1034: 2q+1
      1036: 1
      1038: q+1
      1041: 1
      1042: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: 1
      1058: q
      1059: q+1
      1060: 1
      1062: 1
      1066: q+2
      1068: q+2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 1
      1081: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1102: q+1
      1103: q+1
      1120: 1
      1124: 1
      1146: 2
      1150: 1
      1158: 1
      1164: 1
      1166: 1
      1170: q+1
      1178: 1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1199: 1
      1208: 1
      1210: 2
      1212: 1
      1214: 1
      1219: 1
      1226: 2
      1229: 2
      1236: 1
      1238: 1
      1241: 1
      1244: q+2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1255: 1
      1256: q+1
      1259: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1306: 1
      1307: 1
      1320: 1
      1342: 2
      1354: 1
      1372: 1
      1374: 1
      1386: 1
      1390: 1
      1404: 1
      1407: 1
      1412: 1
      1413: 1
      1415: 1
      1424: 1
      1438: 1
      1443: 1
      1452: 1
      1456: 1
      1458: 1
      1463: 1
      1470: 1
      1472: 1
      1477: 1
      1486: 1
      1488: 1
      1529: 1
      1530: 1
      1547: 1
      1589: 1
      1613: 1
      1651: 1
      1656: 1
      1667: 1
      1767: 1

1768:    0: q^4+9q^3+11q^2+6q+1
         1: q^4+9q^3+11q^2+6q+1
         2: q^4+9q^3+11q^2+6q+1
         3: q^4+9q^3+11q^2+6q+1
         4: 3q^4+8q^3+9q^2+5q+1
         5: q^4+9q^3+11q^2+6q+1
         6: 3q^4+8q^3+9q^2+5q+1
         7: 3q^4+8q^3+9q^2+5q+1
         8: q^4+9q^3+11q^2+6q+1
         9: q^5+4q^4+6q^3+6q^2+4q+1
        10: q^4+9q^3+11q^2+6q+1
        11: q^4+9q^3+11q^2+6q+1
        12: 3q^4+8q^3+9q^2+5q+1
        13: q^4+9q^3+11q^2+6q+1
        14: 3q^4+8q^3+9q^2+5q+1
        15: q^4+9q^3+11q^2+6q+1
        16: 5q^3+10q^2+6q+1
        17: 5q^3+10q^2+6q+1
        18: 2q^4+5q^3+6q^2+4q+1
        19: 5q^3+8q^2+5q+1
        20: 5q^3+8q^2+5q+1
        21: 5q^3+8q^2+5q+1
        22: 6q^3+9q^2+6q+1
        23: 6q^3+9q^2+6q+1
        24: 6q^3+9q^2+6q+1
        25: q^4+9q^3+11q^2+6q+1
        26: q^4+9q^3+11q^2+6q+1
        27: q^4+9q^3+11q^2+6q+1
        28: 5q^3+10q^2+6q+1
        29: 5q^3+8q^2+5q+1
        30: 5q^3+8q^2+5q+1
        31: 6q^3+9q^2+6q+1
        32: 6q^3+9q^2+6q+1
        33: 3q^3+8q^2+6q+1
        34: q^4+9q^3+11q^2+6q+1
        35: q^4+9q^3+11q^2+6q+1
        36: 5q^3+10q^2+6q+1
        37: 2q^3+2q^2+q
        38: 4q^3+7q^2+5q+1
        39: 2q^3+2q^2+q
        40: 4q^3+7q^2+5q+1
        41: 2q^3+2q^2+q
        42: 4q^3+7q^2+5q+1
        43: q^4+9q^3+11q^2+6q+1
        44: 3q^4+8q^3+9q^2+5q+1
        45: q^4+9q^3+11q^2+6q+1
        46: 5q^3+10q^2+6q+1
        47: 5q^3+10q^2+6q+1
        48: 2q^4+5q^3+6q^2+4q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^3+7q^2+5q+1
        51: 3q^3+5q^2+4q+1
        52: 3q^3+6q^2+5q+1
        53: 3q^3+6q^2+5q+1
        54: 3q^3+6q^2+5q+1
        55: 5q^3+8q^2+5q+1
        56: 5q^3+8q^2+5q+1
        57: 5q^3+8q^2+5q+1
        58: q^3+5q^2+3q+1
        59: 2q^3+3q^2+3q
        60: 2q^3+4q^2+2q
        61: 3q^3+6q^2+4q+1
        62: 2q^3+2q^2+q
        63: 4q^3+7q^2+5q+1
        64: 2q^3+2q^2+q
        65: 4q^3+7q^2+5q+1
        66: q^3+2q^2+q
        67: 2q^3+6q^2+5q+1
        68: 5q^3+10q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 5q^3+8q^2+5q+1
        71: 2q^3+7q^2+5q+1
        72: 4q^2+4q+1
        73: q^3+3q^2+4q+1
        75: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        79: q^3+4q^2+4q+1
        80: 6q^3+9q^2+6q+1
        81: 3q^3+8q^2+6q+1
        82: 3q^3+6q^2+5q+1
        83: 3q^3+6q^2+5q+1
        84: q^4+9q^3+11q^2+6q+1
        85: 5q^3+10q^2+6q+1
        86: 5q^3+8q^2+5q+1
        87: 5q^3+8q^2+5q+1
        88: 5q^3+10q^2+6q+1
        89: 5q^3+10q^2+6q+1
        90: 2q^4+5q^3+6q^2+4q+1
        91: 2q^3+7q^2+5q+1
        92: 2q^3+7q^2+5q+1
        93: 3q^3+5q^2+4q+1
        94: 4q^2+5q+1
        95: 4q^2+5q+1
        96: q^3+3q^2+4q+1
        97: 2q^3+7q^2+5q+1
        98: 2q^3+7q^2+5q+1
        99: 3q^3+5q^2+4q+1
       100: 3q^3+6q^2+5q+1
       101: 3q^3+6q^2+5q+1
       102: 3q^3+6q^2+5q+1
       103: q^2
       104: q^3+2q^2+2q
       105: q^3+4q^2+3q+1
       106: q^3+q^2+q
       107: q^2+q
       108: 3q^2+3q+1
       109: 2q^2+2q+1
       110: q^3+q^2+2q
       112: q^2+3q+1
       114: q^3+4q^2+4q+1
       116: q^3+4q^2+4q+1
       117: q^3+5q^2+3q+1
       118: 2q^3+3q^2+3q
       119: 2q^3+4q^2+2q
       120: 3q^3+6q^2+4q+1
       121: 2q^3+2q^2+q
       122: 4q^3+7q^2+5q+1
       123: q^3+2q^2+q
       124: 2q^3+6q^2+5q+1
       125: 5q^3+10q^2+6q+1
       126: q^3+4q^2+4q+1
       128: 2q^2+4q+1
       130: 2q^2+4q+1
       132: 2q^2+3q+1
       133: 2q^3+7q^2+5q+1
       134: q^3+4q^2+4q+1
       135: 4q^2+4q+1
       136: q^3+3q^2+4q+1
       137: 3q^3+8q^2+6q+1
       138: 2q^2+4q+1
       139: 4q^2+5q+1
       140: q^2+2q+1
       141: 3q^3+6q^2+5q+1
       142: 2q^2+4q+1
       143: 5q^3+10q^2+6q+1
       144: q^3+4q^2+4q+1
       145: 2q^3+7q^2+5q+1
       146: 5q^3+8q^2+5q+1
       147: 4q^2+4q+1
       148: q^3+3q^2+4q+1
       149: 3q^3+6q^2+5q+1
       150: 3q^3+6q^2+5q+1
       152: q^3+4q^2+4q+1
       154: q^3+4q^2+4q+1
       156: q^3+4q^2+4q+1
       157: 2q^3+7q^2+5q+1
       158: 2q^3+7q^2+5q+1
       159: 3q^3+5q^2+4q+1
       160: 4q^2+5q+1
       161: 4q^2+5q+1
       162: q^3+3q^2+4q+1
       163: 2q^3+7q^2+5q+1
       164: 2q^3+7q^2+5q+1
       165: 3q^3+5q^2+4q+1
       166: 4q^2+5q+1
       167: 4q^2+5q+1
       168: q^3+3q^2+4q+1
       170: q
       171: q^2+2q+1
       173: q^2
       174: q^3+2q^2+2q
       175: q^3+4q^2+3q+1
       176: q^3+q^2+q
       178: q^2+3q+1
       180: 2q^2+4q+1
       182: 3q+1
       183: q^2+q
       184: 3q^2+3q+1
       185: 2q^2+2q+1
       186: q^3+q^2+2q
       188: q^2+3q+1
       190: q^3+4q^2+4q+1
       191: q^3+5q^2+3q+1
       192: 2q^3+3q^2+3q
       194: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q
       198: q+1
       199: 2q^3+4q^2+2q
       200: 3q^3+6q^2+4q+1
       201: q^2+q
       202: 3q^2+3q+1
       203: 2q^2+2q+1
       204: q^3+q^2+2q
       206: q^2+3q+1
       207: q^3+2q^2+q
       208: 2q^3+6q^2+5q+1
       210: q^3+4q^2+4q+1
       212: q^3+4q^2+4q+1
       214: 2q^2+4q+1
       216: 2q^2+4q+1
       218: 2q^2+3q+1
       219: q^3+4q^2+4q+1
       220: 2q^3+7q^2+5q+1
       221: q^3+4q^2+4q+1
       222: 4q^2+4q+1
       223: 2q^2+3q+1
       224: q^3+3q^2+4q+1
       225: q^2+3q+1
       226: 2q^2+4q+1
       227: 4q^2+5q+1
       228: 2q^2+4q+1
       229: q^2+2q+1
       230: 2q^2+4q+1
       231: q^3+4q^2+4q+1
       232: 2q^3+7q^2+5q+1
       233: q^3+4q^2+4q+1
       234: 4q^2+4q+1
       235: q^3+3q^2+4q+1
       236: 2q^2+4q+1
       238: 2q^2+4q+1
       240: 2q^2+4q+1
       242: 2q^2+3q+1
       243: 4q^2+5q+1
       244: q^2+2q+1
       245: 2q^2+4q+1
       246: 3q^3+6q^2+5q+1
       247: 4q+2
       248: 4q+2
       249: q^2+2q+1
       250: 4q^2+5q+1
       251: 4q^2+5q+1
       252: q^3+3q^2+4q+1
       253: 2q^3+7q^2+5q+1
       254: 2q^3+7q^2+5q+1
       255: 3q^3+5q^2+4q+1
       256: 4q^2+5q+1
       257: 4q^2+5q+1
       258: q^3+3q^2+4q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       272: q^2+2q+1
       274: q
       275: q^2
       276: q^3+2q^2+2q
       277: q^3+4q^2+3q+1
       278: q^3+q^2+q
       280: 2q^2+4q+1
       282: q^2+3q+1
       284: q^2+2q+1
       285: q+1
       286: q
       288: q^2+3q+1
       290: 3q+1
       292: 2q+1
       293: q^2+q
       294: 3q^2+3q+1
       295: 2q^2+2q+1
       296: q^3+q^2+2q
       298: q^2+3q+1
       300: q^2+2q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q
       306: q+1
       307: q^2+q
       308: 3q^2+3q+1
       309: 2q^2+2q+1
       310: q^3+q^2+2q
       312: 3q+1
       314: q^2+3q+1
       316: q^2+3q+1
       318: 2q^2+4q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q
       324: q+1
       326: q^3+4q^2+4q+1
       328: 2q^2+4q+1
       330: 2q^2+4q+1
       332: 2q^2+3q+1
       333: q^3+4q^2+4q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: 4q+2
       339: 4q+2
       341: 4q+2
       343: q^2+2q+1
       344: 2q^2+4q+1
       345: 4q^2+5q+1
       346: 2q^2+4q+1
       347: q^2+2q+1
       348: q+1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: 2q+2
       352: q^3+4q^2+4q+1
       353: 2q^3+7q^2+5q+1
       354: q^3+4q^2+4q+1
       355: 4q^2+4q+1
       356: 2q^2+3q+1
       357: q^3+3q^2+4q+1
       358: q^2+3q+1
       359: 4q+2
       361: 2q^2+4q+1
       363: 2q^2+4q+1
       365: 2q^2+3q+1
       366: 2q^2+4q+1
       367: 4q^2+5q+1
       368: 2q^2+4q+1
       369: q^2+2q+1
       370: 2q^2+4q+1
       371: 4q+2
       372: 4q+2
       373: q^2+2q+1
       374: 4q^2+5q+1
       375: 4q^2+5q+1
       376: q^3+3q^2+4q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q+1
       395: q+1
       398: 2q+1
       400: q
       402: q^2+2q+1
       403: q
       408: q+1
       410: 2q^2+4q+1
       412: q^2+3q+1
       414: q^2+3q+1
       416: 3q+1
       418: 2q+1
       420: q^2+2q+1
       421: q+1
       422: q
       424: 2q+1
       426: q+1
       428: 4q+2
       430: q+1
       431: q+1
       432: q
       434: 1
       436: q+1
       438: q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q
       442: q+1
       444: 2q+2
       446: 2q+2
       448: q^2+2q+1
       449: q+1
       450: q
       452: 2q+1
       453: q^2+q
       454: 3q^2+3q+1
       456: 3q+1
       457: 2q^2+2q+1
       458: q^3+q^2+2q
       460: q^2+3q+1
       461: 2q+1
       462: 2q+1
       464: 4q+2
       466: 2q^2+4q+1
       468: q^2+3q+1
       470: q^2+3q+1
       472: q^2+2q+1
       473: q^2+2q+1
       474: q^2+2q
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2q^2+3q+1
       482: q^2+3q+1
       483: q+1
       484: 4q+2
       486: 4q+2
       488: 4q+2
       490: q^2+2q+1
       491: q+1
       492: 2q^2+4q+1
       493: q+1
       494: q^2+3q+1
       495: 1
       496: 2q+2
       497: q^3+4q^2+4q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q+1
       501: 4q+2
       503: 2q^2+4q+1
       505: 2q^2+4q+1
       507: 2q^2+3q+1
       508: 2q^2+4q+1
       509: 4q^2+5q+1
       510: 2q^2+4q+1
       511: q^2+2q+1
       512: q+1
       513: 2q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+1
       518: 4q+2
       519: 4q+2
       520: q^2+2q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: 1
       540: q+1
       544: q+1
       548: 2q+2
       550: q+1
       554: 2q+1
       556: q
       558: q^2+2q+1
       560: q
       562: 2q+1
       564: 2q+1
       567: q+1
       572: q+1
       575: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q^2+3q+1
       586: 2q+1
       588: 2q+1
       590: q^2+2q+1
       594: 1
       595: q+1
       596: q
       598: q+1
       600: q+1
       602: 4q+2
       604: q+1
       606: 1
       607: q+1
       608: q
       610: 1
       612: q+1
       614: 1
       616: 2q+2
       618: 2q+2
       620: q^2+2q+1
       621: q+1
       622: q
       624: 2q+1
       626: 2q+1
       628: 3q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       634: 4q+2
       636: 2q^2+4q+1
       638: q^2+3q+1
       640: q^2+3q+1
       642: q+1
       643: q+1
       644: q
       646: 1
       648: q^2+2q+1
       649: q^2+2q+1
       650: q^2+2q
       652: q+1
       654: q+1
       655: q+1
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+1
       664: 1
       665: q+1
       667: 4q+2
       669: 4q+2
       671: q^2+2q+1
       672: 4q+2
       673: q+1
       674: 2
       675: q+1
       676: q^2+3q+1
       677: 1
       678: 2q+2
       679: 1
       680: q+2
       681: 2q^2+3q+1
       682: q^2+3q+1
       683: q+1
       684: 4q+2
       685: q+1
       686: 2q^2+4q+1
       687: q+1
       688: q^2+3q+1
       689: 1
       690: q+2
       691: q+2
       692: q+1
       700: q+1
       701: q+1
       707: q+1
       711: q+1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: 2q+2
       738: q+1
       742: q+1
       746: 2q+1
       748: q
       750: 2q+1
       752: 2q+1
       755: 1
       760: q+1
       764: q+1
       767: q+1
       768: q+1
       770: q+1
       773: q+1
       776: 2
       778: 2q+1
       780: 1
       782: q+1
       784: q+1
       786: 1
       790: 4q+2
       794: 2
       796: 2
       798: 1
       800: 1
       802: q+1
       806: 1
       807: q+1
       808: q
       810: 1
       812: 1
       814: 2q+2
       816: 2q+2
       817: 1
       818: 1
       820: q+2
       822: 2q+1
       824: 2q+1
       826: q^2+2q+1
       830: 1
       831: q+1
       832: q
       834: q+1
       836: q+1
       838: 4q+2
       839: 2q+1
       840: 2q+1
       842: q^2+3q+1
       843: 1
       844: 1
       846: q+1
       847: q+1
       848: q
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q+1
       858: q+1
       860: q+2
       862: q+2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: q+1
       869: 2
       870: 1
       871: 1
       872: 1
       873: q+2
       874: 1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+3q+1
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+1
       891: q+1
       892: q+1
       898: q+1
       907: 1
       915: 1
       919: 2
       923: 1
       931: 1
       935: 2q+2
       937: q+1
       941: 1
       943: 1
       945: q+1
       954: 1
       957: 2q+1
       959: 2q+1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       981: q+1
       983: q+1
       986: q+1
       990: q+1
       991: q+1
       993: 2
       995: 1
       997: 1
      1001: 1
      1003: q+1
      1005: 1
      1015: 2
      1017: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: q+2
      1032: 1
      1033: 1
      1035: 2q+1
      1037: 1
      1039: q+1
      1041: 1
      1043: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: 1
      1058: q+1
      1059: q
      1061: 1
      1063: 1
      1067: q+2
      1069: q+2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1077: 1
      1078: 1
      1079: q+2
      1080: 1
      1081: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1094: 1
      1105: q+1
      1106: q+1
      1121: 1
      1125: 1
      1147: 2
      1151: 1
      1159: 1
      1165: 1
      1167: 1
      1169: q+1
      1179: 1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1201: 1
      1209: 1
      1211: 2
      1213: 1
      1215: 1
      1219: 1
      1227: 2
      1229: 2
      1237: 1
      1239: 1
      1241: 1
      1245: q+2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1255: 1
      1257: q+1
      1259: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1282: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1289: 1
      1309: 1
      1310: 1
      1321: 1
      1343: 2
      1355: 1
      1373: 1
      1375: 1
      1387: 1
      1391: 1
      1405: 1
      1408: 1
      1412: 1
      1413: 1
      1417: 1
      1425: 1
      1439: 1
      1443: 1
      1453: 1
      1457: 1
      1459: 1
      1463: 1
      1471: 1
      1473: 1
      1477: 1
      1486: 1
      1488: 1
      1532: 1
      1533: 1
      1548: 1
      1590: 1
      1614: 1
      1652: 1
      1656: 1
      1668: 1
      1768: 1

1769:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: 9q^3+15q^2+5q+1
        23: 9q^3+15q^2+5q+1
        24: q^4+9q^3+12q^2+5q+1
        25: q^4+16q^3+16q^2+5q+1
        26: q^4+16q^3+16q^2+5q+1
        27: 4q^4+13q^3+13q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 5q^3+13q^2+5q+1
        32: 6q^3+12q^2+5q+1
        33: 9q^3+15q^2+5q+1
        34: 10q^3+14q^2+5q+1
        35: 10q^3+13q^2+5q+1
        36: q^4+16q^3+16q^2+5q+1
        37: 6q^3+10q^2+4q+1
        38: 3q^3+5q^2+q
        39: 6q^3+10q^2+4q+1
        40: 3q^3+5q^2+q
        41: q^4+6q^3+8q^2+4q+1
        42: 3q^3+4q^2+q
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 3q^3+12q^2+5q+1
        53: 5q^3+12q^2+5q+1
        54: 4q^3+10q^2+5q+1
        55: 10q^3+13q^2+5q+1
        56: q^4+12q^3+13q^2+5q+1
        57: 2q^4+8q^3+11q^2+5q+1
        58: 4q^3+8q^2+3q+1
        59: q^3+5q^2+2q
        60: 6q^3+9q^2+4q+1
        61: 4q^3+5q^2+q
        62: 4q^3+9q^2+4q+1
        63: q^3+4q^2+q
        64: 4q^3+8q^2+4q+1
        65: 2q^3+4q^2+q
        66: 6q^3+10q^2+4q+1
        67: 3q^3+5q^2+q
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 6q^3+10q^2+5q+1
        73: 2q^3+9q^2+5q+1
        74: q^3+7q^2+4q+1
        75: 3q^2+q
        76: 2q^3+7q^2+4q+1
        77: q^3+3q^2+q
        78: 2q^3+6q^2+4q+1
        79: 3q^2+q
        80: 2q^3+10q^2+5q+1
        81: 6q^3+12q^2+5q+1
        82: 2q^3+10q^2+5q+1
        83: 2q^3+10q^2+5q+1
        84: 4q^3+11q^2+5q+1
        85: 10q^3+13q^2+5q+1
        86: 7q^3+11q^2+5q+1
        87: 6q^3+11q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 3q^3+12q^2+5q+1
        95: 5q^3+12q^2+5q+1
        96: 4q^3+10q^2+5q+1
        97: 10q^3+13q^2+5q+1
        98: q^4+12q^3+13q^2+5q+1
        99: 2q^4+8q^3+11q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: 3q^3+6q^2+3q+1
       104: 2q^2+q
       105: q^3+2q^2
       106: q^3+3q^2+q
       107: 3q^3+6q^2+4q+1
       108: q^3+2q^2+q
       109: q^3+5q^2+3q+1
       110: 2q^2+2q
       111: 5q^2+4q+1
       112: 2q^2+q
       113: q^3+6q^2+4q+1
       114: 2q^2+q
       115: q^3+6q^2+4q+1
       116: 3q^2+q
       117: q^3+5q^2+3q+1
       118: 2q^2+2q
       119: q^3+6q^2+4q+1
       120: 2q^2+q
       121: 2q^3+7q^2+4q+1
       122: 3q^2+q
       123: 4q^3+8q^2+4q+1
       124: 2q^3+4q^2+q
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: q^3+7q^2+4q+1
       128: 3q^2+q
       129: 2q^3+7q^2+4q+1
       130: q^3+3q^2+q
       131: 2q^3+6q^2+4q+1
       132: 3q^2+q
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: 2q^3+8q^2+5q+1
       136: q^3+7q^2+5q+1
       137: 2q^3+10q^2+5q+1
       138: 2q^3+10q^2+5q+1
       139: 2q^3+10q^2+5q+1
       140: 3q^2+4q+1
       141: q^3+8q^2+5q+1
       142: 2q^3+9q^2+5q+1
       143: 4q^3+11q^2+5q+1
       144: 6q^3+11q^2+5q+1
       145: 7q^3+11q^2+5q+1
       146: 3q^3+9q^2+5q+1
       147: 6q^3+10q^2+5q+1
       148: 2q^3+9q^2+5q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: q^3+7q^2+4q+1
       152: 3q^2+q
       153: 2q^3+7q^2+4q+1
       154: q^3+3q^2+q
       155: 2q^3+6q^2+4q+1
       156: 3q^2+q
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: q^3+6q^2+5q+1
       161: 2q^3+6q^2+5q+1
       162: q^3+6q^2+5q+1
       163: 4q^3+10q^2+5q+1
       164: 6q^3+10q^2+5q+1
       165: 4q^3+10q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: 3q^2+3q+1
       170: q
       171: q^2
       172: q^2+q
       173: q^3+4q^2+3q+1
       174: q^2+q
       175: q^2
       176: q^2+q
       177: q^3+6q^2+4q+1
       178: 3q^2+q
       179: q^3+6q^2+4q+1
       180: 2q^2+q
       181: 5q^2+4q+1
       182: 2q^2+q
       183: 4q^2+4q+1
       184: q^2+q
       185: 3q^2+3q+1
       186: 2q
       187: 4q^2+4q+1
       188: 2q^2+q
       189: q^3+5q^2+4q+1
       190: 2q^2+q
       191: q^3+5q^2+3q+1
       192: 2q^2+2q
       193: 3q^2+4q+1
       195: q^3+5q^2+3q+1
       196: 2q^2+2q
       197: q^2+3q+1
       198: q
       199: q^3+6q^2+4q+1
       200: 2q^2+q
       201: 3q^3+6q^2+4q+1
       202: q^3+2q^2+q
       203: q^3+5q^2+3q+1
       204: 2q^2+2q
       205: 5q^2+4q+1
       206: 2q^2+q
       207: 2q^3+7q^2+4q+1
       208: 3q^2+q
       209: q^3+6q^2+4q+1
       210: 2q^2+q
       211: q^3+6q^2+4q+1
       212: 3q^2+q
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: 2q^3+8q^2+5q+1
       224: 3q^2+5q+1
       225: q^3+7q^2+5q+1
       226: q^3+8q^2+5q+1
       227: 3q^2+5q+1
       228: q^3+6q^2+5q+1
       229: q^2+4q+1
       230: q^3+4q^2+5q+1
       231: 3q^3+9q^2+5q+1
       232: 6q^2+5q+1
       233: 4q^3+10q^2+5q+1
       234: 2q^3+8q^2+5q+1
       235: q^3+7q^2+5q+1
       236: 2q^3+10q^2+5q+1
       237: q^3+7q^2+4q+1
       238: 3q^2+q
       239: 2q^3+7q^2+4q+1
       240: q^3+3q^2+q
       241: 2q^3+6q^2+4q+1
       242: 3q^2+q
       243: 2q^3+10q^2+5q+1
       244: 3q^2+4q+1
       245: 2q^3+9q^2+5q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+5q^2+5q+1
       254: q^3+5q^2+5q+1
       255: q^3+5q^2+5q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: 3q^2+3q+1
       260: q
       261: q^2
       262: q^2+q
       263: 2q^2+3q+1
       264: q
       265: q^2
       266: q
       267: q^2+3q+1
       268: q
       271: 3q^2+3q+1
       272: q^2
       273: q^2+q
       274: q
       275: q^3+4q^2+3q+1
       276: q^2+q
       277: q^2
       278: q^2+q
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: 4q^2+4q+1
       284: q^2+q
       285: 3q^2+3q+1
       286: 2q
       287: q^3+5q^2+4q+1
       288: 2q^2+q
       289: q^2+3q+1
       291: 4q^2+4q+1
       292: 2q^2+q
       293: 2q^2+4q+1
       294: q
       295: q^2+3q+1
       296: 2q
       297: 2q^2+4q+1
       298: q
       299: q^2+4q+1
       301: q^2+3q+1
       302: q
       303: q^2+3q+1
       304: 2q
       305: 3q+1
       306: q
       307: 4q^2+4q+1
       308: q^2+q
       309: 3q^2+3q+1
       310: 2q
       311: 5q^2+4q+1
       312: 2q^2+q
       313: 4q^2+4q+1
       314: 2q^2+q
       315: q^3+6q^2+4q+1
       316: 3q^2+q
       317: q^3+6q^2+4q+1
       318: 2q^2+q
       319: 3q^2+4q+1
       321: q^3+5q^2+3q+1
       322: 2q^2+2q
       323: q^2+3q+1
       324: q
       325: q^3+5q^2+4q+1
       326: 2q^2+q
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 4q^2+5q+1
       339: 2q^2+2q
       340: 4q^2+5q+1
       341: 2q^2+2q
       342: q^3+4q^2+3q+1
       343: 2q^2+q
       344: 3q^2+5q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: q^2+4q+1
       349: q^2+3q+1
       350: q^3+4q^2+5q+1
       351: q^2+6q+1
       352: 6q^2+5q+1
       353: 3q^2+5q+1
       354: q^3+5q^2+5q+1
       355: 3q^2+5q+1
       356: 2q^3+8q^2+5q+1
       357: 3q^2+5q+1
       358: q^3+7q^2+5q+1
       359: 6q^2+7q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^2+4q+1
       370: q^3+4q^2+5q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: 2q^2+3q+1
       378: q
       379: q^2
       380: q
       381: 2q+1
       384: q
       385: q^2+3q+1
       386: q
       388: q
       389: q^2+3q+1
       390: q
       393: 3q+1
       394: q
       397: 3q^2+3q+1
       398: q^2
       399: q^2+q
       400: q
       401: 2q^2+3q+1
       402: q^2
       403: q
       404: q
       405: q^2+3q+1
       407: q
       413: q^2+3q+1
       417: q^2+3q+1
       419: 2q^2+4q+1
       420: q
       421: q^2+3q+1
       422: 2q
       423: 2q^2+4q+1
       424: q
       425: 2q^2+3q+1
       426: q^2+q
       427: 3q^2+5q+1
       428: q^2+2q
       429: q^2+4q+1
       431: q^2+3q+1
       432: 2q
       433: 3q+1
       434: q
       435: 2q+1
       437: 2q+1
       439: 2q+1
       440: q
       441: 2q+1
       443: q^2+6q+1
       445: q^2+4q+1
       446: 2q
       447: 4q^2+4q+1
       448: q^2+q
       449: 3q^2+3q+1
       450: 2q
       451: 4q^2+4q+1
       452: 2q^2+q
       453: 2q^2+4q+1
       454: q
       455: q^2+3q+1
       457: q^2+3q+1
       458: 2q
       459: 2q^2+4q+1
       460: q
       461: 3q^2+4q+1
       462: q^2+3q
       463: 4q^2+5q+1
       464: 2q^2+2q
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+5q^2+4q+1
       470: 2q^2+q
       471: q^2+4q+1
       473: q^2+3q+1
       474: 2q
       475: 3q+1
       476: q
       477: q^2+3q+1
       478: q
       479: q^2+4q+1
       480: 2q
       481: q^2+4q+1
       482: 5q+1
       483: q^2+4q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 3q+1
       496: 3q+1
       497: 3q^2+5q+1
       498: 3q^2+5q+1
       499: 3q^2+5q+1
       500: 3q^2+4q+1
       501: 2q^2+4q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: q^2+4q+1
       513: q^2+3q+1
       514: q^3+4q^2+5q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 2q+1
       524: q
       529: q^2+3q+1
       530: q
       532: q
       533: 3q+1
       534: q
       537: 2q+1
       541: 2q+1
       545: q^2+4q+1
       546: 2q
       549: 2q^2+3q+1
       550: q^2
       551: q
       552: q
       553: 2q+1
       555: q
       557: q^2+3q+1
       559: q
       560: q
       561: 2q^2+3q+1
       562: q^2+q
       563: q^2+2q
       564: q
       565: 3q+1
       566: q
       569: q^2+3q+1
       571: q
       573: q^2+4q+1
       574: 2q
       577: q^2+3q+1
       578: q
       580: q
       581: q
       585: 3q+1
       589: q^2+3q+1
       590: q
       591: q+1
       593: 3q+1
       595: 3q+1
       596: 2q
       597: q+1
       599: q^2+3q+1
       600: q
       601: 2q+1
       603: 2q+1
       605: 2q+1
       607: 2q+1
       608: q
       609: 2q+1
       613: 2q+1
       614: q
       615: 3q+1
       617: q+1
       619: 2q^2+4q+1
       620: q
       621: q^2+3q+1
       622: 2q
       623: q^2+3q+1
       625: 2q^2+4q+1
       626: q
       629: 2q^2+3q+1
       630: q^2+q
       631: q^2+2q+1
       632: 2q
       633: 2q+1
       639: q^2+3q+1
       641: q^2+4q+1
       643: q^2+3q+1
       644: 2q
       645: 3q+1
       646: q
       647: 2q+1
       649: 2q+1
       650: q
       651: 2q+1
       653: 2q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: q^2+4q+1
       682: 5q+1
       683: q^2+4q+1
       684: 2q+1
       685: q^2+2q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+3q+1
       694: q
       696: q
       699: q
       709: 2q+1
       712: q
       713: q+1
       717: 2q+1
       718: q
       721: 2q+1
       725: 2q+1
       733: q+1
       737: 2q+1
       739: q
       741: q^2+3q+1
       743: q
       744: q
       749: q+1
       751: q
       753: 3q+1
       754: q
       757: 2q+1
       761: 2q+1
       765: 2q+1
       766: q
       769: q+1
       775: 2q+1
       779: q+1
       781: q+1
       785: q+1
       787: 1
       791: 1
       793: 3q+1
       795: q+1
       797: q+1
       801: q+1
       805: q+1
       807: 2q+1
       808: q
       809: 1
       811: q+1
       815: q+1
       817: q^2+2q+1
       818: 2q
       819: 2q+1
       821: 3q+1
       825: q^2+3q+1
       826: q
       827: q+1
       829: 3q+1
       831: 3q+1
       832: 2q
       833: q+1
       835: q^2+3q+1
       836: q
       839: q+1
       840: q
       843: 2q+1
       844: q
       845: 2q+1
       847: 2q+1
       848: q
       849: 2q+1
       851: 2q+1
       855: 2q+1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: q+1
       920: q+1
       928: q+1
       940: q+1
       942: q
       944: 2q+1
       946: q
       948: q+1
       952: 2q+1
       953: q
       960: 2q+1
       964: 2q+1
       965: q
       968: q+1
       974: 2q+1
       988: q+1
       994: q+1
       998: 1
      1000: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1016: q+1
      1020: 1
      1022: 1
      1026: 1
      1032: q+1
      1033: q
      1036: q+1
      1038: q+1
      1040: q+1
      1044: 1
      1046: q+1
      1048: q+1
      1052: q+1
      1056: q+1
      1058: 2q+1
      1059: q
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: q+1
      1114: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1156: 1
      1172: 1
      1176: 1
      1180: 1
      1194: q+1
      1198: q+1
      1206: q+1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1230: 1
      1234: 1
      1240: 1
      1248: q+1
      1250: 1
      1254: q+1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1388: 1
      1392: 2
      1396: 1
      1400: 1
      1422: 1
      1430: 1
      1432: 1
      1436: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1468: 1
      1474: 1
      1476: 1
      1482: 1
      1487: 1
      1513: 1
      1515: 1
      1537: 1
      1595: 1
      1599: 1
      1615: 1
      1659: 1
      1665: 1
      1769: 1

1770:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: 9q^3+15q^2+5q+1
        23: 9q^3+15q^2+5q+1
        24: q^4+9q^3+12q^2+5q+1
        25: q^4+16q^3+16q^2+5q+1
        26: q^4+16q^3+16q^2+5q+1
        27: 4q^4+13q^3+13q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 5q^3+13q^2+5q+1
        32: 6q^3+12q^2+5q+1
        33: 9q^3+15q^2+5q+1
        34: 10q^3+14q^2+5q+1
        35: 10q^3+13q^2+5q+1
        36: q^4+16q^3+16q^2+5q+1
        37: 6q^3+10q^2+4q+1
        38: 3q^3+5q^2+q
        39: 6q^3+10q^2+4q+1
        40: 3q^3+5q^2+q
        41: q^4+6q^3+8q^2+4q+1
        42: 3q^3+4q^2+q
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 3q^3+12q^2+5q+1
        53: 5q^3+12q^2+5q+1
        54: 4q^3+10q^2+5q+1
        55: 10q^3+13q^2+5q+1
        56: q^4+12q^3+13q^2+5q+1
        57: 2q^4+8q^3+11q^2+5q+1
        58: q^3+5q^2+2q
        59: 4q^3+8q^2+3q+1
        60: 4q^3+5q^2+q
        61: 6q^3+9q^2+4q+1
        62: 4q^3+9q^2+4q+1
        63: q^3+4q^2+q
        64: 4q^3+8q^2+4q+1
        65: 2q^3+4q^2+q
        66: 6q^3+10q^2+4q+1
        67: 3q^3+5q^2+q
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 6q^3+10q^2+5q+1
        73: 2q^3+9q^2+5q+1
        74: q^3+7q^2+4q+1
        75: 3q^2+q
        76: 2q^3+7q^2+4q+1
        77: q^3+3q^2+q
        78: 2q^3+6q^2+4q+1
        79: 3q^2+q
        80: 2q^3+10q^2+5q+1
        81: 6q^3+12q^2+5q+1
        82: 2q^3+10q^2+5q+1
        83: 2q^3+10q^2+5q+1
        84: 4q^3+11q^2+5q+1
        85: 10q^3+13q^2+5q+1
        86: 7q^3+11q^2+5q+1
        87: 6q^3+11q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 3q^3+12q^2+5q+1
        95: 5q^3+12q^2+5q+1
        96: 4q^3+10q^2+5q+1
        97: 10q^3+13q^2+5q+1
        98: q^4+12q^3+13q^2+5q+1
        99: 2q^4+8q^3+11q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: q^3+3q^2+q
       104: q^3+2q^2
       105: 2q^2+q
       106: 3q^3+6q^2+3q+1
       107: q^3+2q^2+q
       108: 3q^3+6q^2+4q+1
       109: 2q^2+2q
       110: q^3+5q^2+3q+1
       111: 5q^2+4q+1
       112: 2q^2+q
       113: q^3+6q^2+4q+1
       114: 2q^2+q
       115: q^3+6q^2+4q+1
       116: 3q^2+q
       117: 2q^2+2q
       118: q^3+5q^2+3q+1
       119: 2q^2+q
       120: q^3+6q^2+4q+1
       121: 2q^3+7q^2+4q+1
       122: 3q^2+q
       123: 4q^3+8q^2+4q+1
       124: 2q^3+4q^2+q
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: q^3+7q^2+4q+1
       128: 3q^2+q
       129: 2q^3+7q^2+4q+1
       130: q^3+3q^2+q
       131: 2q^3+6q^2+4q+1
       132: 3q^2+q
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: 2q^3+8q^2+5q+1
       136: q^3+7q^2+5q+1
       137: 2q^3+10q^2+5q+1
       138: 2q^3+10q^2+5q+1
       139: 2q^3+10q^2+5q+1
       140: 3q^2+4q+1
       141: q^3+8q^2+5q+1
       142: 2q^3+9q^2+5q+1
       143: 4q^3+11q^2+5q+1
       144: 6q^3+11q^2+5q+1
       145: 7q^3+11q^2+5q+1
       146: 3q^3+9q^2+5q+1
       147: 6q^3+10q^2+5q+1
       148: 2q^3+9q^2+5q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: q^3+7q^2+4q+1
       152: 3q^2+q
       153: 2q^3+7q^2+4q+1
       154: q^3+3q^2+q
       155: 2q^3+6q^2+4q+1
       156: 3q^2+q
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: q^3+6q^2+5q+1
       161: 2q^3+6q^2+5q+1
       162: q^3+6q^2+5q+1
       163: 4q^3+10q^2+5q+1
       164: 6q^3+10q^2+5q+1
       165: 4q^3+10q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q^2+q
       170: q^2
       171: q
       172: 3q^2+3q+1
       173: q^2+q
       174: q^2
       175: q^2+q
       176: q^3+4q^2+3q+1
       177: q^3+6q^2+4q+1
       178: 3q^2+q
       179: q^3+6q^2+4q+1
       180: 2q^2+q
       181: 5q^2+4q+1
       182: 2q^2+q
       183: q^2+q
       184: 4q^2+4q+1
       185: 2q
       186: 3q^2+3q+1
       187: 4q^2+4q+1
       188: 2q^2+q
       189: q^3+5q^2+4q+1
       190: 2q^2+q
       191: 2q^2+2q
       192: q^3+5q^2+3q+1
       194: 3q^2+4q+1
       195: 2q^2+2q
       196: q^3+5q^2+3q+1
       197: q^2+3q+1
       198: q
       199: 2q^2+q
       200: q^3+6q^2+4q+1
       201: q^3+2q^2+q
       202: 3q^3+6q^2+4q+1
       203: 2q^2+2q
       204: q^3+5q^2+3q+1
       205: 5q^2+4q+1
       206: 2q^2+q
       207: 2q^3+7q^2+4q+1
       208: 3q^2+q
       209: q^3+6q^2+4q+1
       210: 2q^2+q
       211: q^3+6q^2+4q+1
       212: 3q^2+q
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: 2q^3+8q^2+5q+1
       224: 3q^2+5q+1
       225: q^3+7q^2+5q+1
       226: q^3+8q^2+5q+1
       227: 3q^2+5q+1
       228: q^3+6q^2+5q+1
       229: q^2+4q+1
       230: q^3+4q^2+5q+1
       231: 3q^3+9q^2+5q+1
       232: 6q^2+5q+1
       233: 4q^3+10q^2+5q+1
       234: 2q^3+8q^2+5q+1
       235: q^3+7q^2+5q+1
       236: 2q^3+10q^2+5q+1
       237: q^3+7q^2+4q+1
       238: 3q^2+q
       239: 2q^3+7q^2+4q+1
       240: q^3+3q^2+q
       241: 2q^3+6q^2+4q+1
       242: 3q^2+q
       243: 2q^3+10q^2+5q+1
       244: 3q^2+4q+1
       245: 2q^3+9q^2+5q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+5q^2+5q+1
       254: q^3+5q^2+5q+1
       255: q^3+5q^2+5q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q^2+q
       260: q^2
       261: q
       262: 3q^2+3q+1
       263: q
       264: q^2
       265: q
       266: 2q^2+3q+1
       269: q^2+3q+1
       270: q
       271: q^2+q
       272: q
       273: 3q^2+3q+1
       274: q^2
       275: q^2+q
       276: q^2
       277: q^2+q
       278: q^3+4q^2+3q+1
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: q^2+q
       284: 4q^2+4q+1
       285: 2q
       286: 3q^2+3q+1
       287: q^3+5q^2+4q+1
       288: 2q^2+q
       289: q^2+3q+1
       291: 4q^2+4q+1
       292: 2q^2+q
       293: q
       294: 2q^2+4q+1
       295: 2q
       296: q^2+3q+1
       297: 2q^2+4q+1
       298: q
       300: q^2+4q+1
       301: q^2+3q+1
       302: q
       303: 2q
       304: q^2+3q+1
       305: 3q+1
       306: q
       307: q^2+q
       308: 4q^2+4q+1
       309: 2q
       310: 3q^2+3q+1
       311: 5q^2+4q+1
       312: 2q^2+q
       313: 4q^2+4q+1
       314: 2q^2+q
       315: q^3+6q^2+4q+1
       316: 3q^2+q
       317: q^3+6q^2+4q+1
       318: 2q^2+q
       320: 3q^2+4q+1
       321: 2q^2+2q
       322: q^3+5q^2+3q+1
       323: q^2+3q+1
       324: q
       325: q^3+5q^2+4q+1
       326: 2q^2+q
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 4q^2+5q+1
       339: 2q^2+2q
       340: 4q^2+5q+1
       341: 2q^2+2q
       342: q^3+4q^2+3q+1
       343: 2q^2+q
       344: 3q^2+5q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: q^2+4q+1
       349: q^2+3q+1
       350: q^3+4q^2+5q+1
       351: q^2+6q+1
       352: 6q^2+5q+1
       353: 3q^2+5q+1
       354: q^3+5q^2+5q+1
       355: 3q^2+5q+1
       356: 2q^3+8q^2+5q+1
       357: 3q^2+5q+1
       358: q^3+7q^2+5q+1
       359: 6q^2+7q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^2+4q+1
       370: q^3+4q^2+5q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       378: q^2
       379: q
       380: 2q^2+3q+1
       381: q
       384: 2q+1
       385: q
       387: q
       388: q^2+3q+1
       391: q^2+3q+1
       392: q
       395: q
       396: 3q+1
       397: q^2+q
       398: q
       399: 3q^2+3q+1
       400: q^2
       401: q
       402: q
       403: q^2
       404: 2q^2+3q+1
       406: q^2+3q+1
       408: q
       413: q^2+3q+1
       417: q^2+3q+1
       419: q
       420: 2q^2+4q+1
       421: 2q
       422: q^2+3q+1
       423: 2q^2+4q+1
       424: q
       425: 2q^2+3q+1
       426: q^2+q
       427: 3q^2+5q+1
       428: q^2+2q
       430: q^2+4q+1
       431: 2q
       432: q^2+3q+1
       433: 3q+1
       434: q
       435: 2q+1
       438: 2q+1
       439: q
       440: 2q+1
       441: 2q+1
       444: q^2+6q+1
       445: q^2+4q+1
       446: 2q
       447: q^2+q
       448: 4q^2+4q+1
       449: 2q
       450: 3q^2+3q+1
       451: 4q^2+4q+1
       452: 2q^2+q
       453: q
       454: 2q^2+4q+1
       455: q^2+3q+1
       457: 2q
       458: q^2+3q+1
       459: 2q^2+4q+1
       460: q
       461: q^2+3q
       462: 3q^2+4q+1
       463: 4q^2+5q+1
       464: 2q^2+2q
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+5q^2+4q+1
       470: 2q^2+q
       472: q^2+4q+1
       473: 2q
       474: q^2+3q+1
       475: 3q+1
       476: q
       477: q^2+3q+1
       478: q
       479: q^2+4q+1
       480: 2q
       481: q^2+4q+1
       482: 5q+1
       483: q^2+4q+1
       484: q^2+4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 3q+1
       496: 3q+1
       497: 3q^2+5q+1
       498: 3q^2+5q+1
       499: 3q^2+5q+1
       500: 3q^2+4q+1
       501: 2q^2+4q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: q^2+4q+1
       513: q^2+3q+1
       514: q^3+4q^2+5q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: 2q+1
       529: q
       531: q
       532: q^2+3q+1
       535: q
       536: 3q+1
       539: 2q+1
       543: 2q+1
       547: q^2+4q+1
       548: 2q
       549: q
       550: q
       551: q^2
       552: 2q^2+3q+1
       553: q
       555: 2q+1
       557: q
       558: q
       559: q^2+3q+1
       561: q^2+2q
       562: q
       563: 2q^2+3q+1
       564: q^2+q
       567: q
       568: 3q+1
       570: q^2+3q+1
       572: q
       575: q^2+4q+1
       576: 2q
       577: q^2+3q+1
       578: q
       580: q
       581: q
       585: 3q+1
       589: q
       590: q^2+3q+1
       592: q+1
       594: 3q+1
       595: 2q
       596: 3q+1
       597: q+1
       599: q^2+3q+1
       600: q
       601: 2q+1
       604: 2q+1
       605: 2q+1
       607: q
       608: 2q+1
       609: 2q+1
       613: 2q+1
       614: q
       616: 3q+1
       617: q+1
       619: q
       620: 2q^2+4q+1
       621: 2q
       622: q^2+3q+1
       623: q^2+3q+1
       625: 2q^2+4q+1
       626: q
       629: 2q^2+3q+1
       630: q^2+q
       631: 2q
       632: q^2+2q+1
       633: 2q+1
       639: q^2+3q+1
       642: q^2+4q+1
       643: 2q
       644: q^2+3q+1
       645: 3q+1
       646: q
       648: 2q+1
       649: q
       650: 2q+1
       651: 2q+1
       653: 2q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: q^2+4q+1
       682: 5q+1
       683: q^2+4q+1
       684: 2q+1
       685: q^2+2q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q^2+3q+1
       698: q
       700: q
       701: q
       709: q
       712: 2q+1
       716: q+1
       719: q
       720: 2q+1
       723: 2q+1
       727: 2q+1
       735: q+1
       737: q
       739: 2q+1
       741: q
       742: q
       743: q^2+3q+1
       749: q
       751: q+1
       755: q
       756: 3q+1
       758: 2q+1
       762: 2q+1
       767: q
       768: 2q+1
       769: q+1
       775: 2q+1
       779: q+1
       781: q+1
       786: q+1
       788: 1
       791: 1
       794: 3q+1
       795: q+1
       797: q+1
       802: q+1
       806: q+1
       807: q
       808: 2q+1
       809: 1
       811: q+1
       816: q+1
       817: 2q
       818: q^2+2q+1
       819: 2q+1
       821: 3q+1
       825: q
       826: q^2+3q+1
       828: q+1
       830: 3q+1
       831: 2q
       832: 3q+1
       833: q+1
       835: q^2+3q+1
       836: q
       839: q
       840: q+1
       843: 2q+1
       844: q
       846: 2q+1
       847: q
       848: 2q+1
       849: 2q+1
       851: 2q+1
       855: 2q+1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       918: q+1
       922: q+1
       930: q+1
       940: q
       942: q+1
       944: q
       946: 2q+1
       950: q+1
       954: q
       955: 2q+1
       961: 2q+1
       966: q
       967: 2q+1
       968: q+1
       975: 2q+1
       991: q+1
       994: q+1
       999: 1
      1001: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1017: q+1
      1020: 1
      1022: 1
      1027: 1
      1032: q
      1033: q+1
      1036: q+1
      1038: q+1
      1041: q+1
      1045: 1
      1046: q+1
      1048: q+1
      1053: q+1
      1057: q+1
      1058: q
      1059: 2q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1091: q+1
      1116: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1158: 1
      1174: 1
      1178: 1
      1183: 1
      1197: q+1
      1199: q+1
      1208: q+1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: 1
      1235: 1
      1241: 1
      1248: q+1
      1251: 1
      1255: q+1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1329: 1
      1331: 1
      1358: 1
      1382: 1
      1390: 1
      1393: 2
      1399: 1
      1401: 1
      1424: 1
      1430: 1
      1432: 1
      1436: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1474: 1
      1477: 1
      1482: 1
      1487: 1
      1518: 1
      1522: 1
      1538: 1
      1598: 1
      1600: 1
      1617: 1
      1659: 1
      1666: 1
      1770: 1

1771:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: 9q^3+15q^2+5q+1
        23: 9q^3+15q^2+5q+1
        24: q^4+9q^3+12q^2+5q+1
        25: q^4+16q^3+16q^2+5q+1
        26: q^4+16q^3+16q^2+5q+1
        27: 4q^4+13q^3+13q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 5q^3+13q^2+5q+1
        32: 6q^3+12q^2+5q+1
        33: 9q^3+15q^2+5q+1
        34: 10q^3+14q^2+5q+1
        35: 10q^3+13q^2+5q+1
        36: q^4+16q^3+16q^2+5q+1
        37: 3q^3+5q^2+q
        38: 6q^3+10q^2+4q+1
        39: 3q^3+5q^2+q
        40: 6q^3+10q^2+4q+1
        41: 3q^3+4q^2+q
        42: q^4+6q^3+8q^2+4q+1
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 3q^3+12q^2+5q+1
        53: 5q^3+12q^2+5q+1
        54: 4q^3+10q^2+5q+1
        55: 10q^3+13q^2+5q+1
        56: q^4+12q^3+13q^2+5q+1
        57: 2q^4+8q^3+11q^2+5q+1
        58: q^3+5q^2+2q
        59: 4q^3+8q^2+3q+1
        60: 6q^3+9q^2+4q+1
        61: 4q^3+5q^2+q
        62: q^3+4q^2+q
        63: 4q^3+9q^2+4q+1
        64: 2q^3+4q^2+q
        65: 4q^3+8q^2+4q+1
        66: 3q^3+5q^2+q
        67: 6q^3+10q^2+4q+1
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 6q^3+10q^2+5q+1
        73: 2q^3+9q^2+5q+1
        74: 3q^2+q
        75: q^3+7q^2+4q+1
        76: q^3+3q^2+q
        77: 2q^3+7q^2+4q+1
        78: 3q^2+q
        79: 2q^3+6q^2+4q+1
        80: 2q^3+10q^2+5q+1
        81: 6q^3+12q^2+5q+1
        82: 2q^3+10q^2+5q+1
        83: 2q^3+10q^2+5q+1
        84: 4q^3+11q^2+5q+1
        85: 10q^3+13q^2+5q+1
        86: 7q^3+11q^2+5q+1
        87: 6q^3+11q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 3q^3+12q^2+5q+1
        95: 5q^3+12q^2+5q+1
        96: 4q^3+10q^2+5q+1
        97: 10q^3+13q^2+5q+1
        98: q^4+12q^3+13q^2+5q+1
        99: 2q^4+8q^3+11q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: 2q^2+q
       104: 3q^3+6q^2+3q+1
       105: q^3+3q^2+q
       106: q^3+2q^2
       107: 3q^3+6q^2+4q+1
       108: q^3+2q^2+q
       109: 2q^2+2q
       110: q^3+5q^2+3q+1
       111: 2q^2+q
       112: 5q^2+4q+1
       113: 2q^2+q
       114: q^3+6q^2+4q+1
       115: 3q^2+q
       116: q^3+6q^2+4q+1
       117: 2q^2+2q
       118: q^3+5q^2+3q+1
       119: q^3+6q^2+4q+1
       120: 2q^2+q
       121: 3q^2+q
       122: 2q^3+7q^2+4q+1
       123: 2q^3+4q^2+q
       124: 4q^3+8q^2+4q+1
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: 3q^2+q
       128: q^3+7q^2+4q+1
       129: q^3+3q^2+q
       130: 2q^3+7q^2+4q+1
       131: 3q^2+q
       132: 2q^3+6q^2+4q+1
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: 2q^3+8q^2+5q+1
       136: q^3+7q^2+5q+1
       137: 2q^3+10q^2+5q+1
       138: 2q^3+10q^2+5q+1
       139: 2q^3+10q^2+5q+1
       140: 3q^2+4q+1
       141: q^3+8q^2+5q+1
       142: 2q^3+9q^2+5q+1
       143: 4q^3+11q^2+5q+1
       144: 6q^3+11q^2+5q+1
       145: 7q^3+11q^2+5q+1
       146: 3q^3+9q^2+5q+1
       147: 6q^3+10q^2+5q+1
       148: 2q^3+9q^2+5q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: 3q^2+q
       152: q^3+7q^2+4q+1
       153: q^3+3q^2+q
       154: 2q^3+7q^2+4q+1
       155: 3q^2+q
       156: 2q^3+6q^2+4q+1
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: q^3+6q^2+5q+1
       161: 2q^3+6q^2+5q+1
       162: q^3+6q^2+5q+1
       163: 4q^3+10q^2+5q+1
       164: 6q^3+10q^2+5q+1
       165: 4q^3+10q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q
       170: 3q^2+3q+1
       171: q^2+q
       172: q^2
       173: q^2+q
       174: q^3+4q^2+3q+1
       175: q^2+q
       176: q^2
       177: 3q^2+q
       178: q^3+6q^2+4q+1
       179: 2q^2+q
       180: q^3+6q^2+4q+1
       181: 2q^2+q
       182: 5q^2+4q+1
       183: 4q^2+4q+1
       184: q^2+q
       185: 2q
       186: 3q^2+3q+1
       187: 2q^2+q
       188: 4q^2+4q+1
       189: 2q^2+q
       190: q^3+5q^2+4q+1
       191: 2q^2+2q
       192: q^3+5q^2+3q+1
       193: 3q^2+4q+1
       195: 2q^2+2q
       196: q^3+5q^2+3q+1
       197: q
       198: q^2+3q+1
       199: q^3+6q^2+4q+1
       200: 2q^2+q
       201: 3q^3+6q^2+4q+1
       202: q^3+2q^2+q
       203: 2q^2+2q
       204: q^3+5q^2+3q+1
       205: 2q^2+q
       206: 5q^2+4q+1
       207: 3q^2+q
       208: 2q^3+7q^2+4q+1
       209: 2q^2+q
       210: q^3+6q^2+4q+1
       211: 3q^2+q
       212: q^3+6q^2+4q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: 2q^3+8q^2+5q+1
       224: 3q^2+5q+1
       225: q^3+7q^2+5q+1
       226: q^3+8q^2+5q+1
       227: 3q^2+5q+1
       228: q^3+6q^2+5q+1
       229: q^2+4q+1
       230: q^3+4q^2+5q+1
       231: 3q^3+9q^2+5q+1
       232: 6q^2+5q+1
       233: 4q^3+10q^2+5q+1
       234: 2q^3+8q^2+5q+1
       235: q^3+7q^2+5q+1
       236: 2q^3+10q^2+5q+1
       237: 3q^2+q
       238: q^3+7q^2+4q+1
       239: q^3+3q^2+q
       240: 2q^3+7q^2+4q+1
       241: 3q^2+q
       242: 2q^3+6q^2+4q+1
       243: 2q^3+10q^2+5q+1
       244: 3q^2+4q+1
       245: 2q^3+9q^2+5q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+5q^2+5q+1
       254: q^3+5q^2+5q+1
       255: q^3+5q^2+5q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q
       260: 3q^2+3q+1
       261: q^2+q
       262: q^2
       263: q
       264: 2q^2+3q+1
       265: q
       266: q^2
       267: q
       268: q^2+3q+1
       271: q
       272: q^2+q
       273: q^2
       274: 3q^2+3q+1
       275: q^2+q
       276: q^3+4q^2+3q+1
       277: q^2+q
       278: q^2
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: 4q^2+4q+1
       284: q^2+q
       285: 2q
       286: 3q^2+3q+1
       287: 2q^2+q
       288: q^3+5q^2+4q+1
       290: q^2+3q+1
       291: 2q^2+q
       292: 4q^2+4q+1
       293: 2q^2+4q+1
       294: q
       295: 2q
       296: q^2+3q+1
       297: q
       298: 2q^2+4q+1
       299: q^2+4q+1
       301: q
       302: q^2+3q+1
       303: 2q
       304: q^2+3q+1
       305: q
       306: 3q+1
       307: 4q^2+4q+1
       308: q^2+q
       309: 2q
       310: 3q^2+3q+1
       311: 2q^2+q
       312: 5q^2+4q+1
       313: 2q^2+q
       314: 4q^2+4q+1
       315: 3q^2+q
       316: q^3+6q^2+4q+1
       317: 2q^2+q
       318: q^3+6q^2+4q+1
       319: 3q^2+4q+1
       321: 2q^2+2q
       322: q^3+5q^2+3q+1
       323: q
       324: q^2+3q+1
       325: 2q^2+q
       326: q^3+5q^2+4q+1
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 2q^2+2q
       339: 4q^2+5q+1
       340: 2q^2+2q
       341: 4q^2+5q+1
       342: 2q^2+q
       343: q^3+4q^2+3q+1
       344: 3q^2+5q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: q^2+4q+1
       349: q^2+3q+1
       350: q^3+4q^2+5q+1
       351: q^2+6q+1
       352: 6q^2+5q+1
       353: 3q^2+5q+1
       354: q^3+5q^2+5q+1
       355: 3q^2+5q+1
       356: 2q^3+8q^2+5q+1
       357: 3q^2+5q+1
       358: q^3+7q^2+5q+1
       359: 6q^2+7q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^2+4q+1
       370: q^3+4q^2+5q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       378: 2q^2+3q+1
       379: q
       380: q^2
       382: 2q+1
       383: q
       385: q
       386: q^2+3q+1
       387: q
       389: q
       390: q^2+3q+1
       393: q
       394: 3q+1
       397: q
       398: q^2+q
       399: q^2
       400: 3q^2+3q+1
       401: q
       402: q
       403: 2q^2+3q+1
       404: q^2
       405: q
       407: q^2+3q+1
       414: q^2+3q+1
       418: q^2+3q+1
       419: 2q^2+4q+1
       420: q
       421: 2q
       422: q^2+3q+1
       423: q
       424: 2q^2+4q+1
       425: q^2+q
       426: 2q^2+3q+1
       427: q^2+2q
       428: 3q^2+5q+1
       429: q^2+4q+1
       431: 2q
       432: q^2+3q+1
       433: q
       434: 3q+1
       436: 2q+1
       437: 2q+1
       439: q
       440: 2q+1
       442: 2q+1
       443: q^2+6q+1
       445: 2q
       446: q^2+4q+1
       447: 4q^2+4q+1
       448: q^2+q
       449: 2q
       450: 3q^2+3q+1
       451: 2q^2+q
       452: 4q^2+4q+1
       453: 2q^2+4q+1
       454: q
       456: q^2+3q+1
       457: 2q
       458: q^2+3q+1
       459: q
       460: 2q^2+4q+1
       461: q^2+3q
       462: 3q^2+4q+1
       463: 2q^2+2q
       464: 4q^2+5q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       469: 2q^2+q
       470: q^3+5q^2+4q+1
       471: q^2+4q+1
       473: 2q
       474: q^2+3q+1
       475: q
       476: 3q+1
       477: q
       478: q^2+3q+1
       479: 2q
       480: q^2+4q+1
       481: q^2+4q+1
       482: 5q+1
       483: q^2+4q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 3q+1
       496: 3q+1
       497: 3q^2+5q+1
       498: 3q^2+5q+1
       499: 3q^2+5q+1
       500: 3q^2+4q+1
       501: 2q^2+4q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: q^2+4q+1
       513: q^2+3q+1
       514: q^3+4q^2+5q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 2q+1
       523: q
       529: q
       530: q^2+3q+1
       531: q
       533: q
       534: 3q+1
       538: 2q+1
       542: 2q+1
       545: 2q
       546: q^2+4q+1
       549: q
       550: q
       551: 2q^2+3q+1
       552: q^2
       554: q
       556: 2q+1
       557: q
       558: q
       560: q^2+3q+1
       561: q
       562: q^2+2q
       563: q^2+q
       564: 2q^2+3q+1
       565: q
       566: 3q+1
       569: q
       571: q^2+3q+1
       573: 2q
       574: q^2+4q+1
       577: q
       578: q
       580: q
       581: q^2+3q+1
       586: 3q+1
       589: q^2+3q+1
       590: q
       592: q+1
       593: 3q+1
       595: 2q
       596: 3q+1
       598: q+1
       599: q
       600: q^2+3q+1
       602: 2q+1
       603: 2q+1
       606: 2q+1
       607: q
       608: 2q+1
       610: 2q+1
       613: q
       614: 2q+1
       615: 3q+1
       618: q+1
       619: 2q^2+4q+1
       620: q
       621: 2q
       622: q^2+3q+1
       624: q^2+3q+1
       625: q
       626: 2q^2+4q+1
       629: q^2+q
       630: 2q^2+3q+1
       631: 2q
       632: q^2+2q+1
       634: 2q+1
       640: q^2+3q+1
       641: q^2+4q+1
       643: 2q
       644: q^2+3q+1
       645: q
       646: 3q+1
       647: 2q+1
       649: q
       650: 2q+1
       652: 2q+1
       654: 2q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: q^2+4q+1
       682: 5q+1
       683: q^2+4q+1
       684: 2q+1
       685: q^2+2q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       696: q
       699: q^2+3q+1
       710: 2q+1
       711: q
       715: q+1
       717: q
       718: 2q+1
       722: 2q+1
       726: 2q+1
       734: q+1
       738: q
       740: 2q+1
       741: q
       742: q
       744: q^2+3q+1
       750: q
       752: q+1
       753: q
       754: 3q+1
       759: 2q+1
       763: 2q+1
       765: q
       766: 2q+1
       773: q+1
       776: 2q+1
       780: q+1
       782: q+1
       785: q+1
       788: 1
       792: 1
       793: 3q+1
       796: q+1
       798: q+1
       801: q+1
       805: q+1
       807: q
       808: 2q+1
       810: 1
       812: q+1
       815: q+1
       817: 2q
       818: q^2+2q+1
       820: 2q+1
       822: 3q+1
       825: q^2+3q+1
       826: q
       828: q+1
       829: 3q+1
       831: 2q
       832: 3q+1
       834: q+1
       835: q
       836: q^2+3q+1
       839: q
       840: q+1
       843: q
       844: 2q+1
       845: 2q+1
       847: q
       848: 2q+1
       850: 2q+1
       852: 2q+1
       855: q
       856: 2q+1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       917: q+1
       921: q+1
       929: q+1
       941: q
       943: q+1
       945: q
       947: 2q+1
       951: q+1
       952: q
       953: 2q+1
       962: 2q+1
       964: q
       965: 2q+1
       972: q+1
       976: 2q+1
       989: q+1
       995: q+1
       999: 1
      1000: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1016: q+1
      1021: 1
      1023: 1
      1026: 1
      1032: q
      1033: q+1
      1037: q+1
      1039: q+1
      1040: q+1
      1045: 1
      1047: q+1
      1049: q+1
      1052: q+1
      1056: q+1
      1058: q
      1059: 2q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1092: q+1
      1117: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1157: 1
      1175: 1
      1177: 1
      1181: 1
      1195: q+1
      1200: q+1
      1207: q+1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: 1
      1234: 1
      1240: 1
      1249: q+1
      1251: 1
      1254: q+1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1327: 1
      1332: 1
      1357: 1
      1383: 1
      1389: 1
      1394: 2
      1397: 1
      1402: 1
      1423: 1
      1434: 1
      1435: 1
      1437: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1475: 1
      1476: 1
      1483: 1
      1487: 1
      1519: 1
      1523: 1
      1539: 1
      1596: 1
      1601: 1
      1616: 1
      1660: 1
      1665: 1
      1771: 1

1772:    0: q^4+16q^3+16q^2+5q+1
         1: q^4+16q^3+16q^2+5q+1
         2: 4q^4+13q^3+13q^2+5q+1
         3: q^4+16q^3+16q^2+5q+1
         4: 4q^4+13q^3+13q^2+5q+1
         5: q^4+16q^3+16q^2+5q+1
         6: q^5+7q^4+15q^3+13q^2+5q+1
         7: q^5+5q^4+10q^3+11q^2+5q+1
         8: 4q^4+13q^3+13q^2+5q+1
         9: q^5+5q^4+10q^3+11q^2+5q+1
        10: 10q^3+14q^2+5q+1
        11: 10q^3+14q^2+5q+1
        12: 3q^4+10q^3+11q^2+5q+1
        13: 10q^3+13q^2+5q+1
        14: 2q^4+8q^3+11q^2+5q+1
        15: 10q^3+13q^2+5q+1
        16: q^4+16q^3+16q^2+5q+1
        17: q^4+16q^3+16q^2+5q+1
        18: q^5+5q^4+10q^3+11q^2+5q+1
        19: 10q^3+13q^2+5q+1
        20: q^4+12q^3+13q^2+5q+1
        21: 2q^4+8q^3+11q^2+5q+1
        22: 9q^3+15q^2+5q+1
        23: 9q^3+15q^2+5q+1
        24: q^4+9q^3+12q^2+5q+1
        25: q^4+16q^3+16q^2+5q+1
        26: q^4+16q^3+16q^2+5q+1
        27: 4q^4+13q^3+13q^2+5q+1
        28: 10q^3+14q^2+5q+1
        29: 7q^3+11q^2+5q+1
        30: 6q^3+11q^2+5q+1
        31: 5q^3+13q^2+5q+1
        32: 6q^3+12q^2+5q+1
        33: 9q^3+15q^2+5q+1
        34: 10q^3+14q^2+5q+1
        35: 10q^3+13q^2+5q+1
        36: q^4+16q^3+16q^2+5q+1
        37: 3q^3+5q^2+q
        38: 6q^3+10q^2+4q+1
        39: 3q^3+5q^2+q
        40: 6q^3+10q^2+4q+1
        41: 3q^3+4q^2+q
        42: q^4+6q^3+8q^2+4q+1
        43: 4q^3+11q^2+5q+1
        44: q^4+5q^3+9q^2+5q+1
        45: 4q^3+11q^2+5q+1
        46: 10q^3+13q^2+5q+1
        47: 10q^3+13q^2+5q+1
        48: 2q^4+8q^3+11q^2+5q+1
        49: 10q^3+13q^2+5q+1
        50: q^4+12q^3+13q^2+5q+1
        51: 2q^4+8q^3+11q^2+5q+1
        52: 3q^3+12q^2+5q+1
        53: 5q^3+12q^2+5q+1
        54: 4q^3+10q^2+5q+1
        55: 10q^3+13q^2+5q+1
        56: q^4+12q^3+13q^2+5q+1
        57: 2q^4+8q^3+11q^2+5q+1
        58: 4q^3+8q^2+3q+1
        59: q^3+5q^2+2q
        60: 4q^3+5q^2+q
        61: 6q^3+9q^2+4q+1
        62: q^3+4q^2+q
        63: 4q^3+9q^2+4q+1
        64: 2q^3+4q^2+q
        65: 4q^3+8q^2+4q+1
        66: 3q^3+5q^2+q
        67: 6q^3+10q^2+4q+1
        68: q^3+8q^2+5q+1
        69: 6q^3+11q^2+5q+1
        70: 3q^3+9q^2+5q+1
        71: 7q^3+11q^2+5q+1
        72: 6q^3+10q^2+5q+1
        73: 2q^3+9q^2+5q+1
        74: 3q^2+q
        75: q^3+7q^2+4q+1
        76: q^3+3q^2+q
        77: 2q^3+7q^2+4q+1
        78: 3q^2+q
        79: 2q^3+6q^2+4q+1
        80: 2q^3+10q^2+5q+1
        81: 6q^3+12q^2+5q+1
        82: 2q^3+10q^2+5q+1
        83: 2q^3+10q^2+5q+1
        84: 4q^3+11q^2+5q+1
        85: 10q^3+13q^2+5q+1
        86: 7q^3+11q^2+5q+1
        87: 6q^3+11q^2+5q+1
        88: 4q^3+11q^2+5q+1
        89: 4q^3+11q^2+5q+1
        90: q^4+5q^3+9q^2+5q+1
        91: 4q^3+10q^2+5q+1
        92: 6q^3+10q^2+5q+1
        93: 4q^3+10q^2+5q+1
        94: 3q^3+12q^2+5q+1
        95: 5q^3+12q^2+5q+1
        96: 4q^3+10q^2+5q+1
        97: 10q^3+13q^2+5q+1
        98: q^4+12q^3+13q^2+5q+1
        99: 2q^4+8q^3+11q^2+5q+1
       100: 3q^3+12q^2+5q+1
       101: 5q^3+12q^2+5q+1
       102: 4q^3+10q^2+5q+1
       103: q^3+2q^2
       104: q^3+3q^2+q
       105: 3q^3+6q^2+3q+1
       106: 2q^2+q
       107: q^3+2q^2+q
       108: 3q^3+6q^2+4q+1
       109: q^3+5q^2+3q+1
       110: 2q^2+2q
       111: 2q^2+q
       112: 5q^2+4q+1
       113: 2q^2+q
       114: q^3+6q^2+4q+1
       115: 3q^2+q
       116: q^3+6q^2+4q+1
       117: q^3+5q^2+3q+1
       118: 2q^2+2q
       119: 2q^2+q
       120: q^3+6q^2+4q+1
       121: 3q^2+q
       122: 2q^3+7q^2+4q+1
       123: 2q^3+4q^2+q
       124: 4q^3+8q^2+4q+1
       125: q^3+8q^2+5q+1
       126: 3q^3+9q^2+5q+1
       127: 3q^2+q
       128: q^3+7q^2+4q+1
       129: q^3+3q^2+q
       130: 2q^3+7q^2+4q+1
       131: 3q^2+q
       132: 2q^3+6q^2+4q+1
       133: 6q^2+5q+1
       134: 4q^3+10q^2+5q+1
       135: 2q^3+8q^2+5q+1
       136: q^3+7q^2+5q+1
       137: 2q^3+10q^2+5q+1
       138: 2q^3+10q^2+5q+1
       139: 2q^3+10q^2+5q+1
       140: 3q^2+4q+1
       141: q^3+8q^2+5q+1
       142: 2q^3+9q^2+5q+1
       143: 4q^3+11q^2+5q+1
       144: 6q^3+11q^2+5q+1
       145: 7q^3+11q^2+5q+1
       146: 3q^3+9q^2+5q+1
       147: 6q^3+10q^2+5q+1
       148: 2q^3+9q^2+5q+1
       149: 2q^3+10q^2+5q+1
       150: 2q^3+10q^2+5q+1
       151: 3q^2+q
       152: q^3+7q^2+4q+1
       153: q^3+3q^2+q
       154: 2q^3+7q^2+4q+1
       155: 3q^2+q
       156: 2q^3+6q^2+4q+1
       157: q^3+5q^2+5q+1
       158: q^3+5q^2+5q+1
       159: q^3+5q^2+5q+1
       160: q^3+6q^2+5q+1
       161: 2q^3+6q^2+5q+1
       162: q^3+6q^2+5q+1
       163: 4q^3+10q^2+5q+1
       164: 6q^3+10q^2+5q+1
       165: 4q^3+10q^2+5q+1
       166: 3q^3+12q^2+5q+1
       167: 5q^3+12q^2+5q+1
       168: 4q^3+10q^2+5q+1
       169: q^2
       170: q^2+q
       171: 3q^2+3q+1
       172: q
       173: q^2
       174: q^2+q
       175: q^3+4q^2+3q+1
       176: q^2+q
       177: 3q^2+q
       178: q^3+6q^2+4q+1
       179: 2q^2+q
       180: q^3+6q^2+4q+1
       181: 2q^2+q
       182: 5q^2+4q+1
       183: q^2+q
       184: 4q^2+4q+1
       185: 3q^2+3q+1
       186: 2q
       187: 2q^2+q
       188: 4q^2+4q+1
       189: 2q^2+q
       190: q^3+5q^2+4q+1
       191: q^3+5q^2+3q+1
       192: 2q^2+2q
       194: 3q^2+4q+1
       195: q^3+5q^2+3q+1
       196: 2q^2+2q
       197: q
       198: q^2+3q+1
       199: 2q^2+q
       200: q^3+6q^2+4q+1
       201: q^3+2q^2+q
       202: 3q^3+6q^2+4q+1
       203: q^3+5q^2+3q+1
       204: 2q^2+2q
       205: 2q^2+q
       206: 5q^2+4q+1
       207: 3q^2+q
       208: 2q^3+7q^2+4q+1
       209: 2q^2+q
       210: q^3+6q^2+4q+1
       211: 3q^2+q
       212: q^3+6q^2+4q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 6q^2+5q+1
       220: 3q^2+5q+1
       221: q^3+5q^2+5q+1
       222: 3q^2+5q+1
       223: 2q^3+8q^2+5q+1
       224: 3q^2+5q+1
       225: q^3+7q^2+5q+1
       226: q^3+8q^2+5q+1
       227: 3q^2+5q+1
       228: q^3+6q^2+5q+1
       229: q^2+4q+1
       230: q^3+4q^2+5q+1
       231: 3q^3+9q^2+5q+1
       232: 6q^2+5q+1
       233: 4q^3+10q^2+5q+1
       234: 2q^3+8q^2+5q+1
       235: q^3+7q^2+5q+1
       236: 2q^3+10q^2+5q+1
       237: 3q^2+q
       238: q^3+7q^2+4q+1
       239: q^3+3q^2+q
       240: 2q^3+7q^2+4q+1
       241: 3q^2+q
       242: 2q^3+6q^2+4q+1
       243: 2q^3+10q^2+5q+1
       244: 3q^2+4q+1
       245: 2q^3+9q^2+5q+1
       246: q^3+8q^2+5q+1
       247: 6q^2+7q+1
       248: 6q^2+7q+1
       249: q^3+6q^2+4q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+5q^2+5q+1
       254: q^3+5q^2+5q+1
       255: q^3+5q^2+5q+1
       256: q^3+6q^2+5q+1
       257: 2q^3+6q^2+5q+1
       258: q^3+6q^2+5q+1
       259: q^2
       260: q^2+q
       261: 3q^2+3q+1
       262: q
       263: q^2
       264: q
       265: 2q^2+3q+1
       266: q
       269: q
       270: q^2+3q+1
       271: q^2
       272: 3q^2+3q+1
       273: q
       274: q^2+q
       275: q^2
       276: q^2+q
       277: q^3+4q^2+3q+1
       278: q^2+q
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: q^2+q
       284: 4q^2+4q+1
       285: 3q^2+3q+1
       286: 2q
       287: 2q^2+q
       288: q^3+5q^2+4q+1
       290: q^2+3q+1
       291: 2q^2+q
       292: 4q^2+4q+1
       293: q
       294: 2q^2+4q+1
       295: q^2+3q+1
       296: 2q
       297: q
       298: 2q^2+4q+1
       300: q^2+4q+1
       301: q
       302: q^2+3q+1
       303: q^2+3q+1
       304: 2q
       305: q
       306: 3q+1
       307: q^2+q
       308: 4q^2+4q+1
       309: 3q^2+3q+1
       310: 2q
       311: 2q^2+q
       312: 5q^2+4q+1
       313: 2q^2+q
       314: 4q^2+4q+1
       315: 3q^2+q
       316: q^3+6q^2+4q+1
       317: 2q^2+q
       318: q^3+6q^2+4q+1
       320: 3q^2+4q+1
       321: q^3+5q^2+3q+1
       322: 2q^2+2q
       323: q
       324: q^2+3q+1
       325: 2q^2+q
       326: q^3+5q^2+4q+1
       333: 3q^2+5q+1
       334: 3q^2+5q+1
       335: 3q^2+5q+1
       336: 3q^2+4q+1
       337: 4q^2+7q+1
       338: 2q^2+2q
       339: 4q^2+5q+1
       340: 2q^2+2q
       341: 4q^2+5q+1
       342: 2q^2+q
       343: q^3+4q^2+3q+1
       344: 3q^2+5q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: q^2+4q+1
       349: q^2+3q+1
       350: q^3+4q^2+5q+1
       351: q^2+6q+1
       352: 6q^2+5q+1
       353: 3q^2+5q+1
       354: q^3+5q^2+5q+1
       355: 3q^2+5q+1
       356: 2q^3+8q^2+5q+1
       357: 3q^2+5q+1
       358: q^3+7q^2+5q+1
       359: 6q^2+7q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+8q^2+5q+1
       367: 3q^2+5q+1
       368: q^3+6q^2+5q+1
       369: q^2+4q+1
       370: q^3+4q^2+5q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q^2
       378: q
       379: 2q^2+3q+1
       380: q
       382: q
       383: 2q+1
       386: q
       387: q^2+3q+1
       388: q
       391: q
       392: q^2+3q+1
       395: 3q+1
       396: q
       397: q^2
       398: 3q^2+3q+1
       399: q
       400: q^2+q
       401: q^2
       402: 2q^2+3q+1
       403: q
       404: q
       406: q
       408: q^2+3q+1
       414: q^2+3q+1
       418: q^2+3q+1
       419: q
       420: 2q^2+4q+1
       421: q^2+3q+1
       422: 2q
       423: q
       424: 2q^2+4q+1
       425: q^2+q
       426: 2q^2+3q+1
       427: q^2+2q
       428: 3q^2+5q+1
       430: q^2+4q+1
       431: q^2+3q+1
       432: 2q
       433: q
       434: 3q+1
       436: 2q+1
       438: 2q+1
       439: 2q+1
       440: q
       442: 2q+1
       444: q^2+6q+1
       445: 2q
       446: q^2+4q+1
       447: q^2+q
       448: 4q^2+4q+1
       449: 3q^2+3q+1
       450: 2q
       451: 2q^2+q
       452: 4q^2+4q+1
       453: q
       454: 2q^2+4q+1
       456: q^2+3q+1
       457: q^2+3q+1
       458: 2q
       459: q
       460: 2q^2+4q+1
       461: 3q^2+4q+1
       462: q^2+3q
       463: 2q^2+2q
       464: 4q^2+5q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       469: 2q^2+q
       470: q^3+5q^2+4q+1
       472: q^2+4q+1
       473: q^2+3q+1
       474: 2q
       475: q
       476: 3q+1
       477: q
       478: q^2+3q+1
       479: 2q
       480: q^2+4q+1
       481: q^2+4q+1
       482: 5q+1
       483: q^2+4q+1
       484: q^2+4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 3q+1
       496: 3q+1
       497: 3q^2+5q+1
       498: 3q^2+5q+1
       499: 3q^2+5q+1
       500: 3q^2+4q+1
       501: 2q^2+4q+1
       508: 3q^2+5q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: q^2+4q+1
       513: q^2+3q+1
       514: q^3+4q^2+5q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: 2q+1
       530: q
       531: q^2+3q+1
       532: q
       535: 3q+1
       536: q
       540: 2q+1
       544: 2q+1
       547: 2q
       548: q^2+4q+1
       549: q^2
       550: 2q^2+3q+1
       551: q
       552: q
       554: 2q+1
       556: q
       558: q^2+3q+1
       559: q
       560: q
       561: q^2+q
       562: 2q^2+3q+1
       563: q
       564: q^2+2q
       567: 3q+1
       568: q
       570: q
       572: q^2+3q+1
       575: 2q
       576: q^2+4q+1
       577: q
       578: q
       580: q
       581: q^2+3q+1
       586: 3q+1
       589: q
       590: q^2+3q+1
       591: q+1
       594: 3q+1
       595: 3q+1
       596: 2q
       598: q+1
       599: q
       600: q^2+3q+1
       602: 2q+1
       604: 2q+1
       606: 2q+1
       607: 2q+1
       608: q
       610: 2q+1
       613: q
       614: 2q+1
       616: 3q+1
       618: q+1
       619: q
       620: 2q^2+4q+1
       621: q^2+3q+1
       622: 2q
       624: q^2+3q+1
       625: q
       626: 2q^2+4q+1
       629: q^2+q
       630: 2q^2+3q+1
       631: q^2+2q+1
       632: 2q
       634: 2q+1
       640: q^2+3q+1
       642: q^2+4q+1
       643: q^2+3q+1
       644: 2q
       645: q
       646: 3q+1
       648: 2q+1
       649: 2q+1
       650: q
       652: 2q+1
       654: 2q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: q^2+4q+1
       682: 5q+1
       683: q^2+4q+1
       684: 2q+1
       685: q^2+2q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q
       698: q
       700: q^2+3q+1
       701: q
       710: q
       711: 2q+1
       714: q+1
       719: 2q+1
       720: q
       724: 2q+1
       728: 2q+1
       736: q+1
       738: 2q+1
       740: q
       742: q^2+3q+1
       743: q
       744: q
       750: q+1
       752: q
       755: 3q+1
       756: q
       760: 2q+1
       764: 2q+1
       767: 2q+1
       768: q
       773: q+1
       776: 2q+1
       780: q+1
       782: q+1
       786: q+1
       787: 1
       792: 1
       794: 3q+1
       796: q+1
       798: q+1
       802: q+1
       806: q+1
       807: 2q+1
       808: q
       810: 1
       812: q+1
       816: q+1
       817: q^2+2q+1
       818: 2q
       820: 2q+1
       822: 3q+1
       825: q
       826: q^2+3q+1
       827: q+1
       830: 3q+1
       831: 3q+1
       832: 2q
       834: q+1
       835: q
       836: q^2+3q+1
       839: q+1
       840: q
       843: q
       844: 2q+1
       846: 2q+1
       847: 2q+1
       848: q
       850: 2q+1
       852: 2q+1
       855: q
       856: 2q+1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       919: q+1
       923: q+1
       931: q+1
       941: q+1
       943: q
       945: 2q+1
       947: q
       949: q+1
       954: 2q+1
       955: q
       963: 2q+1
       966: 2q+1
       967: q
       972: q+1
       977: 2q+1
       990: q+1
       995: q+1
       998: 1
      1001: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1017: q+1
      1021: 1
      1023: 1
      1027: 1
      1032: q+1
      1033: q
      1037: q+1
      1039: q+1
      1041: q+1
      1044: 1
      1047: q+1
      1049: q+1
      1053: q+1
      1057: q+1
      1058: 2q+1
      1059: q
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1093: q+1
      1115: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1159: 1
      1173: 1
      1179: 1
      1182: 1
      1196: q+1
      1201: q+1
      1209: q+1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1231: 1
      1235: 1
      1241: 1
      1249: q+1
      1250: 1
      1255: q+1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1391: 1
      1395: 2
      1398: 1
      1403: 1
      1425: 1
      1434: 1
      1435: 1
      1437: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1469: 1
      1475: 1
      1477: 1
      1483: 1
      1487: 1
      1520: 1
      1524: 1
      1540: 1
      1597: 1
      1602: 1
      1618: 1
      1660: 1
      1666: 1
      1772: 1

1773:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 4q^3+9q^2+6q+1
        26: q^4+5q^3+9q^2+6q+1
        27: 4q^3+9q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 2q^3+7q^2+6q+1
        35: 4q^3+9q^2+6q+1
        36: 2q^3+7q^2+6q+1
        37: 3q^2+4q+1
        38: 3q^2+2q
        39: 3q^2+4q+1
        40: q^3+3q^2+2q
        41: 3q^2+4q+1
        42: 3q^2+2q
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 4q^3+9q^2+6q+1
        56: q^4+5q^3+9q^2+6q+1
        57: 4q^3+9q^2+6q+1
        58: 2q^2+4q+1
        59: 2q
        60: q^3+3q^2+4q+1
        61: 2q^2+2q
        62: 2q^2+4q+1
        63: 2q^2+2q
        64: 3q^2+4q+1
        65: 3q^2+2q
        66: 2q^2+4q+1
        67: 2q^2+2q
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 2q^3+7q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+4q+1
        75: 3q^2+2q
        76: 3q^2+4q+1
        77: q^3+3q^2+2q
        78: 3q^2+4q+1
        79: 3q^2+2q
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 2q^3+7q^2+6q+1
        85: 2q^3+7q^2+6q+1
        86: 2q^3+7q^2+6q+1
        87: 4q^3+9q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^3+7q^2+6q+1
        98: 2q^3+7q^2+6q+1
        99: 3q^3+6q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q^2+3q+1
       104: q
       105: q^2+q
       106: q
       107: q^3+3q^2+4q+1
       108: 2q^2+2q
       109: 2q^2+4q+1
       110: 2q
       111: 2q^2+4q+1
       112: 2q^2+2q
       113: 2q^2+4q+1
       114: 2q^2+2q
       115: 3q^2+4q+1
       116: 3q^2+2q
       117: 2q^2+4q+1
       118: 2q
       119: q^3+3q^2+4q+1
       120: 2q^2+2q
       121: 2q^2+4q+1
       122: 2q^2+2q
       123: 2q^2+4q+1
       124: 2q^2+2q
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 2q^3+7q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: 3q^2+6q+1
       144: q^3+4q^2+4q+1
       145: q^3+5q^2+6q+1
       146: 2q^3+7q^2+6q+1
       147: 2q^3+7q^2+6q+1
       148: 4q^2+6q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+4q+1
       152: 3q^2+2q
       153: 3q^2+4q+1
       154: q^3+3q^2+2q
       155: 3q^2+4q+1
       156: 3q^2+2q
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^3+7q^2+6q+1
       164: 2q^3+7q^2+6q+1
       165: 3q^3+6q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q^2+3q+1
       170: q
       171: q^2+q
       172: q
       173: q^2+3q+1
       174: q
       175: q^2+q
       176: q
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: q^3+3q^2+4q+1
       184: 2q^2+2q
       185: 2q^2+4q+1
       186: 2q
       187: 2q^2+4q+1
       188: 2q^2+2q
       189: 2q^2+4q+1
       190: 2q^2+2q
       191: q^2+4q+1
       192: 2q
       193: 3q+1
       195: q^2+4q+1
       196: 2q
       197: 2q+1
       198: q
       199: 2q^2+4q+1
       200: q^2+2q
       201: q^3+3q^2+4q+1
       202: 2q^2+2q
       203: 2q^2+4q+1
       204: 2q
       205: 2q^2+4q+1
       206: 2q^2+2q
       207: q^2+4q+1
       208: 2q
       209: 2q^2+4q+1
       210: 2q^2+2q
       211: 3q^2+4q+1
       212: 3q^2+2q
       213: 3q+1
       214: q^2+2q
       215: 3q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+q
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: 3q^2+6q+1
       223: q^3+4q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 2q^2+4q+1
       232: q^3+5q^2+6q+1
       233: q^3+4q^2+4q+1
       234: 2q^3+7q^2+6q+1
       235: 4q^2+6q+1
       236: q^2+4q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+6q+1
       244: 3q+1
       245: 2q^2+6q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+6q+1
       254: 3q^2+6q+1
       255: q^3+4q^2+4q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: 2q+1
       260: q
       261: q^2+q
       262: q
       263: q^2+3q+1
       264: q
       265: q^2+q
       266: q
       267: 2q+1
       268: q
       271: q^2+3q+1
       272: q^2+q
       273: q
       274: q
       275: q^2+3q+1
       276: q
       277: q
       278: q
       279: 3q+1
       280: q^2+2q
       281: 2q+1
       282: q
       283: q^2+2q+1
       285: 2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: q^2+2q
       291: 2q+1
       292: q
       293: 2q^2+4q+1
       294: q^2+2q
       295: q^2+4q+1
       296: 2q
       297: q^2+4q+1
       298: 2q
       299: 3q+1
       301: q+1
       302: q
       303: q^2+4q+1
       304: 2q
       305: 2q+1
       306: q
       307: q^3+3q^2+4q+1
       308: 2q^2+2q
       309: 2q^2+4q+1
       310: 2q
       311: 3q+1
       312: q^2+2q
       313: 2q^2+4q+1
       314: 2q^2+2q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       319: 3q+1
       321: q^2+4q+1
       322: 2q
       323: 2q+1
       324: q
       325: 2q^2+4q+1
       326: 2q^2+2q
       333: 2q^2+4q+1
       334: 2q^2+4q+1
       335: 4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 2q^2+4q+1
       353: 3q^2+6q+1
       354: 2q^2+4q+1
       355: 3q^2+6q+1
       356: q^3+4q^2+4q+1
       357: q^2+6q+1
       358: q^2+4q+1
       359: 2q^2+6q+1
       360: 3q+1
       361: q^2+2q
       362: 3q+1
       363: q^2+2q
       364: q^2+2q+1
       365: q^2+q
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 3q+1
       370: 2q^2+6q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: q+1
       381: 2q+1
       382: q
       383: q^2+q
       384: q
       385: q^2+3q+1
       386: q
       387: q
       388: q
       389: q+1
       390: q
       393: 2q+1
       394: q
       397: 2q+1
       398: q^2+q
       399: q
       400: q
       401: q^2+3q+1
       402: q^2+q
       403: q
       404: q
       405: 2q+1
       407: q
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       419: q^2+2q+1
       421: 2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       429: q+1
       431: 2q+1
       433: 1
       435: q+1
       436: q
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: 3q+1
       445: q+1
       446: q
       447: q^2+2q+1
       449: 2q+1
       451: 2q+1
       452: q
       453: 2q^2+4q+1
       454: q^2+2q
       455: 3q+1
       456: q^2+2q
       457: q^2+4q+1
       458: 2q
       459: q^2+4q+1
       460: 2q
       461: q^2+4q+1
       462: 2q
       463: 3q+1
       464: q^2+2q
       465: 3q+1
       466: q^2+2q
       467: 2q+1
       468: q
       469: 2q+1
       470: q
       471: 3q+1
       473: q^2+4q+1
       474: 2q
       475: 2q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+4q+1
       482: 4q+1
       483: 4q+1
       484: q^2+6q+1
       485: 3q+1
       486: q^2+2q
       487: 3q+1
       488: q^2+2q
       489: q^2+2q+1
       490: q^2+q
       491: q^2+4q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q^2+4q+1
       498: 2q^2+4q+1
       499: 4q+1
       500: q^2+4q+1
       501: 2q^2+6q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 3q+1
       514: q^2+4q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       521: q+1
       529: q+1
       533: 1
       537: q+1
       538: q
       541: q+1
       545: q+1
       546: q
       549: q+1
       553: 2q+1
       554: q^2+q
       555: q
       556: q
       557: q^2+3q+1
       558: q
       559: q
       560: q
       561: 2q+1
       562: q^2+q
       563: q
       564: q
       565: 2q+1
       566: q
       569: q+1
       571: q
       573: 2q+1
       574: q
       577: q+1
       581: q
       585: 2q+1
       586: q
       589: q^2+2q+1
       591: 2q+1
       593: q+1
       595: 2q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: 3q+1
       602: q^2+2q
       603: 1
       605: 1
       607: q+1
       609: 1
       613: 1
       615: 3q+1
       617: q+1
       618: q
       619: q^2+2q+1
       621: 2q+1
       623: 2q+1
       624: q
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: q^2+4q+1
       632: 2q
       633: 3q+1
       634: q^2+2q
       639: 2q+1
       640: q
       641: q+1
       643: 2q+1
       645: 1
       647: q+1
       649: 2q+1
       650: q
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q+2
       681: 2q^2+4q+1
       682: 4q+1
       683: 4q+1
       684: 3q+1
       685: q^2+4q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       699: q
       709: q+1
       713: q+1
       717: 1
       721: 1
       725: 1
       733: q+1
       734: q
       737: q+1
       741: q+1
       749: 2q+1
       750: q^2+q
       751: q
       752: q
       753: 1
       757: q+1
       759: q
       761: q+1
       765: 2q+1
       766: q
       769: q+1
       773: q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       785: q+1
       787: 2q+1
       791: 1
       793: 2
       795: 1
       796: 1
       797: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       815: q+1
       817: 2
       819: q+1
       820: q+1
       821: 2q+1
       822: q
       825: q^2+2q+1
       827: 2q+1
       829: q+1
       831: 2q+1
       833: 2q+1
       834: q
       835: 2q+1
       836: q
       839: 2q+1
       840: q
       843: 2
       845: 1
       847: q+1
       849: 1
       851: 1
       855: 1
       857: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       890: q
       900: q+1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       928: 1
       940: 1
       941: 1
       944: q+1
       948: q+1
       952: 1
       960: 1
       964: 2
       968: 1
       969: 1
       974: 1
       988: q+1
       994: 1
       995: 1
       998: 2
      1000: 2
      1004: 1
      1006: q+1
      1008: 1
      1010: 1
      1012: 2
      1016: 1
      1020: 1
      1021: 1
      1022: 1
      1026: 1
      1032: 1
      1036: q+1
      1037: q+1
      1038: 2q+1
      1039: q
      1040: q+1
      1044: 2q+1
      1046: 1
      1048: 1
      1052: 1
      1056: 1
      1058: q+1
      1060: 1
      1062: 1
      1064: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1114: 1
      1115: 1
      1122: 1
      1123: 1
      1126: 1
      1130: 2
      1134: 1
      1138: 1
      1139: 1
      1156: 1
      1172: q+1
      1176: 1
      1180: 1
      1194: 1
      1198: 1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1240: 1
      1246: 1
      1248: 1
      1249: 1
      1250: 2
      1254: 2
      1258: 1
      1260: q+1
      1262: 1
      1266: 1
      1268: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1326: 1
      1330: 1
      1380: 1
      1381: 1
      1388: 1
      1389: 1
      1392: 1
      1396: 2
      1400: 1
      1410: 1
      1422: 1
      1430: 1
      1431: 1
      1440: 1
      1442: 1
      1444: 1
      1460: 1
      1462: 1
      1474: 1
      1476: 1
      1482: 1
      1486: 1
      1488: 1
      1513: 1
      1514: 1
      1549: 1
      1595: 1
      1599: 1
      1653: 1
      1655: 1
      1669: 1
      1773: 1

1774:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 4q^3+9q^2+6q+1
        26: q^4+5q^3+9q^2+6q+1
        27: 4q^3+9q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 2q^3+7q^2+6q+1
        35: 4q^3+9q^2+6q+1
        36: 2q^3+7q^2+6q+1
        37: 3q^2+2q
        38: 3q^2+4q+1
        39: q^3+3q^2+2q
        40: 3q^2+4q+1
        41: 3q^2+2q
        42: 3q^2+4q+1
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 4q^3+9q^2+6q+1
        56: q^4+5q^3+9q^2+6q+1
        57: 4q^3+9q^2+6q+1
        58: 2q
        59: 2q^2+4q+1
        60: q^3+3q^2+4q+1
        61: 2q^2+2q
        62: 2q^2+2q
        63: 2q^2+4q+1
        64: 3q^2+2q
        65: 3q^2+4q+1
        66: 2q^2+2q
        67: 2q^2+4q+1
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 2q^3+7q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+2q
        75: 3q^2+4q+1
        76: q^3+3q^2+2q
        77: 3q^2+4q+1
        78: 3q^2+2q
        79: 3q^2+4q+1
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 2q^3+7q^2+6q+1
        85: 2q^3+7q^2+6q+1
        86: 2q^3+7q^2+6q+1
        87: 4q^3+9q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^3+7q^2+6q+1
        98: 2q^3+7q^2+6q+1
        99: 3q^3+6q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q
       104: q^2+3q+1
       105: q
       106: q^2+q
       107: q^3+3q^2+4q+1
       108: 2q^2+2q
       109: 2q
       110: 2q^2+4q+1
       111: 2q^2+2q
       112: 2q^2+4q+1
       113: 2q^2+2q
       114: 2q^2+4q+1
       115: 3q^2+2q
       116: 3q^2+4q+1
       117: 2q
       118: 2q^2+4q+1
       119: q^3+3q^2+4q+1
       120: 2q^2+2q
       121: 2q^2+2q
       122: 2q^2+4q+1
       123: 2q^2+2q
       124: 2q^2+4q+1
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 2q^3+7q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: 3q^2+6q+1
       144: q^3+4q^2+4q+1
       145: q^3+5q^2+6q+1
       146: 2q^3+7q^2+6q+1
       147: 2q^3+7q^2+6q+1
       148: 4q^2+6q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+2q
       152: 3q^2+4q+1
       153: q^3+3q^2+2q
       154: 3q^2+4q+1
       155: 3q^2+2q
       156: 3q^2+4q+1
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^3+7q^2+6q+1
       164: 2q^3+7q^2+6q+1
       165: 3q^3+6q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q
       170: q^2+3q+1
       171: q
       172: q^2+q
       173: q
       174: q^2+3q+1
       175: q
       176: q^2+q
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: q^3+3q^2+4q+1
       184: 2q^2+2q
       185: 2q
       186: 2q^2+4q+1
       187: 2q^2+2q
       188: 2q^2+4q+1
       189: 2q^2+2q
       190: 2q^2+4q+1
       191: 2q
       192: q^2+4q+1
       193: 3q+1
       195: 2q
       196: q^2+4q+1
       197: q
       198: 2q+1
       199: 2q^2+4q+1
       200: q^2+2q
       201: q^3+3q^2+4q+1
       202: 2q^2+2q
       203: 2q
       204: 2q^2+4q+1
       205: 2q^2+2q
       206: 2q^2+4q+1
       207: 2q
       208: q^2+4q+1
       209: 2q^2+2q
       210: 2q^2+4q+1
       211: 3q^2+2q
       212: 3q^2+4q+1
       213: q^2+2q
       214: 3q+1
       215: q^2+2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: 3q^2+6q+1
       223: q^3+4q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 2q^2+4q+1
       232: q^3+5q^2+6q+1
       233: q^3+4q^2+4q+1
       234: 2q^3+7q^2+6q+1
       235: 4q^2+6q+1
       236: q^2+4q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+6q+1
       244: 3q+1
       245: 2q^2+6q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+6q+1
       254: 3q^2+6q+1
       255: q^3+4q^2+4q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q
       260: 2q+1
       261: q
       262: q^2+q
       263: q
       264: q^2+3q+1
       265: q
       266: q^2+q
       267: q
       268: 2q+1
       271: q
       272: q
       273: q^2+q
       274: q^2+3q+1
       275: q
       276: q^2+3q+1
       277: q
       278: q
       279: q^2+2q
       280: 3q+1
       281: q
       282: 2q+1
       283: q^2+2q+1
       286: 2q+1
       287: q
       288: 2q+1
       289: q^2+2q
       290: 3q+1
       291: q
       292: 2q+1
       293: 2q^2+4q+1
       294: q^2+2q
       295: 2q
       296: q^2+4q+1
       297: 2q
       298: q^2+4q+1
       299: 3q+1
       301: q
       302: q+1
       303: 2q
       304: q^2+4q+1
       305: q
       306: 2q+1
       307: q^3+3q^2+4q+1
       308: 2q^2+2q
       309: 2q
       310: 2q^2+4q+1
       311: q^2+2q
       312: 3q+1
       313: 2q^2+2q
       314: 2q^2+4q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       319: 3q+1
       321: 2q
       322: q^2+4q+1
       323: q
       324: 2q+1
       325: 2q^2+2q
       326: 2q^2+4q+1
       333: 2q^2+4q+1
       334: 2q^2+4q+1
       335: 4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 2q^2+4q+1
       353: 3q^2+6q+1
       354: 2q^2+4q+1
       355: 3q^2+6q+1
       356: q^3+4q^2+4q+1
       357: q^2+6q+1
       358: q^2+4q+1
       359: 2q^2+6q+1
       360: q^2+2q
       361: 3q+1
       362: q^2+2q
       363: 3q+1
       364: q^2+q
       365: q^2+2q+1
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 3q+1
       370: 2q^2+6q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: q+1
       381: q
       382: 2q+1
       383: q
       384: q^2+q
       385: q
       386: q^2+3q+1
       387: q
       388: q
       389: q
       390: q+1
       393: q
       394: 2q+1
       397: q
       398: q
       399: q^2+q
       400: 2q+1
       401: q
       402: q
       403: q^2+3q+1
       404: q^2+q
       405: q
       407: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       419: q^2+2q+1
       422: 2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       429: q+1
       432: 2q+1
       434: 1
       435: q
       436: q+1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: 3q+1
       445: q
       446: q+1
       447: q^2+2q+1
       450: 2q+1
       451: q
       452: 2q+1
       453: 2q^2+4q+1
       454: q^2+2q
       455: q^2+2q
       456: 3q+1
       457: 2q
       458: q^2+4q+1
       459: 2q
       460: q^2+4q+1
       461: 2q
       462: q^2+4q+1
       463: q^2+2q
       464: 3q+1
       465: q^2+2q
       466: 3q+1
       467: q
       468: 2q+1
       469: q
       470: 2q+1
       471: 3q+1
       473: 2q
       474: q^2+4q+1
       475: q
       476: 2q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+4q+1
       482: 4q+1
       483: 4q+1
       484: q^2+6q+1
       485: q^2+2q
       486: 3q+1
       487: q^2+2q
       488: 3q+1
       489: q^2+q
       490: q^2+2q+1
       491: q^2+4q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q^2+4q+1
       498: 2q^2+4q+1
       499: 4q+1
       500: q^2+4q+1
       501: 2q^2+6q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 3q+1
       514: q^2+4q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       522: q+1
       530: q+1
       534: 1
       537: q
       538: q+1
       542: q+1
       545: q
       546: q+1
       551: q+1
       553: q
       554: q
       555: q^2+q
       556: 2q+1
       557: q
       558: q
       559: q
       560: q^2+3q+1
       561: q
       562: q
       563: q^2+q
       564: 2q+1
       565: q
       566: 2q+1
       569: q
       571: q+1
       573: q
       574: 2q+1
       577: q
       581: q+1
       585: q
       586: 2q+1
       589: q^2+2q+1
       592: 2q+1
       593: q+1
       596: 2q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+2q
       602: 3q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       614: 1
       615: 3q+1
       617: q
       618: q+1
       619: q^2+2q+1
       622: 2q+1
       623: q
       624: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: 2q
       632: q^2+4q+1
       633: q^2+2q
       634: 3q+1
       639: q
       640: 2q+1
       641: q+1
       644: 2q+1
       646: 1
       647: q+1
       649: q
       650: 2q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q+2
       681: 2q^2+4q+1
       682: 4q+1
       683: 4q+1
       684: 3q+1
       685: q^2+4q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       699: q+1
       710: q+1
       715: q+1
       718: 1
       722: 1
       726: 1
       733: q
       734: q+1
       740: q+1
       744: q+1
       749: q
       750: q
       751: q^2+q
       752: 2q+1
       754: 1
       757: q
       759: q+1
       763: q+1
       765: q
       766: 2q+1
       769: q
       773: q+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       785: q+1
       788: 2q+1
       792: 1
       793: 2
       795: 1
       796: 1
       798: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       815: q+1
       818: 2
       819: q+1
       820: q+1
       821: q
       822: 2q+1
       825: q^2+2q+1
       828: 2q+1
       829: q+1
       832: 2q+1
       833: q
       834: 2q+1
       835: q
       836: 2q+1
       839: q
       840: 2q+1
       844: 2
       845: 1
       848: q+1
       850: 1
       852: 1
       856: 1
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       890: q+1
       903: q+1
       905: 1
       909: 1
       916: 1
       917: 1
       921: 1
       929: 1
       942: 1
       943: 1
       947: q+1
       951: q+1
       953: 1
       962: 1
       965: 2
       971: 1
       972: 1
       976: 1
       989: q+1
       994: 1
       995: 1
       999: 2
      1000: 2
      1004: 1
      1007: q+1
      1009: 1
      1011: 1
      1013: 2
      1016: 1
      1020: 1
      1021: 1
      1023: 1
      1026: 1
      1033: 1
      1036: q+1
      1037: q+1
      1038: q
      1039: 2q+1
      1040: q+1
      1045: 2q+1
      1047: 1
      1049: 1
      1052: 1
      1056: 1
      1059: q+1
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 2
      1085: 1
      1089: 1
      1092: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1128: 1
      1131: 2
      1136: 1
      1141: 1
      1142: 1
      1157: 1
      1175: q+1
      1177: 1
      1181: 1
      1195: 1
      1200: 1
      1207: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1240: 1
      1247: 1
      1248: 1
      1249: 1
      1251: 2
      1254: 2
      1258: 1
      1261: q+1
      1263: 1
      1267: 1
      1268: 1
      1274: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1293: 1
      1296: 1
      1327: 1
      1332: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1394: 1
      1397: 2
      1402: 1
      1411: 1
      1423: 1
      1433: 1
      1434: 1
      1441: 1
      1442: 1
      1445: 1
      1461: 1
      1462: 1
      1475: 1
      1476: 1
      1483: 1
      1486: 1
      1488: 1
      1516: 1
      1519: 1
      1550: 1
      1596: 1
      1601: 1
      1654: 1
      1655: 1
      1670: 1
      1774: 1

1775:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 4q^3+9q^2+6q+1
        26: q^4+5q^3+9q^2+6q+1
        27: 4q^3+9q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 2q^3+7q^2+6q+1
        35: 4q^3+9q^2+6q+1
        36: 2q^3+7q^2+6q+1
        37: 3q^2+2q
        38: 3q^2+4q+1
        39: q^3+3q^2+2q
        40: 3q^2+4q+1
        41: 3q^2+2q
        42: 3q^2+4q+1
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 4q^3+9q^2+6q+1
        56: q^4+5q^3+9q^2+6q+1
        57: 4q^3+9q^2+6q+1
        58: 2q^2+4q+1
        59: 2q
        60: 2q^2+2q
        61: q^3+3q^2+4q+1
        62: 2q^2+2q
        63: 2q^2+4q+1
        64: 3q^2+2q
        65: 3q^2+4q+1
        66: 2q^2+2q
        67: 2q^2+4q+1
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 2q^3+7q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+2q
        75: 3q^2+4q+1
        76: q^3+3q^2+2q
        77: 3q^2+4q+1
        78: 3q^2+2q
        79: 3q^2+4q+1
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 2q^3+7q^2+6q+1
        85: 2q^3+7q^2+6q+1
        86: 2q^3+7q^2+6q+1
        87: 4q^3+9q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^3+7q^2+6q+1
        98: 2q^3+7q^2+6q+1
        99: 3q^3+6q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q^2+q
       104: q
       105: q^2+3q+1
       106: q
       107: 2q^2+2q
       108: q^3+3q^2+4q+1
       109: 2q^2+4q+1
       110: 2q
       111: 2q^2+2q
       112: 2q^2+4q+1
       113: 2q^2+2q
       114: 2q^2+4q+1
       115: 3q^2+2q
       116: 3q^2+4q+1
       117: 2q^2+4q+1
       118: 2q
       119: 2q^2+2q
       120: q^3+3q^2+4q+1
       121: 2q^2+2q
       122: 2q^2+4q+1
       123: 2q^2+2q
       124: 2q^2+4q+1
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: q^2+2q
       128: 3q+1
       129: q^2+2q
       130: 3q+1
       131: q^2+q
       132: q^2+2q+1
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 2q^3+7q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: 3q^2+6q+1
       144: q^3+4q^2+4q+1
       145: q^3+5q^2+6q+1
       146: 2q^3+7q^2+6q+1
       147: 2q^3+7q^2+6q+1
       148: 4q^2+6q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+2q
       152: 3q^2+4q+1
       153: q^3+3q^2+2q
       154: 3q^2+4q+1
       155: 3q^2+2q
       156: 3q^2+4q+1
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^3+7q^2+6q+1
       164: 2q^3+7q^2+6q+1
       165: 3q^3+6q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q^2+q
       170: q
       171: q^2+3q+1
       172: q
       173: q^2+q
       174: q
       175: q^2+3q+1
       176: q
       177: q
       178: 2q+1
       179: q^2+2q
       180: 3q+1
       181: q^2+2q
       182: 3q+1
       183: 2q^2+2q
       184: q^3+3q^2+4q+1
       185: 2q^2+4q+1
       186: 2q
       187: 2q^2+2q
       188: 2q^2+4q+1
       189: 2q^2+2q
       190: 2q^2+4q+1
       191: q^2+4q+1
       192: 2q
       194: 3q+1
       195: q^2+4q+1
       196: 2q
       197: q
       198: 2q+1
       199: q^2+2q
       200: 2q^2+4q+1
       201: 2q^2+2q
       202: q^3+3q^2+4q+1
       203: 2q^2+4q+1
       204: 2q
       205: 2q^2+2q
       206: 2q^2+4q+1
       207: 2q
       208: q^2+4q+1
       209: 2q^2+2q
       210: 2q^2+4q+1
       211: 3q^2+2q
       212: 3q^2+4q+1
       213: q^2+2q
       214: 3q+1
       215: q^2+2q
       216: 3q+1
       217: q^2+q
       218: q^2+2q+1
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: 3q^2+6q+1
       223: q^3+4q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 2q^2+4q+1
       232: q^3+5q^2+6q+1
       233: q^3+4q^2+4q+1
       234: 2q^3+7q^2+6q+1
       235: 4q^2+6q+1
       236: q^2+4q+1
       237: q^2+2q
       238: 3q+1
       239: q^2+2q
       240: 3q+1
       241: q^2+q
       242: q^2+2q+1
       243: q^2+6q+1
       244: 3q+1
       245: 2q^2+6q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+6q+1
       254: 3q^2+6q+1
       255: q^3+4q^2+4q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q^2+q
       260: q
       261: 2q+1
       262: q
       263: q^2+q
       264: q
       265: q^2+3q+1
       266: q
       269: q
       270: 2q+1
       271: q^2+q
       272: q^2+3q+1
       273: q
       274: q
       275: q
       276: q
       277: q^2+3q+1
       278: q
       279: q^2+2q
       280: 3q+1
       281: q
       282: 2q+1
       284: q^2+2q+1
       285: 2q+1
       287: q
       288: 2q+1
       289: q^2+2q
       290: 3q+1
       291: q
       292: 2q+1
       293: q^2+2q
       294: 2q^2+4q+1
       295: q^2+4q+1
       296: 2q
       297: 2q
       298: q^2+4q+1
       300: 3q+1
       301: q
       302: q+1
       303: q^2+4q+1
       304: 2q
       305: q
       306: 2q+1
       307: 2q^2+2q
       308: q^3+3q^2+4q+1
       309: 2q^2+4q+1
       310: 2q
       311: q^2+2q
       312: 3q+1
       313: 2q^2+2q
       314: 2q^2+4q+1
       315: q
       316: 2q+1
       317: q^2+2q
       318: 3q+1
       320: 3q+1
       321: q^2+4q+1
       322: 2q
       323: q
       324: 2q+1
       325: 2q^2+2q
       326: 2q^2+4q+1
       333: 2q^2+4q+1
       334: 2q^2+4q+1
       335: 4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: q^2+2q
       339: 3q+1
       340: q^2+2q
       341: 3q+1
       342: q^2+q
       343: q^2+2q+1
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 2q^2+4q+1
       353: 3q^2+6q+1
       354: 2q^2+4q+1
       355: 3q^2+6q+1
       356: q^3+4q^2+4q+1
       357: q^2+6q+1
       358: q^2+4q+1
       359: 2q^2+6q+1
       360: q^2+2q
       361: 3q+1
       362: q^2+2q
       363: 3q+1
       364: q^2+q
       365: q^2+2q+1
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 3q+1
       370: 2q^2+6q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: q+1
       381: q^2+q
       382: q
       383: 2q+1
       384: q
       385: q
       386: q
       387: q^2+3q+1
       388: q
       391: q
       392: q+1
       395: 2q+1
       396: q
       397: q^2+q
       398: 2q+1
       399: q
       400: q
       401: q^2+q
       402: q^2+3q+1
       403: q
       404: q
       406: q
       408: 2q+1
       413: q
       414: 2q+1
       417: q
       418: 2q+1
       420: q^2+2q+1
       421: 2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+2q
       428: 3q+1
       430: q+1
       431: 2q+1
       434: 1
       435: q
       436: q+1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: 3q+1
       445: q
       446: q+1
       448: q^2+2q+1
       449: 2q+1
       451: q
       452: 2q+1
       453: q^2+2q
       454: 2q^2+4q+1
       455: q^2+2q
       456: 3q+1
       457: q^2+4q+1
       458: 2q
       459: 2q
       460: q^2+4q+1
       461: q^2+4q+1
       462: 2q
       463: q^2+2q
       464: 3q+1
       465: q^2+2q
       466: 3q+1
       467: q
       468: 2q+1
       469: q
       470: 2q+1
       472: 3q+1
       473: q^2+4q+1
       474: 2q
       475: q
       476: 2q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+4q+1
       482: 4q+1
       483: 4q+1
       484: q^2+6q+1
       485: q^2+2q
       486: 3q+1
       487: q^2+2q
       488: 3q+1
       489: q^2+q
       490: q^2+2q+1
       491: q^2+4q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q^2+4q+1
       498: 2q^2+4q+1
       499: 4q+1
       500: q^2+4q+1
       501: 2q^2+6q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 3q+1
       514: q^2+4q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       523: q+1
       531: q+1
       535: 1
       539: q
       540: q+1
       544: q+1
       547: q
       548: q+1
       550: q+1
       553: q^2+q
       554: 2q+1
       555: q
       556: q
       557: q
       558: q^2+3q+1
       559: q
       560: q
       561: q^2+q
       562: 2q+1
       563: q
       564: q
       567: 2q+1
       568: q
       570: q
       572: q+1
       575: q
       576: 2q+1
       577: q
       581: q+1
       585: q
       586: 2q+1
       590: q^2+2q+1
       591: 2q+1
       594: q+1
       595: 2q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+2q
       602: 3q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       614: 1
       616: 3q+1
       617: q
       618: q+1
       620: q^2+2q+1
       621: 2q+1
       623: q
       624: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: q^2+4q+1
       632: 2q
       633: q^2+2q
       634: 3q+1
       639: q
       640: 2q+1
       642: q+1
       643: 2q+1
       646: 1
       648: q+1
       649: 2q+1
       650: q
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q+2
       681: 2q^2+4q+1
       682: 4q+1
       683: 4q+1
       684: 3q+1
       685: q^2+4q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       700: q+1
       711: q+1
       714: q+1
       719: 1
       724: 1
       728: 1
       735: q
       736: q+1
       738: q+1
       742: q+1
       749: q^2+q
       750: 2q+1
       751: q
       752: q
       755: 1
       758: q
       760: q+1
       764: q+1
       767: 2q+1
       768: q
       769: q
       773: q+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       786: q+1
       787: 2q+1
       792: 1
       794: 2
       795: 1
       796: 1
       798: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       816: q+1
       817: 2
       819: q+1
       820: q+1
       821: q
       822: 2q+1
       826: q^2+2q+1
       827: 2q+1
       830: q+1
       831: 2q+1
       833: q
       834: 2q+1
       835: q
       836: 2q+1
       839: 2q+1
       840: q
       844: 2
       846: 1
       847: q+1
       850: 1
       852: 1
       856: 1
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q
       891: q+1
       901: q+1
       907: 1
       910: 1
       918: 1
       919: 1
       923: 1
       931: 1
       940: 1
       941: 1
       945: q+1
       949: q+1
       954: 1
       963: 1
       966: 2
       971: 1
       972: 1
       977: 1
       990: q+1
       994: 1
       995: 1
       998: 2
      1001: 2
      1005: 1
      1006: q+1
      1009: 1
      1011: 1
      1013: 2
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1036: q+1
      1037: q+1
      1038: q
      1039: 2q+1
      1041: q+1
      1044: 2q+1
      1047: 1
      1049: 1
      1053: 1
      1057: 1
      1058: q+1
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 2
      1085: 1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1124: 1
      1125: 1
      1129: 1
      1132: 2
      1137: 1
      1141: 1
      1142: 1
      1159: 1
      1173: q+1
      1179: 1
      1182: 1
      1196: 1
      1201: 1
      1209: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1241: 1
      1246: 1
      1248: 1
      1249: 1
      1250: 2
      1255: 2
      1259: 1
      1260: q+1
      1263: 1
      1267: 1
      1269: 1
      1274: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1294: 1
      1297: 1
      1328: 1
      1333: 1
      1380: 1
      1381: 1
      1390: 1
      1391: 1
      1395: 1
      1398: 2
      1403: 1
      1412: 1
      1425: 1
      1433: 1
      1434: 1
      1440: 1
      1443: 1
      1445: 1
      1460: 1
      1463: 1
      1475: 1
      1477: 1
      1483: 1
      1486: 1
      1488: 1
      1517: 1
      1520: 1
      1551: 1
      1597: 1
      1602: 1
      1653: 1
      1656: 1
      1670: 1
      1775: 1

1776:    0: 4q^3+9q^2+6q+1
         1: q^4+5q^3+9q^2+6q+1
         2: 4q^3+9q^2+6q+1
         3: q^4+5q^3+9q^2+6q+1
         4: 4q^3+9q^2+6q+1
         5: 4q^3+9q^2+6q+1
         6: q^4+5q^3+9q^2+6q+1
         7: 4q^3+9q^2+6q+1
         8: 4q^3+9q^2+6q+1
         9: 2q^4+5q^3+6q^2+4q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 4q^3+9q^2+6q+1
        14: 4q^3+9q^2+6q+1
        15: 4q^3+9q^2+6q+1
        16: 2q^3+7q^2+6q+1
        17: 2q^3+7q^2+6q+1
        18: 3q^3+6q^2+4q+1
        19: 4q^3+9q^2+6q+1
        20: q^4+5q^3+9q^2+6q+1
        21: 4q^3+9q^2+6q+1
        22: 6q^2+6q+1
        23: q^3+6q^2+6q+1
        24: 6q^2+6q+1
        25: 4q^3+9q^2+6q+1
        26: q^4+5q^3+9q^2+6q+1
        27: 4q^3+9q^2+6q+1
        28: q^3+5q^2+6q+1
        29: 2q^3+7q^2+6q+1
        30: 4q^3+9q^2+6q+1
        31: 4q^2+6q+1
        32: 6q^2+6q+1
        33: 4q^2+6q+1
        34: 2q^3+7q^2+6q+1
        35: 4q^3+9q^2+6q+1
        36: 2q^3+7q^2+6q+1
        37: 3q^2+4q+1
        38: 3q^2+2q
        39: 3q^2+4q+1
        40: q^3+3q^2+2q
        41: 3q^2+4q+1
        42: 3q^2+2q
        43: 2q^3+7q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+7q^2+6q+1
        48: 3q^3+6q^2+4q+1
        49: 2q^3+7q^2+6q+1
        50: 2q^3+7q^2+6q+1
        51: 3q^3+6q^2+4q+1
        52: 6q^2+6q+1
        53: q^3+6q^2+6q+1
        54: 6q^2+6q+1
        55: 4q^3+9q^2+6q+1
        56: q^4+5q^3+9q^2+6q+1
        57: 4q^3+9q^2+6q+1
        58: 2q
        59: 2q^2+4q+1
        60: 2q^2+2q
        61: q^3+3q^2+4q+1
        62: 2q^2+4q+1
        63: 2q^2+2q
        64: 3q^2+4q+1
        65: 3q^2+2q
        66: 2q^2+4q+1
        67: 2q^2+2q
        68: q^3+5q^2+6q+1
        69: q^3+4q^2+4q+1
        70: 2q^3+7q^2+6q+1
        71: q^3+5q^2+6q+1
        72: 2q^3+7q^2+6q+1
        73: 4q^2+6q+1
        74: 3q^2+4q+1
        75: 3q^2+2q
        76: 3q^2+4q+1
        77: q^3+3q^2+2q
        78: 3q^2+4q+1
        79: 3q^2+2q
        80: 4q^2+6q+1
        81: 4q^2+6q+1
        82: 4q^2+6q+1
        83: 6q^2+6q+1
        84: 2q^3+7q^2+6q+1
        85: 2q^3+7q^2+6q+1
        86: 2q^3+7q^2+6q+1
        87: 4q^3+9q^2+6q+1
        88: 3q^2+6q+1
        89: 3q^2+6q+1
        90: q^3+4q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: 2q^3+7q^2+6q+1
        93: 3q^3+6q^2+4q+1
        94: 2q^2+6q+1
        95: 2q^2+6q+1
        96: 3q^2+4q+1
        97: 2q^3+7q^2+6q+1
        98: 2q^3+7q^2+6q+1
        99: 3q^3+6q^2+4q+1
       100: 6q^2+6q+1
       101: q^3+6q^2+6q+1
       102: 6q^2+6q+1
       103: q
       104: q^2+q
       105: q
       106: q^2+3q+1
       107: 2q^2+2q
       108: q^3+3q^2+4q+1
       109: 2q
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: 2q^2+2q
       113: 2q^2+4q+1
       114: 2q^2+2q
       115: 3q^2+4q+1
       116: 3q^2+2q
       117: 2q
       118: 2q^2+4q+1
       119: 2q^2+2q
       120: q^3+3q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+2q
       123: 2q^2+4q+1
       124: 2q^2+2q
       125: 3q^2+6q+1
       126: 2q^2+4q+1
       127: 3q+1
       128: q^2+2q
       129: 3q+1
       130: q^2+2q
       131: q^2+2q+1
       132: q^2+q
       133: q^3+5q^2+6q+1
       134: q^3+4q^2+4q+1
       135: 2q^3+7q^2+6q+1
       136: 4q^2+6q+1
       137: q^2+6q+1
       138: q^2+4q+1
       139: q^2+6q+1
       140: 3q+1
       141: 4q^2+6q+1
       142: 2q^2+6q+1
       143: 3q^2+6q+1
       144: q^3+4q^2+4q+1
       145: q^3+5q^2+6q+1
       146: 2q^3+7q^2+6q+1
       147: 2q^3+7q^2+6q+1
       148: 4q^2+6q+1
       149: 4q^2+6q+1
       150: 6q^2+6q+1
       151: 3q^2+4q+1
       152: 3q^2+2q
       153: 3q^2+4q+1
       154: q^3+3q^2+2q
       155: 3q^2+4q+1
       156: 3q^2+2q
       157: 3q^2+6q+1
       158: 3q^2+6q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+6q+1
       161: 2q^2+6q+1
       162: 3q^2+4q+1
       163: 2q^3+7q^2+6q+1
       164: 2q^3+7q^2+6q+1
       165: 3q^3+6q^2+4q+1
       166: 2q^2+6q+1
       167: 2q^2+6q+1
       168: 3q^2+4q+1
       169: q
       170: q^2+q
       171: q
       172: q^2+3q+1
       173: q
       174: q^2+q
       175: q
       176: q^2+3q+1
       177: 2q+1
       178: q
       179: 3q+1
       180: q^2+2q
       181: 3q+1
       182: q^2+2q
       183: 2q^2+2q
       184: q^3+3q^2+4q+1
       185: 2q
       186: 2q^2+4q+1
       187: 2q^2+4q+1
       188: 2q^2+2q
       189: 2q^2+4q+1
       190: 2q^2+2q
       191: 2q
       192: q^2+4q+1
       194: 3q+1
       195: 2q
       196: q^2+4q+1
       197: 2q+1
       198: q
       199: q^2+2q
       200: 2q^2+4q+1
       201: 2q^2+2q
       202: q^3+3q^2+4q+1
       203: 2q
       204: 2q^2+4q+1
       205: 2q^2+4q+1
       206: 2q^2+2q
       207: q^2+4q+1
       208: 2q
       209: 2q^2+4q+1
       210: 2q^2+2q
       211: 3q^2+4q+1
       212: 3q^2+2q
       213: 3q+1
       214: q^2+2q
       215: 3q+1
       216: q^2+2q
       217: q^2+2q+1
       218: q^2+q
       219: 2q^2+4q+1
       220: 3q^2+6q+1
       221: 2q^2+4q+1
       222: 3q^2+6q+1
       223: q^3+4q^2+4q+1
       224: q^2+6q+1
       225: q^2+4q+1
       226: 4q+1
       227: q^2+6q+1
       228: q^2+4q+1
       229: 3q+1
       230: 2q^2+6q+1
       231: 2q^2+4q+1
       232: q^3+5q^2+6q+1
       233: q^3+4q^2+4q+1
       234: 2q^3+7q^2+6q+1
       235: 4q^2+6q+1
       236: q^2+4q+1
       237: 3q+1
       238: q^2+2q
       239: 3q+1
       240: q^2+2q
       241: q^2+2q+1
       242: q^2+q
       243: q^2+6q+1
       244: 3q+1
       245: 2q^2+6q+1
       246: 4q^2+6q+1
       247: 2q^2+6q+1
       248: 2q^2+6q+1
       249: 3q^2+4q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+6q+1
       254: 3q^2+6q+1
       255: q^3+4q^2+4q+1
       256: 2q^2+6q+1
       257: 2q^2+6q+1
       258: 3q^2+4q+1
       259: q
       260: q^2+q
       261: q
       262: 2q+1
       263: q
       264: q^2+q
       265: q
       266: q^2+3q+1
       269: 2q+1
       270: q
       271: q
       272: q
       273: q^2+3q+1
       274: q^2+q
       275: q
       276: q
       277: q
       278: q^2+3q+1
       279: 3q+1
       280: q^2+2q
       281: 2q+1
       282: q
       284: q^2+2q+1
       286: 2q+1
       287: 2q+1
       288: q
       289: 3q+1
       290: q^2+2q
       291: 2q+1
       292: q
       293: q^2+2q
       294: 2q^2+4q+1
       295: 2q
       296: q^2+4q+1
       297: q^2+4q+1
       298: 2q
       300: 3q+1
       301: q+1
       302: q
       303: 2q
       304: q^2+4q+1
       305: 2q+1
       306: q
       307: 2q^2+2q
       308: q^3+3q^2+4q+1
       309: 2q
       310: 2q^2+4q+1
       311: 3q+1
       312: q^2+2q
       313: 2q^2+4q+1
       314: 2q^2+2q
       315: 2q+1
       316: q
       317: 3q+1
       318: q^2+2q
       320: 3q+1
       321: 2q
       322: q^2+4q+1
       323: 2q+1
       324: q
       325: 2q^2+4q+1
       326: 2q^2+2q
       333: 2q^2+4q+1
       334: 2q^2+4q+1
       335: 4q+1
       336: q^2+4q+1
       337: q^2+6q+1
       338: 3q+1
       339: q^2+2q
       340: 3q+1
       341: q^2+2q
       342: q^2+2q+1
       343: q^2+q
       344: 4q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: q+1
       349: 3q+1
       350: q^2+4q+1
       351: 3q+1
       352: 2q^2+4q+1
       353: 3q^2+6q+1
       354: 2q^2+4q+1
       355: 3q^2+6q+1
       356: q^3+4q^2+4q+1
       357: q^2+6q+1
       358: q^2+4q+1
       359: 2q^2+6q+1
       360: 3q+1
       361: q^2+2q
       362: 3q+1
       363: q^2+2q
       364: q^2+2q+1
       365: q^2+q
       366: 4q+1
       367: q^2+6q+1
       368: q^2+4q+1
       369: 3q+1
       370: 2q^2+6q+1
       371: 2q^2+6q+1
       372: 2q^2+6q+1
       373: 3q^2+4q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: q+1
       381: q
       382: q^2+q
       383: q
       384: 2q+1
       385: q
       386: q
       387: q
       388: q^2+3q+1
       391: q+1
       392: q
       395: q
       396: 2q+1
       397: q
       398: q
       399: 2q+1
       400: q^2+q
       401: q
       402: q
       403: q^2+q
       404: q^2+3q+1
       406: 2q+1
       408: q
       413: 2q+1
       414: q
       417: 2q+1
       418: q
       420: q^2+2q+1
       422: 2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: 3q+1
       428: q^2+2q
       430: q+1
       432: 2q+1
       433: 1
       435: q+1
       436: q
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: 3q+1
       445: q+1
       446: q
       448: q^2+2q+1
       450: 2q+1
       451: 2q+1
       452: q
       453: q^2+2q
       454: 2q^2+4q+1
       455: 3q+1
       456: q^2+2q
       457: 2q
       458: q^2+4q+1
       459: q^2+4q+1
       460: 2q
       461: 2q
       462: q^2+4q+1
       463: 3q+1
       464: q^2+2q
       465: 3q+1
       466: q^2+2q
       467: 2q+1
       468: q
       469: 2q+1
       470: q
       472: 3q+1
       473: 2q
       474: q^2+4q+1
       475: 2q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+4q+1
       482: 4q+1
       483: 4q+1
       484: q^2+6q+1
       485: 3q+1
       486: q^2+2q
       487: 3q+1
       488: q^2+2q
       489: q^2+2q+1
       490: q^2+q
       491: q^2+4q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: q+1
       496: 3q+1
       497: 2q^2+4q+1
       498: 2q^2+4q+1
       499: 4q+1
       500: q^2+4q+1
       501: 2q^2+6q+1
       508: 4q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 3q+1
       514: q^2+4q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       524: q+1
       532: q+1
       536: 1
       539: q+1
       540: q
       543: q+1
       547: q+1
       548: q
       552: q+1
       553: q
       554: q
       555: 2q+1
       556: q^2+q
       557: q
       558: q
       559: q^2+3q+1
       560: q
       561: q
       562: q
       563: 2q+1
       564: q^2+q
       567: q
       568: 2q+1
       570: q+1
       572: q
       575: 2q+1
       576: q
       577: q+1
       581: q
       585: 2q+1
       586: q
       590: q^2+2q+1
       592: 2q+1
       594: q+1
       596: 2q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: 3q+1
       602: q^2+2q
       604: 1
       605: 1
       608: q+1
       609: 1
       613: 1
       616: 3q+1
       617: q+1
       618: q
       620: q^2+2q+1
       622: 2q+1
       623: 2q+1
       624: q
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: 2q
       632: q^2+4q+1
       633: 3q+1
       634: q^2+2q
       639: 2q+1
       640: q
       642: q+1
       644: 2q+1
       645: 1
       648: q+1
       649: q
       650: 2q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 4q+1
       672: 3q+1
       673: 2q+1
       674: 2
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q+2
       681: 2q^2+4q+1
       682: 4q+1
       683: 4q+1
       684: 3q+1
       685: q^2+4q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       700: q
       712: q+1
       716: q+1
       720: 1
       723: 1
       727: 1
       735: q+1
       736: q
       739: q+1
       743: q+1
       749: q
       750: q
       751: 2q+1
       752: q^2+q
       756: 1
       758: q+1
       760: q
       762: q+1
       767: q
       768: 2q+1
       769: q+1
       773: q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       786: q+1
       788: 2q+1
       791: 1
       794: 2
       795: 1
       796: 1
       797: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       816: q+1
       818: 2
       819: q+1
       820: q+1
       821: 2q+1
       822: q
       826: q^2+2q+1
       828: 2q+1
       830: q+1
       832: 2q+1
       833: 2q+1
       834: q
       835: 2q+1
       836: q
       839: q
       840: 2q+1
       843: 2
       846: 1
       848: q+1
       849: 1
       851: 1
       855: 1
       857: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: 1
       870: 2
       871: 1
       872: 1
       873: q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q+1
       891: q
       902: q+1
       906: 1
       911: 1
       918: 1
       919: 1
       922: 1
       930: 1
       942: 1
       943: 1
       946: q+1
       950: q+1
       955: 1
       961: 1
       967: 2
       968: 1
       969: 1
       975: 1
       991: q+1
       994: 1
       995: 1
       999: 2
      1001: 2
      1005: 1
      1007: q+1
      1008: 1
      1010: 1
      1012: 2
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1033: 1
      1036: q+1
      1037: q+1
      1038: 2q+1
      1039: q
      1041: q+1
      1045: 2q+1
      1046: 1
      1048: 1
      1053: 1
      1057: 1
      1059: q+1
      1060: 1
      1062: 1
      1064: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 2
      1085: 1
      1091: 1
      1094: 1
      1116: 1
      1117: 1
      1124: 1
      1125: 1
      1127: 1
      1133: 2
      1135: 1
      1138: 1
      1139: 1
      1158: 1
      1174: q+1
      1178: 1
      1183: 1
      1197: 1
      1199: 1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1241: 1
      1247: 1
      1248: 1
      1249: 1
      1251: 2
      1255: 2
      1259: 1
      1261: q+1
      1262: 1
      1266: 1
      1269: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1295: 1
      1298: 1
      1329: 1
      1331: 1
      1382: 1
      1383: 1
      1390: 1
      1391: 1
      1393: 1
      1399: 2
      1401: 1
      1413: 1
      1424: 1
      1430: 1
      1431: 1
      1441: 1
      1443: 1
      1444: 1
      1461: 1
      1463: 1
      1474: 1
      1477: 1
      1482: 1
      1486: 1
      1488: 1
      1518: 1
      1521: 1
      1552: 1
      1598: 1
      1600: 1
      1654: 1
      1656: 1
      1669: 1
      1776: 1

1777:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+3q^2+2q+1
        26: 2q^3+3q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: 2q^3+3q^2+2q+1
        35: 2q^3+3q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+3q^2+2q+1
        56: 2q^3+3q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: q^2+q+1
        59: q
        60: 2q^2+q+1
        61: q
        62: q^3+2q^2+2q+1
        64: q^3+2q^2+2q+1
        66: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^3+2q^2+2q+1
        76: q^3+2q^2+2q+1
        78: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q^3+3q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^3+3q^2+2q+1
        87: 2q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+q+1
       106: q
       107: 2q^2+q+1
       108: q
       109: q^2+q+1
       110: q
       111: q^2+2q+1
       113: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       117: q^2+q+1
       118: q
       119: 2q^2+q+1
       120: q
       121: q^3+2q^2+2q+1
       123: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^3+2q^2+2q+1
       142: 2q+1
       143: 2q^2+2q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: 2q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       151: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+2q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       169: q^2+q+1
       172: q
       173: q^2+q+1
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q^2+q+1
       184: q
       185: q^2+q+1
       186: q
       187: q^2+2q+1
       189: q^3+2q^2+2q+1
       191: q^2+q+1
       192: q
       193: q+1
       195: q+1
       196: q
       197: q+1
       199: 2q^2+q+1
       200: q
       201: 2q^2+q+1
       202: q
       203: q^2+q+1
       204: q
       205: q^2+2q+1
       207: q^2+2q+1
       209: q^3+2q^2+2q+1
       211: q^3+2q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: 2q^2+2q+1
       223: q^2+q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q^2+q+1
       232: 2q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 2q+1
       244: q+1
       245: 2q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+2q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       259: q+1
       262: q
       263: q^2+q+1
       266: q
       267: q+1
       271: q^2+q+1
       273: q
       275: q^2+q+1
       278: q
       279: 2q+1
       281: q+1
       283: q^2+1
       285: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q^2+q+1
       294: q
       295: q^2+q+1
       296: q
       297: q^2+2q+1
       299: q+1
       301: q+1
       303: q+1
       304: q
       305: q+1
       307: 2q^2+q+1
       308: q
       309: q^2+q+1
       310: q
       311: 2q+1
       313: q^2+2q+1
       315: q+1
       317: 2q+1
       319: q+1
       321: q+1
       322: q
       323: q+1
       325: q^3+2q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: q^2+q+1
       353: 2q^2+2q+1
       354: q^2+q+1
       355: 2q^2+2q+1
       356: q^2+q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       377: 1
       381: q+1
       384: q
       385: q^2+q+1
       388: q
       389: q+1
       393: q+1
       397: q+1
       399: q
       401: q^2+q+1
       404: q
       405: q+1
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q^2+1
       421: 1
       423: q+1
       425: q+1
       427: 2q+1
       429: 1
       431: 1
       433: 1
       435: q+1
       437: q+1
       439: q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: q^2+1
       449: 1
       451: q+1
       453: 2q^2+q+1
       454: q
       455: 2q+1
       457: q^2+q+1
       458: q
       459: q^2+2q+1
       461: q+1
       462: q
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q+1
       473: q+1
       474: q
       475: q+1
       477: q+1
       479: q+1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 1
       525: q+1
       528: q
       529: 1
       533: 1
       537: q+1
       541: q+1
       545: q+1
       549: 1
       553: q+1
       555: q
       557: q^2+q+1
       559: q
       561: q+1
       563: q
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+1
       591: 1
       593: 1
       595: 1
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: 1
       607: 1
       609: 1
       611: q+1
       613: 1
       615: q+1
       617: q+1
       619: q^2+1
       621: 1
       623: q+1
       625: q+1
       627: 2q+1
       629: q+1
       631: q+1
       632: q
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: q+1
       649: q+1
       650: q
       651: q+1
       653: q+1
       655: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: 1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       693: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: q+1
       737: 1
       741: 1
       745: q+1
       747: q
       749: q+1
       751: q
       753: 1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       777: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: q+1
       815: q+1
       821: q+1
       823: q+1
       825: q^2+1
       827: 1
       829: 1
       831: 1
       833: q+1
       835: q+1
       837: 2q+1
       839: q+1
       840: q
       841: q+1
       845: 1
       847: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       868: q+1
       871: 1
       872: 1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       920: 1
       928: 1
       932: q+1
       936: 1
       944: 1
       948: 1
       952: 1
       956: q+1
       958: q
       960: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1026: 1
      1034: q+1
      1038: q+1
      1040: 1
      1042: q+1
      1044: 1
      1048: 1
      1050: 1
      1052: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1098: q+1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1156: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1198: 1
      1206: 1
      1220: 1
      1222: 1
      1238: 1
      1240: 1
      1256: q+1
      1258: 1
      1260: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1322: 1
      1330: 1
      1352: 1
      1376: 1
      1384: 1
      1392: 1
      1400: 1
      1414: 1
      1422: 1
      1446: 1
      1470: 1
      1474: 1
      1476: 1
      1480: 1
      1559: 1
      1591: 1
      1599: 1
      1611: 1
      1671: 1
      1777: 1

1778:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+3q^2+2q+1
        26: 2q^3+3q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: 2q^3+3q^2+2q+1
        35: 2q^3+3q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+3q^2+2q+1
        56: 2q^3+3q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: q
        59: q^2+q+1
        60: q
        61: 2q^2+q+1
        62: q^3+2q^2+2q+1
        64: q^3+2q^2+2q+1
        66: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^3+2q^2+2q+1
        76: q^3+2q^2+2q+1
        78: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q^3+3q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^3+3q^2+2q+1
        87: 2q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q
       106: q^2+q+1
       107: q
       108: 2q^2+q+1
       109: q
       110: q^2+q+1
       111: q^2+2q+1
       113: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       117: q
       118: q^2+q+1
       119: q
       120: 2q^2+q+1
       121: q^3+2q^2+2q+1
       123: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^3+2q^2+2q+1
       142: 2q+1
       143: 2q^2+2q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: 2q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       151: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+2q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       169: q
       172: q^2+q+1
       173: q
       176: q^2+q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q
       184: 2q^2+q+1
       185: q
       186: q^2+q+1
       187: q^2+2q+1
       189: q^3+2q^2+2q+1
       191: q
       192: q^2+q+1
       194: q+1
       195: q
       196: q+1
       197: q+1
       199: q
       200: 2q^2+q+1
       201: q
       202: 2q^2+q+1
       203: q
       204: q^2+q+1
       205: q^2+2q+1
       207: q^2+2q+1
       209: q^3+2q^2+2q+1
       211: q^3+2q^2+2q+1
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: 2q^2+2q+1
       223: q^2+q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q^2+q+1
       232: 2q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 2q+1
       244: q+1
       245: 2q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+2q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       259: q
       262: q+1
       263: q
       266: q^2+q+1
       269: q+1
       271: q
       273: q^2+q+1
       275: q
       278: q^2+q+1
       279: 2q+1
       281: q+1
       284: q^2+1
       286: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: q
       294: 2q^2+q+1
       295: q
       296: q^2+q+1
       297: q^2+2q+1
       300: q+1
       301: q+1
       303: q
       304: q+1
       305: q+1
       307: q
       308: 2q^2+q+1
       309: q
       310: q^2+q+1
       311: 2q+1
       313: q^2+2q+1
       315: q+1
       317: 2q+1
       320: q+1
       321: q
       322: q+1
       323: q+1
       325: q^3+2q^2+2q+1
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: q^2+q+1
       353: 2q^2+2q+1
       354: q^2+q+1
       355: 2q^2+2q+1
       356: q^2+q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       380: 1
       381: q
       384: q+1
       385: q
       388: q^2+q+1
       391: q+1
       396: q+1
       397: q
       399: q+1
       401: q
       404: q^2+q+1
       406: q+1
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: q^2+1
       422: 1
       423: q+1
       425: q+1
       427: 2q+1
       430: 1
       432: 1
       433: 1
       435: q+1
       438: q+1
       439: q
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       448: q^2+1
       450: 1
       451: q+1
       453: q
       454: 2q^2+q+1
       455: 2q+1
       457: q
       458: q^2+q+1
       459: q^2+2q+1
       461: q
       462: q+1
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: q+1
       473: q
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: 1
       525: q
       528: q+1
       532: 1
       536: 1
       539: q+1
       543: q+1
       547: q+1
       552: 1
       553: q
       555: q+1
       557: q
       559: q^2+q+1
       561: q
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       590: q^2+1
       592: 1
       594: 1
       596: 1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       613: 1
       616: q+1
       617: q+1
       620: q^2+1
       622: 1
       623: q+1
       625: q+1
       627: 2q+1
       629: q+1
       631: q
       632: q+1
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: q+1
       649: q
       650: q+1
       651: q+1
       653: q+1
       655: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: 1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       697: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: q+1
       739: 1
       743: 1
       745: q
       747: q+1
       749: q
       751: q+1
       756: 1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       777: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       797: 1
       799: 1
       802: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: q+1
       816: q+1
       821: q+1
       823: q+1
       826: q^2+1
       828: 1
       830: 1
       832: 1
       833: q+1
       835: q+1
       837: 2q+1
       839: q
       840: q+1
       841: q+1
       846: 1
       848: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       868: q+1
       871: 1
       872: 1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       922: 1
       930: 1
       934: q+1
       938: 1
       946: 1
       950: 1
       955: 1
       956: q
       958: q+1
       961: 1
       975: 1
       979: q+1
       982: q+1
       991: q+1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1027: 1
      1034: q+1
      1038: q+1
      1041: 1
      1042: q+1
      1045: 1
      1048: 1
      1050: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1102: q+1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1158: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1199: 1
      1208: 1
      1220: 1
      1222: 1
      1238: 1
      1241: 1
      1256: q+1
      1259: 1
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1323: 1
      1331: 1
      1354: 1
      1378: 1
      1386: 1
      1393: 1
      1401: 1
      1415: 1
      1424: 1
      1446: 1
      1470: 1
      1474: 1
      1477: 1
      1480: 1
      1560: 1
      1592: 1
      1600: 1
      1613: 1
      1671: 1
      1778: 1

1779:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+3q^2+2q+1
        26: 2q^3+3q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: 2q^3+3q^2+2q+1
        35: 2q^3+3q^2+2q+1
        36: 2q^2+2q+1
        38: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+3q^2+2q+1
        56: 2q^3+3q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: q
        59: q^2+q+1
        60: 2q^2+q+1
        61: q
        63: q^3+2q^2+2q+1
        65: q^3+2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: q^3+2q^2+2q+1
        77: q^3+2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q^3+3q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^3+3q^2+2q+1
        87: 2q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q^2+q+1
       105: q
       107: 2q^2+q+1
       108: q
       109: q
       110: q^2+q+1
       112: q^2+2q+1
       114: q^3+2q^2+2q+1
       116: q^3+2q^2+2q+1
       117: q
       118: q^2+q+1
       119: 2q^2+q+1
       120: q
       122: q^3+2q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^3+2q^2+2q+1
       142: 2q+1
       143: 2q^2+2q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: 2q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       152: q^3+2q^2+2q+1
       154: q^3+2q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+2q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       170: q^2+q+1
       171: q
       174: q^2+q+1
       175: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q^2+q+1
       184: q
       185: q
       186: q^2+q+1
       188: q^2+2q+1
       190: q^3+2q^2+2q+1
       191: q
       192: q^2+q+1
       193: q+1
       195: q
       196: q+1
       198: q+1
       199: 2q^2+q+1
       200: q
       201: 2q^2+q+1
       202: q
       203: q
       204: q^2+q+1
       206: q^2+2q+1
       208: q^2+2q+1
       210: q^3+2q^2+2q+1
       212: q^3+2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: 2q^2+2q+1
       223: q^2+q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q^2+q+1
       232: 2q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 2q+1
       244: q+1
       245: 2q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+2q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       260: q+1
       261: q
       264: q^2+q+1
       265: q
       268: q+1
       272: q
       274: q^2+q+1
       276: q^2+q+1
       277: q
       280: 2q+1
       282: q+1
       283: q^2+1
       286: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q^2+q+1
       294: q
       295: q
       296: q^2+q+1
       298: q^2+2q+1
       299: q+1
       302: q+1
       303: q
       304: q+1
       306: q+1
       307: 2q^2+q+1
       308: q
       309: q
       310: q^2+q+1
       312: 2q+1
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       319: q+1
       321: q
       322: q+1
       324: q+1
       326: q^3+2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: q^2+q+1
       353: 2q^2+2q+1
       354: q^2+q+1
       355: 2q^2+2q+1
       356: q^2+q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       378: 1
       382: q+1
       383: q
       386: q^2+q+1
       387: q
       390: q+1
       394: q+1
       398: q
       400: q+1
       402: q
       403: q^2+q+1
       407: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q^2+1
       422: 1
       424: q+1
       426: q+1
       428: 2q+1
       429: 1
       432: 1
       434: 1
       436: q+1
       437: q+1
       439: q
       440: q+1
       442: q+1
       443: q+1
       446: q+1
       447: q^2+1
       450: 1
       452: q+1
       453: 2q^2+q+1
       454: q
       456: 2q+1
       457: q
       458: q^2+q+1
       460: q^2+2q+1
       461: q
       462: q+1
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q+1
       473: q
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: 2q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 1
       526: q+1
       527: q
       530: 1
       534: 1
       538: q+1
       542: q+1
       546: q+1
       551: 1
       554: q
       556: q+1
       558: q
       560: q^2+q+1
       562: q
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+1
       592: 1
       593: 1
       596: 1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: 1
       608: 1
       610: 1
       612: q+1
       614: 1
       615: q+1
       618: q+1
       619: q^2+1
       622: 1
       624: q+1
       626: q+1
       628: 2q+1
       630: q+1
       631: q
       632: q+1
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: q+1
       649: q
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: 1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       699: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: q+1
       740: 1
       744: 1
       746: q
       748: q+1
       750: q
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       778: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       798: 1
       800: 1
       801: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: q+1
       815: q+1
       822: q+1
       824: q+1
       825: q^2+1
       828: 1
       829: 1
       832: 1
       834: q+1
       836: q+1
       838: 2q+1
       839: q
       840: q+1
       842: q+1
       845: 1
       848: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       868: q+1
       871: 1
       872: 1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       921: 1
       929: 1
       933: q+1
       939: 1
       947: 1
       951: 1
       953: 1
       957: q
       959: q+1
       962: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1026: 1
      1035: q+1
      1039: q+1
      1040: 1
      1043: q+1
      1045: 1
      1049: 1
      1051: 1
      1052: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1104: q+1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1157: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1200: 1
      1207: 1
      1221: 1
      1223: 1
      1239: 1
      1240: 1
      1257: q+1
      1258: 1
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1324: 1
      1332: 1
      1353: 1
      1379: 1
      1385: 1
      1394: 1
      1402: 1
      1416: 1
      1423: 1
      1447: 1
      1471: 1
      1475: 1
      1476: 1
      1481: 1
      1561: 1
      1593: 1
      1601: 1
      1612: 1
      1672: 1
      1779: 1

1780:    0: 2q^3+3q^2+2q+1
         1: 2q^3+3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 2q^3+3q^2+2q+1
         7: 2q^3+3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 2q^3+3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+q+1
        19: 2q^3+3q^2+2q+1
        20: 2q^3+3q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+3q^2+2q+1
        26: 2q^3+3q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 2q^3+3q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: 2q^3+3q^2+2q+1
        35: 2q^3+3q^2+2q+1
        36: 2q^2+2q+1
        38: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^3+3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: 2q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^3+2q^2+q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+3q^2+2q+1
        56: 2q^3+3q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: q^2+q+1
        59: q
        60: q
        61: 2q^2+q+1
        63: q^3+2q^2+2q+1
        65: q^3+2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: q^2+q+1
        70: 2q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: q^3+2q^2+2q+1
        77: q^3+2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q^3+3q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^3+3q^2+2q+1
        87: 2q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^3+2q^2+q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+q+1
        94: 2q+1
        95: 2q+1
        96: q^2+q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q
       105: q^2+q+1
       107: q
       108: 2q^2+q+1
       109: q^2+q+1
       110: q
       112: q^2+2q+1
       114: q^3+2q^2+2q+1
       116: q^3+2q^2+2q+1
       117: q^2+q+1
       118: q
       119: q
       120: 2q^2+q+1
       122: q^3+2q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^3+2q^2+2q+1
       142: 2q+1
       143: 2q^2+2q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: 2q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       152: q^3+2q^2+2q+1
       154: q^3+2q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^3+2q^2+q+1
       160: 2q+1
       161: 2q+1
       162: q^2+q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+2q^2+q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       170: q
       171: q^2+q+1
       174: q
       175: q^2+q+1
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q
       184: 2q^2+q+1
       185: q^2+q+1
       186: q
       188: q^2+2q+1
       190: q^3+2q^2+2q+1
       191: q^2+q+1
       192: q
       194: q+1
       195: q+1
       196: q
       198: q+1
       199: q
       200: 2q^2+q+1
       201: q
       202: 2q^2+q+1
       203: q^2+q+1
       204: q
       206: q^2+2q+1
       208: q^2+2q+1
       210: q^3+2q^2+2q+1
       212: q^3+2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: q^2+q+1
       222: 2q^2+2q+1
       223: q^2+q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q^2+q+1
       232: 2q^2+2q+1
       233: q^2+q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 2q+1
       244: q+1
       245: 2q+1
       246: q^3+2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q+1
       251: 2q+1
       252: q^2+q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^3+2q^2+q+1
       256: 2q+1
       257: 2q+1
       258: q^2+q+1
       260: q
       261: q+1
       264: q
       265: q^2+q+1
       270: q+1
       272: q^2+q+1
       274: q
       276: q
       277: q^2+q+1
       280: 2q+1
       282: q+1
       284: q^2+1
       285: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: q
       294: 2q^2+q+1
       295: q^2+q+1
       296: q
       298: q^2+2q+1
       300: q+1
       302: q+1
       303: q+1
       304: q
       306: q+1
       307: q
       308: 2q^2+q+1
       309: q^2+q+1
       310: q
       312: 2q+1
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       320: q+1
       321: q+1
       322: q
       324: q+1
       326: q^3+2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: 2q+1
       350: q+1
       351: q+1
       352: q^2+q+1
       353: 2q^2+2q+1
       354: q^2+q+1
       355: 2q^2+2q+1
       356: q^2+q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q+1
       367: 2q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q+1
       375: 2q+1
       376: q^2+q+1
       379: 1
       382: q
       383: q+1
       386: q
       387: q^2+q+1
       392: q+1
       395: q+1
       398: q+1
       400: q
       402: q^2+q+1
       403: q
       408: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: q^2+1
       421: 1
       424: q+1
       426: q+1
       428: 2q+1
       430: 1
       431: 1
       434: 1
       436: q+1
       438: q+1
       439: q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       448: q^2+1
       449: 1
       452: q+1
       453: q
       454: 2q^2+q+1
       456: 2q+1
       457: q^2+q+1
       458: q
       460: q^2+2q+1
       461: q+1
       462: q
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: q+1
       473: q+1
       474: q
       476: q+1
       478: q+1
       480: q+1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: 2q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: q+1
       512: 1
       513: 2q+1
       514: q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: 1
       526: q
       527: q+1
       531: 1
       535: 1
       540: q+1
       544: q+1
       548: q+1
       550: 1
       554: q+1
       556: q
       558: q^2+q+1
       560: q
       562: q+1
       564: q
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       590: q^2+1
       591: 1
       594: 1
       595: 1
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: 1
       607: 1
       610: 1
       612: q+1
       614: 1
       616: q+1
       618: q+1
       620: q^2+1
       621: 1
       624: q+1
       626: q+1
       628: 2q+1
       630: q+1
       631: q+1
       632: q
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: q+1
       649: q+1
       650: q
       652: q+1
       654: q+1
       656: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       675: 1
       676: q+1
       677: 1
       678: q+1
       679: 1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       700: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: q+1
       738: 1
       742: 1
       746: q+1
       748: q
       750: q+1
       752: q
       755: 1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       778: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: q+1
       816: q+1
       822: q+1
       824: q+1
       826: q^2+1
       827: 1
       830: 1
       831: 1
       834: q+1
       836: q+1
       838: 2q+1
       839: q+1
       840: q
       842: q+1
       846: 1
       847: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       868: q+1
       871: 1
       872: 1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       923: 1
       931: 1
       935: q+1
       937: 1
       945: 1
       949: 1
       954: 1
       957: q+1
       959: q
       963: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1027: 1
      1035: q+1
      1039: q+1
      1041: 1
      1043: q+1
      1044: 1
      1049: 1
      1051: 1
      1053: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: q+1
      1083: 1
      1085: 1
      1105: q+1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1159: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1201: 1
      1209: 1
      1221: 1
      1223: 1
      1239: 1
      1241: 1
      1257: q+1
      1259: 1
      1260: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1325: 1
      1333: 1
      1355: 1
      1377: 1
      1387: 1
      1395: 1
      1403: 1
      1417: 1
      1425: 1
      1447: 1
      1471: 1
      1475: 1
      1477: 1
      1481: 1
      1562: 1
      1594: 1
      1602: 1
      1614: 1
      1672: 1
      1780: 1

1781:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q+1
        59: 2q
        60: q^2+2q+1
        61: q
        62: q^2+2q+1
        63: q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 3q^2+3q+1
        84: 2q^2+3q+1
        85: 3q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q+1
       104: q
       106: q
       107: q^2+2q+1
       108: q
       109: q+1
       110: 2q
       111: q^2+2q+1
       112: q^2+q
       113: q^2+2q+1
       114: q
       115: 2q^2+2q+1
       116: q^2+q
       117: q+1
       118: 2q
       119: q^2+2q+1
       120: q
       121: q^2+2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: 3q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: 3q+1
       144: 2q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q+1
       170: q
       172: q
       173: q+1
       174: q
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q^2+2q+1
       184: q
       185: q+1
       186: 2q
       187: q^2+2q+1
       188: q^2+q
       189: q^2+2q+1
       190: q
       191: q+1
       192: 2q
       193: 2q+1
       195: q+1
       196: 2q
       197: q+1
       198: q
       199: 2q+1
       200: q
       201: q^2+2q+1
       202: q
       203: q+1
       204: 2q
       205: q^2+2q+1
       206: q^2+q
       207: 2q+1
       208: q
       209: q^2+2q+1
       210: q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: 2q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: 3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 3q+1
       244: 2q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q+1
       262: q
       263: q+1
       264: q
       266: q
       267: q+1
       268: q
       271: q+1
       273: q
       274: q
       275: q+1
       276: q
       278: q
       279: 2q+1
       281: q+1
       283: q+1
       285: 1
       286: q
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q+1
       294: q
       295: q+1
       296: 2q
       297: 2q+1
       298: q
       299: 2q+1
       301: q+1
       303: q+1
       304: 2q
       305: q+1
       306: q
       307: q^2+2q+1
       308: q
       309: q+1
       310: 2q
       311: 2q+1
       313: q^2+2q+1
       314: q^2+q
       315: q+1
       317: 2q+1
       319: 2q+1
       321: q+1
       322: 2q
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       381: q+1
       384: q
       385: q+1
       386: q
       388: q
       389: q+1
       393: q+1
       394: q
       397: q+1
       399: q
       401: q+1
       403: q
       404: q
       405: q+1
       407: q
       413: q+1
       417: q+1
       419: q+1
       421: 1
       422: q
       423: q+1
       425: q+1
       427: 2q+1
       429: q+1
       431: 1
       432: q
       433: 1
       435: q+1
       437: 1
       439: 1
       440: q
       441: 1
       443: 2q+1
       445: q+1
       447: q+1
       449: 1
       450: q
       451: q+1
       453: 2q+1
       454: q
       455: 2q+1
       457: q+1
       458: 2q
       459: 2q+1
       460: q
       461: q+1
       462: 2q
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 2q+1
       473: q+1
       474: 2q
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       521: 1
       529: 1
       533: 1
       537: q+1
       541: 1
       545: q+1
       549: 1
       553: q+1
       555: q
       557: q+1
       559: q
       560: q
       561: q+1
       563: q
       565: q+1
       566: q
       569: q+1
       573: q+1
       574: q
       577: q+1
       585: q+1
       589: q+1
       591: 1
       592: q
       593: q+1
       595: 1
       596: q
       597: q+1
       599: q+1
       601: 2q+1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       613: 1
       615: 2q+1
       617: q+1
       619: q+1
       621: 1
       622: q
       623: q+1
       625: q+1
       629: q+1
       631: q+1
       632: 2q
       633: 2q+1
       639: q+1
       641: q+1
       643: 1
       644: q
       645: 1
       647: 1
       649: 1
       650: q
       651: q+1
       653: 1
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       693: q+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q+1
       737: 1
       741: 1
       749: q+1
       751: q
       753: 1
       757: q+1
       761: 1
       765: q+1
       766: q
       769: q+1
       775: 2
       779: q+2
       781: q+1
       785: q+1
       787: 1
       788: q
       791: 1
       793: 2
       795: 2
       797: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       815: 1
       817: 1
       818: 1
       819: q+2
       821: q+1
       825: q+1
       827: 1
       828: q
       829: q+1
       831: 1
       832: q
       833: q+1
       835: q+1
       839: 1
       840: q
       843: 1
       844: 1
       845: 1
       847: 1
       848: q
       849: 1
       851: 1
       855: 1
       857: 1
       866: 2
       868: q+1
       870: 2
       871: 1
       872: 1
       874: q+2
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       884: q+1
       900: 1
       904: 1
       908: 1
       916: 2
       920: 1
       928: 1
       940: 1
       942: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       988: 1
       994: 2
       998: 1
       999: 1
      1000: 2
      1004: 1
      1006: 1
      1007: q
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1020: 2
      1022: 1
      1026: 1
      1036: q+2
      1038: q+1
      1040: q+1
      1044: 1
      1045: q
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1076: 1
      1078: 1
      1080: 2
      1082: q+1
      1083: 1
      1084: 2
      1085: 1
      1086: 1
      1089: 1
      1114: 1
      1116: 1
      1122: 2
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1138: 1
      1141: 1
      1156: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1206: 1
      1220: 1
      1230: 1
      1234: 1
      1240: 1
      1248: 2
      1250: 1
      1251: 1
      1254: 2
      1258: 1
      1260: 1
      1261: q
      1266: 1
      1268: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1290: 1
      1293: 1
      1330: 1
      1356: 1
      1380: 1
      1382: 1
      1388: 2
      1392: 1
      1396: 1
      1397: 1
      1400: 1
      1422: 1
      1430: 1
      1433: 1
      1464: 1
      1468: 1
      1474: 1
      1476: 1
      1484: 1
      1513: 1
      1516: 1
      1599: 1
      1615: 1
      1641: 1
      1657: 1
      1781: 1

1782:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: q+1
        60: q^2+2q+1
        61: q
        62: q
        63: q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 3q^2+3q+1
        84: 2q^2+3q+1
        85: 3q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q+1
       105: q
       107: q^2+2q+1
       108: q
       109: 2q
       110: q+1
       111: q^2+q
       112: q^2+2q+1
       113: q
       114: q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: 2q
       118: q+1
       119: q^2+2q+1
       120: q
       121: q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: 3q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: 3q+1
       144: 2q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q+1
       171: q
       173: q
       174: q+1
       175: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q^2+2q+1
       184: q
       185: 2q
       186: q+1
       187: q^2+q
       188: q^2+2q+1
       189: q
       190: q^2+2q+1
       191: 2q
       192: q+1
       193: 2q+1
       195: 2q
       196: q+1
       197: q
       198: q+1
       199: 2q+1
       200: q
       201: q^2+2q+1
       202: q
       203: 2q
       204: q+1
       205: q^2+q
       206: q^2+2q+1
       207: q
       208: 2q+1
       209: q
       210: q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: 2q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: 3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 3q+1
       244: 2q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q+1
       261: q
       263: q
       264: q+1
       265: q
       267: q
       268: q+1
       271: q
       272: q
       274: q+1
       275: q
       276: q+1
       277: q
       280: 2q+1
       282: q+1
       283: q+1
       285: q
       286: 1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q+1
       294: q
       295: 2q
       296: q+1
       297: q
       298: 2q+1
       299: 2q+1
       302: q+1
       303: 2q
       304: q+1
       305: q
       306: q+1
       307: q^2+2q+1
       308: q
       309: 2q
       310: q+1
       312: 2q+1
       313: q^2+q
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       319: 2q+1
       321: 2q
       322: q+1
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       382: q+1
       383: q
       385: q
       386: q+1
       387: q
       390: q+1
       393: q
       394: q+1
       398: q
       400: q+1
       401: q
       402: q
       403: q+1
       405: q
       407: q+1
       414: q+1
       418: q+1
       419: q+1
       421: q
       422: 1
       424: q+1
       426: q+1
       428: 2q+1
       429: q+1
       431: q
       432: 1
       434: 1
       436: q+1
       437: 1
       439: q
       440: 1
       442: 1
       443: 2q+1
       446: q+1
       447: q+1
       449: q
       450: 1
       452: q+1
       453: 2q+1
       454: q
       456: 2q+1
       457: 2q
       458: q+1
       459: q
       460: 2q+1
       461: 2q
       462: q+1
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 2q+1
       473: 2q
       474: q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       522: 1
       530: 1
       534: 1
       538: q+1
       542: 1
       546: q+1
       551: 1
       554: q
       556: q+1
       557: q
       558: q
       560: q+1
       562: q
       564: q+1
       565: q
       566: q+1
       571: q+1
       573: q
       574: q+1
       581: q+1
       586: q+1
       589: q+1
       591: q
       592: 1
       593: q+1
       595: q
       596: 1
       598: q+1
       600: q+1
       602: 2q+1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       614: 1
       615: 2q+1
       618: q+1
       619: q+1
       621: q
       622: 1
       624: q+1
       626: q+1
       630: q+1
       631: 2q
       632: q+1
       634: 2q+1
       640: q+1
       641: q+1
       643: q
       644: 1
       646: 1
       647: 1
       649: q
       650: 1
       652: q+1
       654: 1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       699: q+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: q+1
       740: 1
       744: 1
       750: q
       752: q+1
       754: 1
       759: q+1
       763: 1
       765: q
       766: q+1
       773: q+1
       776: 2
       780: q+2
       782: q+1
       785: q+1
       787: q
       788: 1
       792: 1
       793: 2
       796: 2
       798: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       815: 1
       817: 1
       818: 1
       820: q+2
       822: q+1
       825: q+1
       827: q
       828: 1
       829: q+1
       831: q
       832: 1
       834: q+1
       836: q+1
       839: q
       840: 1
       843: 1
       844: 1
       845: 1
       847: q
       848: 1
       850: 1
       852: 1
       856: 1
       858: 1
       866: 2
       868: q+1
       870: 2
       871: 1
       872: 1
       874: q+2
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       890: q+1
       903: 1
       905: 1
       909: 1
       917: 2
       921: 1
       929: 1
       941: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       989: 1
       995: 2
       998: 1
       999: 1
      1000: 2
      1004: 1
      1006: q
      1007: 1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 2
      1023: 1
      1026: 1
      1037: q+2
      1039: q+1
      1040: q+1
      1044: q
      1045: 1
      1049: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 2
      1082: q+1
      1083: 1
      1084: 2
      1085: 1
      1087: 1
      1092: 1
      1115: 1
      1117: 1
      1123: 2
      1128: 1
      1130: 1
      1131: 1
      1136: 1
      1139: 1
      1142: 1
      1157: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1207: 1
      1221: 1
      1231: 1
      1234: 1
      1240: 1
      1249: 2
      1250: 1
      1251: 1
      1254: 2
      1258: 1
      1260: q
      1261: 1
      1267: 1
      1268: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1291: 1
      1296: 1
      1332: 1
      1357: 1
      1381: 1
      1383: 1
      1389: 2
      1394: 1
      1396: 1
      1397: 1
      1402: 1
      1423: 1
      1431: 1
      1434: 1
      1465: 1
      1468: 1
      1475: 1
      1476: 1
      1484: 1
      1514: 1
      1519: 1
      1601: 1
      1616: 1
      1642: 1
      1657: 1
      1782: 1

1783:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: q+1
        60: q
        61: q^2+2q+1
        62: q^2+2q+1
        63: q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 3q^2+3q+1
        84: 2q^2+3q+1
        85: 3q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       105: q
       106: q+1
       107: q
       108: q^2+2q+1
       109: 2q
       110: q+1
       111: q^2+2q+1
       112: q^2+q
       113: q^2+2q+1
       114: q
       115: 2q^2+2q+1
       116: q^2+q
       117: 2q
       118: q+1
       119: q
       120: q^2+2q+1
       121: q^2+2q+1
       122: q
       123: q^2+2q+1
       124: q^2+q
       125: 3q+1
       126: 2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: 3q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: 3q+1
       144: 2q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       171: q
       172: q+1
       173: q
       175: q
       176: q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q
       184: q^2+2q+1
       185: 2q
       186: q+1
       187: q^2+2q+1
       188: q^2+q
       189: q^2+2q+1
       190: q
       191: 2q
       192: q+1
       194: 2q+1
       195: 2q
       196: q+1
       197: q+1
       198: q
       199: q
       200: 2q+1
       201: q
       202: q^2+2q+1
       203: 2q
       204: q+1
       205: q^2+2q+1
       206: q^2+q
       207: 2q+1
       208: q
       209: q^2+2q+1
       210: q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: 2q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: 3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: 3q+1
       244: 2q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q
       262: q+1
       263: q
       265: q
       266: q+1
       269: q+1
       270: q
       271: q
       272: q
       273: q+1
       275: q
       277: q
       278: q+1
       279: 2q+1
       281: q+1
       284: q+1
       285: q
       286: 1
       287: q+1
       289: 2q+1
       291: q+1
       293: q
       294: 2q+1
       295: 2q
       296: q+1
       297: 2q+1
       298: q
       300: 2q+1
       301: q+1
       303: 2q
       304: q+1
       305: q+1
       306: q
       307: q
       308: q^2+2q+1
       309: 2q
       310: q+1
       311: 2q+1
       313: q^2+2q+1
       314: q^2+q
       315: q+1
       317: 2q+1
       320: 2q+1
       321: 2q
       322: q+1
       323: q+1
       324: q
       325: q^2+2q+1
       326: q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       381: q
       384: q+1
       385: q
       387: q
       388: q+1
       391: q+1
       395: q
       396: q+1
       397: q
       399: q+1
       401: q
       402: q
       404: q+1
       406: q+1
       408: q
       413: q+1
       417: q+1
       420: q+1
       421: q
       422: 1
       423: q+1
       425: q+1
       427: 2q+1
       430: q+1
       431: q
       432: 1
       433: 1
       435: q+1
       438: 1
       439: q
       440: 1
       441: 1
       444: 2q+1
       445: q+1
       448: q+1
       449: q
       450: 1
       451: q+1
       453: q
       454: 2q+1
       455: 2q+1
       457: 2q
       458: q+1
       459: 2q+1
       460: q
       461: 2q
       462: q+1
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: 2q+1
       473: 2q
       474: q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       524: 1
       532: 1
       536: 1
       539: q+1
       543: 1
       547: q+1
       552: 1
       553: q
       555: q+1
       557: q
       558: q
       559: q+1
       561: q
       563: q+1
       567: q
       568: q+1
       570: q+1
       575: q+1
       576: q
       577: q+1
       585: q+1
       590: q+1
       591: q
       592: 1
       594: q+1
       595: q
       596: 1
       597: q+1
       599: q+1
       601: 2q+1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       613: 1
       616: 2q+1
       617: q+1
       620: q+1
       621: q
       622: 1
       623: q+1
       625: q+1
       629: q+1
       631: 2q
       632: q+1
       633: 2q+1
       639: q+1
       642: q+1
       643: q
       644: 1
       645: 1
       648: 1
       649: q
       650: 1
       651: q+1
       653: 1
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       697: q+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: q+1
       739: 1
       743: 1
       749: q
       751: q+1
       756: 1
       758: q+1
       762: 1
       767: q
       768: q+1
       769: q+1
       775: 2
       779: q+2
       781: q+1
       786: q+1
       787: q
       788: 1
       791: 1
       794: 2
       795: 2
       797: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       816: 1
       817: 1
       818: 1
       819: q+2
       821: q+1
       826: q+1
       827: q
       828: 1
       830: q+1
       831: q
       832: 1
       833: q+1
       835: q+1
       839: q
       840: 1
       843: 1
       844: 1
       846: 1
       847: q
       848: 1
       849: 1
       851: 1
       855: 1
       857: 1
       866: 2
       868: q+1
       870: 2
       871: 1
       872: 1
       874: q+2
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       889: q+1
       902: 1
       906: 1
       911: 1
       918: 2
       922: 1
       930: 1
       940: 1
       942: 1
       946: 1
       950: 1
       955: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       991: 1
       994: 2
       998: 1
       999: 1
      1001: 2
      1005: 1
      1006: q
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1020: 2
      1022: 1
      1027: 1
      1036: q+2
      1038: q+1
      1041: q+1
      1044: q
      1045: 1
      1048: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 1
      1078: 1
      1080: 2
      1082: q+1
      1083: 1
      1084: 2
      1085: 1
      1090: 1
      1091: 1
      1114: 1
      1116: 1
      1124: 2
      1127: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1158: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1208: 1
      1220: 1
      1230: 1
      1235: 1
      1241: 1
      1248: 2
      1250: 1
      1251: 1
      1255: 2
      1259: 1
      1260: q
      1261: 1
      1266: 1
      1269: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1294: 1
      1295: 1
      1331: 1
      1358: 1
      1380: 1
      1382: 1
      1390: 2
      1393: 1
      1398: 1
      1399: 1
      1401: 1
      1424: 1
      1430: 1
      1433: 1
      1464: 1
      1469: 1
      1474: 1
      1477: 1
      1484: 1
      1517: 1
      1518: 1
      1600: 1
      1617: 1
      1641: 1
      1658: 1
      1783: 1

1784:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q+1
        59: 2q
        60: q
        61: q^2+2q+1
        62: q
        63: q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 3q^2+3q+1
        84: 2q^2+3q+1
        85: 3q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       104: q
       105: q+1
       106: q
       107: q
       108: q^2+2q+1
       109: q+1
       110: 2q
       111: q^2+q
       112: q^2+2q+1
       113: q
       114: q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: q+1
       118: 2q
       119: q
       120: q^2+2q+1
       121: q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q+1
       126: 2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: 3q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: 3q+1
       144: 2q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       170: q
       171: q+1
       172: q
       174: q
       175: q+1
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q
       184: q^2+2q+1
       185: q+1
       186: 2q
       187: q^2+q
       188: q^2+2q+1
       189: q
       190: q^2+2q+1
       191: q+1
       192: 2q
       194: 2q+1
       195: q+1
       196: 2q
       197: q
       198: q+1
       199: q
       200: 2q+1
       201: q
       202: q^2+2q+1
       203: q+1
       204: 2q
       205: q^2+q
       206: q^2+2q+1
       207: q
       208: 2q+1
       209: q
       210: q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: 2q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: 3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: 3q+1
       244: 2q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q
       261: q+1
       264: q
       265: q+1
       266: q
       269: q
       270: q+1
       272: q+1
       273: q
       274: q
       276: q
       277: q+1
       278: q
       280: 2q+1
       282: q+1
       284: q+1
       285: 1
       286: q
       288: q+1
       290: 2q+1
       292: q+1
       293: q
       294: 2q+1
       295: q+1
       296: 2q
       297: q
       298: 2q+1
       300: 2q+1
       302: q+1
       303: q+1
       304: 2q
       305: q
       306: q+1
       307: q
       308: q^2+2q+1
       309: q+1
       310: 2q
       312: 2q+1
       313: q^2+q
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       320: 2q+1
       321: q+1
       322: 2q
       323: q
       324: q+1
       325: q
       326: q^2+2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q+1
       367: 3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       382: q
       383: q+1
       386: q
       387: q+1
       388: q
       392: q+1
       395: q+1
       396: q
       398: q+1
       400: q
       402: q+1
       403: q
       404: q
       406: q
       408: q+1
       414: q+1
       418: q+1
       420: q+1
       421: 1
       422: q
       424: q+1
       426: q+1
       428: 2q+1
       430: q+1
       431: 1
       432: q
       434: 1
       436: q+1
       438: 1
       439: 1
       440: q
       442: 1
       444: 2q+1
       446: q+1
       448: q+1
       449: 1
       450: q
       452: q+1
       453: q
       454: 2q+1
       456: 2q+1
       457: q+1
       458: 2q
       459: q
       460: 2q+1
       461: q+1
       462: 2q
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: 2q+1
       473: q+1
       474: 2q
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q+1
       519: q+1
       520: q+1
       523: 1
       531: 1
       535: 1
       540: q+1
       544: 1
       548: q+1
       550: 1
       554: q+1
       556: q
       558: q+1
       559: q
       560: q
       562: q+1
       564: q
       567: q+1
       568: q
       572: q+1
       575: q
       576: q+1
       581: q+1
       586: q+1
       590: q+1
       591: 1
       592: q
       594: q+1
       595: 1
       596: q
       598: q+1
       600: q+1
       602: 2q+1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       614: 1
       616: 2q+1
       618: q+1
       620: q+1
       621: 1
       622: q
       624: q+1
       626: q+1
       630: q+1
       631: q+1
       632: 2q
       634: 2q+1
       640: q+1
       642: q+1
       643: 1
       644: q
       646: 1
       648: 1
       649: 1
       650: q
       652: q+1
       654: 1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 2q+1
       672: q+1
       673: q+1
       674: 2
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       700: q+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: q+1
       738: 1
       742: 1
       750: q+1
       752: q
       755: 1
       760: q+1
       764: 1
       767: q+1
       768: q
       773: q+1
       776: 2
       780: q+2
       782: q+1
       786: q+1
       787: 1
       788: q
       792: 1
       794: 2
       796: 2
       798: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       816: 1
       817: 1
       818: 1
       820: q+2
       822: q+1
       826: q+1
       827: 1
       828: q
       830: q+1
       831: 1
       832: q
       834: q+1
       836: q+1
       839: 1
       840: q
       843: 1
       844: 1
       846: 1
       847: 1
       848: q
       850: 1
       852: 1
       856: 1
       858: 1
       866: 2
       868: q+1
       870: 2
       871: 1
       872: 1
       874: q+2
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       891: q+1
       901: 1
       907: 1
       910: 1
       919: 2
       923: 1
       931: 1
       941: 1
       943: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       990: 1
       995: 2
       998: 1
       999: 1
      1001: 2
      1005: 1
      1006: 1
      1007: q
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 2
      1023: 1
      1027: 1
      1037: q+2
      1039: q+1
      1041: q+1
      1044: 1
      1045: q
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 2
      1082: q+1
      1083: 1
      1084: 2
      1085: 1
      1093: 1
      1094: 1
      1115: 1
      1117: 1
      1125: 2
      1129: 1
      1132: 1
      1133: 1
      1137: 1
      1139: 1
      1142: 1
      1159: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1209: 1
      1221: 1
      1231: 1
      1235: 1
      1241: 1
      1249: 2
      1250: 1
      1251: 1
      1255: 2
      1259: 1
      1260: 1
      1261: q
      1267: 1
      1269: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1287: 1
      1289: 1
      1297: 1
      1298: 1
      1333: 1
      1359: 1
      1381: 1
      1383: 1
      1391: 2
      1395: 1
      1398: 1
      1399: 1
      1403: 1
      1425: 1
      1431: 1
      1434: 1
      1465: 1
      1469: 1
      1475: 1
      1477: 1
      1484: 1
      1520: 1
      1521: 1
      1602: 1
      1618: 1
      1642: 1
      1658: 1
      1784: 1

1785:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+3q+1
        38: 2q^2+q
        39: 3q^2+3q+1
        40: 2q^2+q
        41: q^3+2q^2+3q+1
        42: q^3+q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 3q^2+3q+1
        59: 2q^2+q
        60: 3q^2+2q+1
        61: 2q^2+2q
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: 2q^2+2q+1
       104: q^2
       105: q^2+q
       106: q^2+q
       107: q^2+q+1
       108: q^2+q
       109: q^2+2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+3q+1
       118: q
       119: q^2+2q+1
       120: 2q
       121: 2q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: q^2+2q+1
       136: 2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: 2q^2+2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       169: q+1
       173: q^2+2q+1
       175: q
       176: q
       177: q^2+2q+1
       179: q^2+2q+1
       181: q+1
       183: q+1
       184: q
       185: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q^2+q+1
       194: q^2+q
       195: q^2+2q+1
       197: q+1
       199: q^2+2q+1
       200: 2q
       201: q^2+q+1
       202: q^2+q
       203: q^2+2q+1
       205: q+1
       207: 2q^2+3q+1
       208: q^2+q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q^2+2q+1
       230: 2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q^2+3q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: 3q^2+3q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       259: q+1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       277: q
       278: q
       279: q+1
       281: q+1
       283: q+1
       284: q
       285: 2q+1
       287: q^2+2q+1
       289: 1
       291: q+1
       293: q+1
       294: q
       295: 2q+1
       297: q+1
       299: q+1
       300: q
       301: q+1
       303: 2q+1
       305: q+1
       307: q+1
       308: q
       309: 2q+1
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       319: q^2+q+1
       320: q^2+q
       321: q^2+2q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 3q+1
       334: q^2+2q+1
       335: 2q+1
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 2q+2
       360: q+1
       362: q+1
       364: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q+1
       420: q
       421: 2q+1
       423: q+1
       425: q+1
       427: 2q+2
       429: q+1
       430: q
       431: 2q+1
       433: q+1
       435: 1
       437: q+1
       438: q
       439: 2q+1
       441: q+1
       443: q+1
       444: q+1
       445: 2q+2
       447: q+1
       448: q
       449: 2q+1
       451: q+1
       453: q+1
       454: q
       455: 1
       457: 2q+1
       459: q+1
       461: 2q+2
       463: 2q+2
       465: q+1
       467: q+1
       469: q^2+2q+1
       471: q+1
       472: q
       473: 2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: q+1
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 3q+1
       493: q^2+2q+1
       494: 2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: q^2+2q+1
       499: 2q+1
       500: q+1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: 2q+1
       514: 2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q+1
       545: q+1
       547: q+1
       549: q+1
       553: 1
       557: q+1
       561: 2q+2
       565: q+1
       569: q+1
       573: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: 1
       589: q+1
       590: q
       591: q+1
       595: q+1
       597: 1
       599: q+1
       601: 2
       603: q+1
       604: q
       605: 1
       607: 2q+1
       609: q+1
       611: 1
       613: q+1
       615: 1
       616: 1
       617: 2
       619: q+1
       620: q
       621: 2q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       631: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q+1
       642: q
       643: 2q+1
       645: q+1
       647: q+1
       648: q
       649: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2q+1
       676: q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+1
       682: q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: q^2+2q+1
       688: 2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       693: q+1
       698: q+1
       705: 1
       709: 1
       713: q+1
       721: 1
       725: q+1
       729: 1
       733: 1
       735: 1
       737: 1
       741: q+1
       745: 1
       749: 2
       753: q+1
       757: 1
       761: q+1
       765: 1
       767: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 1
       799: 1
       801: q+1
       802: q
       803: q+1
       807: q+1
       809: 1
       811: q+1
       813: 2
       815: 1
       816: 1
       817: 2
       819: 2
       821: 1
       823: 1
       825: q+1
       826: q
       827: q+1
       831: q+1
       833: 1
       835: q+1
       837: 2
       839: 2
       841: q+1
       843: 1
       844: 1
       845: q+1
       846: q
       847: 2q+1
       849: 1
       851: q+1
       853: 1
       855: q+1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       884: 1
       888: 1
       896: 1
       900: 1
       912: 1
       916: 1
       918: 1
       920: 1
       924: q+1
       932: 1
       934: 1
       936: 1
       940: 2
       944: 1
       948: q+1
       956: 2
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: q+1
       978: 1
       982: 1
       985: 1
       988: 1
       990: 1
       992: 2
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1028: 1
      1030: 2
      1032: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1053: q
      1054: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1090: 1
      1098: 1
      1103: 1
      1110: 1
      1114: 1
      1144: 1
      1146: 1
      1148: 1
      1152: 1
      1164: 2
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1198: 1
      1202: q+1
      1214: 1
      1216: 1
      1230: 1
      1232: 1
      1236: 1
      1238: 1
      1242: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1306: 1
      1314: 1
      1344: 1
      1348: 1
      1376: 1
      1380: 1
      1414: 1
      1418: 1
      1448: 1
      1450: 1
      1456: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1478: 1
      1487: 1
      1563: 1
      1583: 1
      1603: 1
      1607: 1
      1661: 1
      1663: 1
      1785: 1

1786:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: 3q^2+3q+1
        39: 2q^2+q
        40: 3q^2+3q+1
        41: q^3+q^2+q
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 3q^2+3q+1
        59: 2q^2+q
        60: 2q^2+2q
        61: 3q^2+2q+1
        62: 2q^2+q
        63: 3q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2+q
       104: q^2+q
       105: 2q^2+2q+1
       106: q^2
       107: q^2+q
       108: q^2+q+1
       109: q^2+2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+3q+1
       118: q
       119: 2q
       120: q^2+2q+1
       121: q^2+q
       122: 2q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: q^2+2q+1
       136: 2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: 2q^2+2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       171: q+1
       173: q
       174: q
       175: q^2+2q+1
       178: q^2+2q+1
       180: q^2+2q+1
       182: q+1
       183: q
       184: q+1
       185: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q^2+3q+1
       192: q
       193: q^2+q
       194: q^2+q+1
       195: q^2+2q+1
       198: q+1
       199: 2q
       200: q^2+2q+1
       201: q^2+q
       202: q^2+q+1
       203: q^2+2q+1
       206: q+1
       207: q^2+q
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q^2+2q+1
       230: 2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q^2+3q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: 3q^2+3q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       261: q+1
       265: q+1
       270: q+1
       272: q+1
       275: q
       276: q
       277: q^2+2q+1
       280: q+1
       282: q+1
       283: q
       284: q+1
       285: 2q+1
       288: q^2+2q+1
       290: 1
       292: q+1
       293: q
       294: q+1
       295: 2q+1
       298: q+1
       299: q
       300: q+1
       302: q+1
       303: 2q+1
       306: q+1
       307: q
       308: q+1
       309: 2q+1
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       319: q^2+q
       320: q^2+q+1
       321: q^2+2q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 3q+1
       334: q^2+2q+1
       335: 2q+1
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 2q+2
       361: q+1
       363: q+1
       365: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q
       420: q+1
       421: 2q+1
       424: q+1
       426: q+1
       428: 2q+2
       429: q
       430: q+1
       431: 2q+1
       434: q+1
       436: 1
       437: q
       438: q+1
       439: 2q+1
       442: q+1
       443: q+1
       444: q+1
       446: 2q+2
       447: q
       448: q+1
       449: 2q+1
       452: q+1
       453: q
       454: q+1
       456: 1
       457: 2q+1
       460: q+1
       461: 2q+2
       464: 2q+2
       466: q+1
       468: q+1
       470: q^2+2q+1
       471: q
       472: q+1
       473: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: q+1
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 3q+1
       493: q^2+2q+1
       494: 2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: q^2+2q+1
       499: 2q+1
       500: q+1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: 2q+1
       514: 2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q+1
       546: q+1
       548: q+1
       550: q+1
       554: 1
       558: q+1
       562: 2q+2
       567: q+1
       572: q+1
       573: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: 1
       589: q
       590: q+1
       591: q+1
       595: q+1
       598: 1
       600: q+1
       602: 2
       603: q
       604: q+1
       606: 1
       607: 2q+1
       610: q+1
       612: 1
       614: q+1
       615: 1
       616: 1
       618: 2
       619: q
       620: q+1
       621: 2q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       631: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q
       642: q+1
       643: 2q+1
       646: q+1
       647: q
       648: q+1
       649: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2q+1
       676: q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+1
       682: q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: q^2+2q+1
       688: 2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       694: q+1
       700: q+1
       707: 1
       711: 1
       714: q+1
       724: 1
       728: q+1
       732: 1
       734: 1
       736: 1
       738: 1
       742: q+1
       746: 1
       750: 2
       755: q+1
       760: 1
       764: q+1
       765: 1
       767: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 1
       800: 1
       801: q
       802: q+1
       803: q+1
       807: q+1
       810: 1
       812: q+1
       814: 2
       815: 1
       816: 1
       817: 2
       820: 2
       822: 1
       824: 1
       825: q
       826: q+1
       827: q+1
       831: q+1
       834: 1
       836: q+1
       838: 2
       839: 2
       842: q+1
       843: 1
       844: 1
       845: q
       846: q+1
       847: 2q+1
       850: 1
       852: q+1
       854: 1
       856: q+1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       885: 1
       891: 1
       898: 1
       901: 1
       915: 1
       917: 1
       919: 1
       923: 1
       925: q+1
       933: 1
       935: 1
       937: 1
       941: 2
       945: 1
       949: q+1
       957: 2
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: q+1
       981: 1
       983: 1
       986: 1
       988: 1
       990: 1
       993: 2
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1028: 1
      1031: 2
      1032: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: q+1
      1054: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1093: 1
      1099: 1
      1105: 1
      1111: 1
      1115: 1
      1145: 1
      1147: 1
      1151: 1
      1153: 1
      1165: 2
      1169: 1
      1173: 1
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1201: 1
      1203: q+1
      1215: 1
      1216: 1
      1231: 1
      1232: 1
      1237: 1
      1239: 1
      1242: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1309: 1
      1315: 1
      1345: 1
      1349: 1
      1377: 1
      1381: 1
      1417: 1
      1419: 1
      1449: 1
      1450: 1
      1457: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1478: 1
      1487: 1
      1564: 1
      1584: 1
      1604: 1
      1608: 1
      1662: 1
      1663: 1
      1786: 1

1787:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+3q+1
        38: 2q^2+q
        39: 3q^2+3q+1
        40: 2q^2+q
        41: q^3+2q^2+3q+1
        42: q^3+q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+q
        59: 3q^2+3q+1
        60: 2q^2+2q
        61: 3q^2+2q+1
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2+q
       104: q^2+q
       105: q^2
       106: 2q^2+2q+1
       107: q^2+q
       108: q^2+q+1
       110: q^2+2q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q
       118: q^2+3q+1
       119: 2q
       120: q^2+2q+1
       121: 2q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: q^2+2q+1
       136: 2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: 2q^2+2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       172: q+1
       173: q
       174: q
       176: q^2+2q+1
       177: q^2+2q+1
       179: q^2+2q+1
       181: q+1
       183: q
       184: q+1
       186: 2q+1
       187: q+1
       189: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q^2+q
       194: q^2+q+1
       196: q^2+2q+1
       197: q+1
       199: 2q
       200: q^2+2q+1
       201: q^2+q
       202: q^2+q+1
       204: q^2+2q+1
       205: q+1
       207: 2q^2+3q+1
       208: q^2+q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q^2+2q+1
       230: 2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q^2+3q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: 3q^2+3q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       262: q+1
       266: q+1
       269: q+1
       273: q+1
       275: q
       276: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       283: q
       284: q+1
       286: 2q+1
       287: q^2+2q+1
       289: 1
       291: q+1
       293: q
       294: q+1
       296: 2q+1
       297: q+1
       299: q
       300: q+1
       301: q+1
       304: 2q+1
       305: q+1
       307: q
       308: q+1
       310: 2q+1
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       319: q^2+q
       320: q^2+q+1
       322: q^2+2q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 3q+1
       334: q^2+2q+1
       335: 2q+1
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 2q+2
       360: q+1
       362: q+1
       364: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q
       420: q+1
       422: 2q+1
       423: q+1
       425: q+1
       427: 2q+2
       429: q
       430: q+1
       432: 2q+1
       433: q+1
       435: 1
       437: q
       438: q+1
       440: 2q+1
       441: q+1
       443: q+1
       444: q+1
       445: 2q+2
       447: q
       448: q+1
       450: 2q+1
       451: q+1
       453: q
       454: q+1
       455: 1
       458: 2q+1
       459: q+1
       462: 2q+2
       463: 2q+2
       465: q+1
       467: q+1
       469: q^2+2q+1
       471: q
       472: q+1
       474: 2q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: q+1
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 3q+1
       493: q^2+2q+1
       494: 2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: q^2+2q+1
       499: 2q+1
       500: q+1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: 2q+1
       514: 2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q+1
       545: q+1
       547: q+1
       552: q+1
       555: 1
       559: q+1
       563: 2q+2
       568: q+1
       570: q+1
       574: q+1
       575: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: 1
       589: q
       590: q+1
       592: q+1
       596: q+1
       597: 1
       599: q+1
       601: 2
       603: q
       604: q+1
       605: 1
       608: 2q+1
       609: q+1
       611: 1
       613: q+1
       615: 1
       616: 1
       617: 2
       619: q
       620: q+1
       622: 2q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       632: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q
       642: q+1
       644: 2q+1
       645: q+1
       647: q
       648: q+1
       650: 2q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2q+1
       676: q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+1
       682: q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: q^2+2q+1
       688: 2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       696: q+1
       697: q+1
       708: 1
       712: 1
       716: q+1
       723: 1
       727: q+1
       731: 1
       733: 1
       735: 1
       739: 1
       743: q+1
       747: 1
       751: 2
       756: q+1
       758: 1
       762: q+1
       766: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 1
       799: 1
       801: q
       802: q+1
       804: q+1
       808: q+1
       809: 1
       811: q+1
       813: 2
       815: 1
       816: 1
       818: 2
       819: 2
       821: 1
       823: 1
       825: q
       826: q+1
       828: q+1
       832: q+1
       833: 1
       835: q+1
       837: 2
       840: 2
       841: q+1
       843: 1
       844: 1
       845: q
       846: q+1
       848: 2q+1
       849: 1
       851: q+1
       853: 1
       855: q+1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       887: 1
       889: 1
       899: 1
       902: 1
       914: 1
       916: 1
       918: 1
       922: 1
       927: q+1
       932: 1
       934: 1
       938: 1
       942: 2
       946: 1
       950: q+1
       958: 2
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: q+1
       979: 1
       982: 1
       985: 1
       989: 1
       991: 1
       992: 2
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1029: 1
      1030: 2
      1033: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q
      1053: q+1
      1055: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1101: 1
      1102: 1
      1112: 1
      1116: 1
      1144: 1
      1146: 1
      1150: 1
      1154: 1
      1166: 2
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1199: 1
      1204: q+1
      1214: 1
      1217: 1
      1230: 1
      1233: 1
      1236: 1
      1238: 1
      1243: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1305: 1
      1307: 1
      1316: 1
      1346: 1
      1350: 1
      1378: 1
      1382: 1
      1415: 1
      1420: 1
      1448: 1
      1451: 1
      1456: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1479: 1
      1487: 1
      1565: 1
      1585: 1
      1605: 1
      1609: 1
      1661: 1
      1664: 1
      1787: 1

1788:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: 3q^2+3q+1
        39: 2q^2+q
        40: 3q^2+3q+1
        41: q^3+q^2+q
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+q
        59: 3q^2+3q+1
        60: 3q^2+2q+1
        61: 2q^2+2q
        62: 2q^2+q
        63: 3q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2
       104: 2q^2+2q+1
       105: q^2+q
       106: q^2+q
       107: q^2+q+1
       108: q^2+q
       110: q^2+2q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q
       118: q^2+3q+1
       119: q^2+2q+1
       120: 2q
       121: q^2+q
       122: 2q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: q^2+2q+1
       136: 2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: 2q^2+2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       170: q+1
       174: q^2+2q+1
       175: q
       176: q
       178: q^2+2q+1
       180: q^2+2q+1
       182: q+1
       183: q+1
       184: q
       186: 2q+1
       188: q+1
       190: q^2+2q+1
       191: q
       192: q^2+3q+1
       193: q^2+q+1
       194: q^2+q
       196: q^2+2q+1
       198: q+1
       199: q^2+2q+1
       200: 2q
       201: q^2+q+1
       202: q^2+q
       204: q^2+2q+1
       206: q+1
       207: q^2+q
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q+1
       225: 2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: q^2+2q+1
       230: 2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: q^2+2q+1
       235: 2q+1
       236: 2q^2+3q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: 3q^2+3q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       260: q+1
       264: q+1
       268: q+1
       274: q+1
       276: q^2+2q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: q+1
       284: q
       286: 2q+1
       288: q^2+2q+1
       290: 1
       292: q+1
       293: q+1
       294: q
       296: 2q+1
       298: q+1
       299: q+1
       300: q
       302: q+1
       304: 2q+1
       306: q+1
       307: q+1
       308: q
       310: 2q+1
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       319: q^2+q+1
       320: q^2+q
       322: q^2+2q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 3q+1
       334: q^2+2q+1
       335: 2q+1
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 2q+1
       358: 2q+1
       359: 2q+2
       361: q+1
       363: q+1
       365: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q+1
       420: q
       422: 2q+1
       424: q+1
       426: q+1
       428: 2q+2
       429: q+1
       430: q
       432: 2q+1
       434: q+1
       436: 1
       437: q+1
       438: q
       440: 2q+1
       442: q+1
       443: q+1
       444: q+1
       446: 2q+2
       447: q+1
       448: q
       450: 2q+1
       452: q+1
       453: q+1
       454: q
       456: 1
       458: 2q+1
       460: q+1
       462: 2q+2
       464: 2q+2
       466: q+1
       468: q+1
       470: q^2+2q+1
       471: q+1
       472: q
       474: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: q+1
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 3q+1
       493: q^2+2q+1
       494: 2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: q^2+2q+1
       499: 2q+1
       500: q+1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: 2q+1
       514: 2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q+1
       546: q+1
       548: q+1
       551: q+1
       556: 1
       560: q+1
       564: 2q+2
       566: q+1
       571: q+1
       574: q+1
       575: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: 1
       589: q+1
       590: q
       592: q+1
       596: q+1
       598: 1
       600: q+1
       602: 2
       603: q+1
       604: q
       606: 1
       608: 2q+1
       610: q+1
       612: 1
       614: q+1
       615: 1
       616: 1
       618: 2
       619: q+1
       620: q
       622: 2q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       632: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q+1
       642: q
       644: 2q+1
       646: q+1
       647: q+1
       648: q
       650: 2q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2q+1
       676: q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2q+1
       682: q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: q^2+2q+1
       688: 2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       699: q+1
       701: q+1
       706: 1
       710: 1
       715: q+1
       722: 1
       726: q+1
       730: 1
       734: 1
       736: 1
       740: 1
       744: q+1
       748: 1
       752: 2
       754: q+1
       759: 1
       763: q+1
       766: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 1
       800: 1
       801: q+1
       802: q
       804: q+1
       808: q+1
       810: 1
       812: q+1
       814: 2
       815: 1
       816: 1
       818: 2
       820: 2
       822: 1
       824: 1
       825: q+1
       826: q
       828: q+1
       832: q+1
       834: 1
       836: q+1
       838: 2
       840: 2
       842: q+1
       843: 1
       844: 1
       845: q+1
       846: q
       848: 2q+1
       850: 1
       852: q+1
       854: 1
       856: q+1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       890: 1
       892: 1
       897: 1
       903: 1
       913: 1
       917: 1
       919: 1
       921: 1
       926: q+1
       933: 1
       935: 1
       939: 1
       943: 2
       947: 1
       951: q+1
       959: 2
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: q+1
       980: 1
       983: 1
       986: 1
       989: 1
       991: 1
       993: 2
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1029: 1
      1031: 2
      1033: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: q
      1055: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1094: 1
      1104: 1
      1106: 1
      1113: 1
      1117: 1
      1145: 1
      1147: 1
      1149: 1
      1155: 1
      1167: 2
      1171: 1
      1175: 1
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1200: 1
      1205: q+1
      1215: 1
      1217: 1
      1231: 1
      1233: 1
      1237: 1
      1239: 1
      1243: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1308: 1
      1310: 1
      1317: 1
      1347: 1
      1351: 1
      1379: 1
      1383: 1
      1416: 1
      1421: 1
      1449: 1
      1451: 1
      1457: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1479: 1
      1487: 1
      1566: 1
      1586: 1
      1606: 1
      1610: 1
      1662: 1
      1664: 1
      1788: 1

1789:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+3q+1
        38: 2q^2+q
        39: 3q^2+3q+1
        40: 2q^2+q
        41: q^3+2q^2+3q+1
        42: q^3+q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 3q^2+2q+1
        59: 2q^2+2q
        60: 3q^2+3q+1
        61: 2q^2+q
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: 2q^2+2q+1
       104: q^2+q
       105: q^2
       106: q^2+q
       107: q^2+2q+1
       109: q^2+q+1
       110: q^2+q
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+2q+1
       118: 2q
       119: q^2+3q+1
       120: q
       121: 2q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q^2+2q+1
       141: 2q^2+3q+1
       142: 2q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       169: q+1
       173: q^2+2q+1
       174: q
       176: q
       177: q^2+2q+1
       179: q^2+2q+1
       181: q+1
       183: 2q+1
       185: q+1
       186: q
       187: q+1
       189: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       193: q^2+2q+1
       195: q^2+q+1
       196: q^2+q
       197: q+1
       199: q^2+3q+1
       200: q
       201: q^2+2q+1
       203: q^2+q+1
       204: q^2+q
       205: q+1
       207: 2q^2+3q+1
       208: q^2+q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: 2q+1
       235: q^2+2q+1
       236: 2q^2+3q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: 3q^2+3q+1
       244: q^2+2q+1
       245: 2q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       259: q+1
       263: q+1
       267: q+1
       271: q+1
       275: q^2+2q+1
       276: q
       278: q
       279: q+1
       281: q+1
       283: 2q+1
       285: q+1
       286: q
       287: q^2+2q+1
       289: 1
       291: q+1
       293: 2q+1
       295: q+1
       296: q
       297: q+1
       299: 2q+1
       301: q+1
       303: q+1
       304: q
       305: q+1
       307: 2q+1
       309: q+1
       310: q
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       319: q^2+2q+1
       321: q^2+q+1
       322: q^2+q
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 3q+1
       334: 2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: 2q+1
       356: 2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+2
       360: q+1
       362: q+1
       364: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       377: q+1
       381: 1
       385: q+1
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: 2q+1
       421: q+1
       422: q
       423: q+1
       425: q+1
       427: 2q+2
       429: 2q+1
       431: q+1
       432: q
       433: q+1
       435: 1
       437: 2q+1
       439: q+1
       440: q
       441: q+1
       443: 2q+2
       445: 2q+2
       447: 2q+1
       449: q+1
       450: q
       451: q+1
       453: 2q+1
       455: 1
       457: q+1
       458: q
       459: q+1
       461: q+1
       462: q+1
       463: 2q+2
       465: q+1
       467: q+1
       469: q^2+2q+1
       471: 2q+1
       473: q+1
       474: q
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: 2q+1
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 3q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: q+1
       533: q+1
       537: 1
       541: q+1
       545: 2q+2
       549: q+1
       553: 1
       557: q+1
       561: q+1
       563: q+1
       565: q+1
       569: q+1
       573: q+1
       574: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: 1
       589: q+1
       593: q+1
       595: q+1
       596: q
       597: 1
       599: q+1
       601: 2
       603: 2q+1
       605: 1
       607: q+1
       608: q
       609: q+1
       611: 1
       613: q+1
       615: 2
       617: 2
       619: 2q+1
       621: q+1
       622: q
       623: 1
       625: q+1
       627: 1
       629: q+1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: 2q+1
       643: q+1
       644: q
       645: q+1
       647: 2q+1
       649: q+1
       650: q
       651: 1
       653: q+1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: 2q+1
       688: q^2+2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       693: q+1
       696: q+1
       705: 1
       709: 1
       717: q+1
       721: 1
       725: q+1
       729: 1
       733: 2
       737: 1
       741: q+1
       745: 1
       749: 1
       751: 1
       753: q+1
       757: 1
       761: q+1
       765: 1
       766: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 2
       793: 2
       795: 2
       797: 1
       799: 1
       801: q+1
       805: q+1
       807: q+1
       808: q
       809: 1
       811: q+1
       813: 2
       815: 2
       817: 1
       818: 1
       819: 2
       821: 1
       823: 1
       825: q+1
       829: q+1
       831: q+1
       832: q
       833: 1
       835: q+1
       837: 2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       845: 2q+1
       847: q+1
       848: q
       849: 1
       851: q+1
       853: 1
       855: q+1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: 1
       884: 1
       887: 1
       896: 1
       904: 1
       912: 1
       916: 2
       920: 1
       928: q+1
       932: 2
       936: 1
       940: 1
       942: 1
       944: 1
       952: q+1
       956: 1
       958: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: q+1
       978: 1
       982: 1
       985: 1
       988: 1
       989: 1
       992: 2
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 2
      1016: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: q+1
      1058: q+1
      1059: q
      1060: 1
      1062: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1098: 1
      1101: 1
      1118: 1
      1122: 1
      1144: 2
      1148: 1
      1156: 1
      1164: 1
      1166: 1
      1168: 1
      1176: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1198: 1
      1206: q+1
      1214: 1
      1218: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1248: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1305: 1
      1318: 1
      1352: 1
      1356: 1
      1384: 1
      1388: 1
      1414: 1
      1422: 1
      1448: 1
      1454: 1
      1456: 1
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1476: 1
      1487: 1
      1567: 1
      1587: 1
      1611: 1
      1615: 1
      1661: 1
      1665: 1
      1789: 1

1790:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: 3q^2+3q+1
        39: 2q^2+q
        40: 3q^2+3q+1
        41: q^3+q^2+q
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+2q
        59: 3q^2+2q+1
        60: 3q^2+3q+1
        61: 2q^2+q
        62: 2q^2+q
        63: 3q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2+q
       104: 2q^2+2q+1
       105: q^2+q
       106: q^2
       107: q^2+2q+1
       109: q^2+q
       110: q^2+q+1
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: 2q
       118: q^2+2q+1
       119: q^2+3q+1
       120: q
       121: q^2+q
       122: 2q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q^2+2q+1
       141: 2q^2+3q+1
       142: 2q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       170: q+1
       173: q
       174: q^2+2q+1
       175: q
       178: q^2+2q+1
       180: q^2+2q+1
       182: q+1
       183: 2q+1
       185: q
       186: q+1
       188: q+1
       190: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       193: q^2+2q+1
       195: q^2+q
       196: q^2+q+1
       198: q+1
       199: q^2+3q+1
       200: q
       201: q^2+2q+1
       203: q^2+q
       204: q^2+q+1
       206: q+1
       207: q^2+q
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: 2q+1
       235: q^2+2q+1
       236: 2q^2+3q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: 3q^2+3q+1
       244: q^2+2q+1
       245: 2q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       260: q+1
       264: q+1
       268: q+1
       274: q+1
       275: q
       276: q^2+2q+1
       277: q
       280: q+1
       282: q+1
       283: 2q+1
       285: q
       286: q+1
       288: q^2+2q+1
       290: 1
       292: q+1
       293: 2q+1
       295: q
       296: q+1
       298: q+1
       299: 2q+1
       302: q+1
       303: q
       304: q+1
       306: q+1
       307: 2q+1
       309: q
       310: q+1
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       319: q^2+2q+1
       321: q^2+q
       322: q^2+q+1
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 3q+1
       334: 2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: 2q+1
       356: 2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+2
       361: q+1
       363: q+1
       365: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       378: q+1
       382: 1
       386: q+1
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: 2q+1
       421: q
       422: q+1
       424: q+1
       426: q+1
       428: 2q+2
       429: 2q+1
       431: q
       432: q+1
       434: q+1
       436: 1
       437: 2q+1
       439: q
       440: q+1
       442: q+1
       443: 2q+2
       446: 2q+2
       447: 2q+1
       449: q
       450: q+1
       452: q+1
       453: 2q+1
       456: 1
       457: q
       458: q+1
       460: q+1
       461: q+1
       462: q+1
       464: 2q+2
       466: q+1
       468: q+1
       470: q^2+2q+1
       471: 2q+1
       473: q
       474: q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: 2q+1
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 3q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: q+1
       534: q+1
       538: 1
       542: q+1
       546: 2q+2
       551: q+1
       556: 1
       560: q+1
       562: q+1
       564: q+1
       566: q+1
       571: q+1
       573: q+1
       574: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: 1
       589: q+1
       593: q+1
       595: q
       596: q+1
       598: 1
       600: q+1
       602: 2
       603: 2q+1
       606: 1
       607: q
       608: q+1
       610: q+1
       612: 1
       614: q+1
       615: 2
       618: 2
       619: 2q+1
       621: q
       622: q+1
       624: 1
       626: q+1
       628: 1
       630: q+1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: 2q+1
       643: q
       644: q+1
       646: q+1
       647: 2q+1
       649: q
       650: q+1
       652: 1
       654: q+1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: 2q+1
       688: q^2+2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       694: q+1
       699: q+1
       706: 1
       710: 1
       718: q+1
       722: 1
       726: q+1
       730: 1
       734: 2
       740: 1
       744: q+1
       748: 1
       750: 1
       752: 1
       754: q+1
       759: 1
       763: q+1
       765: 1
       766: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 2
       793: 2
       796: 2
       798: 1
       800: 1
       801: q+1
       805: q+1
       807: q
       808: q+1
       810: 1
       812: q+1
       814: 2
       815: 2
       817: 1
       818: 1
       820: 2
       822: 1
       824: 1
       825: q+1
       829: q+1
       831: q
       832: q+1
       834: 1
       836: q+1
       838: 2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       845: 2q+1
       847: q
       848: q+1
       850: 1
       852: q+1
       854: 1
       856: q+1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: 1
       885: 1
       890: 1
       897: 1
       905: 1
       913: 1
       917: 2
       921: 1
       929: q+1
       933: 2
       939: 1
       941: 1
       943: 1
       947: 1
       953: q+1
       957: 1
       959: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: q+1
       980: 1
       983: 1
       986: 1
       988: 1
       989: 1
       993: 2
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 2
      1016: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: q+1
      1058: q
      1059: q+1
      1061: 1
      1063: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1099: 1
      1104: 1
      1119: 1
      1123: 1
      1145: 2
      1149: 1
      1157: 1
      1165: 1
      1167: 1
      1171: 1
      1177: 1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1200: 1
      1207: q+1
      1215: 1
      1218: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1249: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1308: 1
      1319: 1
      1353: 1
      1357: 1
      1385: 1
      1389: 1
      1416: 1
      1423: 1
      1449: 1
      1454: 1
      1457: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1476: 1
      1487: 1
      1568: 1
      1588: 1
      1612: 1
      1616: 1
      1662: 1
      1665: 1
      1790: 1

1791:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+3q+1
        38: 2q^2+q
        39: 3q^2+3q+1
        40: 2q^2+q
        41: q^3+2q^2+3q+1
        42: q^3+q^2+q
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 2q^2+2q
        59: 3q^2+2q+1
        60: 2q^2+q
        61: 3q^2+3q+1
        62: 3q^2+3q+1
        63: 2q^2+q
        64: 2q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2+q
       104: q^2
       105: q^2+q
       106: 2q^2+2q+1
       108: q^2+2q+1
       109: q^2+q
       110: q^2+q+1
       111: q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: 2q
       118: q^2+2q+1
       119: q
       120: q^2+3q+1
       121: 2q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: q^2+4q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q^2+2q+1
       141: 2q^2+3q+1
       142: 2q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       153: q^2+2q+1
       155: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       172: q+1
       173: q
       175: q
       176: q^2+2q+1
       177: q^2+2q+1
       179: q^2+2q+1
       181: q+1
       184: 2q+1
       185: q
       186: q+1
       187: q+1
       189: q^2+2q+1
       191: 2q
       192: q^2+2q+1
       194: q^2+2q+1
       195: q^2+q
       196: q^2+q+1
       197: q+1
       199: q
       200: q^2+3q+1
       202: q^2+2q+1
       203: q^2+q
       204: q^2+q+1
       205: q+1
       207: 2q^2+3q+1
       208: q^2+q
       209: q^2+2q+1
       211: q^2+2q+1
       213: q+1
       215: q+1
       217: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: 2q+1
       235: q^2+2q+1
       236: 2q^2+3q+1
       237: q^2+2q+1
       239: q^2+2q+1
       241: q^2+2q+1
       243: 3q^2+3q+1
       244: q^2+2q+1
       245: 2q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       262: q+1
       266: q+1
       269: q+1
       273: q+1
       275: q
       277: q
       278: q^2+2q+1
       279: q+1
       281: q+1
       284: 2q+1
       285: q
       286: q+1
       287: q^2+2q+1
       289: 1
       291: q+1
       294: 2q+1
       295: q
       296: q+1
       297: q+1
       300: 2q+1
       301: q+1
       303: q
       304: q+1
       305: q+1
       308: 2q+1
       309: q
       310: q+1
       311: q+1
       313: q+1
       315: q^2+2q+1
       317: q^2+2q+1
       320: q^2+2q+1
       321: q^2+q
       322: q^2+q+1
       323: q+1
       325: q^2+2q+1
       327: q+1
       329: q+1
       331: q+1
       333: 3q+1
       334: 2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: 2q+1
       356: 2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+2
       360: q+1
       362: q+1
       364: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       380: q+1
       384: 1
       388: q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: 2q+1
       421: q
       422: q+1
       423: q+1
       425: q+1
       427: 2q+2
       430: 2q+1
       431: q
       432: q+1
       433: q+1
       435: 1
       438: 2q+1
       439: q
       440: q+1
       441: q+1
       444: 2q+2
       445: 2q+2
       448: 2q+1
       449: q
       450: q+1
       451: q+1
       454: 2q+1
       455: 1
       457: q
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: 2q+2
       465: q+1
       467: q+1
       469: q^2+2q+1
       472: 2q+1
       473: q
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       480: q+1
       481: q+1
       482: 2q+1
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 3q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: q+1
       536: q+1
       539: 1
       543: q+1
       547: 2q+2
       552: q+1
       555: 1
       559: q+1
       561: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       576: q+1
       577: q+1
       580: q+1
       583: q+1
       585: 1
       587: 1
       590: q+1
       594: q+1
       595: q
       596: q+1
       597: 1
       599: q+1
       601: 2
       604: 2q+1
       605: 1
       607: q
       608: q+1
       609: q+1
       611: 1
       613: q+1
       616: 2
       617: 2
       620: 2q+1
       621: q
       622: q+1
       623: 1
       625: q+1
       627: 1
       629: q+1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       642: 2q+1
       643: q
       644: q+1
       645: q+1
       648: 2q+1
       649: q
       650: q+1
       651: 1
       653: q+1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: 2q+1
       688: q^2+2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       697: q+1
       698: q+1
       708: 1
       712: 1
       720: q+1
       723: 1
       727: q+1
       731: 1
       735: 2
       739: 1
       743: q+1
       747: 1
       749: 1
       751: 1
       756: q+1
       758: 1
       762: q+1
       767: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 2
       794: 2
       795: 2
       797: 1
       799: 1
       802: q+1
       806: q+1
       807: q
       808: q+1
       809: 1
       811: q+1
       813: 2
       816: 2
       817: 1
       818: 1
       819: 2
       821: 1
       823: 1
       826: q+1
       830: q+1
       831: q
       832: q+1
       833: 1
       835: q+1
       837: 2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       846: 2q+1
       847: q
       848: q+1
       849: 1
       851: q+1
       853: 1
       855: q+1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: 1
       888: 1
       889: 1
       899: 1
       906: 1
       914: 1
       918: 2
       922: 1
       930: q+1
       934: 2
       938: 1
       940: 1
       942: 1
       946: 1
       955: q+1
       956: 1
       958: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: q+1
       979: 1
       982: 1
       985: 1
       990: 1
       991: 1
       992: 2
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 2
      1017: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: q+1
      1058: q
      1059: q+1
      1060: 1
      1062: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1102: 1
      1103: 1
      1120: 1
      1124: 1
      1146: 2
      1150: 1
      1158: 1
      1164: 1
      1166: 1
      1170: 1
      1178: 1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1199: 1
      1208: q+1
      1214: 1
      1219: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1248: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1306: 1
      1307: 1
      1320: 1
      1354: 1
      1358: 1
      1386: 1
      1390: 1
      1415: 1
      1424: 1
      1448: 1
      1455: 1
      1456: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1487: 1
      1569: 1
      1589: 1
      1613: 1
      1617: 1
      1661: 1
      1666: 1
      1791: 1

1792:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 2q^3+3q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+4q^2+3q+1
         5: 5q^2+4q+1
         6: 2q^3+4q^2+3q+1
         7: q^4+2q^3+3q^2+3q+1
         8: 2q^3+3q^2+4q+1
         9: q^4+2q^3+3q^2+3q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 2q^3+4q^2+3q+1
        13: 3q^2+4q+1
        14: q^3+3q^2+3q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: q^4+2q^3+3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+2q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 2q^3+3q^2+4q+1
        25: 5q^2+4q+1
        26: 5q^2+4q+1
        27: 2q^3+3q^2+4q+1
        28: 5q^2+4q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 5q^2+4q+1
        32: 3q^2+4q+1
        33: 5q^2+4q+1
        34: 5q^2+4q+1
        35: 3q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: 3q^2+3q+1
        39: 2q^2+q
        40: 3q^2+3q+1
        41: q^3+q^2+q
        42: q^3+2q^2+3q+1
        43: 3q^2+4q+1
        44: q^3+3q^2+3q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+3q^2+3q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+2q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^3+2q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^3+2q^2+3q+1
        58: 3q^2+2q+1
        59: 2q^2+2q
        60: 2q^2+q
        61: 3q^2+3q+1
        62: 2q^2+q
        63: 3q^2+3q+1
        64: q^2+q
        65: 2q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: q^2+4q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+4q+1
        89: 3q^2+4q+1
        90: q^3+3q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+2q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+2q^2+3q+1
       103: q^2
       104: q^2+q
       105: 2q^2+2q+1
       106: q^2+q
       108: q^2+2q+1
       109: q^2+q+1
       110: q^2+q
       112: q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: 2q
       119: q
       120: q^2+3q+1
       121: q^2+q
       122: 2q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: q^2+4q+1
       126: 2q^2+3q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: 3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+2q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 3q^2+3q+1
       140: q^2+2q+1
       141: 2q^2+3q+1
       142: 2q^2+2q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q^2+2q+1
       149: 3q^2+3q+1
       150: 2q^2+3q+1
       152: q^2+2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 3q^2+3q+1
       167: 3q^2+3q+1
       168: q^3+2q^2+3q+1
       171: q+1
       174: q
       175: q^2+2q+1
       176: q
       178: q^2+2q+1
       180: q^2+2q+1
       182: q+1
       184: 2q+1
       185: q+1
       186: q
       188: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: 2q
       194: q^2+2q+1
       195: q^2+q+1
       196: q^2+q
       198: q+1
       199: q
       200: q^2+3q+1
       202: q^2+2q+1
       203: q^2+q+1
       204: q^2+q
       206: q+1
       207: q^2+q
       208: 2q^2+3q+1
       210: q^2+2q+1
       212: q^2+2q+1
       214: q+1
       216: q+1
       218: q+1
       219: 3q+1
       220: 3q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q^2+3q+1
       232: 3q+1
       233: q^2+3q+1
       234: 2q+1
       235: q^2+2q+1
       236: 2q^2+3q+1
       238: q^2+2q+1
       240: q^2+2q+1
       242: q^2+2q+1
       243: 3q^2+3q+1
       244: q^2+2q+1
       245: 2q^2+2q+1
       246: 2q^2+3q+1
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       261: q+1
       265: q+1
       270: q+1
       272: q+1
       276: q
       277: q^2+2q+1
       278: q
       280: q+1
       282: q+1
       284: 2q+1
       285: q+1
       286: q
       288: q^2+2q+1
       290: 1
       292: q+1
       294: 2q+1
       295: q+1
       296: q
       298: q+1
       300: 2q+1
       302: q+1
       303: q+1
       304: q
       306: q+1
       308: 2q+1
       309: q+1
       310: q
       312: q+1
       314: q+1
       316: q^2+2q+1
       318: q^2+2q+1
       320: q^2+2q+1
       321: q^2+q+1
       322: q^2+q
       324: q+1
       326: q^2+2q+1
       328: q+1
       330: q+1
       332: q+1
       333: 3q+1
       334: 2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: 3q+1
       345: 3q+1
       346: q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+2
       352: 3q+1
       353: 3q+1
       354: q^2+3q+1
       355: 2q+1
       356: 2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+2
       361: q+1
       363: q+1
       365: q+1
       366: 2q^2+3q+1
       367: 3q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: q^2+3q+1
       379: q+1
       383: 1
       387: q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: 2q+1
       421: q+1
       422: q
       424: q+1
       426: q+1
       428: 2q+2
       430: 2q+1
       431: q+1
       432: q
       434: q+1
       436: 1
       438: 2q+1
       439: q+1
       440: q
       442: q+1
       444: 2q+2
       446: 2q+2
       448: 2q+1
       449: q+1
       450: q
       452: q+1
       454: 2q+1
       456: 1
       457: q+1
       458: q
       460: q+1
       461: q+1
       462: q+1
       464: 2q+2
       466: q+1
       468: q+1
       470: q^2+2q+1
       472: 2q+1
       473: q+1
       474: q
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: 2q+1
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 3q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: 2
       497: 3q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: 3q+1
       509: 3q+1
       510: q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: q+1
       535: q+1
       540: 1
       544: q+1
       548: 2q+2
       550: q+1
       554: 1
       558: q+1
       562: q+1
       564: q+1
       567: q+1
       572: q+1
       575: q+1
       576: q+1
       578: q+1
       581: q+1
       584: q+1
       586: 1
       588: 1
       590: q+1
       594: q+1
       595: q+1
       596: q
       598: 1
       600: q+1
       602: 2
       604: 2q+1
       606: 1
       607: q+1
       608: q
       610: q+1
       612: 1
       614: q+1
       616: 2
       618: 2
       620: 2q+1
       621: q+1
       622: q
       624: 1
       626: q+1
       628: 1
       630: q+1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       642: 2q+1
       643: q+1
       644: q
       646: q+1
       648: 2q+1
       649: q+1
       650: q
       652: 1
       654: q+1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: 2q+1
       677: q+1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: 2q+1
       683: q+1
       684: 2
       685: 1
       686: 3q+1
       687: 2q+1
       688: q^2+2q+1
       689: q+1
       690: 2
       691: 2
       692: q+1
       700: q+1
       701: q+1
       707: 1
       711: 1
       719: q+1
       724: 1
       728: q+1
       732: 1
       736: 2
       738: 1
       742: q+1
       746: 1
       750: 1
       752: 1
       755: q+1
       760: 1
       764: q+1
       767: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 2
       794: 2
       796: 2
       798: 1
       800: 1
       802: q+1
       806: q+1
       807: q+1
       808: q
       810: 1
       812: q+1
       814: 2
       816: 2
       817: 1
       818: 1
       820: 2
       822: 1
       824: 1
       826: q+1
       830: q+1
       831: q+1
       832: q
       834: 1
       836: q+1
       838: 2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       846: 2q+1
       847: q+1
       848: q
       850: 1
       852: q+1
       854: 1
       856: q+1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: 1
       891: 1
       892: 1
       898: 1
       907: 1
       915: 1
       919: 2
       923: 1
       931: q+1
       935: 2
       937: 1
       941: 1
       943: 1
       945: 1
       954: q+1
       957: 1
       959: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: q+1
       981: 1
       983: 1
       986: 1
       990: 1
       991: 1
       993: 2
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 2
      1017: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: q+1
      1058: q+1
      1059: q
      1061: 1
      1063: q+1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1094: 1
      1105: 1
      1106: 1
      1121: 1
      1125: 1
      1147: 2
      1151: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1179: 1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1201: 1
      1209: q+1
      1215: 1
      1219: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1249: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1309: 1
      1310: 1
      1321: 1
      1355: 1
      1359: 1
      1387: 1
      1391: 1
      1417: 1
      1425: 1
      1449: 1
      1455: 1
      1457: 1
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1477: 1
      1487: 1
      1570: 1
      1590: 1
      1614: 1
      1618: 1
      1662: 1
      1666: 1
      1792: 1

1793:    0: 2q^4+5q^3+8q^2+2q+1
         1: 2q^4+5q^3+8q^2+2q+1
         2: 7q^3+5q^2+2q+1
         3: 2q^4+5q^3+8q^2+2q+1
         4: q^5+2q^4+6q^3+6q^2+2q+1
         5: 2q^4+5q^3+8q^2+2q+1
         6: q^5+2q^4+6q^3+6q^2+2q+1
         7: 2q^4+6q^3+4q^2+2q+1
         8: 7q^3+5q^2+2q+1
         9: 2q^5+3q^4+4q^3+3q^2+2q+1
        10: 2q^4+5q^3+8q^2+2q+1
        11: 2q^4+5q^3+8q^2+2q+1
        12: q^5+2q^4+6q^3+6q^2+2q+1
        13: 4q^3+5q^2+2q+1
        14: q^4+4q^3+4q^2+2q+1
        15: 4q^3+5q^2+2q+1
        16: q^4+2q^3+8q^2+2q+1
        17: q^4+2q^3+8q^2+2q+1
        18: 2q^4+4q^3+3q^2+2q+1
        19: q^4+4q^3+6q^2+2q+1
        20: q^4+4q^3+6q^2+2q+1
        21: 5q^3+4q^2+2q+1
        22: 2q^4+5q^3+8q^2+2q+1
        23: 2q^4+5q^3+8q^2+2q+1
        24: 7q^3+5q^2+2q+1
        25: 2q^4+5q^3+8q^2+2q+1
        26: 2q^4+5q^3+8q^2+2q+1
        27: 7q^3+5q^2+2q+1
        28: q^4+2q^3+8q^2+2q+1
        29: q^4+4q^3+6q^2+2q+1
        30: 3q^3+4q^2+2q+1
        31: 2q^4+5q^3+8q^2+2q+1
        32: 4q^3+5q^2+2q+1
        33: q^4+2q^3+8q^2+2q+1
        34: 2q^4+5q^3+8q^2+2q+1
        35: 4q^3+5q^2+2q+1
        36: q^4+2q^3+8q^2+2q+1
        37: q^4+4q^3+6q^2+2q+1
        38: q^4+q^3+2q^2
        39: q^4+4q^3+6q^2+2q+1
        40: q^4+q^3+2q^2
        41: 5q^3+4q^2+2q+1
        42: 2q^3+q^2
        43: 4q^3+5q^2+2q+1
        44: q^4+4q^3+4q^2+2q+1
        45: 4q^3+5q^2+2q+1
        46: q^3+5q^2+2q+1
        47: q^3+5q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+6q^2+2q+1
        50: q^3+6q^2+2q+1
        51: 3q^3+3q^2+2q+1
        52: q^4+4q^3+6q^2+2q+1
        53: q^4+4q^3+6q^2+2q+1
        54: 5q^3+4q^2+2q+1
        55: q^4+4q^3+6q^2+2q+1
        56: q^4+4q^3+6q^2+2q+1
        57: 5q^3+4q^2+2q+1
        58: q^4+2q^3+5q^2+2q+1
        59: 3q^2
        60: q^4+2q^3+5q^2+2q+1
        61: 3q^2
        62: q^4+4q^3+6q^2+2q+1
        63: q^4+q^3+2q^2
        64: 3q^3+4q^2+2q+1
        65: q^3+q^2
        66: q^4+2q^3+6q^2+2q+1
        67: 2q^2
        68: q^3+2q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^3+4q^2+2q+1
        71: q^3+6q^2+2q+1
        72: q^3+4q^2+2q+1
        73: q^3+4q^2+2q+1
        74: 3q^3+4q^2+2q+1
        76: 3q^3+4q^2+2q+1
        78: 3q^3+3q^2+2q+1
        80: 4q^3+5q^2+2q+1
        81: q^3+5q^2+2q+1
        82: q^4+4q^3+6q^2+2q+1
        83: 3q^3+4q^2+2q+1
        84: 4q^3+5q^2+2q+1
        85: q^3+5q^2+2q+1
        86: q^4+4q^3+6q^2+2q+1
        87: 3q^3+4q^2+2q+1
        88: q^3+5q^2+2q+1
        89: q^3+5q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: 3q^2+2q+1
        92: 3q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+6q^2+2q+1
        95: q^3+6q^2+2q+1
        96: 3q^3+3q^2+2q+1
        97: q^3+6q^2+2q+1
        98: q^3+6q^2+2q+1
        99: 3q^3+3q^2+2q+1
       100: q^4+4q^3+6q^2+2q+1
       101: q^4+4q^3+6q^2+2q+1
       102: 5q^3+4q^2+2q+1
       103: q^4+2q^3+4q^2+2q+1
       104: q^2
       105: q^2
       106: 2q^2
       107: q^3+3q^2+2q+1
       108: q^2
       109: q^3+3q^2+2q+1
       110: q^2
       111: q^3+2q^2+2q+1
       113: 3q^3+4q^2+2q+1
       115: 2q^3+3q^2+2q+1
       117: q^3+2q^2+2q+1
       119: q^3+2q^2+2q+1
       121: 3q^3+4q^2+2q+1
       122: q^3+q^2
       123: q^3+4q^2+2q+1
       124: q^2
       125: q^3+2q^2+2q+1
       126: 3q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^3+5q^2+2q+1
       138: 3q^2+2q+1
       139: q^3+6q^2+2q+1
       140: q^3+4q^2+2q+1
       141: 3q^3+4q^2+2q+1
       142: q^3+4q^2+2q+1
       143: q^3+5q^2+2q+1
       144: 3q^2+2q+1
       145: q^3+6q^2+2q+1
       146: 3q^3+4q^2+2q+1
       147: q^3+4q^2+2q+1
       148: q^3+4q^2+2q+1
       149: q^4+4q^3+6q^2+2q+1
       150: 3q^3+4q^2+2q+1
       151: 3q^3+4q^2+2q+1
       153: 3q^3+4q^2+2q+1
       155: 3q^3+3q^2+2q+1
       157: 3q^2+2q+1
       158: 3q^2+2q+1
       159: q^3+2q^2+2q+1
       160: 3q^2+2q+1
       161: 3q^2+2q+1
       162: q^3+2q^2+2q+1
       163: 3q^2+2q+1
       164: 3q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+6q^2+2q+1
       167: q^3+6q^2+2q+1
       168: 3q^3+3q^2+2q+1
       169: q^3+2q^2+2q+1
       173: q^3+2q^2+2q+1
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       183: q^2+2q+1
       185: q^2+2q+1
       187: q^2+2q+1
       189: 2q^3+3q^2+2q+1
       191: q^3+2q^2+2q+1
       193: q^3+3q^2+2q+1
       194: q^2
       195: q^3+3q^2+2q+1
       196: q^2
       197: q^3+2q^2+2q+1
       199: q^3+2q^2+2q+1
       201: q^3+3q^2+2q+1
       202: q^2
       203: q^3+3q^2+2q+1
       204: q^2
       205: q^3+2q^2+2q+1
       207: q^3+4q^2+2q+1
       208: q^2
       209: 3q^3+4q^2+2q+1
       211: 2q^3+3q^2+2q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: q^2+2q+1
       228: 2q^2+2q+1
       229: 2q^2+2q+1
       230: 2q^2+2q+1
       231: 3q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 3q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: q^3+6q^2+2q+1
       244: q^3+4q^2+2q+1
       245: q^3+4q^2+2q+1
       246: 3q^3+4q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 3q^2+2q+1
       251: 3q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 3q^2+2q+1
       254: 3q^2+2q+1
       255: q^3+2q^2+2q+1
       256: 3q^2+2q+1
       257: 3q^2+2q+1
       258: q^3+2q^2+2q+1
       259: q^2+2q+1
       263: q^2+2q+1
       267: q^3+2q^2+2q+1
       271: q^3+2q^2+2q+1
       275: q^3+2q^2+2q+1
       279: q+1
       281: q^2+q+1
       283: 2q+1
       285: 2q+1
       287: 2q^2+2q+1
       289: q+1
       291: 2q+1
       293: q^2+2q+1
       295: q^2+2q+1
       297: q^2+2q+1
       299: q^2+2q+1
       301: q^2+2q+1
       303: q^2+2q+1
       305: q^2+2q+1
       307: q^2+2q+1
       309: q^2+2q+1
       311: q^2+2q+1
       313: q^2+2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: q^3+3q^2+2q+1
       320: q^2
       321: q^3+3q^2+2q+1
       322: q^2
       323: q^3+2q^2+2q+1
       325: 2q^3+3q^2+2q+1
       327: q^2+q+1
       329: q^2+q+1
       331: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: 2q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: 3q^2+2q+1
       367: q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 3q^2+2q+1
       375: 3q^2+2q+1
       376: q^3+2q^2+2q+1
       377: 2q+1
       381: q+1
       385: q^2+2q+1
       389: q^2+2q+1
       393: q^2+2q+1
       397: q^2+2q+1
       401: q^2+2q+1
       405: q^3+2q^2+2q+1
       409: q+1
       411: q^2+q+1
       413: q+1
       415: q+1
       417: q+1
       419: 2q+1
       421: 2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       429: 2q+1
       431: 2q+1
       433: 2q+1
       435: q+1
       437: q^2+2q+1
       439: q^2+2q+1
       441: q^2+2q+1
       443: q^2+3q+1
       444: q
       445: q^2+4q+1
       447: 2q+1
       449: 2q+1
       451: 2q+1
       453: q^2+2q+1
       455: q+1
       457: q^2+2q+1
       459: q^2+2q+1
       461: q^2+3q+1
       462: q
       463: q^2+4q+1
       465: q+1
       467: q^2+q+1
       469: 2q^2+2q+1
       471: q^2+2q+1
       473: q^2+2q+1
       475: q^2+2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       502: q^2+q+1
       504: q^2+q+1
       506: q^2+q+1
       508: 2q+1
       509: q^2+2q+1
       510: 2q^2+2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q^2+2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q+1
       525: q+1
       529: 2q+1
       533: 2q+1
       537: q+1
       541: q^2+2q+1
       545: q^2+3q+1
       547: q
       549: 2q+1
       553: q+1
       557: q^2+2q+1
       561: q^2+3q+1
       563: q
       565: q^2+2q+1
       569: q^2+2q+1
       573: q^2+2q+1
       574: q
       576: q
       577: q^2+2q+1
       580: 2q
       583: q+1
       585: 1
       587: q+1
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: q+1
       599: 2q+1
       601: q+1
       603: 2q+1
       605: q+1
       607: 2q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       615: q+1
       617: 2q+1
       619: 2q+1
       621: 2q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       631: q+1
       633: 2q+1
       635: q+1
       637: q^2+q+1
       639: q+1
       641: 2q+1
       643: 2q+1
       645: 2q+1
       647: q^2+2q+1
       649: q^2+2q+1
       651: q+1
       653: q^2+2q+1
       655: q+1
       656: q
       665: 1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q+1
       673: q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       693: q^2+2q+1
       696: q
       698: q
       705: q+1
       709: 1
       713: q+1
       717: q+1
       721: q+1
       725: 2q+1
       729: q+1
       733: q+1
       737: q+1
       741: 2q+1
       745: q+1
       749: q+1
       753: 2q+1
       757: q+1
       761: q^2+2q+1
       765: q+1
       769: q+1
       772: q
       777: 1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: q+1
       791: 1
       797: 1
       799: q+1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: q+1
       811: 2q+1
       813: 2q+1
       815: q+1
       821: 1
       823: q+1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: q+1
       835: 2q+1
       837: 2q+1
       839: q+1
       841: q+1
       845: 2q+1
       847: 2q+1
       849: q+1
       851: 2q+1
       853: q+1
       855: 2q+1
       857: q+1
       858: q
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: q+1
       920: 1
       924: q+1
       928: q+1
       932: q+1
       936: q+1
       944: 1
       948: q+1
       952: q+1
       956: q+1
       960: q+1
       974: 2q+1
       978: q+1
       982: q+1
       985: q
       988: q+1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: q+1
      1026: 1
      1028: 1
      1034: 1
      1038: 1
      1040: 1
      1042: q+1
      1044: 1
      1048: 1
      1050: q+1
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: q+1
      1062: 2q+1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1098: q+1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: q+1
      1198: 1
      1202: q+1
      1206: q+1
      1222: 1
      1238: 1
      1240: 1
      1242: 1
      1256: 1
      1258: 1
      1260: 1
      1264: 1
      1266: 1
      1268: 1
      1270: 1
      1272: q+1
      1276: 1
      1278: 1
      1289: 1
      1322: 1
      1344: 1
      1352: 1
      1360: 1
      1368: 1
      1376: 1
      1384: 1
      1392: 1
      1400: 1
      1414: 1
      1418: 1
      1422: 1
      1426: 1
      1470: 1
      1476: 1
      1478: 1
      1480: 1
      1571: 1
      1591: 1
      1603: 1
      1611: 1
      1619: 1
      1627: 1
      1793: 1

1794:    0: 2q^4+5q^3+8q^2+2q+1
         1: 2q^4+5q^3+8q^2+2q+1
         2: 7q^3+5q^2+2q+1
         3: 2q^4+5q^3+8q^2+2q+1
         4: q^5+2q^4+6q^3+6q^2+2q+1
         5: 2q^4+5q^3+8q^2+2q+1
         6: q^5+2q^4+6q^3+6q^2+2q+1
         7: 2q^4+6q^3+4q^2+2q+1
         8: 7q^3+5q^2+2q+1
         9: 2q^5+3q^4+4q^3+3q^2+2q+1
        10: 2q^4+5q^3+8q^2+2q+1
        11: 2q^4+5q^3+8q^2+2q+1
        12: q^5+2q^4+6q^3+6q^2+2q+1
        13: 4q^3+5q^2+2q+1
        14: q^4+4q^3+4q^2+2q+1
        15: 4q^3+5q^2+2q+1
        16: q^4+2q^3+8q^2+2q+1
        17: q^4+2q^3+8q^2+2q+1
        18: 2q^4+4q^3+3q^2+2q+1
        19: q^4+4q^3+6q^2+2q+1
        20: q^4+4q^3+6q^2+2q+1
        21: 5q^3+4q^2+2q+1
        22: 2q^4+5q^3+8q^2+2q+1
        23: 2q^4+5q^3+8q^2+2q+1
        24: 7q^3+5q^2+2q+1
        25: 2q^4+5q^3+8q^2+2q+1
        26: 2q^4+5q^3+8q^2+2q+1
        27: 7q^3+5q^2+2q+1
        28: q^4+2q^3+8q^2+2q+1
        29: q^4+4q^3+6q^2+2q+1
        30: 3q^3+4q^2+2q+1
        31: 2q^4+5q^3+8q^2+2q+1
        32: 4q^3+5q^2+2q+1
        33: q^4+2q^3+8q^2+2q+1
        34: 2q^4+5q^3+8q^2+2q+1
        35: 4q^3+5q^2+2q+1
        36: q^4+2q^3+8q^2+2q+1
        37: q^4+q^3+2q^2
        38: q^4+4q^3+6q^2+2q+1
        39: q^4+q^3+2q^2
        40: q^4+4q^3+6q^2+2q+1
        41: 2q^3+q^2
        42: 5q^3+4q^2+2q+1
        43: 4q^3+5q^2+2q+1
        44: q^4+4q^3+4q^2+2q+1
        45: 4q^3+5q^2+2q+1
        46: q^3+5q^2+2q+1
        47: q^3+5q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+6q^2+2q+1
        50: q^3+6q^2+2q+1
        51: 3q^3+3q^2+2q+1
        52: q^4+4q^3+6q^2+2q+1
        53: q^4+4q^3+6q^2+2q+1
        54: 5q^3+4q^2+2q+1
        55: q^4+4q^3+6q^2+2q+1
        56: q^4+4q^3+6q^2+2q+1
        57: 5q^3+4q^2+2q+1
        58: 3q^2
        59: q^4+2q^3+5q^2+2q+1
        60: q^4+2q^3+5q^2+2q+1
        61: 3q^2
        62: q^4+q^3+2q^2
        63: q^4+4q^3+6q^2+2q+1
        64: q^3+q^2
        65: 3q^3+4q^2+2q+1
        66: 2q^2
        67: q^4+2q^3+6q^2+2q+1
        68: q^3+2q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^3+4q^2+2q+1
        71: q^3+6q^2+2q+1
        72: q^3+4q^2+2q+1
        73: q^3+4q^2+2q+1
        75: 3q^3+4q^2+2q+1
        77: 3q^3+4q^2+2q+1
        79: 3q^3+3q^2+2q+1
        80: 4q^3+5q^2+2q+1
        81: q^3+5q^2+2q+1
        82: q^4+4q^3+6q^2+2q+1
        83: 3q^3+4q^2+2q+1
        84: 4q^3+5q^2+2q+1
        85: q^3+5q^2+2q+1
        86: q^4+4q^3+6q^2+2q+1
        87: 3q^3+4q^2+2q+1
        88: q^3+5q^2+2q+1
        89: q^3+5q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: 3q^2+2q+1
        92: 3q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+6q^2+2q+1
        95: q^3+6q^2+2q+1
        96: 3q^3+3q^2+2q+1
        97: q^3+6q^2+2q+1
        98: q^3+6q^2+2q+1
        99: 3q^3+3q^2+2q+1
       100: q^4+4q^3+6q^2+2q+1
       101: q^4+4q^3+6q^2+2q+1
       102: 5q^3+4q^2+2q+1
       103: q^2
       104: q^4+2q^3+4q^2+2q+1
       105: 2q^2
       106: q^2
       107: q^3+3q^2+2q+1
       108: q^2
       109: q^2
       110: q^3+3q^2+2q+1
       112: q^3+2q^2+2q+1
       114: 3q^3+4q^2+2q+1
       116: 2q^3+3q^2+2q+1
       118: q^3+2q^2+2q+1
       119: q^3+2q^2+2q+1
       121: q^3+q^2
       122: 3q^3+4q^2+2q+1
       123: q^2
       124: q^3+4q^2+2q+1
       125: q^3+2q^2+2q+1
       126: 3q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^3+5q^2+2q+1
       138: 3q^2+2q+1
       139: q^3+6q^2+2q+1
       140: q^3+4q^2+2q+1
       141: 3q^3+4q^2+2q+1
       142: q^3+4q^2+2q+1
       143: q^3+5q^2+2q+1
       144: 3q^2+2q+1
       145: q^3+6q^2+2q+1
       146: 3q^3+4q^2+2q+1
       147: q^3+4q^2+2q+1
       148: q^3+4q^2+2q+1
       149: q^4+4q^3+6q^2+2q+1
       150: 3q^3+4q^2+2q+1
       152: 3q^3+4q^2+2q+1
       154: 3q^3+4q^2+2q+1
       156: 3q^3+3q^2+2q+1
       157: 3q^2+2q+1
       158: 3q^2+2q+1
       159: q^3+2q^2+2q+1
       160: 3q^2+2q+1
       161: 3q^2+2q+1
       162: q^3+2q^2+2q+1
       163: 3q^2+2q+1
       164: 3q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+6q^2+2q+1
       167: q^3+6q^2+2q+1
       168: 3q^3+3q^2+2q+1
       170: q^3+2q^2+2q+1
       174: q^3+2q^2+2q+1
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       186: q^2+2q+1
       188: q^2+2q+1
       190: 2q^3+3q^2+2q+1
       192: q^3+2q^2+2q+1
       193: q^3+3q^2+2q+1
       194: q^2
       195: q^2
       196: q^3+3q^2+2q+1
       198: q^3+2q^2+2q+1
       199: q^3+2q^2+2q+1
       201: q^3+3q^2+2q+1
       202: q^2
       203: q^2
       204: q^3+3q^2+2q+1
       206: q^3+2q^2+2q+1
       207: q^2
       208: q^3+4q^2+2q+1
       210: 3q^3+4q^2+2q+1
       212: 2q^3+3q^2+2q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: q^2+2q+1
       228: 2q^2+2q+1
       229: 2q^2+2q+1
       230: 2q^2+2q+1
       231: 3q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 3q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: q^3+6q^2+2q+1
       244: q^3+4q^2+2q+1
       245: q^3+4q^2+2q+1
       246: 3q^3+4q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 3q^2+2q+1
       251: 3q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 3q^2+2q+1
       254: 3q^2+2q+1
       255: q^3+2q^2+2q+1
       256: 3q^2+2q+1
       257: 3q^2+2q+1
       258: q^3+2q^2+2q+1
       260: q^2+2q+1
       264: q^2+2q+1
       268: q^3+2q^2+2q+1
       274: q^3+2q^2+2q+1
       276: q^3+2q^2+2q+1
       280: q+1
       282: q^2+q+1
       283: 2q+1
       286: 2q+1
       288: 2q^2+2q+1
       290: q+1
       292: 2q+1
       293: q^2+2q+1
       296: q^2+2q+1
       298: q^2+2q+1
       299: q^2+2q+1
       302: q^2+2q+1
       304: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       310: q^2+2q+1
       312: q^2+2q+1
       314: q^2+2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: q^3+3q^2+2q+1
       320: q^2
       321: q^2
       322: q^3+3q^2+2q+1
       324: q^3+2q^2+2q+1
       326: 2q^3+3q^2+2q+1
       328: q^2+q+1
       330: q^2+q+1
       332: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: 2q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: 3q^2+2q+1
       367: q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 3q^2+2q+1
       375: 3q^2+2q+1
       376: q^3+2q^2+2q+1
       378: 2q+1
       382: q+1
       386: q^2+2q+1
       390: q^2+2q+1
       394: q^2+2q+1
       400: q^2+2q+1
       403: q^2+2q+1
       407: q^3+2q^2+2q+1
       410: q+1
       412: q^2+q+1
       414: q+1
       416: q+1
       418: q+1
       419: 2q+1
       422: 2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       429: 2q+1
       432: 2q+1
       434: 2q+1
       436: q+1
       437: q^2+2q+1
       440: q^2+2q+1
       442: q^2+2q+1
       443: q^2+3q+1
       444: q
       446: q^2+4q+1
       447: 2q+1
       450: 2q+1
       452: 2q+1
       453: q^2+2q+1
       456: q+1
       458: q^2+2q+1
       460: q^2+2q+1
       461: q
       462: q^2+3q+1
       464: q^2+4q+1
       466: q+1
       468: q^2+q+1
       470: 2q^2+2q+1
       471: q^2+2q+1
       474: q^2+2q+1
       476: q^2+2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       503: q^2+q+1
       505: q^2+q+1
       507: q^2+q+1
       508: 2q+1
       509: q^2+2q+1
       510: 2q^2+2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q^2+2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q+1
       526: q+1
       530: 2q+1
       534: 2q+1
       538: q+1
       542: q^2+2q+1
       546: q^2+3q+1
       548: q
       551: 2q+1
       556: q+1
       560: q^2+2q+1
       562: q
       564: q^2+3q+1
       566: q^2+2q+1
       571: q^2+2q+1
       573: q
       574: q^2+2q+1
       575: q
       578: 2q
       581: q^2+2q+1
       584: q+1
       586: 1
       588: q+1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       598: q+1
       600: 2q+1
       602: q+1
       603: 2q+1
       606: q+1
       608: 2q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       615: q+1
       618: 2q+1
       619: 2q+1
       622: 2q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       632: q+1
       634: 2q+1
       636: q+1
       638: q^2+q+1
       640: q+1
       641: 2q+1
       644: 2q+1
       646: 2q+1
       647: q^2+2q+1
       650: q^2+2q+1
       652: q+1
       654: q^2+2q+1
       655: q
       656: q+1
       665: 1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q+1
       673: q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       694: q
       699: q^2+2q+1
       701: q
       706: q+1
       710: 1
       715: q+1
       718: q+1
       722: q+1
       726: 2q+1
       730: q+1
       734: q+1
       740: q+1
       744: 2q+1
       748: q+1
       752: q+1
       754: 2q+1
       759: q+1
       763: q^2+2q+1
       766: q+1
       770: q
       773: q+1
       778: 1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: q+1
       792: 1
       798: 1
       800: q+1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       810: q+1
       812: 2q+1
       814: 2q+1
       815: q+1
       822: 1
       824: q+1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       834: q+1
       836: 2q+1
       838: 2q+1
       840: q+1
       842: q+1
       845: 2q+1
       848: 2q+1
       850: q+1
       852: 2q+1
       854: q+1
       856: 2q+1
       857: q
       858: q+1
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: q+1
       921: 1
       926: q+1
       929: q+1
       933: q+1
       939: q+1
       947: 1
       951: q+1
       953: q+1
       959: q+1
       962: q+1
       976: 2q+1
       980: q+1
       983: q
       986: q+1
       989: q+1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: q+1
      1026: 1
      1029: 1
      1035: 1
      1039: 1
      1040: 1
      1043: q+1
      1045: 1
      1049: 1
      1051: q+1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1061: q+1
      1063: 2q+1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1104: q+1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: q+1
      1200: 1
      1205: q+1
      1207: q+1
      1223: 1
      1239: 1
      1240: 1
      1243: 1
      1257: 1
      1258: 1
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1271: 1
      1273: q+1
      1277: 1
      1279: 1
      1289: 1
      1324: 1
      1347: 1
      1353: 1
      1363: 1
      1371: 1
      1379: 1
      1385: 1
      1394: 1
      1402: 1
      1416: 1
      1421: 1
      1423: 1
      1427: 1
      1471: 1
      1476: 1
      1479: 1
      1481: 1
      1574: 1
      1593: 1
      1606: 1
      1612: 1
      1620: 1
      1628: 1
      1794: 1

1795:    0: 2q^4+5q^3+8q^2+2q+1
         1: 2q^4+5q^3+8q^2+2q+1
         2: 7q^3+5q^2+2q+1
         3: 2q^4+5q^3+8q^2+2q+1
         4: q^5+2q^4+6q^3+6q^2+2q+1
         5: 2q^4+5q^3+8q^2+2q+1
         6: q^5+2q^4+6q^3+6q^2+2q+1
         7: 2q^4+6q^3+4q^2+2q+1
         8: 7q^3+5q^2+2q+1
         9: 2q^5+3q^4+4q^3+3q^2+2q+1
        10: 2q^4+5q^3+8q^2+2q+1
        11: 2q^4+5q^3+8q^2+2q+1
        12: q^5+2q^4+6q^3+6q^2+2q+1
        13: 4q^3+5q^2+2q+1
        14: q^4+4q^3+4q^2+2q+1
        15: 4q^3+5q^2+2q+1
        16: q^4+2q^3+8q^2+2q+1
        17: q^4+2q^3+8q^2+2q+1
        18: 2q^4+4q^3+3q^2+2q+1
        19: q^4+4q^3+6q^2+2q+1
        20: q^4+4q^3+6q^2+2q+1
        21: 5q^3+4q^2+2q+1
        22: 2q^4+5q^3+8q^2+2q+1
        23: 2q^4+5q^3+8q^2+2q+1
        24: 7q^3+5q^2+2q+1
        25: 2q^4+5q^3+8q^2+2q+1
        26: 2q^4+5q^3+8q^2+2q+1
        27: 7q^3+5q^2+2q+1
        28: q^4+2q^3+8q^2+2q+1
        29: q^4+4q^3+6q^2+2q+1
        30: 3q^3+4q^2+2q+1
        31: 2q^4+5q^3+8q^2+2q+1
        32: 4q^3+5q^2+2q+1
        33: q^4+2q^3+8q^2+2q+1
        34: 2q^4+5q^3+8q^2+2q+1
        35: 4q^3+5q^2+2q+1
        36: q^4+2q^3+8q^2+2q+1
        37: q^4+q^3+2q^2
        38: q^4+4q^3+6q^2+2q+1
        39: q^4+q^3+2q^2
        40: q^4+4q^3+6q^2+2q+1
        41: 2q^3+q^2
        42: 5q^3+4q^2+2q+1
        43: 4q^3+5q^2+2q+1
        44: q^4+4q^3+4q^2+2q+1
        45: 4q^3+5q^2+2q+1
        46: q^3+5q^2+2q+1
        47: q^3+5q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+6q^2+2q+1
        50: q^3+6q^2+2q+1
        51: 3q^3+3q^2+2q+1
        52: q^4+4q^3+6q^2+2q+1
        53: q^4+4q^3+6q^2+2q+1
        54: 5q^3+4q^2+2q+1
        55: q^4+4q^3+6q^2+2q+1
        56: q^4+4q^3+6q^2+2q+1
        57: 5q^3+4q^2+2q+1
        58: q^4+2q^3+5q^2+2q+1
        59: 3q^2
        60: 3q^2
        61: q^4+2q^3+5q^2+2q+1
        62: q^4+q^3+2q^2
        63: q^4+4q^3+6q^2+2q+1
        64: q^3+q^2
        65: 3q^3+4q^2+2q+1
        66: 2q^2
        67: q^4+2q^3+6q^2+2q+1
        68: q^3+2q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^3+4q^2+2q+1
        71: q^3+6q^2+2q+1
        72: q^3+4q^2+2q+1
        73: q^3+4q^2+2q+1
        75: 3q^3+4q^2+2q+1
        77: 3q^3+4q^2+2q+1
        79: 3q^3+3q^2+2q+1
        80: 4q^3+5q^2+2q+1
        81: q^3+5q^2+2q+1
        82: q^4+4q^3+6q^2+2q+1
        83: 3q^3+4q^2+2q+1
        84: 4q^3+5q^2+2q+1
        85: q^3+5q^2+2q+1
        86: q^4+4q^3+6q^2+2q+1
        87: 3q^3+4q^2+2q+1
        88: q^3+5q^2+2q+1
        89: q^3+5q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: 3q^2+2q+1
        92: 3q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+6q^2+2q+1
        95: q^3+6q^2+2q+1
        96: 3q^3+3q^2+2q+1
        97: q^3+6q^2+2q+1
        98: q^3+6q^2+2q+1
        99: 3q^3+3q^2+2q+1
       100: q^4+4q^3+6q^2+2q+1
       101: q^4+4q^3+6q^2+2q+1
       102: 5q^3+4q^2+2q+1
       103: q^2
       104: 2q^2
       105: q^4+2q^3+4q^2+2q+1
       106: q^2
       107: q^2
       108: q^3+3q^2+2q+1
       109: q^3+3q^2+2q+1
       110: q^2
       112: q^3+2q^2+2q+1
       114: 3q^3+4q^2+2q+1
       116: 2q^3+3q^2+2q+1
       117: q^3+2q^2+2q+1
       120: q^3+2q^2+2q+1
       121: q^3+q^2
       122: 3q^3+4q^2+2q+1
       123: q^2
       124: q^3+4q^2+2q+1
       125: q^3+2q^2+2q+1
       126: 3q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^3+5q^2+2q+1
       138: 3q^2+2q+1
       139: q^3+6q^2+2q+1
       140: q^3+4q^2+2q+1
       141: 3q^3+4q^2+2q+1
       142: q^3+4q^2+2q+1
       143: q^3+5q^2+2q+1
       144: 3q^2+2q+1
       145: q^3+6q^2+2q+1
       146: 3q^3+4q^2+2q+1
       147: q^3+4q^2+2q+1
       148: q^3+4q^2+2q+1
       149: q^4+4q^3+6q^2+2q+1
       150: 3q^3+4q^2+2q+1
       152: 3q^3+4q^2+2q+1
       154: 3q^3+4q^2+2q+1
       156: 3q^3+3q^2+2q+1
       157: 3q^2+2q+1
       158: 3q^2+2q+1
       159: q^3+2q^2+2q+1
       160: 3q^2+2q+1
       161: 3q^2+2q+1
       162: q^3+2q^2+2q+1
       163: 3q^2+2q+1
       164: 3q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+6q^2+2q+1
       167: q^3+6q^2+2q+1
       168: 3q^3+3q^2+2q+1
       171: q^3+2q^2+2q+1
       175: q^3+2q^2+2q+1
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       188: q^2+2q+1
       190: 2q^3+3q^2+2q+1
       191: q^3+2q^2+2q+1
       193: q^2
       194: q^3+3q^2+2q+1
       195: q^3+3q^2+2q+1
       196: q^2
       198: q^3+2q^2+2q+1
       200: q^3+2q^2+2q+1
       201: q^2
       202: q^3+3q^2+2q+1
       203: q^3+3q^2+2q+1
       204: q^2
       206: q^3+2q^2+2q+1
       207: q^2
       208: q^3+4q^2+2q+1
       210: 3q^3+4q^2+2q+1
       212: 2q^3+3q^2+2q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: 2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: q^2+2q+1
       228: 2q^2+2q+1
       229: 2q^2+2q+1
       230: 2q^2+2q+1
       231: 3q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 3q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: q^3+6q^2+2q+1
       244: q^3+4q^2+2q+1
       245: q^3+4q^2+2q+1
       246: 3q^3+4q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 3q^2+2q+1
       251: 3q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 3q^2+2q+1
       254: 3q^2+2q+1
       255: q^3+2q^2+2q+1
       256: 3q^2+2q+1
       257: 3q^2+2q+1
       258: q^3+2q^2+2q+1
       261: q^2+2q+1
       265: q^2+2q+1
       270: q^3+2q^2+2q+1
       272: q^3+2q^2+2q+1
       277: q^3+2q^2+2q+1
       280: q+1
       282: q^2+q+1
       284: 2q+1
       285: 2q+1
       288: 2q^2+2q+1
       290: q+1
       292: 2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       298: q^2+2q+1
       300: q^2+2q+1
       302: q^2+2q+1
       303: q^2+2q+1
       306: q^2+2q+1
       308: q^2+2q+1
       309: q^2+2q+1
       312: q^2+2q+1
       314: q^2+2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: q^2
       320: q^3+3q^2+2q+1
       321: q^3+3q^2+2q+1
       322: q^2
       324: q^3+2q^2+2q+1
       326: 2q^3+3q^2+2q+1
       328: q^2+q+1
       330: q^2+q+1
       332: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: 2q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: 3q^2+2q+1
       367: q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 3q^2+2q+1
       375: 3q^2+2q+1
       376: q^3+2q^2+2q+1
       379: 2q+1
       383: q+1
       387: q^2+2q+1
       392: q^2+2q+1
       395: q^2+2q+1
       398: q^2+2q+1
       402: q^2+2q+1
       408: q^3+2q^2+2q+1
       410: q+1
       412: q^2+q+1
       414: q+1
       416: q+1
       418: q+1
       420: 2q+1
       421: 2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       430: 2q+1
       431: 2q+1
       434: 2q+1
       436: q+1
       438: q^2+2q+1
       439: q^2+2q+1
       442: q^2+2q+1
       443: q
       444: q^2+3q+1
       446: q^2+4q+1
       448: 2q+1
       449: 2q+1
       452: 2q+1
       454: q^2+2q+1
       456: q+1
       457: q^2+2q+1
       460: q^2+2q+1
       461: q^2+3q+1
       462: q
       464: q^2+4q+1
       466: q+1
       468: q^2+q+1
       470: 2q^2+2q+1
       472: q^2+2q+1
       473: q^2+2q+1
       476: q^2+2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       503: q^2+q+1
       505: q^2+q+1
       507: q^2+q+1
       508: 2q+1
       509: q^2+2q+1
       510: 2q^2+2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q^2+2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: q+1
       527: q+1
       531: 2q+1
       535: 2q+1
       540: q+1
       544: q^2+2q+1
       546: q
       548: q^2+3q+1
       550: 2q+1
       554: q+1
       558: q^2+2q+1
       562: q^2+3q+1
       564: q
       567: q^2+2q+1
       572: q^2+2q+1
       573: q
       575: q
       576: q^2+2q+1
       578: 2q
       581: q^2+2q+1
       584: q+1
       586: 1
       588: q+1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       598: q+1
       600: 2q+1
       602: q+1
       604: 2q+1
       606: q+1
       607: 2q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       616: q+1
       618: 2q+1
       620: 2q+1
       621: 2q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       631: q+1
       634: 2q+1
       636: q+1
       638: q^2+q+1
       640: q+1
       642: 2q+1
       643: 2q+1
       646: 2q+1
       648: q^2+2q+1
       649: q^2+2q+1
       652: q+1
       654: q^2+2q+1
       655: q
       656: q+1
       665: 1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q+1
       673: q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       694: q
       700: q^2+2q+1
       701: q
       707: q+1
       711: 1
       714: q+1
       719: q+1
       724: q+1
       728: 2q+1
       732: q+1
       736: q+1
       738: q+1
       742: 2q+1
       746: q+1
       750: q+1
       755: 2q+1
       760: q+1
       764: q^2+2q+1
       767: q+1
       770: q
       773: q+1
       778: 1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: q+1
       792: 1
       798: 1
       800: q+1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       810: q+1
       812: 2q+1
       814: 2q+1
       816: q+1
       822: 1
       824: q+1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       834: q+1
       836: 2q+1
       838: 2q+1
       839: q+1
       842: q+1
       846: 2q+1
       847: 2q+1
       850: q+1
       852: 2q+1
       854: q+1
       856: 2q+1
       857: q
       858: q+1
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: q+1
       923: 1
       925: q+1
       931: q+1
       935: q+1
       937: q+1
       945: 1
       949: q+1
       954: q+1
       957: q+1
       963: q+1
       977: 2q+1
       981: q+1
       983: q
       986: q+1
       990: q+1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: q+1
      1027: 1
      1028: 1
      1035: 1
      1039: 1
      1041: 1
      1043: q+1
      1044: 1
      1049: 1
      1051: q+1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1061: q+1
      1063: 2q+1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1105: q+1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: q+1
      1201: 1
      1203: q+1
      1209: q+1
      1223: 1
      1239: 1
      1241: 1
      1242: 1
      1257: 1
      1259: 1
      1260: 1
      1265: 1
      1267: 1
      1269: 1
      1270: 1
      1273: q+1
      1277: 1
      1279: 1
      1289: 1
      1325: 1
      1345: 1
      1355: 1
      1362: 1
      1370: 1
      1377: 1
      1387: 1
      1395: 1
      1403: 1
      1417: 1
      1419: 1
      1425: 1
      1428: 1
      1471: 1
      1477: 1
      1478: 1
      1481: 1
      1573: 1
      1594: 1
      1604: 1
      1614: 1
      1621: 1
      1629: 1
      1795: 1

1796:    0: 2q^4+5q^3+8q^2+2q+1
         1: 2q^4+5q^3+8q^2+2q+1
         2: 7q^3+5q^2+2q+1
         3: 2q^4+5q^3+8q^2+2q+1
         4: q^5+2q^4+6q^3+6q^2+2q+1
         5: 2q^4+5q^3+8q^2+2q+1
         6: q^5+2q^4+6q^3+6q^2+2q+1
         7: 2q^4+6q^3+4q^2+2q+1
         8: 7q^3+5q^2+2q+1
         9: 2q^5+3q^4+4q^3+3q^2+2q+1
        10: 2q^4+5q^3+8q^2+2q+1
        11: 2q^4+5q^3+8q^2+2q+1
        12: q^5+2q^4+6q^3+6q^2+2q+1
        13: 4q^3+5q^2+2q+1
        14: q^4+4q^3+4q^2+2q+1
        15: 4q^3+5q^2+2q+1
        16: q^4+2q^3+8q^2+2q+1
        17: q^4+2q^3+8q^2+2q+1
        18: 2q^4+4q^3+3q^2+2q+1
        19: q^4+4q^3+6q^2+2q+1
        20: q^4+4q^3+6q^2+2q+1
        21: 5q^3+4q^2+2q+1
        22: 2q^4+5q^3+8q^2+2q+1
        23: 2q^4+5q^3+8q^2+2q+1
        24: 7q^3+5q^2+2q+1
        25: 2q^4+5q^3+8q^2+2q+1
        26: 2q^4+5q^3+8q^2+2q+1
        27: 7q^3+5q^2+2q+1
        28: q^4+2q^3+8q^2+2q+1
        29: q^4+4q^3+6q^2+2q+1
        30: 3q^3+4q^2+2q+1
        31: 2q^4+5q^3+8q^2+2q+1
        32: 4q^3+5q^2+2q+1
        33: q^4+2q^3+8q^2+2q+1
        34: 2q^4+5q^3+8q^2+2q+1
        35: 4q^3+5q^2+2q+1
        36: q^4+2q^3+8q^2+2q+1
        37: q^4+4q^3+6q^2+2q+1
        38: q^4+q^3+2q^2
        39: q^4+4q^3+6q^2+2q+1
        40: q^4+q^3+2q^2
        41: 5q^3+4q^2+2q+1
        42: 2q^3+q^2
        43: 4q^3+5q^2+2q+1
        44: q^4+4q^3+4q^2+2q+1
        45: 4q^3+5q^2+2q+1
        46: q^3+5q^2+2q+1
        47: q^3+5q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+6q^2+2q+1
        50: q^3+6q^2+2q+1
        51: 3q^3+3q^2+2q+1
        52: q^4+4q^3+6q^2+2q+1
        53: q^4+4q^3+6q^2+2q+1
        54: 5q^3+4q^2+2q+1
        55: q^4+4q^3+6q^2+2q+1
        56: q^4+4q^3+6q^2+2q+1
        57: 5q^3+4q^2+2q+1
        58: 3q^2
        59: q^4+2q^3+5q^2+2q+1
        60: 3q^2
        61: q^4+2q^3+5q^2+2q+1
        62: q^4+4q^3+6q^2+2q+1
        63: q^4+q^3+2q^2
        64: 3q^3+4q^2+2q+1
        65: q^3+q^2
        66: q^4+2q^3+6q^2+2q+1
        67: 2q^2
        68: q^3+2q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^3+4q^2+2q+1
        71: q^3+6q^2+2q+1
        72: q^3+4q^2+2q+1
        73: q^3+4q^2+2q+1
        74: 3q^3+4q^2+2q+1
        76: 3q^3+4q^2+2q+1
        78: 3q^3+3q^2+2q+1
        80: 4q^3+5q^2+2q+1
        81: q^3+5q^2+2q+1
        82: q^4+4q^3+6q^2+2q+1
        83: 3q^3+4q^2+2q+1
        84: 4q^3+5q^2+2q+1
        85: q^3+5q^2+2q+1
        86: q^4+4q^3+6q^2+2q+1
        87: 3q^3+4q^2+2q+1
        88: q^3+5q^2+2q+1
        89: q^3+5q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: 3q^2+2q+1
        92: 3q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+6q^2+2q+1
        95: q^3+6q^2+2q+1
        96: 3q^3+3q^2+2q+1
        97: q^3+6q^2+2q+1
        98: q^3+6q^2+2q+1
        99: 3q^3+3q^2+2q+1
       100: q^4+4q^3+6q^2+2q+1
       101: q^4+4q^3+6q^2+2q+1
       102: 5q^3+4q^2+2q+1
       103: 2q^2
       104: q^2
       105: q^2
       106: q^4+2q^3+4q^2+2q+1
       107: q^2
       108: q^3+3q^2+2q+1
       109: q^2
       110: q^3+3q^2+2q+1
       111: q^3+2q^2+2q+1
       113: 3q^3+4q^2+2q+1
       115: 2q^3+3q^2+2q+1
       118: q^3+2q^2+2q+1
       120: q^3+2q^2+2q+1
       121: 3q^3+4q^2+2q+1
       122: q^3+q^2
       123: q^3+4q^2+2q+1
       124: q^2
       125: q^3+2q^2+2q+1
       126: 3q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^3+5q^2+2q+1
       138: 3q^2+2q+1
       139: q^3+6q^2+2q+1
       140: q^3+4q^2+2q+1
       141: 3q^3+4q^2+2q+1
       142: q^3+4q^2+2q+1
       143: q^3+5q^2+2q+1
       144: 3q^2+2q+1
       145: q^3+6q^2+2q+1
       146: 3q^3+4q^2+2q+1
       147: q^3+4q^2+2q+1
       148: q^3+4q^2+2q+1
       149: q^4+4q^3+6q^2+2q+1
       150: 3q^3+4q^2+2q+1
       151: 3q^3+4q^2+2q+1
       153: 3q^3+4q^2+2q+1
       155: 3q^3+3q^2+2q+1
       157: 3q^2+2q+1
       158: 3q^2+2q+1
       159: q^3+2q^2+2q+1
       160: 3q^2+2q+1
       161: 3q^2+2q+1
       162: q^3+2q^2+2q+1
       163: 3q^2+2q+1
       164: 3q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+6q^2+2q+1
       167: q^3+6q^2+2q+1
       168: 3q^3+3q^2+2q+1
       172: q^3+2q^2+2q+1
       176: q^3+2q^2+2q+1
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       184: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       189: 2q^3+3q^2+2q+1
       192: q^3+2q^2+2q+1
       193: q^2
       194: q^3+3q^2+2q+1
       195: q^2
       196: q^3+3q^2+2q+1
       197: q^3+2q^2+2q+1
       200: q^3+2q^2+2q+1
       201: q^2
       202: q^3+3q^2+2q+1
       203: q^2
       204: q^3+3q^2+2q+1
       205: q^3+2q^2+2q+1
       207: q^3+4q^2+2q+1
       208: q^2
       209: 3q^3+4q^2+2q+1
       211: 2q^3+3q^2+2q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: 2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: q^2+2q+1
       228: 2q^2+2q+1
       229: 2q^2+2q+1
       230: 2q^2+2q+1
       231: 3q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 3q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: q^3+6q^2+2q+1
       244: q^3+4q^2+2q+1
       245: q^3+4q^2+2q+1
       246: 3q^3+4q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 3q^2+2q+1
       251: 3q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 3q^2+2q+1
       254: 3q^2+2q+1
       255: q^3+2q^2+2q+1
       256: 3q^2+2q+1
       257: 3q^2+2q+1
       258: q^3+2q^2+2q+1
       262: q^2+2q+1
       266: q^2+2q+1
       269: q^3+2q^2+2q+1
       273: q^3+2q^2+2q+1
       278: q^3+2q^2+2q+1
       279: q+1
       281: q^2+q+1
       284: 2q+1
       286: 2q+1
       287: 2q^2+2q+1
       289: q+1
       291: 2q+1
       294: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       308: q^2+2q+1
       310: q^2+2q+1
       311: q^2+2q+1
       313: q^2+2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: q^2
       320: q^3+3q^2+2q+1
       321: q^2
       322: q^3+3q^2+2q+1
       323: q^3+2q^2+2q+1
       325: 2q^3+3q^2+2q+1
       327: q^2+q+1
       329: q^2+q+1
       331: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: 2q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: 3q^2+2q+1
       367: q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 3q^2+2q+1
       375: 3q^2+2q+1
       376: q^3+2q^2+2q+1
       380: 2q+1
       384: q+1
       388: q^2+2q+1
       391: q^2+2q+1
       396: q^2+2q+1
       399: q^2+2q+1
       404: q^2+2q+1
       406: q^3+2q^2+2q+1
       409: q+1
       411: q^2+q+1
       413: q+1
       415: q+1
       417: q+1
       420: 2q+1
       422: 2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       430: 2q+1
       432: 2q+1
       433: 2q+1
       435: q+1
       438: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       443: q
       444: q^2+3q+1
       445: q^2+4q+1
       448: 2q+1
       450: 2q+1
       451: 2q+1
       454: q^2+2q+1
       455: q+1
       458: q^2+2q+1
       459: q^2+2q+1
       461: q
       462: q^2+3q+1
       463: q^2+4q+1
       465: q+1
       467: q^2+q+1
       469: 2q^2+2q+1
       472: q^2+2q+1
       474: q^2+2q+1
       475: q^2+2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       502: q^2+q+1
       504: q^2+q+1
       506: q^2+q+1
       508: 2q+1
       509: q^2+2q+1
       510: 2q^2+2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q^2+2q+1
       514: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: q+1
       528: q+1
       532: 2q+1
       536: 2q+1
       539: q+1
       543: q^2+2q+1
       545: q
       547: q^2+3q+1
       552: 2q+1
       555: q+1
       559: q^2+2q+1
       561: q
       563: q^2+3q+1
       568: q^2+2q+1
       570: q^2+2q+1
       574: q
       575: q^2+2q+1
       576: q
       577: q^2+2q+1
       580: 2q
       583: q+1
       585: 1
       587: q+1
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: q+1
       599: 2q+1
       601: q+1
       604: 2q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       616: q+1
       617: 2q+1
       620: 2q+1
       622: 2q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       632: q+1
       633: 2q+1
       635: q+1
       637: q^2+q+1
       639: q+1
       642: 2q+1
       644: 2q+1
       645: 2q+1
       648: q^2+2q+1
       650: q^2+2q+1
       651: q+1
       653: q^2+2q+1
       655: q+1
       656: q
       665: 1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q+1
       673: q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       696: q
       697: q^2+2q+1
       698: q
       708: q+1
       712: 1
       716: q+1
       720: q+1
       723: q+1
       727: 2q+1
       731: q+1
       735: q+1
       739: q+1
       743: 2q+1
       747: q+1
       751: q+1
       756: 2q+1
       758: q+1
       762: q^2+2q+1
       768: q+1
       769: q+1
       772: q
       777: 1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: q+1
       791: 1
       797: 1
       799: q+1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: q+1
       811: 2q+1
       813: 2q+1
       816: q+1
       821: 1
       823: q+1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: q+1
       835: 2q+1
       837: 2q+1
       840: q+1
       841: q+1
       846: 2q+1
       848: 2q+1
       849: q+1
       851: 2q+1
       853: q+1
       855: 2q+1
       857: q+1
       858: q
       868: 1
       871: 1
       872: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: q+1
       922: 1
       927: q+1
       930: q+1
       934: q+1
       938: q+1
       946: 1
       950: q+1
       955: q+1
       958: q+1
       961: q+1
       975: 2q+1
       979: q+1
       982: q+1
       985: q
       991: q+1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: q+1
      1027: 1
      1029: 1
      1034: 1
      1038: 1
      1041: 1
      1042: q+1
      1045: 1
      1048: 1
      1050: q+1
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: q+1
      1062: 2q+1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: q+1
      1102: q+1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: q+1
      1199: 1
      1204: q+1
      1208: q+1
      1222: 1
      1238: 1
      1241: 1
      1243: 1
      1256: 1
      1259: 1
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1271: 1
      1272: q+1
      1276: 1
      1278: 1
      1289: 1
      1323: 1
      1346: 1
      1354: 1
      1361: 1
      1369: 1
      1378: 1
      1386: 1
      1393: 1
      1401: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1470: 1
      1477: 1
      1479: 1
      1480: 1
      1572: 1
      1592: 1
      1605: 1
      1613: 1
      1622: 1
      1630: 1
      1796: 1

1797:    0: 3q^3+10q^2+4q+1
         1: 3q^3+10q^2+4q+1
         2: 5q^3+6q^2+3q+1
         3: 3q^3+10q^2+4q+1
         4: q^4+5q^3+7q^2+4q+1
         5: 3q^3+10q^2+4q+1
         6: q^4+5q^3+7q^2+4q+1
         7: 2q^4+4q^3+5q^2+3q+1
         8: 5q^3+6q^2+3q+1
         9: 2q^4+4q^3+5q^2+3q+1
        10: 3q^3+10q^2+4q+1
        11: 3q^3+10q^2+4q+1
        12: q^4+5q^3+7q^2+4q+1
        13: 5q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 5q^2+3q+1
        16: 3q^3+10q^2+4q+1
        17: 3q^3+10q^2+4q+1
        18: 2q^4+4q^3+5q^2+3q+1
        19: 2q^3+7q^2+4q+1
        20: 2q^3+7q^2+4q+1
        21: 3q^3+5q^2+3q+1
        22: 3q^3+10q^2+4q+1
        23: 3q^3+10q^2+4q+1
        24: 5q^3+6q^2+3q+1
        25: 3q^3+10q^2+4q+1
        26: 3q^3+10q^2+4q+1
        27: 5q^3+6q^2+3q+1
        28: 3q^3+10q^2+4q+1
        29: 2q^3+7q^2+4q+1
        30: 4q^2+3q+1
        31: 3q^3+10q^2+4q+1
        32: 5q^2+3q+1
        33: 3q^3+10q^2+4q+1
        34: 3q^3+10q^2+4q+1
        35: 5q^2+3q+1
        36: 3q^3+10q^2+4q+1
        37: q^3+6q^2+2q+1
        38: 2q^3+4q^2+2q
        39: q^3+6q^2+2q+1
        40: 2q^3+4q^2+2q
        41: 3q^3+3q^2+2q+1
        42: 2q^3+3q^2+q
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: 5q^2+3q+1
        47: 5q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+7q^2+4q+1
        50: 2q^3+7q^2+4q+1
        51: 3q^3+5q^2+3q+1
        52: 2q^3+7q^2+4q+1
        53: 2q^3+7q^2+4q+1
        54: 3q^3+5q^2+3q+1
        55: 2q^3+7q^2+4q+1
        56: 2q^3+7q^2+4q+1
        57: 3q^3+5q^2+3q+1
        58: 2q^3+6q^2+3q+1
        59: q^3+4q^2+q
        60: 2q^3+6q^2+3q+1
        61: q^3+4q^2+q
        62: q^3+6q^2+2q+1
        63: 2q^3+4q^2+2q
        64: 3q^2+2q+1
        65: 2q^2+q
        66: q^3+6q^2+2q+1
        67: 2q^3+4q^2+2q
        68: q^2+2q+1
        69: 4q^2+3q+1
        70: 4q^2+3q+1
        71: 2q^3+7q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: 3q^2+2q+1
        75: q^3+q^2+2q
        76: 3q^2+2q+1
        77: q^3+q^2+2q
        78: q^3+2q^2+2q+1
        79: 2q^2+q
        80: 5q^2+3q+1
        81: 5q^2+3q+1
        82: 2q^3+7q^2+4q+1
        83: 4q^2+3q+1
        84: 5q^2+3q+1
        85: 5q^2+3q+1
        86: 2q^3+7q^2+4q+1
        87: 4q^2+3q+1
        88: 5q^2+3q+1
        89: 5q^2+3q+1
        90: q^3+4q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+7q^2+4q+1
        95: 2q^3+7q^2+4q+1
        96: 3q^3+5q^2+3q+1
        97: 2q^3+7q^2+4q+1
        98: 2q^3+7q^2+4q+1
        99: 3q^3+5q^2+3q+1
       100: 2q^3+7q^2+4q+1
       101: 2q^3+7q^2+4q+1
       102: 3q^3+5q^2+3q+1
       103: q^3+4q^2+2q+1
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       106: 2q^2
       107: q^3+3q^2+3q+1
       108: q^2+q
       109: q^3+3q^2+3q+1
       110: q^2+q
       111: q^2+2q+1
       112: 2q
       113: 3q^2+2q+1
       114: q^3+q^2+2q
       115: 2q^2+2q+1
       116: q^2+q
       117: q^2+2q+1
       119: q^2+2q+1
       121: 3q^2+2q+1
       122: 2q^2+q
       123: 3q^2+2q+1
       124: 2q^2+q
       125: q^2+2q+1
       126: 4q^2+3q+1
       127: 3q^2+2q+1
       128: q^3+q^2+2q
       129: 3q^2+2q+1
       130: q^3+q^2+2q
       131: q^3+2q^2+2q+1
       132: 2q^2+q
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: 5q^2+3q+1
       138: 4q^2+3q+1
       139: 2q^3+7q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 5q^2+3q+1
       144: 4q^2+3q+1
       145: 2q^3+7q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: 2q^3+7q^2+4q+1
       150: 4q^2+3q+1
       151: 3q^2+2q+1
       152: q^3+q^2+2q
       153: 3q^2+2q+1
       154: q^3+q^2+2q
       155: q^3+2q^2+2q+1
       156: 2q^2+q
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q^3+7q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: 3q^3+5q^2+3q+1
       169: q^2+2q+1
       170: q
       171: q
       173: q^2+2q+1
       177: 2q^2+2q+1
       178: q^2+q
       179: 3q^2+2q+1
       180: q^3+q^2+2q
       181: q^2+2q+1
       182: 2q
       183: 2q+1
       185: 2q+1
       187: 2q+1
       188: q
       189: 2q^2+2q+1
       190: q^2+q
       191: q^2+2q+1
       193: q^3+3q^2+3q+1
       194: q^2+q
       195: q^3+3q^2+3q+1
       196: q^2+q
       197: q^2+2q+1
       198: 2q
       199: q^2+2q+1
       201: q^3+3q^2+3q+1
       202: q^2+q
       203: q^3+3q^2+3q+1
       204: q^2+q
       205: q^2+2q+1
       206: 2q
       207: 3q^2+2q+1
       208: 2q^2+q
       209: 3q^2+2q+1
       210: q^3+q^2+2q
       211: 2q^2+2q+1
       212: q^2+q
       219: 2q+1
       220: 2q+1
       221: 2q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: 4q^2+3q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 4q^2+3q+1
       237: 3q^2+2q+1
       238: q^3+q^2+2q
       239: 3q^2+2q+1
       240: q^3+q^2+2q
       241: q^3+2q^2+2q+1
       242: 2q^2+q
       243: 2q^3+7q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: 2q^2+7q+1
       248: 2q^2+7q+1
       249: q^3+4q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q^2+2q+1
       260: q
       261: q
       263: 2q+1
       267: q^2+2q+1
       268: q
       270: q
       271: q^2+2q+1
       272: q
       274: q
       275: q^2+2q+1
       283: 2q+1
       285: 2q+1
       287: 2q^2+2q+1
       288: q^2+q
       291: 2q+1
       292: q
       293: 2q+1
       295: 2q+1
       297: 2q+1
       298: q
       299: 2q+1
       301: q^2+2q+1
       302: 2q
       303: 2q+1
       305: 2q+1
       306: q
       307: 2q+1
       309: 2q+1
       311: q^2+2q+1
       312: 2q
       313: 2q+1
       314: q
       315: 2q^2+2q+1
       316: q^2+q
       317: 3q^2+2q+1
       318: q^3+q^2+2q
       319: q^3+3q^2+3q+1
       320: q^2+q
       321: q^3+3q^2+3q+1
       322: q^2+q
       323: q^2+2q+1
       324: 2q
       325: 2q^2+2q+1
       326: q^2+q
       333: 2q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: 3q+1
       337: 2q^2+7q+1
       338: q^2+4q+1
       339: q^2+3q
       340: q^2+4q+1
       341: q^2+3q
       342: q^3+2q^2+2q+1
       343: 2q^2+q
       344: 2q+1
       345: 2q+1
       346: 2q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 2q^2+7q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q^2+3q+1
       358: q^2+3q+1
       359: 2q^2+7q+1
       366: 4q^2+3q+1
       367: 2q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: 2q+1
       385: 2q+1
       389: q^2+2q+1
       390: q
       392: q
       393: 2q+1
       397: q^2+2q+1
       398: q
       400: q
       401: 2q+1
       405: q^2+2q+1
       407: q
       408: q
       419: 2q+1
       421: 2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: q^2+4q+1
       428: q^2+3q
       429: 2q+1
       431: 2q+1
       433: 2q+1
       434: q
       437: 2q+1
       439: 2q+1
       441: 2q+1
       442: q
       443: 2q^2+5q+1
       444: 2q
       445: q^2+4q+1
       446: q^2+3q
       447: 2q+1
       449: 2q+1
       451: 2q+1
       452: q
       453: 2q+1
       457: 2q+1
       459: 2q+1
       460: q
       461: 2q^2+5q+1
       462: 2q
       463: q^2+4q+1
       464: q^2+3q
       469: 2q^2+2q+1
       470: q^2+q
       471: 2q+1
       473: 2q+1
       475: 2q+1
       476: q
       477: q^2+2q+1
       478: 2q
       479: 2q^2+3q+1
       480: 4q
       481: q+1
       482: q+1
       483: 3q+1
       484: q+1
       491: q+1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: 3q+1
       496: 2q+1
       497: 2q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: 3q+1
       501: 2q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       529: 2q+1
       533: 2q+1
       541: 2q+1
       545: q^2+3q+1
       546: q^2+2q
       547: q
       548: q
       549: 2q+1
       557: 2q+1
       561: q^2+3q+1
       562: q^2+2q
       563: q
       564: q
       565: 2q+1
       569: q^2+2q+1
       571: q
       572: q
       573: 2q^2+3q+1
       574: 2q
       576: 2q
       577: q^2+2q+1
       578: q^2+q
       580: 2q
       581: 2q
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       599: 2q+1
       600: q
       603: 2q+1
       607: 2q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: q+1
       619: 2q+1
       621: 2q+1
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: q+1
       641: 2q+1
       643: 2q+1
       645: 2q+1
       646: q
       647: 2q+1
       649: 2q+1
       653: 2q+1
       654: q
       655: q+1
       656: q
       657: q+1
       664: q+1
       665: 1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 3q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 3q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+3q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       694: q^2+q
       696: q
       698: q
       699: q
       700: q
       713: q+1
       717: q+1
       725: 2q+1
       741: 2q+1
       753: 2q+1
       761: 2q+1
       765: q+1
       785: 1
       787: 1
       791: 1
       793: q+1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       811: 2q+1
       812: q
       815: q+1
       817: q+1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       835: 2q+1
       836: q
       839: q+1
       843: q+1
       844: q
       845: 2q+1
       847: 2q+1
       851: 2q+1
       852: q
       855: 2q+1
       856: q
       857: q+1
       858: q
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 3q+1
       880: q+1
       908: 1
       924: q+1
       928: q+1
       948: q+1
       952: q+1
       964: q+1
       974: 2q+1
       988: q+1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1012: 1
      1016: q+1
      1026: 1
      1028: 1
      1032: q+1
      1040: 1
      1044: 1
      1046: q+1
      1047: q
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1062: 2q+1
      1063: q
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1130: 1
      1134: 1
      1160: 1
      1180: 1
      1194: q+1
      1202: q+1
      1206: q+1
      1216: 1
      1218: 1
      1224: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1268: 1
      1270: 1
      1276: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1326: 1
      1364: 1
      1368: 1
      1396: 1
      1400: 1
      1426: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1466: 1
      1468: 1
      1476: 1
      1478: 1
      1482: 1
      1487: 1
      1575: 1
      1595: 1
      1623: 1
      1627: 1
      1663: 1
      1665: 1
      1797: 1

1798:    0: 3q^3+10q^2+4q+1
         1: 3q^3+10q^2+4q+1
         2: 5q^3+6q^2+3q+1
         3: 3q^3+10q^2+4q+1
         4: q^4+5q^3+7q^2+4q+1
         5: 3q^3+10q^2+4q+1
         6: q^4+5q^3+7q^2+4q+1
         7: 2q^4+4q^3+5q^2+3q+1
         8: 5q^3+6q^2+3q+1
         9: 2q^4+4q^3+5q^2+3q+1
        10: 3q^3+10q^2+4q+1
        11: 3q^3+10q^2+4q+1
        12: q^4+5q^3+7q^2+4q+1
        13: 5q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 5q^2+3q+1
        16: 3q^3+10q^2+4q+1
        17: 3q^3+10q^2+4q+1
        18: 2q^4+4q^3+5q^2+3q+1
        19: 2q^3+7q^2+4q+1
        20: 2q^3+7q^2+4q+1
        21: 3q^3+5q^2+3q+1
        22: 3q^3+10q^2+4q+1
        23: 3q^3+10q^2+4q+1
        24: 5q^3+6q^2+3q+1
        25: 3q^3+10q^2+4q+1
        26: 3q^3+10q^2+4q+1
        27: 5q^3+6q^2+3q+1
        28: 3q^3+10q^2+4q+1
        29: 2q^3+7q^2+4q+1
        30: 4q^2+3q+1
        31: 3q^3+10q^2+4q+1
        32: 5q^2+3q+1
        33: 3q^3+10q^2+4q+1
        34: 3q^3+10q^2+4q+1
        35: 5q^2+3q+1
        36: 3q^3+10q^2+4q+1
        37: 2q^3+4q^2+2q
        38: q^3+6q^2+2q+1
        39: 2q^3+4q^2+2q
        40: q^3+6q^2+2q+1
        41: 2q^3+3q^2+q
        42: 3q^3+3q^2+2q+1
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: 5q^2+3q+1
        47: 5q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+7q^2+4q+1
        50: 2q^3+7q^2+4q+1
        51: 3q^3+5q^2+3q+1
        52: 2q^3+7q^2+4q+1
        53: 2q^3+7q^2+4q+1
        54: 3q^3+5q^2+3q+1
        55: 2q^3+7q^2+4q+1
        56: 2q^3+7q^2+4q+1
        57: 3q^3+5q^2+3q+1
        58: q^3+4q^2+q
        59: 2q^3+6q^2+3q+1
        60: 2q^3+6q^2+3q+1
        61: q^3+4q^2+q
        62: 2q^3+4q^2+2q
        63: q^3+6q^2+2q+1
        64: 2q^2+q
        65: 3q^2+2q+1
        66: 2q^3+4q^2+2q
        67: q^3+6q^2+2q+1
        68: q^2+2q+1
        69: 4q^2+3q+1
        70: 4q^2+3q+1
        71: 2q^3+7q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: q^3+q^2+2q
        75: 3q^2+2q+1
        76: q^3+q^2+2q
        77: 3q^2+2q+1
        78: 2q^2+q
        79: q^3+2q^2+2q+1
        80: 5q^2+3q+1
        81: 5q^2+3q+1
        82: 2q^3+7q^2+4q+1
        83: 4q^2+3q+1
        84: 5q^2+3q+1
        85: 5q^2+3q+1
        86: 2q^3+7q^2+4q+1
        87: 4q^2+3q+1
        88: 5q^2+3q+1
        89: 5q^2+3q+1
        90: q^3+4q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+7q^2+4q+1
        95: 2q^3+7q^2+4q+1
        96: 3q^3+5q^2+3q+1
        97: 2q^3+7q^2+4q+1
        98: 2q^3+7q^2+4q+1
        99: 3q^3+5q^2+3q+1
       100: 2q^3+7q^2+4q+1
       101: 2q^3+7q^2+4q+1
       102: 3q^3+5q^2+3q+1
       103: q^3+2q^2+q
       104: q^3+4q^2+2q+1
       105: 2q^2
       106: q^3+2q^2+q
       107: q^3+3q^2+3q+1
       108: q^2+q
       109: q^2+q
       110: q^3+3q^2+3q+1
       111: 2q
       112: q^2+2q+1
       113: q^3+q^2+2q
       114: 3q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       121: 2q^2+q
       122: 3q^2+2q+1
       123: 2q^2+q
       124: 3q^2+2q+1
       125: q^2+2q+1
       126: 4q^2+3q+1
       127: q^3+q^2+2q
       128: 3q^2+2q+1
       129: q^3+q^2+2q
       130: 3q^2+2q+1
       131: 2q^2+q
       132: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: 5q^2+3q+1
       138: 4q^2+3q+1
       139: 2q^3+7q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 5q^2+3q+1
       144: 4q^2+3q+1
       145: 2q^3+7q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: 2q^3+7q^2+4q+1
       150: 4q^2+3q+1
       151: q^3+q^2+2q
       152: 3q^2+2q+1
       153: q^3+q^2+2q
       154: 3q^2+2q+1
       155: 2q^2+q
       156: q^3+2q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q^3+7q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: 3q^3+5q^2+3q+1
       169: q
       170: q^2+2q+1
       172: q
       174: q^2+2q+1
       177: q^2+q
       178: 2q^2+2q+1
       179: q^3+q^2+2q
       180: 3q^2+2q+1
       181: 2q
       182: q^2+2q+1
       183: 2q+1
       186: 2q+1
       187: q
       188: 2q+1
       189: q^2+q
       190: 2q^2+2q+1
       192: q^2+2q+1
       193: q^3+3q^2+3q+1
       194: q^2+q
       195: q^2+q
       196: q^3+3q^2+3q+1
       197: 2q
       198: q^2+2q+1
       199: q^2+2q+1
       201: q^3+3q^2+3q+1
       202: q^2+q
       203: q^2+q
       204: q^3+3q^2+3q+1
       205: 2q
       206: q^2+2q+1
       207: 2q^2+q
       208: 3q^2+2q+1
       209: q^3+q^2+2q
       210: 3q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: 4q^2+3q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 4q^2+3q+1
       237: q^3+q^2+2q
       238: 3q^2+2q+1
       239: q^3+q^2+2q
       240: 3q^2+2q+1
       241: 2q^2+q
       242: q^3+2q^2+2q+1
       243: 2q^3+7q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: 2q^2+7q+1
       248: 2q^2+7q+1
       249: q^3+4q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q
       260: q^2+2q+1
       262: q
       264: 2q+1
       267: q
       268: q^2+2q+1
       269: q
       271: q
       273: q
       274: q^2+2q+1
       276: q^2+2q+1
       283: 2q+1
       286: 2q+1
       287: q^2+q
       288: 2q^2+2q+1
       291: q
       292: 2q+1
       293: 2q+1
       296: 2q+1
       297: q
       298: 2q+1
       299: 2q+1
       301: 2q
       302: q^2+2q+1
       304: 2q+1
       305: q
       306: 2q+1
       307: 2q+1
       310: 2q+1
       311: 2q
       312: q^2+2q+1
       313: q
       314: 2q+1
       315: q^2+q
       316: 2q^2+2q+1
       317: q^3+q^2+2q
       318: 3q^2+2q+1
       319: q^3+3q^2+3q+1
       320: q^2+q
       321: q^2+q
       322: q^3+3q^2+3q+1
       323: 2q
       324: q^2+2q+1
       325: q^2+q
       326: 2q^2+2q+1
       333: 2q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: 3q+1
       337: 2q^2+7q+1
       338: q^2+3q
       339: q^2+4q+1
       340: q^2+3q
       341: q^2+4q+1
       342: 2q^2+q
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 2q^2+7q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q^2+3q+1
       358: q^2+3q+1
       359: 2q^2+7q+1
       366: 4q^2+3q+1
       367: 2q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       378: 2q+1
       386: 2q+1
       389: q
       390: q^2+2q+1
       391: q
       394: 2q+1
       397: q
       399: q
       400: q^2+2q+1
       403: 2q+1
       405: q
       406: q
       407: q^2+2q+1
       419: 2q+1
       422: 2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+3q
       428: q^2+4q+1
       429: 2q+1
       432: 2q+1
       433: q
       434: 2q+1
       437: 2q+1
       440: 2q+1
       441: q
       442: 2q+1
       443: 2q^2+5q+1
       444: 2q
       445: q^2+3q
       446: q^2+4q+1
       447: 2q+1
       450: 2q+1
       451: q
       452: 2q+1
       453: 2q+1
       458: 2q+1
       459: q
       460: 2q+1
       461: 2q
       462: 2q^2+5q+1
       463: q^2+3q
       464: q^2+4q+1
       469: q^2+q
       470: 2q^2+2q+1
       471: 2q+1
       474: 2q+1
       475: q
       476: 2q+1
       477: 2q
       478: q^2+2q+1
       479: 4q
       480: 2q^2+3q+1
       481: q+1
       482: q+1
       483: 3q+1
       484: q+1
       491: q+1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: 3q+1
       496: 2q+1
       497: 2q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: 3q+1
       501: 2q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       530: 2q+1
       534: 2q+1
       542: 2q+1
       545: q^2+2q
       546: q^2+3q+1
       547: q
       548: q
       551: 2q+1
       560: 2q+1
       561: q
       562: q
       563: q^2+2q
       564: q^2+3q+1
       566: 2q+1
       569: q
       570: q
       571: q^2+2q+1
       573: 2q
       574: 2q^2+3q+1
       575: 2q
       577: 2q
       578: 2q
       580: q^2+q
       581: q^2+2q+1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       599: q
       600: 2q+1
       603: 2q+1
       608: 2q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: q+1
       619: 2q+1
       622: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       632: q+1
       641: 2q+1
       644: 2q+1
       645: q
       646: 2q+1
       647: 2q+1
       650: 2q+1
       653: q
       654: 2q+1
       655: q
       656: q+1
       657: q+1
       664: q+1
       665: 1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 3q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 3q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+3q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       696: q^2+q
       697: q
       699: q^2+2q+1
       701: q
       715: q+1
       718: q+1
       726: 2q+1
       744: 2q+1
       754: 2q+1
       763: 2q+1
       766: q+1
       785: 1
       788: 1
       792: 1
       793: q+1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       811: q
       812: 2q+1
       815: q+1
       818: q+1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       835: q
       836: 2q+1
       840: q+1
       843: q
       844: q+1
       845: 2q+1
       848: 2q+1
       851: q
       852: 2q+1
       855: q
       856: 2q+1
       857: q
       858: q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 3q+1
       880: q+1
       909: 1
       926: q+1
       929: q+1
       951: q+1
       953: q+1
       965: q+1
       976: 2q+1
       989: q+1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1013: 1
      1016: q+1
      1026: 1
      1029: 1
      1033: q+1
      1040: 1
      1045: 1
      1046: q
      1047: q+1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1062: q
      1063: 2q+1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1131: 1
      1136: 1
      1162: 1
      1181: 1
      1195: q+1
      1205: q+1
      1207: q+1
      1217: 1
      1218: 1
      1225: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1268: 1
      1271: 1
      1277: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1327: 1
      1366: 1
      1371: 1
      1397: 1
      1402: 1
      1427: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1467: 1
      1468: 1
      1476: 1
      1479: 1
      1483: 1
      1487: 1
      1577: 1
      1596: 1
      1624: 1
      1628: 1
      1664: 1
      1665: 1
      1798: 1

1799:    0: 3q^3+10q^2+4q+1
         1: 3q^3+10q^2+4q+1
         2: 5q^3+6q^2+3q+1
         3: 3q^3+10q^2+4q+1
         4: q^4+5q^3+7q^2+4q+1
         5: 3q^3+10q^2+4q+1
         6: q^4+5q^3+7q^2+4q+1
         7: 2q^4+4q^3+5q^2+3q+1
         8: 5q^3+6q^2+3q+1
         9: 2q^4+4q^3+5q^2+3q+1
        10: 3q^3+10q^2+4q+1
        11: 3q^3+10q^2+4q+1
        12: q^4+5q^3+7q^2+4q+1
        13: 5q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 5q^2+3q+1
        16: 3q^3+10q^2+4q+1
        17: 3q^3+10q^2+4q+1
        18: 2q^4+4q^3+5q^2+3q+1
        19: 2q^3+7q^2+4q+1
        20: 2q^3+7q^2+4q+1
        21: 3q^3+5q^2+3q+1
        22: 3q^3+10q^2+4q+1
        23: 3q^3+10q^2+4q+1
        24: 5q^3+6q^2+3q+1
        25: 3q^3+10q^2+4q+1
        26: 3q^3+10q^2+4q+1
        27: 5q^3+6q^2+3q+1
        28: 3q^3+10q^2+4q+1
        29: 2q^3+7q^2+4q+1
        30: 4q^2+3q+1
        31: 3q^3+10q^2+4q+1
        32: 5q^2+3q+1
        33: 3q^3+10q^2+4q+1
        34: 3q^3+10q^2+4q+1
        35: 5q^2+3q+1
        36: 3q^3+10q^2+4q+1
        37: 2q^3+4q^2+2q
        38: q^3+6q^2+2q+1
        39: 2q^3+4q^2+2q
        40: q^3+6q^2+2q+1
        41: 2q^3+3q^2+q
        42: 3q^3+3q^2+2q+1
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: 5q^2+3q+1
        47: 5q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+7q^2+4q+1
        50: 2q^3+7q^2+4q+1
        51: 3q^3+5q^2+3q+1
        52: 2q^3+7q^2+4q+1
        53: 2q^3+7q^2+4q+1
        54: 3q^3+5q^2+3q+1
        55: 2q^3+7q^2+4q+1
        56: 2q^3+7q^2+4q+1
        57: 3q^3+5q^2+3q+1
        58: 2q^3+6q^2+3q+1
        59: q^3+4q^2+q
        60: q^3+4q^2+q
        61: 2q^3+6q^2+3q+1
        62: 2q^3+4q^2+2q
        63: q^3+6q^2+2q+1
        64: 2q^2+q
        65: 3q^2+2q+1
        66: 2q^3+4q^2+2q
        67: q^3+6q^2+2q+1
        68: q^2+2q+1
        69: 4q^2+3q+1
        70: 4q^2+3q+1
        71: 2q^3+7q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: q^3+q^2+2q
        75: 3q^2+2q+1
        76: q^3+q^2+2q
        77: 3q^2+2q+1
        78: 2q^2+q
        79: q^3+2q^2+2q+1
        80: 5q^2+3q+1
        81: 5q^2+3q+1
        82: 2q^3+7q^2+4q+1
        83: 4q^2+3q+1
        84: 5q^2+3q+1
        85: 5q^2+3q+1
        86: 2q^3+7q^2+4q+1
        87: 4q^2+3q+1
        88: 5q^2+3q+1
        89: 5q^2+3q+1
        90: q^3+4q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+7q^2+4q+1
        95: 2q^3+7q^2+4q+1
        96: 3q^3+5q^2+3q+1
        97: 2q^3+7q^2+4q+1
        98: 2q^3+7q^2+4q+1
        99: 3q^3+5q^2+3q+1
       100: 2q^3+7q^2+4q+1
       101: 2q^3+7q^2+4q+1
       102: 3q^3+5q^2+3q+1
       103: q^3+2q^2+q
       104: 2q^2
       105: q^3+4q^2+2q+1
       106: q^3+2q^2+q
       107: q^2+q
       108: q^3+3q^2+3q+1
       109: q^3+3q^2+3q+1
       110: q^2+q
       111: 2q
       112: q^2+2q+1
       113: q^3+q^2+2q
       114: 3q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+q
       122: 3q^2+2q+1
       123: 2q^2+q
       124: 3q^2+2q+1
       125: q^2+2q+1
       126: 4q^2+3q+1
       127: q^3+q^2+2q
       128: 3q^2+2q+1
       129: q^3+q^2+2q
       130: 3q^2+2q+1
       131: 2q^2+q
       132: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: 5q^2+3q+1
       138: 4q^2+3q+1
       139: 2q^3+7q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 5q^2+3q+1
       144: 4q^2+3q+1
       145: 2q^3+7q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: 2q^3+7q^2+4q+1
       150: 4q^2+3q+1
       151: q^3+q^2+2q
       152: 3q^2+2q+1
       153: q^3+q^2+2q
       154: 3q^2+2q+1
       155: 2q^2+q
       156: q^3+2q^2+2q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q^3+7q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: 3q^3+5q^2+3q+1
       169: q
       171: q^2+2q+1
       172: q
       175: q^2+2q+1
       177: q^2+q
       178: 2q^2+2q+1
       179: q^3+q^2+2q
       180: 3q^2+2q+1
       181: 2q
       182: q^2+2q+1
       184: 2q+1
       185: 2q+1
       187: q
       188: 2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: q^2+2q+1
       193: q^2+q
       194: q^3+3q^2+3q+1
       195: q^3+3q^2+3q+1
       196: q^2+q
       197: 2q
       198: q^2+2q+1
       200: q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+3q+1
       203: q^3+3q^2+3q+1
       204: q^2+q
       205: 2q
       206: q^2+2q+1
       207: 2q^2+q
       208: 3q^2+2q+1
       209: q^3+q^2+2q
       210: 3q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: 4q^2+3q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 4q^2+3q+1
       237: q^3+q^2+2q
       238: 3q^2+2q+1
       239: q^3+q^2+2q
       240: 3q^2+2q+1
       241: 2q^2+q
       242: q^3+2q^2+2q+1
       243: 2q^3+7q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: 2q^2+7q+1
       248: 2q^2+7q+1
       249: q^3+4q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q
       261: q^2+2q+1
       262: q
       265: 2q+1
       267: q
       269: q
       270: q^2+2q+1
       271: q
       272: q^2+2q+1
       273: q
       277: q^2+2q+1
       284: 2q+1
       285: 2q+1
       287: q^2+q
       288: 2q^2+2q+1
       291: q
       292: 2q+1
       294: 2q+1
       295: 2q+1
       297: q
       298: 2q+1
       300: 2q+1
       301: 2q
       302: q^2+2q+1
       303: 2q+1
       305: q
       306: 2q+1
       308: 2q+1
       309: 2q+1
       311: 2q
       312: q^2+2q+1
       313: q
       314: 2q+1
       315: q^2+q
       316: 2q^2+2q+1
       317: q^3+q^2+2q
       318: 3q^2+2q+1
       319: q^2+q
       320: q^3+3q^2+3q+1
       321: q^3+3q^2+3q+1
       322: q^2+q
       323: 2q
       324: q^2+2q+1
       325: q^2+q
       326: 2q^2+2q+1
       333: 2q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: 3q+1
       337: 2q^2+7q+1
       338: q^2+3q
       339: q^2+4q+1
       340: q^2+3q
       341: q^2+4q+1
       342: 2q^2+q
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 2q^2+7q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q^2+3q+1
       358: q^2+3q+1
       359: 2q^2+7q+1
       366: 4q^2+3q+1
       367: 2q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       379: 2q+1
       387: 2q+1
       389: q
       391: q
       392: q^2+2q+1
       395: 2q+1
       397: q
       398: q^2+2q+1
       399: q
       402: 2q+1
       405: q
       406: q
       408: q^2+2q+1
       420: 2q+1
       421: 2q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+3q
       428: q^2+4q+1
       430: 2q+1
       431: 2q+1
       433: q
       434: 2q+1
       438: 2q+1
       439: 2q+1
       441: q
       442: 2q+1
       443: 2q
       444: 2q^2+5q+1
       445: q^2+3q
       446: q^2+4q+1
       448: 2q+1
       449: 2q+1
       451: q
       452: 2q+1
       454: 2q+1
       457: 2q+1
       459: q
       460: 2q+1
       461: 2q^2+5q+1
       462: 2q
       463: q^2+3q
       464: q^2+4q+1
       469: q^2+q
       470: 2q^2+2q+1
       472: 2q+1
       473: 2q+1
       475: q
       476: 2q+1
       477: 2q
       478: q^2+2q+1
       479: 4q
       480: 2q^2+3q+1
       481: q+1
       482: q+1
       483: 3q+1
       484: q+1
       491: q+1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: 3q+1
       496: 2q+1
       497: 2q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: 3q+1
       501: 2q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       531: 2q+1
       535: 2q+1
       544: 2q+1
       545: q
       546: q
       547: q^2+2q
       548: q^2+3q+1
       550: 2q+1
       558: 2q+1
       561: q^2+2q
       562: q^2+3q+1
       563: q
       564: q
       567: 2q+1
       569: q
       570: q
       572: q^2+2q+1
       573: 2q
       575: 2q
       576: 2q^2+3q+1
       577: 2q
       578: 2q
       580: q^2+q
       581: q^2+2q+1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       599: q
       600: 2q+1
       604: 2q+1
       607: 2q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       616: q+1
       620: 2q+1
       621: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: q+1
       642: 2q+1
       643: 2q+1
       645: q
       646: 2q+1
       648: 2q+1
       649: 2q+1
       653: q
       654: 2q+1
       655: q
       656: q+1
       657: q+1
       664: q+1
       665: 1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 3q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 3q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+3q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       697: q
       698: q^2+q
       700: q^2+2q+1
       701: q
       714: q+1
       719: q+1
       728: 2q+1
       742: 2q+1
       755: 2q+1
       764: 2q+1
       767: q+1
       786: 1
       787: 1
       792: 1
       794: q+1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       811: q
       812: 2q+1
       816: q+1
       817: q+1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       835: q
       836: 2q+1
       839: q+1
       843: q
       844: q+1
       846: 2q+1
       847: 2q+1
       851: q
       852: 2q+1
       855: q
       856: 2q+1
       857: q
       858: q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 3q+1
       880: q+1
       910: 1
       925: q+1
       931: q+1
       949: q+1
       954: q+1
       966: q+1
       977: 2q+1
       990: q+1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1013: 1
      1017: q+1
      1027: 1
      1028: 1
      1032: q+1
      1041: 1
      1044: 1
      1046: q
      1047: q+1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1062: q
      1063: 2q+1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1132: 1
      1137: 1
      1161: 1
      1182: 1
      1196: q+1
      1203: q+1
      1209: q+1
      1216: 1
      1219: 1
      1225: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1269: 1
      1270: 1
      1277: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1328: 1
      1365: 1
      1370: 1
      1398: 1
      1403: 1
      1428: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1466: 1
      1469: 1
      1477: 1
      1478: 1
      1483: 1
      1487: 1
      1576: 1
      1597: 1
      1625: 1
      1629: 1
      1663: 1
      1666: 1
      1799: 1

1800:    0: 3q^3+10q^2+4q+1
         1: 3q^3+10q^2+4q+1
         2: 5q^3+6q^2+3q+1
         3: 3q^3+10q^2+4q+1
         4: q^4+5q^3+7q^2+4q+1
         5: 3q^3+10q^2+4q+1
         6: q^4+5q^3+7q^2+4q+1
         7: 2q^4+4q^3+5q^2+3q+1
         8: 5q^3+6q^2+3q+1
         9: 2q^4+4q^3+5q^2+3q+1
        10: 3q^3+10q^2+4q+1
        11: 3q^3+10q^2+4q+1
        12: q^4+5q^3+7q^2+4q+1
        13: 5q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 5q^2+3q+1
        16: 3q^3+10q^2+4q+1
        17: 3q^3+10q^2+4q+1
        18: 2q^4+4q^3+5q^2+3q+1
        19: 2q^3+7q^2+4q+1
        20: 2q^3+7q^2+4q+1
        21: 3q^3+5q^2+3q+1
        22: 3q^3+10q^2+4q+1
        23: 3q^3+10q^2+4q+1
        24: 5q^3+6q^2+3q+1
        25: 3q^3+10q^2+4q+1
        26: 3q^3+10q^2+4q+1
        27: 5q^3+6q^2+3q+1
        28: 3q^3+10q^2+4q+1
        29: 2q^3+7q^2+4q+1
        30: 4q^2+3q+1
        31: 3q^3+10q^2+4q+1
        32: 5q^2+3q+1
        33: 3q^3+10q^2+4q+1
        34: 3q^3+10q^2+4q+1
        35: 5q^2+3q+1
        36: 3q^3+10q^2+4q+1
        37: q^3+6q^2+2q+1
        38: 2q^3+4q^2+2q
        39: q^3+6q^2+2q+1
        40: 2q^3+4q^2+2q
        41: 3q^3+3q^2+2q+1
        42: 2q^3+3q^2+q
        43: 5q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 5q^2+3q+1
        46: 5q^2+3q+1
        47: 5q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+7q^2+4q+1
        50: 2q^3+7q^2+4q+1
        51: 3q^3+5q^2+3q+1
        52: 2q^3+7q^2+4q+1
        53: 2q^3+7q^2+4q+1
        54: 3q^3+5q^2+3q+1
        55: 2q^3+7q^2+4q+1
        56: 2q^3+7q^2+4q+1
        57: 3q^3+5q^2+3q+1
        58: q^3+4q^2+q
        59: 2q^3+6q^2+3q+1
        60: q^3+4q^2+q
        61: 2q^3+6q^2+3q+1
        62: q^3+6q^2+2q+1
        63: 2q^3+4q^2+2q
        64: 3q^2+2q+1
        65: 2q^2+q
        66: q^3+6q^2+2q+1
        67: 2q^3+4q^2+2q
        68: q^2+2q+1
        69: 4q^2+3q+1
        70: 4q^2+3q+1
        71: 2q^3+7q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: 3q^2+2q+1
        75: q^3+q^2+2q
        76: 3q^2+2q+1
        77: q^3+q^2+2q
        78: q^3+2q^2+2q+1
        79: 2q^2+q
        80: 5q^2+3q+1
        81: 5q^2+3q+1
        82: 2q^3+7q^2+4q+1
        83: 4q^2+3q+1
        84: 5q^2+3q+1
        85: 5q^2+3q+1
        86: 2q^3+7q^2+4q+1
        87: 4q^2+3q+1
        88: 5q^2+3q+1
        89: 5q^2+3q+1
        90: q^3+4q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+7q^2+4q+1
        95: 2q^3+7q^2+4q+1
        96: 3q^3+5q^2+3q+1
        97: 2q^3+7q^2+4q+1
        98: 2q^3+7q^2+4q+1
        99: 3q^3+5q^2+3q+1
       100: 2q^3+7q^2+4q+1
       101: 2q^3+7q^2+4q+1
       102: 3q^3+5q^2+3q+1
       103: 2q^2
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       106: q^3+4q^2+2q+1
       107: q^2+q
       108: q^3+3q^2+3q+1
       109: q^2+q
       110: q^3+3q^2+3q+1
       111: q^2+2q+1
       112: 2q
       113: 3q^2+2q+1
       114: q^3+q^2+2q
       115: 2q^2+2q+1
       116: q^2+q
       118: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+2q+1
       122: 2q^2+q
       123: 3q^2+2q+1
       124: 2q^2+q
       125: q^2+2q+1
       126: 4q^2+3q+1
       127: 3q^2+2q+1
       128: q^3+q^2+2q
       129: 3q^2+2q+1
       130: q^3+q^2+2q
       131: q^3+2q^2+2q+1
       132: 2q^2+q
       133: 2q+1
       134: 2q^2+3q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: 5q^2+3q+1
       138: 4q^2+3q+1
       139: 2q^3+7q^2+4q+1
       140: q^3+4q^2+4q+1
       141: 4q^2+3q+1
       142: q^3+4q^2+4q+1
       143: 5q^2+3q+1
       144: 4q^2+3q+1
       145: 2q^3+7q^2+4q+1
       146: 4q^2+3q+1
       147: q^3+4q^2+4q+1
       148: q^3+4q^2+4q+1
       149: 2q^3+7q^2+4q+1
       150: 4q^2+3q+1
       151: 3q^2+2q+1
       152: q^3+q^2+2q
       153: 3q^2+2q+1
       154: q^3+q^2+2q
       155: q^3+2q^2+2q+1
       156: 2q^2+q
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q^3+7q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: 3q^3+5q^2+3q+1
       170: q
       171: q
       172: q^2+2q+1
       176: q^2+2q+1
       177: 2q^2+2q+1
       178: q^2+q
       179: 3q^2+2q+1
       180: q^3+q^2+2q
       181: q^2+2q+1
       182: 2q
       184: 2q+1
       186: 2q+1
       187: 2q+1
       188: q
       189: 2q^2+2q+1
       190: q^2+q
       192: q^2+2q+1
       193: q^2+q
       194: q^3+3q^2+3q+1
       195: q^2+q
       196: q^3+3q^2+3q+1
       197: q^2+2q+1
       198: 2q
       200: q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+3q+1
       203: q^2+q
       204: q^3+3q^2+3q+1
       205: q^2+2q+1
       206: 2q
       207: 3q^2+2q+1
       208: 2q^2+q
       209: 3q^2+2q+1
       210: q^3+q^2+2q
       211: 2q^2+2q+1
       212: q^2+q
       219: 2q+1
       220: 2q+1
       221: 2q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^2+3q+1
       226: 4q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: 4q^2+3q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 4q^2+3q+1
       237: 3q^2+2q+1
       238: q^3+q^2+2q
       239: 3q^2+2q+1
       240: q^3+q^2+2q
       241: q^3+2q^2+2q+1
       242: 2q^2+q
       243: 2q^3+7q^2+4q+1
       244: q^3+4q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 4q^2+3q+1
       247: 2q^2+7q+1
       248: 2q^2+7q+1
       249: q^3+4q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       260: q
       261: q
       262: q^2+2q+1
       266: 2q+1
       268: q
       269: q^2+2q+1
       270: q
       272: q
       273: q^2+2q+1
       274: q
       278: q^2+2q+1
       284: 2q+1
       286: 2q+1
       287: 2q^2+2q+1
       288: q^2+q
       291: 2q+1
       292: q
       294: 2q+1
       296: 2q+1
       297: 2q+1
       298: q
       300: 2q+1
       301: q^2+2q+1
       302: 2q
       304: 2q+1
       305: 2q+1
       306: q
       308: 2q+1
       310: 2q+1
       311: q^2+2q+1
       312: 2q
       313: 2q+1
       314: q
       315: 2q^2+2q+1
       316: q^2+q
       317: 3q^2+2q+1
       318: q^3+q^2+2q
       319: q^2+q
       320: q^3+3q^2+3q+1
       321: q^2+q
       322: q^3+3q^2+3q+1
       323: q^2+2q+1
       324: 2q
       325: 2q^2+2q+1
       326: q^2+q
       333: 2q+1
       334: q^2+3q+1
       335: q^2+3q+1
       336: 3q+1
       337: 2q^2+7q+1
       338: q^2+4q+1
       339: q^2+3q
       340: q^2+4q+1
       341: q^2+3q
       342: q^3+2q^2+2q+1
       343: 2q^2+q
       344: 2q+1
       345: 2q+1
       346: 2q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 2q^2+7q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: q^2+3q+1
       358: q^2+3q+1
       359: 2q^2+7q+1
       366: 4q^2+3q+1
       367: 2q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       380: 2q+1
       388: 2q+1
       390: q
       391: q^2+2q+1
       392: q
       396: 2q+1
       398: q
       399: q^2+2q+1
       400: q
       404: 2q+1
       406: q^2+2q+1
       407: q
       408: q
       420: 2q+1
       422: 2q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: q^2+4q+1
       428: q^2+3q
       430: 2q+1
       432: 2q+1
       433: 2q+1
       434: q
       438: 2q+1
       440: 2q+1
       441: 2q+1
       442: q
       443: 2q
       444: 2q^2+5q+1
       445: q^2+4q+1
       446: q^2+3q
       448: 2q+1
       450: 2q+1
       451: 2q+1
       452: q
       454: 2q+1
       458: 2q+1
       459: 2q+1
       460: q
       461: 2q
       462: 2q^2+5q+1
       463: q^2+4q+1
       464: q^2+3q
       469: 2q^2+2q+1
       470: q^2+q
       472: 2q+1
       474: 2q+1
       475: 2q+1
       476: q
       477: q^2+2q+1
       478: 2q
       479: 2q^2+3q+1
       480: 4q
       481: q+1
       482: q+1
       483: 3q+1
       484: q+1
       491: q+1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: 3q+1
       496: 2q+1
       497: 2q+1
       498: q^2+3q+1
       499: q^2+3q+1
       500: 3q+1
       501: 2q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       532: 2q+1
       536: 2q+1
       543: 2q+1
       545: q
       546: q
       547: q^2+3q+1
       548: q^2+2q
       552: 2q+1
       559: 2q+1
       561: q
       562: q
       563: q^2+3q+1
       564: q^2+2q
       568: 2q+1
       570: q^2+2q+1
       571: q
       572: q
       574: 2q
       575: 2q^2+3q+1
       576: 2q
       577: q^2+2q+1
       578: q^2+q
       580: 2q
       581: 2q
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       599: 2q+1
       600: q
       604: 2q+1
       608: 2q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       616: q+1
       620: 2q+1
       622: 2q+1
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       632: q+1
       642: 2q+1
       644: 2q+1
       645: 2q+1
       646: q
       648: 2q+1
       650: 2q+1
       653: 2q+1
       654: q
       655: q+1
       656: q
       657: q+1
       664: q+1
       665: 1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 3q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 3q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+3q+1
       688: q^2+3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q^2+2q+1
       698: q
       699: q
       700: q
       701: q^2+q
       716: q+1
       720: q+1
       727: 2q+1
       743: 2q+1
       756: 2q+1
       762: 2q+1
       768: q+1
       786: 1
       788: 1
       791: 1
       794: q+1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       811: 2q+1
       812: q
       816: q+1
       818: q+1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       835: 2q+1
       836: q
       840: q+1
       843: q+1
       844: q
       846: 2q+1
       848: 2q+1
       851: 2q+1
       852: q
       855: 2q+1
       856: q
       857: q+1
       858: q
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 3q+1
       880: q+1
       911: 1
       927: q+1
       930: q+1
       950: q+1
       955: q+1
       967: q+1
       975: 2q+1
       991: q+1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1012: 1
      1017: q+1
      1027: 1
      1029: 1
      1033: q+1
      1041: 1
      1045: 1
      1046: q+1
      1047: q
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1062: 2q+1
      1063: q
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1133: 1
      1135: 1
      1163: 1
      1183: 1
      1197: q+1
      1204: q+1
      1208: q+1
      1217: 1
      1219: 1
      1224: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1269: 1
      1271: 1
      1276: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1329: 1
      1367: 1
      1369: 1
      1399: 1
      1401: 1
      1429: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1467: 1
      1469: 1
      1477: 1
      1479: 1
      1482: 1
      1487: 1
      1578: 1
      1598: 1
      1626: 1
      1630: 1
      1664: 1
      1666: 1
      1800: 1

1801:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        37: q+2
        39: q+2
        41: q+2
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        62: q+2
        64: q+2
        66: 2
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+2
       123: 2
       125: 2
       126: 1
       127: 2
       129: 2
       131: q+1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       169: 1
       172: 1
       173: 1
       176: 1
       177: 1
       179: 2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2
       209: q+2
       211: q+2
       213: 2
       215: 2
       217: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       237: 2
       239: 2
       241: q+1
       243: 2
       244: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: 1
       278: 1
       279: 2
       281: 1
       287: 1
       289: 2
       291: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: 1
       317: 2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: q+2
       327: 2
       329: 2
       331: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       360: 2
       362: 2
       364: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 2
       411: 1
       413: 1
       415: 2
       417: 1
       423: 1
       425: 1
       427: 2
       433: 1
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       451: 1
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: 2
       467: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 1
       482: 1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       502: 2
       504: 2
       506: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       525: 1
       528: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: 1
       585: 1
       587: 1
       597: 1
       599: 1
       601: 2
       605: 1
       609: 1
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       623: 1
       625: 1
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: 2
       637: 1
       639: 1
       645: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       697: 1
       729: 1
       731: 1
       733: 1
       735: 1
       745: 1
       747: 1
       749: 1
       751: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       777: 1
       779: 1
       781: 1
       783: 1
       789: 2
       791: 1
       795: 1
       797: 1
       799: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       819: 1
       821: 1
       823: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: 1
       843: 1
       849: 1
       851: 1
       853: 2
       855: 1
       857: 2
       859: 1
       861: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       932: 1
       934: 1
       956: 1
       958: 1
       968: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       996: 1
      1002: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1030: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1046: 1
      1048: 1
      1050: 1
      1060: 1
      1062: 1
      1064: 1
      1066: 1
      1068: 1
      1070: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1102: 1
      1138: 1
      1188: 1
      1212: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1236: 1
      1238: 1
      1244: 1
      1252: 1
      1256: 1
      1262: 1
      1264: 1
      1266: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1334: 1
      1404: 1
      1430: 1
      1444: 1
      1446: 1
      1452: 1
      1458: 1
      1470: 1
      1472: 1
      1474: 1
      1480: 1
      1482: 1
      1488: 1
      1553: 1
      1631: 1
      1667: 1
      1669: 1
      1671: 1
      1801: 1

1802:    0: 4q^2+4q
         1: 4q^2+4q
         2: 4q^2+4q
         3: 4q^2+4q
         4: 4q^2+4q
         5: 4q^2+4q
         6: 4q^2+4q
         7: 4q^2+4q
         8: 4q^2+4q
         9: q^4+2q^3+2q^2+q
        10: 4q^2+4q
        11: 4q^2+4q
        12: 4q^2+4q
        13: 4q^2+4q
        14: 4q^2+4q
        15: 4q^2+4q
        16: 4q
        17: 4q
        18: 2q^2+q
        19: 4q^2+4q
        20: 4q^2+4q
        21: 4q^2+4q
        22: 4q^2+4q
        23: 4q^2+4q
        24: 4q^2+4q
        25: 4q^2+4q
        26: 4q^2+4q
        27: 4q^2+4q
        28: 4q
        29: 4q^2+4q
        30: 4q^2+4q
        31: 4q^2+4q
        32: 4q^2+4q
        33: 4q
        34: 4q^2+4q
        35: 4q^2+4q
        36: 4q
        37: q^2+2q
        38: 3q^2+2q
        39: q^2+2q
        40: 3q^2+2q
        41: q^2+2q
        42: 3q^2+2q
        43: 4q^2+4q
        44: 4q^2+4q
        45: 4q^2+4q
        46: 4q
        47: 4q
        48: 2q^2+q
        49: 4q
        50: 4q
        51: 2q^2+q
        52: 4q^2+4q
        53: 4q^2+4q
        54: 4q^2+4q
        55: 4q^2+4q
        56: 4q^2+4q
        57: 4q^2+4q
        58: 2q
        59: 2q
        60: 2q
        61: 2q
        62: q^2+2q
        63: 3q^2+2q
        64: q^2+2q
        65: 3q^2+2q
        66: 2q
        67: 2q
        68: 4q
        69: q
        70: 4q^2+4q
        71: 4q
        72: 4q
        73: 4q
        74: q^2+2q
        75: 3q^2+2q
        76: q^2+2q
        77: 3q^2+2q
        78: q^2+2q
        79: 3q^2+2q
        80: 4q^2+4q
        81: 4q
        82: 4q^2+4q
        83: 4q^2+4q
        84: 4q^2+4q
        85: 4q
        86: 4q^2+4q
        87: 4q^2+4q
        88: 4q
        89: 4q
        90: 2q^2+q
        91: 4q
        92: 4q
        93: 2q^2+q
        94: 4q
        95: 4q
        96: 2q^2+q
        97: 4q
        98: 4q
        99: 2q^2+q
       100: 4q^2+4q
       101: 4q^2+4q
       102: 4q^2+4q
       103: q
       104: q
       105: q
       106: q
       107: 2q
       108: 2q
       109: 2q
       110: 2q
       111: 2q
       112: 2q
       113: q^2+2q
       114: 3q^2+2q
       115: q^2+2q
       116: 3q^2+2q
       117: 2q
       118: 2q
       119: 2q
       120: 2q
       121: q^2+2q
       122: 3q^2+2q
       123: 2q
       124: 2q
       125: 4q
       126: q
       128: 2q
       130: 2q
       132: q^2
       133: 4q
       134: q
       135: 4q
       136: 4q
       137: 4q
       138: q
       139: 4q
       140: 4q
       141: 4q^2+4q
       142: 4q
       143: 4q
       144: q
       145: 4q
       146: 4q^2+4q
       147: 4q
       148: 4q
       149: 4q^2+4q
       150: 4q^2+4q
       151: q^2+2q
       152: 3q^2+2q
       153: q^2+2q
       154: 3q^2+2q
       155: q^2+2q
       156: 3q^2+2q
       157: 4q
       158: 4q
       159: 2q^2+q
       160: 4q
       161: 4q
       162: 2q^2+q
       163: 4q
       164: 4q
       165: 2q^2+q
       166: 4q
       167: 4q
       168: 2q^2+q
       169: q
       170: q
       171: q
       172: q
       173: q
       174: q
       175: q
       176: q
       180: 2q
       182: 2q
       183: 2q
       184: 2q
       185: 2q
       186: 2q
       187: 2q
       188: 2q
       189: q^2+2q
       190: 3q^2+2q
       191: 2q
       192: 2q
       193: 2q
       194: 2q
       195: 2q
       196: 2q
       197: 2q
       198: 2q
       199: 2q
       200: 2q
       201: 2q
       202: 2q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: 2q
       208: 2q
       209: q^2+2q
       210: 3q^2+2q
       211: q^2+2q
       212: 3q^2+2q
       214: 2q
       216: 2q
       218: q^2
       219: q
       220: 4q
       221: q
       222: 4q
       223: q
       224: 4q
       225: q
       226: q
       227: 4q
       228: q
       229: 4q
       230: 4q
       231: q
       232: 4q
       233: q
       234: 4q
       235: 4q
       236: q
       238: 2q
       240: 2q
       242: q^2
       243: 4q
       244: 4q
       245: 4q
       246: 4q^2+4q
       247: 4q
       248: 4q
       249: 2q^2+q
       250: 4q
       251: 4q
       252: 2q^2+q
       253: 4q
       254: 4q
       255: 2q^2+q
       256: 4q
       257: 4q
       258: 2q^2+q
       260: q
       261: q
       263: q
       264: q
       265: q
       266: q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       275: q
       276: q
       277: q
       278: q
       280: 2q
       290: 2q
       293: 2q
       294: 2q
       295: 2q
       296: 2q
       297: 2q
       298: 2q
       299: 2q
       300: 2q
       302: 2q
       303: 2q
       304: 2q
       305: 2q
       306: 2q
       307: 2q
       308: 2q
       309: 2q
       310: 2q
       312: 2q
       313: 2q
       314: 2q
       318: 2q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       324: 2q
       325: q^2+2q
       326: 3q^2+2q
       328: 2q
       330: 2q
       332: q^2
       333: q
       334: q
       335: q
       336: q
       337: 4q
       339: 2q
       341: 2q
       343: q^2
       344: q
       345: 4q
       346: q
       347: 4q
       348: q
       349: 4q
       350: q
       351: 4q
       352: q
       353: 4q
       354: q
       355: 4q
       356: q
       357: 4q
       358: q
       359: 4q
       361: 2q
       363: 2q
       365: q^2
       366: q
       367: 4q
       368: q
       369: 4q
       370: 4q
       371: 4q
       372: 4q
       373: 2q^2+q
       374: 4q
       375: 4q
       376: 2q^2+q
       382: q
       383: q
       385: q
       386: q
       387: q
       388: q
       390: q
       392: q
       393: q
       394: q
       395: q
       396: q
       398: q
       400: q
       401: q
       402: q
       403: q
       404: q
       405: q
       406: q
       407: q
       408: q
       410: 2q
       416: 2q
       428: 2q
       436: 2q
       437: 2q
       438: 2q
       439: 2q
       440: 2q
       441: 2q
       442: 2q
       443: 2q
       444: 2q
       446: 2q
       453: 2q
       454: 2q
       456: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: 2q
       462: 2q
       464: 2q
       466: 2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       478: 2q
       479: 2q
       480: 2q
       481: q
       482: q
       483: q
       484: 4q
       486: 2q
       488: 2q
       490: q^2
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 4q
       497: q
       498: q
       499: q
       500: q
       501: 4q
       503: 2q
       505: 2q
       507: q^2
       508: q
       509: 4q
       510: q
       511: 4q
       512: q
       513: 4q
       514: q
       515: 1
       516: 1
       517: 1
       518: 4q
       519: 4q
       520: 2q^2+q
       526: q
       527: q
       538: q
       540: q
       541: q
       542: q
       543: q
       544: q
       546: q
       548: q
       554: q
       556: q
       557: q
       558: q
       559: q
       560: q
       562: q
       564: q
       565: q
       566: q
       567: q
       568: q
       571: q
       572: q
       573: q
       574: q
       575: q
       576: q
       581: 2q
       602: 2q
       612: 2q
       615: 2q
       616: 2q
       618: 2q
       628: 2q
       631: 2q
       632: 2q
       634: 2q
       636: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       652: 2q
       653: 2q
       654: 2q
       655: 2q
       656: 2q
       659: 1
       661: 1
       663: 1
       664: 1
       665: q
       667: 2q
       669: 2q
       671: q^2
       672: 4q
       673: q
       674: 1
       675: q
       676: q
       677: q
       678: 4q
       679: q
       680: 1
       681: q
       682: q
       683: q
       684: 4q
       685: q
       686: q
       687: q
       688: q
       689: q
       690: 1
       691: 1
       692: 1
       699: q
       700: q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       761: q
       762: q
       763: q
       764: q
       765: q
       766: q
       767: q
       768: q
       773: 2q
       780: 1
       790: 2q
       796: 1
       814: 2q
       815: 2q
       816: 2q
       820: 1
       838: 2q
       839: 2q
       840: 2q
       843: 1
       854: 2q
       857: 2q
       858: 2q
       860: 1
       862: 1
       864: 1
       867: 1
       868: q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       881: 1
       882: 1
       883: 1
       890: q
       891: q
       933: q
       935: q
       957: q
       959: q
       969: 1
       980: q
       981: q
       986: 2q
       988: q
       989: q
       990: q
       991: q
       997: 1
      1012: 1
      1015: 1
      1021: 1
      1031: 1
      1037: 1
      1046: 1
      1067: 1
      1069: 1
      1071: 1
      1073: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1104: q
      1105: q
      1139: 1
      1189: 1
      1213: 1
      1224: 1
      1227: 1
      1237: 1
      1245: 1
      1253: 1
      1262: 1
      1275: 1
      1280: 1
      1284: 1
      1286: 1
      1288: 1
      1289: q
      1335: 1
      1405: 1
      1431: 1
      1444: 1
      1453: 1
      1459: 1
      1473: 1
      1482: 1
      1488: 1
      1554: 1
      1632: 1
      1668: 1
      1669: 1
      1802: 1

1803:    0: 2q^3+2q^2+2q
         1: 2q^4+2q^3+2q^2+2q
         2: 2q^3+2q^2+2q
         3: 2q^4+2q^3+2q^2+2q
         4: q^5+q^4+q^3+2q^2+2q
         5: 2q^3+2q^2+2q
         6: q^5+2q^4+q^3+2q^2+2q
         7: q^5+q^4+q^3+2q^2+2q
         8: 2q^3+2q^2+2q
         9: q^6+q^5+q^3+2q^2+q
        10: 2q^3+q^2+2q
        11: 2q^3+q^2+2q
        12: q^4+q^3+q^2+2q
        13: 2q^3+2q^2+2q
        14: q^5+q^4+q^3+2q^2+2q
        15: 2q^3+2q^2+2q
        16: 2q^3+q^2+2q
        17: 2q^3+q^2+2q
        18: q^5+2q^2+q
        19: q^3+2q^2+2q
        20: q^4+q^3+2q^2+2q
        21: q^3+2q^2+2q
        22: 2q^3+2q^2+2q
        23: 2q^4+2q^3+2q^2+2q
        24: 2q^3+2q^2+2q
        25: 2q^3+2q^2+2q
        26: 2q^4+2q^3+2q^2+2q
        27: 2q^3+2q^2+2q
        28: 2q^3+2q
        29: q^3+q^2+2q
        30: q^3+2q^2+2q
        31: 2q^3+q^2+2q
        32: 2q^3+2q^2+2q
        33: 2q^3+q^2+2q
        34: 2q^3+q^2+2q
        35: 2q^3+2q^2+2q
        36: 2q^3+q^2+2q
        37: 2q^3+2q^2+2q
        39: 2q^4+2q^3+2q^2+2q
        41: 2q^3+2q^2+2q
        43: 2q^3+q^2+2q
        44: q^4+q^3+q^2+2q
        45: 2q^3+q^2+2q
        46: 2q^3+q^2+2q
        47: 2q^3+q^2+2q
        48: q^5+2q^2+q
        49: q^3+q^2+2q
        50: q^3+q^2+2q
        51: 2q^2+q
        52: q^3+2q^2+2q
        53: q^4+q^3+2q^2+2q
        54: q^3+2q^2+2q
        55: q^3+2q^2+2q
        56: q^4+q^3+2q^2+2q
        57: q^3+2q^2+2q
        58: q^3+q
        59: q^3+q
        60: q^3+q
        61: q^3+q
        62: 2q^3+q^2+2q
        64: 2q^3+2q^2+2q
        66: 2q^3+q^2+2q
        68: 2q^3+2q
        69: q^2+q
        70: q^3+q^2+2q
        71: q^3+2q
        72: q^2+2q
        73: q^2+2q
        74: q^3+2q^2+2q
        76: q^4+q^3+2q^2+2q
        78: q^3+2q^2+2q
        80: 2q^3+q^2+2q
        81: 2q^3+q^2+2q
        82: q^3+q^2+2q
        83: q^3+2q^2+2q
        84: 2q^3+q^2+2q
        85: 2q^3+q^2+2q
        86: q^3+q^2+2q
        87: q^3+2q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: q^3+q^2+2q
        92: q^3+q^2+2q
        93: 2q^2+q
        94: q^3+q^2+2q
        95: q^3+q^2+2q
        96: 2q^2+q
        97: q^3+q^2+2q
        98: q^3+q^2+2q
        99: 2q^2+q
       100: q^3+2q^2+2q
       101: q^4+q^3+2q^2+2q
       102: q^3+2q^2+2q
       103: q^3+q
       106: q^3+q
       107: q
       108: q
       109: q
       110: q
       111: q^2+2q
       113: q^3+q^2+2q
       115: q^3+2q^2+2q
       117: q^3+q
       118: q^3+q
       119: q^3+q
       120: q^3+q
       121: 2q^3+q^2+2q
       123: 2q^3+q^2+2q
       125: 2q
       126: q
       127: q^3+q^2+2q
       129: q^3+q^2+2q
       131: 2q^2+q
       133: q^3+2q
       134: q^2+q
       135: q^2+2q
       136: q^2+2q
       137: 2q
       138: q^2+q
       139: q^3+2q
       140: q^2+2q
       141: q^3+q^2+2q
       142: q^2+2q
       143: 2q
       144: q^2+q
       145: q^3+2q
       146: q^3+q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: q^3+q^2+2q
       150: q^3+2q^2+2q
       151: q^3+2q^2+2q
       153: q^4+q^3+2q^2+2q
       155: q^3+2q^2+2q
       157: 2q
       158: 2q
       159: q^2+q
       160: q^3+q^2+2q
       161: q^3+q^2+2q
       162: 2q^2+q
       163: q^3+q^2+2q
       164: q^3+q^2+2q
       165: 2q^2+q
       166: q^3+q^2+2q
       167: q^3+q^2+2q
       168: 2q^2+q
       169: q
       172: q
       173: q^3+q
       176: q^3+q
       177: q^2+q
       179: q^3+2q
       181: q^2+2q
       183: q
       184: q
       185: q
       186: q
       187: q^2+2q
       189: q^3+q^2+2q
       191: q
       192: q
       193: q
       194: q
       195: q
       196: q
       197: q^2+2q
       199: q
       200: q
       201: q
       202: q
       203: q
       204: q
       205: q^2+2q
       207: 2q
       209: q^3+q^2+2q
       211: q^3+2q^2+2q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: q
       220: 2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: q^3+2q
       228: q^2+q
       229: q^2+2q
       230: q^2+2q
       231: q
       232: q^3+2q
       233: q^2+q
       234: q^2+2q
       235: q^2+2q
       236: q^2+q
       237: q^3+q^2+2q
       239: q^3+q^2+2q
       241: 2q^2+q
       243: q^3+2q
       244: q^2+2q
       245: q^2+2q
       246: q^3+q^2+2q
       247: 2q
       248: 2q
       249: q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: q^3+q^2+2q
       257: q^3+q^2+2q
       258: 2q^2+q
       259: q
       262: q
       263: q
       266: q
       267: q
       269: q
       271: q
       273: q
       275: q
       278: q
       279: q^3+2q
       281: q^2+q
       287: q
       289: q^2+2q
       291: q^2+q
       293: q
       294: q
       295: q
       296: q
       297: 2q
       299: q
       300: q
       301: q^2+2q
       303: q
       304: q
       305: q^2+2q
       307: q
       308: q
       309: q
       310: q
       311: q^2+2q
       313: q^2+2q
       315: q^2+q
       317: q^3+2q
       319: q
       320: q
       321: q
       322: q
       323: q^2+2q
       325: q^3+q^2+2q
       327: 2q
       329: 2q
       331: q^2+q
       333: q
       334: q
       335: q
       336: q
       337: 2q
       338: 2q
       340: 2q
       342: q^2+q
       344: q
       345: 2q
       346: q
       347: 2q
       348: q^2+q
       349: 2q
       350: q^2+q
       351: 2q
       352: q
       353: 2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q^2+q
       359: 2q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: q
       367: q^3+2q
       368: q^2+q
       369: q^2+2q
       370: q^2+2q
       371: 2q
       372: 2q
       373: q^2+q
       374: 2q
       375: 2q
       376: q^2+q
       381: q
       384: q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q^2+q
       423: q
       425: q
       427: 2q
       433: q^2+q
       435: q^2+2q
       437: q
       438: q
       439: q
       440: q
       441: 2q
       443: q
       444: q
       445: 2q
       451: q^2+q
       453: q
       454: q
       455: q^2+2q
       457: q
       458: q
       459: 2q
       461: q
       462: q
       463: 2q
       465: q^3+2q
       467: q^2+q
       469: q
       471: q
       472: q
       473: q
       474: q
       475: q^2+2q
       477: q^2+2q
       479: 2q
       481: q
       482: q
       483: q
       484: 2q
       485: 2q
       487: 2q
       489: q^2+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 2q
       497: q
       498: q
       499: q
       500: q
       501: 2q
       502: 2q
       504: 2q
       506: q^2+q
       508: q
       509: 2q
       510: q
       511: 2q
       512: q^2+q
       513: 2q
       514: q^2+q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       545: q
       547: q
       553: q
       555: q
       557: q
       559: q
       561: q
       563: q
       565: q
       568: q
       569: q
       570: q
       573: q
       575: q
       577: 2q
       583: q
       585: q
       587: q
       597: q
       599: q
       601: 2q
       605: q^2+q
       609: q
       611: 2q
       613: q
       615: q
       616: q
       617: 2q
       623: q^2+q
       625: q
       627: 2q
       629: q
       631: q
       632: q
       633: 2q
       635: 2q
       637: q
       639: q
       645: q^2+q
       647: q
       648: q
       649: q
       650: q
       651: q^2+2q
       653: 2q
       655: 2q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       693: q
       697: q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       765: q
       768: q
       769: 2q
       777: q
       781: q
       791: q
       797: q
       799: q
       809: q
       811: q
       821: q
       823: q
       833: q
       835: q
       841: q
       849: q^2+q
       851: q
       853: 2q
       855: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       884: q
       889: q
       978: q
       979: q
      1010: q
      1018: q
      1022: q
      1034: q
      1038: q
      1048: q
      1050: q
      1060: q
      1062: q
      1064: q
      1083: q
      1222: 1
      1264: q
      1266: q
      1278: q
      1336: 1
      1446: 1
      1480: 1
      1555: 1
      1633: 1
      1671: 1
      1803: 1

1804:    0: 4q^2+4q
         1: 4q^2+4q
         2: 4q^2+4q
         3: 4q^2+4q
         4: 4q^2+4q
         5: 4q^2+4q
         6: 4q^2+4q
         7: 4q^2+4q
         8: 4q^2+4q
         9: q^4+2q^3+2q^2+q
        10: 4q^2+4q
        11: 4q^2+4q
        12: 4q^2+4q
        13: 4q^2+4q
        14: 4q^2+4q
        15: 4q^2+4q
        16: 4q
        17: 4q
        18: 2q^2+q
        19: 4q^2+4q
        20: 4q^2+4q
        21: 4q^2+4q
        22: 4q^2+4q
        23: 4q^2+4q
        24: 4q^2+4q
        25: 4q^2+4q
        26: 4q^2+4q
        27: 4q^2+4q
        28: 4q
        29: 4q^2+4q
        30: 4q^2+4q
        31: 4q^2+4q
        32: 4q^2+4q
        33: 4q
        34: 4q^2+4q
        35: 4q^2+4q
        36: 4q
        37: 3q^2+2q
        38: q^2+2q
        39: 3q^2+2q
        40: q^2+2q
        41: 3q^2+2q
        42: q^2+2q
        43: 4q^2+4q
        44: 4q^2+4q
        45: 4q^2+4q
        46: 4q
        47: 4q
        48: 2q^2+q
        49: 4q
        50: 4q
        51: 2q^2+q
        52: 4q^2+4q
        53: 4q^2+4q
        54: 4q^2+4q
        55: 4q^2+4q
        56: 4q^2+4q
        57: 4q^2+4q
        58: 2q
        59: 2q
        60: 2q
        61: 2q
        62: 3q^2+2q
        63: q^2+2q
        64: 3q^2+2q
        65: q^2+2q
        66: 2q
        67: 2q
        68: 4q
        69: q
        70: 4q^2+4q
        71: 4q
        72: 4q
        73: 4q
        74: 3q^2+2q
        75: q^2+2q
        76: 3q^2+2q
        77: q^2+2q
        78: 3q^2+2q
        79: q^2+2q
        80: 4q^2+4q
        81: 4q
        82: 4q^2+4q
        83: 4q^2+4q
        84: 4q^2+4q
        85: 4q
        86: 4q^2+4q
        87: 4q^2+4q
        88: 4q
        89: 4q
        90: 2q^2+q
        91: 4q
        92: 4q
        93: 2q^2+q
        94: 4q
        95: 4q
        96: 2q^2+q
        97: 4q
        98: 4q
        99: 2q^2+q
       100: 4q^2+4q
       101: 4q^2+4q
       102: 4q^2+4q
       103: q
       104: q
       105: q
       106: q
       107: 2q
       108: 2q
       109: 2q
       110: 2q
       111: 2q
       112: 2q
       113: 3q^2+2q
       114: q^2+2q
       115: 3q^2+2q
       116: q^2+2q
       117: 2q
       118: 2q
       119: 2q
       120: 2q
       121: 3q^2+2q
       122: q^2+2q
       123: 2q
       124: 2q
       125: 4q
       126: q
       127: 2q
       129: 2q
       131: q^2
       133: 4q
       134: q
       135: 4q
       136: 4q
       137: 4q
       138: q
       139: 4q
       140: 4q
       141: 4q^2+4q
       142: 4q
       143: 4q
       144: q
       145: 4q
       146: 4q^2+4q
       147: 4q
       148: 4q
       149: 4q^2+4q
       150: 4q^2+4q
       151: 3q^2+2q
       152: q^2+2q
       153: 3q^2+2q
       154: q^2+2q
       155: 3q^2+2q
       156: q^2+2q
       157: 4q
       158: 4q
       159: 2q^2+q
       160: 4q
       161: 4q
       162: 2q^2+q
       163: 4q
       164: 4q
       165: 2q^2+q
       166: 4q
       167: 4q
       168: 2q^2+q
       169: q
       170: q
       171: q
       172: q
       173: q
       174: q
       175: q
       176: q
       179: 2q
       181: 2q
       183: 2q
       184: 2q
       185: 2q
       186: 2q
       187: 2q
       188: 2q
       189: 3q^2+2q
       190: q^2+2q
       191: 2q
       192: 2q
       193: 2q
       194: 2q
       195: 2q
       196: 2q
       197: 2q
       198: 2q
       199: 2q
       200: 2q
       201: 2q
       202: 2q
       203: 2q
       204: 2q
       205: 2q
       206: 2q
       207: 2q
       208: 2q
       209: 3q^2+2q
       210: q^2+2q
       211: 3q^2+2q
       212: q^2+2q
       213: 2q
       215: 2q
       217: q^2
       219: q
       220: 4q
       221: q
       222: 4q
       223: q
       224: 4q
       225: q
       226: q
       227: 4q
       228: q
       229: 4q
       230: 4q
       231: q
       232: 4q
       233: q
       234: 4q
       235: 4q
       236: q
       237: 2q
       239: 2q
       241: q^2
       243: 4q
       244: 4q
       245: 4q
       246: 4q^2+4q
       247: 4q
       248: 4q
       249: 2q^2+q
       250: 4q
       251: 4q
       252: 2q^2+q
       253: 4q
       254: 4q
       255: 2q^2+q
       256: 4q
       257: 4q
       258: 2q^2+q
       259: q
       262: q
       263: q
       264: q
       265: q
       266: q
       267: q
       268: q
       269: q
       270: q
       271: q
       272: q
       273: q
       274: q
       275: q
       276: q
       277: q
       278: q
       279: 2q
       289: 2q
       293: 2q
       294: 2q
       295: 2q
       296: 2q
       297: 2q
       298: 2q
       299: 2q
       300: 2q
       301: 2q
       303: 2q
       304: 2q
       305: 2q
       306: 2q
       307: 2q
       308: 2q
       309: 2q
       310: 2q
       311: 2q
       313: 2q
       314: 2q
       317: 2q
       319: 2q
       320: 2q
       321: 2q
       322: 2q
       323: 2q
       324: 2q
       325: 3q^2+2q
       326: q^2+2q
       327: 2q
       329: 2q
       331: q^2
       333: q
       334: q
       335: q
       336: q
       337: 4q
       338: 2q
       340: 2q
       342: q^2
       344: q
       345: 4q
       346: q
       347: 4q
       348: q
       349: 4q
       350: q
       351: 4q
       352: q
       353: 4q
       354: q
       355: 4q
       356: q
       357: 4q
       358: q
       359: 4q
       360: 2q
       362: 2q
       364: q^2
       366: q
       367: 4q
       368: q
       369: 4q
       370: 4q
       371: 4q
       372: 4q
       373: 2q^2+q
       374: 4q
       375: 4q
       376: 2q^2+q
       381: q
       384: q
       385: q
       386: q
       387: q
       388: q
       389: q
       391: q
       393: q
       394: q
       395: q
       396: q
       397: q
       399: q
       401: q
       402: q
       403: q
       404: q
       405: q
       406: q
       407: q
       408: q
       409: 2q
       415: 2q
       427: 2q
       435: 2q
       437: 2q
       438: 2q
       439: 2q
       440: 2q
       441: 2q
       442: 2q
       443: 2q
       444: 2q
       445: 2q
       453: 2q
       454: 2q
       455: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: 2q
       462: 2q
       463: 2q
       465: 2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       477: 2q
       479: 2q
       480: 2q
       481: q
       482: q
       483: q
       484: 4q
       485: 2q
       487: 2q
       489: q^2
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 4q
       497: q
       498: q
       499: q
       500: q
       501: 4q
       502: 2q
       504: 2q
       506: q^2
       508: q
       509: 4q
       510: q
       511: 4q
       512: q
       513: 4q
       514: q
       515: 1
       516: 1
       517: 1
       518: 4q
       519: 4q
       520: 2q^2+q
       525: q
       528: q
       537: q
       539: q
       541: q
       542: q
       543: q
       544: q
       545: q
       547: q
       553: q
       555: q
       557: q
       558: q
       559: q
       560: q
       561: q
       563: q
       565: q
       566: q
       567: q
       568: q
       569: q
       570: q
       573: q
       574: q
       575: q
       576: q
       577: 2q
       601: 2q
       611: 2q
       615: 2q
       616: 2q
       617: 2q
       627: 2q
       631: 2q
       632: 2q
       633: 2q
       635: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       651: 2q
       653: 2q
       654: 2q
       655: 2q
       656: 2q
       658: 1
       660: 1
       662: 1
       664: 1
       665: q
       666: 2q
       668: 2q
       670: q^2
       672: 4q
       673: q
       674: 1
       675: q
       676: q
       677: q
       678: 4q
       679: q
       680: 1
       681: q
       682: q
       683: q
       684: 4q
       685: q
       686: q
       687: q
       688: q
       689: q
       690: 1
       691: 1
       692: 1
       693: q
       697: q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       763: q
       764: q
       765: q
       766: q
       767: q
       768: q
       769: 2q
       779: 1
       789: 2q
       795: 1
       813: 2q
       815: 2q
       816: 2q
       819: 1
       837: 2q
       839: 2q
       840: 2q
       844: 1
       853: 2q
       857: 2q
       858: 2q
       859: 1
       861: 1
       863: 1
       867: 1
       868: q
       869: 1
       870: 1
       871: q
       872: q
       873: 1
       874: 1
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       881: 1
       882: 1
       883: 1
       884: q
       889: q
       932: q
       934: q
       956: q
       958: q
       971: 1
       978: q
       979: q
       982: 2q
       988: q
       989: q
       990: q
       991: q
       996: 1
      1013: 1
      1014: 1
      1020: 1
      1030: 1
      1036: 1
      1047: 1
      1066: 1
      1068: 1
      1070: 1
      1073: 1
      1075: 1
      1077: 1
      1078: q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1098: q
      1102: q
      1141: 1
      1191: 1
      1212: 1
      1225: 1
      1226: 1
      1236: 1
      1244: 1
      1252: 1
      1263: 1
      1274: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1289: q
      1337: 1
      1407: 1
      1433: 1
      1445: 1
      1452: 1
      1458: 1
      1472: 1
      1483: 1
      1488: 1
      1556: 1
      1634: 1
      1667: 1
      1670: 1
      1804: 1

1805:    0: q+2
         1: q+2
         2: q+2
         3: q+2
         4: q+2
         5: q+2
         6: q+2
         7: q+2
         8: q+2
         9: q^2+q+1
        10: q+2
        11: q+2
        12: q+2
        13: q+2
        14: q+2
        15: q+2
        16: 2
        17: 2
        18: q+1
        19: q+2
        20: q+2
        21: q+2
        22: q+2
        23: q+2
        24: q+2
        25: q+2
        26: q+2
        27: q+2
        28: 2
        29: q+2
        30: q+2
        31: q+2
        32: q+2
        33: 2
        34: q+2
        35: q+2
        36: 2
        38: q+2
        40: q+2
        42: q+2
        43: q+2
        44: q+2
        45: q+2
        46: 2
        47: 2
        48: q+1
        49: 2
        50: 2
        51: q+1
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: 1
        59: 1
        60: 1
        61: 1
        63: q+2
        65: q+2
        67: 2
        68: 2
        69: 1
        70: q+2
        71: 2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: q+2
        81: 2
        82: q+2
        83: q+2
        84: q+2
        85: 2
        86: q+2
        87: q+2
        88: 2
        89: 2
        90: q+1
        91: 2
        92: 2
        93: q+1
        94: 2
        95: 2
        96: q+1
        97: 2
        98: 2
        99: q+1
       100: q+2
       101: q+2
       102: q+2
       104: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: 1
       118: 1
       119: 1
       120: 1
       122: q+2
       124: 2
       125: 2
       126: 1
       128: 2
       130: 2
       132: q+1
       133: 2
       134: 1
       135: 2
       136: 2
       137: 2
       138: 1
       139: 2
       140: 2
       141: q+2
       142: 2
       143: 2
       144: 1
       145: 2
       146: q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: 2
       158: 2
       159: q+1
       160: 2
       161: 2
       162: q+1
       163: 2
       164: 2
       165: q+1
       166: 2
       167: 2
       168: q+1
       170: 1
       171: 1
       174: 1
       175: 1
       178: 1
       180: 2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2
       210: q+2
       212: q+2
       214: 2
       216: 2
       218: q+1
       219: 1
       220: 2
       221: 1
       222: 2
       223: 1
       224: 2
       225: 1
       226: 1
       227: 2
       228: 1
       229: 2
       230: 2
       231: 1
       232: 2
       233: 1
       234: 2
       235: 2
       236: 1
       238: 2
       240: 2
       242: q+1
       243: 2
       244: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: 2
       251: 2
       252: q+1
       253: 2
       254: 2
       255: q+1
       256: 2
       257: 2
       258: q+1
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: 1
       277: 1
       280: 2
       282: 1
       288: 1
       290: 2
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: 1
       318: 2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: q+2
       328: 2
       330: 2
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: 1
       345: 2
       346: 1
       347: 2
       348: 1
       349: 2
       350: 1
       351: 2
       352: 1
       353: 2
       354: 1
       355: 2
       356: 1
       357: 2
       358: 1
       359: 2
       361: 2
       363: 2
       365: q+1
       366: 1
       367: 2
       368: 1
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: 2
       375: 2
       376: q+1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 2
       412: 1
       414: 1
       416: 2
       418: 1
       424: 1
       426: 1
       428: 2
       434: 1
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       452: 1
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: 2
       468: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 1
       482: 1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 2
       497: 1
       498: 1
       499: 1
       500: 1
       501: 2
       503: 2
       505: 2
       507: q+1
       508: 1
       509: 2
       510: 1
       511: 2
       512: 1
       513: 2
       514: 1
       515: 1
       516: 1
       517: 1
       518: 2
       519: 2
       520: q+1
       526: 1
       527: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: 1
       586: 1
       588: 1
       598: 1
       600: 1
       602: 2
       606: 1
       610: 1
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       624: 1
       626: 1
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: 2
       638: 1
       640: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 2
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 2
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       699: 1
       700: 1
       730: 1
       732: 1
       734: 1
       736: 1
       746: 1
       748: 1
       750: 1
       752: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       778: 1
       780: 1
       782: 1
       784: 1
       790: 2
       792: 1
       796: 1
       798: 1
       800: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       820: 1
       822: 1
       824: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: 1
       844: 1
       850: 1
       852: 1
       854: 2
       856: 1
       858: 2
       860: 1
       862: 1
       864: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       890: 1
       891: 1
       933: 1
       935: 1
       957: 1
       959: 1
       972: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       997: 1
      1003: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1031: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1047: 1
      1049: 1
      1051: 1
      1061: 1
      1063: 1
      1065: 1
      1067: 1
      1069: 1
      1071: 1
      1073: 1
      1075: 1
      1077: 1
      1078: 1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1104: 1
      1105: 1
      1142: 1
      1192: 1
      1213: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1237: 1
      1239: 1
      1245: 1
      1253: 1
      1257: 1
      1263: 1
      1265: 1
      1267: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1289: 1
      1338: 1
      1408: 1
      1434: 1
      1445: 1
      1447: 1
      1453: 1
      1459: 1
      1471: 1
      1473: 1
      1475: 1
      1481: 1
      1483: 1
      1488: 1
      1557: 1
      1635: 1
      1668: 1
      1670: 1
      1672: 1
      1805: 1

1806:    0: 2q^3+2q^2+2q
         1: 2q^4+2q^3+2q^2+2q
         2: 2q^3+2q^2+2q
         3: 2q^4+2q^3+2q^2+2q
         4: q^5+q^4+q^3+2q^2+2q
         5: 2q^3+2q^2+2q
         6: q^5+2q^4+q^3+2q^2+2q
         7: q^5+q^4+q^3+2q^2+2q
         8: 2q^3+2q^2+2q
         9: q^6+q^5+q^3+2q^2+q
        10: 2q^3+q^2+2q
        11: 2q^3+q^2+2q
        12: q^4+q^3+q^2+2q
        13: 2q^3+2q^2+2q
        14: q^5+q^4+q^3+2q^2+2q
        15: 2q^3+2q^2+2q
        16: 2q^3+q^2+2q
        17: 2q^3+q^2+2q
        18: q^5+2q^2+q
        19: q^3+2q^2+2q
        20: q^4+q^3+2q^2+2q
        21: q^3+2q^2+2q
        22: 2q^3+2q^2+2q
        23: 2q^4+2q^3+2q^2+2q
        24: 2q^3+2q^2+2q
        25: 2q^3+2q^2+2q
        26: 2q^4+2q^3+2q^2+2q
        27: 2q^3+2q^2+2q
        28: 2q^3+2q
        29: q^3+q^2+2q
        30: q^3+2q^2+2q
        31: 2q^3+q^2+2q
        32: 2q^3+2q^2+2q
        33: 2q^3+q^2+2q
        34: 2q^3+q^2+2q
        35: 2q^3+2q^2+2q
        36: 2q^3+q^2+2q
        38: 2q^3+2q^2+2q
        40: 2q^4+2q^3+2q^2+2q
        42: 2q^3+2q^2+2q
        43: 2q^3+q^2+2q
        44: q^4+q^3+q^2+2q
        45: 2q^3+q^2+2q
        46: 2q^3+q^2+2q
        47: 2q^3+q^2+2q
        48: q^5+2q^2+q
        49: q^3+q^2+2q
        50: q^3+q^2+2q
        51: 2q^2+q
        52: q^3+2q^2+2q
        53: q^4+q^3+2q^2+2q
        54: q^3+2q^2+2q
        55: q^3+2q^2+2q
        56: q^4+q^3+2q^2+2q
        57: q^3+2q^2+2q
        58: q^3+q
        59: q^3+q
        60: q^3+q
        61: q^3+q
        63: 2q^3+q^2+2q
        65: 2q^3+2q^2+2q
        67: 2q^3+q^2+2q
        68: 2q^3+2q
        69: q^2+q
        70: q^3+q^2+2q
        71: q^3+2q
        72: q^2+2q
        73: q^2+2q
        75: q^3+2q^2+2q
        77: q^4+q^3+2q^2+2q
        79: q^3+2q^2+2q
        80: 2q^3+q^2+2q
        81: 2q^3+q^2+2q
        82: q^3+q^2+2q
        83: q^3+2q^2+2q
        84: 2q^3+q^2+2q
        85: 2q^3+q^2+2q
        86: q^3+q^2+2q
        87: q^3+2q^2+2q
        88: 2q
        89: 2q
        90: q^2+q
        91: q^3+q^2+2q
        92: q^3+q^2+2q
        93: 2q^2+q
        94: q^3+q^2+2q
        95: q^3+q^2+2q
        96: 2q^2+q
        97: q^3+q^2+2q
        98: q^3+q^2+2q
        99: 2q^2+q
       100: q^3+2q^2+2q
       101: q^4+q^3+2q^2+2q
       102: q^3+2q^2+2q
       104: q^3+q
       105: q^3+q
       107: q
       108: q
       109: q
       110: q
       112: q^2+2q
       114: q^3+q^2+2q
       116: q^3+2q^2+2q
       117: q^3+q
       118: q^3+q
       119: q^3+q
       120: q^3+q
       122: 2q^3+q^2+2q
       124: 2q^3+q^2+2q
       125: 2q
       126: q
       128: q^3+q^2+2q
       130: q^3+q^2+2q
       132: 2q^2+q
       133: q^3+2q
       134: q^2+q
       135: q^2+2q
       136: q^2+2q
       137: 2q
       138: q^2+q
       139: q^3+2q
       140: q^2+2q
       141: q^3+q^2+2q
       142: q^2+2q
       143: 2q
       144: q^2+q
       145: q^3+2q
       146: q^3+q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: q^3+q^2+2q
       150: q^3+2q^2+2q
       152: q^3+2q^2+2q
       154: q^4+q^3+2q^2+2q
       156: q^3+2q^2+2q
       157: 2q
       158: 2q
       159: q^2+q
       160: q^3+q^2+2q
       161: q^3+q^2+2q
       162: 2q^2+q
       163: q^3+q^2+2q
       164: q^3+q^2+2q
       165: 2q^2+q
       166: q^3+q^2+2q
       167: q^3+q^2+2q
       168: 2q^2+q
       170: q
       171: q
       174: q^3+q
       175: q^3+q
       178: q^2+q
       180: q^3+2q
       182: q^2+2q
       183: q
       184: q
       185: q
       186: q
       188: q^2+2q
       190: q^3+q^2+2q
       191: q
       192: q
       193: q
       194: q
       195: q
       196: q
       198: q^2+2q
       199: q
       200: q
       201: q
       202: q
       203: q
       204: q
       206: q^2+2q
       208: 2q
       210: q^3+q^2+2q
       212: q^3+2q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: q
       220: 2q
       221: q
       222: 2q
       223: q^2+q
       224: 2q
       225: q^2+q
       226: q
       227: q^3+2q
       228: q^2+q
       229: q^2+2q
       230: q^2+2q
       231: q
       232: q^3+2q
       233: q^2+q
       234: q^2+2q
       235: q^2+2q
       236: q^2+q
       238: q^3+q^2+2q
       240: q^3+q^2+2q
       242: 2q^2+q
       243: q^3+2q
       244: q^2+2q
       245: q^2+2q
       246: q^3+q^2+2q
       247: 2q
       248: 2q
       249: q^2+q
       250: 2q
       251: 2q
       252: q^2+q
       253: 2q
       254: 2q
       255: q^2+q
       256: q^3+q^2+2q
       257: q^3+q^2+2q
       258: 2q^2+q
       260: q
       261: q
       264: q
       265: q
       268: q
       270: q
       272: q
       274: q
       276: q
       277: q
       280: q^3+2q
       282: q^2+q
       288: q
       290: q^2+2q
       292: q^2+q
       293: q
       294: q
       295: q
       296: q
       298: 2q
       299: q
       300: q
       302: q^2+2q
       303: q
       304: q
       306: q^2+2q
       307: q
       308: q
       309: q
       310: q
       312: q^2+2q
       314: q^2+2q
       316: q^2+q
       318: q^3+2q
       319: q
       320: q
       321: q
       322: q
       324: q^2+2q
       326: q^3+q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: q
       334: q
       335: q
       336: q
       337: 2q
       339: 2q
       341: 2q
       343: q^2+q
       344: q
       345: 2q
       346: q
       347: 2q
       348: q^2+q
       349: 2q
       350: q^2+q
       351: 2q
       352: q
       353: 2q
       354: q
       355: 2q
       356: q^2+q
       357: 2q
       358: q^2+q
       359: 2q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: q
       367: q^3+2q
       368: q^2+q
       369: q^2+2q
       370: q^2+2q
       371: 2q
       372: 2q
       373: q^2+q
       374: 2q
       375: 2q
       376: q^2+q
       382: q
       383: q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q^2+q
       424: q
       426: q
       428: 2q
       434: q^2+q
       436: q^2+2q
       437: q
       438: q
       439: q
       440: q
       442: 2q
       443: q
       444: q
       446: 2q
       452: q^2+q
       453: q
       454: q
       456: q^2+2q
       457: q
       458: q
       460: 2q
       461: q
       462: q
       464: 2q
       466: q^3+2q
       468: q^2+q
       470: q
       471: q
       472: q
       473: q
       474: q
       476: q^2+2q
       478: q^2+2q
       480: 2q
       481: q
       482: q
       483: q
       484: 2q
       486: 2q
       488: 2q
       490: q^2+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: 2q
       497: q
       498: q
       499: q
       500: q
       501: 2q
       503: 2q
       505: 2q
       507: q^2+q
       508: q
       509: 2q
       510: q
       511: 2q
       512: q^2+q
       513: 2q
       514: q^2+q
       526: q
       527: q
       538: q
       540: q
       542: q
       544: q
       546: q
       548: q
       554: q
       556: q
       558: q
       560: q
       562: q
       564: q
       566: q
       567: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       584: q
       586: q
       588: q
       598: q
       600: q
       602: 2q
       606: q^2+q
       610: q
       612: 2q
       614: q
       615: q
       616: q
       618: 2q
       624: q^2+q
       626: q
       628: 2q
       630: q
       631: q
       632: q
       634: 2q
       636: 2q
       638: q
       640: q
       646: q^2+q
       647: q
       648: q
       649: q
       650: q
       652: q^2+2q
       654: 2q
       656: 2q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       699: q
       700: q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       763: q
       764: q
       766: q
       767: q
       773: 2q
       778: q
       782: q
       792: q
       798: q
       800: q
       810: q
       812: q
       822: q
       824: q
       834: q
       836: q
       842: q
       850: q^2+q
       852: q
       854: 2q
       856: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       890: q
       891: q
       980: q
       981: q
      1011: q
      1019: q
      1023: q
      1035: q
      1039: q
      1049: q
      1051: q
      1061: q
      1063: q
      1065: q
      1083: q
      1223: 1
      1265: q
      1267: q
      1279: q
      1339: 1
      1447: 1
      1481: 1
      1558: 1
      1636: 1
      1672: 1
      1806: 1

1807:    0: 3q^3+2q^2+1
         1: q^4+3q^3+2q^2+1
         2: 3q^3+2q^2+1
         3: q^4+3q^3+2q^2+1
         4: 3q^3+2q^2+1
         5: 3q^3+2q^2+1
         6: q^4+3q^3+2q^2+1
         7: 3q^3+2q^2+1
         8: 3q^3+2q^2+1
         9: 2q^5+2q^4+2q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: 2q^3+q^2+1
        13: 3q^3+2q^2+1
        14: 3q^3+2q^2+1
        15: 3q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: 2q^3+q^2+1
        19: 3q^3+2q^2+1
        20: q^4+3q^3+2q^2+1
        21: 3q^3+2q^2+1
        22: 3q^3+2q^2+1
        23: q^4+3q^3+2q^2+1
        24: 3q^3+2q^2+1
        25: 3q^3+2q^2+1
        26: q^4+3q^3+2q^2+1
        27: 3q^3+2q^2+1
        28: q^2+1
        29: 2q^3+q^2+1
        30: 3q^3+2q^2+1
        31: 2q^3+q^2+1
        32: 3q^3+2q^2+1
        33: 2q^2+1
        34: 2q^3+q^2+1
        35: 3q^3+2q^2+1
        36: 2q^2+1
        37: 2q^3+q^2+1
        38: q^3+q^2
        39: 2q^3+q^2+1
        40: q^4+q^3+q^2
        41: 2q^3+q^2+1
        42: q^3+q^2
        43: 2q^3+q^2+1
        44: 2q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: 2q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: 2q^3+q^2+1
        52: 3q^3+2q^2+1
        53: q^4+3q^3+2q^2+1
        54: 3q^3+2q^2+1
        55: 3q^3+2q^2+1
        56: q^4+3q^3+2q^2+1
        57: 3q^3+2q^2+1
        58: q^2+1
        60: q^2+1
        62: q^3+q^2+1
        63: q^3
        64: 2q^3+q^2+1
        65: q^3+q^2
        66: q^2+1
        67: q^2
        68: q^2+1
        69: q^2+1
        70: 2q^3+q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: 2q^3+q^2+1
        75: q^3+q^2
        76: 2q^3+q^2+1
        77: q^4+q^3+q^2
        78: 2q^3+q^2+1
        79: q^3+q^2
        80: 2q^3+q^2+1
        81: 2q^2+1
        82: 2q^3+q^2+1
        83: 3q^3+2q^2+1
        84: 2q^3+q^2+1
        85: 2q^2+1
        86: 2q^3+q^2+1
        87: 3q^3+2q^2+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+1
        92: 2q^2+1
        93: 2q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: 2q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: 2q^3+q^2+1
       100: 3q^3+2q^2+1
       101: q^4+3q^3+2q^2+1
       102: 3q^3+2q^2+1
       103: q^2+1
       107: q^2+1
       109: q^2+1
       111: q^2+1
       112: q^2
       113: q^3+q^2+1
       114: q^3
       115: 2q^3+q^2+1
       116: q^3+q^2
       117: q^2+1
       119: q^2+1
       121: q^3+q^2+1
       122: q^3
       123: q^2+1
       124: q^2
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: 2q^3+q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: 2q^3+q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: 2q^3+q^2+1
       150: 3q^3+2q^2+1
       151: 2q^3+q^2+1
       152: q^3+q^2
       153: 2q^3+q^2+1
       154: q^4+q^3+q^2
       155: 2q^3+q^2+1
       156: q^3+q^2
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+1
       161: 2q^2+1
       162: 2q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: 2q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: 2q^3+q^2+1
       169: q^2+1
       173: q^2+1
       177: 1
       179: 1
       181: 1
       183: q^2+1
       185: q^2+1
       187: q^2+1
       188: q^2
       189: q^3+q^2+1
       190: q^3
       191: 1
       193: q^2+1
       195: q^2+1
       197: q^2+1
       198: q^2
       199: 1
       201: q^2+1
       203: q^2+1
       205: q^2+1
       206: q^2
       207: 1
       209: q^3+q^2+1
       210: q^3
       211: 2q^3+q^2+1
       212: q^3+q^2
       213: 1
       215: 1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       237: 1
       239: 1
       241: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: 2q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 2q^2+1
       257: 2q^2+1
       258: 2q^3+q^2+1
       259: 1
       263: q^2+1
       267: q^2+1
       271: q^2+1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: q^2+1
       301: 1
       303: q^2+1
       305: q^2+1
       306: q^2
       307: q^2+1
       309: q^2+1
       311: 1
       313: q^2+1
       314: q^2
       315: 1
       317: 1
       319: q^2+1
       321: q^2+1
       323: q^2+1
       324: q^2
       325: q^3+q^2+1
       326: q^3
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       360: 1
       362: 1
       364: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: 1
       375: 1
       376: q^3+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: q^2+1
       397: 1
       401: q^2+1
       405: q^2+1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: q^2+1
       445: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: q^2+1
       463: 1
       465: 1
       467: 1
       469: 1
       471: q^2+1
       473: q^2+1
       475: q^2+1
       476: q^2
       477: 1
       479: q^2+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: q^2+1
       485: 1
       487: 1
       489: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       518: 1
       519: 1
       520: q^3+1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: q^2+1
       569: 1
       573: q^2+1
       577: 1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: q^2+1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: q^2+1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: q^2+1
       656: q^2
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: q^2+1
       769: 1
       781: 1
       785: 1
       787: 1
       791: 1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       815: 1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       839: 1
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       884: 1
       900: 1
       904: 1
       908: 1
       920: 1
       924: 1
       928: 1
       944: 1
       948: 1
       952: 1
       960: 1
       974: 1
       988: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1022: 1
      1026: 1
      1028: 1
      1038: 1
      1040: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1126: 1
      1134: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1202: 1
      1206: 1
      1220: 1
      1240: 1
      1242: 1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1270: 1
      1276: 1
      1278: 1
      1289: 1
      1330: 1
      1360: 1
      1368: 1
      1392: 1
      1400: 1
      1418: 1
      1422: 1
      1426: 1
      1474: 1
      1476: 1
      1478: 1
      1579: 1
      1599: 1
      1619: 1
      1627: 1
      1807: 1

1808:    0: 3q^3+2q^2+1
         1: q^4+3q^3+2q^2+1
         2: 3q^3+2q^2+1
         3: q^4+3q^3+2q^2+1
         4: 3q^3+2q^2+1
         5: 3q^3+2q^2+1
         6: q^4+3q^3+2q^2+1
         7: 3q^3+2q^2+1
         8: 3q^3+2q^2+1
         9: 2q^5+2q^4+2q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: 2q^3+q^2+1
        13: 3q^3+2q^2+1
        14: 3q^3+2q^2+1
        15: 3q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: 2q^3+q^2+1
        19: 3q^3+2q^2+1
        20: q^4+3q^3+2q^2+1
        21: 3q^3+2q^2+1
        22: 3q^3+2q^2+1
        23: q^4+3q^3+2q^2+1
        24: 3q^3+2q^2+1
        25: 3q^3+2q^2+1
        26: q^4+3q^3+2q^2+1
        27: 3q^3+2q^2+1
        28: q^2+1
        29: 2q^3+q^2+1
        30: 3q^3+2q^2+1
        31: 2q^3+q^2+1
        32: 3q^3+2q^2+1
        33: 2q^2+1
        34: 2q^3+q^2+1
        35: 3q^3+2q^2+1
        36: 2q^2+1
        37: 2q^3+q^2+1
        38: q^3+q^2
        39: 2q^3+q^2+1
        40: q^4+q^3+q^2
        41: 2q^3+q^2+1
        42: q^3+q^2
        43: 2q^3+q^2+1
        44: 2q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: 2q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: 2q^3+q^2+1
        52: 3q^3+2q^2+1
        53: q^4+3q^3+2q^2+1
        54: 3q^3+2q^2+1
        55: 3q^3+2q^2+1
        56: q^4+3q^3+2q^2+1
        57: 3q^3+2q^2+1
        59: q^2+1
        61: q^2+1
        62: q^3+q^2+1
        63: q^3
        64: 2q^3+q^2+1
        65: q^3+q^2
        66: q^2+1
        67: q^2
        68: q^2+1
        69: q^2+1
        70: 2q^3+q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: 2q^3+q^2+1
        75: q^3+q^2
        76: 2q^3+q^2+1
        77: q^4+q^3+q^2
        78: 2q^3+q^2+1
        79: q^3+q^2
        80: 2q^3+q^2+1
        81: 2q^2+1
        82: 2q^3+q^2+1
        83: 3q^3+2q^2+1
        84: 2q^3+q^2+1
        85: 2q^2+1
        86: 2q^3+q^2+1
        87: 3q^3+2q^2+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+1
        92: 2q^2+1
        93: 2q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: 2q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: 2q^3+q^2+1
       100: 3q^3+2q^2+1
       101: q^4+3q^3+2q^2+1
       102: 3q^3+2q^2+1
       106: q^2+1
       108: q^2+1
       110: q^2+1
       111: q^2+1
       112: q^2
       113: q^3+q^2+1
       114: q^3
       115: 2q^3+q^2+1
       116: q^3+q^2
       118: q^2+1
       120: q^2+1
       121: q^3+q^2+1
       122: q^3
       123: q^2+1
       124: q^2
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: 2q^3+q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: 2q^3+q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: 2q^3+q^2+1
       150: 3q^3+2q^2+1
       151: 2q^3+q^2+1
       152: q^3+q^2
       153: 2q^3+q^2+1
       154: q^4+q^3+q^2
       155: 2q^3+q^2+1
       156: q^3+q^2
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+1
       161: 2q^2+1
       162: 2q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: 2q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: 2q^3+q^2+1
       172: q^2+1
       176: q^2+1
       177: 1
       179: 1
       181: 1
       184: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2
       189: q^3+q^2+1
       190: q^3
       192: 1
       194: q^2+1
       196: q^2+1
       197: q^2+1
       198: q^2
       200: 1
       202: q^2+1
       204: q^2+1
       205: q^2+1
       206: q^2
       207: 1
       209: q^3+q^2+1
       210: q^3
       211: 2q^3+q^2+1
       212: q^3+q^2
       213: 1
       215: 1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       237: 1
       239: 1
       241: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: 2q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 2q^2+1
       257: 2q^2+1
       258: 2q^3+q^2+1
       262: 1
       266: q^2+1
       269: q^2+1
       273: q^2+1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: q^2+1
       301: 1
       304: q^2+1
       305: q^2+1
       306: q^2
       308: q^2+1
       310: q^2+1
       311: 1
       313: q^2+1
       314: q^2
       315: 1
       317: 1
       320: q^2+1
       322: q^2+1
       323: q^2+1
       324: q^2
       325: q^3+q^2+1
       326: q^3
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       360: 1
       362: 1
       364: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: 1
       375: 1
       376: q^3+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: q^2+1
       399: 1
       404: q^2+1
       406: q^2+1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: q^2+1
       445: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: q^2+1
       463: 1
       465: 1
       467: 1
       469: 1
       472: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2
       477: 1
       479: q^2+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: q^2+1
       485: 1
       487: 1
       489: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       518: 1
       519: 1
       520: q^3+1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: q^2+1
       570: 1
       575: q^2+1
       577: 1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       616: q^2+1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: q^2+1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: q^2+1
       656: q^2
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: q^2+1
       769: 1
       781: 1
       786: 1
       788: 1
       791: 1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       816: 1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       840: 1
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       889: 1
       902: 1
       906: 1
       911: 1
       922: 1
       927: 1
       930: 1
       946: 1
       950: 1
       955: 1
       961: 1
       975: 1
       991: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1022: 1
      1027: 1
      1029: 1
      1038: 1
      1041: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1127: 1
      1135: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1204: 1
      1208: 1
      1220: 1
      1241: 1
      1243: 1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1271: 1
      1276: 1
      1278: 1
      1289: 1
      1331: 1
      1361: 1
      1369: 1
      1393: 1
      1401: 1
      1420: 1
      1424: 1
      1429: 1
      1474: 1
      1477: 1
      1479: 1
      1580: 1
      1600: 1
      1622: 1
      1630: 1
      1808: 1

1809:    0: 3q^3+2q^2+1
         1: q^4+3q^3+2q^2+1
         2: 3q^3+2q^2+1
         3: q^4+3q^3+2q^2+1
         4: 3q^3+2q^2+1
         5: 3q^3+2q^2+1
         6: q^4+3q^3+2q^2+1
         7: 3q^3+2q^2+1
         8: 3q^3+2q^2+1
         9: 2q^5+2q^4+2q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: 2q^3+q^2+1
        13: 3q^3+2q^2+1
        14: 3q^3+2q^2+1
        15: 3q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: 2q^3+q^2+1
        19: 3q^3+2q^2+1
        20: q^4+3q^3+2q^2+1
        21: 3q^3+2q^2+1
        22: 3q^3+2q^2+1
        23: q^4+3q^3+2q^2+1
        24: 3q^3+2q^2+1
        25: 3q^3+2q^2+1
        26: q^4+3q^3+2q^2+1
        27: 3q^3+2q^2+1
        28: q^2+1
        29: 2q^3+q^2+1
        30: 3q^3+2q^2+1
        31: 2q^3+q^2+1
        32: 3q^3+2q^2+1
        33: 2q^2+1
        34: 2q^3+q^2+1
        35: 3q^3+2q^2+1
        36: 2q^2+1
        37: q^3+q^2
        38: 2q^3+q^2+1
        39: q^4+q^3+q^2
        40: 2q^3+q^2+1
        41: q^3+q^2
        42: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: 2q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: 2q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: 2q^3+q^2+1
        52: 3q^3+2q^2+1
        53: q^4+3q^3+2q^2+1
        54: 3q^3+2q^2+1
        55: 3q^3+2q^2+1
        56: q^4+3q^3+2q^2+1
        57: 3q^3+2q^2+1
        59: q^2+1
        60: q^2+1
        62: q^3
        63: q^3+q^2+1
        64: q^3+q^2
        65: 2q^3+q^2+1
        66: q^2
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: 2q^3+q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^3+q^2
        75: 2q^3+q^2+1
        76: q^4+q^3+q^2
        77: 2q^3+q^2+1
        78: q^3+q^2
        79: 2q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^2+1
        82: 2q^3+q^2+1
        83: 3q^3+2q^2+1
        84: 2q^3+q^2+1
        85: 2q^2+1
        86: 2q^3+q^2+1
        87: 3q^3+2q^2+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+1
        92: 2q^2+1
        93: 2q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: 2q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: 2q^3+q^2+1
       100: 3q^3+2q^2+1
       101: q^4+3q^3+2q^2+1
       102: 3q^3+2q^2+1
       104: q^2+1
       107: q^2+1
       110: q^2+1
       111: q^2
       112: q^2+1
       113: q^3
       114: q^3+q^2+1
       115: q^3+q^2
       116: 2q^3+q^2+1
       118: q^2+1
       119: q^2+1
       121: q^3
       122: q^3+q^2+1
       123: q^2
       124: q^2+1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: 2q^3+q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: 2q^3+q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: 2q^3+q^2+1
       150: 3q^3+2q^2+1
       151: q^3+q^2
       152: 2q^3+q^2+1
       153: q^4+q^3+q^2
       154: 2q^3+q^2+1
       155: q^3+q^2
       156: 2q^3+q^2+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+1
       161: 2q^2+1
       162: 2q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: 2q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: 2q^3+q^2+1
       170: q^2+1
       174: q^2+1
       178: 1
       180: 1
       182: 1
       183: q^2+1
       186: q^2+1
       187: q^2
       188: q^2+1
       189: q^3
       190: q^3+q^2+1
       192: 1
       193: q^2+1
       196: q^2+1
       197: q^2
       198: q^2+1
       199: 1
       201: q^2+1
       204: q^2+1
       205: q^2
       206: q^2+1
       208: 1
       209: q^3
       210: q^3+q^2+1
       211: q^3+q^2
       212: 2q^3+q^2+1
       214: 1
       216: 1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       238: 1
       240: 1
       242: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: 2q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 2q^2+1
       257: 2q^2+1
       258: 2q^3+q^2+1
       260: 1
       264: q^2+1
       268: q^2+1
       274: q^2+1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: q^2+1
       302: 1
       304: q^2+1
       305: q^2
       306: q^2+1
       307: q^2+1
       310: q^2+1
       312: 1
       313: q^2
       314: q^2+1
       316: 1
       318: 1
       319: q^2+1
       322: q^2+1
       323: q^2
       324: q^2+1
       325: q^3
       326: q^3+q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       361: 1
       363: 1
       365: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: 1
       375: 1
       376: q^3+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: q^2+1
       400: 1
       403: q^2+1
       407: q^2+1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q^2+1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q^2+1
       464: 1
       466: 1
       468: 1
       470: 1
       471: q^2+1
       474: q^2+1
       475: q^2
       476: q^2+1
       478: 1
       479: q^2
       480: q^2+1
       481: 1
       482: 1
       483: 1
       484: q^2+1
       486: 1
       488: 1
       490: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       518: 1
       519: 1
       520: q^3+1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: q^2+1
       571: 1
       574: q^2+1
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: q^2+1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       632: q^2+1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       655: q^2
       656: q^2+1
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: q^2+1
       773: 1
       782: 1
       785: 1
       788: 1
       792: 1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: 1
       812: 1
       815: 1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: 1
       836: 1
       840: 1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       890: 1
       903: 1
       905: 1
       909: 1
       921: 1
       926: 1
       929: 1
       947: 1
       951: 1
       953: 1
       962: 1
       976: 1
       989: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1023: 1
      1026: 1
      1029: 1
      1039: 1
      1040: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1128: 1
      1136: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1205: 1
      1207: 1
      1221: 1
      1240: 1
      1243: 1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1271: 1
      1277: 1
      1279: 1
      1289: 1
      1332: 1
      1363: 1
      1371: 1
      1394: 1
      1402: 1
      1421: 1
      1423: 1
      1427: 1
      1475: 1
      1476: 1
      1479: 1
      1582: 1
      1601: 1
      1620: 1
      1628: 1
      1809: 1

1810:    0: 3q^3+2q^2+1
         1: q^4+3q^3+2q^2+1
         2: 3q^3+2q^2+1
         3: q^4+3q^3+2q^2+1
         4: 3q^3+2q^2+1
         5: 3q^3+2q^2+1
         6: q^4+3q^3+2q^2+1
         7: 3q^3+2q^2+1
         8: 3q^3+2q^2+1
         9: 2q^5+2q^4+2q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: 2q^3+q^2+1
        13: 3q^3+2q^2+1
        14: 3q^3+2q^2+1
        15: 3q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: 2q^3+q^2+1
        19: 3q^3+2q^2+1
        20: q^4+3q^3+2q^2+1
        21: 3q^3+2q^2+1
        22: 3q^3+2q^2+1
        23: q^4+3q^3+2q^2+1
        24: 3q^3+2q^2+1
        25: 3q^3+2q^2+1
        26: q^4+3q^3+2q^2+1
        27: 3q^3+2q^2+1
        28: q^2+1
        29: 2q^3+q^2+1
        30: 3q^3+2q^2+1
        31: 2q^3+q^2+1
        32: 3q^3+2q^2+1
        33: 2q^2+1
        34: 2q^3+q^2+1
        35: 3q^3+2q^2+1
        36: 2q^2+1
        37: q^3+q^2
        38: 2q^3+q^2+1
        39: q^4+q^3+q^2
        40: 2q^3+q^2+1
        41: q^3+q^2
        42: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: 2q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: 2q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: 2q^3+q^2+1
        52: 3q^3+2q^2+1
        53: q^4+3q^3+2q^2+1
        54: 3q^3+2q^2+1
        55: 3q^3+2q^2+1
        56: q^4+3q^3+2q^2+1
        57: 3q^3+2q^2+1
        58: q^2+1
        61: q^2+1
        62: q^3
        63: q^3+q^2+1
        64: q^3+q^2
        65: 2q^3+q^2+1
        66: q^2
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: 2q^3+q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^3+q^2
        75: 2q^3+q^2+1
        76: q^4+q^3+q^2
        77: 2q^3+q^2+1
        78: q^3+q^2
        79: 2q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^2+1
        82: 2q^3+q^2+1
        83: 3q^3+2q^2+1
        84: 2q^3+q^2+1
        85: 2q^2+1
        86: 2q^3+q^2+1
        87: 3q^3+2q^2+1
        88: 1
        89: 1
        90: q^3+1
        91: 2q^2+1
        92: 2q^2+1
        93: 2q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: 2q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: 2q^3+q^2+1
       100: 3q^3+2q^2+1
       101: q^4+3q^3+2q^2+1
       102: 3q^3+2q^2+1
       105: q^2+1
       108: q^2+1
       109: q^2+1
       111: q^2
       112: q^2+1
       113: q^3
       114: q^3+q^2+1
       115: q^3+q^2
       116: 2q^3+q^2+1
       117: q^2+1
       120: q^2+1
       121: q^3
       122: q^3+q^2+1
       123: q^2
       124: q^2+1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: 2q^3+q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: 2q^3+q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: 2q^3+q^2+1
       150: 3q^3+2q^2+1
       151: q^3+q^2
       152: 2q^3+q^2+1
       153: q^4+q^3+q^2
       154: 2q^3+q^2+1
       155: q^3+q^2
       156: 2q^3+q^2+1
       157: 1
       158: 1
       159: q^3+1
       160: 2q^2+1
       161: 2q^2+1
       162: 2q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: 2q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: 2q^3+q^2+1
       171: q^2+1
       175: q^2+1
       178: 1
       180: 1
       182: 1
       184: q^2+1
       185: q^2+1
       187: q^2
       188: q^2+1
       189: q^3
       190: q^3+q^2+1
       191: 1
       194: q^2+1
       195: q^2+1
       197: q^2
       198: q^2+1
       200: 1
       202: q^2+1
       203: q^2+1
       205: q^2
       206: q^2+1
       208: 1
       209: q^3
       210: q^3+q^2+1
       211: q^3+q^2
       212: 2q^3+q^2+1
       214: 1
       216: 1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       238: 1
       240: 1
       242: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: 2q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 2q^2+1
       257: 2q^2+1
       258: 2q^3+q^2+1
       261: 1
       265: q^2+1
       270: q^2+1
       272: q^2+1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: q^2+1
       302: 1
       303: q^2+1
       305: q^2
       306: q^2+1
       308: q^2+1
       309: q^2+1
       312: 1
       313: q^2
       314: q^2+1
       316: 1
       318: 1
       320: q^2+1
       321: q^2+1
       323: q^2
       324: q^2+1
       325: q^3
       326: q^3+q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       361: 1
       363: 1
       365: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: 1
       375: 1
       376: q^3+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: q^2+1
       398: 1
       402: q^2+1
       408: q^2+1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q^2+1
       446: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q^2+1
       464: 1
       466: 1
       468: 1
       470: 1
       472: q^2+1
       473: q^2+1
       475: q^2
       476: q^2+1
       478: 1
       479: q^2
       480: q^2+1
       481: 1
       482: 1
       483: 1
       484: q^2+1
       486: 1
       488: 1
       490: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       518: 1
       519: 1
       520: q^3+1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: q^2+1
       572: 1
       576: q^2+1
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       616: q^2+1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: q^2+1
       634: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       655: q^2
       656: q^2+1
       665: 1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: q^2+1
       773: 1
       782: 1
       786: 1
       787: 1
       792: 1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: 1
       812: 1
       816: 1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: 1
       836: 1
       839: 1
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       891: 1
       901: 1
       907: 1
       910: 1
       923: 1
       925: 1
       931: 1
       945: 1
       949: 1
       954: 1
       963: 1
       977: 1
       990: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1023: 1
      1027: 1
      1028: 1
      1039: 1
      1041: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1129: 1
      1137: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1203: 1
      1209: 1
      1221: 1
      1241: 1
      1242: 1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1270: 1
      1277: 1
      1279: 1
      1289: 1
      1333: 1
      1362: 1
      1370: 1
      1395: 1
      1403: 1
      1419: 1
      1425: 1
      1428: 1
      1475: 1
      1477: 1
      1478: 1
      1581: 1
      1602: 1
      1621: 1
      1629: 1
      1810: 1

1811:    0: q^4+3q^3+3q^2+2q+1
         1: q^4+3q^3+3q^2+2q+1
         2: 3q^3+3q^2+q+1
         3: q^4+3q^3+3q^2+2q+1
         4: q^4+3q^3+3q^2+2q+1
         5: q^4+3q^3+3q^2+2q+1
         6: q^4+3q^3+3q^2+2q+1
         7: 3q^3+3q^2+q+1
         8: 3q^3+3q^2+q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: 2q^3+2q^2+q+1
        19: q^4+3q^3+3q^2+2q+1
        20: q^4+3q^3+3q^2+2q+1
        21: 3q^3+3q^2+q+1
        22: q^4+3q^3+3q^2+2q+1
        23: q^4+3q^3+3q^2+2q+1
        24: 3q^3+3q^2+q+1
        25: q^4+3q^3+3q^2+2q+1
        26: q^4+3q^3+3q^2+2q+1
        27: 3q^3+3q^2+q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^3+2q^2+q+1
        31: q^3+2q^2+2q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+2q+1
        37: 2q^3+2q^2+1
        38: q^4+q^3+q^2+2q
        39: 2q^3+2q^2+1
        40: q^4+q^3+q^2+2q
        41: 2q^3+q^2+1
        42: q^3+2q^2+q
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: 2q^3+2q^2+q+1
        52: q^4+3q^3+3q^2+2q+1
        53: q^4+3q^3+3q^2+2q+1
        54: 3q^3+3q^2+q+1
        55: q^4+3q^3+3q^2+2q+1
        56: q^4+3q^3+3q^2+2q+1
        57: 3q^3+3q^2+q+1
        58: 2q^2+q+1
        59: q
        60: 2q^2+q+1
        61: q
        62: 2q^2+1
        63: q^3+2q
        64: q^3+q^2+1
        65: q^3+q^2+q
        66: q^3+2q^2+1
        67: q^2+2q
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: 2q^2+2q+1
        72: q^3+3q^2+2q+1
        73: q^3+3q^2+2q+1
        74: 2q^3+2q^2+1
        75: q^4+q^3+q^2+2q
        76: 2q^3+2q^2+1
        77: q^4+q^3+q^2+2q
        78: 2q^3+q^2+1
        79: q^3+2q^2+q
        80: q^3+q^2+q+1
        81: 2q^2+q+1
        82: q^3+2q^2+2q+1
        83: 2q^3+2q^2+q+1
        84: q^3+q^2+q+1
        85: 2q^2+q+1
        86: q^3+2q^2+2q+1
        87: 2q^3+2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: 2q^3+2q^2+q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: 2q^3+2q^2+q+1
       100: q^4+3q^3+3q^2+2q+1
       101: q^4+3q^3+3q^2+2q+1
       102: 3q^3+3q^2+q+1
       103: 2q^2+1
       104: q
       105: q
       107: 2q^2+q+1
       108: q
       109: 2q^2+q+1
       110: q
       111: q^3+2q^2+1
       112: q^2+2q
       113: 2q^2+1
       114: q^3+2q
       115: q^3+q^2+1
       116: q^3+q^2+q
       117: q^2+1
       119: q^2+1
       121: q^2+1
       122: q^3+q
       123: q^2+1
       124: q^2+q
       125: 1
       126: q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^3+3q^2+2q+1
       141: q^3+q^2+q+1
       142: q^3+3q^2+2q+1
       143: q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: q^3+q^2+q+1
       147: q^3+3q^2+2q+1
       148: q^3+3q^2+2q+1
       149: q^3+2q^2+2q+1
       150: 2q^3+2q^2+q+1
       151: 2q^3+2q^2+1
       152: q^4+q^3+q^2+2q
       153: 2q^3+2q^2+1
       154: q^4+q^3+q^2+2q
       155: 2q^3+q^2+1
       156: q^3+2q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+2q+1
       167: q^3+3q^2+2q+1
       168: 2q^3+2q^2+q+1
       169: 2q^2+1
       170: q
       171: q
       173: q^2+1
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       183: q^2+1
       185: q^2+1
       187: q^2+1
       188: q^2+q
       189: q^2+1
       190: q^3+q
       191: 1
       193: 2q^2+q+1
       194: q
       195: 2q^2+q+1
       196: q
       197: q^3+2q^2+1
       198: q^2+2q
       199: 1
       201: 2q^2+q+1
       202: q
       203: 2q^2+q+1
       204: q
       205: q^3+2q^2+1
       206: q^2+2q
       207: 1
       208: q
       209: 2q^2+1
       210: q^3+2q
       211: q^3+q^2+1
       212: q^3+q^2+q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q^2+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: 2q^2+2q+1
       244: q^3+3q^2+2q+1
       245: q^3+3q^2+2q+1
       246: q^3+q^2+q+1
       247: q^3+3q^2+2q+1
       248: q^3+3q^2+2q+1
       249: 2q^3+2q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       259: q^2+1
       260: q
       261: q
       263: q^2+1
       267: 2q^2+1
       268: q
       270: q
       271: 2q^2+1
       272: q
       274: q
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: 1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: q^2+1
       301: q^2+1
       302: 2q
       303: q^2+1
       305: q^2+1
       306: q^2+q
       307: q^2+1
       309: q^2+1
       311: q^2+1
       312: 2q
       313: q^2+1
       314: q^2+q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: 2q^2+q+1
       320: q
       321: 2q^2+q+1
       322: q
       323: q^3+2q^2+1
       324: q^2+2q
       325: q^2+1
       326: q^3+q
       333: 1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: 2q^2+2q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: q+1
       350: q^2+q+1
       351: q^3+3q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: q+1
       358: q^2+q+1
       359: q^3+3q^2+2q+1
       366: q+1
       367: q^2+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: 1
       389: q^2+1
       390: q
       392: q
       393: q^2+1
       397: q^2+1
       398: q
       400: q
       401: q^2+1
       405: 2q^2+1
       407: q
       408: q
       419: 1
       421: 1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       429: 1
       431: 1
       433: 1
       434: q
       437: 1
       439: 1
       441: 1
       442: q
       443: 2q^2+q+1
       444: q
       445: q^2+1
       446: 2q
       447: 1
       449: 1
       451: 1
       452: q
       453: 1
       457: 1
       459: 1
       460: q
       461: 2q^2+q+1
       462: q
       463: q^2+1
       464: 2q
       469: 1
       470: q
       471: q^2+1
       473: q^2+1
       475: q^2+1
       476: q^2+q
       477: q^2+1
       478: 2q
       479: q^3+2q^2+1
       480: q^2+2q
       481: 1
       482: 1
       483: q+1
       484: q^2+1
       491: q^2+q+1
       492: 1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: 1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 2q^2+q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       529: 1
       533: 1
       541: 1
       545: q^2+1
       546: q
       548: q
       549: 1
       557: 1
       561: q^2+1
       562: q
       564: q
       565: q^2+1
       569: q^2+1
       571: q
       572: q
       573: 2q^2+1
       574: q
       576: q
       577: q^2+1
       581: 2q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       603: 1
       607: 1
       609: 1
       610: q
       613: 1
       614: q
       615: q^2+1
       619: 1
       621: 1
       625: 1
       626: q
       629: 1
       630: q
       631: q^2+1
       641: 1
       643: 1
       645: 1
       646: q
       647: 1
       649: 1
       653: 1
       654: q
       655: q^2+1
       656: q^2+q
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q^2+q+1
       686: 1
       687: q+1
       688: q+1
       689: q^2+q+1
       693: q^2+1
       699: q
       700: q
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: q^2+1
       785: 1
       787: 1
       791: 1
       792: q
       793: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       812: q
       815: 1
       817: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       836: q
       839: 1
       843: 1
       844: q
       845: 1
       847: 1
       851: 1
       852: q
       855: 1
       856: q
       857: 1
       858: q
       866: 1
       868: 1
       870: q+1
       871: 1
       872: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q^2+q+1
       908: 1
       924: 1
       928: 1
       948: 1
       952: 1
       964: 1
       974: 1
       988: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1009: q
      1012: 1
      1013: q
      1026: 1
      1028: 1
      1040: 1
      1044: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1062: 1
      1063: q
      1064: 1
      1065: q
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1130: 1
      1134: 1
      1160: 1
      1180: 1
      1202: 1
      1206: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1268: 1
      1270: 1
      1276: 1
      1277: q
      1280: 1
      1281: q
      1287: 1
      1289: 1
      1364: 1
      1368: 1
      1396: 1
      1400: 1
      1426: 1
      1466: 1
      1468: 1
      1476: 1
      1478: 1
      1484: 1
      1623: 1
      1627: 1
      1649: 1
      1657: 1
      1811: 1

1812:    0: q^4+3q^3+3q^2+2q+1
         1: q^4+3q^3+3q^2+2q+1
         2: 3q^3+3q^2+q+1
         3: q^4+3q^3+3q^2+2q+1
         4: q^4+3q^3+3q^2+2q+1
         5: q^4+3q^3+3q^2+2q+1
         6: q^4+3q^3+3q^2+2q+1
         7: 3q^3+3q^2+q+1
         8: 3q^3+3q^2+q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: 2q^3+2q^2+q+1
        19: q^4+3q^3+3q^2+2q+1
        20: q^4+3q^3+3q^2+2q+1
        21: 3q^3+3q^2+q+1
        22: q^4+3q^3+3q^2+2q+1
        23: q^4+3q^3+3q^2+2q+1
        24: 3q^3+3q^2+q+1
        25: q^4+3q^3+3q^2+2q+1
        26: q^4+3q^3+3q^2+2q+1
        27: 3q^3+3q^2+q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^3+2q^2+q+1
        31: q^3+2q^2+2q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+2q+1
        37: q^4+q^3+q^2+2q
        38: 2q^3+2q^2+1
        39: q^4+q^3+q^2+2q
        40: 2q^3+2q^2+1
        41: q^3+2q^2+q
        42: 2q^3+q^2+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: 2q^3+2q^2+q+1
        52: q^4+3q^3+3q^2+2q+1
        53: q^4+3q^3+3q^2+2q+1
        54: 3q^3+3q^2+q+1
        55: q^4+3q^3+3q^2+2q+1
        56: q^4+3q^3+3q^2+2q+1
        57: 3q^3+3q^2+q+1
        58: q
        59: 2q^2+q+1
        60: 2q^2+q+1
        61: q
        62: q^3+2q
        63: 2q^2+1
        64: q^3+q^2+q
        65: q^3+q^2+1
        66: q^2+2q
        67: q^3+2q^2+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: 2q^2+2q+1
        72: q^3+3q^2+2q+1
        73: q^3+3q^2+2q+1
        74: q^4+q^3+q^2+2q
        75: 2q^3+2q^2+1
        76: q^4+q^3+q^2+2q
        77: 2q^3+2q^2+1
        78: q^3+2q^2+q
        79: 2q^3+q^2+1
        80: q^3+q^2+q+1
        81: 2q^2+q+1
        82: q^3+2q^2+2q+1
        83: 2q^3+2q^2+q+1
        84: q^3+q^2+q+1
        85: 2q^2+q+1
        86: q^3+2q^2+2q+1
        87: 2q^3+2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: 2q^3+2q^2+q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: 2q^3+2q^2+q+1
       100: q^4+3q^3+3q^2+2q+1
       101: q^4+3q^3+3q^2+2q+1
       102: 3q^3+3q^2+q+1
       103: q
       104: 2q^2+1
       106: q
       107: 2q^2+q+1
       108: q
       109: q
       110: 2q^2+q+1
       111: q^2+2q
       112: q^3+2q^2+1
       113: q^3+2q
       114: 2q^2+1
       115: q^3+q^2+q
       116: q^3+q^2+1
       118: q^2+1
       119: q^2+1
       121: q^3+q
       122: q^2+1
       123: q^2+q
       124: q^2+1
       125: 1
       126: q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^3+3q^2+2q+1
       141: q^3+q^2+q+1
       142: q^3+3q^2+2q+1
       143: q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: q^3+q^2+q+1
       147: q^3+3q^2+2q+1
       148: q^3+3q^2+2q+1
       149: q^3+2q^2+2q+1
       150: 2q^3+2q^2+q+1
       151: q^4+q^3+q^2+2q
       152: 2q^3+2q^2+1
       153: q^4+q^3+q^2+2q
       154: 2q^3+2q^2+1
       155: q^3+2q^2+q
       156: 2q^3+q^2+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+2q+1
       167: q^3+3q^2+2q+1
       168: 2q^3+2q^2+q+1
       169: q
       170: 2q^2+1
       172: q
       174: q^2+1
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       183: q^2+1
       186: q^2+1
       187: q^2+q
       188: q^2+1
       189: q^3+q
       190: q^2+1
       192: 1
       193: 2q^2+q+1
       194: q
       195: q
       196: 2q^2+q+1
       197: q^2+2q
       198: q^3+2q^2+1
       199: 1
       201: 2q^2+q+1
       202: q
       203: q
       204: 2q^2+q+1
       205: q^2+2q
       206: q^3+2q^2+1
       207: q
       208: 1
       209: q^3+2q
       210: 2q^2+1
       211: q^3+q^2+q
       212: q^3+q^2+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q^2+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: 2q^2+2q+1
       244: q^3+3q^2+2q+1
       245: q^3+3q^2+2q+1
       246: q^3+q^2+q+1
       247: q^3+3q^2+2q+1
       248: q^3+3q^2+2q+1
       249: 2q^3+2q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       259: q
       260: q^2+1
       262: q
       264: q^2+1
       267: q
       268: 2q^2+1
       269: q
       271: q
       273: q
       274: 2q^2+1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       291: q
       292: 1
       293: 1
       296: 1
       297: q
       298: 1
       299: q^2+1
       301: 2q
       302: q^2+1
       304: q^2+1
       305: q^2+q
       306: q^2+1
       307: q^2+1
       310: q^2+1
       311: 2q
       312: q^2+1
       313: q^2+q
       314: q^2+1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: 2q^2+q+1
       320: q
       321: q
       322: 2q^2+q+1
       323: q^2+2q
       324: q^3+2q^2+1
       325: q^3+q
       326: q^2+1
       333: 1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: 2q^2+2q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: q+1
       350: q^2+q+1
       351: q^3+3q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: q+1
       358: q^2+q+1
       359: q^3+3q^2+2q+1
       366: q+1
       367: q^2+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: 1
       389: q
       390: q^2+1
       391: q
       394: q^2+1
       397: q
       399: q
       400: q^2+1
       403: q^2+1
       405: q
       406: q
       407: 2q^2+1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       429: 1
       432: 1
       433: q
       434: 1
       437: 1
       440: 1
       441: q
       442: 1
       443: 2q^2+q+1
       444: q
       445: 2q
       446: q^2+1
       447: 1
       450: 1
       451: q
       452: 1
       453: 1
       458: 1
       459: q
       460: 1
       461: q
       462: 2q^2+q+1
       463: 2q
       464: q^2+1
       469: q
       470: 1
       471: q^2+1
       474: q^2+1
       475: q^2+q
       476: q^2+1
       477: 2q
       478: q^2+1
       479: q^2+2q
       480: q^3+2q^2+1
       481: 1
       482: 1
       483: q+1
       484: q^2+1
       491: q^2+q+1
       492: 1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: 1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 2q^2+q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       530: 1
       534: 1
       542: 1
       545: q
       546: q^2+1
       547: q
       551: 1
       560: 1
       561: q
       563: q
       564: q^2+1
       566: q^2+1
       569: q
       570: q
       571: q^2+1
       573: q
       574: 2q^2+1
       575: q
       577: 2q
       581: q^2+1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       603: 1
       608: 1
       609: q
       610: 1
       613: q
       614: 1
       615: q^2+1
       619: 1
       622: 1
       625: q
       626: 1
       629: q
       630: 1
       632: q^2+1
       641: 1
       644: 1
       645: q
       646: 1
       647: 1
       650: 1
       653: q
       654: 1
       655: q^2+q
       656: q^2+1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q^2+q+1
       686: 1
       687: q+1
       688: q+1
       689: q^2+q+1
       693: q
       697: q
       699: q^2+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: q^2+1
       785: 1
       788: 1
       791: q
       792: 1
       793: 1
       801: 1
       804: 1
       805: 1
       808: 1
       811: q
       812: 1
       815: 1
       818: 1
       825: 1
       828: 1
       829: 1
       832: 1
       835: q
       836: 1
       840: 1
       843: q
       844: 1
       845: 1
       848: 1
       851: q
       852: 1
       855: q
       856: 1
       857: q
       858: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q^2+q+1
       909: 1
       926: 1
       929: 1
       951: 1
       953: 1
       965: 1
       976: 1
       989: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1008: q
      1009: 1
      1012: q
      1013: 1
      1026: 1
      1029: 1
      1040: 1
      1045: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1131: 1
      1136: 1
      1162: 1
      1181: 1
      1205: 1
      1207: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1268: 1
      1271: 1
      1276: q
      1277: 1
      1280: q
      1281: 1
      1287: 1
      1289: 1
      1366: 1
      1371: 1
      1397: 1
      1402: 1
      1427: 1
      1467: 1
      1468: 1
      1476: 1
      1479: 1
      1484: 1
      1624: 1
      1628: 1
      1650: 1
      1657: 1
      1812: 1

1813:    0: q^4+3q^3+3q^2+2q+1
         1: q^4+3q^3+3q^2+2q+1
         2: 3q^3+3q^2+q+1
         3: q^4+3q^3+3q^2+2q+1
         4: q^4+3q^3+3q^2+2q+1
         5: q^4+3q^3+3q^2+2q+1
         6: q^4+3q^3+3q^2+2q+1
         7: 3q^3+3q^2+q+1
         8: 3q^3+3q^2+q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: 2q^3+2q^2+q+1
        19: q^4+3q^3+3q^2+2q+1
        20: q^4+3q^3+3q^2+2q+1
        21: 3q^3+3q^2+q+1
        22: q^4+3q^3+3q^2+2q+1
        23: q^4+3q^3+3q^2+2q+1
        24: 3q^3+3q^2+q+1
        25: q^4+3q^3+3q^2+2q+1
        26: q^4+3q^3+3q^2+2q+1
        27: 3q^3+3q^2+q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^3+2q^2+q+1
        31: q^3+2q^2+2q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+2q+1
        37: q^4+q^3+q^2+2q
        38: 2q^3+2q^2+1
        39: q^4+q^3+q^2+2q
        40: 2q^3+2q^2+1
        41: q^3+2q^2+q
        42: 2q^3+q^2+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: 2q^3+2q^2+q+1
        52: q^4+3q^3+3q^2+2q+1
        53: q^4+3q^3+3q^2+2q+1
        54: 3q^3+3q^2+q+1
        55: q^4+3q^3+3q^2+2q+1
        56: q^4+3q^3+3q^2+2q+1
        57: 3q^3+3q^2+q+1
        58: 2q^2+q+1
        59: q
        60: q
        61: 2q^2+q+1
        62: q^3+2q
        63: 2q^2+1
        64: q^3+q^2+q
        65: q^3+q^2+1
        66: q^2+2q
        67: q^3+2q^2+1
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: 2q^2+2q+1
        72: q^3+3q^2+2q+1
        73: q^3+3q^2+2q+1
        74: q^4+q^3+q^2+2q
        75: 2q^3+2q^2+1
        76: q^4+q^3+q^2+2q
        77: 2q^3+2q^2+1
        78: q^3+2q^2+q
        79: 2q^3+q^2+1
        80: q^3+q^2+q+1
        81: 2q^2+q+1
        82: q^3+2q^2+2q+1
        83: 2q^3+2q^2+q+1
        84: q^3+q^2+q+1
        85: 2q^2+q+1
        86: q^3+2q^2+2q+1
        87: 2q^3+2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: 2q^3+2q^2+q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: 2q^3+2q^2+q+1
       100: q^4+3q^3+3q^2+2q+1
       101: q^4+3q^3+3q^2+2q+1
       102: 3q^3+3q^2+q+1
       103: q
       105: 2q^2+1
       106: q
       107: q
       108: 2q^2+q+1
       109: 2q^2+q+1
       110: q
       111: q^2+2q
       112: q^3+2q^2+1
       113: q^3+2q
       114: 2q^2+1
       115: q^3+q^2+q
       116: q^3+q^2+1
       117: q^2+1
       120: q^2+1
       121: q^3+q
       122: q^2+1
       123: q^2+q
       124: q^2+1
       125: 1
       126: q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^3+3q^2+2q+1
       141: q^3+q^2+q+1
       142: q^3+3q^2+2q+1
       143: q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: q^3+q^2+q+1
       147: q^3+3q^2+2q+1
       148: q^3+3q^2+2q+1
       149: q^3+2q^2+2q+1
       150: 2q^3+2q^2+q+1
       151: q^4+q^3+q^2+2q
       152: 2q^3+2q^2+1
       153: q^4+q^3+q^2+2q
       154: 2q^3+2q^2+1
       155: q^3+2q^2+q
       156: 2q^3+q^2+1
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+2q+1
       167: q^3+3q^2+2q+1
       168: 2q^3+2q^2+q+1
       169: q
       171: 2q^2+1
       172: q
       175: q^2+1
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       184: q^2+1
       185: q^2+1
       187: q^2+q
       188: q^2+1
       189: q^3+q
       190: q^2+1
       191: 1
       193: q
       194: 2q^2+q+1
       195: 2q^2+q+1
       196: q
       197: q^2+2q
       198: q^3+2q^2+1
       200: 1
       201: q
       202: 2q^2+q+1
       203: 2q^2+q+1
       204: q
       205: q^2+2q
       206: q^3+2q^2+1
       207: q
       208: 1
       209: q^3+2q
       210: 2q^2+1
       211: q^3+q^2+q
       212: q^3+q^2+1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q^2+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: 2q^2+2q+1
       244: q^3+3q^2+2q+1
       245: q^3+3q^2+2q+1
       246: q^3+q^2+q+1
       247: q^3+3q^2+2q+1
       248: q^3+3q^2+2q+1
       249: 2q^3+2q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       259: q
       261: q^2+1
       262: q
       265: q^2+1
       267: q
       269: q
       270: 2q^2+1
       271: q
       272: 2q^2+1
       273: q
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       291: q
       292: 1
       294: 1
       295: 1
       297: q
       298: 1
       300: q^2+1
       301: 2q
       302: q^2+1
       303: q^2+1
       305: q^2+q
       306: q^2+1
       308: q^2+1
       309: q^2+1
       311: 2q
       312: q^2+1
       313: q^2+q
       314: q^2+1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: q
       320: 2q^2+q+1
       321: 2q^2+q+1
       322: q
       323: q^2+2q
       324: q^3+2q^2+1
       325: q^3+q
       326: q^2+1
       333: 1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: 2q^2+2q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: q+1
       350: q^2+q+1
       351: q^3+3q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: q+1
       358: q^2+q+1
       359: q^3+3q^2+2q+1
       366: q+1
       367: q^2+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: 1
       389: q
       391: q
       392: q^2+1
       395: q^2+1
       397: q
       398: q^2+1
       399: q
       402: q^2+1
       405: q
       406: q
       408: 2q^2+1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       430: 1
       431: 1
       433: q
       434: 1
       438: 1
       439: 1
       441: q
       442: 1
       443: q
       444: 2q^2+q+1
       445: 2q
       446: q^2+1
       448: 1
       449: 1
       451: q
       452: 1
       454: 1
       457: 1
       459: q
       460: 1
       461: 2q^2+q+1
       462: q
       463: 2q
       464: q^2+1
       469: q
       470: 1
       472: q^2+1
       473: q^2+1
       475: q^2+q
       476: q^2+1
       477: 2q
       478: q^2+1
       479: q^2+2q
       480: q^3+2q^2+1
       481: 1
       482: 1
       483: q+1
       484: q^2+1
       491: q^2+q+1
       492: 1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: 1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 2q^2+q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       531: 1
       535: 1
       544: 1
       545: q
       547: q
       548: q^2+1
       550: 1
       558: 1
       561: q
       562: q^2+1
       563: q
       567: q^2+1
       569: q
       570: q
       572: q^2+1
       573: q
       575: q
       576: 2q^2+1
       577: 2q
       581: q^2+1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       604: 1
       607: 1
       609: q
       610: 1
       613: q
       614: 1
       616: q^2+1
       620: 1
       621: 1
       625: q
       626: 1
       629: q
       630: 1
       631: q^2+1
       642: 1
       643: 1
       645: q
       646: 1
       648: 1
       649: 1
       653: q
       654: 1
       655: q^2+q
       656: q^2+1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q^2+q+1
       686: 1
       687: q+1
       688: q+1
       689: q^2+q+1
       693: q
       697: q
       700: q^2+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: q^2+1
       786: 1
       787: 1
       791: q
       792: 1
       794: 1
       802: 1
       803: 1
       806: 1
       807: 1
       811: q
       812: 1
       816: 1
       817: 1
       826: 1
       827: 1
       830: 1
       831: 1
       835: q
       836: 1
       839: 1
       843: q
       844: 1
       846: 1
       847: 1
       851: q
       852: 1
       855: q
       856: 1
       857: q
       858: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q^2+q+1
       910: 1
       925: 1
       931: 1
       949: 1
       954: 1
       966: 1
       977: 1
       990: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1008: q
      1009: 1
      1012: q
      1013: 1
      1027: 1
      1028: 1
      1041: 1
      1044: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1132: 1
      1137: 1
      1161: 1
      1182: 1
      1203: 1
      1209: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1269: 1
      1270: 1
      1276: q
      1277: 1
      1280: q
      1281: 1
      1287: 1
      1289: 1
      1365: 1
      1370: 1
      1398: 1
      1403: 1
      1428: 1
      1466: 1
      1469: 1
      1477: 1
      1478: 1
      1484: 1
      1625: 1
      1629: 1
      1649: 1
      1658: 1
      1813: 1

1814:    0: q^4+3q^3+3q^2+2q+1
         1: q^4+3q^3+3q^2+2q+1
         2: 3q^3+3q^2+q+1
         3: q^4+3q^3+3q^2+2q+1
         4: q^4+3q^3+3q^2+2q+1
         5: q^4+3q^3+3q^2+2q+1
         6: q^4+3q^3+3q^2+2q+1
         7: 3q^3+3q^2+q+1
         8: 3q^3+3q^2+q+1
         9: q^5+q^4+2q^3+2q^2+q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: 2q^3+2q^2+q+1
        19: q^4+3q^3+3q^2+2q+1
        20: q^4+3q^3+3q^2+2q+1
        21: 3q^3+3q^2+q+1
        22: q^4+3q^3+3q^2+2q+1
        23: q^4+3q^3+3q^2+2q+1
        24: 3q^3+3q^2+q+1
        25: q^4+3q^3+3q^2+2q+1
        26: q^4+3q^3+3q^2+2q+1
        27: 3q^3+3q^2+q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^3+2q^2+q+1
        31: q^3+2q^2+2q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+2q+1
        37: 2q^3+2q^2+1
        38: q^4+q^3+q^2+2q
        39: 2q^3+2q^2+1
        40: q^4+q^3+q^2+2q
        41: 2q^3+q^2+1
        42: q^3+2q^2+q
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: 2q^3+2q^2+q+1
        52: q^4+3q^3+3q^2+2q+1
        53: q^4+3q^3+3q^2+2q+1
        54: 3q^3+3q^2+q+1
        55: q^4+3q^3+3q^2+2q+1
        56: q^4+3q^3+3q^2+2q+1
        57: 3q^3+3q^2+q+1
        58: q
        59: 2q^2+q+1
        60: q
        61: 2q^2+q+1
        62: 2q^2+1
        63: q^3+2q
        64: q^3+q^2+1
        65: q^3+q^2+q
        66: q^3+2q^2+1
        67: q^2+2q
        68: q^2+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: 2q^2+2q+1
        72: q^3+3q^2+2q+1
        73: q^3+3q^2+2q+1
        74: 2q^3+2q^2+1
        75: q^4+q^3+q^2+2q
        76: 2q^3+2q^2+1
        77: q^4+q^3+q^2+2q
        78: 2q^3+q^2+1
        79: q^3+2q^2+q
        80: q^3+q^2+q+1
        81: 2q^2+q+1
        82: q^3+2q^2+2q+1
        83: 2q^3+2q^2+q+1
        84: q^3+q^2+q+1
        85: 2q^2+q+1
        86: q^3+2q^2+2q+1
        87: 2q^3+2q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: 2q^3+2q^2+q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: 2q^3+2q^2+q+1
       100: q^4+3q^3+3q^2+2q+1
       101: q^4+3q^3+3q^2+2q+1
       102: 3q^3+3q^2+q+1
       104: q
       105: q
       106: 2q^2+1
       107: q
       108: 2q^2+q+1
       109: q
       110: 2q^2+q+1
       111: q^3+2q^2+1
       112: q^2+2q
       113: 2q^2+1
       114: q^3+2q
       115: q^3+q^2+1
       116: q^3+q^2+q
       118: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^3+q
       123: q^2+1
       124: q^2+q
       125: 1
       126: q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: q^2+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: q+1
       138: q^2+q+1
       139: 2q^2+2q+1
       140: q^3+3q^2+2q+1
       141: q^3+q^2+q+1
       142: q^3+3q^2+2q+1
       143: q+1
       144: q^2+q+1
       145: 2q^2+2q+1
       146: q^3+q^2+q+1
       147: q^3+3q^2+2q+1
       148: q^3+3q^2+2q+1
       149: q^3+2q^2+2q+1
       150: 2q^3+2q^2+q+1
       151: 2q^3+2q^2+1
       152: q^4+q^3+q^2+2q
       153: 2q^3+2q^2+1
       154: q^4+q^3+q^2+2q
       155: 2q^3+q^2+1
       156: q^3+2q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+2q+1
       167: q^3+3q^2+2q+1
       168: 2q^3+2q^2+q+1
       170: q
       171: q
       172: 2q^2+1
       176: q^2+1
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       184: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+q
       189: q^2+1
       190: q^3+q
       192: 1
       193: q
       194: 2q^2+q+1
       195: q
       196: 2q^2+q+1
       197: q^3+2q^2+1
       198: q^2+2q
       200: 1
       201: q
       202: 2q^2+q+1
       203: q
       204: 2q^2+q+1
       205: q^3+2q^2+1
       206: q^2+2q
       207: 1
       208: q
       209: 2q^2+1
       210: q^3+2q
       211: q^3+q^2+1
       212: q^3+q^2+q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q+1
       225: q^2+q+1
       226: q+1
       227: q^2+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q+1
       232: q^2+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: 2q^2+2q+1
       244: q^3+3q^2+2q+1
       245: q^3+3q^2+2q+1
       246: q^3+q^2+q+1
       247: q^3+3q^2+2q+1
       248: q^3+3q^2+2q+1
       249: 2q^3+2q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       260: q
       261: q
       262: q^2+1
       266: q^2+1
       268: q
       269: 2q^2+1
       270: q
       272: q
       273: 2q^2+1
       274: q
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: 1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: q^2+1
       301: q^2+1
       302: 2q
       304: q^2+1
       305: q^2+1
       306: q^2+q
       308: q^2+1
       310: q^2+1
       311: q^2+1
       312: 2q
       313: q^2+1
       314: q^2+q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: q
       320: 2q^2+q+1
       321: q
       322: 2q^2+q+1
       323: q^3+2q^2+1
       324: q^2+2q
       325: q^2+1
       326: q^3+q
       333: 1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: 2q^2+2q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q^2+q+1
       349: q+1
       350: q^2+q+1
       351: q^3+3q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q^2+q+1
       357: q+1
       358: q^2+q+1
       359: q^3+3q^2+2q+1
       366: q+1
       367: q^2+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: 1
       390: q
       391: q^2+1
       392: q
       396: q^2+1
       398: q
       399: q^2+1
       400: q
       404: q^2+1
       406: 2q^2+1
       407: q
       408: q
       420: 1
       422: 1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       430: 1
       432: 1
       433: 1
       434: q
       438: 1
       440: 1
       441: 1
       442: q
       443: q
       444: 2q^2+q+1
       445: q^2+1
       446: 2q
       448: 1
       450: 1
       451: 1
       452: q
       454: 1
       458: 1
       459: 1
       460: q
       461: q
       462: 2q^2+q+1
       463: q^2+1
       464: 2q
       469: 1
       470: q
       472: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2+q
       477: q^2+1
       478: 2q
       479: q^3+2q^2+1
       480: q^2+2q
       481: 1
       482: 1
       483: q+1
       484: q^2+1
       491: q^2+q+1
       492: 1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: 1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 2q^2+q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q^2+q+1
       513: q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       532: 1
       536: 1
       543: 1
       546: q
       547: q^2+1
       548: q
       552: 1
       559: 1
       562: q
       563: q^2+1
       564: q
       568: q^2+1
       570: q^2+1
       571: q
       572: q
       574: q
       575: 2q^2+1
       576: q
       577: q^2+1
       581: 2q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       604: 1
       608: 1
       609: 1
       610: q
       613: 1
       614: q
       616: q^2+1
       620: 1
       622: 1
       625: 1
       626: q
       629: 1
       630: q
       632: q^2+1
       642: 1
       644: 1
       645: 1
       646: q
       648: 1
       650: 1
       653: 1
       654: q
       655: q^2+1
       656: q^2+q
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q^2+q+1
       686: 1
       687: q+1
       688: q+1
       689: q^2+q+1
       697: q^2+1
       699: q
       700: q
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: q^2+1
       786: 1
       788: 1
       791: 1
       792: q
       794: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       812: q
       816: 1
       818: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       836: q
       840: 1
       843: 1
       844: q
       846: 1
       848: 1
       851: 1
       852: q
       855: 1
       856: q
       857: 1
       858: q
       866: 1
       868: 1
       870: q+1
       871: 1
       872: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q^2+q+1
       911: 1
       927: 1
       930: 1
       950: 1
       955: 1
       967: 1
       975: 1
       991: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1009: q
      1012: 1
      1013: q
      1027: 1
      1029: 1
      1041: 1
      1045: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1062: 1
      1063: q
      1064: 1
      1065: q
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1133: 1
      1135: 1
      1163: 1
      1183: 1
      1204: 1
      1208: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1269: 1
      1271: 1
      1276: 1
      1277: q
      1280: 1
      1281: q
      1287: 1
      1289: 1
      1367: 1
      1369: 1
      1399: 1
      1401: 1
      1429: 1
      1467: 1
      1469: 1
      1477: 1
      1479: 1
      1484: 1
      1626: 1
      1630: 1
      1650: 1
      1658: 1
      1814: 1

1815:    0: 2q^4+21q^3+34q^2+14q+2
         1: 2q^4+21q^3+34q^2+14q+2
         2: q^5+5q^4+20q^3+27q^2+13q+2
         3: 22q^3+34q^2+14q+2
         4: 2q^4+21q^3+34q^2+14q+2
         5: 22q^3+34q^2+14q+2
         6: 2q^4+21q^3+34q^2+14q+2
         7: q^5+5q^4+20q^3+27q^2+13q+2
         8: 7q^4+23q^3+27q^2+13q+2
         9: q^6+4q^5+10q^4+18q^3+19q^2+10q+2
        10: 2q^4+21q^3+34q^2+14q+2
        11: 22q^3+34q^2+14q+2
        12: 2q^4+21q^3+34q^2+14q+2
        13: q^4+12q^3+26q^2+13q+2
        14: q^4+12q^3+26q^2+13q+2
        15: 15q^3+26q^2+13q+2
        16: 11q^3+31q^2+14q+2
        17: 11q^3+31q^2+14q+2
        18: q^5+5q^4+15q^3+19q^2+10q+2
        19: 2q^4+21q^3+34q^2+14q+2
        20: 2q^4+21q^3+34q^2+14q+2
        21: q^5+5q^4+20q^3+27q^2+13q+2
        22: 11q^3+31q^2+14q+2
        23: 11q^3+31q^2+14q+2
        24: 2q^4+15q^3+24q^2+13q+2
        25: 11q^3+31q^2+14q+2
        26: 11q^3+31q^2+14q+2
        27: 2q^4+15q^3+24q^2+13q+2
        28: 11q^3+31q^2+14q+2
        29: 2q^4+21q^3+34q^2+14q+2
        30: q^4+12q^3+26q^2+13q+2
        31: 11q^3+31q^2+14q+2
        32: 7q^3+23q^2+13q+2
        33: 4q^3+28q^2+14q+2
        34: 11q^3+31q^2+14q+2
        35: 7q^3+23q^2+13q+2
        36: 4q^3+28q^2+14q+2
        37: 4q^3+21q^2+12q+2
        38: 8q^2+2q
        39: 4q^3+21q^2+12q+2
        40: 8q^2+2q
        41: 8q^3+17q^2+11q+2
        42: 3q^3+5q^2+2q
        43: q^4+12q^3+26q^2+13q+2
        44: q^4+12q^3+26q^2+13q+2
        45: 15q^3+26q^2+13q+2
        46: 3q^3+23q^2+13q+2
        47: 5q^3+23q^2+13q+2
        48: q^4+8q^3+18q^2+10q+2
        49: 11q^3+31q^2+14q+2
        50: 11q^3+31q^2+14q+2
        51: q^5+5q^4+15q^3+19q^2+10q+2
        52: 11q^3+31q^2+14q+2
        53: 11q^3+31q^2+14q+2
        54: 2q^4+15q^3+24q^2+13q+2
        55: 11q^3+31q^2+14q+2
        56: 11q^3+31q^2+14q+2
        57: 2q^4+15q^3+24q^2+13q+2
        58: 2q^3+14q^2+7q+1
        59: 2q^3+14q^2+7q+1
        60: 2q^3+14q^2+7q+1
        61: 2q^3+14q^2+7q+1
        62: 4q^3+21q^2+12q+2
        63: 8q^2+2q
        64: 3q^3+16q^2+11q+2
        65: 5q^2+2q
        66: 18q^2+12q+2
        67: 8q^2+2q
        68: q^3+15q^2+12q+2
        69: 3q^3+15q^2+10q+2
        70: q^4+12q^3+26q^2+13q+2
        71: 11q^3+31q^2+14q+2
        72: 4q^3+28q^2+14q+2
        73: 4q^3+28q^2+14q+2
        74: 4q^3+21q^2+12q+2
        75: 8q^2+2q
        76: 4q^3+21q^2+12q+2
        77: 8q^2+2q
        78: 8q^3+17q^2+11q+2
        79: 3q^3+5q^2+2q
        80: 7q^3+23q^2+13q+2
        81: q^3+20q^2+13q+2
        82: 11q^3+31q^2+14q+2
        83: 7q^3+23q^2+13q+2
        84: 7q^3+23q^2+13q+2
        85: q^3+20q^2+13q+2
        86: 11q^3+31q^2+14q+2
        87: 7q^3+23q^2+13q+2
        88: 3q^3+23q^2+13q+2
        89: 5q^3+23q^2+13q+2
        90: q^4+8q^3+18q^2+10q+2
        91: 3q^3+23q^2+13q+2
        92: 5q^3+23q^2+13q+2
        93: q^4+8q^3+18q^2+10q+2
        94: 4q^3+24q^2+14q+2
        95: 4q^3+24q^2+14q+2
        96: 2q^4+10q^3+16q^2+10q+2
        97: 4q^3+24q^2+14q+2
        98: 4q^3+24q^2+14q+2
        99: 2q^4+10q^3+16q^2+10q+2
       100: 4q^3+25q^2+13q+2
       101: 4q^3+25q^2+13q+2
       102: 8q^3+18q^2+12q+2
       103: 9q^2+6q+1
       104: 4q^2+q
       105: 4q^2+q
       106: 9q^2+6q+1
       107: 2q^3+14q^2+7q+1
       108: 2q^3+14q^2+7q+1
       109: 2q^3+14q^2+7q+1
       110: 2q^3+14q^2+7q+1
       111: 18q^2+12q+2
       112: 8q^2+2q
       113: 4q^3+21q^2+12q+2
       114: 8q^2+2q
       115: 3q^3+16q^2+11q+2
       116: 5q^2+2q
       117: 6q^2+6q+1
       118: 6q^2+6q+1
       119: 6q^2+6q+1
       120: 6q^2+6q+1
       121: 3q^3+16q^2+11q+2
       122: 5q^2+2q
       123: 13q^2+11q+2
       124: 5q^2+2q
       125: q^3+15q^2+12q+2
       126: 3q^3+15q^2+10q+2
       127: 12q^2+12q+2
       129: 12q^2+12q+2
       131: 4q^3+10q^2+8q+2
       133: q^3+15q^2+12q+2
       134: 3q^3+15q^2+10q+2
       135: q^3+20q^2+13q+2
       136: q^3+20q^2+13q+2
       137: q^3+20q^2+13q+2
       138: q^3+12q^2+10q+2
       139: 4q^3+24q^2+14q+2
       140: 12q^2+10q+2
       141: 7q^3+23q^2+13q+2
       142: 4q^3+24q^2+14q+2
       143: q^3+20q^2+13q+2
       144: q^3+12q^2+10q+2
       145: 4q^3+24q^2+14q+2
       146: 7q^3+23q^2+13q+2
       147: 4q^3+24q^2+14q+2
       148: 12q^2+10q+2
       149: 4q^3+25q^2+13q+2
       150: 3q^3+17q^2+12q+2
       151: 4q^3+18q^2+11q+2
       152: 7q^2+2q
       153: 4q^3+18q^2+11q+2
       154: 7q^2+2q
       155: 6q^3+14q^2+10q+2
       156: 2q^3+4q^2+2q
       157: 3q^3+23q^2+13q+2
       158: 5q^3+23q^2+13q+2
       159: q^4+8q^3+18q^2+10q+2
       160: q^3+12q^2+13q+2
       161: q^3+12q^2+13q+2
       162: 3q^3+11q^2+10q+2
       163: q^3+12q^2+13q+2
       164: q^3+12q^2+13q+2
       165: 3q^3+11q^2+10q+2
       166: 15q^2+13q+2
       167: 15q^2+13q+2
       168: 4q^3+11q^2+9q+2
       169: 9q^2+6q+1
       170: 4q^2+q
       171: 4q^2+q
       172: 9q^2+6q+1
       173: 4q^2+5q+1
       174: q^2+q
       175: q^2+q
       176: 4q^2+5q+1
       177: 6q^2+8q+2
       179: 12q^2+12q+2
       181: 12q^2+12q+2
       183: 6q^2+6q+1
       184: 6q^2+6q+1
       185: 6q^2+6q+1
       186: 6q^2+6q+1
       187: 13q^2+11q+2
       188: 5q^2+2q
       189: 3q^3+16q^2+11q+2
       190: 5q^2+2q
       191: 6q^2+6q+1
       192: 6q^2+6q+1
       193: 6q^2+5q+1
       194: 6q^2+5q+1
       195: 2q^3+12q^2+7q+1
       196: 2q^3+12q^2+7q+1
       197: 8q^2+8q+2
       198: 4q^2+2q
       199: 6q^2+6q+1
       200: 6q^2+6q+1
       201: 2q^3+12q^2+7q+1
       202: 2q^3+12q^2+7q+1
       203: 6q^2+5q+1
       204: 6q^2+5q+1
       205: 8q^2+8q+2
       206: 4q^2+2q
       207: 13q^2+11q+2
       208: 5q^2+2q
       209: 4q^3+18q^2+11q+2
       210: 7q^2+2q
       211: 3q^3+13q^2+10q+2
       212: 4q^2+2q
       213: 2q^2+9q+2
       215: 2q^2+9q+2
       217: 4q^2+6q+2
       219: q^3+8q^2+9q+2
       220: q^3+15q^2+12q+2
       221: 3q^3+15q^2+10q+2
       222: q^3+20q^2+13q+2
       223: q^3+12q^2+10q+2
       224: q^3+20q^2+13q+2
       225: q^3+12q^2+10q+2
       226: q^3+12q^2+10q+2
       227: 6q^2+12q+2
       228: q^3+8q^2+10q+2
       229: 5q^2+9q+2
       230: q^3+12q^2+13q+2
       231: q^3+12q^2+10q+2
       232: 6q^2+12q+2
       233: q^3+8q^2+10q+2
       234: q^3+12q^2+13q+2
       235: 5q^2+9q+2
       236: 8q^2+9q+2
       237: 8q^2+11q+2
       239: 8q^2+11q+2
       241: 2q^3+7q^2+7q+2
       243: 15q^2+13q+2
       244: 8q^2+10q+2
       245: 8q^2+10q+2
       246: 3q^3+17q^2+12q+2
       247: 15q^2+13q+2
       248: 15q^2+13q+2
       249: 4q^3+11q^2+9q+2
       250: q^3+12q^2+13q+2
       251: q^3+12q^2+13q+2
       252: 3q^3+11q^2+10q+2
       253: q^3+12q^2+13q+2
       254: q^3+12q^2+13q+2
       255: 3q^3+11q^2+10q+2
       256: 3q^2+12q+2
       257: 5q^2+12q+2
       258: 5q^2+9q+2
       259: 6q^2+6q+1
       262: 6q^2+6q+1
       263: 4q^2+5q+1
       264: q^2+q
       265: q^2+q
       266: 4q^2+5q+1
       267: 4q^2+4q+1
       268: 2q^2+q
       269: 4q^2+4q+1
       270: 2q^2+q
       271: 4q^2+4q+1
       272: 2q^2+q
       273: 4q^2+4q+1
       274: 2q^2+q
       275: 4q^2+5q+1
       276: q^2+q
       277: q^2+q
       278: 4q^2+5q+1
       279: 8q+2
       281: q^2+6q+2
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       286: 2q^2+3q+1
       287: 6q^2+8q+2
       289: 2q^2+9q+2
       291: 6q^2+8q+2
       293: 6q^2+6q+1
       294: 6q^2+6q+1
       295: 6q^2+6q+1
       296: 6q^2+6q+1
       297: 13q^2+11q+2
       298: 5q^2+2q
       299: q^2+4q+1
       300: q^2+4q+1
       301: 4q^2+8q+2
       303: 3q^2+6q+1
       304: 3q^2+6q+1
       305: 4q^2+7q+2
       306: q^2+2q
       307: 3q^2+6q+1
       308: 3q^2+6q+1
       309: q^2+4q+1
       310: q^2+4q+1
       311: 4q^2+8q+2
       313: 4q^2+7q+2
       314: q^2+2q
       315: 4q^2+7q+2
       317: 8q^2+11q+2
       319: 4q^2+5q+1
       320: 4q^2+5q+1
       321: 4q^2+5q+1
       322: 4q^2+5q+1
       323: 2q^2+6q+2
       324: 2q^2+2q
       325: 3q^3+13q^2+10q+2
       326: 4q^2+2q
       327: 2q^2+9q+2
       329: 2q^2+9q+2
       331: 4q^2+6q+2
       333: q^3+8q^2+9q+2
       334: q^3+12q^2+10q+2
       335: q^3+12q^2+10q+2
       336: 8q^2+9q+2
       337: 15q^2+13q+2
       338: 8q^2+11q+2
       340: 8q^2+11q+2
       342: 2q^3+7q^2+7q+2
       344: 3q^2+9q+2
       345: 6q^2+12q+2
       346: q^3+8q^2+10q+2
       347: 5q^2+9q+2
       348: 2q^2+6q+2
       349: q^3+12q^2+13q+2
       350: q^3+8q^2+10q+2
       351: 8q^2+10q+2
       352: 3q^2+9q+2
       353: 6q^2+12q+2
       354: q^3+8q^2+10q+2
       355: q^3+12q^2+13q+2
       356: q^3+8q^2+10q+2
       357: 5q^2+9q+2
       358: 2q^2+6q+2
       359: 8q^2+10q+2
       360: 8q+2
       362: q^2+8q+2
       364: 2q^2+5q+2
       366: 8q^2+9q+2
       367: q^2+11q+2
       368: 3q^2+9q+2
       369: q^2+9q+2
       370: q^2+9q+2
       371: 3q^2+12q+2
       372: 5q^2+12q+2
       373: 5q^2+9q+2
       374: 3q^2+12q+2
       375: 5q^2+12q+2
       376: 5q^2+9q+2
       377: q^2+2q+1
       380: q^2+2q+1
       381: 4q+1
       384: 4q+1
       385: 4q^2+5q+1
       386: q^2+q
       387: q^2+q
       388: 4q^2+5q+1
       389: 2q^2+4q+1
       391: 2q^2+4q+1
       393: q^2+3q+1
       394: q
       395: q
       396: q^2+3q+1
       397: 2q^2+4q+1
       399: 2q^2+4q+1
       401: q^2+3q+1
       402: q
       403: q
       404: q^2+3q+1
       405: q^2+3q+1
       406: q^2+3q+1
       407: q^2+q
       408: q^2+q
       409: 8q+2
       411: q^2+6q+2
       413: 5q+2
       415: 2q^2+9q+2
       417: q^2+6q+2
       419: 2q^2+3q+1
       420: 2q^2+3q+1
       421: 2q^2+3q+1
       422: 2q^2+3q+1
       423: 6q^2+8q+2
       425: 4q^2+7q+2
       427: 8q^2+11q+2
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q^2+3q+1
       433: q^2+4q+2
       435: 5q+2
       437: q^2+4q+1
       438: q^2+4q+1
       439: 3q^2+6q+1
       440: 3q^2+6q+1
       441: 4q^2+7q+2
       442: q^2+2q
       443: 4q^2+5q+1
       444: 4q^2+5q+1
       445: 4q^2+8q+2
       447: q^2+3q+1
       448: q^2+3q+1
       449: 2q+1
       450: 2q+1
       451: q^2+4q+2
       453: 3q^2+6q+1
       454: 3q^2+6q+1
       455: 5q+2
       457: q^2+4q+1
       458: q^2+4q+1
       459: 4q^2+7q+2
       460: q^2+2q
       461: 4q^2+5q+1
       462: 4q^2+5q+1
       463: 4q^2+8q+2
       465: 7q+2
       467: 5q+2
       469: 4q^2+7q+2
       471: 4q+1
       472: 4q+1
       473: 4q+1
       474: 4q+1
       475: 5q+2
       476: 2q
       477: 2q^2+8q+2
       479: 2q^2+6q+2
       480: 2q^2+2q
       481: 3q^2+9q+2
       482: 3q^2+9q+2
       483: 8q^2+9q+2
       484: q^2+11q+2
       485: 8q+2
       487: q^2+8q+2
       489: 2q^2+5q+2
       491: 3q^2+9q+2
       492: 3q^2+9q+2
       493: 2q^2+6q+2
       494: q^3+8q^2+10q+2
       495: 2q^2+6q+2
       496: q^2+9q+2
       497: 3q^2+9q+2
       498: q^3+8q^2+10q+2
       499: 2q^2+6q+2
       500: 2q^2+6q+2
       501: q^2+9q+2
       502: 8q+2
       504: q^2+8q+2
       506: 2q^2+5q+2
       508: q^2+8q+2
       509: q^2+11q+2
       510: 3q^2+9q+2
       511: q^2+9q+2
       512: q^2+6q+2
       513: q^2+9q+2
       514: q^2+6q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: 3q^2+12q+2
       519: 5q^2+12q+2
       520: 5q^2+9q+2
       521: q+1
       524: q+1
       525: 4q+1
       528: 4q+1
       529: q^2+2q+1
       532: q^2+2q+1
       533: q+1
       536: q+1
       537: 2q+1
       539: 2q+1
       541: q^2+3q+1
       542: q
       543: q^2+3q+1
       544: q
       545: 2q^2+4q+1
       547: 2q^2+4q+1
       549: q+1
       552: q+1
       553: 2q+1
       555: 2q+1
       557: q^2+3q+1
       558: q
       559: q^2+3q+1
       560: q
       561: 2q^2+4q+1
       563: 2q^2+4q+1
       565: 2q+1
       566: q
       567: q
       568: 2q+1
       569: q^2+4q+1
       570: q^2+4q+1
       573: q^2+3q+1
       574: q^2+q
       575: q^2+3q+1
       576: q^2+q
       577: 2q^2+6q+2
       579: 2q
       583: 5q+2
       585: 5q+2
       587: q^2+6q+2
       589: q^2+3q+1
       590: q^2+3q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: q^2+3q+1
       596: q^2+3q+1
       597: 5q+2
       599: 4q^2+7q+2
       601: 7q+2
       603: 2q+1
       604: 2q+1
       605: 2q+2
       607: q^2+3q+1
       608: q^2+3q+1
       609: q^2+4q+2
       611: 5q+2
       613: q^2+4q+2
       615: 4q+1
       616: 4q+1
       617: 5q+2
       619: q^2+3q+1
       620: q^2+3q+1
       621: 2q+1
       622: 2q+1
       623: 2q+2
       625: q^2+4q+2
       627: 5q+2
       629: q^2+4q+2
       631: 4q+1
       632: 4q+1
       633: 5q+2
       635: 7q+2
       637: 5q+2
       639: 4q+2
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: 3q+2
       647: 4q+1
       648: 4q+1
       649: 4q+1
       650: 4q+1
       651: 4q+2
       653: 5q+2
       654: 2q
       655: 5q+2
       656: 2q
       657: q+4
       658: 3q+4
       660: 4q+4
       662: 3q+4
       664: 3q+4
       665: q^2+8q+2
       666: 8q+2
       668: q^2+8q+2
       670: 2q^2+5q+2
       672: q^2+11q+2
       673: 3q^2+9q+2
       674: q+4
       675: 3q+2
       676: 3q^2+9q+2
       677: 2q^2+6q+2
       678: q^2+9q+2
       679: q^2+6q+2
       680: q+4
       681: 3q^2+9q+2
       682: 3q+2
       683: 2q^2+6q+2
       684: q^2+9q+2
       685: q^2+6q+2
       686: q^2+8q+2
       687: q^2+6q+2
       688: q^2+6q+2
       689: 2q+1
       690: 3q+4
       691: 4q+4
       692: 3q+4
       693: q^2+3q+1
       695: q
       697: q^2+3q+1
       702: q
       705: q+1
       708: q+1
       709: q+1
       712: q+1
       713: q+1
       716: q+1
       717: q+1
       720: q+1
       721: 1
       723: 1
       725: q+1
       727: q+1
       729: 2q+1
       731: 2q+1
       733: 2q+1
       735: 2q+1
       737: 1
       739: 1
       741: q+1
       743: q+1
       745: 2q+1
       747: 2q+1
       749: 2q+1
       751: 2q+1
       753: q+1
       756: q+1
       757: q+1
       758: q+1
       761: 2q+1
       762: 2q+1
       763: q
       764: q
       765: 2q+1
       766: q
       767: q
       768: 2q+1
       769: 3q+2
       771: q
       775: q+4
       777: 5q+2
       779: 3q+4
       781: 4q+2
       783: 5q+2
       785: 2q+1
       786: 2q+1
       787: 2q+1
       788: 2q+1
       789: 7q+2
       791: 3q+2
       793: 2
       794: 2
       795: q+4
       797: q+2
       799: 2q+2
       801: q+1
       802: q+1
       805: 2q+1
       806: 2q+1
       807: q^2+3q+1
       808: q^2+3q+1
       809: 2q+2
       811: q^2+4q+2
       813: 5q+2
       815: 4q+1
       816: 4q+1
       817: 2
       818: 2
       819: q+4
       821: q+2
       823: 2q+2
       825: q^2+3q+1
       826: q^2+3q+1
       827: 2q+1
       828: 2q+1
       831: q+1
       832: q+1
       833: 2q+2
       835: q^2+4q+2
       837: 5q+2
       839: 4q+1
       840: 4q+1
       841: 4q+2
       843: 2
       844: 2
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: q+2
       851: 3q+2
       853: 4q+2
       855: q+1
       857: 5q+2
       858: 2q
       859: 3q+4
       861: 4q+4
       863: 3q+4
       865: q+4
       866: q+4
       867: 3q+4
       868: q^2+8q+2
       869: q+4
       870: q+4
       871: 3q+2
       872: q^2+6q+2
       873: q+4
       874: q+4
       875: 3q+2
       876: q^2+6q+2
       877: 3q+2
       878: 3q+2
       879: 2q+1
       880: 2q+1
       884: q+1
       889: q+1
       896: q+1
       899: q+1
       900: 1
       902: 1
       904: 1
       906: 1
       908: q+1
       911: q+1
       912: 1
       914: 1
       916: 2
       918: 2
       920: 1
       922: 1
       928: q+1
       930: q+1
       932: 2q+1
       934: 2q+1
       936: 1
       938: 1
       940: 2
       942: 2
       944: 1
       946: 1
       948: q+1
       950: q+1
       956: 2q+1
       958: 2q+1
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: q+1
       975: q+1
       978: q+1
       979: q+1
       982: 3q+2
       984: q
       988: 2q+1
       989: q
       990: q
       991: 2q+1
       992: q+4
       994: q+4
       996: 3q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1002: 4q+2
      1004: 2q+1
      1005: 2q+1
      1006: 2q+1
      1007: 2q+1
      1008: 3q+2
      1010: q+2
      1012: 2
      1013: 2
      1014: q+4
      1016: 2
      1017: 2
      1018: q+2
      1020: q+4
      1022: q+2
      1024: 2q+2
      1026: q+1
      1027: q+1
      1030: q+4
      1032: 2
      1033: 2
      1034: q+2
      1036: q+4
      1038: q+2
      1042: 2q+2
      1044: q+1
      1045: q+1
      1046: 2
      1047: 2
      1048: 2
      1050: q+2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: q+4
      1076: 2
      1077: q+4
      1078: 3q+2
      1080: 2
      1081: q+4
      1082: 3q+2
      1083: q+1
      1084: 2
      1085: 2q+1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1098: q+1
      1102: q+1
      1110: 1
      1112: 1
      1114: 2
      1116: 2
      1118: 1
      1120: 1
      1122: 2
      1124: 2
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: q+1
      1135: q+1
      1138: 2
      1141: 2
      1144: 2
      1146: 2
      1148: 1
      1150: 1
      1156: 1
      1158: 1
      1164: 2
      1166: 2
      1168: 1
      1170: 1
      1172: 1
      1174: 1
      1184: 1
      1185: 1
      1188: 2
      1191: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1214: q+4
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1220: 2
      1222: q+2
      1224: 2
      1225: 2
      1230: 2
      1234: 1
      1235: 1
      1236: q+4
      1238: q+2
      1240: q+1
      1241: q+1
      1248: 2
      1250: 1
      1251: 1
      1252: q+4
      1256: q+2
      1260: q+1
      1261: q+1
      1264: 2
      1266: 1
      1272: 1
      1274: 2
      1276: q+1
      1278: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1293: 1
      1294: 1
      1295: 1
      1302: 1
      1305: 1
      1306: 1
      1307: 1
      1314: 2
      1316: 2
      1318: 2
      1320: 2
      1322: 1
      1323: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1334: 2
      1337: 2
      1352: 1
      1354: 1
      1356: 1
      1358: 1
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1414: 1
      1415: 1
      1430: 1
      1433: 1
      1446: 2
      1448: 2
      1454: 1
      1455: 1
      1456: 2
      1460: 1
      1461: 1
      1464: 1
      1470: 1
      1472: 2
      1474: 1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1489: 1
      1492: 1
      1493: 1
      1494: 1
      1559: 1
      1560: 1
      1567: 1
      1569: 1
      1583: 1
      1585: 1
      1631: 1
      1634: 1
      1641: 1
      1661: 1
      1671: 1
      1673: 1
      1815: 1

1816:    0: 2q^4+21q^3+34q^2+14q+2
         1: 2q^4+21q^3+34q^2+14q+2
         2: q^5+5q^4+20q^3+27q^2+13q+2
         3: 22q^3+34q^2+14q+2
         4: 2q^4+21q^3+34q^2+14q+2
         5: 22q^3+34q^2+14q+2
         6: 2q^4+21q^3+34q^2+14q+2
         7: q^5+5q^4+20q^3+27q^2+13q+2
         8: 7q^4+23q^3+27q^2+13q+2
         9: q^6+4q^5+10q^4+18q^3+19q^2+10q+2
        10: 2q^4+21q^3+34q^2+14q+2
        11: 22q^3+34q^2+14q+2
        12: 2q^4+21q^3+34q^2+14q+2
        13: q^4+12q^3+26q^2+13q+2
        14: q^4+12q^3+26q^2+13q+2
        15: 15q^3+26q^2+13q+2
        16: 11q^3+31q^2+14q+2
        17: 11q^3+31q^2+14q+2
        18: q^5+5q^4+15q^3+19q^2+10q+2
        19: 2q^4+21q^3+34q^2+14q+2
        20: 2q^4+21q^3+34q^2+14q+2
        21: q^5+5q^4+20q^3+27q^2+13q+2
        22: 11q^3+31q^2+14q+2
        23: 11q^3+31q^2+14q+2
        24: 2q^4+15q^3+24q^2+13q+2
        25: 11q^3+31q^2+14q+2
        26: 11q^3+31q^2+14q+2
        27: 2q^4+15q^3+24q^2+13q+2
        28: 11q^3+31q^2+14q+2
        29: 2q^4+21q^3+34q^2+14q+2
        30: q^4+12q^3+26q^2+13q+2
        31: 11q^3+31q^2+14q+2
        32: 7q^3+23q^2+13q+2
        33: 4q^3+28q^2+14q+2
        34: 11q^3+31q^2+14q+2
        35: 7q^3+23q^2+13q+2
        36: 4q^3+28q^2+14q+2
        37: 8q^2+2q
        38: 4q^3+21q^2+12q+2
        39: 8q^2+2q
        40: 4q^3+21q^2+12q+2
        41: 3q^3+5q^2+2q
        42: 8q^3+17q^2+11q+2
        43: q^4+12q^3+26q^2+13q+2
        44: q^4+12q^3+26q^2+13q+2
        45: 15q^3+26q^2+13q+2
        46: 3q^3+23q^2+13q+2
        47: 5q^3+23q^2+13q+2
        48: q^4+8q^3+18q^2+10q+2
        49: 11q^3+31q^2+14q+2
        50: 11q^3+31q^2+14q+2
        51: q^5+5q^4+15q^3+19q^2+10q+2
        52: 11q^3+31q^2+14q+2
        53: 11q^3+31q^2+14q+2
        54: 2q^4+15q^3+24q^2+13q+2
        55: 11q^3+31q^2+14q+2
        56: 11q^3+31q^2+14q+2
        57: 2q^4+15q^3+24q^2+13q+2
        58: 2q^3+14q^2+7q+1
        59: 2q^3+14q^2+7q+1
        60: 2q^3+14q^2+7q+1
        61: 2q^3+14q^2+7q+1
        62: 8q^2+2q
        63: 4q^3+21q^2+12q+2
        64: 5q^2+2q
        65: 3q^3+16q^2+11q+2
        66: 8q^2+2q
        67: 18q^2+12q+2
        68: q^3+15q^2+12q+2
        69: 3q^3+15q^2+10q+2
        70: q^4+12q^3+26q^2+13q+2
        71: 11q^3+31q^2+14q+2
        72: 4q^3+28q^2+14q+2
        73: 4q^3+28q^2+14q+2
        74: 8q^2+2q
        75: 4q^3+21q^2+12q+2
        76: 8q^2+2q
        77: 4q^3+21q^2+12q+2
        78: 3q^3+5q^2+2q
        79: 8q^3+17q^2+11q+2
        80: 7q^3+23q^2+13q+2
        81: q^3+20q^2+13q+2
        82: 11q^3+31q^2+14q+2
        83: 7q^3+23q^2+13q+2
        84: 7q^3+23q^2+13q+2
        85: q^3+20q^2+13q+2
        86: 11q^3+31q^2+14q+2
        87: 7q^3+23q^2+13q+2
        88: 3q^3+23q^2+13q+2
        89: 5q^3+23q^2+13q+2
        90: q^4+8q^3+18q^2+10q+2
        91: 3q^3+23q^2+13q+2
        92: 5q^3+23q^2+13q+2
        93: q^4+8q^3+18q^2+10q+2
        94: 4q^3+24q^2+14q+2
        95: 4q^3+24q^2+14q+2
        96: 2q^4+10q^3+16q^2+10q+2
        97: 4q^3+24q^2+14q+2
        98: 4q^3+24q^2+14q+2
        99: 2q^4+10q^3+16q^2+10q+2
       100: 4q^3+25q^2+13q+2
       101: 4q^3+25q^2+13q+2
       102: 8q^3+18q^2+12q+2
       103: 4q^2+q
       104: 9q^2+6q+1
       105: 9q^2+6q+1
       106: 4q^2+q
       107: 2q^3+14q^2+7q+1
       108: 2q^3+14q^2+7q+1
       109: 2q^3+14q^2+7q+1
       110: 2q^3+14q^2+7q+1
       111: 8q^2+2q
       112: 18q^2+12q+2
       113: 8q^2+2q
       114: 4q^3+21q^2+12q+2
       115: 5q^2+2q
       116: 3q^3+16q^2+11q+2
       117: 6q^2+6q+1
       118: 6q^2+6q+1
       119: 6q^2+6q+1
       120: 6q^2+6q+1
       121: 5q^2+2q
       122: 3q^3+16q^2+11q+2
       123: 5q^2+2q
       124: 13q^2+11q+2
       125: q^3+15q^2+12q+2
       126: 3q^3+15q^2+10q+2
       128: 12q^2+12q+2
       130: 12q^2+12q+2
       132: 4q^3+10q^2+8q+2
       133: q^3+15q^2+12q+2
       134: 3q^3+15q^2+10q+2
       135: q^3+20q^2+13q+2
       136: q^3+20q^2+13q+2
       137: q^3+20q^2+13q+2
       138: q^3+12q^2+10q+2
       139: 4q^3+24q^2+14q+2
       140: 12q^2+10q+2
       141: 7q^3+23q^2+13q+2
       142: 4q^3+24q^2+14q+2
       143: q^3+20q^2+13q+2
       144: q^3+12q^2+10q+2
       145: 4q^3+24q^2+14q+2
       146: 7q^3+23q^2+13q+2
       147: 4q^3+24q^2+14q+2
       148: 12q^2+10q+2
       149: 4q^3+25q^2+13q+2
       150: 3q^3+17q^2+12q+2
       151: 7q^2+2q
       152: 4q^3+18q^2+11q+2
       153: 7q^2+2q
       154: 4q^3+18q^2+11q+2
       155: 2q^3+4q^2+2q
       156: 6q^3+14q^2+10q+2
       157: 3q^3+23q^2+13q+2
       158: 5q^3+23q^2+13q+2
       159: q^4+8q^3+18q^2+10q+2
       160: q^3+12q^2+13q+2
       161: q^3+12q^2+13q+2
       162: 3q^3+11q^2+10q+2
       163: q^3+12q^2+13q+2
       164: q^3+12q^2+13q+2
       165: 3q^3+11q^2+10q+2
       166: 15q^2+13q+2
       167: 15q^2+13q+2
       168: 4q^3+11q^2+9q+2
       169: 4q^2+q
       170: 9q^2+6q+1
       171: 9q^2+6q+1
       172: 4q^2+q
       173: q^2+q
       174: 4q^2+5q+1
       175: 4q^2+5q+1
       176: q^2+q
       178: 6q^2+8q+2
       180: 12q^2+12q+2
       182: 12q^2+12q+2
       183: 6q^2+6q+1
       184: 6q^2+6q+1
       185: 6q^2+6q+1
       186: 6q^2+6q+1
       187: 5q^2+2q
       188: 13q^2+11q+2
       189: 5q^2+2q
       190: 3q^3+16q^2+11q+2
       191: 6q^2+6q+1
       192: 6q^2+6q+1
       193: 6q^2+5q+1
       194: 6q^2+5q+1
       195: 2q^3+12q^2+7q+1
       196: 2q^3+12q^2+7q+1
       197: 4q^2+2q
       198: 8q^2+8q+2
       199: 6q^2+6q+1
       200: 6q^2+6q+1
       201: 2q^3+12q^2+7q+1
       202: 2q^3+12q^2+7q+1
       203: 6q^2+5q+1
       204: 6q^2+5q+1
       205: 4q^2+2q
       206: 8q^2+8q+2
       207: 5q^2+2q
       208: 13q^2+11q+2
       209: 7q^2+2q
       210: 4q^3+18q^2+11q+2
       211: 4q^2+2q
       212: 3q^3+13q^2+10q+2
       214: 2q^2+9q+2
       216: 2q^2+9q+2
       218: 4q^2+6q+2
       219: q^3+8q^2+9q+2
       220: q^3+15q^2+12q+2
       221: 3q^3+15q^2+10q+2
       222: q^3+20q^2+13q+2
       223: q^3+12q^2+10q+2
       224: q^3+20q^2+13q+2
       225: q^3+12q^2+10q+2
       226: q^3+12q^2+10q+2
       227: 6q^2+12q+2
       228: q^3+8q^2+10q+2
       229: 5q^2+9q+2
       230: q^3+12q^2+13q+2
       231: q^3+12q^2+10q+2
       232: 6q^2+12q+2
       233: q^3+8q^2+10q+2
       234: q^3+12q^2+13q+2
       235: 5q^2+9q+2
       236: 8q^2+9q+2
       238: 8q^2+11q+2
       240: 8q^2+11q+2
       242: 2q^3+7q^2+7q+2
       243: 15q^2+13q+2
       244: 8q^2+10q+2
       245: 8q^2+10q+2
       246: 3q^3+17q^2+12q+2
       247: 15q^2+13q+2
       248: 15q^2+13q+2
       249: 4q^3+11q^2+9q+2
       250: q^3+12q^2+13q+2
       251: q^3+12q^2+13q+2
       252: 3q^3+11q^2+10q+2
       253: q^3+12q^2+13q+2
       254: q^3+12q^2+13q+2
       255: 3q^3+11q^2+10q+2
       256: 3q^2+12q+2
       257: 5q^2+12q+2
       258: 5q^2+9q+2
       260: 6q^2+6q+1
       261: 6q^2+6q+1
       263: q^2+q
       264: 4q^2+5q+1
       265: 4q^2+5q+1
       266: q^2+q
       267: 2q^2+q
       268: 4q^2+4q+1
       269: 2q^2+q
       270: 4q^2+4q+1
       271: 2q^2+q
       272: 4q^2+4q+1
       273: 2q^2+q
       274: 4q^2+4q+1
       275: q^2+q
       276: 4q^2+5q+1
       277: 4q^2+5q+1
       278: q^2+q
       280: 8q+2
       282: q^2+6q+2
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       286: 2q^2+3q+1
       288: 6q^2+8q+2
       290: 2q^2+9q+2
       292: 6q^2+8q+2
       293: 6q^2+6q+1
       294: 6q^2+6q+1
       295: 6q^2+6q+1
       296: 6q^2+6q+1
       297: 5q^2+2q
       298: 13q^2+11q+2
       299: q^2+4q+1
       300: q^2+4q+1
       302: 4q^2+8q+2
       303: 3q^2+6q+1
       304: 3q^2+6q+1
       305: q^2+2q
       306: 4q^2+7q+2
       307: 3q^2+6q+1
       308: 3q^2+6q+1
       309: q^2+4q+1
       310: q^2+4q+1
       312: 4q^2+8q+2
       313: q^2+2q
       314: 4q^2+7q+2
       316: 4q^2+7q+2
       318: 8q^2+11q+2
       319: 4q^2+5q+1
       320: 4q^2+5q+1
       321: 4q^2+5q+1
       322: 4q^2+5q+1
       323: 2q^2+2q
       324: 2q^2+6q+2
       325: 4q^2+2q
       326: 3q^3+13q^2+10q+2
       328: 2q^2+9q+2
       330: 2q^2+9q+2
       332: 4q^2+6q+2
       333: q^3+8q^2+9q+2
       334: q^3+12q^2+10q+2
       335: q^3+12q^2+10q+2
       336: 8q^2+9q+2
       337: 15q^2+13q+2
       339: 8q^2+11q+2
       341: 8q^2+11q+2
       343: 2q^3+7q^2+7q+2
       344: 3q^2+9q+2
       345: 6q^2+12q+2
       346: q^3+8q^2+10q+2
       347: 5q^2+9q+2
       348: 2q^2+6q+2
       349: q^3+12q^2+13q+2
       350: q^3+8q^2+10q+2
       351: 8q^2+10q+2
       352: 3q^2+9q+2
       353: 6q^2+12q+2
       354: q^3+8q^2+10q+2
       355: q^3+12q^2+13q+2
       356: q^3+8q^2+10q+2
       357: 5q^2+9q+2
       358: 2q^2+6q+2
       359: 8q^2+10q+2
       361: 8q+2
       363: q^2+8q+2
       365: 2q^2+5q+2
       366: 8q^2+9q+2
       367: q^2+11q+2
       368: 3q^2+9q+2
       369: q^2+9q+2
       370: q^2+9q+2
       371: 3q^2+12q+2
       372: 5q^2+12q+2
       373: 5q^2+9q+2
       374: 3q^2+12q+2
       375: 5q^2+12q+2
       376: 5q^2+9q+2
       378: q^2+2q+1
       379: q^2+2q+1
       382: 4q+1
       383: 4q+1
       385: q^2+q
       386: 4q^2+5q+1
       387: 4q^2+5q+1
       388: q^2+q
       390: 2q^2+4q+1
       392: 2q^2+4q+1
       393: q
       394: q^2+3q+1
       395: q^2+3q+1
       396: q
       398: 2q^2+4q+1
       400: 2q^2+4q+1
       401: q
       402: q^2+3q+1
       403: q^2+3q+1
       404: q
       405: q^2+q
       406: q^2+q
       407: q^2+3q+1
       408: q^2+3q+1
       410: 8q+2
       412: q^2+6q+2
       414: 5q+2
       416: 2q^2+9q+2
       418: q^2+6q+2
       419: 2q^2+3q+1
       420: 2q^2+3q+1
       421: 2q^2+3q+1
       422: 2q^2+3q+1
       424: 6q^2+8q+2
       426: 4q^2+7q+2
       428: 8q^2+11q+2
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q^2+3q+1
       434: q^2+4q+2
       436: 5q+2
       437: q^2+4q+1
       438: q^2+4q+1
       439: 3q^2+6q+1
       440: 3q^2+6q+1
       441: q^2+2q
       442: 4q^2+7q+2
       443: 4q^2+5q+1
       444: 4q^2+5q+1
       446: 4q^2+8q+2
       447: q^2+3q+1
       448: q^2+3q+1
       449: 2q+1
       450: 2q+1
       452: q^2+4q+2
       453: 3q^2+6q+1
       454: 3q^2+6q+1
       456: 5q+2
       457: q^2+4q+1
       458: q^2+4q+1
       459: q^2+2q
       460: 4q^2+7q+2
       461: 4q^2+5q+1
       462: 4q^2+5q+1
       464: 4q^2+8q+2
       466: 7q+2
       468: 5q+2
       470: 4q^2+7q+2
       471: 4q+1
       472: 4q+1
       473: 4q+1
       474: 4q+1
       475: 2q
       476: 5q+2
       478: 2q^2+8q+2
       479: 2q^2+2q
       480: 2q^2+6q+2
       481: 3q^2+9q+2
       482: 3q^2+9q+2
       483: 8q^2+9q+2
       484: q^2+11q+2
       486: 8q+2
       488: q^2+8q+2
       490: 2q^2+5q+2
       491: 3q^2+9q+2
       492: 3q^2+9q+2
       493: 2q^2+6q+2
       494: q^3+8q^2+10q+2
       495: 2q^2+6q+2
       496: q^2+9q+2
       497: 3q^2+9q+2
       498: q^3+8q^2+10q+2
       499: 2q^2+6q+2
       500: 2q^2+6q+2
       501: q^2+9q+2
       503: 8q+2
       505: q^2+8q+2
       507: 2q^2+5q+2
       508: q^2+8q+2
       509: q^2+11q+2
       510: 3q^2+9q+2
       511: q^2+9q+2
       512: q^2+6q+2
       513: q^2+9q+2
       514: q^2+6q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: 3q^2+12q+2
       519: 5q^2+12q+2
       520: 5q^2+9q+2
       522: q+1
       523: q+1
       526: 4q+1
       527: 4q+1
       530: q^2+2q+1
       531: q^2+2q+1
       534: q+1
       535: q+1
       538: 2q+1
       540: 2q+1
       541: q
       542: q^2+3q+1
       543: q
       544: q^2+3q+1
       546: 2q^2+4q+1
       548: 2q^2+4q+1
       550: q+1
       551: q+1
       554: 2q+1
       556: 2q+1
       557: q
       558: q^2+3q+1
       559: q
       560: q^2+3q+1
       562: 2q^2+4q+1
       564: 2q^2+4q+1
       565: q
       566: 2q+1
       567: 2q+1
       568: q
       571: q^2+4q+1
       572: q^2+4q+1
       573: q^2+q
       574: q^2+3q+1
       575: q^2+q
       576: q^2+3q+1
       581: 2q^2+6q+2
       582: 2q
       584: 5q+2
       586: 5q+2
       588: q^2+6q+2
       589: q^2+3q+1
       590: q^2+3q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: q^2+3q+1
       596: q^2+3q+1
       598: 5q+2
       600: 4q^2+7q+2
       602: 7q+2
       603: 2q+1
       604: 2q+1
       606: 2q+2
       607: q^2+3q+1
       608: q^2+3q+1
       610: q^2+4q+2
       612: 5q+2
       614: q^2+4q+2
       615: 4q+1
       616: 4q+1
       618: 5q+2
       619: q^2+3q+1
       620: q^2+3q+1
       621: 2q+1
       622: 2q+1
       624: 2q+2
       626: q^2+4q+2
       628: 5q+2
       630: q^2+4q+2
       631: 4q+1
       632: 4q+1
       634: 5q+2
       636: 7q+2
       638: 5q+2
       640: 4q+2
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       646: 3q+2
       647: 4q+1
       648: 4q+1
       649: 4q+1
       650: 4q+1
       652: 4q+2
       653: 2q
       654: 5q+2
       655: 2q
       656: 5q+2
       657: q+4
       659: 3q+4
       661: 4q+4
       663: 3q+4
       664: 3q+4
       665: q^2+8q+2
       667: 8q+2
       669: q^2+8q+2
       671: 2q^2+5q+2
       672: q^2+11q+2
       673: 3q^2+9q+2
       674: q+4
       675: 3q+2
       676: 3q^2+9q+2
       677: 2q^2+6q+2
       678: q^2+9q+2
       679: q^2+6q+2
       680: q+4
       681: 3q^2+9q+2
       682: 3q+2
       683: 2q^2+6q+2
       684: q^2+9q+2
       685: q^2+6q+2
       686: q^2+8q+2
       687: q^2+6q+2
       688: q^2+6q+2
       689: 2q+1
       690: 3q+4
       691: 4q+4
       692: 3q+4
       699: q^2+3q+1
       700: q^2+3q+1
       703: q
       704: q
       706: q+1
       707: q+1
       710: q+1
       711: q+1
       714: q+1
       715: q+1
       718: q+1
       719: q+1
       722: 1
       724: 1
       726: q+1
       728: q+1
       730: 2q+1
       732: 2q+1
       734: 2q+1
       736: 2q+1
       738: 1
       740: 1
       742: q+1
       744: q+1
       746: 2q+1
       748: 2q+1
       750: 2q+1
       752: 2q+1
       754: q+1
       755: q+1
       759: q+1
       760: q+1
       761: q
       762: q
       763: 2q+1
       764: 2q+1
       765: q
       766: 2q+1
       767: 2q+1
       768: q
       773: 3q+2
       774: q
       776: q+4
       778: 5q+2
       780: 3q+4
       782: 4q+2
       784: 5q+2
       785: 2q+1
       786: 2q+1
       787: 2q+1
       788: 2q+1
       790: 7q+2
       792: 3q+2
       793: 2
       794: 2
       796: q+4
       798: q+2
       800: 2q+2
       801: q+1
       802: q+1
       805: 2q+1
       806: 2q+1
       807: q^2+3q+1
       808: q^2+3q+1
       810: 2q+2
       812: q^2+4q+2
       814: 5q+2
       815: 4q+1
       816: 4q+1
       817: 2
       818: 2
       820: q+4
       822: q+2
       824: 2q+2
       825: q^2+3q+1
       826: q^2+3q+1
       827: 2q+1
       828: 2q+1
       831: q+1
       832: q+1
       834: 2q+2
       836: q^2+4q+2
       838: 5q+2
       839: 4q+1
       840: 4q+1
       842: 4q+2
       843: 2
       844: 2
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       850: q+2
       852: 3q+2
       854: 4q+2
       856: q+1
       857: 2q
       858: 5q+2
       860: 3q+4
       862: 4q+4
       864: 3q+4
       865: q+4
       866: q+4
       867: 3q+4
       868: q^2+8q+2
       869: q+4
       870: q+4
       871: 3q+2
       872: q^2+6q+2
       873: q+4
       874: q+4
       875: 3q+2
       876: q^2+6q+2
       877: 3q+2
       878: 3q+2
       879: 2q+1
       880: 2q+1
       890: q+1
       891: q+1
       897: q+1
       898: q+1
       901: 1
       903: 1
       905: 1
       907: 1
       909: q+1
       910: q+1
       913: 1
       915: 1
       917: 2
       919: 2
       921: 1
       923: 1
       929: q+1
       931: q+1
       933: 2q+1
       935: 2q+1
       937: 1
       939: 1
       941: 2
       943: 2
       945: 1
       947: 1
       949: q+1
       951: q+1
       957: 2q+1
       959: 2q+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: q+1
       977: q+1
       980: q+1
       981: q+1
       986: 3q+2
       987: q
       988: q
       989: 2q+1
       990: 2q+1
       991: q
       993: q+4
       995: q+4
       997: 3q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1003: 4q+2
      1004: 2q+1
      1005: 2q+1
      1006: 2q+1
      1007: 2q+1
      1009: 3q+2
      1011: q+2
      1012: 2
      1013: 2
      1015: q+4
      1016: 2
      1017: 2
      1019: q+2
      1021: q+4
      1023: q+2
      1025: 2q+2
      1026: q+1
      1027: q+1
      1031: q+4
      1032: 2
      1033: 2
      1035: q+2
      1037: q+4
      1039: q+2
      1043: 2q+2
      1044: q+1
      1045: q+1
      1046: 2
      1047: 2
      1049: 2
      1051: q+2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: q+4
      1076: 2
      1077: q+4
      1078: 3q+2
      1080: 2
      1081: q+4
      1082: 3q+2
      1083: q+1
      1084: 2
      1085: 2q+1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1104: q+1
      1105: q+1
      1111: 1
      1113: 1
      1115: 2
      1117: 2
      1119: 1
      1121: 1
      1123: 2
      1125: 2
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1136: q+1
      1137: q+1
      1139: 2
      1142: 2
      1145: 2
      1147: 2
      1149: 1
      1151: 1
      1157: 1
      1159: 1
      1165: 2
      1167: 2
      1169: 1
      1171: 1
      1173: 1
      1175: 1
      1186: 1
      1187: 1
      1189: 2
      1192: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1215: q+4
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1221: 2
      1223: q+2
      1224: 2
      1225: 2
      1231: 2
      1234: 1
      1235: 1
      1237: q+4
      1239: q+2
      1240: q+1
      1241: q+1
      1249: 2
      1250: 1
      1251: 1
      1253: q+4
      1257: q+2
      1260: q+1
      1261: q+1
      1265: 2
      1267: 1
      1273: 1
      1275: 2
      1277: q+1
      1279: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1296: 1
      1297: 1
      1298: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 2
      1317: 2
      1319: 2
      1321: 2
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1335: 2
      1338: 2
      1353: 1
      1355: 1
      1357: 1
      1359: 1
      1377: 1
      1379: 1
      1381: 1
      1383: 1
      1416: 1
      1417: 1
      1431: 1
      1434: 1
      1447: 2
      1449: 2
      1454: 1
      1455: 1
      1457: 2
      1460: 1
      1461: 1
      1465: 1
      1471: 1
      1473: 2
      1475: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1490: 1
      1495: 1
      1496: 1
      1497: 1
      1561: 1
      1562: 1
      1568: 1
      1570: 1
      1584: 1
      1586: 1
      1632: 1
      1635: 1
      1642: 1
      1662: 1
      1672: 1
      1673: 1
      1816: 1

1817:    0: 7q^3+11q^2+4q+2
         1: q^4+8q^3+11q^2+4q+2
         2: q^5+2q^4+5q^3+8q^2+4q+2
         3: 7q^3+11q^2+4q+2
         4: 7q^3+11q^2+4q+2
         5: q^4+8q^3+11q^2+4q+2
         6: q^4+8q^3+11q^2+4q+2
         7: q^5+2q^4+5q^3+8q^2+4q+2
         8: 3q^4+6q^3+8q^2+4q+2
         9: q^5+2q^4+5q^3+8q^2+4q+2
        10: 4q^3+7q^2+4q+2
        11: 4q^3+7q^2+4q+2
        12: 4q^3+7q^2+4q+2
        13: 2q^3+8q^2+4q+2
        14: 2q^3+8q^2+4q+2
        15: 3q^3+8q^2+4q+2
        16: 7q^3+11q^2+4q+2
        17: q^4+8q^3+11q^2+4q+2
        18: q^5+2q^4+5q^3+8q^2+4q+2
        19: 7q^3+11q^2+4q+2
        20: q^4+8q^3+11q^2+4q+2
        21: q^5+2q^4+5q^3+8q^2+4q+2
        22: 4q^3+10q^2+4q+2
        23: 4q^3+10q^2+4q+2
        24: q^4+4q^3+7q^2+4q+2
        25: 4q^3+10q^2+4q+2
        26: 4q^3+10q^2+4q+2
        27: q^4+4q^3+7q^2+4q+2
        28: 4q^3+7q^2+4q+2
        29: 4q^3+7q^2+4q+2
        30: 2q^3+8q^2+4q+2
        31: 2q^3+6q^2+4q+2
        32: q^3+7q^2+4q+2
        33: 4q^3+10q^2+4q+2
        34: 2q^3+6q^2+4q+2
        35: q^3+7q^2+4q+2
        36: 4q^3+10q^2+4q+2
        37: q^3+7q^2+2q+2
        38: 3q^2+2q
        39: q^3+7q^2+2q+2
        40: 3q^2+2q
        41: 3q^3+4q^2+2q+2
        42: 3q^2+2q
        43: 4q^2+4q+2
        44: 4q^2+4q+2
        45: 4q^2+4q+2
        46: 2q^3+8q^2+4q+2
        47: 3q^3+8q^2+4q+2
        48: 2q^3+8q^2+4q+2
        49: 7q^3+11q^2+4q+2
        50: q^4+8q^3+11q^2+4q+2
        51: q^5+2q^4+5q^3+8q^2+4q+2
        52: 4q^3+10q^2+4q+2
        53: 4q^3+10q^2+4q+2
        54: q^4+4q^3+7q^2+4q+2
        55: 4q^3+10q^2+4q+2
        56: 4q^3+10q^2+4q+2
        57: q^4+4q^3+7q^2+4q+2
        58: q^3+3q^2+2q+1
        59: q^3+3q^2+2q+1
        60: q^3+3q^2+2q+1
        61: q^3+3q^2+2q+1
        62: 6q^2+2q+2
        63: 2q
        64: 4q^2+2q+2
        65: 3q^2+2q
        66: q^3+7q^2+2q+2
        67: 3q^2+2q
        68: q^2+4q+2
        69: 2q^3+8q^2+4q+2
        70: 4q^2+4q+2
        71: 4q^3+7q^2+4q+2
        72: 4q^3+10q^2+4q+2
        73: 4q^3+10q^2+4q+2
        74: q^3+7q^2+2q+2
        75: 3q^2+2q
        76: q^3+7q^2+2q+2
        77: 3q^2+2q
        78: 3q^3+4q^2+2q+2
        79: 3q^2+2q
        80: 3q^2+4q+2
        81: q^3+7q^2+4q+2
        82: 2q^3+6q^2+4q+2
        83: q^3+7q^2+4q+2
        84: 3q^2+4q+2
        85: q^3+7q^2+4q+2
        86: 2q^3+6q^2+4q+2
        87: q^3+7q^2+4q+2
        88: 4q^2+4q+2
        89: 4q^2+4q+2
        90: 4q^2+4q+2
        91: 2q^3+8q^2+4q+2
        92: 3q^3+8q^2+4q+2
        93: 2q^3+8q^2+4q+2
        94: 4q^3+10q^2+4q+2
        95: 4q^3+10q^2+4q+2
        96: q^4+4q^3+7q^2+4q+2
        97: 4q^3+10q^2+4q+2
        98: 4q^3+10q^2+4q+2
        99: q^4+4q^3+7q^2+4q+2
       100: 9q^2+3q+2
       101: q^3+10q^2+3q+2
       102: 2q^3+6q^2+3q+2
       103: 3q^2+q+1
       104: q
       105: q
       106: 3q^2+q+1
       107: q^3+3q^2+2q+1
       108: q^3+3q^2+2q+1
       109: q^3+3q^2+2q+1
       110: q^3+3q^2+2q+1
       111: q^3+7q^2+2q+2
       112: 3q^2+2q
       113: 6q^2+2q+2
       114: 2q
       115: 4q^2+2q+2
       116: 3q^2+2q
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 3q^2+2q+2
       122: 2q
       123: 4q^2+2q+2
       124: 3q^2+2q
       125: q^2+4q+2
       126: 4q^2+4q+2
       127: q^3+7q^2+2q+2
       128: 3q^2+2q
       129: q^3+7q^2+2q+2
       130: 3q^2+2q
       131: 3q^3+4q^2+2q+2
       132: 3q^2+2q
       133: q^2+4q+2
       134: 2q^3+8q^2+4q+2
       135: q^3+7q^2+4q+2
       136: q^3+7q^2+4q+2
       137: 3q^2+4q+2
       138: q^3+7q^2+4q+2
       139: 2q^3+6q^2+4q+2
       140: 6q^2+2q+2
       141: 3q^2+4q+2
       142: 4q^3+10q^2+4q+2
       143: 3q^2+4q+2
       144: q^3+7q^2+4q+2
       145: 2q^3+6q^2+4q+2
       146: 3q^2+4q+2
       147: 4q^3+10q^2+4q+2
       148: 6q^2+2q+2
       149: 6q^2+3q+2
       150: 6q^2+3q+2
       151: 7q^2+q+2
       152: 2q^2+2q
       153: q^3+7q^2+q+2
       154: 3q^2+2q
       155: 2q^3+4q^2+q+2
       156: 2q^2+2q
       157: 4q^2+4q+2
       158: 4q^2+4q+2
       159: 4q^2+4q+2
       160: q^3+5q^2+4q+2
       161: q^3+5q^2+4q+2
       162: q^3+5q^2+4q+2
       163: q^3+5q^2+4q+2
       164: q^3+5q^2+4q+2
       165: q^3+5q^2+4q+2
       166: 9q^2+3q+2
       167: q^3+10q^2+3q+2
       168: 2q^3+6q^2+3q+2
       169: 3q^2+q+1
       170: q
       171: q
       172: 3q^2+q+1
       173: q+1
       174: q
       175: q
       176: q+1
       177: 4q^2+2q+2
       178: 3q^2+2q
       179: 6q^2+2q+2
       180: 2q
       181: q^3+7q^2+2q+2
       182: 3q^2+2q
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 4q^2+2q+2
       188: 3q^2+2q
       189: 3q^2+2q+2
       190: 2q
       191: 2q+1
       192: 2q+1
       193: 2q^2+q+1
       194: 2q^2+q+1
       195: q^3+3q^2+2q+1
       196: q^3+3q^2+2q+1
       197: 5q^2+2
       198: q^2+2q
       199: 2q+1
       200: 2q+1
       201: q^3+3q^2+2q+1
       202: q^3+3q^2+2q+1
       203: 2q^2+q+1
       204: 2q^2+q+1
       205: 5q^2+2
       206: q^2+2q
       207: 3q^2+2q+2
       208: 2q
       209: 6q^2+q+2
       210: 2q
       211: 4q^2+q+2
       212: 2q^2+2q
       213: q^2+2q+2
       215: q^2+2q+2
       217: q^2+2q+2
       219: q^2+4q+2
       220: q^2+4q+2
       221: 4q^2+4q+2
       222: 3q^2+4q+2
       223: q^3+7q^2+4q+2
       224: 3q^2+4q+2
       225: q^3+7q^2+4q+2
       226: 3q^2+4q+2
       227: 4q+2
       228: q^3+5q^2+4q+2
       229: 3q^2+2q+2
       230: q^3+5q^2+4q+2
       231: 3q^2+4q+2
       232: 4q+2
       233: q^3+5q^2+4q+2
       234: q^3+5q^2+4q+2
       235: 3q^2+2q+2
       236: 6q^2+3q+2
       237: 7q^2+q+2
       238: 2q^2+2q
       239: q^3+7q^2+q+2
       240: 3q^2+2q
       241: 2q^3+4q^2+q+2
       242: 2q^2+2q
       243: 6q^2+3q+2
       244: 6q^2+2q+2
       245: 6q^2+2q+2
       246: 3q^2+3q+2
       247: 9q^2+3q+2
       248: q^3+10q^2+3q+2
       249: 2q^3+6q^2+3q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: 3q^2+q+1
       260: q
       261: q
       262: 3q^2+q+1
       263: q+1
       264: q
       265: q
       266: q+1
       267: 2q^2+1
       268: q
       269: 2q^2+1
       270: q
       271: 2q^2+1
       272: q
       273: 2q^2+1
       274: q
       275: q+1
       276: q
       277: q
       278: q+1
       279: 2q+2
       281: q^2+2q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 3q^2+2q+2
       288: 2q
       289: q^2+2q+2
       291: 4q^2+2q+2
       292: 3q^2+2q
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 3q^2+2q+2
       298: 2q
       299: q+1
       300: q+1
       301: 5q^2+2
       302: q^2+2q
       303: 2q+1
       304: 2q+1
       305: 2q^2+2
       306: q^2+2q
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 5q^2+2
       312: q^2+2q
       313: 2q^2+2
       314: q^2+2q
       315: 4q^2+q+2
       316: 2q^2+2q
       317: 6q^2+q+2
       318: 2q
       319: 2q^2+q+1
       320: 2q^2+q+1
       321: 2q^2+q+1
       322: 2q^2+q+1
       323: 3q^2+2
       324: 2q
       325: 3q^2+q+2
       326: 2q
       333: q^2+4q+2
       334: 3q^2+4q+2
       335: 3q^2+4q+2
       336: 6q^2+3q+2
       337: 6q^2+3q+2
       338: 7q^2+q+2
       339: 2q^2+2q
       340: q^3+7q^2+q+2
       341: 3q^2+2q
       342: 2q^3+4q^2+q+2
       343: 2q^2+2q
       344: 4q+2
       345: 2q+2
       346: q^2+2q+2
       347: q^2+2
       348: 3q^2+2q+2
       349: q^2+2q+2
       350: q^3+5q^2+4q+2
       351: 6q^2+2q+2
       352: 4q+2
       353: 2q+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^3+5q^2+4q+2
       357: q^2+2
       358: 3q^2+2q+2
       359: 6q^2+2q+2
       360: q+2
       362: q+2
       364: q+2
       366: 3q^2+3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 2q^2+3q+2
       372: 3q^2+3q+2
       373: 2q^2+3q+2
       374: q+2
       375: q+2
       376: q+2
       377: q+1
       378: q
       379: q
       380: q+1
       381: q+1
       384: q+1
       385: q+1
       386: q
       387: q
       388: q+1
       389: 2q^2+1
       390: q
       391: 2q^2+1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 2q^2+1
       398: q
       399: 2q^2+1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: q^2+1
       406: q^2+1
       407: q
       408: q
       413: 2q+2
       417: q^2+2q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 3q^2+2q+2
       424: 2q
       425: 4q^2+q+2
       426: 2q^2+2q
       427: 6q^2+q+2
       428: 2q
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 2q^2+2
       434: q^2+2q
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: q^2+2
       443: 2q^2+q+1
       444: 2q^2+q+1
       445: 5q^2+2
       446: q^2+2q
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 2q^2+2
       452: q^2+2q
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: q^2+2
       461: 2q^2+q+1
       462: 2q^2+q+1
       463: 5q^2+2
       464: q^2+2q
       465: q+2
       467: q+2
       469: 3q^2+q+2
       470: 2q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       476: 2q
       477: 3q^2+2
       478: 2q
       479: 3q^2+2
       480: 2q
       481: 4q+2
       482: 4q+2
       483: 3q^2+3q+2
       484: 3q+2
       485: q+2
       487: q+2
       489: q+2
       491: 2q^2+3q+2
       492: 2q+2
       493: q^2+2
       494: q^2+2q+2
       495: 3q^2+2q+2
       496: q^2+2q+2
       497: 2q+2
       498: q^2+2q+2
       499: q^2+2
       500: 3q^2+2q+2
       501: q^2+2q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 2q^2+3q+2
       516: 3q^2+3q+2
       517: 2q^2+3q+2
       518: q+2
       519: q+2
       520: q+2
       521: q+1
       524: q+1
       529: q+1
       530: q
       531: q
       532: q+1
       533: 1
       534: q
       535: q
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2q^2+1
       546: q
       547: 2q^2+1
       548: q
       549: 1
       550: q
       551: q
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2q^2+1
       562: q
       563: 2q^2+1
       564: q
       565: 1
       566: q
       567: q
       568: 1
       569: q^2+1
       570: q^2+1
       571: q
       572: q
       573: q^2+1
       574: q
       575: q^2+1
       576: q
       577: 3q^2+2
       581: 2q
       585: 2q+2
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: q+2
       599: 3q^2+q+2
       600: 2q
       601: q+2
       603: 1
       604: 1
       605: 2
       607: q+1
       608: q+1
       609: q^2+2
       613: 2q^2+2
       614: q^2+2q
       615: q+1
       616: q+1
       617: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       625: q^2+2
       629: 2q^2+2
       630: q^2+2q
       631: q+1
       632: q+1
       633: 2
       639: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       646: 2q
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+2
       653: 2
       655: 2
       656: 2q
       657: 3q+2
       658: q+2
       660: q+2
       662: q+2
       664: 2q^2+3q+2
       665: 3q+2
       672: q+2
       673: q+2
       674: q^2+2q+2
       675: 2
       676: 2q+2
       677: q^2+2
       678: 2
       679: q^2+2q+2
       680: q^2+2q+2
       681: 2q+2
       682: 2
       683: q^2+2
       684: 2
       685: q^2+2q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: q^2+1
       697: q^2+1
       699: q
       700: q
       709: q+1
       712: q+1
       713: 1
       714: q
       715: q
       716: 1
       717: 1
       718: q
       719: q
       720: 1
       721: 1
       723: 1
       725: 1
       727: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       749: 1
       751: 1
       753: 1
       754: q
       755: q
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       771: q
       775: q+2
       779: q+2
       781: q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       791: 2
       792: 2q
       793: q+1
       794: q+1
       795: 2
       797: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2
       811: q^2+2
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       821: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: 2
       835: q^2+2
       839: 1
       840: 1
       843: 2
       844: 2q
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: 2
       855: 1
       856: q
       857: 2
       865: q+2
       866: 3q+2
       867: q+2
       868: q+2
       869: 2
       870: q^2+2q+2
       871: 2
       872: 2
       873: 2
       874: q^2+2q+2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       884: 1
       889: 1
       900: 1
       902: 1
       904: 1
       906: 1
       908: 1
       909: q
       910: q
       911: 1
       916: 1
       918: 1
       920: 1
       922: 1
       928: 1
       930: 1
       940: 1
       942: 1
       944: 1
       946: 1
       948: 1
       950: 1
       960: 1
       961: 1
       964: 1
       965: q
       966: q
       967: 1
       968: 2
       970: q
       974: 1
       975: 1
       988: 1
       991: 1
       994: q+2
       998: q+1
       999: q+1
      1000: q+1
      1001: q+1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 2
      1010: q+2
      1012: 2
      1013: 2q
      1016: 1
      1017: 1
      1020: 2
      1022: 2
      1026: 1
      1027: 1
      1032: 1
      1033: 1
      1036: 2
      1038: 2
      1044: 1
      1045: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q
      1074: q+2
      1076: 2
      1077: 2
      1078: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1091: 1
      1114: 1
      1116: 1
      1122: 1
      1124: 1
      1126: 1
      1127: 1
      1130: 1
      1131: q
      1132: q
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1140: q
      1156: 1
      1158: 1
      1172: 1
      1174: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 2
      1224: 2
      1230: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1248: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1266: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1283: 2
      1285: 2
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1295: 1
      1326: 1
      1329: 1
      1330: 1
      1331: 1
      1356: 1
      1358: 1
      1380: 1
      1382: 1
      1430: 1
      1436: 2
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1464: 1
      1474: 1
      1482: 1
      1484: 1
      1487: 1
      1537: 1
      1538: 1
      1641: 1
      1659: 1
      1673: 1
      1817: 1

1818:    0: 7q^3+11q^2+4q+2
         1: q^4+8q^3+11q^2+4q+2
         2: q^5+2q^4+5q^3+8q^2+4q+2
         3: 7q^3+11q^2+4q+2
         4: 7q^3+11q^2+4q+2
         5: q^4+8q^3+11q^2+4q+2
         6: q^4+8q^3+11q^2+4q+2
         7: q^5+2q^4+5q^3+8q^2+4q+2
         8: 3q^4+6q^3+8q^2+4q+2
         9: q^5+2q^4+5q^3+8q^2+4q+2
        10: 4q^3+7q^2+4q+2
        11: 4q^3+7q^2+4q+2
        12: 4q^3+7q^2+4q+2
        13: 2q^3+8q^2+4q+2
        14: 2q^3+8q^2+4q+2
        15: 3q^3+8q^2+4q+2
        16: 7q^3+11q^2+4q+2
        17: q^4+8q^3+11q^2+4q+2
        18: q^5+2q^4+5q^3+8q^2+4q+2
        19: 7q^3+11q^2+4q+2
        20: q^4+8q^3+11q^2+4q+2
        21: q^5+2q^4+5q^3+8q^2+4q+2
        22: 4q^3+10q^2+4q+2
        23: 4q^3+10q^2+4q+2
        24: q^4+4q^3+7q^2+4q+2
        25: 4q^3+10q^2+4q+2
        26: 4q^3+10q^2+4q+2
        27: q^4+4q^3+7q^2+4q+2
        28: 4q^3+7q^2+4q+2
        29: 4q^3+7q^2+4q+2
        30: 2q^3+8q^2+4q+2
        31: 2q^3+6q^2+4q+2
        32: q^3+7q^2+4q+2
        33: 4q^3+10q^2+4q+2
        34: 2q^3+6q^2+4q+2
        35: q^3+7q^2+4q+2
        36: 4q^3+10q^2+4q+2
        37: 3q^2+2q
        38: q^3+7q^2+2q+2
        39: 3q^2+2q
        40: q^3+7q^2+2q+2
        41: 3q^2+2q
        42: 3q^3+4q^2+2q+2
        43: 4q^2+4q+2
        44: 4q^2+4q+2
        45: 4q^2+4q+2
        46: 2q^3+8q^2+4q+2
        47: 3q^3+8q^2+4q+2
        48: 2q^3+8q^2+4q+2
        49: 7q^3+11q^2+4q+2
        50: q^4+8q^3+11q^2+4q+2
        51: q^5+2q^4+5q^3+8q^2+4q+2
        52: 4q^3+10q^2+4q+2
        53: 4q^3+10q^2+4q+2
        54: q^4+4q^3+7q^2+4q+2
        55: 4q^3+10q^2+4q+2
        56: 4q^3+10q^2+4q+2
        57: q^4+4q^3+7q^2+4q+2
        58: q^3+3q^2+2q+1
        59: q^3+3q^2+2q+1
        60: q^3+3q^2+2q+1
        61: q^3+3q^2+2q+1
        62: 2q
        63: 6q^2+2q+2
        64: 3q^2+2q
        65: 4q^2+2q+2
        66: 3q^2+2q
        67: q^3+7q^2+2q+2
        68: q^2+4q+2
        69: 2q^3+8q^2+4q+2
        70: 4q^2+4q+2
        71: 4q^3+7q^2+4q+2
        72: 4q^3+10q^2+4q+2
        73: 4q^3+10q^2+4q+2
        74: 3q^2+2q
        75: q^3+7q^2+2q+2
        76: 3q^2+2q
        77: q^3+7q^2+2q+2
        78: 3q^2+2q
        79: 3q^3+4q^2+2q+2
        80: 3q^2+4q+2
        81: q^3+7q^2+4q+2
        82: 2q^3+6q^2+4q+2
        83: q^3+7q^2+4q+2
        84: 3q^2+4q+2
        85: q^3+7q^2+4q+2
        86: 2q^3+6q^2+4q+2
        87: q^3+7q^2+4q+2
        88: 4q^2+4q+2
        89: 4q^2+4q+2
        90: 4q^2+4q+2
        91: 2q^3+8q^2+4q+2
        92: 3q^3+8q^2+4q+2
        93: 2q^3+8q^2+4q+2
        94: 4q^3+10q^2+4q+2
        95: 4q^3+10q^2+4q+2
        96: q^4+4q^3+7q^2+4q+2
        97: 4q^3+10q^2+4q+2
        98: 4q^3+10q^2+4q+2
        99: q^4+4q^3+7q^2+4q+2
       100: 9q^2+3q+2
       101: q^3+10q^2+3q+2
       102: 2q^3+6q^2+3q+2
       103: q
       104: 3q^2+q+1
       105: 3q^2+q+1
       106: q
       107: q^3+3q^2+2q+1
       108: q^3+3q^2+2q+1
       109: q^3+3q^2+2q+1
       110: q^3+3q^2+2q+1
       111: 3q^2+2q
       112: q^3+7q^2+2q+2
       113: 2q
       114: 6q^2+2q+2
       115: 3q^2+2q
       116: 4q^2+2q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q
       122: 3q^2+2q+2
       123: 3q^2+2q
       124: 4q^2+2q+2
       125: q^2+4q+2
       126: 4q^2+4q+2
       127: 3q^2+2q
       128: q^3+7q^2+2q+2
       129: 3q^2+2q
       130: q^3+7q^2+2q+2
       131: 3q^2+2q
       132: 3q^3+4q^2+2q+2
       133: q^2+4q+2
       134: 2q^3+8q^2+4q+2
       135: q^3+7q^2+4q+2
       136: q^3+7q^2+4q+2
       137: 3q^2+4q+2
       138: q^3+7q^2+4q+2
       139: 2q^3+6q^2+4q+2
       140: 6q^2+2q+2
       141: 3q^2+4q+2
       142: 4q^3+10q^2+4q+2
       143: 3q^2+4q+2
       144: q^3+7q^2+4q+2
       145: 2q^3+6q^2+4q+2
       146: 3q^2+4q+2
       147: 4q^3+10q^2+4q+2
       148: 6q^2+2q+2
       149: 6q^2+3q+2
       150: 6q^2+3q+2
       151: 2q^2+2q
       152: 7q^2+q+2
       153: 3q^2+2q
       154: q^3+7q^2+q+2
       155: 2q^2+2q
       156: 2q^3+4q^2+q+2
       157: 4q^2+4q+2
       158: 4q^2+4q+2
       159: 4q^2+4q+2
       160: q^3+5q^2+4q+2
       161: q^3+5q^2+4q+2
       162: q^3+5q^2+4q+2
       163: q^3+5q^2+4q+2
       164: q^3+5q^2+4q+2
       165: q^3+5q^2+4q+2
       166: 9q^2+3q+2
       167: q^3+10q^2+3q+2
       168: 2q^3+6q^2+3q+2
       169: q
       170: 3q^2+q+1
       171: 3q^2+q+1
       172: q
       173: q
       174: q+1
       175: q+1
       176: q
       177: 3q^2+2q
       178: 4q^2+2q+2
       179: 2q
       180: 6q^2+2q+2
       181: 3q^2+2q
       182: q^3+7q^2+2q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 3q^2+2q
       188: 4q^2+2q+2
       189: 2q
       190: 3q^2+2q+2
       191: 2q+1
       192: 2q+1
       193: 2q^2+q+1
       194: 2q^2+q+1
       195: q^3+3q^2+2q+1
       196: q^3+3q^2+2q+1
       197: q^2+2q
       198: 5q^2+2
       199: 2q+1
       200: 2q+1
       201: q^3+3q^2+2q+1
       202: q^3+3q^2+2q+1
       203: 2q^2+q+1
       204: 2q^2+q+1
       205: q^2+2q
       206: 5q^2+2
       207: 2q
       208: 3q^2+2q+2
       209: 2q
       210: 6q^2+q+2
       211: 2q^2+2q
       212: 4q^2+q+2
       214: q^2+2q+2
       216: q^2+2q+2
       218: q^2+2q+2
       219: q^2+4q+2
       220: q^2+4q+2
       221: 4q^2+4q+2
       222: 3q^2+4q+2
       223: q^3+7q^2+4q+2
       224: 3q^2+4q+2
       225: q^3+7q^2+4q+2
       226: 3q^2+4q+2
       227: 4q+2
       228: q^3+5q^2+4q+2
       229: 3q^2+2q+2
       230: q^3+5q^2+4q+2
       231: 3q^2+4q+2
       232: 4q+2
       233: q^3+5q^2+4q+2
       234: q^3+5q^2+4q+2
       235: 3q^2+2q+2
       236: 6q^2+3q+2
       237: 2q^2+2q
       238: 7q^2+q+2
       239: 3q^2+2q
       240: q^3+7q^2+q+2
       241: 2q^2+2q
       242: 2q^3+4q^2+q+2
       243: 6q^2+3q+2
       244: 6q^2+2q+2
       245: 6q^2+2q+2
       246: 3q^2+3q+2
       247: 9q^2+3q+2
       248: q^3+10q^2+3q+2
       249: 2q^3+6q^2+3q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: q
       260: 3q^2+q+1
       261: 3q^2+q+1
       262: q
       263: q
       264: q+1
       265: q+1
       266: q
       267: q
       268: 2q^2+1
       269: q
       270: 2q^2+1
       271: q
       272: 2q^2+1
       273: q
       274: 2q^2+1
       275: q
       276: q+1
       277: q+1
       278: q
       280: 2q+2
       282: q^2+2q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 2q
       288: 3q^2+2q+2
       290: q^2+2q+2
       291: 3q^2+2q
       292: 4q^2+2q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q
       298: 3q^2+2q+2
       299: q+1
       300: q+1
       301: q^2+2q
       302: 5q^2+2
       303: 2q+1
       304: 2q+1
       305: q^2+2q
       306: 2q^2+2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: q^2+2q
       312: 5q^2+2
       313: q^2+2q
       314: 2q^2+2
       315: 2q^2+2q
       316: 4q^2+q+2
       317: 2q
       318: 6q^2+q+2
       319: 2q^2+q+1
       320: 2q^2+q+1
       321: 2q^2+q+1
       322: 2q^2+q+1
       323: 2q
       324: 3q^2+2
       325: 2q
       326: 3q^2+q+2
       333: q^2+4q+2
       334: 3q^2+4q+2
       335: 3q^2+4q+2
       336: 6q^2+3q+2
       337: 6q^2+3q+2
       338: 2q^2+2q
       339: 7q^2+q+2
       340: 3q^2+2q
       341: q^3+7q^2+q+2
       342: 2q^2+2q
       343: 2q^3+4q^2+q+2
       344: 4q+2
       345: 2q+2
       346: q^2+2q+2
       347: q^2+2
       348: 3q^2+2q+2
       349: q^2+2q+2
       350: q^3+5q^2+4q+2
       351: 6q^2+2q+2
       352: 4q+2
       353: 2q+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^3+5q^2+4q+2
       357: q^2+2
       358: 3q^2+2q+2
       359: 6q^2+2q+2
       361: q+2
       363: q+2
       365: q+2
       366: 3q^2+3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 2q^2+3q+2
       372: 3q^2+3q+2
       373: 2q^2+3q+2
       374: q+2
       375: q+2
       376: q+2
       377: q
       378: q+1
       379: q+1
       380: q
       382: q+1
       383: q+1
       385: q
       386: q+1
       387: q+1
       388: q
       389: q
       390: 2q^2+1
       391: q
       392: 2q^2+1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 2q^2+1
       399: q
       400: 2q^2+1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: q^2+1
       408: q^2+1
       414: 2q+2
       418: q^2+2q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q
       424: 3q^2+2q+2
       425: 2q^2+2q
       426: 4q^2+q+2
       427: 2q
       428: 6q^2+q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: q^2+2q
       434: 2q^2+2
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: q^2+2
       443: 2q^2+q+1
       444: 2q^2+q+1
       445: q^2+2q
       446: 5q^2+2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: q^2+2q
       452: 2q^2+2
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: q^2+2
       461: 2q^2+q+1
       462: 2q^2+q+1
       463: q^2+2q
       464: 5q^2+2
       466: q+2
       468: q+2
       469: 2q
       470: 3q^2+q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: 2
       477: 2q
       478: 3q^2+2
       479: 2q
       480: 3q^2+2
       481: 4q+2
       482: 4q+2
       483: 3q^2+3q+2
       484: 3q+2
       486: q+2
       488: q+2
       490: q+2
       491: 2q^2+3q+2
       492: 2q+2
       493: q^2+2
       494: q^2+2q+2
       495: 3q^2+2q+2
       496: q^2+2q+2
       497: 2q+2
       498: q^2+2q+2
       499: q^2+2
       500: 3q^2+2q+2
       501: q^2+2q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 2q^2+3q+2
       516: 3q^2+3q+2
       517: 2q^2+3q+2
       518: q+2
       519: q+2
       520: q+2
       522: q+1
       523: q+1
       529: q
       530: q+1
       531: q+1
       532: q
       533: q
       534: 1
       535: 1
       536: q
       538: 1
       540: 1
       542: 1
       544: 1
       545: q
       546: 2q^2+1
       547: q
       548: 2q^2+1
       549: q
       550: 1
       551: 1
       552: q
       554: 1
       556: 1
       558: 1
       560: 1
       561: q
       562: 2q^2+1
       563: q
       564: 2q^2+1
       565: q
       566: 1
       567: 1
       568: q
       569: q
       570: q
       571: q^2+1
       572: q^2+1
       573: q
       574: q^2+1
       575: q
       576: q^2+1
       577: 2q
       581: 3q^2+2
       586: 2q+2
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       598: q+2
       599: 2q
       600: 3q^2+q+2
       602: q+2
       603: 1
       604: 1
       606: 2
       607: q+1
       608: q+1
       610: q^2+2
       613: q^2+2q
       614: 2q^2+2
       615: q+1
       616: q+1
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2
       626: q^2+2
       629: q^2+2q
       630: 2q^2+2
       631: q+1
       632: q+1
       634: 2
       640: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+2
       654: 2
       655: 2q
       656: 2
       657: 3q+2
       659: q+2
       661: q+2
       663: q+2
       664: 2q^2+3q+2
       665: 3q+2
       672: q+2
       673: q+2
       674: q^2+2q+2
       675: 2
       676: 2q+2
       677: q^2+2
       678: 2
       679: q^2+2q+2
       680: q^2+2q+2
       681: 2q+2
       682: 2
       683: q^2+2
       684: 2
       685: q^2+2q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: q
       697: q
       699: q^2+1
       700: q^2+1
       710: q+1
       711: q+1
       713: q
       714: 1
       715: 1
       716: q
       717: q
       718: 1
       719: 1
       720: q
       722: 1
       724: 1
       726: 1
       728: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       750: 1
       752: 1
       753: q
       754: 1
       755: 1
       756: q
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       773: 2
       774: q
       776: q+2
       780: q+2
       782: q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       791: 2q
       792: 2
       793: q+1
       794: q+1
       796: 2
       798: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       810: 2
       812: q^2+2
       815: 1
       816: 1
       817: q+1
       818: q+1
       820: 2
       822: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       834: 2
       836: q^2+2
       839: 1
       840: 1
       843: 2q
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: 2
       855: q
       856: 1
       858: 2
       865: q+2
       866: 3q+2
       867: q+2
       868: q+2
       869: 2
       870: q^2+2q+2
       871: 2
       872: 2
       873: 2
       874: q^2+2q+2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       890: 1
       891: 1
       901: 1
       903: 1
       905: 1
       907: 1
       908: q
       909: 1
       910: 1
       911: q
       917: 1
       919: 1
       921: 1
       923: 1
       929: 1
       931: 1
       941: 1
       943: 1
       945: 1
       947: 1
       949: 1
       951: 1
       962: 1
       963: 1
       964: q
       965: 1
       966: 1
       967: q
       972: 2
       973: q
       976: 1
       977: 1
       989: 1
       990: 1
       995: q+2
       998: q+1
       999: q+1
      1000: q+1
      1001: q+1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1009: 2
      1011: q+2
      1012: 2q
      1013: 2
      1016: 1
      1017: 1
      1021: 2
      1023: 2
      1026: 1
      1027: 1
      1032: 1
      1033: 1
      1037: 2
      1039: 2
      1044: 1
      1045: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1074: q+2
      1076: 2
      1077: 2
      1078: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: q+1
      1085: 1
      1092: 1
      1093: 1
      1115: 1
      1117: 1
      1123: 1
      1125: 1
      1128: 1
      1129: 1
      1130: q
      1131: 1
      1132: 1
      1133: q
      1136: 1
      1137: 1
      1142: 2
      1143: q
      1157: 1
      1159: 1
      1173: 1
      1175: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1221: 2
      1225: 2
      1231: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1249: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1267: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1297: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1357: 1
      1359: 1
      1381: 1
      1383: 1
      1434: 1
      1437: 2
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1465: 1
      1475: 1
      1483: 1
      1484: 1
      1487: 1
      1539: 1
      1540: 1
      1642: 1
      1660: 1
      1673: 1
      1818: 1

1819:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+2q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+2q+2
         8: q^3+3q^2+2q+2
         9: q^3+3q^2+2q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+3q^2+2q+2
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+2q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+2q+2
        25: 4q+2
        26: 4q+2
        27: 2q^2+2q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: q^2+2q+2
        31: 2q^2+4q+2
        32: q^2+2q+2
        33: 2q^2+4q+2
        34: 4q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: 2q^2+4q+2
        50: 2q^2+4q+2
        51: q^3+3q^2+2q+2
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: q^3+3q^2+2q+2
        55: 4q+2
        56: 4q+2
        57: 2q^2+2q+2
        58: 2q^2+2q+2
        59: 2q
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: 2q^2+4q+2
        72: 4q+2
        73: 2q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+2q+2
        81: q^2+2q+2
        82: 2q^2+4q+2
        83: q^2+2q+2
        84: 2q+2
        85: 2q+2
        86: 4q+2
        87: 2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2q^2+4q+2
        95: 2q^2+4q+2
        96: q^3+3q^2+2q+2
        97: 4q+2
        98: 4q+2
        99: 2q^2+2q+2
       100: 4q+2
       101: 4q+2
       102: 2q^2+2q+2
       103: q+1
       104: q
       105: q+1
       106: q
       107: 2q+1
       108: 2q+1
       109: 2q^2+2q+2
       110: 2q
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: q+1
       117: q^2+2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2
       126: q^2+2q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2
       134: q^2+2q+2
       135: 2q+2
       136: q^2+2q+2
       137: q^2+2q+2
       138: q^2+2q+2
       139: 2q^2+4q+2
       140: 4q+2
       141: q^2+2q+2
       142: 2q^2+4q+2
       143: 2q+2
       144: 2q+2
       145: 4q+2
       146: 2q+2
       147: 4q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q+2
       164: q+2
       165: q+2
       166: 4q+2
       167: 4q+2
       168: 2q^2+2q+2
       169: q+1
       170: q
       171: q+1
       172: q
       173: 1
       175: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 1
       184: 1
       185: q^2+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+2
       193: 2q+1
       194: 2q+1
       195: 2q^2+2q+2
       196: 2q
       197: 2q+1
       198: 2q+1
       199: 1
       200: 1
       201: 2q+1
       202: 2q+1
       203: 2q+2
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q^2+2
       220: q^2+2
       221: q^2+2q+2
       222: 2q+2
       223: 2q+2
       224: q^2+2q+2
       225: q^2+2q+2
       226: q^2+2q+2
       227: q^2+2
       228: q^2+2q+2
       229: 2q+2
       230: q^2+2q+2
       231: 2q+2
       232: 2
       233: q+2
       234: q+2
       235: 2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 4q+2
       244: 4q+2
       245: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q^2+2q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       259: q+1
       260: q
       261: q+1
       262: q
       263: 1
       265: 1
       267: q+1
       268: q
       269: q
       270: q+1
       271: q+1
       272: q+1
       275: 1
       277: 1
       283: 1
       284: 1
       285: q^2+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q^2+2
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: 2q+1
       302: 2q+1
       303: q^2+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       309: 2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+1
       320: 2q+1
       321: 2q+2
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       333: q^2+2
       334: 2q+2
       335: q^2+2q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q^2+2
       345: q^2+2
       346: q^2+2q+2
       347: 2q+2
       348: 2q+2
       349: q^2+2q+2
       350: q^2+2q+2
       351: 4q+2
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       357: 2
       358: 2
       359: 2q+2
       366: 2q+2
       367: 2
       368: q+2
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       379: 1
       385: 1
       387: 1
       389: q+1
       390: q
       391: q
       392: q+1
       393: 1
       395: 1
       397: q+1
       398: q+1
       401: 1
       402: 1
       405: q+1
       408: q+1
       419: 1
       420: 1
       421: q^2+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 1
       430: 1
       431: q^2+2
       433: q+1
       434: q+1
       437: 1
       438: 1
       439: q^2+2
       441: q+1
       442: q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 1
       448: 1
       449: 2
       451: 1
       452: 1
       453: 1
       454: 1
       457: 2
       459: 1
       460: 1
       461: 2q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 2
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2
       482: q^2+2
       483: 2q+2
       484: 2
       491: q+2
       492: q^2+2
       493: 2q+2
       494: q^2+2q+2
       495: 2q+2
       496: q+2
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 2
       508: 2
       509: 2
       510: q+2
       511: q+2
       512: q+2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       529: 1
       531: 1
       533: 1
       535: 1
       541: 1
       544: 1
       545: q+1
       546: q
       547: q
       548: q+1
       549: 1
       550: 1
       557: 1
       558: 1
       561: q+1
       562: q+1
       565: 1
       567: 1
       569: q+1
       572: q+1
       573: q+1
       576: q+1
       577: q+1
       581: q+1
       589: 1
       590: 1
       591: 2
       593: 1
       594: 1
       595: q^2+2
       599: q+1
       600: q+1
       603: 1
       604: 1
       607: q^2+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 2
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       641: 1
       642: 1
       643: 2
       645: 1
       646: 1
       647: 1
       648: 1
       649: 2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: q+2
       665: 2
       672: 2
       673: q+2
       674: q+2
       675: 2
       676: q^2+2
       677: 2q+2
       678: q+2
       679: q+2
       680: 2
       681: 2
       682: 1
       683: 2
       684: 2
       685: 2
       686: 2
       687: q+2
       688: 2
       689: 2
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       700: q+1
       713: 1
       714: 1
       717: 1
       719: 1
       725: 1
       728: 1
       741: 1
       742: 1
       753: 1
       755: 1
       761: 1
       764: 1
       765: 1
       767: 1
       785: 1
       786: 1
       787: 2
       791: 1
       792: 1
       793: 1
       794: 1
       801: 1
       802: 1
       803: 2
       805: 1
       806: 1
       807: q^2+2
       811: q+1
       812: q+1
       815: 1
       816: 1
       817: 2
       825: 1
       826: 1
       827: 2
       831: 1
       835: 1
       836: 1
       839: 2
       843: 1
       844: 1
       845: 1
       846: 1
       847: 2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: q+2
       868: 2
       869: q+2
       870: q+2
       871: 2
       872: q+2
       873: 2
       874: 2
       875: 1
       876: 2
       877: 2
       878: 1
       879: 2
       880: 2
       908: 1
       910: 1
       924: 1
       925: 1
       928: 1
       931: 1
       948: 1
       949: 1
       964: 1
       966: 1
       974: 1
       977: 1
       988: 1
       990: 1
       998: 2
      1000: 1
      1001: 1
      1004: 1
      1005: 1
      1006: 2
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1026: 1
      1027: 1
      1028: 2
      1032: 2
      1044: 1
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1054: 2
      1058: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 2
      1076: 2
      1077: q+2
      1078: 2
      1080: 1
      1081: 2
      1082: 1
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1132: 1
      1134: 1
      1137: 1
      1160: 1
      1161: 1
      1194: 1
      1196: 1
      1202: 1
      1203: 1
      1216: 2
      1218: 1
      1219: 1
      1224: 1
      1225: 1
      1232: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1242: 2
      1250: 1
      1260: 1
      1270: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: 1
      1326: 1
      1328: 1
      1364: 1
      1365: 1
      1368: 1
      1370: 1
      1450: 2
      1454: 1
      1455: 1
      1460: 1
      1466: 1
      1478: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1575: 1
      1576: 1
      1649: 1
      1663: 1
      1673: 1
      1819: 1

1820:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+2q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+2q+2
         8: q^3+3q^2+2q+2
         9: q^3+3q^2+2q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+3q^2+2q+2
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+2q+2
        22: 2q^2+4q+2
        23: 2q^2+4q+2
        24: q^3+3q^2+2q+2
        25: 4q+2
        26: 4q+2
        27: 2q^2+2q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: q^2+2q+2
        31: 2q^2+4q+2
        32: q^2+2q+2
        33: 2q^2+4q+2
        34: 4q+2
        35: 2q+2
        36: 4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: 2q^2+4q+2
        50: 2q^2+4q+2
        51: q^3+3q^2+2q+2
        52: 2q^2+4q+2
        53: 2q^2+4q+2
        54: q^3+3q^2+2q+2
        55: 4q+2
        56: 4q+2
        57: 2q^2+2q+2
        58: 2q
        59: 2q^2+2q+2
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: 2q^2+4q+2
        72: 4q+2
        73: 2q^2+4q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+2q+2
        81: q^2+2q+2
        82: 2q^2+4q+2
        83: q^2+2q+2
        84: 2q+2
        85: 2q+2
        86: 4q+2
        87: 2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2q^2+4q+2
        95: 2q^2+4q+2
        96: q^3+3q^2+2q+2
        97: 4q+2
        98: 4q+2
        99: 2q^2+2q+2
       100: 4q+2
       101: 4q+2
       102: 2q^2+2q+2
       103: q
       104: q+1
       105: q
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q
       110: 2q^2+2q+2
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: q+1
       118: q^2+2
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2
       126: q^2+2q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2
       134: q^2+2q+2
       135: 2q+2
       136: q^2+2q+2
       137: q^2+2q+2
       138: q^2+2q+2
       139: 2q^2+4q+2
       140: 4q+2
       141: q^2+2q+2
       142: 2q^2+4q+2
       143: 2q+2
       144: 2q+2
       145: 4q+2
       146: 2q+2
       147: 4q+2
       148: 2q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q+2
       164: q+2
       165: q+2
       166: 4q+2
       167: 4q+2
       168: 2q^2+2q+2
       169: q
       170: q+1
       171: q
       172: q+1
       174: 1
       176: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 1
       184: 1
       186: q^2+2
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       192: q^2+2
       193: 2q+1
       194: 2q+1
       195: 2q
       196: 2q^2+2q+2
       197: 2q+1
       198: 2q+1
       199: 1
       200: 1
       201: 2q+1
       202: 2q+1
       204: 2q+2
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q^2+2
       220: q^2+2
       221: q^2+2q+2
       222: 2q+2
       223: 2q+2
       224: q^2+2q+2
       225: q^2+2q+2
       226: q^2+2q+2
       227: q^2+2
       228: q^2+2q+2
       229: 2q+2
       230: q^2+2q+2
       231: 2q+2
       232: 2
       233: q+2
       234: q+2
       235: 2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 4q+2
       244: 4q+2
       245: 2q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q^2+2q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       259: q
       260: q+1
       261: q
       262: q+1
       264: 1
       266: 1
       267: q
       268: q+1
       269: q+1
       270: q
       273: q+1
       274: q+1
       276: 1
       278: 1
       283: 1
       284: 1
       286: q^2+2
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       296: q^2+2
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: 2q+1
       302: 2q+1
       304: q^2+2
       305: q+1
       306: q+1
       307: 1
       308: 1
       310: 2
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+1
       320: 2q+1
       322: 2q+2
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       333: q^2+2
       334: 2q+2
       335: q^2+2q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q^2+2
       345: q^2+2
       346: q^2+2q+2
       347: 2q+2
       348: 2q+2
       349: q^2+2q+2
       350: q^2+2q+2
       351: 4q+2
       352: 2
       353: 2
       354: q+2
       355: q+2
       356: q+2
       357: 2
       358: 2
       359: 2q+2
       366: 2q+2
       367: 2
       368: q+2
       369: q+2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       378: 1
       380: 1
       386: 1
       388: 1
       389: q
       390: q+1
       391: q+1
       392: q
       394: 1
       396: 1
       399: q+1
       400: q+1
       403: 1
       404: 1
       406: q+1
       407: q+1
       419: 1
       420: 1
       422: q^2+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 1
       430: 1
       432: q^2+2
       433: q+1
       434: q+1
       437: 1
       438: 1
       440: q^2+2
       441: q+1
       442: q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 1
       448: 1
       450: 2
       451: 1
       452: 1
       453: 1
       454: 1
       458: 2
       459: 1
       460: 1
       462: 2q+2
       463: q+1
       464: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: 2
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2
       482: q^2+2
       483: 2q+2
       484: 2
       491: q+2
       492: q^2+2
       493: 2q+2
       494: q^2+2q+2
       495: 2q+2
       496: q+2
       497: 2
       498: q+2
       499: 2
       500: 2
       501: 2
       508: 2
       509: 2
       510: q+2
       511: q+2
       512: q+2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       530: 1
       532: 1
       534: 1
       536: 1
       542: 1
       543: 1
       545: q
       546: q+1
       547: q+1
       548: q
       551: 1
       552: 1
       559: 1
       560: 1
       563: q+1
       564: q+1
       566: 1
       568: 1
       570: q+1
       571: q+1
       574: q+1
       575: q+1
       577: q+1
       581: q+1
       589: 1
       590: 1
       592: 2
       593: 1
       594: 1
       596: q^2+2
       599: q+1
       600: q+1
       603: 1
       604: 1
       608: q^2+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: 1
       616: 1
       619: 1
       620: 1
       622: 2
       625: 1
       626: 1
       629: 1
       630: 1
       632: 2
       641: 1
       642: 1
       644: 2
       645: 1
       646: 1
       647: 1
       648: 1
       650: 2
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: q+2
       665: 2
       672: 2
       673: q+2
       674: q+2
       675: 2
       676: q^2+2
       677: 2q+2
       678: q+2
       679: q+2
       680: 2
       681: 2
       682: 1
       683: 2
       684: 2
       685: 2
       686: 2
       687: q+2
       688: 2
       689: 2
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       699: q+1
       715: 1
       716: 1
       718: 1
       720: 1
       726: 1
       727: 1
       743: 1
       744: 1
       754: 1
       756: 1
       762: 1
       763: 1
       766: 1
       768: 1
       785: 1
       786: 1
       788: 2
       791: 1
       792: 1
       793: 1
       794: 1
       801: 1
       802: 1
       804: 2
       805: 1
       806: 1
       808: q^2+2
       811: q+1
       812: q+1
       815: 1
       816: 1
       818: 2
       825: 1
       826: 1
       828: 2
       832: 1
       835: 1
       836: 1
       840: 2
       843: 1
       844: 1
       845: 1
       846: 1
       848: 2
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: q+2
       868: 2
       869: q+2
       870: q+2
       871: 2
       872: q+2
       873: 2
       874: 2
       875: 1
       876: 2
       877: 2
       878: 1
       879: 2
       880: 2
       909: 1
       911: 1
       926: 1
       927: 1
       929: 1
       930: 1
       950: 1
       951: 1
       965: 1
       967: 1
       975: 1
       976: 1
       989: 1
       991: 1
       999: 2
      1000: 1
      1001: 1
      1004: 1
      1005: 1
      1007: 2
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1026: 1
      1027: 1
      1029: 2
      1033: 2
      1045: 1
      1046: 1
      1047: 1
      1052: 1
      1053: 1
      1055: 2
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 2
      1076: 2
      1077: q+2
      1078: 2
      1080: 1
      1081: 2
      1082: 1
      1083: 1
      1084: 2
      1085: 2
      1131: 1
      1133: 1
      1135: 1
      1136: 1
      1162: 1
      1163: 1
      1195: 1
      1197: 1
      1204: 1
      1205: 1
      1217: 2
      1218: 1
      1219: 1
      1224: 1
      1225: 1
      1233: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1243: 2
      1251: 1
      1261: 1
      1271: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: 1
      1327: 1
      1329: 1
      1366: 1
      1367: 1
      1369: 1
      1371: 1
      1451: 2
      1454: 1
      1455: 1
      1461: 1
      1467: 1
      1479: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1577: 1
      1578: 1
      1650: 1
      1664: 1
      1673: 1
      1820: 1

1821:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+2q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+2q+2
         8: q^3+3q^2+2q+2
         9: q^3+3q^2+2q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+3q^2+2q+2
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+2q+2
        22: 4q+2
        23: 4q+2
        24: 2q^2+2q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+2q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: q^2+2q+2
        31: 4q+2
        32: 2q+2
        33: 4q+2
        34: 2q^2+4q+2
        35: q^2+2q+2
        36: 2q^2+4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: 2q^2+4q+2
        50: 2q^2+4q+2
        51: q^3+3q^2+2q+2
        52: 4q+2
        53: 4q+2
        54: 2q^2+2q+2
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: q^3+3q^2+2q+2
        58: 2q+1
        59: 2q+1
        60: 2q^2+2q+2
        61: 2q
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: 2q^2+4q+2
        72: 2q^2+4q+2
        73: 4q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q^2+q+1
        79: q^2+q+1
        80: 2q+2
        81: 2q+2
        82: 4q+2
        83: 2q+2
        84: q^2+2q+2
        85: q^2+2q+2
        86: 2q^2+4q+2
        87: q^2+2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 4q+2
        95: 4q+2
        96: 2q^2+2q+2
        97: 2q^2+4q+2
        98: 2q^2+4q+2
        99: q^3+3q^2+2q+2
       100: 4q+2
       101: 4q+2
       102: 2q^2+2q+2
       103: q+1
       104: q+1
       105: q
       106: q
       107: 2q^2+2q+2
       108: 2q
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+2
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2
       126: q^2+2q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2
       134: q^2+2q+2
       135: q^2+2q+2
       136: 2q+2
       137: 2q+2
       138: 2q+2
       139: 4q+2
       140: 2q+2
       141: 2q+2
       142: 4q+2
       143: q^2+2q+2
       144: q^2+2q+2
       145: 2q^2+4q+2
       146: q^2+2q+2
       147: 2q^2+4q+2
       148: 4q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q+2
       161: q+2
       162: q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: 4q+2
       167: 4q+2
       168: 2q^2+2q+2
       169: q+1
       170: q+1
       171: q
       172: q
       173: 1
       174: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: q^2+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       199: q^2+2
       201: 2q^2+2q+2
       202: 2q
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q^2+2
       220: q^2+2
       221: q^2+2q+2
       222: q^2+2q+2
       223: q^2+2q+2
       224: 2q+2
       225: 2q+2
       226: 2q+2
       227: 2
       228: q+2
       229: 2
       230: q+2
       231: q^2+2q+2
       232: q^2+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: 2q+2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 4q+2
       244: 2q+2
       245: 4q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q^2+2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: q+2
       257: q+2
       258: q+2
       259: q+1
       260: q+1
       261: q
       262: q
       263: 1
       264: 1
       267: q+1
       268: q+1
       271: q+1
       272: q
       273: q
       274: q+1
       275: 1
       276: 1
       283: q^2+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       293: q^2+2
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: q^2+2
       309: 1
       310: 1
       311: 2q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+2
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       333: q^2+2
       334: q^2+2q+2
       335: 2q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q+2
       351: 2q+2
       352: q^2+2
       353: q^2+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^2+2q+2
       357: 2q+2
       358: 2q+2
       359: 4q+2
       366: 2q+2
       367: 2
       368: q+2
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: 1
       385: 1
       386: 1
       389: q+1
       390: q+1
       393: 1
       394: 1
       397: q+1
       398: q
       399: q
       400: q+1
       401: 1
       403: 1
       405: q+1
       407: q+1
       419: q^2+2
       421: 1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 2
       431: 1
       432: 1
       433: 1
       434: 1
       437: 2
       439: 1
       440: 1
       441: 1
       442: 1
       443: 2q+2
       445: q+1
       446: q+1
       447: q^2+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: q^2+2
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 2q+1
       462: 2q+1
       463: 2q+1
       464: 2q+1
       469: q+1
       470: q+1
       471: 2
       473: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q^2+2
       482: 2
       483: 2q+2
       484: 2
       491: q+2
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 2
       497: q^2+2
       498: q^2+2q+2
       499: 2q+2
       500: 2q+2
       501: q+2
       508: 2
       509: 2
       510: q+2
       511: 2
       512: 2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       529: 1
       530: 1
       533: 1
       534: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       549: 1
       551: 1
       557: 1
       560: 1
       561: q+1
       562: q
       563: q
       564: q+1
       565: 1
       566: 1
       569: q+1
       571: q+1
       573: q+1
       574: q+1
       577: q+1
       581: q+1
       589: q^2+2
       591: 1
       592: 1
       593: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       603: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       619: q^2+2
       621: 1
       622: 1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       641: 2
       643: 1
       644: 1
       645: 1
       646: 1
       647: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: q+2
       665: 2
       672: 2
       673: q+2
       674: 2
       675: 1
       676: 2
       677: 2
       678: 2
       679: 2
       680: q+2
       681: q^2+2
       682: 2
       683: 2q+2
       684: q+2
       685: q+2
       686: 2
       687: 2
       688: q+2
       689: 2
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       699: q+1
       713: 1
       715: 1
       717: 1
       718: 1
       725: 1
       726: 1
       741: 1
       744: 1
       753: 1
       754: 1
       761: 1
       763: 1
       765: 1
       766: 1
       785: 2
       787: 1
       788: 1
       791: 1
       792: 1
       793: 2
       801: 1
       805: 2
       807: 1
       808: 1
       811: 1
       812: 1
       815: 2
       817: 1
       818: 1
       825: q^2+2
       827: 1
       828: 1
       829: 2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       845: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: q+2
       868: 2
       869: 2
       870: 2
       871: 1
       872: 2
       873: q+2
       874: q+2
       875: 2
       876: q+2
       877: 1
       878: 2
       879: 2
       880: 2
       908: 1
       909: 1
       928: 1
       929: 1
       948: 1
       951: 1
       952: 1
       953: 1
       964: 1
       965: 1
       974: 1
       976: 1
       988: 1
       989: 1
       998: 1
       999: 1
      1000: 2
      1004: 2
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1016: 2
      1026: 1
      1032: 1
      1033: 1
      1040: 2
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1052: 1
      1056: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 2
      1076: 1
      1077: 2
      1078: 1
      1080: 2
      1081: q+2
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1130: 1
      1131: 1
      1134: 1
      1136: 1
      1180: 1
      1181: 1
      1194: 1
      1195: 1
      1206: 1
      1207: 1
      1216: 1
      1217: 1
      1218: 2
      1224: 1
      1225: 1
      1234: 1
      1240: 1
      1250: 1
      1251: 1
      1254: 2
      1258: 2
      1260: 1
      1261: 1
      1268: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: 1
      1326: 1
      1327: 1
      1396: 1
      1397: 1
      1400: 1
      1402: 1
      1454: 1
      1460: 1
      1461: 1
      1462: 2
      1468: 1
      1476: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1595: 1
      1596: 1
      1657: 1
      1665: 1
      1673: 1
      1821: 1

1822:    0: 2q^2+4q+2
         1: 2q^2+4q+2
         2: q^3+3q^2+2q+2
         3: 2q^2+4q+2
         4: 2q^2+4q+2
         5: 2q^2+4q+2
         6: 2q^2+4q+2
         7: q^3+3q^2+2q+2
         8: q^3+3q^2+2q+2
         9: q^3+3q^2+2q+2
        10: 2q^2+4q+2
        11: 2q^2+4q+2
        12: 2q^2+4q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: 2q^2+4q+2
        17: 2q^2+4q+2
        18: q^3+3q^2+2q+2
        19: 2q^2+4q+2
        20: 2q^2+4q+2
        21: q^3+3q^2+2q+2
        22: 4q+2
        23: 4q+2
        24: 2q^2+2q+2
        25: 2q^2+4q+2
        26: 2q^2+4q+2
        27: q^3+3q^2+2q+2
        28: 2q^2+4q+2
        29: 2q^2+4q+2
        30: q^2+2q+2
        31: 4q+2
        32: 2q+2
        33: 4q+2
        34: 2q^2+4q+2
        35: q^2+2q+2
        36: 2q^2+4q+2
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: 2q^2+4q+2
        50: 2q^2+4q+2
        51: q^3+3q^2+2q+2
        52: 4q+2
        53: 4q+2
        54: 2q^2+2q+2
        55: 2q^2+4q+2
        56: 2q^2+4q+2
        57: q^3+3q^2+2q+2
        58: 2q+1
        59: 2q+1
        60: 2q
        61: 2q^2+2q+2
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: 2q^2+4q+2
        72: 2q^2+4q+2
        73: 4q+2
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: q^2+q+1
        79: q^2+q+1
        80: 2q+2
        81: 2q+2
        82: 4q+2
        83: 2q+2
        84: q^2+2q+2
        85: q^2+2q+2
        86: 2q^2+4q+2
        87: q^2+2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 4q+2
        95: 4q+2
        96: 2q^2+2q+2
        97: 2q^2+4q+2
        98: 2q^2+4q+2
        99: q^3+3q^2+2q+2
       100: 4q+2
       101: 4q+2
       102: 2q^2+2q+2
       103: q
       104: q
       105: q+1
       106: q+1
       107: 2q
       108: 2q^2+2q+2
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: q^2+2
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2
       126: q^2+2q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+2
       134: q^2+2q+2
       135: q^2+2q+2
       136: 2q+2
       137: 2q+2
       138: 2q+2
       139: 4q+2
       140: 2q+2
       141: 2q+2
       142: 4q+2
       143: q^2+2q+2
       144: q^2+2q+2
       145: 2q^2+4q+2
       146: q^2+2q+2
       147: 2q^2+4q+2
       148: 4q+2
       149: 4q+2
       150: 2q+2
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: q+2
       161: q+2
       162: q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: 4q+2
       167: 4q+2
       168: 2q^2+2q+2
       169: q
       170: q
       171: q+1
       172: q+1
       175: 1
       176: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       184: q^2+2
       185: 1
       186: 1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       194: 2q+2
       195: 2q+1
       196: 2q+1
       197: q+1
       198: q+1
       200: q^2+2
       201: 2q
       202: 2q^2+2q+2
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       219: q^2+2
       220: q^2+2
       221: q^2+2q+2
       222: q^2+2q+2
       223: q^2+2q+2
       224: 2q+2
       225: 2q+2
       226: 2q+2
       227: 2
       228: q+2
       229: 2
       230: q+2
       231: q^2+2q+2
       232: q^2+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: 2q+2
       236: 2q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 4q+2
       244: 2q+2
       245: 4q+2
       246: 2q+2
       247: 4q+2
       248: 4q+2
       249: 2q^2+2q+2
       250: q+2
       251: q+2
       252: q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: q+2
       257: q+2
       258: q+2
       259: q
       260: q
       261: q+1
       262: q+1
       265: 1
       266: 1
       269: q+1
       270: q+1
       271: q
       272: q+1
       273: q+1
       274: q
       277: 1
       278: 1
       284: q^2+2
       285: 1
       286: 1
       287: q+1
       288: q+1
       291: q+1
       292: q+1
       294: q^2+2
       295: 1
       296: 1
       297: q+1
       298: q+1
       300: 2
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       308: q^2+2
       309: 1
       310: 1
       311: 2q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       320: 2q+2
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       333: q^2+2
       334: q^2+2q+2
       335: 2q+2
       336: 2q+2
       337: 4q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: 2
       345: 2
       346: q+2
       347: 2
       348: 2
       349: q+2
       350: q+2
       351: 2q+2
       352: q^2+2
       353: q^2+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^2+2q+2
       357: 2q+2
       358: 2q+2
       359: 4q+2
       366: 2q+2
       367: 2
       368: q+2
       369: 2
       370: q+2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       379: 1
       380: 1
       387: 1
       388: 1
       391: q+1
       392: q+1
       395: 1
       396: 1
       397: q
       398: q+1
       399: q+1
       400: q
       402: 1
       404: 1
       406: q+1
       408: q+1
       420: q^2+2
       421: 1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       430: 2
       431: 1
       432: 1
       433: 1
       434: 1
       438: 2
       439: 1
       440: 1
       441: 1
       442: 1
       444: 2q+2
       445: q+1
       446: q+1
       448: q^2+2
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: q^2+2
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 2q+1
       462: 2q+1
       463: 2q+1
       464: 2q+1
       469: q+1
       470: q+1
       472: 2
       473: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q^2+2
       482: 2
       483: 2q+2
       484: 2
       491: q+2
       492: 2
       493: 2
       494: q+2
       495: 2
       496: 2
       497: q^2+2
       498: q^2+2q+2
       499: 2q+2
       500: 2q+2
       501: q+2
       508: 2
       509: 2
       510: q+2
       511: 2
       512: 2
       513: q+2
       514: q+2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       531: 1
       532: 1
       535: 1
       536: 1
       543: 1
       544: 1
       547: q+1
       548: q+1
       550: 1
       552: 1
       558: 1
       559: 1
       561: q
       562: q+1
       563: q+1
       564: q
       567: 1
       568: 1
       570: q+1
       572: q+1
       575: q+1
       576: q+1
       577: q+1
       581: q+1
       590: q^2+2
       591: 1
       592: 1
       594: 2
       595: 1
       596: 1
       599: q+1
       600: q+1
       604: 2
       607: 1
       608: 1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 2
       620: q^2+2
       621: 1
       622: 1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       642: 2
       643: 1
       644: 1
       645: 1
       646: 1
       648: 2
       649: 1
       650: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 2
       664: q+2
       665: 2
       672: 2
       673: q+2
       674: 2
       675: 1
       676: 2
       677: 2
       678: 2
       679: 2
       680: q+2
       681: q^2+2
       682: 2
       683: 2q+2
       684: q+2
       685: q+2
       686: 2
       687: 2
       688: q+2
       689: 2
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       700: q+1
       714: 1
       716: 1
       719: 1
       720: 1
       727: 1
       728: 1
       742: 1
       743: 1
       755: 1
       756: 1
       762: 1
       764: 1
       767: 1
       768: 1
       786: 2
       787: 1
       788: 1
       791: 1
       792: 1
       794: 2
       802: 1
       806: 2
       807: 1
       808: 1
       811: 1
       812: 1
       816: 2
       817: 1
       818: 1
       826: q^2+2
       827: 1
       828: 1
       830: 2
       831: 1
       832: 1
       835: q+1
       836: q+1
       839: 1
       840: 1
       843: 1
       844: 1
       846: 2
       847: 1
       848: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: q+2
       868: 2
       869: 2
       870: 2
       871: 1
       872: 2
       873: q+2
       874: q+2
       875: 2
       876: q+2
       877: 1
       878: 2
       879: 2
       880: 2
       910: 1
       911: 1
       930: 1
       931: 1
       949: 1
       950: 1
       954: 1
       955: 1
       966: 1
       967: 1
       975: 1
       977: 1
       990: 1
       991: 1
       998: 1
       999: 1
      1001: 2
      1005: 2
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1012: 1
      1013: 1
      1017: 2
      1027: 1
      1032: 1
      1033: 1
      1041: 2
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1053: 1
      1057: 2
      1058: 1
      1059: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 2
      1076: 1
      1077: 2
      1078: 1
      1080: 2
      1081: q+2
      1082: 2
      1083: 1
      1084: 2
      1085: 2
      1132: 1
      1133: 1
      1135: 1
      1137: 1
      1182: 1
      1183: 1
      1196: 1
      1197: 1
      1208: 1
      1209: 1
      1216: 1
      1217: 1
      1219: 2
      1224: 1
      1225: 1
      1235: 1
      1241: 1
      1250: 1
      1251: 1
      1255: 2
      1259: 2
      1260: 1
      1261: 1
      1269: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: 1
      1328: 1
      1329: 1
      1398: 1
      1399: 1
      1401: 1
      1403: 1
      1455: 1
      1460: 1
      1461: 1
      1463: 2
      1469: 1
      1477: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1597: 1
      1598: 1
      1658: 1
      1666: 1
      1673: 1
      1822: 1

1823:    0: 2q^3+4q+2
         1: 2q^3+4q+2
         2: q^4+q^3+q^2+3q+2
         3: 2q^3+4q+2
         4: q^4+q^3+q^2+3q+2
         5: 2q^3+4q+2
         6: q^4+q^3+q^2+3q+2
         7: q^5+q^3+2q^2+2q+2
         8: q^4+q^3+q^2+3q+2
         9: q^5+q^3+2q^2+2q+2
        10: 2q^3+4q+2
        11: 2q^3+4q+2
        12: q^4+q^3+q^2+3q+2
        13: q^3+3q+2
        14: q^3+q^2+2q+2
        15: q^3+3q+2
        16: 2q^3+4q+2
        17: 2q^3+4q+2
        18: q^5+q^3+2q^2+2q+2
        19: q^3+3q+2
        20: q^3+3q+2
        21: q^3+q^2+2q+2
        22: 2q^3+4q+2
        23: 2q^3+4q+2
        24: q^4+q^3+q^2+3q+2
        25: 2q^3+4q+2
        26: 2q^3+4q+2
        27: q^4+q^3+q^2+3q+2
        28: 2q^3+4q+2
        29: q^3+3q+2
        30: q^3+2q+2
        31: 2q^3+4q+2
        32: q^3+3q+2
        33: 2q^3+4q+2
        34: 2q^3+4q+2
        35: q^3+3q+2
        36: 2q^3+4q+2
        37: 2q^3+4q+2
        39: 2q^3+4q+2
        41: q^4+q^3+q^2+3q+2
        43: q^3+3q+2
        44: q^3+q^2+2q+2
        45: q^3+3q+2
        46: q^3+3q+2
        47: q^3+3q+2
        48: q^3+q^2+2q+2
        49: q^3+3q+2
        50: q^3+3q+2
        51: q^3+q^2+2q+2
        52: q^3+3q+2
        53: q^3+3q+2
        54: q^3+q^2+2q+2
        55: q^3+3q+2
        56: q^3+3q+2
        57: q^3+q^2+2q+2
        58: q^3+2q+1
        59: q^3+2q+1
        60: q^3+2q+1
        61: q^3+2q+1
        62: 2q^3+4q+2
        64: q^3+3q+2
        66: 2q^3+4q+2
        68: 2q+2
        69: q^3+2q+2
        70: q^3+2q+2
        71: q^3+3q+2
        72: 2q+2
        73: 2q+2
        74: q^3+3q+2
        76: q^3+3q+2
        78: q^3+q^2+2q+2
        80: q^3+3q+2
        81: q^3+3q+2
        82: q^3+3q+2
        83: q^3+2q+2
        84: q^3+3q+2
        85: q^3+3q+2
        86: q^3+3q+2
        87: q^3+2q+2
        88: q^3+3q+2
        89: q^3+3q+2
        90: q^3+q^2+2q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: q^3+3q+2
        95: q^3+3q+2
        96: q^3+q^2+2q+2
        97: q^3+3q+2
        98: q^3+3q+2
        99: q^3+q^2+2q+2
       100: q^3+3q+2
       101: q^3+3q+2
       102: q^3+q^2+2q+2
       103: q^3+2q+1
       106: q^3+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: q^3+3q+2
       115: q^3+2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^3+3q+2
       123: q^3+3q+2
       125: 2q+2
       126: q^3+2q+2
       127: q^3+3q+2
       129: q^3+3q+2
       131: q^3+q^2+2q+2
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: q^3+3q+2
       138: q^3+2q+2
       139: q^3+3q+2
       140: 2q+2
       141: q^3+2q+2
       142: 2q+2
       143: q^3+3q+2
       144: q^3+2q+2
       145: q^3+3q+2
       146: q^3+2q+2
       147: 2q+2
       148: 2q+2
       149: q^3+3q+2
       150: q^3+2q+2
       151: q^3+3q+2
       153: q^3+3q+2
       155: q^3+q^2+2q+2
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q^3+3q+2
       167: q^3+3q+2
       168: q^3+q^2+2q+2
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: q^3+2q+2
       179: q^3+3q+2
       181: 2q+2
       183: 1
       184: 1
       185: 1
       186: 1
       187: q+2
       189: q^3+2q+2
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+2
       207: q^3+3q+2
       209: q^3+3q+2
       211: q^3+2q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: q^3+2q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: q^3+2q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: q^3+2q+2
       237: q^3+3q+2
       239: q^3+3q+2
       241: q^3+q^2+2q+2
       243: q^3+3q+2
       244: 2q+2
       245: 2q+2
       246: q^3+2q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       259: q+1
       262: q+1
       263: 1
       266: 1
       267: q+1
       269: q+1
       271: q+1
       273: q+1
       275: q+1
       278: q+1
       279: q+2
       281: 2q+2
       283: 1
       284: 1
       285: 1
       286: 1
       287: q^3+2q+2
       289: q+2
       291: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       297: q+2
       299: 1
       300: 1
       301: 2q+2
       303: 1
       304: 1
       305: q+2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2q+2
       313: q+2
       315: q^3+2q+2
       317: q^3+3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q+2
       325: q^3+2q+2
       327: 2q+2
       329: 2q+2
       331: 2q+2
       333: q+2
       334: q+2
       335: q+2
       336: q+1
       337: 2q+2
       338: 2q+2
       340: 2q+2
       342: q^2+2q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 2q+2
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 2q+2
       360: 2q+2
       362: 2q+2
       364: 2q+2
       366: q^3+2q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: q+1
       391: q+1
       393: 1
       396: 1
       397: q+1
       399: q+1
       401: 1
       404: 1
       405: q+1
       406: q+1
       409: q+2
       411: 2q+2
       413: q+2
       415: q+2
       417: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       423: q+2
       425: q+1
       427: 2q+2
       429: 1
       430: 1
       431: 1
       432: 1
       433: q+2
       435: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       441: q+2
       443: q+1
       444: q+1
       445: 2q+2
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+2
       453: 1
       454: 1
       455: q+2
       457: 1
       458: 1
       459: q+2
       461: q+1
       462: q+1
       463: 2q+2
       465: q+2
       467: 2q+2
       469: q^3+2q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+2
       477: 2q+2
       479: 2q+2
       481: 2
       482: 2
       483: q+1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: q+1
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: q+1
       501: 2
       502: 2q+2
       504: 2q+2
       506: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: q+1
       547: q+1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: q+1
       563: q+1
       565: 1
       568: 1
       569: q+1
       570: q+1
       573: q+1
       575: q+1
       577: 2q+2
       583: q+2
       585: 2
       587: q+2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       601: 2
       603: 1
       604: 1
       605: q+2
       607: 1
       608: 1
       609: q+2
       611: q+2
       613: q+1
       615: 1
       616: 1
       617: 2
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+2
       625: q+2
       627: q+2
       629: q+1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: 2q+2
       639: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+2
       653: q+2
       655: 2
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: q+1
       690: 2
       691: 2
       692: q+1
       693: q+1
       697: q+1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       791: 1
       793: 1
       794: 1
       795: 2
       797: 2
       799: q+2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       811: q+1
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: q+2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       835: q+1
       837: 2
       839: 1
       840: 1
       841: q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: q+2
       853: q+2
       855: q+1
       857: 2
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       879: q+1
       880: 1
       884: 1
       889: 1
       896: 1
       899: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1048: 2
      1050: q+2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1091: 1
      1098: 1
      1102: 1
      1138: 1
      1140: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1184: 1
      1185: 1
      1188: 2
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1214: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1236: 1
      1238: 1
      1248: 1
      1252: 1
      1256: 1
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1307: 1
      1334: 1
      1336: 1
      1414: 1
      1415: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: 1
      1456: 1
      1464: 1
      1470: 1
      1472: 1
      1474: 1
      1480: 2
      1482: 1
      1487: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1671: 1
      1823: 1

1824:    0: 2q^3+4q+2
         1: 2q^3+4q+2
         2: q^4+q^3+q^2+3q+2
         3: 2q^3+4q+2
         4: q^4+q^3+q^2+3q+2
         5: 2q^3+4q+2
         6: q^4+q^3+q^2+3q+2
         7: q^5+q^3+2q^2+2q+2
         8: q^4+q^3+q^2+3q+2
         9: q^5+q^3+2q^2+2q+2
        10: 2q^3+4q+2
        11: 2q^3+4q+2
        12: q^4+q^3+q^2+3q+2
        13: q^3+3q+2
        14: q^3+q^2+2q+2
        15: q^3+3q+2
        16: 2q^3+4q+2
        17: 2q^3+4q+2
        18: q^5+q^3+2q^2+2q+2
        19: q^3+3q+2
        20: q^3+3q+2
        21: q^3+q^2+2q+2
        22: 2q^3+4q+2
        23: 2q^3+4q+2
        24: q^4+q^3+q^2+3q+2
        25: 2q^3+4q+2
        26: 2q^3+4q+2
        27: q^4+q^3+q^2+3q+2
        28: 2q^3+4q+2
        29: q^3+3q+2
        30: q^3+2q+2
        31: 2q^3+4q+2
        32: q^3+3q+2
        33: 2q^3+4q+2
        34: 2q^3+4q+2
        35: q^3+3q+2
        36: 2q^3+4q+2
        38: 2q^3+4q+2
        40: 2q^3+4q+2
        42: q^4+q^3+q^2+3q+2
        43: q^3+3q+2
        44: q^3+q^2+2q+2
        45: q^3+3q+2
        46: q^3+3q+2
        47: q^3+3q+2
        48: q^3+q^2+2q+2
        49: q^3+3q+2
        50: q^3+3q+2
        51: q^3+q^2+2q+2
        52: q^3+3q+2
        53: q^3+3q+2
        54: q^3+q^2+2q+2
        55: q^3+3q+2
        56: q^3+3q+2
        57: q^3+q^2+2q+2
        58: q^3+2q+1
        59: q^3+2q+1
        60: q^3+2q+1
        61: q^3+2q+1
        63: 2q^3+4q+2
        65: q^3+3q+2
        67: 2q^3+4q+2
        68: 2q+2
        69: q^3+2q+2
        70: q^3+2q+2
        71: q^3+3q+2
        72: 2q+2
        73: 2q+2
        75: q^3+3q+2
        77: q^3+3q+2
        79: q^3+q^2+2q+2
        80: q^3+3q+2
        81: q^3+3q+2
        82: q^3+3q+2
        83: q^3+2q+2
        84: q^3+3q+2
        85: q^3+3q+2
        86: q^3+3q+2
        87: q^3+2q+2
        88: q^3+3q+2
        89: q^3+3q+2
        90: q^3+q^2+2q+2
        91: 2q+2
        92: 2q+2
        93: 2q+2
        94: q^3+3q+2
        95: q^3+3q+2
        96: q^3+q^2+2q+2
        97: q^3+3q+2
        98: q^3+3q+2
        99: q^3+q^2+2q+2
       100: q^3+3q+2
       101: q^3+3q+2
       102: q^3+q^2+2q+2
       104: q^3+2q+1
       105: q^3+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: q^3+3q+2
       116: q^3+2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^3+3q+2
       124: q^3+3q+2
       125: 2q+2
       126: q^3+2q+2
       128: q^3+3q+2
       130: q^3+3q+2
       132: q^3+q^2+2q+2
       133: q+2
       134: 2q+2
       135: q+2
       136: q+2
       137: q^3+3q+2
       138: q^3+2q+2
       139: q^3+3q+2
       140: 2q+2
       141: q^3+2q+2
       142: 2q+2
       143: q^3+3q+2
       144: q^3+2q+2
       145: q^3+3q+2
       146: q^3+2q+2
       147: 2q+2
       148: 2q+2
       149: q^3+3q+2
       150: q^3+2q+2
       152: q^3+3q+2
       154: q^3+3q+2
       156: q^3+q^2+2q+2
       157: 2q+2
       158: 2q+2
       159: 2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q^3+3q+2
       167: q^3+3q+2
       168: q^3+q^2+2q+2
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: q^3+2q+2
       180: q^3+3q+2
       182: 2q+2
       183: 1
       184: 1
       185: 1
       186: 1
       188: q+2
       190: q^3+2q+2
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2q+2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2q+2
       208: q^3+3q+2
       210: q^3+3q+2
       212: q^3+2q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: q+2
       220: q+2
       221: 2q+2
       222: q+2
       223: q+2
       224: q+2
       225: q+2
       226: q^3+2q+2
       227: q+2
       228: 2q+2
       229: q+2
       230: q+2
       231: q^3+2q+2
       232: q+2
       233: 2q+2
       234: q+2
       235: q+2
       236: q^3+2q+2
       238: q^3+3q+2
       240: q^3+3q+2
       242: q^3+q^2+2q+2
       243: q^3+3q+2
       244: 2q+2
       245: 2q+2
       246: q^3+2q+2
       247: 2q+2
       248: 2q+2
       249: q^2+2q+1
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q+2
       257: 2q+2
       258: 2q+2
       260: q+1
       261: q+1
       264: 1
       265: 1
       268: q+1
       270: q+1
       272: q+1
       274: q+1
       276: q+1
       277: q+1
       280: q+2
       282: 2q+2
       283: 1
       284: 1
       285: 1
       286: 1
       288: q^3+2q+2
       290: q+2
       292: q+2
       293: 1
       294: 1
       295: 1
       296: 1
       298: q+2
       299: 1
       300: 1
       302: 2q+2
       303: 1
       304: 1
       306: q+2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2q+2
       314: q+2
       316: q^3+2q+2
       318: q^3+3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2q+2
       326: q^3+2q+2
       328: 2q+2
       330: 2q+2
       332: 2q+2
       333: q+2
       334: q+2
       335: q+2
       336: q+1
       337: 2q+2
       339: 2q+2
       341: 2q+2
       343: q^2+2q+1
       344: q+2
       345: q+2
       346: 2q+2
       347: q+2
       348: q+2
       349: q+2
       350: q+2
       351: 2q+2
       352: q+2
       353: q+2
       354: 2q+2
       355: q+2
       356: q+2
       357: q+2
       358: q+2
       359: 2q+2
       361: 2q+2
       363: 2q+2
       365: 2q+2
       366: q^3+2q+2
       367: q+2
       368: 2q+2
       369: q+2
       370: q+2
       371: 2
       372: 2
       373: q+1
       374: 2q+2
       375: 2q+2
       376: 2q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: q+1
       392: q+1
       394: 1
       395: 1
       398: q+1
       400: q+1
       402: 1
       403: 1
       407: q+1
       408: q+1
       410: q+2
       412: 2q+2
       414: q+2
       416: q+2
       418: q+2
       419: 1
       420: 1
       421: 1
       422: 1
       424: q+2
       426: q+1
       428: 2q+2
       429: 1
       430: 1
       431: 1
       432: 1
       434: q+2
       436: q+2
       437: 1
       438: 1
       439: 1
       440: 1
       442: q+2
       443: q+1
       444: q+1
       446: 2q+2
       447: 1
       448: 1
       449: 1
       450: 1
       452: q+2
       453: 1
       454: 1
       456: q+2
       457: 1
       458: 1
       460: q+2
       461: q+1
       462: q+1
       464: 2q+2
       466: q+2
       468: 2q+2
       470: q^3+2q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: q+2
       478: 2q+2
       480: 2q+2
       481: 2
       482: 2
       483: q+1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+2
       493: q+2
       494: q+2
       495: q+1
       496: 2
       497: q+2
       498: q+2
       499: q+2
       500: q+1
       501: 2
       503: 2q+2
       505: 2q+2
       507: 2q+2
       508: q+2
       509: q+2
       510: 2q+2
       511: q+2
       512: q+2
       513: q+2
       514: q+2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: q+1
       548: q+1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: q+1
       564: q+1
       566: 1
       567: 1
       571: q+1
       572: q+1
       574: q+1
       576: q+1
       581: 2q+2
       584: q+2
       586: 2
       588: q+2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: q+1
       602: 2
       603: 1
       604: 1
       606: q+2
       607: 1
       608: 1
       610: q+2
       612: q+2
       614: q+1
       615: 1
       616: 1
       618: 2
       619: 1
       620: 1
       621: 1
       622: 1
       624: q+2
       626: q+2
       628: q+2
       630: q+1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: 2q+2
       640: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: q+2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+2
       654: q+2
       656: 2
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2
       677: q+1
       678: 2
       679: 1
       680: 2
       681: 2
       682: 2
       683: q+1
       684: 2
       685: 1
       686: q+2
       687: q+2
       688: q+2
       689: q+1
       690: 2
       691: 2
       692: q+1
       699: q+1
       700: q+1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       792: 1
       793: 1
       794: 1
       796: 2
       798: 2
       800: q+2
       801: 1
       802: 1
       807: 1
       808: 1
       810: 1
       812: q+1
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: q+2
       825: 1
       826: 1
       831: 1
       832: 1
       834: 1
       836: q+1
       838: 2
       839: 1
       840: 1
       842: q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: q+2
       854: q+2
       856: q+1
       858: 2
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       879: q+1
       880: 1
       890: 1
       891: 1
       897: 1
       898: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       962: 1
       963: 1
       965: 1
       966: 1
       972: 2
       976: 1
       977: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1047: 2
      1049: 2
      1051: q+2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1104: 1
      1105: 1
      1142: 1
      1143: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1186: 1
      1187: 1
      1192: 2
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1215: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1237: 1
      1239: 1
      1249: 1
      1253: 1
      1257: 1
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1308: 1
      1309: 1
      1338: 1
      1339: 1
      1416: 1
      1417: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: 1
      1457: 1
      1465: 1
      1471: 1
      1473: 1
      1475: 1
      1481: 2
      1483: 1
      1487: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1672: 1
      1824: 1

1825:    0: 4q^2+4q+2
         1: 4q^2+4q+2
         2: 4q^2+4q+2
         3: 4q^2+4q+2
         4: q^3+3q^2+3q+2
         5: 4q^2+4q+2
         6: 2q^3+4q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: q^3+3q^2+3q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+4q+2
        14: q^3+3q^2+3q+2
        15: 4q^2+4q+2
        16: 4q^2+4q+2
        17: 4q^2+4q+2
        18: q^3+3q^2+3q+2
        19: 2q^2+3q+2
        20: 3q^2+3q+2
        21: 2q^2+3q+2
        22: 4q^2+4q+2
        23: 4q^2+4q+2
        24: 4q^2+4q+2
        25: 4q^2+4q+2
        26: 4q^2+4q+2
        27: 4q^2+4q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+3q+2
        31: 4q+2
        32: 4q^2+4q+2
        33: 4q^2+4q+2
        34: 4q+2
        35: 4q^2+4q+2
        36: 4q^2+4q+2
        37: q^2+2q+2
        38: 3q^2+2q
        39: q^2+2q+2
        40: 3q^2+2q
        41: q^2+2q+2
        42: 3q^2+2q
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+4q+2
        47: 4q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^2+3q+2
        50: 3q^2+3q+2
        51: 2q^2+3q+2
        52: 2q^2+3q+2
        53: 3q^2+3q+2
        54: 2q^2+3q+2
        55: 2q^2+3q+2
        56: 3q^2+3q+2
        57: 2q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+2
        63: 2q
        64: q^2+2q+2
        65: 3q^2+2q
        66: q^2+2q+2
        67: 3q^2+2q
        68: 4q+2
        69: 2q^2+3q+2
        70: 3q+2
        71: 3q+2
        72: q^2+2q+2
        73: q^2+2q+2
        74: q+2
        75: q^2+2q
        76: q+2
        77: 2q^2+2q
        78: q+2
        79: q^2+2q
        80: 4q+2
        81: 4q^2+4q+2
        82: 3q+2
        83: 2q^2+3q+2
        84: 4q+2
        85: 4q^2+4q+2
        86: 3q+2
        87: 2q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+3q+2
        92: 3q^2+3q+2
        93: 2q^2+3q+2
        94: 2q^2+3q+2
        95: 3q^2+3q+2
        96: 2q^2+3q+2
        97: 2q^2+3q+2
        98: 3q^2+3q+2
        99: 2q^2+3q+2
       100: 2q^2+3q+2
       101: 3q^2+3q+2
       102: 2q^2+3q+2
       103: q+1
       104: q
       105: q
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       112: 2q
       113: q+2
       114: 2q
       115: q+2
       116: q^2+2q
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+2
       122: 2q
       123: q^2+2q+2
       124: 3q^2+2q
       125: 4q+2
       126: 3q+2
       127: q+2
       128: q^2+2q
       129: q+2
       130: 2q^2+2q
       131: q+2
       132: q^2+2q
       133: 3q+2
       134: 2q^2+3q+2
       135: q^2+2q+2
       136: q^2+2q+2
       137: 4q+2
       138: 2q^2+3q+2
       139: 3q+2
       140: q^2+2q+2
       141: 3q+2
       142: q^2+2q+2
       143: 4q+2
       144: 2q^2+3q+2
       145: 3q+2
       146: 3q+2
       147: q^2+2q+2
       148: q^2+2q+2
       149: 3q+2
       150: 2q^2+3q+2
       151: q+2
       152: q^2+2q
       153: q+2
       154: 2q^2+2q
       155: q+2
       156: q^2+2q
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+3q+2
       161: 3q^2+3q+2
       162: 2q^2+3q+2
       163: 2q^2+3q+2
       164: 3q^2+3q+2
       165: 2q^2+3q+2
       166: 2q^2+3q+2
       167: 3q^2+3q+2
       168: 2q^2+3q+2
       169: 1
       170: q
       171: q
       172: 1
       173: q+1
       174: q
       175: q
       176: q+1
       177: q+2
       178: q^2+2q
       179: q+2
       180: 2q
       181: 2
       182: 2q
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2
       188: 2q
       189: q+2
       190: 2q
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       198: 2q
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       206: 2q
       207: 2q+2
       208: 2q
       209: q+2
       210: 2q
       211: q+2
       212: q^2+2q
       213: q+2
       214: q^2+2q
       215: q+2
       216: 2q^2+2q
       217: q+2
       218: q^2+2q
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+2q+2
       224: 2
       225: q^2+2q+2
       226: 3q+2
       227: 3q+2
       228: 2q^2+3q+2
       229: q^2+2q+2
       230: q^2+2q+2
       231: 3q+2
       232: 3q+2
       233: 2q^2+3q+2
       234: q^2+2q+2
       235: q^2+2q+2
       236: 2q^2+3q+2
       237: q+2
       238: q^2+2q
       239: q+2
       240: 2q^2+2q
       241: q+2
       242: q^2+2q
       243: 3q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: 3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: 1
       260: q
       261: q
       262: 1
       263: 1
       264: q
       265: q
       266: 1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: q+1
       276: q
       277: q
       278: q+1
       279: q+2
       280: 2q
       281: q+2
       282: q^2+2q
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+2
       288: 2q
       289: 2
       290: 2q
       291: 2
       292: 2q
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: q+1
       300: q+1
       301: 2
       302: 2q
       303: q+1
       304: q+1
       305: 2
       306: 2q
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       312: 2q
       313: 2
       314: 2q
       315: q+2
       316: q^2+2q
       317: q+2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       324: 2q
       325: q+2
       326: 2q
       333: q+2
       334: 2
       335: 2
       336: q+1
       337: 2q+2
       338: 2
       339: 3q
       340: 2
       341: 3q
       342: q+1
       343: q^2+q
       344: 3q+2
       345: q+2
       346: q+2
       347: 2
       348: q^2+2q+2
       349: 2
       350: q^2+2q+2
       351: 3q+2
       352: 3q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+2q+2
       357: 2
       358: q^2+2q+2
       359: 3q+2
       360: q+2
       361: q^2+2q
       362: q+2
       363: 2q^2+2q
       364: q+2
       365: q^2+2q
       366: 3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       378: q
       379: q
       380: 1
       381: 1
       382: q
       383: q
       384: 1
       385: 1
       388: 1
       389: 1
       390: q
       391: 1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       398: q
       399: 1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       407: q
       408: q
       413: q+2
       414: 2q
       417: 2
       418: 2q
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       426: q
       427: 2
       428: 2q
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 2
       434: 2q
       435: 2
       436: 2q
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: q+1
       444: q+1
       445: 2
       446: 3q
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: 2
       452: 2q
       453: 1
       454: 1
       455: 2
       456: 2q
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       464: 3q
       465: q+2
       466: 2q
       467: q+2
       468: q^2+2q
       469: q+2
       470: 2q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       476: 2q
       477: 2
       478: 2q
       479: q+2
       480: 2q
       481: 2
       482: 2
       483: 1
       484: 2q+2
       485: 2
       486: 3q
       487: 2
       488: 3q
       489: q+1
       490: q^2+q
       491: q+1
       492: q+2
       493: 2
       494: 2
       495: q+1
       496: 3q+2
       497: q+2
       498: 2
       499: 2
       500: q+1
       501: 3q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 3q+2
       516: 3q+2
       517: q^2+2q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       522: q
       523: q
       524: 1
       529: 1
       532: 1
       533: 1
       534: q
       535: q
       536: 1
       537: 1
       538: q
       539: 1
       540: q
       541: 1
       543: 1
       545: 1
       546: q
       547: 1
       548: q
       549: 1
       550: q
       551: q
       552: 1
       553: 1
       554: q
       555: 1
       556: q
       557: 1
       559: 1
       561: 1
       562: q
       563: 1
       564: q
       565: 1
       566: q
       567: q
       568: 1
       569: 1
       570: 1
       571: q
       572: q
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       578: q
       581: 2q
       585: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       598: q
       599: 1
       601: 2
       602: 2q
       603: 1
       604: 1
       605: 2
       606: 2q
       607: 1
       608: 1
       609: 2
       613: 1
       614: q
       615: q+1
       616: q+1
       617: 2
       618: 3q
       619: 1
       620: 1
       621: 1
       622: 1
       623: 2
       624: 2q
       625: 2
       629: 1
       630: q
       631: q+1
       632: q+1
       633: 2
       634: 3q
       639: q+2
       640: 2q
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       646: 2q
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       652: 2q
       653: 2
       655: q+2
       656: 2q
       657: 2q+2
       658: 2
       659: 3q
       660: 2
       661: 3q
       662: q+1
       663: q^2+q
       664: q+1
       665: 1
       672: 2
       673: 1
       674: 3q+2
       675: 2
       676: 2
       677: 1
       678: 2
       679: q+1
       680: 3q+2
       681: 2
       682: 2
       683: 1
       684: 2
       685: q+1
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: 2
       691: 2
       692: q+1
       693: 1
       697: 1
       699: q
       700: q
       709: 1
       712: 1
       721: 1
       722: q
       723: 1
       724: q
       725: 1
       727: 1
       733: 1
       734: q
       735: 1
       736: q
       737: 1
       738: q
       739: 1
       740: q
       741: 1
       743: 1
       749: 1
       750: q
       751: 1
       752: q
       753: 1
       754: q
       755: q
       756: 1
       757: 1
       758: 1
       759: q
       760: q
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       770: q
       773: 2q
       775: 2
       776: 2q
       779: 1
       780: q
       781: 1
       791: 1
       793: q+1
       794: q+1
       795: 2
       796: 3q
       797: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       810: q
       811: 1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       820: 3q
       821: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       834: q
       835: 1
       839: 1
       840: 1
       843: q+2
       844: 2q
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       850: 2q
       851: 2
       855: 1
       856: q
       857: 2
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       879: 1
       880: q+1
       881: 2
       882: 2
       883: q+1
       884: 1
       889: 1
       890: q
       891: q
       916: 1
       917: q
       918: 1
       919: q
       920: 1
       922: 1
       940: 1
       941: q
       942: 1
       943: q
       944: 1
       946: 1
       960: 1
       961: 1
       962: q
       963: q
       964: 1
       965: q
       966: q
       967: 1
       968: 2
       969: q
       972: 2q
       974: 1
       975: 1
       988: 1
       991: 1
       994: 1
      1008: 1
      1010: 1
      1012: 1
      1016: 1
      1017: 1
      1020: 1
      1021: q
      1022: 1
      1032: 1
      1033: 1
      1036: 1
      1037: q
      1038: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1091: 1
      1092: q
      1093: q
      1138: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1220: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1246: 1
      1247: 1
      1248: 1
      1262: 2
      1266: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1410: 1
      1413: 1
      1430: 1
      1436: 1
      1444: 1
      1464: 1
      1474: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1639: 1
      1659: 1
      1669: 1
      1674: 1
      1825: 1

1826:    0: 4q^2+4q+2
         1: 4q^2+4q+2
         2: 4q^2+4q+2
         3: 4q^2+4q+2
         4: q^3+3q^2+3q+2
         5: 4q^2+4q+2
         6: 2q^3+4q^2+3q+2
         7: q^3+3q^2+3q+2
         8: 4q^2+4q+2
         9: q^3+3q^2+3q+2
        10: 4q+2
        11: 4q+2
        12: q^2+3q+2
        13: 4q^2+4q+2
        14: q^3+3q^2+3q+2
        15: 4q^2+4q+2
        16: 4q^2+4q+2
        17: 4q^2+4q+2
        18: q^3+3q^2+3q+2
        19: 2q^2+3q+2
        20: 3q^2+3q+2
        21: 2q^2+3q+2
        22: 4q^2+4q+2
        23: 4q^2+4q+2
        24: 4q^2+4q+2
        25: 4q^2+4q+2
        26: 4q^2+4q+2
        27: 4q^2+4q+2
        28: 4q+2
        29: 3q+2
        30: 2q^2+3q+2
        31: 4q+2
        32: 4q^2+4q+2
        33: 4q^2+4q+2
        34: 4q+2
        35: 4q^2+4q+2
        36: 4q^2+4q+2
        37: 3q^2+2q
        38: q^2+2q+2
        39: 3q^2+2q
        40: q^2+2q+2
        41: 3q^2+2q
        42: q^2+2q+2
        43: 4q+2
        44: q^2+3q+2
        45: 4q+2
        46: 4q^2+4q+2
        47: 4q^2+4q+2
        48: q^3+3q^2+3q+2
        49: 2q^2+3q+2
        50: 3q^2+3q+2
        51: 2q^2+3q+2
        52: 2q^2+3q+2
        53: 3q^2+3q+2
        54: 2q^2+3q+2
        55: 2q^2+3q+2
        56: 3q^2+3q+2
        57: 2q^2+3q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q
        63: 2q+2
        64: 3q^2+2q
        65: q^2+2q+2
        66: 3q^2+2q
        67: q^2+2q+2
        68: 4q+2
        69: 2q^2+3q+2
        70: 3q+2
        71: 3q+2
        72: q^2+2q+2
        73: q^2+2q+2
        74: q^2+2q
        75: q+2
        76: 2q^2+2q
        77: q+2
        78: q^2+2q
        79: q+2
        80: 4q+2
        81: 4q^2+4q+2
        82: 3q+2
        83: 2q^2+3q+2
        84: 4q+2
        85: 4q^2+4q+2
        86: 3q+2
        87: 2q^2+3q+2
        88: 4q+2
        89: 4q+2
        90: q^2+3q+2
        91: 2q^2+3q+2
        92: 3q^2+3q+2
        93: 2q^2+3q+2
        94: 2q^2+3q+2
        95: 3q^2+3q+2
        96: 2q^2+3q+2
        97: 2q^2+3q+2
        98: 3q^2+3q+2
        99: 2q^2+3q+2
       100: 2q^2+3q+2
       101: 3q^2+3q+2
       102: 2q^2+3q+2
       103: q
       104: q+1
       105: q+1
       106: q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q
       112: 2
       113: 2q
       114: q+2
       115: q^2+2q
       116: q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q
       122: 2q+2
       123: 3q^2+2q
       124: q^2+2q+2
       125: 4q+2
       126: 3q+2
       127: q^2+2q
       128: q+2
       129: 2q^2+2q
       130: q+2
       131: q^2+2q
       132: q+2
       133: 3q+2
       134: 2q^2+3q+2
       135: q^2+2q+2
       136: q^2+2q+2
       137: 4q+2
       138: 2q^2+3q+2
       139: 3q+2
       140: q^2+2q+2
       141: 3q+2
       142: q^2+2q+2
       143: 4q+2
       144: 2q^2+3q+2
       145: 3q+2
       146: 3q+2
       147: q^2+2q+2
       148: q^2+2q+2
       149: 3q+2
       150: 2q^2+3q+2
       151: q^2+2q
       152: q+2
       153: 2q^2+2q
       154: q+2
       155: q^2+2q
       156: q+2
       157: q+2
       158: q+2
       159: q+2
       160: 2q^2+3q+2
       161: 3q^2+3q+2
       162: 2q^2+3q+2
       163: 2q^2+3q+2
       164: 3q^2+3q+2
       165: 2q^2+3q+2
       166: 2q^2+3q+2
       167: 3q^2+3q+2
       168: 2q^2+3q+2
       169: q
       170: 1
       171: 1
       172: q
       173: q
       174: q+1
       175: q+1
       176: q
       177: q^2+2q
       178: q+2
       179: 2q
       180: q+2
       181: 2q
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q
       188: 2
       189: 2q
       190: q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q
       198: 2
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q
       206: 2
       207: 2q
       208: 2q+2
       209: 2q
       210: q+2
       211: q^2+2q
       212: q+2
       213: q^2+2q
       214: q+2
       215: 2q^2+2q
       216: q+2
       217: q^2+2q
       218: q+2
       219: 3q+2
       220: q+2
       221: q+2
       222: 2
       223: q^2+2q+2
       224: 2
       225: q^2+2q+2
       226: 3q+2
       227: 3q+2
       228: 2q^2+3q+2
       229: q^2+2q+2
       230: q^2+2q+2
       231: 3q+2
       232: 3q+2
       233: 2q^2+3q+2
       234: q^2+2q+2
       235: q^2+2q+2
       236: 2q^2+3q+2
       237: q^2+2q
       238: q+2
       239: 2q^2+2q
       240: q+2
       241: q^2+2q
       242: q+2
       243: 3q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: 3q+2
       247: 3q+2
       248: 3q+2
       249: q^2+2q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: q
       260: 1
       261: 1
       262: q
       263: q
       264: 1
       265: 1
       266: q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       275: q
       276: q+1
       277: q+1
       278: q
       279: 2q
       280: q+2
       281: q^2+2q
       282: q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 2q
       288: q+2
       289: 2q
       290: 2
       291: 2q
       292: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: q+1
       300: q+1
       301: 2q
       302: 2
       303: q+1
       304: q+1
       305: 2q
       306: 2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q
       312: 2
       313: 2q
       314: 2
       315: q^2+2q
       316: q+2
       317: 2q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: 2
       325: 2q
       326: q+2
       333: q+2
       334: 2
       335: 2
       336: q+1
       337: 2q+2
       338: 3q
       339: 2
       340: 3q
       341: 2
       342: q^2+q
       343: q+1
       344: 3q+2
       345: q+2
       346: q+2
       347: 2
       348: q^2+2q+2
       349: 2
       350: q^2+2q+2
       351: 3q+2
       352: 3q+2
       353: q+2
       354: q+2
       355: 2
       356: q^2+2q+2
       357: 2
       358: q^2+2q+2
       359: 3q+2
       360: q^2+2q
       361: q+2
       362: 2q^2+2q
       363: q+2
       364: q^2+2q
       365: q+2
       366: 3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 3q+2
       372: 3q+2
       373: q^2+2q+1
       374: q+2
       375: q+2
       376: q+2
       377: q
       378: 1
       379: 1
       380: q
       381: q
       382: 1
       383: 1
       384: q
       386: 1
       387: 1
       389: q
       390: 1
       391: q
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 1
       399: q
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: 1
       408: 1
       413: 2q
       414: q+2
       417: 2q
       418: 2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       425: q
       426: 1
       427: 2q
       428: 2
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 2q
       434: 2
       435: 2q
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: q+1
       444: q+1
       445: 3q
       446: 2
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: 2q
       452: 2
       453: 1
       454: 1
       455: 2q
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       463: 3q
       464: 2
       465: 2q
       466: q+2
       467: q^2+2q
       468: q+2
       469: 2q
       470: q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: 2
       477: 2q
       478: 2
       479: 2q
       480: q+2
       481: 2
       482: 2
       483: 1
       484: 2q+2
       485: 3q
       486: 2
       487: 3q
       488: 2
       489: q^2+q
       490: q+1
       491: q+1
       492: q+2
       493: 2
       494: 2
       495: q+1
       496: 3q+2
       497: q+2
       498: 2
       499: 2
       500: q+1
       501: 3q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 3q+2
       516: 3q+2
       517: q^2+2q+1
       518: 2
       519: 2
       520: q+1
       521: q
       522: 1
       523: 1
       524: q
       530: 1
       531: 1
       533: q
       534: 1
       535: 1
       536: q
       537: q
       538: 1
       539: q
       540: 1
       542: 1
       544: 1
       545: q
       546: 1
       547: q
       548: 1
       549: q
       550: 1
       551: 1
       552: q
       553: q
       554: 1
       555: q
       556: 1
       558: 1
       560: 1
       561: q
       562: 1
       563: q
       564: 1
       565: q
       566: 1
       567: 1
       568: q
       569: q
       570: q
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       577: 2q
       580: q
       581: 2
       586: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: q
       598: 1
       600: 1
       601: 2q
       602: 2
       603: 1
       604: 1
       605: 2q
       606: 2
       607: 1
       608: 1
       610: 2
       613: q
       614: 1
       615: q+1
       616: q+1
       617: 3q
       618: 2
       619: 1
       620: 1
       621: 1
       622: 1
       623: 2q
       624: 2
       626: 2
       629: q
       630: 1
       631: q+1
       632: q+1
       633: 3q
       634: 2
       639: 2q
       640: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2q
       652: 2
       654: 2
       655: 2q
       656: q+2
       657: 2q+2
       658: 3q
       659: 2
       660: 3q
       661: 2
       662: q^2+q
       663: q+1
       664: q+1
       665: 1
       672: 2
       673: 1
       674: 3q+2
       675: 2
       676: 2
       677: 1
       678: 2
       679: q+1
       680: 3q+2
       681: 2
       682: 2
       683: 1
       684: 2
       685: q+1
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: 2
       691: 2
       692: q+1
       693: q
       697: q
       699: 1
       700: 1
       710: 1
       711: 1
       721: q
       722: 1
       723: q
       724: 1
       726: 1
       728: 1
       733: q
       734: 1
       735: q
       736: 1
       737: q
       738: 1
       739: q
       740: 1
       742: 1
       744: 1
       749: q
       750: 1
       751: q
       752: 1
       753: q
       754: 1
       755: 1
       756: q
       757: q
       758: q
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       769: 2q
       772: q
       773: 2
       775: 2q
       776: 2
       779: q
       780: 1
       782: 1
       792: 1
       793: q+1
       794: q+1
       795: 3q
       796: 2
       798: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: q
       810: 1
       812: 1
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 3q
       820: 2
       822: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: q
       834: 1
       836: 1
       839: 1
       840: 1
       843: 2q
       844: q+2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2q
       850: 2
       852: 2
       855: q
       856: 1
       858: 2
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: q+1
       871: 1
       872: 1
       873: 2
       874: q+1
       875: 1
       876: 1
       877: 2
       878: 2
       879: 1
       880: q+1
       881: 2
       882: 2
       883: q+1
       884: q
       889: q
       890: 1
       891: 1
       916: q
       917: 1
       918: q
       919: 1
       921: 1
       923: 1
       940: q
       941: 1
       942: q
       943: 1
       945: 1
       947: 1
       960: q
       961: q
       962: 1
       963: 1
       964: q
       965: 1
       966: 1
       967: q
       968: 2q
       971: q
       972: 2
       976: 1
       977: 1
       989: 1
       990: 1
       995: 1
      1009: 1
      1011: 1
      1013: 1
      1016: 1
      1017: 1
      1020: q
      1021: 1
      1023: 1
      1032: 1
      1033: 1
      1036: q
      1037: 1
      1039: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: q
      1061: 1
      1063: 1
      1065: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1091: q
      1092: 1
      1093: 1
      1142: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1221: 1
      1225: 1
      1228: 1
      1229: 1
      1231: 1
      1246: 1
      1247: 1
      1249: 1
      1263: 2
      1267: 1
      1274: q
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1411: 1
      1412: 1
      1434: 1
      1437: 1
      1445: 1
      1465: 1
      1475: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1640: 1
      1660: 1
      1670: 1
      1674: 1
      1826: 1

1827:    0: 4q^2+8q+2
         1: 4q^2+8q+2
         2: 4q^2+8q+2
         3: 4q^2+8q+2
         4: 2q^3+4q^2+5q+2
         5: 4q^2+8q+2
         6: 2q^3+4q^2+5q+2
         7: 2q^3+4q^2+5q+2
         8: 4q^2+8q+2
         9: 2q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: 2q^3+4q^2+5q+2
        13: 4q^2+8q+2
        14: 2q^3+4q^2+5q+2
        15: 4q^2+8q+2
        16: 4q^2+8q+2
        17: 4q^2+8q+2
        18: 2q^3+4q^2+5q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+8q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+8q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: 4q^2+8q+2
        33: 4q^2+8q+2
        34: 4q^2+8q+2
        35: 4q^2+8q+2
        36: 4q^2+8q+2
        37: 2q^2+6q+2
        38: 2q^2+2q
        39: 2q^2+6q+2
        40: 2q^2+2q
        41: 2q^2+6q+2
        42: 2q^2+2q
        43: 4q^2+8q+2
        44: 2q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: 4q^2+8q+2
        47: 4q^2+8q+2
        48: 2q^3+4q^2+5q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+5q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+5q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+5q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 2q^2+6q+2
        63: 2q^2+2q
        64: 2q^2+6q+2
        65: 2q^2+2q
        66: 2q^2+6q+2
        67: 2q^2+2q
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: 2q+2
        73: 2q+2
        74: 3q+2
        76: 3q+2
        78: 3q+2
        80: 4q^2+8q+2
        81: 4q^2+8q+2
        82: q^2+5q+2
        83: q^2+5q+2
        84: 4q^2+8q+2
        85: 4q^2+8q+2
        86: q^2+5q+2
        87: q^2+5q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: 2q^3+4q^2+5q+2
        91: q^2+5q+2
        92: q^2+5q+2
        93: q^2+5q+2
        94: q^2+5q+2
        95: q^2+5q+2
        96: q^2+5q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: q^2+5q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+5q+2
       103: q^2+3q+1
       104: q^2+q
       105: q^2+q
       106: q^2+3q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2
       113: 3q+2
       115: 3q+2
       117: 2q^2+4q+1
       118: 2q^2+4q+1
       119: 2q^2+4q+1
       120: 2q^2+4q+1
       121: 2q^2+6q+2
       122: 2q^2+2q
       123: 2q^2+6q+2
       124: 2q^2+2q
       125: 4q^2+8q+2
       126: q^2+5q+2
       127: 3q+2
       129: 3q+2
       131: 3q+2
       133: q^2+5q+2
       134: q^2+5q+2
       135: 2q+2
       136: 2q+2
       137: 4q^2+8q+2
       138: q^2+5q+2
       139: q^2+5q+2
       140: 2q+2
       141: q^2+5q+2
       142: 2q+2
       143: 4q^2+8q+2
       144: q^2+5q+2
       145: q^2+5q+2
       146: q^2+5q+2
       147: 2q+2
       148: 2q+2
       149: q^2+5q+2
       150: q^2+5q+2
       151: 3q+2
       153: 3q+2
       155: 3q+2
       157: q^2+5q+2
       158: q^2+5q+2
       159: q^2+5q+2
       160: q^2+5q+2
       161: q^2+5q+2
       162: q^2+5q+2
       163: q^2+5q+2
       164: q^2+5q+2
       165: q^2+5q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: q^2+5q+2
       169: 1
       172: 1
       173: q^2+3q+1
       174: q^2+q
       175: q^2+q
       176: q^2+3q+1
       177: 3q+2
       179: 3q+2
       181: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2
       189: 3q+2
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2
       207: 2q^2+6q+2
       208: 2q^2+2q
       209: 3q+2
       211: 3q+2
       213: 3q+2
       215: 3q+2
       217: 3q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: q^2+5q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: q^2+5q+2
       227: q^2+5q+2
       228: q^2+5q+2
       229: 2q+2
       230: 2q+2
       231: q^2+5q+2
       232: q^2+5q+2
       233: q^2+5q+2
       234: 2q+2
       235: 2q+2
       236: q^2+5q+2
       237: 3q+2
       239: 3q+2
       241: 3q+2
       243: q^2+5q+2
       244: 2q+2
       245: 2q+2
       246: q^2+5q+2
       247: 4
       248: 4
       249: 2q+1
       250: q^2+5q+2
       251: q^2+5q+2
       252: q^2+5q+2
       253: q^2+5q+2
       254: q^2+5q+2
       255: q^2+5q+2
       256: q^2+5q+2
       257: q^2+5q+2
       258: q^2+5q+2
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q^2+3q+1
       276: q^2+q
       277: q^2+q
       278: q^2+3q+1
       279: 3q+2
       281: 3q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 3q+2
       289: 2
       291: 2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2
       299: q+1
       300: q+1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2
       313: 2
       315: 3q+2
       317: 3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       325: 3q+2
       327: 3q+2
       329: 3q+2
       331: 3q+2
       333: q^2+5q+2
       334: 2q+2
       335: 2q+2
       336: 1
       337: 4
       338: 4
       340: 4
       342: 2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: q^2+5q+2
       347: 2q+2
       348: 2q+2
       349: 2q+2
       350: 2q+2
       351: 4
       352: q^2+5q+2
       353: q^2+5q+2
       354: q^2+5q+2
       355: 2q+2
       356: 2q+2
       357: 2q+2
       358: 2q+2
       359: 4
       360: 3q+2
       362: 3q+2
       364: 3q+2
       366: q^2+5q+2
       367: q^2+5q+2
       368: q^2+5q+2
       369: 2q+2
       370: 2q+2
       371: 4
       372: 4
       373: 2q+1
       374: q^2+5q+2
       375: q^2+5q+2
       376: q^2+5q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 3q+2
       411: 3q+2
       413: 3q+2
       415: 2
       417: 2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2
       425: 1
       427: 4
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 2
       435: 2
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2
       443: 2
       444: 2
       445: 4
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: 2
       453: q+1
       454: q+1
       455: 2
       457: q+1
       458: q+1
       459: 2
       461: 2
       462: 2
       463: 4
       465: 3q+2
       467: 3q+2
       469: 3q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       477: 2
       479: 2
       480: 2
       481: 2q+2
       482: 2q+2
       483: 1
       484: 4
       485: 4
       487: 4
       489: 2q+1
       491: 1
       492: q^2+5q+2
       493: 2q+2
       494: 2q+2
       495: 1
       496: 4
       497: q^2+5q+2
       498: 2q+2
       499: 2q+2
       500: 1
       501: 4
       502: 3q+2
       504: 3q+2
       506: 3q+2
       508: q^2+5q+2
       509: q^2+5q+2
       510: q^2+5q+2
       511: 2q+2
       512: 2q+2
       513: 2q+2
       514: 2q+2
       515: 4
       516: 4
       517: 2q+1
       518: 4
       519: 4
       520: 2q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 2
       547: 2
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 2
       563: 2
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 2
       580: 2
       583: 3q+2
       585: 2
       587: 2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       597: 1
       599: 1
       601: 4
       603: q+1
       604: q+1
       605: 2
       607: q+1
       608: q+1
       609: 2
       611: 2
       613: 1
       615: 2
       616: 2
       617: 4
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2
       625: 2
       627: 2
       629: 1
       631: 2
       632: 2
       633: 4
       635: 3q+2
       637: 3q+2
       639: 3q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 2
       653: 2
       655: 2
       656: 2
       657: 4
       658: 4
       660: 4
       662: 2q+1
       664: 1
       665: 1
       666: 4
       668: 4
       670: 2q+1
       672: 4
       673: 1
       674: 4
       675: 2q+2
       676: 2q+2
       677: 1
       678: 4
       679: 1
       680: 4
       681: 2q+2
       682: 2q+2
       683: 1
       684: 4
       685: 1
       686: q^2+5q+2
       687: 2q+2
       688: 2q+2
       689: 1
       690: 4
       691: 4
       692: 2q+1
       693: 1
       696: 1
       697: 1
       698: 1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 2
       735: 2
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 2
       751: 2
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 2
       772: 2
       775: 4
       777: 2
       779: 1
       781: 1
       783: 1
       789: 4
       793: 2
       794: 2
       795: 4
       797: 2
       799: 2
       801: q+1
       802: q+1
       807: q+1
       808: q+1
       809: 1
       811: 1
       813: 4
       815: 2
       816: 2
       817: 2
       818: 2
       819: 4
       821: 2
       823: 2
       825: q+1
       826: q+1
       831: q+1
       832: q+1
       833: 1
       835: 1
       837: 4
       839: 2
       840: 2
       841: 3q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: 2
       851: 2
       853: 2
       855: 1
       857: 2
       858: 2
       859: 4
       861: 4
       863: 2q+1
       865: 4
       866: 1
       867: 1
       868: 1
       869: 4
       870: 1
       871: 1
       872: 1
       873: 4
       874: 1
       875: 1
       876: 1
       877: 2q+2
       878: 2q+2
       879: 1
       880: 1
       881: 4
       882: 4
       883: 2q+1
       884: 1
       887: 1
       888: 1
       889: 1
       896: 1
       899: 1
       912: 1
       914: 1
       916: 2
       918: 2
       920: 1
       922: 1
       932: 2
       934: 2
       936: 1
       938: 1
       940: 2
       942: 2
       944: 1
       946: 1
       956: 2
       958: 2
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       985: 2
       988: 1
       989: 1
       990: 1
       991: 1
       992: 4
       994: 1
       996: 1
      1002: 1
      1014: 4
      1016: 2
      1017: 2
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 4
      1032: 2
      1033: 2
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1047: 2
      1048: 2
      1050: 2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1062: 1
      1066: 4
      1068: 4
      1070: 2q+1
      1072: 4
      1073: 1
      1074: 1
      1075: 4
      1076: 1
      1077: 1
      1078: 1
      1079: 4
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1098: 1
      1101: 1
      1102: 1
      1103: 1
      1144: 2
      1146: 2
      1148: 1
      1150: 1
      1164: 2
      1166: 2
      1168: 1
      1170: 1
      1184: 1
      1185: 1
      1188: 2
      1191: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1210: 4
      1212: 1
      1214: 1
      1226: 4
      1228: 2
      1229: 2
      1230: 1
      1236: 1
      1238: 1
      1244: 4
      1246: 2
      1247: 2
      1248: 1
      1252: 1
      1256: 1
      1262: 2
      1263: 2
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1305: 1
      1306: 1
      1307: 1
      1340: 2
      1342: 2
      1372: 2
      1374: 2
      1404: 2
      1407: 2
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1438: 1
      1448: 1
      1452: 1
      1456: 1
      1458: 1
      1464: 1
      1470: 1
      1472: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1643: 1
      1651: 1
      1661: 1
      1667: 1
      1674: 1
      1827: 1

1828:    0: 4q^2+8q+2
         1: 4q^2+8q+2
         2: 4q^2+8q+2
         3: 4q^2+8q+2
         4: 2q^3+4q^2+5q+2
         5: 4q^2+8q+2
         6: 2q^3+4q^2+5q+2
         7: 2q^3+4q^2+5q+2
         8: 4q^2+8q+2
         9: 2q^3+4q^2+5q+2
        10: 4q^2+8q+2
        11: 4q^2+8q+2
        12: 2q^3+4q^2+5q+2
        13: 4q^2+8q+2
        14: 2q^3+4q^2+5q+2
        15: 4q^2+8q+2
        16: 4q^2+8q+2
        17: 4q^2+8q+2
        18: 2q^3+4q^2+5q+2
        19: q^2+5q+2
        20: q^2+5q+2
        21: q^2+5q+2
        22: 4q^2+8q+2
        23: 4q^2+8q+2
        24: 4q^2+8q+2
        25: 4q^2+8q+2
        26: 4q^2+8q+2
        27: 4q^2+8q+2
        28: 4q^2+8q+2
        29: q^2+5q+2
        30: q^2+5q+2
        31: 4q^2+8q+2
        32: 4q^2+8q+2
        33: 4q^2+8q+2
        34: 4q^2+8q+2
        35: 4q^2+8q+2
        36: 4q^2+8q+2
        37: 2q^2+2q
        38: 2q^2+6q+2
        39: 2q^2+2q
        40: 2q^2+6q+2
        41: 2q^2+2q
        42: 2q^2+6q+2
        43: 4q^2+8q+2
        44: 2q^3+4q^2+5q+2
        45: 4q^2+8q+2
        46: 4q^2+8q+2
        47: 4q^2+8q+2
        48: 2q^3+4q^2+5q+2
        49: q^2+5q+2
        50: q^2+5q+2
        51: q^2+5q+2
        52: q^2+5q+2
        53: q^2+5q+2
        54: q^2+5q+2
        55: q^2+5q+2
        56: q^2+5q+2
        57: q^2+5q+2
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 2q^2+2q
        63: 2q^2+6q+2
        64: 2q^2+2q
        65: 2q^2+6q+2
        66: 2q^2+2q
        67: 2q^2+6q+2
        68: 4q^2+8q+2
        69: q^2+5q+2
        70: q^2+5q+2
        71: q^2+5q+2
        72: 2q+2
        73: 2q+2
        75: 3q+2
        77: 3q+2
        79: 3q+2
        80: 4q^2+8q+2
        81: 4q^2+8q+2
        82: q^2+5q+2
        83: q^2+5q+2
        84: 4q^2+8q+2
        85: 4q^2+8q+2
        86: q^2+5q+2
        87: q^2+5q+2
        88: 4q^2+8q+2
        89: 4q^2+8q+2
        90: 2q^3+4q^2+5q+2
        91: q^2+5q+2
        92: q^2+5q+2
        93: q^2+5q+2
        94: q^2+5q+2
        95: q^2+5q+2
        96: q^2+5q+2
        97: q^2+5q+2
        98: q^2+5q+2
        99: q^2+5q+2
       100: q^2+5q+2
       101: q^2+5q+2
       102: q^2+5q+2
       103: q^2+q
       104: q^2+3q+1
       105: q^2+3q+1
       106: q^2+q
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2
       114: 3q+2
       116: 3q+2
       117: 2q^2+4q+1
       118: 2q^2+4q+1
       119: 2q^2+4q+1
       120: 2q^2+4q+1
       121: 2q^2+2q
       122: 2q^2+6q+2
       123: 2q^2+2q
       124: 2q^2+6q+2
       125: 4q^2+8q+2
       126: q^2+5q+2
       128: 3q+2
       130: 3q+2
       132: 3q+2
       133: q^2+5q+2
       134: q^2+5q+2
       135: 2q+2
       136: 2q+2
       137: 4q^2+8q+2
       138: q^2+5q+2
       139: q^2+5q+2
       140: 2q+2
       141: q^2+5q+2
       142: 2q+2
       143: 4q^2+8q+2
       144: q^2+5q+2
       145: q^2+5q+2
       146: q^2+5q+2
       147: 2q+2
       148: 2q+2
       149: q^2+5q+2
       150: q^2+5q+2
       152: 3q+2
       154: 3q+2
       156: 3q+2
       157: q^2+5q+2
       158: q^2+5q+2
       159: q^2+5q+2
       160: q^2+5q+2
       161: q^2+5q+2
       162: q^2+5q+2
       163: q^2+5q+2
       164: q^2+5q+2
       165: q^2+5q+2
       166: q^2+5q+2
       167: q^2+5q+2
       168: q^2+5q+2
       170: 1
       171: 1
       173: q^2+q
       174: q^2+3q+1
       175: q^2+3q+1
       176: q^2+q
       178: 3q+2
       180: 3q+2
       182: 2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2
       190: 3q+2
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 2
       207: 2q^2+2q
       208: 2q^2+6q+2
       210: 3q+2
       212: 3q+2
       214: 3q+2
       216: 3q+2
       218: 3q+2
       219: q^2+5q+2
       220: q^2+5q+2
       221: q^2+5q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: q^2+5q+2
       227: q^2+5q+2
       228: q^2+5q+2
       229: 2q+2
       230: 2q+2
       231: q^2+5q+2
       232: q^2+5q+2
       233: q^2+5q+2
       234: 2q+2
       235: 2q+2
       236: q^2+5q+2
       238: 3q+2
       240: 3q+2
       242: 3q+2
       243: q^2+5q+2
       244: 2q+2
       245: 2q+2
       246: q^2+5q+2
       247: 4
       248: 4
       249: 2q+1
       250: q^2+5q+2
       251: q^2+5q+2
       252: q^2+5q+2
       253: q^2+5q+2
       254: q^2+5q+2
       255: q^2+5q+2
       256: q^2+5q+2
       257: q^2+5q+2
       258: q^2+5q+2
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       275: q^2+q
       276: q^2+3q+1
       277: q^2+3q+1
       278: q^2+q
       280: 3q+2
       282: 3q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: 3q+2
       290: 2
       292: 2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2
       299: q+1
       300: q+1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       312: 2
       314: 2
       316: 3q+2
       318: 3q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       324: 2
       326: 3q+2
       328: 3q+2
       330: 3q+2
       332: 3q+2
       333: q^2+5q+2
       334: 2q+2
       335: 2q+2
       336: 1
       337: 4
       339: 4
       341: 4
       343: 2q+1
       344: q^2+5q+2
       345: q^2+5q+2
       346: q^2+5q+2
       347: 2q+2
       348: 2q+2
       349: 2q+2
       350: 2q+2
       351: 4
       352: q^2+5q+2
       353: q^2+5q+2
       354: q^2+5q+2
       355: 2q+2
       356: 2q+2
       357: 2q+2
       358: 2q+2
       359: 4
       361: 3q+2
       363: 3q+2
       365: 3q+2
       366: q^2+5q+2
       367: q^2+5q+2
       368: q^2+5q+2
       369: 2q+2
       370: 2q+2
       371: 4
       372: 4
       373: 2q+1
       374: q^2+5q+2
       375: q^2+5q+2
       376: q^2+5q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 3q+2
       412: 3q+2
       414: 3q+2
       416: 2
       418: 2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       424: 2
       426: 1
       428: 4
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       434: 2
       436: 2
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: 2
       443: 2
       444: 2
       446: 4
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       452: 2
       453: q+1
       454: q+1
       456: 2
       457: q+1
       458: q+1
       460: 2
       461: 2
       462: 2
       464: 4
       466: 3q+2
       468: 3q+2
       470: 3q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       476: 2
       478: 2
       479: 2
       480: 2
       481: 2q+2
       482: 2q+2
       483: 1
       484: 4
       486: 4
       488: 4
       490: 2q+1
       491: 1
       492: q^2+5q+2
       493: 2q+2
       494: 2q+2
       495: 1
       496: 4
       497: q^2+5q+2
       498: 2q+2
       499: 2q+2
       500: 1
       501: 4
       503: 3q+2
       505: 3q+2
       507: 3q+2
       508: q^2+5q+2
       509: q^2+5q+2
       510: q^2+5q+2
       511: 2q+2
       512: 2q+2
       513: 2q+2
       514: 2q+2
       515: 4
       516: 4
       517: 2q+1
       518: 4
       519: 4
       520: 2q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 2
       548: 2
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 2
       564: 2
       566: 1
       567: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       578: 2
       581: 2
       584: 3q+2
       586: 2
       588: 2
       589: q+1
       590: q+1
       595: q+1
       596: q+1
       598: 1
       600: 1
       602: 4
       603: q+1
       604: q+1
       606: 2
       607: q+1
       608: q+1
       610: 2
       612: 2
       614: 1
       615: 2
       616: 2
       618: 4
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       624: 2
       626: 2
       628: 2
       630: 1
       631: 2
       632: 2
       634: 4
       636: 3q+2
       638: 3q+2
       640: 3q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: 2
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       652: 2
       654: 2
       655: 2
       656: 2
       657: 4
       659: 4
       661: 4
       663: 2q+1
       664: 1
       665: 1
       667: 4
       669: 4
       671: 2q+1
       672: 4
       673: 1
       674: 4
       675: 2q+2
       676: 2q+2
       677: 1
       678: 4
       679: 1
       680: 4
       681: 2q+2
       682: 2q+2
       683: 1
       684: 4
       685: 1
       686: q^2+5q+2
       687: 2q+2
       688: 2q+2
       689: 1
       690: 4
       691: 4
       692: 2q+1
       694: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 2
       736: 2
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 2
       752: 2
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 2
       773: 2
       776: 4
       778: 2
       780: 1
       782: 1
       784: 1
       790: 4
       793: 2
       794: 2
       796: 4
       798: 2
       800: 2
       801: q+1
       802: q+1
       807: q+1
       808: q+1
       810: 1
       812: 1
       814: 4
       815: 2
       816: 2
       817: 2
       818: 2
       820: 4
       822: 2
       824: 2
       825: q+1
       826: q+1
       831: q+1
       832: q+1
       834: 1
       836: 1
       838: 4
       839: 2
       840: 2
       842: 3q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       850: 2
       852: 2
       854: 2
       856: 1
       857: 2
       858: 2
       860: 4
       862: 4
       864: 2q+1
       865: 4
       866: 1
       867: 1
       868: 1
       869: 4
       870: 1
       871: 1
       872: 1
       873: 4
       874: 1
       875: 1
       876: 1
       877: 2q+2
       878: 2q+2
       879: 1
       880: 1
       881: 4
       882: 4
       883: 2q+1
       885: 1
       890: 1
       891: 1
       892: 1
       897: 1
       898: 1
       913: 1
       915: 1
       917: 2
       919: 2
       921: 1
       923: 1
       933: 2
       935: 2
       937: 1
       939: 1
       941: 2
       943: 2
       945: 1
       947: 1
       957: 2
       959: 2
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: 1
       977: 1
       980: 1
       981: 1
       983: 2
       986: 2
       988: 1
       989: 1
       990: 1
       991: 1
       993: 4
       995: 1
       997: 1
      1003: 1
      1015: 4
      1016: 2
      1017: 2
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 4
      1032: 2
      1033: 2
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1046: 2
      1047: 2
      1049: 2
      1051: 2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1061: 1
      1063: 1
      1067: 4
      1069: 4
      1071: 2q+1
      1072: 4
      1073: 1
      1074: 1
      1075: 4
      1076: 1
      1077: 1
      1078: 1
      1079: 4
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1145: 2
      1147: 2
      1149: 1
      1151: 1
      1165: 2
      1167: 2
      1169: 1
      1171: 1
      1186: 1
      1187: 1
      1189: 2
      1192: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1211: 4
      1213: 1
      1215: 1
      1227: 4
      1228: 2
      1229: 2
      1231: 1
      1237: 1
      1239: 1
      1245: 4
      1246: 2
      1247: 2
      1249: 1
      1253: 1
      1257: 1
      1262: 2
      1263: 2
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1341: 2
      1343: 2
      1373: 2
      1375: 2
      1405: 2
      1408: 2
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1416: 1
      1417: 1
      1439: 1
      1449: 1
      1453: 1
      1457: 1
      1459: 1
      1465: 1
      1471: 1
      1473: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1526: 1
      1531: 1
      1532: 1
      1533: 1
      1644: 1
      1652: 1
      1662: 1
      1668: 1
      1674: 1
      1828: 1

1829:    0: 2q^2+6q+2
         1: 2q^2+6q+2
         2: 2q^2+6q+2
         3: 2q^2+6q+2
         4: q^3+3q^2+4q+2
         5: 2q^2+6q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+3q^2+4q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+6q+2
        14: q^3+3q^2+4q+2
        15: 2q^2+6q+2
        16: 2q^2+6q+2
        17: 2q^2+6q+2
        18: q^3+3q^2+4q+2
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: 2q^2+6q+2
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: 4q+2
        30: q^2+4q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 2q^2+6q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 2q^2+6q+2
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 2q^2+6q+2
        47: 2q^2+6q+2
        48: q^3+3q^2+4q+2
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^2+4q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+4q+2
        58: 4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 6q+2
        69: q^2+4q+2
        70: 4q+2
        71: 4q+2
        72: q^2+2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: q^2+4q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: q^2+4q+2
        88: 6q+2
        89: 6q+2
        90: 2q^2+4q+2
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^2+4q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+4q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+4q+2
       100: q^2+4q+2
       101: q^2+4q+2
       102: q^2+4q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: q+1
       108: q+1
       109: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 4q+2
       118: 2q
       119: 3q+1
       120: 3q+1
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 6q+2
       126: 4q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 4q+2
       134: q^2+4q+2
       135: q^2+2q+2
       136: 2q+2
       137: 6q+2
       138: q^2+4q+2
       139: 4q+2
       140: q^2+2q+2
       141: 4q+2
       142: 2q+2
       143: 6q+2
       144: q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: q^2+2q+2
       148: 2q+2
       149: 4q+2
       150: q^2+4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 3q+2
       158: 3q+2
       159: 3q+2
       160: q^2+4q+2
       161: q^2+4q+2
       162: q^2+4q+2
       163: q^2+4q+2
       164: q^2+4q+2
       165: q^2+4q+2
       166: q^2+4q+2
       167: q^2+4q+2
       168: q^2+4q+2
       169: 1
       171: 1
       173: 2q+1
       174: q
       175: 2q+1
       176: q
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+1
       184: q+1
       185: 2q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 4q+2
       192: 2q
       193: q+1
       194: q+1
       195: 2q+2
       197: 1
       198: 1
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: 2q+2
       205: 1
       206: 1
       207: 3q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: 4q+2
       220: 3q+2
       221: 3q+2
       222: 2q+2
       223: q^2+2q+2
       224: q+2
       225: 2q+2
       226: 4q+2
       227: 4q+2
       228: q^2+4q+2
       229: q^2+2q+2
       230: 2q+2
       231: 4q+2
       232: 4q+2
       233: q^2+4q+2
       234: q^2+2q+2
       235: 2q+2
       236: q^2+4q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: q^2+2q+2
       245: 2q+2
       246: 4q+2
       247: 4
       248: 4
       249: 2q+2
       250: 3q+2
       251: 3q+2
       252: 3q+2
       253: 3q+2
       254: 3q+2
       255: 3q+2
       256: q^2+4q+2
       257: q^2+4q+2
       258: q^2+4q+2
       259: 1
       261: 1
       263: 1
       265: 1
       267: 1
       270: 1
       271: 1
       272: 1
       275: 2q+1
       276: q
       277: 2q+1
       278: q
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 2q+2
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: q+1
       294: q+1
       295: q+2
       297: 1
       298: 1
       299: q+1
       300: q+1
       301: 1
       302: 1
       303: 2q+2
       305: 1
       306: 1
       307: q+1
       308: q+1
       309: 2q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 3q+2
       334: 2q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 4q+2
       345: 3q+2
       346: 3q+2
       347: 2q+2
       348: q^2+2q+2
       349: q+2
       350: 2q+2
       351: 4
       352: 4q+2
       353: 3q+2
       354: 3q+2
       355: 2q+2
       356: q^2+2q+2
       357: q+2
       358: 2q+2
       359: 4
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 4q+2
       367: 4q+2
       368: q^2+4q+2
       369: q^2+2q+2
       370: 2q+2
       371: 4
       372: 4
       373: 2q+2
       374: 3q+2
       375: 3q+2
       376: 3q+2
       377: 1
       379: 1
       381: 1
       383: 1
       385: 1
       387: 1
       389: 1
       392: 1
       393: 1
       395: 1
       397: 1
       398: 1
       401: 1
       402: 1
       405: 1
       408: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: q+2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: q+1
       430: q+1
       431: 2q+2
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: q+1
       439: q+2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: q+1
       448: q+1
       449: 2q+2
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       457: q+2
       459: 1
       460: 1
       461: 4
       463: 2
       464: 2
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: 2q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2q+2
       482: q+2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: 3q+2
       493: 2q+2
       494: q+2
       495: 2
       496: 4
       497: 3q+2
       498: 2q+2
       499: q+2
       500: 2
       501: 4
       508: 4q+2
       509: 3q+2
       510: 3q+2
       511: 2q+2
       512: q^2+2q+2
       513: q+2
       514: 2q+2
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       521: 1
       523: 1
       529: 1
       531: 1
       533: 1
       535: 1
       537: 1
       540: 1
       541: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       557: 1
       558: 1
       561: 2
       562: 2
       565: 1
       567: 1
       569: 1
       572: 1
       573: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       585: 1
       586: 1
       589: q+1
       590: q+1
       591: 2
       595: q+2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: q+2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       616: 2
       617: 2
       618: 2
       619: q+1
       620: q+1
       621: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 4
       633: 2
       634: 2
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: 2q+2
       645: 1
       646: 1
       647: q+1
       648: q+1
       649: q+2
       651: 1
       652: 1
       653: 1
       654: 1
       655: 2
       656: 2
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 4
       675: 2q+2
       676: q+2
       677: 2
       678: 2
       679: 2
       680: 4
       681: 2q+2
       682: q+2
       683: 2
       684: 2
       685: 2
       686: 3q+2
       687: 2q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       698: 1
       700: 1
       709: 1
       711: 1
       713: 1
       714: 1
       721: 1
       724: 1
       725: 1
       728: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       742: 1
       749: 2
       750: 2
       753: 1
       755: 1
       757: 1
       760: 1
       761: 1
       764: 1
       765: 2
       767: 2
       769: 1
       770: 1
       772: 1
       773: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       787: 2
       793: 2
       794: 2
       795: 2
       796: 2
       797: 1
       798: 1
       801: q+1
       802: q+1
       803: 2
       807: q+2
       809: 1
       810: 1
       811: 1
       812: 1
       815: 1
       816: 1
       817: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       827: 2
       831: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       873: 2
       874: 2
       875: 2
       876: 1
       877: 2q+2
       878: q+2
       879: 2
       880: 2
       881: 2
       882: 2
       883: q+1
       884: 1
       885: 1
       888: 1
       891: 1
       900: 1
       901: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       925: 1
       940: 2
       941: 2
       944: 1
       945: 1
       948: 1
       949: 1
       960: 1
       963: 1
       964: 2
       966: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       977: 1
       988: 1
       990: 1
       994: 1
       995: 1
       998: 2
      1006: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1028: 2
      1032: 2
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1044: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1054: 2
      1058: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 2
      1077: 1
      1078: 1
      1079: 2
      1080: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1152: 1
      1153: 1
      1172: 1
      1173: 1
      1194: 1
      1196: 1
      1198: 1
      1201: 1
      1202: 1
      1203: 1
      1216: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 2
      1242: 1
      1246: 2
      1248: 1
      1249: 1
      1250: 2
      1260: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1270: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 2
      1288: 1
      1289: 1
      1348: 1
      1349: 1
      1380: 1
      1381: 1
      1410: 1
      1412: 1
      1418: 1
      1419: 1
      1440: 1
      1450: 1
      1460: 1
      1464: 1
      1465: 1
      1466: 2
      1478: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1607: 1
      1608: 1
      1645: 1
      1653: 1
      1663: 1
      1674: 1
      1829: 1

1830:    0: 2q^2+6q+2
         1: 2q^2+6q+2
         2: 2q^2+6q+2
         3: 2q^2+6q+2
         4: q^3+3q^2+4q+2
         5: 2q^2+6q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+3q^2+4q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+6q+2
        14: q^3+3q^2+4q+2
        15: 2q^2+6q+2
        16: 2q^2+6q+2
        17: 2q^2+6q+2
        18: q^3+3q^2+4q+2
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: 2q^2+6q+2
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: 4q+2
        30: q^2+4q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 2q^2+6q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 2q^2+6q+2
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 2q^2+6q+2
        47: 2q^2+6q+2
        48: q^3+3q^2+4q+2
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^2+4q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+4q+2
        58: 2q
        59: 4q+2
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 6q+2
        69: q^2+4q+2
        70: 4q+2
        71: 4q+2
        72: q^2+2q+2
        73: 2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: q^2+4q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: q^2+4q+2
        88: 6q+2
        89: 6q+2
        90: 2q^2+4q+2
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^2+4q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+4q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+4q+2
       100: q^2+4q+2
       101: q^2+4q+2
       102: q^2+4q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: q+1
       108: q+1
       110: 2q+2
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 2q
       118: 4q+2
       119: 3q+1
       120: 3q+1
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 6q+2
       126: 4q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 4q+2
       134: q^2+4q+2
       135: q^2+2q+2
       136: 2q+2
       137: 6q+2
       138: q^2+4q+2
       139: 4q+2
       140: q^2+2q+2
       141: 4q+2
       142: 2q+2
       143: 6q+2
       144: q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: q^2+2q+2
       148: 2q+2
       149: 4q+2
       150: q^2+4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 3q+2
       158: 3q+2
       159: 3q+2
       160: q^2+4q+2
       161: q^2+4q+2
       162: q^2+4q+2
       163: q^2+4q+2
       164: q^2+4q+2
       165: q^2+4q+2
       166: q^2+4q+2
       167: q^2+4q+2
       168: q^2+4q+2
       170: 1
       172: 1
       173: q
       174: 2q+1
       175: q
       176: 2q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: q+1
       184: q+1
       186: 2q+2
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 2q
       192: 4q+2
       193: q+1
       194: q+1
       196: 2q+2
       197: 1
       198: 1
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       204: 2q+2
       205: 1
       206: 1
       207: 3q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: 4q+2
       220: 3q+2
       221: 3q+2
       222: 2q+2
       223: q^2+2q+2
       224: q+2
       225: 2q+2
       226: 4q+2
       227: 4q+2
       228: q^2+4q+2
       229: q^2+2q+2
       230: 2q+2
       231: 4q+2
       232: 4q+2
       233: q^2+4q+2
       234: q^2+2q+2
       235: 2q+2
       236: q^2+4q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: q^2+2q+2
       245: 2q+2
       246: 4q+2
       247: 4
       248: 4
       249: 2q+2
       250: 3q+2
       251: 3q+2
       252: 3q+2
       253: 3q+2
       254: 3q+2
       255: 3q+2
       256: q^2+4q+2
       257: q^2+4q+2
       258: q^2+4q+2
       260: 1
       262: 1
       264: 1
       266: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: q
       276: 2q+1
       277: q
       278: 2q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       286: 2q+2
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: q+1
       294: q+1
       296: q+2
       297: 1
       298: 1
       299: q+1
       300: q+1
       301: 1
       302: 1
       304: 2q+2
       305: 1
       306: 1
       307: q+1
       308: q+1
       310: 2q+2
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       322: 2q+2
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 3q+2
       334: 2q+2
       335: q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 4q+2
       345: 3q+2
       346: 3q+2
       347: 2q+2
       348: q^2+2q+2
       349: q+2
       350: 2q+2
       351: 4
       352: 4q+2
       353: 3q+2
       354: 3q+2
       355: 2q+2
       356: q^2+2q+2
       357: q+2
       358: 2q+2
       359: 4
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 4q+2
       367: 4q+2
       368: q^2+4q+2
       369: q^2+2q+2
       370: 2q+2
       371: 4
       372: 4
       373: 2q+2
       374: 3q+2
       375: 3q+2
       376: 3q+2
       378: 1
       380: 1
       382: 1
       384: 1
       386: 1
       388: 1
       390: 1
       391: 1
       394: 1
       396: 1
       399: 1
       400: 1
       403: 1
       404: 1
       406: 1
       407: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: q+1
       420: q+1
       422: q+2
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: q+1
       430: q+1
       432: 2q+2
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: q+1
       440: q+2
       441: 1
       442: 1
       443: 2
       444: 2
       445: 2
       446: 2
       447: q+1
       448: q+1
       450: 2q+2
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: q+2
       459: 1
       460: 1
       462: 4
       463: 2
       464: 2
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       474: 2q+2
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: 2q+2
       482: q+2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: 3q+2
       493: 2q+2
       494: q+2
       495: 2
       496: 4
       497: 3q+2
       498: 2q+2
       499: q+2
       500: 2
       501: 4
       508: 4q+2
       509: 3q+2
       510: 3q+2
       511: 2q+2
       512: q^2+2q+2
       513: q+2
       514: 2q+2
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       522: 1
       524: 1
       530: 1
       532: 1
       534: 1
       536: 1
       538: 1
       539: 1
       542: 1
       543: 1
       545: 1
       546: 1
       547: 1
       548: 1
       551: 1
       552: 1
       555: 1
       556: 1
       559: 1
       560: 1
       563: 2
       564: 2
       566: 1
       568: 1
       570: 1
       571: 1
       574: 2
       575: 2
       577: 1
       578: 1
       580: 1
       581: 1
       585: 1
       586: 1
       589: q+1
       590: q+1
       592: 2
       596: q+2
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       603: q+1
       604: q+1
       605: 1
       606: 1
       608: q+2
       609: 1
       610: 1
       613: 1
       614: 1
       615: 2
       616: 2
       617: 2
       618: 2
       619: q+1
       620: q+1
       622: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       632: 4
       633: 2
       634: 2
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       644: 2q+2
       645: 1
       646: 1
       647: q+1
       648: q+1
       650: q+2
       651: 1
       652: 1
       653: 1
       654: 1
       655: 2
       656: 2
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 4
       675: 2q+2
       676: q+2
       677: 2
       678: 2
       679: 2
       680: 4
       681: 2q+2
       682: q+2
       683: 2
       684: 2
       685: 2
       686: 3q+2
       687: 2q+2
       688: q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       696: 1
       697: 1
       699: 1
       701: 1
       710: 1
       712: 1
       715: 1
       716: 1
       722: 1
       723: 1
       726: 1
       727: 1
       733: 1
       734: 1
       735: 1
       736: 1
       739: 1
       740: 1
       743: 1
       744: 1
       751: 2
       752: 2
       754: 1
       756: 1
       758: 1
       759: 1
       762: 1
       763: 1
       766: 2
       768: 2
       769: 1
       770: 1
       772: 1
       773: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       788: 2
       793: 2
       794: 2
       795: 2
       796: 2
       797: 1
       798: 1
       801: q+1
       802: q+1
       804: 2
       808: q+2
       809: 1
       810: 1
       811: 1
       812: 1
       815: 1
       816: 1
       818: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       828: 2
       832: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       840: 2
       843: 2
       844: 2
       845: q+1
       846: q+1
       848: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       873: 2
       874: 2
       875: 2
       876: 1
       877: 2q+2
       878: q+2
       879: 2
       880: 2
       881: 2
       882: 2
       883: q+1
       887: 1
       889: 1
       890: 1
       892: 1
       902: 1
       903: 1
       916: 1
       917: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       927: 1
       942: 2
       943: 2
       946: 1
       947: 1
       950: 1
       951: 1
       961: 1
       962: 1
       965: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       976: 1
       989: 1
       991: 1
       994: 1
       995: 1
       999: 2
      1007: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1029: 2
      1033: 2
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1045: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1055: 2
      1059: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 2
      1077: 1
      1078: 1
      1079: 2
      1080: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1089: 1
      1091: 1
      1092: 1
      1094: 1
      1116: 1
      1117: 1
      1154: 1
      1155: 1
      1174: 1
      1175: 1
      1195: 1
      1197: 1
      1199: 1
      1200: 1
      1204: 1
      1205: 1
      1217: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1233: 2
      1243: 1
      1247: 2
      1248: 1
      1249: 1
      1251: 2
      1261: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1271: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 2
      1288: 1
      1289: 1
      1350: 1
      1351: 1
      1382: 1
      1383: 1
      1411: 1
      1413: 1
      1420: 1
      1421: 1
      1441: 1
      1451: 1
      1461: 1
      1464: 1
      1465: 1
      1467: 2
      1479: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1609: 1
      1610: 1
      1646: 1
      1654: 1
      1664: 1
      1674: 1
      1830: 1

1831:    0: 2q^2+6q+2
         1: 2q^2+6q+2
         2: 2q^2+6q+2
         3: 2q^2+6q+2
         4: q^3+3q^2+4q+2
         5: 2q^2+6q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+3q^2+4q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+6q+2
        14: q^3+3q^2+4q+2
        15: 2q^2+6q+2
        16: 2q^2+6q+2
        17: 2q^2+6q+2
        18: q^3+3q^2+4q+2
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: 2q^2+6q+2
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: 4q+2
        30: q^2+4q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 2q^2+6q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 2q^2+6q+2
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 2q^2+6q+2
        47: 2q^2+6q+2
        48: q^3+3q^2+4q+2
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^2+4q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 4q+2
        61: 2q
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 6q+2
        69: q^2+4q+2
        70: 4q+2
        71: 4q+2
        72: 2q+2
        73: q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: q^2+4q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: q^2+4q+2
        88: 6q+2
        89: 6q+2
        90: 2q^2+4q+2
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^2+4q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+4q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+4q+2
       100: q^2+4q+2
       101: q^2+4q+2
       102: q^2+4q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 3q+1
       118: 3q+1
       119: 4q+2
       120: 2q
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 6q+2
       126: 4q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 4q+2
       134: q^2+4q+2
       135: 2q+2
       136: q^2+2q+2
       137: 6q+2
       138: q^2+4q+2
       139: 4q+2
       140: 2q+2
       141: 4q+2
       142: q^2+2q+2
       143: 6q+2
       144: q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: 2q+2
       148: q^2+2q+2
       149: 4q+2
       150: q^2+4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 3q+2
       158: 3q+2
       159: 3q+2
       160: q^2+4q+2
       161: q^2+4q+2
       162: q^2+4q+2
       163: q^2+4q+2
       164: q^2+4q+2
       165: q^2+4q+2
       166: q^2+4q+2
       167: q^2+4q+2
       168: q^2+4q+2
       169: 1
       170: 1
       173: 2q+1
       174: 2q+1
       175: q
       176: q
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 2q+2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 3q+1
       192: 3q+1
       193: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 4q+2
       200: 2q
       201: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 3q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: 4q+2
       220: 3q+2
       221: 3q+2
       222: q+2
       223: 2q+2
       224: 2q+2
       225: q^2+2q+2
       226: 4q+2
       227: 4q+2
       228: q^2+4q+2
       229: 2q+2
       230: q^2+2q+2
       231: 4q+2
       232: 4q+2
       233: q^2+4q+2
       234: 2q+2
       235: q^2+2q+2
       236: q^2+4q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: q^2+2q+2
       246: 4q+2
       247: 4
       248: 4
       249: 2q+2
       250: 3q+2
       251: 3q+2
       252: 3q+2
       253: 3q+2
       254: 3q+2
       255: 3q+2
       256: q^2+4q+2
       257: q^2+4q+2
       258: q^2+4q+2
       259: 1
       260: 1
       263: 1
       264: 1
       267: 1
       268: 1
       271: 1
       274: 1
       275: 2q+1
       276: 2q+1
       277: q
       278: q
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: q+2
       295: q+1
       296: q+1
       297: 1
       298: 1
       299: 2q+2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       307: 2q+2
       309: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 3q+2
       334: q+2
       335: 2q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 4q+2
       345: 3q+2
       346: 3q+2
       347: q+2
       348: 2q+2
       349: 2q+2
       350: q^2+2q+2
       351: 4
       352: 4q+2
       353: 3q+2
       354: 3q+2
       355: q+2
       356: 2q+2
       357: 2q+2
       358: q^2+2q+2
       359: 4
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 4q+2
       367: 4q+2
       368: q^2+4q+2
       369: 2q+2
       370: q^2+2q+2
       371: 4
       372: 4
       373: 2q+2
       374: 3q+2
       375: 3q+2
       376: 3q+2
       377: 1
       378: 1
       381: 1
       382: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       397: 1
       400: 1
       401: 1
       403: 1
       405: 1
       407: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       419: q+2
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       429: 2q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+2
       439: q+1
       440: q+1
       441: 1
       442: 1
       443: 4
       445: 2
       446: 2
       447: 2q+2
       449: q+1
       450: q+1
       451: 1
       452: 1
       453: q+2
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 2q+2
       473: q+1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: q+2
       482: 2q+2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: 3q+2
       493: q+2
       494: 2q+2
       495: 2
       496: 4
       497: 3q+2
       498: q+2
       499: 2q+2
       500: 2
       501: 4
       508: 4q+2
       509: 3q+2
       510: 3q+2
       511: q+2
       512: 2q+2
       513: 2q+2
       514: q^2+2q+2
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       521: 1
       522: 1
       529: 1
       530: 1
       533: 1
       534: 1
       537: 1
       538: 1
       541: 1
       542: 1
       545: 2
       546: 2
       549: 1
       551: 1
       553: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       571: 1
       573: 2
       574: 2
       577: 1
       578: 1
       580: 1
       581: 1
       585: 1
       586: 1
       589: q+2
       593: 2
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       603: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 4
       617: 2
       618: 2
       619: q+2
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: q+1
       640: q+1
       641: 2q+2
       643: q+1
       644: q+1
       645: 1
       646: 1
       647: q+2
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 2
       656: 2
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 4
       675: q+2
       676: 2q+2
       677: 2
       678: 2
       679: 2
       680: 4
       681: q+2
       682: 2q+2
       683: 2
       684: 2
       685: 2
       686: 3q+2
       687: q+2
       688: 2q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       693: 1
       694: 1
       696: 1
       699: 1
       709: 1
       710: 1
       717: 1
       718: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: 2
       734: 2
       737: 1
       740: 1
       741: 1
       744: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       757: 1
       759: 1
       761: 1
       763: 1
       765: 2
       766: 2
       769: 1
       770: 1
       772: 1
       773: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       785: 2
       793: 4
       795: 2
       796: 2
       797: 1
       798: 1
       801: q+2
       805: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 2
       817: 2
       818: 2
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+2
       829: 2
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       839: 1
       840: 1
       843: 2
       844: 2
       845: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       873: 2
       874: 2
       875: 2
       876: 1
       877: q+2
       878: 2q+2
       879: 2
       880: 2
       881: 2
       882: 2
       883: q+1
       884: 1
       885: 1
       887: 1
       890: 1
       904: 1
       905: 1
       916: 2
       917: 2
       920: 1
       921: 1
       928: 1
       929: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       947: 1
       952: 1
       953: 1
       960: 1
       962: 1
       964: 2
       965: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       976: 1
       988: 1
       989: 1
       994: 1
       995: 1
      1000: 2
      1004: 1
      1016: 2
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1026: 2
      1032: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+2
      1056: 2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 2
      1077: 1
      1078: 1
      1079: 2
      1080: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1092: 1
      1122: 1
      1123: 1
      1156: 1
      1157: 1
      1176: 1
      1177: 1
      1194: 1
      1195: 1
      1198: 1
      1200: 1
      1206: 1
      1207: 1
      1218: 1
      1228: 2
      1230: 1
      1231: 1
      1234: 2
      1240: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1254: 2
      1258: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1268: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 2
      1288: 1
      1289: 1
      1356: 1
      1357: 1
      1388: 1
      1389: 1
      1410: 1
      1411: 1
      1422: 1
      1423: 1
      1442: 1
      1454: 1
      1462: 1
      1464: 1
      1465: 1
      1468: 2
      1476: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1615: 1
      1616: 1
      1647: 1
      1655: 1
      1665: 1
      1674: 1
      1831: 1

1832:    0: 2q^2+6q+2
         1: 2q^2+6q+2
         2: 2q^2+6q+2
         3: 2q^2+6q+2
         4: q^3+3q^2+4q+2
         5: 2q^2+6q+2
         6: q^3+3q^2+4q+2
         7: q^3+3q^2+4q+2
         8: 2q^2+6q+2
         9: q^3+3q^2+4q+2
        10: 6q+2
        11: 6q+2
        12: 2q^2+4q+2
        13: 2q^2+6q+2
        14: q^3+3q^2+4q+2
        15: 2q^2+6q+2
        16: 2q^2+6q+2
        17: 2q^2+6q+2
        18: q^3+3q^2+4q+2
        19: q^2+4q+2
        20: q^2+4q+2
        21: q^2+4q+2
        22: 2q^2+6q+2
        23: 2q^2+6q+2
        24: 2q^2+6q+2
        25: 2q^2+6q+2
        26: 2q^2+6q+2
        27: 2q^2+6q+2
        28: 6q+2
        29: 4q+2
        30: q^2+4q+2
        31: 6q+2
        32: 2q^2+6q+2
        33: 2q^2+6q+2
        34: 6q+2
        35: 2q^2+6q+2
        36: 2q^2+6q+2
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 6q+2
        44: 2q^2+4q+2
        45: 6q+2
        46: 2q^2+6q+2
        47: 2q^2+6q+2
        48: q^3+3q^2+4q+2
        49: q^2+4q+2
        50: q^2+4q+2
        51: q^2+4q+2
        52: q^2+4q+2
        53: q^2+4q+2
        54: q^2+4q+2
        55: q^2+4q+2
        56: q^2+4q+2
        57: q^2+4q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 4q+2
        62: 3q+1
        63: 3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 6q+2
        69: q^2+4q+2
        70: 4q+2
        71: 4q+2
        72: 2q+2
        73: q^2+2q+2
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 6q+2
        81: 2q^2+6q+2
        82: 4q+2
        83: q^2+4q+2
        84: 6q+2
        85: 2q^2+6q+2
        86: 4q+2
        87: q^2+4q+2
        88: 6q+2
        89: 6q+2
        90: 2q^2+4q+2
        91: q^2+4q+2
        92: q^2+4q+2
        93: q^2+4q+2
        94: q^2+4q+2
        95: q^2+4q+2
        96: q^2+4q+2
        97: q^2+4q+2
        98: q^2+4q+2
        99: q^2+4q+2
       100: q^2+4q+2
       101: q^2+4q+2
       102: q^2+4q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       108: 2q+2
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 3q+1
       118: 3q+1
       119: 2q
       120: 4q+2
       121: 3q+1
       122: 3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: 6q+2
       126: 4q+2
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 4q+2
       134: q^2+4q+2
       135: 2q+2
       136: q^2+2q+2
       137: 6q+2
       138: q^2+4q+2
       139: 4q+2
       140: 2q+2
       141: 4q+2
       142: q^2+2q+2
       143: 6q+2
       144: q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: 2q+2
       148: q^2+2q+2
       149: 4q+2
       150: q^2+4q+2
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 3q+2
       158: 3q+2
       159: 3q+2
       160: q^2+4q+2
       161: q^2+4q+2
       162: q^2+4q+2
       163: q^2+4q+2
       164: q^2+4q+2
       165: q^2+4q+2
       166: q^2+4q+2
       167: q^2+4q+2
       168: q^2+4q+2
       171: 1
       172: 1
       173: q
       174: q
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       184: 2q+2
       185: q+1
       186: q+1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: 3q+1
       192: 3q+1
       194: 2q+2
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 2q
       200: 4q+2
       202: 2q+2
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 3q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: 4q+2
       220: 3q+2
       221: 3q+2
       222: q+2
       223: 2q+2
       224: 2q+2
       225: q^2+2q+2
       226: 4q+2
       227: 4q+2
       228: q^2+4q+2
       229: 2q+2
       230: q^2+2q+2
       231: 4q+2
       232: 4q+2
       233: q^2+4q+2
       234: 2q+2
       235: q^2+2q+2
       236: q^2+4q+2
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 4q+2
       244: 2q+2
       245: q^2+2q+2
       246: 4q+2
       247: 4
       248: 4
       249: 2q+2
       250: 3q+2
       251: 3q+2
       252: 3q+2
       253: 3q+2
       254: 3q+2
       255: 3q+2
       256: q^2+4q+2
       257: q^2+4q+2
       258: q^2+4q+2
       261: 1
       262: 1
       265: 1
       266: 1
       269: 1
       270: 1
       272: 1
       273: 1
       275: q
       276: q
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       284: 2q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       294: q+2
       295: q+1
       296: q+1
       297: 1
       298: 1
       300: 2q+2
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 1
       308: 2q+2
       309: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: 2q+2
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: q+1
       333: 3q+2
       334: q+2
       335: 2q+2
       336: 2
       337: 4
       338: 2
       339: 2
       340: 2
       341: 2
       342: q+1
       343: q+1
       344: 4q+2
       345: 3q+2
       346: 3q+2
       347: q+2
       348: 2q+2
       349: 2q+2
       350: q^2+2q+2
       351: 4
       352: 4q+2
       353: 3q+2
       354: 3q+2
       355: q+2
       356: 2q+2
       357: 2q+2
       358: q^2+2q+2
       359: 4
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 4q+2
       367: 4q+2
       368: q^2+4q+2
       369: 2q+2
       370: q^2+2q+2
       371: 4
       372: 4
       373: 2q+2
       374: 3q+2
       375: 3q+2
       376: 3q+2
       379: 1
       380: 1
       383: 1
       384: 1
       387: 1
       388: 1
       391: 1
       392: 1
       395: 1
       396: 1
       398: 1
       399: 1
       402: 1
       404: 1
       406: 1
       408: 1
       413: q+1
       414: q+1
       417: 1
       418: 1
       420: q+2
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2
       428: 2
       430: 2q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       438: q+2
       439: q+1
       440: q+1
       441: 1
       442: 1
       444: 4
       445: 2
       446: 2
       448: 2q+2
       449: q+1
       450: q+1
       451: 1
       452: 1
       454: q+2
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: 1
       460: 1
       461: 2
       462: 2
       463: 2
       464: 2
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       472: 2q+2
       473: q+1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 2
       480: 2
       481: q+2
       482: 2q+2
       483: 2
       484: 4
       485: 2
       486: 2
       487: 2
       488: 2
       489: q+1
       490: q+1
       491: 2
       492: 3q+2
       493: q+2
       494: 2q+2
       495: 2
       496: 4
       497: 3q+2
       498: q+2
       499: 2q+2
       500: 2
       501: 4
       508: 4q+2
       509: 3q+2
       510: 3q+2
       511: q+2
       512: 2q+2
       513: 2q+2
       514: q^2+2q+2
       515: 4
       516: 4
       517: 2q+2
       518: 2
       519: 2
       520: q+1
       523: 1
       524: 1
       531: 1
       532: 1
       535: 1
       536: 1
       539: 1
       540: 1
       543: 1
       544: 1
       547: 2
       548: 2
       550: 1
       552: 1
       554: 1
       555: 1
       558: 1
       559: 1
       561: 1
       562: 1
       563: 1
       564: 1
       567: 1
       568: 1
       570: 1
       572: 1
       575: 2
       576: 2
       577: 1
       578: 1
       580: 1
       581: 1
       585: 1
       586: 1
       590: q+2
       594: 2
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 2
       602: 2
       604: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 4
       617: 2
       618: 2
       620: q+2
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 2
       632: 2
       633: 2
       634: 2
       639: q+1
       640: q+1
       642: 2q+2
       643: q+1
       644: q+1
       645: 1
       646: 1
       648: q+2
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 2
       656: 2
       657: 4
       658: 2
       659: 2
       660: 2
       661: 2
       662: q+1
       663: q+1
       664: 2
       665: 2
       672: 2
       673: 1
       674: 4
       675: q+2
       676: 2q+2
       677: 2
       678: 2
       679: 2
       680: 4
       681: q+2
       682: 2q+2
       683: 2
       684: 2
       685: 2
       686: 3q+2
       687: q+2
       688: 2q+2
       689: 2
       690: 2
       691: 2
       692: q+1
       697: 1
       698: 1
       700: 1
       701: 1
       711: 1
       712: 1
       719: 1
       720: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: 2
       736: 2
       738: 1
       739: 1
       742: 1
       743: 1
       749: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       758: 1
       760: 1
       762: 1
       764: 1
       767: 2
       768: 2
       769: 1
       770: 1
       772: 1
       773: 1
       775: 2
       776: 2
       779: 1
       780: 1
       781: 1
       782: 1
       786: 2
       794: 4
       795: 2
       796: 2
       797: 1
       798: 1
       802: q+2
       806: 2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       816: 2
       817: 2
       818: 2
       819: 2
       820: 2
       821: 1
       822: 1
       826: q+2
       830: 2
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       839: 1
       840: 1
       843: 2
       844: 2
       846: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       865: 2
       866: 2
       867: 1
       868: 1
       869: 2
       870: 2
       871: 2
       872: 1
       873: 2
       874: 2
       875: 2
       876: 1
       877: q+2
       878: 2q+2
       879: 2
       880: 2
       881: 2
       882: 2
       883: q+1
       888: 1
       889: 1
       891: 1
       892: 1
       906: 1
       907: 1
       918: 2
       919: 2
       922: 1
       923: 1
       930: 1
       931: 1
       940: 1
       941: 1
       942: 1
       943: 1
       945: 1
       946: 1
       954: 1
       955: 1
       961: 1
       963: 1
       966: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       977: 1
       990: 1
       991: 1
       994: 1
       995: 1
      1001: 2
      1005: 1
      1017: 2
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1027: 2
      1032: 1
      1033: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1041: 2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: q+2
      1057: 2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 2
      1077: 1
      1078: 1
      1079: 2
      1080: 2
      1081: 1
      1082: 1
      1083: 2
      1084: 2
      1085: 1
      1090: 1
      1091: 1
      1093: 1
      1094: 1
      1124: 1
      1125: 1
      1158: 1
      1159: 1
      1178: 1
      1179: 1
      1196: 1
      1197: 1
      1199: 1
      1201: 1
      1208: 1
      1209: 1
      1219: 1
      1229: 2
      1230: 1
      1231: 1
      1235: 2
      1241: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1255: 2
      1259: 1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1269: 2
      1274: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 2
      1288: 1
      1289: 1
      1358: 1
      1359: 1
      1390: 1
      1391: 1
      1412: 1
      1413: 1
      1424: 1
      1425: 1
      1443: 1
      1455: 1
      1463: 1
      1464: 1
      1465: 1
      1469: 2
      1477: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1617: 1
      1618: 1
      1648: 1
      1656: 1
      1666: 1
      1674: 1
      1832: 1

1833:    0: q^5+7q^3+26q^2+20q+4
         1: 10q^3+26q^2+20q+4
         2: q^5+7q^3+26q^2+20q+4
         3: 10q^3+26q^2+20q+4
         4: q^5+7q^3+26q^2+20q+4
         5: 10q^3+26q^2+20q+4
         6: 10q^3+26q^2+20q+4
         7: q^5+7q^3+26q^2+20q+4
         8: 10q^3+26q^2+20q+4
         9: q^6+q^5+4q^4+13q^3+19q^2+14q+4
        10: 3q^3+20q^2+20q+4
        11: 4q^3+20q^2+20q+4
        12: 3q^3+20q^2+20q+4
        13: q^5+7q^3+26q^2+20q+4
        14: q^5+7q^3+26q^2+20q+4
        15: 10q^3+26q^2+20q+4
        16: 3q^3+20q^2+20q+4
        17: 4q^3+20q^2+20q+4
        18: q^5+7q^3+19q^2+14q+4
        19: q^5+7q^3+26q^2+20q+4
        20: 10q^3+26q^2+20q+4
        21: q^5+7q^3+26q^2+20q+4
        22: 3q^3+20q^2+20q+4
        23: 4q^3+20q^2+20q+4
        24: 3q^3+20q^2+20q+4
        25: 3q^3+20q^2+20q+4
        26: 4q^3+20q^2+20q+4
        27: 3q^3+20q^2+20q+4
        28: q^3+14q^2+20q+4
        29: 3q^3+20q^2+20q+4
        30: q^5+7q^3+26q^2+20q+4
        31: q^3+14q^2+20q+4
        32: 3q^3+20q^2+20q+4
        33: q^3+14q^2+20q+4
        34: q^3+14q^2+20q+4
        35: 3q^3+20q^2+20q+4
        36: q^3+14q^2+20q+4
        37: 8q^2+10q+2
        38: 8q^2+10q+2
        39: 8q^2+10q+2
        40: 8q^2+10q+2
        41: 8q^2+10q+2
        42: 8q^2+10q+2
        43: 3q^3+20q^2+20q+4
        44: 3q^3+20q^2+20q+4
        45: 4q^3+20q^2+20q+4
        46: 3q^3+20q^2+20q+4
        47: 4q^3+20q^2+20q+4
        48: q^5+7q^3+19q^2+14q+4
        49: 3q^3+20q^2+20q+4
        50: 4q^3+20q^2+20q+4
        51: q^5+7q^3+19q^2+14q+4
        52: 3q^3+20q^2+20q+4
        53: 4q^3+20q^2+20q+4
        54: 3q^3+20q^2+20q+4
        55: 3q^3+20q^2+20q+4
        56: 4q^3+20q^2+20q+4
        57: 3q^3+20q^2+20q+4
        58: 4q^2+10q+2
        59: 4q^2+10q+2
        60: 4q^2+10q+2
        61: 4q^2+10q+2
        62: 5q^2+10q+2
        63: 5q^2+10q+2
        64: 8q^2+10q+2
        65: 8q^2+10q+2
        66: 5q^2+10q+2
        67: 5q^2+10q+2
        68: q^3+14q^2+20q+4
        69: 3q^3+13q^2+14q+4
        70: 3q^3+20q^2+20q+4
        71: q^3+14q^2+20q+4
        72: q^3+14q^2+20q+4
        73: q^3+14q^2+20q+4
        74: 8q^2+10q+2
        75: 8q^2+10q+2
        76: 8q^2+10q+2
        77: 8q^2+10q+2
        78: 8q^2+10q+2
        79: 8q^2+10q+2
        80: q^3+14q^2+20q+4
        81: q^3+14q^2+20q+4
        82: q^3+14q^2+20q+4
        83: 3q^3+20q^2+20q+4
        84: q^3+14q^2+20q+4
        85: q^3+14q^2+20q+4
        86: q^3+14q^2+20q+4
        87: 3q^3+20q^2+20q+4
        88: q^3+10q^2+20q+4
        89: q^3+10q^2+20q+4
        90: 3q^3+13q^2+14q+4
        91: 3q^3+20q^2+20q+4
        92: 4q^3+20q^2+20q+4
        93: q^5+7q^3+19q^2+14q+4
        94: q^3+10q^2+20q+4
        95: q^3+10q^2+20q+4
        96: 3q^3+13q^2+14q+4
        97: q^3+10q^2+20q+4
        98: q^3+10q^2+20q+4
        99: 3q^3+13q^2+14q+4
       100: 12q^2+18q+4
       101: 14q^2+18q+4
       102: 12q^2+18q+4
       103: q^2+5q+1
       104: q^2+5q+1
       105: q^2+5q+1
       106: q^2+5q+1
       107: 4q^2+10q+2
       108: 4q^2+10q+2
       109: 4q^2+10q+2
       110: 4q^2+10q+2
       111: 5q^2+10q+2
       112: 5q^2+10q+2
       113: 5q^2+10q+2
       114: 5q^2+10q+2
       115: 8q^2+10q+2
       116: 8q^2+10q+2
       117: 4q^2+10q+2
       118: 4q^2+10q+2
       119: 4q^2+10q+2
       120: 4q^2+10q+2
       121: 5q^2+10q+2
       122: 5q^2+10q+2
       123: 5q^2+10q+2
       124: 5q^2+10q+2
       125: q^3+10q^2+20q+4
       126: q^3+7q^2+14q+4
       127: 8q+2
       128: 8q+2
       129: 8q+2
       130: 8q+2
       131: 3q^2+5q+2
       132: 3q^2+5q+2
       133: q^3+14q^2+20q+4
       134: 3q^3+13q^2+14q+4
       135: q^3+14q^2+20q+4
       136: q^3+14q^2+20q+4
       137: 6q^2+20q+4
       138: q^3+7q^2+14q+4
       139: 6q^2+20q+4
       140: 2q^2+12q+4
       141: q^3+14q^2+20q+4
       142: q^3+10q^2+20q+4
       143: 6q^2+20q+4
       144: q^3+7q^2+14q+4
       145: 6q^2+20q+4
       146: q^3+14q^2+20q+4
       147: q^3+10q^2+20q+4
       148: 2q^2+12q+4
       149: 8q^2+18q+4
       150: 12q^2+18q+4
       151: 6q^2+9q+2
       152: 6q^2+9q+2
       153: 7q^2+9q+2
       154: 7q^2+9q+2
       155: 6q^2+9q+2
       156: 6q^2+9q+2
       157: q^3+10q^2+20q+4
       158: q^3+10q^2+20q+4
       159: 3q^3+13q^2+14q+4
       160: q^3+10q^2+20q+4
       161: q^3+10q^2+20q+4
       162: 3q^3+13q^2+14q+4
       163: q^3+10q^2+20q+4
       164: q^3+10q^2+20q+4
       165: 3q^3+13q^2+14q+4
       166: 3q^2+18q+4
       167: 4q^2+18q+4
       168: 7q^2+12q+4
       169: q^2+5q+1
       170: q^2+5q+1
       171: q^2+5q+1
       172: q^2+5q+1
       173: q^2+5q+1
       174: q^2+5q+1
       175: q^2+5q+1
       176: q^2+5q+1
       177: 5q+2
       178: 5q+2
       179: 8q+2
       180: 8q+2
       181: 8q+2
       182: 8q+2
       183: 4q^2+10q+2
       184: 4q^2+10q+2
       185: 4q^2+10q+2
       186: 4q^2+10q+2
       187: 5q^2+10q+2
       188: 5q^2+10q+2
       189: 5q^2+10q+2
       190: 5q^2+10q+2
       191: 3q^2+10q+2
       192: 3q^2+10q+2
       193: 6q+2
       194: 6q+2
       195: 3q^2+10q+2
       196: 3q^2+10q+2
       197: q^2+6q+2
       198: q^2+6q+2
       199: 3q^2+10q+2
       200: 3q^2+10q+2
       201: 3q^2+10q+2
       202: 3q^2+10q+2
       203: 6q+2
       204: 6q+2
       205: q^2+6q+2
       206: q^2+6q+2
       207: 2q^2+10q+2
       208: 2q^2+10q+2
       209: 4q^2+9q+2
       210: 4q^2+9q+2
       211: 6q^2+9q+2
       212: 6q^2+9q+2
       213: 8q+2
       214: 8q+2
       215: 8q+2
       216: 8q+2
       217: 3q^2+5q+2
       218: 3q^2+5q+2
       219: q^3+7q^2+14q+4
       220: q^3+10q^2+20q+4
       221: q^3+7q^2+14q+4
       222: 6q^2+20q+4
       223: q^3+7q^2+14q+4
       224: 6q^2+20q+4
       225: q^3+7q^2+14q+4
       226: 3q^2+14q+4
       227: 6q^2+20q+4
       228: q^3+7q^2+14q+4
       229: 2q^2+12q+4
       230: q^3+10q^2+20q+4
       231: 3q^2+14q+4
       232: 6q^2+20q+4
       233: q^3+7q^2+14q+4
       234: q^3+10q^2+20q+4
       235: 2q^2+12q+4
       236: 3q^2+12q+4
       237: 7q+2
       238: 7q+2
       239: 7q+2
       240: 7q+2
       241: 2q^2+4q+2
       242: 2q^2+4q+2
       243: q^2+18q+4
       244: q^2+12q+4
       245: q^2+12q+4
       246: 8q^2+18q+4
       247: 3q^2+18q+4
       248: 4q^2+18q+4
       249: 7q^2+12q+4
       250: 4q^2+14q+4
       251: 4q^2+14q+4
       252: q^3+7q^2+10q+4
       253: 4q^2+14q+4
       254: 4q^2+14q+4
       255: q^3+7q^2+10q+4
       256: 3q^2+18q+4
       257: 4q^2+18q+4
       258: 7q^2+12q+4
       259: 4q+1
       260: 4q+1
       261: 4q+1
       262: 4q+1
       263: q^2+5q+1
       264: q^2+5q+1
       265: q^2+5q+1
       266: q^2+5q+1
       267: 3q+1
       268: 3q+1
       269: 3q+1
       270: 3q+1
       271: 3q+1
       272: 3q+1
       273: 3q+1
       274: 3q+1
       275: q^2+5q+1
       276: q^2+5q+1
       277: q^2+5q+1
       278: q^2+5q+1
       279: 8q+2
       280: 8q+2
       281: 5q+2
       282: 5q+2
       283: q^2+4q+2
       284: q^2+4q+2
       285: q^2+4q+2
       286: q^2+4q+2
       287: 5q+2
       288: 5q+2
       289: 8q+2
       290: 8q+2
       291: 5q+2
       292: 5q+2
       293: 3q^2+10q+2
       294: 3q^2+10q+2
       295: 3q^2+10q+2
       296: 3q^2+10q+2
       297: 2q^2+10q+2
       298: 2q^2+10q+2
       299: 6q+2
       300: 6q+2
       301: 4q+2
       302: 4q+2
       303: 3q^2+10q+2
       304: 3q^2+10q+2
       305: q^2+6q+2
       306: q^2+6q+2
       307: 3q^2+10q+2
       308: 3q^2+10q+2
       309: 6q+2
       310: 6q+2
       311: 4q+2
       312: 4q+2
       313: q^2+6q+2
       314: q^2+6q+2
       315: 4q+2
       316: 4q+2
       317: 7q+2
       318: 7q+2
       319: 6q+2
       320: 6q+2
       321: 6q+2
       322: 6q+2
       323: 4q+2
       324: 4q+2
       325: 4q^2+9q+2
       326: 4q^2+9q+2
       333: q^3+7q^2+14q+4
       334: 3q^2+14q+4
       335: 3q^2+14q+4
       336: 3q^2+12q+4
       337: q^2+18q+4
       338: 7q+2
       339: 7q+2
       340: 7q+2
       341: 7q+2
       342: 2q^2+4q+2
       343: 2q^2+4q+2
       344: 3q^2+14q+4
       345: 4q^2+14q+4
       346: 3q^2+10q+4
       347: 8q+4
       348: q^2+6q+4
       349: 4q^2+14q+4
       350: q^3+7q^2+14q+4
       351: q^2+12q+4
       352: 3q^2+14q+4
       353: 4q^2+14q+4
       354: 3q^2+10q+4
       355: 4q^2+14q+4
       356: q^3+7q^2+14q+4
       357: 8q+4
       358: q^2+6q+4
       359: q^2+12q+4
       360: 7q+2
       361: 7q+2
       362: 7q+2
       363: 7q+2
       364: 2q^2+4q+2
       365: 2q^2+4q+2
       366: q^2+12q+4
       367: q^2+18q+4
       368: 3q^2+12q+4
       369: q^2+12q+4
       370: q^2+12q+4
       371: 3q^2+18q+4
       372: 4q^2+18q+4
       373: 7q^2+12q+4
       374: q^2+10q+4
       375: q^2+10q+4
       376: 3q^2+7q+4
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: 4q+1
       382: 4q+1
       383: 4q+1
       384: 4q+1
       385: q^2+5q+1
       386: q^2+5q+1
       387: q^2+5q+1
       388: q^2+5q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: 2q+1
       393: 3q+1
       394: 3q+1
       395: 3q+1
       396: 3q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 3q+1
       402: 3q+1
       403: 3q+1
       404: 3q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       413: 5q+2
       414: 5q+2
       417: 5q+2
       418: 5q+2
       419: q^2+4q+2
       420: q^2+4q+2
       421: q^2+4q+2
       422: q^2+4q+2
       423: 5q+2
       424: 5q+2
       425: 4q+2
       426: 4q+2
       427: 7q+2
       428: 7q+2
       429: 2q+2
       430: 2q+2
       431: q^2+4q+2
       432: q^2+4q+2
       433: q+2
       434: q+2
       435: 4q+2
       436: 4q+2
       437: 4q+2
       438: 4q+2
       439: 2q^2+7q+2
       440: 2q^2+7q+2
       441: 4q+2
       442: 4q+2
       443: 6q+2
       444: 6q+2
       445: 4q+2
       446: 4q+2
       447: q^2+4q+2
       448: q^2+4q+2
       449: 2q+2
       450: 2q+2
       451: q+2
       452: q+2
       453: 2q^2+7q+2
       454: 2q^2+7q+2
       455: 4q+2
       456: 4q+2
       457: 4q+2
       458: 4q+2
       459: 4q+2
       460: 4q+2
       461: 6q+2
       462: 6q+2
       463: 4q+2
       464: 4q+2
       465: 7q+2
       466: 7q+2
       467: 4q+2
       468: 4q+2
       469: 4q+2
       470: 4q+2
       471: 6q+2
       472: 6q+2
       473: 6q+2
       474: 6q+2
       475: 4q+2
       476: 4q+2
       477: 2q+2
       478: 2q+2
       479: 4q+2
       480: 4q+2
       481: 3q^2+14q+4
       482: 3q^2+14q+4
       483: q^2+12q+4
       484: q^2+18q+4
       485: 7q+2
       486: 7q+2
       487: 7q+2
       488: 7q+2
       489: 2q^2+4q+2
       490: 2q^2+4q+2
       491: 3q^2+12q+4
       492: 3q^2+10q+4
       493: 4q+4
       494: 3q^2+10q+4
       495: q^2+6q+4
       496: q^2+12q+4
       497: 3q^2+10q+4
       498: 3q^2+10q+4
       499: 4q+4
       500: q^2+6q+4
       501: q^2+12q+4
       508: q^2+12q+4
       509: q^2+10q+4
       510: q^2+7q+4
       511: 6q+4
       512: q^2+6q+4
       513: 6q+4
       514: q^2+6q+4
       515: 6q+8
       516: 8q+8
       517: 6q+8
       518: q^2+10q+4
       519: q^2+10q+4
       520: 3q^2+7q+4
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: 2q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 2q+2
       581: 2q+2
       585: 5q+2
       586: 5q+2
       589: q^2+4q+2
       590: q^2+4q+2
       591: 2q+2
       592: 2q+2
       593: 2q+2
       594: 2q+2
       595: q^2+4q+2
       596: q^2+4q+2
       597: 4q+2
       598: 4q+2
       599: 4q+2
       600: 4q+2
       601: 7q+2
       602: 7q+2
       603: q+2
       604: q+2
       605: q+2
       606: q+2
       607: q^2+3q+2
       608: q^2+3q+2
       609: q+2
       610: q+2
       613: q+2
       614: q+2
       615: 6q+2
       616: 6q+2
       617: 4q+2
       618: 4q+2
       619: q^2+3q+2
       620: q^2+3q+2
       621: q+2
       622: q+2
       623: q+2
       624: q+2
       625: q+2
       626: q+2
       629: q+2
       630: q+2
       631: 6q+2
       632: 6q+2
       633: 4q+2
       634: 4q+2
       639: 4q+2
       640: 4q+2
       641: 2q+2
       642: 2q+2
       643: 2q+2
       644: 2q+2
       645: 2
       646: 2
       647: 3q+2
       648: 3q+2
       649: 3q+2
       650: 3q+2
       651: 2q+2
       652: 2q+2
       653: 2q+2
       654: 2q+2
       655: 4q+2
       656: 4q+2
       657: 2q+8
       658: 3q+4
       659: 3q+4
       660: 4q+4
       661: 4q+4
       662: 3q+4
       663: 3q+4
       664: 6q+8
       665: q^2+12q+4
       672: q^2+10q+4
       673: q^2+7q+4
       674: 2q+8
       675: 4q+4
       676: 3q^2+10q+4
       677: 4q+4
       678: 6q+4
       679: q^2+6q+4
       680: 2q+8
       681: 3q^2+10q+4
       682: 4q+4
       683: 4q+4
       684: 6q+4
       685: q^2+6q+4
       686: q^2+7q+4
       687: 3q+4
       688: 3q+4
       689: 2q+2
       690: 3q+4
       691: 4q+4
       692: 3q+4
       693: q+1
       697: q+1
       699: q+1
       700: q+1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       733: 2q+1
       734: 2q+1
       735: 2q+1
       736: 2q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 1
       754: 1
       755: 1
       756: 1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: 2q+2
       773: 2q+2
       775: q+4
       776: q+4
       779: 3q+4
       780: 3q+4
       781: 4q+2
       782: 4q+2
       785: 2q+2
       786: 2q+2
       787: 2q+2
       788: 2q+2
       791: 2
       792: 2
       793: 4
       794: 4
       795: q+4
       796: q+4
       797: q+2
       798: q+2
       801: q+2
       802: q+2
       805: q+2
       806: q+2
       807: q^2+3q+2
       808: q^2+3q+2
       809: q+2
       810: q+2
       811: q+2
       812: q+2
       815: 3q+2
       816: 3q+2
       817: 4
       818: 4
       819: q+4
       820: q+4
       821: q+2
       822: q+2
       825: q^2+3q+2
       826: q^2+3q+2
       827: q+2
       828: q+2
       831: q+2
       832: q+2
       833: q+2
       834: q+2
       835: q+2
       836: q+2
       839: 3q+2
       840: 3q+2
       843: 4
       844: 4
       845: q+2
       846: q+2
       847: q+2
       848: q+2
       849: 2
       850: 2
       851: 2
       852: 2
       855: 1
       856: 1
       857: 2q+2
       858: 2q+2
       865: q+4
       866: 2q+8
       867: 3q+4
       868: q^2+7q+4
       869: q+4
       870: 2q+8
       871: 4q+4
       872: 3q+4
       873: q+4
       874: 2q+8
       875: 4q+4
       876: 3q+4
       877: 3q+4
       878: 3q+4
       879: q+2
       880: 2q+2
       881: 3q+4
       882: 4q+4
       883: 3q+4
       884: q+1
       889: q+1
       890: q+1
       891: q+1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       916: 2
       917: 2
       918: 2
       919: 2
       920: 1
       921: 1
       922: 1
       923: 1
       928: 1
       929: 1
       930: 1
       931: 1
       940: 2
       941: 2
       942: 2
       943: 2
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 2
       965: 2
       966: 2
       967: 2
       968: 2
       969: 2
       971: 2
       972: 2
       974: 1
       975: 1
       976: 1
       977: 1
       988: q+1
       989: q+1
       990: q+1
       991: q+1
       994: q+4
       995: q+4
       998: 4
       999: 4
      1000: 4
      1001: 4
      1004: q+2
      1005: q+2
      1006: q+2
      1007: q+2
      1008: 2
      1009: 2
      1010: 2
      1011: 2
      1012: 4
      1013: 4
      1016: 2
      1017: 2
      1020: q+4
      1021: q+4
      1022: q+2
      1023: q+2
      1026: q+2
      1027: q+2
      1032: 2
      1033: 2
      1036: q+4
      1037: q+4
      1038: q+2
      1039: q+2
      1044: q+2
      1045: q+2
      1046: 2
      1047: 2
      1048: 2
      1049: 2
      1052: q+2
      1053: q+2
      1058: q+2
      1059: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1072: q+4
      1073: 3q+4
      1074: q+4
      1075: q+4
      1076: 4
      1077: q+4
      1078: 3q+4
      1079: q+4
      1080: 4
      1081: q+4
      1082: 3q+4
      1083: q+2
      1084: 4
      1085: q+2
      1086: 1
      1087: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1114: 2
      1115: 2
      1116: 2
      1117: 2
      1122: 2
      1123: 2
      1124: 2
      1125: 2
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 2
      1131: 2
      1132: 2
      1133: 2
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 2
      1139: 2
      1141: 2
      1142: 2
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1220: 2
      1221: 2
      1224: 2
      1225: 2
      1228: 2
      1229: 2
      1230: 2
      1231: 2
      1234: 2
      1235: 2
      1240: q+2
      1241: q+2
      1246: 2
      1247: 2
      1248: 2
      1249: 2
      1250: 2
      1251: 2
      1260: q+2
      1261: q+2
      1262: 2
      1263: 2
      1266: 1
      1267: 1
      1274: 2
      1275: 2
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 2
      1281: 2
      1282: q+4
      1283: 2
      1284: q+4
      1285: 2
      1286: q+4
      1287: 2
      1288: 2
      1289: q+2
      1290: 1
      1291: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1430: 1
      1431: 1
      1433: 1
      1434: 1
      1440: 2
      1441: 2
      1442: 2
      1443: 2
      1444: 2
      1445: 2
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1464: 1
      1465: 1
      1474: 1
      1475: 1
      1482: 1
      1483: 1
      1484: 2
      1485: 2
      1486: 2
      1487: 1
      1488: 2
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1641: 1
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1669: 1
      1670: 1
      1673: 1
      1674: 1
      1833: 1

1834:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^3+2q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       103: q^2+q+1
       106: q
       107: q^2+q+1
       108: q
       109: q^2+q+1
       110: q
       111: q^2+2q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q^2+q+1
       118: q
       119: q^2+q+1
       120: q
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+2q^2+2q+1
       126: q^3+2q^2+2q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: q^3+2q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^3+2q^2+2q+1
       158: q^3+2q^2+2q+1
       159: q^3+2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: q^2+q+1
       172: q
       173: q^2+q+1
       176: q
       177: q^2+2q+1
       179: q^2+2q+1
       181: q^2+2q+1
       183: q^2+q+1
       184: q
       185: q^2+q+1
       186: q
       187: q^2+2q+1
       189: q^2+2q+1
       191: q^2+q+1
       192: q
       193: 1
       195: q^2+q+1
       196: q
       197: 1
       199: q^2+q+1
       200: q
       201: q^2+q+1
       202: q
       203: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q^2+2q+1
       215: q^2+2q+1
       217: q^2+2q+1
       219: q^3+2q^2+2q+1
       220: q^3+2q^2+2q+1
       221: q^3+2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       262: q
       263: q^2+q+1
       266: q
       267: 1
       271: 1
       275: q^2+q+1
       278: q
       279: q^2+2q+1
       281: q^2+2q+1
       283: q^2+q+1
       284: q
       285: q^2+q+1
       286: q
       287: q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: q^2+q+1
       294: q
       295: q^2+q+1
       296: q
       297: q^2+2q+1
       299: 1
       301: 1
       303: q^2+q+1
       304: q
       305: 1
       307: q^2+q+1
       308: q
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: 1
       321: 1
       323: 1
       325: q+1
       327: q^2+2q+1
       329: q^2+2q+1
       331: q^2+2q+1
       333: q^3+2q^2+2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+q+1
       380: q
       381: q^2+q+1
       384: q
       385: q^2+q+1
       388: q
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: q^2+2q+1
       411: q^2+2q+1
       413: q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: q^2+q+1
       420: q
       421: q^2+q+1
       422: q
       423: q^2+2q+1
       425: q+1
       427: q+1
       429: 1
       431: q^2+q+1
       432: q
       433: 1
       435: 1
       437: 1
       439: q^2+q+1
       440: q
       441: 1
       443: 1
       445: 1
       447: q^2+q+1
       448: q
       449: 1
       451: 1
       453: q^2+q+1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q^2+q+1
       524: q
       525: q^2+q+1
       528: q
       529: q^2+q+1
       532: q
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: q^2+q+1
       590: q
       591: 1
       593: 1
       595: q^2+q+1
       596: q
       597: q+1
       599: q+1
       601: q+1
       603: 1
       605: 1
       607: q^2+q+1
       608: q
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q^2+q+1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       705: q^2+q+1
       708: q
       709: q^2+q+1
       712: q
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q^2+q+1
       808: q
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: q^2+q+1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       896: q^2+q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: 1
       936: 1
       940: 1
       944: 1
       948: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1058: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1228: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1244: 1
      1246: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1264: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1352: 1
      1356: 1
      1372: 1
      1376: 1
      1380: 1
      1404: 1
      1410: 1
      1414: 1
      1436: 1
      1438: q+1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1454: 1
      1456: 1
      1458: 1
      1460: 1
      1485: 1
      1486: 1
      1489: 1
      1525: 1
      1537: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1567: 1
      1583: 1
      1637: 1
      1639: 1
      1643: 1
      1647: 1
      1651: 1
      1653: 1
      1675: 1
      1723: 1
      1729: 1
      1733: 1
      1745: 1
      1761: 1
      1834: 1

1835:    0: 2q^4+7q^3+8q^2+3q
         1: 2q^4+7q^3+8q^2+3q
         2: 3q^4+5q^3+7q^2+3q
         3: 2q^4+7q^3+8q^2+3q
         4: 2q^4+7q^3+8q^2+3q
         5: 2q^4+7q^3+8q^2+3q
         6: 2q^4+7q^3+8q^2+3q
         7: 3q^4+5q^3+7q^2+3q
         8: q^5+5q^4+6q^3+7q^2+3q
         9: 3q^4+5q^3+7q^2+3q
        10: 2q^4+7q^3+8q^2+3q
        11: 2q^4+7q^3+8q^2+3q
        12: 2q^4+7q^3+8q^2+3q
        13: q^4+4q^3+7q^2+3q
        14: q^4+4q^3+7q^2+3q
        15: 2q^4+5q^3+7q^2+3q
        16: 2q^4+7q^3+8q^2+3q
        17: 2q^4+7q^3+8q^2+3q
        18: 3q^4+5q^3+7q^2+3q
        19: 2q^4+7q^3+8q^2+3q
        20: 2q^4+7q^3+8q^2+3q
        21: 3q^4+5q^3+7q^2+3q
        22: 3q^3+7q^2+3q
        23: 3q^3+7q^2+3q
        24: q^4+3q^3+6q^2+3q
        25: 3q^3+7q^2+3q
        26: 3q^3+7q^2+3q
        27: q^4+3q^3+6q^2+3q
        28: 2q^4+7q^3+8q^2+3q
        29: 2q^4+7q^3+8q^2+3q
        30: q^4+4q^3+7q^2+3q
        31: 3q^3+7q^2+3q
        32: 2q^3+6q^2+3q
        33: 3q^3+7q^2+3q
        34: 3q^3+7q^2+3q
        35: 2q^3+6q^2+3q
        36: 3q^3+7q^2+3q
        37: q^3+2q^2+q
        38: 4q^2+2q
        39: q^3+2q^2+q
        40: 4q^2+2q
        41: q^3+2q^2+q
        42: q^3+3q^2+2q
        43: q^4+4q^3+7q^2+3q
        44: q^4+4q^3+7q^2+3q
        45: 2q^4+5q^3+7q^2+3q
        46: q^4+4q^3+7q^2+3q
        47: 2q^4+5q^3+7q^2+3q
        48: q^4+4q^3+7q^2+3q
        49: 2q^4+7q^3+8q^2+3q
        50: 2q^4+7q^3+8q^2+3q
        51: 3q^4+5q^3+7q^2+3q
        52: 3q^3+7q^2+3q
        53: 3q^3+7q^2+3q
        54: q^4+3q^3+6q^2+3q
        55: 3q^3+7q^2+3q
        56: 3q^3+7q^2+3q
        57: q^4+3q^3+6q^2+3q
        58: 2q^3+4q^2+2q
        59: q^3+3q^2+q
        60: 2q^3+4q^2+2q
        61: q^3+3q^2+q
        62: q^3+2q^2+q
        63: 4q^2+2q
        64: q^3+2q^2+q
        65: 3q^2+2q
        66: q^3+2q^2+q
        67: 4q^2+2q
        68: q^4+2q^3+6q^2+3q
        69: q^4+4q^3+7q^2+3q
        70: q^4+4q^3+7q^2+3q
        71: 2q^4+7q^3+8q^2+3q
        72: 3q^3+7q^2+3q
        73: 3q^3+7q^2+3q
        74: q^3+2q^2+q
        75: 4q^2+2q
        76: q^3+2q^2+q
        77: 4q^2+2q
        78: q^3+2q^2+q
        79: q^3+3q^2+2q
        80: 2q^3+6q^2+3q
        81: 2q^3+6q^2+3q
        82: 3q^3+7q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: 2q^3+6q^2+3q
        86: 3q^3+7q^2+3q
        87: 2q^3+6q^2+3q
        88: q^4+4q^3+7q^2+3q
        89: 2q^4+5q^3+7q^2+3q
        90: q^4+4q^3+7q^2+3q
        91: q^4+4q^3+7q^2+3q
        92: 2q^4+5q^3+7q^2+3q
        93: q^4+4q^3+7q^2+3q
        94: 3q^3+7q^2+3q
        95: 3q^3+7q^2+3q
        96: q^4+3q^3+6q^2+3q
        97: 3q^3+7q^2+3q
        98: 3q^3+7q^2+3q
        99: q^4+3q^3+6q^2+3q
       100: 4q^2+3q
       101: 4q^2+3q
       102: 3q^2+3q
       103: q^3+q^2+q
       104: 2q^2+q
       105: 2q^2+q
       106: q^2
       107: 2q^3+4q^2+2q
       108: q^3+3q^2+q
       109: 2q^3+4q^2+2q
       110: q^3+3q^2+q
       111: q^3+2q^2+q
       112: 4q^2+2q
       113: q^3+2q^2+q
       114: 4q^2+2q
       115: q^3+2q^2+q
       116: 3q^2+2q
       117: q^3+3q^2+2q
       118: 2q^2+q
       119: q^3+3q^2+2q
       120: 2q^2+q
       121: q^3+2q^2+q
       122: 3q^2+2q
       123: q^3+2q^2+q
       124: 3q^2+2q
       125: q^4+2q^3+6q^2+3q
       126: q^4+4q^3+7q^2+3q
       127: q^3+2q^2+q
       128: 4q^2+2q
       129: q^3+2q^2+q
       130: 4q^2+2q
       131: q^3+2q^2+q
       132: q^3+3q^2+2q
       133: q^4+2q^3+6q^2+3q
       134: q^4+4q^3+7q^2+3q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 2q^3+6q^2+3q
       138: 2q^3+6q^2+3q
       139: 3q^3+7q^2+3q
       140: q^2+2q
       141: 2q^3+6q^2+3q
       142: 3q^3+7q^2+3q
       143: 2q^3+6q^2+3q
       144: 2q^3+6q^2+3q
       145: 3q^3+7q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^3+7q^2+3q
       148: q^2+2q
       149: 4q^2+3q
       150: 3q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: 3q^2+2q
       155: q^2+q
       156: 2q^2+2q
       157: q^4+4q^3+7q^2+3q
       158: 2q^4+5q^3+7q^2+3q
       159: q^4+4q^3+7q^2+3q
       160: q^3+4q^2+3q
       161: q^3+4q^2+3q
       162: q^3+4q^2+3q
       163: q^3+4q^2+3q
       164: q^3+4q^2+3q
       165: q^3+4q^2+3q
       166: 4q^2+3q
       167: 4q^2+3q
       168: 3q^2+3q
       169: q^3+q^2+q
       170: 2q^2+q
       171: 2q^2+q
       172: q^2
       173: q^3+q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2
       177: q^3+2q^2+q
       178: 3q^2+2q
       179: q^3+2q^2+q
       180: 4q^2+2q
       181: q^3+2q^2+q
       182: 4q^2+2q
       183: q^3+3q^2+2q
       184: 2q^2+q
       185: q^3+3q^2+2q
       186: 2q^2+q
       187: q^3+2q^2+q
       188: 3q^2+2q
       189: q^3+2q^2+q
       190: 3q^2+2q
       191: q^3+3q^2+2q
       192: 2q^2+q
       193: q^2+2q
       195: 2q^3+4q^2+2q
       196: q^3+3q^2+q
       197: q
       198: q^2+q
       199: q^3+3q^2+2q
       200: 2q^2+q
       201: 2q^3+4q^2+2q
       202: q^3+3q^2+q
       203: q^2+2q
       205: q
       206: q^2+q
       207: q^3+2q^2+q
       208: 3q^2+2q
       209: q^2+q
       210: 3q^2+2q
       211: q^2+q
       212: 2q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: q^4+2q^3+6q^2+3q
       220: q^4+2q^3+6q^2+3q
       221: q^4+4q^3+7q^2+3q
       222: 2q^3+6q^2+3q
       223: 2q^3+6q^2+3q
       224: 2q^3+6q^2+3q
       225: 2q^3+6q^2+3q
       226: 2q^3+6q^2+3q
       227: 3q^2+3q
       228: q^3+4q^2+3q
       229: 2q
       230: q^3+4q^2+3q
       231: 2q^3+6q^2+3q
       232: 3q^2+3q
       233: q^3+4q^2+3q
       234: q^3+4q^2+3q
       235: 2q
       236: 3q^2+3q
       237: q^2+q
       238: 3q^2+2q
       239: q^2+q
       240: 3q^2+2q
       241: q^2+q
       242: 2q^2+2q
       243: 4q^2+3q
       244: q^2+2q
       245: q^2+2q
       246: 3q^2+3q
       247: 4q^2+3q
       248: 4q^2+3q
       249: 3q^2+3q
       250: q^3+4q^2+3q
       251: q^3+4q^2+3q
       252: q^3+4q^2+3q
       253: q^3+4q^2+3q
       254: q^3+4q^2+3q
       255: q^3+4q^2+3q
       256: q^2+3q
       257: 2q^2+3q
       258: q^2+3q
       259: q^3+q^2+q
       260: 2q^2+q
       261: 2q^2+q
       262: q^2
       263: q^3+q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2
       267: q
       268: q^2+q
       271: q
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       275: q^3+q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: 2q
       282: q^2+2q
       283: q^3+3q^2+2q
       284: 2q^2+q
       285: q^3+3q^2+2q
       286: 2q^2+q
       287: q^3+2q^2+q
       288: 3q^2+2q
       290: q^2+2q
       291: q^3+2q^2+q
       292: 3q^2+2q
       293: q^3+3q^2+2q
       294: 2q^2+q
       295: q^3+3q^2+2q
       296: 2q^2+q
       297: q^3+2q^2+q
       298: 3q^2+2q
       299: 2q
       301: q
       302: q^2+q
       303: 2q^2+2q
       304: q^2+q
       305: q
       306: q
       307: 2q^2+2q
       308: q^2+q
       309: 2q
       311: q
       312: q^2+q
       313: q
       314: q
       315: q^2+q
       316: 2q^2+2q
       317: q^2+q
       318: 3q^2+2q
       319: q^2+2q
       321: q^2+2q
       323: q
       325: q^2+q
       326: 2q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: q^4+2q^3+6q^2+3q
       334: 2q^3+6q^2+3q
       335: 2q^3+6q^2+3q
       336: 3q^2+3q
       337: 4q^2+3q
       338: q^2+q
       339: 3q^2+2q
       340: q^2+q
       341: 3q^2+2q
       342: q^2+q
       343: 2q^2+2q
       344: 3q^2+3q
       345: 3q^2+3q
       346: q^3+4q^2+3q
       347: 2q
       348: 2q
       349: q^3+4q^2+3q
       350: q^3+4q^2+3q
       351: q^2+2q
       352: 3q^2+3q
       353: 3q^2+3q
       354: q^3+4q^2+3q
       355: q^3+4q^2+3q
       356: q^3+4q^2+3q
       357: 2q
       358: 2q
       359: q^2+2q
       361: 2q
       363: q^2+2q
       365: 2q
       366: 3q^2+3q
       367: q^2+3q
       368: q^2+3q
       369: 2q
       370: 2q
       371: q^2+3q
       372: 2q^2+3q
       373: q^2+3q
       374: q^2+3q
       375: 2q^2+3q
       376: q^2+3q
       377: q^3+q^2+q
       378: q^2+q
       379: q^2+q
       380: q^2
       382: q
       383: q
       385: q^3+q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2
       389: q
       390: q^2+q
       393: q
       394: q
       397: q
       398: q^2+q
       401: q
       402: q
       405: q
       410: 2q
       412: q^2+2q
       414: 2q
       416: q^2+2q
       418: q^2+2q
       419: q^3+3q^2+2q
       420: 2q^2+q
       421: q^3+3q^2+2q
       422: 2q^2+q
       423: q^3+2q^2+q
       424: 3q^2+2q
       425: q^2+q
       426: 2q^2+2q
       427: q^2+q
       428: 3q^2+2q
       429: 2q
       431: 2q^2+2q
       432: q^2+q
       433: q
       434: q
       436: q
       437: 2q
       439: 2q^2+2q
       440: q^2+q
       441: q
       442: q
       443: q^2+2q
       445: q
       446: q^2+q
       447: 2q^2+2q
       448: q^2+q
       449: 2q
       451: q
       452: q
       453: 2q^2+2q
       454: q^2+q
       456: q
       457: 2q
       459: q
       460: q
       461: q^2+2q
       463: q
       464: q^2+q
       466: 2q
       468: 2q
       469: q^2+q
       470: 2q^2+2q
       471: 2q
       473: 2q
       475: q
       477: q
       479: q
       481: 3q^2+3q
       482: 3q^2+3q
       483: 3q^2+3q
       484: q^2+3q
       486: 2q
       488: q^2+2q
       490: 2q
       491: q^2+3q
       492: 3q^2+3q
       493: 2q
       494: q^3+4q^2+3q
       495: 2q
       496: 2q
       497: 3q^2+3q
       498: q^3+4q^2+3q
       499: 2q
       500: 2q
       501: 2q
       503: 2q
       505: q^2+2q
       507: 2q
       508: q^2+3q
       509: q^2+3q
       510: q^2+3q
       511: 2q
       512: 2q
       513: 2q
       514: 2q
       515: q^2+3q
       516: 2q^2+3q
       517: q^2+3q
       518: q^2+3q
       519: 2q^2+3q
       520: q^2+3q
       522: q
       523: q
       526: q
       527: q
       529: q^3+q^2+q
       530: q^2+q
       531: q^2+q
       532: q^2
       533: q
       534: q
       538: q
       541: q
       542: q
       545: q
       546: q^2+q
       549: q
       550: q
       554: q
       557: q
       558: q
       561: q
       562: q^2+q
       565: q
       569: q
       573: q
       577: q
       584: 2q
       586: 2q
       588: q^2+2q
       589: 2q^2+2q
       590: q^2+q
       591: 2q
       593: 2q
       595: 2q^2+2q
       596: q^2+q
       598: 2q
       599: q^2+q
       600: 2q^2+2q
       602: 2q
       603: 2q
       606: q
       607: 2q^2+2q
       608: q^2+q
       609: q
       610: q
       612: q
       613: q
       614: q
       615: 2q
       618: q
       619: 2q^2+2q
       620: q^2+q
       621: 2q
       624: q
       625: q
       626: q
       628: q
       629: q
       630: q
       631: 2q
       634: q
       636: 2q
       638: 2q
       640: 2q
       641: 2q
       643: 2q
       645: q
       647: 2q
       649: 2q
       653: q
       655: q
       657: q^2+3q
       659: 2q
       661: q^2+2q
       663: 2q
       664: q^2+3q
       665: q^2+3q
       667: 2q
       669: q^2+2q
       671: 2q
       672: q^2+3q
       673: q^2+3q
       674: 2q
       675: q
       676: 3q^2+3q
       677: 2q
       678: 2q
       679: 2q
       680: 2q
       681: 3q^2+3q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+3q
       687: 2q
       688: 2q
       690: q^2+3q
       691: 2q^2+3q
       692: q^2+3q
       693: q
       706: q
       707: q
       710: q
       711: q
       713: q
       714: q
       717: q
       718: q
       722: q
       725: q
       726: q
       730: q
       734: q
       738: q
       741: q
       742: q
       746: q
       750: q
       753: q
       761: q
       765: q
       776: 2q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       785: 2q
       787: 2q
       790: 2q
       791: q
       793: 2q
       796: q
       800: q
       801: q
       805: 2q
       807: 2q^2+2q
       808: q^2+q
       810: q
       811: q
       812: q
       814: q
       815: 2q
       817: 2q
       820: q
       824: q
       825: 2q^2+2q
       826: q^2+q
       827: 2q
       831: q
       834: q
       835: q
       836: q
       838: q
       839: 2q
       842: 2q
       843: q
       845: 2q
       847: 2q
       851: q
       857: q
       860: 2q
       862: q^2+2q
       864: 2q
       865: q^2+3q
       866: q^2+3q
       867: q^2+3q
       868: q^2+3q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q
       878: q
       881: q+1
       882: q+1
       883: q+1
       897: q
       898: q
       901: q
       905: q
       908: q
       913: q
       917: q
       928: q
       929: q
       933: q
       937: q
       941: q
       948: q
       949: q
       957: q
       964: q
       974: q
       988: q
       993: 2q
       995: 2q
       997: 2q
       998: 2q
      1000: 2q
      1003: 2q
      1004: 2q
      1006: 2q
      1008: q
      1012: q
      1015: q
      1016: 2q
      1021: q
      1025: q
      1026: q
      1031: q
      1032: 2q
      1037: q
      1043: q
      1044: q
      1046: q
      1052: q
      1058: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+3q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1111: q
      1115: q
      1119: q
      1123: q
      1130: q
      1134: q
      1145: q
      1165: q
      1194: q
      1211: q+1
      1213: q+1
      1215: 2q
      1216: 2q
      1218: 2q
      1224: q
      1227: 1
      1228: 1
      1234: q
      1237: q
      1240: q
      1245: 1
      1246: 1
      1250: q
      1253: q
      1260: q
      1262: 1
      1282: q+1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1315: q
      1319: q
      1326: q
      1341: 1
      1373: 1
      1405: 1
      1410: 1
      1439: q+1
      1440: 1
      1442: 1
      1444: 1
      1453: 1
      1454: q
      1459: 1
      1460: q
      1485: 1
      1486: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1639: 1
      1644: 1
      1647: 1
      1652: 1
      1653: 1
      1676: 1
      1724: 1
      1733: 1
      1746: 1
      1762: 1
      1835: 1

1836:    0: q^4+2q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+2q^3+2q^2+q
         4: q^4+2q^3+2q^2+q
         5: q^4+2q^3+2q^2+q
         6: q^4+2q^3+2q^2+q
         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^3+2q^2+q
        11: q^3+2q^2+q
        12: q^3+2q^2+q
        13: q^4+2q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: q^4+2q^3+2q^2+q
        16: q^4+2q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+2q^3+2q^2+q
        19: q^4+2q^3+2q^2+q
        20: q^4+2q^3+2q^2+q
        21: q^4+2q^3+2q^2+q
        22: q^3+2q^2+q
        23: q^3+2q^2+q
        24: q^3+2q^2+q
        25: q^3+2q^2+q
        26: q^3+2q^2+q
        27: q^3+2q^2+q
        28: q^3+2q^2+q
        29: q^3+2q^2+q
        30: q^4+2q^3+2q^2+q
        31: 2q^2+q
        32: q^3+2q^2+q
        33: q^3+2q^2+q
        34: 2q^2+q
        35: q^3+2q^2+q
        36: q^3+2q^2+q
        37: q^3+2q^2+q
        39: q^3+2q^2+q
        41: q^3+2q^2+q
        43: q^3+2q^2+q
        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^4+2q^3+2q^2+q
        47: q^4+2q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+2q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+2q^2+q
        53: q^3+2q^2+q
        54: q^3+2q^2+q
        55: q^3+2q^2+q
        56: q^3+2q^2+q
        57: q^3+2q^2+q
        58: q^2+q
        59: q^2
        60: q^2+q
        61: q^2
        62: 2q^2+q
        64: q^3+2q^2+q
        66: q^3+2q^2+q
        68: q^3+2q^2+q
        69: q^4+2q^3+2q^2+q
        70: q^3+2q^2+q
        71: q^3+2q^2+q
        72: q^3+2q^2+q
        73: q^3+2q^2+q
        74: q^3+2q^2+q
        76: q^3+2q^2+q
        78: q^3+2q^2+q
        80: 2q^2+q
        81: q^3+2q^2+q
        82: 2q^2+q
        83: q^3+2q^2+q
        84: 2q^2+q
        85: q^3+2q^2+q
        86: 2q^2+q
        87: q^3+2q^2+q
        88: q^3+2q^2+q
        89: q^3+2q^2+q
        90: q^3+2q^2+q
        91: q^4+2q^3+2q^2+q
        92: q^4+2q^3+2q^2+q
        93: q^4+2q^3+2q^2+q
        94: q^3+2q^2+q
        95: q^3+2q^2+q
        96: q^3+2q^2+q
        97: q^3+2q^2+q
        98: q^3+2q^2+q
        99: q^3+2q^2+q
       100: q^2+q
       101: q^2+q
       102: q^2+q
       103: q^2+q
       106: q^2
       107: q^2+q
       108: q^2
       109: q^2+q
       110: q^2
       111: q^3+2q^2+q
       113: 2q^2+q
       115: q^3+2q^2+q
       117: q^2+q
       118: q^2
       119: q^2+q
       120: q^2
       121: 2q^2+q
       123: q^3+2q^2+q
       125: q^3+2q^2+q
       126: q^3+2q^2+q
       127: q^3+2q^2+q
       129: q^3+2q^2+q
       131: q^3+2q^2+q
       133: q^3+2q^2+q
       134: q^4+2q^3+2q^2+q
       135: q^3+2q^2+q
       136: q^3+2q^2+q
       137: 2q^2+q
       138: q^3+2q^2+q
       139: 2q^2+q
       140: q
       141: 2q^2+q
       142: q^3+2q^2+q
       143: 2q^2+q
       144: q^3+2q^2+q
       145: 2q^2+q
       146: 2q^2+q
       147: q^3+2q^2+q
       148: q
       149: q^2+q
       150: q^2+q
       151: q^2+q
       153: q^2+q
       155: q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^3+2q^2+q
       161: q^3+2q^2+q
       162: q^3+2q^2+q
       163: q^3+2q^2+q
       164: q^3+2q^2+q
       165: q^3+2q^2+q
       166: q^2+q
       167: q^2+q
       168: q^2+q
       169: q^2+q
       172: q^2
       173: q^2+q
       176: q^2
       177: q^3+2q^2+q
       179: 2q^2+q
       181: q^3+2q^2+q
       183: q^2+q
       184: q^2
       185: q^2+q
       186: q^2
       187: q^3+2q^2+q
       189: 2q^2+q
       191: q^2+q
       192: q^2
       193: q
       195: q^2+q
       196: q^2
       197: q
       199: q^2+q
       200: q^2
       201: q^2+q
       202: q^2
       203: q
       205: q
       207: 2q^2+q
       209: q^2+q
       211: q^2+q
       213: q^3+2q^2+q
       215: q^3+2q^2+q
       217: q^3+2q^2+q
       219: q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: q^3+2q^2+q
       224: 2q^2+q
       225: q^3+2q^2+q
       226: 2q^2+q
       227: 2q^2+q
       228: q^3+2q^2+q
       229: q
       230: q^3+2q^2+q
       231: 2q^2+q
       232: 2q^2+q
       233: q^3+2q^2+q
       234: q^3+2q^2+q
       235: q
       236: q^2+q
       237: q^2+q
       239: q^2+q
       241: q^2+q
       243: q^2+q
       244: q
       245: q
       246: q^2+q
       247: q^2+q
       248: q^2+q
       249: q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2+q
       262: q^2
       263: q^2+q
       266: q^2
       267: q
       271: q
       275: q^2+q
       278: q^2
       279: 2q^2+q
       281: q^3+2q^2+q
       283: q^2+q
       284: q^2
       285: q^2+q
       286: q^2
       287: 2q^2+q
       289: q^3+2q^2+q
       291: q^3+2q^2+q
       293: q^2+q
       294: q^2
       295: q^2+q
       296: q^2
       297: 2q^2+q
       299: q
       301: q
       303: q^2+q
       304: q^2
       305: q
       307: q^2+q
       308: q^2
       309: q
       311: q
       313: q
       315: q^2+q
       317: q^2+q
       319: q
       321: q
       323: q
       325: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: q^2+q
       338: q^2+q
       340: q^2+q
       342: q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^3+2q^2+q
       351: q
       352: 2q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+2q^2+q
       357: q
       358: q
       359: q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: q^2+q
       367: q^2+q
       368: q^2+q
       369: q
       370: q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       377: q^2+q
       380: q^2
       381: q^2+q
       384: q^2
       385: q^2+q
       388: q^2
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q^2+q
       411: q^2+q
       413: 2q^2+q
       415: q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       420: q^2
       421: q^2+q
       422: q^2
       423: 2q^2+q
       425: q^2+q
       427: q^2+q
       429: q
       431: q^2+q
       432: q^2
       433: q
       435: q
       437: q
       439: q
       440: q^2
       441: q
       443: q
       445: q
       447: q^2+q
       448: q^2
       449: q
       451: q
       453: q
       454: q^2
       455: q
       457: q
       459: q
       461: q
       463: q
       465: q^2+q
       467: q^2+q
       469: q^2+q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: q^2+q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q
       508: q^2+q
       512: q
       514: q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       521: q^2+q
       524: q^2
       525: q
       528: q^2
       529: q^2+q
       532: q^2
       533: q
       537: q
       541: q
       545: q
       549: q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       590: q^2
       591: q
       593: q
       595: q^2+q
       596: q^2
       597: q^2+q
       599: q^2+q
       601: q^2+q
       603: q
       605: q
       607: q
       608: q^2
       609: q
       613: q
       615: q
       617: q
       619: q
       620: q^2
       621: q
       623: q
       625: q
       629: q
       631: q
       633: q
       639: q^2+q
       641: q
       643: q
       645: q
       651: q
       655: q
       657: q^2+q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: q^2+q
       665: q^2+q
       674: q
       675: q
       676: q^2+q
       677: q
       679: q
       680: q
       681: q^2+q
       682: q
       683: q
       685: q
       693: q
       705: q
       708: q^2
       709: q^2+q
       712: q^2
       713: q
       717: q
       721: q
       725: q
       733: q
       737: q
       741: q
       749: q
       753: q
       757: q
       765: q
       769: q
       775: q^2+q
       777: q^2+q
       779: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       793: q
       795: q
       797: q
       801: q
       805: q
       807: q
       808: q^2
       809: q
       811: q
       817: q
       819: q
       821: q
       825: q
       826: q^2
       827: q
       831: q
       833: q
       835: q
       843: q
       849: q
       853: 1
       866: q^2+q
       870: q
       871: q
       874: q
       875: q
       884: q
       896: q
       899: q^2
       900: q
       904: q
       908: q
       916: q
       920: q
       928: q
       940: q
       944: q
       948: q
       960: q
       964: q
       968: q
       978: 1
       984: 1
       994: q^2+q
       998: q
      1000: q
      1010: q
      1012: q
      1020: q
      1022: q
      1026: q
      1036: q
      1038: q
      1044: q
      1050: 1
      1076: q
      1080: q
      1086: q
      1100: 1
      1114: q
      1122: q
      1126: q
      1130: q
      1138: q
      1156: q
      1172: q
      1184: 1
      1190: 1
      1222: 1
      1230: q
      1234: q
      1248: q
      1250: q
      1264: 1
      1290: q
      1304: 1
      1322: 1
      1336: 1
      1356: q
      1380: q
      1406: 1
      1414: 1
      1446: 1
      1491: 1
      1527: 1
      1555: 1
      1559: 1
      1637: 1
      1677: 1
      1725: 1
      1729: 1
      1836: 1

1837:    0: 2q^4+7q^3+8q^2+3q
         1: 2q^4+7q^3+8q^2+3q
         2: 3q^4+5q^3+7q^2+3q
         3: 2q^4+7q^3+8q^2+3q
         4: 2q^4+7q^3+8q^2+3q
         5: 2q^4+7q^3+8q^2+3q
         6: 2q^4+7q^3+8q^2+3q
         7: 3q^4+5q^3+7q^2+3q
         8: q^5+5q^4+6q^3+7q^2+3q
         9: 3q^4+5q^3+7q^2+3q
        10: 2q^4+7q^3+8q^2+3q
        11: 2q^4+7q^3+8q^2+3q
        12: 2q^4+7q^3+8q^2+3q
        13: q^4+4q^3+7q^2+3q
        14: q^4+4q^3+7q^2+3q
        15: 2q^4+5q^3+7q^2+3q
        16: 2q^4+7q^3+8q^2+3q
        17: 2q^4+7q^3+8q^2+3q
        18: 3q^4+5q^3+7q^2+3q
        19: 2q^4+7q^3+8q^2+3q
        20: 2q^4+7q^3+8q^2+3q
        21: 3q^4+5q^3+7q^2+3q
        22: 3q^3+7q^2+3q
        23: 3q^3+7q^2+3q
        24: q^4+3q^3+6q^2+3q
        25: 3q^3+7q^2+3q
        26: 3q^3+7q^2+3q
        27: q^4+3q^3+6q^2+3q
        28: 2q^4+7q^3+8q^2+3q
        29: 2q^4+7q^3+8q^2+3q
        30: q^4+4q^3+7q^2+3q
        31: 3q^3+7q^2+3q
        32: 2q^3+6q^2+3q
        33: 3q^3+7q^2+3q
        34: 3q^3+7q^2+3q
        35: 2q^3+6q^2+3q
        36: 3q^3+7q^2+3q
        37: 4q^2+2q
        38: q^3+2q^2+q
        39: 4q^2+2q
        40: q^3+2q^2+q
        41: q^3+3q^2+2q
        42: q^3+2q^2+q
        43: q^4+4q^3+7q^2+3q
        44: q^4+4q^3+7q^2+3q
        45: 2q^4+5q^3+7q^2+3q
        46: q^4+4q^3+7q^2+3q
        47: 2q^4+5q^3+7q^2+3q
        48: q^4+4q^3+7q^2+3q
        49: 2q^4+7q^3+8q^2+3q
        50: 2q^4+7q^3+8q^2+3q
        51: 3q^4+5q^3+7q^2+3q
        52: 3q^3+7q^2+3q
        53: 3q^3+7q^2+3q
        54: q^4+3q^3+6q^2+3q
        55: 3q^3+7q^2+3q
        56: 3q^3+7q^2+3q
        57: q^4+3q^3+6q^2+3q
        58: q^3+3q^2+q
        59: 2q^3+4q^2+2q
        60: 2q^3+4q^2+2q
        61: q^3+3q^2+q
        62: 4q^2+2q
        63: q^3+2q^2+q
        64: 3q^2+2q
        65: q^3+2q^2+q
        66: 4q^2+2q
        67: q^3+2q^2+q
        68: q^4+2q^3+6q^2+3q
        69: q^4+4q^3+7q^2+3q
        70: q^4+4q^3+7q^2+3q
        71: 2q^4+7q^3+8q^2+3q
        72: 3q^3+7q^2+3q
        73: 3q^3+7q^2+3q
        74: 4q^2+2q
        75: q^3+2q^2+q
        76: 4q^2+2q
        77: q^3+2q^2+q
        78: q^3+3q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+6q^2+3q
        81: 2q^3+6q^2+3q
        82: 3q^3+7q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: 2q^3+6q^2+3q
        86: 3q^3+7q^2+3q
        87: 2q^3+6q^2+3q
        88: q^4+4q^3+7q^2+3q
        89: 2q^4+5q^3+7q^2+3q
        90: q^4+4q^3+7q^2+3q
        91: q^4+4q^3+7q^2+3q
        92: 2q^4+5q^3+7q^2+3q
        93: q^4+4q^3+7q^2+3q
        94: 3q^3+7q^2+3q
        95: 3q^3+7q^2+3q
        96: q^4+3q^3+6q^2+3q
        97: 3q^3+7q^2+3q
        98: 3q^3+7q^2+3q
        99: q^4+3q^3+6q^2+3q
       100: 4q^2+3q
       101: 4q^2+3q
       102: 3q^2+3q
       103: 2q^2+q
       104: q^3+q^2+q
       105: q^2
       106: 2q^2+q
       107: 2q^3+4q^2+2q
       108: q^3+3q^2+q
       109: q^3+3q^2+q
       110: 2q^3+4q^2+2q
       111: 4q^2+2q
       112: q^3+2q^2+q
       113: 4q^2+2q
       114: q^3+2q^2+q
       115: 3q^2+2q
       116: q^3+2q^2+q
       117: 2q^2+q
       118: q^3+3q^2+2q
       119: q^3+3q^2+2q
       120: 2q^2+q
       121: 3q^2+2q
       122: q^3+2q^2+q
       123: 3q^2+2q
       124: q^3+2q^2+q
       125: q^4+2q^3+6q^2+3q
       126: q^4+4q^3+7q^2+3q
       127: 4q^2+2q
       128: q^3+2q^2+q
       129: 4q^2+2q
       130: q^3+2q^2+q
       131: q^3+3q^2+2q
       132: q^3+2q^2+q
       133: q^4+2q^3+6q^2+3q
       134: q^4+4q^3+7q^2+3q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 2q^3+6q^2+3q
       138: 2q^3+6q^2+3q
       139: 3q^3+7q^2+3q
       140: q^2+2q
       141: 2q^3+6q^2+3q
       142: 3q^3+7q^2+3q
       143: 2q^3+6q^2+3q
       144: 2q^3+6q^2+3q
       145: 3q^3+7q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^3+7q^2+3q
       148: q^2+2q
       149: 4q^2+3q
       150: 3q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: 3q^2+2q
       154: q^2+q
       155: 2q^2+2q
       156: q^2+q
       157: q^4+4q^3+7q^2+3q
       158: 2q^4+5q^3+7q^2+3q
       159: q^4+4q^3+7q^2+3q
       160: q^3+4q^2+3q
       161: q^3+4q^2+3q
       162: q^3+4q^2+3q
       163: q^3+4q^2+3q
       164: q^3+4q^2+3q
       165: q^3+4q^2+3q
       166: 4q^2+3q
       167: 4q^2+3q
       168: 3q^2+3q
       169: 2q^2+q
       170: q^3+q^2+q
       171: q^2
       172: 2q^2+q
       173: q^2+q
       174: q^3+q^2+q
       175: q^2
       176: q^2+q
       177: 3q^2+2q
       178: q^3+2q^2+q
       179: 4q^2+2q
       180: q^3+2q^2+q
       181: 4q^2+2q
       182: q^3+2q^2+q
       183: q^3+3q^2+2q
       184: 2q^2+q
       185: 2q^2+q
       186: q^3+3q^2+2q
       187: 3q^2+2q
       188: q^3+2q^2+q
       189: 3q^2+2q
       190: q^3+2q^2+q
       191: 2q^2+q
       192: q^3+3q^2+2q
       193: q^2+2q
       195: q^3+3q^2+q
       196: 2q^3+4q^2+2q
       197: q^2+q
       198: q
       199: q^3+3q^2+2q
       200: 2q^2+q
       201: 2q^3+4q^2+2q
       202: q^3+3q^2+q
       204: q^2+2q
       205: q^2+q
       206: q
       207: 3q^2+2q
       208: q^3+2q^2+q
       209: 3q^2+2q
       210: q^2+q
       211: 2q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: q^4+2q^3+6q^2+3q
       220: q^4+2q^3+6q^2+3q
       221: q^4+4q^3+7q^2+3q
       222: 2q^3+6q^2+3q
       223: 2q^3+6q^2+3q
       224: 2q^3+6q^2+3q
       225: 2q^3+6q^2+3q
       226: 2q^3+6q^2+3q
       227: 3q^2+3q
       228: q^3+4q^2+3q
       229: 2q
       230: q^3+4q^2+3q
       231: 2q^3+6q^2+3q
       232: 3q^2+3q
       233: q^3+4q^2+3q
       234: q^3+4q^2+3q
       235: 2q
       236: 3q^2+3q
       237: 3q^2+2q
       238: q^2+q
       239: 3q^2+2q
       240: q^2+q
       241: 2q^2+2q
       242: q^2+q
       243: 4q^2+3q
       244: q^2+2q
       245: q^2+2q
       246: 3q^2+3q
       247: 4q^2+3q
       248: 4q^2+3q
       249: 3q^2+3q
       250: q^3+4q^2+3q
       251: q^3+4q^2+3q
       252: q^3+4q^2+3q
       253: q^3+4q^2+3q
       254: q^3+4q^2+3q
       255: q^3+4q^2+3q
       256: q^2+3q
       257: 2q^2+3q
       258: q^2+3q
       259: 2q^2+q
       260: q^3+q^2+q
       261: q^2
       262: 2q^2+q
       263: q^2+q
       264: q^3+q^2+q
       265: q^2
       266: q^2+q
       267: q^2+q
       268: q
       273: q^2+q
       274: q
       275: q^2+q
       276: q^3+q^2+q
       277: q^2
       278: q^2+q
       279: 2q
       281: q^2+2q
       283: q^3+3q^2+2q
       284: 2q^2+q
       285: 2q^2+q
       286: q^3+3q^2+2q
       287: 3q^2+2q
       288: q^3+2q^2+q
       289: q^2+2q
       291: 3q^2+2q
       292: q^3+2q^2+q
       293: q^3+3q^2+2q
       294: 2q^2+q
       295: 2q^2+q
       296: q^3+3q^2+2q
       297: 3q^2+2q
       298: q^3+2q^2+q
       299: 2q
       301: q^2+q
       302: q
       303: q^2+q
       304: 2q^2+2q
       305: q
       306: q
       307: 2q^2+2q
       308: q^2+q
       310: 2q
       311: q^2+q
       312: q
       313: q
       314: q
       315: 2q^2+2q
       316: q^2+q
       317: 3q^2+2q
       318: q^2+q
       319: q^2+2q
       322: q^2+2q
       324: q
       325: 2q^2+2q
       326: q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: q^4+2q^3+6q^2+3q
       334: 2q^3+6q^2+3q
       335: 2q^3+6q^2+3q
       336: 3q^2+3q
       337: 4q^2+3q
       338: 3q^2+2q
       339: q^2+q
       340: 3q^2+2q
       341: q^2+q
       342: 2q^2+2q
       343: q^2+q
       344: 3q^2+3q
       345: 3q^2+3q
       346: q^3+4q^2+3q
       347: 2q
       348: 2q
       349: q^3+4q^2+3q
       350: q^3+4q^2+3q
       351: q^2+2q
       352: 3q^2+3q
       353: 3q^2+3q
       354: q^3+4q^2+3q
       355: q^3+4q^2+3q
       356: q^3+4q^2+3q
       357: 2q
       358: 2q
       359: q^2+2q
       360: 2q
       362: q^2+2q
       364: 2q
       366: 3q^2+3q
       367: q^2+3q
       368: q^2+3q
       369: 2q
       370: 2q
       371: q^2+3q
       372: 2q^2+3q
       373: q^2+3q
       374: q^2+3q
       375: 2q^2+3q
       376: q^2+3q
       377: q^2+q
       378: q^3+q^2+q
       379: q^2
       380: q^2+q
       381: q
       384: q
       385: q^2+q
       386: q^3+q^2+q
       387: q^2
       388: q^2+q
       389: q^2+q
       390: q
       393: q
       394: q
       399: q^2+q
       400: q
       403: q
       404: q
       407: q
       409: 2q
       411: q^2+2q
       413: 2q
       415: q^2+2q
       417: q^2+2q
       419: q^3+3q^2+2q
       420: 2q^2+q
       421: 2q^2+q
       422: q^3+3q^2+2q
       423: 3q^2+2q
       424: q^3+2q^2+q
       425: 2q^2+2q
       426: q^2+q
       427: 3q^2+2q
       428: q^2+q
       429: 2q
       431: q^2+q
       432: 2q^2+2q
       433: q
       434: q
       435: q
       437: 2q
       439: q^2+q
       440: 2q^2+2q
       441: q
       442: q
       443: q^2+2q
       445: q^2+q
       446: q
       447: 2q^2+2q
       448: q^2+q
       450: 2q
       451: q
       452: q
       453: 2q^2+2q
       454: q^2+q
       455: q
       458: 2q
       459: q
       460: q
       462: q^2+2q
       463: q^2+q
       464: q
       465: 2q
       467: 2q
       469: 2q^2+2q
       470: q^2+q
       471: 2q
       474: 2q
       476: q
       478: q
       480: q
       481: 3q^2+3q
       482: 3q^2+3q
       483: 3q^2+3q
       484: q^2+3q
       485: 2q
       487: q^2+2q
       489: 2q
       491: q^2+3q
       492: 3q^2+3q
       493: 2q
       494: q^3+4q^2+3q
       495: 2q
       496: 2q
       497: 3q^2+3q
       498: q^3+4q^2+3q
       499: 2q
       500: 2q
       501: 2q
       502: 2q
       504: q^2+2q
       506: 2q
       508: q^2+3q
       509: q^2+3q
       510: q^2+3q
       511: 2q
       512: 2q
       513: 2q
       514: 2q
       515: q^2+3q
       516: 2q^2+3q
       517: q^2+3q
       518: q^2+3q
       519: 2q^2+3q
       520: q^2+3q
       521: q
       524: q
       525: q
       528: q
       529: q^2+q
       530: q^3+q^2+q
       531: q^2
       532: q^2+q
       533: q
       534: q
       537: q
       541: q
       542: q
       545: q^2+q
       546: q
       551: q
       552: q
       555: q
       559: q
       560: q
       563: q^2+q
       564: q
       566: q
       571: q
       574: q
       581: q
       583: 2q
       585: 2q
       587: q^2+2q
       589: 2q^2+2q
       590: q^2+q
       592: 2q
       593: 2q
       595: q^2+q
       596: 2q^2+2q
       597: 2q
       599: 2q^2+2q
       600: q^2+q
       601: 2q
       603: 2q
       605: q
       607: q^2+q
       608: 2q^2+2q
       609: q
       610: q
       611: q
       613: q
       614: q
       615: 2q
       617: q
       619: 2q^2+2q
       620: q^2+q
       622: 2q
       623: q
       625: q
       626: q
       627: q
       629: q
       630: q
       632: 2q
       633: q
       635: 2q
       637: 2q
       639: 2q
       641: 2q
       644: 2q
       646: q
       647: 2q
       650: 2q
       654: q
       656: q
       657: q^2+3q
       658: 2q
       660: q^2+2q
       662: 2q
       664: q^2+3q
       665: q^2+3q
       666: 2q
       668: q^2+2q
       670: 2q
       672: q^2+3q
       673: q^2+3q
       674: 2q
       675: q
       676: 3q^2+3q
       677: 2q
       678: 2q
       679: 2q
       680: 2q
       681: 3q^2+3q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+3q
       687: 2q
       688: 2q
       690: q^2+3q
       691: 2q^2+3q
       692: q^2+3q
       699: q
       705: q
       708: q
       709: q
       712: q
       715: q
       716: q
       717: q
       718: q
       721: q
       725: q
       726: q
       729: q
       733: q
       739: q
       743: q
       744: q
       747: q
       751: q
       754: q
       763: q
       766: q
       775: 2q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       785: 2q
       788: 2q
       789: 2q
       792: q
       793: 2q
       795: q
       799: q
       801: q
       805: 2q
       807: q^2+q
       808: 2q^2+2q
       809: q
       811: q
       812: q
       813: q
       815: 2q
       818: 2q
       819: q
       823: q
       825: 2q^2+2q
       826: q^2+q
       828: 2q
       832: q
       833: q
       835: q
       836: q
       837: q
       840: 2q
       841: 2q
       844: q
       845: 2q
       848: 2q
       852: q
       858: q
       859: 2q
       861: q^2+2q
       863: 2q
       865: q^2+3q
       866: q^2+3q
       867: q^2+3q
       868: q^2+3q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q
       878: q
       881: q+1
       882: q+1
       883: q+1
       896: q
       899: q
       902: q
       904: q
       909: q
       912: q
       916: q
       928: q
       929: q
       932: q
       938: q
       942: q
       950: q
       951: q
       958: q
       965: q
       976: q
       989: q
       992: 2q
       994: 2q
       996: 2q
       999: 2q
      1000: 2q
      1002: 2q
      1004: 2q
      1007: 2q
      1009: q
      1013: q
      1014: q
      1016: 2q
      1020: q
      1024: q
      1026: q
      1030: q
      1033: 2q
      1036: q
      1042: q
      1045: q
      1047: q
      1052: q
      1059: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+3q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1112: q
      1116: q
      1118: q
      1122: q
      1131: q
      1136: q
      1144: q
      1166: q
      1195: q
      1210: q+1
      1212: q+1
      1214: 2q
      1217: 2q
      1218: 2q
      1225: q
      1226: 1
      1228: 1
      1234: q
      1236: q
      1240: q
      1244: 1
      1247: 1
      1251: q
      1252: q
      1261: q
      1263: 1
      1282: q+1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1316: q
      1318: q
      1327: q
      1340: 1
      1374: 1
      1407: 1
      1411: 1
      1438: q+1
      1441: 1
      1442: 1
      1445: 1
      1452: 1
      1454: q
      1458: 1
      1461: q
      1485: 1
      1486: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1640: 1
      1643: 1
      1647: 1
      1651: 1
      1654: 1
      1678: 1
      1726: 1
      1734: 1
      1745: 1
      1763: 1
      1837: 1

1838:    0: 2q^4+7q^3+8q^2+3q
         1: 2q^4+7q^3+8q^2+3q
         2: 3q^4+5q^3+7q^2+3q
         3: 2q^4+7q^3+8q^2+3q
         4: 2q^4+7q^3+8q^2+3q
         5: 2q^4+7q^3+8q^2+3q
         6: 2q^4+7q^3+8q^2+3q
         7: 3q^4+5q^3+7q^2+3q
         8: q^5+5q^4+6q^3+7q^2+3q
         9: 3q^4+5q^3+7q^2+3q
        10: 2q^4+7q^3+8q^2+3q
        11: 2q^4+7q^3+8q^2+3q
        12: 2q^4+7q^3+8q^2+3q
        13: q^4+4q^3+7q^2+3q
        14: q^4+4q^3+7q^2+3q
        15: 2q^4+5q^3+7q^2+3q
        16: 2q^4+7q^3+8q^2+3q
        17: 2q^4+7q^3+8q^2+3q
        18: 3q^4+5q^3+7q^2+3q
        19: 2q^4+7q^3+8q^2+3q
        20: 2q^4+7q^3+8q^2+3q
        21: 3q^4+5q^3+7q^2+3q
        22: 3q^3+7q^2+3q
        23: 3q^3+7q^2+3q
        24: q^4+3q^3+6q^2+3q
        25: 3q^3+7q^2+3q
        26: 3q^3+7q^2+3q
        27: q^4+3q^3+6q^2+3q
        28: 2q^4+7q^3+8q^2+3q
        29: 2q^4+7q^3+8q^2+3q
        30: q^4+4q^3+7q^2+3q
        31: 3q^3+7q^2+3q
        32: 2q^3+6q^2+3q
        33: 3q^3+7q^2+3q
        34: 3q^3+7q^2+3q
        35: 2q^3+6q^2+3q
        36: 3q^3+7q^2+3q
        37: 4q^2+2q
        38: q^3+2q^2+q
        39: 4q^2+2q
        40: q^3+2q^2+q
        41: q^3+3q^2+2q
        42: q^3+2q^2+q
        43: q^4+4q^3+7q^2+3q
        44: q^4+4q^3+7q^2+3q
        45: 2q^4+5q^3+7q^2+3q
        46: q^4+4q^3+7q^2+3q
        47: 2q^4+5q^3+7q^2+3q
        48: q^4+4q^3+7q^2+3q
        49: 2q^4+7q^3+8q^2+3q
        50: 2q^4+7q^3+8q^2+3q
        51: 3q^4+5q^3+7q^2+3q
        52: 3q^3+7q^2+3q
        53: 3q^3+7q^2+3q
        54: q^4+3q^3+6q^2+3q
        55: 3q^3+7q^2+3q
        56: 3q^3+7q^2+3q
        57: q^4+3q^3+6q^2+3q
        58: 2q^3+4q^2+2q
        59: q^3+3q^2+q
        60: q^3+3q^2+q
        61: 2q^3+4q^2+2q
        62: 4q^2+2q
        63: q^3+2q^2+q
        64: 3q^2+2q
        65: q^3+2q^2+q
        66: 4q^2+2q
        67: q^3+2q^2+q
        68: q^4+2q^3+6q^2+3q
        69: q^4+4q^3+7q^2+3q
        70: q^4+4q^3+7q^2+3q
        71: 2q^4+7q^3+8q^2+3q
        72: 3q^3+7q^2+3q
        73: 3q^3+7q^2+3q
        74: 4q^2+2q
        75: q^3+2q^2+q
        76: 4q^2+2q
        77: q^3+2q^2+q
        78: q^3+3q^2+2q
        79: q^3+2q^2+q
        80: 2q^3+6q^2+3q
        81: 2q^3+6q^2+3q
        82: 3q^3+7q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: 2q^3+6q^2+3q
        86: 3q^3+7q^2+3q
        87: 2q^3+6q^2+3q
        88: q^4+4q^3+7q^2+3q
        89: 2q^4+5q^3+7q^2+3q
        90: q^4+4q^3+7q^2+3q
        91: q^4+4q^3+7q^2+3q
        92: 2q^4+5q^3+7q^2+3q
        93: q^4+4q^3+7q^2+3q
        94: 3q^3+7q^2+3q
        95: 3q^3+7q^2+3q
        96: q^4+3q^3+6q^2+3q
        97: 3q^3+7q^2+3q
        98: 3q^3+7q^2+3q
        99: q^4+3q^3+6q^2+3q
       100: 4q^2+3q
       101: 4q^2+3q
       102: 3q^2+3q
       103: 2q^2+q
       104: q^2
       105: q^3+q^2+q
       106: 2q^2+q
       107: q^3+3q^2+q
       108: 2q^3+4q^2+2q
       109: 2q^3+4q^2+2q
       110: q^3+3q^2+q
       111: 4q^2+2q
       112: q^3+2q^2+q
       113: 4q^2+2q
       114: q^3+2q^2+q
       115: 3q^2+2q
       116: q^3+2q^2+q
       117: q^3+3q^2+2q
       118: 2q^2+q
       119: 2q^2+q
       120: q^3+3q^2+2q
       121: 3q^2+2q
       122: q^3+2q^2+q
       123: 3q^2+2q
       124: q^3+2q^2+q
       125: q^4+2q^3+6q^2+3q
       126: q^4+4q^3+7q^2+3q
       127: 4q^2+2q
       128: q^3+2q^2+q
       129: 4q^2+2q
       130: q^3+2q^2+q
       131: q^3+3q^2+2q
       132: q^3+2q^2+q
       133: q^4+2q^3+6q^2+3q
       134: q^4+4q^3+7q^2+3q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 2q^3+6q^2+3q
       138: 2q^3+6q^2+3q
       139: 3q^3+7q^2+3q
       140: q^2+2q
       141: 2q^3+6q^2+3q
       142: 3q^3+7q^2+3q
       143: 2q^3+6q^2+3q
       144: 2q^3+6q^2+3q
       145: 3q^3+7q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^3+7q^2+3q
       148: q^2+2q
       149: 4q^2+3q
       150: 3q^2+3q
       151: 3q^2+2q
       152: q^2+q
       153: 3q^2+2q
       154: q^2+q
       155: 2q^2+2q
       156: q^2+q
       157: q^4+4q^3+7q^2+3q
       158: 2q^4+5q^3+7q^2+3q
       159: q^4+4q^3+7q^2+3q
       160: q^3+4q^2+3q
       161: q^3+4q^2+3q
       162: q^3+4q^2+3q
       163: q^3+4q^2+3q
       164: q^3+4q^2+3q
       165: q^3+4q^2+3q
       166: 4q^2+3q
       167: 4q^2+3q
       168: 3q^2+3q
       169: 2q^2+q
       170: q^2
       171: q^3+q^2+q
       172: 2q^2+q
       173: q^2+q
       174: q^2
       175: q^3+q^2+q
       176: q^2+q
       177: 3q^2+2q
       178: q^3+2q^2+q
       179: 4q^2+2q
       180: q^3+2q^2+q
       181: 4q^2+2q
       182: q^3+2q^2+q
       183: 2q^2+q
       184: q^3+3q^2+2q
       185: q^3+3q^2+2q
       186: 2q^2+q
       187: 3q^2+2q
       188: q^3+2q^2+q
       189: 3q^2+2q
       190: q^3+2q^2+q
       191: q^3+3q^2+2q
       192: 2q^2+q
       194: q^2+2q
       195: 2q^3+4q^2+2q
       196: q^3+3q^2+q
       197: q^2+q
       198: q
       199: 2q^2+q
       200: q^3+3q^2+2q
       201: q^3+3q^2+q
       202: 2q^3+4q^2+2q
       203: q^2+2q
       205: q^2+q
       206: q
       207: 3q^2+2q
       208: q^3+2q^2+q
       209: 3q^2+2q
       210: q^2+q
       211: 2q^2+2q
       212: q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: q^4+2q^3+6q^2+3q
       220: q^4+2q^3+6q^2+3q
       221: q^4+4q^3+7q^2+3q
       222: 2q^3+6q^2+3q
       223: 2q^3+6q^2+3q
       224: 2q^3+6q^2+3q
       225: 2q^3+6q^2+3q
       226: 2q^3+6q^2+3q
       227: 3q^2+3q
       228: q^3+4q^2+3q
       229: 2q
       230: q^3+4q^2+3q
       231: 2q^3+6q^2+3q
       232: 3q^2+3q
       233: q^3+4q^2+3q
       234: q^3+4q^2+3q
       235: 2q
       236: 3q^2+3q
       237: 3q^2+2q
       238: q^2+q
       239: 3q^2+2q
       240: q^2+q
       241: 2q^2+2q
       242: q^2+q
       243: 4q^2+3q
       244: q^2+2q
       245: q^2+2q
       246: 3q^2+3q
       247: 4q^2+3q
       248: 4q^2+3q
       249: 3q^2+3q
       250: q^3+4q^2+3q
       251: q^3+4q^2+3q
       252: q^3+4q^2+3q
       253: q^3+4q^2+3q
       254: q^3+4q^2+3q
       255: q^3+4q^2+3q
       256: q^2+3q
       257: 2q^2+3q
       258: q^2+3q
       259: 2q^2+q
       260: q^2
       261: q^3+q^2+q
       262: 2q^2+q
       263: q^2+q
       264: q^2
       265: q^3+q^2+q
       266: q^2+q
       269: q^2+q
       270: q
       271: q^2+q
       272: q
       275: q^2+q
       276: q^2
       277: q^3+q^2+q
       278: q^2+q
       279: 2q
       281: q^2+2q
       283: 2q^2+q
       284: q^3+3q^2+2q
       285: q^3+3q^2+2q
       286: 2q^2+q
       287: 3q^2+2q
       288: q^3+2q^2+q
       289: q^2+2q
       291: 3q^2+2q
       292: q^3+2q^2+q
       293: 2q^2+q
       294: q^3+3q^2+2q
       295: q^3+3q^2+2q
       296: 2q^2+q
       297: 3q^2+2q
       298: q^3+2q^2+q
       300: 2q
       301: q^2+q
       302: q
       303: 2q^2+2q
       304: q^2+q
       305: q
       306: q
       307: q^2+q
       308: 2q^2+2q
       309: 2q
       311: q^2+q
       312: q
       313: q
       314: q
       315: 2q^2+2q
       316: q^2+q
       317: 3q^2+2q
       318: q^2+q
       320: q^2+2q
       321: q^2+2q
       324: q
       325: 2q^2+2q
       326: q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: q^4+2q^3+6q^2+3q
       334: 2q^3+6q^2+3q
       335: 2q^3+6q^2+3q
       336: 3q^2+3q
       337: 4q^2+3q
       338: 3q^2+2q
       339: q^2+q
       340: 3q^2+2q
       341: q^2+q
       342: 2q^2+2q
       343: q^2+q
       344: 3q^2+3q
       345: 3q^2+3q
       346: q^3+4q^2+3q
       347: 2q
       348: 2q
       349: q^3+4q^2+3q
       350: q^3+4q^2+3q
       351: q^2+2q
       352: 3q^2+3q
       353: 3q^2+3q
       354: q^3+4q^2+3q
       355: q^3+4q^2+3q
       356: q^3+4q^2+3q
       357: 2q
       358: 2q
       359: q^2+2q
       360: 2q
       362: q^2+2q
       364: 2q
       366: 3q^2+3q
       367: q^2+3q
       368: q^2+3q
       369: 2q
       370: 2q
       371: q^2+3q
       372: 2q^2+3q
       373: q^2+3q
       374: q^2+3q
       375: 2q^2+3q
       376: q^2+3q
       377: q^2+q
       378: q^2
       379: q^3+q^2+q
       380: q^2+q
       381: q
       384: q
       385: q^2+q
       386: q^2
       387: q^3+q^2+q
       388: q^2+q
       391: q^2+q
       392: q
       395: q
       396: q
       397: q^2+q
       398: q
       401: q
       402: q
       408: q
       409: 2q
       411: q^2+2q
       413: 2q
       415: q^2+2q
       417: q^2+2q
       419: 2q^2+q
       420: q^3+3q^2+2q
       421: q^3+3q^2+2q
       422: 2q^2+q
       423: 3q^2+2q
       424: q^3+2q^2+q
       425: 2q^2+2q
       426: q^2+q
       427: 3q^2+2q
       428: q^2+q
       430: 2q
       431: 2q^2+2q
       432: q^2+q
       433: q
       434: q
       435: q
       438: 2q
       439: 2q^2+2q
       440: q^2+q
       441: q
       442: q
       444: q^2+2q
       445: q^2+q
       446: q
       447: q^2+q
       448: 2q^2+2q
       449: 2q
       451: q
       452: q
       453: q^2+q
       454: 2q^2+2q
       455: q
       457: 2q
       459: q
       460: q
       461: q^2+2q
       463: q^2+q
       464: q
       465: 2q
       467: 2q
       469: 2q^2+2q
       470: q^2+q
       472: 2q
       473: 2q
       476: q
       478: q
       480: q
       481: 3q^2+3q
       482: 3q^2+3q
       483: 3q^2+3q
       484: q^2+3q
       485: 2q
       487: q^2+2q
       489: 2q
       491: q^2+3q
       492: 3q^2+3q
       493: 2q
       494: q^3+4q^2+3q
       495: 2q
       496: 2q
       497: 3q^2+3q
       498: q^3+4q^2+3q
       499: 2q
       500: 2q
       501: 2q
       502: 2q
       504: q^2+2q
       506: 2q
       508: q^2+3q
       509: q^2+3q
       510: q^2+3q
       511: 2q
       512: 2q
       513: 2q
       514: 2q
       515: q^2+3q
       516: 2q^2+3q
       517: q^2+3q
       518: q^2+3q
       519: 2q^2+3q
       520: q^2+3q
       521: q
       524: q
       525: q
       528: q
       529: q^2+q
       530: q^2
       531: q^3+q^2+q
       532: q^2+q
       535: q
       536: q
       539: q
       543: q
       544: q
       547: q^2+q
       548: q
       549: q
       550: q
       553: q
       557: q
       558: q
       561: q^2+q
       562: q
       567: q
       572: q
       576: q
       581: q
       583: 2q
       585: 2q
       587: q^2+2q
       589: q^2+q
       590: 2q^2+2q
       591: 2q
       594: 2q
       595: 2q^2+2q
       596: q^2+q
       597: 2q
       599: 2q^2+2q
       600: q^2+q
       601: 2q
       604: 2q
       605: q
       607: 2q^2+2q
       608: q^2+q
       609: q
       610: q
       611: q
       613: q
       614: q
       616: 2q
       617: q
       619: q^2+q
       620: 2q^2+2q
       621: 2q
       623: q
       625: q
       626: q
       627: q
       629: q
       630: q
       631: 2q
       633: q
       635: 2q
       637: 2q
       639: 2q
       642: 2q
       643: 2q
       646: q
       648: 2q
       649: 2q
       654: q
       656: q
       657: q^2+3q
       658: 2q
       660: q^2+2q
       662: 2q
       664: q^2+3q
       665: q^2+3q
       666: 2q
       668: q^2+2q
       670: 2q
       672: q^2+3q
       673: q^2+3q
       674: 2q
       675: q
       676: 3q^2+3q
       677: 2q
       678: 2q
       679: 2q
       680: 2q
       681: 3q^2+3q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+3q
       687: 2q
       688: 2q
       690: q^2+3q
       691: 2q^2+3q
       692: q^2+3q
       700: q
       705: q
       708: q
       709: q
       712: q
       713: q
       714: q
       719: q
       720: q
       723: q
       727: q
       728: q
       731: q
       735: q
       737: q
       741: q
       742: q
       745: q
       749: q
       755: q
       764: q
       767: q
       775: 2q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       786: 2q
       787: 2q
       789: 2q
       792: q
       794: 2q
       795: q
       799: q
       802: q
       806: 2q
       807: 2q^2+2q
       808: q^2+q
       809: q
       811: q
       812: q
       813: q
       816: 2q
       817: 2q
       819: q
       823: q
       825: q^2+q
       826: 2q^2+2q
       827: 2q
       831: q
       833: q
       835: q
       836: q
       837: q
       839: 2q
       841: 2q
       844: q
       846: 2q
       847: 2q
       852: q
       858: q
       859: 2q
       861: q^2+2q
       863: 2q
       865: q^2+3q
       866: q^2+3q
       867: q^2+3q
       868: q^2+3q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q
       878: q
       881: q+1
       882: q+1
       883: q+1
       896: q
       899: q
       900: q
       906: q
       910: q
       914: q
       918: q
       930: q
       931: q
       934: q
       936: q
       940: q
       948: q
       949: q
       956: q
       966: q
       977: q
       990: q
       992: 2q
       994: 2q
       996: 2q
       998: 2q
      1001: 2q
      1002: 2q
      1005: 2q
      1006: 2q
      1009: q
      1013: q
      1014: q
      1017: 2q
      1020: q
      1024: q
      1027: q
      1030: q
      1032: 2q
      1036: q
      1042: q
      1044: q
      1047: q
      1053: q
      1058: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+3q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1110: q
      1114: q
      1120: q
      1124: q
      1132: q
      1137: q
      1146: q
      1164: q
      1196: q
      1210: q+1
      1212: q+1
      1214: 2q
      1216: 2q
      1219: 2q
      1225: q
      1226: 1
      1229: 1
      1235: q
      1236: q
      1241: q
      1244: 1
      1246: 1
      1250: q
      1252: q
      1260: q
      1263: 1
      1282: q+1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1314: q
      1320: q
      1328: q
      1342: 1
      1372: 1
      1407: 1
      1412: 1
      1438: q+1
      1440: 1
      1443: 1
      1445: 1
      1452: 1
      1455: q
      1458: 1
      1460: q
      1485: 1
      1486: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1640: 1
      1643: 1
      1648: 1
      1651: 1
      1653: 1
      1679: 1
      1726: 1
      1735: 1
      1747: 1
      1761: 1
      1838: 1

1839:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q^2+2q+1
        41: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q
        61: q^2+q+1
        62: q^2+2q+1
        64: q^2+2q+1
        66: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^3+2q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: q^2+q+1
       107: q
       108: q^2+q+1
       109: q
       110: q^2+q+1
       111: q^2+2q+1
       113: q^2+2q+1
       115: q^2+2q+1
       117: q
       118: q^2+q+1
       119: q
       120: q^2+q+1
       121: q^2+2q+1
       123: q^2+2q+1
       125: q^3+2q^2+2q+1
       126: q^3+2q^2+2q+1
       127: q^2+2q+1
       129: q^2+2q+1
       131: q^2+2q+1
       133: q^3+2q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^3+2q^2+2q+1
       158: q^3+2q^2+2q+1
       159: q^3+2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       169: q
       172: q^2+q+1
       173: q
       176: q^2+q+1
       177: q^2+2q+1
       179: q^2+2q+1
       181: q^2+2q+1
       183: q
       184: q^2+q+1
       185: q
       186: q^2+q+1
       187: q^2+2q+1
       189: q^2+2q+1
       191: q
       192: q^2+q+1
       194: 1
       195: q
       196: q^2+q+1
       197: 1
       199: q
       200: q^2+q+1
       201: q
       202: q^2+q+1
       204: 1
       205: 1
       207: q^2+2q+1
       209: q+1
       211: q+1
       213: q^2+2q+1
       215: q^2+2q+1
       217: q^2+2q+1
       219: q^3+2q^2+2q+1
       220: q^3+2q^2+2q+1
       221: q^3+2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: q^2+q+1
       263: q
       266: q^2+q+1
       269: 1
       273: 1
       275: q
       278: q^2+q+1
       279: q^2+2q+1
       281: q^2+2q+1
       283: q
       284: q^2+q+1
       285: q
       286: q^2+q+1
       287: q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: q
       294: q^2+q+1
       295: q
       296: q^2+q+1
       297: q^2+2q+1
       300: 1
       301: 1
       303: q
       304: q^2+q+1
       305: 1
       307: q
       308: q^2+q+1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: 1
       322: 1
       323: 1
       325: q+1
       327: q^2+2q+1
       329: q^2+2q+1
       331: q^2+2q+1
       333: q^3+2q^2+2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: q^2+q+1
       381: q
       384: q^2+q+1
       385: q
       388: q^2+q+1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: q^2+2q+1
       411: q^2+2q+1
       413: q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: q
       420: q^2+q+1
       421: q
       422: q^2+q+1
       423: q^2+2q+1
       425: q+1
       427: q+1
       430: 1
       431: q
       432: q^2+q+1
       433: 1
       435: 1
       438: 1
       439: q
       440: q^2+q+1
       441: 1
       444: 1
       445: 1
       447: q
       448: q^2+q+1
       450: 1
       451: 1
       453: q
       454: q^2+q+1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: q^2+q+1
       525: q
       528: q^2+q+1
       529: q
       532: q^2+q+1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: q
       590: q^2+q+1
       592: 1
       594: 1
       595: q
       596: q^2+q+1
       597: q+1
       599: q+1
       601: q+1
       604: 1
       605: 1
       607: q
       608: q^2+q+1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       619: q
       620: q^2+q+1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       705: q
       708: q^2+q+1
       709: q
       712: q^2+q+1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       807: q
       808: q^2+q+1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: q^2+q+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: q+1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       896: q
       899: q^2+q+1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: 1
       938: 1
       942: 1
       946: 1
       950: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1059: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1158: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1244: 1
      1247: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1264: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1354: 1
      1358: 1
      1374: 1
      1378: 1
      1382: 1
      1404: 1
      1413: 1
      1415: 1
      1436: 1
      1438: q+1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1455: 1
      1456: 1
      1458: 1
      1461: 1
      1485: 1
      1486: 1
      1494: 1
      1530: 1
      1538: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1569: 1
      1585: 1
      1637: 1
      1639: 1
      1643: 1
      1648: 1
      1651: 1
      1654: 1
      1680: 1
      1723: 1
      1730: 1
      1736: 1
      1747: 1
      1763: 1
      1839: 1

1840:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: q^2+q+1
        61: q
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^3+2q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       104: q^2+q+1
       105: q
       107: q^2+q+1
       108: q
       109: q
       110: q^2+q+1
       112: q^2+2q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q
       118: q^2+q+1
       119: q^2+q+1
       120: q
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+2q^2+2q+1
       126: q^3+2q^2+2q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: q^3+2q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^3+2q^2+2q+1
       158: q^3+2q^2+2q+1
       159: q^3+2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: q^2+q+1
       171: q
       174: q^2+q+1
       175: q
       178: q^2+2q+1
       180: q^2+2q+1
       182: q^2+2q+1
       183: q^2+q+1
       184: q
       185: q
       186: q^2+q+1
       188: q^2+2q+1
       190: q^2+2q+1
       191: q
       192: q^2+q+1
       193: 1
       195: q
       196: q^2+q+1
       198: 1
       199: q^2+q+1
       200: q
       201: q^2+q+1
       202: q
       204: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q^2+2q+1
       216: q^2+2q+1
       218: q^2+2q+1
       219: q^3+2q^2+2q+1
       220: q^3+2q^2+2q+1
       221: q^3+2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^2+q+1
       261: q
       264: q^2+q+1
       265: q
       268: 1
       274: 1
       276: q^2+q+1
       277: q
       280: q^2+2q+1
       282: q^2+2q+1
       283: q^2+q+1
       284: q
       285: q
       286: q^2+q+1
       288: q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: q^2+q+1
       294: q
       295: q
       296: q^2+q+1
       298: q^2+2q+1
       299: 1
       302: 1
       303: q
       304: q^2+q+1
       306: 1
       307: q^2+q+1
       308: q
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: 1
       322: 1
       324: 1
       326: q+1
       328: q^2+2q+1
       330: q^2+2q+1
       332: q^2+2q+1
       333: q^3+2q^2+2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q^2+q+1
       379: q
       382: q^2+q+1
       383: q
       386: q^2+q+1
       387: q
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: q^2+2q+1
       412: q^2+2q+1
       414: q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: q^2+q+1
       420: q
       421: q
       422: q^2+q+1
       424: q^2+2q+1
       426: q+1
       428: q+1
       429: 1
       431: q
       432: q^2+q+1
       434: 1
       436: 1
       437: 1
       439: q
       440: q^2+q+1
       442: 1
       443: 1
       446: 1
       447: q^2+q+1
       448: q
       450: 1
       452: 1
       453: q^2+q+1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q^2+q+1
       523: q
       526: q^2+q+1
       527: q
       530: q^2+q+1
       531: q
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: q^2+q+1
       590: q
       592: 1
       593: 1
       595: q
       596: q^2+q+1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       606: 1
       607: q
       608: q^2+q+1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q^2+q+1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       699: 1
       706: q^2+q+1
       707: q
       710: q^2+q+1
       711: q
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       807: q
       808: q^2+q+1
       810: 1
       812: 1
       814: 1
       815: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: q^2+q+1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       890: 1
       897: q^2+q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: 1
       939: 1
       943: 1
       947: 1
       951: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1059: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1157: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1245: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1263: 1
      1265: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1353: 1
      1357: 1
      1375: 1
      1379: 1
      1383: 1
      1408: 1
      1411: 1
      1416: 1
      1437: 1
      1439: q+1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1454: 1
      1457: 1
      1459: 1
      1461: 1
      1485: 1
      1486: 1
      1495: 1
      1531: 1
      1539: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1568: 1
      1586: 1
      1638: 1
      1640: 1
      1644: 1
      1647: 1
      1652: 1
      1654: 1
      1681: 1
      1727: 1
      1731: 1
      1734: 1
      1746: 1
      1764: 1
      1840: 1

1841:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        38: q^2+2q+1
        40: q^2+2q+1
        42: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        63: q^2+2q+1
        65: q^2+2q+1
        67: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: q^2+2q+1
        77: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^3+2q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: q^2+q+1
       107: q
       108: q^2+q+1
       109: q^2+q+1
       110: q
       112: q^2+2q+1
       114: q^2+2q+1
       116: q^2+2q+1
       117: q^2+q+1
       118: q
       119: q
       120: q^2+q+1
       122: q^2+2q+1
       124: q^2+2q+1
       125: q^3+2q^2+2q+1
       126: q^3+2q^2+2q+1
       128: q^2+2q+1
       130: q^2+2q+1
       132: q^2+2q+1
       133: q^3+2q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^3+2q^2+2q+1
       158: q^3+2q^2+2q+1
       159: q^3+2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q+1
       170: q
       171: q^2+q+1
       174: q
       175: q^2+q+1
       178: q^2+2q+1
       180: q^2+2q+1
       182: q^2+2q+1
       183: q
       184: q^2+q+1
       185: q^2+q+1
       186: q
       188: q^2+2q+1
       190: q^2+2q+1
       191: q^2+q+1
       192: q
       194: 1
       195: q^2+q+1
       196: q
       198: 1
       199: q
       200: q^2+q+1
       201: q
       202: q^2+q+1
       203: 1
       206: 1
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q^2+2q+1
       216: q^2+2q+1
       218: q^2+2q+1
       219: q^3+2q^2+2q+1
       220: q^3+2q^2+2q+1
       221: q^3+2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q^2+q+1
       264: q
       265: q^2+q+1
       270: 1
       272: 1
       276: q
       277: q^2+q+1
       280: q^2+2q+1
       282: q^2+2q+1
       283: q
       284: q^2+q+1
       285: q^2+q+1
       286: q
       288: q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: q
       294: q^2+q+1
       295: q^2+q+1
       296: q
       298: q^2+2q+1
       300: 1
       302: 1
       303: q^2+q+1
       304: q
       306: 1
       307: q
       308: q^2+q+1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: 1
       321: 1
       324: 1
       326: q+1
       328: q^2+2q+1
       330: q^2+2q+1
       332: q^2+2q+1
       333: q^3+2q^2+2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: 1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: q^2+q+1
       382: q
       383: q^2+q+1
       386: q
       387: q^2+q+1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: q^2+2q+1
       412: q^2+2q+1
       414: q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: q
       420: q^2+q+1
       421: q^2+q+1
       422: q
       424: q^2+2q+1
       426: q+1
       428: q+1
       430: 1
       431: q^2+q+1
       432: q
       434: 1
       436: 1
       438: 1
       439: q^2+q+1
       440: q
       442: 1
       444: 1
       446: 1
       447: q
       448: q^2+q+1
       449: 1
       452: 1
       453: q
       454: q^2+q+1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+2q+1
       493: 1
       494: q^2+2q+1
       495: 1
       496: 1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: q^2+q+1
       526: q
       527: q^2+q+1
       530: q
       531: q^2+q+1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       584: q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: q
       590: q^2+q+1
       591: 1
       594: 1
       595: q^2+q+1
       596: q
       598: q+1
       600: q+1
       602: q+1
       604: 1
       606: 1
       607: q^2+q+1
       608: q
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       619: q
       620: q^2+q+1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q^2+2q+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+2q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: 1
       688: 1
       690: q+1
       691: q+1
       692: q+1
       700: 1
       706: q
       707: q^2+q+1
       710: q
       711: q^2+q+1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q^2+q+1
       808: q
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: q^2+q+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: q+1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       881: q+1
       882: q+1
       883: q+1
       891: 1
       897: q
       898: q^2+q+1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: 1
       937: 1
       941: 1
       945: 1
       949: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1058: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1229: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1263: 1
      1265: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1355: 1
      1359: 1
      1373: 1
      1377: 1
      1381: 1
      1408: 1
      1412: 1
      1417: 1
      1437: 1
      1439: q+1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1455: 1
      1457: 1
      1459: 1
      1460: 1
      1485: 1
      1486: 1
      1496: 1
      1532: 1
      1540: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1570: 1
      1584: 1
      1638: 1
      1640: 1
      1644: 1
      1648: 1
      1652: 1
      1653: 1
      1682: 1
      1727: 1
      1732: 1
      1735: 1
      1748: 1
      1762: 1
      1841: 1

1842:    0: 2q^4+7q^3+8q^2+3q
         1: 2q^4+7q^3+8q^2+3q
         2: 3q^4+5q^3+7q^2+3q
         3: 2q^4+7q^3+8q^2+3q
         4: 2q^4+7q^3+8q^2+3q
         5: 2q^4+7q^3+8q^2+3q
         6: 2q^4+7q^3+8q^2+3q
         7: 3q^4+5q^3+7q^2+3q
         8: q^5+5q^4+6q^3+7q^2+3q
         9: 3q^4+5q^3+7q^2+3q
        10: 2q^4+7q^3+8q^2+3q
        11: 2q^4+7q^3+8q^2+3q
        12: 2q^4+7q^3+8q^2+3q
        13: q^4+4q^3+7q^2+3q
        14: q^4+4q^3+7q^2+3q
        15: 2q^4+5q^3+7q^2+3q
        16: 2q^4+7q^3+8q^2+3q
        17: 2q^4+7q^3+8q^2+3q
        18: 3q^4+5q^3+7q^2+3q
        19: 2q^4+7q^3+8q^2+3q
        20: 2q^4+7q^3+8q^2+3q
        21: 3q^4+5q^3+7q^2+3q
        22: 3q^3+7q^2+3q
        23: 3q^3+7q^2+3q
        24: q^4+3q^3+6q^2+3q
        25: 3q^3+7q^2+3q
        26: 3q^3+7q^2+3q
        27: q^4+3q^3+6q^2+3q
        28: 2q^4+7q^3+8q^2+3q
        29: 2q^4+7q^3+8q^2+3q
        30: q^4+4q^3+7q^2+3q
        31: 3q^3+7q^2+3q
        32: 2q^3+6q^2+3q
        33: 3q^3+7q^2+3q
        34: 3q^3+7q^2+3q
        35: 2q^3+6q^2+3q
        36: 3q^3+7q^2+3q
        37: q^3+2q^2+q
        38: 4q^2+2q
        39: q^3+2q^2+q
        40: 4q^2+2q
        41: q^3+2q^2+q
        42: q^3+3q^2+2q
        43: q^4+4q^3+7q^2+3q
        44: q^4+4q^3+7q^2+3q
        45: 2q^4+5q^3+7q^2+3q
        46: q^4+4q^3+7q^2+3q
        47: 2q^4+5q^3+7q^2+3q
        48: q^4+4q^3+7q^2+3q
        49: 2q^4+7q^3+8q^2+3q
        50: 2q^4+7q^3+8q^2+3q
        51: 3q^4+5q^3+7q^2+3q
        52: 3q^3+7q^2+3q
        53: 3q^3+7q^2+3q
        54: q^4+3q^3+6q^2+3q
        55: 3q^3+7q^2+3q
        56: 3q^3+7q^2+3q
        57: q^4+3q^3+6q^2+3q
        58: q^3+3q^2+q
        59: 2q^3+4q^2+2q
        60: q^3+3q^2+q
        61: 2q^3+4q^2+2q
        62: q^3+2q^2+q
        63: 4q^2+2q
        64: q^3+2q^2+q
        65: 3q^2+2q
        66: q^3+2q^2+q
        67: 4q^2+2q
        68: q^4+2q^3+6q^2+3q
        69: q^4+4q^3+7q^2+3q
        70: q^4+4q^3+7q^2+3q
        71: 2q^4+7q^3+8q^2+3q
        72: 3q^3+7q^2+3q
        73: 3q^3+7q^2+3q
        74: q^3+2q^2+q
        75: 4q^2+2q
        76: q^3+2q^2+q
        77: 4q^2+2q
        78: q^3+2q^2+q
        79: q^3+3q^2+2q
        80: 2q^3+6q^2+3q
        81: 2q^3+6q^2+3q
        82: 3q^3+7q^2+3q
        83: 2q^3+6q^2+3q
        84: 2q^3+6q^2+3q
        85: 2q^3+6q^2+3q
        86: 3q^3+7q^2+3q
        87: 2q^3+6q^2+3q
        88: q^4+4q^3+7q^2+3q
        89: 2q^4+5q^3+7q^2+3q
        90: q^4+4q^3+7q^2+3q
        91: q^4+4q^3+7q^2+3q
        92: 2q^4+5q^3+7q^2+3q
        93: q^4+4q^3+7q^2+3q
        94: 3q^3+7q^2+3q
        95: 3q^3+7q^2+3q
        96: q^4+3q^3+6q^2+3q
        97: 3q^3+7q^2+3q
        98: 3q^3+7q^2+3q
        99: q^4+3q^3+6q^2+3q
       100: 4q^2+3q
       101: 4q^2+3q
       102: 3q^2+3q
       103: q^2
       104: 2q^2+q
       105: 2q^2+q
       106: q^3+q^2+q
       107: q^3+3q^2+q
       108: 2q^3+4q^2+2q
       109: q^3+3q^2+q
       110: 2q^3+4q^2+2q
       111: q^3+2q^2+q
       112: 4q^2+2q
       113: q^3+2q^2+q
       114: 4q^2+2q
       115: q^3+2q^2+q
       116: 3q^2+2q
       117: 2q^2+q
       118: q^3+3q^2+2q
       119: 2q^2+q
       120: q^3+3q^2+2q
       121: q^3+2q^2+q
       122: 3q^2+2q
       123: q^3+2q^2+q
       124: 3q^2+2q
       125: q^4+2q^3+6q^2+3q
       126: q^4+4q^3+7q^2+3q
       127: q^3+2q^2+q
       128: 4q^2+2q
       129: q^3+2q^2+q
       130: 4q^2+2q
       131: q^3+2q^2+q
       132: q^3+3q^2+2q
       133: q^4+2q^3+6q^2+3q
       134: q^4+4q^3+7q^2+3q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 2q^3+6q^2+3q
       138: 2q^3+6q^2+3q
       139: 3q^3+7q^2+3q
       140: q^2+2q
       141: 2q^3+6q^2+3q
       142: 3q^3+7q^2+3q
       143: 2q^3+6q^2+3q
       144: 2q^3+6q^2+3q
       145: 3q^3+7q^2+3q
       146: 2q^3+6q^2+3q
       147: 3q^3+7q^2+3q
       148: q^2+2q
       149: 4q^2+3q
       150: 3q^2+3q
       151: q^2+q
       152: 3q^2+2q
       153: q^2+q
       154: 3q^2+2q
       155: q^2+q
       156: 2q^2+2q
       157: q^4+4q^3+7q^2+3q
       158: 2q^4+5q^3+7q^2+3q
       159: q^4+4q^3+7q^2+3q
       160: q^3+4q^2+3q
       161: q^3+4q^2+3q
       162: q^3+4q^2+3q
       163: q^3+4q^2+3q
       164: q^3+4q^2+3q
       165: q^3+4q^2+3q
       166: 4q^2+3q
       167: 4q^2+3q
       168: 3q^2+3q
       169: q^2
       170: 2q^2+q
       171: 2q^2+q
       172: q^3+q^2+q
       173: q^2
       174: q^2+q
       175: q^2+q
       176: q^3+q^2+q
       177: q^3+2q^2+q
       178: 3q^2+2q
       179: q^3+2q^2+q
       180: 4q^2+2q
       181: q^3+2q^2+q
       182: 4q^2+2q
       183: 2q^2+q
       184: q^3+3q^2+2q
       185: 2q^2+q
       186: q^3+3q^2+2q
       187: q^3+2q^2+q
       188: 3q^2+2q
       189: q^3+2q^2+q
       190: 3q^2+2q
       191: 2q^2+q
       192: q^3+3q^2+2q
       194: q^2+2q
       195: q^3+3q^2+q
       196: 2q^3+4q^2+2q
       197: q
       198: q^2+q
       199: 2q^2+q
       200: q^3+3q^2+2q
       201: q^3+3q^2+q
       202: 2q^3+4q^2+2q
       204: q^2+2q
       205: q
       206: q^2+q
       207: q^3+2q^2+q
       208: 3q^2+2q
       209: q^2+q
       210: 3q^2+2q
       211: q^2+q
       212: 2q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: q^4+2q^3+6q^2+3q
       220: q^4+2q^3+6q^2+3q
       221: q^4+4q^3+7q^2+3q
       222: 2q^3+6q^2+3q
       223: 2q^3+6q^2+3q
       224: 2q^3+6q^2+3q
       225: 2q^3+6q^2+3q
       226: 2q^3+6q^2+3q
       227: 3q^2+3q
       228: q^3+4q^2+3q
       229: 2q
       230: q^3+4q^2+3q
       231: 2q^3+6q^2+3q
       232: 3q^2+3q
       233: q^3+4q^2+3q
       234: q^3+4q^2+3q
       235: 2q
       236: 3q^2+3q
       237: q^2+q
       238: 3q^2+2q
       239: q^2+q
       240: 3q^2+2q
       241: q^2+q
       242: 2q^2+2q
       243: 4q^2+3q
       244: q^2+2q
       245: q^2+2q
       246: 3q^2+3q
       247: 4q^2+3q
       248: 4q^2+3q
       249: 3q^2+3q
       250: q^3+4q^2+3q
       251: q^3+4q^2+3q
       252: q^3+4q^2+3q
       253: q^3+4q^2+3q
       254: q^3+4q^2+3q
       255: q^3+4q^2+3q
       256: q^2+3q
       257: 2q^2+3q
       258: q^2+3q
       259: q^2
       260: 2q^2+q
       261: 2q^2+q
       262: q^3+q^2+q
       263: q^2
       264: q^2+q
       265: q^2+q
       266: q^3+q^2+q
       269: q
       270: q^2+q
       273: q
       274: q^2+q
       275: q^2
       276: q^2+q
       277: q^2+q
       278: q^3+q^2+q
       280: 2q
       282: q^2+2q
       283: 2q^2+q
       284: q^3+3q^2+2q
       285: 2q^2+q
       286: q^3+3q^2+2q
       287: q^3+2q^2+q
       288: 3q^2+2q
       290: q^2+2q
       291: q^3+2q^2+q
       292: 3q^2+2q
       293: 2q^2+q
       294: q^3+3q^2+2q
       295: 2q^2+q
       296: q^3+3q^2+2q
       297: q^3+2q^2+q
       298: 3q^2+2q
       300: 2q
       301: q
       302: q^2+q
       303: q^2+q
       304: 2q^2+2q
       305: q
       306: q
       307: q^2+q
       308: 2q^2+2q
       310: 2q
       311: q
       312: q^2+q
       313: q
       314: q
       315: q^2+q
       316: 2q^2+2q
       317: q^2+q
       318: 3q^2+2q
       320: q^2+2q
       322: q^2+2q
       323: q
       325: q^2+q
       326: 2q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: q^4+2q^3+6q^2+3q
       334: 2q^3+6q^2+3q
       335: 2q^3+6q^2+3q
       336: 3q^2+3q
       337: 4q^2+3q
       338: q^2+q
       339: 3q^2+2q
       340: q^2+q
       341: 3q^2+2q
       342: q^2+q
       343: 2q^2+2q
       344: 3q^2+3q
       345: 3q^2+3q
       346: q^3+4q^2+3q
       347: 2q
       348: 2q
       349: q^3+4q^2+3q
       350: q^3+4q^2+3q
       351: q^2+2q
       352: 3q^2+3q
       353: 3q^2+3q
       354: q^3+4q^2+3q
       355: q^3+4q^2+3q
       356: q^3+4q^2+3q
       357: 2q
       358: 2q
       359: q^2+2q
       361: 2q
       363: q^2+2q
       365: 2q
       366: 3q^2+3q
       367: q^2+3q
       368: q^2+3q
       369: 2q
       370: 2q
       371: q^2+3q
       372: 2q^2+3q
       373: q^2+3q
       374: q^2+3q
       375: 2q^2+3q
       376: q^2+3q
       377: q^2
       378: q^2+q
       379: q^2+q
       380: q^3+q^2+q
       382: q
       383: q
       385: q^2
       386: q^2+q
       387: q^2+q
       388: q^3+q^2+q
       391: q
       392: q^2+q
       395: q
       396: q
       399: q
       400: q^2+q
       403: q
       404: q
       406: q
       410: 2q
       412: q^2+2q
       414: 2q
       416: q^2+2q
       418: q^2+2q
       419: 2q^2+q
       420: q^3+3q^2+2q
       421: 2q^2+q
       422: q^3+3q^2+2q
       423: q^3+2q^2+q
       424: 3q^2+2q
       425: q^2+q
       426: 2q^2+2q
       427: q^2+q
       428: 3q^2+2q
       430: 2q
       431: q^2+q
       432: 2q^2+2q
       433: q
       434: q
       436: q
       438: 2q
       439: q^2+q
       440: 2q^2+2q
       441: q
       442: q
       444: q^2+2q
       445: q
       446: q^2+q
       447: q^2+q
       448: 2q^2+2q
       450: 2q
       451: q
       452: q
       453: q^2+q
       454: 2q^2+2q
       456: q
       458: 2q
       459: q
       460: q
       462: q^2+2q
       463: q
       464: q^2+q
       466: 2q
       468: 2q
       469: q^2+q
       470: 2q^2+2q
       472: 2q
       474: 2q
       475: q
       477: q
       479: q
       481: 3q^2+3q
       482: 3q^2+3q
       483: 3q^2+3q
       484: q^2+3q
       486: 2q
       488: q^2+2q
       490: 2q
       491: q^2+3q
       492: 3q^2+3q
       493: 2q
       494: q^3+4q^2+3q
       495: 2q
       496: 2q
       497: 3q^2+3q
       498: q^3+4q^2+3q
       499: 2q
       500: 2q
       501: 2q
       503: 2q
       505: q^2+2q
       507: 2q
       508: q^2+3q
       509: q^2+3q
       510: q^2+3q
       511: 2q
       512: 2q
       513: 2q
       514: 2q
       515: q^2+3q
       516: 2q^2+3q
       517: q^2+3q
       518: q^2+3q
       519: 2q^2+3q
       520: q^2+3q
       522: q
       523: q
       526: q
       527: q
       529: q^2
       530: q^2+q
       531: q^2+q
       532: q^3+q^2+q
       535: q
       536: q
       540: q
       543: q
       544: q
       547: q
       548: q^2+q
       551: q
       552: q
       556: q
       559: q
       560: q
       563: q
       564: q^2+q
       568: q
       570: q
       575: q
       577: q
       584: 2q
       586: 2q
       588: q^2+2q
       589: q^2+q
       590: 2q^2+2q
       592: 2q
       594: 2q
       595: q^2+q
       596: 2q^2+2q
       598: 2q
       599: q^2+q
       600: 2q^2+2q
       602: 2q
       604: 2q
       606: q
       607: q^2+q
       608: 2q^2+2q
       609: q
       610: q
       612: q
       613: q
       614: q
       616: 2q
       618: q
       619: q^2+q
       620: 2q^2+2q
       622: 2q
       624: q
       625: q
       626: q
       628: q
       629: q
       630: q
       632: 2q
       634: q
       636: 2q
       638: 2q
       640: 2q
       642: 2q
       644: 2q
       645: q
       648: 2q
       650: 2q
       653: q
       655: q
       657: q^2+3q
       659: 2q
       661: q^2+2q
       663: 2q
       664: q^2+3q
       665: q^2+3q
       667: 2q
       669: q^2+2q
       671: 2q
       672: q^2+3q
       673: q^2+3q
       674: 2q
       675: q
       676: 3q^2+3q
       677: 2q
       678: 2q
       679: 2q
       680: 2q
       681: 3q^2+3q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+3q
       687: 2q
       688: 2q
       690: q^2+3q
       691: 2q^2+3q
       692: q^2+3q
       697: q
       706: q
       707: q
       710: q
       711: q
       715: q
       716: q
       719: q
       720: q
       724: q
       727: q
       728: q
       732: q
       736: q
       740: q
       743: q
       744: q
       748: q
       752: q
       756: q
       762: q
       768: q
       776: 2q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       786: 2q
       788: 2q
       790: 2q
       791: q
       794: 2q
       796: q
       800: q
       802: q
       806: 2q
       807: q^2+q
       808: 2q^2+2q
       810: q
       811: q
       812: q
       814: q
       816: 2q
       818: 2q
       820: q
       824: q
       825: q^2+q
       826: 2q^2+2q
       828: 2q
       832: q
       834: q
       835: q
       836: q
       838: q
       840: 2q
       842: 2q
       843: q
       846: 2q
       848: 2q
       851: q
       857: q
       860: 2q
       862: q^2+2q
       864: 2q
       865: q^2+3q
       866: q^2+3q
       867: q^2+3q
       868: q^2+3q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q
       878: q
       881: q+1
       882: q+1
       883: q+1
       897: q
       898: q
       903: q
       907: q
       911: q
       915: q
       919: q
       930: q
       931: q
       935: q
       939: q
       943: q
       950: q
       951: q
       959: q
       967: q
       975: q
       991: q
       993: 2q
       995: 2q
       997: 2q
       999: 2q
      1001: 2q
      1003: 2q
      1005: 2q
      1007: 2q
      1008: q
      1012: q
      1015: q
      1017: 2q
      1021: q
      1025: q
      1027: q
      1031: q
      1033: 2q
      1037: q
      1043: q
      1045: q
      1046: q
      1053: q
      1059: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+3q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1113: q
      1117: q
      1121: q
      1125: q
      1133: q
      1135: q
      1147: q
      1167: q
      1197: q
      1211: q+1
      1213: q+1
      1215: 2q
      1217: 2q
      1219: 2q
      1224: q
      1227: 1
      1229: 1
      1235: q
      1237: q
      1241: q
      1245: 1
      1247: 1
      1251: q
      1253: q
      1261: q
      1262: 1
      1282: q+1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1317: q
      1321: q
      1329: q
      1343: 1
      1375: 1
      1405: 1
      1413: 1
      1439: q+1
      1441: 1
      1443: 1
      1444: 1
      1453: 1
      1455: q
      1459: 1
      1461: q
      1485: 1
      1486: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1639: 1
      1644: 1
      1648: 1
      1652: 1
      1654: 1
      1683: 1
      1724: 1
      1736: 1
      1748: 1
      1764: 1
      1842: 1

1843:    0: q^4+2q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
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        31: 2q^2+q
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        55: q^3+2q^2+q
        56: q^3+2q^2+q
        57: q^3+2q^2+q
        58: q^2
        59: q^2+q
        60: q^2
        61: q^2+q
        62: 2q^2+q
        64: q^3+2q^2+q
        66: q^3+2q^2+q
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        80: 2q^2+q
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        84: 2q^2+q
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        86: 2q^2+q
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       465: q^2+q
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       481: 2q^2+q
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       568: q
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       583: q^2+q
       585: 2q^2+q
       587: q^2+q
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       590: q^2+q
       592: q
       594: q
       595: q^2
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       599: q^2+q
       601: q^2+q
       604: q
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       613: q
       616: q
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       619: q^2
       620: q
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       632: q
       633: q
       639: q^2+q
       642: q
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       657: q^2+q
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       664: q^2+q
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       674: q
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       677: q
       679: q
       680: q
       681: q^2+q
       682: q
       683: q
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       697: q
       705: q^2
       708: q
       709: q^2
       712: q^2+q
       716: q
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       735: q
       739: q
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       751: q
       756: q
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       768: q
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       786: q
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       802: q
       806: q
       807: q^2
       808: q
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       821: q
       825: q^2
       826: q
       828: q
       832: q
       833: q
       835: q
       843: q
       849: q
       853: 1
       866: q^2+q
       870: q
       871: q
       874: q
       875: q
       889: q
       896: q^2
       899: q
       902: q
       906: q
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       922: q
       930: q
       942: q
       946: q
       950: q
       961: q
       967: q
       968: q
       979: 1
       984: 1
       994: q^2+q
       999: q
      1001: q
      1010: q
      1012: q
      1020: q
      1022: q
      1027: q
      1036: q
      1038: q
      1045: q
      1050: 1
      1076: q
      1080: q
      1091: q
      1107: 1
      1116: q
      1124: q
      1127: q
      1133: q
      1138: q
      1158: q
      1174: q
      1185: 1
      1190: 1
      1222: 1
      1230: q
      1235: q
      1248: q
      1251: q
      1264: 1
      1295: q
      1311: 1
      1323: 1
      1336: 1
      1358: q
      1382: q
      1406: 1
      1415: 1
      1446: 1
      1498: 1
      1534: 1
      1555: 1
      1560: 1
      1637: 1
      1684: 1
      1725: 1
      1730: 1
      1843: 1

1844:    0: q^4+2q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
         2: q^4+2q^3+2q^2+q
         3: q^4+2q^3+2q^2+q
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         5: q^4+2q^3+2q^2+q
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         7: q^4+2q^3+2q^2+q
         8: q^4+2q^3+2q^2+q
         9: q^4+2q^3+2q^2+q
        10: q^3+2q^2+q
        11: q^3+2q^2+q
        12: q^3+2q^2+q
        13: q^4+2q^3+2q^2+q
        14: q^4+2q^3+2q^2+q
        15: q^4+2q^3+2q^2+q
        16: q^4+2q^3+2q^2+q
        17: q^4+2q^3+2q^2+q
        18: q^4+2q^3+2q^2+q
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        30: q^4+2q^3+2q^2+q
        31: 2q^2+q
        32: q^3+2q^2+q
        33: q^3+2q^2+q
        34: 2q^2+q
        35: q^3+2q^2+q
        36: q^3+2q^2+q
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        40: q^3+2q^2+q
        42: q^3+2q^2+q
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        44: q^3+2q^2+q
        45: q^3+2q^2+q
        46: q^4+2q^3+2q^2+q
        47: q^4+2q^3+2q^2+q
        48: q^4+2q^3+2q^2+q
        49: q^4+2q^3+2q^2+q
        50: q^4+2q^3+2q^2+q
        51: q^4+2q^3+2q^2+q
        52: q^3+2q^2+q
        53: q^3+2q^2+q
        54: q^3+2q^2+q
        55: q^3+2q^2+q
        56: q^3+2q^2+q
        57: q^3+2q^2+q
        58: q^2
        59: q^2+q
        60: q^2+q
        61: q^2
        63: 2q^2+q
        65: q^3+2q^2+q
        67: q^3+2q^2+q
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        69: q^4+2q^3+2q^2+q
        70: q^3+2q^2+q
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        80: 2q^2+q
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        82: 2q^2+q
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        84: 2q^2+q
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        86: 2q^2+q
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        90: q^3+2q^2+q
        91: q^4+2q^3+2q^2+q
        92: q^4+2q^3+2q^2+q
        93: q^4+2q^3+2q^2+q
        94: q^3+2q^2+q
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        98: q^3+2q^2+q
        99: q^3+2q^2+q
       100: q^2+q
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       105: q^2
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       140: q
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       145: 2q^2+q
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       148: q
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       166: q^2+q
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       170: q^2+q
       171: q^2
       174: q^2+q
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       826: q^2
       828: q
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       850: q
       854: 1
       866: q^2+q
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       898: q^2
       903: q
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       951: q
       962: q
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       972: q
       980: 1
       987: 1
       995: q^2+q
       999: q
      1000: q
      1011: q
      1013: q
      1021: q
      1023: q
      1026: q
      1037: q
      1039: q
      1045: q
      1051: 1
      1076: q
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      1092: q
      1108: 1
      1117: q
      1123: q
      1128: q
      1131: q
      1142: q
      1157: q
      1175: q
      1186: 1
      1193: 1
      1223: 1
      1231: q
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      1249: q
      1251: q
      1265: 1
      1296: q
      1312: 1
      1324: 1
      1339: 1
      1357: q
      1383: q
      1409: 1
      1416: 1
      1447: 1
      1499: 1
      1535: 1
      1558: 1
      1561: 1
      1638: 1
      1685: 1
      1728: 1
      1731: 1
      1844: 1

1845:    0: q^4+2q^3+2q^2+q
         1: q^4+2q^3+2q^2+q
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       295: q^2+q
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       382: q^2
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       604: q
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       619: q^2
       620: q
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       782: q^2+q
       786: q
       787: q
       792: q
       794: q
       796: q
       798: q
       802: q
       806: q
       807: q
       808: q^2
       810: q
       812: q
       817: q
       820: q
       822: q
       825: q^2
       826: q
       827: q
       831: q
       834: q
       836: q
       844: q
       850: q
       854: 1
       866: q^2+q
       870: q
       871: q
       874: q
       875: q
       891: q
       897: q^2
       898: q
       901: q
       907: q
       910: q
       919: q
       923: q
       931: q
       941: q
       945: q
       949: q
       963: q
       966: q
       972: q
       981: 1
       987: 1
       995: q^2+q
       998: q
      1001: q
      1011: q
      1013: q
      1021: q
      1023: q
      1027: q
      1037: q
      1039: q
      1044: q
      1051: 1
      1076: q
      1080: q
      1093: q
      1109: 1
      1115: q
      1125: q
      1129: q
      1132: q
      1142: q
      1159: q
      1173: q
      1187: 1
      1193: 1
      1223: 1
      1231: q
      1235: q
      1249: q
      1250: q
      1265: 1
      1297: q
      1313: 1
      1325: 1
      1339: 1
      1359: q
      1381: q
      1409: 1
      1417: 1
      1447: 1
      1500: 1
      1536: 1
      1558: 1
      1562: 1
      1638: 1
      1686: 1
      1728: 1
      1732: 1
      1845: 1

1846:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: q^2+2q+1
        61: q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       106: q
       107: q^2+2q+1
       108: q
       109: 2q^2+2q+1
       110: q^2+q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: 2q^2+2q+1
       118: q^2+q
       119: q^2+2q+1
       120: q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+2q+1
       184: q
       185: 2q^2+2q+1
       186: q^2+q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: 2q^2+2q+1
       192: q^2+q
       193: q^2+2q+1
       194: q
       195: 2q^2+2q+1
       196: q^2+q
       197: q^2+3q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       203: q+1
       205: q+1
       207: q^2+3q+1
       209: 2q^2+3q+1
       211: 2q^2+3q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q^2+2q+1
       269: q
       271: q+1
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q+1
       285: q^2+q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+2q+1
       294: q
       295: 2q^2+2q+1
       296: q^2+q
       297: q^2+3q+1
       299: q^2+2q+1
       300: q
       301: 3q+1
       303: 2q^2+2q+1
       304: q^2+q
       305: q^2+3q+1
       307: 2q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: 2q+1
       317: 3q+1
       319: 2q+1
       320: q
       321: q+1
       323: q+1
       325: 2q^2+3q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: q^2+3q+1
       348: 2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 3q+1
       362: 3q+1
       364: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 3q+1
       370: q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: 2q+1
       391: q
       393: q^2+2q+1
       396: q
       397: q+1
       401: q+1
       405: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q+1
       421: q^2+q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: q+1
       431: q^2+q+1
       433: 2q+1
       435: 3q+1
       437: q^2+2q+1
       438: q
       439: 2q^2+2q+1
       440: q^2+q
       441: q^2+3q+1
       443: 2q+1
       444: q
       445: 3q+1
       447: q+1
       449: 1
       451: 1
       453: 2q+1
       454: q
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 3q+1
       467: 2q+1
       469: 2q+1
       471: 2q+1
       472: q
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: 3q+1
       485: 3q+1
       487: 3q+1
       489: q^2+2q+1
       491: 2q+1
       492: 2q^2+2q+1
       493: 2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       502: 3q+1
       504: 3q+1
       506: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: 2q+1
       513: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: q+1
       537: 2q+1
       539: q
       541: q^2+2q+1
       543: q
       545: 2q+1
       547: q
       549: 1
       553: q+1
       557: q+1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q+1
       591: 1
       593: q+1
       595: q^2+q+1
       597: 2q+1
       599: 2q+1
       601: 3q+1
       603: q+1
       605: 2q+1
       607: q^2+q+1
       609: 2q+1
       611: 3q+1
       613: 2q+1
       615: 2q+1
       616: q
       617: 3q+1
       619: q+1
       621: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: q+1
       633: q+1
       635: 3q+1
       637: 2q+1
       639: 2q+1
       641: q+1
       643: 1
       645: 1
       647: 2q+1
       648: q
       649: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q+1
       666: 3q+1
       668: 3q+1
       670: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: q+1
       675: 2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       705: q+1
       709: q+1
       713: 1
       717: q+1
       721: q+1
       725: q+1
       729: 2q+1
       731: q
       733: 2q+1
       735: q
       737: 1
       741: 1
       745: q+1
       749: q+1
       753: 1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       785: q+1
       787: 1
       789: 3q+1
       791: 1
       793: 1
       795: q+1
       797: 2q+1
       799: 2q+1
       801: q+1
       803: 1
       805: q+1
       807: q^2+q+1
       809: 2q+1
       811: 2q+1
       813: 3q+1
       815: 2q+1
       816: q
       817: 1
       819: 1
       821: 1
       823: 1
       825: q+1
       827: 1
       831: 1
       833: 1
       835: 1
       837: q+1
       839: q+1
       841: 2q+1
       843: 1
       845: q+1
       847: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       896: q+1
       900: 1
       904: q+1
       908: 1
       912: q+1
       916: 1
       920: q+1
       924: 1
       928: q+1
       932: 2q+1
       934: q
       936: 1
       940: 1
       944: 1
       948: 1
       956: q+1
       960: 1
       964: 1
       968: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 2q+1
      1004: q+1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: 1
      1018: 2q+1
      1020: q+1
      1022: 2q+1
      1024: 2q+1
      1026: q+1
      1028: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: q+1
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: q+1
      1110: 1
      1114: 1
      1118: q+1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: q+1
      1152: 1
      1156: q+1
      1160: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1202: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1228: 1
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 2q+1
      1240: q+1
      1242: 1
      1244: 1
      1246: 1
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1344: 1
      1348: 1
      1352: q+1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1372: 1
      1376: 1
      1404: 1
      1410: 1
      1414: 1
      1418: 1
      1430: 1
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1450: 1
      1452: q+1
      1454: 1
      1458: 1
      1470: 1
      1472: 1
      1474: 1
      1478: 1
      1480: 1
      1482: 1
      1485: 1
      1488: 1
      1489: 1
      1501: 1
      1525: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1603: 1
      1631: 1
      1643: 1
      1645: 1
      1647: 1
      1667: 1
      1669: 1
      1671: 1
      1675: 1
      1687: 1
      1737: 1
      1745: 1
      1749: 1
      1753: 1
      1801: 1
      1846: 1

1847:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 2q^4+7q^3+6q^2+3q
        23: 2q^4+7q^3+6q^2+3q
        24: 2q^4+7q^3+6q^2+3q
        25: 4q^3+5q^2+3q
        26: 4q^3+5q^2+3q
        27: 4q^3+5q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 2q^4+7q^3+6q^2+3q
        32: 2q^4+7q^3+6q^2+3q
        33: 3q^3+5q^2+3q
        34: 4q^3+5q^2+3q
        35: 4q^3+5q^2+3q
        36: q^3+4q^2+3q
        37: 2q^3+2q^2+q
        38: 2q^3+3q^2+2q
        39: 2q^3+2q^2+q
        40: 2q^3+3q^2+2q
        41: 2q^3+2q^2+q
        42: 2q^3+3q^2+2q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 2q^4+7q^3+6q^2+3q
        53: 2q^4+7q^3+6q^2+3q
        54: 2q^4+7q^3+6q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: 4q^3+5q^2+3q
        58: 2q^3+3q^2+2q
        59: q^3+2q^2+q
        60: q^3+2q^2+2q
        61: 2q^2+q
        62: 2q^3+2q^2+q
        63: 2q^3+3q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: q^3+4q^2+3q
        73: 3q^3+5q^2+3q
        74: 2q^3+2q^2+q
        75: 2q^3+3q^2+2q
        76: 2q^3+2q^2+q
        77: 2q^3+3q^2+2q
        78: 2q^3+2q^2+q
        79: 2q^3+3q^2+2q
        80: 2q^4+7q^3+6q^2+3q
        81: 3q^3+5q^2+3q
        82: 2q^4+7q^3+6q^2+3q
        83: 2q^4+7q^3+6q^2+3q
        84: 4q^3+5q^2+3q
        85: q^3+4q^2+3q
        86: 4q^3+5q^2+3q
        87: 4q^3+5q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^3+5q^2+3q
        95: 3q^3+5q^2+3q
        96: q^4+3q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+2q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^3+q^2+q
       104: q^2+q
       105: q^2+q
       106: q^2
       107: q^3+2q^2+2q
       108: 2q^2+q
       109: 2q^3+3q^2+2q
       110: q^3+2q^2+q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: 2q^3+2q^2+q
       114: 2q^3+3q^2+2q
       115: 2q^3+2q^2+q
       116: 2q^3+3q^2+2q
       117: 2q^3+3q^2+2q
       118: q^3+2q^2+q
       119: q^3+2q^2+2q
       120: 2q^2+q
       121: 2q^3+2q^2+q
       122: 2q^3+3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: q^3+4q^2+3q
       136: 3q^3+5q^2+3q
       137: 3q^3+5q^2+3q
       138: q^3+2q^2+2q
       139: 3q^3+5q^2+3q
       140: q^3+4q^2+3q
       141: 2q^4+7q^3+6q^2+3q
       142: 3q^3+5q^2+3q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: 3q^2+3q
       146: 4q^3+5q^2+3q
       147: 3q^2+3q
       148: q^2+2q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+2q^2+q
       152: 2q^3+3q^2+2q
       153: 2q^3+2q^2+q
       154: 2q^3+3q^2+2q
       155: 2q^3+2q^2+q
       156: 2q^3+3q^2+2q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+5q^2+3q
       161: 3q^3+5q^2+3q
       162: q^4+3q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+2q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^3+q^2+q
       170: q^2+q
       171: q^2+q
       172: q^2
       173: q^3+q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q
       180: q^2+2q
       182: q^2+2q
       183: q^3+2q^2+2q
       184: 2q^2+q
       185: 2q^3+3q^2+2q
       186: q^3+2q^2+q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: 2q^3+2q^2+q
       190: 2q^3+3q^2+2q
       191: 2q^3+3q^2+2q
       192: q^3+2q^2+q
       193: q^3+2q^2+2q
       194: 2q^2+q
       195: 2q^3+3q^2+2q
       196: q^3+2q^2+q
       197: q^3+2q^2+q
       198: 2q^2+2q
       199: q^3+2q^2+2q
       200: 2q^2+q
       201: 2q^2+2q
       202: q^2+q
       203: q^2+2q
       205: q^2+q
       206: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: 2q^3+2q^2+q
       210: 2q^3+3q^2+2q
       211: 2q^3+2q^2+q
       212: 2q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: q^3+4q^2+3q
       223: q^2+2q
       224: 3q^3+5q^2+3q
       225: q^3+2q^2+2q
       226: q^3+2q^2+2q
       227: 3q^3+5q^2+3q
       228: q^3+2q^2+2q
       229: q^3+4q^2+3q
       230: 3q^3+5q^2+3q
       231: q^2+2q
       232: 3q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: q^2+2q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q^2+3q
       244: 3q^2+3q
       245: q^2+2q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^3+5q^2+3q
       251: 3q^3+5q^2+3q
       252: q^4+3q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+2q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       260: q^2+q
       261: q
       263: q^3+q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2
       267: q^3+q^2+q
       268: q^2+q
       269: q^2
       270: q^2+q
       271: q^2+q
       272: q
       275: q^3+q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: q^2+2q
       282: q
       283: q
       285: q^2+q
       288: q
       290: q^2+2q
       292: q
       293: q^3+2q^2+2q
       294: 2q^2+q
       295: 2q^3+3q^2+2q
       296: q^3+2q^2+q
       297: q^3+2q^2+q
       298: 2q^2+2q
       299: q^3+2q^2+2q
       300: 2q^2+q
       302: q^2+2q
       303: 2q^3+3q^2+2q
       304: q^3+2q^2+q
       305: q^3+2q^2+q
       306: 2q^2+2q
       307: 2q^2+2q
       308: q^2+q
       309: q^2+2q
       312: q
       313: q^2+q
       314: q
       316: q
       318: q^2+2q
       319: 2q^2+2q
       320: q^2+q
       321: q^2+2q
       323: q^2+q
       324: q
       325: 2q^3+2q^2+q
       326: 2q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: q^3+2q^2+2q
       334: q^2+2q
       335: q^3+2q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: q^3+2q^2+2q
       345: 3q^3+5q^2+3q
       346: q^3+2q^2+2q
       347: q^3+4q^2+3q
       348: q^2+2q
       349: 3q^3+5q^2+3q
       350: q^3+2q^2+2q
       351: 3q^2+3q
       352: q^2+2q
       353: 3q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: q^2+2q
       358: q
       359: q^2+2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: 3q^2+3q
       370: q^2+2q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       382: q^2+q
       383: q
       385: q^3+q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2
       390: q^2+q
       392: q
       393: q^3+q^2+q
       394: q^2+q
       395: q^2+q
       396: q^2
       398: q
       401: q^2+q
       402: q
       405: q^2+q
       408: q
       410: q^2+2q
       412: q
       414: q
       416: q^2+2q
       418: q
       419: q
       421: q^2+q
       424: q
       426: q
       428: q^2+2q
       429: q
       431: q^2+q
       434: q
       436: q^2+2q
       437: q^3+2q^2+2q
       438: 2q^2+q
       439: 2q^3+3q^2+2q
       440: q^3+2q^2+q
       441: q^3+2q^2+q
       442: 2q^2+2q
       443: 2q^2+2q
       444: q^2+q
       446: q^2+2q
       447: q
       449: q
       453: 2q^2+2q
       454: q^2+q
       456: q
       457: q^2+2q
       459: q^2+q
       460: q
       461: q^2+2q
       464: q
       466: q^2+2q
       468: q
       470: q
       471: 2q^2+2q
       472: q^2+q
       473: q^2+2q
       475: q^2+q
       476: q
       478: q
       479: q^2+q
       480: q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: q^3+2q^2+2q
       493: q^2+2q
       494: q^3+2q^2+2q
       495: q^2+2q
       496: 3q^2+3q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: q^2+2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: 3q^2+3q
       512: q^2+2q
       513: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       526: q^2+q
       527: q
       538: q^2+q
       540: q
       541: q^3+q^2+q
       542: q^2+q
       543: q^2
       544: q^2+q
       546: q^2+q
       548: q
       554: q
       557: q^2+q
       558: q
       562: q
       565: q^2+q
       567: q
       572: q
       573: q^2+q
       576: q
       581: q
       584: q
       586: q
       588: q
       589: q
       591: q
       593: q
       595: q^2+q
       598: q
       600: q
       602: q^2+2q
       603: q
       606: q
       607: q^2+q
       610: q
       612: q^2+2q
       614: q
       615: 2q^2+2q
       616: q^2+q
       618: q^2+2q
       619: q
       621: q
       628: q
       631: q^2+2q
       634: q
       636: q^2+2q
       638: q
       640: q
       641: q
       643: q
       647: 2q^2+2q
       648: q^2+q
       649: q^2+2q
       652: q
       653: q^2+q
       654: q
       655: q^2+q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q^2+2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: q+1
       675: q^2+2q
       676: q^3+2q^2+2q
       677: q^2+2q
       678: 3q^2+3q
       679: q^2+2q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: q^2+2q
       685: q
       686: q^2+2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       700: q
       730: q^2+q
       732: q
       734: q^2+q
       736: q
       746: q
       750: q
       760: q
       761: q^2+q
       764: q
       765: q^2+q
       767: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: q^2+2q
       793: 1
       796: q+1
       798: q
       800: q
       801: q
       803: q
       805: q
       807: q^2+q
       810: q
       812: q
       814: q^2+2q
       815: 2q^2+2q
       816: q^2+q
       817: 1
       820: 1
       825: q
       827: q
       831: q
       838: q
       839: q^2+2q
       842: q
       843: 1
       845: q
       847: q
       854: q
       857: q^2+q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: q+1
       870: q+1
       871: q^2+2q
       872: q^2+2q
       873: 1
       874: 1
       875: q
       876: q
       877: q^2+2q
       878: q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       891: q
       917: 1
       933: q^2+q
       935: q
       941: 1
       957: q
       964: 1
       969: 1
       981: q
       986: q
       988: q^2+q
       990: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: q+1
      1016: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: 1
      1032: 1
      1037: 1
      1044: q
      1046: 1
      1052: q
      1054: q
      1058: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: q^2+2q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1087: 1
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1227: q+1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1245: 1
      1246: 1
      1253: 1
      1260: q
      1262: 1
      1270: q
      1275: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: q
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1341: 1
      1349: 1
      1357: 1
      1364: 1
      1373: 1
      1405: 1
      1410: 1
      1431: 1
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1449: 1
      1450: 1
      1453: q+1
      1454: 1
      1459: 1
      1473: 1
      1478: q
      1482: 1
      1485: 1
      1488: 1
      1490: 1
      1502: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1564: 1
      1568: 1
      1575: 1
      1632: 1
      1644: 1
      1645: 1
      1647: 1
      1668: 1
      1669: 1
      1676: 1
      1688: 1
      1738: 1
      1746: 1
      1749: 1
      1802: 1
      1847: 1

1848:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 7q^4+7q^3+3q^2+q
        23: 2q^5+8q^4+7q^3+3q^2+q
        24: 7q^4+7q^3+3q^2+q
        25: 4q^4+6q^3+3q^2+q
        26: q^5+5q^4+6q^3+3q^2+q
        27: 4q^4+6q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 5q^4+6q^3+3q^2+q
        32: 7q^4+7q^3+3q^2+q
        33: 5q^4+6q^3+3q^2+q
        34: 3q^4+5q^3+3q^2+q
        35: 4q^4+6q^3+3q^2+q
        36: 3q^4+5q^3+3q^2+q
        37: 4q^4+6q^3+3q^2+q
        39: q^5+5q^4+6q^3+3q^2+q
        41: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: 4q^4+6q^3+3q^2+q
        53: q^5+5q^4+6q^3+3q^2+q
        54: 4q^4+6q^3+3q^2+q
        55: q^4+5q^3+3q^2+q
        56: 2q^4+5q^3+3q^2+q
        57: q^4+5q^3+3q^2+q
        58: 2q^4+4q^3+2q^2+q
        59: q^4+q^3+q^2
        60: 2q^4+3q^3+2q^2+q
        61: q^3+q^2
        62: 3q^4+5q^3+3q^2+q
        64: 4q^4+6q^3+3q^2+q
        66: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 4q^3+3q^2+q
        74: q^4+5q^3+3q^2+q
        76: 2q^4+5q^3+3q^2+q
        78: q^4+5q^3+3q^2+q
        80: 5q^4+6q^3+3q^2+q
        81: 5q^4+6q^3+3q^2+q
        82: 3q^4+5q^3+3q^2+q
        83: 4q^4+6q^3+3q^2+q
        84: 3q^4+5q^3+3q^2+q
        85: 3q^4+5q^3+3q^2+q
        86: q^4+4q^3+3q^2+q
        87: q^4+5q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 2q^4+5q^3+3q^2+q
        95: 2q^4+5q^3+3q^2+q
        96: 2q^4+4q^3+2q^2+q
        97: 3q^3+3q^2+q
        98: 3q^3+3q^2+q
        99: 3q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       103: 2q^4+3q^3+2q^2+q
       106: q^3+q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: 3q^3+2q^2+q
       110: q^2
       111: 3q^3+3q^2+q
       113: q^4+4q^3+3q^2+q
       115: q^4+5q^3+3q^2+q
       117: 2q^4+4q^3+2q^2+q
       118: q^4+q^3+q^2
       119: 2q^4+3q^3+2q^2+q
       120: q^3+q^2
       121: 3q^4+5q^3+3q^2+q
       123: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       127: 3q^3+3q^2+q
       129: 3q^3+3q^2+q
       131: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 4q^3+3q^2+q
       137: q^4+4q^3+3q^2+q
       138: q^4+3q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: 3q^3+3q^2+q
       141: 3q^4+5q^3+3q^2+q
       142: 4q^3+3q^2+q
       143: q^4+3q^3+3q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^4+4q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: 2q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       151: q^4+5q^3+3q^2+q
       153: 2q^4+5q^3+3q^2+q
       155: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^4+5q^3+3q^2+q
       161: 2q^4+5q^3+3q^2+q
       162: 2q^4+4q^3+2q^2+q
       163: 3q^3+3q^2+q
       164: 3q^3+3q^2+q
       165: 3q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       169: 2q^3+2q^2+q
       172: q^2
       173: 2q^4+3q^3+2q^2+q
       176: q^3+q^2
       177: 2q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: 2q^3+2q^2+q
       184: q^2
       185: 3q^3+2q^2+q
       186: q^2
       187: 3q^3+3q^2+q
       189: q^4+4q^3+3q^2+q
       191: q^4+3q^3+2q^2+q
       192: q^3+q^2
       193: 2q^3+2q^2+q
       194: q^2
       195: 3q^3+2q^2+q
       196: q^2
       197: 3q^3+3q^2+q
       199: q^4+2q^3+2q^2+q
       200: q^3+q^2
       201: q^3+2q^2+q
       202: q^2
       203: 2q^2+q
       205: 2q^2+q
       207: q^4+3q^3+3q^2+q
       209: q^4+4q^3+3q^2+q
       211: q^4+5q^3+3q^2+q
       213: 3q^3+3q^2+q
       215: 3q^3+3q^2+q
       217: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^4+4q^3+3q^2+q
       228: q^4+3q^3+2q^2+q
       229: 3q^3+3q^2+q
       230: 4q^3+3q^2+q
       231: q^3+2q^2+q
       232: 2q^3+3q^2+q
       233: 2q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: 2q^2+q
       236: 2q^3+2q^2+q
       237: 3q^3+3q^2+q
       239: 3q^3+3q^2+q
       241: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^3+3q^2+q
       245: 2q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^3+3q^2+q
       251: 2q^3+3q^2+q
       252: q^4+2q^3+2q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: 2q^3+2q^2+q
       266: q^2
       267: 2q^3+2q^2+q
       269: q^2
       271: 2q^2+q
       275: q^4+2q^3+2q^2+q
       278: q^3+q^2
       279: 2q^3+3q^2+q
       281: 2q^3+2q^2+q
       283: q^2+q
       285: q^3+q^2+q
       287: q^3+2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^3+2q^2+q
       296: q^2
       297: q^3+3q^2+q
       299: 2q^3+2q^2+q
       300: q^2
       301: 2q^3+3q^2+q
       303: 3q^3+2q^2+q
       304: q^2
       305: 3q^3+3q^2+q
       307: q^3+2q^2+q
       308: q^2
       309: 2q^2+q
       311: 2q^2+q
       313: 2q^2+q
       315: 2q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: q^3+2q^2+q
       320: q^2
       321: 2q^2+q
       323: 2q^2+q
       325: q^4+4q^3+3q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: 2q^3+3q^2+q
       346: q^3+2q^2+q
       347: q^3+3q^2+q
       348: q^3+2q^2+q
       349: q^3+3q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: 3q^3+3q^2+q
       362: 3q^3+3q^2+q
       364: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^3+3q^2+q
       370: 2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       377: q^2+q
       381: q^3+2q^2+q
       384: q^2
       385: q^3+2q^2+q
       388: q^2
       389: q^3+2q^2+q
       391: q^2
       393: 2q^3+2q^2+q
       396: q^2
       397: 2q^2+q
       401: 2q^2+q
       405: 2q^2+q
       409: 2q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2+q
       431: q^3+q^2+q
       433: q^3+2q^2+q
       435: 2q^3+3q^2+q
       437: q^3+2q^2+q
       438: q^2
       439: q^3+2q^2+q
       440: q^2
       441: q^3+3q^2+q
       443: q^2+q
       444: q^2
       445: 2q^2+q
       447: q^2+q
       449: q^2+q
       451: q^2+q
       453: q^2+q
       454: q^2
       455: 2q^2+q
       457: q^2+q
       459: q^2+q
       461: q^2+q
       463: q^2+q
       465: 2q^3+3q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: q^3+2q^2+q
       472: q^2
       473: 2q^2+q
       475: 2q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       502: 2q^2+q
       504: 2q^2+q
       506: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: 2q^2+q
       512: q^3+2q^2+q
       513: q^2+q
       514: q^2+q
       521: q^2+q
       525: q^2+q
       528: q^2
       529: q^2+q
       533: q^2+q
       537: q^3+2q^2+q
       539: q^2
       541: q^3+2q^2+q
       543: q^2
       545: q^2+q
       547: q^2
       549: q^2+q
       553: 2q^2+q
       557: q^2+q
       561: q^2+q
       565: 2q^2+q
       569: 2q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       591: q
       593: q
       595: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       603: q^2+q
       605: q^3+2q^2+q
       607: q^2+q
       609: 2q^2+q
       611: 2q^2+q
       613: q^2+q
       615: q^2+q
       616: q^2
       617: 2q^2+q
       619: q
       621: q
       623: q^2+q
       625: q
       627: q^2+q
       629: q
       631: q^2+q
       633: q^2+q
       635: 2q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q^2+q
       648: q^2
       649: q^2+q
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       665: q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       693: q^2+q
       705: q
       709: q^2+q
       713: q
       717: q
       721: q^2+q
       725: q^2+q
       729: q^2+q
       731: q^2
       733: q^2+q
       735: q^2
       737: q^2+q
       741: q
       745: q^2+q
       749: q^2+q
       753: q^2+q
       757: 2q^2+q
       761: q^2+q
       765: q^2+q
       769: q^2+q
       777: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       797: 2q^2+q
       799: q^2+q
       801: q^2+q
       803: q
       805: q
       807: q^2+q
       809: q^2+q
       811: q^2+q
       821: q
       823: q
       825: q
       827: q
       831: q
       833: q
       835: q
       841: q^2+q
       845: q
       847: q
       849: q^2+q
       851: q
       853: q^2+q
       855: q
       871: q^2+q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       884: q^2+q
       896: q
       900: q
       904: q
       908: q
       912: q
       920: q^2+q
       924: q
       928: q
       936: q
       944: q
       948: q
       960: q^2+q
       974: q
       978: q^2+q
      1010: q
      1018: q^2+q
      1022: q^2+q
      1026: q
      1028: q
      1034: q
      1038: q
      1044: q
      1048: q
      1050: q
      1052: q
      1054: q
      1058: q
      1060: q
      1062: q
      1064: q
      1083: q
      1126: q
      1148: q
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1184: q
      1198: q
      1202: q
      1222: 1
      1264: q
      1266: q
      1270: q
      1278: q
      1322: 1
      1336: 1
      1360: q
      1414: q
      1418: q
      1446: 1
      1480: 1
      1491: 1
      1555: 1
      1559: 1
      1571: 1
      1633: 1
      1671: 1
      1677: 1
      1689: 1
      1753: 1
      1803: 1
      1848: 1

1849:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 2q^4+7q^3+6q^2+3q
        23: 2q^4+7q^3+6q^2+3q
        24: 2q^4+7q^3+6q^2+3q
        25: 4q^3+5q^2+3q
        26: 4q^3+5q^2+3q
        27: 4q^3+5q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 2q^4+7q^3+6q^2+3q
        32: 2q^4+7q^3+6q^2+3q
        33: 3q^3+5q^2+3q
        34: 4q^3+5q^2+3q
        35: 4q^3+5q^2+3q
        36: q^3+4q^2+3q
        37: 2q^3+3q^2+2q
        38: 2q^3+2q^2+q
        39: 2q^3+3q^2+2q
        40: 2q^3+2q^2+q
        41: 2q^3+3q^2+2q
        42: 2q^3+2q^2+q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 2q^4+7q^3+6q^2+3q
        53: 2q^4+7q^3+6q^2+3q
        54: 2q^4+7q^3+6q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: 4q^3+5q^2+3q
        58: 2q^3+3q^2+2q
        59: q^3+2q^2+q
        60: 2q^2+q
        61: q^3+2q^2+2q
        62: 2q^3+3q^2+2q
        63: 2q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: q^3+4q^2+3q
        73: 3q^3+5q^2+3q
        74: 2q^3+3q^2+2q
        75: 2q^3+2q^2+q
        76: 2q^3+3q^2+2q
        77: 2q^3+2q^2+q
        78: 2q^3+3q^2+2q
        79: 2q^3+2q^2+q
        80: 2q^4+7q^3+6q^2+3q
        81: 3q^3+5q^2+3q
        82: 2q^4+7q^3+6q^2+3q
        83: 2q^4+7q^3+6q^2+3q
        84: 4q^3+5q^2+3q
        85: q^3+4q^2+3q
        86: 4q^3+5q^2+3q
        87: 4q^3+5q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^3+5q^2+3q
        95: 3q^3+5q^2+3q
        96: q^4+3q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+2q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2+q
       104: q^2
       105: q^3+q^2+q
       106: q^2+q
       107: 2q^2+q
       108: q^3+2q^2+2q
       109: 2q^3+3q^2+2q
       110: q^3+2q^2+q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 2q^3+3q^2+2q
       114: 2q^3+2q^2+q
       115: 2q^3+3q^2+2q
       116: 2q^3+2q^2+q
       117: 2q^3+3q^2+2q
       118: q^3+2q^2+q
       119: 2q^2+q
       120: q^3+2q^2+2q
       121: 2q^3+3q^2+2q
       122: 2q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: q^3+4q^2+3q
       136: 3q^3+5q^2+3q
       137: 3q^3+5q^2+3q
       138: q^3+2q^2+2q
       139: 3q^3+5q^2+3q
       140: q^3+4q^2+3q
       141: 2q^4+7q^3+6q^2+3q
       142: 3q^3+5q^2+3q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: 3q^2+3q
       146: 4q^3+5q^2+3q
       147: 3q^2+3q
       148: q^2+2q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: 2q^3+2q^2+q
       153: 2q^3+3q^2+2q
       154: 2q^3+2q^2+q
       155: 2q^3+3q^2+2q
       156: 2q^3+2q^2+q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+5q^2+3q
       161: 3q^3+5q^2+3q
       162: q^4+3q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+2q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2+q
       170: q^2
       171: q^3+q^2+q
       172: q^2+q
       173: q^2+q
       174: q^2
       175: q^3+q^2+q
       176: q^2+q
       177: q
       179: q^2+2q
       181: q^2+2q
       183: 2q^2+q
       184: q^3+2q^2+2q
       185: 2q^3+3q^2+2q
       186: q^3+2q^2+q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 2q^3+3q^2+2q
       190: 2q^3+2q^2+q
       191: 2q^3+3q^2+2q
       192: q^3+2q^2+q
       193: 2q^2+q
       194: q^3+2q^2+2q
       195: 2q^3+3q^2+2q
       196: q^3+2q^2+q
       197: 2q^2+2q
       198: q^3+2q^2+q
       199: 2q^2+q
       200: q^3+2q^2+2q
       201: q^2+q
       202: 2q^2+2q
       203: q^2+2q
       205: q
       206: q^2+q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^3+3q^2+2q
       210: 2q^3+2q^2+q
       211: 2q^3+3q^2+2q
       212: 2q^3+2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: q^3+4q^2+3q
       223: q^2+2q
       224: 3q^3+5q^2+3q
       225: q^3+2q^2+2q
       226: q^3+2q^2+2q
       227: 3q^3+5q^2+3q
       228: q^3+2q^2+2q
       229: q^3+4q^2+3q
       230: 3q^3+5q^2+3q
       231: q^2+2q
       232: 3q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: q^2+2q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q^2+3q
       244: 3q^2+3q
       245: q^2+2q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^3+5q^2+3q
       251: 3q^3+5q^2+3q
       252: q^4+3q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+2q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       259: q
       262: q^2+q
       263: q^2+q
       264: q^2
       265: q^3+q^2+q
       266: q^2+q
       267: q^2+q
       268: q^2
       269: q^2+q
       270: q^3+q^2+q
       271: q
       272: q^2+q
       275: q^2+q
       276: q^2
       277: q^3+q^2+q
       278: q^2+q
       279: q^2+2q
       281: q
       284: q
       285: q^2+q
       287: q
       289: q^2+2q
       291: q
       293: 2q^2+q
       294: q^3+2q^2+2q
       295: 2q^3+3q^2+2q
       296: q^3+2q^2+q
       297: 2q^2+2q
       298: q^3+2q^2+q
       299: 2q^2+q
       300: q^3+2q^2+2q
       301: q^2+2q
       303: 2q^3+3q^2+2q
       304: q^3+2q^2+q
       305: 2q^2+2q
       306: q^3+2q^2+q
       307: q^2+q
       308: 2q^2+2q
       309: q^2+2q
       311: q
       313: q
       314: q^2+q
       315: q
       317: q^2+2q
       319: q^2+q
       320: 2q^2+2q
       321: q^2+2q
       323: q
       324: q^2+q
       325: 2q^3+3q^2+2q
       326: 2q^3+2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: q^3+2q^2+2q
       334: q^2+2q
       335: q^3+2q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: q^3+2q^2+2q
       345: 3q^3+5q^2+3q
       346: q^3+2q^2+2q
       347: q^3+4q^2+3q
       348: q^2+2q
       349: 3q^3+5q^2+3q
       350: q^3+2q^2+2q
       351: 3q^2+3q
       352: q^2+2q
       353: 3q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: q^2+2q
       358: q
       359: q^2+2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: 3q^2+3q
       370: q^2+2q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       381: q
       384: q^2+q
       385: q^2+q
       386: q^2
       387: q^3+q^2+q
       388: q^2+q
       389: q
       391: q^2+q
       393: q^2+q
       394: q^2
       395: q^3+q^2+q
       396: q^2+q
       397: q
       401: q
       402: q^2+q
       405: q
       408: q^2+q
       409: q^2+2q
       411: q
       413: q
       415: q^2+2q
       417: q
       420: q
       421: q^2+q
       423: q
       425: q
       427: q^2+2q
       430: q
       431: q^2+q
       433: q
       435: q^2+2q
       437: 2q^2+q
       438: q^3+2q^2+2q
       439: 2q^3+3q^2+2q
       440: q^3+2q^2+q
       441: 2q^2+2q
       442: q^3+2q^2+q
       443: q^2+q
       444: 2q^2+2q
       445: q^2+2q
       448: q
       449: q
       453: q^2+q
       454: 2q^2+2q
       455: q
       457: q^2+2q
       459: q
       460: q^2+q
       461: q^2+2q
       463: q
       465: q^2+2q
       467: q
       469: q
       471: q^2+q
       472: 2q^2+2q
       473: q^2+2q
       475: q
       476: q^2+q
       477: q
       479: q
       480: q^2+q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: q^3+2q^2+2q
       493: q^2+2q
       494: q^3+2q^2+2q
       495: q^2+2q
       496: 3q^2+3q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: q^2+2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: 3q^2+3q
       512: q^2+2q
       513: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       525: q
       528: q^2+q
       537: q
       539: q^2+q
       541: q^2+q
       542: q^2
       543: q^2+q
       544: q^3+q^2+q
       545: q
       547: q^2+q
       553: q
       557: q
       558: q^2+q
       561: q
       565: q
       567: q^2+q
       569: q
       573: q
       576: q^2+q
       577: q
       583: q
       585: q
       587: q
       590: q
       591: q
       594: q
       595: q^2+q
       597: q
       599: q
       601: q^2+2q
       604: q
       605: q
       607: q^2+q
       609: q
       611: q^2+2q
       613: q
       615: q^2+q
       616: 2q^2+2q
       617: q^2+2q
       620: q
       621: q
       627: q
       631: q^2+2q
       633: q
       635: q^2+2q
       637: q
       639: q
       642: q
       643: q
       647: q^2+q
       648: 2q^2+2q
       649: q^2+2q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q^2+2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: q+1
       675: q^2+2q
       676: q^3+2q^2+2q
       677: q^2+2q
       678: 3q^2+3q
       679: q^2+2q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: q^2+2q
       685: q
       686: q^2+2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       693: q
       729: q
       731: q^2+q
       733: q
       735: q^2+q
       745: q
       749: q
       757: q
       761: q
       764: q^2+q
       765: q
       767: q^2+q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: q^2+2q
       794: 1
       795: q+1
       797: q
       799: q
       802: q
       803: q
       806: q
       807: q^2+q
       809: q
       811: q
       813: q^2+2q
       815: q^2+q
       816: 2q^2+2q
       817: 1
       819: 1
       826: q
       827: q
       831: q
       837: q
       839: q^2+2q
       841: q
       844: 1
       846: q
       847: q
       853: q
       857: q
       858: q^2+q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: q+1
       870: q+1
       871: q^2+2q
       872: q^2+2q
       873: 1
       874: 1
       875: q
       876: q
       877: q^2+2q
       878: q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       884: q
       918: 1
       932: q
       934: q^2+q
       940: 1
       956: q
       966: 1
       971: 1
       978: q
       982: q
       988: q
       990: q^2+q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: q+1
      1017: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: 1
      1032: 1
      1036: 1
      1044: q
      1047: 1
      1053: q
      1054: q
      1058: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: q^2+2q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1090: 1
      1098: q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1226: q+1
      1229: 1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1244: 1
      1246: 1
      1252: 1
      1260: q
      1263: 1
      1270: q
      1274: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: q
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1342: 1
      1348: 1
      1358: 1
      1365: 1
      1372: 1
      1407: 1
      1412: 1
      1433: 1
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1448: 1
      1450: 1
      1452: q+1
      1455: 1
      1458: 1
      1472: 1
      1478: q
      1483: 1
      1485: 1
      1488: 1
      1493: 1
      1504: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1563: 1
      1569: 1
      1576: 1
      1634: 1
      1643: 1
      1645: 1
      1648: 1
      1667: 1
      1670: 1
      1679: 1
      1690: 1
      1737: 1
      1747: 1
      1750: 1
      1804: 1
      1849: 1

1850:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 2q^4+7q^3+6q^2+3q
        23: 2q^4+7q^3+6q^2+3q
        24: 2q^4+7q^3+6q^2+3q
        25: 4q^3+5q^2+3q
        26: 4q^3+5q^2+3q
        27: 4q^3+5q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 2q^4+7q^3+6q^2+3q
        32: 2q^4+7q^3+6q^2+3q
        33: 3q^3+5q^2+3q
        34: 4q^3+5q^2+3q
        35: 4q^3+5q^2+3q
        36: q^3+4q^2+3q
        37: 2q^3+3q^2+2q
        38: 2q^3+2q^2+q
        39: 2q^3+3q^2+2q
        40: 2q^3+2q^2+q
        41: 2q^3+3q^2+2q
        42: 2q^3+2q^2+q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 2q^4+7q^3+6q^2+3q
        53: 2q^4+7q^3+6q^2+3q
        54: 2q^4+7q^3+6q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: 4q^3+5q^2+3q
        58: q^3+2q^2+q
        59: 2q^3+3q^2+2q
        60: q^3+2q^2+2q
        61: 2q^2+q
        62: 2q^3+3q^2+2q
        63: 2q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: q^3+4q^2+3q
        73: 3q^3+5q^2+3q
        74: 2q^3+3q^2+2q
        75: 2q^3+2q^2+q
        76: 2q^3+3q^2+2q
        77: 2q^3+2q^2+q
        78: 2q^3+3q^2+2q
        79: 2q^3+2q^2+q
        80: 2q^4+7q^3+6q^2+3q
        81: 3q^3+5q^2+3q
        82: 2q^4+7q^3+6q^2+3q
        83: 2q^4+7q^3+6q^2+3q
        84: 4q^3+5q^2+3q
        85: q^3+4q^2+3q
        86: 4q^3+5q^2+3q
        87: 4q^3+5q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^3+5q^2+3q
        95: 3q^3+5q^2+3q
        96: q^4+3q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+2q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2+q
       104: q^3+q^2+q
       105: q^2
       106: q^2+q
       107: q^3+2q^2+2q
       108: 2q^2+q
       109: q^3+2q^2+q
       110: 2q^3+3q^2+2q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 2q^3+3q^2+2q
       114: 2q^3+2q^2+q
       115: 2q^3+3q^2+2q
       116: 2q^3+2q^2+q
       117: q^3+2q^2+q
       118: 2q^3+3q^2+2q
       119: q^3+2q^2+2q
       120: 2q^2+q
       121: 2q^3+3q^2+2q
       122: 2q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: q^3+4q^2+3q
       136: 3q^3+5q^2+3q
       137: 3q^3+5q^2+3q
       138: q^3+2q^2+2q
       139: 3q^3+5q^2+3q
       140: q^3+4q^2+3q
       141: 2q^4+7q^3+6q^2+3q
       142: 3q^3+5q^2+3q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: 3q^2+3q
       146: 4q^3+5q^2+3q
       147: 3q^2+3q
       148: q^2+2q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: 2q^3+2q^2+q
       153: 2q^3+3q^2+2q
       154: 2q^3+2q^2+q
       155: 2q^3+3q^2+2q
       156: 2q^3+2q^2+q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+5q^2+3q
       161: 3q^3+5q^2+3q
       162: q^4+3q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+2q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2+q
       170: q^3+q^2+q
       171: q^2
       172: q^2+q
       173: q^2+q
       174: q^3+q^2+q
       175: q^2
       176: q^2+q
       177: q
       179: q^2+2q
       181: q^2+2q
       183: q^3+2q^2+2q
       184: 2q^2+q
       185: q^3+2q^2+q
       186: 2q^3+3q^2+2q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 2q^3+3q^2+2q
       190: 2q^3+2q^2+q
       191: q^3+2q^2+q
       192: 2q^3+3q^2+2q
       193: q^3+2q^2+2q
       194: 2q^2+q
       195: q^3+2q^2+q
       196: 2q^3+3q^2+2q
       197: 2q^2+2q
       198: q^3+2q^2+q
       199: q^3+2q^2+2q
       200: 2q^2+q
       201: 2q^2+2q
       202: q^2+q
       204: q^2+2q
       205: q
       206: q^2+q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^3+3q^2+2q
       210: 2q^3+2q^2+q
       211: 2q^3+3q^2+2q
       212: 2q^3+2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: q^3+4q^2+3q
       223: q^2+2q
       224: 3q^3+5q^2+3q
       225: q^3+2q^2+2q
       226: q^3+2q^2+2q
       227: 3q^3+5q^2+3q
       228: q^3+2q^2+2q
       229: q^3+4q^2+3q
       230: 3q^3+5q^2+3q
       231: q^2+2q
       232: 3q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: q^2+2q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q^2+3q
       244: 3q^2+3q
       245: q^2+2q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^3+5q^2+3q
       251: 3q^3+5q^2+3q
       252: q^4+3q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+2q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       259: q^2+q
       262: q
       263: q^2+q
       264: q^3+q^2+q
       265: q^2
       266: q^2+q
       267: q^2+q
       268: q^3+q^2+q
       269: q^2+q
       270: q^2
       273: q
       274: q^2+q
       275: q^2+q
       276: q^3+q^2+q
       277: q^2
       278: q^2+q
       279: q^2+2q
       281: q
       283: q
       286: q^2+q
       287: q
       289: q^2+2q
       291: q
       293: q^3+2q^2+2q
       294: 2q^2+q
       295: q^3+2q^2+q
       296: 2q^3+3q^2+2q
       297: 2q^2+2q
       298: q^3+2q^2+q
       299: q^3+2q^2+2q
       300: 2q^2+q
       301: q^2+2q
       303: q^3+2q^2+q
       304: 2q^3+3q^2+2q
       305: 2q^2+2q
       306: q^3+2q^2+q
       307: 2q^2+2q
       308: q^2+q
       310: q^2+2q
       311: q
       313: q
       314: q^2+q
       315: q
       317: q^2+2q
       319: 2q^2+2q
       320: q^2+q
       322: q^2+2q
       323: q
       324: q^2+q
       325: 2q^3+3q^2+2q
       326: 2q^3+2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: q^3+2q^2+2q
       334: q^2+2q
       335: q^3+2q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: q^3+2q^2+2q
       345: 3q^3+5q^2+3q
       346: q^3+2q^2+2q
       347: q^3+4q^2+3q
       348: q^2+2q
       349: 3q^3+5q^2+3q
       350: q^3+2q^2+2q
       351: 3q^2+3q
       352: q^2+2q
       353: 3q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: q^2+2q
       358: q
       359: q^2+2q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: 3q^2+3q
       370: q^2+2q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       381: q^2+q
       384: q
       385: q^2+q
       386: q^3+q^2+q
       387: q^2
       388: q^2+q
       389: q^2+q
       391: q
       393: q^2+q
       394: q^3+q^2+q
       395: q^2
       396: q^2+q
       399: q
       403: q^2+q
       404: q
       406: q
       407: q^2+q
       409: q^2+2q
       411: q
       413: q
       415: q^2+2q
       417: q
       419: q
       422: q^2+q
       423: q
       425: q
       427: q^2+2q
       429: q
       432: q^2+q
       433: q
       435: q^2+2q
       437: q^3+2q^2+2q
       438: 2q^2+q
       439: q^3+2q^2+q
       440: 2q^3+3q^2+2q
       441: 2q^2+2q
       442: q^3+2q^2+q
       443: 2q^2+2q
       444: q^2+q
       445: q^2+2q
       447: q
       450: q
       453: 2q^2+2q
       454: q^2+q
       455: q
       458: q^2+2q
       459: q
       460: q^2+q
       462: q^2+2q
       463: q
       465: q^2+2q
       467: q
       469: q
       471: 2q^2+2q
       472: q^2+q
       474: q^2+2q
       475: q
       476: q^2+q
       477: q
       479: q
       480: q^2+q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: q^3+2q^2+2q
       493: q^2+2q
       494: q^3+2q^2+2q
       495: q^2+2q
       496: 3q^2+3q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: q^2+2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: 3q^2+3q
       512: q^2+2q
       513: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       525: q^2+q
       528: q
       537: q^2+q
       539: q
       541: q^2+q
       542: q^3+q^2+q
       543: q^2+q
       544: q^2
       545: q^2+q
       547: q
       555: q
       559: q
       560: q^2+q
       563: q
       566: q^2+q
       568: q
       570: q
       574: q^2+q
       575: q
       577: q
       583: q
       585: q
       587: q
       589: q
       592: q
       593: q
       596: q^2+q
       597: q
       599: q
       601: q^2+2q
       603: q
       605: q
       608: q^2+q
       609: q
       611: q^2+2q
       613: q
       615: 2q^2+2q
       616: q^2+q
       617: q^2+2q
       619: q
       622: q
       627: q
       632: q^2+2q
       633: q
       635: q^2+2q
       637: q
       639: q
       641: q
       644: q
       647: 2q^2+2q
       648: q^2+q
       650: q^2+2q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q^2+2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: q+1
       675: q^2+2q
       676: q^3+2q^2+2q
       677: q^2+2q
       678: 3q^2+3q
       679: q^2+2q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: q^2+2q
       685: q
       686: q^2+2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       697: q
       729: q^2+q
       731: q
       733: q^2+q
       735: q
       747: q
       751: q
       758: q
       762: q
       763: q^2+q
       766: q^2+q
       768: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: q^2+2q
       793: 1
       795: q+1
       797: q
       799: q
       801: q
       804: q
       805: q
       808: q^2+q
       809: q
       811: q
       813: q^2+2q
       815: 2q^2+2q
       816: q^2+q
       818: 1
       819: 1
       825: q
       828: q
       832: q
       837: q
       840: q^2+2q
       841: q
       844: 1
       845: q
       848: q
       853: q
       857: q
       858: q^2+q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: q+1
       870: q+1
       871: q^2+2q
       872: q^2+2q
       873: 1
       874: 1
       875: q
       876: q
       877: q^2+2q
       878: q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       889: q
       916: 1
       932: q^2+q
       934: q
       942: 1
       958: q
       965: 1
       971: 1
       979: q
       982: q
       989: q^2+q
       991: q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: q+1
      1016: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: 1
      1033: 1
      1036: 1
      1045: q
      1047: 1
      1052: q
      1055: q
      1059: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: q^2+2q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1089: 1
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1226: q+1
      1228: 1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1244: 1
      1247: 1
      1252: 1
      1261: q
      1263: 1
      1271: q
      1274: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: q
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1340: 1
      1350: 1
      1356: 1
      1366: 1
      1374: 1
      1407: 1
      1411: 1
      1433: 1
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1448: 1
      1451: 1
      1452: q+1
      1454: 1
      1458: 1
      1472: 1
      1479: q
      1483: 1
      1485: 1
      1488: 1
      1492: 1
      1505: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1565: 1
      1567: 1
      1577: 1
      1634: 1
      1643: 1
      1646: 1
      1647: 1
      1667: 1
      1670: 1
      1678: 1
      1691: 1
      1739: 1
      1745: 1
      1751: 1
      1804: 1
      1850: 1

1851:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: q
        61: q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       106: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: q^2+q
       110: 2q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+q
       118: 2q^2+2q+1
       119: q
       120: q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q
       184: q^2+2q+1
       185: q^2+q
       186: 2q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+q
       192: 2q^2+2q+1
       193: q
       194: q^2+2q+1
       195: q^2+q
       196: 2q^2+2q+1
       197: q^2+3q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       204: q+1
       205: q+1
       207: q^2+3q+1
       209: 2q^2+3q+1
       211: 2q^2+3q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       267: q
       269: q^2+2q+1
       273: q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       284: q+1
       286: q^2+q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q
       294: q^2+2q+1
       295: q^2+q
       296: 2q^2+2q+1
       297: q^2+3q+1
       299: q
       300: q^2+2q+1
       301: 3q+1
       303: q^2+q
       304: 2q^2+2q+1
       305: q^2+3q+1
       307: q
       308: 2q+1
       310: q+1
       311: q+1
       313: q+1
       315: 2q+1
       317: 3q+1
       319: q
       320: 2q+1
       322: q+1
       323: q+1
       325: 2q^2+3q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: q^2+3q+1
       348: 2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       360: 3q+1
       362: 3q+1
       364: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 3q+1
       370: q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       389: q
       391: 2q+1
       393: q
       396: q^2+2q+1
       399: q+1
       404: q+1
       406: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       420: q+1
       422: q^2+q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: q+1
       432: q^2+q+1
       433: 2q+1
       435: 3q+1
       437: q
       438: q^2+2q+1
       439: q^2+q
       440: 2q^2+2q+1
       441: q^2+3q+1
       443: q
       444: 2q+1
       445: 3q+1
       448: q+1
       450: 1
       451: 1
       453: q
       454: 2q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 3q+1
       467: 2q+1
       469: 2q+1
       471: q
       472: 2q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: 3q+1
       485: 3q+1
       487: 3q+1
       489: q^2+2q+1
       491: 2q+1
       492: 2q^2+2q+1
       493: 2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       502: 3q+1
       504: 3q+1
       506: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: 2q+1
       513: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: q+1
       537: q
       539: 2q+1
       541: q
       543: q^2+2q+1
       545: q
       547: 2q+1
       552: 1
       555: q+1
       559: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       590: q+1
       592: 1
       594: q+1
       596: q^2+q+1
       597: 2q+1
       599: 2q+1
       601: 3q+1
       604: q+1
       605: 2q+1
       608: q^2+q+1
       609: 2q+1
       611: 3q+1
       613: 2q+1
       615: q
       616: 2q+1
       617: 3q+1
       620: q+1
       622: 1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: q+1
       633: q+1
       635: 3q+1
       637: 2q+1
       639: 2q+1
       642: q+1
       644: 1
       645: 1
       647: q
       648: 2q+1
       650: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q+1
       666: 3q+1
       668: 3q+1
       670: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: q+1
       675: 2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       708: q+1
       712: q+1
       716: 1
       720: q+1
       723: q+1
       727: q+1
       729: q
       731: 2q+1
       733: q
       735: 2q+1
       739: 1
       743: 1
       747: q+1
       751: q+1
       756: 1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       786: q+1
       788: 1
       789: 3q+1
       791: 1
       794: 1
       795: q+1
       797: 2q+1
       799: 2q+1
       802: q+1
       804: 1
       806: q+1
       808: q^2+q+1
       809: 2q+1
       811: 2q+1
       813: 3q+1
       815: q
       816: 2q+1
       818: 1
       819: 1
       821: 1
       823: 1
       826: q+1
       828: 1
       832: 1
       833: 1
       835: 1
       837: q+1
       840: q+1
       841: 2q+1
       843: 1
       846: q+1
       848: 1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       889: q+1
       899: q+1
       902: 1
       906: q+1
       911: 1
       914: q+1
       918: 1
       922: q+1
       927: 1
       930: q+1
       932: q
       934: 2q+1
       938: 1
       942: 1
       946: 1
       950: 1
       958: q+1
       961: 1
       967: 1
       968: 1
       975: 1
       979: q+1
       982: q+1
       991: q+1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 2q+1
      1005: q+1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1017: 1
      1018: 2q+1
      1020: q+1
      1022: 2q+1
      1024: 2q+1
      1027: q+1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: q+1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: q+1
      1112: 1
      1116: 1
      1120: q+1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: q+1
      1154: 1
      1158: q+1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1204: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 2q+1
      1241: q+1
      1243: 1
      1244: 1
      1247: 1
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1346: 1
      1350: 1
      1354: q+1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: 1
      1378: 1
      1404: 1
      1413: 1
      1415: 1
      1420: 1
      1430: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1451: 1
      1452: q+1
      1455: 1
      1458: 1
      1470: 1
      1472: 1
      1474: 1
      1479: 1
      1480: 1
      1482: 1
      1485: 1
      1488: 1
      1494: 1
      1506: 1
      1530: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1605: 1
      1631: 1
      1643: 1
      1646: 1
      1648: 1
      1667: 1
      1669: 1
      1671: 1
      1680: 1
      1692: 1
      1739: 1
      1747: 1
      1752: 1
      1754: 1
      1801: 1
      1851: 1

1852:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: q
        61: q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+3q+1
        73: 3q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q
       105: q^2+2q+1
       107: q
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: q^2+q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 2q^2+2q+1
       118: q^2+q
       119: q
       120: q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q
       184: q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: 2q^2+2q+1
       192: q^2+q
       193: q
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+q
       198: q^2+3q+1
       199: q
       200: q^2+2q+1
       201: q
       202: 2q+1
       203: q+1
       206: q+1
       208: q^2+3q+1
       210: 2q^2+3q+1
       212: 2q^2+3q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       268: q
       270: q^2+2q+1
       272: q+1
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       284: q+1
       285: q^2+q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: q^2+q
       298: q^2+3q+1
       299: q
       300: q^2+2q+1
       302: 3q+1
       303: 2q^2+2q+1
       304: q^2+q
       306: q^2+3q+1
       307: q
       308: 2q+1
       309: q+1
       312: q+1
       314: q+1
       316: 2q+1
       318: 3q+1
       319: q
       320: 2q+1
       321: q+1
       324: q+1
       326: 2q^2+3q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: q^2+3q+1
       348: 2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 3q+1
       363: 3q+1
       365: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 3q+1
       370: q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       390: q
       392: 2q+1
       394: q
       395: q^2+2q+1
       398: q+1
       402: q+1
       408: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       420: q+1
       421: q^2+q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: q+1
       431: q^2+q+1
       434: 2q+1
       436: 3q+1
       437: q
       438: q^2+2q+1
       439: 2q^2+2q+1
       440: q^2+q
       442: q^2+3q+1
       443: q
       444: 2q+1
       446: 3q+1
       448: q+1
       449: 1
       452: 1
       453: q
       454: 2q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 3q+1
       468: 2q+1
       470: 2q+1
       471: q
       472: 2q+1
       473: q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: 3q+1
       486: 3q+1
       488: 3q+1
       490: q^2+2q+1
       491: 2q+1
       492: 2q^2+2q+1
       493: 2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       503: 3q+1
       505: 3q+1
       507: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: 2q+1
       513: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: q+1
       538: q
       540: 2q+1
       542: q
       544: q^2+2q+1
       546: q
       548: 2q+1
       550: 1
       554: q+1
       558: q+1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       590: q+1
       591: 1
       594: q+1
       595: q^2+q+1
       598: 2q+1
       600: 2q+1
       602: 3q+1
       604: q+1
       606: 2q+1
       607: q^2+q+1
       610: 2q+1
       612: 3q+1
       614: 2q+1
       615: q
       616: 2q+1
       618: 3q+1
       620: q+1
       621: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: q+1
       634: q+1
       636: 3q+1
       638: 2q+1
       640: 2q+1
       642: q+1
       643: 1
       646: 1
       647: q
       648: 2q+1
       649: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q+1
       667: 3q+1
       669: 3q+1
       671: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: q+1
       675: 2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       707: q+1
       711: q+1
       714: 1
       719: q+1
       724: q+1
       728: q+1
       730: q
       732: 2q+1
       734: q
       736: 2q+1
       738: 1
       742: 1
       746: q+1
       750: q+1
       755: 1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       786: q+1
       787: 1
       790: 3q+1
       792: 1
       794: 1
       796: q+1
       798: 2q+1
       800: 2q+1
       802: q+1
       803: 1
       806: q+1
       807: q^2+q+1
       810: 2q+1
       812: 2q+1
       814: 3q+1
       815: q
       816: 2q+1
       817: 1
       820: 1
       822: 1
       824: 1
       826: q+1
       827: 1
       831: 1
       834: 1
       836: 1
       838: q+1
       839: q+1
       842: 2q+1
       844: 1
       846: q+1
       847: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       891: q+1
       898: q+1
       901: 1
       907: q+1
       910: 1
       915: q+1
       919: 1
       923: q+1
       925: 1
       931: q+1
       933: q
       935: 2q+1
       937: 1
       941: 1
       945: 1
       949: 1
       957: q+1
       963: 1
       966: 1
       972: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 2q+1
      1005: q+1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1017: 1
      1019: 2q+1
      1021: q+1
      1023: 2q+1
      1025: 2q+1
      1027: q+1
      1028: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: q+1
      1111: 1
      1115: 1
      1121: q+1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: q+1
      1153: 1
      1159: q+1
      1161: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1203: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1229: 1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 2q+1
      1241: q+1
      1242: 1
      1245: 1
      1246: 1
      1253: 1
      1257: 1
      1260: 1
      1263: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1345: 1
      1349: 1
      1355: q+1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: 1
      1377: 1
      1408: 1
      1412: 1
      1417: 1
      1419: 1
      1434: 1
      1439: 1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1450: 1
      1453: q+1
      1455: 1
      1459: 1
      1471: 1
      1473: 1
      1475: 1
      1478: 1
      1481: 1
      1483: 1
      1485: 1
      1488: 1
      1496: 1
      1507: 1
      1532: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1604: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1668: 1
      1670: 1
      1672: 1
      1682: 1
      1693: 1
      1738: 1
      1748: 1
      1750: 1
      1755: 1
      1805: 1
      1852: 1

1853:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: q^2+2q+1
        61: q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+3q+1
        73: 3q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q^2+2q+1
       105: q
       107: q^2+2q+1
       108: q
       109: q^2+q
       110: 2q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+q
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: 3q+1
       146: 2q^2+3q+1
       147: 3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+2q+1
       184: q
       185: q^2+q
       186: 2q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+q
       192: 2q^2+2q+1
       193: q^2+2q+1
       194: q
       195: q^2+q
       196: 2q^2+2q+1
       198: q^2+3q+1
       199: q^2+2q+1
       200: q
       201: 2q+1
       202: q
       204: q+1
       206: q+1
       208: q^2+3q+1
       210: 2q^2+3q+1
       212: 2q^2+3q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: q^2+3q+1
       223: 2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: q^2+3q+1
       230: 3q^2+3q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 3q+1
       235: q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: 3q+1
       245: q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q^2+2q+1
       270: q
       274: q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q+1
       286: q^2+q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+2q+1
       294: q
       295: q^2+q
       296: 2q^2+2q+1
       298: q^2+3q+1
       299: q^2+2q+1
       300: q
       302: 3q+1
       303: q^2+q
       304: 2q^2+2q+1
       306: q^2+3q+1
       307: 2q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: 2q+1
       318: 3q+1
       319: 2q+1
       320: q
       322: q+1
       324: q+1
       326: 2q^2+3q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: q^2+3q+1
       348: 2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: 3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: 2q+1
       357: q+1
       358: 1
       359: q+1
       361: 3q+1
       363: 3q+1
       365: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: 3q+1
       370: q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: 2q+1
       392: q
       394: q^2+2q+1
       395: q
       400: q+1
       403: q+1
       407: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q+1
       422: q^2+q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: q+1
       432: q^2+q+1
       434: 2q+1
       436: 3q+1
       437: q^2+2q+1
       438: q
       439: q^2+q
       440: 2q^2+2q+1
       442: q^2+3q+1
       443: 2q+1
       444: q
       446: 3q+1
       447: q+1
       450: 1
       452: 1
       453: 2q+1
       454: q
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 3q+1
       468: 2q+1
       470: 2q+1
       471: 2q+1
       472: q
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: 3q+1
       486: 3q+1
       488: 3q+1
       490: q^2+2q+1
       491: 2q+1
       492: 2q^2+2q+1
       493: 2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: 3q+1
       497: 2q+1
       498: 2q+1
       499: 1
       500: 1
       501: q+1
       503: 3q+1
       505: 3q+1
       507: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: 2q+1
       513: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: q+1
       538: 2q+1
       540: q
       542: q^2+2q+1
       544: q
       546: 2q+1
       548: q
       551: 1
       556: q+1
       560: q+1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q+1
       592: 1
       593: q+1
       596: q^2+q+1
       598: 2q+1
       600: 2q+1
       602: 3q+1
       603: q+1
       606: 2q+1
       608: q^2+q+1
       610: 2q+1
       612: 3q+1
       614: 2q+1
       615: 2q+1
       616: q
       618: 3q+1
       619: q+1
       622: 1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: q+1
       634: q+1
       636: 3q+1
       638: 2q+1
       640: 2q+1
       641: q+1
       644: 1
       646: 1
       647: 2q+1
       648: q
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q+1
       667: 3q+1
       669: 3q+1
       671: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: q+1
       675: 2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: 1
       681: 2q+1
       682: 1
       683: 1
       684: q+1
       685: 1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       706: q+1
       710: q+1
       715: 1
       718: q+1
       722: q+1
       726: q+1
       730: 2q+1
       732: q
       734: 2q+1
       736: q
       740: 1
       744: 1
       748: q+1
       752: q+1
       754: 1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       785: q+1
       788: 1
       790: 3q+1
       792: 1
       793: 1
       796: q+1
       798: 2q+1
       800: 2q+1
       801: q+1
       804: 1
       805: q+1
       808: q^2+q+1
       810: 2q+1
       812: 2q+1
       814: 3q+1
       815: 2q+1
       816: q
       818: 1
       820: 1
       822: 1
       824: 1
       825: q+1
       828: 1
       832: 1
       834: 1
       836: 1
       838: q+1
       840: q+1
       842: 2q+1
       844: 1
       845: q+1
       848: 1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 2q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       890: q+1
       897: q+1
       903: 1
       905: q+1
       909: 1
       913: q+1
       917: 1
       921: q+1
       926: 1
       929: q+1
       933: 2q+1
       935: q
       939: 1
       943: 1
       947: 1
       951: 1
       959: q+1
       962: 1
       965: 1
       972: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 2q+1
      1004: q+1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: 1
      1019: 2q+1
      1021: q+1
      1023: 2q+1
      1025: 2q+1
      1026: q+1
      1029: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: q+1
      1113: 1
      1117: 1
      1119: q+1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: q+1
      1155: 1
      1157: q+1
      1162: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1205: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1228: 1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 2q+1
      1240: q+1
      1243: 1
      1245: 1
      1247: 1
      1253: 1
      1257: 1
      1261: 1
      1263: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1347: 1
      1351: 1
      1353: q+1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1408: 1
      1411: 1
      1416: 1
      1421: 1
      1434: 1
      1439: 1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1451: 1
      1453: q+1
      1454: 1
      1459: 1
      1471: 1
      1473: 1
      1475: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1488: 1
      1495: 1
      1508: 1
      1531: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1606: 1
      1635: 1
      1644: 1
      1646: 1
      1647: 1
      1668: 1
      1670: 1
      1672: 1
      1681: 1
      1694: 1
      1740: 1
      1746: 1
      1751: 1
      1756: 1
      1805: 1
      1853: 1

1854:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 2q^4+7q^3+6q^2+3q
        23: 2q^4+7q^3+6q^2+3q
        24: 2q^4+7q^3+6q^2+3q
        25: 4q^3+5q^2+3q
        26: 4q^3+5q^2+3q
        27: 4q^3+5q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 2q^4+7q^3+6q^2+3q
        32: 2q^4+7q^3+6q^2+3q
        33: 3q^3+5q^2+3q
        34: 4q^3+5q^2+3q
        35: 4q^3+5q^2+3q
        36: q^3+4q^2+3q
        37: 2q^3+2q^2+q
        38: 2q^3+3q^2+2q
        39: 2q^3+2q^2+q
        40: 2q^3+3q^2+2q
        41: 2q^3+2q^2+q
        42: 2q^3+3q^2+2q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 2q^4+7q^3+6q^2+3q
        53: 2q^4+7q^3+6q^2+3q
        54: 2q^4+7q^3+6q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: 4q^3+5q^2+3q
        58: q^3+2q^2+q
        59: 2q^3+3q^2+2q
        60: 2q^2+q
        61: q^3+2q^2+2q
        62: 2q^3+2q^2+q
        63: 2q^3+3q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: q^3+4q^2+3q
        73: 3q^3+5q^2+3q
        74: 2q^3+2q^2+q
        75: 2q^3+3q^2+2q
        76: 2q^3+2q^2+q
        77: 2q^3+3q^2+2q
        78: 2q^3+2q^2+q
        79: 2q^3+3q^2+2q
        80: 2q^4+7q^3+6q^2+3q
        81: 3q^3+5q^2+3q
        82: 2q^4+7q^3+6q^2+3q
        83: 2q^4+7q^3+6q^2+3q
        84: 4q^3+5q^2+3q
        85: q^3+4q^2+3q
        86: 4q^3+5q^2+3q
        87: 4q^3+5q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^3+5q^2+3q
        95: 3q^3+5q^2+3q
        96: q^4+3q^3+3q^2+2q
        97: 3q^2+3q
        98: 3q^2+3q
        99: q^3+2q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2
       104: q^2+q
       105: q^2+q
       106: q^3+q^2+q
       107: 2q^2+q
       108: q^3+2q^2+2q
       109: q^3+2q^2+q
       110: 2q^3+3q^2+2q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: 2q^3+2q^2+q
       114: 2q^3+3q^2+2q
       115: 2q^3+2q^2+q
       116: 2q^3+3q^2+2q
       117: q^3+2q^2+q
       118: 2q^3+3q^2+2q
       119: 2q^2+q
       120: q^3+2q^2+2q
       121: 2q^3+2q^2+q
       122: 2q^3+3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: q^3+4q^2+3q
       136: 3q^3+5q^2+3q
       137: 3q^3+5q^2+3q
       138: q^3+2q^2+2q
       139: 3q^3+5q^2+3q
       140: q^3+4q^2+3q
       141: 2q^4+7q^3+6q^2+3q
       142: 3q^3+5q^2+3q
       143: q^3+4q^2+3q
       144: q^2+2q
       145: 3q^2+3q
       146: 4q^3+5q^2+3q
       147: 3q^2+3q
       148: q^2+2q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+2q^2+q
       152: 2q^3+3q^2+2q
       153: 2q^3+2q^2+q
       154: 2q^3+3q^2+2q
       155: 2q^3+2q^2+q
       156: 2q^3+3q^2+2q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+5q^2+3q
       161: 3q^3+5q^2+3q
       162: q^4+3q^3+3q^2+2q
       163: 3q^2+3q
       164: 3q^2+3q
       165: q^3+2q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2
       170: q^2+q
       171: q^2+q
       172: q^3+q^2+q
       173: q^2
       174: q^2+q
       175: q^2+q
       176: q^3+q^2+q
       178: q
       180: q^2+2q
       182: q^2+2q
       183: 2q^2+q
       184: q^3+2q^2+2q
       185: q^3+2q^2+q
       186: 2q^3+3q^2+2q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: 2q^3+2q^2+q
       190: 2q^3+3q^2+2q
       191: q^3+2q^2+q
       192: 2q^3+3q^2+2q
       193: 2q^2+q
       194: q^3+2q^2+2q
       195: q^3+2q^2+q
       196: 2q^3+3q^2+2q
       197: q^3+2q^2+q
       198: 2q^2+2q
       199: 2q^2+q
       200: q^3+2q^2+2q
       201: q^2+q
       202: 2q^2+2q
       204: q^2+2q
       205: q^2+q
       206: q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: 2q^3+2q^2+q
       210: 2q^3+3q^2+2q
       211: 2q^3+2q^2+q
       212: 2q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: q^3+4q^2+3q
       223: q^2+2q
       224: 3q^3+5q^2+3q
       225: q^3+2q^2+2q
       226: q^3+2q^2+2q
       227: 3q^3+5q^2+3q
       228: q^3+2q^2+2q
       229: q^3+4q^2+3q
       230: 3q^3+5q^2+3q
       231: q^2+2q
       232: 3q^2+3q
       233: q^2+2q
       234: 3q^2+3q
       235: q^2+2q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q^2+3q
       244: 3q^2+3q
       245: q^2+2q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^3+5q^2+3q
       251: 3q^3+5q^2+3q
       252: q^4+3q^3+3q^2+2q
       253: 3q^2+3q
       254: 3q^2+3q
       255: q^3+2q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       260: q
       261: q^2+q
       263: q^2
       264: q^2+q
       265: q^2+q
       266: q^3+q^2+q
       267: q^2
       268: q^2+q
       269: q^3+q^2+q
       270: q^2+q
       273: q^2+q
       274: q
       275: q^2
       276: q^2+q
       277: q^2+q
       278: q^3+q^2+q
       280: q^2+2q
       282: q
       284: q
       286: q^2+q
       288: q
       290: q^2+2q
       292: q
       293: 2q^2+q
       294: q^3+2q^2+2q
       295: q^3+2q^2+q
       296: 2q^3+3q^2+2q
       297: q^3+2q^2+q
       298: 2q^2+2q
       299: 2q^2+q
       300: q^3+2q^2+2q
       302: q^2+2q
       303: q^3+2q^2+q
       304: 2q^3+3q^2+2q
       305: q^3+2q^2+q
       306: 2q^2+2q
       307: q^2+q
       308: 2q^2+2q
       310: q^2+2q
       312: q
       313: q^2+q
       314: q
       316: q
       318: q^2+2q
       319: q^2+q
       320: 2q^2+2q
       322: q^2+2q
       323: q^2+q
       324: q
       325: 2q^3+2q^2+q
       326: 2q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: q^3+2q^2+2q
       334: q^2+2q
       335: q^3+2q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: q^3+2q^2+2q
       345: 3q^3+5q^2+3q
       346: q^3+2q^2+2q
       347: q^3+4q^2+3q
       348: q^2+2q
       349: 3q^3+5q^2+3q
       350: q^3+2q^2+2q
       351: 3q^2+3q
       352: q^2+2q
       353: 3q^2+3q
       354: q^2+2q
       355: 3q^2+3q
       356: q^2+2q
       357: q^2+2q
       358: q
       359: q^2+2q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: 3q^2+3q
       370: q^2+2q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       382: q
       383: q^2+q
       385: q^2
       386: q^2+q
       387: q^2+q
       388: q^3+q^2+q
       390: q
       392: q^2+q
       393: q^2
       394: q^2+q
       395: q^2+q
       396: q^3+q^2+q
       400: q
       403: q
       404: q^2+q
       406: q^2+q
       407: q
       410: q^2+2q
       412: q
       414: q
       416: q^2+2q
       418: q
       420: q
       422: q^2+q
       424: q
       426: q
       428: q^2+2q
       430: q
       432: q^2+q
       434: q
       436: q^2+2q
       437: 2q^2+q
       438: q^3+2q^2+2q
       439: q^3+2q^2+q
       440: 2q^3+3q^2+2q
       441: q^3+2q^2+q
       442: 2q^2+2q
       443: q^2+q
       444: 2q^2+2q
       446: q^2+2q
       448: q
       450: q
       453: q^2+q
       454: 2q^2+2q
       456: q
       458: q^2+2q
       459: q^2+q
       460: q
       462: q^2+2q
       464: q
       466: q^2+2q
       468: q
       470: q
       471: q^2+q
       472: 2q^2+2q
       474: q^2+2q
       475: q^2+q
       476: q
       478: q
       479: q^2+q
       480: q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: q^3+2q^2+2q
       493: q^2+2q
       494: q^3+2q^2+2q
       495: q^2+2q
       496: 3q^2+3q
       497: q^2+2q
       498: q^2+2q
       499: q
       500: q
       501: q^2+2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: 3q^2+3q
       512: q^2+2q
       513: q^2+2q
       514: q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       526: q
       527: q^2+q
       538: q
       540: q^2+q
       541: q^2
       542: q^2+q
       543: q^3+q^2+q
       544: q^2+q
       546: q
       548: q^2+q
       556: q
       559: q^2+q
       560: q
       564: q
       566: q
       568: q^2+q
       571: q
       574: q
       575: q^2+q
       581: q
       584: q
       586: q
       588: q
       590: q
       592: q
       594: q
       596: q^2+q
       598: q
       600: q
       602: q^2+2q
       604: q
       606: q
       608: q^2+q
       610: q
       612: q^2+2q
       614: q
       615: q^2+q
       616: 2q^2+2q
       618: q^2+2q
       620: q
       622: q
       628: q
       632: q^2+2q
       634: q
       636: q^2+2q
       638: q
       640: q
       642: q
       644: q
       647: q^2+q
       648: 2q^2+2q
       650: q^2+2q
       652: q
       653: q^2+q
       654: q
       655: q^2+q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q^2+2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: q+1
       675: q^2+2q
       676: q^3+2q^2+2q
       677: q^2+2q
       678: 3q^2+3q
       679: q^2+2q
       680: 1
       681: q^2+2q
       682: q
       683: q
       684: q^2+2q
       685: q
       686: q^2+2q
       687: q^2+2q
       688: q
       689: q
       690: q+1
       691: q+1
       692: q+1
       699: q
       730: q
       732: q^2+q
       734: q
       736: q^2+q
       748: q
       752: q
       759: q
       762: q^2+q
       763: q
       766: q
       768: q^2+q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: q^2+2q
       794: 1
       796: q+1
       798: q
       800: q
       802: q
       804: q
       806: q
       808: q^2+q
       810: q
       812: q
       814: q^2+2q
       815: q^2+q
       816: 2q^2+2q
       818: 1
       820: 1
       826: q
       828: q
       832: q
       838: q
       840: q^2+2q
       842: q
       843: 1
       846: q
       848: q
       854: q
       857: q^2+q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: q+1
       870: q+1
       871: q^2+2q
       872: q^2+2q
       873: 1
       874: 1
       875: q
       876: q
       877: q^2+2q
       878: q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       890: q
       919: 1
       933: q
       935: q^2+q
       943: 1
       959: q
       967: 1
       969: 1
       980: q
       986: q
       989: q
       991: q^2+q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: q+1
      1017: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: 1
      1033: 1
      1037: 1
      1045: q
      1046: 1
      1053: q
      1055: q
      1059: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: q^2+2q
      1079: 1
      1081: 1
      1082: q
      1083: q
      1084: 1
      1085: q
      1094: 1
      1104: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1227: q+1
      1229: 1
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1245: 1
      1247: 1
      1253: 1
      1261: q
      1262: 1
      1271: q
      1275: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1286: 1
      1288: 1
      1289: q
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1343: 1
      1351: 1
      1359: 1
      1367: 1
      1375: 1
      1405: 1
      1413: 1
      1431: 1
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1449: 1
      1451: 1
      1453: q+1
      1455: 1
      1459: 1
      1473: 1
      1479: q
      1482: 1
      1485: 1
      1488: 1
      1497: 1
      1509: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1566: 1
      1570: 1
      1578: 1
      1632: 1
      1644: 1
      1646: 1
      1648: 1
      1668: 1
      1669: 1
      1683: 1
      1695: 1
      1740: 1
      1748: 1
      1752: 1
      1802: 1
      1854: 1

1855:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 7q^4+7q^3+3q^2+q
        23: 2q^5+8q^4+7q^3+3q^2+q
        24: 7q^4+7q^3+3q^2+q
        25: 4q^4+6q^3+3q^2+q
        26: q^5+5q^4+6q^3+3q^2+q
        27: 4q^4+6q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 5q^4+6q^3+3q^2+q
        32: 7q^4+7q^3+3q^2+q
        33: 5q^4+6q^3+3q^2+q
        34: 3q^4+5q^3+3q^2+q
        35: 4q^4+6q^3+3q^2+q
        36: 3q^4+5q^3+3q^2+q
        37: 4q^4+6q^3+3q^2+q
        39: q^5+5q^4+6q^3+3q^2+q
        41: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: 4q^4+6q^3+3q^2+q
        53: q^5+5q^4+6q^3+3q^2+q
        54: 4q^4+6q^3+3q^2+q
        55: q^4+5q^3+3q^2+q
        56: 2q^4+5q^3+3q^2+q
        57: q^4+5q^3+3q^2+q
        58: q^4+q^3+q^2
        59: 2q^4+4q^3+2q^2+q
        60: q^3+q^2
        61: 2q^4+3q^3+2q^2+q
        62: 3q^4+5q^3+3q^2+q
        64: 4q^4+6q^3+3q^2+q
        66: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 4q^3+3q^2+q
        74: q^4+5q^3+3q^2+q
        76: 2q^4+5q^3+3q^2+q
        78: q^4+5q^3+3q^2+q
        80: 5q^4+6q^3+3q^2+q
        81: 5q^4+6q^3+3q^2+q
        82: 3q^4+5q^3+3q^2+q
        83: 4q^4+6q^3+3q^2+q
        84: 3q^4+5q^3+3q^2+q
        85: 3q^4+5q^3+3q^2+q
        86: q^4+4q^3+3q^2+q
        87: q^4+5q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 2q^4+5q^3+3q^2+q
        95: 2q^4+5q^3+3q^2+q
        96: 2q^4+4q^3+2q^2+q
        97: 3q^3+3q^2+q
        98: 3q^3+3q^2+q
        99: 3q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       103: q^3+q^2
       106: 2q^4+3q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: q^2
       110: 3q^3+2q^2+q
       111: 3q^3+3q^2+q
       113: q^4+4q^3+3q^2+q
       115: q^4+5q^3+3q^2+q
       117: q^4+q^3+q^2
       118: 2q^4+4q^3+2q^2+q
       119: q^3+q^2
       120: 2q^4+3q^3+2q^2+q
       121: 3q^4+5q^3+3q^2+q
       123: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       127: 3q^3+3q^2+q
       129: 3q^3+3q^2+q
       131: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 4q^3+3q^2+q
       137: q^4+4q^3+3q^2+q
       138: q^4+3q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: 3q^3+3q^2+q
       141: 3q^4+5q^3+3q^2+q
       142: 4q^3+3q^2+q
       143: q^4+3q^3+3q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^4+4q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: 2q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       151: q^4+5q^3+3q^2+q
       153: 2q^4+5q^3+3q^2+q
       155: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^4+5q^3+3q^2+q
       161: 2q^4+5q^3+3q^2+q
       162: 2q^4+4q^3+2q^2+q
       163: 3q^3+3q^2+q
       164: 3q^3+3q^2+q
       165: 3q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       169: q^2
       172: 2q^3+2q^2+q
       173: q^3+q^2
       176: 2q^4+3q^3+2q^2+q
       177: 2q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: q^2
       184: 2q^3+2q^2+q
       185: q^2
       186: 3q^3+2q^2+q
       187: 3q^3+3q^2+q
       189: q^4+4q^3+3q^2+q
       191: q^3+q^2
       192: q^4+3q^3+2q^2+q
       193: q^2
       194: 2q^3+2q^2+q
       195: q^2
       196: 3q^3+2q^2+q
       197: 3q^3+3q^2+q
       199: q^3+q^2
       200: q^4+2q^3+2q^2+q
       201: q^2
       202: q^3+2q^2+q
       204: 2q^2+q
       205: 2q^2+q
       207: q^4+3q^3+3q^2+q
       209: q^4+4q^3+3q^2+q
       211: q^4+5q^3+3q^2+q
       213: 3q^3+3q^2+q
       215: 3q^3+3q^2+q
       217: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^4+4q^3+3q^2+q
       228: q^4+3q^3+2q^2+q
       229: 3q^3+3q^2+q
       230: 4q^3+3q^2+q
       231: q^3+2q^2+q
       232: 2q^3+3q^2+q
       233: 2q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: 2q^2+q
       236: 2q^3+2q^2+q
       237: 3q^3+3q^2+q
       239: 3q^3+3q^2+q
       241: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^3+3q^2+q
       245: 2q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^3+3q^2+q
       251: 2q^3+3q^2+q
       252: q^4+2q^3+2q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       259: q^2
       262: q^3+2q^2+q
       263: q^2
       266: 2q^3+2q^2+q
       267: q^2
       269: 2q^3+2q^2+q
       273: 2q^2+q
       275: q^3+q^2
       278: q^4+2q^3+2q^2+q
       279: 2q^3+3q^2+q
       281: 2q^3+2q^2+q
       284: q^2+q
       286: q^3+q^2+q
       287: q^3+2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^2
       296: q^3+2q^2+q
       297: q^3+3q^2+q
       299: q^2
       300: 2q^3+2q^2+q
       301: 2q^3+3q^2+q
       303: q^2
       304: 3q^3+2q^2+q
       305: 3q^3+3q^2+q
       307: q^2
       308: q^3+2q^2+q
       310: 2q^2+q
       311: 2q^2+q
       313: 2q^2+q
       315: 2q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: q^2
       320: q^3+2q^2+q
       322: 2q^2+q
       323: 2q^2+q
       325: q^4+4q^3+3q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: 2q^3+3q^2+q
       346: q^3+2q^2+q
       347: q^3+3q^2+q
       348: q^3+2q^2+q
       349: q^3+3q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: 3q^3+3q^2+q
       362: 3q^3+3q^2+q
       364: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^3+3q^2+q
       370: 2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       380: q^2+q
       381: q^2
       384: q^3+2q^2+q
       385: q^2
       388: q^3+2q^2+q
       389: q^2
       391: q^3+2q^2+q
       393: q^2
       396: 2q^3+2q^2+q
       399: 2q^2+q
       404: 2q^2+q
       406: 2q^2+q
       409: 2q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       430: q^2+q
       432: q^3+q^2+q
       433: q^3+2q^2+q
       435: 2q^3+3q^2+q
       437: q^2
       438: q^3+2q^2+q
       439: q^2
       440: q^3+2q^2+q
       441: q^3+3q^2+q
       443: q^2
       444: q^2+q
       445: 2q^2+q
       448: q^2+q
       450: q^2+q
       451: q^2+q
       453: q^2
       454: q^2+q
       455: 2q^2+q
       458: q^2+q
       459: q^2+q
       462: q^2+q
       463: q^2+q
       465: 2q^3+3q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: q^2
       472: q^3+2q^2+q
       474: 2q^2+q
       475: 2q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       502: 2q^2+q
       504: 2q^2+q
       506: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: 2q^2+q
       512: q^3+2q^2+q
       513: q^2+q
       514: q^2+q
       524: q^2+q
       525: q^2
       528: q^2+q
       532: q^2+q
       536: q^2+q
       537: q^2
       539: q^3+2q^2+q
       541: q^2
       543: q^3+2q^2+q
       545: q^2
       547: q^2+q
       552: q^2+q
       555: 2q^2+q
       559: q^2+q
       563: q^2+q
       568: 2q^2+q
       570: 2q^2+q
       575: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       590: q^2+q
       592: q
       594: q
       596: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       604: q^2+q
       605: q^3+2q^2+q
       608: q^2+q
       609: 2q^2+q
       611: 2q^2+q
       613: q^2+q
       615: q^2
       616: q^2+q
       617: 2q^2+q
       620: q
       622: q
       623: q^2+q
       625: q
       627: q^2+q
       629: q
       632: q^2+q
       633: q^2+q
       635: 2q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       647: q^2
       648: q^2+q
       650: q^2+q
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       665: q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       697: q^2+q
       708: q
       712: q^2+q
       716: q
       720: q
       723: q^2+q
       727: q^2+q
       729: q^2
       731: q^2+q
       733: q^2
       735: q^2+q
       739: q^2+q
       743: q
       747: q^2+q
       751: q^2+q
       756: q^2+q
       758: 2q^2+q
       762: q^2+q
       768: q^2+q
       769: q^2+q
       777: q^2+q
       781: q^2+q
       786: q
       788: q
       791: q
       797: 2q^2+q
       799: q^2+q
       802: q^2+q
       804: q
       806: q
       808: q^2+q
       809: q^2+q
       811: q^2+q
       821: q
       823: q
       826: q
       828: q
       832: q
       833: q
       835: q
       841: q^2+q
       846: q
       848: q
       849: q^2+q
       851: q
       853: q^2+q
       855: q
       871: q^2+q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       889: q^2+q
       899: q
       902: q
       906: q
       911: q
       914: q
       922: q^2+q
       927: q
       930: q
       938: q
       946: q
       950: q
       961: q^2+q
       975: q
       979: q^2+q
      1010: q
      1018: q^2+q
      1022: q^2+q
      1027: q
      1029: q
      1034: q
      1038: q
      1045: q
      1048: q
      1050: q
      1053: q
      1055: q
      1059: q
      1060: q
      1062: q
      1064: q
      1083: q
      1127: q
      1150: q
      1154: q
      1158: q
      1163: q
      1170: q
      1174: q
      1185: q
      1199: q
      1204: q
      1222: 1
      1264: q
      1266: q
      1271: q
      1278: q
      1323: 1
      1336: 1
      1361: q
      1415: q
      1420: q
      1446: 1
      1480: 1
      1498: 1
      1555: 1
      1560: 1
      1572: 1
      1633: 1
      1671: 1
      1684: 1
      1696: 1
      1754: 1
      1803: 1
      1855: 1

1856:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 7q^4+7q^3+3q^2+q
        23: 2q^5+8q^4+7q^3+3q^2+q
        24: 7q^4+7q^3+3q^2+q
        25: 4q^4+6q^3+3q^2+q
        26: q^5+5q^4+6q^3+3q^2+q
        27: 4q^4+6q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 5q^4+6q^3+3q^2+q
        32: 7q^4+7q^3+3q^2+q
        33: 5q^4+6q^3+3q^2+q
        34: 3q^4+5q^3+3q^2+q
        35: 4q^4+6q^3+3q^2+q
        36: 3q^4+5q^3+3q^2+q
        38: 4q^4+6q^3+3q^2+q
        40: q^5+5q^4+6q^3+3q^2+q
        42: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: 4q^4+6q^3+3q^2+q
        53: q^5+5q^4+6q^3+3q^2+q
        54: 4q^4+6q^3+3q^2+q
        55: q^4+5q^3+3q^2+q
        56: 2q^4+5q^3+3q^2+q
        57: q^4+5q^3+3q^2+q
        58: 2q^4+4q^3+2q^2+q
        59: q^4+q^3+q^2
        60: q^3+q^2
        61: 2q^4+3q^3+2q^2+q
        63: 3q^4+5q^3+3q^2+q
        65: 4q^4+6q^3+3q^2+q
        67: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 4q^3+3q^2+q
        75: q^4+5q^3+3q^2+q
        77: 2q^4+5q^3+3q^2+q
        79: q^4+5q^3+3q^2+q
        80: 5q^4+6q^3+3q^2+q
        81: 5q^4+6q^3+3q^2+q
        82: 3q^4+5q^3+3q^2+q
        83: 4q^4+6q^3+3q^2+q
        84: 3q^4+5q^3+3q^2+q
        85: 3q^4+5q^3+3q^2+q
        86: q^4+4q^3+3q^2+q
        87: q^4+5q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 2q^4+5q^3+3q^2+q
        95: 2q^4+5q^3+3q^2+q
        96: 2q^4+4q^3+2q^2+q
        97: 3q^3+3q^2+q
        98: 3q^3+3q^2+q
        99: 3q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       104: q^3+q^2
       105: 2q^4+3q^3+2q^2+q
       107: q^2
       108: 2q^3+2q^2+q
       109: 3q^3+2q^2+q
       110: q^2
       112: 3q^3+3q^2+q
       114: q^4+4q^3+3q^2+q
       116: q^4+5q^3+3q^2+q
       117: 2q^4+4q^3+2q^2+q
       118: q^4+q^3+q^2
       119: q^3+q^2
       120: 2q^4+3q^3+2q^2+q
       122: 3q^4+5q^3+3q^2+q
       124: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       128: 3q^3+3q^2+q
       130: 3q^3+3q^2+q
       132: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 4q^3+3q^2+q
       137: q^4+4q^3+3q^2+q
       138: q^4+3q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: 3q^3+3q^2+q
       141: 3q^4+5q^3+3q^2+q
       142: 4q^3+3q^2+q
       143: q^4+3q^3+3q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^4+4q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: 2q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       152: q^4+5q^3+3q^2+q
       154: 2q^4+5q^3+3q^2+q
       156: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^4+5q^3+3q^2+q
       161: 2q^4+5q^3+3q^2+q
       162: 2q^4+4q^3+2q^2+q
       163: 3q^3+3q^2+q
       164: 3q^3+3q^2+q
       165: 3q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       170: q^2
       171: 2q^3+2q^2+q
       174: q^3+q^2
       175: 2q^4+3q^3+2q^2+q
       178: 2q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: q^2
       184: 2q^3+2q^2+q
       185: 3q^3+2q^2+q
       186: q^2
       188: 3q^3+3q^2+q
       190: q^4+4q^3+3q^2+q
       191: q^4+3q^3+2q^2+q
       192: q^3+q^2
       193: q^2
       194: 2q^3+2q^2+q
       195: 3q^3+2q^2+q
       196: q^2
       198: 3q^3+3q^2+q
       199: q^3+q^2
       200: q^4+2q^3+2q^2+q
       201: q^2
       202: q^3+2q^2+q
       203: 2q^2+q
       206: 2q^2+q
       208: q^4+3q^3+3q^2+q
       210: q^4+4q^3+3q^2+q
       212: q^4+5q^3+3q^2+q
       214: 3q^3+3q^2+q
       216: 3q^3+3q^2+q
       218: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^4+4q^3+3q^2+q
       228: q^4+3q^3+2q^2+q
       229: 3q^3+3q^2+q
       230: 4q^3+3q^2+q
       231: q^3+2q^2+q
       232: 2q^3+3q^2+q
       233: 2q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: 2q^2+q
       236: 2q^3+2q^2+q
       238: 3q^3+3q^2+q
       240: 3q^3+3q^2+q
       242: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^3+3q^2+q
       245: 2q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^3+3q^2+q
       251: 2q^3+3q^2+q
       252: q^4+2q^3+2q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       260: q^2
       261: q^3+2q^2+q
       264: q^2
       265: 2q^3+2q^2+q
       268: q^2
       270: 2q^3+2q^2+q
       272: 2q^2+q
       276: q^3+q^2
       277: q^4+2q^3+2q^2+q
       280: 2q^3+3q^2+q
       282: 2q^3+2q^2+q
       284: q^2+q
       285: q^3+q^2+q
       288: q^3+2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       296: q^2
       298: q^3+3q^2+q
       299: q^2
       300: 2q^3+2q^2+q
       302: 2q^3+3q^2+q
       303: 3q^3+2q^2+q
       304: q^2
       306: 3q^3+3q^2+q
       307: q^2
       308: q^3+2q^2+q
       309: 2q^2+q
       312: 2q^2+q
       314: 2q^2+q
       316: 2q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: q^2
       320: q^3+2q^2+q
       321: 2q^2+q
       324: 2q^2+q
       326: q^4+4q^3+3q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: 2q^3+3q^2+q
       346: q^3+2q^2+q
       347: q^3+3q^2+q
       348: q^3+2q^2+q
       349: q^3+3q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: 3q^3+3q^2+q
       363: 3q^3+3q^2+q
       365: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^3+3q^2+q
       370: 2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       379: q^2+q
       382: q^2
       383: q^3+2q^2+q
       386: q^2
       387: q^3+2q^2+q
       390: q^2
       392: q^3+2q^2+q
       394: q^2
       395: 2q^3+2q^2+q
       398: 2q^2+q
       402: 2q^2+q
       408: 2q^2+q
       410: 2q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       430: q^2+q
       431: q^3+q^2+q
       434: q^3+2q^2+q
       436: 2q^3+3q^2+q
       437: q^2
       438: q^3+2q^2+q
       439: q^3+2q^2+q
       440: q^2
       442: q^3+3q^2+q
       443: q^2
       444: q^2+q
       446: 2q^2+q
       448: q^2+q
       449: q^2+q
       452: q^2+q
       453: q^2
       454: q^2+q
       456: 2q^2+q
       457: q^2+q
       460: q^2+q
       461: q^2+q
       464: q^2+q
       466: 2q^3+3q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: q^2
       472: q^3+2q^2+q
       473: 2q^2+q
       476: 2q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       503: 2q^2+q
       505: 2q^2+q
       507: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: 2q^2+q
       512: q^3+2q^2+q
       513: q^2+q
       514: q^2+q
       523: q^2+q
       526: q^2
       527: q^2+q
       531: q^2+q
       535: q^2+q
       538: q^2
       540: q^3+2q^2+q
       542: q^2
       544: q^3+2q^2+q
       546: q^2
       548: q^2+q
       550: q^2+q
       554: 2q^2+q
       558: q^2+q
       562: q^2+q
       567: 2q^2+q
       572: 2q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       604: q^2+q
       606: q^3+2q^2+q
       607: q^2+q
       610: 2q^2+q
       612: 2q^2+q
       614: q^2+q
       615: q^2
       616: q^2+q
       618: 2q^2+q
       620: q
       621: q
       624: q^2+q
       626: q
       628: q^2+q
       630: q
       631: q^2+q
       634: q^2+q
       636: 2q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       647: q^2
       648: q^2+q
       649: q^2+q
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       665: q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       700: q^2+q
       707: q
       711: q^2+q
       714: q
       719: q
       724: q^2+q
       728: q^2+q
       730: q^2
       732: q^2+q
       734: q^2
       736: q^2+q
       738: q^2+q
       742: q
       746: q^2+q
       750: q^2+q
       755: q^2+q
       760: 2q^2+q
       764: q^2+q
       767: q^2+q
       773: q^2+q
       778: q^2+q
       782: q^2+q
       786: q
       787: q
       792: q
       798: 2q^2+q
       800: q^2+q
       802: q^2+q
       803: q
       806: q
       807: q^2+q
       810: q^2+q
       812: q^2+q
       822: q
       824: q
       826: q
       827: q
       831: q
       834: q
       836: q
       842: q^2+q
       846: q
       847: q
       850: q^2+q
       852: q
       854: q^2+q
       856: q
       871: q^2+q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       891: q^2+q
       898: q
       901: q
       907: q
       910: q
       915: q
       923: q^2+q
       925: q
       931: q
       937: q
       945: q
       949: q
       963: q^2+q
       977: q
       981: q^2+q
      1011: q
      1019: q^2+q
      1023: q^2+q
      1027: q
      1028: q
      1035: q
      1039: q
      1044: q
      1049: q
      1051: q
      1053: q
      1054: q
      1058: q
      1061: q
      1063: q
      1065: q
      1083: q
      1129: q
      1151: q
      1153: q
      1159: q
      1161: q
      1169: q
      1173: q
      1187: q
      1201: q
      1203: q
      1223: 1
      1265: q
      1267: q
      1270: q
      1279: q
      1325: 1
      1339: 1
      1362: q
      1417: q
      1419: q
      1447: 1
      1481: 1
      1500: 1
      1558: 1
      1562: 1
      1573: 1
      1636: 1
      1672: 1
      1686: 1
      1697: 1
      1755: 1
      1806: 1
      1856: 1

1857:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 7q^4+7q^3+3q^2+q
        23: 2q^5+8q^4+7q^3+3q^2+q
        24: 7q^4+7q^3+3q^2+q
        25: 4q^4+6q^3+3q^2+q
        26: q^5+5q^4+6q^3+3q^2+q
        27: 4q^4+6q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 5q^4+6q^3+3q^2+q
        32: 7q^4+7q^3+3q^2+q
        33: 5q^4+6q^3+3q^2+q
        34: 3q^4+5q^3+3q^2+q
        35: 4q^4+6q^3+3q^2+q
        36: 3q^4+5q^3+3q^2+q
        38: 4q^4+6q^3+3q^2+q
        40: q^5+5q^4+6q^3+3q^2+q
        42: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: 4q^4+6q^3+3q^2+q
        53: q^5+5q^4+6q^3+3q^2+q
        54: 4q^4+6q^3+3q^2+q
        55: q^4+5q^3+3q^2+q
        56: 2q^4+5q^3+3q^2+q
        57: q^4+5q^3+3q^2+q
        58: q^4+q^3+q^2
        59: 2q^4+4q^3+2q^2+q
        60: 2q^4+3q^3+2q^2+q
        61: q^3+q^2
        63: 3q^4+5q^3+3q^2+q
        65: 4q^4+6q^3+3q^2+q
        67: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 3q^3+3q^2+q
        73: 4q^3+3q^2+q
        75: q^4+5q^3+3q^2+q
        77: 2q^4+5q^3+3q^2+q
        79: q^4+5q^3+3q^2+q
        80: 5q^4+6q^3+3q^2+q
        81: 5q^4+6q^3+3q^2+q
        82: 3q^4+5q^3+3q^2+q
        83: 4q^4+6q^3+3q^2+q
        84: 3q^4+5q^3+3q^2+q
        85: 3q^4+5q^3+3q^2+q
        86: q^4+4q^3+3q^2+q
        87: q^4+5q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 2q^4+5q^3+3q^2+q
        95: 2q^4+5q^3+3q^2+q
        96: 2q^4+4q^3+2q^2+q
        97: 3q^3+3q^2+q
        98: 3q^3+3q^2+q
        99: 3q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       104: 2q^4+3q^3+2q^2+q
       105: q^3+q^2
       107: 2q^3+2q^2+q
       108: q^2
       109: q^2
       110: 3q^3+2q^2+q
       112: 3q^3+3q^2+q
       114: q^4+4q^3+3q^2+q
       116: q^4+5q^3+3q^2+q
       117: q^4+q^3+q^2
       118: 2q^4+4q^3+2q^2+q
       119: 2q^4+3q^3+2q^2+q
       120: q^3+q^2
       122: 3q^4+5q^3+3q^2+q
       124: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       128: 3q^3+3q^2+q
       130: 3q^3+3q^2+q
       132: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 3q^3+3q^2+q
       136: 4q^3+3q^2+q
       137: q^4+4q^3+3q^2+q
       138: q^4+3q^3+2q^2+q
       139: q^4+4q^3+3q^2+q
       140: 3q^3+3q^2+q
       141: 3q^4+5q^3+3q^2+q
       142: 4q^3+3q^2+q
       143: q^4+3q^3+3q^2+q
       144: 2q^3+2q^2+q
       145: 2q^3+3q^2+q
       146: q^4+4q^3+3q^2+q
       147: 2q^3+3q^2+q
       148: 2q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       152: q^4+5q^3+3q^2+q
       154: 2q^4+5q^3+3q^2+q
       156: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 2q^4+5q^3+3q^2+q
       161: 2q^4+5q^3+3q^2+q
       162: 2q^4+4q^3+2q^2+q
       163: 3q^3+3q^2+q
       164: 3q^3+3q^2+q
       165: 3q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       170: 2q^3+2q^2+q
       171: q^2
       174: 2q^4+3q^3+2q^2+q
       175: q^3+q^2
       178: 2q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: 2q^3+2q^2+q
       184: q^2
       185: q^2
       186: 3q^3+2q^2+q
       188: 3q^3+3q^2+q
       190: q^4+4q^3+3q^2+q
       191: q^3+q^2
       192: q^4+3q^3+2q^2+q
       193: 2q^3+2q^2+q
       194: q^2
       195: q^2
       196: 3q^3+2q^2+q
       198: 3q^3+3q^2+q
       199: q^4+2q^3+2q^2+q
       200: q^3+q^2
       201: q^3+2q^2+q
       202: q^2
       204: 2q^2+q
       206: 2q^2+q
       208: q^4+3q^3+3q^2+q
       210: q^4+4q^3+3q^2+q
       212: q^4+5q^3+3q^2+q
       214: 3q^3+3q^2+q
       216: 3q^3+3q^2+q
       218: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: q^3+2q^2+q
       224: q^3+3q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^4+4q^3+3q^2+q
       228: q^4+3q^3+2q^2+q
       229: 3q^3+3q^2+q
       230: 4q^3+3q^2+q
       231: q^3+2q^2+q
       232: 2q^3+3q^2+q
       233: 2q^3+2q^2+q
       234: 2q^3+3q^2+q
       235: 2q^2+q
       236: 2q^3+2q^2+q
       238: 3q^3+3q^2+q
       240: 3q^3+3q^2+q
       242: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^3+3q^2+q
       245: 2q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^3+3q^2+q
       251: 2q^3+3q^2+q
       252: q^4+2q^3+2q^2+q
       253: 2q^2+q
       254: 2q^2+q
       255: q^3+q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: 2q^3+2q^2+q
       265: q^2
       268: 2q^3+2q^2+q
       270: q^2
       274: 2q^2+q
       276: q^4+2q^3+2q^2+q
       277: q^3+q^2
       280: 2q^3+3q^2+q
       282: 2q^3+2q^2+q
       283: q^2+q
       286: q^3+q^2+q
       288: q^3+2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^2
       296: q^3+2q^2+q
       298: q^3+3q^2+q
       299: 2q^3+2q^2+q
       300: q^2
       302: 2q^3+3q^2+q
       303: q^2
       304: 3q^3+2q^2+q
       306: 3q^3+3q^2+q
       307: q^3+2q^2+q
       308: q^2
       310: 2q^2+q
       312: 2q^2+q
       314: 2q^2+q
       316: 2q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: q^3+2q^2+q
       320: q^2
       322: 2q^2+q
       324: 2q^2+q
       326: q^4+4q^3+3q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: 2q^3+3q^2+q
       346: q^3+2q^2+q
       347: q^3+3q^2+q
       348: q^3+2q^2+q
       349: q^3+3q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: 2q^2+q
       354: q^2+q
       355: 2q^2+q
       356: q^3+2q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: 3q^3+3q^2+q
       363: 3q^3+3q^2+q
       365: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^3+3q^2+q
       370: 2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       378: q^2+q
       382: q^3+2q^2+q
       383: q^2
       386: q^3+2q^2+q
       387: q^2
       390: q^3+2q^2+q
       392: q^2
       394: 2q^3+2q^2+q
       395: q^2
       400: 2q^2+q
       403: 2q^2+q
       407: 2q^2+q
       410: 2q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2+q
       432: q^3+q^2+q
       434: q^3+2q^2+q
       436: 2q^3+3q^2+q
       437: q^3+2q^2+q
       438: q^2
       439: q^2
       440: q^3+2q^2+q
       442: q^3+3q^2+q
       443: q^2+q
       444: q^2
       446: 2q^2+q
       447: q^2+q
       450: q^2+q
       452: q^2+q
       453: q^2+q
       454: q^2
       456: 2q^2+q
       458: q^2+q
       460: q^2+q
       462: q^2+q
       464: q^2+q
       466: 2q^3+3q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: q^3+2q^2+q
       472: q^2
       474: 2q^2+q
       476: 2q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       503: 2q^2+q
       505: 2q^2+q
       507: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: 2q^2+q
       512: q^3+2q^2+q
       513: q^2+q
       514: q^2+q
       522: q^2+q
       526: q^2+q
       527: q^2
       530: q^2+q
       534: q^2+q
       538: q^3+2q^2+q
       540: q^2
       542: q^3+2q^2+q
       544: q^2
       546: q^2+q
       548: q^2
       551: q^2+q
       556: 2q^2+q
       560: q^2+q
       564: q^2+q
       566: 2q^2+q
       571: 2q^2+q
       574: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2+q
       592: q
       593: q
       596: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       603: q^2+q
       606: q^3+2q^2+q
       608: q^2+q
       610: 2q^2+q
       612: 2q^2+q
       614: q^2+q
       615: q^2+q
       616: q^2
       618: 2q^2+q
       619: q
       622: q
       624: q^2+q
       626: q
       628: q^2+q
       630: q
       632: q^2+q
       634: q^2+q
       636: 2q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q^2+q
       648: q^2
       650: q^2+q
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       665: q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       699: q^2+q
       706: q
       710: q^2+q
       715: q
       718: q
       722: q^2+q
       726: q^2+q
       730: q^2+q
       732: q^2
       734: q^2+q
       736: q^2
       740: q^2+q
       744: q
       748: q^2+q
       752: q^2+q
       754: q^2+q
       759: 2q^2+q
       763: q^2+q
       766: q^2+q
       773: q^2+q
       778: q^2+q
       782: q^2+q
       785: q
       788: q
       792: q
       798: 2q^2+q
       800: q^2+q
       801: q^2+q
       804: q
       805: q
       808: q^2+q
       810: q^2+q
       812: q^2+q
       822: q
       824: q
       825: q
       828: q
       832: q
       834: q
       836: q
       842: q^2+q
       845: q
       848: q
       850: q^2+q
       852: q
       854: q^2+q
       856: q
       871: q^2+q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       890: q^2+q
       897: q
       903: q
       905: q
       909: q
       913: q
       921: q^2+q
       926: q
       929: q
       939: q
       947: q
       951: q
       962: q^2+q
       976: q
       980: q^2+q
      1011: q
      1019: q^2+q
      1023: q^2+q
      1026: q
      1029: q
      1035: q
      1039: q
      1045: q
      1049: q
      1051: q
      1052: q
      1055: q
      1059: q
      1061: q
      1063: q
      1065: q
      1083: q
      1128: q
      1149: q
      1155: q
      1157: q
      1162: q
      1171: q
      1175: q
      1186: q
      1200: q
      1205: q
      1223: 1
      1265: q
      1267: q
      1271: q
      1279: q
      1324: 1
      1339: 1
      1363: q
      1416: q
      1421: q
      1447: 1
      1481: 1
      1499: 1
      1558: 1
      1561: 1
      1574: 1
      1636: 1
      1672: 1
      1685: 1
      1698: 1
      1756: 1
      1806: 1
      1857: 1

1858:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q^2+2q+1
        59: q
        60: 2q^2+2q+1
        61: q^2+q
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       106: q
       107: 2q^2+2q+1
       108: q^2+q
       109: q^2+2q+1
       110: q
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: 2q^2+2q+1
       120: q^2+q
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q^2+2q+1
       172: q
       173: q^2+2q+1
       176: q
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: 2q^2+2q+1
       184: q^2+q
       185: q^2+2q+1
       186: q
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       193: q+1
       195: 2q+1
       196: q
       197: q+1
       199: 2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       203: q^2+2q+1
       204: q
       205: q^2+3q+1
       207: q^2+3q+1
       209: 2q^2+3q+1
       211: 2q^2+3q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: 2q+1
       262: q
       263: q^2+2q+1
       266: q
       267: q+1
       271: q^2+2q+1
       273: q
       275: q^2+2q+1
       278: q
       279: 3q+1
       281: 2q+1
       283: q^2+q+1
       285: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: 2q^2+2q+1
       294: q^2+q
       295: q^2+2q+1
       296: q
       297: q^2+3q+1
       299: q+1
       301: q+1
       303: 2q+1
       304: q
       305: q+1
       307: 2q^2+2q+1
       308: q^2+q
       309: q^2+2q+1
       310: q
       311: 3q+1
       313: q^2+3q+1
       315: 2q+1
       317: 3q+1
       319: q+1
       321: 2q+1
       322: q
       323: q+1
       325: 2q^2+3q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: q^2+3q+1
       358: 2q+1
       359: 3q+1
       360: 3q+1
       362: 3q+1
       364: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: q+1
       370: 3q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: q+1
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q+1
       393: q+1
       397: 2q+1
       399: q
       401: q^2+2q+1
       404: q
       405: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       419: q^2+q+1
       421: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       429: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       439: 2q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: q^2+q+1
       449: q+1
       451: 2q+1
       453: 2q^2+2q+1
       454: q^2+q
       455: 3q+1
       457: q^2+2q+1
       458: q
       459: q^2+3q+1
       461: 2q+1
       462: q
       463: 3q+1
       465: 3q+1
       467: 2q+1
       469: 2q+1
       471: q+1
       473: 2q+1
       474: q
       475: q+1
       477: q+1
       479: q+1
       481: 2q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 3q+1
       487: 3q+1
       489: q^2+2q+1
       491: 2q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       502: 3q+1
       504: 3q+1
       506: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: 1
       513: 3q+1
       514: 2q+1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       521: q+1
       525: 2q+1
       528: q
       529: q+1
       533: 1
       537: q+1
       541: q+1
       545: q+1
       549: q+1
       553: 2q+1
       555: q
       557: q^2+2q+1
       559: q
       561: 2q+1
       563: q
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       589: q^2+q+1
       591: q+1
       593: 1
       595: q+1
       597: 2q+1
       599: 2q+1
       601: 3q+1
       603: 1
       605: 1
       607: q+1
       609: 1
       611: q+1
       613: 1
       615: q+1
       617: q+1
       619: q^2+q+1
       621: q+1
       623: 2q+1
       625: 2q+1
       627: 3q+1
       629: 2q+1
       631: 2q+1
       632: q
       633: 3q+1
       635: 3q+1
       637: 2q+1
       639: 2q+1
       641: 1
       643: q+1
       645: 1
       647: q+1
       649: 2q+1
       650: q
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q+1
       666: 3q+1
       668: 3q+1
       670: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: q+1
       681: 2q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       705: q+1
       709: q+1
       713: q+1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: q+1
       737: q+1
       741: q+1
       745: 2q+1
       747: q
       749: 2q+1
       751: q
       753: 1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       785: 1
       787: q+1
       789: 3q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: q+1
       809: 1
       811: 1
       813: q+1
       815: q+1
       817: 1
       819: q+1
       821: 2q+1
       823: 2q+1
       825: q^2+q+1
       827: q+1
       829: 1
       831: q+1
       833: 2q+1
       835: 2q+1
       837: 3q+1
       839: 2q+1
       840: q
       841: 2q+1
       843: 1
       845: 1
       847: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       896: q+1
       900: q+1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: q+1
       936: q+1
       940: 1
       944: q+1
       948: q+1
       952: 1
       956: 2q+1
       958: q
       960: 1
       964: 1
       968: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 2q+1
      1004: 1
      1006: q+1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: q+1
      1032: 1
      1034: 2q+1
      1036: q+1
      1038: 2q+1
      1040: 1
      1042: 2q+1
      1044: q+1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1056: 1
      1058: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: q+1
      1110: q+1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1168: q+1
      1172: q+1
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1206: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1228: 1
      1236: 1
      1238: 1
      1240: 1
      1244: q+1
      1246: 1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 2q+1
      1258: 1
      1260: q+1
      1262: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1352: 1
      1372: 1
      1376: q+1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: 1
      1410: 1
      1414: 1
      1422: 1
      1430: 1
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1452: 1
      1456: 1
      1458: q+1
      1460: 1
      1462: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1480: 1
      1482: 1
      1486: 1
      1488: 1
      1489: 1
      1513: 1
      1525: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1611: 1
      1631: 1
      1651: 1
      1653: 1
      1655: 1
      1667: 1
      1669: 1
      1671: 1
      1675: 1
      1699: 1
      1761: 1
      1765: 1
      1773: 1
      1777: 1
      1801: 1
      1858: 1

1859:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 4q^3+5q^2+3q
        23: 4q^3+5q^2+3q
        24: 4q^3+5q^2+3q
        25: 2q^4+7q^3+6q^2+3q
        26: 2q^4+7q^3+6q^2+3q
        27: 2q^4+7q^3+6q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 4q^3+5q^2+3q
        32: 4q^3+5q^2+3q
        33: q^3+4q^2+3q
        34: 2q^4+7q^3+6q^2+3q
        35: 2q^4+7q^3+6q^2+3q
        36: 3q^3+5q^2+3q
        37: 2q^3+2q^2+q
        38: 2q^3+3q^2+2q
        39: 2q^3+2q^2+q
        40: 2q^3+3q^2+2q
        41: 2q^3+2q^2+q
        42: 2q^3+3q^2+2q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: 4q^3+5q^2+3q
        55: 2q^4+7q^3+6q^2+3q
        56: 2q^4+7q^3+6q^2+3q
        57: 2q^4+7q^3+6q^2+3q
        58: q^3+2q^2+2q
        59: 2q^2+q
        60: 2q^3+3q^2+2q
        61: q^3+2q^2+q
        62: 2q^3+2q^2+q
        63: 2q^3+3q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: 3q^3+5q^2+3q
        73: q^3+4q^2+3q
        74: 2q^3+2q^2+q
        75: 2q^3+3q^2+2q
        76: 2q^3+2q^2+q
        77: 2q^3+3q^2+2q
        78: 2q^3+2q^2+q
        79: 2q^3+3q^2+2q
        80: 4q^3+5q^2+3q
        81: q^3+4q^2+3q
        82: 4q^3+5q^2+3q
        83: 4q^3+5q^2+3q
        84: 2q^4+7q^3+6q^2+3q
        85: 3q^3+5q^2+3q
        86: 2q^4+7q^3+6q^2+3q
        87: 2q^4+7q^3+6q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+2q^2+2q
        97: 3q^3+5q^2+3q
        98: 3q^3+5q^2+3q
        99: q^4+3q^3+3q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^3+q^2+q
       104: q^2+q
       105: q^2+q
       106: q^2
       107: 2q^3+3q^2+2q
       108: q^3+2q^2+q
       109: q^3+2q^2+2q
       110: 2q^2+q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: 2q^3+2q^2+q
       114: 2q^3+3q^2+2q
       115: 2q^3+2q^2+q
       116: 2q^3+3q^2+2q
       117: q^3+2q^2+2q
       118: 2q^2+q
       119: 2q^3+3q^2+2q
       120: q^3+2q^2+q
       121: 2q^3+2q^2+q
       122: 2q^3+3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: 3q^3+5q^2+3q
       136: q^3+4q^2+3q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: 3q^2+3q
       140: q^2+2q
       141: 4q^3+5q^2+3q
       142: 3q^2+3q
       143: 3q^3+5q^2+3q
       144: q^3+2q^2+2q
       145: 3q^3+5q^2+3q
       146: 2q^4+7q^3+6q^2+3q
       147: 3q^3+5q^2+3q
       148: q^3+4q^2+3q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+2q^2+q
       152: 2q^3+3q^2+2q
       153: 2q^3+2q^2+q
       154: 2q^3+3q^2+2q
       155: 2q^3+2q^2+q
       156: 2q^3+3q^2+2q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+2q^2+2q
       163: 3q^3+5q^2+3q
       164: 3q^3+5q^2+3q
       165: q^4+3q^3+3q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^3+q^2+q
       170: q^2+q
       171: q^2+q
       172: q^2
       173: q^3+q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q
       180: q^2+2q
       182: q^2+2q
       183: 2q^3+3q^2+2q
       184: q^3+2q^2+q
       185: q^3+2q^2+2q
       186: 2q^2+q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: 2q^3+2q^2+q
       190: 2q^3+3q^2+2q
       191: q^3+2q^2+2q
       192: 2q^2+q
       193: q^2+2q
       195: 2q^2+2q
       196: q^2+q
       197: q^2+q
       198: q
       199: 2q^3+3q^2+2q
       200: q^3+2q^2+q
       201: 2q^3+3q^2+2q
       202: q^3+2q^2+q
       203: q^3+2q^2+2q
       204: 2q^2+q
       205: q^3+2q^2+q
       206: 2q^2+2q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: 2q^3+2q^2+q
       210: 2q^3+3q^2+2q
       211: 2q^3+2q^2+q
       212: 2q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: 3q^3+5q^2+3q
       223: q^3+2q^2+2q
       224: q^3+4q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q^2+3q
       228: q^2+2q
       229: q^2+2q
       230: 3q^2+3q
       231: q^3+2q^2+2q
       232: 3q^3+5q^2+3q
       233: q^3+2q^2+2q
       234: 3q^3+5q^2+3q
       235: q^3+4q^2+3q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q^2+3q
       244: q^2+2q
       245: 3q^2+3q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+2q^2+2q
       253: 3q^3+5q^2+3q
       254: 3q^3+5q^2+3q
       255: q^4+3q^3+3q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       260: q
       261: q^2+q
       263: q^3+q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2
       267: q^2+q
       268: q
       271: q^3+q^2+q
       272: q^2+q
       273: q^2
       274: q^2+q
       275: q^3+q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: q^2+2q
       282: q
       283: q^2+q
       285: q
       288: q
       290: q^2+2q
       292: q
       293: 2q^3+3q^2+2q
       294: q^3+2q^2+q
       295: q^3+2q^2+2q
       296: 2q^2+q
       297: q^3+2q^2+q
       298: 2q^2+2q
       299: q^2+2q
       302: q
       303: 2q^2+2q
       304: q^2+q
       305: q^2+q
       306: q
       307: 2q^3+3q^2+2q
       308: q^3+2q^2+q
       309: q^3+2q^2+2q
       310: 2q^2+q
       312: q^2+2q
       313: q^3+2q^2+q
       314: 2q^2+2q
       316: q
       318: q^2+2q
       319: q^2+2q
       321: 2q^2+2q
       322: q^2+q
       323: q^2+q
       324: q
       325: 2q^3+2q^2+q
       326: 2q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: q^3+2q^2+2q
       334: q^3+2q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: q^2+2q
       345: 3q^2+3q
       346: q^2+2q
       347: q^2+2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: 3q^3+5q^2+3q
       354: q^3+2q^2+2q
       355: 3q^3+5q^2+3q
       356: q^3+2q^2+2q
       357: q^3+4q^2+3q
       358: q^2+2q
       359: 3q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: q^2+2q
       370: 3q^2+3q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       382: q
       383: q^2+q
       385: q^3+q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2
       390: q
       393: q^2+q
       394: q
       398: q^2+q
       400: q
       401: q^3+q^2+q
       402: q^2+q
       403: q^2+q
       404: q^2
       405: q^2+q
       407: q
       410: q^2+2q
       412: q
       414: q
       416: q^2+2q
       418: q
       419: q^2+q
       421: q
       424: q
       426: q
       428: q^2+2q
       429: q
       431: q
       436: q
       437: q^2+2q
       439: 2q^2+2q
       440: q^2+q
       441: q^2+q
       442: q
       443: q^2+2q
       446: q
       447: q^2+q
       449: q
       452: q
       453: 2q^3+3q^2+2q
       454: q^3+2q^2+q
       456: q^2+2q
       457: q^3+2q^2+2q
       458: 2q^2+q
       459: q^3+2q^2+q
       460: 2q^2+2q
       461: 2q^2+2q
       462: q^2+q
       464: q^2+2q
       466: q^2+2q
       468: q
       470: q
       471: q^2+2q
       473: 2q^2+2q
       474: q^2+q
       475: q^2+q
       476: q
       478: q
       479: q^2+q
       480: q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: q^2+2q
       497: q^3+2q^2+2q
       498: q^3+2q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 3q^2+3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: q^2+2q
       512: q
       513: 3q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       526: q
       527: q^2+q
       538: q
       541: q^2+q
       542: q
       546: q
       554: q^2+q
       556: q
       557: q^3+q^2+q
       558: q^2+q
       559: q^2
       560: q^2+q
       562: q^2+q
       564: q
       565: q^2+q
       566: q
       571: q
       573: q^2+q
       574: q
       581: q
       584: q
       586: q
       588: q
       589: q^2+q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: q^2+2q
       603: q
       607: q
       612: q
       615: q^2+2q
       618: q
       619: q^2+q
       621: q
       624: q
       626: q
       628: q^2+2q
       630: q
       631: 2q^2+2q
       632: q^2+q
       634: q^2+2q
       636: q^2+2q
       638: q
       640: q
       641: q
       643: q
       647: q^2+2q
       649: 2q^2+2q
       650: q^2+q
       652: q
       653: q^2+q
       654: q
       655: q^2+q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q^2+2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: q^2+2q
       679: q
       680: q+1
       681: q^3+2q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 3q^2+3q
       685: q^2+2q
       686: q^2+2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       699: q
       730: q
       734: q
       746: q^2+q
       748: q
       750: q^2+q
       752: q
       759: q
       761: q^2+q
       763: q
       765: q^2+q
       766: q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: q^2+2q
       793: 1
       796: 1
       801: q
       805: q
       807: q
       814: q
       815: q^2+2q
       817: 1
       820: q+1
       822: q
       824: q
       825: q^2+q
       827: q
       829: q
       831: q
       834: q
       836: q
       838: q^2+2q
       839: 2q^2+2q
       840: q^2+q
       842: q
       843: 1
       845: q
       847: q
       854: q
       857: q^2+q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: q+1
       874: q+1
       875: q^2+2q
       876: q^2+2q
       877: q
       878: q^2+2q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       890: q
       917: 1
       933: q
       941: 1
       957: q^2+q
       959: q
       964: 1
       969: 1
       980: q
       986: q
       988: q^2+q
       989: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 1
      1016: 1
      1021: 1
      1026: q
      1031: q+1
      1032: 1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: 1
      1052: q
      1056: q
      1058: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: q+1
      1080: 1
      1081: q+1
      1082: q^2+2q
      1083: q
      1084: 1
      1085: q
      1087: 1
      1104: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: 1
      1165: 1
      1189: 1
      1194: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1227: 1
      1228: 1
      1237: 1
      1240: q
      1245: q+1
      1246: 1
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1262: 1
      1268: q
      1275: 1
      1280: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: q
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1341: 1
      1373: 1
      1381: 1
      1389: 1
      1396: 1
      1405: 1
      1410: 1
      1431: 1
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1453: 1
      1457: 1
      1459: q+1
      1460: 1
      1462: 1
      1473: 1
      1476: q
      1482: 1
      1486: 1
      1488: 1
      1490: 1
      1514: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1584: 1
      1588: 1
      1595: 1
      1632: 1
      1652: 1
      1653: 1
      1655: 1
      1668: 1
      1669: 1
      1676: 1
      1700: 1
      1762: 1
      1766: 1
      1773: 1
      1802: 1
      1859: 1

1860:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 4q^4+6q^3+3q^2+q
        23: q^5+5q^4+6q^3+3q^2+q
        24: 4q^4+6q^3+3q^2+q
        25: 7q^4+7q^3+3q^2+q
        26: 2q^5+8q^4+7q^3+3q^2+q
        27: 7q^4+7q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 3q^4+5q^3+3q^2+q
        32: 4q^4+6q^3+3q^2+q
        33: 3q^4+5q^3+3q^2+q
        34: 5q^4+6q^3+3q^2+q
        35: 7q^4+7q^3+3q^2+q
        36: 5q^4+6q^3+3q^2+q
        37: 4q^4+6q^3+3q^2+q
        39: q^5+5q^4+6q^3+3q^2+q
        41: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: q^4+5q^3+3q^2+q
        53: 2q^4+5q^3+3q^2+q
        54: q^4+5q^3+3q^2+q
        55: 4q^4+6q^3+3q^2+q
        56: q^5+5q^4+6q^3+3q^2+q
        57: 4q^4+6q^3+3q^2+q
        58: 2q^4+3q^3+2q^2+q
        59: q^3+q^2
        60: 2q^4+4q^3+2q^2+q
        61: q^4+q^3+q^2
        62: 3q^4+5q^3+3q^2+q
        64: 4q^4+6q^3+3q^2+q
        66: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 4q^3+3q^2+q
        73: 3q^3+3q^2+q
        74: q^4+5q^3+3q^2+q
        76: 2q^4+5q^3+3q^2+q
        78: q^4+5q^3+3q^2+q
        80: 3q^4+5q^3+3q^2+q
        81: 3q^4+5q^3+3q^2+q
        82: q^4+4q^3+3q^2+q
        83: q^4+5q^3+3q^2+q
        84: 5q^4+6q^3+3q^2+q
        85: 5q^4+6q^3+3q^2+q
        86: 3q^4+5q^3+3q^2+q
        87: 4q^4+6q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 3q^3+3q^2+q
        95: 3q^3+3q^2+q
        96: 3q^3+2q^2+q
        97: 2q^4+5q^3+3q^2+q
        98: 2q^4+5q^3+3q^2+q
        99: 2q^4+4q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       103: 2q^4+3q^3+2q^2+q
       106: q^3+q^2
       107: 3q^3+2q^2+q
       108: q^2
       109: 2q^3+2q^2+q
       110: q^2
       111: 3q^3+3q^2+q
       113: q^4+4q^3+3q^2+q
       115: q^4+5q^3+3q^2+q
       117: 2q^4+3q^3+2q^2+q
       118: q^3+q^2
       119: 2q^4+4q^3+2q^2+q
       120: q^4+q^3+q^2
       121: 3q^4+5q^3+3q^2+q
       123: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       127: 3q^3+3q^2+q
       129: 3q^3+3q^2+q
       131: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 4q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^4+3q^3+3q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: 2q^2+q
       141: q^4+4q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^4+4q^3+3q^2+q
       144: q^4+3q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 3q^4+5q^3+3q^2+q
       147: 4q^3+3q^2+q
       148: 3q^3+3q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       151: q^4+5q^3+3q^2+q
       153: 2q^4+5q^3+3q^2+q
       155: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 3q^3+3q^2+q
       161: 3q^3+3q^2+q
       162: 3q^3+2q^2+q
       163: 2q^4+5q^3+3q^2+q
       164: 2q^4+5q^3+3q^2+q
       165: 2q^4+4q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       169: 2q^3+2q^2+q
       172: q^2
       173: 2q^4+3q^3+2q^2+q
       176: q^3+q^2
       177: 2q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: 3q^3+2q^2+q
       184: q^2
       185: 2q^3+2q^2+q
       186: q^2
       187: 3q^3+3q^2+q
       189: q^4+4q^3+3q^2+q
       191: q^4+2q^3+2q^2+q
       192: q^3+q^2
       193: 2q^2+q
       195: q^3+2q^2+q
       196: q^2
       197: 2q^2+q
       199: q^4+3q^3+2q^2+q
       200: q^3+q^2
       201: 3q^3+2q^2+q
       202: q^2
       203: 2q^3+2q^2+q
       204: q^2
       205: 3q^3+3q^2+q
       207: q^4+3q^3+3q^2+q
       209: q^4+4q^3+3q^2+q
       211: q^4+5q^3+3q^2+q
       213: 3q^3+3q^2+q
       215: 3q^3+3q^2+q
       217: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: 2q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: 2q^3+3q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: 2q^3+3q^2+q
       231: 2q^3+2q^2+q
       232: q^4+4q^3+3q^2+q
       233: q^4+3q^3+2q^2+q
       234: 4q^3+3q^2+q
       235: 3q^3+3q^2+q
       236: 2q^3+2q^2+q
       237: 3q^3+3q^2+q
       239: 3q^3+3q^2+q
       241: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^2+q
       245: 2q^3+3q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^3+3q^2+q
       254: 2q^3+3q^2+q
       255: q^4+2q^3+2q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       259: q^3+2q^2+q
       262: q^2
       263: 2q^3+2q^2+q
       266: q^2
       267: 2q^2+q
       271: 2q^3+2q^2+q
       273: q^2
       275: q^4+2q^3+2q^2+q
       278: q^3+q^2
       279: 2q^3+3q^2+q
       281: 2q^3+2q^2+q
       283: q^3+q^2+q
       285: q^2+q
       287: q^3+2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^3+2q^2+q
       296: q^2
       297: q^3+3q^2+q
       299: 2q^2+q
       301: 2q^2+q
       303: q^3+2q^2+q
       304: q^2
       305: 2q^2+q
       307: 3q^3+2q^2+q
       308: q^2
       309: 2q^3+2q^2+q
       310: q^2
       311: 2q^3+3q^2+q
       313: 3q^3+3q^2+q
       315: 2q^3+2q^2+q
       317: 2q^3+3q^2+q
       319: 2q^2+q
       321: q^3+2q^2+q
       322: q^2
       323: 2q^2+q
       325: q^4+4q^3+3q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^3+2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: 2q^3+3q^2+q
       354: q^3+2q^2+q
       355: q^3+3q^2+q
       356: 2q^3+2q^2+q
       357: q^3+3q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       360: 3q^3+3q^2+q
       362: 3q^3+3q^2+q
       364: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^2+q
       370: 2q^3+3q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       377: q^2+q
       381: q^3+2q^2+q
       384: q^2
       385: q^3+2q^2+q
       388: q^2
       389: 2q^2+q
       393: 2q^2+q
       397: q^3+2q^2+q
       399: q^2
       401: 2q^3+2q^2+q
       404: q^2
       405: 2q^2+q
       409: 2q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       421: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2+q
       431: q^2+q
       433: q^2+q
       435: 2q^2+q
       437: q^2+q
       439: q^2+q
       440: q^2
       441: q^2+q
       443: q^2+q
       445: q^2+q
       447: q^3+q^2+q
       449: q^2+q
       451: q^3+2q^2+q
       453: q^3+2q^2+q
       454: q^2
       455: 2q^3+3q^2+q
       457: q^3+2q^2+q
       458: q^2
       459: q^3+3q^2+q
       461: q^2+q
       462: q^2
       463: 2q^2+q
       465: 2q^3+3q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: 2q^2+q
       473: q^3+2q^2+q
       474: q^2
       475: 2q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       502: 2q^2+q
       504: 2q^2+q
       506: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: 2q^2+q
       514: q^3+2q^2+q
       521: q^2+q
       525: q^2+q
       528: q^2
       529: q^2+q
       533: q^2+q
       537: 2q^2+q
       541: q^2+q
       545: q^2+q
       549: q^2+q
       553: q^3+2q^2+q
       555: q^2
       557: q^3+2q^2+q
       559: q^2
       561: q^2+q
       563: q^2
       565: 2q^2+q
       569: 2q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       591: q
       593: q
       595: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       603: q
       605: q^2+q
       607: q
       609: q
       611: q^2+q
       613: q
       615: q^2+q
       617: q^2+q
       619: q^2+q
       621: q^2+q
       623: q^3+2q^2+q
       625: 2q^2+q
       627: 2q^2+q
       629: q^2+q
       631: q^2+q
       632: q^2
       633: 2q^2+q
       635: 2q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q^2+q
       649: q^2+q
       650: q^2
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       693: q^2+q
       705: q
       709: q^2+q
       713: q
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       721: q^2+q
       725: q
       729: q^2+q
       733: q^2+q
       737: q^2+q
       741: q^2+q
       745: q^2+q
       747: q^2
       749: q^2+q
       751: q^2
       753: q^2+q
       757: 2q^2+q
       761: q^2+q
       765: q^2+q
       769: q^2+q
       777: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       797: q
       799: q
       801: q
       805: q
       807: q
       809: q
       811: q
       821: 2q^2+q
       823: q^2+q
       825: q^2+q
       827: q
       829: q
       831: q^2+q
       833: q^2+q
       835: q^2+q
       841: q^2+q
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       849: q^2+q
       851: q
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       855: q
       871: q
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       884: q^2+q
       896: q
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       928: q
       936: q
       944: q^2+q
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       974: q
       978: q^2+q
      1010: q
      1018: q
      1022: q
      1026: q
      1034: q^2+q
      1038: q^2+q
      1040: q
      1044: q
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      1056: q
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      1126: q
      1148: q
      1156: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: q
      1198: q
      1206: q
      1222: 1
      1264: q
      1266: q
      1268: q
      1278: q
      1322: 1
      1336: 1
      1392: q
      1414: q
      1422: q
      1446: 1
      1480: 1
      1491: 1
      1555: 1
      1559: 1
      1591: 1
      1633: 1
      1671: 1
      1677: 1
      1701: 1
      1777: 1
      1803: 1
      1860: 1

1861:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 4q^3+5q^2+3q
        23: 4q^3+5q^2+3q
        24: 4q^3+5q^2+3q
        25: 2q^4+7q^3+6q^2+3q
        26: 2q^4+7q^3+6q^2+3q
        27: 2q^4+7q^3+6q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 4q^3+5q^2+3q
        32: 4q^3+5q^2+3q
        33: q^3+4q^2+3q
        34: 2q^4+7q^3+6q^2+3q
        35: 2q^4+7q^3+6q^2+3q
        36: 3q^3+5q^2+3q
        37: 2q^3+3q^2+2q
        38: 2q^3+2q^2+q
        39: 2q^3+3q^2+2q
        40: 2q^3+2q^2+q
        41: 2q^3+3q^2+2q
        42: 2q^3+2q^2+q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: 4q^3+5q^2+3q
        55: 2q^4+7q^3+6q^2+3q
        56: 2q^4+7q^3+6q^2+3q
        57: 2q^4+7q^3+6q^2+3q
        58: 2q^2+q
        59: q^3+2q^2+2q
        60: 2q^3+3q^2+2q
        61: q^3+2q^2+q
        62: 2q^3+3q^2+2q
        63: 2q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: 3q^3+5q^2+3q
        73: q^3+4q^2+3q
        74: 2q^3+3q^2+2q
        75: 2q^3+2q^2+q
        76: 2q^3+3q^2+2q
        77: 2q^3+2q^2+q
        78: 2q^3+3q^2+2q
        79: 2q^3+2q^2+q
        80: 4q^3+5q^2+3q
        81: q^3+4q^2+3q
        82: 4q^3+5q^2+3q
        83: 4q^3+5q^2+3q
        84: 2q^4+7q^3+6q^2+3q
        85: 3q^3+5q^2+3q
        86: 2q^4+7q^3+6q^2+3q
        87: 2q^4+7q^3+6q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+2q^2+2q
        97: 3q^3+5q^2+3q
        98: 3q^3+5q^2+3q
        99: q^4+3q^3+3q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2+q
       104: q^3+q^2+q
       105: q^2
       106: q^2+q
       107: 2q^3+3q^2+2q
       108: q^3+2q^2+q
       109: 2q^2+q
       110: q^3+2q^2+2q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 2q^3+3q^2+2q
       114: 2q^3+2q^2+q
       115: 2q^3+3q^2+2q
       116: 2q^3+2q^2+q
       117: 2q^2+q
       118: q^3+2q^2+2q
       119: 2q^3+3q^2+2q
       120: q^3+2q^2+q
       121: 2q^3+3q^2+2q
       122: 2q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: 3q^3+5q^2+3q
       136: q^3+4q^2+3q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: 3q^2+3q
       140: q^2+2q
       141: 4q^3+5q^2+3q
       142: 3q^2+3q
       143: 3q^3+5q^2+3q
       144: q^3+2q^2+2q
       145: 3q^3+5q^2+3q
       146: 2q^4+7q^3+6q^2+3q
       147: 3q^3+5q^2+3q
       148: q^3+4q^2+3q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: 2q^3+2q^2+q
       153: 2q^3+3q^2+2q
       154: 2q^3+2q^2+q
       155: 2q^3+3q^2+2q
       156: 2q^3+2q^2+q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+2q^2+2q
       163: 3q^3+5q^2+3q
       164: 3q^3+5q^2+3q
       165: q^4+3q^3+3q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2+q
       170: q^3+q^2+q
       171: q^2
       172: q^2+q
       173: q^2+q
       174: q^3+q^2+q
       175: q^2
       176: q^2+q
       177: q
       179: q^2+2q
       181: q^2+2q
       183: 2q^3+3q^2+2q
       184: q^3+2q^2+q
       185: 2q^2+q
       186: q^3+2q^2+2q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 2q^3+3q^2+2q
       190: 2q^3+2q^2+q
       191: 2q^2+q
       192: q^3+2q^2+2q
       193: q^2+2q
       195: q^2+q
       196: 2q^2+2q
       197: q
       198: q^2+q
       199: 2q^3+3q^2+2q
       200: q^3+2q^2+q
       201: 2q^3+3q^2+2q
       202: q^3+2q^2+q
       203: 2q^2+q
       204: q^3+2q^2+2q
       205: 2q^2+2q
       206: q^3+2q^2+q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^3+3q^2+2q
       210: 2q^3+2q^2+q
       211: 2q^3+3q^2+2q
       212: 2q^3+2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: 3q^3+5q^2+3q
       223: q^3+2q^2+2q
       224: q^3+4q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q^2+3q
       228: q^2+2q
       229: q^2+2q
       230: 3q^2+3q
       231: q^3+2q^2+2q
       232: 3q^3+5q^2+3q
       233: q^3+2q^2+2q
       234: 3q^3+5q^2+3q
       235: q^3+4q^2+3q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q^2+3q
       244: q^2+2q
       245: 3q^2+3q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+2q^2+2q
       253: 3q^3+5q^2+3q
       254: 3q^3+5q^2+3q
       255: q^4+3q^3+3q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       259: q
       262: q^2+q
       263: q^2+q
       264: q^3+q^2+q
       265: q^2
       266: q^2+q
       267: q
       268: q^2+q
       271: q^2+q
       272: q^2
       273: q^2+q
       274: q^3+q^2+q
       275: q^2+q
       276: q^3+q^2+q
       277: q^2
       278: q^2+q
       279: q^2+2q
       281: q
       283: q^2+q
       286: q
       287: q
       289: q^2+2q
       291: q
       293: 2q^3+3q^2+2q
       294: q^3+2q^2+q
       295: 2q^2+q
       296: q^3+2q^2+2q
       297: 2q^2+2q
       298: q^3+2q^2+q
       299: q^2+2q
       301: q
       303: q^2+q
       304: 2q^2+2q
       305: q
       306: q^2+q
       307: 2q^3+3q^2+2q
       308: q^3+2q^2+q
       309: 2q^2+q
       310: q^3+2q^2+2q
       311: q^2+2q
       313: 2q^2+2q
       314: q^3+2q^2+q
       315: q
       317: q^2+2q
       319: q^2+2q
       321: q^2+q
       322: 2q^2+2q
       323: q
       324: q^2+q
       325: 2q^3+3q^2+2q
       326: 2q^3+2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: q^3+2q^2+2q
       334: q^3+2q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: q^2+2q
       345: 3q^2+3q
       346: q^2+2q
       347: q^2+2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: 3q^3+5q^2+3q
       354: q^3+2q^2+2q
       355: 3q^3+5q^2+3q
       356: q^3+2q^2+2q
       357: q^3+4q^2+3q
       358: q^2+2q
       359: 3q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: q^2+2q
       370: 3q^2+3q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       381: q
       384: q^2+q
       385: q^2+q
       386: q^3+q^2+q
       387: q^2
       388: q^2+q
       389: q
       393: q
       394: q^2+q
       397: q
       399: q^2+q
       401: q^2+q
       402: q^2
       403: q^3+q^2+q
       404: q^2+q
       405: q
       407: q^2+q
       409: q^2+2q
       411: q
       413: q
       415: q^2+2q
       417: q
       419: q^2+q
       422: q
       423: q
       425: q
       427: q^2+2q
       429: q
       432: q
       435: q
       437: q^2+2q
       439: q^2+q
       440: 2q^2+2q
       441: q
       442: q^2+q
       443: q^2+2q
       445: q
       447: q^2+q
       450: q
       451: q
       453: 2q^3+3q^2+2q
       454: q^3+2q^2+q
       455: q^2+2q
       457: 2q^2+q
       458: q^3+2q^2+2q
       459: 2q^2+2q
       460: q^3+2q^2+q
       461: q^2+q
       462: 2q^2+2q
       463: q^2+2q
       465: q^2+2q
       467: q
       469: q
       471: q^2+2q
       473: q^2+q
       474: 2q^2+2q
       475: q
       476: q^2+q
       477: q
       479: q
       480: q^2+q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: q^2+2q
       497: q^3+2q^2+2q
       498: q^3+2q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 3q^2+3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: q^2+2q
       512: q
       513: 3q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       525: q
       528: q^2+q
       537: q
       541: q
       542: q^2+q
       545: q
       553: q
       555: q^2+q
       557: q^2+q
       558: q^2
       559: q^2+q
       560: q^3+q^2+q
       561: q
       563: q^2+q
       565: q
       566: q^2+q
       569: q
       573: q
       574: q^2+q
       577: q
       583: q
       585: q
       587: q
       589: q^2+q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: q^2+2q
       603: q
       608: q
       611: q
       615: q^2+2q
       617: q
       619: q^2+q
       622: q
       623: q
       625: q
       627: q^2+2q
       629: q
       631: q^2+q
       632: 2q^2+2q
       633: q^2+2q
       635: q^2+2q
       637: q
       639: q
       641: q
       644: q
       647: q^2+2q
       649: q^2+q
       650: 2q^2+2q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q^2+2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: q^2+2q
       679: q
       680: q+1
       681: q^3+2q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 3q^2+3q
       685: q^2+2q
       686: q^2+2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       693: q
       729: q
       733: q
       745: q
       747: q^2+q
       749: q
       751: q^2+q
       757: q
       761: q
       763: q^2+q
       765: q
       766: q^2+q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: q^2+2q
       793: 1
       795: 1
       801: q
       805: q
       808: q
       813: q
       815: q^2+2q
       818: 1
       819: q+1
       821: q
       823: q
       825: q^2+q
       828: q
       829: q
       832: q
       833: q
       835: q
       837: q^2+2q
       839: q^2+q
       840: 2q^2+2q
       841: q
       844: 1
       845: q
       848: q
       853: q
       857: q
       858: q^2+q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: q+1
       874: q+1
       875: q^2+2q
       876: q^2+2q
       877: q
       878: q^2+2q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       884: q
       916: 1
       932: q
       942: 1
       956: q
       958: q^2+q
       965: 1
       971: 1
       978: q
       982: q
       988: q
       989: q^2+q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 1
      1016: 1
      1020: 1
      1026: q
      1030: q+1
      1033: 1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1047: 1
      1052: q
      1056: q
      1059: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: q+1
      1080: 1
      1081: q+1
      1082: q^2+2q
      1083: q
      1084: 1
      1085: q
      1089: 1
      1098: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: 1
      1166: 1
      1191: 1
      1195: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1226: 1
      1228: 1
      1236: 1
      1240: q
      1244: q+1
      1247: 1
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1263: 1
      1268: q
      1274: 1
      1281: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: q
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1340: 1
      1374: 1
      1382: 1
      1388: 1
      1397: 1
      1407: 1
      1411: 1
      1433: 1
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1452: 1
      1456: 1
      1458: q+1
      1461: 1
      1462: 1
      1472: 1
      1476: q
      1483: 1
      1486: 1
      1488: 1
      1492: 1
      1516: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1585: 1
      1587: 1
      1596: 1
      1634: 1
      1651: 1
      1654: 1
      1655: 1
      1667: 1
      1670: 1
      1678: 1
      1702: 1
      1763: 1
      1765: 1
      1774: 1
      1804: 1
      1861: 1

1862:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 4q^3+5q^2+3q
        23: 4q^3+5q^2+3q
        24: 4q^3+5q^2+3q
        25: 2q^4+7q^3+6q^2+3q
        26: 2q^4+7q^3+6q^2+3q
        27: 2q^4+7q^3+6q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 4q^3+5q^2+3q
        32: 4q^3+5q^2+3q
        33: q^3+4q^2+3q
        34: 2q^4+7q^3+6q^2+3q
        35: 2q^4+7q^3+6q^2+3q
        36: 3q^3+5q^2+3q
        37: 2q^3+3q^2+2q
        38: 2q^3+2q^2+q
        39: 2q^3+3q^2+2q
        40: 2q^3+2q^2+q
        41: 2q^3+3q^2+2q
        42: 2q^3+2q^2+q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: 4q^3+5q^2+3q
        55: 2q^4+7q^3+6q^2+3q
        56: 2q^4+7q^3+6q^2+3q
        57: 2q^4+7q^3+6q^2+3q
        58: q^3+2q^2+2q
        59: 2q^2+q
        60: q^3+2q^2+q
        61: 2q^3+3q^2+2q
        62: 2q^3+3q^2+2q
        63: 2q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 2q^2+2q
        67: q^3+2q^2+q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: 3q^3+5q^2+3q
        73: q^3+4q^2+3q
        74: 2q^3+3q^2+2q
        75: 2q^3+2q^2+q
        76: 2q^3+3q^2+2q
        77: 2q^3+2q^2+q
        78: 2q^3+3q^2+2q
        79: 2q^3+2q^2+q
        80: 4q^3+5q^2+3q
        81: q^3+4q^2+3q
        82: 4q^3+5q^2+3q
        83: 4q^3+5q^2+3q
        84: 2q^4+7q^3+6q^2+3q
        85: 3q^3+5q^2+3q
        86: 2q^4+7q^3+6q^2+3q
        87: 2q^4+7q^3+6q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+2q^2+2q
        97: 3q^3+5q^2+3q
        98: 3q^3+5q^2+3q
        99: q^4+3q^3+3q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2+q
       104: q^2
       105: q^3+q^2+q
       106: q^2+q
       107: q^3+2q^2+q
       108: 2q^3+3q^2+2q
       109: q^3+2q^2+2q
       110: 2q^2+q
       111: 2q^2+2q
       112: q^3+2q^2+q
       113: 2q^3+3q^2+2q
       114: 2q^3+2q^2+q
       115: 2q^3+3q^2+2q
       116: 2q^3+2q^2+q
       117: q^3+2q^2+2q
       118: 2q^2+q
       119: q^3+2q^2+q
       120: 2q^3+3q^2+2q
       121: 2q^3+3q^2+2q
       122: 2q^3+2q^2+q
       123: 2q^2+2q
       124: q^3+2q^2+q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: 3q^3+5q^2+3q
       136: q^3+4q^2+3q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: 3q^2+3q
       140: q^2+2q
       141: 4q^3+5q^2+3q
       142: 3q^2+3q
       143: 3q^3+5q^2+3q
       144: q^3+2q^2+2q
       145: 3q^3+5q^2+3q
       146: 2q^4+7q^3+6q^2+3q
       147: 3q^3+5q^2+3q
       148: q^3+4q^2+3q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+3q^2+2q
       152: 2q^3+2q^2+q
       153: 2q^3+3q^2+2q
       154: 2q^3+2q^2+q
       155: 2q^3+3q^2+2q
       156: 2q^3+2q^2+q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+2q^2+2q
       163: 3q^3+5q^2+3q
       164: 3q^3+5q^2+3q
       165: q^4+3q^3+3q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2+q
       170: q^2
       171: q^3+q^2+q
       172: q^2+q
       173: q^2+q
       174: q^2
       175: q^3+q^2+q
       176: q^2+q
       177: q
       179: q^2+2q
       181: q^2+2q
       183: q^3+2q^2+q
       184: 2q^3+3q^2+2q
       185: q^3+2q^2+2q
       186: 2q^2+q
       187: 2q^2+2q
       188: q^3+2q^2+q
       189: 2q^3+3q^2+2q
       190: 2q^3+2q^2+q
       191: q^3+2q^2+2q
       192: 2q^2+q
       194: q^2+2q
       195: 2q^2+2q
       196: q^2+q
       197: q
       198: q^2+q
       199: q^3+2q^2+q
       200: 2q^3+3q^2+2q
       201: q^3+2q^2+q
       202: 2q^3+3q^2+2q
       203: q^3+2q^2+2q
       204: 2q^2+q
       205: 2q^2+2q
       206: q^3+2q^2+q
       207: 2q^2+2q
       208: q^3+2q^2+q
       209: 2q^3+3q^2+2q
       210: 2q^3+2q^2+q
       211: 2q^3+3q^2+2q
       212: 2q^3+2q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: 3q^3+5q^2+3q
       223: q^3+2q^2+2q
       224: q^3+4q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q^2+3q
       228: q^2+2q
       229: q^2+2q
       230: 3q^2+3q
       231: q^3+2q^2+2q
       232: 3q^3+5q^2+3q
       233: q^3+2q^2+2q
       234: 3q^3+5q^2+3q
       235: q^3+4q^2+3q
       236: q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+q
       243: 3q^2+3q
       244: q^2+2q
       245: 3q^2+3q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+2q^2+2q
       253: 3q^3+5q^2+3q
       254: 3q^3+5q^2+3q
       255: q^4+3q^3+3q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       259: q^2+q
       262: q
       263: q^2+q
       264: q^2
       265: q^3+q^2+q
       266: q^2+q
       269: q
       270: q^2+q
       271: q^2+q
       272: q^3+q^2+q
       273: q^2+q
       274: q^2
       275: q^2+q
       276: q^2
       277: q^3+q^2+q
       278: q^2+q
       279: q^2+2q
       281: q
       284: q^2+q
       285: q
       287: q
       289: q^2+2q
       291: q
       293: q^3+2q^2+q
       294: 2q^3+3q^2+2q
       295: q^3+2q^2+2q
       296: 2q^2+q
       297: 2q^2+2q
       298: q^3+2q^2+q
       300: q^2+2q
       301: q
       303: 2q^2+2q
       304: q^2+q
       305: q
       306: q^2+q
       307: q^3+2q^2+q
       308: 2q^3+3q^2+2q
       309: q^3+2q^2+2q
       310: 2q^2+q
       311: q^2+2q
       313: 2q^2+2q
       314: q^3+2q^2+q
       315: q
       317: q^2+2q
       320: q^2+2q
       321: 2q^2+2q
       322: q^2+q
       323: q
       324: q^2+q
       325: 2q^3+3q^2+2q
       326: 2q^3+2q^2+q
       327: q^2+2q
       329: q^2+2q
       331: q^2+q
       333: q^3+2q^2+2q
       334: q^3+2q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       338: q^2+2q
       340: q^2+2q
       342: q^2+q
       344: q^2+2q
       345: 3q^2+3q
       346: q^2+2q
       347: q^2+2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: 3q^3+5q^2+3q
       354: q^3+2q^2+2q
       355: 3q^3+5q^2+3q
       356: q^3+2q^2+2q
       357: q^3+4q^2+3q
       358: q^2+2q
       359: 3q^2+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: q^2+2q
       370: 3q^2+3q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       381: q^2+q
       384: q
       385: q^2+q
       386: q^2
       387: q^3+q^2+q
       388: q^2+q
       391: q
       395: q^2+q
       396: q
       397: q^2+q
       399: q
       401: q^2+q
       402: q^3+q^2+q
       403: q^2
       404: q^2+q
       406: q
       408: q^2+q
       409: q^2+2q
       411: q
       413: q
       415: q^2+2q
       417: q
       420: q^2+q
       421: q
       423: q
       425: q
       427: q^2+2q
       430: q
       431: q
       435: q
       438: q^2+2q
       439: 2q^2+2q
       440: q^2+q
       441: q
       442: q^2+q
       444: q^2+2q
       445: q
       448: q^2+q
       449: q
       451: q
       453: q^3+2q^2+q
       454: 2q^3+3q^2+2q
       455: q^2+2q
       457: q^3+2q^2+2q
       458: 2q^2+q
       459: 2q^2+2q
       460: q^3+2q^2+q
       461: 2q^2+2q
       462: q^2+q
       463: q^2+2q
       465: q^2+2q
       467: q
       469: q
       472: q^2+2q
       473: 2q^2+2q
       474: q^2+q
       475: q
       476: q^2+q
       477: q
       479: q
       480: q^2+q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       485: q^2+2q
       487: q^2+2q
       489: q^2+q
       491: q^2+2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: q^2+2q
       497: q^3+2q^2+2q
       498: q^3+2q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 3q^2+3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: q^2+2q
       512: q
       513: 3q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       525: q^2+q
       528: q
       539: q
       543: q
       544: q^2+q
       547: q
       553: q^2+q
       555: q
       557: q^2+q
       558: q^3+q^2+q
       559: q^2+q
       560: q^2
       561: q^2+q
       563: q
       567: q^2+q
       568: q
       570: q
       575: q
       576: q^2+q
       577: q
       583: q
       585: q
       587: q
       590: q^2+q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: q^2+2q
       604: q
       607: q
       611: q
       616: q^2+2q
       617: q
       620: q^2+q
       621: q
       623: q
       625: q
       627: q^2+2q
       629: q
       631: 2q^2+2q
       632: q^2+q
       633: q^2+2q
       635: q^2+2q
       637: q
       639: q
       642: q
       643: q
       648: q^2+2q
       649: 2q^2+2q
       650: q^2+q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q^2+2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: q^2+2q
       679: q
       680: q+1
       681: q^3+2q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 3q^2+3q
       685: q^2+2q
       686: q^2+2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       697: q
       731: q
       735: q
       745: q^2+q
       747: q
       749: q^2+q
       751: q
       758: q
       762: q
       764: q^2+q
       767: q^2+q
       768: q
       769: q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: q^2+2q
       794: 1
       795: 1
       802: q
       806: q
       807: q
       813: q
       816: q^2+2q
       817: 1
       819: q+1
       821: q
       823: q
       826: q^2+q
       827: q
       830: q
       831: q
       833: q
       835: q
       837: q^2+2q
       839: 2q^2+2q
       840: q^2+q
       841: q
       844: 1
       846: q
       847: q
       853: q
       857: q
       858: q^2+q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: q+1
       874: q+1
       875: q^2+2q
       876: q^2+2q
       877: q
       878: q^2+2q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       889: q
       918: 1
       934: q
       940: 1
       956: q^2+q
       958: q
       966: 1
       971: 1
       979: q
       982: q
       990: q^2+q
       991: q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 1
      1017: 1
      1020: 1
      1027: q
      1030: q+1
      1032: 1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1047: 1
      1053: q
      1057: q
      1058: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: q+1
      1080: 1
      1081: q+1
      1082: q^2+2q
      1083: q
      1084: 1
      1085: q
      1090: 1
      1102: q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: 1
      1164: 1
      1191: 1
      1196: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1226: 1
      1229: 1
      1236: 1
      1241: q
      1244: q+1
      1246: 1
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1263: 1
      1269: q
      1274: 1
      1281: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: q
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1342: 1
      1372: 1
      1380: 1
      1390: 1
      1398: 1
      1407: 1
      1412: 1
      1433: 1
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1452: 1
      1456: 1
      1458: q+1
      1460: 1
      1463: 1
      1472: 1
      1477: q
      1483: 1
      1486: 1
      1488: 1
      1493: 1
      1517: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1583: 1
      1589: 1
      1597: 1
      1634: 1
      1651: 1
      1653: 1
      1656: 1
      1667: 1
      1670: 1
      1679: 1
      1703: 1
      1761: 1
      1767: 1
      1775: 1
      1804: 1
      1862: 1

1863:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        39: 2q^2+3q+1
        41: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q^2+q
        61: 2q^2+2q+1
        62: 2q^2+3q+1
        64: 2q^2+3q+1
        66: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q
       106: q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+3q+1
       113: 2q^2+3q+1
       115: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: q^2+q
       120: 2q^2+2q+1
       121: 2q^2+3q+1
       123: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 3q+1
       129: 3q+1
       131: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       153: 2q^2+3q+1
       155: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       169: q
       172: q^2+2q+1
       173: q
       176: q^2+2q+1
       177: 2q+1
       179: 3q+1
       181: 3q+1
       183: q^2+q
       184: 2q^2+2q+1
       185: q
       186: q^2+2q+1
       187: q^2+3q+1
       189: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       194: q+1
       195: q
       196: 2q+1
       197: q+1
       199: q^2+q
       200: 2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: q
       204: q^2+2q+1
       205: q^2+3q+1
       207: q^2+3q+1
       209: 2q^2+3q+1
       211: 2q^2+3q+1
       213: 3q+1
       215: 3q+1
       217: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: 3q+1
       239: 3q+1
       241: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       259: q
       262: 2q+1
       263: q
       266: q^2+2q+1
       269: q+1
       271: q
       273: q^2+2q+1
       275: q
       278: q^2+2q+1
       279: 3q+1
       281: 2q+1
       284: q^2+q+1
       286: q+1
       287: 2q+1
       289: 3q+1
       291: 2q+1
       293: q^2+q
       294: 2q^2+2q+1
       295: q
       296: q^2+2q+1
       297: q^2+3q+1
       300: q+1
       301: q+1
       303: q
       304: 2q+1
       305: q+1
       307: q^2+q
       308: 2q^2+2q+1
       309: q
       310: q^2+2q+1
       311: 3q+1
       313: q^2+3q+1
       315: 2q+1
       317: 3q+1
       320: q+1
       321: q
       322: 2q+1
       323: q+1
       325: 2q^2+3q+1
       327: 3q+1
       329: 3q+1
       331: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       338: 3q+1
       340: 3q+1
       342: q^2+2q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: q^2+3q+1
       358: 2q+1
       359: 3q+1
       360: 3q+1
       362: 3q+1
       364: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: q+1
       370: 3q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q+1
       396: q+1
       397: q
       399: 2q+1
       401: q
       404: q^2+2q+1
       406: q+1
       409: 3q+1
       411: 2q+1
       413: 2q+1
       415: 3q+1
       417: 2q+1
       420: q^2+q+1
       422: q+1
       423: 2q+1
       425: 2q+1
       427: 3q+1
       430: 1
       432: q+1
       433: 1
       435: q+1
       438: q+1
       439: q
       440: 2q+1
       441: q+1
       444: q+1
       445: q+1
       448: q^2+q+1
       450: q+1
       451: 2q+1
       453: q^2+q
       454: 2q^2+2q+1
       455: 3q+1
       457: q
       458: q^2+2q+1
       459: q^2+3q+1
       461: q
       462: 2q+1
       463: 3q+1
       465: 3q+1
       467: 2q+1
       469: 2q+1
       472: q+1
       473: q
       474: 2q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       485: 3q+1
       487: 3q+1
       489: q^2+2q+1
       491: 2q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       502: 3q+1
       504: 3q+1
       506: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: 1
       513: 3q+1
       514: 2q+1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       524: q+1
       525: q
       528: 2q+1
       532: q+1
       536: 1
       539: q+1
       543: q+1
       547: q+1
       552: q+1
       553: q
       555: 2q+1
       557: q
       559: q^2+2q+1
       561: q
       563: 2q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: 2q+1
       585: 2q+1
       587: 2q+1
       590: q^2+q+1
       592: q+1
       594: 1
       596: q+1
       597: 2q+1
       599: 2q+1
       601: 3q+1
       604: 1
       605: 1
       608: q+1
       609: 1
       611: q+1
       613: 1
       616: q+1
       617: q+1
       620: q^2+q+1
       622: q+1
       623: 2q+1
       625: 2q+1
       627: 3q+1
       629: 2q+1
       631: q
       632: 2q+1
       633: 3q+1
       635: 3q+1
       637: 2q+1
       639: 2q+1
       642: 1
       644: q+1
       645: 1
       648: q+1
       649: q
       650: 2q+1
       651: q+1
       653: q+1
       655: q+1
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q+1
       666: 3q+1
       668: 3q+1
       670: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: q+1
       681: 2q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q+1
       708: q+1
       712: q+1
       716: q+1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: q+1
       739: q+1
       743: q+1
       745: q
       747: 2q+1
       749: q
       751: 2q+1
       756: 1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       775: 1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       786: 1
       788: q+1
       789: 3q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       808: q+1
       809: 1
       811: 1
       813: q+1
       816: q+1
       818: 1
       819: q+1
       821: 2q+1
       823: 2q+1
       826: q^2+q+1
       828: q+1
       830: 1
       832: q+1
       833: 2q+1
       835: 2q+1
       837: 3q+1
       839: q
       840: 2q+1
       841: 2q+1
       843: 1
       846: 1
       848: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       889: q+1
       899: q+1
       902: q+1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: q+1
       938: q+1
       942: 1
       946: q+1
       950: q+1
       955: 1
       956: q
       958: 2q+1
       961: 1
       967: 1
       968: 1
       975: 1
       979: q+1
       982: q+1
       991: q+1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 2q+1
      1005: 1
      1007: q+1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: q+1
      1033: 1
      1034: 2q+1
      1036: q+1
      1038: 2q+1
      1041: 1
      1042: 2q+1
      1045: q+1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1057: 1
      1059: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: q+1
      1112: q+1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1158: 1
      1166: 1
      1170: q+1
      1174: q+1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1208: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1236: 1
      1238: 1
      1241: 1
      1244: q+1
      1247: 1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 2q+1
      1259: 1
      1261: q+1
      1262: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1354: 1
      1374: 1
      1378: q+1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: 1
      1413: 1
      1415: 1
      1424: 1
      1430: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1452: 1
      1456: 1
      1458: q+1
      1461: 1
      1463: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1480: 1
      1482: 1
      1486: 1
      1488: 1
      1494: 1
      1518: 1
      1530: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1613: 1
      1631: 1
      1651: 1
      1654: 1
      1656: 1
      1667: 1
      1669: 1
      1671: 1
      1680: 1
      1704: 1
      1763: 1
      1767: 1
      1776: 1
      1778: 1
      1801: 1
      1863: 1

1864:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q
        59: q^2+2q+1
        60: 2q^2+2q+1
        61: q^2+q
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q^2+2q+1
       105: q
       107: 2q^2+2q+1
       108: q^2+q
       109: q
       110: q^2+2q+1
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q
       118: q^2+2q+1
       119: 2q^2+2q+1
       120: q^2+q
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q^2+2q+1
       171: q
       174: q^2+2q+1
       175: q
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: 2q^2+2q+1
       184: q^2+q
       185: q
       186: q^2+2q+1
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q
       192: q^2+2q+1
       193: q+1
       195: q
       196: 2q+1
       198: q+1
       199: 2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       203: q
       204: q^2+2q+1
       206: q^2+3q+1
       208: q^2+3q+1
       210: 2q^2+3q+1
       212: 2q^2+3q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: 2q+1
       261: q
       264: q^2+2q+1
       265: q
       268: q+1
       272: q
       274: q^2+2q+1
       276: q^2+2q+1
       277: q
       280: 3q+1
       282: 2q+1
       283: q^2+q+1
       286: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: 2q^2+2q+1
       294: q^2+q
       295: q
       296: q^2+2q+1
       298: q^2+3q+1
       299: q+1
       302: q+1
       303: q
       304: 2q+1
       306: q+1
       307: 2q^2+2q+1
       308: q^2+q
       309: q
       310: q^2+2q+1
       312: 3q+1
       314: q^2+3q+1
       316: 2q+1
       318: 3q+1
       319: q+1
       321: q
       322: 2q+1
       324: q+1
       326: 2q^2+3q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: q^2+3q+1
       358: 2q+1
       359: 3q+1
       361: 3q+1
       363: 3q+1
       365: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: q+1
       370: 3q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: q+1
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q+1
       394: q+1
       398: q
       400: 2q+1
       402: q
       403: q^2+2q+1
       407: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       419: q^2+q+1
       422: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       429: 1
       432: q+1
       434: 1
       436: q+1
       437: q+1
       439: q
       440: 2q+1
       442: q+1
       443: q+1
       446: q+1
       447: q^2+q+1
       450: q+1
       452: 2q+1
       453: 2q^2+2q+1
       454: q^2+q
       456: 3q+1
       457: q
       458: q^2+2q+1
       460: q^2+3q+1
       461: q
       462: 2q+1
       464: 3q+1
       466: 3q+1
       468: 2q+1
       470: 2q+1
       471: q+1
       473: q
       474: 2q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 3q+1
       488: 3q+1
       490: q^2+2q+1
       491: 2q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       503: 3q+1
       505: 3q+1
       507: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: 1
       513: 3q+1
       514: 2q+1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       522: q+1
       526: 2q+1
       527: q
       530: q+1
       534: 1
       538: q+1
       542: q+1
       546: q+1
       551: q+1
       554: q
       556: 2q+1
       558: q
       560: q^2+2q+1
       562: q
       564: 2q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       589: q^2+q+1
       592: q+1
       593: 1
       596: q+1
       598: 2q+1
       600: 2q+1
       602: 3q+1
       603: 1
       606: 1
       608: q+1
       610: 1
       612: q+1
       614: 1
       615: q+1
       618: q+1
       619: q^2+q+1
       622: q+1
       624: 2q+1
       626: 2q+1
       628: 3q+1
       630: 2q+1
       631: q
       632: 2q+1
       634: 3q+1
       636: 3q+1
       638: 2q+1
       640: 2q+1
       641: 1
       644: q+1
       646: 1
       647: q+1
       649: q
       650: 2q+1
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q+1
       667: 3q+1
       669: 3q+1
       671: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: q+1
       681: 2q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q+1
       706: q+1
       710: q+1
       715: q+1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: q+1
       740: q+1
       744: q+1
       746: q
       748: 2q+1
       750: q
       752: 2q+1
       754: 1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       785: 1
       788: q+1
       790: 3q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       808: q+1
       810: 1
       812: 1
       814: q+1
       815: q+1
       818: 1
       820: q+1
       822: 2q+1
       824: 2q+1
       825: q^2+q+1
       828: q+1
       829: 1
       832: q+1
       834: 2q+1
       836: 2q+1
       838: 3q+1
       839: q
       840: 2q+1
       842: 2q+1
       844: 1
       845: 1
       848: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       890: q+1
       897: q+1
       903: q+1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: q+1
       939: q+1
       943: 1
       947: q+1
       951: q+1
       953: 1
       957: q
       959: 2q+1
       962: 1
       965: 1
       972: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 2q+1
      1004: 1
      1007: q+1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: q+1
      1033: 1
      1035: 2q+1
      1037: q+1
      1039: 2q+1
      1040: 1
      1043: 2q+1
      1045: q+1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1056: 1
      1059: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: q+1
      1113: q+1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1157: 1
      1167: 1
      1171: q+1
      1175: q+1
      1177: 1
      1181: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1207: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1228: 1
      1237: 1
      1239: 1
      1240: 1
      1245: q+1
      1247: 1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 2q+1
      1258: 1
      1261: q+1
      1263: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1353: 1
      1375: 1
      1379: q+1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1408: 1
      1411: 1
      1416: 1
      1423: 1
      1434: 1
      1439: 1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1453: 1
      1457: 1
      1459: q+1
      1461: 1
      1462: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1481: 1
      1483: 1
      1486: 1
      1488: 1
      1495: 1
      1519: 1
      1531: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1612: 1
      1635: 1
      1652: 1
      1654: 1
      1655: 1
      1668: 1
      1670: 1
      1672: 1
      1681: 1
      1705: 1
      1764: 1
      1766: 1
      1774: 1
      1779: 1
      1805: 1
      1864: 1

1865:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        38: 2q^2+3q+1
        40: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q^2+q
        61: 2q^2+2q+1
        63: 2q^2+3q+1
        65: 2q^2+3q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: q^2+3q+1
        75: 2q^2+3q+1
        77: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q+1
        95: 3q+1
        96: q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       104: q
       105: q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: q
       112: q^2+3q+1
       114: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+2q+1
       118: q
       119: q^2+q
       120: 2q^2+2q+1
       122: 2q^2+3q+1
       124: q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 3q+1
       130: 3q+1
       132: q^2+2q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: 3q+1
       140: q+1
       141: 2q^2+3q+1
       142: 3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       152: 2q^2+3q+1
       154: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q+1
       161: 3q+1
       162: q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: 3q+1
       167: 3q+1
       168: q^2+2q+1
       170: q
       171: q^2+2q+1
       174: q
       175: q^2+2q+1
       178: 2q+1
       180: 3q+1
       182: 3q+1
       183: q^2+q
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q
       188: q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: q
       194: q+1
       195: 2q+1
       196: q
       198: q+1
       199: q^2+q
       200: 2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: q^2+2q+1
       204: q
       206: q^2+3q+1
       208: q^2+3q+1
       210: 2q^2+3q+1
       212: 2q^2+3q+1
       214: 3q+1
       216: 3q+1
       218: q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 3q+1
       228: 2q+1
       229: q+1
       230: 3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       238: 3q+1
       240: 3q+1
       242: q^2+2q+1
       243: 3q+1
       244: q+1
       245: 3q+1
       246: 2q^2+3q+1
       247: 3q+1
       248: 3q+1
       249: q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: 3q+1
       257: 3q+1
       258: q^2+2q+1
       260: q
       261: 2q+1
       264: q
       265: q^2+2q+1
       270: q+1
       272: q^2+2q+1
       274: q
       276: q
       277: q^2+2q+1
       280: 3q+1
       282: 2q+1
       284: q^2+q+1
       285: q+1
       288: 2q+1
       290: 3q+1
       292: 2q+1
       293: q^2+q
       294: 2q^2+2q+1
       295: q^2+2q+1
       296: q
       298: q^2+3q+1
       300: q+1
       302: q+1
       303: 2q+1
       304: q
       306: q+1
       307: q^2+q
       308: 2q^2+2q+1
       309: q^2+2q+1
       310: q
       312: 3q+1
       314: q^2+3q+1
       316: 2q+1
       318: 3q+1
       320: q+1
       321: 2q+1
       322: q
       324: q+1
       326: 2q^2+3q+1
       328: 3q+1
       330: 3q+1
       332: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q+1
       336: 2q+1
       337: 3q+1
       339: 3q+1
       341: 3q+1
       343: q^2+2q+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: q+1
       348: 1
       349: 3q+1
       350: 2q+1
       351: q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: q^2+3q+1
       358: 2q+1
       359: 3q+1
       361: 3q+1
       363: 3q+1
       365: q^2+2q+1
       366: 2q+1
       367: 3q+1
       368: 2q+1
       369: q+1
       370: 3q+1
       371: 3q+1
       372: 3q+1
       373: q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q+1
       395: q+1
       398: 2q+1
       400: q
       402: q^2+2q+1
       403: q
       408: q+1
       410: 3q+1
       412: 2q+1
       414: 2q+1
       416: 3q+1
       418: 2q+1
       420: q^2+q+1
       421: q+1
       424: 2q+1
       426: 2q+1
       428: 3q+1
       430: 1
       431: q+1
       434: 1
       436: q+1
       438: q+1
       439: 2q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       448: q^2+q+1
       449: q+1
       452: 2q+1
       453: q^2+q
       454: 2q^2+2q+1
       456: 3q+1
       457: q^2+2q+1
       458: q
       460: q^2+3q+1
       461: 2q+1
       462: q
       464: 3q+1
       466: 3q+1
       468: 2q+1
       470: 2q+1
       472: q+1
       473: 2q+1
       474: q
       476: q+1
       478: q+1
       480: q+1
       481: 2q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 3q+1
       486: 3q+1
       488: 3q+1
       490: q^2+2q+1
       491: 2q+1
       492: 2q+1
       493: 1
       494: 2q+1
       495: 1
       496: q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       503: 3q+1
       505: 3q+1
       507: q^2+2q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: q+1
       512: 1
       513: 3q+1
       514: 2q+1
       515: q+1
       516: q+1
       517: q+1
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       523: q+1
       526: q
       527: 2q+1
       531: q+1
       535: 1
       540: q+1
       544: q+1
       548: q+1
       550: q+1
       554: 2q+1
       556: q
       558: q^2+2q+1
       560: q
       562: 2q+1
       564: q
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: 2q+1
       586: 2q+1
       588: 2q+1
       590: q^2+q+1
       591: q+1
       594: 1
       595: q+1
       598: 2q+1
       600: 2q+1
       602: 3q+1
       604: 1
       606: 1
       607: q+1
       610: 1
       612: q+1
       614: 1
       616: q+1
       618: q+1
       620: q^2+q+1
       621: q+1
       624: 2q+1
       626: 2q+1
       628: 3q+1
       630: 2q+1
       631: 2q+1
       632: q
       634: 3q+1
       636: 3q+1
       638: 2q+1
       640: 2q+1
       642: 1
       643: q+1
       646: 1
       648: q+1
       649: 2q+1
       650: q
       652: q+1
       654: q+1
       656: q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q+1
       667: 3q+1
       669: 3q+1
       671: q^2+2q+1
       672: 3q+1
       673: 2q+1
       674: 1
       675: 1
       676: 2q+1
       677: 1
       678: q+1
       679: 1
       680: q+1
       681: 2q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 2q+1
       687: 1
       688: 2q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q+1
       707: q+1
       711: q+1
       714: q+1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: q+1
       738: q+1
       742: q+1
       746: 2q+1
       748: q
       750: 2q+1
       752: q
       755: 1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       776: 1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       786: 1
       787: q+1
       790: 3q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: q+1
       810: 1
       812: 1
       814: q+1
       816: q+1
       817: 1
       820: q+1
       822: 2q+1
       824: 2q+1
       826: q^2+q+1
       827: q+1
       830: 1
       831: q+1
       834: 2q+1
       836: 2q+1
       838: 3q+1
       839: 2q+1
       840: q
       842: 2q+1
       844: 1
       846: 1
       847: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       858: q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 1
       878: 2q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       891: q+1
       898: q+1
       901: q+1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: q+1
       937: q+1
       941: 1
       945: q+1
       949: q+1
       954: 1
       957: 2q+1
       959: q
       963: 1
       966: 1
       972: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 2q+1
      1005: 1
      1006: q+1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: q+1
      1032: 1
      1035: 2q+1
      1037: q+1
      1039: 2q+1
      1041: 1
      1043: 2q+1
      1044: q+1
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1057: 1
      1058: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: q+1
      1111: q+1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1169: q+1
      1173: q+1
      1179: 1
      1182: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1209: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1229: 1
      1237: 1
      1239: 1
      1241: 1
      1245: q+1
      1246: 1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 2q+1
      1259: 1
      1260: q+1
      1263: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1355: 1
      1373: 1
      1377: q+1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1408: 1
      1412: 1
      1417: 1
      1425: 1
      1434: 1
      1439: 1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1453: 1
      1457: 1
      1459: q+1
      1460: 1
      1463: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1481: 1
      1483: 1
      1486: 1
      1488: 1
      1496: 1
      1520: 1
      1532: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1614: 1
      1635: 1
      1652: 1
      1653: 1
      1656: 1
      1668: 1
      1670: 1
      1672: 1
      1682: 1
      1706: 1
      1762: 1
      1768: 1
      1775: 1
      1780: 1
      1805: 1
      1865: 1

1866:    0: 2q^4+7q^3+6q^2+3q
         1: 2q^4+7q^3+6q^2+3q
         2: 2q^4+7q^3+6q^2+3q
         3: 2q^4+7q^3+6q^2+3q
         4: 2q^4+7q^3+6q^2+3q
         5: 2q^4+7q^3+6q^2+3q
         6: 2q^4+7q^3+6q^2+3q
         7: 2q^4+7q^3+6q^2+3q
         8: 2q^4+7q^3+6q^2+3q
         9: 2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+7q^3+6q^2+3q
        11: 2q^4+7q^3+6q^2+3q
        12: 2q^4+7q^3+6q^2+3q
        13: 2q^4+7q^3+6q^2+3q
        14: 2q^4+7q^3+6q^2+3q
        15: 2q^4+7q^3+6q^2+3q
        16: 3q^3+5q^2+3q
        17: 3q^3+5q^2+3q
        18: q^4+3q^3+3q^2+2q
        19: 2q^4+7q^3+6q^2+3q
        20: 2q^4+7q^3+6q^2+3q
        21: 2q^4+7q^3+6q^2+3q
        22: 4q^3+5q^2+3q
        23: 4q^3+5q^2+3q
        24: 4q^3+5q^2+3q
        25: 2q^4+7q^3+6q^2+3q
        26: 2q^4+7q^3+6q^2+3q
        27: 2q^4+7q^3+6q^2+3q
        28: 3q^3+5q^2+3q
        29: 2q^4+7q^3+6q^2+3q
        30: 2q^4+7q^3+6q^2+3q
        31: 4q^3+5q^2+3q
        32: 4q^3+5q^2+3q
        33: q^3+4q^2+3q
        34: 2q^4+7q^3+6q^2+3q
        35: 2q^4+7q^3+6q^2+3q
        36: 3q^3+5q^2+3q
        37: 2q^3+2q^2+q
        38: 2q^3+3q^2+2q
        39: 2q^3+2q^2+q
        40: 2q^3+3q^2+2q
        41: 2q^3+2q^2+q
        42: 2q^3+3q^2+2q
        43: 2q^4+7q^3+6q^2+3q
        44: 2q^4+7q^3+6q^2+3q
        45: 2q^4+7q^3+6q^2+3q
        46: 3q^3+5q^2+3q
        47: 3q^3+5q^2+3q
        48: q^4+3q^3+3q^2+2q
        49: 3q^3+5q^2+3q
        50: 3q^3+5q^2+3q
        51: q^4+3q^3+3q^2+2q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: 4q^3+5q^2+3q
        55: 2q^4+7q^3+6q^2+3q
        56: 2q^4+7q^3+6q^2+3q
        57: 2q^4+7q^3+6q^2+3q
        58: 2q^2+q
        59: q^3+2q^2+2q
        60: q^3+2q^2+q
        61: 2q^3+3q^2+2q
        62: 2q^3+2q^2+q
        63: 2q^3+3q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: q^3+2q^2+q
        67: 2q^2+2q
        68: 3q^3+5q^2+3q
        69: q^3+2q^2+2q
        70: 2q^4+7q^3+6q^2+3q
        71: 3q^3+5q^2+3q
        72: 3q^3+5q^2+3q
        73: q^3+4q^2+3q
        74: 2q^3+2q^2+q
        75: 2q^3+3q^2+2q
        76: 2q^3+2q^2+q
        77: 2q^3+3q^2+2q
        78: 2q^3+2q^2+q
        79: 2q^3+3q^2+2q
        80: 4q^3+5q^2+3q
        81: q^3+4q^2+3q
        82: 4q^3+5q^2+3q
        83: 4q^3+5q^2+3q
        84: 2q^4+7q^3+6q^2+3q
        85: 3q^3+5q^2+3q
        86: 2q^4+7q^3+6q^2+3q
        87: 2q^4+7q^3+6q^2+3q
        88: 3q^3+5q^2+3q
        89: 3q^3+5q^2+3q
        90: q^4+3q^3+3q^2+2q
        91: 3q^3+5q^2+3q
        92: 3q^3+5q^2+3q
        93: q^4+3q^3+3q^2+2q
        94: 3q^2+3q
        95: 3q^2+3q
        96: q^3+2q^2+2q
        97: 3q^3+5q^2+3q
        98: 3q^3+5q^2+3q
        99: q^4+3q^3+3q^2+2q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: 4q^3+5q^2+3q
       103: q^2
       104: q^2+q
       105: q^2+q
       106: q^3+q^2+q
       107: q^3+2q^2+q
       108: 2q^3+3q^2+2q
       109: 2q^2+q
       110: q^3+2q^2+2q
       111: q^3+2q^2+q
       112: 2q^2+2q
       113: 2q^3+2q^2+q
       114: 2q^3+3q^2+2q
       115: 2q^3+2q^2+q
       116: 2q^3+3q^2+2q
       117: 2q^2+q
       118: q^3+2q^2+2q
       119: q^3+2q^2+q
       120: 2q^3+3q^2+2q
       121: 2q^3+2q^2+q
       122: 2q^3+3q^2+2q
       123: q^3+2q^2+q
       124: 2q^2+2q
       125: 3q^3+5q^2+3q
       126: q^3+2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+q
       133: 3q^3+5q^2+3q
       134: q^3+2q^2+2q
       135: 3q^3+5q^2+3q
       136: q^3+4q^2+3q
       137: q^3+4q^2+3q
       138: q^2+2q
       139: 3q^2+3q
       140: q^2+2q
       141: 4q^3+5q^2+3q
       142: 3q^2+3q
       143: 3q^3+5q^2+3q
       144: q^3+2q^2+2q
       145: 3q^3+5q^2+3q
       146: 2q^4+7q^3+6q^2+3q
       147: 3q^3+5q^2+3q
       148: q^3+4q^2+3q
       149: 4q^3+5q^2+3q
       150: 4q^3+5q^2+3q
       151: 2q^3+2q^2+q
       152: 2q^3+3q^2+2q
       153: 2q^3+2q^2+q
       154: 2q^3+3q^2+2q
       155: 2q^3+2q^2+q
       156: 2q^3+3q^2+2q
       157: 3q^3+5q^2+3q
       158: 3q^3+5q^2+3q
       159: q^4+3q^3+3q^2+2q
       160: 3q^2+3q
       161: 3q^2+3q
       162: q^3+2q^2+2q
       163: 3q^3+5q^2+3q
       164: 3q^3+5q^2+3q
       165: q^4+3q^3+3q^2+2q
       166: 3q^2+3q
       167: 3q^2+3q
       168: q^3+2q^2+2q
       169: q^2
       170: q^2+q
       171: q^2+q
       172: q^3+q^2+q
       173: q^2
       174: q^2+q
       175: q^2+q
       176: q^3+q^2+q
       178: q
       180: q^2+2q
       182: q^2+2q
       183: q^3+2q^2+q
       184: 2q^3+3q^2+2q
       185: 2q^2+q
       186: q^3+2q^2+2q
       187: q^3+2q^2+q
       188: 2q^2+2q
       189: 2q^3+2q^2+q
       190: 2q^3+3q^2+2q
       191: 2q^2+q
       192: q^3+2q^2+2q
       194: q^2+2q
       195: q^2+q
       196: 2q^2+2q
       197: q^2+q
       198: q
       199: q^3+2q^2+q
       200: 2q^3+3q^2+2q
       201: q^3+2q^2+q
       202: 2q^3+3q^2+2q
       203: 2q^2+q
       204: q^3+2q^2+2q
       205: q^3+2q^2+q
       206: 2q^2+2q
       207: q^3+2q^2+q
       208: 2q^2+2q
       209: 2q^3+2q^2+q
       210: 2q^3+3q^2+2q
       211: 2q^3+2q^2+q
       212: 2q^3+3q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+q
       219: q^3+2q^2+2q
       220: 3q^3+5q^2+3q
       221: q^3+2q^2+2q
       222: 3q^3+5q^2+3q
       223: q^3+2q^2+2q
       224: q^3+4q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q^2+3q
       228: q^2+2q
       229: q^2+2q
       230: 3q^2+3q
       231: q^3+2q^2+2q
       232: 3q^3+5q^2+3q
       233: q^3+2q^2+2q
       234: 3q^3+5q^2+3q
       235: q^3+4q^2+3q
       236: q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+q
       243: 3q^2+3q
       244: q^2+2q
       245: 3q^2+3q
       246: 4q^3+5q^2+3q
       247: 3q^2+3q
       248: 3q^2+3q
       249: q^3+2q^2+2q
       250: 3q^2+3q
       251: 3q^2+3q
       252: q^3+2q^2+2q
       253: 3q^3+5q^2+3q
       254: 3q^3+5q^2+3q
       255: q^4+3q^3+3q^2+2q
       256: 3q^2+3q
       257: 3q^2+3q
       258: q^3+2q^2+2q
       260: q^2+q
       261: q
       263: q^2
       264: q^2+q
       265: q^2+q
       266: q^3+q^2+q
       269: q^2+q
       270: q
       271: q^2
       272: q^2+q
       273: q^3+q^2+q
       274: q^2+q
       275: q^2
       276: q^2+q
       277: q^2+q
       278: q^3+q^2+q
       280: q^2+2q
       282: q
       284: q^2+q
       286: q
       288: q
       290: q^2+2q
       292: q
       293: q^3+2q^2+q
       294: 2q^3+3q^2+2q
       295: 2q^2+q
       296: q^3+2q^2+2q
       297: q^3+2q^2+q
       298: 2q^2+2q
       300: q^2+2q
       302: q
       303: q^2+q
       304: 2q^2+2q
       305: q^2+q
       306: q
       307: q^3+2q^2+q
       308: 2q^3+3q^2+2q
       309: 2q^2+q
       310: q^3+2q^2+2q
       312: q^2+2q
       313: q^3+2q^2+q
       314: 2q^2+2q
       316: q
       318: q^2+2q
       320: q^2+2q
       321: q^2+q
       322: 2q^2+2q
       323: q^2+q
       324: q
       325: 2q^3+2q^2+q
       326: 2q^3+3q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+q
       333: q^3+2q^2+2q
       334: q^3+2q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: 3q^2+3q
       339: q^2+2q
       341: q^2+2q
       343: q^2+q
       344: q^2+2q
       345: 3q^2+3q
       346: q^2+2q
       347: q^2+2q
       348: q
       349: 3q^2+3q
       350: q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: 3q^3+5q^2+3q
       354: q^3+2q^2+2q
       355: 3q^3+5q^2+3q
       356: q^3+2q^2+2q
       357: q^3+4q^2+3q
       358: q^2+2q
       359: 3q^2+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+q
       366: q^2+2q
       367: 3q^2+3q
       368: q^2+2q
       369: q^2+2q
       370: 3q^2+3q
       371: 3q^2+3q
       372: 3q^2+3q
       373: q^3+2q^2+2q
       374: 3q^2+3q
       375: 3q^2+3q
       376: q^3+2q^2+2q
       382: q^2+q
       383: q
       385: q^2
       386: q^2+q
       387: q^2+q
       388: q^3+q^2+q
       392: q
       395: q
       396: q^2+q
       398: q
       400: q^2+q
       401: q^2
       402: q^2+q
       403: q^2+q
       404: q^3+q^2+q
       406: q^2+q
       408: q
       410: q^2+2q
       412: q
       414: q
       416: q^2+2q
       418: q
       420: q^2+q
       422: q
       424: q
       426: q
       428: q^2+2q
       430: q
       432: q
       436: q
       438: q^2+2q
       439: q^2+q
       440: 2q^2+2q
       441: q^2+q
       442: q
       444: q^2+2q
       446: q
       448: q^2+q
       450: q
       452: q
       453: q^3+2q^2+q
       454: 2q^3+3q^2+2q
       456: q^2+2q
       457: 2q^2+q
       458: q^3+2q^2+2q
       459: q^3+2q^2+q
       460: 2q^2+2q
       461: q^2+q
       462: 2q^2+2q
       464: q^2+2q
       466: q^2+2q
       468: q
       470: q
       472: q^2+2q
       473: q^2+q
       474: 2q^2+2q
       475: q^2+q
       476: q
       478: q
       479: q^2+q
       480: q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: q^2+2q
       484: 3q^2+3q
       486: q^2+2q
       488: q^2+2q
       490: q^2+q
       491: q^2+2q
       492: q^2+2q
       493: q
       494: q^2+2q
       495: q
       496: q^2+2q
       497: q^3+2q^2+2q
       498: q^3+2q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 3q^2+3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+q
       508: q^2+2q
       509: 3q^2+3q
       510: q^2+2q
       511: q^2+2q
       512: q
       513: 3q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q^2+3q
       519: 3q^2+3q
       520: q^3+2q^2+2q
       526: q^2+q
       527: q
       540: q
       543: q^2+q
       544: q
       548: q
       554: q
       556: q^2+q
       557: q^2
       558: q^2+q
       559: q^3+q^2+q
       560: q^2+q
       562: q
       564: q^2+q
       567: q
       568: q^2+q
       572: q
       575: q^2+q
       576: q
       581: q
       584: q
       586: q
       588: q
       590: q^2+q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: q^2+2q
       604: q
       608: q
       612: q
       616: q^2+2q
       618: q
       620: q^2+q
       622: q
       624: q
       626: q
       628: q^2+2q
       630: q
       631: q^2+q
       632: 2q^2+2q
       634: q^2+2q
       636: q^2+2q
       638: q
       640: q
       642: q
       644: q
       648: q^2+2q
       649: q^2+q
       650: 2q^2+2q
       652: q
       653: q^2+q
       654: q
       655: q^2+q
       656: q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q^2+2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+q
       672: 3q^2+3q
       673: q^2+2q
       674: 1
       675: q
       676: q^2+2q
       677: q
       678: q^2+2q
       679: q
       680: q+1
       681: q^3+2q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 3q^2+3q
       685: q^2+2q
       686: q^2+2q
       687: q
       688: q^2+2q
       689: q
       690: q+1
       691: q+1
       692: q+1
       700: q
       732: q
       736: q
       746: q
       748: q^2+q
       750: q
       752: q^2+q
       760: q
       762: q^2+q
       764: q
       767: q
       768: q^2+q
       773: q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: q^2+2q
       794: 1
       796: 1
       802: q
       806: q
       808: q
       814: q
       816: q^2+2q
       818: 1
       820: q+1
       822: q
       824: q
       826: q^2+q
       828: q
       830: q
       832: q
       834: q
       836: q
       838: q^2+2q
       839: q^2+q
       840: 2q^2+2q
       842: q
       843: 1
       846: q
       848: q
       854: q
       857: q^2+q
       858: q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q^2+2q
       869: 1
       870: 1
       871: q
       872: q
       873: q+1
       874: q+1
       875: q^2+2q
       876: q^2+2q
       877: q
       878: q^2+2q
       879: q
       880: q
       881: q+1
       882: q+1
       883: q+1
       891: q
       919: 1
       935: q
       943: 1
       957: q
       959: q^2+q
       967: 1
       969: 1
       981: q
       986: q
       990: q
       991: q^2+q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 1
      1017: 1
      1021: 1
      1027: q
      1031: q+1
      1033: 1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: 1
      1053: q
      1057: q
      1059: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1077: 1
      1078: q
      1079: q+1
      1080: 1
      1081: q+1
      1082: q^2+2q
      1083: q
      1084: 1
      1085: q
      1094: 1
      1105: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: 1
      1167: 1
      1189: 1
      1197: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1227: 1
      1229: 1
      1237: 1
      1241: q
      1245: q+1
      1247: 1
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1262: 1
      1269: q
      1275: 1
      1280: 1
      1282: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: 1
      1289: q
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1343: 1
      1375: 1
      1383: 1
      1391: 1
      1399: 1
      1405: 1
      1413: 1
      1431: 1
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1453: 1
      1457: 1
      1459: q+1
      1461: 1
      1463: 1
      1473: 1
      1477: q
      1482: 1
      1486: 1
      1488: 1
      1497: 1
      1521: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1586: 1
      1590: 1
      1598: 1
      1632: 1
      1652: 1
      1654: 1
      1656: 1
      1668: 1
      1669: 1
      1683: 1
      1707: 1
      1764: 1
      1768: 1
      1776: 1
      1802: 1
      1866: 1

1867:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 4q^4+6q^3+3q^2+q
        23: q^5+5q^4+6q^3+3q^2+q
        24: 4q^4+6q^3+3q^2+q
        25: 7q^4+7q^3+3q^2+q
        26: 2q^5+8q^4+7q^3+3q^2+q
        27: 7q^4+7q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 3q^4+5q^3+3q^2+q
        32: 4q^4+6q^3+3q^2+q
        33: 3q^4+5q^3+3q^2+q
        34: 5q^4+6q^3+3q^2+q
        35: 7q^4+7q^3+3q^2+q
        36: 5q^4+6q^3+3q^2+q
        37: 4q^4+6q^3+3q^2+q
        39: q^5+5q^4+6q^3+3q^2+q
        41: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: q^4+5q^3+3q^2+q
        53: 2q^4+5q^3+3q^2+q
        54: q^4+5q^3+3q^2+q
        55: 4q^4+6q^3+3q^2+q
        56: q^5+5q^4+6q^3+3q^2+q
        57: 4q^4+6q^3+3q^2+q
        58: q^3+q^2
        59: 2q^4+3q^3+2q^2+q
        60: q^4+q^3+q^2
        61: 2q^4+4q^3+2q^2+q
        62: 3q^4+5q^3+3q^2+q
        64: 4q^4+6q^3+3q^2+q
        66: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 4q^3+3q^2+q
        73: 3q^3+3q^2+q
        74: q^4+5q^3+3q^2+q
        76: 2q^4+5q^3+3q^2+q
        78: q^4+5q^3+3q^2+q
        80: 3q^4+5q^3+3q^2+q
        81: 3q^4+5q^3+3q^2+q
        82: q^4+4q^3+3q^2+q
        83: q^4+5q^3+3q^2+q
        84: 5q^4+6q^3+3q^2+q
        85: 5q^4+6q^3+3q^2+q
        86: 3q^4+5q^3+3q^2+q
        87: 4q^4+6q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 3q^3+3q^2+q
        95: 3q^3+3q^2+q
        96: 3q^3+2q^2+q
        97: 2q^4+5q^3+3q^2+q
        98: 2q^4+5q^3+3q^2+q
        99: 2q^4+4q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       103: q^3+q^2
       106: 2q^4+3q^3+2q^2+q
       107: q^2
       108: 3q^3+2q^2+q
       109: q^2
       110: 2q^3+2q^2+q
       111: 3q^3+3q^2+q
       113: q^4+4q^3+3q^2+q
       115: q^4+5q^3+3q^2+q
       117: q^3+q^2
       118: 2q^4+3q^3+2q^2+q
       119: q^4+q^3+q^2
       120: 2q^4+4q^3+2q^2+q
       121: 3q^4+5q^3+3q^2+q
       123: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       127: 3q^3+3q^2+q
       129: 3q^3+3q^2+q
       131: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 4q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^4+3q^3+3q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: 2q^2+q
       141: q^4+4q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^4+4q^3+3q^2+q
       144: q^4+3q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 3q^4+5q^3+3q^2+q
       147: 4q^3+3q^2+q
       148: 3q^3+3q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       151: q^4+5q^3+3q^2+q
       153: 2q^4+5q^3+3q^2+q
       155: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 3q^3+3q^2+q
       161: 3q^3+3q^2+q
       162: 3q^3+2q^2+q
       163: 2q^4+5q^3+3q^2+q
       164: 2q^4+5q^3+3q^2+q
       165: 2q^4+4q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       169: q^2
       172: 2q^3+2q^2+q
       173: q^3+q^2
       176: 2q^4+3q^3+2q^2+q
       177: 2q^3+2q^2+q
       179: 2q^3+3q^2+q
       181: 2q^3+3q^2+q
       183: q^2
       184: 3q^3+2q^2+q
       185: q^2
       186: 2q^3+2q^2+q
       187: 3q^3+3q^2+q
       189: q^4+4q^3+3q^2+q
       191: q^3+q^2
       192: q^4+2q^3+2q^2+q
       194: 2q^2+q
       195: q^2
       196: q^3+2q^2+q
       197: 2q^2+q
       199: q^3+q^2
       200: q^4+3q^3+2q^2+q
       201: q^2
       202: 3q^3+2q^2+q
       203: q^2
       204: 2q^3+2q^2+q
       205: 3q^3+3q^2+q
       207: q^4+3q^3+3q^2+q
       209: q^4+4q^3+3q^2+q
       211: q^4+5q^3+3q^2+q
       213: 3q^3+3q^2+q
       215: 3q^3+3q^2+q
       217: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: 2q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: 2q^3+3q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: 2q^3+3q^2+q
       231: 2q^3+2q^2+q
       232: q^4+4q^3+3q^2+q
       233: q^4+3q^3+2q^2+q
       234: 4q^3+3q^2+q
       235: 3q^3+3q^2+q
       236: 2q^3+2q^2+q
       237: 3q^3+3q^2+q
       239: 3q^3+3q^2+q
       241: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^2+q
       245: 2q^3+3q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^3+3q^2+q
       254: 2q^3+3q^2+q
       255: q^4+2q^3+2q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       259: q^2
       262: q^3+2q^2+q
       263: q^2
       266: 2q^3+2q^2+q
       269: 2q^2+q
       271: q^2
       273: 2q^3+2q^2+q
       275: q^3+q^2
       278: q^4+2q^3+2q^2+q
       279: 2q^3+3q^2+q
       281: 2q^3+2q^2+q
       284: q^3+q^2+q
       286: q^2+q
       287: q^3+2q^2+q
       289: 2q^3+3q^2+q
       291: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^2
       296: q^3+2q^2+q
       297: q^3+3q^2+q
       300: 2q^2+q
       301: 2q^2+q
       303: q^2
       304: q^3+2q^2+q
       305: 2q^2+q
       307: q^2
       308: 3q^3+2q^2+q
       309: q^2
       310: 2q^3+2q^2+q
       311: 2q^3+3q^2+q
       313: 3q^3+3q^2+q
       315: 2q^3+2q^2+q
       317: 2q^3+3q^2+q
       320: 2q^2+q
       321: q^2
       322: q^3+2q^2+q
       323: 2q^2+q
       325: q^4+4q^3+3q^2+q
       327: 2q^2+q
       329: 2q^2+q
       331: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^3+2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: 2q^3+3q^2+q
       354: q^3+2q^2+q
       355: q^3+3q^2+q
       356: 2q^3+2q^2+q
       357: q^3+3q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       360: 3q^3+3q^2+q
       362: 3q^3+3q^2+q
       364: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^2+q
       370: 2q^3+3q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       380: q^2+q
       381: q^2
       384: q^3+2q^2+q
       385: q^2
       388: q^3+2q^2+q
       391: 2q^2+q
       396: 2q^2+q
       397: q^2
       399: q^3+2q^2+q
       401: q^2
       404: 2q^3+2q^2+q
       406: 2q^2+q
       409: 2q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: 2q^2+q
       417: q^3+2q^2+q
       420: q^2+q
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       430: q^2+q
       432: q^2+q
       433: q^2+q
       435: 2q^2+q
       438: q^2+q
       439: q^2
       440: q^2+q
       441: q^2+q
       444: q^2+q
       445: q^2+q
       448: q^3+q^2+q
       450: q^2+q
       451: q^3+2q^2+q
       453: q^2
       454: q^3+2q^2+q
       455: 2q^3+3q^2+q
       457: q^2
       458: q^3+2q^2+q
       459: q^3+3q^2+q
       461: q^2
       462: q^2+q
       463: 2q^2+q
       465: 2q^3+3q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       472: 2q^2+q
       473: q^2
       474: q^3+2q^2+q
       475: 2q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       502: 2q^2+q
       504: 2q^2+q
       506: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: 2q^2+q
       514: q^3+2q^2+q
       524: q^2+q
       525: q^2
       528: q^2+q
       532: q^2+q
       536: q^2+q
       539: 2q^2+q
       543: q^2+q
       547: q^2+q
       552: q^2+q
       553: q^2
       555: q^3+2q^2+q
       557: q^2
       559: q^3+2q^2+q
       561: q^2
       563: q^2+q
       568: 2q^2+q
       570: 2q^2+q
       575: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       590: q^2+q
       592: q
       594: q
       596: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       604: q
       605: q^2+q
       608: q
       609: q
       611: q^2+q
       613: q
       616: q^2+q
       617: q^2+q
       620: q^2+q
       622: q^2+q
       623: q^3+2q^2+q
       625: 2q^2+q
       627: 2q^2+q
       629: q^2+q
       631: q^2
       632: q^2+q
       633: 2q^2+q
       635: 2q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       648: q^2+q
       649: q^2
       650: q^2+q
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       697: q^2+q
       708: q
       712: q^2+q
       716: q
       720: q
       723: q^2+q
       727: q
       731: q^2+q
       735: q^2+q
       739: q^2+q
       743: q^2+q
       745: q^2
       747: q^2+q
       749: q^2
       751: q^2+q
       756: q^2+q
       758: 2q^2+q
       762: q^2+q
       768: q^2+q
       769: q^2+q
       777: q^2+q
       781: q^2+q
       786: q
       788: q
       791: q
       797: q
       799: q
       802: q
       806: q
       808: q
       809: q
       811: q
       821: 2q^2+q
       823: q^2+q
       826: q^2+q
       828: q
       830: q
       832: q^2+q
       833: q^2+q
       835: q^2+q
       841: q^2+q
       846: q
       848: q
       849: q^2+q
       851: q
       853: q^2+q
       855: q
       871: q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       889: q^2+q
       899: q
       902: q
       906: q
       911: q
       914: q
       922: q
       930: q
       938: q
       946: q^2+q
       950: q
       955: q
       961: q^2+q
       975: q
       979: q^2+q
      1010: q
      1018: q
      1022: q
      1027: q
      1034: q^2+q
      1038: q^2+q
      1041: q
      1045: q
      1048: q
      1050: q
      1053: q
      1057: q
      1059: q
      1060: q
      1062: q
      1064: q
      1083: q
      1127: q
      1150: q
      1158: q
      1170: q
      1174: q
      1178: q
      1183: q
      1185: q
      1199: q
      1208: q
      1222: 1
      1264: q
      1266: q
      1269: q
      1278: q
      1323: 1
      1336: 1
      1393: q
      1415: q
      1424: q
      1446: 1
      1480: 1
      1498: 1
      1555: 1
      1560: 1
      1592: 1
      1633: 1
      1671: 1
      1684: 1
      1708: 1
      1778: 1
      1803: 1
      1867: 1

1868:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 4q^4+6q^3+3q^2+q
        23: q^5+5q^4+6q^3+3q^2+q
        24: 4q^4+6q^3+3q^2+q
        25: 7q^4+7q^3+3q^2+q
        26: 2q^5+8q^4+7q^3+3q^2+q
        27: 7q^4+7q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 3q^4+5q^3+3q^2+q
        32: 4q^4+6q^3+3q^2+q
        33: 3q^4+5q^3+3q^2+q
        34: 5q^4+6q^3+3q^2+q
        35: 7q^4+7q^3+3q^2+q
        36: 5q^4+6q^3+3q^2+q
        38: 4q^4+6q^3+3q^2+q
        40: q^5+5q^4+6q^3+3q^2+q
        42: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: q^4+5q^3+3q^2+q
        53: 2q^4+5q^3+3q^2+q
        54: q^4+5q^3+3q^2+q
        55: 4q^4+6q^3+3q^2+q
        56: q^5+5q^4+6q^3+3q^2+q
        57: 4q^4+6q^3+3q^2+q
        58: q^3+q^2
        59: 2q^4+3q^3+2q^2+q
        60: 2q^4+4q^3+2q^2+q
        61: q^4+q^3+q^2
        63: 3q^4+5q^3+3q^2+q
        65: 4q^4+6q^3+3q^2+q
        67: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 4q^3+3q^2+q
        73: 3q^3+3q^2+q
        75: q^4+5q^3+3q^2+q
        77: 2q^4+5q^3+3q^2+q
        79: q^4+5q^3+3q^2+q
        80: 3q^4+5q^3+3q^2+q
        81: 3q^4+5q^3+3q^2+q
        82: q^4+4q^3+3q^2+q
        83: q^4+5q^3+3q^2+q
        84: 5q^4+6q^3+3q^2+q
        85: 5q^4+6q^3+3q^2+q
        86: 3q^4+5q^3+3q^2+q
        87: 4q^4+6q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 3q^3+3q^2+q
        95: 3q^3+3q^2+q
        96: 3q^3+2q^2+q
        97: 2q^4+5q^3+3q^2+q
        98: 2q^4+5q^3+3q^2+q
        99: 2q^4+4q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       104: 2q^4+3q^3+2q^2+q
       105: q^3+q^2
       107: 3q^3+2q^2+q
       108: q^2
       109: q^2
       110: 2q^3+2q^2+q
       112: 3q^3+3q^2+q
       114: q^4+4q^3+3q^2+q
       116: q^4+5q^3+3q^2+q
       117: q^3+q^2
       118: 2q^4+3q^3+2q^2+q
       119: 2q^4+4q^3+2q^2+q
       120: q^4+q^3+q^2
       122: 3q^4+5q^3+3q^2+q
       124: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       128: 3q^3+3q^2+q
       130: 3q^3+3q^2+q
       132: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 4q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^4+3q^3+3q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: 2q^2+q
       141: q^4+4q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^4+4q^3+3q^2+q
       144: q^4+3q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 3q^4+5q^3+3q^2+q
       147: 4q^3+3q^2+q
       148: 3q^3+3q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       152: q^4+5q^3+3q^2+q
       154: 2q^4+5q^3+3q^2+q
       156: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 3q^3+3q^2+q
       161: 3q^3+3q^2+q
       162: 3q^3+2q^2+q
       163: 2q^4+5q^3+3q^2+q
       164: 2q^4+5q^3+3q^2+q
       165: 2q^4+4q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       170: 2q^3+2q^2+q
       171: q^2
       174: 2q^4+3q^3+2q^2+q
       175: q^3+q^2
       178: 2q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: 3q^3+2q^2+q
       184: q^2
       185: q^2
       186: 2q^3+2q^2+q
       188: 3q^3+3q^2+q
       190: q^4+4q^3+3q^2+q
       191: q^3+q^2
       192: q^4+2q^3+2q^2+q
       193: 2q^2+q
       195: q^2
       196: q^3+2q^2+q
       198: 2q^2+q
       199: q^4+3q^3+2q^2+q
       200: q^3+q^2
       201: 3q^3+2q^2+q
       202: q^2
       203: q^2
       204: 2q^3+2q^2+q
       206: 3q^3+3q^2+q
       208: q^4+3q^3+3q^2+q
       210: q^4+4q^3+3q^2+q
       212: q^4+5q^3+3q^2+q
       214: 3q^3+3q^2+q
       216: 3q^3+3q^2+q
       218: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: 2q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: 2q^3+3q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: 2q^3+3q^2+q
       231: 2q^3+2q^2+q
       232: q^4+4q^3+3q^2+q
       233: q^4+3q^3+2q^2+q
       234: 4q^3+3q^2+q
       235: 3q^3+3q^2+q
       236: 2q^3+2q^2+q
       238: 3q^3+3q^2+q
       240: 3q^3+3q^2+q
       242: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^2+q
       245: 2q^3+3q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^3+3q^2+q
       254: 2q^3+3q^2+q
       255: q^4+2q^3+2q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       260: q^3+2q^2+q
       261: q^2
       264: 2q^3+2q^2+q
       265: q^2
       268: 2q^2+q
       272: q^2
       274: 2q^3+2q^2+q
       276: q^4+2q^3+2q^2+q
       277: q^3+q^2
       280: 2q^3+3q^2+q
       282: 2q^3+2q^2+q
       283: q^3+q^2+q
       286: q^2+q
       288: q^3+2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^3+2q^2+q
       294: q^2
       295: q^2
       296: q^3+2q^2+q
       298: q^3+3q^2+q
       299: 2q^2+q
       302: 2q^2+q
       303: q^2
       304: q^3+2q^2+q
       306: 2q^2+q
       307: 3q^3+2q^2+q
       308: q^2
       309: q^2
       310: 2q^3+2q^2+q
       312: 2q^3+3q^2+q
       314: 3q^3+3q^2+q
       316: 2q^3+2q^2+q
       318: 2q^3+3q^2+q
       319: 2q^2+q
       321: q^2
       322: q^3+2q^2+q
       324: 2q^2+q
       326: q^4+4q^3+3q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^3+2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: 2q^3+3q^2+q
       354: q^3+2q^2+q
       355: q^3+3q^2+q
       356: 2q^3+2q^2+q
       357: q^3+3q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       361: 3q^3+3q^2+q
       363: 3q^3+3q^2+q
       365: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^2+q
       370: 2q^3+3q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       378: q^2+q
       382: q^3+2q^2+q
       383: q^2
       386: q^3+2q^2+q
       387: q^2
       390: 2q^2+q
       394: 2q^2+q
       398: q^2
       400: q^3+2q^2+q
       402: q^2
       403: 2q^3+2q^2+q
       407: 2q^2+q
       410: 2q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       419: q^2+q
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2+q
       432: q^2+q
       434: q^2+q
       436: 2q^2+q
       437: q^2+q
       439: q^2
       440: q^2+q
       442: q^2+q
       443: q^2+q
       446: q^2+q
       447: q^3+q^2+q
       450: q^2+q
       452: q^3+2q^2+q
       453: q^3+2q^2+q
       454: q^2
       456: 2q^3+3q^2+q
       457: q^2
       458: q^3+2q^2+q
       460: q^3+3q^2+q
       461: q^2
       462: q^2+q
       464: 2q^2+q
       466: 2q^3+3q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: 2q^2+q
       473: q^2
       474: q^3+2q^2+q
       476: 2q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       503: 2q^2+q
       505: 2q^2+q
       507: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: 2q^2+q
       514: q^3+2q^2+q
       522: q^2+q
       526: q^2+q
       527: q^2
       530: q^2+q
       534: q^2+q
       538: 2q^2+q
       542: q^2+q
       546: q^2+q
       551: q^2+q
       554: q^2
       556: q^3+2q^2+q
       558: q^2
       560: q^3+2q^2+q
       562: q^2
       564: q^2+q
       566: 2q^2+q
       571: 2q^2+q
       574: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2+q
       592: q
       593: q
       596: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       603: q
       606: q^2+q
       608: q
       610: q
       612: q^2+q
       614: q
       615: q^2+q
       618: q^2+q
       619: q^2+q
       622: q^2+q
       624: q^3+2q^2+q
       626: 2q^2+q
       628: 2q^2+q
       630: q^2+q
       631: q^2
       632: q^2+q
       634: 2q^2+q
       636: 2q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q^2+q
       649: q^2
       650: q^2+q
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       699: q^2+q
       706: q
       710: q^2+q
       715: q
       718: q
       722: q^2+q
       726: q
       730: q^2+q
       734: q^2+q
       740: q^2+q
       744: q^2+q
       746: q^2
       748: q^2+q
       750: q^2
       752: q^2+q
       754: q^2+q
       759: 2q^2+q
       763: q^2+q
       766: q^2+q
       773: q^2+q
       778: q^2+q
       782: q^2+q
       785: q
       788: q
       792: q
       798: q
       800: q
       801: q
       805: q
       808: q
       810: q
       812: q
       822: 2q^2+q
       824: q^2+q
       825: q^2+q
       828: q
       829: q
       832: q^2+q
       834: q^2+q
       836: q^2+q
       842: q^2+q
       845: q
       848: q
       850: q^2+q
       852: q
       854: q^2+q
       856: q
       871: q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       890: q^2+q
       897: q
       903: q
       905: q
       909: q
       913: q
       921: q
       929: q
       939: q
       947: q^2+q
       951: q
       953: q
       962: q^2+q
       976: q
       980: q^2+q
      1011: q
      1019: q
      1023: q
      1026: q
      1035: q^2+q
      1039: q^2+q
      1040: q
      1045: q
      1049: q
      1051: q
      1052: q
      1056: q
      1059: q
      1061: q
      1063: q
      1065: q
      1083: q
      1128: q
      1149: q
      1157: q
      1171: q
      1175: q
      1177: q
      1181: q
      1186: q
      1200: q
      1207: q
      1223: 1
      1265: q
      1267: q
      1268: q
      1279: q
      1324: 1
      1339: 1
      1394: q
      1416: q
      1423: q
      1447: 1
      1481: 1
      1499: 1
      1558: 1
      1561: 1
      1593: 1
      1636: 1
      1672: 1
      1685: 1
      1709: 1
      1779: 1
      1806: 1
      1868: 1

1869:    0: 7q^4+7q^3+3q^2+q
         1: 2q^5+8q^4+7q^3+3q^2+q
         2: 7q^4+7q^3+3q^2+q
         3: 2q^5+8q^4+7q^3+3q^2+q
         4: 3q^5+5q^4+6q^3+3q^2+q
         5: 7q^4+7q^3+3q^2+q
         6: q^6+4q^5+6q^4+6q^3+3q^2+q
         7: 3q^5+5q^4+6q^3+3q^2+q
         8: 7q^4+7q^3+3q^2+q
         9: q^6+3q^5+4q^4+4q^3+2q^2+q
        10: 5q^4+6q^3+3q^2+q
        11: 5q^4+6q^3+3q^2+q
        12: 2q^5+4q^4+5q^3+3q^2+q
        13: 7q^4+7q^3+3q^2+q
        14: 3q^5+5q^4+6q^3+3q^2+q
        15: 7q^4+7q^3+3q^2+q
        16: 5q^4+6q^3+3q^2+q
        17: 5q^4+6q^3+3q^2+q
        18: 2q^5+3q^4+4q^3+2q^2+q
        19: 4q^4+6q^3+3q^2+q
        20: q^5+5q^4+6q^3+3q^2+q
        21: 4q^4+6q^3+3q^2+q
        22: 4q^4+6q^3+3q^2+q
        23: q^5+5q^4+6q^3+3q^2+q
        24: 4q^4+6q^3+3q^2+q
        25: 7q^4+7q^3+3q^2+q
        26: 2q^5+8q^4+7q^3+3q^2+q
        27: 7q^4+7q^3+3q^2+q
        28: 3q^4+5q^3+3q^2+q
        29: 3q^4+5q^3+3q^2+q
        30: 4q^4+6q^3+3q^2+q
        31: 3q^4+5q^3+3q^2+q
        32: 4q^4+6q^3+3q^2+q
        33: 3q^4+5q^3+3q^2+q
        34: 5q^4+6q^3+3q^2+q
        35: 7q^4+7q^3+3q^2+q
        36: 5q^4+6q^3+3q^2+q
        38: 4q^4+6q^3+3q^2+q
        40: q^5+5q^4+6q^3+3q^2+q
        42: 4q^4+6q^3+3q^2+q
        43: 5q^4+6q^3+3q^2+q
        44: 2q^5+4q^4+5q^3+3q^2+q
        45: 5q^4+6q^3+3q^2+q
        46: 5q^4+6q^3+3q^2+q
        47: 5q^4+6q^3+3q^2+q
        48: 2q^5+3q^4+4q^3+2q^2+q
        49: 2q^4+5q^3+3q^2+q
        50: 2q^4+5q^3+3q^2+q
        51: 2q^4+4q^3+2q^2+q
        52: q^4+5q^3+3q^2+q
        53: 2q^4+5q^3+3q^2+q
        54: q^4+5q^3+3q^2+q
        55: 4q^4+6q^3+3q^2+q
        56: q^5+5q^4+6q^3+3q^2+q
        57: 4q^4+6q^3+3q^2+q
        58: 2q^4+3q^3+2q^2+q
        59: q^3+q^2
        60: q^4+q^3+q^2
        61: 2q^4+4q^3+2q^2+q
        63: 3q^4+5q^3+3q^2+q
        65: 4q^4+6q^3+3q^2+q
        67: 3q^4+5q^3+3q^2+q
        68: 3q^4+5q^3+3q^2+q
        69: q^4+3q^3+2q^2+q
        70: 3q^4+5q^3+3q^2+q
        71: q^4+4q^3+3q^2+q
        72: 4q^3+3q^2+q
        73: 3q^3+3q^2+q
        75: q^4+5q^3+3q^2+q
        77: 2q^4+5q^3+3q^2+q
        79: q^4+5q^3+3q^2+q
        80: 3q^4+5q^3+3q^2+q
        81: 3q^4+5q^3+3q^2+q
        82: q^4+4q^3+3q^2+q
        83: q^4+5q^3+3q^2+q
        84: 5q^4+6q^3+3q^2+q
        85: 5q^4+6q^3+3q^2+q
        86: 3q^4+5q^3+3q^2+q
        87: 4q^4+6q^3+3q^2+q
        88: q^4+4q^3+3q^2+q
        89: q^4+4q^3+3q^2+q
        90: q^5+2q^4+3q^3+2q^2+q
        91: 2q^4+5q^3+3q^2+q
        92: 2q^4+5q^3+3q^2+q
        93: 2q^4+4q^3+2q^2+q
        94: 3q^3+3q^2+q
        95: 3q^3+3q^2+q
        96: 3q^3+2q^2+q
        97: 2q^4+5q^3+3q^2+q
        98: 2q^4+5q^3+3q^2+q
        99: 2q^4+4q^3+2q^2+q
       100: q^4+5q^3+3q^2+q
       101: 2q^4+5q^3+3q^2+q
       102: q^4+5q^3+3q^2+q
       104: q^3+q^2
       105: 2q^4+3q^3+2q^2+q
       107: q^2
       108: 3q^3+2q^2+q
       109: 2q^3+2q^2+q
       110: q^2
       112: 3q^3+3q^2+q
       114: q^4+4q^3+3q^2+q
       116: q^4+5q^3+3q^2+q
       117: 2q^4+3q^3+2q^2+q
       118: q^3+q^2
       119: q^4+q^3+q^2
       120: 2q^4+4q^3+2q^2+q
       122: 3q^4+5q^3+3q^2+q
       124: 3q^4+5q^3+3q^2+q
       125: q^4+4q^3+3q^2+q
       126: 2q^3+2q^2+q
       128: 3q^3+3q^2+q
       130: 3q^3+3q^2+q
       132: 3q^3+2q^2+q
       133: q^4+4q^3+3q^2+q
       134: q^4+3q^3+2q^2+q
       135: 4q^3+3q^2+q
       136: 3q^3+3q^2+q
       137: q^4+3q^3+3q^2+q
       138: 2q^3+2q^2+q
       139: 2q^3+3q^2+q
       140: 2q^2+q
       141: q^4+4q^3+3q^2+q
       142: 2q^3+3q^2+q
       143: q^4+4q^3+3q^2+q
       144: q^4+3q^3+2q^2+q
       145: q^4+4q^3+3q^2+q
       146: 3q^4+5q^3+3q^2+q
       147: 4q^3+3q^2+q
       148: 3q^3+3q^2+q
       149: q^4+4q^3+3q^2+q
       150: q^4+5q^3+3q^2+q
       152: q^4+5q^3+3q^2+q
       154: 2q^4+5q^3+3q^2+q
       156: q^4+5q^3+3q^2+q
       157: 2q^3+3q^2+q
       158: 2q^3+3q^2+q
       159: q^4+2q^3+2q^2+q
       160: 3q^3+3q^2+q
       161: 3q^3+3q^2+q
       162: 3q^3+2q^2+q
       163: 2q^4+5q^3+3q^2+q
       164: 2q^4+5q^3+3q^2+q
       165: 2q^4+4q^3+2q^2+q
       166: 3q^3+3q^2+q
       167: 3q^3+3q^2+q
       168: 3q^3+2q^2+q
       170: q^2
       171: 2q^3+2q^2+q
       174: q^3+q^2
       175: 2q^4+3q^3+2q^2+q
       178: 2q^3+2q^2+q
       180: 2q^3+3q^2+q
       182: 2q^3+3q^2+q
       183: q^2
       184: 3q^3+2q^2+q
       185: 2q^3+2q^2+q
       186: q^2
       188: 3q^3+3q^2+q
       190: q^4+4q^3+3q^2+q
       191: q^4+2q^3+2q^2+q
       192: q^3+q^2
       194: 2q^2+q
       195: q^3+2q^2+q
       196: q^2
       198: 2q^2+q
       199: q^3+q^2
       200: q^4+3q^3+2q^2+q
       201: q^2
       202: 3q^3+2q^2+q
       203: 2q^3+2q^2+q
       204: q^2
       206: 3q^3+3q^2+q
       208: q^4+3q^3+3q^2+q
       210: q^4+4q^3+3q^2+q
       212: q^4+5q^3+3q^2+q
       214: 3q^3+3q^2+q
       216: 3q^3+3q^2+q
       218: 3q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: 2q^3+3q^2+q
       221: q^3+2q^2+q
       222: q^3+3q^2+q
       223: 2q^3+2q^2+q
       224: q^3+3q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: 2q^3+3q^2+q
       228: 2q^3+2q^2+q
       229: 2q^2+q
       230: 2q^3+3q^2+q
       231: 2q^3+2q^2+q
       232: q^4+4q^3+3q^2+q
       233: q^4+3q^3+2q^2+q
       234: 4q^3+3q^2+q
       235: 3q^3+3q^2+q
       236: 2q^3+2q^2+q
       238: 3q^3+3q^2+q
       240: 3q^3+3q^2+q
       242: 3q^3+2q^2+q
       243: 2q^3+3q^2+q
       244: 2q^2+q
       245: 2q^3+3q^2+q
       246: q^4+4q^3+3q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: 2q^2+q
       251: 2q^2+q
       252: q^3+q^2+q
       253: 2q^3+3q^2+q
       254: 2q^3+3q^2+q
       255: q^4+2q^3+2q^2+q
       256: 3q^3+3q^2+q
       257: 3q^3+3q^2+q
       258: 3q^3+2q^2+q
       260: q^2
       261: q^3+2q^2+q
       264: q^2
       265: 2q^3+2q^2+q
       270: 2q^2+q
       272: 2q^3+2q^2+q
       274: q^2
       276: q^3+q^2
       277: q^4+2q^3+2q^2+q
       280: 2q^3+3q^2+q
       282: 2q^3+2q^2+q
       284: q^3+q^2+q
       285: q^2+q
       288: q^3+2q^2+q
       290: 2q^3+3q^2+q
       292: q^3+2q^2+q
       293: q^2
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       296: q^2
       298: q^3+3q^2+q
       300: 2q^2+q
       302: 2q^2+q
       303: q^3+2q^2+q
       304: q^2
       306: 2q^2+q
       307: q^2
       308: 3q^3+2q^2+q
       309: 2q^3+2q^2+q
       310: q^2
       312: 2q^3+3q^2+q
       314: 3q^3+3q^2+q
       316: 2q^3+2q^2+q
       318: 2q^3+3q^2+q
       320: 2q^2+q
       321: q^3+2q^2+q
       322: q^2
       324: 2q^2+q
       326: q^4+4q^3+3q^2+q
       328: 2q^2+q
       330: 2q^2+q
       332: q^3+q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^3+2q^2+q
       345: 2q^2+q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: 2q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: 2q^3+3q^2+q
       354: q^3+2q^2+q
       355: q^3+3q^2+q
       356: 2q^3+2q^2+q
       357: q^3+3q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       361: 3q^3+3q^2+q
       363: 3q^3+3q^2+q
       365: 3q^3+2q^2+q
       366: q^3+2q^2+q
       367: 2q^3+3q^2+q
       368: 2q^3+2q^2+q
       369: 2q^2+q
       370: 2q^3+3q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: 2q^2+q
       375: 2q^2+q
       376: q^3+q^2+q
       379: q^2+q
       382: q^2
       383: q^3+2q^2+q
       386: q^2
       387: q^3+2q^2+q
       392: 2q^2+q
       395: 2q^2+q
       398: q^3+2q^2+q
       400: q^2
       402: 2q^3+2q^2+q
       403: q^2
       408: 2q^2+q
       410: 2q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: 2q^2+q
       418: q^3+2q^2+q
       420: q^2+q
       421: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       430: q^2+q
       431: q^2+q
       434: q^2+q
       436: 2q^2+q
       438: q^2+q
       439: q^2+q
       440: q^2
       442: q^2+q
       444: q^2+q
       446: q^2+q
       448: q^3+q^2+q
       449: q^2+q
       452: q^3+2q^2+q
       453: q^2
       454: q^3+2q^2+q
       456: 2q^3+3q^2+q
       457: q^3+2q^2+q
       458: q^2
       460: q^3+3q^2+q
       461: q^2+q
       462: q^2
       464: 2q^2+q
       466: 2q^3+3q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       472: 2q^2+q
       473: q^3+2q^2+q
       474: q^2
       476: 2q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       503: 2q^2+q
       505: 2q^2+q
       507: q^3+q^2+q
       508: q^3+2q^2+q
       509: 2q^2+q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: 2q^2+q
       514: q^3+2q^2+q
       523: q^2+q
       526: q^2
       527: q^2+q
       531: q^2+q
       535: q^2+q
       540: 2q^2+q
       544: q^2+q
       548: q^2+q
       550: q^2+q
       554: q^3+2q^2+q
       556: q^2
       558: q^3+2q^2+q
       560: q^2
       562: q^2+q
       564: q^2
       567: 2q^2+q
       572: 2q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       604: q
       606: q^2+q
       607: q
       610: q
       612: q^2+q
       614: q
       616: q^2+q
       618: q^2+q
       620: q^2+q
       621: q^2+q
       624: q^3+2q^2+q
       626: 2q^2+q
       628: 2q^2+q
       630: q^2+q
       631: q^2+q
       632: q^2
       634: 2q^2+q
       636: 2q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       648: q^2+q
       649: q^2+q
       650: q^2
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       665: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       700: q^2+q
       707: q
       711: q^2+q
       714: q
       719: q
       724: q^2+q
       728: q
       732: q^2+q
       736: q^2+q
       738: q^2+q
       742: q^2+q
       746: q^2+q
       748: q^2
       750: q^2+q
       752: q^2
       755: q^2+q
       760: 2q^2+q
       764: q^2+q
       767: q^2+q
       773: q^2+q
       778: q^2+q
       782: q^2+q
       786: q
       787: q
       792: q
       798: q
       800: q
       802: q
       806: q
       807: q
       810: q
       812: q
       822: 2q^2+q
       824: q^2+q
       826: q^2+q
       827: q
       830: q
       831: q^2+q
       834: q^2+q
       836: q^2+q
       842: q^2+q
       846: q
       847: q
       850: q^2+q
       852: q
       854: q^2+q
       856: q
       871: q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       891: q^2+q
       898: q
       901: q
       907: q
       910: q
       915: q
       923: q
       931: q
       937: q
       945: q^2+q
       949: q
       954: q
       963: q^2+q
       977: q
       981: q^2+q
      1011: q
      1019: q
      1023: q
      1027: q
      1035: q^2+q
      1039: q^2+q
      1041: q
      1044: q
      1049: q
      1051: q
      1053: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q
      1083: q
      1129: q
      1151: q
      1159: q
      1169: q
      1173: q
      1179: q
      1182: q
      1187: q
      1201: q
      1209: q
      1223: 1
      1265: q
      1267: q
      1269: q
      1279: q
      1325: 1
      1339: 1
      1395: q
      1417: q
      1425: q
      1447: 1
      1481: 1
      1500: 1
      1558: 1
      1562: 1
      1594: 1
      1636: 1
      1672: 1
      1686: 1
      1710: 1
      1780: 1
      1806: 1
      1869: 1

1870:    0: 7q^2+2q+1
         1: 7q^2+2q+1
         2: 3q^3+4q^2+2q+1
         3: 7q^2+2q+1
         4: 2q^3+5q^2+2q+1
         5: 7q^2+2q+1
         6: 2q^3+5q^2+2q+1
         7: q^4+3q^3+3q^2+2q+1
         8: 3q^3+4q^2+2q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 7q^2+2q+1
        11: 7q^2+2q+1
        12: 2q^3+5q^2+2q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 7q^2+2q+1
        17: 7q^2+2q+1
        18: q^4+3q^3+3q^2+2q+1
        19: 5q^2+2q+1
        20: 5q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 7q^2+2q+1
        23: 7q^2+2q+1
        24: 3q^3+4q^2+2q+1
        25: 7q^2+2q+1
        26: 7q^2+2q+1
        27: 3q^3+4q^2+2q+1
        28: 7q^2+2q+1
        29: 5q^2+2q+1
        30: 3q^2+2q+1
        31: 7q^2+2q+1
        32: 4q^2+2q+1
        33: 7q^2+2q+1
        34: 7q^2+2q+1
        35: 4q^2+2q+1
        36: 7q^2+2q+1
        37: 5q^2+2q+1
        38: 2q^2
        39: 5q^2+2q+1
        40: 2q^2
        41: 2q^3+3q^2+2q+1
        42: q^3+q^2
        43: 4q^2+2q+1
        44: q^3+3q^2+2q+1
        45: 4q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 5q^2+2q+1
        50: 5q^2+2q+1
        51: 2q^3+3q^2+2q+1
        52: 5q^2+2q+1
        53: 5q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: 5q^2+2q+1
        56: 5q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: 4q^2+2q+1
        59: 3q^2
        60: 4q^2+2q+1
        61: 3q^2
        62: 5q^2+2q+1
        63: 2q^2
        64: 3q^2+2q+1
        65: q^2
        66: 5q^2+2q+1
        67: 2q^2
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^2+2q+1
        71: 5q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        74: 3q^2+2q+1
        76: 3q^2+2q+1
        78: q^3+2q^2+2q+1
        80: 4q^2+2q+1
        81: 4q^2+2q+1
        82: 5q^2+2q+1
        83: 3q^2+2q+1
        84: 4q^2+2q+1
        85: 4q^2+2q+1
        86: 5q^2+2q+1
        87: 3q^2+2q+1
        88: 4q^2+2q+1
        89: 4q^2+2q+1
        90: q^3+3q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 5q^2+2q+1
        95: 5q^2+2q+1
        96: 2q^3+3q^2+2q+1
        97: 5q^2+2q+1
        98: 5q^2+2q+1
        99: 2q^3+3q^2+2q+1
       100: 5q^2+2q+1
       101: 5q^2+2q+1
       102: 2q^3+3q^2+2q+1
       103: 3q^2+2q+1
       104: q^2
       105: q^2
       106: 2q^2
       107: 2q^2+2q+1
       108: q^2
       109: 2q^2+2q+1
       110: q^2
       111: q^2+2q+1
       113: 3q^2+2q+1
       115: 2q^2+2q+1
       117: q^2+2q+1
       119: q^2+2q+1
       121: 3q^2+2q+1
       122: q^2
       123: 3q^2+2q+1
       124: q^2
       125: q^2+2q+1
       126: 3q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 4q^2+2q+1
       138: 3q^2+2q+1
       139: 5q^2+2q+1
       140: 3q^2+2q+1
       141: 3q^2+2q+1
       142: 3q^2+2q+1
       143: 4q^2+2q+1
       144: 3q^2+2q+1
       145: 5q^2+2q+1
       146: 3q^2+2q+1
       147: 3q^2+2q+1
       148: 3q^2+2q+1
       149: 5q^2+2q+1
       150: 3q^2+2q+1
       151: 3q^2+2q+1
       153: 3q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 5q^2+2q+1
       167: 5q^2+2q+1
       168: 2q^3+3q^2+2q+1
       169: q^2+2q+1
       173: q^2+2q+1
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       183: 2q+1
       185: 2q+1
       187: 2q+1
       189: 2q^2+2q+1
       191: q^2+2q+1
       193: 2q^2+2q+1
       194: q^2
       195: 2q^2+2q+1
       196: q^2
       197: q^2+2q+1
       199: q^2+2q+1
       201: 2q^2+2q+1
       202: q^2
       203: 2q^2+2q+1
       204: q^2
       205: q^2+2q+1
       207: 3q^2+2q+1
       208: q^2
       209: 3q^2+2q+1
       211: 2q^2+2q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 3q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: 5q^2+2q+1
       244: 3q^2+2q+1
       245: 3q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q^2+2q+1
       263: 2q+1
       267: q^2+2q+1
       271: q^2+2q+1
       275: q^2+2q+1
       279: q+1
       281: q^2+q+1
       283: 2q+1
       285: 2q+1
       287: 2q^2+2q+1
       289: q+1
       291: 2q+1
       293: 2q+1
       295: 2q+1
       297: 2q+1
       299: 2q+1
       301: q^2+2q+1
       303: 2q+1
       305: 2q+1
       307: 2q+1
       309: 2q+1
       311: q^2+2q+1
       313: 2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: 2q^2+2q+1
       320: q^2
       321: 2q^2+2q+1
       322: q^2
       323: q^2+2q+1
       325: 2q^2+2q+1
       327: q^2+q+1
       329: q^2+q+1
       331: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: 3q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: 2q+1
       381: q+1
       385: 2q+1
       389: q^2+2q+1
       393: 2q+1
       397: q^2+2q+1
       401: 2q+1
       405: q^2+2q+1
       409: q+1
       411: q^2+q+1
       413: q+1
       415: q+1
       417: q+1
       419: 2q+1
       421: 2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       429: 2q+1
       431: 2q+1
       433: 2q+1
       435: q+1
       437: 2q+1
       439: 2q+1
       441: 2q+1
       443: q^2+3q+1
       444: q
       445: q^2+4q+1
       447: 2q+1
       449: 2q+1
       451: 2q+1
       453: 2q+1
       455: q+1
       457: 2q+1
       459: 2q+1
       461: q^2+3q+1
       462: q
       463: q^2+4q+1
       465: q+1
       467: q^2+q+1
       469: 2q^2+2q+1
       471: 2q+1
       473: 2q+1
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       502: q^2+q+1
       504: q^2+q+1
       506: q^2+q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q+1
       525: q+1
       529: 2q+1
       533: 2q+1
       537: q+1
       541: 2q+1
       545: q^2+3q+1
       547: q
       549: 2q+1
       553: q+1
       557: 2q+1
       561: q^2+3q+1
       563: q
       565: 2q+1
       569: q^2+2q+1
       573: q^2+2q+1
       574: q
       576: q
       577: q^2+2q+1
       580: 2q
       583: q+1
       585: 1
       587: q+1
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: q+1
       599: 2q+1
       601: q+1
       603: 2q+1
       605: q+1
       607: 2q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       615: q+1
       617: 2q+1
       619: 2q+1
       621: 2q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       631: q+1
       633: 2q+1
       635: q+1
       637: q^2+q+1
       639: q+1
       641: 2q+1
       643: 2q+1
       645: 2q+1
       647: 2q+1
       649: 2q+1
       651: q+1
       653: 2q+1
       655: q+1
       656: q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       696: q
       698: q
       705: q+1
       709: 1
       713: q+1
       717: q+1
       721: q+1
       725: 2q+1
       729: q+1
       733: q+1
       737: q+1
       741: 2q+1
       745: q+1
       749: q+1
       753: 2q+1
       757: q+1
       761: 2q+1
       765: q+1
       769: q+1
       772: q
       775: q+1
       777: 1
       779: q+1
       781: 1
       783: q+1
       785: 1
       787: 1
       789: q+1
       791: 1
       793: q+1
       795: 2q+1
       797: 1
       799: q+1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: q+1
       811: 2q+1
       813: 2q+1
       815: q+1
       817: q+1
       819: 2q+1
       821: 1
       823: q+1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: q+1
       835: 2q+1
       837: 2q+1
       839: q+1
       841: q+1
       843: q+1
       844: q
       845: 2q+1
       847: 2q+1
       849: q+1
       851: 2q+1
       853: q+1
       855: 2q+1
       857: q+1
       858: q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: q+1
       916: q+1
       920: 1
       924: q+1
       928: q+1
       932: q+1
       936: q+1
       940: q+1
       944: 1
       948: q+1
       952: q+1
       956: q+1
       960: q+1
       964: q+1
       968: q+1
       971: q
       974: 2q+1
       978: q+1
       982: q+1
       985: q
       988: q+1
       992: q+1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1016: q+1
      1018: 1
      1020: q+1
      1022: 1
      1024: q+1
      1026: 1
      1028: 1
      1030: 2q+1
      1032: q+1
      1034: 1
      1036: q+1
      1038: 1
      1040: 1
      1042: q+1
      1044: 1
      1046: q+1
      1047: q
      1048: 1
      1050: q+1
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: q+1
      1062: 2q+1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1086: q+1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: q+1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1164: q+1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: q+1
      1188: q+1
      1191: q
      1194: q+1
      1198: 1
      1202: q+1
      1206: q+1
      1214: 1
      1216: 1
      1218: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 1
      1258: 1
      1260: 1
      1264: 1
      1266: 1
      1268: 1
      1270: 1
      1272: q+1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1290: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1334: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1414: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1448: 1
      1450: 1
      1454: 1
      1456: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: q+1
      1476: 1
      1478: 1
      1480: 1
      1482: 1
      1487: 1
      1489: 1
      1501: 1
      1513: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1631: 1
      1661: 1
      1663: 1
      1665: 1
      1687: 1
      1699: 1
      1711: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1870: 1

1871:    0: 4q^4+22q^3+10q^2+3q
         1: 4q^4+22q^3+10q^2+3q
         2: 9q^4+15q^3+9q^2+3q
         3: 4q^4+22q^3+10q^2+3q
         4: q^5+10q^4+16q^3+9q^2+3q
         5: 4q^4+22q^3+10q^2+3q
         6: q^5+10q^4+16q^3+9q^2+3q
         7: 3q^5+10q^4+12q^3+8q^2+3q
         8: 9q^4+15q^3+9q^2+3q
         9: q^6+4q^5+8q^4+9q^3+6q^2+2q
        10: 4q^4+22q^3+10q^2+3q
        11: 4q^4+22q^3+10q^2+3q
        12: q^5+10q^4+16q^3+9q^2+3q
        13: q^4+14q^3+9q^2+3q
        14: 5q^4+11q^3+8q^2+3q
        15: q^4+14q^3+9q^2+3q
        16: 18q^3+9q^2+3q
        17: 18q^3+9q^2+3q
        18: 2q^5+6q^4+8q^3+6q^2+2q
        19: 3q^4+15q^3+9q^2+3q
        20: 3q^4+15q^3+9q^2+3q
        21: 6q^4+11q^3+8q^2+3q
        22: 4q^4+22q^3+10q^2+3q
        23: 4q^4+22q^3+10q^2+3q
        24: 9q^4+15q^3+9q^2+3q
        25: 4q^4+22q^3+10q^2+3q
        26: 4q^4+22q^3+10q^2+3q
        27: 9q^4+15q^3+9q^2+3q
        28: 18q^3+9q^2+3q
        29: 3q^4+15q^3+9q^2+3q
        30: q^4+10q^3+8q^2+3q
        31: 4q^4+22q^3+10q^2+3q
        32: q^4+14q^3+9q^2+3q
        33: 18q^3+9q^2+3q
        34: 4q^4+22q^3+10q^2+3q
        35: q^4+14q^3+9q^2+3q
        36: 18q^3+9q^2+3q
        37: q^4+10q^3+3q^2+q
        38: 3q^4+12q^3+7q^2+2q
        39: q^4+10q^3+3q^2+q
        40: 3q^4+12q^3+7q^2+2q
        41: 4q^4+6q^3+3q^2+q
        42: 5q^4+9q^3+6q^2+2q
        43: q^4+14q^3+9q^2+3q
        44: 5q^4+11q^3+8q^2+3q
        45: q^4+14q^3+9q^2+3q
        46: 10q^3+8q^2+3q
        47: 10q^3+8q^2+3q
        48: 3q^4+7q^3+6q^2+2q
        49: 11q^3+8q^2+3q
        50: 11q^3+8q^2+3q
        51: 3q^4+7q^3+6q^2+2q
        52: 3q^4+15q^3+9q^2+3q
        53: 3q^4+15q^3+9q^2+3q
        54: 6q^4+11q^3+8q^2+3q
        55: 3q^4+15q^3+9q^2+3q
        56: 3q^4+15q^3+9q^2+3q
        57: 6q^4+11q^3+8q^2+3q
        58: 10q^3+6q^2+2q
        59: 8q^3+3q^2+q
        60: 10q^3+6q^2+2q
        61: 8q^3+3q^2+q
        62: q^4+10q^3+3q^2+q
        63: 3q^4+12q^3+7q^2+2q
        64: 6q^3+3q^2+q
        65: q^4+8q^3+6q^2+2q
        66: 8q^3+3q^2+q
        67: 10q^3+6q^2+2q
        68: 3q^3+7q^2+3q
        69: 4q^3+5q^2+2q
        70: q^4+10q^3+8q^2+3q
        71: 11q^3+8q^2+3q
        72: 6q^3+7q^2+3q
        73: 6q^3+7q^2+3q
        74: 3q^3+2q^2+q
        75: 2q^4+5q^3+6q^2+2q
        76: 3q^3+2q^2+q
        77: 2q^4+5q^3+6q^2+2q
        78: q^4+2q^3+2q^2+q
        79: 2q^4+5q^3+5q^2+2q
        80: q^4+14q^3+9q^2+3q
        81: 10q^3+8q^2+3q
        82: 3q^4+15q^3+9q^2+3q
        83: q^4+10q^3+8q^2+3q
        84: q^4+14q^3+9q^2+3q
        85: 10q^3+8q^2+3q
        86: 3q^4+15q^3+9q^2+3q
        87: q^4+10q^3+8q^2+3q
        88: 10q^3+8q^2+3q
        89: 10q^3+8q^2+3q
        90: 3q^4+7q^3+6q^2+2q
        91: 4q^3+7q^2+3q
        92: 4q^3+7q^2+3q
        93: 4q^3+6q^2+2q
        94: 11q^3+8q^2+3q
        95: 11q^3+8q^2+3q
        96: 3q^4+7q^3+6q^2+2q
        97: 11q^3+8q^2+3q
        98: 11q^3+8q^2+3q
        99: 3q^4+7q^3+6q^2+2q
       100: 3q^4+15q^3+9q^2+3q
       101: 3q^4+15q^3+9q^2+3q
       102: 6q^4+11q^3+8q^2+3q
       103: 5q^3+3q^2+q
       104: 5q^3+3q^2+q
       105: 5q^3+3q^2+q
       106: 3q^3
       107: 4q^3+5q^2+2q
       108: 2q^3+2q^2+q
       109: 4q^3+5q^2+2q
       110: 2q^3+2q^2+q
       111: q^3+2q^2+q
       112: 4q^2+2q
       113: 3q^3+2q^2+q
       114: 2q^4+5q^3+6q^2+2q
       115: 2q^3+2q^2+q
       116: q^4+4q^3+5q^2+2q
       117: 2q^3+5q^2+2q
       118: q^3+2q^2+q
       119: 2q^3+5q^2+2q
       120: q^3+2q^2+q
       121: 6q^3+3q^2+q
       122: q^4+8q^3+6q^2+2q
       123: 4q^3+3q^2+q
       124: 6q^3+5q^2+2q
       125: 3q^3+7q^2+3q
       126: 4q^3+5q^2+2q
       128: 3q^3+3q^2+2q
       130: 3q^3+3q^2+2q
       132: 2q^3+3q^2+q
       133: 6q^2+3q
       134: 2q^3+5q^2+2q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 10q^3+8q^2+3q
       138: 4q^3+5q^2+2q
       139: 11q^3+8q^2+3q
       140: 6q^3+7q^2+3q
       141: q^4+10q^3+8q^2+3q
       142: 6q^3+7q^2+3q
       143: 10q^3+8q^2+3q
       144: 4q^3+5q^2+2q
       145: 11q^3+8q^2+3q
       146: q^4+10q^3+8q^2+3q
       147: 6q^3+7q^2+3q
       148: 6q^3+7q^2+3q
       149: 3q^4+15q^3+9q^2+3q
       150: q^4+10q^3+8q^2+3q
       151: 3q^3+2q^2+q
       152: 2q^4+5q^3+6q^2+2q
       153: 3q^3+2q^2+q
       154: 2q^4+5q^3+6q^2+2q
       155: q^4+2q^3+2q^2+q
       156: 2q^4+5q^3+5q^2+2q
       157: 4q^3+7q^2+3q
       158: 4q^3+7q^2+3q
       159: 4q^3+6q^2+2q
       160: 4q^3+7q^2+3q
       161: 4q^3+7q^2+3q
       162: 4q^3+6q^2+2q
       163: 4q^3+7q^2+3q
       164: 4q^3+7q^2+3q
       165: 4q^3+6q^2+2q
       166: 11q^3+8q^2+3q
       167: 11q^3+8q^2+3q
       168: 3q^4+7q^3+6q^2+2q
       169: q^3+2q^2+q
       170: 2q^2+q
       171: 2q^2+q
       173: q^3+3q^2+q
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       178: q^3+2q^2+q
       180: 3q^3+3q^2+2q
       182: 2q^2+2q
       183: 4q^2+2q
       184: q^2+q
       185: 4q^2+2q
       186: q^2+q
       187: 2q^2+q
       188: 3q^2+2q
       189: 2q^3+2q^2+q
       190: q^4+4q^3+5q^2+2q
       191: 2q^3+5q^2+2q
       192: q^3+2q^2+q
       193: 4q^3+5q^2+2q
       194: 2q^3+2q^2+q
       195: 4q^3+5q^2+2q
       196: 2q^3+2q^2+q
       197: q^3+2q^2+q
       198: 4q^2+2q
       199: 2q^3+5q^2+2q
       200: q^3+2q^2+q
       201: 4q^3+5q^2+2q
       202: 2q^3+2q^2+q
       203: 4q^3+5q^2+2q
       204: 2q^3+2q^2+q
       205: q^3+2q^2+q
       206: 4q^2+2q
       207: 4q^3+3q^2+q
       208: 6q^3+5q^2+2q
       209: 3q^3+2q^2+q
       210: 2q^4+5q^3+6q^2+2q
       211: 2q^3+2q^2+q
       212: q^4+4q^3+5q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 4q^2+2q
       220: 6q^2+3q
       221: 2q^3+5q^2+2q
       222: 2q^3+6q^2+3q
       223: q^3+4q^2+2q
       224: 2q^3+6q^2+3q
       225: q^3+4q^2+2q
       226: 4q^3+5q^2+2q
       227: 6q^2+3q
       228: 2q^3+5q^2+2q
       229: 2q^3+6q^2+3q
       230: 2q^3+6q^2+3q
       231: 4q^3+5q^2+2q
       232: 6q^2+3q
       233: 2q^3+5q^2+2q
       234: 2q^3+6q^2+3q
       235: 2q^3+6q^2+3q
       236: 4q^3+5q^2+2q
       238: 3q^3+3q^2+2q
       240: 3q^3+3q^2+2q
       242: 2q^3+3q^2+q
       243: 11q^3+8q^2+3q
       244: 6q^3+7q^2+3q
       245: 6q^3+7q^2+3q
       246: q^4+10q^3+8q^2+3q
       247: q^3+9q^2+4q
       248: q^3+9q^2+4q
       249: q^4+4q^3+5q^2+2q
       250: 4q^3+7q^2+3q
       251: 4q^3+7q^2+3q
       252: 4q^3+6q^2+2q
       253: 4q^3+7q^2+3q
       254: 4q^3+7q^2+3q
       255: 4q^3+6q^2+2q
       256: 4q^3+7q^2+3q
       257: 4q^3+7q^2+3q
       258: 4q^3+6q^2+2q
       260: q^2+q
       261: q^2+q
       263: 2q^2+q
       264: q^2+q
       265: q^2+q
       267: q^3+2q^2+q
       268: 2q^2+q
       270: 2q^2+q
       271: q^3+2q^2+q
       272: 2q^2+q
       274: 2q^2+q
       275: q^3+3q^2+q
       276: q^3+2q^2+q
       277: q^3+2q^2+q
       280: q^2+2q
       282: q^2+q
       283: 2q^2+q
       285: 2q^2+q
       288: q^3+2q^2+q
       290: 2q
       292: q^2+q
       293: 4q^2+2q
       294: q^2+q
       295: 4q^2+2q
       296: q^2+q
       297: 2q^2+q
       298: 3q^2+2q
       299: 4q^2+2q
       300: q^2+q
       302: 2q^2+2q
       303: 4q^2+2q
       304: q^2+q
       305: 2q^2+q
       306: 3q^2+2q
       307: 4q^2+2q
       308: q^2+q
       309: 4q^2+2q
       310: q^2+q
       312: 2q^2+2q
       313: 2q^2+q
       314: 3q^2+2q
       316: q^3+2q^2+q
       318: 3q^3+3q^2+2q
       319: 4q^3+5q^2+2q
       320: 2q^3+2q^2+q
       321: 4q^3+5q^2+2q
       322: 2q^3+2q^2+q
       323: q^3+2q^2+q
       324: 4q^2+2q
       325: 2q^3+2q^2+q
       326: q^4+4q^3+5q^2+2q
       328: q^3+q^2+2q
       330: q^3+q^2+2q
       332: 2q^2+q
       333: 4q^2+2q
       334: q^3+4q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: q^3+9q^2+4q
       339: 5q^2+3q
       341: 5q^2+3q
       343: 2q^3+3q^2+q
       344: 4q^2+2q
       345: 6q^2+3q
       346: 2q^3+5q^2+2q
       347: 2q^3+6q^2+3q
       348: q^3+4q^2+2q
       349: 2q^3+6q^2+3q
       350: q^3+4q^2+2q
       351: q^3+9q^2+4q
       352: 4q^2+2q
       353: 6q^2+3q
       354: 2q^3+5q^2+2q
       355: 2q^3+6q^2+3q
       356: q^3+4q^2+2q
       357: 2q^3+6q^2+3q
       358: q^3+4q^2+2q
       359: q^3+9q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 4q^3+5q^2+2q
       367: 6q^2+3q
       368: 2q^3+5q^2+2q
       369: 2q^3+6q^2+3q
       370: 2q^3+6q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 4q^3+7q^2+3q
       375: 4q^3+7q^2+3q
       376: 4q^3+6q^2+2q
       382: q
       383: q
       385: 2q^2+q
       386: q^2+q
       387: q^2+q
       390: q^2+q
       392: q^2+q
       393: 2q^2+q
       394: q^2+q
       395: q^2+q
       398: q^2+q
       400: q^2+q
       401: 2q^2+q
       402: q^2+q
       403: q^2+q
       405: q^3+2q^2+q
       407: 2q^2+q
       408: 2q^2+q
       410: q^2+2q
       412: q^2+q
       414: q^2+q
       416: 2q
       418: q
       419: 2q^2+q
       421: 2q^2+q
       424: q^2+q
       426: q^2+q
       428: 5q^2+3q
       429: 2q^2+q
       431: 2q^2+q
       434: q^2+q
       436: 2q
       437: 4q^2+2q
       438: q^2+q
       439: 4q^2+2q
       440: q^2+q
       441: 2q^2+q
       442: 3q^2+2q
       443: q^3+6q^2+3q
       444: 3q^2+q
       446: 5q^2+3q
       447: 2q^2+q
       449: 2q^2+q
       452: q^2+q
       453: 4q^2+2q
       454: q^2+q
       456: 2q
       457: 4q^2+2q
       458: q^2+q
       459: 2q^2+q
       460: 3q^2+2q
       461: q^3+6q^2+3q
       462: 3q^2+q
       464: 5q^2+3q
       466: q^2+2q
       468: q^2+q
       470: q^3+2q^2+q
       471: 4q^2+2q
       472: q^2+q
       473: 4q^2+2q
       474: q^2+q
       475: 2q^2+q
       476: 3q^2+2q
       478: 2q^2+2q
       479: q^3+5q^2+2q
       480: 4q^2+2q
       481: 2q^2+2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: q^2+2q
       492: 4q^2+2q
       493: q^3+4q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 3q^2+4q
       497: 4q^2+2q
       498: q^3+4q^2+2q
       499: q^3+4q^2+2q
       500: 3q^2+2q
       501: 3q^2+4q
       503: q^3+q^2+2q
       505: q^3+q^2+2q
       507: 2q^2+q
       508: 4q^2+2q
       509: 6q^2+3q
       510: 2q^3+5q^2+2q
       511: 2q^3+6q^2+3q
       512: q^3+4q^2+2q
       513: 2q^3+6q^2+3q
       514: q^3+4q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 3q^2+4q
       519: 3q^2+4q
       520: q^3+3q^2+2q
       526: q
       527: q
       538: q
       540: q
       541: 2q^2+q
       542: q^2+q
       544: q^2+q
       546: 3q^2+2q
       548: 2q^2+q
       554: q
       556: q
       557: 2q^2+q
       558: q^2+q
       560: q^2+q
       562: 3q^2+2q
       564: 2q^2+q
       565: 2q^2+q
       566: q^2+q
       567: q^2+q
       571: q^2+q
       572: q^2+q
       573: q^3+4q^2+2q
       574: 2q^2+q
       575: q^2
       576: 2q^2+q
       578: 3q^2+q
       581: 2q^2+2q
       584: q^2+q
       586: q
       588: q
       589: q^2+q
       591: q^2+q
       593: q^2+q
       595: q^2+q
       598: q
       600: q^2+q
       602: 3q
       603: 2q^2+q
       606: q
       607: 2q^2+q
       610: q^2+q
       612: 2q
       614: q^2+q
       615: q^2+3q
       616: q
       618: q^2+3q
       619: 2q^2+q
       621: 2q^2+q
       624: q
       626: q^2+q
       628: 2q
       630: q^2+q
       631: q^2+3q
       632: q
       634: q^2+3q
       636: q^2+2q
       638: q^2+q
       640: q^2+q
       641: 2q^2+q
       643: 2q^2+q
       646: q^2+q
       647: 4q^2+2q
       648: q^2+q
       649: 4q^2+2q
       650: q^2+q
       652: 2q
       653: 2q^2+q
       654: 3q^2+2q
       655: 2q^2+2q
       656: q^2+2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       667: q^2+3q
       669: q^2+3q
       671: 2q^2+q
       672: q^2+4q
       673: q^2+2q
       674: 2q+1
       675: 2q^2+2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 3q^2+4q
       679: q^2+2q
       680: 2q+1
       681: 2q^2+2q
       682: 2q^2+2q
       683: 3q^2+2q
       684: 3q^2+4q
       685: q^2+2q
       686: 4q^2+2q
       687: q^3+4q^2+2q
       688: q^3+4q^2+2q
       689: 3q^2+2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: 2q^2+q
       699: q^2+q
       700: q^2+q
       701: q^2
       730: q
       732: q
       734: 2q
       736: q
       746: q
       748: q
       750: 2q
       752: q
       759: q
       760: q
       761: 2q^2+q
       763: q^2+q
       764: q^2+q
       765: q^2+2q
       766: q
       767: q
       770: q^2+q
       773: 2q
       776: q+1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: 3q
       793: q+1
       796: 2q+1
       798: q
       800: q
       801: q^2+q
       803: q^2+q
       805: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       814: q^2+3q
       815: q^2+3q
       816: q
       817: q+1
       820: 2q+1
       822: q
       824: q
       825: q^2+q
       827: q^2+q
       829: q^2+q
       831: q^2+q
       834: q
       836: q^2+q
       838: q^2+3q
       839: q^2+3q
       840: q
       842: q^2+q
       843: q+1
       844: q
       845: 2q^2+q
       847: 2q^2+q
       850: q
       852: q^2+q
       854: 2q
       856: q^2+q
       857: 2q^2+2q
       858: q^2+2q
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 2q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q^2+2q
       878: 2q^2+2q
       879: 3q^2+2q
       880: q^2+2q
       885: q
       890: q
       891: q
       917: q+1
       933: 2q
       935: q
       941: q+1
       957: 2q
       959: q
       964: q+1
       969: q+1
       972: q
       980: q
       981: q
       983: q^2+q
       986: 2q
       988: q^2+2q
       989: q
       990: q
       993: q+1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 2q+1
      1016: q+1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: 2q+1
      1032: q+1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: q+1
      1047: q
      1049: q
      1051: q
      1052: q^2+q
      1054: q^2+q
      1056: q^2+q
      1058: q^2+q
      1061: q
      1063: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1087: q+1
      1099: q
      1104: q
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: q+1
      1165: q+1
      1189: q+1
      1192: q
      1194: q+1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1265: q
      1267: q
      1268: q
      1270: q
      1273: q
      1275: q+1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1291: 1
      1303: q+1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1349: 1
      1357: 1
      1364: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1449: 1
      1450: 1
      1454: 1
      1457: 1
      1460: 1
      1462: 1
      1465: 1
      1466: 1
      1468: 1
      1471: q
      1473: q+1
      1476: q
      1478: q
      1482: 1
      1487: 1
      1490: 1
      1502: 1
      1514: 1
      1564: 1
      1568: 1
      1575: 1
      1584: 1
      1588: 1
      1595: 1
      1608: 1
      1616: 1
      1623: 1
      1632: 1
      1662: 1
      1663: 1
      1665: 1
      1688: 1
      1700: 1
      1712: 1
      1786: 1
      1790: 1
      1797: 1
      1871: 1

1872:    0: q^5+q^4+2q^3+q
         1: q^5+q^4+2q^3+q
         2: 2q^4+q^3+q
         3: q^5+q^4+2q^3+q
         4: q^4+q^3+q
         5: q^5+q^4+2q^3+q
         6: q^4+q^3+q
         7: q^5+2q^4+q^3+q
         8: 2q^4+q^3+q
         9: q^5+2q^4+q^3+q
        10: q^5+q^4+2q^3+q
        11: q^5+q^4+2q^3+q
        12: q^4+q^3+q
        13: q^4+q^3+q
        14: q^4+q^3+q
        15: q^4+q^3+q
        16: q^5+q^4+2q^3+q
        17: q^5+q^4+2q^3+q
        18: q^5+2q^4+q^3+q
        19: q^3+q
        20: q^3+q
        21: q^4+q^3+q
        22: q^5+q^4+2q^3+q
        23: q^5+q^4+2q^3+q
        24: 2q^4+q^3+q
        25: q^5+q^4+2q^3+q
        26: q^5+q^4+2q^3+q
        27: 2q^4+q^3+q
        28: q^5+q^4+2q^3+q
        29: q^3+q
        30: q^3+q
        31: q^5+q^4+2q^3+q
        32: q^4+q^3+q
        33: q^5+q^4+2q^3+q
        34: q^5+q^4+2q^3+q
        35: q^4+q^3+q
        36: q^5+q^4+2q^3+q
        37: q^5+q^4+2q^3+q
        39: q^5+q^4+2q^3+q
        41: 2q^4+q^3+q
        43: q^4+q^3+q
        44: q^4+q^3+q
        45: q^4+q^3+q
        46: q^4+q^3+q
        47: q^4+q^3+q
        48: q^4+q^3+q
        49: q^3+q
        50: q^3+q
        51: q^4+q^3+q
        52: q^3+q
        53: q^3+q
        54: q^4+q^3+q
        55: q^3+q
        56: q^3+q
        57: q^4+q^3+q
        58: q^5+q^4+q^3+q
        59: q^3
        60: q^5+q^4+q^3+q
        61: q^3
        62: q^5+q^4+2q^3+q
        64: q^4+q^3+q
        66: q^5+q^4+2q^3+q
        68: q^4+q
        69: q^3+q
        70: q^3+q
        71: q^3+q
        72: q
        73: q
        74: q^3+q
        76: q^3+q
        78: q^4+q^3+q
        80: q^4+q^3+q
        81: q^4+q^3+q
        82: q^3+q
        83: q^3+q
        84: q^4+q^3+q
        85: q^4+q^3+q
        86: q^3+q
        87: q^3+q
        88: q^4+q^3+q
        89: q^4+q^3+q
        90: q^4+q^3+q
        91: q^3+q
        92: q
        93: q^3+q
        94: q^3+q
        95: q^3+q
        96: q^4+q^3+q
        97: q^3+q
        98: q^3+q
        99: q^4+q^3+q
       100: q^3+q
       101: q^3+q
       102: q^4+q^3+q
       103: q^5+q^4+q^3+q
       106: q^3
       107: q
       109: q
       111: q
       113: q^3+q
       115: q^3+q
       117: q^4+q
       119: q^4+q
       121: q^4+q^3+q
       123: q^4+q^3+q
       125: q^4+q
       126: q^3+q
       127: q^3+q
       129: q^3+q
       131: q^4+q^3+q
       133: q
       134: q^3+q
       135: q
       136: q
       137: q^4+q^3+q
       138: q^3+q
       139: q^3+q
       140: q
       141: q^3+q
       142: q
       143: q^4+q^3+q
       144: q^3+q
       145: q^3+q
       146: q^3+q
       147: q
       148: q
       149: q^3+q
       150: q^3+q
       151: q^3+q
       153: q^3+q
       155: q^4+q^3+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^3+q
       161: q
       162: q^3+q
       163: q^3+q
       164: q
       165: q^3+q
       166: q^3+q
       167: q^3+q
       168: q^4+q^3+q
       169: q
       173: q^4+q
       177: q^3+q
       179: q^3+q
       181: q
       183: q
       185: q
       187: q
       189: q^3+q
       191: q^4+q
       193: q
       195: q
       197: q
       199: q^4+q
       201: q
       203: q
       205: q
       207: q^4+q^3+q
       209: q^3+q
       211: q^3+q
       213: q^3+q
       215: q
       217: q^3+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q
       224: q
       225: q
       226: q^3+q
       227: q
       228: q^3+q
       229: q
       230: q
       231: q^3+q
       232: q
       233: q^3+q
       234: q
       235: q
       236: q^3+q
       237: q^3+q
       239: q^3+q
       241: q^4+q^3+q
       243: q^3+q
       244: q
       245: q
       246: q^3+q
       247: q
       248: q
       249: q^4+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^3+q
       257: q
       258: q^3+q
       259: q
       263: q
       267: q
       271: q
       275: q^4+q
       279: q
       281: q^3+q
       283: q
       285: q
       287: q^3+q
       289: q
       291: q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q^3+q
       317: q^3+q
       319: q
       321: q
       323: q
       325: q^3+q
       327: q^3+q
       329: q
       331: q^3+q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q^3+q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q^3+q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q
       367: q
       368: q^3+q
       369: q
       370: q
       374: q^3+q
       375: q
       376: q^3+q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q^3+q
       413: q
       415: q
       417: q
       419: q
       421: q
       423: q
       425: q
       427: q
       429: q
       431: q
       433: q
       435: q
       437: q
       439: q
       441: q
       443: q
       445: q
       447: q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       461: q
       463: q
       465: q
       467: q^3+q
       469: q^3+q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q
       497: q
       498: q
       499: q
       500: q
       502: q^3+q
       504: q
       506: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       521: q
       525: q
       529: q
       533: q
       537: q
       541: q
       545: q
       549: q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       583: q
       585: q
       587: q
       589: q
       591: q
       593: q
       595: q
       599: q
       603: q
       605: q
       607: q
       609: q
       611: q
       613: q
       619: q
       621: q
       623: q
       625: q
       627: q
       629: q
       635: q
       637: q^3+q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q
       693: q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q
       729: q
       737: q
       741: q
       745: q
       753: q
       757: q
       761: q
       777: q
       797: q
       799: q
       801: q
       803: q
       805: q
       807: q
       811: q
       821: q
       823: q
       825: q
       827: q
       829: q
       831: q
       835: q
       841: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       877: q
       878: q
       879: q
       896: q
       912: q
       920: q
       924: q
       928: q
       936: q
       944: q
       948: q
       952: q
       960: q
       974: q
       978: q
      1010: 1
      1018: q
      1034: q
      1048: q
      1050: q
      1052: q
      1054: q
      1056: q
      1058: q
      1062: q
      1126: 1
      1140: 1
      1148: q
      1168: q
      1184: q
      1198: q
      1202: q
      1206: q
      1222: 1
      1264: q
      1278: 1
      1292: 1
      1322: 1
      1336: 1
      1360: 1
      1392: 1
      1414: q
      1432: 1
      1480: 1
      1491: 1
      1503: 1
      1515: 1
      1571: 1
      1591: 1
      1619: 1
      1633: 1
      1689: 1
      1701: 1
      1713: 1
      1793: 1
      1872: 1

1873:    0: 4q^4+22q^3+10q^2+3q
         1: 4q^4+22q^3+10q^2+3q
         2: 9q^4+15q^3+9q^2+3q
         3: 4q^4+22q^3+10q^2+3q
         4: q^5+10q^4+16q^3+9q^2+3q
         5: 4q^4+22q^3+10q^2+3q
         6: q^5+10q^4+16q^3+9q^2+3q
         7: 3q^5+10q^4+12q^3+8q^2+3q
         8: 9q^4+15q^3+9q^2+3q
         9: q^6+4q^5+8q^4+9q^3+6q^2+2q
        10: 4q^4+22q^3+10q^2+3q
        11: 4q^4+22q^3+10q^2+3q
        12: q^5+10q^4+16q^3+9q^2+3q
        13: q^4+14q^3+9q^2+3q
        14: 5q^4+11q^3+8q^2+3q
        15: q^4+14q^3+9q^2+3q
        16: 18q^3+9q^2+3q
        17: 18q^3+9q^2+3q
        18: 2q^5+6q^4+8q^3+6q^2+2q
        19: 3q^4+15q^3+9q^2+3q
        20: 3q^4+15q^3+9q^2+3q
        21: 6q^4+11q^3+8q^2+3q
        22: 4q^4+22q^3+10q^2+3q
        23: 4q^4+22q^3+10q^2+3q
        24: 9q^4+15q^3+9q^2+3q
        25: 4q^4+22q^3+10q^2+3q
        26: 4q^4+22q^3+10q^2+3q
        27: 9q^4+15q^3+9q^2+3q
        28: 18q^3+9q^2+3q
        29: 3q^4+15q^3+9q^2+3q
        30: q^4+10q^3+8q^2+3q
        31: 4q^4+22q^3+10q^2+3q
        32: q^4+14q^3+9q^2+3q
        33: 18q^3+9q^2+3q
        34: 4q^4+22q^3+10q^2+3q
        35: q^4+14q^3+9q^2+3q
        36: 18q^3+9q^2+3q
        37: 3q^4+12q^3+7q^2+2q
        38: q^4+10q^3+3q^2+q
        39: 3q^4+12q^3+7q^2+2q
        40: q^4+10q^3+3q^2+q
        41: 5q^4+9q^3+6q^2+2q
        42: 4q^4+6q^3+3q^2+q
        43: q^4+14q^3+9q^2+3q
        44: 5q^4+11q^3+8q^2+3q
        45: q^4+14q^3+9q^2+3q
        46: 10q^3+8q^2+3q
        47: 10q^3+8q^2+3q
        48: 3q^4+7q^3+6q^2+2q
        49: 11q^3+8q^2+3q
        50: 11q^3+8q^2+3q
        51: 3q^4+7q^3+6q^2+2q
        52: 3q^4+15q^3+9q^2+3q
        53: 3q^4+15q^3+9q^2+3q
        54: 6q^4+11q^3+8q^2+3q
        55: 3q^4+15q^3+9q^2+3q
        56: 3q^4+15q^3+9q^2+3q
        57: 6q^4+11q^3+8q^2+3q
        58: 8q^3+3q^2+q
        59: 10q^3+6q^2+2q
        60: 10q^3+6q^2+2q
        61: 8q^3+3q^2+q
        62: 3q^4+12q^3+7q^2+2q
        63: q^4+10q^3+3q^2+q
        64: q^4+8q^3+6q^2+2q
        65: 6q^3+3q^2+q
        66: 10q^3+6q^2+2q
        67: 8q^3+3q^2+q
        68: 3q^3+7q^2+3q
        69: 4q^3+5q^2+2q
        70: q^4+10q^3+8q^2+3q
        71: 11q^3+8q^2+3q
        72: 6q^3+7q^2+3q
        73: 6q^3+7q^2+3q
        74: 2q^4+5q^3+6q^2+2q
        75: 3q^3+2q^2+q
        76: 2q^4+5q^3+6q^2+2q
        77: 3q^3+2q^2+q
        78: 2q^4+5q^3+5q^2+2q
        79: q^4+2q^3+2q^2+q
        80: q^4+14q^3+9q^2+3q
        81: 10q^3+8q^2+3q
        82: 3q^4+15q^3+9q^2+3q
        83: q^4+10q^3+8q^2+3q
        84: q^4+14q^3+9q^2+3q
        85: 10q^3+8q^2+3q
        86: 3q^4+15q^3+9q^2+3q
        87: q^4+10q^3+8q^2+3q
        88: 10q^3+8q^2+3q
        89: 10q^3+8q^2+3q
        90: 3q^4+7q^3+6q^2+2q
        91: 4q^3+7q^2+3q
        92: 4q^3+7q^2+3q
        93: 4q^3+6q^2+2q
        94: 11q^3+8q^2+3q
        95: 11q^3+8q^2+3q
        96: 3q^4+7q^3+6q^2+2q
        97: 11q^3+8q^2+3q
        98: 11q^3+8q^2+3q
        99: 3q^4+7q^3+6q^2+2q
       100: 3q^4+15q^3+9q^2+3q
       101: 3q^4+15q^3+9q^2+3q
       102: 6q^4+11q^3+8q^2+3q
       103: 5q^3+3q^2+q
       104: 5q^3+3q^2+q
       105: 3q^3
       106: 5q^3+3q^2+q
       107: 4q^3+5q^2+2q
       108: 2q^3+2q^2+q
       109: 2q^3+2q^2+q
       110: 4q^3+5q^2+2q
       111: 4q^2+2q
       112: q^3+2q^2+q
       113: 2q^4+5q^3+6q^2+2q
       114: 3q^3+2q^2+q
       115: q^4+4q^3+5q^2+2q
       116: 2q^3+2q^2+q
       117: q^3+2q^2+q
       118: 2q^3+5q^2+2q
       119: 2q^3+5q^2+2q
       120: q^3+2q^2+q
       121: q^4+8q^3+6q^2+2q
       122: 6q^3+3q^2+q
       123: 6q^3+5q^2+2q
       124: 4q^3+3q^2+q
       125: 3q^3+7q^2+3q
       126: 4q^3+5q^2+2q
       127: 3q^3+3q^2+2q
       129: 3q^3+3q^2+2q
       131: 2q^3+3q^2+q
       133: 6q^2+3q
       134: 2q^3+5q^2+2q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 10q^3+8q^2+3q
       138: 4q^3+5q^2+2q
       139: 11q^3+8q^2+3q
       140: 6q^3+7q^2+3q
       141: q^4+10q^3+8q^2+3q
       142: 6q^3+7q^2+3q
       143: 10q^3+8q^2+3q
       144: 4q^3+5q^2+2q
       145: 11q^3+8q^2+3q
       146: q^4+10q^3+8q^2+3q
       147: 6q^3+7q^2+3q
       148: 6q^3+7q^2+3q
       149: 3q^4+15q^3+9q^2+3q
       150: q^4+10q^3+8q^2+3q
       151: 2q^4+5q^3+6q^2+2q
       152: 3q^3+2q^2+q
       153: 2q^4+5q^3+6q^2+2q
       154: 3q^3+2q^2+q
       155: 2q^4+5q^3+5q^2+2q
       156: q^4+2q^3+2q^2+q
       157: 4q^3+7q^2+3q
       158: 4q^3+7q^2+3q
       159: 4q^3+6q^2+2q
       160: 4q^3+7q^2+3q
       161: 4q^3+7q^2+3q
       162: 4q^3+6q^2+2q
       163: 4q^3+7q^2+3q
       164: 4q^3+7q^2+3q
       165: 4q^3+6q^2+2q
       166: 11q^3+8q^2+3q
       167: 11q^3+8q^2+3q
       168: 3q^4+7q^3+6q^2+2q
       169: 2q^2+q
       170: q^3+2q^2+q
       172: 2q^2+q
       173: q^3+2q^2+q
       174: q^3+3q^2+q
       176: q^3+2q^2+q
       177: q^3+2q^2+q
       179: 3q^3+3q^2+2q
       181: 2q^2+2q
       183: 4q^2+2q
       184: q^2+q
       185: q^2+q
       186: 4q^2+2q
       187: 3q^2+2q
       188: 2q^2+q
       189: q^4+4q^3+5q^2+2q
       190: 2q^3+2q^2+q
       191: q^3+2q^2+q
       192: 2q^3+5q^2+2q
       193: 4q^3+5q^2+2q
       194: 2q^3+2q^2+q
       195: 2q^3+2q^2+q
       196: 4q^3+5q^2+2q
       197: 4q^2+2q
       198: q^3+2q^2+q
       199: 2q^3+5q^2+2q
       200: q^3+2q^2+q
       201: 4q^3+5q^2+2q
       202: 2q^3+2q^2+q
       203: 2q^3+2q^2+q
       204: 4q^3+5q^2+2q
       205: 4q^2+2q
       206: q^3+2q^2+q
       207: 6q^3+5q^2+2q
       208: 4q^3+3q^2+q
       209: 2q^4+5q^3+6q^2+2q
       210: 3q^3+2q^2+q
       211: q^4+4q^3+5q^2+2q
       212: 2q^3+2q^2+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 4q^2+2q
       220: 6q^2+3q
       221: 2q^3+5q^2+2q
       222: 2q^3+6q^2+3q
       223: q^3+4q^2+2q
       224: 2q^3+6q^2+3q
       225: q^3+4q^2+2q
       226: 4q^3+5q^2+2q
       227: 6q^2+3q
       228: 2q^3+5q^2+2q
       229: 2q^3+6q^2+3q
       230: 2q^3+6q^2+3q
       231: 4q^3+5q^2+2q
       232: 6q^2+3q
       233: 2q^3+5q^2+2q
       234: 2q^3+6q^2+3q
       235: 2q^3+6q^2+3q
       236: 4q^3+5q^2+2q
       237: 3q^3+3q^2+2q
       239: 3q^3+3q^2+2q
       241: 2q^3+3q^2+q
       243: 11q^3+8q^2+3q
       244: 6q^3+7q^2+3q
       245: 6q^3+7q^2+3q
       246: q^4+10q^3+8q^2+3q
       247: q^3+9q^2+4q
       248: q^3+9q^2+4q
       249: q^4+4q^3+5q^2+2q
       250: 4q^3+7q^2+3q
       251: 4q^3+7q^2+3q
       252: 4q^3+6q^2+2q
       253: 4q^3+7q^2+3q
       254: 4q^3+7q^2+3q
       255: 4q^3+6q^2+2q
       256: 4q^3+7q^2+3q
       257: 4q^3+7q^2+3q
       258: 4q^3+6q^2+2q
       259: q^2+q
       262: q^2+q
       263: q^2+q
       264: 2q^2+q
       266: q^2+q
       267: 2q^2+q
       268: q^3+2q^2+q
       269: 2q^2+q
       271: 2q^2+q
       273: 2q^2+q
       274: q^3+2q^2+q
       275: q^3+2q^2+q
       276: q^3+3q^2+q
       278: q^3+2q^2+q
       279: q^2+2q
       281: q^2+q
       283: 2q^2+q
       286: 2q^2+q
       287: q^3+2q^2+q
       289: 2q
       291: q^2+q
       293: 4q^2+2q
       294: q^2+q
       295: q^2+q
       296: 4q^2+2q
       297: 3q^2+2q
       298: 2q^2+q
       299: 4q^2+2q
       300: q^2+q
       301: 2q^2+2q
       303: q^2+q
       304: 4q^2+2q
       305: 3q^2+2q
       306: 2q^2+q
       307: 4q^2+2q
       308: q^2+q
       309: q^2+q
       310: 4q^2+2q
       311: 2q^2+2q
       313: 3q^2+2q
       314: 2q^2+q
       315: q^3+2q^2+q
       317: 3q^3+3q^2+2q
       319: 4q^3+5q^2+2q
       320: 2q^3+2q^2+q
       321: 2q^3+2q^2+q
       322: 4q^3+5q^2+2q
       323: 4q^2+2q
       324: q^3+2q^2+q
       325: q^4+4q^3+5q^2+2q
       326: 2q^3+2q^2+q
       327: q^3+q^2+2q
       329: q^3+q^2+2q
       331: 2q^2+q
       333: 4q^2+2q
       334: q^3+4q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: q^3+9q^2+4q
       338: 5q^2+3q
       340: 5q^2+3q
       342: 2q^3+3q^2+q
       344: 4q^2+2q
       345: 6q^2+3q
       346: 2q^3+5q^2+2q
       347: 2q^3+6q^2+3q
       348: q^3+4q^2+2q
       349: 2q^3+6q^2+3q
       350: q^3+4q^2+2q
       351: q^3+9q^2+4q
       352: 4q^2+2q
       353: 6q^2+3q
       354: 2q^3+5q^2+2q
       355: 2q^3+6q^2+3q
       356: q^3+4q^2+2q
       357: 2q^3+6q^2+3q
       358: q^3+4q^2+2q
       359: q^3+9q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 4q^3+5q^2+2q
       367: 6q^2+3q
       368: 2q^3+5q^2+2q
       369: 2q^3+6q^2+3q
       370: 2q^3+6q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 4q^3+7q^2+3q
       375: 4q^3+7q^2+3q
       376: 4q^3+6q^2+2q
       381: q
       384: q
       385: q^2+q
       386: 2q^2+q
       388: q^2+q
       389: q^2+q
       391: q^2+q
       393: q^2+q
       394: 2q^2+q
       396: q^2+q
       397: q^2+q
       399: q^2+q
       401: q^2+q
       403: 2q^2+q
       404: q^2+q
       405: 2q^2+q
       406: 2q^2+q
       407: q^3+2q^2+q
       409: q^2+2q
       411: q^2+q
       413: q^2+q
       415: 2q
       417: q
       419: 2q^2+q
       422: 2q^2+q
       423: q^2+q
       425: q^2+q
       427: 5q^2+3q
       429: 2q^2+q
       432: 2q^2+q
       433: q^2+q
       435: 2q
       437: 4q^2+2q
       438: q^2+q
       439: q^2+q
       440: 4q^2+2q
       441: 3q^2+2q
       442: 2q^2+q
       443: q^3+6q^2+3q
       444: 3q^2+q
       445: 5q^2+3q
       447: 2q^2+q
       450: 2q^2+q
       451: q^2+q
       453: 4q^2+2q
       454: q^2+q
       455: 2q
       457: q^2+q
       458: 4q^2+2q
       459: 3q^2+2q
       460: 2q^2+q
       461: 3q^2+q
       462: q^3+6q^2+3q
       463: 5q^2+3q
       465: q^2+2q
       467: q^2+q
       469: q^3+2q^2+q
       471: 4q^2+2q
       472: q^2+q
       473: q^2+q
       474: 4q^2+2q
       475: 3q^2+2q
       476: 2q^2+q
       477: 2q^2+2q
       479: 4q^2+2q
       480: q^3+5q^2+2q
       481: 2q^2+2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: q^2+2q
       492: 4q^2+2q
       493: q^3+4q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 3q^2+4q
       497: 4q^2+2q
       498: q^3+4q^2+2q
       499: q^3+4q^2+2q
       500: 3q^2+2q
       501: 3q^2+4q
       502: q^3+q^2+2q
       504: q^3+q^2+2q
       506: 2q^2+q
       508: 4q^2+2q
       509: 6q^2+3q
       510: 2q^3+5q^2+2q
       511: 2q^3+6q^2+3q
       512: q^3+4q^2+2q
       513: 2q^3+6q^2+3q
       514: q^3+4q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 3q^2+4q
       519: 3q^2+4q
       520: q^3+3q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q^2+q
       542: 2q^2+q
       543: q^2+q
       545: 3q^2+2q
       547: 2q^2+q
       553: q
       555: q
       557: q^2+q
       559: q^2+q
       560: 2q^2+q
       561: 2q^2+q
       563: 3q^2+2q
       565: q^2+q
       566: 2q^2+q
       568: q^2+q
       569: q^2+q
       570: q^2+q
       573: 2q^2+q
       574: q^3+4q^2+2q
       575: 2q^2+q
       576: q^2
       577: 2q^2+2q
       580: 3q^2+q
       583: q^2+q
       585: q
       587: q
       589: q^2+q
       592: q^2+q
       593: q^2+q
       596: q^2+q
       597: q
       599: q^2+q
       601: 3q
       603: 2q^2+q
       605: q
       608: 2q^2+q
       609: q^2+q
       611: 2q
       613: q^2+q
       615: q^2+3q
       616: q
       617: q^2+3q
       619: 2q^2+q
       622: 2q^2+q
       623: q
       625: q^2+q
       627: 2q
       629: q^2+q
       631: q
       632: q^2+3q
       633: q^2+3q
       635: q^2+2q
       637: q^2+q
       639: q^2+q
       641: 2q^2+q
       644: 2q^2+q
       645: q^2+q
       647: 4q^2+2q
       648: q^2+q
       649: q^2+q
       650: 4q^2+2q
       651: 2q
       653: 3q^2+2q
       654: 2q^2+q
       655: q^2+2q
       656: 2q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       666: q^2+3q
       668: q^2+3q
       670: 2q^2+q
       672: q^2+4q
       673: q^2+2q
       674: 2q+1
       675: 2q^2+2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 3q^2+4q
       679: q^2+2q
       680: 2q+1
       681: 2q^2+2q
       682: 2q^2+2q
       683: 3q^2+2q
       684: 3q^2+4q
       685: q^2+2q
       686: 4q^2+2q
       687: q^3+4q^2+2q
       688: q^3+4q^2+2q
       689: 3q^2+2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+q
       696: 2q^2+q
       697: q^2+q
       698: q^2
       729: q
       731: q
       733: 2q
       735: q
       745: q
       747: q
       749: q
       751: 2q
       757: q
       758: q
       761: q^2+q
       762: q^2+q
       763: 2q^2+q
       765: q
       766: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: 3q
       793: q+1
       795: 2q+1
       797: q
       799: q
       801: q^2+q
       804: q^2+q
       805: q^2+q
       808: q^2+q
       809: q
       811: q^2+q
       813: q^2+3q
       815: q^2+3q
       816: q
       818: q+1
       819: 2q+1
       821: q
       823: q
       825: q^2+q
       828: q^2+q
       829: q^2+q
       832: q^2+q
       833: q
       835: q^2+q
       837: q^2+3q
       839: q
       840: q^2+3q
       841: q^2+q
       843: q
       844: q+1
       845: 2q^2+q
       848: 2q^2+q
       849: q
       851: q^2+q
       853: 2q
       855: q^2+q
       857: q^2+2q
       858: 2q^2+2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 2q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q^2+2q
       878: 2q^2+2q
       879: 3q^2+2q
       880: q^2+2q
       884: q
       887: q
       889: q
       916: q+1
       932: 2q
       934: q
       942: q+1
       956: q
       958: 2q
       965: q+1
       968: q
       971: q+1
       978: q
       979: q
       982: 2q
       985: q^2+q
       988: q
       989: q^2+2q
       991: q
       992: q+1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 2q+1
      1016: q+1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: 2q+1
      1033: q+1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1046: q
      1047: q+1
      1048: q
      1050: q
      1052: q^2+q
      1055: q^2+q
      1056: q^2+q
      1059: q^2+q
      1060: q
      1062: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1089: q+1
      1098: q
      1101: q
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: q+1
      1166: q+1
      1188: q
      1191: q+1
      1195: q+1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1264: q
      1266: q
      1268: q
      1271: q
      1272: q
      1274: q+1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1293: 1
      1305: q+1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1350: 1
      1356: 1
      1366: 1
      1382: 1
      1388: 1
      1397: 1
      1433: 1
      1448: 1
      1451: 1
      1454: 1
      1456: 1
      1461: 1
      1462: 1
      1464: 1
      1467: 1
      1468: 1
      1470: q
      1472: q+1
      1476: q
      1479: q
      1483: 1
      1487: 1
      1492: 1
      1505: 1
      1516: 1
      1565: 1
      1567: 1
      1577: 1
      1585: 1
      1587: 1
      1596: 1
      1609: 1
      1615: 1
      1624: 1
      1634: 1
      1661: 1
      1664: 1
      1665: 1
      1691: 1
      1702: 1
      1714: 1
      1787: 1
      1789: 1
      1798: 1
      1873: 1

1874:    0: 4q^4+22q^3+10q^2+3q
         1: 4q^4+22q^3+10q^2+3q
         2: 9q^4+15q^3+9q^2+3q
         3: 4q^4+22q^3+10q^2+3q
         4: q^5+10q^4+16q^3+9q^2+3q
         5: 4q^4+22q^3+10q^2+3q
         6: q^5+10q^4+16q^3+9q^2+3q
         7: 3q^5+10q^4+12q^3+8q^2+3q
         8: 9q^4+15q^3+9q^2+3q
         9: q^6+4q^5+8q^4+9q^3+6q^2+2q
        10: 4q^4+22q^3+10q^2+3q
        11: 4q^4+22q^3+10q^2+3q
        12: q^5+10q^4+16q^3+9q^2+3q
        13: q^4+14q^3+9q^2+3q
        14: 5q^4+11q^3+8q^2+3q
        15: q^4+14q^3+9q^2+3q
        16: 18q^3+9q^2+3q
        17: 18q^3+9q^2+3q
        18: 2q^5+6q^4+8q^3+6q^2+2q
        19: 3q^4+15q^3+9q^2+3q
        20: 3q^4+15q^3+9q^2+3q
        21: 6q^4+11q^3+8q^2+3q
        22: 4q^4+22q^3+10q^2+3q
        23: 4q^4+22q^3+10q^2+3q
        24: 9q^4+15q^3+9q^2+3q
        25: 4q^4+22q^3+10q^2+3q
        26: 4q^4+22q^3+10q^2+3q
        27: 9q^4+15q^3+9q^2+3q
        28: 18q^3+9q^2+3q
        29: 3q^4+15q^3+9q^2+3q
        30: q^4+10q^3+8q^2+3q
        31: 4q^4+22q^3+10q^2+3q
        32: q^4+14q^3+9q^2+3q
        33: 18q^3+9q^2+3q
        34: 4q^4+22q^3+10q^2+3q
        35: q^4+14q^3+9q^2+3q
        36: 18q^3+9q^2+3q
        37: 3q^4+12q^3+7q^2+2q
        38: q^4+10q^3+3q^2+q
        39: 3q^4+12q^3+7q^2+2q
        40: q^4+10q^3+3q^2+q
        41: 5q^4+9q^3+6q^2+2q
        42: 4q^4+6q^3+3q^2+q
        43: q^4+14q^3+9q^2+3q
        44: 5q^4+11q^3+8q^2+3q
        45: q^4+14q^3+9q^2+3q
        46: 10q^3+8q^2+3q
        47: 10q^3+8q^2+3q
        48: 3q^4+7q^3+6q^2+2q
        49: 11q^3+8q^2+3q
        50: 11q^3+8q^2+3q
        51: 3q^4+7q^3+6q^2+2q
        52: 3q^4+15q^3+9q^2+3q
        53: 3q^4+15q^3+9q^2+3q
        54: 6q^4+11q^3+8q^2+3q
        55: 3q^4+15q^3+9q^2+3q
        56: 3q^4+15q^3+9q^2+3q
        57: 6q^4+11q^3+8q^2+3q
        58: 10q^3+6q^2+2q
        59: 8q^3+3q^2+q
        60: 8q^3+3q^2+q
        61: 10q^3+6q^2+2q
        62: 3q^4+12q^3+7q^2+2q
        63: q^4+10q^3+3q^2+q
        64: q^4+8q^3+6q^2+2q
        65: 6q^3+3q^2+q
        66: 10q^3+6q^2+2q
        67: 8q^3+3q^2+q
        68: 3q^3+7q^2+3q
        69: 4q^3+5q^2+2q
        70: q^4+10q^3+8q^2+3q
        71: 11q^3+8q^2+3q
        72: 6q^3+7q^2+3q
        73: 6q^3+7q^2+3q
        74: 2q^4+5q^3+6q^2+2q
        75: 3q^3+2q^2+q
        76: 2q^4+5q^3+6q^2+2q
        77: 3q^3+2q^2+q
        78: 2q^4+5q^3+5q^2+2q
        79: q^4+2q^3+2q^2+q
        80: q^4+14q^3+9q^2+3q
        81: 10q^3+8q^2+3q
        82: 3q^4+15q^3+9q^2+3q
        83: q^4+10q^3+8q^2+3q
        84: q^4+14q^3+9q^2+3q
        85: 10q^3+8q^2+3q
        86: 3q^4+15q^3+9q^2+3q
        87: q^4+10q^3+8q^2+3q
        88: 10q^3+8q^2+3q
        89: 10q^3+8q^2+3q
        90: 3q^4+7q^3+6q^2+2q
        91: 4q^3+7q^2+3q
        92: 4q^3+7q^2+3q
        93: 4q^3+6q^2+2q
        94: 11q^3+8q^2+3q
        95: 11q^3+8q^2+3q
        96: 3q^4+7q^3+6q^2+2q
        97: 11q^3+8q^2+3q
        98: 11q^3+8q^2+3q
        99: 3q^4+7q^3+6q^2+2q
       100: 3q^4+15q^3+9q^2+3q
       101: 3q^4+15q^3+9q^2+3q
       102: 6q^4+11q^3+8q^2+3q
       103: 5q^3+3q^2+q
       104: 3q^3
       105: 5q^3+3q^2+q
       106: 5q^3+3q^2+q
       107: 2q^3+2q^2+q
       108: 4q^3+5q^2+2q
       109: 4q^3+5q^2+2q
       110: 2q^3+2q^2+q
       111: 4q^2+2q
       112: q^3+2q^2+q
       113: 2q^4+5q^3+6q^2+2q
       114: 3q^3+2q^2+q
       115: q^4+4q^3+5q^2+2q
       116: 2q^3+2q^2+q
       117: 2q^3+5q^2+2q
       118: q^3+2q^2+q
       119: q^3+2q^2+q
       120: 2q^3+5q^2+2q
       121: q^4+8q^3+6q^2+2q
       122: 6q^3+3q^2+q
       123: 6q^3+5q^2+2q
       124: 4q^3+3q^2+q
       125: 3q^3+7q^2+3q
       126: 4q^3+5q^2+2q
       127: 3q^3+3q^2+2q
       129: 3q^3+3q^2+2q
       131: 2q^3+3q^2+q
       133: 6q^2+3q
       134: 2q^3+5q^2+2q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 10q^3+8q^2+3q
       138: 4q^3+5q^2+2q
       139: 11q^3+8q^2+3q
       140: 6q^3+7q^2+3q
       141: q^4+10q^3+8q^2+3q
       142: 6q^3+7q^2+3q
       143: 10q^3+8q^2+3q
       144: 4q^3+5q^2+2q
       145: 11q^3+8q^2+3q
       146: q^4+10q^3+8q^2+3q
       147: 6q^3+7q^2+3q
       148: 6q^3+7q^2+3q
       149: 3q^4+15q^3+9q^2+3q
       150: q^4+10q^3+8q^2+3q
       151: 2q^4+5q^3+6q^2+2q
       152: 3q^3+2q^2+q
       153: 2q^4+5q^3+6q^2+2q
       154: 3q^3+2q^2+q
       155: 2q^4+5q^3+5q^2+2q
       156: q^4+2q^3+2q^2+q
       157: 4q^3+7q^2+3q
       158: 4q^3+7q^2+3q
       159: 4q^3+6q^2+2q
       160: 4q^3+7q^2+3q
       161: 4q^3+7q^2+3q
       162: 4q^3+6q^2+2q
       163: 4q^3+7q^2+3q
       164: 4q^3+7q^2+3q
       165: 4q^3+6q^2+2q
       166: 11q^3+8q^2+3q
       167: 11q^3+8q^2+3q
       168: 3q^4+7q^3+6q^2+2q
       169: 2q^2+q
       171: q^3+2q^2+q
       172: 2q^2+q
       173: q^3+2q^2+q
       175: q^3+3q^2+q
       176: q^3+2q^2+q
       177: q^3+2q^2+q
       179: 3q^3+3q^2+2q
       181: 2q^2+2q
       183: q^2+q
       184: 4q^2+2q
       185: 4q^2+2q
       186: q^2+q
       187: 3q^2+2q
       188: 2q^2+q
       189: q^4+4q^3+5q^2+2q
       190: 2q^3+2q^2+q
       191: 2q^3+5q^2+2q
       192: q^3+2q^2+q
       193: 2q^3+2q^2+q
       194: 4q^3+5q^2+2q
       195: 4q^3+5q^2+2q
       196: 2q^3+2q^2+q
       197: 4q^2+2q
       198: q^3+2q^2+q
       199: q^3+2q^2+q
       200: 2q^3+5q^2+2q
       201: 2q^3+2q^2+q
       202: 4q^3+5q^2+2q
       203: 4q^3+5q^2+2q
       204: 2q^3+2q^2+q
       205: 4q^2+2q
       206: q^3+2q^2+q
       207: 6q^3+5q^2+2q
       208: 4q^3+3q^2+q
       209: 2q^4+5q^3+6q^2+2q
       210: 3q^3+2q^2+q
       211: q^4+4q^3+5q^2+2q
       212: 2q^3+2q^2+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 4q^2+2q
       220: 6q^2+3q
       221: 2q^3+5q^2+2q
       222: 2q^3+6q^2+3q
       223: q^3+4q^2+2q
       224: 2q^3+6q^2+3q
       225: q^3+4q^2+2q
       226: 4q^3+5q^2+2q
       227: 6q^2+3q
       228: 2q^3+5q^2+2q
       229: 2q^3+6q^2+3q
       230: 2q^3+6q^2+3q
       231: 4q^3+5q^2+2q
       232: 6q^2+3q
       233: 2q^3+5q^2+2q
       234: 2q^3+6q^2+3q
       235: 2q^3+6q^2+3q
       236: 4q^3+5q^2+2q
       237: 3q^3+3q^2+2q
       239: 3q^3+3q^2+2q
       241: 2q^3+3q^2+q
       243: 11q^3+8q^2+3q
       244: 6q^3+7q^2+3q
       245: 6q^3+7q^2+3q
       246: q^4+10q^3+8q^2+3q
       247: q^3+9q^2+4q
       248: q^3+9q^2+4q
       249: q^4+4q^3+5q^2+2q
       250: 4q^3+7q^2+3q
       251: 4q^3+7q^2+3q
       252: 4q^3+6q^2+2q
       253: 4q^3+7q^2+3q
       254: 4q^3+7q^2+3q
       255: 4q^3+6q^2+2q
       256: 4q^3+7q^2+3q
       257: 4q^3+7q^2+3q
       258: 4q^3+6q^2+2q
       259: q^2+q
       262: q^2+q
       263: q^2+q
       265: 2q^2+q
       266: q^2+q
       267: 2q^2+q
       269: 2q^2+q
       270: q^3+2q^2+q
       271: 2q^2+q
       272: q^3+2q^2+q
       273: 2q^2+q
       275: q^3+2q^2+q
       277: q^3+3q^2+q
       278: q^3+2q^2+q
       279: q^2+2q
       281: q^2+q
       284: 2q^2+q
       285: 2q^2+q
       287: q^3+2q^2+q
       289: 2q
       291: q^2+q
       293: q^2+q
       294: 4q^2+2q
       295: 4q^2+2q
       296: q^2+q
       297: 3q^2+2q
       298: 2q^2+q
       299: q^2+q
       300: 4q^2+2q
       301: 2q^2+2q
       303: 4q^2+2q
       304: q^2+q
       305: 3q^2+2q
       306: 2q^2+q
       307: q^2+q
       308: 4q^2+2q
       309: 4q^2+2q
       310: q^2+q
       311: 2q^2+2q
       313: 3q^2+2q
       314: 2q^2+q
       315: q^3+2q^2+q
       317: 3q^3+3q^2+2q
       319: 2q^3+2q^2+q
       320: 4q^3+5q^2+2q
       321: 4q^3+5q^2+2q
       322: 2q^3+2q^2+q
       323: 4q^2+2q
       324: q^3+2q^2+q
       325: q^4+4q^3+5q^2+2q
       326: 2q^3+2q^2+q
       327: q^3+q^2+2q
       329: q^3+q^2+2q
       331: 2q^2+q
       333: 4q^2+2q
       334: q^3+4q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: q^3+9q^2+4q
       338: 5q^2+3q
       340: 5q^2+3q
       342: 2q^3+3q^2+q
       344: 4q^2+2q
       345: 6q^2+3q
       346: 2q^3+5q^2+2q
       347: 2q^3+6q^2+3q
       348: q^3+4q^2+2q
       349: 2q^3+6q^2+3q
       350: q^3+4q^2+2q
       351: q^3+9q^2+4q
       352: 4q^2+2q
       353: 6q^2+3q
       354: 2q^3+5q^2+2q
       355: 2q^3+6q^2+3q
       356: q^3+4q^2+2q
       357: 2q^3+6q^2+3q
       358: q^3+4q^2+2q
       359: q^3+9q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 4q^3+5q^2+2q
       367: 6q^2+3q
       368: 2q^3+5q^2+2q
       369: 2q^3+6q^2+3q
       370: 2q^3+6q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 4q^3+7q^2+3q
       375: 4q^3+7q^2+3q
       376: 4q^3+6q^2+2q
       381: q
       384: q
       385: q^2+q
       387: 2q^2+q
       388: q^2+q
       389: q^2+q
       391: q^2+q
       393: q^2+q
       395: 2q^2+q
       396: q^2+q
       397: q^2+q
       399: q^2+q
       401: q^2+q
       402: 2q^2+q
       404: q^2+q
       405: 2q^2+q
       406: 2q^2+q
       408: q^3+2q^2+q
       409: q^2+2q
       411: q^2+q
       413: q^2+q
       415: 2q
       417: q
       420: 2q^2+q
       421: 2q^2+q
       423: q^2+q
       425: q^2+q
       427: 5q^2+3q
       430: 2q^2+q
       431: 2q^2+q
       433: q^2+q
       435: 2q
       437: q^2+q
       438: 4q^2+2q
       439: 4q^2+2q
       440: q^2+q
       441: 3q^2+2q
       442: 2q^2+q
       443: 3q^2+q
       444: q^3+6q^2+3q
       445: 5q^2+3q
       448: 2q^2+q
       449: 2q^2+q
       451: q^2+q
       453: q^2+q
       454: 4q^2+2q
       455: 2q
       457: 4q^2+2q
       458: q^2+q
       459: 3q^2+2q
       460: 2q^2+q
       461: q^3+6q^2+3q
       462: 3q^2+q
       463: 5q^2+3q
       465: q^2+2q
       467: q^2+q
       469: q^3+2q^2+q
       471: q^2+q
       472: 4q^2+2q
       473: 4q^2+2q
       474: q^2+q
       475: 3q^2+2q
       476: 2q^2+q
       477: 2q^2+2q
       479: 4q^2+2q
       480: q^3+5q^2+2q
       481: 2q^2+2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: q^2+2q
       492: 4q^2+2q
       493: q^3+4q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 3q^2+4q
       497: 4q^2+2q
       498: q^3+4q^2+2q
       499: q^3+4q^2+2q
       500: 3q^2+2q
       501: 3q^2+4q
       502: q^3+q^2+2q
       504: q^3+q^2+2q
       506: 2q^2+q
       508: 4q^2+2q
       509: 6q^2+3q
       510: 2q^3+5q^2+2q
       511: 2q^3+6q^2+3q
       512: q^3+4q^2+2q
       513: 2q^3+6q^2+3q
       514: q^3+4q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 3q^2+4q
       519: 3q^2+4q
       520: q^3+3q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q^2+q
       543: q^2+q
       544: 2q^2+q
       545: 2q^2+q
       547: 3q^2+2q
       553: q
       555: q
       557: q^2+q
       558: 2q^2+q
       559: q^2+q
       561: 3q^2+2q
       563: 2q^2+q
       565: q^2+q
       567: 2q^2+q
       568: q^2+q
       569: q^2+q
       570: q^2+q
       573: 2q^2+q
       574: q^2
       575: 2q^2+q
       576: q^3+4q^2+2q
       577: 2q^2+2q
       580: 3q^2+q
       583: q^2+q
       585: q
       587: q
       590: q^2+q
       591: q^2+q
       594: q^2+q
       595: q^2+q
       597: q
       599: q^2+q
       601: 3q
       604: 2q^2+q
       605: q
       607: 2q^2+q
       609: q^2+q
       611: 2q
       613: q^2+q
       615: q
       616: q^2+3q
       617: q^2+3q
       620: 2q^2+q
       621: 2q^2+q
       623: q
       625: q^2+q
       627: 2q
       629: q^2+q
       631: q^2+3q
       632: q
       633: q^2+3q
       635: q^2+2q
       637: q^2+q
       639: q^2+q
       642: 2q^2+q
       643: 2q^2+q
       645: q^2+q
       647: q^2+q
       648: 4q^2+2q
       649: 4q^2+2q
       650: q^2+q
       651: 2q
       653: 3q^2+2q
       654: 2q^2+q
       655: q^2+2q
       656: 2q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       666: q^2+3q
       668: q^2+3q
       670: 2q^2+q
       672: q^2+4q
       673: q^2+2q
       674: 2q+1
       675: 2q^2+2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 3q^2+4q
       679: q^2+2q
       680: 2q+1
       681: 2q^2+2q
       682: 2q^2+2q
       683: 3q^2+2q
       684: 3q^2+4q
       685: q^2+2q
       686: 4q^2+2q
       687: q^3+4q^2+2q
       688: q^3+4q^2+2q
       689: 3q^2+2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+q
       696: q^2
       697: q^2+q
       698: 2q^2+q
       729: q
       731: q
       733: q
       735: 2q
       745: q
       747: q
       749: 2q
       751: q
       757: q
       758: q
       761: q^2+q
       762: q^2+q
       764: 2q^2+q
       765: q
       767: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: 3q
       794: q+1
       795: 2q+1
       797: q
       799: q
       802: q^2+q
       803: q^2+q
       806: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       813: q^2+3q
       815: q
       816: q^2+3q
       817: q+1
       819: 2q+1
       821: q
       823: q
       826: q^2+q
       827: q^2+q
       830: q^2+q
       831: q^2+q
       833: q
       835: q^2+q
       837: q^2+3q
       839: q^2+3q
       840: q
       841: q^2+q
       843: q
       844: q+1
       846: 2q^2+q
       847: 2q^2+q
       849: q
       851: q^2+q
       853: 2q
       855: q^2+q
       857: q^2+2q
       858: 2q^2+2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 2q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q^2+2q
       878: 2q^2+2q
       879: 3q^2+2q
       880: q^2+2q
       884: q
       888: q
       889: q
       918: q+1
       932: q
       934: 2q
       940: q+1
       956: 2q
       958: q
       966: q+1
       968: q
       971: q+1
       978: q
       979: q
       982: 2q
       985: q^2+q
       988: q
       990: q^2+2q
       991: q
       992: q+1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 2q+1
      1017: q+1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: 2q+1
      1032: q+1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1046: q
      1047: q+1
      1048: q
      1050: q
      1053: q^2+q
      1054: q^2+q
      1057: q^2+q
      1058: q^2+q
      1060: q
      1062: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1090: q+1
      1098: q
      1102: q
      1103: q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: q+1
      1164: q+1
      1188: q
      1191: q+1
      1196: q+1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1264: q
      1266: q
      1269: q
      1270: q
      1272: q
      1274: q+1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1294: 1
      1306: q+1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1348: 1
      1358: 1
      1365: 1
      1380: 1
      1390: 1
      1398: 1
      1433: 1
      1448: 1
      1450: 1
      1455: 1
      1456: 1
      1460: 1
      1463: 1
      1464: 1
      1466: 1
      1469: 1
      1470: q
      1472: q+1
      1477: q
      1478: q
      1483: 1
      1487: 1
      1493: 1
      1504: 1
      1517: 1
      1563: 1
      1569: 1
      1576: 1
      1583: 1
      1589: 1
      1597: 1
      1607: 1
      1617: 1
      1625: 1
      1634: 1
      1661: 1
      1663: 1
      1666: 1
      1690: 1
      1703: 1
      1715: 1
      1785: 1
      1791: 1
      1799: 1
      1874: 1

1875:    0: 7q^2+2q+1
         1: 7q^2+2q+1
         2: 3q^3+4q^2+2q+1
         3: 7q^2+2q+1
         4: 2q^3+5q^2+2q+1
         5: 7q^2+2q+1
         6: 2q^3+5q^2+2q+1
         7: q^4+3q^3+3q^2+2q+1
         8: 3q^3+4q^2+2q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 7q^2+2q+1
        11: 7q^2+2q+1
        12: 2q^3+5q^2+2q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 7q^2+2q+1
        17: 7q^2+2q+1
        18: q^4+3q^3+3q^2+2q+1
        19: 5q^2+2q+1
        20: 5q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 7q^2+2q+1
        23: 7q^2+2q+1
        24: 3q^3+4q^2+2q+1
        25: 7q^2+2q+1
        26: 7q^2+2q+1
        27: 3q^3+4q^2+2q+1
        28: 7q^2+2q+1
        29: 5q^2+2q+1
        30: 3q^2+2q+1
        31: 7q^2+2q+1
        32: 4q^2+2q+1
        33: 7q^2+2q+1
        34: 7q^2+2q+1
        35: 4q^2+2q+1
        36: 7q^2+2q+1
        37: 2q^2
        38: 5q^2+2q+1
        39: 2q^2
        40: 5q^2+2q+1
        41: q^3+q^2
        42: 2q^3+3q^2+2q+1
        43: 4q^2+2q+1
        44: q^3+3q^2+2q+1
        45: 4q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 5q^2+2q+1
        50: 5q^2+2q+1
        51: 2q^3+3q^2+2q+1
        52: 5q^2+2q+1
        53: 5q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: 5q^2+2q+1
        56: 5q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: 3q^2
        59: 4q^2+2q+1
        60: 4q^2+2q+1
        61: 3q^2
        62: 2q^2
        63: 5q^2+2q+1
        64: q^2
        65: 3q^2+2q+1
        66: 2q^2
        67: 5q^2+2q+1
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^2+2q+1
        71: 5q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        75: 3q^2+2q+1
        77: 3q^2+2q+1
        79: q^3+2q^2+2q+1
        80: 4q^2+2q+1
        81: 4q^2+2q+1
        82: 5q^2+2q+1
        83: 3q^2+2q+1
        84: 4q^2+2q+1
        85: 4q^2+2q+1
        86: 5q^2+2q+1
        87: 3q^2+2q+1
        88: 4q^2+2q+1
        89: 4q^2+2q+1
        90: q^3+3q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 5q^2+2q+1
        95: 5q^2+2q+1
        96: 2q^3+3q^2+2q+1
        97: 5q^2+2q+1
        98: 5q^2+2q+1
        99: 2q^3+3q^2+2q+1
       100: 5q^2+2q+1
       101: 5q^2+2q+1
       102: 2q^3+3q^2+2q+1
       103: q^2
       104: 3q^2+2q+1
       105: 2q^2
       106: q^2
       107: 2q^2+2q+1
       108: q^2
       109: q^2
       110: 2q^2+2q+1
       112: q^2+2q+1
       114: 3q^2+2q+1
       116: 2q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       121: q^2
       122: 3q^2+2q+1
       123: q^2
       124: 3q^2+2q+1
       125: q^2+2q+1
       126: 3q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 4q^2+2q+1
       138: 3q^2+2q+1
       139: 5q^2+2q+1
       140: 3q^2+2q+1
       141: 3q^2+2q+1
       142: 3q^2+2q+1
       143: 4q^2+2q+1
       144: 3q^2+2q+1
       145: 5q^2+2q+1
       146: 3q^2+2q+1
       147: 3q^2+2q+1
       148: 3q^2+2q+1
       149: 5q^2+2q+1
       150: 3q^2+2q+1
       152: 3q^2+2q+1
       154: 3q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 5q^2+2q+1
       167: 5q^2+2q+1
       168: 2q^3+3q^2+2q+1
       170: q^2+2q+1
       174: q^2+2q+1
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       186: 2q+1
       188: 2q+1
       190: 2q^2+2q+1
       192: q^2+2q+1
       193: 2q^2+2q+1
       194: q^2
       195: q^2
       196: 2q^2+2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       201: 2q^2+2q+1
       202: q^2
       203: q^2
       204: 2q^2+2q+1
       206: q^2+2q+1
       207: q^2
       208: 3q^2+2q+1
       210: 3q^2+2q+1
       212: 2q^2+2q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 3q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: 5q^2+2q+1
       244: 3q^2+2q+1
       245: 3q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q^2+2q+1
       264: 2q+1
       268: q^2+2q+1
       274: q^2+2q+1
       276: q^2+2q+1
       280: q+1
       282: q^2+q+1
       283: 2q+1
       286: 2q+1
       288: 2q^2+2q+1
       290: q+1
       292: 2q+1
       293: 2q+1
       296: 2q+1
       298: 2q+1
       299: 2q+1
       302: q^2+2q+1
       304: 2q+1
       306: 2q+1
       307: 2q+1
       310: 2q+1
       312: q^2+2q+1
       314: 2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: 2q^2+2q+1
       320: q^2
       321: q^2
       322: 2q^2+2q+1
       324: q^2+2q+1
       326: 2q^2+2q+1
       328: q^2+q+1
       330: q^2+q+1
       332: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: 3q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       378: 2q+1
       382: q+1
       386: 2q+1
       390: q^2+2q+1
       394: 2q+1
       400: q^2+2q+1
       403: 2q+1
       407: q^2+2q+1
       410: q+1
       412: q^2+q+1
       414: q+1
       416: q+1
       418: q+1
       419: 2q+1
       422: 2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       429: 2q+1
       432: 2q+1
       434: 2q+1
       436: q+1
       437: 2q+1
       440: 2q+1
       442: 2q+1
       443: q^2+3q+1
       444: q
       446: q^2+4q+1
       447: 2q+1
       450: 2q+1
       452: 2q+1
       453: 2q+1
       456: q+1
       458: 2q+1
       460: 2q+1
       461: q
       462: q^2+3q+1
       464: q^2+4q+1
       466: q+1
       468: q^2+q+1
       470: 2q^2+2q+1
       471: 2q+1
       474: 2q+1
       476: 2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       503: q^2+q+1
       505: q^2+q+1
       507: q^2+q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q+1
       526: q+1
       530: 2q+1
       534: 2q+1
       538: q+1
       542: 2q+1
       546: q^2+3q+1
       548: q
       551: 2q+1
       556: q+1
       560: 2q+1
       562: q
       564: q^2+3q+1
       566: 2q+1
       571: q^2+2q+1
       573: q
       574: q^2+2q+1
       575: q
       578: 2q
       581: q^2+2q+1
       584: q+1
       586: 1
       588: q+1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       598: q+1
       600: 2q+1
       602: q+1
       603: 2q+1
       606: q+1
       608: 2q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       615: q+1
       618: 2q+1
       619: 2q+1
       622: 2q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       632: q+1
       634: 2q+1
       636: q+1
       638: q^2+q+1
       640: q+1
       641: 2q+1
       644: 2q+1
       646: 2q+1
       647: 2q+1
       650: 2q+1
       652: q+1
       654: 2q+1
       655: q
       656: q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q
       699: q^2+2q+1
       701: q
       706: q+1
       710: 1
       715: q+1
       718: q+1
       722: q+1
       726: 2q+1
       730: q+1
       734: q+1
       740: q+1
       744: 2q+1
       748: q+1
       752: q+1
       754: 2q+1
       759: q+1
       763: 2q+1
       766: q+1
       770: q
       773: q+1
       776: q+1
       778: 1
       780: q+1
       782: 1
       784: q+1
       785: 1
       788: 1
       790: q+1
       792: 1
       793: q+1
       796: 2q+1
       798: 1
       800: q+1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       810: q+1
       812: 2q+1
       814: 2q+1
       815: q+1
       818: q+1
       820: 2q+1
       822: 1
       824: q+1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       834: q+1
       836: 2q+1
       838: 2q+1
       840: q+1
       842: q+1
       843: q
       844: q+1
       845: 2q+1
       848: 2q+1
       850: q+1
       852: 2q+1
       854: q+1
       856: 2q+1
       857: q
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: q+1
       917: q+1
       921: 1
       926: q+1
       929: q+1
       933: q+1
       939: q+1
       943: q+1
       947: 1
       951: q+1
       953: q+1
       959: q+1
       962: q+1
       965: q+1
       969: q
       972: q+1
       976: 2q+1
       980: q+1
       983: q
       986: q+1
       989: q+1
       993: q+1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1016: q+1
      1019: 1
      1021: q+1
      1023: 1
      1025: q+1
      1026: 1
      1029: 1
      1031: 2q+1
      1033: q+1
      1035: 1
      1037: q+1
      1039: 1
      1040: 1
      1043: q+1
      1045: 1
      1046: q
      1047: q+1
      1049: 1
      1051: q+1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1061: q+1
      1063: 2q+1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1092: q+1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: q+1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1167: q+1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: q+1
      1189: q
      1192: q+1
      1195: q+1
      1200: 1
      1205: q+1
      1207: q+1
      1215: 1
      1217: 1
      1218: 1
      1223: 1
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 1
      1258: 1
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1271: 1
      1273: q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1296: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1338: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1416: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1449: 1
      1451: 1
      1454: 1
      1457: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: q+1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1487: 1
      1495: 1
      1508: 1
      1519: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1635: 1
      1662: 1
      1664: 1
      1665: 1
      1694: 1
      1705: 1
      1716: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1875: 1

1876:    0: 7q^2+2q+1
         1: 7q^2+2q+1
         2: 3q^3+4q^2+2q+1
         3: 7q^2+2q+1
         4: 2q^3+5q^2+2q+1
         5: 7q^2+2q+1
         6: 2q^3+5q^2+2q+1
         7: q^4+3q^3+3q^2+2q+1
         8: 3q^3+4q^2+2q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 7q^2+2q+1
        11: 7q^2+2q+1
        12: 2q^3+5q^2+2q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 7q^2+2q+1
        17: 7q^2+2q+1
        18: q^4+3q^3+3q^2+2q+1
        19: 5q^2+2q+1
        20: 5q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 7q^2+2q+1
        23: 7q^2+2q+1
        24: 3q^3+4q^2+2q+1
        25: 7q^2+2q+1
        26: 7q^2+2q+1
        27: 3q^3+4q^2+2q+1
        28: 7q^2+2q+1
        29: 5q^2+2q+1
        30: 3q^2+2q+1
        31: 7q^2+2q+1
        32: 4q^2+2q+1
        33: 7q^2+2q+1
        34: 7q^2+2q+1
        35: 4q^2+2q+1
        36: 7q^2+2q+1
        37: 2q^2
        38: 5q^2+2q+1
        39: 2q^2
        40: 5q^2+2q+1
        41: q^3+q^2
        42: 2q^3+3q^2+2q+1
        43: 4q^2+2q+1
        44: q^3+3q^2+2q+1
        45: 4q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 5q^2+2q+1
        50: 5q^2+2q+1
        51: 2q^3+3q^2+2q+1
        52: 5q^2+2q+1
        53: 5q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: 5q^2+2q+1
        56: 5q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: 4q^2+2q+1
        59: 3q^2
        60: 3q^2
        61: 4q^2+2q+1
        62: 2q^2
        63: 5q^2+2q+1
        64: q^2
        65: 3q^2+2q+1
        66: 2q^2
        67: 5q^2+2q+1
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^2+2q+1
        71: 5q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        75: 3q^2+2q+1
        77: 3q^2+2q+1
        79: q^3+2q^2+2q+1
        80: 4q^2+2q+1
        81: 4q^2+2q+1
        82: 5q^2+2q+1
        83: 3q^2+2q+1
        84: 4q^2+2q+1
        85: 4q^2+2q+1
        86: 5q^2+2q+1
        87: 3q^2+2q+1
        88: 4q^2+2q+1
        89: 4q^2+2q+1
        90: q^3+3q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 5q^2+2q+1
        95: 5q^2+2q+1
        96: 2q^3+3q^2+2q+1
        97: 5q^2+2q+1
        98: 5q^2+2q+1
        99: 2q^3+3q^2+2q+1
       100: 5q^2+2q+1
       101: 5q^2+2q+1
       102: 2q^3+3q^2+2q+1
       103: q^2
       104: 2q^2
       105: 3q^2+2q+1
       106: q^2
       107: q^2
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: q^2
       112: q^2+2q+1
       114: 3q^2+2q+1
       116: 2q^2+2q+1
       117: q^2+2q+1
       120: q^2+2q+1
       121: q^2
       122: 3q^2+2q+1
       123: q^2
       124: 3q^2+2q+1
       125: q^2+2q+1
       126: 3q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 4q^2+2q+1
       138: 3q^2+2q+1
       139: 5q^2+2q+1
       140: 3q^2+2q+1
       141: 3q^2+2q+1
       142: 3q^2+2q+1
       143: 4q^2+2q+1
       144: 3q^2+2q+1
       145: 5q^2+2q+1
       146: 3q^2+2q+1
       147: 3q^2+2q+1
       148: 3q^2+2q+1
       149: 5q^2+2q+1
       150: 3q^2+2q+1
       152: 3q^2+2q+1
       154: 3q^2+2q+1
       156: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 5q^2+2q+1
       167: 5q^2+2q+1
       168: 2q^3+3q^2+2q+1
       171: q^2+2q+1
       175: q^2+2q+1
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       184: 2q+1
       185: 2q+1
       188: 2q+1
       190: 2q^2+2q+1
       191: q^2+2q+1
       193: q^2
       194: 2q^2+2q+1
       195: 2q^2+2q+1
       196: q^2
       198: q^2+2q+1
       200: q^2+2q+1
       201: q^2
       202: 2q^2+2q+1
       203: 2q^2+2q+1
       204: q^2
       206: q^2+2q+1
       207: q^2
       208: 3q^2+2q+1
       210: 3q^2+2q+1
       212: 2q^2+2q+1
       214: q^2+q+1
       216: q^2+q+1
       218: q^2+q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 3q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: 5q^2+2q+1
       244: 3q^2+2q+1
       245: 3q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       261: q^2+2q+1
       265: 2q+1
       270: q^2+2q+1
       272: q^2+2q+1
       277: q^2+2q+1
       280: q+1
       282: q^2+q+1
       284: 2q+1
       285: 2q+1
       288: 2q^2+2q+1
       290: q+1
       292: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       300: 2q+1
       302: q^2+2q+1
       303: 2q+1
       306: 2q+1
       308: 2q+1
       309: 2q+1
       312: q^2+2q+1
       314: 2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: q^2
       320: 2q^2+2q+1
       321: 2q^2+2q+1
       322: q^2
       324: q^2+2q+1
       326: 2q^2+2q+1
       328: q^2+q+1
       330: q^2+q+1
       332: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       361: q^2+q+1
       363: q^2+q+1
       365: q^2+q+1
       366: 3q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       379: 2q+1
       383: q+1
       387: 2q+1
       392: q^2+2q+1
       395: 2q+1
       398: q^2+2q+1
       402: 2q+1
       408: q^2+2q+1
       410: q+1
       412: q^2+q+1
       414: q+1
       416: q+1
       418: q+1
       420: 2q+1
       421: 2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       430: 2q+1
       431: 2q+1
       434: 2q+1
       436: q+1
       438: 2q+1
       439: 2q+1
       442: 2q+1
       443: q
       444: q^2+3q+1
       446: q^2+4q+1
       448: 2q+1
       449: 2q+1
       452: 2q+1
       454: 2q+1
       456: q+1
       457: 2q+1
       460: 2q+1
       461: q^2+3q+1
       462: q
       464: q^2+4q+1
       466: q+1
       468: q^2+q+1
       470: 2q^2+2q+1
       472: 2q+1
       473: 2q+1
       476: 2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       503: q^2+q+1
       505: q^2+q+1
       507: q^2+q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       523: q+1
       527: q+1
       531: 2q+1
       535: 2q+1
       540: q+1
       544: 2q+1
       546: q
       548: q^2+3q+1
       550: 2q+1
       554: q+1
       558: 2q+1
       562: q^2+3q+1
       564: q
       567: 2q+1
       572: q^2+2q+1
       573: q
       575: q
       576: q^2+2q+1
       578: 2q
       581: q^2+2q+1
       584: q+1
       586: 1
       588: q+1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       598: q+1
       600: 2q+1
       602: q+1
       604: 2q+1
       606: q+1
       607: 2q+1
       610: 2q+1
       612: q+1
       614: 2q+1
       616: q+1
       618: 2q+1
       620: 2q+1
       621: 2q+1
       624: q+1
       626: 2q+1
       628: q+1
       630: 2q+1
       631: q+1
       634: 2q+1
       636: q+1
       638: q^2+q+1
       640: q+1
       642: 2q+1
       643: 2q+1
       646: 2q+1
       648: 2q+1
       649: 2q+1
       652: q+1
       654: 2q+1
       655: q
       656: q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q
       700: q^2+2q+1
       701: q
       707: q+1
       711: 1
       714: q+1
       719: q+1
       724: q+1
       728: 2q+1
       732: q+1
       736: q+1
       738: q+1
       742: 2q+1
       746: q+1
       750: q+1
       755: 2q+1
       760: q+1
       764: 2q+1
       767: q+1
       770: q
       773: q+1
       776: q+1
       778: 1
       780: q+1
       782: 1
       784: q+1
       786: 1
       787: 1
       790: q+1
       792: 1
       794: q+1
       796: 2q+1
       798: 1
       800: q+1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       810: q+1
       812: 2q+1
       814: 2q+1
       816: q+1
       817: q+1
       820: 2q+1
       822: 1
       824: q+1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       834: q+1
       836: 2q+1
       838: 2q+1
       839: q+1
       842: q+1
       843: q
       844: q+1
       846: 2q+1
       847: 2q+1
       850: q+1
       852: 2q+1
       854: q+1
       856: 2q+1
       857: q
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: q+1
       919: q+1
       923: 1
       925: q+1
       931: q+1
       935: q+1
       937: q+1
       941: q+1
       945: 1
       949: q+1
       954: q+1
       957: q+1
       963: q+1
       966: q+1
       969: q
       972: q+1
       977: 2q+1
       981: q+1
       983: q
       986: q+1
       990: q+1
       993: q+1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1017: q+1
      1019: 1
      1021: q+1
      1023: 1
      1025: q+1
      1027: 1
      1028: 1
      1031: 2q+1
      1032: q+1
      1035: 1
      1037: q+1
      1039: 1
      1041: 1
      1043: q+1
      1044: 1
      1046: q
      1047: q+1
      1049: 1
      1051: q+1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1061: q+1
      1063: 2q+1
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1093: q+1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: q+1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1165: q+1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: q+1
      1189: q
      1192: q+1
      1196: q+1
      1201: 1
      1203: q+1
      1209: q+1
      1215: 1
      1216: 1
      1219: 1
      1223: 1
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 1
      1259: 1
      1260: 1
      1265: 1
      1267: 1
      1269: 1
      1270: 1
      1273: q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1297: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1338: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1417: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1449: 1
      1450: 1
      1455: 1
      1457: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: q+1
      1477: 1
      1478: 1
      1481: 1
      1483: 1
      1487: 1
      1496: 1
      1507: 1
      1520: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1635: 1
      1662: 1
      1663: 1
      1666: 1
      1693: 1
      1706: 1
      1717: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1876: 1

1877:    0: 7q^2+2q+1
         1: 7q^2+2q+1
         2: 3q^3+4q^2+2q+1
         3: 7q^2+2q+1
         4: 2q^3+5q^2+2q+1
         5: 7q^2+2q+1
         6: 2q^3+5q^2+2q+1
         7: q^4+3q^3+3q^2+2q+1
         8: 3q^3+4q^2+2q+1
         9: q^4+3q^3+3q^2+2q+1
        10: 7q^2+2q+1
        11: 7q^2+2q+1
        12: 2q^3+5q^2+2q+1
        13: 4q^2+2q+1
        14: q^3+3q^2+2q+1
        15: 4q^2+2q+1
        16: 7q^2+2q+1
        17: 7q^2+2q+1
        18: q^4+3q^3+3q^2+2q+1
        19: 5q^2+2q+1
        20: 5q^2+2q+1
        21: 2q^3+3q^2+2q+1
        22: 7q^2+2q+1
        23: 7q^2+2q+1
        24: 3q^3+4q^2+2q+1
        25: 7q^2+2q+1
        26: 7q^2+2q+1
        27: 3q^3+4q^2+2q+1
        28: 7q^2+2q+1
        29: 5q^2+2q+1
        30: 3q^2+2q+1
        31: 7q^2+2q+1
        32: 4q^2+2q+1
        33: 7q^2+2q+1
        34: 7q^2+2q+1
        35: 4q^2+2q+1
        36: 7q^2+2q+1
        37: 5q^2+2q+1
        38: 2q^2
        39: 5q^2+2q+1
        40: 2q^2
        41: 2q^3+3q^2+2q+1
        42: q^3+q^2
        43: 4q^2+2q+1
        44: q^3+3q^2+2q+1
        45: 4q^2+2q+1
        46: 4q^2+2q+1
        47: 4q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 5q^2+2q+1
        50: 5q^2+2q+1
        51: 2q^3+3q^2+2q+1
        52: 5q^2+2q+1
        53: 5q^2+2q+1
        54: 2q^3+3q^2+2q+1
        55: 5q^2+2q+1
        56: 5q^2+2q+1
        57: 2q^3+3q^2+2q+1
        58: 3q^2
        59: 4q^2+2q+1
        60: 3q^2
        61: 4q^2+2q+1
        62: 5q^2+2q+1
        63: 2q^2
        64: 3q^2+2q+1
        65: q^2
        66: 5q^2+2q+1
        67: 2q^2
        68: q^2+2q+1
        69: 3q^2+2q+1
        70: 3q^2+2q+1
        71: 5q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        74: 3q^2+2q+1
        76: 3q^2+2q+1
        78: q^3+2q^2+2q+1
        80: 4q^2+2q+1
        81: 4q^2+2q+1
        82: 5q^2+2q+1
        83: 3q^2+2q+1
        84: 4q^2+2q+1
        85: 4q^2+2q+1
        86: 5q^2+2q+1
        87: 3q^2+2q+1
        88: 4q^2+2q+1
        89: 4q^2+2q+1
        90: q^3+3q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 5q^2+2q+1
        95: 5q^2+2q+1
        96: 2q^3+3q^2+2q+1
        97: 5q^2+2q+1
        98: 5q^2+2q+1
        99: 2q^3+3q^2+2q+1
       100: 5q^2+2q+1
       101: 5q^2+2q+1
       102: 2q^3+3q^2+2q+1
       103: 2q^2
       104: q^2
       105: q^2
       106: 3q^2+2q+1
       107: q^2
       108: 2q^2+2q+1
       109: q^2
       110: 2q^2+2q+1
       111: q^2+2q+1
       113: 3q^2+2q+1
       115: 2q^2+2q+1
       118: q^2+2q+1
       120: q^2+2q+1
       121: 3q^2+2q+1
       122: q^2
       123: 3q^2+2q+1
       124: q^2
       125: q^2+2q+1
       126: 3q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: 2q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 4q^2+2q+1
       138: 3q^2+2q+1
       139: 5q^2+2q+1
       140: 3q^2+2q+1
       141: 3q^2+2q+1
       142: 3q^2+2q+1
       143: 4q^2+2q+1
       144: 3q^2+2q+1
       145: 5q^2+2q+1
       146: 3q^2+2q+1
       147: 3q^2+2q+1
       148: 3q^2+2q+1
       149: 5q^2+2q+1
       150: 3q^2+2q+1
       151: 3q^2+2q+1
       153: 3q^2+2q+1
       155: q^3+2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 5q^2+2q+1
       167: 5q^2+2q+1
       168: 2q^3+3q^2+2q+1
       172: q^2+2q+1
       176: q^2+2q+1
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       184: 2q+1
       186: 2q+1
       187: 2q+1
       189: 2q^2+2q+1
       192: q^2+2q+1
       193: q^2
       194: 2q^2+2q+1
       195: q^2
       196: 2q^2+2q+1
       197: q^2+2q+1
       200: q^2+2q+1
       201: q^2
       202: 2q^2+2q+1
       203: q^2
       204: 2q^2+2q+1
       205: q^2+2q+1
       207: 3q^2+2q+1
       208: q^2
       209: 3q^2+2q+1
       211: 2q^2+2q+1
       213: q^2+q+1
       215: q^2+q+1
       217: q^2+q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 3q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 3q^2+2q+1
       232: 2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: 5q^2+2q+1
       244: 3q^2+2q+1
       245: 3q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       262: q^2+2q+1
       266: 2q+1
       269: q^2+2q+1
       273: q^2+2q+1
       278: q^2+2q+1
       279: q+1
       281: q^2+q+1
       284: 2q+1
       286: 2q+1
       287: 2q^2+2q+1
       289: q+1
       291: 2q+1
       294: 2q+1
       296: 2q+1
       297: 2q+1
       300: 2q+1
       301: q^2+2q+1
       304: 2q+1
       305: 2q+1
       308: 2q+1
       310: 2q+1
       311: q^2+2q+1
       313: 2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: q^2
       320: 2q^2+2q+1
       321: q^2
       322: 2q^2+2q+1
       323: q^2+2q+1
       325: 2q^2+2q+1
       327: q^2+q+1
       329: q^2+q+1
       331: q^2+q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q^2+4q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+4q+1
       360: q^2+q+1
       362: q^2+q+1
       364: q^2+q+1
       366: 3q^2+2q+1
       367: 2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       380: 2q+1
       384: q+1
       388: 2q+1
       391: q^2+2q+1
       396: 2q+1
       399: q^2+2q+1
       404: 2q+1
       406: q^2+2q+1
       409: q+1
       411: q^2+q+1
       413: q+1
       415: q+1
       417: q+1
       420: 2q+1
       422: 2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       430: 2q+1
       432: 2q+1
       433: 2q+1
       435: q+1
       438: 2q+1
       440: 2q+1
       441: 2q+1
       443: q
       444: q^2+3q+1
       445: q^2+4q+1
       448: 2q+1
       450: 2q+1
       451: 2q+1
       454: 2q+1
       455: q+1
       458: 2q+1
       459: 2q+1
       461: q
       462: q^2+3q+1
       463: q^2+4q+1
       465: q+1
       467: q^2+q+1
       469: 2q^2+2q+1
       472: 2q+1
       474: 2q+1
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: q+1
       482: q+1
       483: 2q+1
       484: q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: 2q+1
       501: 2q+1
       502: q^2+q+1
       504: q^2+q+1
       506: q^2+q+1
       508: 2q+1
       509: 2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       524: q+1
       528: q+1
       532: 2q+1
       536: 2q+1
       539: q+1
       543: 2q+1
       545: q
       547: q^2+3q+1
       552: 2q+1
       555: q+1
       559: 2q+1
       561: q
       563: q^2+3q+1
       568: 2q+1
       570: q^2+2q+1
       574: q
       575: q^2+2q+1
       576: q
       577: q^2+2q+1
       580: 2q
       583: q+1
       585: 1
       587: q+1
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: q+1
       599: 2q+1
       601: q+1
       604: 2q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       613: 2q+1
       616: q+1
       617: 2q+1
       620: 2q+1
       622: 2q+1
       623: q+1
       625: 2q+1
       627: q+1
       629: 2q+1
       632: q+1
       633: 2q+1
       635: q+1
       637: q^2+q+1
       639: q+1
       642: 2q+1
       644: 2q+1
       645: 2q+1
       648: 2q+1
       650: 2q+1
       651: q+1
       653: 2q+1
       655: q+1
       656: q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: q+1
       676: q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q^2+2q+1
       698: q
       708: q+1
       712: 1
       716: q+1
       720: q+1
       723: q+1
       727: 2q+1
       731: q+1
       735: q+1
       739: q+1
       743: 2q+1
       747: q+1
       751: q+1
       756: 2q+1
       758: q+1
       762: 2q+1
       768: q+1
       769: q+1
       772: q
       775: q+1
       777: 1
       779: q+1
       781: 1
       783: q+1
       786: 1
       788: 1
       789: q+1
       791: 1
       794: q+1
       795: 2q+1
       797: 1
       799: q+1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: q+1
       811: 2q+1
       813: 2q+1
       816: q+1
       818: q+1
       819: 2q+1
       821: 1
       823: q+1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: q+1
       835: 2q+1
       837: 2q+1
       840: q+1
       841: q+1
       843: q+1
       844: q
       846: 2q+1
       848: 2q+1
       849: q+1
       851: 2q+1
       853: q+1
       855: 2q+1
       857: q+1
       858: q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: 2q+1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       878: q+1
       879: 2q+1
       880: q+1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: q+1
       918: q+1
       922: 1
       927: q+1
       930: q+1
       934: q+1
       938: q+1
       942: q+1
       946: 1
       950: q+1
       955: q+1
       958: q+1
       961: q+1
       967: q+1
       968: q+1
       971: q
       975: 2q+1
       979: q+1
       982: q+1
       985: q
       991: q+1
       992: q+1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1017: q+1
      1018: 1
      1020: q+1
      1022: 1
      1024: q+1
      1027: 1
      1029: 1
      1030: 2q+1
      1033: q+1
      1034: 1
      1036: q+1
      1038: 1
      1041: 1
      1042: q+1
      1045: 1
      1046: q+1
      1047: q
      1048: 1
      1050: q+1
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: q+1
      1062: 2q+1
      1064: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1091: q+1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: q+1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: q+1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: q+1
      1188: q+1
      1191: q
      1197: q+1
      1199: 1
      1204: q+1
      1208: q+1
      1214: 1
      1217: 1
      1219: 1
      1222: 1
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1271: 1
      1272: q+1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1295: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1334: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1448: 1
      1451: 1
      1455: 1
      1456: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: q+1
      1477: 1
      1479: 1
      1480: 1
      1482: 1
      1487: 1
      1494: 1
      1506: 1
      1518: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1661: 1
      1664: 1
      1666: 1
      1692: 1
      1704: 1
      1718: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1877: 1

1878:    0: q^5+q^4+2q^3+q
         1: q^5+q^4+2q^3+q
         2: 2q^4+q^3+q
         3: q^5+q^4+2q^3+q
         4: q^4+q^3+q
         5: q^5+q^4+2q^3+q
         6: q^4+q^3+q
         7: q^5+2q^4+q^3+q
         8: 2q^4+q^3+q
         9: q^5+2q^4+q^3+q
        10: q^5+q^4+2q^3+q
        11: q^5+q^4+2q^3+q
        12: q^4+q^3+q
        13: q^4+q^3+q
        14: q^4+q^3+q
        15: q^4+q^3+q
        16: q^5+q^4+2q^3+q
        17: q^5+q^4+2q^3+q
        18: q^5+2q^4+q^3+q
        19: q^3+q
        20: q^3+q
        21: q^4+q^3+q
        22: q^5+q^4+2q^3+q
        23: q^5+q^4+2q^3+q
        24: 2q^4+q^3+q
        25: q^5+q^4+2q^3+q
        26: q^5+q^4+2q^3+q
        27: 2q^4+q^3+q
        28: q^5+q^4+2q^3+q
        29: q^3+q
        30: q^3+q
        31: q^5+q^4+2q^3+q
        32: q^4+q^3+q
        33: q^5+q^4+2q^3+q
        34: q^5+q^4+2q^3+q
        35: q^4+q^3+q
        36: q^5+q^4+2q^3+q
        38: q^5+q^4+2q^3+q
        40: q^5+q^4+2q^3+q
        42: 2q^4+q^3+q
        43: q^4+q^3+q
        44: q^4+q^3+q
        45: q^4+q^3+q
        46: q^4+q^3+q
        47: q^4+q^3+q
        48: q^4+q^3+q
        49: q^3+q
        50: q^3+q
        51: q^4+q^3+q
        52: q^3+q
        53: q^3+q
        54: q^4+q^3+q
        55: q^3+q
        56: q^3+q
        57: q^4+q^3+q
        58: q^3
        59: q^5+q^4+q^3+q
        60: q^5+q^4+q^3+q
        61: q^3
        63: q^5+q^4+2q^3+q
        65: q^4+q^3+q
        67: q^5+q^4+2q^3+q
        68: q^4+q
        69: q^3+q
        70: q^3+q
        71: q^3+q
        72: q
        73: q
        75: q^3+q
        77: q^3+q
        79: q^4+q^3+q
        80: q^4+q^3+q
        81: q^4+q^3+q
        82: q^3+q
        83: q^3+q
        84: q^4+q^3+q
        85: q^4+q^3+q
        86: q^3+q
        87: q^3+q
        88: q^4+q^3+q
        89: q^4+q^3+q
        90: q^4+q^3+q
        91: q^3+q
        92: q
        93: q^3+q
        94: q^3+q
        95: q^3+q
        96: q^4+q^3+q
        97: q^3+q
        98: q^3+q
        99: q^4+q^3+q
       100: q^3+q
       101: q^3+q
       102: q^4+q^3+q
       104: q^5+q^4+q^3+q
       105: q^3
       107: q
       110: q
       112: q
       114: q^3+q
       116: q^3+q
       118: q^4+q
       119: q^4+q
       122: q^4+q^3+q
       124: q^4+q^3+q
       125: q^4+q
       126: q^3+q
       128: q^3+q
       130: q^3+q
       132: q^4+q^3+q
       133: q
       134: q^3+q
       135: q
       136: q
       137: q^4+q^3+q
       138: q^3+q
       139: q^3+q
       140: q
       141: q^3+q
       142: q
       143: q^4+q^3+q
       144: q^3+q
       145: q^3+q
       146: q^3+q
       147: q
       148: q
       149: q^3+q
       150: q^3+q
       152: q^3+q
       154: q^3+q
       156: q^4+q^3+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^3+q
       161: q
       162: q^3+q
       163: q^3+q
       164: q
       165: q^3+q
       166: q^3+q
       167: q^3+q
       168: q^4+q^3+q
       170: q
       174: q^4+q
       178: q^3+q
       180: q^3+q
       182: q
       183: q
       186: q
       188: q
       190: q^3+q
       192: q^4+q
       193: q
       196: q
       198: q
       199: q^4+q
       201: q
       204: q
       206: q
       208: q^4+q^3+q
       210: q^3+q
       212: q^3+q
       214: q^3+q
       216: q
       218: q^3+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q
       224: q
       225: q
       226: q^3+q
       227: q
       228: q^3+q
       229: q
       230: q
       231: q^3+q
       232: q
       233: q^3+q
       234: q
       235: q
       236: q^3+q
       238: q^3+q
       240: q^3+q
       242: q^4+q^3+q
       243: q^3+q
       244: q
       245: q
       246: q^3+q
       247: q
       248: q
       249: q^4+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^3+q
       257: q
       258: q^3+q
       260: q
       264: q
       268: q
       274: q
       276: q^4+q
       280: q
       282: q^3+q
       283: q
       286: q
       288: q^3+q
       290: q
       292: q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q^3+q
       318: q^3+q
       319: q
       322: q
       324: q
       326: q^3+q
       328: q^3+q
       330: q
       332: q^3+q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q
       343: q^4+q
       344: q
       345: q
       346: q^3+q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q^3+q
       355: q
       356: q
       357: q
       358: q
       359: q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q
       367: q
       368: q^3+q
       369: q
       370: q
       374: q^3+q
       375: q
       376: q^3+q
       378: q
       382: q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q
       412: q^3+q
       414: q
       416: q
       418: q
       419: q
       422: q
       424: q
       426: q
       428: q
       429: q
       432: q
       434: q
       436: q
       437: q
       440: q
       442: q
       443: q
       446: q
       447: q
       450: q
       452: q
       453: q
       456: q
       458: q
       460: q
       462: q
       464: q
       466: q
       468: q^3+q
       470: q^3+q
       471: q
       474: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q
       497: q
       498: q
       499: q
       500: q
       503: q^3+q
       505: q
       507: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       522: q
       526: q
       530: q
       534: q
       538: q
       542: q
       546: q
       551: q
       556: q
       560: q
       564: q
       566: q
       571: q
       574: q
       581: q
       584: q
       586: q
       588: q
       589: q
       592: q
       593: q
       596: q
       600: q
       603: q
       606: q
       608: q
       610: q
       612: q
       614: q
       619: q
       622: q
       624: q
       626: q
       628: q
       630: q
       636: q
       638: q^3+q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: q
       654: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q
       699: q
       706: q
       710: q
       715: q
       718: q
       722: q
       726: q
       730: q
       740: q
       744: q
       748: q
       754: q
       759: q
       763: q
       778: q
       798: q
       800: q
       801: q
       804: q
       805: q
       808: q
       812: q
       822: q
       824: q
       825: q
       828: q
       829: q
       832: q
       836: q
       842: q
       845: q
       848: q
       850: q
       852: q
       854: q
       856: q
       877: q
       878: q
       879: q
       897: q
       913: q
       921: q
       926: q
       929: q
       939: q
       947: q
       951: q
       953: q
       962: q
       976: q
       980: q
      1011: 1
      1019: q
      1035: q
      1049: q
      1051: q
      1052: q
      1055: q
      1056: q
      1059: q
      1063: q
      1128: 1
      1143: 1
      1149: q
      1171: q
      1186: q
      1200: q
      1205: q
      1207: q
      1223: 1
      1265: q
      1279: 1
      1300: 1
      1324: 1
      1339: 1
      1363: 1
      1394: 1
      1416: q
      1435: 1
      1481: 1
      1499: 1
      1512: 1
      1523: 1
      1574: 1
      1593: 1
      1620: 1
      1636: 1
      1698: 1
      1709: 1
      1719: 1
      1794: 1
      1878: 1

1879:    0: 4q^4+22q^3+10q^2+3q
         1: 4q^4+22q^3+10q^2+3q
         2: 9q^4+15q^3+9q^2+3q
         3: 4q^4+22q^3+10q^2+3q
         4: q^5+10q^4+16q^3+9q^2+3q
         5: 4q^4+22q^3+10q^2+3q
         6: q^5+10q^4+16q^3+9q^2+3q
         7: 3q^5+10q^4+12q^3+8q^2+3q
         8: 9q^4+15q^3+9q^2+3q
         9: q^6+4q^5+8q^4+9q^3+6q^2+2q
        10: 4q^4+22q^3+10q^2+3q
        11: 4q^4+22q^3+10q^2+3q
        12: q^5+10q^4+16q^3+9q^2+3q
        13: q^4+14q^3+9q^2+3q
        14: 5q^4+11q^3+8q^2+3q
        15: q^4+14q^3+9q^2+3q
        16: 18q^3+9q^2+3q
        17: 18q^3+9q^2+3q
        18: 2q^5+6q^4+8q^3+6q^2+2q
        19: 3q^4+15q^3+9q^2+3q
        20: 3q^4+15q^3+9q^2+3q
        21: 6q^4+11q^3+8q^2+3q
        22: 4q^4+22q^3+10q^2+3q
        23: 4q^4+22q^3+10q^2+3q
        24: 9q^4+15q^3+9q^2+3q
        25: 4q^4+22q^3+10q^2+3q
        26: 4q^4+22q^3+10q^2+3q
        27: 9q^4+15q^3+9q^2+3q
        28: 18q^3+9q^2+3q
        29: 3q^4+15q^3+9q^2+3q
        30: q^4+10q^3+8q^2+3q
        31: 4q^4+22q^3+10q^2+3q
        32: q^4+14q^3+9q^2+3q
        33: 18q^3+9q^2+3q
        34: 4q^4+22q^3+10q^2+3q
        35: q^4+14q^3+9q^2+3q
        36: 18q^3+9q^2+3q
        37: q^4+10q^3+3q^2+q
        38: 3q^4+12q^3+7q^2+2q
        39: q^4+10q^3+3q^2+q
        40: 3q^4+12q^3+7q^2+2q
        41: 4q^4+6q^3+3q^2+q
        42: 5q^4+9q^3+6q^2+2q
        43: q^4+14q^3+9q^2+3q
        44: 5q^4+11q^3+8q^2+3q
        45: q^4+14q^3+9q^2+3q
        46: 10q^3+8q^2+3q
        47: 10q^3+8q^2+3q
        48: 3q^4+7q^3+6q^2+2q
        49: 11q^3+8q^2+3q
        50: 11q^3+8q^2+3q
        51: 3q^4+7q^3+6q^2+2q
        52: 3q^4+15q^3+9q^2+3q
        53: 3q^4+15q^3+9q^2+3q
        54: 6q^4+11q^3+8q^2+3q
        55: 3q^4+15q^3+9q^2+3q
        56: 3q^4+15q^3+9q^2+3q
        57: 6q^4+11q^3+8q^2+3q
        58: 8q^3+3q^2+q
        59: 10q^3+6q^2+2q
        60: 8q^3+3q^2+q
        61: 10q^3+6q^2+2q
        62: q^4+10q^3+3q^2+q
        63: 3q^4+12q^3+7q^2+2q
        64: 6q^3+3q^2+q
        65: q^4+8q^3+6q^2+2q
        66: 8q^3+3q^2+q
        67: 10q^3+6q^2+2q
        68: 3q^3+7q^2+3q
        69: 4q^3+5q^2+2q
        70: q^4+10q^3+8q^2+3q
        71: 11q^3+8q^2+3q
        72: 6q^3+7q^2+3q
        73: 6q^3+7q^2+3q
        74: 3q^3+2q^2+q
        75: 2q^4+5q^3+6q^2+2q
        76: 3q^3+2q^2+q
        77: 2q^4+5q^3+6q^2+2q
        78: q^4+2q^3+2q^2+q
        79: 2q^4+5q^3+5q^2+2q
        80: q^4+14q^3+9q^2+3q
        81: 10q^3+8q^2+3q
        82: 3q^4+15q^3+9q^2+3q
        83: q^4+10q^3+8q^2+3q
        84: q^4+14q^3+9q^2+3q
        85: 10q^3+8q^2+3q
        86: 3q^4+15q^3+9q^2+3q
        87: q^4+10q^3+8q^2+3q
        88: 10q^3+8q^2+3q
        89: 10q^3+8q^2+3q
        90: 3q^4+7q^3+6q^2+2q
        91: 4q^3+7q^2+3q
        92: 4q^3+7q^2+3q
        93: 4q^3+6q^2+2q
        94: 11q^3+8q^2+3q
        95: 11q^3+8q^2+3q
        96: 3q^4+7q^3+6q^2+2q
        97: 11q^3+8q^2+3q
        98: 11q^3+8q^2+3q
        99: 3q^4+7q^3+6q^2+2q
       100: 3q^4+15q^3+9q^2+3q
       101: 3q^4+15q^3+9q^2+3q
       102: 6q^4+11q^3+8q^2+3q
       103: 3q^3
       104: 5q^3+3q^2+q
       105: 5q^3+3q^2+q
       106: 5q^3+3q^2+q
       107: 2q^3+2q^2+q
       108: 4q^3+5q^2+2q
       109: 2q^3+2q^2+q
       110: 4q^3+5q^2+2q
       111: q^3+2q^2+q
       112: 4q^2+2q
       113: 3q^3+2q^2+q
       114: 2q^4+5q^3+6q^2+2q
       115: 2q^3+2q^2+q
       116: q^4+4q^3+5q^2+2q
       117: q^3+2q^2+q
       118: 2q^3+5q^2+2q
       119: q^3+2q^2+q
       120: 2q^3+5q^2+2q
       121: 6q^3+3q^2+q
       122: q^4+8q^3+6q^2+2q
       123: 4q^3+3q^2+q
       124: 6q^3+5q^2+2q
       125: 3q^3+7q^2+3q
       126: 4q^3+5q^2+2q
       128: 3q^3+3q^2+2q
       130: 3q^3+3q^2+2q
       132: 2q^3+3q^2+q
       133: 6q^2+3q
       134: 2q^3+5q^2+2q
       135: 2q^3+6q^2+3q
       136: 2q^3+6q^2+3q
       137: 10q^3+8q^2+3q
       138: 4q^3+5q^2+2q
       139: 11q^3+8q^2+3q
       140: 6q^3+7q^2+3q
       141: q^4+10q^3+8q^2+3q
       142: 6q^3+7q^2+3q
       143: 10q^3+8q^2+3q
       144: 4q^3+5q^2+2q
       145: 11q^3+8q^2+3q
       146: q^4+10q^3+8q^2+3q
       147: 6q^3+7q^2+3q
       148: 6q^3+7q^2+3q
       149: 3q^4+15q^3+9q^2+3q
       150: q^4+10q^3+8q^2+3q
       151: 3q^3+2q^2+q
       152: 2q^4+5q^3+6q^2+2q
       153: 3q^3+2q^2+q
       154: 2q^4+5q^3+6q^2+2q
       155: q^4+2q^3+2q^2+q
       156: 2q^4+5q^3+5q^2+2q
       157: 4q^3+7q^2+3q
       158: 4q^3+7q^2+3q
       159: 4q^3+6q^2+2q
       160: 4q^3+7q^2+3q
       161: 4q^3+7q^2+3q
       162: 4q^3+6q^2+2q
       163: 4q^3+7q^2+3q
       164: 4q^3+7q^2+3q
       165: 4q^3+6q^2+2q
       166: 11q^3+8q^2+3q
       167: 11q^3+8q^2+3q
       168: 3q^4+7q^3+6q^2+2q
       170: 2q^2+q
       171: 2q^2+q
       172: q^3+2q^2+q
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       176: q^3+3q^2+q
       178: q^3+2q^2+q
       180: 3q^3+3q^2+2q
       182: 2q^2+2q
       183: q^2+q
       184: 4q^2+2q
       185: q^2+q
       186: 4q^2+2q
       187: 2q^2+q
       188: 3q^2+2q
       189: 2q^3+2q^2+q
       190: q^4+4q^3+5q^2+2q
       191: q^3+2q^2+q
       192: 2q^3+5q^2+2q
       193: 2q^3+2q^2+q
       194: 4q^3+5q^2+2q
       195: 2q^3+2q^2+q
       196: 4q^3+5q^2+2q
       197: q^3+2q^2+q
       198: 4q^2+2q
       199: q^3+2q^2+q
       200: 2q^3+5q^2+2q
       201: 2q^3+2q^2+q
       202: 4q^3+5q^2+2q
       203: 2q^3+2q^2+q
       204: 4q^3+5q^2+2q
       205: q^3+2q^2+q
       206: 4q^2+2q
       207: 4q^3+3q^2+q
       208: 6q^3+5q^2+2q
       209: 3q^3+2q^2+q
       210: 2q^4+5q^3+6q^2+2q
       211: 2q^3+2q^2+q
       212: q^4+4q^3+5q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 4q^2+2q
       220: 6q^2+3q
       221: 2q^3+5q^2+2q
       222: 2q^3+6q^2+3q
       223: q^3+4q^2+2q
       224: 2q^3+6q^2+3q
       225: q^3+4q^2+2q
       226: 4q^3+5q^2+2q
       227: 6q^2+3q
       228: 2q^3+5q^2+2q
       229: 2q^3+6q^2+3q
       230: 2q^3+6q^2+3q
       231: 4q^3+5q^2+2q
       232: 6q^2+3q
       233: 2q^3+5q^2+2q
       234: 2q^3+6q^2+3q
       235: 2q^3+6q^2+3q
       236: 4q^3+5q^2+2q
       238: 3q^3+3q^2+2q
       240: 3q^3+3q^2+2q
       242: 2q^3+3q^2+q
       243: 11q^3+8q^2+3q
       244: 6q^3+7q^2+3q
       245: 6q^3+7q^2+3q
       246: q^4+10q^3+8q^2+3q
       247: q^3+9q^2+4q
       248: q^3+9q^2+4q
       249: q^4+4q^3+5q^2+2q
       250: 4q^3+7q^2+3q
       251: 4q^3+7q^2+3q
       252: 4q^3+6q^2+2q
       253: 4q^3+7q^2+3q
       254: 4q^3+7q^2+3q
       255: 4q^3+6q^2+2q
       256: 4q^3+7q^2+3q
       257: 4q^3+7q^2+3q
       258: 4q^3+6q^2+2q
       260: q^2+q
       261: q^2+q
       264: q^2+q
       265: q^2+q
       266: 2q^2+q
       268: 2q^2+q
       269: q^3+2q^2+q
       270: 2q^2+q
       272: 2q^2+q
       273: q^3+2q^2+q
       274: 2q^2+q
       276: q^3+2q^2+q
       277: q^3+2q^2+q
       278: q^3+3q^2+q
       280: q^2+2q
       282: q^2+q
       284: 2q^2+q
       286: 2q^2+q
       288: q^3+2q^2+q
       290: 2q
       292: q^2+q
       293: q^2+q
       294: 4q^2+2q
       295: q^2+q
       296: 4q^2+2q
       297: 2q^2+q
       298: 3q^2+2q
       299: q^2+q
       300: 4q^2+2q
       302: 2q^2+2q
       303: q^2+q
       304: 4q^2+2q
       305: 2q^2+q
       306: 3q^2+2q
       307: q^2+q
       308: 4q^2+2q
       309: q^2+q
       310: 4q^2+2q
       312: 2q^2+2q
       313: 2q^2+q
       314: 3q^2+2q
       316: q^3+2q^2+q
       318: 3q^3+3q^2+2q
       319: 2q^3+2q^2+q
       320: 4q^3+5q^2+2q
       321: 2q^3+2q^2+q
       322: 4q^3+5q^2+2q
       323: q^3+2q^2+q
       324: 4q^2+2q
       325: 2q^3+2q^2+q
       326: q^4+4q^3+5q^2+2q
       328: q^3+q^2+2q
       330: q^3+q^2+2q
       332: 2q^2+q
       333: 4q^2+2q
       334: q^3+4q^2+2q
       335: q^3+4q^2+2q
       336: 3q^2+2q
       337: q^3+9q^2+4q
       339: 5q^2+3q
       341: 5q^2+3q
       343: 2q^3+3q^2+q
       344: 4q^2+2q
       345: 6q^2+3q
       346: 2q^3+5q^2+2q
       347: 2q^3+6q^2+3q
       348: q^3+4q^2+2q
       349: 2q^3+6q^2+3q
       350: q^3+4q^2+2q
       351: q^3+9q^2+4q
       352: 4q^2+2q
       353: 6q^2+3q
       354: 2q^3+5q^2+2q
       355: 2q^3+6q^2+3q
       356: q^3+4q^2+2q
       357: 2q^3+6q^2+3q
       358: q^3+4q^2+2q
       359: q^3+9q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 4q^3+5q^2+2q
       367: 6q^2+3q
       368: 2q^3+5q^2+2q
       369: 2q^3+6q^2+3q
       370: 2q^3+6q^2+3q
       371: 3q^2+4q
       372: 3q^2+4q
       373: q^3+3q^2+2q
       374: 4q^3+7q^2+3q
       375: 4q^3+7q^2+3q
       376: 4q^3+6q^2+2q
       382: q
       383: q
       386: q^2+q
       387: q^2+q
       388: 2q^2+q
       390: q^2+q
       392: q^2+q
       394: q^2+q
       395: q^2+q
       396: 2q^2+q
       398: q^2+q
       400: q^2+q
       402: q^2+q
       403: q^2+q
       404: 2q^2+q
       406: q^3+2q^2+q
       407: 2q^2+q
       408: 2q^2+q
       410: q^2+2q
       412: q^2+q
       414: q^2+q
       416: 2q
       418: q
       420: 2q^2+q
       422: 2q^2+q
       424: q^2+q
       426: q^2+q
       428: 5q^2+3q
       430: 2q^2+q
       432: 2q^2+q
       434: q^2+q
       436: 2q
       437: q^2+q
       438: 4q^2+2q
       439: q^2+q
       440: 4q^2+2q
       441: 2q^2+q
       442: 3q^2+2q
       443: 3q^2+q
       444: q^3+6q^2+3q
       446: 5q^2+3q
       448: 2q^2+q
       450: 2q^2+q
       452: q^2+q
       453: q^2+q
       454: 4q^2+2q
       456: 2q
       457: q^2+q
       458: 4q^2+2q
       459: 2q^2+q
       460: 3q^2+2q
       461: 3q^2+q
       462: q^3+6q^2+3q
       464: 5q^2+3q
       466: q^2+2q
       468: q^2+q
       470: q^3+2q^2+q
       471: q^2+q
       472: 4q^2+2q
       473: q^2+q
       474: 4q^2+2q
       475: 2q^2+q
       476: 3q^2+2q
       478: 2q^2+2q
       479: q^3+5q^2+2q
       480: 4q^2+2q
       481: 2q^2+2q
       482: 2q^2+2q
       483: 3q^2+2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: q^2+2q
       492: 4q^2+2q
       493: q^3+4q^2+2q
       494: q^3+4q^2+2q
       495: 3q^2+2q
       496: 3q^2+4q
       497: 4q^2+2q
       498: q^3+4q^2+2q
       499: q^3+4q^2+2q
       500: 3q^2+2q
       501: 3q^2+4q
       503: q^3+q^2+2q
       505: q^3+q^2+2q
       507: 2q^2+q
       508: 4q^2+2q
       509: 6q^2+3q
       510: 2q^3+5q^2+2q
       511: 2q^3+6q^2+3q
       512: q^3+4q^2+2q
       513: 2q^3+6q^2+3q
       514: q^3+4q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 3q^2+4q
       519: 3q^2+4q
       520: q^3+3q^2+2q
       526: q
       527: q
       538: q
       540: q
       542: q^2+q
       543: 2q^2+q
       544: q^2+q
       546: 2q^2+q
       548: 3q^2+2q
       554: q
       556: q
       558: q^2+q
       559: 2q^2+q
       560: q^2+q
       562: 2q^2+q
       564: 3q^2+2q
       566: q^2+q
       567: q^2+q
       568: 2q^2+q
       571: q^2+q
       572: q^2+q
       573: q^2
       574: 2q^2+q
       575: q^3+4q^2+2q
       576: 2q^2+q
       578: 3q^2+q
       581: 2q^2+2q
       584: q^2+q
       586: q
       588: q
       590: q^2+q
       592: q^2+q
       594: q^2+q
       596: q^2+q
       598: q
       600: q^2+q
       602: 3q
       604: 2q^2+q
       606: q
       608: 2q^2+q
       610: q^2+q
       612: 2q
       614: q^2+q
       615: q
       616: q^2+3q
       618: q^2+3q
       620: 2q^2+q
       622: 2q^2+q
       624: q
       626: q^2+q
       628: 2q
       630: q^2+q
       631: q
       632: q^2+3q
       634: q^2+3q
       636: q^2+2q
       638: q^2+q
       640: q^2+q
       642: 2q^2+q
       644: 2q^2+q
       646: q^2+q
       647: q^2+q
       648: 4q^2+2q
       649: q^2+q
       650: 4q^2+2q
       652: 2q
       653: 2q^2+q
       654: 3q^2+2q
       655: 2q^2+2q
       656: q^2+2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       667: q^2+3q
       669: q^2+3q
       671: 2q^2+q
       672: q^2+4q
       673: q^2+2q
       674: 2q+1
       675: 2q^2+2q
       676: 2q^2+2q
       677: 3q^2+2q
       678: 3q^2+4q
       679: q^2+2q
       680: 2q+1
       681: 2q^2+2q
       682: 2q^2+2q
       683: 3q^2+2q
       684: 3q^2+4q
       685: q^2+2q
       686: 4q^2+2q
       687: q^3+4q^2+2q
       688: q^3+4q^2+2q
       689: 3q^2+2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q^2
       699: q^2+q
       700: q^2+q
       701: 2q^2+q
       730: q
       732: q
       734: q
       736: 2q
       746: q
       748: q
       750: q
       752: 2q
       759: q
       760: q
       762: 2q^2+q
       763: q^2+q
       764: q^2+q
       766: q
       767: q
       768: q^2+2q
       770: q^2+q
       773: 2q
       776: q+1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: 3q
       794: q+1
       796: 2q+1
       798: q
       800: q
       802: q^2+q
       804: q^2+q
       806: q^2+q
       808: q^2+q
       810: q
       812: q^2+q
       814: q^2+3q
       815: q
       816: q^2+3q
       818: q+1
       820: 2q+1
       822: q
       824: q
       826: q^2+q
       828: q^2+q
       830: q^2+q
       832: q^2+q
       834: q
       836: q^2+q
       838: q^2+3q
       839: q
       840: q^2+3q
       842: q^2+q
       843: q+1
       844: q
       846: 2q^2+q
       848: 2q^2+q
       850: q
       852: q^2+q
       854: 2q
       856: q^2+q
       857: 2q^2+2q
       858: q^2+2q
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: 2q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q^2+2q
       878: 2q^2+2q
       879: 3q^2+2q
       880: q^2+2q
       890: q
       891: q
       892: q
       919: q+1
       933: q
       935: 2q
       943: q+1
       957: q
       959: 2q
       967: q+1
       969: q+1
       972: q
       980: q
       981: q
       983: q^2+q
       986: 2q
       989: q
       990: q
       991: q^2+2q
       993: q+1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 2q+1
      1017: q+1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: 2q+1
      1033: q+1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: q+1
      1047: q
      1049: q
      1051: q
      1053: q^2+q
      1055: q^2+q
      1057: q^2+q
      1059: q^2+q
      1061: q
      1063: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1094: q+1
      1104: q
      1105: q
      1106: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: q+1
      1167: q+1
      1189: q+1
      1192: q
      1197: q+1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1265: q
      1267: q
      1269: q
      1271: q
      1273: q
      1275: q+1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1298: 1
      1310: q+1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1351: 1
      1359: 1
      1367: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1449: 1
      1451: 1
      1455: 1
      1457: 1
      1461: 1
      1463: 1
      1465: 1
      1467: 1
      1469: 1
      1471: q
      1473: q+1
      1477: q
      1479: q
      1482: 1
      1487: 1
      1497: 1
      1509: 1
      1521: 1
      1566: 1
      1570: 1
      1578: 1
      1586: 1
      1590: 1
      1598: 1
      1610: 1
      1618: 1
      1626: 1
      1632: 1
      1662: 1
      1664: 1
      1666: 1
      1695: 1
      1707: 1
      1720: 1
      1788: 1
      1792: 1
      1800: 1
      1879: 1

1880:    0: q^5+q^4+2q^3+q
         1: q^5+q^4+2q^3+q
         2: 2q^4+q^3+q
         3: q^5+q^4+2q^3+q
         4: q^4+q^3+q
         5: q^5+q^4+2q^3+q
         6: q^4+q^3+q
         7: q^5+2q^4+q^3+q
         8: 2q^4+q^3+q
         9: q^5+2q^4+q^3+q
        10: q^5+q^4+2q^3+q
        11: q^5+q^4+2q^3+q
        12: q^4+q^3+q
        13: q^4+q^3+q
        14: q^4+q^3+q
        15: q^4+q^3+q
        16: q^5+q^4+2q^3+q
        17: q^5+q^4+2q^3+q
        18: q^5+2q^4+q^3+q
        19: q^3+q
        20: q^3+q
        21: q^4+q^3+q
        22: q^5+q^4+2q^3+q
        23: q^5+q^4+2q^3+q
        24: 2q^4+q^3+q
        25: q^5+q^4+2q^3+q
        26: q^5+q^4+2q^3+q
        27: 2q^4+q^3+q
        28: q^5+q^4+2q^3+q
        29: q^3+q
        30: q^3+q
        31: q^5+q^4+2q^3+q
        32: q^4+q^3+q
        33: q^5+q^4+2q^3+q
        34: q^5+q^4+2q^3+q
        35: q^4+q^3+q
        36: q^5+q^4+2q^3+q
        38: q^5+q^4+2q^3+q
        40: q^5+q^4+2q^3+q
        42: 2q^4+q^3+q
        43: q^4+q^3+q
        44: q^4+q^3+q
        45: q^4+q^3+q
        46: q^4+q^3+q
        47: q^4+q^3+q
        48: q^4+q^3+q
        49: q^3+q
        50: q^3+q
        51: q^4+q^3+q
        52: q^3+q
        53: q^3+q
        54: q^4+q^3+q
        55: q^3+q
        56: q^3+q
        57: q^4+q^3+q
        58: q^5+q^4+q^3+q
        59: q^3
        60: q^3
        61: q^5+q^4+q^3+q
        63: q^5+q^4+2q^3+q
        65: q^4+q^3+q
        67: q^5+q^4+2q^3+q
        68: q^4+q
        69: q^3+q
        70: q^3+q
        71: q^3+q
        72: q
        73: q
        75: q^3+q
        77: q^3+q
        79: q^4+q^3+q
        80: q^4+q^3+q
        81: q^4+q^3+q
        82: q^3+q
        83: q^3+q
        84: q^4+q^3+q
        85: q^4+q^3+q
        86: q^3+q
        87: q^3+q
        88: q^4+q^3+q
        89: q^4+q^3+q
        90: q^4+q^3+q
        91: q^3+q
        92: q
        93: q^3+q
        94: q^3+q
        95: q^3+q
        96: q^4+q^3+q
        97: q^3+q
        98: q^3+q
        99: q^4+q^3+q
       100: q^3+q
       101: q^3+q
       102: q^4+q^3+q
       104: q^3
       105: q^5+q^4+q^3+q
       108: q
       109: q
       112: q
       114: q^3+q
       116: q^3+q
       117: q^4+q
       120: q^4+q
       122: q^4+q^3+q
       124: q^4+q^3+q
       125: q^4+q
       126: q^3+q
       128: q^3+q
       130: q^3+q
       132: q^4+q^3+q
       133: q
       134: q^3+q
       135: q
       136: q
       137: q^4+q^3+q
       138: q^3+q
       139: q^3+q
       140: q
       141: q^3+q
       142: q
       143: q^4+q^3+q
       144: q^3+q
       145: q^3+q
       146: q^3+q
       147: q
       148: q
       149: q^3+q
       150: q^3+q
       152: q^3+q
       154: q^3+q
       156: q^4+q^3+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^3+q
       161: q
       162: q^3+q
       163: q^3+q
       164: q
       165: q^3+q
       166: q^3+q
       167: q^3+q
       168: q^4+q^3+q
       171: q
       175: q^4+q
       178: q^3+q
       180: q^3+q
       182: q
       184: q
       185: q
       188: q
       190: q^3+q
       191: q^4+q
       194: q
       195: q
       198: q
       200: q^4+q
       202: q
       203: q
       206: q
       208: q^4+q^3+q
       210: q^3+q
       212: q^3+q
       214: q^3+q
       216: q
       218: q^3+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q
       224: q
       225: q
       226: q^3+q
       227: q
       228: q^3+q
       229: q
       230: q
       231: q^3+q
       232: q
       233: q^3+q
       234: q
       235: q
       236: q^3+q
       238: q^3+q
       240: q^3+q
       242: q^4+q^3+q
       243: q^3+q
       244: q
       245: q
       246: q^3+q
       247: q
       248: q
       249: q^4+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^3+q
       257: q
       258: q^3+q
       261: q
       265: q
       270: q
       272: q
       277: q^4+q
       280: q
       282: q^3+q
       284: q
       285: q
       288: q^3+q
       290: q
       292: q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q^3+q
       318: q^3+q
       320: q
       321: q
       324: q
       326: q^3+q
       328: q^3+q
       330: q
       332: q^3+q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q
       343: q^4+q
       344: q
       345: q
       346: q^3+q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q^3+q
       355: q
       356: q
       357: q
       358: q
       359: q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q
       367: q
       368: q^3+q
       369: q
       370: q
       374: q^3+q
       375: q
       376: q^3+q
       379: q
       383: q
       387: q
       392: q
       395: q
       398: q
       402: q
       408: q
       410: q
       412: q^3+q
       414: q
       416: q
       418: q
       420: q
       421: q
       424: q
       426: q
       428: q
       430: q
       431: q
       434: q
       436: q
       438: q
       439: q
       442: q
       444: q
       446: q
       448: q
       449: q
       452: q
       454: q
       456: q
       457: q
       460: q
       461: q
       464: q
       466: q
       468: q^3+q
       470: q^3+q
       472: q
       473: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q
       497: q
       498: q
       499: q
       500: q
       503: q^3+q
       505: q
       507: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       523: q
       527: q
       531: q
       535: q
       540: q
       544: q
       548: q
       550: q
       554: q
       558: q
       562: q
       567: q
       572: q
       576: q
       581: q
       584: q
       586: q
       588: q
       590: q
       591: q
       594: q
       595: q
       600: q
       604: q
       606: q
       607: q
       610: q
       612: q
       614: q
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       636: q
       638: q^3+q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q
       700: q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q
       732: q
       738: q
       742: q
       746: q
       755: q
       760: q
       764: q
       778: q
       798: q
       800: q
       802: q
       803: q
       806: q
       807: q
       812: q
       822: q
       824: q
       826: q
       827: q
       830: q
       831: q
       836: q
       842: q
       846: q
       847: q
       850: q
       852: q
       854: q
       856: q
       877: q
       878: q
       879: q
       898: q
       915: q
       923: q
       925: q
       931: q
       937: q
       945: q
       949: q
       954: q
       963: q
       977: q
       981: q
      1011: 1
      1019: q
      1035: q
      1049: q
      1051: q
      1053: q
      1054: q
      1057: q
      1058: q
      1063: q
      1129: 1
      1143: 1
      1151: q
      1169: q
      1187: q
      1201: q
      1203: q
      1209: q
      1223: 1
      1265: q
      1279: 1
      1301: 1
      1325: 1
      1339: 1
      1362: 1
      1395: 1
      1417: q
      1435: 1
      1481: 1
      1500: 1
      1511: 1
      1524: 1
      1573: 1
      1594: 1
      1621: 1
      1636: 1
      1697: 1
      1710: 1
      1721: 1
      1795: 1
      1880: 1

1881:    0: q^5+q^4+2q^3+q
         1: q^5+q^4+2q^3+q
         2: 2q^4+q^3+q
         3: q^5+q^4+2q^3+q
         4: q^4+q^3+q
         5: q^5+q^4+2q^3+q
         6: q^4+q^3+q
         7: q^5+2q^4+q^3+q
         8: 2q^4+q^3+q
         9: q^5+2q^4+q^3+q
        10: q^5+q^4+2q^3+q
        11: q^5+q^4+2q^3+q
        12: q^4+q^3+q
        13: q^4+q^3+q
        14: q^4+q^3+q
        15: q^4+q^3+q
        16: q^5+q^4+2q^3+q
        17: q^5+q^4+2q^3+q
        18: q^5+2q^4+q^3+q
        19: q^3+q
        20: q^3+q
        21: q^4+q^3+q
        22: q^5+q^4+2q^3+q
        23: q^5+q^4+2q^3+q
        24: 2q^4+q^3+q
        25: q^5+q^4+2q^3+q
        26: q^5+q^4+2q^3+q
        27: 2q^4+q^3+q
        28: q^5+q^4+2q^3+q
        29: q^3+q
        30: q^3+q
        31: q^5+q^4+2q^3+q
        32: q^4+q^3+q
        33: q^5+q^4+2q^3+q
        34: q^5+q^4+2q^3+q
        35: q^4+q^3+q
        36: q^5+q^4+2q^3+q
        37: q^5+q^4+2q^3+q
        39: q^5+q^4+2q^3+q
        41: 2q^4+q^3+q
        43: q^4+q^3+q
        44: q^4+q^3+q
        45: q^4+q^3+q
        46: q^4+q^3+q
        47: q^4+q^3+q
        48: q^4+q^3+q
        49: q^3+q
        50: q^3+q
        51: q^4+q^3+q
        52: q^3+q
        53: q^3+q
        54: q^4+q^3+q
        55: q^3+q
        56: q^3+q
        57: q^4+q^3+q
        58: q^3
        59: q^5+q^4+q^3+q
        60: q^3
        61: q^5+q^4+q^3+q
        62: q^5+q^4+2q^3+q
        64: q^4+q^3+q
        66: q^5+q^4+2q^3+q
        68: q^4+q
        69: q^3+q
        70: q^3+q
        71: q^3+q
        72: q
        73: q
        74: q^3+q
        76: q^3+q
        78: q^4+q^3+q
        80: q^4+q^3+q
        81: q^4+q^3+q
        82: q^3+q
        83: q^3+q
        84: q^4+q^3+q
        85: q^4+q^3+q
        86: q^3+q
        87: q^3+q
        88: q^4+q^3+q
        89: q^4+q^3+q
        90: q^4+q^3+q
        91: q^3+q
        92: q
        93: q^3+q
        94: q^3+q
        95: q^3+q
        96: q^4+q^3+q
        97: q^3+q
        98: q^3+q
        99: q^4+q^3+q
       100: q^3+q
       101: q^3+q
       102: q^4+q^3+q
       103: q^3
       106: q^5+q^4+q^3+q
       108: q
       110: q
       111: q
       113: q^3+q
       115: q^3+q
       118: q^4+q
       120: q^4+q
       121: q^4+q^3+q
       123: q^4+q^3+q
       125: q^4+q
       126: q^3+q
       127: q^3+q
       129: q^3+q
       131: q^4+q^3+q
       133: q
       134: q^3+q
       135: q
       136: q
       137: q^4+q^3+q
       138: q^3+q
       139: q^3+q
       140: q
       141: q^3+q
       142: q
       143: q^4+q^3+q
       144: q^3+q
       145: q^3+q
       146: q^3+q
       147: q
       148: q
       149: q^3+q
       150: q^3+q
       151: q^3+q
       153: q^3+q
       155: q^4+q^3+q
       157: q^3+q
       158: q
       159: q^3+q
       160: q^3+q
       161: q
       162: q^3+q
       163: q^3+q
       164: q
       165: q^3+q
       166: q^3+q
       167: q^3+q
       168: q^4+q^3+q
       172: q
       176: q^4+q
       177: q^3+q
       179: q^3+q
       181: q
       184: q
       186: q
       187: q
       189: q^3+q
       192: q^4+q
       194: q
       196: q
       197: q
       200: q^4+q
       202: q
       204: q
       205: q
       207: q^4+q^3+q
       209: q^3+q
       211: q^3+q
       213: q^3+q
       215: q
       217: q^3+q
       219: q
       220: q
       221: q^3+q
       222: q
       223: q
       224: q
       225: q
       226: q^3+q
       227: q
       228: q^3+q
       229: q
       230: q
       231: q^3+q
       232: q
       233: q^3+q
       234: q
       235: q
       236: q^3+q
       237: q^3+q
       239: q^3+q
       241: q^4+q^3+q
       243: q^3+q
       244: q
       245: q
       246: q^3+q
       247: q
       248: q
       249: q^4+q
       250: q^3+q
       251: q
       252: q^3+q
       253: q^3+q
       254: q
       255: q^3+q
       256: q^3+q
       257: q
       258: q^3+q
       262: q
       266: q
       269: q
       273: q
       278: q^4+q
       279: q
       281: q^3+q
       284: q
       286: q
       287: q^3+q
       289: q
       291: q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q^3+q
       317: q^3+q
       320: q
       322: q
       323: q
       325: q^3+q
       327: q^3+q
       329: q
       331: q^3+q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q^3+q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q^3+q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q
       367: q
       368: q^3+q
       369: q
       370: q
       374: q^3+q
       375: q
       376: q^3+q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q
       411: q^3+q
       413: q
       415: q
       417: q
       420: q
       422: q
       423: q
       425: q
       427: q
       430: q
       432: q
       433: q
       435: q
       438: q
       440: q
       441: q
       444: q
       445: q
       448: q
       450: q
       451: q
       454: q
       455: q
       458: q
       459: q
       462: q
       463: q
       465: q
       467: q^3+q
       469: q^3+q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       492: q
       493: q
       494: q
       495: q
       497: q
       498: q
       499: q
       500: q
       502: q^3+q
       504: q
       506: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       524: q
       528: q
       532: q
       536: q
       539: q
       543: q
       547: q
       552: q
       555: q
       559: q
       563: q
       568: q
       570: q
       575: q
       577: q
       583: q
       585: q
       587: q
       590: q
       592: q
       594: q
       596: q
       599: q
       604: q
       605: q
       608: q
       609: q
       611: q
       613: q
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       635: q
       637: q^3+q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: q
       653: q
       675: q
       676: q
       677: q
       681: q
       682: q
       683: q
       686: q
       687: q
       688: q
       689: q
       697: q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q
       731: q
       739: q
       743: q
       747: q
       756: q
       758: q
       762: q
       777: q
       797: q
       799: q
       802: q
       804: q
       806: q
       808: q
       811: q
       821: q
       823: q
       826: q
       828: q
       830: q
       832: q
       835: q
       841: q
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       877: q
       878: q
       879: q
       899: q
       914: q
       922: q
       927: q
       930: q
       938: q
       946: q
       950: q
       955: q
       961: q
       975: q
       979: q
      1010: 1
      1018: q
      1034: q
      1048: q
      1050: q
      1053: q
      1055: q
      1057: q
      1059: q
      1062: q
      1127: 1
      1140: 1
      1150: q
      1170: q
      1185: q
      1199: q
      1204: q
      1208: q
      1222: 1
      1264: q
      1278: 1
      1299: 1
      1323: 1
      1336: 1
      1361: 1
      1393: 1
      1415: q
      1432: 1
      1480: 1
      1498: 1
      1510: 1
      1522: 1
      1572: 1
      1592: 1
      1622: 1
      1633: 1
      1696: 1
      1708: 1
      1722: 1
      1796: 1
      1881: 1

1882:    0: q^3+2q^2+1
         1: q^3+2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: q^3+2q^2+1
         7: q^3+2q^2+1
         8: q^3+2q^2+1
         9: q^4+q^3+q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^3+2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: q^3+q^2+1
        19: q^3+2q^2+1
        20: q^3+2q^2+1
        21: q^3+2q^2+1
        22: q^3+2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: q^3+2q^2+1
        26: q^3+2q^2+1
        27: q^3+2q^2+1
        28: q^2+1
        29: q^2+1
        30: q^3+2q^2+1
        31: q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^3+q^2+1
        38: q^2
        39: q^3+q^2+1
        40: q^2
        41: q^3+q^2+1
        42: q^2
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: q^3+q^2+1
        52: q^3+2q^2+1
        53: q^3+2q^2+1
        54: q^3+2q^2+1
        55: q^3+2q^2+1
        56: q^3+2q^2+1
        57: q^3+2q^2+1
        58: q^2+1
        60: q^2+1
        62: q^2+1
        64: q^3+q^2+1
        65: q^2
        66: q^2+1
        67: q^2
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^3+q^2+1
        75: q^2
        76: q^3+q^2+1
        77: q^2
        78: q^3+q^2+1
        79: q^2
        80: q^2+1
        81: 2q^2+1
        82: q^2+1
        83: q^3+2q^2+1
        84: q^2+1
        85: 2q^2+1
        86: q^2+1
        87: q^3+2q^2+1
        88: 1
        89: 1
        90: 1
        91: 2q^2+1
        92: 2q^2+1
        93: q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+q^2+1
       100: q^3+2q^2+1
       101: q^3+2q^2+1
       102: q^3+2q^2+1
       103: q^2+1
       107: q^2+1
       109: q^2+1
       111: q^2+1
       112: q^2
       113: q^2+1
       115: q^3+q^2+1
       116: q^2
       117: q^2+1
       119: q^2+1
       121: q^2+1
       123: q^2+1
       124: q^2
       125: 1
       126: 1
       127: q^2+1
       129: q^2+1
       131: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: q^2+1
       150: q^3+2q^2+1
       151: q^3+q^2+1
       152: q^2
       153: q^3+q^2+1
       154: q^2
       155: q^3+q^2+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: 2q^2+1
       161: 2q^2+1
       162: q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: q^3+q^2+1
       169: q^2+1
       173: q^2+1
       177: 1
       179: q^2+1
       181: q^2+1
       183: q^2+1
       185: q^2+1
       187: q^2+1
       188: q^2
       189: q^2+1
       191: 1
       193: q^2+1
       195: q^2+1
       197: q^2+1
       198: q^2
       199: 1
       201: q^2+1
       203: q^2+1
       205: q^2+1
       206: q^2
       207: 1
       209: q^2+1
       211: q^3+q^2+1
       212: q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       237: q^2+1
       239: q^2+1
       241: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: q^3+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+1
       257: 2q^2+1
       258: q^3+q^2+1
       259: q^2+1
       263: q^2+1
       267: q^2+1
       271: q^2+1
       275: 1
       279: q^2+1
       281: 1
       283: 1
       285: 1
       287: 1
       289: q^2+1
       291: 1
       293: 1
       295: 1
       297: 1
       299: q^2+1
       301: q^2+1
       303: q^2+1
       305: q^2+1
       306: q^2
       307: q^2+1
       309: q^2+1
       311: q^2+1
       313: q^2+1
       314: q^2
       315: 1
       317: q^2+1
       319: q^2+1
       321: q^2+1
       323: q^2+1
       324: q^2
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       338: q^2+1
       340: q^2+1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: q^3+q^2+1
       374: 1
       375: 1
       376: 1
       377: 1
       381: q^2+1
       385: 1
       389: q^2+1
       393: q^2+1
       397: q^2+1
       401: q^2+1
       405: q^2+1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: q^2+1
       429: 1
       431: 1
       433: 1
       435: q^2+1
       437: 1
       439: 1
       441: 1
       443: q^2+1
       445: q^2+1
       447: 1
       449: 1
       451: 1
       453: 1
       455: q^2+1
       457: 1
       459: 1
       461: q^2+1
       463: q^2+1
       465: q^2+1
       467: 1
       469: 1
       471: q^2+1
       473: q^2+1
       475: q^2+1
       476: q^2
       477: q^2+1
       479: q^2+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: q^2+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       529: 1
       533: 1
       537: q^2+1
       541: 1
       545: q^2+1
       549: 1
       553: q^2+1
       557: 1
       561: q^2+1
       565: q^2+1
       569: q^2+1
       573: q^2+1
       577: q^2+1
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: q^2+1
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       615: q^2+1
       617: q^2+1
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       631: q^2+1
       633: q^2+1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: q^2+1
       653: 1
       655: q^2+1
       656: q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       672: 1
       673: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       693: q^2+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q^2+1
       737: 1
       741: 1
       749: q^2+1
       753: 1
       757: q^2+1
       761: 1
       765: q^2+1
       769: q^2+1
       775: 1
       779: q+1
       781: 1
       785: 1
       787: 1
       791: 1
       793: 1
       795: q+1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       815: 1
       817: 1
       819: q+1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       839: 1
       843: 1
       844: q
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       857: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       884: q^2+1
       900: 1
       904: 1
       908: 1
       916: 1
       920: 1
       924: 1
       928: 1
       940: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 1
       968: 1
       971: q
       974: 1
       988: 1
       994: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1020: q+1
      1022: 1
      1026: 1
      1028: 1
      1036: q+1
      1038: 1
      1040: 1
      1044: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1141: q
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1198: 1
      1202: 1
      1206: 1
      1220: 1
      1230: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1270: 1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1287: 1
      1289: 1
      1290: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1433: q
      1464: 1
      1466: 1
      1468: 1
      1474: 1
      1476: 1
      1478: 1
      1484: 1
      1501: 1
      1513: 1
      1579: 1
      1599: 1
      1607: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1641: 1
      1649: 1
      1657: 1
      1711: 1
      1757: 1
      1781: 1
      1807: 1
      1811: 1
      1882: 1

1883:    0: 2q^3+3q^2+3q
         1: 2q^3+3q^2+3q
         2: 2q^3+3q^2+3q
         3: 2q^3+3q^2+3q
         4: 2q^3+3q^2+3q
         5: 2q^3+3q^2+3q
         6: 2q^3+3q^2+3q
         7: 2q^3+3q^2+3q
         8: 2q^3+3q^2+3q
         9: q^5+q^4+2q^3+2q^2+2q
        10: q^3+2q^2+3q
        11: q^3+2q^2+3q
        12: q^3+2q^2+3q
        13: 2q^3+3q^2+3q
        14: 2q^3+3q^2+3q
        15: 2q^3+3q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^3+2q^2+2q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 2q^3+3q^2+3q
        23: 2q^3+3q^2+3q
        24: 2q^3+3q^2+3q
        25: 2q^3+3q^2+3q
        26: 2q^3+3q^2+3q
        27: 2q^3+3q^2+3q
        28: q^2+3q
        29: q^3+2q^2+3q
        30: 2q^3+3q^2+3q
        31: q^3+2q^2+3q
        32: 2q^3+3q^2+3q
        33: 2q^2+3q
        34: q^3+2q^2+3q
        35: 2q^3+3q^2+3q
        36: 2q^2+3q
        37: q^3+q^2+q
        38: q^3+2q^2+2q
        39: q^3+q^2+q
        40: q^3+2q^2+2q
        41: q^3+q^2+q
        42: q^3+2q^2+2q
        43: q^3+2q^2+3q
        44: q^3+2q^2+3q
        45: q^3+2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^3+2q^2+2q
        49: 2q^2+3q
        50: 2q^2+3q
        51: q^3+2q^2+2q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q^2+2q
        59: q
        60: q^2+2q
        61: q
        62: q^2+q
        63: q^3+q^2+2q
        64: q^3+q^2+q
        65: q^3+2q^2+2q
        66: q^2+q
        67: q^2+2q
        68: q^2+3q
        69: q^2+2q
        70: q^3+2q^2+3q
        71: q^2+3q
        72: 2q^2+3q
        73: 2q^2+3q
        74: q^3+q^2+q
        75: q^3+2q^2+2q
        76: q^3+q^2+q
        77: q^3+2q^2+2q
        78: q^3+q^2+q
        79: q^3+2q^2+2q
        80: q^3+2q^2+3q
        81: 2q^2+3q
        82: q^3+2q^2+3q
        83: 2q^3+3q^2+3q
        84: q^3+2q^2+3q
        85: 2q^2+3q
        86: q^3+2q^2+3q
        87: 2q^3+3q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^2+3q
        92: 2q^2+3q
        93: q^3+2q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: q^3+2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: q^3+2q^2+2q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: q^2+q
       104: q
       105: q
       107: q^2+2q
       108: q
       109: q^2+2q
       110: q
       111: q^2+q
       112: q^2+2q
       113: q^2+q
       114: q^3+q^2+2q
       115: q^3+q^2+q
       116: q^3+2q^2+2q
       117: q^2+2q
       118: q
       119: q^2+2q
       120: q
       121: q^2+q
       122: q^3+q^2+2q
       123: q^2+q
       124: q^2+2q
       125: 3q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       133: q^2+3q
       134: q^2+2q
       135: 2q^2+3q
       136: 2q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q^2+3q
       141: q^3+2q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: q^3+2q^2+3q
       147: 2q^2+3q
       148: 2q^2+3q
       149: q^3+2q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+q^2+q
       152: q^3+2q^2+2q
       153: q^3+q^2+q
       154: q^3+2q^2+2q
       155: q^3+q^2+q
       156: q^3+2q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: q^3+2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: q^3+2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: q^3+2q^2+2q
       169: q^2+q
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       180: 2q
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       183: q^2+2q
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       189: q^2+q
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       191: 2q
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       210: q^3+q^2+2q
       211: q^3+q^2+q
       212: q^3+2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q^2+3q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q^2+3q
       236: q^2+2q
       238: 2q
       240: 2q
       242: q^2+q
       243: q^2+3q
       244: 2q^2+3q
       245: 2q^2+3q
       246: q^3+2q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: q^3+2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: q^3+2q^2+2q
       260: q
       261: q
       263: q^2+q
       264: q
       265: q
       267: q^2+q
       268: q
       270: q
       271: q^2+q
       272: q
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       277: q
       280: 2q
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       296: q
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       298: 2q
       299: q^2+2q
       300: q
       302: 2q
       303: q^2+2q
       304: q
       305: q^2+q
       306: q^2+2q
       307: q^2+2q
       308: q
       309: q^2+2q
       310: q
       312: 2q
       313: q^2+q
       314: q^2+2q
       316: q
       318: 2q
       319: q^2+2q
       320: q
       321: q^2+2q
       322: q
       323: q^2+q
       324: q^2+2q
       325: q^2+q
       326: q^3+q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+3q
       339: 2q
       341: 2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^2+2q
       351: 2q^2+3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       361: 2q
       363: 2q
       365: q^2+q
       366: 2q
       367: q^2+3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: q^3+2q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
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       390: q
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       393: q^2+q
       394: q
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       405: q^2+q
       407: q
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       434: q
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       438: q
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       440: q
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       442: 2q
       443: q^2+2q
       444: q
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       456: 2q
       457: 2q
       458: q
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       460: 2q
       461: q^2+2q
       462: q
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       466: 2q
       468: q
       470: q
       471: q^2+2q
       472: q
       473: q^2+2q
       474: q
       475: q^2+q
       476: q^2+2q
       478: 2q
       479: q^2+q
       480: q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+3q
       486: 2q
       488: 2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: q^2+2q
       513: 3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       538: q
       540: q
       541: q
       542: q
       544: q
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       548: q
       554: q
       556: q
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       565: q^2+q
       566: q
       567: q
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       573: q^2+q
       574: q
       576: q
       581: 2q
       586: q
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       598: q
       600: q
       602: 2q
       603: q
       606: q
       607: q
       610: q
       614: q
       615: q^2+2q
       616: q
       618: 2q
       619: q
       621: q
       624: q
       626: q
       630: q
       631: q^2+2q
       632: q
       634: 2q
       640: q
       641: q
       643: q
       646: q
       647: 2q
       648: q
       649: 2q
       650: q
       652: 2q
       653: q
       654: 2q
       655: q^2+q
       656: q^2+2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       699: q
       700: q
       734: q
       736: q
       750: q
       752: q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q^2+q
       766: q
       767: q
       773: 2q
       776: 1
       780: q+1
       782: q
       785: q
       787: q
       792: q
       793: 1
       796: q+1
       798: q
       801: q
       803: q
       805: q
       807: q
       810: q
       812: q
       815: 2q
       816: q
       817: 1
       820: q+1
       822: q
       825: q
       827: q
       829: q
       831: q
       834: q
       836: q
       839: 2q
       840: q
       843: 1
       844: q
       845: q
       847: q
       850: q
       852: q
       856: q
       857: q
       858: 2q
       866: 1
       868: 2q
       870: q+1
       871: 2q
       872: 2q
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       890: q
       891: q
       917: 1
       941: 1
       964: 1
       969: 1
       972: q
       988: q
       989: q
       990: q
       995: 1
       998: 1
      1000: 1
      1004: q
      1006: q
      1009: q
      1011: q
      1012: 1
      1013: q
      1021: q+1
      1023: q
      1026: q
      1028: q
      1037: q+1
      1039: q
      1040: q
      1044: q
      1049: q
      1052: q
      1054: q
      1056: q
      1058: q
      1061: q
      1063: q
      1065: q
      1076: 1
      1078: 2q
      1080: 1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1087: 1
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1142: q
      1221: q
      1231: 1
      1232: 1
      1234: 1
      1240: q
      1242: q
      1249: 1
      1250: 1
      1254: 1
      1258: q
      1260: q
      1267: q
      1268: q
      1270: q
      1275: q+1
      1277: q
      1279: q
      1280: 1
      1281: q
      1287: 1
      1289: 2q
      1291: 1
      1349: 1
      1357: 1
      1364: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1434: q
      1465: 1
      1466: 1
      1468: 1
      1475: q
      1476: q
      1478: q
      1484: 1
      1502: 1
      1514: 1
      1608: 1
      1616: 1
      1623: 1
      1642: 1
      1649: 1
      1657: 1
      1712: 1
      1758: 1
      1782: 1
      1811: 1
      1883: 1

1884:    0: 2q^3+3q^2+3q
         1: 2q^3+3q^2+3q
         2: 2q^3+3q^2+3q
         3: 2q^3+3q^2+3q
         4: 2q^3+3q^2+3q
         5: 2q^3+3q^2+3q
         6: 2q^3+3q^2+3q
         7: 2q^3+3q^2+3q
         8: 2q^3+3q^2+3q
         9: q^5+q^4+2q^3+2q^2+2q
        10: q^3+2q^2+3q
        11: q^3+2q^2+3q
        12: q^3+2q^2+3q
        13: 2q^3+3q^2+3q
        14: 2q^3+3q^2+3q
        15: 2q^3+3q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^3+2q^2+2q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 2q^3+3q^2+3q
        23: 2q^3+3q^2+3q
        24: 2q^3+3q^2+3q
        25: 2q^3+3q^2+3q
        26: 2q^3+3q^2+3q
        27: 2q^3+3q^2+3q
        28: q^2+3q
        29: q^3+2q^2+3q
        30: 2q^3+3q^2+3q
        31: q^3+2q^2+3q
        32: 2q^3+3q^2+3q
        33: 2q^2+3q
        34: q^3+2q^2+3q
        35: 2q^3+3q^2+3q
        36: 2q^2+3q
        37: q^3+2q^2+2q
        38: q^3+q^2+q
        39: q^3+2q^2+2q
        40: q^3+q^2+q
        41: q^3+2q^2+2q
        42: q^3+q^2+q
        43: q^3+2q^2+3q
        44: q^3+2q^2+3q
        45: q^3+2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^3+2q^2+2q
        49: 2q^2+3q
        50: 2q^2+3q
        51: q^3+2q^2+2q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q
        59: q^2+2q
        60: q^2+2q
        61: q
        62: q^3+q^2+2q
        63: q^2+q
        64: q^3+2q^2+2q
        65: q^3+q^2+q
        66: q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^2+2q
        70: q^3+2q^2+3q
        71: q^2+3q
        72: 2q^2+3q
        73: 2q^2+3q
        74: q^3+2q^2+2q
        75: q^3+q^2+q
        76: q^3+2q^2+2q
        77: q^3+q^2+q
        78: q^3+2q^2+2q
        79: q^3+q^2+q
        80: q^3+2q^2+3q
        81: 2q^2+3q
        82: q^3+2q^2+3q
        83: 2q^3+3q^2+3q
        84: q^3+2q^2+3q
        85: 2q^2+3q
        86: q^3+2q^2+3q
        87: 2q^3+3q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^2+3q
        92: 2q^2+3q
        93: q^3+2q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: q^3+2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: q^3+2q^2+2q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: q
       104: q^2+q
       106: q
       107: q^2+2q
       108: q
       109: q
       110: q^2+2q
       111: q^2+2q
       112: q^2+q
       113: q^3+q^2+2q
       114: q^2+q
       115: q^3+2q^2+2q
       116: q^3+q^2+q
       117: q
       118: q^2+2q
       119: q^2+2q
       120: q
       121: q^3+q^2+2q
       122: q^2+q
       123: q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       133: q^2+3q
       134: q^2+2q
       135: 2q^2+3q
       136: 2q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q^2+3q
       141: q^3+2q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: q^3+2q^2+3q
       147: 2q^2+3q
       148: 2q^2+3q
       149: q^3+2q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+2q^2+2q
       152: q^3+q^2+q
       153: q^3+2q^2+2q
       154: q^3+q^2+q
       155: q^3+2q^2+2q
       156: q^3+q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: q^3+2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: q^3+2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: q^3+2q^2+2q
       169: q
       170: q^2+q
       172: q
       173: q
       174: q^2+q
       176: q
       177: q
       179: 2q
       181: 2q
       183: q^2+2q
       184: q
       185: q
       186: q^2+2q
       187: q^2+2q
       188: q^2+q
       189: q^3+q^2+2q
       190: q^2+q
       191: q
       192: 2q
       193: q^2+2q
       194: q
       195: q
       196: q^2+2q
       197: q^2+2q
       198: q^2+q
       199: 2q
       200: q
       201: q^2+2q
       202: q
       203: q
       204: q^2+2q
       205: q^2+2q
       206: q^2+q
       207: 2q
       208: q
       209: q^3+q^2+2q
       210: q^2+q
       211: q^3+2q^2+2q
       212: q^3+q^2+q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q^2+3q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q^2+3q
       236: q^2+2q
       237: 2q
       239: 2q
       241: q^2+q
       243: q^2+3q
       244: 2q^2+3q
       245: 2q^2+3q
       246: q^3+2q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: q^3+2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: q^3+2q^2+2q
       259: q
       262: q
       263: q
       264: q^2+q
       266: q
       267: q
       268: q^2+q
       269: q
       271: q
       273: q
       274: q^2+q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q
       289: 2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: q^2+2q
       300: q
       301: 2q
       303: q
       304: q^2+2q
       305: q^2+2q
       306: q^2+q
       307: q^2+2q
       308: q
       309: q
       310: q^2+2q
       311: 2q
       313: q^2+2q
       314: q^2+q
       315: q
       317: 2q
       319: q^2+2q
       320: q
       321: q
       322: q^2+2q
       323: q^2+2q
       324: q^2+q
       325: q^3+q^2+2q
       326: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+3q
       338: 2q
       340: 2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^2+2q
       351: 2q^2+3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       360: 2q
       362: 2q
       364: q^2+q
       366: 2q
       367: q^2+3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: q^3+2q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       391: q
       393: q
       394: q^2+q
       396: q
       397: q
       399: q
       401: q
       403: q^2+q
       404: q
       405: q
       406: q
       407: q^2+q
       413: q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 2q
       429: q
       432: q
       433: q
       435: 2q
       437: 2q
       438: q
       439: q
       440: 2q
       441: 2q
       442: q
       443: q^2+2q
       444: q
       445: 2q
       447: q
       450: q
       451: q
       453: 2q
       454: q
       455: 2q
       457: q
       458: 2q
       459: 2q
       460: q
       461: q
       462: q^2+2q
       463: 2q
       465: 2q
       467: q
       469: q
       471: q^2+2q
       472: q
       473: q
       474: q^2+2q
       475: q^2+2q
       476: q^2+q
       477: 2q
       479: q^2+2q
       480: q^2+q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+3q
       485: 2q
       487: 2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: q^2+2q
       513: 3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       537: q
       539: q
       541: q
       542: q
       543: q
       545: q
       547: q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q
       563: q
       565: q
       566: q^2+q
       568: q
       569: q
       570: q
       573: q
       574: q^2+q
       575: q
       577: 2q
       585: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 2q
       603: q
       605: q
       608: q
       609: q
       613: q
       615: q^2+2q
       616: q
       617: 2q
       619: q
       622: q
       623: q
       625: q
       629: q
       631: q
       632: q^2+2q
       633: 2q
       639: q
       641: q
       644: q
       645: q
       647: 2q
       648: q
       649: q
       650: 2q
       651: 2q
       653: 2q
       654: q
       655: q^2+2q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       693: q
       697: q
       733: q
       735: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       763: q
       765: q
       766: q^2+q
       768: q
       769: 2q
       775: 1
       779: q+1
       781: q
       785: q
       788: q
       791: q
       793: 1
       795: q+1
       797: q
       801: q
       804: q
       805: q
       808: q
       809: q
       811: q
       815: 2q
       816: q
       818: 1
       819: q+1
       821: q
       825: q
       828: q
       829: q
       832: q
       833: q
       835: q
       839: q
       840: 2q
       843: q
       844: 1
       845: q
       848: q
       849: q
       851: q
       855: q
       857: 2q
       858: q
       866: 1
       868: 2q
       870: q+1
       871: 2q
       872: 2q
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       884: q
       889: q
       916: 1
       942: 1
       965: 1
       968: q
       971: 1
       988: q
       989: q
       991: q
       994: 1
       999: 1
      1000: 1
      1004: q
      1007: q
      1008: q
      1010: q
      1012: q
      1013: 1
      1020: q+1
      1022: q
      1026: q
      1029: q
      1036: q+1
      1038: q
      1040: q
      1045: q
      1048: q
      1052: q
      1055: q
      1056: q
      1059: q
      1060: q
      1062: q
      1064: q
      1076: 1
      1078: 2q
      1080: 1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1089: 1
      1116: 1
      1122: 1
      1131: 1
      1138: q
      1141: 1
      1220: q
      1230: 1
      1233: 1
      1234: 1
      1240: q
      1243: q
      1248: 1
      1251: 1
      1254: 1
      1258: q
      1261: q
      1266: q
      1268: q
      1271: q
      1274: q+1
      1276: q
      1278: q
      1280: q
      1281: 1
      1287: 1
      1289: 2q
      1293: 1
      1350: 1
      1356: 1
      1366: 1
      1382: 1
      1388: 1
      1397: 1
      1430: q
      1433: 1
      1464: 1
      1467: 1
      1468: 1
      1474: q
      1476: q
      1479: q
      1484: 1
      1505: 1
      1516: 1
      1609: 1
      1615: 1
      1624: 1
      1641: 1
      1650: 1
      1657: 1
      1714: 1
      1759: 1
      1781: 1
      1812: 1
      1884: 1

1885:    0: 2q^3+3q^2+3q
         1: 2q^3+3q^2+3q
         2: 2q^3+3q^2+3q
         3: 2q^3+3q^2+3q
         4: 2q^3+3q^2+3q
         5: 2q^3+3q^2+3q
         6: 2q^3+3q^2+3q
         7: 2q^3+3q^2+3q
         8: 2q^3+3q^2+3q
         9: q^5+q^4+2q^3+2q^2+2q
        10: q^3+2q^2+3q
        11: q^3+2q^2+3q
        12: q^3+2q^2+3q
        13: 2q^3+3q^2+3q
        14: 2q^3+3q^2+3q
        15: 2q^3+3q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^3+2q^2+2q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 2q^3+3q^2+3q
        23: 2q^3+3q^2+3q
        24: 2q^3+3q^2+3q
        25: 2q^3+3q^2+3q
        26: 2q^3+3q^2+3q
        27: 2q^3+3q^2+3q
        28: q^2+3q
        29: q^3+2q^2+3q
        30: 2q^3+3q^2+3q
        31: q^3+2q^2+3q
        32: 2q^3+3q^2+3q
        33: 2q^2+3q
        34: q^3+2q^2+3q
        35: 2q^3+3q^2+3q
        36: 2q^2+3q
        37: q^3+2q^2+2q
        38: q^3+q^2+q
        39: q^3+2q^2+2q
        40: q^3+q^2+q
        41: q^3+2q^2+2q
        42: q^3+q^2+q
        43: q^3+2q^2+3q
        44: q^3+2q^2+3q
        45: q^3+2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^3+2q^2+2q
        49: 2q^2+3q
        50: 2q^2+3q
        51: q^3+2q^2+2q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q^2+2q
        59: q
        60: q
        61: q^2+2q
        62: q^3+q^2+2q
        63: q^2+q
        64: q^3+2q^2+2q
        65: q^3+q^2+q
        66: q^2+2q
        67: q^2+q
        68: q^2+3q
        69: q^2+2q
        70: q^3+2q^2+3q
        71: q^2+3q
        72: 2q^2+3q
        73: 2q^2+3q
        74: q^3+2q^2+2q
        75: q^3+q^2+q
        76: q^3+2q^2+2q
        77: q^3+q^2+q
        78: q^3+2q^2+2q
        79: q^3+q^2+q
        80: q^3+2q^2+3q
        81: 2q^2+3q
        82: q^3+2q^2+3q
        83: 2q^3+3q^2+3q
        84: q^3+2q^2+3q
        85: 2q^2+3q
        86: q^3+2q^2+3q
        87: 2q^3+3q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^2+3q
        92: 2q^2+3q
        93: q^3+2q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: q^3+2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: q^3+2q^2+2q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: q
       105: q^2+q
       106: q
       107: q
       108: q^2+2q
       109: q^2+2q
       110: q
       111: q^2+2q
       112: q^2+q
       113: q^3+q^2+2q
       114: q^2+q
       115: q^3+2q^2+2q
       116: q^3+q^2+q
       117: q^2+2q
       118: q
       119: q
       120: q^2+2q
       121: q^3+q^2+2q
       122: q^2+q
       123: q^2+2q
       124: q^2+q
       125: 3q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       133: q^2+3q
       134: q^2+2q
       135: 2q^2+3q
       136: 2q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q^2+3q
       141: q^3+2q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: q^3+2q^2+3q
       147: 2q^2+3q
       148: 2q^2+3q
       149: q^3+2q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+2q^2+2q
       152: q^3+q^2+q
       153: q^3+2q^2+2q
       154: q^3+q^2+q
       155: q^3+2q^2+2q
       156: q^3+q^2+q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: q^3+2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: q^3+2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: q^3+2q^2+2q
       169: q
       171: q^2+q
       172: q
       173: q
       175: q^2+q
       176: q
       177: q
       179: 2q
       181: 2q
       183: q
       184: q^2+2q
       185: q^2+2q
       186: q
       187: q^2+2q
       188: q^2+q
       189: q^3+q^2+2q
       190: q^2+q
       191: 2q
       192: q
       193: q
       194: q^2+2q
       195: q^2+2q
       196: q
       197: q^2+2q
       198: q^2+q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       203: q^2+2q
       204: q
       205: q^2+2q
       206: q^2+q
       207: 2q
       208: q
       209: q^3+q^2+2q
       210: q^2+q
       211: q^3+2q^2+2q
       212: q^3+q^2+q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q^2+3q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q^2+3q
       236: q^2+2q
       237: 2q
       239: 2q
       241: q^2+q
       243: q^2+3q
       244: 2q^2+3q
       245: 2q^2+3q
       246: q^3+2q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: q^3+2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: q^3+2q^2+2q
       259: q
       262: q
       263: q
       265: q^2+q
       266: q
       267: q
       269: q
       270: q^2+q
       271: q
       272: q^2+q
       273: q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q
       289: 2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       299: q
       300: q^2+2q
       301: 2q
       303: q^2+2q
       304: q
       305: q^2+2q
       306: q^2+q
       307: q
       308: q^2+2q
       309: q^2+2q
       310: q
       311: 2q
       313: q^2+2q
       314: q^2+q
       315: q
       317: 2q
       319: q
       320: q^2+2q
       321: q^2+2q
       322: q
       323: q^2+2q
       324: q^2+q
       325: q^3+q^2+2q
       326: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+3q
       338: 2q
       340: 2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^2+2q
       351: 2q^2+3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       360: 2q
       362: 2q
       364: q^2+q
       366: 2q
       367: q^2+3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: q^3+2q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       389: q
       391: q
       393: q
       395: q^2+q
       396: q
       397: q
       399: q
       401: q
       402: q^2+q
       404: q
       405: q
       406: q
       408: q^2+q
       413: q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 2q
       430: q
       431: q
       433: q
       435: 2q
       437: q
       438: 2q
       439: 2q
       440: q
       441: 2q
       442: q
       443: q
       444: q^2+2q
       445: 2q
       448: q
       449: q
       451: q
       453: q
       454: 2q
       455: 2q
       457: 2q
       458: q
       459: 2q
       460: q
       461: q^2+2q
       462: q
       463: 2q
       465: 2q
       467: q
       469: q
       471: q
       472: q^2+2q
       473: q^2+2q
       474: q
       475: q^2+2q
       476: q^2+q
       477: 2q
       479: q^2+2q
       480: q^2+q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+3q
       485: 2q
       487: 2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: q^2+2q
       513: 3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       537: q
       539: q
       541: q
       543: q
       544: q
       545: q
       547: q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: q
       563: q
       565: q
       567: q^2+q
       568: q
       569: q
       570: q
       573: q
       575: q
       576: q^2+q
       577: 2q
       585: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 2q
       604: q
       605: q
       607: q
       609: q
       613: q
       615: q
       616: q^2+2q
       617: 2q
       620: q
       621: q
       623: q
       625: q
       629: q
       631: q^2+2q
       632: q
       633: 2q
       639: q
       642: q
       643: q
       645: q
       647: q
       648: 2q
       649: 2q
       650: q
       651: 2q
       653: 2q
       654: q
       655: q^2+2q
       656: q^2+q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       693: q
       697: q
       733: q
       735: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       764: q
       765: q
       767: q^2+q
       768: q
       769: 2q
       775: 1
       779: q+1
       781: q
       786: q
       787: q
       791: q
       794: 1
       795: q+1
       797: q
       802: q
       803: q
       806: q
       807: q
       809: q
       811: q
       815: q
       816: 2q
       817: 1
       819: q+1
       821: q
       826: q
       827: q
       830: q
       831: q
       833: q
       835: q
       839: 2q
       840: q
       843: q
       844: 1
       846: q
       847: q
       849: q
       851: q
       855: q
       857: 2q
       858: q
       866: 1
       868: 2q
       870: q+1
       871: 2q
       872: 2q
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       884: q
       889: q
       918: 1
       940: 1
       966: 1
       968: q
       971: 1
       988: q
       990: q
       991: q
       994: 1
       998: 1
      1001: 1
      1005: q
      1006: q
      1008: q
      1010: q
      1012: q
      1013: 1
      1020: q+1
      1022: q
      1027: q
      1028: q
      1036: q+1
      1038: q
      1041: q
      1044: q
      1048: q
      1053: q
      1054: q
      1057: q
      1058: q
      1060: q
      1062: q
      1064: q
      1076: 1
      1078: 2q
      1080: 1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1090: 1
      1114: 1
      1124: 1
      1132: 1
      1138: q
      1141: 1
      1220: q
      1230: 1
      1232: 1
      1235: 1
      1241: q
      1242: q
      1248: 1
      1250: 1
      1255: 1
      1259: q
      1260: q
      1266: q
      1269: q
      1270: q
      1274: q+1
      1276: q
      1278: q
      1280: q
      1281: 1
      1287: 1
      1289: 2q
      1294: 1
      1348: 1
      1358: 1
      1365: 1
      1380: 1
      1390: 1
      1398: 1
      1430: q
      1433: 1
      1464: 1
      1466: 1
      1469: 1
      1474: q
      1477: q
      1478: q
      1484: 1
      1504: 1
      1517: 1
      1607: 1
      1617: 1
      1625: 1
      1641: 1
      1649: 1
      1658: 1
      1715: 1
      1757: 1
      1783: 1
      1813: 1
      1885: 1

1886:    0: 12q^4+9q^3+2q^2+q
         1: 3q^5+12q^4+9q^3+2q^2+q
         2: 3q^5+10q^4+7q^3+2q^2+q
         3: 3q^5+12q^4+9q^3+2q^2+q
         4: 12q^4+9q^3+2q^2+q
         5: 3q^5+12q^4+9q^3+2q^2+q
         6: 3q^5+12q^4+9q^3+2q^2+q
         7: 3q^5+10q^4+7q^3+2q^2+q
         8: 3q^5+9q^4+7q^3+2q^2+q
         9: 2q^6+6q^5+8q^4+5q^3+2q^2+q
        10: 7q^4+6q^3+2q^2+q
        11: q^5+7q^4+6q^3+2q^2+q
        12: 7q^4+6q^3+2q^2+q
        13: 8q^4+7q^3+2q^2+q
        14: 8q^4+7q^3+2q^2+q
        15: q^5+7q^4+7q^3+2q^2+q
        16: 8q^4+9q^3+2q^2+q
        17: q^5+8q^4+9q^3+2q^2+q
        18: 3q^5+8q^4+5q^3+2q^2+q
        19: 12q^4+9q^3+2q^2+q
        20: 3q^5+12q^4+9q^3+2q^2+q
        21: 3q^5+10q^4+7q^3+2q^2+q
        22: 8q^4+9q^3+2q^2+q
        23: q^5+8q^4+9q^3+2q^2+q
        24: q^5+7q^4+7q^3+2q^2+q
        25: 8q^4+9q^3+2q^2+q
        26: q^5+8q^4+9q^3+2q^2+q
        27: q^5+7q^4+7q^3+2q^2+q
        28: 4q^4+6q^3+2q^2+q
        29: 7q^4+6q^3+2q^2+q
        30: 8q^4+7q^3+2q^2+q
        31: 4q^4+6q^3+2q^2+q
        32: 5q^4+7q^3+2q^2+q
        33: 5q^4+9q^3+2q^2+q
        34: 4q^4+6q^3+2q^2+q
        35: 5q^4+7q^3+2q^2+q
        36: 5q^4+9q^3+2q^2+q
        37: 4q^4+6q^3+2q^2+q
        38: q^4+3q^3
        39: 4q^4+6q^3+2q^2+q
        40: q^4+3q^3
        41: 4q^4+5q^3+2q^2+q
        42: q^4+2q^3
        43: 4q^4+4q^3+2q^2+q
        44: 4q^4+4q^3+2q^2+q
        45: 3q^4+4q^3+2q^2+q
        46: 4q^4+7q^3+2q^2+q
        47: 3q^4+7q^3+2q^2+q
        48: 6q^4+5q^3+2q^2+q
        49: 8q^4+9q^3+2q^2+q
        50: q^5+8q^4+9q^3+2q^2+q
        51: 3q^5+8q^4+5q^3+2q^2+q
        52: 8q^4+9q^3+2q^2+q
        53: q^5+8q^4+9q^3+2q^2+q
        54: q^5+7q^4+7q^3+2q^2+q
        55: 8q^4+9q^3+2q^2+q
        56: q^5+8q^4+9q^3+2q^2+q
        57: q^5+7q^4+7q^3+2q^2+q
        58: 2q^4+4q^3+2q^2+q
        59: 2q^3
        60: 2q^4+4q^3+2q^2+q
        61: 2q^3
        62: 2q^4+4q^3+2q^2+q
        63: 2q^3
        64: 3q^4+5q^3+2q^2+q
        65: 2q^3
        66: 2q^4+6q^3+2q^2+q
        67: q^4+3q^3
        68: 2q^3+2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: 4q^4+4q^3+2q^2+q
        71: 4q^4+6q^3+2q^2+q
        72: 5q^4+9q^3+2q^2+q
        73: 5q^4+9q^3+2q^2+q
        74: 4q^4+6q^3+2q^2+q
        75: q^4+3q^3
        76: 4q^4+6q^3+2q^2+q
        77: q^4+3q^3
        78: 4q^4+5q^3+2q^2+q
        79: q^4+2q^3
        80: 2q^4+4q^3+2q^2+q
        81: 2q^4+7q^3+2q^2+q
        82: 4q^4+6q^3+2q^2+q
        83: 5q^4+7q^3+2q^2+q
        84: 2q^4+4q^3+2q^2+q
        85: 2q^4+7q^3+2q^2+q
        86: 4q^4+6q^3+2q^2+q
        87: 5q^4+7q^3+2q^2+q
        88: q^4+3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: 3q^4+2q^3+2q^2+q
        91: 4q^4+7q^3+2q^2+q
        92: 3q^4+7q^3+2q^2+q
        93: 6q^4+5q^3+2q^2+q
        94: 3q^4+8q^3+2q^2+q
        95: 3q^4+8q^3+2q^2+q
        96: q^5+5q^4+5q^3+2q^2+q
        97: 3q^4+8q^3+2q^2+q
        98: 3q^4+8q^3+2q^2+q
        99: q^5+5q^4+5q^3+2q^2+q
       100: 2q^4+8q^3+2q^2+q
       101: 4q^4+8q^3+2q^2+q
       102: 4q^4+7q^3+2q^2+q
       103: q^4+3q^3+2q^2+q
       104: q^3
       105: q^3
       106: q^3
       107: 2q^4+4q^3+2q^2+q
       108: 2q^3
       109: 2q^4+4q^3+2q^2+q
       110: 2q^3
       111: 2q^4+6q^3+2q^2+q
       112: q^4+3q^3
       113: 2q^4+4q^3+2q^2+q
       114: 2q^3
       115: 3q^4+5q^3+2q^2+q
       116: 2q^3
       117: 2q^3+2q^2+q
       119: 2q^3+2q^2+q
       121: q^4+3q^3+2q^2+q
       122: q^3
       123: q^4+5q^3+2q^2+q
       124: 2q^3
       125: q^3+2q^2+q
       126: q^4+2q^3+2q^2+q
       127: 4q^3+2q^2+q
       129: 4q^3+2q^2+q
       131: 2q^4+3q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: 2q^4+7q^3+2q^2+q
       136: 2q^4+7q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+5q^3+2q^2+q
       140: 4q^3+2q^2+q
       141: 2q^4+4q^3+2q^2+q
       142: 3q^4+8q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+5q^3+2q^2+q
       146: 2q^4+4q^3+2q^2+q
       147: 3q^4+8q^3+2q^2+q
       148: 4q^3+2q^2+q
       149: q^4+5q^3+2q^2+q
       150: 2q^4+7q^3+2q^2+q
       151: 2q^4+5q^3+2q^2+q
       152: 3q^3
       153: 3q^4+5q^3+2q^2+q
       154: q^4+3q^3
       155: 3q^4+5q^3+2q^2+q
       156: q^4+2q^3
       157: q^4+3q^3+2q^2+q
       158: 3q^3+2q^2+q
       159: 3q^4+2q^3+2q^2+q
       160: q^4+5q^3+2q^2+q
       161: q^4+5q^3+2q^2+q
       162: 3q^4+4q^3+2q^2+q
       163: q^4+5q^3+2q^2+q
       164: q^4+5q^3+2q^2+q
       165: 3q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^4+3q^3+2q^2+q
       170: q^3
       171: q^3
       172: q^3
       173: 2q^3+2q^2+q
       177: 3q^3+2q^2+q
       179: 2q^3+2q^2+q
       181: 4q^3+2q^2+q
       183: 2q^3+2q^2+q
       185: 2q^3+2q^2+q
       187: q^4+5q^3+2q^2+q
       188: 2q^3
       189: q^4+3q^3+2q^2+q
       190: q^3
       191: q^3+2q^2+q
       193: 2q^3+2q^2+q
       195: q^4+3q^3+2q^2+q
       196: 2q^3
       197: 2q^3+2q^2+q
       198: 2q^3
       199: q^3+2q^2+q
       201: q^4+3q^3+2q^2+q
       202: 2q^3
       203: 2q^3+2q^2+q
       205: 2q^3+2q^2+q
       206: 2q^3
       207: 2q^3+2q^2+q
       208: q^3
       209: q^4+3q^3+2q^2+q
       210: 2q^3
       211: 2q^4+5q^3+2q^2+q
       212: 2q^3
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^2+q
       220: q^3+2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 3q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 3q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^3+2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 3q^3+2q^2+q
       230: q^4+5q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: q^3+2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+5q^3+2q^2+q
       235: 3q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3+2q^2+q
       239: 3q^3+2q^2+q
       241: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: q^4+4q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3+2q^2+q
       262: q^3
       263: 2q^3+2q^2+q
       267: q^3+2q^2+q
       268: q^3
       271: q^3+2q^2+q
       272: q^3
       275: q^3+2q^2+q
       279: q^2+q
       281: q^3+q^2+q
       283: 2q^2+q
       285: 2q^2+q
       287: q^3+2q^2+q
       289: q^3+q^2+q
       291: 3q^3+2q^2+q
       293: q^3+2q^2+q
       295: q^3+2q^2+q
       297: 2q^3+2q^2+q
       298: q^3
       299: q^3+2q^2+q
       301: q^3+2q^2+q
       303: q^3+2q^2+q
       305: 2q^3+2q^2+q
       306: q^3
       307: q^3+2q^2+q
       309: q^3+2q^2+q
       311: q^3+2q^2+q
       313: 2q^3+2q^2+q
       314: q^3
       315: 3q^3+2q^2+q
       317: q^3+2q^2+q
       319: q^3+2q^2+q
       321: q^3+2q^2+q
       323: 2q^2+q
       324: q^3
       325: q^4+3q^3+2q^2+q
       326: q^3
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3+2q^2+q
       340: 3q^3+2q^2+q
       342: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       377: 2q^2+q
       381: q^2+q
       385: q^3+2q^2+q
       389: 2q^2+q
       393: q^3+2q^2+q
       397: 2q^2+q
       401: q^3+2q^2+q
       405: 2q^2+q
       413: q^2+q
       417: q^3+q^2+q
       419: 2q^2+q
       421: 2q^2+q
       423: q^3+2q^2+q
       425: 3q^3+2q^2+q
       427: q^3+2q^2+q
       429: 2q^2+q
       431: 2q^2+q
       433: q^3+2q^2+q
       435: q
       437: q^2+q
       439: q^2+q
       441: q^2+q
       443: q^3+2q^2+q
       445: q^3+2q^2+q
       447: 2q^2+q
       449: 2q^2+q
       451: q^3+2q^2+q
       453: q^2+q
       455: q
       457: q^2+q
       459: q^2+q
       461: q^3+2q^2+q
       463: q^3+2q^2+q
       465: q
       467: q^3+q
       469: q^3+2q^2+q
       471: q^2+q
       473: q^2+q
       475: q^2+q
       477: 2q^2+q
       479: 2q^2+q
       480: q^3
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       485: q^3+q
       487: q
       489: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       521: q^2+q
       529: 2q^2+q
       533: 2q^2+q
       537: q
       541: q^2+q
       545: 2q^2+q
       549: 2q^2+q
       553: q
       557: q^2+q
       561: 2q^2+q
       565: q^2+q
       569: 2q^2+q
       573: 2q^2+q
       577: 2q^2+q
       585: q^2+q
       589: 2q^2+q
       591: 2q^2+q
       593: 2q^2+q
       595: 2q^2+q
       597: q^3+q
       599: q^3+2q^2+q
       601: q
       603: q^2+q
       605: q
       607: q^2+q
       609: q^2+q
       613: q^3+2q^2+q
       615: q^2+q
       617: q
       619: q^2+q
       621: q^2+q
       623: q
       625: q^2+q
       629: q^3+2q^2+q
       631: q^2+q
       633: q
       639: q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q
       649: q
       651: 2q
       653: q
       655: q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       693: 2q^2+q
       709: q^2+q
       713: 2q^2+q
       717: 2q^2+q
       721: q
       725: q^2+q
       733: q
       737: q
       741: q^2+q
       749: q
       753: q^2+q
       757: 2q
       761: q
       765: q^2+q
       769: q
       771: q
       781: q
       785: q^2+q
       787: q^2+q
       791: q^2+q
       797: q
       801: q
       803: q
       805: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       815: q
       821: q
       825: q^2+q
       827: q^2+q
       829: q
       831: q
       833: q
       835: q^2+q
       839: q
       845: q
       847: q
       849: 2q
       851: q
       855: q^2+q
       857: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       884: q
       886: q
       900: q
       904: q
       908: q^2+q
       920: q
       924: q
       928: q^2+q
       944: q
       948: q^2+q
       952: q
       960: 2q
       970: q
       974: q
       988: q
      1004: q
      1006: q
      1008: q
      1010: 2q
      1022: q
      1026: q
      1028: q
      1038: q
      1040: q
      1044: q
      1048: q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q^2+q
      1078: q
      1082: q
      1085: q
      1088: q
      1126: 2q
      1134: q
      1140: q
      1152: q
      1156: q
      1160: q
      1172: q
      1176: q
      1180: q
      1198: q
      1202: q
      1206: q
      1220: q
      1240: q
      1242: q
      1258: q
      1260: q
      1276: q
      1278: q
      1292: q
      1330: q
      1360: q
      1368: q
      1392: q
      1400: q
      1619: 1
      1713: 1
      1807: 1
      1886: 1

1887:    0: q^3+2q^2+1
         1: q^3+2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: q^3+2q^2+1
         7: q^3+2q^2+1
         8: q^3+2q^2+1
         9: q^4+q^3+q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^3+2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: q^3+q^2+1
        19: q^3+2q^2+1
        20: q^3+2q^2+1
        21: q^3+2q^2+1
        22: q^3+2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: q^3+2q^2+1
        26: q^3+2q^2+1
        27: q^3+2q^2+1
        28: q^2+1
        29: q^2+1
        30: q^3+2q^2+1
        31: q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^2
        38: q^3+q^2+1
        39: q^2
        40: q^3+q^2+1
        41: q^2
        42: q^3+q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: q^3+q^2+1
        52: q^3+2q^2+1
        53: q^3+2q^2+1
        54: q^3+2q^2+1
        55: q^3+2q^2+1
        56: q^3+2q^2+1
        57: q^3+2q^2+1
        59: q^2+1
        60: q^2+1
        63: q^2+1
        64: q^2
        65: q^3+q^2+1
        66: q^2
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^2
        75: q^3+q^2+1
        76: q^2
        77: q^3+q^2+1
        78: q^2
        79: q^3+q^2+1
        80: q^2+1
        81: 2q^2+1
        82: q^2+1
        83: q^3+2q^2+1
        84: q^2+1
        85: 2q^2+1
        86: q^2+1
        87: q^3+2q^2+1
        88: 1
        89: 1
        90: 1
        91: 2q^2+1
        92: 2q^2+1
        93: q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+q^2+1
       100: q^3+2q^2+1
       101: q^3+2q^2+1
       102: q^3+2q^2+1
       104: q^2+1
       107: q^2+1
       110: q^2+1
       111: q^2
       112: q^2+1
       114: q^2+1
       115: q^2
       116: q^3+q^2+1
       118: q^2+1
       119: q^2+1
       122: q^2+1
       123: q^2
       124: q^2+1
       125: 1
       126: 1
       128: q^2+1
       130: q^2+1
       132: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: q^2+1
       150: q^3+2q^2+1
       151: q^2
       152: q^3+q^2+1
       153: q^2
       154: q^3+q^2+1
       155: q^2
       156: q^3+q^2+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+1
       161: 2q^2+1
       162: q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: q^3+q^2+1
       170: q^2+1
       174: q^2+1
       178: 1
       180: q^2+1
       182: q^2+1
       183: q^2+1
       186: q^2+1
       187: q^2
       188: q^2+1
       190: q^2+1
       192: 1
       193: q^2+1
       196: q^2+1
       197: q^2
       198: q^2+1
       199: 1
       201: q^2+1
       204: q^2+1
       205: q^2
       206: q^2+1
       208: 1
       210: q^2+1
       211: q^2
       212: q^3+q^2+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       238: q^2+1
       240: q^2+1
       242: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: q^3+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+1
       257: 2q^2+1
       258: q^3+q^2+1
       260: q^2+1
       264: q^2+1
       268: q^2+1
       274: q^2+1
       276: 1
       280: q^2+1
       282: 1
       283: 1
       286: 1
       288: 1
       290: q^2+1
       292: 1
       293: 1
       296: 1
       298: 1
       299: q^2+1
       302: q^2+1
       304: q^2+1
       305: q^2
       306: q^2+1
       307: q^2+1
       310: q^2+1
       312: q^2+1
       313: q^2
       314: q^2+1
       316: 1
       318: q^2+1
       319: q^2+1
       322: q^2+1
       323: q^2
       324: q^2+1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       339: q^2+1
       341: q^2+1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: q^3+q^2+1
       374: 1
       375: 1
       376: 1
       378: 1
       382: q^2+1
       386: 1
       390: q^2+1
       394: q^2+1
       400: q^2+1
       403: q^2+1
       407: q^2+1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: q^2+1
       429: 1
       432: 1
       434: 1
       436: q^2+1
       437: 1
       440: 1
       442: 1
       443: q^2+1
       446: q^2+1
       447: 1
       450: 1
       452: 1
       453: 1
       456: q^2+1
       458: 1
       460: 1
       462: q^2+1
       464: q^2+1
       466: q^2+1
       468: 1
       470: 1
       471: q^2+1
       474: q^2+1
       475: q^2
       476: q^2+1
       478: q^2+1
       479: q^2
       480: q^2+1
       481: 1
       482: 1
       483: 1
       484: q^2+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       530: 1
       534: 1
       538: q^2+1
       542: 1
       546: q^2+1
       551: 1
       556: q^2+1
       560: 1
       564: q^2+1
       566: q^2+1
       571: q^2+1
       574: q^2+1
       581: q^2+1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: q^2+1
       603: 1
       606: 1
       608: 1
       610: 1
       614: 1
       615: q^2+1
       618: q^2+1
       619: 1
       622: 1
       624: 1
       626: 1
       630: 1
       632: q^2+1
       634: q^2+1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: q^2+1
       654: 1
       655: q^2
       656: q^2+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       672: 1
       673: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       699: q^2+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: q^2+1
       740: 1
       744: 1
       752: q^2+1
       754: 1
       759: q^2+1
       763: 1
       766: q^2+1
       773: q^2+1
       776: 1
       780: q+1
       782: 1
       785: 1
       788: 1
       792: 1
       793: 1
       796: q+1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: 1
       812: 1
       815: 1
       818: 1
       820: q+1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: 1
       836: 1
       840: 1
       843: q
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       856: 1
       858: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       890: q^2+1
       903: 1
       905: 1
       909: 1
       917: 1
       921: 1
       926: 1
       929: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       965: 1
       969: q
       972: 1
       976: 1
       989: 1
       995: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1021: q+1
      1023: 1
      1026: 1
      1029: 1
      1037: q+1
      1039: 1
      1040: 1
      1045: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1139: q
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1200: 1
      1205: 1
      1207: 1
      1221: 1
      1231: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1271: 1
      1275: q+1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1287: 1
      1289: 1
      1296: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1421: 1
      1423: 1
      1427: 1
      1431: q
      1434: 1
      1465: 1
      1467: 1
      1468: 1
      1475: 1
      1476: 1
      1479: 1
      1484: 1
      1508: 1
      1519: 1
      1582: 1
      1601: 1
      1610: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1642: 1
      1650: 1
      1657: 1
      1716: 1
      1760: 1
      1782: 1
      1809: 1
      1812: 1
      1887: 1

1888:    0: q^3+2q^2+1
         1: q^3+2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: q^3+2q^2+1
         7: q^3+2q^2+1
         8: q^3+2q^2+1
         9: q^4+q^3+q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^3+2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: q^3+q^2+1
        19: q^3+2q^2+1
        20: q^3+2q^2+1
        21: q^3+2q^2+1
        22: q^3+2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: q^3+2q^2+1
        26: q^3+2q^2+1
        27: q^3+2q^2+1
        28: q^2+1
        29: q^2+1
        30: q^3+2q^2+1
        31: q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^2
        38: q^3+q^2+1
        39: q^2
        40: q^3+q^2+1
        41: q^2
        42: q^3+q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: q^3+q^2+1
        52: q^3+2q^2+1
        53: q^3+2q^2+1
        54: q^3+2q^2+1
        55: q^3+2q^2+1
        56: q^3+2q^2+1
        57: q^3+2q^2+1
        58: q^2+1
        61: q^2+1
        63: q^2+1
        64: q^2
        65: q^3+q^2+1
        66: q^2
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^2
        75: q^3+q^2+1
        76: q^2
        77: q^3+q^2+1
        78: q^2
        79: q^3+q^2+1
        80: q^2+1
        81: 2q^2+1
        82: q^2+1
        83: q^3+2q^2+1
        84: q^2+1
        85: 2q^2+1
        86: q^2+1
        87: q^3+2q^2+1
        88: 1
        89: 1
        90: 1
        91: 2q^2+1
        92: 2q^2+1
        93: q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+q^2+1
       100: q^3+2q^2+1
       101: q^3+2q^2+1
       102: q^3+2q^2+1
       105: q^2+1
       108: q^2+1
       109: q^2+1
       111: q^2
       112: q^2+1
       114: q^2+1
       115: q^2
       116: q^3+q^2+1
       117: q^2+1
       120: q^2+1
       122: q^2+1
       123: q^2
       124: q^2+1
       125: 1
       126: 1
       128: q^2+1
       130: q^2+1
       132: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: q^2+1
       150: q^3+2q^2+1
       151: q^2
       152: q^3+q^2+1
       153: q^2
       154: q^3+q^2+1
       155: q^2
       156: q^3+q^2+1
       157: 1
       158: 1
       159: 1
       160: 2q^2+1
       161: 2q^2+1
       162: q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: q^3+q^2+1
       171: q^2+1
       175: q^2+1
       178: 1
       180: q^2+1
       182: q^2+1
       184: q^2+1
       185: q^2+1
       187: q^2
       188: q^2+1
       190: q^2+1
       191: 1
       194: q^2+1
       195: q^2+1
       197: q^2
       198: q^2+1
       200: 1
       202: q^2+1
       203: q^2+1
       205: q^2
       206: q^2+1
       208: 1
       210: q^2+1
       211: q^2
       212: q^3+q^2+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       238: q^2+1
       240: q^2+1
       242: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: q^3+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+1
       257: 2q^2+1
       258: q^3+q^2+1
       261: q^2+1
       265: q^2+1
       270: q^2+1
       272: q^2+1
       277: 1
       280: q^2+1
       282: 1
       284: 1
       285: 1
       288: 1
       290: q^2+1
       292: 1
       294: 1
       295: 1
       298: 1
       300: q^2+1
       302: q^2+1
       303: q^2+1
       305: q^2
       306: q^2+1
       308: q^2+1
       309: q^2+1
       312: q^2+1
       313: q^2
       314: q^2+1
       316: 1
       318: q^2+1
       320: q^2+1
       321: q^2+1
       323: q^2
       324: q^2+1
       326: q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       339: q^2+1
       341: q^2+1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: q^3+q^2+1
       374: 1
       375: 1
       376: 1
       379: 1
       383: q^2+1
       387: 1
       392: q^2+1
       395: q^2+1
       398: q^2+1
       402: q^2+1
       408: q^2+1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: q^2+1
       430: 1
       431: 1
       434: 1
       436: q^2+1
       438: 1
       439: 1
       442: 1
       444: q^2+1
       446: q^2+1
       448: 1
       449: 1
       452: 1
       454: 1
       456: q^2+1
       457: 1
       460: 1
       461: q^2+1
       464: q^2+1
       466: q^2+1
       468: 1
       470: 1
       472: q^2+1
       473: q^2+1
       475: q^2
       476: q^2+1
       478: q^2+1
       479: q^2
       480: q^2+1
       481: 1
       482: 1
       483: 1
       484: q^2+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 1
       519: 1
       520: 1
       523: 1
       531: 1
       535: 1
       540: q^2+1
       544: 1
       548: q^2+1
       550: 1
       554: q^2+1
       558: 1
       562: q^2+1
       567: q^2+1
       572: q^2+1
       576: q^2+1
       581: q^2+1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: q^2+1
       604: 1
       606: 1
       607: 1
       610: 1
       614: 1
       616: q^2+1
       618: q^2+1
       620: 1
       621: 1
       624: 1
       626: 1
       630: 1
       631: q^2+1
       634: q^2+1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: q^2+1
       654: 1
       655: q^2
       656: q^2+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 1
       672: 1
       673: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       700: q^2+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: q^2+1
       738: 1
       742: 1
       750: q^2+1
       755: 1
       760: q^2+1
       764: 1
       767: q^2+1
       773: q^2+1
       776: 1
       780: q+1
       782: 1
       786: 1
       787: 1
       792: 1
       794: 1
       796: q+1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: 1
       812: 1
       816: 1
       817: 1
       820: q+1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: 1
       836: 1
       839: 1
       843: q
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       856: 1
       858: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       891: q^2+1
       901: 1
       907: 1
       910: 1
       919: 1
       923: 1
       925: 1
       931: 1
       941: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 1
       969: q
       972: 1
       977: 1
       990: 1
       995: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1021: q+1
      1023: 1
      1027: 1
      1028: 1
      1037: q+1
      1039: 1
      1041: 1
      1044: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1139: q
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1201: 1
      1203: 1
      1209: 1
      1221: 1
      1231: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1270: 1
      1275: q+1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1287: 1
      1289: 1
      1297: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1419: 1
      1425: 1
      1428: 1
      1431: q
      1434: 1
      1465: 1
      1466: 1
      1469: 1
      1475: 1
      1477: 1
      1478: 1
      1484: 1
      1507: 1
      1520: 1
      1581: 1
      1602: 1
      1608: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1642: 1
      1649: 1
      1658: 1
      1717: 1
      1758: 1
      1784: 1
      1810: 1
      1813: 1
      1888: 1

1889:    0: q^3+2q^2+1
         1: q^3+2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: q^3+2q^2+1
         7: q^3+2q^2+1
         8: q^3+2q^2+1
         9: q^4+q^3+q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^3+2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: 2q^2+1
        18: q^3+q^2+1
        19: q^3+2q^2+1
        20: q^3+2q^2+1
        21: q^3+2q^2+1
        22: q^3+2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: q^3+2q^2+1
        26: q^3+2q^2+1
        27: q^3+2q^2+1
        28: q^2+1
        29: q^2+1
        30: q^3+2q^2+1
        31: q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^3+q^2+1
        38: q^2
        39: q^3+q^2+1
        40: q^2
        41: q^3+q^2+1
        42: q^2
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 2q^2+1
        47: 2q^2+1
        48: q^3+q^2+1
        49: 2q^2+1
        50: 2q^2+1
        51: q^3+q^2+1
        52: q^3+2q^2+1
        53: q^3+2q^2+1
        54: q^3+2q^2+1
        55: q^3+2q^2+1
        56: q^3+2q^2+1
        57: q^3+2q^2+1
        59: q^2+1
        61: q^2+1
        62: q^2+1
        64: q^3+q^2+1
        65: q^2
        66: q^2+1
        67: q^2
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^3+q^2+1
        75: q^2
        76: q^3+q^2+1
        77: q^2
        78: q^3+q^2+1
        79: q^2
        80: q^2+1
        81: 2q^2+1
        82: q^2+1
        83: q^3+2q^2+1
        84: q^2+1
        85: 2q^2+1
        86: q^2+1
        87: q^3+2q^2+1
        88: 1
        89: 1
        90: 1
        91: 2q^2+1
        92: 2q^2+1
        93: q^3+q^2+1
        94: 2q^2+1
        95: 2q^2+1
        96: q^3+q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+q^2+1
       100: q^3+2q^2+1
       101: q^3+2q^2+1
       102: q^3+2q^2+1
       106: q^2+1
       108: q^2+1
       110: q^2+1
       111: q^2+1
       112: q^2
       113: q^2+1
       115: q^3+q^2+1
       116: q^2
       118: q^2+1
       120: q^2+1
       121: q^2+1
       123: q^2+1
       124: q^2
       125: 1
       126: 1
       127: q^2+1
       129: q^2+1
       131: q^3+1
       133: q^2+1
       134: q^2+1
       135: 2q^2+1
       136: 2q^2+1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: q^2+1
       142: 2q^2+1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 2q^2+1
       148: 2q^2+1
       149: q^2+1
       150: q^3+2q^2+1
       151: q^3+q^2+1
       152: q^2
       153: q^3+q^2+1
       154: q^2
       155: q^3+q^2+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: 2q^2+1
       161: 2q^2+1
       162: q^3+q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: q^3+q^2+1
       166: 2q^2+1
       167: 2q^2+1
       168: q^3+q^2+1
       172: q^2+1
       176: q^2+1
       177: 1
       179: q^2+1
       181: q^2+1
       184: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2
       189: q^2+1
       192: 1
       194: q^2+1
       196: q^2+1
       197: q^2+1
       198: q^2
       200: 1
       202: q^2+1
       204: q^2+1
       205: q^2+1
       206: q^2
       207: 1
       209: q^2+1
       211: q^3+q^2+1
       212: q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 2q^2+1
       230: 2q^2+1
       231: 1
       232: q^2+1
       233: q^2+1
       234: 2q^2+1
       235: 2q^2+1
       236: q^2+1
       237: q^2+1
       239: q^2+1
       241: q^3+1
       243: q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: q^3+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q^2+1
       257: 2q^2+1
       258: q^3+q^2+1
       262: q^2+1
       266: q^2+1
       269: q^2+1
       273: q^2+1
       278: 1
       279: q^2+1
       281: 1
       284: 1
       286: 1
       287: 1
       289: q^2+1
       291: 1
       294: 1
       296: 1
       297: 1
       300: q^2+1
       301: q^2+1
       304: q^2+1
       305: q^2+1
       306: q^2
       308: q^2+1
       310: q^2+1
       311: q^2+1
       313: q^2+1
       314: q^2
       315: 1
       317: q^2+1
       320: q^2+1
       322: q^2+1
       323: q^2+1
       324: q^2
       325: q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       338: q^2+1
       340: q^2+1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: 2q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: 2q^2+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: q^3+q^2+1
       374: 1
       375: 1
       376: 1
       380: 1
       384: q^2+1
       388: 1
       391: q^2+1
       396: q^2+1
       399: q^2+1
       404: q^2+1
       406: q^2+1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: q^2+1
       430: 1
       432: 1
       433: 1
       435: q^2+1
       438: 1
       440: 1
       441: 1
       444: q^2+1
       445: q^2+1
       448: 1
       450: 1
       451: 1
       454: 1
       455: q^2+1
       458: 1
       459: 1
       462: q^2+1
       463: q^2+1
       465: q^2+1
       467: 1
       469: 1
       472: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2
       477: q^2+1
       479: q^2+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: q^2+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 2q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: 2q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 1
       519: 1
       520: 1
       524: 1
       532: 1
       536: 1
       539: q^2+1
       543: 1
       547: q^2+1
       552: 1
       555: q^2+1
       559: 1
       563: q^2+1
       568: q^2+1
       570: q^2+1
       575: q^2+1
       577: q^2+1
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: q^2+1
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       616: q^2+1
       617: q^2+1
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       632: q^2+1
       633: q^2+1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: q^2+1
       653: 1
       655: q^2+1
       656: q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 1
       672: 1
       673: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       697: q^2+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: q^2+1
       739: 1
       743: 1
       751: q^2+1
       756: 1
       758: q^2+1
       762: 1
       768: q^2+1
       769: q^2+1
       775: 1
       779: q+1
       781: 1
       786: 1
       788: 1
       791: 1
       794: 1
       795: q+1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       816: 1
       818: 1
       819: q+1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       840: 1
       843: 1
       844: q
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       857: 1
       866: 1
       868: 1
       870: q+1
       871: 1
       872: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       889: q^2+1
       902: 1
       906: 1
       911: 1
       918: 1
       922: 1
       927: 1
       930: 1
       942: 1
       946: 1
       950: 1
       955: 1
       961: 1
       967: 1
       968: 1
       971: q
       975: 1
       991: 1
       994: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1020: q+1
      1022: 1
      1027: 1
      1029: 1
      1036: q+1
      1038: 1
      1041: 1
      1045: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1076: 1
      1078: 1
      1080: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1141: q
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1199: 1
      1204: 1
      1208: 1
      1220: 1
      1230: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1271: 1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1287: 1
      1289: 1
      1295: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1433: q
      1464: 1
      1467: 1
      1469: 1
      1474: 1
      1477: 1
      1479: 1
      1484: 1
      1506: 1
      1518: 1
      1580: 1
      1600: 1
      1609: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1641: 1
      1650: 1
      1658: 1
      1718: 1
      1759: 1
      1783: 1
      1808: 1
      1814: 1
      1889: 1

1890:    0: 2q^3+3q^2+3q
         1: 2q^3+3q^2+3q
         2: 2q^3+3q^2+3q
         3: 2q^3+3q^2+3q
         4: 2q^3+3q^2+3q
         5: 2q^3+3q^2+3q
         6: 2q^3+3q^2+3q
         7: 2q^3+3q^2+3q
         8: 2q^3+3q^2+3q
         9: q^5+q^4+2q^3+2q^2+2q
        10: q^3+2q^2+3q
        11: q^3+2q^2+3q
        12: q^3+2q^2+3q
        13: 2q^3+3q^2+3q
        14: 2q^3+3q^2+3q
        15: 2q^3+3q^2+3q
        16: 2q^2+3q
        17: 2q^2+3q
        18: q^3+2q^2+2q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 2q^3+3q^2+3q
        23: 2q^3+3q^2+3q
        24: 2q^3+3q^2+3q
        25: 2q^3+3q^2+3q
        26: 2q^3+3q^2+3q
        27: 2q^3+3q^2+3q
        28: q^2+3q
        29: q^3+2q^2+3q
        30: 2q^3+3q^2+3q
        31: q^3+2q^2+3q
        32: 2q^3+3q^2+3q
        33: 2q^2+3q
        34: q^3+2q^2+3q
        35: 2q^3+3q^2+3q
        36: 2q^2+3q
        37: q^3+q^2+q
        38: q^3+2q^2+2q
        39: q^3+q^2+q
        40: q^3+2q^2+2q
        41: q^3+q^2+q
        42: q^3+2q^2+2q
        43: q^3+2q^2+3q
        44: q^3+2q^2+3q
        45: q^3+2q^2+3q
        46: 2q^2+3q
        47: 2q^2+3q
        48: q^3+2q^2+2q
        49: 2q^2+3q
        50: 2q^2+3q
        51: q^3+2q^2+2q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q
        59: q^2+2q
        60: q
        61: q^2+2q
        62: q^2+q
        63: q^3+q^2+2q
        64: q^3+q^2+q
        65: q^3+2q^2+2q
        66: q^2+q
        67: q^2+2q
        68: q^2+3q
        69: q^2+2q
        70: q^3+2q^2+3q
        71: q^2+3q
        72: 2q^2+3q
        73: 2q^2+3q
        74: q^3+q^2+q
        75: q^3+2q^2+2q
        76: q^3+q^2+q
        77: q^3+2q^2+2q
        78: q^3+q^2+q
        79: q^3+2q^2+2q
        80: q^3+2q^2+3q
        81: 2q^2+3q
        82: q^3+2q^2+3q
        83: 2q^3+3q^2+3q
        84: q^3+2q^2+3q
        85: 2q^2+3q
        86: q^3+2q^2+3q
        87: 2q^3+3q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 2q^2+3q
        92: 2q^2+3q
        93: q^3+2q^2+2q
        94: 2q^2+3q
        95: 2q^2+3q
        96: q^3+2q^2+2q
        97: 2q^2+3q
        98: 2q^2+3q
        99: q^3+2q^2+2q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       104: q
       105: q
       106: q^2+q
       107: q
       108: q^2+2q
       109: q
       110: q^2+2q
       111: q^2+q
       112: q^2+2q
       113: q^2+q
       114: q^3+q^2+2q
       115: q^3+q^2+q
       116: q^3+2q^2+2q
       117: q
       118: q^2+2q
       119: q
       120: q^2+2q
       121: q^2+q
       122: q^3+q^2+2q
       123: q^2+q
       124: q^2+2q
       125: 3q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       133: q^2+3q
       134: q^2+2q
       135: 2q^2+3q
       136: 2q^2+3q
       137: 3q
       138: q^2+2q
       139: q^2+3q
       140: 2q^2+3q
       141: q^3+2q^2+3q
       142: 2q^2+3q
       143: 3q
       144: q^2+2q
       145: q^2+3q
       146: q^3+2q^2+3q
       147: 2q^2+3q
       148: 2q^2+3q
       149: q^3+2q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+q^2+q
       152: q^3+2q^2+2q
       153: q^3+q^2+q
       154: q^3+2q^2+2q
       155: q^3+q^2+q
       156: q^3+2q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 2q^2+3q
       161: 2q^2+3q
       162: q^3+2q^2+2q
       163: 2q^2+3q
       164: 2q^2+3q
       165: q^3+2q^2+2q
       166: 2q^2+3q
       167: 2q^2+3q
       168: q^3+2q^2+2q
       170: q
       171: q
       172: q^2+q
       174: q
       175: q
       176: q^2+q
       178: q
       180: 2q
       182: 2q
       183: q
       184: q^2+2q
       185: q
       186: q^2+2q
       187: q^2+q
       188: q^2+2q
       189: q^2+q
       190: q^3+q^2+2q
       191: q
       192: 2q
       193: q
       194: q^2+2q
       195: q
       196: q^2+2q
       197: q^2+q
       198: q^2+2q
       199: q
       200: 2q
       201: q
       202: q^2+2q
       203: q
       204: q^2+2q
       205: q^2+q
       206: q^2+2q
       207: q
       208: 2q
       209: q^2+q
       210: q^3+q^2+2q
       211: q^3+q^2+q
       212: q^3+2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: q^2+2q
       224: 3q
       225: q^2+2q
       226: 2q
       227: q^2+3q
       228: q^2+2q
       229: 2q^2+3q
       230: 2q^2+3q
       231: 2q
       232: q^2+3q
       233: q^2+2q
       234: 2q^2+3q
       235: 2q^2+3q
       236: q^2+2q
       238: 2q
       240: 2q
       242: q^2+q
       243: q^2+3q
       244: 2q^2+3q
       245: 2q^2+3q
       246: q^3+2q^2+3q
       247: 2q^2+3q
       248: 2q^2+3q
       249: q^3+2q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 2q^2+3q
       257: 2q^2+3q
       258: q^3+2q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q^2+q
       268: q
       269: q^2+q
       270: q
       272: q
       273: q^2+q
       274: q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q
       290: 2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       299: q
       300: q^2+2q
       302: 2q
       303: q
       304: q^2+2q
       305: q^2+q
       306: q^2+2q
       307: q
       308: q^2+2q
       309: q
       310: q^2+2q
       312: 2q
       313: q^2+q
       314: q^2+2q
       316: q
       318: 2q
       319: q
       320: q^2+2q
       321: q
       322: q^2+2q
       323: q^2+q
       324: q^2+2q
       325: q^2+q
       326: q^3+q^2+2q
       333: 2q
       334: 2q
       335: 2q
       336: q^2+2q
       337: q^2+3q
       339: 2q
       341: 2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: q^2+2q
       349: 3q
       350: q^2+2q
       351: 2q^2+3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: q^2+2q
       357: 3q
       358: q^2+2q
       359: 2q^2+3q
       361: 2q
       363: 2q
       365: q^2+q
       366: 2q
       367: q^2+3q
       368: q^2+2q
       369: 2q^2+3q
       370: 2q^2+3q
       371: 2q^2+3q
       372: 2q^2+3q
       373: q^3+2q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q
       392: q
       394: q
       395: q
       396: q^2+q
       398: q
       400: q
       402: q
       403: q
       404: q^2+q
       406: q^2+q
       407: q
       408: q
       414: q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 2q
       430: q
       432: q
       434: q
       436: 2q
       437: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: 2q
       443: q
       444: q^2+2q
       446: 2q
       448: q
       450: q
       452: q
       453: q
       454: 2q
       456: 2q
       457: q
       458: 2q
       459: q
       460: 2q
       461: q
       462: q^2+2q
       464: 2q
       466: 2q
       468: q
       470: q
       471: q
       472: q^2+2q
       473: q
       474: q^2+2q
       475: q^2+q
       476: q^2+2q
       478: 2q
       479: q^2+q
       480: q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: q^2+3q
       486: 2q
       488: 2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: 2q
       494: 2q
       495: q^2+2q
       496: 2q^2+3q
       497: 2q
       498: 2q
       499: 2q
       500: q^2+2q
       501: 2q^2+3q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: q^2+2q
       513: 3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q
       548: q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q
       564: q
       566: q
       567: q
       568: q^2+q
       571: q
       572: q
       574: q
       575: q^2+q
       576: q
       581: 2q
       586: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 2q
       604: q
       606: q
       608: q
       610: q
       614: q
       615: q
       616: q^2+2q
       618: 2q
       620: q
       622: q
       624: q
       626: q
       630: q
       631: q
       632: q^2+2q
       634: 2q
       640: q
       642: q
       644: q
       646: q
       647: q
       648: 2q
       649: q
       650: 2q
       652: 2q
       653: q
       654: 2q
       655: q^2+q
       656: q^2+2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: q^2+2q
       686: 2q
       687: 2q
       688: 2q
       689: q^2+2q
       699: q
       700: q
       734: q
       736: q
       750: q
       752: q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q^2+q
       773: 2q
       776: 1
       780: q+1
       782: q
       786: q
       788: q
       792: q
       794: 1
       796: q+1
       798: q
       802: q
       804: q
       806: q
       808: q
       810: q
       812: q
       815: q
       816: 2q
       818: 1
       820: q+1
       822: q
       826: q
       828: q
       830: q
       832: q
       834: q
       836: q
       839: q
       840: 2q
       843: 1
       844: q
       846: q
       848: q
       850: q
       852: q
       856: q
       857: q
       858: 2q
       866: 1
       868: 2q
       870: q+1
       871: 2q
       872: 2q
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: q^2+2q
       890: q
       891: q
       919: 1
       943: 1
       967: 1
       969: 1
       972: q
       989: q
       990: q
       991: q
       995: 1
       999: 1
      1001: 1
      1005: q
      1007: q
      1009: q
      1011: q
      1012: 1
      1013: q
      1021: q+1
      1023: q
      1027: q
      1029: q
      1037: q+1
      1039: q
      1041: q
      1045: q
      1049: q
      1053: q
      1055: q
      1057: q
      1059: q
      1061: q
      1063: q
      1065: q
      1076: 1
      1078: 2q
      1080: 1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1094: 1
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1142: q
      1221: q
      1231: 1
      1233: 1
      1235: 1
      1241: q
      1243: q
      1249: 1
      1251: 1
      1255: 1
      1259: q
      1261: q
      1267: q
      1269: q
      1271: q
      1275: q+1
      1277: q
      1279: q
      1280: 1
      1281: q
      1287: 1
      1289: 2q
      1298: 1
      1351: 1
      1359: 1
      1367: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1434: q
      1465: 1
      1467: 1
      1469: 1
      1475: q
      1477: q
      1479: q
      1484: 1
      1509: 1
      1521: 1
      1610: 1
      1618: 1
      1626: 1
      1642: 1
      1650: 1
      1658: 1
      1720: 1
      1760: 1
      1784: 1
      1814: 1
      1890: 1

1891:    0: 12q^4+9q^3+2q^2+q
         1: 3q^5+12q^4+9q^3+2q^2+q
         2: 3q^5+10q^4+7q^3+2q^2+q
         3: 3q^5+12q^4+9q^3+2q^2+q
         4: 12q^4+9q^3+2q^2+q
         5: 3q^5+12q^4+9q^3+2q^2+q
         6: 3q^5+12q^4+9q^3+2q^2+q
         7: 3q^5+10q^4+7q^3+2q^2+q
         8: 3q^5+9q^4+7q^3+2q^2+q
         9: 2q^6+6q^5+8q^4+5q^3+2q^2+q
        10: 7q^4+6q^3+2q^2+q
        11: q^5+7q^4+6q^3+2q^2+q
        12: 7q^4+6q^3+2q^2+q
        13: 8q^4+7q^3+2q^2+q
        14: 8q^4+7q^3+2q^2+q
        15: q^5+7q^4+7q^3+2q^2+q
        16: 8q^4+9q^3+2q^2+q
        17: q^5+8q^4+9q^3+2q^2+q
        18: 3q^5+8q^4+5q^3+2q^2+q
        19: 12q^4+9q^3+2q^2+q
        20: 3q^5+12q^4+9q^3+2q^2+q
        21: 3q^5+10q^4+7q^3+2q^2+q
        22: 8q^4+9q^3+2q^2+q
        23: q^5+8q^4+9q^3+2q^2+q
        24: q^5+7q^4+7q^3+2q^2+q
        25: 8q^4+9q^3+2q^2+q
        26: q^5+8q^4+9q^3+2q^2+q
        27: q^5+7q^4+7q^3+2q^2+q
        28: 4q^4+6q^3+2q^2+q
        29: 7q^4+6q^3+2q^2+q
        30: 8q^4+7q^3+2q^2+q
        31: 4q^4+6q^3+2q^2+q
        32: 5q^4+7q^3+2q^2+q
        33: 5q^4+9q^3+2q^2+q
        34: 4q^4+6q^3+2q^2+q
        35: 5q^4+7q^3+2q^2+q
        36: 5q^4+9q^3+2q^2+q
        37: 4q^4+6q^3+2q^2+q
        38: q^4+3q^3
        39: 4q^4+6q^3+2q^2+q
        40: q^4+3q^3
        41: 4q^4+5q^3+2q^2+q
        42: q^4+2q^3
        43: 4q^4+4q^3+2q^2+q
        44: 4q^4+4q^3+2q^2+q
        45: 3q^4+4q^3+2q^2+q
        46: 4q^4+7q^3+2q^2+q
        47: 3q^4+7q^3+2q^2+q
        48: 6q^4+5q^3+2q^2+q
        49: 8q^4+9q^3+2q^2+q
        50: q^5+8q^4+9q^3+2q^2+q
        51: 3q^5+8q^4+5q^3+2q^2+q
        52: 8q^4+9q^3+2q^2+q
        53: q^5+8q^4+9q^3+2q^2+q
        54: q^5+7q^4+7q^3+2q^2+q
        55: 8q^4+9q^3+2q^2+q
        56: q^5+8q^4+9q^3+2q^2+q
        57: q^5+7q^4+7q^3+2q^2+q
        58: 2q^3
        59: 2q^4+4q^3+2q^2+q
        60: 2q^3
        61: 2q^4+4q^3+2q^2+q
        62: 2q^4+4q^3+2q^2+q
        63: 2q^3
        64: 3q^4+5q^3+2q^2+q
        65: 2q^3
        66: 2q^4+6q^3+2q^2+q
        67: q^4+3q^3
        68: 2q^3+2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: 4q^4+4q^3+2q^2+q
        71: 4q^4+6q^3+2q^2+q
        72: 5q^4+9q^3+2q^2+q
        73: 5q^4+9q^3+2q^2+q
        74: 4q^4+6q^3+2q^2+q
        75: q^4+3q^3
        76: 4q^4+6q^3+2q^2+q
        77: q^4+3q^3
        78: 4q^4+5q^3+2q^2+q
        79: q^4+2q^3
        80: 2q^4+4q^3+2q^2+q
        81: 2q^4+7q^3+2q^2+q
        82: 4q^4+6q^3+2q^2+q
        83: 5q^4+7q^3+2q^2+q
        84: 2q^4+4q^3+2q^2+q
        85: 2q^4+7q^3+2q^2+q
        86: 4q^4+6q^3+2q^2+q
        87: 5q^4+7q^3+2q^2+q
        88: q^4+3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: 3q^4+2q^3+2q^2+q
        91: 4q^4+7q^3+2q^2+q
        92: 3q^4+7q^3+2q^2+q
        93: 6q^4+5q^3+2q^2+q
        94: 3q^4+8q^3+2q^2+q
        95: 3q^4+8q^3+2q^2+q
        96: q^5+5q^4+5q^3+2q^2+q
        97: 3q^4+8q^3+2q^2+q
        98: 3q^4+8q^3+2q^2+q
        99: q^5+5q^4+5q^3+2q^2+q
       100: 2q^4+8q^3+2q^2+q
       101: 4q^4+8q^3+2q^2+q
       102: 4q^4+7q^3+2q^2+q
       103: q^3
       104: q^3
       105: q^3
       106: q^4+3q^3+2q^2+q
       107: 2q^3
       108: 2q^4+4q^3+2q^2+q
       109: 2q^3
       110: 2q^4+4q^3+2q^2+q
       111: 2q^4+6q^3+2q^2+q
       112: q^4+3q^3
       113: 2q^4+4q^3+2q^2+q
       114: 2q^3
       115: 3q^4+5q^3+2q^2+q
       116: 2q^3
       118: 2q^3+2q^2+q
       120: 2q^3+2q^2+q
       121: q^4+3q^3+2q^2+q
       122: q^3
       123: q^4+5q^3+2q^2+q
       124: 2q^3
       125: q^3+2q^2+q
       126: q^4+2q^3+2q^2+q
       127: 4q^3+2q^2+q
       129: 4q^3+2q^2+q
       131: 2q^4+3q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: 2q^4+7q^3+2q^2+q
       136: 2q^4+7q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+5q^3+2q^2+q
       140: 4q^3+2q^2+q
       141: 2q^4+4q^3+2q^2+q
       142: 3q^4+8q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+5q^3+2q^2+q
       146: 2q^4+4q^3+2q^2+q
       147: 3q^4+8q^3+2q^2+q
       148: 4q^3+2q^2+q
       149: q^4+5q^3+2q^2+q
       150: 2q^4+7q^3+2q^2+q
       151: 2q^4+5q^3+2q^2+q
       152: 3q^3
       153: 3q^4+5q^3+2q^2+q
       154: q^4+3q^3
       155: 3q^4+5q^3+2q^2+q
       156: q^4+2q^3
       157: q^4+3q^3+2q^2+q
       158: 3q^3+2q^2+q
       159: 3q^4+2q^3+2q^2+q
       160: q^4+5q^3+2q^2+q
       161: q^4+5q^3+2q^2+q
       162: 3q^4+4q^3+2q^2+q
       163: q^4+5q^3+2q^2+q
       164: q^4+5q^3+2q^2+q
       165: 3q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^3
       171: q^3
       172: q^4+3q^3+2q^2+q
       176: 2q^3+2q^2+q
       177: 3q^3+2q^2+q
       179: 2q^3+2q^2+q
       181: 4q^3+2q^2+q
       184: 2q^3+2q^2+q
       186: 2q^3+2q^2+q
       187: q^4+5q^3+2q^2+q
       188: 2q^3
       189: q^4+3q^3+2q^2+q
       190: q^3
       192: q^3+2q^2+q
       194: 2q^3+2q^2+q
       195: 2q^3
       196: q^4+3q^3+2q^2+q
       197: 2q^3+2q^2+q
       198: 2q^3
       200: q^3+2q^2+q
       201: 2q^3
       202: q^4+3q^3+2q^2+q
       204: 2q^3+2q^2+q
       205: 2q^3+2q^2+q
       206: 2q^3
       207: 2q^3+2q^2+q
       208: q^3
       209: q^4+3q^3+2q^2+q
       210: 2q^3
       211: 2q^4+5q^3+2q^2+q
       212: 2q^3
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^2+q
       220: q^3+2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 3q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 3q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^3+2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 3q^3+2q^2+q
       230: q^4+5q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: q^3+2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+5q^3+2q^2+q
       235: 3q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3+2q^2+q
       239: 3q^3+2q^2+q
       241: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: q^4+4q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3
       262: q^3+2q^2+q
       266: 2q^3+2q^2+q
       269: q^3+2q^2+q
       270: q^3
       273: q^3+2q^2+q
       274: q^3
       278: q^3+2q^2+q
       279: q^2+q
       281: q^3+q^2+q
       284: 2q^2+q
       286: 2q^2+q
       287: q^3+2q^2+q
       289: q^3+q^2+q
       291: 3q^3+2q^2+q
       294: q^3+2q^2+q
       296: q^3+2q^2+q
       297: 2q^3+2q^2+q
       298: q^3
       300: q^3+2q^2+q
       301: q^3+2q^2+q
       304: q^3+2q^2+q
       305: 2q^3+2q^2+q
       306: q^3
       308: q^3+2q^2+q
       310: q^3+2q^2+q
       311: q^3+2q^2+q
       313: 2q^3+2q^2+q
       314: q^3
       315: 3q^3+2q^2+q
       317: q^3+2q^2+q
       320: q^3+2q^2+q
       322: q^3+2q^2+q
       323: 2q^2+q
       324: q^3
       325: q^4+3q^3+2q^2+q
       326: q^3
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3+2q^2+q
       340: 3q^3+2q^2+q
       342: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       380: 2q^2+q
       384: q^2+q
       388: q^3+2q^2+q
       391: 2q^2+q
       396: q^3+2q^2+q
       399: 2q^2+q
       404: q^3+2q^2+q
       406: 2q^2+q
       413: q^2+q
       417: q^3+q^2+q
       420: 2q^2+q
       422: 2q^2+q
       423: q^3+2q^2+q
       425: 3q^3+2q^2+q
       427: q^3+2q^2+q
       430: 2q^2+q
       432: 2q^2+q
       433: q^3+2q^2+q
       435: q
       438: q^2+q
       440: q^2+q
       441: q^2+q
       444: q^3+2q^2+q
       445: q^3+2q^2+q
       448: 2q^2+q
       450: 2q^2+q
       451: q^3+2q^2+q
       454: q^2+q
       455: q
       458: q^2+q
       459: q^2+q
       462: q^3+2q^2+q
       463: q^3+2q^2+q
       465: q
       467: q^3+q
       469: q^3+2q^2+q
       472: q^2+q
       474: q^2+q
       475: q^2+q
       477: 2q^2+q
       479: 2q^2+q
       480: q^3
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       485: q^3+q
       487: q
       489: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       524: q^2+q
       532: 2q^2+q
       536: 2q^2+q
       539: q
       543: q^2+q
       547: 2q^2+q
       552: 2q^2+q
       555: q
       559: q^2+q
       563: 2q^2+q
       568: q^2+q
       570: 2q^2+q
       575: 2q^2+q
       577: 2q^2+q
       585: q^2+q
       590: 2q^2+q
       592: 2q^2+q
       594: 2q^2+q
       596: 2q^2+q
       597: q^3+q
       599: q^3+2q^2+q
       601: q
       604: q^2+q
       605: q
       608: q^2+q
       609: q^2+q
       613: q^3+2q^2+q
       616: q^2+q
       617: q
       620: q^2+q
       622: q^2+q
       623: q
       625: q^2+q
       629: q^3+2q^2+q
       632: q^2+q
       633: q
       639: q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       648: q
       650: q
       651: 2q
       653: q
       655: q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       697: 2q^2+q
       712: q^2+q
       716: 2q^2+q
       720: 2q^2+q
       723: q
       727: q^2+q
       735: q
       739: q
       743: q^2+q
       751: q
       756: q^2+q
       758: 2q
       762: q
       768: q^2+q
       769: q
       771: q
       781: q
       786: q^2+q
       788: q^2+q
       791: q^2+q
       797: q
       802: q
       804: q
       806: q^2+q
       808: q^2+q
       809: q
       811: q^2+q
       816: q
       821: q
       826: q^2+q
       828: q^2+q
       830: q
       832: q
       833: q
       835: q^2+q
       840: q
       846: q
       848: q
       849: 2q
       851: q
       855: q^2+q
       857: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       889: q
       893: q
       902: q
       906: q
       911: q^2+q
       922: q
       927: q
       930: q^2+q
       946: q
       950: q^2+q
       955: q
       961: 2q
       970: q
       975: q
       991: q
      1005: q
      1007: q
      1008: q
      1010: 2q
      1022: q
      1027: q
      1029: q
      1038: q
      1041: q
      1045: q
      1048: q
      1053: q
      1055: q
      1057: q
      1059: q
      1060: q
      1062: q
      1064: q^2+q
      1078: q
      1082: q
      1085: q
      1095: q
      1127: 2q
      1135: q
      1140: q
      1154: q
      1158: q
      1163: q
      1174: q
      1178: q
      1183: q
      1199: q
      1204: q
      1208: q
      1220: q
      1241: q
      1243: q
      1259: q
      1261: q
      1276: q
      1278: q
      1299: q
      1331: q
      1361: q
      1369: q
      1393: q
      1401: q
      1622: 1
      1722: 1
      1808: 1
      1891: 1

1892:    0: 12q^4+9q^3+2q^2+q
         1: 3q^5+12q^4+9q^3+2q^2+q
         2: 3q^5+10q^4+7q^3+2q^2+q
         3: 3q^5+12q^4+9q^3+2q^2+q
         4: 12q^4+9q^3+2q^2+q
         5: 3q^5+12q^4+9q^3+2q^2+q
         6: 3q^5+12q^4+9q^3+2q^2+q
         7: 3q^5+10q^4+7q^3+2q^2+q
         8: 3q^5+9q^4+7q^3+2q^2+q
         9: 2q^6+6q^5+8q^4+5q^3+2q^2+q
        10: 7q^4+6q^3+2q^2+q
        11: q^5+7q^4+6q^3+2q^2+q
        12: 7q^4+6q^3+2q^2+q
        13: 8q^4+7q^3+2q^2+q
        14: 8q^4+7q^3+2q^2+q
        15: q^5+7q^4+7q^3+2q^2+q
        16: 8q^4+9q^3+2q^2+q
        17: q^5+8q^4+9q^3+2q^2+q
        18: 3q^5+8q^4+5q^3+2q^2+q
        19: 12q^4+9q^3+2q^2+q
        20: 3q^5+12q^4+9q^3+2q^2+q
        21: 3q^5+10q^4+7q^3+2q^2+q
        22: 8q^4+9q^3+2q^2+q
        23: q^5+8q^4+9q^3+2q^2+q
        24: q^5+7q^4+7q^3+2q^2+q
        25: 8q^4+9q^3+2q^2+q
        26: q^5+8q^4+9q^3+2q^2+q
        27: q^5+7q^4+7q^3+2q^2+q
        28: 4q^4+6q^3+2q^2+q
        29: 7q^4+6q^3+2q^2+q
        30: 8q^4+7q^3+2q^2+q
        31: 4q^4+6q^3+2q^2+q
        32: 5q^4+7q^3+2q^2+q
        33: 5q^4+9q^3+2q^2+q
        34: 4q^4+6q^3+2q^2+q
        35: 5q^4+7q^3+2q^2+q
        36: 5q^4+9q^3+2q^2+q
        37: q^4+3q^3
        38: 4q^4+6q^3+2q^2+q
        39: q^4+3q^3
        40: 4q^4+6q^3+2q^2+q
        41: q^4+2q^3
        42: 4q^4+5q^3+2q^2+q
        43: 4q^4+4q^3+2q^2+q
        44: 4q^4+4q^3+2q^2+q
        45: 3q^4+4q^3+2q^2+q
        46: 4q^4+7q^3+2q^2+q
        47: 3q^4+7q^3+2q^2+q
        48: 6q^4+5q^3+2q^2+q
        49: 8q^4+9q^3+2q^2+q
        50: q^5+8q^4+9q^3+2q^2+q
        51: 3q^5+8q^4+5q^3+2q^2+q
        52: 8q^4+9q^3+2q^2+q
        53: q^5+8q^4+9q^3+2q^2+q
        54: q^5+7q^4+7q^3+2q^2+q
        55: 8q^4+9q^3+2q^2+q
        56: q^5+8q^4+9q^3+2q^2+q
        57: q^5+7q^4+7q^3+2q^2+q
        58: 2q^3
        59: 2q^4+4q^3+2q^2+q
        60: 2q^4+4q^3+2q^2+q
        61: 2q^3
        62: 2q^3
        63: 2q^4+4q^3+2q^2+q
        64: 2q^3
        65: 3q^4+5q^3+2q^2+q
        66: q^4+3q^3
        67: 2q^4+6q^3+2q^2+q
        68: 2q^3+2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: 4q^4+4q^3+2q^2+q
        71: 4q^4+6q^3+2q^2+q
        72: 5q^4+9q^3+2q^2+q
        73: 5q^4+9q^3+2q^2+q
        74: q^4+3q^3
        75: 4q^4+6q^3+2q^2+q
        76: q^4+3q^3
        77: 4q^4+6q^3+2q^2+q
        78: q^4+2q^3
        79: 4q^4+5q^3+2q^2+q
        80: 2q^4+4q^3+2q^2+q
        81: 2q^4+7q^3+2q^2+q
        82: 4q^4+6q^3+2q^2+q
        83: 5q^4+7q^3+2q^2+q
        84: 2q^4+4q^3+2q^2+q
        85: 2q^4+7q^3+2q^2+q
        86: 4q^4+6q^3+2q^2+q
        87: 5q^4+7q^3+2q^2+q
        88: q^4+3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: 3q^4+2q^3+2q^2+q
        91: 4q^4+7q^3+2q^2+q
        92: 3q^4+7q^3+2q^2+q
        93: 6q^4+5q^3+2q^2+q
        94: 3q^4+8q^3+2q^2+q
        95: 3q^4+8q^3+2q^2+q
        96: q^5+5q^4+5q^3+2q^2+q
        97: 3q^4+8q^3+2q^2+q
        98: 3q^4+8q^3+2q^2+q
        99: q^5+5q^4+5q^3+2q^2+q
       100: 2q^4+8q^3+2q^2+q
       101: 4q^4+8q^3+2q^2+q
       102: 4q^4+7q^3+2q^2+q
       103: q^3
       104: q^4+3q^3+2q^2+q
       105: q^3
       106: q^3
       107: 2q^4+4q^3+2q^2+q
       108: 2q^3
       109: 2q^3
       110: 2q^4+4q^3+2q^2+q
       111: q^4+3q^3
       112: 2q^4+6q^3+2q^2+q
       113: 2q^3
       114: 2q^4+4q^3+2q^2+q
       115: 2q^3
       116: 3q^4+5q^3+2q^2+q
       118: 2q^3+2q^2+q
       119: 2q^3+2q^2+q
       121: q^3
       122: q^4+3q^3+2q^2+q
       123: 2q^3
       124: q^4+5q^3+2q^2+q
       125: q^3+2q^2+q
       126: q^4+2q^3+2q^2+q
       128: 4q^3+2q^2+q
       130: 4q^3+2q^2+q
       132: 2q^4+3q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: 2q^4+7q^3+2q^2+q
       136: 2q^4+7q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+5q^3+2q^2+q
       140: 4q^3+2q^2+q
       141: 2q^4+4q^3+2q^2+q
       142: 3q^4+8q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+5q^3+2q^2+q
       146: 2q^4+4q^3+2q^2+q
       147: 3q^4+8q^3+2q^2+q
       148: 4q^3+2q^2+q
       149: q^4+5q^3+2q^2+q
       150: 2q^4+7q^3+2q^2+q
       151: 3q^3
       152: 2q^4+5q^3+2q^2+q
       153: q^4+3q^3
       154: 3q^4+5q^3+2q^2+q
       155: q^4+2q^3
       156: 3q^4+5q^3+2q^2+q
       157: q^4+3q^3+2q^2+q
       158: 3q^3+2q^2+q
       159: 3q^4+2q^3+2q^2+q
       160: q^4+5q^3+2q^2+q
       161: q^4+5q^3+2q^2+q
       162: 3q^4+4q^3+2q^2+q
       163: q^4+5q^3+2q^2+q
       164: q^4+5q^3+2q^2+q
       165: 3q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^4+3q^3+2q^2+q
       171: q^3
       172: q^3
       174: 2q^3+2q^2+q
       178: 3q^3+2q^2+q
       180: 2q^3+2q^2+q
       182: 4q^3+2q^2+q
       183: 2q^3+2q^2+q
       186: 2q^3+2q^2+q
       187: 2q^3
       188: q^4+5q^3+2q^2+q
       189: q^3
       190: q^4+3q^3+2q^2+q
       192: q^3+2q^2+q
       193: 2q^3+2q^2+q
       195: 2q^3
       196: q^4+3q^3+2q^2+q
       197: 2q^3
       198: 2q^3+2q^2+q
       199: q^3+2q^2+q
       201: q^4+3q^3+2q^2+q
       202: 2q^3
       204: 2q^3+2q^2+q
       205: 2q^3
       206: 2q^3+2q^2+q
       207: q^3
       208: 2q^3+2q^2+q
       209: 2q^3
       210: q^4+3q^3+2q^2+q
       211: 2q^3
       212: 2q^4+5q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^2+q
       220: q^3+2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 3q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 3q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^3+2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 3q^3+2q^2+q
       230: q^4+5q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: q^3+2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+5q^3+2q^2+q
       235: 3q^3+2q^2+q
       236: 5q^3+2q^2+q
       238: 3q^3+2q^2+q
       240: 3q^3+2q^2+q
       242: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: q^4+4q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       260: q^3+2q^2+q
       261: q^3
       264: 2q^3+2q^2+q
       267: q^3
       268: q^3+2q^2+q
       273: q^3
       274: q^3+2q^2+q
       276: q^3+2q^2+q
       280: q^2+q
       282: q^3+q^2+q
       283: 2q^2+q
       286: 2q^2+q
       288: q^3+2q^2+q
       290: q^3+q^2+q
       292: 3q^3+2q^2+q
       293: q^3+2q^2+q
       296: q^3+2q^2+q
       297: q^3
       298: 2q^3+2q^2+q
       299: q^3+2q^2+q
       302: q^3+2q^2+q
       304: q^3+2q^2+q
       305: q^3
       306: 2q^3+2q^2+q
       307: q^3+2q^2+q
       310: q^3+2q^2+q
       312: q^3+2q^2+q
       313: q^3
       314: 2q^3+2q^2+q
       316: 3q^3+2q^2+q
       318: q^3+2q^2+q
       319: q^3+2q^2+q
       322: q^3+2q^2+q
       323: q^3
       324: 2q^2+q
       325: q^3
       326: q^4+3q^3+2q^2+q
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       339: 3q^3+2q^2+q
       341: 3q^3+2q^2+q
       343: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       378: 2q^2+q
       382: q^2+q
       386: q^3+2q^2+q
       390: 2q^2+q
       394: q^3+2q^2+q
       400: 2q^2+q
       403: q^3+2q^2+q
       407: 2q^2+q
       414: q^2+q
       418: q^3+q^2+q
       419: 2q^2+q
       422: 2q^2+q
       424: q^3+2q^2+q
       426: 3q^3+2q^2+q
       428: q^3+2q^2+q
       429: 2q^2+q
       432: 2q^2+q
       434: q^3+2q^2+q
       436: q
       437: q^2+q
       440: q^2+q
       442: q^2+q
       443: q^3+2q^2+q
       446: q^3+2q^2+q
       447: 2q^2+q
       450: 2q^2+q
       452: q^3+2q^2+q
       453: q^2+q
       456: q
       458: q^2+q
       460: q^2+q
       462: q^3+2q^2+q
       464: q^3+2q^2+q
       466: q
       468: q^3+q
       470: q^3+2q^2+q
       471: q^2+q
       474: q^2+q
       476: q^2+q
       478: 2q^2+q
       479: q^3
       480: 2q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       486: q^3+q
       488: q
       490: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       522: q^2+q
       530: 2q^2+q
       534: 2q^2+q
       538: q
       542: q^2+q
       546: 2q^2+q
       551: 2q^2+q
       556: q
       560: q^2+q
       564: 2q^2+q
       566: q^2+q
       571: 2q^2+q
       574: 2q^2+q
       581: 2q^2+q
       586: q^2+q
       589: 2q^2+q
       592: 2q^2+q
       593: 2q^2+q
       596: 2q^2+q
       598: q^3+q
       600: q^3+2q^2+q
       602: q
       603: q^2+q
       606: q
       608: q^2+q
       610: q^2+q
       614: q^3+2q^2+q
       615: q^2+q
       618: q
       619: q^2+q
       622: q^2+q
       624: q
       626: q^2+q
       630: q^3+2q^2+q
       632: q^2+q
       634: q
       640: q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q
       650: q
       652: 2q
       654: q
       656: q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       699: 2q^2+q
       710: q^2+q
       715: 2q^2+q
       718: 2q^2+q
       722: q
       726: q^2+q
       734: q
       740: q
       744: q^2+q
       752: q
       754: q^2+q
       759: 2q
       763: q
       766: q^2+q
       773: q
       774: q
       782: q
       785: q^2+q
       788: q^2+q
       792: q^2+q
       798: q
       801: q
       804: q
       805: q^2+q
       808: q^2+q
       810: q
       812: q^2+q
       815: q
       822: q
       825: q^2+q
       828: q^2+q
       829: q
       832: q
       834: q
       836: q^2+q
       840: q
       845: q
       848: q
       850: 2q
       852: q
       856: q^2+q
       858: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       890: q
       894: q
       903: q
       905: q
       909: q^2+q
       921: q
       926: q
       929: q^2+q
       947: q
       951: q^2+q
       953: q
       962: 2q
       973: q
       976: q
       989: q
      1004: q
      1007: q
      1009: q
      1011: 2q
      1023: q
      1026: q
      1029: q
      1039: q
      1040: q
      1045: q
      1049: q
      1052: q
      1055: q
      1056: q
      1059: q
      1061: q
      1063: q
      1065: q^2+q
      1078: q
      1082: q
      1085: q
      1096: q
      1128: 2q
      1136: q
      1143: q
      1155: q
      1157: q
      1162: q
      1175: q
      1177: q
      1181: q
      1200: q
      1205: q
      1207: q
      1221: q
      1240: q
      1243: q
      1258: q
      1261: q
      1277: q
      1279: q
      1300: q
      1332: q
      1363: q
      1371: q
      1394: q
      1402: q
      1620: 1
      1719: 1
      1809: 1
      1892: 1

1893:    0: 12q^4+9q^3+2q^2+q
         1: 3q^5+12q^4+9q^3+2q^2+q
         2: 3q^5+10q^4+7q^3+2q^2+q
         3: 3q^5+12q^4+9q^3+2q^2+q
         4: 12q^4+9q^3+2q^2+q
         5: 3q^5+12q^4+9q^3+2q^2+q
         6: 3q^5+12q^4+9q^3+2q^2+q
         7: 3q^5+10q^4+7q^3+2q^2+q
         8: 3q^5+9q^4+7q^3+2q^2+q
         9: 2q^6+6q^5+8q^4+5q^3+2q^2+q
        10: 7q^4+6q^3+2q^2+q
        11: q^5+7q^4+6q^3+2q^2+q
        12: 7q^4+6q^3+2q^2+q
        13: 8q^4+7q^3+2q^2+q
        14: 8q^4+7q^3+2q^2+q
        15: q^5+7q^4+7q^3+2q^2+q
        16: 8q^4+9q^3+2q^2+q
        17: q^5+8q^4+9q^3+2q^2+q
        18: 3q^5+8q^4+5q^3+2q^2+q
        19: 12q^4+9q^3+2q^2+q
        20: 3q^5+12q^4+9q^3+2q^2+q
        21: 3q^5+10q^4+7q^3+2q^2+q
        22: 8q^4+9q^3+2q^2+q
        23: q^5+8q^4+9q^3+2q^2+q
        24: q^5+7q^4+7q^3+2q^2+q
        25: 8q^4+9q^3+2q^2+q
        26: q^5+8q^4+9q^3+2q^2+q
        27: q^5+7q^4+7q^3+2q^2+q
        28: 4q^4+6q^3+2q^2+q
        29: 7q^4+6q^3+2q^2+q
        30: 8q^4+7q^3+2q^2+q
        31: 4q^4+6q^3+2q^2+q
        32: 5q^4+7q^3+2q^2+q
        33: 5q^4+9q^3+2q^2+q
        34: 4q^4+6q^3+2q^2+q
        35: 5q^4+7q^3+2q^2+q
        36: 5q^4+9q^3+2q^2+q
        37: q^4+3q^3
        38: 4q^4+6q^3+2q^2+q
        39: q^4+3q^3
        40: 4q^4+6q^3+2q^2+q
        41: q^4+2q^3
        42: 4q^4+5q^3+2q^2+q
        43: 4q^4+4q^3+2q^2+q
        44: 4q^4+4q^3+2q^2+q
        45: 3q^4+4q^3+2q^2+q
        46: 4q^4+7q^3+2q^2+q
        47: 3q^4+7q^3+2q^2+q
        48: 6q^4+5q^3+2q^2+q
        49: 8q^4+9q^3+2q^2+q
        50: q^5+8q^4+9q^3+2q^2+q
        51: 3q^5+8q^4+5q^3+2q^2+q
        52: 8q^4+9q^3+2q^2+q
        53: q^5+8q^4+9q^3+2q^2+q
        54: q^5+7q^4+7q^3+2q^2+q
        55: 8q^4+9q^3+2q^2+q
        56: q^5+8q^4+9q^3+2q^2+q
        57: q^5+7q^4+7q^3+2q^2+q
        58: 2q^4+4q^3+2q^2+q
        59: 2q^3
        60: 2q^3
        61: 2q^4+4q^3+2q^2+q
        62: 2q^3
        63: 2q^4+4q^3+2q^2+q
        64: 2q^3
        65: 3q^4+5q^3+2q^2+q
        66: q^4+3q^3
        67: 2q^4+6q^3+2q^2+q
        68: 2q^3+2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: 4q^4+4q^3+2q^2+q
        71: 4q^4+6q^3+2q^2+q
        72: 5q^4+9q^3+2q^2+q
        73: 5q^4+9q^3+2q^2+q
        74: q^4+3q^3
        75: 4q^4+6q^3+2q^2+q
        76: q^4+3q^3
        77: 4q^4+6q^3+2q^2+q
        78: q^4+2q^3
        79: 4q^4+5q^3+2q^2+q
        80: 2q^4+4q^3+2q^2+q
        81: 2q^4+7q^3+2q^2+q
        82: 4q^4+6q^3+2q^2+q
        83: 5q^4+7q^3+2q^2+q
        84: 2q^4+4q^3+2q^2+q
        85: 2q^4+7q^3+2q^2+q
        86: 4q^4+6q^3+2q^2+q
        87: 5q^4+7q^3+2q^2+q
        88: q^4+3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: 3q^4+2q^3+2q^2+q
        91: 4q^4+7q^3+2q^2+q
        92: 3q^4+7q^3+2q^2+q
        93: 6q^4+5q^3+2q^2+q
        94: 3q^4+8q^3+2q^2+q
        95: 3q^4+8q^3+2q^2+q
        96: q^5+5q^4+5q^3+2q^2+q
        97: 3q^4+8q^3+2q^2+q
        98: 3q^4+8q^3+2q^2+q
        99: q^5+5q^4+5q^3+2q^2+q
       100: 2q^4+8q^3+2q^2+q
       101: 4q^4+8q^3+2q^2+q
       102: 4q^4+7q^3+2q^2+q
       103: q^3
       104: q^3
       105: q^4+3q^3+2q^2+q
       106: q^3
       107: 2q^3
       108: 2q^4+4q^3+2q^2+q
       109: 2q^4+4q^3+2q^2+q
       110: 2q^3
       111: q^4+3q^3
       112: 2q^4+6q^3+2q^2+q
       113: 2q^3
       114: 2q^4+4q^3+2q^2+q
       115: 2q^3
       116: 3q^4+5q^3+2q^2+q
       117: 2q^3+2q^2+q
       120: 2q^3+2q^2+q
       121: q^3
       122: q^4+3q^3+2q^2+q
       123: 2q^3
       124: q^4+5q^3+2q^2+q
       125: q^3+2q^2+q
       126: q^4+2q^3+2q^2+q
       128: 4q^3+2q^2+q
       130: 4q^3+2q^2+q
       132: 2q^4+3q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: 2q^4+7q^3+2q^2+q
       136: 2q^4+7q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+5q^3+2q^2+q
       140: 4q^3+2q^2+q
       141: 2q^4+4q^3+2q^2+q
       142: 3q^4+8q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+5q^3+2q^2+q
       146: 2q^4+4q^3+2q^2+q
       147: 3q^4+8q^3+2q^2+q
       148: 4q^3+2q^2+q
       149: q^4+5q^3+2q^2+q
       150: 2q^4+7q^3+2q^2+q
       151: 3q^3
       152: 2q^4+5q^3+2q^2+q
       153: q^4+3q^3
       154: 3q^4+5q^3+2q^2+q
       155: q^4+2q^3
       156: 3q^4+5q^3+2q^2+q
       157: q^4+3q^3+2q^2+q
       158: 3q^3+2q^2+q
       159: 3q^4+2q^3+2q^2+q
       160: q^4+5q^3+2q^2+q
       161: q^4+5q^3+2q^2+q
       162: 3q^4+4q^3+2q^2+q
       163: q^4+5q^3+2q^2+q
       164: q^4+5q^3+2q^2+q
       165: 3q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^3
       171: q^4+3q^3+2q^2+q
       172: q^3
       175: 2q^3+2q^2+q
       178: 3q^3+2q^2+q
       180: 2q^3+2q^2+q
       182: 4q^3+2q^2+q
       184: 2q^3+2q^2+q
       185: 2q^3+2q^2+q
       187: 2q^3
       188: q^4+5q^3+2q^2+q
       189: q^3
       190: q^4+3q^3+2q^2+q
       191: q^3+2q^2+q
       194: 2q^3+2q^2+q
       195: q^4+3q^3+2q^2+q
       196: 2q^3
       197: 2q^3
       198: 2q^3+2q^2+q
       200: q^3+2q^2+q
       201: 2q^3
       202: q^4+3q^3+2q^2+q
       203: 2q^3+2q^2+q
       205: 2q^3
       206: 2q^3+2q^2+q
       207: q^3
       208: 2q^3+2q^2+q
       209: 2q^3
       210: q^4+3q^3+2q^2+q
       211: 2q^3
       212: 2q^4+5q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^2+q
       220: q^3+2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 3q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 3q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: q^3+2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 3q^3+2q^2+q
       230: q^4+5q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: q^3+2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+5q^3+2q^2+q
       235: 3q^3+2q^2+q
       236: 5q^3+2q^2+q
       238: 3q^3+2q^2+q
       240: 3q^3+2q^2+q
       242: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: q^4+4q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       260: q^3
       261: q^3+2q^2+q
       265: 2q^3+2q^2+q
       269: q^3
       270: q^3+2q^2+q
       271: q^3
       272: q^3+2q^2+q
       277: q^3+2q^2+q
       280: q^2+q
       282: q^3+q^2+q
       284: 2q^2+q
       285: 2q^2+q
       288: q^3+2q^2+q
       290: q^3+q^2+q
       292: 3q^3+2q^2+q
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       297: q^3
       298: 2q^3+2q^2+q
       300: q^3+2q^2+q
       302: q^3+2q^2+q
       303: q^3+2q^2+q
       305: q^3
       306: 2q^3+2q^2+q
       308: q^3+2q^2+q
       309: q^3+2q^2+q
       312: q^3+2q^2+q
       313: q^3
       314: 2q^3+2q^2+q
       316: 3q^3+2q^2+q
       318: q^3+2q^2+q
       320: q^3+2q^2+q
       321: q^3+2q^2+q
       323: q^3
       324: 2q^2+q
       325: q^3
       326: q^4+3q^3+2q^2+q
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       339: 3q^3+2q^2+q
       341: 3q^3+2q^2+q
       343: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       379: 2q^2+q
       383: q^2+q
       387: q^3+2q^2+q
       392: 2q^2+q
       395: q^3+2q^2+q
       398: 2q^2+q
       402: q^3+2q^2+q
       408: 2q^2+q
       414: q^2+q
       418: q^3+q^2+q
       420: 2q^2+q
       421: 2q^2+q
       424: q^3+2q^2+q
       426: 3q^3+2q^2+q
       428: q^3+2q^2+q
       430: 2q^2+q
       431: 2q^2+q
       434: q^3+2q^2+q
       436: q
       438: q^2+q
       439: q^2+q
       442: q^2+q
       444: q^3+2q^2+q
       446: q^3+2q^2+q
       448: 2q^2+q
       449: 2q^2+q
       452: q^3+2q^2+q
       454: q^2+q
       456: q
       457: q^2+q
       460: q^2+q
       461: q^3+2q^2+q
       464: q^3+2q^2+q
       466: q
       468: q^3+q
       470: q^3+2q^2+q
       472: q^2+q
       473: q^2+q
       476: q^2+q
       478: 2q^2+q
       479: q^3
       480: 2q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       486: q^3+q
       488: q
       490: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       523: q^2+q
       531: 2q^2+q
       535: 2q^2+q
       540: q
       544: q^2+q
       548: 2q^2+q
       550: 2q^2+q
       554: q
       558: q^2+q
       562: 2q^2+q
       567: q^2+q
       572: 2q^2+q
       576: 2q^2+q
       581: 2q^2+q
       586: q^2+q
       590: 2q^2+q
       591: 2q^2+q
       594: 2q^2+q
       595: 2q^2+q
       598: q^3+q
       600: q^3+2q^2+q
       602: q
       604: q^2+q
       606: q
       607: q^2+q
       610: q^2+q
       614: q^3+2q^2+q
       616: q^2+q
       618: q
       620: q^2+q
       621: q^2+q
       624: q
       626: q^2+q
       630: q^3+2q^2+q
       631: q^2+q
       634: q
       640: q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       648: q
       649: q
       652: 2q
       654: q
       656: q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       700: 2q^2+q
       711: q^2+q
       714: 2q^2+q
       719: 2q^2+q
       724: q
       728: q^2+q
       736: q
       738: q
       742: q^2+q
       750: q
       755: q^2+q
       760: 2q
       764: q
       767: q^2+q
       773: q
       774: q
       782: q
       786: q^2+q
       787: q^2+q
       792: q^2+q
       798: q
       802: q
       803: q
       806: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       816: q
       822: q
       826: q^2+q
       827: q^2+q
       830: q
       831: q
       834: q
       836: q^2+q
       839: q
       846: q
       847: q
       850: 2q
       852: q
       856: q^2+q
       858: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       891: q
       895: q
       901: q
       907: q
       910: q^2+q
       923: q
       925: q
       931: q^2+q
       945: q
       949: q^2+q
       954: q
       963: 2q
       973: q
       977: q
       990: q
      1005: q
      1006: q
      1009: q
      1011: 2q
      1023: q
      1027: q
      1028: q
      1039: q
      1041: q
      1044: q
      1049: q
      1053: q
      1054: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q^2+q
      1078: q
      1082: q
      1085: q
      1097: q
      1129: 2q
      1137: q
      1143: q
      1153: q
      1159: q
      1161: q
      1173: q
      1179: q
      1182: q
      1201: q
      1203: q
      1209: q
      1221: q
      1241: q
      1242: q
      1259: q
      1260: q
      1277: q
      1279: q
      1301: q
      1333: q
      1362: q
      1370: q
      1395: q
      1403: q
      1621: 1
      1721: 1
      1810: 1
      1893: 1

1894:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 5q^3+6q^2+3q+1
        23: 5q^3+6q^2+3q+1
        24: 2q^4+4q^3+5q^2+3q+1
        25: 3q^3+5q^2+3q+1
        26: 3q^3+5q^2+3q+1
        27: q^4+3q^3+4q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 5q^3+6q^2+3q+1
        32: 3q^3+5q^2+3q+1
        33: 5q^3+6q^2+3q+1
        34: 3q^3+5q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: 3q^3+5q^2+3q+1
        37: 3q^3+5q^2+3q+1
        39: 3q^3+5q^2+3q+1
        41: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+5q^2+3q+1
        53: 3q^3+5q^2+3q+1
        54: q^4+3q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 2q^3+3q^2+3q+1
        58: 3q^3+4q^2+2q+1
        59: 2q^3+2q^2+q
        60: 2q^3+3q^2+2q+1
        61: q^3+2q^2+q
        62: 3q^3+5q^2+3q+1
        64: 2q^3+4q^2+3q+1
        66: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: 3q^2+3q+1
        73: q^3+4q^2+3q+1
        74: q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        78: 2q^3+3q^2+3q+1
        80: 3q^3+5q^2+3q+1
        81: 3q^3+5q^2+3q+1
        82: 3q^3+5q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 2q^3+4q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: 3q^3+5q^2+3q+1
        95: 3q^3+5q^2+3q+1
        96: q^4+3q^3+4q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       103: 2q^3+3q^2+2q+1
       106: q^3+2q^2+q
       107: 2q^2+2q+1
       108: q^2+q
       109: q^3+3q^2+2q+1
       110: q^2+q
       111: 3q^2+3q+1
       113: q^3+4q^2+3q+1
       115: q^3+3q^2+3q+1
       117: q^3+3q^2+2q+1
       118: q^2+q
       119: q^3+2q^2+2q+1
       120: q^2+q
       121: 2q^3+4q^2+3q+1
       123: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       127: q^3+4q^2+3q+1
       129: q^3+4q^2+3q+1
       131: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^3+5q^2+3q+1
       138: 2q^3+4q^2+3q+1
       139: 3q^3+5q^2+3q+1
       140: 3q^2+3q+1
       141: 2q^3+4q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 2q^3+4q^2+3q+1
       144: q^3+3q^2+3q+1
       145: q^3+4q^2+3q+1
       146: q^3+3q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+2q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       155: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: q^3+4q^2+3q+1
       162: q^3+4q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       169: 2q^2+2q+1
       172: q^2+q
       173: q^3+2q^2+2q+1
       176: q^2+q
       177: q^3+3q^2+3q+1
       179: q^3+4q^2+3q+1
       181: 3q^2+3q+1
       183: q^2+2q+1
       184: q
       185: 2q^2+2q+1
       186: q
       187: 2q^2+3q+1
       189: q^3+3q^2+3q+1
       191: q^3+3q^2+2q+1
       192: q^2+q
       193: 2q^2+2q+1
       194: q^2+q
       195: q^3+3q^2+2q+1
       196: q^2+q
       197: 3q^2+3q+1
       199: q^3+2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       203: q^2+2q+1
       205: q^2+2q+1
       207: 2q^3+4q^2+3q+1
       209: q^3+4q^2+3q+1
       211: q^3+3q^2+3q+1
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 3q^2+3q+1
       225: 3q^2+3q+1
       226: 2q^3+4q^2+3q+1
       227: 3q^2+3q+1
       228: q^3+4q^2+3q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^3+3q^2+3q+1
       232: q^2+3q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^3+3q^2+3q+1
       237: q^3+4q^2+3q+1
       239: q^3+4q^2+3q+1
       241: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: 3q^2+3q+1
       245: q^2+2q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: 2q^2+2q+1
       262: q^2+q
       263: q^2+2q+1
       266: q
       267: 2q^2+2q+1
       269: q^2+q
       271: q^2+2q+1
       275: q^3+2q^2+2q+1
       278: q^2+q
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: q^2+2q+1
       284: q
       285: 2q^2+2q+1
       286: q
       287: q^3+3q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: q^2+2q+1
       294: q
       295: 2q^2+2q+1
       296: q
       297: 2q^2+3q+1
       299: q^2+2q+1
       300: q
       301: 3q^2+3q+1
       303: 2q^2+2q+1
       304: q
       305: 2q^2+3q+1
       307: 2q+1
       308: q
       309: 2q+1
       311: q^2+2q+1
       313: 2q+1
       315: q^3+3q^2+3q+1
       317: q^3+4q^2+3q+1
       319: 2q^2+2q+1
       320: q^2+q
       321: q^2+2q+1
       323: q^2+2q+1
       325: q^3+3q^2+3q+1
       327: 2q^2+3q+1
       329: 2q^2+3q+1
       331: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: 3q^2+3q+1
       345: 3q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: 3q^2+3q+1
       350: 3q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q+1
       358: 2q+1
       359: q^2+2q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q^2+2q+1
       380: q
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: 2q^2+2q+1
       391: q^2+q
       393: q^2+2q+1
       396: q
       397: q^2+2q+1
       401: 2q+1
       405: q^2+2q+1
       409: q^2+3q+1
       411: 2q^2+3q+1
       413: q^2+3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: q^2+2q+1
       420: q
       421: 2q^2+2q+1
       422: q
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: q^2+2q+1
       430: q
       431: 2q^2+2q+1
       432: q
       433: 2q^2+3q+1
       435: q^2+3q+1
       437: q^2+2q+1
       438: q
       439: 2q^2+2q+1
       440: q
       441: 2q^2+3q+1
       443: q^2+2q+1
       444: q^2+q
       445: 2q^2+3q+1
       447: 2q+1
       448: q
       449: 2q+1
       451: 2q+1
       453: 2q+1
       454: q
       455: 2q+1
       457: 2q+1
       459: 2q+1
       461: q^2+2q+1
       463: q^2+2q+1
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+3q^2+3q+1
       471: 2q+1
       472: q
       473: 2q+1
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: q^2+2q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 3q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q^2+3q+1
       504: 2q^2+3q+1
       506: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 2q+1
       524: q
       525: 2q+1
       528: q
       529: q^2+2q+1
       532: q
       533: q^2+2q+1
       536: q
       537: 2q+1
       539: q
       541: q^2+2q+1
       543: q
       545: q^2+2q+1
       547: q^2+q
       549: 2q+1
       553: 2q+1
       557: 2q+1
       561: q^2+2q+1
       565: 2q+1
       569: q^2+2q+1
       573: q^2+2q+1
       577: q^2+2q+1
       583: q^2+3q+1
       585: 3q+1
       587: q^2+3q+1
       589: 2q+1
       590: q
       591: q+1
       593: q+1
       595: q^2+2q+1
       596: q
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: q^2+2q+1
       604: q
       605: q^2+3q+1
       607: 2q^2+2q+1
       608: q
       609: 2q^2+3q+1
       611: q^2+3q+1
       613: q^2+2q+1
       615: q+1
       616: q
       617: 2q+1
       619: 2q+1
       620: q
       621: 2q+1
       623: 2q+1
       625: 2q+1
       627: 2q+1
       629: q+1
       631: q+1
       633: q+1
       635: q^2+3q+1
       637: 2q^2+3q+1
       639: q^2+3q+1
       641: 2q+1
       642: q
       643: 2q+1
       645: 2q+1
       647: 2q+1
       648: q
       649: 2q+1
       651: 2q+1
       653: 2q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: 3q+1
       676: q^2+3q+1
       677: q^2+2q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: 1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       705: 2q+1
       708: q
       709: 2q+1
       712: q
       713: q+1
       717: q+1
       721: 2q+1
       723: q
       725: q^2+2q+1
       727: q
       729: 2q+1
       731: q
       733: q+1
       735: q
       737: 2q+1
       741: 2q+1
       745: 2q+1
       749: q+1
       753: 2q+1
       757: 2q+1
       761: 2q+1
       765: q+1
       769: q+1
       775: 2q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       793: q+1
       794: q
       795: 2q+1
       797: 3q+1
       799: q^2+3q+1
       801: 2q+1
       802: q
       803: q+1
       805: q+1
       807: q^2+2q+1
       808: q
       809: q+1
       811: q^2+2q+1
       813: 2q+1
       815: q+1
       816: q
       817: q+1
       819: q+1
       821: q+1
       823: 2q+1
       825: 2q+1
       826: q
       827: q+1
       831: q+1
       833: 1
       835: q+1
       837: q+1
       839: q+1
       841: q^2+3q+1
       843: q+1
       845: 2q+1
       846: q
       847: 2q+1
       849: 2q+1
       851: 2q+1
       853: 2q+1
       855: q+1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: 1
       884: q+1
       896: 2q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: 2q+1
       914: q
       916: q+1
       918: q
       920: 2q+1
       922: q
       924: q+1
       928: q+1
       932: q+1
       934: q
       936: 2q+1
       940: q+1
       944: q+1
       948: q+1
       956: q+1
       960: 2q+1
       964: q+1
       968: q+1
       974: 2q+1
       978: 2q+1
       982: q+1
       988: q+1
       992: 2q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 2q+1
      1016: q+1
      1017: q
      1018: 3q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: 1
      1028: 1
      1030: q+1
      1032: q+1
      1034: q+1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: q+1
      1048: q+1
      1050: 2q+1
      1052: 2q+1
      1053: q
      1054: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1144: q+1
      1146: q
      1148: 2q+1
      1150: q
      1152: 1
      1156: 1
      1160: 1
      1164: q+1
      1168: q+1
      1172: 1
      1184: 2q+1
      1188: q+1
      1194: q+1
      1198: q+1
      1202: q+1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 2
      1224: 1
      1230: q+1
      1232: 1
      1234: 1
      1236: q+1
      1238: q+1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1264: q+1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 2
      1326: 1
      1330: 1
      1334: 1
      1336: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 2
      1364: 1
      1368: 1
      1376: 1
      1380: 1
      1414: q+1
      1418: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: q+1
      1450: 1
      1454: 1
      1456: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1474: 1
      1478: 1
      1480: 2
      1482: 1
      1487: 1
      1489: 1
      1491: 1
      1501: 1
      1503: 1
      1537: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 2
      1575: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1663: 1
      1671: 1
      1687: 1
      1689: 1
      1729: 1
      1741: 1
      1753: 1
      1785: 1
      1823: 1
      1894: 1

1895:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 5q^3+6q^2+3q+1
        23: 5q^3+6q^2+3q+1
        24: 2q^4+4q^3+5q^2+3q+1
        25: 3q^3+5q^2+3q+1
        26: 3q^3+5q^2+3q+1
        27: q^4+3q^3+4q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 5q^3+6q^2+3q+1
        32: 3q^3+5q^2+3q+1
        33: 5q^3+6q^2+3q+1
        34: 3q^3+5q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: 3q^3+5q^2+3q+1
        37: 3q^3+5q^2+3q+1
        39: 3q^3+5q^2+3q+1
        41: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+5q^2+3q+1
        53: 3q^3+5q^2+3q+1
        54: q^4+3q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 2q^3+3q^2+3q+1
        58: 2q^3+2q^2+q
        59: 3q^3+4q^2+2q+1
        60: q^3+2q^2+q
        61: 2q^3+3q^2+2q+1
        62: 3q^3+5q^2+3q+1
        64: 2q^3+4q^2+3q+1
        66: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: 3q^2+3q+1
        73: q^3+4q^2+3q+1
        74: q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        78: 2q^3+3q^2+3q+1
        80: 3q^3+5q^2+3q+1
        81: 3q^3+5q^2+3q+1
        82: 3q^3+5q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 2q^3+4q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: 3q^3+5q^2+3q+1
        95: 3q^3+5q^2+3q+1
        96: q^4+3q^3+4q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       103: q^3+2q^2+q
       106: 2q^3+3q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: q^2+q
       110: q^3+3q^2+2q+1
       111: 3q^2+3q+1
       113: q^3+4q^2+3q+1
       115: q^3+3q^2+3q+1
       117: q^2+q
       118: q^3+3q^2+2q+1
       119: q^2+q
       120: q^3+2q^2+2q+1
       121: 2q^3+4q^2+3q+1
       123: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       127: q^3+4q^2+3q+1
       129: q^3+4q^2+3q+1
       131: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^3+5q^2+3q+1
       138: 2q^3+4q^2+3q+1
       139: 3q^3+5q^2+3q+1
       140: 3q^2+3q+1
       141: 2q^3+4q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 2q^3+4q^2+3q+1
       144: q^3+3q^2+3q+1
       145: q^3+4q^2+3q+1
       146: q^3+3q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+2q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       155: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: q^3+4q^2+3q+1
       162: q^3+4q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       172: 2q^2+2q+1
       173: q^2+q
       176: q^3+2q^2+2q+1
       177: q^3+3q^2+3q+1
       179: q^3+4q^2+3q+1
       181: 3q^2+3q+1
       183: q
       184: q^2+2q+1
       185: q
       186: 2q^2+2q+1
       187: 2q^2+3q+1
       189: q^3+3q^2+3q+1
       191: q^2+q
       192: q^3+3q^2+2q+1
       193: q^2+q
       194: 2q^2+2q+1
       195: q^2+q
       196: q^3+3q^2+2q+1
       197: 3q^2+3q+1
       199: q^2+q
       200: q^3+2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       204: q^2+2q+1
       205: q^2+2q+1
       207: 2q^3+4q^2+3q+1
       209: q^3+4q^2+3q+1
       211: q^3+3q^2+3q+1
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 3q^2+3q+1
       225: 3q^2+3q+1
       226: 2q^3+4q^2+3q+1
       227: 3q^2+3q+1
       228: q^3+4q^2+3q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^3+3q^2+3q+1
       232: q^2+3q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^3+3q^2+3q+1
       237: q^3+4q^2+3q+1
       239: q^3+4q^2+3q+1
       241: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: 3q^2+3q+1
       245: q^2+2q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q^2+q
       262: 2q^2+2q+1
       263: q
       266: q^2+2q+1
       267: q^2+q
       269: 2q^2+2q+1
       273: q^2+2q+1
       275: q^2+q
       278: q^3+2q^2+2q+1
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: q
       284: q^2+2q+1
       285: q
       286: 2q^2+2q+1
       287: q^3+3q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: q
       294: q^2+2q+1
       295: q
       296: 2q^2+2q+1
       297: 2q^2+3q+1
       299: q
       300: q^2+2q+1
       301: 3q^2+3q+1
       303: q
       304: 2q^2+2q+1
       305: 2q^2+3q+1
       307: q
       308: 2q+1
       310: 2q+1
       311: q^2+2q+1
       313: 2q+1
       315: q^3+3q^2+3q+1
       317: q^3+4q^2+3q+1
       319: q^2+q
       320: 2q^2+2q+1
       322: q^2+2q+1
       323: q^2+2q+1
       325: q^3+3q^2+3q+1
       327: 2q^2+3q+1
       329: 2q^2+3q+1
       331: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: 3q^2+3q+1
       345: 3q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: 3q^2+3q+1
       350: 3q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q+1
       358: 2q+1
       359: q^2+2q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       380: q^2+2q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       389: q^2+q
       391: 2q^2+2q+1
       393: q
       396: q^2+2q+1
       399: q^2+2q+1
       404: 2q+1
       406: q^2+2q+1
       409: q^2+3q+1
       411: 2q^2+3q+1
       413: q^2+3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: q
       420: q^2+2q+1
       421: q
       422: 2q^2+2q+1
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: q
       430: q^2+2q+1
       431: q
       432: 2q^2+2q+1
       433: 2q^2+3q+1
       435: q^2+3q+1
       437: q
       438: q^2+2q+1
       439: q
       440: 2q^2+2q+1
       441: 2q^2+3q+1
       443: q^2+q
       444: q^2+2q+1
       445: 2q^2+3q+1
       447: q
       448: 2q+1
       450: 2q+1
       451: 2q+1
       453: q
       454: 2q+1
       455: 2q+1
       458: 2q+1
       459: 2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+3q^2+3q+1
       471: q
       472: 2q+1
       474: 2q+1
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: q^2+2q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 3q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q^2+3q+1
       504: 2q^2+3q+1
       506: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: 2q+1
       525: q
       528: 2q+1
       529: q
       532: q^2+2q+1
       533: q
       536: q^2+2q+1
       537: q
       539: 2q+1
       541: q
       543: q^2+2q+1
       545: q^2+q
       547: q^2+2q+1
       552: 2q+1
       555: 2q+1
       559: 2q+1
       563: q^2+2q+1
       568: 2q+1
       570: q^2+2q+1
       575: q^2+2q+1
       577: q^2+2q+1
       583: q^2+3q+1
       585: 3q+1
       587: q^2+3q+1
       589: q
       590: 2q+1
       592: q+1
       594: q+1
       595: q
       596: q^2+2q+1
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: q
       604: q^2+2q+1
       605: q^2+3q+1
       607: q
       608: 2q^2+2q+1
       609: 2q^2+3q+1
       611: q^2+3q+1
       613: q^2+2q+1
       615: q
       616: q+1
       617: 2q+1
       619: q
       620: 2q+1
       622: 2q+1
       623: 2q+1
       625: 2q+1
       627: 2q+1
       629: q+1
       632: q+1
       633: q+1
       635: q^2+3q+1
       637: 2q^2+3q+1
       639: q^2+3q+1
       641: q
       642: 2q+1
       644: 2q+1
       645: 2q+1
       647: q
       648: 2q+1
       650: 2q+1
       651: 2q+1
       653: 2q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: 3q+1
       676: q^2+3q+1
       677: q^2+2q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: 1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q^2+2q+1
       705: q
       708: 2q+1
       709: q
       712: 2q+1
       716: q+1
       720: q+1
       721: q
       723: 2q+1
       725: q
       727: q^2+2q+1
       729: q
       731: 2q+1
       733: q
       735: q+1
       739: 2q+1
       743: 2q+1
       747: 2q+1
       751: q+1
       756: 2q+1
       758: 2q+1
       762: 2q+1
       768: q+1
       769: q+1
       775: 2q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       793: q
       794: q+1
       795: 2q+1
       797: 3q+1
       799: q^2+3q+1
       801: q
       802: 2q+1
       804: q+1
       806: q+1
       807: q
       808: q^2+2q+1
       809: q+1
       811: q^2+2q+1
       813: 2q+1
       815: q
       816: q+1
       818: q+1
       819: q+1
       821: q+1
       823: 2q+1
       825: q
       826: 2q+1
       828: q+1
       832: q+1
       833: 1
       835: q+1
       837: q+1
       840: q+1
       841: q^2+3q+1
       843: q+1
       845: q
       846: 2q+1
       848: 2q+1
       849: 2q+1
       851: 2q+1
       853: 2q+1
       855: q+1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: 1
       889: q+1
       896: q
       899: 2q+1
       902: 1
       906: 1
       911: 1
       912: q
       914: 2q+1
       916: q
       918: q+1
       920: q
       922: 2q+1
       927: q+1
       930: q+1
       932: q
       934: q+1
       938: 2q+1
       942: q+1
       946: q+1
       950: q+1
       958: q+1
       961: 2q+1
       967: q+1
       968: q+1
       975: 2q+1
       979: 2q+1
       982: q+1
       991: q+1
       992: 2q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 2q+1
      1016: q
      1017: q+1
      1018: 3q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1027: 1
      1029: 1
      1030: q+1
      1033: q+1
      1034: q+1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: q+1
      1048: q+1
      1050: 2q+1
      1052: q
      1053: 2q+1
      1055: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: q+1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1144: q
      1146: q+1
      1148: q
      1150: 2q+1
      1154: 1
      1158: 1
      1163: 1
      1166: q+1
      1170: q+1
      1174: 1
      1185: 2q+1
      1188: q+1
      1197: q+1
      1199: q+1
      1204: q+1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 2
      1224: 1
      1230: q+1
      1233: 1
      1235: 1
      1236: q+1
      1238: q+1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1264: q+1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 2
      1329: 1
      1331: 1
      1334: 1
      1336: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 2
      1367: 1
      1369: 1
      1378: 1
      1382: 1
      1415: q+1
      1420: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: q+1
      1451: 1
      1455: 1
      1456: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1474: 1
      1479: 1
      1480: 2
      1482: 1
      1487: 1
      1494: 1
      1498: 1
      1506: 1
      1510: 1
      1538: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 2
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1664: 1
      1671: 1
      1692: 1
      1696: 1
      1730: 1
      1742: 1
      1754: 1
      1787: 1
      1823: 1
      1895: 1

1896:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 5q^3+6q^2+3q+1
        23: 5q^3+6q^2+3q+1
        24: 2q^4+4q^3+5q^2+3q+1
        25: 3q^3+5q^2+3q+1
        26: 3q^3+5q^2+3q+1
        27: q^4+3q^3+4q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 5q^3+6q^2+3q+1
        32: 3q^3+5q^2+3q+1
        33: 5q^3+6q^2+3q+1
        34: 3q^3+5q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: 3q^3+5q^2+3q+1
        38: 3q^3+5q^2+3q+1
        40: 3q^3+5q^2+3q+1
        42: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+5q^2+3q+1
        53: 3q^3+5q^2+3q+1
        54: q^4+3q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 2q^3+3q^2+3q+1
        58: 3q^3+4q^2+2q+1
        59: 2q^3+2q^2+q
        60: q^3+2q^2+q
        61: 2q^3+3q^2+2q+1
        63: 3q^3+5q^2+3q+1
        65: 2q^3+4q^2+3q+1
        67: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: 3q^2+3q+1
        73: q^3+4q^2+3q+1
        75: q^3+4q^2+3q+1
        77: q^3+4q^2+3q+1
        79: 2q^3+3q^2+3q+1
        80: 3q^3+5q^2+3q+1
        81: 3q^3+5q^2+3q+1
        82: 3q^3+5q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 2q^3+4q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: 3q^3+5q^2+3q+1
        95: 3q^3+5q^2+3q+1
        96: q^4+3q^3+4q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       104: q^3+2q^2+q
       105: 2q^3+3q^2+2q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: q^3+3q^2+2q+1
       110: q^2+q
       112: 3q^2+3q+1
       114: q^3+4q^2+3q+1
       116: q^3+3q^2+3q+1
       117: q^3+3q^2+2q+1
       118: q^2+q
       119: q^2+q
       120: q^3+2q^2+2q+1
       122: 2q^3+4q^2+3q+1
       124: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       128: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       132: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^3+5q^2+3q+1
       138: 2q^3+4q^2+3q+1
       139: 3q^3+5q^2+3q+1
       140: 3q^2+3q+1
       141: 2q^3+4q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 2q^3+4q^2+3q+1
       144: q^3+3q^2+3q+1
       145: q^3+4q^2+3q+1
       146: q^3+3q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+2q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       152: q^3+4q^2+3q+1
       154: q^3+4q^2+3q+1
       156: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: q^3+4q^2+3q+1
       162: q^3+4q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       170: q^2+q
       171: 2q^2+2q+1
       174: q^2+q
       175: q^3+2q^2+2q+1
       178: q^3+3q^2+3q+1
       180: q^3+4q^2+3q+1
       182: 3q^2+3q+1
       183: q
       184: q^2+2q+1
       185: 2q^2+2q+1
       186: q
       188: 2q^2+3q+1
       190: q^3+3q^2+3q+1
       191: q^3+3q^2+2q+1
       192: q^2+q
       193: q^2+q
       194: 2q^2+2q+1
       195: q^3+3q^2+2q+1
       196: q^2+q
       198: 3q^2+3q+1
       199: q^2+q
       200: q^3+2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: q^2+2q+1
       206: q^2+2q+1
       208: 2q^3+4q^2+3q+1
       210: q^3+4q^2+3q+1
       212: q^3+3q^2+3q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 3q^2+3q+1
       225: 3q^2+3q+1
       226: 2q^3+4q^2+3q+1
       227: 3q^2+3q+1
       228: q^3+4q^2+3q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^3+3q^2+3q+1
       232: q^2+3q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^3+3q^2+3q+1
       238: q^3+4q^2+3q+1
       240: q^3+4q^2+3q+1
       242: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: 3q^2+3q+1
       245: q^2+2q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       260: q^2+q
       261: 2q^2+2q+1
       264: q
       265: q^2+2q+1
       268: q^2+q
       270: 2q^2+2q+1
       272: q^2+2q+1
       276: q^2+q
       277: q^3+2q^2+2q+1
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: q
       284: q^2+2q+1
       285: 2q^2+2q+1
       286: q
       288: q^3+3q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: q
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: q
       298: 2q^2+3q+1
       299: q
       300: q^2+2q+1
       302: 3q^2+3q+1
       303: 2q^2+2q+1
       304: q
       306: 2q^2+3q+1
       307: q
       308: 2q+1
       309: 2q+1
       312: q^2+2q+1
       314: 2q+1
       316: q^3+3q^2+3q+1
       318: q^3+4q^2+3q+1
       319: q^2+q
       320: 2q^2+2q+1
       321: q^2+2q+1
       324: q^2+2q+1
       326: q^3+3q^2+3q+1
       328: 2q^2+3q+1
       330: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: 3q^2+3q+1
       345: 3q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: 3q^2+3q+1
       350: 3q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q+1
       358: 2q+1
       359: q^2+2q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       378: q
       379: q^2+2q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       390: q^2+q
       392: 2q^2+2q+1
       394: q
       395: q^2+2q+1
       398: q^2+2q+1
       402: 2q+1
       408: q^2+2q+1
       410: q^2+3q+1
       412: 2q^2+3q+1
       414: q^2+3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: q
       420: q^2+2q+1
       421: 2q^2+2q+1
       422: q
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: q
       430: q^2+2q+1
       431: 2q^2+2q+1
       432: q
       434: 2q^2+3q+1
       436: q^2+3q+1
       437: q
       438: q^2+2q+1
       439: 2q^2+2q+1
       440: q
       442: 2q^2+3q+1
       443: q^2+q
       444: q^2+2q+1
       446: 2q^2+3q+1
       447: q
       448: 2q+1
       449: 2q+1
       452: 2q+1
       453: q
       454: 2q+1
       456: 2q+1
       457: 2q+1
       460: 2q+1
       461: q^2+2q+1
       464: q^2+2q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       470: q^3+3q^2+3q+1
       471: q
       472: 2q+1
       473: 2q+1
       476: 2q+1
       478: q^2+2q+1
       480: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: q^2+2q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 3q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: q+1
       501: q+1
       503: 2q^2+3q+1
       505: 2q^2+3q+1
       507: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: 2q+1
       526: q
       527: 2q+1
       530: q
       531: q^2+2q+1
       534: q
       535: q^2+2q+1
       538: q
       540: 2q+1
       542: q
       544: q^2+2q+1
       546: q^2+q
       548: q^2+2q+1
       550: 2q+1
       554: 2q+1
       558: 2q+1
       562: q^2+2q+1
       567: 2q+1
       572: q^2+2q+1
       576: q^2+2q+1
       581: q^2+2q+1
       584: q^2+3q+1
       586: 3q+1
       588: q^2+3q+1
       589: q
       590: 2q+1
       591: q+1
       594: q+1
       595: q^2+2q+1
       596: q
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: q
       604: q^2+2q+1
       606: q^2+3q+1
       607: 2q^2+2q+1
       608: q
       610: 2q^2+3q+1
       612: q^2+3q+1
       614: q^2+2q+1
       615: q
       616: q+1
       618: 2q+1
       619: q
       620: 2q+1
       621: 2q+1
       624: 2q+1
       626: 2q+1
       628: 2q+1
       630: q+1
       631: q+1
       634: q+1
       636: q^2+3q+1
       638: 2q^2+3q+1
       640: q^2+3q+1
       641: q
       642: 2q+1
       643: 2q+1
       646: 2q+1
       647: q
       648: 2q+1
       649: 2q+1
       652: 2q+1
       654: 2q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: 3q+1
       676: q^2+3q+1
       677: q^2+2q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: 1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       700: q^2+2q+1
       706: q
       707: 2q+1
       710: q
       711: 2q+1
       714: q+1
       719: q+1
       722: q
       724: 2q+1
       726: q
       728: q^2+2q+1
       730: q
       732: 2q+1
       734: q
       736: q+1
       738: 2q+1
       742: 2q+1
       746: 2q+1
       750: q+1
       755: 2q+1
       760: 2q+1
       764: 2q+1
       767: q+1
       773: q+1
       776: 2q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       793: q
       794: q+1
       796: 2q+1
       798: 3q+1
       800: q^2+3q+1
       801: q
       802: 2q+1
       803: q+1
       806: q+1
       807: q^2+2q+1
       808: q
       810: q+1
       812: q^2+2q+1
       814: 2q+1
       815: q
       816: q+1
       817: q+1
       820: q+1
       822: q+1
       824: 2q+1
       825: q
       826: 2q+1
       827: q+1
       831: q+1
       834: 1
       836: q+1
       838: q+1
       839: q+1
       842: q^2+3q+1
       844: q+1
       845: q
       846: 2q+1
       847: 2q+1
       850: 2q+1
       852: 2q+1
       854: 2q+1
       856: q+1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: 1
       891: q+1
       897: q
       898: 2q+1
       901: 1
       907: 1
       910: 1
       913: q
       915: 2q+1
       917: q
       919: q+1
       921: q
       923: 2q+1
       925: q+1
       931: q+1
       933: q
       935: q+1
       937: 2q+1
       941: q+1
       945: q+1
       949: q+1
       957: q+1
       963: 2q+1
       966: q+1
       972: q+1
       977: 2q+1
       981: 2q+1
       986: q+1
       990: q+1
       993: 2q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 2q+1
      1016: q
      1017: q+1
      1019: 3q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1027: 1
      1028: 1
      1031: q+1
      1032: q+1
      1035: q+1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: q+1
      1049: q+1
      1051: 2q+1
      1052: q
      1053: 2q+1
      1054: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: q+1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1145: q
      1147: q+1
      1149: q
      1151: 2q+1
      1153: 1
      1159: 1
      1161: 1
      1165: q+1
      1169: q+1
      1173: 1
      1187: 2q+1
      1192: q+1
      1196: q+1
      1201: q+1
      1203: q+1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 2
      1225: 1
      1231: q+1
      1232: 1
      1235: 1
      1237: q+1
      1239: q+1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1265: q+1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 2
      1328: 1
      1333: 1
      1338: 1
      1339: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 2
      1365: 1
      1370: 1
      1377: 1
      1381: 1
      1417: q+1
      1419: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: q+1
      1450: 1
      1455: 1
      1457: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1475: 1
      1478: 1
      1481: 2
      1483: 1
      1487: 1
      1496: 1
      1500: 1
      1507: 1
      1511: 1
      1540: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 2
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1663: 1
      1672: 1
      1693: 1
      1697: 1
      1732: 1
      1743: 1
      1755: 1
      1786: 1
      1824: 1
      1896: 1

1897:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 5q^3+6q^2+3q+1
        23: 5q^3+6q^2+3q+1
        24: 2q^4+4q^3+5q^2+3q+1
        25: 3q^3+5q^2+3q+1
        26: 3q^3+5q^2+3q+1
        27: q^4+3q^3+4q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 5q^3+6q^2+3q+1
        32: 3q^3+5q^2+3q+1
        33: 5q^3+6q^2+3q+1
        34: 3q^3+5q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: 3q^3+5q^2+3q+1
        38: 3q^3+5q^2+3q+1
        40: 3q^3+5q^2+3q+1
        42: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+5q^2+3q+1
        53: 3q^3+5q^2+3q+1
        54: q^4+3q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 2q^3+3q^2+3q+1
        58: 2q^3+2q^2+q
        59: 3q^3+4q^2+2q+1
        60: 2q^3+3q^2+2q+1
        61: q^3+2q^2+q
        63: 3q^3+5q^2+3q+1
        65: 2q^3+4q^2+3q+1
        67: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: 3q^2+3q+1
        73: q^3+4q^2+3q+1
        75: q^3+4q^2+3q+1
        77: q^3+4q^2+3q+1
        79: 2q^3+3q^2+3q+1
        80: 3q^3+5q^2+3q+1
        81: 3q^3+5q^2+3q+1
        82: 3q^3+5q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 2q^3+4q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: 3q^3+5q^2+3q+1
        95: 3q^3+5q^2+3q+1
        96: q^4+3q^3+4q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       104: 2q^3+3q^2+2q+1
       105: q^3+2q^2+q
       107: 2q^2+2q+1
       108: q^2+q
       109: q^2+q
       110: q^3+3q^2+2q+1
       112: 3q^2+3q+1
       114: q^3+4q^2+3q+1
       116: q^3+3q^2+3q+1
       117: q^2+q
       118: q^3+3q^2+2q+1
       119: q^3+2q^2+2q+1
       120: q^2+q
       122: 2q^3+4q^2+3q+1
       124: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       128: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       132: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^3+5q^2+3q+1
       138: 2q^3+4q^2+3q+1
       139: 3q^3+5q^2+3q+1
       140: 3q^2+3q+1
       141: 2q^3+4q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 2q^3+4q^2+3q+1
       144: q^3+3q^2+3q+1
       145: q^3+4q^2+3q+1
       146: q^3+3q^2+3q+1
       147: 3q^2+3q+1
       148: q^2+2q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       152: q^3+4q^2+3q+1
       154: q^3+4q^2+3q+1
       156: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: q^3+4q^2+3q+1
       162: q^3+4q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       170: 2q^2+2q+1
       171: q^2+q
       174: q^3+2q^2+2q+1
       175: q^2+q
       178: q^3+3q^2+3q+1
       180: q^3+4q^2+3q+1
       182: 3q^2+3q+1
       183: q^2+2q+1
       184: q
       185: q
       186: 2q^2+2q+1
       188: 2q^2+3q+1
       190: q^3+3q^2+3q+1
       191: q^2+q
       192: q^3+3q^2+2q+1
       193: 2q^2+2q+1
       194: q^2+q
       195: q^2+q
       196: q^3+3q^2+2q+1
       198: 3q^2+3q+1
       199: q^3+2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       204: q^2+2q+1
       206: q^2+2q+1
       208: 2q^3+4q^2+3q+1
       210: q^3+4q^2+3q+1
       212: q^3+3q^2+3q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 3q^2+3q+1
       225: 3q^2+3q+1
       226: 2q^3+4q^2+3q+1
       227: 3q^2+3q+1
       228: q^3+4q^2+3q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^3+3q^2+3q+1
       232: q^2+3q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^3+3q^2+3q+1
       238: q^3+4q^2+3q+1
       240: q^3+4q^2+3q+1
       242: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: 3q^2+3q+1
       245: q^2+2q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       260: 2q^2+2q+1
       261: q^2+q
       264: q^2+2q+1
       265: q
       268: 2q^2+2q+1
       270: q^2+q
       274: q^2+2q+1
       276: q^3+2q^2+2q+1
       277: q^2+q
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: q^2+2q+1
       284: q
       285: q
       286: 2q^2+2q+1
       288: q^3+3q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: q^2+2q+1
       294: q
       295: q
       296: 2q^2+2q+1
       298: 2q^2+3q+1
       299: q^2+2q+1
       300: q
       302: 3q^2+3q+1
       303: q
       304: 2q^2+2q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q
       310: 2q+1
       312: q^2+2q+1
       314: 2q+1
       316: q^3+3q^2+3q+1
       318: q^3+4q^2+3q+1
       319: 2q^2+2q+1
       320: q^2+q
       322: q^2+2q+1
       324: q^2+2q+1
       326: q^3+3q^2+3q+1
       328: 2q^2+3q+1
       330: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: 3q^2+3q+1
       345: 3q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: 3q^2+3q+1
       350: 3q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: q^2+3q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q^2+3q+1
       357: 2q+1
       358: 2q+1
       359: q^2+2q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       378: q^2+2q+1
       379: q
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: 2q^2+2q+1
       392: q^2+q
       394: q^2+2q+1
       395: q
       400: q^2+2q+1
       403: 2q+1
       407: q^2+2q+1
       410: q^2+3q+1
       412: 2q^2+3q+1
       414: q^2+3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: q^2+2q+1
       420: q
       421: q
       422: 2q^2+2q+1
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: q^2+2q+1
       430: q
       431: q
       432: 2q^2+2q+1
       434: 2q^2+3q+1
       436: q^2+3q+1
       437: q^2+2q+1
       438: q
       439: q
       440: 2q^2+2q+1
       442: 2q^2+3q+1
       443: q^2+2q+1
       444: q^2+q
       446: 2q^2+3q+1
       447: 2q+1
       448: q
       450: 2q+1
       452: 2q+1
       453: 2q+1
       454: q
       456: 2q+1
       458: 2q+1
       460: 2q+1
       462: q^2+2q+1
       464: q^2+2q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       470: q^3+3q^2+3q+1
       471: 2q+1
       472: q
       474: 2q+1
       476: 2q+1
       478: q^2+2q+1
       480: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: q^2+2q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 3q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+3q+1
       498: q^2+3q+1
       499: 2q+1
       500: q+1
       501: q+1
       503: 2q^2+3q+1
       505: 2q^2+3q+1
       507: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 2q+1
       523: q
       526: 2q+1
       527: q
       530: q^2+2q+1
       531: q
       534: q^2+2q+1
       535: q
       538: 2q+1
       540: q
       542: q^2+2q+1
       544: q
       546: q^2+2q+1
       548: q^2+q
       551: 2q+1
       556: 2q+1
       560: 2q+1
       564: q^2+2q+1
       566: 2q+1
       571: q^2+2q+1
       574: q^2+2q+1
       581: q^2+2q+1
       584: q^2+3q+1
       586: 3q+1
       588: q^2+3q+1
       589: 2q+1
       590: q
       592: q+1
       593: q+1
       595: q
       596: q^2+2q+1
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: q^2+2q+1
       604: q
       606: q^2+3q+1
       607: q
       608: 2q^2+2q+1
       610: 2q^2+3q+1
       612: q^2+3q+1
       614: q^2+2q+1
       615: q+1
       616: q
       618: 2q+1
       619: 2q+1
       620: q
       622: 2q+1
       624: 2q+1
       626: 2q+1
       628: 2q+1
       630: q+1
       632: q+1
       634: q+1
       636: q^2+3q+1
       638: 2q^2+3q+1
       640: q^2+3q+1
       641: 2q+1
       642: q
       644: 2q+1
       646: 2q+1
       647: 2q+1
       648: q
       650: 2q+1
       652: 2q+1
       654: 2q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: 3q+1
       676: q^2+3q+1
       677: q^2+2q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 3q+1
       682: q+1
       683: q+1
       684: q+1
       685: 1
       686: q^2+3q+1
       687: q^2+3q+1
       688: 2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       699: q^2+2q+1
       706: 2q+1
       707: q
       710: 2q+1
       711: q
       715: q+1
       718: q+1
       722: 2q+1
       724: q
       726: q^2+2q+1
       728: q
       730: 2q+1
       732: q
       734: q+1
       736: q
       740: 2q+1
       744: 2q+1
       748: 2q+1
       752: q+1
       754: 2q+1
       759: 2q+1
       763: 2q+1
       766: q+1
       773: q+1
       776: 2q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       793: q+1
       794: q
       796: 2q+1
       798: 3q+1
       800: q^2+3q+1
       801: 2q+1
       802: q
       804: q+1
       805: q+1
       807: q
       808: q^2+2q+1
       810: q+1
       812: q^2+2q+1
       814: 2q+1
       815: q+1
       816: q
       818: q+1
       820: q+1
       822: q+1
       824: 2q+1
       825: 2q+1
       826: q
       828: q+1
       832: q+1
       834: 1
       836: q+1
       838: q+1
       840: q+1
       842: q^2+3q+1
       844: q+1
       845: 2q+1
       846: q
       848: 2q+1
       850: 2q+1
       852: 2q+1
       854: 2q+1
       856: q+1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       878: q+1
       879: q+1
       880: 1
       890: q+1
       897: 2q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: 2q+1
       915: q
       917: q+1
       919: q
       921: 2q+1
       923: q
       926: q+1
       929: q+1
       933: q+1
       935: q
       939: 2q+1
       943: q+1
       947: q+1
       951: q+1
       959: q+1
       962: 2q+1
       965: q+1
       972: q+1
       976: 2q+1
       980: 2q+1
       986: q+1
       989: q+1
       993: 2q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 2q+1
      1016: q+1
      1017: q
      1019: 3q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: 1
      1029: 1
      1031: q+1
      1033: q+1
      1035: q+1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: q+1
      1049: q+1
      1051: 2q+1
      1052: 2q+1
      1053: q
      1055: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: q+1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1145: q+1
      1147: q
      1149: 2q+1
      1151: q
      1155: 1
      1157: 1
      1162: 1
      1167: q+1
      1171: q+1
      1175: 1
      1186: 2q+1
      1192: q+1
      1195: q+1
      1200: q+1
      1205: q+1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 2
      1225: 1
      1231: q+1
      1233: 1
      1234: 1
      1237: q+1
      1239: q+1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1265: q+1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 2
      1327: 1
      1332: 1
      1338: 1
      1339: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 2
      1366: 1
      1371: 1
      1379: 1
      1383: 1
      1416: q+1
      1421: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: q+1
      1451: 1
      1454: 1
      1457: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1475: 1
      1479: 1
      1481: 2
      1483: 1
      1487: 1
      1495: 1
      1499: 1
      1508: 1
      1512: 1
      1539: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 2
      1577: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1664: 1
      1672: 1
      1694: 1
      1698: 1
      1731: 1
      1744: 1
      1756: 1
      1788: 1
      1824: 1
      1897: 1

1898:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 2q^4+7q^3+9q^2+3q+1
        23: 2q^4+7q^3+9q^2+3q+1
        24: 2q^4+7q^3+9q^2+3q+1
        25: 4q^3+8q^2+3q+1
        26: 4q^3+8q^2+3q+1
        27: 4q^3+8q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: 3q^3+8q^2+3q+1
        32: 2q^4+7q^3+9q^2+3q+1
        33: 2q^4+7q^3+9q^2+3q+1
        34: q^3+7q^2+3q+1
        35: 4q^3+8q^2+3q+1
        36: 4q^3+8q^2+3q+1
        37: 2q^3+4q^2+2q+1
        38: 2q^3+4q^2+q
        39: 2q^3+4q^2+2q+1
        40: 2q^3+4q^2+q
        41: 2q^3+4q^2+2q+1
        42: 2q^3+4q^2+q
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^4+4q^3+7q^2+3q+1
        53: 2q^4+5q^3+7q^2+3q+1
        54: q^4+4q^3+7q^2+3q+1
        55: q^3+6q^2+3q+1
        56: 2q^3+6q^2+3q+1
        57: q^3+6q^2+3q+1
        58: 2q^3+5q^2+2q+1
        59: q^3+3q^2+q
        60: q^3+5q^2+q+1
        61: 2q^2+2q
        62: q^3+4q^2+2q+1
        63: 3q^2+q
        64: 2q^3+4q^2+2q+1
        65: 2q^3+4q^2+q
        66: 2q^3+4q^2+2q+1
        67: 2q^3+4q^2+q
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^4+2q^3+5q^2+3q+1
        74: 2q^2+2q+1
        75: 3q^2+q
        76: 2q^2+2q+1
        77: q^3+3q^2+q
        78: 2q^2+2q+1
        79: 3q^2+q
        80: 3q^3+8q^2+3q+1
        81: 2q^4+7q^3+9q^2+3q+1
        82: 2q^3+6q^2+3q+1
        83: q^4+4q^3+7q^2+3q+1
        84: q^3+7q^2+3q+1
        85: 4q^3+8q^2+3q+1
        86: 5q^2+3q+1
        87: q^3+6q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^4+4q^3+7q^2+3q+1
        95: 2q^4+5q^3+7q^2+3q+1
        96: q^4+4q^3+7q^2+3q+1
        97: q^3+6q^2+3q+1
        98: 2q^3+6q^2+3q+1
        99: q^3+6q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^3+3q^2+q+1
       104: 2q^2
       105: q^2+q
       106: q^2+q
       107: 3q^2+q+1
       108: 2q
       109: q^3+3q^2+2q+1
       110: q^2+q
       111: q^2+2q+1
       112: 2q^2+q
       113: 2q^2+2q+1
       114: 2q^2+q
       115: 2q^2+2q+1
       116: 3q^2+q
       117: 2q^3+5q^2+2q+1
       118: q^3+3q^2+q
       119: q^3+5q^2+q+1
       120: 2q^2+2q
       121: q^3+4q^2+2q+1
       122: 3q^2+q
       123: 2q^3+4q^2+2q+1
       124: 2q^3+4q^2+q
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 2q^2+2q+1
       128: 3q^2+q
       129: 2q^2+2q+1
       130: q^3+3q^2+q
       131: 2q^2+2q+1
       132: 3q^2+q
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^3+4q^2+3q+1
       136: q^4+2q^3+5q^2+3q+1
       137: 3q^3+8q^2+3q+1
       138: q^4+4q^3+7q^2+3q+1
       139: 2q^3+6q^2+3q+1
       140: q^3+4q^2+3q+1
       141: 2q^3+6q^2+3q+1
       142: q^4+2q^3+5q^2+3q+1
       143: q^3+7q^2+3q+1
       144: q^3+6q^2+3q+1
       145: 5q^2+3q+1
       146: 5q^2+3q+1
       147: q^3+4q^2+3q+1
       148: q^2+2q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 2q^2+2q+1
       152: 3q^2+q
       153: 2q^2+2q+1
       154: q^3+3q^2+q
       155: 2q^2+2q+1
       156: 3q^2+q
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^4+4q^3+7q^2+3q+1
       161: 2q^4+5q^3+7q^2+3q+1
       162: q^4+4q^3+7q^2+3q+1
       163: q^3+6q^2+3q+1
       164: 2q^3+6q^2+3q+1
       165: q^3+6q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q^2+q+1
       170: q^2
       171: q
       172: q
       173: q^3+3q^2+q+1
       174: 2q^2
       175: q^2+q
       176: q^2+q
       177: 2q^2+2q+1
       178: 3q^2+q
       179: 2q^2+2q+1
       180: 2q^2+q
       181: q^2+2q+1
       182: 2q^2+q
       183: 3q^2+q+1
       184: 2q
       185: q^3+3q^2+2q+1
       186: q^2+q
       187: q^2+2q+1
       188: 2q^2+q
       189: 2q^2+2q+1
       190: 2q^2+q
       191: 2q^3+5q^2+2q+1
       192: q^3+3q^2+q
       193: 3q^2+q+1
       194: 2q
       195: q^3+3q^2+2q+1
       196: q^2+q
       197: q^2+2q+1
       198: 2q^2+q
       199: q^3+5q^2+q+1
       200: 2q^2+2q
       201: 3q^2+q+1
       202: 2q
       203: q^2+2q+1
       205: q+1
       206: q
       207: q^3+4q^2+2q+1
       208: 3q^2+q
       209: 2q^2+2q+1
       210: 2q^2+q
       211: 2q^2+2q+1
       212: 3q^2+q
       213: 2q^2+2q+1
       214: 3q^2+q
       215: 2q^2+2q+1
       216: q^3+3q^2+q
       217: 2q^2+2q+1
       218: 3q^2+q
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^3+4q^2+3q+1
       224: 2q^2+3q+1
       225: q^4+2q^3+5q^2+3q+1
       226: 2q^3+6q^2+3q+1
       227: 2q^3+6q^2+3q+1
       228: q^4+4q^3+7q^2+3q+1
       229: q^3+4q^2+3q+1
       230: q^4+2q^3+5q^2+3q+1
       231: 5q^2+3q+1
       232: 5q^2+3q+1
       233: q^3+6q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^2+2q+1
       236: q^3+6q^2+3q+1
       237: 2q^2+2q+1
       238: 3q^2+q
       239: 2q^2+2q+1
       240: q^3+3q^2+q
       241: 2q^2+2q+1
       242: 3q^2+q
       243: 5q^2+3q+1
       244: q^3+4q^2+3q+1
       245: q^2+2q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q^2+q+1
       260: q^2
       261: q
       262: q
       263: q^2+q+1
       264: q^2
       265: q
       266: q
       267: q^2+q+1
       268: q^2
       269: q
       270: q
       271: q+1
       272: q
       275: q^3+3q^2+q+1
       276: 2q^2
       277: q^2+q
       278: q^2+q
       279: 2q^2+2q+1
       280: 2q^2+q
       281: 2q^2+2q+1
       282: 3q^2+q
       283: 3q^2+q+1
       284: 2q
       285: q^3+3q^2+2q+1
       286: q^2+q
       287: 2q^2+2q+1
       288: 2q^2+q
       289: q^2+2q+1
       290: 2q^2+q
       291: q^2+2q+1
       292: 2q^2+q
       293: 2q^2+q+1
       294: 2q
       295: 2q^2+2q+1
       296: q
       297: q^2+2q+1
       298: q
       299: 3q^2+q+1
       300: 2q
       301: q^2+2q+1
       302: 2q^2+q
       303: q^3+3q^2+2q+1
       304: q^2+q
       305: q^2+2q+1
       306: 2q^2+q
       307: 3q^2+q+1
       308: 2q
       309: q^2+2q+1
       311: q+1
       312: q
       313: q+1
       314: q
       315: 2q^2+2q+1
       316: 3q^2+q
       317: 2q^2+2q+1
       318: 2q^2+q
       319: 3q^2+q+1
       320: 2q
       321: q^2+2q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: 2q^2+q
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       339: 2q^2+2q
       340: 2q+1
       341: 2q^2+2q
       342: q^2+q+1
       343: 2q^2+q
       344: 2q^3+6q^2+3q+1
       345: q^3+4q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: q^3+4q^2+3q+1
       349: 2q^2+3q+1
       350: q^4+2q^3+5q^2+3q+1
       351: 2q^2+4q+1
       352: 5q^2+3q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^3+4q^2+3q+1
       357: q+1
       358: q^2+2q+1
       359: 3q+1
       360: 2q^2+2q+1
       361: 3q^2+q
       362: 2q^2+2q+1
       363: q^3+3q^2+q
       364: 2q^2+2q+1
       365: 3q^2+q
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^3+4q^2+3q+1
       370: q^2+2q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2+q+1
       378: q^2
       379: q
       380: q
       381: q^2+q+1
       382: q^2
       383: q
       384: q
       385: q^2+q+1
       387: q
       388: q
       389: q^2+q+1
       390: q^2
       391: q
       392: q
       393: q^2+q+1
       394: q^2
       395: q
       396: q
       397: q+1
       398: q
       401: q+1
       402: q
       405: q+1
       408: q
       413: 2q^2+2q+1
       414: 2q^2+q
       417: q^2+2q+1
       418: 2q^2+q
       419: 2q^2+q+1
       420: 2q
       421: 2q^2+2q+1
       422: q
       423: q^2+2q+1
       424: q
       425: q+1
       426: q^2+q
       427: 2q+1
       428: q^2+2q
       429: 3q^2+q+1
       430: 2q
       431: q^3+3q^2+2q+1
       432: q^2+q
       433: q^2+2q+1
       434: 2q^2+q
       435: q^2+2q+1
       436: 2q^2+q
       437: 2q^2+q+1
       438: 2q
       439: 2q^2+2q+1
       440: q
       441: q^2+2q+1
       442: q
       443: q^2+2q+1
       444: 2q
       445: 2q+1
       446: 2q^2+2q
       447: 3q^2+q+1
       448: 2q
       449: q^2+2q+1
       451: q+1
       452: q
       453: q^2+q+1
       454: q
       455: q+1
       456: q
       457: q+1
       459: q+1
       461: 3q+1
       463: q+1
       464: 2q
       465: 2q^2+2q+1
       466: 2q^2+q
       467: 2q^2+2q+1
       468: 3q^2+q
       469: 2q^2+2q+1
       470: 2q^2+q
       471: 3q^2+q+1
       472: 2q
       473: q^2+2q+1
       475: q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       486: 2q^2+2q
       487: 2q+1
       488: 2q^2+2q
       489: q^2+q+1
       490: 2q^2+q
       491: q^2+2q+1
       492: q^3+4q^2+3q+1
       493: 2q^2+3q+1
       494: 2q^2+3q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 3q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^3+4q^2+3q+1
       513: q+1
       514: q^2+2q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2+q+1
       522: q^2
       523: q
       524: q
       529: q^2+q+1
       531: q
       532: q
       533: q^2+q+1
       534: q^2
       535: q
       536: q
       537: q^2+q+1
       538: q^2
       539: q
       540: q
       541: q^2+q+1
       543: q
       544: q
       545: q+1
       546: q^2+q
       547: q
       548: q
       549: q+1
       550: q
       553: q+1
       554: q
       557: q+1
       561: q+1
       562: 2q
       565: q+1
       567: q
       569: q+1
       572: q
       573: 2q+1
       576: q
       577: q+1
       578: q
       581: q
       585: q^2+2q+1
       586: q
       589: 2q^2+q+1
       590: 2q
       591: q+1
       593: 1
       595: 2q^2+2q+1
       596: q
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: 2q+1
       602: q^2+2q
       603: 2q^2+q+1
       604: 2q
       605: q^2+2q+1
       606: 2q^2+q
       607: 2q^2+2q+1
       608: q
       609: q^2+2q+1
       610: q
       613: q+1
       614: q^2+q
       615: q^2+2q+1
       616: 2q
       617: 2q+1
       618: 2q^2+2q
       619: q^2+q+1
       620: q
       621: q+1
       623: q+1
       624: q
       625: q+1
       629: 1
       630: q
       631: 3q+1
       633: q+1
       634: 2q
       639: 2q^2+2q+1
       640: 2q^2+q
       641: 3q^2+q+1
       642: 2q
       643: q^2+2q+1
       645: q+1
       646: q
       647: q^2+q+1
       648: q
       649: q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       659: 2q^2+2q
       660: 2q+1
       661: 2q^2+2q
       662: q^2+q+1
       663: 2q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 2q^2+3q+1
       676: 2q^2+3q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q+1
       694: q
       700: q
       709: q^2+q+1
       711: q
       712: q
       713: 1
       714: q
       717: 1
       721: q^2+q+1
       722: q^2
       723: q
       724: q
       725: q^2+q+1
       727: q
       728: q
       733: q+1
       734: q^2+q
       735: q
       736: q
       737: q+1
       738: q
       741: q+1
       749: q+1
       750: 2q
       753: q+1
       755: q
       757: q+1
       760: q
       761: q+1
       765: 2q+1
       767: q
       769: q+1
       770: q
       773: q
       775: 2q+1
       776: q^2+2q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       785: 1
       787: q+1
       791: 1
       793: q^2+2q+1
       794: 2q
       795: 2q+1
       796: 2q^2+2q
       797: q^2+2q+1
       798: q
       801: 2q^2+q+1
       802: 2q
       803: q+1
       805: 1
       807: 2q^2+2q+1
       808: q
       809: q+1
       810: q^2+q
       811: q+1
       812: q
       815: q+1
       816: q
       817: 3q+1
       819: q+1
       820: 2q
       821: q+1
       825: q^2+q+1
       826: q
       827: 1
       831: q+1
       833: 1
       834: q
       835: 1
       839: q+1
       843: 2q+1
       844: q
       845: q^2+q+1
       846: q
       847: q+1
       849: q+1
       850: q
       851: q+1
       855: 1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q+1
       885: q
       891: q
       900: 1
       901: q
       904: 1
       908: 1
       916: q+1
       917: q^2+q
       918: q
       919: q
       920: q^2+q+1
       922: q
       923: q
       924: 1
       925: q
       928: 1
       940: q+1
       941: 2q
       944: q+1
       948: 1
       960: q+1
       963: q
       964: 2q+1
       966: q
       968: q+1
       969: q
       972: q
       974: q+1
       988: q+1
       994: q+1
       995: q
       998: q+1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1016: q+1
      1017: q
      1020: q+1
      1021: q^2+q
      1022: q+1
      1023: q
      1026: 1
      1028: q+1
      1032: q+1
      1036: 1
      1037: q
      1038: 1
      1044: 1
      1046: q+1
      1048: q+1
      1052: q^2+q+1
      1053: q
      1054: 1
      1058: q+1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: q+1
      1087: q
      1093: q
      1114: 1
      1115: q
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1152: 1
      1153: q
      1156: 1
      1160: 1
      1172: 1
      1194: q+1
      1198: q+1
      1202: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: q+1
      1229: q
      1230: q+1
      1231: q
      1232: q+1
      1234: 1
      1240: 1
      1242: 1
      1246: q+1
      1248: 1
      1250: 1
      1260: 1
      1262: q+1
      1266: 1
      1270: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1348: 1
      1349: q
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1380: 1
      1410: q+1
      1418: 1
      1430: 1
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1450: 1
      1454: 1
      1460: 1
      1464: 1
      1466: 1
      1474: 1
      1478: 1
      1482: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1501: 1
      1537: 1
      1549: 1
      1575: 1
      1579: 1
      1607: 1
      1639: 1
      1645: 1
      1647: 1
      1653: 1
      1659: 1
      1663: 1
      1669: 1
      1674: 1
      1733: 1
      1741: 1
      1749: 1
      1825: 1
      1829: 1
      1898: 1

1899:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 2q^4+7q^3+9q^2+3q+1
        23: 2q^4+7q^3+9q^2+3q+1
        24: 2q^4+7q^3+9q^2+3q+1
        25: 4q^3+8q^2+3q+1
        26: 4q^3+8q^2+3q+1
        27: 4q^3+8q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: 3q^3+8q^2+3q+1
        32: 2q^4+7q^3+9q^2+3q+1
        33: 2q^4+7q^3+9q^2+3q+1
        34: q^3+7q^2+3q+1
        35: 4q^3+8q^2+3q+1
        36: 4q^3+8q^2+3q+1
        37: 2q^3+4q^2+q
        38: 2q^3+4q^2+2q+1
        39: 2q^3+4q^2+q
        40: 2q^3+4q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+4q^2+2q+1
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^4+4q^3+7q^2+3q+1
        53: 2q^4+5q^3+7q^2+3q+1
        54: q^4+4q^3+7q^2+3q+1
        55: q^3+6q^2+3q+1
        56: 2q^3+6q^2+3q+1
        57: q^3+6q^2+3q+1
        58: 2q^3+5q^2+2q+1
        59: q^3+3q^2+q
        60: 2q^2+2q
        61: q^3+5q^2+q+1
        62: 3q^2+q
        63: q^3+4q^2+2q+1
        64: 2q^3+4q^2+q
        65: 2q^3+4q^2+2q+1
        66: 2q^3+4q^2+q
        67: 2q^3+4q^2+2q+1
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^4+2q^3+5q^2+3q+1
        74: 3q^2+q
        75: 2q^2+2q+1
        76: q^3+3q^2+q
        77: 2q^2+2q+1
        78: 3q^2+q
        79: 2q^2+2q+1
        80: 3q^3+8q^2+3q+1
        81: 2q^4+7q^3+9q^2+3q+1
        82: 2q^3+6q^2+3q+1
        83: q^4+4q^3+7q^2+3q+1
        84: q^3+7q^2+3q+1
        85: 4q^3+8q^2+3q+1
        86: 5q^2+3q+1
        87: q^3+6q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^4+4q^3+7q^2+3q+1
        95: 2q^4+5q^3+7q^2+3q+1
        96: q^4+4q^3+7q^2+3q+1
        97: q^3+6q^2+3q+1
        98: 2q^3+6q^2+3q+1
        99: q^3+6q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^2+q
       104: q^2+q
       105: q^3+3q^2+q+1
       106: 2q^2
       107: 2q
       108: 3q^2+q+1
       109: q^3+3q^2+2q+1
       110: q^2+q
       111: 2q^2+q
       112: q^2+2q+1
       113: 2q^2+q
       114: 2q^2+2q+1
       115: 3q^2+q
       116: 2q^2+2q+1
       117: 2q^3+5q^2+2q+1
       118: q^3+3q^2+q
       119: 2q^2+2q
       120: q^3+5q^2+q+1
       121: 3q^2+q
       122: q^3+4q^2+2q+1
       123: 2q^3+4q^2+q
       124: 2q^3+4q^2+2q+1
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 3q^2+q
       128: 2q^2+2q+1
       129: q^3+3q^2+q
       130: 2q^2+2q+1
       131: 3q^2+q
       132: 2q^2+2q+1
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^3+4q^2+3q+1
       136: q^4+2q^3+5q^2+3q+1
       137: 3q^3+8q^2+3q+1
       138: q^4+4q^3+7q^2+3q+1
       139: 2q^3+6q^2+3q+1
       140: q^3+4q^2+3q+1
       141: 2q^3+6q^2+3q+1
       142: q^4+2q^3+5q^2+3q+1
       143: q^3+7q^2+3q+1
       144: q^3+6q^2+3q+1
       145: 5q^2+3q+1
       146: 5q^2+3q+1
       147: q^3+4q^2+3q+1
       148: q^2+2q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 3q^2+q
       152: 2q^2+2q+1
       153: q^3+3q^2+q
       154: 2q^2+2q+1
       155: 3q^2+q
       156: 2q^2+2q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^4+4q^3+7q^2+3q+1
       161: 2q^4+5q^3+7q^2+3q+1
       162: q^4+4q^3+7q^2+3q+1
       163: q^3+6q^2+3q+1
       164: 2q^3+6q^2+3q+1
       165: q^3+6q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q
       170: q
       171: q^2+q+1
       172: q^2
       173: q^2+q
       174: q^2+q
       175: q^3+3q^2+q+1
       176: 2q^2
       177: 3q^2+q
       178: 2q^2+2q+1
       179: 2q^2+q
       180: 2q^2+2q+1
       181: 2q^2+q
       182: q^2+2q+1
       183: 2q
       184: 3q^2+q+1
       185: q^3+3q^2+2q+1
       186: q^2+q
       187: 2q^2+q
       188: q^2+2q+1
       189: 2q^2+q
       190: 2q^2+2q+1
       191: 2q^3+5q^2+2q+1
       192: q^3+3q^2+q
       193: 2q
       194: 3q^2+q+1
       195: q^3+3q^2+2q+1
       196: q^2+q
       197: 2q^2+q
       198: q^2+2q+1
       199: 2q^2+2q
       200: q^3+5q^2+q+1
       201: 2q
       202: 3q^2+q+1
       203: q^2+2q+1
       205: q
       206: q+1
       207: 3q^2+q
       208: q^3+4q^2+2q+1
       209: 2q^2+q
       210: 2q^2+2q+1
       211: 3q^2+q
       212: 2q^2+2q+1
       213: 3q^2+q
       214: 2q^2+2q+1
       215: q^3+3q^2+q
       216: 2q^2+2q+1
       217: 3q^2+q
       218: 2q^2+2q+1
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^3+4q^2+3q+1
       224: 2q^2+3q+1
       225: q^4+2q^3+5q^2+3q+1
       226: 2q^3+6q^2+3q+1
       227: 2q^3+6q^2+3q+1
       228: q^4+4q^3+7q^2+3q+1
       229: q^3+4q^2+3q+1
       230: q^4+2q^3+5q^2+3q+1
       231: 5q^2+3q+1
       232: 5q^2+3q+1
       233: q^3+6q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^2+2q+1
       236: q^3+6q^2+3q+1
       237: 3q^2+q
       238: 2q^2+2q+1
       239: q^3+3q^2+q
       240: 2q^2+2q+1
       241: 3q^2+q
       242: 2q^2+2q+1
       243: 5q^2+3q+1
       244: q^3+4q^2+3q+1
       245: q^2+2q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q
       260: q
       261: q^2+q+1
       262: q^2
       263: q
       264: q
       265: q^2+q+1
       266: q^2
       267: q
       268: q
       269: q^2
       270: q^2+q+1
       271: q
       272: q+1
       275: q^2+q
       276: q^2+q
       277: q^3+3q^2+q+1
       278: 2q^2
       279: 2q^2+q
       280: 2q^2+2q+1
       281: 3q^2+q
       282: 2q^2+2q+1
       283: 2q
       284: 3q^2+q+1
       285: q^3+3q^2+2q+1
       286: q^2+q
       287: 2q^2+q
       288: 2q^2+2q+1
       289: 2q^2+q
       290: q^2+2q+1
       291: 2q^2+q
       292: q^2+2q+1
       293: 2q
       294: 2q^2+q+1
       295: 2q^2+2q+1
       296: q
       297: q
       298: q^2+2q+1
       299: 2q
       300: 3q^2+q+1
       301: 2q^2+q
       302: q^2+2q+1
       303: q^3+3q^2+2q+1
       304: q^2+q
       305: 2q^2+q
       306: q^2+2q+1
       307: 2q
       308: 3q^2+q+1
       309: q^2+2q+1
       311: q
       312: q+1
       313: q
       314: q+1
       315: 3q^2+q
       316: 2q^2+2q+1
       317: 2q^2+q
       318: 2q^2+2q+1
       319: 2q
       320: 3q^2+q+1
       321: q^2+2q+1
       323: q
       324: q+1
       325: 2q^2+q
       326: 2q^2+2q+1
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q^2+2q
       339: 2q+1
       340: 2q^2+2q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: 2q^3+6q^2+3q+1
       345: q^3+4q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: q^3+4q^2+3q+1
       349: 2q^2+3q+1
       350: q^4+2q^3+5q^2+3q+1
       351: 2q^2+4q+1
       352: 5q^2+3q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^3+4q^2+3q+1
       357: q+1
       358: q^2+2q+1
       359: 3q+1
       360: 3q^2+q
       361: 2q^2+2q+1
       362: q^3+3q^2+q
       363: 2q^2+2q+1
       364: 3q^2+q
       365: 2q^2+2q+1
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^3+4q^2+3q+1
       370: q^2+2q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       378: q
       379: q^2+q+1
       380: q^2
       381: q
       382: q
       383: q^2+q+1
       384: q^2
       385: q
       386: q
       387: q^2+q+1
       389: q
       390: q
       391: q^2
       392: q^2+q+1
       393: q
       394: q
       395: q^2+q+1
       396: q^2
       397: q
       398: q+1
       401: q
       402: q+1
       405: q
       408: q+1
       413: 2q^2+q
       414: 2q^2+2q+1
       417: 2q^2+q
       418: q^2+2q+1
       419: 2q
       420: 2q^2+q+1
       421: 2q^2+2q+1
       422: q
       423: q
       424: q^2+2q+1
       425: q^2+q
       426: q+1
       427: q^2+2q
       428: 2q+1
       429: 2q
       430: 3q^2+q+1
       431: q^3+3q^2+2q+1
       432: q^2+q
       433: 2q^2+q
       434: q^2+2q+1
       435: 2q^2+q
       436: q^2+2q+1
       437: 2q
       438: 2q^2+q+1
       439: 2q^2+2q+1
       440: q
       441: q
       442: q^2+2q+1
       443: 2q
       444: q^2+2q+1
       445: 2q^2+2q
       446: 2q+1
       447: 2q
       448: 3q^2+q+1
       449: q^2+2q+1
       451: q
       452: q+1
       453: q
       454: q^2+q+1
       455: q
       456: q+1
       457: q+1
       460: q+1
       461: 3q+1
       463: 2q
       464: q+1
       465: 2q^2+q
       466: 2q^2+2q+1
       467: 3q^2+q
       468: 2q^2+2q+1
       469: 2q^2+q
       470: 2q^2+2q+1
       471: 2q
       472: 3q^2+q+1
       473: q^2+2q+1
       475: q
       476: q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q^2+2q
       486: 2q+1
       487: 2q^2+2q
       488: 2q+1
       489: 2q^2+q
       490: q^2+q+1
       491: q^2+2q+1
       492: q^3+4q^2+3q+1
       493: 2q^2+3q+1
       494: 2q^2+3q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 3q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^3+4q^2+3q+1
       513: q+1
       514: q^2+2q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       522: q
       523: q^2+q+1
       524: q^2
       529: q
       530: q
       531: q^2+q+1
       533: q
       534: q
       535: q^2+q+1
       536: q^2
       537: q
       538: q
       539: q^2
       540: q^2+q+1
       541: q
       542: q
       544: q^2+q+1
       545: q
       546: q
       547: q^2+q
       548: q+1
       549: q
       550: q+1
       553: q
       554: q+1
       558: q+1
       561: 2q
       562: q+1
       565: q
       567: q+1
       569: q
       572: q+1
       573: q
       576: 2q+1
       577: q
       580: q
       581: q+1
       585: q
       586: q^2+2q+1
       589: 2q
       590: 2q^2+q+1
       591: q+1
       594: 1
       595: 2q^2+2q+1
       596: q
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q^2+2q
       602: 2q+1
       603: 2q
       604: 2q^2+q+1
       605: 2q^2+q
       606: q^2+2q+1
       607: 2q^2+2q+1
       608: q
       609: q
       610: q^2+2q+1
       613: q^2+q
       614: q+1
       615: 2q
       616: q^2+2q+1
       617: 2q^2+2q
       618: 2q+1
       619: q
       620: q^2+q+1
       621: q+1
       623: q
       624: q+1
       626: q+1
       629: q
       630: 1
       631: 3q+1
       633: 2q
       634: q+1
       639: 2q^2+q
       640: 2q^2+2q+1
       641: 2q
       642: 3q^2+q+1
       643: q^2+2q+1
       645: q
       646: q+1
       647: q
       648: q^2+q+1
       649: q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       658: 2q^2+2q
       659: 2q+1
       660: 2q^2+2q
       661: 2q+1
       662: 2q^2+q
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 2q^2+3q+1
       676: 2q^2+3q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       698: q
       700: q+1
       709: q
       710: q
       711: q^2+q+1
       713: q
       714: 1
       719: 1
       721: q
       722: q
       723: q^2
       724: q^2+q+1
       725: q
       726: q
       728: q^2+q+1
       733: q
       734: q
       735: q^2+q
       736: q+1
       737: q
       738: q+1
       742: q+1
       749: 2q
       750: q+1
       753: q
       755: q+1
       757: q
       760: q+1
       764: q+1
       765: q
       767: 2q+1
       769: q
       772: q
       773: q+1
       775: q^2+2q
       776: 2q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       786: 1
       787: q+1
       792: 1
       793: 2q
       794: q^2+2q+1
       795: 2q^2+2q
       796: 2q+1
       797: q
       798: q^2+2q+1
       801: 2q
       802: 2q^2+q+1
       803: q+1
       806: 1
       807: 2q^2+2q+1
       808: q
       809: q^2+q
       810: q+1
       811: q
       812: q+1
       815: q
       816: q+1
       817: 3q+1
       819: 2q
       820: q+1
       822: q+1
       825: q
       826: q^2+q+1
       827: 1
       831: q+1
       833: q
       834: 1
       836: 1
       839: q+1
       843: q
       844: 2q+1
       845: q
       846: q^2+q+1
       847: q+1
       849: q
       850: q+1
       852: q+1
       855: q
       856: 1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       888: q
       891: q+1
       900: q
       901: 1
       907: 1
       910: 1
       916: q
       917: q
       918: q^2+q
       919: q+1
       920: q
       921: q
       923: q^2+q+1
       924: q
       925: 1
       931: 1
       940: 2q
       941: q+1
       945: q+1
       949: 1
       960: q
       963: q+1
       964: q
       966: 2q+1
       968: q
       971: q
       972: q+1
       977: q+1
       990: q+1
       994: q
       995: q+1
       998: q+1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1016: q
      1017: q+1
      1020: q^2+q
      1021: q+1
      1022: q
      1023: q+1
      1027: 1
      1028: q+1
      1032: q+1
      1036: q
      1037: 1
      1039: 1
      1044: 1
      1047: q+1
      1049: q+1
      1052: q
      1053: q^2+q+1
      1054: 1
      1058: q+1
      1060: q
      1061: 1
      1063: 1
      1065: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1090: q
      1093: q+1
      1114: q
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1152: q
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1196: q+1
      1201: q+1
      1203: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1228: q
      1229: q+1
      1230: q
      1231: q+1
      1232: q+1
      1235: 1
      1241: 1
      1242: 1
      1246: q+1
      1249: 1
      1250: 1
      1260: 1
      1263: q+1
      1267: 1
      1270: 1
      1274: q
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1348: q
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1381: 1
      1412: q+1
      1419: 1
      1434: 1
      1437: 1
      1440: 1
      1443: 1
      1445: 1
      1450: 1
      1455: 1
      1460: 1
      1465: 1
      1466: 1
      1475: 1
      1478: 1
      1483: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1507: 1
      1540: 1
      1551: 1
      1576: 1
      1581: 1
      1608: 1
      1640: 1
      1645: 1
      1648: 1
      1653: 1
      1660: 1
      1663: 1
      1670: 1
      1674: 1
      1735: 1
      1743: 1
      1750: 1
      1826: 1
      1829: 1
      1899: 1

1900:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 2q^4+7q^3+9q^2+3q+1
        23: 2q^4+7q^3+9q^2+3q+1
        24: 2q^4+7q^3+9q^2+3q+1
        25: 4q^3+8q^2+3q+1
        26: 4q^3+8q^2+3q+1
        27: 4q^3+8q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: 3q^3+8q^2+3q+1
        32: 2q^4+7q^3+9q^2+3q+1
        33: 2q^4+7q^3+9q^2+3q+1
        34: q^3+7q^2+3q+1
        35: 4q^3+8q^2+3q+1
        36: 4q^3+8q^2+3q+1
        37: 2q^3+4q^2+2q+1
        38: 2q^3+4q^2+q
        39: 2q^3+4q^2+2q+1
        40: 2q^3+4q^2+q
        41: 2q^3+4q^2+2q+1
        42: 2q^3+4q^2+q
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^4+4q^3+7q^2+3q+1
        53: 2q^4+5q^3+7q^2+3q+1
        54: q^4+4q^3+7q^2+3q+1
        55: q^3+6q^2+3q+1
        56: 2q^3+6q^2+3q+1
        57: q^3+6q^2+3q+1
        58: q^3+3q^2+q
        59: 2q^3+5q^2+2q+1
        60: 2q^2+2q
        61: q^3+5q^2+q+1
        62: q^3+4q^2+2q+1
        63: 3q^2+q
        64: 2q^3+4q^2+2q+1
        65: 2q^3+4q^2+q
        66: 2q^3+4q^2+2q+1
        67: 2q^3+4q^2+q
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^4+2q^3+5q^2+3q+1
        74: 2q^2+2q+1
        75: 3q^2+q
        76: 2q^2+2q+1
        77: q^3+3q^2+q
        78: 2q^2+2q+1
        79: 3q^2+q
        80: 3q^3+8q^2+3q+1
        81: 2q^4+7q^3+9q^2+3q+1
        82: 2q^3+6q^2+3q+1
        83: q^4+4q^3+7q^2+3q+1
        84: q^3+7q^2+3q+1
        85: 4q^3+8q^2+3q+1
        86: 5q^2+3q+1
        87: q^3+6q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^4+4q^3+7q^2+3q+1
        95: 2q^4+5q^3+7q^2+3q+1
        96: q^4+4q^3+7q^2+3q+1
        97: q^3+6q^2+3q+1
        98: 2q^3+6q^2+3q+1
        99: q^3+6q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^2+q
       104: q^2+q
       105: 2q^2
       106: q^3+3q^2+q+1
       107: 2q
       108: 3q^2+q+1
       109: q^2+q
       110: q^3+3q^2+2q+1
       111: q^2+2q+1
       112: 2q^2+q
       113: 2q^2+2q+1
       114: 2q^2+q
       115: 2q^2+2q+1
       116: 3q^2+q
       117: q^3+3q^2+q
       118: 2q^3+5q^2+2q+1
       119: 2q^2+2q
       120: q^3+5q^2+q+1
       121: q^3+4q^2+2q+1
       122: 3q^2+q
       123: 2q^3+4q^2+2q+1
       124: 2q^3+4q^2+q
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 2q^2+2q+1
       128: 3q^2+q
       129: 2q^2+2q+1
       130: q^3+3q^2+q
       131: 2q^2+2q+1
       132: 3q^2+q
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^3+4q^2+3q+1
       136: q^4+2q^3+5q^2+3q+1
       137: 3q^3+8q^2+3q+1
       138: q^4+4q^3+7q^2+3q+1
       139: 2q^3+6q^2+3q+1
       140: q^3+4q^2+3q+1
       141: 2q^3+6q^2+3q+1
       142: q^4+2q^3+5q^2+3q+1
       143: q^3+7q^2+3q+1
       144: q^3+6q^2+3q+1
       145: 5q^2+3q+1
       146: 5q^2+3q+1
       147: q^3+4q^2+3q+1
       148: q^2+2q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 2q^2+2q+1
       152: 3q^2+q
       153: 2q^2+2q+1
       154: q^3+3q^2+q
       155: 2q^2+2q+1
       156: 3q^2+q
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^4+4q^3+7q^2+3q+1
       161: 2q^4+5q^3+7q^2+3q+1
       162: q^4+4q^3+7q^2+3q+1
       163: q^3+6q^2+3q+1
       164: 2q^3+6q^2+3q+1
       165: q^3+6q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q
       170: q
       171: q^2
       172: q^2+q+1
       173: q^2+q
       174: q^2+q
       175: 2q^2
       176: q^3+3q^2+q+1
       177: 2q^2+2q+1
       178: 3q^2+q
       179: 2q^2+2q+1
       180: 2q^2+q
       181: q^2+2q+1
       182: 2q^2+q
       183: 2q
       184: 3q^2+q+1
       185: q^2+q
       186: q^3+3q^2+2q+1
       187: q^2+2q+1
       188: 2q^2+q
       189: 2q^2+2q+1
       190: 2q^2+q
       191: q^3+3q^2+q
       192: 2q^3+5q^2+2q+1
       193: 2q
       194: 3q^2+q+1
       195: q^2+q
       196: q^3+3q^2+2q+1
       197: q^2+2q+1
       198: 2q^2+q
       199: 2q^2+2q
       200: q^3+5q^2+q+1
       201: 2q
       202: 3q^2+q+1
       204: q^2+2q+1
       205: q+1
       206: q
       207: q^3+4q^2+2q+1
       208: 3q^2+q
       209: 2q^2+2q+1
       210: 2q^2+q
       211: 2q^2+2q+1
       212: 3q^2+q
       213: 2q^2+2q+1
       214: 3q^2+q
       215: 2q^2+2q+1
       216: q^3+3q^2+q
       217: 2q^2+2q+1
       218: 3q^2+q
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^3+4q^2+3q+1
       224: 2q^2+3q+1
       225: q^4+2q^3+5q^2+3q+1
       226: 2q^3+6q^2+3q+1
       227: 2q^3+6q^2+3q+1
       228: q^4+4q^3+7q^2+3q+1
       229: q^3+4q^2+3q+1
       230: q^4+2q^3+5q^2+3q+1
       231: 5q^2+3q+1
       232: 5q^2+3q+1
       233: q^3+6q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^2+2q+1
       236: q^3+6q^2+3q+1
       237: 2q^2+2q+1
       238: 3q^2+q
       239: 2q^2+2q+1
       240: q^3+3q^2+q
       241: 2q^2+2q+1
       242: 3q^2+q
       243: 5q^2+3q+1
       244: q^3+4q^2+3q+1
       245: q^2+2q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q
       260: q
       261: q^2
       262: q^2+q+1
       263: q
       264: q
       265: q^2
       266: q^2+q+1
       267: q
       268: q
       269: q^2+q+1
       270: q^2
       273: q+1
       274: q
       275: q^2+q
       276: q^2+q
       277: 2q^2
       278: q^3+3q^2+q+1
       279: 2q^2+2q+1
       280: 2q^2+q
       281: 2q^2+2q+1
       282: 3q^2+q
       283: 2q
       284: 3q^2+q+1
       285: q^2+q
       286: q^3+3q^2+2q+1
       287: 2q^2+2q+1
       288: 2q^2+q
       289: q^2+2q+1
       290: 2q^2+q
       291: q^2+2q+1
       292: 2q^2+q
       293: 2q
       294: 2q^2+q+1
       295: q
       296: 2q^2+2q+1
       297: q^2+2q+1
       298: q
       299: 2q
       300: 3q^2+q+1
       301: q^2+2q+1
       302: 2q^2+q
       303: q^2+q
       304: q^3+3q^2+2q+1
       305: q^2+2q+1
       306: 2q^2+q
       307: 2q
       308: 3q^2+q+1
       310: q^2+2q+1
       311: q+1
       312: q
       313: q+1
       314: q
       315: 2q^2+2q+1
       316: 3q^2+q
       317: 2q^2+2q+1
       318: 2q^2+q
       319: 2q
       320: 3q^2+q+1
       322: q^2+2q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: 2q^2+q
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       339: 2q^2+2q
       340: 2q+1
       341: 2q^2+2q
       342: q^2+q+1
       343: 2q^2+q
       344: 2q^3+6q^2+3q+1
       345: q^3+4q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: q^3+4q^2+3q+1
       349: 2q^2+3q+1
       350: q^4+2q^3+5q^2+3q+1
       351: 2q^2+4q+1
       352: 5q^2+3q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^3+4q^2+3q+1
       357: q+1
       358: q^2+2q+1
       359: 3q+1
       360: 2q^2+2q+1
       361: 3q^2+q
       362: 2q^2+2q+1
       363: q^3+3q^2+q
       364: 2q^2+2q+1
       365: 3q^2+q
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^3+4q^2+3q+1
       370: q^2+2q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       378: q
       379: q^2
       380: q^2+q+1
       381: q
       382: q
       383: q^2
       384: q^2+q+1
       385: q
       386: q
       388: q^2+q+1
       389: q
       390: q
       391: q^2+q+1
       392: q^2
       393: q
       394: q
       395: q^2
       396: q^2+q+1
       399: q+1
       400: q
       403: q
       404: q+1
       406: q+1
       407: q
       413: 2q^2+2q+1
       414: 2q^2+q
       417: q^2+2q+1
       418: 2q^2+q
       419: 2q
       420: 2q^2+q+1
       421: q
       422: 2q^2+2q+1
       423: q^2+2q+1
       424: q
       425: q+1
       426: q^2+q
       427: 2q+1
       428: q^2+2q
       429: 2q
       430: 3q^2+q+1
       431: q^2+q
       432: q^3+3q^2+2q+1
       433: q^2+2q+1
       434: 2q^2+q
       435: q^2+2q+1
       436: 2q^2+q
       437: 2q
       438: 2q^2+q+1
       439: q
       440: 2q^2+2q+1
       441: q^2+2q+1
       442: q
       443: 2q
       444: q^2+2q+1
       445: 2q+1
       446: 2q^2+2q
       447: 2q
       448: 3q^2+q+1
       450: q^2+2q+1
       451: q+1
       452: q
       453: q
       454: q^2+q+1
       455: q+1
       456: q
       458: q+1
       459: q+1
       462: 3q+1
       463: q+1
       464: 2q
       465: 2q^2+2q+1
       466: 2q^2+q
       467: 2q^2+2q+1
       468: 3q^2+q
       469: 2q^2+2q+1
       470: 2q^2+q
       471: 2q
       472: 3q^2+q+1
       474: q^2+2q+1
       475: q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       486: 2q^2+2q
       487: 2q+1
       488: 2q^2+2q
       489: q^2+q+1
       490: 2q^2+q
       491: q^2+2q+1
       492: q^3+4q^2+3q+1
       493: 2q^2+3q+1
       494: 2q^2+3q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 3q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^3+4q^2+3q+1
       513: q+1
       514: q^2+2q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       522: q
       523: q^2
       524: q^2+q+1
       529: q
       530: q
       532: q^2+q+1
       533: q
       534: q
       535: q^2
       536: q^2+q+1
       537: q
       538: q
       539: q^2+q+1
       540: q^2
       541: q
       542: q
       543: q^2+q+1
       545: q
       546: q
       547: q+1
       548: q^2+q
       551: q
       552: q+1
       555: q+1
       556: q
       559: q+1
       563: q+1
       564: 2q
       566: q
       568: q+1
       570: q+1
       571: q
       574: q
       575: 2q+1
       577: q+1
       578: q
       581: q
       585: q^2+2q+1
       586: q
       589: 2q
       590: 2q^2+q+1
       592: q+1
       594: 1
       595: q
       596: 2q^2+2q+1
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: 2q+1
       602: q^2+2q
       603: 2q
       604: 2q^2+q+1
       605: q^2+2q+1
       606: 2q^2+q
       607: q
       608: 2q^2+2q+1
       609: q^2+2q+1
       610: q
       613: q+1
       614: q^2+q
       615: 2q
       616: q^2+2q+1
       617: 2q+1
       618: 2q^2+2q
       619: q
       620: q^2+q+1
       622: q+1
       623: q+1
       624: q
       625: q+1
       629: 1
       630: q
       632: 3q+1
       633: q+1
       634: 2q
       639: 2q^2+2q+1
       640: 2q^2+q
       641: 2q
       642: 3q^2+q+1
       644: q^2+2q+1
       645: q+1
       646: q
       647: q
       648: q^2+q+1
       650: q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       659: 2q^2+2q
       660: 2q+1
       661: 2q^2+2q
       662: q^2+q+1
       663: 2q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 2q^2+3q+1
       676: 2q^2+3q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q+1
       699: q
       701: q
       709: q
       710: q
       712: q^2+q+1
       715: q
       716: 1
       720: 1
       721: q
       722: q
       723: q^2+q+1
       724: q^2
       725: q
       726: q
       727: q^2+q+1
       733: q
       734: q
       735: q+1
       736: q^2+q
       739: q+1
       740: q
       743: q+1
       751: q+1
       752: 2q
       754: q
       756: q+1
       758: q+1
       759: q
       762: q+1
       766: q
       768: 2q+1
       769: q+1
       770: q
       773: q
       775: 2q+1
       776: q^2+2q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       786: 1
       788: q+1
       791: 1
       793: 2q
       794: q^2+2q+1
       795: 2q+1
       796: 2q^2+2q
       797: q^2+2q+1
       798: q
       801: 2q
       802: 2q^2+q+1
       804: q+1
       806: 1
       807: q
       808: 2q^2+2q+1
       809: q+1
       810: q^2+q
       811: q+1
       812: q
       815: q
       816: q+1
       818: 3q+1
       819: q+1
       820: 2q
       821: q+1
       825: q
       826: q^2+q+1
       828: 1
       832: q+1
       833: 1
       834: q
       835: 1
       840: q+1
       843: 2q+1
       844: q
       845: q
       846: q^2+q+1
       848: q+1
       849: q+1
       850: q
       851: q+1
       855: 1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       889: q+1
       890: q
       892: q
       902: 1
       903: q
       906: 1
       911: 1
       916: q
       917: q
       918: q+1
       919: q^2+q
       920: q
       921: q
       922: q^2+q+1
       926: q
       927: 1
       930: 1
       942: q+1
       943: 2q
       946: q+1
       950: 1
       961: q+1
       962: q
       965: q
       967: 2q+1
       968: q+1
       969: q
       972: q
       975: q+1
       991: q+1
       994: q+1
       995: q
       999: q+1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1016: q
      1017: q+1
      1020: q+1
      1021: q^2+q
      1022: q+1
      1023: q
      1027: 1
      1029: q+1
      1033: q+1
      1036: 1
      1037: q
      1038: 1
      1045: 1
      1046: q+1
      1048: q+1
      1052: q
      1053: q^2+q+1
      1055: 1
      1059: q+1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: q+1
      1092: q
      1094: q
      1116: 1
      1117: q
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1154: 1
      1155: q
      1158: 1
      1163: 1
      1174: 1
      1197: q+1
      1199: q+1
      1204: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1228: q
      1229: q+1
      1230: q+1
      1231: q
      1233: q+1
      1235: 1
      1241: 1
      1243: 1
      1247: q+1
      1248: 1
      1251: 1
      1261: 1
      1262: q+1
      1266: 1
      1271: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1350: 1
      1351: q
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1382: 1
      1413: q+1
      1420: 1
      1430: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1451: 1
      1455: 1
      1461: 1
      1464: 1
      1467: 1
      1474: 1
      1479: 1
      1482: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1506: 1
      1538: 1
      1552: 1
      1578: 1
      1580: 1
      1609: 1
      1639: 1
      1646: 1
      1648: 1
      1654: 1
      1659: 1
      1664: 1
      1669: 1
      1674: 1
      1736: 1
      1742: 1
      1752: 1
      1825: 1
      1830: 1
      1900: 1

1901:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 2q^4+7q^3+9q^2+3q+1
        23: 2q^4+7q^3+9q^2+3q+1
        24: 2q^4+7q^3+9q^2+3q+1
        25: 4q^3+8q^2+3q+1
        26: 4q^3+8q^2+3q+1
        27: 4q^3+8q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: 3q^3+8q^2+3q+1
        32: 2q^4+7q^3+9q^2+3q+1
        33: 2q^4+7q^3+9q^2+3q+1
        34: q^3+7q^2+3q+1
        35: 4q^3+8q^2+3q+1
        36: 4q^3+8q^2+3q+1
        37: 2q^3+4q^2+q
        38: 2q^3+4q^2+2q+1
        39: 2q^3+4q^2+q
        40: 2q^3+4q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+4q^2+2q+1
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^4+4q^3+7q^2+3q+1
        53: 2q^4+5q^3+7q^2+3q+1
        54: q^4+4q^3+7q^2+3q+1
        55: q^3+6q^2+3q+1
        56: 2q^3+6q^2+3q+1
        57: q^3+6q^2+3q+1
        58: q^3+3q^2+q
        59: 2q^3+5q^2+2q+1
        60: q^3+5q^2+q+1
        61: 2q^2+2q
        62: 3q^2+q
        63: q^3+4q^2+2q+1
        64: 2q^3+4q^2+q
        65: 2q^3+4q^2+2q+1
        66: 2q^3+4q^2+q
        67: 2q^3+4q^2+2q+1
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^4+2q^3+5q^2+3q+1
        74: 3q^2+q
        75: 2q^2+2q+1
        76: q^3+3q^2+q
        77: 2q^2+2q+1
        78: 3q^2+q
        79: 2q^2+2q+1
        80: 3q^3+8q^2+3q+1
        81: 2q^4+7q^3+9q^2+3q+1
        82: 2q^3+6q^2+3q+1
        83: q^4+4q^3+7q^2+3q+1
        84: q^3+7q^2+3q+1
        85: 4q^3+8q^2+3q+1
        86: 5q^2+3q+1
        87: q^3+6q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^4+4q^3+7q^2+3q+1
        95: 2q^4+5q^3+7q^2+3q+1
        96: q^4+4q^3+7q^2+3q+1
        97: q^3+6q^2+3q+1
        98: 2q^3+6q^2+3q+1
        99: q^3+6q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: 2q^2
       104: q^3+3q^2+q+1
       105: q^2+q
       106: q^2+q
       107: 3q^2+q+1
       108: 2q
       109: q^2+q
       110: q^3+3q^2+2q+1
       111: 2q^2+q
       112: q^2+2q+1
       113: 2q^2+q
       114: 2q^2+2q+1
       115: 3q^2+q
       116: 2q^2+2q+1
       117: q^3+3q^2+q
       118: 2q^3+5q^2+2q+1
       119: q^3+5q^2+q+1
       120: 2q^2+2q
       121: 3q^2+q
       122: q^3+4q^2+2q+1
       123: 2q^3+4q^2+q
       124: 2q^3+4q^2+2q+1
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 3q^2+q
       128: 2q^2+2q+1
       129: q^3+3q^2+q
       130: 2q^2+2q+1
       131: 3q^2+q
       132: 2q^2+2q+1
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^3+4q^2+3q+1
       136: q^4+2q^3+5q^2+3q+1
       137: 3q^3+8q^2+3q+1
       138: q^4+4q^3+7q^2+3q+1
       139: 2q^3+6q^2+3q+1
       140: q^3+4q^2+3q+1
       141: 2q^3+6q^2+3q+1
       142: q^4+2q^3+5q^2+3q+1
       143: q^3+7q^2+3q+1
       144: q^3+6q^2+3q+1
       145: 5q^2+3q+1
       146: 5q^2+3q+1
       147: q^3+4q^2+3q+1
       148: q^2+2q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 3q^2+q
       152: 2q^2+2q+1
       153: q^3+3q^2+q
       154: 2q^2+2q+1
       155: 3q^2+q
       156: 2q^2+2q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^4+4q^3+7q^2+3q+1
       161: 2q^4+5q^3+7q^2+3q+1
       162: q^4+4q^3+7q^2+3q+1
       163: q^3+6q^2+3q+1
       164: 2q^3+6q^2+3q+1
       165: q^3+6q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q^2
       170: q^2+q+1
       171: q
       172: q
       173: 2q^2
       174: q^3+3q^2+q+1
       175: q^2+q
       176: q^2+q
       177: 3q^2+q
       178: 2q^2+2q+1
       179: 2q^2+q
       180: 2q^2+2q+1
       181: 2q^2+q
       182: q^2+2q+1
       183: 3q^2+q+1
       184: 2q
       185: q^2+q
       186: q^3+3q^2+2q+1
       187: 2q^2+q
       188: q^2+2q+1
       189: 2q^2+q
       190: 2q^2+2q+1
       191: q^3+3q^2+q
       192: 2q^3+5q^2+2q+1
       193: 3q^2+q+1
       194: 2q
       195: q^2+q
       196: q^3+3q^2+2q+1
       197: 2q^2+q
       198: q^2+2q+1
       199: q^3+5q^2+q+1
       200: 2q^2+2q
       201: 3q^2+q+1
       202: 2q
       204: q^2+2q+1
       205: q
       206: q+1
       207: 3q^2+q
       208: q^3+4q^2+2q+1
       209: 2q^2+q
       210: 2q^2+2q+1
       211: 3q^2+q
       212: 2q^2+2q+1
       213: 3q^2+q
       214: 2q^2+2q+1
       215: q^3+3q^2+q
       216: 2q^2+2q+1
       217: 3q^2+q
       218: 2q^2+2q+1
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^3+4q^2+3q+1
       224: 2q^2+3q+1
       225: q^4+2q^3+5q^2+3q+1
       226: 2q^3+6q^2+3q+1
       227: 2q^3+6q^2+3q+1
       228: q^4+4q^3+7q^2+3q+1
       229: q^3+4q^2+3q+1
       230: q^4+2q^3+5q^2+3q+1
       231: 5q^2+3q+1
       232: 5q^2+3q+1
       233: q^3+6q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^2+2q+1
       236: q^3+6q^2+3q+1
       237: 3q^2+q
       238: 2q^2+2q+1
       239: q^3+3q^2+q
       240: 2q^2+2q+1
       241: 3q^2+q
       242: 2q^2+2q+1
       243: 5q^2+3q+1
       244: q^3+4q^2+3q+1
       245: q^2+2q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: q^3+4q^2+3q+1
       251: q^3+4q^2+3q+1
       252: q^3+4q^2+3q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q^2
       260: q^2+q+1
       261: q
       262: q
       263: q^2
       264: q^2+q+1
       265: q
       266: q
       267: q^2
       268: q^2+q+1
       269: q
       270: q
       273: q
       274: q+1
       275: 2q^2
       276: q^3+3q^2+q+1
       277: q^2+q
       278: q^2+q
       279: 2q^2+q
       280: 2q^2+2q+1
       281: 3q^2+q
       282: 2q^2+2q+1
       283: 3q^2+q+1
       284: 2q
       285: q^2+q
       286: q^3+3q^2+2q+1
       287: 2q^2+q
       288: 2q^2+2q+1
       289: 2q^2+q
       290: q^2+2q+1
       291: 2q^2+q
       292: q^2+2q+1
       293: 2q^2+q+1
       294: 2q
       295: q
       296: 2q^2+2q+1
       297: q
       298: q^2+2q+1
       299: 3q^2+q+1
       300: 2q
       301: 2q^2+q
       302: q^2+2q+1
       303: q^2+q
       304: q^3+3q^2+2q+1
       305: 2q^2+q
       306: q^2+2q+1
       307: 3q^2+q+1
       308: 2q
       310: q^2+2q+1
       311: q
       312: q+1
       313: q
       314: q+1
       315: 3q^2+q
       316: 2q^2+2q+1
       317: 2q^2+q
       318: 2q^2+2q+1
       319: 3q^2+q+1
       320: 2q
       322: q^2+2q+1
       323: q
       324: q+1
       325: 2q^2+q
       326: 2q^2+2q+1
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q^2+2q
       339: 2q+1
       340: 2q^2+2q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: 2q^3+6q^2+3q+1
       345: q^3+4q^2+3q+1
       346: q^3+4q^2+3q+1
       347: 2q^2+3q+1
       348: q^3+4q^2+3q+1
       349: 2q^2+3q+1
       350: q^4+2q^3+5q^2+3q+1
       351: 2q^2+4q+1
       352: 5q^2+3q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^3+4q^2+3q+1
       357: q+1
       358: q^2+2q+1
       359: 3q+1
       360: 3q^2+q
       361: 2q^2+2q+1
       362: q^3+3q^2+q
       363: 2q^2+2q+1
       364: 3q^2+q
       365: 2q^2+2q+1
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^3+4q^2+3q+1
       370: q^2+2q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2
       378: q^2+q+1
       379: q
       380: q
       381: q^2
       382: q^2+q+1
       383: q
       384: q
       386: q^2+q+1
       387: q
       388: q
       389: q^2
       390: q^2+q+1
       391: q
       392: q
       393: q^2
       394: q^2+q+1
       395: q
       396: q
       399: q
       400: q+1
       403: q+1
       404: q
       406: q
       407: q+1
       413: 2q^2+q
       414: 2q^2+2q+1
       417: 2q^2+q
       418: q^2+2q+1
       419: 2q^2+q+1
       420: 2q
       421: q
       422: 2q^2+2q+1
       423: q
       424: q^2+2q+1
       425: q^2+q
       426: q+1
       427: q^2+2q
       428: 2q+1
       429: 3q^2+q+1
       430: 2q
       431: q^2+q
       432: q^3+3q^2+2q+1
       433: 2q^2+q
       434: q^2+2q+1
       435: 2q^2+q
       436: q^2+2q+1
       437: 2q^2+q+1
       438: 2q
       439: q
       440: 2q^2+2q+1
       441: q
       442: q^2+2q+1
       443: q^2+2q+1
       444: 2q
       445: 2q^2+2q
       446: 2q+1
       447: 3q^2+q+1
       448: 2q
       450: q^2+2q+1
       451: q
       452: q+1
       453: q^2+q+1
       454: q
       455: q
       456: q+1
       458: q+1
       460: q+1
       462: 3q+1
       463: 2q
       464: q+1
       465: 2q^2+q
       466: 2q^2+2q+1
       467: 3q^2+q
       468: 2q^2+2q+1
       469: 2q^2+q
       470: 2q^2+2q+1
       471: 3q^2+q+1
       472: 2q
       474: q^2+2q+1
       475: q
       476: q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q^2+2q
       486: 2q+1
       487: 2q^2+2q
       488: 2q+1
       489: 2q^2+q
       490: q^2+q+1
       491: q^2+2q+1
       492: q^3+4q^2+3q+1
       493: 2q^2+3q+1
       494: 2q^2+3q+1
       495: q^2+2q+1
       496: 2q^2+4q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 3q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^3+4q^2+3q+1
       513: q+1
       514: q^2+2q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2
       522: q^2+q+1
       523: q
       524: q
       530: q^2+q+1
       531: q
       532: q
       533: q^2
       534: q^2+q+1
       535: q
       536: q
       537: q^2
       538: q^2+q+1
       539: q
       540: q
       542: q^2+q+1
       543: q
       544: q
       545: q^2+q
       546: q+1
       547: q
       548: q
       551: q+1
       552: q
       555: q
       556: q+1
       560: q+1
       563: 2q
       564: q+1
       566: q+1
       568: q
       570: q
       571: q+1
       574: 2q+1
       575: q
       577: q
       580: q
       581: q+1
       585: q
       586: q^2+2q+1
       589: 2q^2+q+1
       590: 2q
       592: q+1
       593: 1
       595: q
       596: 2q^2+2q+1
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q^2+2q
       602: 2q+1
       603: 2q^2+q+1
       604: 2q
       605: 2q^2+q
       606: q^2+2q+1
       607: q
       608: 2q^2+2q+1
       609: q
       610: q^2+2q+1
       613: q^2+q
       614: q+1
       615: q^2+2q+1
       616: 2q
       617: 2q^2+2q
       618: 2q+1
       619: q^2+q+1
       620: q
       622: q+1
       623: q
       624: q+1
       626: q+1
       629: q
       630: 1
       632: 3q+1
       633: 2q
       634: q+1
       639: 2q^2+q
       640: 2q^2+2q+1
       641: 3q^2+q+1
       642: 2q
       644: q^2+2q+1
       645: q
       646: q+1
       647: q^2+q+1
       648: q
       650: q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       658: 2q^2+2q
       659: 2q+1
       660: 2q^2+2q
       661: 2q+1
       662: 2q^2+q
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 2q^2+4q+1
       675: 2q^2+3q+1
       676: 2q^2+3q+1
       677: 2q+1
       678: 2q+1
       679: q^2+2q+1
       680: 3q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q
       699: q+1
       710: q^2+q+1
       711: q
       712: q
       715: 1
       716: q
       718: 1
       721: q^2
       722: q^2+q+1
       723: q
       724: q
       726: q^2+q+1
       727: q
       728: q
       733: q^2+q
       734: q+1
       735: q
       736: q
       739: q
       740: q+1
       744: q+1
       751: 2q
       752: q+1
       754: q+1
       756: q
       758: q
       759: q+1
       763: q+1
       766: 2q+1
       768: q
       769: q
       772: q
       773: q+1
       775: q^2+2q
       776: 2q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       785: 1
       788: q+1
       792: 1
       793: q^2+2q+1
       794: 2q
       795: 2q^2+2q
       796: 2q+1
       797: q
       798: q^2+2q+1
       801: 2q^2+q+1
       802: 2q
       804: q+1
       805: 1
       807: q
       808: 2q^2+2q+1
       809: q^2+q
       810: q+1
       811: q
       812: q+1
       815: q+1
       816: q
       818: 3q+1
       819: 2q
       820: q+1
       822: q+1
       825: q^2+q+1
       826: q
       828: 1
       832: q+1
       833: q
       834: 1
       836: 1
       840: q+1
       843: q
       844: 2q+1
       845: q^2+q+1
       846: q
       848: q+1
       849: q
       850: q+1
       852: q+1
       855: q
       856: 1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       887: q
       889: q
       890: q+1
       902: q
       903: 1
       905: 1
       909: 1
       916: q^2+q
       917: q+1
       918: q
       919: q
       921: q^2+q+1
       922: q
       923: q
       926: 1
       927: q
       929: 1
       942: 2q
       943: q+1
       947: q+1
       951: 1
       961: q
       962: q+1
       965: 2q+1
       967: q
       968: q
       971: q
       972: q+1
       976: q+1
       989: q+1
       994: q
       995: q+1
       999: q+1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1016: q+1
      1017: q
      1020: q^2+q
      1021: q+1
      1022: q
      1023: q+1
      1026: 1
      1029: q+1
      1033: q+1
      1036: q
      1037: 1
      1039: 1
      1045: 1
      1047: q+1
      1049: q+1
      1052: q^2+q+1
      1053: q
      1055: 1
      1059: q+1
      1060: q
      1061: 1
      1063: 1
      1065: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1089: q
      1091: q
      1092: q+1
      1116: q
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1154: q
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1195: q+1
      1200: q+1
      1205: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: q+1
      1229: q
      1230: q
      1231: q+1
      1233: q+1
      1234: 1
      1240: 1
      1243: 1
      1247: q+1
      1249: 1
      1251: 1
      1261: 1
      1263: q+1
      1267: 1
      1271: 1
      1274: q
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1350: q
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1383: 1
      1411: q+1
      1421: 1
      1434: 1
      1437: 1
      1441: 1
      1442: 1
      1445: 1
      1451: 1
      1454: 1
      1461: 1
      1465: 1
      1467: 1
      1475: 1
      1479: 1
      1483: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1508: 1
      1539: 1
      1550: 1
      1577: 1
      1582: 1
      1610: 1
      1640: 1
      1646: 1
      1647: 1
      1654: 1
      1660: 1
      1664: 1
      1670: 1
      1674: 1
      1734: 1
      1744: 1
      1751: 1
      1826: 1
      1830: 1
      1901: 1

1902:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: 3q^3+7q^2+4q+1
        23: 3q^3+7q^2+4q+1
        24: q^4+4q^3+5q^2+4q+1
        25: q^3+6q^2+4q+1
        26: q^3+6q^2+4q+1
        27: 3q^3+4q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+4q^2+4q+1
        36: 5q^2+4q+1
        37: q^3+4q^2+3q+1
        38: 2q^2+q
        39: q^3+4q^2+3q+1
        40: 2q^2+q
        41: 2q^3+3q^2+3q+1
        42: q^3+q^2+q
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+7q^2+4q+1
        53: 3q^3+7q^2+4q+1
        54: q^4+4q^3+5q^2+4q+1
        55: q^3+6q^2+4q+1
        56: q^3+6q^2+4q+1
        57: 3q^3+4q^2+4q+1
        58: q^3+4q^2+3q+1
        59: 2q^2+q
        60: 3q^2+2q+1
        61: 2q^2+2q
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+3q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: 5q^2+4q+1
        73: q^3+6q^2+4q+1
        74: q^3+4q^2+3q+1
        75: 2q^2+q
        76: q^3+4q^2+3q+1
        77: 2q^2+q
        78: 2q^3+3q^2+3q+1
        79: q^3+q^2+q
        80: 2q^3+5q^2+4q+1
        81: 4q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 2q^3+5q^2+4q+1
        84: q^3+4q^2+4q+1
        85: 3q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: q^3+6q^2+4q+1
        95: q^3+6q^2+4q+1
        96: q^4+3q^3+4q^2+3q+1
        97: 4q^2+4q+1
        98: 4q^2+4q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: 2q^2+2q+1
       104: q^2
       105: q^2+q
       106: q^2+q
       107: 3q^2+2q+1
       108: 2q^2+2q
       109: q^3+4q^2+3q+1
       110: 2q^2+q
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+3q^2+3q+1
       116: q^2+q
       117: 2q^2+3q+1
       118: q
       119: q^2+2q+1
       120: 2q
       121: q^3+3q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       127: 2q^2+3q+1
       129: 2q^2+3q+1
       131: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 3q^2+4q+1
       136: 4q^2+4q+1
       137: 4q^2+4q+1
       138: 3q^2+3q+1
       139: q^3+6q^2+4q+1
       140: 5q^2+4q+1
       141: 2q^3+5q^2+4q+1
       142: q^3+6q^2+4q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 4q^2+4q+1
       146: q^3+4q^2+4q+1
       147: 4q^2+4q+1
       148: 2q^2+3q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: q^3+4q^2+3q+1
       152: 2q^2+q
       153: q^3+4q^2+3q+1
       154: 2q^2+q
       155: 2q^3+3q^2+3q+1
       156: q^3+q^2+q
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: 4q^2+4q+1
       161: 4q^2+4q+1
       162: q^3+4q^2+3q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: 2q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: 2q^2+2q+1
       170: q^2
       171: q^2+q
       172: q^2+q
       173: q^2+2q+1
       175: q
       176: q
       177: q^2+2q+1
       179: 2q^2+3q+1
       181: 2q^2+3q+1
       183: q^2+2q+1
       184: 2q
       185: 2q^2+3q+1
       186: q
       187: 2q^2+3q+1
       188: q^2+q
       189: q^3+3q^2+3q+1
       190: q^2+q
       191: 2q^2+3q+1
       192: q
       193: 3q^2+2q+1
       194: 2q^2+2q
       195: q^3+4q^2+3q+1
       196: 2q^2+q
       197: 3q^2+3q+1
       198: 2q^2+q
       199: q^2+2q+1
       200: 2q
       201: 2q^2+2q+1
       202: 2q^2+2q
       203: 2q^2+3q+1
       205: q^2+2q+1
       206: q^2+q
       207: 2q^2+3q+1
       208: q^2+q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+3q^2+3q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 3q^2+4q+1
       223: 2q^2+3q+1
       224: 4q^2+4q+1
       225: 3q^2+3q+1
       226: 3q^2+3q+1
       227: 2q^2+4q+1
       228: 3q^2+3q+1
       229: 3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+3q+1
       232: 4q+1
       233: q^2+3q+1
       234: q^2+4q+1
       235: 3q+1
       236: 2q^2+3q+1
       237: 2q^2+3q+1
       239: 2q^2+3q+1
       241: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 4q^2+4q+1
       245: 2q^2+3q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: 4q^2+4q+1
       251: 4q^2+4q+1
       252: q^3+4q^2+3q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: 2q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       259: q^2+2q+1
       262: q^2+q
       263: q^2+2q+1
       265: q
       266: q
       267: 2q^2+2q+1
       268: q^2
       269: q^2+q
       270: q^2+q
       271: q^2+2q+1
       272: q^2+q
       275: q^2+2q+1
       277: q
       278: q
       279: 2q+1
       281: q+1
       283: q+1
       284: q
       285: q^2+2q+1
       287: q^2+2q+1
       289: 2q+1
       291: q^2+2q+1
       293: q^2+2q+1
       294: 2q
       295: 2q^2+3q+1
       296: q
       297: 2q^2+3q+1
       298: q^2+q
       299: q^2+2q+1
       300: 2q
       301: 2q^2+3q+1
       303: 2q^2+3q+1
       304: q
       305: 2q^2+3q+1
       306: q^2+q
       307: 2q+1
       308: 2q
       309: 3q+1
       311: q^2+2q+1
       313: 2q+1
       314: q
       315: q^2+2q+1
       317: 2q^2+3q+1
       319: 2q^2+2q+1
       320: 2q^2+2q
       321: 2q^2+3q+1
       323: q^2+2q+1
       324: q^2+q
       325: q^3+3q^2+3q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: 3q^2+3q+1
       347: 3q^2+4q+1
       348: 2q^2+3q+1
       349: 4q^2+4q+1
       350: 3q^2+3q+1
       351: 4q^2+4q+1
       352: 3q+1
       353: 4q+1
       354: q^2+3q+1
       355: q^2+4q+1
       356: q^2+3q+1
       357: 3q+1
       358: 2q+1
       359: 2q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: q^2+4q+1
       370: 3q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       377: q+1
       381: q+1
       384: q
       385: q^2+2q+1
       387: q
       388: q
       389: q^2+2q+1
       391: q^2+q
       393: q^2+2q+1
       395: q
       396: q
       397: q^2+2q+1
       401: 2q+1
       402: q
       405: q^2+2q+1
       408: q^2+q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q+1
       420: q
       421: q^2+2q+1
       423: q^2+2q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: q+1
       430: q
       431: q^2+2q+1
       433: q^2+2q+1
       435: 2q+1
       437: q^2+2q+1
       438: 2q
       439: 2q^2+3q+1
       440: q
       441: 2q^2+3q+1
       442: q^2+q
       443: 2q^2+2q+1
       444: 2q^2+2q
       445: 2q^2+3q+1
       447: q+1
       448: q
       449: 2q+1
       451: q+1
       453: 2q+1
       454: 2q
       455: q+1
       457: 3q+1
       459: 2q+1
       460: q
       461: 2q^2+3q+1
       463: q^2+2q+1
       465: 2q+1
       467: q+1
       469: q^2+2q+1
       471: 2q+1
       472: 2q
       473: 3q+1
       475: 2q+1
       476: q
       477: q^2+2q+1
       479: q^2+2q+1
       480: q^2+q
       481: 3q+1
       482: q^2+3q+1
       483: 2q^2+3q+1
       484: 4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+3q+1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+4q+1
       497: 3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: q^2+4q+1
       512: q^2+3q+1
       513: 3q+1
       514: 2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       521: 1
       525: q+1
       528: q
       529: q+1
       533: q+1
       537: q+1
       539: q
       541: q^2+2q+1
       543: q
       544: q
       545: q^2+2q+1
       547: q^2+q
       549: q+1
       553: q+1
       557: 2q+1
       558: q
       561: q^2+2q+1
       565: 2q+1
       567: q
       569: q^2+2q+1
       573: q^2+2q+1
       576: q^2+q
       577: q^2+2q+1
       583: q+1
       585: q+1
       587: q+1
       589: q+1
       590: q
       591: 2q+1
       593: q+1
       594: q
       595: q^2+2q+1
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: q+1
       604: q
       605: q+1
       607: q^2+2q+1
       609: q^2+2q+1
       611: 2q+1
       613: q^2+2q+1
       615: 2q+1
       616: 2q
       617: 2q+1
       619: q+1
       620: q
       621: 2q+1
       623: 1
       625: q+1
       627: q+1
       629: q+1
       631: 3q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: q+1
       642: q
       643: 2q+1
       645: q+1
       647: 2q+1
       648: 2q
       649: 3q+1
       651: q+1
       653: 2q+1
       654: q
       655: 2q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 3q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: q+2
       675: 3q+1
       676: q^2+3q+1
       677: 2q^2+3q+1
       678: q^2+4q+1
       679: q^2+3q+1
       680: 2
       681: 3q+1
       682: q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       693: q^2+2q+1
       705: 1
       709: 1
       713: q+1
       717: q+1
       721: 1
       725: q+1
       729: q+1
       731: q
       733: q+1
       735: q
       737: 1
       741: q+1
       745: q+1
       749: q+1
       753: q+1
       757: q+1
       761: 2q+1
       764: q
       765: 2q+1
       767: q
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: q+1
       786: q
       787: 2q+1
       789: 2q+1
       791: q+1
       793: 1
       794: 1
       795: q+2
       797: q+1
       799: q+1
       801: q+1
       802: q
       803: 2q+1
       805: q+1
       806: q
       807: q^2+2q+1
       809: q+1
       811: q^2+2q+1
       813: 2q+1
       815: 2q+1
       816: 2q
       817: 2
       819: 2
       821: 1
       823: 1
       825: q+1
       826: q
       827: 2q+1
       831: q+1
       833: 1
       835: q+1
       837: q+1
       839: 3q+1
       841: q+1
       843: 1
       844: 1
       845: q+1
       846: q
       847: 2q+1
       849: 1
       851: q+1
       853: q+1
       855: q+1
       857: 2q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: q+2
       870: q+2
       871: 3q+1
       872: q^2+3q+1
       873: 2
       874: 2
       875: q+1
       876: 2q+1
       877: 3q+1
       878: q+1
       879: 2q+1
       880: 2q+1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: q+1
       912: 1
       916: 1
       918: 1
       920: 1
       924: q+1
       928: q+1
       932: q+1
       934: q
       936: 1
       940: 2
       944: 1
       948: q+1
       956: q+1
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: q+1
       978: q+1
       982: q+1
       988: 2q+1
       990: q
       992: 2
       994: 2
       996: q+2
       998: 2
      1000: 1
      1001: 1
      1002: q+1
      1004: q+1
      1005: q
      1006: 2q+1
      1008: q+1
      1010: 1
      1012: 1
      1013: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: q+1
      1020: q+2
      1022: q+1
      1024: q+1
      1026: q+1
      1027: q
      1028: 2q+1
      1030: 2
      1032: 2
      1034: 1
      1036: 2
      1038: 1
      1042: 1
      1044: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1053: q
      1054: 2q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: 2
      1076: 2
      1077: q+2
      1078: 3q+1
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1086: 1
      1090: 1
      1098: q+1
      1110: 1
      1114: 2
      1118: 1
      1122: 1
      1124: 1
      1126: 1
      1130: 1
      1132: 1
      1134: q+1
      1138: 1
      1141: 1
      1144: 1
      1146: 1
      1148: 1
      1152: 1
      1156: 1
      1160: q+1
      1164: 2
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1198: 1
      1202: q+1
      1214: 2
      1216: 2
      1218: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1230: 2
      1232: 2
      1234: 1
      1235: 1
      1236: q+2
      1238: q+1
      1240: q+1
      1241: q
      1242: 2q+1
      1248: 1
      1250: 1
      1252: 2
      1256: 1
      1260: q+1
      1264: 1
      1266: 1
      1270: q+1
      1272: 1
      1274: 2
      1276: q+1
      1278: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1294: 1
      1302: 1
      1306: 1
      1314: 2
      1318: 1
      1320: 1
      1322: 1
      1326: 1
      1328: 1
      1330: 1
      1334: 1
      1337: 1
      1344: 1
      1348: 2
      1352: 1
      1356: 1
      1358: 1
      1360: 1
      1364: 1
      1365: 1
      1368: q+1
      1376: 1
      1380: 1
      1414: 1
      1418: 1
      1430: 1
      1433: 1
      1446: 1
      1448: 2
      1450: 2
      1454: 1
      1455: 1
      1456: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 2
      1474: 1
      1478: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1489: 1
      1493: 1
      1501: 1
      1504: 1
      1559: 1
      1563: 2
      1567: 1
      1569: 1
      1571: 1
      1575: 1
      1576: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1634: 1
      1641: 1
      1649: 1
      1661: 1
      1663: 1
      1671: 1
      1673: 1
      1687: 1
      1690: 1
      1753: 1
      1757: 1
      1785: 1
      1815: 1
      1819: 1
      1902: 1

1903:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: 3q^3+7q^2+4q+1
        23: 3q^3+7q^2+4q+1
        24: q^4+4q^3+5q^2+4q+1
        25: q^3+6q^2+4q+1
        26: q^3+6q^2+4q+1
        27: 3q^3+4q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+4q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: q^3+4q^2+3q+1
        39: 2q^2+q
        40: q^3+4q^2+3q+1
        41: q^3+q^2+q
        42: 2q^3+3q^2+3q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+7q^2+4q+1
        53: 3q^3+7q^2+4q+1
        54: q^4+4q^3+5q^2+4q+1
        55: q^3+6q^2+4q+1
        56: q^3+6q^2+4q+1
        57: 3q^3+4q^2+4q+1
        58: q^3+4q^2+3q+1
        59: 2q^2+q
        60: 2q^2+2q
        61: 3q^2+2q+1
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: q^2+q
        65: q^3+3q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: 5q^2+4q+1
        73: q^3+6q^2+4q+1
        74: 2q^2+q
        75: q^3+4q^2+3q+1
        76: 2q^2+q
        77: q^3+4q^2+3q+1
        78: q^3+q^2+q
        79: 2q^3+3q^2+3q+1
        80: 2q^3+5q^2+4q+1
        81: 4q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 2q^3+5q^2+4q+1
        84: q^3+4q^2+4q+1
        85: 3q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: q^3+6q^2+4q+1
        95: q^3+6q^2+4q+1
        96: q^4+3q^3+4q^2+3q+1
        97: 4q^2+4q+1
        98: 4q^2+4q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2+q
       104: q^2+q
       105: 2q^2+2q+1
       106: q^2
       107: 2q^2+2q
       108: 3q^2+2q+1
       109: q^3+4q^2+3q+1
       110: 2q^2+q
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: q^2+q
       116: q^3+3q^2+3q+1
       117: 2q^2+3q+1
       118: q
       119: 2q
       120: q^2+2q+1
       121: q^2+q
       122: q^3+3q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       128: 2q^2+3q+1
       130: 2q^2+3q+1
       132: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 3q^2+4q+1
       136: 4q^2+4q+1
       137: 4q^2+4q+1
       138: 3q^2+3q+1
       139: q^3+6q^2+4q+1
       140: 5q^2+4q+1
       141: 2q^3+5q^2+4q+1
       142: q^3+6q^2+4q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 4q^2+4q+1
       146: q^3+4q^2+4q+1
       147: 4q^2+4q+1
       148: 2q^2+3q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: 2q^2+q
       152: q^3+4q^2+3q+1
       153: 2q^2+q
       154: q^3+4q^2+3q+1
       155: q^3+q^2+q
       156: 2q^3+3q^2+3q+1
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: 4q^2+4q+1
       161: 4q^2+4q+1
       162: q^3+4q^2+3q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: 2q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       170: q^2+q
       171: 2q^2+2q+1
       172: q^2
       173: q
       174: q
       175: q^2+2q+1
       178: q^2+2q+1
       180: 2q^2+3q+1
       182: 2q^2+3q+1
       183: 2q
       184: q^2+2q+1
       185: 2q^2+3q+1
       186: q
       187: q^2+q
       188: 2q^2+3q+1
       189: q^2+q
       190: q^3+3q^2+3q+1
       191: 2q^2+3q+1
       192: q
       193: 2q^2+2q
       194: 3q^2+2q+1
       195: q^3+4q^2+3q+1
       196: 2q^2+q
       197: 2q^2+q
       198: 3q^2+3q+1
       199: 2q
       200: q^2+2q+1
       201: 2q^2+2q
       202: 2q^2+2q+1
       203: 2q^2+3q+1
       205: q^2+q
       206: q^2+2q+1
       207: q^2+q
       208: 2q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: q^2+q
       212: q^3+3q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 3q^2+4q+1
       223: 2q^2+3q+1
       224: 4q^2+4q+1
       225: 3q^2+3q+1
       226: 3q^2+3q+1
       227: 2q^2+4q+1
       228: 3q^2+3q+1
       229: 3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+3q+1
       232: 4q+1
       233: q^2+3q+1
       234: q^2+4q+1
       235: 3q+1
       236: 2q^2+3q+1
       238: 2q^2+3q+1
       240: 2q^2+3q+1
       242: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 4q^2+4q+1
       245: 2q^2+3q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: 4q^2+4q+1
       251: 4q^2+4q+1
       252: q^3+4q^2+3q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: 2q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       260: q^2+q
       261: q^2+2q+1
       263: q
       264: q
       265: q^2+2q+1
       267: q^2+q
       268: q^2+q
       269: q^2
       270: 2q^2+2q+1
       271: q^2+q
       272: q^2+2q+1
       275: q
       276: q
       277: q^2+2q+1
       280: 2q+1
       282: q+1
       283: q
       284: q+1
       285: q^2+2q+1
       288: q^2+2q+1
       290: 2q+1
       292: q^2+2q+1
       293: 2q
       294: q^2+2q+1
       295: 2q^2+3q+1
       296: q
       297: q^2+q
       298: 2q^2+3q+1
       299: 2q
       300: q^2+2q+1
       302: 2q^2+3q+1
       303: 2q^2+3q+1
       304: q
       305: q^2+q
       306: 2q^2+3q+1
       307: 2q
       308: 2q+1
       309: 3q+1
       312: q^2+2q+1
       313: q
       314: 2q+1
       316: q^2+2q+1
       318: 2q^2+3q+1
       319: 2q^2+2q
       320: 2q^2+2q+1
       321: 2q^2+3q+1
       323: q^2+q
       324: q^2+2q+1
       325: q^2+q
       326: q^3+3q^2+3q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: 3q^2+3q+1
       347: 3q^2+4q+1
       348: 2q^2+3q+1
       349: 4q^2+4q+1
       350: 3q^2+3q+1
       351: 4q^2+4q+1
       352: 3q+1
       353: 4q+1
       354: q^2+3q+1
       355: q^2+4q+1
       356: q^2+3q+1
       357: 3q+1
       358: 2q+1
       359: 2q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: q^2+4q+1
       370: 3q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       379: q+1
       382: q
       383: q+1
       385: q
       386: q
       387: q^2+2q+1
       390: q^2+q
       392: q^2+2q+1
       393: q
       394: q
       395: q^2+2q+1
       398: q^2+2q+1
       401: q
       402: 2q+1
       405: q^2+q
       408: q^2+2q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q
       420: q+1
       421: q^2+2q+1
       424: q^2+2q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: q
       430: q+1
       431: q^2+2q+1
       434: q^2+2q+1
       436: 2q+1
       437: 2q
       438: q^2+2q+1
       439: 2q^2+3q+1
       440: q
       441: q^2+q
       442: 2q^2+3q+1
       443: 2q^2+2q
       444: 2q^2+2q+1
       446: 2q^2+3q+1
       447: q
       448: q+1
       449: 2q+1
       452: q+1
       453: 2q
       454: 2q+1
       456: q+1
       457: 3q+1
       459: q
       460: 2q+1
       461: 2q^2+3q+1
       464: q^2+2q+1
       466: 2q+1
       468: q+1
       470: q^2+2q+1
       471: 2q
       472: 2q+1
       473: 3q+1
       475: q
       476: 2q+1
       478: q^2+2q+1
       479: q^2+q
       480: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: 2q^2+3q+1
       484: 4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+3q+1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+4q+1
       497: 3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: q^2+4q+1
       512: q^2+3q+1
       513: 3q+1
       514: 2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       523: 1
       526: q
       527: q+1
       531: q+1
       535: q+1
       538: q
       540: q+1
       541: q
       542: q
       544: q^2+2q+1
       546: q^2+q
       548: q^2+2q+1
       550: q+1
       554: q+1
       557: q
       558: 2q+1
       562: q^2+2q+1
       565: q
       567: 2q+1
       572: q^2+2q+1
       573: q^2+q
       576: q^2+2q+1
       581: q^2+2q+1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: q+1
       591: 2q+1
       593: q
       594: q+1
       595: q^2+2q+1
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: q
       604: q+1
       606: q+1
       607: q^2+2q+1
       610: q^2+2q+1
       612: 2q+1
       614: q^2+2q+1
       615: 2q
       616: 2q+1
       618: 2q+1
       619: q
       620: q+1
       621: 2q+1
       624: 1
       626: q+1
       628: q+1
       630: q+1
       631: 3q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: q
       642: q+1
       643: 2q+1
       646: q+1
       647: 2q
       648: 2q+1
       649: 3q+1
       652: q+1
       653: q
       654: 2q+1
       655: q
       656: 2q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 3q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: q+2
       675: 3q+1
       676: q^2+3q+1
       677: 2q^2+3q+1
       678: q^2+4q+1
       679: q^2+3q+1
       680: 2
       681: 3q+1
       682: q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       700: q^2+2q+1
       707: 1
       711: 1
       714: q+1
       719: q+1
       724: 1
       728: q+1
       730: q
       732: q+1
       734: q
       736: q+1
       738: 1
       742: q+1
       746: q+1
       750: q+1
       755: q+1
       760: q+1
       761: q
       764: 2q+1
       765: q
       767: 2q+1
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: q
       786: q+1
       787: 2q+1
       790: 2q+1
       792: q+1
       793: 1
       794: 1
       796: q+2
       798: q+1
       800: q+1
       801: q
       802: q+1
       803: 2q+1
       805: q
       806: q+1
       807: q^2+2q+1
       810: q+1
       812: q^2+2q+1
       814: 2q+1
       815: 2q
       816: 2q+1
       817: 2
       820: 2
       822: 1
       824: 1
       825: q
       826: q+1
       827: 2q+1
       831: q+1
       834: 1
       836: q+1
       838: q+1
       839: 3q+1
       842: q+1
       843: 1
       844: 1
       845: q
       846: q+1
       847: 2q+1
       850: 1
       852: q+1
       854: q+1
       856: q+1
       857: q
       858: 2q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: q+2
       870: q+2
       871: 3q+1
       872: q^2+3q+1
       873: 2
       874: 2
       875: q+1
       876: 2q+1
       877: 3q+1
       878: q+1
       879: 2q+1
       880: 2q+1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: q+1
       915: 1
       917: 1
       919: 1
       923: 1
       925: q+1
       931: q+1
       933: q
       935: q+1
       937: 1
       941: 2
       945: 1
       949: q+1
       957: q+1
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: q+1
       981: q+1
       986: q+1
       988: q
       990: 2q+1
       993: 2
       995: 2
       997: q+2
       998: 2
      1000: 1
      1001: 1
      1003: q+1
      1004: q
      1005: q+1
      1006: 2q+1
      1009: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: q+1
      1021: q+2
      1023: q+1
      1025: q+1
      1026: q
      1027: q+1
      1028: 2q+1
      1031: 2
      1032: 2
      1035: 1
      1037: 2
      1039: 1
      1043: 1
      1044: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: q+1
      1054: 2q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: 2
      1076: 2
      1077: q+2
      1078: 3q+1
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1087: 1
      1093: 1
      1105: q+1
      1111: 1
      1115: 2
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1137: q+1
      1139: 1
      1142: 1
      1145: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: q+1
      1165: 2
      1169: 1
      1173: 1
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1201: 1
      1203: q+1
      1215: 2
      1216: 2
      1218: 1
      1219: 1
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1231: 2
      1232: 2
      1234: 1
      1235: 1
      1237: q+2
      1239: q+1
      1240: q
      1241: q+1
      1242: 2q+1
      1249: 1
      1250: 1
      1253: 2
      1257: 1
      1260: q+1
      1265: 1
      1267: 1
      1270: q+1
      1273: 1
      1275: 2
      1277: q+1
      1279: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1297: 1
      1303: 1
      1309: 1
      1315: 2
      1319: 1
      1321: 1
      1325: 1
      1326: 1
      1328: 1
      1333: 1
      1335: 1
      1338: 1
      1345: 1
      1349: 2
      1355: 1
      1357: 1
      1359: 1
      1362: 1
      1364: 1
      1365: 1
      1370: q+1
      1377: 1
      1381: 1
      1417: 1
      1419: 1
      1431: 1
      1434: 1
      1447: 1
      1449: 2
      1450: 2
      1454: 1
      1455: 1
      1457: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 2
      1475: 1
      1478: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1490: 1
      1496: 1
      1502: 1
      1507: 1
      1562: 1
      1564: 2
      1568: 1
      1570: 1
      1573: 1
      1575: 1
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1632: 1
      1635: 1
      1642: 1
      1649: 1
      1662: 1
      1663: 1
      1672: 1
      1673: 1
      1688: 1
      1693: 1
      1755: 1
      1758: 1
      1786: 1
      1816: 1
      1819: 1
      1903: 1

1904:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: 3q^3+7q^2+4q+1
        23: 3q^3+7q^2+4q+1
        24: q^4+4q^3+5q^2+4q+1
        25: q^3+6q^2+4q+1
        26: q^3+6q^2+4q+1
        27: 3q^3+4q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+4q^2+4q+1
        36: 5q^2+4q+1
        37: q^3+4q^2+3q+1
        38: 2q^2+q
        39: q^3+4q^2+3q+1
        40: 2q^2+q
        41: 2q^3+3q^2+3q+1
        42: q^3+q^2+q
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+7q^2+4q+1
        53: 3q^3+7q^2+4q+1
        54: q^4+4q^3+5q^2+4q+1
        55: q^3+6q^2+4q+1
        56: q^3+6q^2+4q+1
        57: 3q^3+4q^2+4q+1
        58: 2q^2+q
        59: q^3+4q^2+3q+1
        60: 2q^2+2q
        61: 3q^2+2q+1
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+3q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: 5q^2+4q+1
        73: q^3+6q^2+4q+1
        74: q^3+4q^2+3q+1
        75: 2q^2+q
        76: q^3+4q^2+3q+1
        77: 2q^2+q
        78: 2q^3+3q^2+3q+1
        79: q^3+q^2+q
        80: 2q^3+5q^2+4q+1
        81: 4q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 2q^3+5q^2+4q+1
        84: q^3+4q^2+4q+1
        85: 3q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: q^3+6q^2+4q+1
        95: q^3+6q^2+4q+1
        96: q^4+3q^3+4q^2+3q+1
        97: 4q^2+4q+1
        98: 4q^2+4q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2+q
       104: q^2+q
       105: q^2
       106: 2q^2+2q+1
       107: 2q^2+2q
       108: 3q^2+2q+1
       109: 2q^2+q
       110: q^3+4q^2+3q+1
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+3q^2+3q+1
       116: q^2+q
       117: q
       118: 2q^2+3q+1
       119: 2q
       120: q^2+2q+1
       121: q^3+3q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       127: 2q^2+3q+1
       129: 2q^2+3q+1
       131: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 3q^2+4q+1
       136: 4q^2+4q+1
       137: 4q^2+4q+1
       138: 3q^2+3q+1
       139: q^3+6q^2+4q+1
       140: 5q^2+4q+1
       141: 2q^3+5q^2+4q+1
       142: q^3+6q^2+4q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 4q^2+4q+1
       146: q^3+4q^2+4q+1
       147: 4q^2+4q+1
       148: 2q^2+3q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: q^3+4q^2+3q+1
       152: 2q^2+q
       153: q^3+4q^2+3q+1
       154: 2q^2+q
       155: 2q^3+3q^2+3q+1
       156: q^3+q^2+q
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: 4q^2+4q+1
       161: 4q^2+4q+1
       162: q^3+4q^2+3q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: 2q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       170: q^2+q
       171: q^2
       172: 2q^2+2q+1
       173: q
       174: q
       176: q^2+2q+1
       177: q^2+2q+1
       179: 2q^2+3q+1
       181: 2q^2+3q+1
       183: 2q
       184: q^2+2q+1
       185: q
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: q^2+q
       189: q^3+3q^2+3q+1
       190: q^2+q
       191: q
       192: 2q^2+3q+1
       193: 2q^2+2q
       194: 3q^2+2q+1
       195: 2q^2+q
       196: q^3+4q^2+3q+1
       197: 3q^2+3q+1
       198: 2q^2+q
       199: 2q
       200: q^2+2q+1
       201: 2q^2+2q
       202: 2q^2+2q+1
       204: 2q^2+3q+1
       205: q^2+2q+1
       206: q^2+q
       207: 2q^2+3q+1
       208: q^2+q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+3q^2+3q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 3q^2+4q+1
       223: 2q^2+3q+1
       224: 4q^2+4q+1
       225: 3q^2+3q+1
       226: 3q^2+3q+1
       227: 2q^2+4q+1
       228: 3q^2+3q+1
       229: 3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+3q+1
       232: 4q+1
       233: q^2+3q+1
       234: q^2+4q+1
       235: 3q+1
       236: 2q^2+3q+1
       237: 2q^2+3q+1
       239: 2q^2+3q+1
       241: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 4q^2+4q+1
       245: 2q^2+3q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: 4q^2+4q+1
       251: 4q^2+4q+1
       252: q^3+4q^2+3q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: 2q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       259: q^2+q
       262: q^2+2q+1
       263: q
       264: q
       266: q^2+2q+1
       267: q^2+q
       268: q^2+q
       269: 2q^2+2q+1
       270: q^2
       273: q^2+2q+1
       274: q^2+q
       275: q
       276: q
       278: q^2+2q+1
       279: 2q+1
       281: q+1
       283: q
       284: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       289: 2q+1
       291: q^2+2q+1
       293: 2q
       294: q^2+2q+1
       295: q
       296: 2q^2+3q+1
       297: 2q^2+3q+1
       298: q^2+q
       299: 2q
       300: q^2+2q+1
       301: 2q^2+3q+1
       303: q
       304: 2q^2+3q+1
       305: 2q^2+3q+1
       306: q^2+q
       307: 2q
       308: 2q+1
       310: 3q+1
       311: q^2+2q+1
       313: 2q+1
       314: q
       315: q^2+2q+1
       317: 2q^2+3q+1
       319: 2q^2+2q
       320: 2q^2+2q+1
       322: 2q^2+3q+1
       323: q^2+2q+1
       324: q^2+q
       325: q^3+3q^2+3q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: 3q^2+3q+1
       347: 3q^2+4q+1
       348: 2q^2+3q+1
       349: 4q^2+4q+1
       350: 3q^2+3q+1
       351: 4q^2+4q+1
       352: 3q+1
       353: 4q+1
       354: q^2+3q+1
       355: q^2+4q+1
       356: q^2+3q+1
       357: 3q+1
       358: 2q+1
       359: 2q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: q^2+4q+1
       370: 3q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       380: q+1
       381: q
       384: q+1
       385: q
       386: q
       388: q^2+2q+1
       389: q^2+q
       391: q^2+2q+1
       393: q
       394: q
       396: q^2+2q+1
       399: q^2+2q+1
       403: q
       404: 2q+1
       406: q^2+2q+1
       407: q^2+q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q
       420: q+1
       422: q^2+2q+1
       423: q^2+2q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: q
       430: q+1
       432: q^2+2q+1
       433: q^2+2q+1
       435: 2q+1
       437: 2q
       438: q^2+2q+1
       439: q
       440: 2q^2+3q+1
       441: 2q^2+3q+1
       442: q^2+q
       443: 2q^2+2q
       444: 2q^2+2q+1
       445: 2q^2+3q+1
       447: q
       448: q+1
       450: 2q+1
       451: q+1
       453: 2q
       454: 2q+1
       455: q+1
       458: 3q+1
       459: 2q+1
       460: q
       462: 2q^2+3q+1
       463: q^2+2q+1
       465: 2q+1
       467: q+1
       469: q^2+2q+1
       471: 2q
       472: 2q+1
       474: 3q+1
       475: 2q+1
       476: q
       477: q^2+2q+1
       479: q^2+2q+1
       480: q^2+q
       481: 3q+1
       482: q^2+3q+1
       483: 2q^2+3q+1
       484: 4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+3q+1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+4q+1
       497: 3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: q^2+4q+1
       512: q^2+3q+1
       513: 3q+1
       514: 2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       524: 1
       525: q
       528: q+1
       532: q+1
       536: q+1
       537: q
       539: q+1
       541: q
       542: q
       543: q^2+2q+1
       545: q^2+q
       547: q^2+2q+1
       552: q+1
       555: q+1
       559: 2q+1
       560: q
       563: q^2+2q+1
       566: q
       568: 2q+1
       570: q^2+2q+1
       574: q^2+q
       575: q^2+2q+1
       577: q^2+2q+1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: q+1
       592: 2q+1
       593: q
       594: q+1
       596: q^2+2q+1
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: q
       604: q+1
       605: q+1
       608: q^2+2q+1
       609: q^2+2q+1
       611: 2q+1
       613: q^2+2q+1
       615: 2q
       616: 2q+1
       617: 2q+1
       619: q
       620: q+1
       622: 2q+1
       623: 1
       625: q+1
       627: q+1
       629: q+1
       632: 3q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: q
       642: q+1
       644: 2q+1
       645: q+1
       647: 2q
       648: 2q+1
       650: 3q+1
       651: q+1
       653: 2q+1
       654: q
       655: 2q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 3q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: q+2
       675: 3q+1
       676: q^2+3q+1
       677: 2q^2+3q+1
       678: q^2+4q+1
       679: q^2+3q+1
       680: 2
       681: 3q+1
       682: q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       697: q^2+2q+1
       708: 1
       712: 1
       716: q+1
       720: q+1
       723: 1
       727: q+1
       729: q
       731: q+1
       733: q
       735: q+1
       739: 1
       743: q+1
       747: q+1
       751: q+1
       756: q+1
       758: q+1
       762: 2q+1
       763: q
       766: q
       768: 2q+1
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: q
       786: q+1
       788: 2q+1
       789: 2q+1
       791: q+1
       793: 1
       794: 1
       795: q+2
       797: q+1
       799: q+1
       801: q
       802: q+1
       804: 2q+1
       805: q
       806: q+1
       808: q^2+2q+1
       809: q+1
       811: q^2+2q+1
       813: 2q+1
       815: 2q
       816: 2q+1
       818: 2
       819: 2
       821: 1
       823: 1
       825: q
       826: q+1
       828: 2q+1
       832: q+1
       833: 1
       835: q+1
       837: q+1
       840: 3q+1
       841: q+1
       843: 1
       844: 1
       845: q
       846: q+1
       848: 2q+1
       849: 1
       851: q+1
       853: q+1
       855: q+1
       857: 2q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: q+2
       870: q+2
       871: 3q+1
       872: q^2+3q+1
       873: 2
       874: 2
       875: q+1
       876: 2q+1
       877: 3q+1
       878: q+1
       879: 2q+1
       880: 2q+1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: q+1
       914: 1
       916: 1
       918: 1
       922: 1
       927: q+1
       930: q+1
       932: q
       934: q+1
       938: 1
       942: 2
       946: 1
       950: q+1
       958: q+1
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: q+1
       979: q+1
       982: q+1
       989: q
       991: 2q+1
       992: 2
       994: 2
       996: q+2
       999: 2
      1000: 1
      1001: 1
      1002: q+1
      1004: q
      1005: q+1
      1007: 2q+1
      1008: q+1
      1010: 1
      1012: 1
      1013: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: q+1
      1020: q+2
      1022: q+1
      1024: q+1
      1026: q
      1027: q+1
      1029: 2q+1
      1030: 2
      1033: 2
      1034: 1
      1036: 2
      1038: 1
      1042: 1
      1045: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q
      1053: q+1
      1055: 2q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: 2
      1076: 2
      1077: q+2
      1078: 3q+1
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1089: 1
      1091: 1
      1102: q+1
      1112: 1
      1116: 2
      1120: 1
      1122: 1
      1124: 1
      1127: 1
      1131: 1
      1133: 1
      1135: q+1
      1138: 1
      1141: 1
      1144: 1
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: q+1
      1166: 2
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1199: 1
      1204: q+1
      1214: 2
      1217: 2
      1218: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1230: 2
      1233: 2
      1234: 1
      1235: 1
      1236: q+2
      1238: q+1
      1240: q
      1241: q+1
      1243: 2q+1
      1248: 1
      1251: 1
      1252: 2
      1256: 1
      1261: q+1
      1264: 1
      1266: 1
      1271: q+1
      1272: 1
      1274: 2
      1276: q+1
      1278: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: q+1
      1293: 1
      1295: 1
      1305: 1
      1307: 1
      1316: 2
      1318: 1
      1320: 1
      1323: 1
      1327: 1
      1329: 1
      1331: 1
      1334: 1
      1337: 1
      1346: 1
      1350: 2
      1354: 1
      1356: 1
      1358: 1
      1361: 1
      1366: 1
      1367: 1
      1369: q+1
      1378: 1
      1382: 1
      1415: 1
      1420: 1
      1430: 1
      1433: 1
      1446: 1
      1448: 2
      1451: 2
      1454: 1
      1455: 1
      1456: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 2
      1474: 1
      1479: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1492: 1
      1494: 1
      1505: 1
      1506: 1
      1560: 1
      1565: 2
      1567: 1
      1569: 1
      1572: 1
      1577: 1
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1634: 1
      1641: 1
      1650: 1
      1661: 1
      1664: 1
      1671: 1
      1673: 1
      1691: 1
      1692: 1
      1754: 1
      1759: 1
      1787: 1
      1815: 1
      1820: 1
      1904: 1

1905:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: 3q^3+7q^2+4q+1
        23: 3q^3+7q^2+4q+1
        24: q^4+4q^3+5q^2+4q+1
        25: q^3+6q^2+4q+1
        26: q^3+6q^2+4q+1
        27: 3q^3+4q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+6q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+4q^2+4q+1
        36: 5q^2+4q+1
        37: 2q^2+q
        38: q^3+4q^2+3q+1
        39: 2q^2+q
        40: q^3+4q^2+3q+1
        41: q^3+q^2+q
        42: 2q^3+3q^2+3q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: 3q^3+7q^2+4q+1
        53: 3q^3+7q^2+4q+1
        54: q^4+4q^3+5q^2+4q+1
        55: q^3+6q^2+4q+1
        56: q^3+6q^2+4q+1
        57: 3q^3+4q^2+4q+1
        58: 2q^2+q
        59: q^3+4q^2+3q+1
        60: 3q^2+2q+1
        61: 2q^2+2q
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: q^2+q
        65: q^3+3q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: 5q^2+4q+1
        73: q^3+6q^2+4q+1
        74: 2q^2+q
        75: q^3+4q^2+3q+1
        76: 2q^2+q
        77: q^3+4q^2+3q+1
        78: q^3+q^2+q
        79: 2q^3+3q^2+3q+1
        80: 2q^3+5q^2+4q+1
        81: 4q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 2q^3+5q^2+4q+1
        84: q^3+4q^2+4q+1
        85: 3q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: q^3+6q^2+4q+1
        95: q^3+6q^2+4q+1
        96: q^4+3q^3+4q^2+3q+1
        97: 4q^2+4q+1
        98: 4q^2+4q+1
        99: 2q^3+3q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2
       104: 2q^2+2q+1
       105: q^2+q
       106: q^2+q
       107: 3q^2+2q+1
       108: 2q^2+2q
       109: 2q^2+q
       110: q^3+4q^2+3q+1
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: q^2+q
       116: q^3+3q^2+3q+1
       117: q
       118: 2q^2+3q+1
       119: q^2+2q+1
       120: 2q
       121: q^2+q
       122: q^3+3q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       128: 2q^2+3q+1
       130: 2q^2+3q+1
       132: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 3q^2+4q+1
       136: 4q^2+4q+1
       137: 4q^2+4q+1
       138: 3q^2+3q+1
       139: q^3+6q^2+4q+1
       140: 5q^2+4q+1
       141: 2q^3+5q^2+4q+1
       142: q^3+6q^2+4q+1
       143: 3q^2+4q+1
       144: 2q^2+3q+1
       145: 4q^2+4q+1
       146: q^3+4q^2+4q+1
       147: 4q^2+4q+1
       148: 2q^2+3q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: 2q^2+q
       152: q^3+4q^2+3q+1
       153: 2q^2+q
       154: q^3+4q^2+3q+1
       155: q^3+q^2+q
       156: 2q^3+3q^2+3q+1
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: 4q^2+4q+1
       161: 4q^2+4q+1
       162: q^3+4q^2+3q+1
       163: q^2+4q+1
       164: q^2+4q+1
       165: 2q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2
       170: 2q^2+2q+1
       171: q^2+q
       172: q^2+q
       174: q^2+2q+1
       175: q
       176: q
       178: q^2+2q+1
       180: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q^2+2q+1
       184: 2q
       185: q
       186: 2q^2+3q+1
       187: q^2+q
       188: 2q^2+3q+1
       189: q^2+q
       190: q^3+3q^2+3q+1
       191: q
       192: 2q^2+3q+1
       193: 3q^2+2q+1
       194: 2q^2+2q
       195: 2q^2+q
       196: q^3+4q^2+3q+1
       197: 2q^2+q
       198: 3q^2+3q+1
       199: q^2+2q+1
       200: 2q
       201: 2q^2+2q+1
       202: 2q^2+2q
       204: 2q^2+3q+1
       205: q^2+q
       206: q^2+2q+1
       207: q^2+q
       208: 2q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: q^2+q
       212: q^3+3q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 3q^2+4q+1
       223: 2q^2+3q+1
       224: 4q^2+4q+1
       225: 3q^2+3q+1
       226: 3q^2+3q+1
       227: 2q^2+4q+1
       228: 3q^2+3q+1
       229: 3q^2+4q+1
       230: 4q^2+4q+1
       231: 2q^2+3q+1
       232: 4q+1
       233: q^2+3q+1
       234: q^2+4q+1
       235: 3q+1
       236: 2q^2+3q+1
       238: 2q^2+3q+1
       240: 2q^2+3q+1
       242: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 4q^2+4q+1
       245: 2q^2+3q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: 4q^2+4q+1
       251: 4q^2+4q+1
       252: q^3+4q^2+3q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: 2q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       260: q^2+2q+1
       261: q^2+q
       264: q^2+2q+1
       265: q
       266: q
       267: q^2
       268: 2q^2+2q+1
       269: q^2+q
       270: q^2+q
       273: q^2+q
       274: q^2+2q+1
       276: q^2+2q+1
       277: q
       278: q
       280: 2q+1
       282: q+1
       283: q+1
       284: q
       286: q^2+2q+1
       288: q^2+2q+1
       290: 2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: 2q
       295: q
       296: 2q^2+3q+1
       297: q^2+q
       298: 2q^2+3q+1
       299: q^2+2q+1
       300: 2q
       302: 2q^2+3q+1
       303: q
       304: 2q^2+3q+1
       305: q^2+q
       306: 2q^2+3q+1
       307: 2q+1
       308: 2q
       310: 3q+1
       312: q^2+2q+1
       313: q
       314: 2q+1
       316: q^2+2q+1
       318: 2q^2+3q+1
       319: 2q^2+2q+1
       320: 2q^2+2q
       322: 2q^2+3q+1
       323: q^2+q
       324: q^2+2q+1
       325: q^2+q
       326: q^3+3q^2+3q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+3q+1
       334: 2q^2+3q+1
       335: 3q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: 2q^2+4q+1
       346: 3q^2+3q+1
       347: 3q^2+4q+1
       348: 2q^2+3q+1
       349: 4q^2+4q+1
       350: 3q^2+3q+1
       351: 4q^2+4q+1
       352: 3q+1
       353: 4q+1
       354: q^2+3q+1
       355: q^2+4q+1
       356: q^2+3q+1
       357: 3q+1
       358: 2q+1
       359: 2q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: q^2+4q+1
       370: 3q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       378: q+1
       382: q+1
       383: q
       386: q^2+2q+1
       387: q
       388: q
       390: q^2+2q+1
       392: q^2+q
       394: q^2+2q+1
       395: q
       396: q
       400: q^2+2q+1
       403: 2q+1
       404: q
       406: q^2+q
       407: q^2+2q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q+1
       420: q
       422: q^2+2q+1
       424: q^2+2q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: q+1
       430: q
       432: q^2+2q+1
       434: q^2+2q+1
       436: 2q+1
       437: q^2+2q+1
       438: 2q
       439: q
       440: 2q^2+3q+1
       441: q^2+q
       442: 2q^2+3q+1
       443: 2q^2+2q+1
       444: 2q^2+2q
       446: 2q^2+3q+1
       447: q+1
       448: q
       450: 2q+1
       452: q+1
       453: 2q+1
       454: 2q
       456: q+1
       458: 3q+1
       459: q
       460: 2q+1
       462: 2q^2+3q+1
       464: q^2+2q+1
       466: 2q+1
       468: q+1
       470: q^2+2q+1
       471: 2q+1
       472: 2q
       474: 3q+1
       475: q
       476: 2q+1
       478: q^2+2q+1
       479: q^2+q
       480: q^2+2q+1
       481: 3q+1
       482: q^2+3q+1
       483: 2q^2+3q+1
       484: 4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+3q+1
       492: q^2+3q+1
       493: 2q^2+3q+1
       494: 3q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+4q+1
       497: 3q+1
       498: q^2+3q+1
       499: 2q+1
       500: 2q+1
       501: 3q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: q^2+4q+1
       512: q^2+3q+1
       513: 3q+1
       514: 2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       522: 1
       526: q+1
       527: q
       530: q+1
       534: q+1
       538: q+1
       540: q
       542: q^2+2q+1
       543: q
       544: q
       546: q^2+2q+1
       548: q^2+q
       551: q+1
       556: q+1
       559: q
       560: 2q+1
       564: q^2+2q+1
       566: 2q+1
       568: q
       571: q^2+2q+1
       574: q^2+2q+1
       575: q^2+q
       581: q^2+2q+1
       584: q+1
       586: q+1
       588: q+1
       589: q+1
       590: q
       592: 2q+1
       593: q+1
       594: q
       596: q^2+2q+1
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: q+1
       604: q
       606: q+1
       608: q^2+2q+1
       610: q^2+2q+1
       612: 2q+1
       614: q^2+2q+1
       615: 2q+1
       616: 2q
       618: 2q+1
       619: q+1
       620: q
       622: 2q+1
       624: 1
       626: q+1
       628: q+1
       630: q+1
       632: 3q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: q+1
       642: q
       644: 2q+1
       646: q+1
       647: 2q+1
       648: 2q
       650: 3q+1
       652: q+1
       653: q
       654: 2q+1
       655: q
       656: 2q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 3q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: q+2
       675: 3q+1
       676: q^2+3q+1
       677: 2q^2+3q+1
       678: q^2+4q+1
       679: q^2+3q+1
       680: 2
       681: 3q+1
       682: q+1
       683: 2q+1
       684: 3q+1
       685: 2q+1
       686: 3q+1
       687: q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       699: q^2+2q+1
       706: 1
       710: 1
       715: q+1
       718: q+1
       722: 1
       726: q+1
       730: q+1
       732: q
       734: q+1
       736: q
       740: 1
       744: q+1
       748: q+1
       752: q+1
       754: q+1
       759: q+1
       762: q
       763: 2q+1
       766: 2q+1
       768: q
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: q+1
       786: q
       788: 2q+1
       790: 2q+1
       792: q+1
       793: 1
       794: 1
       796: q+2
       798: q+1
       800: q+1
       801: q+1
       802: q
       804: 2q+1
       805: q+1
       806: q
       808: q^2+2q+1
       810: q+1
       812: q^2+2q+1
       814: 2q+1
       815: 2q+1
       816: 2q
       818: 2
       820: 2
       822: 1
       824: 1
       825: q+1
       826: q
       828: 2q+1
       832: q+1
       834: 1
       836: q+1
       838: q+1
       840: 3q+1
       842: q+1
       843: 1
       844: 1
       845: q+1
       846: q
       848: 2q+1
       850: 1
       852: q+1
       854: q+1
       856: q+1
       857: q
       858: 2q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: q+2
       870: q+2
       871: 3q+1
       872: q^2+3q+1
       873: 2
       874: 2
       875: q+1
       876: 2q+1
       877: 3q+1
       878: q+1
       879: 2q+1
       880: 2q+1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: q+1
       913: 1
       917: 1
       919: 1
       921: 1
       926: q+1
       929: q+1
       933: q+1
       935: q
       939: 1
       943: 2
       947: 1
       951: q+1
       959: q+1
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: q+1
       980: q+1
       986: q+1
       989: 2q+1
       991: q
       993: 2
       995: 2
       997: q+2
       999: 2
      1000: 1
      1001: 1
      1003: q+1
      1004: q+1
      1005: q
      1007: 2q+1
      1009: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: q+1
      1021: q+2
      1023: q+1
      1025: q+1
      1026: q+1
      1027: q
      1029: 2q+1
      1031: 2
      1033: 2
      1035: 1
      1037: 2
      1039: 1
      1043: 1
      1045: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: q
      1055: 2q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: 2
      1076: 2
      1077: q+2
      1078: 3q+1
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1092: 1
      1094: 1
      1104: q+1
      1113: 1
      1117: 2
      1119: 1
      1123: 1
      1125: 1
      1128: 1
      1131: 1
      1133: 1
      1136: q+1
      1139: 1
      1142: 1
      1145: 1
      1147: 1
      1149: 1
      1155: 1
      1157: 1
      1162: q+1
      1167: 2
      1171: 1
      1175: 1
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1200: 1
      1205: q+1
      1215: 2
      1217: 2
      1218: 1
      1219: 1
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1231: 2
      1233: 2
      1234: 1
      1235: 1
      1237: q+2
      1239: q+1
      1240: q+1
      1241: q
      1243: 2q+1
      1249: 1
      1251: 1
      1253: 2
      1257: 1
      1261: q+1
      1265: 1
      1267: 1
      1271: q+1
      1273: 1
      1275: 2
      1277: q+1
      1279: 1
      1280: 1
      1281: 1
      1283: 2
      1285: 1
      1287: 1
      1288: 2
      1289: q+1
      1296: 1
      1298: 1
      1308: 1
      1310: 1
      1317: 2
      1319: 1
      1321: 1
      1324: 1
      1327: 1
      1329: 1
      1332: 1
      1335: 1
      1338: 1
      1347: 1
      1351: 2
      1353: 1
      1357: 1
      1359: 1
      1363: 1
      1366: 1
      1367: 1
      1371: q+1
      1379: 1
      1383: 1
      1416: 1
      1421: 1
      1431: 1
      1434: 1
      1447: 1
      1449: 2
      1451: 2
      1454: 1
      1455: 1
      1457: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 2
      1475: 1
      1479: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1497: 1
      1508: 1
      1509: 1
      1561: 1
      1566: 2
      1568: 1
      1570: 1
      1574: 1
      1577: 1
      1578: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1632: 1
      1635: 1
      1642: 1
      1650: 1
      1662: 1
      1664: 1
      1672: 1
      1673: 1
      1694: 1
      1695: 1
      1756: 1
      1760: 1
      1788: 1
      1816: 1
      1820: 1
      1905: 1

1906:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: q^4+2q^3+3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 3q^2+2q+1
        37: 2q^2+q+1
        38: q^2+q
        39: 2q^2+q+1
        40: q^2+q
        41: q^3+q^2+q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 2q^3+4q^2+2q+1
        53: 2q^3+4q^2+2q+1
        54: q^4+2q^3+3q^2+2q+1
        55: 3q^2+2q+1
        56: 3q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+q+1
        59: q^2+q
        60: q^2+1
        61: q^2+2q
        62: 2q^2+q+1
        63: q
        64: q^2+q+1
        65: q^2+q
        66: 2q^2+q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 3q^2+2q+1
        73: 2q^3+4q^2+2q+1
        74: 2q^2+q+1
        75: q^2+q
        76: 2q^2+q+1
        77: q^2+q
        78: q^3+q^2+q+1
        79: q^2+q
        80: 2q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^3+4q^2+2q+1
        95: 2q^3+4q^2+2q+1
        96: q^4+2q^3+3q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+1
       105: q
       106: q^2+q
       107: q^2+1
       108: q^2+2q
       109: q^3+2q^2+q+1
       110: q^2+q
       111: 2q^2+q+1
       112: q^2+q
       113: 2q^2+q+1
       114: q
       115: q^2+q+1
       116: q^2+q
       117: q^2+q+1
       118: q
       119: 1
       120: 2q
       121: q^2+q+1
       122: q
       123: q^2+q+1
       124: q^2+q
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+q+1
       128: q^2+q
       129: 2q^2+q+1
       130: q^2+q
       131: q^3+q^2+q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^3+3q^2+2q+1
       137: 2q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: 3q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^3+4q^2+2q+1
       143: q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 3q^2+2q+1
       148: q^2+q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+q+1
       152: q^2+q
       153: 2q^2+q+1
       154: q^2+q
       155: q^3+q^2+q+1
       156: q^2+q
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q^2+1
       171: q
       172: q^2+q
       173: 1
       175: q
       176: q
       177: q^2+q+1
       178: q^2+q
       179: 2q^2+q+1
       180: q
       181: 2q^2+q+1
       182: q^2+q
       183: 1
       184: 2q
       185: q^2+q+1
       186: q
       187: q^2+q+1
       188: q^2+q
       189: q^2+q+1
       190: q
       191: q^2+q+1
       192: q
       193: q^2+1
       194: q^2+2q
       195: q^3+2q^2+q+1
       196: q^2+q
       197: 2q^2+q+1
       198: q^2+q
       199: 1
       200: 2q
       201: q^2+1
       202: q^2+2q
       203: q^2+q+1
       205: q^2+1
       206: q
       207: q^2+q+1
       208: q
       209: 2q^2+q+1
       210: q
       211: q^2+q+1
       212: q^2+q
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: 2q^2+2q+1
       224: 2q^2+2q+1
       225: q^3+3q^2+2q+1
       226: 2q^2+2q+1
       227: q^2+2q+1
       228: q^3+3q^2+2q+1
       229: 2q^2+2q+1
       230: q^3+3q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: 2q^2+q+1
       238: q^2+q
       239: 2q^2+q+1
       240: q^2+q
       241: q^3+q^2+q+1
       242: q^2+q
       243: 2q^2+2q+1
       244: 3q^2+2q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+1
       261: q
       262: q^2+q
       263: 1
       265: q
       266: q
       267: q^2+1
       269: q^2+q
       270: q
       271: q^2+1
       272: q
       275: 1
       277: q
       278: q
       279: q+1
       281: q+1
       283: 1
       284: 2q
       285: q^2+q+1
       286: q
       287: q^2+q+1
       288: q
       289: q+1
       291: q^2+q+1
       292: q^2+q
       293: 1
       294: 2q
       295: q^2+q+1
       296: q
       297: q^2+q+1
       298: q
       299: 1
       300: 2q
       301: 2q^2+q+1
       302: q^2+q
       303: q^2+q+1
       304: q
       305: q^2+q+1
       306: q^2+q
       307: 1
       308: 2q
       309: q+1
       311: q^2+1
       312: q
       313: 1
       314: q
       315: q^2+q+1
       316: q^2+q
       317: 2q^2+q+1
       318: q
       319: q^2+1
       320: q^2+2q
       321: q^2+q+1
       323: q^2+1
       324: q
       325: q^2+q+1
       326: q
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: 2q^2+q+1
       339: q^2+q
       340: 2q^2+q+1
       341: q^2+q
       342: q^3+q^2+q+1
       343: q^2+q
       344: q^2+2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: 2q^2+2q+1
       349: 2q^2+2q+1
       350: q^3+3q^2+2q+1
       351: 3q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q^2+q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       379: q
       380: q
       381: 1
       384: q
       385: 1
       387: q
       388: q
       389: q^2+1
       391: q^2+q
       392: q
       393: 1
       395: q
       396: q
       397: q^2+1
       398: q
       401: 1
       402: q
       405: q^2+1
       408: q
       413: q+1
       417: q+1
       419: 1
       420: 2q
       421: q^2+q+1
       422: q
       423: q^2+q+1
       424: q
       425: q^2+q+1
       426: q^2+q
       427: 2q^2+q+1
       428: q
       429: 1
       430: 2q
       431: q^2+q+1
       432: q
       433: q^2+q+1
       434: q^2+q
       435: q+1
       437: 1
       438: 2q
       439: q^2+q+1
       440: q
       441: q^2+q+1
       442: q
       443: q^2+1
       444: q^2+2q
       445: 2q^2+q+1
       446: q^2+q
       447: 1
       448: 2q
       449: q+1
       451: 1
       452: q
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: q^2+q+1
       463: q^2+1
       464: q
       465: q+1
       467: q+1
       469: q^2+q+1
       470: q
       471: 1
       472: 2q
       473: q+1
       475: 1
       476: q
       477: q^2+1
       478: q
       479: q^2+1
       480: q
       481: 2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: 2q+1
       485: q+1
       487: q+1
       489: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: 2q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       529: 1
       531: q
       532: q
       533: 1
       535: q
       536: q
       537: 1
       539: q
       541: 1
       543: q
       544: q
       545: q^2+1
       547: q^2+q
       548: q
       549: 1
       550: q
       553: 1
       557: 1
       561: q^2+1
       562: q
       565: 1
       567: q
       569: q^2+1
       572: q
       573: q^2+1
       576: q
       577: q^2+1
       581: q
       585: q+1
       589: 1
       590: 2q
       591: q+1
       593: 1
       594: 2q
       595: q^2+q+1
       596: q
       597: q+1
       599: q^2+q+1
       600: q
       601: q+1
       603: 1
       604: 2q
       605: q+1
       607: q^2+q+1
       608: q
       609: q^2+q+1
       610: q
       613: q^2+q+1
       614: q^2+q
       615: 1
       616: 2q
       617: q+1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       629: 1
       630: q
       631: q+1
       633: 1
       639: q+1
       641: 1
       642: 2q
       643: q+1
       645: 1
       646: q
       647: 1
       648: q
       649: 1
       651: 1
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       660: q+1
       662: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: q^2+2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+1
       700: q
       709: 1
       712: q
       713: 1
       714: q
       717: 1
       719: q
       720: q
       721: 1
       723: q
       725: 1
       727: q
       728: q
       733: 1
       735: q
       737: 1
       741: 1
       749: 1
       753: 1
       755: q
       757: 1
       761: 1
       765: 1
       767: q
       769: 1
       775: q+1
       779: q+1
       781: q+1
       785: 1
       786: 2q
       787: q+1
       791: 1
       792: q
       793: 1
       794: 2q
       795: q+1
       797: q+1
       801: 1
       802: 2q
       803: q+1
       805: 1
       806: 2q
       807: q^2+q+1
       808: q
       809: q+1
       811: q^2+q+1
       812: q
       815: 1
       816: q
       817: q+1
       819: 1
       821: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       839: 1
       843: 1
       844: q
       845: 1
       846: q
       847: 1
       849: 1
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       884: 1
       900: 1
       904: 1
       906: q
       908: 1
       910: q
       916: 1
       918: q
       920: 1
       922: q
       924: 1
       925: q
       928: 1
       930: q
       931: q
       940: 1
       944: 1
       948: 1
       960: 1
       964: 1
       966: q
       968: 1
       974: 1
       988: 1
       994: q+1
       998: q+1
      1000: 1
      1001: 2q
      1004: 1
      1005: q
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1016: 1
      1017: q
      1020: q+1
      1022: q+1
      1026: 1
      1027: 2q
      1028: q+1
      1032: 1
      1036: 1
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1114: 1
      1122: 1
      1124: q
      1126: 1
      1130: 1
      1132: q
      1134: 1
      1138: 1
      1152: 1
      1156: 1
      1158: q
      1160: 1
      1161: q
      1172: 1
      1194: 1
      1198: 1
      1202: 1
      1216: 1
      1218: 1
      1219: q
      1220: 1
      1224: 1
      1230: q+1
      1232: q+1
      1234: 1
      1235: 2q
      1240: 1
      1241: q
      1242: 1
      1248: 1
      1250: 1
      1260: 1
      1266: 1
      1270: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1358: q
      1360: 1
      1364: 1
      1365: q
      1368: 1
      1380: 1
      1418: 1
      1430: 1
      1436: 1
      1450: 1
      1454: 1
      1455: q
      1460: 1
      1464: 1
      1466: 1
      1474: 1
      1478: 1
      1482: 1
      1484: 1
      1487: 1
      1501: 1
      1537: 1
      1575: 1
      1579: 1
      1607: 1
      1641: 1
      1649: 1
      1659: 1
      1663: 1
      1673: 1
      1741: 1
      1757: 1
      1817: 1
      1819: 1
      1906: 1

1907:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: q^4+2q^3+3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 3q^2+2q+1
        37: 2q^2+q+1
        38: q^2+q
        39: 2q^2+q+1
        40: q^2+q
        41: q^3+q^2+q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 2q^3+4q^2+2q+1
        53: 2q^3+4q^2+2q+1
        54: q^4+2q^3+3q^2+2q+1
        55: 3q^2+2q+1
        56: 3q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+q+1
        60: q^2+2q
        61: q^2+1
        62: 2q^2+q+1
        63: q
        64: q^2+q+1
        65: q^2+q
        66: 2q^2+q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 3q^2+2q+1
        73: 2q^3+4q^2+2q+1
        74: 2q^2+q+1
        75: q^2+q
        76: 2q^2+q+1
        77: q^2+q
        78: q^3+q^2+q+1
        79: q^2+q
        80: 2q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^3+4q^2+2q+1
        95: 2q^3+4q^2+2q+1
        96: q^4+2q^3+3q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+q
       104: q
       106: q^2+1
       107: q^2+2q
       108: q^2+1
       109: q^2+q
       110: q^3+2q^2+q+1
       111: 2q^2+q+1
       112: q^2+q
       113: 2q^2+q+1
       114: q
       115: q^2+q+1
       116: q^2+q
       117: q
       118: q^2+q+1
       119: 2q
       120: 1
       121: q^2+q+1
       122: q
       123: q^2+q+1
       124: q^2+q
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+q+1
       128: q^2+q
       129: 2q^2+q+1
       130: q^2+q
       131: q^3+q^2+q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^3+3q^2+2q+1
       137: 2q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: 3q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^3+4q^2+2q+1
       143: q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 3q^2+2q+1
       148: q^2+q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+q+1
       152: q^2+q
       153: 2q^2+q+1
       154: q^2+q
       155: q^3+q^2+q+1
       156: q^2+q
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q^2+q
       170: q
       172: q^2+1
       173: q
       174: q
       176: 1
       177: q^2+q+1
       178: q^2+q
       179: 2q^2+q+1
       180: q
       181: 2q^2+q+1
       182: q^2+q
       183: 2q
       184: 1
       185: q
       186: q^2+q+1
       187: q^2+q+1
       188: q^2+q
       189: q^2+q+1
       190: q
       191: q
       192: q^2+q+1
       193: q^2+2q
       194: q^2+1
       195: q^2+q
       196: q^3+2q^2+q+1
       197: 2q^2+q+1
       198: q^2+q
       199: 2q
       200: 1
       201: q^2+2q
       202: q^2+1
       204: q^2+q+1
       205: q^2+1
       206: q
       207: q^2+q+1
       208: q
       209: 2q^2+q+1
       210: q
       211: q^2+q+1
       212: q^2+q
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: 2q^2+2q+1
       224: 2q^2+2q+1
       225: q^3+3q^2+2q+1
       226: 2q^2+2q+1
       227: q^2+2q+1
       228: q^3+3q^2+2q+1
       229: 2q^2+2q+1
       230: q^3+3q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: 2q^2+q+1
       238: q^2+q
       239: 2q^2+q+1
       240: q^2+q
       241: q^3+q^2+q+1
       242: q^2+q
       243: 2q^2+2q+1
       244: 3q^2+2q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+q
       260: q
       262: q^2+1
       263: q
       264: q
       266: 1
       267: q^2+q
       268: q
       269: q^2+1
       273: q^2+1
       274: q
       275: q
       276: q
       278: 1
       279: q+1
       281: q+1
       283: 2q
       284: 1
       285: q
       286: q^2+q+1
       287: q^2+q+1
       288: q
       289: q+1
       291: q^2+q+1
       292: q^2+q
       293: 2q
       294: 1
       295: q
       296: q^2+q+1
       297: q^2+q+1
       298: q
       299: 2q
       300: 1
       301: 2q^2+q+1
       302: q^2+q
       303: q
       304: q^2+q+1
       305: q^2+q+1
       306: q^2+q
       307: 2q
       308: 1
       310: q+1
       311: q^2+1
       312: q
       313: 1
       314: q
       315: q^2+q+1
       316: q^2+q
       317: 2q^2+q+1
       318: q
       319: q^2+2q
       320: q^2+1
       322: q^2+q+1
       323: q^2+1
       324: q
       325: q^2+q+1
       326: q
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: 2q^2+q+1
       339: q^2+q
       340: 2q^2+q+1
       341: q^2+q
       342: q^3+q^2+q+1
       343: q^2+q
       344: q^2+2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: 2q^2+2q+1
       349: 2q^2+2q+1
       350: q^3+3q^2+2q+1
       351: 3q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q^2+q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       380: 1
       381: q
       384: 1
       385: q
       386: q
       388: 1
       389: q^2+q
       390: q
       391: q^2+1
       393: q
       394: q
       396: 1
       399: q^2+1
       400: q
       403: q
       404: 1
       406: q^2+1
       407: q
       413: q+1
       417: q+1
       419: 2q
       420: 1
       421: q
       422: q^2+q+1
       423: q^2+q+1
       424: q
       425: q^2+q+1
       426: q^2+q
       427: 2q^2+q+1
       428: q
       429: 2q
       430: 1
       431: q
       432: q^2+q+1
       433: q^2+q+1
       434: q^2+q
       435: q+1
       437: 2q
       438: 1
       439: q
       440: q^2+q+1
       441: q^2+q+1
       442: q
       443: q^2+2q
       444: q^2+1
       445: 2q^2+q+1
       446: q^2+q
       447: 2q
       448: 1
       450: q+1
       451: 1
       452: q
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: q^2+q+1
       463: q^2+1
       464: q
       465: q+1
       467: q+1
       469: q^2+q+1
       470: q
       471: 2q
       472: 1
       474: q+1
       475: 1
       476: q
       477: q^2+1
       478: q
       479: q^2+1
       480: q
       481: 2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: 2q+1
       485: q+1
       487: q+1
       489: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: 2q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       529: q
       530: q
       532: 1
       533: q
       534: q
       536: 1
       537: q
       539: 1
       541: q
       542: q
       543: 1
       545: q^2+q
       546: q
       547: q^2+1
       551: q
       552: 1
       555: 1
       559: 1
       563: q^2+1
       564: q
       566: q
       568: 1
       570: q^2+1
       571: q
       574: q
       575: q^2+1
       577: q^2+1
       581: q
       585: q+1
       589: 2q
       590: 1
       592: q+1
       593: 2q
       594: 1
       595: q
       596: q^2+q+1
       597: q+1
       599: q^2+q+1
       600: q
       601: q+1
       603: 2q
       604: 1
       605: q+1
       607: q
       608: q^2+q+1
       609: q^2+q+1
       610: q
       613: q^2+q+1
       614: q^2+q
       615: 2q
       616: 1
       617: q+1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       630: q
       632: q+1
       633: 1
       639: q+1
       641: 2q
       642: 1
       644: q+1
       645: 1
       646: q
       647: q
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       660: q+1
       662: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: q^2+2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q^2+1
       699: q
       709: q
       712: 1
       715: q
       716: 1
       717: q
       718: q
       720: 1
       721: q
       723: 1
       725: q
       726: q
       727: 1
       733: q
       735: 1
       739: 1
       743: 1
       751: 1
       754: q
       756: 1
       758: 1
       762: 1
       766: q
       768: 1
       769: 1
       775: q+1
       779: q+1
       781: q+1
       785: 2q
       786: 1
       788: q+1
       791: 1
       792: q
       793: 2q
       794: 1
       795: q+1
       797: q+1
       801: 2q
       802: 1
       804: q+1
       805: 2q
       806: 1
       807: q
       808: q^2+q+1
       809: q+1
       811: q^2+q+1
       812: q
       815: q
       816: 1
       818: q+1
       819: 1
       821: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       840: 1
       843: 1
       844: q
       845: q
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       889: 1
       902: 1
       904: q
       906: 1
       909: q
       911: 1
       916: q
       918: 1
       920: q
       922: 1
       926: q
       927: 1
       928: q
       929: q
       930: 1
       942: 1
       946: 1
       950: 1
       961: 1
       965: q
       967: 1
       968: 1
       975: 1
       991: 1
       994: q+1
       999: q+1
      1000: 2q
      1001: 1
      1004: q
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1016: q
      1017: 1
      1020: q+1
      1022: q+1
      1026: 2q
      1027: 1
      1029: q+1
      1033: 1
      1036: 1
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: 1
      1116: 1
      1122: q
      1124: 1
      1127: 1
      1131: q
      1133: 1
      1135: 1
      1138: 1
      1154: 1
      1156: q
      1158: 1
      1162: q
      1163: 1
      1174: 1
      1197: 1
      1199: 1
      1204: 1
      1217: 1
      1218: q
      1219: 1
      1220: 1
      1224: 1
      1230: q+1
      1233: q+1
      1234: 2q
      1235: 1
      1240: q
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1261: 1
      1266: 1
      1271: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1350: 1
      1356: q
      1358: 1
      1361: 1
      1366: q
      1367: 1
      1369: 1
      1382: 1
      1420: 1
      1430: 1
      1436: 1
      1451: 1
      1454: q
      1455: 1
      1461: 1
      1464: 1
      1467: 1
      1474: 1
      1479: 1
      1482: 1
      1484: 1
      1487: 1
      1506: 1
      1538: 1
      1578: 1
      1580: 1
      1609: 1
      1641: 1
      1650: 1
      1659: 1
      1664: 1
      1673: 1
      1742: 1
      1759: 1
      1817: 1
      1820: 1
      1907: 1

1908:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: q^4+2q^3+3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 3q^2+2q+1
        37: q^2+q
        38: 2q^2+q+1
        39: q^2+q
        40: 2q^2+q+1
        41: q^2+q
        42: q^3+q^2+q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 2q^3+4q^2+2q+1
        53: 2q^3+4q^2+2q+1
        54: q^4+2q^3+3q^2+2q+1
        55: 3q^2+2q+1
        56: 3q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+q+1
        59: q^2+q
        60: q^2+2q
        61: q^2+1
        62: q
        63: 2q^2+q+1
        64: q^2+q
        65: q^2+q+1
        66: q^2+q
        67: 2q^2+q+1
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 3q^2+2q+1
        73: 2q^3+4q^2+2q+1
        74: q^2+q
        75: 2q^2+q+1
        76: q^2+q
        77: 2q^2+q+1
        78: q^2+q
        79: q^3+q^2+q+1
        80: 2q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^3+4q^2+2q+1
        95: 2q^3+4q^2+2q+1
        96: q^4+2q^3+3q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q
       104: q^2+q
       105: q^2+1
       107: q^2+2q
       108: q^2+1
       109: q^3+2q^2+q+1
       110: q^2+q
       111: q^2+q
       112: 2q^2+q+1
       113: q
       114: 2q^2+q+1
       115: q^2+q
       116: q^2+q+1
       117: q^2+q+1
       118: q
       119: 2q
       120: 1
       121: q
       122: q^2+q+1
       123: q^2+q
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: q^2+q
       128: 2q^2+q+1
       129: q^2+q
       130: 2q^2+q+1
       131: q^2+q
       132: q^3+q^2+q+1
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^3+3q^2+2q+1
       137: 2q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: 3q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^3+4q^2+2q+1
       143: q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 3q^2+2q+1
       148: q^2+q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+q
       152: 2q^2+q+1
       153: q^2+q
       154: 2q^2+q+1
       155: q^2+q
       156: q^3+q^2+q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q
       170: q^2+q
       171: q^2+1
       173: q
       174: q
       175: 1
       177: q^2+q
       178: q^2+q+1
       179: q
       180: 2q^2+q+1
       181: q^2+q
       182: 2q^2+q+1
       183: 2q
       184: 1
       185: q^2+q+1
       186: q
       187: q^2+q
       188: q^2+q+1
       189: q
       190: q^2+q+1
       191: q^2+q+1
       192: q
       193: q^2+2q
       194: q^2+1
       195: q^3+2q^2+q+1
       196: q^2+q
       197: q^2+q
       198: 2q^2+q+1
       199: 2q
       200: 1
       201: q^2+2q
       202: q^2+1
       203: q^2+q+1
       205: q
       206: q^2+1
       207: q
       208: q^2+q+1
       209: q
       210: 2q^2+q+1
       211: q^2+q
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: 2q^2+2q+1
       224: 2q^2+2q+1
       225: q^3+3q^2+2q+1
       226: 2q^2+2q+1
       227: q^2+2q+1
       228: q^3+3q^2+2q+1
       229: 2q^2+2q+1
       230: q^3+3q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: q^2+q
       238: 2q^2+q+1
       239: q^2+q
       240: 2q^2+q+1
       241: q^2+q
       242: q^3+q^2+q+1
       243: 2q^2+2q+1
       244: 3q^2+2q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       260: q^2+q
       261: q^2+1
       263: q
       264: q
       265: 1
       267: q
       268: q^2+q
       270: q^2+1
       271: q
       272: q^2+1
       275: q
       276: q
       277: 1
       280: q+1
       282: q+1
       283: 2q
       284: 1
       285: q^2+q+1
       286: q
       287: q
       288: q^2+q+1
       290: q+1
       291: q^2+q
       292: q^2+q+1
       293: 2q
       294: 1
       295: q^2+q+1
       296: q
       297: q
       298: q^2+q+1
       299: 2q
       300: 1
       301: q^2+q
       302: 2q^2+q+1
       303: q^2+q+1
       304: q
       305: q^2+q
       306: q^2+q+1
       307: 2q
       308: 1
       309: q+1
       311: q
       312: q^2+1
       313: q
       314: 1
       315: q^2+q
       316: q^2+q+1
       317: q
       318: 2q^2+q+1
       319: q^2+2q
       320: q^2+1
       321: q^2+q+1
       323: q
       324: q^2+1
       325: q
       326: q^2+q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: q^2+q
       339: 2q^2+q+1
       340: q^2+q
       341: 2q^2+q+1
       342: q^2+q
       343: q^3+q^2+q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: 2q^2+2q+1
       349: 2q^2+2q+1
       350: q^3+3q^2+2q+1
       351: 3q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q^2+q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: 1
       382: q
       383: 1
       385: q
       386: q
       387: 1
       389: q
       390: q^2+q
       392: q^2+1
       393: q
       394: q
       395: 1
       397: q
       398: q^2+1
       401: q
       402: 1
       405: q
       408: q^2+1
       414: q+1
       418: q+1
       419: 2q
       420: 1
       421: q^2+q+1
       422: q
       423: q
       424: q^2+q+1
       425: q^2+q
       426: q^2+q+1
       427: q
       428: 2q^2+q+1
       429: 2q
       430: 1
       431: q^2+q+1
       432: q
       433: q^2+q
       434: q^2+q+1
       436: q+1
       437: 2q
       438: 1
       439: q^2+q+1
       440: q
       441: q
       442: q^2+q+1
       443: q^2+2q
       444: q^2+1
       445: q^2+q
       446: 2q^2+q+1
       447: 2q
       448: 1
       449: q+1
       451: q
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: q^2+q+1
       463: q
       464: q^2+1
       466: q+1
       468: q+1
       469: q
       470: q^2+q+1
       471: 2q
       472: 1
       473: q+1
       475: q
       476: 1
       477: q
       478: q^2+1
       479: q
       480: q^2+1
       481: 2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: 2q+1
       486: q+1
       488: q+1
       490: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: 2q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       529: q
       530: q
       531: 1
       533: q
       534: q
       535: 1
       538: q
       540: 1
       541: q
       542: q
       544: 1
       545: q
       546: q^2+q
       548: q^2+1
       549: q
       550: 1
       554: 1
       558: 1
       561: q
       562: q^2+1
       565: q
       567: 1
       569: q
       572: q^2+1
       573: q
       576: q^2+1
       577: q
       581: q^2+1
       586: q+1
       589: 2q
       590: 1
       591: q+1
       593: 2q
       594: 1
       595: q^2+q+1
       596: q
       598: q+1
       599: q
       600: q^2+q+1
       602: q+1
       603: 2q
       604: 1
       606: q+1
       607: q^2+q+1
       608: q
       609: q
       610: q^2+q+1
       613: q^2+q
       614: q^2+q+1
       615: 2q
       616: 1
       618: q+1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       629: q
       630: 1
       631: q+1
       634: 1
       640: q+1
       641: 2q
       642: 1
       643: q+1
       645: q
       646: 1
       647: q
       648: 1
       649: 1
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       659: q+1
       661: q+1
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: q^2+2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       700: q^2+1
       710: q
       711: 1
       713: q
       714: 1
       717: q
       718: q
       719: 1
       722: q
       724: 1
       725: q
       726: q
       728: 1
       734: q
       736: 1
       738: 1
       742: 1
       750: 1
       753: q
       755: 1
       760: 1
       764: 1
       765: q
       767: 1
       773: 1
       776: q+1
       780: q+1
       782: q+1
       785: 2q
       786: 1
       787: q+1
       791: q
       792: 1
       793: 2q
       794: 1
       796: q+1
       798: q+1
       801: 2q
       802: 1
       803: q+1
       805: 2q
       806: 1
       807: q^2+q+1
       808: q
       810: q+1
       811: q
       812: q^2+q+1
       815: q
       816: 1
       817: q+1
       820: 1
       822: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       839: 1
       843: q
       844: 1
       845: q
       846: 1
       847: 1
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       891: 1
       901: 1
       905: q
       907: 1
       908: q
       910: 1
       917: q
       919: 1
       921: q
       923: 1
       924: q
       925: 1
       928: q
       929: q
       931: 1
       941: 1
       945: 1
       949: 1
       963: 1
       964: q
       966: 1
       972: 1
       977: 1
       990: 1
       995: q+1
       998: q+1
      1000: 2q
      1001: 1
      1004: q
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1016: q
      1017: 1
      1021: q+1
      1023: q+1
      1026: 2q
      1027: 1
      1028: q+1
      1032: 1
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1093: 1
      1115: 1
      1123: q
      1125: 1
      1129: 1
      1130: q
      1132: 1
      1137: 1
      1142: 1
      1153: 1
      1157: q
      1159: 1
      1160: q
      1161: 1
      1173: 1
      1196: 1
      1201: 1
      1203: 1
      1216: 1
      1218: q
      1219: 1
      1221: 1
      1225: 1
      1231: q+1
      1232: q+1
      1234: 2q
      1235: 1
      1240: q
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1260: 1
      1267: 1
      1270: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1349: 1
      1357: q
      1359: 1
      1362: 1
      1364: q
      1365: 1
      1370: 1
      1381: 1
      1419: 1
      1434: 1
      1437: 1
      1450: 1
      1454: q
      1455: 1
      1460: 1
      1465: 1
      1466: 1
      1475: 1
      1478: 1
      1483: 1
      1484: 1
      1487: 1
      1507: 1
      1540: 1
      1576: 1
      1581: 1
      1608: 1
      1642: 1
      1649: 1
      1660: 1
      1663: 1
      1673: 1
      1743: 1
      1758: 1
      1818: 1
      1819: 1
      1908: 1

1909:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: q^4+2q^3+3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 3q^2+2q+1
        37: q^2+q
        38: 2q^2+q+1
        39: q^2+q
        40: 2q^2+q+1
        41: q^2+q
        42: q^3+q^2+q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 2q^3+4q^2+2q+1
        53: 2q^3+4q^2+2q+1
        54: q^4+2q^3+3q^2+2q+1
        55: 3q^2+2q+1
        56: 3q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+q+1
        60: q^2+1
        61: q^2+2q
        62: q
        63: 2q^2+q+1
        64: q^2+q
        65: q^2+q+1
        66: q^2+q
        67: 2q^2+q+1
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 3q^2+2q+1
        73: 2q^3+4q^2+2q+1
        74: q^2+q
        75: 2q^2+q+1
        76: q^2+q
        77: 2q^2+q+1
        78: q^2+q
        79: q^3+q^2+q+1
        80: 2q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^3+4q^2+2q+1
        95: 2q^3+4q^2+2q+1
        96: q^4+2q^3+3q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q^2+1
       105: q^2+q
       106: q
       107: q^2+1
       108: q^2+2q
       109: q^2+q
       110: q^3+2q^2+q+1
       111: q^2+q
       112: 2q^2+q+1
       113: q
       114: 2q^2+q+1
       115: q^2+q
       116: q^2+q+1
       117: q
       118: q^2+q+1
       119: 1
       120: 2q
       121: q
       122: q^2+q+1
       123: q^2+q
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: q^2+q
       128: 2q^2+q+1
       129: q^2+q
       130: 2q^2+q+1
       131: q^2+q
       132: q^3+q^2+q+1
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^3+3q^2+2q+1
       137: 2q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: 3q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^3+4q^2+2q+1
       143: q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 3q^2+2q+1
       148: q^2+q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+q
       152: 2q^2+q+1
       153: q^2+q
       154: 2q^2+q+1
       155: q^2+q
       156: q^3+q^2+q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       170: q^2+1
       171: q^2+q
       172: q
       174: 1
       175: q
       176: q
       177: q^2+q
       178: q^2+q+1
       179: q
       180: 2q^2+q+1
       181: q^2+q
       182: 2q^2+q+1
       183: 1
       184: 2q
       185: q
       186: q^2+q+1
       187: q^2+q
       188: q^2+q+1
       189: q
       190: q^2+q+1
       191: q
       192: q^2+q+1
       193: q^2+1
       194: q^2+2q
       195: q^2+q
       196: q^3+2q^2+q+1
       197: q^2+q
       198: 2q^2+q+1
       199: 1
       200: 2q
       201: q^2+1
       202: q^2+2q
       204: q^2+q+1
       205: q
       206: q^2+1
       207: q
       208: q^2+q+1
       209: q
       210: 2q^2+q+1
       211: q^2+q
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: 2q^2+2q+1
       224: 2q^2+2q+1
       225: q^3+3q^2+2q+1
       226: 2q^2+2q+1
       227: q^2+2q+1
       228: q^3+3q^2+2q+1
       229: 2q^2+2q+1
       230: q^3+3q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: q^2+q
       238: 2q^2+q+1
       239: q^2+q
       240: 2q^2+q+1
       241: q^2+q
       242: q^3+q^2+q+1
       243: 2q^2+2q+1
       244: 3q^2+2q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: q^2+1
       261: q^2+q
       262: q
       264: 1
       265: q
       266: q
       268: q^2+1
       269: q
       270: q^2+q
       273: q
       274: q^2+1
       276: 1
       277: q
       278: q
       280: q+1
       282: q+1
       283: 1
       284: 2q
       285: q
       286: q^2+q+1
       287: q
       288: q^2+q+1
       290: q+1
       291: q^2+q
       292: q^2+q+1
       293: 1
       294: 2q
       295: q
       296: q^2+q+1
       297: q
       298: q^2+q+1
       299: 1
       300: 2q
       301: q^2+q
       302: 2q^2+q+1
       303: q
       304: q^2+q+1
       305: q^2+q
       306: q^2+q+1
       307: 1
       308: 2q
       310: q+1
       311: q
       312: q^2+1
       313: q
       314: 1
       315: q^2+q
       316: q^2+q+1
       317: q
       318: 2q^2+q+1
       319: q^2+1
       320: q^2+2q
       322: q^2+q+1
       323: q
       324: q^2+1
       325: q
       326: q^2+q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: q^2+q
       339: 2q^2+q+1
       340: q^2+q
       341: 2q^2+q+1
       342: q^2+q
       343: q^3+q^2+q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: 2q^2+2q+1
       347: q^2+2q+1
       348: 2q^2+2q+1
       349: 2q^2+2q+1
       350: q^3+3q^2+2q+1
       351: 3q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q^2+q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       380: q
       382: 1
       383: q
       386: 1
       387: q
       388: q
       390: q^2+1
       391: q
       392: q^2+q
       394: 1
       395: q
       396: q
       399: q
       400: q^2+1
       403: 1
       404: q
       406: q
       407: q^2+1
       414: q+1
       418: q+1
       419: 1
       420: 2q
       421: q
       422: q^2+q+1
       423: q
       424: q^2+q+1
       425: q^2+q
       426: q^2+q+1
       427: q
       428: 2q^2+q+1
       429: 1
       430: 2q
       431: q
       432: q^2+q+1
       433: q^2+q
       434: q^2+q+1
       436: q+1
       437: 1
       438: 2q
       439: q
       440: q^2+q+1
       441: q
       442: q^2+q+1
       443: q^2+1
       444: q^2+2q
       445: q^2+q
       446: 2q^2+q+1
       447: 1
       448: 2q
       450: q+1
       451: q
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: q^2+q+1
       463: q
       464: q^2+1
       466: q+1
       468: q+1
       469: q
       470: q^2+q+1
       471: 1
       472: 2q
       474: q+1
       475: q
       476: 1
       477: q
       478: q^2+1
       479: q
       480: q^2+1
       481: 2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: 2q+1
       486: q+1
       488: q+1
       490: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: 2q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       530: 1
       531: q
       532: q
       534: 1
       535: q
       536: q
       538: 1
       540: q
       542: 1
       543: q
       544: q
       546: q^2+1
       547: q
       548: q^2+q
       551: 1
       552: q
       556: 1
       560: 1
       563: q
       564: q^2+1
       566: 1
       568: q
       570: q
       571: q^2+1
       574: q^2+1
       575: q
       577: q
       581: q^2+1
       586: q+1
       589: 1
       590: 2q
       592: q+1
       593: 1
       594: 2q
       595: q
       596: q^2+q+1
       598: q+1
       599: q
       600: q^2+q+1
       602: q+1
       603: 1
       604: 2q
       606: q+1
       607: q
       608: q^2+q+1
       609: q
       610: q^2+q+1
       613: q^2+q
       614: q^2+q+1
       615: 1
       616: 2q
       618: q+1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       629: q
       630: 1
       632: q+1
       634: 1
       640: q+1
       641: 1
       642: 2q
       644: q+1
       645: q
       646: 1
       647: 1
       648: q
       650: 1
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       659: q+1
       661: q+1
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: q^2+2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       699: q^2+1
       710: 1
       711: q
       715: 1
       716: q
       718: 1
       719: q
       720: q
       722: 1
       724: q
       726: 1
       727: q
       728: q
       734: 1
       736: q
       740: 1
       744: 1
       752: 1
       754: 1
       756: q
       759: 1
       763: 1
       766: 1
       768: q
       773: 1
       776: q+1
       780: q+1
       782: q+1
       785: 1
       786: 2q
       788: q+1
       791: q
       792: 1
       793: 1
       794: 2q
       796: q+1
       798: q+1
       801: 1
       802: 2q
       804: q+1
       805: 1
       806: 2q
       807: q
       808: q^2+q+1
       810: q+1
       811: q
       812: q^2+q+1
       815: 1
       816: q
       818: q+1
       820: 1
       822: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       840: 1
       843: q
       844: 1
       845: 1
       846: q
       848: 1
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       890: 1
       903: 1
       905: 1
       907: q
       909: 1
       911: q
       917: 1
       919: q
       921: 1
       923: q
       926: 1
       927: q
       929: 1
       930: q
       931: q
       943: 1
       947: 1
       951: 1
       962: 1
       965: 1
       967: q
       972: 1
       976: 1
       989: 1
       995: q+1
       999: q+1
      1000: 1
      1001: 2q
      1004: 1
      1005: q
      1007: 1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1016: 1
      1017: q
      1021: q+1
      1023: q+1
      1026: 1
      1027: 2q
      1029: q+1
      1033: 1
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1074: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1092: 1
      1117: 1
      1123: 1
      1125: q
      1128: 1
      1131: 1
      1133: q
      1136: 1
      1142: 1
      1155: 1
      1157: 1
      1159: q
      1162: 1
      1163: q
      1175: 1
      1195: 1
      1200: 1
      1205: 1
      1217: 1
      1218: 1
      1219: q
      1221: 1
      1225: 1
      1231: q+1
      1233: q+1
      1234: 1
      1235: 2q
      1240: 1
      1241: q
      1243: 1
      1249: 1
      1251: 1
      1261: 1
      1267: 1
      1271: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1359: q
      1363: 1
      1366: 1
      1367: q
      1371: 1
      1383: 1
      1421: 1
      1434: 1
      1437: 1
      1451: 1
      1454: 1
      1455: q
      1461: 1
      1465: 1
      1467: 1
      1475: 1
      1479: 1
      1483: 1
      1484: 1
      1487: 1
      1508: 1
      1539: 1
      1577: 1
      1582: 1
      1610: 1
      1642: 1
      1650: 1
      1660: 1
      1664: 1
      1673: 1
      1744: 1
      1760: 1
      1818: 1
      1820: 1
      1909: 1

1910:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 3q^3+5q^2+3q+1
        23: 3q^3+5q^2+3q+1
        24: q^4+3q^3+4q^2+3q+1
        25: 5q^3+6q^2+3q+1
        26: 5q^3+6q^2+3q+1
        27: 2q^4+4q^3+5q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 3q^3+5q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 3q^3+5q^2+3q+1
        34: 5q^3+6q^2+3q+1
        35: 3q^3+5q^2+3q+1
        36: 5q^3+6q^2+3q+1
        37: 3q^3+5q^2+3q+1
        39: 3q^3+5q^2+3q+1
        41: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 2q^3+3q^2+3q+1
        55: 3q^3+5q^2+3q+1
        56: 3q^3+5q^2+3q+1
        57: q^4+3q^3+4q^2+3q+1
        58: 2q^3+3q^2+2q+1
        59: q^3+2q^2+q
        60: 3q^3+4q^2+2q+1
        61: 2q^3+2q^2+q
        62: 3q^3+5q^2+3q+1
        64: 2q^3+4q^2+3q+1
        66: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 3q^2+3q+1
        74: q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        78: 2q^3+3q^2+3q+1
        80: 2q^3+4q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 3q^3+5q^2+3q+1
        85: 3q^3+5q^2+3q+1
        86: 3q^3+5q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: 2q^3+3q^2+3q+1
        97: 3q^3+5q^2+3q+1
        98: 3q^3+5q^2+3q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       103: 2q^3+3q^2+2q+1
       106: q^3+2q^2+q
       107: q^3+3q^2+2q+1
       108: q^2+q
       109: 2q^2+2q+1
       110: q^2+q
       111: 3q^2+3q+1
       113: q^3+4q^2+3q+1
       115: q^3+3q^2+3q+1
       117: q^3+2q^2+2q+1
       118: q^2+q
       119: q^3+3q^2+2q+1
       120: q^2+q
       121: 2q^3+4q^2+3q+1
       123: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       127: q^3+4q^2+3q+1
       129: q^3+4q^2+3q+1
       131: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^3+4q^2+3q+1
       138: q^3+3q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^2+2q+1
       141: q^3+3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^3+5q^2+3q+1
       144: 2q^3+4q^2+3q+1
       145: 3q^3+5q^2+3q+1
       146: 2q^3+4q^2+3q+1
       147: q^3+4q^2+3q+1
       148: 3q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       155: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: q^3+4q^2+3q+1
       164: q^3+4q^2+3q+1
       165: q^3+4q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       169: 2q^2+2q+1
       172: q^2+q
       173: q^3+2q^2+2q+1
       176: q^2+q
       177: q^3+3q^2+3q+1
       179: q^3+4q^2+3q+1
       181: 3q^2+3q+1
       183: 2q^2+2q+1
       184: q
       185: q^2+2q+1
       186: q
       187: 2q^2+3q+1
       189: q^3+3q^2+3q+1
       191: q^3+2q^2+2q+1
       192: q^2+q
       193: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+q
       197: q^2+2q+1
       199: q^3+3q^2+2q+1
       200: q^2+q
       201: q^3+3q^2+2q+1
       202: q^2+q
       203: 2q^2+2q+1
       204: q^2+q
       205: 3q^2+3q+1
       207: 2q^3+4q^2+3q+1
       209: q^3+4q^2+3q+1
       211: q^3+3q^2+3q+1
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 3q^2+3q+1
       223: 3q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 2q^2+3q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^3+4q^2+3q+1
       232: 3q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^3+3q^2+3q+1
       237: q^3+4q^2+3q+1
       239: q^3+4q^2+3q+1
       241: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: q^2+2q+1
       245: 3q^2+3q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: 2q^2+2q+1
       262: q^2+q
       263: q^2+2q+1
       266: q
       267: q^2+2q+1
       271: 2q^2+2q+1
       273: q^2+q
       275: q^3+2q^2+2q+1
       278: q^2+q
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: 2q^2+2q+1
       284: q
       285: q^2+2q+1
       286: q
       287: q^3+3q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: 2q^2+2q+1
       294: q
       295: q^2+2q+1
       296: q
       297: 2q^2+3q+1
       299: 2q+1
       301: q^2+2q+1
       303: 2q+1
       304: q
       305: 2q+1
       307: 2q^2+2q+1
       308: q
       309: q^2+2q+1
       310: q
       311: 3q^2+3q+1
       313: 2q^2+3q+1
       315: q^3+3q^2+3q+1
       317: q^3+4q^2+3q+1
       319: q^2+2q+1
       321: 2q^2+2q+1
       322: q^2+q
       323: q^2+2q+1
       325: q^3+3q^2+3q+1
       327: 2q^2+3q+1
       329: 2q^2+3q+1
       331: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+2q+1
       352: 3q^2+3q+1
       353: 3q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 3q^2+3q+1
       356: 3q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q^2+2q+1
       380: q
       381: 2q+1
       384: q
       385: q^2+2q+1
       388: q
       389: q^2+2q+1
       393: 2q+1
       397: 2q^2+2q+1
       399: q^2+q
       401: q^2+2q+1
       404: q
       405: q^2+2q+1
       409: q^2+3q+1
       411: 2q^2+3q+1
       413: q^2+3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: 2q^2+2q+1
       420: q
       421: q^2+2q+1
       422: q
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: 2q+1
       431: 2q+1
       432: q
       433: 2q+1
       435: 2q+1
       437: 2q+1
       439: 2q+1
       440: q
       441: 2q+1
       443: q^2+2q+1
       445: q^2+2q+1
       447: 2q^2+2q+1
       448: q
       449: q^2+2q+1
       450: q
       451: 2q^2+3q+1
       453: 2q^2+2q+1
       454: q
       455: q^2+3q+1
       457: q^2+2q+1
       458: q
       459: 2q^2+3q+1
       461: q^2+2q+1
       462: q^2+q
       463: 2q^2+3q+1
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+3q^2+3q+1
       471: 2q+1
       473: 2q+1
       474: q
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: q^2+2q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: q+1
       496: q+1
       497: 3q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q+1
       502: 2q^2+3q+1
       504: 2q^2+3q+1
       506: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: 2q+1
       524: q
       525: 2q+1
       528: q
       529: q^2+2q+1
       532: q
       533: 2q+1
       537: 2q+1
       541: 2q+1
       545: q^2+2q+1
       549: q^2+2q+1
       552: q
       553: 2q+1
       555: q
       557: q^2+2q+1
       559: q
       561: q^2+2q+1
       563: q^2+q
       565: 2q+1
       569: q^2+2q+1
       573: q^2+2q+1
       577: q^2+2q+1
       583: q^2+3q+1
       585: 3q+1
       587: q^2+3q+1
       589: q^2+2q+1
       590: q
       591: q+1
       593: q+1
       595: 2q+1
       596: q
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: 2q+1
       605: 2q+1
       607: 2q+1
       608: q
       609: 2q+1
       611: 2q+1
       613: q+1
       615: q+1
       617: q+1
       619: 2q^2+2q+1
       620: q
       621: q^2+2q+1
       622: q
       623: q^2+3q+1
       625: 2q^2+3q+1
       627: q^2+3q+1
       629: q^2+2q+1
       631: q+1
       632: q
       633: 2q+1
       635: q^2+3q+1
       637: 2q^2+3q+1
       639: q^2+3q+1
       641: 2q+1
       643: 2q+1
       644: q
       645: 2q+1
       647: 2q+1
       649: 2q+1
       650: q
       651: 2q+1
       653: 2q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: 1
       680: 2q+1
       681: q^2+3q+1
       682: 3q+1
       683: q^2+2q+1
       684: 2q+1
       685: q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       705: 2q+1
       708: q
       709: 2q+1
       712: q
       713: q+1
       717: q+1
       721: 2q+1
       725: 2q+1
       729: 2q+1
       733: q+1
       737: 2q+1
       739: q
       741: q^2+2q+1
       743: q
       745: 2q+1
       747: q
       749: q+1
       751: q
       753: 2q+1
       757: 2q+1
       761: 2q+1
       765: q+1
       769: q+1
       775: 2q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       793: q+1
       795: q+1
       797: q+1
       799: 2q+1
       801: q+1
       805: q+1
       807: 2q+1
       808: q
       809: 1
       811: q+1
       813: q+1
       815: q+1
       817: q+1
       818: q
       819: 2q+1
       821: 3q+1
       823: q^2+3q+1
       825: q^2+2q+1
       826: q
       827: q+1
       829: q+1
       831: 2q+1
       832: q
       833: q+1
       835: q^2+2q+1
       837: 2q+1
       839: q+1
       840: q
       841: q^2+3q+1
       843: q+1
       845: 2q+1
       847: 2q+1
       848: q
       849: 2q+1
       851: 2q+1
       853: 2q+1
       855: q+1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: 1
       884: q+1
       896: 2q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: 2q+1
       916: q+1
       920: q+1
       928: q+1
       932: q+1
       936: 2q+1
       938: q
       940: q+1
       942: q
       944: 2q+1
       946: q
       948: q+1
       952: q+1
       956: q+1
       958: q
       960: 2q+1
       964: q+1
       968: q+1
       974: 2q+1
       978: 2q+1
       982: q+1
       988: q+1
       992: 2q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1014: q+1
      1016: q+1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 2q+1
      1032: q+1
      1033: q
      1034: 3q+1
      1036: q+1
      1038: q+1
      1040: 1
      1042: q+1
      1044: 1
      1046: q+1
      1048: q+1
      1050: 2q+1
      1052: q+1
      1056: q+1
      1058: 2q+1
      1059: q
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1144: q+1
      1148: q+1
      1156: 1
      1164: q+1
      1166: q
      1168: 2q+1
      1170: q
      1172: 1
      1176: 1
      1180: 1
      1184: 2q+1
      1188: q+1
      1194: q+1
      1198: q+1
      1206: q+1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1248: q+1
      1250: 1
      1252: q+1
      1254: 1
      1256: q+1
      1258: 1
      1260: 1
      1264: q+1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 2
      1326: 1
      1330: 1
      1334: 1
      1336: 1
      1352: 1
      1356: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 2
      1396: 1
      1400: 1
      1414: q+1
      1422: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: 1
      1454: 1
      1456: q+1
      1460: 1
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1480: 2
      1482: 1
      1487: 1
      1489: 1
      1491: 1
      1513: 1
      1515: 1
      1537: 1
      1559: 1
      1567: 1
      1583: 1
      1587: 1
      1591: 2
      1595: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1665: 1
      1671: 1
      1699: 1
      1701: 1
      1729: 1
      1769: 1
      1777: 1
      1789: 1
      1823: 1
      1910: 1

1911:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 3q^3+5q^2+3q+1
        23: 3q^3+5q^2+3q+1
        24: q^4+3q^3+4q^2+3q+1
        25: 5q^3+6q^2+3q+1
        26: 5q^3+6q^2+3q+1
        27: 2q^4+4q^3+5q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 3q^3+5q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 3q^3+5q^2+3q+1
        34: 5q^3+6q^2+3q+1
        35: 3q^3+5q^2+3q+1
        36: 5q^3+6q^2+3q+1
        37: 3q^3+5q^2+3q+1
        39: 3q^3+5q^2+3q+1
        41: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 2q^3+3q^2+3q+1
        55: 3q^3+5q^2+3q+1
        56: 3q^3+5q^2+3q+1
        57: q^4+3q^3+4q^2+3q+1
        58: q^3+2q^2+q
        59: 2q^3+3q^2+2q+1
        60: 2q^3+2q^2+q
        61: 3q^3+4q^2+2q+1
        62: 3q^3+5q^2+3q+1
        64: 2q^3+4q^2+3q+1
        66: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 3q^2+3q+1
        74: q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        78: 2q^3+3q^2+3q+1
        80: 2q^3+4q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 3q^3+5q^2+3q+1
        85: 3q^3+5q^2+3q+1
        86: 3q^3+5q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: 2q^3+3q^2+3q+1
        97: 3q^3+5q^2+3q+1
        98: 3q^3+5q^2+3q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       103: q^3+2q^2+q
       106: 2q^3+3q^2+2q+1
       107: q^2+q
       108: q^3+3q^2+2q+1
       109: q^2+q
       110: 2q^2+2q+1
       111: 3q^2+3q+1
       113: q^3+4q^2+3q+1
       115: q^3+3q^2+3q+1
       117: q^2+q
       118: q^3+2q^2+2q+1
       119: q^2+q
       120: q^3+3q^2+2q+1
       121: 2q^3+4q^2+3q+1
       123: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       127: q^3+4q^2+3q+1
       129: q^3+4q^2+3q+1
       131: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^3+4q^2+3q+1
       138: q^3+3q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^2+2q+1
       141: q^3+3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^3+5q^2+3q+1
       144: 2q^3+4q^2+3q+1
       145: 3q^3+5q^2+3q+1
       146: 2q^3+4q^2+3q+1
       147: q^3+4q^2+3q+1
       148: 3q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       155: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: q^3+4q^2+3q+1
       164: q^3+4q^2+3q+1
       165: q^3+4q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       172: 2q^2+2q+1
       173: q^2+q
       176: q^3+2q^2+2q+1
       177: q^3+3q^2+3q+1
       179: q^3+4q^2+3q+1
       181: 3q^2+3q+1
       183: q
       184: 2q^2+2q+1
       185: q
       186: q^2+2q+1
       187: 2q^2+3q+1
       189: q^3+3q^2+3q+1
       191: q^2+q
       192: q^3+2q^2+2q+1
       194: q^2+2q+1
       195: q^2+q
       196: 2q^2+2q+1
       197: q^2+2q+1
       199: q^2+q
       200: q^3+3q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+2q+1
       203: q^2+q
       204: 2q^2+2q+1
       205: 3q^2+3q+1
       207: 2q^3+4q^2+3q+1
       209: q^3+4q^2+3q+1
       211: q^3+3q^2+3q+1
       213: 2q^2+3q+1
       215: 2q^2+3q+1
       217: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 3q^2+3q+1
       223: 3q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 2q^2+3q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^3+4q^2+3q+1
       232: 3q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^3+3q^2+3q+1
       237: q^3+4q^2+3q+1
       239: q^3+4q^2+3q+1
       241: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: q^2+2q+1
       245: 3q^2+3q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q^2+q
       262: 2q^2+2q+1
       263: q
       266: q^2+2q+1
       269: q^2+2q+1
       271: q^2+q
       273: 2q^2+2q+1
       275: q^2+q
       278: q^3+2q^2+2q+1
       279: q^2+3q+1
       281: 2q^2+3q+1
       283: q
       284: 2q^2+2q+1
       285: q
       286: q^2+2q+1
       287: q^3+3q^2+3q+1
       289: q^2+3q+1
       291: 2q^2+3q+1
       293: q
       294: 2q^2+2q+1
       295: q
       296: q^2+2q+1
       297: 2q^2+3q+1
       300: 2q+1
       301: q^2+2q+1
       303: q
       304: 2q+1
       305: 2q+1
       307: q
       308: 2q^2+2q+1
       309: q
       310: q^2+2q+1
       311: 3q^2+3q+1
       313: 2q^2+3q+1
       315: q^3+3q^2+3q+1
       317: q^3+4q^2+3q+1
       320: q^2+2q+1
       321: q^2+q
       322: 2q^2+2q+1
       323: q^2+2q+1
       325: q^3+3q^2+3q+1
       327: 2q^2+3q+1
       329: 2q^2+3q+1
       331: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+2q+1
       352: 3q^2+3q+1
       353: 3q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 3q^2+3q+1
       356: 3q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       360: 2q^2+3q+1
       362: 2q^2+3q+1
       364: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       377: q
       380: q^2+2q+1
       381: q
       384: 2q+1
       385: q
       388: q^2+2q+1
       391: q^2+2q+1
       396: 2q+1
       397: q^2+q
       399: 2q^2+2q+1
       401: q
       404: q^2+2q+1
       406: q^2+2q+1
       409: q^2+3q+1
       411: 2q^2+3q+1
       413: q^2+3q+1
       415: q^2+3q+1
       417: q^2+3q+1
       419: q
       420: 2q^2+2q+1
       421: q
       422: q^2+2q+1
       423: 2q^2+3q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       430: 2q+1
       431: q
       432: 2q+1
       433: 2q+1
       435: 2q+1
       438: 2q+1
       439: q
       440: 2q+1
       441: 2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       447: q
       448: 2q^2+2q+1
       449: q
       450: q^2+2q+1
       451: 2q^2+3q+1
       453: q
       454: 2q^2+2q+1
       455: q^2+3q+1
       457: q
       458: q^2+2q+1
       459: 2q^2+3q+1
       461: q^2+q
       462: q^2+2q+1
       463: 2q^2+3q+1
       465: q^2+3q+1
       467: 2q^2+3q+1
       469: q^3+3q^2+3q+1
       472: 2q+1
       473: q
       474: 2q+1
       475: 2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: q^2+2q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: q+1
       496: q+1
       497: 3q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q+1
       502: 2q^2+3q+1
       504: 2q^2+3q+1
       506: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: 2q+1
       525: q
       528: 2q+1
       529: q
       532: q^2+2q+1
       536: 2q+1
       539: 2q+1
       543: 2q+1
       547: q^2+2q+1
       549: q
       552: q^2+2q+1
       553: q
       555: 2q+1
       557: q
       559: q^2+2q+1
       561: q^2+q
       563: q^2+2q+1
       568: 2q+1
       570: q^2+2q+1
       575: q^2+2q+1
       577: q^2+2q+1
       583: q^2+3q+1
       585: 3q+1
       587: q^2+3q+1
       589: q
       590: q^2+2q+1
       592: q+1
       594: q+1
       595: q
       596: 2q+1
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       604: 2q+1
       605: 2q+1
       607: q
       608: 2q+1
       609: 2q+1
       611: 2q+1
       613: q+1
       616: q+1
       617: q+1
       619: q
       620: 2q^2+2q+1
       621: q
       622: q^2+2q+1
       623: q^2+3q+1
       625: 2q^2+3q+1
       627: q^2+3q+1
       629: q^2+2q+1
       631: q
       632: q+1
       633: 2q+1
       635: q^2+3q+1
       637: 2q^2+3q+1
       639: q^2+3q+1
       642: 2q+1
       643: q
       644: 2q+1
       645: 2q+1
       648: 2q+1
       649: q
       650: 2q+1
       651: 2q+1
       653: 2q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: 1
       680: 2q+1
       681: q^2+3q+1
       682: 3q+1
       683: q^2+2q+1
       684: 2q+1
       685: q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q^2+2q+1
       705: q
       708: 2q+1
       709: q
       712: 2q+1
       716: q+1
       720: q+1
       723: 2q+1
       727: 2q+1
       731: 2q+1
       735: q+1
       737: q
       739: 2q+1
       741: q
       743: q^2+2q+1
       745: q
       747: 2q+1
       749: q
       751: q+1
       756: 2q+1
       758: 2q+1
       762: 2q+1
       768: q+1
       769: q+1
       775: 2q+1
       777: 3q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       794: q+1
       795: q+1
       797: q+1
       799: 2q+1
       802: q+1
       806: q+1
       807: q
       808: 2q+1
       809: 1
       811: q+1
       813: q+1
       816: q+1
       817: q
       818: q+1
       819: 2q+1
       821: 3q+1
       823: q^2+3q+1
       825: q
       826: q^2+2q+1
       828: q+1
       830: q+1
       831: q
       832: 2q+1
       833: q+1
       835: q^2+2q+1
       837: 2q+1
       839: q
       840: q+1
       841: q^2+3q+1
       843: q+1
       846: 2q+1
       847: q
       848: 2q+1
       849: 2q+1
       851: 2q+1
       853: 2q+1
       855: q+1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: 1
       889: q+1
       896: q
       899: 2q+1
       902: 1
       906: 1
       911: 1
       914: 2q+1
       918: q+1
       922: q+1
       930: q+1
       934: q+1
       936: q
       938: 2q+1
       940: q
       942: q+1
       944: q
       946: 2q+1
       950: q+1
       955: q+1
       956: q
       958: q+1
       961: 2q+1
       967: q+1
       968: q+1
       975: 2q+1
       979: 2q+1
       982: q+1
       991: q+1
       992: 2q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1014: q+1
      1017: q+1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 2q+1
      1032: q
      1033: q+1
      1034: 3q+1
      1036: q+1
      1038: q+1
      1041: 1
      1042: q+1
      1045: 1
      1046: q+1
      1048: q+1
      1050: 2q+1
      1053: q+1
      1057: q+1
      1058: q
      1059: 2q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1091: q+1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1146: q+1
      1150: q+1
      1158: 1
      1164: q
      1166: q+1
      1168: q
      1170: 2q+1
      1174: 1
      1178: 1
      1183: 1
      1185: 2q+1
      1188: q+1
      1197: q+1
      1199: q+1
      1208: q+1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1248: q+1
      1251: 1
      1252: q+1
      1255: 1
      1256: q+1
      1259: 1
      1261: 1
      1264: q+1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 2
      1329: 1
      1331: 1
      1334: 1
      1336: 1
      1354: 1
      1358: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 2
      1399: 1
      1401: 1
      1415: q+1
      1424: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: 1
      1455: 1
      1456: q+1
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1480: 2
      1482: 1
      1487: 1
      1494: 1
      1498: 1
      1518: 1
      1522: 1
      1538: 1
      1560: 1
      1569: 1
      1585: 1
      1589: 1
      1592: 2
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1666: 1
      1671: 1
      1704: 1
      1708: 1
      1730: 1
      1770: 1
      1778: 1
      1791: 1
      1823: 1
      1911: 1

1912:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 3q^3+5q^2+3q+1
        23: 3q^3+5q^2+3q+1
        24: q^4+3q^3+4q^2+3q+1
        25: 5q^3+6q^2+3q+1
        26: 5q^3+6q^2+3q+1
        27: 2q^4+4q^3+5q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 3q^3+5q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 3q^3+5q^2+3q+1
        34: 5q^3+6q^2+3q+1
        35: 3q^3+5q^2+3q+1
        36: 5q^3+6q^2+3q+1
        38: 3q^3+5q^2+3q+1
        40: 3q^3+5q^2+3q+1
        42: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 2q^3+3q^2+3q+1
        55: 3q^3+5q^2+3q+1
        56: 3q^3+5q^2+3q+1
        57: q^4+3q^3+4q^2+3q+1
        58: q^3+2q^2+q
        59: 2q^3+3q^2+2q+1
        60: 3q^3+4q^2+2q+1
        61: 2q^3+2q^2+q
        63: 3q^3+5q^2+3q+1
        65: 2q^3+4q^2+3q+1
        67: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 3q^2+3q+1
        75: q^3+4q^2+3q+1
        77: q^3+4q^2+3q+1
        79: 2q^3+3q^2+3q+1
        80: 2q^3+4q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 3q^3+5q^2+3q+1
        85: 3q^3+5q^2+3q+1
        86: 3q^3+5q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: 2q^3+3q^2+3q+1
        97: 3q^3+5q^2+3q+1
        98: 3q^3+5q^2+3q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       104: 2q^3+3q^2+2q+1
       105: q^3+2q^2+q
       107: q^3+3q^2+2q+1
       108: q^2+q
       109: q^2+q
       110: 2q^2+2q+1
       112: 3q^2+3q+1
       114: q^3+4q^2+3q+1
       116: q^3+3q^2+3q+1
       117: q^2+q
       118: q^3+2q^2+2q+1
       119: q^3+3q^2+2q+1
       120: q^2+q
       122: 2q^3+4q^2+3q+1
       124: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       128: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       132: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^3+4q^2+3q+1
       138: q^3+3q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^2+2q+1
       141: q^3+3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^3+5q^2+3q+1
       144: 2q^3+4q^2+3q+1
       145: 3q^3+5q^2+3q+1
       146: 2q^3+4q^2+3q+1
       147: q^3+4q^2+3q+1
       148: 3q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       152: q^3+4q^2+3q+1
       154: q^3+4q^2+3q+1
       156: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: q^3+4q^2+3q+1
       164: q^3+4q^2+3q+1
       165: q^3+4q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       170: 2q^2+2q+1
       171: q^2+q
       174: q^3+2q^2+2q+1
       175: q^2+q
       178: q^3+3q^2+3q+1
       180: q^3+4q^2+3q+1
       182: 3q^2+3q+1
       183: 2q^2+2q+1
       184: q
       185: q
       186: q^2+2q+1
       188: 2q^2+3q+1
       190: q^3+3q^2+3q+1
       191: q^2+q
       192: q^3+2q^2+2q+1
       193: q^2+2q+1
       195: q^2+q
       196: 2q^2+2q+1
       198: q^2+2q+1
       199: q^3+3q^2+2q+1
       200: q^2+q
       201: q^3+3q^2+2q+1
       202: q^2+q
       203: q^2+q
       204: 2q^2+2q+1
       206: 3q^2+3q+1
       208: 2q^3+4q^2+3q+1
       210: q^3+4q^2+3q+1
       212: q^3+3q^2+3q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 3q^2+3q+1
       223: 3q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 2q^2+3q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^3+4q^2+3q+1
       232: 3q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^3+3q^2+3q+1
       238: q^3+4q^2+3q+1
       240: q^3+4q^2+3q+1
       242: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: q^2+2q+1
       245: 3q^2+3q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       260: 2q^2+2q+1
       261: q^2+q
       264: q^2+2q+1
       265: q
       268: q^2+2q+1
       272: q^2+q
       274: 2q^2+2q+1
       276: q^3+2q^2+2q+1
       277: q^2+q
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: 2q^2+2q+1
       284: q
       285: q
       286: q^2+2q+1
       288: q^3+3q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: 2q^2+2q+1
       294: q
       295: q
       296: q^2+2q+1
       298: 2q^2+3q+1
       299: 2q+1
       302: q^2+2q+1
       303: q
       304: 2q+1
       306: 2q+1
       307: 2q^2+2q+1
       308: q
       309: q
       310: q^2+2q+1
       312: 3q^2+3q+1
       314: 2q^2+3q+1
       316: q^3+3q^2+3q+1
       318: q^3+4q^2+3q+1
       319: q^2+2q+1
       321: q^2+q
       322: 2q^2+2q+1
       324: q^2+2q+1
       326: q^3+3q^2+3q+1
       328: 2q^2+3q+1
       330: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+2q+1
       352: 3q^2+3q+1
       353: 3q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 3q^2+3q+1
       356: 3q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       378: q^2+2q+1
       379: q
       382: 2q+1
       383: q
       386: q^2+2q+1
       387: q
       390: q^2+2q+1
       394: 2q+1
       398: q^2+q
       400: 2q^2+2q+1
       402: q
       403: q^2+2q+1
       407: q^2+2q+1
       410: q^2+3q+1
       412: 2q^2+3q+1
       414: q^2+3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: 2q^2+2q+1
       420: q
       421: q
       422: q^2+2q+1
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: 2q+1
       431: q
       432: 2q+1
       434: 2q+1
       436: 2q+1
       437: 2q+1
       439: q
       440: 2q+1
       442: 2q+1
       443: q^2+2q+1
       446: q^2+2q+1
       447: 2q^2+2q+1
       448: q
       449: q
       450: q^2+2q+1
       452: 2q^2+3q+1
       453: 2q^2+2q+1
       454: q
       456: q^2+3q+1
       457: q
       458: q^2+2q+1
       460: 2q^2+3q+1
       461: q^2+q
       462: q^2+2q+1
       464: 2q^2+3q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       470: q^3+3q^2+3q+1
       471: 2q+1
       473: q
       474: 2q+1
       476: 2q+1
       478: q^2+2q+1
       480: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: q^2+2q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: q+1
       496: q+1
       497: 3q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q+1
       503: 2q^2+3q+1
       505: 2q^2+3q+1
       507: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: 2q+1
       523: q
       526: 2q+1
       527: q
       530: q^2+2q+1
       531: q
       534: 2q+1
       538: 2q+1
       542: 2q+1
       546: q^2+2q+1
       550: q
       551: q^2+2q+1
       554: q
       556: 2q+1
       558: q
       560: q^2+2q+1
       562: q^2+q
       564: q^2+2q+1
       566: 2q+1
       571: q^2+2q+1
       574: q^2+2q+1
       581: q^2+2q+1
       584: q^2+3q+1
       586: 3q+1
       588: q^2+3q+1
       589: q^2+2q+1
       590: q
       592: q+1
       593: q+1
       595: q
       596: 2q+1
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: 2q+1
       606: 2q+1
       607: q
       608: 2q+1
       610: 2q+1
       612: 2q+1
       614: q+1
       615: q+1
       618: q+1
       619: 2q^2+2q+1
       620: q
       621: q
       622: q^2+2q+1
       624: q^2+3q+1
       626: 2q^2+3q+1
       628: q^2+3q+1
       630: q^2+2q+1
       631: q
       632: q+1
       634: 2q+1
       636: q^2+3q+1
       638: 2q^2+3q+1
       640: q^2+3q+1
       641: 2q+1
       643: q
       644: 2q+1
       646: 2q+1
       647: 2q+1
       649: q
       650: 2q+1
       652: 2q+1
       654: 2q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: 1
       680: 2q+1
       681: q^2+3q+1
       682: 3q+1
       683: q^2+2q+1
       684: 2q+1
       685: q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       699: q^2+2q+1
       706: 2q+1
       707: q
       710: 2q+1
       711: q
       715: q+1
       718: q+1
       722: 2q+1
       726: 2q+1
       730: 2q+1
       734: q+1
       738: q
       740: 2q+1
       742: q
       744: q^2+2q+1
       746: q
       748: 2q+1
       750: q
       752: q+1
       754: 2q+1
       759: 2q+1
       763: 2q+1
       766: q+1
       773: q+1
       776: 2q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       793: q+1
       796: q+1
       798: q+1
       800: 2q+1
       801: q+1
       805: q+1
       807: q
       808: 2q+1
       810: 1
       812: q+1
       814: q+1
       815: q+1
       817: q
       818: q+1
       820: 2q+1
       822: 3q+1
       824: q^2+3q+1
       825: q^2+2q+1
       826: q
       828: q+1
       829: q+1
       831: q
       832: 2q+1
       834: q+1
       836: q^2+2q+1
       838: 2q+1
       839: q
       840: q+1
       842: q^2+3q+1
       844: q+1
       845: 2q+1
       847: q
       848: 2q+1
       850: 2q+1
       852: 2q+1
       854: 2q+1
       856: q+1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: 1
       890: q+1
       897: 2q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: 2q+1
       917: q+1
       921: q+1
       929: q+1
       933: q+1
       937: q
       939: 2q+1
       941: q
       943: q+1
       945: q
       947: 2q+1
       951: q+1
       953: q+1
       957: q
       959: q+1
       962: 2q+1
       965: q+1
       972: q+1
       976: 2q+1
       980: 2q+1
       986: q+1
       989: q+1
       993: 2q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1015: q+1
      1016: q+1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 2q+1
      1032: q
      1033: q+1
      1035: 3q+1
      1037: q+1
      1039: q+1
      1040: 1
      1043: q+1
      1045: 1
      1047: q+1
      1049: q+1
      1051: 2q+1
      1052: q+1
      1056: q+1
      1058: q
      1059: 2q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1092: q+1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1145: q+1
      1149: q+1
      1157: 1
      1165: q
      1167: q+1
      1169: q
      1171: 2q+1
      1175: 1
      1177: 1
      1181: 1
      1186: 2q+1
      1192: q+1
      1195: q+1
      1200: q+1
      1207: q+1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1249: q+1
      1251: 1
      1253: q+1
      1254: 1
      1257: q+1
      1258: 1
      1261: 1
      1265: q+1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 2
      1327: 1
      1332: 1
      1338: 1
      1339: 1
      1353: 1
      1357: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 2
      1397: 1
      1402: 1
      1416: q+1
      1423: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: 1
      1454: 1
      1457: q+1
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1481: 2
      1483: 1
      1487: 1
      1495: 1
      1499: 1
      1519: 1
      1523: 1
      1539: 1
      1561: 1
      1568: 1
      1586: 1
      1588: 1
      1593: 2
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1665: 1
      1672: 1
      1705: 1
      1709: 1
      1731: 1
      1771: 1
      1779: 1
      1790: 1
      1824: 1
      1912: 1

1913:    0: 5q^3+6q^2+3q+1
         1: 5q^3+6q^2+3q+1
         2: 2q^4+4q^3+5q^2+3q+1
         3: 5q^3+6q^2+3q+1
         4: 2q^4+4q^3+5q^2+3q+1
         5: 5q^3+6q^2+3q+1
         6: 2q^4+4q^3+5q^2+3q+1
         7: q^5+2q^4+4q^3+4q^2+3q+1
         8: 2q^4+4q^3+5q^2+3q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 5q^3+6q^2+3q+1
        11: 5q^3+6q^2+3q+1
        12: 2q^4+4q^3+5q^2+3q+1
        13: 3q^3+5q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 3q^3+5q^2+3q+1
        16: 5q^3+6q^2+3q+1
        17: 5q^3+6q^2+3q+1
        18: q^5+2q^4+4q^3+4q^2+3q+1
        19: 3q^3+5q^2+3q+1
        20: 3q^3+5q^2+3q+1
        21: q^4+3q^3+4q^2+3q+1
        22: 3q^3+5q^2+3q+1
        23: 3q^3+5q^2+3q+1
        24: q^4+3q^3+4q^2+3q+1
        25: 5q^3+6q^2+3q+1
        26: 5q^3+6q^2+3q+1
        27: 2q^4+4q^3+5q^2+3q+1
        28: 5q^3+6q^2+3q+1
        29: 3q^3+5q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 3q^3+5q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 3q^3+5q^2+3q+1
        34: 5q^3+6q^2+3q+1
        35: 3q^3+5q^2+3q+1
        36: 5q^3+6q^2+3q+1
        38: 3q^3+5q^2+3q+1
        40: 3q^3+5q^2+3q+1
        42: q^4+3q^3+4q^2+3q+1
        43: 3q^3+5q^2+3q+1
        44: q^4+3q^3+4q^2+3q+1
        45: 3q^3+5q^2+3q+1
        46: 3q^3+5q^2+3q+1
        47: 3q^3+5q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 3q^3+5q^2+3q+1
        50: 3q^3+5q^2+3q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: 2q^3+3q^2+3q+1
        55: 3q^3+5q^2+3q+1
        56: 3q^3+5q^2+3q+1
        57: q^4+3q^3+4q^2+3q+1
        58: 2q^3+3q^2+2q+1
        59: q^3+2q^2+q
        60: 2q^3+2q^2+q
        61: 3q^3+4q^2+2q+1
        63: 3q^3+5q^2+3q+1
        65: 2q^3+4q^2+3q+1
        67: 3q^3+5q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^3+4q^2+3q+1
        71: 3q^3+5q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 3q^2+3q+1
        75: q^3+4q^2+3q+1
        77: q^3+4q^2+3q+1
        79: 2q^3+3q^2+3q+1
        80: 2q^3+4q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 3q^3+5q^2+3q+1
        85: 3q^3+5q^2+3q+1
        86: 3q^3+5q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 3q^3+5q^2+3q+1
        89: 3q^3+5q^2+3q+1
        90: q^4+3q^3+4q^2+3q+1
        91: q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: 2q^3+3q^2+3q+1
        97: 3q^3+5q^2+3q+1
        98: 3q^3+5q^2+3q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: 2q^3+3q^2+3q+1
       104: q^3+2q^2+q
       105: 2q^3+3q^2+2q+1
       107: q^2+q
       108: q^3+3q^2+2q+1
       109: 2q^2+2q+1
       110: q^2+q
       112: 3q^2+3q+1
       114: q^3+4q^2+3q+1
       116: q^3+3q^2+3q+1
       117: q^3+2q^2+2q+1
       118: q^2+q
       119: q^2+q
       120: q^3+3q^2+2q+1
       122: 2q^3+4q^2+3q+1
       124: 2q^3+4q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^3+4q^2+3q+1
       128: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       132: 2q^3+3q^2+3q+1
       133: 3q^2+3q+1
       134: q^3+4q^2+3q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^3+4q^2+3q+1
       138: q^3+3q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^2+2q+1
       141: q^3+3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^3+5q^2+3q+1
       144: 2q^3+4q^2+3q+1
       145: 3q^3+5q^2+3q+1
       146: 2q^3+4q^2+3q+1
       147: q^3+4q^2+3q+1
       148: 3q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^3+3q^2+3q+1
       152: q^3+4q^2+3q+1
       154: q^3+4q^2+3q+1
       156: 2q^3+3q^2+3q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: q^3+4q^2+3q+1
       164: q^3+4q^2+3q+1
       165: q^3+4q^2+3q+1
       166: q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^3+3q^2+3q+1
       170: q^2+q
       171: 2q^2+2q+1
       174: q^2+q
       175: q^3+2q^2+2q+1
       178: q^3+3q^2+3q+1
       180: q^3+4q^2+3q+1
       182: 3q^2+3q+1
       183: q
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q
       188: 2q^2+3q+1
       190: q^3+3q^2+3q+1
       191: q^3+2q^2+2q+1
       192: q^2+q
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+q
       198: q^2+2q+1
       199: q^2+q
       200: q^3+3q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+2q+1
       203: 2q^2+2q+1
       204: q^2+q
       206: 3q^2+3q+1
       208: 2q^3+4q^2+3q+1
       210: q^3+4q^2+3q+1
       212: q^3+3q^2+3q+1
       214: 2q^2+3q+1
       216: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 3q^2+3q+1
       220: 3q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 3q^2+3q+1
       223: 3q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 2q^2+3q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^3+4q^2+3q+1
       232: 3q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^3+3q^2+3q+1
       238: q^3+4q^2+3q+1
       240: q^3+4q^2+3q+1
       242: 2q^3+3q^2+3q+1
       243: q^3+4q^2+3q+1
       244: q^2+2q+1
       245: 3q^2+3q+1
       246: q^3+3q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       260: q^2+q
       261: 2q^2+2q+1
       264: q
       265: q^2+2q+1
       270: q^2+2q+1
       272: 2q^2+2q+1
       274: q^2+q
       276: q^2+q
       277: q^3+2q^2+2q+1
       280: q^2+3q+1
       282: 2q^2+3q+1
       283: q
       284: 2q^2+2q+1
       285: q^2+2q+1
       286: q
       288: q^3+3q^2+3q+1
       290: q^2+3q+1
       292: 2q^2+3q+1
       293: q
       294: 2q^2+2q+1
       295: q^2+2q+1
       296: q
       298: 2q^2+3q+1
       300: 2q+1
       302: q^2+2q+1
       303: 2q+1
       304: q
       306: 2q+1
       307: q
       308: 2q^2+2q+1
       309: q^2+2q+1
       310: q
       312: 3q^2+3q+1
       314: 2q^2+3q+1
       316: q^3+3q^2+3q+1
       318: q^3+4q^2+3q+1
       320: q^2+2q+1
       321: 2q^2+2q+1
       322: q^2+q
       324: q^2+2q+1
       326: q^3+3q^2+3q+1
       328: 2q^2+3q+1
       330: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 3q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: 2q^2+3q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+2q+1
       352: 3q^2+3q+1
       353: 3q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 3q^2+3q+1
       356: 3q^2+3q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       361: 2q^2+3q+1
       363: 2q^2+3q+1
       365: 2q^2+3q+1
       366: q^3+3q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q^2+3q+1
       378: q
       379: q^2+2q+1
       382: q
       383: 2q+1
       386: q
       387: q^2+2q+1
       392: q^2+2q+1
       395: 2q+1
       398: 2q^2+2q+1
       400: q^2+q
       402: q^2+2q+1
       403: q
       408: q^2+2q+1
       410: q^2+3q+1
       412: 2q^2+3q+1
       414: q^2+3q+1
       416: q^2+3q+1
       418: q^2+3q+1
       419: q
       420: 2q^2+2q+1
       421: q^2+2q+1
       422: q
       424: 2q^2+3q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       430: 2q+1
       431: 2q+1
       432: q
       434: 2q+1
       436: 2q+1
       438: 2q+1
       439: 2q+1
       440: q
       442: 2q+1
       444: q^2+2q+1
       446: q^2+2q+1
       447: q
       448: 2q^2+2q+1
       449: q^2+2q+1
       450: q
       452: 2q^2+3q+1
       453: q
       454: 2q^2+2q+1
       456: q^2+3q+1
       457: q^2+2q+1
       458: q
       460: 2q^2+3q+1
       461: q^2+2q+1
       462: q^2+q
       464: 2q^2+3q+1
       466: q^2+3q+1
       468: 2q^2+3q+1
       470: q^3+3q^2+3q+1
       472: 2q+1
       473: 2q+1
       474: q
       476: 2q+1
       478: q^2+2q+1
       480: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: q^2+2q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^2+3q+1
       493: 2q+1
       494: q^2+3q+1
       495: q+1
       496: q+1
       497: 3q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q+1
       503: 2q^2+3q+1
       505: 2q^2+3q+1
       507: 2q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: 2q+1
       526: q
       527: 2q+1
       530: q
       531: q^2+2q+1
       535: 2q+1
       540: 2q+1
       544: 2q+1
       548: q^2+2q+1
       550: q^2+2q+1
       551: q
       554: 2q+1
       556: q
       558: q^2+2q+1
       560: q
       562: q^2+2q+1
       564: q^2+q
       567: 2q+1
       572: q^2+2q+1
       576: q^2+2q+1
       581: q^2+2q+1
       584: q^2+3q+1
       586: 3q+1
       588: q^2+3q+1
       589: q
       590: q^2+2q+1
       591: q+1
       594: q+1
       595: 2q+1
       596: q
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       604: 2q+1
       606: 2q+1
       607: 2q+1
       608: q
       610: 2q+1
       612: 2q+1
       614: q+1
       616: q+1
       618: q+1
       619: q
       620: 2q^2+2q+1
       621: q^2+2q+1
       622: q
       624: q^2+3q+1
       626: 2q^2+3q+1
       628: q^2+3q+1
       630: q^2+2q+1
       631: q+1
       632: q
       634: 2q+1
       636: q^2+3q+1
       638: 2q^2+3q+1
       640: q^2+3q+1
       642: 2q+1
       643: 2q+1
       644: q
       646: 2q+1
       648: 2q+1
       649: 2q+1
       650: q
       652: 2q+1
       654: 2q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: 3q+1
       677: q+1
       678: q+1
       679: 1
       680: 2q+1
       681: q^2+3q+1
       682: 3q+1
       683: q^2+2q+1
       684: 2q+1
       685: q+1
       686: q^2+3q+1
       687: 2q+1
       688: q^2+3q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       700: q^2+2q+1
       706: q
       707: 2q+1
       710: q
       711: 2q+1
       714: q+1
       719: q+1
       724: 2q+1
       728: 2q+1
       732: 2q+1
       736: q+1
       738: 2q+1
       740: q
       742: q^2+2q+1
       744: q
       746: 2q+1
       748: q
       750: q+1
       752: q
       755: 2q+1
       760: 2q+1
       764: 2q+1
       767: q+1
       773: q+1
       776: 2q+1
       778: 3q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       794: q+1
       796: q+1
       798: q+1
       800: 2q+1
       802: q+1
       806: q+1
       807: 2q+1
       808: q
       810: 1
       812: q+1
       814: q+1
       816: q+1
       817: q+1
       818: q
       820: 2q+1
       822: 3q+1
       824: q^2+3q+1
       825: q
       826: q^2+2q+1
       827: q+1
       830: q+1
       831: 2q+1
       832: q
       834: q+1
       836: q^2+2q+1
       838: 2q+1
       839: q+1
       840: q
       842: q^2+3q+1
       844: q+1
       846: 2q+1
       847: 2q+1
       848: q
       850: 2q+1
       852: 2q+1
       854: 2q+1
       856: q+1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: 3q+1
       879: q+1
       880: 1
       891: q+1
       897: q
       898: 2q+1
       901: 1
       907: 1
       910: 1
       915: 2q+1
       919: q+1
       923: q+1
       931: q+1
       935: q+1
       937: 2q+1
       939: q
       941: q+1
       943: q
       945: 2q+1
       947: q
       949: q+1
       954: q+1
       957: q+1
       959: q
       963: 2q+1
       966: q+1
       972: q+1
       977: 2q+1
       981: 2q+1
       986: q+1
       990: q+1
       993: 2q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1015: q+1
      1017: q+1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 2q+1
      1032: q+1
      1033: q
      1035: 3q+1
      1037: q+1
      1039: q+1
      1041: 1
      1043: q+1
      1044: 1
      1047: q+1
      1049: q+1
      1051: 2q+1
      1053: q+1
      1057: q+1
      1058: 2q+1
      1059: q
      1061: 1
      1063: q+1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1093: q+1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1147: q+1
      1151: q+1
      1159: 1
      1165: q+1
      1167: q
      1169: 2q+1
      1171: q
      1173: 1
      1179: 1
      1182: 1
      1187: 2q+1
      1192: q+1
      1196: q+1
      1201: q+1
      1209: q+1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1249: q+1
      1250: 1
      1253: q+1
      1255: 1
      1257: q+1
      1259: 1
      1260: 1
      1265: q+1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 2
      1328: 1
      1333: 1
      1338: 1
      1339: 1
      1355: 1
      1359: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 2
      1398: 1
      1403: 1
      1417: q+1
      1425: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: 1
      1455: 1
      1457: q+1
      1460: 1
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1481: 2
      1483: 1
      1487: 1
      1496: 1
      1500: 1
      1520: 1
      1524: 1
      1540: 1
      1562: 1
      1570: 1
      1584: 1
      1590: 1
      1594: 2
      1597: 1
      1602: 1
      1614: 1
      1618: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1666: 1
      1672: 1
      1706: 1
      1710: 1
      1732: 1
      1772: 1
      1780: 1
      1792: 1
      1824: 1
      1913: 1

1914:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 4q^3+8q^2+3q+1
        23: 4q^3+8q^2+3q+1
        24: 4q^3+8q^2+3q+1
        25: 2q^4+7q^3+9q^2+3q+1
        26: 2q^4+7q^3+9q^2+3q+1
        27: 2q^4+7q^3+9q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: q^3+7q^2+3q+1
        32: 4q^3+8q^2+3q+1
        33: 4q^3+8q^2+3q+1
        34: 3q^3+8q^2+3q+1
        35: 2q^4+7q^3+9q^2+3q+1
        36: 2q^4+7q^3+9q^2+3q+1
        37: 2q^3+4q^2+2q+1
        38: 2q^3+4q^2+q
        39: 2q^3+4q^2+2q+1
        40: 2q^3+4q^2+q
        41: 2q^3+4q^2+2q+1
        42: 2q^3+4q^2+q
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^3+6q^2+3q+1
        53: 2q^3+6q^2+3q+1
        54: q^3+6q^2+3q+1
        55: q^4+4q^3+7q^2+3q+1
        56: 2q^4+5q^3+7q^2+3q+1
        57: q^4+4q^3+7q^2+3q+1
        58: q^3+5q^2+q+1
        59: 2q^2+2q
        60: 2q^3+5q^2+2q+1
        61: q^3+3q^2+q
        62: q^3+4q^2+2q+1
        63: 3q^2+q
        64: 2q^3+4q^2+2q+1
        65: 2q^3+4q^2+q
        66: 2q^3+4q^2+2q+1
        67: 2q^3+4q^2+q
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^4+2q^3+5q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 2q^2+2q+1
        75: 3q^2+q
        76: 2q^2+2q+1
        77: q^3+3q^2+q
        78: 2q^2+2q+1
        79: 3q^2+q
        80: q^3+7q^2+3q+1
        81: 4q^3+8q^2+3q+1
        82: 5q^2+3q+1
        83: q^3+6q^2+3q+1
        84: 3q^3+8q^2+3q+1
        85: 2q^4+7q^3+9q^2+3q+1
        86: 2q^3+6q^2+3q+1
        87: q^4+4q^3+7q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^3+6q^2+3q+1
        95: 2q^3+6q^2+3q+1
        96: q^3+6q^2+3q+1
        97: q^4+4q^3+7q^2+3q+1
        98: 2q^4+5q^3+7q^2+3q+1
        99: q^4+4q^3+7q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^3+3q^2+q+1
       104: q^2+q
       105: 2q^2
       106: q^2+q
       107: q^3+3q^2+2q+1
       108: q^2+q
       109: 3q^2+q+1
       110: 2q
       111: q^2+2q+1
       112: 2q^2+q
       113: 2q^2+2q+1
       114: 2q^2+q
       115: 2q^2+2q+1
       116: 3q^2+q
       117: q^3+5q^2+q+1
       118: 2q^2+2q
       119: 2q^3+5q^2+2q+1
       120: q^3+3q^2+q
       121: q^3+4q^2+2q+1
       122: 3q^2+q
       123: 2q^3+4q^2+2q+1
       124: 2q^3+4q^2+q
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 2q^2+2q+1
       128: 3q^2+q
       129: 2q^2+2q+1
       130: q^3+3q^2+q
       131: 2q^2+2q+1
       132: 3q^2+q
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^4+2q^3+5q^2+3q+1
       136: q^3+4q^2+3q+1
       137: q^3+7q^2+3q+1
       138: q^3+6q^2+3q+1
       139: 5q^2+3q+1
       140: q^2+2q+1
       141: 5q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 3q^3+8q^2+3q+1
       144: q^4+4q^3+7q^2+3q+1
       145: 2q^3+6q^2+3q+1
       146: 2q^3+6q^2+3q+1
       147: q^4+2q^3+5q^2+3q+1
       148: q^3+4q^2+3q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 2q^2+2q+1
       152: 3q^2+q
       153: 2q^2+2q+1
       154: q^3+3q^2+q
       155: 2q^2+2q+1
       156: 3q^2+q
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+6q^2+3q+1
       161: 2q^3+6q^2+3q+1
       162: q^3+6q^2+3q+1
       163: q^4+4q^3+7q^2+3q+1
       164: 2q^4+5q^3+7q^2+3q+1
       165: q^4+4q^3+7q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q^2+q+1
       170: q
       171: q^2
       172: q
       173: q^3+3q^2+q+1
       174: q^2+q
       175: 2q^2
       176: q^2+q
       177: 2q^2+2q+1
       178: 3q^2+q
       179: 2q^2+2q+1
       180: 2q^2+q
       181: q^2+2q+1
       182: 2q^2+q
       183: q^3+3q^2+2q+1
       184: q^2+q
       185: 3q^2+q+1
       186: 2q
       187: q^2+2q+1
       188: 2q^2+q
       189: 2q^2+2q+1
       190: 2q^2+q
       191: q^3+5q^2+q+1
       192: 2q^2+2q
       193: q^2+2q+1
       195: 3q^2+q+1
       196: 2q
       197: q+1
       198: q
       199: 2q^3+5q^2+2q+1
       200: q^3+3q^2+q
       201: q^3+3q^2+2q+1
       202: q^2+q
       203: 3q^2+q+1
       204: 2q
       205: q^2+2q+1
       206: 2q^2+q
       207: q^3+4q^2+2q+1
       208: 3q^2+q
       209: 2q^2+2q+1
       210: 2q^2+q
       211: 2q^2+2q+1
       212: 3q^2+q
       213: 2q^2+2q+1
       214: 3q^2+q
       215: 2q^2+2q+1
       216: q^3+3q^2+q
       217: 2q^2+2q+1
       218: 3q^2+q
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^4+2q^3+5q^2+3q+1
       224: 2q^2+3q+1
       225: q^3+4q^2+3q+1
       226: 5q^2+3q+1
       227: 5q^2+3q+1
       228: q^3+6q^2+3q+1
       229: q^2+2q+1
       230: q^3+4q^2+3q+1
       231: 2q^3+6q^2+3q+1
       232: 2q^3+6q^2+3q+1
       233: q^4+4q^3+7q^2+3q+1
       234: q^4+2q^3+5q^2+3q+1
       235: q^3+4q^2+3q+1
       236: q^3+6q^2+3q+1
       237: 2q^2+2q+1
       238: 3q^2+q
       239: 2q^2+2q+1
       240: q^3+3q^2+q
       241: 2q^2+2q+1
       242: 3q^2+q
       243: 5q^2+3q+1
       244: q^2+2q+1
       245: q^3+4q^2+3q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q^2+q+1
       260: q
       261: q^2
       262: q
       263: q^2+q+1
       264: q
       265: q^2
       266: q
       267: q+1
       268: q
       271: q^2+q+1
       272: q^2
       273: q
       274: q
       275: q^3+3q^2+q+1
       276: q^2+q
       277: 2q^2
       278: q^2+q
       279: 2q^2+2q+1
       280: 2q^2+q
       281: 2q^2+2q+1
       282: 3q^2+q
       283: q^3+3q^2+2q+1
       284: q^2+q
       285: 3q^2+q+1
       286: 2q
       287: 2q^2+2q+1
       288: 2q^2+q
       289: q^2+2q+1
       290: 2q^2+q
       291: q^2+2q+1
       292: 2q^2+q
       293: 2q^2+2q+1
       294: q
       295: 2q^2+q+1
       296: 2q
       297: q^2+2q+1
       298: q
       299: q^2+2q+1
       301: q+1
       302: q
       303: 3q^2+q+1
       304: 2q
       305: q+1
       306: q
       307: q^3+3q^2+2q+1
       308: q^2+q
       309: 3q^2+q+1
       310: 2q
       311: q^2+2q+1
       312: 2q^2+q
       313: q^2+2q+1
       314: 2q^2+q
       315: 2q^2+2q+1
       316: 3q^2+q
       317: 2q^2+2q+1
       318: 2q^2+q
       319: q^2+2q+1
       321: 3q^2+q+1
       322: 2q
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: 2q^2+q
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       339: 2q^2+2q
       340: 2q+1
       341: 2q^2+2q
       342: q^2+q+1
       343: 2q^2+q
       344: 5q^2+3q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+4q^2+3q+1
       351: 3q+1
       352: 2q^3+6q^2+3q+1
       353: q^3+4q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 2q^2+3q+1
       356: q^4+2q^3+5q^2+3q+1
       357: 2q^2+3q+1
       358: q^3+4q^2+3q+1
       359: 2q^2+4q+1
       360: 2q^2+2q+1
       361: 3q^2+q
       362: 2q^2+2q+1
       363: q^3+3q^2+q
       364: 2q^2+2q+1
       365: 3q^2+q
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^2+2q+1
       370: q^3+4q^2+3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2+q+1
       378: q
       379: q^2
       380: q
       381: q^2+q+1
       382: q
       383: q^2
       384: q
       385: q^2+q+1
       386: q
       388: q
       389: q+1
       390: q
       393: q+1
       394: q
       397: q^2+q+1
       398: q^2
       399: q
       400: q
       401: q^2+q+1
       402: q^2
       403: q
       404: q
       405: q+1
       407: q
       413: 2q^2+2q+1
       414: 2q^2+q
       417: q^2+2q+1
       418: 2q^2+q
       419: 2q^2+2q+1
       420: q
       421: 2q^2+q+1
       422: 2q
       423: q^2+2q+1
       424: q
       425: q+1
       426: q^2+q
       427: 2q+1
       428: q^2+2q
       429: q^2+2q+1
       431: 3q^2+q+1
       432: 2q
       433: q+1
       434: q
       435: q+1
       436: q
       437: q+1
       439: q^2+q+1
       440: q
       441: q+1
       443: 3q+1
       445: q+1
       446: 2q
       447: q^3+3q^2+2q+1
       448: q^2+q
       449: 3q^2+q+1
       450: 2q
       451: q^2+2q+1
       452: 2q^2+q
       453: 2q^2+2q+1
       454: q
       455: q^2+2q+1
       456: 2q^2+q
       457: 2q^2+q+1
       458: 2q
       459: q^2+2q+1
       460: q
       461: q^2+2q+1
       462: 2q
       463: 2q+1
       464: 2q^2+2q
       465: 2q^2+2q+1
       466: 2q^2+q
       467: 2q^2+2q+1
       468: 3q^2+q
       469: 2q^2+2q+1
       470: 2q^2+q
       471: q^2+2q+1
       473: 3q^2+q+1
       474: 2q
       475: q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       486: 2q^2+2q
       487: 2q+1
       488: 2q^2+2q
       489: q^2+q+1
       490: 2q^2+q
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 3q+1
       497: q^3+4q^2+3q+1
       498: 2q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^3+4q^2+3q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2+q+1
       522: q
       523: q^2
       524: q
       529: q^2+q+1
       530: q
       532: q
       533: q+1
       534: q
       537: q+1
       538: q
       541: q+1
       545: q+1
       546: 2q
       549: q^2+q+1
       550: q^2
       551: q
       552: q
       553: q^2+q+1
       554: q^2
       555: q
       556: q
       557: q^2+q+1
       559: q
       560: q
       561: q+1
       562: q^2+q
       563: q
       564: q
       565: q+1
       566: q
       569: q+1
       571: q
       573: 2q+1
       574: q
       577: q+1
       578: q
       581: q
       585: q^2+2q+1
       586: q
       589: 2q^2+2q+1
       590: q
       591: 1
       593: q+1
       595: 2q^2+q+1
       596: 2q
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: 2q+1
       602: q^2+2q
       603: q+1
       605: q+1
       606: q
       607: q^2+q+1
       608: q
       609: q+1
       613: 1
       614: q
       615: 3q+1
       617: q+1
       618: 2q
       619: 2q^2+2q+1
       620: q
       621: 2q^2+q+1
       622: 2q
       623: q^2+2q+1
       624: 2q^2+q
       625: q^2+2q+1
       626: q
       629: q+1
       630: q^2+q
       631: q^2+2q+1
       632: 2q
       633: 2q+1
       634: 2q^2+2q
       639: 2q^2+2q+1
       640: 2q^2+q
       641: q^2+2q+1
       643: 3q^2+q+1
       644: 2q
       645: q+1
       646: q
       647: q+1
       649: q^2+q+1
       650: q
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       659: 2q^2+2q
       660: 2q+1
       661: 2q^2+2q
       662: q^2+q+1
       663: 2q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: 2q^2+3q+1
       682: 2q^2+3q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q+1
       694: q
       699: q
       709: q^2+q+1
       710: q
       712: q
       713: 1
       717: 1
       718: q
       721: q+1
       722: q
       725: q+1
       733: q+1
       734: 2q
       737: q^2+q+1
       738: q^2
       739: q
       740: q
       741: q^2+q+1
       743: q
       744: q
       749: q+1
       750: q^2+q
       751: q
       752: q
       753: q+1
       754: q
       757: q+1
       759: q
       761: q+1
       765: 2q+1
       766: q
       769: q+1
       770: q
       773: q
       775: 2q+1
       776: q^2+2q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       785: q+1
       787: 1
       791: 1
       793: 3q+1
       795: q+1
       796: 2q
       797: q+1
       801: q+1
       805: 1
       807: q^2+q+1
       808: q
       809: 1
       810: q
       811: 1
       815: q+1
       817: q^2+2q+1
       818: 2q
       819: 2q+1
       820: 2q^2+2q
       821: q^2+2q+1
       822: q
       825: 2q^2+2q+1
       826: q
       827: 1
       829: q+1
       831: 2q^2+q+1
       832: 2q
       833: q+1
       834: q^2+q
       835: q+1
       836: q
       839: q+1
       840: q
       843: 2q+1
       844: q
       845: q+1
       847: q^2+q+1
       848: q
       849: q+1
       850: q
       851: q+1
       855: 1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q+1
       885: q
       890: q
       900: 1
       904: 1
       905: q
       908: 1
       916: q+1
       917: 2q
       920: q+1
       928: 1
       940: q+1
       941: q^2+q
       942: q
       943: q
       944: q^2+q+1
       946: q
       947: q
       948: 1
       952: 1
       953: q
       960: q+1
       962: q
       964: 2q+1
       965: q
       968: q+1
       969: q
       972: q
       974: q+1
       988: q+1
       994: q+1
       995: q
       998: 1
      1000: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1016: q+1
      1020: 1
      1021: q
      1022: 1
      1026: 1
      1032: q+1
      1033: q
      1036: q+1
      1037: q^2+q
      1038: q+1
      1039: q
      1040: q+1
      1044: 1
      1046: q+1
      1048: q+1
      1052: q+1
      1056: 1
      1058: q^2+q+1
      1059: q
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: q+1
      1087: q
      1092: q
      1114: 1
      1122: 1
      1123: q
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1156: 1
      1172: 1
      1176: 1
      1177: q
      1180: 1
      1194: q+1
      1198: q+1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: q+1
      1230: 1
      1234: 1
      1240: 1
      1246: q+1
      1247: q
      1248: q+1
      1249: q
      1250: 1
      1254: q+1
      1258: 1
      1260: 1
      1262: q+1
      1266: 1
      1268: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1388: 1
      1389: q
      1392: 1
      1396: 1
      1400: 1
      1410: q+1
      1422: 1
      1430: 1
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1468: 1
      1474: 1
      1476: 1
      1482: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1513: 1
      1537: 1
      1549: 1
      1595: 1
      1599: 1
      1615: 1
      1639: 1
      1647: 1
      1653: 1
      1655: 1
      1659: 1
      1665: 1
      1669: 1
      1674: 1
      1733: 1
      1769: 1
      1773: 1
      1825: 1
      1831: 1
      1914: 1

1915:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 4q^3+8q^2+3q+1
        23: 4q^3+8q^2+3q+1
        24: 4q^3+8q^2+3q+1
        25: 2q^4+7q^3+9q^2+3q+1
        26: 2q^4+7q^3+9q^2+3q+1
        27: 2q^4+7q^3+9q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: q^3+7q^2+3q+1
        32: 4q^3+8q^2+3q+1
        33: 4q^3+8q^2+3q+1
        34: 3q^3+8q^2+3q+1
        35: 2q^4+7q^3+9q^2+3q+1
        36: 2q^4+7q^3+9q^2+3q+1
        37: 2q^3+4q^2+q
        38: 2q^3+4q^2+2q+1
        39: 2q^3+4q^2+q
        40: 2q^3+4q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+4q^2+2q+1
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^3+6q^2+3q+1
        53: 2q^3+6q^2+3q+1
        54: q^3+6q^2+3q+1
        55: q^4+4q^3+7q^2+3q+1
        56: 2q^4+5q^3+7q^2+3q+1
        57: q^4+4q^3+7q^2+3q+1
        58: 2q^2+2q
        59: q^3+5q^2+q+1
        60: 2q^3+5q^2+2q+1
        61: q^3+3q^2+q
        62: 3q^2+q
        63: q^3+4q^2+2q+1
        64: 2q^3+4q^2+q
        65: 2q^3+4q^2+2q+1
        66: 2q^3+4q^2+q
        67: 2q^3+4q^2+2q+1
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^4+2q^3+5q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 3q^2+q
        75: 2q^2+2q+1
        76: q^3+3q^2+q
        77: 2q^2+2q+1
        78: 3q^2+q
        79: 2q^2+2q+1
        80: q^3+7q^2+3q+1
        81: 4q^3+8q^2+3q+1
        82: 5q^2+3q+1
        83: q^3+6q^2+3q+1
        84: 3q^3+8q^2+3q+1
        85: 2q^4+7q^3+9q^2+3q+1
        86: 2q^3+6q^2+3q+1
        87: q^4+4q^3+7q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^3+6q^2+3q+1
        95: 2q^3+6q^2+3q+1
        96: q^3+6q^2+3q+1
        97: q^4+4q^3+7q^2+3q+1
        98: 2q^4+5q^3+7q^2+3q+1
        99: q^4+4q^3+7q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^2+q
       104: q^3+3q^2+q+1
       105: q^2+q
       106: 2q^2
       107: q^3+3q^2+2q+1
       108: q^2+q
       109: 2q
       110: 3q^2+q+1
       111: 2q^2+q
       112: q^2+2q+1
       113: 2q^2+q
       114: 2q^2+2q+1
       115: 3q^2+q
       116: 2q^2+2q+1
       117: 2q^2+2q
       118: q^3+5q^2+q+1
       119: 2q^3+5q^2+2q+1
       120: q^3+3q^2+q
       121: 3q^2+q
       122: q^3+4q^2+2q+1
       123: 2q^3+4q^2+q
       124: 2q^3+4q^2+2q+1
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 3q^2+q
       128: 2q^2+2q+1
       129: q^3+3q^2+q
       130: 2q^2+2q+1
       131: 3q^2+q
       132: 2q^2+2q+1
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^4+2q^3+5q^2+3q+1
       136: q^3+4q^2+3q+1
       137: q^3+7q^2+3q+1
       138: q^3+6q^2+3q+1
       139: 5q^2+3q+1
       140: q^2+2q+1
       141: 5q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 3q^3+8q^2+3q+1
       144: q^4+4q^3+7q^2+3q+1
       145: 2q^3+6q^2+3q+1
       146: 2q^3+6q^2+3q+1
       147: q^4+2q^3+5q^2+3q+1
       148: q^3+4q^2+3q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 3q^2+q
       152: 2q^2+2q+1
       153: q^3+3q^2+q
       154: 2q^2+2q+1
       155: 3q^2+q
       156: 2q^2+2q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+6q^2+3q+1
       161: 2q^3+6q^2+3q+1
       162: q^3+6q^2+3q+1
       163: q^4+4q^3+7q^2+3q+1
       164: 2q^4+5q^3+7q^2+3q+1
       165: q^4+4q^3+7q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q
       170: q^2+q+1
       171: q
       172: q^2
       173: q^2+q
       174: q^3+3q^2+q+1
       175: q^2+q
       176: 2q^2
       177: 3q^2+q
       178: 2q^2+2q+1
       179: 2q^2+q
       180: 2q^2+2q+1
       181: 2q^2+q
       182: q^2+2q+1
       183: q^3+3q^2+2q+1
       184: q^2+q
       185: 2q
       186: 3q^2+q+1
       187: 2q^2+q
       188: q^2+2q+1
       189: 2q^2+q
       190: 2q^2+2q+1
       191: 2q^2+2q
       192: q^3+5q^2+q+1
       193: q^2+2q+1
       195: 2q
       196: 3q^2+q+1
       197: q
       198: q+1
       199: 2q^3+5q^2+2q+1
       200: q^3+3q^2+q
       201: q^3+3q^2+2q+1
       202: q^2+q
       203: 2q
       204: 3q^2+q+1
       205: 2q^2+q
       206: q^2+2q+1
       207: 3q^2+q
       208: q^3+4q^2+2q+1
       209: 2q^2+q
       210: 2q^2+2q+1
       211: 3q^2+q
       212: 2q^2+2q+1
       213: 3q^2+q
       214: 2q^2+2q+1
       215: q^3+3q^2+q
       216: 2q^2+2q+1
       217: 3q^2+q
       218: 2q^2+2q+1
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^4+2q^3+5q^2+3q+1
       224: 2q^2+3q+1
       225: q^3+4q^2+3q+1
       226: 5q^2+3q+1
       227: 5q^2+3q+1
       228: q^3+6q^2+3q+1
       229: q^2+2q+1
       230: q^3+4q^2+3q+1
       231: 2q^3+6q^2+3q+1
       232: 2q^3+6q^2+3q+1
       233: q^4+4q^3+7q^2+3q+1
       234: q^4+2q^3+5q^2+3q+1
       235: q^3+4q^2+3q+1
       236: q^3+6q^2+3q+1
       237: 3q^2+q
       238: 2q^2+2q+1
       239: q^3+3q^2+q
       240: 2q^2+2q+1
       241: 3q^2+q
       242: 2q^2+2q+1
       243: 5q^2+3q+1
       244: q^2+2q+1
       245: q^3+4q^2+3q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q
       260: q^2+q+1
       261: q
       262: q^2
       263: q
       264: q^2+q+1
       265: q
       266: q^2
       267: q
       268: q+1
       271: q
       272: q
       273: q^2
       274: q^2+q+1
       275: q^2+q
       276: q^3+3q^2+q+1
       277: q^2+q
       278: 2q^2
       279: 2q^2+q
       280: 2q^2+2q+1
       281: 3q^2+q
       282: 2q^2+2q+1
       283: q^3+3q^2+2q+1
       284: q^2+q
       285: 2q
       286: 3q^2+q+1
       287: 2q^2+q
       288: 2q^2+2q+1
       289: 2q^2+q
       290: q^2+2q+1
       291: 2q^2+q
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q
       295: 2q
       296: 2q^2+q+1
       297: q
       298: q^2+2q+1
       299: q^2+2q+1
       301: q
       302: q+1
       303: 2q
       304: 3q^2+q+1
       305: q
       306: q+1
       307: q^3+3q^2+2q+1
       308: q^2+q
       309: 2q
       310: 3q^2+q+1
       311: 2q^2+q
       312: q^2+2q+1
       313: 2q^2+q
       314: q^2+2q+1
       315: 3q^2+q
       316: 2q^2+2q+1
       317: 2q^2+q
       318: 2q^2+2q+1
       319: q^2+2q+1
       321: 2q
       322: 3q^2+q+1
       323: q
       324: q+1
       325: 2q^2+q
       326: 2q^2+2q+1
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q^2+2q
       339: 2q+1
       340: 2q^2+2q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: 5q^2+3q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+4q^2+3q+1
       351: 3q+1
       352: 2q^3+6q^2+3q+1
       353: q^3+4q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 2q^2+3q+1
       356: q^4+2q^3+5q^2+3q+1
       357: 2q^2+3q+1
       358: q^3+4q^2+3q+1
       359: 2q^2+4q+1
       360: 3q^2+q
       361: 2q^2+2q+1
       362: q^3+3q^2+q
       363: 2q^2+2q+1
       364: 3q^2+q
       365: 2q^2+2q+1
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^2+2q+1
       370: q^3+4q^2+3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       378: q^2+q+1
       379: q
       380: q^2
       381: q
       382: q^2+q+1
       383: q
       384: q^2
       385: q
       386: q^2+q+1
       387: q
       389: q
       390: q+1
       393: q
       394: q+1
       397: q
       398: q
       399: q^2
       400: q^2+q+1
       401: q
       402: q
       403: q^2+q+1
       404: q^2
       405: q
       407: q+1
       413: 2q^2+q
       414: 2q^2+2q+1
       417: 2q^2+q
       418: q^2+2q+1
       419: 2q^2+2q+1
       420: q
       421: 2q
       422: 2q^2+q+1
       423: q
       424: q^2+2q+1
       425: q^2+q
       426: q+1
       427: q^2+2q
       428: 2q+1
       429: q^2+2q+1
       431: 2q
       432: 3q^2+q+1
       433: q
       434: q+1
       435: q
       436: q+1
       437: q+1
       439: q
       440: q^2+q+1
       442: q+1
       443: 3q+1
       445: 2q
       446: q+1
       447: q^3+3q^2+2q+1
       448: q^2+q
       449: 2q
       450: 3q^2+q+1
       451: 2q^2+q
       452: q^2+2q+1
       453: 2q^2+2q+1
       454: q
       455: 2q^2+q
       456: q^2+2q+1
       457: 2q
       458: 2q^2+q+1
       459: q
       460: q^2+2q+1
       461: 2q
       462: q^2+2q+1
       463: 2q^2+2q
       464: 2q+1
       465: 2q^2+q
       466: 2q^2+2q+1
       467: 3q^2+q
       468: 2q^2+2q+1
       469: 2q^2+q
       470: 2q^2+2q+1
       471: q^2+2q+1
       473: 2q
       474: 3q^2+q+1
       475: q
       476: q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q^2+2q
       486: 2q+1
       487: 2q^2+2q
       488: 2q+1
       489: 2q^2+q
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 3q+1
       497: q^3+4q^2+3q+1
       498: 2q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^3+4q^2+3q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       522: q^2+q+1
       523: q
       524: q^2
       529: q
       530: q^2+q+1
       531: q
       533: q
       534: q+1
       537: q
       538: q+1
       542: q+1
       545: 2q
       546: q+1
       549: q
       550: q
       551: q^2+q+1
       552: q^2
       553: q
       554: q
       555: q^2
       556: q^2+q+1
       557: q
       558: q
       560: q^2+q+1
       561: q
       562: q
       563: q^2+q
       564: q+1
       565: q
       566: q+1
       569: q
       571: q+1
       573: q
       574: 2q+1
       577: q
       580: q
       581: q+1
       585: q
       586: q^2+2q+1
       589: 2q^2+2q+1
       590: q
       592: 1
       593: q+1
       595: 2q
       596: 2q^2+q+1
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q^2+2q
       602: 2q+1
       603: q+1
       605: q
       606: q+1
       607: q
       608: q^2+q+1
       610: q+1
       613: q
       614: 1
       615: 3q+1
       617: 2q
       618: q+1
       619: 2q^2+2q+1
       620: q
       621: 2q
       622: 2q^2+q+1
       623: 2q^2+q
       624: q^2+2q+1
       625: q
       626: q^2+2q+1
       629: q^2+q
       630: q+1
       631: 2q
       632: q^2+2q+1
       633: 2q^2+2q
       634: 2q+1
       639: 2q^2+q
       640: 2q^2+2q+1
       641: q^2+2q+1
       643: 2q
       644: 3q^2+q+1
       645: q
       646: q+1
       647: q+1
       649: q
       650: q^2+q+1
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       658: 2q^2+2q
       659: 2q+1
       660: 2q^2+2q
       661: 2q+1
       662: 2q^2+q
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: 2q^2+3q+1
       682: 2q^2+3q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       696: q
       699: q+1
       709: q
       710: q^2+q+1
       711: q
       715: 1
       717: q
       718: 1
       721: q
       722: q+1
       726: q+1
       733: 2q
       734: q+1
       737: q
       738: q
       739: q^2
       740: q^2+q+1
       741: q
       742: q
       744: q^2+q+1
       749: q
       750: q
       751: q^2+q
       752: q+1
       753: q
       754: q+1
       757: q
       759: q+1
       763: q+1
       765: q
       766: 2q+1
       769: q
       772: q
       773: q+1
       775: q^2+2q
       776: 2q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       785: q+1
       788: 1
       792: 1
       793: 3q+1
       795: 2q
       796: q+1
       798: q+1
       801: q+1
       805: 1
       807: q
       808: q^2+q+1
       809: q
       810: 1
       812: 1
       815: q+1
       817: 2q
       818: q^2+2q+1
       819: 2q^2+2q
       820: 2q+1
       821: q
       822: q^2+2q+1
       825: 2q^2+2q+1
       826: q
       828: 1
       829: q+1
       831: 2q
       832: 2q^2+q+1
       833: q^2+q
       834: q+1
       835: q
       836: q+1
       839: q
       840: q+1
       843: q
       844: 2q+1
       845: q+1
       847: q
       848: q^2+q+1
       849: q
       850: q+1
       852: q+1
       855: q
       856: 1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       887: q
       890: q+1
       903: 1
       904: q
       905: 1
       909: 1
       916: 2q
       917: q+1
       921: q+1
       929: 1
       940: q
       941: q
       942: q^2+q
       943: q+1
       944: q
       945: q
       947: q^2+q+1
       951: 1
       952: q
       953: 1
       960: q
       962: q+1
       964: q
       965: 2q+1
       968: q
       971: q
       972: q+1
       976: q+1
       989: q+1
       994: q
       995: q+1
       999: 1
      1000: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1016: q+1
      1020: q
      1021: 1
      1023: 1
      1026: 1
      1032: q
      1033: q+1
      1036: q^2+q
      1037: q+1
      1038: q
      1039: q+1
      1040: q+1
      1045: 1
      1047: q+1
      1049: q+1
      1052: q+1
      1056: 1
      1058: q
      1059: q^2+q+1
      1060: q
      1061: 1
      1063: 1
      1065: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1089: q
      1092: q+1
      1117: 1
      1122: q
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1157: 1
      1175: 1
      1176: q
      1177: 1
      1181: 1
      1195: q+1
      1200: q+1
      1207: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: q+1
      1231: 1
      1234: 1
      1240: 1
      1246: q
      1247: q+1
      1248: q
      1249: q+1
      1251: 1
      1254: q+1
      1258: 1
      1261: 1
      1263: q+1
      1267: 1
      1268: 1
      1274: q
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1357: 1
      1383: 1
      1388: q
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1411: q+1
      1423: 1
      1434: 1
      1437: 1
      1441: 1
      1442: 1
      1445: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1475: 1
      1476: 1
      1483: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1519: 1
      1539: 1
      1550: 1
      1596: 1
      1601: 1
      1616: 1
      1640: 1
      1647: 1
      1654: 1
      1655: 1
      1660: 1
      1665: 1
      1670: 1
      1674: 1
      1734: 1
      1771: 1
      1774: 1
      1826: 1
      1831: 1
      1915: 1

1916:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 4q^3+8q^2+3q+1
        23: 4q^3+8q^2+3q+1
        24: 4q^3+8q^2+3q+1
        25: 2q^4+7q^3+9q^2+3q+1
        26: 2q^4+7q^3+9q^2+3q+1
        27: 2q^4+7q^3+9q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: q^3+7q^2+3q+1
        32: 4q^3+8q^2+3q+1
        33: 4q^3+8q^2+3q+1
        34: 3q^3+8q^2+3q+1
        35: 2q^4+7q^3+9q^2+3q+1
        36: 2q^4+7q^3+9q^2+3q+1
        37: 2q^3+4q^2+2q+1
        38: 2q^3+4q^2+q
        39: 2q^3+4q^2+2q+1
        40: 2q^3+4q^2+q
        41: 2q^3+4q^2+2q+1
        42: 2q^3+4q^2+q
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^3+6q^2+3q+1
        53: 2q^3+6q^2+3q+1
        54: q^3+6q^2+3q+1
        55: q^4+4q^3+7q^2+3q+1
        56: 2q^4+5q^3+7q^2+3q+1
        57: q^4+4q^3+7q^2+3q+1
        58: 2q^2+2q
        59: q^3+5q^2+q+1
        60: q^3+3q^2+q
        61: 2q^3+5q^2+2q+1
        62: q^3+4q^2+2q+1
        63: 3q^2+q
        64: 2q^3+4q^2+2q+1
        65: 2q^3+4q^2+q
        66: 2q^3+4q^2+2q+1
        67: 2q^3+4q^2+q
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^4+2q^3+5q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 2q^2+2q+1
        75: 3q^2+q
        76: 2q^2+2q+1
        77: q^3+3q^2+q
        78: 2q^2+2q+1
        79: 3q^2+q
        80: q^3+7q^2+3q+1
        81: 4q^3+8q^2+3q+1
        82: 5q^2+3q+1
        83: q^3+6q^2+3q+1
        84: 3q^3+8q^2+3q+1
        85: 2q^4+7q^3+9q^2+3q+1
        86: 2q^3+6q^2+3q+1
        87: q^4+4q^3+7q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^3+6q^2+3q+1
        95: 2q^3+6q^2+3q+1
        96: q^3+6q^2+3q+1
        97: q^4+4q^3+7q^2+3q+1
        98: 2q^4+5q^3+7q^2+3q+1
        99: q^4+4q^3+7q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: q^2+q
       104: 2q^2
       105: q^2+q
       106: q^3+3q^2+q+1
       107: q^2+q
       108: q^3+3q^2+2q+1
       109: 2q
       110: 3q^2+q+1
       111: q^2+2q+1
       112: 2q^2+q
       113: 2q^2+2q+1
       114: 2q^2+q
       115: 2q^2+2q+1
       116: 3q^2+q
       117: 2q^2+2q
       118: q^3+5q^2+q+1
       119: q^3+3q^2+q
       120: 2q^3+5q^2+2q+1
       121: q^3+4q^2+2q+1
       122: 3q^2+q
       123: 2q^3+4q^2+2q+1
       124: 2q^3+4q^2+q
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 2q^2+2q+1
       128: 3q^2+q
       129: 2q^2+2q+1
       130: q^3+3q^2+q
       131: 2q^2+2q+1
       132: 3q^2+q
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^4+2q^3+5q^2+3q+1
       136: q^3+4q^2+3q+1
       137: q^3+7q^2+3q+1
       138: q^3+6q^2+3q+1
       139: 5q^2+3q+1
       140: q^2+2q+1
       141: 5q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 3q^3+8q^2+3q+1
       144: q^4+4q^3+7q^2+3q+1
       145: 2q^3+6q^2+3q+1
       146: 2q^3+6q^2+3q+1
       147: q^4+2q^3+5q^2+3q+1
       148: q^3+4q^2+3q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 2q^2+2q+1
       152: 3q^2+q
       153: 2q^2+2q+1
       154: q^3+3q^2+q
       155: 2q^2+2q+1
       156: 3q^2+q
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+6q^2+3q+1
       161: 2q^3+6q^2+3q+1
       162: q^3+6q^2+3q+1
       163: q^4+4q^3+7q^2+3q+1
       164: 2q^4+5q^3+7q^2+3q+1
       165: q^4+4q^3+7q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q
       170: q^2
       171: q
       172: q^2+q+1
       173: q^2+q
       174: 2q^2
       175: q^2+q
       176: q^3+3q^2+q+1
       177: 2q^2+2q+1
       178: 3q^2+q
       179: 2q^2+2q+1
       180: 2q^2+q
       181: q^2+2q+1
       182: 2q^2+q
       183: q^2+q
       184: q^3+3q^2+2q+1
       185: 2q
       186: 3q^2+q+1
       187: q^2+2q+1
       188: 2q^2+q
       189: 2q^2+2q+1
       190: 2q^2+q
       191: 2q^2+2q
       192: q^3+5q^2+q+1
       194: q^2+2q+1
       195: 2q
       196: 3q^2+q+1
       197: q+1
       198: q
       199: q^3+3q^2+q
       200: 2q^3+5q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+2q+1
       203: 2q
       204: 3q^2+q+1
       205: q^2+2q+1
       206: 2q^2+q
       207: q^3+4q^2+2q+1
       208: 3q^2+q
       209: 2q^2+2q+1
       210: 2q^2+q
       211: 2q^2+2q+1
       212: 3q^2+q
       213: 2q^2+2q+1
       214: 3q^2+q
       215: 2q^2+2q+1
       216: q^3+3q^2+q
       217: 2q^2+2q+1
       218: 3q^2+q
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^4+2q^3+5q^2+3q+1
       224: 2q^2+3q+1
       225: q^3+4q^2+3q+1
       226: 5q^2+3q+1
       227: 5q^2+3q+1
       228: q^3+6q^2+3q+1
       229: q^2+2q+1
       230: q^3+4q^2+3q+1
       231: 2q^3+6q^2+3q+1
       232: 2q^3+6q^2+3q+1
       233: q^4+4q^3+7q^2+3q+1
       234: q^4+2q^3+5q^2+3q+1
       235: q^3+4q^2+3q+1
       236: q^3+6q^2+3q+1
       237: 2q^2+2q+1
       238: 3q^2+q
       239: 2q^2+2q+1
       240: q^3+3q^2+q
       241: 2q^2+2q+1
       242: 3q^2+q
       243: 5q^2+3q+1
       244: q^2+2q+1
       245: q^3+4q^2+3q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q
       260: q^2
       261: q
       262: q^2+q+1
       263: q
       264: q^2
       265: q
       266: q^2+q+1
       269: q+1
       270: q
       271: q
       272: q
       273: q^2+q+1
       274: q^2
       275: q^2+q
       276: 2q^2
       277: q^2+q
       278: q^3+3q^2+q+1
       279: 2q^2+2q+1
       280: 2q^2+q
       281: 2q^2+2q+1
       282: 3q^2+q
       283: q^2+q
       284: q^3+3q^2+2q+1
       285: 2q
       286: 3q^2+q+1
       287: 2q^2+2q+1
       288: 2q^2+q
       289: q^2+2q+1
       290: 2q^2+q
       291: q^2+2q+1
       292: 2q^2+q
       293: q
       294: 2q^2+2q+1
       295: 2q
       296: 2q^2+q+1
       297: q^2+2q+1
       298: q
       300: q^2+2q+1
       301: q+1
       302: q
       303: 2q
       304: 3q^2+q+1
       305: q+1
       306: q
       307: q^2+q
       308: q^3+3q^2+2q+1
       309: 2q
       310: 3q^2+q+1
       311: q^2+2q+1
       312: 2q^2+q
       313: q^2+2q+1
       314: 2q^2+q
       315: 2q^2+2q+1
       316: 3q^2+q
       317: 2q^2+2q+1
       318: 2q^2+q
       320: q^2+2q+1
       321: 2q
       322: 3q^2+q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: 2q^2+q
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q+1
       339: 2q^2+2q
       340: 2q+1
       341: 2q^2+2q
       342: q^2+q+1
       343: 2q^2+q
       344: 5q^2+3q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+4q^2+3q+1
       351: 3q+1
       352: 2q^3+6q^2+3q+1
       353: q^3+4q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 2q^2+3q+1
       356: q^4+2q^3+5q^2+3q+1
       357: 2q^2+3q+1
       358: q^3+4q^2+3q+1
       359: 2q^2+4q+1
       360: 2q^2+2q+1
       361: 3q^2+q
       362: 2q^2+2q+1
       363: q^3+3q^2+q
       364: 2q^2+2q+1
       365: 3q^2+q
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^2+2q+1
       370: q^3+4q^2+3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       378: q^2
       379: q
       380: q^2+q+1
       381: q
       382: q^2
       383: q
       384: q^2+q+1
       385: q
       387: q
       388: q^2+q+1
       391: q+1
       392: q
       395: q
       396: q+1
       397: q
       398: q
       399: q^2+q+1
       400: q^2
       401: q
       402: q
       403: q^2
       404: q^2+q+1
       406: q+1
       408: q
       413: 2q^2+2q+1
       414: 2q^2+q
       417: q^2+2q+1
       418: 2q^2+q
       419: q
       420: 2q^2+2q+1
       421: 2q
       422: 2q^2+q+1
       423: q^2+2q+1
       424: q
       425: q+1
       426: q^2+q
       427: 2q+1
       428: q^2+2q
       430: q^2+2q+1
       431: 2q
       432: 3q^2+q+1
       433: q+1
       434: q
       435: q+1
       436: q
       438: q+1
       439: q
       440: q^2+q+1
       441: q+1
       444: 3q+1
       445: q+1
       446: 2q
       447: q^2+q
       448: q^3+3q^2+2q+1
       449: 2q
       450: 3q^2+q+1
       451: q^2+2q+1
       452: 2q^2+q
       453: q
       454: 2q^2+2q+1
       455: q^2+2q+1
       456: 2q^2+q
       457: 2q
       458: 2q^2+q+1
       459: q^2+2q+1
       460: q
       461: 2q
       462: q^2+2q+1
       463: 2q+1
       464: 2q^2+2q
       465: 2q^2+2q+1
       466: 2q^2+q
       467: 2q^2+2q+1
       468: 3q^2+q
       469: 2q^2+2q+1
       470: 2q^2+q
       472: q^2+2q+1
       473: 2q
       474: 3q^2+q+1
       475: q+1
       476: q
       477: q+1
       478: q
       479: 2q+1
       480: q
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q+1
       486: 2q^2+2q
       487: 2q+1
       488: 2q^2+2q
       489: q^2+q+1
       490: 2q^2+q
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 3q+1
       497: q^3+4q^2+3q+1
       498: 2q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^3+4q^2+3q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       522: q^2
       523: q
       524: q^2+q+1
       529: q
       531: q
       532: q^2+q+1
       535: q
       536: q+1
       539: q+1
       540: q
       543: q+1
       547: q+1
       548: 2q
       549: q
       550: q
       551: q^2
       552: q^2+q+1
       553: q
       554: q
       555: q^2+q+1
       556: q^2
       557: q
       558: q
       559: q^2+q+1
       561: q
       562: q
       563: q+1
       564: q^2+q
       567: q
       568: q+1
       570: q+1
       572: q
       575: 2q+1
       576: q
       577: q+1
       578: q
       581: q
       585: q^2+2q+1
       586: q
       589: q
       590: 2q^2+2q+1
       592: 1
       594: q+1
       595: 2q
       596: 2q^2+q+1
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: 2q+1
       602: q^2+2q
       604: q+1
       605: q+1
       606: q
       607: q
       608: q^2+q+1
       609: q+1
       613: 1
       614: q
       616: 3q+1
       617: q+1
       618: 2q
       619: q
       620: 2q^2+2q+1
       621: 2q
       622: 2q^2+q+1
       623: q^2+2q+1
       624: 2q^2+q
       625: q^2+2q+1
       626: q
       629: q+1
       630: q^2+q
       631: 2q
       632: q^2+2q+1
       633: 2q+1
       634: 2q^2+2q
       639: 2q^2+2q+1
       640: 2q^2+q
       642: q^2+2q+1
       643: 2q
       644: 3q^2+q+1
       645: q+1
       646: q
       648: q+1
       649: q
       650: q^2+q+1
       651: q+1
       652: q
       653: q+1
       655: 2q+1
       656: q
       657: q^2+4q+1
       658: 2q+1
       659: 2q^2+2q
       660: 2q+1
       661: 2q^2+2q
       662: q^2+q+1
       663: 2q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: 2q^2+3q+1
       682: 2q^2+3q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q+1
       700: q
       701: q
       709: q
       711: q
       712: q^2+q+1
       716: 1
       719: q
       720: 1
       723: q+1
       724: q
       727: q+1
       735: q+1
       736: 2q
       737: q
       738: q
       739: q^2+q+1
       740: q^2
       741: q
       742: q
       743: q^2+q+1
       749: q
       750: q
       751: q+1
       752: q^2+q
       755: q
       756: q+1
       758: q+1
       760: q
       762: q+1
       767: q
       768: 2q+1
       769: q+1
       770: q
       773: q
       775: 2q+1
       776: q^2+2q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       786: q+1
       788: 1
       791: 1
       794: 3q+1
       795: q+1
       796: 2q
       797: q+1
       802: q+1
       806: 1
       807: q
       808: q^2+q+1
       809: 1
       810: q
       811: 1
       816: q+1
       817: 2q
       818: q^2+2q+1
       819: 2q+1
       820: 2q^2+2q
       821: q^2+2q+1
       822: q
       825: q
       826: 2q^2+2q+1
       828: 1
       830: q+1
       831: 2q
       832: 2q^2+q+1
       833: q+1
       834: q^2+q
       835: q+1
       836: q
       839: q
       840: q+1
       843: 2q+1
       844: q
       846: q+1
       847: q
       848: q^2+q+1
       849: q+1
       850: q
       851: q+1
       855: 1
       856: q
       857: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       889: q+1
       891: q
       892: q
       902: 1
       906: 1
       907: q
       911: 1
       918: q+1
       919: 2q
       922: q+1
       930: 1
       940: q
       941: q
       942: q+1
       943: q^2+q
       944: q
       945: q
       946: q^2+q+1
       950: 1
       954: q
       955: 1
       961: q+1
       963: q
       966: q
       967: 2q+1
       968: q+1
       969: q
       972: q
       975: q+1
       991: q+1
       994: q+1
       995: q
       999: 1
      1001: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1017: q+1
      1020: 1
      1021: q
      1022: 1
      1027: 1
      1032: q
      1033: q+1
      1036: q+1
      1037: q^2+q
      1038: q+1
      1039: q
      1041: q+1
      1045: 1
      1046: q+1
      1048: q+1
      1053: q+1
      1057: 1
      1058: q
      1059: q^2+q+1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1091: q+1
      1093: q
      1094: q
      1116: 1
      1124: 1
      1125: q
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1158: 1
      1174: 1
      1178: 1
      1179: q
      1183: 1
      1197: q+1
      1199: q+1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: q+1
      1230: 1
      1235: 1
      1241: 1
      1246: q
      1247: q+1
      1248: q+1
      1249: q
      1251: 1
      1255: q+1
      1259: 1
      1261: 1
      1262: q+1
      1266: 1
      1269: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1358: 1
      1382: 1
      1390: 1
      1391: q
      1393: 1
      1399: 1
      1401: 1
      1413: q+1
      1424: 1
      1430: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1474: 1
      1477: 1
      1482: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1518: 1
      1538: 1
      1552: 1
      1598: 1
      1600: 1
      1617: 1
      1639: 1
      1648: 1
      1654: 1
      1656: 1
      1659: 1
      1666: 1
      1669: 1
      1674: 1
      1736: 1
      1770: 1
      1776: 1
      1825: 1
      1832: 1
      1916: 1

1917:    0: 2q^4+7q^3+9q^2+3q+1
         1: 2q^4+7q^3+9q^2+3q+1
         2: 2q^4+7q^3+9q^2+3q+1
         3: 2q^4+7q^3+9q^2+3q+1
         4: 3q^4+6q^3+7q^2+3q+1
         5: 2q^4+7q^3+9q^2+3q+1
         6: q^5+5q^4+7q^3+7q^2+3q+1
         7: 3q^4+6q^3+7q^2+3q+1
         8: 2q^4+7q^3+9q^2+3q+1
         9: 3q^4+6q^3+7q^2+3q+1
        10: 3q^3+8q^2+3q+1
        11: 3q^3+8q^2+3q+1
        12: q^4+4q^3+6q^2+3q+1
        13: 2q^4+7q^3+9q^2+3q+1
        14: 3q^4+6q^3+7q^2+3q+1
        15: 2q^4+7q^3+9q^2+3q+1
        16: 2q^4+7q^3+9q^2+3q+1
        17: 2q^4+7q^3+9q^2+3q+1
        18: 3q^4+6q^3+7q^2+3q+1
        19: q^4+4q^3+7q^2+3q+1
        20: 2q^4+5q^3+7q^2+3q+1
        21: q^4+4q^3+7q^2+3q+1
        22: 4q^3+8q^2+3q+1
        23: 4q^3+8q^2+3q+1
        24: 4q^3+8q^2+3q+1
        25: 2q^4+7q^3+9q^2+3q+1
        26: 2q^4+7q^3+9q^2+3q+1
        27: 2q^4+7q^3+9q^2+3q+1
        28: 3q^3+8q^2+3q+1
        29: 2q^3+6q^2+3q+1
        30: q^4+4q^3+7q^2+3q+1
        31: q^3+7q^2+3q+1
        32: 4q^3+8q^2+3q+1
        33: 4q^3+8q^2+3q+1
        34: 3q^3+8q^2+3q+1
        35: 2q^4+7q^3+9q^2+3q+1
        36: 2q^4+7q^3+9q^2+3q+1
        37: 2q^3+4q^2+q
        38: 2q^3+4q^2+2q+1
        39: 2q^3+4q^2+q
        40: 2q^3+4q^2+2q+1
        41: 2q^3+4q^2+q
        42: 2q^3+4q^2+2q+1
        43: 3q^3+8q^2+3q+1
        44: q^4+4q^3+6q^2+3q+1
        45: 3q^3+8q^2+3q+1
        46: 2q^4+7q^3+9q^2+3q+1
        47: 2q^4+7q^3+9q^2+3q+1
        48: 3q^4+6q^3+7q^2+3q+1
        49: q^4+4q^3+7q^2+3q+1
        50: 2q^4+5q^3+7q^2+3q+1
        51: q^4+4q^3+7q^2+3q+1
        52: q^3+6q^2+3q+1
        53: 2q^3+6q^2+3q+1
        54: q^3+6q^2+3q+1
        55: q^4+4q^3+7q^2+3q+1
        56: 2q^4+5q^3+7q^2+3q+1
        57: q^4+4q^3+7q^2+3q+1
        58: q^3+5q^2+q+1
        59: 2q^2+2q
        60: q^3+3q^2+q
        61: 2q^3+5q^2+2q+1
        62: 3q^2+q
        63: q^3+4q^2+2q+1
        64: 2q^3+4q^2+q
        65: 2q^3+4q^2+2q+1
        66: 2q^3+4q^2+q
        67: 2q^3+4q^2+2q+1
        68: 3q^3+8q^2+3q+1
        69: q^4+4q^3+7q^2+3q+1
        70: 2q^3+6q^2+3q+1
        71: 2q^3+6q^2+3q+1
        72: q^4+2q^3+5q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 3q^2+q
        75: 2q^2+2q+1
        76: q^3+3q^2+q
        77: 2q^2+2q+1
        78: 3q^2+q
        79: 2q^2+2q+1
        80: q^3+7q^2+3q+1
        81: 4q^3+8q^2+3q+1
        82: 5q^2+3q+1
        83: q^3+6q^2+3q+1
        84: 3q^3+8q^2+3q+1
        85: 2q^4+7q^3+9q^2+3q+1
        86: 2q^3+6q^2+3q+1
        87: q^4+4q^3+7q^2+3q+1
        88: 3q^3+8q^2+3q+1
        89: 3q^3+8q^2+3q+1
        90: q^4+4q^3+6q^2+3q+1
        91: q^4+4q^3+7q^2+3q+1
        92: 2q^4+5q^3+7q^2+3q+1
        93: q^4+4q^3+7q^2+3q+1
        94: q^3+6q^2+3q+1
        95: 2q^3+6q^2+3q+1
        96: q^3+6q^2+3q+1
        97: q^4+4q^3+7q^2+3q+1
        98: 2q^4+5q^3+7q^2+3q+1
        99: q^4+4q^3+7q^2+3q+1
       100: q^3+6q^2+3q+1
       101: 2q^3+6q^2+3q+1
       102: q^3+6q^2+3q+1
       103: 2q^2
       104: q^2+q
       105: q^3+3q^2+q+1
       106: q^2+q
       107: q^2+q
       108: q^3+3q^2+2q+1
       109: 3q^2+q+1
       110: 2q
       111: 2q^2+q
       112: q^2+2q+1
       113: 2q^2+q
       114: 2q^2+2q+1
       115: 3q^2+q
       116: 2q^2+2q+1
       117: q^3+5q^2+q+1
       118: 2q^2+2q
       119: q^3+3q^2+q
       120: 2q^3+5q^2+2q+1
       121: 3q^2+q
       122: q^3+4q^2+2q+1
       123: 2q^3+4q^2+q
       124: 2q^3+4q^2+2q+1
       125: 3q^3+8q^2+3q+1
       126: 2q^3+6q^2+3q+1
       127: 3q^2+q
       128: 2q^2+2q+1
       129: q^3+3q^2+q
       130: 2q^2+2q+1
       131: 3q^2+q
       132: 2q^2+2q+1
       133: 2q^3+6q^2+3q+1
       134: q^4+4q^3+7q^2+3q+1
       135: q^4+2q^3+5q^2+3q+1
       136: q^3+4q^2+3q+1
       137: q^3+7q^2+3q+1
       138: q^3+6q^2+3q+1
       139: 5q^2+3q+1
       140: q^2+2q+1
       141: 5q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 3q^3+8q^2+3q+1
       144: q^4+4q^3+7q^2+3q+1
       145: 2q^3+6q^2+3q+1
       146: 2q^3+6q^2+3q+1
       147: q^4+2q^3+5q^2+3q+1
       148: q^3+4q^2+3q+1
       149: 5q^2+3q+1
       150: q^3+6q^2+3q+1
       151: 3q^2+q
       152: 2q^2+2q+1
       153: q^3+3q^2+q
       154: 2q^2+2q+1
       155: 3q^2+q
       156: 2q^2+2q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+6q^2+3q+1
       161: 2q^3+6q^2+3q+1
       162: q^3+6q^2+3q+1
       163: q^4+4q^3+7q^2+3q+1
       164: 2q^4+5q^3+7q^2+3q+1
       165: q^4+4q^3+7q^2+3q+1
       166: q^3+6q^2+3q+1
       167: 2q^3+6q^2+3q+1
       168: q^3+6q^2+3q+1
       169: q^2
       170: q
       171: q^2+q+1
       172: q
       173: 2q^2
       174: q^2+q
       175: q^3+3q^2+q+1
       176: q^2+q
       177: 3q^2+q
       178: 2q^2+2q+1
       179: 2q^2+q
       180: 2q^2+2q+1
       181: 2q^2+q
       182: q^2+2q+1
       183: q^2+q
       184: q^3+3q^2+2q+1
       185: 3q^2+q+1
       186: 2q
       187: 2q^2+q
       188: q^2+2q+1
       189: 2q^2+q
       190: 2q^2+2q+1
       191: q^3+5q^2+q+1
       192: 2q^2+2q
       194: q^2+2q+1
       195: 3q^2+q+1
       196: 2q
       197: q
       198: q+1
       199: q^3+3q^2+q
       200: 2q^3+5q^2+2q+1
       201: q^2+q
       202: q^3+3q^2+2q+1
       203: 3q^2+q+1
       204: 2q
       205: 2q^2+q
       206: q^2+2q+1
       207: 3q^2+q
       208: q^3+4q^2+2q+1
       209: 2q^2+q
       210: 2q^2+2q+1
       211: 3q^2+q
       212: 2q^2+2q+1
       213: 3q^2+q
       214: 2q^2+2q+1
       215: q^3+3q^2+q
       216: 2q^2+2q+1
       217: 3q^2+q
       218: 2q^2+2q+1
       219: 2q^3+6q^2+3q+1
       220: q^3+4q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^4+2q^3+5q^2+3q+1
       224: 2q^2+3q+1
       225: q^3+4q^2+3q+1
       226: 5q^2+3q+1
       227: 5q^2+3q+1
       228: q^3+6q^2+3q+1
       229: q^2+2q+1
       230: q^3+4q^2+3q+1
       231: 2q^3+6q^2+3q+1
       232: 2q^3+6q^2+3q+1
       233: q^4+4q^3+7q^2+3q+1
       234: q^4+2q^3+5q^2+3q+1
       235: q^3+4q^2+3q+1
       236: q^3+6q^2+3q+1
       237: 3q^2+q
       238: 2q^2+2q+1
       239: q^3+3q^2+q
       240: 2q^2+2q+1
       241: 3q^2+q
       242: 2q^2+2q+1
       243: 5q^2+3q+1
       244: q^2+2q+1
       245: q^3+4q^2+3q+1
       246: 5q^2+3q+1
       247: 2q^2+4q+1
       248: 2q^2+4q+1
       249: 3q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: q^3+4q^2+3q+1
       256: q^3+6q^2+3q+1
       257: 2q^3+6q^2+3q+1
       258: q^3+6q^2+3q+1
       259: q^2
       260: q
       261: q^2+q+1
       262: q
       263: q^2
       264: q
       265: q^2+q+1
       266: q
       269: q
       270: q+1
       271: q^2
       272: q^2+q+1
       273: q
       274: q
       275: 2q^2
       276: q^2+q
       277: q^3+3q^2+q+1
       278: q^2+q
       279: 2q^2+q
       280: 2q^2+2q+1
       281: 3q^2+q
       282: 2q^2+2q+1
       283: q^2+q
       284: q^3+3q^2+2q+1
       285: 3q^2+q+1
       286: 2q
       287: 2q^2+q
       288: 2q^2+2q+1
       289: 2q^2+q
       290: q^2+2q+1
       291: 2q^2+q
       292: q^2+2q+1
       293: q
       294: 2q^2+2q+1
       295: 2q^2+q+1
       296: 2q
       297: q
       298: q^2+2q+1
       300: q^2+2q+1
       301: q
       302: q+1
       303: 3q^2+q+1
       304: 2q
       305: q
       306: q+1
       307: q^2+q
       308: q^3+3q^2+2q+1
       309: 3q^2+q+1
       310: 2q
       311: 2q^2+q
       312: q^2+2q+1
       313: 2q^2+q
       314: q^2+2q+1
       315: 3q^2+q
       316: 2q^2+2q+1
       317: 2q^2+q
       318: 2q^2+2q+1
       320: q^2+2q+1
       321: 3q^2+q+1
       322: 2q
       323: q
       324: q+1
       325: 2q^2+q
       326: 2q^2+2q+1
       333: q^3+4q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q^2+2q+1
       337: q^2+4q+1
       338: 2q^2+2q
       339: 2q+1
       340: 2q^2+2q
       341: 2q+1
       342: 2q^2+q
       343: q^2+q+1
       344: 5q^2+3q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+4q^2+3q+1
       351: 3q+1
       352: 2q^3+6q^2+3q+1
       353: q^3+4q^2+3q+1
       354: q^3+4q^2+3q+1
       355: 2q^2+3q+1
       356: q^4+2q^3+5q^2+3q+1
       357: 2q^2+3q+1
       358: q^3+4q^2+3q+1
       359: 2q^2+4q+1
       360: 3q^2+q
       361: 2q^2+2q+1
       362: q^3+3q^2+q
       363: 2q^2+2q+1
       364: 3q^2+q
       365: 2q^2+2q+1
       366: 5q^2+3q+1
       367: 5q^2+3q+1
       368: q^3+6q^2+3q+1
       369: q^2+2q+1
       370: q^3+4q^2+3q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 3q^2+2q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2
       378: q
       379: q^2+q+1
       380: q
       381: q^2
       382: q
       383: q^2+q+1
       384: q
       386: q
       387: q^2+q+1
       388: q
       391: q
       392: q+1
       395: q+1
       396: q
       397: q^2
       398: q^2+q+1
       399: q
       400: q
       401: q^2
       402: q^2+q+1
       403: q
       404: q
       406: q
       408: q+1
       413: 2q^2+q
       414: 2q^2+2q+1
       417: 2q^2+q
       418: q^2+2q+1
       419: q
       420: 2q^2+2q+1
       421: 2q^2+q+1
       422: 2q
       423: q
       424: q^2+2q+1
       425: q^2+q
       426: q+1
       427: q^2+2q
       428: 2q+1
       430: q^2+2q+1
       431: 3q^2+q+1
       432: 2q
       433: q
       434: q+1
       435: q
       436: q+1
       438: q+1
       439: q^2+q+1
       440: q
       442: q+1
       444: 3q+1
       445: 2q
       446: q+1
       447: q^2+q
       448: q^3+3q^2+2q+1
       449: 3q^2+q+1
       450: 2q
       451: 2q^2+q
       452: q^2+2q+1
       453: q
       454: 2q^2+2q+1
       455: 2q^2+q
       456: q^2+2q+1
       457: 2q^2+q+1
       458: 2q
       459: q
       460: q^2+2q+1
       461: q^2+2q+1
       462: 2q
       463: 2q^2+2q
       464: 2q+1
       465: 2q^2+q
       466: 2q^2+2q+1
       467: 3q^2+q
       468: 2q^2+2q+1
       469: 2q^2+q
       470: 2q^2+2q+1
       472: q^2+2q+1
       473: 3q^2+q+1
       474: 2q
       475: q
       476: q+1
       477: q
       478: q+1
       479: q
       480: 2q+1
       481: 2q^2+3q+1
       482: 2q^2+3q+1
       483: 2q+1
       484: q^2+4q+1
       485: 2q^2+2q
       486: 2q+1
       487: 2q^2+2q
       488: 2q+1
       489: 2q^2+q
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 3q+1
       497: q^3+4q^2+3q+1
       498: 2q^2+3q+1
       499: 2q^2+3q+1
       500: q^2+2q+1
       501: 2q^2+4q+1
       508: 5q^2+3q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q^2+2q+1
       513: q^2+2q+1
       514: q^3+4q^2+3q+1
       515: 2q^2+4q+1
       516: 2q^2+4q+1
       517: 3q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2
       522: q
       523: q^2+q+1
       524: q
       530: q
       531: q^2+q+1
       532: q
       535: q+1
       536: q
       539: q
       540: q+1
       544: q+1
       547: 2q
       548: q+1
       549: q^2
       550: q^2+q+1
       551: q
       552: q
       553: q^2
       554: q^2+q+1
       555: q
       556: q
       558: q^2+q+1
       559: q
       560: q
       561: q^2+q
       562: q+1
       563: q
       564: q
       567: q+1
       568: q
       570: q
       572: q+1
       575: q
       576: 2q+1
       577: q
       580: q
       581: q+1
       585: q
       586: q^2+2q+1
       589: q
       590: 2q^2+2q+1
       591: 1
       594: q+1
       595: 2q^2+q+1
       596: 2q
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q^2+2q
       602: 2q+1
       604: q+1
       605: q
       606: q+1
       607: q^2+q+1
       608: q
       610: q+1
       613: q
       614: 1
       616: 3q+1
       617: 2q
       618: q+1
       619: q
       620: 2q^2+2q+1
       621: 2q^2+q+1
       622: 2q
       623: 2q^2+q
       624: q^2+2q+1
       625: q
       626: q^2+2q+1
       629: q^2+q
       630: q+1
       631: q^2+2q+1
       632: 2q
       633: 2q^2+2q
       634: 2q+1
       639: 2q^2+q
       640: 2q^2+2q+1
       642: q^2+2q+1
       643: 3q^2+q+1
       644: 2q
       645: q
       646: q+1
       648: q+1
       649: q^2+q+1
       650: q
       651: q
       652: q+1
       654: q+1
       655: q
       656: 2q+1
       657: q^2+4q+1
       658: 2q^2+2q
       659: 2q+1
       660: 2q^2+2q
       661: 2q+1
       662: 2q^2+q
       663: q^2+q+1
       664: q^2+2q+1
       665: 2q+1
       672: 2q+1
       673: q+1
       674: 3q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: q+1
       680: 2q^2+4q+1
       681: 2q^2+3q+1
       682: 2q^2+3q+1
       683: 2q+1
       684: 2q+1
       685: q^2+2q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q
       698: q
       700: q+1
       710: q
       711: q^2+q+1
       712: q
       714: 1
       719: 1
       720: q
       723: q
       724: q+1
       728: q+1
       735: 2q
       736: q+1
       737: q^2
       738: q^2+q+1
       739: q
       740: q
       742: q^2+q+1
       743: q
       744: q
       749: q^2+q
       750: q+1
       751: q
       752: q
       755: q+1
       756: q
       758: q
       760: q+1
       764: q+1
       767: 2q+1
       768: q
       769: q
       772: q
       773: q+1
       775: q^2+2q
       776: 2q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       786: q+1
       787: 1
       792: 1
       794: 3q+1
       795: 2q
       796: q+1
       798: q+1
       802: q+1
       806: 1
       807: q^2+q+1
       808: q
       809: q
       810: 1
       812: 1
       816: q+1
       817: q^2+2q+1
       818: 2q
       819: 2q^2+2q
       820: 2q+1
       821: q
       822: q^2+2q+1
       825: q
       826: 2q^2+2q+1
       827: 1
       830: q+1
       831: 2q^2+q+1
       832: 2q
       833: q^2+q
       834: q+1
       835: q
       836: q+1
       839: q+1
       840: q
       843: q
       844: 2q+1
       846: q+1
       847: q^2+q+1
       848: q
       849: q
       850: q+1
       852: q+1
       855: q
       856: 1
       858: q+1
       865: 2q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: 1
       873: 2q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       888: q
       889: q
       891: q+1
       901: 1
       906: q
       907: 1
       910: 1
       918: 2q
       919: q+1
       923: q+1
       931: 1
       940: q^2+q
       941: q+1
       942: q
       943: q
       945: q^2+q+1
       946: q
       947: q
       949: 1
       954: 1
       955: q
       961: q
       963: q+1
       966: 2q+1
       967: q
       968: q
       971: q
       972: q+1
       977: q+1
       990: q+1
       994: q
       995: q+1
       998: 1
      1001: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1017: q+1
      1020: q
      1021: 1
      1023: 1
      1027: 1
      1032: q+1
      1033: q
      1036: q^2+q
      1037: q+1
      1038: q
      1039: q+1
      1041: q+1
      1044: 1
      1047: q+1
      1049: q+1
      1053: q+1
      1057: 1
      1058: q^2+q+1
      1059: q
      1060: q
      1061: 1
      1063: 1
      1065: 1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1090: q
      1091: q
      1093: q+1
      1115: 1
      1124: q
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1159: 1
      1173: 1
      1178: q
      1179: 1
      1182: 1
      1196: q+1
      1201: q+1
      1209: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: q+1
      1231: 1
      1235: 1
      1241: 1
      1246: q+1
      1247: q
      1248: q
      1249: q+1
      1250: 1
      1255: q+1
      1259: 1
      1260: 1
      1263: q+1
      1267: 1
      1269: 1
      1274: q
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1390: q
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1412: q+1
      1425: 1
      1434: 1
      1437: 1
      1440: 1
      1443: 1
      1445: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1469: 1
      1475: 1
      1477: 1
      1483: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1520: 1
      1540: 1
      1551: 1
      1597: 1
      1602: 1
      1618: 1
      1640: 1
      1648: 1
      1653: 1
      1656: 1
      1660: 1
      1666: 1
      1670: 1
      1674: 1
      1735: 1
      1772: 1
      1775: 1
      1826: 1
      1832: 1
      1917: 1

1918:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: q^3+6q^2+4q+1
        23: q^3+6q^2+4q+1
        24: 3q^3+4q^2+4q+1
        25: 3q^3+7q^2+4q+1
        26: 3q^3+7q^2+4q+1
        27: q^4+4q^3+5q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+4q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 2q^3+5q^2+4q+1
        36: q^3+6q^2+4q+1
        37: q^3+4q^2+3q+1
        38: 2q^2+q
        39: q^3+4q^2+3q+1
        40: 2q^2+q
        41: 2q^3+3q^2+3q+1
        42: q^3+q^2+q
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+6q^2+4q+1
        53: q^3+6q^2+4q+1
        54: 3q^3+4q^2+4q+1
        55: 3q^3+7q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: q^4+4q^3+5q^2+4q+1
        58: 3q^2+2q+1
        59: 2q^2+2q
        60: q^3+4q^2+3q+1
        61: 2q^2+q
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+3q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: q^3+6q^2+4q+1
        73: 5q^2+4q+1
        74: q^3+4q^2+3q+1
        75: 2q^2+q
        76: q^3+4q^2+3q+1
        77: 2q^2+q
        78: 2q^3+3q^2+3q+1
        79: q^3+q^2+q
        80: q^3+4q^2+4q+1
        81: 3q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+4q^2+4q+1
        84: 2q^3+5q^2+4q+1
        85: 4q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 2q^3+5q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: 4q^2+4q+1
        95: 4q^2+4q+1
        96: 2q^3+3q^2+3q+1
        97: q^3+6q^2+4q+1
        98: q^3+6q^2+4q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: 2q^2+2q+1
       104: q^2+q
       105: q^2
       106: q^2+q
       107: q^3+4q^2+3q+1
       108: 2q^2+q
       109: 3q^2+2q+1
       110: 2q^2+2q
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+3q^2+3q+1
       116: q^2+q
       117: q^2+2q+1
       118: 2q
       119: 2q^2+3q+1
       120: q
       121: q^3+3q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       127: 2q^2+3q+1
       129: 2q^2+3q+1
       131: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 4q^2+4q+1
       136: 3q^2+4q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 4q^2+4q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 3q^2+3q+1
       145: q^3+6q^2+4q+1
       146: 2q^3+5q^2+4q+1
       147: q^3+6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: q^3+4q^2+3q+1
       152: 2q^2+q
       153: q^3+4q^2+3q+1
       154: 2q^2+q
       155: 2q^3+3q^2+3q+1
       156: q^3+q^2+q
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: 2q^2+3q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^3+4q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: 2q^2+2q+1
       170: q^2+q
       171: q^2
       172: q^2+q
       173: q^2+2q+1
       174: q
       176: q
       177: q^2+2q+1
       179: 2q^2+3q+1
       181: 2q^2+3q+1
       183: 2q^2+3q+1
       184: q
       185: q^2+2q+1
       186: 2q
       187: 2q^2+3q+1
       188: q^2+q
       189: q^3+3q^2+3q+1
       190: q^2+q
       191: q^2+2q+1
       192: 2q
       193: 2q^2+3q+1
       195: 2q^2+2q+1
       196: 2q^2+2q
       197: q^2+2q+1
       198: q^2+q
       199: 2q^2+3q+1
       200: q
       201: q^3+4q^2+3q+1
       202: 2q^2+q
       203: 3q^2+2q+1
       204: 2q^2+2q
       205: 3q^2+3q+1
       206: 2q^2+q
       207: 2q^2+3q+1
       208: q^2+q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+3q^2+3q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 4q^2+4q+1
       223: 3q^2+3q+1
       224: 3q^2+4q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 4q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+4q+1
       231: 3q^2+3q+1
       232: 2q^2+4q+1
       233: 3q^2+3q+1
       234: 4q^2+4q+1
       235: 3q^2+4q+1
       236: 2q^2+3q+1
       237: 2q^2+3q+1
       239: 2q^2+3q+1
       241: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 2q^2+3q+1
       245: 4q^2+4q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: 2q^2+3q+1
       253: 4q^2+4q+1
       254: 4q^2+4q+1
       255: q^3+4q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       259: q^2+2q+1
       262: q^2+q
       263: q^2+2q+1
       264: q
       266: q
       267: q^2+2q+1
       268: q^2+q
       271: 2q^2+2q+1
       272: q^2
       273: q^2+q
       274: q^2+q
       275: q^2+2q+1
       276: q
       278: q
       279: 2q+1
       281: q+1
       283: q^2+2q+1
       285: q+1
       286: q
       287: q^2+2q+1
       289: 2q+1
       291: q^2+2q+1
       293: 2q^2+3q+1
       294: q
       295: q^2+2q+1
       296: 2q
       297: 2q^2+3q+1
       298: q^2+q
       299: 3q+1
       301: q^2+2q+1
       303: 2q+1
       304: 2q
       305: 2q+1
       306: q
       307: 2q^2+3q+1
       308: q
       309: q^2+2q+1
       310: 2q
       311: 2q^2+3q+1
       313: 2q^2+3q+1
       314: q^2+q
       315: q^2+2q+1
       317: 2q^2+3q+1
       319: 2q^2+3q+1
       321: 2q^2+2q+1
       322: 2q^2+2q
       323: q^2+2q+1
       324: q^2+q
       325: q^3+3q^2+3q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: 3q+1
       345: 4q+1
       346: q^2+3q+1
       347: 3q+1
       348: 2q+1
       349: q^2+4q+1
       350: q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: 3q^2+3q+1
       355: 4q^2+4q+1
       356: 3q^2+3q+1
       357: 3q^2+4q+1
       358: 2q^2+3q+1
       359: 4q^2+4q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: 3q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       377: q+1
       381: q+1
       384: q
       385: q^2+2q+1
       386: q
       388: q
       389: q^2+2q+1
       393: 2q+1
       394: q
       397: q^2+2q+1
       399: q^2+q
       401: q^2+2q+1
       403: q
       404: q
       405: q^2+2q+1
       407: q^2+q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q^2+2q+1
       421: q+1
       422: q
       423: q^2+2q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       429: 2q+1
       431: q+1
       432: q
       433: q+1
       435: q+1
       437: 3q+1
       439: 2q+1
       440: 2q
       441: 2q+1
       442: q
       443: 2q^2+3q+1
       445: q^2+2q+1
       447: q^2+2q+1
       449: q+1
       450: q
       451: q^2+2q+1
       453: 2q^2+3q+1
       454: q
       455: 2q+1
       457: q^2+2q+1
       458: 2q
       459: 2q^2+3q+1
       460: q^2+q
       461: 2q^2+2q+1
       462: 2q^2+2q
       463: 2q^2+3q+1
       465: 2q+1
       467: q+1
       469: q^2+2q+1
       471: 3q+1
       473: 2q+1
       474: 2q
       475: 2q+1
       476: q
       477: q^2+2q+1
       479: q^2+2q+1
       480: q^2+q
       481: q^2+3q+1
       482: 3q+1
       483: 2q^2+3q+1
       484: 4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+3q+1
       492: 3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: 3q+1
       497: q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: 2q^2+3q+1
       501: q^2+4q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: 3q+1
       512: 2q+1
       513: q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       521: 1
       525: q+1
       528: q
       529: q+1
       533: q+1
       537: q+1
       541: 2q+1
       542: q
       545: q^2+2q+1
       549: q+1
       553: q+1
       555: q
       557: q^2+2q+1
       559: q
       560: q
       561: q^2+2q+1
       563: q^2+q
       565: 2q+1
       566: q
       569: q^2+2q+1
       573: q^2+2q+1
       574: q^2+q
       577: q^2+2q+1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+2q+1
       591: q+1
       592: q
       593: 2q+1
       595: q+1
       596: q
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       603: 2q+1
       605: 1
       607: q+1
       608: q
       609: q+1
       611: q+1
       613: q+1
       615: 3q+1
       617: q+1
       619: q^2+2q+1
       621: q+1
       622: q
       623: q+1
       625: q^2+2q+1
       627: 2q+1
       629: q^2+2q+1
       631: 2q+1
       632: 2q
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: 2q+1
       643: q+1
       644: q
       645: q+1
       647: 3q+1
       649: 2q+1
       650: 2q
       651: q+1
       653: 2q+1
       654: q
       655: 2q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 3q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: 2
       675: q+1
       676: 3q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: q+2
       681: q^2+3q+1
       682: 3q+1
       683: 2q^2+3q+1
       684: q^2+4q+1
       685: q^2+3q+1
       686: 3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       693: q^2+2q+1
       705: 1
       709: 1
       713: q+1
       717: q+1
       721: 1
       725: q+1
       729: q+1
       733: q+1
       737: 1
       741: q+1
       745: q+1
       747: q
       749: q+1
       751: q
       753: q+1
       757: q+1
       761: 2q+1
       763: q
       765: 2q+1
       766: q
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: 2q+1
       787: q+1
       788: q
       789: 2q+1
       791: q+1
       793: 2
       795: 2
       797: 1
       799: 1
       801: q+1
       805: 2q+1
       807: q+1
       808: q
       809: 1
       811: q+1
       813: q+1
       815: 3q+1
       817: 1
       818: 1
       819: q+2
       821: q+1
       823: q+1
       825: q^2+2q+1
       827: q+1
       828: q
       829: 2q+1
       831: q+1
       832: q
       833: q+1
       835: q^2+2q+1
       837: 2q+1
       839: 2q+1
       840: 2q
       841: q+1
       843: 1
       844: 1
       845: 2q+1
       847: q+1
       848: q
       849: 1
       851: q+1
       853: q+1
       855: q+1
       857: 2q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: 2
       870: 2
       871: q+1
       872: 2q+1
       873: q+2
       874: q+2
       875: 3q+1
       876: q^2+3q+1
       877: q+1
       878: 3q+1
       879: 2q+1
       880: 2q+1
       884: q+1
       896: 1
       900: 1
       904: 1
       908: q+1
       912: 1
       916: 2
       920: 1
       928: q+1
       932: q+1
       936: 1
       940: 1
       942: 1
       944: 1
       948: q+1
       952: q+1
       956: q+1
       958: q
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: q+1
       978: q+1
       982: q+1
       988: 2q+1
       989: q
       992: 2
       994: 2
       996: q+2
       998: 1
       999: 1
      1000: 2
      1002: q+1
      1004: 2q+1
      1006: q+1
      1007: q
      1008: q+1
      1010: 1
      1012: 1
      1013: 1
      1014: 2
      1016: 2
      1018: 1
      1020: 2
      1022: 1
      1024: 1
      1026: q+1
      1030: q+2
      1032: 1
      1033: 1
      1034: q+1
      1036: q+2
      1038: q+1
      1040: 2q+1
      1042: q+1
      1044: q+1
      1045: q
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: 2q+1
      1058: q+1
      1059: q
      1060: 1
      1062: q+1
      1064: q+1
      1074: 2
      1076: 1
      1077: 2
      1078: q+1
      1080: 2
      1081: q+2
      1082: 3q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1086: 1
      1089: 1
      1098: q+1
      1110: 1
      1114: 1
      1116: 1
      1118: 1
      1122: 2
      1126: 1
      1130: 1
      1131: 1
      1134: q+1
      1138: 1
      1141: 1
      1144: 2
      1148: 1
      1156: 1
      1164: 1
      1166: 1
      1168: 1
      1172: 1
      1176: 1
      1180: q+1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1198: 1
      1206: q+1
      1214: 2
      1216: 1
      1217: 1
      1218: 2
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1230: 1
      1234: 1
      1236: 2
      1238: 1
      1240: q+1
      1248: 2
      1250: 1
      1251: 1
      1252: q+2
      1254: 2
      1256: q+1
      1258: 2q+1
      1260: q+1
      1261: q
      1264: 1
      1266: 1
      1268: q+1
      1272: 1
      1274: 2
      1276: q+1
      1278: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1293: 1
      1302: 1
      1305: 1
      1314: 1
      1316: 1
      1318: 2
      1322: 1
      1326: 1
      1327: 1
      1330: 1
      1334: 1
      1337: 1
      1352: 1
      1356: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1388: 2
      1392: 1
      1396: 1
      1397: 1
      1400: q+1
      1414: 1
      1422: 1
      1430: 1
      1433: 1
      1446: 1
      1448: 1
      1454: 1
      1456: 2
      1460: 1
      1461: 1
      1462: 2
      1464: 1
      1468: 1
      1470: 1
      1472: 2
      1474: 1
      1476: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1489: 1
      1492: 1
      1513: 1
      1516: 1
      1559: 1
      1567: 1
      1583: 1
      1585: 1
      1587: 2
      1591: 1
      1595: 1
      1596: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1634: 1
      1641: 1
      1657: 1
      1661: 1
      1665: 1
      1671: 1
      1673: 1
      1699: 1
      1702: 1
      1777: 1
      1781: 1
      1789: 1
      1815: 1
      1821: 1
      1918: 1

1919:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: q^3+6q^2+4q+1
        23: q^3+6q^2+4q+1
        24: 3q^3+4q^2+4q+1
        25: 3q^3+7q^2+4q+1
        26: 3q^3+7q^2+4q+1
        27: q^4+4q^3+5q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+4q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 2q^3+5q^2+4q+1
        36: q^3+6q^2+4q+1
        37: 2q^2+q
        38: q^3+4q^2+3q+1
        39: 2q^2+q
        40: q^3+4q^2+3q+1
        41: q^3+q^2+q
        42: 2q^3+3q^2+3q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+6q^2+4q+1
        53: q^3+6q^2+4q+1
        54: 3q^3+4q^2+4q+1
        55: 3q^3+7q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: q^4+4q^3+5q^2+4q+1
        58: 2q^2+2q
        59: 3q^2+2q+1
        60: q^3+4q^2+3q+1
        61: 2q^2+q
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: q^2+q
        65: q^3+3q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: q^3+6q^2+4q+1
        73: 5q^2+4q+1
        74: 2q^2+q
        75: q^3+4q^2+3q+1
        76: 2q^2+q
        77: q^3+4q^2+3q+1
        78: q^3+q^2+q
        79: 2q^3+3q^2+3q+1
        80: q^3+4q^2+4q+1
        81: 3q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+4q^2+4q+1
        84: 2q^3+5q^2+4q+1
        85: 4q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 2q^3+5q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: 4q^2+4q+1
        95: 4q^2+4q+1
        96: 2q^3+3q^2+3q+1
        97: q^3+6q^2+4q+1
        98: q^3+6q^2+4q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2+q
       104: 2q^2+2q+1
       105: q^2+q
       106: q^2
       107: q^3+4q^2+3q+1
       108: 2q^2+q
       109: 2q^2+2q
       110: 3q^2+2q+1
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: q^2+q
       116: q^3+3q^2+3q+1
       117: 2q
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: q
       121: q^2+q
       122: q^3+3q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       128: 2q^2+3q+1
       130: 2q^2+3q+1
       132: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 4q^2+4q+1
       136: 3q^2+4q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 4q^2+4q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 3q^2+3q+1
       145: q^3+6q^2+4q+1
       146: 2q^3+5q^2+4q+1
       147: q^3+6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: 2q^2+q
       152: q^3+4q^2+3q+1
       153: 2q^2+q
       154: q^3+4q^2+3q+1
       155: q^3+q^2+q
       156: 2q^3+3q^2+3q+1
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: 2q^2+3q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^3+4q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       170: 2q^2+2q+1
       171: q^2+q
       172: q^2
       173: q
       174: q^2+2q+1
       175: q
       178: q^2+2q+1
       180: 2q^2+3q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: q
       185: 2q
       186: q^2+2q+1
       187: q^2+q
       188: 2q^2+3q+1
       189: q^2+q
       190: q^3+3q^2+3q+1
       191: 2q
       192: q^2+2q+1
       193: 2q^2+3q+1
       195: 2q^2+2q
       196: 2q^2+2q+1
       197: q^2+q
       198: q^2+2q+1
       199: 2q^2+3q+1
       200: q
       201: q^3+4q^2+3q+1
       202: 2q^2+q
       203: 2q^2+2q
       204: 3q^2+2q+1
       205: 2q^2+q
       206: 3q^2+3q+1
       207: q^2+q
       208: 2q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: q^2+q
       212: q^3+3q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 4q^2+4q+1
       223: 3q^2+3q+1
       224: 3q^2+4q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 4q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+4q+1
       231: 3q^2+3q+1
       232: 2q^2+4q+1
       233: 3q^2+3q+1
       234: 4q^2+4q+1
       235: 3q^2+4q+1
       236: 2q^2+3q+1
       238: 2q^2+3q+1
       240: 2q^2+3q+1
       242: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 2q^2+3q+1
       245: 4q^2+4q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: 2q^2+3q+1
       253: 4q^2+4q+1
       254: 4q^2+4q+1
       255: q^3+4q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       260: q^2+2q+1
       261: q^2+q
       263: q
       264: q^2+2q+1
       265: q
       267: q^2+q
       268: q^2+2q+1
       271: q^2+q
       272: q^2+q
       273: q^2
       274: 2q^2+2q+1
       275: q
       276: q^2+2q+1
       277: q
       280: 2q+1
       282: q+1
       283: q^2+2q+1
       285: q
       286: q+1
       288: q^2+2q+1
       290: 2q+1
       292: q^2+2q+1
       293: 2q^2+3q+1
       294: q
       295: 2q
       296: q^2+2q+1
       297: q^2+q
       298: 2q^2+3q+1
       299: 3q+1
       302: q^2+2q+1
       303: 2q
       304: 2q+1
       305: q
       306: 2q+1
       307: 2q^2+3q+1
       308: q
       309: 2q
       310: q^2+2q+1
       312: 2q^2+3q+1
       313: q^2+q
       314: 2q^2+3q+1
       316: q^2+2q+1
       318: 2q^2+3q+1
       319: 2q^2+3q+1
       321: 2q^2+2q
       322: 2q^2+2q+1
       323: q^2+q
       324: q^2+2q+1
       325: q^2+q
       326: q^3+3q^2+3q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: 3q+1
       345: 4q+1
       346: q^2+3q+1
       347: 3q+1
       348: 2q+1
       349: q^2+4q+1
       350: q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: 3q^2+3q+1
       355: 4q^2+4q+1
       356: 3q^2+3q+1
       357: 3q^2+4q+1
       358: 2q^2+3q+1
       359: 4q^2+4q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: 3q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       378: q+1
       382: q+1
       383: q
       385: q
       386: q^2+2q+1
       387: q
       390: q^2+2q+1
       393: q
       394: 2q+1
       398: q^2+q
       400: q^2+2q+1
       401: q
       402: q
       403: q^2+2q+1
       405: q^2+q
       407: q^2+2q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q^2+2q+1
       421: q
       422: q+1
       424: q^2+2q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       429: 2q+1
       431: q
       432: q+1
       434: q+1
       436: q+1
       437: 3q+1
       439: 2q
       440: 2q+1
       441: q
       442: 2q+1
       443: 2q^2+3q+1
       446: q^2+2q+1
       447: q^2+2q+1
       449: q
       450: q+1
       452: q^2+2q+1
       453: 2q^2+3q+1
       454: q
       456: 2q+1
       457: 2q
       458: q^2+2q+1
       459: q^2+q
       460: 2q^2+3q+1
       461: 2q^2+2q
       462: 2q^2+2q+1
       464: 2q^2+3q+1
       466: 2q+1
       468: q+1
       470: q^2+2q+1
       471: 3q+1
       473: 2q
       474: 2q+1
       475: q
       476: 2q+1
       478: q^2+2q+1
       479: q^2+q
       480: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: 2q^2+3q+1
       484: 4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+3q+1
       492: 3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: 3q+1
       497: q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: 2q^2+3q+1
       501: q^2+4q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: 3q+1
       512: 2q+1
       513: q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       522: 1
       526: q+1
       527: q
       530: q+1
       534: q+1
       538: q+1
       541: q
       542: 2q+1
       546: q^2+2q+1
       551: q+1
       554: q
       556: q+1
       557: q
       558: q
       560: q^2+2q+1
       562: q^2+q
       564: q^2+2q+1
       565: q
       566: 2q+1
       571: q^2+2q+1
       573: q^2+q
       574: q^2+2q+1
       581: q^2+2q+1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+2q+1
       591: q
       592: q+1
       593: 2q+1
       595: q
       596: q+1
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       603: 2q+1
       606: 1
       607: q
       608: q+1
       610: q+1
       612: q+1
       614: q+1
       615: 3q+1
       618: q+1
       619: q^2+2q+1
       621: q
       622: q+1
       624: q+1
       626: q^2+2q+1
       628: 2q+1
       630: q^2+2q+1
       631: 2q
       632: 2q+1
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: 2q+1
       643: q
       644: q+1
       646: q+1
       647: 3q+1
       649: 2q
       650: 2q+1
       652: q+1
       653: q
       654: 2q+1
       655: q
       656: 2q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 3q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: 2
       675: q+1
       676: 3q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: q+2
       681: q^2+3q+1
       682: 3q+1
       683: 2q^2+3q+1
       684: q^2+4q+1
       685: q^2+3q+1
       686: 3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       699: q^2+2q+1
       706: 1
       710: 1
       715: q+1
       718: q+1
       722: 1
       726: q+1
       730: q+1
       734: q+1
       740: 1
       744: q+1
       746: q
       748: q+1
       750: q
       752: q+1
       754: q+1
       759: q+1
       761: q
       763: 2q+1
       765: q
       766: 2q+1
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: 2q+1
       787: q
       788: q+1
       790: 2q+1
       792: q+1
       793: 2
       796: 2
       798: 1
       800: 1
       801: q+1
       805: 2q+1
       807: q
       808: q+1
       810: 1
       812: q+1
       814: q+1
       815: 3q+1
       817: 1
       818: 1
       820: q+2
       822: q+1
       824: q+1
       825: q^2+2q+1
       827: q
       828: q+1
       829: 2q+1
       831: q
       832: q+1
       834: q+1
       836: q^2+2q+1
       838: 2q+1
       839: 2q
       840: 2q+1
       842: q+1
       843: 1
       844: 1
       845: 2q+1
       847: q
       848: q+1
       850: 1
       852: q+1
       854: q+1
       856: q+1
       857: q
       858: 2q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: 2
       870: 2
       871: q+1
       872: 2q+1
       873: q+2
       874: q+2
       875: 3q+1
       876: q^2+3q+1
       877: q+1
       878: 3q+1
       879: 2q+1
       880: 2q+1
       890: q+1
       897: 1
       903: 1
       905: 1
       909: q+1
       913: 1
       917: 2
       921: 1
       929: q+1
       933: q+1
       939: 1
       941: 1
       943: 1
       947: 1
       951: q+1
       953: q+1
       957: q
       959: q+1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: q+1
       980: q+1
       986: q+1
       988: q
       989: 2q+1
       993: 2
       995: 2
       997: q+2
       998: 1
       999: 1
      1000: 2
      1003: q+1
      1004: 2q+1
      1006: q
      1007: q+1
      1009: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: 2
      1016: 2
      1019: 1
      1021: 2
      1023: 1
      1025: 1
      1026: q+1
      1031: q+2
      1032: 1
      1033: 1
      1035: q+1
      1037: q+2
      1039: q+1
      1040: 2q+1
      1043: q+1
      1044: q
      1045: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: 2q+1
      1058: q
      1059: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: 2
      1076: 1
      1077: 2
      1078: q+1
      1080: 2
      1081: q+2
      1082: 3q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1087: 1
      1092: 1
      1104: q+1
      1113: 1
      1115: 1
      1117: 1
      1119: 1
      1123: 2
      1128: 1
      1130: 1
      1131: 1
      1136: q+1
      1139: 1
      1142: 1
      1145: 2
      1149: 1
      1157: 1
      1165: 1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: q+1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1200: 1
      1207: q+1
      1215: 2
      1216: 1
      1217: 1
      1218: 2
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1231: 1
      1234: 1
      1237: 2
      1239: 1
      1240: q+1
      1249: 2
      1250: 1
      1251: 1
      1253: q+2
      1254: 2
      1257: q+1
      1258: 2q+1
      1260: q
      1261: q+1
      1265: 1
      1267: 1
      1268: q+1
      1273: 1
      1275: 2
      1277: q+1
      1279: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1296: 1
      1303: 1
      1308: 1
      1315: 1
      1317: 1
      1319: 2
      1324: 1
      1326: 1
      1327: 1
      1332: 1
      1335: 1
      1338: 1
      1353: 1
      1357: 1
      1379: 1
      1381: 1
      1383: 1
      1385: 1
      1389: 2
      1394: 1
      1396: 1
      1397: 1
      1402: q+1
      1416: 1
      1423: 1
      1431: 1
      1434: 1
      1447: 1
      1449: 1
      1454: 1
      1457: 2
      1460: 1
      1461: 1
      1462: 2
      1465: 1
      1468: 1
      1471: 1
      1473: 2
      1475: 1
      1476: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1490: 1
      1495: 1
      1514: 1
      1519: 1
      1561: 1
      1568: 1
      1584: 1
      1586: 1
      1588: 2
      1593: 1
      1595: 1
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1632: 1
      1635: 1
      1642: 1
      1657: 1
      1662: 1
      1665: 1
      1672: 1
      1673: 1
      1700: 1
      1705: 1
      1779: 1
      1782: 1
      1790: 1
      1816: 1
      1821: 1
      1919: 1

1920:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: q^3+6q^2+4q+1
        23: q^3+6q^2+4q+1
        24: 3q^3+4q^2+4q+1
        25: 3q^3+7q^2+4q+1
        26: 3q^3+7q^2+4q+1
        27: q^4+4q^3+5q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+4q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 2q^3+5q^2+4q+1
        36: q^3+6q^2+4q+1
        37: q^3+4q^2+3q+1
        38: 2q^2+q
        39: q^3+4q^2+3q+1
        40: 2q^2+q
        41: 2q^3+3q^2+3q+1
        42: q^3+q^2+q
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+6q^2+4q+1
        53: q^3+6q^2+4q+1
        54: 3q^3+4q^2+4q+1
        55: 3q^3+7q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: q^4+4q^3+5q^2+4q+1
        58: 2q^2+2q
        59: 3q^2+2q+1
        60: 2q^2+q
        61: q^3+4q^2+3q+1
        62: q^3+4q^2+3q+1
        63: 2q^2+q
        64: q^3+3q^2+3q+1
        65: q^2+q
        66: 3q^2+3q+1
        67: 2q^2+q
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: q^3+6q^2+4q+1
        73: 5q^2+4q+1
        74: q^3+4q^2+3q+1
        75: 2q^2+q
        76: q^3+4q^2+3q+1
        77: 2q^2+q
        78: 2q^3+3q^2+3q+1
        79: q^3+q^2+q
        80: q^3+4q^2+4q+1
        81: 3q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+4q^2+4q+1
        84: 2q^3+5q^2+4q+1
        85: 4q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 2q^3+5q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: 4q^2+4q+1
        95: 4q^2+4q+1
        96: 2q^3+3q^2+3q+1
        97: q^3+6q^2+4q+1
        98: q^3+6q^2+4q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2+q
       104: q^2
       105: q^2+q
       106: 2q^2+2q+1
       107: 2q^2+q
       108: q^3+4q^2+3q+1
       109: 2q^2+2q
       110: 3q^2+2q+1
       111: 3q^2+3q+1
       112: 2q^2+q
       113: q^3+4q^2+3q+1
       114: 2q^2+q
       115: q^3+3q^2+3q+1
       116: q^2+q
       117: 2q
       118: q^2+2q+1
       119: q
       120: 2q^2+3q+1
       121: q^3+3q^2+3q+1
       122: q^2+q
       123: 2q^2+3q+1
       124: q^2+q
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       127: 2q^2+3q+1
       129: 2q^2+3q+1
       131: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 4q^2+4q+1
       136: 3q^2+4q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 4q^2+4q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 3q^2+3q+1
       145: q^3+6q^2+4q+1
       146: 2q^3+5q^2+4q+1
       147: q^3+6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: q^3+4q^2+3q+1
       152: 2q^2+q
       153: q^3+4q^2+3q+1
       154: 2q^2+q
       155: 2q^3+3q^2+3q+1
       156: q^3+q^2+q
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: 2q^2+3q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^3+4q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2+q
       170: q^2
       171: q^2+q
       172: 2q^2+2q+1
       173: q
       175: q
       176: q^2+2q+1
       177: q^2+2q+1
       179: 2q^2+3q+1
       181: 2q^2+3q+1
       183: q
       184: 2q^2+3q+1
       185: 2q
       186: q^2+2q+1
       187: 2q^2+3q+1
       188: q^2+q
       189: q^3+3q^2+3q+1
       190: q^2+q
       191: 2q
       192: q^2+2q+1
       194: 2q^2+3q+1
       195: 2q^2+2q
       196: 2q^2+2q+1
       197: q^2+2q+1
       198: q^2+q
       199: q
       200: 2q^2+3q+1
       201: 2q^2+q
       202: q^3+4q^2+3q+1
       203: 2q^2+2q
       204: 3q^2+2q+1
       205: 3q^2+3q+1
       206: 2q^2+q
       207: 2q^2+3q+1
       208: q^2+q
       209: q^3+4q^2+3q+1
       210: 2q^2+q
       211: q^3+3q^2+3q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 4q^2+4q+1
       223: 3q^2+3q+1
       224: 3q^2+4q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 4q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+4q+1
       231: 3q^2+3q+1
       232: 2q^2+4q+1
       233: 3q^2+3q+1
       234: 4q^2+4q+1
       235: 3q^2+4q+1
       236: 2q^2+3q+1
       237: 2q^2+3q+1
       239: 2q^2+3q+1
       241: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 2q^2+3q+1
       245: 4q^2+4q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: 2q^2+3q+1
       253: 4q^2+4q+1
       254: 4q^2+4q+1
       255: q^3+4q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       259: q^2+q
       262: q^2+2q+1
       263: q
       265: q
       266: q^2+2q+1
       269: q^2+2q+1
       270: q^2+q
       271: q^2+q
       272: q^2+q
       273: 2q^2+2q+1
       274: q^2
       275: q
       277: q
       278: q^2+2q+1
       279: 2q+1
       281: q+1
       284: q^2+2q+1
       285: q
       286: q+1
       287: q^2+2q+1
       289: 2q+1
       291: q^2+2q+1
       293: q
       294: 2q^2+3q+1
       295: 2q
       296: q^2+2q+1
       297: 2q^2+3q+1
       298: q^2+q
       300: 3q+1
       301: q^2+2q+1
       303: 2q
       304: 2q+1
       305: 2q+1
       306: q
       307: q
       308: 2q^2+3q+1
       309: 2q
       310: q^2+2q+1
       311: 2q^2+3q+1
       313: 2q^2+3q+1
       314: q^2+q
       315: q^2+2q+1
       317: 2q^2+3q+1
       320: 2q^2+3q+1
       321: 2q^2+2q
       322: 2q^2+2q+1
       323: q^2+2q+1
       324: q^2+q
       325: q^3+3q^2+3q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       338: 2q^2+3q+1
       340: 2q^2+3q+1
       342: q^3+2q^2+2q+1
       344: 3q+1
       345: 4q+1
       346: q^2+3q+1
       347: 3q+1
       348: 2q+1
       349: q^2+4q+1
       350: q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: 3q^2+3q+1
       355: 4q^2+4q+1
       356: 3q^2+3q+1
       357: 3q^2+4q+1
       358: 2q^2+3q+1
       359: 4q^2+4q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: 3q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       380: q+1
       381: q
       384: q+1
       385: q
       387: q
       388: q^2+2q+1
       391: q^2+2q+1
       395: q
       396: 2q+1
       397: q^2+q
       399: q^2+2q+1
       401: q
       402: q
       404: q^2+2q+1
       406: q^2+2q+1
       408: q^2+q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: q^2+2q+1
       421: q
       422: q+1
       423: q^2+2q+1
       425: q^2+2q+1
       427: 2q^2+3q+1
       430: 2q+1
       431: q
       432: q+1
       433: q+1
       435: q+1
       438: 3q+1
       439: 2q
       440: 2q+1
       441: 2q+1
       442: q
       444: 2q^2+3q+1
       445: q^2+2q+1
       448: q^2+2q+1
       449: q
       450: q+1
       451: q^2+2q+1
       453: q
       454: 2q^2+3q+1
       455: 2q+1
       457: 2q
       458: q^2+2q+1
       459: 2q^2+3q+1
       460: q^2+q
       461: 2q^2+2q
       462: 2q^2+2q+1
       463: 2q^2+3q+1
       465: 2q+1
       467: q+1
       469: q^2+2q+1
       472: 3q+1
       473: 2q
       474: 2q+1
       475: 2q+1
       476: q
       477: q^2+2q+1
       479: q^2+2q+1
       480: q^2+q
       481: q^2+3q+1
       482: 3q+1
       483: 2q^2+3q+1
       484: 4q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+3q+1
       492: 3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: 3q+1
       497: q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: 2q^2+3q+1
       501: q^2+4q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: 3q+1
       512: 2q+1
       513: q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       524: 1
       525: q
       528: q+1
       532: q+1
       536: q+1
       539: q+1
       543: 2q+1
       544: q
       547: q^2+2q+1
       552: q+1
       553: q
       555: q+1
       557: q
       558: q
       559: q^2+2q+1
       561: q^2+q
       563: q^2+2q+1
       567: q
       568: 2q+1
       570: q^2+2q+1
       575: q^2+2q+1
       576: q^2+q
       577: q^2+2q+1
       583: q+1
       585: q+1
       587: q+1
       590: q^2+2q+1
       591: q
       592: q+1
       594: 2q+1
       595: q
       596: q+1
       597: q+1
       599: q^2+2q+1
       601: 2q+1
       604: 2q+1
       605: 1
       607: q
       608: q+1
       609: q+1
       611: q+1
       613: q+1
       616: 3q+1
       617: q+1
       620: q^2+2q+1
       621: q
       622: q+1
       623: q+1
       625: q^2+2q+1
       627: 2q+1
       629: q^2+2q+1
       631: 2q
       632: 2q+1
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: 2q+1
       643: q
       644: q+1
       645: q+1
       648: 3q+1
       649: 2q
       650: 2q+1
       651: q+1
       653: 2q+1
       654: q
       655: 2q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: 3q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: 2
       675: q+1
       676: 3q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: q+2
       681: q^2+3q+1
       682: 3q+1
       683: 2q^2+3q+1
       684: q^2+4q+1
       685: q^2+3q+1
       686: 3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       697: q^2+2q+1
       708: 1
       712: 1
       716: q+1
       720: q+1
       723: 1
       727: q+1
       731: q+1
       735: q+1
       739: 1
       743: q+1
       745: q
       747: q+1
       749: q
       751: q+1
       756: q+1
       758: q+1
       762: 2q+1
       764: q
       767: q
       768: 2q+1
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       786: 2q+1
       787: q
       788: q+1
       789: 2q+1
       791: q+1
       794: 2
       795: 2
       797: 1
       799: 1
       802: q+1
       806: 2q+1
       807: q
       808: q+1
       809: 1
       811: q+1
       813: q+1
       816: 3q+1
       817: 1
       818: 1
       819: q+2
       821: q+1
       823: q+1
       826: q^2+2q+1
       827: q
       828: q+1
       830: 2q+1
       831: q
       832: q+1
       833: q+1
       835: q^2+2q+1
       837: 2q+1
       839: 2q
       840: 2q+1
       841: q+1
       843: 1
       844: 1
       846: 2q+1
       847: q
       848: q+1
       849: 1
       851: q+1
       853: q+1
       855: q+1
       857: 2q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: 2
       870: 2
       871: q+1
       872: 2q+1
       873: q+2
       874: q+2
       875: 3q+1
       876: q^2+3q+1
       877: q+1
       878: 3q+1
       879: 2q+1
       880: 2q+1
       889: q+1
       899: 1
       902: 1
       906: 1
       911: q+1
       914: 1
       918: 2
       922: 1
       930: q+1
       934: q+1
       938: 1
       940: 1
       942: 1
       946: 1
       950: q+1
       955: q+1
       956: q
       958: q+1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: q+1
       979: q+1
       982: q+1
       990: q
       991: 2q+1
       992: 2
       994: 2
       996: q+2
       998: 1
       999: 1
      1001: 2
      1002: q+1
      1005: 2q+1
      1006: q
      1007: q+1
      1008: q+1
      1010: 1
      1012: 1
      1013: 1
      1014: 2
      1017: 2
      1018: 1
      1020: 2
      1022: 1
      1024: 1
      1027: q+1
      1030: q+2
      1032: 1
      1033: 1
      1034: q+1
      1036: q+2
      1038: q+1
      1041: 2q+1
      1042: q+1
      1044: q
      1045: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: 2q+1
      1058: q
      1059: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: 2
      1076: 1
      1077: 2
      1078: q+1
      1080: 2
      1081: q+2
      1082: 3q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1090: 1
      1091: 1
      1102: q+1
      1112: 1
      1114: 1
      1116: 1
      1120: 1
      1124: 2
      1127: 1
      1132: 1
      1133: 1
      1135: q+1
      1138: 1
      1141: 1
      1146: 2
      1150: 1
      1158: 1
      1164: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: q+1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1199: 1
      1208: q+1
      1214: 2
      1216: 1
      1217: 1
      1219: 2
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1230: 1
      1235: 1
      1236: 2
      1238: 1
      1241: q+1
      1248: 2
      1250: 1
      1251: 1
      1252: q+2
      1255: 2
      1256: q+1
      1259: 2q+1
      1260: q
      1261: q+1
      1264: 1
      1266: 1
      1269: q+1
      1272: 1
      1274: 2
      1276: q+1
      1278: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1294: 1
      1295: 1
      1306: 1
      1307: 1
      1314: 1
      1316: 1
      1320: 2
      1323: 1
      1328: 1
      1329: 1
      1331: 1
      1334: 1
      1337: 1
      1354: 1
      1358: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1390: 2
      1393: 1
      1398: 1
      1399: 1
      1401: q+1
      1415: 1
      1424: 1
      1430: 1
      1433: 1
      1446: 1
      1448: 1
      1455: 1
      1456: 2
      1460: 1
      1461: 1
      1463: 2
      1464: 1
      1469: 1
      1470: 1
      1472: 2
      1474: 1
      1477: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1493: 1
      1494: 1
      1517: 1
      1518: 1
      1560: 1
      1569: 1
      1583: 1
      1585: 1
      1589: 2
      1592: 1
      1597: 1
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1634: 1
      1641: 1
      1658: 1
      1661: 1
      1666: 1
      1671: 1
      1673: 1
      1703: 1
      1704: 1
      1778: 1
      1783: 1
      1791: 1
      1815: 1
      1822: 1
      1920: 1

1921:    0: 3q^3+7q^2+4q+1
         1: 3q^3+7q^2+4q+1
         2: q^4+4q^3+5q^2+4q+1
         3: 3q^3+7q^2+4q+1
         4: 3q^3+7q^2+4q+1
         5: 3q^3+7q^2+4q+1
         6: 3q^3+7q^2+4q+1
         7: q^4+4q^3+5q^2+4q+1
         8: q^4+4q^3+5q^2+4q+1
         9: q^5+2q^4+4q^3+4q^2+3q+1
        10: 3q^3+7q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^4+3q^3+4q^2+3q+1
        19: 3q^3+7q^2+4q+1
        20: 3q^3+7q^2+4q+1
        21: q^4+4q^3+5q^2+4q+1
        22: q^3+6q^2+4q+1
        23: q^3+6q^2+4q+1
        24: 3q^3+4q^2+4q+1
        25: 3q^3+7q^2+4q+1
        26: 3q^3+7q^2+4q+1
        27: q^4+4q^3+5q^2+4q+1
        28: q^3+6q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: q^3+6q^2+4q+1
        32: q^3+4q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^3+7q^2+4q+1
        35: 2q^3+5q^2+4q+1
        36: q^3+6q^2+4q+1
        37: 2q^2+q
        38: q^3+4q^2+3q+1
        39: 2q^2+q
        40: q^3+4q^2+3q+1
        41: q^3+q^2+q
        42: 2q^3+3q^2+3q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 4q^2+4q+1
        47: 4q^2+4q+1
        48: q^3+4q^2+3q+1
        49: q^3+6q^2+4q+1
        50: q^3+6q^2+4q+1
        51: q^4+3q^3+4q^2+3q+1
        52: q^3+6q^2+4q+1
        53: q^3+6q^2+4q+1
        54: 3q^3+4q^2+4q+1
        55: 3q^3+7q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: q^4+4q^3+5q^2+4q+1
        58: 3q^2+2q+1
        59: 2q^2+2q
        60: 2q^2+q
        61: q^3+4q^2+3q+1
        62: 2q^2+q
        63: q^3+4q^2+3q+1
        64: q^2+q
        65: q^3+3q^2+3q+1
        66: 2q^2+q
        67: 3q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+3q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+4q+1
        72: q^3+6q^2+4q+1
        73: 5q^2+4q+1
        74: 2q^2+q
        75: q^3+4q^2+3q+1
        76: 2q^2+q
        77: q^3+4q^2+3q+1
        78: q^3+q^2+q
        79: 2q^3+3q^2+3q+1
        80: q^3+4q^2+4q+1
        81: 3q^2+4q+1
        82: q^3+6q^2+4q+1
        83: q^3+4q^2+4q+1
        84: 2q^3+5q^2+4q+1
        85: 4q^2+4q+1
        86: 3q^3+7q^2+4q+1
        87: 2q^3+5q^2+4q+1
        88: 4q^2+4q+1
        89: 4q^2+4q+1
        90: q^3+4q^2+3q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: q^3+4q^2+3q+1
        94: 4q^2+4q+1
        95: 4q^2+4q+1
        96: 2q^3+3q^2+3q+1
        97: q^3+6q^2+4q+1
        98: q^3+6q^2+4q+1
        99: q^4+3q^3+4q^2+3q+1
       100: q^3+6q^2+4q+1
       101: q^3+6q^2+4q+1
       102: 3q^3+4q^2+4q+1
       103: q^2
       104: q^2+q
       105: 2q^2+2q+1
       106: q^2+q
       107: 2q^2+q
       108: q^3+4q^2+3q+1
       109: 3q^2+2q+1
       110: 2q^2+2q
       111: 2q^2+q
       112: 3q^2+3q+1
       113: 2q^2+q
       114: q^3+4q^2+3q+1
       115: q^2+q
       116: q^3+3q^2+3q+1
       117: q^2+2q+1
       118: 2q
       119: q
       120: 2q^2+3q+1
       121: q^2+q
       122: q^3+3q^2+3q+1
       123: q^2+q
       124: 2q^2+3q+1
       125: 2q^2+4q+1
       126: 3q^2+3q+1
       128: 2q^2+3q+1
       130: 2q^2+3q+1
       132: q^3+2q^2+2q+1
       133: 2q^2+4q+1
       134: 3q^2+3q+1
       135: 4q^2+4q+1
       136: 3q^2+4q+1
       137: 3q^2+4q+1
       138: 2q^2+3q+1
       139: 4q^2+4q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 3q^2+3q+1
       145: q^3+6q^2+4q+1
       146: 2q^3+5q^2+4q+1
       147: q^3+6q^2+4q+1
       148: 5q^2+4q+1
       149: q^3+6q^2+4q+1
       150: q^3+4q^2+4q+1
       151: 2q^2+q
       152: q^3+4q^2+3q+1
       153: 2q^2+q
       154: q^3+4q^2+3q+1
       155: q^3+q^2+q
       156: 2q^3+3q^2+3q+1
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: q^3+4q^2+3q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: 2q^2+3q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^3+4q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: 2q^3+3q^2+3q+1
       169: q^2
       170: q^2+q
       171: 2q^2+2q+1
       172: q^2+q
       174: q
       175: q^2+2q+1
       176: q
       178: q^2+2q+1
       180: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q
       184: 2q^2+3q+1
       185: q^2+2q+1
       186: 2q
       187: q^2+q
       188: 2q^2+3q+1
       189: q^2+q
       190: q^3+3q^2+3q+1
       191: q^2+2q+1
       192: 2q
       194: 2q^2+3q+1
       195: 2q^2+2q+1
       196: 2q^2+2q
       197: q^2+q
       198: q^2+2q+1
       199: q
       200: 2q^2+3q+1
       201: 2q^2+q
       202: q^3+4q^2+3q+1
       203: 3q^2+2q+1
       204: 2q^2+2q
       205: 2q^2+q
       206: 3q^2+3q+1
       207: q^2+q
       208: 2q^2+3q+1
       209: 2q^2+q
       210: q^3+4q^2+3q+1
       211: q^2+q
       212: q^3+3q^2+3q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: q^2+3q+1
       220: 2q^2+4q+1
       221: 3q^2+3q+1
       222: 4q^2+4q+1
       223: 3q^2+3q+1
       224: 3q^2+4q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 4q+1
       228: q^2+3q+1
       229: 3q+1
       230: q^2+4q+1
       231: 3q^2+3q+1
       232: 2q^2+4q+1
       233: 3q^2+3q+1
       234: 4q^2+4q+1
       235: 3q^2+4q+1
       236: 2q^2+3q+1
       238: 2q^2+3q+1
       240: 2q^2+3q+1
       242: q^3+2q^2+2q+1
       243: 4q^2+4q+1
       244: 2q^2+3q+1
       245: 4q^2+4q+1
       246: q^3+4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+3q^2+3q+1
       250: q^2+4q+1
       251: q^2+4q+1
       252: 2q^2+3q+1
       253: 4q^2+4q+1
       254: 4q^2+4q+1
       255: q^3+4q^2+3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q^2+3q+1
       260: q^2+q
       261: q^2+2q+1
       264: q
       265: q^2+2q+1
       266: q
       269: q^2+q
       270: q^2+2q+1
       271: q^2
       272: 2q^2+2q+1
       273: q^2+q
       274: q^2+q
       276: q
       277: q^2+2q+1
       278: q
       280: 2q+1
       282: q+1
       284: q^2+2q+1
       285: q+1
       286: q
       288: q^2+2q+1
       290: 2q+1
       292: q^2+2q+1
       293: q
       294: 2q^2+3q+1
       295: q^2+2q+1
       296: 2q
       297: q^2+q
       298: 2q^2+3q+1
       300: 3q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q
       305: q
       306: 2q+1
       307: q
       308: 2q^2+3q+1
       309: q^2+2q+1
       310: 2q
       312: 2q^2+3q+1
       313: q^2+q
       314: 2q^2+3q+1
       316: q^2+2q+1
       318: 2q^2+3q+1
       320: 2q^2+3q+1
       321: 2q^2+2q+1
       322: 2q^2+2q
       323: q^2+q
       324: q^2+2q+1
       325: q^2+q
       326: q^3+3q^2+3q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: q^2+3q+1
       334: 3q^2+3q+1
       335: 2q^2+3q+1
       336: 2q^2+3q+1
       337: 4q^2+4q+1
       339: 2q^2+3q+1
       341: 2q^2+3q+1
       343: q^3+2q^2+2q+1
       344: 3q+1
       345: 4q+1
       346: q^2+3q+1
       347: 3q+1
       348: 2q+1
       349: q^2+4q+1
       350: q^2+3q+1
       351: 2q^2+3q+1
       352: q^2+3q+1
       353: 2q^2+4q+1
       354: 3q^2+3q+1
       355: 4q^2+4q+1
       356: 3q^2+3q+1
       357: 3q^2+4q+1
       358: 2q^2+3q+1
       359: 4q^2+4q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: 2q^2+3q+1
       367: 4q+1
       368: q^2+3q+1
       369: 3q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+3q+1
       374: q^2+4q+1
       375: q^2+4q+1
       376: 2q^2+3q+1
       379: q+1
       382: q
       383: q+1
       386: q
       387: q^2+2q+1
       388: q
       392: q^2+2q+1
       395: 2q+1
       396: q
       398: q^2+2q+1
       400: q^2+q
       402: q^2+2q+1
       403: q
       404: q
       406: q^2+q
       408: q^2+2q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: q^2+2q+1
       421: q+1
       422: q
       424: q^2+2q+1
       426: q^2+2q+1
       428: 2q^2+3q+1
       430: 2q+1
       431: q+1
       432: q
       434: q+1
       436: q+1
       438: 3q+1
       439: 2q+1
       440: 2q
       441: q
       442: 2q+1
       444: 2q^2+3q+1
       446: q^2+2q+1
       448: q^2+2q+1
       449: q+1
       450: q
       452: q^2+2q+1
       453: q
       454: 2q^2+3q+1
       456: 2q+1
       457: q^2+2q+1
       458: 2q
       459: q^2+q
       460: 2q^2+3q+1
       461: 2q^2+2q+1
       462: 2q^2+2q
       464: 2q^2+3q+1
       466: 2q+1
       468: q+1
       470: q^2+2q+1
       472: 3q+1
       473: 2q+1
       474: 2q
       475: q
       476: 2q+1
       478: q^2+2q+1
       479: q^2+q
       480: q^2+2q+1
       481: q^2+3q+1
       482: 3q+1
       483: 2q^2+3q+1
       484: 4q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+3q+1
       492: 3q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: 3q+1
       497: q^2+3q+1
       498: 3q^2+3q+1
       499: 2q^2+3q+1
       500: 2q^2+3q+1
       501: q^2+4q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: 3q+1
       509: 4q+1
       510: q^2+3q+1
       511: 3q+1
       512: 2q+1
       513: q^2+4q+1
       514: q^2+3q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: 2q^2+3q+1
       523: 1
       526: q
       527: q+1
       531: q+1
       535: q+1
       540: q+1
       543: q
       544: 2q+1
       548: q^2+2q+1
       550: q+1
       554: q+1
       556: q
       558: q^2+2q+1
       559: q
       560: q
       562: q^2+2q+1
       564: q^2+q
       567: 2q+1
       568: q
       572: q^2+2q+1
       575: q^2+q
       576: q^2+2q+1
       581: q^2+2q+1
       584: q+1
       586: q+1
       588: q+1
       590: q^2+2q+1
       591: q+1
       592: q
       594: 2q+1
       595: q+1
       596: q
       598: q+1
       600: q^2+2q+1
       602: 2q+1
       604: 2q+1
       606: 1
       607: q+1
       608: q
       610: q+1
       612: q+1
       614: q+1
       616: 3q+1
       618: q+1
       620: q^2+2q+1
       621: q+1
       622: q
       624: q+1
       626: q^2+2q+1
       628: 2q+1
       630: q^2+2q+1
       631: 2q+1
       632: 2q
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: 2q+1
       643: q+1
       644: q
       646: q+1
       648: 3q+1
       649: 2q+1
       650: 2q
       652: q+1
       653: q
       654: 2q+1
       655: q
       656: 2q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: 3q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 4q+1
       673: q^2+3q+1
       674: 2
       675: q+1
       676: 3q+1
       677: 2q+1
       678: 3q+1
       679: 2q+1
       680: q+2
       681: q^2+3q+1
       682: 3q+1
       683: 2q^2+3q+1
       684: q^2+4q+1
       685: q^2+3q+1
       686: 3q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+2
       691: q+2
       692: q+2
       700: q^2+2q+1
       707: 1
       711: 1
       714: q+1
       719: q+1
       724: 1
       728: q+1
       732: q+1
       736: q+1
       738: 1
       742: q+1
       746: q+1
       748: q
       750: q+1
       752: q
       755: q+1
       760: q+1
       762: q
       764: 2q+1
       767: 2q+1
       768: q
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       786: 2q+1
       787: q+1
       788: q
       790: 2q+1
       792: q+1
       794: 2
       796: 2
       798: 1
       800: 1
       802: q+1
       806: 2q+1
       807: q+1
       808: q
       810: 1
       812: q+1
       814: q+1
       816: 3q+1
       817: 1
       818: 1
       820: q+2
       822: q+1
       824: q+1
       826: q^2+2q+1
       827: q+1
       828: q
       830: 2q+1
       831: q+1
       832: q
       834: q+1
       836: q^2+2q+1
       838: 2q+1
       839: 2q+1
       840: 2q
       842: q+1
       843: 1
       844: 1
       846: 2q+1
       847: q+1
       848: q
       850: 1
       852: q+1
       854: q+1
       856: q+1
       857: q
       858: 2q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: 3q+1
       869: 2
       870: 2
       871: q+1
       872: 2q+1
       873: q+2
       874: q+2
       875: 3q+1
       876: q^2+3q+1
       877: q+1
       878: 3q+1
       879: 2q+1
       880: 2q+1
       891: q+1
       898: 1
       901: 1
       907: 1
       910: q+1
       915: 1
       919: 2
       923: 1
       931: q+1
       935: q+1
       937: 1
       941: 1
       943: 1
       945: 1
       949: q+1
       954: q+1
       957: q+1
       959: q
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: q+1
       981: q+1
       986: q+1
       990: 2q+1
       991: q
       993: 2
       995: 2
       997: q+2
       998: 1
       999: 1
      1001: 2
      1003: q+1
      1005: 2q+1
      1006: q+1
      1007: q
      1009: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: 2
      1017: 2
      1019: 1
      1021: 2
      1023: 1
      1025: 1
      1027: q+1
      1031: q+2
      1032: 1
      1033: 1
      1035: q+1
      1037: q+2
      1039: q+1
      1041: 2q+1
      1043: q+1
      1044: q+1
      1045: q
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: 2q+1
      1058: q+1
      1059: q
      1061: 1
      1063: q+1
      1065: q+1
      1074: 2
      1076: 1
      1077: 2
      1078: q+1
      1080: 2
      1081: q+2
      1082: 3q+1
      1083: q+1
      1084: 2
      1085: 2q+1
      1093: 1
      1094: 1
      1105: q+1
      1111: 1
      1115: 1
      1117: 1
      1121: 1
      1125: 2
      1129: 1
      1132: 1
      1133: 1
      1137: q+1
      1139: 1
      1142: 1
      1147: 2
      1151: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1173: 1
      1179: 1
      1182: q+1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1201: 1
      1209: q+1
      1215: 2
      1216: 1
      1217: 1
      1219: 2
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1231: 1
      1235: 1
      1237: 2
      1239: 1
      1241: q+1
      1249: 2
      1250: 1
      1251: 1
      1253: q+2
      1255: 2
      1257: q+1
      1259: 2q+1
      1260: q+1
      1261: q
      1265: 1
      1267: 1
      1269: q+1
      1273: 1
      1275: 2
      1277: q+1
      1279: 1
      1280: 1
      1281: 1
      1283: 1
      1285: 2
      1287: 1
      1288: 2
      1289: q+1
      1297: 1
      1298: 1
      1309: 1
      1310: 1
      1315: 1
      1317: 1
      1321: 2
      1325: 1
      1328: 1
      1329: 1
      1333: 1
      1335: 1
      1338: 1
      1355: 1
      1359: 1
      1377: 1
      1381: 1
      1383: 1
      1387: 1
      1391: 2
      1395: 1
      1398: 1
      1399: 1
      1403: q+1
      1417: 1
      1425: 1
      1431: 1
      1434: 1
      1447: 1
      1449: 1
      1455: 1
      1457: 2
      1460: 1
      1461: 1
      1463: 2
      1465: 1
      1469: 1
      1471: 1
      1473: 2
      1475: 1
      1477: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1496: 1
      1497: 1
      1520: 1
      1521: 1
      1562: 1
      1570: 1
      1584: 1
      1586: 1
      1590: 2
      1594: 1
      1597: 1
      1598: 1
      1602: 1
      1614: 1
      1618: 1
      1632: 1
      1635: 1
      1642: 1
      1658: 1
      1662: 1
      1666: 1
      1672: 1
      1673: 1
      1706: 1
      1707: 1
      1780: 1
      1784: 1
      1792: 1
      1816: 1
      1822: 1
      1921: 1

1922:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 3q^2+2q+1
        23: 3q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: q^4+2q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 3q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: 2q^2+q+1
        38: q^2+q
        39: 2q^2+q+1
        40: q^2+q
        41: q^3+q^2+q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 3q^2+2q+1
        53: 3q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+4q^2+2q+1
        56: 2q^3+4q^2+2q+1
        57: q^4+2q^3+3q^2+2q+1
        58: q^2+1
        59: q^2+2q
        60: q^3+2q^2+q+1
        61: q^2+q
        62: 2q^2+q+1
        63: q
        64: q^2+q+1
        65: q^2+q
        66: 2q^2+q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^3+4q^2+2q+1
        73: 3q^2+2q+1
        74: 2q^2+q+1
        75: q^2+q
        76: 2q^2+q+1
        77: q^2+q
        78: q^3+q^2+q+1
        79: q^2+q
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^3+3q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^3+4q^2+2q+1
        98: 2q^3+4q^2+2q+1
        99: q^4+2q^3+3q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+1
       104: q
       106: q^2+q
       107: q^3+2q^2+q+1
       108: q^2+q
       109: q^2+1
       110: q^2+2q
       111: 2q^2+q+1
       112: q^2+q
       113: 2q^2+q+1
       114: q
       115: q^2+q+1
       116: q^2+q
       117: 1
       118: 2q
       119: q^2+q+1
       120: q
       121: q^2+q+1
       122: q
       123: q^2+q+1
       124: q^2+q
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+q+1
       128: q^2+q
       129: 2q^2+q+1
       130: q^2+q
       131: q^3+q^2+q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^3+3q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: 3q^2+2q+1
       143: 2q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^3+4q^2+2q+1
       148: 3q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+q+1
       152: q^2+q
       153: 2q^2+q+1
       154: q^2+q
       155: q^3+q^2+q+1
       156: q^2+q
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q^2+1
       170: q
       172: q^2+q
       173: 1
       174: q
       176: q
       177: q^2+q+1
       178: q^2+q
       179: 2q^2+q+1
       180: q
       181: 2q^2+q+1
       182: q^2+q
       183: q^2+q+1
       184: q
       185: 1
       186: 2q
       187: q^2+q+1
       188: q^2+q
       189: q^2+q+1
       190: q
       191: 1
       192: 2q
       193: q^2+q+1
       195: q^2+1
       196: q^2+2q
       197: q^2+1
       198: q
       199: q^2+q+1
       200: q
       201: q^3+2q^2+q+1
       202: q^2+q
       203: q^2+1
       204: q^2+2q
       205: 2q^2+q+1
       206: q^2+q
       207: q^2+q+1
       208: q
       209: 2q^2+q+1
       210: q
       211: q^2+q+1
       212: q^2+q
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^3+3q^2+2q+1
       224: q^2+2q+1
       225: 2q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: q^3+3q^2+2q+1
       234: q^3+3q^2+2q+1
       235: 2q^2+2q+1
       236: 2q^2+2q+1
       237: 2q^2+q+1
       238: q^2+q
       239: 2q^2+q+1
       240: q^2+q
       241: q^3+q^2+q+1
       242: q^2+q
       243: 2q^2+2q+1
       244: q^2+q+1
       245: 3q^2+2q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+1
       260: q
       262: q^2+q
       263: 1
       264: q
       266: q
       267: q^2+1
       268: q
       271: q^2+1
       273: q^2+q
       274: q
       275: 1
       276: q
       278: q
       279: q+1
       281: q+1
       283: q^2+q+1
       284: q
       285: 1
       286: 2q
       287: q^2+q+1
       288: q
       289: q+1
       291: q^2+q+1
       292: q^2+q
       293: q^2+q+1
       294: q
       295: 1
       296: 2q
       297: q^2+q+1
       298: q
       299: q+1
       301: q^2+1
       302: q
       303: 1
       304: 2q
       305: 1
       306: q
       307: q^2+q+1
       308: q
       309: 1
       310: 2q
       311: 2q^2+q+1
       312: q^2+q
       313: q^2+q+1
       314: q^2+q
       315: q^2+q+1
       316: q^2+q
       317: 2q^2+q+1
       318: q
       319: q^2+q+1
       321: q^2+1
       322: q^2+2q
       323: q^2+1
       324: q
       325: q^2+q+1
       326: q
       333: q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: 2q^2+q+1
       339: q^2+q
       340: 2q^2+q+1
       341: q^2+q
       342: q^3+q^2+q+1
       343: q^2+q
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^3+3q^2+2q+1
       357: q^2+2q+1
       358: 2q^2+2q+1
       359: 3q^2+2q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q
       380: q
       381: 1
       384: q
       385: 1
       386: q
       388: q
       389: q^2+1
       390: q
       393: 1
       394: q
       397: q^2+1
       399: q^2+q
       400: q
       401: 1
       403: q
       404: q
       405: q^2+1
       407: q
       413: q+1
       417: q+1
       419: q^2+q+1
       420: q
       421: 1
       422: 2q
       423: q^2+q+1
       424: q
       425: q^2+q+1
       426: q^2+q
       427: 2q^2+q+1
       428: q
       429: q+1
       431: 1
       432: 2q
       433: 1
       434: q
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: q^2+q+1
       445: q^2+1
       446: q
       447: q^2+q+1
       448: q
       449: 1
       450: 2q
       451: q^2+q+1
       452: q^2+q
       453: q^2+q+1
       454: q
       455: q+1
       457: 1
       458: 2q
       459: q^2+q+1
       460: q
       461: q^2+1
       462: q^2+2q
       463: 2q^2+q+1
       464: q^2+q
       465: q+1
       467: q+1
       469: q^2+q+1
       470: q
       471: q+1
       473: 1
       474: 2q
       475: 1
       476: q
       477: q^2+1
       478: q
       479: q^2+1
       480: q
       481: q^2+2q+1
       482: 2q+1
       483: q^2+2q+1
       484: 2q+1
       485: q+1
       487: q+1
       489: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: 2q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       529: 1
       530: q
       532: q
       533: 1
       534: q
       537: 1
       541: 1
       545: q^2+1
       546: q
       549: 1
       551: q
       552: q
       553: 1
       555: q
       557: 1
       559: q
       560: q
       561: q^2+1
       563: q^2+q
       564: q
       565: 1
       566: q
       569: q^2+1
       571: q
       573: q^2+1
       574: q
       577: q^2+1
       581: q
       585: q+1
       589: q^2+q+1
       590: q
       591: 1
       592: 2q
       593: q+1
       595: 1
       596: 2q
       597: q+1
       599: q^2+q+1
       600: q
       601: q+1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       613: 1
       614: q
       615: q+1
       617: 1
       619: q^2+q+1
       620: q
       621: 1
       622: 2q
       623: q+1
       625: q^2+q+1
       626: q
       629: q^2+q+1
       630: q^2+q
       631: 1
       632: 2q
       633: q+1
       639: q+1
       641: q+1
       643: 1
       644: 2q
       645: 1
       646: q
       647: 1
       649: 1
       650: q
       651: 1
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       660: q+1
       662: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: q^2+2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+1
       699: q
       709: 1
       712: q
       713: 1
       715: q
       716: q
       717: 1
       718: q
       721: 1
       725: 1
       733: 1
       737: 1
       739: q
       741: 1
       743: q
       744: q
       749: 1
       751: q
       753: 1
       754: q
       757: 1
       761: 1
       765: 1
       766: q
       769: 1
       775: q+1
       779: q+1
       781: q+1
       785: q+1
       787: 1
       788: 2q
       791: 1
       792: q
       793: q+1
       795: 1
       797: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       815: 1
       817: 1
       818: 2q
       819: q+1
       821: q+1
       825: q^2+q+1
       826: q
       827: 1
       828: 2q
       829: q+1
       831: 1
       832: 2q
       833: q+1
       835: q^2+q+1
       836: q
       839: 1
       840: q
       843: 1
       844: q
       845: 1
       847: 1
       848: q
       849: 1
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       884: 1
       900: 1
       902: q
       904: 1
       908: 1
       909: q
       916: 1
       920: 1
       928: 1
       940: 1
       942: q
       944: 1
       946: q
       948: 1
       950: q
       951: q
       952: 1
       953: q
       960: 1
       964: 1
       965: q
       968: 1
       974: 1
       988: 1
       994: q+1
       998: 1
       999: 2q
      1000: q+1
      1004: 1
      1006: 1
      1007: q
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1016: 1
      1020: 1
      1022: 1
      1026: 1
      1032: 1
      1033: q
      1036: q+1
      1038: q+1
      1040: q+1
      1044: 1
      1045: 2q
      1046: 1
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1065: q
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1114: 1
      1116: q
      1122: 1
      1126: 1
      1130: 1
      1131: q
      1134: 1
      1138: 1
      1156: 1
      1172: 1
      1174: q
      1176: 1
      1180: 1
      1181: q
      1194: 1
      1198: 1
      1206: 1
      1216: 1
      1217: q
      1218: 1
      1220: 1
      1224: 1
      1230: 1
      1234: 1
      1240: 1
      1248: q+1
      1250: 1
      1251: 2q
      1254: q+1
      1258: 1
      1260: 1
      1261: q
      1266: 1
      1268: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1382: q
      1388: 1
      1392: 1
      1396: 1
      1397: q
      1400: 1
      1422: 1
      1430: 1
      1436: 1
      1454: 1
      1460: 1
      1461: q
      1462: 1
      1464: 1
      1468: 1
      1474: 1
      1476: 1
      1482: 1
      1484: 1
      1487: 1
      1513: 1
      1537: 1
      1595: 1
      1599: 1
      1615: 1
      1641: 1
      1657: 1
      1659: 1
      1665: 1
      1673: 1
      1769: 1
      1781: 1
      1817: 1
      1821: 1
      1922: 1

1923:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 3q^2+2q+1
        23: 3q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: q^4+2q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 3q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: 2q^2+q+1
        38: q^2+q
        39: 2q^2+q+1
        40: q^2+q
        41: q^3+q^2+q+1
        42: q^2+q
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 3q^2+2q+1
        53: 3q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+4q^2+2q+1
        56: 2q^3+4q^2+2q+1
        57: q^4+2q^3+3q^2+2q+1
        58: q^2+2q
        59: q^2+1
        60: q^2+q
        61: q^3+2q^2+q+1
        62: 2q^2+q+1
        63: q
        64: q^2+q+1
        65: q^2+q
        66: 2q^2+q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^3+4q^2+2q+1
        73: 3q^2+2q+1
        74: 2q^2+q+1
        75: q^2+q
        76: 2q^2+q+1
        77: q^2+q
        78: q^3+q^2+q+1
        79: q^2+q
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^3+3q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^3+4q^2+2q+1
        98: 2q^3+4q^2+2q+1
        99: q^4+2q^3+3q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+q
       105: q
       106: q^2+1
       107: q^2+q
       108: q^3+2q^2+q+1
       109: q^2+2q
       110: q^2+1
       111: 2q^2+q+1
       112: q^2+q
       113: 2q^2+q+1
       114: q
       115: q^2+q+1
       116: q^2+q
       117: 2q
       118: 1
       119: q
       120: q^2+q+1
       121: q^2+q+1
       122: q
       123: q^2+q+1
       124: q^2+q
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+q+1
       128: q^2+q
       129: 2q^2+q+1
       130: q^2+q
       131: q^3+q^2+q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^3+3q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: 3q^2+2q+1
       143: 2q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^3+4q^2+2q+1
       148: 3q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+q+1
       152: q^2+q
       153: 2q^2+q+1
       154: q^2+q
       155: q^3+q^2+q+1
       156: q^2+q
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q^2+q
       171: q
       172: q^2+1
       173: q
       175: q
       176: 1
       177: q^2+q+1
       178: q^2+q
       179: 2q^2+q+1
       180: q
       181: 2q^2+q+1
       182: q^2+q
       183: q
       184: q^2+q+1
       185: 2q
       186: 1
       187: q^2+q+1
       188: q^2+q
       189: q^2+q+1
       190: q
       191: 2q
       192: 1
       194: q^2+q+1
       195: q^2+2q
       196: q^2+1
       197: q^2+1
       198: q
       199: q
       200: q^2+q+1
       201: q^2+q
       202: q^3+2q^2+q+1
       203: q^2+2q
       204: q^2+1
       205: 2q^2+q+1
       206: q^2+q
       207: q^2+q+1
       208: q
       209: 2q^2+q+1
       210: q
       211: q^2+q+1
       212: q^2+q
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^3+3q^2+2q+1
       224: q^2+2q+1
       225: 2q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: q^3+3q^2+2q+1
       234: q^3+3q^2+2q+1
       235: 2q^2+2q+1
       236: 2q^2+2q+1
       237: 2q^2+q+1
       238: q^2+q
       239: 2q^2+q+1
       240: q^2+q
       241: q^3+q^2+q+1
       242: q^2+q
       243: 2q^2+2q+1
       244: q^2+q+1
       245: 3q^2+2q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+q
       261: q
       262: q^2+1
       263: q
       265: q
       266: 1
       269: q^2+1
       270: q
       271: q^2+q
       272: q
       273: q^2+1
       275: q
       277: q
       278: 1
       279: q+1
       281: q+1
       283: q
       284: q^2+q+1
       285: 2q
       286: 1
       287: q^2+q+1
       288: q
       289: q+1
       291: q^2+q+1
       292: q^2+q
       293: q
       294: q^2+q+1
       295: 2q
       296: 1
       297: q^2+q+1
       298: q
       300: q+1
       301: q^2+1
       302: q
       303: 2q
       304: 1
       305: 1
       306: q
       307: q
       308: q^2+q+1
       309: 2q
       310: 1
       311: 2q^2+q+1
       312: q^2+q
       313: q^2+q+1
       314: q^2+q
       315: q^2+q+1
       316: q^2+q
       317: 2q^2+q+1
       318: q
       320: q^2+q+1
       321: q^2+2q
       322: q^2+1
       323: q^2+1
       324: q
       325: q^2+q+1
       326: q
       333: q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: 2q^2+q+1
       339: q^2+q
       340: 2q^2+q+1
       341: q^2+q
       342: q^3+q^2+q+1
       343: q^2+q
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^3+3q^2+2q+1
       357: q^2+2q+1
       358: 2q^2+2q+1
       359: 3q^2+2q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       379: q
       380: 1
       381: q
       384: 1
       385: q
       387: q
       388: 1
       391: q^2+1
       392: q
       395: q
       396: 1
       397: q^2+q
       398: q
       399: q^2+1
       401: q
       402: q
       404: 1
       406: q^2+1
       408: q
       413: q+1
       417: q+1
       419: q
       420: q^2+q+1
       421: 2q
       422: 1
       423: q^2+q+1
       424: q
       425: q^2+q+1
       426: q^2+q
       427: 2q^2+q+1
       428: q
       430: q+1
       431: 2q
       432: 1
       433: 1
       434: q
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: q^2+q+1
       445: q^2+1
       446: q
       447: q
       448: q^2+q+1
       449: 2q
       450: 1
       451: q^2+q+1
       452: q^2+q
       453: q
       454: q^2+q+1
       455: q+1
       457: 2q
       458: 1
       459: q^2+q+1
       460: q
       461: q^2+2q
       462: q^2+1
       463: 2q^2+q+1
       464: q^2+q
       465: q+1
       467: q+1
       469: q^2+q+1
       470: q
       472: q+1
       473: 2q
       474: 1
       475: 1
       476: q
       477: q^2+1
       478: q
       479: q^2+1
       480: q
       481: q^2+2q+1
       482: 2q+1
       483: q^2+2q+1
       484: 2q+1
       485: q+1
       487: q+1
       489: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: 2q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       529: q
       531: q
       532: 1
       535: q
       536: 1
       539: 1
       543: 1
       547: q^2+1
       548: q
       549: q
       550: q
       552: 1
       553: q
       555: 1
       557: q
       558: q
       559: 1
       561: q^2+q
       562: q
       563: q^2+1
       567: q
       568: 1
       570: q^2+1
       572: q
       575: q^2+1
       576: q
       577: q^2+1
       581: q
       585: q+1
       589: q
       590: q^2+q+1
       591: 2q
       592: 1
       594: q+1
       595: 2q
       596: 1
       597: q+1
       599: q^2+q+1
       600: q
       601: q+1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       613: 1
       614: q
       616: q+1
       617: 1
       619: q
       620: q^2+q+1
       621: 2q
       622: 1
       623: q+1
       625: q^2+q+1
       626: q
       629: q^2+q+1
       630: q^2+q
       631: 2q
       632: 1
       633: q+1
       639: q+1
       642: q+1
       643: 2q
       644: 1
       645: 1
       646: q
       648: 1
       649: q
       650: 1
       651: 1
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       660: q+1
       662: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: q^2+2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q^2+1
       700: q
       709: q
       712: 1
       713: q
       714: q
       716: 1
       719: q
       720: 1
       723: 1
       727: 1
       735: 1
       737: q
       739: 1
       741: q
       742: q
       743: 1
       749: q
       751: 1
       755: q
       756: 1
       758: 1
       762: 1
       767: q
       768: 1
       769: 1
       775: q+1
       779: q+1
       781: q+1
       786: q+1
       787: 2q
       788: 1
       791: 1
       792: q
       794: q+1
       795: 1
       797: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       816: 1
       817: 2q
       818: 1
       819: q+1
       821: q+1
       825: q
       826: q^2+q+1
       827: 2q
       828: 1
       830: q+1
       831: 2q
       832: 1
       833: q+1
       835: q^2+q+1
       836: q
       839: q
       840: 1
       843: 1
       844: q
       846: 1
       847: q
       848: 1
       849: 1
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       889: 1
       900: q
       902: 1
       906: 1
       910: q
       911: 1
       918: 1
       922: 1
       930: 1
       940: q
       942: 1
       944: q
       946: 1
       948: q
       949: q
       950: 1
       954: q
       955: 1
       961: 1
       966: q
       967: 1
       968: 1
       975: 1
       991: 1
       994: q+1
       998: 2q
       999: 1
      1001: q+1
      1005: 1
      1006: q
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1017: 1
      1020: 1
      1022: 1
      1027: 1
      1032: q
      1033: 1
      1036: q+1
      1038: q+1
      1041: q+1
      1044: 2q
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1091: 1
      1114: q
      1116: 1
      1124: 1
      1127: 1
      1132: q
      1133: 1
      1135: 1
      1138: 1
      1158: 1
      1172: q
      1174: 1
      1178: 1
      1182: q
      1183: 1
      1197: 1
      1199: 1
      1208: 1
      1216: q
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: 1
      1235: 1
      1241: 1
      1248: q+1
      1250: 2q
      1251: 1
      1255: q+1
      1259: 1
      1260: q
      1261: 1
      1266: 1
      1269: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1358: 1
      1380: q
      1382: 1
      1390: 1
      1393: 1
      1398: q
      1399: 1
      1401: 1
      1424: 1
      1430: 1
      1436: 1
      1455: 1
      1460: q
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1474: 1
      1477: 1
      1482: 1
      1484: 1
      1487: 1
      1518: 1
      1538: 1
      1598: 1
      1600: 1
      1617: 1
      1641: 1
      1658: 1
      1659: 1
      1666: 1
      1673: 1
      1770: 1
      1783: 1
      1817: 1
      1822: 1
      1923: 1

1924:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 3q^2+2q+1
        23: 3q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: q^4+2q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 3q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: q^2+q
        38: 2q^2+q+1
        39: q^2+q
        40: 2q^2+q+1
        41: q^2+q
        42: q^3+q^2+q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 3q^2+2q+1
        53: 3q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+4q^2+2q+1
        56: 2q^3+4q^2+2q+1
        57: q^4+2q^3+3q^2+2q+1
        58: q^2+2q
        59: q^2+1
        60: q^3+2q^2+q+1
        61: q^2+q
        62: q
        63: 2q^2+q+1
        64: q^2+q
        65: q^2+q+1
        66: q^2+q
        67: 2q^2+q+1
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^3+4q^2+2q+1
        73: 3q^2+2q+1
        74: q^2+q
        75: 2q^2+q+1
        76: q^2+q
        77: 2q^2+q+1
        78: q^2+q
        79: q^3+q^2+q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^3+3q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^3+4q^2+2q+1
        98: 2q^3+4q^2+2q+1
        99: q^4+2q^3+3q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q
       104: q^2+1
       105: q^2+q
       107: q^3+2q^2+q+1
       108: q^2+q
       109: q^2+2q
       110: q^2+1
       111: q^2+q
       112: 2q^2+q+1
       113: q
       114: 2q^2+q+1
       115: q^2+q
       116: q^2+q+1
       117: 2q
       118: 1
       119: q^2+q+1
       120: q
       121: q
       122: q^2+q+1
       123: q^2+q
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: q^2+q
       128: 2q^2+q+1
       129: q^2+q
       130: 2q^2+q+1
       131: q^2+q
       132: q^3+q^2+q+1
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^3+3q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: 3q^2+2q+1
       143: 2q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^3+4q^2+2q+1
       148: 3q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+q
       152: 2q^2+q+1
       153: q^2+q
       154: 2q^2+q+1
       155: q^2+q
       156: q^3+q^2+q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q
       170: q^2+1
       171: q^2+q
       173: q
       174: 1
       175: q
       177: q^2+q
       178: q^2+q+1
       179: q
       180: 2q^2+q+1
       181: q^2+q
       182: 2q^2+q+1
       183: q^2+q+1
       184: q
       185: 2q
       186: 1
       187: q^2+q
       188: q^2+q+1
       189: q
       190: q^2+q+1
       191: 2q
       192: 1
       193: q^2+q+1
       195: q^2+2q
       196: q^2+1
       197: q
       198: q^2+1
       199: q^2+q+1
       200: q
       201: q^3+2q^2+q+1
       202: q^2+q
       203: q^2+2q
       204: q^2+1
       205: q^2+q
       206: 2q^2+q+1
       207: q
       208: q^2+q+1
       209: q
       210: 2q^2+q+1
       211: q^2+q
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^3+3q^2+2q+1
       224: q^2+2q+1
       225: 2q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: q^3+3q^2+2q+1
       234: q^3+3q^2+2q+1
       235: 2q^2+2q+1
       236: 2q^2+2q+1
       237: q^2+q
       238: 2q^2+q+1
       239: q^2+q
       240: 2q^2+q+1
       241: q^2+q
       242: q^3+q^2+q+1
       243: 2q^2+2q+1
       244: q^2+q+1
       245: 3q^2+2q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       260: q^2+1
       261: q^2+q
       263: q
       264: 1
       265: q
       267: q
       268: q^2+1
       271: q
       272: q^2+q
       274: q^2+1
       275: q
       276: 1
       277: q
       280: q+1
       282: q+1
       283: q^2+q+1
       284: q
       285: 2q
       286: 1
       287: q
       288: q^2+q+1
       290: q+1
       291: q^2+q
       292: q^2+q+1
       293: q^2+q+1
       294: q
       295: 2q
       296: 1
       297: q
       298: q^2+q+1
       299: q+1
       301: q
       302: q^2+1
       303: 2q
       304: 1
       305: q
       306: 1
       307: q^2+q+1
       308: q
       309: 2q
       310: 1
       311: q^2+q
       312: 2q^2+q+1
       313: q^2+q
       314: q^2+q+1
       315: q^2+q
       316: q^2+q+1
       317: q
       318: 2q^2+q+1
       319: q^2+q+1
       321: q^2+2q
       322: q^2+1
       323: q
       324: q^2+1
       325: q
       326: q^2+q+1
       333: q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: q^2+q
       339: 2q^2+q+1
       340: q^2+q
       341: 2q^2+q+1
       342: q^2+q
       343: q^3+q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^3+3q^2+2q+1
       357: q^2+2q+1
       358: 2q^2+2q+1
       359: 3q^2+2q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: 1
       379: q
       382: 1
       383: q
       385: q
       386: 1
       387: q
       389: q
       390: q^2+1
       393: q
       394: 1
       397: q
       398: q^2+q
       400: q^2+1
       401: q
       402: q
       403: 1
       405: q
       407: q^2+1
       414: q+1
       418: q+1
       419: q^2+q+1
       420: q
       421: 2q
       422: 1
       423: q
       424: q^2+q+1
       425: q^2+q
       426: q^2+q+1
       427: q
       428: 2q^2+q+1
       429: q+1
       431: 2q
       432: 1
       433: q
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: q^2+q+1
       445: q
       446: q^2+1
       447: q^2+q+1
       448: q
       449: 2q
       450: 1
       451: q^2+q
       452: q^2+q+1
       453: q^2+q+1
       454: q
       456: q+1
       457: 2q
       458: 1
       459: q
       460: q^2+q+1
       461: q^2+2q
       462: q^2+1
       463: q^2+q
       464: 2q^2+q+1
       466: q+1
       468: q+1
       469: q
       470: q^2+q+1
       471: q+1
       473: 2q
       474: 1
       475: q
       476: 1
       477: q
       478: q^2+1
       479: q
       480: q^2+1
       481: q^2+2q+1
       482: 2q+1
       483: q^2+2q+1
       484: 2q+1
       486: q+1
       488: q+1
       490: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: 2q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       529: q
       530: 1
       531: q
       533: q
       534: 1
       538: 1
       542: 1
       545: q
       546: q^2+1
       549: q
       550: q
       551: 1
       554: q
       556: 1
       557: q
       558: q
       560: 1
       561: q
       562: q^2+q
       564: q^2+1
       565: q
       566: 1
       569: q
       571: q^2+1
       573: q
       574: q^2+1
       577: q
       581: q^2+1
       586: q+1
       589: q^2+q+1
       590: q
       591: 2q
       592: 1
       593: q+1
       595: 2q
       596: 1
       598: q+1
       599: q
       600: q^2+q+1
       602: q+1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       613: q
       614: 1
       615: q+1
       618: 1
       619: q^2+q+1
       620: q
       621: 2q
       622: 1
       624: q+1
       625: q
       626: q^2+q+1
       629: q^2+q
       630: q^2+q+1
       631: 2q
       632: 1
       634: q+1
       640: q+1
       641: q+1
       643: 2q
       644: 1
       645: q
       646: 1
       647: 1
       649: q
       650: 1
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       659: q+1
       661: q+1
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: q^2+2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       699: q^2+1
       710: 1
       711: q
       713: q
       714: q
       715: 1
       717: q
       718: 1
       722: 1
       726: 1
       734: 1
       738: q
       740: 1
       741: q
       742: q
       744: 1
       750: q
       752: 1
       753: q
       754: 1
       759: 1
       763: 1
       765: q
       766: 1
       773: 1
       776: q+1
       780: q+1
       782: q+1
       785: q+1
       787: 2q
       788: 1
       791: q
       792: 1
       793: q+1
       796: 1
       798: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       815: 1
       817: 2q
       818: 1
       820: q+1
       822: q+1
       825: q^2+q+1
       826: q
       827: 2q
       828: 1
       829: q+1
       831: 2q
       832: 1
       834: q+1
       835: q
       836: q^2+q+1
       839: q
       840: 1
       843: q
       844: 1
       845: 1
       847: q
       848: 1
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       890: 1
       901: q
       903: 1
       905: 1
       908: q
       909: 1
       917: 1
       921: 1
       929: 1
       941: q
       943: 1
       945: q
       947: 1
       948: q
       949: q
       951: 1
       952: q
       953: 1
       962: 1
       964: q
       965: 1
       972: 1
       976: 1
       989: 1
       995: q+1
       998: 2q
       999: 1
      1000: q+1
      1004: 1
      1006: q
      1007: 1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1016: 1
      1021: 1
      1023: 1
      1026: 1
      1032: q
      1033: 1
      1037: q+1
      1039: q+1
      1040: q+1
      1044: 2q
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1092: 1
      1115: q
      1117: 1
      1123: 1
      1128: 1
      1130: q
      1131: 1
      1136: 1
      1142: 1
      1157: 1
      1173: q
      1175: 1
      1177: 1
      1180: q
      1181: 1
      1195: 1
      1200: 1
      1207: 1
      1216: q
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: 1
      1234: 1
      1240: 1
      1249: q+1
      1250: 2q
      1251: 1
      1254: q+1
      1258: 1
      1260: q
      1261: 1
      1267: 1
      1268: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1357: 1
      1381: q
      1383: 1
      1389: 1
      1394: 1
      1396: q
      1397: 1
      1402: 1
      1423: 1
      1434: 1
      1437: 1
      1454: 1
      1460: q
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1475: 1
      1476: 1
      1483: 1
      1484: 1
      1487: 1
      1519: 1
      1539: 1
      1596: 1
      1601: 1
      1616: 1
      1642: 1
      1657: 1
      1660: 1
      1665: 1
      1673: 1
      1771: 1
      1782: 1
      1818: 1
      1821: 1
      1924: 1

1925:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: 2q^3+4q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: 2q^3+4q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^4+2q^3+3q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: 2q^3+4q^2+2q+1
        20: 2q^3+4q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: 3q^2+2q+1
        23: 3q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: q^4+2q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 3q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: q^2+q
        38: 2q^2+q+1
        39: q^2+q
        40: 2q^2+q+1
        41: q^2+q
        42: q^3+q^2+q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^3+3q^2+2q+1
        49: 2q^3+4q^2+2q+1
        50: 2q^3+4q^2+2q+1
        51: q^4+2q^3+3q^2+2q+1
        52: 3q^2+2q+1
        53: 3q^2+2q+1
        54: q^3+2q^2+2q+1
        55: 2q^3+4q^2+2q+1
        56: 2q^3+4q^2+2q+1
        57: q^4+2q^3+3q^2+2q+1
        58: q^2+1
        59: q^2+2q
        60: q^2+q
        61: q^3+2q^2+q+1
        62: q
        63: 2q^2+q+1
        64: q^2+q
        65: q^2+q+1
        66: q^2+q
        67: 2q^2+q+1
        68: q^2+2q+1
        69: q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^3+4q^2+2q+1
        73: 3q^2+2q+1
        74: q^2+q
        75: 2q^2+q+1
        76: q^2+q
        77: 2q^2+q+1
        78: q^2+q
        79: q^3+q^2+q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^3+3q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^3+4q^2+2q+1
        98: 2q^3+4q^2+2q+1
        99: q^4+2q^3+3q^2+2q+1
       100: 3q^2+2q+1
       101: 3q^2+2q+1
       102: q^3+2q^2+2q+1
       104: q^2+q
       105: q^2+1
       106: q
       107: q^2+q
       108: q^3+2q^2+q+1
       109: q^2+1
       110: q^2+2q
       111: q^2+q
       112: 2q^2+q+1
       113: q
       114: 2q^2+q+1
       115: q^2+q
       116: q^2+q+1
       117: 1
       118: 2q
       119: q
       120: q^2+q+1
       121: q
       122: q^2+q+1
       123: q^2+q
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: q^2+q
       128: 2q^2+q+1
       129: q^2+q
       130: 2q^2+q+1
       131: q^2+q
       132: q^3+q^2+q+1
       133: q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^3+3q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: 3q^2+2q+1
       143: 2q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^3+4q^2+2q+1
       148: 3q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+q
       152: 2q^2+q+1
       153: q^2+q
       154: 2q^2+q+1
       155: q^2+q
       156: q^3+q^2+q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: q^3+2q^2+2q+1
       170: q^2+q
       171: q^2+1
       172: q
       174: q
       175: 1
       176: q
       177: q^2+q
       178: q^2+q+1
       179: q
       180: 2q^2+q+1
       181: q^2+q
       182: 2q^2+q+1
       183: q
       184: q^2+q+1
       185: 1
       186: 2q
       187: q^2+q
       188: q^2+q+1
       189: q
       190: q^2+q+1
       191: 1
       192: 2q
       194: q^2+q+1
       195: q^2+1
       196: q^2+2q
       197: q
       198: q^2+1
       199: q
       200: q^2+q+1
       201: q^2+q
       202: q^3+2q^2+q+1
       203: q^2+1
       204: q^2+2q
       205: q^2+q
       206: 2q^2+q+1
       207: q
       208: q^2+q+1
       209: q
       210: 2q^2+q+1
       211: q^2+q
       212: q^2+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q^2+2q+1
       222: 2q^2+2q+1
       223: q^3+3q^2+2q+1
       224: q^2+2q+1
       225: 2q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: q^3+3q^2+2q+1
       234: q^3+3q^2+2q+1
       235: 2q^2+2q+1
       236: 2q^2+2q+1
       237: q^2+q
       238: 2q^2+q+1
       239: q^2+q
       240: 2q^2+q+1
       241: q^2+q
       242: q^3+q^2+q+1
       243: 2q^2+2q+1
       244: q^2+q+1
       245: 3q^2+2q+1
       246: q^2+2q+1
       247: 3q^2+2q+1
       248: 3q^2+2q+1
       249: q^3+2q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: q^2+q
       261: q^2+1
       262: q
       264: q
       265: 1
       266: q
       269: q
       270: q^2+1
       272: q^2+1
       273: q
       274: q^2+q
       276: q
       277: 1
       278: q
       280: q+1
       282: q+1
       283: q
       284: q^2+q+1
       285: 1
       286: 2q
       287: q
       288: q^2+q+1
       290: q+1
       291: q^2+q
       292: q^2+q+1
       293: q
       294: q^2+q+1
       295: 1
       296: 2q
       297: q
       298: q^2+q+1
       300: q+1
       301: q
       302: q^2+1
       303: 1
       304: 2q
       305: q
       306: 1
       307: q
       308: q^2+q+1
       309: 1
       310: 2q
       311: q^2+q
       312: 2q^2+q+1
       313: q^2+q
       314: q^2+q+1
       315: q^2+q
       316: q^2+q+1
       317: q
       318: 2q^2+q+1
       320: q^2+q+1
       321: q^2+1
       322: q^2+2q
       323: q
       324: q^2+1
       325: q
       326: q^2+q+1
       333: q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: 2q^2+2q+1
       337: 2q^2+2q+1
       338: q^2+q
       339: 2q^2+q+1
       340: q^2+q
       341: 2q^2+q+1
       342: q^2+q
       343: q^3+q^2+q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q^2+q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q^3+3q^2+2q+1
       357: q^2+2q+1
       358: 2q^2+2q+1
       359: 3q^2+2q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       380: q
       382: q
       383: 1
       386: q
       387: 1
       388: q
       391: q
       392: q^2+1
       395: 1
       396: q
       398: q^2+1
       399: q
       400: q^2+q
       402: 1
       403: q
       404: q
       406: q
       408: q^2+1
       414: q+1
       418: q+1
       419: q
       420: q^2+q+1
       421: 1
       422: 2q
       423: q
       424: q^2+q+1
       425: q^2+q
       426: q^2+q+1
       427: q
       428: 2q^2+q+1
       430: q+1
       431: 1
       432: 2q
       433: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: q^2+q+1
       445: q
       446: q^2+1
       447: q
       448: q^2+q+1
       449: 1
       450: 2q
       451: q^2+q
       452: q^2+q+1
       453: q
       454: q^2+q+1
       456: q+1
       457: 1
       458: 2q
       459: q
       460: q^2+q+1
       461: q^2+1
       462: q^2+2q
       463: q^2+q
       464: 2q^2+q+1
       466: q+1
       468: q+1
       469: q
       470: q^2+q+1
       472: q+1
       473: 1
       474: 2q
       475: q
       476: 1
       477: q
       478: q^2+1
       479: q
       480: q^2+1
       481: q^2+2q+1
       482: 2q+1
       483: q^2+2q+1
       484: 2q+1
       486: q+1
       488: q+1
       490: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: 2q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       530: q
       531: 1
       532: q
       535: 1
       536: q
       540: 1
       544: 1
       547: q
       548: q^2+1
       550: 1
       551: q
       552: q
       554: 1
       556: q
       558: 1
       559: q
       560: q
       562: q^2+1
       563: q
       564: q^2+q
       567: 1
       568: q
       570: q
       572: q^2+1
       575: q
       576: q^2+1
       577: q
       581: q^2+1
       586: q+1
       589: q
       590: q^2+q+1
       591: 1
       592: 2q
       594: q+1
       595: 1
       596: 2q
       598: q+1
       599: q
       600: q^2+q+1
       602: q+1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       613: q
       614: 1
       616: q+1
       618: 1
       619: q
       620: q^2+q+1
       621: 1
       622: 2q
       624: q+1
       625: q
       626: q^2+q+1
       629: q^2+q
       630: q^2+q+1
       631: 1
       632: 2q
       634: q+1
       640: q+1
       642: q+1
       643: 1
       644: 2q
       645: q
       646: 1
       648: 1
       649: 1
       650: q
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       659: q+1
       661: q+1
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: q^2+2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       700: q^2+1
       710: q
       711: 1
       714: 1
       715: q
       716: q
       719: 1
       720: q
       724: 1
       728: 1
       736: 1
       738: 1
       740: q
       742: 1
       743: q
       744: q
       750: 1
       752: q
       755: 1
       756: q
       760: 1
       764: 1
       767: 1
       768: q
       773: 1
       776: q+1
       780: q+1
       782: q+1
       786: q+1
       787: 1
       788: 2q
       791: q
       792: 1
       794: q+1
       796: 1
       798: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       816: 1
       817: 1
       818: 2q
       820: q+1
       822: q+1
       825: q
       826: q^2+q+1
       827: 1
       828: 2q
       830: q+1
       831: 1
       832: 2q
       834: q+1
       835: q
       836: q^2+q+1
       839: 1
       840: q
       843: q
       844: 1
       846: 1
       847: 1
       848: q
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       891: 1
       901: 1
       903: q
       907: 1
       910: 1
       911: q
       919: 1
       923: 1
       931: 1
       941: 1
       943: q
       945: 1
       947: q
       949: 1
       950: q
       951: q
       954: 1
       955: q
       963: 1
       966: 1
       967: q
       972: 1
       977: 1
       990: 1
       995: q+1
       998: 1
       999: 2q
      1001: q+1
      1005: 1
      1006: 1
      1007: q
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1017: 1
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1033: q
      1037: q+1
      1039: q+1
      1041: q+1
      1044: 1
      1045: 2q
      1047: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1093: 1
      1115: 1
      1117: q
      1125: 1
      1129: 1
      1132: 1
      1133: q
      1137: 1
      1142: 1
      1159: 1
      1173: 1
      1175: q
      1179: 1
      1182: 1
      1183: q
      1196: 1
      1201: 1
      1209: 1
      1216: 1
      1217: q
      1219: 1
      1221: 1
      1225: 1
      1231: 1
      1235: 1
      1241: 1
      1249: q+1
      1250: 1
      1251: 2q
      1255: q+1
      1259: 1
      1260: 1
      1261: q
      1267: 1
      1269: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1383: q
      1391: 1
      1395: 1
      1398: 1
      1399: q
      1403: 1
      1425: 1
      1434: 1
      1437: 1
      1455: 1
      1460: 1
      1461: q
      1463: 1
      1465: 1
      1469: 1
      1475: 1
      1477: 1
      1483: 1
      1484: 1
      1487: 1
      1520: 1
      1540: 1
      1597: 1
      1602: 1
      1618: 1
      1642: 1
      1658: 1
      1660: 1
      1666: 1
      1673: 1
      1772: 1
      1784: 1
      1818: 1
      1822: 1
      1925: 1

1926:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+q+2
         5: 2q+2
         6: q^2+q+2
         7: q^2+q+2
         8: 2q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: q^2+q+2
        13: 2q+2
        14: q^2+q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: q+2
        20: q+2
        21: q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: q+2
        30: q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: 2q+2
        44: q^2+q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: q^2+q+2
        49: q+2
        50: q+2
        51: q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: 2q+2
        69: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        74: q+2
        76: q+2
        78: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+q+2
        91: q+2
        92: q+2
        93: q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 2
       113: q+2
       115: q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: 2q+2
       125: 2q+2
       126: q+2
       127: q+2
       129: q+2
       131: q+2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       140: 2
       141: q+2
       142: 2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+2
       167: q+2
       168: q+2
       169: 1
       172: 1
       173: q+1
       176: q+1
       177: q+2
       179: q+2
       181: 2
       183: 1
       184: 1
       185: 1
       186: 1
       187: 2
       189: q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: q+2
       211: q+2
       213: q+2
       215: q+2
       217: q+2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       229: 2
       230: 2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       235: 2
       236: q+2
       237: q+2
       239: q+2
       241: q+2
       243: q+2
       244: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       259: 1
       262: 1
       263: 1
       266: 1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: q+2
       281: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       287: q+2
       289: 2
       291: 2
       293: 1
       294: 1
       295: 1
       296: 1
       297: 2
       299: 1
       300: 1
       301: 2
       303: 1
       304: 1
       305: 2
       307: 1
       308: 1
       309: 1
       310: 1
       311: 2
       313: 2
       315: q+2
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: q+2
       327: q+2
       329: q+2
       331: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q+2
       345: q+2
       346: q+2
       347: 2
       348: 2
       349: 2
       350: 2
       351: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       357: 2
       358: 2
       359: 2
       360: q+2
       362: q+2
       364: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       377: 1
       380: 1
       381: 1
       384: 1
       385: 1
       388: 1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: q+2
       411: q+2
       413: q+2
       415: 2
       417: 2
       419: 1
       420: 1
       421: 1
       422: 1
       423: 2
       425: 1
       427: 2
       429: 1
       430: 1
       431: 1
       432: 1
       433: 2
       435: 2
       437: 1
       438: 1
       439: 1
       440: 1
       441: 2
       443: 1
       444: 1
       445: 2
       447: 1
       448: 1
       449: 1
       450: 1
       451: 2
       453: 1
       454: 1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: q+2
       469: q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 2
       482: 2
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 2
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 2
       502: q+2
       504: q+2
       506: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       524: 1
       525: 1
       528: 1
       529: 1
       532: 1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: q+2
       585: 2
       587: 2
       589: 1
       590: 1
       595: 1
       596: 1
       597: 1
       599: 1
       601: 2
       603: 1
       604: 1
       605: 2
       607: 1
       608: 1
       609: 2
       611: 2
       613: 1
       615: 1
       616: 1
       617: 2
       619: 1
       620: 1
       621: 1
       622: 1
       623: 2
       625: 2
       627: 2
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+2
       637: q+2
       639: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2
       677: 1
       678: 2
       679: 1
       680: 2
       681: 2
       682: 2
       683: 1
       684: 2
       685: 1
       686: q+2
       687: 2
       688: 2
       689: 1
       690: 2
       691: 2
       692: q+1
       693: 1
       697: 1
       705: 1
       708: 1
       709: 1
       712: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       775: 2
       777: 2
       779: 1
       781: 1
       783: 1
       789: 2
       791: 1
       793: 1
       794: 1
       795: 2
       797: 2
       799: 2
       801: 1
       802: 1
       807: 1
       808: 1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: 2
       825: 1
       826: 1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       851: 2
       853: 2
       855: 1
       857: 2
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       884: 1
       889: 1
       896: 1
       899: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       956: 1
       958: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       992: 2
       994: 1
       996: 1
      1002: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 1
      1022: 1
      1024: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 1
      1038: 1
      1042: 1
      1046: 2
      1048: 2
      1050: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1091: 1
      1098: 1
      1102: 1
      1138: 1
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1184: 1
      1185: 1
      1188: 2
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1210: 2
      1212: 1
      1214: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2
      1228: 1
      1229: 1
      1230: 1
      1236: 1
      1238: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1256: 1
      1262: 2
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1307: 1
      1334: 1
      1340: 1
      1342: 1
      1372: 1
      1374: 1
      1404: 2
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1436: 1
      1438: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1456: 1
      1458: 1
      1464: 1
      1470: 1
      1472: 1
      1474: 1
      1480: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1525: 1
      1530: 1
      1553: 1
      1631: 1
      1637: 1
      1639: 1
      1643: 1
      1651: 1
      1659: 1
      1661: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1723: 1
      1801: 1
      1823: 1
      1825: 1
      1827: 1
      1926: 1

1927:    0: 12q^2+4q
         1: 12q^2+4q
         2: 4q^3+8q^2+4q
         3: 12q^2+4q
         4: 4q^3+8q^2+4q
         5: 12q^2+4q
         6: 4q^3+8q^2+4q
         7: q^4+4q^3+5q^2+4q
         8: 4q^3+8q^2+4q
         9: q^4+4q^3+5q^2+4q
        10: 12q^2+4q
        11: 12q^2+4q
        12: 4q^3+8q^2+4q
        13: 8q^2+4q
        14: 2q^3+5q^2+4q
        15: 8q^2+4q
        16: 12q^2+4q
        17: 12q^2+4q
        18: q^4+4q^3+5q^2+4q
        19: 8q^2+4q
        20: 8q^2+4q
        21: 2q^3+5q^2+4q
        22: 12q^2+4q
        23: 12q^2+4q
        24: 4q^3+8q^2+4q
        25: 12q^2+4q
        26: 12q^2+4q
        27: 4q^3+8q^2+4q
        28: 12q^2+4q
        29: 8q^2+4q
        30: 5q^2+4q
        31: 12q^2+4q
        32: 8q^2+4q
        33: 12q^2+4q
        34: 12q^2+4q
        35: 8q^2+4q
        36: 12q^2+4q
        37: 4q^2+2q
        38: 8q^2+2q
        39: 4q^2+2q
        40: 8q^2+2q
        41: q^3+3q^2+2q
        42: 3q^3+5q^2+2q
        43: 8q^2+4q
        44: 2q^3+5q^2+4q
        45: 8q^2+4q
        46: 8q^2+4q
        47: 8q^2+4q
        48: 2q^3+5q^2+4q
        49: 8q^2+4q
        50: 8q^2+4q
        51: 2q^3+5q^2+4q
        52: 8q^2+4q
        53: 8q^2+4q
        54: 2q^3+5q^2+4q
        55: 8q^2+4q
        56: 8q^2+4q
        57: 2q^3+5q^2+4q
        58: 6q^2+2q
        59: 6q^2+2q
        60: 6q^2+2q
        61: 6q^2+2q
        62: 4q^2+2q
        63: 8q^2+2q
        64: 3q^2+2q
        65: 5q^2+2q
        66: 4q^2+2q
        67: 8q^2+2q
        68: 4q^2+4q
        69: 5q^2+4q
        70: 5q^2+4q
        71: 8q^2+4q
        72: 4q^2+4q
        73: 4q^2+4q
        74: q^2+2q
        75: 5q^2+2q
        76: q^2+2q
        77: 5q^2+2q
        78: q^2+2q
        79: q^3+3q^2+2q
        80: 8q^2+4q
        81: 8q^2+4q
        82: 8q^2+4q
        83: 5q^2+4q
        84: 8q^2+4q
        85: 8q^2+4q
        86: 8q^2+4q
        87: 5q^2+4q
        88: 8q^2+4q
        89: 8q^2+4q
        90: 2q^3+5q^2+4q
        91: 3q^2+4q
        92: 4q^2+4q
        93: 3q^2+4q
        94: 8q^2+4q
        95: 8q^2+4q
        96: 2q^3+5q^2+4q
        97: 8q^2+4q
        98: 8q^2+4q
        99: 2q^3+5q^2+4q
       100: 8q^2+4q
       101: 8q^2+4q
       102: 2q^3+5q^2+4q
       103: 2q^2+q
       104: 4q^2+q
       105: 4q^2+q
       106: 2q^2+q
       107: 2q^2+2q
       108: 2q^2+2q
       109: 2q^2+2q
       110: 2q^2+2q
       111: 2q
       112: 2q^2+2q
       113: q^2+2q
       114: 5q^2+2q
       115: q^2+2q
       116: 3q^2+2q
       117: 2q^2+2q
       118: 2q^2+2q
       119: 2q^2+2q
       120: 2q^2+2q
       121: 3q^2+2q
       122: 5q^2+2q
       123: 3q^2+2q
       124: 5q^2+2q
       125: 4q^2+4q
       126: 5q^2+4q
       127: q^2+2q
       128: 5q^2+2q
       129: q^2+2q
       130: 5q^2+2q
       131: q^2+2q
       132: q^3+3q^2+2q
       133: q^2+4q
       134: 3q^2+4q
       135: q^2+4q
       136: q^2+4q
       137: 8q^2+4q
       138: 5q^2+4q
       139: 8q^2+4q
       140: 4q^2+4q
       141: 5q^2+4q
       142: 4q^2+4q
       143: 8q^2+4q
       144: 5q^2+4q
       145: 8q^2+4q
       146: 5q^2+4q
       147: 4q^2+4q
       148: 4q^2+4q
       149: 8q^2+4q
       150: 5q^2+4q
       151: q^2+2q
       152: 5q^2+2q
       153: q^2+2q
       154: 5q^2+2q
       155: q^2+2q
       156: q^3+3q^2+2q
       157: 3q^2+4q
       158: 4q^2+4q
       159: 3q^2+4q
       160: 3q^2+4q
       161: 4q^2+4q
       162: 3q^2+4q
       163: 3q^2+4q
       164: 4q^2+4q
       165: 3q^2+4q
       166: 8q^2+4q
       167: 8q^2+4q
       168: 2q^3+5q^2+4q
       169: q
       170: q^2+q
       171: q^2+q
       172: q
       173: q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       177: q^2+2q
       178: 3q^2+2q
       179: q^2+2q
       180: 5q^2+2q
       181: 2q
       182: 2q^2+2q
       183: 2q
       184: 2q
       185: 2q
       186: 2q
       187: 2q
       188: 2q
       189: q^2+2q
       190: 3q^2+2q
       191: 2q^2+2q
       192: 2q^2+2q
       193: 2q^2+2q
       194: 2q^2+2q
       195: 2q^2+2q
       196: 2q^2+2q
       197: 2q
       198: 2q^2+2q
       199: 2q^2+2q
       200: 2q^2+2q
       201: 2q^2+2q
       202: 2q^2+2q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 2q
       206: 2q^2+2q
       207: 3q^2+2q
       208: 5q^2+2q
       209: q^2+2q
       210: 5q^2+2q
       211: q^2+2q
       212: 3q^2+2q
       214: q^2+2q
       216: 2q^2+2q
       218: q^2+2q
       219: q^2+4q
       220: q^2+4q
       221: 3q^2+4q
       222: q^2+4q
       223: q^2+4q
       224: q^2+4q
       225: q^2+4q
       226: 5q^2+4q
       227: q^2+4q
       228: 3q^2+4q
       229: q^2+4q
       230: q^2+4q
       231: 5q^2+4q
       232: q^2+4q
       233: 3q^2+4q
       234: q^2+4q
       235: q^2+4q
       236: 5q^2+4q
       237: q^2+2q
       238: 5q^2+2q
       239: q^2+2q
       240: 5q^2+2q
       241: q^2+2q
       242: q^3+3q^2+2q
       243: 8q^2+4q
       244: 4q^2+4q
       245: 4q^2+4q
       246: 5q^2+4q
       247: 2q^2+6q
       248: 2q^2+6q
       249: q^3+3q^2+2q
       250: 3q^2+4q
       251: 4q^2+4q
       252: 3q^2+4q
       253: 3q^2+4q
       254: 4q^2+4q
       255: 3q^2+4q
       256: 3q^2+4q
       257: 4q^2+4q
       258: 3q^2+4q
       259: q
       260: q^2+q
       261: q^2+q
       262: q
       263: q
       264: q
       265: q
       266: q
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       278: q^2+q
       280: 2q
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       283: 2q
       284: 2q
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       287: q^2+2q
       288: 3q^2+2q
       290: 2q
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       303: 2q
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       306: 2q
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       309: 2q
       310: 2q
       311: 2q
       312: 2q^2+2q
       313: 2q
       314: 2q
       315: q^2+2q
       316: 3q^2+2q
       317: q^2+2q
       318: 5q^2+2q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       323: 2q
       324: 2q^2+2q
       325: q^2+2q
       326: 3q^2+2q
       328: q^2+2q
       330: 2q^2+2q
       332: q^2+2q
       333: q^2+4q
       334: q^2+4q
       335: q^2+4q
       336: 2q
       337: 2q^2+6q
       338: 2q
       339: 2q^2+4q
       340: 2q
       341: 2q^2+4q
       342: q^2+q
       343: q^3+2q^2+q
       344: q^2+4q
       345: q^2+4q
       346: 3q^2+4q
       347: q^2+4q
       348: q^2+4q
       349: q^2+4q
       350: q^2+4q
       351: 2q^2+6q
       352: q^2+4q
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       354: 3q^2+4q
       355: q^2+4q
       356: q^2+4q
       357: q^2+4q
       358: q^2+4q
       359: 2q^2+6q
       361: q^2+2q
       363: 2q^2+2q
       365: q^2+2q
       366: 5q^2+4q
       367: q^2+4q
       368: 3q^2+4q
       369: q^2+4q
       370: q^2+4q
       371: 5q
       372: 5q
       373: 2q^2+2q
       374: 3q^2+4q
       375: 4q^2+4q
       376: 3q^2+4q
       377: q
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       443: q^2+3q
       444: q^2+3q
       445: 2q
       446: 2q^2+4q
       447: 2q
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       460: 2q
       461: q^2+3q
       462: q^2+3q
       463: 2q
       464: 2q^2+4q
       466: 2q
       468: q^2+2q
       469: q^2+2q
       470: 3q^2+2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       477: 2q
       478: 2q^2+2q
       479: 4q
       480: 2q^2+2q
       481: 2q
       482: 2q
       483: 2q
       484: 4q
       486: 3q
       488: 3q
       490: q^2+q
       491: 2q
       492: q^2+4q
       493: q^2+4q
       494: q^2+4q
       495: 2q
       496: 5q
       497: q^2+4q
       498: q^2+4q
       499: q^2+4q
       500: 2q
       501: 5q
       503: q^2+2q
       505: 2q^2+2q
       507: q^2+2q
       508: q^2+4q
       509: q^2+4q
       510: 3q^2+4q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: 5q
       516: 5q
       517: 2q^2+2q
       518: 5q
       519: 5q
       520: 2q^2+2q
       522: q
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       573: 2q
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       575: 2q
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       577: 2q
       578: 2q
       581: 2q^2+2q
       584: 2q
       588: 2q
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       600: q
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       618: 3q
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       632: 2q
       634: 3q
       636: 2q
       638: q^2+2q
       640: 2q
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       661: 3q
       663: q^2+q
       664: 2q
       665: q
       667: 3q
       669: 3q
       671: q^2+q
       672: 4q
       673: 2q
       674: 5q
       675: 2q
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       686: q^2+4q
       687: q^2+4q
       688: q^2+4q
       689: 2q
       690: 5q
       691: 5q
       692: 2q^2+2q
       693: q
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       800: 2q
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       850: 2q
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       864: q^2+q
       865: 4q
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       881: 2
       882: 2
       883: q+1
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      1031: 3q
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      1037: q
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      1046: 3q
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      1051: 2q
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      1058: q
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      1061: q
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      1063: q
      1064: q
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: q
      1075: 2
      1076: q
      1077: 2q
      1078: q
      1079: 2
      1080: q
      1081: 2q
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      1084: 2q
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      1092: q
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      1192: 2q
      1194: q
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      1196: q
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      1211: 2
      1213: 1
      1224: q
      1227: 2
      1228: 1
      1229: 1
      1237: q
      1245: 2
      1246: 1
      1247: 1
      1253: q
      1262: 2
      1273: q
      1275: q
      1276: q
      1280: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1308: q
      1309: q
      1341: 1
      1343: 1
      1373: 1
      1375: 1
      1405: 2
      1410: 1
      1413: 1
      1439: 1
      1444: 1
      1453: 1
      1459: 1
      1473: q
      1482: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1526: 1
      1533: 1
      1554: 1
      1639: 1
      1644: 1
      1652: 1
      1668: 1
      1669: 1
      1674: 1
      1724: 1
      1802: 1
      1825: 1
      1828: 1
      1927: 1

1928:    0: q^4+2q^3+3q^2+2q
         1: q^4+2q^3+3q^2+2q
         2: q^4+2q^3+3q^2+2q
         3: q^4+2q^3+3q^2+2q
         4: q^5+q^4+2q^3+2q^2+2q
         5: q^4+2q^3+3q^2+2q
         6: q^5+q^4+2q^3+2q^2+2q
         7: q^5+q^4+2q^3+2q^2+2q
         8: q^4+2q^3+3q^2+2q
         9: q^5+q^4+2q^3+2q^2+2q
        10: 2q^3+2q^2+2q
        11: 2q^3+2q^2+2q
        12: q^4+2q^3+q^2+2q
        13: q^4+2q^3+3q^2+2q
        14: q^5+q^4+2q^3+2q^2+2q
        15: q^4+2q^3+3q^2+2q
        16: q^4+2q^3+3q^2+2q
        17: q^4+2q^3+3q^2+2q
        18: q^5+q^4+2q^3+2q^2+2q
        19: q^3+2q^2+2q
        20: q^3+2q^2+2q
        21: q^3+2q^2+2q
        22: q^4+2q^3+3q^2+2q
        23: q^4+2q^3+3q^2+2q
        24: q^4+2q^3+3q^2+2q
        25: q^4+2q^3+3q^2+2q
        26: q^4+2q^3+3q^2+2q
        27: q^4+2q^3+3q^2+2q
        28: 2q^3+2q^2+2q
        29: q^3+q^2+2q
        30: q^3+2q^2+2q
        31: 2q^3+2q^2+2q
        32: q^4+2q^3+3q^2+2q
        33: q^4+2q^3+3q^2+2q
        34: 2q^3+2q^2+2q
        35: q^4+2q^3+3q^2+2q
        36: q^4+2q^3+3q^2+2q
        37: q^4+2q^3+3q^2+2q
        39: q^4+2q^3+3q^2+2q
        41: q^4+2q^3+3q^2+2q
        43: 2q^3+2q^2+2q
        44: q^4+2q^3+q^2+2q
        45: 2q^3+2q^2+2q
        46: q^4+2q^3+3q^2+2q
        47: q^4+2q^3+3q^2+2q
        48: q^5+q^4+2q^3+2q^2+2q
        49: q^3+2q^2+2q
        50: q^3+2q^2+2q
        51: q^3+2q^2+2q
        52: q^3+2q^2+2q
        53: q^3+2q^2+2q
        54: q^3+2q^2+2q
        55: q^3+2q^2+2q
        56: q^3+2q^2+2q
        57: q^3+2q^2+2q
        58: q^3+q^2+q
        59: q^3+q^2+q
        60: q^3+q^2+q
        61: q^3+q^2+q
        62: 2q^3+2q^2+2q
        64: q^4+2q^3+3q^2+2q
        66: q^4+2q^3+3q^2+2q
        68: 2q^3+2q^2+2q
        69: q^3+2q^2+2q
        70: q^3+q^2+2q
        71: q^3+q^2+2q
        72: q^2+2q
        73: q^2+2q
        74: q^3+2q^2+2q
        76: q^3+2q^2+2q
        78: q^3+2q^2+2q
        80: 2q^3+2q^2+2q
        81: q^4+2q^3+3q^2+2q
        82: q^3+q^2+2q
        83: q^3+2q^2+2q
        84: 2q^3+2q^2+2q
        85: q^4+2q^3+3q^2+2q
        86: q^3+q^2+2q
        87: q^3+2q^2+2q
        88: 2q^3+2q^2+2q
        89: 2q^3+2q^2+2q
        90: q^4+2q^3+q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: q^3+2q^2+2q
        95: q^3+2q^2+2q
        96: q^3+2q^2+2q
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        99: q^3+2q^2+2q
       100: q^3+2q^2+2q
       101: q^3+2q^2+2q
       102: q^3+2q^2+2q
       103: q^3+q^2+q
       106: q^3+q^2+q
       107: q
       108: q
       109: q
       110: q
       111: q^2+2q
       113: q^3+q^2+2q
       115: q^3+2q^2+2q
       117: q^3+q^2+q
       118: q^3+q^2+q
       119: q^3+q^2+q
       120: q^3+q^2+q
       121: 2q^3+2q^2+2q
       123: q^4+2q^3+3q^2+2q
       125: 2q^3+2q^2+2q
       126: q^3+q^2+2q
       127: q^3+2q^2+2q
       129: q^3+2q^2+2q
       131: q^3+2q^2+2q
       133: q^3+q^2+2q
       134: q^3+2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 2q^3+2q^2+2q
       138: q^3+2q^2+2q
       139: q^3+q^2+2q
       140: q^2+2q
       141: q^3+q^2+2q
       142: q^2+2q
       143: 2q^3+2q^2+2q
       144: q^3+2q^2+2q
       145: q^3+q^2+2q
       146: q^3+q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: q^3+q^2+2q
       150: q^3+2q^2+2q
       151: q^3+2q^2+2q
       153: q^3+2q^2+2q
       155: q^3+2q^2+2q
       157: q^2+2q
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       160: q^3+2q^2+2q
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       168: q^3+2q^2+2q
       169: q
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       176: q^3+q^2+q
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       179: q^3+q^2+2q
       181: q^2+2q
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       217: q^3+2q^2+2q
       219: q^3+q^2+2q
       220: q^2+2q
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       225: q^2+2q
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       227: q^3+q^2+2q
       228: q^3+2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: q^3+q^2+2q
       232: q^3+q^2+2q
       233: q^3+2q^2+2q
       234: q^2+2q
       235: q^2+2q
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       237: q^3+2q^2+2q
       239: q^3+2q^2+2q
       241: q^3+2q^2+2q
       243: q^3+q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: q^3+q^2+2q
       247: 2q
       248: 2q
       249: q^2+q
       250: q^2+2q
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       275: q^3+q^2+q
       278: q^3+q^2+q
       279: q^3+q^2+2q
       281: q^3+2q^2+2q
       283: q
       284: q
       285: q
       286: q
       287: q^3+q^2+2q
       289: q^2+2q
       291: q^2+2q
       293: q
       294: q
       295: q
       296: q
       297: 2q
       299: q
       300: q
       301: q^2+2q
       303: q
       304: q
       305: q^2+2q
       307: q
       308: q
       309: q
       310: q
       311: q^2+2q
       313: q^2+2q
       315: q^3+2q^2+2q
       317: q^3+q^2+2q
       319: q
       320: q
       321: q
       322: q
       323: q^2+2q
       325: q^3+q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: q^2+2q
       334: 2q
       335: 2q
       336: q
       337: 2q
       338: 2q
       340: 2q
       342: q^2+q
       344: q^3+q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: 2q
       348: q^2+2q
       349: 2q
       350: q^2+2q
       351: 2q
       352: q^3+q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: 2q
       356: q^2+2q
       357: 2q
       358: q^2+2q
       359: 2q
       360: q^3+2q^2+2q
       362: q^3+2q^2+2q
       364: q^3+2q^2+2q
       366: q^3+q^2+2q
       367: q^3+q^2+2q
       368: q^3+2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 2q
       372: 2q
       373: q^2+q
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       377: q
       380: q
       381: q
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       396: q
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       401: q
       404: q
       405: q
       406: q
       409: q^2+2q
       411: q^2+2q
       413: q^3+q^2+2q
       415: 2q
       417: q^2+2q
       419: q
       420: q
       421: q
       422: q
       423: 2q
       425: q
       427: 2q
       429: q
       430: q
       431: q
       432: q
       433: q^2+2q
       435: q^2+2q
       437: q
       438: q
       439: q
       440: q
       441: 2q
       443: q
       444: q
       445: 2q
       447: q
       448: q
       449: q
       450: q
       451: q^2+2q
       453: q
       454: q
       455: q^2+2q
       457: q
       458: q
       459: 2q
       461: q
       462: q
       463: 2q
       465: q^3+q^2+2q
       467: q^3+2q^2+2q
       469: q^3+q^2+2q
       471: q
       472: q
       473: q
       474: q
       475: q^2+2q
       477: q^2+2q
       479: 2q
       481: 2q
       482: 2q
       483: q
       484: 2q
       485: 2q
       487: 2q
       489: q^2+q
       491: q
       492: q^2+2q
       493: 2q
       494: 2q
       495: q
       496: 2q
       497: q^2+2q
       498: 2q
       499: 2q
       500: q
       501: 2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: q^3+q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: 2q
       512: q^2+2q
       513: 2q
       514: q^2+2q
       515: 2q
       516: 2q
       517: q^2+q
       521: q
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       569: q
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       573: q
       575: q
       577: 2q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q
       590: q
       595: q
       596: q
       597: q
       599: q
       601: 2q
       603: q
       604: q
       605: q^2+2q
       607: q
       608: q
       609: 2q
       611: 2q
       613: q
       615: q
       616: q
       617: 2q
       619: q
       620: q
       621: q
       622: q
       623: q^2+2q
       625: 2q
       627: 2q
       629: q
       631: q
       632: q
       633: 2q
       635: q^2+2q
       637: q^2+2q
       639: q^3+q^2+2q
       641: q
       642: q
       643: q
       644: q
       645: q^2+2q
       647: q
       648: q
       649: q
       650: q
       651: q^2+2q
       653: 2q
       655: 2q
       657: 2q
       658: 2q
       660: 2q
       662: q^2+q
       664: q
       665: q
       674: 2q
       675: 2q
       676: 2q
       677: q
       679: q
       680: 2q
       681: 2q
       682: 2q
       683: q
       685: q
       686: q^2+2q
       687: 2q
       688: 2q
       689: q
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       705: q
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       721: q
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       769: 2q
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       795: 2q
       797: 2q
       799: 2q
       801: q
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       811: q
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       819: 2q
       821: 2q
       823: 2q
       825: q
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       831: q
       832: q
       833: q
       835: q
       841: q^2+2q
       843: 2q
       845: q
       846: q
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       848: q
       849: q^2+2q
       851: 2q
       853: 2q
       855: q
       866: q
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       874: q
       875: q
       877: 2q
       878: 2q
       879: q
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       899: q
       912: q
       914: q
       916: q
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       922: q
       936: q
       938: q
       940: q
       942: q
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       946: q
       960: q
       961: q
       964: q
       967: q
       968: 2q
       974: q
       975: q
       978: q
       979: q
       994: q
      1010: q
      1012: q
      1018: 2q
      1020: q
      1022: q
      1034: 2q
      1036: q
      1038: q
      1048: 2q
      1050: 2q
      1052: q
      1053: q
      1058: q
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      1062: q
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      1076: q
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      1083: q
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      1138: q
      1148: q
      1150: q
      1168: q
      1170: q
      1184: q
      1185: q
      1198: q
      1199: q
      1222: 1
      1230: q
      1248: q
      1264: 2q
      1266: q
      1274: q
      1278: q
      1280: q
      1287: q
      1336: 1
      1414: q
      1415: q
      1430: q
      1446: 1
      1464: q
      1480: 1
      1555: 1
      1633: 1
      1637: 1
      1671: 1
      1725: 1
      1803: 1
      1823: 1
      1928: 1

1929:    0: 12q^2+4q
         1: 12q^2+4q
         2: 4q^3+8q^2+4q
         3: 12q^2+4q
         4: 4q^3+8q^2+4q
         5: 12q^2+4q
         6: 4q^3+8q^2+4q
         7: q^4+4q^3+5q^2+4q
         8: 4q^3+8q^2+4q
         9: q^4+4q^3+5q^2+4q
        10: 12q^2+4q
        11: 12q^2+4q
        12: 4q^3+8q^2+4q
        13: 8q^2+4q
        14: 2q^3+5q^2+4q
        15: 8q^2+4q
        16: 12q^2+4q
        17: 12q^2+4q
        18: q^4+4q^3+5q^2+4q
        19: 8q^2+4q
        20: 8q^2+4q
        21: 2q^3+5q^2+4q
        22: 12q^2+4q
        23: 12q^2+4q
        24: 4q^3+8q^2+4q
        25: 12q^2+4q
        26: 12q^2+4q
        27: 4q^3+8q^2+4q
        28: 12q^2+4q
        29: 8q^2+4q
        30: 5q^2+4q
        31: 12q^2+4q
        32: 8q^2+4q
        33: 12q^2+4q
        34: 12q^2+4q
        35: 8q^2+4q
        36: 12q^2+4q
        37: 8q^2+2q
        38: 4q^2+2q
        39: 8q^2+2q
        40: 4q^2+2q
        41: 3q^3+5q^2+2q
        42: q^3+3q^2+2q
        43: 8q^2+4q
        44: 2q^3+5q^2+4q
        45: 8q^2+4q
        46: 8q^2+4q
        47: 8q^2+4q
        48: 2q^3+5q^2+4q
        49: 8q^2+4q
        50: 8q^2+4q
        51: 2q^3+5q^2+4q
        52: 8q^2+4q
        53: 8q^2+4q
        54: 2q^3+5q^2+4q
        55: 8q^2+4q
        56: 8q^2+4q
        57: 2q^3+5q^2+4q
        58: 6q^2+2q
        59: 6q^2+2q
        60: 6q^2+2q
        61: 6q^2+2q
        62: 8q^2+2q
        63: 4q^2+2q
        64: 5q^2+2q
        65: 3q^2+2q
        66: 8q^2+2q
        67: 4q^2+2q
        68: 4q^2+4q
        69: 5q^2+4q
        70: 5q^2+4q
        71: 8q^2+4q
        72: 4q^2+4q
        73: 4q^2+4q
        74: 5q^2+2q
        75: q^2+2q
        76: 5q^2+2q
        77: q^2+2q
        78: q^3+3q^2+2q
        79: q^2+2q
        80: 8q^2+4q
        81: 8q^2+4q
        82: 8q^2+4q
        83: 5q^2+4q
        84: 8q^2+4q
        85: 8q^2+4q
        86: 8q^2+4q
        87: 5q^2+4q
        88: 8q^2+4q
        89: 8q^2+4q
        90: 2q^3+5q^2+4q
        91: 3q^2+4q
        92: 4q^2+4q
        93: 3q^2+4q
        94: 8q^2+4q
        95: 8q^2+4q
        96: 2q^3+5q^2+4q
        97: 8q^2+4q
        98: 8q^2+4q
        99: 2q^3+5q^2+4q
       100: 8q^2+4q
       101: 8q^2+4q
       102: 2q^3+5q^2+4q
       103: 4q^2+q
       104: 2q^2+q
       105: 2q^2+q
       106: 4q^2+q
       107: 2q^2+2q
       108: 2q^2+2q
       109: 2q^2+2q
       110: 2q^2+2q
       111: 2q^2+2q
       112: 2q
       113: 5q^2+2q
       114: q^2+2q
       115: 3q^2+2q
       116: q^2+2q
       117: 2q^2+2q
       118: 2q^2+2q
       119: 2q^2+2q
       120: 2q^2+2q
       121: 5q^2+2q
       122: 3q^2+2q
       123: 5q^2+2q
       124: 3q^2+2q
       125: 4q^2+4q
       126: 5q^2+4q
       127: 5q^2+2q
       128: q^2+2q
       129: 5q^2+2q
       130: q^2+2q
       131: q^3+3q^2+2q
       132: q^2+2q
       133: q^2+4q
       134: 3q^2+4q
       135: q^2+4q
       136: q^2+4q
       137: 8q^2+4q
       138: 5q^2+4q
       139: 8q^2+4q
       140: 4q^2+4q
       141: 5q^2+4q
       142: 4q^2+4q
       143: 8q^2+4q
       144: 5q^2+4q
       145: 8q^2+4q
       146: 5q^2+4q
       147: 4q^2+4q
       148: 4q^2+4q
       149: 8q^2+4q
       150: 5q^2+4q
       151: 5q^2+2q
       152: q^2+2q
       153: 5q^2+2q
       154: q^2+2q
       155: q^3+3q^2+2q
       156: q^2+2q
       157: 3q^2+4q
       158: 4q^2+4q
       159: 3q^2+4q
       160: 3q^2+4q
       161: 4q^2+4q
       162: 3q^2+4q
       163: 3q^2+4q
       164: 4q^2+4q
       165: 3q^2+4q
       166: 8q^2+4q
       167: 8q^2+4q
       168: 2q^3+5q^2+4q
       169: q^2+q
       170: q
       171: q
       172: q^2+q
       173: q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       177: 3q^2+2q
       178: q^2+2q
       179: 5q^2+2q
       180: q^2+2q
       181: 2q^2+2q
       182: 2q
       183: 2q
       184: 2q
       185: 2q
       186: 2q
       187: 2q
       188: 2q
       189: 3q^2+2q
       190: q^2+2q
       191: 2q^2+2q
       192: 2q^2+2q
       193: 2q^2+2q
       194: 2q^2+2q
       195: 2q^2+2q
       196: 2q^2+2q
       197: 2q^2+2q
       198: 2q
       199: 2q^2+2q
       200: 2q^2+2q
       201: 2q^2+2q
       202: 2q^2+2q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 2q^2+2q
       206: 2q
       207: 5q^2+2q
       208: 3q^2+2q
       209: 5q^2+2q
       210: q^2+2q
       211: 3q^2+2q
       212: q^2+2q
       213: q^2+2q
       215: 2q^2+2q
       217: q^2+2q
       219: q^2+4q
       220: q^2+4q
       221: 3q^2+4q
       222: q^2+4q
       223: q^2+4q
       224: q^2+4q
       225: q^2+4q
       226: 5q^2+4q
       227: q^2+4q
       228: 3q^2+4q
       229: q^2+4q
       230: q^2+4q
       231: 5q^2+4q
       232: q^2+4q
       233: 3q^2+4q
       234: q^2+4q
       235: q^2+4q
       236: 5q^2+4q
       237: 5q^2+2q
       238: q^2+2q
       239: 5q^2+2q
       240: q^2+2q
       241: q^3+3q^2+2q
       242: q^2+2q
       243: 8q^2+4q
       244: 4q^2+4q
       245: 4q^2+4q
       246: 5q^2+4q
       247: 2q^2+6q
       248: 2q^2+6q
       249: q^3+3q^2+2q
       250: 3q^2+4q
       251: 4q^2+4q
       252: 3q^2+4q
       253: 3q^2+4q
       254: 4q^2+4q
       255: 3q^2+4q
       256: 3q^2+4q
       257: 4q^2+4q
       258: 3q^2+4q
       259: q^2+q
       260: q
       261: q
       262: q^2+q
       263: q
       264: q
       265: q
       266: q
       267: q^2+q
       268: q
       269: q^2+q
       270: q
       271: q^2+q
       272: q
       273: q^2+q
       274: q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       279: 2q
       281: q^2+2q
       283: 2q
       284: 2q
       285: 2q
       286: 2q
       287: 3q^2+2q
       288: q^2+2q
       289: 2q
       291: 2q
       292: 2q
       293: 2q
       294: 2q
       295: 2q
       296: 2q
       297: 2q
       298: 2q
       299: 2q
       300: 2q
       301: 2q^2+2q
       302: 2q
       303: 2q
       304: 2q
       305: 2q
       306: 2q
       307: 2q
       308: 2q
       309: 2q
       310: 2q
       311: 2q^2+2q
       312: 2q
       313: 2q
       314: 2q
       315: 3q^2+2q
       316: q^2+2q
       317: 5q^2+2q
       318: q^2+2q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       323: 2q^2+2q
       324: 2q
       325: 3q^2+2q
       326: q^2+2q
       327: q^2+2q
       329: 2q^2+2q
       331: q^2+2q
       333: q^2+4q
       334: q^2+4q
       335: q^2+4q
       336: 2q
       337: 2q^2+6q
       338: 2q^2+4q
       339: 2q
       340: 2q^2+4q
       341: 2q
       342: q^3+2q^2+q
       343: q^2+q
       344: q^2+4q
       345: q^2+4q
       346: 3q^2+4q
       347: q^2+4q
       348: q^2+4q
       349: q^2+4q
       350: q^2+4q
       351: 2q^2+6q
       352: q^2+4q
       353: q^2+4q
       354: 3q^2+4q
       355: q^2+4q
       356: q^2+4q
       357: q^2+4q
       358: q^2+4q
       359: 2q^2+6q
       360: q^2+2q
       362: 2q^2+2q
       364: q^2+2q
       366: 5q^2+4q
       367: q^2+4q
       368: 3q^2+4q
       369: q^2+4q
       370: q^2+4q
       371: 5q
       372: 5q
       373: 2q^2+2q
       374: 3q^2+4q
       375: 4q^2+4q
       376: 3q^2+4q
       377: q
       378: q
       379: q
       380: q
       381: q
       384: q
       385: q
       386: q
       387: q
       388: q
       389: q^2+q
       390: q
       391: q^2+q
       392: q
       393: q
       394: q
       395: q
       396: q
       397: q^2+q
       398: q
       399: q^2+q
       400: q
       401: q
       402: q
       403: q
       404: q
       405: q^2+q
       406: q^2+q
       407: q
       408: q
       409: 2q
       411: q^2+2q
       413: 2q
       415: 2q
       417: 2q
       419: 2q
       420: 2q
       421: 2q
       422: 2q
       423: 2q
       424: 2q
       425: q
       426: q
       427: 2q^2+4q
       428: 2q
       429: 2q
       430: 2q
       431: 2q
       432: 2q
       433: 2q
       434: 2q
       435: 2q
       437: 2q
       438: 2q
       439: 2q
       440: 2q
       441: 2q
       442: 2q
       443: q^2+3q
       444: q^2+3q
       445: 2q^2+4q
       446: 2q
       447: 2q
       448: 2q
       449: 2q
       450: 2q
       451: 2q
       452: 2q
       453: 2q
       454: 2q
       455: 2q
       457: 2q
       458: 2q
       459: 2q
       460: 2q
       461: q^2+3q
       462: q^2+3q
       463: 2q^2+4q
       464: 2q
       465: 2q
       467: q^2+2q
       469: 3q^2+2q
       470: q^2+2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       477: 2q^2+2q
       478: 2q
       479: 2q^2+2q
       480: 4q
       481: 2q
       482: 2q
       483: 2q
       484: 4q
       485: 3q
       487: 3q
       489: q^2+q
       491: 2q
       492: q^2+4q
       493: q^2+4q
       494: q^2+4q
       495: 2q
       496: 5q
       497: q^2+4q
       498: q^2+4q
       499: q^2+4q
       500: 2q
       501: 5q
       502: q^2+2q
       504: 2q^2+2q
       506: q^2+2q
       508: q^2+4q
       509: q^2+4q
       510: 3q^2+4q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: 5q
       516: 5q
       517: 2q^2+2q
       518: 5q
       519: 5q
       520: 2q^2+2q
       521: q
       524: q
       525: q
       528: q
       529: q
       530: q
       531: q
       532: q
       533: q
       534: q
       535: q
       536: q
       537: q
       539: q
       541: q
       542: q
       543: q
       544: q
       545: q^2+2q
       546: q
       547: q^2+2q
       548: q
       549: q
       550: q
       551: q
       552: q
       553: q
       555: q
       557: q
       558: q
       559: q
       560: q
       561: q^2+2q
       562: q
       563: q^2+2q
       564: q
       565: q
       566: q
       567: q
       568: q
       569: q^2+q
       570: q^2+q
       571: q
       572: q
       573: q^2+q
       574: 2q
       575: q^2+q
       576: 2q
       577: 2q^2+2q
       580: 2q
       581: 2q
       583: 2q
       587: 2q
       589: q
       590: q
       595: q
       596: q
       597: q
       599: q
       600: q
       601: 2q
       603: 2q
       604: 2q
       605: 2q
       607: 2q
       608: 2q
       609: 2q
       610: 2q
       611: 2q
       613: q
       614: q
       615: 2q
       616: 2q
       617: 3q
       619: 2q
       620: 2q
       621: 2q
       622: 2q
       623: 2q
       625: 2q
       626: 2q
       627: 2q
       629: q
       630: q
       631: 2q
       632: 2q
       633: 3q
       635: 2q
       637: q^2+2q
       639: 2q
       641: 2q
       642: 2q
       643: 2q
       644: 2q
       645: 2q
       646: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       651: 2q
       653: 2q
       654: 2q
       655: 2q
       656: 3q
       657: 4q
       658: 3q
       660: 3q
       662: q^2+q
       664: 2q
       665: q
       666: 3q
       668: 3q
       670: q^2+q
       672: 4q
       673: 2q
       674: 5q
       675: 2q
       676: 2q
       677: 2q
       678: 5q
       679: 2q
       680: 5q
       681: 2q
       682: 2q
       683: 2q
       684: 5q
       685: 2q
       686: q^2+4q
       687: q^2+4q
       688: q^2+4q
       689: 2q
       690: 5q
       691: 5q
       692: 2q^2+2q
       693: q^2+q
       696: q
       697: q^2+q
       698: q
       699: q
       700: q
       705: q
       708: q
       721: q
       723: q
       725: q
       726: q
       727: q
       728: q
       729: q
       731: q
       733: q
       735: q
       737: q
       739: q
       741: q
       742: q
       743: q
       744: q
       745: q
       747: q
       749: q
       751: q
       753: q
       754: q
       755: q
       756: q
       757: q
       758: q
       761: q
       762: q
       763: q
       764: q
       765: q
       766: q
       767: q
       768: q
       769: 2q
       772: q
       775: 2q
       779: q
       783: q
       789: 2q
       792: q
       793: 2q
       794: 2q
       795: 3q
       799: 2q
       801: q
       802: q
       807: q
       808: q
       809: q
       811: q
       812: q
       813: 3q
       815: 2q
       816: 2q
       817: 2q
       818: 2q
       819: 3q
       823: 2q
       825: q
       826: q
       831: q
       832: q
       833: q
       835: q
       836: q
       837: 3q
       839: 2q
       840: 2q
       841: 2q
       843: 2q
       844: 3q
       845: 2q
       846: 2q
       847: 2q
       848: 2q
       849: 2q
       851: 2q
       852: 2q
       853: 2q
       855: q
       856: q
       857: 2q
       858: 3q
       859: 3q
       861: 3q
       863: q^2+q
       865: 4q
       866: q
       867: 2q
       868: q
       869: 5q
       870: 2q
       871: q
       872: 2q
       873: 5q
       874: 2q
       875: q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: 2
       882: 2
       883: q+1
       884: q
       889: q
       912: q
       914: q
       916: q
       918: q
       932: q
       934: q
       936: q
       938: q
       940: q
       942: q
       956: q
       958: q
       960: q
       961: q
       964: q
       965: q
       966: q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       976: q
       977: q
       978: q
       979: q
       982: 2q
       985: q
       988: q
       989: q
       990: q
       991: q
       992: 2q
       996: q
      1009: q
      1013: q
      1014: 3q
      1016: 2q
      1017: 2q
      1020: q
      1024: q
      1030: 3q
      1032: 2q
      1033: 2q
      1036: q
      1042: q
      1046: 2q
      1047: 3q
      1050: 2q
      1052: q
      1053: q
      1058: q
      1059: q
      1060: q
      1062: q
      1063: q
      1065: q
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: q
      1075: 2
      1076: q
      1077: 2q
      1078: q
      1079: 2
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1091: q
      1098: q
      1102: q
      1144: q
      1146: q
      1164: q
      1166: q
      1184: q
      1185: q
      1188: 2q
      1191: q
      1194: q
      1195: q
      1196: q
      1197: q
      1210: 2
      1212: 1
      1225: q
      1226: 2
      1228: 1
      1229: 1
      1236: q
      1244: 2
      1246: 1
      1247: 1
      1252: q
      1263: 2
      1272: q
      1274: q
      1277: q
      1281: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1302: q
      1307: q
      1340: 1
      1342: 1
      1372: 1
      1374: 1
      1407: 2
      1411: 1
      1412: 1
      1438: 1
      1445: 1
      1452: 1
      1458: 1
      1472: q
      1483: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1528: 1
      1529: 1
      1556: 1
      1640: 1
      1643: 1
      1651: 1
      1667: 1
      1670: 1
      1674: 1
      1726: 1
      1804: 1
      1826: 1
      1827: 1
      1929: 1

1930:    0: 2q+2
         1: 2q+2
         2: 2q+2
         3: 2q+2
         4: q^2+q+2
         5: 2q+2
         6: q^2+q+2
         7: q^2+q+2
         8: 2q+2
         9: q^2+q+2
        10: 2q+2
        11: 2q+2
        12: q^2+q+2
        13: 2q+2
        14: q^2+q+2
        15: 2q+2
        16: 2q+2
        17: 2q+2
        18: q^2+q+2
        19: q+2
        20: q+2
        21: q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: 2q+2
        29: q+2
        30: q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: 2q+2
        44: q^2+q+2
        45: 2q+2
        46: 2q+2
        47: 2q+2
        48: q^2+q+2
        49: q+2
        50: q+2
        51: q+2
        52: q+2
        53: q+2
        54: q+2
        55: q+2
        56: q+2
        57: q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: 2q+2
        69: q+2
        70: q+2
        71: q+2
        72: 2
        73: 2
        75: q+2
        77: q+2
        79: q+2
        80: 2q+2
        81: 2q+2
        82: q+2
        83: q+2
        84: 2q+2
        85: 2q+2
        86: q+2
        87: q+2
        88: 2q+2
        89: 2q+2
        90: q^2+q+2
        91: q+2
        92: q+2
        93: q+2
        94: q+2
        95: q+2
        96: q+2
        97: q+2
        98: q+2
        99: q+2
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 2
       114: q+2
       116: q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: 2q+2
       125: 2q+2
       126: q+2
       128: q+2
       130: q+2
       132: q+2
       133: q+2
       134: q+2
       135: 2
       136: 2
       137: 2q+2
       138: q+2
       139: q+2
       140: 2
       141: q+2
       142: 2
       143: 2q+2
       144: q+2
       145: q+2
       146: q+2
       147: 2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: q+2
       158: q+2
       159: q+2
       160: q+2
       161: q+2
       162: q+2
       163: q+2
       164: q+2
       165: q+2
       166: q+2
       167: q+2
       168: q+2
       170: 1
       171: 1
       174: q+1
       175: q+1
       178: q+2
       180: q+2
       182: 2
       183: 1
       184: 1
       185: 1
       186: 1
       188: 2
       190: q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 2
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: q+2
       212: q+2
       214: q+2
       216: q+2
       218: q+2
       219: q+2
       220: q+2
       221: q+2
       222: 2
       223: 2
       224: 2
       225: 2
       226: q+2
       227: q+2
       228: q+2
       229: 2
       230: 2
       231: q+2
       232: q+2
       233: q+2
       234: 2
       235: 2
       236: q+2
       238: q+2
       240: q+2
       242: q+2
       243: q+2
       244: 2
       245: 2
       246: q+2
       247: 2
       248: 2
       249: q+1
       250: q+2
       251: q+2
       252: q+2
       253: q+2
       254: q+2
       255: q+2
       256: q+2
       257: q+2
       258: q+2
       260: 1
       261: 1
       264: 1
       265: 1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: q+2
       282: q+2
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+2
       290: 2
       292: 2
       293: 1
       294: 1
       295: 1
       296: 1
       298: 2
       299: 1
       300: 1
       302: 2
       303: 1
       304: 1
       306: 2
       307: 1
       308: 1
       309: 1
       310: 1
       312: 2
       314: 2
       316: q+2
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: q+2
       328: q+2
       330: q+2
       332: q+2
       333: q+2
       334: 2
       335: 2
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q+2
       345: q+2
       346: q+2
       347: 2
       348: 2
       349: 2
       350: 2
       351: 2
       352: q+2
       353: q+2
       354: q+2
       355: 2
       356: 2
       357: 2
       358: 2
       359: 2
       361: q+2
       363: q+2
       365: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: 2
       372: 2
       373: q+1
       374: q+2
       375: q+2
       376: q+2
       378: 1
       379: 1
       382: 1
       383: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: q+2
       412: q+2
       414: q+2
       416: 2
       418: 2
       419: 1
       420: 1
       421: 1
       422: 1
       424: 2
       426: 1
       428: 2
       429: 1
       430: 1
       431: 1
       432: 1
       434: 2
       436: 2
       437: 1
       438: 1
       439: 1
       440: 1
       442: 2
       443: 1
       444: 1
       446: 2
       447: 1
       448: 1
       449: 1
       450: 1
       452: 2
       453: 1
       454: 1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: q+2
       470: q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 2
       482: 2
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q+2
       493: 2
       494: 2
       495: 1
       496: 2
       497: q+2
       498: 2
       499: 2
       500: 1
       501: 2
       503: q+2
       505: q+2
       507: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       523: 1
       526: 1
       527: 1
       530: 1
       531: 1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: q+2
       586: 2
       588: 2
       589: 1
       590: 1
       595: 1
       596: 1
       598: 1
       600: 1
       602: 2
       603: 1
       604: 1
       606: 2
       607: 1
       608: 1
       610: 2
       612: 2
       614: 1
       615: 1
       616: 1
       618: 2
       619: 1
       620: 1
       621: 1
       622: 1
       624: 2
       626: 2
       628: 2
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+2
       638: q+2
       640: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: 2
       676: 2
       677: 1
       678: 2
       679: 1
       680: 2
       681: 2
       682: 2
       683: 1
       684: 2
       685: 1
       686: q+2
       687: 2
       688: 2
       689: 1
       690: 2
       691: 2
       692: q+1
       699: 1
       700: 1
       706: 1
       707: 1
       710: 1
       711: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       776: 2
       778: 2
       780: 1
       782: 1
       784: 1
       790: 2
       792: 1
       793: 1
       794: 1
       796: 2
       798: 2
       800: 2
       801: 1
       802: 1
       807: 1
       808: 1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: 2
       825: 1
       826: 1
       831: 1
       832: 1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: 2
       852: 2
       854: 2
       856: 1
       858: 2
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: 2
       878: 2
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       890: 1
       891: 1
       897: 1
       898: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       957: 1
       959: 1
       962: 1
       963: 1
       965: 1
       966: 1
       972: 2
       976: 1
       977: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       993: 2
       995: 1
       997: 1
      1003: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 1
      1023: 1
      1025: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 1
      1039: 1
      1043: 1
      1047: 2
      1049: 2
      1051: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1104: 1
      1105: 1
      1142: 1
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1186: 1
      1187: 1
      1192: 2
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1211: 2
      1213: 1
      1215: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2
      1228: 1
      1229: 1
      1231: 1
      1237: 1
      1239: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1257: 1
      1263: 2
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1308: 1
      1309: 1
      1338: 1
      1341: 1
      1343: 1
      1373: 1
      1375: 1
      1408: 2
      1411: 1
      1412: 1
      1416: 1
      1417: 1
      1434: 1
      1437: 1
      1439: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1457: 1
      1459: 1
      1465: 1
      1471: 1
      1473: 1
      1475: 1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1531: 1
      1532: 1
      1557: 1
      1635: 1
      1638: 1
      1640: 1
      1644: 1
      1652: 1
      1660: 1
      1662: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1727: 1
      1805: 1
      1824: 1
      1826: 1
      1828: 1
      1930: 1

1931:    0: q^4+2q^3+3q^2+2q
         1: q^4+2q^3+3q^2+2q
         2: q^4+2q^3+3q^2+2q
         3: q^4+2q^3+3q^2+2q
         4: q^5+q^4+2q^3+2q^2+2q
         5: q^4+2q^3+3q^2+2q
         6: q^5+q^4+2q^3+2q^2+2q
         7: q^5+q^4+2q^3+2q^2+2q
         8: q^4+2q^3+3q^2+2q
         9: q^5+q^4+2q^3+2q^2+2q
        10: 2q^3+2q^2+2q
        11: 2q^3+2q^2+2q
        12: q^4+2q^3+q^2+2q
        13: q^4+2q^3+3q^2+2q
        14: q^5+q^4+2q^3+2q^2+2q
        15: q^4+2q^3+3q^2+2q
        16: q^4+2q^3+3q^2+2q
        17: q^4+2q^3+3q^2+2q
        18: q^5+q^4+2q^3+2q^2+2q
        19: q^3+2q^2+2q
        20: q^3+2q^2+2q
        21: q^3+2q^2+2q
        22: q^4+2q^3+3q^2+2q
        23: q^4+2q^3+3q^2+2q
        24: q^4+2q^3+3q^2+2q
        25: q^4+2q^3+3q^2+2q
        26: q^4+2q^3+3q^2+2q
        27: q^4+2q^3+3q^2+2q
        28: 2q^3+2q^2+2q
        29: q^3+q^2+2q
        30: q^3+2q^2+2q
        31: 2q^3+2q^2+2q
        32: q^4+2q^3+3q^2+2q
        33: q^4+2q^3+3q^2+2q
        34: 2q^3+2q^2+2q
        35: q^4+2q^3+3q^2+2q
        36: q^4+2q^3+3q^2+2q
        38: q^4+2q^3+3q^2+2q
        40: q^4+2q^3+3q^2+2q
        42: q^4+2q^3+3q^2+2q
        43: 2q^3+2q^2+2q
        44: q^4+2q^3+q^2+2q
        45: 2q^3+2q^2+2q
        46: q^4+2q^3+3q^2+2q
        47: q^4+2q^3+3q^2+2q
        48: q^5+q^4+2q^3+2q^2+2q
        49: q^3+2q^2+2q
        50: q^3+2q^2+2q
        51: q^3+2q^2+2q
        52: q^3+2q^2+2q
        53: q^3+2q^2+2q
        54: q^3+2q^2+2q
        55: q^3+2q^2+2q
        56: q^3+2q^2+2q
        57: q^3+2q^2+2q
        58: q^3+q^2+q
        59: q^3+q^2+q
        60: q^3+q^2+q
        61: q^3+q^2+q
        63: 2q^3+2q^2+2q
        65: q^4+2q^3+3q^2+2q
        67: q^4+2q^3+3q^2+2q
        68: 2q^3+2q^2+2q
        69: q^3+2q^2+2q
        70: q^3+q^2+2q
        71: q^3+q^2+2q
        72: q^2+2q
        73: q^2+2q
        75: q^3+2q^2+2q
        77: q^3+2q^2+2q
        79: q^3+2q^2+2q
        80: 2q^3+2q^2+2q
        81: q^4+2q^3+3q^2+2q
        82: q^3+q^2+2q
        83: q^3+2q^2+2q
        84: 2q^3+2q^2+2q
        85: q^4+2q^3+3q^2+2q
        86: q^3+q^2+2q
        87: q^3+2q^2+2q
        88: 2q^3+2q^2+2q
        89: 2q^3+2q^2+2q
        90: q^4+2q^3+q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: q^3+2q^2+2q
        95: q^3+2q^2+2q
        96: q^3+2q^2+2q
        97: q^3+2q^2+2q
        98: q^3+2q^2+2q
        99: q^3+2q^2+2q
       100: q^3+2q^2+2q
       101: q^3+2q^2+2q
       102: q^3+2q^2+2q
       104: q^3+q^2+q
       105: q^3+q^2+q
       107: q
       108: q
       109: q
       110: q
       112: q^2+2q
       114: q^3+q^2+2q
       116: q^3+2q^2+2q
       117: q^3+q^2+q
       118: q^3+q^2+q
       119: q^3+q^2+q
       120: q^3+q^2+q
       122: 2q^3+2q^2+2q
       124: q^4+2q^3+3q^2+2q
       125: 2q^3+2q^2+2q
       126: q^3+q^2+2q
       128: q^3+2q^2+2q
       130: q^3+2q^2+2q
       132: q^3+2q^2+2q
       133: q^3+q^2+2q
       134: q^3+2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 2q^3+2q^2+2q
       138: q^3+2q^2+2q
       139: q^3+q^2+2q
       140: q^2+2q
       141: q^3+q^2+2q
       142: q^2+2q
       143: 2q^3+2q^2+2q
       144: q^3+2q^2+2q
       145: q^3+q^2+2q
       146: q^3+q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: q^3+q^2+2q
       150: q^3+2q^2+2q
       152: q^3+2q^2+2q
       154: q^3+2q^2+2q
       156: q^3+2q^2+2q
       157: q^2+2q
       158: q^2+2q
       159: q^2+2q
       160: q^3+2q^2+2q
       161: q^3+2q^2+2q
       162: q^3+2q^2+2q
       163: q^3+2q^2+2q
       164: q^3+2q^2+2q
       165: q^3+2q^2+2q
       166: q^3+2q^2+2q
       167: q^3+2q^2+2q
       168: q^3+2q^2+2q
       170: q
       171: q
       174: q^3+q^2+q
       175: q^3+q^2+q
       178: q^3+2q^2+2q
       180: q^3+q^2+2q
       182: q^2+2q
       183: q
       184: q
       185: q
       186: q
       188: q^2+2q
       190: q^3+q^2+2q
       191: q^3+q^2+q
       192: q^3+q^2+q
       193: q
       194: q
       195: q
       196: q
       198: q^2+2q
       199: q^3+q^2+q
       200: q^3+q^2+q
       201: q
       202: q
       203: q
       204: q
       206: q^2+2q
       208: 2q^3+2q^2+2q
       210: q^3+q^2+2q
       212: q^3+2q^2+2q
       214: q^3+2q^2+2q
       216: q^3+2q^2+2q
       218: q^3+2q^2+2q
       219: q^3+q^2+2q
       220: q^2+2q
       221: q^2+2q
       222: 2q
       223: q^2+2q
       224: 2q
       225: q^2+2q
       226: q^3+q^2+2q
       227: q^3+q^2+2q
       228: q^3+2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: q^3+q^2+2q
       232: q^3+q^2+2q
       233: q^3+2q^2+2q
       234: q^2+2q
       235: q^2+2q
       236: q^3+2q^2+2q
       238: q^3+2q^2+2q
       240: q^3+2q^2+2q
       242: q^3+2q^2+2q
       243: q^3+q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: q^3+q^2+2q
       247: 2q
       248: 2q
       249: q^2+q
       250: q^2+2q
       251: q^2+2q
       252: q^2+2q
       253: q^2+2q
       254: q^2+2q
       255: q^2+2q
       256: q^3+2q^2+2q
       257: q^3+2q^2+2q
       258: q^3+2q^2+2q
       260: q
       261: q
       264: q
       265: q
       268: q
       270: q
       272: q
       274: q
       276: q^3+q^2+q
       277: q^3+q^2+q
       280: q^3+q^2+2q
       282: q^3+2q^2+2q
       283: q
       284: q
       285: q
       286: q
       288: q^3+q^2+2q
       290: q^2+2q
       292: q^2+2q
       293: q
       294: q
       295: q
       296: q
       298: 2q
       299: q
       300: q
       302: q^2+2q
       303: q
       304: q
       306: q^2+2q
       307: q
       308: q
       309: q
       310: q
       312: q^2+2q
       314: q^2+2q
       316: q^3+2q^2+2q
       318: q^3+q^2+2q
       319: q
       320: q
       321: q
       322: q
       324: q^2+2q
       326: q^3+q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: q^2+2q
       334: 2q
       335: 2q
       336: q
       337: 2q
       339: 2q
       341: 2q
       343: q^2+q
       344: q^3+q^2+2q
       345: q^2+2q
       346: q^2+2q
       347: 2q
       348: q^2+2q
       349: 2q
       350: q^2+2q
       351: 2q
       352: q^3+q^2+2q
       353: q^2+2q
       354: q^2+2q
       355: 2q
       356: q^2+2q
       357: 2q
       358: q^2+2q
       359: 2q
       361: q^3+2q^2+2q
       363: q^3+2q^2+2q
       365: q^3+2q^2+2q
       366: q^3+q^2+2q
       367: q^3+q^2+2q
       368: q^3+2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 2q
       372: 2q
       373: q^2+q
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       378: q
       379: q
       382: q
       383: q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: q^2+2q
       412: q^2+2q
       414: q^3+q^2+2q
       416: 2q
       418: q^2+2q
       419: q
       420: q
       421: q
       422: q
       424: 2q
       426: q
       428: 2q
       429: q
       430: q
       431: q
       432: q
       434: q^2+2q
       436: q^2+2q
       437: q
       438: q
       439: q
       440: q
       442: 2q
       443: q
       444: q
       446: 2q
       447: q
       448: q
       449: q
       450: q
       452: q^2+2q
       453: q
       454: q
       456: q^2+2q
       457: q
       458: q
       460: 2q
       461: q
       462: q
       464: 2q
       466: q^3+q^2+2q
       468: q^3+2q^2+2q
       470: q^3+q^2+2q
       471: q
       472: q
       473: q
       474: q
       476: q^2+2q
       478: q^2+2q
       480: 2q
       481: 2q
       482: 2q
       483: q
       484: 2q
       486: 2q
       488: 2q
       490: q^2+q
       491: q
       492: q^2+2q
       493: 2q
       494: 2q
       495: q
       496: 2q
       497: q^2+2q
       498: 2q
       499: 2q
       500: q
       501: 2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: q^3+q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: 2q
       512: q^2+2q
       513: 2q
       514: q^2+2q
       515: 2q
       516: 2q
       517: q^2+q
       522: q
       523: q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: q
       548: q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: q
       564: q
       566: q
       567: q
       571: q
       572: q
       574: q
       576: q
       581: 2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q
       590: q
       595: q
       596: q
       598: q
       600: q
       602: 2q
       603: q
       604: q
       606: q^2+2q
       607: q
       608: q
       610: 2q
       612: 2q
       614: q
       615: q
       616: q
       618: 2q
       619: q
       620: q
       621: q
       622: q
       624: q^2+2q
       626: 2q
       628: 2q
       630: q
       631: q
       632: q
       634: 2q
       636: q^2+2q
       638: q^2+2q
       640: q^3+q^2+2q
       641: q
       642: q
       643: q
       644: q
       646: q^2+2q
       647: q
       648: q
       649: q
       650: q
       652: q^2+2q
       654: 2q
       656: 2q
       657: 2q
       659: 2q
       661: 2q
       663: q^2+q
       664: q
       665: q
       674: 2q
       675: 2q
       676: 2q
       677: q
       679: q
       680: 2q
       681: 2q
       682: 2q
       683: q
       685: q
       686: q^2+2q
       687: 2q
       688: 2q
       689: q
       699: q
       700: q
       706: q
       707: q
       710: q
       711: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: q
       736: q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: q
       752: q
       754: q
       755: q
       759: q
       760: q
       763: q
       764: q
       766: q
       767: q
       773: 2q
       776: 2q
       778: 2q
       780: q
       782: q
       792: q
       793: q
       794: q
       796: 2q
       798: 2q
       800: 2q
       801: q
       802: q
       807: q
       808: q
       810: q
       812: q
       817: q
       818: q
       820: 2q
       822: 2q
       824: 2q
       825: q
       826: q
       831: q
       832: q
       834: q
       836: q
       842: q^2+2q
       844: 2q
       845: q
       846: q
       847: q
       848: q
       850: q^2+2q
       852: 2q
       854: 2q
       856: q
       866: q
       870: q
       871: q
       874: q
       875: q
       877: 2q
       878: 2q
       879: q
       880: q
       890: q
       891: q
       897: q
       898: q
       913: q
       915: q
       917: q
       919: q
       921: q
       923: q
       937: q
       939: q
       941: q
       943: q
       945: q
       947: q
       962: q
       963: q
       965: q
       966: q
       972: 2q
       976: q
       977: q
       980: q
       981: q
       995: q
      1011: q
      1013: q
      1019: 2q
      1021: q
      1023: q
      1035: 2q
      1037: q
      1039: q
      1049: 2q
      1051: 2q
      1052: q
      1053: q
      1058: q
      1059: q
      1061: q
      1063: q
      1065: q
      1076: q
      1080: q
      1083: q
      1084: q
      1092: q
      1093: q
      1142: q
      1149: q
      1151: q
      1169: q
      1171: q
      1186: q
      1187: q
      1200: q
      1201: q
      1223: 1
      1231: q
      1249: q
      1265: 2q
      1267: q
      1275: q
      1279: q
      1281: q
      1287: q
      1339: 1
      1416: q
      1417: q
      1434: q
      1447: 1
      1465: q
      1481: 1
      1558: 1
      1636: 1
      1638: 1
      1672: 1
      1728: 1
      1806: 1
      1824: 1
      1931: 1

1932:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+q
        60: 2q^2+q+1
        61: 2q
        62: q^2+2q+1
        63: q^2+q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+q+1
       104: q^2
       105: q
       106: q
       107: q^2+1
       108: q
       109: q+1
       111: 1
       113: q+1
       115: q+1
       117: q^2+2q+1
       118: q^2+q
       119: 2q^2+q+1
       120: 2q
       121: q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       173: q^2+q+1
       174: q^2
       175: q
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q^2+1
       184: q
       185: q+1
       187: 1
       189: q+1
       191: q^2+2q+1
       192: q^2+q
       193: q^2+1
       194: q
       195: q+1
       197: 1
       199: 2q^2+q+1
       200: 2q
       201: q^2+1
       202: q
       203: q+1
       205: 1
       207: q^2+2q+1
       208: q^2+q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+2q+1
       244: q^2+q+1
       245: q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+q+1
       276: q^2
       277: q
       278: q
       279: q+1
       281: q+1
       283: q^2+1
       284: q
       285: q+1
       287: q+1
       289: 1
       291: 1
       293: q^2+1
       294: q
       295: q+1
       297: 1
       299: q^2+1
       300: q
       301: 1
       303: q+1
       305: 1
       307: q^2+1
       308: q
       309: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q^2+1
       320: q
       321: q+1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q^2+q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q^2+q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q^2+1
       420: q
       421: q+1
       423: 1
       425: 1
       427: 2
       429: q^2+1
       430: q
       431: q+1
       433: 1
       435: 1
       437: q^2+1
       438: q
       439: q+1
       441: 1
       443: 1
       444: 1
       445: 2
       447: q^2+1
       448: q
       449: q+1
       451: 1
       453: q^2+1
       454: q
       455: 1
       457: q+1
       459: 1
       461: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q^2+1
       472: q
       473: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+2q+1
       493: q^2+q+1
       494: q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q^2+q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       547: 1
       549: 1
       553: 1
       557: 1
       561: 2
       565: 1
       569: 1
       573: 1
       576: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       589: q^2+1
       590: q
       591: 1
       595: q+1
       597: 1
       599: 1
       601: 2
       603: q^2+1
       604: q
       605: 1
       607: q+1
       609: 1
       611: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: q^2+1
       620: q
       621: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q^2+1
       642: q
       643: q+1
       645: 1
       647: q^2+1
       648: q
       649: q+1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q^2+q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q^2+q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q^2+q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       693: 1
       698: 1
       705: 1
       709: 1
       713: 1
       721: 1
       725: 1
       729: 1
       733: 1
       735: 1
       737: 1
       741: 1
       745: 1
       749: 2
       753: 1
       757: 1
       761: 1
       765: 1
       767: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       787: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 1
       799: 1
       801: q^2+1
       802: q
       803: 1
       807: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       817: 2
       819: 2
       821: 1
       823: 1
       825: q^2+1
       826: q
       827: 1
       831: q+1
       833: 1
       835: 1
       837: 2
       839: 2
       841: q+1
       843: 1
       844: 1
       845: q^2+1
       846: q
       847: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       884: 1
       888: 1
       896: 1
       900: 1
       912: 1
       916: 1
       918: 1
       920: 1
       924: 1
       932: 1
       934: 1
       936: 1
       940: 2
       944: 1
       948: 1
       956: 2
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       990: 1
       992: 2
       994: 1
       996: 1
       998: 1
      1002: 1
      1006: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1028: 1
      1030: 2
      1032: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q^2+1
      1053: q
      1054: 1
      1058: q+1
      1060: 1
      1062: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1090: 1
      1098: 1
      1103: 1
      1110: 1
      1114: 1
      1144: 1
      1146: 1
      1148: 1
      1152: 1
      1164: 2
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1198: 1
      1202: 1
      1210: 2
      1212: 1
      1214: 1
      1216: 1
      1226: 2
      1228: 1
      1229: 1
      1230: 1
      1232: 1
      1236: 1
      1238: 1
      1242: 1
      1244: 2
      1246: 2
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1306: 1
      1314: 1
      1340: 1
      1342: 1
      1344: 1
      1348: 1
      1372: 2
      1376: 1
      1380: 1
      1404: 1
      1407: 1
      1410: 1
      1412: 1
      1414: 1
      1418: 1
      1438: 1
      1440: 1
      1448: 1
      1450: 1
      1452: 1
      1456: 1
      1458: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1478: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1525: 1
      1529: 1
      1541: 1
      1563: 1
      1583: 1
      1603: 1
      1607: 1
      1643: 1
      1645: 1
      1651: 1
      1653: 1
      1661: 1
      1663: 1
      1667: 1
      1674: 1
      1737: 1
      1761: 1
      1785: 1
      1827: 1
      1829: 1
      1932: 1

1933:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+q
        60: 2q
        61: 2q^2+q+1
        62: q^2+q
        63: q^2+2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       105: q^2+q+1
       106: q^2
       107: q
       108: q^2+1
       109: q+1
       112: 1
       114: q+1
       116: q+1
       117: q^2+2q+1
       118: q^2+q
       119: 2q
       120: 2q^2+q+1
       121: q^2+q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       171: 1
       173: q
       174: q
       175: q^2+q+1
       176: q^2
       178: q+1
       180: q+1
       182: 1
       183: q
       184: q^2+1
       185: q+1
       188: 1
       190: q+1
       191: q^2+2q+1
       192: q^2+q
       193: q
       194: q^2+1
       195: q+1
       198: 1
       199: 2q
       200: 2q^2+q+1
       201: q
       202: q^2+1
       203: q+1
       206: 1
       207: q^2+q
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+2q+1
       244: q^2+q+1
       245: q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q
       276: q
       277: q^2+q+1
       278: q^2
       280: q+1
       282: q+1
       283: q
       284: q^2+1
       285: q+1
       288: q+1
       290: 1
       292: 1
       293: q
       294: q^2+1
       295: q+1
       298: 1
       299: q
       300: q^2+1
       302: 1
       303: q+1
       306: 1
       307: q
       308: q^2+1
       309: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q
       320: q^2+1
       321: q+1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q^2+q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q^2+q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q
       420: q^2+1
       421: q+1
       424: 1
       426: 1
       428: 2
       429: q
       430: q^2+1
       431: q+1
       434: 1
       436: 1
       437: q
       438: q^2+1
       439: q+1
       442: 1
       443: 1
       444: 1
       446: 2
       447: q
       448: q^2+1
       449: q+1
       452: 1
       453: q
       454: q^2+1
       456: 1
       457: q+1
       460: 1
       461: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q
       472: q^2+1
       473: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+2q+1
       493: q^2+q+1
       494: q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q^2+q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       546: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 2
       567: 1
       572: 1
       573: 1
       576: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: q
       590: q^2+1
       591: 1
       595: q+1
       598: 1
       600: 1
       602: 2
       603: q
       604: q^2+1
       606: 1
       607: q+1
       610: 1
       612: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: q
       620: q^2+1
       621: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q
       642: q^2+1
       643: q+1
       646: 1
       647: q
       648: q^2+1
       649: q+1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q^2+q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q^2+q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q^2+q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       694: 1
       700: 1
       707: 1
       711: 1
       714: 1
       724: 1
       728: 1
       732: 1
       734: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 2
       755: 1
       760: 1
       764: 1
       765: 1
       767: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       787: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 1
       800: 1
       801: q
       802: q^2+1
       803: 1
       807: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       817: 2
       820: 2
       822: 1
       824: 1
       825: q
       826: q^2+1
       827: 1
       831: q+1
       834: 1
       836: 1
       838: 2
       839: 2
       842: q+1
       843: 1
       844: 1
       845: q
       846: q^2+1
       847: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       885: 1
       891: 1
       898: 1
       901: 1
       915: 1
       917: 1
       919: 1
       923: 1
       925: 1
       933: 1
       935: 1
       937: 1
       941: 2
       945: 1
       949: 1
       957: 2
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       981: 1
       983: 1
       986: 1
       988: 1
       990: 1
       993: 2
       995: 1
       997: 1
       998: 1
      1003: 1
      1006: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1028: 1
      1031: 2
      1032: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: q^2+1
      1054: 1
      1058: q+1
      1061: 1
      1063: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1093: 1
      1099: 1
      1105: 1
      1111: 1
      1115: 1
      1145: 1
      1147: 1
      1151: 1
      1153: 1
      1165: 2
      1169: 1
      1173: 1
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1211: 2
      1213: 1
      1215: 1
      1216: 1
      1227: 2
      1228: 1
      1229: 1
      1231: 1
      1232: 1
      1237: 1
      1239: 1
      1242: 1
      1245: 2
      1246: 2
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1309: 1
      1315: 1
      1341: 1
      1343: 1
      1345: 1
      1349: 1
      1373: 2
      1377: 1
      1381: 1
      1405: 1
      1408: 1
      1410: 1
      1412: 1
      1417: 1
      1419: 1
      1439: 1
      1440: 1
      1449: 1
      1450: 1
      1453: 1
      1457: 1
      1459: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1478: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1526: 1
      1532: 1
      1542: 1
      1564: 1
      1584: 1
      1604: 1
      1608: 1
      1644: 1
      1645: 1
      1652: 1
      1653: 1
      1662: 1
      1663: 1
      1668: 1
      1674: 1
      1738: 1
      1762: 1
      1786: 1
      1828: 1
      1829: 1
      1933: 1

1934:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+2q+1
        60: 2q
        61: 2q^2+q+1
        62: q^2+2q+1
        63: q^2+q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       105: q^2
       106: q^2+q+1
       107: q
       108: q^2+1
       110: q+1
       111: 1
       113: q+1
       115: q+1
       117: q^2+q
       118: q^2+2q+1
       119: 2q
       120: 2q^2+q+1
       121: q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       172: 1
       173: q
       174: q
       175: q^2
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       183: q
       184: q^2+1
       186: q+1
       187: 1
       189: q+1
       191: q^2+q
       192: q^2+2q+1
       193: q
       194: q^2+1
       196: q+1
       197: 1
       199: 2q
       200: 2q^2+q+1
       201: q
       202: q^2+1
       204: q+1
       205: 1
       207: q^2+2q+1
       208: q^2+q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+2q+1
       244: q^2+q+1
       245: q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q
       277: q^2
       278: q^2+q+1
       279: q+1
       281: q+1
       283: q
       284: q^2+1
       286: q+1
       287: q+1
       289: 1
       291: 1
       293: q
       294: q^2+1
       296: q+1
       297: 1
       299: q
       300: q^2+1
       301: 1
       304: q+1
       305: 1
       307: q
       308: q^2+1
       310: q+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q
       320: q^2+1
       322: q+1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q^2+q+1
       335: q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q^2+q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q
       420: q^2+1
       422: q+1
       423: 1
       425: 1
       427: 2
       429: q
       430: q^2+1
       432: q+1
       433: 1
       435: 1
       437: q
       438: q^2+1
       440: q+1
       441: 1
       443: 1
       444: 1
       445: 2
       447: q
       448: q^2+1
       450: q+1
       451: 1
       453: q
       454: q^2+1
       455: 1
       458: q+1
       459: 1
       462: 2
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q
       472: q^2+1
       474: q+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+2q+1
       493: q^2+q+1
       494: q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q^2+q+1
       499: q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       545: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 2
       568: 1
       570: 1
       574: 1
       575: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       589: q
       590: q^2+1
       592: 1
       596: q+1
       597: 1
       599: 1
       601: 2
       603: q
       604: q^2+1
       605: 1
       608: q+1
       609: 1
       611: 1
       613: 1
       615: 1
       616: 1
       617: 2
       619: q
       620: q^2+1
       622: q+1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 2
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q
       642: q^2+1
       644: q+1
       645: 1
       647: q
       648: q^2+1
       650: q+1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q^2+q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q^2+q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q^2+q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       696: 1
       697: 1
       708: 1
       712: 1
       716: 1
       723: 1
       727: 1
       731: 1
       733: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 2
       756: 1
       758: 1
       762: 1
       766: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       788: 1
       789: 2
       793: 1
       794: 1
       795: 2
       797: 1
       799: 1
       801: q
       802: q^2+1
       804: 1
       808: q+1
       809: 1
       811: 1
       813: 2
       815: 1
       816: 1
       818: 2
       819: 2
       821: 1
       823: 1
       825: q
       826: q^2+1
       828: 1
       832: q+1
       833: 1
       835: 1
       837: 2
       840: 2
       841: q+1
       843: 1
       844: 1
       845: q
       846: q^2+1
       848: q+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       887: 1
       889: 1
       899: 1
       902: 1
       914: 1
       916: 1
       918: 1
       922: 1
       927: 1
       932: 1
       934: 1
       938: 1
       942: 2
       946: 1
       950: 1
       958: 2
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: 1
       982: 1
       985: 1
       989: 1
       991: 1
       992: 2
       994: 1
       996: 1
       999: 1
      1002: 1
      1007: 1
      1014: 2
      1016: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1029: 1
      1030: 2
      1033: 2
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q
      1053: q^2+1
      1055: 1
      1059: q+1
      1060: 1
      1062: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1101: 1
      1102: 1
      1112: 1
      1116: 1
      1144: 1
      1146: 1
      1150: 1
      1154: 1
      1166: 2
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1199: 1
      1204: 1
      1210: 2
      1212: 1
      1214: 1
      1217: 1
      1226: 2
      1228: 1
      1229: 1
      1230: 1
      1233: 1
      1236: 1
      1238: 1
      1243: 1
      1244: 2
      1247: 2
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1305: 1
      1307: 1
      1316: 1
      1340: 1
      1342: 1
      1346: 1
      1350: 1
      1374: 2
      1378: 1
      1382: 1
      1404: 1
      1407: 1
      1411: 1
      1413: 1
      1415: 1
      1420: 1
      1438: 1
      1441: 1
      1448: 1
      1451: 1
      1452: 1
      1456: 1
      1458: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1479: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1528: 1
      1530: 1
      1543: 1
      1565: 1
      1585: 1
      1605: 1
      1609: 1
      1643: 1
      1646: 1
      1651: 1
      1654: 1
      1661: 1
      1664: 1
      1667: 1
      1674: 1
      1739: 1
      1763: 1
      1787: 1
      1827: 1
      1830: 1
      1934: 1

1935:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q
        59: q^2+2q+1
        60: 2q^2+q+1
        61: 2q
        62: q^2+q
        63: q^2+2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2
       104: q^2+q+1
       105: q
       106: q
       107: q^2+1
       108: q
       110: q+1
       112: 1
       114: q+1
       116: q+1
       117: q^2+q
       118: q^2+2q+1
       119: 2q^2+q+1
       120: 2q
       121: q^2+q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+q+1
       141: q^2+2q+1
       142: q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 1
       173: q^2
       174: q^2+q+1
       175: q
       176: q
       178: q+1
       180: q+1
       182: 1
       183: q^2+1
       184: q
       186: q+1
       188: 1
       190: q+1
       191: q^2+q
       192: q^2+2q+1
       193: q^2+1
       194: q
       196: q+1
       198: 1
       199: 2q^2+q+1
       200: 2q
       201: q^2+1
       202: q
       204: q+1
       206: 1
       207: q^2+q
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+q+1
       235: q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+2q+1
       244: q^2+q+1
       245: q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q^2
       276: q^2+q+1
       277: q
       278: q
       280: q+1
       282: q+1
       283: q^2+1
       284: q
       286: q+1
       288: q+1
       290: 1
       292: 1
       293: q^2+1
       294: q
       296: q+1
       298: 1
       299: q^2+1
       300: q
       302: 1
       304: q+1
       306: 1
       307: q^2+1
       308: q
       310: q+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q^2+1
       320: q
       322: q+1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q^2+q+1
       335: q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q^2+q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+q+1
       370: q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q^2+1
       420: q
       422: q+1
       424: 1
       426: 1
       428: 2
       429: q^2+1
       430: q
       432: q+1
       434: 1
       436: 1
       437: q^2+1
       438: q
       440: q+1
       442: 1
       443: 1
       444: 1
       446: 2
       447: q^2+1
       448: q
       450: q+1
       452: 1
       453: q^2+1
       454: q
       456: 1
       458: q+1
       460: 1
       462: 2
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q^2+1
       472: q
       474: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+2q+1
       493: q^2+q+1
       494: q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q^2+q+1
       499: q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       548: 1
       551: 1
       556: 1
       560: 1
       564: 2
       566: 1
       571: 1
       574: 1
       575: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: q^2+1
       590: q
       592: 1
       596: q+1
       598: 1
       600: 1
       602: 2
       603: q^2+1
       604: q
       606: 1
       608: q+1
       610: 1
       612: 1
       614: 1
       615: 1
       616: 1
       618: 2
       619: q^2+1
       620: q
       622: q+1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 2
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q^2+1
       642: q
       644: q+1
       646: 1
       647: q^2+1
       648: q
       650: q+1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q^2+q+1
       676: q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q^2+q+1
       682: q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q^2+q+1
       688: q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       699: 1
       701: 1
       706: 1
       710: 1
       715: 1
       722: 1
       726: 1
       730: 1
       734: 1
       736: 1
       740: 1
       744: 1
       748: 1
       752: 2
       754: 1
       759: 1
       763: 1
       766: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       788: 1
       790: 2
       793: 1
       794: 1
       796: 2
       798: 1
       800: 1
       801: q^2+1
       802: q
       804: 1
       808: q+1
       810: 1
       812: 1
       814: 2
       815: 1
       816: 1
       818: 2
       820: 2
       822: 1
       824: 1
       825: q^2+1
       826: q
       828: 1
       832: q+1
       834: 1
       836: 1
       838: 2
       840: 2
       842: q+1
       843: 1
       844: 1
       845: q^2+1
       846: q
       848: q+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q^2+q+1
       878: q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       890: 1
       892: 1
       897: 1
       903: 1
       913: 1
       917: 1
       919: 1
       921: 1
       926: 1
       933: 1
       935: 1
       939: 1
       943: 2
       947: 1
       951: 1
       959: 2
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       980: 1
       983: 1
       986: 1
       989: 1
       991: 1
       993: 2
       995: 1
       997: 1
       999: 1
      1003: 1
      1007: 1
      1015: 2
      1016: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1029: 1
      1031: 2
      1033: 2
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q^2+1
      1053: q
      1055: 1
      1059: q+1
      1061: 1
      1063: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1094: 1
      1104: 1
      1106: 1
      1113: 1
      1117: 1
      1145: 1
      1147: 1
      1149: 1
      1155: 1
      1167: 2
      1171: 1
      1175: 1
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1200: 1
      1205: 1
      1211: 2
      1213: 1
      1215: 1
      1217: 1
      1227: 2
      1228: 1
      1229: 1
      1231: 1
      1233: 1
      1237: 1
      1239: 1
      1243: 1
      1245: 2
      1247: 2
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1308: 1
      1310: 1
      1317: 1
      1341: 1
      1343: 1
      1347: 1
      1351: 1
      1375: 2
      1379: 1
      1383: 1
      1405: 1
      1408: 1
      1411: 1
      1413: 1
      1416: 1
      1421: 1
      1439: 1
      1441: 1
      1449: 1
      1451: 1
      1453: 1
      1457: 1
      1459: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1479: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1531: 1
      1533: 1
      1544: 1
      1566: 1
      1586: 1
      1606: 1
      1610: 1
      1644: 1
      1646: 1
      1652: 1
      1654: 1
      1662: 1
      1664: 1
      1668: 1
      1674: 1
      1740: 1
      1764: 1
      1788: 1
      1828: 1
      1830: 1
      1935: 1

1936:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+q+1
        59: 2q
        60: q^2+2q+1
        61: q^2+q
        62: q^2+2q+1
        63: q^2+q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+q+1
       104: q
       105: q^2
       106: q
       107: q+1
       109: q^2+1
       110: q
       111: 1
       113: q+1
       115: q+1
       117: 2q^2+q+1
       118: 2q
       119: q^2+2q+1
       120: q^2+q
       121: q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       173: q^2+q+1
       174: q
       175: q^2
       176: q
       177: q+1
       179: q+1
       181: 1
       183: q+1
       185: q^2+1
       186: q
       187: 1
       189: q+1
       191: 2q^2+q+1
       192: 2q
       193: q+1
       195: q^2+1
       196: q
       197: 1
       199: q^2+2q+1
       200: q^2+q
       201: q+1
       203: q^2+1
       204: q
       205: 1
       207: q^2+2q+1
       208: q^2+q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+2q+1
       244: q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: q^2+q+1
       276: q
       277: q^2
       278: q
       279: q+1
       281: q+1
       283: q+1
       285: q^2+1
       286: q
       287: q+1
       289: 1
       291: 1
       293: q+1
       295: q^2+1
       296: q
       297: 1
       299: q+1
       301: 1
       303: q^2+1
       304: q
       305: 1
       307: q+1
       309: q^2+1
       310: q
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q+1
       321: q^2+1
       322: q
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       419: q+1
       421: q^2+1
       422: q
       423: 1
       425: 1
       427: 2
       429: q+1
       431: q^2+1
       432: q
       433: 1
       435: 1
       437: q+1
       439: q^2+1
       440: q
       441: 1
       443: 2
       445: 2
       447: q+1
       449: q^2+1
       450: q
       451: 1
       453: q+1
       455: 1
       457: q^2+1
       458: q
       459: 1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       471: q+1
       473: q^2+1
       474: q
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+2q+1
       493: q+1
       494: q^2+q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q+1
       499: q^2+q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 2
       549: 1
       553: 1
       557: 1
       561: 1
       563: 1
       565: 1
       569: 1
       573: 1
       574: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       589: q+1
       593: 1
       595: q^2+1
       596: q
       597: 1
       599: 1
       601: 2
       603: q+1
       605: 1
       607: q^2+1
       608: q
       609: 1
       611: 1
       613: 1
       615: 2
       617: 2
       619: q+1
       621: q^2+1
       622: q
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       641: q+1
       643: q^2+1
       644: q
       645: 1
       647: q+1
       649: q^2+1
       650: q
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: q^2+q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: q^2+q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q+1
       688: q^2+q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       693: 1
       696: 1
       705: 1
       709: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 2
       737: 1
       741: 1
       745: 1
       749: 1
       751: 1
       753: 1
       757: 1
       761: 1
       765: 1
       766: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       789: 2
       793: 2
       795: 2
       797: 1
       799: 1
       801: q+1
       805: 1
       807: q^2+1
       808: q
       809: 1
       811: 1
       813: 2
       815: 2
       817: 1
       818: 1
       819: 2
       821: 1
       823: 1
       825: q+1
       829: 1
       831: q^2+1
       832: q
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       845: q+1
       847: q^2+1
       848: q
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q^2+q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       884: 1
       887: 1
       896: 1
       904: 1
       912: 1
       916: 2
       920: 1
       928: 1
       932: 2
       936: 1
       940: 1
       942: 1
       944: 1
       952: 1
       956: 1
       958: 1
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       978: 1
       982: 1
       985: 1
       988: 1
       989: 1
       992: 2
       994: 1
       996: 1
      1000: 1
      1002: 1
      1004: 1
      1014: 2
      1016: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: 1
      1058: q^2+1
      1059: q
      1060: 1
      1062: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1089: 1
      1098: 1
      1101: 1
      1118: 1
      1122: 1
      1144: 2
      1148: 1
      1156: 1
      1164: 1
      1166: 1
      1168: 1
      1176: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1198: 1
      1206: 1
      1210: 2
      1212: 1
      1214: 1
      1218: 1
      1226: 2
      1228: 2
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1302: 1
      1305: 1
      1318: 1
      1340: 2
      1352: 1
      1356: 1
      1372: 1
      1374: 1
      1384: 1
      1388: 1
      1404: 1
      1407: 1
      1410: 1
      1411: 1
      1414: 1
      1422: 1
      1438: 1
      1442: 1
      1448: 1
      1452: 1
      1454: 1
      1456: 1
      1458: 1
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1476: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1525: 1
      1528: 1
      1545: 1
      1567: 1
      1587: 1
      1611: 1
      1615: 1
      1643: 1
      1647: 1
      1651: 1
      1655: 1
      1661: 1
      1665: 1
      1667: 1
      1674: 1
      1745: 1
      1765: 1
      1789: 1
      1827: 1
      1831: 1
      1936: 1

1937:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q
        59: 2q^2+q+1
        60: q^2+2q+1
        61: q^2+q
        62: q^2+q
        63: q^2+2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q^2+q+1
       105: q
       106: q^2
       107: q+1
       109: q
       110: q^2+1
       112: 1
       114: q+1
       116: q+1
       117: 2q
       118: 2q^2+q+1
       119: q^2+2q+1
       120: q^2+q
       121: q^2+q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 1
       173: q
       174: q^2+q+1
       175: q
       176: q^2
       178: q+1
       180: q+1
       182: 1
       183: q+1
       185: q
       186: q^2+1
       188: 1
       190: q+1
       191: 2q
       192: 2q^2+q+1
       193: q+1
       195: q
       196: q^2+1
       198: 1
       199: q^2+2q+1
       200: q^2+q
       201: q+1
       203: q
       204: q^2+1
       206: 1
       207: q^2+q
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+2q+1
       244: q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: 1
       264: 1
       268: 1
       274: 1
       275: q
       276: q^2+q+1
       277: q
       278: q^2
       280: q+1
       282: q+1
       283: q+1
       285: q
       286: q^2+1
       288: q+1
       290: 1
       292: 1
       293: q+1
       295: q
       296: q^2+1
       298: 1
       299: q+1
       302: 1
       303: q
       304: q^2+1
       306: 1
       307: q+1
       309: q
       310: q^2+1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q+1
       321: q
       322: q^2+1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       419: q+1
       421: q
       422: q^2+1
       424: 1
       426: 1
       428: 2
       429: q+1
       431: q
       432: q^2+1
       434: 1
       436: 1
       437: q+1
       439: q
       440: q^2+1
       442: 1
       443: 2
       446: 2
       447: q+1
       449: q
       450: q^2+1
       452: 1
       453: q+1
       456: 1
       457: q
       458: q^2+1
       460: 1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       471: q+1
       473: q
       474: q^2+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+2q+1
       493: q+1
       494: q^2+q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q+1
       499: q^2+q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 2
       551: 1
       556: 1
       560: 1
       562: 1
       564: 1
       566: 1
       571: 1
       573: 1
       574: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       589: q+1
       593: 1
       595: q
       596: q^2+1
       598: 1
       600: 1
       602: 2
       603: q+1
       606: 1
       607: q
       608: q^2+1
       610: 1
       612: 1
       614: 1
       615: 2
       618: 2
       619: q+1
       621: q
       622: q^2+1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       641: q+1
       643: q
       644: q^2+1
       646: 1
       647: q+1
       649: q
       650: q^2+1
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: q^2+q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: q^2+q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q+1
       688: q^2+q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       694: 1
       699: 1
       706: 1
       710: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 2
       740: 1
       744: 1
       748: 1
       750: 1
       752: 1
       754: 1
       759: 1
       763: 1
       765: 1
       766: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       790: 2
       793: 2
       796: 2
       798: 1
       800: 1
       801: q+1
       805: 1
       807: q
       808: q^2+1
       810: 1
       812: 1
       814: 2
       815: 2
       817: 1
       818: 1
       820: 2
       822: 1
       824: 1
       825: q+1
       829: 1
       831: q
       832: q^2+1
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       845: q+1
       847: q
       848: q^2+1
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q^2+q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       885: 1
       890: 1
       897: 1
       905: 1
       913: 1
       917: 2
       921: 1
       929: 1
       933: 2
       939: 1
       941: 1
       943: 1
       947: 1
       953: 1
       957: 1
       959: 1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       980: 1
       983: 1
       986: 1
       988: 1
       989: 1
       993: 2
       995: 1
       997: 1
      1000: 1
      1003: 1
      1004: 1
      1015: 2
      1016: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: 1
      1058: q
      1059: q^2+1
      1061: 1
      1063: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1092: 1
      1099: 1
      1104: 1
      1119: 1
      1123: 1
      1145: 2
      1149: 1
      1157: 1
      1165: 1
      1167: 1
      1171: 1
      1177: 1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1200: 1
      1207: 1
      1211: 2
      1213: 1
      1215: 1
      1218: 1
      1227: 2
      1228: 2
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1303: 1
      1308: 1
      1319: 1
      1341: 2
      1353: 1
      1357: 1
      1373: 1
      1375: 1
      1385: 1
      1389: 1
      1405: 1
      1408: 1
      1410: 1
      1411: 1
      1416: 1
      1423: 1
      1439: 1
      1442: 1
      1449: 1
      1453: 1
      1454: 1
      1457: 1
      1459: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1476: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1526: 1
      1531: 1
      1546: 1
      1568: 1
      1588: 1
      1612: 1
      1616: 1
      1644: 1
      1647: 1
      1652: 1
      1655: 1
      1662: 1
      1665: 1
      1668: 1
      1674: 1
      1746: 1
      1766: 1
      1790: 1
      1828: 1
      1831: 1
      1937: 1

1938:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+q
        39: q^2+2q+1
        40: q^2+q
        41: q^2+2q+1
        42: q^2+q
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q
        59: 2q^2+q+1
        60: q^2+q
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+q
        64: q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q^2
       105: q
       106: q^2+q+1
       108: q+1
       109: q
       110: q^2+1
       111: 1
       113: q+1
       115: q+1
       117: 2q
       118: 2q^2+q+1
       119: q^2+q
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       172: 1
       173: q
       174: q^2
       175: q
       176: q^2+q+1
       177: q+1
       179: q+1
       181: 1
       184: q+1
       185: q
       186: q^2+1
       187: 1
       189: q+1
       191: 2q
       192: 2q^2+q+1
       194: q+1
       195: q
       196: q^2+1
       197: 1
       199: q^2+q
       200: q^2+2q+1
       202: q+1
       203: q
       204: q^2+1
       205: 1
       207: q^2+2q+1
       208: q^2+q
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       237: q+1
       239: q+1
       241: q+1
       243: q^2+2q+1
       244: q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       262: 1
       266: 1
       269: 1
       273: 1
       275: q
       276: q^2
       277: q
       278: q^2+q+1
       279: q+1
       281: q+1
       284: q+1
       285: q
       286: q^2+1
       287: q+1
       289: 1
       291: 1
       294: q+1
       295: q
       296: q^2+1
       297: 1
       300: q+1
       301: 1
       303: q
       304: q^2+1
       305: 1
       308: q+1
       309: q
       310: q^2+1
       311: 1
       313: 1
       315: q+1
       317: q+1
       320: q+1
       321: q
       322: q^2+1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+2q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 2
       338: 2
       340: 2
       342: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^2+q+1
       359: 2
       360: q+1
       362: q+1
       364: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: 1
       417: 1
       420: q+1
       421: q
       422: q^2+1
       423: 1
       425: 1
       427: 2
       430: q+1
       431: q
       432: q^2+1
       433: 1
       435: 1
       438: q+1
       439: q
       440: q^2+1
       441: 1
       444: 2
       445: 2
       448: q+1
       449: q
       450: q^2+1
       451: 1
       454: q+1
       455: 1
       457: q
       458: q^2+1
       459: 1
       461: 1
       462: 1
       463: 2
       465: q+1
       467: q+1
       469: q+1
       472: q+1
       473: q
       474: q^2+1
       475: 1
       477: 1
       479: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: 1
       484: 2
       485: 2
       487: 2
       489: q+1
       491: 1
       492: q^2+2q+1
       493: q+1
       494: q^2+q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q+1
       499: q^2+q+1
       500: 1
       501: 2
       502: q+1
       504: q+1
       506: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 2
       552: 1
       555: 1
       559: 1
       561: 1
       563: 1
       568: 1
       570: 1
       575: 1
       576: 1
       577: 1
       580: 1
       583: q+1
       585: 1
       587: 1
       590: q+1
       594: 1
       595: q
       596: q^2+1
       597: 1
       599: 1
       601: 2
       604: q+1
       605: 1
       607: q
       608: q^2+1
       609: 1
       611: 1
       613: 1
       616: 2
       617: 2
       620: q+1
       621: q
       622: q^2+1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       632: 1
       633: 2
       635: q+1
       637: q+1
       639: q+1
       642: q+1
       643: q
       644: q^2+1
       645: 1
       648: q+1
       649: q
       650: q^2+1
       651: 1
       653: 1
       655: 1
       656: 1
       657: 2
       658: 2
       660: 2
       662: q+1
       664: 1
       665: 1
       666: 2
       668: 2
       670: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: q^2+q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: q^2+q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q+1
       688: q^2+q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       697: 1
       698: 1
       708: 1
       712: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 2
       739: 1
       743: 1
       747: 1
       749: 1
       751: 1
       756: 1
       758: 1
       762: 1
       767: 1
       768: 1
       769: 1
       772: 1
       775: 2
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       789: 2
       794: 2
       795: 2
       797: 1
       799: 1
       802: q+1
       806: 1
       807: q
       808: q^2+1
       809: 1
       811: 1
       813: 2
       816: 2
       817: 1
       818: 1
       819: 2
       821: 1
       823: 1
       826: q+1
       830: 1
       831: q
       832: q^2+1
       833: 1
       835: 1
       837: 2
       839: 1
       840: 1
       841: q+1
       843: 1
       844: 1
       846: q+1
       847: q
       848: q^2+1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       858: 1
       859: 2
       861: 2
       863: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q^2+q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       888: 1
       889: 1
       899: 1
       906: 1
       914: 1
       918: 2
       922: 1
       930: 1
       934: 2
       938: 1
       940: 1
       942: 1
       946: 1
       955: 1
       956: 1
       958: 1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: 1
       982: 1
       985: 1
       990: 1
       991: 1
       992: 2
       994: 1
       996: 1
      1001: 1
      1002: 1
      1005: 1
      1014: 2
      1017: 2
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: 1
      1058: q
      1059: q^2+1
      1060: 1
      1062: 1
      1066: 2
      1068: 2
      1070: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1102: 1
      1103: 1
      1120: 1
      1124: 1
      1146: 2
      1150: 1
      1158: 1
      1164: 1
      1166: 1
      1170: 1
      1178: 1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1199: 1
      1208: 1
      1210: 2
      1212: 1
      1214: 1
      1219: 1
      1226: 2
      1229: 2
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1306: 1
      1307: 1
      1320: 1
      1342: 2
      1354: 1
      1358: 1
      1372: 1
      1374: 1
      1386: 1
      1390: 1
      1404: 1
      1407: 1
      1412: 1
      1413: 1
      1415: 1
      1424: 1
      1438: 1
      1443: 1
      1448: 1
      1452: 1
      1455: 1
      1456: 1
      1458: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1529: 1
      1530: 1
      1547: 1
      1569: 1
      1589: 1
      1613: 1
      1617: 1
      1643: 1
      1648: 1
      1651: 1
      1656: 1
      1661: 1
      1666: 1
      1667: 1
      1674: 1
      1747: 1
      1767: 1
      1791: 1
      1827: 1
      1832: 1
      1938: 1

1939:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+2q^2+2q+1
         5: 2q^2+3q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+3q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+3q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: q^2+2q+1
        39: q^2+q
        40: q^2+2q+1
        41: q^2+q
        42: q^2+2q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+q+1
        59: 2q
        60: q^2+q
        61: q^2+2q+1
        62: q^2+q
        63: q^2+2q+1
        64: q^2+q
        65: q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q^2+3q+1
        90: q^3+2q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2
       104: q
       105: q^2+q+1
       106: q
       108: q+1
       109: q^2+1
       110: q
       112: 1
       114: q+1
       116: q+1
       117: 2q^2+q+1
       118: 2q
       119: q^2+q
       120: q^2+2q+1
       121: q^2+q
       122: q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+q+1
       149: q^2+2q+1
       150: q^2+2q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       171: 1
       173: q^2
       174: q
       175: q^2+q+1
       176: q
       178: q+1
       180: q+1
       182: 1
       184: q+1
       185: q^2+1
       186: q
       188: 1
       190: q+1
       191: 2q^2+q+1
       192: 2q
       194: q+1
       195: q^2+1
       196: q
       198: 1
       199: q^2+q
       200: q^2+2q+1
       202: q+1
       203: q^2+1
       204: q
       206: 1
       207: q^2+q
       208: q^2+2q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q+1
       235: q^2+q+1
       236: q^2+2q+1
       238: q+1
       240: q+1
       242: q+1
       243: q^2+2q+1
       244: q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: 2
       248: 2
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       261: 1
       265: 1
       270: 1
       272: 1
       275: q^2
       276: q
       277: q^2+q+1
       278: q
       280: q+1
       282: q+1
       284: q+1
       285: q^2+1
       286: q
       288: q+1
       290: 1
       292: 1
       294: q+1
       295: q^2+1
       296: q
       298: 1
       300: q+1
       302: 1
       303: q^2+1
       304: q
       306: 1
       308: q+1
       309: q^2+1
       310: q
       312: 1
       314: 1
       316: q+1
       318: q+1
       320: q+1
       321: q^2+1
       322: q
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+2q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 2
       339: 2
       341: 2
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 2
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^2+q+1
       359: 2
       361: q+1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+q+1
       371: 2
       372: 2
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: 1
       418: 1
       420: q+1
       421: q^2+1
       422: q
       424: 1
       426: 1
       428: 2
       430: q+1
       431: q^2+1
       432: q
       434: 1
       436: 1
       438: q+1
       439: q^2+1
       440: q
       442: 1
       444: 2
       446: 2
       448: q+1
       449: q^2+1
       450: q
       452: 1
       454: q+1
       456: 1
       457: q^2+1
       458: q
       460: 1
       461: 1
       462: 1
       464: 2
       466: q+1
       468: q+1
       470: q+1
       472: q+1
       473: q^2+1
       474: q
       476: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: 1
       484: 2
       486: 2
       488: 2
       490: q+1
       491: 1
       492: q^2+2q+1
       493: q+1
       494: q^2+q+1
       495: 1
       496: 2
       497: q^2+2q+1
       498: q+1
       499: q^2+q+1
       500: 1
       501: 2
       503: q+1
       505: q+1
       507: q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q^2+q+1
       515: 2
       516: 2
       517: q+1
       518: 2
       519: 2
       520: q+1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 2
       550: 1
       554: 1
       558: 1
       562: 1
       564: 1
       567: 1
       572: 1
       575: 1
       576: 1
       578: 1
       581: 1
       584: q+1
       586: 1
       588: 1
       590: q+1
       594: 1
       595: q^2+1
       596: q
       598: 1
       600: 1
       602: 2
       604: q+1
       606: 1
       607: q^2+1
       608: q
       610: 1
       612: 1
       614: 1
       616: 2
       618: 2
       620: q+1
       621: q^2+1
       622: q
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       632: 1
       634: 2
       636: q+1
       638: q+1
       640: q+1
       642: q+1
       643: q^2+1
       644: q
       646: 1
       648: q+1
       649: q^2+1
       650: q
       652: 1
       654: 1
       655: 1
       656: 1
       657: 2
       659: 2
       661: 2
       663: q+1
       664: 1
       665: 1
       667: 2
       669: 2
       671: q+1
       672: 2
       673: 1
       674: 2
       675: q+1
       676: q^2+q+1
       677: 1
       678: 2
       679: 1
       680: 2
       681: q+1
       682: q^2+q+1
       683: 1
       684: 2
       685: 1
       686: q^2+2q+1
       687: q+1
       688: q^2+q+1
       689: 1
       690: 2
       691: 2
       692: q+1
       700: 1
       701: 1
       707: 1
       711: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 2
       738: 1
       742: 1
       746: 1
       750: 1
       752: 1
       755: 1
       760: 1
       764: 1
       767: 1
       768: 1
       770: 1
       773: 1
       776: 2
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       790: 2
       794: 2
       796: 2
       798: 1
       800: 1
       802: q+1
       806: 1
       807: q^2+1
       808: q
       810: 1
       812: 1
       814: 2
       816: 2
       817: 1
       818: 1
       820: 2
       822: 1
       824: 1
       826: q+1
       830: 1
       831: q^2+1
       832: q
       834: 1
       836: 1
       838: 2
       839: 1
       840: 1
       842: q+1
       843: 1
       844: 1
       846: q+1
       847: q^2+1
       848: q
       850: 1
       852: 1
       854: 1
       856: 1
       857: 1
       858: 1
       860: 2
       862: 2
       864: q+1
       865: 2
       866: 1
       867: 1
       868: 1
       869: 2
       870: 1
       871: 1
       872: 1
       873: 2
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q^2+q+1
       879: 1
       880: 1
       881: 2
       882: 2
       883: q+1
       891: 1
       892: 1
       898: 1
       907: 1
       915: 1
       919: 2
       923: 1
       931: 1
       935: 2
       937: 1
       941: 1
       943: 1
       945: 1
       954: 1
       957: 1
       959: 1
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       981: 1
       983: 1
       986: 1
       990: 1
       991: 1
       993: 2
       995: 1
       997: 1
      1001: 1
      1003: 1
      1005: 1
      1015: 2
      1017: 2
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: 1
      1058: q^2+1
      1059: q
      1061: 1
      1063: 1
      1067: 2
      1069: 2
      1071: q+1
      1072: 2
      1073: 1
      1074: 1
      1075: 2
      1076: 1
      1077: 1
      1078: 1
      1079: 2
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1094: 1
      1105: 1
      1106: 1
      1121: 1
      1125: 1
      1147: 2
      1151: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1179: 1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1201: 1
      1209: 1
      1211: 2
      1213: 1
      1215: 1
      1219: 1
      1227: 2
      1229: 2
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1309: 1
      1310: 1
      1321: 1
      1343: 2
      1355: 1
      1359: 1
      1373: 1
      1375: 1
      1387: 1
      1391: 1
      1405: 1
      1408: 1
      1412: 1
      1413: 1
      1417: 1
      1425: 1
      1439: 1
      1443: 1
      1449: 1
      1453: 1
      1455: 1
      1457: 1
      1459: 1
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1477: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1532: 1
      1533: 1
      1548: 1
      1570: 1
      1590: 1
      1614: 1
      1618: 1
      1644: 1
      1648: 1
      1652: 1
      1656: 1
      1662: 1
      1666: 1
      1668: 1
      1674: 1
      1748: 1
      1768: 1
      1792: 1
      1828: 1
      1832: 1
      1939: 1

1940:    0: 13q^3+14q^2+5q+1
         1: 3q^4+13q^3+14q^2+5q+1
         2: 13q^3+14q^2+5q+1
         3: 3q^4+13q^3+14q^2+5q+1
         4: 4q^4+12q^3+11q^2+5q+1
         5: 13q^3+14q^2+5q+1
         6: q^5+6q^4+12q^3+11q^2+5q+1
         7: 4q^4+12q^3+11q^2+5q+1
         8: 13q^3+14q^2+5q+1
         9: 2q^5+6q^4+9q^3+8q^2+4q+1
        10: 8q^3+13q^2+5q+1
        11: 8q^3+13q^2+5q+1
        12: 2q^4+9q^3+10q^2+5q+1
        13: 13q^3+14q^2+5q+1
        14: 4q^4+12q^3+11q^2+5q+1
        15: 13q^3+14q^2+5q+1
        16: 8q^3+13q^2+5q+1
        17: 8q^3+13q^2+5q+1
        18: 3q^4+8q^3+8q^2+4q+1
        19: 9q^3+11q^2+5q+1
        20: 2q^4+9q^3+11q^2+5q+1
        21: 9q^3+11q^2+5q+1
        22: 13q^3+14q^2+5q+1
        23: 3q^4+13q^3+14q^2+5q+1
        24: 13q^3+14q^2+5q+1
        25: 13q^3+14q^2+5q+1
        26: 3q^4+13q^3+14q^2+5q+1
        27: 13q^3+14q^2+5q+1
        28: 4q^3+12q^2+5q+1
        29: 6q^3+10q^2+5q+1
        30: 9q^3+11q^2+5q+1
        31: 8q^3+13q^2+5q+1
        32: 13q^3+14q^2+5q+1
        33: 8q^3+13q^2+5q+1
        34: 8q^3+13q^2+5q+1
        35: 13q^3+14q^2+5q+1
        36: 8q^3+13q^2+5q+1
        37: 7q^3+8q^2+3q+1
        38: 6q^3+6q^2+2q
        39: q^4+7q^3+8q^2+3q+1
        40: 2q^4+6q^3+6q^2+2q
        41: 7q^3+8q^2+3q+1
        42: 6q^3+6q^2+2q
        43: 8q^3+13q^2+5q+1
        44: 2q^4+9q^3+10q^2+5q+1
        45: 8q^3+13q^2+5q+1
        46: 8q^3+13q^2+5q+1
        47: 8q^3+13q^2+5q+1
        48: 3q^4+8q^3+8q^2+4q+1
        49: 4q^3+10q^2+5q+1
        50: 4q^3+10q^2+5q+1
        51: 5q^3+8q^2+4q+1
        52: 9q^3+11q^2+5q+1
        53: 2q^4+9q^3+11q^2+5q+1
        54: 9q^3+11q^2+5q+1
        55: 9q^3+11q^2+5q+1
        56: 2q^4+9q^3+11q^2+5q+1
        57: 9q^3+11q^2+5q+1
        58: 3q^3+8q^2+4q+1
        59: q^3+4q^2+q
        60: 3q^3+8q^2+4q+1
        61: q^3+4q^2+q
        62: 4q^3+8q^2+3q+1
        63: 4q^3+5q^2+2q
        64: 7q^3+8q^2+3q+1
        65: 6q^3+6q^2+2q
        66: 4q^3+8q^2+3q+1
        67: 4q^3+5q^2+2q
        68: 4q^3+12q^2+5q+1
        69: 2q^3+7q^2+4q+1
        70: 6q^3+10q^2+5q+1
        71: 2q^3+9q^2+5q+1
        72: 2q^3+7q^2+5q+1
        73: 2q^3+7q^2+5q+1
        74: 3q^3+5q^2+3q+1
        75: 2q^3+3q^2+2q
        76: 3q^3+5q^2+3q+1
        77: q^4+2q^3+3q^2+2q
        78: 3q^3+5q^2+3q+1
        79: 2q^3+3q^2+2q
        80: 8q^3+13q^2+5q+1
        81: 8q^3+13q^2+5q+1
        82: 6q^3+10q^2+5q+1
        83: 9q^3+11q^2+5q+1
        84: 8q^3+13q^2+5q+1
        85: 8q^3+13q^2+5q+1
        86: 6q^3+10q^2+5q+1
        87: 9q^3+11q^2+5q+1
        88: q^3+11q^2+5q+1
        89: q^3+11q^2+5q+1
        90: q^4+5q^3+7q^2+4q+1
        91: 4q^3+10q^2+5q+1
        92: 4q^3+10q^2+5q+1
        93: 5q^3+8q^2+4q+1
        94: 4q^3+10q^2+5q+1
        95: 4q^3+10q^2+5q+1
        96: 5q^3+8q^2+4q+1
        97: 4q^3+10q^2+5q+1
        98: 4q^3+10q^2+5q+1
        99: 5q^3+8q^2+4q+1
       100: 9q^3+11q^2+5q+1
       101: 2q^4+9q^3+11q^2+5q+1
       102: 9q^3+11q^2+5q+1
       103: 2q^3+6q^2+3q+1
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       106: 2q^2
       107: q^3+5q^2+4q+1
       108: q^2+q
       109: q^3+5q^2+4q+1
       110: q^2+q
       111: 3q^2+3q+1
       112: q^2+2q
       113: 2q^3+5q^2+3q+1
       114: 2q^3+2q^2+2q
       115: 3q^3+5q^2+3q+1
       116: 2q^3+3q^2+2q
       117: 3q^3+8q^2+4q+1
       118: q^3+4q^2+q
       119: 3q^3+8q^2+4q+1
       120: q^3+4q^2+q
       121: 4q^3+8q^2+3q+1
       122: 4q^3+5q^2+2q
       123: 4q^3+8q^2+3q+1
       124: 4q^3+5q^2+2q
       125: q^3+11q^2+5q+1
       126: 6q^2+4q+1
       127: 3q^2+2q+1
       128: q^3+q^2+2q
       129: 3q^2+2q+1
       130: q^3+q^2+2q
       131: q^3+2q^2+2q+1
       132: 2q^2+q
       133: 2q^3+9q^2+5q+1
       134: 2q^3+7q^2+4q+1
       135: 2q^3+7q^2+5q+1
       136: 2q^3+7q^2+5q+1
       137: q^3+11q^2+5q+1
       138: 2q^3+7q^2+4q+1
       139: 2q^3+9q^2+5q+1
       140: 2q^3+7q^2+5q+1
       141: 6q^3+10q^2+5q+1
       142: 2q^3+7q^2+5q+1
       143: q^3+11q^2+5q+1
       144: 2q^3+7q^2+4q+1
       145: 2q^3+9q^2+5q+1
       146: 6q^3+10q^2+5q+1
       147: 2q^3+7q^2+5q+1
       148: 2q^3+7q^2+5q+1
       149: 6q^3+10q^2+5q+1
       150: 9q^3+11q^2+5q+1
       151: 3q^3+5q^2+3q+1
       152: 2q^3+3q^2+2q
       153: 3q^3+5q^2+3q+1
       154: q^4+2q^3+3q^2+2q
       155: 3q^3+5q^2+3q+1
       156: 2q^3+3q^2+2q
       157: 6q^2+5q+1
       158: 6q^2+5q+1
       159: 2q^3+5q^2+4q+1
       160: 4q^3+10q^2+5q+1
       161: 4q^3+10q^2+5q+1
       162: 5q^3+8q^2+4q+1
       163: 4q^3+10q^2+5q+1
       164: 4q^3+10q^2+5q+1
       165: 5q^3+8q^2+4q+1
       166: 4q^3+10q^2+5q+1
       167: 4q^3+10q^2+5q+1
       168: 5q^3+8q^2+4q+1
       169: 3q^2+3q+1
       170: q
       171: q
       173: 2q^3+6q^2+3q+1
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       176: 2q^2
       177: 2q^2+2q+1
       178: q^2+q
       179: 3q^2+2q+1
       180: q^3+q^2+2q
       181: q^2+2q+1
       182: 2q
       183: q^3+5q^2+4q+1
       184: q^2+q
       185: q^3+5q^2+4q+1
       186: q^2+q
       187: 3q^2+3q+1
       188: q^2+2q
       189: 2q^3+5q^2+3q+1
       190: 2q^3+2q^2+2q
       191: q^3+7q^2+4q+1
       192: 4q^2+q
       193: q^3+5q^2+4q+1
       194: q^2+q
       195: q^3+5q^2+4q+1
       196: q^2+q
       197: 3q^2+3q+1
       198: q^2+2q
       199: q^3+7q^2+4q+1
       200: 4q^2+q
       201: q^3+5q^2+4q+1
       202: q^2+q
       203: q^3+5q^2+4q+1
       204: q^2+q
       205: 3q^2+3q+1
       206: q^2+2q
       207: q^3+7q^2+3q+1
       208: 4q^2+2q
       209: 2q^3+5q^2+3q+1
       210: 2q^3+2q^2+2q
       211: 3q^3+5q^2+3q+1
       212: 2q^3+3q^2+2q
       213: 3q^2+2q+1
       214: q^3+q^2+2q
       215: 3q^2+2q+1
       216: q^3+q^2+2q
       217: q^3+2q^2+2q+1
       218: 2q^2+q
       219: 6q^2+4q+1
       220: 6q^2+5q+1
       221: 4q^2+4q+1
       222: 4q^2+5q+1
       223: q^3+4q^2+4q+1
       224: 4q^2+5q+1
       225: q^3+4q^2+4q+1
       226: 6q^2+4q+1
       227: 2q^3+9q^2+5q+1
       228: 2q^3+7q^2+4q+1
       229: 2q^3+7q^2+5q+1
       230: 2q^3+7q^2+5q+1
       231: 6q^2+4q+1
       232: 2q^3+9q^2+5q+1
       233: 2q^3+7q^2+4q+1
       234: 2q^3+7q^2+5q+1
       235: 2q^3+7q^2+5q+1
       236: 2q^3+7q^2+4q+1
       237: 3q^2+2q+1
       238: q^3+q^2+2q
       239: 3q^2+2q+1
       240: q^3+q^2+2q
       241: q^3+2q^2+2q+1
       242: 2q^2+q
       243: 2q^3+9q^2+5q+1
       244: 2q^3+7q^2+5q+1
       245: 2q^3+7q^2+5q+1
       246: 6q^3+10q^2+5q+1
       247: 4q^2+8q+1
       248: 4q^2+8q+1
       249: 2q^3+5q^2+4q+1
       250: 6q^2+5q+1
       251: 6q^2+5q+1
       252: 2q^3+5q^2+4q+1
       253: 6q^2+5q+1
       254: 6q^2+5q+1
       255: 2q^3+5q^2+4q+1
       256: 4q^3+10q^2+5q+1
       257: 4q^3+10q^2+5q+1
       258: 5q^3+8q^2+4q+1
       259: q^2+2q+1
       260: q
       261: q
       263: 3q^2+3q+1
       264: q
       265: q
       267: 3q^2+3q+1
       268: q
       270: q
       271: 3q^2+3q+1
       272: q
       274: q
       275: q^3+5q^2+3q+1
       276: 2q^2+q
       277: 2q^2+q
       278: 2q^2
       279: 3q^2+2q+1
       280: q^3+q^2+2q
       281: 2q^2+2q+1
       282: q^2+q
       283: 2q^2+3q+1
       285: 2q^2+3q+1
       287: 2q^2+2q+1
       288: q^2+q
       289: q^2+2q+1
       290: 2q
       291: 2q+1
       292: q
       293: 3q^2+4q+1
       294: q^2+q
       295: 3q^2+4q+1
       296: q^2+q
       297: 2q^2+3q+1
       298: 2q
       299: q^3+5q^2+4q+1
       300: q^2+q
       301: q^2+2q+1
       302: 2q
       303: q^3+5q^2+4q+1
       304: q^2+q
       305: 3q^2+3q+1
       306: q^2+2q
       307: q^3+5q^2+4q+1
       308: q^2+q
       309: q^3+5q^2+4q+1
       310: q^2+q
       311: q^2+2q+1
       312: 2q
       313: 3q^2+3q+1
       314: q^2+2q
       315: 2q^2+2q+1
       316: q^2+q
       317: 3q^2+2q+1
       318: q^3+q^2+2q
       319: q^3+5q^2+4q+1
       320: q^2+q
       321: q^3+5q^2+4q+1
       322: q^2+q
       323: 3q^2+3q+1
       324: q^2+2q
       325: 2q^3+5q^2+3q+1
       326: 2q^3+2q^2+2q
       333: 4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: 3q^2+8q+1
       338: q^2+4q+1
       339: q^2+3q
       340: q^2+4q+1
       341: q^2+3q
       342: q^3+2q^2+2q+1
       343: 2q^2+q
       344: 6q^2+4q+1
       345: 6q^2+5q+1
       346: 4q^2+4q+1
       347: 4q^2+5q+1
       348: q^3+4q^2+4q+1
       349: 4q^2+5q+1
       350: q^3+4q^2+4q+1
       351: 4q^2+8q+1
       352: 6q^2+4q+1
       353: 6q^2+5q+1
       354: 4q^2+4q+1
       355: 4q^2+5q+1
       356: q^3+4q^2+4q+1
       357: 4q^2+5q+1
       358: q^3+4q^2+4q+1
       359: 4q^2+8q+1
       360: 3q^2+2q+1
       361: q^3+q^2+2q
       362: 3q^2+2q+1
       363: q^3+q^2+2q
       364: q^3+2q^2+2q+1
       365: 2q^2+q
       366: 6q^2+4q+1
       367: 2q^3+9q^2+5q+1
       368: 2q^3+7q^2+4q+1
       369: 2q^3+7q^2+5q+1
       370: 2q^3+7q^2+5q+1
       371: 4q^2+8q+1
       372: 4q^2+8q+1
       373: 2q^3+5q^2+4q+1
       374: 6q^2+5q+1
       375: 6q^2+5q+1
       376: 2q^3+5q^2+4q+1
       377: 2q+1
       381: q^2+2q+1
       382: q
       383: q
       385: 2q^2+3q+1
       386: q
       387: q
       389: q^2+2q+1
       390: q
       392: q
       393: 3q^2+3q+1
       394: q
       395: q
       397: q^2+2q+1
       398: q
       400: q
       401: 3q^2+3q+1
       402: q
       403: q
       405: 3q^2+3q+1
       407: q
       408: q
       413: 2q^2+2q+1
       414: q^2+q
       417: 2q+1
       418: q
       419: q^2+3q+1
       421: q^2+3q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: q^2+4q+1
       428: q^2+3q
       429: 2q^2+3q+1
       431: 2q^2+3q+1
       433: 2q+1
       434: q
       435: q^2+2q+1
       436: 2q
       437: 3q^2+4q+1
       438: q^2+q
       439: 3q^2+4q+1
       440: q^2+q
       441: 2q^2+3q+1
       442: 2q
       443: 3q^2+6q+1
       444: 2q
       445: q^2+4q+1
       446: q^2+3q
       447: 2q^2+3q+1
       449: 2q^2+3q+1
       451: 2q+1
       452: q
       453: 3q^2+4q+1
       454: q^2+q
       455: q^2+2q+1
       456: 2q
       457: 3q^2+4q+1
       458: q^2+q
       459: 2q^2+3q+1
       460: 2q
       461: 3q^2+6q+1
       462: 2q
       463: q^2+4q+1
       464: q^2+3q
       465: 3q^2+2q+1
       466: q^3+q^2+2q
       467: 2q^2+2q+1
       468: q^2+q
       469: 2q^2+2q+1
       470: q^2+q
       471: q^3+5q^2+4q+1
       472: q^2+q
       473: q^3+5q^2+4q+1
       474: q^2+q
       475: 3q^2+3q+1
       476: q^2+2q
       477: q^2+2q+1
       478: 2q
       479: 3q^2+4q+1
       480: q^2+4q
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: 3q^2+8q+1
       485: q^2+4q+1
       486: q^2+3q
       487: q^2+4q+1
       488: q^2+3q
       489: q^3+2q^2+2q+1
       490: 2q^2+q
       491: q^2+4q+1
       492: 4q^2+4q+1
       493: 2q^2+4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 4q^2+8q+1
       497: 4q^2+4q+1
       498: 2q^2+4q+1
       499: 2q^2+4q+1
       500: q^2+4q+1
       501: 4q^2+8q+1
       508: 6q^2+4q+1
       509: 6q^2+5q+1
       510: 4q^2+4q+1
       511: 4q^2+5q+1
       512: q^3+4q^2+4q+1
       513: 4q^2+5q+1
       514: q^3+4q^2+4q+1
       515: 4q+2
       516: 4q+2
       517: 2q^2+2q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       521: 2q+1
       529: 2q+1
       533: 2q+1
       537: q^2+2q+1
       538: q
       540: q
       541: 2q^2+3q+1
       542: q
       544: q
       545: q^2+3q+1
       546: q^2+2q
       547: q
       548: q
       549: 2q+1
       553: q^2+2q+1
       554: q
       556: q
       557: 2q^2+3q+1
       558: q
       560: q
       561: q^2+3q+1
       562: q^2+2q
       563: q
       564: q
       565: 3q^2+3q+1
       566: q
       567: q
       569: q^2+2q+1
       571: q
       572: q
       573: 3q^2+4q+1
       574: 2q
       576: 2q
       577: q^2+2q+1
       578: q^2+q
       580: 2q
       581: 2q
       585: 2q+1
       586: q
       589: q^2+3q+1
       591: 2q+1
       593: 2q+1
       595: q^2+3q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: q^2+4q+1
       602: q^2+3q
       603: q^2+3q+1
       605: 2q+1
       606: q
       607: q^2+3q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: 3q^2+6q+1
       616: 2q
       617: q^2+4q+1
       618: q^2+3q
       619: q^2+3q+1
       621: q^2+3q+1
       623: 2q+1
       624: q
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: 3q^2+6q+1
       632: 2q
       633: q^2+4q+1
       634: q^2+3q
       639: 2q^2+2q+1
       640: q^2+q
       641: 2q^2+3q+1
       643: 2q^2+3q+1
       645: 2q+1
       646: q
       647: 3q^2+4q+1
       648: q^2+q
       649: 3q^2+4q+1
       650: q^2+q
       651: q^2+2q+1
       652: 2q
       653: 2q^2+3q+1
       654: 2q
       655: 3q^2+4q+1
       656: q^2+4q
       657: 2q+2
       658: 2q+1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: q^2+q+1
       663: q^2+q+1
       664: 2q+2
       665: 4q+1
       672: q^2+4q+1
       673: 2q+1
       674: 4q+2
       675: 2q^2+4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: q^2+4q+1
       679: q^2+4q+1
       680: 4q+2
       681: 2q^2+4q+1
       682: 2q^2+4q+1
       683: 4q+1
       684: q^2+4q+1
       685: q^2+4q+1
       686: 4q^2+4q+1
       687: 2q^2+4q+1
       688: 2q^2+4q+1
       689: q^2+4q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       694: q^2+q
       696: q
       698: q
       699: q
       700: q
       709: 2q+1
       713: q+1
       717: q+1
       721: 2q+1
       725: 2q+1
       733: q^2+3q+1
       734: q^2+2q
       735: q
       736: q
       737: 2q+1
       741: 2q+1
       749: q^2+3q+1
       750: q^2+2q
       751: q
       752: q
       753: 2q+1
       757: q^2+2q+1
       759: q
       760: q
       761: 2q^2+3q+1
       763: q
       764: q
       765: 3q^2+4q+1
       766: 2q
       767: 2q
       769: q^2+2q+1
       770: q^2+q
       772: 2q
       773: 2q
       775: q+1
       776: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       785: 2q+1
       787: 2q+1
       791: 1
       793: 2q+2
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: q
       801: q^2+3q+1
       803: 2q+1
       805: 2q+1
       807: q^2+3q+1
       809: 2q+1
       810: q
       811: 2q+1
       812: q
       815: q^2+3q+1
       816: q
       817: 2q+2
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: q
       825: q^2+3q+1
       827: 2q+1
       829: 2q+1
       831: q^2+3q+1
       833: 2q+1
       834: q
       835: 2q+1
       836: q
       839: q^2+3q+1
       840: q
       843: 2q+2
       844: 2q
       845: q^2+3q+1
       847: q^2+3q+1
       849: 2q+1
       850: q
       851: 2q+1
       852: q
       855: 2q+1
       856: q
       857: q^2+2q+1
       858: 2q
       865: q+1
       866: 2
       867: q+1
       868: 2q+1
       869: 2q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 2q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 2q^2+4q+1
       878: 2q^2+4q+1
       879: 4q+1
       880: q^2+4q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q^2+2q+1
       885: q^2+q
       887: q
       888: q
       890: q
       891: q
       900: q+1
       904: q+1
       908: 1
       916: q+1
       917: q+1
       920: 2q+1
       924: q+1
       928: q+1
       940: q+1
       941: q+1
       944: 2q+1
       948: q+1
       952: q+1
       960: 2q+1
       964: 2q+2
       968: q+1
       969: q+1
       971: q
       972: q
       974: 2q+1
       988: q^2+2q+1
       989: q
       990: q
       994: 1
       995: 1
       998: 2
      1000: 2
      1004: q+1
      1006: q+1
      1008: 1
      1010: 1
      1012: 2
      1016: q+1
      1020: q+1
      1021: q+1
      1022: 2q+1
      1023: q
      1026: 2q+1
      1028: 2q+1
      1032: q+1
      1036: q+1
      1037: q+1
      1038: 2q+1
      1039: q
      1040: 2q+1
      1044: 2q+1
      1046: q+1
      1047: q
      1048: 2q+1
      1049: q
      1052: q^2+3q+1
      1054: 2q+1
      1056: 2q+1
      1058: q^2+3q+1
      1060: 2q+1
      1061: q
      1062: 2q+1
      1063: q
      1064: 1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 4q+1
      1084: 2q+2
      1085: 2q+1
      1086: q+1
      1087: q+1
      1114: 1
      1115: 1
      1122: 1
      1123: 1
      1126: 1
      1130: 2
      1134: 1
      1138: 1
      1139: 1
      1152: q+1
      1156: q+1
      1160: 1
      1172: q+1
      1176: q+1
      1180: 1
      1194: q+1
      1198: 2q+1
      1202: q+1
      1206: q+1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: q+1
      1230: 1
      1231: 1
      1232: 2
      1234: 2
      1240: q+1
      1242: q+1
      1246: q+1
      1248: 1
      1249: 1
      1250: 2
      1254: 2
      1258: q+1
      1260: q+1
      1262: q+1
      1263: q
      1266: 2q+1
      1267: q
      1268: 2q+1
      1270: 2q+1
      1274: q+1
      1275: q+1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1290: 1
      1291: 1
      1326: 1
      1330: 1
      1348: 1
      1349: 1
      1356: 1
      1357: 1
      1360: 1
      1364: 2
      1368: 1
      1380: 1
      1381: 1
      1388: 1
      1389: 1
      1392: 1
      1396: 2
      1400: 1
      1410: q+1
      1418: q+1
      1422: q+1
      1426: 1
      1430: 1
      1431: 1
      1440: 1
      1442: 1
      1444: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1465: 1
      1466: 2
      1468: 2
      1474: 1
      1476: q+1
      1478: q+1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1501: 1
      1502: 1
      1513: 1
      1514: 1
      1549: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1608: 1
      1615: 1
      1616: 1
      1619: 1
      1623: 2
      1627: 1
      1645: 1
      1647: 1
      1653: 1
      1655: 1
      1663: 1
      1665: 1
      1669: 1
      1674: 1
      1711: 1
      1712: 1
      1749: 1
      1773: 1
      1797: 1
      1807: 1
      1829: 1
      1831: 1
      1940: 1

1941:    0: 13q^3+14q^2+5q+1
         1: 3q^4+13q^3+14q^2+5q+1
         2: 13q^3+14q^2+5q+1
         3: 3q^4+13q^3+14q^2+5q+1
         4: 4q^4+12q^3+11q^2+5q+1
         5: 13q^3+14q^2+5q+1
         6: q^5+6q^4+12q^3+11q^2+5q+1
         7: 4q^4+12q^3+11q^2+5q+1
         8: 13q^3+14q^2+5q+1
         9: 2q^5+6q^4+9q^3+8q^2+4q+1
        10: 8q^3+13q^2+5q+1
        11: 8q^3+13q^2+5q+1
        12: 2q^4+9q^3+10q^2+5q+1
        13: 13q^3+14q^2+5q+1
        14: 4q^4+12q^3+11q^2+5q+1
        15: 13q^3+14q^2+5q+1
        16: 8q^3+13q^2+5q+1
        17: 8q^3+13q^2+5q+1
        18: 3q^4+8q^3+8q^2+4q+1
        19: 9q^3+11q^2+5q+1
        20: 2q^4+9q^3+11q^2+5q+1
        21: 9q^3+11q^2+5q+1
        22: 13q^3+14q^2+5q+1
        23: 3q^4+13q^3+14q^2+5q+1
        24: 13q^3+14q^2+5q+1
        25: 13q^3+14q^2+5q+1
        26: 3q^4+13q^3+14q^2+5q+1
        27: 13q^3+14q^2+5q+1
        28: 4q^3+12q^2+5q+1
        29: 6q^3+10q^2+5q+1
        30: 9q^3+11q^2+5q+1
        31: 8q^3+13q^2+5q+1
        32: 13q^3+14q^2+5q+1
        33: 8q^3+13q^2+5q+1
        34: 8q^3+13q^2+5q+1
        35: 13q^3+14q^2+5q+1
        36: 8q^3+13q^2+5q+1
        37: 6q^3+6q^2+2q
        38: 7q^3+8q^2+3q+1
        39: 2q^4+6q^3+6q^2+2q
        40: q^4+7q^3+8q^2+3q+1
        41: 6q^3+6q^2+2q
        42: 7q^3+8q^2+3q+1
        43: 8q^3+13q^2+5q+1
        44: 2q^4+9q^3+10q^2+5q+1
        45: 8q^3+13q^2+5q+1
        46: 8q^3+13q^2+5q+1
        47: 8q^3+13q^2+5q+1
        48: 3q^4+8q^3+8q^2+4q+1
        49: 4q^3+10q^2+5q+1
        50: 4q^3+10q^2+5q+1
        51: 5q^3+8q^2+4q+1
        52: 9q^3+11q^2+5q+1
        53: 2q^4+9q^3+11q^2+5q+1
        54: 9q^3+11q^2+5q+1
        55: 9q^3+11q^2+5q+1
        56: 2q^4+9q^3+11q^2+5q+1
        57: 9q^3+11q^2+5q+1
        58: q^3+4q^2+q
        59: 3q^3+8q^2+4q+1
        60: 3q^3+8q^2+4q+1
        61: q^3+4q^2+q
        62: 4q^3+5q^2+2q
        63: 4q^3+8q^2+3q+1
        64: 6q^3+6q^2+2q
        65: 7q^3+8q^2+3q+1
        66: 4q^3+5q^2+2q
        67: 4q^3+8q^2+3q+1
        68: 4q^3+12q^2+5q+1
        69: 2q^3+7q^2+4q+1
        70: 6q^3+10q^2+5q+1
        71: 2q^3+9q^2+5q+1
        72: 2q^3+7q^2+5q+1
        73: 2q^3+7q^2+5q+1
        74: 2q^3+3q^2+2q
        75: 3q^3+5q^2+3q+1
        76: q^4+2q^3+3q^2+2q
        77: 3q^3+5q^2+3q+1
        78: 2q^3+3q^2+2q
        79: 3q^3+5q^2+3q+1
        80: 8q^3+13q^2+5q+1
        81: 8q^3+13q^2+5q+1
        82: 6q^3+10q^2+5q+1
        83: 9q^3+11q^2+5q+1
        84: 8q^3+13q^2+5q+1
        85: 8q^3+13q^2+5q+1
        86: 6q^3+10q^2+5q+1
        87: 9q^3+11q^2+5q+1
        88: q^3+11q^2+5q+1
        89: q^3+11q^2+5q+1
        90: q^4+5q^3+7q^2+4q+1
        91: 4q^3+10q^2+5q+1
        92: 4q^3+10q^2+5q+1
        93: 5q^3+8q^2+4q+1
        94: 4q^3+10q^2+5q+1
        95: 4q^3+10q^2+5q+1
        96: 5q^3+8q^2+4q+1
        97: 4q^3+10q^2+5q+1
        98: 4q^3+10q^2+5q+1
        99: 5q^3+8q^2+4q+1
       100: 9q^3+11q^2+5q+1
       101: 2q^4+9q^3+11q^2+5q+1
       102: 9q^3+11q^2+5q+1
       103: q^3+2q^2+q
       104: 2q^3+6q^2+3q+1
       105: 2q^2
       106: q^3+2q^2+q
       107: q^3+5q^2+4q+1
       108: q^2+q
       109: q^2+q
       110: q^3+5q^2+4q+1
       111: q^2+2q
       112: 3q^2+3q+1
       113: 2q^3+2q^2+2q
       114: 2q^3+5q^2+3q+1
       115: 2q^3+3q^2+2q
       116: 3q^3+5q^2+3q+1
       117: q^3+4q^2+q
       118: 3q^3+8q^2+4q+1
       119: 3q^3+8q^2+4q+1
       120: q^3+4q^2+q
       121: 4q^3+5q^2+2q
       122: 4q^3+8q^2+3q+1
       123: 4q^3+5q^2+2q
       124: 4q^3+8q^2+3q+1
       125: q^3+11q^2+5q+1
       126: 6q^2+4q+1
       127: q^3+q^2+2q
       128: 3q^2+2q+1
       129: q^3+q^2+2q
       130: 3q^2+2q+1
       131: 2q^2+q
       132: q^3+2q^2+2q+1
       133: 2q^3+9q^2+5q+1
       134: 2q^3+7q^2+4q+1
       135: 2q^3+7q^2+5q+1
       136: 2q^3+7q^2+5q+1
       137: q^3+11q^2+5q+1
       138: 2q^3+7q^2+4q+1
       139: 2q^3+9q^2+5q+1
       140: 2q^3+7q^2+5q+1
       141: 6q^3+10q^2+5q+1
       142: 2q^3+7q^2+5q+1
       143: q^3+11q^2+5q+1
       144: 2q^3+7q^2+4q+1
       145: 2q^3+9q^2+5q+1
       146: 6q^3+10q^2+5q+1
       147: 2q^3+7q^2+5q+1
       148: 2q^3+7q^2+5q+1
       149: 6q^3+10q^2+5q+1
       150: 9q^3+11q^2+5q+1
       151: 2q^3+3q^2+2q
       152: 3q^3+5q^2+3q+1
       153: q^4+2q^3+3q^2+2q
       154: 3q^3+5q^2+3q+1
       155: 2q^3+3q^2+2q
       156: 3q^3+5q^2+3q+1
       157: 6q^2+5q+1
       158: 6q^2+5q+1
       159: 2q^3+5q^2+4q+1
       160: 4q^3+10q^2+5q+1
       161: 4q^3+10q^2+5q+1
       162: 5q^3+8q^2+4q+1
       163: 4q^3+10q^2+5q+1
       164: 4q^3+10q^2+5q+1
       165: 5q^3+8q^2+4q+1
       166: 4q^3+10q^2+5q+1
       167: 4q^3+10q^2+5q+1
       168: 5q^3+8q^2+4q+1
       169: q
       170: 3q^2+3q+1
       172: q
       173: q^3+2q^2+q
       174: 2q^3+6q^2+3q+1
       175: 2q^2
       176: q^3+2q^2+q
       177: q^2+q
       178: 2q^2+2q+1
       179: q^3+q^2+2q
       180: 3q^2+2q+1
       181: 2q
       182: q^2+2q+1
       183: q^3+5q^2+4q+1
       184: q^2+q
       185: q^2+q
       186: q^3+5q^2+4q+1
       187: q^2+2q
       188: 3q^2+3q+1
       189: 2q^3+2q^2+2q
       190: 2q^3+5q^2+3q+1
       191: 4q^2+q
       192: q^3+7q^2+4q+1
       193: q^3+5q^2+4q+1
       194: q^2+q
       195: q^2+q
       196: q^3+5q^2+4q+1
       197: q^2+2q
       198: 3q^2+3q+1
       199: q^3+7q^2+4q+1
       200: 4q^2+q
       201: q^3+5q^2+4q+1
       202: q^2+q
       203: q^2+q
       204: q^3+5q^2+4q+1
       205: q^2+2q
       206: 3q^2+3q+1
       207: 4q^2+2q
       208: q^3+7q^2+3q+1
       209: 2q^3+2q^2+2q
       210: 2q^3+5q^2+3q+1
       211: 2q^3+3q^2+2q
       212: 3q^3+5q^2+3q+1
       213: q^3+q^2+2q
       214: 3q^2+2q+1
       215: q^3+q^2+2q
       216: 3q^2+2q+1
       217: 2q^2+q
       218: q^3+2q^2+2q+1
       219: 6q^2+4q+1
       220: 6q^2+5q+1
       221: 4q^2+4q+1
       222: 4q^2+5q+1
       223: q^3+4q^2+4q+1
       224: 4q^2+5q+1
       225: q^3+4q^2+4q+1
       226: 6q^2+4q+1
       227: 2q^3+9q^2+5q+1
       228: 2q^3+7q^2+4q+1
       229: 2q^3+7q^2+5q+1
       230: 2q^3+7q^2+5q+1
       231: 6q^2+4q+1
       232: 2q^3+9q^2+5q+1
       233: 2q^3+7q^2+4q+1
       234: 2q^3+7q^2+5q+1
       235: 2q^3+7q^2+5q+1
       236: 2q^3+7q^2+4q+1
       237: q^3+q^2+2q
       238: 3q^2+2q+1
       239: q^3+q^2+2q
       240: 3q^2+2q+1
       241: 2q^2+q
       242: q^3+2q^2+2q+1
       243: 2q^3+9q^2+5q+1
       244: 2q^3+7q^2+5q+1
       245: 2q^3+7q^2+5q+1
       246: 6q^3+10q^2+5q+1
       247: 4q^2+8q+1
       248: 4q^2+8q+1
       249: 2q^3+5q^2+4q+1
       250: 6q^2+5q+1
       251: 6q^2+5q+1
       252: 2q^3+5q^2+4q+1
       253: 6q^2+5q+1
       254: 6q^2+5q+1
       255: 2q^3+5q^2+4q+1
       256: 4q^3+10q^2+5q+1
       257: 4q^3+10q^2+5q+1
       258: 5q^3+8q^2+4q+1
       259: q
       260: q^2+2q+1
       262: q
       263: q
       264: 3q^2+3q+1
       266: q
       267: q
       268: 3q^2+3q+1
       269: q
       271: q
       273: q
       274: 3q^2+3q+1
       275: 2q^2+q
       276: q^3+5q^2+3q+1
       277: 2q^2
       278: 2q^2+q
       279: q^3+q^2+2q
       280: 3q^2+2q+1
       281: q^2+q
       282: 2q^2+2q+1
       283: 2q^2+3q+1
       286: 2q^2+3q+1
       287: q^2+q
       288: 2q^2+2q+1
       289: 2q
       290: q^2+2q+1
       291: q
       292: 2q+1
       293: 3q^2+4q+1
       294: q^2+q
       295: q^2+q
       296: 3q^2+4q+1
       297: 2q
       298: 2q^2+3q+1
       299: q^3+5q^2+4q+1
       300: q^2+q
       301: 2q
       302: q^2+2q+1
       303: q^2+q
       304: q^3+5q^2+4q+1
       305: q^2+2q
       306: 3q^2+3q+1
       307: q^3+5q^2+4q+1
       308: q^2+q
       309: q^2+q
       310: q^3+5q^2+4q+1
       311: 2q
       312: q^2+2q+1
       313: q^2+2q
       314: 3q^2+3q+1
       315: q^2+q
       316: 2q^2+2q+1
       317: q^3+q^2+2q
       318: 3q^2+2q+1
       319: q^3+5q^2+4q+1
       320: q^2+q
       321: q^2+q
       322: q^3+5q^2+4q+1
       323: q^2+2q
       324: 3q^2+3q+1
       325: 2q^3+2q^2+2q
       326: 2q^3+5q^2+3q+1
       333: 4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: 3q^2+8q+1
       338: q^2+3q
       339: q^2+4q+1
       340: q^2+3q
       341: q^2+4q+1
       342: 2q^2+q
       343: q^3+2q^2+2q+1
       344: 6q^2+4q+1
       345: 6q^2+5q+1
       346: 4q^2+4q+1
       347: 4q^2+5q+1
       348: q^3+4q^2+4q+1
       349: 4q^2+5q+1
       350: q^3+4q^2+4q+1
       351: 4q^2+8q+1
       352: 6q^2+4q+1
       353: 6q^2+5q+1
       354: 4q^2+4q+1
       355: 4q^2+5q+1
       356: q^3+4q^2+4q+1
       357: 4q^2+5q+1
       358: q^3+4q^2+4q+1
       359: 4q^2+8q+1
       360: q^3+q^2+2q
       361: 3q^2+2q+1
       362: q^3+q^2+2q
       363: 3q^2+2q+1
       364: 2q^2+q
       365: q^3+2q^2+2q+1
       366: 6q^2+4q+1
       367: 2q^3+9q^2+5q+1
       368: 2q^3+7q^2+4q+1
       369: 2q^3+7q^2+5q+1
       370: 2q^3+7q^2+5q+1
       371: 4q^2+8q+1
       372: 4q^2+8q+1
       373: 2q^3+5q^2+4q+1
       374: 6q^2+5q+1
       375: 6q^2+5q+1
       376: 2q^3+5q^2+4q+1
       378: 2q+1
       381: q
       382: q^2+2q+1
       384: q
       385: q
       386: 2q^2+3q+1
       388: q
       389: q
       390: q^2+2q+1
       391: q
       393: q
       394: 3q^2+3q+1
       396: q
       397: q
       399: q
       400: q^2+2q+1
       401: q
       403: 3q^2+3q+1
       404: q
       405: q
       406: q
       407: 3q^2+3q+1
       413: q^2+q
       414: 2q^2+2q+1
       417: q
       418: 2q+1
       419: q^2+3q+1
       422: q^2+3q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+3q
       428: q^2+4q+1
       429: 2q^2+3q+1
       432: 2q^2+3q+1
       433: q
       434: 2q+1
       435: 2q
       436: q^2+2q+1
       437: 3q^2+4q+1
       438: q^2+q
       439: q^2+q
       440: 3q^2+4q+1
       441: 2q
       442: 2q^2+3q+1
       443: 3q^2+6q+1
       444: 2q
       445: q^2+3q
       446: q^2+4q+1
       447: 2q^2+3q+1
       450: 2q^2+3q+1
       451: q
       452: 2q+1
       453: 3q^2+4q+1
       454: q^2+q
       455: 2q
       456: q^2+2q+1
       457: q^2+q
       458: 3q^2+4q+1
       459: 2q
       460: 2q^2+3q+1
       461: 2q
       462: 3q^2+6q+1
       463: q^2+3q
       464: q^2+4q+1
       465: q^3+q^2+2q
       466: 3q^2+2q+1
       467: q^2+q
       468: 2q^2+2q+1
       469: q^2+q
       470: 2q^2+2q+1
       471: q^3+5q^2+4q+1
       472: q^2+q
       473: q^2+q
       474: q^3+5q^2+4q+1
       475: q^2+2q
       476: 3q^2+3q+1
       477: 2q
       478: q^2+2q+1
       479: q^2+4q
       480: 3q^2+4q+1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: 3q^2+8q+1
       485: q^2+3q
       486: q^2+4q+1
       487: q^2+3q
       488: q^2+4q+1
       489: 2q^2+q
       490: q^3+2q^2+2q+1
       491: q^2+4q+1
       492: 4q^2+4q+1
       493: 2q^2+4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 4q^2+8q+1
       497: 4q^2+4q+1
       498: 2q^2+4q+1
       499: 2q^2+4q+1
       500: q^2+4q+1
       501: 4q^2+8q+1
       508: 6q^2+4q+1
       509: 6q^2+5q+1
       510: 4q^2+4q+1
       511: 4q^2+5q+1
       512: q^3+4q^2+4q+1
       513: 4q^2+5q+1
       514: q^3+4q^2+4q+1
       515: 4q+2
       516: 4q+2
       517: 2q^2+2q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       522: 2q+1
       530: 2q+1
       534: 2q+1
       537: q
       538: q^2+2q+1
       539: q
       541: q
       542: 2q^2+3q+1
       543: q
       545: q^2+2q
       546: q^2+3q+1
       547: q
       548: q
       551: 2q+1
       553: q
       555: q
       556: q^2+2q+1
       557: q
       559: q
       560: 2q^2+3q+1
       561: q
       562: q
       563: q^2+2q
       564: q^2+3q+1
       565: q
       566: 3q^2+3q+1
       568: q
       569: q
       570: q
       571: q^2+2q+1
       573: 2q
       574: 3q^2+4q+1
       575: 2q
       577: 2q
       578: 2q
       580: q^2+q
       581: q^2+2q+1
       585: q
       586: 2q+1
       589: q^2+3q+1
       592: 2q+1
       593: 2q+1
       596: q^2+3q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+3q
       602: q^2+4q+1
       603: q^2+3q+1
       605: q
       606: 2q+1
       608: q^2+3q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: 3q^2+6q+1
       616: 2q
       617: q^2+3q
       618: q^2+4q+1
       619: q^2+3q+1
       622: q^2+3q+1
       623: q
       624: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: 2q
       632: 3q^2+6q+1
       633: q^2+3q
       634: q^2+4q+1
       639: q^2+q
       640: 2q^2+2q+1
       641: 2q^2+3q+1
       644: 2q^2+3q+1
       645: q
       646: 2q+1
       647: 3q^2+4q+1
       648: q^2+q
       649: q^2+q
       650: 3q^2+4q+1
       651: 2q
       652: q^2+2q+1
       653: 2q
       654: 2q^2+3q+1
       655: q^2+4q
       656: 3q^2+4q+1
       657: 2q+2
       658: 2q+1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: q^2+q+1
       663: q^2+q+1
       664: 2q+2
       665: 4q+1
       672: q^2+4q+1
       673: 2q+1
       674: 4q+2
       675: 2q^2+4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: q^2+4q+1
       679: q^2+4q+1
       680: 4q+2
       681: 2q^2+4q+1
       682: 2q^2+4q+1
       683: 4q+1
       684: q^2+4q+1
       685: q^2+4q+1
       686: 4q^2+4q+1
       687: 2q^2+4q+1
       688: 2q^2+4q+1
       689: q^2+4q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       696: q^2+q
       697: q
       699: q^2+2q+1
       701: q
       710: 2q+1
       715: q+1
       718: q+1
       722: 2q+1
       726: 2q+1
       733: q^2+2q
       734: q^2+3q+1
       735: q
       736: q
       740: 2q+1
       744: 2q+1
       749: q
       750: q
       751: q^2+2q
       752: q^2+3q+1
       754: 2q+1
       757: q
       758: q
       759: q^2+2q+1
       761: q
       762: q
       763: 2q^2+3q+1
       765: 2q
       766: 3q^2+4q+1
       768: 2q
       769: 2q
       770: 2q
       772: q^2+q
       773: q^2+2q+1
       775: q+1
       776: q+1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       785: 2q+1
       788: 2q+1
       792: 1
       793: 2q+2
       795: 2q+1
       796: 2q+1
       797: q
       798: 2q+1
       801: q^2+3q+1
       804: 2q+1
       805: 2q+1
       808: q^2+3q+1
       809: q
       810: 2q+1
       811: q
       812: 2q+1
       815: q^2+3q+1
       816: q
       818: 2q+2
       819: 2q+1
       820: 2q+1
       821: q
       822: 2q+1
       825: q^2+3q+1
       828: 2q+1
       829: 2q+1
       832: q^2+3q+1
       833: q
       834: 2q+1
       835: q
       836: 2q+1
       839: q
       840: q^2+3q+1
       843: 2q
       844: 2q+2
       845: q^2+3q+1
       848: q^2+3q+1
       849: q
       850: 2q+1
       851: q
       852: 2q+1
       855: q
       856: 2q+1
       857: 2q
       858: q^2+2q+1
       865: q+1
       866: 2
       867: q+1
       868: 2q+1
       869: 2q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 2q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 2q^2+4q+1
       878: 2q^2+4q+1
       879: 4q+1
       880: q^2+4q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       885: q
       887: q^2+q
       889: q
       890: q^2+2q+1
       892: q
       903: q+1
       905: q+1
       909: 1
       916: q+1
       917: q+1
       921: 2q+1
       926: q+1
       929: q+1
       942: q+1
       943: q+1
       947: 2q+1
       951: q+1
       953: q+1
       962: 2q+1
       965: 2q+2
       968: q
       969: q
       971: q+1
       972: q+1
       976: 2q+1
       988: q
       989: q^2+2q+1
       991: q
       994: 1
       995: 1
       999: 2
      1000: 2
      1004: q+1
      1007: q+1
      1009: 1
      1011: 1
      1013: 2
      1016: q+1
      1020: q+1
      1021: q+1
      1022: q
      1023: 2q+1
      1026: 2q+1
      1029: 2q+1
      1033: q+1
      1036: q+1
      1037: q+1
      1038: q
      1039: 2q+1
      1040: 2q+1
      1045: 2q+1
      1046: q
      1047: q+1
      1048: q
      1049: 2q+1
      1052: q^2+3q+1
      1055: 2q+1
      1056: 2q+1
      1059: q^2+3q+1
      1060: q
      1061: 2q+1
      1062: q
      1063: 2q+1
      1065: 1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 4q+1
      1084: 2q+2
      1085: 2q+1
      1089: q+1
      1092: q+1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1128: 1
      1131: 2
      1136: 1
      1141: 1
      1142: 1
      1155: q+1
      1157: q+1
      1162: 1
      1175: q+1
      1177: q+1
      1181: 1
      1195: q+1
      1200: 2q+1
      1205: q+1
      1207: q+1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: q+1
      1230: 1
      1231: 1
      1233: 2
      1234: 2
      1240: q+1
      1243: q+1
      1247: q+1
      1248: 1
      1249: 1
      1251: 2
      1254: 2
      1258: q+1
      1261: q+1
      1262: q
      1263: q+1
      1266: q
      1267: 2q+1
      1268: 2q+1
      1271: 2q+1
      1274: q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1293: 1
      1296: 1
      1327: 1
      1332: 1
      1350: 1
      1351: 1
      1356: 1
      1357: 1
      1363: 1
      1366: 2
      1371: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1394: 1
      1397: 2
      1402: 1
      1411: q+1
      1421: q+1
      1423: q+1
      1427: 1
      1433: 1
      1434: 1
      1441: 1
      1442: 1
      1445: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1464: 1
      1465: 1
      1467: 2
      1468: 2
      1475: 1
      1476: q+1
      1479: q+1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1505: 1
      1508: 1
      1516: 1
      1519: 1
      1550: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1609: 1
      1610: 1
      1615: 1
      1616: 1
      1620: 1
      1624: 2
      1628: 1
      1646: 1
      1647: 1
      1654: 1
      1655: 1
      1664: 1
      1665: 1
      1670: 1
      1674: 1
      1714: 1
      1716: 1
      1751: 1
      1774: 1
      1798: 1
      1809: 1
      1830: 1
      1831: 1
      1941: 1

1942:    0: 13q^3+14q^2+5q+1
         1: 3q^4+13q^3+14q^2+5q+1
         2: 13q^3+14q^2+5q+1
         3: 3q^4+13q^3+14q^2+5q+1
         4: 4q^4+12q^3+11q^2+5q+1
         5: 13q^3+14q^2+5q+1
         6: q^5+6q^4+12q^3+11q^2+5q+1
         7: 4q^4+12q^3+11q^2+5q+1
         8: 13q^3+14q^2+5q+1
         9: 2q^5+6q^4+9q^3+8q^2+4q+1
        10: 8q^3+13q^2+5q+1
        11: 8q^3+13q^2+5q+1
        12: 2q^4+9q^3+10q^2+5q+1
        13: 13q^3+14q^2+5q+1
        14: 4q^4+12q^3+11q^2+5q+1
        15: 13q^3+14q^2+5q+1
        16: 8q^3+13q^2+5q+1
        17: 8q^3+13q^2+5q+1
        18: 3q^4+8q^3+8q^2+4q+1
        19: 9q^3+11q^2+5q+1
        20: 2q^4+9q^3+11q^2+5q+1
        21: 9q^3+11q^2+5q+1
        22: 13q^3+14q^2+5q+1
        23: 3q^4+13q^3+14q^2+5q+1
        24: 13q^3+14q^2+5q+1
        25: 13q^3+14q^2+5q+1
        26: 3q^4+13q^3+14q^2+5q+1
        27: 13q^3+14q^2+5q+1
        28: 4q^3+12q^2+5q+1
        29: 6q^3+10q^2+5q+1
        30: 9q^3+11q^2+5q+1
        31: 8q^3+13q^2+5q+1
        32: 13q^3+14q^2+5q+1
        33: 8q^3+13q^2+5q+1
        34: 8q^3+13q^2+5q+1
        35: 13q^3+14q^2+5q+1
        36: 8q^3+13q^2+5q+1
        37: 6q^3+6q^2+2q
        38: 7q^3+8q^2+3q+1
        39: 2q^4+6q^3+6q^2+2q
        40: q^4+7q^3+8q^2+3q+1
        41: 6q^3+6q^2+2q
        42: 7q^3+8q^2+3q+1
        43: 8q^3+13q^2+5q+1
        44: 2q^4+9q^3+10q^2+5q+1
        45: 8q^3+13q^2+5q+1
        46: 8q^3+13q^2+5q+1
        47: 8q^3+13q^2+5q+1
        48: 3q^4+8q^3+8q^2+4q+1
        49: 4q^3+10q^2+5q+1
        50: 4q^3+10q^2+5q+1
        51: 5q^3+8q^2+4q+1
        52: 9q^3+11q^2+5q+1
        53: 2q^4+9q^3+11q^2+5q+1
        54: 9q^3+11q^2+5q+1
        55: 9q^3+11q^2+5q+1
        56: 2q^4+9q^3+11q^2+5q+1
        57: 9q^3+11q^2+5q+1
        58: 3q^3+8q^2+4q+1
        59: q^3+4q^2+q
        60: q^3+4q^2+q
        61: 3q^3+8q^2+4q+1
        62: 4q^3+5q^2+2q
        63: 4q^3+8q^2+3q+1
        64: 6q^3+6q^2+2q
        65: 7q^3+8q^2+3q+1
        66: 4q^3+5q^2+2q
        67: 4q^3+8q^2+3q+1
        68: 4q^3+12q^2+5q+1
        69: 2q^3+7q^2+4q+1
        70: 6q^3+10q^2+5q+1
        71: 2q^3+9q^2+5q+1
        72: 2q^3+7q^2+5q+1
        73: 2q^3+7q^2+5q+1
        74: 2q^3+3q^2+2q
        75: 3q^3+5q^2+3q+1
        76: q^4+2q^3+3q^2+2q
        77: 3q^3+5q^2+3q+1
        78: 2q^3+3q^2+2q
        79: 3q^3+5q^2+3q+1
        80: 8q^3+13q^2+5q+1
        81: 8q^3+13q^2+5q+1
        82: 6q^3+10q^2+5q+1
        83: 9q^3+11q^2+5q+1
        84: 8q^3+13q^2+5q+1
        85: 8q^3+13q^2+5q+1
        86: 6q^3+10q^2+5q+1
        87: 9q^3+11q^2+5q+1
        88: q^3+11q^2+5q+1
        89: q^3+11q^2+5q+1
        90: q^4+5q^3+7q^2+4q+1
        91: 4q^3+10q^2+5q+1
        92: 4q^3+10q^2+5q+1
        93: 5q^3+8q^2+4q+1
        94: 4q^3+10q^2+5q+1
        95: 4q^3+10q^2+5q+1
        96: 5q^3+8q^2+4q+1
        97: 4q^3+10q^2+5q+1
        98: 4q^3+10q^2+5q+1
        99: 5q^3+8q^2+4q+1
       100: 9q^3+11q^2+5q+1
       101: 2q^4+9q^3+11q^2+5q+1
       102: 9q^3+11q^2+5q+1
       103: q^3+2q^2+q
       104: 2q^2
       105: 2q^3+6q^2+3q+1
       106: q^3+2q^2+q
       107: q^2+q
       108: q^3+5q^2+4q+1
       109: q^3+5q^2+4q+1
       110: q^2+q
       111: q^2+2q
       112: 3q^2+3q+1
       113: 2q^3+2q^2+2q
       114: 2q^3+5q^2+3q+1
       115: 2q^3+3q^2+2q
       116: 3q^3+5q^2+3q+1
       117: 3q^3+8q^2+4q+1
       118: q^3+4q^2+q
       119: q^3+4q^2+q
       120: 3q^3+8q^2+4q+1
       121: 4q^3+5q^2+2q
       122: 4q^3+8q^2+3q+1
       123: 4q^3+5q^2+2q
       124: 4q^3+8q^2+3q+1
       125: q^3+11q^2+5q+1
       126: 6q^2+4q+1
       127: q^3+q^2+2q
       128: 3q^2+2q+1
       129: q^3+q^2+2q
       130: 3q^2+2q+1
       131: 2q^2+q
       132: q^3+2q^2+2q+1
       133: 2q^3+9q^2+5q+1
       134: 2q^3+7q^2+4q+1
       135: 2q^3+7q^2+5q+1
       136: 2q^3+7q^2+5q+1
       137: q^3+11q^2+5q+1
       138: 2q^3+7q^2+4q+1
       139: 2q^3+9q^2+5q+1
       140: 2q^3+7q^2+5q+1
       141: 6q^3+10q^2+5q+1
       142: 2q^3+7q^2+5q+1
       143: q^3+11q^2+5q+1
       144: 2q^3+7q^2+4q+1
       145: 2q^3+9q^2+5q+1
       146: 6q^3+10q^2+5q+1
       147: 2q^3+7q^2+5q+1
       148: 2q^3+7q^2+5q+1
       149: 6q^3+10q^2+5q+1
       150: 9q^3+11q^2+5q+1
       151: 2q^3+3q^2+2q
       152: 3q^3+5q^2+3q+1
       153: q^4+2q^3+3q^2+2q
       154: 3q^3+5q^2+3q+1
       155: 2q^3+3q^2+2q
       156: 3q^3+5q^2+3q+1
       157: 6q^2+5q+1
       158: 6q^2+5q+1
       159: 2q^3+5q^2+4q+1
       160: 4q^3+10q^2+5q+1
       161: 4q^3+10q^2+5q+1
       162: 5q^3+8q^2+4q+1
       163: 4q^3+10q^2+5q+1
       164: 4q^3+10q^2+5q+1
       165: 5q^3+8q^2+4q+1
       166: 4q^3+10q^2+5q+1
       167: 4q^3+10q^2+5q+1
       168: 5q^3+8q^2+4q+1
       169: q
       171: 3q^2+3q+1
       172: q
       173: q^3+2q^2+q
       174: 2q^2
       175: 2q^3+6q^2+3q+1
       176: q^3+2q^2+q
       177: q^2+q
       178: 2q^2+2q+1
       179: q^3+q^2+2q
       180: 3q^2+2q+1
       181: 2q
       182: q^2+2q+1
       183: q^2+q
       184: q^3+5q^2+4q+1
       185: q^3+5q^2+4q+1
       186: q^2+q
       187: q^2+2q
       188: 3q^2+3q+1
       189: 2q^3+2q^2+2q
       190: 2q^3+5q^2+3q+1
       191: q^3+7q^2+4q+1
       192: 4q^2+q
       193: q^2+q
       194: q^3+5q^2+4q+1
       195: q^3+5q^2+4q+1
       196: q^2+q
       197: q^2+2q
       198: 3q^2+3q+1
       199: 4q^2+q
       200: q^3+7q^2+4q+1
       201: q^2+q
       202: q^3+5q^2+4q+1
       203: q^3+5q^2+4q+1
       204: q^2+q
       205: q^2+2q
       206: 3q^2+3q+1
       207: 4q^2+2q
       208: q^3+7q^2+3q+1
       209: 2q^3+2q^2+2q
       210: 2q^3+5q^2+3q+1
       211: 2q^3+3q^2+2q
       212: 3q^3+5q^2+3q+1
       213: q^3+q^2+2q
       214: 3q^2+2q+1
       215: q^3+q^2+2q
       216: 3q^2+2q+1
       217: 2q^2+q
       218: q^3+2q^2+2q+1
       219: 6q^2+4q+1
       220: 6q^2+5q+1
       221: 4q^2+4q+1
       222: 4q^2+5q+1
       223: q^3+4q^2+4q+1
       224: 4q^2+5q+1
       225: q^3+4q^2+4q+1
       226: 6q^2+4q+1
       227: 2q^3+9q^2+5q+1
       228: 2q^3+7q^2+4q+1
       229: 2q^3+7q^2+5q+1
       230: 2q^3+7q^2+5q+1
       231: 6q^2+4q+1
       232: 2q^3+9q^2+5q+1
       233: 2q^3+7q^2+4q+1
       234: 2q^3+7q^2+5q+1
       235: 2q^3+7q^2+5q+1
       236: 2q^3+7q^2+4q+1
       237: q^3+q^2+2q
       238: 3q^2+2q+1
       239: q^3+q^2+2q
       240: 3q^2+2q+1
       241: 2q^2+q
       242: q^3+2q^2+2q+1
       243: 2q^3+9q^2+5q+1
       244: 2q^3+7q^2+5q+1
       245: 2q^3+7q^2+5q+1
       246: 6q^3+10q^2+5q+1
       247: 4q^2+8q+1
       248: 4q^2+8q+1
       249: 2q^3+5q^2+4q+1
       250: 6q^2+5q+1
       251: 6q^2+5q+1
       252: 2q^3+5q^2+4q+1
       253: 6q^2+5q+1
       254: 6q^2+5q+1
       255: 2q^3+5q^2+4q+1
       256: 4q^3+10q^2+5q+1
       257: 4q^3+10q^2+5q+1
       258: 5q^3+8q^2+4q+1
       259: q
       261: q^2+2q+1
       262: q
       263: q
       265: 3q^2+3q+1
       266: q
       267: q
       269: q
       270: 3q^2+3q+1
       271: q
       272: 3q^2+3q+1
       273: q
       275: 2q^2+q
       276: 2q^2
       277: q^3+5q^2+3q+1
       278: 2q^2+q
       279: q^3+q^2+2q
       280: 3q^2+2q+1
       281: q^2+q
       282: 2q^2+2q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       287: q^2+q
       288: 2q^2+2q+1
       289: 2q
       290: q^2+2q+1
       291: q
       292: 2q+1
       293: q^2+q
       294: 3q^2+4q+1
       295: 3q^2+4q+1
       296: q^2+q
       297: 2q
       298: 2q^2+3q+1
       299: q^2+q
       300: q^3+5q^2+4q+1
       301: 2q
       302: q^2+2q+1
       303: q^3+5q^2+4q+1
       304: q^2+q
       305: q^2+2q
       306: 3q^2+3q+1
       307: q^2+q
       308: q^3+5q^2+4q+1
       309: q^3+5q^2+4q+1
       310: q^2+q
       311: 2q
       312: q^2+2q+1
       313: q^2+2q
       314: 3q^2+3q+1
       315: q^2+q
       316: 2q^2+2q+1
       317: q^3+q^2+2q
       318: 3q^2+2q+1
       319: q^2+q
       320: q^3+5q^2+4q+1
       321: q^3+5q^2+4q+1
       322: q^2+q
       323: q^2+2q
       324: 3q^2+3q+1
       325: 2q^3+2q^2+2q
       326: 2q^3+5q^2+3q+1
       333: 4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: 3q^2+8q+1
       338: q^2+3q
       339: q^2+4q+1
       340: q^2+3q
       341: q^2+4q+1
       342: 2q^2+q
       343: q^3+2q^2+2q+1
       344: 6q^2+4q+1
       345: 6q^2+5q+1
       346: 4q^2+4q+1
       347: 4q^2+5q+1
       348: q^3+4q^2+4q+1
       349: 4q^2+5q+1
       350: q^3+4q^2+4q+1
       351: 4q^2+8q+1
       352: 6q^2+4q+1
       353: 6q^2+5q+1
       354: 4q^2+4q+1
       355: 4q^2+5q+1
       356: q^3+4q^2+4q+1
       357: 4q^2+5q+1
       358: q^3+4q^2+4q+1
       359: 4q^2+8q+1
       360: q^3+q^2+2q
       361: 3q^2+2q+1
       362: q^3+q^2+2q
       363: 3q^2+2q+1
       364: 2q^2+q
       365: q^3+2q^2+2q+1
       366: 6q^2+4q+1
       367: 2q^3+9q^2+5q+1
       368: 2q^3+7q^2+4q+1
       369: 2q^3+7q^2+5q+1
       370: 2q^3+7q^2+5q+1
       371: 4q^2+8q+1
       372: 4q^2+8q+1
       373: 2q^3+5q^2+4q+1
       374: 6q^2+5q+1
       375: 6q^2+5q+1
       376: 2q^3+5q^2+4q+1
       379: 2q+1
       381: q
       383: q^2+2q+1
       384: q
       385: q
       387: 2q^2+3q+1
       388: q
       389: q
       391: q
       392: q^2+2q+1
       393: q
       395: 3q^2+3q+1
       396: q
       397: q
       398: q^2+2q+1
       399: q
       401: q
       402: 3q^2+3q+1
       404: q
       405: q
       406: q
       408: 3q^2+3q+1
       413: q^2+q
       414: 2q^2+2q+1
       417: q
       418: 2q+1
       420: q^2+3q+1
       421: q^2+3q+1
       423: q
       424: 2q+1
       425: q
       426: 2q+1
       427: q^2+3q
       428: q^2+4q+1
       430: 2q^2+3q+1
       431: 2q^2+3q+1
       433: q
       434: 2q+1
       435: 2q
       436: q^2+2q+1
       437: q^2+q
       438: 3q^2+4q+1
       439: 3q^2+4q+1
       440: q^2+q
       441: 2q
       442: 2q^2+3q+1
       443: 2q
       444: 3q^2+6q+1
       445: q^2+3q
       446: q^2+4q+1
       448: 2q^2+3q+1
       449: 2q^2+3q+1
       451: q
       452: 2q+1
       453: q^2+q
       454: 3q^2+4q+1
       455: 2q
       456: q^2+2q+1
       457: 3q^2+4q+1
       458: q^2+q
       459: 2q
       460: 2q^2+3q+1
       461: 3q^2+6q+1
       462: 2q
       463: q^2+3q
       464: q^2+4q+1
       465: q^3+q^2+2q
       466: 3q^2+2q+1
       467: q^2+q
       468: 2q^2+2q+1
       469: q^2+q
       470: 2q^2+2q+1
       471: q^2+q
       472: q^3+5q^2+4q+1
       473: q^3+5q^2+4q+1
       474: q^2+q
       475: q^2+2q
       476: 3q^2+3q+1
       477: 2q
       478: q^2+2q+1
       479: q^2+4q
       480: 3q^2+4q+1
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: 3q^2+8q+1
       485: q^2+3q
       486: q^2+4q+1
       487: q^2+3q
       488: q^2+4q+1
       489: 2q^2+q
       490: q^3+2q^2+2q+1
       491: q^2+4q+1
       492: 4q^2+4q+1
       493: 2q^2+4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 4q^2+8q+1
       497: 4q^2+4q+1
       498: 2q^2+4q+1
       499: 2q^2+4q+1
       500: q^2+4q+1
       501: 4q^2+8q+1
       508: 6q^2+4q+1
       509: 6q^2+5q+1
       510: 4q^2+4q+1
       511: 4q^2+5q+1
       512: q^3+4q^2+4q+1
       513: 4q^2+5q+1
       514: q^3+4q^2+4q+1
       515: 4q+2
       516: 4q+2
       517: 2q^2+2q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       523: 2q+1
       531: 2q+1
       535: 2q+1
       537: q
       539: q
       540: q^2+2q+1
       541: q
       543: q
       544: 2q^2+3q+1
       545: q
       546: q
       547: q^2+2q
       548: q^2+3q+1
       550: 2q+1
       553: q
       554: q^2+2q+1
       555: q
       557: q
       558: 2q^2+3q+1
       559: q
       561: q^2+2q
       562: q^2+3q+1
       563: q
       564: q
       565: q
       567: 3q^2+3q+1
       568: q
       569: q
       570: q
       572: q^2+2q+1
       573: 2q
       575: 2q
       576: 3q^2+4q+1
       577: 2q
       578: 2q
       580: q^2+q
       581: q^2+2q+1
       585: q
       586: 2q+1
       590: q^2+3q+1
       591: 2q+1
       594: 2q+1
       595: q^2+3q+1
       597: q
       598: 2q+1
       599: q
       600: 2q+1
       601: q^2+3q
       602: q^2+4q+1
       604: q^2+3q+1
       605: q
       606: 2q+1
       607: q^2+3q+1
       609: q
       610: 2q+1
       613: q
       614: 2q+1
       615: 2q
       616: 3q^2+6q+1
       617: q^2+3q
       618: q^2+4q+1
       620: q^2+3q+1
       621: q^2+3q+1
       623: q
       624: 2q+1
       625: q
       626: 2q+1
       629: q
       630: 2q+1
       631: 3q^2+6q+1
       632: 2q
       633: q^2+3q
       634: q^2+4q+1
       639: q^2+q
       640: 2q^2+2q+1
       642: 2q^2+3q+1
       643: 2q^2+3q+1
       645: q
       646: 2q+1
       647: q^2+q
       648: 3q^2+4q+1
       649: 3q^2+4q+1
       650: q^2+q
       651: 2q
       652: q^2+2q+1
       653: 2q
       654: 2q^2+3q+1
       655: q^2+4q
       656: 3q^2+4q+1
       657: 2q+2
       658: 2q+1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: q^2+q+1
       663: q^2+q+1
       664: 2q+2
       665: 4q+1
       672: q^2+4q+1
       673: 2q+1
       674: 4q+2
       675: 2q^2+4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: q^2+4q+1
       679: q^2+4q+1
       680: 4q+2
       681: 2q^2+4q+1
       682: 2q^2+4q+1
       683: 4q+1
       684: q^2+4q+1
       685: q^2+4q+1
       686: 4q^2+4q+1
       687: 2q^2+4q+1
       688: 2q^2+4q+1
       689: q^2+4q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       694: q
       697: q
       698: q^2+q
       700: q^2+2q+1
       701: q
       711: 2q+1
       714: q+1
       719: q+1
       724: 2q+1
       728: 2q+1
       733: q
       734: q
       735: q^2+2q
       736: q^2+3q+1
       738: 2q+1
       742: 2q+1
       749: q^2+2q
       750: q^2+3q+1
       751: q
       752: q
       755: 2q+1
       757: q
       758: q
       760: q^2+2q+1
       761: q
       762: q
       764: 2q^2+3q+1
       765: 2q
       767: 3q^2+4q+1
       768: 2q
       769: 2q
       770: 2q
       772: q^2+q
       773: q^2+2q+1
       775: q+1
       776: q+1
       779: q+1
       780: q+1
       781: q
       782: 2q+1
       786: 2q+1
       787: 2q+1
       792: 1
       794: 2q+2
       795: 2q+1
       796: 2q+1
       797: q
       798: 2q+1
       802: q^2+3q+1
       803: 2q+1
       806: 2q+1
       807: q^2+3q+1
       809: q
       810: 2q+1
       811: q
       812: 2q+1
       815: q
       816: q^2+3q+1
       817: 2q+2
       819: 2q+1
       820: 2q+1
       821: q
       822: 2q+1
       826: q^2+3q+1
       827: 2q+1
       830: 2q+1
       831: q^2+3q+1
       833: q
       834: 2q+1
       835: q
       836: 2q+1
       839: q^2+3q+1
       840: q
       843: 2q
       844: 2q+2
       846: q^2+3q+1
       847: q^2+3q+1
       849: q
       850: 2q+1
       851: q
       852: 2q+1
       855: q
       856: 2q+1
       857: 2q
       858: q^2+2q+1
       865: q+1
       866: 2
       867: q+1
       868: 2q+1
       869: 2q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 2q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 2q^2+4q+1
       878: 2q^2+4q+1
       879: 4q+1
       880: q^2+4q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       885: q
       888: q^2+q
       889: q
       891: q^2+2q+1
       892: q
       901: q+1
       907: q+1
       910: 1
       918: q+1
       919: q+1
       923: 2q+1
       925: q+1
       931: q+1
       940: q+1
       941: q+1
       945: 2q+1
       949: q+1
       954: q+1
       963: 2q+1
       966: 2q+2
       968: q
       969: q
       971: q+1
       972: q+1
       977: 2q+1
       988: q
       990: q^2+2q+1
       991: q
       994: 1
       995: 1
       998: 2
      1001: 2
      1005: q+1
      1006: q+1
      1009: 1
      1011: 1
      1013: 2
      1017: q+1
      1020: q+1
      1021: q+1
      1022: q
      1023: 2q+1
      1027: 2q+1
      1028: 2q+1
      1032: q+1
      1036: q+1
      1037: q+1
      1038: q
      1039: 2q+1
      1041: 2q+1
      1044: 2q+1
      1046: q
      1047: q+1
      1048: q
      1049: 2q+1
      1053: q^2+3q+1
      1054: 2q+1
      1057: 2q+1
      1058: q^2+3q+1
      1060: q
      1061: 2q+1
      1062: q
      1063: 2q+1
      1065: 1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 4q+1
      1084: 2q+2
      1085: 2q+1
      1090: q+1
      1093: q+1
      1114: 1
      1115: 1
      1124: 1
      1125: 1
      1129: 1
      1132: 2
      1137: 1
      1141: 1
      1142: 1
      1153: q+1
      1159: q+1
      1161: 1
      1173: q+1
      1179: q+1
      1182: 1
      1196: q+1
      1201: 2q+1
      1203: q+1
      1209: q+1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 2
      1235: 2
      1241: q+1
      1242: q+1
      1246: q+1
      1248: 1
      1249: 1
      1250: 2
      1255: 2
      1259: q+1
      1260: q+1
      1262: q
      1263: q+1
      1266: q
      1267: 2q+1
      1269: 2q+1
      1270: 2q+1
      1274: q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1294: 1
      1297: 1
      1328: 1
      1333: 1
      1348: 1
      1349: 1
      1358: 1
      1359: 1
      1362: 1
      1365: 2
      1370: 1
      1380: 1
      1381: 1
      1390: 1
      1391: 1
      1395: 1
      1398: 2
      1403: 1
      1412: q+1
      1419: q+1
      1425: q+1
      1428: 1
      1433: 1
      1434: 1
      1440: 1
      1443: 1
      1445: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 2
      1469: 2
      1475: 1
      1477: q+1
      1478: q+1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1504: 1
      1507: 1
      1517: 1
      1520: 1
      1551: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1607: 1
      1608: 1
      1617: 1
      1618: 1
      1621: 1
      1625: 2
      1629: 1
      1645: 1
      1648: 1
      1653: 1
      1656: 1
      1663: 1
      1666: 1
      1670: 1
      1674: 1
      1715: 1
      1717: 1
      1750: 1
      1775: 1
      1799: 1
      1810: 1
      1829: 1
      1832: 1
      1942: 1

1943:    0: 13q^3+14q^2+5q+1
         1: 3q^4+13q^3+14q^2+5q+1
         2: 13q^3+14q^2+5q+1
         3: 3q^4+13q^3+14q^2+5q+1
         4: 4q^4+12q^3+11q^2+5q+1
         5: 13q^3+14q^2+5q+1
         6: q^5+6q^4+12q^3+11q^2+5q+1
         7: 4q^4+12q^3+11q^2+5q+1
         8: 13q^3+14q^2+5q+1
         9: 2q^5+6q^4+9q^3+8q^2+4q+1
        10: 8q^3+13q^2+5q+1
        11: 8q^3+13q^2+5q+1
        12: 2q^4+9q^3+10q^2+5q+1
        13: 13q^3+14q^2+5q+1
        14: 4q^4+12q^3+11q^2+5q+1
        15: 13q^3+14q^2+5q+1
        16: 8q^3+13q^2+5q+1
        17: 8q^3+13q^2+5q+1
        18: 3q^4+8q^3+8q^2+4q+1
        19: 9q^3+11q^2+5q+1
        20: 2q^4+9q^3+11q^2+5q+1
        21: 9q^3+11q^2+5q+1
        22: 13q^3+14q^2+5q+1
        23: 3q^4+13q^3+14q^2+5q+1
        24: 13q^3+14q^2+5q+1
        25: 13q^3+14q^2+5q+1
        26: 3q^4+13q^3+14q^2+5q+1
        27: 13q^3+14q^2+5q+1
        28: 4q^3+12q^2+5q+1
        29: 6q^3+10q^2+5q+1
        30: 9q^3+11q^2+5q+1
        31: 8q^3+13q^2+5q+1
        32: 13q^3+14q^2+5q+1
        33: 8q^3+13q^2+5q+1
        34: 8q^3+13q^2+5q+1
        35: 13q^3+14q^2+5q+1
        36: 8q^3+13q^2+5q+1
        37: 7q^3+8q^2+3q+1
        38: 6q^3+6q^2+2q
        39: q^4+7q^3+8q^2+3q+1
        40: 2q^4+6q^3+6q^2+2q
        41: 7q^3+8q^2+3q+1
        42: 6q^3+6q^2+2q
        43: 8q^3+13q^2+5q+1
        44: 2q^4+9q^3+10q^2+5q+1
        45: 8q^3+13q^2+5q+1
        46: 8q^3+13q^2+5q+1
        47: 8q^3+13q^2+5q+1
        48: 3q^4+8q^3+8q^2+4q+1
        49: 4q^3+10q^2+5q+1
        50: 4q^3+10q^2+5q+1
        51: 5q^3+8q^2+4q+1
        52: 9q^3+11q^2+5q+1
        53: 2q^4+9q^3+11q^2+5q+1
        54: 9q^3+11q^2+5q+1
        55: 9q^3+11q^2+5q+1
        56: 2q^4+9q^3+11q^2+5q+1
        57: 9q^3+11q^2+5q+1
        58: q^3+4q^2+q
        59: 3q^3+8q^2+4q+1
        60: q^3+4q^2+q
        61: 3q^3+8q^2+4q+1
        62: 4q^3+8q^2+3q+1
        63: 4q^3+5q^2+2q
        64: 7q^3+8q^2+3q+1
        65: 6q^3+6q^2+2q
        66: 4q^3+8q^2+3q+1
        67: 4q^3+5q^2+2q
        68: 4q^3+12q^2+5q+1
        69: 2q^3+7q^2+4q+1
        70: 6q^3+10q^2+5q+1
        71: 2q^3+9q^2+5q+1
        72: 2q^3+7q^2+5q+1
        73: 2q^3+7q^2+5q+1
        74: 3q^3+5q^2+3q+1
        75: 2q^3+3q^2+2q
        76: 3q^3+5q^2+3q+1
        77: q^4+2q^3+3q^2+2q
        78: 3q^3+5q^2+3q+1
        79: 2q^3+3q^2+2q
        80: 8q^3+13q^2+5q+1
        81: 8q^3+13q^2+5q+1
        82: 6q^3+10q^2+5q+1
        83: 9q^3+11q^2+5q+1
        84: 8q^3+13q^2+5q+1
        85: 8q^3+13q^2+5q+1
        86: 6q^3+10q^2+5q+1
        87: 9q^3+11q^2+5q+1
        88: q^3+11q^2+5q+1
        89: q^3+11q^2+5q+1
        90: q^4+5q^3+7q^2+4q+1
        91: 4q^3+10q^2+5q+1
        92: 4q^3+10q^2+5q+1
        93: 5q^3+8q^2+4q+1
        94: 4q^3+10q^2+5q+1
        95: 4q^3+10q^2+5q+1
        96: 5q^3+8q^2+4q+1
        97: 4q^3+10q^2+5q+1
        98: 4q^3+10q^2+5q+1
        99: 5q^3+8q^2+4q+1
       100: 9q^3+11q^2+5q+1
       101: 2q^4+9q^3+11q^2+5q+1
       102: 9q^3+11q^2+5q+1
       103: 2q^2
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       106: 2q^3+6q^2+3q+1
       107: q^2+q
       108: q^3+5q^2+4q+1
       109: q^2+q
       110: q^3+5q^2+4q+1
       111: 3q^2+3q+1
       112: q^2+2q
       113: 2q^3+5q^2+3q+1
       114: 2q^3+2q^2+2q
       115: 3q^3+5q^2+3q+1
       116: 2q^3+3q^2+2q
       117: q^3+4q^2+q
       118: 3q^3+8q^2+4q+1
       119: q^3+4q^2+q
       120: 3q^3+8q^2+4q+1
       121: 4q^3+8q^2+3q+1
       122: 4q^3+5q^2+2q
       123: 4q^3+8q^2+3q+1
       124: 4q^3+5q^2+2q
       125: q^3+11q^2+5q+1
       126: 6q^2+4q+1
       127: 3q^2+2q+1
       128: q^3+q^2+2q
       129: 3q^2+2q+1
       130: q^3+q^2+2q
       131: q^3+2q^2+2q+1
       132: 2q^2+q
       133: 2q^3+9q^2+5q+1
       134: 2q^3+7q^2+4q+1
       135: 2q^3+7q^2+5q+1
       136: 2q^3+7q^2+5q+1
       137: q^3+11q^2+5q+1
       138: 2q^3+7q^2+4q+1
       139: 2q^3+9q^2+5q+1
       140: 2q^3+7q^2+5q+1
       141: 6q^3+10q^2+5q+1
       142: 2q^3+7q^2+5q+1
       143: q^3+11q^2+5q+1
       144: 2q^3+7q^2+4q+1
       145: 2q^3+9q^2+5q+1
       146: 6q^3+10q^2+5q+1
       147: 2q^3+7q^2+5q+1
       148: 2q^3+7q^2+5q+1
       149: 6q^3+10q^2+5q+1
       150: 9q^3+11q^2+5q+1
       151: 3q^3+5q^2+3q+1
       152: 2q^3+3q^2+2q
       153: 3q^3+5q^2+3q+1
       154: q^4+2q^3+3q^2+2q
       155: 3q^3+5q^2+3q+1
       156: 2q^3+3q^2+2q
       157: 6q^2+5q+1
       158: 6q^2+5q+1
       159: 2q^3+5q^2+4q+1
       160: 4q^3+10q^2+5q+1
       161: 4q^3+10q^2+5q+1
       162: 5q^3+8q^2+4q+1
       163: 4q^3+10q^2+5q+1
       164: 4q^3+10q^2+5q+1
       165: 5q^3+8q^2+4q+1
       166: 4q^3+10q^2+5q+1
       167: 4q^3+10q^2+5q+1
       168: 5q^3+8q^2+4q+1
       170: q
       171: q
       172: 3q^2+3q+1
       173: 2q^2
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       176: 2q^3+6q^2+3q+1
       177: 2q^2+2q+1
       178: q^2+q
       179: 3q^2+2q+1
       180: q^3+q^2+2q
       181: q^2+2q+1
       182: 2q
       183: q^2+q
       184: q^3+5q^2+4q+1
       185: q^2+q
       186: q^3+5q^2+4q+1
       187: 3q^2+3q+1
       188: q^2+2q
       189: 2q^3+5q^2+3q+1
       190: 2q^3+2q^2+2q
       191: 4q^2+q
       192: q^3+7q^2+4q+1
       193: q^2+q
       194: q^3+5q^2+4q+1
       195: q^2+q
       196: q^3+5q^2+4q+1
       197: 3q^2+3q+1
       198: q^2+2q
       199: 4q^2+q
       200: q^3+7q^2+4q+1
       201: q^2+q
       202: q^3+5q^2+4q+1
       203: q^2+q
       204: q^3+5q^2+4q+1
       205: 3q^2+3q+1
       206: q^2+2q
       207: q^3+7q^2+3q+1
       208: 4q^2+2q
       209: 2q^3+5q^2+3q+1
       210: 2q^3+2q^2+2q
       211: 3q^3+5q^2+3q+1
       212: 2q^3+3q^2+2q
       213: 3q^2+2q+1
       214: q^3+q^2+2q
       215: 3q^2+2q+1
       216: q^3+q^2+2q
       217: q^3+2q^2+2q+1
       218: 2q^2+q
       219: 6q^2+4q+1
       220: 6q^2+5q+1
       221: 4q^2+4q+1
       222: 4q^2+5q+1
       223: q^3+4q^2+4q+1
       224: 4q^2+5q+1
       225: q^3+4q^2+4q+1
       226: 6q^2+4q+1
       227: 2q^3+9q^2+5q+1
       228: 2q^3+7q^2+4q+1
       229: 2q^3+7q^2+5q+1
       230: 2q^3+7q^2+5q+1
       231: 6q^2+4q+1
       232: 2q^3+9q^2+5q+1
       233: 2q^3+7q^2+4q+1
       234: 2q^3+7q^2+5q+1
       235: 2q^3+7q^2+5q+1
       236: 2q^3+7q^2+4q+1
       237: 3q^2+2q+1
       238: q^3+q^2+2q
       239: 3q^2+2q+1
       240: q^3+q^2+2q
       241: q^3+2q^2+2q+1
       242: 2q^2+q
       243: 2q^3+9q^2+5q+1
       244: 2q^3+7q^2+5q+1
       245: 2q^3+7q^2+5q+1
       246: 6q^3+10q^2+5q+1
       247: 4q^2+8q+1
       248: 4q^2+8q+1
       249: 2q^3+5q^2+4q+1
       250: 6q^2+5q+1
       251: 6q^2+5q+1
       252: 2q^3+5q^2+4q+1
       253: 6q^2+5q+1
       254: 6q^2+5q+1
       255: 2q^3+5q^2+4q+1
       256: 4q^3+10q^2+5q+1
       257: 4q^3+10q^2+5q+1
       258: 5q^3+8q^2+4q+1
       260: q
       261: q
       262: q^2+2q+1
       264: q
       265: q
       266: 3q^2+3q+1
       268: q
       269: 3q^2+3q+1
       270: q
       272: q
       273: 3q^2+3q+1
       274: q
       275: 2q^2
       276: 2q^2+q
       277: 2q^2+q
       278: q^3+5q^2+3q+1
       279: 3q^2+2q+1
       280: q^3+q^2+2q
       281: 2q^2+2q+1
       282: q^2+q
       284: 2q^2+3q+1
       286: 2q^2+3q+1
       287: 2q^2+2q+1
       288: q^2+q
       289: q^2+2q+1
       290: 2q
       291: 2q+1
       292: q
       293: q^2+q
       294: 3q^2+4q+1
       295: q^2+q
       296: 3q^2+4q+1
       297: 2q^2+3q+1
       298: 2q
       299: q^2+q
       300: q^3+5q^2+4q+1
       301: q^2+2q+1
       302: 2q
       303: q^2+q
       304: q^3+5q^2+4q+1
       305: 3q^2+3q+1
       306: q^2+2q
       307: q^2+q
       308: q^3+5q^2+4q+1
       309: q^2+q
       310: q^3+5q^2+4q+1
       311: q^2+2q+1
       312: 2q
       313: 3q^2+3q+1
       314: q^2+2q
       315: 2q^2+2q+1
       316: q^2+q
       317: 3q^2+2q+1
       318: q^3+q^2+2q
       319: q^2+q
       320: q^3+5q^2+4q+1
       321: q^2+q
       322: q^3+5q^2+4q+1
       323: 3q^2+3q+1
       324: q^2+2q
       325: 2q^3+5q^2+3q+1
       326: 2q^3+2q^2+2q
       333: 4q^2+4q+1
       334: 2q^2+4q+1
       335: 2q^2+4q+1
       336: q^2+4q+1
       337: 3q^2+8q+1
       338: q^2+4q+1
       339: q^2+3q
       340: q^2+4q+1
       341: q^2+3q
       342: q^3+2q^2+2q+1
       343: 2q^2+q
       344: 6q^2+4q+1
       345: 6q^2+5q+1
       346: 4q^2+4q+1
       347: 4q^2+5q+1
       348: q^3+4q^2+4q+1
       349: 4q^2+5q+1
       350: q^3+4q^2+4q+1
       351: 4q^2+8q+1
       352: 6q^2+4q+1
       353: 6q^2+5q+1
       354: 4q^2+4q+1
       355: 4q^2+5q+1
       356: q^3+4q^2+4q+1
       357: 4q^2+5q+1
       358: q^3+4q^2+4q+1
       359: 4q^2+8q+1
       360: 3q^2+2q+1
       361: q^3+q^2+2q
       362: 3q^2+2q+1
       363: q^3+q^2+2q
       364: q^3+2q^2+2q+1
       365: 2q^2+q
       366: 6q^2+4q+1
       367: 2q^3+9q^2+5q+1
       368: 2q^3+7q^2+4q+1
       369: 2q^3+7q^2+5q+1
       370: 2q^3+7q^2+5q+1
       371: 4q^2+8q+1
       372: 4q^2+8q+1
       373: 2q^3+5q^2+4q+1
       374: 6q^2+5q+1
       375: 6q^2+5q+1
       376: 2q^3+5q^2+4q+1
       380: 2q+1
       382: q
       383: q
       384: q^2+2q+1
       386: q
       387: q
       388: 2q^2+3q+1
       390: q
       391: q^2+2q+1
       392: q
       394: q
       395: q
       396: 3q^2+3q+1
       398: q
       399: q^2+2q+1
       400: q
       402: q
       403: q
       404: 3q^2+3q+1
       406: 3q^2+3q+1
       407: q
       408: q
       413: 2q^2+2q+1
       414: q^2+q
       417: 2q+1
       418: q
       420: q^2+3q+1
       422: q^2+3q+1
       423: 2q+1
       424: q
       425: 2q+1
       426: q
       427: q^2+4q+1
       428: q^2+3q
       430: 2q^2+3q+1
       432: 2q^2+3q+1
       433: 2q+1
       434: q
       435: q^2+2q+1
       436: 2q
       437: q^2+q
       438: 3q^2+4q+1
       439: q^2+q
       440: 3q^2+4q+1
       441: 2q^2+3q+1
       442: 2q
       443: 2q
       444: 3q^2+6q+1
       445: q^2+4q+1
       446: q^2+3q
       448: 2q^2+3q+1
       450: 2q^2+3q+1
       451: 2q+1
       452: q
       453: q^2+q
       454: 3q^2+4q+1
       455: q^2+2q+1
       456: 2q
       457: q^2+q
       458: 3q^2+4q+1
       459: 2q^2+3q+1
       460: 2q
       461: 2q
       462: 3q^2+6q+1
       463: q^2+4q+1
       464: q^2+3q
       465: 3q^2+2q+1
       466: q^3+q^2+2q
       467: 2q^2+2q+1
       468: q^2+q
       469: 2q^2+2q+1
       470: q^2+q
       471: q^2+q
       472: q^3+5q^2+4q+1
       473: q^2+q
       474: q^3+5q^2+4q+1
       475: 3q^2+3q+1
       476: q^2+2q
       477: q^2+2q+1
       478: 2q
       479: 3q^2+4q+1
       480: q^2+4q
       481: 2q^2+4q+1
       482: 2q^2+4q+1
       483: 4q+1
       484: 3q^2+8q+1
       485: q^2+4q+1
       486: q^2+3q
       487: q^2+4q+1
       488: q^2+3q
       489: q^3+2q^2+2q+1
       490: 2q^2+q
       491: q^2+4q+1
       492: 4q^2+4q+1
       493: 2q^2+4q+1
       494: 2q^2+4q+1
       495: q^2+4q+1
       496: 4q^2+8q+1
       497: 4q^2+4q+1
       498: 2q^2+4q+1
       499: 2q^2+4q+1
       500: q^2+4q+1
       501: 4q^2+8q+1
       508: 6q^2+4q+1
       509: 6q^2+5q+1
       510: 4q^2+4q+1
       511: 4q^2+5q+1
       512: q^3+4q^2+4q+1
       513: 4q^2+5q+1
       514: q^3+4q^2+4q+1
       515: 4q+2
       516: 4q+2
       517: 2q^2+2q+2
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       524: 2q+1
       532: 2q+1
       536: 2q+1
       538: q
       539: q^2+2q+1
       540: q
       542: q
       543: 2q^2+3q+1
       544: q
       545: q
       546: q
       547: q^2+3q+1
       548: q^2+2q
       552: 2q+1
       554: q
       555: q^2+2q+1
       556: q
       558: q
       559: 2q^2+3q+1
       560: q
       561: q
       562: q
       563: q^2+3q+1
       564: q^2+2q
       566: q
       567: q
       568: 3q^2+3q+1
       570: q^2+2q+1
       571: q
       572: q
       574: 2q
       575: 3q^2+4q+1
       576: 2q
       577: q^2+2q+1
       578: q^2+q
       580: 2q
       581: 2q
       585: 2q+1
       586: q
       590: q^2+3q+1
       592: 2q+1
       594: 2q+1
       596: q^2+3q+1
       597: 2q+1
       598: q
       599: 2q+1
       600: q
       601: q^2+4q+1
       602: q^2+3q
       604: q^2+3q+1
       605: 2q+1
       606: q
       608: q^2+3q+1
       609: 2q+1
       610: q
       613: 2q+1
       614: q
       615: 2q
       616: 3q^2+6q+1
       617: q^2+4q+1
       618: q^2+3q
       620: q^2+3q+1
       622: q^2+3q+1
       623: 2q+1
       624: q
       625: 2q+1
       626: q
       629: 2q+1
       630: q
       631: 2q
       632: 3q^2+6q+1
       633: q^2+4q+1
       634: q^2+3q
       639: 2q^2+2q+1
       640: q^2+q
       642: 2q^2+3q+1
       644: 2q^2+3q+1
       645: 2q+1
       646: q
       647: q^2+q
       648: 3q^2+4q+1
       649: q^2+q
       650: 3q^2+4q+1
       651: q^2+2q+1
       652: 2q
       653: 2q^2+3q+1
       654: 2q
       655: 3q^2+4q+1
       656: q^2+4q
       657: 2q+2
       658: 2q+1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: q^2+q+1
       663: q^2+q+1
       664: 2q+2
       665: 4q+1
       672: q^2+4q+1
       673: 2q+1
       674: 4q+2
       675: 2q^2+4q+1
       676: 2q^2+4q+1
       677: 4q+1
       678: q^2+4q+1
       679: q^2+4q+1
       680: 4q+2
       681: 2q^2+4q+1
       682: 2q^2+4q+1
       683: 4q+1
       684: q^2+4q+1
       685: q^2+4q+1
       686: 4q^2+4q+1
       687: 2q^2+4q+1
       688: 2q^2+4q+1
       689: q^2+4q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q^2+2q+1
       698: q
       699: q
       700: q
       701: q^2+q
       712: 2q+1
       716: q+1
       720: q+1
       723: 2q+1
       727: 2q+1
       733: q
       734: q
       735: q^2+3q+1
       736: q^2+2q
       739: 2q+1
       743: 2q+1
       749: q
       750: q
       751: q^2+3q+1
       752: q^2+2q
       756: 2q+1
       758: q^2+2q+1
       759: q
       760: q
       762: 2q^2+3q+1
       763: q
       764: q
       766: 2q
       767: 2q
       768: 3q^2+4q+1
       769: q^2+2q+1
       770: q^2+q
       772: 2q
       773: 2q
       775: q+1
       776: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q
       786: 2q+1
       788: 2q+1
       791: 1
       794: 2q+2
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: q
       802: q^2+3q+1
       804: 2q+1
       806: 2q+1
       808: q^2+3q+1
       809: 2q+1
       810: q
       811: 2q+1
       812: q
       815: q
       816: q^2+3q+1
       818: 2q+2
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: q
       826: q^2+3q+1
       828: 2q+1
       830: 2q+1
       832: q^2+3q+1
       833: 2q+1
       834: q
       835: 2q+1
       836: q
       839: q
       840: q^2+3q+1
       843: 2q+2
       844: 2q
       846: q^2+3q+1
       848: q^2+3q+1
       849: 2q+1
       850: q
       851: 2q+1
       852: q
       855: 2q+1
       856: q
       857: q^2+2q+1
       858: 2q
       865: q+1
       866: 2
       867: q+1
       868: 2q+1
       869: 2q+1
       870: 2q+2
       871: 4q+1
       872: 2q+1
       873: 2q+1
       874: 2q+2
       875: 4q+1
       876: 2q+1
       877: 2q^2+4q+1
       878: 2q^2+4q+1
       879: 4q+1
       880: q^2+4q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       887: q
       888: q
       889: q^2+2q+1
       890: q
       891: q
       892: q^2+q
       902: q+1
       906: q+1
       911: 1
       918: q+1
       919: q+1
       922: 2q+1
       927: q+1
       930: q+1
       942: q+1
       943: q+1
       946: 2q+1
       950: q+1
       955: q+1
       961: 2q+1
       967: 2q+2
       968: q+1
       969: q+1
       971: q
       972: q
       975: 2q+1
       989: q
       990: q
       991: q^2+2q+1
       994: 1
       995: 1
       999: 2
      1001: 2
      1005: q+1
      1007: q+1
      1008: 1
      1010: 1
      1012: 2
      1017: q+1
      1020: q+1
      1021: q+1
      1022: 2q+1
      1023: q
      1027: 2q+1
      1029: 2q+1
      1033: q+1
      1036: q+1
      1037: q+1
      1038: 2q+1
      1039: q
      1041: 2q+1
      1045: 2q+1
      1046: q+1
      1047: q
      1048: 2q+1
      1049: q
      1053: q^2+3q+1
      1055: 2q+1
      1057: 2q+1
      1059: q^2+3q+1
      1060: 2q+1
      1061: q
      1062: 2q+1
      1063: q
      1064: 1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 4q+1
      1084: 2q+2
      1085: 2q+1
      1091: q+1
      1094: q+1
      1116: 1
      1117: 1
      1124: 1
      1125: 1
      1127: 1
      1133: 2
      1135: 1
      1138: 1
      1139: 1
      1154: q+1
      1158: q+1
      1163: 1
      1174: q+1
      1178: q+1
      1183: 1
      1197: q+1
      1199: 2q+1
      1204: q+1
      1208: q+1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: q+1
      1230: 1
      1231: 1
      1233: 2
      1235: 2
      1241: q+1
      1243: q+1
      1247: q+1
      1248: 1
      1249: 1
      1251: 2
      1255: 2
      1259: q+1
      1261: q+1
      1262: q+1
      1263: q
      1266: 2q+1
      1267: q
      1269: 2q+1
      1271: 2q+1
      1274: q+1
      1275: q+1
      1276: 1
      1278: 1
      1280: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1295: 1
      1298: 1
      1329: 1
      1331: 1
      1350: 1
      1351: 1
      1358: 1
      1359: 1
      1361: 1
      1367: 2
      1369: 1
      1382: 1
      1383: 1
      1390: 1
      1391: 1
      1393: 1
      1399: 2
      1401: 1
      1413: q+1
      1420: q+1
      1424: q+1
      1429: 1
      1430: 1
      1431: 1
      1441: 1
      1443: 1
      1444: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 2
      1469: 2
      1474: 1
      1477: q+1
      1479: q+1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1506: 1
      1509: 1
      1518: 1
      1521: 1
      1552: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1610: 1
      1617: 1
      1618: 1
      1622: 1
      1626: 2
      1630: 1
      1646: 1
      1648: 1
      1654: 1
      1656: 1
      1664: 1
      1666: 1
      1669: 1
      1674: 1
      1718: 1
      1720: 1
      1752: 1
      1776: 1
      1800: 1
      1808: 1
      1830: 1
      1832: 1
      1943: 1

1944:    0: q^4+8q^3+2q^2+q+1
         1: q^4+8q^3+2q^2+q+1
         2: 3q^4+5q^3+2q^2+q+1
         3: q^4+8q^3+2q^2+q+1
         4: 3q^4+5q^3+2q^2+q+1
         5: q^4+8q^3+2q^2+q+1
         6: q^5+4q^4+5q^3+2q^2+q+1
         7: 2q^5+4q^4+4q^3+2q^2+q+1
         8: 3q^4+5q^3+2q^2+q+1
         9: 2q^5+4q^4+4q^3+2q^2+q+1
        10: 5q^3+q^2+q+1
        11: 5q^3+q^2+q+1
        12: 2q^4+3q^3+q^2+q+1
        13: 5q^3+2q^2+q+1
        14: 2q^4+4q^3+2q^2+q+1
        15: 5q^3+2q^2+q+1
        16: q^4+8q^3+2q^2+q+1
        17: q^4+8q^3+2q^2+q+1
        18: 2q^5+4q^4+4q^3+2q^2+q+1
        19: 5q^3+2q^2+q+1
        20: q^4+5q^3+2q^2+q+1
        21: 2q^4+4q^3+2q^2+q+1
        22: q^4+8q^3+2q^2+q+1
        23: q^4+8q^3+2q^2+q+1
        24: 3q^4+5q^3+2q^2+q+1
        25: q^4+8q^3+2q^2+q+1
        26: q^4+8q^3+2q^2+q+1
        27: 3q^4+5q^3+2q^2+q+1
        28: 5q^3+q^2+q+1
        29: 3q^3+q^2+q+1
        30: 4q^3+2q^2+q+1
        31: 5q^3+q^2+q+1
        32: 5q^3+2q^2+q+1
        33: q^4+8q^3+2q^2+q+1
        34: 5q^3+q^2+q+1
        35: 5q^3+2q^2+q+1
        36: q^4+8q^3+2q^2+q+1
        37: 5q^3+q^2+q+1
        38: q^4+3q^3+q^2
        39: 5q^3+q^2+q+1
        40: q^4+3q^3+q^2
        41: 2q^4+3q^3+q^2+q+1
        42: q^4+2q^3+q^2
        43: 2q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 2q^3+q^2+q+1
        46: 5q^3+2q^2+q+1
        47: 5q^3+2q^2+q+1
        48: 2q^4+4q^3+2q^2+q+1
        49: 5q^3+2q^2+q+1
        50: q^4+5q^3+2q^2+q+1
        51: 2q^4+4q^3+2q^2+q+1
        52: 5q^3+2q^2+q+1
        53: q^4+5q^3+2q^2+q+1
        54: 2q^4+4q^3+2q^2+q+1
        55: 5q^3+2q^2+q+1
        56: q^4+5q^3+2q^2+q+1
        57: 2q^4+4q^3+2q^2+q+1
        58: 3q^3+q^2+q+1
        59: 2q^3
        60: 3q^3+q^2+q+1
        61: 2q^3
        62: 3q^3+q^2+q+1
        63: 2q^3
        64: 3q^3+q^2+q+1
        65: 2q^3+q^2
        66: 5q^3+q^2+q+1
        67: q^4+3q^3+q^2
        68: q^2+q+1
        69: 4q^3+2q^2+q+1
        70: 2q^3+q^2+q+1
        71: 3q^3+q^2+q+1
        72: 2q^3+2q^2+q+1
        73: 2q^3+2q^2+q+1
        74: 2q^3+q^2+q+1
        75: q^3+q^2
        76: 2q^3+q^2+q+1
        77: q^4+q^3+q^2
        78: q^4+2q^3+q^2+q+1
        79: q^3+q^2
        80: 2q^3+q^2+q+1
        81: 5q^3+2q^2+q+1
        82: 3q^3+q^2+q+1
        83: 4q^3+2q^2+q+1
        84: 2q^3+q^2+q+1
        85: 5q^3+2q^2+q+1
        86: 3q^3+q^2+q+1
        87: 4q^3+2q^2+q+1
        88: 2q^3+q^2+q+1
        89: 2q^3+q^2+q+1
        90: q^4+2q^3+q^2+q+1
        91: 3q^3+2q^2+q+1
        92: 2q^3+2q^2+q+1
        93: 3q^3+2q^2+q+1
        94: 5q^3+2q^2+q+1
        95: q^4+5q^3+2q^2+q+1
        96: 2q^4+4q^3+2q^2+q+1
        97: 5q^3+2q^2+q+1
        98: q^4+5q^3+2q^2+q+1
        99: 2q^4+4q^3+2q^2+q+1
       100: 5q^3+2q^2+q+1
       101: q^4+5q^3+2q^2+q+1
       102: 2q^4+4q^3+2q^2+q+1
       103: 2q^3+q^2+q+1
       104: q^3
       105: q^3
       106: q^3
       107: q^3+q^2+q+1
       109: q^3+q^2+q+1
       111: q^2+q+1
       112: q^2
       113: q^3+q^2+q+1
       114: q^3
       115: 2q^3+q^2+q+1
       116: q^3+q^2
       117: q^2+q+1
       119: q^2+q+1
       121: q^3+q^2+q+1
       122: q^3
       123: 3q^3+q^2+q+1
       124: 2q^3+q^2
       125: q^2+q+1
       126: 2q^3+q^2+q+1
       127: 2q^3+q^2+q+1
       128: q^3+q^2
       129: 2q^3+q^2+q+1
       130: q^4+q^3+q^2
       131: q^4+2q^3+q^2+q+1
       132: q^3+q^2
       133: q^2+q+1
       134: 3q^3+2q^2+q+1
       135: q^3+2q^2+q+1
       136: q^3+2q^2+q+1
       137: 2q^3+q^2+q+1
       138: 4q^3+2q^2+q+1
       139: 3q^3+q^2+q+1
       140: 2q^3+2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^3+2q^2+q+1
       143: 2q^3+q^2+q+1
       144: 4q^3+2q^2+q+1
       145: 3q^3+q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^3+2q^2+q+1
       148: 2q^3+2q^2+q+1
       149: 3q^3+q^2+q+1
       150: 4q^3+2q^2+q+1
       151: 2q^3+q^2+q+1
       152: q^3+q^2
       153: 2q^3+q^2+q+1
       154: q^4+q^3+q^2
       155: q^4+2q^3+q^2+q+1
       156: q^3+q^2
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: 3q^3+2q^2+q+1
       161: 2q^3+2q^2+q+1
       162: 3q^3+2q^2+q+1
       163: 3q^3+2q^2+q+1
       164: 2q^3+2q^2+q+1
       165: 3q^3+2q^2+q+1
       166: 5q^3+2q^2+q+1
       167: q^4+5q^3+2q^2+q+1
       168: 2q^4+4q^3+2q^2+q+1
       169: q^2+q+1
       173: q^2+q+1
       177: 2q^3+q^2+q+1
       178: q^3+q^2
       179: q^3+q^2+q+1
       180: q^3
       181: q^2+q+1
       182: q^2
       183: q^2+q+1
       185: q^2+q+1
       187: q^2+q+1
       188: q^2
       189: q^3+q^2+q+1
       190: q^3
       191: q^2+q+1
       193: q^3+q^2+q+1
       195: q^3+q^2+q+1
       197: q^2+q+1
       198: q^2
       199: q^2+q+1
       201: q^3+q^2+q+1
       203: q^3+q^2+q+1
       205: q^2+q+1
       206: q^2
       207: q^3+q^2+q+1
       208: q^3
       209: q^3+q^2+q+1
       210: q^3
       211: 2q^3+q^2+q+1
       212: q^3+q^2
       213: q^3+q+1
       215: q+1
       217: q^3+q+1
       219: q^2+q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q^3+2q^2+q+1
       224: q+1
       225: q^3+2q^2+q+1
       226: 2q^3+q^2+q+1
       227: q^2+q+1
       228: 3q^3+2q^2+q+1
       229: q^3+2q^2+q+1
       230: q^3+2q^2+q+1
       231: 2q^3+q^2+q+1
       232: q^2+q+1
       233: 3q^3+2q^2+q+1
       234: q^3+2q^2+q+1
       235: q^3+2q^2+q+1
       236: 4q^3+2q^2+q+1
       237: 2q^3+q^2+q+1
       238: q^3+q^2
       239: 2q^3+q^2+q+1
       240: q^4+q^3+q^2
       241: q^4+2q^3+q^2+q+1
       242: q^3+q^2
       243: 3q^3+q^2+q+1
       244: 2q^3+2q^2+q+1
       245: 2q^3+2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 4q^2+q+1
       248: 4q^2+q+1
       249: q^4+3q^3+2q^2+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: 3q^3+2q^2+q+1
       257: 2q^3+2q^2+q+1
       258: 3q^3+2q^2+q+1
       259: q^2+q+1
       263: q^2+q+1
       267: q^2+q+1
       271: q^2+q+1
       275: q^2+q+1
       279: q+1
       281: q^3+q+1
       283: q^2+q+1
       285: q^2+q+1
       287: q^3+q^2+q+1
       288: q^3
       289: q+1
       291: q^2+q+1
       292: q^2
       293: q+1
       295: q+1
       297: q+1
       299: q^2+q+1
       301: q^2+q+1
       302: q^2
       303: q^2+q+1
       305: q^2+q+1
       306: q^2
       307: q^2+q+1
       309: q^2+q+1
       311: q^2+q+1
       312: q^2
       313: q^2+q+1
       314: q^2
       315: 2q^3+q^2+q+1
       316: q^3+q^2
       317: q^3+q^2+q+1
       318: q^3
       319: q^3+q^2+q+1
       321: q^3+q^2+q+1
       323: q^2+q+1
       324: q^2
       325: q^3+q^2+q+1
       326: q^3
       333: q+1
       334: q+1
       335: q+1
       336: 2q^2+q+1
       337: 2q^2+q+1
       338: 2q^2+q+1
       339: 2q^2
       340: 2q^2+q+1
       341: 2q^2
       342: q^4+2q^3+q^2+q+1
       343: q^3+q^2
       344: q^2+q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q^3+2q^2+q+1
       349: q+1
       350: q^3+2q^2+q+1
       351: 4q^2+q+1
       352: q^2+q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q^3+2q^2+q+1
       357: q+1
       358: q^3+2q^2+q+1
       359: 4q^2+q+1
       360: q^3+q+1
       362: q+1
       364: q^3+q+1
       366: 2q^3+q^2+q+1
       367: q^2+q+1
       368: 3q^3+2q^2+q+1
       369: q^3+2q^2+q+1
       370: q^3+2q^2+q+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       377: q^2+q+1
       381: q+1
       385: q+1
       389: q^2+q+1
       393: q^2+q+1
       397: q^2+q+1
       401: q^2+q+1
       405: q^2+q+1
       413: q+1
       417: q+1
       419: q+1
       421: q+1
       423: q+1
       425: q^2+q+1
       426: q^2
       427: q^2+q+1
       428: q^2
       429: q^2+q+1
       431: q^2+q+1
       433: q^2+q+1
       434: q^2
       435: q+1
       437: q+1
       439: q+1
       441: q+1
       443: 2q^2+q+1
       445: 2q^2+q+1
       446: 2q^2
       447: q^2+q+1
       449: q^2+q+1
       451: q^2+q+1
       452: q^2
       453: q+1
       455: q+1
       457: q+1
       459: q+1
       461: 2q^2+q+1
       463: 2q^2+q+1
       464: 2q^2
       465: q+1
       467: q^3+q+1
       469: q^3+q^2+q+1
       470: q^3
       471: q^2+q+1
       473: q^2+q+1
       475: q^2+q+1
       476: q^2
       477: q^2+q+1
       478: q^2
       479: 2q^2+q+1
       480: 2q^2
       481: q+1
       482: q+1
       483: q+1
       484: q^2+1
       485: 1
       487: 1
       489: q^3+1
       491: q^2+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q^2+q+1
       496: 2q^2+1
       497: q+1
       498: q+1
       499: q+1
       500: 2q^2+q+1
       501: 2q^2+1
       508: q^2+q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q^3+2q^2+q+1
       513: q+1
       514: q^3+2q^2+q+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       521: q+1
       529: q+1
       533: q^2+q+1
       537: q+1
       541: q+1
       545: q^2+q+1
       546: q^2
       549: q^2+q+1
       553: q+1
       557: q+1
       561: q^2+q+1
       562: q^2
       565: q^2+q+1
       569: q^2+q+1
       573: 2q^2+q+1
       577: q^2+q+1
       578: q^2
       580: q^2
       581: q^2
       585: q+1
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: 1
       599: q+1
       601: 1
       603: q+1
       605: q+1
       607: q+1
       609: q+1
       613: q^2+q+1
       614: q^2
       615: q^2+1
       617: 1
       619: q+1
       621: q+1
       623: q+1
       625: q+1
       629: q^2+q+1
       630: q^2
       631: q^2+1
       633: 1
       639: q+1
       641: q^2+q+1
       643: q^2+q+1
       645: q^2+q+1
       646: q^2
       647: q+1
       649: q+1
       651: q+1
       653: q+1
       655: q^2+1
       656: q^2
       657: q^2+1
       658: 1
       660: 1
       662: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q^2+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q^2+q+1
       690: 1
       691: 1
       692: q^3+1
       693: q^2+q+1
       694: q^2
       709: q+1
       713: q+1
       717: q+1
       721: q+1
       725: q+1
       733: 1
       737: q+1
       741: q+1
       749: 1
       753: q^2+q+1
       757: q+1
       761: q+1
       765: q^2+1
       769: 1
       775: 1
       779: 1
       781: 1
       785: 1
       787: 1
       791: 1
       793: q^2+1
       795: 1
       797: q+1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: 1
       811: q+1
       815: 1
       817: q^2+1
       819: 1
       821: q+1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: 1
       835: q+1
       839: 1
       843: q^2+1
       844: q^2
       845: q+1
       847: q+1
       849: q+1
       851: q+1
       855: q^2+q+1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q^2+1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       920: q+1
       924: q+1
       928: q+1
       940: 1
       944: q+1
       948: q+1
       952: q+1
       960: q+1
       964: q^2+1
       968: 1
       974: q+1
       988: 1
       994: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1016: 1
      1020: 1
      1022: 1
      1026: 1
      1028: 1
      1032: 1
      1036: 1
      1038: 1
      1040: 1
      1044: 1
      1046: 1
      1048: q+1
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1194: 1
      1198: q+1
      1202: q+1
      1206: q+1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1270: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 2
      1364: 1
      1368: 1
      1380: 1
      1388: 1
      1392: 2
      1396: 1
      1400: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1432: 1
      1436: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1474: 1
      1476: 1
      1478: 1
      1482: 1
      1487: 1
      1501: 1
      1503: 1
      1513: 1
      1515: 1
      1537: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1615: 1
      1619: 2
      1623: 1
      1627: 1
      1659: 1
      1663: 1
      1665: 1
      1711: 1
      1713: 1
      1741: 1
      1769: 1
      1797: 1
      1807: 1
      1944: 1

1945:    0: q^4+8q^3+2q^2+q+1
         1: q^4+8q^3+2q^2+q+1
         2: 3q^4+5q^3+2q^2+q+1
         3: q^4+8q^3+2q^2+q+1
         4: 3q^4+5q^3+2q^2+q+1
         5: q^4+8q^3+2q^2+q+1
         6: q^5+4q^4+5q^3+2q^2+q+1
         7: 2q^5+4q^4+4q^3+2q^2+q+1
         8: 3q^4+5q^3+2q^2+q+1
         9: 2q^5+4q^4+4q^3+2q^2+q+1
        10: 5q^3+q^2+q+1
        11: 5q^3+q^2+q+1
        12: 2q^4+3q^3+q^2+q+1
        13: 5q^3+2q^2+q+1
        14: 2q^4+4q^3+2q^2+q+1
        15: 5q^3+2q^2+q+1
        16: q^4+8q^3+2q^2+q+1
        17: q^4+8q^3+2q^2+q+1
        18: 2q^5+4q^4+4q^3+2q^2+q+1
        19: 5q^3+2q^2+q+1
        20: q^4+5q^3+2q^2+q+1
        21: 2q^4+4q^3+2q^2+q+1
        22: q^4+8q^3+2q^2+q+1
        23: q^4+8q^3+2q^2+q+1
        24: 3q^4+5q^3+2q^2+q+1
        25: q^4+8q^3+2q^2+q+1
        26: q^4+8q^3+2q^2+q+1
        27: 3q^4+5q^3+2q^2+q+1
        28: 5q^3+q^2+q+1
        29: 3q^3+q^2+q+1
        30: 4q^3+2q^2+q+1
        31: 5q^3+q^2+q+1
        32: 5q^3+2q^2+q+1
        33: q^4+8q^3+2q^2+q+1
        34: 5q^3+q^2+q+1
        35: 5q^3+2q^2+q+1
        36: q^4+8q^3+2q^2+q+1
        37: 5q^3+q^2+q+1
        38: q^4+3q^3+q^2
        39: 5q^3+q^2+q+1
        40: q^4+3q^3+q^2
        41: 2q^4+3q^3+q^2+q+1
        42: q^4+2q^3+q^2
        43: 2q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 2q^3+q^2+q+1
        46: 5q^3+2q^2+q+1
        47: 5q^3+2q^2+q+1
        48: 2q^4+4q^3+2q^2+q+1
        49: 5q^3+2q^2+q+1
        50: q^4+5q^3+2q^2+q+1
        51: 2q^4+4q^3+2q^2+q+1
        52: 5q^3+2q^2+q+1
        53: q^4+5q^3+2q^2+q+1
        54: 2q^4+4q^3+2q^2+q+1
        55: 5q^3+2q^2+q+1
        56: q^4+5q^3+2q^2+q+1
        57: 2q^4+4q^3+2q^2+q+1
        58: 2q^3
        59: 3q^3+q^2+q+1
        60: 2q^3
        61: 3q^3+q^2+q+1
        62: 3q^3+q^2+q+1
        63: 2q^3
        64: 3q^3+q^2+q+1
        65: 2q^3+q^2
        66: 5q^3+q^2+q+1
        67: q^4+3q^3+q^2
        68: q^2+q+1
        69: 4q^3+2q^2+q+1
        70: 2q^3+q^2+q+1
        71: 3q^3+q^2+q+1
        72: 2q^3+2q^2+q+1
        73: 2q^3+2q^2+q+1
        74: 2q^3+q^2+q+1
        75: q^3+q^2
        76: 2q^3+q^2+q+1
        77: q^4+q^3+q^2
        78: q^4+2q^3+q^2+q+1
        79: q^3+q^2
        80: 2q^3+q^2+q+1
        81: 5q^3+2q^2+q+1
        82: 3q^3+q^2+q+1
        83: 4q^3+2q^2+q+1
        84: 2q^3+q^2+q+1
        85: 5q^3+2q^2+q+1
        86: 3q^3+q^2+q+1
        87: 4q^3+2q^2+q+1
        88: 2q^3+q^2+q+1
        89: 2q^3+q^2+q+1
        90: q^4+2q^3+q^2+q+1
        91: 3q^3+2q^2+q+1
        92: 2q^3+2q^2+q+1
        93: 3q^3+2q^2+q+1
        94: 5q^3+2q^2+q+1
        95: q^4+5q^3+2q^2+q+1
        96: 2q^4+4q^3+2q^2+q+1
        97: 5q^3+2q^2+q+1
        98: q^4+5q^3+2q^2+q+1
        99: 2q^4+4q^3+2q^2+q+1
       100: 5q^3+2q^2+q+1
       101: q^4+5q^3+2q^2+q+1
       102: 2q^4+4q^3+2q^2+q+1
       103: q^3
       104: q^3
       105: q^3
       106: 2q^3+q^2+q+1
       108: q^3+q^2+q+1
       110: q^3+q^2+q+1
       111: q^2+q+1
       112: q^2
       113: q^3+q^2+q+1
       114: q^3
       115: 2q^3+q^2+q+1
       116: q^3+q^2
       118: q^2+q+1
       120: q^2+q+1
       121: q^3+q^2+q+1
       122: q^3
       123: 3q^3+q^2+q+1
       124: 2q^3+q^2
       125: q^2+q+1
       126: 2q^3+q^2+q+1
       127: 2q^3+q^2+q+1
       128: q^3+q^2
       129: 2q^3+q^2+q+1
       130: q^4+q^3+q^2
       131: q^4+2q^3+q^2+q+1
       132: q^3+q^2
       133: q^2+q+1
       134: 3q^3+2q^2+q+1
       135: q^3+2q^2+q+1
       136: q^3+2q^2+q+1
       137: 2q^3+q^2+q+1
       138: 4q^3+2q^2+q+1
       139: 3q^3+q^2+q+1
       140: 2q^3+2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^3+2q^2+q+1
       143: 2q^3+q^2+q+1
       144: 4q^3+2q^2+q+1
       145: 3q^3+q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^3+2q^2+q+1
       148: 2q^3+2q^2+q+1
       149: 3q^3+q^2+q+1
       150: 4q^3+2q^2+q+1
       151: 2q^3+q^2+q+1
       152: q^3+q^2
       153: 2q^3+q^2+q+1
       154: q^4+q^3+q^2
       155: q^4+2q^3+q^2+q+1
       156: q^3+q^2
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: 3q^3+2q^2+q+1
       161: 2q^3+2q^2+q+1
       162: 3q^3+2q^2+q+1
       163: 3q^3+2q^2+q+1
       164: 2q^3+2q^2+q+1
       165: 3q^3+2q^2+q+1
       166: 5q^3+2q^2+q+1
       167: q^4+5q^3+2q^2+q+1
       168: 2q^4+4q^3+2q^2+q+1
       172: q^2+q+1
       176: q^2+q+1
       177: 2q^3+q^2+q+1
       178: q^3+q^2
       179: q^3+q^2+q+1
       180: q^3
       181: q^2+q+1
       182: q^2
       184: q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q^2
       189: q^3+q^2+q+1
       190: q^3
       192: q^2+q+1
       194: q^3+q^2+q+1
       196: q^3+q^2+q+1
       197: q^2+q+1
       198: q^2
       200: q^2+q+1
       202: q^3+q^2+q+1
       204: q^3+q^2+q+1
       205: q^2+q+1
       206: q^2
       207: q^3+q^2+q+1
       208: q^3
       209: q^3+q^2+q+1
       210: q^3
       211: 2q^3+q^2+q+1
       212: q^3+q^2
       213: q^3+q+1
       215: q+1
       217: q^3+q+1
       219: q^2+q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q^3+2q^2+q+1
       224: q+1
       225: q^3+2q^2+q+1
       226: 2q^3+q^2+q+1
       227: q^2+q+1
       228: 3q^3+2q^2+q+1
       229: q^3+2q^2+q+1
       230: q^3+2q^2+q+1
       231: 2q^3+q^2+q+1
       232: q^2+q+1
       233: 3q^3+2q^2+q+1
       234: q^3+2q^2+q+1
       235: q^3+2q^2+q+1
       236: 4q^3+2q^2+q+1
       237: 2q^3+q^2+q+1
       238: q^3+q^2
       239: 2q^3+q^2+q+1
       240: q^4+q^3+q^2
       241: q^4+2q^3+q^2+q+1
       242: q^3+q^2
       243: 3q^3+q^2+q+1
       244: 2q^3+2q^2+q+1
       245: 2q^3+2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 4q^2+q+1
       248: 4q^2+q+1
       249: q^4+3q^3+2q^2+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: 3q^3+2q^2+q+1
       257: 2q^3+2q^2+q+1
       258: 3q^3+2q^2+q+1
       262: q^2+q+1
       266: q^2+q+1
       269: q^2+q+1
       273: q^2+q+1
       278: q^2+q+1
       279: q+1
       281: q^3+q+1
       284: q^2+q+1
       286: q^2+q+1
       287: q^3+q^2+q+1
       288: q^3
       289: q+1
       291: q^2+q+1
       292: q^2
       294: q+1
       296: q+1
       297: q+1
       300: q^2+q+1
       301: q^2+q+1
       302: q^2
       304: q^2+q+1
       305: q^2+q+1
       306: q^2
       308: q^2+q+1
       310: q^2+q+1
       311: q^2+q+1
       312: q^2
       313: q^2+q+1
       314: q^2
       315: 2q^3+q^2+q+1
       316: q^3+q^2
       317: q^3+q^2+q+1
       318: q^3
       320: q^3+q^2+q+1
       322: q^3+q^2+q+1
       323: q^2+q+1
       324: q^2
       325: q^3+q^2+q+1
       326: q^3
       333: q+1
       334: q+1
       335: q+1
       336: 2q^2+q+1
       337: 2q^2+q+1
       338: 2q^2+q+1
       339: 2q^2
       340: 2q^2+q+1
       341: 2q^2
       342: q^4+2q^3+q^2+q+1
       343: q^3+q^2
       344: q^2+q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q^3+2q^2+q+1
       349: q+1
       350: q^3+2q^2+q+1
       351: 4q^2+q+1
       352: q^2+q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q^3+2q^2+q+1
       357: q+1
       358: q^3+2q^2+q+1
       359: 4q^2+q+1
       360: q^3+q+1
       362: q+1
       364: q^3+q+1
       366: 2q^3+q^2+q+1
       367: q^2+q+1
       368: 3q^3+2q^2+q+1
       369: q^3+2q^2+q+1
       370: q^3+2q^2+q+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       380: q^2+q+1
       384: q+1
       388: q+1
       391: q^2+q+1
       396: q^2+q+1
       399: q^2+q+1
       404: q^2+q+1
       406: q^2+q+1
       413: q+1
       417: q+1
       420: q+1
       422: q+1
       423: q+1
       425: q^2+q+1
       426: q^2
       427: q^2+q+1
       428: q^2
       430: q^2+q+1
       432: q^2+q+1
       433: q^2+q+1
       434: q^2
       435: q+1
       438: q+1
       440: q+1
       441: q+1
       444: 2q^2+q+1
       445: 2q^2+q+1
       446: 2q^2
       448: q^2+q+1
       450: q^2+q+1
       451: q^2+q+1
       452: q^2
       454: q+1
       455: q+1
       458: q+1
       459: q+1
       462: 2q^2+q+1
       463: 2q^2+q+1
       464: 2q^2
       465: q+1
       467: q^3+q+1
       469: q^3+q^2+q+1
       470: q^3
       472: q^2+q+1
       474: q^2+q+1
       475: q^2+q+1
       476: q^2
       477: q^2+q+1
       478: q^2
       479: 2q^2+q+1
       480: 2q^2
       481: q+1
       482: q+1
       483: q+1
       484: q^2+1
       485: 1
       487: 1
       489: q^3+1
       491: q^2+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q^2+q+1
       496: 2q^2+1
       497: q+1
       498: q+1
       499: q+1
       500: 2q^2+q+1
       501: 2q^2+1
       508: q^2+q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q^3+2q^2+q+1
       513: q+1
       514: q^3+2q^2+q+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       524: q+1
       532: q+1
       536: q^2+q+1
       539: q+1
       543: q+1
       547: q^2+q+1
       548: q^2
       552: q^2+q+1
       555: q+1
       559: q+1
       563: q^2+q+1
       564: q^2
       568: q^2+q+1
       570: q^2+q+1
       575: 2q^2+q+1
       577: q^2+q+1
       578: q^2
       580: q^2
       581: q^2
       585: q+1
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: 1
       599: q+1
       601: 1
       604: q+1
       605: q+1
       608: q+1
       609: q+1
       613: q^2+q+1
       614: q^2
       616: q^2+1
       617: 1
       620: q+1
       622: q+1
       623: q+1
       625: q+1
       629: q^2+q+1
       630: q^2
       632: q^2+1
       633: 1
       639: q+1
       642: q^2+q+1
       644: q^2+q+1
       645: q^2+q+1
       646: q^2
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: q^2+1
       656: q^2
       657: q^2+1
       658: 1
       660: 1
       662: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q^2+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q^2+q+1
       690: 1
       691: 1
       692: q^3+1
       697: q^2+q+1
       701: q^2
       712: q+1
       716: q+1
       720: q+1
       723: q+1
       727: q+1
       735: 1
       739: q+1
       743: q+1
       751: 1
       756: q^2+q+1
       758: q+1
       762: q+1
       768: q^2+1
       769: 1
       775: 1
       779: 1
       781: 1
       786: 1
       788: 1
       791: 1
       794: q^2+1
       795: 1
       797: q+1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: 1
       811: q+1
       816: 1
       818: q^2+1
       819: 1
       821: q+1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: 1
       835: q+1
       840: 1
       843: q^2+1
       844: q^2
       846: q+1
       848: q+1
       849: q+1
       851: q+1
       855: q^2+q+1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q^2+1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       922: q+1
       927: q+1
       930: q+1
       942: 1
       946: q+1
       950: q+1
       955: q+1
       961: q+1
       967: q^2+1
       968: 1
       975: q+1
       991: 1
       994: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1017: 1
      1020: 1
      1022: 1
      1027: 1
      1029: 1
      1033: 1
      1036: 1
      1038: 1
      1041: 1
      1045: 1
      1046: 1
      1048: q+1
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1197: 1
      1199: q+1
      1204: q+1
      1208: q+1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1271: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1329: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 2
      1367: 1
      1369: 1
      1382: 1
      1390: 1
      1393: 2
      1399: 1
      1401: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1432: 1
      1436: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1474: 1
      1477: 1
      1479: 1
      1482: 1
      1487: 1
      1506: 1
      1510: 1
      1518: 1
      1522: 1
      1538: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1617: 1
      1622: 2
      1626: 1
      1630: 1
      1659: 1
      1664: 1
      1666: 1
      1718: 1
      1722: 1
      1742: 1
      1770: 1
      1800: 1
      1808: 1
      1945: 1

1946:    0: q^4+8q^3+2q^2+q+1
         1: q^4+8q^3+2q^2+q+1
         2: 3q^4+5q^3+2q^2+q+1
         3: q^4+8q^3+2q^2+q+1
         4: 3q^4+5q^3+2q^2+q+1
         5: q^4+8q^3+2q^2+q+1
         6: q^5+4q^4+5q^3+2q^2+q+1
         7: 2q^5+4q^4+4q^3+2q^2+q+1
         8: 3q^4+5q^3+2q^2+q+1
         9: 2q^5+4q^4+4q^3+2q^2+q+1
        10: 5q^3+q^2+q+1
        11: 5q^3+q^2+q+1
        12: 2q^4+3q^3+q^2+q+1
        13: 5q^3+2q^2+q+1
        14: 2q^4+4q^3+2q^2+q+1
        15: 5q^3+2q^2+q+1
        16: q^4+8q^3+2q^2+q+1
        17: q^4+8q^3+2q^2+q+1
        18: 2q^5+4q^4+4q^3+2q^2+q+1
        19: 5q^3+2q^2+q+1
        20: q^4+5q^3+2q^2+q+1
        21: 2q^4+4q^3+2q^2+q+1
        22: q^4+8q^3+2q^2+q+1
        23: q^4+8q^3+2q^2+q+1
        24: 3q^4+5q^3+2q^2+q+1
        25: q^4+8q^3+2q^2+q+1
        26: q^4+8q^3+2q^2+q+1
        27: 3q^4+5q^3+2q^2+q+1
        28: 5q^3+q^2+q+1
        29: 3q^3+q^2+q+1
        30: 4q^3+2q^2+q+1
        31: 5q^3+q^2+q+1
        32: 5q^3+2q^2+q+1
        33: q^4+8q^3+2q^2+q+1
        34: 5q^3+q^2+q+1
        35: 5q^3+2q^2+q+1
        36: q^4+8q^3+2q^2+q+1
        37: q^4+3q^3+q^2
        38: 5q^3+q^2+q+1
        39: q^4+3q^3+q^2
        40: 5q^3+q^2+q+1
        41: q^4+2q^3+q^2
        42: 2q^4+3q^3+q^2+q+1
        43: 2q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 2q^3+q^2+q+1
        46: 5q^3+2q^2+q+1
        47: 5q^3+2q^2+q+1
        48: 2q^4+4q^3+2q^2+q+1
        49: 5q^3+2q^2+q+1
        50: q^4+5q^3+2q^2+q+1
        51: 2q^4+4q^3+2q^2+q+1
        52: 5q^3+2q^2+q+1
        53: q^4+5q^3+2q^2+q+1
        54: 2q^4+4q^3+2q^2+q+1
        55: 5q^3+2q^2+q+1
        56: q^4+5q^3+2q^2+q+1
        57: 2q^4+4q^3+2q^2+q+1
        58: 2q^3
        59: 3q^3+q^2+q+1
        60: 3q^3+q^2+q+1
        61: 2q^3
        62: 2q^3
        63: 3q^3+q^2+q+1
        64: 2q^3+q^2
        65: 3q^3+q^2+q+1
        66: q^4+3q^3+q^2
        67: 5q^3+q^2+q+1
        68: q^2+q+1
        69: 4q^3+2q^2+q+1
        70: 2q^3+q^2+q+1
        71: 3q^3+q^2+q+1
        72: 2q^3+2q^2+q+1
        73: 2q^3+2q^2+q+1
        74: q^3+q^2
        75: 2q^3+q^2+q+1
        76: q^4+q^3+q^2
        77: 2q^3+q^2+q+1
        78: q^3+q^2
        79: q^4+2q^3+q^2+q+1
        80: 2q^3+q^2+q+1
        81: 5q^3+2q^2+q+1
        82: 3q^3+q^2+q+1
        83: 4q^3+2q^2+q+1
        84: 2q^3+q^2+q+1
        85: 5q^3+2q^2+q+1
        86: 3q^3+q^2+q+1
        87: 4q^3+2q^2+q+1
        88: 2q^3+q^2+q+1
        89: 2q^3+q^2+q+1
        90: q^4+2q^3+q^2+q+1
        91: 3q^3+2q^2+q+1
        92: 2q^3+2q^2+q+1
        93: 3q^3+2q^2+q+1
        94: 5q^3+2q^2+q+1
        95: q^4+5q^3+2q^2+q+1
        96: 2q^4+4q^3+2q^2+q+1
        97: 5q^3+2q^2+q+1
        98: q^4+5q^3+2q^2+q+1
        99: 2q^4+4q^3+2q^2+q+1
       100: 5q^3+2q^2+q+1
       101: q^4+5q^3+2q^2+q+1
       102: 2q^4+4q^3+2q^2+q+1
       103: q^3
       104: 2q^3+q^2+q+1
       105: q^3
       106: q^3
       107: q^3+q^2+q+1
       110: q^3+q^2+q+1
       111: q^2
       112: q^2+q+1
       113: q^3
       114: q^3+q^2+q+1
       115: q^3+q^2
       116: 2q^3+q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       121: q^3
       122: q^3+q^2+q+1
       123: 2q^3+q^2
       124: 3q^3+q^2+q+1
       125: q^2+q+1
       126: 2q^3+q^2+q+1
       127: q^3+q^2
       128: 2q^3+q^2+q+1
       129: q^4+q^3+q^2
       130: 2q^3+q^2+q+1
       131: q^3+q^2
       132: q^4+2q^3+q^2+q+1
       133: q^2+q+1
       134: 3q^3+2q^2+q+1
       135: q^3+2q^2+q+1
       136: q^3+2q^2+q+1
       137: 2q^3+q^2+q+1
       138: 4q^3+2q^2+q+1
       139: 3q^3+q^2+q+1
       140: 2q^3+2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^3+2q^2+q+1
       143: 2q^3+q^2+q+1
       144: 4q^3+2q^2+q+1
       145: 3q^3+q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^3+2q^2+q+1
       148: 2q^3+2q^2+q+1
       149: 3q^3+q^2+q+1
       150: 4q^3+2q^2+q+1
       151: q^3+q^2
       152: 2q^3+q^2+q+1
       153: q^4+q^3+q^2
       154: 2q^3+q^2+q+1
       155: q^3+q^2
       156: q^4+2q^3+q^2+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: 3q^3+2q^2+q+1
       161: 2q^3+2q^2+q+1
       162: 3q^3+2q^2+q+1
       163: 3q^3+2q^2+q+1
       164: 2q^3+2q^2+q+1
       165: 3q^3+2q^2+q+1
       166: 5q^3+2q^2+q+1
       167: q^4+5q^3+2q^2+q+1
       168: 2q^4+4q^3+2q^2+q+1
       170: q^2+q+1
       174: q^2+q+1
       177: q^3+q^2
       178: 2q^3+q^2+q+1
       179: q^3
       180: q^3+q^2+q+1
       181: q^2
       182: q^2+q+1
       183: q^2+q+1
       186: q^2+q+1
       187: q^2
       188: q^2+q+1
       189: q^3
       190: q^3+q^2+q+1
       192: q^2+q+1
       193: q^3+q^2+q+1
       196: q^3+q^2+q+1
       197: q^2
       198: q^2+q+1
       199: q^2+q+1
       201: q^3+q^2+q+1
       204: q^3+q^2+q+1
       205: q^2
       206: q^2+q+1
       207: q^3
       208: q^3+q^2+q+1
       209: q^3
       210: q^3+q^2+q+1
       211: q^3+q^2
       212: 2q^3+q^2+q+1
       214: q^3+q+1
       216: q+1
       218: q^3+q+1
       219: q^2+q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q^3+2q^2+q+1
       224: q+1
       225: q^3+2q^2+q+1
       226: 2q^3+q^2+q+1
       227: q^2+q+1
       228: 3q^3+2q^2+q+1
       229: q^3+2q^2+q+1
       230: q^3+2q^2+q+1
       231: 2q^3+q^2+q+1
       232: q^2+q+1
       233: 3q^3+2q^2+q+1
       234: q^3+2q^2+q+1
       235: q^3+2q^2+q+1
       236: 4q^3+2q^2+q+1
       237: q^3+q^2
       238: 2q^3+q^2+q+1
       239: q^4+q^3+q^2
       240: 2q^3+q^2+q+1
       241: q^3+q^2
       242: q^4+2q^3+q^2+q+1
       243: 3q^3+q^2+q+1
       244: 2q^3+2q^2+q+1
       245: 2q^3+2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 4q^2+q+1
       248: 4q^2+q+1
       249: q^4+3q^3+2q^2+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: 3q^3+2q^2+q+1
       257: 2q^3+2q^2+q+1
       258: 3q^3+2q^2+q+1
       260: q^2+q+1
       264: q^2+q+1
       268: q^2+q+1
       274: q^2+q+1
       276: q^2+q+1
       280: q+1
       282: q^3+q+1
       283: q^2+q+1
       286: q^2+q+1
       287: q^3
       288: q^3+q^2+q+1
       290: q+1
       291: q^2
       292: q^2+q+1
       293: q+1
       296: q+1
       298: q+1
       299: q^2+q+1
       301: q^2
       302: q^2+q+1
       304: q^2+q+1
       305: q^2
       306: q^2+q+1
       307: q^2+q+1
       310: q^2+q+1
       311: q^2
       312: q^2+q+1
       313: q^2
       314: q^2+q+1
       315: q^3+q^2
       316: 2q^3+q^2+q+1
       317: q^3
       318: q^3+q^2+q+1
       319: q^3+q^2+q+1
       322: q^3+q^2+q+1
       323: q^2
       324: q^2+q+1
       325: q^3
       326: q^3+q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: 2q^2+q+1
       337: 2q^2+q+1
       338: 2q^2
       339: 2q^2+q+1
       340: 2q^2
       341: 2q^2+q+1
       342: q^3+q^2
       343: q^4+2q^3+q^2+q+1
       344: q^2+q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q^3+2q^2+q+1
       349: q+1
       350: q^3+2q^2+q+1
       351: 4q^2+q+1
       352: q^2+q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q^3+2q^2+q+1
       357: q+1
       358: q^3+2q^2+q+1
       359: 4q^2+q+1
       361: q^3+q+1
       363: q+1
       365: q^3+q+1
       366: 2q^3+q^2+q+1
       367: q^2+q+1
       368: 3q^3+2q^2+q+1
       369: q^3+2q^2+q+1
       370: q^3+2q^2+q+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       378: q^2+q+1
       382: q+1
       386: q+1
       390: q^2+q+1
       394: q^2+q+1
       400: q^2+q+1
       403: q^2+q+1
       407: q^2+q+1
       414: q+1
       418: q+1
       419: q+1
       422: q+1
       424: q+1
       425: q^2
       426: q^2+q+1
       427: q^2
       428: q^2+q+1
       429: q^2+q+1
       432: q^2+q+1
       433: q^2
       434: q^2+q+1
       436: q+1
       437: q+1
       440: q+1
       442: q+1
       443: 2q^2+q+1
       445: 2q^2
       446: 2q^2+q+1
       447: q^2+q+1
       450: q^2+q+1
       451: q^2
       452: q^2+q+1
       453: q+1
       456: q+1
       458: q+1
       460: q+1
       462: 2q^2+q+1
       463: 2q^2
       464: 2q^2+q+1
       466: q+1
       468: q^3+q+1
       469: q^3
       470: q^3+q^2+q+1
       471: q^2+q+1
       474: q^2+q+1
       475: q^2
       476: q^2+q+1
       477: q^2
       478: q^2+q+1
       479: 2q^2
       480: 2q^2+q+1
       481: q+1
       482: q+1
       483: q+1
       484: q^2+1
       486: 1
       488: 1
       490: q^3+1
       491: q^2+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q^2+q+1
       496: 2q^2+1
       497: q+1
       498: q+1
       499: q+1
       500: 2q^2+q+1
       501: 2q^2+1
       508: q^2+q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q^3+2q^2+q+1
       513: q+1
       514: q^3+2q^2+q+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       522: q+1
       530: q+1
       534: q^2+q+1
       538: q+1
       542: q+1
       545: q^2
       546: q^2+q+1
       551: q^2+q+1
       556: q+1
       560: q+1
       563: q^2
       564: q^2+q+1
       566: q^2+q+1
       571: q^2+q+1
       574: 2q^2+q+1
       577: q^2
       578: q^2
       580: q^2
       581: q^2+q+1
       586: q+1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       598: 1
       600: q+1
       602: 1
       603: q+1
       606: q+1
       608: q+1
       610: q+1
       613: q^2
       614: q^2+q+1
       615: q^2+1
       618: 1
       619: q+1
       622: q+1
       624: q+1
       626: q+1
       629: q^2
       630: q^2+q+1
       632: q^2+1
       634: 1
       640: q+1
       641: q^2+q+1
       644: q^2+q+1
       645: q^2
       646: q^2+q+1
       647: q+1
       650: q+1
       652: q+1
       654: q+1
       655: q^2
       656: q^2+1
       657: q^2+1
       659: 1
       661: 1
       663: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q^2+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q^2+q+1
       690: 1
       691: 1
       692: q^3+1
       696: q^2
       699: q^2+q+1
       710: q+1
       715: q+1
       718: q+1
       722: q+1
       726: q+1
       734: 1
       740: q+1
       744: q+1
       752: 1
       754: q^2+q+1
       759: q+1
       763: q+1
       766: q^2+1
       773: 1
       776: 1
       780: 1
       782: 1
       785: 1
       788: 1
       792: 1
       793: q^2+1
       796: 1
       798: q+1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       810: 1
       812: q+1
       815: 1
       818: q^2+1
       820: 1
       822: q+1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       834: 1
       836: q+1
       840: 1
       843: q^2
       844: q^2+1
       845: q+1
       848: q+1
       850: q+1
       852: q+1
       855: q^2
       856: q^2+q+1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q^2+1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       921: q+1
       926: q+1
       929: q+1
       943: 1
       947: q+1
       951: q+1
       953: q+1
       962: q+1
       965: q^2+1
       972: 1
       976: q+1
       989: 1
       995: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1016: 1
      1021: 1
      1023: 1
      1026: 1
      1029: 1
      1033: 1
      1037: 1
      1039: 1
      1040: 1
      1045: 1
      1047: 1
      1049: q+1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1195: 1
      1200: q+1
      1205: q+1
      1207: q+1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1271: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 2
      1366: 1
      1371: 1
      1383: 1
      1389: 1
      1394: 2
      1397: 1
      1402: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1435: 1
      1437: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1475: 1
      1476: 1
      1479: 1
      1483: 1
      1487: 1
      1508: 1
      1512: 1
      1519: 1
      1523: 1
      1539: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1610: 1
      1616: 1
      1620: 2
      1624: 1
      1628: 1
      1660: 1
      1664: 1
      1665: 1
      1716: 1
      1719: 1
      1744: 1
      1771: 1
      1798: 1
      1809: 1
      1946: 1

1947:    0: q^4+8q^3+2q^2+q+1
         1: q^4+8q^3+2q^2+q+1
         2: 3q^4+5q^3+2q^2+q+1
         3: q^4+8q^3+2q^2+q+1
         4: 3q^4+5q^3+2q^2+q+1
         5: q^4+8q^3+2q^2+q+1
         6: q^5+4q^4+5q^3+2q^2+q+1
         7: 2q^5+4q^4+4q^3+2q^2+q+1
         8: 3q^4+5q^3+2q^2+q+1
         9: 2q^5+4q^4+4q^3+2q^2+q+1
        10: 5q^3+q^2+q+1
        11: 5q^3+q^2+q+1
        12: 2q^4+3q^3+q^2+q+1
        13: 5q^3+2q^2+q+1
        14: 2q^4+4q^3+2q^2+q+1
        15: 5q^3+2q^2+q+1
        16: q^4+8q^3+2q^2+q+1
        17: q^4+8q^3+2q^2+q+1
        18: 2q^5+4q^4+4q^3+2q^2+q+1
        19: 5q^3+2q^2+q+1
        20: q^4+5q^3+2q^2+q+1
        21: 2q^4+4q^3+2q^2+q+1
        22: q^4+8q^3+2q^2+q+1
        23: q^4+8q^3+2q^2+q+1
        24: 3q^4+5q^3+2q^2+q+1
        25: q^4+8q^3+2q^2+q+1
        26: q^4+8q^3+2q^2+q+1
        27: 3q^4+5q^3+2q^2+q+1
        28: 5q^3+q^2+q+1
        29: 3q^3+q^2+q+1
        30: 4q^3+2q^2+q+1
        31: 5q^3+q^2+q+1
        32: 5q^3+2q^2+q+1
        33: q^4+8q^3+2q^2+q+1
        34: 5q^3+q^2+q+1
        35: 5q^3+2q^2+q+1
        36: q^4+8q^3+2q^2+q+1
        37: q^4+3q^3+q^2
        38: 5q^3+q^2+q+1
        39: q^4+3q^3+q^2
        40: 5q^3+q^2+q+1
        41: q^4+2q^3+q^2
        42: 2q^4+3q^3+q^2+q+1
        43: 2q^3+q^2+q+1
        44: q^4+2q^3+q^2+q+1
        45: 2q^3+q^2+q+1
        46: 5q^3+2q^2+q+1
        47: 5q^3+2q^2+q+1
        48: 2q^4+4q^3+2q^2+q+1
        49: 5q^3+2q^2+q+1
        50: q^4+5q^3+2q^2+q+1
        51: 2q^4+4q^3+2q^2+q+1
        52: 5q^3+2q^2+q+1
        53: q^4+5q^3+2q^2+q+1
        54: 2q^4+4q^3+2q^2+q+1
        55: 5q^3+2q^2+q+1
        56: q^4+5q^3+2q^2+q+1
        57: 2q^4+4q^3+2q^2+q+1
        58: 3q^3+q^2+q+1
        59: 2q^3
        60: 2q^3
        61: 3q^3+q^2+q+1
        62: 2q^3
        63: 3q^3+q^2+q+1
        64: 2q^3+q^2
        65: 3q^3+q^2+q+1
        66: q^4+3q^3+q^2
        67: 5q^3+q^2+q+1
        68: q^2+q+1
        69: 4q^3+2q^2+q+1
        70: 2q^3+q^2+q+1
        71: 3q^3+q^2+q+1
        72: 2q^3+2q^2+q+1
        73: 2q^3+2q^2+q+1
        74: q^3+q^2
        75: 2q^3+q^2+q+1
        76: q^4+q^3+q^2
        77: 2q^3+q^2+q+1
        78: q^3+q^2
        79: q^4+2q^3+q^2+q+1
        80: 2q^3+q^2+q+1
        81: 5q^3+2q^2+q+1
        82: 3q^3+q^2+q+1
        83: 4q^3+2q^2+q+1
        84: 2q^3+q^2+q+1
        85: 5q^3+2q^2+q+1
        86: 3q^3+q^2+q+1
        87: 4q^3+2q^2+q+1
        88: 2q^3+q^2+q+1
        89: 2q^3+q^2+q+1
        90: q^4+2q^3+q^2+q+1
        91: 3q^3+2q^2+q+1
        92: 2q^3+2q^2+q+1
        93: 3q^3+2q^2+q+1
        94: 5q^3+2q^2+q+1
        95: q^4+5q^3+2q^2+q+1
        96: 2q^4+4q^3+2q^2+q+1
        97: 5q^3+2q^2+q+1
        98: q^4+5q^3+2q^2+q+1
        99: 2q^4+4q^3+2q^2+q+1
       100: 5q^3+2q^2+q+1
       101: q^4+5q^3+2q^2+q+1
       102: 2q^4+4q^3+2q^2+q+1
       103: q^3
       104: q^3
       105: 2q^3+q^2+q+1
       106: q^3
       108: q^3+q^2+q+1
       109: q^3+q^2+q+1
       111: q^2
       112: q^2+q+1
       113: q^3
       114: q^3+q^2+q+1
       115: q^3+q^2
       116: 2q^3+q^2+q+1
       117: q^2+q+1
       120: q^2+q+1
       121: q^3
       122: q^3+q^2+q+1
       123: 2q^3+q^2
       124: 3q^3+q^2+q+1
       125: q^2+q+1
       126: 2q^3+q^2+q+1
       127: q^3+q^2
       128: 2q^3+q^2+q+1
       129: q^4+q^3+q^2
       130: 2q^3+q^2+q+1
       131: q^3+q^2
       132: q^4+2q^3+q^2+q+1
       133: q^2+q+1
       134: 3q^3+2q^2+q+1
       135: q^3+2q^2+q+1
       136: q^3+2q^2+q+1
       137: 2q^3+q^2+q+1
       138: 4q^3+2q^2+q+1
       139: 3q^3+q^2+q+1
       140: 2q^3+2q^2+q+1
       141: 2q^3+q^2+q+1
       142: 2q^3+2q^2+q+1
       143: 2q^3+q^2+q+1
       144: 4q^3+2q^2+q+1
       145: 3q^3+q^2+q+1
       146: 2q^3+q^2+q+1
       147: 2q^3+2q^2+q+1
       148: 2q^3+2q^2+q+1
       149: 3q^3+q^2+q+1
       150: 4q^3+2q^2+q+1
       151: q^3+q^2
       152: 2q^3+q^2+q+1
       153: q^4+q^3+q^2
       154: 2q^3+q^2+q+1
       155: q^3+q^2
       156: q^4+2q^3+q^2+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: 3q^3+2q^2+q+1
       161: 2q^3+2q^2+q+1
       162: 3q^3+2q^2+q+1
       163: 3q^3+2q^2+q+1
       164: 2q^3+2q^2+q+1
       165: 3q^3+2q^2+q+1
       166: 5q^3+2q^2+q+1
       167: q^4+5q^3+2q^2+q+1
       168: 2q^4+4q^3+2q^2+q+1
       171: q^2+q+1
       175: q^2+q+1
       177: q^3+q^2
       178: 2q^3+q^2+q+1
       179: q^3
       180: q^3+q^2+q+1
       181: q^2
       182: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       187: q^2
       188: q^2+q+1
       189: q^3
       190: q^3+q^2+q+1
       191: q^2+q+1
       194: q^3+q^2+q+1
       195: q^3+q^2+q+1
       197: q^2
       198: q^2+q+1
       200: q^2+q+1
       202: q^3+q^2+q+1
       203: q^3+q^2+q+1
       205: q^2
       206: q^2+q+1
       207: q^3
       208: q^3+q^2+q+1
       209: q^3
       210: q^3+q^2+q+1
       211: q^3+q^2
       212: 2q^3+q^2+q+1
       214: q^3+q+1
       216: q+1
       218: q^3+q+1
       219: q^2+q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q^3+2q^2+q+1
       224: q+1
       225: q^3+2q^2+q+1
       226: 2q^3+q^2+q+1
       227: q^2+q+1
       228: 3q^3+2q^2+q+1
       229: q^3+2q^2+q+1
       230: q^3+2q^2+q+1
       231: 2q^3+q^2+q+1
       232: q^2+q+1
       233: 3q^3+2q^2+q+1
       234: q^3+2q^2+q+1
       235: q^3+2q^2+q+1
       236: 4q^3+2q^2+q+1
       237: q^3+q^2
       238: 2q^3+q^2+q+1
       239: q^4+q^3+q^2
       240: 2q^3+q^2+q+1
       241: q^3+q^2
       242: q^4+2q^3+q^2+q+1
       243: 3q^3+q^2+q+1
       244: 2q^3+2q^2+q+1
       245: 2q^3+2q^2+q+1
       246: 2q^3+q^2+q+1
       247: 4q^2+q+1
       248: 4q^2+q+1
       249: q^4+3q^3+2q^2+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: 3q^3+2q^2+q+1
       257: 2q^3+2q^2+q+1
       258: 3q^3+2q^2+q+1
       261: q^2+q+1
       265: q^2+q+1
       270: q^2+q+1
       272: q^2+q+1
       277: q^2+q+1
       280: q+1
       282: q^3+q+1
       284: q^2+q+1
       285: q^2+q+1
       287: q^3
       288: q^3+q^2+q+1
       290: q+1
       291: q^2
       292: q^2+q+1
       294: q+1
       295: q+1
       298: q+1
       300: q^2+q+1
       301: q^2
       302: q^2+q+1
       303: q^2+q+1
       305: q^2
       306: q^2+q+1
       308: q^2+q+1
       309: q^2+q+1
       311: q^2
       312: q^2+q+1
       313: q^2
       314: q^2+q+1
       315: q^3+q^2
       316: 2q^3+q^2+q+1
       317: q^3
       318: q^3+q^2+q+1
       320: q^3+q^2+q+1
       321: q^3+q^2+q+1
       323: q^2
       324: q^2+q+1
       325: q^3
       326: q^3+q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: 2q^2+q+1
       337: 2q^2+q+1
       338: 2q^2
       339: 2q^2+q+1
       340: 2q^2
       341: 2q^2+q+1
       342: q^3+q^2
       343: q^4+2q^3+q^2+q+1
       344: q^2+q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q^3+2q^2+q+1
       349: q+1
       350: q^3+2q^2+q+1
       351: 4q^2+q+1
       352: q^2+q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q^3+2q^2+q+1
       357: q+1
       358: q^3+2q^2+q+1
       359: 4q^2+q+1
       361: q^3+q+1
       363: q+1
       365: q^3+q+1
       366: 2q^3+q^2+q+1
       367: q^2+q+1
       368: 3q^3+2q^2+q+1
       369: q^3+2q^2+q+1
       370: q^3+2q^2+q+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       379: q^2+q+1
       383: q+1
       387: q+1
       392: q^2+q+1
       395: q^2+q+1
       398: q^2+q+1
       402: q^2+q+1
       408: q^2+q+1
       414: q+1
       418: q+1
       420: q+1
       421: q+1
       424: q+1
       425: q^2
       426: q^2+q+1
       427: q^2
       428: q^2+q+1
       430: q^2+q+1
       431: q^2+q+1
       433: q^2
       434: q^2+q+1
       436: q+1
       438: q+1
       439: q+1
       442: q+1
       444: 2q^2+q+1
       445: 2q^2
       446: 2q^2+q+1
       448: q^2+q+1
       449: q^2+q+1
       451: q^2
       452: q^2+q+1
       454: q+1
       456: q+1
       457: q+1
       460: q+1
       461: 2q^2+q+1
       463: 2q^2
       464: 2q^2+q+1
       466: q+1
       468: q^3+q+1
       469: q^3
       470: q^3+q^2+q+1
       472: q^2+q+1
       473: q^2+q+1
       475: q^2
       476: q^2+q+1
       477: q^2
       478: q^2+q+1
       479: 2q^2
       480: 2q^2+q+1
       481: q+1
       482: q+1
       483: q+1
       484: q^2+1
       486: 1
       488: 1
       490: q^3+1
       491: q^2+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q^2+q+1
       496: 2q^2+1
       497: q+1
       498: q+1
       499: q+1
       500: 2q^2+q+1
       501: 2q^2+1
       508: q^2+q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q^3+2q^2+q+1
       513: q+1
       514: q^3+2q^2+q+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       523: q+1
       531: q+1
       535: q^2+q+1
       540: q+1
       544: q+1
       547: q^2
       548: q^2+q+1
       550: q^2+q+1
       554: q+1
       558: q+1
       561: q^2
       562: q^2+q+1
       567: q^2+q+1
       572: q^2+q+1
       576: 2q^2+q+1
       577: q^2
       578: q^2
       580: q^2
       581: q^2+q+1
       586: q+1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       598: 1
       600: q+1
       602: 1
       604: q+1
       606: q+1
       607: q+1
       610: q+1
       613: q^2
       614: q^2+q+1
       616: q^2+1
       618: 1
       620: q+1
       621: q+1
       624: q+1
       626: q+1
       629: q^2
       630: q^2+q+1
       631: q^2+1
       634: 1
       640: q+1
       642: q^2+q+1
       643: q^2+q+1
       645: q^2
       646: q^2+q+1
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       655: q^2
       656: q^2+1
       657: q^2+1
       659: 1
       661: 1
       663: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q^2+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q^2+q+1
       690: 1
       691: 1
       692: q^3+1
       698: q^2
       700: q^2+q+1
       711: q+1
       714: q+1
       719: q+1
       724: q+1
       728: q+1
       736: 1
       738: q+1
       742: q+1
       750: 1
       755: q^2+q+1
       760: q+1
       764: q+1
       767: q^2+1
       773: 1
       776: 1
       780: 1
       782: 1
       786: 1
       787: 1
       792: 1
       794: q^2+1
       796: 1
       798: q+1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       810: 1
       812: q+1
       816: 1
       817: q^2+1
       820: 1
       822: q+1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       834: 1
       836: q+1
       839: 1
       843: q^2
       844: q^2+1
       846: q+1
       847: q+1
       850: q+1
       852: q+1
       855: q^2
       856: q^2+q+1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q^2+1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       923: q+1
       925: q+1
       931: q+1
       941: 1
       945: q+1
       949: q+1
       954: q+1
       963: q+1
       966: q^2+1
       972: 1
       977: q+1
       990: 1
       995: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1017: 1
      1021: 1
      1023: 1
      1027: 1
      1028: 1
      1032: 1
      1037: 1
      1039: 1
      1041: 1
      1044: 1
      1047: 1
      1049: q+1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1196: 1
      1201: q+1
      1203: q+1
      1209: q+1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1270: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1328: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 2
      1365: 1
      1370: 1
      1381: 1
      1391: 1
      1395: 2
      1398: 1
      1403: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1435: 1
      1437: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1475: 1
      1477: 1
      1478: 1
      1483: 1
      1487: 1
      1507: 1
      1511: 1
      1520: 1
      1524: 1
      1540: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1608: 1
      1618: 1
      1621: 2
      1625: 1
      1629: 1
      1660: 1
      1663: 1
      1666: 1
      1717: 1
      1721: 1
      1743: 1
      1772: 1
      1799: 1
      1810: 1
      1947: 1

1948:    0: q^3+1
         1: q^3+1
         2: q^3+1
         3: q^3+1
         4: q^3+1
         5: q^3+1
         6: q^3+1
         7: q^3+1
         8: q^3+1
         9: q^5+q^4+q^3+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^3+1
        14: q^3+1
        15: q^3+1
        16: 1
        17: 1
        18: q^3+1
        19: q^3+1
        20: q^3+1
        21: q^3+1
        22: q^3+1
        23: q^3+1
        24: q^3+1
        25: q^3+1
        26: q^3+1
        27: q^3+1
        28: 1
        29: q^3+1
        30: q^3+1
        31: q^3+1
        32: q^3+1
        33: 1
        34: q^3+1
        35: q^3+1
        36: 1
        37: q^3+1
        39: q^3+1
        41: q^3+1
        43: q^3+1
        44: q^3+1
        45: q^3+1
        46: 1
        47: 1
        48: q^3+1
        49: 1
        50: 1
        51: q^3+1
        52: q^3+1
        53: q^3+1
        54: q^3+1
        55: q^3+1
        56: q^3+1
        57: q^3+1
        58: 1
        60: 1
        62: q^3+1
        64: q^3+1
        66: 1
        68: 1
        69: 1
        70: q^3+1
        71: 1
        72: 1
        73: 1
        74: q^3+1
        76: q^3+1
        78: q^3+1
        80: q^3+1
        81: 1
        82: q^3+1
        83: q^3+1
        84: q^3+1
        85: 1
        86: q^3+1
        87: q^3+1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: 1
        93: q^3+1
        94: 1
        95: 1
        96: q^3+1
        97: 1
        98: 1
        99: q^3+1
       100: q^3+1
       101: q^3+1
       102: q^3+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: q^3+1
       115: q^3+1
       117: 1
       119: 1
       121: q^3+1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^3+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^3+1
       142: 1
       143: 1
       144: 1
       145: 1
       146: q^3+1
       147: 1
       148: 1
       149: q^3+1
       150: q^3+1
       151: q^3+1
       153: q^3+1
       155: q^3+1
       157: 1
       158: 1
       159: q^3+1
       160: 1
       161: 1
       162: q^3+1
       163: 1
       164: 1
       165: q^3+1
       166: 1
       167: 1
       168: q^3+1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: q^3+1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: q^3+1
       211: q^3+1
       213: 1
       215: 1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: q^3+1
       243: 1
       244: 1
       245: 1
       246: q^3+1
       247: 1
       248: 1
       249: q^3+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 1
       257: 1
       258: q^3+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: q^3+1
       327: 1
       329: 1
       331: q^3+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: q^3+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^3+1
       374: 1
       375: 1
       376: q^3+1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: q^3+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: q^3+1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: 1
       585: 1
       587: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       693: 1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       777: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       797: 1
       799: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       821: 1
       823: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       920: 1
       924: 1
       928: 1
       932: 1
       936: 1
       944: 1
       948: 1
       952: 1
       956: 1
       960: 1
       974: 1
       978: 1
       982: 1
       988: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1026: 1
      1028: 1
      1034: 1
      1038: 1
      1040: 1
      1042: 1
      1044: 1
      1048: 1
      1050: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1098: 1
      1110: 1
      1118: 1
      1126: 1
      1134: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1198: 1
      1202: 1
      1206: 1
      1220: 1
      1222: 1
      1238: 1
      1240: 1
      1242: 1
      1256: 1
      1258: 1
      1260: 1
      1264: 1
      1266: 1
      1268: 1
      1270: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1322: 1
      1330: 1
      1344: 1
      1352: 1
      1360: 1
      1368: 1
      1376: 1
      1384: 1
      1392: 1
      1400: 1
      1414: 1
      1418: 1
      1422: 1
      1426: 1
      1446: 1
      1470: 1
      1474: 1
      1476: 1
      1478: 1
      1480: 1
      1559: 1
      1571: 1
      1579: 1
      1591: 1
      1599: 1
      1603: 1
      1611: 1
      1619: 1
      1627: 1
      1671: 1
      1753: 1
      1777: 1
      1793: 1
      1807: 1
      1948: 1

1949:    0: q^3+1
         1: q^3+1
         2: q^3+1
         3: q^3+1
         4: q^3+1
         5: q^3+1
         6: q^3+1
         7: q^3+1
         8: q^3+1
         9: q^5+q^4+q^3+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^3+1
        14: q^3+1
        15: q^3+1
        16: 1
        17: 1
        18: q^3+1
        19: q^3+1
        20: q^3+1
        21: q^3+1
        22: q^3+1
        23: q^3+1
        24: q^3+1
        25: q^3+1
        26: q^3+1
        27: q^3+1
        28: 1
        29: q^3+1
        30: q^3+1
        31: q^3+1
        32: q^3+1
        33: 1
        34: q^3+1
        35: q^3+1
        36: 1
        37: q^3+1
        39: q^3+1
        41: q^3+1
        43: q^3+1
        44: q^3+1
        45: q^3+1
        46: 1
        47: 1
        48: q^3+1
        49: 1
        50: 1
        51: q^3+1
        52: q^3+1
        53: q^3+1
        54: q^3+1
        55: q^3+1
        56: q^3+1
        57: q^3+1
        59: 1
        61: 1
        62: q^3+1
        64: q^3+1
        66: 1
        68: 1
        69: 1
        70: q^3+1
        71: 1
        72: 1
        73: 1
        74: q^3+1
        76: q^3+1
        78: q^3+1
        80: q^3+1
        81: 1
        82: q^3+1
        83: q^3+1
        84: q^3+1
        85: 1
        86: q^3+1
        87: q^3+1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: 1
        93: q^3+1
        94: 1
        95: 1
        96: q^3+1
        97: 1
        98: 1
        99: q^3+1
       100: q^3+1
       101: q^3+1
       102: q^3+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: q^3+1
       115: q^3+1
       118: 1
       120: 1
       121: q^3+1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^3+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^3+1
       142: 1
       143: 1
       144: 1
       145: 1
       146: q^3+1
       147: 1
       148: 1
       149: q^3+1
       150: q^3+1
       151: q^3+1
       153: q^3+1
       155: q^3+1
       157: 1
       158: 1
       159: q^3+1
       160: 1
       161: 1
       162: q^3+1
       163: 1
       164: 1
       165: q^3+1
       166: 1
       167: 1
       168: q^3+1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: q^3+1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: q^3+1
       211: q^3+1
       213: 1
       215: 1
       217: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: q^3+1
       243: 1
       244: 1
       245: 1
       246: q^3+1
       247: 1
       248: 1
       249: q^3+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 1
       257: 1
       258: q^3+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: q^3+1
       327: 1
       329: 1
       331: q^3+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: q^3+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^3+1
       374: 1
       375: 1
       376: q^3+1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: q^3+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: q^3+1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: 1
       585: 1
       587: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       697: 1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       777: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       797: 1
       799: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       821: 1
       823: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       922: 1
       927: 1
       930: 1
       934: 1
       938: 1
       946: 1
       950: 1
       955: 1
       958: 1
       961: 1
       975: 1
       979: 1
       982: 1
       991: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1018: 1
      1022: 1
      1024: 1
      1027: 1
      1029: 1
      1034: 1
      1038: 1
      1041: 1
      1042: 1
      1045: 1
      1048: 1
      1050: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1102: 1
      1112: 1
      1120: 1
      1127: 1
      1135: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1199: 1
      1204: 1
      1208: 1
      1220: 1
      1222: 1
      1238: 1
      1241: 1
      1243: 1
      1256: 1
      1259: 1
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1271: 1
      1272: 1
      1276: 1
      1278: 1
      1289: 1
      1323: 1
      1331: 1
      1346: 1
      1354: 1
      1361: 1
      1369: 1
      1378: 1
      1386: 1
      1393: 1
      1401: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1446: 1
      1470: 1
      1474: 1
      1477: 1
      1479: 1
      1480: 1
      1560: 1
      1572: 1
      1580: 1
      1592: 1
      1600: 1
      1605: 1
      1613: 1
      1622: 1
      1630: 1
      1671: 1
      1754: 1
      1778: 1
      1796: 1
      1808: 1
      1949: 1

1950:    0: q^3+1
         1: q^3+1
         2: q^3+1
         3: q^3+1
         4: q^3+1
         5: q^3+1
         6: q^3+1
         7: q^3+1
         8: q^3+1
         9: q^5+q^4+q^3+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^3+1
        14: q^3+1
        15: q^3+1
        16: 1
        17: 1
        18: q^3+1
        19: q^3+1
        20: q^3+1
        21: q^3+1
        22: q^3+1
        23: q^3+1
        24: q^3+1
        25: q^3+1
        26: q^3+1
        27: q^3+1
        28: 1
        29: q^3+1
        30: q^3+1
        31: q^3+1
        32: q^3+1
        33: 1
        34: q^3+1
        35: q^3+1
        36: 1
        38: q^3+1
        40: q^3+1
        42: q^3+1
        43: q^3+1
        44: q^3+1
        45: q^3+1
        46: 1
        47: 1
        48: q^3+1
        49: 1
        50: 1
        51: q^3+1
        52: q^3+1
        53: q^3+1
        54: q^3+1
        55: q^3+1
        56: q^3+1
        57: q^3+1
        59: 1
        60: 1
        63: q^3+1
        65: q^3+1
        67: 1
        68: 1
        69: 1
        70: q^3+1
        71: 1
        72: 1
        73: 1
        75: q^3+1
        77: q^3+1
        79: q^3+1
        80: q^3+1
        81: 1
        82: q^3+1
        83: q^3+1
        84: q^3+1
        85: 1
        86: q^3+1
        87: q^3+1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: 1
        93: q^3+1
        94: 1
        95: 1
        96: q^3+1
        97: 1
        98: 1
        99: q^3+1
       100: q^3+1
       101: q^3+1
       102: q^3+1
       104: 1
       107: 1
       110: 1
       112: 1
       114: q^3+1
       116: q^3+1
       118: 1
       119: 1
       122: q^3+1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^3+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^3+1
       142: 1
       143: 1
       144: 1
       145: 1
       146: q^3+1
       147: 1
       148: 1
       149: q^3+1
       150: q^3+1
       152: q^3+1
       154: q^3+1
       156: q^3+1
       157: 1
       158: 1
       159: q^3+1
       160: 1
       161: 1
       162: q^3+1
       163: 1
       164: 1
       165: q^3+1
       166: 1
       167: 1
       168: q^3+1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: q^3+1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: q^3+1
       212: q^3+1
       214: 1
       216: 1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: q^3+1
       243: 1
       244: 1
       245: 1
       246: q^3+1
       247: 1
       248: 1
       249: q^3+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 1
       257: 1
       258: q^3+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: q^3+1
       328: 1
       330: 1
       332: q^3+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: q^3+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^3+1
       374: 1
       375: 1
       376: q^3+1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: q^3+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: q^3+1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: 1
       586: 1
       588: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       699: 1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       778: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       798: 1
       800: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       822: 1
       824: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       921: 1
       926: 1
       929: 1
       933: 1
       939: 1
       947: 1
       951: 1
       953: 1
       959: 1
       962: 1
       976: 1
       980: 1
       986: 1
       989: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1026: 1
      1029: 1
      1035: 1
      1039: 1
      1040: 1
      1043: 1
      1045: 1
      1049: 1
      1051: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1104: 1
      1113: 1
      1119: 1
      1128: 1
      1136: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1200: 1
      1205: 1
      1207: 1
      1221: 1
      1223: 1
      1239: 1
      1240: 1
      1243: 1
      1257: 1
      1258: 1
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1271: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1324: 1
      1332: 1
      1347: 1
      1353: 1
      1363: 1
      1371: 1
      1379: 1
      1385: 1
      1394: 1
      1402: 1
      1416: 1
      1421: 1
      1423: 1
      1427: 1
      1447: 1
      1471: 1
      1475: 1
      1476: 1
      1479: 1
      1481: 1
      1561: 1
      1574: 1
      1582: 1
      1593: 1
      1601: 1
      1606: 1
      1612: 1
      1620: 1
      1628: 1
      1672: 1
      1756: 1
      1779: 1
      1794: 1
      1809: 1
      1950: 1

1951:    0: q^3+1
         1: q^3+1
         2: q^3+1
         3: q^3+1
         4: q^3+1
         5: q^3+1
         6: q^3+1
         7: q^3+1
         8: q^3+1
         9: q^5+q^4+q^3+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^3+1
        14: q^3+1
        15: q^3+1
        16: 1
        17: 1
        18: q^3+1
        19: q^3+1
        20: q^3+1
        21: q^3+1
        22: q^3+1
        23: q^3+1
        24: q^3+1
        25: q^3+1
        26: q^3+1
        27: q^3+1
        28: 1
        29: q^3+1
        30: q^3+1
        31: q^3+1
        32: q^3+1
        33: 1
        34: q^3+1
        35: q^3+1
        36: 1
        38: q^3+1
        40: q^3+1
        42: q^3+1
        43: q^3+1
        44: q^3+1
        45: q^3+1
        46: 1
        47: 1
        48: q^3+1
        49: 1
        50: 1
        51: q^3+1
        52: q^3+1
        53: q^3+1
        54: q^3+1
        55: q^3+1
        56: q^3+1
        57: q^3+1
        58: 1
        61: 1
        63: q^3+1
        65: q^3+1
        67: 1
        68: 1
        69: 1
        70: q^3+1
        71: 1
        72: 1
        73: 1
        75: q^3+1
        77: q^3+1
        79: q^3+1
        80: q^3+1
        81: 1
        82: q^3+1
        83: q^3+1
        84: q^3+1
        85: 1
        86: q^3+1
        87: q^3+1
        88: 1
        89: 1
        90: q^3+1
        91: 1
        92: 1
        93: q^3+1
        94: 1
        95: 1
        96: q^3+1
        97: 1
        98: 1
        99: q^3+1
       100: q^3+1
       101: q^3+1
       102: q^3+1
       105: 1
       108: 1
       109: 1
       112: 1
       114: q^3+1
       116: q^3+1
       117: 1
       120: 1
       122: q^3+1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^3+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^3+1
       142: 1
       143: 1
       144: 1
       145: 1
       146: q^3+1
       147: 1
       148: 1
       149: q^3+1
       150: q^3+1
       152: q^3+1
       154: q^3+1
       156: q^3+1
       157: 1
       158: 1
       159: q^3+1
       160: 1
       161: 1
       162: q^3+1
       163: 1
       164: 1
       165: q^3+1
       166: 1
       167: 1
       168: q^3+1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: q^3+1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: q^3+1
       212: q^3+1
       214: 1
       216: 1
       218: q^3+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: q^3+1
       243: 1
       244: 1
       245: 1
       246: q^3+1
       247: 1
       248: 1
       249: q^3+1
       250: 1
       251: 1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 1
       257: 1
       258: q^3+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: q^3+1
       328: 1
       330: 1
       332: q^3+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: q^3+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^3+1
       374: 1
       375: 1
       376: q^3+1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: q^3+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       518: 1
       519: 1
       520: q^3+1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       584: 1
       586: 1
       588: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       700: 1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       778: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       798: 1
       800: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       822: 1
       824: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       923: 1
       925: 1
       931: 1
       935: 1
       937: 1
       945: 1
       949: 1
       954: 1
       957: 1
       963: 1
       977: 1
       981: 1
       986: 1
       990: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1019: 1
      1023: 1
      1025: 1
      1027: 1
      1028: 1
      1035: 1
      1039: 1
      1041: 1
      1043: 1
      1044: 1
      1049: 1
      1051: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1078: 1
      1082: 1
      1083: 1
      1085: 1
      1105: 1
      1111: 1
      1121: 1
      1129: 1
      1137: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1201: 1
      1203: 1
      1209: 1
      1221: 1
      1223: 1
      1239: 1
      1241: 1
      1242: 1
      1257: 1
      1259: 1
      1260: 1
      1265: 1
      1267: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1279: 1
      1289: 1
      1325: 1
      1333: 1
      1345: 1
      1355: 1
      1362: 1
      1370: 1
      1377: 1
      1387: 1
      1395: 1
      1403: 1
      1417: 1
      1419: 1
      1425: 1
      1428: 1
      1447: 1
      1471: 1
      1475: 1
      1477: 1
      1478: 1
      1481: 1
      1562: 1
      1573: 1
      1581: 1
      1594: 1
      1602: 1
      1604: 1
      1614: 1
      1621: 1
      1629: 1
      1672: 1
      1755: 1
      1780: 1
      1795: 1
      1810: 1
      1951: 1

1952:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^3+q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^3+q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^3+q^2+q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^3+q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+1
        38: 2q
        39: q^2+1
        40: 2q
        41: q^3+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^3+q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^3+q^2+q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+q+1
        58: q^2+q+1
        59: q
        60: q^2+q+1
        61: q
        62: q^2+1
        63: 2q
        64: 1
        65: q
        66: q^2+1
        67: 2q
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+1
        75: 2q
        76: q^2+1
        77: 2q
        78: q^3+1
        79: q^2+q
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^3+q^2+q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^3+q^2+q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^3+q^2+q+1
       103: q^2+1
       104: q
       105: q
       107: q^2+q+1
       108: q
       109: q^2+q+1
       110: q
       111: q^2+1
       112: 2q
       113: q^2+1
       114: 2q
       115: 1
       116: q
       117: 1
       119: 1
       121: 1
       122: q
       123: 1
       124: q
       125: 1
       126: q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+1
       152: 2q
       153: q^2+1
       154: 2q
       155: q^3+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^3+q^2+q+1
       169: q^2+1
       170: q
       171: q
       173: 1
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       183: 1
       185: 1
       187: 1
       188: q
       189: 1
       190: q
       191: 1
       193: q^2+q+1
       194: q
       195: q^2+q+1
       196: q
       197: q^2+1
       198: 2q
       199: 1
       201: q^2+q+1
       202: q
       203: q^2+q+1
       204: q
       205: q^2+1
       206: 2q
       207: 1
       208: q
       209: q^2+1
       210: 2q
       211: 1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^3+q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+1
       260: q
       261: q
       263: 1
       267: q^2+1
       268: q
       270: q
       271: q^2+1
       272: q
       274: q
       275: 1
       283: 1
       285: 1
       287: 1
       288: q
       291: 1
       292: q
       293: 1
       295: 1
       297: 1
       298: q
       299: 1
       301: q^2+1
       302: 2q
       303: 1
       305: 1
       306: q
       307: 1
       309: 1
       311: q^2+1
       312: 2q
       313: 1
       314: q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: q^2+q+1
       320: q
       321: q^2+q+1
       322: q
       323: q^2+1
       324: 2q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       385: 1
       389: q^2+1
       390: q
       392: q
       393: 1
       397: q^2+1
       398: q
       400: q
       401: 1
       405: q^2+1
       407: q
       408: q
       419: 1
       421: 1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       429: 1
       431: 1
       433: 1
       434: q
       437: 1
       439: 1
       441: 1
       442: q
       443: q^2+q+1
       444: q
       445: q^2+1
       446: 2q
       447: 1
       449: 1
       451: 1
       452: q
       453: 1
       457: 1
       459: 1
       460: q
       461: q^2+q+1
       462: q
       463: q^2+1
       464: 2q
       469: 1
       470: q
       471: 1
       473: 1
       475: 1
       476: q
       477: q^2+1
       478: 2q
       479: q^2+1
       480: 2q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       529: 1
       533: 1
       541: 1
       545: q^2+1
       546: q
       548: q
       549: 1
       557: 1
       561: q^2+1
       562: q
       564: q
       565: 1
       569: q^2+1
       571: q
       572: q
       573: q^2+1
       574: q
       576: q
       577: q^2+1
       581: 2q
       589: 1
       591: 1
       593: 1
       595: 1
       599: 1
       600: q
       603: 1
       607: 1
       609: 1
       610: q
       613: 1
       614: q
       615: 1
       619: 1
       621: 1
       625: 1
       626: q
       629: 1
       630: q
       631: 1
       641: 1
       643: 1
       645: 1
       646: q
       647: 1
       649: 1
       653: 1
       654: q
       655: 1
       656: q
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+1
       699: q
       700: q
       713: 1
       717: 1
       725: 1
       741: 1
       753: 1
       761: 1
       765: 1
       785: 1
       787: 1
       791: 1
       792: q
       793: 1
       801: 1
       803: 1
       805: 1
       807: 1
       811: 1
       812: q
       815: 1
       817: 1
       825: 1
       827: 1
       829: 1
       831: 1
       835: 1
       836: q
       839: 1
       843: 1
       844: q
       845: 1
       847: 1
       851: 1
       852: q
       855: 1
       856: q
       857: 1
       858: q
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       908: 1
       924: 1
       928: 1
       948: 1
       952: 1
       964: 1
       974: 1
       988: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1009: q
      1012: 1
      1013: q
      1016: 1
      1026: 1
      1028: 1
      1032: 1
      1040: 1
      1044: 1
      1046: 1
      1047: q
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1062: 1
      1063: q
      1064: 1
      1065: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1130: 1
      1134: 1
      1160: 1
      1180: 1
      1194: 1
      1202: 1
      1206: 1
      1216: 1
      1218: 1
      1224: 1
      1225: q
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1268: 1
      1270: 1
      1276: 1
      1277: q
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1326: 1
      1364: 1
      1368: 1
      1396: 1
      1400: 1
      1426: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1466: 1
      1468: 1
      1476: 1
      1478: 1
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1575: 1
      1595: 1
      1623: 1
      1627: 1
      1649: 1
      1657: 1
      1663: 1
      1665: 1
      1673: 1
      1797: 1
      1811: 1
      1819: 1
      1821: 1
      1952: 1

1953:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^3+q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^3+q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^3+q^2+q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^3+q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: 2q
        38: q^2+1
        39: 2q
        40: q^2+1
        41: q^2+q
        42: q^3+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^3+q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^3+q^2+q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+q+1
        58: q
        59: q^2+q+1
        60: q^2+q+1
        61: q
        62: 2q
        63: q^2+1
        64: q
        65: 1
        66: 2q
        67: q^2+1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q
        75: q^2+1
        76: 2q
        77: q^2+1
        78: q^2+q
        79: q^3+1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^3+q^2+q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^3+q^2+q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^3+q^2+q+1
       103: q
       104: q^2+1
       106: q
       107: q^2+q+1
       108: q
       109: q
       110: q^2+q+1
       111: 2q
       112: q^2+1
       113: 2q
       114: q^2+1
       115: q
       116: 1
       118: 1
       119: 1
       121: q
       122: 1
       123: q
       124: 1
       125: 1
       126: q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: 2q
       152: q^2+1
       153: 2q
       154: q^2+1
       155: q^2+q
       156: q^3+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^3+q^2+q+1
       169: q
       170: q^2+1
       172: q
       174: 1
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       183: 1
       186: 1
       187: q
       188: 1
       189: q
       190: 1
       192: 1
       193: q^2+q+1
       194: q
       195: q
       196: q^2+q+1
       197: 2q
       198: q^2+1
       199: 1
       201: q^2+q+1
       202: q
       203: q
       204: q^2+q+1
       205: 2q
       206: q^2+1
       207: q
       208: 1
       209: 2q
       210: q^2+1
       211: q
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^3+q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       260: q^2+1
       262: q
       264: 1
       267: q
       268: q^2+1
       269: q
       271: q
       273: q
       274: q^2+1
       276: 1
       283: 1
       286: 1
       287: q
       288: 1
       291: q
       292: 1
       293: 1
       296: 1
       297: q
       298: 1
       299: 1
       301: 2q
       302: q^2+1
       304: 1
       305: q
       306: 1
       307: 1
       310: 1
       311: 2q
       312: q^2+1
       313: q
       314: 1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: q^2+q+1
       320: q
       321: q
       322: q^2+q+1
       323: 2q
       324: q^2+1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       386: 1
       389: q
       390: q^2+1
       391: q
       394: 1
       397: q
       399: q
       400: q^2+1
       403: 1
       405: q
       406: q
       407: q^2+1
       419: 1
       422: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       429: 1
       432: 1
       433: q
       434: 1
       437: 1
       440: 1
       441: q
       442: 1
       443: q^2+q+1
       444: q
       445: 2q
       446: q^2+1
       447: 1
       450: 1
       451: q
       452: 1
       453: 1
       458: 1
       459: q
       460: 1
       461: q
       462: q^2+q+1
       463: 2q
       464: q^2+1
       469: q
       470: 1
       471: 1
       474: 1
       475: q
       476: 1
       477: 2q
       478: q^2+1
       479: 2q
       480: q^2+1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       530: 1
       534: 1
       542: 1
       545: q
       546: q^2+1
       547: q
       551: 1
       560: 1
       561: q
       563: q
       564: q^2+1
       566: 1
       569: q
       570: q
       571: q^2+1
       573: q
       574: q^2+1
       575: q
       577: 2q
       581: q^2+1
       589: 1
       592: 1
       593: 1
       596: 1
       599: q
       600: 1
       603: 1
       608: 1
       609: q
       610: 1
       613: q
       614: 1
       615: 1
       619: 1
       622: 1
       625: q
       626: 1
       629: q
       630: 1
       632: 1
       641: 1
       644: 1
       645: q
       646: 1
       647: 1
       650: 1
       653: q
       654: 1
       655: q
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       699: q^2+1
       715: 1
       718: 1
       726: 1
       744: 1
       754: 1
       763: 1
       766: 1
       785: 1
       788: 1
       791: q
       792: 1
       793: 1
       801: 1
       804: 1
       805: 1
       808: 1
       811: q
       812: 1
       815: 1
       818: 1
       825: 1
       828: 1
       829: 1
       832: 1
       835: q
       836: 1
       840: 1
       843: q
       844: 1
       845: 1
       848: 1
       851: q
       852: 1
       855: q
       856: 1
       857: q
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       909: 1
       926: 1
       929: 1
       951: 1
       953: 1
       965: 1
       976: 1
       989: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1008: q
      1009: 1
      1012: q
      1013: 1
      1016: 1
      1026: 1
      1029: 1
      1033: 1
      1040: 1
      1045: 1
      1046: q
      1047: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1131: 1
      1136: 1
      1162: 1
      1181: 1
      1195: 1
      1205: 1
      1207: 1
      1217: 1
      1218: 1
      1224: q
      1225: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1268: 1
      1271: 1
      1276: q
      1277: 1
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1327: 1
      1366: 1
      1371: 1
      1397: 1
      1402: 1
      1427: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1467: 1
      1468: 1
      1476: 1
      1479: 1
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1577: 1
      1596: 1
      1624: 1
      1628: 1
      1650: 1
      1657: 1
      1664: 1
      1665: 1
      1673: 1
      1798: 1
      1812: 1
      1820: 1
      1821: 1
      1953: 1

1954:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^3+q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^3+q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^3+q^2+q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^3+q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: 2q
        38: q^2+1
        39: 2q
        40: q^2+1
        41: q^2+q
        42: q^3+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^3+q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^3+q^2+q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+q+1
        58: q^2+q+1
        59: q
        60: q
        61: q^2+q+1
        62: 2q
        63: q^2+1
        64: q
        65: 1
        66: 2q
        67: q^2+1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q
        75: q^2+1
        76: 2q
        77: q^2+1
        78: q^2+q
        79: q^3+1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^3+q^2+q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^3+q^2+q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^3+q^2+q+1
       103: q
       105: q^2+1
       106: q
       107: q
       108: q^2+q+1
       109: q^2+q+1
       110: q
       111: 2q
       112: q^2+1
       113: 2q
       114: q^2+1
       115: q
       116: 1
       117: 1
       120: 1
       121: q
       122: 1
       123: q
       124: 1
       125: 1
       126: q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: 2q
       152: q^2+1
       153: 2q
       154: q^2+1
       155: q^2+q
       156: q^3+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^3+q^2+q+1
       169: q
       171: q^2+1
       172: q
       175: 1
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       184: 1
       185: 1
       187: q
       188: 1
       189: q
       190: 1
       191: 1
       193: q
       194: q^2+q+1
       195: q^2+q+1
       196: q
       197: 2q
       198: q^2+1
       200: 1
       201: q
       202: q^2+q+1
       203: q^2+q+1
       204: q
       205: 2q
       206: q^2+1
       207: q
       208: 1
       209: 2q
       210: q^2+1
       211: q
       212: 1
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^3+q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       261: q^2+1
       262: q
       265: 1
       267: q
       269: q
       270: q^2+1
       271: q
       272: q^2+1
       273: q
       277: 1
       284: 1
       285: 1
       287: q
       288: 1
       291: q
       292: 1
       294: 1
       295: 1
       297: q
       298: 1
       300: 1
       301: 2q
       302: q^2+1
       303: 1
       305: q
       306: 1
       308: 1
       309: 1
       311: 2q
       312: q^2+1
       313: q
       314: 1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: q
       320: q^2+q+1
       321: q^2+q+1
       322: q
       323: 2q
       324: q^2+1
       325: q
       326: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       379: 1
       387: 1
       389: q
       391: q
       392: q^2+1
       395: 1
       397: q
       398: q^2+1
       399: q
       402: 1
       405: q
       406: q
       408: q^2+1
       420: 1
       421: 1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       430: 1
       431: 1
       433: q
       434: 1
       438: 1
       439: 1
       441: q
       442: 1
       443: q
       444: q^2+q+1
       445: 2q
       446: q^2+1
       448: 1
       449: 1
       451: q
       452: 1
       454: 1
       457: 1
       459: q
       460: 1
       461: q^2+q+1
       462: q
       463: 2q
       464: q^2+1
       469: q
       470: 1
       472: 1
       473: 1
       475: q
       476: 1
       477: 2q
       478: q^2+1
       479: 2q
       480: q^2+1
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       531: 1
       535: 1
       544: 1
       545: q
       547: q
       548: q^2+1
       550: 1
       558: 1
       561: q
       562: q^2+1
       563: q
       567: 1
       569: q
       570: q
       572: q^2+1
       573: q
       575: q
       576: q^2+1
       577: 2q
       581: q^2+1
       590: 1
       591: 1
       594: 1
       595: 1
       599: q
       600: 1
       604: 1
       607: 1
       609: q
       610: 1
       613: q
       614: 1
       616: 1
       620: 1
       621: 1
       625: q
       626: 1
       629: q
       630: 1
       631: 1
       642: 1
       643: 1
       645: q
       646: 1
       648: 1
       649: 1
       653: q
       654: 1
       655: q
       656: 1
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       700: q^2+1
       714: 1
       719: 1
       728: 1
       742: 1
       755: 1
       764: 1
       767: 1
       786: 1
       787: 1
       791: q
       792: 1
       794: 1
       802: 1
       803: 1
       806: 1
       807: 1
       811: q
       812: 1
       816: 1
       817: 1
       826: 1
       827: 1
       830: 1
       831: 1
       835: q
       836: 1
       839: 1
       843: q
       844: 1
       846: 1
       847: 1
       851: q
       852: 1
       855: q
       856: 1
       857: q
       858: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       910: 1
       925: 1
       931: 1
       949: 1
       954: 1
       966: 1
       977: 1
       990: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1008: q
      1009: 1
      1012: q
      1013: 1
      1017: 1
      1027: 1
      1028: 1
      1032: 1
      1041: 1
      1044: 1
      1046: q
      1047: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1132: 1
      1137: 1
      1161: 1
      1182: 1
      1196: 1
      1203: 1
      1209: 1
      1216: 1
      1219: 1
      1224: q
      1225: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1269: 1
      1270: 1
      1276: q
      1277: 1
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1328: 1
      1365: 1
      1370: 1
      1398: 1
      1403: 1
      1428: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1466: 1
      1469: 1
      1477: 1
      1478: 1
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1576: 1
      1597: 1
      1625: 1
      1629: 1
      1649: 1
      1658: 1
      1663: 1
      1666: 1
      1673: 1
      1799: 1
      1813: 1
      1819: 1
      1822: 1
      1954: 1

1955:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^3+q^2+q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^3+q^2+q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^3+q^2+q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^3+q^2+q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^3+q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+1
        38: 2q
        39: q^2+1
        40: 2q
        41: q^3+1
        42: q^2+q
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^3+q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^3+q^2+q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+q+1
        58: q
        59: q^2+q+1
        60: q
        61: q^2+q+1
        62: q^2+1
        63: 2q
        64: 1
        65: q
        66: q^2+1
        67: 2q
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+1
        75: 2q
        76: q^2+1
        77: 2q
        78: q^3+1
        79: q^2+q
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^3+q^2+q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^3+q^2+q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^3+q^2+q+1
       104: q
       105: q
       106: q^2+1
       107: q
       108: q^2+q+1
       109: q
       110: q^2+q+1
       111: q^2+1
       112: 2q
       113: q^2+1
       114: 2q
       115: 1
       116: q
       118: 1
       120: 1
       121: 1
       122: q
       123: 1
       124: q
       125: 1
       126: q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+1
       152: 2q
       153: q^2+1
       154: 2q
       155: q^3+1
       156: q^2+q
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^3+q^2+q+1
       170: q
       171: q
       172: q^2+1
       176: 1
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       184: 1
       186: 1
       187: 1
       188: q
       189: 1
       190: q
       192: 1
       193: q
       194: q^2+q+1
       195: q
       196: q^2+q+1
       197: q^2+1
       198: 2q
       200: 1
       201: q
       202: q^2+q+1
       203: q
       204: q^2+q+1
       205: q^2+1
       206: 2q
       207: 1
       208: q
       209: q^2+1
       210: 2q
       211: 1
       212: q
       219: 1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^3+q^2+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: q
       262: q^2+1
       266: 1
       268: q
       269: q^2+1
       270: q
       272: q
       273: q^2+1
       274: q
       278: 1
       284: 1
       286: 1
       287: 1
       288: q
       291: 1
       292: q
       294: 1
       296: 1
       297: 1
       298: q
       300: 1
       301: q^2+1
       302: 2q
       304: 1
       305: 1
       306: q
       308: 1
       310: 1
       311: q^2+1
       312: 2q
       313: 1
       314: q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: q
       320: q^2+q+1
       321: q
       322: q^2+q+1
       323: q^2+1
       324: 2q
       325: 1
       326: q
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       380: 1
       388: 1
       390: q
       391: q^2+1
       392: q
       396: 1
       398: q
       399: q^2+1
       400: q
       404: 1
       406: q^2+1
       407: q
       408: q
       420: 1
       422: 1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       430: 1
       432: 1
       433: 1
       434: q
       438: 1
       440: 1
       441: 1
       442: q
       443: q
       444: q^2+q+1
       445: q^2+1
       446: 2q
       448: 1
       450: 1
       451: 1
       452: q
       454: 1
       458: 1
       459: 1
       460: q
       461: q
       462: q^2+q+1
       463: q^2+1
       464: 2q
       469: 1
       470: q
       472: 1
       474: 1
       475: 1
       476: q
       477: q^2+1
       478: 2q
       479: q^2+1
       480: 2q
       481: 1
       482: 1
       483: q+1
       484: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       532: 1
       536: 1
       543: 1
       546: q
       547: q^2+1
       548: q
       552: 1
       559: 1
       562: q
       563: q^2+1
       564: q
       568: 1
       570: q^2+1
       571: q
       572: q
       574: q
       575: q^2+1
       576: q
       577: q^2+1
       581: 2q
       590: 1
       592: 1
       594: 1
       596: 1
       599: 1
       600: q
       604: 1
       608: 1
       609: 1
       610: q
       613: 1
       614: q
       616: 1
       620: 1
       622: 1
       625: 1
       626: q
       629: 1
       630: q
       632: 1
       642: 1
       644: 1
       645: 1
       646: q
       648: 1
       650: 1
       653: 1
       654: q
       655: 1
       656: q
       657: 1
       664: q+1
       665: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: 1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q^2+1
       699: q
       700: q
       716: 1
       720: 1
       727: 1
       743: 1
       756: 1
       762: 1
       768: 1
       786: 1
       788: 1
       791: 1
       792: q
       794: 1
       802: 1
       804: 1
       806: 1
       808: 1
       811: 1
       812: q
       816: 1
       818: 1
       826: 1
       828: 1
       830: 1
       832: 1
       835: 1
       836: q
       840: 1
       843: 1
       844: q
       846: 1
       848: 1
       851: 1
       852: q
       855: 1
       856: q
       857: 1
       858: q
       865: 1
       866: 1
       867: q+1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       877: 1
       878: 1
       879: q+1
       880: q+1
       911: 1
       927: 1
       930: 1
       950: 1
       955: 1
       967: 1
       975: 1
       991: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1009: q
      1012: 1
      1013: q
      1017: 1
      1027: 1
      1029: 1
      1033: 1
      1041: 1
      1045: 1
      1046: 1
      1047: q
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1062: 1
      1063: q
      1064: 1
      1065: q
      1074: 1
      1076: 1
      1077: q+1
      1078: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1133: 1
      1135: 1
      1163: 1
      1183: 1
      1197: 1
      1204: 1
      1208: 1
      1217: 1
      1219: 1
      1224: 1
      1225: q
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1269: 1
      1271: 1
      1276: 1
      1277: q
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 1
      1329: 1
      1367: 1
      1369: 1
      1399: 1
      1401: 1
      1429: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1467: 1
      1469: 1
      1477: 1
      1479: 1
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1578: 1
      1598: 1
      1626: 1
      1630: 1
      1650: 1
      1658: 1
      1664: 1
      1666: 1
      1673: 1
      1800: 1
      1814: 1
      1820: 1
      1822: 1
      1955: 1

1956:    0: 3q^3+12q^2+10q+2
         1: 3q^3+12q^2+10q+2
         2: 3q^3+12q^2+10q+2
         3: 4q^3+12q^2+10q+2
         4: 3q^3+12q^2+10q+2
         5: 4q^3+12q^2+10q+2
         6: 3q^3+12q^2+10q+2
         7: 3q^3+12q^2+10q+2
         8: 4q^3+12q^2+10q+2
         9: 2q^4+6q^3+9q^2+7q+2
        10: 3q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 3q^3+12q^2+10q+2
        13: 3q^3+12q^2+10q+2
        14: 3q^3+12q^2+10q+2
        15: 4q^3+12q^2+10q+2
        16: q^3+9q^2+10q+2
        17: q^3+9q^2+10q+2
        18: 3q^3+9q^2+7q+2
        19: 3q^3+12q^2+10q+2
        20: 3q^3+12q^2+10q+2
        21: 3q^3+12q^2+10q+2
        22: q^3+9q^2+10q+2
        23: q^3+9q^2+10q+2
        24: q^3+9q^2+10q+2
        25: q^3+9q^2+10q+2
        26: q^3+9q^2+10q+2
        27: q^3+9q^2+10q+2
        28: q^3+9q^2+10q+2
        29: 3q^3+12q^2+10q+2
        30: 3q^3+12q^2+10q+2
        31: q^3+9q^2+10q+2
        32: q^3+9q^2+10q+2
        33: 6q^2+10q+2
        34: q^3+9q^2+10q+2
        35: q^3+9q^2+10q+2
        36: 6q^2+10q+2
        37: 5q^2+8q+2
        38: 2q^2+2q
        39: 5q^2+8q+2
        40: 2q^2+2q
        41: 5q^2+8q+2
        42: 2q^2+2q
        43: 3q^3+12q^2+10q+2
        44: 3q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: q^3+9q^2+10q+2
        47: q^3+9q^2+10q+2
        48: 3q^3+9q^2+7q+2
        49: q^3+9q^2+10q+2
        50: q^3+9q^2+10q+2
        51: 3q^3+9q^2+7q+2
        52: q^3+9q^2+10q+2
        53: q^3+9q^2+10q+2
        54: q^3+9q^2+10q+2
        55: q^3+9q^2+10q+2
        56: q^3+9q^2+10q+2
        57: q^3+9q^2+10q+2
        58: 3q^2+5q+1
        59: 3q^2+5q+1
        60: 3q^2+5q+1
        61: 3q^2+5q+1
        62: 5q^2+8q+2
        63: 2q^2+2q
        64: 5q^2+8q+2
        65: 2q^2+2q
        66: 2q^2+8q+2
        67: 2q^2+2q
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 3q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: 6q^2+10q+2
        73: 6q^2+10q+2
        74: 5q^2+8q+2
        75: 2q^2+2q
        76: 5q^2+8q+2
        77: 2q^2+2q
        78: 5q^2+8q+2
        79: 2q^2+2q
        80: q^3+9q^2+10q+2
        81: 6q^2+10q+2
        82: q^3+9q^2+10q+2
        83: q^3+9q^2+10q+2
        84: q^3+9q^2+10q+2
        85: 6q^2+10q+2
        86: q^3+9q^2+10q+2
        87: q^3+9q^2+10q+2
        88: q^3+9q^2+10q+2
        89: q^3+9q^2+10q+2
        90: 3q^3+9q^2+7q+2
        91: q^3+9q^2+10q+2
        92: q^3+9q^2+10q+2
        93: 3q^3+9q^2+7q+2
        94: 4q^2+10q+2
        95: 4q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 4q^2+10q+2
        98: 4q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 5q^2+9q+2
       101: 5q^2+9q+2
       102: 5q^2+9q+2
       103: q^2+4q+1
       104: q^2+q
       105: q^2+q
       106: q^2+4q+1
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+8q+2
       112: 2q^2+2q
       113: 5q^2+8q+2
       114: 2q^2+2q
       115: 5q^2+8q+2
       116: 2q^2+2q
       117: 3q^2+5q+1
       118: 3q^2+5q+1
       119: 3q^2+5q+1
       120: 3q^2+5q+1
       121: 5q^2+8q+2
       122: 2q^2+2q
       123: 2q^2+8q+2
       124: 2q^2+2q
       125: q^3+9q^2+10q+2
       126: q^3+6q^2+7q+2
       127: 8q+2
       129: 8q+2
       131: 3q^2+5q+2
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: 6q^2+10q+2
       136: 6q^2+10q+2
       137: 6q^2+10q+2
       138: 3q^2+7q+2
       139: 4q^2+10q+2
       140: 6q+2
       141: q^3+9q^2+10q+2
       142: 4q^2+10q+2
       143: 6q^2+10q+2
       144: 3q^2+7q+2
       145: 4q^2+10q+2
       146: q^3+9q^2+10q+2
       147: 4q^2+10q+2
       148: 6q+2
       149: 5q^2+9q+2
       150: 5q^2+9q+2
       151: 4q^2+7q+2
       152: q^2+2q
       153: 4q^2+7q+2
       154: q^2+2q
       155: 4q^2+7q+2
       156: q^2+2q
       157: q^3+9q^2+10q+2
       158: q^3+9q^2+10q+2
       159: 3q^3+9q^2+7q+2
       160: 4q^2+10q+2
       161: 4q^2+10q+2
       162: q^3+6q^2+7q+2
       163: 4q^2+10q+2
       164: 4q^2+10q+2
       165: q^3+6q^2+7q+2
       166: q^2+9q+2
       167: q^2+9q+2
       168: 3q^2+6q+2
       169: q^2+4q+1
       170: q^2+q
       171: q^2+q
       172: q^2+4q+1
       173: q^2+4q+1
       174: q^2+q
       175: q^2+q
       176: q^2+4q+1
       177: 5q+2
       179: 8q+2
       181: 8q+2
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+8q+2
       188: 2q^2+2q
       189: 5q^2+8q+2
       190: 2q^2+2q
       191: 3q^2+5q+1
       192: 3q^2+5q+1
       193: 3q+1
       194: 3q+1
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 4q+2
       198: 2q
       199: 3q^2+5q+1
       200: 3q^2+5q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 4q+2
       206: 2q
       207: 2q^2+8q+2
       208: 2q^2+2q
       209: 4q^2+7q+2
       210: q^2+2q
       211: 4q^2+7q+2
       212: q^2+2q
       213: 8q+2
       215: 8q+2
       217: 3q^2+5q+2
       219: q^3+6q^2+7q+2
       220: q^3+9q^2+10q+2
       221: q^3+6q^2+7q+2
       222: 6q^2+10q+2
       223: 3q^2+7q+2
       224: 6q^2+10q+2
       225: 3q^2+7q+2
       226: 3q^2+7q+2
       227: 4q^2+10q+2
       228: 3q^2+7q+2
       229: 6q+2
       230: 4q^2+10q+2
       231: 3q^2+7q+2
       232: 4q^2+10q+2
       233: 3q^2+7q+2
       234: 4q^2+10q+2
       235: 6q+2
       236: q^2+6q+2
       237: 7q+2
       239: 7q+2
       241: 2q^2+4q+2
       243: q^2+9q+2
       244: 6q+2
       245: 6q+2
       246: 5q^2+9q+2
       247: q^2+9q+2
       248: q^2+9q+2
       249: 3q^2+6q+2
       250: 4q^2+10q+2
       251: 4q^2+10q+2
       252: q^3+6q^2+7q+2
       253: 4q^2+10q+2
       254: 4q^2+10q+2
       255: q^3+6q^2+7q+2
       256: q^2+9q+2
       257: q^2+9q+2
       258: 3q^2+6q+2
       259: 4q+1
       262: 4q+1
       263: q^2+4q+1
       264: q^2+q
       265: q^2+q
       266: q^2+4q+1
       267: 2q+1
       268: q
       269: 2q+1
       270: q
       271: 2q+1
       272: q
       273: 2q+1
       274: q
       275: q^2+4q+1
       276: q^2+q
       277: q^2+q
       278: q^2+4q+1
       279: 8q+2
       281: 5q+2
       283: q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: 5q+2
       289: 8q+2
       291: 5q+2
       293: 3q^2+5q+1
       294: 3q^2+5q+1
       295: 3q^2+5q+1
       296: 3q^2+5q+1
       297: 2q^2+8q+2
       298: 2q^2+2q
       299: 3q+1
       300: 3q+1
       301: 4q+2
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 4q+2
       306: 2q
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       309: 3q+1
       310: 3q+1
       311: 4q+2
       313: 4q+2
       314: 2q
       315: 4q+2
       317: 7q+2
       319: 3q+1
       320: 3q+1
       321: 3q+1
       322: 3q+1
       323: 2q+2
       324: 2q
       325: 4q^2+7q+2
       326: q^2+2q
       327: 8q+2
       329: 8q+2
       331: 3q^2+5q+2
       333: q^3+6q^2+7q+2
       334: 3q^2+7q+2
       335: 3q^2+7q+2
       336: q^2+6q+2
       337: q^2+9q+2
       338: 7q+2
       340: 7q+2
       342: 2q^2+4q+2
       344: 3q^2+7q+2
       345: 4q^2+10q+2
       346: 3q^2+7q+2
       347: 6q+2
       348: 3q+2
       349: 4q^2+10q+2
       350: 3q^2+7q+2
       351: 6q+2
       352: 3q^2+7q+2
       353: 4q^2+10q+2
       354: 3q^2+7q+2
       355: 4q^2+10q+2
       356: 3q^2+7q+2
       357: 6q+2
       358: 3q+2
       359: 6q+2
       360: 7q+2
       362: 7q+2
       364: 2q^2+4q+2
       366: q^2+6q+2
       367: q^2+9q+2
       368: q^2+6q+2
       369: 6q+2
       370: 6q+2
       371: q^2+9q+2
       372: q^2+9q+2
       373: 3q^2+6q+2
       374: q^2+9q+2
       375: q^2+9q+2
       376: 3q^2+6q+2
       377: q+1
       380: q+1
       381: 4q+1
       384: 4q+1
       385: q^2+4q+1
       386: q^2+q
       387: q^2+q
       388: q^2+4q+1
       389: 2q+1
       391: 2q+1
       393: 2q+1
       394: q
       395: q
       396: 2q+1
       397: 2q+1
       399: 2q+1
       401: 2q+1
       402: q
       403: q
       404: 2q+1
       405: q+1
       406: q+1
       407: q
       408: q
       409: 8q+2
       411: 5q+2
       413: 5q+2
       415: 8q+2
       417: 5q+2
       419: q^2+2q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: 5q+2
       425: 4q+2
       427: 7q+2
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+2
       435: 4q+2
       437: 3q+1
       438: 3q+1
       439: 2q^2+5q+1
       440: 2q^2+5q+1
       441: 4q+2
       442: 2q
       443: 3q+1
       444: 3q+1
       445: 4q+2
       447: q^2+2q+1
       448: q^2+2q+1
       449: q+1
       450: q+1
       451: q+2
       453: 2q^2+5q+1
       454: 2q^2+5q+1
       455: 4q+2
       457: 3q+1
       458: 3q+1
       459: 4q+2
       460: 2q
       461: 3q+1
       462: 3q+1
       463: 4q+2
       465: 7q+2
       467: 4q+2
       469: 4q+2
       471: 3q+1
       472: 3q+1
       473: 3q+1
       474: 3q+1
       475: 2q+2
       476: 2q
       477: 2q+2
       479: 2q+2
       480: 2q
       481: 3q^2+7q+2
       482: 3q^2+7q+2
       483: q^2+6q+2
       484: q^2+9q+2
       485: 7q+2
       487: 7q+2
       489: 2q^2+4q+2
       491: q^2+6q+2
       492: 3q^2+7q+2
       493: 3q+2
       494: 3q^2+7q+2
       495: 3q+2
       496: 6q+2
       497: 3q^2+7q+2
       498: 3q^2+7q+2
       499: 3q+2
       500: 3q+2
       501: 6q+2
       502: 7q+2
       504: 7q+2
       506: 2q^2+4q+2
       508: q^2+6q+2
       509: q^2+9q+2
       510: q^2+6q+2
       511: 6q+2
       512: 3q+2
       513: 6q+2
       514: 3q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: q^2+9q+2
       519: q^2+9q+2
       520: 3q^2+6q+2
       521: q+1
       524: q+1
       525: 4q+1
       528: 4q+1
       529: q+1
       532: q+1
       533: 1
       536: 1
       537: 2q+1
       539: 2q+1
       541: 2q+1
       542: q
       543: 2q+1
       544: q
       545: 2q+1
       547: 2q+1
       549: 1
       552: 1
       553: 2q+1
       555: 2q+1
       557: 2q+1
       558: q
       559: 2q+1
       560: q
       561: 2q+1
       563: 2q+1
       565: q+1
       566: q
       567: q
       568: q+1
       569: q+1
       570: q+1
       573: q+1
       574: q
       575: q+1
       576: q
       577: 2q+2
       583: 5q+2
       585: 5q+2
       587: 5q+2
       589: q^2+2q+1
       590: q^2+2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q^2+2q+1
       596: q^2+2q+1
       597: 4q+2
       599: 4q+2
       601: 7q+2
       603: q+1
       604: q+1
       605: q+2
       607: q^2+2q+1
       608: q^2+2q+1
       609: q+2
       611: 4q+2
       613: q+2
       615: 3q+1
       616: 3q+1
       617: 4q+2
       619: q^2+2q+1
       620: q^2+2q+1
       621: q+1
       622: q+1
       623: q+2
       625: q+2
       627: 4q+2
       629: q+2
       631: 3q+1
       632: 3q+1
       633: 4q+2
       635: 7q+2
       637: 4q+2
       639: 4q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       647: 3q+1
       648: 3q+1
       649: 3q+1
       650: 3q+1
       651: 2q+2
       653: 2q+2
       654: 2q
       655: 2q+2
       656: 2q
       657: q+4
       658: 3q+4
       660: 4q+4
       662: 3q+4
       664: 3q+4
       665: q^2+6q+2
       666: 7q+2
       668: 7q+2
       670: 2q^2+4q+2
       672: q^2+9q+2
       673: q^2+6q+2
       674: q+4
       675: 3q+2
       676: 3q^2+7q+2
       677: 3q+2
       678: 6q+2
       679: 3q+2
       680: q+4
       681: 3q^2+7q+2
       682: 3q+2
       683: 3q+2
       684: 6q+2
       685: 3q+2
       686: q^2+6q+2
       687: 3q+2
       688: 3q+2
       689: q+1
       690: 3q+4
       691: 4q+4
       692: 3q+4
       693: q+1
       697: q+1
       705: q+1
       708: q+1
       709: q+1
       712: q+1
       713: 1
       716: 1
       717: 1
       720: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 2q+1
       731: 2q+1
       733: 2q+1
       735: 2q+1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 2q+1
       747: 2q+1
       749: 2q+1
       751: 2q+1
       753: 1
       756: 1
       757: q+1
       758: q+1
       761: q+1
       762: q+1
       763: q
       764: q
       765: q+1
       766: q
       767: q
       768: q+1
       769: 2q+2
       775: q+4
       777: 5q+2
       779: 3q+4
       781: 4q+2
       783: 4q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: 7q+2
       791: 2
       793: 2
       794: 2
       795: q+4
       797: q+2
       799: q+2
       801: q+1
       802: q+1
       805: q+1
       806: q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: q+2
       811: q+2
       813: 4q+2
       815: 3q+1
       816: 3q+1
       817: 2
       818: 2
       819: q+4
       821: q+2
       823: q+2
       825: q^2+2q+1
       826: q^2+2q+1
       827: q+1
       828: q+1
       831: q+1
       832: q+1
       833: q+2
       835: q+2
       837: 4q+2
       839: 3q+1
       840: 3q+1
       841: 4q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: 2
       851: 2
       853: 2q+2
       855: 1
       857: 2q+2
       858: 2q
       859: 3q+4
       861: 4q+4
       863: 3q+4
       865: q+4
       866: q+4
       867: 3q+4
       868: q^2+6q+2
       869: q+4
       870: q+4
       871: 3q+2
       872: 3q+2
       873: q+4
       874: q+4
       875: 3q+2
       876: 3q+2
       877: 3q+2
       878: 3q+2
       879: q+1
       880: q+1
       881: 3q+4
       882: 4q+4
       883: 3q+4
       884: q+1
       889: q+1
       896: q+1
       899: q+1
       900: 1
       902: 1
       904: 1
       906: 1
       908: 1
       911: 1
       912: 1
       914: 1
       916: 2
       918: 2
       920: 1
       922: 1
       928: 1
       930: 1
       932: 2q+1
       934: 2q+1
       936: 1
       938: 1
       940: 2
       942: 2
       944: 1
       946: 1
       948: 1
       950: 1
       956: 2q+1
       958: 2q+1
       960: 1
       961: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 2
       971: 2
       974: 1
       975: 1
       978: q+1
       979: q+1
       982: 2q+2
       988: q+1
       989: q
       990: q
       991: q+1
       992: q+4
       994: q+4
       996: 3q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1002: 4q+2
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: 2
      1010: 2
      1012: 2
      1013: 2
      1014: q+4
      1016: 2
      1017: 2
      1018: q+2
      1020: q+4
      1022: q+2
      1024: q+2
      1026: q+1
      1027: q+1
      1030: q+4
      1032: 2
      1033: 2
      1034: q+2
      1036: q+4
      1038: q+2
      1042: q+2
      1044: q+1
      1045: q+1
      1046: 2
      1047: 2
      1048: 2
      1050: 2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: 3q+4
      1068: 4q+4
      1070: 3q+4
      1072: q+4
      1073: 3q+4
      1074: q+4
      1075: q+4
      1076: 2
      1077: q+4
      1078: 3q+2
      1079: q+4
      1080: 2
      1081: q+4
      1082: 3q+2
      1083: q+1
      1084: 2
      1085: q+1
      1086: 1
      1089: 1
      1090: 1
      1091: 1
      1098: q+1
      1102: q+1
      1110: 1
      1112: 1
      1114: 2
      1116: 2
      1118: 1
      1120: 1
      1122: 2
      1124: 2
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1141: 2
      1144: 2
      1146: 2
      1148: 1
      1150: 1
      1156: 1
      1158: 1
      1164: 2
      1166: 2
      1168: 1
      1170: 1
      1172: 1
      1174: 1
      1184: 1
      1185: 1
      1188: 2
      1191: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1210: q+4
      1212: 3q+4
      1214: q+4
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1220: 2
      1222: 2
      1224: 2
      1225: 2
      1226: q+4
      1228: 2
      1229: 2
      1230: 2
      1234: 1
      1235: 1
      1236: q+4
      1238: q+2
      1240: q+1
      1241: q+1
      1244: q+4
      1246: 2
      1247: 2
      1248: 2
      1250: 1
      1251: 1
      1252: q+4
      1256: q+2
      1260: q+1
      1261: q+1
      1262: 2
      1263: 2
      1264: 2
      1266: 1
      1272: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1282: q+4
      1283: 2
      1284: q+4
      1285: 2
      1286: q+4
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1293: 1
      1294: 1
      1295: 1
      1302: 1
      1305: 1
      1306: 1
      1307: 1
      1314: 2
      1316: 2
      1318: 2
      1320: 2
      1322: 1
      1323: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1334: 2
      1337: 2
      1340: 2
      1342: 2
      1352: 1
      1354: 1
      1356: 1
      1358: 1
      1372: 2
      1374: 2
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1404: 2
      1407: 2
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1433: 1
      1438: q+4
      1440: 2
      1441: 2
      1442: 2
      1443: 2
      1444: 2
      1445: 2
      1446: 2
      1448: 2
      1452: q+4
      1454: 1
      1455: 1
      1456: 2
      1458: q+4
      1460: 1
      1461: 1
      1464: 1
      1470: 1
      1472: 2
      1474: 1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 2
      1489: 1
      1492: 1
      1493: 1
      1494: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1541: 2
      1543: 2
      1545: 2
      1547: 2
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 2
      1556: 2
      1559: 1
      1560: 1
      1567: 1
      1569: 1
      1583: 1
      1585: 1
      1631: 1
      1634: 1
      1641: 1
      1643: 2
      1647: 1
      1648: 1
      1651: 2
      1653: 1
      1654: 1
      1661: 1
      1667: 2
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1678: 1
      1679: 1
      1680: 1
      1745: 1
      1747: 1
      1761: 1
      1763: 1
      1801: 1
      1804: 1
      1815: 1
      1827: 1
      1833: 1
      1956: 1

1957:    0: 3q^3+12q^2+10q+2
         1: 3q^3+12q^2+10q+2
         2: 3q^3+12q^2+10q+2
         3: 4q^3+12q^2+10q+2
         4: 3q^3+12q^2+10q+2
         5: 4q^3+12q^2+10q+2
         6: 3q^3+12q^2+10q+2
         7: 3q^3+12q^2+10q+2
         8: 4q^3+12q^2+10q+2
         9: 2q^4+6q^3+9q^2+7q+2
        10: 3q^3+12q^2+10q+2
        11: 4q^3+12q^2+10q+2
        12: 3q^3+12q^2+10q+2
        13: 3q^3+12q^2+10q+2
        14: 3q^3+12q^2+10q+2
        15: 4q^3+12q^2+10q+2
        16: q^3+9q^2+10q+2
        17: q^3+9q^2+10q+2
        18: 3q^3+9q^2+7q+2
        19: 3q^3+12q^2+10q+2
        20: 3q^3+12q^2+10q+2
        21: 3q^3+12q^2+10q+2
        22: q^3+9q^2+10q+2
        23: q^3+9q^2+10q+2
        24: q^3+9q^2+10q+2
        25: q^3+9q^2+10q+2
        26: q^3+9q^2+10q+2
        27: q^3+9q^2+10q+2
        28: q^3+9q^2+10q+2
        29: 3q^3+12q^2+10q+2
        30: 3q^3+12q^2+10q+2
        31: q^3+9q^2+10q+2
        32: q^3+9q^2+10q+2
        33: 6q^2+10q+2
        34: q^3+9q^2+10q+2
        35: q^3+9q^2+10q+2
        36: 6q^2+10q+2
        37: 2q^2+2q
        38: 5q^2+8q+2
        39: 2q^2+2q
        40: 5q^2+8q+2
        41: 2q^2+2q
        42: 5q^2+8q+2
        43: 3q^3+12q^2+10q+2
        44: 3q^3+12q^2+10q+2
        45: 4q^3+12q^2+10q+2
        46: q^3+9q^2+10q+2
        47: q^3+9q^2+10q+2
        48: 3q^3+9q^2+7q+2
        49: q^3+9q^2+10q+2
        50: q^3+9q^2+10q+2
        51: 3q^3+9q^2+7q+2
        52: q^3+9q^2+10q+2
        53: q^3+9q^2+10q+2
        54: q^3+9q^2+10q+2
        55: q^3+9q^2+10q+2
        56: q^3+9q^2+10q+2
        57: q^3+9q^2+10q+2
        58: 3q^2+5q+1
        59: 3q^2+5q+1
        60: 3q^2+5q+1
        61: 3q^2+5q+1
        62: 2q^2+2q
        63: 5q^2+8q+2
        64: 2q^2+2q
        65: 5q^2+8q+2
        66: 2q^2+2q
        67: 2q^2+8q+2
        68: q^3+9q^2+10q+2
        69: q^3+6q^2+7q+2
        70: 3q^3+12q^2+10q+2
        71: q^3+9q^2+10q+2
        72: 6q^2+10q+2
        73: 6q^2+10q+2
        74: 2q^2+2q
        75: 5q^2+8q+2
        76: 2q^2+2q
        77: 5q^2+8q+2
        78: 2q^2+2q
        79: 5q^2+8q+2
        80: q^3+9q^2+10q+2
        81: 6q^2+10q+2
        82: q^3+9q^2+10q+2
        83: q^3+9q^2+10q+2
        84: q^3+9q^2+10q+2
        85: 6q^2+10q+2
        86: q^3+9q^2+10q+2
        87: q^3+9q^2+10q+2
        88: q^3+9q^2+10q+2
        89: q^3+9q^2+10q+2
        90: 3q^3+9q^2+7q+2
        91: q^3+9q^2+10q+2
        92: q^3+9q^2+10q+2
        93: 3q^3+9q^2+7q+2
        94: 4q^2+10q+2
        95: 4q^2+10q+2
        96: q^3+6q^2+7q+2
        97: 4q^2+10q+2
        98: 4q^2+10q+2
        99: q^3+6q^2+7q+2
       100: 5q^2+9q+2
       101: 5q^2+9q+2
       102: 5q^2+9q+2
       103: q^2+q
       104: q^2+4q+1
       105: q^2+4q+1
       106: q^2+q
       107: 3q^2+5q+1
       108: 3q^2+5q+1
       109: 3q^2+5q+1
       110: 3q^2+5q+1
       111: 2q^2+2q
       112: 2q^2+8q+2
       113: 2q^2+2q
       114: 5q^2+8q+2
       115: 2q^2+2q
       116: 5q^2+8q+2
       117: 3q^2+5q+1
       118: 3q^2+5q+1
       119: 3q^2+5q+1
       120: 3q^2+5q+1
       121: 2q^2+2q
       122: 5q^2+8q+2
       123: 2q^2+2q
       124: 2q^2+8q+2
       125: q^3+9q^2+10q+2
       126: q^3+6q^2+7q+2
       128: 8q+2
       130: 8q+2
       132: 3q^2+5q+2
       133: q^3+9q^2+10q+2
       134: q^3+6q^2+7q+2
       135: 6q^2+10q+2
       136: 6q^2+10q+2
       137: 6q^2+10q+2
       138: 3q^2+7q+2
       139: 4q^2+10q+2
       140: 6q+2
       141: q^3+9q^2+10q+2
       142: 4q^2+10q+2
       143: 6q^2+10q+2
       144: 3q^2+7q+2
       145: 4q^2+10q+2
       146: q^3+9q^2+10q+2
       147: 4q^2+10q+2
       148: 6q+2
       149: 5q^2+9q+2
       150: 5q^2+9q+2
       151: q^2+2q
       152: 4q^2+7q+2
       153: q^2+2q
       154: 4q^2+7q+2
       155: q^2+2q
       156: 4q^2+7q+2
       157: q^3+9q^2+10q+2
       158: q^3+9q^2+10q+2
       159: 3q^3+9q^2+7q+2
       160: 4q^2+10q+2
       161: 4q^2+10q+2
       162: q^3+6q^2+7q+2
       163: 4q^2+10q+2
       164: 4q^2+10q+2
       165: q^3+6q^2+7q+2
       166: q^2+9q+2
       167: q^2+9q+2
       168: 3q^2+6q+2
       169: q^2+q
       170: q^2+4q+1
       171: q^2+4q+1
       172: q^2+q
       173: q^2+q
       174: q^2+4q+1
       175: q^2+4q+1
       176: q^2+q
       178: 5q+2
       180: 8q+2
       182: 8q+2
       183: 3q^2+5q+1
       184: 3q^2+5q+1
       185: 3q^2+5q+1
       186: 3q^2+5q+1
       187: 2q^2+2q
       188: 2q^2+8q+2
       189: 2q^2+2q
       190: 5q^2+8q+2
       191: 3q^2+5q+1
       192: 3q^2+5q+1
       193: 3q+1
       194: 3q+1
       195: 2q^2+5q+1
       196: 2q^2+5q+1
       197: 2q
       198: 4q+2
       199: 3q^2+5q+1
       200: 3q^2+5q+1
       201: 2q^2+5q+1
       202: 2q^2+5q+1
       203: 3q+1
       204: 3q+1
       205: 2q
       206: 4q+2
       207: 2q^2+2q
       208: 2q^2+8q+2
       209: q^2+2q
       210: 4q^2+7q+2
       211: q^2+2q
       212: 4q^2+7q+2
       214: 8q+2
       216: 8q+2
       218: 3q^2+5q+2
       219: q^3+6q^2+7q+2
       220: q^3+9q^2+10q+2
       221: q^3+6q^2+7q+2
       222: 6q^2+10q+2
       223: 3q^2+7q+2
       224: 6q^2+10q+2
       225: 3q^2+7q+2
       226: 3q^2+7q+2
       227: 4q^2+10q+2
       228: 3q^2+7q+2
       229: 6q+2
       230: 4q^2+10q+2
       231: 3q^2+7q+2
       232: 4q^2+10q+2
       233: 3q^2+7q+2
       234: 4q^2+10q+2
       235: 6q+2
       236: q^2+6q+2
       238: 7q+2
       240: 7q+2
       242: 2q^2+4q+2
       243: q^2+9q+2
       244: 6q+2
       245: 6q+2
       246: 5q^2+9q+2
       247: q^2+9q+2
       248: q^2+9q+2
       249: 3q^2+6q+2
       250: 4q^2+10q+2
       251: 4q^2+10q+2
       252: q^3+6q^2+7q+2
       253: 4q^2+10q+2
       254: 4q^2+10q+2
       255: q^3+6q^2+7q+2
       256: q^2+9q+2
       257: q^2+9q+2
       258: 3q^2+6q+2
       260: 4q+1
       261: 4q+1
       263: q^2+q
       264: q^2+4q+1
       265: q^2+4q+1
       266: q^2+q
       267: q
       268: 2q+1
       269: q
       270: 2q+1
       271: q
       272: 2q+1
       273: q
       274: 2q+1
       275: q^2+q
       276: q^2+4q+1
       277: q^2+4q+1
       278: q^2+q
       280: 8q+2
       282: 5q+2
       283: q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       288: 5q+2
       290: 8q+2
       292: 5q+2
       293: 3q^2+5q+1
       294: 3q^2+5q+1
       295: 3q^2+5q+1
       296: 3q^2+5q+1
       297: 2q^2+2q
       298: 2q^2+8q+2
       299: 3q+1
       300: 3q+1
       302: 4q+2
       303: 2q^2+5q+1
       304: 2q^2+5q+1
       305: 2q
       306: 4q+2
       307: 2q^2+5q+1
       308: 2q^2+5q+1
       309: 3q+1
       310: 3q+1
       312: 4q+2
       313: 2q
       314: 4q+2
       316: 4q+2
       318: 7q+2
       319: 3q+1
       320: 3q+1
       321: 3q+1
       322: 3q+1
       323: 2q
       324: 2q+2
       325: q^2+2q
       326: 4q^2+7q+2
       328: 8q+2
       330: 8q+2
       332: 3q^2+5q+2
       333: q^3+6q^2+7q+2
       334: 3q^2+7q+2
       335: 3q^2+7q+2
       336: q^2+6q+2
       337: q^2+9q+2
       339: 7q+2
       341: 7q+2
       343: 2q^2+4q+2
       344: 3q^2+7q+2
       345: 4q^2+10q+2
       346: 3q^2+7q+2
       347: 6q+2
       348: 3q+2
       349: 4q^2+10q+2
       350: 3q^2+7q+2
       351: 6q+2
       352: 3q^2+7q+2
       353: 4q^2+10q+2
       354: 3q^2+7q+2
       355: 4q^2+10q+2
       356: 3q^2+7q+2
       357: 6q+2
       358: 3q+2
       359: 6q+2
       361: 7q+2
       363: 7q+2
       365: 2q^2+4q+2
       366: q^2+6q+2
       367: q^2+9q+2
       368: q^2+6q+2
       369: 6q+2
       370: 6q+2
       371: q^2+9q+2
       372: q^2+9q+2
       373: 3q^2+6q+2
       374: q^2+9q+2
       375: q^2+9q+2
       376: 3q^2+6q+2
       378: q+1
       379: q+1
       382: 4q+1
       383: 4q+1
       385: q^2+q
       386: q^2+4q+1
       387: q^2+4q+1
       388: q^2+q
       390: 2q+1
       392: 2q+1
       393: q
       394: 2q+1
       395: 2q+1
       396: q
       398: 2q+1
       400: 2q+1
       401: q
       402: 2q+1
       403: 2q+1
       404: q
       405: q
       406: q
       407: q+1
       408: q+1
       410: 8q+2
       412: 5q+2
       414: 5q+2
       416: 8q+2
       418: 5q+2
       419: q^2+2q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q^2+2q+1
       424: 5q+2
       426: 4q+2
       428: 7q+2
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       434: q+2
       436: 4q+2
       437: 3q+1
       438: 3q+1
       439: 2q^2+5q+1
       440: 2q^2+5q+1
       441: 2q
       442: 4q+2
       443: 3q+1
       444: 3q+1
       446: 4q+2
       447: q^2+2q+1
       448: q^2+2q+1
       449: q+1
       450: q+1
       452: q+2
       453: 2q^2+5q+1
       454: 2q^2+5q+1
       456: 4q+2
       457: 3q+1
       458: 3q+1
       459: 2q
       460: 4q+2
       461: 3q+1
       462: 3q+1
       464: 4q+2
       466: 7q+2
       468: 4q+2
       470: 4q+2
       471: 3q+1
       472: 3q+1
       473: 3q+1
       474: 3q+1
       475: 2q
       476: 2q+2
       478: 2q+2
       479: 2q
       480: 2q+2
       481: 3q^2+7q+2
       482: 3q^2+7q+2
       483: q^2+6q+2
       484: q^2+9q+2
       486: 7q+2
       488: 7q+2
       490: 2q^2+4q+2
       491: q^2+6q+2
       492: 3q^2+7q+2
       493: 3q+2
       494: 3q^2+7q+2
       495: 3q+2
       496: 6q+2
       497: 3q^2+7q+2
       498: 3q^2+7q+2
       499: 3q+2
       500: 3q+2
       501: 6q+2
       503: 7q+2
       505: 7q+2
       507: 2q^2+4q+2
       508: q^2+6q+2
       509: q^2+9q+2
       510: q^2+6q+2
       511: 6q+2
       512: 3q+2
       513: 6q+2
       514: 3q+2
       515: 3q+4
       516: 4q+4
       517: 3q+4
       518: q^2+9q+2
       519: q^2+9q+2
       520: 3q^2+6q+2
       522: q+1
       523: q+1
       526: 4q+1
       527: 4q+1
       530: q+1
       531: q+1
       534: 1
       535: 1
       538: 2q+1
       540: 2q+1
       541: q
       542: 2q+1
       543: q
       544: 2q+1
       546: 2q+1
       548: 2q+1
       550: 1
       551: 1
       554: 2q+1
       556: 2q+1
       557: q
       558: 2q+1
       559: q
       560: 2q+1
       562: 2q+1
       564: 2q+1
       565: q
       566: q+1
       567: q+1
       568: q
       571: q+1
       572: q+1
       573: q
       574: q+1
       575: q
       576: q+1
       581: 2q+2
       584: 5q+2
       586: 5q+2
       588: 5q+2
       589: q^2+2q+1
       590: q^2+2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q^2+2q+1
       596: q^2+2q+1
       598: 4q+2
       600: 4q+2
       602: 7q+2
       603: q+1
       604: q+1
       606: q+2
       607: q^2+2q+1
       608: q^2+2q+1
       610: q+2
       612: 4q+2
       614: q+2
       615: 3q+1
       616: 3q+1
       618: 4q+2
       619: q^2+2q+1
       620: q^2+2q+1
       621: q+1
       622: q+1
       624: q+2
       626: q+2
       628: 4q+2
       630: q+2
       631: 3q+1
       632: 3q+1
       634: 4q+2
       636: 7q+2
       638: 4q+2
       640: 4q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: 2
       647: 3q+1
       648: 3q+1
       649: 3q+1
       650: 3q+1
       652: 2q+2
       653: 2q
       654: 2q+2
       655: 2q
       656: 2q+2
       657: q+4
       659: 3q+4
       661: 4q+4
       663: 3q+4
       664: 3q+4
       665: q^2+6q+2
       667: 7q+2
       669: 7q+2
       671: 2q^2+4q+2
       672: q^2+9q+2
       673: q^2+6q+2
       674: q+4
       675: 3q+2
       676: 3q^2+7q+2
       677: 3q+2
       678: 6q+2
       679: 3q+2
       680: q+4
       681: 3q^2+7q+2
       682: 3q+2
       683: 3q+2
       684: 6q+2
       685: 3q+2
       686: q^2+6q+2
       687: 3q+2
       688: 3q+2
       689: q+1
       690: 3q+4
       691: 4q+4
       692: 3q+4
       699: q+1
       700: q+1
       706: q+1
       707: q+1
       710: q+1
       711: q+1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 2q+1
       732: 2q+1
       734: 2q+1
       736: 2q+1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 2q+1
       748: 2q+1
       750: 2q+1
       752: 2q+1
       754: 1
       755: 1
       759: q+1
       760: q+1
       761: q
       762: q
       763: q+1
       764: q+1
       765: q
       766: q+1
       767: q+1
       768: q
       773: 2q+2
       776: q+4
       778: 5q+2
       780: 3q+4
       782: 4q+2
       784: 4q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       790: 7q+2
       792: 2
       793: 2
       794: 2
       796: q+4
       798: q+2
       800: q+2
       801: q+1
       802: q+1
       805: q+1
       806: q+1
       807: q^2+2q+1
       808: q^2+2q+1
       810: q+2
       812: q+2
       814: 4q+2
       815: 3q+1
       816: 3q+1
       817: 2
       818: 2
       820: q+4
       822: q+2
       824: q+2
       825: q^2+2q+1
       826: q^2+2q+1
       827: q+1
       828: q+1
       831: q+1
       832: q+1
       834: q+2
       836: q+2
       838: 4q+2
       839: 3q+1
       840: 3q+1
       842: 4q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       850: 2
       852: 2
       854: 2q+2
       856: 1
       857: 2q
       858: 2q+2
       860: 3q+4
       862: 4q+4
       864: 3q+4
       865: q+4
       866: q+4
       867: 3q+4
       868: q^2+6q+2
       869: q+4
       870: q+4
       871: 3q+2
       872: 3q+2
       873: q+4
       874: q+4
       875: 3q+2
       876: 3q+2
       877: 3q+2
       878: 3q+2
       879: q+1
       880: q+1
       881: 3q+4
       882: 4q+4
       883: 3q+4
       890: q+1
       891: q+1
       897: q+1
       898: q+1
       901: 1
       903: 1
       905: 1
       907: 1
       909: 1
       910: 1
       913: 1
       915: 1
       917: 2
       919: 2
       921: 1
       923: 1
       929: 1
       931: 1
       933: 2q+1
       935: 2q+1
       937: 1
       939: 1
       941: 2
       943: 2
       945: 1
       947: 1
       949: 1
       951: 1
       957: 2q+1
       959: 2q+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 2
       972: 2
       976: 1
       977: 1
       980: q+1
       981: q+1
       986: 2q+2
       988: q
       989: q+1
       990: q+1
       991: q
       993: q+4
       995: q+4
       997: 3q+4
       998: 2
       999: 2
      1000: 2
      1001: 2
      1003: 4q+2
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1009: 2
      1011: 2
      1012: 2
      1013: 2
      1015: q+4
      1016: 2
      1017: 2
      1019: q+2
      1021: q+4
      1023: q+2
      1025: q+2
      1026: q+1
      1027: q+1
      1031: q+4
      1032: 2
      1033: 2
      1035: q+2
      1037: q+4
      1039: q+2
      1043: q+2
      1044: q+1
      1045: q+1
      1046: 2
      1047: 2
      1049: 2
      1051: 2
      1052: q+1
      1053: q+1
      1058: q+1
      1059: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: 3q+4
      1069: 4q+4
      1071: 3q+4
      1072: q+4
      1073: 3q+4
      1074: q+4
      1075: q+4
      1076: 2
      1077: q+4
      1078: 3q+2
      1079: q+4
      1080: 2
      1081: q+4
      1082: 3q+2
      1083: q+1
      1084: 2
      1085: q+1
      1087: 1
      1092: 1
      1093: 1
      1094: 1
      1104: q+1
      1105: q+1
      1111: 1
      1113: 1
      1115: 2
      1117: 2
      1119: 1
      1121: 1
      1123: 2
      1125: 2
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1136: 1
      1137: 1
      1139: 2
      1142: 2
      1145: 2
      1147: 2
      1149: 1
      1151: 1
      1157: 1
      1159: 1
      1165: 2
      1167: 2
      1169: 1
      1171: 1
      1173: 1
      1175: 1
      1186: 1
      1187: 1
      1189: 2
      1192: 2
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1211: q+4
      1213: 3q+4
      1215: q+4
      1216: 2
      1217: 2
      1218: 2
      1219: 2
      1221: 2
      1223: 2
      1224: 2
      1225: 2
      1227: q+4
      1228: 2
      1229: 2
      1231: 2
      1234: 1
      1235: 1
      1237: q+4
      1239: q+2
      1240: q+1
      1241: q+1
      1245: q+4
      1246: 2
      1247: 2
      1249: 2
      1250: 1
      1251: 1
      1253: q+4
      1257: q+2
      1260: q+1
      1261: q+1
      1262: 2
      1263: 2
      1265: 2
      1267: 1
      1273: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+4
      1283: 2
      1284: q+4
      1285: 2
      1286: q+4
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1296: 1
      1297: 1
      1298: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 2
      1317: 2
      1319: 2
      1321: 2
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1335: 2
      1338: 2
      1341: 2
      1343: 2
      1353: 1
      1355: 1
      1357: 1
      1359: 1
      1373: 2
      1375: 2
      1377: 1
      1379: 1
      1381: 1
      1383: 1
      1405: 2
      1408: 2
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1416: 1
      1417: 1
      1431: 1
      1434: 1
      1439: q+4
      1440: 2
      1441: 2
      1442: 2
      1443: 2
      1444: 2
      1445: 2
      1447: 2
      1449: 2
      1453: q+4
      1454: 1
      1455: 1
      1457: 2
      1459: q+4
      1460: 1
      1461: 1
      1465: 1
      1471: 1
      1473: 2
      1475: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 2
      1490: 1
      1495: 1
      1496: 1
      1497: 1
      1526: 1
      1531: 1
      1532: 1
      1533: 1
      1542: 2
      1544: 2
      1546: 2
      1548: 2
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1554: 2
      1557: 2
      1561: 1
      1562: 1
      1568: 1
      1570: 1
      1584: 1
      1586: 1
      1632: 1
      1635: 1
      1642: 1
      1644: 2
      1647: 1
      1648: 1
      1652: 2
      1653: 1
      1654: 1
      1662: 1
      1668: 2
      1669: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1681: 1
      1682: 1
      1683: 1
      1746: 1
      1748: 1
      1762: 1
      1764: 1
      1802: 1
      1805: 1
      1816: 1
      1828: 1
      1833: 1
      1957: 1

1958:    0: q^4+2q^3+3q^2+2q+2
         1: q^4+2q^3+3q^2+2q+2
         2: q^5+q^4+2q^3+2q^2+2q+2
         3: q^4+2q^3+3q^2+2q+2
         4: q^4+2q^3+3q^2+2q+2
         5: q^4+2q^3+3q^2+2q+2
         6: q^4+2q^3+3q^2+2q+2
         7: q^5+q^4+2q^3+2q^2+2q+2
         8: q^5+q^4+2q^3+2q^2+2q+2
         9: q^5+q^4+2q^3+2q^2+2q+2
        10: q^4+2q^3+3q^2+2q+2
        11: q^4+2q^3+3q^2+2q+2
        12: q^4+2q^3+3q^2+2q+2
        13: q^3+2q^2+2q+2
        14: q^3+2q^2+2q+2
        15: q^3+2q^2+2q+2
        16: q^4+2q^3+3q^2+2q+2
        17: q^4+2q^3+3q^2+2q+2
        18: q^5+q^4+2q^3+2q^2+2q+2
        19: q^4+2q^3+3q^2+2q+2
        20: q^4+2q^3+3q^2+2q+2
        21: q^5+q^4+2q^3+2q^2+2q+2
        22: 2q^3+2q^2+2q+2
        23: 2q^3+2q^2+2q+2
        24: q^4+2q^3+q^2+2q+2
        25: 2q^3+2q^2+2q+2
        26: 2q^3+2q^2+2q+2
        27: q^4+2q^3+q^2+2q+2
        28: q^4+2q^3+3q^2+2q+2
        29: q^4+2q^3+3q^2+2q+2
        30: q^3+2q^2+2q+2
        31: 2q^3+2q^2+2q+2
        32: q^3+q^2+2q+2
        33: 2q^3+2q^2+2q+2
        34: 2q^3+2q^2+2q+2
        35: q^3+q^2+2q+2
        36: 2q^3+2q^2+2q+2
        37: 2q^3+2q^2+2q+2
        39: 2q^3+2q^2+2q+2
        41: q^4+2q^3+q^2+2q+2
        43: q^3+2q^2+2q+2
        44: q^3+2q^2+2q+2
        45: q^3+2q^2+2q+2
        46: q^3+2q^2+2q+2
        47: q^3+2q^2+2q+2
        48: q^3+2q^2+2q+2
        49: q^4+2q^3+3q^2+2q+2
        50: q^4+2q^3+3q^2+2q+2
        51: q^5+q^4+2q^3+2q^2+2q+2
        52: 2q^3+2q^2+2q+2
        53: 2q^3+2q^2+2q+2
        54: q^4+2q^3+q^2+2q+2
        55: 2q^3+2q^2+2q+2
        56: 2q^3+2q^2+2q+2
        57: q^4+2q^3+q^2+2q+2
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^3+q^2+q+1
        61: q^3+q^2+q+1
        62: 2q^3+2q^2+2q+2
        64: q^3+q^2+2q+2
        66: 2q^3+2q^2+2q+2
        68: q^2+2q+2
        69: q^3+2q^2+2q+2
        70: q^3+2q^2+2q+2
        71: q^4+2q^3+3q^2+2q+2
        72: 2q^3+2q^2+2q+2
        73: 2q^3+2q^2+2q+2
        74: 2q^3+2q^2+2q+2
        76: 2q^3+2q^2+2q+2
        78: q^4+2q^3+q^2+2q+2
        80: q^3+q^2+2q+2
        81: q^3+q^2+2q+2
        82: 2q^3+2q^2+2q+2
        83: q^3+q^2+2q+2
        84: q^3+q^2+2q+2
        85: q^3+q^2+2q+2
        86: 2q^3+2q^2+2q+2
        87: q^3+q^2+2q+2
        88: q^3+2q^2+2q+2
        89: q^3+2q^2+2q+2
        90: q^3+2q^2+2q+2
        91: q^3+2q^2+2q+2
        92: q^3+2q^2+2q+2
        93: q^3+2q^2+2q+2
        94: 2q^3+2q^2+2q+2
        95: 2q^3+2q^2+2q+2
        96: q^4+2q^3+q^2+2q+2
        97: 2q^3+2q^2+2q+2
        98: 2q^3+2q^2+2q+2
        99: q^4+2q^3+q^2+2q+2
       100: q^3+2q^2+q+2
       101: q^3+2q^2+q+2
       102: 2q^3+q^2+q+2
       103: q^3+q^2+q+1
       106: q^3+q^2+q+1
       107: q^3+q^2+q+1
       108: q^3+q^2+q+1
       109: q^3+q^2+q+1
       110: q^3+q^2+q+1
       111: 2q^3+2q^2+2q+2
       113: 2q^3+2q^2+2q+2
       115: q^3+q^2+2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^3+q^2+2q+2
       123: q^3+q^2+2q+2
       125: q^2+2q+2
       126: q^3+2q^2+2q+2
       127: 2q^3+2q^2+2q+2
       129: 2q^3+2q^2+2q+2
       131: q^4+2q^3+q^2+2q+2
       133: q^2+2q+2
       134: q^3+2q^2+2q+2
       135: q^3+q^2+2q+2
       136: q^3+q^2+2q+2
       137: q^3+q^2+2q+2
       138: q^3+q^2+2q+2
       139: 2q^3+2q^2+2q+2
       140: 2q^2+2
       141: q^3+q^2+2q+2
       142: 2q^3+2q^2+2q+2
       143: q^3+q^2+2q+2
       144: q^3+q^2+2q+2
       145: 2q^3+2q^2+2q+2
       146: q^3+q^2+2q+2
       147: 2q^3+2q^2+2q+2
       148: 2q^2+2
       149: q^3+2q^2+q+2
       150: q^3+q^2+q+2
       151: q^3+2q^2+q+2
       153: q^3+2q^2+q+2
       155: 2q^3+q^2+q+2
       157: q^3+2q^2+2q+2
       158: q^3+2q^2+2q+2
       159: q^3+2q^2+2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+2q^2+q+2
       167: q^3+2q^2+q+2
       168: 2q^3+q^2+q+2
       169: q^3+q^2+q+1
       172: q^3+q^2+q+1
       173: q+1
       176: q+1
       177: q^3+q^2+2q+2
       179: 2q^3+2q^2+2q+2
       181: 2q^3+2q^2+2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q^3+q^2+2q+2
       189: q^3+q^2+2q+2
       191: q+1
       192: q+1
       193: q^2+1
       194: q^2+1
       195: q^3+q^2+q+1
       196: q^3+q^2+q+1
       197: 2q^2+2
       199: q+1
       200: q+1
       201: q^3+q^2+q+1
       202: q^3+q^2+q+1
       203: q^2+1
       204: q^2+1
       205: 2q^2+2
       207: q^3+q^2+2q+2
       209: q^3+2q^2+q+2
       211: q^3+q^2+q+2
       213: q^2+2q+2
       215: q^2+2q+2
       217: q^2+2q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^3+2q^2+2q+2
       222: q^3+q^2+2q+2
       223: q^3+q^2+2q+2
       224: q^3+q^2+2q+2
       225: q^3+q^2+2q+2
       226: q^3+q^2+2q+2
       227: 2q+2
       228: q^2+2q+2
       229: q^2+2
       230: q^2+2q+2
       231: q^3+q^2+2q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: q^2+2
       236: q^3+q^2+q+2
       237: q^3+2q^2+q+2
       239: q^3+2q^2+q+2
       241: 2q^3+q^2+q+2
       243: q^3+2q^2+q+2
       244: 2q^2+2
       245: 2q^2+2
       246: q^3+q^2+q+2
       247: q^3+2q^2+q+2
       248: q^3+2q^2+q+2
       249: 2q^3+q^2+q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: q+2
       257: q+2
       258: q+2
       259: q^3+q^2+q+1
       262: q^3+q^2+q+1
       263: q+1
       266: q+1
       267: q^2+1
       269: q^2+1
       271: q^2+1
       273: q^2+1
       275: q+1
       278: q+1
       279: 2q+2
       281: q^2+2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q^3+q^2+2q+2
       289: q^2+2q+2
       291: q^3+q^2+2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q^3+q^2+2q+2
       299: 1
       300: 1
       301: 2q^2+2
       303: q+1
       304: q+1
       305: q^2+2
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2q^2+2
       313: q^2+2
       315: q^3+q^2+q+2
       317: q^3+2q^2+q+2
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       323: 2q^2+2
       325: q^3+q^2+q+2
       327: q^2+2q+2
       329: q^2+2q+2
       331: q^2+2q+2
       333: q^2+2q+2
       334: q^3+q^2+2q+2
       335: q^3+q^2+2q+2
       336: q^3+q^2+q+2
       337: q^3+2q^2+q+2
       338: q^3+2q^2+q+2
       340: q^3+2q^2+q+2
       342: 2q^3+q^2+q+2
       344: 2q+2
       345: 2q+2
       346: q^2+2q+2
       347: q^2+2
       348: q^2+2
       349: q^2+2q+2
       350: q^2+2q+2
       351: 2q^2+2
       352: 2q+2
       353: 2q+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^2+2q+2
       357: q^2+2
       358: q^2+2
       359: 2q^2+2
       360: q+2
       362: q+2
       364: q+2
       366: q^3+q^2+q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       377: q+1
       380: q+1
       381: q+1
       384: q+1
       385: q+1
       388: q+1
       389: q^2+1
       391: q^2+1
       393: 1
       396: 1
       397: q^2+1
       399: q^2+1
       401: 1
       404: 1
       405: q^2+1
       406: q^2+1
       409: 2q+2
       411: q^2+2q+2
       413: 2q+2
       415: q^2+2q+2
       417: q^2+2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q^3+q^2+2q+2
       425: q^3+q^2+q+2
       427: q^3+2q^2+q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q^2+2
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: q^2+2
       443: q^2+1
       444: q^2+1
       445: 2q^2+2
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q^2+2
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: q^2+2
       461: q^2+1
       462: q^2+1
       463: 2q^2+2
       465: q+2
       467: q+2
       469: q^3+q^2+q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2q^2+2
       479: 2q^2+2
       481: 2q+2
       482: 2q+2
       483: q^3+q^2+q+2
       484: q+2
       485: q+2
       487: q+2
       489: q+2
       491: q+2
       492: 2q+2
       493: q^2+2
       494: q^2+2q+2
       495: q^2+2
       496: 2
       497: 2q+2
       498: q^2+2q+2
       499: q^2+2
       500: q^2+2
       501: 2
       502: q+2
       504: q+2
       506: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       521: q+1
       524: q+1
       525: q+1
       528: q+1
       529: q+1
       532: q+1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: q^2+1
       547: q^2+1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: q^2+1
       563: q^2+1
       565: 1
       568: 1
       569: q^2+1
       570: q^2+1
       573: q^2+1
       575: q^2+1
       577: 2q^2+2
       583: 2q+2
       585: 2q+2
       587: q^2+2q+2
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: q+1
       596: q+1
       597: q+2
       599: q^3+q^2+q+2
       601: q+2
       603: 1
       604: 1
       605: 2
       607: q+1
       608: q+1
       609: q^2+2
       611: 2
       613: q^2+2
       615: 1
       616: 1
       617: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       625: q^2+2
       627: 2
       629: q^2+2
       631: 1
       632: 1
       633: 2
       635: q+2
       637: q+2
       639: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+2
       653: 2
       655: 2
       657: q+2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q+2
       666: q+2
       668: q+2
       670: q+2
       672: q+2
       673: q+2
       674: 2
       675: 2
       676: 2q+2
       677: q^2+2
       678: 2
       679: 2
       680: 2
       681: 2q+2
       682: 2
       683: q^2+2
       684: 2
       685: 2
       686: q+2
       687: 2
       688: 2
       689: 1
       690: q+2
       691: q+2
       692: q+2
       693: q^2+1
       697: q^2+1
       705: q+1
       708: q+1
       709: q+1
       712: q+1
       713: 1
       716: 1
       717: 1
       720: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       771: q
       775: q+2
       777: 2q+2
       779: q+2
       781: q+2
       783: q+2
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+2
       791: 2
       793: 1
       794: 1
       795: 2
       797: 2
       799: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2
       811: q^2+2
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: 2
       835: q^2+2
       837: 2
       839: 1
       840: 1
       841: q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+2
       851: 2
       853: q+2
       855: 1
       857: 2
       859: q+2
       861: q+2
       863: q+2
       865: q+2
       866: q+2
       867: q+2
       868: q+2
       869: 2
       870: 2
       871: 2
       872: 2
       873: 2
       874: 2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: 1
       884: 1
       889: 1
       896: q+1
       899: q+1
       900: 1
       902: 1
       904: 1
       906: 1
       908: 1
       911: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       928: 1
       930: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       948: 1
       950: 1
       956: 1
       958: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       970: q
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       984: q
       988: 1
       991: 1
       992: q+2
       994: q+2
       996: q+2
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: q+2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 2
      1010: q+2
      1012: 2
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 2
      1022: 2
      1024: 2
      1026: 1
      1027: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 2
      1038: 2
      1042: 2
      1044: 1
      1045: 1
      1046: 2
      1048: 2
      1050: q+2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1074: q+2
      1076: 2
      1077: 2
      1078: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1091: 1
      1098: 1
      1102: 1
      1110: 1
      1112: 1
      1114: 1
      1116: 1
      1118: 1
      1120: 1
      1122: 1
      1124: 1
      1126: 1
      1127: 1
      1130: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1140: q
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1156: 1
      1158: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1172: 1
      1174: 1
      1184: 1
      1185: 1
      1188: 2
      1190: q
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1214: q+2
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 2
      1222: q+2
      1224: 2
      1230: 2
      1234: 1
      1235: 1
      1236: 2
      1238: 2
      1240: 1
      1241: 1
      1248: 2
      1250: 1
      1251: 1
      1252: 2
      1256: 2
      1260: 1
      1261: 1
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1295: 1
      1302: 1
      1307: 1
      1314: 1
      1316: 1
      1318: 1
      1320: 1
      1322: 1
      1323: 1
      1326: 1
      1329: 1
      1330: 1
      1331: 1
      1334: 2
      1336: q
      1352: 1
      1354: 1
      1356: 1
      1358: 1
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1414: 1
      1415: 1
      1430: 1
      1436: 2
      1446: 2
      1448: 2
      1454: 1
      1455: 1
      1456: 2
      1460: 1
      1461: 1
      1464: 1
      1470: 1
      1472: 1
      1474: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1489: 1
      1494: 1
      1537: 1
      1538: 1
      1559: 1
      1560: 1
      1567: 1
      1569: 1
      1583: 1
      1585: 1
      1631: 1
      1637: 2
      1641: 1
      1659: 1
      1661: 1
      1671: 1
      1673: 1
      1729: 1
      1730: 1
      1815: 1
      1817: 1
      1823: 1
      1958: 1

1959:    0: q^4+2q^3+3q^2+2q+2
         1: q^4+2q^3+3q^2+2q+2
         2: q^5+q^4+2q^3+2q^2+2q+2
         3: q^4+2q^3+3q^2+2q+2
         4: q^4+2q^3+3q^2+2q+2
         5: q^4+2q^3+3q^2+2q+2
         6: q^4+2q^3+3q^2+2q+2
         7: q^5+q^4+2q^3+2q^2+2q+2
         8: q^5+q^4+2q^3+2q^2+2q+2
         9: q^5+q^4+2q^3+2q^2+2q+2
        10: q^4+2q^3+3q^2+2q+2
        11: q^4+2q^3+3q^2+2q+2
        12: q^4+2q^3+3q^2+2q+2
        13: q^3+2q^2+2q+2
        14: q^3+2q^2+2q+2
        15: q^3+2q^2+2q+2
        16: q^4+2q^3+3q^2+2q+2
        17: q^4+2q^3+3q^2+2q+2
        18: q^5+q^4+2q^3+2q^2+2q+2
        19: q^4+2q^3+3q^2+2q+2
        20: q^4+2q^3+3q^2+2q+2
        21: q^5+q^4+2q^3+2q^2+2q+2
        22: 2q^3+2q^2+2q+2
        23: 2q^3+2q^2+2q+2
        24: q^4+2q^3+q^2+2q+2
        25: 2q^3+2q^2+2q+2
        26: 2q^3+2q^2+2q+2
        27: q^4+2q^3+q^2+2q+2
        28: q^4+2q^3+3q^2+2q+2
        29: q^4+2q^3+3q^2+2q+2
        30: q^3+2q^2+2q+2
        31: 2q^3+2q^2+2q+2
        32: q^3+q^2+2q+2
        33: 2q^3+2q^2+2q+2
        34: 2q^3+2q^2+2q+2
        35: q^3+q^2+2q+2
        36: 2q^3+2q^2+2q+2
        38: 2q^3+2q^2+2q+2
        40: 2q^3+2q^2+2q+2
        42: q^4+2q^3+q^2+2q+2
        43: q^3+2q^2+2q+2
        44: q^3+2q^2+2q+2
        45: q^3+2q^2+2q+2
        46: q^3+2q^2+2q+2
        47: q^3+2q^2+2q+2
        48: q^3+2q^2+2q+2
        49: q^4+2q^3+3q^2+2q+2
        50: q^4+2q^3+3q^2+2q+2
        51: q^5+q^4+2q^3+2q^2+2q+2
        52: 2q^3+2q^2+2q+2
        53: 2q^3+2q^2+2q+2
        54: q^4+2q^3+q^2+2q+2
        55: 2q^3+2q^2+2q+2
        56: 2q^3+2q^2+2q+2
        57: q^4+2q^3+q^2+2q+2
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^3+q^2+q+1
        61: q^3+q^2+q+1
        63: 2q^3+2q^2+2q+2
        65: q^3+q^2+2q+2
        67: 2q^3+2q^2+2q+2
        68: q^2+2q+2
        69: q^3+2q^2+2q+2
        70: q^3+2q^2+2q+2
        71: q^4+2q^3+3q^2+2q+2
        72: 2q^3+2q^2+2q+2
        73: 2q^3+2q^2+2q+2
        75: 2q^3+2q^2+2q+2
        77: 2q^3+2q^2+2q+2
        79: q^4+2q^3+q^2+2q+2
        80: q^3+q^2+2q+2
        81: q^3+q^2+2q+2
        82: 2q^3+2q^2+2q+2
        83: q^3+q^2+2q+2
        84: q^3+q^2+2q+2
        85: q^3+q^2+2q+2
        86: 2q^3+2q^2+2q+2
        87: q^3+q^2+2q+2
        88: q^3+2q^2+2q+2
        89: q^3+2q^2+2q+2
        90: q^3+2q^2+2q+2
        91: q^3+2q^2+2q+2
        92: q^3+2q^2+2q+2
        93: q^3+2q^2+2q+2
        94: 2q^3+2q^2+2q+2
        95: 2q^3+2q^2+2q+2
        96: q^4+2q^3+q^2+2q+2
        97: 2q^3+2q^2+2q+2
        98: 2q^3+2q^2+2q+2
        99: q^4+2q^3+q^2+2q+2
       100: q^3+2q^2+q+2
       101: q^3+2q^2+q+2
       102: 2q^3+q^2+q+2
       104: q^3+q^2+q+1
       105: q^3+q^2+q+1
       107: q^3+q^2+q+1
       108: q^3+q^2+q+1
       109: q^3+q^2+q+1
       110: q^3+q^2+q+1
       112: 2q^3+2q^2+2q+2
       114: 2q^3+2q^2+2q+2
       116: q^3+q^2+2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: q^3+q^2+2q+2
       124: q^3+q^2+2q+2
       125: q^2+2q+2
       126: q^3+2q^2+2q+2
       128: 2q^3+2q^2+2q+2
       130: 2q^3+2q^2+2q+2
       132: q^4+2q^3+q^2+2q+2
       133: q^2+2q+2
       134: q^3+2q^2+2q+2
       135: q^3+q^2+2q+2
       136: q^3+q^2+2q+2
       137: q^3+q^2+2q+2
       138: q^3+q^2+2q+2
       139: 2q^3+2q^2+2q+2
       140: 2q^2+2
       141: q^3+q^2+2q+2
       142: 2q^3+2q^2+2q+2
       143: q^3+q^2+2q+2
       144: q^3+q^2+2q+2
       145: 2q^3+2q^2+2q+2
       146: q^3+q^2+2q+2
       147: 2q^3+2q^2+2q+2
       148: 2q^2+2
       149: q^3+2q^2+q+2
       150: q^3+q^2+q+2
       152: q^3+2q^2+q+2
       154: q^3+2q^2+q+2
       156: 2q^3+q^2+q+2
       157: q^3+2q^2+2q+2
       158: q^3+2q^2+2q+2
       159: q^3+2q^2+2q+2
       160: q^2+2q+2
       161: q^2+2q+2
       162: q^2+2q+2
       163: q^2+2q+2
       164: q^2+2q+2
       165: q^2+2q+2
       166: q^3+2q^2+q+2
       167: q^3+2q^2+q+2
       168: 2q^3+q^2+q+2
       170: q^3+q^2+q+1
       171: q^3+q^2+q+1
       174: q+1
       175: q+1
       178: q^3+q^2+2q+2
       180: 2q^3+2q^2+2q+2
       182: 2q^3+2q^2+2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: q^3+q^2+2q+2
       190: q^3+q^2+2q+2
       191: q+1
       192: q+1
       193: q^2+1
       194: q^2+1
       195: q^3+q^2+q+1
       196: q^3+q^2+q+1
       198: 2q^2+2
       199: q+1
       200: q+1
       201: q^3+q^2+q+1
       202: q^3+q^2+q+1
       203: q^2+1
       204: q^2+1
       206: 2q^2+2
       208: q^3+q^2+2q+2
       210: q^3+2q^2+q+2
       212: q^3+q^2+q+2
       214: q^2+2q+2
       216: q^2+2q+2
       218: q^2+2q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^3+2q^2+2q+2
       222: q^3+q^2+2q+2
       223: q^3+q^2+2q+2
       224: q^3+q^2+2q+2
       225: q^3+q^2+2q+2
       226: q^3+q^2+2q+2
       227: 2q+2
       228: q^2+2q+2
       229: q^2+2
       230: q^2+2q+2
       231: q^3+q^2+2q+2
       232: 2q+2
       233: q^2+2q+2
       234: q^2+2q+2
       235: q^2+2
       236: q^3+q^2+q+2
       238: q^3+2q^2+q+2
       240: q^3+2q^2+q+2
       242: 2q^3+q^2+q+2
       243: q^3+2q^2+q+2
       244: 2q^2+2
       245: 2q^2+2
       246: q^3+q^2+q+2
       247: q^3+2q^2+q+2
       248: q^3+2q^2+q+2
       249: 2q^3+q^2+q+2
       250: q^2+2q+2
       251: q^2+2q+2
       252: q^2+2q+2
       253: q^2+2q+2
       254: q^2+2q+2
       255: q^2+2q+2
       256: q+2
       257: q+2
       258: q+2
       260: q^3+q^2+q+1
       261: q^3+q^2+q+1
       264: q+1
       265: q+1
       268: q^2+1
       270: q^2+1
       272: q^2+1
       274: q^2+1
       276: q+1
       277: q+1
       280: 2q+2
       282: q^2+2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: q^3+q^2+2q+2
       290: q^2+2q+2
       292: q^3+q^2+2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: q^3+q^2+2q+2
       299: 1
       300: 1
       302: 2q^2+2
       303: q+1
       304: q+1
       306: q^2+2
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2q^2+2
       314: q^2+2
       316: q^3+q^2+q+2
       318: q^3+2q^2+q+2
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       324: 2q^2+2
       326: q^3+q^2+q+2
       328: q^2+2q+2
       330: q^2+2q+2
       332: q^2+2q+2
       333: q^2+2q+2
       334: q^3+q^2+2q+2
       335: q^3+q^2+2q+2
       336: q^3+q^2+q+2
       337: q^3+2q^2+q+2
       339: q^3+2q^2+q+2
       341: q^3+2q^2+q+2
       343: 2q^3+q^2+q+2
       344: 2q+2
       345: 2q+2
       346: q^2+2q+2
       347: q^2+2
       348: q^2+2
       349: q^2+2q+2
       350: q^2+2q+2
       351: 2q^2+2
       352: 2q+2
       353: 2q+2
       354: q^2+2q+2
       355: q^2+2q+2
       356: q^2+2q+2
       357: q^2+2
       358: q^2+2
       359: 2q^2+2
       361: q+2
       363: q+2
       365: q+2
       366: q^3+q^2+q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       378: q+1
       379: q+1
       382: q+1
       383: q+1
       386: q+1
       387: q+1
       390: q^2+1
       392: q^2+1
       394: 1
       395: 1
       398: q^2+1
       400: q^2+1
       402: 1
       403: 1
       407: q^2+1
       408: q^2+1
       410: 2q+2
       412: q^2+2q+2
       414: 2q+2
       416: q^2+2q+2
       418: q^2+2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       424: q^3+q^2+2q+2
       426: q^3+q^2+q+2
       428: q^3+2q^2+q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       434: q^2+2
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: q^2+2
       443: q^2+1
       444: q^2+1
       446: 2q^2+2
       447: q+1
       448: q+1
       449: 1
       450: 1
       452: q^2+2
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: q^2+2
       461: q^2+1
       462: q^2+1
       464: 2q^2+2
       466: q+2
       468: q+2
       470: q^3+q^2+q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2q^2+2
       480: 2q^2+2
       481: 2q+2
       482: 2q+2
       483: q^3+q^2+q+2
       484: q+2
       486: q+2
       488: q+2
       490: q+2
       491: q+2
       492: 2q+2
       493: q^2+2
       494: q^2+2q+2
       495: q^2+2
       496: 2
       497: 2q+2
       498: q^2+2q+2
       499: q^2+2
       500: q^2+2
       501: 2
       503: q+2
       505: q+2
       507: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       522: q+1
       523: q+1
       526: q+1
       527: q+1
       530: q+1
       531: q+1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: q^2+1
       548: q^2+1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: q^2+1
       564: q^2+1
       566: 1
       567: 1
       571: q^2+1
       572: q^2+1
       574: q^2+1
       576: q^2+1
       581: 2q^2+2
       584: 2q+2
       586: 2q+2
       588: q^2+2q+2
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: q+1
       596: q+1
       598: q+2
       600: q^3+q^2+q+2
       602: q+2
       603: 1
       604: 1
       606: 2
       607: q+1
       608: q+1
       610: q^2+2
       612: 2
       614: q^2+2
       615: 1
       616: 1
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2
       626: q^2+2
       628: 2
       630: q^2+2
       631: 1
       632: 1
       634: 2
       636: q+2
       638: q+2
       640: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+2
       654: 2
       656: 2
       657: q+2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q+2
       667: q+2
       669: q+2
       671: q+2
       672: q+2
       673: q+2
       674: 2
       675: 2
       676: 2q+2
       677: q^2+2
       678: 2
       679: 2
       680: 2
       681: 2q+2
       682: 2
       683: q^2+2
       684: 2
       685: 2
       686: q+2
       687: 2
       688: 2
       689: 1
       690: q+2
       691: q+2
       692: q+2
       699: q^2+1
       700: q^2+1
       706: q+1
       707: q+1
       710: q+1
       711: q+1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       774: q
       776: q+2
       778: 2q+2
       780: q+2
       782: q+2
       784: q+2
       785: 1
       786: 1
       787: 1
       788: 1
       790: q+2
       792: 2
       793: 1
       794: 1
       796: 2
       798: 2
       800: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       810: 2
       812: q^2+2
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       834: 2
       836: q^2+2
       838: 2
       839: 1
       840: 1
       842: q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+2
       852: 2
       854: q+2
       856: 1
       858: 2
       860: q+2
       862: q+2
       864: q+2
       865: q+2
       866: q+2
       867: q+2
       868: q+2
       869: 2
       870: 2
       871: 2
       872: 2
       873: 2
       874: 2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: 1
       890: 1
       891: 1
       897: q+1
       898: q+1
       901: 1
       903: 1
       905: 1
       907: 1
       909: 1
       910: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       929: 1
       931: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       949: 1
       951: 1
       957: 1
       959: 1
       962: 1
       963: 1
       965: 1
       966: 1
       972: 2
       973: q
       976: 1
       977: 1
       980: 1
       981: 1
       986: 2
       987: q
       989: 1
       990: 1
       993: q+2
       995: q+2
       997: q+2
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: q+2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1009: 2
      1011: q+2
      1013: 2
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 2
      1023: 2
      1025: 2
      1026: 1
      1027: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 2
      1039: 2
      1043: 2
      1044: 1
      1045: 1
      1047: 2
      1049: 2
      1051: q+2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1074: q+2
      1076: 2
      1077: 2
      1078: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1104: 1
      1105: 1
      1111: 1
      1113: 1
      1115: 1
      1117: 1
      1119: 1
      1121: 1
      1123: 1
      1125: 1
      1128: 1
      1129: 1
      1131: 1
      1132: 1
      1136: 1
      1137: 1
      1142: 2
      1143: q
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1157: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1173: 1
      1175: 1
      1186: 1
      1187: 1
      1192: 2
      1193: q
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1215: q+2
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1221: 2
      1223: q+2
      1225: 2
      1231: 2
      1234: 1
      1235: 1
      1237: 2
      1239: 2
      1240: 1
      1241: 1
      1249: 2
      1250: 1
      1251: 1
      1253: 2
      1257: 2
      1260: 1
      1261: 1
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 2
      1285: 2
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1297: 1
      1308: 1
      1309: 1
      1315: 1
      1317: 1
      1319: 1
      1321: 1
      1324: 1
      1325: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1338: 2
      1339: q
      1353: 1
      1355: 1
      1357: 1
      1359: 1
      1377: 1
      1379: 1
      1381: 1
      1383: 1
      1416: 1
      1417: 1
      1434: 1
      1437: 2
      1447: 2
      1449: 2
      1454: 1
      1455: 1
      1457: 2
      1460: 1
      1461: 1
      1465: 1
      1471: 1
      1473: 1
      1475: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1496: 1
      1539: 1
      1540: 1
      1561: 1
      1562: 1
      1568: 1
      1570: 1
      1584: 1
      1586: 1
      1635: 1
      1638: 2
      1642: 1
      1660: 1
      1662: 1
      1672: 1
      1673: 1
      1731: 1
      1732: 1
      1816: 1
      1818: 1
      1824: 1
      1959: 1

1960:    0: 2q^3+4q^2+4q+2
         1: 3q^3+4q^2+4q+2
         2: 2q^3+4q^2+4q+2
         3: 2q^3+4q^2+4q+2
         4: 2q^3+4q^2+4q+2
         5: 3q^3+4q^2+4q+2
         6: 3q^3+4q^2+4q+2
         7: 2q^3+4q^2+4q+2
         8: 3q^3+4q^2+4q+2
         9: 2q^3+4q^2+4q+2
        10: q^2+4q+2
        11: q^2+4q+2
        12: q^2+4q+2
        13: 2q^3+4q^2+4q+2
        14: 2q^3+4q^2+4q+2
        15: 3q^3+4q^2+4q+2
        16: 2q^3+4q^2+4q+2
        17: 3q^3+4q^2+4q+2
        18: 2q^3+4q^2+4q+2
        19: 2q^3+4q^2+4q+2
        20: 3q^3+4q^2+4q+2
        21: 2q^3+4q^2+4q+2
        22: q^3+3q^2+4q+2
        23: q^3+3q^2+4q+2
        24: q^3+3q^2+4q+2
        25: q^3+3q^2+4q+2
        26: q^3+3q^2+4q+2
        27: q^3+3q^2+4q+2
        28: q^2+4q+2
        29: q^2+4q+2
        30: 2q^3+4q^2+4q+2
        31: 4q+2
        32: q^3+3q^2+4q+2
        33: q^3+3q^2+4q+2
        34: 4q+2
        35: q^3+3q^2+4q+2
        36: q^3+3q^2+4q+2
        37: 2q+2
        38: 3q^2+2q
        39: 2q+2
        40: 3q^2+2q
        41: 2q+2
        42: 3q^2+2q
        43: q^2+4q+2
        44: q^2+4q+2
        45: q^2+4q+2
        46: 2q^3+4q^2+4q+2
        47: 3q^3+4q^2+4q+2
        48: 2q^3+4q^2+4q+2
        49: 2q^3+4q^2+4q+2
        50: 3q^3+4q^2+4q+2
        51: 2q^3+4q^2+4q+2
        52: q^3+3q^2+4q+2
        53: q^3+3q^2+4q+2
        54: q^3+3q^2+4q+2
        55: q^3+3q^2+4q+2
        56: q^3+3q^2+4q+2
        57: q^3+3q^2+4q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+2
        63: 2q
        64: 2q+2
        65: 3q^2+2q
        66: 2q+2
        67: 3q^2+2q
        68: q^2+4q+2
        69: 2q^3+4q^2+4q+2
        70: q^2+4q+2
        71: q^2+4q+2
        72: q^3+3q^2+4q+2
        73: q^3+3q^2+4q+2
        74: 2q+2
        75: 3q^2+2q
        76: 2q+2
        77: 3q^2+2q
        78: 2q+2
        79: 3q^2+2q
        80: 4q+2
        81: q^3+3q^2+4q+2
        82: 4q+2
        83: q^3+3q^2+4q+2
        84: 4q+2
        85: q^3+3q^2+4q+2
        86: 4q+2
        87: q^3+3q^2+4q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: q^2+4q+2
        91: 2q^3+4q^2+4q+2
        92: 3q^3+4q^2+4q+2
        93: 2q^3+4q^2+4q+2
        94: q^3+3q^2+4q+2
        95: q^3+3q^2+4q+2
        96: q^3+3q^2+4q+2
        97: q^3+3q^2+4q+2
        98: q^3+3q^2+4q+2
        99: q^3+3q^2+4q+2
       100: 2q^2+3q+2
       101: 3q^2+3q+2
       102: 2q^2+3q+2
       103: q+1
       104: q
       105: q
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 2q+2
       112: 3q^2+2q
       113: 2q+2
       114: 2q
       115: 2q+2
       116: 3q^2+2q
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+2
       122: 2q
       123: 2q+2
       124: 3q^2+2q
       125: q^2+4q+2
       126: q^2+4q+2
       127: 2q+2
       128: 3q^2+2q
       129: 2q+2
       130: 3q^2+2q
       131: 2q+2
       132: 3q^2+2q
       133: q^2+4q+2
       134: 2q^3+4q^2+4q+2
       135: q^3+3q^2+4q+2
       136: q^3+3q^2+4q+2
       137: 4q+2
       138: q^3+3q^2+4q+2
       139: 4q+2
       140: q^2+2q+2
       141: 4q+2
       142: q^3+3q^2+4q+2
       143: 4q+2
       144: q^3+3q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: q^3+3q^2+4q+2
       148: q^2+2q+2
       149: 3q+2
       150: 2q^2+3q+2
       151: q+2
       152: 2q^2+2q
       153: q+2
       154: 3q^2+2q
       155: q+2
       156: 2q^2+2q
       157: q^2+4q+2
       158: q^2+4q+2
       159: q^2+4q+2
       160: q^3+3q^2+4q+2
       161: q^3+3q^2+4q+2
       162: q^3+3q^2+4q+2
       163: q^3+3q^2+4q+2
       164: q^3+3q^2+4q+2
       165: q^3+3q^2+4q+2
       166: 2q^2+3q+2
       167: 3q^2+3q+2
       168: 2q^2+3q+2
       169: q+1
       170: q
       171: q
       172: q+1
       173: q+1
       174: q
       175: q
       176: q+1
       177: 2q+2
       178: 3q^2+2q
       179: 2q+2
       180: 2q
       181: 2q+2
       182: 3q^2+2q
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+2
       188: 3q^2+2q
       189: 2q+2
       190: 2q
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: 2
       198: q^2+2q
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 2
       206: q^2+2q
       207: 2q+2
       208: 2q
       209: q+2
       210: 2q
       211: q+2
       212: 2q^2+2q
       213: 2q+2
       214: 3q^2+2q
       215: 2q+2
       216: 3q^2+2q
       217: 2q+2
       218: 3q^2+2q
       219: q^2+4q+2
       220: q^2+4q+2
       221: q^2+4q+2
       222: 4q+2
       223: q^3+3q^2+4q+2
       224: 4q+2
       225: q^3+3q^2+4q+2
       226: 4q+2
       227: 4q+2
       228: q^3+3q^2+4q+2
       229: q^2+2q+2
       230: q^3+3q^2+4q+2
       231: 4q+2
       232: 4q+2
       233: q^3+3q^2+4q+2
       234: q^3+3q^2+4q+2
       235: q^2+2q+2
       236: 2q^2+3q+2
       237: q+2
       238: 2q^2+2q
       239: q+2
       240: 3q^2+2q
       241: q+2
       242: 2q^2+2q
       243: 3q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: 3q+2
       247: 2q^2+3q+2
       248: 3q^2+3q+2
       249: 2q^2+3q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: q+1
       260: q
       261: q
       262: q+1
       263: q+1
       264: q
       265: q
       266: q+1
       267: 1
       268: q
       269: 1
       270: q
       271: 1
       272: q
       273: 1
       274: q
       275: q+1
       276: q
       277: q
       278: q+1
       279: 2q+2
       280: 2q
       281: 2q+2
       282: 3q^2+2q
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 2q+2
       288: 2q
       289: 2q+2
       290: 3q^2+2q
       291: 2q+2
       292: 3q^2+2q
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+2
       298: 2q
       299: q+1
       300: q+1
       301: 2
       302: q^2+2q
       303: 2q+1
       304: 2q+1
       305: 2
       306: q^2+2q
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: 2
       312: q^2+2q
       313: 2
       314: q^2+2q
       315: q+2
       316: 2q^2+2q
       317: q+2
       318: 2q
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2
       324: 2q
       325: q+2
       326: 2q
       333: q^2+4q+2
       334: 4q+2
       335: 4q+2
       336: 2q^2+3q+2
       337: 3q+2
       338: q+2
       339: 2q^2+2q
       340: q+2
       341: 3q^2+2q
       342: q+2
       343: 2q^2+2q
       344: 4q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: q^2+2q+2
       349: 2q+2
       350: q^3+3q^2+4q+2
       351: q^2+2q+2
       352: 4q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: q^3+3q^2+4q+2
       357: 2
       358: q^2+2q+2
       359: q^2+2q+2
       360: q+2
       361: 2q^2+2q
       362: q+2
       363: 3q^2+2q
       364: q+2
       365: 2q^2+2q
       366: 3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 2q^2+3q+2
       372: 3q^2+3q+2
       373: 2q^2+3q+2
       374: q+2
       375: q+2
       376: q+2
       377: q+1
       378: q
       379: q
       380: q+1
       381: q+1
       382: q
       383: q
       384: q+1
       385: q+1
       386: q
       387: q
       388: q+1
       389: 1
       390: q
       391: 1
       392: q
       393: 1
       394: q
       395: q
       396: 1
       397: 1
       398: q
       399: 1
       400: q
       401: 1
       402: q
       403: q
       404: 1
       405: 1
       406: 1
       407: q
       408: q
       413: 2q+2
       414: 2q
       417: 2q+2
       418: 3q^2+2q
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+2
       424: 2q
       425: q+2
       426: 2q^2+2q
       427: q+2
       428: 2q
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 2
       434: q^2+2q
       435: 2
       436: q^2+2q
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: q+1
       444: q+1
       445: 2
       446: q^2+2q
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 2
       452: q^2+2q
       453: q+1
       454: q+1
       455: 2
       456: q^2+2q
       457: 1
       458: 1
       459: 2
       461: q+1
       462: q+1
       463: 2
       464: q^2+2q
       465: q+2
       466: 2q
       467: q+2
       468: 2q^2+2q
       469: q+2
       470: 2q
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2
       476: 2q
       477: 2
       478: 2q
       479: 2
       480: 2q
       481: 4q+2
       482: 4q+2
       483: 3q+2
       484: 3q+2
       485: q+2
       486: 2q^2+2q
       487: q+2
       488: 3q^2+2q
       489: q+2
       490: 2q^2+2q
       491: 2q^2+3q+2
       492: 2q+2
       493: 2
       494: 2q+2
       495: q^2+2q+2
       496: q^2+2q+2
       497: 2q+2
       498: 2q+2
       499: 2
       500: q^2+2q+2
       501: q^2+2q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 2q^2+3q+2
       516: 3q^2+3q+2
       517: 2q^2+3q+2
       518: q+2
       519: q+2
       520: q+2
       521: q+1
       522: q
       523: q
       524: q+1
       529: q+1
       530: q
       531: q
       532: q+1
       533: 1
       534: q
       535: q
       536: 1
       537: 1
       538: q
       539: 1
       540: q
       541: 1
       543: 1
       545: 1
       546: q
       547: 1
       548: q
       549: 1
       550: q
       551: q
       552: 1
       553: 1
       554: q
       555: 1
       556: q
       557: 1
       559: 1
       561: 1
       562: q
       563: 1
       564: q
       565: 1
       566: q
       567: q
       568: 1
       569: 1
       570: 1
       571: q
       572: q
       573: 1
       574: q
       575: 1
       576: q
       577: 2
       581: 2q
       585: 2q+2
       586: 2q
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: q+2
       598: 2q^2+2q
       599: q+2
       600: 2q
       601: q+2
       602: 2q
       603: 1
       604: 1
       605: 2
       606: q^2+2q
       607: q+1
       608: q+1
       609: 2
       613: 2
       614: q^2+2q
       615: q+1
       616: q+1
       617: 2
       618: q^2+2q
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       624: q^2+2q
       625: 2
       629: 2
       630: q^2+2q
       631: q+1
       632: q+1
       633: 2
       634: q^2+2q
       639: q+2
       640: 2q
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2
       646: 2q
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       652: 2q
       653: 2
       655: 2
       656: 2q
       657: 3q+2
       658: q+2
       659: 2q^2+2q
       660: q+2
       661: 3q^2+2q
       662: q+2
       663: 2q^2+2q
       664: 2q^2+3q+2
       665: 3q+2
       672: q+2
       673: q+2
       674: q^2+2q+2
       675: 2
       676: 2q+2
       677: 2
       678: 2
       679: q^2+2q+2
       680: q^2+2q+2
       681: 2q+2
       682: 2
       683: 2
       684: 2
       685: q^2+2q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: 1
       697: 1
       699: q
       700: q
       709: q+1
       710: q
       711: q
       712: q+1
       713: 1
       714: q
       715: q
       716: 1
       717: 1
       718: q
       719: q
       720: 1
       721: 1
       722: q
       723: 1
       724: q
       725: 1
       727: 1
       733: 1
       734: q
       735: 1
       736: q
       737: 1
       738: q
       739: 1
       740: q
       741: 1
       743: 1
       749: 1
       750: q
       751: 1
       752: q
       753: 1
       754: q
       755: q
       756: 1
       757: 1
       758: 1
       759: q
       760: q
       761: 1
       762: 1
       765: 1
       766: q
       767: q
       768: 1
       769: 2
       773: 2q
       775: q+2
       776: 2q
       779: q+2
       780: 2q^2+2q
       781: q+2
       782: 2q
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       791: 2
       792: 2q
       793: q+1
       794: q+1
       795: 2
       796: q^2+2q
       797: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2
       810: q^2+2q
       811: 2
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: 2
       820: q^2+2q
       821: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: 2
       834: q^2+2q
       835: 2
       839: 1
       840: 1
       843: 2
       844: 2q
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       850: 2q
       851: 2
       855: 1
       856: q
       857: 2
       865: q+2
       866: 3q+2
       867: q+2
       868: q+2
       869: 2
       870: q^2+2q+2
       871: 2
       872: 2
       873: 2
       874: q^2+2q+2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       884: 1
       889: 1
       890: q
       891: q
       900: 1
       901: q
       902: 1
       903: q
       904: 1
       905: q
       906: 1
       907: q
       908: 1
       909: q
       910: q
       911: 1
       916: 1
       917: q
       918: 1
       919: q
       920: 1
       922: 1
       928: 1
       930: 1
       940: 1
       941: q
       942: 1
       943: q
       944: 1
       946: 1
       948: 1
       950: 1
       960: 1
       961: 1
       962: q
       963: q
       964: 1
       965: q
       966: q
       967: 1
       968: 2
       972: 2q
       974: 1
       975: 1
       988: 1
       991: 1
       994: q+2
       995: 2q
       998: q+1
       999: q+1
      1000: q+1
      1001: q+1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 2
      1010: 2
      1011: 2q
      1012: 2
      1013: 2q
      1016: 1
      1017: 1
      1020: 2
      1021: q^2+2q
      1022: 2
      1026: 1
      1027: 1
      1032: 1
      1033: 1
      1036: 2
      1037: q^2+2q
      1038: 2
      1044: 1
      1045: 1
      1046: 2
      1048: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1065: q
      1072: q+2
      1073: q+2
      1074: q+2
      1075: 2
      1076: 2
      1077: 2
      1078: 2
      1079: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1091: 1
      1092: q
      1093: q
      1114: 1
      1115: q
      1116: 1
      1117: q
      1122: 1
      1123: q
      1124: 1
      1125: q
      1126: 1
      1127: 1
      1128: q
      1129: q
      1130: 1
      1131: q
      1132: q
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1142: 2q
      1156: 1
      1158: 1
      1172: 1
      1174: 1
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 2
      1224: 2
      1228: 1
      1229: 1
      1230: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1246: 1
      1247: 1
      1248: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1262: 2
      1266: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1279: q
      1280: 1
      1281: q
      1282: q+2
      1283: 2
      1284: 2
      1285: 2
      1286: 2
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1295: 1
      1296: q
      1297: q
      1326: 1
      1329: 1
      1330: 1
      1331: 1
      1356: 1
      1358: 1
      1380: 1
      1382: 1
      1410: 1
      1413: 1
      1430: 1
      1434: q
      1436: 2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 2
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1464: 1
      1474: 1
      1482: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 1
      1537: 1
      1538: 1
      1549: 1
      1552: 1
      1639: 2
      1641: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1659: 1
      1669: 1
      1673: 1
      1674: 1
      1733: 1
      1736: 1
      1817: 1
      1825: 1
      1833: 1
      1960: 1

1961:    0: 2q^3+4q^2+4q+2
         1: 3q^3+4q^2+4q+2
         2: 2q^3+4q^2+4q+2
         3: 2q^3+4q^2+4q+2
         4: 2q^3+4q^2+4q+2
         5: 3q^3+4q^2+4q+2
         6: 3q^3+4q^2+4q+2
         7: 2q^3+4q^2+4q+2
         8: 3q^3+4q^2+4q+2
         9: 2q^3+4q^2+4q+2
        10: q^2+4q+2
        11: q^2+4q+2
        12: q^2+4q+2
        13: 2q^3+4q^2+4q+2
        14: 2q^3+4q^2+4q+2
        15: 3q^3+4q^2+4q+2
        16: 2q^3+4q^2+4q+2
        17: 3q^3+4q^2+4q+2
        18: 2q^3+4q^2+4q+2
        19: 2q^3+4q^2+4q+2
        20: 3q^3+4q^2+4q+2
        21: 2q^3+4q^2+4q+2
        22: q^3+3q^2+4q+2
        23: q^3+3q^2+4q+2
        24: q^3+3q^2+4q+2
        25: q^3+3q^2+4q+2
        26: q^3+3q^2+4q+2
        27: q^3+3q^2+4q+2
        28: q^2+4q+2
        29: q^2+4q+2
        30: 2q^3+4q^2+4q+2
        31: 4q+2
        32: q^3+3q^2+4q+2
        33: q^3+3q^2+4q+2
        34: 4q+2
        35: q^3+3q^2+4q+2
        36: q^3+3q^2+4q+2
        37: 3q^2+2q
        38: 2q+2
        39: 3q^2+2q
        40: 2q+2
        41: 3q^2+2q
        42: 2q+2
        43: q^2+4q+2
        44: q^2+4q+2
        45: q^2+4q+2
        46: 2q^3+4q^2+4q+2
        47: 3q^3+4q^2+4q+2
        48: 2q^3+4q^2+4q+2
        49: 2q^3+4q^2+4q+2
        50: 3q^3+4q^2+4q+2
        51: 2q^3+4q^2+4q+2
        52: q^3+3q^2+4q+2
        53: q^3+3q^2+4q+2
        54: q^3+3q^2+4q+2
        55: q^3+3q^2+4q+2
        56: q^3+3q^2+4q+2
        57: q^3+3q^2+4q+2
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q
        63: 2q+2
        64: 3q^2+2q
        65: 2q+2
        66: 3q^2+2q
        67: 2q+2
        68: q^2+4q+2
        69: 2q^3+4q^2+4q+2
        70: q^2+4q+2
        71: q^2+4q+2
        72: q^3+3q^2+4q+2
        73: q^3+3q^2+4q+2
        74: 3q^2+2q
        75: 2q+2
        76: 3q^2+2q
        77: 2q+2
        78: 3q^2+2q
        79: 2q+2
        80: 4q+2
        81: q^3+3q^2+4q+2
        82: 4q+2
        83: q^3+3q^2+4q+2
        84: 4q+2
        85: q^3+3q^2+4q+2
        86: 4q+2
        87: q^3+3q^2+4q+2
        88: q^2+4q+2
        89: q^2+4q+2
        90: q^2+4q+2
        91: 2q^3+4q^2+4q+2
        92: 3q^3+4q^2+4q+2
        93: 2q^3+4q^2+4q+2
        94: q^3+3q^2+4q+2
        95: q^3+3q^2+4q+2
        96: q^3+3q^2+4q+2
        97: q^3+3q^2+4q+2
        98: q^3+3q^2+4q+2
        99: q^3+3q^2+4q+2
       100: 2q^2+3q+2
       101: 3q^2+3q+2
       102: 2q^2+3q+2
       103: q
       104: q+1
       105: q+1
       106: q
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 3q^2+2q
       112: 2q+2
       113: 2q
       114: 2q+2
       115: 3q^2+2q
       116: 2q+2
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q
       122: 2q+2
       123: 3q^2+2q
       124: 2q+2
       125: q^2+4q+2
       126: q^2+4q+2
       127: 3q^2+2q
       128: 2q+2
       129: 3q^2+2q
       130: 2q+2
       131: 3q^2+2q
       132: 2q+2
       133: q^2+4q+2
       134: 2q^3+4q^2+4q+2
       135: q^3+3q^2+4q+2
       136: q^3+3q^2+4q+2
       137: 4q+2
       138: q^3+3q^2+4q+2
       139: 4q+2
       140: q^2+2q+2
       141: 4q+2
       142: q^3+3q^2+4q+2
       143: 4q+2
       144: q^3+3q^2+4q+2
       145: 4q+2
       146: 4q+2
       147: q^3+3q^2+4q+2
       148: q^2+2q+2
       149: 3q+2
       150: 2q^2+3q+2
       151: 2q^2+2q
       152: q+2
       153: 3q^2+2q
       154: q+2
       155: 2q^2+2q
       156: q+2
       157: q^2+4q+2
       158: q^2+4q+2
       159: q^2+4q+2
       160: q^3+3q^2+4q+2
       161: q^3+3q^2+4q+2
       162: q^3+3q^2+4q+2
       163: q^3+3q^2+4q+2
       164: q^3+3q^2+4q+2
       165: q^3+3q^2+4q+2
       166: 2q^2+3q+2
       167: 3q^2+3q+2
       168: 2q^2+3q+2
       169: q
       170: q+1
       171: q+1
       172: q
       173: q
       174: q+1
       175: q+1
       176: q
       177: 3q^2+2q
       178: 2q+2
       179: 2q
       180: 2q+2
       181: 3q^2+2q
       182: 2q+2
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 3q^2+2q
       188: 2q+2
       189: 2q
       190: 2q+2
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: 2q+1
       197: q^2+2q
       198: 2
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: q^2+2q
       206: 2
       207: 2q
       208: 2q+2
       209: 2q
       210: q+2
       211: 2q^2+2q
       212: q+2
       213: 3q^2+2q
       214: 2q+2
       215: 3q^2+2q
       216: 2q+2
       217: 3q^2+2q
       218: 2q+2
       219: q^2+4q+2
       220: q^2+4q+2
       221: q^2+4q+2
       222: 4q+2
       223: q^3+3q^2+4q+2
       224: 4q+2
       225: q^3+3q^2+4q+2
       226: 4q+2
       227: 4q+2
       228: q^3+3q^2+4q+2
       229: q^2+2q+2
       230: q^3+3q^2+4q+2
       231: 4q+2
       232: 4q+2
       233: q^3+3q^2+4q+2
       234: q^3+3q^2+4q+2
       235: q^2+2q+2
       236: 2q^2+3q+2
       237: 2q^2+2q
       238: q+2
       239: 3q^2+2q
       240: q+2
       241: 2q^2+2q
       242: q+2
       243: 3q+2
       244: q^2+2q+2
       245: q^2+2q+2
       246: 3q+2
       247: 2q^2+3q+2
       248: 3q^2+3q+2
       249: 2q^2+3q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: 2q^2+3q+2
       257: 3q^2+3q+2
       258: 2q^2+3q+2
       259: q
       260: q+1
       261: q+1
       262: q
       263: q
       264: q+1
       265: q+1
       266: q
       267: q
       268: 1
       269: q
       270: 1
       271: q
       272: 1
       273: q
       274: 1
       275: q
       276: q+1
       277: q+1
       278: q
       279: 2q
       280: 2q+2
       281: 3q^2+2q
       282: 2q+2
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: 2q
       288: 2q+2
       289: 3q^2+2q
       290: 2q+2
       291: 3q^2+2q
       292: 2q+2
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q
       298: 2q+2
       299: q+1
       300: q+1
       301: q^2+2q
       302: 2
       303: 2q+1
       304: 2q+1
       305: q^2+2q
       306: 2
       307: 2q+1
       308: 2q+1
       309: q+1
       310: q+1
       311: q^2+2q
       312: 2
       313: q^2+2q
       314: 2
       315: 2q^2+2q
       316: q+2
       317: 2q
       318: q+2
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q
       324: 2
       325: 2q
       326: q+2
       333: q^2+4q+2
       334: 4q+2
       335: 4q+2
       336: 2q^2+3q+2
       337: 3q+2
       338: 2q^2+2q
       339: q+2
       340: 3q^2+2q
       341: q+2
       342: 2q^2+2q
       343: q+2
       344: 4q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: q^2+2q+2
       349: 2q+2
       350: q^3+3q^2+4q+2
       351: q^2+2q+2
       352: 4q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: q^3+3q^2+4q+2
       357: 2
       358: q^2+2q+2
       359: q^2+2q+2
       360: 2q^2+2q
       361: q+2
       362: 3q^2+2q
       363: q+2
       364: 2q^2+2q
       365: q+2
       366: 3q+2
       367: 3q+2
       368: 2q^2+3q+2
       369: q^2+2q+2
       370: q^2+2q+2
       371: 2q^2+3q+2
       372: 3q^2+3q+2
       373: 2q^2+3q+2
       374: q+2
       375: q+2
       376: q+2
       377: q
       378: q+1
       379: q+1
       380: q
       381: q
       382: q+1
       383: q+1
       384: q
       385: q
       386: q+1
       387: q+1
       388: q
       389: q
       390: 1
       391: q
       392: 1
       393: q
       394: 1
       395: 1
       396: q
       397: q
       398: 1
       399: q
       400: 1
       401: q
       402: 1
       403: 1
       404: q
       405: q
       406: q
       407: 1
       408: 1
       413: 2q
       414: 2q+2
       417: 3q^2+2q
       418: 2q+2
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q
       424: 2q+2
       425: 2q^2+2q
       426: q+2
       427: 2q
       428: q+2
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: q^2+2q
       434: 2
       435: q^2+2q
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: q+1
       444: q+1
       445: q^2+2q
       446: 2
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: q^2+2q
       452: 2
       453: q+1
       454: q+1
       455: q^2+2q
       456: 2
       457: 1
       458: 1
       460: 2
       461: q+1
       462: q+1
       463: q^2+2q
       464: 2
       465: 2q
       466: q+2
       467: 2q^2+2q
       468: q+2
       469: 2q
       470: q+2
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: 2q
       476: 2
       477: 2q
       478: 2
       479: 2q
       480: 2
       481: 4q+2
       482: 4q+2
       483: 3q+2
       484: 3q+2
       485: 2q^2+2q
       486: q+2
       487: 3q^2+2q
       488: q+2
       489: 2q^2+2q
       490: q+2
       491: 2q^2+3q+2
       492: 2q+2
       493: 2
       494: 2q+2
       495: q^2+2q+2
       496: q^2+2q+2
       497: 2q+2
       498: 2q+2
       499: 2
       500: q^2+2q+2
       501: q^2+2q+2
       508: 3q+2
       509: q+2
       510: q+2
       511: 2
       512: q^2+2q+2
       513: 2
       514: q^2+2q+2
       515: 2q^2+3q+2
       516: 3q^2+3q+2
       517: 2q^2+3q+2
       518: q+2
       519: q+2
       520: q+2
       521: q
       522: q+1
       523: q+1
       524: q
       529: q
       530: q+1
       531: q+1
       532: q
       533: q
       534: 1
       535: 1
       536: q
       537: q
       538: 1
       539: q
       540: 1
       542: 1
       544: 1
       545: q
       546: 1
       547: q
       548: 1
       549: q
       550: 1
       551: 1
       552: q
       553: q
       554: 1
       555: q
       556: 1
       558: 1
       560: 1
       561: q
       562: 1
       563: q
       564: 1
       565: q
       566: 1
       567: 1
       568: q
       569: q
       570: q
       571: 1
       572: 1
       573: q
       574: 1
       575: q
       576: 1
       577: 2q
       581: 2
       585: 2q
       586: 2q+2
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: 2q^2+2q
       598: q+2
       599: 2q
       600: q+2
       601: 2q
       602: q+2
       603: 1
       604: 1
       605: q^2+2q
       606: 2
       607: q+1
       608: q+1
       610: 2
       613: q^2+2q
       614: 2
       615: q+1
       616: q+1
       617: q^2+2q
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: q^2+2q
       624: 2
       626: 2
       629: q^2+2q
       630: 2
       631: q+1
       632: q+1
       633: q^2+2q
       634: 2
       639: 2q
       640: q+2
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2q
       652: 2
       654: 2
       655: 2q
       656: 2
       657: 3q+2
       658: 2q^2+2q
       659: q+2
       660: 3q^2+2q
       661: q+2
       662: 2q^2+2q
       663: q+2
       664: 2q^2+3q+2
       665: 3q+2
       672: q+2
       673: q+2
       674: q^2+2q+2
       675: 2
       676: 2q+2
       677: 2
       678: 2
       679: q^2+2q+2
       680: q^2+2q+2
       681: 2q+2
       682: 2
       683: 2
       684: 2
       685: q^2+2q+2
       686: q+2
       687: 2
       688: 2
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: q
       697: q
       699: 1
       700: 1
       709: q
       710: q+1
       711: q+1
       712: q
       713: q
       714: 1
       715: 1
       716: q
       717: q
       718: 1
       719: 1
       720: q
       721: q
       722: 1
       723: q
       724: 1
       726: 1
       728: 1
       733: q
       734: 1
       735: q
       736: 1
       737: q
       738: 1
       739: q
       740: 1
       742: 1
       744: 1
       749: q
       750: 1
       751: q
       752: 1
       753: q
       754: 1
       755: 1
       756: q
       757: q
       758: q
       759: 1
       760: 1
       763: 1
       764: 1
       765: q
       766: 1
       767: 1
       768: q
       769: 2q
       773: 2
       775: 2q
       776: q+2
       779: 2q^2+2q
       780: q+2
       781: 2q
       782: q+2
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       791: 2q
       792: 2
       793: q+1
       794: q+1
       795: q^2+2q
       796: 2
       798: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q^2+2q
       810: 2
       812: 2
       815: 1
       816: 1
       817: q+1
       818: q+1
       819: q^2+2q
       820: 2
       822: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: q^2+2q
       834: 2
       836: 2
       839: 1
       840: 1
       843: 2q
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2q
       850: 2
       852: 2
       855: q
       856: 1
       858: 2
       865: q+2
       866: 3q+2
       867: q+2
       868: q+2
       869: 2
       870: q^2+2q+2
       871: 2
       872: 2
       873: 2
       874: q^2+2q+2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       884: q
       889: q
       890: 1
       891: 1
       900: q
       901: 1
       902: q
       903: 1
       904: q
       905: 1
       906: q
       907: 1
       908: q
       909: 1
       910: 1
       911: q
       916: q
       917: 1
       918: q
       919: 1
       921: 1
       923: 1
       929: 1
       931: 1
       940: q
       941: 1
       942: q
       943: 1
       945: 1
       947: 1
       949: 1
       951: 1
       960: q
       961: q
       962: 1
       963: 1
       964: q
       965: 1
       966: 1
       967: q
       968: 2q
       972: 2
       976: 1
       977: 1
       989: 1
       990: 1
       994: 2q
       995: q+2
       998: q+1
       999: q+1
      1000: q+1
      1001: q+1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1009: 2
      1010: 2q
      1011: 2
      1012: 2q
      1013: 2
      1016: 1
      1017: 1
      1020: q^2+2q
      1021: 2
      1023: 2
      1026: 1
      1027: 1
      1032: 1
      1033: 1
      1036: q^2+2q
      1037: 2
      1039: 2
      1044: 1
      1045: 1
      1047: 2
      1049: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1072: q+2
      1073: q+2
      1074: q+2
      1075: 2
      1076: 2
      1077: 2
      1078: 2
      1079: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1091: q
      1092: 1
      1093: 1
      1114: q
      1115: 1
      1116: q
      1117: 1
      1122: q
      1123: 1
      1124: q
      1125: 1
      1126: q
      1127: q
      1128: 1
      1129: 1
      1130: q
      1131: 1
      1132: 1
      1133: q
      1136: 1
      1137: 1
      1138: 2q
      1142: 2
      1157: 1
      1159: 1
      1173: 1
      1175: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1221: 2
      1225: 2
      1228: 1
      1229: 1
      1231: 2
      1234: 1
      1235: 1
      1240: 1
      1241: 1
      1246: 1
      1247: 1
      1249: 2
      1250: 1
      1251: 1
      1260: 1
      1261: 1
      1263: 2
      1267: 1
      1274: q
      1275: 1
      1277: 1
      1278: q
      1279: 1
      1280: q
      1281: 1
      1282: q+2
      1283: 2
      1284: 2
      1285: 2
      1286: 2
      1287: 1
      1288: 1
      1289: 1
      1290: q
      1295: q
      1296: 1
      1297: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1357: 1
      1359: 1
      1381: 1
      1383: 1
      1411: 1
      1412: 1
      1430: q
      1434: 1
      1437: 2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1445: 2
      1454: 1
      1455: 1
      1460: 1
      1461: 1
      1465: 1
      1475: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 1
      1539: 1
      1540: 1
      1550: 1
      1551: 1
      1640: 2
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1660: 1
      1670: 1
      1673: 1
      1674: 1
      1734: 1
      1735: 1
      1818: 1
      1826: 1
      1833: 1
      1961: 1

1962:    0: q^3+6q^2+6q+2
         1: q^3+6q^2+6q+2
         2: q^3+6q^2+6q+2
         3: q^3+6q^2+6q+2
         4: q^3+6q^2+6q+2
         5: q^3+6q^2+6q+2
         6: q^3+6q^2+6q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+3q^3+5q^2+4q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+6q^2+6q+2
        14: q^3+6q^2+6q+2
        15: q^3+6q^2+6q+2
        16: 4q^2+6q+2
        17: 4q^2+6q+2
        18: q^3+5q^2+4q+2
        19: q^3+6q^2+6q+2
        20: q^3+6q^2+6q+2
        21: q^3+6q^2+6q+2
        22: q^3+6q^2+6q+2
        23: q^3+6q^2+6q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: 4q^2+6q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+6q^2+6q+2
        31: 4q^2+6q+2
        32: q^3+6q^2+6q+2
        33: 4q^2+6q+2
        34: 2q^2+6q+2
        35: 4q^2+6q+2
        36: 2q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: q^3+5q^2+4q+2
        49: 4q^2+6q+2
        50: 4q^2+6q+2
        51: q^3+5q^2+4q+2
        52: q^3+6q^2+6q+2
        53: q^3+6q^2+6q+2
        54: q^3+6q^2+6q+2
        55: 4q^2+6q+2
        56: 4q^2+6q+2
        57: 4q^2+6q+2
        58: 2q^2+4q+2
        59: 2q
        60: 3q+1
        61: 3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+6q+2
        69: 3q^2+4q+2
        70: 4q^2+6q+2
        71: 2q^2+6q+2
        72: 2q^2+6q+2
        73: 4q^2+6q+2
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 4q^2+6q+2
        81: 4q^2+6q+2
        82: 4q^2+6q+2
        83: q^3+6q^2+6q+2
        84: 2q^2+6q+2
        85: 2q^2+6q+2
        86: 2q^2+6q+2
        87: 4q^2+6q+2
        88: q^2+6q+2
        89: q^2+6q+2
        90: 3q^2+4q+2
        91: 4q^2+6q+2
        92: 4q^2+6q+2
        93: q^3+5q^2+4q+2
        94: 4q^2+6q+2
        95: 4q^2+6q+2
        96: q^3+5q^2+4q+2
        97: q^2+6q+2
        98: q^2+6q+2
        99: 3q^2+4q+2
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 4q^2+6q+2
       103: 2q+1
       104: q
       105: 2q+1
       106: q
       107: 3q+1
       108: 3q+1
       109: 2q^2+4q+2
       110: 2q
       111: q^2+3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 2q^2+4q+2
       118: 2q
       119: 3q+1
       120: 3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+6q+2
       126: q^2+4q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 2q^2+6q+2
       134: 3q^2+4q+2
       135: 2q^2+6q+2
       136: 4q^2+6q+2
       137: q^2+6q+2
       138: 3q^2+4q+2
       139: 2q^2+6q+2
       140: 2q^2+6q+2
       141: 4q^2+6q+2
       142: 4q^2+6q+2
       143: 6q+2
       144: q^2+4q+2
       145: 6q+2
       146: 2q^2+6q+2
       147: q^2+6q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 4q^2+6q+2
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: q^2+6q+2
       158: q^2+6q+2
       159: 3q^2+4q+2
       160: 4q^2+6q+2
       161: 4q^2+6q+2
       162: q^3+5q^2+4q+2
       163: q^2+6q+2
       164: q^2+6q+2
       165: 3q^2+4q+2
       166: q^2+6q+2
       167: q^2+6q+2
       168: 3q^2+4q+2
       169: 2q+1
       170: q
       171: 2q+1
       172: q
       173: 2q+1
       174: q
       175: 2q+1
       176: q
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 3q+1
       184: 3q+1
       185: 2q^2+4q+2
       186: 2q
       187: q^2+3q+1
       188: q^2+3q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: q^2+4q+2
       192: 2q
       193: 3q+1
       194: 3q+1
       195: 2q^2+4q+2
       196: 2q
       197: q^2+3q+1
       198: q^2+3q+1
       199: 3q+1
       200: 3q+1
       201: 3q+1
       202: 3q+1
       203: 4q+2
       205: 2q+1
       206: 2q+1
       207: 3q+1
       208: 3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+4q+2
       220: q^2+6q+2
       221: q^2+4q+2
       222: 6q+2
       223: q^2+4q+2
       224: q^2+6q+2
       225: 3q^2+4q+2
       226: q^2+4q+2
       227: 2q^2+6q+2
       228: 3q^2+4q+2
       229: 2q^2+6q+2
       230: 4q^2+6q+2
       231: 4q+2
       232: 6q+2
       233: q^2+4q+2
       234: q^2+6q+2
       235: 4q+2
       236: q^2+4q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: q^2+6q+2
       245: 4q+2
       246: 2q^2+6q+2
       247: q^2+6q+2
       248: q^2+6q+2
       249: 3q^2+4q+2
       250: q^2+6q+2
       251: q^2+6q+2
       252: 3q^2+4q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: q^2+6q+2
       257: q^2+6q+2
       258: 3q^2+4q+2
       259: q+1
       260: q
       261: q+1
       262: q
       263: 2q+1
       264: q
       265: 2q+1
       266: q
       267: 2q+1
       268: q
       269: q
       270: 2q+1
       271: 2q+1
       272: 2q+1
       275: 2q+1
       276: q
       277: 2q+1
       278: q
       279: 2q+1
       280: 2q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q^2+2q+2
       287: q+1
       288: q+1
       289: 2q+1
       290: 2q+1
       291: q+1
       292: q+1
       293: 3q+1
       294: 3q+1
       295: q^2+4q+2
       296: 2q
       297: 3q+1
       298: 3q+1
       299: 3q+1
       300: 3q+1
       301: 2q+1
       302: 2q+1
       303: 2q^2+4q+2
       304: 2q
       305: q^2+3q+1
       306: q^2+3q+1
       307: 3q+1
       308: 3q+1
       309: 4q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 3q+1
       320: 3q+1
       321: 4q+2
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: q^2+4q+2
       334: 4q+2
       335: q^2+4q+2
       336: q^2+4q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q^2+4q+2
       345: q^2+6q+2
       346: q^2+4q+2
       347: 6q+2
       348: q^2+4q+2
       349: q^2+6q+2
       350: 3q^2+4q+2
       351: q^2+6q+2
       352: 4q+2
       353: 4q+2
       354: 3q+2
       355: 4q+2
       356: q^2+4q+2
       357: 2q+2
       358: 2q+2
       359: 4q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q^2+q+1
       365: q^2+q+1
       366: 4q+2
       367: 6q+2
       368: q^2+4q+2
       369: q^2+6q+2
       370: 4q+2
       371: q^2+6q+2
       372: q^2+6q+2
       373: 3q^2+4q+2
       374: 4q+2
       375: 4q+2
       376: q^2+3q+2
       377: 1
       379: 1
       381: q+1
       382: q
       383: q+1
       384: q
       385: 2q+1
       386: q
       387: 2q+1
       388: q
       389: q+1
       390: q
       391: q
       392: q+1
       393: 2q+1
       394: q
       395: 2q+1
       396: q
       397: q+1
       398: q+1
       401: 2q+1
       402: 2q+1
       405: 2q+1
       408: 2q+1
       413: q+1
       414: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q^2+2q+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: q+1
       431: q^2+2q+2
       433: q+1
       434: q+1
       435: 2q+1
       436: 2q+1
       437: 3q+1
       438: 3q+1
       439: q^2+4q+2
       440: 2q
       441: 3q+1
       442: 3q+1
       443: 3q+1
       444: 3q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: q+1
       449: 2q+2
       451: 1
       452: 1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+2
       459: q+1
       460: q+1
       461: 4q+2
       463: q+1
       464: q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 3q+1
       472: 3q+1
       473: 4q+2
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: 4q+2
       482: q^2+4q+2
       483: 4q+2
       484: 6q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q^2+q+1
       490: q^2+q+1
       491: q^2+4q+2
       492: q^2+4q+2
       493: 4q+2
       494: q^2+4q+2
       495: q^2+4q+2
       496: q^2+6q+2
       497: 3q+2
       498: 3q+2
       499: q+2
       500: 2q+2
       501: 4q+2
       508: 4q+2
       509: 4q+2
       510: 3q+2
       511: 4q+2
       512: q^2+4q+2
       513: 2q+2
       514: 2q+2
       515: 2q+4
       516: 2q+4
       517: 2q+4
       518: 4q+2
       519: 4q+2
       520: q^2+3q+2
       521: 1
       523: 1
       529: 1
       531: 1
       533: 1
       535: 1
       537: q+1
       538: q
       539: q
       540: q+1
       541: 2q+1
       542: q
       543: q
       544: 2q+1
       545: q+1
       546: q
       547: q
       548: q+1
       549: 1
       550: 1
       553: q+1
       554: q+1
       557: q+1
       558: q+1
       561: q+1
       562: q+1
       565: 2q+1
       567: 2q+1
       569: q+1
       572: q+1
       573: 2q+1
       576: 2q+1
       577: q+1
       581: q+1
       585: q+1
       586: q+1
       589: q+1
       590: q+1
       591: 2q+2
       593: q+1
       594: q+1
       595: q^2+2q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q^2+2q+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: 3q+1
       616: 3q+1
       617: 2q+1
       618: 2q+1
       619: q+1
       620: q+1
       621: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 4q+2
       633: q+1
       634: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: 2q+2
       645: 1
       646: 1
       647: 2q+1
       648: 2q+1
       649: 2q+2
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 2q+1
       656: 2q+1
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+2
       663: q+2
       664: 2q+4
       665: 4q+2
       672: 4q+2
       673: 3q+2
       674: 2q+4
       675: 4q+2
       676: q^2+4q+2
       677: 4q+2
       678: 4q+2
       679: q^2+4q+2
       680: 4
       681: 3q+2
       682: q+2
       683: q+2
       684: 2q+2
       685: 2q+2
       686: 3q+2
       687: 3q+2
       688: q+2
       689: 2q+2
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       700: q+1
       709: 1
       711: 1
       713: 1
       714: 1
       717: 1
       719: 1
       721: 1
       724: 1
       725: 1
       728: 1
       733: q+1
       734: q
       735: q
       736: q+1
       737: 1
       738: 1
       741: 1
       742: 1
       749: q+1
       750: q+1
       753: 1
       755: 1
       757: q+1
       760: q+1
       761: q+1
       764: q+1
       765: 2q+1
       767: 2q+1
       769: q+1
       773: q+1
       775: 2
       776: 2
       779: q+2
       780: q+2
       781: q+1
       782: q+1
       785: q+1
       786: q+1
       787: 2q+2
       791: 1
       792: 1
       793: 2
       794: 2
       795: q+2
       796: q+2
       797: q+1
       798: q+1
       801: q+1
       802: q+1
       803: 2q+2
       805: q+1
       806: q+1
       807: q^2+2q+2
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       815: 2q+1
       816: 2q+1
       817: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       827: q+2
       831: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       839: 2q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       847: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 4
       867: q+2
       868: 3q+2
       869: q+2
       870: 2q+4
       871: 4q+2
       872: 3q+2
       873: 2
       874: 4
       875: q+2
       876: q+2
       877: 3q+2
       878: q+2
       879: q+2
       880: 2q+2
       881: q+2
       882: q+2
       883: q+2
       884: q+1
       891: q+1
       900: 1
       901: 1
       904: 1
       907: 1
       908: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       925: 1
       928: 1
       931: 1
       940: 2
       941: 2
       944: 1
       945: 1
       948: 1
       949: 1
       960: 1
       963: 1
       964: 2
       966: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       977: 1
       988: q+1
       990: q+1
       994: 2
       995: 2
       998: 4
      1000: 2
      1001: 2
      1004: q+1
      1005: q+1
      1006: q+2
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 2
      1013: 2
      1016: 1
      1017: 1
      1020: q+2
      1021: q+2
      1022: q+1
      1023: q+1
      1026: q+1
      1027: q+1
      1028: 2q+2
      1032: 2
      1036: 2
      1037: 2
      1038: 1
      1039: 1
      1044: q+2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1054: q+2
      1058: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 4
      1077: q+2
      1078: 3q+2
      1079: 2
      1080: 2
      1081: 2
      1082: q+2
      1083: q+2
      1084: 4
      1085: q+2
      1086: 1
      1087: 1
      1090: 1
      1093: 1
      1114: 2
      1115: 2
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 2
      1132: 2
      1134: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1152: 1
      1153: 1
      1156: 1
      1159: 1
      1160: 1
      1161: 1
      1172: 1
      1173: 1
      1194: 1
      1196: 1
      1198: 1
      1201: 1
      1202: 1
      1203: 1
      1216: 2
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1224: 1
      1225: 1
      1228: 1
      1229: 1
      1230: 2
      1231: 2
      1232: 4
      1234: 2
      1235: 2
      1240: q+1
      1241: q+1
      1242: q+2
      1246: 2
      1248: 1
      1249: 1
      1250: 2
      1260: q+2
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1270: q+2
      1274: 2
      1275: 2
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 2
      1281: 2
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 2
      1288: 2
      1289: q+2
      1290: 1
      1291: 1
      1294: 1
      1297: 1
      1326: 1
      1328: 1
      1330: 1
      1333: 1
      1348: 2
      1349: 2
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1362: 1
      1364: 2
      1365: 2
      1368: 1
      1370: 1
      1380: 1
      1381: 1
      1410: 1
      1412: 1
      1418: 1
      1419: 1
      1430: 1
      1431: 1
      1433: 1
      1434: 1
      1440: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1450: 2
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1466: 2
      1474: 1
      1475: 1
      1478: q+2
      1482: 1
      1483: 1
      1484: 2
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1501: 1
      1502: 1
      1504: 1
      1507: 1
      1549: 1
      1551: 1
      1575: 1
      1576: 1
      1579: 1
      1581: 1
      1607: 1
      1608: 1
      1641: 1
      1642: 1
      1645: 2
      1647: 1
      1648: 1
      1649: 2
      1653: 1
      1663: 1
      1669: 1
      1670: 1
      1673: 1
      1674: 1
      1749: 1
      1750: 1
      1757: 1
      1758: 1
      1819: 1
      1829: 1
      1833: 1
      1962: 1

1963:    0: q^3+6q^2+6q+2
         1: q^3+6q^2+6q+2
         2: q^3+6q^2+6q+2
         3: q^3+6q^2+6q+2
         4: q^3+6q^2+6q+2
         5: q^3+6q^2+6q+2
         6: q^3+6q^2+6q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+3q^3+5q^2+4q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+6q^2+6q+2
        14: q^3+6q^2+6q+2
        15: q^3+6q^2+6q+2
        16: 4q^2+6q+2
        17: 4q^2+6q+2
        18: q^3+5q^2+4q+2
        19: q^3+6q^2+6q+2
        20: q^3+6q^2+6q+2
        21: q^3+6q^2+6q+2
        22: q^3+6q^2+6q+2
        23: q^3+6q^2+6q+2
        24: q^3+6q^2+6q+2
        25: 4q^2+6q+2
        26: 4q^2+6q+2
        27: 4q^2+6q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+6q^2+6q+2
        31: 4q^2+6q+2
        32: q^3+6q^2+6q+2
        33: 4q^2+6q+2
        34: 2q^2+6q+2
        35: 4q^2+6q+2
        36: 2q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: q^3+5q^2+4q+2
        49: 4q^2+6q+2
        50: 4q^2+6q+2
        51: q^3+5q^2+4q+2
        52: q^3+6q^2+6q+2
        53: q^3+6q^2+6q+2
        54: q^3+6q^2+6q+2
        55: 4q^2+6q+2
        56: 4q^2+6q+2
        57: 4q^2+6q+2
        58: 2q
        59: 2q^2+4q+2
        60: 3q+1
        61: 3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+6q+2
        69: 3q^2+4q+2
        70: 4q^2+6q+2
        71: 2q^2+6q+2
        72: 2q^2+6q+2
        73: 4q^2+6q+2
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 4q^2+6q+2
        81: 4q^2+6q+2
        82: 4q^2+6q+2
        83: q^3+6q^2+6q+2
        84: 2q^2+6q+2
        85: 2q^2+6q+2
        86: 2q^2+6q+2
        87: 4q^2+6q+2
        88: q^2+6q+2
        89: q^2+6q+2
        90: 3q^2+4q+2
        91: 4q^2+6q+2
        92: 4q^2+6q+2
        93: q^3+5q^2+4q+2
        94: 4q^2+6q+2
        95: 4q^2+6q+2
        96: q^3+5q^2+4q+2
        97: q^2+6q+2
        98: q^2+6q+2
        99: 3q^2+4q+2
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 4q^2+6q+2
       103: q
       104: 2q+1
       105: q
       106: 2q+1
       107: 3q+1
       108: 3q+1
       109: 2q
       110: 2q^2+4q+2
       111: q^2+3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 2q
       118: 2q^2+4q+2
       119: 3q+1
       120: 3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+6q+2
       126: q^2+4q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 2q^2+6q+2
       134: 3q^2+4q+2
       135: 2q^2+6q+2
       136: 4q^2+6q+2
       137: q^2+6q+2
       138: 3q^2+4q+2
       139: 2q^2+6q+2
       140: 2q^2+6q+2
       141: 4q^2+6q+2
       142: 4q^2+6q+2
       143: 6q+2
       144: q^2+4q+2
       145: 6q+2
       146: 2q^2+6q+2
       147: q^2+6q+2
       148: 4q+2
       149: 2q^2+6q+2
       150: 4q^2+6q+2
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: q^2+6q+2
       158: q^2+6q+2
       159: 3q^2+4q+2
       160: 4q^2+6q+2
       161: 4q^2+6q+2
       162: q^3+5q^2+4q+2
       163: q^2+6q+2
       164: q^2+6q+2
       165: 3q^2+4q+2
       166: q^2+6q+2
       167: q^2+6q+2
       168: 3q^2+4q+2
       169: q
       170: 2q+1
       171: q
       172: 2q+1
       173: q
       174: 2q+1
       175: q
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 3q+1
       184: 3q+1
       185: 2q
       186: 2q^2+4q+2
       187: q^2+3q+1
       188: q^2+3q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 2q
       192: q^2+4q+2
       193: 3q+1
       194: 3q+1
       195: 2q
       196: 2q^2+4q+2
       197: q^2+3q+1
       198: q^2+3q+1
       199: 3q+1
       200: 3q+1
       201: 3q+1
       202: 3q+1
       204: 4q+2
       205: 2q+1
       206: 2q+1
       207: 3q+1
       208: 3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+4q+2
       220: q^2+6q+2
       221: q^2+4q+2
       222: 6q+2
       223: q^2+4q+2
       224: q^2+6q+2
       225: 3q^2+4q+2
       226: q^2+4q+2
       227: 2q^2+6q+2
       228: 3q^2+4q+2
       229: 2q^2+6q+2
       230: 4q^2+6q+2
       231: 4q+2
       232: 6q+2
       233: q^2+4q+2
       234: q^2+6q+2
       235: 4q+2
       236: q^2+4q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: q^2+6q+2
       245: 4q+2
       246: 2q^2+6q+2
       247: q^2+6q+2
       248: q^2+6q+2
       249: 3q^2+4q+2
       250: q^2+6q+2
       251: q^2+6q+2
       252: 3q^2+4q+2
       253: 4q+2
       254: 4q+2
       255: q^2+3q+2
       256: q^2+6q+2
       257: q^2+6q+2
       258: 3q^2+4q+2
       259: q
       260: q+1
       261: q
       262: q+1
       263: q
       264: 2q+1
       265: q
       266: 2q+1
       267: q
       268: 2q+1
       269: 2q+1
       270: q
       273: 2q+1
       274: 2q+1
       275: q
       276: 2q+1
       277: q
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       286: q^2+2q+2
       287: q+1
       288: q+1
       289: 2q+1
       290: 2q+1
       291: q+1
       292: q+1
       293: 3q+1
       294: 3q+1
       295: 2q
       296: q^2+4q+2
       297: 3q+1
       298: 3q+1
       299: 3q+1
       300: 3q+1
       301: 2q+1
       302: 2q+1
       303: 2q
       304: 2q^2+4q+2
       305: q^2+3q+1
       306: q^2+3q+1
       307: 3q+1
       308: 3q+1
       310: 4q+2
       311: q+1
       312: q+1
       313: 2q+1
       314: 2q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 3q+1
       320: 3q+1
       322: 4q+2
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: q^2+4q+2
       334: 4q+2
       335: q^2+4q+2
       336: q^2+4q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q^2+4q+2
       345: q^2+6q+2
       346: q^2+4q+2
       347: 6q+2
       348: q^2+4q+2
       349: q^2+6q+2
       350: 3q^2+4q+2
       351: q^2+6q+2
       352: 4q+2
       353: 4q+2
       354: 3q+2
       355: 4q+2
       356: q^2+4q+2
       357: 2q+2
       358: 2q+2
       359: 4q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q^2+q+1
       365: q^2+q+1
       366: 4q+2
       367: 6q+2
       368: q^2+4q+2
       369: q^2+6q+2
       370: 4q+2
       371: q^2+6q+2
       372: q^2+6q+2
       373: 3q^2+4q+2
       374: 4q+2
       375: 4q+2
       376: q^2+3q+2
       378: 1
       380: 1
       381: q
       382: q+1
       383: q
       384: q+1
       385: q
       386: 2q+1
       387: q
       388: 2q+1
       389: q
       390: q+1
       391: q+1
       392: q
       393: q
       394: 2q+1
       395: q
       396: 2q+1
       399: q+1
       400: q+1
       403: 2q+1
       404: 2q+1
       406: 2q+1
       407: 2q+1
       413: q+1
       414: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       422: q^2+2q+2
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: q+1
       432: q^2+2q+2
       433: q+1
       434: q+1
       435: 2q+1
       436: 2q+1
       437: 3q+1
       438: 3q+1
       439: 2q
       440: q^2+4q+2
       441: 3q+1
       442: 3q+1
       443: 3q+1
       444: 3q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: q+1
       450: 2q+2
       451: 1
       452: 1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q+1
       458: 2q+2
       459: q+1
       460: q+1
       462: 4q+2
       463: q+1
       464: q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 3q+1
       472: 3q+1
       474: 4q+2
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: 4q+2
       482: q^2+4q+2
       483: 4q+2
       484: 6q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q^2+q+1
       490: q^2+q+1
       491: q^2+4q+2
       492: q^2+4q+2
       493: 4q+2
       494: q^2+4q+2
       495: q^2+4q+2
       496: q^2+6q+2
       497: 3q+2
       498: 3q+2
       499: q+2
       500: 2q+2
       501: 4q+2
       508: 4q+2
       509: 4q+2
       510: 3q+2
       511: 4q+2
       512: q^2+4q+2
       513: 2q+2
       514: 2q+2
       515: 2q+4
       516: 2q+4
       517: 2q+4
       518: 4q+2
       519: 4q+2
       520: q^2+3q+2
       522: 1
       524: 1
       530: 1
       532: 1
       534: 1
       536: 1
       537: q
       538: q+1
       539: q+1
       540: q
       541: q
       542: 2q+1
       543: 2q+1
       544: q
       545: q
       546: q+1
       547: q+1
       548: q
       551: 1
       552: 1
       555: q+1
       556: q+1
       559: q+1
       560: q+1
       563: q+1
       564: q+1
       566: 2q+1
       568: 2q+1
       570: q+1
       571: q+1
       574: 2q+1
       575: 2q+1
       577: q+1
       581: q+1
       585: q+1
       586: q+1
       589: q+1
       590: q+1
       592: 2q+2
       593: q+1
       594: q+1
       596: q^2+2q+2
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       608: q^2+2q+2
       609: q+1
       610: q+1
       613: q+1
       614: q+1
       615: 3q+1
       616: 3q+1
       617: 2q+1
       618: 2q+1
       619: q+1
       620: q+1
       622: q+2
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       632: 4q+2
       633: q+1
       634: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       644: 2q+2
       645: 1
       646: 1
       647: 2q+1
       648: 2q+1
       650: 2q+2
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 2q+1
       656: 2q+1
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+2
       663: q+2
       664: 2q+4
       665: 4q+2
       672: 4q+2
       673: 3q+2
       674: 2q+4
       675: 4q+2
       676: q^2+4q+2
       677: 4q+2
       678: 4q+2
       679: q^2+4q+2
       680: 4
       681: 3q+2
       682: q+2
       683: q+2
       684: 2q+2
       685: 2q+2
       686: 3q+2
       687: 3q+2
       688: q+2
       689: 2q+2
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       699: q+1
       710: 1
       712: 1
       715: 1
       716: 1
       718: 1
       720: 1
       722: 1
       723: 1
       726: 1
       727: 1
       733: q
       734: q+1
       735: q+1
       736: q
       739: 1
       740: 1
       743: 1
       744: 1
       751: q+1
       752: q+1
       754: 1
       756: 1
       758: q+1
       759: q+1
       762: q+1
       763: q+1
       766: 2q+1
       768: 2q+1
       769: q+1
       773: q+1
       775: 2
       776: 2
       779: q+2
       780: q+2
       781: q+1
       782: q+1
       785: q+1
       786: q+1
       788: 2q+2
       791: 1
       792: 1
       793: 2
       794: 2
       795: q+2
       796: q+2
       797: q+1
       798: q+1
       801: q+1
       802: q+1
       804: 2q+2
       805: q+1
       806: q+1
       808: q^2+2q+2
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       815: 2q+1
       816: 2q+1
       818: 4
       819: 2
       820: 2
       821: 1
       822: 1
       825: q+1
       826: q+1
       828: q+2
       832: q+2
       833: 1
       834: 1
       835: 1
       836: 1
       840: 2q+2
       843: 2
       844: 2
       845: q+1
       846: q+1
       848: q+2
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 4
       867: q+2
       868: 3q+2
       869: q+2
       870: 2q+4
       871: 4q+2
       872: 3q+2
       873: 2
       874: 4
       875: q+2
       876: q+2
       877: 3q+2
       878: q+2
       879: q+2
       880: 2q+2
       881: q+2
       882: q+2
       883: q+2
       889: q+1
       890: q+1
       902: 1
       903: 1
       905: 1
       906: 1
       909: 1
       911: 1
       916: 1
       917: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       927: 1
       929: 1
       930: 1
       942: 2
       943: 2
       946: 1
       947: 1
       950: 1
       951: 1
       961: 1
       962: 1
       965: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       976: 1
       989: q+1
       991: q+1
       994: 2
       995: 2
       999: 4
      1000: 2
      1001: 2
      1004: q+1
      1005: q+1
      1007: q+2
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 2
      1013: 2
      1016: 1
      1017: 1
      1020: q+2
      1021: q+2
      1022: q+1
      1023: q+1
      1026: q+1
      1027: q+1
      1029: 2q+2
      1033: 2
      1036: 2
      1037: 2
      1038: 1
      1039: 1
      1045: q+2
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1053: q+1
      1055: q+2
      1059: q+2
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 4
      1077: q+2
      1078: 3q+2
      1079: 2
      1080: 2
      1081: 2
      1082: q+2
      1083: q+2
      1084: 4
      1085: q+2
      1089: 1
      1091: 1
      1092: 1
      1094: 1
      1116: 2
      1117: 2
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1127: 1
      1128: 1
      1131: 2
      1133: 2
      1135: 1
      1136: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1162: 1
      1163: 1
      1174: 1
      1175: 1
      1195: 1
      1197: 1
      1199: 1
      1200: 1
      1204: 1
      1205: 1
      1217: 2
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1224: 1
      1225: 1
      1228: 1
      1229: 1
      1230: 2
      1231: 2
      1233: 4
      1234: 2
      1235: 2
      1240: q+1
      1241: q+1
      1243: q+2
      1247: 2
      1248: 1
      1249: 1
      1251: 2
      1261: q+2
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1271: q+2
      1274: 2
      1275: 2
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 2
      1281: 2
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 2
      1288: 2
      1289: q+2
      1293: 1
      1295: 1
      1296: 1
      1298: 1
      1327: 1
      1329: 1
      1331: 1
      1332: 1
      1350: 2
      1351: 2
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1363: 1
      1366: 2
      1367: 2
      1369: 1
      1371: 1
      1382: 1
      1383: 1
      1411: 1
      1413: 1
      1420: 1
      1421: 1
      1430: 1
      1431: 1
      1433: 1
      1434: 1
      1441: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1451: 2
      1454: 1
      1455: 1
      1461: 1
      1464: 1
      1465: 1
      1467: 2
      1474: 1
      1475: 1
      1479: q+2
      1482: 1
      1483: 1
      1484: 2
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1505: 1
      1506: 1
      1508: 1
      1509: 1
      1550: 1
      1552: 1
      1577: 1
      1578: 1
      1580: 1
      1582: 1
      1609: 1
      1610: 1
      1641: 1
      1642: 1
      1646: 2
      1647: 1
      1648: 1
      1650: 2
      1654: 1
      1664: 1
      1669: 1
      1670: 1
      1673: 1
      1674: 1
      1751: 1
      1752: 1
      1759: 1
      1760: 1
      1820: 1
      1830: 1
      1833: 1
      1963: 1

1964:    0: q^3+6q^2+6q+2
         1: q^3+6q^2+6q+2
         2: q^3+6q^2+6q+2
         3: q^3+6q^2+6q+2
         4: q^3+6q^2+6q+2
         5: q^3+6q^2+6q+2
         6: q^3+6q^2+6q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+3q^3+5q^2+4q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+6q^2+6q+2
        14: q^3+6q^2+6q+2
        15: q^3+6q^2+6q+2
        16: 4q^2+6q+2
        17: 4q^2+6q+2
        18: q^3+5q^2+4q+2
        19: q^3+6q^2+6q+2
        20: q^3+6q^2+6q+2
        21: q^3+6q^2+6q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: 4q^2+6q+2
        25: q^3+6q^2+6q+2
        26: q^3+6q^2+6q+2
        27: q^3+6q^2+6q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+6q^2+6q+2
        31: 2q^2+6q+2
        32: 4q^2+6q+2
        33: 2q^2+6q+2
        34: 4q^2+6q+2
        35: q^3+6q^2+6q+2
        36: 4q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: q^3+5q^2+4q+2
        49: 4q^2+6q+2
        50: 4q^2+6q+2
        51: q^3+5q^2+4q+2
        52: 4q^2+6q+2
        53: 4q^2+6q+2
        54: 4q^2+6q+2
        55: q^3+6q^2+6q+2
        56: q^3+6q^2+6q+2
        57: q^3+6q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: 2q^2+4q+2
        61: 2q
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+6q+2
        69: 3q^2+4q+2
        70: 4q^2+6q+2
        71: 2q^2+6q+2
        72: 4q^2+6q+2
        73: 2q^2+6q+2
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+6q+2
        81: 2q^2+6q+2
        82: 2q^2+6q+2
        83: 4q^2+6q+2
        84: 4q^2+6q+2
        85: 4q^2+6q+2
        86: 4q^2+6q+2
        87: q^3+6q^2+6q+2
        88: q^2+6q+2
        89: q^2+6q+2
        90: 3q^2+4q+2
        91: 4q^2+6q+2
        92: 4q^2+6q+2
        93: q^3+5q^2+4q+2
        94: q^2+6q+2
        95: q^2+6q+2
        96: 3q^2+4q+2
        97: 4q^2+6q+2
        98: 4q^2+6q+2
        99: q^3+5q^2+4q+2
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 4q^2+6q+2
       103: 2q+1
       104: 2q+1
       105: q
       106: q
       107: 2q^2+4q+2
       108: 2q
       109: 3q+1
       110: 3q+1
       111: q^2+3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 3q+1
       118: 3q+1
       119: 2q^2+4q+2
       120: 2q
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+6q+2
       126: q^2+4q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 2q^2+6q+2
       134: 3q^2+4q+2
       135: 4q^2+6q+2
       136: 2q^2+6q+2
       137: 6q+2
       138: q^2+4q+2
       139: 6q+2
       140: 4q+2
       141: 2q^2+6q+2
       142: q^2+6q+2
       143: q^2+6q+2
       144: 3q^2+4q+2
       145: 2q^2+6q+2
       146: 4q^2+6q+2
       147: 4q^2+6q+2
       148: 2q^2+6q+2
       149: 2q^2+6q+2
       150: 4q^2+6q+2
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: q^2+6q+2
       158: q^2+6q+2
       159: 3q^2+4q+2
       160: q^2+6q+2
       161: q^2+6q+2
       162: 3q^2+4q+2
       163: 4q^2+6q+2
       164: 4q^2+6q+2
       165: q^3+5q^2+4q+2
       166: q^2+6q+2
       167: q^2+6q+2
       168: 3q^2+4q+2
       169: 2q+1
       170: 2q+1
       171: q
       172: q
       173: 2q+1
       174: 2q+1
       175: q
       176: q
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q^2+4q+2
       184: 2q
       185: 3q+1
       186: 3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 3q+1
       192: 3q+1
       193: 4q+2
       195: 3q+1
       196: 3q+1
       197: 2q+1
       198: 2q+1
       199: q^2+4q+2
       200: 2q
       201: 2q^2+4q+2
       202: 2q
       203: 3q+1
       204: 3q+1
       205: q^2+3q+1
       206: q^2+3q+1
       207: 3q+1
       208: 3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+4q+2
       220: q^2+6q+2
       221: q^2+4q+2
       222: q^2+6q+2
       223: 3q^2+4q+2
       224: 6q+2
       225: q^2+4q+2
       226: 4q+2
       227: 6q+2
       228: q^2+4q+2
       229: 4q+2
       230: q^2+6q+2
       231: q^2+4q+2
       232: 2q^2+6q+2
       233: 3q^2+4q+2
       234: 4q^2+6q+2
       235: 2q^2+6q+2
       236: q^2+4q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: 4q+2
       245: q^2+6q+2
       246: 2q^2+6q+2
       247: q^2+6q+2
       248: q^2+6q+2
       249: 3q^2+4q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: q^2+6q+2
       254: q^2+6q+2
       255: 3q^2+4q+2
       256: q^2+6q+2
       257: q^2+6q+2
       258: 3q^2+4q+2
       259: q+1
       260: q+1
       261: q
       262: q
       263: 2q+1
       264: 2q+1
       265: q
       266: q
       267: 2q+1
       268: 2q+1
       271: 2q+1
       272: q
       273: q
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: q
       278: q
       279: 2q+1
       280: 2q+1
       281: q+1
       282: q+1
       283: q^2+2q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 2q+1
       290: 2q+1
       291: q+1
       292: q+1
       293: q^2+4q+2
       294: 2q
       295: 3q+1
       296: 3q+1
       297: 3q+1
       298: 3q+1
       299: 4q+2
       301: q+1
       302: q+1
       303: 3q+1
       304: 3q+1
       305: 2q+1
       306: 2q+1
       307: 2q^2+4q+2
       308: 2q
       309: 3q+1
       310: 3q+1
       311: 2q+1
       312: 2q+1
       313: q^2+3q+1
       314: q^2+3q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 4q+2
       321: 3q+1
       322: 3q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: q^2+4q+2
       334: q^2+4q+2
       335: 4q+2
       336: q^2+4q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: 4q+2
       345: 4q+2
       346: 3q+2
       347: 2q+2
       348: 2q+2
       349: 4q+2
       350: q^2+4q+2
       351: 4q+2
       352: q^2+4q+2
       353: q^2+6q+2
       354: q^2+4q+2
       355: q^2+6q+2
       356: 3q^2+4q+2
       357: 6q+2
       358: q^2+4q+2
       359: q^2+6q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q^2+q+1
       365: q^2+q+1
       366: 4q+2
       367: 6q+2
       368: q^2+4q+2
       369: 4q+2
       370: q^2+6q+2
       371: q^2+6q+2
       372: q^2+6q+2
       373: 3q^2+4q+2
       374: 4q+2
       375: 4q+2
       376: q^2+3q+2
       377: 1
       378: 1
       381: q+1
       382: q+1
       383: q
       384: q
       385: 2q+1
       386: 2q+1
       387: q
       388: q
       389: q+1
       390: q+1
       393: 2q+1
       394: 2q+1
       397: q+1
       398: q
       399: q
       400: q+1
       401: 2q+1
       402: q
       403: 2q+1
       404: q
       405: 2q+1
       407: 2q+1
       413: q+1
       414: q+1
       417: q+1
       418: q+1
       419: q^2+2q+2
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       429: 2q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: 2q+2
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: 4q+2
       445: q+1
       446: q+1
       447: q^2+2q+2
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q^2+4q+2
       454: 2q
       455: 2q+1
       456: 2q+1
       457: 3q+1
       458: 3q+1
       459: 3q+1
       460: 3q+1
       461: 3q+1
       462: 3q+1
       463: 2q+1
       464: 2q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 4q+2
       473: 3q+1
       474: 3q+1
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q^2+4q+2
       482: 4q+2
       483: 4q+2
       484: 6q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q^2+q+1
       490: q^2+q+1
       491: q^2+4q+2
       492: 3q+2
       493: q+2
       494: 3q+2
       495: 2q+2
       496: 4q+2
       497: q^2+4q+2
       498: q^2+4q+2
       499: 4q+2
       500: q^2+4q+2
       501: q^2+6q+2
       508: 4q+2
       509: 4q+2
       510: 3q+2
       511: 2q+2
       512: 2q+2
       513: 4q+2
       514: q^2+4q+2
       515: 2q+4
       516: 2q+4
       517: 2q+4
       518: 4q+2
       519: 4q+2
       520: q^2+3q+2
       521: 1
       522: 1
       529: 1
       530: 1
       533: 1
       534: 1
       537: q+1
       538: q+1
       541: q+1
       542: q+1
       545: q+1
       546: q+1
       549: 1
       551: 1
       553: q+1
       554: q
       555: q
       556: q+1
       557: 2q+1
       558: q
       559: q
       560: 2q+1
       561: q+1
       562: q
       563: q
       564: q+1
       565: 2q+1
       566: 2q+1
       569: q+1
       571: q+1
       573: 2q+1
       574: 2q+1
       577: q+1
       581: q+1
       585: q+1
       586: q+1
       589: q^2+2q+2
       591: q+1
       592: q+1
       593: 2q+2
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       615: 4q+2
       617: q+1
       618: q+1
       619: q^2+2q+2
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: 3q+1
       632: 3q+1
       633: 2q+1
       634: 2q+1
       639: q+1
       640: q+1
       641: 2q+2
       643: q+1
       644: q+1
       645: 1
       646: 1
       647: 2q+2
       649: 2q+1
       650: 2q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 2q+1
       656: 2q+1
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+2
       663: q+2
       664: 2q+4
       665: 4q+2
       672: 4q+2
       673: 3q+2
       674: 4
       675: q+2
       676: 3q+2
       677: q+2
       678: 2q+2
       679: 2q+2
       680: 2q+4
       681: q^2+4q+2
       682: 4q+2
       683: 4q+2
       684: 4q+2
       685: q^2+4q+2
       686: 3q+2
       687: q+2
       688: 3q+2
       689: 2q+2
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       699: q+1
       709: 1
       710: 1
       713: 1
       715: 1
       717: 1
       718: 1
       721: 1
       722: 1
       725: 1
       726: 1
       733: q+1
       734: q+1
       737: 1
       740: 1
       741: 1
       744: 1
       749: q+1
       750: q
       751: q
       752: q+1
       753: 1
       754: 1
       757: q+1
       759: q+1
       761: q+1
       763: q+1
       765: 2q+1
       766: 2q+1
       769: q+1
       773: q+1
       775: 2
       776: 2
       779: q+2
       780: q+2
       781: q+1
       782: q+1
       785: 2q+2
       787: q+1
       788: q+1
       791: 1
       792: 1
       793: 4
       795: 2
       796: 2
       797: 1
       798: 1
       801: q+2
       805: q+2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       815: 2q+2
       817: 2
       818: 2
       819: q+2
       820: q+2
       821: q+1
       822: q+1
       825: q^2+2q+2
       827: q+1
       828: q+1
       829: 2q+2
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       839: 2q+1
       840: 2q+1
       843: 2
       844: 2
       845: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 4
       867: q+2
       868: 3q+2
       869: 2
       870: 4
       871: q+2
       872: q+2
       873: q+2
       874: 2q+4
       875: 4q+2
       876: 3q+2
       877: q+2
       878: 3q+2
       879: q+2
       880: 2q+2
       881: q+2
       882: q+2
       883: q+2
       884: q+1
       890: q+1
       900: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       916: 2
       917: 2
       920: 1
       921: 1
       928: 1
       929: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       947: 1
       948: 1
       951: 1
       952: 1
       953: 1
       960: 1
       962: 1
       964: 2
       965: 2
       968: 1
       969: 1
       971: 1
       972: 1
       974: 1
       976: 1
       988: q+1
       989: q+1
       994: 2
       995: 2
       998: 2
       999: 2
      1000: 4
      1004: q+2
      1006: q+1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 2
      1013: 2
      1016: 2
      1020: 2
      1021: 2
      1022: 1
      1023: 1
      1026: q+2
      1032: 1
      1033: 1
      1036: q+2
      1037: q+2
      1038: q+1
      1039: q+1
      1040: 2q+2
      1044: q+1
      1045: q+1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+2
      1056: q+2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 2
      1077: 2
      1078: q+2
      1079: q+2
      1080: 4
      1081: q+2
      1082: 3q+2
      1083: q+2
      1084: 4
      1085: q+2
      1086: 1
      1087: 1
      1089: 1
      1092: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1122: 2
      1123: 2
      1126: 1
      1128: 1
      1130: 2
      1131: 2
      1134: 1
      1136: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1156: 1
      1157: 1
      1172: 1
      1175: 1
      1176: 1
      1177: 1
      1180: 1
      1181: 1
      1194: 1
      1195: 1
      1198: 1
      1200: 1
      1206: 1
      1207: 1
      1216: 1
      1217: 1
      1218: 2
      1220: 1
      1221: 1
      1224: 1
      1225: 1
      1228: 2
      1230: 1
      1231: 1
      1234: 2
      1240: q+2
      1246: 1
      1247: 1
      1248: 2
      1249: 2
      1250: 2
      1251: 2
      1254: 4
      1258: q+2
      1260: q+1
      1261: q+1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1268: q+2
      1274: 2
      1275: 2
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 2
      1281: 2
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 2
      1288: 2
      1289: q+2
      1290: 1
      1291: 1
      1293: 1
      1296: 1
      1326: 1
      1327: 1
      1330: 1
      1332: 1
      1356: 1
      1357: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 2
      1389: 2
      1392: 1
      1394: 1
      1396: 2
      1397: 2
      1400: 1
      1402: 1
      1410: 1
      1411: 1
      1422: 1
      1423: 1
      1430: 1
      1431: 1
      1433: 1
      1434: 1
      1440: 1
      1441: 1
      1442: 2
      1444: 1
      1445: 1
      1454: 1
      1460: 1
      1461: 1
      1462: 2
      1464: 1
      1465: 1
      1468: 2
      1474: 1
      1475: 1
      1476: q+2
      1482: 1
      1483: 1
      1484: 2
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1513: 1
      1514: 1
      1516: 1
      1519: 1
      1549: 1
      1550: 1
      1595: 1
      1596: 1
      1599: 1
      1601: 1
      1615: 1
      1616: 1
      1641: 1
      1642: 1
      1647: 1
      1653: 1
      1654: 1
      1655: 2
      1657: 2
      1665: 1
      1669: 1
      1670: 1
      1673: 1
      1674: 1
      1773: 1
      1774: 1
      1781: 1
      1782: 1
      1821: 1
      1831: 1
      1833: 1
      1964: 1

1965:    0: q^3+6q^2+6q+2
         1: q^3+6q^2+6q+2
         2: q^3+6q^2+6q+2
         3: q^3+6q^2+6q+2
         4: q^3+6q^2+6q+2
         5: q^3+6q^2+6q+2
         6: q^3+6q^2+6q+2
         7: q^3+6q^2+6q+2
         8: q^3+6q^2+6q+2
         9: q^4+3q^3+5q^2+4q+2
        10: 4q^2+6q+2
        11: 4q^2+6q+2
        12: 4q^2+6q+2
        13: q^3+6q^2+6q+2
        14: q^3+6q^2+6q+2
        15: q^3+6q^2+6q+2
        16: 4q^2+6q+2
        17: 4q^2+6q+2
        18: q^3+5q^2+4q+2
        19: q^3+6q^2+6q+2
        20: q^3+6q^2+6q+2
        21: q^3+6q^2+6q+2
        22: 4q^2+6q+2
        23: 4q^2+6q+2
        24: 4q^2+6q+2
        25: q^3+6q^2+6q+2
        26: q^3+6q^2+6q+2
        27: q^3+6q^2+6q+2
        28: 2q^2+6q+2
        29: 4q^2+6q+2
        30: q^3+6q^2+6q+2
        31: 2q^2+6q+2
        32: 4q^2+6q+2
        33: 2q^2+6q+2
        34: 4q^2+6q+2
        35: q^3+6q^2+6q+2
        36: 4q^2+6q+2
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 4q^2+6q+2
        44: 4q^2+6q+2
        45: 4q^2+6q+2
        46: 4q^2+6q+2
        47: 4q^2+6q+2
        48: q^3+5q^2+4q+2
        49: 4q^2+6q+2
        50: 4q^2+6q+2
        51: q^3+5q^2+4q+2
        52: 4q^2+6q+2
        53: 4q^2+6q+2
        54: 4q^2+6q+2
        55: q^3+6q^2+6q+2
        56: q^3+6q^2+6q+2
        57: q^3+6q^2+6q+2
        58: 3q+1
        59: 3q+1
        60: 2q
        61: 2q^2+4q+2
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+6q+2
        69: 3q^2+4q+2
        70: 4q^2+6q+2
        71: 2q^2+6q+2
        72: 4q^2+6q+2
        73: 2q^2+6q+2
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+6q+2
        81: 2q^2+6q+2
        82: 2q^2+6q+2
        83: 4q^2+6q+2
        84: 4q^2+6q+2
        85: 4q^2+6q+2
        86: 4q^2+6q+2
        87: q^3+6q^2+6q+2
        88: q^2+6q+2
        89: q^2+6q+2
        90: 3q^2+4q+2
        91: 4q^2+6q+2
        92: 4q^2+6q+2
        93: q^3+5q^2+4q+2
        94: q^2+6q+2
        95: q^2+6q+2
        96: 3q^2+4q+2
        97: 4q^2+6q+2
        98: 4q^2+6q+2
        99: q^3+5q^2+4q+2
       100: 4q^2+6q+2
       101: 4q^2+6q+2
       102: 4q^2+6q+2
       103: q
       104: q
       105: 2q+1
       106: 2q+1
       107: 2q
       108: 2q^2+4q+2
       109: 3q+1
       110: 3q+1
       111: q^2+3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 3q+1
       118: 3q+1
       119: 2q
       120: 2q^2+4q+2
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+6q+2
       126: q^2+4q+2
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 2q^2+6q+2
       134: 3q^2+4q+2
       135: 4q^2+6q+2
       136: 2q^2+6q+2
       137: 6q+2
       138: q^2+4q+2
       139: 6q+2
       140: 4q+2
       141: 2q^2+6q+2
       142: q^2+6q+2
       143: q^2+6q+2
       144: 3q^2+4q+2
       145: 2q^2+6q+2
       146: 4q^2+6q+2
       147: 4q^2+6q+2
       148: 2q^2+6q+2
       149: 2q^2+6q+2
       150: 4q^2+6q+2
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: q^2+6q+2
       158: q^2+6q+2
       159: 3q^2+4q+2
       160: q^2+6q+2
       161: q^2+6q+2
       162: 3q^2+4q+2
       163: 4q^2+6q+2
       164: 4q^2+6q+2
       165: q^3+5q^2+4q+2
       166: q^2+6q+2
       167: q^2+6q+2
       168: 3q^2+4q+2
       169: q
       170: q
       171: 2q+1
       172: 2q+1
       173: q
       174: q
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q
       184: 2q^2+4q+2
       185: 3q+1
       186: 3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 3q+1
       192: 3q+1
       194: 4q+2
       195: 3q+1
       196: 3q+1
       197: 2q+1
       198: 2q+1
       199: 2q
       200: q^2+4q+2
       201: 2q
       202: 2q^2+4q+2
       203: 3q+1
       204: 3q+1
       205: q^2+3q+1
       206: q^2+3q+1
       207: 3q+1
       208: 3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+4q+2
       220: q^2+6q+2
       221: q^2+4q+2
       222: q^2+6q+2
       223: 3q^2+4q+2
       224: 6q+2
       225: q^2+4q+2
       226: 4q+2
       227: 6q+2
       228: q^2+4q+2
       229: 4q+2
       230: q^2+6q+2
       231: q^2+4q+2
       232: 2q^2+6q+2
       233: 3q^2+4q+2
       234: 4q^2+6q+2
       235: 2q^2+6q+2
       236: q^2+4q+2
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 6q+2
       244: 4q+2
       245: q^2+6q+2
       246: 2q^2+6q+2
       247: q^2+6q+2
       248: q^2+6q+2
       249: 3q^2+4q+2
       250: 4q+2
       251: 4q+2
       252: q^2+3q+2
       253: q^2+6q+2
       254: q^2+6q+2
       255: 3q^2+4q+2
       256: q^2+6q+2
       257: q^2+6q+2
       258: 3q^2+4q+2
       259: q
       260: q
       261: q+1
       262: q+1
       263: q
       264: q
       265: 2q+1
       266: 2q+1
       269: 2q+1
       270: 2q+1
       271: q
       272: 2q+1
       273: 2q+1
       274: q
       275: q
       276: q
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: q+1
       282: q+1
       284: q^2+2q+2
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 2q+1
       290: 2q+1
       291: q+1
       292: q+1
       293: 2q
       294: q^2+4q+2
       295: 3q+1
       296: 3q+1
       297: 3q+1
       298: 3q+1
       300: 4q+2
       301: q+1
       302: q+1
       303: 3q+1
       304: 3q+1
       305: 2q+1
       306: 2q+1
       307: 2q
       308: 2q^2+4q+2
       309: 3q+1
       310: 3q+1
       311: 2q+1
       312: 2q+1
       313: q^2+3q+1
       314: q^2+3q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       320: 4q+2
       321: 3q+1
       322: 3q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: q^2+3q+1
       333: q^2+4q+2
       334: q^2+4q+2
       335: 4q+2
       336: q^2+4q+2
       337: 6q+2
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+q+1
       343: q^2+q+1
       344: 4q+2
       345: 4q+2
       346: 3q+2
       347: 2q+2
       348: 2q+2
       349: 4q+2
       350: q^2+4q+2
       351: 4q+2
       352: q^2+4q+2
       353: q^2+6q+2
       354: q^2+4q+2
       355: q^2+6q+2
       356: 3q^2+4q+2
       357: 6q+2
       358: q^2+4q+2
       359: q^2+6q+2
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: 2q+1
       364: q^2+q+1
       365: q^2+q+1
       366: 4q+2
       367: 6q+2
       368: q^2+4q+2
       369: 4q+2
       370: q^2+6q+2
       371: q^2+6q+2
       372: q^2+6q+2
       373: 3q^2+4q+2
       374: 4q+2
       375: 4q+2
       376: q^2+3q+2
       379: 1
       380: 1
       381: q
       382: q
       383: q+1
       384: q+1
       385: q
       386: q
       387: 2q+1
       388: 2q+1
       391: q+1
       392: q+1
       395: 2q+1
       396: 2q+1
       397: q
       398: q+1
       399: q+1
       400: q
       401: q
       402: 2q+1
       403: q
       404: 2q+1
       406: 2q+1
       408: 2q+1
       413: q+1
       414: q+1
       417: q+1
       418: q+1
       420: q^2+2q+2
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q+1
       428: 2q+1
       430: 2q+2
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: q+1
       436: q+1
       438: 2q+2
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       444: 4q+2
       445: q+1
       446: q+1
       448: q^2+2q+2
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 2q
       454: q^2+4q+2
       455: 2q+1
       456: 2q+1
       457: 3q+1
       458: 3q+1
       459: 3q+1
       460: 3q+1
       461: 3q+1
       462: 3q+1
       463: 2q+1
       464: 2q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       472: 4q+2
       473: 3q+1
       474: 3q+1
       475: 2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 2q+1
       481: q^2+4q+2
       482: 4q+2
       483: 4q+2
       484: 6q+2
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: q^2+q+1
       490: q^2+q+1
       491: q^2+4q+2
       492: 3q+2
       493: q+2
       494: 3q+2
       495: 2q+2
       496: 4q+2
       497: q^2+4q+2
       498: q^2+4q+2
       499: 4q+2
       500: q^2+4q+2
       501: q^2+6q+2
       508: 4q+2
       509: 4q+2
       510: 3q+2
       511: 2q+2
       512: 2q+2
       513: 4q+2
       514: q^2+4q+2
       515: 2q+4
       516: 2q+4
       517: 2q+4
       518: 4q+2
       519: 4q+2
       520: q^2+3q+2
       523: 1
       524: 1
       531: 1
       532: 1
       535: 1
       536: 1
       539: q+1
       540: q+1
       543: q+1
       544: q+1
       547: q+1
       548: q+1
       550: 1
       552: 1
       553: q
       554: q+1
       555: q+1
       556: q
       557: q
       558: 2q+1
       559: 2q+1
       560: q
       561: q
       562: q+1
       563: q+1
       564: q
       567: 2q+1
       568: 2q+1
       570: q+1
       572: q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       581: q+1
       585: q+1
       586: q+1
       590: q^2+2q+2
       591: q+1
       592: q+1
       594: 2q+2
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       604: q+2
       605: 1
       606: 1
       607: q+1
       608: q+1
       609: 1
       610: 1
       613: 1
       614: 1
       616: 4q+2
       617: q+1
       618: q+1
       620: q^2+2q+2
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       629: q+1
       630: q+1
       631: 3q+1
       632: 3q+1
       633: 2q+1
       634: 2q+1
       639: q+1
       640: q+1
       642: 2q+2
       643: q+1
       644: q+1
       645: 1
       646: 1
       648: 2q+2
       649: 2q+1
       650: 2q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: 2q+1
       656: 2q+1
       657: 4
       658: q+2
       659: q+2
       660: q+2
       661: q+2
       662: q+2
       663: q+2
       664: 2q+4
       665: 4q+2
       672: 4q+2
       673: 3q+2
       674: 4
       675: q+2
       676: 3q+2
       677: q+2
       678: 2q+2
       679: 2q+2
       680: 2q+4
       681: q^2+4q+2
       682: 4q+2
       683: 4q+2
       684: 4q+2
       685: q^2+4q+2
       686: 3q+2
       687: q+2
       688: 3q+2
       689: 2q+2
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       700: q+1
       711: 1
       712: 1
       714: 1
       716: 1
       719: 1
       720: 1
       723: 1
       724: 1
       727: 1
       728: 1
       735: q+1
       736: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       749: q
       750: q+1
       751: q+1
       752: q
       755: 1
       756: 1
       758: q+1
       760: q+1
       762: q+1
       764: q+1
       767: 2q+1
       768: 2q+1
       769: q+1
       773: q+1
       775: 2
       776: 2
       779: q+2
       780: q+2
       781: q+1
       782: q+1
       786: 2q+2
       787: q+1
       788: q+1
       791: 1
       792: 1
       794: 4
       795: 2
       796: 2
       797: 1
       798: 1
       802: q+2
       806: q+2
       807: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       816: 2q+2
       817: 2
       818: 2
       819: q+2
       820: q+2
       821: q+1
       822: q+1
       826: q^2+2q+2
       827: q+1
       828: q+1
       830: 2q+2
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       839: 2q+1
       840: 2q+1
       843: 2
       844: 2
       846: q+2
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       855: 1
       856: 1
       857: q+1
       858: q+1
       865: 2
       866: 4
       867: q+2
       868: 3q+2
       869: 2
       870: 4
       871: q+2
       872: q+2
       873: q+2
       874: 2q+4
       875: 4q+2
       876: 3q+2
       877: q+2
       878: 3q+2
       879: q+2
       880: 2q+2
       881: q+2
       882: q+2
       883: q+2
       889: q+1
       891: q+1
       901: 1
       902: 1
       906: 1
       907: 1
       910: 1
       911: 1
       918: 2
       919: 2
       922: 1
       923: 1
       930: 1
       931: 1
       940: 1
       941: 1
       942: 1
       943: 1
       945: 1
       946: 1
       949: 1
       950: 1
       954: 1
       955: 1
       961: 1
       963: 1
       966: 2
       967: 2
       968: 1
       969: 1
       971: 1
       972: 1
       975: 1
       977: 1
       990: q+1
       991: q+1
       994: 2
       995: 2
       998: 2
       999: 2
      1001: 4
      1005: q+2
      1006: q+1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 2
      1013: 2
      1017: 2
      1020: 2
      1021: 2
      1022: 1
      1023: 1
      1027: q+2
      1032: 1
      1033: 1
      1036: q+2
      1037: q+2
      1038: q+1
      1039: q+1
      1041: 2q+2
      1044: q+1
      1045: q+1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: q+2
      1057: q+2
      1058: q+1
      1059: q+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 2
      1077: 2
      1078: q+2
      1079: q+2
      1080: 4
      1081: q+2
      1082: 3q+2
      1083: q+2
      1084: 4
      1085: q+2
      1090: 1
      1091: 1
      1093: 1
      1094: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1124: 2
      1125: 2
      1127: 1
      1129: 1
      1132: 2
      1133: 2
      1135: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1158: 1
      1159: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1182: 1
      1183: 1
      1196: 1
      1197: 1
      1199: 1
      1201: 1
      1208: 1
      1209: 1
      1216: 1
      1217: 1
      1219: 2
      1220: 1
      1221: 1
      1224: 1
      1225: 1
      1229: 2
      1230: 1
      1231: 1
      1235: 2
      1241: q+2
      1246: 1
      1247: 1
      1248: 2
      1249: 2
      1250: 2
      1251: 2
      1255: 4
      1259: q+2
      1260: q+1
      1261: q+1
      1262: 1
      1263: 1
      1266: 1
      1267: 1
      1269: q+2
      1274: 2
      1275: 2
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 2
      1281: 2
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 2
      1288: 2
      1289: q+2
      1294: 1
      1295: 1
      1297: 1
      1298: 1
      1328: 1
      1329: 1
      1331: 1
      1333: 1
      1358: 1
      1359: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1390: 2
      1391: 2
      1393: 1
      1395: 1
      1398: 2
      1399: 2
      1401: 1
      1403: 1
      1412: 1
      1413: 1
      1424: 1
      1425: 1
      1430: 1
      1431: 1
      1433: 1
      1434: 1
      1440: 1
      1441: 1
      1443: 2
      1444: 1
      1445: 1
      1455: 1
      1460: 1
      1461: 1
      1463: 2
      1464: 1
      1465: 1
      1469: 2
      1474: 1
      1475: 1
      1477: q+2
      1482: 1
      1483: 1
      1484: 2
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1551: 1
      1552: 1
      1597: 1
      1598: 1
      1600: 1
      1602: 1
      1617: 1
      1618: 1
      1641: 1
      1642: 1
      1648: 1
      1653: 1
      1654: 1
      1656: 2
      1658: 2
      1666: 1
      1669: 1
      1670: 1
      1673: 1
      1674: 1
      1775: 1
      1776: 1
      1783: 1
      1784: 1
      1822: 1
      1832: 1
      1833: 1
      1965: 1

1966:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: 2q^3+4q^2+2q+1
        25: q^3+3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^3+4q^2+2q+1
        32: 2q^3+4q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        41: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: q^3+3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: q^3+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^3+3q^2+q+1
        59: q^3+q^2+q
        60: q^3+2q^2+q+1
        61: q^2+q
        62: q^3+3q^2+2q+1
        64: q^3+3q^2+2q+1
        66: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        76: 2q^2+2q+1
        78: 2q^2+2q+1
        80: 2q^3+4q^2+2q+1
        81: 2q^3+4q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^3+3q^2+2q+1
        85: q^3+3q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^3+2q^2+q+1
       106: q^2+q
       107: q^2+q+1
       108: q
       109: 2q^2+q+1
       110: q
       111: q^2+2q+1
       113: 2q^2+2q+1
       115: 2q^2+2q+1
       117: q^3+3q^2+q+1
       118: q^3+q^2+q
       119: q^3+2q^2+q+1
       120: q^2+q
       121: q^3+3q^2+2q+1
       123: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       127: 2q^2+2q+1
       129: 2q^2+2q+1
       131: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^3+4q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: q^2+2q+1
       141: q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^3+3q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       153: 2q^2+2q+1
       155: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^2+q+1
       172: q
       173: q^3+2q^2+q+1
       176: q^2+q
       177: 2q^2+2q+1
       179: 2q^2+2q+1
       181: q^2+2q+1
       183: q^2+q+1
       184: q
       185: 2q^2+q+1
       186: q
       187: q^2+2q+1
       189: 2q^2+2q+1
       191: q^3+3q^2+q+1
       192: q^3+q^2+q
       193: q^2+q+1
       194: q
       195: 2q^2+q+1
       196: q
       197: q^2+2q+1
       199: q^3+2q^2+q+1
       200: q^2+q
       201: q^2+q+1
       202: q
       203: q+1
       205: q+1
       207: q^3+3q^2+2q+1
       209: 2q^2+2q+1
       211: 2q^2+2q+1
       213: 2q^2+2q+1
       215: 2q^2+2q+1
       217: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: 2q^2+2q+1
       226: q^3+3q^2+2q+1
       227: q^3+3q^2+2q+1
       228: q^3+3q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: 2q^2+2q+1
       239: 2q^2+2q+1
       241: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: q^3+3q^2+2q+1
       251: q^3+3q^2+2q+1
       252: q^3+3q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q^2+q+1
       262: q
       263: q^2+q+1
       266: q
       267: q^2+q+1
       269: q
       271: q+1
       275: q^3+2q^2+q+1
       278: q^2+q
       279: 2q^2+2q+1
       281: 2q^2+2q+1
       283: q^2+q+1
       284: q
       285: 2q^2+q+1
       286: q
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: q^2+q+1
       294: q
       295: 2q^2+q+1
       296: q
       297: q^2+2q+1
       299: q^2+q+1
       300: q
       301: q^2+2q+1
       303: 2q^2+q+1
       304: q
       305: q^2+2q+1
       307: q^2+q+1
       308: q
       309: q+1
       311: q+1
       313: q+1
       315: 2q^2+2q+1
       317: 2q^2+2q+1
       319: q^2+q+1
       320: q
       321: q+1
       323: q+1
       325: 2q^2+2q+1
       327: 2q^2+2q+1
       329: 2q^2+2q+1
       331: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^3+3q^2+2q+1
       345: q^3+3q^2+2q+1
       346: q^3+3q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: 2q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       360: 2q^2+2q+1
       362: 2q^2+2q+1
       364: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2+q+1
       380: q
       381: q^2+q+1
       384: q
       385: q^2+q+1
       388: q
       389: q^2+q+1
       391: q
       393: q^2+q+1
       396: q
       397: q+1
       401: q+1
       405: q+1
       409: 2q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: q^2+q+1
       420: q
       421: 2q^2+q+1
       422: q
       423: q^2+2q+1
       425: q+1
       427: 2q+1
       429: q^2+q+1
       430: q
       431: 2q^2+q+1
       432: q
       433: q^2+2q+1
       435: q^2+2q+1
       437: q^2+q+1
       438: q
       439: 2q^2+q+1
       440: q
       441: q^2+2q+1
       443: q+1
       444: q
       445: 2q+1
       447: q^2+q+1
       448: q
       449: q+1
       451: q+1
       453: q^2+q+1
       454: q
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: 2q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       471: q^2+q+1
       472: q
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^3+3q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: q+1
       502: 2q^2+2q+1
       504: 2q^2+2q+1
       506: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2+q+1
       524: q
       525: q^2+q+1
       528: q
       529: q^2+q+1
       532: q
       533: q^2+q+1
       536: q
       537: q^2+q+1
       539: q
       541: q^2+q+1
       543: q
       545: q+1
       547: q
       549: q+1
       553: q+1
       557: q+1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: 2q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: q^2+q+1
       590: q
       591: 1
       593: 1
       595: 2q^2+q+1
       596: q
       597: q+1
       599: q+1
       601: 2q+1
       603: q^2+q+1
       604: q
       605: q^2+2q+1
       607: 2q^2+q+1
       608: q
       609: q^2+2q+1
       611: q^2+2q+1
       613: q+1
       615: q+1
       616: q
       617: 2q+1
       619: q^2+q+1
       620: q
       621: q+1
       623: q+1
       625: q+1
       627: q+1
       629: 1
       631: q+1
       633: q+1
       635: 2q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       641: q^2+q+1
       642: q
       643: q+1
       645: q+1
       647: q^2+q+1
       648: q
       649: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: 1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q+1
       705: q^2+q+1
       708: q
       709: q^2+q+1
       712: q
       713: 1
       717: 1
       721: q^2+q+1
       723: q
       725: q^2+q+1
       727: q
       729: q^2+q+1
       731: q
       733: q+1
       735: q
       737: q+1
       741: q+1
       745: q+1
       749: q+1
       753: q+1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       775: 2q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       793: q+1
       794: q
       795: 2q+1
       797: q^2+2q+1
       799: q^2+2q+1
       801: q^2+q+1
       802: q
       803: 1
       805: 1
       807: 2q^2+q+1
       808: q
       809: q+1
       811: q+1
       813: 2q+1
       815: q+1
       816: q
       817: q+1
       819: q+1
       821: q+1
       823: q+1
       825: q^2+q+1
       826: q
       827: 1
       831: q+1
       833: 1
       835: 1
       837: q+1
       839: q+1
       841: 2q^2+2q+1
       843: q+1
       845: q^2+q+1
       846: q
       847: q+1
       849: q+1
       851: q+1
       853: q+1
       855: 1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q+1
       896: q^2+q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: q^2+q+1
       914: q
       916: q+1
       918: q
       920: q^2+q+1
       922: q
       924: 1
       928: 1
       932: q+1
       934: q
       936: q+1
       940: q+1
       944: q+1
       948: 1
       956: q+1
       960: q+1
       964: q+1
       968: q+1
       974: q+1
       978: q+1
       982: q+1
       988: q+1
       992: 2q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1016: q+1
      1017: q
      1018: q^2+2q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: 1
      1028: 1
      1030: q+1
      1032: q+1
      1034: q+1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: q+1
      1048: q+1
      1050: q+1
      1052: q^2+q+1
      1053: q
      1054: 1
      1058: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: q+1
      1146: q
      1148: q^2+q+1
      1150: q
      1152: 1
      1156: 1
      1160: 1
      1164: q+1
      1168: q+1
      1172: 1
      1184: q+1
      1188: q+1
      1194: q+1
      1198: q+1
      1202: 1
      1210: 2q+1
      1212: q+1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2q+1
      1228: q+1
      1229: q
      1230: q+1
      1232: 1
      1234: 1
      1236: q+1
      1238: q+1
      1240: 1
      1242: 1
      1244: q+1
      1246: q+1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1262: q+1
      1264: q+1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: q+1
      1342: q
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1372: q+1
      1376: 1
      1380: 1
      1404: q+1
      1410: q+1
      1414: q+1
      1418: 1
      1430: 1
      1436: 1
      1438: q+1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: q+1
      1450: 1
      1452: q+1
      1454: 1
      1456: 1
      1458: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1474: 1
      1478: 1
      1480: 1
      1482: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1501: 1
      1525: q+1
      1537: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1637: 1
      1639: 1
      1643: q+1
      1645: 1
      1647: 1
      1651: 1
      1653: 1
      1659: 1
      1661: 1
      1663: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1675: 1
      1687: 1
      1723: 1
      1729: 1
      1733: 1
      1737: 1
      1741: 1
      1745: 1
      1749: 1
      1753: 1
      1761: 1
      1785: 1
      1801: 1
      1823: 1
      1825: 1
      1827: 1
      1829: 1
      1834: 1
      1846: 1
      1894: 1
      1898: 1
      1926: 1
      1932: 1
      1966: 1

1967:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: 7q^4+15q^3+9q^2+2q
        23: 7q^4+15q^3+9q^2+2q
        24: 2q^5+9q^4+12q^3+8q^2+2q
        25: q^4+11q^3+9q^2+2q
        26: q^4+11q^3+9q^2+2q
        27: 4q^4+9q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: 7q^4+15q^3+9q^2+2q
        32: 5q^4+11q^3+8q^2+2q
        33: 7q^4+15q^3+9q^2+2q
        34: q^4+11q^3+9q^2+2q
        35: q^4+8q^3+8q^2+2q
        36: q^4+11q^3+9q^2+2q
        37: q^4+5q^3+3q^2+q
        38: 6q^3+6q^2+q
        39: q^4+5q^3+3q^2+q
        40: 6q^3+6q^2+q
        41: 2q^4+4q^3+3q^2+q
        42: 2q^4+5q^3+5q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 5q^4+11q^3+8q^2+2q
        53: 5q^4+11q^3+8q^2+2q
        54: q^5+5q^4+9q^3+7q^2+2q
        55: 7q^3+8q^2+2q
        56: 7q^3+8q^2+2q
        57: q^4+6q^3+7q^2+2q
        58: 4q^4+9q^3+5q^2+2q
        59: 3q^4+6q^3+4q^2
        60: q^4+6q^3+5q^2+q
        61: 5q^3+4q^2+q
        62: q^4+5q^3+3q^2+q
        63: 6q^3+6q^2+q
        64: q^4+4q^3+3q^2+q
        65: 4q^3+5q^2+q
        66: q^4+5q^3+3q^2+q
        67: 6q^3+6q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 4q^3+7q^2+2q
        73: 3q^4+7q^3+7q^2+2q
        74: 2q^3+2q^2+q
        75: 3q^3+5q^2+q
        76: 2q^3+2q^2+q
        77: 3q^3+5q^2+q
        78: 2q^3+2q^2+q
        79: 3q^3+4q^2+q
        80: 5q^4+11q^3+8q^2+2q
        81: 5q^4+11q^3+8q^2+2q
        82: 5q^4+11q^3+8q^2+2q
        83: 3q^4+8q^3+7q^2+2q
        84: q^4+8q^3+8q^2+2q
        85: q^4+8q^3+8q^2+2q
        86: 7q^3+8q^2+2q
        87: 5q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 5q^4+11q^3+8q^2+2q
        95: 5q^4+11q^3+8q^2+2q
        96: q^5+5q^4+9q^3+7q^2+2q
        97: 7q^3+8q^2+2q
        98: 7q^3+8q^2+2q
        99: q^4+6q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: q^4+3q^3+2q^2+q
       104: 3q^3+3q^2
       105: 3q^3+3q^2+q
       106: 2q^3+q^2
       107: 3q^3+4q^2+q
       108: q^3+3q^2+q
       109: 2q^4+5q^3+4q^2+2q
       110: q^4+2q^3+3q^2
       111: q^3+2q^2+q
       112: q^3+4q^2+q
       113: 2q^3+2q^2+q
       114: 3q^3+5q^2+q
       115: 2q^3+2q^2+q
       116: 2q^3+4q^2+q
       117: 2q^4+5q^3+4q^2+2q
       118: q^4+2q^3+3q^2
       119: q^4+3q^3+4q^2+q
       120: 2q^3+3q^2+q
       121: q^4+4q^3+3q^2+q
       122: 4q^3+5q^2+q
       123: q^4+4q^3+3q^2+q
       124: 4q^3+5q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 2q^3+2q^2+q
       128: 3q^3+5q^2+q
       129: 2q^3+2q^2+q
       130: 3q^3+5q^2+q
       131: 2q^3+2q^2+q
       132: 3q^3+4q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: 2q^3+6q^2+2q
       136: q^4+4q^3+6q^2+2q
       137: 5q^4+11q^3+8q^2+2q
       138: 3q^4+8q^3+7q^2+2q
       139: 5q^4+11q^3+8q^2+2q
       140: 4q^3+7q^2+2q
       141: 3q^4+8q^3+7q^2+2q
       142: 3q^4+7q^3+7q^2+2q
       143: q^4+8q^3+8q^2+2q
       144: 5q^3+7q^2+2q
       145: 7q^3+8q^2+2q
       146: 5q^3+7q^2+2q
       147: 4q^3+7q^2+2q
       148: q^3+3q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 2q^3+2q^2+q
       152: 3q^3+5q^2+q
       153: 2q^3+2q^2+q
       154: 3q^3+5q^2+q
       155: 2q^3+2q^2+q
       156: 3q^3+4q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^4+6q^3+7q^2+2q
       161: 3q^4+7q^3+7q^2+2q
       162: 2q^4+6q^3+7q^2+2q
       163: 2q^3+6q^2+2q
       164: 3q^3+6q^2+2q
       165: 2q^3+6q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^3+q^2+q
       170: q^3+2q^2
       171: 2q^2+q
       172: q^2
       173: q^4+2q^3+2q^2+q
       174: q^3+2q^2
       175: q^3+2q^2+q
       176: q^3+q^2
       177: 2q^3+2q^2+q
       178: 2q^3+4q^2+q
       179: 2q^3+2q^2+q
       180: 3q^3+5q^2+q
       181: q^3+2q^2+q
       182: q^3+4q^2+q
       183: q^3+3q^2+q
       184: 2q^2+q
       185: 3q^3+3q^2+2q
       186: 2q^2
       187: q^3+2q^2+q
       188: 3q^2+q
       189: 2q^3+2q^2+q
       190: 2q^3+4q^2+q
       191: 2q^4+5q^3+4q^2+2q
       192: q^4+2q^3+3q^2
       193: 3q^3+4q^2+q
       194: q^3+3q^2+q
       195: 2q^4+5q^3+4q^2+2q
       196: q^4+2q^3+3q^2
       197: q^3+2q^2+q
       198: q^3+4q^2+q
       199: q^4+3q^3+4q^2+q
       200: 2q^3+3q^2+q
       201: 3q^3+4q^2+q
       202: q^3+3q^2+q
       203: q^3+3q^2+2q
       205: q^2+q
       206: q^2+q
       207: q^4+4q^3+3q^2+q
       208: 4q^3+5q^2+q
       209: 2q^3+2q^2+q
       210: 3q^3+5q^2+q
       211: 2q^3+2q^2+q
       212: 2q^3+4q^2+q
       214: 3q^2+q
       216: q^3+3q^2+q
       218: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: 2q^3+6q^2+2q
       223: 2q^3+6q^2+2q
       224: q^4+4q^3+6q^2+2q
       225: q^4+4q^3+6q^2+2q
       226: 3q^4+8q^3+7q^2+2q
       227: q^4+4q^3+6q^2+2q
       228: 2q^4+6q^3+7q^2+2q
       229: 2q^3+6q^2+2q
       230: q^4+4q^3+6q^2+2q
       231: 5q^3+7q^2+2q
       232: q^3+5q^2+2q
       233: 2q^3+6q^2+2q
       234: q^3+5q^2+2q
       235: 2q^2+2q
       236: 5q^3+7q^2+2q
       237: 2q^3+2q^2+q
       238: 3q^3+5q^2+q
       239: 2q^3+2q^2+q
       240: 3q^3+5q^2+q
       241: 2q^3+2q^2+q
       242: 3q^3+4q^2+q
       243: 7q^3+8q^2+2q
       244: 4q^3+7q^2+2q
       245: q^3+3q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^4+6q^3+7q^2+2q
       251: 3q^4+7q^3+7q^2+2q
       252: 2q^4+6q^3+7q^2+2q
       253: 2q^3+6q^2+2q
       254: 3q^3+6q^2+2q
       255: 2q^3+6q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^3+q^2+q
       260: q^3+2q^2
       261: 2q^2+q
       262: q^2
       263: q^3+q^2+q
       264: q^2
       265: q^2+q
       266: q^2
       267: q^3+q^2+q
       268: q^3+2q^2
       269: q^2
       270: 2q^2+q
       271: q^2+q
       272: q^2+q
       275: q^4+2q^3+2q^2+q
       276: q^3+2q^2
       277: q^3+2q^2+q
       278: q^3+q^2
       280: 2q^2+q
       282: 3q^2+q
       283: q^3+3q^2+q
       284: 2q^2+q
       285: 3q^3+3q^2+2q
       286: 2q^2
       287: 2q^3+2q^2+q
       288: 2q^3+4q^2+q
       290: 2q^2+q
       291: q^3+2q^2+q
       292: 3q^2+q
       293: q^3+3q^2+q
       294: 2q^2+q
       295: 3q^3+3q^2+2q
       296: 2q^2
       297: q^3+2q^2+q
       298: 3q^2+q
       299: q^3+3q^2+q
       300: 2q^2+q
       301: q^3+2q^2+q
       302: q^3+4q^2+q
       303: 3q^3+3q^2+2q
       304: 2q^2
       305: q^3+2q^2+q
       306: 3q^2+q
       307: 3q^2+q
       308: q^2+q
       309: 2q^2+2q
       311: q^2+q
       312: q^2+q
       313: q^2+q
       314: q
       315: 2q^3+2q^2+q
       316: 2q^3+4q^2+q
       317: 2q^3+2q^2+q
       318: 3q^3+5q^2+q
       319: 3q^3+4q^2+q
       320: q^3+3q^2+q
       321: q^3+3q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^3+2q^2+q
       326: 2q^3+4q^2+q
       328: 3q^2+q
       330: q^3+3q^2+q
       332: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: 2q^3+6q^2+2q
       335: q^4+4q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: 2q^2+q
       339: q^3+5q^2+2q
       340: 2q^2+q
       341: q^3+5q^2+2q
       342: q^3+q^2+q
       343: 2q^3+3q^2+q
       344: q^4+4q^3+6q^2+2q
       345: q^4+4q^3+6q^2+2q
       346: 2q^4+6q^3+7q^2+2q
       347: 2q^3+6q^2+2q
       348: 2q^3+6q^2+2q
       349: q^4+4q^3+6q^2+2q
       350: q^4+4q^3+6q^2+2q
       351: q^3+7q^2+3q
       352: q^3+5q^2+2q
       353: q^3+5q^2+2q
       354: 2q^3+6q^2+2q
       355: q^3+5q^2+2q
       356: q^3+5q^2+2q
       357: 2q^2+2q
       358: 2q^2+2q
       359: 3q^2+3q
       361: 3q^2+q
       363: q^3+3q^2+q
       365: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: q^3+5q^2+2q
       370: 2q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^3+q^2+q
       378: q^2
       379: q^2+q
       380: q^2
       382: q^2
       383: q
       385: q^3+q^2+q
       386: q^2
       387: q^2+q
       388: q^2
       389: q^3+q^2+q
       390: q^3+2q^2
       391: q^2
       392: 2q^2+q
       393: q^3+q^2+q
       394: q^2
       395: q^2+q
       396: q^2
       397: q^2+q
       398: q^2+q
       401: q^2+q
       402: q
       405: q^2+q
       408: q^2+q
       410: 2q^2+q
       412: 3q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: 2q^2+q
       419: q^3+3q^2+q
       420: 2q^2+q
       421: 3q^3+3q^2+2q
       422: 2q^2
       423: q^3+2q^2+q
       424: 3q^2+q
       425: q^2+q
       426: 2q^2+q
       427: 2q^2+q
       428: q^3+5q^2+2q
       429: q^3+3q^2+q
       430: 2q^2+q
       431: 3q^3+3q^2+2q
       432: 2q^2
       433: q^3+2q^2+q
       434: 3q^2+q
       436: 2q^2+q
       437: q^3+3q^2+q
       438: 2q^2+q
       439: 3q^3+3q^2+2q
       440: 2q^2
       441: q^3+2q^2+q
       442: 3q^2+q
       443: q^3+4q^2+2q
       444: 3q^2+q
       445: 2q^2+q
       446: q^3+5q^2+2q
       447: 3q^2+q
       448: q^2+q
       449: 2q^2+2q
       451: q^2+q
       452: q
       453: 3q^2+q
       454: q^2+q
       456: q
       457: 2q^2+2q
       459: q^2+q
       460: q
       461: 3q^2+3q
       463: q^2+q
       464: 2q^2+2q
       466: 2q^2+q
       468: 3q^2+q
       469: 2q^3+2q^2+q
       470: 2q^3+4q^2+q
       471: 3q^2+q
       472: q^2+q
       473: 2q^2+2q
       475: q^2+q
       476: q
       477: q^2+q
       478: q^2+q
       479: 2q^2+2q
       480: q^2+q
       481: 3q^2+2q
       482: 2q^3+3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       486: 2q^2+2q
       488: 2q^2+2q
       490: 2q^2+q
       491: 2q^2+2q
       492: q^4+4q^3+6q^2+2q
       493: 2q^3+6q^2+2q
       494: q^4+4q^3+6q^2+2q
       495: 3q^2+2q
       496: 4q^2+3q
       497: q^3+5q^2+2q
       498: q^3+5q^2+2q
       499: 2q^2+2q
       500: 2q
       501: q^2+3q
       503: 3q^2+q
       505: q^3+3q^2+q
       507: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: q^3+5q^2+2q
       512: q^3+5q^2+2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       522: q^2
       523: q
       526: q^2
       527: q
       529: q^3+q^2+q
       530: q^2
       531: q^2+q
       532: q^2
       533: q^3+q^2+q
       534: q^2
       535: q^2+q
       536: q^2
       538: q^2
       540: q
       541: q^3+q^2+q
       542: q^2
       543: q^2
       544: q^2+q
       545: q^2+q
       546: q^3+3q^2+q
       547: q^2
       548: 2q^2+q
       549: q^2+q
       550: q
       554: q
       557: q^2+q
       558: q
       561: q^2+q
       562: 2q^2+2q
       565: q^2+q
       567: q
       569: q^2+q
       572: q^2+q
       573: 2q^2+2q
       576: q^2+q
       577: q^2+q
       578: q^2+q
       581: q^2+q
       584: 2q^2+q
       586: q
       588: 2q^2+q
       589: 2q^2+q
       590: q^2+q
       591: 2q
       593: q
       595: 2q^3+2q^2+2q
       596: q^2
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q^2+2q
       603: q^3+3q^2+q
       604: 2q^2+q
       606: 2q^2+q
       607: 3q^3+3q^2+2q
       608: 2q^2
       609: q^3+2q^2+q
       610: 3q^2+q
       612: 2q^2+q
       613: q^2+q
       614: 2q^2+q
       615: 2q^2+2q
       616: q^2+q
       618: 2q^2+2q
       619: 3q^2+q
       620: q^2+q
       621: 2q^2+2q
       624: q
       625: q^2+q
       626: q
       628: q
       629: q
       630: q
       631: q^2+3q
       634: 2q
       636: 2q^2+q
       638: 3q^2+q
       640: 2q^2+q
       641: 3q^2+q
       642: q^2+q
       643: 2q^2+2q
       645: q^2+q
       646: q
       647: 3q^2+q
       648: q^2+q
       649: 2q^2+2q
       652: q
       653: q^2+q
       654: q
       655: q^2+2q
       656: q
       657: 3q^2+3q
       659: 2q^2+2q
       661: 2q^2+2q
       663: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: 2q^2+2q
       669: 2q^2+2q
       671: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: 4q^2+3q
       675: 3q^2+2q
       676: 2q^3+3q^2+2q
       677: 3q^2+2q
       678: 4q^2+3q
       679: 2q^2+2q
       680: q^2+3q
       681: 3q^2+2q
       682: q^2+q
       683: 2q
       684: q^2+3q
       685: 2q
       686: q^3+5q^2+2q
       687: q^3+5q^2+2q
       688: 2q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       693: q^2+q
       694: q^2+q
       700: q^2+q
       706: q^2
       707: q
       711: q
       713: q
       714: q
       717: q
       722: q^2
       724: q
       725: q^3+q^2+q
       726: q^2
       727: q^2
       728: q^2+q
       730: q^2
       732: q
       734: q^2+q
       736: q
       738: q
       741: q^2+q
       742: q
       746: q
       750: 2q
       753: q^2+q
       755: q
       760: q
       761: q^2+q
       764: q
       765: q^2+2q
       767: q
       770: q
       773: q
       776: q^2+2q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: q
       787: 2q
       790: q^2+2q
       791: q
       793: 2q^2+2q
       794: q^2+q
       796: 2q^2+2q
       798: q
       800: 2q^2+q
       801: 2q^2+q
       802: q^2+q
       803: 2q
       805: q
       807: 2q^3+2q^2+2q
       808: q^2
       810: q^2+q
       811: q^2+q
       812: 2q^2+q
       814: 2q^2+2q
       815: 2q^2+2q
       816: q^2+q
       817: q^2+3q
       820: 2q
       824: q
       825: 2q^2+q
       826: q^2+q
       827: 2q
       831: q^2+q
       834: q
       835: q
       836: q
       838: 2q
       839: q^2+3q
       842: 2q^2+q
       843: q^2+2q
       844: q
       845: 3q^2+q
       846: q^2+q
       847: 2q^2+2q
       850: q
       851: q^2+q
       852: q
       854: q
       855: q
       856: q
       857: q^2+2q
       858: q
       860: 2q^2+2q
       862: 2q^2+2q
       864: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 4q^2+3q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: q^2+3q
       874: 2q
       875: q
       876: 2q
       877: 3q^2+2q
       878: q^2+q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       885: q
       891: q
       898: q
       901: q
       908: q
       913: q^2
       915: q
       917: q^2+q
       919: q
       923: q
       924: q
       925: q
       928: q
       933: q^2+q
       935: q
       937: q
       941: 2q
       948: q
       949: q
       957: 2q
       963: q
       964: q^2+2q
       966: q
       969: q
       972: q
       974: q^2+q
       977: q
       981: q
       983: q
       986: q
       988: q^2+2q
       990: q
       993: q^2+2q
       995: q
       997: q^2+q
       998: 2q
      1000: q
      1003: q
      1004: q
      1006: 2q
      1008: q
      1012: q
      1015: 2q^2+2q
      1016: 2q^2+2q
      1017: q^2+q
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1026: q
      1028: 2q
      1031: 2q
      1032: q^2+3q
      1037: q
      1043: q
      1044: q
      1046: q^2+2q
      1047: q
      1051: q
      1052: 2q^2+q
      1053: q^2+q
      1054: 2q
      1058: q^2+q
      1061: q
      1062: q
      1063: q
      1064: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: 2q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: q+1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1087: q
      1093: q
      1099: q
      1105: q
      1111: q
      1115: q
      1130: q
      1134: q
      1145: q^2+q
      1147: q
      1151: q
      1153: q
      1160: q
      1165: 2q
      1187: q
      1189: q
      1192: q
      1194: q^2+2q
      1196: q
      1202: q
      1203: q
      1211: 2q+1
      1213: q+1
      1215: q
      1216: 2q
      1218: q
      1224: q
      1227: 2q+1
      1228: q+1
      1229: q
      1231: q
      1232: 2q
      1234: q
      1237: q^2+q
      1239: q
      1240: q
      1242: 2q
      1245: q+1
      1246: q+1
      1250: q
      1253: q
      1260: q
      1262: q+1
      1270: q
      1273: q
      1275: q
      1276: q
      1280: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1303: q
      1309: q
      1315: q
      1326: q
      1341: q+1
      1343: q
      1345: q
      1349: q
      1364: q
      1368: q
      1373: q+1
      1405: q+1
      1410: q+1
      1439: q+1
      1440: 1
      1442: 1
      1444: 1
      1449: q
      1450: 2q
      1453: q+1
      1454: q
      1459: 1
      1460: q
      1466: q
      1473: q
      1478: q
      1482: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1526: q+1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1564: q
      1575: q
      1639: 1
      1644: q+1
      1645: 1
      1647: 1
      1652: 1
      1653: 1
      1663: q
      1668: 1
      1669: 1
      1674: 1
      1676: 1
      1724: 1
      1733: 1
      1738: 1
      1746: 1
      1749: 1
      1762: 1
      1802: 1
      1825: 1
      1828: 1
      1829: 1
      1835: 1
      1847: 1
      1898: 1
      1927: 1
      1933: 1
      1967: 1

1968:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+4q^3+2q^2+q
        23: 2q^4+4q^3+2q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+3q^3+2q^2+q
        26: q^4+3q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 3q^3+2q^2+q
        32: 2q^4+4q^3+2q^2+q
        33: 2q^4+4q^3+2q^2+q
        34: 2q^3+2q^2+q
        35: q^4+3q^3+2q^2+q
        36: q^4+3q^3+2q^2+q
        37: q^4+3q^3+2q^2+q
        39: q^4+3q^3+2q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+3q^3+2q^2+q
        53: q^4+3q^3+2q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+2q^2+q
        56: 2q^3+2q^2+q
        57: 2q^3+2q^2+q
        58: 2q^3+q^2+q
        59: q^3+q^2
        60: q^3+q^2+q
        61: q^3+q^2
        62: 2q^3+2q^2+q
        64: q^4+3q^3+2q^2+q
        66: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: q^3+2q^2+q
        73: 2q^3+2q^2+q
        74: 2q^3+2q^2+q
        76: 2q^3+2q^2+q
        78: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 2q^4+4q^3+2q^2+q
        82: 2q^3+2q^2+q
        83: q^4+3q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+3q^3+2q^2+q
        86: q^3+2q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: q^4+3q^3+2q^2+q
        95: q^4+3q^3+2q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+2q^2+q
        98: 2q^3+2q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2+q
       106: q^3+q^2
       107: q^2+q
       108: q^2
       109: q^3+q^2+q
       110: q^2
       111: q^3+2q^2+q
       113: q^3+2q^2+q
       115: 2q^3+2q^2+q
       117: 2q^3+q^2+q
       118: q^3+q^2
       119: q^3+q^2+q
       120: q^3+q^2
       121: 2q^3+2q^2+q
       123: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+2q^2+q
       129: 2q^3+2q^2+q
       131: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+3q^3+2q^2+q
       139: 2q^3+2q^2+q
       140: q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^3+2q^2+q
       146: q^3+2q^2+q
       147: q^3+2q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       151: 2q^3+2q^2+q
       153: 2q^3+2q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^4+3q^3+2q^2+q
       161: q^4+3q^3+2q^2+q
       162: q^4+3q^3+2q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       169: q^2+q
       172: q^2
       173: q^3+q^2+q
       176: q^3+q^2
       177: 2q^3+2q^2+q
       179: q^3+2q^2+q
       181: q^3+2q^2+q
       183: q^2+q
       184: q^2
       185: q^3+q^2+q
       186: q^2
       187: q^3+2q^2+q
       189: q^3+2q^2+q
       191: 2q^3+q^2+q
       192: q^3+q^2
       193: q^2+q
       194: q^2
       195: q^3+q^2+q
       196: q^2
       197: q^3+2q^2+q
       199: q^3+q^2+q
       200: q^3+q^2
       201: q^2+q
       202: q^2
       203: q^2+q
       205: q^2+q
       207: 2q^3+2q^2+q
       209: q^3+2q^2+q
       211: 2q^3+2q^2+q
       213: 2q^3+2q^2+q
       215: 2q^3+2q^2+q
       217: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: q^3+2q^2+q
       224: 2q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^3+2q^2+q
       228: q^4+3q^3+2q^2+q
       229: q^3+2q^2+q
       230: 2q^3+2q^2+q
       231: q^3+2q^2+q
       232: q^3+2q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: q^2+q
       236: 2q^3+2q^2+q
       237: 2q^3+2q^2+q
       239: 2q^3+2q^2+q
       241: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^3+2q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       259: q^2+q
       262: q^2
       263: q^2+q
       266: q^2
       267: q^2+q
       269: q^2
       271: q^2+q
       275: q^3+q^2+q
       278: q^3+q^2
       279: q^3+2q^2+q
       281: 2q^3+2q^2+q
       283: q^2+q
       284: q^2
       285: q^3+q^2+q
       286: q^2
       287: q^3+2q^2+q
       289: q^3+2q^2+q
       291: q^3+2q^2+q
       293: q^2+q
       294: q^2
       295: q^2+q
       296: q^2
       297: 2q^2+q
       299: q^2+q
       300: q^2
       301: q^3+2q^2+q
       303: q^3+q^2+q
       304: q^2
       305: q^3+2q^2+q
       307: q^2+q
       308: q^2
       309: q^2+q
       311: q^2+q
       313: q^2+q
       315: 2q^3+2q^2+q
       317: q^3+2q^2+q
       319: q^2+q
       320: q^2
       321: q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: q^3+2q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: q^3+2q^2+q
       349: 2q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+2q^2+q
       357: q
       358: q^2+q
       359: q^2+q
       360: 2q^3+2q^2+q
       362: 2q^3+2q^2+q
       364: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^3+2q^2+q
       370: q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2+q
       380: q^2
       381: q^2+q
       384: q^2
       385: q^2+q
       388: q^2
       389: q^2+q
       391: q^2
       393: q^2+q
       396: q^2
       397: q^2+q
       401: q^2+q
       405: q^2+q
       409: q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       420: q^2
       421: q^2+q
       422: q^2
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2+q
       430: q^2
       431: q^3+q^2+q
       432: q^2
       433: q^3+2q^2+q
       435: q^3+2q^2+q
       437: q^2+q
       438: q^2
       439: q^2+q
       440: q^2
       441: 2q^2+q
       443: q^2+q
       444: q^2
       445: 2q^2+q
       447: q^2+q
       448: q^2
       449: q^2+q
       451: q^2+q
       453: q
       454: q^2
       455: q^2+q
       457: q
       459: q
       461: q^2+q
       463: q^2+q
       465: q^3+2q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: q^2+q
       472: q^2
       473: q^2+q
       475: q^2+q
       477: q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+2q^2+q
       513: q
       514: q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       521: q^2+q
       524: q^2
       525: q
       528: q^2
       529: q^2+q
       532: q^2
       533: q^2+q
       536: q^2
       537: q^2+q
       539: q^2
       541: q^2+q
       543: q^2
       545: q^2+q
       547: q^2
       549: q^2+q
       553: q^2+q
       557: q
       561: q^2+q
       565: q^2+q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       590: q^2
       591: q
       593: q
       595: q^2+q
       596: q^2
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       603: q^2+q
       604: q^2
       605: q^3+2q^2+q
       607: q^2+q
       608: q^2
       609: 2q^2+q
       611: q^2+q
       613: q^2+q
       615: q^2+q
       616: q^2
       617: 2q^2+q
       619: q
       620: q^2
       621: q
       623: q^2+q
       625: q
       627: q
       629: q
       631: q^2+q
       633: q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       641: q^2+q
       642: q^2
       643: q^2+q
       645: q^2+q
       647: q
       648: q^2
       649: q
       651: q^2+q
       653: q
       655: q^2+q
       657: 2q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: 2q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       680: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       693: q^2+q
       705: q
       708: q^2
       709: q^2+q
       712: q^2
       713: q
       717: q
       721: q^2+q
       723: q^2
       725: q^2+q
       727: q^2
       729: q
       731: q^2
       733: q^2+q
       735: q^2
       737: q^2+q
       741: q
       745: q
       749: q^2+q
       753: q^2+q
       757: q^2+q
       761: q
       765: q^2+q
       769: q^2+q
       775: 2q^2+q
       777: q^2+q
       779: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       793: q^2+q
       794: q^2
       795: 2q^2+q
       797: 2q^2+q
       799: q^2+q
       801: q^2+q
       802: q^2
       803: q
       805: q
       807: q^2+q
       808: q^2
       809: q^2+q
       811: q^2+q
       817: q^2+q
       819: q^2+q
       821: q
       823: q
       825: q
       826: q^2
       827: q
       831: q
       833: q
       835: q
       841: q^2+q
       843: q^2+q
       845: q
       846: q^2
       847: q
       849: q^2+q
       851: q
       853: q
       855: q
       866: q^2+q
       870: q^2+q
       871: q^2+q
       874: q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       884: q^2+q
       896: q
       899: q^2
       900: q
       904: q
       908: q
       912: q
       914: q^2
       916: q^2+q
       918: q^2
       920: q^2+q
       922: q^2
       924: q
       928: q
       936: q
       940: q^2+q
       944: q
       948: q
       960: q^2+q
       964: q^2+q
       968: q^2+q
       974: q
       978: q
       994: q^2+q
       998: q
      1000: q
      1010: q
      1012: q
      1018: q^2+q
      1020: q^2+q
      1022: q^2+q
      1026: q
      1028: q
      1034: q
      1036: q
      1038: q
      1044: q
      1048: q
      1050: q
      1052: q
      1053: q^2
      1054: q
      1058: q
      1060: q
      1062: q
      1064: q
      1076: q^2+q
      1080: q
      1083: q
      1084: q
      1086: q^2+q
      1114: q
      1122: q
      1126: q
      1130: q
      1138: q
      1148: q
      1150: q^2
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1184: q
      1198: q
      1202: q
      1222: 1
      1230: q^2+q
      1232: q
      1234: q
      1248: q
      1250: q
      1264: q
      1266: q
      1270: q
      1274: q
      1278: q
      1280: q
      1287: q
      1290: q
      1322: 1
      1336: 1
      1348: q
      1356: q
      1360: q
      1364: q
      1380: q
      1414: q
      1418: q
      1430: q
      1446: 1
      1464: q
      1466: q
      1480: 1
      1491: 1
      1501: q
      1555: 1
      1559: 1
      1571: 1
      1607: q
      1633: 1
      1637: 1
      1671: 1
      1677: 1
      1689: 1
      1725: 1
      1729: 1
      1753: 1
      1803: 1
      1823: 1
      1836: 1
      1848: 1
      1894: 1
      1928: 1
      1968: 1

1969:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: 7q^4+15q^3+9q^2+2q
        23: 7q^4+15q^3+9q^2+2q
        24: 2q^5+9q^4+12q^3+8q^2+2q
        25: q^4+11q^3+9q^2+2q
        26: q^4+11q^3+9q^2+2q
        27: 4q^4+9q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: 7q^4+15q^3+9q^2+2q
        32: 5q^4+11q^3+8q^2+2q
        33: 7q^4+15q^3+9q^2+2q
        34: q^4+11q^3+9q^2+2q
        35: q^4+8q^3+8q^2+2q
        36: q^4+11q^3+9q^2+2q
        37: 6q^3+6q^2+q
        38: q^4+5q^3+3q^2+q
        39: 6q^3+6q^2+q
        40: q^4+5q^3+3q^2+q
        41: 2q^4+5q^3+5q^2+q
        42: 2q^4+4q^3+3q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 5q^4+11q^3+8q^2+2q
        53: 5q^4+11q^3+8q^2+2q
        54: q^5+5q^4+9q^3+7q^2+2q
        55: 7q^3+8q^2+2q
        56: 7q^3+8q^2+2q
        57: q^4+6q^3+7q^2+2q
        58: 4q^4+9q^3+5q^2+2q
        59: 3q^4+6q^3+4q^2
        60: 5q^3+4q^2+q
        61: q^4+6q^3+5q^2+q
        62: 6q^3+6q^2+q
        63: q^4+5q^3+3q^2+q
        64: 4q^3+5q^2+q
        65: q^4+4q^3+3q^2+q
        66: 6q^3+6q^2+q
        67: q^4+5q^3+3q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 4q^3+7q^2+2q
        73: 3q^4+7q^3+7q^2+2q
        74: 3q^3+5q^2+q
        75: 2q^3+2q^2+q
        76: 3q^3+5q^2+q
        77: 2q^3+2q^2+q
        78: 3q^3+4q^2+q
        79: 2q^3+2q^2+q
        80: 5q^4+11q^3+8q^2+2q
        81: 5q^4+11q^3+8q^2+2q
        82: 5q^4+11q^3+8q^2+2q
        83: 3q^4+8q^3+7q^2+2q
        84: q^4+8q^3+8q^2+2q
        85: q^4+8q^3+8q^2+2q
        86: 7q^3+8q^2+2q
        87: 5q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 5q^4+11q^3+8q^2+2q
        95: 5q^4+11q^3+8q^2+2q
        96: q^5+5q^4+9q^3+7q^2+2q
        97: 7q^3+8q^2+2q
        98: 7q^3+8q^2+2q
        99: q^4+6q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 3q^3+3q^2+q
       104: 2q^3+q^2
       105: q^4+3q^3+2q^2+q
       106: 3q^3+3q^2
       107: q^3+3q^2+q
       108: 3q^3+4q^2+q
       109: 2q^4+5q^3+4q^2+2q
       110: q^4+2q^3+3q^2
       111: q^3+4q^2+q
       112: q^3+2q^2+q
       113: 3q^3+5q^2+q
       114: 2q^3+2q^2+q
       115: 2q^3+4q^2+q
       116: 2q^3+2q^2+q
       117: 2q^4+5q^3+4q^2+2q
       118: q^4+2q^3+3q^2
       119: 2q^3+3q^2+q
       120: q^4+3q^3+4q^2+q
       121: 4q^3+5q^2+q
       122: q^4+4q^3+3q^2+q
       123: 4q^3+5q^2+q
       124: q^4+4q^3+3q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 3q^3+5q^2+q
       128: 2q^3+2q^2+q
       129: 3q^3+5q^2+q
       130: 2q^3+2q^2+q
       131: 3q^3+4q^2+q
       132: 2q^3+2q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: 2q^3+6q^2+2q
       136: q^4+4q^3+6q^2+2q
       137: 5q^4+11q^3+8q^2+2q
       138: 3q^4+8q^3+7q^2+2q
       139: 5q^4+11q^3+8q^2+2q
       140: 4q^3+7q^2+2q
       141: 3q^4+8q^3+7q^2+2q
       142: 3q^4+7q^3+7q^2+2q
       143: q^4+8q^3+8q^2+2q
       144: 5q^3+7q^2+2q
       145: 7q^3+8q^2+2q
       146: 5q^3+7q^2+2q
       147: 4q^3+7q^2+2q
       148: q^3+3q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 3q^3+5q^2+q
       152: 2q^3+2q^2+q
       153: 3q^3+5q^2+q
       154: 2q^3+2q^2+q
       155: 3q^3+4q^2+q
       156: 2q^3+2q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^4+6q^3+7q^2+2q
       161: 3q^4+7q^3+7q^2+2q
       162: 2q^4+6q^3+7q^2+2q
       163: 2q^3+6q^2+2q
       164: 3q^3+6q^2+2q
       165: 2q^3+6q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: 2q^2+q
       170: q^2
       171: q^3+q^2+q
       172: q^3+2q^2
       173: q^3+2q^2+q
       174: q^3+q^2
       175: q^4+2q^3+2q^2+q
       176: q^3+2q^2
       177: 2q^3+4q^2+q
       178: 2q^3+2q^2+q
       179: 3q^3+5q^2+q
       180: 2q^3+2q^2+q
       181: q^3+4q^2+q
       182: q^3+2q^2+q
       183: 2q^2+q
       184: q^3+3q^2+q
       185: 3q^3+3q^2+2q
       186: 2q^2
       187: 3q^2+q
       188: q^3+2q^2+q
       189: 2q^3+4q^2+q
       190: 2q^3+2q^2+q
       191: 2q^4+5q^3+4q^2+2q
       192: q^4+2q^3+3q^2
       193: q^3+3q^2+q
       194: 3q^3+4q^2+q
       195: 2q^4+5q^3+4q^2+2q
       196: q^4+2q^3+3q^2
       197: q^3+4q^2+q
       198: q^3+2q^2+q
       199: 2q^3+3q^2+q
       200: q^4+3q^3+4q^2+q
       201: q^3+3q^2+q
       202: 3q^3+4q^2+q
       203: q^3+3q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^3+5q^2+q
       208: q^4+4q^3+3q^2+q
       209: 3q^3+5q^2+q
       210: 2q^3+2q^2+q
       211: 2q^3+4q^2+q
       212: 2q^3+2q^2+q
       213: 3q^2+q
       215: q^3+3q^2+q
       217: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: 2q^3+6q^2+2q
       223: 2q^3+6q^2+2q
       224: q^4+4q^3+6q^2+2q
       225: q^4+4q^3+6q^2+2q
       226: 3q^4+8q^3+7q^2+2q
       227: q^4+4q^3+6q^2+2q
       228: 2q^4+6q^3+7q^2+2q
       229: 2q^3+6q^2+2q
       230: q^4+4q^3+6q^2+2q
       231: 5q^3+7q^2+2q
       232: q^3+5q^2+2q
       233: 2q^3+6q^2+2q
       234: q^3+5q^2+2q
       235: 2q^2+2q
       236: 5q^3+7q^2+2q
       237: 3q^3+5q^2+q
       238: 2q^3+2q^2+q
       239: 3q^3+5q^2+q
       240: 2q^3+2q^2+q
       241: 3q^3+4q^2+q
       242: 2q^3+2q^2+q
       243: 7q^3+8q^2+2q
       244: 4q^3+7q^2+2q
       245: q^3+3q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^4+6q^3+7q^2+2q
       251: 3q^4+7q^3+7q^2+2q
       252: 2q^4+6q^3+7q^2+2q
       253: 2q^3+6q^2+2q
       254: 3q^3+6q^2+2q
       255: 2q^3+6q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: 2q^2+q
       260: q^2
       261: q^3+q^2+q
       262: q^3+2q^2
       263: q^2+q
       264: q^2
       265: q^3+q^2+q
       266: q^2
       267: 2q^2+q
       268: q^2
       269: q^3+2q^2
       270: q^3+q^2+q
       271: q^2+q
       272: q^2+q
       275: q^3+2q^2+q
       276: q^3+q^2
       277: q^4+2q^3+2q^2+q
       278: q^3+2q^2
       279: 2q^2+q
       281: 3q^2+q
       283: 2q^2+q
       284: q^3+3q^2+q
       285: 3q^3+3q^2+2q
       286: 2q^2
       287: 2q^3+4q^2+q
       288: 2q^3+2q^2+q
       289: 2q^2+q
       291: 3q^2+q
       292: q^3+2q^2+q
       293: 2q^2+q
       294: q^3+3q^2+q
       295: 3q^3+3q^2+2q
       296: 2q^2
       297: 3q^2+q
       298: q^3+2q^2+q
       299: 2q^2+q
       300: q^3+3q^2+q
       301: q^3+4q^2+q
       302: q^3+2q^2+q
       303: 3q^3+3q^2+2q
       304: 2q^2
       305: 3q^2+q
       306: q^3+2q^2+q
       307: q^2+q
       308: 3q^2+q
       309: 2q^2+2q
       311: q^2+q
       312: q^2+q
       313: q
       314: q^2+q
       315: 2q^3+4q^2+q
       316: 2q^3+2q^2+q
       317: 3q^3+5q^2+q
       318: 2q^3+2q^2+q
       319: q^3+3q^2+q
       320: 3q^3+4q^2+q
       321: q^3+3q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^3+4q^2+q
       326: 2q^3+2q^2+q
       327: 3q^2+q
       329: q^3+3q^2+q
       331: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: 2q^3+6q^2+2q
       335: q^4+4q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: q^3+5q^2+2q
       339: 2q^2+q
       340: q^3+5q^2+2q
       341: 2q^2+q
       342: 2q^3+3q^2+q
       343: q^3+q^2+q
       344: q^4+4q^3+6q^2+2q
       345: q^4+4q^3+6q^2+2q
       346: 2q^4+6q^3+7q^2+2q
       347: 2q^3+6q^2+2q
       348: 2q^3+6q^2+2q
       349: q^4+4q^3+6q^2+2q
       350: q^4+4q^3+6q^2+2q
       351: q^3+7q^2+3q
       352: q^3+5q^2+2q
       353: q^3+5q^2+2q
       354: 2q^3+6q^2+2q
       355: q^3+5q^2+2q
       356: q^3+5q^2+2q
       357: 2q^2+2q
       358: 2q^2+2q
       359: 3q^2+3q
       360: 3q^2+q
       362: q^3+3q^2+q
       364: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: q^3+5q^2+2q
       370: 2q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2+q
       378: q^2
       379: q^3+q^2+q
       380: q^2
       381: q
       384: q^2
       385: q^2+q
       386: q^2
       387: q^3+q^2+q
       388: q^2
       389: 2q^2+q
       390: q^2
       391: q^3+2q^2
       392: q^3+q^2+q
       393: q^2+q
       394: q^2
       395: q^3+q^2+q
       396: q^2
       397: q^2+q
       398: q^2+q
       401: q
       402: q^2+q
       405: q^2+q
       408: q^2+q
       409: 2q^2+q
       411: 3q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: 2q^2+q
       419: 2q^2+q
       420: q^3+3q^2+q
       421: 3q^3+3q^2+2q
       422: 2q^2
       423: 3q^2+q
       424: q^3+2q^2+q
       425: 2q^2+q
       426: q^2+q
       427: q^3+5q^2+2q
       428: 2q^2+q
       429: 2q^2+q
       430: q^3+3q^2+q
       431: 3q^3+3q^2+2q
       432: 2q^2
       433: 3q^2+q
       434: q^3+2q^2+q
       435: 2q^2+q
       437: 2q^2+q
       438: q^3+3q^2+q
       439: 3q^3+3q^2+2q
       440: 2q^2
       441: 3q^2+q
       442: q^3+2q^2+q
       443: 3q^2+q
       444: q^3+4q^2+2q
       445: q^3+5q^2+2q
       446: 2q^2+q
       447: q^2+q
       448: 3q^2+q
       449: 2q^2+2q
       451: q
       452: q^2+q
       453: q^2+q
       454: 3q^2+q
       455: q
       457: 2q^2+2q
       459: q
       460: q^2+q
       461: 3q^2+3q
       463: 2q^2+2q
       464: q^2+q
       465: 2q^2+q
       467: 3q^2+q
       469: 2q^3+4q^2+q
       470: 2q^3+2q^2+q
       471: q^2+q
       472: 3q^2+q
       473: 2q^2+2q
       475: q
       476: q^2+q
       477: q^2+q
       478: q^2+q
       479: q^2+q
       480: 2q^2+2q
       481: 3q^2+2q
       482: 2q^3+3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       485: 2q^2+2q
       487: 2q^2+2q
       489: 2q^2+q
       491: 2q^2+2q
       492: q^4+4q^3+6q^2+2q
       493: 2q^3+6q^2+2q
       494: q^4+4q^3+6q^2+2q
       495: 3q^2+2q
       496: 4q^2+3q
       497: q^3+5q^2+2q
       498: q^3+5q^2+2q
       499: 2q^2+2q
       500: 2q
       501: q^2+3q
       502: 3q^2+q
       504: q^3+3q^2+q
       506: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: q^3+5q^2+2q
       512: q^3+5q^2+2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       521: q
       524: q^2
       525: q
       528: q^2
       529: q^2+q
       530: q^2
       531: q^3+q^2+q
       532: q^2
       533: q^2+q
       534: q^2
       535: q^3+q^2+q
       536: q^2
       537: q
       539: q^2
       541: q^2+q
       542: q^2
       543: q^2
       544: q^3+q^2+q
       545: 2q^2+q
       546: q^2
       547: q^3+3q^2+q
       548: q^2+q
       549: q
       550: q^2+q
       553: q
       557: q
       558: q^2+q
       561: 2q^2+2q
       562: q^2+q
       565: q
       567: q^2+q
       569: q^2+q
       572: q^2+q
       573: q^2+q
       576: 2q^2+2q
       577: q^2+q
       580: q^2+q
       581: q^2+q
       583: 2q^2+q
       585: q
       587: 2q^2+q
       589: q^2+q
       590: 2q^2+q
       591: 2q
       594: q
       595: 2q^3+2q^2+2q
       596: q^2
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q^2+2q
       603: 2q^2+q
       604: q^3+3q^2+q
       605: 2q^2+q
       607: 3q^3+3q^2+2q
       608: 2q^2
       609: 3q^2+q
       610: q^3+2q^2+q
       611: 2q^2+q
       613: 2q^2+q
       614: q^2+q
       615: q^2+q
       616: 2q^2+2q
       617: 2q^2+2q
       619: q^2+q
       620: 3q^2+q
       621: 2q^2+2q
       623: q
       625: q
       626: q^2+q
       627: q
       629: q
       630: q
       631: q^2+3q
       633: 2q
       635: 2q^2+q
       637: 3q^2+q
       639: 2q^2+q
       641: q^2+q
       642: 3q^2+q
       643: 2q^2+2q
       645: q
       646: q^2+q
       647: q^2+q
       648: 3q^2+q
       649: 2q^2+2q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+2q
       657: 3q^2+3q
       658: 2q^2+2q
       660: 2q^2+2q
       662: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: 2q^2+2q
       668: 2q^2+2q
       670: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: 4q^2+3q
       675: 3q^2+2q
       676: 2q^3+3q^2+2q
       677: 3q^2+2q
       678: 4q^2+3q
       679: 2q^2+2q
       680: q^2+3q
       681: 3q^2+2q
       682: q^2+q
       683: 2q
       684: q^2+3q
       685: 2q
       686: q^3+5q^2+2q
       687: q^3+5q^2+2q
       688: 2q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       693: q^2+q
       698: q^2+q
       700: q^2+q
       705: q
       708: q^2
       709: q
       713: q
       714: q
       719: q
       721: q
       723: q^2
       725: q^2+q
       726: q^2
       727: q^2
       728: q^3+q^2+q
       729: q
       731: q^2
       733: q
       735: q^2+q
       737: q
       741: q
       742: q^2+q
       745: q
       749: 2q
       753: q
       755: q^2+q
       757: q
       761: q
       764: q^2+q
       765: q
       767: q^2+2q
       769: q
       772: q
       775: q^2+2q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       786: q
       787: 2q
       789: q^2+2q
       792: q
       793: q^2+q
       794: 2q^2+2q
       795: 2q^2+2q
       797: q
       799: 2q^2+q
       801: q^2+q
       802: 2q^2+q
       803: 2q
       806: q
       807: 2q^3+2q^2+2q
       808: q^2
       809: q^2+q
       811: 2q^2+q
       812: q^2+q
       813: 2q^2+2q
       815: q^2+q
       816: 2q^2+2q
       817: q^2+3q
       819: 2q
       823: q
       825: q^2+q
       826: 2q^2+q
       827: 2q
       831: q^2+q
       833: q
       835: q
       836: q
       837: 2q
       839: q^2+3q
       841: 2q^2+q
       843: q
       844: q^2+2q
       845: q^2+q
       846: 3q^2+q
       847: 2q^2+2q
       849: q
       851: q
       852: q^2+q
       853: q
       855: q
       856: q
       857: q
       858: q^2+2q
       859: 2q^2+2q
       861: 2q^2+2q
       863: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 4q^2+3q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: q^2+3q
       874: 2q
       875: q
       876: 2q
       877: 3q^2+2q
       878: q^2+q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       888: q
       896: q
       900: q
       910: q
       912: q
       914: q^2
       916: q
       918: q^2+q
       920: q
       924: q
       925: q
       931: q
       932: q
       934: q^2+q
       936: q
       940: 2q
       948: q
       949: q
       956: 2q
       960: q
       964: q
       966: q^2+2q
       968: q
       971: q
       974: q
       977: q^2+q
       978: q
       982: q
       985: q
       988: q
       990: q^2+2q
       992: q^2+2q
       994: q
       996: q^2+q
       998: 2q
      1001: q
      1002: q
      1005: q
      1006: 2q
      1009: q
      1013: q
      1014: 2q^2+2q
      1016: q^2+q
      1017: 2q^2+2q
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1027: q
      1028: 2q
      1030: 2q
      1032: q^2+3q
      1036: q
      1042: q
      1044: q
      1046: q
      1047: q^2+2q
      1050: q
      1052: q^2+q
      1053: 2q^2+q
      1054: 2q
      1058: q^2+q
      1060: q
      1062: q
      1063: q
      1065: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: 2q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: q+1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1090: q
      1098: q
      1103: q
      1110: q
      1114: q
      1132: q
      1137: q
      1144: q
      1146: q^2+q
      1148: q
      1152: q
      1161: q
      1164: 2q
      1184: q
      1188: q
      1191: q
      1194: q
      1196: q^2+2q
      1202: q
      1203: q
      1210: 2q+1
      1212: q+1
      1214: q
      1216: 2q
      1219: q
      1225: q
      1226: 2q+1
      1228: q
      1229: q+1
      1230: q
      1232: 2q
      1235: q
      1236: q^2+q
      1238: q
      1241: q
      1242: 2q
      1244: q+1
      1246: q+1
      1250: q
      1252: q
      1260: q
      1263: q+1
      1270: q
      1272: q
      1274: q
      1277: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1302: q
      1306: q
      1314: q
      1328: q
      1340: q
      1342: q+1
      1344: q
      1348: q
      1365: q
      1370: q
      1372: q+1
      1407: q+1
      1412: q+1
      1438: q+1
      1440: 1
      1443: 1
      1445: 1
      1448: q
      1450: 2q
      1452: q+1
      1455: q
      1458: 1
      1460: q
      1466: q
      1472: q
      1478: q
      1483: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1529: q+1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1563: q
      1576: q
      1640: 1
      1643: q+1
      1645: 1
      1648: 1
      1651: 1
      1653: 1
      1663: q
      1667: 1
      1670: 1
      1674: 1
      1679: 1
      1726: 1
      1735: 1
      1737: 1
      1747: 1
      1750: 1
      1761: 1
      1804: 1
      1826: 1
      1827: 1
      1829: 1
      1838: 1
      1849: 1
      1899: 1
      1929: 1
      1932: 1
      1969: 1

1970:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: 2q^3+4q^2+2q+1
        25: q^3+3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^3+4q^2+2q+1
        32: 2q^3+4q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        41: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: q^3+3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: q^3+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^3+q^2+q
        59: q^3+3q^2+q+1
        60: q^2+q
        61: q^3+2q^2+q+1
        62: q^3+3q^2+2q+1
        64: q^3+3q^2+2q+1
        66: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        76: 2q^2+2q+1
        78: 2q^2+2q+1
        80: 2q^3+4q^2+2q+1
        81: 2q^3+4q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^3+3q^2+2q+1
        85: q^3+3q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+q
       106: q^3+2q^2+q+1
       107: q
       108: q^2+q+1
       109: q
       110: 2q^2+q+1
       111: q^2+2q+1
       113: 2q^2+2q+1
       115: 2q^2+2q+1
       117: q^3+q^2+q
       118: q^3+3q^2+q+1
       119: q^2+q
       120: q^3+2q^2+q+1
       121: q^3+3q^2+2q+1
       123: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       127: 2q^2+2q+1
       129: 2q^2+2q+1
       131: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^3+4q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: q^2+2q+1
       141: q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^3+3q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       153: 2q^2+2q+1
       155: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q
       172: q^2+q+1
       173: q^2+q
       176: q^3+2q^2+q+1
       177: 2q^2+2q+1
       179: 2q^2+2q+1
       181: q^2+2q+1
       183: q
       184: q^2+q+1
       185: q
       186: 2q^2+q+1
       187: q^2+2q+1
       189: 2q^2+2q+1
       191: q^3+q^2+q
       192: q^3+3q^2+q+1
       193: q
       194: q^2+q+1
       195: q
       196: 2q^2+q+1
       197: q^2+2q+1
       199: q^2+q
       200: q^3+2q^2+q+1
       201: q
       202: q^2+q+1
       204: q+1
       205: q+1
       207: q^3+3q^2+2q+1
       209: 2q^2+2q+1
       211: 2q^2+2q+1
       213: 2q^2+2q+1
       215: 2q^2+2q+1
       217: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: 2q^2+2q+1
       226: q^3+3q^2+2q+1
       227: q^3+3q^2+2q+1
       228: q^3+3q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       237: 2q^2+2q+1
       239: 2q^2+2q+1
       241: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: q^3+3q^2+2q+1
       251: q^3+3q^2+2q+1
       252: q^3+3q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q
       262: q^2+q+1
       263: q
       266: q^2+q+1
       267: q
       269: q^2+q+1
       273: q+1
       275: q^2+q
       278: q^3+2q^2+q+1
       279: 2q^2+2q+1
       281: 2q^2+2q+1
       283: q
       284: q^2+q+1
       285: q
       286: 2q^2+q+1
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: q
       294: q^2+q+1
       295: q
       296: 2q^2+q+1
       297: q^2+2q+1
       299: q
       300: q^2+q+1
       301: q^2+2q+1
       303: q
       304: 2q^2+q+1
       305: q^2+2q+1
       307: q
       308: q^2+q+1
       310: q+1
       311: q+1
       313: q+1
       315: 2q^2+2q+1
       317: 2q^2+2q+1
       319: q
       320: q^2+q+1
       322: q+1
       323: q+1
       325: 2q^2+2q+1
       327: 2q^2+2q+1
       329: 2q^2+2q+1
       331: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^3+3q^2+2q+1
       345: q^3+3q^2+2q+1
       346: q^3+3q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: 2q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       360: 2q^2+2q+1
       362: 2q^2+2q+1
       364: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       380: q^2+q+1
       381: q
       384: q^2+q+1
       385: q
       388: q^2+q+1
       389: q
       391: q^2+q+1
       393: q
       396: q^2+q+1
       399: q+1
       404: q+1
       406: q+1
       409: 2q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: q
       420: q^2+q+1
       421: q
       422: 2q^2+q+1
       423: q^2+2q+1
       425: q+1
       427: 2q+1
       429: q
       430: q^2+q+1
       431: q
       432: 2q^2+q+1
       433: q^2+2q+1
       435: q^2+2q+1
       437: q
       438: q^2+q+1
       439: q
       440: 2q^2+q+1
       441: q^2+2q+1
       443: q
       444: q+1
       445: 2q+1
       447: q
       448: q^2+q+1
       450: q+1
       451: q+1
       453: q
       454: q^2+q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 2q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       471: q
       472: q^2+q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: q^3+3q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: q+1
       502: 2q^2+2q+1
       504: 2q^2+2q+1
       506: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: q^2+q+1
       525: q
       528: q^2+q+1
       529: q
       532: q^2+q+1
       533: q
       536: q^2+q+1
       537: q
       539: q^2+q+1
       541: q
       543: q^2+q+1
       545: q
       547: q+1
       552: q+1
       555: q+1
       559: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: 2q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: q
       590: q^2+q+1
       592: 1
       594: 1
       595: q
       596: 2q^2+q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: q
       604: q^2+q+1
       605: q^2+2q+1
       607: q
       608: 2q^2+q+1
       609: q^2+2q+1
       611: q^2+2q+1
       613: q+1
       615: q
       616: q+1
       617: 2q+1
       619: q
       620: q^2+q+1
       622: q+1
       623: q+1
       625: q+1
       627: q+1
       629: 1
       632: q+1
       633: q+1
       635: 2q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       641: q
       642: q^2+q+1
       644: q+1
       645: q+1
       647: q
       648: q^2+q+1
       650: q+1
       651: q+1
       653: q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: 1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q+1
       705: q
       708: q^2+q+1
       709: q
       712: q^2+q+1
       716: 1
       720: 1
       721: q
       723: q^2+q+1
       725: q
       727: q^2+q+1
       729: q
       731: q^2+q+1
       733: q
       735: q+1
       739: q+1
       743: q+1
       747: q+1
       751: q+1
       756: q+1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       775: 2q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       793: q
       794: q+1
       795: 2q+1
       797: q^2+2q+1
       799: q^2+2q+1
       801: q
       802: q^2+q+1
       804: 1
       806: 1
       807: q
       808: 2q^2+q+1
       809: q+1
       811: q+1
       813: 2q+1
       815: q
       816: q+1
       818: q+1
       819: q+1
       821: q+1
       823: q+1
       825: q
       826: q^2+q+1
       828: 1
       832: q+1
       833: 1
       835: 1
       837: q+1
       840: q+1
       841: 2q^2+2q+1
       843: q+1
       845: q
       846: q^2+q+1
       848: q+1
       849: q+1
       851: q+1
       853: q+1
       855: 1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       889: q+1
       896: q
       899: q^2+q+1
       902: 1
       906: 1
       911: 1
       912: q
       914: q^2+q+1
       916: q
       918: q+1
       920: q
       922: q^2+q+1
       927: 1
       930: 1
       932: q
       934: q+1
       938: q+1
       942: q+1
       946: q+1
       950: 1
       958: q+1
       961: q+1
       967: q+1
       968: q+1
       975: q+1
       979: q+1
       982: q+1
       991: q+1
       992: 2q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1016: q
      1017: q+1
      1018: q^2+2q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1027: 1
      1029: 1
      1030: q+1
      1033: q+1
      1034: q+1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: q+1
      1048: q+1
      1050: q+1
      1052: q
      1053: q^2+q+1
      1055: 1
      1059: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: q+1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1144: q
      1146: q+1
      1148: q
      1150: q^2+q+1
      1154: 1
      1158: 1
      1163: 1
      1166: q+1
      1170: q+1
      1174: 1
      1185: q+1
      1188: q+1
      1197: q+1
      1199: q+1
      1204: 1
      1210: 2q+1
      1212: q+1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2q+1
      1228: q
      1229: q+1
      1230: q+1
      1233: 1
      1235: 1
      1236: q+1
      1238: q+1
      1241: 1
      1243: 1
      1244: q+1
      1247: q+1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1262: q+1
      1264: q+1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1340: q
      1342: q+1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: q+1
      1378: 1
      1382: 1
      1404: q+1
      1413: q+1
      1415: q+1
      1420: 1
      1430: 1
      1436: 1
      1438: q+1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: q+1
      1451: 1
      1452: q+1
      1455: 1
      1456: 1
      1458: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1474: 1
      1479: 1
      1480: 1
      1482: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1494: 1
      1506: 1
      1530: q+1
      1538: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1637: 1
      1639: 1
      1643: q+1
      1646: 1
      1648: 1
      1651: 1
      1654: 1
      1659: 1
      1661: 1
      1664: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1680: 1
      1692: 1
      1723: 1
      1730: 1
      1736: 1
      1739: 1
      1742: 1
      1747: 1
      1752: 1
      1754: 1
      1763: 1
      1787: 1
      1801: 1
      1823: 1
      1825: 1
      1827: 1
      1830: 1
      1839: 1
      1851: 1
      1895: 1
      1900: 1
      1926: 1
      1934: 1
      1970: 1

1971:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: 2q^3+4q^2+2q+1
        25: q^3+3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^3+4q^2+2q+1
        32: 2q^3+4q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        38: q^3+3q^2+2q+1
        40: q^3+3q^2+2q+1
        42: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: q^3+3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: q^3+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^3+3q^2+q+1
        59: q^3+q^2+q
        60: q^2+q
        61: q^3+2q^2+q+1
        63: q^3+3q^2+2q+1
        65: q^3+3q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: 2q^2+2q+1
        77: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^3+4q^2+2q+1
        81: 2q^3+4q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^3+3q^2+2q+1
        85: q^3+3q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       104: q^2+q
       105: q^3+2q^2+q+1
       107: q
       108: q^2+q+1
       109: 2q^2+q+1
       110: q
       112: q^2+2q+1
       114: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^3+3q^2+q+1
       118: q^3+q^2+q
       119: q^2+q
       120: q^3+2q^2+q+1
       122: q^3+3q^2+2q+1
       124: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       128: 2q^2+2q+1
       130: 2q^2+2q+1
       132: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^3+4q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: q^2+2q+1
       141: q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^3+3q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       152: 2q^2+2q+1
       154: 2q^2+2q+1
       156: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       170: q
       171: q^2+q+1
       174: q^2+q
       175: q^3+2q^2+q+1
       178: 2q^2+2q+1
       180: 2q^2+2q+1
       182: q^2+2q+1
       183: q
       184: q^2+q+1
       185: 2q^2+q+1
       186: q
       188: q^2+2q+1
       190: 2q^2+2q+1
       191: q^3+3q^2+q+1
       192: q^3+q^2+q
       193: q
       194: q^2+q+1
       195: 2q^2+q+1
       196: q
       198: q^2+2q+1
       199: q^2+q
       200: q^3+2q^2+q+1
       201: q
       202: q^2+q+1
       203: q+1
       206: q+1
       208: q^3+3q^2+2q+1
       210: 2q^2+2q+1
       212: 2q^2+2q+1
       214: 2q^2+2q+1
       216: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: 2q^2+2q+1
       226: q^3+3q^2+2q+1
       227: q^3+3q^2+2q+1
       228: q^3+3q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       238: 2q^2+2q+1
       240: 2q^2+2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: q^3+3q^2+2q+1
       251: q^3+3q^2+2q+1
       252: q^3+3q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q
       261: q^2+q+1
       264: q
       265: q^2+q+1
       268: q
       270: q^2+q+1
       272: q+1
       276: q^2+q
       277: q^3+2q^2+q+1
       280: 2q^2+2q+1
       282: 2q^2+2q+1
       283: q
       284: q^2+q+1
       285: 2q^2+q+1
       286: q
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: q
       294: q^2+q+1
       295: 2q^2+q+1
       296: q
       298: q^2+2q+1
       299: q
       300: q^2+q+1
       302: q^2+2q+1
       303: 2q^2+q+1
       304: q
       306: q^2+2q+1
       307: q
       308: q^2+q+1
       309: q+1
       312: q+1
       314: q+1
       316: 2q^2+2q+1
       318: 2q^2+2q+1
       319: q
       320: q^2+q+1
       321: q+1
       324: q+1
       326: 2q^2+2q+1
       328: 2q^2+2q+1
       330: 2q^2+2q+1
       332: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^3+3q^2+2q+1
       345: q^3+3q^2+2q+1
       346: q^3+3q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: 2q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       361: 2q^2+2q+1
       363: 2q^2+2q+1
       365: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       378: q
       379: q^2+q+1
       382: q
       383: q^2+q+1
       386: q
       387: q^2+q+1
       390: q
       392: q^2+q+1
       394: q
       395: q^2+q+1
       398: q+1
       402: q+1
       408: q+1
       410: 2q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: q
       420: q^2+q+1
       421: 2q^2+q+1
       422: q
       424: q^2+2q+1
       426: q+1
       428: 2q+1
       429: q
       430: q^2+q+1
       431: 2q^2+q+1
       432: q
       434: q^2+2q+1
       436: q^2+2q+1
       437: q
       438: q^2+q+1
       439: 2q^2+q+1
       440: q
       442: q^2+2q+1
       443: q
       444: q+1
       446: 2q+1
       447: q
       448: q^2+q+1
       449: q+1
       452: q+1
       453: q
       454: q^2+q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: 2q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       471: q
       472: q^2+q+1
       473: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^3+3q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: q+1
       503: 2q^2+2q+1
       505: 2q^2+2q+1
       507: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: q^2+q+1
       526: q
       527: q^2+q+1
       530: q
       531: q^2+q+1
       534: q
       535: q^2+q+1
       538: q
       540: q^2+q+1
       542: q
       544: q^2+q+1
       546: q
       548: q+1
       550: q+1
       554: q+1
       558: q+1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: 2q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: q
       590: q^2+q+1
       591: 1
       594: 1
       595: 2q^2+q+1
       596: q
       598: q+1
       600: q+1
       602: 2q+1
       603: q
       604: q^2+q+1
       606: q^2+2q+1
       607: 2q^2+q+1
       608: q
       610: q^2+2q+1
       612: q^2+2q+1
       614: q+1
       615: q
       616: q+1
       618: 2q+1
       619: q
       620: q^2+q+1
       621: q+1
       624: q+1
       626: q+1
       628: q+1
       630: 1
       631: q+1
       634: q+1
       636: 2q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       641: q
       642: q^2+q+1
       643: q+1
       646: q+1
       647: q
       648: q^2+q+1
       649: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: 1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       700: q+1
       706: q
       707: q^2+q+1
       710: q
       711: q^2+q+1
       714: 1
       719: 1
       722: q
       724: q^2+q+1
       726: q
       728: q^2+q+1
       730: q
       732: q^2+q+1
       734: q
       736: q+1
       738: q+1
       742: q+1
       746: q+1
       750: q+1
       755: q+1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       776: 2q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       793: q
       794: q+1
       796: 2q+1
       798: q^2+2q+1
       800: q^2+2q+1
       801: q
       802: q^2+q+1
       803: 1
       806: 1
       807: 2q^2+q+1
       808: q
       810: q+1
       812: q+1
       814: 2q+1
       815: q
       816: q+1
       817: q+1
       820: q+1
       822: q+1
       824: q+1
       825: q
       826: q^2+q+1
       827: 1
       831: q+1
       834: 1
       836: 1
       838: q+1
       839: q+1
       842: 2q^2+2q+1
       844: q+1
       845: q
       846: q^2+q+1
       847: q+1
       850: q+1
       852: q+1
       854: q+1
       856: 1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       891: q+1
       897: q
       898: q^2+q+1
       901: 1
       907: 1
       910: 1
       913: q
       915: q^2+q+1
       917: q
       919: q+1
       921: q
       923: q^2+q+1
       925: 1
       931: 1
       933: q
       935: q+1
       937: q+1
       941: q+1
       945: q+1
       949: 1
       957: q+1
       963: q+1
       966: q+1
       972: q+1
       977: q+1
       981: q+1
       986: q+1
       990: q+1
       993: 2q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1016: q
      1017: q+1
      1019: q^2+2q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1027: 1
      1028: 1
      1031: q+1
      1032: q+1
      1035: q+1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: q+1
      1049: q+1
      1051: q+1
      1052: q
      1053: q^2+q+1
      1054: 1
      1058: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: q+1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1145: q
      1147: q+1
      1149: q
      1151: q^2+q+1
      1153: 1
      1159: 1
      1161: 1
      1165: q+1
      1169: q+1
      1173: 1
      1187: q+1
      1192: q+1
      1196: q+1
      1201: q+1
      1203: 1
      1211: 2q+1
      1213: q+1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2q+1
      1228: q
      1229: q+1
      1231: q+1
      1232: 1
      1235: 1
      1237: q+1
      1239: q+1
      1241: 1
      1242: 1
      1245: q+1
      1246: q+1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1263: q+1
      1265: q+1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1341: q
      1343: q+1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: q+1
      1377: 1
      1381: 1
      1408: q+1
      1412: q+1
      1417: q+1
      1419: 1
      1434: 1
      1437: 1
      1439: q+1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: q+1
      1450: 1
      1453: q+1
      1455: 1
      1457: 1
      1459: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1475: 1
      1478: 1
      1481: 1
      1483: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1496: 1
      1507: 1
      1532: q+1
      1540: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1635: 1
      1638: 1
      1640: 1
      1644: q+1
      1645: 1
      1648: 1
      1652: 1
      1653: 1
      1660: 1
      1662: 1
      1663: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1682: 1
      1693: 1
      1727: 1
      1732: 1
      1735: 1
      1738: 1
      1743: 1
      1748: 1
      1750: 1
      1755: 1
      1762: 1
      1786: 1
      1805: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1841: 1
      1852: 1
      1896: 1
      1899: 1
      1930: 1
      1933: 1
      1971: 1

1972:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: 7q^4+15q^3+9q^2+2q
        23: 7q^4+15q^3+9q^2+2q
        24: 2q^5+9q^4+12q^3+8q^2+2q
        25: q^4+11q^3+9q^2+2q
        26: q^4+11q^3+9q^2+2q
        27: 4q^4+9q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: 7q^4+15q^3+9q^2+2q
        32: 5q^4+11q^3+8q^2+2q
        33: 7q^4+15q^3+9q^2+2q
        34: q^4+11q^3+9q^2+2q
        35: q^4+8q^3+8q^2+2q
        36: q^4+11q^3+9q^2+2q
        37: q^4+5q^3+3q^2+q
        38: 6q^3+6q^2+q
        39: q^4+5q^3+3q^2+q
        40: 6q^3+6q^2+q
        41: 2q^4+4q^3+3q^2+q
        42: 2q^4+5q^3+5q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 5q^4+11q^3+8q^2+2q
        53: 5q^4+11q^3+8q^2+2q
        54: q^5+5q^4+9q^3+7q^2+2q
        55: 7q^3+8q^2+2q
        56: 7q^3+8q^2+2q
        57: q^4+6q^3+7q^2+2q
        58: 3q^4+6q^3+4q^2
        59: 4q^4+9q^3+5q^2+2q
        60: 5q^3+4q^2+q
        61: q^4+6q^3+5q^2+q
        62: q^4+5q^3+3q^2+q
        63: 6q^3+6q^2+q
        64: q^4+4q^3+3q^2+q
        65: 4q^3+5q^2+q
        66: q^4+5q^3+3q^2+q
        67: 6q^3+6q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 4q^3+7q^2+2q
        73: 3q^4+7q^3+7q^2+2q
        74: 2q^3+2q^2+q
        75: 3q^3+5q^2+q
        76: 2q^3+2q^2+q
        77: 3q^3+5q^2+q
        78: 2q^3+2q^2+q
        79: 3q^3+4q^2+q
        80: 5q^4+11q^3+8q^2+2q
        81: 5q^4+11q^3+8q^2+2q
        82: 5q^4+11q^3+8q^2+2q
        83: 3q^4+8q^3+7q^2+2q
        84: q^4+8q^3+8q^2+2q
        85: q^4+8q^3+8q^2+2q
        86: 7q^3+8q^2+2q
        87: 5q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 5q^4+11q^3+8q^2+2q
        95: 5q^4+11q^3+8q^2+2q
        96: q^5+5q^4+9q^3+7q^2+2q
        97: 7q^3+8q^2+2q
        98: 7q^3+8q^2+2q
        99: q^4+6q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 2q^3+q^2
       104: 3q^3+3q^2+q
       105: 3q^3+3q^2
       106: q^4+3q^3+2q^2+q
       107: q^3+3q^2+q
       108: 3q^3+4q^2+q
       109: q^4+2q^3+3q^2
       110: 2q^4+5q^3+4q^2+2q
       111: q^3+2q^2+q
       112: q^3+4q^2+q
       113: 2q^3+2q^2+q
       114: 3q^3+5q^2+q
       115: 2q^3+2q^2+q
       116: 2q^3+4q^2+q
       117: q^4+2q^3+3q^2
       118: 2q^4+5q^3+4q^2+2q
       119: 2q^3+3q^2+q
       120: q^4+3q^3+4q^2+q
       121: q^4+4q^3+3q^2+q
       122: 4q^3+5q^2+q
       123: q^4+4q^3+3q^2+q
       124: 4q^3+5q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 2q^3+2q^2+q
       128: 3q^3+5q^2+q
       129: 2q^3+2q^2+q
       130: 3q^3+5q^2+q
       131: 2q^3+2q^2+q
       132: 3q^3+4q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: 2q^3+6q^2+2q
       136: q^4+4q^3+6q^2+2q
       137: 5q^4+11q^3+8q^2+2q
       138: 3q^4+8q^3+7q^2+2q
       139: 5q^4+11q^3+8q^2+2q
       140: 4q^3+7q^2+2q
       141: 3q^4+8q^3+7q^2+2q
       142: 3q^4+7q^3+7q^2+2q
       143: q^4+8q^3+8q^2+2q
       144: 5q^3+7q^2+2q
       145: 7q^3+8q^2+2q
       146: 5q^3+7q^2+2q
       147: 4q^3+7q^2+2q
       148: q^3+3q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 2q^3+2q^2+q
       152: 3q^3+5q^2+q
       153: 2q^3+2q^2+q
       154: 3q^3+5q^2+q
       155: 2q^3+2q^2+q
       156: 3q^3+4q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^4+6q^3+7q^2+2q
       161: 3q^4+7q^3+7q^2+2q
       162: 2q^4+6q^3+7q^2+2q
       163: 2q^3+6q^2+2q
       164: 3q^3+6q^2+2q
       165: 2q^3+6q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^2
       170: 2q^2+q
       171: q^3+2q^2
       172: q^3+q^2+q
       173: q^3+q^2
       174: q^3+2q^2+q
       175: q^3+2q^2
       176: q^4+2q^3+2q^2+q
       177: 2q^3+2q^2+q
       178: 2q^3+4q^2+q
       179: 2q^3+2q^2+q
       180: 3q^3+5q^2+q
       181: q^3+2q^2+q
       182: q^3+4q^2+q
       183: 2q^2+q
       184: q^3+3q^2+q
       185: 2q^2
       186: 3q^3+3q^2+2q
       187: q^3+2q^2+q
       188: 3q^2+q
       189: 2q^3+2q^2+q
       190: 2q^3+4q^2+q
       191: q^4+2q^3+3q^2
       192: 2q^4+5q^3+4q^2+2q
       193: q^3+3q^2+q
       194: 3q^3+4q^2+q
       195: q^4+2q^3+3q^2
       196: 2q^4+5q^3+4q^2+2q
       197: q^3+2q^2+q
       198: q^3+4q^2+q
       199: 2q^3+3q^2+q
       200: q^4+3q^3+4q^2+q
       201: q^3+3q^2+q
       202: 3q^3+4q^2+q
       204: q^3+3q^2+2q
       205: q^2+q
       206: q^2+q
       207: q^4+4q^3+3q^2+q
       208: 4q^3+5q^2+q
       209: 2q^3+2q^2+q
       210: 3q^3+5q^2+q
       211: 2q^3+2q^2+q
       212: 2q^3+4q^2+q
       214: 3q^2+q
       216: q^3+3q^2+q
       218: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: 2q^3+6q^2+2q
       223: 2q^3+6q^2+2q
       224: q^4+4q^3+6q^2+2q
       225: q^4+4q^3+6q^2+2q
       226: 3q^4+8q^3+7q^2+2q
       227: q^4+4q^3+6q^2+2q
       228: 2q^4+6q^3+7q^2+2q
       229: 2q^3+6q^2+2q
       230: q^4+4q^3+6q^2+2q
       231: 5q^3+7q^2+2q
       232: q^3+5q^2+2q
       233: 2q^3+6q^2+2q
       234: q^3+5q^2+2q
       235: 2q^2+2q
       236: 5q^3+7q^2+2q
       237: 2q^3+2q^2+q
       238: 3q^3+5q^2+q
       239: 2q^3+2q^2+q
       240: 3q^3+5q^2+q
       241: 2q^3+2q^2+q
       242: 3q^3+4q^2+q
       243: 7q^3+8q^2+2q
       244: 4q^3+7q^2+2q
       245: q^3+3q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^4+6q^3+7q^2+2q
       251: 3q^4+7q^3+7q^2+2q
       252: 2q^4+6q^3+7q^2+2q
       253: 2q^3+6q^2+2q
       254: 3q^3+6q^2+2q
       255: 2q^3+6q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^2
       260: 2q^2+q
       261: q^3+2q^2
       262: q^3+q^2+q
       263: q^2
       264: q^2+q
       265: q^2
       266: q^3+q^2+q
       267: q^2
       268: 2q^2+q
       269: q^3+q^2+q
       270: q^3+2q^2
       273: q^2+q
       274: q^2+q
       275: q^3+q^2
       276: q^3+2q^2+q
       277: q^3+2q^2
       278: q^4+2q^3+2q^2+q
       280: 2q^2+q
       282: 3q^2+q
       283: 2q^2+q
       284: q^3+3q^2+q
       285: 2q^2
       286: 3q^3+3q^2+2q
       287: 2q^3+2q^2+q
       288: 2q^3+4q^2+q
       290: 2q^2+q
       291: q^3+2q^2+q
       292: 3q^2+q
       293: 2q^2+q
       294: q^3+3q^2+q
       295: 2q^2
       296: 3q^3+3q^2+2q
       297: q^3+2q^2+q
       298: 3q^2+q
       299: 2q^2+q
       300: q^3+3q^2+q
       301: q^3+2q^2+q
       302: q^3+4q^2+q
       303: 2q^2
       304: 3q^3+3q^2+2q
       305: q^3+2q^2+q
       306: 3q^2+q
       307: q^2+q
       308: 3q^2+q
       310: 2q^2+2q
       311: q^2+q
       312: q^2+q
       313: q^2+q
       314: q
       315: 2q^3+2q^2+q
       316: 2q^3+4q^2+q
       317: 2q^3+2q^2+q
       318: 3q^3+5q^2+q
       319: q^3+3q^2+q
       320: 3q^3+4q^2+q
       322: q^3+3q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^3+2q^2+q
       326: 2q^3+4q^2+q
       328: 3q^2+q
       330: q^3+3q^2+q
       332: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: 2q^3+6q^2+2q
       335: q^4+4q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: 2q^2+q
       339: q^3+5q^2+2q
       340: 2q^2+q
       341: q^3+5q^2+2q
       342: q^3+q^2+q
       343: 2q^3+3q^2+q
       344: q^4+4q^3+6q^2+2q
       345: q^4+4q^3+6q^2+2q
       346: 2q^4+6q^3+7q^2+2q
       347: 2q^3+6q^2+2q
       348: 2q^3+6q^2+2q
       349: q^4+4q^3+6q^2+2q
       350: q^4+4q^3+6q^2+2q
       351: q^3+7q^2+3q
       352: q^3+5q^2+2q
       353: q^3+5q^2+2q
       354: 2q^3+6q^2+2q
       355: q^3+5q^2+2q
       356: q^3+5q^2+2q
       357: 2q^2+2q
       358: 2q^2+2q
       359: 3q^2+3q
       361: 3q^2+q
       363: q^3+3q^2+q
       365: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: q^3+5q^2+2q
       370: 2q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2
       378: q^2+q
       379: q^2
       380: q^3+q^2+q
       382: q
       383: q^2
       385: q^2
       386: q^2+q
       387: q^2
       388: q^3+q^2+q
       389: q^2
       390: 2q^2+q
       391: q^3+q^2+q
       392: q^3+2q^2
       393: q^2
       394: q^2+q
       395: q^2
       396: q^3+q^2+q
       399: q^2+q
       400: q^2+q
       403: q
       404: q^2+q
       406: q^2+q
       407: q^2+q
       410: 2q^2+q
       412: 3q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: 2q^2+q
       419: 2q^2+q
       420: q^3+3q^2+q
       421: 2q^2
       422: 3q^3+3q^2+2q
       423: q^3+2q^2+q
       424: 3q^2+q
       425: q^2+q
       426: 2q^2+q
       427: 2q^2+q
       428: q^3+5q^2+2q
       429: 2q^2+q
       430: q^3+3q^2+q
       431: 2q^2
       432: 3q^3+3q^2+2q
       433: q^3+2q^2+q
       434: 3q^2+q
       436: 2q^2+q
       437: 2q^2+q
       438: q^3+3q^2+q
       439: 2q^2
       440: 3q^3+3q^2+2q
       441: q^3+2q^2+q
       442: 3q^2+q
       443: 3q^2+q
       444: q^3+4q^2+2q
       445: 2q^2+q
       446: q^3+5q^2+2q
       447: q^2+q
       448: 3q^2+q
       450: 2q^2+2q
       451: q^2+q
       452: q
       453: q^2+q
       454: 3q^2+q
       456: q
       458: 2q^2+2q
       459: q^2+q
       460: q
       462: 3q^2+3q
       463: q^2+q
       464: 2q^2+2q
       466: 2q^2+q
       468: 3q^2+q
       469: 2q^3+2q^2+q
       470: 2q^3+4q^2+q
       471: q^2+q
       472: 3q^2+q
       474: 2q^2+2q
       475: q^2+q
       476: q
       477: q^2+q
       478: q^2+q
       479: 2q^2+2q
       480: q^2+q
       481: 3q^2+2q
       482: 2q^3+3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       486: 2q^2+2q
       488: 2q^2+2q
       490: 2q^2+q
       491: 2q^2+2q
       492: q^4+4q^3+6q^2+2q
       493: 2q^3+6q^2+2q
       494: q^4+4q^3+6q^2+2q
       495: 3q^2+2q
       496: 4q^2+3q
       497: q^3+5q^2+2q
       498: q^3+5q^2+2q
       499: 2q^2+2q
       500: 2q
       501: q^2+3q
       503: 3q^2+q
       505: q^3+3q^2+q
       507: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: q^3+5q^2+2q
       512: q^3+5q^2+2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       522: q
       523: q^2
       526: q
       527: q^2
       529: q^2
       530: q^2+q
       531: q^2
       532: q^3+q^2+q
       533: q^2
       534: q^2+q
       535: q^2
       536: q^3+q^2+q
       538: q
       540: q^2
       541: q^2
       542: q^2+q
       543: q^3+q^2+q
       544: q^2
       545: q^2
       546: 2q^2+q
       547: q^2+q
       548: q^3+3q^2+q
       551: q
       552: q^2+q
       556: q
       559: q^2+q
       560: q
       563: q^2+q
       564: 2q^2+2q
       566: q
       568: q^2+q
       570: q^2+q
       571: q^2+q
       574: q^2+q
       575: 2q^2+2q
       577: q^2+q
       578: q^2+q
       581: q^2+q
       584: 2q^2+q
       586: q
       588: 2q^2+q
       589: q^2+q
       590: 2q^2+q
       592: 2q
       594: q
       595: q^2
       596: 2q^3+2q^2+2q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q^2+2q
       603: 2q^2+q
       604: q^3+3q^2+q
       606: 2q^2+q
       607: 2q^2
       608: 3q^3+3q^2+2q
       609: q^3+2q^2+q
       610: 3q^2+q
       612: 2q^2+q
       613: q^2+q
       614: 2q^2+q
       615: q^2+q
       616: 2q^2+2q
       618: 2q^2+2q
       619: q^2+q
       620: 3q^2+q
       622: 2q^2+2q
       624: q
       625: q^2+q
       626: q
       628: q
       629: q
       630: q
       632: q^2+3q
       634: 2q
       636: 2q^2+q
       638: 3q^2+q
       640: 2q^2+q
       641: q^2+q
       642: 3q^2+q
       644: 2q^2+2q
       645: q^2+q
       646: q
       647: q^2+q
       648: 3q^2+q
       650: 2q^2+2q
       652: q
       653: q^2+q
       654: q
       655: q^2+2q
       656: q
       657: 3q^2+3q
       659: 2q^2+2q
       661: 2q^2+2q
       663: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: 2q^2+2q
       669: 2q^2+2q
       671: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: 4q^2+3q
       675: 3q^2+2q
       676: 2q^3+3q^2+2q
       677: 3q^2+2q
       678: 4q^2+3q
       679: 2q^2+2q
       680: q^2+3q
       681: 3q^2+2q
       682: q^2+q
       683: 2q
       684: q^2+3q
       685: 2q
       686: q^3+5q^2+2q
       687: q^3+5q^2+2q
       688: 2q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       697: q^2+q
       699: q^2+q
       701: q^2+q
       706: q
       707: q^2
       710: q
       715: q
       716: q
       720: q
       722: q
       724: q^2
       725: q^2
       726: q^2+q
       727: q^3+q^2+q
       728: q^2
       730: q
       732: q^2
       734: q
       736: q^2+q
       740: q
       743: q^2+q
       744: q
       748: q
       752: 2q
       754: q
       756: q^2+q
       759: q
       762: q^2+q
       763: q
       766: q
       768: q^2+2q
       770: q
       773: q
       776: q^2+2q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       786: q
       788: 2q
       790: q^2+2q
       791: q
       793: q^2+q
       794: 2q^2+2q
       796: 2q^2+2q
       798: q
       800: 2q^2+q
       801: q^2+q
       802: 2q^2+q
       804: 2q
       806: q
       807: q^2
       808: 2q^3+2q^2+2q
       810: q^2+q
       811: q^2+q
       812: 2q^2+q
       814: 2q^2+2q
       815: q^2+q
       816: 2q^2+2q
       818: q^2+3q
       820: 2q
       824: q
       825: q^2+q
       826: 2q^2+q
       828: 2q
       832: q^2+q
       834: q
       835: q
       836: q
       838: 2q
       840: q^2+3q
       842: 2q^2+q
       843: q^2+2q
       844: q
       845: q^2+q
       846: 3q^2+q
       848: 2q^2+2q
       850: q
       851: q^2+q
       852: q
       854: q
       855: q
       856: q
       857: q^2+2q
       858: q
       860: 2q^2+2q
       862: 2q^2+2q
       864: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 4q^2+3q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: q^2+3q
       874: 2q
       875: q
       876: 2q
       877: 3q^2+2q
       878: q^2+q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       890: q
       892: q
       897: q
       903: q
       911: q
       913: q
       915: q^2
       917: q
       919: q^2+q
       921: q
       926: q
       927: q
       930: q
       933: q
       935: q^2+q
       939: q
       943: 2q
       950: q
       951: q
       959: 2q
       962: q
       965: q
       967: q^2+2q
       969: q
       972: q
       975: q^2+q
       976: q
       980: q
       983: q
       986: q
       989: q
       991: q^2+2q
       993: q^2+2q
       995: q
       997: q^2+q
       999: 2q
      1001: q
      1003: q
      1005: q
      1007: 2q
      1008: q
      1012: q
      1015: 2q^2+2q
      1016: q^2+q
      1017: 2q^2+2q
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1027: q
      1029: 2q
      1031: 2q
      1033: q^2+3q
      1037: q
      1043: q
      1045: q
      1046: q^2+2q
      1047: q
      1051: q
      1052: q^2+q
      1053: 2q^2+q
      1055: 2q
      1059: q^2+q
      1061: q
      1062: q
      1063: q
      1064: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: 2q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: q+1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1092: q
      1094: q
      1104: q
      1106: q
      1113: q
      1117: q
      1133: q
      1135: q
      1145: q
      1147: q^2+q
      1149: q
      1155: q
      1163: q
      1167: 2q
      1186: q
      1189: q
      1192: q
      1195: q
      1197: q^2+2q
      1204: q
      1205: q
      1211: 2q+1
      1213: q+1
      1215: q
      1217: 2q
      1219: q
      1224: q
      1227: 2q+1
      1228: q
      1229: q+1
      1231: q
      1233: 2q
      1235: q
      1237: q^2+q
      1239: q
      1241: q
      1243: 2q
      1245: q+1
      1247: q+1
      1251: q
      1253: q
      1261: q
      1262: q+1
      1271: q
      1273: q
      1275: q
      1276: q
      1280: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1308: q
      1310: q
      1317: q
      1329: q
      1341: q
      1343: q+1
      1347: q
      1351: q
      1367: q
      1369: q
      1375: q+1
      1405: q+1
      1413: q+1
      1439: q+1
      1441: 1
      1443: 1
      1444: 1
      1449: q
      1451: 2q
      1453: q+1
      1455: q
      1459: 1
      1461: q
      1467: q
      1473: q
      1479: q
      1482: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1533: q+1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1566: q
      1578: q
      1639: 1
      1644: q+1
      1646: 1
      1648: 1
      1652: 1
      1654: 1
      1664: q
      1668: 1
      1669: 1
      1674: 1
      1683: 1
      1724: 1
      1736: 1
      1740: 1
      1748: 1
      1752: 1
      1764: 1
      1802: 1
      1825: 1
      1828: 1
      1830: 1
      1842: 1
      1854: 1
      1900: 1
      1927: 1
      1935: 1
      1972: 1

1973:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+4q^3+2q^2+q
        23: 2q^4+4q^3+2q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+3q^3+2q^2+q
        26: q^4+3q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 3q^3+2q^2+q
        32: 2q^4+4q^3+2q^2+q
        33: 2q^4+4q^3+2q^2+q
        34: 2q^3+2q^2+q
        35: q^4+3q^3+2q^2+q
        36: q^4+3q^3+2q^2+q
        37: q^4+3q^3+2q^2+q
        39: q^4+3q^3+2q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+3q^3+2q^2+q
        53: q^4+3q^3+2q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+2q^2+q
        56: 2q^3+2q^2+q
        57: 2q^3+2q^2+q
        58: q^3+q^2
        59: 2q^3+q^2+q
        60: q^3+q^2
        61: q^3+q^2+q
        62: 2q^3+2q^2+q
        64: q^4+3q^3+2q^2+q
        66: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: q^3+2q^2+q
        73: 2q^3+2q^2+q
        74: 2q^3+2q^2+q
        76: 2q^3+2q^2+q
        78: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 2q^4+4q^3+2q^2+q
        82: 2q^3+2q^2+q
        83: q^4+3q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+3q^3+2q^2+q
        86: q^3+2q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: q^4+3q^3+2q^2+q
        95: q^4+3q^3+2q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+2q^2+q
        98: 2q^3+2q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2
       106: q^3+q^2+q
       107: q^2
       108: q^2+q
       109: q^2
       110: q^3+q^2+q
       111: q^3+2q^2+q
       113: q^3+2q^2+q
       115: 2q^3+2q^2+q
       117: q^3+q^2
       118: 2q^3+q^2+q
       119: q^3+q^2
       120: q^3+q^2+q
       121: 2q^3+2q^2+q
       123: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+2q^2+q
       129: 2q^3+2q^2+q
       131: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+3q^3+2q^2+q
       139: 2q^3+2q^2+q
       140: q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^3+2q^2+q
       146: q^3+2q^2+q
       147: q^3+2q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       151: 2q^3+2q^2+q
       153: 2q^3+2q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^4+3q^3+2q^2+q
       161: q^4+3q^3+2q^2+q
       162: q^4+3q^3+2q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       169: q^2
       172: q^2+q
       173: q^3+q^2
       176: q^3+q^2+q
       177: 2q^3+2q^2+q
       179: q^3+2q^2+q
       181: q^3+2q^2+q
       183: q^2
       184: q^2+q
       185: q^2
       186: q^3+q^2+q
       187: q^3+2q^2+q
       189: q^3+2q^2+q
       191: q^3+q^2
       192: 2q^3+q^2+q
       193: q^2
       194: q^2+q
       195: q^2
       196: q^3+q^2+q
       197: q^3+2q^2+q
       199: q^3+q^2
       200: q^3+q^2+q
       201: q^2
       202: q^2+q
       204: q^2+q
       205: q^2+q
       207: 2q^3+2q^2+q
       209: q^3+2q^2+q
       211: 2q^3+2q^2+q
       213: 2q^3+2q^2+q
       215: 2q^3+2q^2+q
       217: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: q^3+2q^2+q
       224: 2q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^3+2q^2+q
       228: q^4+3q^3+2q^2+q
       229: q^3+2q^2+q
       230: 2q^3+2q^2+q
       231: q^3+2q^2+q
       232: q^3+2q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: q^2+q
       236: 2q^3+2q^2+q
       237: 2q^3+2q^2+q
       239: 2q^3+2q^2+q
       241: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^3+2q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       259: q^2
       262: q^2+q
       263: q^2
       266: q^2+q
       267: q^2
       269: q^2+q
       273: q^2+q
       275: q^3+q^2
       278: q^3+q^2+q
       279: q^3+2q^2+q
       281: 2q^3+2q^2+q
       283: q^2
       284: q^2+q
       285: q^2
       286: q^3+q^2+q
       287: q^3+2q^2+q
       289: q^3+2q^2+q
       291: q^3+2q^2+q
       293: q^2
       294: q^2+q
       295: q^2
       296: q^2+q
       297: 2q^2+q
       299: q^2
       300: q^2+q
       301: q^3+2q^2+q
       303: q^2
       304: q^3+q^2+q
       305: q^3+2q^2+q
       307: q^2
       308: q^2+q
       310: q^2+q
       311: q^2+q
       313: q^2+q
       315: 2q^3+2q^2+q
       317: q^3+2q^2+q
       319: q^2
       320: q^2+q
       322: q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: q^3+2q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: q^3+2q^2+q
       349: 2q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+2q^2+q
       357: q
       358: q^2+q
       359: q^2+q
       360: 2q^3+2q^2+q
       362: 2q^3+2q^2+q
       364: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^3+2q^2+q
       370: q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2
       380: q^2+q
       381: q^2
       384: q^2+q
       385: q^2
       388: q^2+q
       389: q^2
       391: q^2+q
       393: q^2
       396: q^2+q
       399: q^2+q
       404: q^2+q
       406: q^2+q
       409: q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: q^2+q
       417: q^3+2q^2+q
       419: q^2
       420: q^2+q
       421: q^2
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2
       430: q^2+q
       431: q^2
       432: q^3+q^2+q
       433: q^3+2q^2+q
       435: q^3+2q^2+q
       437: q^2
       438: q^2+q
       439: q^2
       440: q^2+q
       441: 2q^2+q
       443: q^2
       444: q^2+q
       445: 2q^2+q
       447: q^2
       448: q^2+q
       450: q^2+q
       451: q^2+q
       453: q^2
       454: q
       455: q^2+q
       458: q
       459: q
       462: q^2+q
       463: q^2+q
       465: q^3+2q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: q^2
       472: q^2+q
       474: q^2+q
       475: q^2+q
       477: q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+2q^2+q
       513: q
       514: q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       521: q^2
       524: q^2+q
       525: q^2
       528: q
       529: q^2
       532: q^2+q
       533: q^2
       536: q^2+q
       537: q^2
       539: q^2+q
       541: q^2
       543: q^2+q
       545: q^2
       547: q^2+q
       552: q^2+q
       555: q^2+q
       559: q
       563: q^2+q
       568: q^2+q
       570: q^2+q
       575: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2
       590: q^2+q
       592: q
       594: q
       595: q^2
       596: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       603: q^2
       604: q^2+q
       605: q^3+2q^2+q
       607: q^2
       608: q^2+q
       609: 2q^2+q
       611: q^2+q
       613: q^2+q
       615: q^2
       616: q^2+q
       617: 2q^2+q
       619: q^2
       620: q
       622: q
       623: q^2+q
       625: q
       627: q
       629: q
       632: q^2+q
       633: q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       641: q^2
       642: q^2+q
       644: q^2+q
       645: q^2+q
       647: q^2
       648: q
       650: q
       651: q^2+q
       653: q
       655: q^2+q
       657: 2q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: 2q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       680: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       697: q^2+q
       705: q^2
       708: q
       709: q^2
       712: q^2+q
       716: q
       720: q
       721: q^2
       723: q^2+q
       725: q^2
       727: q^2+q
       729: q^2
       731: q
       733: q^2
       735: q^2+q
       739: q^2+q
       743: q
       747: q
       751: q^2+q
       756: q^2+q
       758: q^2+q
       762: q
       768: q^2+q
       769: q^2+q
       775: 2q^2+q
       777: q^2+q
       779: q^2+q
       781: q^2+q
       786: q
       788: q
       791: q
       793: q^2
       794: q^2+q
       795: 2q^2+q
       797: 2q^2+q
       799: q^2+q
       801: q^2
       802: q^2+q
       804: q
       806: q
       807: q^2
       808: q^2+q
       809: q^2+q
       811: q^2+q
       818: q^2+q
       819: q^2+q
       821: q
       823: q
       825: q^2
       826: q
       828: q
       832: q
       833: q
       835: q
       841: q^2+q
       843: q^2+q
       845: q^2
       846: q
       848: q
       849: q^2+q
       851: q
       853: q
       855: q
       866: q^2+q
       870: q^2+q
       871: q^2+q
       874: q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       889: q^2+q
       896: q^2
       899: q
       902: q
       906: q
       911: q
       912: q^2
       914: q
       916: q^2
       918: q^2+q
       920: q^2
       922: q^2+q
       927: q
       930: q
       938: q
       942: q^2+q
       946: q
       950: q
       961: q^2+q
       967: q^2+q
       968: q^2+q
       975: q
       979: q
       994: q^2+q
       999: q
      1001: q
      1010: q
      1012: q
      1018: q^2+q
      1020: q^2+q
      1022: q^2+q
      1027: q
      1029: q
      1034: q
      1036: q
      1038: q
      1045: q
      1048: q
      1050: q
      1052: q^2
      1053: q
      1055: q
      1059: q
      1060: q
      1062: q
      1064: q
      1076: q^2+q
      1080: q
      1083: q
      1084: q
      1091: q^2+q
      1116: q
      1124: q
      1127: q
      1133: q
      1138: q
      1148: q^2
      1150: q
      1154: q
      1158: q
      1163: q
      1170: q
      1174: q
      1185: q
      1199: q
      1204: q
      1222: 1
      1230: q^2+q
      1233: q
      1235: q
      1248: q
      1251: q
      1264: q
      1266: q
      1271: q
      1274: q
      1278: q
      1280: q
      1287: q
      1295: q
      1323: 1
      1336: 1
      1350: q
      1358: q
      1361: q
      1367: q
      1382: q
      1415: q
      1420: q
      1430: q
      1446: 1
      1464: q
      1467: q
      1480: 1
      1498: 1
      1506: q
      1555: 1
      1560: 1
      1572: 1
      1609: q
      1633: 1
      1637: 1
      1671: 1
      1684: 1
      1696: 1
      1725: 1
      1730: 1
      1754: 1
      1803: 1
      1823: 1
      1843: 1
      1855: 1
      1895: 1
      1928: 1
      1973: 1

1974:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: 7q^4+15q^3+9q^2+2q
        23: 7q^4+15q^3+9q^2+2q
        24: 2q^5+9q^4+12q^3+8q^2+2q
        25: q^4+11q^3+9q^2+2q
        26: q^4+11q^3+9q^2+2q
        27: 4q^4+9q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: 7q^4+15q^3+9q^2+2q
        32: 5q^4+11q^3+8q^2+2q
        33: 7q^4+15q^3+9q^2+2q
        34: q^4+11q^3+9q^2+2q
        35: q^4+8q^3+8q^2+2q
        36: q^4+11q^3+9q^2+2q
        37: 6q^3+6q^2+q
        38: q^4+5q^3+3q^2+q
        39: 6q^3+6q^2+q
        40: q^4+5q^3+3q^2+q
        41: 2q^4+5q^3+5q^2+q
        42: 2q^4+4q^3+3q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 5q^4+11q^3+8q^2+2q
        53: 5q^4+11q^3+8q^2+2q
        54: q^5+5q^4+9q^3+7q^2+2q
        55: 7q^3+8q^2+2q
        56: 7q^3+8q^2+2q
        57: q^4+6q^3+7q^2+2q
        58: 3q^4+6q^3+4q^2
        59: 4q^4+9q^3+5q^2+2q
        60: q^4+6q^3+5q^2+q
        61: 5q^3+4q^2+q
        62: 6q^3+6q^2+q
        63: q^4+5q^3+3q^2+q
        64: 4q^3+5q^2+q
        65: q^4+4q^3+3q^2+q
        66: 6q^3+6q^2+q
        67: q^4+5q^3+3q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 4q^3+7q^2+2q
        73: 3q^4+7q^3+7q^2+2q
        74: 3q^3+5q^2+q
        75: 2q^3+2q^2+q
        76: 3q^3+5q^2+q
        77: 2q^3+2q^2+q
        78: 3q^3+4q^2+q
        79: 2q^3+2q^2+q
        80: 5q^4+11q^3+8q^2+2q
        81: 5q^4+11q^3+8q^2+2q
        82: 5q^4+11q^3+8q^2+2q
        83: 3q^4+8q^3+7q^2+2q
        84: q^4+8q^3+8q^2+2q
        85: q^4+8q^3+8q^2+2q
        86: 7q^3+8q^2+2q
        87: 5q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 5q^4+11q^3+8q^2+2q
        95: 5q^4+11q^3+8q^2+2q
        96: q^5+5q^4+9q^3+7q^2+2q
        97: 7q^3+8q^2+2q
        98: 7q^3+8q^2+2q
        99: q^4+6q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 3q^3+3q^2
       104: q^4+3q^3+2q^2+q
       105: 2q^3+q^2
       106: 3q^3+3q^2+q
       107: 3q^3+4q^2+q
       108: q^3+3q^2+q
       109: q^4+2q^3+3q^2
       110: 2q^4+5q^3+4q^2+2q
       111: q^3+4q^2+q
       112: q^3+2q^2+q
       113: 3q^3+5q^2+q
       114: 2q^3+2q^2+q
       115: 2q^3+4q^2+q
       116: 2q^3+2q^2+q
       117: q^4+2q^3+3q^2
       118: 2q^4+5q^3+4q^2+2q
       119: q^4+3q^3+4q^2+q
       120: 2q^3+3q^2+q
       121: 4q^3+5q^2+q
       122: q^4+4q^3+3q^2+q
       123: 4q^3+5q^2+q
       124: q^4+4q^3+3q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 3q^3+5q^2+q
       128: 2q^3+2q^2+q
       129: 3q^3+5q^2+q
       130: 2q^3+2q^2+q
       131: 3q^3+4q^2+q
       132: 2q^3+2q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: 2q^3+6q^2+2q
       136: q^4+4q^3+6q^2+2q
       137: 5q^4+11q^3+8q^2+2q
       138: 3q^4+8q^3+7q^2+2q
       139: 5q^4+11q^3+8q^2+2q
       140: 4q^3+7q^2+2q
       141: 3q^4+8q^3+7q^2+2q
       142: 3q^4+7q^3+7q^2+2q
       143: q^4+8q^3+8q^2+2q
       144: 5q^3+7q^2+2q
       145: 7q^3+8q^2+2q
       146: 5q^3+7q^2+2q
       147: 4q^3+7q^2+2q
       148: q^3+3q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 3q^3+5q^2+q
       152: 2q^3+2q^2+q
       153: 3q^3+5q^2+q
       154: 2q^3+2q^2+q
       155: 3q^3+4q^2+q
       156: 2q^3+2q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^4+6q^3+7q^2+2q
       161: 3q^4+7q^3+7q^2+2q
       162: 2q^4+6q^3+7q^2+2q
       163: 2q^3+6q^2+2q
       164: 3q^3+6q^2+2q
       165: 2q^3+6q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^3+2q^2
       170: q^3+q^2+q
       171: q^2
       172: 2q^2+q
       173: q^3+2q^2
       174: q^4+2q^3+2q^2+q
       175: q^3+q^2
       176: q^3+2q^2+q
       177: 2q^3+4q^2+q
       178: 2q^3+2q^2+q
       179: 3q^3+5q^2+q
       180: 2q^3+2q^2+q
       181: q^3+4q^2+q
       182: q^3+2q^2+q
       183: q^3+3q^2+q
       184: 2q^2+q
       185: 2q^2
       186: 3q^3+3q^2+2q
       187: 3q^2+q
       188: q^3+2q^2+q
       189: 2q^3+4q^2+q
       190: 2q^3+2q^2+q
       191: q^4+2q^3+3q^2
       192: 2q^4+5q^3+4q^2+2q
       193: 3q^3+4q^2+q
       194: q^3+3q^2+q
       195: q^4+2q^3+3q^2
       196: 2q^4+5q^3+4q^2+2q
       197: q^3+4q^2+q
       198: q^3+2q^2+q
       199: q^4+3q^3+4q^2+q
       200: 2q^3+3q^2+q
       201: 3q^3+4q^2+q
       202: q^3+3q^2+q
       204: q^3+3q^2+2q
       205: q^2+q
       206: q^2+q
       207: 4q^3+5q^2+q
       208: q^4+4q^3+3q^2+q
       209: 3q^3+5q^2+q
       210: 2q^3+2q^2+q
       211: 2q^3+4q^2+q
       212: 2q^3+2q^2+q
       213: 3q^2+q
       215: q^3+3q^2+q
       217: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: 2q^3+6q^2+2q
       223: 2q^3+6q^2+2q
       224: q^4+4q^3+6q^2+2q
       225: q^4+4q^3+6q^2+2q
       226: 3q^4+8q^3+7q^2+2q
       227: q^4+4q^3+6q^2+2q
       228: 2q^4+6q^3+7q^2+2q
       229: 2q^3+6q^2+2q
       230: q^4+4q^3+6q^2+2q
       231: 5q^3+7q^2+2q
       232: q^3+5q^2+2q
       233: 2q^3+6q^2+2q
       234: q^3+5q^2+2q
       235: 2q^2+2q
       236: 5q^3+7q^2+2q
       237: 3q^3+5q^2+q
       238: 2q^3+2q^2+q
       239: 3q^3+5q^2+q
       240: 2q^3+2q^2+q
       241: 3q^3+4q^2+q
       242: 2q^3+2q^2+q
       243: 7q^3+8q^2+2q
       244: 4q^3+7q^2+2q
       245: q^3+3q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^4+6q^3+7q^2+2q
       251: 3q^4+7q^3+7q^2+2q
       252: 2q^4+6q^3+7q^2+2q
       253: 2q^3+6q^2+2q
       254: 3q^3+6q^2+2q
       255: 2q^3+6q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^3+2q^2
       260: q^3+q^2+q
       261: q^2
       262: 2q^2+q
       263: q^2
       264: q^3+q^2+q
       265: q^2
       266: q^2+q
       267: q^3+2q^2
       268: q^3+q^2+q
       269: 2q^2+q
       270: q^2
       273: q^2+q
       274: q^2+q
       275: q^3+2q^2
       276: q^4+2q^3+2q^2+q
       277: q^3+q^2
       278: q^3+2q^2+q
       279: 2q^2+q
       281: 3q^2+q
       283: q^3+3q^2+q
       284: 2q^2+q
       285: 2q^2
       286: 3q^3+3q^2+2q
       287: 2q^3+4q^2+q
       288: 2q^3+2q^2+q
       289: 2q^2+q
       291: 3q^2+q
       292: q^3+2q^2+q
       293: q^3+3q^2+q
       294: 2q^2+q
       295: 2q^2
       296: 3q^3+3q^2+2q
       297: 3q^2+q
       298: q^3+2q^2+q
       299: q^3+3q^2+q
       300: 2q^2+q
       301: q^3+4q^2+q
       302: q^3+2q^2+q
       303: 2q^2
       304: 3q^3+3q^2+2q
       305: 3q^2+q
       306: q^3+2q^2+q
       307: 3q^2+q
       308: q^2+q
       310: 2q^2+2q
       311: q^2+q
       312: q^2+q
       313: q
       314: q^2+q
       315: 2q^3+4q^2+q
       316: 2q^3+2q^2+q
       317: 3q^3+5q^2+q
       318: 2q^3+2q^2+q
       319: 3q^3+4q^2+q
       320: q^3+3q^2+q
       322: q^3+3q^2+2q
       323: q^2+q
       324: q^2+q
       325: 2q^3+4q^2+q
       326: 2q^3+2q^2+q
       327: 3q^2+q
       329: q^3+3q^2+q
       331: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: 2q^3+6q^2+2q
       335: q^4+4q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: q^3+5q^2+2q
       339: 2q^2+q
       340: q^3+5q^2+2q
       341: 2q^2+q
       342: 2q^3+3q^2+q
       343: q^3+q^2+q
       344: q^4+4q^3+6q^2+2q
       345: q^4+4q^3+6q^2+2q
       346: 2q^4+6q^3+7q^2+2q
       347: 2q^3+6q^2+2q
       348: 2q^3+6q^2+2q
       349: q^4+4q^3+6q^2+2q
       350: q^4+4q^3+6q^2+2q
       351: q^3+7q^2+3q
       352: q^3+5q^2+2q
       353: q^3+5q^2+2q
       354: 2q^3+6q^2+2q
       355: q^3+5q^2+2q
       356: q^3+5q^2+2q
       357: 2q^2+2q
       358: 2q^2+2q
       359: 3q^2+3q
       360: 3q^2+q
       362: q^3+3q^2+q
       364: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: q^3+5q^2+2q
       370: 2q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2
       378: q^3+q^2+q
       379: q^2
       380: q^2+q
       381: q^2
       384: q
       385: q^2
       386: q^3+q^2+q
       387: q^2
       388: q^2+q
       389: q^3+2q^2
       390: q^3+q^2+q
       391: 2q^2+q
       392: q^2
       393: q^2
       394: q^3+q^2+q
       395: q^2
       396: q^2+q
       399: q^2+q
       400: q^2+q
       403: q^2+q
       404: q
       406: q^2+q
       407: q^2+q
       409: 2q^2+q
       411: 3q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: 2q^2+q
       419: q^3+3q^2+q
       420: 2q^2+q
       421: 2q^2
       422: 3q^3+3q^2+2q
       423: 3q^2+q
       424: q^3+2q^2+q
       425: 2q^2+q
       426: q^2+q
       427: q^3+5q^2+2q
       428: 2q^2+q
       429: q^3+3q^2+q
       430: 2q^2+q
       431: 2q^2
       432: 3q^3+3q^2+2q
       433: 3q^2+q
       434: q^3+2q^2+q
       435: 2q^2+q
       437: q^3+3q^2+q
       438: 2q^2+q
       439: 2q^2
       440: 3q^3+3q^2+2q
       441: 3q^2+q
       442: q^3+2q^2+q
       443: q^3+4q^2+2q
       444: 3q^2+q
       445: q^3+5q^2+2q
       446: 2q^2+q
       447: 3q^2+q
       448: q^2+q
       450: 2q^2+2q
       451: q
       452: q^2+q
       453: 3q^2+q
       454: q^2+q
       455: q
       458: 2q^2+2q
       459: q
       460: q^2+q
       462: 3q^2+3q
       463: 2q^2+2q
       464: q^2+q
       465: 2q^2+q
       467: 3q^2+q
       469: 2q^3+4q^2+q
       470: 2q^3+2q^2+q
       471: 3q^2+q
       472: q^2+q
       474: 2q^2+2q
       475: q
       476: q^2+q
       477: q^2+q
       478: q^2+q
       479: q^2+q
       480: 2q^2+2q
       481: 3q^2+2q
       482: 2q^3+3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       485: 2q^2+2q
       487: 2q^2+2q
       489: 2q^2+q
       491: 2q^2+2q
       492: q^4+4q^3+6q^2+2q
       493: 2q^3+6q^2+2q
       494: q^4+4q^3+6q^2+2q
       495: 3q^2+2q
       496: 4q^2+3q
       497: q^3+5q^2+2q
       498: q^3+5q^2+2q
       499: 2q^2+2q
       500: 2q
       501: q^2+3q
       502: 3q^2+q
       504: q^3+3q^2+q
       506: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: q^3+5q^2+2q
       512: q^3+5q^2+2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       521: q^2
       524: q
       525: q^2
       528: q
       529: q^2
       530: q^3+q^2+q
       531: q^2
       532: q^2+q
       533: q^2
       534: q^3+q^2+q
       535: q^2
       536: q^2+q
       537: q^2
       539: q
       541: q^2
       542: q^3+q^2+q
       543: q^2+q
       544: q^2
       545: q^3+3q^2+q
       546: q^2+q
       547: 2q^2+q
       548: q^2
       551: q^2+q
       552: q
       555: q
       559: q
       560: q^2+q
       563: 2q^2+2q
       564: q^2+q
       566: q^2+q
       568: q
       570: q^2+q
       571: q^2+q
       574: 2q^2+2q
       575: q^2+q
       577: q^2+q
       580: q^2+q
       581: q^2+q
       583: 2q^2+q
       585: q
       587: 2q^2+q
       589: 2q^2+q
       590: q^2+q
       592: 2q
       593: q
       595: q^2
       596: 2q^3+2q^2+2q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q^2+2q
       603: q^3+3q^2+q
       604: 2q^2+q
       605: 2q^2+q
       607: 2q^2
       608: 3q^3+3q^2+2q
       609: 3q^2+q
       610: q^3+2q^2+q
       611: 2q^2+q
       613: 2q^2+q
       614: q^2+q
       615: 2q^2+2q
       616: q^2+q
       617: 2q^2+2q
       619: 3q^2+q
       620: q^2+q
       622: 2q^2+2q
       623: q
       625: q
       626: q^2+q
       627: q
       629: q
       630: q
       632: q^2+3q
       633: 2q
       635: 2q^2+q
       637: 3q^2+q
       639: 2q^2+q
       641: 3q^2+q
       642: q^2+q
       644: 2q^2+2q
       645: q
       646: q^2+q
       647: 3q^2+q
       648: q^2+q
       650: 2q^2+2q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+2q
       657: 3q^2+3q
       658: 2q^2+2q
       660: 2q^2+2q
       662: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: 2q^2+2q
       668: 2q^2+2q
       670: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: 4q^2+3q
       675: 3q^2+2q
       676: 2q^3+3q^2+2q
       677: 3q^2+2q
       678: 4q^2+3q
       679: 2q^2+2q
       680: q^2+3q
       681: 3q^2+2q
       682: q^2+q
       683: 2q
       684: q^2+3q
       685: 2q
       686: q^3+5q^2+2q
       687: q^3+5q^2+2q
       688: 2q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       696: q^2+q
       697: q^2+q
       699: q^2+q
       705: q^2
       708: q
       712: q
       715: q
       716: q
       718: q
       721: q^2
       723: q
       725: q^2
       726: q^3+q^2+q
       727: q^2+q
       728: q^2
       729: q^2
       731: q
       733: q^2+q
       735: q
       739: q
       743: q
       744: q^2+q
       747: q
       751: 2q
       754: q^2+q
       756: q
       758: q
       762: q
       763: q^2+q
       766: q^2+2q
       768: q
       769: q
       772: q
       775: q^2+2q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: q
       788: 2q
       789: q^2+2q
       792: q
       793: 2q^2+2q
       794: q^2+q
       795: 2q^2+2q
       797: q
       799: 2q^2+q
       801: 2q^2+q
       802: q^2+q
       804: 2q
       805: q
       807: q^2
       808: 2q^3+2q^2+2q
       809: q^2+q
       811: 2q^2+q
       812: q^2+q
       813: 2q^2+2q
       815: 2q^2+2q
       816: q^2+q
       818: q^2+3q
       819: 2q
       823: q
       825: 2q^2+q
       826: q^2+q
       828: 2q
       832: q^2+q
       833: q
       835: q
       836: q
       837: 2q
       840: q^2+3q
       841: 2q^2+q
       843: q
       844: q^2+2q
       845: 3q^2+q
       846: q^2+q
       848: 2q^2+2q
       849: q
       851: q
       852: q^2+q
       853: q
       855: q
       856: q
       857: q
       858: q^2+2q
       859: 2q^2+2q
       861: 2q^2+2q
       863: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 4q^2+3q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: q^2+3q
       874: 2q
       875: q
       876: 2q
       877: 3q^2+2q
       878: q^2+q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       887: q
       889: q
       899: q
       902: q
       909: q
       912: q^2
       914: q
       916: q^2+q
       918: q
       922: q
       926: q
       927: q
       929: q
       932: q^2+q
       934: q
       938: q
       942: 2q
       950: q
       951: q
       958: 2q
       961: q
       965: q^2+2q
       967: q
       968: q
       971: q
       975: q
       976: q^2+q
       979: q
       982: q
       985: q
       989: q^2+2q
       991: q
       992: q^2+2q
       994: q
       996: q^2+q
       999: 2q
      1000: q
      1002: q
      1004: q
      1007: 2q
      1009: q
      1013: q
      1014: 2q^2+2q
      1016: 2q^2+2q
      1017: q^2+q
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1026: q
      1029: 2q
      1030: 2q
      1033: q^2+3q
      1036: q
      1042: q
      1045: q
      1046: q
      1047: q^2+2q
      1050: q
      1052: 2q^2+q
      1053: q^2+q
      1055: 2q
      1059: q^2+q
      1060: q
      1062: q
      1063: q
      1065: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: 2q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: q+1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1089: q
      1091: q
      1101: q
      1102: q
      1112: q
      1116: q
      1131: q
      1136: q
      1144: q^2+q
      1146: q
      1150: q
      1154: q
      1162: q
      1166: 2q
      1185: q
      1188: q
      1191: q
      1195: q^2+2q
      1197: q
      1204: q
      1205: q
      1210: 2q+1
      1212: q+1
      1214: q
      1217: 2q
      1218: q
      1225: q
      1226: 2q+1
      1228: q+1
      1229: q
      1230: q
      1233: 2q
      1234: q
      1236: q^2+q
      1238: q
      1240: q
      1243: 2q
      1244: q+1
      1247: q+1
      1251: q
      1252: q
      1261: q
      1263: q+1
      1271: q
      1272: q
      1274: q
      1277: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1305: q
      1307: q
      1316: q
      1327: q
      1340: q+1
      1342: q
      1346: q
      1350: q
      1366: q
      1371: q
      1374: q+1
      1407: q+1
      1411: q+1
      1438: q+1
      1441: 1
      1442: 1
      1445: 1
      1448: q
      1451: 2q
      1452: q+1
      1454: q
      1458: 1
      1461: q
      1467: q
      1472: q
      1479: q
      1483: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1528: q+1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1565: q
      1577: q
      1640: 1
      1643: q+1
      1646: 1
      1647: 1
      1651: 1
      1654: 1
      1664: q
      1667: 1
      1670: 1
      1674: 1
      1678: 1
      1726: 1
      1734: 1
      1739: 1
      1745: 1
      1751: 1
      1763: 1
      1804: 1
      1826: 1
      1827: 1
      1830: 1
      1837: 1
      1850: 1
      1901: 1
      1929: 1
      1934: 1
      1974: 1

1975:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+4q^3+2q^2+q
        23: 2q^4+4q^3+2q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+3q^3+2q^2+q
        26: q^4+3q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 3q^3+2q^2+q
        32: 2q^4+4q^3+2q^2+q
        33: 2q^4+4q^3+2q^2+q
        34: 2q^3+2q^2+q
        35: q^4+3q^3+2q^2+q
        36: q^4+3q^3+2q^2+q
        38: q^4+3q^3+2q^2+q
        40: q^4+3q^3+2q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+3q^3+2q^2+q
        53: q^4+3q^3+2q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+2q^2+q
        56: 2q^3+2q^2+q
        57: 2q^3+2q^2+q
        58: 2q^3+q^2+q
        59: q^3+q^2
        60: q^3+q^2
        61: q^3+q^2+q
        63: 2q^3+2q^2+q
        65: q^4+3q^3+2q^2+q
        67: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: q^3+2q^2+q
        73: 2q^3+2q^2+q
        75: 2q^3+2q^2+q
        77: 2q^3+2q^2+q
        79: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 2q^4+4q^3+2q^2+q
        82: 2q^3+2q^2+q
        83: q^4+3q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+3q^3+2q^2+q
        86: q^3+2q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: q^4+3q^3+2q^2+q
        95: q^4+3q^3+2q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+2q^2+q
        98: 2q^3+2q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2
       105: q^3+q^2+q
       107: q^2
       108: q^2+q
       109: q^3+q^2+q
       110: q^2
       112: q^3+2q^2+q
       114: q^3+2q^2+q
       116: 2q^3+2q^2+q
       117: 2q^3+q^2+q
       118: q^3+q^2
       119: q^3+q^2
       120: q^3+q^2+q
       122: 2q^3+2q^2+q
       124: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+2q^2+q
       130: 2q^3+2q^2+q
       132: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+3q^3+2q^2+q
       139: 2q^3+2q^2+q
       140: q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^3+2q^2+q
       146: q^3+2q^2+q
       147: q^3+2q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       152: 2q^3+2q^2+q
       154: 2q^3+2q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^4+3q^3+2q^2+q
       161: q^4+3q^3+2q^2+q
       162: q^4+3q^3+2q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       170: q^2
       171: q^2+q
       174: q^3+q^2
       175: q^3+q^2+q
       178: 2q^3+2q^2+q
       180: q^3+2q^2+q
       182: q^3+2q^2+q
       183: q^2
       184: q^2+q
       185: q^3+q^2+q
       186: q^2
       188: q^3+2q^2+q
       190: q^3+2q^2+q
       191: 2q^3+q^2+q
       192: q^3+q^2
       193: q^2
       194: q^2+q
       195: q^3+q^2+q
       196: q^2
       198: q^3+2q^2+q
       199: q^3+q^2
       200: q^3+q^2+q
       201: q^2
       202: q^2+q
       203: q^2+q
       206: q^2+q
       208: 2q^3+2q^2+q
       210: q^3+2q^2+q
       212: 2q^3+2q^2+q
       214: 2q^3+2q^2+q
       216: 2q^3+2q^2+q
       218: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: q^3+2q^2+q
       224: 2q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^3+2q^2+q
       228: q^4+3q^3+2q^2+q
       229: q^3+2q^2+q
       230: 2q^3+2q^2+q
       231: q^3+2q^2+q
       232: q^3+2q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: q^2+q
       236: 2q^3+2q^2+q
       238: 2q^3+2q^2+q
       240: 2q^3+2q^2+q
       242: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^3+2q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       260: q^2
       261: q^2+q
       264: q^2
       265: q^2+q
       268: q^2
       270: q^2+q
       272: q^2+q
       276: q^3+q^2
       277: q^3+q^2+q
       280: q^3+2q^2+q
       282: 2q^3+2q^2+q
       283: q^2
       284: q^2+q
       285: q^3+q^2+q
       286: q^2
       288: q^3+2q^2+q
       290: q^3+2q^2+q
       292: q^3+2q^2+q
       293: q^2
       294: q^2+q
       295: q^2+q
       296: q^2
       298: 2q^2+q
       299: q^2
       300: q^2+q
       302: q^3+2q^2+q
       303: q^3+q^2+q
       304: q^2
       306: q^3+2q^2+q
       307: q^2
       308: q^2+q
       309: q^2+q
       312: q^2+q
       314: q^2+q
       316: 2q^3+2q^2+q
       318: q^3+2q^2+q
       319: q^2
       320: q^2+q
       321: q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: q^3+2q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: q^3+2q^2+q
       349: 2q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+2q^2+q
       357: q
       358: q^2+q
       359: q^2+q
       361: 2q^3+2q^2+q
       363: 2q^3+2q^2+q
       365: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^3+2q^2+q
       370: q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2
       379: q^2+q
       382: q^2
       383: q^2+q
       386: q^2
       387: q^2+q
       390: q^2
       392: q^2+q
       394: q^2
       395: q^2+q
       398: q^2+q
       402: q^2+q
       408: q^2+q
       410: q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: q^2+q
       418: q^3+2q^2+q
       419: q^2
       420: q^2+q
       421: q^2+q
       422: q^2
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2
       430: q^2+q
       431: q^3+q^2+q
       432: q^2
       434: q^3+2q^2+q
       436: q^3+2q^2+q
       437: q^2
       438: q^2+q
       439: q^2+q
       440: q^2
       442: 2q^2+q
       443: q^2
       444: q^2+q
       446: 2q^2+q
       447: q^2
       448: q^2+q
       449: q^2+q
       452: q^2+q
       453: q^2
       454: q
       456: q^2+q
       457: q
       460: q
       461: q^2+q
       464: q^2+q
       466: q^3+2q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: q^2
       472: q^2+q
       473: q^2+q
       476: q^2+q
       478: q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+2q^2+q
       513: q
       514: q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       522: q^2
       523: q^2+q
       526: q^2
       527: q
       530: q^2
       531: q^2+q
       534: q^2
       535: q^2+q
       538: q^2
       540: q^2+q
       542: q^2
       544: q^2+q
       546: q^2
       548: q^2+q
       550: q^2+q
       554: q^2+q
       558: q
       562: q^2+q
       567: q^2+q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       596: q^2
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       603: q^2
       604: q^2+q
       606: q^3+2q^2+q
       607: q^2+q
       608: q^2
       610: 2q^2+q
       612: q^2+q
       614: q^2+q
       615: q^2
       616: q^2+q
       618: 2q^2+q
       619: q^2
       620: q
       621: q
       624: q^2+q
       626: q
       628: q
       630: q
       631: q^2+q
       634: q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       641: q^2
       642: q^2+q
       643: q^2+q
       646: q^2+q
       647: q^2
       648: q
       649: q
       652: q^2+q
       654: q
       656: q^2+q
       657: 2q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: 2q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       680: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       700: q^2+q
       706: q^2
       707: q
       710: q^2
       711: q^2+q
       714: q
       719: q
       722: q^2
       724: q^2+q
       726: q^2
       728: q^2+q
       730: q^2
       732: q
       734: q^2
       736: q^2+q
       738: q^2+q
       742: q
       746: q
       750: q^2+q
       755: q^2+q
       760: q^2+q
       764: q
       767: q^2+q
       773: q^2+q
       776: 2q^2+q
       778: q^2+q
       780: q^2+q
       782: q^2+q
       786: q
       787: q
       792: q
       793: q^2
       794: q^2+q
       796: 2q^2+q
       798: 2q^2+q
       800: q^2+q
       801: q^2
       802: q^2+q
       803: q
       806: q
       807: q^2+q
       808: q^2
       810: q^2+q
       812: q^2+q
       817: q^2+q
       820: q^2+q
       822: q
       824: q
       825: q^2
       826: q
       827: q
       831: q
       834: q
       836: q
       842: q^2+q
       844: q^2+q
       845: q^2
       846: q
       847: q
       850: q^2+q
       852: q
       854: q
       856: q
       866: q^2+q
       870: q^2+q
       871: q^2+q
       874: q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       891: q^2+q
       897: q^2
       898: q
       901: q
       907: q
       910: q
       913: q^2
       915: q
       917: q^2
       919: q^2+q
       921: q^2
       923: q^2+q
       925: q
       931: q
       937: q
       941: q^2+q
       945: q
       949: q
       963: q^2+q
       966: q^2+q
       972: q^2+q
       977: q
       981: q
       995: q^2+q
       998: q
      1001: q
      1011: q
      1013: q
      1019: q^2+q
      1021: q^2+q
      1023: q^2+q
      1027: q
      1028: q
      1035: q
      1037: q
      1039: q
      1044: q
      1049: q
      1051: q
      1052: q^2
      1053: q
      1054: q
      1058: q
      1061: q
      1063: q
      1065: q
      1076: q^2+q
      1080: q
      1083: q
      1084: q
      1093: q^2+q
      1115: q
      1125: q
      1129: q
      1132: q
      1142: q
      1149: q^2
      1151: q
      1153: q
      1159: q
      1161: q
      1169: q
      1173: q
      1187: q
      1201: q
      1203: q
      1223: 1
      1231: q^2+q
      1232: q
      1235: q
      1249: q
      1250: q
      1265: q
      1267: q
      1270: q
      1275: q
      1279: q
      1281: q
      1287: q
      1297: q
      1325: 1
      1339: 1
      1349: q
      1359: q
      1362: q
      1365: q
      1381: q
      1417: q
      1419: q
      1434: q
      1447: 1
      1465: q
      1466: q
      1481: 1
      1500: 1
      1507: q
      1558: 1
      1562: 1
      1573: 1
      1608: q
      1636: 1
      1638: 1
      1672: 1
      1686: 1
      1697: 1
      1728: 1
      1732: 1
      1755: 1
      1806: 1
      1824: 1
      1845: 1
      1856: 1
      1896: 1
      1931: 1
      1975: 1

1976:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: 2q^3+4q^2+2q+1
        23: 2q^3+4q^2+2q+1
        24: 2q^3+4q^2+2q+1
        25: q^3+3q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 2q^3+4q^2+2q+1
        32: 2q^3+4q^2+2q+1
        33: 2q^3+4q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        38: q^3+3q^2+2q+1
        40: q^3+3q^2+2q+1
        42: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: q^3+3q^2+2q+1
        53: q^3+3q^2+2q+1
        54: q^3+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^3+q^2+q
        59: q^3+3q^2+q+1
        60: q^3+2q^2+q+1
        61: q^2+q
        63: q^3+3q^2+2q+1
        65: q^3+3q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        75: 2q^2+2q+1
        77: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^3+4q^2+2q+1
        81: 2q^3+4q^2+2q+1
        82: q^3+3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^3+3q^2+2q+1
        85: q^3+3q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: q^3+3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       104: q^3+2q^2+q+1
       105: q^2+q
       107: q^2+q+1
       108: q
       109: q
       110: 2q^2+q+1
       112: q^2+2q+1
       114: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^3+q^2+q
       118: q^3+3q^2+q+1
       119: q^3+2q^2+q+1
       120: q^2+q
       122: q^3+3q^2+2q+1
       124: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       128: 2q^2+2q+1
       130: 2q^2+2q+1
       132: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^3+4q^2+2q+1
       138: q^3+3q^2+2q+1
       139: q^3+3q^2+2q+1
       140: q^2+2q+1
       141: q^3+3q^2+2q+1
       142: 2q^2+2q+1
       143: q^3+3q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       152: 2q^2+2q+1
       154: 2q^2+2q+1
       156: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: q^3+3q^2+2q+1
       161: q^3+3q^2+2q+1
       162: q^3+3q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       170: q^2+q+1
       171: q
       174: q^3+2q^2+q+1
       175: q^2+q
       178: 2q^2+2q+1
       180: 2q^2+2q+1
       182: q^2+2q+1
       183: q^2+q+1
       184: q
       185: q
       186: 2q^2+q+1
       188: q^2+2q+1
       190: 2q^2+2q+1
       191: q^3+q^2+q
       192: q^3+3q^2+q+1
       193: q^2+q+1
       194: q
       195: q
       196: 2q^2+q+1
       198: q^2+2q+1
       199: q^3+2q^2+q+1
       200: q^2+q
       201: q^2+q+1
       202: q
       204: q+1
       206: q+1
       208: q^3+3q^2+2q+1
       210: 2q^2+2q+1
       212: 2q^2+2q+1
       214: 2q^2+2q+1
       216: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: 2q^2+2q+1
       226: q^3+3q^2+2q+1
       227: q^3+3q^2+2q+1
       228: q^3+3q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: 2q^2+2q+1
       238: 2q^2+2q+1
       240: 2q^2+2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: q^3+3q^2+2q+1
       251: q^3+3q^2+2q+1
       252: q^3+3q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q^2+q+1
       261: q
       264: q^2+q+1
       265: q
       268: q^2+q+1
       270: q
       274: q+1
       276: q^3+2q^2+q+1
       277: q^2+q
       280: 2q^2+2q+1
       282: 2q^2+2q+1
       283: q^2+q+1
       284: q
       285: q
       286: 2q^2+q+1
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: q^2+q+1
       294: q
       295: q
       296: 2q^2+q+1
       298: q^2+2q+1
       299: q^2+q+1
       300: q
       302: q^2+2q+1
       303: q
       304: 2q^2+q+1
       306: q^2+2q+1
       307: q^2+q+1
       308: q
       310: q+1
       312: q+1
       314: q+1
       316: 2q^2+2q+1
       318: 2q^2+2q+1
       319: q^2+q+1
       320: q
       322: q+1
       324: q+1
       326: 2q^2+2q+1
       328: 2q^2+2q+1
       330: 2q^2+2q+1
       332: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^3+3q^2+2q+1
       345: q^3+3q^2+2q+1
       346: q^3+3q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: 2q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q+1
       358: q+1
       359: q+1
       361: 2q^2+2q+1
       363: 2q^2+2q+1
       365: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       378: q^2+q+1
       379: q
       382: q^2+q+1
       383: q
       386: q^2+q+1
       387: q
       390: q^2+q+1
       392: q
       394: q^2+q+1
       395: q
       400: q+1
       403: q+1
       407: q+1
       410: 2q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: q^2+q+1
       420: q
       421: q
       422: 2q^2+q+1
       424: q^2+2q+1
       426: q+1
       428: 2q+1
       429: q^2+q+1
       430: q
       431: q
       432: 2q^2+q+1
       434: q^2+2q+1
       436: q^2+2q+1
       437: q^2+q+1
       438: q
       439: q
       440: 2q^2+q+1
       442: q^2+2q+1
       443: q+1
       444: q
       446: 2q+1
       447: q^2+q+1
       448: q
       450: q+1
       452: q+1
       453: q^2+q+1
       454: q
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: 2q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       471: q^2+q+1
       472: q
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: q^3+3q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: 1
       501: q+1
       503: 2q^2+2q+1
       505: 2q^2+2q+1
       507: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q^2+2q+1
       512: q^2+2q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q^2+q+1
       523: q
       526: q^2+q+1
       527: q
       530: q^2+q+1
       531: q
       534: q^2+q+1
       535: q
       538: q^2+q+1
       540: q
       542: q^2+q+1
       544: q
       546: q+1
       548: q
       551: q+1
       556: q+1
       560: q+1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: 2q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: q^2+q+1
       590: q
       592: 1
       593: 1
       595: q
       596: 2q^2+q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q^2+q+1
       604: q
       606: q^2+2q+1
       607: q
       608: 2q^2+q+1
       610: q^2+2q+1
       612: q^2+2q+1
       614: q+1
       615: q+1
       616: q
       618: 2q+1
       619: q^2+q+1
       620: q
       622: q+1
       624: q+1
       626: q+1
       628: q+1
       630: 1
       632: q+1
       634: q+1
       636: 2q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       641: q^2+q+1
       642: q
       644: q+1
       646: q+1
       647: q^2+q+1
       648: q
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: 2q+1
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q+1
       683: 1
       684: q+1
       685: 1
       686: 2q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       699: q+1
       706: q^2+q+1
       707: q
       710: q^2+q+1
       711: q
       715: 1
       718: 1
       722: q^2+q+1
       724: q
       726: q^2+q+1
       728: q
       730: q^2+q+1
       732: q
       734: q+1
       736: q
       740: q+1
       744: q+1
       748: q+1
       752: q+1
       754: q+1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       776: 2q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       793: q+1
       794: q
       796: 2q+1
       798: q^2+2q+1
       800: q^2+2q+1
       801: q^2+q+1
       802: q
       804: 1
       805: 1
       807: q
       808: 2q^2+q+1
       810: q+1
       812: q+1
       814: 2q+1
       815: q+1
       816: q
       818: q+1
       820: q+1
       822: q+1
       824: q+1
       825: q^2+q+1
       826: q
       828: 1
       832: q+1
       834: 1
       836: 1
       838: q+1
       840: q+1
       842: 2q^2+2q+1
       844: q+1
       845: q^2+q+1
       846: q
       848: q+1
       850: q+1
       852: q+1
       854: q+1
       856: 1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: q+1
       871: q+1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q^2+2q+1
       878: q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       890: q+1
       897: q^2+q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: q^2+q+1
       915: q
       917: q+1
       919: q
       921: q^2+q+1
       923: q
       926: 1
       929: 1
       933: q+1
       935: q
       939: q+1
       943: q+1
       947: q+1
       951: 1
       959: q+1
       962: q+1
       965: q+1
       972: q+1
       976: q+1
       980: q+1
       986: q+1
       989: q+1
       993: 2q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1016: q+1
      1017: q
      1019: q^2+2q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: 1
      1029: 1
      1031: q+1
      1033: q+1
      1035: q+1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: q+1
      1049: q+1
      1051: q+1
      1052: q^2+q+1
      1053: q
      1055: 1
      1059: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: q+1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: q+1
      1147: q
      1149: q^2+q+1
      1151: q
      1155: 1
      1157: 1
      1162: 1
      1167: q+1
      1171: q+1
      1175: 1
      1186: q+1
      1192: q+1
      1195: q+1
      1200: q+1
      1205: 1
      1211: 2q+1
      1213: q+1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2q+1
      1228: q+1
      1229: q
      1231: q+1
      1233: 1
      1234: 1
      1237: q+1
      1239: q+1
      1240: 1
      1243: 1
      1245: q+1
      1247: q+1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1263: q+1
      1265: q+1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: q+1
      1343: q
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1375: q+1
      1379: 1
      1383: 1
      1408: q+1
      1411: q+1
      1416: q+1
      1421: 1
      1434: 1
      1437: 1
      1439: q+1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: q+1
      1451: 1
      1453: q+1
      1454: 1
      1457: 1
      1459: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1475: 1
      1479: 1
      1481: 1
      1483: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1495: 1
      1508: 1
      1531: q+1
      1539: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1635: 1
      1638: 1
      1640: 1
      1644: q+1
      1646: 1
      1647: 1
      1652: 1
      1654: 1
      1660: 1
      1662: 1
      1664: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1681: 1
      1694: 1
      1727: 1
      1731: 1
      1734: 1
      1740: 1
      1744: 1
      1746: 1
      1751: 1
      1756: 1
      1764: 1
      1788: 1
      1805: 1
      1824: 1
      1826: 1
      1828: 1
      1830: 1
      1840: 1
      1853: 1
      1897: 1
      1901: 1
      1930: 1
      1935: 1
      1976: 1

1977:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: 2q^4+4q^3+2q^2+q
        23: 2q^4+4q^3+2q^2+q
        24: 2q^4+4q^3+2q^2+q
        25: q^4+3q^3+2q^2+q
        26: q^4+3q^3+2q^2+q
        27: q^4+3q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 3q^3+2q^2+q
        32: 2q^4+4q^3+2q^2+q
        33: 2q^4+4q^3+2q^2+q
        34: 2q^3+2q^2+q
        35: q^4+3q^3+2q^2+q
        36: q^4+3q^3+2q^2+q
        38: q^4+3q^3+2q^2+q
        40: q^4+3q^3+2q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: q^4+3q^3+2q^2+q
        53: q^4+3q^3+2q^2+q
        54: q^4+3q^3+2q^2+q
        55: 2q^3+2q^2+q
        56: 2q^3+2q^2+q
        57: 2q^3+2q^2+q
        58: q^3+q^2
        59: 2q^3+q^2+q
        60: q^3+q^2+q
        61: q^3+q^2
        63: 2q^3+2q^2+q
        65: q^4+3q^3+2q^2+q
        67: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: q^3+2q^2+q
        73: 2q^3+2q^2+q
        75: 2q^3+2q^2+q
        77: 2q^3+2q^2+q
        79: 2q^3+2q^2+q
        80: 3q^3+2q^2+q
        81: 2q^4+4q^3+2q^2+q
        82: 2q^3+2q^2+q
        83: q^4+3q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+3q^3+2q^2+q
        86: q^3+2q^2+q
        87: 2q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: q^4+3q^3+2q^2+q
        95: q^4+3q^3+2q^2+q
        96: q^4+3q^3+2q^2+q
        97: 2q^3+2q^2+q
        98: 2q^3+2q^2+q
        99: 2q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2+q
       105: q^3+q^2
       107: q^2+q
       108: q^2
       109: q^2
       110: q^3+q^2+q
       112: q^3+2q^2+q
       114: q^3+2q^2+q
       116: 2q^3+2q^2+q
       117: q^3+q^2
       118: 2q^3+q^2+q
       119: q^3+q^2+q
       120: q^3+q^2
       122: 2q^3+2q^2+q
       124: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+2q^2+q
       130: 2q^3+2q^2+q
       132: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: q^3+2q^2+q
       136: 2q^3+2q^2+q
       137: 3q^3+2q^2+q
       138: q^4+3q^3+2q^2+q
       139: 2q^3+2q^2+q
       140: q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 2q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: 2q^3+2q^2+q
       145: q^3+2q^2+q
       146: q^3+2q^2+q
       147: q^3+2q^2+q
       148: q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       152: 2q^3+2q^2+q
       154: 2q^3+2q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: q^4+3q^3+2q^2+q
       161: q^4+3q^3+2q^2+q
       162: q^4+3q^3+2q^2+q
       163: 2q^3+2q^2+q
       164: 2q^3+2q^2+q
       165: 2q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       170: q^2+q
       171: q^2
       174: q^3+q^2+q
       175: q^3+q^2
       178: 2q^3+2q^2+q
       180: q^3+2q^2+q
       182: q^3+2q^2+q
       183: q^2+q
       184: q^2
       185: q^2
       186: q^3+q^2+q
       188: q^3+2q^2+q
       190: q^3+2q^2+q
       191: q^3+q^2
       192: 2q^3+q^2+q
       193: q^2+q
       194: q^2
       195: q^2
       196: q^3+q^2+q
       198: q^3+2q^2+q
       199: q^3+q^2+q
       200: q^3+q^2
       201: q^2+q
       202: q^2
       204: q^2+q
       206: q^2+q
       208: 2q^3+2q^2+q
       210: q^3+2q^2+q
       212: 2q^3+2q^2+q
       214: 2q^3+2q^2+q
       216: 2q^3+2q^2+q
       218: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: q^3+2q^2+q
       224: 2q^2+q
       225: 2q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^3+2q^2+q
       228: q^4+3q^3+2q^2+q
       229: q^3+2q^2+q
       230: 2q^3+2q^2+q
       231: q^3+2q^2+q
       232: q^3+2q^2+q
       233: 2q^3+2q^2+q
       234: q^3+2q^2+q
       235: q^2+q
       236: 2q^3+2q^2+q
       238: 2q^3+2q^2+q
       240: 2q^3+2q^2+q
       242: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^3+2q^2+q
       245: q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^3+2q^2+q
       251: q^3+2q^2+q
       252: q^3+2q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       260: q^2+q
       261: q^2
       264: q^2+q
       265: q^2
       268: q^2+q
       270: q^2
       274: q^2+q
       276: q^3+q^2+q
       277: q^3+q^2
       280: q^3+2q^2+q
       282: 2q^3+2q^2+q
       283: q^2+q
       284: q^2
       285: q^2
       286: q^3+q^2+q
       288: q^3+2q^2+q
       290: q^3+2q^2+q
       292: q^3+2q^2+q
       293: q^2+q
       294: q^2
       295: q^2
       296: q^2+q
       298: 2q^2+q
       299: q^2+q
       300: q^2
       302: q^3+2q^2+q
       303: q^2
       304: q^3+q^2+q
       306: q^3+2q^2+q
       307: q^2+q
       308: q^2
       310: q^2+q
       312: q^2+q
       314: q^2+q
       316: 2q^3+2q^2+q
       318: q^3+2q^2+q
       319: q^2+q
       320: q^2
       322: q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: 2q^3+2q^2+q
       345: q^3+2q^2+q
       346: q^3+2q^2+q
       347: 2q^2+q
       348: q^3+2q^2+q
       349: 2q^2+q
       350: 2q^3+2q^2+q
       351: 2q^2+q
       352: q^3+2q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+2q^2+q
       357: q
       358: q^2+q
       359: q^2+q
       361: 2q^3+2q^2+q
       363: 2q^3+2q^2+q
       365: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^3+2q^2+q
       370: q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2+q
       379: q^2
       382: q^2+q
       383: q^2
       386: q^2+q
       387: q^2
       390: q^2+q
       392: q^2
       394: q^2+q
       395: q^2
       400: q^2+q
       403: q^2+q
       407: q^2+q
       410: q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: q^2+q
       418: q^3+2q^2+q
       419: q^2+q
       420: q^2
       421: q^2
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2+q
       430: q^2
       431: q^2
       432: q^3+q^2+q
       434: q^3+2q^2+q
       436: q^3+2q^2+q
       437: q^2+q
       438: q^2
       439: q^2
       440: q^2+q
       442: 2q^2+q
       443: q^2+q
       444: q^2
       446: 2q^2+q
       447: q^2+q
       448: q^2
       450: q^2+q
       452: q^2+q
       453: q
       454: q^2
       456: q^2+q
       458: q
       460: q
       462: q^2+q
       464: q^2+q
       466: q^3+2q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: q^2+q
       472: q^2
       474: q^2+q
       476: q^2+q
       478: q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^3+2q^2+q
       493: 2q^2+q
       494: 2q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+2q^2+q
       513: q
       514: q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       522: q^2+q
       523: q^2
       526: q
       527: q^2
       530: q^2+q
       531: q^2
       534: q^2+q
       535: q^2
       538: q^2+q
       540: q^2
       542: q^2+q
       544: q^2
       546: q^2+q
       548: q^2
       551: q^2+q
       556: q^2+q
       560: q
       564: q^2+q
       566: q^2+q
       571: q^2+q
       574: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2+q
       590: q^2
       592: q
       593: q
       595: q^2
       596: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       603: q^2+q
       604: q^2
       606: q^3+2q^2+q
       607: q^2
       608: q^2+q
       610: 2q^2+q
       612: q^2+q
       614: q^2+q
       615: q^2+q
       616: q^2
       618: 2q^2+q
       619: q
       620: q^2
       622: q
       624: q^2+q
       626: q
       628: q
       630: q
       632: q^2+q
       634: q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       641: q^2+q
       642: q^2
       644: q^2+q
       646: q^2+q
       647: q
       648: q^2
       650: q
       652: q^2+q
       654: q
       656: q^2+q
       657: 2q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: 2q^2+q
       675: 2q^2+q
       676: 2q^2+q
       677: q^2+q
       679: q^2+q
       680: q^2+q
       681: q^2+q
       682: q
       683: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       699: q^2+q
       706: q
       707: q^2
       710: q^2+q
       711: q^2
       715: q
       718: q
       722: q^2+q
       724: q^2
       726: q^2+q
       728: q^2
       730: q
       732: q^2
       734: q^2+q
       736: q^2
       740: q^2+q
       744: q
       748: q
       752: q^2+q
       754: q^2+q
       759: q^2+q
       763: q
       766: q^2+q
       773: q^2+q
       776: 2q^2+q
       778: q^2+q
       780: q^2+q
       782: q^2+q
       785: q
       788: q
       792: q
       793: q^2+q
       794: q^2
       796: 2q^2+q
       798: 2q^2+q
       800: q^2+q
       801: q^2+q
       802: q^2
       804: q
       805: q
       807: q^2
       808: q^2+q
       810: q^2+q
       812: q^2+q
       818: q^2+q
       820: q^2+q
       822: q
       824: q
       825: q
       826: q^2
       828: q
       832: q
       834: q
       836: q
       842: q^2+q
       844: q^2+q
       845: q
       846: q^2
       848: q
       850: q^2+q
       852: q
       854: q
       856: q
       866: q^2+q
       870: q^2+q
       871: q^2+q
       874: q
       875: q
       877: q^2+q
       878: q
       879: q
       880: q
       890: q^2+q
       897: q
       898: q^2
       903: q
       905: q
       909: q
       913: q
       915: q^2
       917: q^2+q
       919: q^2
       921: q^2+q
       923: q^2
       926: q
       929: q
       939: q
       943: q^2+q
       947: q
       951: q
       962: q^2+q
       965: q^2+q
       972: q^2+q
       976: q
       980: q
       995: q^2+q
       999: q
      1000: q
      1011: q
      1013: q
      1019: q^2+q
      1021: q^2+q
      1023: q^2+q
      1026: q
      1029: q
      1035: q
      1037: q
      1039: q
      1045: q
      1049: q
      1051: q
      1052: q
      1053: q^2
      1055: q
      1059: q
      1061: q
      1063: q
      1065: q
      1076: q^2+q
      1080: q
      1083: q
      1084: q
      1092: q^2+q
      1117: q
      1123: q
      1128: q
      1131: q
      1142: q
      1149: q
      1151: q^2
      1155: q
      1157: q
      1162: q
      1171: q
      1175: q
      1186: q
      1200: q
      1205: q
      1223: 1
      1231: q^2+q
      1233: q
      1234: q
      1249: q
      1251: q
      1265: q
      1267: q
      1271: q
      1275: q
      1279: q
      1281: q
      1287: q
      1296: q
      1324: 1
      1339: 1
      1351: q
      1357: q
      1363: q
      1366: q
      1383: q
      1416: q
      1421: q
      1434: q
      1447: 1
      1465: q
      1467: q
      1481: 1
      1499: 1
      1508: q
      1558: 1
      1561: 1
      1574: 1
      1610: q
      1636: 1
      1638: 1
      1672: 1
      1685: 1
      1698: 1
      1728: 1
      1731: 1
      1756: 1
      1806: 1
      1824: 1
      1844: 1
      1857: 1
      1897: 1
      1931: 1
      1977: 1

1978:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: q^3+3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: q^3+3q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: 2q^3+4q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^3+3q^2+2q+1
        34: 2q^3+4q^2+2q+1
        35: 2q^3+4q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        41: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^3+3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: q^3+3q^2+2q+1
        58: q^3+2q^2+q+1
        59: q^2+q
        60: q^3+3q^2+q+1
        61: q^3+q^2+q
        62: q^3+3q^2+2q+1
        64: q^3+3q^2+2q+1
        66: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+2q+1
        76: 2q^2+2q+1
        78: 2q^2+2q+1
        80: q^3+3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^3+4q^2+2q+1
        85: 2q^3+4q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^3+2q^2+q+1
       106: q^2+q
       107: 2q^2+q+1
       108: q
       109: q^2+q+1
       110: q
       111: q^2+2q+1
       113: 2q^2+2q+1
       115: 2q^2+2q+1
       117: q^3+2q^2+q+1
       118: q^2+q
       119: q^3+3q^2+q+1
       120: q^3+q^2+q
       121: q^3+3q^2+2q+1
       123: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       127: 2q^2+2q+1
       129: 2q^2+2q+1
       131: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^3+3q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: 2q^3+4q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       153: 2q^2+2q+1
       155: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^2+q+1
       172: q
       173: q^3+2q^2+q+1
       176: q^2+q
       177: 2q^2+2q+1
       179: 2q^2+2q+1
       181: q^2+2q+1
       183: 2q^2+q+1
       184: q
       185: q^2+q+1
       186: q
       187: q^2+2q+1
       189: 2q^2+2q+1
       191: q^3+2q^2+q+1
       192: q^2+q
       193: q+1
       195: q^2+q+1
       196: q
       197: q+1
       199: q^3+3q^2+q+1
       200: q^3+q^2+q
       201: 2q^2+q+1
       202: q
       203: q^2+q+1
       204: q
       205: q^2+2q+1
       207: q^3+3q^2+2q+1
       209: 2q^2+2q+1
       211: 2q^2+2q+1
       213: 2q^2+2q+1
       215: 2q^2+2q+1
       217: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: 2q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^3+3q^2+2q+1
       232: q^3+3q^2+2q+1
       233: q^3+3q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       237: 2q^2+2q+1
       239: 2q^2+2q+1
       241: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+3q^2+2q+1
       254: q^3+3q^2+2q+1
       255: q^3+3q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q^2+q+1
       262: q
       263: q^2+q+1
       266: q
       267: q+1
       271: q^2+q+1
       273: q
       275: q^3+2q^2+q+1
       278: q^2+q
       279: 2q^2+2q+1
       281: 2q^2+2q+1
       283: 2q^2+q+1
       284: q
       285: q^2+q+1
       286: q
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: 2q^2+q+1
       294: q
       295: q^2+q+1
       296: q
       297: q^2+2q+1
       299: q+1
       301: q+1
       303: q^2+q+1
       304: q
       305: q+1
       307: 2q^2+q+1
       308: q
       309: q^2+q+1
       310: q
       311: q^2+2q+1
       313: q^2+2q+1
       315: 2q^2+2q+1
       317: 2q^2+2q+1
       319: q+1
       321: q^2+q+1
       322: q
       323: q+1
       325: 2q^2+2q+1
       327: 2q^2+2q+1
       329: 2q^2+2q+1
       331: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q^2+2q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q^3+3q^2+2q+1
       353: q^3+3q^2+2q+1
       354: q^3+3q^2+2q+1
       355: 2q^2+2q+1
       356: 2q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+1
       360: 2q^2+2q+1
       362: 2q^2+2q+1
       364: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q^2+q+1
       380: q
       381: q^2+q+1
       384: q
       385: q^2+q+1
       388: q
       389: q+1
       393: q+1
       397: q^2+q+1
       399: q
       401: q^2+q+1
       404: q
       405: q+1
       409: 2q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: 2q^2+q+1
       420: q
       421: q^2+q+1
       422: q
       423: q^2+2q+1
       425: q+1
       427: 2q+1
       429: q+1
       431: q^2+q+1
       432: q
       433: q+1
       435: q+1
       437: q+1
       439: q^2+q+1
       440: q
       441: q+1
       443: q+1
       445: q+1
       447: 2q^2+q+1
       448: q
       449: q^2+q+1
       450: q
       451: q^2+2q+1
       453: 2q^2+q+1
       454: q
       455: q^2+2q+1
       457: q^2+q+1
       458: q
       459: q^2+2q+1
       461: q+1
       462: q
       463: 2q+1
       465: 2q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       471: q+1
       473: q^2+q+1
       474: q
       475: q+1
       477: q+1
       479: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: q+1
       497: q^3+3q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q+1
       501: 2q+1
       502: 2q^2+2q+1
       504: 2q^2+2q+1
       506: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q^2+q+1
       524: q
       525: q^2+q+1
       528: q
       529: q^2+q+1
       532: q
       533: q+1
       537: q+1
       541: q+1
       545: q+1
       549: q^2+q+1
       552: q
       553: q^2+q+1
       555: q
       557: q^2+q+1
       559: q
       561: q+1
       563: q
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: 2q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: 2q^2+q+1
       590: q
       591: 1
       593: 1
       595: q^2+q+1
       596: q
       597: q+1
       599: q+1
       601: 2q+1
       603: q+1
       605: q+1
       607: q^2+q+1
       608: q
       609: q+1
       611: q+1
       613: 1
       615: q+1
       617: q+1
       619: 2q^2+q+1
       620: q
       621: q^2+q+1
       622: q
       623: q^2+2q+1
       625: q^2+2q+1
       627: q^2+2q+1
       629: q+1
       631: q+1
       632: q
       633: 2q+1
       635: 2q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       641: q+1
       643: q^2+q+1
       644: q
       645: q+1
       647: q+1
       649: q^2+q+1
       650: q
       651: q+1
       653: q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: 1
       680: 2q+1
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q+1
       705: q^2+q+1
       708: q
       709: q^2+q+1
       712: q
       713: 1
       717: 1
       721: q+1
       725: q+1
       729: q+1
       733: q+1
       737: q^2+q+1
       739: q
       741: q^2+q+1
       743: q
       745: q^2+q+1
       747: q
       749: q+1
       751: q
       753: q+1
       757: q+1
       761: q+1
       765: q+1
       769: q+1
       775: 2q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       789: 2q+1
       791: 1
       793: q+1
       795: q+1
       797: q+1
       799: q+1
       801: q+1
       805: 1
       807: q^2+q+1
       808: q
       809: 1
       811: 1
       813: q+1
       815: q+1
       817: q+1
       818: q
       819: 2q+1
       821: q^2+2q+1
       823: q^2+2q+1
       825: 2q^2+q+1
       826: q
       827: 1
       829: 1
       831: q^2+q+1
       832: q
       833: q+1
       835: q+1
       837: 2q+1
       839: q+1
       840: q
       841: 2q^2+2q+1
       843: q+1
       845: q+1
       847: q^2+q+1
       848: q
       849: q+1
       851: q+1
       853: q+1
       855: 1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q+1
       896: q^2+q+1
       899: q
       900: 1
       904: 1
       908: 1
       912: q+1
       916: q+1
       920: q+1
       928: 1
       932: q+1
       936: q^2+q+1
       938: q
       940: q+1
       942: q
       944: q^2+q+1
       946: q
       948: 1
       952: 1
       956: q+1
       958: q
       960: q+1
       964: q+1
       968: q+1
       974: q+1
       978: q+1
       982: q+1
       988: q+1
       992: 2q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: q+1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: 2q+1
      1032: q+1
      1033: q
      1034: q^2+2q+1
      1036: q+1
      1038: q+1
      1040: 1
      1042: q+1
      1044: 1
      1046: q+1
      1048: q+1
      1050: q+1
      1052: q+1
      1056: 1
      1058: q^2+q+1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1098: q+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: q+1
      1148: q+1
      1156: 1
      1164: q+1
      1166: q
      1168: q^2+q+1
      1170: q
      1172: 1
      1176: 1
      1180: 1
      1184: q+1
      1188: q+1
      1194: q+1
      1198: q+1
      1206: 1
      1210: 2q+1
      1212: q+1
      1214: q+1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1228: q+1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1244: 2q+1
      1246: q+1
      1247: q
      1248: q+1
      1250: 1
      1252: q+1
      1254: 1
      1256: q+1
      1258: 1
      1260: 1
      1262: q+1
      1264: q+1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: q+1
      1352: 1
      1356: 1
      1372: q+1
      1374: q
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: q+1
      1410: q+1
      1414: q+1
      1422: 1
      1430: 1
      1436: 1
      1438: q+1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1454: 1
      1456: q+1
      1458: q+1
      1460: 1
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1480: 1
      1482: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1489: 1
      1513: 1
      1525: q+1
      1537: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1567: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1637: 1
      1639: 1
      1643: 1
      1647: 1
      1651: q+1
      1653: 1
      1655: 1
      1659: 1
      1661: 1
      1665: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1675: 1
      1699: 1
      1723: 1
      1729: 1
      1733: 1
      1745: 1
      1761: 1
      1765: 1
      1769: 1
      1773: 1
      1777: 1
      1789: 1
      1801: 1
      1823: 1
      1825: 1
      1827: 1
      1831: 1
      1834: 1
      1858: 1
      1910: 1
      1914: 1
      1926: 1
      1936: 1
      1978: 1

1979:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: q^4+11q^3+9q^2+2q
        23: q^4+11q^3+9q^2+2q
        24: 4q^4+9q^3+8q^2+2q
        25: 7q^4+15q^3+9q^2+2q
        26: 7q^4+15q^3+9q^2+2q
        27: 2q^5+9q^4+12q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: q^4+11q^3+9q^2+2q
        32: q^4+8q^3+8q^2+2q
        33: q^4+11q^3+9q^2+2q
        34: 7q^4+15q^3+9q^2+2q
        35: 5q^4+11q^3+8q^2+2q
        36: 7q^4+15q^3+9q^2+2q
        37: q^4+5q^3+3q^2+q
        38: 6q^3+6q^2+q
        39: q^4+5q^3+3q^2+q
        40: 6q^3+6q^2+q
        41: 2q^4+4q^3+3q^2+q
        42: 2q^4+5q^3+5q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 7q^3+8q^2+2q
        53: 7q^3+8q^2+2q
        54: q^4+6q^3+7q^2+2q
        55: 5q^4+11q^3+8q^2+2q
        56: 5q^4+11q^3+8q^2+2q
        57: q^5+5q^4+9q^3+7q^2+2q
        58: q^4+6q^3+5q^2+q
        59: 5q^3+4q^2+q
        60: 4q^4+9q^3+5q^2+2q
        61: 3q^4+6q^3+4q^2
        62: q^4+5q^3+3q^2+q
        63: 6q^3+6q^2+q
        64: q^4+4q^3+3q^2+q
        65: 4q^3+5q^2+q
        66: q^4+5q^3+3q^2+q
        67: 6q^3+6q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 3q^4+7q^3+7q^2+2q
        73: 4q^3+7q^2+2q
        74: 2q^3+2q^2+q
        75: 3q^3+5q^2+q
        76: 2q^3+2q^2+q
        77: 3q^3+5q^2+q
        78: 2q^3+2q^2+q
        79: 3q^3+4q^2+q
        80: q^4+8q^3+8q^2+2q
        81: q^4+8q^3+8q^2+2q
        82: 7q^3+8q^2+2q
        83: 5q^3+7q^2+2q
        84: 5q^4+11q^3+8q^2+2q
        85: 5q^4+11q^3+8q^2+2q
        86: 5q^4+11q^3+8q^2+2q
        87: 3q^4+8q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 7q^3+8q^2+2q
        95: 7q^3+8q^2+2q
        96: q^4+6q^3+7q^2+2q
        97: 5q^4+11q^3+8q^2+2q
        98: 5q^4+11q^3+8q^2+2q
        99: q^5+5q^4+9q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: q^4+3q^3+2q^2+q
       104: 3q^3+3q^2+q
       105: 3q^3+3q^2
       106: 2q^3+q^2
       107: 2q^4+5q^3+4q^2+2q
       108: q^4+2q^3+3q^2
       109: 3q^3+4q^2+q
       110: q^3+3q^2+q
       111: q^3+2q^2+q
       112: q^3+4q^2+q
       113: 2q^3+2q^2+q
       114: 3q^3+5q^2+q
       115: 2q^3+2q^2+q
       116: 2q^3+4q^2+q
       117: q^4+3q^3+4q^2+q
       118: 2q^3+3q^2+q
       119: 2q^4+5q^3+4q^2+2q
       120: q^4+2q^3+3q^2
       121: q^4+4q^3+3q^2+q
       122: 4q^3+5q^2+q
       123: q^4+4q^3+3q^2+q
       124: 4q^3+5q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 2q^3+2q^2+q
       128: 3q^3+5q^2+q
       129: 2q^3+2q^2+q
       130: 3q^3+5q^2+q
       131: 2q^3+2q^2+q
       132: 3q^3+4q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: q^4+4q^3+6q^2+2q
       136: 2q^3+6q^2+2q
       137: q^4+8q^3+8q^2+2q
       138: 5q^3+7q^2+2q
       139: 7q^3+8q^2+2q
       140: q^3+3q^2+2q
       141: 5q^3+7q^2+2q
       142: 4q^3+7q^2+2q
       143: 5q^4+11q^3+8q^2+2q
       144: 3q^4+8q^3+7q^2+2q
       145: 5q^4+11q^3+8q^2+2q
       146: 3q^4+8q^3+7q^2+2q
       147: 3q^4+7q^3+7q^2+2q
       148: 4q^3+7q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 2q^3+2q^2+q
       152: 3q^3+5q^2+q
       153: 2q^3+2q^2+q
       154: 3q^3+5q^2+q
       155: 2q^3+2q^2+q
       156: 3q^3+4q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^3+6q^2+2q
       161: 3q^3+6q^2+2q
       162: 2q^3+6q^2+2q
       163: 2q^4+6q^3+7q^2+2q
       164: 3q^4+7q^3+7q^2+2q
       165: 2q^4+6q^3+7q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^3+q^2+q
       170: 2q^2+q
       171: q^3+2q^2
       172: q^2
       173: q^4+2q^3+2q^2+q
       174: q^3+2q^2+q
       175: q^3+2q^2
       176: q^3+q^2
       177: 2q^3+2q^2+q
       178: 2q^3+4q^2+q
       179: 2q^3+2q^2+q
       180: 3q^3+5q^2+q
       181: q^3+2q^2+q
       182: q^3+4q^2+q
       183: 3q^3+3q^2+2q
       184: 2q^2
       185: q^3+3q^2+q
       186: 2q^2+q
       187: q^3+2q^2+q
       188: 3q^2+q
       189: 2q^3+2q^2+q
       190: 2q^3+4q^2+q
       191: q^4+3q^3+4q^2+q
       192: 2q^3+3q^2+q
       193: q^3+3q^2+2q
       195: 3q^3+4q^2+q
       196: q^3+3q^2+q
       197: q^2+q
       198: q^2+q
       199: 2q^4+5q^3+4q^2+2q
       200: q^4+2q^3+3q^2
       201: 2q^4+5q^3+4q^2+2q
       202: q^4+2q^3+3q^2
       203: 3q^3+4q^2+q
       204: q^3+3q^2+q
       205: q^3+2q^2+q
       206: q^3+4q^2+q
       207: q^4+4q^3+3q^2+q
       208: 4q^3+5q^2+q
       209: 2q^3+2q^2+q
       210: 3q^3+5q^2+q
       211: 2q^3+2q^2+q
       212: 2q^3+4q^2+q
       214: 3q^2+q
       216: q^3+3q^2+q
       218: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: q^4+4q^3+6q^2+2q
       223: q^4+4q^3+6q^2+2q
       224: 2q^3+6q^2+2q
       225: 2q^3+6q^2+2q
       226: 5q^3+7q^2+2q
       227: q^3+5q^2+2q
       228: 2q^3+6q^2+2q
       229: 2q^2+2q
       230: q^3+5q^2+2q
       231: 3q^4+8q^3+7q^2+2q
       232: q^4+4q^3+6q^2+2q
       233: 2q^4+6q^3+7q^2+2q
       234: q^4+4q^3+6q^2+2q
       235: 2q^3+6q^2+2q
       236: 5q^3+7q^2+2q
       237: 2q^3+2q^2+q
       238: 3q^3+5q^2+q
       239: 2q^3+2q^2+q
       240: 3q^3+5q^2+q
       241: 2q^3+2q^2+q
       242: 3q^3+4q^2+q
       243: 7q^3+8q^2+2q
       244: q^3+3q^2+2q
       245: 4q^3+7q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^3+6q^2+2q
       251: 3q^3+6q^2+2q
       252: 2q^3+6q^2+2q
       253: 2q^4+6q^3+7q^2+2q
       254: 3q^4+7q^3+7q^2+2q
       255: 2q^4+6q^3+7q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^3+q^2+q
       260: 2q^2+q
       261: q^3+2q^2
       262: q^2
       263: q^3+q^2+q
       264: q^2+q
       265: q^2
       266: q^2
       267: q^2+q
       268: q^2+q
       271: q^3+q^2+q
       272: q^3+2q^2
       273: q^2
       274: 2q^2+q
       275: q^4+2q^3+2q^2+q
       276: q^3+2q^2+q
       277: q^3+2q^2
       278: q^3+q^2
       280: 2q^2+q
       282: 3q^2+q
       283: 3q^3+3q^2+2q
       284: 2q^2
       285: q^3+3q^2+q
       286: 2q^2+q
       287: 2q^3+2q^2+q
       288: 2q^3+4q^2+q
       290: 2q^2+q
       291: q^3+2q^2+q
       292: 3q^2+q
       293: 3q^3+3q^2+2q
       294: 2q^2
       295: q^3+3q^2+q
       296: 2q^2+q
       297: q^3+2q^2+q
       298: 3q^2+q
       299: 2q^2+2q
       301: q^2+q
       302: q^2+q
       303: 3q^2+q
       304: q^2+q
       305: q^2+q
       306: q
       307: 3q^3+3q^2+2q
       308: 2q^2
       309: q^3+3q^2+q
       310: 2q^2+q
       311: q^3+2q^2+q
       312: q^3+4q^2+q
       313: q^3+2q^2+q
       314: 3q^2+q
       315: 2q^3+2q^2+q
       316: 2q^3+4q^2+q
       317: 2q^3+2q^2+q
       318: 3q^3+5q^2+q
       319: q^3+3q^2+2q
       321: 3q^3+4q^2+q
       322: q^3+3q^2+q
       323: q^2+q
       324: q^2+q
       325: 2q^3+2q^2+q
       326: 2q^3+4q^2+q
       328: 3q^2+q
       330: q^3+3q^2+q
       332: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: q^4+4q^3+6q^2+2q
       335: 2q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: 2q^2+q
       339: q^3+5q^2+2q
       340: 2q^2+q
       341: q^3+5q^2+2q
       342: q^3+q^2+q
       343: 2q^3+3q^2+q
       344: q^3+5q^2+2q
       345: q^3+5q^2+2q
       346: 2q^3+6q^2+2q
       347: 2q^2+2q
       348: 2q^2+2q
       349: q^3+5q^2+2q
       350: q^3+5q^2+2q
       351: 3q^2+3q
       352: q^4+4q^3+6q^2+2q
       353: q^4+4q^3+6q^2+2q
       354: 2q^4+6q^3+7q^2+2q
       355: q^4+4q^3+6q^2+2q
       356: q^4+4q^3+6q^2+2q
       357: 2q^3+6q^2+2q
       358: 2q^3+6q^2+2q
       359: q^3+7q^2+3q
       361: 3q^2+q
       363: q^3+3q^2+q
       365: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: 2q^2+2q
       370: q^3+5q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^3+q^2+q
       378: q^2+q
       379: q^2
       380: q^2
       382: q
       383: q^2
       385: q^3+q^2+q
       386: q^2+q
       387: q^2
       388: q^2
       389: q^2+q
       390: q^2+q
       393: q^2+q
       394: q
       397: q^3+q^2+q
       398: q^3+2q^2
       399: q^2
       400: 2q^2+q
       401: q^3+q^2+q
       402: q^2
       403: q^2+q
       404: q^2
       405: q^2+q
       407: q^2+q
       410: 2q^2+q
       412: 3q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: 2q^2+q
       419: 3q^3+3q^2+2q
       420: 2q^2
       421: q^3+3q^2+q
       422: 2q^2+q
       423: q^3+2q^2+q
       424: 3q^2+q
       425: q^2+q
       426: 2q^2+q
       427: 2q^2+q
       428: q^3+5q^2+2q
       429: 2q^2+2q
       431: 3q^2+q
       432: q^2+q
       433: q^2+q
       434: q
       436: q
       437: 2q^2+2q
       439: 3q^2+q
       440: q^2+q
       441: q^2+q
       442: q
       443: 3q^2+3q
       445: q^2+q
       446: 2q^2+2q
       447: 3q^3+3q^2+2q
       448: 2q^2
       449: q^3+3q^2+q
       450: 2q^2+q
       451: q^3+2q^2+q
       452: 3q^2+q
       453: 3q^3+3q^2+2q
       454: 2q^2
       456: 2q^2+q
       457: q^3+3q^2+q
       458: 2q^2+q
       459: q^3+2q^2+q
       460: 3q^2+q
       461: q^3+4q^2+2q
       462: 3q^2+q
       463: 2q^2+q
       464: q^3+5q^2+2q
       466: 2q^2+q
       468: 3q^2+q
       469: 2q^3+2q^2+q
       470: 2q^3+4q^2+q
       471: 2q^2+2q
       473: 3q^2+q
       474: q^2+q
       475: q^2+q
       476: q
       477: q^2+q
       478: q^2+q
       479: 2q^2+2q
       480: q^2+q
       481: 2q^3+3q^2+2q
       482: 3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       486: 2q^2+2q
       488: 2q^2+2q
       490: 2q^2+q
       491: 2q^2+2q
       492: q^3+5q^2+2q
       493: 2q^2+2q
       494: q^3+5q^2+2q
       495: 2q
       496: q^2+3q
       497: q^4+4q^3+6q^2+2q
       498: q^4+4q^3+6q^2+2q
       499: 2q^3+6q^2+2q
       500: 3q^2+2q
       501: 4q^2+3q
       503: 3q^2+q
       505: q^3+3q^2+q
       507: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: q^3+5q^2+2q
       514: q^3+5q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       522: q
       523: q^2
       526: q
       527: q^2
       529: q^3+q^2+q
       530: q^2+q
       531: q^2
       532: q^2
       533: q^2+q
       534: q
       538: q
       541: q^2+q
       542: q
       545: q^2+q
       546: 2q^2+2q
       549: q^3+q^2+q
       550: q^2
       551: q^2+q
       552: q^2
       554: q^2
       556: q
       557: q^3+q^2+q
       558: q^2
       559: q^2
       560: q^2+q
       561: q^2+q
       562: q^3+3q^2+q
       563: q^2
       564: 2q^2+q
       565: q^2+q
       566: q
       569: q^2+q
       571: q^2+q
       573: 2q^2+2q
       574: q^2+q
       577: q^2+q
       578: q^2+q
       581: q^2+q
       584: 2q^2+q
       586: q
       588: 2q^2+q
       589: 2q^3+2q^2+2q
       590: q^2
       591: q
       593: 2q
       595: 2q^2+q
       596: q^2+q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q^2+2q
       603: 2q^2+2q
       606: q
       607: 3q^2+q
       608: q^2+q
       609: q^2+q
       610: q
       612: q
       613: q
       614: q
       615: q^2+3q
       618: 2q
       619: 3q^3+3q^2+2q
       620: 2q^2
       621: q^3+3q^2+q
       622: 2q^2+q
       624: 2q^2+q
       625: q^3+2q^2+q
       626: 3q^2+q
       628: 2q^2+q
       629: q^2+q
       630: 2q^2+q
       631: 2q^2+2q
       632: q^2+q
       634: 2q^2+2q
       636: 2q^2+q
       638: 3q^2+q
       640: 2q^2+q
       641: 2q^2+2q
       643: 3q^2+q
       644: q^2+q
       645: q^2+q
       646: q
       647: 2q^2+2q
       649: 3q^2+q
       650: q^2+q
       652: q
       653: q^2+q
       654: q
       655: q^2+2q
       656: q
       657: 3q^2+3q
       659: 2q^2+2q
       661: 2q^2+2q
       663: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: 2q^2+2q
       669: 2q^2+2q
       671: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: q^2+3q
       675: q^2+q
       676: 3q^2+2q
       677: 2q
       678: q^2+3q
       679: 2q
       680: 4q^2+3q
       681: 2q^3+3q^2+2q
       682: 3q^2+2q
       683: 3q^2+2q
       684: 4q^2+3q
       685: 2q^2+2q
       686: q^3+5q^2+2q
       687: 2q^2+2q
       688: q^3+5q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       693: q^2+q
       694: q^2+q
       699: q^2+q
       706: q
       707: q^2
       710: q
       713: q
       717: q
       718: q
       722: q
       725: q^2+q
       726: q
       730: q
       734: 2q
       738: q^2
       740: q
       741: q^3+q^2+q
       742: q^2
       743: q^2
       744: q^2+q
       746: q^2
       748: q
       750: q^2+q
       752: q
       753: q^2+q
       754: q
       759: q
       761: q^2+q
       763: q
       765: q^2+2q
       766: q
       770: q
       773: q
       776: q^2+2q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: 2q
       787: q
       790: q^2+2q
       791: q
       793: q^2+3q
       796: 2q
       800: q
       801: q^2+q
       805: 2q
       807: 2q^2+q
       808: q^2+q
       810: q
       811: q
       812: q
       814: 2q
       815: q^2+3q
       817: 2q^2+2q
       818: q^2+q
       820: 2q^2+2q
       822: q
       824: 2q^2+q
       825: 2q^3+2q^2+2q
       826: q^2
       827: q
       829: 2q
       831: 2q^2+q
       832: q^2+q
       834: q^2+q
       835: q^2+q
       836: 2q^2+q
       838: 2q^2+2q
       839: 2q^2+2q
       840: q^2+q
       842: 2q^2+q
       843: q^2+2q
       844: q
       845: 2q^2+2q
       847: 3q^2+q
       848: q^2+q
       850: q
       851: q^2+q
       852: q
       854: q
       855: q
       856: q
       857: q^2+2q
       858: q
       860: 2q^2+2q
       862: 2q^2+2q
       864: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: q^2+3q
       870: 2q
       871: q
       872: 2q
       873: 4q^2+3q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q^2+q
       878: 3q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       885: q
       890: q
       897: q
       905: q
       908: q
       913: q
       917: 2q
       928: q
       929: q
       933: 2q
       937: q^2
       939: q
       941: q^2+q
       943: q
       947: q
       948: q
       952: q
       953: q
       957: q^2+q
       959: q
       962: q
       964: q^2+2q
       965: q
       969: q
       972: q
       974: q^2+q
       976: q
       980: q
       983: q
       986: q
       988: q^2+2q
       989: q
       993: q^2+2q
       995: q
       997: q^2+q
       998: q
      1000: 2q
      1003: q
      1004: 2q
      1006: q
      1008: q
      1012: q
      1015: 2q
      1016: q^2+3q
      1021: q
      1025: q
      1026: q
      1031: 2q^2+2q
      1032: 2q^2+2q
      1033: q^2+q
      1035: q
      1037: q^2+q
      1039: q
      1040: 2q
      1043: q^2+q
      1044: q
      1046: q^2+2q
      1047: q
      1051: q
      1052: q^2+q
      1056: 2q
      1058: 2q^2+q
      1059: q^2+q
      1061: q
      1062: q
      1063: q
      1064: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q
      1077: 2q
      1078: q
      1079: 2q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1087: q
      1092: q
      1099: q
      1104: q
      1119: q
      1123: q
      1130: q
      1134: q
      1145: 2q
      1165: q^2+q
      1167: q
      1171: q
      1177: q
      1180: q
      1186: q
      1189: q
      1192: q
      1194: q^2+2q
      1195: q
      1206: q
      1207: q
      1211: 2q+1
      1213: q+1
      1215: q
      1216: q
      1218: 2q
      1224: q
      1227: q+1
      1228: q+1
      1234: q
      1237: q
      1240: q
      1245: 2q+1
      1246: q+1
      1247: q
      1249: q
      1250: q
      1253: q^2+q
      1254: 2q
      1257: q
      1258: 2q
      1260: q
      1262: q+1
      1268: q
      1273: q
      1275: q
      1276: q
      1280: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1303: q
      1308: q
      1319: q
      1326: q
      1341: q+1
      1373: q+1
      1375: q
      1385: q
      1389: q
      1396: q
      1400: q
      1405: q+1
      1410: q+1
      1439: q+1
      1440: 1
      1442: 1
      1444: 1
      1453: 1
      1454: q
      1457: q
      1459: q+1
      1460: q
      1462: 2q
      1468: q
      1473: q
      1476: q
      1482: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1526: q+1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1588: q
      1595: q
      1639: 1
      1644: 1
      1647: 1
      1652: q+1
      1653: 1
      1655: 1
      1665: q
      1668: 1
      1669: 1
      1674: 1
      1676: 1
      1724: 1
      1733: 1
      1746: 1
      1762: 1
      1766: 1
      1773: 1
      1802: 1
      1825: 1
      1828: 1
      1831: 1
      1835: 1
      1859: 1
      1914: 1
      1927: 1
      1937: 1
      1979: 1

1980:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+3q^3+2q^2+q
        23: q^4+3q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+4q^3+2q^2+q
        26: 2q^4+4q^3+2q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 2q^3+2q^2+q
        32: q^4+3q^3+2q^2+q
        33: q^4+3q^3+2q^2+q
        34: 3q^3+2q^2+q
        35: 2q^4+4q^3+2q^2+q
        36: 2q^4+4q^3+2q^2+q
        37: q^4+3q^3+2q^2+q
        39: q^4+3q^3+2q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+2q^2+q
        53: 2q^3+2q^2+q
        54: 2q^3+2q^2+q
        55: q^4+3q^3+2q^2+q
        56: q^4+3q^3+2q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2+q
        59: q^3+q^2
        60: 2q^3+q^2+q
        61: q^3+q^2
        62: 2q^3+2q^2+q
        64: q^4+3q^3+2q^2+q
        66: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: 2q^3+2q^2+q
        73: q^3+2q^2+q
        74: 2q^3+2q^2+q
        76: 2q^3+2q^2+q
        78: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+3q^3+2q^2+q
        82: q^3+2q^2+q
        83: 2q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 2q^4+4q^3+2q^2+q
        86: 2q^3+2q^2+q
        87: q^4+3q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: 2q^3+2q^2+q
        95: 2q^3+2q^2+q
        96: 2q^3+2q^2+q
        97: q^4+3q^3+2q^2+q
        98: q^4+3q^3+2q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2+q
       106: q^3+q^2
       107: q^3+q^2+q
       108: q^2
       109: q^2+q
       110: q^2
       111: q^3+2q^2+q
       113: q^3+2q^2+q
       115: 2q^3+2q^2+q
       117: q^3+q^2+q
       118: q^3+q^2
       119: 2q^3+q^2+q
       120: q^3+q^2
       121: 2q^3+2q^2+q
       123: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+2q^2+q
       129: 2q^3+2q^2+q
       131: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: 2q^3+2q^2+q
       136: q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^3+2q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+3q^3+2q^2+q
       145: 2q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+2q^2+q
       148: q^3+2q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       151: 2q^3+2q^2+q
       153: 2q^3+2q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^4+3q^3+2q^2+q
       164: q^4+3q^3+2q^2+q
       165: q^4+3q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       169: q^2+q
       172: q^2
       173: q^3+q^2+q
       176: q^3+q^2
       177: 2q^3+2q^2+q
       179: q^3+2q^2+q
       181: q^3+2q^2+q
       183: q^3+q^2+q
       184: q^2
       185: q^2+q
       186: q^2
       187: q^3+2q^2+q
       189: q^3+2q^2+q
       191: q^3+q^2+q
       192: q^3+q^2
       193: q^2+q
       195: q^2+q
       196: q^2
       197: q^2+q
       199: 2q^3+q^2+q
       200: q^3+q^2
       201: q^3+q^2+q
       202: q^2
       203: q^2+q
       204: q^2
       205: q^3+2q^2+q
       207: 2q^3+2q^2+q
       209: q^3+2q^2+q
       211: 2q^3+2q^2+q
       213: 2q^3+2q^2+q
       215: 2q^3+2q^2+q
       217: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^3+2q^2+q
       224: 2q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: q^3+2q^2+q
       228: 2q^3+2q^2+q
       229: q^2+q
       230: q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^3+2q^2+q
       233: q^4+3q^3+2q^2+q
       234: 2q^3+2q^2+q
       235: q^3+2q^2+q
       236: 2q^3+2q^2+q
       237: 2q^3+2q^2+q
       239: 2q^3+2q^2+q
       241: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^2+q
       245: q^3+2q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       259: q^2+q
       262: q^2
       263: q^2+q
       266: q^2
       267: q^2+q
       271: q^2+q
       273: q^2
       275: q^3+q^2+q
       278: q^3+q^2
       279: q^3+2q^2+q
       281: 2q^3+2q^2+q
       283: q^3+q^2+q
       284: q^2
       285: q^2+q
       286: q^2
       287: q^3+2q^2+q
       289: q^3+2q^2+q
       291: q^3+2q^2+q
       293: q^2+q
       294: q^2
       295: q^2+q
       296: q^2
       297: 2q^2+q
       299: q^2+q
       301: q^2+q
       303: q^2+q
       304: q^2
       305: q^2+q
       307: q^3+q^2+q
       308: q^2
       309: q^2+q
       310: q^2
       311: q^3+2q^2+q
       313: q^3+2q^2+q
       315: 2q^3+2q^2+q
       317: q^3+2q^2+q
       319: q^2+q
       321: q^2+q
       322: q^2
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^3+2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q^2+q
       349: q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: q^3+2q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^3+2q^2+q
       357: 2q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       360: 2q^3+2q^2+q
       362: 2q^3+2q^2+q
       364: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^2+q
       370: q^3+2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2+q
       380: q^2
       381: q^2+q
       384: q^2
       385: q^2+q
       388: q^2
       389: q^2+q
       393: q^2+q
       397: q^2+q
       399: q^2
       401: q^2+q
       404: q^2
       405: q^2+q
       409: q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: q^2+q
       417: q^3+2q^2+q
       419: q^2+q
       420: q^2
       421: q^2+q
       422: q^2
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       429: q^2+q
       431: q^2+q
       432: q^2
       433: q^2+q
       435: q^2+q
       437: q
       439: q
       440: q^2
       441: q
       443: q^2+q
       445: q^2+q
       447: q^3+q^2+q
       448: q^2
       449: q^2+q
       450: q^2
       451: q^3+2q^2+q
       453: q^2+q
       454: q^2
       455: q^3+2q^2+q
       457: q^2+q
       458: q^2
       459: 2q^2+q
       461: q^2+q
       462: q^2
       463: 2q^2+q
       465: q^3+2q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       471: q^2+q
       473: q^2+q
       474: q^2
       475: q^2+q
       477: q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q^2+q
       513: q^2+q
       514: q^3+2q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       521: q^2+q
       524: q^2
       525: q
       528: q^2
       529: q^2+q
       532: q^2
       533: q^2+q
       537: q^2+q
       541: q
       545: q^2+q
       549: q^2+q
       552: q^2
       553: q^2+q
       555: q^2
       557: q^2+q
       559: q^2
       561: q^2+q
       563: q^2
       565: q^2+q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2+q
       590: q^2
       591: q
       593: q
       595: q^2+q
       596: q^2
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       603: q
       605: q^2+q
       607: q
       608: q^2
       609: q
       611: q
       613: q
       615: q^2+q
       617: q^2+q
       619: q^2+q
       620: q^2
       621: q^2+q
       622: q^2
       623: q^3+2q^2+q
       625: 2q^2+q
       627: q^2+q
       629: q^2+q
       631: q^2+q
       632: q^2
       633: 2q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       641: q^2+q
       643: q^2+q
       644: q^2
       645: q^2+q
       647: q
       649: q
       650: q^2
       651: q^2+q
       653: q
       655: q^2+q
       657: 2q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       680: 2q^2+q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       693: q^2+q
       705: q
       708: q^2
       709: q^2+q
       712: q^2
       713: q
       717: q
       721: q^2+q
       725: q
       729: q
       733: q^2+q
       737: q^2+q
       739: q^2
       741: q^2+q
       743: q^2
       745: q
       747: q^2
       749: q^2+q
       751: q^2
       753: q^2+q
       757: q^2+q
       761: q
       765: q^2+q
       769: q^2+q
       775: 2q^2+q
       777: q^2+q
       779: q^2+q
       781: q^2+q
       785: q
       787: q
       791: q
       793: q^2+q
       795: q^2+q
       797: q
       799: q
       801: q
       805: q
       807: q
       808: q^2
       809: q
       811: q
       817: q^2+q
       818: q^2
       819: 2q^2+q
       821: 2q^2+q
       823: q^2+q
       825: q^2+q
       826: q^2
       827: q
       829: q
       831: q^2+q
       832: q^2
       833: q^2+q
       835: q^2+q
       841: q^2+q
       843: q^2+q
       845: q
       847: q
       848: q^2
       849: q^2+q
       851: q
       853: q
       855: q
       866: q^2+q
       870: q
       871: q
       874: q^2+q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       884: q^2+q
       896: q
       899: q^2
       900: q
       904: q
       908: q
       912: q
       916: q^2+q
       920: q
       928: q
       936: q
       938: q^2
       940: q^2+q
       942: q^2
       944: q^2+q
       946: q^2
       948: q
       952: q
       960: q^2+q
       964: q^2+q
       968: q^2+q
       974: q
       978: q
       994: q^2+q
       998: q
      1000: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1026: q
      1034: q^2+q
      1036: q^2+q
      1038: q^2+q
      1040: q
      1044: q
      1048: q
      1050: q
      1052: q
      1056: q
      1058: q
      1059: q^2
      1060: q
      1062: q
      1064: q
      1076: q
      1080: q^2+q
      1083: q
      1084: q
      1086: q^2+q
      1114: q
      1122: q
      1126: q
      1130: q
      1138: q
      1148: q
      1156: q
      1168: q
      1170: q^2
      1172: q
      1176: q
      1180: q
      1184: q
      1198: q
      1206: q
      1222: 1
      1230: q
      1234: q
      1248: q^2+q
      1250: q
      1254: q
      1264: q
      1266: q
      1268: q
      1274: q
      1278: q
      1280: q
      1287: q
      1290: q
      1322: 1
      1336: 1
      1356: q
      1380: q
      1388: q
      1392: q
      1396: q
      1414: q
      1422: q
      1430: q
      1446: 1
      1464: q
      1468: q
      1480: 1
      1491: 1
      1513: q
      1555: 1
      1559: 1
      1591: 1
      1615: q
      1633: 1
      1637: 1
      1671: 1
      1677: 1
      1701: 1
      1725: 1
      1729: 1
      1777: 1
      1803: 1
      1823: 1
      1836: 1
      1860: 1
      1910: 1
      1928: 1
      1980: 1

1981:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: q^4+11q^3+9q^2+2q
        23: q^4+11q^3+9q^2+2q
        24: 4q^4+9q^3+8q^2+2q
        25: 7q^4+15q^3+9q^2+2q
        26: 7q^4+15q^3+9q^2+2q
        27: 2q^5+9q^4+12q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: q^4+11q^3+9q^2+2q
        32: q^4+8q^3+8q^2+2q
        33: q^4+11q^3+9q^2+2q
        34: 7q^4+15q^3+9q^2+2q
        35: 5q^4+11q^3+8q^2+2q
        36: 7q^4+15q^3+9q^2+2q
        37: 6q^3+6q^2+q
        38: q^4+5q^3+3q^2+q
        39: 6q^3+6q^2+q
        40: q^4+5q^3+3q^2+q
        41: 2q^4+5q^3+5q^2+q
        42: 2q^4+4q^3+3q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 7q^3+8q^2+2q
        53: 7q^3+8q^2+2q
        54: q^4+6q^3+7q^2+2q
        55: 5q^4+11q^3+8q^2+2q
        56: 5q^4+11q^3+8q^2+2q
        57: q^5+5q^4+9q^3+7q^2+2q
        58: 5q^3+4q^2+q
        59: q^4+6q^3+5q^2+q
        60: 4q^4+9q^3+5q^2+2q
        61: 3q^4+6q^3+4q^2
        62: 6q^3+6q^2+q
        63: q^4+5q^3+3q^2+q
        64: 4q^3+5q^2+q
        65: q^4+4q^3+3q^2+q
        66: 6q^3+6q^2+q
        67: q^4+5q^3+3q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 3q^4+7q^3+7q^2+2q
        73: 4q^3+7q^2+2q
        74: 3q^3+5q^2+q
        75: 2q^3+2q^2+q
        76: 3q^3+5q^2+q
        77: 2q^3+2q^2+q
        78: 3q^3+4q^2+q
        79: 2q^3+2q^2+q
        80: q^4+8q^3+8q^2+2q
        81: q^4+8q^3+8q^2+2q
        82: 7q^3+8q^2+2q
        83: 5q^3+7q^2+2q
        84: 5q^4+11q^3+8q^2+2q
        85: 5q^4+11q^3+8q^2+2q
        86: 5q^4+11q^3+8q^2+2q
        87: 3q^4+8q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 7q^3+8q^2+2q
        95: 7q^3+8q^2+2q
        96: q^4+6q^3+7q^2+2q
        97: 5q^4+11q^3+8q^2+2q
        98: 5q^4+11q^3+8q^2+2q
        99: q^5+5q^4+9q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 3q^3+3q^2+q
       104: q^4+3q^3+2q^2+q
       105: 2q^3+q^2
       106: 3q^3+3q^2
       107: 2q^4+5q^3+4q^2+2q
       108: q^4+2q^3+3q^2
       109: q^3+3q^2+q
       110: 3q^3+4q^2+q
       111: q^3+4q^2+q
       112: q^3+2q^2+q
       113: 3q^3+5q^2+q
       114: 2q^3+2q^2+q
       115: 2q^3+4q^2+q
       116: 2q^3+2q^2+q
       117: 2q^3+3q^2+q
       118: q^4+3q^3+4q^2+q
       119: 2q^4+5q^3+4q^2+2q
       120: q^4+2q^3+3q^2
       121: 4q^3+5q^2+q
       122: q^4+4q^3+3q^2+q
       123: 4q^3+5q^2+q
       124: q^4+4q^3+3q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 3q^3+5q^2+q
       128: 2q^3+2q^2+q
       129: 3q^3+5q^2+q
       130: 2q^3+2q^2+q
       131: 3q^3+4q^2+q
       132: 2q^3+2q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: q^4+4q^3+6q^2+2q
       136: 2q^3+6q^2+2q
       137: q^4+8q^3+8q^2+2q
       138: 5q^3+7q^2+2q
       139: 7q^3+8q^2+2q
       140: q^3+3q^2+2q
       141: 5q^3+7q^2+2q
       142: 4q^3+7q^2+2q
       143: 5q^4+11q^3+8q^2+2q
       144: 3q^4+8q^3+7q^2+2q
       145: 5q^4+11q^3+8q^2+2q
       146: 3q^4+8q^3+7q^2+2q
       147: 3q^4+7q^3+7q^2+2q
       148: 4q^3+7q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 3q^3+5q^2+q
       152: 2q^3+2q^2+q
       153: 3q^3+5q^2+q
       154: 2q^3+2q^2+q
       155: 3q^3+4q^2+q
       156: 2q^3+2q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^3+6q^2+2q
       161: 3q^3+6q^2+2q
       162: 2q^3+6q^2+2q
       163: 2q^4+6q^3+7q^2+2q
       164: 3q^4+7q^3+7q^2+2q
       165: 2q^4+6q^3+7q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: 2q^2+q
       170: q^3+q^2+q
       171: q^2
       172: q^3+2q^2
       173: q^3+2q^2+q
       174: q^4+2q^3+2q^2+q
       175: q^3+q^2
       176: q^3+2q^2
       177: 2q^3+4q^2+q
       178: 2q^3+2q^2+q
       179: 3q^3+5q^2+q
       180: 2q^3+2q^2+q
       181: q^3+4q^2+q
       182: q^3+2q^2+q
       183: 3q^3+3q^2+2q
       184: 2q^2
       185: 2q^2+q
       186: q^3+3q^2+q
       187: 3q^2+q
       188: q^3+2q^2+q
       189: 2q^3+4q^2+q
       190: 2q^3+2q^2+q
       191: 2q^3+3q^2+q
       192: q^4+3q^3+4q^2+q
       193: q^3+3q^2+2q
       195: q^3+3q^2+q
       196: 3q^3+4q^2+q
       197: q^2+q
       198: q^2+q
       199: 2q^4+5q^3+4q^2+2q
       200: q^4+2q^3+3q^2
       201: 2q^4+5q^3+4q^2+2q
       202: q^4+2q^3+3q^2
       203: q^3+3q^2+q
       204: 3q^3+4q^2+q
       205: q^3+4q^2+q
       206: q^3+2q^2+q
       207: 4q^3+5q^2+q
       208: q^4+4q^3+3q^2+q
       209: 3q^3+5q^2+q
       210: 2q^3+2q^2+q
       211: 2q^3+4q^2+q
       212: 2q^3+2q^2+q
       213: 3q^2+q
       215: q^3+3q^2+q
       217: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: q^4+4q^3+6q^2+2q
       223: q^4+4q^3+6q^2+2q
       224: 2q^3+6q^2+2q
       225: 2q^3+6q^2+2q
       226: 5q^3+7q^2+2q
       227: q^3+5q^2+2q
       228: 2q^3+6q^2+2q
       229: 2q^2+2q
       230: q^3+5q^2+2q
       231: 3q^4+8q^3+7q^2+2q
       232: q^4+4q^3+6q^2+2q
       233: 2q^4+6q^3+7q^2+2q
       234: q^4+4q^3+6q^2+2q
       235: 2q^3+6q^2+2q
       236: 5q^3+7q^2+2q
       237: 3q^3+5q^2+q
       238: 2q^3+2q^2+q
       239: 3q^3+5q^2+q
       240: 2q^3+2q^2+q
       241: 3q^3+4q^2+q
       242: 2q^3+2q^2+q
       243: 7q^3+8q^2+2q
       244: q^3+3q^2+2q
       245: 4q^3+7q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^3+6q^2+2q
       251: 3q^3+6q^2+2q
       252: 2q^3+6q^2+2q
       253: 2q^4+6q^3+7q^2+2q
       254: 3q^4+7q^3+7q^2+2q
       255: 2q^4+6q^3+7q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: 2q^2+q
       260: q^3+q^2+q
       261: q^2
       262: q^3+2q^2
       263: q^2+q
       264: q^3+q^2+q
       265: q^2
       266: q^2
       267: q^2+q
       268: q^2+q
       271: 2q^2+q
       272: q^2
       273: q^3+2q^2
       274: q^3+q^2+q
       275: q^3+2q^2+q
       276: q^4+2q^3+2q^2+q
       277: q^3+q^2
       278: q^3+2q^2
       279: 2q^2+q
       281: 3q^2+q
       283: 3q^3+3q^2+2q
       284: 2q^2
       285: 2q^2+q
       286: q^3+3q^2+q
       287: 2q^3+4q^2+q
       288: 2q^3+2q^2+q
       289: 2q^2+q
       291: 3q^2+q
       292: q^3+2q^2+q
       293: 3q^3+3q^2+2q
       294: 2q^2
       295: 2q^2+q
       296: q^3+3q^2+q
       297: 3q^2+q
       298: q^3+2q^2+q
       299: 2q^2+2q
       301: q^2+q
       302: q^2+q
       303: q^2+q
       304: 3q^2+q
       305: q
       306: q^2+q
       307: 3q^3+3q^2+2q
       308: 2q^2
       309: 2q^2+q
       310: q^3+3q^2+q
       311: q^3+4q^2+q
       312: q^3+2q^2+q
       313: 3q^2+q
       314: q^3+2q^2+q
       315: 2q^3+4q^2+q
       316: 2q^3+2q^2+q
       317: 3q^3+5q^2+q
       318: 2q^3+2q^2+q
       319: q^3+3q^2+2q
       321: q^3+3q^2+q
       322: 3q^3+4q^2+q
       323: q^2+q
       324: q^2+q
       325: 2q^3+4q^2+q
       326: 2q^3+2q^2+q
       327: 3q^2+q
       329: q^3+3q^2+q
       331: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: q^4+4q^3+6q^2+2q
       335: 2q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: q^3+5q^2+2q
       339: 2q^2+q
       340: q^3+5q^2+2q
       341: 2q^2+q
       342: 2q^3+3q^2+q
       343: q^3+q^2+q
       344: q^3+5q^2+2q
       345: q^3+5q^2+2q
       346: 2q^3+6q^2+2q
       347: 2q^2+2q
       348: 2q^2+2q
       349: q^3+5q^2+2q
       350: q^3+5q^2+2q
       351: 3q^2+3q
       352: q^4+4q^3+6q^2+2q
       353: q^4+4q^3+6q^2+2q
       354: 2q^4+6q^3+7q^2+2q
       355: q^4+4q^3+6q^2+2q
       356: q^4+4q^3+6q^2+2q
       357: 2q^3+6q^2+2q
       358: 2q^3+6q^2+2q
       359: q^3+7q^2+3q
       360: 3q^2+q
       362: q^3+3q^2+q
       364: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: 2q^2+2q
       370: q^3+5q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2+q
       378: q^3+q^2+q
       379: q^2
       380: q^2
       381: q
       384: q^2
       385: q^2+q
       386: q^3+q^2+q
       387: q^2
       388: q^2
       389: q^2+q
       390: q^2+q
       393: q
       394: q^2+q
       397: 2q^2+q
       398: q^2
       399: q^3+2q^2
       400: q^3+q^2+q
       401: q^2+q
       402: q^2
       403: q^3+q^2+q
       404: q^2
       405: q^2+q
       407: q^2+q
       409: 2q^2+q
       411: 3q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: 2q^2+q
       419: 3q^3+3q^2+2q
       420: 2q^2
       421: 2q^2+q
       422: q^3+3q^2+q
       423: 3q^2+q
       424: q^3+2q^2+q
       425: 2q^2+q
       426: q^2+q
       427: q^3+5q^2+2q
       428: 2q^2+q
       429: 2q^2+2q
       431: q^2+q
       432: 3q^2+q
       433: q
       434: q^2+q
       435: q
       437: 2q^2+2q
       439: q^2+q
       440: 3q^2+q
       441: q
       442: q^2+q
       443: 3q^2+3q
       445: 2q^2+2q
       446: q^2+q
       447: 3q^3+3q^2+2q
       448: 2q^2
       449: 2q^2+q
       450: q^3+3q^2+q
       451: 3q^2+q
       452: q^3+2q^2+q
       453: 3q^3+3q^2+2q
       454: 2q^2
       455: 2q^2+q
       457: 2q^2+q
       458: q^3+3q^2+q
       459: 3q^2+q
       460: q^3+2q^2+q
       461: 3q^2+q
       462: q^3+4q^2+2q
       463: q^3+5q^2+2q
       464: 2q^2+q
       465: 2q^2+q
       467: 3q^2+q
       469: 2q^3+4q^2+q
       470: 2q^3+2q^2+q
       471: 2q^2+2q
       473: q^2+q
       474: 3q^2+q
       475: q
       476: q^2+q
       477: q^2+q
       478: q^2+q
       479: q^2+q
       480: 2q^2+2q
       481: 2q^3+3q^2+2q
       482: 3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       485: 2q^2+2q
       487: 2q^2+2q
       489: 2q^2+q
       491: 2q^2+2q
       492: q^3+5q^2+2q
       493: 2q^2+2q
       494: q^3+5q^2+2q
       495: 2q
       496: q^2+3q
       497: q^4+4q^3+6q^2+2q
       498: q^4+4q^3+6q^2+2q
       499: 2q^3+6q^2+2q
       500: 3q^2+2q
       501: 4q^2+3q
       502: 3q^2+q
       504: q^3+3q^2+q
       506: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: q^3+5q^2+2q
       514: q^3+5q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       521: q
       524: q^2
       525: q
       528: q^2
       529: q^2+q
       530: q^3+q^2+q
       531: q^2
       532: q^2
       533: q
       534: q^2+q
       537: q
       541: q
       542: q^2+q
       545: 2q^2+2q
       546: q^2+q
       549: q^2+q
       550: q^2
       551: q^3+q^2+q
       552: q^2
       553: q
       555: q^2
       557: q^2+q
       558: q^2
       559: q^2
       560: q^3+q^2+q
       561: 2q^2+q
       562: q^2
       563: q^3+3q^2+q
       564: q^2+q
       565: q
       566: q^2+q
       569: q^2+q
       571: q^2+q
       573: q^2+q
       574: 2q^2+2q
       577: q^2+q
       580: q^2+q
       581: q^2+q
       583: 2q^2+q
       585: q
       587: 2q^2+q
       589: 2q^3+2q^2+2q
       590: q^2
       592: q
       593: 2q
       595: q^2+q
       596: 2q^2+q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q^2+2q
       603: 2q^2+2q
       605: q
       607: q^2+q
       608: 3q^2+q
       609: q
       610: q^2+q
       611: q
       613: q
       614: q
       615: q^2+3q
       617: 2q
       619: 3q^3+3q^2+2q
       620: 2q^2
       621: 2q^2+q
       622: q^3+3q^2+q
       623: 2q^2+q
       625: 3q^2+q
       626: q^3+2q^2+q
       627: 2q^2+q
       629: 2q^2+q
       630: q^2+q
       631: q^2+q
       632: 2q^2+2q
       633: 2q^2+2q
       635: 2q^2+q
       637: 3q^2+q
       639: 2q^2+q
       641: 2q^2+2q
       643: q^2+q
       644: 3q^2+q
       645: q
       646: q^2+q
       647: 2q^2+2q
       649: q^2+q
       650: 3q^2+q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+2q
       657: 3q^2+3q
       658: 2q^2+2q
       660: 2q^2+2q
       662: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: 2q^2+2q
       668: 2q^2+2q
       670: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: q^2+3q
       675: q^2+q
       676: 3q^2+2q
       677: 2q
       678: q^2+3q
       679: 2q
       680: 4q^2+3q
       681: 2q^3+3q^2+2q
       682: 3q^2+2q
       683: 3q^2+2q
       684: 4q^2+3q
       685: 2q^2+2q
       686: q^3+5q^2+2q
       687: 2q^2+2q
       688: q^3+5q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       693: q^2+q
       696: q^2+q
       699: q^2+q
       705: q
       708: q^2
       709: q
       715: q
       717: q
       718: q
       721: q
       725: q
       726: q^2+q
       729: q
       733: 2q
       737: q
       739: q^2
       741: q^2+q
       742: q^2
       743: q^2
       744: q^3+q^2+q
       745: q
       747: q^2
       749: q
       751: q^2+q
       753: q
       754: q^2+q
       757: q
       761: q
       763: q^2+q
       765: q
       766: q^2+2q
       769: q
       772: q
       775: q^2+2q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: 2q
       788: q
       789: q^2+2q
       792: q
       793: q^2+3q
       795: 2q
       799: q
       801: q^2+q
       805: 2q
       807: q^2+q
       808: 2q^2+q
       809: q
       811: q
       812: q
       813: 2q
       815: q^2+3q
       817: q^2+q
       818: 2q^2+2q
       819: 2q^2+2q
       821: q
       823: 2q^2+q
       825: 2q^3+2q^2+2q
       826: q^2
       828: q
       829: 2q
       831: q^2+q
       832: 2q^2+q
       833: q^2+q
       835: 2q^2+q
       836: q^2+q
       837: 2q^2+2q
       839: q^2+q
       840: 2q^2+2q
       841: 2q^2+q
       843: q
       844: q^2+2q
       845: 2q^2+2q
       847: q^2+q
       848: 3q^2+q
       849: q
       851: q
       852: q^2+q
       853: q
       855: q
       856: q
       857: q
       858: q^2+2q
       859: 2q^2+2q
       861: 2q^2+2q
       863: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: q^2+3q
       870: 2q
       871: q
       872: 2q
       873: 4q^2+3q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q^2+q
       878: 3q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       887: q
       896: q
       904: q
       909: q
       912: q
       916: 2q
       928: q
       929: q
       932: 2q
       936: q
       938: q^2
       940: q
       942: q^2+q
       944: q
       951: q
       952: q
       953: q
       956: q
       958: q^2+q
       960: q
       964: q
       965: q^2+2q
       968: q
       971: q
       974: q
       976: q^2+q
       978: q
       982: q
       985: q
       988: q
       989: q^2+2q
       992: q^2+2q
       994: q
       996: q^2+q
       999: q
      1000: 2q
      1002: q
      1004: 2q
      1007: q
      1009: q
      1013: q
      1014: 2q
      1016: q^2+3q
      1020: q
      1024: q
      1026: q
      1030: 2q^2+2q
      1032: q^2+q
      1033: 2q^2+2q
      1034: q
      1036: q^2+q
      1038: q
      1040: 2q
      1042: q^2+q
      1045: q
      1046: q
      1047: q^2+2q
      1050: q
      1052: q^2+q
      1056: 2q
      1058: q^2+q
      1059: 2q^2+q
      1060: q
      1062: q
      1063: q
      1065: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q
      1077: 2q
      1078: q
      1079: 2q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1089: q
      1098: q
      1101: q
      1118: q
      1122: q
      1131: q
      1136: q
      1144: 2q
      1164: q
      1166: q^2+q
      1168: q
      1176: q
      1181: q
      1184: q
      1188: q
      1191: q
      1194: q
      1195: q^2+2q
      1206: q
      1207: q
      1210: 2q+1
      1212: q+1
      1214: q
      1217: q
      1218: 2q
      1225: q
      1226: q+1
      1228: q+1
      1234: q
      1236: q
      1240: q
      1244: 2q+1
      1246: q
      1247: q+1
      1248: q
      1251: q
      1252: q^2+q
      1254: 2q
      1256: q
      1258: 2q
      1261: q
      1263: q+1
      1268: q
      1272: q
      1274: q
      1277: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1302: q
      1305: q
      1318: q
      1327: q
      1340: q+1
      1372: q
      1374: q+1
      1384: q
      1388: q
      1397: q
      1402: q
      1407: q+1
      1411: q+1
      1438: q+1
      1441: 1
      1442: 1
      1445: 1
      1452: 1
      1454: q
      1456: q
      1458: q+1
      1461: q
      1462: 2q
      1468: q
      1472: q
      1476: q
      1483: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1528: q+1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1587: q
      1596: q
      1640: 1
      1643: 1
      1647: 1
      1651: q+1
      1654: 1
      1655: 1
      1665: q
      1667: 1
      1670: 1
      1674: 1
      1678: 1
      1726: 1
      1734: 1
      1745: 1
      1763: 1
      1765: 1
      1774: 1
      1804: 1
      1826: 1
      1827: 1
      1831: 1
      1837: 1
      1861: 1
      1915: 1
      1929: 1
      1936: 1
      1981: 1

1982:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: q^3+3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: q^3+3q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: 2q^3+4q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^3+3q^2+2q+1
        34: 2q^3+4q^2+2q+1
        35: 2q^3+4q^2+2q+1
        36: 2q^3+4q^2+2q+1
        37: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        41: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^3+3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: q^3+3q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+q+1
        60: q^3+q^2+q
        61: q^3+3q^2+q+1
        62: q^3+3q^2+2q+1
        64: q^3+3q^2+2q+1
        66: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+2q+1
        76: 2q^2+2q+1
        78: 2q^2+2q+1
        80: q^3+3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^3+4q^2+2q+1
        85: 2q^3+4q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+q
       106: q^3+2q^2+q+1
       107: q
       108: 2q^2+q+1
       109: q
       110: q^2+q+1
       111: q^2+2q+1
       113: 2q^2+2q+1
       115: 2q^2+2q+1
       117: q^2+q
       118: q^3+2q^2+q+1
       119: q^3+q^2+q
       120: q^3+3q^2+q+1
       121: q^3+3q^2+2q+1
       123: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       127: 2q^2+2q+1
       129: 2q^2+2q+1
       131: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^3+3q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: 2q^3+4q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       153: 2q^2+2q+1
       155: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q
       172: q^2+q+1
       173: q^2+q
       176: q^3+2q^2+q+1
       177: 2q^2+2q+1
       179: 2q^2+2q+1
       181: q^2+2q+1
       183: q
       184: 2q^2+q+1
       185: q
       186: q^2+q+1
       187: q^2+2q+1
       189: 2q^2+2q+1
       191: q^2+q
       192: q^3+2q^2+q+1
       194: q+1
       195: q
       196: q^2+q+1
       197: q+1
       199: q^3+q^2+q
       200: q^3+3q^2+q+1
       201: q
       202: 2q^2+q+1
       203: q
       204: q^2+q+1
       205: q^2+2q+1
       207: q^3+3q^2+2q+1
       209: 2q^2+2q+1
       211: 2q^2+2q+1
       213: 2q^2+2q+1
       215: 2q^2+2q+1
       217: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: 2q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^3+3q^2+2q+1
       232: q^3+3q^2+2q+1
       233: q^3+3q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       237: 2q^2+2q+1
       239: 2q^2+2q+1
       241: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+3q^2+2q+1
       254: q^3+3q^2+2q+1
       255: q^3+3q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       259: q
       262: q^2+q+1
       263: q
       266: q^2+q+1
       269: q+1
       271: q
       273: q^2+q+1
       275: q^2+q
       278: q^3+2q^2+q+1
       279: 2q^2+2q+1
       281: 2q^2+2q+1
       283: q
       284: 2q^2+q+1
       285: q
       286: q^2+q+1
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: q^2+2q+1
       293: q
       294: 2q^2+q+1
       295: q
       296: q^2+q+1
       297: q^2+2q+1
       300: q+1
       301: q+1
       303: q
       304: q^2+q+1
       305: q+1
       307: q
       308: 2q^2+q+1
       309: q
       310: q^2+q+1
       311: q^2+2q+1
       313: q^2+2q+1
       315: 2q^2+2q+1
       317: 2q^2+2q+1
       320: q+1
       321: q
       322: q^2+q+1
       323: q+1
       325: 2q^2+2q+1
       327: 2q^2+2q+1
       329: 2q^2+2q+1
       331: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q^2+2q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q^3+3q^2+2q+1
       353: q^3+3q^2+2q+1
       354: q^3+3q^2+2q+1
       355: 2q^2+2q+1
       356: 2q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+1
       360: 2q^2+2q+1
       362: 2q^2+2q+1
       364: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       377: q
       380: q^2+q+1
       381: q
       384: q^2+q+1
       385: q
       388: q^2+q+1
       391: q+1
       396: q+1
       397: q
       399: q^2+q+1
       401: q
       404: q^2+q+1
       406: q+1
       409: 2q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: q^2+2q+1
       419: q
       420: 2q^2+q+1
       421: q
       422: q^2+q+1
       423: q^2+2q+1
       425: q+1
       427: 2q+1
       430: q+1
       431: q
       432: q^2+q+1
       433: q+1
       435: q+1
       438: q+1
       439: q
       440: q^2+q+1
       441: q+1
       444: q+1
       445: q+1
       447: q
       448: 2q^2+q+1
       449: q
       450: q^2+q+1
       451: q^2+2q+1
       453: q
       454: 2q^2+q+1
       455: q^2+2q+1
       457: q
       458: q^2+q+1
       459: q^2+2q+1
       461: q
       462: q+1
       463: 2q+1
       465: 2q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       472: q+1
       473: q
       474: q^2+q+1
       475: q+1
       477: q+1
       479: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: q+1
       497: q^3+3q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q+1
       501: 2q+1
       502: 2q^2+2q+1
       504: 2q^2+2q+1
       506: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       521: q
       524: q^2+q+1
       525: q
       528: q^2+q+1
       529: q
       532: q^2+q+1
       536: q+1
       539: q+1
       543: q+1
       547: q+1
       549: q
       552: q^2+q+1
       553: q
       555: q^2+q+1
       557: q
       559: q^2+q+1
       561: q
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: 2q^2+2q+1
       585: q^2+2q+1
       587: q^2+2q+1
       589: q
       590: 2q^2+q+1
       592: 1
       594: 1
       595: q
       596: q^2+q+1
       597: q+1
       599: q+1
       601: 2q+1
       604: q+1
       605: q+1
       607: q
       608: q^2+q+1
       609: q+1
       611: q+1
       613: 1
       616: q+1
       617: q+1
       619: q
       620: 2q^2+q+1
       621: q
       622: q^2+q+1
       623: q^2+2q+1
       625: q^2+2q+1
       627: q^2+2q+1
       629: q+1
       631: q
       632: q+1
       633: 2q+1
       635: 2q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       642: q+1
       643: q
       644: q^2+q+1
       645: q+1
       648: q+1
       649: q
       650: q^2+q+1
       651: q+1
       653: q+1
       655: q+1
       657: 2q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: 1
       680: 2q+1
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       697: q+1
       705: q
       708: q^2+q+1
       709: q
       712: q^2+q+1
       716: 1
       720: 1
       723: q+1
       727: q+1
       731: q+1
       735: q+1
       737: q
       739: q^2+q+1
       741: q
       743: q^2+q+1
       745: q
       747: q^2+q+1
       749: q
       751: q+1
       756: q+1
       758: q+1
       762: q+1
       768: q+1
       769: q+1
       775: 2q+1
       777: q^2+2q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       788: 1
       789: 2q+1
       791: 1
       794: q+1
       795: q+1
       797: q+1
       799: q+1
       802: q+1
       806: 1
       807: q
       808: q^2+q+1
       809: 1
       811: 1
       813: q+1
       816: q+1
       817: q
       818: q+1
       819: 2q+1
       821: q^2+2q+1
       823: q^2+2q+1
       825: q
       826: 2q^2+q+1
       828: 1
       830: 1
       831: q
       832: q^2+q+1
       833: q+1
       835: q+1
       837: 2q+1
       839: q
       840: q+1
       841: 2q^2+2q+1
       843: q+1
       846: q+1
       847: q
       848: q^2+q+1
       849: q+1
       851: q+1
       853: q+1
       855: 1
       857: q+1
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       889: q+1
       896: q
       899: q^2+q+1
       902: 1
       906: 1
       911: 1
       914: q+1
       918: q+1
       922: q+1
       930: 1
       934: q+1
       936: q
       938: q^2+q+1
       940: q
       942: q+1
       944: q
       946: q^2+q+1
       950: 1
       955: 1
       956: q
       958: q+1
       961: q+1
       967: q+1
       968: q+1
       975: q+1
       979: q+1
       982: q+1
       991: q+1
       992: 2q+1
       994: q+1
       996: q+1
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1017: q+1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: 2q+1
      1032: q
      1033: q+1
      1034: q^2+2q+1
      1036: q+1
      1038: q+1
      1041: 1
      1042: q+1
      1045: 1
      1046: q+1
      1048: q+1
      1050: q+1
      1053: q+1
      1057: 1
      1058: q
      1059: q^2+q+1
      1060: 1
      1062: 1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1091: q+1
      1102: q+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: q+1
      1150: q+1
      1158: 1
      1164: q
      1166: q+1
      1168: q
      1170: q^2+q+1
      1174: 1
      1178: 1
      1183: 1
      1185: q+1
      1188: q+1
      1197: q+1
      1199: q+1
      1208: 1
      1210: 2q+1
      1212: q+1
      1214: q+1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1229: q+1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1244: 2q+1
      1246: q
      1247: q+1
      1248: q+1
      1251: 1
      1252: q+1
      1255: 1
      1256: q+1
      1259: 1
      1261: 1
      1262: q+1
      1264: q+1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: q+1
      1354: 1
      1358: 1
      1372: q
      1374: q+1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: q+1
      1413: q+1
      1415: q+1
      1424: 1
      1430: 1
      1436: 1
      1438: q+1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1455: 1
      1456: q+1
      1458: q+1
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1480: 1
      1482: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1494: 1
      1518: 1
      1530: q+1
      1538: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1569: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1637: 1
      1639: 1
      1643: 1
      1648: 1
      1651: q+1
      1654: 1
      1656: 1
      1659: 1
      1661: 1
      1666: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1680: 1
      1704: 1
      1723: 1
      1730: 1
      1736: 1
      1747: 1
      1763: 1
      1767: 1
      1770: 1
      1776: 1
      1778: 1
      1791: 1
      1801: 1
      1823: 1
      1825: 1
      1827: 1
      1832: 1
      1839: 1
      1863: 1
      1911: 1
      1916: 1
      1926: 1
      1938: 1
      1982: 1

1983:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: q^3+3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: q^3+3q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: 2q^3+4q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^3+3q^2+2q+1
        34: 2q^3+4q^2+2q+1
        35: 2q^3+4q^2+2q+1
        36: 2q^3+4q^2+2q+1
        38: q^3+3q^2+2q+1
        40: q^3+3q^2+2q+1
        42: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^3+3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: q^3+3q^2+2q+1
        58: q^2+q
        59: q^3+2q^2+q+1
        60: q^3+3q^2+q+1
        61: q^3+q^2+q
        63: q^3+3q^2+2q+1
        65: q^3+3q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: 2q^2+2q+1
        77: 2q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^3+4q^2+2q+1
        85: 2q^3+4q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       104: q^3+2q^2+q+1
       105: q^2+q
       107: 2q^2+q+1
       108: q
       109: q
       110: q^2+q+1
       112: q^2+2q+1
       114: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^2+q
       118: q^3+2q^2+q+1
       119: q^3+3q^2+q+1
       120: q^3+q^2+q
       122: q^3+3q^2+2q+1
       124: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       128: 2q^2+2q+1
       130: 2q^2+2q+1
       132: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^3+3q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: 2q^3+4q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       152: 2q^2+2q+1
       154: 2q^2+2q+1
       156: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       170: q^2+q+1
       171: q
       174: q^3+2q^2+q+1
       175: q^2+q
       178: 2q^2+2q+1
       180: 2q^2+2q+1
       182: q^2+2q+1
       183: 2q^2+q+1
       184: q
       185: q
       186: q^2+q+1
       188: q^2+2q+1
       190: 2q^2+2q+1
       191: q^2+q
       192: q^3+2q^2+q+1
       193: q+1
       195: q
       196: q^2+q+1
       198: q+1
       199: q^3+3q^2+q+1
       200: q^3+q^2+q
       201: 2q^2+q+1
       202: q
       203: q
       204: q^2+q+1
       206: q^2+2q+1
       208: q^3+3q^2+2q+1
       210: 2q^2+2q+1
       212: 2q^2+2q+1
       214: 2q^2+2q+1
       216: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: 2q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^3+3q^2+2q+1
       232: q^3+3q^2+2q+1
       233: q^3+3q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       238: 2q^2+2q+1
       240: 2q^2+2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+3q^2+2q+1
       254: q^3+3q^2+2q+1
       255: q^3+3q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q^2+q+1
       261: q
       264: q^2+q+1
       265: q
       268: q+1
       272: q
       274: q^2+q+1
       276: q^3+2q^2+q+1
       277: q^2+q
       280: 2q^2+2q+1
       282: 2q^2+2q+1
       283: 2q^2+q+1
       284: q
       285: q
       286: q^2+q+1
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: 2q^2+q+1
       294: q
       295: q
       296: q^2+q+1
       298: q^2+2q+1
       299: q+1
       302: q+1
       303: q
       304: q^2+q+1
       306: q+1
       307: 2q^2+q+1
       308: q
       309: q
       310: q^2+q+1
       312: q^2+2q+1
       314: q^2+2q+1
       316: 2q^2+2q+1
       318: 2q^2+2q+1
       319: q+1
       321: q
       322: q^2+q+1
       324: q+1
       326: 2q^2+2q+1
       328: 2q^2+2q+1
       330: 2q^2+2q+1
       332: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q^2+2q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q^3+3q^2+2q+1
       353: q^3+3q^2+2q+1
       354: q^3+3q^2+2q+1
       355: 2q^2+2q+1
       356: 2q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+1
       361: 2q^2+2q+1
       363: 2q^2+2q+1
       365: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       378: q^2+q+1
       379: q
       382: q^2+q+1
       383: q
       386: q^2+q+1
       387: q
       390: q+1
       394: q+1
       398: q
       400: q^2+q+1
       402: q
       403: q^2+q+1
       407: q+1
       410: 2q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: 2q^2+q+1
       420: q
       421: q
       422: q^2+q+1
       424: q^2+2q+1
       426: q+1
       428: 2q+1
       429: q+1
       431: q
       432: q^2+q+1
       434: q+1
       436: q+1
       437: q+1
       439: q
       440: q^2+q+1
       442: q+1
       443: q+1
       446: q+1
       447: 2q^2+q+1
       448: q
       449: q
       450: q^2+q+1
       452: q^2+2q+1
       453: 2q^2+q+1
       454: q
       456: q^2+2q+1
       457: q
       458: q^2+q+1
       460: q^2+2q+1
       461: q
       462: q+1
       464: 2q+1
       466: 2q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       471: q+1
       473: q
       474: q^2+q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: q+1
       497: q^3+3q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q+1
       501: 2q+1
       503: 2q^2+2q+1
       505: 2q^2+2q+1
       507: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q^2+q+1
       523: q
       526: q^2+q+1
       527: q
       530: q^2+q+1
       531: q
       534: q+1
       538: q+1
       542: q+1
       546: q+1
       550: q
       551: q^2+q+1
       554: q
       556: q^2+q+1
       558: q
       560: q^2+q+1
       562: q
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: 2q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: 2q^2+q+1
       590: q
       592: 1
       593: 1
       595: q
       596: q^2+q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q+1
       606: q+1
       607: q
       608: q^2+q+1
       610: q+1
       612: q+1
       614: 1
       615: q+1
       618: q+1
       619: 2q^2+q+1
       620: q
       621: q
       622: q^2+q+1
       624: q^2+2q+1
       626: q^2+2q+1
       628: q^2+2q+1
       630: q+1
       631: q
       632: q+1
       634: 2q+1
       636: 2q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       641: q+1
       643: q
       644: q^2+q+1
       646: q+1
       647: q+1
       649: q
       650: q^2+q+1
       652: q+1
       654: q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: 1
       680: 2q+1
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       699: q+1
       706: q^2+q+1
       707: q
       710: q^2+q+1
       711: q
       715: 1
       718: 1
       722: q+1
       726: q+1
       730: q+1
       734: q+1
       738: q
       740: q^2+q+1
       742: q
       744: q^2+q+1
       746: q
       748: q^2+q+1
       750: q
       752: q+1
       754: q+1
       759: q+1
       763: q+1
       766: q+1
       773: q+1
       776: 2q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       788: 1
       790: 2q+1
       792: 1
       793: q+1
       796: q+1
       798: q+1
       800: q+1
       801: q+1
       805: 1
       807: q
       808: q^2+q+1
       810: 1
       812: 1
       814: q+1
       815: q+1
       817: q
       818: q+1
       820: 2q+1
       822: q^2+2q+1
       824: q^2+2q+1
       825: 2q^2+q+1
       826: q
       828: 1
       829: 1
       831: q
       832: q^2+q+1
       834: q+1
       836: q+1
       838: 2q+1
       839: q
       840: q+1
       842: 2q^2+2q+1
       844: q+1
       845: q+1
       847: q
       848: q^2+q+1
       850: q+1
       852: q+1
       854: q+1
       856: 1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       890: q+1
       897: q^2+q+1
       898: q
       903: 1
       905: 1
       909: 1
       913: q+1
       917: q+1
       921: q+1
       929: 1
       933: q+1
       937: q
       939: q^2+q+1
       941: q
       943: q+1
       945: q
       947: q^2+q+1
       951: 1
       953: 1
       957: q
       959: q+1
       962: q+1
       965: q+1
       972: q+1
       976: q+1
       980: q+1
       986: q+1
       989: q+1
       993: 2q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: q+1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: 2q+1
      1032: q
      1033: q+1
      1035: q^2+2q+1
      1037: q+1
      1039: q+1
      1040: 1
      1043: q+1
      1045: 1
      1047: q+1
      1049: q+1
      1051: q+1
      1052: q+1
      1056: 1
      1058: q
      1059: q^2+q+1
      1061: 1
      1063: 1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1092: q+1
      1104: q+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: q+1
      1149: q+1
      1157: 1
      1165: q
      1167: q+1
      1169: q
      1171: q^2+q+1
      1175: 1
      1177: 1
      1181: 1
      1186: q+1
      1192: q+1
      1195: q+1
      1200: q+1
      1207: 1
      1211: 2q+1
      1213: q+1
      1215: q+1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1228: q+1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1245: 2q+1
      1246: q
      1247: q+1
      1249: q+1
      1251: 1
      1253: q+1
      1254: 1
      1257: q+1
      1258: 1
      1261: 1
      1263: q+1
      1265: q+1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: q+1
      1353: 1
      1357: 1
      1373: q
      1375: q+1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1408: q+1
      1411: q+1
      1416: q+1
      1423: 1
      1434: 1
      1437: 1
      1439: q+1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1454: 1
      1457: q+1
      1459: q+1
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1481: 1
      1483: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1495: 1
      1519: 1
      1531: q+1
      1539: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1568: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1635: 1
      1638: 1
      1640: 1
      1644: 1
      1647: 1
      1652: q+1
      1654: 1
      1655: 1
      1660: 1
      1662: 1
      1665: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1681: 1
      1705: 1
      1727: 1
      1731: 1
      1734: 1
      1746: 1
      1764: 1
      1766: 1
      1771: 1
      1774: 1
      1779: 1
      1790: 1
      1805: 1
      1824: 1
      1826: 1
      1828: 1
      1831: 1
      1840: 1
      1864: 1
      1912: 1
      1915: 1
      1930: 1
      1937: 1
      1983: 1

1984:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: q^4+11q^3+9q^2+2q
        23: q^4+11q^3+9q^2+2q
        24: 4q^4+9q^3+8q^2+2q
        25: 7q^4+15q^3+9q^2+2q
        26: 7q^4+15q^3+9q^2+2q
        27: 2q^5+9q^4+12q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: q^4+11q^3+9q^2+2q
        32: q^4+8q^3+8q^2+2q
        33: q^4+11q^3+9q^2+2q
        34: 7q^4+15q^3+9q^2+2q
        35: 5q^4+11q^3+8q^2+2q
        36: 7q^4+15q^3+9q^2+2q
        37: q^4+5q^3+3q^2+q
        38: 6q^3+6q^2+q
        39: q^4+5q^3+3q^2+q
        40: 6q^3+6q^2+q
        41: 2q^4+4q^3+3q^2+q
        42: 2q^4+5q^3+5q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 7q^3+8q^2+2q
        53: 7q^3+8q^2+2q
        54: q^4+6q^3+7q^2+2q
        55: 5q^4+11q^3+8q^2+2q
        56: 5q^4+11q^3+8q^2+2q
        57: q^5+5q^4+9q^3+7q^2+2q
        58: 5q^3+4q^2+q
        59: q^4+6q^3+5q^2+q
        60: 3q^4+6q^3+4q^2
        61: 4q^4+9q^3+5q^2+2q
        62: q^4+5q^3+3q^2+q
        63: 6q^3+6q^2+q
        64: q^4+4q^3+3q^2+q
        65: 4q^3+5q^2+q
        66: q^4+5q^3+3q^2+q
        67: 6q^3+6q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 3q^4+7q^3+7q^2+2q
        73: 4q^3+7q^2+2q
        74: 2q^3+2q^2+q
        75: 3q^3+5q^2+q
        76: 2q^3+2q^2+q
        77: 3q^3+5q^2+q
        78: 2q^3+2q^2+q
        79: 3q^3+4q^2+q
        80: q^4+8q^3+8q^2+2q
        81: q^4+8q^3+8q^2+2q
        82: 7q^3+8q^2+2q
        83: 5q^3+7q^2+2q
        84: 5q^4+11q^3+8q^2+2q
        85: 5q^4+11q^3+8q^2+2q
        86: 5q^4+11q^3+8q^2+2q
        87: 3q^4+8q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 7q^3+8q^2+2q
        95: 7q^3+8q^2+2q
        96: q^4+6q^3+7q^2+2q
        97: 5q^4+11q^3+8q^2+2q
        98: 5q^4+11q^3+8q^2+2q
        99: q^5+5q^4+9q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 2q^3+q^2
       104: 3q^3+3q^2
       105: 3q^3+3q^2+q
       106: q^4+3q^3+2q^2+q
       107: q^4+2q^3+3q^2
       108: 2q^4+5q^3+4q^2+2q
       109: q^3+3q^2+q
       110: 3q^3+4q^2+q
       111: q^3+2q^2+q
       112: q^3+4q^2+q
       113: 2q^3+2q^2+q
       114: 3q^3+5q^2+q
       115: 2q^3+2q^2+q
       116: 2q^3+4q^2+q
       117: 2q^3+3q^2+q
       118: q^4+3q^3+4q^2+q
       119: q^4+2q^3+3q^2
       120: 2q^4+5q^3+4q^2+2q
       121: q^4+4q^3+3q^2+q
       122: 4q^3+5q^2+q
       123: q^4+4q^3+3q^2+q
       124: 4q^3+5q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 2q^3+2q^2+q
       128: 3q^3+5q^2+q
       129: 2q^3+2q^2+q
       130: 3q^3+5q^2+q
       131: 2q^3+2q^2+q
       132: 3q^3+4q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: q^4+4q^3+6q^2+2q
       136: 2q^3+6q^2+2q
       137: q^4+8q^3+8q^2+2q
       138: 5q^3+7q^2+2q
       139: 7q^3+8q^2+2q
       140: q^3+3q^2+2q
       141: 5q^3+7q^2+2q
       142: 4q^3+7q^2+2q
       143: 5q^4+11q^3+8q^2+2q
       144: 3q^4+8q^3+7q^2+2q
       145: 5q^4+11q^3+8q^2+2q
       146: 3q^4+8q^3+7q^2+2q
       147: 3q^4+7q^3+7q^2+2q
       148: 4q^3+7q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 2q^3+2q^2+q
       152: 3q^3+5q^2+q
       153: 2q^3+2q^2+q
       154: 3q^3+5q^2+q
       155: 2q^3+2q^2+q
       156: 3q^3+4q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^3+6q^2+2q
       161: 3q^3+6q^2+2q
       162: 2q^3+6q^2+2q
       163: 2q^4+6q^3+7q^2+2q
       164: 3q^4+7q^3+7q^2+2q
       165: 2q^4+6q^3+7q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^2
       170: q^3+2q^2
       171: 2q^2+q
       172: q^3+q^2+q
       173: q^3+q^2
       174: q^3+2q^2
       175: q^3+2q^2+q
       176: q^4+2q^3+2q^2+q
       177: 2q^3+2q^2+q
       178: 2q^3+4q^2+q
       179: 2q^3+2q^2+q
       180: 3q^3+5q^2+q
       181: q^3+2q^2+q
       182: q^3+4q^2+q
       183: 2q^2
       184: 3q^3+3q^2+2q
       185: 2q^2+q
       186: q^3+3q^2+q
       187: q^3+2q^2+q
       188: 3q^2+q
       189: 2q^3+2q^2+q
       190: 2q^3+4q^2+q
       191: 2q^3+3q^2+q
       192: q^4+3q^3+4q^2+q
       194: q^3+3q^2+2q
       195: q^3+3q^2+q
       196: 3q^3+4q^2+q
       197: q^2+q
       198: q^2+q
       199: q^4+2q^3+3q^2
       200: 2q^4+5q^3+4q^2+2q
       201: q^4+2q^3+3q^2
       202: 2q^4+5q^3+4q^2+2q
       203: q^3+3q^2+q
       204: 3q^3+4q^2+q
       205: q^3+2q^2+q
       206: q^3+4q^2+q
       207: q^4+4q^3+3q^2+q
       208: 4q^3+5q^2+q
       209: 2q^3+2q^2+q
       210: 3q^3+5q^2+q
       211: 2q^3+2q^2+q
       212: 2q^3+4q^2+q
       214: 3q^2+q
       216: q^3+3q^2+q
       218: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: q^4+4q^3+6q^2+2q
       223: q^4+4q^3+6q^2+2q
       224: 2q^3+6q^2+2q
       225: 2q^3+6q^2+2q
       226: 5q^3+7q^2+2q
       227: q^3+5q^2+2q
       228: 2q^3+6q^2+2q
       229: 2q^2+2q
       230: q^3+5q^2+2q
       231: 3q^4+8q^3+7q^2+2q
       232: q^4+4q^3+6q^2+2q
       233: 2q^4+6q^3+7q^2+2q
       234: q^4+4q^3+6q^2+2q
       235: 2q^3+6q^2+2q
       236: 5q^3+7q^2+2q
       237: 2q^3+2q^2+q
       238: 3q^3+5q^2+q
       239: 2q^3+2q^2+q
       240: 3q^3+5q^2+q
       241: 2q^3+2q^2+q
       242: 3q^3+4q^2+q
       243: 7q^3+8q^2+2q
       244: q^3+3q^2+2q
       245: 4q^3+7q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^3+6q^2+2q
       251: 3q^3+6q^2+2q
       252: 2q^3+6q^2+2q
       253: 2q^4+6q^3+7q^2+2q
       254: 3q^4+7q^3+7q^2+2q
       255: 2q^4+6q^3+7q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^2
       260: q^3+2q^2
       261: 2q^2+q
       262: q^3+q^2+q
       263: q^2
       264: q^2
       265: q^2+q
       266: q^3+q^2+q
       269: q^2+q
       270: q^2+q
       271: q^2
       272: 2q^2+q
       273: q^3+q^2+q
       274: q^3+2q^2
       275: q^3+q^2
       276: q^3+2q^2
       277: q^3+2q^2+q
       278: q^4+2q^3+2q^2+q
       280: 2q^2+q
       282: 3q^2+q
       283: 2q^2
       284: 3q^3+3q^2+2q
       285: 2q^2+q
       286: q^3+3q^2+q
       287: 2q^3+2q^2+q
       288: 2q^3+4q^2+q
       290: 2q^2+q
       291: q^3+2q^2+q
       292: 3q^2+q
       293: 2q^2
       294: 3q^3+3q^2+2q
       295: 2q^2+q
       296: q^3+3q^2+q
       297: q^3+2q^2+q
       298: 3q^2+q
       300: 2q^2+2q
       301: q^2+q
       302: q^2+q
       303: q^2+q
       304: 3q^2+q
       305: q^2+q
       306: q
       307: 2q^2
       308: 3q^3+3q^2+2q
       309: 2q^2+q
       310: q^3+3q^2+q
       311: q^3+2q^2+q
       312: q^3+4q^2+q
       313: q^3+2q^2+q
       314: 3q^2+q
       315: 2q^3+2q^2+q
       316: 2q^3+4q^2+q
       317: 2q^3+2q^2+q
       318: 3q^3+5q^2+q
       320: q^3+3q^2+2q
       321: q^3+3q^2+q
       322: 3q^3+4q^2+q
       323: q^2+q
       324: q^2+q
       325: 2q^3+2q^2+q
       326: 2q^3+4q^2+q
       328: 3q^2+q
       330: q^3+3q^2+q
       332: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: q^4+4q^3+6q^2+2q
       335: 2q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: 2q^2+q
       339: q^3+5q^2+2q
       340: 2q^2+q
       341: q^3+5q^2+2q
       342: q^3+q^2+q
       343: 2q^3+3q^2+q
       344: q^3+5q^2+2q
       345: q^3+5q^2+2q
       346: 2q^3+6q^2+2q
       347: 2q^2+2q
       348: 2q^2+2q
       349: q^3+5q^2+2q
       350: q^3+5q^2+2q
       351: 3q^2+3q
       352: q^4+4q^3+6q^2+2q
       353: q^4+4q^3+6q^2+2q
       354: 2q^4+6q^3+7q^2+2q
       355: q^4+4q^3+6q^2+2q
       356: q^4+4q^3+6q^2+2q
       357: 2q^3+6q^2+2q
       358: 2q^3+6q^2+2q
       359: q^3+7q^2+3q
       361: 3q^2+q
       363: q^3+3q^2+q
       365: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: 2q^2+2q
       370: q^3+5q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2
       378: q^2
       379: q^2+q
       380: q^3+q^2+q
       382: q^2
       383: q
       385: q^2
       386: q^2
       387: q^2+q
       388: q^3+q^2+q
       391: q^2+q
       392: q^2+q
       395: q
       396: q^2+q
       397: q^2
       398: 2q^2+q
       399: q^3+q^2+q
       400: q^3+2q^2
       401: q^2
       402: q^2+q
       403: q^2
       404: q^3+q^2+q
       406: q^2+q
       408: q^2+q
       410: 2q^2+q
       412: 3q^2+q
       414: 2q^2+q
       416: 2q^2+q
       418: 2q^2+q
       419: 2q^2
       420: 3q^3+3q^2+2q
       421: 2q^2+q
       422: q^3+3q^2+q
       423: q^3+2q^2+q
       424: 3q^2+q
       425: q^2+q
       426: 2q^2+q
       427: 2q^2+q
       428: q^3+5q^2+2q
       430: 2q^2+2q
       431: q^2+q
       432: 3q^2+q
       433: q^2+q
       434: q
       436: q
       438: 2q^2+2q
       439: q^2+q
       440: 3q^2+q
       441: q^2+q
       442: q
       444: 3q^2+3q
       445: q^2+q
       446: 2q^2+2q
       447: 2q^2
       448: 3q^3+3q^2+2q
       449: 2q^2+q
       450: q^3+3q^2+q
       451: q^3+2q^2+q
       452: 3q^2+q
       453: 2q^2
       454: 3q^3+3q^2+2q
       456: 2q^2+q
       457: 2q^2+q
       458: q^3+3q^2+q
       459: q^3+2q^2+q
       460: 3q^2+q
       461: 3q^2+q
       462: q^3+4q^2+2q
       463: 2q^2+q
       464: q^3+5q^2+2q
       466: 2q^2+q
       468: 3q^2+q
       469: 2q^3+2q^2+q
       470: 2q^3+4q^2+q
       472: 2q^2+2q
       473: q^2+q
       474: 3q^2+q
       475: q^2+q
       476: q
       477: q^2+q
       478: q^2+q
       479: 2q^2+2q
       480: q^2+q
       481: 2q^3+3q^2+2q
       482: 3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       486: 2q^2+2q
       488: 2q^2+2q
       490: 2q^2+q
       491: 2q^2+2q
       492: q^3+5q^2+2q
       493: 2q^2+2q
       494: q^3+5q^2+2q
       495: 2q
       496: q^2+3q
       497: q^4+4q^3+6q^2+2q
       498: q^4+4q^3+6q^2+2q
       499: 2q^3+6q^2+2q
       500: 3q^2+2q
       501: 4q^2+3q
       503: 3q^2+q
       505: q^3+3q^2+q
       507: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: q^3+5q^2+2q
       514: q^3+5q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       522: q^2
       523: q
       526: q^2
       527: q
       529: q^2
       530: q^2
       531: q^2+q
       532: q^3+q^2+q
       535: q
       536: q^2+q
       540: q
       543: q^2+q
       544: q
       547: q^2+q
       548: 2q^2+2q
       549: q^2
       550: q^2+q
       551: q^2
       552: q^3+q^2+q
       554: q
       556: q^2
       557: q^2
       558: q^2+q
       559: q^3+q^2+q
       560: q^2
       561: q^2
       562: 2q^2+q
       563: q^2+q
       564: q^3+3q^2+q
       567: q
       568: q^2+q
       570: q^2+q
       572: q^2+q
       575: 2q^2+2q
       576: q^2+q
       577: q^2+q
       578: q^2+q
       581: q^2+q
       584: 2q^2+q
       586: q
       588: 2q^2+q
       589: q^2
       590: 2q^3+2q^2+2q
       592: q
       594: 2q
       595: q^2+q
       596: 2q^2+q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q^2+2q
       604: 2q^2+2q
       606: q
       607: q^2+q
       608: 3q^2+q
       609: q^2+q
       610: q
       612: q
       613: q
       614: q
       616: q^2+3q
       618: 2q
       619: 2q^2
       620: 3q^3+3q^2+2q
       621: 2q^2+q
       622: q^3+3q^2+q
       624: 2q^2+q
       625: q^3+2q^2+q
       626: 3q^2+q
       628: 2q^2+q
       629: q^2+q
       630: 2q^2+q
       631: q^2+q
       632: 2q^2+2q
       634: 2q^2+2q
       636: 2q^2+q
       638: 3q^2+q
       640: 2q^2+q
       642: 2q^2+2q
       643: q^2+q
       644: 3q^2+q
       645: q^2+q
       646: q
       648: 2q^2+2q
       649: q^2+q
       650: 3q^2+q
       652: q
       653: q^2+q
       654: q
       655: q^2+2q
       656: q
       657: 3q^2+3q
       659: 2q^2+2q
       661: 2q^2+2q
       663: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: 2q^2+2q
       669: 2q^2+2q
       671: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: q^2+3q
       675: q^2+q
       676: 3q^2+2q
       677: 2q
       678: q^2+3q
       679: 2q
       680: 4q^2+3q
       681: 2q^3+3q^2+2q
       682: 3q^2+2q
       683: 3q^2+2q
       684: 4q^2+3q
       685: 2q^2+2q
       686: q^3+5q^2+2q
       687: 2q^2+2q
       688: q^3+5q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       697: q^2+q
       700: q^2+q
       701: q^2+q
       706: q^2
       707: q
       711: q
       716: q
       719: q
       720: q
       724: q
       727: q^2+q
       728: q
       732: q
       736: 2q
       738: q
       740: q^2
       741: q^2
       742: q^2+q
       743: q^3+q^2+q
       744: q^2
       746: q
       748: q^2
       750: q
       752: q^2+q
       755: q
       756: q^2+q
       760: q
       762: q^2+q
       764: q
       767: q
       768: q^2+2q
       770: q
       773: q
       776: q^2+2q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       786: 2q
       788: q
       790: q^2+2q
       791: q
       794: q^2+3q
       796: 2q
       800: q
       802: q^2+q
       806: 2q
       807: q^2+q
       808: 2q^2+q
       810: q
       811: q
       812: q
       814: 2q
       816: q^2+3q
       817: q^2+q
       818: 2q^2+2q
       820: 2q^2+2q
       822: q
       824: 2q^2+q
       825: q^2
       826: 2q^3+2q^2+2q
       828: q
       830: 2q
       831: q^2+q
       832: 2q^2+q
       834: q^2+q
       835: q^2+q
       836: 2q^2+q
       838: 2q^2+2q
       839: q^2+q
       840: 2q^2+2q
       842: 2q^2+q
       843: q^2+2q
       844: q
       846: 2q^2+2q
       847: q^2+q
       848: 3q^2+q
       850: q
       851: q^2+q
       852: q
       854: q
       855: q
       856: q
       857: q^2+2q
       858: q
       860: 2q^2+2q
       862: 2q^2+2q
       864: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: q^2+3q
       870: 2q
       871: q
       872: 2q
       873: 4q^2+3q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q^2+q
       878: 3q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       891: q
       892: q
       898: q
       907: q
       911: q
       915: q
       919: 2q
       930: q
       931: q
       935: 2q
       937: q
       939: q^2
       941: q
       943: q^2+q
       945: q
       950: q
       954: q
       955: q
       957: q
       959: q^2+q
       963: q
       966: q
       967: q^2+2q
       969: q
       972: q
       975: q^2+q
       977: q
       981: q
       983: q
       986: q
       990: q
       991: q^2+2q
       993: q^2+2q
       995: q
       997: q^2+q
       999: q
      1001: 2q
      1003: q
      1005: 2q
      1007: q
      1008: q
      1012: q
      1015: 2q
      1017: q^2+3q
      1021: q
      1025: q
      1027: q
      1031: 2q^2+2q
      1032: q^2+q
      1033: 2q^2+2q
      1035: q
      1037: q^2+q
      1039: q
      1041: 2q
      1043: q^2+q
      1045: q
      1046: q^2+2q
      1047: q
      1051: q
      1053: q^2+q
      1057: 2q
      1058: q^2+q
      1059: 2q^2+q
      1061: q
      1062: q
      1063: q
      1064: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q
      1077: 2q
      1078: q
      1079: 2q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1093: q
      1094: q
      1105: q
      1106: q
      1121: q
      1125: q
      1133: q
      1135: q
      1147: 2q
      1165: q
      1167: q^2+q
      1169: q
      1179: q
      1183: q
      1187: q
      1189: q
      1192: q
      1196: q
      1197: q^2+2q
      1208: q
      1209: q
      1211: 2q+1
      1213: q+1
      1215: q
      1217: q
      1219: 2q
      1224: q
      1227: q+1
      1229: q+1
      1235: q
      1237: q
      1241: q
      1245: 2q+1
      1246: q
      1247: q+1
      1249: q
      1251: q
      1253: q^2+q
      1255: 2q
      1257: q
      1259: 2q
      1261: q
      1262: q+1
      1269: q
      1273: q
      1275: q
      1276: q
      1280: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1309: q
      1310: q
      1321: q
      1329: q
      1343: q+1
      1373: q
      1375: q+1
      1387: q
      1391: q
      1399: q
      1401: q
      1405: q+1
      1413: q+1
      1439: q+1
      1441: 1
      1443: 1
      1444: 1
      1453: 1
      1455: q
      1457: q
      1459: q+1
      1461: q
      1463: 2q
      1469: q
      1473: q
      1477: q
      1482: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1533: q+1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1590: q
      1598: q
      1639: 1
      1644: 1
      1648: 1
      1652: q+1
      1654: 1
      1656: 1
      1666: q
      1668: 1
      1669: 1
      1674: 1
      1683: 1
      1724: 1
      1736: 1
      1748: 1
      1764: 1
      1768: 1
      1776: 1
      1802: 1
      1825: 1
      1828: 1
      1832: 1
      1842: 1
      1866: 1
      1916: 1
      1927: 1
      1939: 1
      1984: 1

1985:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+3q^3+2q^2+q
        23: q^4+3q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+4q^3+2q^2+q
        26: 2q^4+4q^3+2q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 2q^3+2q^2+q
        32: q^4+3q^3+2q^2+q
        33: q^4+3q^3+2q^2+q
        34: 3q^3+2q^2+q
        35: 2q^4+4q^3+2q^2+q
        36: 2q^4+4q^3+2q^2+q
        37: q^4+3q^3+2q^2+q
        39: q^4+3q^3+2q^2+q
        41: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+2q^2+q
        53: 2q^3+2q^2+q
        54: 2q^3+2q^2+q
        55: q^4+3q^3+2q^2+q
        56: q^4+3q^3+2q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2
        59: q^3+q^2+q
        60: q^3+q^2
        61: 2q^3+q^2+q
        62: 2q^3+2q^2+q
        64: q^4+3q^3+2q^2+q
        66: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: 2q^3+2q^2+q
        73: q^3+2q^2+q
        74: 2q^3+2q^2+q
        76: 2q^3+2q^2+q
        78: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+3q^3+2q^2+q
        82: q^3+2q^2+q
        83: 2q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 2q^4+4q^3+2q^2+q
        86: 2q^3+2q^2+q
        87: q^4+3q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: 2q^3+2q^2+q
        95: 2q^3+2q^2+q
        96: 2q^3+2q^2+q
        97: q^4+3q^3+2q^2+q
        98: q^4+3q^3+2q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       103: q^3+q^2
       106: q^3+q^2+q
       107: q^2
       108: q^3+q^2+q
       109: q^2
       110: q^2+q
       111: q^3+2q^2+q
       113: q^3+2q^2+q
       115: 2q^3+2q^2+q
       117: q^3+q^2
       118: q^3+q^2+q
       119: q^3+q^2
       120: 2q^3+q^2+q
       121: 2q^3+2q^2+q
       123: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       127: 2q^3+2q^2+q
       129: 2q^3+2q^2+q
       131: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: 2q^3+2q^2+q
       136: q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^3+2q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+3q^3+2q^2+q
       145: 2q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+2q^2+q
       148: q^3+2q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       151: 2q^3+2q^2+q
       153: 2q^3+2q^2+q
       155: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^4+3q^3+2q^2+q
       164: q^4+3q^3+2q^2+q
       165: q^4+3q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       169: q^2
       172: q^2+q
       173: q^3+q^2
       176: q^3+q^2+q
       177: 2q^3+2q^2+q
       179: q^3+2q^2+q
       181: q^3+2q^2+q
       183: q^2
       184: q^3+q^2+q
       185: q^2
       186: q^2+q
       187: q^3+2q^2+q
       189: q^3+2q^2+q
       191: q^3+q^2
       192: q^3+q^2+q
       194: q^2+q
       195: q^2
       196: q^2+q
       197: q^2+q
       199: q^3+q^2
       200: 2q^3+q^2+q
       201: q^2
       202: q^3+q^2+q
       203: q^2
       204: q^2+q
       205: q^3+2q^2+q
       207: 2q^3+2q^2+q
       209: q^3+2q^2+q
       211: 2q^3+2q^2+q
       213: 2q^3+2q^2+q
       215: 2q^3+2q^2+q
       217: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^3+2q^2+q
       224: 2q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: q^3+2q^2+q
       228: 2q^3+2q^2+q
       229: q^2+q
       230: q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^3+2q^2+q
       233: q^4+3q^3+2q^2+q
       234: 2q^3+2q^2+q
       235: q^3+2q^2+q
       236: 2q^3+2q^2+q
       237: 2q^3+2q^2+q
       239: 2q^3+2q^2+q
       241: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^2+q
       245: q^3+2q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       259: q^2
       262: q^2+q
       263: q^2
       266: q^2+q
       269: q^2+q
       271: q^2
       273: q^2+q
       275: q^3+q^2
       278: q^3+q^2+q
       279: q^3+2q^2+q
       281: 2q^3+2q^2+q
       283: q^2
       284: q^3+q^2+q
       285: q^2
       286: q^2+q
       287: q^3+2q^2+q
       289: q^3+2q^2+q
       291: q^3+2q^2+q
       293: q^2
       294: q^2+q
       295: q^2
       296: q^2+q
       297: 2q^2+q
       300: q^2+q
       301: q^2+q
       303: q^2
       304: q^2+q
       305: q^2+q
       307: q^2
       308: q^3+q^2+q
       309: q^2
       310: q^2+q
       311: q^3+2q^2+q
       313: q^3+2q^2+q
       315: 2q^3+2q^2+q
       317: q^3+2q^2+q
       320: q^2+q
       321: q^2
       322: q^2+q
       323: q^2+q
       325: q^3+2q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2+q
       340: 2q^2+q
       342: q^3+q^2+q
       344: q^3+2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q^2+q
       349: q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: q^3+2q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^3+2q^2+q
       357: 2q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       360: 2q^3+2q^2+q
       362: 2q^3+2q^2+q
       364: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^2+q
       370: q^3+2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2
       380: q^2+q
       381: q^2
       384: q^2+q
       385: q^2
       388: q^2+q
       391: q^2+q
       396: q^2+q
       397: q^2
       399: q^2+q
       401: q^2
       404: q^2+q
       406: q^2+q
       409: q^2+q
       411: q^2+q
       413: q^3+2q^2+q
       415: q^2+q
       417: q^3+2q^2+q
       419: q^2
       420: q^2+q
       421: q^2
       422: q^2+q
       423: 2q^2+q
       425: q^2+q
       427: 2q^2+q
       430: q^2+q
       431: q^2
       432: q^2+q
       433: q^2+q
       435: q^2+q
       438: q
       439: q^2
       440: q
       441: q
       444: q^2+q
       445: q^2+q
       447: q^2
       448: q^3+q^2+q
       449: q^2
       450: q^2+q
       451: q^3+2q^2+q
       453: q^2
       454: q^2+q
       455: q^3+2q^2+q
       457: q^2
       458: q^2+q
       459: 2q^2+q
       461: q^2
       462: q^2+q
       463: 2q^2+q
       465: q^3+2q^2+q
       467: 2q^3+2q^2+q
       469: q^3+2q^2+q
       472: q^2+q
       473: q^2
       474: q^2+q
       475: q^2+q
       477: q^2+q
       479: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q^2+q
       513: q^2+q
       514: q^3+2q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       521: q^2
       524: q^2+q
       525: q^2
       528: q
       529: q^2
       532: q^2+q
       536: q^2+q
       539: q^2+q
       543: q
       547: q^2+q
       549: q^2
       552: q^2+q
       553: q^2
       555: q^2+q
       557: q^2
       559: q^2+q
       561: q^2
       563: q^2+q
       568: q^2+q
       570: q^2+q
       575: q^2+q
       577: q^2+q
       583: q^2+q
       585: 2q^2+q
       587: q^2+q
       589: q^2
       590: q^2+q
       592: q
       594: q
       595: q^2
       596: q^2+q
       597: q^2+q
       599: q^2+q
       601: 2q^2+q
       604: q
       605: q^2+q
       607: q^2
       608: q
       609: q
       611: q
       613: q
       616: q^2+q
       617: q^2+q
       619: q^2
       620: q^2+q
       621: q^2
       622: q^2+q
       623: q^3+2q^2+q
       625: 2q^2+q
       627: q^2+q
       629: q^2+q
       631: q^2
       632: q^2+q
       633: 2q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+2q^2+q
       642: q^2+q
       643: q^2
       644: q^2+q
       645: q^2+q
       648: q
       649: q^2
       650: q
       651: q^2+q
       653: q
       655: q^2+q
       657: 2q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       680: 2q^2+q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       697: q^2+q
       705: q^2
       708: q
       709: q^2
       712: q^2+q
       716: q
       720: q
       723: q^2+q
       727: q
       731: q
       735: q^2+q
       737: q^2
       739: q^2+q
       741: q^2
       743: q^2+q
       745: q^2
       747: q
       749: q^2
       751: q^2+q
       756: q^2+q
       758: q^2+q
       762: q
       768: q^2+q
       769: q^2+q
       775: 2q^2+q
       777: q^2+q
       779: q^2+q
       781: q^2+q
       786: q
       788: q
       791: q
       794: q^2+q
       795: q^2+q
       797: q
       799: q
       802: q
       806: q
       807: q^2
       808: q
       809: q
       811: q
       817: q^2
       818: q^2+q
       819: 2q^2+q
       821: 2q^2+q
       823: q^2+q
       825: q^2
       826: q^2+q
       828: q
       830: q
       831: q^2
       832: q^2+q
       833: q^2+q
       835: q^2+q
       841: q^2+q
       843: q^2+q
       846: q
       847: q^2
       848: q
       849: q^2+q
       851: q
       853: q
       855: q
       866: q^2+q
       870: q
       871: q
       874: q^2+q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       889: q^2+q
       896: q^2
       899: q
       902: q
       906: q
       911: q
       914: q
       918: q^2+q
       922: q
       930: q
       936: q^2
       938: q
       940: q^2
       942: q^2+q
       944: q^2
       946: q^2+q
       950: q
       955: q
       961: q^2+q
       967: q^2+q
       968: q^2+q
       975: q
       979: q
       994: q^2+q
       999: q
      1001: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1027: q
      1034: q^2+q
      1036: q^2+q
      1038: q^2+q
      1041: q
      1045: q
      1048: q
      1050: q
      1053: q
      1057: q
      1058: q^2
      1059: q
      1060: q
      1062: q
      1064: q
      1076: q
      1080: q^2+q
      1083: q
      1084: q
      1091: q^2+q
      1116: q
      1124: q
      1127: q
      1133: q
      1138: q
      1150: q
      1158: q
      1168: q^2
      1170: q
      1174: q
      1178: q
      1183: q
      1185: q
      1199: q
      1208: q
      1222: 1
      1230: q
      1235: q
      1248: q^2+q
      1251: q
      1255: q
      1264: q
      1266: q
      1269: q
      1274: q
      1278: q
      1280: q
      1287: q
      1295: q
      1323: 1
      1336: 1
      1358: q
      1382: q
      1390: q
      1393: q
      1399: q
      1415: q
      1424: q
      1430: q
      1446: 1
      1464: q
      1469: q
      1480: 1
      1498: 1
      1518: q
      1555: 1
      1560: 1
      1592: 1
      1617: q
      1633: 1
      1637: 1
      1671: 1
      1684: 1
      1708: 1
      1725: 1
      1730: 1
      1778: 1
      1803: 1
      1823: 1
      1843: 1
      1867: 1
      1911: 1
      1928: 1
      1985: 1

1986:    0: 7q^4+15q^3+9q^2+2q
         1: 7q^4+15q^3+9q^2+2q
         2: 2q^5+9q^4+12q^3+8q^2+2q
         3: 7q^4+15q^3+9q^2+2q
         4: 2q^5+9q^4+12q^3+8q^2+2q
         5: 7q^4+15q^3+9q^2+2q
         6: 2q^5+9q^4+12q^3+8q^2+2q
         7: 3q^5+7q^4+10q^3+7q^2+2q
         8: 2q^5+9q^4+12q^3+8q^2+2q
         9: 3q^5+7q^4+10q^3+7q^2+2q
        10: 7q^4+15q^3+9q^2+2q
        11: 7q^4+15q^3+9q^2+2q
        12: 2q^5+9q^4+12q^3+8q^2+2q
        13: 5q^4+11q^3+8q^2+2q
        14: q^5+5q^4+9q^3+7q^2+2q
        15: 5q^4+11q^3+8q^2+2q
        16: 7q^4+15q^3+9q^2+2q
        17: 7q^4+15q^3+9q^2+2q
        18: 3q^5+7q^4+10q^3+7q^2+2q
        19: 5q^4+11q^3+8q^2+2q
        20: 5q^4+11q^3+8q^2+2q
        21: q^5+5q^4+9q^3+7q^2+2q
        22: q^4+11q^3+9q^2+2q
        23: q^4+11q^3+9q^2+2q
        24: 4q^4+9q^3+8q^2+2q
        25: 7q^4+15q^3+9q^2+2q
        26: 7q^4+15q^3+9q^2+2q
        27: 2q^5+9q^4+12q^3+8q^2+2q
        28: 7q^4+15q^3+9q^2+2q
        29: 5q^4+11q^3+8q^2+2q
        30: 3q^4+8q^3+7q^2+2q
        31: q^4+11q^3+9q^2+2q
        32: q^4+8q^3+8q^2+2q
        33: q^4+11q^3+9q^2+2q
        34: 7q^4+15q^3+9q^2+2q
        35: 5q^4+11q^3+8q^2+2q
        36: 7q^4+15q^3+9q^2+2q
        37: 6q^3+6q^2+q
        38: q^4+5q^3+3q^2+q
        39: 6q^3+6q^2+q
        40: q^4+5q^3+3q^2+q
        41: 2q^4+5q^3+5q^2+q
        42: 2q^4+4q^3+3q^2+q
        43: 5q^4+11q^3+8q^2+2q
        44: q^5+5q^4+9q^3+7q^2+2q
        45: 5q^4+11q^3+8q^2+2q
        46: 5q^4+11q^3+8q^2+2q
        47: 5q^4+11q^3+8q^2+2q
        48: q^5+5q^4+9q^3+7q^2+2q
        49: 5q^4+11q^3+8q^2+2q
        50: 5q^4+11q^3+8q^2+2q
        51: q^5+5q^4+9q^3+7q^2+2q
        52: 7q^3+8q^2+2q
        53: 7q^3+8q^2+2q
        54: q^4+6q^3+7q^2+2q
        55: 5q^4+11q^3+8q^2+2q
        56: 5q^4+11q^3+8q^2+2q
        57: q^5+5q^4+9q^3+7q^2+2q
        58: q^4+6q^3+5q^2+q
        59: 5q^3+4q^2+q
        60: 3q^4+6q^3+4q^2
        61: 4q^4+9q^3+5q^2+2q
        62: 6q^3+6q^2+q
        63: q^4+5q^3+3q^2+q
        64: 4q^3+5q^2+q
        65: q^4+4q^3+3q^2+q
        66: 6q^3+6q^2+q
        67: q^4+5q^3+3q^2+q
        68: 3q^4+7q^3+7q^2+2q
        69: 3q^4+8q^3+7q^2+2q
        70: 3q^4+8q^3+7q^2+2q
        71: 5q^4+11q^3+8q^2+2q
        72: 3q^4+7q^3+7q^2+2q
        73: 4q^3+7q^2+2q
        74: 3q^3+5q^2+q
        75: 2q^3+2q^2+q
        76: 3q^3+5q^2+q
        77: 2q^3+2q^2+q
        78: 3q^3+4q^2+q
        79: 2q^3+2q^2+q
        80: q^4+8q^3+8q^2+2q
        81: q^4+8q^3+8q^2+2q
        82: 7q^3+8q^2+2q
        83: 5q^3+7q^2+2q
        84: 5q^4+11q^3+8q^2+2q
        85: 5q^4+11q^3+8q^2+2q
        86: 5q^4+11q^3+8q^2+2q
        87: 3q^4+8q^3+7q^2+2q
        88: 5q^4+11q^3+8q^2+2q
        89: 5q^4+11q^3+8q^2+2q
        90: q^5+5q^4+9q^3+7q^2+2q
        91: 2q^4+6q^3+7q^2+2q
        92: 3q^4+7q^3+7q^2+2q
        93: 2q^4+6q^3+7q^2+2q
        94: 7q^3+8q^2+2q
        95: 7q^3+8q^2+2q
        96: q^4+6q^3+7q^2+2q
        97: 5q^4+11q^3+8q^2+2q
        98: 5q^4+11q^3+8q^2+2q
        99: q^5+5q^4+9q^3+7q^2+2q
       100: 7q^3+8q^2+2q
       101: 7q^3+8q^2+2q
       102: q^4+6q^3+7q^2+2q
       103: 3q^3+3q^2
       104: 2q^3+q^2
       105: q^4+3q^3+2q^2+q
       106: 3q^3+3q^2+q
       107: q^4+2q^3+3q^2
       108: 2q^4+5q^3+4q^2+2q
       109: 3q^3+4q^2+q
       110: q^3+3q^2+q
       111: q^3+4q^2+q
       112: q^3+2q^2+q
       113: 3q^3+5q^2+q
       114: 2q^3+2q^2+q
       115: 2q^3+4q^2+q
       116: 2q^3+2q^2+q
       117: q^4+3q^3+4q^2+q
       118: 2q^3+3q^2+q
       119: q^4+2q^3+3q^2
       120: 2q^4+5q^3+4q^2+2q
       121: 4q^3+5q^2+q
       122: q^4+4q^3+3q^2+q
       123: 4q^3+5q^2+q
       124: q^4+4q^3+3q^2+q
       125: 3q^4+7q^3+7q^2+2q
       126: 3q^4+8q^3+7q^2+2q
       127: 3q^3+5q^2+q
       128: 2q^3+2q^2+q
       129: 3q^3+5q^2+q
       130: 2q^3+2q^2+q
       131: 3q^3+4q^2+q
       132: 2q^3+2q^2+q
       133: q^4+4q^3+6q^2+2q
       134: 2q^4+6q^3+7q^2+2q
       135: q^4+4q^3+6q^2+2q
       136: 2q^3+6q^2+2q
       137: q^4+8q^3+8q^2+2q
       138: 5q^3+7q^2+2q
       139: 7q^3+8q^2+2q
       140: q^3+3q^2+2q
       141: 5q^3+7q^2+2q
       142: 4q^3+7q^2+2q
       143: 5q^4+11q^3+8q^2+2q
       144: 3q^4+8q^3+7q^2+2q
       145: 5q^4+11q^3+8q^2+2q
       146: 3q^4+8q^3+7q^2+2q
       147: 3q^4+7q^3+7q^2+2q
       148: 4q^3+7q^2+2q
       149: 7q^3+8q^2+2q
       150: 5q^3+7q^2+2q
       151: 3q^3+5q^2+q
       152: 2q^3+2q^2+q
       153: 3q^3+5q^2+q
       154: 2q^3+2q^2+q
       155: 3q^3+4q^2+q
       156: 2q^3+2q^2+q
       157: 2q^4+6q^3+7q^2+2q
       158: 3q^4+7q^3+7q^2+2q
       159: 2q^4+6q^3+7q^2+2q
       160: 2q^3+6q^2+2q
       161: 3q^3+6q^2+2q
       162: 2q^3+6q^2+2q
       163: 2q^4+6q^3+7q^2+2q
       164: 3q^4+7q^3+7q^2+2q
       165: 2q^4+6q^3+7q^2+2q
       166: 7q^3+8q^2+2q
       167: 7q^3+8q^2+2q
       168: q^4+6q^3+7q^2+2q
       169: q^3+2q^2
       170: q^2
       171: q^3+q^2+q
       172: 2q^2+q
       173: q^3+2q^2
       174: q^3+q^2
       175: q^4+2q^3+2q^2+q
       176: q^3+2q^2+q
       177: 2q^3+4q^2+q
       178: 2q^3+2q^2+q
       179: 3q^3+5q^2+q
       180: 2q^3+2q^2+q
       181: q^3+4q^2+q
       182: q^3+2q^2+q
       183: 2q^2
       184: 3q^3+3q^2+2q
       185: q^3+3q^2+q
       186: 2q^2+q
       187: 3q^2+q
       188: q^3+2q^2+q
       189: 2q^3+4q^2+q
       190: 2q^3+2q^2+q
       191: q^4+3q^3+4q^2+q
       192: 2q^3+3q^2+q
       194: q^3+3q^2+2q
       195: 3q^3+4q^2+q
       196: q^3+3q^2+q
       197: q^2+q
       198: q^2+q
       199: q^4+2q^3+3q^2
       200: 2q^4+5q^3+4q^2+2q
       201: q^4+2q^3+3q^2
       202: 2q^4+5q^3+4q^2+2q
       203: 3q^3+4q^2+q
       204: q^3+3q^2+q
       205: q^3+4q^2+q
       206: q^3+2q^2+q
       207: 4q^3+5q^2+q
       208: q^4+4q^3+3q^2+q
       209: 3q^3+5q^2+q
       210: 2q^3+2q^2+q
       211: 2q^3+4q^2+q
       212: 2q^3+2q^2+q
       213: 3q^2+q
       215: q^3+3q^2+q
       217: 3q^2+q
       219: q^4+4q^3+6q^2+2q
       220: q^4+4q^3+6q^2+2q
       221: 2q^4+6q^3+7q^2+2q
       222: q^4+4q^3+6q^2+2q
       223: q^4+4q^3+6q^2+2q
       224: 2q^3+6q^2+2q
       225: 2q^3+6q^2+2q
       226: 5q^3+7q^2+2q
       227: q^3+5q^2+2q
       228: 2q^3+6q^2+2q
       229: 2q^2+2q
       230: q^3+5q^2+2q
       231: 3q^4+8q^3+7q^2+2q
       232: q^4+4q^3+6q^2+2q
       233: 2q^4+6q^3+7q^2+2q
       234: q^4+4q^3+6q^2+2q
       235: 2q^3+6q^2+2q
       236: 5q^3+7q^2+2q
       237: 3q^3+5q^2+q
       238: 2q^3+2q^2+q
       239: 3q^3+5q^2+q
       240: 2q^3+2q^2+q
       241: 3q^3+4q^2+q
       242: 2q^3+2q^2+q
       243: 7q^3+8q^2+2q
       244: q^3+3q^2+2q
       245: 4q^3+7q^2+2q
       246: 5q^3+7q^2+2q
       247: q^3+7q^2+3q
       248: q^3+7q^2+3q
       249: 3q^3+4q^2+2q
       250: 2q^3+6q^2+2q
       251: 3q^3+6q^2+2q
       252: 2q^3+6q^2+2q
       253: 2q^4+6q^3+7q^2+2q
       254: 3q^4+7q^3+7q^2+2q
       255: 2q^4+6q^3+7q^2+2q
       256: 2q^3+6q^2+2q
       257: 3q^3+6q^2+2q
       258: 2q^3+6q^2+2q
       259: q^3+2q^2
       260: q^2
       261: q^3+q^2+q
       262: 2q^2+q
       263: q^2
       264: q^2
       265: q^3+q^2+q
       266: q^2+q
       269: q^2+q
       270: q^2+q
       271: q^3+2q^2
       272: q^3+q^2+q
       273: 2q^2+q
       274: q^2
       275: q^3+2q^2
       276: q^3+q^2
       277: q^4+2q^3+2q^2+q
       278: q^3+2q^2+q
       279: 2q^2+q
       281: 3q^2+q
       283: 2q^2
       284: 3q^3+3q^2+2q
       285: q^3+3q^2+q
       286: 2q^2+q
       287: 2q^3+4q^2+q
       288: 2q^3+2q^2+q
       289: 2q^2+q
       291: 3q^2+q
       292: q^3+2q^2+q
       293: 2q^2
       294: 3q^3+3q^2+2q
       295: q^3+3q^2+q
       296: 2q^2+q
       297: 3q^2+q
       298: q^3+2q^2+q
       300: 2q^2+2q
       301: q^2+q
       302: q^2+q
       303: 3q^2+q
       304: q^2+q
       305: q
       306: q^2+q
       307: 2q^2
       308: 3q^3+3q^2+2q
       309: q^3+3q^2+q
       310: 2q^2+q
       311: q^3+4q^2+q
       312: q^3+2q^2+q
       313: 3q^2+q
       314: q^3+2q^2+q
       315: 2q^3+4q^2+q
       316: 2q^3+2q^2+q
       317: 3q^3+5q^2+q
       318: 2q^3+2q^2+q
       320: q^3+3q^2+2q
       321: 3q^3+4q^2+q
       322: q^3+3q^2+q
       323: q^2+q
       324: q^2+q
       325: 2q^3+4q^2+q
       326: 2q^3+2q^2+q
       327: 3q^2+q
       329: q^3+3q^2+q
       331: 3q^2+q
       333: q^4+4q^3+6q^2+2q
       334: q^4+4q^3+6q^2+2q
       335: 2q^3+6q^2+2q
       336: 3q^2+2q
       337: q^3+7q^2+3q
       338: q^3+5q^2+2q
       339: 2q^2+q
       340: q^3+5q^2+2q
       341: 2q^2+q
       342: 2q^3+3q^2+q
       343: q^3+q^2+q
       344: q^3+5q^2+2q
       345: q^3+5q^2+2q
       346: 2q^3+6q^2+2q
       347: 2q^2+2q
       348: 2q^2+2q
       349: q^3+5q^2+2q
       350: q^3+5q^2+2q
       351: 3q^2+3q
       352: q^4+4q^3+6q^2+2q
       353: q^4+4q^3+6q^2+2q
       354: 2q^4+6q^3+7q^2+2q
       355: q^4+4q^3+6q^2+2q
       356: q^4+4q^3+6q^2+2q
       357: 2q^3+6q^2+2q
       358: 2q^3+6q^2+2q
       359: q^3+7q^2+3q
       360: 3q^2+q
       362: q^3+3q^2+q
       364: 3q^2+q
       366: 5q^3+7q^2+2q
       367: q^3+5q^2+2q
       368: 2q^3+6q^2+2q
       369: 2q^2+2q
       370: q^3+5q^2+2q
       371: 4q^2+3q
       372: 4q^2+3q
       373: q^3+3q^2+2q
       374: 2q^3+6q^2+2q
       375: 3q^3+6q^2+2q
       376: 2q^3+6q^2+2q
       377: q^2
       378: q^2
       379: q^3+q^2+q
       380: q^2+q
       381: q^2
       384: q
       385: q^2
       386: q^2
       387: q^3+q^2+q
       388: q^2+q
       391: q^2+q
       392: q^2+q
       395: q^2+q
       396: q
       397: q^3+2q^2
       398: q^3+q^2+q
       399: 2q^2+q
       400: q^2
       401: q^2
       402: q^3+q^2+q
       403: q^2
       404: q^2+q
       406: q^2+q
       408: q^2+q
       409: 2q^2+q
       411: 3q^2+q
       413: 2q^2+q
       415: 2q^2+q
       417: 2q^2+q
       419: 2q^2
       420: 3q^3+3q^2+2q
       421: q^3+3q^2+q
       422: 2q^2+q
       423: 3q^2+q
       424: q^3+2q^2+q
       425: 2q^2+q
       426: q^2+q
       427: q^3+5q^2+2q
       428: 2q^2+q
       430: 2q^2+2q
       431: 3q^2+q
       432: q^2+q
       433: q
       434: q^2+q
       435: q
       438: 2q^2+2q
       439: 3q^2+q
       440: q^2+q
       441: q
       442: q^2+q
       444: 3q^2+3q
       445: 2q^2+2q
       446: q^2+q
       447: 2q^2
       448: 3q^3+3q^2+2q
       449: q^3+3q^2+q
       450: 2q^2+q
       451: 3q^2+q
       452: q^3+2q^2+q
       453: 2q^2
       454: 3q^3+3q^2+2q
       455: 2q^2+q
       457: q^3+3q^2+q
       458: 2q^2+q
       459: 3q^2+q
       460: q^3+2q^2+q
       461: q^3+4q^2+2q
       462: 3q^2+q
       463: q^3+5q^2+2q
       464: 2q^2+q
       465: 2q^2+q
       467: 3q^2+q
       469: 2q^3+4q^2+q
       470: 2q^3+2q^2+q
       472: 2q^2+2q
       473: 3q^2+q
       474: q^2+q
       475: q
       476: q^2+q
       477: q^2+q
       478: q^2+q
       479: q^2+q
       480: 2q^2+2q
       481: 2q^3+3q^2+2q
       482: 3q^2+2q
       483: 3q^2+2q
       484: 3q^2+3q
       485: 2q^2+2q
       487: 2q^2+2q
       489: 2q^2+q
       491: 2q^2+2q
       492: q^3+5q^2+2q
       493: 2q^2+2q
       494: q^3+5q^2+2q
       495: 2q
       496: q^2+3q
       497: q^4+4q^3+6q^2+2q
       498: q^4+4q^3+6q^2+2q
       499: 2q^3+6q^2+2q
       500: 3q^2+2q
       501: 4q^2+3q
       502: 3q^2+q
       504: q^3+3q^2+q
       506: 3q^2+q
       508: q^3+5q^2+2q
       509: q^3+5q^2+2q
       510: 2q^3+6q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: q^3+5q^2+2q
       514: q^3+5q^2+2q
       515: 4q^2+3q
       516: 4q^2+3q
       517: q^3+3q^2+2q
       518: 4q^2+3q
       519: 4q^2+3q
       520: q^3+3q^2+2q
       521: q^2
       524: q
       525: q^2
       528: q
       529: q^2
       530: q^2
       531: q^3+q^2+q
       532: q^2+q
       535: q^2+q
       536: q
       539: q
       543: q
       544: q^2+q
       547: 2q^2+2q
       548: q^2+q
       549: q^2
       550: q^3+q^2+q
       551: q^2
       552: q^2+q
       553: q^2
       555: q
       557: q^2
       558: q^3+q^2+q
       559: q^2+q
       560: q^2
       561: q^3+3q^2+q
       562: q^2+q
       563: 2q^2+q
       564: q^2
       567: q^2+q
       568: q
       570: q^2+q
       572: q^2+q
       575: q^2+q
       576: 2q^2+2q
       577: q^2+q
       580: q^2+q
       581: q^2+q
       583: 2q^2+q
       585: q
       587: 2q^2+q
       589: q^2
       590: 2q^3+2q^2+2q
       591: q
       594: 2q
       595: 2q^2+q
       596: q^2+q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q^2+2q
       604: 2q^2+2q
       605: q
       607: 3q^2+q
       608: q^2+q
       609: q
       610: q^2+q
       611: q
       613: q
       614: q
       616: q^2+3q
       617: 2q
       619: 2q^2
       620: 3q^3+3q^2+2q
       621: q^3+3q^2+q
       622: 2q^2+q
       623: 2q^2+q
       625: 3q^2+q
       626: q^3+2q^2+q
       627: 2q^2+q
       629: 2q^2+q
       630: q^2+q
       631: 2q^2+2q
       632: q^2+q
       633: 2q^2+2q
       635: 2q^2+q
       637: 3q^2+q
       639: 2q^2+q
       642: 2q^2+2q
       643: 3q^2+q
       644: q^2+q
       645: q
       646: q^2+q
       648: 2q^2+2q
       649: 3q^2+q
       650: q^2+q
       651: q
       653: q
       654: q^2+q
       655: q
       656: q^2+2q
       657: 3q^2+3q
       658: 2q^2+2q
       660: 2q^2+2q
       662: 2q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: 2q^2+2q
       668: 2q^2+2q
       670: 2q^2+q
       672: 3q^2+3q
       673: 2q^2+2q
       674: q^2+3q
       675: q^2+q
       676: 3q^2+2q
       677: 2q
       678: q^2+3q
       679: 2q
       680: 4q^2+3q
       681: 2q^3+3q^2+2q
       682: 3q^2+2q
       683: 3q^2+2q
       684: 4q^2+3q
       685: 2q^2+2q
       686: q^3+5q^2+2q
       687: 2q^2+2q
       688: q^3+5q^2+2q
       689: 2q
       690: 4q^2+3q
       691: 4q^2+3q
       692: q^3+3q^2+2q
       697: q^2+q
       698: q^2+q
       700: q^2+q
       705: q^2
       708: q
       712: q
       714: q
       719: q
       720: q
       723: q
       727: q
       728: q^2+q
       731: q
       735: 2q
       737: q^2
       739: q
       741: q^2
       742: q^3+q^2+q
       743: q^2+q
       744: q^2
       745: q^2
       747: q
       749: q^2+q
       751: q
       755: q^2+q
       756: q
       758: q
       762: q
       764: q^2+q
       767: q^2+2q
       768: q
       769: q
       772: q
       775: q^2+2q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       786: 2q
       787: q
       789: q^2+2q
       792: q
       794: q^2+3q
       795: 2q
       799: q
       802: q^2+q
       806: 2q
       807: 2q^2+q
       808: q^2+q
       809: q
       811: q
       812: q
       813: 2q
       816: q^2+3q
       817: 2q^2+2q
       818: q^2+q
       819: 2q^2+2q
       821: q
       823: 2q^2+q
       825: q^2
       826: 2q^3+2q^2+2q
       827: q
       830: 2q
       831: 2q^2+q
       832: q^2+q
       833: q^2+q
       835: 2q^2+q
       836: q^2+q
       837: 2q^2+2q
       839: 2q^2+2q
       840: q^2+q
       841: 2q^2+q
       843: q
       844: q^2+2q
       846: 2q^2+2q
       847: 3q^2+q
       848: q^2+q
       849: q
       851: q
       852: q^2+q
       853: q
       855: q
       856: q
       857: q
       858: q^2+2q
       859: 2q^2+2q
       861: 2q^2+2q
       863: 2q^2+q
       865: 3q^2+3q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: q^2+3q
       870: 2q
       871: q
       872: 2q
       873: 4q^2+3q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q^2+q
       878: 3q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       888: q
       889: q
       899: q
       906: q
       910: q
       914: q
       918: 2q
       930: q
       931: q
       934: 2q
       936: q^2
       938: q
       940: q^2+q
       942: q
       946: q
       949: q
       954: q
       955: q
       956: q^2+q
       958: q
       961: q
       966: q^2+2q
       967: q
       968: q
       971: q
       975: q
       977: q^2+q
       979: q
       982: q
       985: q
       990: q^2+2q
       991: q
       992: q^2+2q
       994: q
       996: q^2+q
       998: q
      1001: 2q
      1002: q
      1005: 2q
      1006: q
      1009: q
      1013: q
      1014: 2q
      1017: q^2+3q
      1020: q
      1024: q
      1027: q
      1030: 2q^2+2q
      1032: 2q^2+2q
      1033: q^2+q
      1034: q
      1036: q^2+q
      1038: q
      1041: 2q
      1042: q^2+q
      1044: q
      1046: q
      1047: q^2+2q
      1050: q
      1053: q^2+q
      1057: 2q
      1058: 2q^2+q
      1059: q^2+q
      1060: q
      1062: q
      1063: q
      1065: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q
      1077: 2q
      1078: q
      1079: 2q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1090: q
      1091: q
      1102: q
      1103: q
      1120: q
      1124: q
      1132: q
      1137: q
      1146: 2q
      1164: q^2+q
      1166: q
      1170: q
      1178: q
      1182: q
      1185: q
      1188: q
      1191: q
      1196: q^2+2q
      1197: q
      1208: q
      1209: q
      1210: 2q+1
      1212: q+1
      1214: q
      1216: q
      1219: 2q
      1225: q
      1226: q+1
      1229: q+1
      1235: q
      1236: q
      1241: q
      1244: 2q+1
      1246: q+1
      1247: q
      1248: q
      1250: q
      1252: q^2+q
      1255: 2q
      1256: q
      1259: 2q
      1260: q
      1263: q+1
      1269: q
      1272: q
      1274: q
      1277: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1306: q
      1307: q
      1320: q
      1328: q
      1342: q+1
      1372: q+1
      1374: q
      1386: q
      1390: q
      1398: q
      1403: q
      1407: q+1
      1412: q+1
      1438: q+1
      1440: 1
      1443: 1
      1445: 1
      1452: 1
      1455: q
      1456: q
      1458: q+1
      1460: q
      1463: 2q
      1469: q
      1472: q
      1477: q
      1483: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1529: q+1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1589: q
      1597: q
      1640: 1
      1643: 1
      1648: 1
      1651: q+1
      1653: 1
      1656: 1
      1666: q
      1667: 1
      1670: 1
      1674: 1
      1679: 1
      1726: 1
      1735: 1
      1747: 1
      1761: 1
      1767: 1
      1775: 1
      1804: 1
      1826: 1
      1827: 1
      1832: 1
      1838: 1
      1862: 1
      1917: 1
      1929: 1
      1938: 1
      1986: 1

1987:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+3q^3+2q^2+q
        23: q^4+3q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+4q^3+2q^2+q
        26: 2q^4+4q^3+2q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 2q^3+2q^2+q
        32: q^4+3q^3+2q^2+q
        33: q^4+3q^3+2q^2+q
        34: 3q^3+2q^2+q
        35: 2q^4+4q^3+2q^2+q
        36: 2q^4+4q^3+2q^2+q
        38: q^4+3q^3+2q^2+q
        40: q^4+3q^3+2q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+2q^2+q
        53: 2q^3+2q^2+q
        54: 2q^3+2q^2+q
        55: q^4+3q^3+2q^2+q
        56: q^4+3q^3+2q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2
        59: q^3+q^2+q
        60: 2q^3+q^2+q
        61: q^3+q^2
        63: 2q^3+2q^2+q
        65: q^4+3q^3+2q^2+q
        67: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: 2q^3+2q^2+q
        73: q^3+2q^2+q
        75: 2q^3+2q^2+q
        77: 2q^3+2q^2+q
        79: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+3q^3+2q^2+q
        82: q^3+2q^2+q
        83: 2q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 2q^4+4q^3+2q^2+q
        86: 2q^3+2q^2+q
        87: q^4+3q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: 2q^3+2q^2+q
        95: 2q^3+2q^2+q
        96: 2q^3+2q^2+q
        97: q^4+3q^3+2q^2+q
        98: q^4+3q^3+2q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2+q
       105: q^3+q^2
       107: q^3+q^2+q
       108: q^2
       109: q^2
       110: q^2+q
       112: q^3+2q^2+q
       114: q^3+2q^2+q
       116: 2q^3+2q^2+q
       117: q^3+q^2
       118: q^3+q^2+q
       119: 2q^3+q^2+q
       120: q^3+q^2
       122: 2q^3+2q^2+q
       124: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+2q^2+q
       130: 2q^3+2q^2+q
       132: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: 2q^3+2q^2+q
       136: q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^3+2q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+3q^3+2q^2+q
       145: 2q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+2q^2+q
       148: q^3+2q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       152: 2q^3+2q^2+q
       154: 2q^3+2q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^4+3q^3+2q^2+q
       164: q^4+3q^3+2q^2+q
       165: q^4+3q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       170: q^2+q
       171: q^2
       174: q^3+q^2+q
       175: q^3+q^2
       178: 2q^3+2q^2+q
       180: q^3+2q^2+q
       182: q^3+2q^2+q
       183: q^3+q^2+q
       184: q^2
       185: q^2
       186: q^2+q
       188: q^3+2q^2+q
       190: q^3+2q^2+q
       191: q^3+q^2
       192: q^3+q^2+q
       193: q^2+q
       195: q^2
       196: q^2+q
       198: q^2+q
       199: 2q^3+q^2+q
       200: q^3+q^2
       201: q^3+q^2+q
       202: q^2
       203: q^2
       204: q^2+q
       206: q^3+2q^2+q
       208: 2q^3+2q^2+q
       210: q^3+2q^2+q
       212: 2q^3+2q^2+q
       214: 2q^3+2q^2+q
       216: 2q^3+2q^2+q
       218: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^3+2q^2+q
       224: 2q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: q^3+2q^2+q
       228: 2q^3+2q^2+q
       229: q^2+q
       230: q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^3+2q^2+q
       233: q^4+3q^3+2q^2+q
       234: 2q^3+2q^2+q
       235: q^3+2q^2+q
       236: 2q^3+2q^2+q
       238: 2q^3+2q^2+q
       240: 2q^3+2q^2+q
       242: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^2+q
       245: q^3+2q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       260: q^2+q
       261: q^2
       264: q^2+q
       265: q^2
       268: q^2+q
       272: q^2
       274: q^2+q
       276: q^3+q^2+q
       277: q^3+q^2
       280: q^3+2q^2+q
       282: 2q^3+2q^2+q
       283: q^3+q^2+q
       284: q^2
       285: q^2
       286: q^2+q
       288: q^3+2q^2+q
       290: q^3+2q^2+q
       292: q^3+2q^2+q
       293: q^2+q
       294: q^2
       295: q^2
       296: q^2+q
       298: 2q^2+q
       299: q^2+q
       302: q^2+q
       303: q^2
       304: q^2+q
       306: q^2+q
       307: q^3+q^2+q
       308: q^2
       309: q^2
       310: q^2+q
       312: q^3+2q^2+q
       314: q^3+2q^2+q
       316: 2q^3+2q^2+q
       318: q^3+2q^2+q
       319: q^2+q
       321: q^2
       322: q^2+q
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^3+2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q^2+q
       349: q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: q^3+2q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^3+2q^2+q
       357: 2q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       361: 2q^3+2q^2+q
       363: 2q^3+2q^2+q
       365: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^2+q
       370: q^3+2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2+q
       379: q^2
       382: q^2+q
       383: q^2
       386: q^2+q
       387: q^2
       390: q^2+q
       394: q^2+q
       398: q^2
       400: q^2+q
       402: q^2
       403: q^2+q
       407: q^2+q
       410: q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: q^2+q
       418: q^3+2q^2+q
       419: q^2+q
       420: q^2
       421: q^2
       422: q^2+q
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       429: q^2+q
       431: q^2
       432: q^2+q
       434: q^2+q
       436: q^2+q
       437: q
       439: q^2
       440: q
       442: q
       443: q^2+q
       446: q^2+q
       447: q^3+q^2+q
       448: q^2
       449: q^2
       450: q^2+q
       452: q^3+2q^2+q
       453: q^2+q
       454: q^2
       456: q^3+2q^2+q
       457: q^2
       458: q^2+q
       460: 2q^2+q
       461: q^2
       462: q^2+q
       464: 2q^2+q
       466: q^3+2q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       471: q^2+q
       473: q^2
       474: q^2+q
       476: q^2+q
       478: q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q^2+q
       513: q^2+q
       514: q^3+2q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       522: q^2+q
       523: q^2
       526: q
       527: q^2
       530: q^2+q
       531: q^2
       534: q^2+q
       538: q^2+q
       542: q
       546: q^2+q
       550: q^2
       551: q^2+q
       554: q^2
       556: q^2+q
       558: q^2
       560: q^2+q
       562: q^2
       564: q^2+q
       566: q^2+q
       571: q^2+q
       574: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2+q
       590: q^2
       592: q
       593: q
       595: q^2
       596: q^2+q
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       603: q
       606: q^2+q
       607: q^2
       608: q
       610: q
       612: q
       614: q
       615: q^2+q
       618: q^2+q
       619: q^2+q
       620: q^2
       621: q^2
       622: q^2+q
       624: q^3+2q^2+q
       626: 2q^2+q
       628: q^2+q
       630: q^2+q
       631: q^2
       632: q^2+q
       634: 2q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       641: q^2+q
       643: q^2
       644: q^2+q
       646: q^2+q
       647: q
       649: q^2
       650: q
       652: q^2+q
       654: q
       656: q^2+q
       657: 2q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       680: 2q^2+q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       699: q^2+q
       706: q
       707: q^2
       710: q^2+q
       711: q^2
       715: q
       718: q
       722: q^2+q
       726: q
       730: q
       734: q^2+q
       738: q^2
       740: q^2+q
       742: q^2
       744: q^2+q
       746: q^2
       748: q
       750: q^2
       752: q^2+q
       754: q^2+q
       759: q^2+q
       763: q
       766: q^2+q
       773: q^2+q
       776: 2q^2+q
       778: q^2+q
       780: q^2+q
       782: q^2+q
       785: q
       788: q
       792: q
       793: q^2+q
       796: q^2+q
       798: q
       800: q
       801: q
       805: q
       807: q^2
       808: q
       810: q
       812: q
       817: q^2
       818: q^2+q
       820: 2q^2+q
       822: 2q^2+q
       824: q^2+q
       825: q^2+q
       826: q^2
       828: q
       829: q
       831: q^2
       832: q^2+q
       834: q^2+q
       836: q^2+q
       842: q^2+q
       844: q^2+q
       845: q
       847: q^2
       848: q
       850: q^2+q
       852: q
       854: q
       856: q
       866: q^2+q
       870: q
       871: q
       874: q^2+q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       890: q^2+q
       897: q
       898: q^2
       903: q
       905: q
       909: q
       913: q
       917: q^2+q
       921: q
       929: q
       937: q^2
       939: q
       941: q^2
       943: q^2+q
       945: q^2
       947: q^2+q
       951: q
       953: q
       962: q^2+q
       965: q^2+q
       972: q^2+q
       976: q
       980: q
       995: q^2+q
       999: q
      1000: q
      1011: q
      1013: q
      1019: q
      1021: q
      1023: q
      1026: q
      1035: q^2+q
      1037: q^2+q
      1039: q^2+q
      1040: q
      1045: q
      1049: q
      1051: q
      1052: q
      1056: q
      1058: q^2
      1059: q
      1061: q
      1063: q
      1065: q
      1076: q
      1080: q^2+q
      1083: q
      1084: q
      1092: q^2+q
      1117: q
      1123: q
      1128: q
      1131: q
      1142: q
      1149: q
      1157: q
      1169: q^2
      1171: q
      1175: q
      1177: q
      1181: q
      1186: q
      1200: q
      1207: q
      1223: 1
      1231: q
      1234: q
      1249: q^2+q
      1251: q
      1254: q
      1265: q
      1267: q
      1268: q
      1275: q
      1279: q
      1281: q
      1287: q
      1296: q
      1324: 1
      1339: 1
      1357: q
      1383: q
      1389: q
      1394: q
      1397: q
      1416: q
      1423: q
      1434: q
      1447: 1
      1465: q
      1468: q
      1481: 1
      1499: 1
      1519: q
      1558: 1
      1561: 1
      1593: 1
      1616: q
      1636: 1
      1638: 1
      1672: 1
      1685: 1
      1709: 1
      1728: 1
      1731: 1
      1779: 1
      1806: 1
      1824: 1
      1844: 1
      1868: 1
      1912: 1
      1931: 1
      1987: 1

1988:    0: 2q^3+4q^2+2q+1
         1: 2q^3+4q^2+2q+1
         2: 2q^3+4q^2+2q+1
         3: 2q^3+4q^2+2q+1
         4: q^4+2q^3+3q^2+2q+1
         5: 2q^3+4q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: 2q^3+4q^2+2q+1
         9: q^4+2q^3+3q^2+2q+1
        10: 2q^3+4q^2+2q+1
        11: 2q^3+4q^2+2q+1
        12: q^4+2q^3+3q^2+2q+1
        13: 2q^3+4q^2+2q+1
        14: q^4+2q^3+3q^2+2q+1
        15: 2q^3+4q^2+2q+1
        16: 2q^3+4q^2+2q+1
        17: 2q^3+4q^2+2q+1
        18: q^4+2q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^3+3q^2+2q+1
        22: q^3+3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: q^3+3q^2+2q+1
        25: 2q^3+4q^2+2q+1
        26: 2q^3+4q^2+2q+1
        27: 2q^3+4q^2+2q+1
        28: 2q^3+4q^2+2q+1
        29: q^3+3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^3+3q^2+2q+1
        34: 2q^3+4q^2+2q+1
        35: 2q^3+4q^2+2q+1
        36: 2q^3+4q^2+2q+1
        38: q^3+3q^2+2q+1
        40: q^3+3q^2+2q+1
        42: q^3+3q^2+2q+1
        43: 2q^3+4q^2+2q+1
        44: q^4+2q^3+3q^2+2q+1
        45: 2q^3+4q^2+2q+1
        46: 2q^3+4q^2+2q+1
        47: 2q^3+4q^2+2q+1
        48: q^4+2q^3+3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^3+3q^2+2q+1
        51: q^3+3q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^3+3q^2+2q+1
        56: q^3+3q^2+2q+1
        57: q^3+3q^2+2q+1
        58: q^3+2q^2+q+1
        59: q^2+q
        60: q^3+q^2+q
        61: q^3+3q^2+q+1
        63: q^3+3q^2+2q+1
        65: q^3+3q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^3+4q^2+2q+1
        69: q^3+3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^3+3q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        75: 2q^2+2q+1
        77: 2q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^3+4q^2+2q+1
        85: 2q^3+4q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: 2q^3+4q^2+2q+1
        89: 2q^3+4q^2+2q+1
        90: q^4+2q^3+3q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^3+3q^2+2q+1
        98: q^3+3q^2+2q+1
        99: q^3+3q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       104: q^2+q
       105: q^3+2q^2+q+1
       107: q
       108: 2q^2+q+1
       109: q^2+q+1
       110: q
       112: q^2+2q+1
       114: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^3+2q^2+q+1
       118: q^2+q
       119: q^3+q^2+q
       120: q^3+3q^2+q+1
       122: q^3+3q^2+2q+1
       124: q^3+3q^2+2q+1
       125: 2q^3+4q^2+2q+1
       126: q^3+3q^2+2q+1
       128: 2q^2+2q+1
       130: 2q^2+2q+1
       132: 2q^2+2q+1
       133: q^3+3q^2+2q+1
       134: q^3+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^3+3q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: 2q^3+4q^2+2q+1
       144: q^3+3q^2+2q+1
       145: q^3+3q^2+2q+1
       146: q^3+3q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       152: 2q^2+2q+1
       154: 2q^2+2q+1
       156: 2q^2+2q+1
       157: q^3+3q^2+2q+1
       158: q^3+3q^2+2q+1
       159: q^3+3q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: q^3+3q^2+2q+1
       164: q^3+3q^2+2q+1
       165: q^3+3q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       170: q
       171: q^2+q+1
       174: q^2+q
       175: q^3+2q^2+q+1
       178: 2q^2+2q+1
       180: 2q^2+2q+1
       182: q^2+2q+1
       183: q
       184: 2q^2+q+1
       185: q^2+q+1
       186: q
       188: q^2+2q+1
       190: 2q^2+2q+1
       191: q^3+2q^2+q+1
       192: q^2+q
       194: q+1
       195: q^2+q+1
       196: q
       198: q+1
       199: q^3+q^2+q
       200: q^3+3q^2+q+1
       201: q
       202: 2q^2+q+1
       203: q^2+q+1
       204: q
       206: q^2+2q+1
       208: q^3+3q^2+2q+1
       210: 2q^2+2q+1
       212: 2q^2+2q+1
       214: 2q^2+2q+1
       216: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+3q^2+2q+1
       220: q^3+3q^2+2q+1
       221: q^3+3q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: 2q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^3+3q^2+2q+1
       232: q^3+3q^2+2q+1
       233: q^3+3q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       238: 2q^2+2q+1
       240: 2q^2+2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q^2+2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^3+3q^2+2q+1
       254: q^3+3q^2+2q+1
       255: q^3+3q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q^2+2q+1
       260: q
       261: q^2+q+1
       264: q
       265: q^2+q+1
       270: q+1
       272: q^2+q+1
       274: q
       276: q^2+q
       277: q^3+2q^2+q+1
       280: 2q^2+2q+1
       282: 2q^2+2q+1
       283: q
       284: 2q^2+q+1
       285: q^2+q+1
       286: q
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: q^2+2q+1
       293: q
       294: 2q^2+q+1
       295: q^2+q+1
       296: q
       298: q^2+2q+1
       300: q+1
       302: q+1
       303: q^2+q+1
       304: q
       306: q+1
       307: q
       308: 2q^2+q+1
       309: q^2+q+1
       310: q
       312: q^2+2q+1
       314: q^2+2q+1
       316: 2q^2+2q+1
       318: 2q^2+2q+1
       320: q+1
       321: q^2+q+1
       322: q
       324: q+1
       326: 2q^2+2q+1
       328: 2q^2+2q+1
       330: 2q^2+2q+1
       332: 2q^2+2q+1
       333: q^3+3q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: 2q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q^2+2q+1
       345: 2q^2+2q+1
       346: 2q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q^3+3q^2+2q+1
       353: q^3+3q^2+2q+1
       354: q^3+3q^2+2q+1
       355: 2q^2+2q+1
       356: 2q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+1
       361: 2q^2+2q+1
       363: 2q^2+2q+1
       365: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+q+1
       374: 2q^2+2q+1
       375: 2q^2+2q+1
       376: 2q^2+2q+1
       378: q
       379: q^2+q+1
       382: q
       383: q^2+q+1
       386: q
       387: q^2+q+1
       392: q+1
       395: q+1
       398: q^2+q+1
       400: q
       402: q^2+q+1
       403: q
       408: q+1
       410: 2q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: q^2+2q+1
       419: q
       420: 2q^2+q+1
       421: q^2+q+1
       422: q
       424: q^2+2q+1
       426: q+1
       428: 2q+1
       430: q+1
       431: q^2+q+1
       432: q
       434: q+1
       436: q+1
       438: q+1
       439: q^2+q+1
       440: q
       442: q+1
       444: q+1
       446: q+1
       447: q
       448: 2q^2+q+1
       449: q^2+q+1
       450: q
       452: q^2+2q+1
       453: q
       454: 2q^2+q+1
       456: q^2+2q+1
       457: q^2+q+1
       458: q
       460: q^2+2q+1
       461: q+1
       462: q
       464: 2q+1
       466: 2q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       472: q+1
       473: q^2+q+1
       474: q
       476: q+1
       478: q+1
       480: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q+1
       484: 2q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q+1
       492: 2q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: 1
       496: q+1
       497: q^3+3q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q+1
       501: 2q+1
       503: 2q^2+2q+1
       505: 2q^2+2q+1
       507: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q^2+2q+1
       510: 2q^2+2q+1
       511: q+1
       512: q+1
       513: q^2+2q+1
       514: q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: 2q+1
       519: 2q+1
       520: q^2+q+1
       522: q
       523: q^2+q+1
       526: q
       527: q^2+q+1
       530: q
       531: q^2+q+1
       535: q+1
       540: q+1
       544: q+1
       548: q+1
       550: q^2+q+1
       551: q
       554: q^2+q+1
       556: q
       558: q^2+q+1
       560: q
       562: q+1
       564: q
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: 2q^2+2q+1
       586: q^2+2q+1
       588: q^2+2q+1
       589: q
       590: 2q^2+q+1
       591: 1
       594: 1
       595: q^2+q+1
       596: q
       598: q+1
       600: q+1
       602: 2q+1
       604: q+1
       606: q+1
       607: q^2+q+1
       608: q
       610: q+1
       612: q+1
       614: 1
       616: q+1
       618: q+1
       619: q
       620: 2q^2+q+1
       621: q^2+q+1
       622: q
       624: q^2+2q+1
       626: q^2+2q+1
       628: q^2+2q+1
       630: q+1
       631: q+1
       632: q
       634: 2q+1
       636: 2q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       642: q+1
       643: q^2+q+1
       644: q
       646: q+1
       648: q+1
       649: q^2+q+1
       650: q
       652: q+1
       654: q+1
       656: q+1
       657: 2q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: 2q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+2q+1
       677: 1
       678: q+1
       679: 1
       680: 2q+1
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: 2q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: 1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       700: q+1
       706: q
       707: q^2+q+1
       710: q
       711: q^2+q+1
       714: 1
       719: 1
       724: q+1
       728: q+1
       732: q+1
       736: q+1
       738: q^2+q+1
       740: q
       742: q^2+q+1
       744: q
       746: q^2+q+1
       748: q
       750: q+1
       752: q
       755: q+1
       760: q+1
       764: q+1
       767: q+1
       773: q+1
       776: 2q+1
       778: q^2+2q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       790: 2q+1
       792: 1
       794: q+1
       796: q+1
       798: q+1
       800: q+1
       802: q+1
       806: 1
       807: q^2+q+1
       808: q
       810: 1
       812: 1
       814: q+1
       816: q+1
       817: q+1
       818: q
       820: 2q+1
       822: q^2+2q+1
       824: q^2+2q+1
       825: q
       826: 2q^2+q+1
       827: 1
       830: 1
       831: q^2+q+1
       832: q
       834: q+1
       836: q+1
       838: 2q+1
       839: q+1
       840: q
       842: 2q^2+2q+1
       844: q+1
       846: q+1
       847: q^2+q+1
       848: q
       850: q+1
       852: q+1
       854: q+1
       856: 1
       858: q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: 2q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: 1
       871: 1
       872: 1
       873: 2q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+2q+1
       879: 1
       880: 1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       891: q+1
       897: q
       898: q^2+q+1
       901: 1
       907: 1
       910: 1
       915: q+1
       919: q+1
       923: q+1
       931: 1
       935: q+1
       937: q^2+q+1
       939: q
       941: q+1
       943: q
       945: q^2+q+1
       947: q
       949: 1
       954: 1
       957: q+1
       959: q
       963: q+1
       966: q+1
       972: q+1
       977: q+1
       981: q+1
       986: q+1
       990: q+1
       993: 2q+1
       995: q+1
       997: q+1
       998: 1
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1017: q+1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: 2q+1
      1032: q+1
      1033: q
      1035: q^2+2q+1
      1037: q+1
      1039: q+1
      1041: 1
      1043: q+1
      1044: 1
      1047: q+1
      1049: q+1
      1051: q+1
      1053: q+1
      1057: 1
      1058: q^2+q+1
      1059: q
      1061: 1
      1063: 1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 1
      1077: 1
      1078: 1
      1079: 2q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1093: q+1
      1105: q+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: q+1
      1151: q+1
      1159: 1
      1165: q+1
      1167: q
      1169: q^2+q+1
      1171: q
      1173: 1
      1179: 1
      1182: 1
      1187: q+1
      1192: q+1
      1196: q+1
      1201: q+1
      1209: 1
      1211: 2q+1
      1213: q+1
      1215: q+1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1229: q+1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1245: 2q+1
      1246: q+1
      1247: q
      1249: q+1
      1250: 1
      1253: q+1
      1255: 1
      1257: q+1
      1259: 1
      1260: 1
      1263: q+1
      1265: q+1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: q+1
      1355: 1
      1359: 1
      1373: q+1
      1375: q
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1408: q+1
      1412: q+1
      1417: q+1
      1425: 1
      1434: 1
      1437: 1
      1439: q+1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1455: 1
      1457: q+1
      1459: q+1
      1460: 1
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1481: 1
      1483: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1496: 1
      1520: 1
      1532: q+1
      1540: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1570: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1614: 1
      1618: 1
      1635: 1
      1638: 1
      1640: 1
      1644: 1
      1648: 1
      1652: q+1
      1653: 1
      1656: 1
      1660: 1
      1662: 1
      1666: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1682: 1
      1706: 1
      1727: 1
      1732: 1
      1735: 1
      1748: 1
      1762: 1
      1768: 1
      1772: 1
      1775: 1
      1780: 1
      1792: 1
      1805: 1
      1824: 1
      1826: 1
      1828: 1
      1832: 1
      1841: 1
      1865: 1
      1913: 1
      1917: 1
      1930: 1
      1939: 1
      1988: 1

1989:    0: 2q^4+4q^3+2q^2+q
         1: 2q^4+4q^3+2q^2+q
         2: 2q^4+4q^3+2q^2+q
         3: 2q^4+4q^3+2q^2+q
         4: q^5+2q^4+3q^3+2q^2+q
         5: 2q^4+4q^3+2q^2+q
         6: q^5+2q^4+3q^3+2q^2+q
         7: q^5+2q^4+3q^3+2q^2+q
         8: 2q^4+4q^3+2q^2+q
         9: q^5+2q^4+3q^3+2q^2+q
        10: 3q^3+2q^2+q
        11: 3q^3+2q^2+q
        12: q^4+2q^3+2q^2+q
        13: 2q^4+4q^3+2q^2+q
        14: q^5+2q^4+3q^3+2q^2+q
        15: 2q^4+4q^3+2q^2+q
        16: 2q^4+4q^3+2q^2+q
        17: 2q^4+4q^3+2q^2+q
        18: q^5+2q^4+3q^3+2q^2+q
        19: q^4+3q^3+2q^2+q
        20: q^4+3q^3+2q^2+q
        21: q^4+3q^3+2q^2+q
        22: q^4+3q^3+2q^2+q
        23: q^4+3q^3+2q^2+q
        24: q^4+3q^3+2q^2+q
        25: 2q^4+4q^3+2q^2+q
        26: 2q^4+4q^3+2q^2+q
        27: 2q^4+4q^3+2q^2+q
        28: 3q^3+2q^2+q
        29: 2q^3+2q^2+q
        30: q^4+3q^3+2q^2+q
        31: 2q^3+2q^2+q
        32: q^4+3q^3+2q^2+q
        33: q^4+3q^3+2q^2+q
        34: 3q^3+2q^2+q
        35: 2q^4+4q^3+2q^2+q
        36: 2q^4+4q^3+2q^2+q
        38: q^4+3q^3+2q^2+q
        40: q^4+3q^3+2q^2+q
        42: q^4+3q^3+2q^2+q
        43: 3q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 3q^3+2q^2+q
        46: 2q^4+4q^3+2q^2+q
        47: 2q^4+4q^3+2q^2+q
        48: q^5+2q^4+3q^3+2q^2+q
        49: q^4+3q^3+2q^2+q
        50: q^4+3q^3+2q^2+q
        51: q^4+3q^3+2q^2+q
        52: 2q^3+2q^2+q
        53: 2q^3+2q^2+q
        54: 2q^3+2q^2+q
        55: q^4+3q^3+2q^2+q
        56: q^4+3q^3+2q^2+q
        57: q^4+3q^3+2q^2+q
        58: q^3+q^2+q
        59: q^3+q^2
        60: q^3+q^2
        61: 2q^3+q^2+q
        63: 2q^3+2q^2+q
        65: q^4+3q^3+2q^2+q
        67: q^4+3q^3+2q^2+q
        68: 3q^3+2q^2+q
        69: q^4+3q^3+2q^2+q
        70: 2q^3+2q^2+q
        71: 2q^3+2q^2+q
        72: 2q^3+2q^2+q
        73: q^3+2q^2+q
        75: 2q^3+2q^2+q
        77: 2q^3+2q^2+q
        79: 2q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+3q^3+2q^2+q
        82: q^3+2q^2+q
        83: 2q^3+2q^2+q
        84: 3q^3+2q^2+q
        85: 2q^4+4q^3+2q^2+q
        86: 2q^3+2q^2+q
        87: q^4+3q^3+2q^2+q
        88: 3q^3+2q^2+q
        89: 3q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: q^4+3q^3+2q^2+q
        92: q^4+3q^3+2q^2+q
        93: q^4+3q^3+2q^2+q
        94: 2q^3+2q^2+q
        95: 2q^3+2q^2+q
        96: 2q^3+2q^2+q
        97: q^4+3q^3+2q^2+q
        98: q^4+3q^3+2q^2+q
        99: q^4+3q^3+2q^2+q
       100: 2q^3+2q^2+q
       101: 2q^3+2q^2+q
       102: 2q^3+2q^2+q
       104: q^3+q^2
       105: q^3+q^2+q
       107: q^2
       108: q^3+q^2+q
       109: q^2+q
       110: q^2
       112: q^3+2q^2+q
       114: q^3+2q^2+q
       116: 2q^3+2q^2+q
       117: q^3+q^2+q
       118: q^3+q^2
       119: q^3+q^2
       120: 2q^3+q^2+q
       122: 2q^3+2q^2+q
       124: q^4+3q^3+2q^2+q
       125: 3q^3+2q^2+q
       126: 2q^3+2q^2+q
       128: 2q^3+2q^2+q
       130: 2q^3+2q^2+q
       132: 2q^3+2q^2+q
       133: 2q^3+2q^2+q
       134: q^4+3q^3+2q^2+q
       135: 2q^3+2q^2+q
       136: q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: 2q^3+2q^2+q
       139: q^3+2q^2+q
       140: q^2+q
       141: q^3+2q^2+q
       142: q^3+2q^2+q
       143: 3q^3+2q^2+q
       144: q^4+3q^3+2q^2+q
       145: 2q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 2q^3+2q^2+q
       148: q^3+2q^2+q
       149: q^3+2q^2+q
       150: 2q^3+2q^2+q
       152: 2q^3+2q^2+q
       154: 2q^3+2q^2+q
       156: 2q^3+2q^2+q
       157: q^3+2q^2+q
       158: q^3+2q^2+q
       159: q^3+2q^2+q
       160: 2q^3+2q^2+q
       161: 2q^3+2q^2+q
       162: 2q^3+2q^2+q
       163: q^4+3q^3+2q^2+q
       164: q^4+3q^3+2q^2+q
       165: q^4+3q^3+2q^2+q
       166: 2q^3+2q^2+q
       167: 2q^3+2q^2+q
       168: 2q^3+2q^2+q
       170: q^2
       171: q^2+q
       174: q^3+q^2
       175: q^3+q^2+q
       178: 2q^3+2q^2+q
       180: q^3+2q^2+q
       182: q^3+2q^2+q
       183: q^2
       184: q^3+q^2+q
       185: q^2+q
       186: q^2
       188: q^3+2q^2+q
       190: q^3+2q^2+q
       191: q^3+q^2+q
       192: q^3+q^2
       194: q^2+q
       195: q^2+q
       196: q^2
       198: q^2+q
       199: q^3+q^2
       200: 2q^3+q^2+q
       201: q^2
       202: q^3+q^2+q
       203: q^2+q
       204: q^2
       206: q^3+2q^2+q
       208: 2q^3+2q^2+q
       210: q^3+2q^2+q
       212: 2q^3+2q^2+q
       214: 2q^3+2q^2+q
       216: 2q^3+2q^2+q
       218: 2q^3+2q^2+q
       219: 2q^3+2q^2+q
       220: q^3+2q^2+q
       221: q^3+2q^2+q
       222: 2q^2+q
       223: 2q^3+2q^2+q
       224: 2q^2+q
       225: q^3+2q^2+q
       226: q^3+2q^2+q
       227: q^3+2q^2+q
       228: 2q^3+2q^2+q
       229: q^2+q
       230: q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^3+2q^2+q
       233: q^4+3q^3+2q^2+q
       234: 2q^3+2q^2+q
       235: q^3+2q^2+q
       236: 2q^3+2q^2+q
       238: 2q^3+2q^2+q
       240: 2q^3+2q^2+q
       242: 2q^3+2q^2+q
       243: q^3+2q^2+q
       244: q^2+q
       245: q^3+2q^2+q
       246: q^3+2q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^3+2q^2+q
       254: q^3+2q^2+q
       255: q^3+2q^2+q
       256: 2q^3+2q^2+q
       257: 2q^3+2q^2+q
       258: 2q^3+2q^2+q
       260: q^2
       261: q^2+q
       264: q^2
       265: q^2+q
       270: q^2+q
       272: q^2+q
       274: q^2
       276: q^3+q^2
       277: q^3+q^2+q
       280: q^3+2q^2+q
       282: 2q^3+2q^2+q
       283: q^2
       284: q^3+q^2+q
       285: q^2+q
       286: q^2
       288: q^3+2q^2+q
       290: q^3+2q^2+q
       292: q^3+2q^2+q
       293: q^2
       294: q^2+q
       295: q^2+q
       296: q^2
       298: 2q^2+q
       300: q^2+q
       302: q^2+q
       303: q^2+q
       304: q^2
       306: q^2+q
       307: q^2
       308: q^3+q^2+q
       309: q^2+q
       310: q^2
       312: q^3+2q^2+q
       314: q^3+2q^2+q
       316: 2q^3+2q^2+q
       318: q^3+2q^2+q
       320: q^2+q
       321: q^2+q
       322: q^2
       324: q^2+q
       326: q^3+2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+q
       334: 2q^2+q
       335: 2q^2+q
       336: q^2+q
       337: 2q^2+q
       339: 2q^2+q
       341: 2q^2+q
       343: q^3+q^2+q
       344: q^3+2q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q^2+q
       349: q^2+q
       350: q^3+2q^2+q
       351: q^2+q
       352: 2q^3+2q^2+q
       353: q^3+2q^2+q
       354: q^3+2q^2+q
       355: 2q^2+q
       356: 2q^3+2q^2+q
       357: 2q^2+q
       358: q^3+2q^2+q
       359: 2q^2+q
       361: 2q^3+2q^2+q
       363: 2q^3+2q^2+q
       365: 2q^3+2q^2+q
       366: q^3+2q^2+q
       367: q^3+2q^2+q
       368: 2q^3+2q^2+q
       369: q^2+q
       370: q^3+2q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2
       379: q^2+q
       382: q^2
       383: q^2+q
       386: q^2
       387: q^2+q
       392: q^2+q
       395: q^2+q
       398: q^2+q
       400: q^2
       402: q^2+q
       403: q^2
       408: q^2+q
       410: q^2+q
       412: q^2+q
       414: q^3+2q^2+q
       416: q^2+q
       418: q^3+2q^2+q
       419: q^2
       420: q^2+q
       421: q^2+q
       422: q^2
       424: 2q^2+q
       426: q^2+q
       428: 2q^2+q
       430: q^2+q
       431: q^2+q
       432: q^2
       434: q^2+q
       436: q^2+q
       438: q
       439: q
       440: q^2
       442: q
       444: q^2+q
       446: q^2+q
       447: q^2
       448: q^3+q^2+q
       449: q^2+q
       450: q^2
       452: q^3+2q^2+q
       453: q^2
       454: q^2+q
       456: q^3+2q^2+q
       457: q^2+q
       458: q^2
       460: 2q^2+q
       461: q^2+q
       462: q^2
       464: 2q^2+q
       466: q^3+2q^2+q
       468: 2q^3+2q^2+q
       470: q^3+2q^2+q
       472: q^2+q
       473: q^2+q
       474: q^2
       476: q^2+q
       478: q^2+q
       480: q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: q^2+q
       484: 2q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^2+q
       497: q^3+2q^2+q
       498: 2q^2+q
       499: 2q^2+q
       500: q^2+q
       501: 2q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+2q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q^2+q
       513: q^2+q
       514: q^3+2q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^3+q^2+q
       522: q^2
       523: q^2+q
       526: q^2
       527: q
       530: q^2
       531: q^2+q
       535: q^2+q
       540: q^2+q
       544: q
       548: q^2+q
       550: q^2+q
       551: q^2
       554: q^2+q
       556: q^2
       558: q^2+q
       560: q^2
       562: q^2+q
       564: q^2
       567: q^2+q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: 2q^2+q
       588: q^2+q
       589: q^2
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       596: q^2
       598: q^2+q
       600: q^2+q
       602: 2q^2+q
       604: q
       606: q^2+q
       607: q
       608: q^2
       610: q
       612: q
       614: q
       616: q^2+q
       618: q^2+q
       619: q^2
       620: q^2+q
       621: q^2+q
       622: q^2
       624: q^3+2q^2+q
       626: 2q^2+q
       628: q^2+q
       630: q^2+q
       631: q^2+q
       632: q^2
       634: 2q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+2q^2+q
       642: q^2+q
       643: q^2+q
       644: q^2
       646: q^2+q
       648: q
       649: q
       650: q^2
       652: q^2+q
       654: q
       656: q^2+q
       657: 2q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: q^2+q
       665: q^2+q
       674: q^2+q
       675: q
       676: q^2+q
       677: q
       679: q
       680: 2q^2+q
       681: 2q^2+q
       682: 2q^2+q
       683: q^2+q
       685: q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       700: q^2+q
       706: q^2
       707: q
       710: q^2
       711: q^2+q
       714: q
       719: q
       724: q^2+q
       728: q
       732: q
       736: q^2+q
       738: q^2+q
       740: q^2
       742: q^2+q
       744: q^2
       746: q
       748: q^2
       750: q^2+q
       752: q^2
       755: q^2+q
       760: q^2+q
       764: q
       767: q^2+q
       773: q^2+q
       776: 2q^2+q
       778: q^2+q
       780: q^2+q
       782: q^2+q
       786: q
       787: q
       792: q
       794: q^2+q
       796: q^2+q
       798: q
       800: q
       802: q
       806: q
       807: q
       808: q^2
       810: q
       812: q
       817: q^2+q
       818: q^2
       820: 2q^2+q
       822: 2q^2+q
       824: q^2+q
       825: q^2
       826: q^2+q
       827: q
       830: q
       831: q^2+q
       832: q^2
       834: q^2+q
       836: q^2+q
       842: q^2+q
       844: q^2+q
       846: q
       847: q
       848: q^2
       850: q^2+q
       852: q
       854: q
       856: q
       866: q^2+q
       870: q
       871: q
       874: q^2+q
       875: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       891: q^2+q
       897: q^2
       898: q
       901: q
       907: q
       910: q
       915: q
       919: q^2+q
       923: q
       931: q
       937: q
       939: q^2
       941: q^2+q
       943: q^2
       945: q^2+q
       947: q^2
       949: q
       954: q
       963: q^2+q
       966: q^2+q
       972: q^2+q
       977: q
       981: q
       995: q^2+q
       998: q
      1001: q
      1011: q
      1013: q
      1019: q
      1021: q
      1023: q
      1027: q
      1035: q^2+q
      1037: q^2+q
      1039: q^2+q
      1041: q
      1044: q
      1049: q
      1051: q
      1053: q
      1057: q
      1058: q
      1059: q^2
      1061: q
      1063: q
      1065: q
      1076: q
      1080: q^2+q
      1083: q
      1084: q
      1093: q^2+q
      1115: q
      1125: q
      1129: q
      1132: q
      1142: q
      1151: q
      1159: q
      1169: q
      1171: q^2
      1173: q
      1179: q
      1182: q
      1187: q
      1201: q
      1209: q
      1223: 1
      1231: q
      1235: q
      1249: q^2+q
      1250: q
      1255: q
      1265: q
      1267: q
      1269: q
      1275: q
      1279: q
      1281: q
      1287: q
      1297: q
      1325: 1
      1339: 1
      1359: q
      1381: q
      1391: q
      1395: q
      1398: q
      1417: q
      1425: q
      1434: q
      1447: 1
      1465: q
      1469: q
      1481: 1
      1500: 1
      1520: q
      1558: 1
      1562: 1
      1594: 1
      1618: q
      1636: 1
      1638: 1
      1672: 1
      1686: 1
      1710: 1
      1728: 1
      1732: 1
      1780: 1
      1806: 1
      1824: 1
      1845: 1
      1869: 1
      1913: 1
      1931: 1
      1989: 1

1990:    0: 4q^3+8q^2+2q+1
         1: 4q^3+8q^2+2q+1
         2: 4q^3+8q^2+2q+1
         3: 4q^3+8q^2+2q+1
         4: q^4+5q^3+6q^2+2q+1
         5: 4q^3+8q^2+2q+1
         6: q^4+5q^3+6q^2+2q+1
         7: q^4+5q^3+6q^2+2q+1
         8: 4q^3+8q^2+2q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 4q^3+8q^2+2q+1
        11: 4q^3+8q^2+2q+1
        12: q^4+5q^3+6q^2+2q+1
        13: 4q^3+8q^2+2q+1
        14: q^4+5q^3+6q^2+2q+1
        15: 4q^3+8q^2+2q+1
        16: q^3+8q^2+2q+1
        17: q^3+8q^2+2q+1
        18: q^4+4q^3+4q^2+2q+1
        19: 3q^3+6q^2+2q+1
        20: 3q^3+6q^2+2q+1
        21: 3q^3+6q^2+2q+1
        22: 4q^3+8q^2+2q+1
        23: 4q^3+8q^2+2q+1
        24: 4q^3+8q^2+2q+1
        25: 4q^3+8q^2+2q+1
        26: 4q^3+8q^2+2q+1
        27: 4q^3+8q^2+2q+1
        28: q^3+8q^2+2q+1
        29: 3q^3+6q^2+2q+1
        30: 3q^3+6q^2+2q+1
        31: 4q^3+8q^2+2q+1
        32: 4q^3+8q^2+2q+1
        33: q^3+8q^2+2q+1
        34: 4q^3+8q^2+2q+1
        35: 4q^3+8q^2+2q+1
        36: q^3+8q^2+2q+1
        37: 3q^3+6q^2+2q+1
        38: q^3+2q^2
        39: 3q^3+6q^2+2q+1
        40: q^3+2q^2
        41: 3q^3+6q^2+2q+1
        42: q^3+2q^2
        43: 4q^3+8q^2+2q+1
        44: q^4+5q^3+6q^2+2q+1
        45: 4q^3+8q^2+2q+1
        46: q^3+8q^2+2q+1
        47: q^3+8q^2+2q+1
        48: q^4+4q^3+4q^2+2q+1
        49: 6q^2+2q+1
        50: 6q^2+2q+1
        51: 2q^3+4q^2+2q+1
        52: 3q^3+6q^2+2q+1
        53: 3q^3+6q^2+2q+1
        54: 3q^3+6q^2+2q+1
        55: 3q^3+6q^2+2q+1
        56: 3q^3+6q^2+2q+1
        57: 3q^3+6q^2+2q+1
        58: q^3+5q^2+2q+1
        59: 3q^2
        60: q^3+5q^2+2q+1
        61: 3q^2
        62: 3q^3+6q^2+2q+1
        63: q^3+2q^2
        64: 3q^3+6q^2+2q+1
        65: q^3+2q^2
        66: q^3+6q^2+2q+1
        67: 2q^2
        68: q^3+8q^2+2q+1
        69: 4q^2+2q+1
        70: 3q^3+6q^2+2q+1
        71: 6q^2+2q+1
        72: 4q^2+2q+1
        73: 4q^2+2q+1
        74: 2q^3+4q^2+2q+1
        76: 2q^3+4q^2+2q+1
        78: 2q^3+4q^2+2q+1
        80: 4q^3+8q^2+2q+1
        81: q^3+8q^2+2q+1
        82: 3q^3+6q^2+2q+1
        83: 3q^3+6q^2+2q+1
        84: 4q^3+8q^2+2q+1
        85: q^3+8q^2+2q+1
        86: 3q^3+6q^2+2q+1
        87: 3q^3+6q^2+2q+1
        88: q^3+8q^2+2q+1
        89: q^3+8q^2+2q+1
        90: q^4+4q^3+4q^2+2q+1
        91: 6q^2+2q+1
        92: 6q^2+2q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+2q+1
        95: 6q^2+2q+1
        96: 2q^3+4q^2+2q+1
        97: 6q^2+2q+1
        98: 6q^2+2q+1
        99: 2q^3+4q^2+2q+1
       100: 3q^3+6q^2+2q+1
       101: 3q^3+6q^2+2q+1
       102: 3q^3+6q^2+2q+1
       103: q^3+4q^2+2q+1
       104: q^2
       105: q^2
       106: 2q^2
       107: 3q^2+2q+1
       108: q^2
       109: 3q^2+2q+1
       110: q^2
       111: 2q^2+2q+1
       113: 2q^3+4q^2+2q+1
       115: 2q^3+4q^2+2q+1
       117: q^3+5q^2+2q+1
       118: 3q^2
       119: q^3+5q^2+2q+1
       120: 3q^2
       121: 3q^3+6q^2+2q+1
       122: q^3+2q^2
       123: q^3+6q^2+2q+1
       124: 2q^2
       125: q^3+8q^2+2q+1
       126: 4q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: 6q^2+2q+1
       134: 4q^2+2q+1
       135: 4q^2+2q+1
       136: 4q^2+2q+1
       137: q^3+8q^2+2q+1
       138: 4q^2+2q+1
       139: 6q^2+2q+1
       140: 4q^2+2q+1
       141: 3q^3+6q^2+2q+1
       142: 4q^2+2q+1
       143: q^3+8q^2+2q+1
       144: 4q^2+2q+1
       145: 6q^2+2q+1
       146: 3q^3+6q^2+2q+1
       147: 4q^2+2q+1
       148: 4q^2+2q+1
       149: 3q^3+6q^2+2q+1
       150: 3q^3+6q^2+2q+1
       151: 2q^3+4q^2+2q+1
       153: 2q^3+4q^2+2q+1
       155: 2q^3+4q^2+2q+1
       157: 6q^2+2q+1
       158: 6q^2+2q+1
       159: 2q^3+4q^2+2q+1
       160: 6q^2+2q+1
       161: 6q^2+2q+1
       162: 2q^3+4q^2+2q+1
       163: 6q^2+2q+1
       164: 6q^2+2q+1
       165: 2q^3+4q^2+2q+1
       166: 6q^2+2q+1
       167: 6q^2+2q+1
       168: 2q^3+4q^2+2q+1
       169: 2q^2+2q+1
       173: q^3+4q^2+2q+1
       174: q^2
       175: q^2
       176: 2q^2
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       183: 3q^2+2q+1
       184: q^2
       185: 3q^2+2q+1
       186: q^2
       187: 2q^2+2q+1
       189: 2q^3+4q^2+2q+1
       191: q^3+5q^2+2q+1
       192: 3q^2
       193: 3q^2+2q+1
       194: q^2
       195: 3q^2+2q+1
       196: q^2
       197: 2q^2+2q+1
       199: q^3+5q^2+2q+1
       200: 3q^2
       201: 3q^2+2q+1
       202: q^2
       203: 3q^2+2q+1
       204: q^2
       205: 2q^2+2q+1
       207: q^3+6q^2+2q+1
       208: 2q^2
       209: 2q^3+4q^2+2q+1
       211: 2q^3+4q^2+2q+1
       213: 3q^2+2q+1
       215: 3q^2+2q+1
       217: q^3+2q^2+2q+1
       219: 4q^2+2q+1
       220: 6q^2+2q+1
       221: 4q^2+2q+1
       222: 4q^2+2q+1
       223: 2q^2+2q+1
       224: 4q^2+2q+1
       225: 2q^2+2q+1
       226: 4q^2+2q+1
       227: 6q^2+2q+1
       228: 4q^2+2q+1
       229: 4q^2+2q+1
       230: 4q^2+2q+1
       231: 4q^2+2q+1
       232: 6q^2+2q+1
       233: 4q^2+2q+1
       234: 4q^2+2q+1
       235: 4q^2+2q+1
       236: 4q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: 6q^2+2q+1
       244: 4q^2+2q+1
       245: 4q^2+2q+1
       246: 3q^3+6q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 6q^2+2q+1
       251: 6q^2+2q+1
       252: 2q^3+4q^2+2q+1
       253: 6q^2+2q+1
       254: 6q^2+2q+1
       255: 2q^3+4q^2+2q+1
       256: 6q^2+2q+1
       257: 6q^2+2q+1
       258: 2q^3+4q^2+2q+1
       259: q^2+2q+1
       263: 2q^2+2q+1
       267: 2q^2+2q+1
       271: 2q^2+2q+1
       275: q^3+4q^2+2q+1
       276: q^2
       277: q^2
       278: 2q^2
       279: 3q^2+2q+1
       281: 2q^2+2q+1
       283: q^2+2q+1
       285: q^2+2q+1
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: 2q+1
       293: 3q^2+2q+1
       294: q^2
       295: 3q^2+2q+1
       296: q^2
       297: 2q^2+2q+1
       299: 3q^2+2q+1
       300: q^2
       301: q^2+2q+1
       303: 3q^2+2q+1
       304: q^2
       305: 2q^2+2q+1
       307: 3q^2+2q+1
       308: q^2
       309: 3q^2+2q+1
       310: q^2
       311: q^2+2q+1
       313: 2q^2+2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: 3q^2+2q+1
       320: q^2
       321: 3q^2+2q+1
       322: q^2
       323: 2q^2+2q+1
       325: 2q^3+4q^2+2q+1
       327: 3q^2+2q+1
       329: 3q^2+2q+1
       331: q^3+2q^2+2q+1
       333: 4q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 4q^2+2q+1
       345: 6q^2+2q+1
       346: 4q^2+2q+1
       347: 4q^2+2q+1
       348: 2q^2+2q+1
       349: 4q^2+2q+1
       350: 2q^2+2q+1
       351: q^2+4q+1
       352: 4q^2+2q+1
       353: 6q^2+2q+1
       354: 4q^2+2q+1
       355: 4q^2+2q+1
       356: 2q^2+2q+1
       357: 4q^2+2q+1
       358: 2q^2+2q+1
       359: q^2+4q+1
       360: 3q^2+2q+1
       362: 3q^2+2q+1
       364: q^3+2q^2+2q+1
       366: 4q^2+2q+1
       367: 6q^2+2q+1
       368: 4q^2+2q+1
       369: 4q^2+2q+1
       370: 4q^2+2q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: q^3+2q^2+2q+1
       374: 6q^2+2q+1
       375: 6q^2+2q+1
       376: 2q^3+4q^2+2q+1
       377: 2q+1
       381: q^2+2q+1
       385: 2q^2+2q+1
       389: q^2+2q+1
       393: 2q^2+2q+1
       397: q^2+2q+1
       401: 2q^2+2q+1
       405: 2q^2+2q+1
       409: 3q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: 2q+1
       419: q^2+2q+1
       421: q^2+2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       429: q^2+2q+1
       431: q^2+2q+1
       433: 2q+1
       435: q^2+2q+1
       437: 3q^2+2q+1
       438: q^2
       439: 3q^2+2q+1
       440: q^2
       441: 2q^2+2q+1
       443: q^2+3q+1
       444: q
       445: q^2+4q+1
       447: q^2+2q+1
       449: q^2+2q+1
       451: 2q+1
       453: 3q^2+2q+1
       454: q^2
       455: q^2+2q+1
       457: 3q^2+2q+1
       458: q^2
       459: 2q^2+2q+1
       461: q^2+3q+1
       462: q
       463: q^2+4q+1
       465: 3q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       471: 3q^2+2q+1
       472: q^2
       473: 3q^2+2q+1
       474: q^2
       475: 2q^2+2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: 2q^2+2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: q^2+4q+1
       485: q^2+4q+1
       487: q^2+4q+1
       489: q^3+2q^2+2q+1
       491: 2q+1
       492: 4q^2+2q+1
       493: 2q^2+2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: q^2+4q+1
       497: 4q^2+2q+1
       498: 2q^2+2q+1
       499: 2q^2+2q+1
       500: 2q+1
       501: q^2+4q+1
       502: 3q^2+2q+1
       504: 3q^2+2q+1
       506: q^3+2q^2+2q+1
       508: 4q^2+2q+1
       509: 6q^2+2q+1
       510: 4q^2+2q+1
       511: 4q^2+2q+1
       512: 2q^2+2q+1
       513: 4q^2+2q+1
       514: 2q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       521: 2q+1
       525: q^2+2q+1
       529: 2q+1
       533: 2q+1
       537: q^2+2q+1
       541: 2q^2+2q+1
       545: q^2+3q+1
       547: q
       549: 2q+1
       553: q^2+2q+1
       557: 2q^2+2q+1
       561: q^2+3q+1
       563: q
       565: 2q^2+2q+1
       569: q^2+2q+1
       573: q^2+2q+1
       574: q
       576: q
       577: q^2+2q+1
       580: 2q
       583: 2q^2+2q+1
       585: 2q+1
       587: 2q+1
       589: q^2+2q+1
       591: q+1
       593: q+1
       595: q^2+2q+1
       597: 2q+1
       599: 2q+1
       601: q^2+4q+1
       603: q^2+2q+1
       605: 2q+1
       607: q^2+2q+1
       609: 2q+1
       611: q^2+2q+1
       613: 2q+1
       615: q^2+3q+1
       616: q
       617: q^2+4q+1
       619: q^2+2q+1
       621: q^2+2q+1
       623: 2q+1
       625: 2q+1
       627: q^2+2q+1
       629: 2q+1
       631: q^2+3q+1
       632: q
       633: q^2+4q+1
       635: 3q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       641: q^2+2q+1
       643: q^2+2q+1
       645: 2q+1
       647: 3q^2+2q+1
       648: q^2
       649: 3q^2+2q+1
       650: q^2
       651: q^2+2q+1
       653: 2q^2+2q+1
       655: q^2+2q+1
       656: 2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q+1
       666: q^2+4q+1
       668: q^2+4q+1
       670: q^3+2q^2+2q+1
       672: q^2+4q+1
       673: 2q+1
       674: 2q+1
       675: 2q^2+2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: q^2+4q+1
       679: 2q+1
       680: 2q+1
       681: 2q^2+2q+1
       682: 2q^2+2q+1
       683: 2q+1
       684: q^2+4q+1
       685: 2q+1
       686: 4q^2+2q+1
       687: 2q^2+2q+1
       688: 2q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q^2+2q+1
       696: q
       698: q
       705: 2q+1
       709: 2q+1
       713: q+1
       717: q+1
       721: 2q+1
       725: 2q+1
       729: q^2+2q+1
       733: q^2+3q+1
       735: q
       737: 2q+1
       741: 2q+1
       745: q^2+2q+1
       749: q^2+3q+1
       751: q
       753: 2q+1
       757: q^2+2q+1
       761: 2q^2+2q+1
       765: q^2+2q+1
       766: q
       767: q
       769: q^2+2q+1
       772: 2q
       775: q+1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       785: q+1
       787: q+1
       789: q^2+4q+1
       791: 1
       793: q+1
       795: 2q+1
       797: 2q+1
       799: 2q+1
       801: q^2+2q+1
       803: q+1
       805: q+1
       807: q^2+2q+1
       809: 2q+1
       811: 2q+1
       813: q^2+4q+1
       815: q^2+3q+1
       816: q
       817: q+1
       819: 2q+1
       821: 2q+1
       823: 2q+1
       825: q^2+2q+1
       827: q+1
       829: q+1
       831: q^2+2q+1
       833: 2q+1
       835: 2q+1
       837: q^2+4q+1
       839: q^2+3q+1
       840: q
       841: 2q^2+2q+1
       843: q+1
       844: q
       845: q^2+2q+1
       847: q^2+2q+1
       849: 2q+1
       851: 2q+1
       853: q^2+2q+1
       855: 2q+1
       857: q^2+2q+1
       858: 2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q+1
       869: 2q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 2q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 2q^2+2q+1
       878: 2q^2+2q+1
       879: 2q+1
       880: 2q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q^2+2q+1
       887: q
       888: q
       896: 2q+1
       900: q+1
       904: q+1
       908: 1
       912: 2q+1
       916: q+1
       920: 2q+1
       924: q+1
       928: q+1
       932: q^2+3q+1
       934: q
       936: 2q+1
       940: q+1
       944: 2q+1
       948: q+1
       952: q+1
       956: q^2+3q+1
       958: q
       960: 2q+1
       964: q+1
       968: q+1
       971: q
       974: 2q+1
       978: q^2+2q+1
       982: q^2+2q+1
       985: 2q
       988: q^2+2q+1
       989: q
       990: q
       992: q+1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 2q+1
      1004: q+1
      1006: q+1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1016: q+1
      1018: 2q+1
      1020: q+1
      1022: 2q+1
      1024: 2q+1
      1026: q+1
      1028: q+1
      1030: 2q+1
      1032: q+1
      1034: 2q+1
      1036: q+1
      1038: 2q+1
      1040: q+1
      1042: 2q+1
      1044: q+1
      1046: q+1
      1047: q
      1048: 2q+1
      1050: 2q+1
      1052: q^2+2q+1
      1054: q+1
      1056: q+1
      1058: q^2+2q+1
      1060: 2q+1
      1062: 2q+1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: q+1
      1085: 2q+1
      1086: q+1
      1098: q^2+2q+1
      1101: q
      1103: q
      1110: q+1
      1114: 1
      1118: q+1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: q+1
      1148: 2q+1
      1152: q+1
      1156: q+1
      1160: 1
      1164: q+1
      1168: 2q+1
      1172: q+1
      1176: q+1
      1180: 1
      1184: 2q+1
      1188: q+1
      1191: q
      1194: q+1
      1198: 2q+1
      1202: q+1
      1206: q+1
      1210: q+1
      1212: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2q+1
      1228: q+1
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 2q+1
      1240: q+1
      1242: q+1
      1244: 2q+1
      1246: q+1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 2q+1
      1258: q+1
      1260: q+1
      1262: q+1
      1263: q
      1264: 2q+1
      1266: 2q+1
      1268: q+1
      1270: q+1
      1272: 2q+1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q+1
      1290: 1
      1302: q+1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: q+1
      1344: q+1
      1348: 1
      1352: q+1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1372: q+1
      1376: q+1
      1380: 1
      1384: q+1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: q+1
      1407: q
      1410: q+1
      1414: 2q+1
      1418: q+1
      1422: q+1
      1426: 1
      1430: 1
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1450: 1
      1452: q+1
      1454: 1
      1456: 1
      1458: q+1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 2q+1
      1472: q+1
      1474: 1
      1476: q+1
      1478: q+1
      1480: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1489: 1
      1501: 1
      1513: 1
      1525: q+1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1603: q+1
      1607: 1
      1611: q+1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1631: 1
      1643: 1
      1645: 1
      1647: 1
      1651: 1
      1653: 1
      1655: 1
      1661: 1
      1663: 1
      1665: 1
      1667: q+1
      1669: 1
      1671: 1
      1674: 1
      1675: 1
      1687: 1
      1699: 1
      1711: 1
      1737: 1
      1745: 1
      1749: 1
      1753: 1
      1761: 1
      1765: 1
      1773: 1
      1777: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1801: 1
      1807: 1
      1827: 1
      1829: 1
      1831: 1
      1846: 1
      1858: 1
      1870: 1
      1932: 1
      1936: 1
      1940: 1
      1948: 1
      1990: 1

1991:    0: 6q^4+8q^3+4q^2+3q
         1: 6q^4+8q^3+4q^2+3q
         2: 6q^4+8q^3+4q^2+3q
         3: 6q^4+8q^3+4q^2+3q
         4: 2q^5+7q^4+6q^3+3q^2+3q
         5: 6q^4+8q^3+4q^2+3q
         6: 2q^5+7q^4+6q^3+3q^2+3q
         7: 2q^5+7q^4+6q^3+3q^2+3q
         8: 6q^4+8q^3+4q^2+3q
         9: 2q^6+3q^5+4q^4+4q^3+3q^2+2q
        10: 6q^4+8q^3+4q^2+3q
        11: 6q^4+8q^3+4q^2+3q
        12: 2q^5+7q^4+6q^3+3q^2+3q
        13: 6q^4+8q^3+4q^2+3q
        14: 2q^5+7q^4+6q^3+3q^2+3q
        15: 6q^4+8q^3+4q^2+3q
        16: q^4+8q^3+3q^2+3q
        17: q^4+8q^3+3q^2+3q
        18: q^5+4q^4+3q^3+3q^2+2q
        19: 4q^4+5q^3+3q^2+3q
        20: 4q^4+5q^3+3q^2+3q
        21: 4q^4+5q^3+3q^2+3q
        22: 6q^4+8q^3+4q^2+3q
        23: 6q^4+8q^3+4q^2+3q
        24: 6q^4+8q^3+4q^2+3q
        25: 6q^4+8q^3+4q^2+3q
        26: 6q^4+8q^3+4q^2+3q
        27: 6q^4+8q^3+4q^2+3q
        28: q^4+8q^3+3q^2+3q
        29: 4q^4+5q^3+3q^2+3q
        30: 4q^4+5q^3+3q^2+3q
        31: 6q^4+8q^3+4q^2+3q
        32: 6q^4+8q^3+4q^2+3q
        33: q^4+8q^3+3q^2+3q
        34: 6q^4+8q^3+4q^2+3q
        35: 6q^4+8q^3+4q^2+3q
        36: q^4+8q^3+3q^2+3q
        37: 3q^4+4q^3+q^2+q
        38: 3q^4+4q^3+3q^2+2q
        39: 3q^4+4q^3+q^2+q
        40: 3q^4+4q^3+3q^2+2q
        41: 3q^4+4q^3+q^2+q
        42: 3q^4+4q^3+3q^2+2q
        43: 6q^4+8q^3+4q^2+3q
        44: 2q^5+7q^4+6q^3+3q^2+3q
        45: 6q^4+8q^3+4q^2+3q
        46: q^4+8q^3+3q^2+3q
        47: q^4+8q^3+3q^2+3q
        48: q^5+4q^4+3q^3+3q^2+2q
        49: 5q^3+2q^2+3q
        50: 5q^3+2q^2+3q
        51: 2q^4+2q^3+3q^2+2q
        52: 4q^4+5q^3+3q^2+3q
        53: 4q^4+5q^3+3q^2+3q
        54: 4q^4+5q^3+3q^2+3q
        55: 4q^4+5q^3+3q^2+3q
        56: 4q^4+5q^3+3q^2+3q
        57: 4q^4+5q^3+3q^2+3q
        58: q^4+4q^3+2q^2+2q
        59: 4q^3+q^2+q
        60: q^4+4q^3+2q^2+2q
        61: 4q^3+q^2+q
        62: 3q^4+4q^3+q^2+q
        63: 3q^4+4q^3+3q^2+2q
        64: 3q^4+4q^3+q^2+q
        65: 3q^4+4q^3+3q^2+2q
        66: q^4+4q^3+q^2+q
        67: 4q^3+2q^2+2q
        68: q^4+8q^3+3q^2+3q
        69: 2q^3+2q^2+2q
        70: 4q^4+5q^3+3q^2+3q
        71: 5q^3+2q^2+3q
        72: 3q^3+q^2+3q
        73: 3q^3+q^2+3q
        74: q^4+q^3+q
        75: q^4+q^3+2q^2+2q
        76: q^4+q^3+q
        77: q^4+q^3+2q^2+2q
        78: q^4+q^3+q
        79: q^4+q^3+2q^2+2q
        80: 6q^4+8q^3+4q^2+3q
        81: q^4+8q^3+3q^2+3q
        82: 4q^4+5q^3+3q^2+3q
        83: 4q^4+5q^3+3q^2+3q
        84: 6q^4+8q^3+4q^2+3q
        85: q^4+8q^3+3q^2+3q
        86: 4q^4+5q^3+3q^2+3q
        87: 4q^4+5q^3+3q^2+3q
        88: q^4+8q^3+3q^2+3q
        89: q^4+8q^3+3q^2+3q
        90: q^5+4q^4+3q^3+3q^2+2q
        91: 5q^3+2q^2+3q
        92: 5q^3+2q^2+3q
        93: 2q^4+2q^3+3q^2+2q
        94: 5q^3+2q^2+3q
        95: 5q^3+2q^2+3q
        96: 2q^4+2q^3+3q^2+2q
        97: 5q^3+2q^2+3q
        98: 5q^3+2q^2+3q
        99: 2q^4+2q^3+3q^2+2q
       100: 4q^4+5q^3+3q^2+3q
       101: 4q^4+5q^3+3q^2+3q
       102: 4q^4+5q^3+3q^2+3q
       103: q^4+2q^3+q^2+q
       104: 2q^3+q^2+q
       105: 2q^3+q^2+q
       106: 2q^3
       107: 2q^3+q^2+2q
       108: q^3+q
       109: 2q^3+q^2+2q
       110: q^3+q
       111: q^3+q
       112: 2q
       113: q^4+q^3+q
       114: q^4+q^3+2q^2+2q
       115: q^4+q^3+q
       116: q^4+q^3+2q^2+2q
       117: q^4+4q^3+2q^2+2q
       118: 4q^3+q^2+q
       119: q^4+4q^3+2q^2+2q
       120: 4q^3+q^2+q
       121: 3q^4+4q^3+q^2+q
       122: 3q^4+4q^3+3q^2+2q
       123: q^4+4q^3+q^2+q
       124: 4q^3+2q^2+2q
       125: q^4+8q^3+3q^2+3q
       126: 2q^3+2q^2+2q
       128: q^3+q^2+2q
       130: q^3+q^2+2q
       132: 2q^2+q
       133: 5q^3+2q^2+3q
       134: 2q^3+2q^2+2q
       135: 3q^3+q^2+3q
       136: 3q^3+q^2+3q
       137: q^4+8q^3+3q^2+3q
       138: 2q^3+2q^2+2q
       139: 5q^3+2q^2+3q
       140: 3q^3+q^2+3q
       141: 4q^4+5q^3+3q^2+3q
       142: 3q^3+q^2+3q
       143: q^4+8q^3+3q^2+3q
       144: 2q^3+2q^2+2q
       145: 5q^3+2q^2+3q
       146: 4q^4+5q^3+3q^2+3q
       147: 3q^3+q^2+3q
       148: 3q^3+q^2+3q
       149: 4q^4+5q^3+3q^2+3q
       150: 4q^4+5q^3+3q^2+3q
       151: q^4+q^3+q
       152: q^4+q^3+2q^2+2q
       153: q^4+q^3+q
       154: q^4+q^3+2q^2+2q
       155: q^4+q^3+q
       156: q^4+q^3+2q^2+2q
       157: 5q^3+2q^2+3q
       158: 5q^3+2q^2+3q
       159: 2q^4+2q^3+3q^2+2q
       160: 5q^3+2q^2+3q
       161: 5q^3+2q^2+3q
       162: 2q^4+2q^3+3q^2+2q
       163: 5q^3+2q^2+3q
       164: 5q^3+2q^2+3q
       165: 2q^4+2q^3+3q^2+2q
       166: 5q^3+2q^2+3q
       167: 5q^3+2q^2+3q
       168: 2q^4+2q^3+3q^2+2q
       169: q^3+q
       170: q
       171: q
       173: q^4+2q^3+q^2+q
       174: 2q^3+q^2+q
       175: 2q^3+q^2+q
       176: 2q^3
       178: q^2+q
       180: q^3+q^2+2q
       182: 2q
       183: 2q^3+q^2+2q
       184: q^3+q
       185: 2q^3+q^2+2q
       186: q^3+q
       187: q^3+q
       188: 2q
       189: q^4+q^3+q
       190: q^4+q^3+2q^2+2q
       191: q^4+4q^3+2q^2+2q
       192: 4q^3+q^2+q
       193: 2q^3+q^2+2q
       194: q^3+q
       195: 2q^3+q^2+2q
       196: q^3+q
       197: q^3+q
       198: 2q
       199: q^4+4q^3+2q^2+2q
       200: 4q^3+q^2+q
       201: 2q^3+q^2+2q
       202: q^3+q
       203: 2q^3+q^2+2q
       204: q^3+q
       205: q^3+q
       206: 2q
       207: q^4+4q^3+q^2+q
       208: 4q^3+2q^2+2q
       209: q^4+q^3+q
       210: q^4+q^3+2q^2+2q
       211: q^4+q^3+q
       212: q^4+q^3+2q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 2q^3+2q^2+2q
       220: 5q^3+2q^2+3q
       221: 2q^3+2q^2+2q
       222: 3q^3+q^2+3q
       223: q^3+q^2+2q
       224: 3q^3+q^2+3q
       225: q^3+q^2+2q
       226: 2q^3+2q^2+2q
       227: 5q^3+2q^2+3q
       228: 2q^3+2q^2+2q
       229: 3q^3+q^2+3q
       230: 3q^3+q^2+3q
       231: 2q^3+2q^2+2q
       232: 5q^3+2q^2+3q
       233: 2q^3+2q^2+2q
       234: 3q^3+q^2+3q
       235: 3q^3+q^2+3q
       236: 2q^3+2q^2+2q
       238: q^3+q^2+2q
       240: q^3+q^2+2q
       242: 2q^2+q
       243: 5q^3+2q^2+3q
       244: 3q^3+q^2+3q
       245: 3q^3+q^2+3q
       246: 4q^4+5q^3+3q^2+3q
       247: q^2+4q
       248: q^2+4q
       249: q^4+2q^2+2q
       250: 5q^3+2q^2+3q
       251: 5q^3+2q^2+3q
       252: 2q^4+2q^3+3q^2+2q
       253: 5q^3+2q^2+3q
       254: 5q^3+2q^2+3q
       255: 2q^4+2q^3+3q^2+2q
       256: 5q^3+2q^2+3q
       257: 5q^3+2q^2+3q
       258: 2q^4+2q^3+3q^2+2q
       260: q
       261: q
       263: q^3+q
       264: q
       265: q
       267: q^3+q
       268: q
       270: q
       271: q^3+q
       272: q
       274: q
       275: q^4+2q^3+q^2+q
       276: 2q^3+q^2+q
       277: 2q^3+q^2+q
       278: 2q^3
       280: q^3+q^2+2q
       282: q^2+q
       283: q^2+q
       285: q^2+q
       288: q^2+q
       290: 2q
       292: q
       293: 2q^3+q^2+2q
       294: q^3+q
       295: 2q^3+q^2+2q
       296: q^3+q
       297: q^3+q
       298: 2q
       299: 2q^3+q^2+2q
       300: q^3+q
       302: 2q
       303: 2q^3+q^2+2q
       304: q^3+q
       305: q^3+q
       306: 2q
       307: 2q^3+q^2+2q
       308: q^3+q
       309: 2q^3+q^2+2q
       310: q^3+q
       312: 2q
       313: q^3+q
       314: 2q
       316: q^2+q
       318: q^3+q^2+2q
       319: 2q^3+q^2+2q
       320: q^3+q
       321: 2q^3+q^2+2q
       322: q^3+q
       323: q^3+q
       324: 2q
       325: q^4+q^3+q
       326: q^4+q^3+2q^2+2q
       328: q^3+q^2+2q
       330: q^3+q^2+2q
       332: 2q^2+q
       333: 2q^3+2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: 2q
       337: q^2+4q
       339: q^2+3q
       341: q^2+3q
       343: 2q^2+q
       344: 2q^3+2q^2+2q
       345: 5q^3+2q^2+3q
       346: 2q^3+2q^2+2q
       347: 3q^3+q^2+3q
       348: q^3+q^2+2q
       349: 3q^3+q^2+3q
       350: q^3+q^2+2q
       351: q^2+4q
       352: 2q^3+2q^2+2q
       353: 5q^3+2q^2+3q
       354: 2q^3+2q^2+2q
       355: 3q^3+q^2+3q
       356: q^3+q^2+2q
       357: 3q^3+q^2+3q
       358: q^3+q^2+2q
       359: q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 2q^3+2q^2+2q
       367: 5q^3+2q^2+3q
       368: 2q^3+2q^2+2q
       369: 3q^3+q^2+3q
       370: 3q^3+q^2+3q
       371: q^2+4q
       372: q^2+4q
       373: q^4+2q^2+2q
       374: 5q^3+2q^2+3q
       375: 5q^3+2q^2+3q
       376: 2q^4+2q^3+3q^2+2q
       382: q
       383: q
       385: q^3+q
       386: q
       387: q
       390: q
       392: q
       393: q^3+q
       394: q
       395: q
       398: q
       400: q
       401: q^3+q
       402: q
       403: q
       405: q^3+q
       407: q
       408: q
       410: q^3+q^2+2q
       412: q^2+q
       414: q^2+q
       416: 2q
       418: q
       419: q^2+q
       421: q^2+q
       424: q
       426: q
       428: q^2+3q
       429: q^2+q
       431: q^2+q
       434: q
       436: 2q
       437: 2q^3+q^2+2q
       438: q^3+q
       439: 2q^3+q^2+2q
       440: q^3+q
       441: q^3+q
       442: 2q
       443: q^2+3q
       444: q
       446: q^2+3q
       447: q^2+q
       449: q^2+q
       452: q
       453: 2q^3+q^2+2q
       454: q^3+q
       456: 2q
       457: 2q^3+q^2+2q
       458: q^3+q
       459: q^3+q
       460: 2q
       461: q^2+3q
       462: q
       464: q^2+3q
       466: q^3+q^2+2q
       468: q^2+q
       470: q^2+q
       471: 2q^3+q^2+2q
       472: q^3+q
       473: 2q^3+q^2+2q
       474: q^3+q
       475: q^3+q
       476: 2q
       478: 2q
       479: q^2+2q
       480: 2q
       481: q^3+q^2+2q
       482: q^3+q^2+2q
       483: 2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: 2q
       492: 2q^3+2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: 2q
       496: q^2+4q
       497: 2q^3+2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: 2q
       501: q^2+4q
       503: q^3+q^2+2q
       505: q^3+q^2+2q
       507: 2q^2+q
       508: 2q^3+2q^2+2q
       509: 5q^3+2q^2+3q
       510: 2q^3+2q^2+2q
       511: 3q^3+q^2+3q
       512: q^3+q^2+2q
       513: 3q^3+q^2+3q
       514: q^3+q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q
       519: q^2+4q
       520: q^4+2q^2+2q
       526: q
       527: q
       538: q
       540: q
       541: q^3+q
       542: q
       544: q
       546: q^2+2q
       548: q
       554: q
       556: q
       557: q^3+q
       558: q
       560: q
       562: q^2+2q
       564: q
       565: q^3+q
       566: q
       567: q
       571: q
       572: q
       573: q^2+2q
       574: q
       576: q
       578: q^2+q
       581: 2q
       584: q^2+q
       586: q
       588: q
       589: q^2+q
       591: q
       593: q
       595: q^2+q
       598: q
       600: q
       602: q^2+3q
       603: q^2+q
       606: q
       607: q^2+q
       610: q
       612: 2q
       614: q
       615: q^2+3q
       616: q
       618: q^2+3q
       619: q^2+q
       621: q^2+q
       624: q
       626: q
       628: 2q
       630: q
       631: q^2+3q
       632: q
       634: q^2+3q
       636: q^3+q^2+2q
       638: q^2+q
       640: q^2+q
       641: q^2+q
       643: q^2+q
       646: q
       647: 2q^3+q^2+2q
       648: q^3+q
       649: 2q^3+q^2+2q
       650: q^3+q
       652: 2q
       653: q^3+q
       654: 2q
       655: q^2+2q
       656: 2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       667: q^2+3q
       669: q^2+3q
       671: 2q^2+q
       672: q^2+4q
       673: 2q
       674: 2q+1
       675: q^3+q^2+2q
       676: q^3+q^2+2q
       677: 2q
       678: q^2+4q
       679: 2q
       680: 2q+1
       681: q^3+q^2+2q
       682: q^3+q^2+2q
       683: 2q
       684: q^2+4q
       685: 2q
       686: 2q^3+2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: 2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q^2+q
       699: q
       700: q
       730: q
       732: q
       734: q^2+2q
       736: q
       746: q
       748: q
       750: q^2+2q
       752: q
       759: q
       760: q
       761: q^3+q
       763: q
       764: q
       765: q^2+2q
       766: q
       767: q
       770: q^2+q
       773: 2q
       776: q+1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: q^2+3q
       793: q+1
       796: 2q+1
       798: q
       800: q
       801: q^2+q
       803: q
       805: q
       807: q^2+q
       810: q
       812: q
       814: q^2+3q
       815: q^2+3q
       816: q
       817: q+1
       820: 2q+1
       822: q
       824: q
       825: q^2+q
       827: q
       829: q
       831: q^2+q
       834: q
       836: q
       838: q^2+3q
       839: q^2+3q
       840: q
       842: q^2+q
       843: q+1
       844: q
       845: q^2+q
       847: q^2+q
       850: q
       852: q
       854: 2q
       856: q
       857: q^2+2q
       858: 2q
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: 2q
       873: 2q+1
       874: q+1
       875: 2q
       876: 2q
       877: q^3+q^2+2q
       878: q^3+q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       885: q^2+q
       890: q
       891: q
       917: q+1
       933: q^2+2q
       935: q
       941: q+1
       957: q^2+2q
       959: q
       964: q+1
       969: q+1
       972: q
       980: q
       981: q
       983: q^2+q
       986: 2q
       988: q^2+2q
       989: q
       990: q
       993: q+1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1012: 1
      1015: 2q+1
      1016: q+1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: 2q+1
      1032: q+1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: q+1
      1047: q
      1049: q
      1051: q
      1052: q^2+q
      1054: q
      1056: q
      1058: q^2+q
      1061: q
      1063: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1087: q+1
      1099: q^2+q
      1104: q
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1145: q+1
      1165: q+1
      1189: q+1
      1192: q
      1194: q+1
      1211: q+1
      1213: q+1
      1215: 1
      1216: 1
      1218: 1
      1224: 1
      1227: 2q+1
      1228: q+1
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1245: 2q+1
      1246: q+1
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1262: q+1
      1263: q
      1265: q
      1267: q
      1268: q
      1270: q
      1273: q
      1275: q+1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1291: 1
      1303: q+1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1341: q+1
      1349: 1
      1357: 1
      1364: 1
      1373: q+1
      1381: 1
      1389: 1
      1396: 1
      1405: q+1
      1408: q
      1410: q+1
      1431: 1
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1449: 1
      1450: 1
      1453: q+1
      1454: 1
      1457: 1
      1459: q+1
      1460: 1
      1462: 1
      1465: 1
      1466: 1
      1468: 1
      1471: q
      1473: q+1
      1476: q
      1478: q
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1490: 1
      1502: 1
      1514: 1
      1526: q+1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1564: 1
      1568: 1
      1575: 1
      1584: 1
      1588: 1
      1595: 1
      1608: 1
      1616: 1
      1623: 1
      1632: 1
      1644: 1
      1645: 1
      1647: 1
      1652: 1
      1653: 1
      1655: 1
      1662: 1
      1663: 1
      1665: 1
      1668: q+1
      1669: 1
      1674: 1
      1676: 1
      1688: 1
      1700: 1
      1712: 1
      1738: 1
      1746: 1
      1749: 1
      1762: 1
      1766: 1
      1773: 1
      1786: 1
      1790: 1
      1797: 1
      1802: 1
      1828: 1
      1829: 1
      1831: 1
      1847: 1
      1859: 1
      1871: 1
      1933: 1
      1937: 1
      1940: 1
      1991: 1

1992:    0: q^5+2q^4+q
         1: q^6+q^5+2q^4+q
         2: q^5+2q^4+q
         3: q^6+q^5+2q^4+q
         4: q^5+2q^4+q
         5: q^5+2q^4+q
         6: q^4+q
         7: q^5+2q^4+q
         8: q^5+2q^4+q
         9: q^6+2q^5+2q^4+q
        10: q^5+q^4+q
        11: q^5+q^4+q
        12: q^4+q
        13: q^5+2q^4+q
        14: q^5+2q^4+q
        15: q^5+2q^4+q
        16: q^5+q^4+q
        17: q^5+q^4+q
        18: q^5+2q^4+q
        19: 2q^4+q
        20: q^4+q
        21: 2q^4+q
        22: q^5+2q^4+q
        23: q^6+q^5+2q^4+q
        24: q^5+2q^4+q
        25: q^5+2q^4+q
        26: q^6+q^5+2q^4+q
        27: q^5+2q^4+q
        28: q^5+q
        29: q^4+q
        30: 2q^4+q
        31: q^5+q^4+q
        32: q^5+2q^4+q
        33: q^5+q^4+q
        34: q^5+q^4+q
        35: q^5+2q^4+q
        36: q^5+q^4+q
        37: q^5+2q^4+q
        39: q^6+q^5+2q^4+q
        41: q^5+2q^4+q
        43: q^5+q^4+q
        44: q^4+q
        45: q^5+q^4+q
        46: q^5+q^4+q
        47: q^5+q^4+q
        48: q^5+2q^4+q
        49: q^4+q
        50: q
        51: 2q^4+q
        52: 2q^4+q
        53: q^4+q
        54: 2q^4+q
        55: 2q^4+q
        56: q^4+q
        57: 2q^4+q
        58: q^5+q
        60: q^5+q
        62: q^5+q^4+q
        64: q^5+2q^4+q
        66: q^5+q^4+q
        68: q^5+q
        69: q^4+q
        70: q^4+q
        71: q
        72: q
        73: q
        74: 2q^4+q
        76: q^4+q
        78: 2q^4+q
        80: q^5+q^4+q
        81: q^5+q^4+q
        82: q^4+q
        83: 2q^4+q
        84: q^5+q^4+q
        85: q^5+q^4+q
        86: q^4+q
        87: 2q^4+q
        88: q
        89: q
        90: q^4+q
        91: q^4+q
        92: q
        93: 2q^4+q
        94: q^4+q
        95: q
        96: 2q^4+q
        97: q^4+q
        98: q
        99: 2q^4+q
       100: 2q^4+q
       101: q^4+q
       102: 2q^4+q
       103: q^5+q
       107: q
       109: q
       111: q
       113: q^4+q
       115: 2q^4+q
       117: q^5+q
       119: q^5+q
       121: q^5+q^4+q
       123: q^5+q^4+q
       125: q
       126: q
       127: q^4+q
       129: q
       131: 2q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q^4+q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q^4+q
       147: q
       148: q
       149: q^4+q
       150: 2q^4+q
       151: 2q^4+q
       153: q^4+q
       155: 2q^4+q
       157: q
       158: q
       159: q^4+q
       160: q^4+q
       161: q
       162: 2q^4+q
       163: q^4+q
       164: q
       165: 2q^4+q
       166: q^4+q
       167: q
       168: 2q^4+q
       169: q
       173: q^5+q
       177: q^4+q
       179: q
       181: q
       183: q
       185: q
       187: q
       189: q^4+q
       191: q
       193: q
       195: q
       197: q
       199: q
       201: q
       203: q
       205: q
       207: q
       209: q^4+q
       211: 2q^4+q
       213: q^4+q
       215: q
       217: 2q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       237: q^4+q
       239: q
       241: 2q^4+q
       243: q
       244: q
       245: q
       246: q^4+q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q^4+q
       253: q
       254: q
       255: q^4+q
       256: q^4+q
       257: q
       258: 2q^4+q
       259: q
       263: q
       267: q
       271: q
       275: q
       279: q
       281: q^4+q
       283: q
       285: q
       287: q
       289: q
       291: q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q^4+q
       317: q
       319: q
       321: q
       323: q
       325: q^4+q
       327: q
       329: q
       331: q^4+q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^4+q
       362: q
       364: 2q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q^4+q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q
       413: q
       415: q
       417: q
       419: q
       421: q
       423: q
       425: q
       427: q
       429: q
       431: q
       433: q
       435: q
       437: q
       439: q
       441: q
       443: q
       445: q
       447: q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       461: q
       463: q
       465: q
       467: q^4+q
       469: q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       502: q
       504: q
       506: q^4+q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       521: q
       525: q
       529: q
       533: q
       537: q
       541: q
       545: q
       549: q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       583: q
       585: q
       587: q
       589: q
       591: q
       593: q
       595: q
       597: q
       599: q
       601: q
       603: q
       605: q
       607: q
       609: q
       611: q
       613: q
       615: q
       617: q
       619: q
       621: q
       623: q
       625: q
       627: q
       629: q
       631: q
       633: q
       635: q
       637: q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       655: q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       693: q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q
       729: q
       733: q
       737: q
       741: q
       745: q
       749: q
       753: q
       757: q
       761: q
       765: q
       769: q
       777: q
       781: q
       785: q
       787: q
       791: q
       797: q
       799: q
       801: q
       803: q
       805: q
       807: q
       809: q
       811: q
       821: q
       823: q
       825: q
       827: q
       829: q
       831: q
       833: q
       835: q
       841: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       884: q
       896: q
       900: q
       904: q
       908: q
       912: q
       920: q
       924: q
       928: q
       936: q
       944: q
       948: q
       952: q
       960: q
       974: q
       978: q
      1010: q
      1018: q
      1022: q
      1026: q
      1028: q
      1034: q
      1038: q
      1040: q
      1044: q
      1048: q
      1050: q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q
      1083: q
      1126: q
      1148: q
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: q
      1198: q
      1202: q
      1206: q
      1222: 1
      1264: q
      1266: q
      1268: q
      1270: q
      1278: q
      1322: 1
      1336: 1
      1360: q
      1392: q
      1414: q
      1418: q
      1422: q
      1426: q
      1446: 1
      1480: 1
      1491: 1
      1555: 1
      1559: 1
      1571: 1
      1591: 1
      1619: q
      1633: 1
      1671: 1
      1677: 1
      1689: 1
      1701: 1
      1753: 1
      1777: 1
      1793: 1
      1803: 1
      1848: 1
      1860: 1
      1872: 1
      1948: 1
      1992: 1

1993:    0: 6q^4+8q^3+4q^2+3q
         1: 6q^4+8q^3+4q^2+3q
         2: 6q^4+8q^3+4q^2+3q
         3: 6q^4+8q^3+4q^2+3q
         4: 2q^5+7q^4+6q^3+3q^2+3q
         5: 6q^4+8q^3+4q^2+3q
         6: 2q^5+7q^4+6q^3+3q^2+3q
         7: 2q^5+7q^4+6q^3+3q^2+3q
         8: 6q^4+8q^3+4q^2+3q
         9: 2q^6+3q^5+4q^4+4q^3+3q^2+2q
        10: 6q^4+8q^3+4q^2+3q
        11: 6q^4+8q^3+4q^2+3q
        12: 2q^5+7q^4+6q^3+3q^2+3q
        13: 6q^4+8q^3+4q^2+3q
        14: 2q^5+7q^4+6q^3+3q^2+3q
        15: 6q^4+8q^3+4q^2+3q
        16: q^4+8q^3+3q^2+3q
        17: q^4+8q^3+3q^2+3q
        18: q^5+4q^4+3q^3+3q^2+2q
        19: 4q^4+5q^3+3q^2+3q
        20: 4q^4+5q^3+3q^2+3q
        21: 4q^4+5q^3+3q^2+3q
        22: 6q^4+8q^3+4q^2+3q
        23: 6q^4+8q^3+4q^2+3q
        24: 6q^4+8q^3+4q^2+3q
        25: 6q^4+8q^3+4q^2+3q
        26: 6q^4+8q^3+4q^2+3q
        27: 6q^4+8q^3+4q^2+3q
        28: q^4+8q^3+3q^2+3q
        29: 4q^4+5q^3+3q^2+3q
        30: 4q^4+5q^3+3q^2+3q
        31: 6q^4+8q^3+4q^2+3q
        32: 6q^4+8q^3+4q^2+3q
        33: q^4+8q^3+3q^2+3q
        34: 6q^4+8q^3+4q^2+3q
        35: 6q^4+8q^3+4q^2+3q
        36: q^4+8q^3+3q^2+3q
        37: 3q^4+4q^3+3q^2+2q
        38: 3q^4+4q^3+q^2+q
        39: 3q^4+4q^3+3q^2+2q
        40: 3q^4+4q^3+q^2+q
        41: 3q^4+4q^3+3q^2+2q
        42: 3q^4+4q^3+q^2+q
        43: 6q^4+8q^3+4q^2+3q
        44: 2q^5+7q^4+6q^3+3q^2+3q
        45: 6q^4+8q^3+4q^2+3q
        46: q^4+8q^3+3q^2+3q
        47: q^4+8q^3+3q^2+3q
        48: q^5+4q^4+3q^3+3q^2+2q
        49: 5q^3+2q^2+3q
        50: 5q^3+2q^2+3q
        51: 2q^4+2q^3+3q^2+2q
        52: 4q^4+5q^3+3q^2+3q
        53: 4q^4+5q^3+3q^2+3q
        54: 4q^4+5q^3+3q^2+3q
        55: 4q^4+5q^3+3q^2+3q
        56: 4q^4+5q^3+3q^2+3q
        57: 4q^4+5q^3+3q^2+3q
        58: 4q^3+q^2+q
        59: q^4+4q^3+2q^2+2q
        60: q^4+4q^3+2q^2+2q
        61: 4q^3+q^2+q
        62: 3q^4+4q^3+3q^2+2q
        63: 3q^4+4q^3+q^2+q
        64: 3q^4+4q^3+3q^2+2q
        65: 3q^4+4q^3+q^2+q
        66: 4q^3+2q^2+2q
        67: q^4+4q^3+q^2+q
        68: q^4+8q^3+3q^2+3q
        69: 2q^3+2q^2+2q
        70: 4q^4+5q^3+3q^2+3q
        71: 5q^3+2q^2+3q
        72: 3q^3+q^2+3q
        73: 3q^3+q^2+3q
        74: q^4+q^3+2q^2+2q
        75: q^4+q^3+q
        76: q^4+q^3+2q^2+2q
        77: q^4+q^3+q
        78: q^4+q^3+2q^2+2q
        79: q^4+q^3+q
        80: 6q^4+8q^3+4q^2+3q
        81: q^4+8q^3+3q^2+3q
        82: 4q^4+5q^3+3q^2+3q
        83: 4q^4+5q^3+3q^2+3q
        84: 6q^4+8q^3+4q^2+3q
        85: q^4+8q^3+3q^2+3q
        86: 4q^4+5q^3+3q^2+3q
        87: 4q^4+5q^3+3q^2+3q
        88: q^4+8q^3+3q^2+3q
        89: q^4+8q^3+3q^2+3q
        90: q^5+4q^4+3q^3+3q^2+2q
        91: 5q^3+2q^2+3q
        92: 5q^3+2q^2+3q
        93: 2q^4+2q^3+3q^2+2q
        94: 5q^3+2q^2+3q
        95: 5q^3+2q^2+3q
        96: 2q^4+2q^3+3q^2+2q
        97: 5q^3+2q^2+3q
        98: 5q^3+2q^2+3q
        99: 2q^4+2q^3+3q^2+2q
       100: 4q^4+5q^3+3q^2+3q
       101: 4q^4+5q^3+3q^2+3q
       102: 4q^4+5q^3+3q^2+3q
       103: 2q^3+q^2+q
       104: q^4+2q^3+q^2+q
       105: 2q^3
       106: 2q^3+q^2+q
       107: 2q^3+q^2+2q
       108: q^3+q
       109: q^3+q
       110: 2q^3+q^2+2q
       111: 2q
       112: q^3+q
       113: q^4+q^3+2q^2+2q
       114: q^4+q^3+q
       115: q^4+q^3+2q^2+2q
       116: q^4+q^3+q
       117: 4q^3+q^2+q
       118: q^4+4q^3+2q^2+2q
       119: q^4+4q^3+2q^2+2q
       120: 4q^3+q^2+q
       121: 3q^4+4q^3+3q^2+2q
       122: 3q^4+4q^3+q^2+q
       123: 4q^3+2q^2+2q
       124: q^4+4q^3+q^2+q
       125: q^4+8q^3+3q^2+3q
       126: 2q^3+2q^2+2q
       127: q^3+q^2+2q
       129: q^3+q^2+2q
       131: 2q^2+q
       133: 5q^3+2q^2+3q
       134: 2q^3+2q^2+2q
       135: 3q^3+q^2+3q
       136: 3q^3+q^2+3q
       137: q^4+8q^3+3q^2+3q
       138: 2q^3+2q^2+2q
       139: 5q^3+2q^2+3q
       140: 3q^3+q^2+3q
       141: 4q^4+5q^3+3q^2+3q
       142: 3q^3+q^2+3q
       143: q^4+8q^3+3q^2+3q
       144: 2q^3+2q^2+2q
       145: 5q^3+2q^2+3q
       146: 4q^4+5q^3+3q^2+3q
       147: 3q^3+q^2+3q
       148: 3q^3+q^2+3q
       149: 4q^4+5q^3+3q^2+3q
       150: 4q^4+5q^3+3q^2+3q
       151: q^4+q^3+2q^2+2q
       152: q^4+q^3+q
       153: q^4+q^3+2q^2+2q
       154: q^4+q^3+q
       155: q^4+q^3+2q^2+2q
       156: q^4+q^3+q
       157: 5q^3+2q^2+3q
       158: 5q^3+2q^2+3q
       159: 2q^4+2q^3+3q^2+2q
       160: 5q^3+2q^2+3q
       161: 5q^3+2q^2+3q
       162: 2q^4+2q^3+3q^2+2q
       163: 5q^3+2q^2+3q
       164: 5q^3+2q^2+3q
       165: 2q^4+2q^3+3q^2+2q
       166: 5q^3+2q^2+3q
       167: 5q^3+2q^2+3q
       168: 2q^4+2q^3+3q^2+2q
       169: q
       170: q^3+q
       172: q
       173: 2q^3+q^2+q
       174: q^4+2q^3+q^2+q
       175: 2q^3
       176: 2q^3+q^2+q
       177: q^2+q
       179: q^3+q^2+2q
       181: 2q
       183: 2q^3+q^2+2q
       184: q^3+q
       185: q^3+q
       186: 2q^3+q^2+2q
       187: 2q
       188: q^3+q
       189: q^4+q^3+2q^2+2q
       190: q^4+q^3+q
       191: 4q^3+q^2+q
       192: q^4+4q^3+2q^2+2q
       193: 2q^3+q^2+2q
       194: q^3+q
       195: q^3+q
       196: 2q^3+q^2+2q
       197: 2q
       198: q^3+q
       199: q^4+4q^3+2q^2+2q
       200: 4q^3+q^2+q
       201: 2q^3+q^2+2q
       202: q^3+q
       203: q^3+q
       204: 2q^3+q^2+2q
       205: 2q
       206: q^3+q
       207: 4q^3+2q^2+2q
       208: q^4+4q^3+q^2+q
       209: q^4+q^3+2q^2+2q
       210: q^4+q^3+q
       211: q^4+q^3+2q^2+2q
       212: q^4+q^3+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 2q^3+2q^2+2q
       220: 5q^3+2q^2+3q
       221: 2q^3+2q^2+2q
       222: 3q^3+q^2+3q
       223: q^3+q^2+2q
       224: 3q^3+q^2+3q
       225: q^3+q^2+2q
       226: 2q^3+2q^2+2q
       227: 5q^3+2q^2+3q
       228: 2q^3+2q^2+2q
       229: 3q^3+q^2+3q
       230: 3q^3+q^2+3q
       231: 2q^3+2q^2+2q
       232: 5q^3+2q^2+3q
       233: 2q^3+2q^2+2q
       234: 3q^3+q^2+3q
       235: 3q^3+q^2+3q
       236: 2q^3+2q^2+2q
       237: q^3+q^2+2q
       239: q^3+q^2+2q
       241: 2q^2+q
       243: 5q^3+2q^2+3q
       244: 3q^3+q^2+3q
       245: 3q^3+q^2+3q
       246: 4q^4+5q^3+3q^2+3q
       247: q^2+4q
       248: q^2+4q
       249: q^4+2q^2+2q
       250: 5q^3+2q^2+3q
       251: 5q^3+2q^2+3q
       252: 2q^4+2q^3+3q^2+2q
       253: 5q^3+2q^2+3q
       254: 5q^3+2q^2+3q
       255: 2q^4+2q^3+3q^2+2q
       256: 5q^3+2q^2+3q
       257: 5q^3+2q^2+3q
       258: 2q^4+2q^3+3q^2+2q
       259: q
       262: q
       263: q
       264: q^3+q
       266: q
       267: q
       268: q^3+q
       269: q
       271: q
       273: q
       274: q^3+q
       275: 2q^3+q^2+q
       276: q^4+2q^3+q^2+q
       277: 2q^3
       278: 2q^3+q^2+q
       279: q^3+q^2+2q
       281: q^2+q
       283: q^2+q
       286: q^2+q
       287: q^2+q
       289: 2q
       291: q
       293: 2q^3+q^2+2q
       294: q^3+q
       295: q^3+q
       296: 2q^3+q^2+2q
       297: 2q
       298: q^3+q
       299: 2q^3+q^2+2q
       300: q^3+q
       301: 2q
       303: q^3+q
       304: 2q^3+q^2+2q
       305: 2q
       306: q^3+q
       307: 2q^3+q^2+2q
       308: q^3+q
       309: q^3+q
       310: 2q^3+q^2+2q
       311: 2q
       313: 2q
       314: q^3+q
       315: q^2+q
       317: q^3+q^2+2q
       319: 2q^3+q^2+2q
       320: q^3+q
       321: q^3+q
       322: 2q^3+q^2+2q
       323: 2q
       324: q^3+q
       325: q^4+q^3+2q^2+2q
       326: q^4+q^3+q
       327: q^3+q^2+2q
       329: q^3+q^2+2q
       331: 2q^2+q
       333: 2q^3+2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: 2q
       337: q^2+4q
       338: q^2+3q
       340: q^2+3q
       342: 2q^2+q
       344: 2q^3+2q^2+2q
       345: 5q^3+2q^2+3q
       346: 2q^3+2q^2+2q
       347: 3q^3+q^2+3q
       348: q^3+q^2+2q
       349: 3q^3+q^2+3q
       350: q^3+q^2+2q
       351: q^2+4q
       352: 2q^3+2q^2+2q
       353: 5q^3+2q^2+3q
       354: 2q^3+2q^2+2q
       355: 3q^3+q^2+3q
       356: q^3+q^2+2q
       357: 3q^3+q^2+3q
       358: q^3+q^2+2q
       359: q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 2q^3+2q^2+2q
       367: 5q^3+2q^2+3q
       368: 2q^3+2q^2+2q
       369: 3q^3+q^2+3q
       370: 3q^3+q^2+3q
       371: q^2+4q
       372: q^2+4q
       373: q^4+2q^2+2q
       374: 5q^3+2q^2+3q
       375: 5q^3+2q^2+3q
       376: 2q^4+2q^3+3q^2+2q
       381: q
       384: q
       385: q
       386: q^3+q
       388: q
       389: q
       391: q
       393: q
       394: q^3+q
       396: q
       397: q
       399: q
       401: q
       403: q^3+q
       404: q
       405: q
       406: q
       407: q^3+q
       409: q^3+q^2+2q
       411: q^2+q
       413: q^2+q
       415: 2q
       417: q
       419: q^2+q
       422: q^2+q
       423: q
       425: q
       427: q^2+3q
       429: q^2+q
       432: q^2+q
       433: q
       435: 2q
       437: 2q^3+q^2+2q
       438: q^3+q
       439: q^3+q
       440: 2q^3+q^2+2q
       441: 2q
       442: q^3+q
       443: q^2+3q
       444: q
       445: q^2+3q
       447: q^2+q
       450: q^2+q
       451: q
       453: 2q^3+q^2+2q
       454: q^3+q
       455: 2q
       457: q^3+q
       458: 2q^3+q^2+2q
       459: 2q
       460: q^3+q
       461: q
       462: q^2+3q
       463: q^2+3q
       465: q^3+q^2+2q
       467: q^2+q
       469: q^2+q
       471: 2q^3+q^2+2q
       472: q^3+q
       473: q^3+q
       474: 2q^3+q^2+2q
       475: 2q
       476: q^3+q
       477: 2q
       479: 2q
       480: q^2+2q
       481: q^3+q^2+2q
       482: q^3+q^2+2q
       483: 2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: 2q
       492: 2q^3+2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: 2q
       496: q^2+4q
       497: 2q^3+2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: 2q
       501: q^2+4q
       502: q^3+q^2+2q
       504: q^3+q^2+2q
       506: 2q^2+q
       508: 2q^3+2q^2+2q
       509: 5q^3+2q^2+3q
       510: 2q^3+2q^2+2q
       511: 3q^3+q^2+3q
       512: q^3+q^2+2q
       513: 3q^3+q^2+3q
       514: q^3+q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q
       519: q^2+4q
       520: q^4+2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       542: q^3+q
       543: q
       545: q^2+2q
       547: q
       553: q
       555: q
       557: q
       559: q
       560: q^3+q
       561: q
       563: q^2+2q
       565: q
       566: q^3+q
       568: q
       569: q
       570: q
       573: q
       574: q^2+2q
       575: q
       577: 2q
       580: q^2+q
       583: q^2+q
       585: q
       587: q
       589: q^2+q
       592: q
       593: q
       596: q^2+q
       597: q
       599: q
       601: q^2+3q
       603: q^2+q
       605: q
       608: q^2+q
       609: q
       611: 2q
       613: q
       615: q^2+3q
       616: q
       617: q^2+3q
       619: q^2+q
       622: q^2+q
       623: q
       625: q
       627: 2q
       629: q
       631: q
       632: q^2+3q
       633: q^2+3q
       635: q^3+q^2+2q
       637: q^2+q
       639: q^2+q
       641: q^2+q
       644: q^2+q
       645: q
       647: 2q^3+q^2+2q
       648: q^3+q
       649: q^3+q
       650: 2q^3+q^2+2q
       651: 2q
       653: 2q
       654: q^3+q
       655: 2q
       656: q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       666: q^2+3q
       668: q^2+3q
       670: 2q^2+q
       672: q^2+4q
       673: 2q
       674: 2q+1
       675: q^3+q^2+2q
       676: q^3+q^2+2q
       677: 2q
       678: q^2+4q
       679: 2q
       680: 2q+1
       681: q^3+q^2+2q
       682: q^3+q^2+2q
       683: 2q
       684: q^2+4q
       685: 2q
       686: 2q^3+2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: 2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       696: q^2+q
       697: q
       729: q
       731: q
       733: q^2+2q
       735: q
       745: q
       747: q
       749: q
       751: q^2+2q
       757: q
       758: q
       761: q
       762: q
       763: q^3+q
       765: q
       766: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: q^2+3q
       793: q+1
       795: 2q+1
       797: q
       799: q
       801: q^2+q
       804: q
       805: q
       808: q^2+q
       809: q
       811: q
       813: q^2+3q
       815: q^2+3q
       816: q
       818: q+1
       819: 2q+1
       821: q
       823: q
       825: q^2+q
       828: q
       829: q
       832: q^2+q
       833: q
       835: q
       837: q^2+3q
       839: q
       840: q^2+3q
       841: q^2+q
       843: q
       844: q+1
       845: q^2+q
       848: q^2+q
       849: q
       851: q
       853: 2q
       855: q
       857: 2q
       858: q^2+2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: 2q
       873: 2q+1
       874: q+1
       875: 2q
       876: 2q
       877: q^3+q^2+2q
       878: q^3+q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       887: q^2+q
       889: q
       916: q+1
       932: q^2+2q
       934: q
       942: q+1
       956: q
       958: q^2+2q
       965: q+1
       968: q
       971: q+1
       978: q
       979: q
       982: 2q
       985: q^2+q
       988: q
       989: q^2+2q
       991: q
       992: q+1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1013: 1
      1014: 2q+1
      1016: q+1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: 2q+1
      1033: q+1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1046: q
      1047: q+1
      1048: q
      1050: q
      1052: q^2+q
      1055: q
      1056: q
      1059: q^2+q
      1060: q
      1062: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1089: q+1
      1098: q
      1101: q^2+q
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1141: 1
      1144: q+1
      1166: q+1
      1188: q
      1191: q+1
      1195: q+1
      1210: q+1
      1212: q+1
      1214: 1
      1217: 1
      1218: 1
      1225: 1
      1226: 2q+1
      1228: q+1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1244: 2q+1
      1247: q+1
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1262: q
      1263: q+1
      1264: q
      1266: q
      1268: q
      1271: q
      1272: q
      1274: q+1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1293: 1
      1305: q+1
      1316: 1
      1318: 1
      1327: 1
      1337: 1
      1340: q+1
      1350: 1
      1356: 1
      1366: 1
      1374: q+1
      1382: 1
      1388: 1
      1397: 1
      1404: q
      1407: q+1
      1411: q+1
      1433: 1
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1448: 1
      1451: 1
      1452: q+1
      1454: 1
      1456: 1
      1458: q+1
      1461: 1
      1462: 1
      1464: 1
      1467: 1
      1468: 1
      1470: q
      1472: q+1
      1476: q
      1479: q
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1492: 1
      1505: 1
      1516: 1
      1528: q+1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1565: 1
      1567: 1
      1577: 1
      1585: 1
      1587: 1
      1596: 1
      1609: 1
      1615: 1
      1624: 1
      1634: 1
      1643: 1
      1646: 1
      1647: 1
      1651: 1
      1654: 1
      1655: 1
      1661: 1
      1664: 1
      1665: 1
      1667: q+1
      1670: 1
      1674: 1
      1678: 1
      1691: 1
      1702: 1
      1714: 1
      1739: 1
      1745: 1
      1751: 1
      1763: 1
      1765: 1
      1774: 1
      1787: 1
      1789: 1
      1798: 1
      1804: 1
      1827: 1
      1830: 1
      1831: 1
      1850: 1
      1861: 1
      1873: 1
      1934: 1
      1936: 1
      1941: 1
      1993: 1

1994:    0: 6q^4+8q^3+4q^2+3q
         1: 6q^4+8q^3+4q^2+3q
         2: 6q^4+8q^3+4q^2+3q
         3: 6q^4+8q^3+4q^2+3q
         4: 2q^5+7q^4+6q^3+3q^2+3q
         5: 6q^4+8q^3+4q^2+3q
         6: 2q^5+7q^4+6q^3+3q^2+3q
         7: 2q^5+7q^4+6q^3+3q^2+3q
         8: 6q^4+8q^3+4q^2+3q
         9: 2q^6+3q^5+4q^4+4q^3+3q^2+2q
        10: 6q^4+8q^3+4q^2+3q
        11: 6q^4+8q^3+4q^2+3q
        12: 2q^5+7q^4+6q^3+3q^2+3q
        13: 6q^4+8q^3+4q^2+3q
        14: 2q^5+7q^4+6q^3+3q^2+3q
        15: 6q^4+8q^3+4q^2+3q
        16: q^4+8q^3+3q^2+3q
        17: q^4+8q^3+3q^2+3q
        18: q^5+4q^4+3q^3+3q^2+2q
        19: 4q^4+5q^3+3q^2+3q
        20: 4q^4+5q^3+3q^2+3q
        21: 4q^4+5q^3+3q^2+3q
        22: 6q^4+8q^3+4q^2+3q
        23: 6q^4+8q^3+4q^2+3q
        24: 6q^4+8q^3+4q^2+3q
        25: 6q^4+8q^3+4q^2+3q
        26: 6q^4+8q^3+4q^2+3q
        27: 6q^4+8q^3+4q^2+3q
        28: q^4+8q^3+3q^2+3q
        29: 4q^4+5q^3+3q^2+3q
        30: 4q^4+5q^3+3q^2+3q
        31: 6q^4+8q^3+4q^2+3q
        32: 6q^4+8q^3+4q^2+3q
        33: q^4+8q^3+3q^2+3q
        34: 6q^4+8q^3+4q^2+3q
        35: 6q^4+8q^3+4q^2+3q
        36: q^4+8q^3+3q^2+3q
        37: 3q^4+4q^3+3q^2+2q
        38: 3q^4+4q^3+q^2+q
        39: 3q^4+4q^3+3q^2+2q
        40: 3q^4+4q^3+q^2+q
        41: 3q^4+4q^3+3q^2+2q
        42: 3q^4+4q^3+q^2+q
        43: 6q^4+8q^3+4q^2+3q
        44: 2q^5+7q^4+6q^3+3q^2+3q
        45: 6q^4+8q^3+4q^2+3q
        46: q^4+8q^3+3q^2+3q
        47: q^4+8q^3+3q^2+3q
        48: q^5+4q^4+3q^3+3q^2+2q
        49: 5q^3+2q^2+3q
        50: 5q^3+2q^2+3q
        51: 2q^4+2q^3+3q^2+2q
        52: 4q^4+5q^3+3q^2+3q
        53: 4q^4+5q^3+3q^2+3q
        54: 4q^4+5q^3+3q^2+3q
        55: 4q^4+5q^3+3q^2+3q
        56: 4q^4+5q^3+3q^2+3q
        57: 4q^4+5q^3+3q^2+3q
        58: q^4+4q^3+2q^2+2q
        59: 4q^3+q^2+q
        60: 4q^3+q^2+q
        61: q^4+4q^3+2q^2+2q
        62: 3q^4+4q^3+3q^2+2q
        63: 3q^4+4q^3+q^2+q
        64: 3q^4+4q^3+3q^2+2q
        65: 3q^4+4q^3+q^2+q
        66: 4q^3+2q^2+2q
        67: q^4+4q^3+q^2+q
        68: q^4+8q^3+3q^2+3q
        69: 2q^3+2q^2+2q
        70: 4q^4+5q^3+3q^2+3q
        71: 5q^3+2q^2+3q
        72: 3q^3+q^2+3q
        73: 3q^3+q^2+3q
        74: q^4+q^3+2q^2+2q
        75: q^4+q^3+q
        76: q^4+q^3+2q^2+2q
        77: q^4+q^3+q
        78: q^4+q^3+2q^2+2q
        79: q^4+q^3+q
        80: 6q^4+8q^3+4q^2+3q
        81: q^4+8q^3+3q^2+3q
        82: 4q^4+5q^3+3q^2+3q
        83: 4q^4+5q^3+3q^2+3q
        84: 6q^4+8q^3+4q^2+3q
        85: q^4+8q^3+3q^2+3q
        86: 4q^4+5q^3+3q^2+3q
        87: 4q^4+5q^3+3q^2+3q
        88: q^4+8q^3+3q^2+3q
        89: q^4+8q^3+3q^2+3q
        90: q^5+4q^4+3q^3+3q^2+2q
        91: 5q^3+2q^2+3q
        92: 5q^3+2q^2+3q
        93: 2q^4+2q^3+3q^2+2q
        94: 5q^3+2q^2+3q
        95: 5q^3+2q^2+3q
        96: 2q^4+2q^3+3q^2+2q
        97: 5q^3+2q^2+3q
        98: 5q^3+2q^2+3q
        99: 2q^4+2q^3+3q^2+2q
       100: 4q^4+5q^3+3q^2+3q
       101: 4q^4+5q^3+3q^2+3q
       102: 4q^4+5q^3+3q^2+3q
       103: 2q^3+q^2+q
       104: 2q^3
       105: q^4+2q^3+q^2+q
       106: 2q^3+q^2+q
       107: q^3+q
       108: 2q^3+q^2+2q
       109: 2q^3+q^2+2q
       110: q^3+q
       111: 2q
       112: q^3+q
       113: q^4+q^3+2q^2+2q
       114: q^4+q^3+q
       115: q^4+q^3+2q^2+2q
       116: q^4+q^3+q
       117: q^4+4q^3+2q^2+2q
       118: 4q^3+q^2+q
       119: 4q^3+q^2+q
       120: q^4+4q^3+2q^2+2q
       121: 3q^4+4q^3+3q^2+2q
       122: 3q^4+4q^3+q^2+q
       123: 4q^3+2q^2+2q
       124: q^4+4q^3+q^2+q
       125: q^4+8q^3+3q^2+3q
       126: 2q^3+2q^2+2q
       127: q^3+q^2+2q
       129: q^3+q^2+2q
       131: 2q^2+q
       133: 5q^3+2q^2+3q
       134: 2q^3+2q^2+2q
       135: 3q^3+q^2+3q
       136: 3q^3+q^2+3q
       137: q^4+8q^3+3q^2+3q
       138: 2q^3+2q^2+2q
       139: 5q^3+2q^2+3q
       140: 3q^3+q^2+3q
       141: 4q^4+5q^3+3q^2+3q
       142: 3q^3+q^2+3q
       143: q^4+8q^3+3q^2+3q
       144: 2q^3+2q^2+2q
       145: 5q^3+2q^2+3q
       146: 4q^4+5q^3+3q^2+3q
       147: 3q^3+q^2+3q
       148: 3q^3+q^2+3q
       149: 4q^4+5q^3+3q^2+3q
       150: 4q^4+5q^3+3q^2+3q
       151: q^4+q^3+2q^2+2q
       152: q^4+q^3+q
       153: q^4+q^3+2q^2+2q
       154: q^4+q^3+q
       155: q^4+q^3+2q^2+2q
       156: q^4+q^3+q
       157: 5q^3+2q^2+3q
       158: 5q^3+2q^2+3q
       159: 2q^4+2q^3+3q^2+2q
       160: 5q^3+2q^2+3q
       161: 5q^3+2q^2+3q
       162: 2q^4+2q^3+3q^2+2q
       163: 5q^3+2q^2+3q
       164: 5q^3+2q^2+3q
       165: 2q^4+2q^3+3q^2+2q
       166: 5q^3+2q^2+3q
       167: 5q^3+2q^2+3q
       168: 2q^4+2q^3+3q^2+2q
       169: q
       171: q^3+q
       172: q
       173: 2q^3+q^2+q
       174: 2q^3
       175: q^4+2q^3+q^2+q
       176: 2q^3+q^2+q
       177: q^2+q
       179: q^3+q^2+2q
       181: 2q
       183: q^3+q
       184: 2q^3+q^2+2q
       185: 2q^3+q^2+2q
       186: q^3+q
       187: 2q
       188: q^3+q
       189: q^4+q^3+2q^2+2q
       190: q^4+q^3+q
       191: q^4+4q^3+2q^2+2q
       192: 4q^3+q^2+q
       193: q^3+q
       194: 2q^3+q^2+2q
       195: 2q^3+q^2+2q
       196: q^3+q
       197: 2q
       198: q^3+q
       199: 4q^3+q^2+q
       200: q^4+4q^3+2q^2+2q
       201: q^3+q
       202: 2q^3+q^2+2q
       203: 2q^3+q^2+2q
       204: q^3+q
       205: 2q
       206: q^3+q
       207: 4q^3+2q^2+2q
       208: q^4+4q^3+q^2+q
       209: q^4+q^3+2q^2+2q
       210: q^4+q^3+q
       211: q^4+q^3+2q^2+2q
       212: q^4+q^3+q
       213: q^3+q^2+2q
       215: q^3+q^2+2q
       217: 2q^2+q
       219: 2q^3+2q^2+2q
       220: 5q^3+2q^2+3q
       221: 2q^3+2q^2+2q
       222: 3q^3+q^2+3q
       223: q^3+q^2+2q
       224: 3q^3+q^2+3q
       225: q^3+q^2+2q
       226: 2q^3+2q^2+2q
       227: 5q^3+2q^2+3q
       228: 2q^3+2q^2+2q
       229: 3q^3+q^2+3q
       230: 3q^3+q^2+3q
       231: 2q^3+2q^2+2q
       232: 5q^3+2q^2+3q
       233: 2q^3+2q^2+2q
       234: 3q^3+q^2+3q
       235: 3q^3+q^2+3q
       236: 2q^3+2q^2+2q
       237: q^3+q^2+2q
       239: q^3+q^2+2q
       241: 2q^2+q
       243: 5q^3+2q^2+3q
       244: 3q^3+q^2+3q
       245: 3q^3+q^2+3q
       246: 4q^4+5q^3+3q^2+3q
       247: q^2+4q
       248: q^2+4q
       249: q^4+2q^2+2q
       250: 5q^3+2q^2+3q
       251: 5q^3+2q^2+3q
       252: 2q^4+2q^3+3q^2+2q
       253: 5q^3+2q^2+3q
       254: 5q^3+2q^2+3q
       255: 2q^4+2q^3+3q^2+2q
       256: 5q^3+2q^2+3q
       257: 5q^3+2q^2+3q
       258: 2q^4+2q^3+3q^2+2q
       259: q
       262: q
       263: q
       265: q^3+q
       266: q
       267: q
       269: q
       270: q^3+q
       271: q
       272: q^3+q
       273: q
       275: 2q^3+q^2+q
       276: 2q^3
       277: q^4+2q^3+q^2+q
       278: 2q^3+q^2+q
       279: q^3+q^2+2q
       281: q^2+q
       284: q^2+q
       285: q^2+q
       287: q^2+q
       289: 2q
       291: q
       293: q^3+q
       294: 2q^3+q^2+2q
       295: 2q^3+q^2+2q
       296: q^3+q
       297: 2q
       298: q^3+q
       299: q^3+q
       300: 2q^3+q^2+2q
       301: 2q
       303: 2q^3+q^2+2q
       304: q^3+q
       305: 2q
       306: q^3+q
       307: q^3+q
       308: 2q^3+q^2+2q
       309: 2q^3+q^2+2q
       310: q^3+q
       311: 2q
       313: 2q
       314: q^3+q
       315: q^2+q
       317: q^3+q^2+2q
       319: q^3+q
       320: 2q^3+q^2+2q
       321: 2q^3+q^2+2q
       322: q^3+q
       323: 2q
       324: q^3+q
       325: q^4+q^3+2q^2+2q
       326: q^4+q^3+q
       327: q^3+q^2+2q
       329: q^3+q^2+2q
       331: 2q^2+q
       333: 2q^3+2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: 2q
       337: q^2+4q
       338: q^2+3q
       340: q^2+3q
       342: 2q^2+q
       344: 2q^3+2q^2+2q
       345: 5q^3+2q^2+3q
       346: 2q^3+2q^2+2q
       347: 3q^3+q^2+3q
       348: q^3+q^2+2q
       349: 3q^3+q^2+3q
       350: q^3+q^2+2q
       351: q^2+4q
       352: 2q^3+2q^2+2q
       353: 5q^3+2q^2+3q
       354: 2q^3+2q^2+2q
       355: 3q^3+q^2+3q
       356: q^3+q^2+2q
       357: 3q^3+q^2+3q
       358: q^3+q^2+2q
       359: q^2+4q
       360: q^3+q^2+2q
       362: q^3+q^2+2q
       364: 2q^2+q
       366: 2q^3+2q^2+2q
       367: 5q^3+2q^2+3q
       368: 2q^3+2q^2+2q
       369: 3q^3+q^2+3q
       370: 3q^3+q^2+3q
       371: q^2+4q
       372: q^2+4q
       373: q^4+2q^2+2q
       374: 5q^3+2q^2+3q
       375: 5q^3+2q^2+3q
       376: 2q^4+2q^3+3q^2+2q
       381: q
       384: q
       385: q
       387: q^3+q
       388: q
       389: q
       391: q
       393: q
       395: q^3+q
       396: q
       397: q
       399: q
       401: q
       402: q^3+q
       404: q
       405: q
       406: q
       408: q^3+q
       409: q^3+q^2+2q
       411: q^2+q
       413: q^2+q
       415: 2q
       417: q
       420: q^2+q
       421: q^2+q
       423: q
       425: q
       427: q^2+3q
       430: q^2+q
       431: q^2+q
       433: q
       435: 2q
       437: q^3+q
       438: 2q^3+q^2+2q
       439: 2q^3+q^2+2q
       440: q^3+q
       441: 2q
       442: q^3+q
       443: q
       444: q^2+3q
       445: q^2+3q
       448: q^2+q
       449: q^2+q
       451: q
       453: q^3+q
       454: 2q^3+q^2+2q
       455: 2q
       457: 2q^3+q^2+2q
       458: q^3+q
       459: 2q
       460: q^3+q
       461: q^2+3q
       462: q
       463: q^2+3q
       465: q^3+q^2+2q
       467: q^2+q
       469: q^2+q
       471: q^3+q
       472: 2q^3+q^2+2q
       473: 2q^3+q^2+2q
       474: q^3+q
       475: 2q
       476: q^3+q
       477: 2q
       479: 2q
       480: q^2+2q
       481: q^3+q^2+2q
       482: q^3+q^2+2q
       483: 2q
       484: q^2+4q
       485: q^2+3q
       487: q^2+3q
       489: 2q^2+q
       491: 2q
       492: 2q^3+2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: 2q
       496: q^2+4q
       497: 2q^3+2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: 2q
       501: q^2+4q
       502: q^3+q^2+2q
       504: q^3+q^2+2q
       506: 2q^2+q
       508: 2q^3+2q^2+2q
       509: 5q^3+2q^2+3q
       510: 2q^3+2q^2+2q
       511: 3q^3+q^2+3q
       512: q^3+q^2+2q
       513: 3q^3+q^2+3q
       514: q^3+q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q
       519: q^2+4q
       520: q^4+2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       544: q^3+q
       545: q
       547: q^2+2q
       553: q
       555: q
       557: q
       558: q^3+q
       559: q
       561: q^2+2q
       563: q
       565: q
       567: q^3+q
       568: q
       569: q
       570: q
       573: q
       575: q
       576: q^2+2q
       577: 2q
       580: q^2+q
       583: q^2+q
       585: q
       587: q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       597: q
       599: q
       601: q^2+3q
       604: q^2+q
       605: q
       607: q^2+q
       609: q
       611: 2q
       613: q
       615: q
       616: q^2+3q
       617: q^2+3q
       620: q^2+q
       621: q^2+q
       623: q
       625: q
       627: 2q
       629: q
       631: q^2+3q
       632: q
       633: q^2+3q
       635: q^3+q^2+2q
       637: q^2+q
       639: q^2+q
       642: q^2+q
       643: q^2+q
       645: q
       647: q^3+q
       648: 2q^3+q^2+2q
       649: 2q^3+q^2+2q
       650: q^3+q
       651: 2q
       653: 2q
       654: q^3+q
       655: 2q
       656: q^2+2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q
       666: q^2+3q
       668: q^2+3q
       670: 2q^2+q
       672: q^2+4q
       673: 2q
       674: 2q+1
       675: q^3+q^2+2q
       676: q^3+q^2+2q
       677: 2q
       678: q^2+4q
       679: 2q
       680: 2q+1
       681: q^3+q^2+2q
       682: q^3+q^2+2q
       683: 2q
       684: q^2+4q
       685: 2q
       686: 2q^3+2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: 2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       693: q
       697: q
       698: q^2+q
       729: q
       731: q
       733: q
       735: q^2+2q
       745: q
       747: q
       749: q^2+2q
       751: q
       757: q
       758: q
       761: q
       762: q
       764: q^3+q
       765: q
       767: q^2+2q
       768: q
       769: 2q
       772: q^2+q
       775: q+1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: q^2+3q
       794: q+1
       795: 2q+1
       797: q
       799: q
       802: q^2+q
       803: q
       806: q
       807: q^2+q
       809: q
       811: q
       813: q^2+3q
       815: q
       816: q^2+3q
       817: q+1
       819: 2q+1
       821: q
       823: q
       826: q^2+q
       827: q
       830: q
       831: q^2+q
       833: q
       835: q
       837: q^2+3q
       839: q^2+3q
       840: q
       841: q^2+q
       843: q
       844: q+1
       846: q^2+q
       847: q^2+q
       849: q
       851: q
       853: 2q
       855: q
       857: 2q
       858: q^2+2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: 2q
       873: 2q+1
       874: q+1
       875: 2q
       876: 2q
       877: q^3+q^2+2q
       878: q^3+q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       884: q
       888: q^2+q
       889: q
       918: q+1
       932: q
       934: q^2+2q
       940: q+1
       956: q^2+2q
       958: q
       966: q+1
       968: q
       971: q+1
       978: q
       979: q
       982: 2q
       985: q^2+q
       988: q
       990: q^2+2q
       991: q
       992: q+1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1013: 1
      1014: 2q+1
      1017: q+1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: 2q+1
      1032: q+1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1046: q
      1047: q+1
      1048: q
      1050: q
      1053: q^2+q
      1054: q
      1057: q
      1058: q^2+q
      1060: q
      1062: q
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1090: q+1
      1098: q
      1102: q
      1103: q^2+q
      1114: 1
      1124: 1
      1132: 1
      1141: 1
      1146: q+1
      1164: q+1
      1188: q
      1191: q+1
      1196: q+1
      1210: q+1
      1212: q+1
      1214: 1
      1216: 1
      1219: 1
      1225: 1
      1226: 2q+1
      1229: q+1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1244: 2q+1
      1246: q+1
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1262: q
      1263: q+1
      1264: q
      1266: q
      1269: q
      1270: q
      1272: q
      1274: q+1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1294: 1
      1306: q+1
      1314: 1
      1320: 1
      1328: 1
      1337: 1
      1342: q+1
      1348: 1
      1358: 1
      1365: 1
      1372: q+1
      1380: 1
      1390: 1
      1398: 1
      1404: q
      1407: q+1
      1412: q+1
      1433: 1
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1448: 1
      1450: 1
      1452: q+1
      1455: 1
      1456: 1
      1458: q+1
      1460: 1
      1463: 1
      1464: 1
      1466: 1
      1469: 1
      1470: q
      1472: q+1
      1477: q
      1478: q
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1493: 1
      1504: 1
      1517: 1
      1529: q+1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1563: 1
      1569: 1
      1576: 1
      1583: 1
      1589: 1
      1597: 1
      1607: 1
      1617: 1
      1625: 1
      1634: 1
      1643: 1
      1645: 1
      1648: 1
      1651: 1
      1653: 1
      1656: 1
      1661: 1
      1663: 1
      1666: 1
      1667: q+1
      1670: 1
      1674: 1
      1679: 1
      1690: 1
      1703: 1
      1715: 1
      1737: 1
      1747: 1
      1750: 1
      1761: 1
      1767: 1
      1775: 1
      1785: 1
      1791: 1
      1799: 1
      1804: 1
      1827: 1
      1829: 1
      1832: 1
      1849: 1
      1862: 1
      1874: 1
      1932: 1
      1938: 1
      1942: 1
      1994: 1

1995:    0: 4q^3+8q^2+2q+1
         1: 4q^3+8q^2+2q+1
         2: 4q^3+8q^2+2q+1
         3: 4q^3+8q^2+2q+1
         4: q^4+5q^3+6q^2+2q+1
         5: 4q^3+8q^2+2q+1
         6: q^4+5q^3+6q^2+2q+1
         7: q^4+5q^3+6q^2+2q+1
         8: 4q^3+8q^2+2q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 4q^3+8q^2+2q+1
        11: 4q^3+8q^2+2q+1
        12: q^4+5q^3+6q^2+2q+1
        13: 4q^3+8q^2+2q+1
        14: q^4+5q^3+6q^2+2q+1
        15: 4q^3+8q^2+2q+1
        16: q^3+8q^2+2q+1
        17: q^3+8q^2+2q+1
        18: q^4+4q^3+4q^2+2q+1
        19: 3q^3+6q^2+2q+1
        20: 3q^3+6q^2+2q+1
        21: 3q^3+6q^2+2q+1
        22: 4q^3+8q^2+2q+1
        23: 4q^3+8q^2+2q+1
        24: 4q^3+8q^2+2q+1
        25: 4q^3+8q^2+2q+1
        26: 4q^3+8q^2+2q+1
        27: 4q^3+8q^2+2q+1
        28: q^3+8q^2+2q+1
        29: 3q^3+6q^2+2q+1
        30: 3q^3+6q^2+2q+1
        31: 4q^3+8q^2+2q+1
        32: 4q^3+8q^2+2q+1
        33: q^3+8q^2+2q+1
        34: 4q^3+8q^2+2q+1
        35: 4q^3+8q^2+2q+1
        36: q^3+8q^2+2q+1
        37: q^3+2q^2
        38: 3q^3+6q^2+2q+1
        39: q^3+2q^2
        40: 3q^3+6q^2+2q+1
        41: q^3+2q^2
        42: 3q^3+6q^2+2q+1
        43: 4q^3+8q^2+2q+1
        44: q^4+5q^3+6q^2+2q+1
        45: 4q^3+8q^2+2q+1
        46: q^3+8q^2+2q+1
        47: q^3+8q^2+2q+1
        48: q^4+4q^3+4q^2+2q+1
        49: 6q^2+2q+1
        50: 6q^2+2q+1
        51: 2q^3+4q^2+2q+1
        52: 3q^3+6q^2+2q+1
        53: 3q^3+6q^2+2q+1
        54: 3q^3+6q^2+2q+1
        55: 3q^3+6q^2+2q+1
        56: 3q^3+6q^2+2q+1
        57: 3q^3+6q^2+2q+1
        58: 3q^2
        59: q^3+5q^2+2q+1
        60: q^3+5q^2+2q+1
        61: 3q^2
        62: q^3+2q^2
        63: 3q^3+6q^2+2q+1
        64: q^3+2q^2
        65: 3q^3+6q^2+2q+1
        66: 2q^2
        67: q^3+6q^2+2q+1
        68: q^3+8q^2+2q+1
        69: 4q^2+2q+1
        70: 3q^3+6q^2+2q+1
        71: 6q^2+2q+1
        72: 4q^2+2q+1
        73: 4q^2+2q+1
        75: 2q^3+4q^2+2q+1
        77: 2q^3+4q^2+2q+1
        79: 2q^3+4q^2+2q+1
        80: 4q^3+8q^2+2q+1
        81: q^3+8q^2+2q+1
        82: 3q^3+6q^2+2q+1
        83: 3q^3+6q^2+2q+1
        84: 4q^3+8q^2+2q+1
        85: q^3+8q^2+2q+1
        86: 3q^3+6q^2+2q+1
        87: 3q^3+6q^2+2q+1
        88: q^3+8q^2+2q+1
        89: q^3+8q^2+2q+1
        90: q^4+4q^3+4q^2+2q+1
        91: 6q^2+2q+1
        92: 6q^2+2q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+2q+1
        95: 6q^2+2q+1
        96: 2q^3+4q^2+2q+1
        97: 6q^2+2q+1
        98: 6q^2+2q+1
        99: 2q^3+4q^2+2q+1
       100: 3q^3+6q^2+2q+1
       101: 3q^3+6q^2+2q+1
       102: 3q^3+6q^2+2q+1
       103: q^2
       104: q^3+4q^2+2q+1
       105: 2q^2
       106: q^2
       107: 3q^2+2q+1
       108: q^2
       109: q^2
       110: 3q^2+2q+1
       112: 2q^2+2q+1
       114: 2q^3+4q^2+2q+1
       116: 2q^3+4q^2+2q+1
       117: 3q^2
       118: q^3+5q^2+2q+1
       119: q^3+5q^2+2q+1
       120: 3q^2
       121: q^3+2q^2
       122: 3q^3+6q^2+2q+1
       123: 2q^2
       124: q^3+6q^2+2q+1
       125: q^3+8q^2+2q+1
       126: 4q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: 6q^2+2q+1
       134: 4q^2+2q+1
       135: 4q^2+2q+1
       136: 4q^2+2q+1
       137: q^3+8q^2+2q+1
       138: 4q^2+2q+1
       139: 6q^2+2q+1
       140: 4q^2+2q+1
       141: 3q^3+6q^2+2q+1
       142: 4q^2+2q+1
       143: q^3+8q^2+2q+1
       144: 4q^2+2q+1
       145: 6q^2+2q+1
       146: 3q^3+6q^2+2q+1
       147: 4q^2+2q+1
       148: 4q^2+2q+1
       149: 3q^3+6q^2+2q+1
       150: 3q^3+6q^2+2q+1
       152: 2q^3+4q^2+2q+1
       154: 2q^3+4q^2+2q+1
       156: 2q^3+4q^2+2q+1
       157: 6q^2+2q+1
       158: 6q^2+2q+1
       159: 2q^3+4q^2+2q+1
       160: 6q^2+2q+1
       161: 6q^2+2q+1
       162: 2q^3+4q^2+2q+1
       163: 6q^2+2q+1
       164: 6q^2+2q+1
       165: 2q^3+4q^2+2q+1
       166: 6q^2+2q+1
       167: 6q^2+2q+1
       168: 2q^3+4q^2+2q+1
       170: 2q^2+2q+1
       173: q^2
       174: q^3+4q^2+2q+1
       175: 2q^2
       176: q^2
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       183: 3q^2+2q+1
       184: q^2
       185: q^2
       186: 3q^2+2q+1
       188: 2q^2+2q+1
       190: 2q^3+4q^2+2q+1
       191: 3q^2
       192: q^3+5q^2+2q+1
       193: 3q^2+2q+1
       194: q^2
       195: q^2
       196: 3q^2+2q+1
       198: 2q^2+2q+1
       199: q^3+5q^2+2q+1
       200: 3q^2
       201: 3q^2+2q+1
       202: q^2
       203: q^2
       204: 3q^2+2q+1
       206: 2q^2+2q+1
       207: 2q^2
       208: q^3+6q^2+2q+1
       210: 2q^3+4q^2+2q+1
       212: 2q^3+4q^2+2q+1
       214: 3q^2+2q+1
       216: 3q^2+2q+1
       218: q^3+2q^2+2q+1
       219: 4q^2+2q+1
       220: 6q^2+2q+1
       221: 4q^2+2q+1
       222: 4q^2+2q+1
       223: 2q^2+2q+1
       224: 4q^2+2q+1
       225: 2q^2+2q+1
       226: 4q^2+2q+1
       227: 6q^2+2q+1
       228: 4q^2+2q+1
       229: 4q^2+2q+1
       230: 4q^2+2q+1
       231: 4q^2+2q+1
       232: 6q^2+2q+1
       233: 4q^2+2q+1
       234: 4q^2+2q+1
       235: 4q^2+2q+1
       236: 4q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: 6q^2+2q+1
       244: 4q^2+2q+1
       245: 4q^2+2q+1
       246: 3q^3+6q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 6q^2+2q+1
       251: 6q^2+2q+1
       252: 2q^3+4q^2+2q+1
       253: 6q^2+2q+1
       254: 6q^2+2q+1
       255: 2q^3+4q^2+2q+1
       256: 6q^2+2q+1
       257: 6q^2+2q+1
       258: 2q^3+4q^2+2q+1
       260: q^2+2q+1
       264: 2q^2+2q+1
       268: 2q^2+2q+1
       274: 2q^2+2q+1
       275: q^2
       276: q^3+4q^2+2q+1
       277: 2q^2
       278: q^2
       280: 3q^2+2q+1
       282: 2q^2+2q+1
       283: q^2+2q+1
       286: q^2+2q+1
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: 2q+1
       293: 3q^2+2q+1
       294: q^2
       295: q^2
       296: 3q^2+2q+1
       298: 2q^2+2q+1
       299: 3q^2+2q+1
       300: q^2
       302: q^2+2q+1
       303: q^2
       304: 3q^2+2q+1
       306: 2q^2+2q+1
       307: 3q^2+2q+1
       308: q^2
       309: q^2
       310: 3q^2+2q+1
       312: q^2+2q+1
       314: 2q^2+2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: 3q^2+2q+1
       320: q^2
       321: q^2
       322: 3q^2+2q+1
       324: 2q^2+2q+1
       326: 2q^3+4q^2+2q+1
       328: 3q^2+2q+1
       330: 3q^2+2q+1
       332: q^3+2q^2+2q+1
       333: 4q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 4q^2+2q+1
       345: 6q^2+2q+1
       346: 4q^2+2q+1
       347: 4q^2+2q+1
       348: 2q^2+2q+1
       349: 4q^2+2q+1
       350: 2q^2+2q+1
       351: q^2+4q+1
       352: 4q^2+2q+1
       353: 6q^2+2q+1
       354: 4q^2+2q+1
       355: 4q^2+2q+1
       356: 2q^2+2q+1
       357: 4q^2+2q+1
       358: 2q^2+2q+1
       359: q^2+4q+1
       361: 3q^2+2q+1
       363: 3q^2+2q+1
       365: q^3+2q^2+2q+1
       366: 4q^2+2q+1
       367: 6q^2+2q+1
       368: 4q^2+2q+1
       369: 4q^2+2q+1
       370: 4q^2+2q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: q^3+2q^2+2q+1
       374: 6q^2+2q+1
       375: 6q^2+2q+1
       376: 2q^3+4q^2+2q+1
       378: 2q+1
       382: q^2+2q+1
       386: 2q^2+2q+1
       390: q^2+2q+1
       394: 2q^2+2q+1
       400: q^2+2q+1
       403: 2q^2+2q+1
       407: 2q^2+2q+1
       410: 3q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: 2q+1
       419: q^2+2q+1
       422: q^2+2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       429: q^2+2q+1
       432: q^2+2q+1
       434: 2q+1
       436: q^2+2q+1
       437: 3q^2+2q+1
       438: q^2
       439: q^2
       440: 3q^2+2q+1
       442: 2q^2+2q+1
       443: q^2+3q+1
       444: q
       446: q^2+4q+1
       447: q^2+2q+1
       450: q^2+2q+1
       452: 2q+1
       453: 3q^2+2q+1
       454: q^2
       456: q^2+2q+1
       457: q^2
       458: 3q^2+2q+1
       460: 2q^2+2q+1
       461: q
       462: q^2+3q+1
       464: q^2+4q+1
       466: 3q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       471: 3q^2+2q+1
       472: q^2
       473: q^2
       474: 3q^2+2q+1
       476: 2q^2+2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: 2q^2+2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: q^2+4q+1
       486: q^2+4q+1
       488: q^2+4q+1
       490: q^3+2q^2+2q+1
       491: 2q+1
       492: 4q^2+2q+1
       493: 2q^2+2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: q^2+4q+1
       497: 4q^2+2q+1
       498: 2q^2+2q+1
       499: 2q^2+2q+1
       500: 2q+1
       501: q^2+4q+1
       503: 3q^2+2q+1
       505: 3q^2+2q+1
       507: q^3+2q^2+2q+1
       508: 4q^2+2q+1
       509: 6q^2+2q+1
       510: 4q^2+2q+1
       511: 4q^2+2q+1
       512: 2q^2+2q+1
       513: 4q^2+2q+1
       514: 2q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       522: 2q+1
       526: q^2+2q+1
       530: 2q+1
       534: 2q+1
       538: q^2+2q+1
       542: 2q^2+2q+1
       546: q^2+3q+1
       548: q
       551: 2q+1
       556: q^2+2q+1
       560: 2q^2+2q+1
       562: q
       564: q^2+3q+1
       566: 2q^2+2q+1
       571: q^2+2q+1
       573: q
       574: q^2+2q+1
       575: q
       578: 2q
       581: q^2+2q+1
       584: 2q^2+2q+1
       586: 2q+1
       588: 2q+1
       589: q^2+2q+1
       592: q+1
       593: q+1
       596: q^2+2q+1
       598: 2q+1
       600: 2q+1
       602: q^2+4q+1
       603: q^2+2q+1
       606: 2q+1
       608: q^2+2q+1
       610: 2q+1
       612: q^2+2q+1
       614: 2q+1
       615: q^2+3q+1
       616: q
       618: q^2+4q+1
       619: q^2+2q+1
       622: q^2+2q+1
       624: 2q+1
       626: 2q+1
       628: q^2+2q+1
       630: 2q+1
       631: q
       632: q^2+3q+1
       634: q^2+4q+1
       636: 3q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       641: q^2+2q+1
       644: q^2+2q+1
       646: 2q+1
       647: 3q^2+2q+1
       648: q^2
       649: q^2
       650: 3q^2+2q+1
       652: q^2+2q+1
       654: 2q^2+2q+1
       655: 2q
       656: q^2+2q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q+1
       667: q^2+4q+1
       669: q^2+4q+1
       671: q^3+2q^2+2q+1
       672: q^2+4q+1
       673: 2q+1
       674: 2q+1
       675: 2q^2+2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: q^2+4q+1
       679: 2q+1
       680: 2q+1
       681: 2q^2+2q+1
       682: 2q^2+2q+1
       683: 2q+1
       684: q^2+4q+1
       685: 2q+1
       686: 4q^2+2q+1
       687: 2q^2+2q+1
       688: 2q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q
       699: q^2+2q+1
       701: q
       706: 2q+1
       710: 2q+1
       715: q+1
       718: q+1
       722: 2q+1
       726: 2q+1
       730: q^2+2q+1
       734: q^2+3q+1
       736: q
       740: 2q+1
       744: 2q+1
       748: q^2+2q+1
       750: q
       752: q^2+3q+1
       754: 2q+1
       759: q^2+2q+1
       763: 2q^2+2q+1
       765: q
       766: q^2+2q+1
       768: q
       770: 2q
       773: q^2+2q+1
       776: q+1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       785: q+1
       788: q+1
       790: q^2+4q+1
       792: 1
       793: q+1
       796: 2q+1
       798: 2q+1
       800: 2q+1
       801: q^2+2q+1
       804: q+1
       805: q+1
       808: q^2+2q+1
       810: 2q+1
       812: 2q+1
       814: q^2+4q+1
       815: q^2+3q+1
       816: q
       818: q+1
       820: 2q+1
       822: 2q+1
       824: 2q+1
       825: q^2+2q+1
       828: q+1
       829: q+1
       832: q^2+2q+1
       834: 2q+1
       836: 2q+1
       838: q^2+4q+1
       839: q
       840: q^2+3q+1
       842: 2q^2+2q+1
       843: q
       844: q+1
       845: q^2+2q+1
       848: q^2+2q+1
       850: 2q+1
       852: 2q+1
       854: q^2+2q+1
       856: 2q+1
       857: 2q
       858: q^2+2q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q+1
       869: 2q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 2q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 2q^2+2q+1
       878: 2q^2+2q+1
       879: 2q+1
       880: 2q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       885: q
       890: q^2+2q+1
       892: q
       897: 2q+1
       903: q+1
       905: q+1
       909: 1
       913: 2q+1
       917: q+1
       921: 2q+1
       926: q+1
       929: q+1
       933: q^2+3q+1
       935: q
       939: 2q+1
       943: q+1
       947: 2q+1
       951: q+1
       953: q+1
       957: q
       959: q^2+3q+1
       962: 2q+1
       965: q+1
       969: q
       972: q+1
       976: 2q+1
       980: q^2+2q+1
       983: 2q
       986: q^2+2q+1
       988: q
       989: q^2+2q+1
       991: q
       993: q+1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 2q+1
      1004: q+1
      1007: q+1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1016: q+1
      1019: 2q+1
      1021: q+1
      1023: 2q+1
      1025: 2q+1
      1026: q+1
      1029: q+1
      1031: 2q+1
      1033: q+1
      1035: 2q+1
      1037: q+1
      1039: 2q+1
      1040: q+1
      1043: 2q+1
      1045: q+1
      1046: q
      1047: q+1
      1049: 2q+1
      1051: 2q+1
      1052: q^2+2q+1
      1055: q+1
      1056: q+1
      1059: q^2+2q+1
      1061: 2q+1
      1063: 2q+1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: q+1
      1085: 2q+1
      1092: q+1
      1099: q
      1104: q^2+2q+1
      1106: q
      1113: q+1
      1117: 1
      1119: q+1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: q+1
      1149: 2q+1
      1155: q+1
      1157: q+1
      1162: 1
      1167: q+1
      1171: 2q+1
      1175: q+1
      1177: q+1
      1181: 1
      1186: 2q+1
      1189: q
      1192: q+1
      1195: q+1
      1200: 2q+1
      1205: q+1
      1207: q+1
      1211: q+1
      1213: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2q+1
      1228: q+1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 2q+1
      1240: q+1
      1243: q+1
      1245: 2q+1
      1247: q+1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 2q+1
      1258: q+1
      1261: q+1
      1262: q
      1263: q+1
      1265: 2q+1
      1267: 2q+1
      1268: q+1
      1271: q+1
      1273: 2q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q+1
      1296: 1
      1308: q+1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: q+1
      1347: q+1
      1351: 1
      1353: q+1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1375: q+1
      1379: q+1
      1383: 1
      1385: q+1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1405: q
      1408: q+1
      1411: q+1
      1416: 2q+1
      1421: q+1
      1423: q+1
      1427: 1
      1434: 1
      1439: 1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1451: 1
      1453: q+1
      1454: 1
      1457: 1
      1459: q+1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 2q+1
      1473: q+1
      1475: 1
      1476: q+1
      1479: q+1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1495: 1
      1508: 1
      1519: 1
      1531: q+1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1606: q+1
      1610: 1
      1612: q+1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1635: 1
      1644: 1
      1646: 1
      1647: 1
      1652: 1
      1654: 1
      1655: 1
      1662: 1
      1664: 1
      1665: 1
      1668: q+1
      1670: 1
      1672: 1
      1674: 1
      1681: 1
      1694: 1
      1705: 1
      1716: 1
      1740: 1
      1746: 1
      1751: 1
      1756: 1
      1764: 1
      1766: 1
      1774: 1
      1779: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1805: 1
      1809: 1
      1828: 1
      1830: 1
      1831: 1
      1853: 1
      1864: 1
      1875: 1
      1935: 1
      1937: 1
      1941: 1
      1950: 1
      1995: 1

1996:    0: 4q^3+8q^2+2q+1
         1: 4q^3+8q^2+2q+1
         2: 4q^3+8q^2+2q+1
         3: 4q^3+8q^2+2q+1
         4: q^4+5q^3+6q^2+2q+1
         5: 4q^3+8q^2+2q+1
         6: q^4+5q^3+6q^2+2q+1
         7: q^4+5q^3+6q^2+2q+1
         8: 4q^3+8q^2+2q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 4q^3+8q^2+2q+1
        11: 4q^3+8q^2+2q+1
        12: q^4+5q^3+6q^2+2q+1
        13: 4q^3+8q^2+2q+1
        14: q^4+5q^3+6q^2+2q+1
        15: 4q^3+8q^2+2q+1
        16: q^3+8q^2+2q+1
        17: q^3+8q^2+2q+1
        18: q^4+4q^3+4q^2+2q+1
        19: 3q^3+6q^2+2q+1
        20: 3q^3+6q^2+2q+1
        21: 3q^3+6q^2+2q+1
        22: 4q^3+8q^2+2q+1
        23: 4q^3+8q^2+2q+1
        24: 4q^3+8q^2+2q+1
        25: 4q^3+8q^2+2q+1
        26: 4q^3+8q^2+2q+1
        27: 4q^3+8q^2+2q+1
        28: q^3+8q^2+2q+1
        29: 3q^3+6q^2+2q+1
        30: 3q^3+6q^2+2q+1
        31: 4q^3+8q^2+2q+1
        32: 4q^3+8q^2+2q+1
        33: q^3+8q^2+2q+1
        34: 4q^3+8q^2+2q+1
        35: 4q^3+8q^2+2q+1
        36: q^3+8q^2+2q+1
        37: q^3+2q^2
        38: 3q^3+6q^2+2q+1
        39: q^3+2q^2
        40: 3q^3+6q^2+2q+1
        41: q^3+2q^2
        42: 3q^3+6q^2+2q+1
        43: 4q^3+8q^2+2q+1
        44: q^4+5q^3+6q^2+2q+1
        45: 4q^3+8q^2+2q+1
        46: q^3+8q^2+2q+1
        47: q^3+8q^2+2q+1
        48: q^4+4q^3+4q^2+2q+1
        49: 6q^2+2q+1
        50: 6q^2+2q+1
        51: 2q^3+4q^2+2q+1
        52: 3q^3+6q^2+2q+1
        53: 3q^3+6q^2+2q+1
        54: 3q^3+6q^2+2q+1
        55: 3q^3+6q^2+2q+1
        56: 3q^3+6q^2+2q+1
        57: 3q^3+6q^2+2q+1
        58: q^3+5q^2+2q+1
        59: 3q^2
        60: 3q^2
        61: q^3+5q^2+2q+1
        62: q^3+2q^2
        63: 3q^3+6q^2+2q+1
        64: q^3+2q^2
        65: 3q^3+6q^2+2q+1
        66: 2q^2
        67: q^3+6q^2+2q+1
        68: q^3+8q^2+2q+1
        69: 4q^2+2q+1
        70: 3q^3+6q^2+2q+1
        71: 6q^2+2q+1
        72: 4q^2+2q+1
        73: 4q^2+2q+1
        75: 2q^3+4q^2+2q+1
        77: 2q^3+4q^2+2q+1
        79: 2q^3+4q^2+2q+1
        80: 4q^3+8q^2+2q+1
        81: q^3+8q^2+2q+1
        82: 3q^3+6q^2+2q+1
        83: 3q^3+6q^2+2q+1
        84: 4q^3+8q^2+2q+1
        85: q^3+8q^2+2q+1
        86: 3q^3+6q^2+2q+1
        87: 3q^3+6q^2+2q+1
        88: q^3+8q^2+2q+1
        89: q^3+8q^2+2q+1
        90: q^4+4q^3+4q^2+2q+1
        91: 6q^2+2q+1
        92: 6q^2+2q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+2q+1
        95: 6q^2+2q+1
        96: 2q^3+4q^2+2q+1
        97: 6q^2+2q+1
        98: 6q^2+2q+1
        99: 2q^3+4q^2+2q+1
       100: 3q^3+6q^2+2q+1
       101: 3q^3+6q^2+2q+1
       102: 3q^3+6q^2+2q+1
       103: q^2
       104: 2q^2
       105: q^3+4q^2+2q+1
       106: q^2
       107: q^2
       108: 3q^2+2q+1
       109: 3q^2+2q+1
       110: q^2
       112: 2q^2+2q+1
       114: 2q^3+4q^2+2q+1
       116: 2q^3+4q^2+2q+1
       117: q^3+5q^2+2q+1
       118: 3q^2
       119: 3q^2
       120: q^3+5q^2+2q+1
       121: q^3+2q^2
       122: 3q^3+6q^2+2q+1
       123: 2q^2
       124: q^3+6q^2+2q+1
       125: q^3+8q^2+2q+1
       126: 4q^2+2q+1
       128: 3q^2+2q+1
       130: 3q^2+2q+1
       132: q^3+2q^2+2q+1
       133: 6q^2+2q+1
       134: 4q^2+2q+1
       135: 4q^2+2q+1
       136: 4q^2+2q+1
       137: q^3+8q^2+2q+1
       138: 4q^2+2q+1
       139: 6q^2+2q+1
       140: 4q^2+2q+1
       141: 3q^3+6q^2+2q+1
       142: 4q^2+2q+1
       143: q^3+8q^2+2q+1
       144: 4q^2+2q+1
       145: 6q^2+2q+1
       146: 3q^3+6q^2+2q+1
       147: 4q^2+2q+1
       148: 4q^2+2q+1
       149: 3q^3+6q^2+2q+1
       150: 3q^3+6q^2+2q+1
       152: 2q^3+4q^2+2q+1
       154: 2q^3+4q^2+2q+1
       156: 2q^3+4q^2+2q+1
       157: 6q^2+2q+1
       158: 6q^2+2q+1
       159: 2q^3+4q^2+2q+1
       160: 6q^2+2q+1
       161: 6q^2+2q+1
       162: 2q^3+4q^2+2q+1
       163: 6q^2+2q+1
       164: 6q^2+2q+1
       165: 2q^3+4q^2+2q+1
       166: 6q^2+2q+1
       167: 6q^2+2q+1
       168: 2q^3+4q^2+2q+1
       171: 2q^2+2q+1
       173: q^2
       174: 2q^2
       175: q^3+4q^2+2q+1
       176: q^2
       178: 2q^2+2q+1
       180: 3q^2+2q+1
       182: q^2+2q+1
       183: q^2
       184: 3q^2+2q+1
       185: 3q^2+2q+1
       186: q^2
       188: 2q^2+2q+1
       190: 2q^3+4q^2+2q+1
       191: q^3+5q^2+2q+1
       192: 3q^2
       193: q^2
       194: 3q^2+2q+1
       195: 3q^2+2q+1
       196: q^2
       198: 2q^2+2q+1
       199: 3q^2
       200: q^3+5q^2+2q+1
       201: q^2
       202: 3q^2+2q+1
       203: 3q^2+2q+1
       204: q^2
       206: 2q^2+2q+1
       207: 2q^2
       208: q^3+6q^2+2q+1
       210: 2q^3+4q^2+2q+1
       212: 2q^3+4q^2+2q+1
       214: 3q^2+2q+1
       216: 3q^2+2q+1
       218: q^3+2q^2+2q+1
       219: 4q^2+2q+1
       220: 6q^2+2q+1
       221: 4q^2+2q+1
       222: 4q^2+2q+1
       223: 2q^2+2q+1
       224: 4q^2+2q+1
       225: 2q^2+2q+1
       226: 4q^2+2q+1
       227: 6q^2+2q+1
       228: 4q^2+2q+1
       229: 4q^2+2q+1
       230: 4q^2+2q+1
       231: 4q^2+2q+1
       232: 6q^2+2q+1
       233: 4q^2+2q+1
       234: 4q^2+2q+1
       235: 4q^2+2q+1
       236: 4q^2+2q+1
       238: 3q^2+2q+1
       240: 3q^2+2q+1
       242: q^3+2q^2+2q+1
       243: 6q^2+2q+1
       244: 4q^2+2q+1
       245: 4q^2+2q+1
       246: 3q^3+6q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 6q^2+2q+1
       251: 6q^2+2q+1
       252: 2q^3+4q^2+2q+1
       253: 6q^2+2q+1
       254: 6q^2+2q+1
       255: 2q^3+4q^2+2q+1
       256: 6q^2+2q+1
       257: 6q^2+2q+1
       258: 2q^3+4q^2+2q+1
       261: q^2+2q+1
       265: 2q^2+2q+1
       270: 2q^2+2q+1
       272: 2q^2+2q+1
       275: q^2
       276: 2q^2
       277: q^3+4q^2+2q+1
       278: q^2
       280: 3q^2+2q+1
       282: 2q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       288: 2q^2+2q+1
       290: q^2+2q+1
       292: 2q+1
       293: q^2
       294: 3q^2+2q+1
       295: 3q^2+2q+1
       296: q^2
       298: 2q^2+2q+1
       299: q^2
       300: 3q^2+2q+1
       302: q^2+2q+1
       303: 3q^2+2q+1
       304: q^2
       306: 2q^2+2q+1
       307: q^2
       308: 3q^2+2q+1
       309: 3q^2+2q+1
       310: q^2
       312: q^2+2q+1
       314: 2q^2+2q+1
       316: 2q^2+2q+1
       318: 3q^2+2q+1
       319: q^2
       320: 3q^2+2q+1
       321: 3q^2+2q+1
       322: q^2
       324: 2q^2+2q+1
       326: 2q^3+4q^2+2q+1
       328: 3q^2+2q+1
       330: 3q^2+2q+1
       332: q^3+2q^2+2q+1
       333: 4q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       339: q^2+4q+1
       341: q^2+4q+1
       343: q^3+2q^2+2q+1
       344: 4q^2+2q+1
       345: 6q^2+2q+1
       346: 4q^2+2q+1
       347: 4q^2+2q+1
       348: 2q^2+2q+1
       349: 4q^2+2q+1
       350: 2q^2+2q+1
       351: q^2+4q+1
       352: 4q^2+2q+1
       353: 6q^2+2q+1
       354: 4q^2+2q+1
       355: 4q^2+2q+1
       356: 2q^2+2q+1
       357: 4q^2+2q+1
       358: 2q^2+2q+1
       359: q^2+4q+1
       361: 3q^2+2q+1
       363: 3q^2+2q+1
       365: q^3+2q^2+2q+1
       366: 4q^2+2q+1
       367: 6q^2+2q+1
       368: 4q^2+2q+1
       369: 4q^2+2q+1
       370: 4q^2+2q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: q^3+2q^2+2q+1
       374: 6q^2+2q+1
       375: 6q^2+2q+1
       376: 2q^3+4q^2+2q+1
       379: 2q+1
       383: q^2+2q+1
       387: 2q^2+2q+1
       392: q^2+2q+1
       395: 2q^2+2q+1
       398: q^2+2q+1
       402: 2q^2+2q+1
       408: 2q^2+2q+1
       410: 3q^2+2q+1
       412: 2q^2+2q+1
       414: 2q^2+2q+1
       416: q^2+2q+1
       418: 2q+1
       420: q^2+2q+1
       421: q^2+2q+1
       424: 2q+1
       426: 2q+1
       428: q^2+4q+1
       430: q^2+2q+1
       431: q^2+2q+1
       434: 2q+1
       436: q^2+2q+1
       437: q^2
       438: 3q^2+2q+1
       439: 3q^2+2q+1
       440: q^2
       442: 2q^2+2q+1
       443: q
       444: q^2+3q+1
       446: q^2+4q+1
       448: q^2+2q+1
       449: q^2+2q+1
       452: 2q+1
       453: q^2
       454: 3q^2+2q+1
       456: q^2+2q+1
       457: 3q^2+2q+1
       458: q^2
       460: 2q^2+2q+1
       461: q^2+3q+1
       462: q
       464: q^2+4q+1
       466: 3q^2+2q+1
       468: 2q^2+2q+1
       470: 2q^2+2q+1
       471: q^2
       472: 3q^2+2q+1
       473: 3q^2+2q+1
       474: q^2
       476: 2q^2+2q+1
       478: q^2+2q+1
       479: 2q
       480: q^2+2q+1
       481: 2q^2+2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: q^2+4q+1
       486: q^2+4q+1
       488: q^2+4q+1
       490: q^3+2q^2+2q+1
       491: 2q+1
       492: 4q^2+2q+1
       493: 2q^2+2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: q^2+4q+1
       497: 4q^2+2q+1
       498: 2q^2+2q+1
       499: 2q^2+2q+1
       500: 2q+1
       501: q^2+4q+1
       503: 3q^2+2q+1
       505: 3q^2+2q+1
       507: q^3+2q^2+2q+1
       508: 4q^2+2q+1
       509: 6q^2+2q+1
       510: 4q^2+2q+1
       511: 4q^2+2q+1
       512: 2q^2+2q+1
       513: 4q^2+2q+1
       514: 2q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       523: 2q+1
       527: q^2+2q+1
       531: 2q+1
       535: 2q+1
       540: q^2+2q+1
       544: 2q^2+2q+1
       546: q
       548: q^2+3q+1
       550: 2q+1
       554: q^2+2q+1
       558: 2q^2+2q+1
       562: q^2+3q+1
       564: q
       567: 2q^2+2q+1
       572: q^2+2q+1
       573: q
       575: q
       576: q^2+2q+1
       578: 2q
       581: q^2+2q+1
       584: 2q^2+2q+1
       586: 2q+1
       588: 2q+1
       590: q^2+2q+1
       591: q+1
       594: q+1
       595: q^2+2q+1
       598: 2q+1
       600: 2q+1
       602: q^2+4q+1
       604: q^2+2q+1
       606: 2q+1
       607: q^2+2q+1
       610: 2q+1
       612: q^2+2q+1
       614: 2q+1
       615: q
       616: q^2+3q+1
       618: q^2+4q+1
       620: q^2+2q+1
       621: q^2+2q+1
       624: 2q+1
       626: 2q+1
       628: q^2+2q+1
       630: 2q+1
       631: q^2+3q+1
       632: q
       634: q^2+4q+1
       636: 3q^2+2q+1
       638: 2q^2+2q+1
       640: 2q^2+2q+1
       642: q^2+2q+1
       643: q^2+2q+1
       646: 2q+1
       647: q^2
       648: 3q^2+2q+1
       649: 3q^2+2q+1
       650: q^2
       652: q^2+2q+1
       654: 2q^2+2q+1
       655: 2q
       656: q^2+2q+1
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q+1
       667: q^2+4q+1
       669: q^2+4q+1
       671: q^3+2q^2+2q+1
       672: q^2+4q+1
       673: 2q+1
       674: 2q+1
       675: 2q^2+2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: q^2+4q+1
       679: 2q+1
       680: 2q+1
       681: 2q^2+2q+1
       682: 2q^2+2q+1
       683: 2q+1
       684: q^2+4q+1
       685: 2q+1
       686: 4q^2+2q+1
       687: 2q^2+2q+1
       688: 2q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       694: q
       700: q^2+2q+1
       701: q
       707: 2q+1
       711: 2q+1
       714: q+1
       719: q+1
       724: 2q+1
       728: 2q+1
       732: q^2+2q+1
       734: q
       736: q^2+3q+1
       738: 2q+1
       742: 2q+1
       746: q^2+2q+1
       750: q^2+3q+1
       752: q
       755: 2q+1
       760: q^2+2q+1
       764: 2q^2+2q+1
       765: q
       767: q^2+2q+1
       768: q
       770: 2q
       773: q^2+2q+1
       776: q+1
       778: 2q+1
       780: q+1
       782: 2q+1
       784: 2q+1
       786: q+1
       787: q+1
       790: q^2+4q+1
       792: 1
       794: q+1
       796: 2q+1
       798: 2q+1
       800: 2q+1
       802: q^2+2q+1
       803: q+1
       806: q+1
       807: q^2+2q+1
       810: 2q+1
       812: 2q+1
       814: q^2+4q+1
       815: q
       816: q^2+3q+1
       817: q+1
       820: 2q+1
       822: 2q+1
       824: 2q+1
       826: q^2+2q+1
       827: q+1
       830: q+1
       831: q^2+2q+1
       834: 2q+1
       836: 2q+1
       838: q^2+4q+1
       839: q^2+3q+1
       840: q
       842: 2q^2+2q+1
       843: q
       844: q+1
       846: q^2+2q+1
       847: q^2+2q+1
       850: 2q+1
       852: 2q+1
       854: q^2+2q+1
       856: 2q+1
       857: 2q
       858: q^2+2q+1
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q+1
       869: 2q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 2q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 2q^2+2q+1
       878: 2q^2+2q+1
       879: 2q+1
       880: 2q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       885: q
       891: q^2+2q+1
       892: q
       898: 2q+1
       901: q+1
       907: q+1
       910: 1
       915: 2q+1
       919: q+1
       923: 2q+1
       925: q+1
       931: q+1
       933: q
       935: q^2+3q+1
       937: 2q+1
       941: q+1
       945: 2q+1
       949: q+1
       954: q+1
       957: q^2+3q+1
       959: q
       963: 2q+1
       966: q+1
       969: q
       972: q+1
       977: 2q+1
       981: q^2+2q+1
       983: 2q
       986: q^2+2q+1
       988: q
       990: q^2+2q+1
       991: q
       993: q+1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 2q+1
      1005: q+1
      1006: q+1
      1009: 1
      1011: 1
      1013: 1
      1015: 2q+1
      1017: q+1
      1019: 2q+1
      1021: q+1
      1023: 2q+1
      1025: 2q+1
      1027: q+1
      1028: q+1
      1031: 2q+1
      1032: q+1
      1035: 2q+1
      1037: q+1
      1039: 2q+1
      1041: q+1
      1043: 2q+1
      1044: q+1
      1046: q
      1047: q+1
      1049: 2q+1
      1051: 2q+1
      1053: q^2+2q+1
      1054: q+1
      1057: q+1
      1058: q^2+2q+1
      1061: 2q+1
      1063: 2q+1
      1065: 1
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: q+1
      1085: 2q+1
      1093: q+1
      1099: q
      1105: q^2+2q+1
      1106: q
      1111: q+1
      1115: 1
      1121: q+1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: q+1
      1151: 2q+1
      1153: q+1
      1159: q+1
      1161: 1
      1165: q+1
      1169: 2q+1
      1173: q+1
      1179: q+1
      1182: 1
      1187: 2q+1
      1189: q
      1192: q+1
      1196: q+1
      1201: 2q+1
      1203: q+1
      1209: q+1
      1211: q+1
      1213: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 2q+1
      1229: q+1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 2q+1
      1241: q+1
      1242: q+1
      1245: 2q+1
      1246: q+1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 2q+1
      1259: q+1
      1260: q+1
      1262: q
      1263: q+1
      1265: 2q+1
      1267: 2q+1
      1269: q+1
      1270: q+1
      1273: 2q+1
      1275: q+1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q+1
      1297: 1
      1309: q+1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: q+1
      1345: q+1
      1349: 1
      1355: q+1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: q+1
      1377: q+1
      1381: 1
      1387: q+1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1405: q
      1408: q+1
      1412: q+1
      1417: 2q+1
      1419: q+1
      1425: q+1
      1428: 1
      1434: 1
      1439: 1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1450: 1
      1453: q+1
      1455: 1
      1457: 1
      1459: q+1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 2q+1
      1473: q+1
      1475: 1
      1477: q+1
      1478: q+1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1496: 1
      1507: 1
      1520: 1
      1532: q+1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1604: q+1
      1608: 1
      1614: q+1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1652: 1
      1653: 1
      1656: 1
      1662: 1
      1663: 1
      1666: 1
      1668: q+1
      1670: 1
      1672: 1
      1674: 1
      1682: 1
      1693: 1
      1706: 1
      1717: 1
      1738: 1
      1748: 1
      1750: 1
      1755: 1
      1762: 1
      1768: 1
      1775: 1
      1780: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1805: 1
      1810: 1
      1828: 1
      1829: 1
      1832: 1
      1852: 1
      1865: 1
      1876: 1
      1933: 1
      1939: 1
      1942: 1
      1951: 1
      1996: 1

1997:    0: 4q^3+8q^2+2q+1
         1: 4q^3+8q^2+2q+1
         2: 4q^3+8q^2+2q+1
         3: 4q^3+8q^2+2q+1
         4: q^4+5q^3+6q^2+2q+1
         5: 4q^3+8q^2+2q+1
         6: q^4+5q^3+6q^2+2q+1
         7: q^4+5q^3+6q^2+2q+1
         8: 4q^3+8q^2+2q+1
         9: q^5+3q^4+4q^3+4q^2+2q+1
        10: 4q^3+8q^2+2q+1
        11: 4q^3+8q^2+2q+1
        12: q^4+5q^3+6q^2+2q+1
        13: 4q^3+8q^2+2q+1
        14: q^4+5q^3+6q^2+2q+1
        15: 4q^3+8q^2+2q+1
        16: q^3+8q^2+2q+1
        17: q^3+8q^2+2q+1
        18: q^4+4q^3+4q^2+2q+1
        19: 3q^3+6q^2+2q+1
        20: 3q^3+6q^2+2q+1
        21: 3q^3+6q^2+2q+1
        22: 4q^3+8q^2+2q+1
        23: 4q^3+8q^2+2q+1
        24: 4q^3+8q^2+2q+1
        25: 4q^3+8q^2+2q+1
        26: 4q^3+8q^2+2q+1
        27: 4q^3+8q^2+2q+1
        28: q^3+8q^2+2q+1
        29: 3q^3+6q^2+2q+1
        30: 3q^3+6q^2+2q+1
        31: 4q^3+8q^2+2q+1
        32: 4q^3+8q^2+2q+1
        33: q^3+8q^2+2q+1
        34: 4q^3+8q^2+2q+1
        35: 4q^3+8q^2+2q+1
        36: q^3+8q^2+2q+1
        37: 3q^3+6q^2+2q+1
        38: q^3+2q^2
        39: 3q^3+6q^2+2q+1
        40: q^3+2q^2
        41: 3q^3+6q^2+2q+1
        42: q^3+2q^2
        43: 4q^3+8q^2+2q+1
        44: q^4+5q^3+6q^2+2q+1
        45: 4q^3+8q^2+2q+1
        46: q^3+8q^2+2q+1
        47: q^3+8q^2+2q+1
        48: q^4+4q^3+4q^2+2q+1
        49: 6q^2+2q+1
        50: 6q^2+2q+1
        51: 2q^3+4q^2+2q+1
        52: 3q^3+6q^2+2q+1
        53: 3q^3+6q^2+2q+1
        54: 3q^3+6q^2+2q+1
        55: 3q^3+6q^2+2q+1
        56: 3q^3+6q^2+2q+1
        57: 3q^3+6q^2+2q+1
        58: 3q^2
        59: q^3+5q^2+2q+1
        60: 3q^2
        61: q^3+5q^2+2q+1
        62: 3q^3+6q^2+2q+1
        63: q^3+2q^2
        64: 3q^3+6q^2+2q+1
        65: q^3+2q^2
        66: q^3+6q^2+2q+1
        67: 2q^2
        68: q^3+8q^2+2q+1
        69: 4q^2+2q+1
        70: 3q^3+6q^2+2q+1
        71: 6q^2+2q+1
        72: 4q^2+2q+1
        73: 4q^2+2q+1
        74: 2q^3+4q^2+2q+1
        76: 2q^3+4q^2+2q+1
        78: 2q^3+4q^2+2q+1
        80: 4q^3+8q^2+2q+1
        81: q^3+8q^2+2q+1
        82: 3q^3+6q^2+2q+1
        83: 3q^3+6q^2+2q+1
        84: 4q^3+8q^2+2q+1
        85: q^3+8q^2+2q+1
        86: 3q^3+6q^2+2q+1
        87: 3q^3+6q^2+2q+1
        88: q^3+8q^2+2q+1
        89: q^3+8q^2+2q+1
        90: q^4+4q^3+4q^2+2q+1
        91: 6q^2+2q+1
        92: 6q^2+2q+1
        93: 2q^3+4q^2+2q+1
        94: 6q^2+2q+1
        95: 6q^2+2q+1
        96: 2q^3+4q^2+2q+1
        97: 6q^2+2q+1
        98: 6q^2+2q+1
        99: 2q^3+4q^2+2q+1
       100: 3q^3+6q^2+2q+1
       101: 3q^3+6q^2+2q+1
       102: 3q^3+6q^2+2q+1
       103: 2q^2
       104: q^2
       105: q^2
       106: q^3+4q^2+2q+1
       107: q^2
       108: 3q^2+2q+1
       109: q^2
       110: 3q^2+2q+1
       111: 2q^2+2q+1
       113: 2q^3+4q^2+2q+1
       115: 2q^3+4q^2+2q+1
       117: 3q^2
       118: q^3+5q^2+2q+1
       119: 3q^2
       120: q^3+5q^2+2q+1
       121: 3q^3+6q^2+2q+1
       122: q^3+2q^2
       123: q^3+6q^2+2q+1
       124: 2q^2
       125: q^3+8q^2+2q+1
       126: 4q^2+2q+1
       127: 3q^2+2q+1
       129: 3q^2+2q+1
       131: q^3+2q^2+2q+1
       133: 6q^2+2q+1
       134: 4q^2+2q+1
       135: 4q^2+2q+1
       136: 4q^2+2q+1
       137: q^3+8q^2+2q+1
       138: 4q^2+2q+1
       139: 6q^2+2q+1
       140: 4q^2+2q+1
       141: 3q^3+6q^2+2q+1
       142: 4q^2+2q+1
       143: q^3+8q^2+2q+1
       144: 4q^2+2q+1
       145: 6q^2+2q+1
       146: 3q^3+6q^2+2q+1
       147: 4q^2+2q+1
       148: 4q^2+2q+1
       149: 3q^3+6q^2+2q+1
       150: 3q^3+6q^2+2q+1
       151: 2q^3+4q^2+2q+1
       153: 2q^3+4q^2+2q+1
       155: 2q^3+4q^2+2q+1
       157: 6q^2+2q+1
       158: 6q^2+2q+1
       159: 2q^3+4q^2+2q+1
       160: 6q^2+2q+1
       161: 6q^2+2q+1
       162: 2q^3+4q^2+2q+1
       163: 6q^2+2q+1
       164: 6q^2+2q+1
       165: 2q^3+4q^2+2q+1
       166: 6q^2+2q+1
       167: 6q^2+2q+1
       168: 2q^3+4q^2+2q+1
       172: 2q^2+2q+1
       173: 2q^2
       174: q^2
       175: q^2
       176: q^3+4q^2+2q+1
       177: 2q^2+2q+1
       179: 3q^2+2q+1
       181: q^2+2q+1
       183: q^2
       184: 3q^2+2q+1
       185: q^2
       186: 3q^2+2q+1
       187: 2q^2+2q+1
       189: 2q^3+4q^2+2q+1
       191: 3q^2
       192: q^3+5q^2+2q+1
       193: q^2
       194: 3q^2+2q+1
       195: q^2
       196: 3q^2+2q+1
       197: 2q^2+2q+1
       199: 3q^2
       200: q^3+5q^2+2q+1
       201: q^2
       202: 3q^2+2q+1
       203: q^2
       204: 3q^2+2q+1
       205: 2q^2+2q+1
       207: q^3+6q^2+2q+1
       208: 2q^2
       209: 2q^3+4q^2+2q+1
       211: 2q^3+4q^2+2q+1
       213: 3q^2+2q+1
       215: 3q^2+2q+1
       217: q^3+2q^2+2q+1
       219: 4q^2+2q+1
       220: 6q^2+2q+1
       221: 4q^2+2q+1
       222: 4q^2+2q+1
       223: 2q^2+2q+1
       224: 4q^2+2q+1
       225: 2q^2+2q+1
       226: 4q^2+2q+1
       227: 6q^2+2q+1
       228: 4q^2+2q+1
       229: 4q^2+2q+1
       230: 4q^2+2q+1
       231: 4q^2+2q+1
       232: 6q^2+2q+1
       233: 4q^2+2q+1
       234: 4q^2+2q+1
       235: 4q^2+2q+1
       236: 4q^2+2q+1
       237: 3q^2+2q+1
       239: 3q^2+2q+1
       241: q^3+2q^2+2q+1
       243: 6q^2+2q+1
       244: 4q^2+2q+1
       245: 4q^2+2q+1
       246: 3q^3+6q^2+2q+1
       247: q^2+4q+1
       248: q^2+4q+1
       249: q^3+2q^2+2q+1
       250: 6q^2+2q+1
       251: 6q^2+2q+1
       252: 2q^3+4q^2+2q+1
       253: 6q^2+2q+1
       254: 6q^2+2q+1
       255: 2q^3+4q^2+2q+1
       256: 6q^2+2q+1
       257: 6q^2+2q+1
       258: 2q^3+4q^2+2q+1
       262: q^2+2q+1
       266: 2q^2+2q+1
       269: 2q^2+2q+1
       273: 2q^2+2q+1
       275: 2q^2
       276: q^2
       277: q^2
       278: q^3+4q^2+2q+1
       279: 3q^2+2q+1
       281: 2q^2+2q+1
       284: q^2+2q+1
       286: q^2+2q+1
       287: 2q^2+2q+1
       289: q^2+2q+1
       291: 2q+1
       293: q^2
       294: 3q^2+2q+1
       295: q^2
       296: 3q^2+2q+1
       297: 2q^2+2q+1
       299: q^2
       300: 3q^2+2q+1
       301: q^2+2q+1
       303: q^2
       304: 3q^2+2q+1
       305: 2q^2+2q+1
       307: q^2
       308: 3q^2+2q+1
       309: q^2
       310: 3q^2+2q+1
       311: q^2+2q+1
       313: 2q^2+2q+1
       315: 2q^2+2q+1
       317: 3q^2+2q+1
       319: q^2
       320: 3q^2+2q+1
       321: q^2
       322: 3q^2+2q+1
       323: 2q^2+2q+1
       325: 2q^3+4q^2+2q+1
       327: 3q^2+2q+1
       329: 3q^2+2q+1
       331: q^3+2q^2+2q+1
       333: 4q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: q^2+4q+1
       338: q^2+4q+1
       340: q^2+4q+1
       342: q^3+2q^2+2q+1
       344: 4q^2+2q+1
       345: 6q^2+2q+1
       346: 4q^2+2q+1
       347: 4q^2+2q+1
       348: 2q^2+2q+1
       349: 4q^2+2q+1
       350: 2q^2+2q+1
       351: q^2+4q+1
       352: 4q^2+2q+1
       353: 6q^2+2q+1
       354: 4q^2+2q+1
       355: 4q^2+2q+1
       356: 2q^2+2q+1
       357: 4q^2+2q+1
       358: 2q^2+2q+1
       359: q^2+4q+1
       360: 3q^2+2q+1
       362: 3q^2+2q+1
       364: q^3+2q^2+2q+1
       366: 4q^2+2q+1
       367: 6q^2+2q+1
       368: 4q^2+2q+1
       369: 4q^2+2q+1
       370: 4q^2+2q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: q^3+2q^2+2q+1
       374: 6q^2+2q+1
       375: 6q^2+2q+1
       376: 2q^3+4q^2+2q+1
       380: 2q+1
       384: q^2+2q+1
       388: 2q^2+2q+1
       391: q^2+2q+1
       396: 2q^2+2q+1
       399: q^2+2q+1
       404: 2q^2+2q+1
       406: 2q^2+2q+1
       409: 3q^2+2q+1
       411: 2q^2+2q+1
       413: 2q^2+2q+1
       415: q^2+2q+1
       417: 2q+1
       420: q^2+2q+1
       422: q^2+2q+1
       423: 2q+1
       425: 2q+1
       427: q^2+4q+1
       430: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       435: q^2+2q+1
       437: q^2
       438: 3q^2+2q+1
       439: q^2
       440: 3q^2+2q+1
       441: 2q^2+2q+1
       443: q
       444: q^2+3q+1
       445: q^2+4q+1
       448: q^2+2q+1
       450: q^2+2q+1
       451: 2q+1
       453: q^2
       454: 3q^2+2q+1
       455: q^2+2q+1
       457: q^2
       458: 3q^2+2q+1
       459: 2q^2+2q+1
       461: q
       462: q^2+3q+1
       463: q^2+4q+1
       465: 3q^2+2q+1
       467: 2q^2+2q+1
       469: 2q^2+2q+1
       471: q^2
       472: 3q^2+2q+1
       473: q^2
       474: 3q^2+2q+1
       475: 2q^2+2q+1
       477: q^2+2q+1
       479: q^2+2q+1
       480: 2q
       481: 2q^2+2q+1
       482: 2q^2+2q+1
       483: 2q+1
       484: q^2+4q+1
       485: q^2+4q+1
       487: q^2+4q+1
       489: q^3+2q^2+2q+1
       491: 2q+1
       492: 4q^2+2q+1
       493: 2q^2+2q+1
       494: 2q^2+2q+1
       495: 2q+1
       496: q^2+4q+1
       497: 4q^2+2q+1
       498: 2q^2+2q+1
       499: 2q^2+2q+1
       500: 2q+1
       501: q^2+4q+1
       502: 3q^2+2q+1
       504: 3q^2+2q+1
       506: q^3+2q^2+2q+1
       508: 4q^2+2q+1
       509: 6q^2+2q+1
       510: 4q^2+2q+1
       511: 4q^2+2q+1
       512: 2q^2+2q+1
       513: 4q^2+2q+1
       514: 2q^2+2q+1
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q+1
       519: q^2+4q+1
       520: q^3+2q^2+2q+1
       524: 2q+1
       528: q^2+2q+1
       532: 2q+1
       536: 2q+1
       539: q^2+2q+1
       543: 2q^2+2q+1
       545: q
       547: q^2+3q+1
       552: 2q+1
       555: q^2+2q+1
       559: 2q^2+2q+1
       561: q
       563: q^2+3q+1
       568: 2q^2+2q+1
       570: q^2+2q+1
       574: q
       575: q^2+2q+1
       576: q
       577: q^2+2q+1
       580: 2q
       583: 2q^2+2q+1
       585: 2q+1
       587: 2q+1
       590: q^2+2q+1
       592: q+1
       594: q+1
       596: q^2+2q+1
       597: 2q+1
       599: 2q+1
       601: q^2+4q+1
       604: q^2+2q+1
       605: 2q+1
       608: q^2+2q+1
       609: 2q+1
       611: q^2+2q+1
       613: 2q+1
       615: q
       616: q^2+3q+1
       617: q^2+4q+1
       620: q^2+2q+1
       622: q^2+2q+1
       623: 2q+1
       625: 2q+1
       627: q^2+2q+1
       629: 2q+1
       631: q
       632: q^2+3q+1
       633: q^2+4q+1
       635: 3q^2+2q+1
       637: 2q^2+2q+1
       639: 2q^2+2q+1
       642: q^2+2q+1
       644: q^2+2q+1
       645: 2q+1
       647: q^2
       648: 3q^2+2q+1
       649: q^2
       650: 3q^2+2q+1
       651: q^2+2q+1
       653: 2q^2+2q+1
       655: q^2+2q+1
       656: 2q
       657: q+1
       658: 2q+1
       660: 2q+1
       662: q^2+q+1
       664: q+1
       665: 2q+1
       666: q^2+4q+1
       668: q^2+4q+1
       670: q^3+2q^2+2q+1
       672: q^2+4q+1
       673: 2q+1
       674: 2q+1
       675: 2q^2+2q+1
       676: 2q^2+2q+1
       677: 2q+1
       678: q^2+4q+1
       679: 2q+1
       680: 2q+1
       681: 2q^2+2q+1
       682: 2q^2+2q+1
       683: 2q+1
       684: q^2+4q+1
       685: 2q+1
       686: 4q^2+2q+1
       687: 2q^2+2q+1
       688: 2q^2+2q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       696: q
       697: q^2+2q+1
       698: q
       708: 2q+1
       712: 2q+1
       716: q+1
       720: q+1
       723: 2q+1
       727: 2q+1
       731: q^2+2q+1
       733: q
       735: q^2+3q+1
       739: 2q+1
       743: 2q+1
       747: q^2+2q+1
       749: q
       751: q^2+3q+1
       756: 2q+1
       758: q^2+2q+1
       762: 2q^2+2q+1
       766: q
       767: q
       768: q^2+2q+1
       769: q^2+2q+1
       772: 2q
       775: q+1
       777: 2q+1
       779: q+1
       781: 2q+1
       783: 2q+1
       786: q+1
       788: q+1
       789: q^2+4q+1
       791: 1
       794: q+1
       795: 2q+1
       797: 2q+1
       799: 2q+1
       802: q^2+2q+1
       804: q+1
       806: q+1
       808: q^2+2q+1
       809: 2q+1
       811: 2q+1
       813: q^2+4q+1
       815: q
       816: q^2+3q+1
       818: q+1
       819: 2q+1
       821: 2q+1
       823: 2q+1
       826: q^2+2q+1
       828: q+1
       830: q+1
       832: q^2+2q+1
       833: 2q+1
       835: 2q+1
       837: q^2+4q+1
       839: q
       840: q^2+3q+1
       841: 2q^2+2q+1
       843: q+1
       844: q
       846: q^2+2q+1
       848: q^2+2q+1
       849: 2q+1
       851: 2q+1
       853: q^2+2q+1
       855: 2q+1
       857: q^2+2q+1
       858: 2q
       859: 2q+1
       861: 2q+1
       863: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q+1
       869: 2q+1
       870: q+1
       871: 2q+1
       872: 2q+1
       873: 2q+1
       874: q+1
       875: 2q+1
       876: 2q+1
       877: 2q^2+2q+1
       878: 2q^2+2q+1
       879: 2q+1
       880: 2q+1
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       887: q
       888: q
       889: q^2+2q+1
       899: 2q+1
       902: q+1
       906: q+1
       911: 1
       914: 2q+1
       918: q+1
       922: 2q+1
       927: q+1
       930: q+1
       932: q
       934: q^2+3q+1
       938: 2q+1
       942: q+1
       946: 2q+1
       950: q+1
       955: q+1
       956: q
       958: q^2+3q+1
       961: 2q+1
       967: q+1
       968: q+1
       971: q
       975: 2q+1
       979: q^2+2q+1
       982: q^2+2q+1
       985: 2q
       989: q
       990: q
       991: q^2+2q+1
       992: q+1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 2q+1
      1005: q+1
      1007: q+1
      1008: 1
      1010: 1
      1012: 1
      1014: 2q+1
      1017: q+1
      1018: 2q+1
      1020: q+1
      1022: 2q+1
      1024: 2q+1
      1027: q+1
      1029: q+1
      1030: 2q+1
      1033: q+1
      1034: 2q+1
      1036: q+1
      1038: 2q+1
      1041: q+1
      1042: 2q+1
      1045: q+1
      1046: q+1
      1047: q
      1048: 2q+1
      1050: 2q+1
      1053: q^2+2q+1
      1055: q+1
      1057: q+1
      1059: q^2+2q+1
      1060: 2q+1
      1062: 2q+1
      1064: 1
      1066: 2q+1
      1068: 2q+1
      1070: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q+1
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: q+1
      1085: 2q+1
      1091: q+1
      1101: q
      1102: q^2+2q+1
      1103: q
      1112: q+1
      1116: 1
      1120: q+1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: q+1
      1150: 2q+1
      1154: q+1
      1158: q+1
      1163: 1
      1166: q+1
      1170: 2q+1
      1174: q+1
      1178: q+1
      1183: 1
      1185: 2q+1
      1188: q+1
      1191: q
      1197: q+1
      1199: 2q+1
      1204: q+1
      1208: q+1
      1210: q+1
      1212: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 2q+1
      1229: q+1
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 2q+1
      1241: q+1
      1243: q+1
      1244: 2q+1
      1247: q+1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 2q+1
      1259: q+1
      1261: q+1
      1262: q+1
      1263: q
      1264: 2q+1
      1266: 2q+1
      1269: q+1
      1271: q+1
      1272: 2q+1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q+1
      1295: 1
      1307: q+1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: q+1
      1346: q+1
      1350: 1
      1354: q+1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: q+1
      1378: q+1
      1382: 1
      1386: q+1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: q+1
      1407: q
      1413: q+1
      1415: 2q+1
      1420: q+1
      1424: q+1
      1429: 1
      1430: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1451: 1
      1452: q+1
      1455: 1
      1456: 1
      1458: q+1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 2q+1
      1472: q+1
      1474: 1
      1477: q+1
      1479: q+1
      1480: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1494: 1
      1506: 1
      1518: 1
      1530: q+1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: q+1
      1609: 1
      1613: q+1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1643: 1
      1646: 1
      1648: 1
      1651: 1
      1654: 1
      1656: 1
      1661: 1
      1664: 1
      1666: 1
      1667: q+1
      1669: 1
      1671: 1
      1674: 1
      1680: 1
      1692: 1
      1704: 1
      1718: 1
      1739: 1
      1747: 1
      1752: 1
      1754: 1
      1763: 1
      1767: 1
      1776: 1
      1778: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1801: 1
      1808: 1
      1827: 1
      1830: 1
      1832: 1
      1851: 1
      1863: 1
      1877: 1
      1934: 1
      1938: 1
      1943: 1
      1949: 1
      1997: 1

1998:    0: 6q^4+8q^3+4q^2+3q
         1: 6q^4+8q^3+4q^2+3q
         2: 6q^4+8q^3+4q^2+3q
         3: 6q^4+8q^3+4q^2+3q
         4: 2q^5+7q^4+6q^3+3q^2+3q
         5: 6q^4+8q^3+4q^2+3q
         6: 2q^5+7q^4+6q^3+3q^2+3q
         7: 2q^5+7q^4+6q^3+3q^2+3q
         8: 6q^4+8q^3+4q^2+3q
         9: 2q^6+3q^5+4q^4+4q^3+3q^2+2q
        10: 6q^4+8q^3+4q^2+3q
        11: 6q^4+8q^3+4q^2+3q
        12: 2q^5+7q^4+6q^3+3q^2+3q
        13: 6q^4+8q^3+4q^2+3q
        14: 2q^5+7q^4+6q^3+3q^2+3q
        15: 6q^4+8q^3+4q^2+3q
        16: q^4+8q^3+3q^2+3q
        17: q^4+8q^3+3q^2+3q
        18: q^5+4q^4+3q^3+3q^2+2q
        19: 4q^4+5q^3+3q^2+3q
        20: 4q^4+5q^3+3q^2+3q
        21: 4q^4+5q^3+3q^2+3q
        22: 6q^4+8q^3+4q^2+3q
        23: 6q^4+8q^3+4q^2+3q
        24: 6q^4+8q^3+4q^2+3q
        25: 6q^4+8q^3+4q^2+3q
        26: 6q^4+8q^3+4q^2+3q
        27: 6q^4+8q^3+4q^2+3q
        28: q^4+8q^3+3q^2+3q
        29: 4q^4+5q^3+3q^2+3q
        30: 4q^4+5q^3+3q^2+3q
        31: 6q^4+8q^3+4q^2+3q
        32: 6q^4+8q^3+4q^2+3q
        33: q^4+8q^3+3q^2+3q
        34: 6q^4+8q^3+4q^2+3q
        35: 6q^4+8q^3+4q^2+3q
        36: q^4+8q^3+3q^2+3q
        37: 3q^4+4q^3+q^2+q
        38: 3q^4+4q^3+3q^2+2q
        39: 3q^4+4q^3+q^2+q
        40: 3q^4+4q^3+3q^2+2q
        41: 3q^4+4q^3+q^2+q
        42: 3q^4+4q^3+3q^2+2q
        43: 6q^4+8q^3+4q^2+3q
        44: 2q^5+7q^4+6q^3+3q^2+3q
        45: 6q^4+8q^3+4q^2+3q
        46: q^4+8q^3+3q^2+3q
        47: q^4+8q^3+3q^2+3q
        48: q^5+4q^4+3q^3+3q^2+2q
        49: 5q^3+2q^2+3q
        50: 5q^3+2q^2+3q
        51: 2q^4+2q^3+3q^2+2q
        52: 4q^4+5q^3+3q^2+3q
        53: 4q^4+5q^3+3q^2+3q
        54: 4q^4+5q^3+3q^2+3q
        55: 4q^4+5q^3+3q^2+3q
        56: 4q^4+5q^3+3q^2+3q
        57: 4q^4+5q^3+3q^2+3q
        58: 4q^3+q^2+q
        59: q^4+4q^3+2q^2+2q
        60: 4q^3+q^2+q
        61: q^4+4q^3+2q^2+2q
        62: 3q^4+4q^3+q^2+q
        63: 3q^4+4q^3+3q^2+2q
        64: 3q^4+4q^3+q^2+q
        65: 3q^4+4q^3+3q^2+2q
        66: q^4+4q^3+q^2+q
        67: 4q^3+2q^2+2q
        68: q^4+8q^3+3q^2+3q
        69: 2q^3+2q^2+2q
        70: 4q^4+5q^3+3q^2+3q
        71: 5q^3+2q^2+3q
        72: 3q^3+q^2+3q
        73: 3q^3+q^2+3q
        74: q^4+q^3+q
        75: q^4+q^3+2q^2+2q
        76: q^4+q^3+q
        77: q^4+q^3+2q^2+2q
        78: q^4+q^3+q
        79: q^4+q^3+2q^2+2q
        80: 6q^4+8q^3+4q^2+3q
        81: q^4+8q^3+3q^2+3q
        82: 4q^4+5q^3+3q^2+3q
        83: 4q^4+5q^3+3q^2+3q
        84: 6q^4+8q^3+4q^2+3q
        85: q^4+8q^3+3q^2+3q
        86: 4q^4+5q^3+3q^2+3q
        87: 4q^4+5q^3+3q^2+3q
        88: q^4+8q^3+3q^2+3q
        89: q^4+8q^3+3q^2+3q
        90: q^5+4q^4+3q^3+3q^2+2q
        91: 5q^3+2q^2+3q
        92: 5q^3+2q^2+3q
        93: 2q^4+2q^3+3q^2+2q
        94: 5q^3+2q^2+3q
        95: 5q^3+2q^2+3q
        96: 2q^4+2q^3+3q^2+2q
        97: 5q^3+2q^2+3q
        98: 5q^3+2q^2+3q
        99: 2q^4+2q^3+3q^2+2q
       100: 4q^4+5q^3+3q^2+3q
       101: 4q^4+5q^3+3q^2+3q
       102: 4q^4+5q^3+3q^2+3q
       103: 2q^3
       104: 2q^3+q^2+q
       105: 2q^3+q^2+q
       106: q^4+2q^3+q^2+q
       107: q^3+q
       108: 2q^3+q^2+2q
       109: q^3+q
       110: 2q^3+q^2+2q
       111: q^3+q
       112: 2q
       113: q^4+q^3+q
       114: q^4+q^3+2q^2+2q
       115: q^4+q^3+q
       116: q^4+q^3+2q^2+2q
       117: 4q^3+q^2+q
       118: q^4+4q^3+2q^2+2q
       119: 4q^3+q^2+q
       120: q^4+4q^3+2q^2+2q
       121: 3q^4+4q^3+q^2+q
       122: 3q^4+4q^3+3q^2+2q
       123: q^4+4q^3+q^2+q
       124: 4q^3+2q^2+2q
       125: q^4+8q^3+3q^2+3q
       126: 2q^3+2q^2+2q
       128: q^3+q^2+2q
       130: q^3+q^2+2q
       132: 2q^2+q
       133: 5q^3+2q^2+3q
       134: 2q^3+2q^2+2q
       135: 3q^3+q^2+3q
       136: 3q^3+q^2+3q
       137: q^4+8q^3+3q^2+3q
       138: 2q^3+2q^2+2q
       139: 5q^3+2q^2+3q
       140: 3q^3+q^2+3q
       141: 4q^4+5q^3+3q^2+3q
       142: 3q^3+q^2+3q
       143: q^4+8q^3+3q^2+3q
       144: 2q^3+2q^2+2q
       145: 5q^3+2q^2+3q
       146: 4q^4+5q^3+3q^2+3q
       147: 3q^3+q^2+3q
       148: 3q^3+q^2+3q
       149: 4q^4+5q^3+3q^2+3q
       150: 4q^4+5q^3+3q^2+3q
       151: q^4+q^3+q
       152: q^4+q^3+2q^2+2q
       153: q^4+q^3+q
       154: q^4+q^3+2q^2+2q
       155: q^4+q^3+q
       156: q^4+q^3+2q^2+2q
       157: 5q^3+2q^2+3q
       158: 5q^3+2q^2+3q
       159: 2q^4+2q^3+3q^2+2q
       160: 5q^3+2q^2+3q
       161: 5q^3+2q^2+3q
       162: 2q^4+2q^3+3q^2+2q
       163: 5q^3+2q^2+3q
       164: 5q^3+2q^2+3q
       165: 2q^4+2q^3+3q^2+2q
       166: 5q^3+2q^2+3q
       167: 5q^3+2q^2+3q
       168: 2q^4+2q^3+3q^2+2q
       170: q
       171: q
       172: q^3+q
       173: 2q^3
       174: 2q^3+q^2+q
       175: 2q^3+q^2+q
       176: q^4+2q^3+q^2+q
       178: q^2+q
       180: q^3+q^2+2q
       182: 2q
       183: q^3+q
       184: 2q^3+q^2+2q
       185: q^3+q
       186: 2q^3+q^2+2q
       187: q^3+q
       188: 2q
       189: q^4+q^3+q
       190: q^4+q^3+2q^2+2q
       191: 4q^3+q^2+q
       192: q^4+4q^3+2q^2+2q
       193: q^3+q
       194: 2q^3+q^2+2q
       195: q^3+q
       196: 2q^3+q^2+2q
       197: q^3+q
       198: 2q
       199: 4q^3+q^2+q
       200: q^4+4q^3+2q^2+2q
       201: q^3+q
       202: 2q^3+q^2+2q
       203: q^3+q
       204: 2q^3+q^2+2q
       205: q^3+q
       206: 2q
       207: q^4+4q^3+q^2+q
       208: 4q^3+2q^2+2q
       209: q^4+q^3+q
       210: q^4+q^3+2q^2+2q
       211: q^4+q^3+q
       212: q^4+q^3+2q^2+2q
       214: q^3+q^2+2q
       216: q^3+q^2+2q
       218: 2q^2+q
       219: 2q^3+2q^2+2q
       220: 5q^3+2q^2+3q
       221: 2q^3+2q^2+2q
       222: 3q^3+q^2+3q
       223: q^3+q^2+2q
       224: 3q^3+q^2+3q
       225: q^3+q^2+2q
       226: 2q^3+2q^2+2q
       227: 5q^3+2q^2+3q
       228: 2q^3+2q^2+2q
       229: 3q^3+q^2+3q
       230: 3q^3+q^2+3q
       231: 2q^3+2q^2+2q
       232: 5q^3+2q^2+3q
       233: 2q^3+2q^2+2q
       234: 3q^3+q^2+3q
       235: 3q^3+q^2+3q
       236: 2q^3+2q^2+2q
       238: q^3+q^2+2q
       240: q^3+q^2+2q
       242: 2q^2+q
       243: 5q^3+2q^2+3q
       244: 3q^3+q^2+3q
       245: 3q^3+q^2+3q
       246: 4q^4+5q^3+3q^2+3q
       247: q^2+4q
       248: q^2+4q
       249: q^4+2q^2+2q
       250: 5q^3+2q^2+3q
       251: 5q^3+2q^2+3q
       252: 2q^4+2q^3+3q^2+2q
       253: 5q^3+2q^2+3q
       254: 5q^3+2q^2+3q
       255: 2q^4+2q^3+3q^2+2q
       256: 5q^3+2q^2+3q
       257: 5q^3+2q^2+3q
       258: 2q^4+2q^3+3q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q^3+q
       268: q
       269: q^3+q
       270: q
       272: q
       273: q^3+q
       274: q
       275: 2q^3
       276: 2q^3+q^2+q
       277: 2q^3+q^2+q
       278: q^4+2q^3+q^2+q
       280: q^3+q^2+2q
       282: q^2+q
       284: q^2+q
       286: q^2+q
       288: q^2+q
       290: 2q
       292: q
       293: q^3+q
       294: 2q^3+q^2+2q
       295: q^3+q
       296: 2q^3+q^2+2q
       297: q^3+q
       298: 2q
       299: q^3+q
       300: 2q^3+q^2+2q
       302: 2q
       303: q^3+q
       304: 2q^3+q^2+2q
       305: q^3+q
       306: 2q
       307: q^3+q
       308: 2q^3+q^2+2q
       309: q^3+q
       310: 2q^3+q^2+2q
       312: 2q
       313: q^3+q
       314: 2q
       316: q^2+q
       318: q^3+q^2+2q
       319: q^3+q
       320: 2q^3+q^2+2q
       321: q^3+q
       322: 2q^3+q^2+2q
       323: q^3+q
       324: 2q
       325: q^4+q^3+q
       326: q^4+q^3+2q^2+2q
       328: q^3+q^2+2q
       330: q^3+q^2+2q
       332: 2q^2+q
       333: 2q^3+2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: 2q
       337: q^2+4q
       339: q^2+3q
       341: q^2+3q
       343: 2q^2+q
       344: 2q^3+2q^2+2q
       345: 5q^3+2q^2+3q
       346: 2q^3+2q^2+2q
       347: 3q^3+q^2+3q
       348: q^3+q^2+2q
       349: 3q^3+q^2+3q
       350: q^3+q^2+2q
       351: q^2+4q
       352: 2q^3+2q^2+2q
       353: 5q^3+2q^2+3q
       354: 2q^3+2q^2+2q
       355: 3q^3+q^2+3q
       356: q^3+q^2+2q
       357: 3q^3+q^2+3q
       358: q^3+q^2+2q
       359: q^2+4q
       361: q^3+q^2+2q
       363: q^3+q^2+2q
       365: 2q^2+q
       366: 2q^3+2q^2+2q
       367: 5q^3+2q^2+3q
       368: 2q^3+2q^2+2q
       369: 3q^3+q^2+3q
       370: 3q^3+q^2+3q
       371: q^2+4q
       372: q^2+4q
       373: q^4+2q^2+2q
       374: 5q^3+2q^2+3q
       375: 5q^3+2q^2+3q
       376: 2q^4+2q^3+3q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q^3+q
       390: q
       392: q
       394: q
       395: q
       396: q^3+q
       398: q
       400: q
       402: q
       403: q
       404: q^3+q
       406: q^3+q
       407: q
       408: q
       410: q^3+q^2+2q
       412: q^2+q
       414: q^2+q
       416: 2q
       418: q
       420: q^2+q
       422: q^2+q
       424: q
       426: q
       428: q^2+3q
       430: q^2+q
       432: q^2+q
       434: q
       436: 2q
       437: q^3+q
       438: 2q^3+q^2+2q
       439: q^3+q
       440: 2q^3+q^2+2q
       441: q^3+q
       442: 2q
       443: q
       444: q^2+3q
       446: q^2+3q
       448: q^2+q
       450: q^2+q
       452: q
       453: q^3+q
       454: 2q^3+q^2+2q
       456: 2q
       457: q^3+q
       458: 2q^3+q^2+2q
       459: q^3+q
       460: 2q
       461: q
       462: q^2+3q
       464: q^2+3q
       466: q^3+q^2+2q
       468: q^2+q
       470: q^2+q
       471: q^3+q
       472: 2q^3+q^2+2q
       473: q^3+q
       474: 2q^3+q^2+2q
       475: q^3+q
       476: 2q
       478: 2q
       479: q^2+2q
       480: 2q
       481: q^3+q^2+2q
       482: q^3+q^2+2q
       483: 2q
       484: q^2+4q
       486: q^2+3q
       488: q^2+3q
       490: 2q^2+q
       491: 2q
       492: 2q^3+2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: 2q
       496: q^2+4q
       497: 2q^3+2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: 2q
       501: q^2+4q
       503: q^3+q^2+2q
       505: q^3+q^2+2q
       507: 2q^2+q
       508: 2q^3+2q^2+2q
       509: 5q^3+2q^2+3q
       510: 2q^3+2q^2+2q
       511: 3q^3+q^2+3q
       512: q^3+q^2+2q
       513: 3q^3+q^2+3q
       514: q^3+q^2+2q
       515: 2q+1
       516: 2q+1
       517: q^2+q+1
       518: q^2+4q
       519: q^2+4q
       520: q^4+2q^2+2q
       526: q
       527: q
       538: q
       540: q
       542: q
       543: q^3+q
       544: q
       546: q
       548: q^2+2q
       554: q
       556: q
       558: q
       559: q^3+q
       560: q
       562: q
       564: q^2+2q
       566: q
       567: q
       568: q^3+q
       571: q
       572: q
       574: q
       575: q^2+2q
       576: q
       578: q^2+q
       581: 2q
       584: q^2+q
       586: q
       588: q
       590: q^2+q
       592: q
       594: q
       596: q^2+q
       598: q
       600: q
       602: q^2+3q
       604: q^2+q
       606: q
       608: q^2+q
       610: q
       612: 2q
       614: q
       615: q
       616: q^2+3q
       618: q^2+3q
       620: q^2+q
       622: q^2+q
       624: q
       626: q
       628: 2q
       630: q
       631: q
       632: q^2+3q
       634: q^2+3q
       636: q^3+q^2+2q
       638: q^2+q
       640: q^2+q
       642: q^2+q
       644: q^2+q
       646: q
       647: q^3+q
       648: 2q^3+q^2+2q
       649: q^3+q
       650: 2q^3+q^2+2q
       652: 2q
       653: q^3+q
       654: 2q
       655: q^2+2q
       656: 2q
       657: q+1
       659: 2q+1
       661: 2q+1
       663: q^2+q+1
       664: q+1
       665: 2q
       667: q^2+3q
       669: q^2+3q
       671: 2q^2+q
       672: q^2+4q
       673: 2q
       674: 2q+1
       675: q^3+q^2+2q
       676: q^3+q^2+2q
       677: 2q
       678: q^2+4q
       679: 2q
       680: 2q+1
       681: q^3+q^2+2q
       682: q^3+q^2+2q
       683: 2q
       684: q^2+4q
       685: 2q
       686: 2q^3+2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: 2q
       690: 2q+1
       691: 2q+1
       692: q^2+q+1
       699: q
       700: q
       701: q^2+q
       730: q
       732: q
       734: q
       736: q^2+2q
       746: q
       748: q
       750: q
       752: q^2+2q
       759: q
       760: q
       762: q^3+q
       763: q
       764: q
       766: q
       767: q
       768: q^2+2q
       770: q^2+q
       773: 2q
       776: q+1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: q^2+3q
       794: q+1
       796: 2q+1
       798: q
       800: q
       802: q^2+q
       804: q
       806: q
       808: q^2+q
       810: q
       812: q
       814: q^2+3q
       815: q
       816: q^2+3q
       818: q+1
       820: 2q+1
       822: q
       824: q
       826: q^2+q
       828: q
       830: q
       832: q^2+q
       834: q
       836: q
       838: q^2+3q
       839: q
       840: q^2+3q
       842: q^2+q
       843: q+1
       844: q
       846: q^2+q
       848: q^2+q
       850: q
       852: q
       854: 2q
       856: q
       857: q^2+2q
       858: 2q
       860: 2q+1
       862: 2q+1
       864: q^2+q+1
       865: q+1
       866: 1
       867: q+1
       868: 2q
       869: 2q+1
       870: q+1
       871: 2q
       872: 2q
       873: 2q+1
       874: q+1
       875: 2q
       876: 2q
       877: q^3+q^2+2q
       878: q^3+q^2+2q
       879: 2q
       880: 2q
       881: 2q+1
       882: 2q+1
       883: q^2+q+1
       890: q
       891: q
       892: q^2+q
       919: q+1
       933: q
       935: q^2+2q
       943: q+1
       957: q
       959: q^2+2q
       967: q+1
       969: q+1
       972: q
       980: q
       981: q
       983: q^2+q
       986: 2q
       989: q
       990: q
       991: q^2+2q
       993: q+1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1012: 1
      1015: 2q+1
      1017: q+1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: 2q+1
      1033: q+1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: q+1
      1047: q
      1049: q
      1051: q
      1053: q^2+q
      1055: q
      1057: q
      1059: q^2+q
      1061: q
      1063: q
      1067: 2q+1
      1069: 2q+1
      1071: q^2+q+1
      1072: q+1
      1073: q+1
      1074: 1
      1075: 2q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: 2q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1094: q+1
      1104: q
      1105: q
      1106: q^2+q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1147: q+1
      1167: q+1
      1189: q+1
      1192: q
      1197: q+1
      1211: q+1
      1213: q+1
      1215: 1
      1217: 1
      1219: 1
      1224: 1
      1227: 2q+1
      1229: q+1
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1245: 2q+1
      1247: q+1
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1262: q+1
      1263: q
      1265: q
      1267: q
      1269: q
      1271: q
      1273: q
      1275: q+1
      1280: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1298: 1
      1310: q+1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1343: q+1
      1351: 1
      1359: 1
      1367: 1
      1375: q+1
      1383: 1
      1391: 1
      1399: 1
      1405: q+1
      1408: q
      1413: q+1
      1431: 1
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1449: 1
      1451: 1
      1453: q+1
      1455: 1
      1457: 1
      1459: q+1
      1461: 1
      1463: 1
      1465: 1
      1467: 1
      1469: 1
      1471: q
      1473: q+1
      1477: q
      1479: q
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1497: 1
      1509: 1
      1521: 1
      1533: q+1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1566: 1
      1570: 1
      1578: 1
      1586: 1
      1590: 1
      1598: 1
      1610: 1
      1618: 1
      1626: 1
      1632: 1
      1644: 1
      1646: 1
      1648: 1
      1652: 1
      1654: 1
      1656: 1
      1662: 1
      1664: 1
      1666: 1
      1668: q+1
      1669: 1
      1674: 1
      1683: 1
      1695: 1
      1707: 1
      1720: 1
      1740: 1
      1748: 1
      1752: 1
      1764: 1
      1768: 1
      1776: 1
      1788: 1
      1792: 1
      1800: 1
      1802: 1
      1828: 1
      1830: 1
      1832: 1
      1854: 1
      1866: 1
      1879: 1
      1935: 1
      1939: 1
      1943: 1
      1998: 1

1999:    0: q^5+2q^4+q
         1: q^6+q^5+2q^4+q
         2: q^5+2q^4+q
         3: q^6+q^5+2q^4+q
         4: q^5+2q^4+q
         5: q^5+2q^4+q
         6: q^4+q
         7: q^5+2q^4+q
         8: q^5+2q^4+q
         9: q^6+2q^5+2q^4+q
        10: q^5+q^4+q
        11: q^5+q^4+q
        12: q^4+q
        13: q^5+2q^4+q
        14: q^5+2q^4+q
        15: q^5+2q^4+q
        16: q^5+q^4+q
        17: q^5+q^4+q
        18: q^5+2q^4+q
        19: 2q^4+q
        20: q^4+q
        21: 2q^4+q
        22: q^5+2q^4+q
        23: q^6+q^5+2q^4+q
        24: q^5+2q^4+q
        25: q^5+2q^4+q
        26: q^6+q^5+2q^4+q
        27: q^5+2q^4+q
        28: q^5+q
        29: q^4+q
        30: 2q^4+q
        31: q^5+q^4+q
        32: q^5+2q^4+q
        33: q^5+q^4+q
        34: q^5+q^4+q
        35: q^5+2q^4+q
        36: q^5+q^4+q
        37: q^5+2q^4+q
        39: q^6+q^5+2q^4+q
        41: q^5+2q^4+q
        43: q^5+q^4+q
        44: q^4+q
        45: q^5+q^4+q
        46: q^5+q^4+q
        47: q^5+q^4+q
        48: q^5+2q^4+q
        49: q^4+q
        50: q
        51: 2q^4+q
        52: 2q^4+q
        53: q^4+q
        54: 2q^4+q
        55: 2q^4+q
        56: q^4+q
        57: 2q^4+q
        59: q^5+q
        61: q^5+q
        62: q^5+q^4+q
        64: q^5+2q^4+q
        66: q^5+q^4+q
        68: q^5+q
        69: q^4+q
        70: q^4+q
        71: q
        72: q
        73: q
        74: 2q^4+q
        76: q^4+q
        78: 2q^4+q
        80: q^5+q^4+q
        81: q^5+q^4+q
        82: q^4+q
        83: 2q^4+q
        84: q^5+q^4+q
        85: q^5+q^4+q
        86: q^4+q
        87: 2q^4+q
        88: q
        89: q
        90: q^4+q
        91: q^4+q
        92: q
        93: 2q^4+q
        94: q^4+q
        95: q
        96: 2q^4+q
        97: q^4+q
        98: q
        99: 2q^4+q
       100: 2q^4+q
       101: q^4+q
       102: 2q^4+q
       106: q^5+q
       108: q
       110: q
       111: q
       113: q^4+q
       115: 2q^4+q
       118: q^5+q
       120: q^5+q
       121: q^5+q^4+q
       123: q^5+q^4+q
       125: q
       126: q
       127: q^4+q
       129: q
       131: 2q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q^4+q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q^4+q
       147: q
       148: q
       149: q^4+q
       150: 2q^4+q
       151: 2q^4+q
       153: q^4+q
       155: 2q^4+q
       157: q
       158: q
       159: q^4+q
       160: q^4+q
       161: q
       162: 2q^4+q
       163: q^4+q
       164: q
       165: 2q^4+q
       166: q^4+q
       167: q
       168: 2q^4+q
       172: q
       176: q^5+q
       177: q^4+q
       179: q
       181: q
       184: q
       186: q
       187: q
       189: q^4+q
       192: q
       194: q
       196: q
       197: q
       200: q
       202: q
       204: q
       205: q
       207: q
       209: q^4+q
       211: 2q^4+q
       213: q^4+q
       215: q
       217: 2q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       237: q^4+q
       239: q
       241: 2q^4+q
       243: q
       244: q
       245: q
       246: q^4+q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q^4+q
       253: q
       254: q
       255: q^4+q
       256: q^4+q
       257: q
       258: 2q^4+q
       262: q
       266: q
       269: q
       273: q
       278: q
       279: q
       281: q^4+q
       284: q
       286: q
       287: q
       289: q
       291: q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q^4+q
       317: q
       320: q
       322: q
       323: q
       325: q^4+q
       327: q
       329: q
       331: q^4+q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^4+q
       362: q
       364: 2q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q^4+q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q
       411: q
       413: q
       415: q
       417: q
       420: q
       422: q
       423: q
       425: q
       427: q
       430: q
       432: q
       433: q
       435: q
       438: q
       440: q
       441: q
       444: q
       445: q
       448: q
       450: q
       451: q
       454: q
       455: q
       458: q
       459: q
       462: q
       463: q
       465: q
       467: q^4+q
       469: q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       502: q
       504: q
       506: q^4+q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       524: q
       528: q
       532: q
       536: q
       539: q
       543: q
       547: q
       552: q
       555: q
       559: q
       563: q
       568: q
       570: q
       575: q
       577: q
       583: q
       585: q
       587: q
       590: q
       592: q
       594: q
       596: q
       597: q
       599: q
       601: q
       604: q
       605: q
       608: q
       609: q
       611: q
       613: q
       616: q
       617: q
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       632: q
       633: q
       635: q
       637: q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: q
       653: q
       655: q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       697: q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q
       731: q
       735: q
       739: q
       743: q
       747: q
       751: q
       756: q
       758: q
       762: q
       768: q
       769: q
       777: q
       781: q
       786: q
       788: q
       791: q
       797: q
       799: q
       802: q
       804: q
       806: q
       808: q
       809: q
       811: q
       821: q
       823: q
       826: q
       828: q
       830: q
       832: q
       833: q
       835: q
       841: q
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       889: q
       899: q
       902: q
       906: q
       911: q
       914: q
       922: q
       927: q
       930: q
       938: q
       946: q
       950: q
       955: q
       961: q
       975: q
       979: q
      1010: q
      1018: q
      1022: q
      1027: q
      1029: q
      1034: q
      1038: q
      1041: q
      1045: q
      1048: q
      1050: q
      1053: q
      1055: q
      1057: q
      1059: q
      1060: q
      1062: q
      1064: q
      1083: q
      1127: q
      1150: q
      1154: q
      1158: q
      1163: q
      1170: q
      1174: q
      1178: q
      1183: q
      1185: q
      1199: q
      1204: q
      1208: q
      1222: 1
      1264: q
      1266: q
      1269: q
      1271: q
      1278: q
      1323: 1
      1336: 1
      1361: q
      1393: q
      1415: q
      1420: q
      1424: q
      1429: q
      1446: 1
      1480: 1
      1498: 1
      1555: 1
      1560: 1
      1572: 1
      1592: 1
      1622: q
      1633: 1
      1671: 1
      1684: 1
      1696: 1
      1708: 1
      1754: 1
      1778: 1
      1796: 1
      1803: 1
      1855: 1
      1867: 1
      1881: 1
      1949: 1
      1999: 1

2000:    0: q^5+2q^4+q
         1: q^6+q^5+2q^4+q
         2: q^5+2q^4+q
         3: q^6+q^5+2q^4+q
         4: q^5+2q^4+q
         5: q^5+2q^4+q
         6: q^4+q
         7: q^5+2q^4+q
         8: q^5+2q^4+q
         9: q^6+2q^5+2q^4+q
        10: q^5+q^4+q
        11: q^5+q^4+q
        12: q^4+q
        13: q^5+2q^4+q
        14: q^5+2q^4+q
        15: q^5+2q^4+q
        16: q^5+q^4+q
        17: q^5+q^4+q
        18: q^5+2q^4+q
        19: 2q^4+q
        20: q^4+q
        21: 2q^4+q
        22: q^5+2q^4+q
        23: q^6+q^5+2q^4+q
        24: q^5+2q^4+q
        25: q^5+2q^4+q
        26: q^6+q^5+2q^4+q
        27: q^5+2q^4+q
        28: q^5+q
        29: q^4+q
        30: 2q^4+q
        31: q^5+q^4+q
        32: q^5+2q^4+q
        33: q^5+q^4+q
        34: q^5+q^4+q
        35: q^5+2q^4+q
        36: q^5+q^4+q
        38: q^5+2q^4+q
        40: q^6+q^5+2q^4+q
        42: q^5+2q^4+q
        43: q^5+q^4+q
        44: q^4+q
        45: q^5+q^4+q
        46: q^5+q^4+q
        47: q^5+q^4+q
        48: q^5+2q^4+q
        49: q^4+q
        50: q
        51: 2q^4+q
        52: 2q^4+q
        53: q^4+q
        54: 2q^4+q
        55: 2q^4+q
        56: q^4+q
        57: 2q^4+q
        59: q^5+q
        60: q^5+q
        63: q^5+q^4+q
        65: q^5+2q^4+q
        67: q^5+q^4+q
        68: q^5+q
        69: q^4+q
        70: q^4+q
        71: q
        72: q
        73: q
        75: 2q^4+q
        77: q^4+q
        79: 2q^4+q
        80: q^5+q^4+q
        81: q^5+q^4+q
        82: q^4+q
        83: 2q^4+q
        84: q^5+q^4+q
        85: q^5+q^4+q
        86: q^4+q
        87: 2q^4+q
        88: q
        89: q
        90: q^4+q
        91: q^4+q
        92: q
        93: 2q^4+q
        94: q^4+q
        95: q
        96: 2q^4+q
        97: q^4+q
        98: q
        99: 2q^4+q
       100: 2q^4+q
       101: q^4+q
       102: 2q^4+q
       104: q^5+q
       107: q
       110: q
       112: q
       114: q^4+q
       116: 2q^4+q
       118: q^5+q
       119: q^5+q
       122: q^5+q^4+q
       124: q^5+q^4+q
       125: q
       126: q
       128: q^4+q
       130: q
       132: 2q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q^4+q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q^4+q
       147: q
       148: q
       149: q^4+q
       150: 2q^4+q
       152: 2q^4+q
       154: q^4+q
       156: 2q^4+q
       157: q
       158: q
       159: q^4+q
       160: q^4+q
       161: q
       162: 2q^4+q
       163: q^4+q
       164: q
       165: 2q^4+q
       166: q^4+q
       167: q
       168: 2q^4+q
       170: q
       174: q^5+q
       178: q^4+q
       180: q
       182: q
       183: q
       186: q
       188: q
       190: q^4+q
       192: q
       193: q
       196: q
       198: q
       199: q
       201: q
       204: q
       206: q
       208: q
       210: q^4+q
       212: 2q^4+q
       214: q^4+q
       216: q
       218: 2q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       238: q^4+q
       240: q
       242: 2q^4+q
       243: q
       244: q
       245: q
       246: q^4+q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q^4+q
       253: q
       254: q
       255: q^4+q
       256: q^4+q
       257: q
       258: 2q^4+q
       260: q
       264: q
       268: q
       274: q
       276: q
       280: q
       282: q^4+q
       283: q
       286: q
       288: q
       290: q
       292: q
       293: q
       296: q
       298: q
       299: q
       302: q
       304: q
       306: q
       307: q
       310: q
       312: q
       314: q
       316: q^4+q
       318: q
       319: q
       322: q
       324: q
       326: q^4+q
       328: q
       330: q
       332: q^4+q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q
       343: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       361: q^4+q
       363: q
       365: 2q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q^4+q
       378: q
       382: q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q
       412: q
       414: q
       416: q
       418: q
       419: q
       422: q
       424: q
       426: q
       428: q
       429: q
       432: q
       434: q
       436: q
       437: q
       440: q
       442: q
       443: q
       446: q
       447: q
       450: q
       452: q
       453: q
       456: q
       458: q
       460: q
       462: q
       464: q
       466: q
       468: q^4+q
       470: q
       471: q
       474: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       484: q
       486: q
       488: q
       490: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       503: q
       505: q
       507: q^4+q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       522: q
       526: q
       530: q
       534: q
       538: q
       542: q
       546: q
       551: q
       556: q
       560: q
       564: q
       566: q
       571: q
       574: q
       581: q
       584: q
       586: q
       588: q
       589: q
       592: q
       593: q
       596: q
       598: q
       600: q
       602: q
       603: q
       606: q
       608: q
       610: q
       612: q
       614: q
       615: q
       618: q
       619: q
       622: q
       624: q
       626: q
       628: q
       630: q
       632: q
       634: q
       636: q
       638: q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: q
       654: q
       656: q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       699: q
       706: q
       710: q
       715: q
       718: q
       722: q
       726: q
       730: q
       734: q
       740: q
       744: q
       748: q
       752: q
       754: q
       759: q
       763: q
       766: q
       773: q
       778: q
       782: q
       785: q
       788: q
       792: q
       798: q
       800: q
       801: q
       804: q
       805: q
       808: q
       810: q
       812: q
       822: q
       824: q
       825: q
       828: q
       829: q
       832: q
       834: q
       836: q
       842: q
       845: q
       848: q
       850: q
       852: q
       854: q
       856: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       890: q
       897: q
       903: q
       905: q
       909: q
       913: q
       921: q
       926: q
       929: q
       939: q
       947: q
       951: q
       953: q
       962: q
       976: q
       980: q
      1011: q
      1019: q
      1023: q
      1026: q
      1029: q
      1035: q
      1039: q
      1040: q
      1045: q
      1049: q
      1051: q
      1052: q
      1055: q
      1056: q
      1059: q
      1061: q
      1063: q
      1065: q
      1083: q
      1128: q
      1149: q
      1155: q
      1157: q
      1162: q
      1171: q
      1175: q
      1177: q
      1181: q
      1186: q
      1200: q
      1205: q
      1207: q
      1223: 1
      1265: q
      1267: q
      1268: q
      1271: q
      1279: q
      1324: 1
      1339: 1
      1363: q
      1394: q
      1416: q
      1421: q
      1423: q
      1427: q
      1447: 1
      1481: 1
      1499: 1
      1558: 1
      1561: 1
      1574: 1
      1593: 1
      1620: q
      1636: 1
      1672: 1
      1685: 1
      1698: 1
      1709: 1
      1756: 1
      1779: 1
      1794: 1
      1806: 1
      1857: 1
      1868: 1
      1878: 1
      1950: 1
      2000: 1

2001:    0: q^5+2q^4+q
         1: q^6+q^5+2q^4+q
         2: q^5+2q^4+q
         3: q^6+q^5+2q^4+q
         4: q^5+2q^4+q
         5: q^5+2q^4+q
         6: q^4+q
         7: q^5+2q^4+q
         8: q^5+2q^4+q
         9: q^6+2q^5+2q^4+q
        10: q^5+q^4+q
        11: q^5+q^4+q
        12: q^4+q
        13: q^5+2q^4+q
        14: q^5+2q^4+q
        15: q^5+2q^4+q
        16: q^5+q^4+q
        17: q^5+q^4+q
        18: q^5+2q^4+q
        19: 2q^4+q
        20: q^4+q
        21: 2q^4+q
        22: q^5+2q^4+q
        23: q^6+q^5+2q^4+q
        24: q^5+2q^4+q
        25: q^5+2q^4+q
        26: q^6+q^5+2q^4+q
        27: q^5+2q^4+q
        28: q^5+q
        29: q^4+q
        30: 2q^4+q
        31: q^5+q^4+q
        32: q^5+2q^4+q
        33: q^5+q^4+q
        34: q^5+q^4+q
        35: q^5+2q^4+q
        36: q^5+q^4+q
        38: q^5+2q^4+q
        40: q^6+q^5+2q^4+q
        42: q^5+2q^4+q
        43: q^5+q^4+q
        44: q^4+q
        45: q^5+q^4+q
        46: q^5+q^4+q
        47: q^5+q^4+q
        48: q^5+2q^4+q
        49: q^4+q
        50: q
        51: 2q^4+q
        52: 2q^4+q
        53: q^4+q
        54: 2q^4+q
        55: 2q^4+q
        56: q^4+q
        57: 2q^4+q
        58: q^5+q
        61: q^5+q
        63: q^5+q^4+q
        65: q^5+2q^4+q
        67: q^5+q^4+q
        68: q^5+q
        69: q^4+q
        70: q^4+q
        71: q
        72: q
        73: q
        75: 2q^4+q
        77: q^4+q
        79: 2q^4+q
        80: q^5+q^4+q
        81: q^5+q^4+q
        82: q^4+q
        83: 2q^4+q
        84: q^5+q^4+q
        85: q^5+q^4+q
        86: q^4+q
        87: 2q^4+q
        88: q
        89: q
        90: q^4+q
        91: q^4+q
        92: q
        93: 2q^4+q
        94: q^4+q
        95: q
        96: 2q^4+q
        97: q^4+q
        98: q
        99: 2q^4+q
       100: 2q^4+q
       101: q^4+q
       102: 2q^4+q
       105: q^5+q
       108: q
       109: q
       112: q
       114: q^4+q
       116: 2q^4+q
       117: q^5+q
       120: q^5+q
       122: q^5+q^4+q
       124: q^5+q^4+q
       125: q
       126: q
       128: q^4+q
       130: q
       132: 2q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q^4+q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q^4+q
       147: q
       148: q
       149: q^4+q
       150: 2q^4+q
       152: 2q^4+q
       154: q^4+q
       156: 2q^4+q
       157: q
       158: q
       159: q^4+q
       160: q^4+q
       161: q
       162: 2q^4+q
       163: q^4+q
       164: q
       165: 2q^4+q
       166: q^4+q
       167: q
       168: 2q^4+q
       171: q
       175: q^5+q
       178: q^4+q
       180: q
       182: q
       184: q
       185: q
       188: q
       190: q^4+q
       191: q
       194: q
       195: q
       198: q
       200: q
       202: q
       203: q
       206: q
       208: q
       210: q^4+q
       212: 2q^4+q
       214: q^4+q
       216: q
       218: 2q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       238: q^4+q
       240: q
       242: 2q^4+q
       243: q
       244: q
       245: q
       246: q^4+q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q^4+q
       253: q
       254: q
       255: q^4+q
       256: q^4+q
       257: q
       258: 2q^4+q
       261: q
       265: q
       270: q
       272: q
       277: q
       280: q
       282: q^4+q
       284: q
       285: q
       288: q
       290: q
       292: q
       294: q
       295: q
       298: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q^4+q
       318: q
       320: q
       321: q
       324: q
       326: q^4+q
       328: q
       330: q
       332: q^4+q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q
       343: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       361: q^4+q
       363: q
       365: 2q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q^4+q
       379: q
       383: q
       387: q
       392: q
       395: q
       398: q
       402: q
       408: q
       410: q
       412: q
       414: q
       416: q
       418: q
       420: q
       421: q
       424: q
       426: q
       428: q
       430: q
       431: q
       434: q
       436: q
       438: q
       439: q
       442: q
       444: q
       446: q
       448: q
       449: q
       452: q
       454: q
       456: q
       457: q
       460: q
       461: q
       464: q
       466: q
       468: q^4+q
       470: q
       472: q
       473: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       484: q
       486: q
       488: q
       490: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       503: q
       505: q
       507: q^4+q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       523: q
       527: q
       531: q
       535: q
       540: q
       544: q
       548: q
       550: q
       554: q
       558: q
       562: q
       567: q
       572: q
       576: q
       581: q
       584: q
       586: q
       588: q
       590: q
       591: q
       594: q
       595: q
       598: q
       600: q
       602: q
       604: q
       606: q
       607: q
       610: q
       612: q
       614: q
       616: q
       618: q
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       631: q
       634: q
       636: q
       638: q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       656: q
       665: q
       675: q
       676: q
       677: q
       679: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       700: q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q
       732: q
       736: q
       738: q
       742: q
       746: q
       750: q
       755: q
       760: q
       764: q
       767: q
       773: q
       778: q
       782: q
       786: q
       787: q
       792: q
       798: q
       800: q
       802: q
       803: q
       806: q
       807: q
       810: q
       812: q
       822: q
       824: q
       826: q
       827: q
       830: q
       831: q
       834: q
       836: q
       842: q
       846: q
       847: q
       850: q
       852: q
       854: q
       856: q
       871: q
       875: q
       877: q
       878: q
       879: q
       880: q
       891: q
       898: q
       901: q
       907: q
       910: q
       915: q
       923: q
       925: q
       931: q
       937: q
       945: q
       949: q
       954: q
       963: q
       977: q
       981: q
      1011: q
      1019: q
      1023: q
      1027: q
      1028: q
      1035: q
      1039: q
      1041: q
      1044: q
      1049: q
      1051: q
      1053: q
      1054: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q
      1083: q
      1129: q
      1151: q
      1153: q
      1159: q
      1161: q
      1169: q
      1173: q
      1179: q
      1182: q
      1187: q
      1201: q
      1203: q
      1209: q
      1223: 1
      1265: q
      1267: q
      1269: q
      1270: q
      1279: q
      1325: 1
      1339: 1
      1362: q
      1395: q
      1417: q
      1419: q
      1425: q
      1428: q
      1447: 1
      1481: 1
      1500: 1
      1558: 1
      1562: 1
      1573: 1
      1594: 1
      1621: q
      1636: 1
      1672: 1
      1686: 1
      1697: 1
      1710: 1
      1755: 1
      1780: 1
      1795: 1
      1806: 1
      1856: 1
      1869: 1
      1880: 1
      1951: 1
      2001: 1

2002:    0: 3q^3+3q^2+q+1
         1: 3q^3+3q^2+q+1
         2: q^4+3q^3+2q^2+q+1
         3: 3q^3+3q^2+q+1
         4: 3q^3+3q^2+q+1
         5: 3q^3+3q^2+q+1
         6: 3q^3+3q^2+q+1
         7: q^4+3q^3+2q^2+q+1
         8: q^4+3q^3+2q^2+q+1
         9: q^5+2q^4+2q^3+q^2+q+1
        10: 3q^3+3q^2+q+1
        11: 3q^3+3q^2+q+1
        12: 3q^3+3q^2+q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+q+1
        17: q^3+3q^2+q+1
        18: q^4+2q^3+q^2+q+1
        19: 3q^3+3q^2+q+1
        20: 3q^3+3q^2+q+1
        21: q^4+3q^3+2q^2+q+1
        22: 3q^3+3q^2+q+1
        23: 3q^3+3q^2+q+1
        24: q^4+3q^3+2q^2+q+1
        25: 3q^3+3q^2+q+1
        26: 3q^3+3q^2+q+1
        27: q^4+3q^3+2q^2+q+1
        28: q^3+3q^2+q+1
        29: 3q^3+3q^2+q+1
        30: 2q^3+2q^2+q+1
        31: 3q^3+3q^2+q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+q+1
        34: 3q^3+3q^2+q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+q+1
        37: 3q^3+q^2+q+1
        38: 2q^2
        39: 3q^3+q^2+q+1
        40: 2q^2
        41: q^4+2q^3+q^2+q+1
        42: q^3+q^2
        43: 2q^3+2q^2+q+1
        44: 2q^3+2q^2+q+1
        45: 2q^3+2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+q+1
        50: q^3+3q^2+q+1
        51: q^4+2q^3+q^2+q+1
        52: 3q^3+3q^2+q+1
        53: 3q^3+3q^2+q+1
        54: q^4+3q^3+2q^2+q+1
        55: 3q^3+3q^2+q+1
        56: 3q^3+3q^2+q+1
        57: q^4+3q^3+2q^2+q+1
        58: q^3+2q^2+q+1
        59: q^2
        60: q^3+2q^2+q+1
        61: q^2
        62: 3q^3+q^2+q+1
        63: 2q^2
        64: 2q^3+q^2+q+1
        65: q^2
        66: q^3+q^2+q+1
        67: 2q^2
        68: q^2+q+1
        69: q^2+q+1
        70: 2q^3+2q^2+q+1
        71: q^3+3q^2+q+1
        72: q^3+3q^2+q+1
        73: q^3+3q^2+q+1
        74: 3q^3+q^2+q+1
        75: 2q^2
        76: 3q^3+q^2+q+1
        77: 2q^2
        78: q^4+2q^3+q^2+q+1
        79: q^3+q^2
        80: 2q^3+2q^2+q+1
        81: 2q^2+q+1
        82: 3q^3+3q^2+q+1
        83: 2q^3+2q^2+q+1
        84: 2q^3+2q^2+q+1
        85: 2q^2+q+1
        86: 3q^3+3q^2+q+1
        87: 2q^3+2q^2+q+1
        88: 2q^2+q+1
        89: 2q^2+q+1
        90: q^3+q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+q+1
        95: q^3+3q^2+q+1
        96: q^4+2q^3+q^2+q+1
        97: q^3+3q^2+q+1
        98: q^3+3q^2+q+1
        99: q^4+2q^3+q^2+q+1
       100: 3q^3+3q^2+q+1
       101: 3q^3+3q^2+q+1
       102: q^4+3q^3+2q^2+q+1
       103: q^3+q^2+q+1
       104: q^2
       105: q^2
       107: q^3+2q^2+q+1
       108: q^2
       109: q^3+2q^2+q+1
       110: q^2
       111: q^3+q^2+q+1
       112: 2q^2
       113: 3q^3+q^2+q+1
       114: 2q^2
       115: 2q^3+q^2+q+1
       116: q^2
       117: q^2+q+1
       119: q^2+q+1
       121: 2q^3+q^2+q+1
       122: q^2
       123: q^2+q+1
       124: q^2
       125: q^2+q+1
       126: q^2+q+1
       127: q^3+q^2+q+1
       129: q^3+q^2+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: 2q^2+q+1
       138: q^2+q+1
       139: q^3+3q^2+q+1
       140: q^3+3q^2+q+1
       141: 2q^3+2q^2+q+1
       142: q^3+3q^2+q+1
       143: 2q^2+q+1
       144: q^2+q+1
       145: q^3+3q^2+q+1
       146: 2q^3+2q^2+q+1
       147: q^3+3q^2+q+1
       148: q^3+3q^2+q+1
       149: 3q^3+3q^2+q+1
       150: 2q^3+2q^2+q+1
       151: 3q^3+q^2+q+1
       152: 2q^2
       153: 3q^3+q^2+q+1
       154: 2q^2
       155: q^4+2q^3+q^2+q+1
       156: q^3+q^2
       157: 2q^2+q+1
       158: 2q^2+q+1
       159: q^3+q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+q+1
       167: q^3+3q^2+q+1
       168: q^4+2q^3+q^2+q+1
       169: q^3+q^2+q+1
       170: q^2
       171: q^2
       173: q^2+q+1
       177: q+1
       179: q^3+q^2+q+1
       181: q^3+q^2+q+1
       183: q^2+q+1
       185: q^2+q+1
       187: q^2+q+1
       188: q^2
       189: 2q^3+q^2+q+1
       190: q^2
       191: q^2+q+1
       193: q^3+2q^2+q+1
       194: q^2
       195: q^3+2q^2+q+1
       196: q^2
       197: q^3+q^2+q+1
       198: 2q^2
       199: q^2+q+1
       201: q^3+2q^2+q+1
       202: q^2
       203: q^3+2q^2+q+1
       204: q^2
       205: q^3+q^2+q+1
       206: 2q^2
       207: q^2+q+1
       208: q^2
       209: 3q^3+q^2+q+1
       210: 2q^2
       211: 2q^3+q^2+q+1
       212: q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: q^2+q+1
       224: 2q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: q^3+q^2+q+1
       239: q^3+q^2+q+1
       241: q^4+q^3+q+1
       243: q^3+3q^2+q+1
       244: q^3+3q^2+q+1
       245: q^3+3q^2+q+1
       246: 2q^3+2q^2+q+1
       247: q^3+3q^2+q+1
       248: q^3+3q^2+q+1
       249: q^4+2q^3+q^2+q+1
       250: 2q^2+q+1
       251: 2q^2+q+1
       252: q^3+q^2+q+1
       253: 2q^2+q+1
       254: 2q^2+q+1
       255: q^3+q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       259: q^3+q^2+q+1
       263: q^2+q+1
       267: q^3+q^2+q+1
       268: q^2
       270: q^2
       271: q^3+q^2+q+1
       272: q^2
       274: q^2
       275: q^2+q+1
       279: q^2+1
       281: 1
       283: q+1
       285: q+1
       287: q+1
       289: q^2+1
       291: q+1
       293: q^2+q+1
       295: q^2+q+1
       297: q^2+q+1
       298: q^2
       299: q^2+q+1
       301: q^3+q^2+q+1
       303: q^2+q+1
       305: q^2+q+1
       306: q^2
       307: q^2+q+1
       309: q^2+q+1
       311: q^3+q^2+q+1
       313: q^2+q+1
       314: q^2
       315: q+1
       317: q^3+q^2+q+1
       319: q^3+2q^2+q+1
       320: q^2
       321: q^3+2q^2+q+1
       322: q^2
       323: q^3+q^2+q+1
       324: 2q^2
       325: 2q^3+q^2+q+1
       326: q^2
       327: q^2+1
       329: q^2+1
       331: q^3+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+q+1
       337: q^3+3q^2+q+1
       338: q^3+q^2+q+1
       340: q^3+q^2+q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 2q^2+q+1
       348: q^2+q+1
       349: 2q^2+q+1
       350: q^2+q+1
       351: q^3+3q^2+q+1
       352: q+1
       353: q^2+q+1
       354: q^2+q+1
       355: 2q^2+q+1
       356: q^2+q+1
       357: 2q^2+q+1
       358: q^2+q+1
       359: q^3+3q^2+q+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: q^2+q+1
       367: q^2+q+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: 2q^2+q+1
       375: 2q^2+q+1
       376: q^3+q^2+q+1
       377: q+1
       381: q^2+1
       385: q^2+q+1
       389: q^3+q^2+q+1
       393: q^2+q+1
       397: q^3+q^2+q+1
       401: q^2+q+1
       405: q^3+q^2+q+1
       407: q^2
       408: q^2
       409: q^2+1
       411: 1
       413: 1
       415: q^2+1
       417: 1
       419: q+1
       421: q+1
       423: q+1
       425: q+1
       427: q^3+q^2+q+1
       429: q+1
       431: q+1
       433: q+1
       435: q^2+1
       437: q^2+q+1
       439: q^2+q+1
       441: q^2+q+1
       442: q^2
       443: q^3+2q^2+q+1
       444: q^2
       445: q^3+q^2+q+1
       447: q+1
       449: q+1
       451: q+1
       453: q^2+q+1
       455: q^2+1
       457: q^2+q+1
       459: q^2+q+1
       460: q^2
       461: q^3+2q^2+q+1
       462: q^2
       463: q^3+q^2+q+1
       465: q^2+1
       467: 1
       469: q+1
       471: q^2+q+1
       473: q^2+q+1
       475: q^2+q+1
       476: q^2
       477: q^3+q^2+q+1
       479: q^3+q^2+q+1
       480: 2q^2
       481: q+1
       482: q+1
       483: q^2+q+1
       484: q^2+q+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: q^2+q+1
       492: q+1
       493: q^2+q+1
       494: q^2+q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: q+1
       498: q^2+q+1
       499: q^2+q+1
       500: q^2+q+1
       501: 2q^2+q+1
       502: q^2+1
       504: q^2+1
       506: q^3+1
       508: q+1
       509: q^2+q+1
       510: q^2+q+1
       511: 2q^2+q+1
       512: q^2+q+1
       513: 2q^2+q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+q+1
       519: 2q^2+q+1
       520: q^3+q^2+q+1
       521: 1
       525: q^2+1
       529: q+1
       533: q+1
       537: q^2+1
       541: q^2+q+1
       545: q^3+q^2+q+1
       549: q+1
       553: q^2+1
       557: q^2+q+1
       561: q^3+q^2+q+1
       565: q^2+q+1
       569: q^3+q^2+q+1
       573: q^3+q^2+q+1
       574: q^2
       576: q^2
       577: q^3+q^2+q+1
       583: 1
       585: 1
       587: 1
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: 1
       599: q+1
       601: q^2+1
       603: q+1
       605: 1
       607: q+1
       609: q+1
       611: q^2+1
       613: q+1
       615: q^2+q+1
       617: q^2+1
       619: q+1
       621: q+1
       623: 1
       625: q+1
       627: q^2+1
       629: q+1
       631: q^2+q+1
       633: q^2+1
       635: q^2+1
       637: 1
       639: 1
       641: q+1
       643: q+1
       645: q+1
       647: q^2+q+1
       649: q^2+q+1
       651: q^2+1
       653: q^2+q+1
       654: q^2
       655: q^2+q+1
       656: q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q^2+1
       668: q^2+1
       670: q^3+1
       672: q^2+q+1
       673: q^2+q+1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+q+1
       678: 2q^2+q+1
       679: q^2+q+1
       680: q+1
       681: q+1
       682: q+1
       683: q^2+q+1
       684: 2q^2+q+1
       685: q^2+q+1
       686: q+1
       687: q^2+q+1
       688: q^2+q+1
       689: q^2+q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^3+q^2+q+1
       705: 1
       709: 1
       713: q+1
       717: q+1
       721: 1
       725: q+1
       729: q^2+1
       733: q^2+1
       737: 1
       741: q+1
       745: q^2+1
       749: q^2+1
       753: q+1
       757: q^2+1
       761: q^2+q+1
       765: q^2+q+1
       769: q^2+1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: 1
       785: q+1
       787: q+1
       789: q^2+1
       791: q+1
       793: 1
       795: q+1
       797: 1
       799: 1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: 1
       811: q+1
       813: q^2+1
       815: q^2+q+1
       817: 1
       819: q+1
       821: 1
       823: 1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: 1
       835: q+1
       837: q^2+1
       839: q^2+q+1
       841: 1
       843: 1
       844: q
       845: q+1
       847: q+1
       849: 1
       851: q+1
       853: q^2+1
       855: q+1
       857: q^2+q+1
       858: q^2
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+q+1
       873: q+1
       874: q+1
       875: q+1
       876: q^2+q+1
       877: q+1
       878: q+1
       879: q^2+q+1
       880: q^2+q+1
       884: q^2+1
       896: 1
       900: 1
       904: 1
       908: q+1
       912: 1
       916: 1
       920: 1
       924: q+1
       928: q+1
       932: q^2+1
       936: 1
       940: 1
       944: 1
       948: q+1
       952: q+1
       956: q^2+1
       960: 1
       964: 1
       968: 1
       971: q
       974: q+1
       978: q^2+1
       982: q^2+1
       988: q^2+q+1
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 1
      1004: q+1
      1006: q+1
      1008: q+1
      1010: 1
      1012: 1
      1013: q
      1014: q+1
      1016: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: 1
      1026: q+1
      1028: q+1
      1030: q+1
      1032: 1
      1034: 1
      1036: q+1
      1038: 1
      1040: q+1
      1042: 1
      1044: q+1
      1046: 1
      1047: q
      1048: 1
      1050: 1
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: 1
      1076: 1
      1077: q+1
      1078: q+1
      1080: 1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q^2+q+1
      1086: 1
      1098: q^2+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: q+1
      1138: 1
      1141: q
      1144: 1
      1148: 1
      1152: 1
      1156: 1
      1160: q+1
      1164: 1
      1168: 1
      1172: 1
      1176: 1
      1180: q+1
      1184: 1
      1188: 1
      1191: q
      1194: 1
      1198: 1
      1202: q+1
      1206: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: q
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 1
      1240: q+1
      1242: q+1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 1
      1258: q+1
      1260: q+1
      1264: 1
      1266: 1
      1268: q+1
      1270: q+1
      1272: 1
      1274: q+1
      1276: q+1
      1278: 1
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: q+1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1337: q
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: q+1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: q+1
      1414: 1
      1418: 1
      1422: 1
      1426: q+1
      1430: 1
      1433: q
      1446: 1
      1448: 1
      1450: 1
      1454: 1
      1456: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: q+1
      1474: 1
      1476: q+1
      1478: q+1
      1480: 1
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1489: 1
      1501: 1
      1513: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 1
      1623: 1
      1627: q+1
      1631: 1
      1634: q
      1641: 1
      1649: 1
      1657: 1
      1661: 1
      1663: 1
      1665: 1
      1671: 1
      1673: 1
      1687: 1
      1699: 1
      1711: 1
      1753: 1
      1757: 1
      1777: 1
      1781: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1807: 1
      1811: 1
      1815: 1
      1819: 1
      1821: 1
      1870: 1
      1882: 1
      1902: 1
      1918: 1
      1948: 1
      1952: 1
      2002: 1

2003:    0: q^4+q^3+3q^2+3q
         1: q^4+q^3+3q^2+3q
         2: 2q^4+q^3+2q^2+3q
         3: q^4+q^3+3q^2+3q
         4: q^4+q^3+3q^2+3q
         5: q^4+q^3+3q^2+3q
         6: q^4+q^3+3q^2+3q
         7: 2q^4+q^3+2q^2+3q
         8: 2q^4+q^3+2q^2+3q
         9: q^6+q^4+2q^3+2q^2+2q
        10: q^4+q^3+3q^2+3q
        11: q^4+q^3+3q^2+3q
        12: q^4+q^3+3q^2+3q
        13: q^4+2q^2+3q
        14: q^4+2q^2+3q
        15: q^4+2q^2+3q
        16: q^3+2q^2+3q
        17: q^3+2q^2+3q
        18: q^4+q^3+2q^2+2q
        19: q^4+q^3+3q^2+3q
        20: q^4+q^3+3q^2+3q
        21: 2q^4+q^3+2q^2+3q
        22: q^4+q^3+3q^2+3q
        23: q^4+q^3+3q^2+3q
        24: 2q^4+q^3+2q^2+3q
        25: q^4+q^3+3q^2+3q
        26: q^4+q^3+3q^2+3q
        27: 2q^4+q^3+2q^2+3q
        28: q^3+2q^2+3q
        29: q^4+q^3+3q^2+3q
        30: q^4+2q^2+3q
        31: q^4+q^3+3q^2+3q
        32: q^4+2q^2+3q
        33: q^3+2q^2+3q
        34: q^4+q^3+3q^2+3q
        35: q^4+2q^2+3q
        36: q^3+2q^2+3q
        37: q^3+q
        38: q^4+3q^2+2q
        39: q^3+q
        40: q^4+3q^2+2q
        41: q^4+q
        42: q^4+q^3+2q^2+2q
        43: q^4+2q^2+3q
        44: q^4+2q^2+3q
        45: q^4+2q^2+3q
        46: q^2+3q
        47: q^2+3q
        48: 2q^2+2q
        49: q^3+2q^2+3q
        50: q^3+2q^2+3q
        51: q^4+q^3+2q^2+2q
        52: q^4+q^3+3q^2+3q
        53: q^4+q^3+3q^2+3q
        54: 2q^4+q^3+2q^2+3q
        55: q^4+q^3+3q^2+3q
        56: q^4+q^3+3q^2+3q
        57: 2q^4+q^3+2q^2+3q
        58: q^3+q^2+2q
        59: q^2+q
        60: q^3+q^2+2q
        61: q^2+q
        62: q^3+q
        63: q^4+3q^2+2q
        64: q
        65: q^4+2q^2+2q
        66: q^3+q
        67: 2q^2+2q
        68: 3q
        69: q^2+2q
        70: q^4+2q^2+3q
        71: q^3+2q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^3+q
        75: q^4+3q^2+2q
        76: q^3+q
        77: q^4+3q^2+2q
        78: q^4+q
        79: q^4+q^3+2q^2+2q
        80: q^4+2q^2+3q
        81: q^2+3q
        82: q^4+q^3+3q^2+3q
        83: q^4+2q^2+3q
        84: q^4+2q^2+3q
        85: q^2+3q
        86: q^4+q^3+3q^2+3q
        87: q^4+2q^2+3q
        88: q^2+3q
        89: q^2+3q
        90: 2q^2+2q
        91: q^2+3q
        92: q^2+3q
        93: 2q^2+2q
        94: q^3+2q^2+3q
        95: q^3+2q^2+3q
        96: q^4+q^3+2q^2+2q
        97: q^3+2q^2+3q
        98: q^3+2q^2+3q
        99: q^4+q^3+2q^2+2q
       100: q^4+q^3+3q^2+3q
       101: q^4+q^3+3q^2+3q
       102: 2q^4+q^3+2q^2+3q
       103: q^3+q
       104: q^2+q
       105: q^2+q
       107: q^3+q^2+2q
       108: q^2+q
       109: q^3+q^2+2q
       110: q^2+q
       111: q^3+q
       112: 2q^2+2q
       113: q^3+q
       114: q^4+3q^2+2q
       115: q
       116: q^4+2q^2+2q
       117: 2q
       118: q
       119: 2q
       120: q
       121: q
       122: q^4+2q^2+2q
       123: q
       124: q^2+2q
       125: 3q
       126: q^2+2q
       128: 2q^2+2q
       130: 2q^2+2q
       132: q^3+2q^2+q
       133: 3q
       134: q^2+2q
       135: q^2+3q
       136: q^2+3q
       137: q^2+3q
       138: q^2+2q
       139: q^3+2q^2+3q
       140: q^3+2q^2+3q
       141: q^4+2q^2+3q
       142: q^3+2q^2+3q
       143: q^2+3q
       144: q^2+2q
       145: q^3+2q^2+3q
       146: q^4+2q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: q^4+q^3+3q^2+3q
       150: q^4+2q^2+3q
       151: q^3+q
       152: q^4+3q^2+2q
       153: q^3+q
       154: q^4+3q^2+2q
       155: q^4+q
       156: q^4+q^3+2q^2+2q
       157: q^2+3q
       158: q^2+3q
       159: 2q^2+2q
       160: q^2+3q
       161: q^2+3q
       162: 2q^2+2q
       163: q^2+3q
       164: q^2+3q
       165: 2q^2+2q
       166: q^3+2q^2+3q
       167: q^3+2q^2+3q
       168: q^4+q^3+2q^2+2q
       169: q^3+q
       170: q^2+q
       171: q^2+q
       173: q
       174: q
       175: q
       178: q^2+q
       180: 2q^2+2q
       182: 2q^2+2q
       183: 2q
       184: q
       185: 2q
       186: q
       187: q
       188: q^2+2q
       189: q
       190: q^4+2q^2+2q
       191: 2q
       192: q
       193: q^3+q^2+2q
       194: q^2+q
       195: q^3+q^2+2q
       196: q^2+q
       197: q^3+q
       198: 2q^2+2q
       199: 2q
       200: q
       201: q^3+q^2+2q
       202: q^2+q
       203: q^3+q^2+2q
       204: q^2+q
       205: q^3+q
       206: 2q^2+2q
       207: q
       208: q^2+2q
       209: q^3+q
       210: q^4+3q^2+2q
       211: q
       212: q^4+2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: q^2+2q
       222: q^2+3q
       223: q^2+2q
       224: q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q
       228: q^2+2q
       229: q^2+3q
       230: q^2+3q
       231: q^2+2q
       232: 3q
       233: q^2+2q
       234: q^2+3q
       235: q^2+3q
       236: q^2+2q
       238: 2q^2+2q
       240: 2q^2+2q
       242: q^3+2q^2+q
       243: q^3+2q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: q^4+2q^2+3q
       247: q^3+2q^2+3q
       248: q^3+2q^2+3q
       249: q^4+q^3+2q^2+2q
       250: q^2+3q
       251: q^2+3q
       252: 2q^2+2q
       253: q^2+3q
       254: q^2+3q
       255: 2q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: 2q^2+2q
       260: q^2+q
       261: q^2+q
       263: q
       264: q
       265: q
       267: q^3+q
       268: q^2+q
       270: q^2+q
       271: q^3+q
       272: q^2+q
       274: q^2+q
       275: q
       276: q
       277: q
       280: 2q
       282: q
       283: q
       285: q
       288: q^2+q
       290: 2q
       292: q^2+q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: q^2+2q
       299: 2q
       300: q
       302: 2q^2+2q
       303: 2q
       304: q
       305: q
       306: q^2+2q
       307: 2q
       308: q
       309: 2q
       310: q
       312: 2q^2+2q
       313: q
       314: q^2+2q
       316: q^2+q
       318: 2q^2+2q
       319: q^3+q^2+2q
       320: q^2+q
       321: q^3+q^2+2q
       322: q^2+q
       323: q^3+q
       324: 2q^2+2q
       325: q
       326: q^4+2q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: 2q
       334: q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: q^3+2q^2+3q
       339: 2q^2+2q
       341: 2q^2+2q
       343: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: q^2+3q
       348: q^2+2q
       349: q^2+3q
       350: q^2+2q
       351: q^3+2q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: q^2+3q
       356: q^2+2q
       357: q^2+3q
       358: q^2+2q
       359: q^3+2q^2+3q
       361: 2q
       363: 2q
       365: q^2+q
       366: q^2+2q
       367: 3q
       368: q^2+2q
       369: q^2+3q
       370: q^2+3q
       371: q^2+3q
       372: q^2+3q
       373: 2q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q^2+q
       392: q^2+q
       393: q
       394: q
       395: q
       398: q^2+q
       400: q^2+q
       401: q
       402: q
       403: q
       405: q^3+q
       407: q^2+q
       408: q^2+q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       419: q
       421: q
       424: q^2+q
       426: q^2+q
       428: 2q^2+2q
       429: q
       431: q
       434: q^2+q
       436: 2q
       437: 2q
       438: q
       439: 2q
       440: q
       441: q
       442: q^2+2q
       443: q^3+q^2+2q
       444: q^2+q
       446: 2q^2+2q
       447: q
       449: q
       452: q^2+q
       453: 2q
       454: q
       456: 2q
       457: 2q
       458: q
       459: q
       460: q^2+2q
       461: q^3+q^2+2q
       462: q^2+q
       464: 2q^2+2q
       466: 2q
       468: q
       470: q^2+q
       471: 2q
       472: q
       473: 2q
       474: q
       475: q
       476: q^2+2q
       478: 2q^2+2q
       479: q^3+q
       480: 2q^2+2q
       481: 2q
       482: 2q
       483: q^2+2q
       484: 3q
       486: 2q
       488: 2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: q^2+2q
       494: q^2+2q
       495: q^2+2q
       496: q^2+3q
       497: 2q
       498: q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: q^2+3q
       503: 2q
       505: 2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: q^2+3q
       512: q^2+2q
       513: q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: q^2+3q
       519: q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       538: q
       540: q
       541: q
       542: q
       544: q
       546: q^2+q
       548: q^2+q
       554: q
       556: q
       557: q
       558: q
       560: q
       562: q^2+q
       564: q^2+q
       565: q
       566: q
       567: q
       571: q^2+q
       572: q^2+q
       573: q^3+q
       574: q^2+q
       576: q^2+q
       581: 2q^2+2q
       584: q
       586: q
       588: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q^2+q
       602: 2q
       603: q
       606: q
       607: q
       610: q^2+q
       612: 2q
       614: q^2+q
       615: 2q
       616: q
       618: 2q
       619: q
       621: q
       624: q
       626: q^2+q
       628: 2q
       630: q^2+q
       631: 2q
       632: q
       634: 2q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       646: q^2+q
       647: 2q
       648: q
       649: 2q
       650: q
       652: 2q
       653: q
       654: q^2+2q
       655: q
       656: q^2+2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: 2q
       669: 2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q
       677: q^2+2q
       678: q^2+3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: q^2+2q
       684: q^2+3q
       685: q^2+2q
       686: 2q
       687: q^2+2q
       688: q^2+2q
       689: q^2+2q
       690: q+1
       691: q+1
       692: q+1
       699: q^2+q
       700: q^2+q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q
       766: q
       767: q
       773: 2q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       792: q^2+q
       793: 1
       796: q+1
       798: q
       800: q
       801: q
       803: q
       805: q
       807: q
       810: q
       812: q^2+q
       814: 2q
       815: 2q
       816: q
       817: 1
       820: q+1
       822: q
       824: q
       825: q
       827: q
       829: q
       831: q
       834: q
       836: q^2+q
       838: 2q
       839: 2q
       840: q
       842: q
       843: 1
       844: q
       845: q
       847: q
       850: q
       852: q^2+q
       854: 2q
       856: q^2+q
       857: q
       858: q^2+2q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q
       878: 2q
       879: q^2+2q
       880: q^2+2q
       890: q
       891: q
       917: 1
       933: q
       935: q
       941: 1
       957: q
       959: q
       964: 1
       969: 1
       972: q
       980: q
       981: q
       986: 2q
       988: q
       989: q
       990: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1009: q^2+q
      1011: q
      1012: 1
      1013: q
      1015: q+1
      1016: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: q+1
      1032: 1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: 1
      1047: q
      1049: q
      1051: q
      1052: q
      1054: q
      1056: q
      1058: q
      1061: q
      1063: q^2+q
      1065: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1087: 1
      1104: q
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1142: q
      1145: 1
      1165: 1
      1189: 1
      1192: q
      1194: 1
      1215: 1
      1216: 1
      1218: 1
      1221: q
      1223: q
      1224: 1
      1225: q
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1265: q
      1267: q
      1268: q
      1270: q
      1273: q
      1275: q+1
      1277: q^2+q
      1279: q
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1338: q
      1349: 1
      1357: 1
      1364: 1
      1381: 1
      1389: 1
      1396: 1
      1431: 1
      1434: q
      1447: q
      1449: 1
      1450: 1
      1454: 1
      1457: 1
      1460: 1
      1462: 1
      1465: 1
      1466: 1
      1468: 1
      1471: q
      1473: q+1
      1475: q
      1476: q
      1478: q
      1481: q
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1490: 1
      1502: 1
      1514: 1
      1564: 1
      1568: 1
      1575: 1
      1584: 1
      1588: 1
      1595: 1
      1608: 1
      1616: 1
      1623: 1
      1632: 1
      1635: q
      1642: 1
      1649: 1
      1657: 1
      1662: 1
      1663: 1
      1665: 1
      1672: q
      1673: 1
      1688: 1
      1700: 1
      1712: 1
      1758: 1
      1782: 1
      1786: 1
      1790: 1
      1797: 1
      1811: 1
      1816: 1
      1819: 1
      1821: 1
      1871: 1
      1883: 1
      1903: 1
      1919: 1
      1952: 1
      2003: 1

2004:    0: q^4+q^3+3q^2+3q
         1: q^4+q^3+3q^2+3q
         2: 2q^4+q^3+2q^2+3q
         3: q^4+q^3+3q^2+3q
         4: q^4+q^3+3q^2+3q
         5: q^4+q^3+3q^2+3q
         6: q^4+q^3+3q^2+3q
         7: 2q^4+q^3+2q^2+3q
         8: 2q^4+q^3+2q^2+3q
         9: q^6+q^4+2q^3+2q^2+2q
        10: q^4+q^3+3q^2+3q
        11: q^4+q^3+3q^2+3q
        12: q^4+q^3+3q^2+3q
        13: q^4+2q^2+3q
        14: q^4+2q^2+3q
        15: q^4+2q^2+3q
        16: q^3+2q^2+3q
        17: q^3+2q^2+3q
        18: q^4+q^3+2q^2+2q
        19: q^4+q^3+3q^2+3q
        20: q^4+q^3+3q^2+3q
        21: 2q^4+q^3+2q^2+3q
        22: q^4+q^3+3q^2+3q
        23: q^4+q^3+3q^2+3q
        24: 2q^4+q^3+2q^2+3q
        25: q^4+q^3+3q^2+3q
        26: q^4+q^3+3q^2+3q
        27: 2q^4+q^3+2q^2+3q
        28: q^3+2q^2+3q
        29: q^4+q^3+3q^2+3q
        30: q^4+2q^2+3q
        31: q^4+q^3+3q^2+3q
        32: q^4+2q^2+3q
        33: q^3+2q^2+3q
        34: q^4+q^3+3q^2+3q
        35: q^4+2q^2+3q
        36: q^3+2q^2+3q
        37: q^4+3q^2+2q
        38: q^3+q
        39: q^4+3q^2+2q
        40: q^3+q
        41: q^4+q^3+2q^2+2q
        42: q^4+q
        43: q^4+2q^2+3q
        44: q^4+2q^2+3q
        45: q^4+2q^2+3q
        46: q^2+3q
        47: q^2+3q
        48: 2q^2+2q
        49: q^3+2q^2+3q
        50: q^3+2q^2+3q
        51: q^4+q^3+2q^2+2q
        52: q^4+q^3+3q^2+3q
        53: q^4+q^3+3q^2+3q
        54: 2q^4+q^3+2q^2+3q
        55: q^4+q^3+3q^2+3q
        56: q^4+q^3+3q^2+3q
        57: 2q^4+q^3+2q^2+3q
        58: q^2+q
        59: q^3+q^2+2q
        60: q^3+q^2+2q
        61: q^2+q
        62: q^4+3q^2+2q
        63: q^3+q
        64: q^4+2q^2+2q
        65: q
        66: 2q^2+2q
        67: q^3+q
        68: 3q
        69: q^2+2q
        70: q^4+2q^2+3q
        71: q^3+2q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^4+3q^2+2q
        75: q^3+q
        76: q^4+3q^2+2q
        77: q^3+q
        78: q^4+q^3+2q^2+2q
        79: q^4+q
        80: q^4+2q^2+3q
        81: q^2+3q
        82: q^4+q^3+3q^2+3q
        83: q^4+2q^2+3q
        84: q^4+2q^2+3q
        85: q^2+3q
        86: q^4+q^3+3q^2+3q
        87: q^4+2q^2+3q
        88: q^2+3q
        89: q^2+3q
        90: 2q^2+2q
        91: q^2+3q
        92: q^2+3q
        93: 2q^2+2q
        94: q^3+2q^2+3q
        95: q^3+2q^2+3q
        96: q^4+q^3+2q^2+2q
        97: q^3+2q^2+3q
        98: q^3+2q^2+3q
        99: q^4+q^3+2q^2+2q
       100: q^4+q^3+3q^2+3q
       101: q^4+q^3+3q^2+3q
       102: 2q^4+q^3+2q^2+3q
       103: q^2+q
       104: q^3+q
       106: q^2+q
       107: q^3+q^2+2q
       108: q^2+q
       109: q^2+q
       110: q^3+q^2+2q
       111: 2q^2+2q
       112: q^3+q
       113: q^4+3q^2+2q
       114: q^3+q
       115: q^4+2q^2+2q
       116: q
       117: q
       118: 2q
       119: 2q
       120: q
       121: q^4+2q^2+2q
       122: q
       123: q^2+2q
       124: q
       125: 3q
       126: q^2+2q
       127: 2q^2+2q
       129: 2q^2+2q
       131: q^3+2q^2+q
       133: 3q
       134: q^2+2q
       135: q^2+3q
       136: q^2+3q
       137: q^2+3q
       138: q^2+2q
       139: q^3+2q^2+3q
       140: q^3+2q^2+3q
       141: q^4+2q^2+3q
       142: q^3+2q^2+3q
       143: q^2+3q
       144: q^2+2q
       145: q^3+2q^2+3q
       146: q^4+2q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: q^4+q^3+3q^2+3q
       150: q^4+2q^2+3q
       151: q^4+3q^2+2q
       152: q^3+q
       153: q^4+3q^2+2q
       154: q^3+q
       155: q^4+q^3+2q^2+2q
       156: q^4+q
       157: q^2+3q
       158: q^2+3q
       159: 2q^2+2q
       160: q^2+3q
       161: q^2+3q
       162: 2q^2+2q
       163: q^2+3q
       164: q^2+3q
       165: 2q^2+2q
       166: q^3+2q^2+3q
       167: q^3+2q^2+3q
       168: q^4+q^3+2q^2+2q
       169: q^2+q
       170: q^3+q
       172: q^2+q
       173: q
       174: q
       176: q
       177: q^2+q
       179: 2q^2+2q
       181: 2q^2+2q
       183: 2q
       184: q
       185: q
       186: 2q
       187: q^2+2q
       188: q
       189: q^4+2q^2+2q
       190: q
       191: q
       192: 2q
       193: q^3+q^2+2q
       194: q^2+q
       195: q^2+q
       196: q^3+q^2+2q
       197: 2q^2+2q
       198: q^3+q
       199: 2q
       200: q
       201: q^3+q^2+2q
       202: q^2+q
       203: q^2+q
       204: q^3+q^2+2q
       205: 2q^2+2q
       206: q^3+q
       207: q^2+2q
       208: q
       209: q^4+3q^2+2q
       210: q^3+q
       211: q^4+2q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: q^2+2q
       222: q^2+3q
       223: q^2+2q
       224: q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q
       228: q^2+2q
       229: q^2+3q
       230: q^2+3q
       231: q^2+2q
       232: 3q
       233: q^2+2q
       234: q^2+3q
       235: q^2+3q
       236: q^2+2q
       237: 2q^2+2q
       239: 2q^2+2q
       241: q^3+2q^2+q
       243: q^3+2q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: q^4+2q^2+3q
       247: q^3+2q^2+3q
       248: q^3+2q^2+3q
       249: q^4+q^3+2q^2+2q
       250: q^2+3q
       251: q^2+3q
       252: 2q^2+2q
       253: q^2+3q
       254: q^2+3q
       255: 2q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: 2q^2+2q
       259: q^2+q
       262: q^2+q
       263: q
       264: q
       266: q
       267: q^2+q
       268: q^3+q
       269: q^2+q
       271: q^2+q
       273: q^2+q
       274: q^3+q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q^2+q
       289: 2q
       291: q^2+q
       293: 2q
       294: q
       295: q
       296: 2q
       297: q^2+2q
       298: q
       299: 2q
       300: q
       301: 2q^2+2q
       303: q
       304: 2q
       305: q^2+2q
       306: q
       307: 2q
       308: q
       309: q
       310: 2q
       311: 2q^2+2q
       313: q^2+2q
       314: q
       315: q^2+q
       317: 2q^2+2q
       319: q^3+q^2+2q
       320: q^2+q
       321: q^2+q
       322: q^3+q^2+2q
       323: 2q^2+2q
       324: q^3+q
       325: q^4+2q^2+2q
       326: q
       327: 2q
       329: 2q
       331: q^2+q
       333: 2q
       334: q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: q^3+2q^2+3q
       338: 2q^2+2q
       340: 2q^2+2q
       342: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: q^2+3q
       348: q^2+2q
       349: q^2+3q
       350: q^2+2q
       351: q^3+2q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: q^2+3q
       356: q^2+2q
       357: q^2+3q
       358: q^2+2q
       359: q^3+2q^2+3q
       360: 2q
       362: 2q
       364: q^2+q
       366: q^2+2q
       367: 3q
       368: q^2+2q
       369: q^2+3q
       370: q^2+3q
       371: q^2+3q
       372: q^2+3q
       373: 2q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q^2+q
       391: q^2+q
       393: q
       394: q
       396: q
       397: q^2+q
       399: q^2+q
       401: q
       403: q
       404: q
       405: q^2+q
       406: q^2+q
       407: q^3+q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       419: q
       422: q
       423: q^2+q
       425: q^2+q
       427: 2q^2+2q
       429: q
       432: q
       433: q^2+q
       435: 2q
       437: 2q
       438: q
       439: q
       440: 2q
       441: q^2+2q
       442: q
       443: q^3+q^2+2q
       444: q^2+q
       445: 2q^2+2q
       447: q
       450: q
       451: q^2+q
       453: 2q
       454: q
       455: 2q
       457: q
       458: 2q
       459: q^2+2q
       460: q
       461: q^2+q
       462: q^3+q^2+2q
       463: 2q^2+2q
       465: 2q
       467: q
       469: q^2+q
       471: 2q
       472: q
       473: q
       474: 2q
       475: q^2+2q
       476: q
       477: 2q^2+2q
       479: 2q^2+2q
       480: q^3+q
       481: 2q
       482: 2q
       483: q^2+2q
       484: 3q
       485: 2q
       487: 2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: q^2+2q
       494: q^2+2q
       495: q^2+2q
       496: q^2+3q
       497: 2q
       498: q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: q^2+3q
       502: 2q
       504: 2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: q^2+3q
       512: q^2+2q
       513: q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: q^2+3q
       519: q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       542: q
       543: q
       545: q^2+q
       547: q^2+q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q^2+q
       563: q^2+q
       565: q
       566: q
       568: q
       569: q^2+q
       570: q^2+q
       573: q^2+q
       574: q^3+q
       575: q^2+q
       577: 2q^2+2q
       583: q
       585: q
       587: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q^2+q
       601: 2q
       603: q
       605: q
       608: q
       609: q^2+q
       611: 2q
       613: q^2+q
       615: 2q
       616: q
       617: 2q
       619: q
       622: q
       623: q
       625: q^2+q
       627: 2q
       629: q^2+q
       631: q
       632: 2q
       633: 2q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       645: q^2+q
       647: 2q
       648: q
       649: q
       650: 2q
       651: 2q
       653: q^2+2q
       654: q
       655: q^2+2q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: 2q
       668: 2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q
       677: q^2+2q
       678: q^2+3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: q^2+2q
       684: q^2+3q
       685: q^2+2q
       686: 2q
       687: q^2+2q
       688: q^2+2q
       689: q^2+2q
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q
       697: q^2+q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       763: q
       765: q
       766: q
       768: q
       769: 2q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       791: q^2+q
       793: 1
       795: q+1
       797: q
       799: q
       801: q
       804: q
       805: q
       808: q
       809: q
       811: q^2+q
       813: 2q
       815: 2q
       816: q
       818: 1
       819: q+1
       821: q
       823: q
       825: q
       828: q
       829: q
       832: q
       833: q
       835: q^2+q
       837: 2q
       839: q
       840: 2q
       841: q
       843: q
       844: 1
       845: q
       848: q
       849: q
       851: q^2+q
       853: 2q
       855: q^2+q
       857: q^2+2q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q
       878: 2q
       879: q^2+2q
       880: q^2+2q
       884: q
       889: q
       916: 1
       932: q
       934: q
       942: 1
       956: q
       958: q
       965: 1
       968: q
       971: 1
       978: q
       979: q
       982: 2q
       988: q
       989: q
       991: q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1008: q^2+q
      1010: q
      1012: q
      1013: 1
      1014: q+1
      1016: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: q+1
      1033: 1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1046: q
      1047: 1
      1048: q
      1050: q
      1052: q
      1055: q
      1056: q
      1059: q
      1060: q
      1062: q^2+q
      1064: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1089: 1
      1098: q
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1138: q
      1141: 1
      1144: 1
      1166: 1
      1188: q
      1191: 1
      1195: 1
      1214: 1
      1217: 1
      1218: 1
      1220: q
      1222: q
      1224: q
      1225: 1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1264: q
      1266: q
      1268: q
      1271: q
      1272: q
      1274: q+1
      1276: q^2+q
      1278: q
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1334: q
      1337: 1
      1350: 1
      1356: 1
      1366: 1
      1382: 1
      1388: 1
      1397: 1
      1430: q
      1433: 1
      1446: q
      1448: 1
      1451: 1
      1454: 1
      1456: 1
      1461: 1
      1462: 1
      1464: 1
      1467: 1
      1468: 1
      1470: q
      1472: q+1
      1474: q
      1476: q
      1479: q
      1480: q
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1492: 1
      1505: 1
      1516: 1
      1565: 1
      1567: 1
      1577: 1
      1585: 1
      1587: 1
      1596: 1
      1609: 1
      1615: 1
      1624: 1
      1631: q
      1634: 1
      1641: 1
      1650: 1
      1657: 1
      1661: 1
      1664: 1
      1665: 1
      1671: q
      1673: 1
      1691: 1
      1702: 1
      1714: 1
      1759: 1
      1781: 1
      1787: 1
      1789: 1
      1798: 1
      1812: 1
      1815: 1
      1820: 1
      1821: 1
      1873: 1
      1884: 1
      1904: 1
      1918: 1
      1953: 1
      2004: 1

2005:    0: q^4+q^3+3q^2+3q
         1: q^4+q^3+3q^2+3q
         2: 2q^4+q^3+2q^2+3q
         3: q^4+q^3+3q^2+3q
         4: q^4+q^3+3q^2+3q
         5: q^4+q^3+3q^2+3q
         6: q^4+q^3+3q^2+3q
         7: 2q^4+q^3+2q^2+3q
         8: 2q^4+q^3+2q^2+3q
         9: q^6+q^4+2q^3+2q^2+2q
        10: q^4+q^3+3q^2+3q
        11: q^4+q^3+3q^2+3q
        12: q^4+q^3+3q^2+3q
        13: q^4+2q^2+3q
        14: q^4+2q^2+3q
        15: q^4+2q^2+3q
        16: q^3+2q^2+3q
        17: q^3+2q^2+3q
        18: q^4+q^3+2q^2+2q
        19: q^4+q^3+3q^2+3q
        20: q^4+q^3+3q^2+3q
        21: 2q^4+q^3+2q^2+3q
        22: q^4+q^3+3q^2+3q
        23: q^4+q^3+3q^2+3q
        24: 2q^4+q^3+2q^2+3q
        25: q^4+q^3+3q^2+3q
        26: q^4+q^3+3q^2+3q
        27: 2q^4+q^3+2q^2+3q
        28: q^3+2q^2+3q
        29: q^4+q^3+3q^2+3q
        30: q^4+2q^2+3q
        31: q^4+q^3+3q^2+3q
        32: q^4+2q^2+3q
        33: q^3+2q^2+3q
        34: q^4+q^3+3q^2+3q
        35: q^4+2q^2+3q
        36: q^3+2q^2+3q
        37: q^4+3q^2+2q
        38: q^3+q
        39: q^4+3q^2+2q
        40: q^3+q
        41: q^4+q^3+2q^2+2q
        42: q^4+q
        43: q^4+2q^2+3q
        44: q^4+2q^2+3q
        45: q^4+2q^2+3q
        46: q^2+3q
        47: q^2+3q
        48: 2q^2+2q
        49: q^3+2q^2+3q
        50: q^3+2q^2+3q
        51: q^4+q^3+2q^2+2q
        52: q^4+q^3+3q^2+3q
        53: q^4+q^3+3q^2+3q
        54: 2q^4+q^3+2q^2+3q
        55: q^4+q^3+3q^2+3q
        56: q^4+q^3+3q^2+3q
        57: 2q^4+q^3+2q^2+3q
        58: q^3+q^2+2q
        59: q^2+q
        60: q^2+q
        61: q^3+q^2+2q
        62: q^4+3q^2+2q
        63: q^3+q
        64: q^4+2q^2+2q
        65: q
        66: 2q^2+2q
        67: q^3+q
        68: 3q
        69: q^2+2q
        70: q^4+2q^2+3q
        71: q^3+2q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^4+3q^2+2q
        75: q^3+q
        76: q^4+3q^2+2q
        77: q^3+q
        78: q^4+q^3+2q^2+2q
        79: q^4+q
        80: q^4+2q^2+3q
        81: q^2+3q
        82: q^4+q^3+3q^2+3q
        83: q^4+2q^2+3q
        84: q^4+2q^2+3q
        85: q^2+3q
        86: q^4+q^3+3q^2+3q
        87: q^4+2q^2+3q
        88: q^2+3q
        89: q^2+3q
        90: 2q^2+2q
        91: q^2+3q
        92: q^2+3q
        93: 2q^2+2q
        94: q^3+2q^2+3q
        95: q^3+2q^2+3q
        96: q^4+q^3+2q^2+2q
        97: q^3+2q^2+3q
        98: q^3+2q^2+3q
        99: q^4+q^3+2q^2+2q
       100: q^4+q^3+3q^2+3q
       101: q^4+q^3+3q^2+3q
       102: 2q^4+q^3+2q^2+3q
       103: q^2+q
       105: q^3+q
       106: q^2+q
       107: q^2+q
       108: q^3+q^2+2q
       109: q^3+q^2+2q
       110: q^2+q
       111: 2q^2+2q
       112: q^3+q
       113: q^4+3q^2+2q
       114: q^3+q
       115: q^4+2q^2+2q
       116: q
       117: 2q
       118: q
       119: q
       120: 2q
       121: q^4+2q^2+2q
       122: q
       123: q^2+2q
       124: q
       125: 3q
       126: q^2+2q
       127: 2q^2+2q
       129: 2q^2+2q
       131: q^3+2q^2+q
       133: 3q
       134: q^2+2q
       135: q^2+3q
       136: q^2+3q
       137: q^2+3q
       138: q^2+2q
       139: q^3+2q^2+3q
       140: q^3+2q^2+3q
       141: q^4+2q^2+3q
       142: q^3+2q^2+3q
       143: q^2+3q
       144: q^2+2q
       145: q^3+2q^2+3q
       146: q^4+2q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: q^4+q^3+3q^2+3q
       150: q^4+2q^2+3q
       151: q^4+3q^2+2q
       152: q^3+q
       153: q^4+3q^2+2q
       154: q^3+q
       155: q^4+q^3+2q^2+2q
       156: q^4+q
       157: q^2+3q
       158: q^2+3q
       159: 2q^2+2q
       160: q^2+3q
       161: q^2+3q
       162: 2q^2+2q
       163: q^2+3q
       164: q^2+3q
       165: 2q^2+2q
       166: q^3+2q^2+3q
       167: q^3+2q^2+3q
       168: q^4+q^3+2q^2+2q
       169: q^2+q
       171: q^3+q
       172: q^2+q
       173: q
       175: q
       176: q
       177: q^2+q
       179: 2q^2+2q
       181: 2q^2+2q
       183: q
       184: 2q
       185: 2q
       186: q
       187: q^2+2q
       188: q
       189: q^4+2q^2+2q
       190: q
       191: 2q
       192: q
       193: q^2+q
       194: q^3+q^2+2q
       195: q^3+q^2+2q
       196: q^2+q
       197: 2q^2+2q
       198: q^3+q
       199: q
       200: 2q
       201: q^2+q
       202: q^3+q^2+2q
       203: q^3+q^2+2q
       204: q^2+q
       205: 2q^2+2q
       206: q^3+q
       207: q^2+2q
       208: q
       209: q^4+3q^2+2q
       210: q^3+q
       211: q^4+2q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: q^2+2q
       222: q^2+3q
       223: q^2+2q
       224: q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q
       228: q^2+2q
       229: q^2+3q
       230: q^2+3q
       231: q^2+2q
       232: 3q
       233: q^2+2q
       234: q^2+3q
       235: q^2+3q
       236: q^2+2q
       237: 2q^2+2q
       239: 2q^2+2q
       241: q^3+2q^2+q
       243: q^3+2q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: q^4+2q^2+3q
       247: q^3+2q^2+3q
       248: q^3+2q^2+3q
       249: q^4+q^3+2q^2+2q
       250: q^2+3q
       251: q^2+3q
       252: 2q^2+2q
       253: q^2+3q
       254: q^2+3q
       255: 2q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: 2q^2+2q
       259: q^2+q
       262: q^2+q
       263: q
       265: q
       266: q
       267: q^2+q
       269: q^2+q
       270: q^3+q
       271: q^2+q
       272: q^3+q
       273: q^2+q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q^2+q
       289: 2q
       291: q^2+q
       293: q
       294: 2q
       295: 2q
       296: q
       297: q^2+2q
       298: q
       299: q
       300: 2q
       301: 2q^2+2q
       303: 2q
       304: q
       305: q^2+2q
       306: q
       307: q
       308: 2q
       309: 2q
       310: q
       311: 2q^2+2q
       313: q^2+2q
       314: q
       315: q^2+q
       317: 2q^2+2q
       319: q^2+q
       320: q^3+q^2+2q
       321: q^3+q^2+2q
       322: q^2+q
       323: 2q^2+2q
       324: q^3+q
       325: q^4+2q^2+2q
       326: q
       327: 2q
       329: 2q
       331: q^2+q
       333: 2q
       334: q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: q^3+2q^2+3q
       338: 2q^2+2q
       340: 2q^2+2q
       342: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: q^2+3q
       348: q^2+2q
       349: q^2+3q
       350: q^2+2q
       351: q^3+2q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: q^2+3q
       356: q^2+2q
       357: q^2+3q
       358: q^2+2q
       359: q^3+2q^2+3q
       360: 2q
       362: 2q
       364: q^2+q
       366: q^2+2q
       367: 3q
       368: q^2+2q
       369: q^2+3q
       370: q^2+3q
       371: q^2+3q
       372: q^2+3q
       373: 2q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: 2q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       389: q^2+q
       391: q^2+q
       393: q
       395: q
       396: q
       397: q^2+q
       399: q^2+q
       401: q
       402: q
       404: q
       405: q^2+q
       406: q^2+q
       408: q^3+q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       420: q
       421: q
       423: q^2+q
       425: q^2+q
       427: 2q^2+2q
       430: q
       431: q
       433: q^2+q
       435: 2q
       437: q
       438: 2q
       439: 2q
       440: q
       441: q^2+2q
       442: q
       443: q^2+q
       444: q^3+q^2+2q
       445: 2q^2+2q
       448: q
       449: q
       451: q^2+q
       453: q
       454: 2q
       455: 2q
       457: 2q
       458: q
       459: q^2+2q
       460: q
       461: q^3+q^2+2q
       462: q^2+q
       463: 2q^2+2q
       465: 2q
       467: q
       469: q^2+q
       471: q
       472: 2q
       473: 2q
       474: q
       475: q^2+2q
       476: q
       477: 2q^2+2q
       479: 2q^2+2q
       480: q^3+q
       481: 2q
       482: 2q
       483: q^2+2q
       484: 3q
       485: 2q
       487: 2q
       489: q^2+q
       491: q^2+2q
       492: 2q
       493: q^2+2q
       494: q^2+2q
       495: q^2+2q
       496: q^2+3q
       497: 2q
       498: q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: q^2+3q
       502: 2q
       504: 2q
       506: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: q^2+3q
       512: q^2+2q
       513: q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: q^2+3q
       519: q^2+3q
       520: 2q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       544: q
       545: q^2+q
       547: q^2+q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: q^2+q
       563: q^2+q
       565: q
       567: q
       568: q
       569: q^2+q
       570: q^2+q
       573: q^2+q
       575: q^2+q
       576: q^3+q
       577: 2q^2+2q
       583: q
       585: q
       587: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q^2+q
       601: 2q
       604: q
       605: q
       607: q
       609: q^2+q
       611: 2q
       613: q^2+q
       615: q
       616: 2q
       617: 2q
       620: q
       621: q
       623: q
       625: q^2+q
       627: 2q
       629: q^2+q
       631: 2q
       632: q
       633: 2q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       645: q^2+q
       647: q
       648: 2q
       649: 2q
       650: q
       651: 2q
       653: q^2+2q
       654: q
       655: q^2+2q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: 2q
       668: 2q
       670: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q
       677: q^2+2q
       678: q^2+3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: q^2+2q
       684: q^2+3q
       685: q^2+2q
       686: 2q
       687: q^2+2q
       688: q^2+2q
       689: q^2+2q
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q
       697: q^2+q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       764: q
       765: q
       767: q
       768: q
       769: 2q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       791: q^2+q
       794: 1
       795: q+1
       797: q
       799: q
       802: q
       803: q
       806: q
       807: q
       809: q
       811: q^2+q
       813: 2q
       815: q
       816: 2q
       817: 1
       819: q+1
       821: q
       823: q
       826: q
       827: q
       830: q
       831: q
       833: q
       835: q^2+q
       837: 2q
       839: 2q
       840: q
       841: q
       843: q
       844: 1
       846: q
       847: q
       849: q
       851: q^2+q
       853: 2q
       855: q^2+q
       857: q^2+2q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q
       878: 2q
       879: q^2+2q
       880: q^2+2q
       884: q
       889: q
       918: 1
       932: q
       934: q
       940: 1
       956: q
       958: q
       966: 1
       968: q
       971: 1
       978: q
       979: q
       982: 2q
       988: q
       990: q
       991: q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1008: q^2+q
      1010: q
      1012: q
      1013: 1
      1014: q+1
      1017: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: q+1
      1032: 1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1046: q
      1047: 1
      1048: q
      1050: q
      1053: q
      1054: q
      1057: q
      1058: q
      1060: q
      1062: q^2+q
      1064: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1090: 1
      1098: q
      1102: q
      1114: 1
      1124: 1
      1132: 1
      1138: q
      1141: 1
      1146: 1
      1164: 1
      1188: q
      1191: 1
      1196: 1
      1214: 1
      1216: 1
      1219: 1
      1220: q
      1222: q
      1224: q
      1225: 1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1264: q
      1266: q
      1269: q
      1270: q
      1272: q
      1274: q+1
      1276: q^2+q
      1278: q
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1334: q
      1337: 1
      1348: 1
      1358: 1
      1365: 1
      1380: 1
      1390: 1
      1398: 1
      1430: q
      1433: 1
      1446: q
      1448: 1
      1450: 1
      1455: 1
      1456: 1
      1460: 1
      1463: 1
      1464: 1
      1466: 1
      1469: 1
      1470: q
      1472: q+1
      1474: q
      1477: q
      1478: q
      1480: q
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1493: 1
      1504: 1
      1517: 1
      1563: 1
      1569: 1
      1576: 1
      1583: 1
      1589: 1
      1597: 1
      1607: 1
      1617: 1
      1625: 1
      1631: q
      1634: 1
      1641: 1
      1649: 1
      1658: 1
      1661: 1
      1663: 1
      1666: 1
      1671: q
      1673: 1
      1690: 1
      1703: 1
      1715: 1
      1757: 1
      1783: 1
      1785: 1
      1791: 1
      1799: 1
      1813: 1
      1815: 1
      1819: 1
      1822: 1
      1874: 1
      1885: 1
      1902: 1
      1920: 1
      1954: 1
      2005: 1

2006:    0: q^5+3q^4+2q^3+q^2+q
         1: q^5+3q^4+2q^3+q^2+q
         2: q^5+4q^4+q^3+q^2+q
         3: q^6+2q^5+3q^4+2q^3+q^2+q
         4: q^5+3q^4+2q^3+q^2+q
         5: q^6+2q^5+3q^4+2q^3+q^2+q
         6: q^5+3q^4+2q^3+q^2+q
         7: q^5+4q^4+q^3+q^2+q
         8: q^5+3q^4+q^3+q^2+q
         9: q^6+2q^5+3q^4+q^3+q^2+q
        10: q^5+3q^4+2q^3+q^2+q
        11: q^6+2q^5+3q^4+2q^3+q^2+q
        12: q^5+3q^4+2q^3+q^2+q
        13: 3q^4+q^3+q^2+q
        14: 3q^4+q^3+q^2+q
        15: q^5+2q^4+q^3+q^2+q
        16: q^5+2q^4+2q^3+q^2+q
        17: q^5+2q^4+2q^3+q^2+q
        18: q^5+3q^4+q^3+q^2+q
        19: q^5+3q^4+2q^3+q^2+q
        20: q^5+3q^4+2q^3+q^2+q
        21: q^5+4q^4+q^3+q^2+q
        22: q^5+2q^4+2q^3+q^2+q
        23: q^5+2q^4+2q^3+q^2+q
        24: 3q^4+q^3+q^2+q
        25: q^5+2q^4+2q^3+q^2+q
        26: q^5+2q^4+2q^3+q^2+q
        27: 3q^4+q^3+q^2+q
        28: q^5+2q^4+2q^3+q^2+q
        29: q^5+3q^4+2q^3+q^2+q
        30: 3q^4+q^3+q^2+q
        31: q^5+2q^4+2q^3+q^2+q
        32: 2q^4+q^3+q^2+q
        33: q^5+q^4+2q^3+q^2+q
        34: q^5+2q^4+2q^3+q^2+q
        35: 2q^4+q^3+q^2+q
        36: q^5+q^4+2q^3+q^2+q
        37: q^5+2q^4+2q^3+q^2+q
        39: q^5+2q^4+2q^3+q^2+q
        41: 3q^4+q^3+q^2+q
        43: 3q^4+q^3+q^2+q
        44: 3q^4+q^3+q^2+q
        45: q^5+2q^4+q^3+q^2+q
        46: 2q^4+q^3+q^2+q
        47: q^4+q^3+q^2+q
        48: 2q^4+q^3+q^2+q
        49: q^5+2q^4+2q^3+q^2+q
        50: q^5+2q^4+2q^3+q^2+q
        51: q^5+3q^4+q^3+q^2+q
        52: q^5+2q^4+2q^3+q^2+q
        53: q^5+2q^4+2q^3+q^2+q
        54: 3q^4+q^3+q^2+q
        55: q^5+2q^4+2q^3+q^2+q
        56: q^5+2q^4+2q^3+q^2+q
        57: 3q^4+q^3+q^2+q
        58: q^5+q^4+q^3+q^2+q
        59: q^3
        60: q^5+q^4+q^3+q^2+q
        61: q^3
        62: q^5+2q^4+2q^3+q^2+q
        64: 2q^4+q^3+q^2+q
        66: q^5+q^4+2q^3+q^2+q
        68: q^4+q^2+q
        69: q^4+q^3+q^2+q
        70: 3q^4+q^3+q^2+q
        71: q^5+2q^4+2q^3+q^2+q
        72: q^5+q^4+2q^3+q^2+q
        73: q^5+q^4+2q^3+q^2+q
        74: q^5+2q^4+2q^3+q^2+q
        76: q^5+2q^4+2q^3+q^2+q
        78: 3q^4+q^3+q^2+q
        80: 2q^4+q^3+q^2+q
        81: q^4+q^3+q^2+q
        82: q^5+2q^4+2q^3+q^2+q
        83: 2q^4+q^3+q^2+q
        84: 2q^4+q^3+q^2+q
        85: q^4+q^3+q^2+q
        86: q^5+2q^4+2q^3+q^2+q
        87: 2q^4+q^3+q^2+q
        88: 2q^4+q^3+q^2+q
        89: q^4+q^3+q^2+q
        90: 2q^4+q^3+q^2+q
        91: 2q^4+q^3+q^2+q
        92: q^4+q^3+q^2+q
        93: 2q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: 2q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: 2q^4+q^3+q^2+q
       100: q^4+q^3+q^2+q
       101: q^4+q^3+q^2+q
       102: 2q^4+q^3+q^2+q
       103: q^5+q^4+q^3+q^2+q
       106: q^3
       107: q^5+q^4+q^3+q^2+q
       108: q^3
       109: q^5+q^4+q^3+q^2+q
       110: q^3
       111: q^5+q^4+2q^3+q^2+q
       113: q^5+2q^4+2q^3+q^2+q
       115: 2q^4+q^3+q^2+q
       117: q^4+q^2+q
       119: q^4+q^2+q
       121: 2q^4+q^3+q^2+q
       123: q^4+q^3+q^2+q
       125: q^4+q^2+q
       126: q^4+q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: 2q^4+q^3+q^2+q
       133: q^4+q^2+q
       134: q^4+q^3+q^2+q
       135: q^4+q^3+q^2+q
       136: q^4+q^3+q^2+q
       137: q^4+q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: 2q^4+q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^4+q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: 2q^4+q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^4+q^3+q^2+q
       150: q^4+q^3+q^2+q
       151: q^4+q^3+q^2+q
       153: q^4+q^3+q^2+q
       155: 2q^4+q^3+q^2+q
       157: 2q^4+q^3+q^2+q
       158: q^4+q^3+q^2+q
       159: 2q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^5+q^4+q^3+q^2+q
       172: q^3
       173: q^4+q^2+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^4+q^2+q
       185: q^4+q^2+q
       187: q^4+q^3+q^2+q
       189: 2q^4+q^3+q^2+q
       191: q^4+q^2+q
       193: q^2+q
       195: q^3+q^2+q
       196: q^3
       197: q^2+q
       199: q^4+q^2+q
       201: q^3+q^2+q
       202: q^3
       203: q^2+q
       205: q^2+q
       207: q^4+q^3+q^2+q
       209: q^4+q^3+q^2+q
       211: q^4+q^3+q^2+q
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: q^2+q
       220: q^4+q^2+q
       221: q^4+q^3+q^2+q
       222: q^4+q^3+q^2+q
       223: q^3+q^2+q
       224: q^4+q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
       230: q^3+q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: q^3+q^2+q
       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       259: q^3+q^2+q
       262: q^3
       263: q^4+q^2+q
       267: q^2+q
       271: q^2+q
       275: q^4+q^2+q
       279: q^2+q
       281: q^3+q^2+q
       283: q^2+q
       285: q^2+q
       287: q^3+q^2+q
       289: q^3+q^2+q
       291: q^3+q^2+q
       293: q^4+q^2+q
       295: q^4+q^2+q
       297: q^4+q^3+q^2+q
       299: q^2+q
       301: q^2+q
       303: q^2+q
       305: q^2+q
       307: q^2+q
       309: q^2+q
       311: q^2+q
       313: q^2+q
       315: q^3+q^2+q
       317: q^3+q^2+q
       319: q^2+q
       321: q^2+q
       323: q^2+q
       325: q^4+q^3+q^2+q
       327: q^3+q^2+q
       329: q^3+q^2+q
       331: q^4+q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       377: q^2+q
       381: q^2+q
       385: q^4+q^2+q
       389: q^2+q
       393: q^2+q
       397: q^2+q
       401: q^2+q
       405: q^2+q
       409: q^2+q
       411: q^3+q^2+q
       413: q^2+q
       415: q^3+q^2+q
       417: q^3+q^2+q
       419: q^2+q
       421: q^2+q
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: q^3+q^2+q
       429: q^2+q
       431: q^2+q
       433: q^2+q
       435: q
       437: q^2+q
       439: q^2+q
       441: q^2+q
       443: q^2+q
       445: q^2+q
       447: q^2+q
       449: q^2+q
       451: q^2+q
       453: q^2+q
       455: q
       457: q^2+q
       459: q^2+q
       461: q^2+q
       463: q^2+q
       465: q
       467: q^3+q
       469: q^3+q^2+q
       471: q
       473: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       485: q^3+q
       487: q
       489: q^3+q
       491: q^3+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: q^2+q
       496: q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q
       502: q^3+q
       504: q
       506: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       518: q^3+q
       519: q
       520: q^3+q
       521: q^2+q
       525: q^2+q
       529: q^2+q
       533: q^2+q
       537: q
       541: q^2+q
       545: q^2+q
       549: q^2+q
       553: q
       557: q^2+q
       561: q^2+q
       565: q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: q^2+q
       587: q^3+q^2+q
       589: q^2+q
       591: q^2+q
       593: q^2+q
       595: q^2+q
       597: q^3+q
       599: q^3+q^2+q
       601: q
       603: q^2+q
       605: q
       607: q^2+q
       609: q^2+q
       611: q
       613: q^2+q
       615: q
       617: q
       619: q^2+q
       621: q^2+q
       623: q
       625: q^2+q
       627: q
       629: q^2+q
       631: q
       633: q
       635: q
       637: q^3+q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: 2q
       653: q
       655: q
       665: q
       666: q^3+q
       668: q
       670: q^3+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       693: q^2+q
       705: q^2+q
       709: q^2+q
       713: q^2+q
       717: q^2+q
       721: q
       725: q^2+q
       729: q
       733: q
       737: q
       741: q^2+q
       745: q
       749: q
       753: q
       757: 2q
       761: q
       765: q
       769: q
       771: q
       777: q^2+q
       781: q
       783: q^3+q
       785: q
       787: q
       789: q
       791: q
       797: q
       799: q
       801: q
       803: q
       805: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       813: q
       815: q
       821: q
       823: q
       825: q^2+q
       827: q^2+q
       829: q
       831: q
       833: q
       835: q^2+q
       837: q
       839: q
       841: q
       845: q
       847: q
       849: 2q
       851: q
       853: 2q
       855: q
       857: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       884: q
       886: q
       896: q^2+q
       900: q
       904: q
       908: q
       912: q
       920: q
       924: q
       928: q^2+q
       932: q
       936: q
       944: q
       948: q^2+q
       952: q
       956: q
       960: 2q
       970: q
       974: q
       978: 2q
       982: q
       984: q
       988: q
      1002: q
      1004: q
      1006: q
      1008: q
      1010: 2q
      1018: q
      1022: q
      1024: q
      1026: q
      1028: q
      1034: q
      1038: q
      1040: q
      1042: q
      1044: q
      1048: q
      1050: 2q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q
      1078: q
      1082: q
      1085: q
      1088: q
      1098: q
      1100: q
      1110: q
      1118: q
      1126: 2q
      1134: q
      1140: q
      1148: q
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: 2q
      1190: q
      1198: q
      1202: q
      1206: q
      1220: q
      1222: 2q
      1238: q
      1240: q
      1242: q
      1256: q
      1258: q
      1260: q
      1264: q
      1272: q
      1276: q
      1278: q
      1292: q
      1304: q
      1322: 2q
      1330: q
      1336: q
      1344: q
      1352: q
      1360: q
      1368: q
      1376: q
      1384: q
      1392: q
      1400: q
      1414: q
      1446: q
      1480: q
      1491: q
      1559: q
      1571: q
      1591: q
      1619: 1
      1713: 1
      1793: 1
      1807: 1
      1872: 1
      1886: 1
      1948: 1
      2006: 1

2007:    0: 3q^3+3q^2+q+1
         1: 3q^3+3q^2+q+1
         2: q^4+3q^3+2q^2+q+1
         3: 3q^3+3q^2+q+1
         4: 3q^3+3q^2+q+1
         5: 3q^3+3q^2+q+1
         6: 3q^3+3q^2+q+1
         7: q^4+3q^3+2q^2+q+1
         8: q^4+3q^3+2q^2+q+1
         9: q^5+2q^4+2q^3+q^2+q+1
        10: 3q^3+3q^2+q+1
        11: 3q^3+3q^2+q+1
        12: 3q^3+3q^2+q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+q+1
        17: q^3+3q^2+q+1
        18: q^4+2q^3+q^2+q+1
        19: 3q^3+3q^2+q+1
        20: 3q^3+3q^2+q+1
        21: q^4+3q^3+2q^2+q+1
        22: 3q^3+3q^2+q+1
        23: 3q^3+3q^2+q+1
        24: q^4+3q^3+2q^2+q+1
        25: 3q^3+3q^2+q+1
        26: 3q^3+3q^2+q+1
        27: q^4+3q^3+2q^2+q+1
        28: q^3+3q^2+q+1
        29: 3q^3+3q^2+q+1
        30: 2q^3+2q^2+q+1
        31: 3q^3+3q^2+q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+q+1
        34: 3q^3+3q^2+q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+q+1
        37: 2q^2
        38: 3q^3+q^2+q+1
        39: 2q^2
        40: 3q^3+q^2+q+1
        41: q^3+q^2
        42: q^4+2q^3+q^2+q+1
        43: 2q^3+2q^2+q+1
        44: 2q^3+2q^2+q+1
        45: 2q^3+2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+q+1
        50: q^3+3q^2+q+1
        51: q^4+2q^3+q^2+q+1
        52: 3q^3+3q^2+q+1
        53: 3q^3+3q^2+q+1
        54: q^4+3q^3+2q^2+q+1
        55: 3q^3+3q^2+q+1
        56: 3q^3+3q^2+q+1
        57: q^4+3q^3+2q^2+q+1
        58: q^2
        59: q^3+2q^2+q+1
        60: q^3+2q^2+q+1
        61: q^2
        62: 2q^2
        63: 3q^3+q^2+q+1
        64: q^2
        65: 2q^3+q^2+q+1
        66: 2q^2
        67: q^3+q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: 2q^3+2q^2+q+1
        71: q^3+3q^2+q+1
        72: q^3+3q^2+q+1
        73: q^3+3q^2+q+1
        74: 2q^2
        75: 3q^3+q^2+q+1
        76: 2q^2
        77: 3q^3+q^2+q+1
        78: q^3+q^2
        79: q^4+2q^3+q^2+q+1
        80: 2q^3+2q^2+q+1
        81: 2q^2+q+1
        82: 3q^3+3q^2+q+1
        83: 2q^3+2q^2+q+1
        84: 2q^3+2q^2+q+1
        85: 2q^2+q+1
        86: 3q^3+3q^2+q+1
        87: 2q^3+2q^2+q+1
        88: 2q^2+q+1
        89: 2q^2+q+1
        90: q^3+q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+q+1
        95: q^3+3q^2+q+1
        96: q^4+2q^3+q^2+q+1
        97: q^3+3q^2+q+1
        98: q^3+3q^2+q+1
        99: q^4+2q^3+q^2+q+1
       100: 3q^3+3q^2+q+1
       101: 3q^3+3q^2+q+1
       102: q^4+3q^3+2q^2+q+1
       103: q^2
       104: q^3+q^2+q+1
       106: q^2
       107: q^3+2q^2+q+1
       108: q^2
       109: q^2
       110: q^3+2q^2+q+1
       111: 2q^2
       112: q^3+q^2+q+1
       113: 2q^2
       114: 3q^3+q^2+q+1
       115: q^2
       116: 2q^3+q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       121: q^2
       122: 2q^3+q^2+q+1
       123: q^2
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q^3+q^2+q+1
       130: q^3+q^2+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: 2q^2+q+1
       138: q^2+q+1
       139: q^3+3q^2+q+1
       140: q^3+3q^2+q+1
       141: 2q^3+2q^2+q+1
       142: q^3+3q^2+q+1
       143: 2q^2+q+1
       144: q^2+q+1
       145: q^3+3q^2+q+1
       146: 2q^3+2q^2+q+1
       147: q^3+3q^2+q+1
       148: q^3+3q^2+q+1
       149: 3q^3+3q^2+q+1
       150: 2q^3+2q^2+q+1
       151: 2q^2
       152: 3q^3+q^2+q+1
       153: 2q^2
       154: 3q^3+q^2+q+1
       155: q^3+q^2
       156: q^4+2q^3+q^2+q+1
       157: 2q^2+q+1
       158: 2q^2+q+1
       159: q^3+q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+q+1
       167: q^3+3q^2+q+1
       168: q^4+2q^3+q^2+q+1
       169: q^2
       170: q^3+q^2+q+1
       172: q^2
       174: q^2+q+1
       178: q+1
       180: q^3+q^2+q+1
       182: q^3+q^2+q+1
       183: q^2+q+1
       186: q^2+q+1
       187: q^2
       188: q^2+q+1
       189: q^2
       190: 2q^3+q^2+q+1
       192: q^2+q+1
       193: q^3+2q^2+q+1
       194: q^2
       195: q^2
       196: q^3+2q^2+q+1
       197: 2q^2
       198: q^3+q^2+q+1
       199: q^2+q+1
       201: q^3+2q^2+q+1
       202: q^2
       203: q^2
       204: q^3+2q^2+q+1
       205: 2q^2
       206: q^3+q^2+q+1
       207: q^2
       208: q^2+q+1
       209: 2q^2
       210: 3q^3+q^2+q+1
       211: q^2
       212: 2q^3+q^2+q+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: q^2+q+1
       224: 2q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       238: q^3+q^2+q+1
       240: q^3+q^2+q+1
       242: q^4+q^3+q+1
       243: q^3+3q^2+q+1
       244: q^3+3q^2+q+1
       245: q^3+3q^2+q+1
       246: 2q^3+2q^2+q+1
       247: q^3+3q^2+q+1
       248: q^3+3q^2+q+1
       249: q^4+2q^3+q^2+q+1
       250: 2q^2+q+1
       251: 2q^2+q+1
       252: q^3+q^2+q+1
       253: 2q^2+q+1
       254: 2q^2+q+1
       255: q^3+q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       260: q^3+q^2+q+1
       264: q^2+q+1
       267: q^2
       268: q^3+q^2+q+1
       269: q^2
       271: q^2
       273: q^2
       274: q^3+q^2+q+1
       276: q^2+q+1
       280: q^2+1
       282: 1
       283: q+1
       286: q+1
       288: q+1
       290: q^2+1
       292: q+1
       293: q^2+q+1
       296: q^2+q+1
       297: q^2
       298: q^2+q+1
       299: q^2+q+1
       302: q^3+q^2+q+1
       304: q^2+q+1
       305: q^2
       306: q^2+q+1
       307: q^2+q+1
       310: q^2+q+1
       312: q^3+q^2+q+1
       313: q^2
       314: q^2+q+1
       316: q+1
       318: q^3+q^2+q+1
       319: q^3+2q^2+q+1
       320: q^2
       321: q^2
       322: q^3+2q^2+q+1
       323: 2q^2
       324: q^3+q^2+q+1
       325: q^2
       326: 2q^3+q^2+q+1
       328: q^2+1
       330: q^2+1
       332: q^3+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+q+1
       337: q^3+3q^2+q+1
       339: q^3+q^2+q+1
       341: q^3+q^2+q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 2q^2+q+1
       348: q^2+q+1
       349: 2q^2+q+1
       350: q^2+q+1
       351: q^3+3q^2+q+1
       352: q+1
       353: q^2+q+1
       354: q^2+q+1
       355: 2q^2+q+1
       356: q^2+q+1
       357: 2q^2+q+1
       358: q^2+q+1
       359: q^3+3q^2+q+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: q^2+q+1
       367: q^2+q+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: 2q^2+q+1
       375: 2q^2+q+1
       376: q^3+q^2+q+1
       378: q+1
       382: q^2+1
       386: q^2+q+1
       390: q^3+q^2+q+1
       394: q^2+q+1
       400: q^3+q^2+q+1
       403: q^2+q+1
       405: q^2
       406: q^2
       407: q^3+q^2+q+1
       410: q^2+1
       412: 1
       414: 1
       416: q^2+1
       418: 1
       419: q+1
       422: q+1
       424: q+1
       426: q+1
       428: q^3+q^2+q+1
       429: q+1
       432: q+1
       434: q+1
       436: q^2+1
       437: q^2+q+1
       440: q^2+q+1
       441: q^2
       442: q^2+q+1
       443: q^3+2q^2+q+1
       444: q^2
       446: q^3+q^2+q+1
       447: q+1
       450: q+1
       452: q+1
       453: q^2+q+1
       456: q^2+1
       458: q^2+q+1
       459: q^2
       460: q^2+q+1
       461: q^2
       462: q^3+2q^2+q+1
       464: q^3+q^2+q+1
       466: q^2+1
       468: 1
       470: q+1
       471: q^2+q+1
       474: q^2+q+1
       475: q^2
       476: q^2+q+1
       478: q^3+q^2+q+1
       479: 2q^2
       480: q^3+q^2+q+1
       481: q+1
       482: q+1
       483: q^2+q+1
       484: q^2+q+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: q^2+q+1
       492: q+1
       493: q^2+q+1
       494: q^2+q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: q+1
       498: q^2+q+1
       499: q^2+q+1
       500: q^2+q+1
       501: 2q^2+q+1
       503: q^2+1
       505: q^2+1
       507: q^3+1
       508: q+1
       509: q^2+q+1
       510: q^2+q+1
       511: 2q^2+q+1
       512: q^2+q+1
       513: 2q^2+q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+q+1
       519: 2q^2+q+1
       520: q^3+q^2+q+1
       522: 1
       526: q^2+1
       530: q+1
       534: q+1
       538: q^2+1
       542: q^2+q+1
       546: q^3+q^2+q+1
       551: q+1
       556: q^2+1
       560: q^2+q+1
       564: q^3+q^2+q+1
       566: q^2+q+1
       571: q^3+q^2+q+1
       573: q^2
       574: q^3+q^2+q+1
       575: q^2
       581: q^3+q^2+q+1
       584: 1
       586: 1
       588: 1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       598: 1
       600: q+1
       602: q^2+1
       603: q+1
       606: 1
       608: q+1
       610: q+1
       612: q^2+1
       614: q+1
       615: q^2+q+1
       618: q^2+1
       619: q+1
       622: q+1
       624: 1
       626: q+1
       628: q^2+1
       630: q+1
       632: q^2+q+1
       634: q^2+1
       636: q^2+1
       638: 1
       640: 1
       641: q+1
       644: q+1
       646: q+1
       647: q^2+q+1
       650: q^2+q+1
       652: q^2+1
       653: q^2
       654: q^2+q+1
       655: q^2
       656: q^2+q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q^2+1
       669: q^2+1
       671: q^3+1
       672: q^2+q+1
       673: q^2+q+1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+q+1
       678: 2q^2+q+1
       679: q^2+q+1
       680: q+1
       681: q+1
       682: q+1
       683: q^2+q+1
       684: 2q^2+q+1
       685: q^2+q+1
       686: q+1
       687: q^2+q+1
       688: q^2+q+1
       689: q^2+q+1
       690: q+1
       691: q+1
       692: q+1
       699: q^3+q^2+q+1
       706: 1
       710: 1
       715: q+1
       718: q+1
       722: 1
       726: q+1
       730: q^2+1
       734: q^2+1
       740: 1
       744: q+1
       748: q^2+1
       752: q^2+1
       754: q+1
       759: q^2+1
       763: q^2+q+1
       766: q^2+q+1
       773: q^2+1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: 1
       785: q+1
       788: q+1
       790: q^2+1
       792: q+1
       793: 1
       796: q+1
       798: 1
       800: 1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       810: 1
       812: q+1
       814: q^2+1
       815: q^2+q+1
       818: 1
       820: q+1
       822: 1
       824: 1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       834: 1
       836: q+1
       838: q^2+1
       840: q^2+q+1
       842: 1
       843: q
       844: 1
       845: q+1
       848: q+1
       850: 1
       852: q+1
       854: q^2+1
       856: q+1
       857: q^2
       858: q^2+q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+q+1
       873: q+1
       874: q+1
       875: q+1
       876: q^2+q+1
       877: q+1
       878: q+1
       879: q^2+q+1
       880: q^2+q+1
       890: q^2+1
       897: 1
       903: 1
       905: 1
       909: q+1
       913: 1
       917: 1
       921: 1
       926: q+1
       929: q+1
       933: q^2+1
       939: 1
       943: 1
       947: 1
       951: q+1
       953: q+1
       959: q^2+1
       962: 1
       965: 1
       969: q
       972: 1
       976: q+1
       980: q^2+1
       986: q^2+1
       989: q^2+q+1
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 1
      1004: q+1
      1007: q+1
      1009: q+1
      1011: 1
      1012: q
      1013: 1
      1015: q+1
      1016: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: 1
      1026: q+1
      1029: q+1
      1031: q+1
      1033: 1
      1035: 1
      1037: q+1
      1039: 1
      1040: q+1
      1043: 1
      1045: q+1
      1046: q
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: 1
      1076: 1
      1077: q+1
      1078: q+1
      1080: 1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q^2+q+1
      1092: 1
      1104: q^2+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: q+1
      1139: q
      1142: 1
      1145: 1
      1149: 1
      1155: 1
      1157: 1
      1162: q+1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: q+1
      1186: 1
      1189: q
      1192: 1
      1195: 1
      1200: 1
      1205: q+1
      1207: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1224: q
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 1
      1240: q+1
      1243: q+1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 1
      1258: q+1
      1261: q+1
      1265: 1
      1267: 1
      1268: q+1
      1271: q+1
      1273: 1
      1275: q+1
      1277: q+1
      1279: 1
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: q+1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1335: q
      1338: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: q+1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: q+1
      1416: 1
      1421: 1
      1423: 1
      1427: q+1
      1431: q
      1434: 1
      1447: 1
      1449: 1
      1451: 1
      1454: 1
      1457: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: q+1
      1475: 1
      1476: q+1
      1479: q+1
      1481: 1
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1508: 1
      1519: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 1
      1624: 1
      1628: q+1
      1632: q
      1635: 1
      1642: 1
      1650: 1
      1657: 1
      1662: 1
      1664: 1
      1665: 1
      1672: 1
      1673: 1
      1694: 1
      1705: 1
      1716: 1
      1756: 1
      1760: 1
      1779: 1
      1782: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1809: 1
      1812: 1
      1816: 1
      1820: 1
      1821: 1
      1875: 1
      1887: 1
      1905: 1
      1919: 1
      1950: 1
      1953: 1
      2007: 1

2008:    0: 3q^3+3q^2+q+1
         1: 3q^3+3q^2+q+1
         2: q^4+3q^3+2q^2+q+1
         3: 3q^3+3q^2+q+1
         4: 3q^3+3q^2+q+1
         5: 3q^3+3q^2+q+1
         6: 3q^3+3q^2+q+1
         7: q^4+3q^3+2q^2+q+1
         8: q^4+3q^3+2q^2+q+1
         9: q^5+2q^4+2q^3+q^2+q+1
        10: 3q^3+3q^2+q+1
        11: 3q^3+3q^2+q+1
        12: 3q^3+3q^2+q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+q+1
        17: q^3+3q^2+q+1
        18: q^4+2q^3+q^2+q+1
        19: 3q^3+3q^2+q+1
        20: 3q^3+3q^2+q+1
        21: q^4+3q^3+2q^2+q+1
        22: 3q^3+3q^2+q+1
        23: 3q^3+3q^2+q+1
        24: q^4+3q^3+2q^2+q+1
        25: 3q^3+3q^2+q+1
        26: 3q^3+3q^2+q+1
        27: q^4+3q^3+2q^2+q+1
        28: q^3+3q^2+q+1
        29: 3q^3+3q^2+q+1
        30: 2q^3+2q^2+q+1
        31: 3q^3+3q^2+q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+q+1
        34: 3q^3+3q^2+q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+q+1
        37: 2q^2
        38: 3q^3+q^2+q+1
        39: 2q^2
        40: 3q^3+q^2+q+1
        41: q^3+q^2
        42: q^4+2q^3+q^2+q+1
        43: 2q^3+2q^2+q+1
        44: 2q^3+2q^2+q+1
        45: 2q^3+2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+q+1
        50: q^3+3q^2+q+1
        51: q^4+2q^3+q^2+q+1
        52: 3q^3+3q^2+q+1
        53: 3q^3+3q^2+q+1
        54: q^4+3q^3+2q^2+q+1
        55: 3q^3+3q^2+q+1
        56: 3q^3+3q^2+q+1
        57: q^4+3q^3+2q^2+q+1
        58: q^3+2q^2+q+1
        59: q^2
        60: q^2
        61: q^3+2q^2+q+1
        62: 2q^2
        63: 3q^3+q^2+q+1
        64: q^2
        65: 2q^3+q^2+q+1
        66: 2q^2
        67: q^3+q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: 2q^3+2q^2+q+1
        71: q^3+3q^2+q+1
        72: q^3+3q^2+q+1
        73: q^3+3q^2+q+1
        74: 2q^2
        75: 3q^3+q^2+q+1
        76: 2q^2
        77: 3q^3+q^2+q+1
        78: q^3+q^2
        79: q^4+2q^3+q^2+q+1
        80: 2q^3+2q^2+q+1
        81: 2q^2+q+1
        82: 3q^3+3q^2+q+1
        83: 2q^3+2q^2+q+1
        84: 2q^3+2q^2+q+1
        85: 2q^2+q+1
        86: 3q^3+3q^2+q+1
        87: 2q^3+2q^2+q+1
        88: 2q^2+q+1
        89: 2q^2+q+1
        90: q^3+q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+q+1
        95: q^3+3q^2+q+1
        96: q^4+2q^3+q^2+q+1
        97: q^3+3q^2+q+1
        98: q^3+3q^2+q+1
        99: q^4+2q^3+q^2+q+1
       100: 3q^3+3q^2+q+1
       101: 3q^3+3q^2+q+1
       102: q^4+3q^3+2q^2+q+1
       103: q^2
       105: q^3+q^2+q+1
       106: q^2
       107: q^2
       108: q^3+2q^2+q+1
       109: q^3+2q^2+q+1
       110: q^2
       111: 2q^2
       112: q^3+q^2+q+1
       113: 2q^2
       114: 3q^3+q^2+q+1
       115: q^2
       116: 2q^3+q^2+q+1
       117: q^2+q+1
       120: q^2+q+1
       121: q^2
       122: 2q^3+q^2+q+1
       123: q^2
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q^3+q^2+q+1
       130: q^3+q^2+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: 2q^2+q+1
       138: q^2+q+1
       139: q^3+3q^2+q+1
       140: q^3+3q^2+q+1
       141: 2q^3+2q^2+q+1
       142: q^3+3q^2+q+1
       143: 2q^2+q+1
       144: q^2+q+1
       145: q^3+3q^2+q+1
       146: 2q^3+2q^2+q+1
       147: q^3+3q^2+q+1
       148: q^3+3q^2+q+1
       149: 3q^3+3q^2+q+1
       150: 2q^3+2q^2+q+1
       151: 2q^2
       152: 3q^3+q^2+q+1
       153: 2q^2
       154: 3q^3+q^2+q+1
       155: q^3+q^2
       156: q^4+2q^3+q^2+q+1
       157: 2q^2+q+1
       158: 2q^2+q+1
       159: q^3+q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+q+1
       167: q^3+3q^2+q+1
       168: q^4+2q^3+q^2+q+1
       169: q^2
       171: q^3+q^2+q+1
       172: q^2
       175: q^2+q+1
       178: q+1
       180: q^3+q^2+q+1
       182: q^3+q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       187: q^2
       188: q^2+q+1
       189: q^2
       190: 2q^3+q^2+q+1
       191: q^2+q+1
       193: q^2
       194: q^3+2q^2+q+1
       195: q^3+2q^2+q+1
       196: q^2
       197: 2q^2
       198: q^3+q^2+q+1
       200: q^2+q+1
       201: q^2
       202: q^3+2q^2+q+1
       203: q^3+2q^2+q+1
       204: q^2
       205: 2q^2
       206: q^3+q^2+q+1
       207: q^2
       208: q^2+q+1
       209: 2q^2
       210: 3q^3+q^2+q+1
       211: q^2
       212: 2q^3+q^2+q+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: q^2+q+1
       224: 2q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       238: q^3+q^2+q+1
       240: q^3+q^2+q+1
       242: q^4+q^3+q+1
       243: q^3+3q^2+q+1
       244: q^3+3q^2+q+1
       245: q^3+3q^2+q+1
       246: 2q^3+2q^2+q+1
       247: q^3+3q^2+q+1
       248: q^3+3q^2+q+1
       249: q^4+2q^3+q^2+q+1
       250: 2q^2+q+1
       251: 2q^2+q+1
       252: q^3+q^2+q+1
       253: 2q^2+q+1
       254: 2q^2+q+1
       255: q^3+q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       261: q^3+q^2+q+1
       265: q^2+q+1
       267: q^2
       269: q^2
       270: q^3+q^2+q+1
       271: q^2
       272: q^3+q^2+q+1
       273: q^2
       277: q^2+q+1
       280: q^2+1
       282: 1
       284: q+1
       285: q+1
       288: q+1
       290: q^2+1
       292: q+1
       294: q^2+q+1
       295: q^2+q+1
       297: q^2
       298: q^2+q+1
       300: q^2+q+1
       302: q^3+q^2+q+1
       303: q^2+q+1
       305: q^2
       306: q^2+q+1
       308: q^2+q+1
       309: q^2+q+1
       312: q^3+q^2+q+1
       313: q^2
       314: q^2+q+1
       316: q+1
       318: q^3+q^2+q+1
       319: q^2
       320: q^3+2q^2+q+1
       321: q^3+2q^2+q+1
       322: q^2
       323: 2q^2
       324: q^3+q^2+q+1
       325: q^2
       326: 2q^3+q^2+q+1
       328: q^2+1
       330: q^2+1
       332: q^3+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+q+1
       337: q^3+3q^2+q+1
       339: q^3+q^2+q+1
       341: q^3+q^2+q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 2q^2+q+1
       348: q^2+q+1
       349: 2q^2+q+1
       350: q^2+q+1
       351: q^3+3q^2+q+1
       352: q+1
       353: q^2+q+1
       354: q^2+q+1
       355: 2q^2+q+1
       356: q^2+q+1
       357: 2q^2+q+1
       358: q^2+q+1
       359: q^3+3q^2+q+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: q^2+q+1
       367: q^2+q+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: 2q^2+q+1
       375: 2q^2+q+1
       376: q^3+q^2+q+1
       379: q+1
       383: q^2+1
       387: q^2+q+1
       392: q^3+q^2+q+1
       395: q^2+q+1
       398: q^3+q^2+q+1
       402: q^2+q+1
       405: q^2
       406: q^2
       408: q^3+q^2+q+1
       410: q^2+1
       412: 1
       414: 1
       416: q^2+1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       428: q^3+q^2+q+1
       430: q+1
       431: q+1
       434: q+1
       436: q^2+1
       438: q^2+q+1
       439: q^2+q+1
       441: q^2
       442: q^2+q+1
       443: q^2
       444: q^3+2q^2+q+1
       446: q^3+q^2+q+1
       448: q+1
       449: q+1
       452: q+1
       454: q^2+q+1
       456: q^2+1
       457: q^2+q+1
       459: q^2
       460: q^2+q+1
       461: q^3+2q^2+q+1
       462: q^2
       464: q^3+q^2+q+1
       466: q^2+1
       468: 1
       470: q+1
       472: q^2+q+1
       473: q^2+q+1
       475: q^2
       476: q^2+q+1
       478: q^3+q^2+q+1
       479: 2q^2
       480: q^3+q^2+q+1
       481: q+1
       482: q+1
       483: q^2+q+1
       484: q^2+q+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: q^2+q+1
       492: q+1
       493: q^2+q+1
       494: q^2+q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: q+1
       498: q^2+q+1
       499: q^2+q+1
       500: q^2+q+1
       501: 2q^2+q+1
       503: q^2+1
       505: q^2+1
       507: q^3+1
       508: q+1
       509: q^2+q+1
       510: q^2+q+1
       511: 2q^2+q+1
       512: q^2+q+1
       513: 2q^2+q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+q+1
       519: 2q^2+q+1
       520: q^3+q^2+q+1
       523: 1
       527: q^2+1
       531: q+1
       535: q+1
       540: q^2+1
       544: q^2+q+1
       548: q^3+q^2+q+1
       550: q+1
       554: q^2+1
       558: q^2+q+1
       562: q^3+q^2+q+1
       567: q^2+q+1
       572: q^3+q^2+q+1
       573: q^2
       575: q^2
       576: q^3+q^2+q+1
       581: q^3+q^2+q+1
       584: 1
       586: 1
       588: 1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       598: 1
       600: q+1
       602: q^2+1
       604: q+1
       606: 1
       607: q+1
       610: q+1
       612: q^2+1
       614: q+1
       616: q^2+q+1
       618: q^2+1
       620: q+1
       621: q+1
       624: 1
       626: q+1
       628: q^2+1
       630: q+1
       631: q^2+q+1
       634: q^2+1
       636: q^2+1
       638: 1
       640: 1
       642: q+1
       643: q+1
       646: q+1
       648: q^2+q+1
       649: q^2+q+1
       652: q^2+1
       653: q^2
       654: q^2+q+1
       655: q^2
       656: q^2+q+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q^2+1
       669: q^2+1
       671: q^3+1
       672: q^2+q+1
       673: q^2+q+1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+q+1
       678: 2q^2+q+1
       679: q^2+q+1
       680: q+1
       681: q+1
       682: q+1
       683: q^2+q+1
       684: 2q^2+q+1
       685: q^2+q+1
       686: q+1
       687: q^2+q+1
       688: q^2+q+1
       689: q^2+q+1
       690: q+1
       691: q+1
       692: q+1
       700: q^3+q^2+q+1
       707: 1
       711: 1
       714: q+1
       719: q+1
       724: 1
       728: q+1
       732: q^2+1
       736: q^2+1
       738: 1
       742: q+1
       746: q^2+1
       750: q^2+1
       755: q+1
       760: q^2+1
       764: q^2+q+1
       767: q^2+q+1
       773: q^2+1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: 1
       786: q+1
       787: q+1
       790: q^2+1
       792: q+1
       794: 1
       796: q+1
       798: 1
       800: 1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       810: 1
       812: q+1
       814: q^2+1
       816: q^2+q+1
       817: 1
       820: q+1
       822: 1
       824: 1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       834: 1
       836: q+1
       838: q^2+1
       839: q^2+q+1
       842: 1
       843: q
       844: 1
       846: q+1
       847: q+1
       850: 1
       852: q+1
       854: q^2+1
       856: q+1
       857: q^2
       858: q^2+q+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+q+1
       873: q+1
       874: q+1
       875: q+1
       876: q^2+q+1
       877: q+1
       878: q+1
       879: q^2+q+1
       880: q^2+q+1
       891: q^2+1
       898: 1
       901: 1
       907: 1
       910: q+1
       915: 1
       919: 1
       923: 1
       925: q+1
       931: q+1
       935: q^2+1
       937: 1
       941: 1
       945: 1
       949: q+1
       954: q+1
       957: q^2+1
       963: 1
       966: 1
       969: q
       972: 1
       977: q+1
       981: q^2+1
       986: q^2+1
       990: q^2+q+1
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 1
      1005: q+1
      1006: q+1
      1009: q+1
      1011: 1
      1012: q
      1013: 1
      1015: q+1
      1017: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: 1
      1027: q+1
      1028: q+1
      1031: q+1
      1032: 1
      1035: 1
      1037: q+1
      1039: 1
      1041: q+1
      1043: 1
      1044: q+1
      1046: q
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: q+1
      1074: 1
      1076: 1
      1077: q+1
      1078: q+1
      1080: 1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q^2+q+1
      1093: 1
      1105: q^2+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: q+1
      1139: q
      1142: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: q+1
      1165: 1
      1169: 1
      1173: 1
      1179: 1
      1182: q+1
      1187: 1
      1189: q
      1192: 1
      1196: 1
      1201: 1
      1203: q+1
      1209: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1224: q
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 1
      1241: q+1
      1242: q+1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 1
      1259: q+1
      1260: q+1
      1265: 1
      1267: 1
      1269: q+1
      1270: q+1
      1273: 1
      1275: q+1
      1277: q+1
      1279: 1
      1280: q
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: q+1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1335: q
      1338: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: q+1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: q+1
      1417: 1
      1419: 1
      1425: 1
      1428: q+1
      1431: q
      1434: 1
      1447: 1
      1449: 1
      1450: 1
      1455: 1
      1457: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: q+1
      1475: 1
      1477: q+1
      1478: q+1
      1481: 1
      1482: q
      1483: 1
      1484: 1
      1487: 1
      1496: 1
      1507: 1
      1520: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 1
      1625: 1
      1629: q+1
      1632: q
      1635: 1
      1642: 1
      1649: 1
      1658: 1
      1662: 1
      1663: 1
      1666: 1
      1672: 1
      1673: 1
      1693: 1
      1706: 1
      1717: 1
      1755: 1
      1758: 1
      1780: 1
      1784: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1810: 1
      1813: 1
      1816: 1
      1819: 1
      1822: 1
      1876: 1
      1888: 1
      1903: 1
      1921: 1
      1951: 1
      1954: 1
      2008: 1

2009:    0: 3q^3+3q^2+q+1
         1: 3q^3+3q^2+q+1
         2: q^4+3q^3+2q^2+q+1
         3: 3q^3+3q^2+q+1
         4: 3q^3+3q^2+q+1
         5: 3q^3+3q^2+q+1
         6: 3q^3+3q^2+q+1
         7: q^4+3q^3+2q^2+q+1
         8: q^4+3q^3+2q^2+q+1
         9: q^5+2q^4+2q^3+q^2+q+1
        10: 3q^3+3q^2+q+1
        11: 3q^3+3q^2+q+1
        12: 3q^3+3q^2+q+1
        13: 2q^3+2q^2+q+1
        14: 2q^3+2q^2+q+1
        15: 2q^3+2q^2+q+1
        16: q^3+3q^2+q+1
        17: q^3+3q^2+q+1
        18: q^4+2q^3+q^2+q+1
        19: 3q^3+3q^2+q+1
        20: 3q^3+3q^2+q+1
        21: q^4+3q^3+2q^2+q+1
        22: 3q^3+3q^2+q+1
        23: 3q^3+3q^2+q+1
        24: q^4+3q^3+2q^2+q+1
        25: 3q^3+3q^2+q+1
        26: 3q^3+3q^2+q+1
        27: q^4+3q^3+2q^2+q+1
        28: q^3+3q^2+q+1
        29: 3q^3+3q^2+q+1
        30: 2q^3+2q^2+q+1
        31: 3q^3+3q^2+q+1
        32: 2q^3+2q^2+q+1
        33: q^3+3q^2+q+1
        34: 3q^3+3q^2+q+1
        35: 2q^3+2q^2+q+1
        36: q^3+3q^2+q+1
        37: 3q^3+q^2+q+1
        38: 2q^2
        39: 3q^3+q^2+q+1
        40: 2q^2
        41: q^4+2q^3+q^2+q+1
        42: q^3+q^2
        43: 2q^3+2q^2+q+1
        44: 2q^3+2q^2+q+1
        45: 2q^3+2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+3q^2+q+1
        50: q^3+3q^2+q+1
        51: q^4+2q^3+q^2+q+1
        52: 3q^3+3q^2+q+1
        53: 3q^3+3q^2+q+1
        54: q^4+3q^3+2q^2+q+1
        55: 3q^3+3q^2+q+1
        56: 3q^3+3q^2+q+1
        57: q^4+3q^3+2q^2+q+1
        58: q^2
        59: q^3+2q^2+q+1
        60: q^2
        61: q^3+2q^2+q+1
        62: 3q^3+q^2+q+1
        63: 2q^2
        64: 2q^3+q^2+q+1
        65: q^2
        66: q^3+q^2+q+1
        67: 2q^2
        68: q^2+q+1
        69: q^2+q+1
        70: 2q^3+2q^2+q+1
        71: q^3+3q^2+q+1
        72: q^3+3q^2+q+1
        73: q^3+3q^2+q+1
        74: 3q^3+q^2+q+1
        75: 2q^2
        76: 3q^3+q^2+q+1
        77: 2q^2
        78: q^4+2q^3+q^2+q+1
        79: q^3+q^2
        80: 2q^3+2q^2+q+1
        81: 2q^2+q+1
        82: 3q^3+3q^2+q+1
        83: 2q^3+2q^2+q+1
        84: 2q^3+2q^2+q+1
        85: 2q^2+q+1
        86: 3q^3+3q^2+q+1
        87: 2q^3+2q^2+q+1
        88: 2q^2+q+1
        89: 2q^2+q+1
        90: q^3+q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+3q^2+q+1
        95: q^3+3q^2+q+1
        96: q^4+2q^3+q^2+q+1
        97: q^3+3q^2+q+1
        98: q^3+3q^2+q+1
        99: q^4+2q^3+q^2+q+1
       100: 3q^3+3q^2+q+1
       101: 3q^3+3q^2+q+1
       102: q^4+3q^3+2q^2+q+1
       104: q^2
       105: q^2
       106: q^3+q^2+q+1
       107: q^2
       108: q^3+2q^2+q+1
       109: q^2
       110: q^3+2q^2+q+1
       111: q^3+q^2+q+1
       112: 2q^2
       113: 3q^3+q^2+q+1
       114: 2q^2
       115: 2q^3+q^2+q+1
       116: q^2
       118: q^2+q+1
       120: q^2+q+1
       121: 2q^3+q^2+q+1
       122: q^2
       123: q^2+q+1
       124: q^2
       125: q^2+q+1
       126: q^2+q+1
       127: q^3+q^2+q+1
       129: q^3+q^2+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 2q^2+q+1
       137: 2q^2+q+1
       138: q^2+q+1
       139: q^3+3q^2+q+1
       140: q^3+3q^2+q+1
       141: 2q^3+2q^2+q+1
       142: q^3+3q^2+q+1
       143: 2q^2+q+1
       144: q^2+q+1
       145: q^3+3q^2+q+1
       146: 2q^3+2q^2+q+1
       147: q^3+3q^2+q+1
       148: q^3+3q^2+q+1
       149: 3q^3+3q^2+q+1
       150: 2q^3+2q^2+q+1
       151: 3q^3+q^2+q+1
       152: 2q^2
       153: 3q^3+q^2+q+1
       154: 2q^2
       155: q^4+2q^3+q^2+q+1
       156: q^3+q^2
       157: 2q^2+q+1
       158: 2q^2+q+1
       159: q^3+q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^3+q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^3+q^2+q+1
       166: q^3+3q^2+q+1
       167: q^3+3q^2+q+1
       168: q^4+2q^3+q^2+q+1
       170: q^2
       171: q^2
       172: q^3+q^2+q+1
       176: q^2+q+1
       177: q+1
       179: q^3+q^2+q+1
       181: q^3+q^2+q+1
       184: q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q^2
       189: 2q^3+q^2+q+1
       190: q^2
       192: q^2+q+1
       193: q^2
       194: q^3+2q^2+q+1
       195: q^2
       196: q^3+2q^2+q+1
       197: q^3+q^2+q+1
       198: 2q^2
       200: q^2+q+1
       201: q^2
       202: q^3+2q^2+q+1
       203: q^2
       204: q^3+2q^2+q+1
       205: q^3+q^2+q+1
       206: 2q^2
       207: q^2+q+1
       208: q^2
       209: 3q^3+q^2+q+1
       210: 2q^2
       211: 2q^3+q^2+q+1
       212: q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: q^2+q+1
       224: 2q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: 2q^2+q+1
       230: 2q^2+q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: q^3+q^2+q+1
       239: q^3+q^2+q+1
       241: q^4+q^3+q+1
       243: q^3+3q^2+q+1
       244: q^3+3q^2+q+1
       245: q^3+3q^2+q+1
       246: 2q^3+2q^2+q+1
       247: q^3+3q^2+q+1
       248: q^3+3q^2+q+1
       249: q^4+2q^3+q^2+q+1
       250: 2q^2+q+1
       251: 2q^2+q+1
       252: q^3+q^2+q+1
       253: 2q^2+q+1
       254: 2q^2+q+1
       255: q^3+q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q^3+q^2+q+1
       262: q^3+q^2+q+1
       266: q^2+q+1
       268: q^2
       269: q^3+q^2+q+1
       270: q^2
       272: q^2
       273: q^3+q^2+q+1
       274: q^2
       278: q^2+q+1
       279: q^2+1
       281: 1
       284: q+1
       286: q+1
       287: q+1
       289: q^2+1
       291: q+1
       294: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^2
       300: q^2+q+1
       301: q^3+q^2+q+1
       304: q^2+q+1
       305: q^2+q+1
       306: q^2
       308: q^2+q+1
       310: q^2+q+1
       311: q^3+q^2+q+1
       313: q^2+q+1
       314: q^2
       315: q+1
       317: q^3+q^2+q+1
       319: q^2
       320: q^3+2q^2+q+1
       321: q^2
       322: q^3+2q^2+q+1
       323: q^3+q^2+q+1
       324: 2q^2
       325: 2q^3+q^2+q+1
       326: q^2
       327: q^2+1
       329: q^2+1
       331: q^3+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+q+1
       337: q^3+3q^2+q+1
       338: q^3+q^2+q+1
       340: q^3+q^2+q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q^2+q+1
       346: q^2+q+1
       347: 2q^2+q+1
       348: q^2+q+1
       349: 2q^2+q+1
       350: q^2+q+1
       351: q^3+3q^2+q+1
       352: q+1
       353: q^2+q+1
       354: q^2+q+1
       355: 2q^2+q+1
       356: q^2+q+1
       357: 2q^2+q+1
       358: q^2+q+1
       359: q^3+3q^2+q+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: q^2+q+1
       367: q^2+q+1
       368: q^2+q+1
       369: 2q^2+q+1
       370: 2q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^3+q^2+q+1
       374: 2q^2+q+1
       375: 2q^2+q+1
       376: q^3+q^2+q+1
       380: q+1
       384: q^2+1
       388: q^2+q+1
       391: q^3+q^2+q+1
       396: q^2+q+1
       399: q^3+q^2+q+1
       404: q^2+q+1
       406: q^3+q^2+q+1
       407: q^2
       408: q^2
       409: q^2+1
       411: 1
       413: 1
       415: q^2+1
       417: 1
       420: q+1
       422: q+1
       423: q+1
       425: q+1
       427: q^3+q^2+q+1
       430: q+1
       432: q+1
       433: q+1
       435: q^2+1
       438: q^2+q+1
       440: q^2+q+1
       441: q^2+q+1
       442: q^2
       443: q^2
       444: q^3+2q^2+q+1
       445: q^3+q^2+q+1
       448: q+1
       450: q+1
       451: q+1
       454: q^2+q+1
       455: q^2+1
       458: q^2+q+1
       459: q^2+q+1
       460: q^2
       461: q^2
       462: q^3+2q^2+q+1
       463: q^3+q^2+q+1
       465: q^2+1
       467: 1
       469: q+1
       472: q^2+q+1
       474: q^2+q+1
       475: q^2+q+1
       476: q^2
       477: q^3+q^2+q+1
       479: q^3+q^2+q+1
       480: 2q^2
       481: q+1
       482: q+1
       483: q^2+q+1
       484: q^2+q+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: q^2+q+1
       492: q+1
       493: q^2+q+1
       494: q^2+q+1
       495: q^2+q+1
       496: 2q^2+q+1
       497: q+1
       498: q^2+q+1
       499: q^2+q+1
       500: q^2+q+1
       501: 2q^2+q+1
       502: q^2+1
       504: q^2+1
       506: q^3+1
       508: q+1
       509: q^2+q+1
       510: q^2+q+1
       511: 2q^2+q+1
       512: q^2+q+1
       513: 2q^2+q+1
       514: q^2+q+1
       515: q+1
       516: q+1
       517: q+1
       518: 2q^2+q+1
       519: 2q^2+q+1
       520: q^3+q^2+q+1
       524: 1
       528: q^2+1
       532: q+1
       536: q+1
       539: q^2+1
       543: q^2+q+1
       547: q^3+q^2+q+1
       552: q+1
       555: q^2+1
       559: q^2+q+1
       563: q^3+q^2+q+1
       568: q^2+q+1
       570: q^3+q^2+q+1
       574: q^2
       575: q^3+q^2+q+1
       576: q^2
       577: q^3+q^2+q+1
       583: 1
       585: 1
       587: 1
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: 1
       599: q+1
       601: q^2+1
       604: q+1
       605: 1
       608: q+1
       609: q+1
       611: q^2+1
       613: q+1
       616: q^2+q+1
       617: q^2+1
       620: q+1
       622: q+1
       623: 1
       625: q+1
       627: q^2+1
       629: q+1
       632: q^2+q+1
       633: q^2+1
       635: q^2+1
       637: 1
       639: 1
       642: q+1
       644: q+1
       645: q+1
       648: q^2+q+1
       650: q^2+q+1
       651: q^2+1
       653: q^2+q+1
       654: q^2
       655: q^2+q+1
       656: q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q^2+1
       668: q^2+1
       670: q^3+1
       672: q^2+q+1
       673: q^2+q+1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+q+1
       678: 2q^2+q+1
       679: q^2+q+1
       680: q+1
       681: q+1
       682: q+1
       683: q^2+q+1
       684: 2q^2+q+1
       685: q^2+q+1
       686: q+1
       687: q^2+q+1
       688: q^2+q+1
       689: q^2+q+1
       690: q+1
       691: q+1
       692: q+1
       697: q^3+q^2+q+1
       708: 1
       712: 1
       716: q+1
       720: q+1
       723: 1
       727: q+1
       731: q^2+1
       735: q^2+1
       739: 1
       743: q+1
       747: q^2+1
       751: q^2+1
       756: q+1
       758: q^2+1
       762: q^2+q+1
       768: q^2+q+1
       769: q^2+1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: 1
       786: q+1
       788: q+1
       789: q^2+1
       791: q+1
       794: 1
       795: q+1
       797: 1
       799: 1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: 1
       811: q+1
       813: q^2+1
       816: q^2+q+1
       818: 1
       819: q+1
       821: 1
       823: 1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: 1
       835: q+1
       837: q^2+1
       840: q^2+q+1
       841: 1
       843: 1
       844: q
       846: q+1
       848: q+1
       849: 1
       851: q+1
       853: q^2+1
       855: q+1
       857: q^2+q+1
       858: q^2
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+q+1
       873: q+1
       874: q+1
       875: q+1
       876: q^2+q+1
       877: q+1
       878: q+1
       879: q^2+q+1
       880: q^2+q+1
       889: q^2+1
       899: 1
       902: 1
       906: 1
       911: q+1
       914: 1
       918: 1
       922: 1
       927: q+1
       930: q+1
       934: q^2+1
       938: 1
       942: 1
       946: 1
       950: q+1
       955: q+1
       958: q^2+1
       961: 1
       967: 1
       968: 1
       971: q
       975: q+1
       979: q^2+1
       982: q^2+1
       991: q^2+q+1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1005: q+1
      1007: q+1
      1008: q+1
      1010: 1
      1012: 1
      1013: q
      1014: q+1
      1017: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: 1
      1027: q+1
      1029: q+1
      1030: q+1
      1033: 1
      1034: 1
      1036: q+1
      1038: 1
      1041: q+1
      1042: 1
      1045: q+1
      1046: 1
      1047: q
      1048: 1
      1050: 1
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: q+1
      1074: 1
      1076: 1
      1077: q+1
      1078: q+1
      1080: 1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q^2+q+1
      1091: 1
      1102: q^2+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: q+1
      1138: 1
      1141: q
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: q+1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: q+1
      1185: 1
      1188: 1
      1191: q
      1197: 1
      1199: 1
      1204: q+1
      1208: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: q
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 1
      1241: q+1
      1243: q+1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1259: q+1
      1261: q+1
      1264: 1
      1266: 1
      1269: q+1
      1271: q+1
      1272: 1
      1274: q+1
      1276: q+1
      1278: 1
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: q+1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1337: q
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: q+1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: q+1
      1415: 1
      1420: 1
      1424: 1
      1429: q+1
      1430: 1
      1433: q
      1446: 1
      1448: 1
      1451: 1
      1455: 1
      1456: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: q+1
      1474: 1
      1477: q+1
      1479: q+1
      1480: 1
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1494: 1
      1506: 1
      1518: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: q+1
      1631: 1
      1634: q
      1641: 1
      1650: 1
      1658: 1
      1661: 1
      1664: 1
      1666: 1
      1671: 1
      1673: 1
      1692: 1
      1704: 1
      1718: 1
      1754: 1
      1759: 1
      1778: 1
      1783: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1808: 1
      1814: 1
      1815: 1
      1820: 1
      1822: 1
      1877: 1
      1889: 1
      1904: 1
      1920: 1
      1949: 1
      1955: 1
      2009: 1

2010:    0: q^4+q^3+3q^2+3q
         1: q^4+q^3+3q^2+3q
         2: 2q^4+q^3+2q^2+3q
         3: q^4+q^3+3q^2+3q
         4: q^4+q^3+3q^2+3q
         5: q^4+q^3+3q^2+3q
         6: q^4+q^3+3q^2+3q
         7: 2q^4+q^3+2q^2+3q
         8: 2q^4+q^3+2q^2+3q
         9: q^6+q^4+2q^3+2q^2+2q
        10: q^4+q^3+3q^2+3q
        11: q^4+q^3+3q^2+3q
        12: q^4+q^3+3q^2+3q
        13: q^4+2q^2+3q
        14: q^4+2q^2+3q
        15: q^4+2q^2+3q
        16: q^3+2q^2+3q
        17: q^3+2q^2+3q
        18: q^4+q^3+2q^2+2q
        19: q^4+q^3+3q^2+3q
        20: q^4+q^3+3q^2+3q
        21: 2q^4+q^3+2q^2+3q
        22: q^4+q^3+3q^2+3q
        23: q^4+q^3+3q^2+3q
        24: 2q^4+q^3+2q^2+3q
        25: q^4+q^3+3q^2+3q
        26: q^4+q^3+3q^2+3q
        27: 2q^4+q^3+2q^2+3q
        28: q^3+2q^2+3q
        29: q^4+q^3+3q^2+3q
        30: q^4+2q^2+3q
        31: q^4+q^3+3q^2+3q
        32: q^4+2q^2+3q
        33: q^3+2q^2+3q
        34: q^4+q^3+3q^2+3q
        35: q^4+2q^2+3q
        36: q^3+2q^2+3q
        37: q^3+q
        38: q^4+3q^2+2q
        39: q^3+q
        40: q^4+3q^2+2q
        41: q^4+q
        42: q^4+q^3+2q^2+2q
        43: q^4+2q^2+3q
        44: q^4+2q^2+3q
        45: q^4+2q^2+3q
        46: q^2+3q
        47: q^2+3q
        48: 2q^2+2q
        49: q^3+2q^2+3q
        50: q^3+2q^2+3q
        51: q^4+q^3+2q^2+2q
        52: q^4+q^3+3q^2+3q
        53: q^4+q^3+3q^2+3q
        54: 2q^4+q^3+2q^2+3q
        55: q^4+q^3+3q^2+3q
        56: q^4+q^3+3q^2+3q
        57: 2q^4+q^3+2q^2+3q
        58: q^2+q
        59: q^3+q^2+2q
        60: q^2+q
        61: q^3+q^2+2q
        62: q^3+q
        63: q^4+3q^2+2q
        64: q
        65: q^4+2q^2+2q
        66: q^3+q
        67: 2q^2+2q
        68: 3q
        69: q^2+2q
        70: q^4+2q^2+3q
        71: q^3+2q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^3+q
        75: q^4+3q^2+2q
        76: q^3+q
        77: q^4+3q^2+2q
        78: q^4+q
        79: q^4+q^3+2q^2+2q
        80: q^4+2q^2+3q
        81: q^2+3q
        82: q^4+q^3+3q^2+3q
        83: q^4+2q^2+3q
        84: q^4+2q^2+3q
        85: q^2+3q
        86: q^4+q^3+3q^2+3q
        87: q^4+2q^2+3q
        88: q^2+3q
        89: q^2+3q
        90: 2q^2+2q
        91: q^2+3q
        92: q^2+3q
        93: 2q^2+2q
        94: q^3+2q^2+3q
        95: q^3+2q^2+3q
        96: q^4+q^3+2q^2+2q
        97: q^3+2q^2+3q
        98: q^3+2q^2+3q
        99: q^4+q^3+2q^2+2q
       100: q^4+q^3+3q^2+3q
       101: q^4+q^3+3q^2+3q
       102: 2q^4+q^3+2q^2+3q
       104: q^2+q
       105: q^2+q
       106: q^3+q
       107: q^2+q
       108: q^3+q^2+2q
       109: q^2+q
       110: q^3+q^2+2q
       111: q^3+q
       112: 2q^2+2q
       113: q^3+q
       114: q^4+3q^2+2q
       115: q
       116: q^4+2q^2+2q
       117: q
       118: 2q
       119: q
       120: 2q
       121: q
       122: q^4+2q^2+2q
       123: q
       124: q^2+2q
       125: 3q
       126: q^2+2q
       128: 2q^2+2q
       130: 2q^2+2q
       132: q^3+2q^2+q
       133: 3q
       134: q^2+2q
       135: q^2+3q
       136: q^2+3q
       137: q^2+3q
       138: q^2+2q
       139: q^3+2q^2+3q
       140: q^3+2q^2+3q
       141: q^4+2q^2+3q
       142: q^3+2q^2+3q
       143: q^2+3q
       144: q^2+2q
       145: q^3+2q^2+3q
       146: q^4+2q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: q^4+q^3+3q^2+3q
       150: q^4+2q^2+3q
       151: q^3+q
       152: q^4+3q^2+2q
       153: q^3+q
       154: q^4+3q^2+2q
       155: q^4+q
       156: q^4+q^3+2q^2+2q
       157: q^2+3q
       158: q^2+3q
       159: 2q^2+2q
       160: q^2+3q
       161: q^2+3q
       162: 2q^2+2q
       163: q^2+3q
       164: q^2+3q
       165: 2q^2+2q
       166: q^3+2q^2+3q
       167: q^3+2q^2+3q
       168: q^4+q^3+2q^2+2q
       170: q^2+q
       171: q^2+q
       172: q^3+q
       174: q
       175: q
       176: q
       178: q^2+q
       180: 2q^2+2q
       182: 2q^2+2q
       183: q
       184: 2q
       185: q
       186: 2q
       187: q
       188: q^2+2q
       189: q
       190: q^4+2q^2+2q
       191: q
       192: 2q
       193: q^2+q
       194: q^3+q^2+2q
       195: q^2+q
       196: q^3+q^2+2q
       197: q^3+q
       198: 2q^2+2q
       199: q
       200: 2q
       201: q^2+q
       202: q^3+q^2+2q
       203: q^2+q
       204: q^3+q^2+2q
       205: q^3+q
       206: 2q^2+2q
       207: q
       208: q^2+2q
       209: q^3+q
       210: q^4+3q^2+2q
       211: q
       212: q^4+2q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: q^2+2q
       222: q^2+3q
       223: q^2+2q
       224: q^2+3q
       225: q^2+2q
       226: q^2+2q
       227: 3q
       228: q^2+2q
       229: q^2+3q
       230: q^2+3q
       231: q^2+2q
       232: 3q
       233: q^2+2q
       234: q^2+3q
       235: q^2+3q
       236: q^2+2q
       238: 2q^2+2q
       240: 2q^2+2q
       242: q^3+2q^2+q
       243: q^3+2q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: q^4+2q^2+3q
       247: q^3+2q^2+3q
       248: q^3+2q^2+3q
       249: q^4+q^3+2q^2+2q
       250: q^2+3q
       251: q^2+3q
       252: 2q^2+2q
       253: q^2+3q
       254: q^2+3q
       255: 2q^2+2q
       256: q^2+3q
       257: q^2+3q
       258: 2q^2+2q
       260: q^2+q
       261: q^2+q
       264: q
       265: q
       266: q
       268: q^2+q
       269: q^3+q
       270: q^2+q
       272: q^2+q
       273: q^3+q
       274: q^2+q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q^2+q
       290: 2q
       292: q^2+q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: q^2+2q
       299: q
       300: 2q
       302: 2q^2+2q
       303: q
       304: 2q
       305: q
       306: q^2+2q
       307: q
       308: 2q
       309: q
       310: 2q
       312: 2q^2+2q
       313: q
       314: q^2+2q
       316: q^2+q
       318: 2q^2+2q
       319: q^2+q
       320: q^3+q^2+2q
       321: q^2+q
       322: q^3+q^2+2q
       323: q^3+q
       324: 2q^2+2q
       325: q
       326: q^4+2q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: 2q
       334: q^2+2q
       335: q^2+2q
       336: q^2+2q
       337: q^3+2q^2+3q
       339: 2q^2+2q
       341: 2q^2+2q
       343: q^3+2q^2+q
       344: 2q
       345: 3q
       346: q^2+2q
       347: q^2+3q
       348: q^2+2q
       349: q^2+3q
       350: q^2+2q
       351: q^3+2q^2+3q
       352: 2q
       353: 3q
       354: q^2+2q
       355: q^2+3q
       356: q^2+2q
       357: q^2+3q
       358: q^2+2q
       359: q^3+2q^2+3q
       361: 2q
       363: 2q
       365: q^2+q
       366: q^2+2q
       367: 3q
       368: q^2+2q
       369: q^2+3q
       370: q^2+3q
       371: q^2+3q
       372: q^2+3q
       373: 2q^2+2q
       374: q^2+3q
       375: q^2+3q
       376: 2q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q^2+q
       392: q^2+q
       394: q
       395: q
       396: q
       398: q^2+q
       400: q^2+q
       402: q
       403: q
       404: q
       406: q^3+q
       407: q^2+q
       408: q^2+q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       420: q
       422: q
       424: q^2+q
       426: q^2+q
       428: 2q^2+2q
       430: q
       432: q
       434: q^2+q
       436: 2q
       437: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: q^2+2q
       443: q^2+q
       444: q^3+q^2+2q
       446: 2q^2+2q
       448: q
       450: q
       452: q^2+q
       453: q
       454: 2q
       456: 2q
       457: q
       458: 2q
       459: q
       460: q^2+2q
       461: q^2+q
       462: q^3+q^2+2q
       464: 2q^2+2q
       466: 2q
       468: q
       470: q^2+q
       471: q
       472: 2q
       473: q
       474: 2q
       475: q
       476: q^2+2q
       478: 2q^2+2q
       479: q^3+q
       480: 2q^2+2q
       481: 2q
       482: 2q
       483: q^2+2q
       484: 3q
       486: 2q
       488: 2q
       490: q^2+q
       491: q^2+2q
       492: 2q
       493: q^2+2q
       494: q^2+2q
       495: q^2+2q
       496: q^2+3q
       497: 2q
       498: q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: q^2+3q
       503: 2q
       505: 2q
       507: q^2+q
       508: 2q
       509: 3q
       510: q^2+2q
       511: q^2+3q
       512: q^2+2q
       513: q^2+3q
       514: q^2+2q
       515: q+1
       516: q+1
       517: q+1
       518: q^2+3q
       519: q^2+3q
       520: 2q^2+2q
       526: q
       527: q
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q^2+q
       548: q^2+q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q^2+q
       564: q^2+q
       566: q
       567: q
       568: q
       571: q^2+q
       572: q^2+q
       574: q^2+q
       575: q^3+q
       576: q^2+q
       581: 2q^2+2q
       584: q
       586: q
       588: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q^2+q
       602: 2q
       604: q
       606: q
       608: q
       610: q^2+q
       612: 2q
       614: q^2+q
       615: q
       616: 2q
       618: 2q
       620: q
       622: q
       624: q
       626: q^2+q
       628: 2q
       630: q^2+q
       631: q
       632: 2q
       634: 2q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       646: q^2+q
       647: q
       648: 2q
       649: q
       650: 2q
       652: 2q
       653: q
       654: q^2+2q
       655: q
       656: q^2+2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: 2q
       669: 2q
       671: q^2+q
       672: 3q
       673: q^2+2q
       674: q+1
       675: 2q
       676: 2q
       677: q^2+2q
       678: q^2+3q
       679: q^2+2q
       680: q+1
       681: 2q
       682: 2q
       683: q^2+2q
       684: q^2+3q
       685: q^2+2q
       686: 2q
       687: q^2+2q
       688: q^2+2q
       689: q^2+2q
       690: q+1
       691: q+1
       692: q+1
       699: q^2+q
       700: q^2+q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q
       773: 2q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       792: q^2+q
       794: 1
       796: q+1
       798: q
       800: q
       802: q
       804: q
       806: q
       808: q
       810: q
       812: q^2+q
       814: 2q
       815: q
       816: 2q
       818: 1
       820: q+1
       822: q
       824: q
       826: q
       828: q
       830: q
       832: q
       834: q
       836: q^2+q
       838: 2q
       839: q
       840: 2q
       842: q
       843: 1
       844: q
       846: q
       848: q
       850: q
       852: q^2+q
       854: 2q
       856: q^2+q
       857: q
       858: q^2+2q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: q^2+2q
       873: q+1
       874: q+1
       875: 2q
       876: q^2+2q
       877: 2q
       878: 2q
       879: q^2+2q
       880: q^2+2q
       890: q
       891: q
       919: 1
       933: q
       935: q
       943: 1
       957: q
       959: q
       967: 1
       969: 1
       972: q
       980: q
       981: q
       986: 2q
       989: q
       990: q
       991: q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1009: q^2+q
      1011: q
      1012: 1
      1013: q
      1015: q+1
      1017: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: q+1
      1033: 1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: 1
      1047: q
      1049: q
      1051: q
      1053: q
      1055: q
      1057: q
      1059: q
      1061: q
      1063: q^2+q
      1065: q^2+q
      1074: 1
      1076: 1
      1077: q+1
      1078: 2q
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: q^2+2q
      1094: 1
      1104: q
      1105: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1142: q
      1147: 1
      1167: 1
      1189: 1
      1192: q
      1197: 1
      1215: 1
      1217: 1
      1219: 1
      1221: q
      1223: q
      1224: 1
      1225: q
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1265: q
      1267: q
      1269: q
      1271: q
      1273: q
      1275: q+1
      1277: q^2+q
      1279: q
      1280: 1
      1281: q
      1283: 1
      1285: 1
      1287: 1
      1288: q+1
      1289: 2q
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1338: q
      1351: 1
      1359: 1
      1367: 1
      1383: 1
      1391: 1
      1399: 1
      1431: 1
      1434: q
      1447: q
      1449: 1
      1451: 1
      1455: 1
      1457: 1
      1461: 1
      1463: 1
      1465: 1
      1467: 1
      1469: 1
      1471: q
      1473: q+1
      1475: q
      1477: q
      1479: q
      1481: q
      1482: 1
      1483: q
      1484: 1
      1487: 1
      1497: 1
      1509: 1
      1521: 1
      1566: 1
      1570: 1
      1578: 1
      1586: 1
      1590: 1
      1598: 1
      1610: 1
      1618: 1
      1626: 1
      1632: 1
      1635: q
      1642: 1
      1650: 1
      1658: 1
      1662: 1
      1664: 1
      1666: 1
      1672: q
      1673: 1
      1695: 1
      1707: 1
      1720: 1
      1760: 1
      1784: 1
      1788: 1
      1792: 1
      1800: 1
      1814: 1
      1816: 1
      1820: 1
      1822: 1
      1879: 1
      1890: 1
      1905: 1
      1921: 1
      1955: 1
      2010: 1

2011:    0: q^5+3q^4+2q^3+q^2+q
         1: q^5+3q^4+2q^3+q^2+q
         2: q^5+4q^4+q^3+q^2+q
         3: q^6+2q^5+3q^4+2q^3+q^2+q
         4: q^5+3q^4+2q^3+q^2+q
         5: q^6+2q^5+3q^4+2q^3+q^2+q
         6: q^5+3q^4+2q^3+q^2+q
         7: q^5+4q^4+q^3+q^2+q
         8: q^5+3q^4+q^3+q^2+q
         9: q^6+2q^5+3q^4+q^3+q^2+q
        10: q^5+3q^4+2q^3+q^2+q
        11: q^6+2q^5+3q^4+2q^3+q^2+q
        12: q^5+3q^4+2q^3+q^2+q
        13: 3q^4+q^3+q^2+q
        14: 3q^4+q^3+q^2+q
        15: q^5+2q^4+q^3+q^2+q
        16: q^5+2q^4+2q^3+q^2+q
        17: q^5+2q^4+2q^3+q^2+q
        18: q^5+3q^4+q^3+q^2+q
        19: q^5+3q^4+2q^3+q^2+q
        20: q^5+3q^4+2q^3+q^2+q
        21: q^5+4q^4+q^3+q^2+q
        22: q^5+2q^4+2q^3+q^2+q
        23: q^5+2q^4+2q^3+q^2+q
        24: 3q^4+q^3+q^2+q
        25: q^5+2q^4+2q^3+q^2+q
        26: q^5+2q^4+2q^3+q^2+q
        27: 3q^4+q^3+q^2+q
        28: q^5+2q^4+2q^3+q^2+q
        29: q^5+3q^4+2q^3+q^2+q
        30: 3q^4+q^3+q^2+q
        31: q^5+2q^4+2q^3+q^2+q
        32: 2q^4+q^3+q^2+q
        33: q^5+q^4+2q^3+q^2+q
        34: q^5+2q^4+2q^3+q^2+q
        35: 2q^4+q^3+q^2+q
        36: q^5+q^4+2q^3+q^2+q
        37: q^5+2q^4+2q^3+q^2+q
        39: q^5+2q^4+2q^3+q^2+q
        41: 3q^4+q^3+q^2+q
        43: 3q^4+q^3+q^2+q
        44: 3q^4+q^3+q^2+q
        45: q^5+2q^4+q^3+q^2+q
        46: 2q^4+q^3+q^2+q
        47: q^4+q^3+q^2+q
        48: 2q^4+q^3+q^2+q
        49: q^5+2q^4+2q^3+q^2+q
        50: q^5+2q^4+2q^3+q^2+q
        51: q^5+3q^4+q^3+q^2+q
        52: q^5+2q^4+2q^3+q^2+q
        53: q^5+2q^4+2q^3+q^2+q
        54: 3q^4+q^3+q^2+q
        55: q^5+2q^4+2q^3+q^2+q
        56: q^5+2q^4+2q^3+q^2+q
        57: 3q^4+q^3+q^2+q
        58: q^3
        59: q^5+q^4+q^3+q^2+q
        60: q^3
        61: q^5+q^4+q^3+q^2+q
        62: q^5+2q^4+2q^3+q^2+q
        64: 2q^4+q^3+q^2+q
        66: q^5+q^4+2q^3+q^2+q
        68: q^4+q^2+q
        69: q^4+q^3+q^2+q
        70: 3q^4+q^3+q^2+q
        71: q^5+2q^4+2q^3+q^2+q
        72: q^5+q^4+2q^3+q^2+q
        73: q^5+q^4+2q^3+q^2+q
        74: q^5+2q^4+2q^3+q^2+q
        76: q^5+2q^4+2q^3+q^2+q
        78: 3q^4+q^3+q^2+q
        80: 2q^4+q^3+q^2+q
        81: q^4+q^3+q^2+q
        82: q^5+2q^4+2q^3+q^2+q
        83: 2q^4+q^3+q^2+q
        84: 2q^4+q^3+q^2+q
        85: q^4+q^3+q^2+q
        86: q^5+2q^4+2q^3+q^2+q
        87: 2q^4+q^3+q^2+q
        88: 2q^4+q^3+q^2+q
        89: q^4+q^3+q^2+q
        90: 2q^4+q^3+q^2+q
        91: 2q^4+q^3+q^2+q
        92: q^4+q^3+q^2+q
        93: 2q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: 2q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: 2q^4+q^3+q^2+q
       100: q^4+q^3+q^2+q
       101: q^4+q^3+q^2+q
       102: 2q^4+q^3+q^2+q
       103: q^3
       106: q^5+q^4+q^3+q^2+q
       107: q^3
       108: q^5+q^4+q^3+q^2+q
       109: q^3
       110: q^5+q^4+q^3+q^2+q
       111: q^5+q^4+2q^3+q^2+q
       113: q^5+2q^4+2q^3+q^2+q
       115: 2q^4+q^3+q^2+q
       118: q^4+q^2+q
       120: q^4+q^2+q
       121: 2q^4+q^3+q^2+q
       123: q^4+q^3+q^2+q
       125: q^4+q^2+q
       126: q^4+q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: 2q^4+q^3+q^2+q
       133: q^4+q^2+q
       134: q^4+q^3+q^2+q
       135: q^4+q^3+q^2+q
       136: q^4+q^3+q^2+q
       137: q^4+q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: 2q^4+q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^4+q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: 2q^4+q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^4+q^3+q^2+q
       150: q^4+q^3+q^2+q
       151: q^4+q^3+q^2+q
       153: q^4+q^3+q^2+q
       155: 2q^4+q^3+q^2+q
       157: 2q^4+q^3+q^2+q
       158: q^4+q^3+q^2+q
       159: 2q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3
       172: q^5+q^4+q^3+q^2+q
       176: q^4+q^2+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       184: q^4+q^2+q
       186: q^4+q^2+q
       187: q^4+q^3+q^2+q
       189: 2q^4+q^3+q^2+q
       192: q^4+q^2+q
       194: q^2+q
       195: q^3
       196: q^3+q^2+q
       197: q^2+q
       200: q^4+q^2+q
       201: q^3
       202: q^3+q^2+q
       204: q^2+q
       205: q^2+q
       207: q^4+q^3+q^2+q
       209: q^4+q^3+q^2+q
       211: q^4+q^3+q^2+q
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: q^2+q
       220: q^4+q^2+q
       221: q^4+q^3+q^2+q
       222: q^4+q^3+q^2+q
       223: q^3+q^2+q
       224: q^4+q^3+q^2+q
       225: q^3+q^2+q
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       227: q^2+q
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       231: q^3+q^2+q
       232: q^2+q
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       234: q^3+q^2+q
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       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       259: q^3
       262: q^3+q^2+q
       266: q^4+q^2+q
       269: q^2+q
       273: q^2+q
       278: q^4+q^2+q
       279: q^2+q
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       289: q^3+q^2+q
       291: q^3+q^2+q
       294: q^4+q^2+q
       296: q^4+q^2+q
       297: q^4+q^3+q^2+q
       300: q^2+q
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       304: q^2+q
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       308: q^2+q
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       313: q^2+q
       315: q^3+q^2+q
       317: q^3+q^2+q
       320: q^2+q
       322: q^2+q
       323: q^2+q
       325: q^4+q^3+q^2+q
       327: q^3+q^2+q
       329: q^3+q^2+q
       331: q^4+q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
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       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^2+q
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       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
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       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
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       372: q
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       374: q^3+q
       375: q
       376: q^3+q
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       384: q^2+q
       388: q^4+q^2+q
       391: q^2+q
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       484: q
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       492: q^2+q
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       495: q^2+q
       496: q
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       508: q
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       583: q^2+q
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       590: q^2+q
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       601: q
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       616: q
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       629: q^2+q
       632: q
       633: q
       635: q
       637: q^3+q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: 2q
       653: q
       655: q
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       758: 2q
       762: q
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       777: q^2+q
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       802: q
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       826: q^2+q
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       830: q
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       835: q^2+q
       837: q
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       849: 2q
       851: q
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       855: q
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       899: q^2+q
       902: q
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       914: q
       922: q
       927: q
       930: q^2+q
       934: q
       938: q
       946: q
       950: q^2+q
       955: q
       958: q
       961: 2q
       970: q
       975: q
       979: 2q
       982: q
       984: q
       991: q
      1002: q
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      1010: 2q
      1018: q
      1022: q
      1024: q
      1027: q
      1029: q
      1034: q
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      1041: q
      1042: q
      1045: q
      1048: q
      1050: 2q
      1053: q
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      1127: 2q
      1135: q
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      1185: 2q
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      1222: 2q
      1238: q
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      1323: 2q
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      1560: q
      1572: q
      1592: q
      1622: 1
      1722: 1
      1796: 1
      1808: 1
      1881: 1
      1891: 1
      1949: 1
      2011: 1

2012:    0: q^5+3q^4+2q^3+q^2+q
         1: q^5+3q^4+2q^3+q^2+q
         2: q^5+4q^4+q^3+q^2+q
         3: q^6+2q^5+3q^4+2q^3+q^2+q
         4: q^5+3q^4+2q^3+q^2+q
         5: q^6+2q^5+3q^4+2q^3+q^2+q
         6: q^5+3q^4+2q^3+q^2+q
         7: q^5+4q^4+q^3+q^2+q
         8: q^5+3q^4+q^3+q^2+q
         9: q^6+2q^5+3q^4+q^3+q^2+q
        10: q^5+3q^4+2q^3+q^2+q
        11: q^6+2q^5+3q^4+2q^3+q^2+q
        12: q^5+3q^4+2q^3+q^2+q
        13: 3q^4+q^3+q^2+q
        14: 3q^4+q^3+q^2+q
        15: q^5+2q^4+q^3+q^2+q
        16: q^5+2q^4+2q^3+q^2+q
        17: q^5+2q^4+2q^3+q^2+q
        18: q^5+3q^4+q^3+q^2+q
        19: q^5+3q^4+2q^3+q^2+q
        20: q^5+3q^4+2q^3+q^2+q
        21: q^5+4q^4+q^3+q^2+q
        22: q^5+2q^4+2q^3+q^2+q
        23: q^5+2q^4+2q^3+q^2+q
        24: 3q^4+q^3+q^2+q
        25: q^5+2q^4+2q^3+q^2+q
        26: q^5+2q^4+2q^3+q^2+q
        27: 3q^4+q^3+q^2+q
        28: q^5+2q^4+2q^3+q^2+q
        29: q^5+3q^4+2q^3+q^2+q
        30: 3q^4+q^3+q^2+q
        31: q^5+2q^4+2q^3+q^2+q
        32: 2q^4+q^3+q^2+q
        33: q^5+q^4+2q^3+q^2+q
        34: q^5+2q^4+2q^3+q^2+q
        35: 2q^4+q^3+q^2+q
        36: q^5+q^4+2q^3+q^2+q
        38: q^5+2q^4+2q^3+q^2+q
        40: q^5+2q^4+2q^3+q^2+q
        42: 3q^4+q^3+q^2+q
        43: 3q^4+q^3+q^2+q
        44: 3q^4+q^3+q^2+q
        45: q^5+2q^4+q^3+q^2+q
        46: 2q^4+q^3+q^2+q
        47: q^4+q^3+q^2+q
        48: 2q^4+q^3+q^2+q
        49: q^5+2q^4+2q^3+q^2+q
        50: q^5+2q^4+2q^3+q^2+q
        51: q^5+3q^4+q^3+q^2+q
        52: q^5+2q^4+2q^3+q^2+q
        53: q^5+2q^4+2q^3+q^2+q
        54: 3q^4+q^3+q^2+q
        55: q^5+2q^4+2q^3+q^2+q
        56: q^5+2q^4+2q^3+q^2+q
        57: 3q^4+q^3+q^2+q
        58: q^3
        59: q^5+q^4+q^3+q^2+q
        60: q^5+q^4+q^3+q^2+q
        61: q^3
        63: q^5+2q^4+2q^3+q^2+q
        65: 2q^4+q^3+q^2+q
        67: q^5+q^4+2q^3+q^2+q
        68: q^4+q^2+q
        69: q^4+q^3+q^2+q
        70: 3q^4+q^3+q^2+q
        71: q^5+2q^4+2q^3+q^2+q
        72: q^5+q^4+2q^3+q^2+q
        73: q^5+q^4+2q^3+q^2+q
        75: q^5+2q^4+2q^3+q^2+q
        77: q^5+2q^4+2q^3+q^2+q
        79: 3q^4+q^3+q^2+q
        80: 2q^4+q^3+q^2+q
        81: q^4+q^3+q^2+q
        82: q^5+2q^4+2q^3+q^2+q
        83: 2q^4+q^3+q^2+q
        84: 2q^4+q^3+q^2+q
        85: q^4+q^3+q^2+q
        86: q^5+2q^4+2q^3+q^2+q
        87: 2q^4+q^3+q^2+q
        88: 2q^4+q^3+q^2+q
        89: q^4+q^3+q^2+q
        90: 2q^4+q^3+q^2+q
        91: 2q^4+q^3+q^2+q
        92: q^4+q^3+q^2+q
        93: 2q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: 2q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: 2q^4+q^3+q^2+q
       100: q^4+q^3+q^2+q
       101: q^4+q^3+q^2+q
       102: 2q^4+q^3+q^2+q
       104: q^5+q^4+q^3+q^2+q
       105: q^3
       107: q^5+q^4+q^3+q^2+q
       108: q^3
       109: q^3
       110: q^5+q^4+q^3+q^2+q
       112: q^5+q^4+2q^3+q^2+q
       114: q^5+2q^4+2q^3+q^2+q
       116: 2q^4+q^3+q^2+q
       118: q^4+q^2+q
       119: q^4+q^2+q
       122: 2q^4+q^3+q^2+q
       124: q^4+q^3+q^2+q
       125: q^4+q^2+q
       126: q^4+q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: 2q^4+q^3+q^2+q
       133: q^4+q^2+q
       134: q^4+q^3+q^2+q
       135: q^4+q^3+q^2+q
       136: q^4+q^3+q^2+q
       137: q^4+q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: 2q^4+q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^4+q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: 2q^4+q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^4+q^3+q^2+q
       150: q^4+q^3+q^2+q
       152: q^4+q^3+q^2+q
       154: q^4+q^3+q^2+q
       156: 2q^4+q^3+q^2+q
       157: 2q^4+q^3+q^2+q
       158: q^4+q^3+q^2+q
       159: 2q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^5+q^4+q^3+q^2+q
       171: q^3
       174: q^4+q^2+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^4+q^2+q
       186: q^4+q^2+q
       188: q^4+q^3+q^2+q
       190: 2q^4+q^3+q^2+q
       192: q^4+q^2+q
       193: q^2+q
       195: q^3
       196: q^3+q^2+q
       198: q^2+q
       199: q^4+q^2+q
       201: q^3+q^2+q
       202: q^3
       204: q^2+q
       206: q^2+q
       208: q^4+q^3+q^2+q
       210: q^4+q^3+q^2+q
       212: q^4+q^3+q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: q^2+q
       220: q^4+q^2+q
       221: q^4+q^3+q^2+q
       222: q^4+q^3+q^2+q
       223: q^3+q^2+q
       224: q^4+q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
       230: q^3+q^2+q
       231: q^3+q^2+q
       232: q^2+q
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       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       260: q^3+q^2+q
       261: q^3
       264: q^4+q^2+q
       268: q^2+q
       274: q^2+q
       276: q^4+q^2+q
       280: q^2+q
       282: q^3+q^2+q
       283: q^2+q
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       288: q^3+q^2+q
       290: q^3+q^2+q
       292: q^3+q^2+q
       293: q^4+q^2+q
       296: q^4+q^2+q
       298: q^4+q^3+q^2+q
       299: q^2+q
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       304: q^2+q
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       318: q^3+q^2+q
       319: q^2+q
       322: q^2+q
       324: q^2+q
       326: q^4+q^3+q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^4+q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
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       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       378: q^2+q
       382: q^2+q
       386: q^4+q^2+q
       390: q^2+q
       394: q^2+q
       400: q^2+q
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       426: q^3+q^2+q
       428: q^3+q^2+q
       429: q^2+q
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       436: q
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       491: q^3+q
       492: q^2+q
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       494: q^3+q^2+q
       495: q^2+q
       496: q
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       499: q^2+q
       500: q^2+q
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       503: q^3+q
       505: q
       507: q^3+q
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       518: q^3+q
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       520: q^3+q
       522: q^2+q
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       534: q^2+q
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       586: q^2+q
       588: q^3+q^2+q
       589: q^2+q
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       596: q^2+q
       598: q^3+q
       600: q^3+q^2+q
       602: q
       603: q^2+q
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       638: q^3+q
       640: q
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       644: q
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       647: q
       650: q
       652: 2q
       654: q
       656: q
       665: q
       667: q^3+q
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       675: q
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       836: q^2+q
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       850: 2q
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       897: q^2+q
       903: q
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       913: q
       921: q
       926: q
       929: q^2+q
       933: q
       939: q
       947: q
       951: q^2+q
       953: q
       959: q
       962: 2q
       973: q
       976: q
       980: 2q
       986: q
       987: q
       989: q
      1003: q
      1004: q
      1007: q
      1009: q
      1011: 2q
      1019: q
      1023: q
      1025: q
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      1029: q
      1035: q
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      1043: q
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      1049: q
      1051: 2q
      1052: q
      1055: q
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      1078: q
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      1113: q
      1119: q
      1128: 2q
      1136: q
      1143: q
      1149: q
      1155: q
      1157: q
      1162: q
      1171: q
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      1177: q
      1181: q
      1186: 2q
      1193: q
      1200: q
      1205: q
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      1221: q
      1223: 2q
      1239: q
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      1265: q
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      1324: 2q
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      1416: q
      1447: q
      1481: q
      1499: q
      1561: q
      1574: q
      1593: q
      1620: 1
      1719: 1
      1794: 1
      1809: 1
      1878: 1
      1892: 1
      1950: 1
      2012: 1

2013:    0: q^5+3q^4+2q^3+q^2+q
         1: q^5+3q^4+2q^3+q^2+q
         2: q^5+4q^4+q^3+q^2+q
         3: q^6+2q^5+3q^4+2q^3+q^2+q
         4: q^5+3q^4+2q^3+q^2+q
         5: q^6+2q^5+3q^4+2q^3+q^2+q
         6: q^5+3q^4+2q^3+q^2+q
         7: q^5+4q^4+q^3+q^2+q
         8: q^5+3q^4+q^3+q^2+q
         9: q^6+2q^5+3q^4+q^3+q^2+q
        10: q^5+3q^4+2q^3+q^2+q
        11: q^6+2q^5+3q^4+2q^3+q^2+q
        12: q^5+3q^4+2q^3+q^2+q
        13: 3q^4+q^3+q^2+q
        14: 3q^4+q^3+q^2+q
        15: q^5+2q^4+q^3+q^2+q
        16: q^5+2q^4+2q^3+q^2+q
        17: q^5+2q^4+2q^3+q^2+q
        18: q^5+3q^4+q^3+q^2+q
        19: q^5+3q^4+2q^3+q^2+q
        20: q^5+3q^4+2q^3+q^2+q
        21: q^5+4q^4+q^3+q^2+q
        22: q^5+2q^4+2q^3+q^2+q
        23: q^5+2q^4+2q^3+q^2+q
        24: 3q^4+q^3+q^2+q
        25: q^5+2q^4+2q^3+q^2+q
        26: q^5+2q^4+2q^3+q^2+q
        27: 3q^4+q^3+q^2+q
        28: q^5+2q^4+2q^3+q^2+q
        29: q^5+3q^4+2q^3+q^2+q
        30: 3q^4+q^3+q^2+q
        31: q^5+2q^4+2q^3+q^2+q
        32: 2q^4+q^3+q^2+q
        33: q^5+q^4+2q^3+q^2+q
        34: q^5+2q^4+2q^3+q^2+q
        35: 2q^4+q^3+q^2+q
        36: q^5+q^4+2q^3+q^2+q
        38: q^5+2q^4+2q^3+q^2+q
        40: q^5+2q^4+2q^3+q^2+q
        42: 3q^4+q^3+q^2+q
        43: 3q^4+q^3+q^2+q
        44: 3q^4+q^3+q^2+q
        45: q^5+2q^4+q^3+q^2+q
        46: 2q^4+q^3+q^2+q
        47: q^4+q^3+q^2+q
        48: 2q^4+q^3+q^2+q
        49: q^5+2q^4+2q^3+q^2+q
        50: q^5+2q^4+2q^3+q^2+q
        51: q^5+3q^4+q^3+q^2+q
        52: q^5+2q^4+2q^3+q^2+q
        53: q^5+2q^4+2q^3+q^2+q
        54: 3q^4+q^3+q^2+q
        55: q^5+2q^4+2q^3+q^2+q
        56: q^5+2q^4+2q^3+q^2+q
        57: 3q^4+q^3+q^2+q
        58: q^5+q^4+q^3+q^2+q
        59: q^3
        60: q^3
        61: q^5+q^4+q^3+q^2+q
        63: q^5+2q^4+2q^3+q^2+q
        65: 2q^4+q^3+q^2+q
        67: q^5+q^4+2q^3+q^2+q
        68: q^4+q^2+q
        69: q^4+q^3+q^2+q
        70: 3q^4+q^3+q^2+q
        71: q^5+2q^4+2q^3+q^2+q
        72: q^5+q^4+2q^3+q^2+q
        73: q^5+q^4+2q^3+q^2+q
        75: q^5+2q^4+2q^3+q^2+q
        77: q^5+2q^4+2q^3+q^2+q
        79: 3q^4+q^3+q^2+q
        80: 2q^4+q^3+q^2+q
        81: q^4+q^3+q^2+q
        82: q^5+2q^4+2q^3+q^2+q
        83: 2q^4+q^3+q^2+q
        84: 2q^4+q^3+q^2+q
        85: q^4+q^3+q^2+q
        86: q^5+2q^4+2q^3+q^2+q
        87: 2q^4+q^3+q^2+q
        88: 2q^4+q^3+q^2+q
        89: q^4+q^3+q^2+q
        90: 2q^4+q^3+q^2+q
        91: 2q^4+q^3+q^2+q
        92: q^4+q^3+q^2+q
        93: 2q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: 2q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: 2q^4+q^3+q^2+q
       100: q^4+q^3+q^2+q
       101: q^4+q^3+q^2+q
       102: 2q^4+q^3+q^2+q
       104: q^3
       105: q^5+q^4+q^3+q^2+q
       107: q^3
       108: q^5+q^4+q^3+q^2+q
       109: q^5+q^4+q^3+q^2+q
       110: q^3
       112: q^5+q^4+2q^3+q^2+q
       114: q^5+2q^4+2q^3+q^2+q
       116: 2q^4+q^3+q^2+q
       117: q^4+q^2+q
       120: q^4+q^2+q
       122: 2q^4+q^3+q^2+q
       124: q^4+q^3+q^2+q
       125: q^4+q^2+q
       126: q^4+q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: 2q^4+q^3+q^2+q
       133: q^4+q^2+q
       134: q^4+q^3+q^2+q
       135: q^4+q^3+q^2+q
       136: q^4+q^3+q^2+q
       137: q^4+q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: 2q^4+q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^4+q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: 2q^4+q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^4+q^3+q^2+q
       150: q^4+q^3+q^2+q
       152: q^4+q^3+q^2+q
       154: q^4+q^3+q^2+q
       156: 2q^4+q^3+q^2+q
       157: 2q^4+q^3+q^2+q
       158: q^4+q^3+q^2+q
       159: 2q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3
       171: q^5+q^4+q^3+q^2+q
       175: q^4+q^2+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       184: q^4+q^2+q
       185: q^4+q^2+q
       188: q^4+q^3+q^2+q
       190: 2q^4+q^3+q^2+q
       191: q^4+q^2+q
       194: q^2+q
       195: q^3+q^2+q
       196: q^3
       198: q^2+q
       200: q^4+q^2+q
       201: q^3
       202: q^3+q^2+q
       203: q^2+q
       206: q^2+q
       208: q^4+q^3+q^2+q
       210: q^4+q^3+q^2+q
       212: q^4+q^3+q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: q^2+q
       220: q^4+q^2+q
       221: q^4+q^3+q^2+q
       222: q^4+q^3+q^2+q
       223: q^3+q^2+q
       224: q^4+q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
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       231: q^3+q^2+q
       232: q^2+q
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       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^4+q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^4+q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       260: q^3
       261: q^3+q^2+q
       265: q^4+q^2+q
       270: q^2+q
       272: q^2+q
       277: q^4+q^2+q
       280: q^2+q
       282: q^3+q^2+q
       284: q^2+q
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       290: q^3+q^2+q
       292: q^3+q^2+q
       294: q^4+q^2+q
       295: q^4+q^2+q
       298: q^4+q^3+q^2+q
       300: q^2+q
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       320: q^2+q
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       324: q^2+q
       326: q^4+q^3+q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^4+q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
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       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       379: q^2+q
       383: q^2+q
       387: q^4+q^2+q
       392: q^2+q
       395: q^2+q
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       410: q^2+q
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       414: q^2+q
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       418: q^3+q^2+q
       420: q^2+q
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       424: q^3+q^2+q
       426: q^3+q^2+q
       428: q^3+q^2+q
       430: q^2+q
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       436: q
       438: q^2+q
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       457: q^2+q
       460: q^2+q
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       464: q^2+q
       466: q
       468: q^3+q
       470: q^3+q^2+q
       472: q
       473: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       486: q^3+q
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       490: q^3+q
       491: q^3+q
       492: q^2+q
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       500: q^2+q
       501: q
       503: q^3+q
       505: q
       507: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       518: q^3+q
       519: q
       520: q^3+q
       523: q^2+q
       527: q^2+q
       531: q^2+q
       535: q^2+q
       540: q
       544: q^2+q
       548: q^2+q
       550: q^2+q
       554: q
       558: q^2+q
       562: q^2+q
       567: q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: q^2+q
       588: q^3+q^2+q
       590: q^2+q
       591: q^2+q
       594: q^2+q
       595: q^2+q
       598: q^3+q
       600: q^3+q^2+q
       602: q
       604: q^2+q
       606: q
       607: q^2+q
       610: q^2+q
       612: q
       614: q^2+q
       616: q
       618: q
       620: q^2+q
       621: q^2+q
       624: q
       626: q^2+q
       628: q
       630: q^2+q
       631: q
       634: q
       636: q
       638: q^3+q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: 2q
       654: q
       656: q
       665: q
       667: q^3+q
       669: q
       671: q^3+q
       672: q
       673: q^3+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       700: q^2+q
       707: q^2+q
       711: q^2+q
       714: q^2+q
       719: q^2+q
       724: q
       728: q^2+q
       732: q
       736: q
       738: q
       742: q^2+q
       746: q
       750: q
       755: q
       760: 2q
       764: q
       767: q
       773: q
       774: q
       778: q^2+q
       782: q
       784: q^3+q
       786: q
       787: q
       790: q
       792: q
       798: q
       800: q
       802: q
       803: q
       806: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       814: q
       816: q
       822: q
       824: q
       826: q^2+q
       827: q^2+q
       830: q
       831: q
       834: q
       836: q^2+q
       838: q
       839: q
       842: q
       846: q
       847: q
       850: 2q
       852: q
       854: 2q
       856: q
       858: q
       868: q
       871: q
       872: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       891: q
       895: q
       898: q^2+q
       901: q
       907: q
       910: q
       915: q
       923: q
       925: q
       931: q^2+q
       935: q
       937: q
       945: q
       949: q^2+q
       954: q
       957: q
       963: 2q
       973: q
       977: q
       981: 2q
       986: q
       987: q
       990: q
      1003: q
      1005: q
      1006: q
      1009: q
      1011: 2q
      1019: q
      1023: q
      1025: q
      1027: q
      1028: q
      1035: q
      1039: q
      1041: q
      1043: q
      1044: q
      1049: q
      1051: 2q
      1053: q
      1054: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q
      1078: q
      1082: q
      1085: q
      1097: q
      1105: q
      1109: q
      1111: q
      1121: q
      1129: 2q
      1137: q
      1143: q
      1151: q
      1153: q
      1159: q
      1161: q
      1169: q
      1173: q
      1179: q
      1182: q
      1187: 2q
      1193: q
      1201: q
      1203: q
      1209: q
      1221: q
      1223: 2q
      1239: q
      1241: q
      1242: q
      1257: q
      1259: q
      1260: q
      1265: q
      1273: q
      1277: q
      1279: q
      1301: q
      1313: q
      1325: 2q
      1333: q
      1339: q
      1345: q
      1355: q
      1362: q
      1370: q
      1377: q
      1387: q
      1395: q
      1403: q
      1417: q
      1447: q
      1481: q
      1500: q
      1562: q
      1573: q
      1594: q
      1621: 1
      1721: 1
      1795: 1
      1810: 1
      1880: 1
      1893: 1
      1951: 1
      2013: 1

2014:    0: q^3+q^2+1
         1: q^3+q^2+1
         2: q^4+q^2+1
         3: q^3+q^2+1
         4: q^3+q^2+1
         5: q^3+q^2+1
         6: q^3+q^2+1
         7: q^4+q^2+1
         8: q^4+q^2+1
         9: q^4+q^2+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^3+q^2+1
        17: q^3+q^2+1
        18: q^4+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^4+q^2+1
        22: q^3+q^2+1
        23: q^3+q^2+1
        24: q^4+q^2+1
        25: q^3+q^2+1
        26: q^3+q^2+1
        27: q^4+q^2+1
        28: q^3+1
        29: q^3+1
        30: q^2+1
        31: q^3+1
        32: q^2+1
        33: q^3+q^2+1
        34: q^3+1
        35: q^2+1
        36: q^3+q^2+1
        37: q^3+1
        38: q^2
        39: q^3+1
        40: q^2
        41: q^4+1
        42: q^2
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^4+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^4+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^4+q^2+1
        58: q^3+1
        60: q^3+1
        62: q^3+1
        64: 1
        65: q^2
        66: q^3+1
        67: q^2
        68: 1
        69: q^2+1
        70: 1
        71: q^3+1
        72: q^3+q^2+1
        73: q^3+q^2+1
        74: q^3+1
        75: q^2
        76: q^3+1
        77: q^2
        78: q^4+1
        79: q^2
        80: 1
        81: q^2+1
        82: q^3+1
        83: q^2+1
        84: 1
        85: q^2+1
        86: q^3+1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^4+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^4+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^4+q^2+1
       103: q^3+1
       107: q^3+1
       109: q^3+1
       111: q^3+1
       112: q^2
       113: q^3+1
       115: 1
       116: q^2
       117: 1
       119: 1
       121: 1
       123: 1
       124: q^2
       125: 1
       126: 1
       127: q^3+1
       128: q^2
       129: q^3+1
       130: q^2
       131: q^4+1
       132: q^2
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: q^3+1
       140: q^3+q^2+1
       141: 1
       142: q^3+q^2+1
       143: 1
       144: q^2+1
       145: q^3+1
       146: 1
       147: q^3+q^2+1
       148: q^3+q^2+1
       149: q^3+1
       150: q^2+1
       151: q^3+1
       152: q^2
       153: q^3+1
       154: q^2
       155: q^4+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^4+q^2+1
       169: q^3+1
       173: 1
       177: 1
       178: q^2
       179: q^3+1
       181: q^3+1
       182: q^2
       183: 1
       185: 1
       187: 1
       188: q^2
       189: 1
       191: 1
       193: q^3+1
       195: q^3+1
       197: q^3+1
       198: q^2
       199: 1
       201: q^3+1
       203: q^3+1
       205: q^3+1
       206: q^2
       207: 1
       209: q^3+1
       211: 1
       212: q^2
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^3+1
       238: q^2
       239: q^3+1
       240: q^2
       241: q^4+1
       242: q^2
       243: q^3+1
       244: q^3+q^2+1
       245: q^3+q^2+1
       246: 1
       247: q^3+q^2+1
       248: q^3+q^2+1
       249: q^4+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       259: q^3+1
       263: 1
       267: q^3+1
       271: q^3+1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       292: q^2
       293: 1
       295: 1
       297: 1
       299: 1
       301: q^3+1
       302: q^2
       303: 1
       305: 1
       306: q^2
       307: 1
       309: 1
       311: q^3+1
       312: q^2
       313: 1
       314: q^2
       315: 1
       316: q^2
       317: q^3+1
       319: q^3+1
       321: q^3+1
       323: q^3+1
       324: q^2
       325: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^3+1
       338: q^3+1
       339: q^2
       340: q^3+1
       341: q^2
       342: q^4+1
       343: q^2
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^3+q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^3+q^2+1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: q^3+1
       393: 1
       397: q^3+1
       401: 1
       405: q^3+1
       413: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       426: q^2
       427: q^3+1
       429: 1
       431: 1
       433: 1
       434: q^2
       435: 1
       437: 1
       439: 1
       441: 1
       443: q^3+1
       445: q^3+1
       446: q^2
       447: 1
       449: 1
       451: 1
       452: q^2
       453: 1
       455: 1
       457: 1
       459: 1
       461: q^3+1
       463: q^3+1
       464: q^2
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       476: q^2
       477: q^3+1
       478: q^2
       479: q^3+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: q^3+1
       549: 1
       553: 1
       557: 1
       561: q^3+1
       565: 1
       569: q^3+1
       573: q^3+1
       577: q^3+1
       581: q^2
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       613: 1
       614: q^2
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       629: 1
       630: q^2
       631: 1
       633: 1
       639: 1
       641: 1
       643: 1
       645: 1
       646: q^2
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       656: q^2
       657: 1
       658: 1
       660: 1
       662: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       693: q^3+1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       779: 1
       781: 1
       785: 1
       787: 1
       791: 1
       792: q^2
       793: 1
       795: 1
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       815: 1
       817: 1
       819: 1
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       839: 1
       843: 1
       844: q^2
       845: 1
       847: 1
       849: 1
       851: 1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       920: 1
       924: 1
       928: 1
       940: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 1
       968: 1
       974: 1
       988: 1
       994: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q^2
      1016: 1
      1020: 1
      1022: 1
      1026: 1
      1028: 1
      1032: 1
      1036: 1
      1038: 1
      1040: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q^2
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1194: 1
      1198: 1
      1202: 1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1266: 1
      1268: 1
      1270: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q^2
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1436: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1474: 1
      1476: 1
      1478: 1
      1482: 1
      1484: 1
      1487: 1
      1501: 1
      1513: 1
      1537: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1641: 1
      1649: 1
      1657: 1
      1659: 1
      1663: 1
      1665: 1
      1673: 1
      1711: 1
      1741: 1
      1757: 1
      1769: 1
      1781: 1
      1797: 1
      1807: 1
      1811: 1
      1817: 1
      1819: 1
      1821: 1
      1882: 1
      1906: 1
      1922: 1
      1944: 1
      1952: 1
      2014: 1

2015:    0: 6q^4+7q^3+2q^2+q
         1: q^5+6q^4+7q^3+2q^2+q
         2: 3q^5+5q^4+5q^3+2q^2+q
         3: 6q^4+7q^3+2q^2+q
         4: 6q^4+7q^3+2q^2+q
         5: q^5+6q^4+7q^3+2q^2+q
         6: q^5+6q^4+7q^3+2q^2+q
         7: 3q^5+5q^4+5q^3+2q^2+q
         8: 2q^5+4q^4+5q^3+2q^2+q
         9: 3q^5+5q^4+5q^3+2q^2+q
        10: 3q^4+4q^3+2q^2+q
        11: 3q^4+4q^3+2q^2+q
        12: 3q^4+4q^3+2q^2+q
        13: 3q^4+5q^3+2q^2+q
        14: 3q^4+5q^3+2q^2+q
        15: 2q^4+5q^3+2q^2+q
        16: 6q^4+7q^3+2q^2+q
        17: q^5+6q^4+7q^3+2q^2+q
        18: 3q^5+5q^4+5q^3+2q^2+q
        19: 6q^4+7q^3+2q^2+q
        20: q^5+6q^4+7q^3+2q^2+q
        21: 3q^5+5q^4+5q^3+2q^2+q
        22: 3q^4+7q^3+2q^2+q
        23: 3q^4+7q^3+2q^2+q
        24: q^5+3q^4+5q^3+2q^2+q
        25: 3q^4+7q^3+2q^2+q
        26: 3q^4+7q^3+2q^2+q
        27: q^5+3q^4+5q^3+2q^2+q
        28: 3q^4+4q^3+2q^2+q
        29: 3q^4+4q^3+2q^2+q
        30: 3q^4+5q^3+2q^2+q
        31: q^4+4q^3+2q^2+q
        32: q^4+5q^3+2q^2+q
        33: 3q^4+7q^3+2q^2+q
        34: q^4+4q^3+2q^2+q
        35: q^4+5q^3+2q^2+q
        36: 3q^4+7q^3+2q^2+q
        37: 4q^3+2q^2+q
        38: q^4+3q^3
        39: 4q^3+2q^2+q
        40: q^4+3q^3
        41: q^4+3q^3+2q^2+q
        42: q^4+2q^3
        43: q^4+2q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+2q^2+q
        46: 3q^4+5q^3+2q^2+q
        47: 2q^4+5q^3+2q^2+q
        48: 3q^4+5q^3+2q^2+q
        49: 6q^4+7q^3+2q^2+q
        50: q^5+6q^4+7q^3+2q^2+q
        51: 3q^5+5q^4+5q^3+2q^2+q
        52: 3q^4+7q^3+2q^2+q
        53: 3q^4+7q^3+2q^2+q
        54: q^5+3q^4+5q^3+2q^2+q
        55: 3q^4+7q^3+2q^2+q
        56: 3q^4+7q^3+2q^2+q
        57: q^5+3q^4+5q^3+2q^2+q
        58: q^4+2q^3+2q^2+q
        59: 2q^3
        60: q^4+2q^3+2q^2+q
        61: 2q^3
        62: 2q^3+2q^2+q
        63: 2q^3
        64: 3q^3+2q^2+q
        65: 2q^3
        66: 4q^3+2q^2+q
        67: q^4+3q^3
        68: 2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: q^4+2q^3+2q^2+q
        71: 3q^4+4q^3+2q^2+q
        72: 3q^4+7q^3+2q^2+q
        73: 3q^4+7q^3+2q^2+q
        74: 4q^3+2q^2+q
        75: q^4+3q^3
        76: 4q^3+2q^2+q
        77: q^4+3q^3
        78: q^4+3q^3+2q^2+q
        79: q^4+2q^3
        80: 2q^3+2q^2+q
        81: q^4+5q^3+2q^2+q
        82: q^4+4q^3+2q^2+q
        83: q^4+5q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+5q^3+2q^2+q
        86: q^4+4q^3+2q^2+q
        87: q^4+5q^3+2q^2+q
        88: q^4+2q^3+2q^2+q
        89: 2q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: 3q^4+5q^3+2q^2+q
        92: 2q^4+5q^3+2q^2+q
        93: 3q^4+5q^3+2q^2+q
        94: 3q^4+7q^3+2q^2+q
        95: 3q^4+7q^3+2q^2+q
        96: q^5+3q^4+5q^3+2q^2+q
        97: 3q^4+7q^3+2q^2+q
        98: 3q^4+7q^3+2q^2+q
        99: q^5+3q^4+5q^3+2q^2+q
       100: 6q^3+2q^2+q
       101: q^4+6q^3+2q^2+q
       102: 2q^4+5q^3+2q^2+q
       103: q^3+2q^2+q
       104: q^3
       105: q^3
       106: q^3
       107: q^4+2q^3+2q^2+q
       108: 2q^3
       109: q^4+2q^3+2q^2+q
       110: 2q^3
       111: 4q^3+2q^2+q
       112: q^4+3q^3
       113: 2q^3+2q^2+q
       114: 2q^3
       115: 3q^3+2q^2+q
       116: 2q^3
       117: 2q^2+q
       119: 2q^2+q
       121: q^3+2q^2+q
       122: q^3
       123: 3q^3+2q^2+q
       124: 2q^3
       125: 2q^2+q
       126: q^4+2q^3+2q^2+q
       127: 4q^3+2q^2+q
       128: q^4+3q^3
       129: 4q^3+2q^2+q
       130: q^4+3q^3
       131: q^4+3q^3+2q^2+q
       132: q^4+2q^3
       133: 2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: q^4+5q^3+2q^2+q
       136: q^4+5q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+4q^3+2q^2+q
       140: 3q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 3q^4+7q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+4q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 3q^4+7q^3+2q^2+q
       148: 3q^3+2q^2+q
       149: 3q^3+2q^2+q
       150: 5q^3+2q^2+q
       151: 3q^3+2q^2+q
       152: 3q^3
       153: 3q^3+2q^2+q
       154: q^4+3q^3
       155: q^4+3q^3+2q^2+q
       156: q^4+2q^3
       157: q^4+2q^3+2q^2+q
       158: 2q^3+2q^2+q
       159: q^4+2q^3+2q^2+q
       160: q^4+4q^3+2q^2+q
       161: q^4+4q^3+2q^2+q
       162: q^4+4q^3+2q^2+q
       163: q^4+4q^3+2q^2+q
       164: q^4+4q^3+2q^2+q
       165: q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3+2q^2+q
       170: q^3
       171: q^3
       172: q^3
       173: 2q^2+q
       177: 3q^3+2q^2+q
       178: 2q^3
       179: 2q^3+2q^2+q
       180: 2q^3
       181: 4q^3+2q^2+q
       182: q^4+3q^3
       183: 2q^2+q
       185: 2q^2+q
       187: 3q^3+2q^2+q
       188: 2q^3
       189: q^3+2q^2+q
       190: q^3
       191: 2q^2+q
       193: q^3+2q^2+q
       195: q^4+2q^3+2q^2+q
       196: 2q^3
       197: q^3+2q^2+q
       198: 2q^3
       199: 2q^2+q
       201: q^4+2q^3+2q^2+q
       202: 2q^3
       203: q^3+2q^2+q
       205: q^3+2q^2+q
       206: 2q^3
       207: q^3+2q^2+q
       208: q^3
       209: q^3+2q^2+q
       210: 2q^3
       211: 3q^3+2q^2+q
       212: 2q^3
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^3+q^2+q
       219: 2q^2+q
       220: 2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 2q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 2q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 2q^3+2q^2+q
       230: q^4+4q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+4q^3+2q^2+q
       235: 2q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3+2q^2+q
       238: 3q^3
       239: 3q^3+2q^2+q
       240: q^4+3q^3
       241: q^4+3q^3+2q^2+q
       242: q^4+2q^3
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: 2q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3+2q^2+q
       260: q^3
       261: q^3
       262: q^3
       263: 2q^2+q
       267: 2q^2+q
       268: q^3
       271: 2q^2+q
       272: q^3
       275: 2q^2+q
       279: q^2+q
       281: q^3+q^2+q
       283: 2q^2+q
       285: 2q^2+q
       287: q^3+2q^2+q
       288: q^3
       289: q^3+q^2+q
       291: 3q^3+2q^2+q
       292: 2q^3
       293: 2q^2+q
       295: 2q^2+q
       297: q^3+2q^2+q
       298: q^3
       299: 2q^2+q
       301: q^3+2q^2+q
       302: 2q^3
       303: 2q^2+q
       305: q^3+2q^2+q
       306: q^3
       307: 2q^2+q
       309: 2q^2+q
       311: q^3+2q^2+q
       312: 2q^3
       313: q^3+2q^2+q
       314: q^3
       315: 3q^3+2q^2+q
       316: 2q^3
       317: q^3+2q^2+q
       318: 2q^3
       319: q^3+2q^2+q
       321: q^3+2q^2+q
       323: 2q^2+q
       324: q^3
       325: q^3+2q^2+q
       326: q^3
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3+2q^2+q
       339: 3q^3
       340: 3q^3+2q^2+q
       341: q^4+3q^3
       342: q^4+3q^3+2q^2+q
       343: q^4+2q^3
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       377: 2q^2+q
       381: q^2+q
       385: 2q^2+q
       389: 2q^2+q
       390: q^3
       393: 2q^2+q
       397: 2q^2+q
       398: q^3
       401: 2q^2+q
       405: 2q^2+q
       413: q^2+q
       417: q^3+q^2+q
       419: 2q^2+q
       421: 2q^2+q
       423: q^3+2q^2+q
       424: q^3
       425: 3q^3+2q^2+q
       426: 2q^3
       427: q^3+2q^2+q
       428: 2q^3
       429: 2q^2+q
       431: 2q^2+q
       433: q^3+2q^2+q
       434: q^3
       435: q
       437: q^2+q
       439: q^2+q
       441: q^2+q
       443: q^3+2q^2+q
       445: q^3+2q^2+q
       446: 2q^3
       447: 2q^2+q
       449: 2q^2+q
       451: q^3+2q^2+q
       452: q^3
       453: q^2+q
       455: q
       457: q^2+q
       459: q^2+q
       461: q^3+2q^2+q
       463: q^3+2q^2+q
       464: 2q^3
       465: q
       467: q^3+q
       469: q^3+2q^2+q
       470: q^3
       471: q^2+q
       473: q^2+q
       475: q^2+q
       477: 2q^2+q
       478: q^3
       479: 2q^2+q
       480: q^3
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       485: q^3+q
       487: q
       489: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       521: q^2+q
       529: 2q^2+q
       533: 2q^2+q
       537: q
       541: q^2+q
       545: 2q^2+q
       546: q^3
       549: 2q^2+q
       553: q
       557: q^2+q
       561: 2q^2+q
       562: q^3
       565: q^2+q
       569: 2q^2+q
       573: 2q^2+q
       577: 2q^2+q
       581: q^3
       585: q^2+q
       589: 2q^2+q
       591: 2q^2+q
       593: 2q^2+q
       595: 2q^2+q
       597: q^3+q
       599: q^3+2q^2+q
       600: q^3
       601: q
       603: q^2+q
       605: q
       607: q^2+q
       609: q^2+q
       613: q^3+2q^2+q
       614: q^3
       615: q^2+q
       617: q
       619: q^2+q
       621: q^2+q
       623: q
       625: q^2+q
       629: q^3+2q^2+q
       630: q^3
       631: q^2+q
       633: q
       639: q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q
       649: q
       651: 2q
       653: q
       655: q^2+q
       657: q^2+q
       658: q^3+q
       660: q
       662: q^3+q
       664: 3q^3+q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       674: q^3+q^2+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       680: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       690: q^3+q
       691: q
       692: q^3+q
       693: 2q^2+q
       709: q^2+q
       713: 2q^2+q
       717: 2q^2+q
       721: q
       725: q^2+q
       733: q
       737: q
       741: q^2+q
       749: q
       753: q^2+q
       757: 2q
       761: q
       765: q^2+q
       769: q
       771: q
       775: q
       779: q^3+q
       781: q
       785: q^2+q
       787: q^2+q
       791: q^2+q
       793: q^2+q
       795: q
       797: q
       801: q
       803: q
       805: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       815: q
       817: q^2+q
       819: q
       821: q
       825: q^2+q
       827: q^2+q
       829: q
       831: q
       833: q
       835: q^2+q
       839: q
       843: q^2+q
       845: q
       847: q
       849: 2q
       851: q
       855: q^2+q
       857: q
       865: q
       866: q^2+q
       867: q^3+q
       868: q
       869: q
       870: q^3+q^2+q
       871: q
       872: q
       873: q
       874: q^3+q^2+q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       884: q
       886: q
       900: q
       904: q
       908: q^2+q
       916: q
       920: q
       924: q
       928: q^2+q
       940: q
       944: q
       948: q^2+q
       952: q
       960: 2q
       964: q^2+q
       968: q
       970: q
       974: q
       988: q
       994: q
       998: q^2+q
      1000: q^2+q
      1004: q
      1006: q
      1008: q
      1010: 2q
      1012: q^2+q
      1016: q
      1020: q
      1022: q
      1026: q
      1028: q
      1032: q
      1036: q
      1038: q
      1040: q
      1044: q
      1046: q
      1048: q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q^2+q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q^2+q
      1085: q
      1086: q
      1088: q
      1114: q
      1122: q
      1126: 2q
      1130: q^2+q
      1134: q
      1138: q
      1140: q
      1152: q
      1156: q
      1160: q
      1172: q
      1176: q
      1180: q
      1194: q
      1198: q
      1202: q
      1206: q
      1216: q
      1218: q
      1220: q
      1224: q
      1230: q
      1232: q
      1234: q
      1240: q
      1242: q
      1248: q
      1250: q
      1254: q
      1258: q
      1260: q
      1274: q
      1276: q
      1278: q
      1280: q^2+q
      1283: q
      1285: q
      1288: q
      1290: q
      1292: q
      1326: q
      1330: q
      1348: q
      1356: q
      1360: q
      1364: q
      1368: q
      1380: q
      1388: q
      1392: q
      1396: q
      1400: q
      1430: q
      1436: q
      1450: q
      1454: q
      1460: q
      1462: q
      1482: q
      1501: q
      1513: q
      1537: q
      1575: q
      1595: q
      1619: 1
      1713: 1
      1807: 1
      1886: 1
      1944: 1
      2015: 1

2016:    0: 6q^3+6q^2+3q
         1: 6q^3+6q^2+3q
         2: 2q^4+5q^3+5q^2+3q
         3: 6q^3+6q^2+3q
         4: 2q^4+5q^3+5q^2+3q
         5: 6q^3+6q^2+3q
         6: 2q^4+5q^3+5q^2+3q
         7: q^5+2q^4+5q^3+4q^2+3q
         8: 2q^4+5q^3+5q^2+3q
         9: q^5+2q^4+5q^3+4q^2+3q
        10: 3q^3+6q^2+3q
        11: 3q^3+6q^2+3q
        12: q^4+3q^3+5q^2+3q
        13: 4q^3+5q^2+3q
        14: q^4+4q^3+4q^2+3q
        15: 4q^3+5q^2+3q
        16: 6q^3+6q^2+3q
        17: 6q^3+6q^2+3q
        18: q^5+2q^4+5q^3+4q^2+3q
        19: 4q^3+5q^2+3q
        20: 4q^3+5q^2+3q
        21: q^4+4q^3+4q^2+3q
        22: 6q^3+6q^2+3q
        23: 6q^3+6q^2+3q
        24: 2q^4+5q^3+5q^2+3q
        25: 6q^3+6q^2+3q
        26: 6q^3+6q^2+3q
        27: 2q^4+5q^3+5q^2+3q
        28: 3q^3+6q^2+3q
        29: 2q^3+5q^2+3q
        30: 3q^3+4q^2+3q
        31: 3q^3+6q^2+3q
        32: 4q^3+5q^2+3q
        33: 6q^3+6q^2+3q
        34: 3q^3+6q^2+3q
        35: 4q^3+5q^2+3q
        36: 6q^3+6q^2+3q
        37: 3q^3+4q^2+2q
        38: 3q^3+2q^2+q
        39: 3q^3+4q^2+2q
        40: 3q^3+2q^2+q
        41: q^4+3q^3+3q^2+2q
        42: q^4+2q^3+2q^2+q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 4q^3+5q^2+3q
        47: 4q^3+5q^2+3q
        48: q^4+4q^3+4q^2+3q
        49: 4q^3+5q^2+3q
        50: 4q^3+5q^2+3q
        51: q^4+4q^3+4q^2+3q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: q^4+4q^3+4q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: q^4+4q^3+4q^2+3q
        58: q^3+2q^2+q
        59: 2q^3+4q^2+2q
        60: 2q^3+4q^2+2q
        61: q^3+2q^2+q
        62: 2q^3+4q^2+2q
        63: q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 3q^3+4q^2+2q
        67: 3q^3+2q^2+q
        68: 4q^2+3q
        69: 3q^3+4q^2+3q
        70: q^3+4q^2+3q
        71: 2q^3+5q^2+3q
        72: 2q^3+4q^2+3q
        73: 2q^3+4q^2+3q
        74: q^3+3q^2+2q
        75: q^3+q^2+q
        76: q^3+3q^2+2q
        77: q^3+q^2+q
        78: 2q^3+2q^2+2q
        79: q^3+q^2+q
        80: q^3+5q^2+3q
        81: 4q^3+5q^2+3q
        82: 2q^3+5q^2+3q
        83: 3q^3+4q^2+3q
        84: q^3+5q^2+3q
        85: 4q^3+5q^2+3q
        86: 2q^3+5q^2+3q
        87: 3q^3+4q^2+3q
        88: q^3+5q^2+3q
        89: q^3+5q^2+3q
        90: 2q^3+4q^2+3q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+4q^2+3q
        94: 4q^3+5q^2+3q
        95: 4q^3+5q^2+3q
        96: q^4+4q^3+4q^2+3q
        97: 4q^3+5q^2+3q
        98: 4q^3+5q^2+3q
        99: q^4+4q^3+4q^2+3q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: q^4+4q^3+4q^2+3q
       103: q^3+2q^2+q
       104: q^3+2q^2+q
       106: q^3+2q^2+q
       107: q^3+3q^2+2q
       108: q^2+q
       109: q^2+q
       110: q^3+3q^2+2q
       111: 2q^2+2q
       112: q^2+q
       113: q^3+3q^2+2q
       114: q^2+q
       115: q^3+2q^2+2q
       116: q^3+q^2+q
       117: q^2+q
       118: 3q^2+2q
       119: 3q^2+2q
       120: q^2+q
       121: q^3+3q^2+2q
       122: 2q^2+q
       123: 2q^3+3q^2+2q
       124: 2q^3+2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+3q
       127: q^3+3q^2+2q
       128: q^3+q^2+q
       129: q^3+3q^2+2q
       130: q^3+q^2+q
       131: 2q^3+2q^2+2q
       132: q^3+q^2+q
       133: 3q^2+3q
       134: 2q^3+4q^2+3q
       135: q^3+3q^2+3q
       136: q^3+3q^2+3q
       137: q^3+5q^2+3q
       138: 3q^3+4q^2+3q
       139: 2q^3+5q^2+3q
       140: 2q^3+4q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+4q^2+3q
       143: q^3+5q^2+3q
       144: 3q^3+4q^2+3q
       145: 2q^3+5q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+4q^2+3q
       148: 2q^3+4q^2+3q
       149: 2q^3+5q^2+3q
       150: 3q^3+4q^2+3q
       151: q^3+3q^2+2q
       152: q^3+q^2+q
       153: q^3+3q^2+2q
       154: q^3+q^2+q
       155: 2q^3+2q^2+2q
       156: q^3+q^2+q
       157: 3q^2+3q
       158: 3q^2+3q
       159: 3q^2+3q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+4q^2+3q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+4q^2+3q
       166: 4q^3+5q^2+3q
       167: 4q^3+5q^2+3q
       168: q^4+4q^3+4q^2+3q
       169: q^2+q
       170: q^2+q
       172: q^2+q
       173: q^2+q
       174: 2q^2+q
       176: q^2+q
       177: q^3+2q^2+2q
       178: q^3+q^2+q
       179: q^3+3q^2+2q
       180: q^2+q
       181: 2q^2+2q
       182: q^2+q
       183: 2q^2+2q
       184: q
       185: q
       186: 2q^2+2q
       187: q^2+2q
       188: q^2+q
       189: q^3+2q^2+2q
       190: q^2+q
       191: q^2+q
       192: 3q^2+2q
       193: q^3+3q^2+2q
       194: q^2+q
       195: q^2+q
       196: q^3+3q^2+2q
       197: 2q^2+2q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: q^3+3q^2+2q
       202: q^2+q
       203: q^2+q
       204: q^3+3q^2+2q
       205: 2q^2+2q
       206: q^2+q
       207: q^3+3q^2+2q
       208: 2q^2+q
       209: q^3+3q^2+2q
       210: q^2+q
       211: q^3+2q^2+2q
       212: q^3+q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 3q^2+3q
       222: 2q^2+3q
       223: q^3+3q^2+3q
       224: 2q^2+3q
       225: q^3+3q^2+3q
       226: q^3+4q^2+3q
       227: 3q^2+3q
       228: 2q^3+4q^2+3q
       229: q^3+3q^2+3q
       230: q^3+3q^2+3q
       231: q^3+4q^2+3q
       232: 3q^2+3q
       233: 2q^3+4q^2+3q
       234: q^3+3q^2+3q
       235: q^3+3q^2+3q
       236: 3q^3+4q^2+3q
       237: q^3+3q^2+2q
       238: q^3+q^2+q
       239: q^3+3q^2+2q
       240: q^3+q^2+q
       241: 2q^3+2q^2+2q
       242: q^3+q^2+q
       243: 2q^3+5q^2+3q
       244: 2q^3+4q^2+3q
       245: 2q^3+4q^2+3q
       246: q^3+4q^2+3q
       247: 5q^2+4q
       248: 5q^2+4q
       249: 3q^3+3q^2+3q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 3q^2+3q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 3q^2+3q
       256: 2q^3+4q^2+3q
       257: 2q^3+4q^2+3q
       258: 2q^3+4q^2+3q
       259: q^2+q
       260: q^2+q
       262: q^2+q
       263: q
       264: q^2+q
       266: q
       267: q^2+q
       268: q^2+q
       269: q^2+q
       271: q^2+q
       273: q^2+q
       274: q^2+q
       275: q^2+q
       276: 2q^2+q
       278: q^2+q
       279: q^2+2q
       281: q^2+2q
       283: 2q^2+2q
       284: q
       285: q
       286: 2q^2+2q
       287: q^3+2q^2+2q
       288: q^2+q
       289: 2q
       291: q^2+2q
       292: q^2+q
       293: q^2+2q
       294: q
       295: q
       296: q^2+2q
       297: q^2+2q
       298: q
       299: 2q^2+2q
       300: q
       301: 2q^2+2q
       302: q^2+q
       303: q
       304: 2q^2+2q
       305: q^2+2q
       306: q^2+q
       307: 2q^2+2q
       308: q
       309: q
       310: 2q^2+2q
       311: 2q^2+2q
       312: q^2+q
       313: q^2+2q
       314: q^2+q
       315: q^3+2q^2+2q
       316: q^3+q^2+q
       317: q^3+3q^2+2q
       318: q^2+q
       319: q^3+3q^2+2q
       320: q^2+q
       321: q^2+q
       322: q^3+3q^2+2q
       323: 2q^2+2q
       324: q^2+q
       325: q^3+2q^2+2q
       326: q^2+q
       333: 2q^2+3q
       334: 2q^2+3q
       335: 2q^2+3q
       336: 2q^2+3q
       337: 4q^2+4q
       338: 3q^2+3q
       339: 2q^2+q
       340: 3q^2+3q
       341: 2q^2+q
       342: 2q^3+2q^2+2q
       343: q^3+q^2+q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 3q^2+3q
       347: 2q^2+3q
       348: q^3+3q^2+3q
       349: 2q^2+3q
       350: q^3+3q^2+3q
       351: 5q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 3q^2+3q
       355: 2q^2+3q
       356: q^3+3q^2+3q
       357: 2q^2+3q
       358: q^3+3q^2+3q
       359: 5q^2+4q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: q^3+4q^2+3q
       367: 3q^2+3q
       368: 2q^3+4q^2+3q
       369: q^3+3q^2+3q
       370: q^3+3q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 3q^2+3q
       375: 3q^2+3q
       376: 3q^2+3q
       377: q
       378: q^2+q
       380: q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q^2+q
       390: q^2+q
       391: q^2+q
       393: q
       394: q^2+q
       396: q
       397: q^2+q
       399: q^2+q
       400: q^2+q
       401: q
       403: q^2+q
       404: q
       405: q^2+q
       406: q^2+q
       407: q^2+q
       413: q^2+2q
       417: 2q
       419: q^2+2q
       420: q
       421: q
       422: q^2+2q
       423: q^2+2q
       424: q
       425: q^2+2q
       426: q^2+q
       427: 3q^2+3q
       428: q^2+q
       429: 2q^2+2q
       430: q
       431: q
       432: 2q^2+2q
       433: q^2+2q
       434: q^2+q
       435: 2q
       437: q^2+2q
       438: q
       439: q
       440: q^2+2q
       441: q^2+2q
       442: q
       443: 3q^2+3q
       444: q^2+q
       445: 3q^2+3q
       446: 2q^2+q
       447: 2q^2+2q
       448: q
       449: q
       450: 2q^2+2q
       451: q^2+2q
       452: q^2+q
       453: q^2+2q
       454: q
       455: 2q
       457: q
       458: q^2+2q
       459: q^2+2q
       460: q
       461: q^2+q
       462: 3q^2+3q
       463: 3q^2+3q
       464: 2q^2+q
       465: q^2+2q
       467: q^2+2q
       469: q^3+2q^2+2q
       470: q^2+q
       471: 2q^2+2q
       472: q
       473: q
       474: 2q^2+2q
       475: q^2+2q
       476: q^2+q
       477: 2q^2+2q
       478: q^2+q
       479: 3q^2+2q
       480: 2q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: q^2+3q
       484: q^2+4q
       485: 3q
       487: 3q
       489: q^2+2q
       491: q^2+3q
       492: 2q^2+3q
       493: 2q^2+3q
       494: 2q^2+3q
       495: 2q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: 2q^2+3q
       499: 2q^2+3q
       500: 2q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 3q^2+3q
       511: 2q^2+3q
       512: q^3+3q^2+3q
       513: 2q^2+3q
       514: q^3+3q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       529: q
       530: q
       532: q
       533: q
       534: q^2+q
       536: q
       537: q
       539: q
       541: q
       542: q
       543: q
       545: 2q^2+2q
       546: q^2+q
       547: q^2+q
       549: q
       551: q^2+q
       552: q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q^2+q
       563: 2q^2+2q
       564: q^2+q
       565: q
       566: q^2+q
       568: q
       569: q^2+q
       570: q^2+q
       571: q^2+q
       573: q^2+q
       574: 2q^2+2q
       575: q^2+q
       577: 2q^2+2q
       578: q^2
       580: q^2+q
       581: q^2+q
       585: 2q
       589: q^2+2q
       590: q
       592: 2q
       593: 2q
       595: q
       596: q^2+2q
       597: 2q
       599: q^2+2q
       600: q
       601: 3q
       603: q^2+2q
       604: q
       605: 2q
       607: q
       608: q^2+2q
       609: q^2+2q
       610: q
       613: q^2+2q
       614: q^2+q
       615: q^2+3q
       616: q
       617: 3q
       619: q^2+2q
       620: q
       621: q
       622: q^2+2q
       623: 2q
       625: q^2+2q
       626: q
       629: q^2+2q
       630: q^2+q
       631: q
       632: q^2+3q
       633: 3q
       639: q^2+2q
       641: 2q^2+2q
       642: q
       643: q
       644: 2q^2+2q
       645: q^2+2q
       646: q^2+q
       647: q^2+2q
       648: q
       649: q
       650: q^2+2q
       651: 2q
       653: q^2+2q
       654: q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 3q
       660: 3q
       662: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: q^2+3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: q^2+3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: 2q^2+3q
       688: 2q^2+3q
       689: 2q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^2+q
       696: q^2+q
       697: q^2+q
       699: q^2+q
       709: q
       712: q
       715: q
       716: q
       717: q
       718: q
       721: q
       723: q
       725: q
       726: q
       727: q
       733: 2q
       735: q
       737: q
       739: q
       741: q
       743: q
       744: q
       749: q
       751: 2q
       753: q
       754: q^2+q
       756: q
       757: q
       758: q
       761: q
       762: q
       763: q
       765: q
       766: q^2+2q
       768: q
       769: 2q
       772: q
       775: 3q
       779: 2q
       781: 2q
       785: 2q
       788: 2q
       791: q
       792: q
       793: q^2+3q
       794: q
       795: 3q
       797: 2q
       801: q^2+2q
       802: q
       804: 2q
       805: 2q
       807: q
       808: q^2+2q
       809: 2q
       811: q^2+2q
       812: q
       815: 2q
       816: q
       817: q
       818: q^2+3q
       819: 3q
       821: 2q
       825: q^2+2q
       826: q
       828: 2q
       829: 2q
       831: q
       832: q^2+2q
       833: 2q
       835: q^2+2q
       836: q
       839: q
       840: 2q
       843: q^2+2q
       844: q^2+2q
       845: q^2+2q
       846: q
       847: q
       848: q^2+2q
       849: 2q
       851: q^2+2q
       852: q
       855: q^2+2q
       856: q^2+q
       857: 2q
       858: q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
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       878: q^2+3q
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       880: q^2+3q
       884: q
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       902: q
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       916: 2q
       918: q
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       940: q
       942: 2q
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       953: q
       960: q
       961: q
       964: q
       965: q^2+2q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       976: q
       988: q
       989: q
       991: q
       994: 2q
       999: 2q
      1000: 2q
      1004: q
      1007: q
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      1010: q
      1012: q
      1013: q
      1016: 2q
      1017: q
      1020: 2q
      1022: 2q
      1026: 2q
      1029: 2q
      1032: q
      1033: 2q
      1036: 2q
      1038: 2q
      1040: 2q
      1045: 2q
      1046: 2q
      1047: q
      1048: 2q
      1052: q^2+2q
      1053: q
      1055: 2q
      1056: 2q
      1058: q
      1059: q^2+2q
      1060: 2q
      1062: q^2+2q
      1063: q
      1064: q
      1065: q
      1074: 2q
      1076: 3q
      1077: 2q
      1078: 2q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1086: q
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      1484: 1
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      1641: 1
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      1673: 1
      1759: 1
      1781: 1
      1812: 1
      1817: 1
      1820: 1
      1821: 1
      1884: 1
      1907: 1
      1922: 1
      1953: 1
      2016: 1

2017:    0: 6q^3+6q^2+3q
         1: 6q^3+6q^2+3q
         2: 2q^4+5q^3+5q^2+3q
         3: 6q^3+6q^2+3q
         4: 2q^4+5q^3+5q^2+3q
         5: 6q^3+6q^2+3q
         6: 2q^4+5q^3+5q^2+3q
         7: q^5+2q^4+5q^3+4q^2+3q
         8: 2q^4+5q^3+5q^2+3q
         9: q^5+2q^4+5q^3+4q^2+3q
        10: 3q^3+6q^2+3q
        11: 3q^3+6q^2+3q
        12: q^4+3q^3+5q^2+3q
        13: 4q^3+5q^2+3q
        14: q^4+4q^3+4q^2+3q
        15: 4q^3+5q^2+3q
        16: 6q^3+6q^2+3q
        17: 6q^3+6q^2+3q
        18: q^5+2q^4+5q^3+4q^2+3q
        19: 4q^3+5q^2+3q
        20: 4q^3+5q^2+3q
        21: q^4+4q^3+4q^2+3q
        22: 6q^3+6q^2+3q
        23: 6q^3+6q^2+3q
        24: 2q^4+5q^3+5q^2+3q
        25: 6q^3+6q^2+3q
        26: 6q^3+6q^2+3q
        27: 2q^4+5q^3+5q^2+3q
        28: 3q^3+6q^2+3q
        29: 2q^3+5q^2+3q
        30: 3q^3+4q^2+3q
        31: 3q^3+6q^2+3q
        32: 4q^3+5q^2+3q
        33: 6q^3+6q^2+3q
        34: 3q^3+6q^2+3q
        35: 4q^3+5q^2+3q
        36: 6q^3+6q^2+3q
        37: 3q^3+4q^2+2q
        38: 3q^3+2q^2+q
        39: 3q^3+4q^2+2q
        40: 3q^3+2q^2+q
        41: q^4+3q^3+3q^2+2q
        42: q^4+2q^3+2q^2+q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 4q^3+5q^2+3q
        47: 4q^3+5q^2+3q
        48: q^4+4q^3+4q^2+3q
        49: 4q^3+5q^2+3q
        50: 4q^3+5q^2+3q
        51: q^4+4q^3+4q^2+3q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: q^4+4q^3+4q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: q^4+4q^3+4q^2+3q
        58: 2q^3+4q^2+2q
        59: q^3+2q^2+q
        60: q^3+2q^2+q
        61: 2q^3+4q^2+2q
        62: 2q^3+4q^2+2q
        63: q^3+2q^2+q
        64: 2q^3+3q^2+2q
        65: 2q^3+2q^2+q
        66: 3q^3+4q^2+2q
        67: 3q^3+2q^2+q
        68: 4q^2+3q
        69: 3q^3+4q^2+3q
        70: q^3+4q^2+3q
        71: 2q^3+5q^2+3q
        72: 2q^3+4q^2+3q
        73: 2q^3+4q^2+3q
        74: q^3+3q^2+2q
        75: q^3+q^2+q
        76: q^3+3q^2+2q
        77: q^3+q^2+q
        78: 2q^3+2q^2+2q
        79: q^3+q^2+q
        80: q^3+5q^2+3q
        81: 4q^3+5q^2+3q
        82: 2q^3+5q^2+3q
        83: 3q^3+4q^2+3q
        84: q^3+5q^2+3q
        85: 4q^3+5q^2+3q
        86: 2q^3+5q^2+3q
        87: 3q^3+4q^2+3q
        88: q^3+5q^2+3q
        89: q^3+5q^2+3q
        90: 2q^3+4q^2+3q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+4q^2+3q
        94: 4q^3+5q^2+3q
        95: 4q^3+5q^2+3q
        96: q^4+4q^3+4q^2+3q
        97: 4q^3+5q^2+3q
        98: 4q^3+5q^2+3q
        99: q^4+4q^3+4q^2+3q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: q^4+4q^3+4q^2+3q
       103: q^3+2q^2+q
       105: q^3+2q^2+q
       106: q^3+2q^2+q
       107: q^2+q
       108: q^3+3q^2+2q
       109: q^3+3q^2+2q
       110: q^2+q
       111: 2q^2+2q
       112: q^2+q
       113: q^3+3q^2+2q
       114: q^2+q
       115: q^3+2q^2+2q
       116: q^3+q^2+q
       117: 3q^2+2q
       118: q^2+q
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       120: 3q^2+2q
       121: q^3+3q^2+2q
       122: 2q^2+q
       123: 2q^3+3q^2+2q
       124: 2q^3+2q^2+q
       125: 4q^2+3q
       126: q^3+4q^2+3q
       127: q^3+3q^2+2q
       128: q^3+q^2+q
       129: q^3+3q^2+2q
       130: q^3+q^2+q
       131: 2q^3+2q^2+2q
       132: q^3+q^2+q
       133: 3q^2+3q
       134: 2q^3+4q^2+3q
       135: q^3+3q^2+3q
       136: q^3+3q^2+3q
       137: q^3+5q^2+3q
       138: 3q^3+4q^2+3q
       139: 2q^3+5q^2+3q
       140: 2q^3+4q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+4q^2+3q
       143: q^3+5q^2+3q
       144: 3q^3+4q^2+3q
       145: 2q^3+5q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+4q^2+3q
       148: 2q^3+4q^2+3q
       149: 2q^3+5q^2+3q
       150: 3q^3+4q^2+3q
       151: q^3+3q^2+2q
       152: q^3+q^2+q
       153: q^3+3q^2+2q
       154: q^3+q^2+q
       155: 2q^3+2q^2+2q
       156: q^3+q^2+q
       157: 3q^2+3q
       158: 3q^2+3q
       159: 3q^2+3q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+4q^2+3q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+4q^2+3q
       166: 4q^3+5q^2+3q
       167: 4q^3+5q^2+3q
       168: q^4+4q^3+4q^2+3q
       169: q^2+q
       171: q^2+q
       172: q^2+q
       173: q^2+q
       175: 2q^2+q
       176: q^2+q
       177: q^3+2q^2+2q
       178: q^3+q^2+q
       179: q^3+3q^2+2q
       180: q^2+q
       181: 2q^2+2q
       182: q^2+q
       183: q
       184: 2q^2+2q
       185: 2q^2+2q
       186: q
       187: q^2+2q
       188: q^2+q
       189: q^3+2q^2+2q
       190: q^2+q
       191: 3q^2+2q
       192: q^2+q
       193: q^2+q
       194: q^3+3q^2+2q
       195: q^3+3q^2+2q
       196: q^2+q
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       200: 3q^2+2q
       201: q^2+q
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       203: q^3+3q^2+2q
       204: q^2+q
       205: 2q^2+2q
       206: q^2+q
       207: q^3+3q^2+2q
       208: 2q^2+q
       209: q^3+3q^2+2q
       210: q^2+q
       211: q^3+2q^2+2q
       212: q^3+q^2+q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 3q^2+3q
       222: 2q^2+3q
       223: q^3+3q^2+3q
       224: 2q^2+3q
       225: q^3+3q^2+3q
       226: q^3+4q^2+3q
       227: 3q^2+3q
       228: 2q^3+4q^2+3q
       229: q^3+3q^2+3q
       230: q^3+3q^2+3q
       231: q^3+4q^2+3q
       232: 3q^2+3q
       233: 2q^3+4q^2+3q
       234: q^3+3q^2+3q
       235: q^3+3q^2+3q
       236: 3q^3+4q^2+3q
       237: q^3+3q^2+2q
       238: q^3+q^2+q
       239: q^3+3q^2+2q
       240: q^3+q^2+q
       241: 2q^3+2q^2+2q
       242: q^3+q^2+q
       243: 2q^3+5q^2+3q
       244: 2q^3+4q^2+3q
       245: 2q^3+4q^2+3q
       246: q^3+4q^2+3q
       247: 5q^2+4q
       248: 5q^2+4q
       249: 3q^3+3q^2+3q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 3q^2+3q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 3q^2+3q
       256: 2q^3+4q^2+3q
       257: 2q^3+4q^2+3q
       258: 2q^3+4q^2+3q
       259: q^2+q
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       285: 2q^2+2q
       286: q
       287: q^3+2q^2+2q
       288: q^2+q
       289: 2q
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       296: q
       297: q^2+2q
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       302: q^2+q
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       304: q
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       306: q^2+q
       307: q
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       309: 2q^2+2q
       310: q
       311: 2q^2+2q
       312: q^2+q
       313: q^2+2q
       314: q^2+q
       315: q^3+2q^2+2q
       316: q^3+q^2+q
       317: q^3+3q^2+2q
       318: q^2+q
       319: q^2+q
       320: q^3+3q^2+2q
       321: q^3+3q^2+2q
       322: q^2+q
       323: 2q^2+2q
       324: q^2+q
       325: q^3+2q^2+2q
       326: q^2+q
       333: 2q^2+3q
       334: 2q^2+3q
       335: 2q^2+3q
       336: 2q^2+3q
       337: 4q^2+4q
       338: 3q^2+3q
       339: 2q^2+q
       340: 3q^2+3q
       341: 2q^2+q
       342: 2q^3+2q^2+2q
       343: q^3+q^2+q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 3q^2+3q
       347: 2q^2+3q
       348: q^3+3q^2+3q
       349: 2q^2+3q
       350: q^3+3q^2+3q
       351: 5q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 3q^2+3q
       355: 2q^2+3q
       356: q^3+3q^2+3q
       357: 2q^2+3q
       358: q^3+3q^2+3q
       359: 5q^2+4q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: q^3+4q^2+3q
       367: 3q^2+3q
       368: 2q^3+4q^2+3q
       369: q^3+3q^2+3q
       370: q^3+3q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 3q^2+3q
       375: 3q^2+3q
       376: 3q^2+3q
       377: q
       379: q^2+q
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       384: q
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       388: q
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       405: q^2+q
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       408: q^2+q
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       417: 2q
       419: q
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       422: q
       423: q^2+2q
       424: q
       425: q^2+2q
       426: q^2+q
       427: 3q^2+3q
       428: q^2+q
       429: q
       430: 2q^2+2q
       431: 2q^2+2q
       432: q
       433: q^2+2q
       434: q^2+q
       435: 2q
       437: q
       438: q^2+2q
       439: q^2+2q
       440: q
       441: q^2+2q
       442: q
       443: q^2+q
       444: 3q^2+3q
       445: 3q^2+3q
       446: 2q^2+q
       447: q
       448: 2q^2+2q
       449: 2q^2+2q
       450: q
       451: q^2+2q
       452: q^2+q
       453: q
       454: q^2+2q
       455: 2q
       457: q^2+2q
       458: q
       459: q^2+2q
       460: q
       461: 3q^2+3q
       462: q^2+q
       463: 3q^2+3q
       464: 2q^2+q
       465: q^2+2q
       467: q^2+2q
       469: q^3+2q^2+2q
       470: q^2+q
       471: q
       472: 2q^2+2q
       473: 2q^2+2q
       474: q
       475: q^2+2q
       476: q^2+q
       477: 2q^2+2q
       478: q^2+q
       479: 3q^2+2q
       480: 2q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: q^2+3q
       484: q^2+4q
       485: 3q
       487: 3q
       489: q^2+2q
       491: q^2+3q
       492: 2q^2+3q
       493: 2q^2+3q
       494: 2q^2+3q
       495: 2q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: 2q^2+3q
       499: 2q^2+3q
       500: 2q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 3q^2+3q
       511: 2q^2+3q
       512: q^3+3q^2+3q
       513: 2q^2+3q
       514: q^3+3q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       529: q
       531: q
       532: q
       533: q
       535: q^2+q
       536: q
       537: q
       539: q
       541: q
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       544: q
       545: q^2+q
       547: 2q^2+2q
       548: q^2+q
       549: q
       550: q^2+q
       552: q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: 2q^2+2q
       562: q^2+q
       563: q^2+q
       565: q
       567: q^2+q
       568: q
       569: q^2+q
       570: q^2+q
       572: q^2+q
       573: q^2+q
       575: q^2+q
       576: 2q^2+2q
       577: 2q^2+2q
       578: q^2
       580: q^2+q
       581: q^2+q
       585: 2q
       589: q
       590: q^2+2q
       591: 2q
       594: 2q
       595: q^2+2q
       596: q
       597: 2q
       599: q^2+2q
       600: q
       601: 3q
       603: q
       604: q^2+2q
       605: 2q
       607: q^2+2q
       608: q
       609: q^2+2q
       610: q
       613: q^2+2q
       614: q^2+q
       615: q
       616: q^2+3q
       617: 3q
       619: q
       620: q^2+2q
       621: q^2+2q
       622: q
       623: 2q
       625: q^2+2q
       626: q
       629: q^2+2q
       630: q^2+q
       631: q^2+3q
       632: q
       633: 3q
       639: q^2+2q
       641: q
       642: 2q^2+2q
       643: 2q^2+2q
       644: q
       645: q^2+2q
       646: q^2+q
       647: q
       648: q^2+2q
       649: q^2+2q
       650: q
       651: 2q
       653: q^2+2q
       654: q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 3q
       660: 3q
       662: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: q^2+3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: q^2+3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: 2q^2+3q
       688: 2q^2+3q
       689: 2q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^2+q
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       698: q^2+q
       700: q^2+q
       709: q
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       721: q
       723: q
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       728: q
       733: q
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       739: q
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       743: q
       749: 2q
       751: q
       753: q
       755: q^2+q
       756: q
       757: q
       758: q
       761: q
       762: q
       764: q
       765: q
       767: q^2+2q
       768: q
       769: 2q
       772: q
       775: 3q
       779: 2q
       781: 2q
       786: 2q
       787: 2q
       791: q
       792: q
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      1484: 1
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      1673: 1
      1757: 1
      1783: 1
      1813: 1
      1817: 1
      1819: 1
      1822: 1
      1885: 1
      1906: 1
      1923: 1
      1954: 1
      2017: 1

2018:    0: 6q^3+6q^2+3q
         1: 6q^3+6q^2+3q
         2: 2q^4+5q^3+5q^2+3q
         3: 6q^3+6q^2+3q
         4: 2q^4+5q^3+5q^2+3q
         5: 6q^3+6q^2+3q
         6: 2q^4+5q^3+5q^2+3q
         7: q^5+2q^4+5q^3+4q^2+3q
         8: 2q^4+5q^3+5q^2+3q
         9: q^5+2q^4+5q^3+4q^2+3q
        10: 3q^3+6q^2+3q
        11: 3q^3+6q^2+3q
        12: q^4+3q^3+5q^2+3q
        13: 4q^3+5q^2+3q
        14: q^4+4q^3+4q^2+3q
        15: 4q^3+5q^2+3q
        16: 6q^3+6q^2+3q
        17: 6q^3+6q^2+3q
        18: q^5+2q^4+5q^3+4q^2+3q
        19: 4q^3+5q^2+3q
        20: 4q^3+5q^2+3q
        21: q^4+4q^3+4q^2+3q
        22: 6q^3+6q^2+3q
        23: 6q^3+6q^2+3q
        24: 2q^4+5q^3+5q^2+3q
        25: 6q^3+6q^2+3q
        26: 6q^3+6q^2+3q
        27: 2q^4+5q^3+5q^2+3q
        28: 3q^3+6q^2+3q
        29: 2q^3+5q^2+3q
        30: 3q^3+4q^2+3q
        31: 3q^3+6q^2+3q
        32: 4q^3+5q^2+3q
        33: 6q^3+6q^2+3q
        34: 3q^3+6q^2+3q
        35: 4q^3+5q^2+3q
        36: 6q^3+6q^2+3q
        37: 3q^3+2q^2+q
        38: 3q^3+4q^2+2q
        39: 3q^3+2q^2+q
        40: 3q^3+4q^2+2q
        41: q^4+2q^3+2q^2+q
        42: q^4+3q^3+3q^2+2q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 4q^3+5q^2+3q
        47: 4q^3+5q^2+3q
        48: q^4+4q^3+4q^2+3q
        49: 4q^3+5q^2+3q
        50: 4q^3+5q^2+3q
        51: q^4+4q^3+4q^2+3q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: q^4+4q^3+4q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: q^4+4q^3+4q^2+3q
        58: 2q^3+4q^2+2q
        59: q^3+2q^2+q
        60: 2q^3+4q^2+2q
        61: q^3+2q^2+q
        62: q^3+2q^2+q
        63: 2q^3+4q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: 3q^3+2q^2+q
        67: 3q^3+4q^2+2q
        68: 4q^2+3q
        69: 3q^3+4q^2+3q
        70: q^3+4q^2+3q
        71: 2q^3+5q^2+3q
        72: 2q^3+4q^2+3q
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        74: q^3+q^2+q
        75: q^3+3q^2+2q
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        79: 2q^3+2q^2+2q
        80: q^3+5q^2+3q
        81: 4q^3+5q^2+3q
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        86: 2q^3+5q^2+3q
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        88: q^3+5q^2+3q
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        90: 2q^3+4q^2+3q
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        93: 2q^3+4q^2+3q
        94: 4q^3+5q^2+3q
        95: 4q^3+5q^2+3q
        96: q^4+4q^3+4q^2+3q
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        99: q^4+4q^3+4q^2+3q
       100: 4q^3+5q^2+3q
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       102: q^4+4q^3+4q^2+3q
       103: q^3+2q^2+q
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       105: q^3+2q^2+q
       107: q^3+3q^2+2q
       108: q^2+q
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       137: q^3+5q^2+3q
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       165: 2q^3+4q^2+3q
       166: 4q^3+5q^2+3q
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       168: q^4+4q^3+4q^2+3q
       169: q^2+q
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       226: q^3+4q^2+3q
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       236: 3q^3+4q^2+3q
       237: q^3+q^2+q
       238: q^3+3q^2+2q
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       240: q^3+3q^2+2q
       241: q^3+q^2+q
       242: 2q^3+2q^2+2q
       243: 2q^3+5q^2+3q
       244: 2q^3+4q^2+3q
       245: 2q^3+4q^2+3q
       246: q^3+4q^2+3q
       247: 5q^2+4q
       248: 5q^2+4q
       249: 3q^3+3q^2+3q
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       316: q^3+2q^2+2q
       317: q^2+q
       318: q^3+3q^2+2q
       319: q^3+3q^2+2q
       320: q^2+q
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       322: q^2+q
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       324: 2q^2+2q
       325: q^2+q
       326: q^3+2q^2+2q
       333: 2q^2+3q
       334: 2q^2+3q
       335: 2q^2+3q
       336: 2q^2+3q
       337: 4q^2+4q
       338: 2q^2+q
       339: 3q^2+3q
       340: 2q^2+q
       341: 3q^2+3q
       342: q^3+q^2+q
       343: 2q^3+2q^2+2q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 3q^2+3q
       347: 2q^2+3q
       348: q^3+3q^2+3q
       349: 2q^2+3q
       350: q^3+3q^2+3q
       351: 5q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 3q^2+3q
       355: 2q^2+3q
       356: q^3+3q^2+3q
       357: 2q^2+3q
       358: q^3+3q^2+3q
       359: 5q^2+4q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: q^3+4q^2+3q
       367: 3q^2+3q
       368: 2q^3+4q^2+3q
       369: q^3+3q^2+3q
       370: q^3+3q^2+3q
       371: 2q^2+4q
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       374: 3q^2+3q
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       466: q^2+2q
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       469: q^2+q
       470: q^3+2q^2+2q
       471: 2q^2+2q
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       477: q^2+q
       478: 2q^2+2q
       479: 2q^2+2q
       480: 3q^2+2q
       481: q^2+3q
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       484: q^2+4q
       486: 3q
       488: 3q
       490: q^2+2q
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       492: 2q^2+3q
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       496: 2q^2+4q
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       508: 3q^2+3q
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       510: 3q^2+3q
       511: 2q^2+3q
       512: q^3+3q^2+3q
       513: 2q^2+3q
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       515: 2q^2+4q
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       517: q^3+2q^2+3q
       518: 3q
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       520: q^2+2q
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       566: q
       567: q
       569: q^2+q
       571: q^2+q
       572: q^2+q
       573: 2q^2+2q
       574: q^2+q
       576: q^2+q
       577: q^2+q
       578: q^2+q
       580: q^2
       581: 2q^2+2q
       586: 2q
       589: q^2+2q
       590: q
       591: 2q
       593: 2q
       595: q^2+2q
       596: q
       598: 2q
       599: q
       600: q^2+2q
       602: 3q
       603: q^2+2q
       604: q
       606: 2q
       607: q^2+2q
       608: q
       609: q
       610: q^2+2q
       613: q^2+q
       614: q^2+2q
       615: q^2+3q
       616: q
       618: 3q
       619: q^2+2q
       620: q
       621: q^2+2q
       622: q
       624: 2q
       625: q
       626: q^2+2q
       629: q^2+q
       630: q^2+2q
       631: q^2+3q
       632: q
       634: 3q
       640: q^2+2q
       641: 2q^2+2q
       642: q
       643: 2q^2+2q
       644: q
       645: q^2+q
       646: q^2+2q
       647: q^2+2q
       648: q
       649: q^2+2q
       650: q
       652: 2q
       653: q
       654: q^2+2q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       659: 3q
       661: 3q
       663: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: q^2+3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: q^2+3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: 2q^2+3q
       688: 2q^2+3q
       689: 2q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^2+q
       694: q^2+q
       699: q^2+q
       700: q^2+q
       710: q
       711: q
       713: q
       714: q
       717: q
       718: q
       722: q
       724: q
       725: q
       726: q
       728: q
       734: 2q
       736: q
       738: q
       740: q
       741: q
       742: q
       744: q
       750: 2q
       752: q
       753: q^2+q
       754: q
       755: q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q^2+2q
       766: q
       767: q
       770: q
       773: 2q
       776: 3q
       780: 2q
       782: 2q
       785: 2q
       787: 2q
       791: q
       792: q
       793: q^2+3q
       794: q
       796: 3q
       798: 2q
       801: q^2+2q
       802: q
       803: 2q
       805: 2q
       807: q^2+2q
       808: q
       810: 2q
       811: q
       812: q^2+2q
       815: 2q
       816: q
       817: q^2+3q
       818: q
       820: 3q
       822: 2q
       825: q^2+2q
       826: q
       827: 2q
       829: 2q
       831: q^2+2q
       832: q
       834: 2q
       835: q
       836: q^2+2q
       839: 2q
       840: q
       843: q^2+2q
       844: q^2+2q
       845: q^2+2q
       846: q
       847: q^2+2q
       848: q
       850: 2q
       851: q
       852: q^2+2q
       855: q^2+q
       856: q^2+2q
       857: q
       858: 2q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: q^2+3q
       880: q^2+3q
       885: q
       890: q
       891: q
       901: q
       905: q
       908: q
       917: 2q
       919: q
       921: q
       923: q
       924: q
       925: q
       928: q
       929: q
       941: 2q
       943: q
       945: q
       947: q
       948: q
       949: q
       952: q
       953: q
       962: q
       963: q
       964: q^2+2q
       965: q
       966: q
       969: q
       972: 2q
       974: q
       976: q
       977: q
       988: q
       989: q
       990: q
       995: 2q
       998: 2q
      1000: 2q
      1004: q
      1006: q
      1009: q
      1011: q
      1012: q
      1013: q
      1016: 2q
      1017: q
      1021: 2q
      1023: 2q
      1026: 2q
      1028: 2q
      1032: 2q
      1033: q
      1037: 2q
      1039: 2q
      1040: 2q
      1044: 2q
      1046: q
      1047: 2q
      1049: 2q
      1052: q^2+2q
      1053: q
      1054: 2q
      1056: 2q
      1058: q^2+2q
      1059: q
      1061: 2q
      1062: q
      1063: q^2+2q
      1064: q
      1065: q
      1074: 2q
      1076: 3q
      1077: 2q
      1078: 2q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1087: q
      1092: q
      1093: q
      1115: q
      1123: q
      1130: q
      1142: q
      1153: q
      1157: q
      1160: q
      1173: q
      1177: q
      1180: q
      1194: q
      1195: q
      1196: q
      1200: q
      1201: q
      1202: q
      1203: q
      1206: q
      1207: q
      1216: q
      1218: q
      1221: q
      1225: q
      1231: 2q
      1232: 2q
      1234: 2q
      1240: q
      1242: q
      1249: 2q
      1250: 2q
      1254: 2q
      1258: q
      1260: q
      1267: 2q
      1268: 2q
      1270: 2q
      1275: 2q
      1277: q
      1279: q
      1280: q
      1281: q
      1283: 2q
      1285: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1349: q
      1357: q
      1364: q
      1381: q
      1389: q
      1396: q
      1419: q
      1423: q
      1426: q
      1434: q
      1437: q
      1450: q
      1454: q
      1460: q
      1462: q
      1465: 2q
      1466: 2q
      1468: 2q
      1475: q
      1476: q
      1478: q
      1483: q
      1484: 1
      1487: 2q
      1608: q
      1616: q
      1623: q
      1642: 1
      1649: 1
      1657: 1
      1660: q
      1663: q
      1665: q
      1673: 1
      1758: 1
      1782: 1
      1811: 1
      1818: 1
      1819: 1
      1821: 1
      1883: 1
      1908: 1
      1924: 1
      1952: 1
      2018: 1

2019:    0: q^3+q^2+1
         1: q^3+q^2+1
         2: q^4+q^2+1
         3: q^3+q^2+1
         4: q^3+q^2+1
         5: q^3+q^2+1
         6: q^3+q^2+1
         7: q^4+q^2+1
         8: q^4+q^2+1
         9: q^4+q^2+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^3+q^2+1
        17: q^3+q^2+1
        18: q^4+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^4+q^2+1
        22: q^3+q^2+1
        23: q^3+q^2+1
        24: q^4+q^2+1
        25: q^3+q^2+1
        26: q^3+q^2+1
        27: q^4+q^2+1
        28: q^3+1
        29: q^3+1
        30: q^2+1
        31: q^3+1
        32: q^2+1
        33: q^3+q^2+1
        34: q^3+1
        35: q^2+1
        36: q^3+q^2+1
        37: q^3+1
        38: q^2
        39: q^3+1
        40: q^2
        41: q^4+1
        42: q^2
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^4+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^4+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^4+q^2+1
        59: q^3+1
        61: q^3+1
        62: q^3+1
        64: 1
        65: q^2
        66: q^3+1
        67: q^2
        68: 1
        69: q^2+1
        70: 1
        71: q^3+1
        72: q^3+q^2+1
        73: q^3+q^2+1
        74: q^3+1
        75: q^2
        76: q^3+1
        77: q^2
        78: q^4+1
        79: q^2
        80: 1
        81: q^2+1
        82: q^3+1
        83: q^2+1
        84: 1
        85: q^2+1
        86: q^3+1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^4+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^4+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^4+q^2+1
       106: q^3+1
       108: q^3+1
       110: q^3+1
       111: q^3+1
       112: q^2
       113: q^3+1
       115: 1
       116: q^2
       118: 1
       120: 1
       121: 1
       123: 1
       124: q^2
       125: 1
       126: 1
       127: q^3+1
       128: q^2
       129: q^3+1
       130: q^2
       131: q^4+1
       132: q^2
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: q^3+1
       140: q^3+q^2+1
       141: 1
       142: q^3+q^2+1
       143: 1
       144: q^2+1
       145: q^3+1
       146: 1
       147: q^3+q^2+1
       148: q^3+q^2+1
       149: q^3+1
       150: q^2+1
       151: q^3+1
       152: q^2
       153: q^3+1
       154: q^2
       155: q^4+1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^4+q^2+1
       172: q^3+1
       176: 1
       177: 1
       178: q^2
       179: q^3+1
       181: q^3+1
       182: q^2
       184: 1
       186: 1
       187: 1
       188: q^2
       189: 1
       192: 1
       194: q^3+1
       196: q^3+1
       197: q^3+1
       198: q^2
       200: 1
       202: q^3+1
       204: q^3+1
       205: q^3+1
       206: q^2
       207: 1
       209: q^3+1
       211: 1
       212: q^2
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^3+1
       238: q^2
       239: q^3+1
       240: q^2
       241: q^4+1
       242: q^2
       243: q^3+1
       244: q^3+q^2+1
       245: q^3+q^2+1
       246: 1
       247: q^3+q^2+1
       248: q^3+q^2+1
       249: q^4+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       262: q^3+1
       266: 1
       269: q^3+1
       273: q^3+1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       292: q^2
       294: 1
       296: 1
       297: 1
       300: 1
       301: q^3+1
       302: q^2
       304: 1
       305: 1
       306: q^2
       308: 1
       310: 1
       311: q^3+1
       312: q^2
       313: 1
       314: q^2
       315: 1
       316: q^2
       317: q^3+1
       320: q^3+1
       322: q^3+1
       323: q^3+1
       324: q^2
       325: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^3+1
       338: q^3+1
       339: q^2
       340: q^3+1
       341: q^2
       342: q^4+1
       343: q^2
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^3+q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^3+q^2+1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: q^3+1
       396: 1
       399: q^3+1
       404: 1
       406: q^3+1
       413: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       426: q^2
       427: q^3+1
       430: 1
       432: 1
       433: 1
       434: q^2
       435: 1
       438: 1
       440: 1
       441: 1
       444: q^3+1
       445: q^3+1
       446: q^2
       448: 1
       450: 1
       451: 1
       452: q^2
       454: 1
       455: 1
       458: 1
       459: 1
       462: q^3+1
       463: q^3+1
       464: q^2
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       476: q^2
       477: q^3+1
       478: q^2
       479: q^3+1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: q^3+1
       552: 1
       555: 1
       559: 1
       563: q^3+1
       568: 1
       570: q^3+1
       575: q^3+1
       577: q^3+1
       581: q^2
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       613: 1
       614: q^2
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       629: 1
       630: q^2
       632: 1
       633: 1
       639: 1
       642: 1
       644: 1
       645: 1
       646: q^2
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       656: q^2
       657: 1
       658: 1
       660: 1
       662: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       697: q^3+1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       779: 1
       781: 1
       786: 1
       788: 1
       791: 1
       792: q^2
       794: 1
       795: 1
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       816: 1
       818: 1
       819: 1
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       840: 1
       843: 1
       844: q^2
       846: 1
       848: 1
       849: 1
       851: 1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       922: 1
       927: 1
       930: 1
       942: 1
       946: 1
       950: 1
       955: 1
       961: 1
       967: 1
       968: 1
       975: 1
       991: 1
       994: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1013: q^2
      1017: 1
      1020: 1
      1022: 1
      1027: 1
      1029: 1
      1033: 1
      1036: 1
      1038: 1
      1041: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1065: q^2
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1266: 1
      1269: 1
      1271: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1281: q^2
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1436: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1474: 1
      1477: 1
      1479: 1
      1482: 1
      1484: 1
      1487: 1
      1506: 1
      1518: 1
      1538: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1641: 1
      1650: 1
      1658: 1
      1659: 1
      1664: 1
      1666: 1
      1673: 1
      1718: 1
      1742: 1
      1759: 1
      1770: 1
      1783: 1
      1800: 1
      1808: 1
      1814: 1
      1817: 1
      1820: 1
      1822: 1
      1889: 1
      1907: 1
      1923: 1
      1945: 1
      1955: 1
      2019: 1

2020:    0: q^3+q^2+1
         1: q^3+q^2+1
         2: q^4+q^2+1
         3: q^3+q^2+1
         4: q^3+q^2+1
         5: q^3+q^2+1
         6: q^3+q^2+1
         7: q^4+q^2+1
         8: q^4+q^2+1
         9: q^4+q^2+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^3+q^2+1
        17: q^3+q^2+1
        18: q^4+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^4+q^2+1
        22: q^3+q^2+1
        23: q^3+q^2+1
        24: q^4+q^2+1
        25: q^3+q^2+1
        26: q^3+q^2+1
        27: q^4+q^2+1
        28: q^3+1
        29: q^3+1
        30: q^2+1
        31: q^3+1
        32: q^2+1
        33: q^3+q^2+1
        34: q^3+1
        35: q^2+1
        36: q^3+q^2+1
        37: q^2
        38: q^3+1
        39: q^2
        40: q^3+1
        41: q^2
        42: q^4+1
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^4+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^4+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^4+q^2+1
        59: q^3+1
        60: q^3+1
        63: q^3+1
        64: q^2
        65: 1
        66: q^2
        67: q^3+1
        68: 1
        69: q^2+1
        70: 1
        71: q^3+1
        72: q^3+q^2+1
        73: q^3+q^2+1
        74: q^2
        75: q^3+1
        76: q^2
        77: q^3+1
        78: q^2
        79: q^4+1
        80: 1
        81: q^2+1
        82: q^3+1
        83: q^2+1
        84: 1
        85: q^2+1
        86: q^3+1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^4+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^4+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^4+q^2+1
       104: q^3+1
       107: q^3+1
       110: q^3+1
       111: q^2
       112: q^3+1
       114: q^3+1
       115: q^2
       116: 1
       118: 1
       119: 1
       122: 1
       123: q^2
       124: 1
       125: 1
       126: 1
       127: q^2
       128: q^3+1
       129: q^2
       130: q^3+1
       131: q^2
       132: q^4+1
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: q^3+1
       140: q^3+q^2+1
       141: 1
       142: q^3+q^2+1
       143: 1
       144: q^2+1
       145: q^3+1
       146: 1
       147: q^3+q^2+1
       148: q^3+q^2+1
       149: q^3+1
       150: q^2+1
       151: q^2
       152: q^3+1
       153: q^2
       154: q^3+1
       155: q^2
       156: q^4+1
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^4+q^2+1
       170: q^3+1
       174: 1
       177: q^2
       178: 1
       180: q^3+1
       181: q^2
       182: q^3+1
       183: 1
       186: 1
       187: q^2
       188: 1
       190: 1
       192: 1
       193: q^3+1
       196: q^3+1
       197: q^2
       198: q^3+1
       199: 1
       201: q^3+1
       204: q^3+1
       205: q^2
       206: q^3+1
       208: 1
       210: q^3+1
       211: q^2
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^2
       238: q^3+1
       239: q^2
       240: q^3+1
       241: q^2
       242: q^4+1
       243: q^3+1
       244: q^3+q^2+1
       245: q^3+q^2+1
       246: 1
       247: q^3+q^2+1
       248: q^3+q^2+1
       249: q^4+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       260: q^3+1
       264: 1
       268: q^3+1
       274: q^3+1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       291: q^2
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       301: q^2
       302: q^3+1
       304: 1
       305: q^2
       306: 1
       307: 1
       310: 1
       311: q^2
       312: q^3+1
       313: q^2
       314: 1
       315: q^2
       316: 1
       318: q^3+1
       319: q^3+1
       322: q^3+1
       323: q^2
       324: q^3+1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^3+1
       338: q^2
       339: q^3+1
       340: q^2
       341: q^3+1
       342: q^2
       343: q^4+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^3+q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^3+q^2+1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: q^3+1
       394: 1
       400: q^3+1
       403: 1
       407: q^3+1
       414: 1
       418: 1
       419: 1
       422: 1
       424: 1
       425: q^2
       426: 1
       428: q^3+1
       429: 1
       432: 1
       433: q^2
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: q^3+1
       445: q^2
       446: q^3+1
       447: 1
       450: 1
       451: q^2
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: q^3+1
       463: q^2
       464: q^3+1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       475: q^2
       476: 1
       477: q^2
       478: q^3+1
       479: q^2
       480: q^3+1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: q^3+1
       551: 1
       556: 1
       560: 1
       564: q^3+1
       566: 1
       571: q^3+1
       574: q^3+1
       577: q^2
       581: q^3+1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       613: q^2
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       629: q^2
       630: 1
       632: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: q^2
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       655: q^2
       656: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       699: q^3+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       780: 1
       782: 1
       785: 1
       788: 1
       791: q^2
       792: 1
       793: 1
       796: 1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: 1
       812: 1
       815: 1
       818: 1
       820: 1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: 1
       836: 1
       840: 1
       843: q^2
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       921: 1
       926: 1
       929: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       965: 1
       972: 1
       976: 1
       989: 1
       995: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1012: q^2
      1013: 1
      1016: 1
      1021: 1
      1023: 1
      1026: 1
      1029: 1
      1033: 1
      1037: 1
      1039: 1
      1040: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1064: q^2
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1195: 1
      1200: 1
      1205: 1
      1207: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1267: 1
      1268: 1
      1271: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q^2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1437: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1475: 1
      1476: 1
      1479: 1
      1483: 1
      1484: 1
      1487: 1
      1508: 1
      1519: 1
      1539: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1610: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1642: 1
      1650: 1
      1657: 1
      1660: 1
      1664: 1
      1665: 1
      1673: 1
      1716: 1
      1744: 1
      1760: 1
      1771: 1
      1782: 1
      1798: 1
      1809: 1
      1812: 1
      1818: 1
      1820: 1
      1821: 1
      1887: 1
      1909: 1
      1924: 1
      1946: 1
      1953: 1
      2020: 1

2021:    0: q^3+q^2+1
         1: q^3+q^2+1
         2: q^4+q^2+1
         3: q^3+q^2+1
         4: q^3+q^2+1
         5: q^3+q^2+1
         6: q^3+q^2+1
         7: q^4+q^2+1
         8: q^4+q^2+1
         9: q^4+q^2+1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^3+q^2+1
        17: q^3+q^2+1
        18: q^4+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^4+q^2+1
        22: q^3+q^2+1
        23: q^3+q^2+1
        24: q^4+q^2+1
        25: q^3+q^2+1
        26: q^3+q^2+1
        27: q^4+q^2+1
        28: q^3+1
        29: q^3+1
        30: q^2+1
        31: q^3+1
        32: q^2+1
        33: q^3+q^2+1
        34: q^3+1
        35: q^2+1
        36: q^3+q^2+1
        37: q^2
        38: q^3+1
        39: q^2
        40: q^3+1
        41: q^2
        42: q^4+1
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^4+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^4+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^4+q^2+1
        58: q^3+1
        61: q^3+1
        63: q^3+1
        64: q^2
        65: 1
        66: q^2
        67: q^3+1
        68: 1
        69: q^2+1
        70: 1
        71: q^3+1
        72: q^3+q^2+1
        73: q^3+q^2+1
        74: q^2
        75: q^3+1
        76: q^2
        77: q^3+1
        78: q^2
        79: q^4+1
        80: 1
        81: q^2+1
        82: q^3+1
        83: q^2+1
        84: 1
        85: q^2+1
        86: q^3+1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^4+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^4+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^4+q^2+1
       105: q^3+1
       108: q^3+1
       109: q^3+1
       111: q^2
       112: q^3+1
       114: q^3+1
       115: q^2
       116: 1
       117: 1
       120: 1
       122: 1
       123: q^2
       124: 1
       125: 1
       126: 1
       127: q^2
       128: q^3+1
       129: q^2
       130: q^3+1
       131: q^2
       132: q^4+1
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: q^3+1
       140: q^3+q^2+1
       141: 1
       142: q^3+q^2+1
       143: 1
       144: q^2+1
       145: q^3+1
       146: 1
       147: q^3+q^2+1
       148: q^3+q^2+1
       149: q^3+1
       150: q^2+1
       151: q^2
       152: q^3+1
       153: q^2
       154: q^3+1
       155: q^2
       156: q^4+1
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^4+q^2+1
       171: q^3+1
       175: 1
       177: q^2
       178: 1
       180: q^3+1
       181: q^2
       182: q^3+1
       184: 1
       185: 1
       187: q^2
       188: 1
       190: 1
       191: 1
       194: q^3+1
       195: q^3+1
       197: q^2
       198: q^3+1
       200: 1
       202: q^3+1
       203: q^3+1
       205: q^2
       206: q^3+1
       208: 1
       210: q^3+1
       211: q^2
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^2
       238: q^3+1
       239: q^2
       240: q^3+1
       241: q^2
       242: q^4+1
       243: q^3+1
       244: q^3+q^2+1
       245: q^3+q^2+1
       246: 1
       247: q^3+q^2+1
       248: q^3+q^2+1
       249: q^4+q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       261: q^3+1
       265: 1
       270: q^3+1
       272: q^3+1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       291: q^2
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       301: q^2
       302: q^3+1
       303: 1
       305: q^2
       306: 1
       308: 1
       309: 1
       311: q^2
       312: q^3+1
       313: q^2
       314: 1
       315: q^2
       316: 1
       318: q^3+1
       320: q^3+1
       321: q^3+1
       323: q^2
       324: q^3+1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^3+1
       338: q^2
       339: q^3+1
       340: q^2
       341: q^3+1
       342: q^2
       343: q^4+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^3+q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^3+q^2+1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       392: q^3+1
       395: 1
       398: q^3+1
       402: 1
       408: q^3+1
       414: 1
       418: 1
       420: 1
       421: 1
       424: 1
       425: q^2
       426: 1
       428: q^3+1
       430: 1
       431: 1
       433: q^2
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: q^3+1
       445: q^2
       446: q^3+1
       448: 1
       449: 1
       451: q^2
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: q^3+1
       463: q^2
       464: q^3+1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       475: q^2
       476: 1
       477: q^2
       478: q^3+1
       479: q^2
       480: q^3+1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: q^3+1
       550: 1
       554: 1
       558: 1
       562: q^3+1
       567: 1
       572: q^3+1
       576: q^3+1
       577: q^2
       581: q^3+1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       613: q^2
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       629: q^2
       630: 1
       631: 1
       634: 1
       640: 1
       642: 1
       643: 1
       645: q^2
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       655: q^2
       656: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       700: q^3+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       780: 1
       782: 1
       786: 1
       787: 1
       791: q^2
       792: 1
       794: 1
       796: 1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: 1
       812: 1
       816: 1
       817: 1
       820: 1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: 1
       836: 1
       839: 1
       843: q^2
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       923: 1
       925: 1
       931: 1
       941: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 1
       972: 1
       977: 1
       990: 1
       995: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1012: q^2
      1013: 1
      1017: 1
      1021: 1
      1023: 1
      1027: 1
      1028: 1
      1032: 1
      1037: 1
      1039: 1
      1041: 1
      1044: 1
      1047: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1064: q^2
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1196: 1
      1201: 1
      1203: 1
      1209: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1267: 1
      1269: 1
      1270: 1
      1275: 1
      1277: 1
      1279: 1
      1280: q^2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1437: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1475: 1
      1477: 1
      1478: 1
      1483: 1
      1484: 1
      1487: 1
      1507: 1
      1520: 1
      1540: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1608: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1642: 1
      1649: 1
      1658: 1
      1660: 1
      1663: 1
      1666: 1
      1673: 1
      1717: 1
      1743: 1
      1758: 1
      1772: 1
      1784: 1
      1799: 1
      1810: 1
      1813: 1
      1818: 1
      1819: 1
      1822: 1
      1888: 1
      1908: 1
      1925: 1
      1947: 1
      1954: 1
      2021: 1

2022:    0: 6q^4+7q^3+2q^2+q
         1: q^5+6q^4+7q^3+2q^2+q
         2: 3q^5+5q^4+5q^3+2q^2+q
         3: 6q^4+7q^3+2q^2+q
         4: 6q^4+7q^3+2q^2+q
         5: q^5+6q^4+7q^3+2q^2+q
         6: q^5+6q^4+7q^3+2q^2+q
         7: 3q^5+5q^4+5q^3+2q^2+q
         8: 2q^5+4q^4+5q^3+2q^2+q
         9: 3q^5+5q^4+5q^3+2q^2+q
        10: 3q^4+4q^3+2q^2+q
        11: 3q^4+4q^3+2q^2+q
        12: 3q^4+4q^3+2q^2+q
        13: 3q^4+5q^3+2q^2+q
        14: 3q^4+5q^3+2q^2+q
        15: 2q^4+5q^3+2q^2+q
        16: 6q^4+7q^3+2q^2+q
        17: q^5+6q^4+7q^3+2q^2+q
        18: 3q^5+5q^4+5q^3+2q^2+q
        19: 6q^4+7q^3+2q^2+q
        20: q^5+6q^4+7q^3+2q^2+q
        21: 3q^5+5q^4+5q^3+2q^2+q
        22: 3q^4+7q^3+2q^2+q
        23: 3q^4+7q^3+2q^2+q
        24: q^5+3q^4+5q^3+2q^2+q
        25: 3q^4+7q^3+2q^2+q
        26: 3q^4+7q^3+2q^2+q
        27: q^5+3q^4+5q^3+2q^2+q
        28: 3q^4+4q^3+2q^2+q
        29: 3q^4+4q^3+2q^2+q
        30: 3q^4+5q^3+2q^2+q
        31: q^4+4q^3+2q^2+q
        32: q^4+5q^3+2q^2+q
        33: 3q^4+7q^3+2q^2+q
        34: q^4+4q^3+2q^2+q
        35: q^4+5q^3+2q^2+q
        36: 3q^4+7q^3+2q^2+q
        37: 4q^3+2q^2+q
        38: q^4+3q^3
        39: 4q^3+2q^2+q
        40: q^4+3q^3
        41: q^4+3q^3+2q^2+q
        42: q^4+2q^3
        43: q^4+2q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+2q^2+q
        46: 3q^4+5q^3+2q^2+q
        47: 2q^4+5q^3+2q^2+q
        48: 3q^4+5q^3+2q^2+q
        49: 6q^4+7q^3+2q^2+q
        50: q^5+6q^4+7q^3+2q^2+q
        51: 3q^5+5q^4+5q^3+2q^2+q
        52: 3q^4+7q^3+2q^2+q
        53: 3q^4+7q^3+2q^2+q
        54: q^5+3q^4+5q^3+2q^2+q
        55: 3q^4+7q^3+2q^2+q
        56: 3q^4+7q^3+2q^2+q
        57: q^5+3q^4+5q^3+2q^2+q
        58: 2q^3
        59: q^4+2q^3+2q^2+q
        60: 2q^3
        61: q^4+2q^3+2q^2+q
        62: 2q^3+2q^2+q
        63: 2q^3
        64: 3q^3+2q^2+q
        65: 2q^3
        66: 4q^3+2q^2+q
        67: q^4+3q^3
        68: 2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: q^4+2q^3+2q^2+q
        71: 3q^4+4q^3+2q^2+q
        72: 3q^4+7q^3+2q^2+q
        73: 3q^4+7q^3+2q^2+q
        74: 4q^3+2q^2+q
        75: q^4+3q^3
        76: 4q^3+2q^2+q
        77: q^4+3q^3
        78: q^4+3q^3+2q^2+q
        79: q^4+2q^3
        80: 2q^3+2q^2+q
        81: q^4+5q^3+2q^2+q
        82: q^4+4q^3+2q^2+q
        83: q^4+5q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+5q^3+2q^2+q
        86: q^4+4q^3+2q^2+q
        87: q^4+5q^3+2q^2+q
        88: q^4+2q^3+2q^2+q
        89: 2q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: 3q^4+5q^3+2q^2+q
        92: 2q^4+5q^3+2q^2+q
        93: 3q^4+5q^3+2q^2+q
        94: 3q^4+7q^3+2q^2+q
        95: 3q^4+7q^3+2q^2+q
        96: q^5+3q^4+5q^3+2q^2+q
        97: 3q^4+7q^3+2q^2+q
        98: 3q^4+7q^3+2q^2+q
        99: q^5+3q^4+5q^3+2q^2+q
       100: 6q^3+2q^2+q
       101: q^4+6q^3+2q^2+q
       102: 2q^4+5q^3+2q^2+q
       103: q^3
       104: q^3
       105: q^3
       106: q^3+2q^2+q
       107: 2q^3
       108: q^4+2q^3+2q^2+q
       109: 2q^3
       110: q^4+2q^3+2q^2+q
       111: 4q^3+2q^2+q
       112: q^4+3q^3
       113: 2q^3+2q^2+q
       114: 2q^3
       115: 3q^3+2q^2+q
       116: 2q^3
       118: 2q^2+q
       120: 2q^2+q
       121: q^3+2q^2+q
       122: q^3
       123: 3q^3+2q^2+q
       124: 2q^3
       125: 2q^2+q
       126: q^4+2q^3+2q^2+q
       127: 4q^3+2q^2+q
       128: q^4+3q^3
       129: 4q^3+2q^2+q
       130: q^4+3q^3
       131: q^4+3q^3+2q^2+q
       132: q^4+2q^3
       133: 2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: q^4+5q^3+2q^2+q
       136: q^4+5q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+4q^3+2q^2+q
       140: 3q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 3q^4+7q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+4q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 3q^4+7q^3+2q^2+q
       148: 3q^3+2q^2+q
       149: 3q^3+2q^2+q
       150: 5q^3+2q^2+q
       151: 3q^3+2q^2+q
       152: 3q^3
       153: 3q^3+2q^2+q
       154: q^4+3q^3
       155: q^4+3q^3+2q^2+q
       156: q^4+2q^3
       157: q^4+2q^3+2q^2+q
       158: 2q^3+2q^2+q
       159: q^4+2q^3+2q^2+q
       160: q^4+4q^3+2q^2+q
       161: q^4+4q^3+2q^2+q
       162: q^4+4q^3+2q^2+q
       163: q^4+4q^3+2q^2+q
       164: q^4+4q^3+2q^2+q
       165: q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^3
       171: q^3
       172: q^3+2q^2+q
       176: 2q^2+q
       177: 3q^3+2q^2+q
       178: 2q^3
       179: 2q^3+2q^2+q
       180: 2q^3
       181: 4q^3+2q^2+q
       182: q^4+3q^3
       184: 2q^2+q
       186: 2q^2+q
       187: 3q^3+2q^2+q
       188: 2q^3
       189: q^3+2q^2+q
       190: q^3
       192: 2q^2+q
       194: q^3+2q^2+q
       195: 2q^3
       196: q^4+2q^3+2q^2+q
       197: q^3+2q^2+q
       198: 2q^3
       200: 2q^2+q
       201: 2q^3
       202: q^4+2q^3+2q^2+q
       204: q^3+2q^2+q
       205: q^3+2q^2+q
       206: 2q^3
       207: q^3+2q^2+q
       208: q^3
       209: q^3+2q^2+q
       210: 2q^3
       211: 3q^3+2q^2+q
       212: 2q^3
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^3+q^2+q
       219: 2q^2+q
       220: 2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 2q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 2q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 2q^3+2q^2+q
       230: q^4+4q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+4q^3+2q^2+q
       235: 2q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3+2q^2+q
       238: 3q^3
       239: 3q^3+2q^2+q
       240: q^4+3q^3
       241: q^4+3q^3+2q^2+q
       242: q^4+2q^3
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: 2q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3
       260: q^3
       261: q^3
       262: q^3+2q^2+q
       266: 2q^2+q
       269: 2q^2+q
       270: q^3
       273: 2q^2+q
       274: q^3
       278: 2q^2+q
       279: q^2+q
       281: q^3+q^2+q
       284: 2q^2+q
       286: 2q^2+q
       287: q^3+2q^2+q
       288: q^3
       289: q^3+q^2+q
       291: 3q^3+2q^2+q
       292: 2q^3
       294: 2q^2+q
       296: 2q^2+q
       297: q^3+2q^2+q
       298: q^3
       300: 2q^2+q
       301: q^3+2q^2+q
       302: 2q^3
       304: 2q^2+q
       305: q^3+2q^2+q
       306: q^3
       308: 2q^2+q
       310: 2q^2+q
       311: q^3+2q^2+q
       312: 2q^3
       313: q^3+2q^2+q
       314: q^3
       315: 3q^3+2q^2+q
       316: 2q^3
       317: q^3+2q^2+q
       318: 2q^3
       320: q^3+2q^2+q
       322: q^3+2q^2+q
       323: 2q^2+q
       324: q^3
       325: q^3+2q^2+q
       326: q^3
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3+2q^2+q
       339: 3q^3
       340: 3q^3+2q^2+q
       341: q^4+3q^3
       342: q^4+3q^3+2q^2+q
       343: q^4+2q^3
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       380: 2q^2+q
       384: q^2+q
       388: 2q^2+q
       391: 2q^2+q
       392: q^3
       396: 2q^2+q
       399: 2q^2+q
       400: q^3
       404: 2q^2+q
       406: 2q^2+q
       413: q^2+q
       417: q^3+q^2+q
       420: 2q^2+q
       422: 2q^2+q
       423: q^3+2q^2+q
       424: q^3
       425: 3q^3+2q^2+q
       426: 2q^3
       427: q^3+2q^2+q
       428: 2q^3
       430: 2q^2+q
       432: 2q^2+q
       433: q^3+2q^2+q
       434: q^3
       435: q
       438: q^2+q
       440: q^2+q
       441: q^2+q
       444: q^3+2q^2+q
       445: q^3+2q^2+q
       446: 2q^3
       448: 2q^2+q
       450: 2q^2+q
       451: q^3+2q^2+q
       452: q^3
       454: q^2+q
       455: q
       458: q^2+q
       459: q^2+q
       462: q^3+2q^2+q
       463: q^3+2q^2+q
       464: 2q^3
       465: q
       467: q^3+q
       469: q^3+2q^2+q
       470: q^3
       472: q^2+q
       474: q^2+q
       475: q^2+q
       477: 2q^2+q
       478: q^3
       479: 2q^2+q
       480: q^3
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       485: q^3+q
       487: q
       489: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       524: q^2+q
       532: 2q^2+q
       536: 2q^2+q
       539: q
       543: q^2+q
       547: 2q^2+q
       548: q^3
       552: 2q^2+q
       555: q
       559: q^2+q
       563: 2q^2+q
       564: q^3
       568: q^2+q
       570: 2q^2+q
       575: 2q^2+q
       577: 2q^2+q
       581: q^3
       585: q^2+q
       590: 2q^2+q
       592: 2q^2+q
       594: 2q^2+q
       596: 2q^2+q
       597: q^3+q
       599: q^3+2q^2+q
       600: q^3
       601: q
       604: q^2+q
       605: q
       608: q^2+q
       609: q^2+q
       613: q^3+2q^2+q
       614: q^3
       616: q^2+q
       617: q
       620: q^2+q
       622: q^2+q
       623: q
       625: q^2+q
       629: q^3+2q^2+q
       630: q^3
       632: q^2+q
       633: q
       639: q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       648: q
       650: q
       651: 2q
       653: q
       655: q^2+q
       657: q^2+q
       658: q^3+q
       660: q
       662: q^3+q
       664: 3q^3+q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       674: q^3+q^2+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       680: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       690: q^3+q
       691: q
       692: q^3+q
       697: 2q^2+q
       712: q^2+q
       716: 2q^2+q
       720: 2q^2+q
       723: q
       727: q^2+q
       735: q
       739: q
       743: q^2+q
       751: q
       756: q^2+q
       758: 2q
       762: q
       768: q^2+q
       769: q
       771: q
       775: q
       779: q^3+q
       781: q
       786: q^2+q
       788: q^2+q
       791: q^2+q
       794: q^2+q
       795: q
       797: q
       802: q
       804: q
       806: q^2+q
       808: q^2+q
       809: q
       811: q^2+q
       816: q
       818: q^2+q
       819: q
       821: q
       826: q^2+q
       828: q^2+q
       830: q
       832: q
       833: q
       835: q^2+q
       840: q
       843: q^2+q
       846: q
       848: q
       849: 2q
       851: q
       855: q^2+q
       857: q
       865: q
       866: q^2+q
       867: q^3+q
       868: q
       869: q
       870: q^3+q^2+q
       871: q
       872: q
       873: q
       874: q^3+q^2+q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       889: q
       893: q
       902: q
       906: q
       911: q^2+q
       918: q
       922: q
       927: q
       930: q^2+q
       942: q
       946: q
       950: q^2+q
       955: q
       961: 2q
       967: q^2+q
       968: q
       970: q
       975: q
       991: q
       994: q
       999: q^2+q
      1001: q^2+q
      1005: q
      1007: q
      1008: q
      1010: 2q
      1012: q^2+q
      1017: q
      1020: q
      1022: q
      1027: q
      1029: q
      1033: q
      1036: q
      1038: q
      1041: q
      1045: q
      1046: q
      1048: q
      1053: q
      1055: q
      1057: q
      1059: q
      1060: q
      1062: q
      1064: q^2+q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q^2+q
      1085: q
      1091: q
      1095: q
      1116: q
      1124: q
      1127: 2q
      1133: q^2+q
      1135: q
      1138: q
      1140: q
      1154: q
      1158: q
      1163: q
      1174: q
      1178: q
      1183: q
      1197: q
      1199: q
      1204: q
      1208: q
      1217: q
      1219: q
      1220: q
      1224: q
      1230: q
      1233: q
      1235: q
      1241: q
      1243: q
      1248: q
      1251: q
      1255: q
      1259: q
      1261: q
      1274: q
      1276: q
      1278: q
      1280: q^2+q
      1283: q
      1285: q
      1288: q
      1295: q
      1299: q
      1329: q
      1331: q
      1350: q
      1358: q
      1361: q
      1367: q
      1369: q
      1382: q
      1390: q
      1393: q
      1399: q
      1401: q
      1430: q
      1436: q
      1451: q
      1455: q
      1461: q
      1463: q
      1482: q
      1506: q
      1518: q
      1538: q
      1578: q
      1598: q
      1622: 1
      1722: 1
      1808: 1
      1891: 1
      1945: 1
      2022: 1

2023:    0: 6q^4+7q^3+2q^2+q
         1: q^5+6q^4+7q^3+2q^2+q
         2: 3q^5+5q^4+5q^3+2q^2+q
         3: 6q^4+7q^3+2q^2+q
         4: 6q^4+7q^3+2q^2+q
         5: q^5+6q^4+7q^3+2q^2+q
         6: q^5+6q^4+7q^3+2q^2+q
         7: 3q^5+5q^4+5q^3+2q^2+q
         8: 2q^5+4q^4+5q^3+2q^2+q
         9: 3q^5+5q^4+5q^3+2q^2+q
        10: 3q^4+4q^3+2q^2+q
        11: 3q^4+4q^3+2q^2+q
        12: 3q^4+4q^3+2q^2+q
        13: 3q^4+5q^3+2q^2+q
        14: 3q^4+5q^3+2q^2+q
        15: 2q^4+5q^3+2q^2+q
        16: 6q^4+7q^3+2q^2+q
        17: q^5+6q^4+7q^3+2q^2+q
        18: 3q^5+5q^4+5q^3+2q^2+q
        19: 6q^4+7q^3+2q^2+q
        20: q^5+6q^4+7q^3+2q^2+q
        21: 3q^5+5q^4+5q^3+2q^2+q
        22: 3q^4+7q^3+2q^2+q
        23: 3q^4+7q^3+2q^2+q
        24: q^5+3q^4+5q^3+2q^2+q
        25: 3q^4+7q^3+2q^2+q
        26: 3q^4+7q^3+2q^2+q
        27: q^5+3q^4+5q^3+2q^2+q
        28: 3q^4+4q^3+2q^2+q
        29: 3q^4+4q^3+2q^2+q
        30: 3q^4+5q^3+2q^2+q
        31: q^4+4q^3+2q^2+q
        32: q^4+5q^3+2q^2+q
        33: 3q^4+7q^3+2q^2+q
        34: q^4+4q^3+2q^2+q
        35: q^4+5q^3+2q^2+q
        36: 3q^4+7q^3+2q^2+q
        37: q^4+3q^3
        38: 4q^3+2q^2+q
        39: q^4+3q^3
        40: 4q^3+2q^2+q
        41: q^4+2q^3
        42: q^4+3q^3+2q^2+q
        43: q^4+2q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+2q^2+q
        46: 3q^4+5q^3+2q^2+q
        47: 2q^4+5q^3+2q^2+q
        48: 3q^4+5q^3+2q^2+q
        49: 6q^4+7q^3+2q^2+q
        50: q^5+6q^4+7q^3+2q^2+q
        51: 3q^5+5q^4+5q^3+2q^2+q
        52: 3q^4+7q^3+2q^2+q
        53: 3q^4+7q^3+2q^2+q
        54: q^5+3q^4+5q^3+2q^2+q
        55: 3q^4+7q^3+2q^2+q
        56: 3q^4+7q^3+2q^2+q
        57: q^5+3q^4+5q^3+2q^2+q
        58: 2q^3
        59: q^4+2q^3+2q^2+q
        60: q^4+2q^3+2q^2+q
        61: 2q^3
        62: 2q^3
        63: 2q^3+2q^2+q
        64: 2q^3
        65: 3q^3+2q^2+q
        66: q^4+3q^3
        67: 4q^3+2q^2+q
        68: 2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: q^4+2q^3+2q^2+q
        71: 3q^4+4q^3+2q^2+q
        72: 3q^4+7q^3+2q^2+q
        73: 3q^4+7q^3+2q^2+q
        74: q^4+3q^3
        75: 4q^3+2q^2+q
        76: q^4+3q^3
        77: 4q^3+2q^2+q
        78: q^4+2q^3
        79: q^4+3q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+5q^3+2q^2+q
        82: q^4+4q^3+2q^2+q
        83: q^4+5q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+5q^3+2q^2+q
        86: q^4+4q^3+2q^2+q
        87: q^4+5q^3+2q^2+q
        88: q^4+2q^3+2q^2+q
        89: 2q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: 3q^4+5q^3+2q^2+q
        92: 2q^4+5q^3+2q^2+q
        93: 3q^4+5q^3+2q^2+q
        94: 3q^4+7q^3+2q^2+q
        95: 3q^4+7q^3+2q^2+q
        96: q^5+3q^4+5q^3+2q^2+q
        97: 3q^4+7q^3+2q^2+q
        98: 3q^4+7q^3+2q^2+q
        99: q^5+3q^4+5q^3+2q^2+q
       100: 6q^3+2q^2+q
       101: q^4+6q^3+2q^2+q
       102: 2q^4+5q^3+2q^2+q
       103: q^3
       104: q^3+2q^2+q
       105: q^3
       106: q^3
       107: q^4+2q^3+2q^2+q
       108: 2q^3
       109: 2q^3
       110: q^4+2q^3+2q^2+q
       111: q^4+3q^3
       112: 4q^3+2q^2+q
       113: 2q^3
       114: 2q^3+2q^2+q
       115: 2q^3
       116: 3q^3+2q^2+q
       118: 2q^2+q
       119: 2q^2+q
       121: q^3
       122: q^3+2q^2+q
       123: 2q^3
       124: 3q^3+2q^2+q
       125: 2q^2+q
       126: q^4+2q^3+2q^2+q
       127: q^4+3q^3
       128: 4q^3+2q^2+q
       129: q^4+3q^3
       130: 4q^3+2q^2+q
       131: q^4+2q^3
       132: q^4+3q^3+2q^2+q
       133: 2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: q^4+5q^3+2q^2+q
       136: q^4+5q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+4q^3+2q^2+q
       140: 3q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 3q^4+7q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+4q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 3q^4+7q^3+2q^2+q
       148: 3q^3+2q^2+q
       149: 3q^3+2q^2+q
       150: 5q^3+2q^2+q
       151: 3q^3
       152: 3q^3+2q^2+q
       153: q^4+3q^3
       154: 3q^3+2q^2+q
       155: q^4+2q^3
       156: q^4+3q^3+2q^2+q
       157: q^4+2q^3+2q^2+q
       158: 2q^3+2q^2+q
       159: q^4+2q^3+2q^2+q
       160: q^4+4q^3+2q^2+q
       161: q^4+4q^3+2q^2+q
       162: q^4+4q^3+2q^2+q
       163: q^4+4q^3+2q^2+q
       164: q^4+4q^3+2q^2+q
       165: q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^3+2q^2+q
       171: q^3
       172: q^3
       174: 2q^2+q
       177: 2q^3
       178: 3q^3+2q^2+q
       179: 2q^3
       180: 2q^3+2q^2+q
       181: q^4+3q^3
       182: 4q^3+2q^2+q
       183: 2q^2+q
       186: 2q^2+q
       187: 2q^3
       188: 3q^3+2q^2+q
       189: q^3
       190: q^3+2q^2+q
       192: 2q^2+q
       193: q^3+2q^2+q
       195: 2q^3
       196: q^4+2q^3+2q^2+q
       197: 2q^3
       198: q^3+2q^2+q
       199: 2q^2+q
       201: q^4+2q^3+2q^2+q
       202: 2q^3
       204: q^3+2q^2+q
       205: 2q^3
       206: q^3+2q^2+q
       207: q^3
       208: q^3+2q^2+q
       209: 2q^3
       210: q^3+2q^2+q
       211: 2q^3
       212: 3q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: 2q^2+q
       220: 2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 2q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 2q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 2q^3+2q^2+q
       230: q^4+4q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+4q^3+2q^2+q
       235: 2q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3
       238: 3q^3+2q^2+q
       239: q^4+3q^3
       240: 3q^3+2q^2+q
       241: q^4+2q^3
       242: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: 2q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3
       260: q^3+2q^2+q
       261: q^3
       262: q^3
       264: 2q^2+q
       267: q^3
       268: 2q^2+q
       273: q^3
       274: 2q^2+q
       276: 2q^2+q
       280: q^2+q
       282: q^3+q^2+q
       283: 2q^2+q
       286: 2q^2+q
       287: q^3
       288: q^3+2q^2+q
       290: q^3+q^2+q
       291: 2q^3
       292: 3q^3+2q^2+q
       293: 2q^2+q
       296: 2q^2+q
       297: q^3
       298: q^3+2q^2+q
       299: 2q^2+q
       301: 2q^3
       302: q^3+2q^2+q
       304: 2q^2+q
       305: q^3
       306: q^3+2q^2+q
       307: 2q^2+q
       310: 2q^2+q
       311: 2q^3
       312: q^3+2q^2+q
       313: q^3
       314: q^3+2q^2+q
       315: 2q^3
       316: 3q^3+2q^2+q
       317: 2q^3
       318: q^3+2q^2+q
       319: q^3+2q^2+q
       322: q^3+2q^2+q
       323: q^3
       324: 2q^2+q
       325: q^3
       326: q^3+2q^2+q
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3
       339: 3q^3+2q^2+q
       340: q^4+3q^3
       341: 3q^3+2q^2+q
       342: q^4+2q^3
       343: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       378: 2q^2+q
       382: q^2+q
       386: 2q^2+q
       389: q^3
       390: 2q^2+q
       394: 2q^2+q
       399: q^3
       400: 2q^2+q
       403: 2q^2+q
       407: 2q^2+q
       414: q^2+q
       418: q^3+q^2+q
       419: 2q^2+q
       422: 2q^2+q
       423: q^3
       424: q^3+2q^2+q
       425: 2q^3
       426: 3q^3+2q^2+q
       427: 2q^3
       428: q^3+2q^2+q
       429: 2q^2+q
       432: 2q^2+q
       433: q^3
       434: q^3+2q^2+q
       436: q
       437: q^2+q
       440: q^2+q
       442: q^2+q
       443: q^3+2q^2+q
       445: 2q^3
       446: q^3+2q^2+q
       447: 2q^2+q
       450: 2q^2+q
       451: q^3
       452: q^3+2q^2+q
       453: q^2+q
       456: q
       458: q^2+q
       460: q^2+q
       462: q^3+2q^2+q
       463: 2q^3
       464: q^3+2q^2+q
       466: q
       468: q^3+q
       469: q^3
       470: q^3+2q^2+q
       471: q^2+q
       474: q^2+q
       476: q^2+q
       477: q^3
       478: 2q^2+q
       479: q^3
       480: 2q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       486: q^3+q
       488: q
       490: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       522: q^2+q
       530: 2q^2+q
       534: 2q^2+q
       538: q
       542: q^2+q
       545: q^3
       546: 2q^2+q
       551: 2q^2+q
       556: q
       560: q^2+q
       563: q^3
       564: 2q^2+q
       566: q^2+q
       571: 2q^2+q
       574: 2q^2+q
       577: q^3
       581: 2q^2+q
       586: q^2+q
       589: 2q^2+q
       592: 2q^2+q
       593: 2q^2+q
       596: 2q^2+q
       598: q^3+q
       599: q^3
       600: q^3+2q^2+q
       602: q
       603: q^2+q
       606: q
       608: q^2+q
       610: q^2+q
       613: q^3
       614: q^3+2q^2+q
       615: q^2+q
       618: q
       619: q^2+q
       622: q^2+q
       624: q
       626: q^2+q
       629: q^3
       630: q^3+2q^2+q
       632: q^2+q
       634: q
       640: q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q
       650: q
       652: 2q
       654: q
       656: q^2+q
       657: q^2+q
       659: q^3+q
       661: q
       663: q^3+q
       664: 3q^3+q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       674: q^3+q^2+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       680: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       690: q^3+q
       691: q
       692: q^3+q
       699: 2q^2+q
       710: q^2+q
       715: 2q^2+q
       718: 2q^2+q
       722: q
       726: q^2+q
       734: q
       740: q
       744: q^2+q
       752: q
       754: q^2+q
       759: 2q
       763: q
       766: q^2+q
       773: q
       774: q
       776: q
       780: q^3+q
       782: q
       785: q^2+q
       788: q^2+q
       792: q^2+q
       793: q^2+q
       796: q
       798: q
       801: q
       804: q
       805: q^2+q
       808: q^2+q
       810: q
       812: q^2+q
       815: q
       818: q^2+q
       820: q
       822: q
       825: q^2+q
       828: q^2+q
       829: q
       832: q
       834: q
       836: q^2+q
       840: q
       844: q^2+q
       845: q
       848: q
       850: 2q
       852: q
       856: q^2+q
       858: q
       865: q
       866: q^2+q
       867: q^3+q
       868: q
       869: q
       870: q^3+q^2+q
       871: q
       872: q
       873: q
       874: q^3+q^2+q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       890: q
       894: q
       903: q
       905: q
       909: q^2+q
       917: q
       921: q
       926: q
       929: q^2+q
       943: q
       947: q
       951: q^2+q
       953: q
       962: 2q
       965: q^2+q
       972: q
       973: q
       976: q
       989: q
       995: q
       999: q^2+q
      1000: q^2+q
      1004: q
      1007: q
      1009: q
      1011: 2q
      1013: q^2+q
      1016: q
      1021: q
      1023: q
      1026: q
      1029: q
      1033: q
      1037: q
      1039: q
      1040: q
      1045: q
      1047: q
      1049: q
      1052: q
      1055: q
      1056: q
      1059: q
      1061: q
      1063: q
      1065: q^2+q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q^2+q
      1085: q
      1092: q
      1096: q
      1117: q
      1123: q
      1128: 2q
      1131: q^2+q
      1136: q
      1142: q
      1143: q
      1155: q
      1157: q
      1162: q
      1175: q
      1177: q
      1181: q
      1195: q
      1200: q
      1205: q
      1207: q
      1217: q
      1218: q
      1221: q
      1225: q
      1231: q
      1233: q
      1234: q
      1240: q
      1243: q
      1249: q
      1251: q
      1254: q
      1258: q
      1261: q
      1275: q
      1277: q
      1279: q
      1281: q^2+q
      1283: q
      1285: q
      1288: q
      1296: q
      1300: q
      1327: q
      1332: q
      1351: q
      1357: q
      1363: q
      1366: q
      1371: q
      1383: q
      1389: q
      1394: q
      1397: q
      1402: q
      1434: q
      1437: q
      1451: q
      1454: q
      1461: q
      1462: q
      1483: q
      1508: q
      1519: q
      1539: q
      1577: q
      1596: q
      1620: 1
      1719: 1
      1809: 1
      1892: 1
      1946: 1
      2023: 1

2024:    0: 6q^3+6q^2+3q
         1: 6q^3+6q^2+3q
         2: 2q^4+5q^3+5q^2+3q
         3: 6q^3+6q^2+3q
         4: 2q^4+5q^3+5q^2+3q
         5: 6q^3+6q^2+3q
         6: 2q^4+5q^3+5q^2+3q
         7: q^5+2q^4+5q^3+4q^2+3q
         8: 2q^4+5q^3+5q^2+3q
         9: q^5+2q^4+5q^3+4q^2+3q
        10: 3q^3+6q^2+3q
        11: 3q^3+6q^2+3q
        12: q^4+3q^3+5q^2+3q
        13: 4q^3+5q^2+3q
        14: q^4+4q^3+4q^2+3q
        15: 4q^3+5q^2+3q
        16: 6q^3+6q^2+3q
        17: 6q^3+6q^2+3q
        18: q^5+2q^4+5q^3+4q^2+3q
        19: 4q^3+5q^2+3q
        20: 4q^3+5q^2+3q
        21: q^4+4q^3+4q^2+3q
        22: 6q^3+6q^2+3q
        23: 6q^3+6q^2+3q
        24: 2q^4+5q^3+5q^2+3q
        25: 6q^3+6q^2+3q
        26: 6q^3+6q^2+3q
        27: 2q^4+5q^3+5q^2+3q
        28: 3q^3+6q^2+3q
        29: 2q^3+5q^2+3q
        30: 3q^3+4q^2+3q
        31: 3q^3+6q^2+3q
        32: 4q^3+5q^2+3q
        33: 6q^3+6q^2+3q
        34: 3q^3+6q^2+3q
        35: 4q^3+5q^2+3q
        36: 6q^3+6q^2+3q
        37: 3q^3+2q^2+q
        38: 3q^3+4q^2+2q
        39: 3q^3+2q^2+q
        40: 3q^3+4q^2+2q
        41: q^4+2q^3+2q^2+q
        42: q^4+3q^3+3q^2+2q
        43: q^3+5q^2+3q
        44: 2q^3+4q^2+3q
        45: q^3+5q^2+3q
        46: 4q^3+5q^2+3q
        47: 4q^3+5q^2+3q
        48: q^4+4q^3+4q^2+3q
        49: 4q^3+5q^2+3q
        50: 4q^3+5q^2+3q
        51: q^4+4q^3+4q^2+3q
        52: 4q^3+5q^2+3q
        53: 4q^3+5q^2+3q
        54: q^4+4q^3+4q^2+3q
        55: 4q^3+5q^2+3q
        56: 4q^3+5q^2+3q
        57: q^4+4q^3+4q^2+3q
        58: q^3+2q^2+q
        59: 2q^3+4q^2+2q
        60: q^3+2q^2+q
        61: 2q^3+4q^2+2q
        62: q^3+2q^2+q
        63: 2q^3+4q^2+2q
        64: 2q^3+2q^2+q
        65: 2q^3+3q^2+2q
        66: 3q^3+2q^2+q
        67: 3q^3+4q^2+2q
        68: 4q^2+3q
        69: 3q^3+4q^2+3q
        70: q^3+4q^2+3q
        71: 2q^3+5q^2+3q
        72: 2q^3+4q^2+3q
        73: 2q^3+4q^2+3q
        74: q^3+q^2+q
        75: q^3+3q^2+2q
        76: q^3+q^2+q
        77: q^3+3q^2+2q
        78: q^3+q^2+q
        79: 2q^3+2q^2+2q
        80: q^3+5q^2+3q
        81: 4q^3+5q^2+3q
        82: 2q^3+5q^2+3q
        83: 3q^3+4q^2+3q
        84: q^3+5q^2+3q
        85: 4q^3+5q^2+3q
        86: 2q^3+5q^2+3q
        87: 3q^3+4q^2+3q
        88: q^3+5q^2+3q
        89: q^3+5q^2+3q
        90: 2q^3+4q^2+3q
        91: 2q^3+4q^2+3q
        92: 2q^3+4q^2+3q
        93: 2q^3+4q^2+3q
        94: 4q^3+5q^2+3q
        95: 4q^3+5q^2+3q
        96: q^4+4q^3+4q^2+3q
        97: 4q^3+5q^2+3q
        98: 4q^3+5q^2+3q
        99: q^4+4q^3+4q^2+3q
       100: 4q^3+5q^2+3q
       101: 4q^3+5q^2+3q
       102: q^4+4q^3+4q^2+3q
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       106: q^3+2q^2+q
       107: q^2+q
       108: q^3+3q^2+2q
       109: q^2+q
       110: q^3+3q^2+2q
       111: q^2+q
       112: 2q^2+2q
       113: q^2+q
       114: q^3+3q^2+2q
       115: q^3+q^2+q
       116: q^3+2q^2+2q
       117: q^2+q
       118: 3q^2+2q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+q
       122: q^3+3q^2+2q
       123: 2q^3+2q^2+q
       124: 2q^3+3q^2+2q
       125: 4q^2+3q
       126: q^3+4q^2+3q
       127: q^3+q^2+q
       128: q^3+3q^2+2q
       129: q^3+q^2+q
       130: q^3+3q^2+2q
       131: q^3+q^2+q
       132: 2q^3+2q^2+2q
       133: 3q^2+3q
       134: 2q^3+4q^2+3q
       135: q^3+3q^2+3q
       136: q^3+3q^2+3q
       137: q^3+5q^2+3q
       138: 3q^3+4q^2+3q
       139: 2q^3+5q^2+3q
       140: 2q^3+4q^2+3q
       141: q^3+4q^2+3q
       142: 2q^3+4q^2+3q
       143: q^3+5q^2+3q
       144: 3q^3+4q^2+3q
       145: 2q^3+5q^2+3q
       146: q^3+4q^2+3q
       147: 2q^3+4q^2+3q
       148: 2q^3+4q^2+3q
       149: 2q^3+5q^2+3q
       150: 3q^3+4q^2+3q
       151: q^3+q^2+q
       152: q^3+3q^2+2q
       153: q^3+q^2+q
       154: q^3+3q^2+2q
       155: q^3+q^2+q
       156: 2q^3+2q^2+2q
       157: 3q^2+3q
       158: 3q^2+3q
       159: 3q^2+3q
       160: 2q^3+4q^2+3q
       161: 2q^3+4q^2+3q
       162: 2q^3+4q^2+3q
       163: 2q^3+4q^2+3q
       164: 2q^3+4q^2+3q
       165: 2q^3+4q^2+3q
       166: 4q^3+5q^2+3q
       167: 4q^3+5q^2+3q
       168: q^4+4q^3+4q^2+3q
       170: q^2+q
       171: q^2+q
       172: q^2+q
       174: q^2+q
       175: q^2+q
       176: 2q^2+q
       177: q^3+q^2+q
       178: q^3+2q^2+2q
       179: q^2+q
       180: q^3+3q^2+2q
       181: q^2+q
       182: 2q^2+2q
       183: q
       184: 2q^2+2q
       185: q
       186: 2q^2+2q
       187: q^2+q
       188: q^2+2q
       189: q^2+q
       190: q^3+2q^2+2q
       191: q^2+q
       192: 3q^2+2q
       193: q^2+q
       194: q^3+3q^2+2q
       195: q^2+q
       196: q^3+3q^2+2q
       197: q^2+q
       198: 2q^2+2q
       199: q^2+q
       200: 3q^2+2q
       201: q^2+q
       202: q^3+3q^2+2q
       203: q^2+q
       204: q^3+3q^2+2q
       205: q^2+q
       206: 2q^2+2q
       207: 2q^2+q
       208: q^3+3q^2+2q
       209: q^2+q
       210: q^3+3q^2+2q
       211: q^3+q^2+q
       212: q^3+2q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 3q^2+3q
       222: 2q^2+3q
       223: q^3+3q^2+3q
       224: 2q^2+3q
       225: q^3+3q^2+3q
       226: q^3+4q^2+3q
       227: 3q^2+3q
       228: 2q^3+4q^2+3q
       229: q^3+3q^2+3q
       230: q^3+3q^2+3q
       231: q^3+4q^2+3q
       232: 3q^2+3q
       233: 2q^3+4q^2+3q
       234: q^3+3q^2+3q
       235: q^3+3q^2+3q
       236: 3q^3+4q^2+3q
       237: q^3+q^2+q
       238: q^3+3q^2+2q
       239: q^3+q^2+q
       240: q^3+3q^2+2q
       241: q^3+q^2+q
       242: 2q^3+2q^2+2q
       243: 2q^3+5q^2+3q
       244: 2q^3+4q^2+3q
       245: 2q^3+4q^2+3q
       246: q^3+4q^2+3q
       247: 5q^2+4q
       248: 5q^2+4q
       249: 3q^3+3q^2+3q
       250: 3q^2+3q
       251: 3q^2+3q
       252: 3q^2+3q
       253: 3q^2+3q
       254: 3q^2+3q
       255: 3q^2+3q
       256: 2q^3+4q^2+3q
       257: 2q^3+4q^2+3q
       258: 2q^3+4q^2+3q
       260: q^2+q
       261: q^2+q
       262: q^2+q
       264: q
       265: q
       266: q^2+q
       268: q^2+q
       269: q^2+q
       270: q^2+q
       272: q^2+q
       273: q^2+q
       274: q^2+q
       276: q^2+q
       277: q^2+q
       278: 2q^2+q
       280: q^2+2q
       282: q^2+2q
       283: q
       284: 2q^2+2q
       285: q
       286: 2q^2+2q
       287: q^2+q
       288: q^3+2q^2+2q
       290: 2q
       291: q^2+q
       292: q^2+2q
       293: q
       294: q^2+2q
       295: q
       296: q^2+2q
       297: q
       298: q^2+2q
       299: q
       300: 2q^2+2q
       301: q^2+q
       302: 2q^2+2q
       303: q
       304: 2q^2+2q
       305: q^2+q
       306: q^2+2q
       307: q
       308: 2q^2+2q
       309: q
       310: 2q^2+2q
       311: q^2+q
       312: 2q^2+2q
       313: q^2+q
       314: q^2+2q
       315: q^3+q^2+q
       316: q^3+2q^2+2q
       317: q^2+q
       318: q^3+3q^2+2q
       319: q^2+q
       320: q^3+3q^2+2q
       321: q^2+q
       322: q^3+3q^2+2q
       323: q^2+q
       324: 2q^2+2q
       325: q^2+q
       326: q^3+2q^2+2q
       333: 2q^2+3q
       334: 2q^2+3q
       335: 2q^2+3q
       336: 2q^2+3q
       337: 4q^2+4q
       338: 2q^2+q
       339: 3q^2+3q
       340: 2q^2+q
       341: 3q^2+3q
       342: q^3+q^2+q
       343: 2q^3+2q^2+2q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 3q^2+3q
       347: 2q^2+3q
       348: q^3+3q^2+3q
       349: 2q^2+3q
       350: q^3+3q^2+3q
       351: 5q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 3q^2+3q
       355: 2q^2+3q
       356: q^3+3q^2+3q
       357: 2q^2+3q
       358: q^3+3q^2+3q
       359: 5q^2+4q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: q^3+4q^2+3q
       367: 3q^2+3q
       368: 2q^3+4q^2+3q
       369: q^3+3q^2+3q
       370: q^3+3q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 3q^2+3q
       375: 3q^2+3q
       376: 3q^2+3q
       378: q
       379: q
       380: q^2+q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q^2+q
       391: q^2+q
       392: q^2+q
       394: q
       395: q
       396: q^2+q
       398: q^2+q
       399: q^2+q
       400: q^2+q
       402: q
       403: q
       404: q^2+q
       406: q^2+q
       407: q^2+q
       408: q^2+q
       414: q^2+2q
       418: 2q
       419: q
       420: q^2+2q
       421: q
       422: q^2+2q
       423: q
       424: q^2+2q
       425: q^2+q
       426: q^2+2q
       427: q^2+q
       428: 3q^2+3q
       429: q
       430: 2q^2+2q
       431: q
       432: 2q^2+2q
       433: q^2+q
       434: q^2+2q
       436: 2q
       437: q
       438: q^2+2q
       439: q
       440: q^2+2q
       441: q
       442: q^2+2q
       443: q^2+q
       444: 3q^2+3q
       445: 2q^2+q
       446: 3q^2+3q
       447: q
       448: 2q^2+2q
       449: q
       450: 2q^2+2q
       451: q^2+q
       452: q^2+2q
       453: q
       454: q^2+2q
       456: 2q
       457: q
       458: q^2+2q
       459: q
       460: q^2+2q
       461: q^2+q
       462: 3q^2+3q
       463: 2q^2+q
       464: 3q^2+3q
       466: q^2+2q
       468: q^2+2q
       469: q^2+q
       470: q^3+2q^2+2q
       471: q
       472: 2q^2+2q
       473: q
       474: 2q^2+2q
       475: q^2+q
       476: q^2+2q
       477: q^2+q
       478: 2q^2+2q
       479: 2q^2+2q
       480: 3q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: q^2+3q
       484: q^2+4q
       486: 3q
       488: 3q
       490: q^2+2q
       491: q^2+3q
       492: 2q^2+3q
       493: 2q^2+3q
       494: 2q^2+3q
       495: 2q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: 2q^2+3q
       499: 2q^2+3q
       500: 2q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 3q^2+3q
       511: 2q^2+3q
       512: q^3+3q^2+3q
       513: 2q^2+3q
       514: q^3+3q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       530: q
       531: q
       532: q
       534: q
       535: q
       536: q^2+q
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q^2+q
       547: q^2+q
       548: 2q^2+2q
       550: q
       551: q
       552: q^2+q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q^2+q
       563: q^2+q
       564: 2q^2+2q
       566: q
       567: q
       568: q^2+q
       570: q^2+q
       571: q^2+q
       572: q^2+q
       574: q^2+q
       575: 2q^2+2q
       576: q^2+q
       577: q^2+q
       578: q^2+q
       580: q^2
       581: 2q^2+2q
       586: 2q
       589: q
       590: q^2+2q
       592: 2q
       594: 2q
       595: q
       596: q^2+2q
       598: 2q
       599: q
       600: q^2+2q
       602: 3q
       603: q
       604: q^2+2q
       606: 2q
       607: q
       608: q^2+2q
       609: q
       610: q^2+2q
       613: q^2+q
       614: q^2+2q
       615: q
       616: q^2+3q
       618: 3q
       619: q
       620: q^2+2q
       621: q
       622: q^2+2q
       624: 2q
       625: q
       626: q^2+2q
       629: q^2+q
       630: q^2+2q
       631: q
       632: q^2+3q
       634: 3q
       640: q^2+2q
       641: q
       642: 2q^2+2q
       643: q
       644: 2q^2+2q
       645: q^2+q
       646: q^2+2q
       647: q
       648: q^2+2q
       649: q
       650: q^2+2q
       652: 2q
       653: q
       654: q^2+2q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       659: 3q
       661: 3q
       663: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: q^2+3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: q^2+3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: 2q^2+3q
       688: 2q^2+3q
       689: 2q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       697: q^2+q
       699: q^2+q
       700: q^2+q
       701: q^2+q
       710: q
       711: q
       715: q
       716: q
       719: q
       720: q
       722: q
       724: q
       726: q
       727: q
       728: q
       734: q
       736: 2q
       738: q
       740: q
       742: q
       743: q
       744: q
       750: q
       752: 2q
       754: q
       755: q
       756: q^2+q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q^2+2q
       770: q
       773: 2q
       776: 3q
       780: 2q
       782: 2q
       786: 2q
       788: 2q
       791: q
       792: q
       793: q
       794: q^2+3q
       796: 3q
       798: 2q
       801: q
       802: q^2+2q
       804: 2q
       806: 2q
       807: q
       808: q^2+2q
       810: 2q
       811: q
       812: q^2+2q
       815: q
       816: 2q
       817: q
       818: q^2+3q
       820: 3q
       822: 2q
       825: q
       826: q^2+2q
       828: 2q
       830: 2q
       831: q
       832: q^2+2q
       834: 2q
       835: q
       836: q^2+2q
       839: q
       840: 2q
       843: q^2+2q
       844: q^2+2q
       845: q
       846: q^2+2q
       847: q
       848: q^2+2q
       850: 2q
       851: q
       852: q^2+2q
       855: q^2+q
       856: q^2+2q
       857: q
       858: 2q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: q^2+3q
       880: q^2+3q
       890: q
       891: q
       892: q
       903: q
       907: q
       911: q
       917: q
       919: 2q
       921: q
       923: q
       926: q
       927: q
       930: q
       931: q
       941: q
       943: 2q
       945: q
       947: q
       950: q
       951: q
       954: q
       955: q
       962: q
       963: q
       965: q
       966: q
       967: q^2+2q
       969: q
       972: 2q
       975: q
       976: q
       977: q
       989: q
       990: q
       991: q
       995: 2q
       999: 2q
      1001: 2q
      1005: q
      1007: q
      1009: q
      1011: q
      1012: q
      1013: q
      1016: q
      1017: 2q
      1021: 2q
      1023: 2q
      1027: 2q
      1029: 2q
      1032: q
      1033: 2q
      1037: 2q
      1039: 2q
      1041: 2q
      1045: 2q
      1046: q
      1047: 2q
      1049: 2q
      1052: q
      1053: q^2+2q
      1055: 2q
      1057: 2q
      1058: q
      1059: q^2+2q
      1061: 2q
      1062: q
      1063: q^2+2q
      1064: q
      1065: q
      1074: 2q
      1076: 3q
      1077: 2q
      1078: 2q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1092: q
      1093: q
      1094: q
      1117: q
      1125: q
      1133: q
      1142: q
      1155: q
      1159: q
      1163: q
      1175: q
      1179: q
      1183: q
      1195: q
      1196: q
      1197: q
      1200: q
      1201: q
      1204: q
      1205: q
      1208: q
      1209: q
      1217: q
      1219: q
      1221: q
      1225: q
      1231: 2q
      1233: 2q
      1235: 2q
      1241: q
      1243: q
      1249: 2q
      1251: 2q
      1255: 2q
      1259: q
      1261: q
      1267: 2q
      1269: 2q
      1271: 2q
      1275: 2q
      1277: q
      1279: q
      1280: q
      1281: q
      1283: 2q
      1285: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1351: q
      1359: q
      1367: q
      1383: q
      1391: q
      1399: q
      1421: q
      1425: q
      1429: q
      1434: q
      1437: q
      1451: q
      1455: q
      1461: q
      1463: q
      1465: 2q
      1467: 2q
      1469: 2q
      1475: q
      1477: q
      1479: q
      1483: q
      1484: 1
      1487: 2q
      1610: q
      1618: q
      1626: q
      1642: 1
      1650: 1
      1658: 1
      1660: q
      1664: q
      1666: q
      1673: 1
      1760: 1
      1784: 1
      1814: 1
      1818: 1
      1820: 1
      1822: 1
      1890: 1
      1909: 1
      1925: 1
      1955: 1
      2024: 1

2025:    0: 6q^4+7q^3+2q^2+q
         1: q^5+6q^4+7q^3+2q^2+q
         2: 3q^5+5q^4+5q^3+2q^2+q
         3: 6q^4+7q^3+2q^2+q
         4: 6q^4+7q^3+2q^2+q
         5: q^5+6q^4+7q^3+2q^2+q
         6: q^5+6q^4+7q^3+2q^2+q
         7: 3q^5+5q^4+5q^3+2q^2+q
         8: 2q^5+4q^4+5q^3+2q^2+q
         9: 3q^5+5q^4+5q^3+2q^2+q
        10: 3q^4+4q^3+2q^2+q
        11: 3q^4+4q^3+2q^2+q
        12: 3q^4+4q^3+2q^2+q
        13: 3q^4+5q^3+2q^2+q
        14: 3q^4+5q^3+2q^2+q
        15: 2q^4+5q^3+2q^2+q
        16: 6q^4+7q^3+2q^2+q
        17: q^5+6q^4+7q^3+2q^2+q
        18: 3q^5+5q^4+5q^3+2q^2+q
        19: 6q^4+7q^3+2q^2+q
        20: q^5+6q^4+7q^3+2q^2+q
        21: 3q^5+5q^4+5q^3+2q^2+q
        22: 3q^4+7q^3+2q^2+q
        23: 3q^4+7q^3+2q^2+q
        24: q^5+3q^4+5q^3+2q^2+q
        25: 3q^4+7q^3+2q^2+q
        26: 3q^4+7q^3+2q^2+q
        27: q^5+3q^4+5q^3+2q^2+q
        28: 3q^4+4q^3+2q^2+q
        29: 3q^4+4q^3+2q^2+q
        30: 3q^4+5q^3+2q^2+q
        31: q^4+4q^3+2q^2+q
        32: q^4+5q^3+2q^2+q
        33: 3q^4+7q^3+2q^2+q
        34: q^4+4q^3+2q^2+q
        35: q^4+5q^3+2q^2+q
        36: 3q^4+7q^3+2q^2+q
        37: q^4+3q^3
        38: 4q^3+2q^2+q
        39: q^4+3q^3
        40: 4q^3+2q^2+q
        41: q^4+2q^3
        42: q^4+3q^3+2q^2+q
        43: q^4+2q^3+2q^2+q
        44: q^4+2q^3+2q^2+q
        45: 2q^3+2q^2+q
        46: 3q^4+5q^3+2q^2+q
        47: 2q^4+5q^3+2q^2+q
        48: 3q^4+5q^3+2q^2+q
        49: 6q^4+7q^3+2q^2+q
        50: q^5+6q^4+7q^3+2q^2+q
        51: 3q^5+5q^4+5q^3+2q^2+q
        52: 3q^4+7q^3+2q^2+q
        53: 3q^4+7q^3+2q^2+q
        54: q^5+3q^4+5q^3+2q^2+q
        55: 3q^4+7q^3+2q^2+q
        56: 3q^4+7q^3+2q^2+q
        57: q^5+3q^4+5q^3+2q^2+q
        58: q^4+2q^3+2q^2+q
        59: 2q^3
        60: 2q^3
        61: q^4+2q^3+2q^2+q
        62: 2q^3
        63: 2q^3+2q^2+q
        64: 2q^3
        65: 3q^3+2q^2+q
        66: q^4+3q^3
        67: 4q^3+2q^2+q
        68: 2q^2+q
        69: 3q^4+5q^3+2q^2+q
        70: q^4+2q^3+2q^2+q
        71: 3q^4+4q^3+2q^2+q
        72: 3q^4+7q^3+2q^2+q
        73: 3q^4+7q^3+2q^2+q
        74: q^4+3q^3
        75: 4q^3+2q^2+q
        76: q^4+3q^3
        77: 4q^3+2q^2+q
        78: q^4+2q^3
        79: q^4+3q^3+2q^2+q
        80: 2q^3+2q^2+q
        81: q^4+5q^3+2q^2+q
        82: q^4+4q^3+2q^2+q
        83: q^4+5q^3+2q^2+q
        84: 2q^3+2q^2+q
        85: q^4+5q^3+2q^2+q
        86: q^4+4q^3+2q^2+q
        87: q^4+5q^3+2q^2+q
        88: q^4+2q^3+2q^2+q
        89: 2q^3+2q^2+q
        90: q^4+2q^3+2q^2+q
        91: 3q^4+5q^3+2q^2+q
        92: 2q^4+5q^3+2q^2+q
        93: 3q^4+5q^3+2q^2+q
        94: 3q^4+7q^3+2q^2+q
        95: 3q^4+7q^3+2q^2+q
        96: q^5+3q^4+5q^3+2q^2+q
        97: 3q^4+7q^3+2q^2+q
        98: 3q^4+7q^3+2q^2+q
        99: q^5+3q^4+5q^3+2q^2+q
       100: 6q^3+2q^2+q
       101: q^4+6q^3+2q^2+q
       102: 2q^4+5q^3+2q^2+q
       103: q^3
       104: q^3
       105: q^3+2q^2+q
       106: q^3
       107: 2q^3
       108: q^4+2q^3+2q^2+q
       109: q^4+2q^3+2q^2+q
       110: 2q^3
       111: q^4+3q^3
       112: 4q^3+2q^2+q
       113: 2q^3
       114: 2q^3+2q^2+q
       115: 2q^3
       116: 3q^3+2q^2+q
       117: 2q^2+q
       120: 2q^2+q
       121: q^3
       122: q^3+2q^2+q
       123: 2q^3
       124: 3q^3+2q^2+q
       125: 2q^2+q
       126: q^4+2q^3+2q^2+q
       127: q^4+3q^3
       128: 4q^3+2q^2+q
       129: q^4+3q^3
       130: 4q^3+2q^2+q
       131: q^4+2q^3
       132: q^4+3q^3+2q^2+q
       133: 2q^2+q
       134: 3q^4+5q^3+2q^2+q
       135: q^4+5q^3+2q^2+q
       136: q^4+5q^3+2q^2+q
       137: 2q^3+2q^2+q
       138: q^4+5q^3+2q^2+q
       139: q^4+4q^3+2q^2+q
       140: 3q^3+2q^2+q
       141: 2q^3+2q^2+q
       142: 3q^4+7q^3+2q^2+q
       143: 2q^3+2q^2+q
       144: q^4+5q^3+2q^2+q
       145: q^4+4q^3+2q^2+q
       146: 2q^3+2q^2+q
       147: 3q^4+7q^3+2q^2+q
       148: 3q^3+2q^2+q
       149: 3q^3+2q^2+q
       150: 5q^3+2q^2+q
       151: 3q^3
       152: 3q^3+2q^2+q
       153: q^4+3q^3
       154: 3q^3+2q^2+q
       155: q^4+2q^3
       156: q^4+3q^3+2q^2+q
       157: q^4+2q^3+2q^2+q
       158: 2q^3+2q^2+q
       159: q^4+2q^3+2q^2+q
       160: q^4+4q^3+2q^2+q
       161: q^4+4q^3+2q^2+q
       162: q^4+4q^3+2q^2+q
       163: q^4+4q^3+2q^2+q
       164: q^4+4q^3+2q^2+q
       165: q^4+4q^3+2q^2+q
       166: 6q^3+2q^2+q
       167: q^4+6q^3+2q^2+q
       168: 2q^4+5q^3+2q^2+q
       169: q^3
       170: q^3
       171: q^3+2q^2+q
       172: q^3
       175: 2q^2+q
       177: 2q^3
       178: 3q^3+2q^2+q
       179: 2q^3
       180: 2q^3+2q^2+q
       181: q^4+3q^3
       182: 4q^3+2q^2+q
       184: 2q^2+q
       185: 2q^2+q
       187: 2q^3
       188: 3q^3+2q^2+q
       189: q^3
       190: q^3+2q^2+q
       191: 2q^2+q
       194: q^3+2q^2+q
       195: q^4+2q^3+2q^2+q
       196: 2q^3
       197: 2q^3
       198: q^3+2q^2+q
       200: 2q^2+q
       201: 2q^3
       202: q^4+2q^3+2q^2+q
       203: q^3+2q^2+q
       205: 2q^3
       206: q^3+2q^2+q
       207: q^3
       208: q^3+2q^2+q
       209: 2q^3
       210: q^3+2q^2+q
       211: 2q^3
       212: 3q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: 2q^2+q
       220: 2q^2+q
       221: q^4+2q^3+2q^2+q
       222: 2q^3+2q^2+q
       223: q^4+5q^3+2q^2+q
       224: 2q^3+2q^2+q
       225: q^4+5q^3+2q^2+q
       226: 2q^3+2q^2+q
       227: 2q^2+q
       228: q^4+4q^3+2q^2+q
       229: 2q^3+2q^2+q
       230: q^4+4q^3+2q^2+q
       231: 2q^3+2q^2+q
       232: 2q^2+q
       233: q^4+4q^3+2q^2+q
       234: q^4+4q^3+2q^2+q
       235: 2q^3+2q^2+q
       236: 5q^3+2q^2+q
       237: 3q^3
       238: 3q^3+2q^2+q
       239: q^4+3q^3
       240: 3q^3+2q^2+q
       241: q^4+2q^3
       242: q^4+3q^3+2q^2+q
       243: 3q^3+2q^2+q
       244: 3q^3+2q^2+q
       245: 3q^3+2q^2+q
       246: 2q^3+2q^2+q
       247: 6q^3+2q^2+q
       248: q^4+6q^3+2q^2+q
       249: 2q^4+5q^3+2q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: 3q^3+q^2+q
       257: 2q^3+q^2+q
       258: 3q^3+q^2+q
       259: q^3
       260: q^3
       261: q^3+2q^2+q
       262: q^3
       265: 2q^2+q
       269: q^3
       270: 2q^2+q
       271: q^3
       272: 2q^2+q
       277: 2q^2+q
       280: q^2+q
       282: q^3+q^2+q
       284: 2q^2+q
       285: 2q^2+q
       287: q^3
       288: q^3+2q^2+q
       290: q^3+q^2+q
       291: 2q^3
       292: 3q^3+2q^2+q
       294: 2q^2+q
       295: 2q^2+q
       297: q^3
       298: q^3+2q^2+q
       300: 2q^2+q
       301: 2q^3
       302: q^3+2q^2+q
       303: 2q^2+q
       305: q^3
       306: q^3+2q^2+q
       308: 2q^2+q
       309: 2q^2+q
       311: 2q^3
       312: q^3+2q^2+q
       313: q^3
       314: q^3+2q^2+q
       315: 2q^3
       316: 3q^3+2q^2+q
       317: 2q^3
       318: q^3+2q^2+q
       320: q^3+2q^2+q
       321: q^3+2q^2+q
       323: q^3
       324: 2q^2+q
       325: q^3
       326: q^3+2q^2+q
       333: 2q^2+q
       334: 2q^3+2q^2+q
       335: 2q^3+2q^2+q
       336: 5q^3+2q^2+q
       337: 3q^3+2q^2+q
       338: 3q^3
       339: 3q^3+2q^2+q
       340: q^4+3q^3
       341: 3q^3+2q^2+q
       342: q^4+2q^3
       343: q^4+3q^3+2q^2+q
       344: 2q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: 2q^3+2q^2+q
       349: q^3+q^2+q
       350: q^4+4q^3+2q^2+q
       351: 3q^3+2q^2+q
       352: 2q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^4+4q^3+2q^2+q
       357: q^2+q
       358: 2q^3+2q^2+q
       359: 3q^3+2q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: 2q^3+2q^2+q
       367: q^2+q
       368: 3q^3+q^2+q
       369: q^3+q^2+q
       370: q^3+q^2+q
       371: 3q^3+q^2+q
       372: 2q^3+q^2+q
       373: 3q^3+q^2+q
       374: q^3+q
       375: q
       376: q^3+q
       379: 2q^2+q
       383: q^2+q
       387: 2q^2+q
       391: q^3
       392: 2q^2+q
       395: 2q^2+q
       397: q^3
       398: 2q^2+q
       402: 2q^2+q
       408: 2q^2+q
       414: q^2+q
       418: q^3+q^2+q
       420: 2q^2+q
       421: 2q^2+q
       423: q^3
       424: q^3+2q^2+q
       425: 2q^3
       426: 3q^3+2q^2+q
       427: 2q^3
       428: q^3+2q^2+q
       430: 2q^2+q
       431: 2q^2+q
       433: q^3
       434: q^3+2q^2+q
       436: q
       438: q^2+q
       439: q^2+q
       442: q^2+q
       444: q^3+2q^2+q
       445: 2q^3
       446: q^3+2q^2+q
       448: 2q^2+q
       449: 2q^2+q
       451: q^3
       452: q^3+2q^2+q
       454: q^2+q
       456: q
       457: q^2+q
       460: q^2+q
       461: q^3+2q^2+q
       463: 2q^3
       464: q^3+2q^2+q
       466: q
       468: q^3+q
       469: q^3
       470: q^3+2q^2+q
       472: q^2+q
       473: q^2+q
       476: q^2+q
       477: q^3
       478: 2q^2+q
       479: q^3
       480: 2q^2+q
       481: 2q^2+q
       482: 2q^2+q
       483: 2q^3+2q^2+q
       484: q^2+q
       486: q^3+q
       488: q
       490: q^3+q
       491: 3q^3+q^2+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: 2q^3+2q^2+q
       496: q^3+q^2+q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: 2q^3+2q^2+q
       501: q^3+q^2+q
       508: q^2+q
       509: q
       510: q^3+q
       511: q
       512: q^3+q^2+q
       513: q
       514: q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q
       519: q
       520: q^3+q
       523: q^2+q
       531: 2q^2+q
       535: 2q^2+q
       540: q
       544: q^2+q
       547: q^3
       548: 2q^2+q
       550: 2q^2+q
       554: q
       558: q^2+q
       561: q^3
       562: 2q^2+q
       567: q^2+q
       572: 2q^2+q
       576: 2q^2+q
       577: q^3
       581: 2q^2+q
       586: q^2+q
       590: 2q^2+q
       591: 2q^2+q
       594: 2q^2+q
       595: 2q^2+q
       598: q^3+q
       599: q^3
       600: q^3+2q^2+q
       602: q
       604: q^2+q
       606: q
       607: q^2+q
       610: q^2+q
       613: q^3
       614: q^3+2q^2+q
       616: q^2+q
       618: q
       620: q^2+q
       621: q^2+q
       624: q
       626: q^2+q
       629: q^3
       630: q^3+2q^2+q
       631: q^2+q
       634: q
       640: q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       648: q
       649: q
       652: 2q
       654: q
       656: q^2+q
       657: q^2+q
       659: q^3+q
       661: q
       663: q^3+q
       664: 3q^3+q^2+q
       665: q^2+q
       672: q
       673: q^3+q
       674: q^3+q^2+q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q^3+q^2+q
       680: q^3+q^2+q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q^3+q^2+q
       686: q
       687: q
       688: q
       689: q^2+q
       690: q^3+q
       691: q
       692: q^3+q
       700: 2q^2+q
       711: q^2+q
       714: 2q^2+q
       719: 2q^2+q
       724: q
       728: q^2+q
       736: q
       738: q
       742: q^2+q
       750: q
       755: q^2+q
       760: 2q
       764: q
       767: q^2+q
       773: q
       774: q
       776: q
       780: q^3+q
       782: q
       786: q^2+q
       787: q^2+q
       792: q^2+q
       794: q^2+q
       796: q
       798: q
       802: q
       803: q
       806: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       816: q
       817: q^2+q
       820: q
       822: q
       826: q^2+q
       827: q^2+q
       830: q
       831: q
       834: q
       836: q^2+q
       839: q
       844: q^2+q
       846: q
       847: q
       850: 2q
       852: q
       856: q^2+q
       858: q
       865: q
       866: q^2+q
       867: q^3+q
       868: q
       869: q
       870: q^3+q^2+q
       871: q
       872: q
       873: q
       874: q^3+q^2+q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q^2+q
       891: q
       895: q
       901: q
       907: q
       910: q^2+q
       919: q
       923: q
       925: q
       931: q^2+q
       941: q
       945: q
       949: q^2+q
       954: q
       963: 2q
       966: q^2+q
       972: q
       973: q
       977: q
       990: q
       995: q
       998: q^2+q
      1001: q^2+q
      1005: q
      1006: q
      1009: q
      1011: 2q
      1013: q^2+q
      1017: q
      1021: q
      1023: q
      1027: q
      1028: q
      1032: q
      1037: q
      1039: q
      1041: q
      1044: q
      1047: q
      1049: q
      1053: q
      1054: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q^2+q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q^2+q
      1085: q
      1093: q
      1097: q
      1115: q
      1125: q
      1129: 2q
      1132: q^2+q
      1137: q
      1142: q
      1143: q
      1153: q
      1159: q
      1161: q
      1173: q
      1179: q
      1182: q
      1196: q
      1201: q
      1203: q
      1209: q
      1216: q
      1219: q
      1221: q
      1225: q
      1231: q
      1232: q
      1235: q
      1241: q
      1242: q
      1249: q
      1250: q
      1255: q
      1259: q
      1260: q
      1275: q
      1277: q
      1279: q
      1281: q^2+q
      1283: q
      1285: q
      1288: q
      1297: q
      1301: q
      1328: q
      1333: q
      1349: q
      1359: q
      1362: q
      1365: q
      1370: q
      1381: q
      1391: q
      1395: q
      1398: q
      1403: q
      1434: q
      1437: q
      1450: q
      1455: q
      1460: q
      1463: q
      1483: q
      1507: q
      1520: q
      1540: q
      1576: q
      1597: q
      1621: 1
      1721: 1
      1810: 1
      1893: 1
      1947: 1
      2025: 1

2026:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        37: 2q+2
        39: 2q+2
        41: 2q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+2
        64: 2q+2
        66: 2q+2
        68: q^2+2q+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        74: 2q+2
        76: 2q+2
        78: 2q+2
        80: 2q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2q+2
        95: 2q+2
        96: 2q+2
        97: 2q+2
        98: 2q+2
        99: 2q+2
       100: q+2
       101: q+2
       102: q+2
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+2
       113: 2q+2
       115: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+2
       123: 2q+2
       125: q^2+2q+2
       126: q^2+2q+2
       127: 2q+2
       129: 2q+2
       131: 2q+2
       133: q^2+2q+2
       134: q^2+2q+2
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: 2q+2
       139: 2q+2
       140: 2
       141: 2q+2
       142: 2q+2
       143: 2q+2
       144: 2q+2
       145: 2q+2
       146: 2q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       151: q+2
       153: q+2
       155: q+2
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q+2
       167: q+2
       168: q+2
       169: q+1
       172: q+1
       173: q+1
       176: q+1
       177: 2q+2
       179: 2q+2
       181: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 2q+2
       189: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 2
       207: 2q+2
       209: q+2
       211: q+2
       213: 2q+2
       215: 2q+2
       217: 2q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^2+2q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: 2q+2
       227: 2q+2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 2q+2
       232: 2q+2
       233: 2q+2
       234: 2q+2
       235: 2
       236: q+2
       237: q+2
       239: q+2
       241: q+2
       243: q+2
       244: 2
       245: 2
       246: q+2
       247: q+2
       248: q+2
       249: q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: q+2
       257: q+2
       258: q+2
       259: q+1
       262: q+1
       263: q+1
       266: q+1
       267: 1
       269: 1
       271: 1
       273: 1
       275: q+1
       278: q+1
       279: 2q+2
       281: 2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 2q+2
       289: 2q+2
       291: 2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 2q+2
       299: 1
       300: 1
       301: 2
       303: q+1
       304: q+1
       305: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 2
       313: 2
       315: q+2
       317: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       323: 2
       325: q+2
       327: 2q+2
       329: 2q+2
       331: 2q+2
       333: q^2+2q+2
       334: 2q+2
       335: 2q+2
       336: q+2
       337: q+2
       338: q+2
       340: q+2
       342: q+2
       344: 2q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: 2q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       360: q+2
       362: q+2
       364: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       377: q+1
       380: q+1
       381: q+1
       384: q+1
       385: q+1
       388: q+1
       389: 1
       391: 1
       393: 1
       396: 1
       397: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       409: 2q+2
       411: 2q+2
       413: 2q+2
       415: 2q+2
       417: 2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2q+2
       425: q+2
       427: q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 2
       435: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       441: 2
       443: 1
       444: 1
       445: 2
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: 2
       453: q+1
       454: q+1
       455: 2
       457: 1
       458: 1
       459: 2
       461: 1
       462: 1
       463: 2
       465: q+2
       467: q+2
       469: q+2
       471: 1
       472: 1
       473: 1
       474: 1
       475: 2
       477: 2
       479: 2
       481: 2q+2
       482: 2q+2
       483: q+2
       484: q+2
       485: q+2
       487: q+2
       489: q+2
       491: q+2
       492: 2q+2
       493: 2
       494: 2q+2
       495: 2
       496: 2
       497: 2q+2
       498: 2q+2
       499: 2
       500: 2
       501: 2
       502: q+2
       504: q+2
       506: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       521: q+1
       524: q+1
       525: q+1
       528: q+1
       529: q+1
       532: q+1
       533: 1
       536: 1
       537: 1
       539: 1
       541: 1
       543: 1
       545: 1
       547: 1
       549: 1
       552: 1
       553: 1
       555: 1
       557: 1
       559: 1
       561: 1
       563: 1
       565: 1
       568: 1
       569: 1
       570: 1
       573: 1
       575: 1
       577: 2
       583: 2q+2
       585: 2q+2
       587: 2q+2
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: q+1
       596: q+1
       597: q+2
       599: q+2
       601: q+2
       603: 1
       604: 1
       605: 2
       607: q+1
       608: q+1
       609: 2
       611: 2
       613: 2
       615: 1
       616: 1
       617: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 2
       625: 2
       627: 2
       629: 2
       631: 1
       632: 1
       633: 2
       635: q+2
       637: q+2
       639: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       645: 2
       647: 1
       648: 1
       649: 1
       650: 1
       651: 2
       653: 2
       655: 2
       657: q+2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q+2
       666: q+2
       668: q+2
       670: q+2
       672: q+2
       673: q+2
       674: 2
       675: 2
       676: 2q+2
       677: 2
       678: 2
       679: 2
       680: 2
       681: 2q+2
       682: 2
       683: 2
       684: 2
       685: 2
       686: q+2
       687: 2
       688: 2
       689: 1
       690: q+2
       691: q+2
       692: q+2
       693: 1
       697: 1
       705: q+1
       708: q+1
       709: q+1
       712: q+1
       713: 1
       716: 1
       717: 1
       720: 1
       721: 1
       723: 1
       725: 1
       727: 1
       729: 1
       731: 1
       733: 1
       735: 1
       737: 1
       739: 1
       741: 1
       743: 1
       745: 1
       747: 1
       749: 1
       751: 1
       753: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       765: 1
       768: 1
       769: 2
       775: q+2
       777: 2q+2
       779: q+2
       781: q+2
       783: q+2
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+2
       791: 2
       793: 1
       794: 1
       795: 2
       797: 2
       799: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2
       811: 2
       813: 2
       815: 1
       816: 1
       817: 1
       818: 1
       819: 2
       821: 2
       823: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       833: 2
       835: 2
       837: 2
       839: 1
       840: 1
       841: q+2
       843: 2
       845: 1
       846: 1
       847: 1
       848: 1
       849: 2
       851: 2
       853: 2
       855: 1
       857: 2
       859: q+2
       861: q+2
       863: q+2
       865: q+2
       866: q+2
       867: q+2
       868: q+2
       869: 2
       870: 2
       871: 2
       872: 2
       873: 2
       874: 2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+2
       884: 1
       889: 1
       896: q+1
       899: q+1
       900: 1
       902: 1
       904: 1
       906: 1
       908: 1
       911: 1
       912: 1
       914: 1
       916: 1
       918: 1
       920: 1
       922: 1
       928: 1
       930: 1
       932: 1
       934: 1
       936: 1
       938: 1
       940: 1
       942: 1
       944: 1
       946: 1
       948: 1
       950: 1
       956: 1
       958: 1
       960: 1
       961: 1
       964: 1
       967: 1
       968: 2
       974: 1
       975: 1
       978: 1
       979: 1
       982: 2
       988: 1
       991: 1
       992: q+2
       994: q+2
       996: q+2
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: q+2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 2
      1010: 2
      1012: 2
      1014: 2
      1016: 1
      1017: 1
      1018: 2
      1020: 2
      1022: 2
      1024: 2
      1026: 1
      1027: 1
      1030: 2
      1032: 1
      1033: 1
      1034: 2
      1036: 2
      1038: 2
      1042: 2
      1044: 1
      1045: 1
      1046: 2
      1048: 2
      1050: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+2
      1068: q+2
      1070: q+2
      1072: q+2
      1073: q+2
      1074: q+2
      1075: 2
      1076: 2
      1077: 2
      1078: 2
      1079: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1091: 1
      1098: 1
      1102: 1
      1110: 1
      1112: 1
      1114: 1
      1116: 1
      1118: 1
      1120: 1
      1122: 1
      1124: 1
      1126: 1
      1127: 1
      1130: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 2
      1144: 1
      1146: 1
      1148: 1
      1150: 1
      1156: 1
      1158: 1
      1164: 1
      1166: 1
      1168: 1
      1170: 1
      1172: 1
      1174: 1
      1184: 1
      1185: 1
      1188: 2
      1194: 1
      1197: 1
      1198: 1
      1199: 1
      1210: q+2
      1212: q+2
      1214: q+2
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 2
      1222: 2
      1224: 2
      1226: 2
      1228: 1
      1229: 1
      1230: 2
      1234: 1
      1235: 1
      1236: 2
      1238: 2
      1240: 1
      1241: 1
      1244: 2
      1246: 1
      1247: 1
      1248: 2
      1250: 1
      1251: 1
      1252: 2
      1256: 2
      1260: 1
      1261: 1
      1262: 2
      1264: 2
      1266: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+2
      1283: 2
      1284: 2
      1285: 2
      1286: 2
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1295: 1
      1302: 1
      1307: 1
      1314: 1
      1316: 1
      1318: 1
      1320: 1
      1322: 1
      1323: 1
      1326: 1
      1329: 1
      1330: 1
      1331: 1
      1334: 2
      1340: 1
      1342: 1
      1352: 1
      1354: 1
      1356: 1
      1358: 1
      1372: 1
      1374: 1
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1404: 2
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1436: 2
      1438: q+2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 2
      1446: 2
      1448: 2
      1452: 2
      1454: 1
      1455: 1
      1456: 2
      1458: 2
      1460: 1
      1461: 1
      1464: 1
      1470: 1
      1472: 1
      1474: 1
      1480: 1
      1482: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 1
      1489: 1
      1494: 1
      1525: 1
      1530: 1
      1537: 1
      1538: 1
      1541: 1
      1543: 1
      1545: 1
      1547: 1
      1549: 1
      1552: 1
      1553: 2
      1559: 1
      1560: 1
      1567: 1
      1569: 1
      1583: 1
      1585: 1
      1631: 1
      1637: 2
      1639: 2
      1641: 1
      1643: 2
      1647: 1
      1648: 1
      1651: 2
      1653: 1
      1654: 1
      1659: 1
      1661: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1680: 1
      1723: 2
      1729: 1
      1730: 1
      1733: 1
      1736: 1
      1745: 1
      1747: 1
      1761: 1
      1763: 1
      1801: 1
      1815: 1
      1817: 1
      1823: 1
      1825: 1
      1827: 1
      1833: 1
      1834: 1
      1839: 1
      1926: 1
      1956: 1
      1958: 1
      1960: 1
      2026: 1

2027:    0: 6q^3+10q^2+4q
         1: 6q^3+10q^2+4q
         2: 2q^4+6q^3+7q^2+4q
         3: 6q^3+10q^2+4q
         4: 6q^3+10q^2+4q
         5: 6q^3+10q^2+4q
         6: 6q^3+10q^2+4q
         7: 2q^4+6q^3+7q^2+4q
         8: 3q^4+7q^3+7q^2+4q
         9: 2q^4+6q^3+7q^2+4q
        10: 6q^3+10q^2+4q
        11: 6q^3+10q^2+4q
        12: 6q^3+10q^2+4q
        13: 3q^3+7q^2+4q
        14: 3q^3+7q^2+4q
        15: 4q^3+7q^2+4q
        16: 6q^3+10q^2+4q
        17: 6q^3+10q^2+4q
        18: 2q^4+6q^3+7q^2+4q
        19: 6q^3+10q^2+4q
        20: 6q^3+10q^2+4q
        21: 2q^4+6q^3+7q^2+4q
        22: 2q^3+10q^2+4q
        23: 2q^3+10q^2+4q
        24: q^4+4q^3+7q^2+4q
        25: 2q^3+10q^2+4q
        26: 2q^3+10q^2+4q
        27: q^4+4q^3+7q^2+4q
        28: 6q^3+10q^2+4q
        29: 6q^3+10q^2+4q
        30: 3q^3+7q^2+4q
        31: 2q^3+10q^2+4q
        32: q^3+7q^2+4q
        33: 2q^3+10q^2+4q
        34: 2q^3+10q^2+4q
        35: q^3+7q^2+4q
        36: 2q^3+10q^2+4q
        37: 2q^2+2q
        38: 8q^2+2q
        39: 2q^2+2q
        40: 8q^2+2q
        41: 2q^2+2q
        42: 3q^3+5q^2+2q
        43: 3q^3+7q^2+4q
        44: 3q^3+7q^2+4q
        45: 4q^3+7q^2+4q
        46: 3q^3+7q^2+4q
        47: 4q^3+7q^2+4q
        48: 3q^3+7q^2+4q
        49: 6q^3+10q^2+4q
        50: 6q^3+10q^2+4q
        51: 2q^4+6q^3+7q^2+4q
        52: 2q^3+10q^2+4q
        53: 2q^3+10q^2+4q
        54: q^4+4q^3+7q^2+4q
        55: 2q^3+10q^2+4q
        56: 2q^3+10q^2+4q
        57: q^4+4q^3+7q^2+4q
        58: q^3+5q^2+2q
        59: q^3+5q^2+2q
        60: q^3+5q^2+2q
        61: q^3+5q^2+2q
        62: 2q^2+2q
        63: 8q^2+2q
        64: 2q^2+2q
        65: 5q^2+2q
        66: 2q^2+2q
        67: 8q^2+2q
        68: q^3+4q^2+4q
        69: 3q^3+7q^2+4q
        70: 3q^3+7q^2+4q
        71: 6q^3+10q^2+4q
        72: 2q^3+10q^2+4q
        73: 2q^3+10q^2+4q
        74: 2q^2+2q
        75: 8q^2+2q
        76: 2q^2+2q
        77: 8q^2+2q
        78: 2q^2+2q
        79: 3q^3+5q^2+2q
        80: q^3+7q^2+4q
        81: q^3+7q^2+4q
        82: 2q^3+10q^2+4q
        83: q^3+7q^2+4q
        84: q^3+7q^2+4q
        85: q^3+7q^2+4q
        86: 2q^3+10q^2+4q
        87: q^3+7q^2+4q
        88: 3q^3+7q^2+4q
        89: 4q^3+7q^2+4q
        90: 3q^3+7q^2+4q
        91: 3q^3+7q^2+4q
        92: 4q^3+7q^2+4q
        93: 3q^3+7q^2+4q
        94: 2q^3+10q^2+4q
        95: 2q^3+10q^2+4q
        96: q^4+4q^3+7q^2+4q
        97: 2q^3+10q^2+4q
        98: 2q^3+10q^2+4q
        99: q^4+4q^3+7q^2+4q
       100: 8q^2+4q
       101: 8q^2+4q
       102: 2q^3+5q^2+4q
       103: q^2+q
       104: 4q^2+q
       105: 4q^2+q
       106: q^2+q
       107: q^3+5q^2+2q
       108: q^3+5q^2+2q
       109: q^3+5q^2+2q
       110: q^3+5q^2+2q
       111: 2q^2+2q
       112: 8q^2+2q
       113: 2q^2+2q
       114: 8q^2+2q
       115: 2q^2+2q
       116: 5q^2+2q
       117: 2q^2+2q
       118: 2q^2+2q
       119: 2q^2+2q
       120: 2q^2+2q
       121: 2q^2+2q
       122: 5q^2+2q
       123: 2q^2+2q
       124: 5q^2+2q
       125: q^3+4q^2+4q
       126: 3q^3+7q^2+4q
       127: 2q^2+2q
       128: 8q^2+2q
       129: 2q^2+2q
       130: 8q^2+2q
       131: 2q^2+2q
       132: 3q^3+5q^2+2q
       133: q^3+4q^2+4q
       134: 3q^3+7q^2+4q
       135: q^3+7q^2+4q
       136: q^3+7q^2+4q
       137: q^3+7q^2+4q
       138: q^3+7q^2+4q
       139: 2q^3+10q^2+4q
       140: 4q^2+4q
       141: q^3+7q^2+4q
       142: 2q^3+10q^2+4q
       143: q^3+7q^2+4q
       144: q^3+7q^2+4q
       145: 2q^3+10q^2+4q
       146: q^3+7q^2+4q
       147: 2q^3+10q^2+4q
       148: 4q^2+4q
       149: 8q^2+4q
       150: 5q^2+4q
       151: q^2+2q
       152: 7q^2+2q
       153: q^2+2q
       154: 7q^2+2q
       155: q^2+2q
       156: 2q^3+4q^2+2q
       157: 3q^3+7q^2+4q
       158: 4q^3+7q^2+4q
       159: 3q^3+7q^2+4q
       160: q^3+5q^2+4q
       161: q^3+5q^2+4q
       162: q^3+5q^2+4q
       163: q^3+5q^2+4q
       164: q^3+5q^2+4q
       165: q^3+5q^2+4q
       166: 8q^2+4q
       167: 8q^2+4q
       168: 2q^3+5q^2+4q
       169: q^2+q
       170: 4q^2+q
       171: 4q^2+q
       172: q^2+q
       173: q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       177: 2q^2+2q
       178: 5q^2+2q
       179: 2q^2+2q
       180: 8q^2+2q
       181: 2q^2+2q
       182: 8q^2+2q
       183: 2q^2+2q
       184: 2q^2+2q
       185: 2q^2+2q
       186: 2q^2+2q
       187: 2q^2+2q
       188: 5q^2+2q
       189: 2q^2+2q
       190: 5q^2+2q
       191: 2q^2+2q
       192: 2q^2+2q
       193: 2q^2+2q
       194: 2q^2+2q
       195: q^3+5q^2+2q
       196: q^3+5q^2+2q
       197: 2q
       198: 4q^2+2q
       199: 2q^2+2q
       200: 2q^2+2q
       201: q^3+5q^2+2q
       202: q^3+5q^2+2q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 2q
       206: 4q^2+2q
       207: 2q^2+2q
       208: 5q^2+2q
       209: q^2+2q
       210: 7q^2+2q
       211: q^2+2q
       212: 4q^2+2q
       214: 3q^2+2q
       216: 3q^2+2q
       218: 3q^2+2q
       219: q^3+4q^2+4q
       220: q^3+4q^2+4q
       221: 3q^3+7q^2+4q
       222: q^3+7q^2+4q
       223: q^3+7q^2+4q
       224: q^3+7q^2+4q
       225: q^3+7q^2+4q
       226: q^3+7q^2+4q
       227: 2q^2+4q
       228: q^3+5q^2+4q
       229: q^2+4q
       230: q^3+5q^2+4q
       231: q^3+7q^2+4q
       232: 2q^2+4q
       233: q^3+5q^2+4q
       234: q^3+5q^2+4q
       235: q^2+4q
       236: 5q^2+4q
       237: q^2+2q
       238: 7q^2+2q
       239: q^2+2q
       240: 7q^2+2q
       241: q^2+2q
       242: 2q^3+4q^2+2q
       243: 8q^2+4q
       244: 4q^2+4q
       245: 4q^2+4q
       246: 5q^2+4q
       247: 8q^2+4q
       248: 8q^2+4q
       249: 2q^3+5q^2+4q
       250: q^3+5q^2+4q
       251: q^3+5q^2+4q
       252: q^3+5q^2+4q
       253: q^3+5q^2+4q
       254: q^3+5q^2+4q
       255: q^3+5q^2+4q
       256: 3q^2+4q
       257: 4q^2+4q
       258: 3q^2+4q
       259: q^2+q
       260: 4q^2+q
       261: 4q^2+q
       262: q^2+q
       263: q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2+q
       267: q
       268: 2q^2+q
       269: q
       270: 2q^2+q
       271: q
       272: 2q^2+q
       273: q
       274: 2q^2+q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       280: 2q
       282: 3q^2+2q
       283: 2q^2+2q
       284: 2q^2+2q
       285: 2q^2+2q
       286: 2q^2+2q
       287: 2q^2+2q
       288: 5q^2+2q
       290: 3q^2+2q
       291: 2q^2+2q
       292: 5q^2+2q
       293: 2q^2+2q
       294: 2q^2+2q
       295: 2q^2+2q
       296: 2q^2+2q
       297: 2q^2+2q
       298: 5q^2+2q
       299: 2q
       300: 2q
       301: 2q
       302: 4q^2+2q
       303: q^2+2q
       304: q^2+2q
       305: 2q
       306: q^2+2q
       307: q^2+2q
       308: q^2+2q
       309: 2q
       310: 2q
       311: 2q
       312: 4q^2+2q
       313: 2q
       314: q^2+2q
       315: q^2+2q
       316: 4q^2+2q
       317: q^2+2q
       318: 7q^2+2q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       323: 2q
       324: 2q^2+2q
       325: q^2+2q
       326: 4q^2+2q
       328: 3q^2+2q
       330: 3q^2+2q
       332: 3q^2+2q
       333: q^3+4q^2+4q
       334: q^3+7q^2+4q
       335: q^3+7q^2+4q
       336: 5q^2+4q
       337: 8q^2+4q
       338: q^2+2q
       339: 7q^2+2q
       340: q^2+2q
       341: 7q^2+2q
       342: q^2+2q
       343: 2q^3+4q^2+2q
       344: 2q^2+4q
       345: 2q^2+4q
       346: q^3+5q^2+4q
       347: q^2+4q
       348: q^2+4q
       349: q^3+5q^2+4q
       350: q^3+5q^2+4q
       351: 4q^2+4q
       352: 2q^2+4q
       353: 2q^2+4q
       354: q^3+5q^2+4q
       355: q^3+5q^2+4q
       356: q^3+5q^2+4q
       357: q^2+4q
       358: q^2+4q
       359: 4q^2+4q
       361: 2q^2+2q
       363: 3q^2+2q
       365: 2q^2+2q
       366: 5q^2+4q
       367: q^2+4q
       368: 3q^2+4q
       369: q^2+4q
       370: q^2+4q
       371: 3q^2+4q
       372: 4q^2+4q
       373: 3q^2+4q
       374: 3q^2+4q
       375: 4q^2+4q
       376: 3q^2+4q
       377: q^2+q
       378: q^2+q
       379: q^2+q
       380: q^2+q
       382: q
       383: q
       385: q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2+q
       389: q
       390: 2q^2+q
       391: q
       392: 2q^2+q
       393: q
       394: q
       395: q
       396: q
       397: q
       398: 2q^2+q
       399: q
       400: 2q^2+q
       401: q
       402: q
       403: q
       404: q
       405: q
       406: q
       407: q^2+q
       408: q^2+q
       410: 2q
       412: 3q^2+2q
       414: 2q
       416: 3q^2+2q
       418: 3q^2+2q
       419: 2q^2+2q
       420: 2q^2+2q
       421: 2q^2+2q
       422: 2q^2+2q
       423: 2q^2+2q
       424: 5q^2+2q
       425: q^2+2q
       426: 4q^2+2q
       427: q^2+2q
       428: 7q^2+2q
       429: 2q
       430: 2q
       431: q^2+2q
       432: q^2+2q
       433: 2q
       434: q^2+2q
       436: q^2+2q
       437: 2q
       438: 2q
       439: q^2+2q
       440: q^2+2q
       441: 2q
       442: q^2+2q
       443: 2q^2+2q
       444: 2q^2+2q
       445: 2q
       446: 4q^2+2q
       447: q^2+2q
       448: q^2+2q
       449: 2q
       450: 2q
       451: 2q
       452: q^2+2q
       453: q^2+2q
       454: q^2+2q
       456: q^2+2q
       457: 2q
       458: 2q
       459: 2q
       460: q^2+2q
       461: 2q^2+2q
       462: 2q^2+2q
       463: 2q
       464: 4q^2+2q
       466: 2q
       468: 2q^2+2q
       469: q^2+2q
       470: 4q^2+2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       477: 2q
       478: 2q^2+2q
       479: 2q
       480: 2q^2+2q
       481: 2q^2+4q
       482: 2q^2+4q
       483: 5q^2+4q
       484: q^2+4q
       486: 2q^2+2q
       488: 3q^2+2q
       490: 2q^2+2q
       491: 3q^2+4q
       492: 2q^2+4q
       493: q^2+4q
       494: q^3+5q^2+4q
       495: q^2+4q
       496: q^2+4q
       497: 2q^2+4q
       498: q^3+5q^2+4q
       499: q^2+4q
       500: q^2+4q
       501: q^2+4q
       503: 2q^2+2q
       505: 3q^2+2q
       507: 2q^2+2q
       508: q^2+4q
       509: q^2+4q
       510: 3q^2+4q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: 3q^2+4q
       516: 4q^2+4q
       517: 3q^2+4q
       518: 3q^2+4q
       519: 4q^2+4q
       520: 3q^2+4q
       522: q
       523: q
       526: q
       527: q
       529: q^2+q
       530: q^2+q
       531: q^2+q
       532: q^2+q
       533: q
       534: q
       535: q
       536: q
       538: q
       540: q
       541: q
       542: q
       543: q
       544: q
       545: q
       546: 2q^2+q
       547: q
       548: 2q^2+q
       549: q
       550: q
       551: q
       552: q
       554: q
       556: q
       557: q
       558: q
       559: q
       560: q
       561: q
       562: 2q^2+q
       563: q
       564: 2q^2+q
       565: q
       566: q
       567: q
       568: q
       569: q
       570: q
       571: q^2+q
       572: q^2+q
       573: q
       574: q^2+q
       575: q
       576: q^2+q
       577: 2q
       581: 2q^2+2q
       584: 2q
       586: 2q
       588: 3q^2+2q
       589: q^2+2q
       590: q^2+2q
       591: 2q
       592: 2q
       593: 2q
       594: 2q
       595: q^2+2q
       596: q^2+2q
       598: 2q^2+2q
       599: q^2+2q
       600: 4q^2+2q
       602: 2q
       603: 2q
       604: 2q
       606: q^2+2q
       607: q^2+2q
       608: q^2+2q
       609: 2q
       610: q^2+2q
       612: q^2+2q
       613: 2q
       614: q^2+2q
       615: 2q
       616: 2q
       618: q^2+2q
       619: q^2+2q
       620: q^2+2q
       621: 2q
       622: 2q
       624: q^2+2q
       625: 2q
       626: q^2+2q
       628: q^2+2q
       629: 2q
       630: q^2+2q
       631: 2q
       632: 2q
       634: q^2+2q
       636: 2q
       638: 2q^2+2q
       640: 2q
       641: 2q
       642: 2q
       643: 2q
       644: 2q
       645: 2q
       646: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       652: 2q
       653: 2q
       654: 2q
       655: 2q
       656: 2q
       657: q^2+4q
       659: 2q^2+2q
       661: 3q^2+2q
       663: 2q^2+2q
       664: 3q^2+4q
       665: q^2+4q
       667: 2q^2+2q
       669: 3q^2+2q
       671: 2q^2+2q
       672: q^2+4q
       673: 3q^2+4q
       674: q^2+4q
       675: 2q
       676: 2q^2+4q
       677: q^2+4q
       678: q^2+4q
       679: q^2+4q
       680: q^2+4q
       681: 2q^2+4q
       682: 2q
       683: q^2+4q
       684: q^2+4q
       685: q^2+4q
       686: q^2+4q
       687: q^2+4q
       688: q^2+4q
       689: 2q
       690: 3q^2+4q
       691: 4q^2+4q
       692: 3q^2+4q
       693: q
       697: q
       699: q^2+q
       700: q^2+q
       706: q
       707: q
       710: q
       711: q
       713: q
       714: q
       715: q
       716: q
       717: q
       718: q
       719: q
       720: q
       722: q
       724: q
       725: q
       726: q
       727: q
       728: q
       730: q
       732: q
       734: q
       736: q
       738: q
       740: q
       741: q
       742: q
       743: q
       744: q
       746: q
       748: q
       750: q
       752: q
       753: q
       754: q
       755: q
       756: q
       759: q
       760: q
       761: q
       762: q
       763: q
       764: q
       765: q
       766: q
       767: q
       768: q
       773: 2q
       776: 2q
       778: 2q
       780: 2q^2+2q
       782: 2q
       784: 2q^2+2q
       785: 2q
       786: 2q
       787: 2q
       788: 2q
       790: 2q
       791: 2q
       792: 2q
       793: 2q
       794: 2q
       796: q^2+2q
       800: q^2+2q
       801: q
       802: q
       805: 2q
       806: 2q
       807: q^2+2q
       808: q^2+2q
       810: q^2+2q
       811: 2q
       812: q^2+2q
       814: q^2+2q
       815: 2q
       816: 2q
       817: 2q
       818: 2q
       820: q^2+2q
       824: q^2+2q
       825: q^2+2q
       826: q^2+2q
       827: 2q
       828: 2q
       831: q
       832: q
       834: q^2+2q
       835: 2q
       836: q^2+2q
       838: q^2+2q
       839: 2q
       840: 2q
       842: 2q
       843: 2q
       844: 2q
       845: 2q
       846: 2q
       847: 2q
       848: 2q
       850: 2q
       851: 2q
       852: 2q
       854: 2q
       855: q
       856: q
       857: 2q
       858: 2q
       860: 2q^2+2q
       862: 3q^2+2q
       864: 2q^2+2q
       865: q^2+4q
       866: q^2+4q
       867: 3q^2+4q
       868: q^2+4q
       869: q^2+4q
       870: q^2+4q
       871: 2q
       872: q^2+4q
       873: q^2+4q
       874: q^2+4q
       875: 2q
       876: q^2+4q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+2
       882: q+2
       883: q+2
       890: q
       891: q
       897: q
       898: q
       901: q
       903: q
       905: q
       907: q
       908: q
       909: q
       910: q
       911: q
       913: q
       915: q
       917: q
       919: q
       928: q
       929: q
       930: q
       931: q
       933: q
       935: q
       937: q
       939: q
       941: q
       943: q
       948: q
       949: q
       950: q
       951: q
       957: q
       959: q
       962: q
       963: q
       964: q
       965: q
       966: q
       967: q
       972: 2q
       974: q
       975: q
       976: q
       977: q
       980: q
       981: q
       986: 2q
       988: q
       989: q
       990: q
       991: q
       993: 2q
       995: 2q
       997: 2q^2+2q
       998: 2q
       999: 2q
      1000: 2q
      1001: 2q
      1003: 2q
      1004: 2q
      1005: 2q
      1006: 2q
      1007: 2q
      1008: 2q
      1009: 2q
      1011: 2q
      1012: 2q
      1013: 2q
      1015: q^2+2q
      1016: 2q
      1017: 2q
      1021: q^2+2q
      1025: q^2+2q
      1026: q
      1027: q
      1031: q^2+2q
      1032: 2q
      1033: 2q
      1037: q^2+2q
      1043: q^2+2q
      1044: q
      1045: q
      1046: 2q
      1047: 2q
      1051: 2q
      1052: q
      1053: q
      1058: q
      1059: q
      1061: q
      1062: q
      1063: q
      1064: q
      1065: q
      1067: q+2
      1069: q+2
      1071: q+2
      1072: q+2
      1073: q+2
      1074: q^2+4q
      1075: 2
      1076: 2q
      1077: q^2+4q
      1078: 2q
      1079: 2
      1080: 2q
      1081: q^2+4q
      1082: 2q
      1083: q
      1084: 2q
      1085: 2q
      1092: q
      1093: q
      1104: q
      1105: q
      1111: q
      1113: q
      1115: q
      1117: q
      1119: q
      1121: q
      1123: q
      1125: q
      1128: q
      1129: q
      1130: q
      1131: q
      1132: q
      1133: q
      1134: q
      1135: q
      1136: q
      1137: q
      1142: 2q
      1145: q
      1147: q
      1165: q
      1167: q
      1186: q
      1187: q
      1192: 2q
      1194: q
      1195: q
      1196: q
      1197: q
      1211: q+2
      1213: q+2
      1215: 2q
      1216: 2q
      1217: 2q
      1218: 2q
      1219: 2q
      1223: 2q
      1224: 2q
      1225: 2q
      1227: 2
      1228: 1
      1229: 1
      1234: q
      1235: q
      1237: q^2+2q
      1240: q
      1241: q
      1245: 2
      1246: 1
      1247: 1
      1250: q
      1251: q
      1253: q^2+2q
      1260: q
      1261: q
      1262: 2
      1273: q
      1275: q
      1276: q
      1277: q
      1279: q
      1280: q
      1281: q
      1282: q+2
      1283: 2q
      1284: 2
      1285: 2q
      1286: 2
      1287: q
      1288: 2q
      1289: q
      1296: q
      1297: q
      1308: q
      1309: q
      1315: q
      1317: q
      1319: q
      1321: q
      1324: q
      1325: q
      1326: q
      1327: q
      1328: q
      1329: q
      1338: 2q
      1341: 1
      1343: 1
      1373: 1
      1375: 1
      1405: 2
      1410: 1
      1413: 1
      1434: q
      1439: q+2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 2
      1453: 2
      1454: q
      1455: q
      1459: 2
      1460: q
      1461: q
      1473: q
      1481: q
      1482: q
      1483: q
      1484: q
      1485: 2
      1486: 2
      1487: q
      1488: 1
      1495: q
      1496: q
      1526: 1
      1533: 1
      1542: 1
      1544: 1
      1546: 1
      1548: 1
      1549: 1
      1552: 1
      1554: 2
      1635: q
      1639: 2
      1644: 2
      1647: 1
      1648: 1
      1652: 2
      1653: 1
      1654: 1
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1676: 1
      1683: 1
      1724: 2
      1733: 1
      1736: 1
      1746: 1
      1748: 1
      1762: 1
      1764: 1
      1802: 1
      1825: 1
      1828: 1
      1833: 1
      1835: 1
      1842: 1
      1927: 1
      1957: 1
      1960: 1
      2027: 1

2028:    0: q^5+3q^4+5q^3+4q^2+2q
         1: q^5+3q^4+5q^3+4q^2+2q
         2: q^5+3q^4+5q^3+4q^2+2q
         3: q^5+3q^4+5q^3+4q^2+2q
         4: q^5+3q^4+5q^3+4q^2+2q
         5: q^5+3q^4+5q^3+4q^2+2q
         6: q^5+3q^4+5q^3+4q^2+2q
         7: q^5+3q^4+5q^3+4q^2+2q
         8: q^5+3q^4+5q^3+4q^2+2q
         9: q^6+2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+4q^3+4q^2+2q
        11: 2q^4+4q^3+4q^2+2q
        12: 2q^4+4q^3+4q^2+2q
        13: q^5+3q^4+5q^3+4q^2+2q
        14: q^5+3q^4+5q^3+4q^2+2q
        15: q^5+3q^4+5q^3+4q^2+2q
        16: 2q^4+4q^3+4q^2+2q
        17: 2q^4+4q^3+4q^2+2q
        18: q^5+2q^4+4q^3+3q^2+2q
        19: q^5+3q^4+5q^3+4q^2+2q
        20: q^5+3q^4+5q^3+4q^2+2q
        21: q^5+3q^4+5q^3+4q^2+2q
        22: 2q^4+4q^3+4q^2+2q
        23: 2q^4+4q^3+4q^2+2q
        24: 2q^4+4q^3+4q^2+2q
        25: 2q^4+4q^3+4q^2+2q
        26: 2q^4+4q^3+4q^2+2q
        27: 2q^4+4q^3+4q^2+2q
        28: q^4+3q^3+4q^2+2q
        29: 2q^4+4q^3+4q^2+2q
        30: q^5+3q^4+5q^3+4q^2+2q
        31: q^4+3q^3+4q^2+2q
        32: 2q^4+4q^3+4q^2+2q
        33: q^4+3q^3+4q^2+2q
        34: q^4+3q^3+4q^2+2q
        35: 2q^4+4q^3+4q^2+2q
        36: q^4+3q^3+4q^2+2q
        37: 2q^4+4q^3+4q^2+2q
        39: 2q^4+4q^3+4q^2+2q
        41: 2q^4+4q^3+4q^2+2q
        43: 2q^4+4q^3+4q^2+2q
        44: 2q^4+4q^3+4q^2+2q
        45: 2q^4+4q^3+4q^2+2q
        46: 2q^4+4q^3+4q^2+2q
        47: 2q^4+4q^3+4q^2+2q
        48: q^5+2q^4+4q^3+3q^2+2q
        49: 2q^4+4q^3+4q^2+2q
        50: 2q^4+4q^3+4q^2+2q
        51: q^5+2q^4+4q^3+3q^2+2q
        52: 2q^4+4q^3+4q^2+2q
        53: 2q^4+4q^3+4q^2+2q
        54: 2q^4+4q^3+4q^2+2q
        55: 2q^4+4q^3+4q^2+2q
        56: 2q^4+4q^3+4q^2+2q
        57: 2q^4+4q^3+4q^2+2q
        58: q^3+2q^2+q
        59: q^3+2q^2+q
        60: q^3+2q^2+q
        61: q^3+2q^2+q
        62: q^4+3q^3+4q^2+2q
        64: 2q^4+4q^3+4q^2+2q
        66: q^4+3q^3+4q^2+2q
        68: q^4+3q^3+4q^2+2q
        69: q^4+3q^3+3q^2+2q
        70: 2q^4+4q^3+4q^2+2q
        71: q^4+3q^3+4q^2+2q
        72: q^4+3q^3+4q^2+2q
        73: q^4+3q^3+4q^2+2q
        74: 2q^4+4q^3+4q^2+2q
        76: 2q^4+4q^3+4q^2+2q
        78: 2q^4+4q^3+4q^2+2q
        80: q^4+3q^3+4q^2+2q
        81: q^4+3q^3+4q^2+2q
        82: q^4+3q^3+4q^2+2q
        83: 2q^4+4q^3+4q^2+2q
        84: q^4+3q^3+4q^2+2q
        85: q^4+3q^3+4q^2+2q
        86: q^4+3q^3+4q^2+2q
        87: 2q^4+4q^3+4q^2+2q
        88: 3q^3+4q^2+2q
        89: 3q^3+4q^2+2q
        90: q^4+3q^3+3q^2+2q
        91: 2q^4+4q^3+4q^2+2q
        92: 2q^4+4q^3+4q^2+2q
        93: q^5+2q^4+4q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: q^4+3q^3+3q^2+2q
       101: q^4+3q^3+3q^2+2q
       102: q^4+3q^3+3q^2+2q
       103: q^3+2q^2+q
       106: q^3+2q^2+q
       107: q^3+2q^2+q
       108: q^3+2q^2+q
       109: q^3+2q^2+q
       110: q^3+2q^2+q
       111: q^4+3q^3+4q^2+2q
       113: q^4+3q^3+4q^2+2q
       115: 2q^4+4q^3+4q^2+2q
       117: q^3+2q^2+q
       118: q^3+2q^2+q
       119: q^3+2q^2+q
       120: q^3+2q^2+q
       121: q^4+3q^3+4q^2+2q
       123: q^4+3q^3+4q^2+2q
       125: 3q^3+4q^2+2q
       126: 2q^3+3q^2+2q
       127: 3q^3+4q^2+2q
       129: 3q^3+4q^2+2q
       131: q^4+3q^3+3q^2+2q
       133: q^4+3q^3+4q^2+2q
       134: q^4+3q^3+3q^2+2q
       135: q^4+3q^3+4q^2+2q
       136: q^4+3q^3+4q^2+2q
       137: 2q^3+4q^2+2q
       138: 2q^3+3q^2+2q
       139: 2q^3+4q^2+2q
       140: q^3+2q^2+2q
       141: q^4+3q^3+4q^2+2q
       142: 3q^3+4q^2+2q
       143: 2q^3+4q^2+2q
       144: 2q^3+3q^2+2q
       145: 2q^3+4q^2+2q
       146: q^4+3q^3+4q^2+2q
       147: 3q^3+4q^2+2q
       148: q^3+2q^2+2q
       149: q^4+2q^3+3q^2+2q
       150: q^4+3q^3+3q^2+2q
       151: q^4+3q^3+3q^2+2q
       153: q^4+3q^3+3q^2+2q
       155: q^4+3q^3+3q^2+2q
       157: 3q^3+4q^2+2q
       158: 3q^3+4q^2+2q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+4q^2+2q
       161: 3q^3+4q^2+2q
       162: q^4+3q^3+3q^2+2q
       163: 3q^3+4q^2+2q
       164: 3q^3+4q^2+2q
       165: q^4+3q^3+3q^2+2q
       166: q^3+3q^2+2q
       167: q^3+3q^2+2q
       168: 2q^3+2q^2+2q
       169: q^3+2q^2+q
       172: q^3+2q^2+q
       173: q^3+2q^2+q
       176: q^3+2q^2+q
       177: 2q^3+3q^2+2q
       179: 2q^3+4q^2+2q
       181: 3q^3+4q^2+2q
       183: q^3+2q^2+q
       184: q^3+2q^2+q
       185: q^3+2q^2+q
       186: q^3+2q^2+q
       187: q^4+3q^3+4q^2+2q
       189: q^4+3q^3+4q^2+2q
       191: q^3+2q^2+q
       192: q^3+2q^2+q
       193: q^2+q
       194: q^2+q
       195: q^3+2q^2+q
       196: q^3+2q^2+q
       197: q^3+2q^2+2q
       199: q^3+2q^2+q
       200: q^3+2q^2+q
       201: q^3+2q^2+q
       202: q^3+2q^2+q
       203: q^2+q
       204: q^2+q
       205: q^3+2q^2+2q
       207: 2q^3+4q^2+2q
       209: q^4+2q^3+3q^2+2q
       211: q^4+3q^3+3q^2+2q
       213: 3q^3+4q^2+2q
       215: 3q^3+4q^2+2q
       217: q^4+3q^3+3q^2+2q
       219: 2q^3+3q^2+2q
       220: 3q^3+4q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+4q^2+2q
       223: 2q^3+3q^2+2q
       224: 2q^3+4q^2+2q
       225: 2q^3+3q^2+2q
       226: q^3+3q^2+2q
       227: 2q^3+4q^2+2q
       228: 2q^3+3q^2+2q
       229: q^3+2q^2+2q
       230: 3q^3+4q^2+2q
       231: q^3+3q^2+2q
       232: 2q^3+4q^2+2q
       233: 2q^3+3q^2+2q
       234: 3q^3+4q^2+2q
       235: q^3+2q^2+2q
       236: q^3+2q^2+2q
       237: q^3+3q^2+2q
       239: q^3+3q^2+2q
       241: 2q^3+2q^2+2q
       243: q^3+3q^2+2q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^4+2q^3+3q^2+2q
       247: q^3+3q^2+2q
       248: q^3+3q^2+2q
       249: 2q^3+2q^2+2q
       250: 4q^2+2q
       251: 4q^2+2q
       252: q^3+3q^2+2q
       253: 4q^2+2q
       254: 4q^2+2q
       255: q^3+3q^2+2q
       256: q^3+3q^2+2q
       257: q^3+3q^2+2q
       258: 2q^3+2q^2+2q
       259: q^3+2q^2+q
       262: q^3+2q^2+q
       263: q^3+2q^2+q
       266: q^3+2q^2+q
       267: q^2+q
       269: q^2+q
       271: q^2+q
       273: q^2+q
       275: q^3+2q^2+q
       278: q^3+2q^2+q
       279: 2q^3+4q^2+2q
       281: 2q^3+3q^2+2q
       283: q^2+q
       284: q^2+q
       285: q^2+q
       286: q^2+q
       287: q^3+3q^2+2q
       289: 3q^3+4q^2+2q
       291: 2q^3+3q^2+2q
       293: q^3+2q^2+q
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       296: q^3+2q^2+q
       297: 2q^3+4q^2+2q
       299: q^2+q
       300: q^2+q
       301: 2q^2+2q
       303: q^3+2q^2+q
       304: q^3+2q^2+q
       305: q^3+2q^2+2q
       307: q^3+2q^2+q
       308: q^3+2q^2+q
       309: q^2+q
       310: q^2+q
       311: 2q^2+2q
       313: q^3+2q^2+2q
       315: q^3+2q^2+2q
       317: q^3+3q^2+2q
       319: q^2+q
       320: q^2+q
       321: q^2+q
       322: q^2+q
       323: 2q^2+2q
       325: q^4+2q^3+3q^2+2q
       327: 4q^2+2q
       329: 4q^2+2q
       331: q^3+3q^2+2q
       333: 2q^3+3q^2+2q
       334: q^3+3q^2+2q
       335: q^3+3q^2+2q
       336: q^3+2q^2+2q
       337: q^3+3q^2+2q
       338: q^3+3q^2+2q
       340: q^3+3q^2+2q
       342: 2q^3+2q^2+2q
       344: q^3+3q^2+2q
       345: 4q^2+2q
       346: 3q^2+2q
       347: 2q^2+2q
       348: q^2+2q
       349: 4q^2+2q
       350: 2q^3+3q^2+2q
       351: 2q^2+2q
       352: q^3+3q^2+2q
       353: 4q^2+2q
       354: 3q^2+2q
       355: 4q^2+2q
       356: 2q^3+3q^2+2q
       357: 2q^2+2q
       358: q^2+2q
       359: 2q^2+2q
       360: q^3+3q^2+2q
       362: q^3+3q^2+2q
       364: 2q^3+2q^2+2q
       366: q^3+2q^2+2q
       367: q^3+3q^2+2q
       368: q^3+2q^2+2q
       369: 2q^2+2q
       370: 2q^2+2q
       371: q^3+3q^2+2q
       372: q^3+3q^2+2q
       373: 2q^3+2q^2+2q
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       377: q^2+q
       380: q^2+q
       381: q^3+2q^2+q
       384: q^3+2q^2+q
       385: q^3+2q^2+q
       388: q^3+2q^2+q
       389: q^2+q
       391: q^2+q
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       396: q^2+q
       397: q^2+q
       399: q^2+q
       401: q^2+q
       404: q^2+q
       405: q^2+q
       406: q^2+q
       409: 4q^2+2q
       411: 3q^2+2q
       413: q^3+3q^2+2q
       415: 4q^2+2q
       417: 2q^3+3q^2+2q
       419: q^2+q
       420: q^2+q
       421: q^2+q
       422: q^2+q
       423: q^3+3q^2+2q
       425: q^3+2q^2+2q
       427: q^3+3q^2+2q
       429: q
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       432: q^2+q
       433: q^2+2q
       435: 2q^2+2q
       437: q^2+q
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       439: 2q^2+q
       440: 2q^2+q
       441: 2q^2+2q
       443: q^2+q
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       445: 2q^2+2q
       447: q^2+q
       448: q^2+q
       449: q
       450: q
       451: q^2+2q
       453: 2q^2+q
       454: 2q^2+q
       455: 2q^2+2q
       457: q^2+q
       458: q^2+q
       459: 2q^2+2q
       461: q^2+q
       462: q^2+q
       463: 2q^2+2q
       465: q^3+3q^2+2q
       467: q^3+2q^2+2q
       469: q^3+2q^2+2q
       471: q^2+q
       472: q^2+q
       473: q^2+q
       474: q^2+q
       475: 2q^2+2q
       477: 3q^2+2q
       479: 2q^2+2q
       481: q^3+3q^2+2q
       482: q^3+3q^2+2q
       483: q^3+2q^2+2q
       484: q^3+3q^2+2q
       485: q^3+3q^2+2q
       487: q^3+3q^2+2q
       489: 2q^3+2q^2+2q
       491: q^3+2q^2+2q
       492: 3q^2+2q
       493: q^2+2q
       494: 3q^2+2q
       495: q^2+2q
       496: 2q^2+2q
       497: 3q^2+2q
       498: 3q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 2q^2+2q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: q^3+2q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: 2q
       512: q^2+2q
       513: 2q
       514: q^2+2q
       515: q^2+2q
       516: q^2+2q
       517: q^2+2q
       518: q^2+2q
       519: q^2+2q
       520: q^2+2q
       521: q^2+q
       524: q^2+q
       525: 2q^2+q
       528: 2q^2+q
       529: q^2+q
       532: q^2+q
       533: q
       536: q
       537: q^2+q
       539: q^2+q
       541: q^2+q
       543: q^2+q
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       547: q^2+q
       549: q
       552: q
       553: q^2+q
       555: q^2+q
       557: q^2+q
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       561: q^2+q
       563: q^2+q
       565: q^2+q
       568: q^2+q
       569: q^2+q
       570: q^2+q
       573: q^2+q
       575: q^2+q
       577: 2q^2+2q
       579: q^2
       583: 3q^2+2q
       585: q^3+3q^2+2q
       587: 3q^2+2q
       589: q^2+q
       590: q^2+q
       591: q
       592: q
       593: q
       594: q
       595: q^2+q
       596: q^2+q
       597: q^3+2q^2+2q
       599: q^3+2q^2+2q
       601: q^3+3q^2+2q
       603: q
       604: q
       605: q^2+2q
       607: q^2+q
       608: q^2+q
       609: q^2+2q
       611: 2q
       613: q^2+2q
       615: q^2+q
       616: q^2+q
       617: 2q^2+2q
       619: q^2+q
       620: q^2+q
       621: q
       622: q
       623: q^2+2q
       625: q^2+2q
       627: 2q
       629: q^2+2q
       631: q^2+q
       632: q^2+q
       633: 2q^2+2q
       635: q^2+2q
       637: q^2+2q
       639: q^3+2q^2+2q
       641: q
       642: q
       643: q
       644: q
       645: q^2+2q
       647: q
       648: q
       649: q
       650: q
       651: 3q^2+2q
       653: 2q
       655: 2q^2+2q
       657: q^2+2q
       658: q^2+2q
       660: q^2+2q
       662: q^2+2q
       664: q^2+2q
       665: q^3+2q^2+2q
       666: q^2+2q
       668: q^2+2q
       670: q^2+2q
       672: q^2+2q
       673: q^2+2q
       674: 2q
       675: q^2+2q
       676: 3q^2+2q
       677: q^2+2q
       678: 2q
       679: q^2+2q
       680: 2q
       681: 3q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 2q
       685: q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q
       689: q
       693: q^2+q
       697: q^2+q
       705: q^2+q
       708: q^2+q
       709: q^2+q
       712: q^2+q
       713: q
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       729: q
       731: q
       733: q^2+q
       735: q^2+q
       737: q
       739: q
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       747: q
       749: q^2+q
       751: q^2+q
       753: q
       756: q
       757: q^2+q
       758: q^2+q
       761: q
       762: q
       765: q^2+q
       768: q^2+q
       769: 2q^2+2q
       771: q^2
       775: q^2+2q
       777: 3q^2+2q
       779: q^2+2q
       781: q^3+2q^2+2q
       783: q^2+2q
       785: q
       786: q
       787: q
       788: q
       789: q^2+2q
       791: q^2+2q
       793: q
       794: q
       795: 2q
       797: q^2+2q
       799: 2q
       801: q
       802: q
       805: q
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       807: q^2+q
       808: q^2+q
       809: q^2+2q
       811: q^2+2q
       813: 2q
       815: q
       816: q
       817: q
       818: q
       819: 2q
       821: q^2+2q
       823: 2q
       825: q^2+q
       826: q^2+q
       827: q
       828: q
       831: q
       832: q
       833: q^2+2q
       835: q^2+2q
       837: 2q
       839: q
       840: q
       841: q^2+2q
       843: 2q
       845: q
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       848: q
       849: q^2+2q
       851: 2q
       853: 4q
       855: q
       857: 2q
       866: q^2+2q
       868: q^2+2q
       870: 2q
       871: q^2+2q
       872: 2q
       874: 2q
       875: q^2+2q
       876: 2q
       877: 2q
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       879: q
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       884: q^2+q
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       968: 2q
       974: q
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       978: 2q
       979: 2q
       982: 2q
       984: 2q
       988: q
       991: q
       994: q^2+2q
       998: q
       999: q
      1000: q
      1001: q
      1002: q^2+2q
      1004: q
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      1006: q
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      1008: 2q
      1010: q^2+2q
      1012: 2q
      1018: 2q
      1020: 2q
      1022: q^2+2q
      1024: 2q
      1026: q
      1027: q
      1034: 2q
      1036: 2q
      1038: q^2+2q
      1042: 2q
      1044: q
      1045: q
      1048: 2q
      1050: 3q
      1052: q
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      1058: q
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      1064: q
      1076: 2q
      1078: 2q
      1080: 2q
      1082: 2q
      1083: q
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      1120: q
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      1130: q
      1133: q
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      1135: q
      1138: 2q
      1148: q
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      1168: q
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      1174: q
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      1185: q
      1190: q
      1198: q
      1199: q
      1220: 2q
      1222: 3q
      1230: 2q
      1234: q
      1235: q
      1238: 2q
      1240: q
      1241: q
      1248: 2q
      1250: q
      1251: q
      1256: 2q
      1260: q
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      1264: 3q
      1266: q
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      1406: q
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      1430: q
      1446: 3q
      1464: q
      1470: q
      1474: q
      1480: q
      1484: q
      1555: q
      1559: q
      1560: q
      1637: 2
      1641: q
      1671: q
      1725: 2
      1729: 1
      1730: 1
      1823: 1
      1836: 1
      1843: 1
      1928: 1
      1958: 1
      2028: 1

2029:    0: 6q^3+10q^2+4q
         1: 6q^3+10q^2+4q
         2: 2q^4+6q^3+7q^2+4q
         3: 6q^3+10q^2+4q
         4: 6q^3+10q^2+4q
         5: 6q^3+10q^2+4q
         6: 6q^3+10q^2+4q
         7: 2q^4+6q^3+7q^2+4q
         8: 3q^4+7q^3+7q^2+4q
         9: 2q^4+6q^3+7q^2+4q
        10: 6q^3+10q^2+4q
        11: 6q^3+10q^2+4q
        12: 6q^3+10q^2+4q
        13: 3q^3+7q^2+4q
        14: 3q^3+7q^2+4q
        15: 4q^3+7q^2+4q
        16: 6q^3+10q^2+4q
        17: 6q^3+10q^2+4q
        18: 2q^4+6q^3+7q^2+4q
        19: 6q^3+10q^2+4q
        20: 6q^3+10q^2+4q
        21: 2q^4+6q^3+7q^2+4q
        22: 2q^3+10q^2+4q
        23: 2q^3+10q^2+4q
        24: q^4+4q^3+7q^2+4q
        25: 2q^3+10q^2+4q
        26: 2q^3+10q^2+4q
        27: q^4+4q^3+7q^2+4q
        28: 6q^3+10q^2+4q
        29: 6q^3+10q^2+4q
        30: 3q^3+7q^2+4q
        31: 2q^3+10q^2+4q
        32: q^3+7q^2+4q
        33: 2q^3+10q^2+4q
        34: 2q^3+10q^2+4q
        35: q^3+7q^2+4q
        36: 2q^3+10q^2+4q
        37: 8q^2+2q
        38: 2q^2+2q
        39: 8q^2+2q
        40: 2q^2+2q
        41: 3q^3+5q^2+2q
        42: 2q^2+2q
        43: 3q^3+7q^2+4q
        44: 3q^3+7q^2+4q
        45: 4q^3+7q^2+4q
        46: 3q^3+7q^2+4q
        47: 4q^3+7q^2+4q
        48: 3q^3+7q^2+4q
        49: 6q^3+10q^2+4q
        50: 6q^3+10q^2+4q
        51: 2q^4+6q^3+7q^2+4q
        52: 2q^3+10q^2+4q
        53: 2q^3+10q^2+4q
        54: q^4+4q^3+7q^2+4q
        55: 2q^3+10q^2+4q
        56: 2q^3+10q^2+4q
        57: q^4+4q^3+7q^2+4q
        58: q^3+5q^2+2q
        59: q^3+5q^2+2q
        60: q^3+5q^2+2q
        61: q^3+5q^2+2q
        62: 8q^2+2q
        63: 2q^2+2q
        64: 5q^2+2q
        65: 2q^2+2q
        66: 8q^2+2q
        67: 2q^2+2q
        68: q^3+4q^2+4q
        69: 3q^3+7q^2+4q
        70: 3q^3+7q^2+4q
        71: 6q^3+10q^2+4q
        72: 2q^3+10q^2+4q
        73: 2q^3+10q^2+4q
        74: 8q^2+2q
        75: 2q^2+2q
        76: 8q^2+2q
        77: 2q^2+2q
        78: 3q^3+5q^2+2q
        79: 2q^2+2q
        80: q^3+7q^2+4q
        81: q^3+7q^2+4q
        82: 2q^3+10q^2+4q
        83: q^3+7q^2+4q
        84: q^3+7q^2+4q
        85: q^3+7q^2+4q
        86: 2q^3+10q^2+4q
        87: q^3+7q^2+4q
        88: 3q^3+7q^2+4q
        89: 4q^3+7q^2+4q
        90: 3q^3+7q^2+4q
        91: 3q^3+7q^2+4q
        92: 4q^3+7q^2+4q
        93: 3q^3+7q^2+4q
        94: 2q^3+10q^2+4q
        95: 2q^3+10q^2+4q
        96: q^4+4q^3+7q^2+4q
        97: 2q^3+10q^2+4q
        98: 2q^3+10q^2+4q
        99: q^4+4q^3+7q^2+4q
       100: 8q^2+4q
       101: 8q^2+4q
       102: 2q^3+5q^2+4q
       103: 4q^2+q
       104: q^2+q
       105: q^2+q
       106: 4q^2+q
       107: q^3+5q^2+2q
       108: q^3+5q^2+2q
       109: q^3+5q^2+2q
       110: q^3+5q^2+2q
       111: 8q^2+2q
       112: 2q^2+2q
       113: 8q^2+2q
       114: 2q^2+2q
       115: 5q^2+2q
       116: 2q^2+2q
       117: 2q^2+2q
       118: 2q^2+2q
       119: 2q^2+2q
       120: 2q^2+2q
       121: 5q^2+2q
       122: 2q^2+2q
       123: 5q^2+2q
       124: 2q^2+2q
       125: q^3+4q^2+4q
       126: 3q^3+7q^2+4q
       127: 8q^2+2q
       128: 2q^2+2q
       129: 8q^2+2q
       130: 2q^2+2q
       131: 3q^3+5q^2+2q
       132: 2q^2+2q
       133: q^3+4q^2+4q
       134: 3q^3+7q^2+4q
       135: q^3+7q^2+4q
       136: q^3+7q^2+4q
       137: q^3+7q^2+4q
       138: q^3+7q^2+4q
       139: 2q^3+10q^2+4q
       140: 4q^2+4q
       141: q^3+7q^2+4q
       142: 2q^3+10q^2+4q
       143: q^3+7q^2+4q
       144: q^3+7q^2+4q
       145: 2q^3+10q^2+4q
       146: q^3+7q^2+4q
       147: 2q^3+10q^2+4q
       148: 4q^2+4q
       149: 8q^2+4q
       150: 5q^2+4q
       151: 7q^2+2q
       152: q^2+2q
       153: 7q^2+2q
       154: q^2+2q
       155: 2q^3+4q^2+2q
       156: q^2+2q
       157: 3q^3+7q^2+4q
       158: 4q^3+7q^2+4q
       159: 3q^3+7q^2+4q
       160: q^3+5q^2+4q
       161: q^3+5q^2+4q
       162: q^3+5q^2+4q
       163: q^3+5q^2+4q
       164: q^3+5q^2+4q
       165: q^3+5q^2+4q
       166: 8q^2+4q
       167: 8q^2+4q
       168: 2q^3+5q^2+4q
       169: 4q^2+q
       170: q^2+q
       171: q^2+q
       172: 4q^2+q
       173: q^2+q
       174: q^2+q
       175: q^2+q
       176: q^2+q
       177: 5q^2+2q
       178: 2q^2+2q
       179: 8q^2+2q
       180: 2q^2+2q
       181: 8q^2+2q
       182: 2q^2+2q
       183: 2q^2+2q
       184: 2q^2+2q
       185: 2q^2+2q
       186: 2q^2+2q
       187: 5q^2+2q
       188: 2q^2+2q
       189: 5q^2+2q
       190: 2q^2+2q
       191: 2q^2+2q
       192: 2q^2+2q
       193: 2q^2+2q
       194: 2q^2+2q
       195: q^3+5q^2+2q
       196: q^3+5q^2+2q
       197: 4q^2+2q
       198: 2q
       199: 2q^2+2q
       200: 2q^2+2q
       201: q^3+5q^2+2q
       202: q^3+5q^2+2q
       203: 2q^2+2q
       204: 2q^2+2q
       205: 4q^2+2q
       206: 2q
       207: 5q^2+2q
       208: 2q^2+2q
       209: 7q^2+2q
       210: q^2+2q
       211: 4q^2+2q
       212: q^2+2q
       213: 3q^2+2q
       215: 3q^2+2q
       217: 3q^2+2q
       219: q^3+4q^2+4q
       220: q^3+4q^2+4q
       221: 3q^3+7q^2+4q
       222: q^3+7q^2+4q
       223: q^3+7q^2+4q
       224: q^3+7q^2+4q
       225: q^3+7q^2+4q
       226: q^3+7q^2+4q
       227: 2q^2+4q
       228: q^3+5q^2+4q
       229: q^2+4q
       230: q^3+5q^2+4q
       231: q^3+7q^2+4q
       232: 2q^2+4q
       233: q^3+5q^2+4q
       234: q^3+5q^2+4q
       235: q^2+4q
       236: 5q^2+4q
       237: 7q^2+2q
       238: q^2+2q
       239: 7q^2+2q
       240: q^2+2q
       241: 2q^3+4q^2+2q
       242: q^2+2q
       243: 8q^2+4q
       244: 4q^2+4q
       245: 4q^2+4q
       246: 5q^2+4q
       247: 8q^2+4q
       248: 8q^2+4q
       249: 2q^3+5q^2+4q
       250: q^3+5q^2+4q
       251: q^3+5q^2+4q
       252: q^3+5q^2+4q
       253: q^3+5q^2+4q
       254: q^3+5q^2+4q
       255: q^3+5q^2+4q
       256: 3q^2+4q
       257: 4q^2+4q
       258: 3q^2+4q
       259: 4q^2+q
       260: q^2+q
       261: q^2+q
       262: 4q^2+q
       263: q^2+q
       264: q^2+q
       265: q^2+q
       266: q^2+q
       267: 2q^2+q
       268: q
       269: 2q^2+q
       270: q
       271: 2q^2+q
       272: q
       273: 2q^2+q
       274: q
       275: q^2+q
       276: q^2+q
       277: q^2+q
       278: q^2+q
       279: 2q
       281: 3q^2+2q
       283: 2q^2+2q
       284: 2q^2+2q
       285: 2q^2+2q
       286: 2q^2+2q
       287: 5q^2+2q
       288: 2q^2+2q
       289: 3q^2+2q
       291: 5q^2+2q
       292: 2q^2+2q
       293: 2q^2+2q
       294: 2q^2+2q
       295: 2q^2+2q
       296: 2q^2+2q
       297: 5q^2+2q
       298: 2q^2+2q
       299: 2q
       300: 2q
       301: 4q^2+2q
       302: 2q
       303: q^2+2q
       304: q^2+2q
       305: q^2+2q
       306: 2q
       307: q^2+2q
       308: q^2+2q
       309: 2q
       310: 2q
       311: 4q^2+2q
       312: 2q
       313: q^2+2q
       314: 2q
       315: 4q^2+2q
       316: q^2+2q
       317: 7q^2+2q
       318: q^2+2q
       319: 2q^2+2q
       320: 2q^2+2q
       321: 2q^2+2q
       322: 2q^2+2q
       323: 2q^2+2q
       324: 2q
       325: 4q^2+2q
       326: q^2+2q
       327: 3q^2+2q
       329: 3q^2+2q
       331: 3q^2+2q
       333: q^3+4q^2+4q
       334: q^3+7q^2+4q
       335: q^3+7q^2+4q
       336: 5q^2+4q
       337: 8q^2+4q
       338: 7q^2+2q
       339: q^2+2q
       340: 7q^2+2q
       341: q^2+2q
       342: 2q^3+4q^2+2q
       343: q^2+2q
       344: 2q^2+4q
       345: 2q^2+4q
       346: q^3+5q^2+4q
       347: q^2+4q
       348: q^2+4q
       349: q^3+5q^2+4q
       350: q^3+5q^2+4q
       351: 4q^2+4q
       352: 2q^2+4q
       353: 2q^2+4q
       354: q^3+5q^2+4q
       355: q^3+5q^2+4q
       356: q^3+5q^2+4q
       357: q^2+4q
       358: q^2+4q
       359: 4q^2+4q
       360: 2q^2+2q
       362: 3q^2+2q
       364: 2q^2+2q
       366: 5q^2+4q
       367: q^2+4q
       368: 3q^2+4q
       369: q^2+4q
       370: q^2+4q
       371: 3q^2+4q
       372: 4q^2+4q
       373: 3q^2+4q
       374: 3q^2+4q
       375: 4q^2+4q
       376: 3q^2+4q
       377: q^2+q
       378: q^2+q
       379: q^2+q
       380: q^2+q
       381: q
       384: q
       385: q^2+q
       386: q^2+q
       387: q^2+q
       388: q^2+q
       389: 2q^2+q
       390: q
       391: 2q^2+q
       392: q
       393: q
       394: q
       395: q
       396: q
       397: 2q^2+q
       398: q
       399: 2q^2+q
       400: q
       401: q
       402: q
       403: q
       404: q
       405: q^2+q
       406: q^2+q
       407: q
       408: q
       409: 2q
       411: 3q^2+2q
       413: 2q
       415: 3q^2+2q
       417: 3q^2+2q
       419: 2q^2+2q
       420: 2q^2+2q
       421: 2q^2+2q
       422: 2q^2+2q
       423: 5q^2+2q
       424: 2q^2+2q
       425: 4q^2+2q
       426: q^2+2q
       427: 7q^2+2q
       428: q^2+2q
       429: 2q
       430: 2q
       431: q^2+2q
       432: q^2+2q
       433: q^2+2q
       434: 2q
       435: q^2+2q
       437: 2q
       438: 2q
       439: q^2+2q
       440: q^2+2q
       441: q^2+2q
       442: 2q
       443: 2q^2+2q
       444: 2q^2+2q
       445: 4q^2+2q
       446: 2q
       447: q^2+2q
       448: q^2+2q
       449: 2q
       450: 2q
       451: q^2+2q
       452: 2q
       453: q^2+2q
       454: q^2+2q
       455: q^2+2q
       457: 2q
       458: 2q
       459: q^2+2q
       460: 2q
       461: 2q^2+2q
       462: 2q^2+2q
       463: 4q^2+2q
       464: 2q
       465: 2q
       467: 2q^2+2q
       469: 4q^2+2q
       470: q^2+2q
       471: 2q
       472: 2q
       473: 2q
       474: 2q
       475: 2q
       476: 2q
       477: 2q^2+2q
       478: 2q
       479: 2q^2+2q
       480: 2q
       481: 2q^2+4q
       482: 2q^2+4q
       483: 5q^2+4q
       484: q^2+4q
       485: 2q^2+2q
       487: 3q^2+2q
       489: 2q^2+2q
       491: 3q^2+4q
       492: 2q^2+4q
       493: q^2+4q
       494: q^3+5q^2+4q
       495: q^2+4q
       496: q^2+4q
       497: 2q^2+4q
       498: q^3+5q^2+4q
       499: q^2+4q
       500: q^2+4q
       501: q^2+4q
       502: 2q^2+2q
       504: 3q^2+2q
       506: 2q^2+2q
       508: q^2+4q
       509: q^2+4q
       510: 3q^2+4q
       511: q^2+4q
       512: q^2+4q
       513: q^2+4q
       514: q^2+4q
       515: 3q^2+4q
       516: 4q^2+4q
       517: 3q^2+4q
       518: 3q^2+4q
       519: 4q^2+4q
       520: 3q^2+4q
       521: q
       524: q
       525: q
       528: q
       529: q^2+q
       530: q^2+q
       531: q^2+q
       532: q^2+q
       533: q
       534: q
       535: q
       536: q
       537: q
       539: q
       541: q
       542: q
       543: q
       544: q
       545: 2q^2+q
       546: q
       547: 2q^2+q
       548: q
       549: q
       550: q
       551: q
       552: q
       553: q
       555: q
       557: q
       558: q
       559: q
       560: q
       561: 2q^2+q
       562: q
       563: 2q^2+q
       564: q
       565: q
       566: q
       567: q
       568: q
       569: q^2+q
       570: q^2+q
       571: q
       572: q
       573: q^2+q
       574: q
       575: q^2+q
       576: q
       577: 2q^2+2q
       581: 2q
       583: 2q
       585: 2q
       587: 3q^2+2q
       589: q^2+2q
       590: q^2+2q
       591: 2q
       592: 2q
       593: 2q
       594: 2q
       595: q^2+2q
       596: q^2+2q
       597: 2q^2+2q
       599: 4q^2+2q
       600: q^2+2q
       601: 2q
       603: 2q
       604: 2q
       605: q^2+2q
       607: q^2+2q
       608: q^2+2q
       609: q^2+2q
       610: 2q
       611: q^2+2q
       613: q^2+2q
       614: 2q
       615: 2q
       616: 2q
       617: q^2+2q
       619: q^2+2q
       620: q^2+2q
       621: 2q
       622: 2q
       623: q^2+2q
       625: q^2+2q
       626: 2q
       627: q^2+2q
       629: q^2+2q
       630: 2q
       631: 2q
       632: 2q
       633: q^2+2q
       635: 2q
       637: 2q^2+2q
       639: 2q
       641: 2q
       642: 2q
       643: 2q
       644: 2q
       645: 2q
       646: 2q
       647: 2q
       648: 2q
       649: 2q
       650: 2q
       651: 2q
       653: 2q
       654: 2q
       655: 2q
       656: 2q
       657: q^2+4q
       658: 2q^2+2q
       660: 3q^2+2q
       662: 2q^2+2q
       664: 3q^2+4q
       665: q^2+4q
       666: 2q^2+2q
       668: 3q^2+2q
       670: 2q^2+2q
       672: q^2+4q
       673: 3q^2+4q
       674: q^2+4q
       675: 2q
       676: 2q^2+4q
       677: q^2+4q
       678: q^2+4q
       679: q^2+4q
       680: q^2+4q
       681: 2q^2+4q
       682: 2q
       683: q^2+4q
       684: q^2+4q
       685: q^2+4q
       686: q^2+4q
       687: q^2+4q
       688: q^2+4q
       689: 2q
       690: 3q^2+4q
       691: 4q^2+4q
       692: 3q^2+4q
       693: q^2+q
       697: q^2+q
       699: q
       700: q
       705: q
       708: q
       709: q
       712: q
       713: q
       714: q
       715: q
       716: q
       717: q
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       721: q
       723: q
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       731: q
       733: q
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       739: q
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       751: q
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       762: q
       763: q
       764: q
       765: q
       766: q
       767: q
       768: q
       769: 2q
       775: 2q
       777: 2q
       779: 2q^2+2q
       781: 2q
       783: 2q^2+2q
       785: 2q
       786: 2q
       787: 2q
       788: 2q
       789: 2q
       791: 2q
       792: 2q
       793: 2q
       794: 2q
       795: q^2+2q
       799: q^2+2q
       801: q
       802: q
       805: 2q
       806: 2q
       807: q^2+2q
       808: q^2+2q
       809: q^2+2q
       811: q^2+2q
       812: 2q
       813: q^2+2q
       815: 2q
       816: 2q
       817: 2q
       818: 2q
       819: q^2+2q
       823: q^2+2q
       825: q^2+2q
       826: q^2+2q
       827: 2q
       828: 2q
       831: q
       832: q
       833: q^2+2q
       835: q^2+2q
       836: 2q
       837: q^2+2q
       839: 2q
       840: 2q
       841: 2q
       843: 2q
       844: 2q
       845: 2q
       846: 2q
       847: 2q
       848: 2q
       849: 2q
       851: 2q
       852: 2q
       853: 2q
       855: q
       856: q
       857: 2q
       858: 2q
       859: 2q^2+2q
       861: 3q^2+2q
       863: 2q^2+2q
       865: q^2+4q
       866: q^2+4q
       867: 3q^2+4q
       868: q^2+4q
       869: q^2+4q
       870: q^2+4q
       871: 2q
       872: q^2+4q
       873: q^2+4q
       874: q^2+4q
       875: 2q
       876: q^2+4q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+2
       882: q+2
       883: q+2
       884: q
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       904: q
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       968: 2q
       974: q
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       978: q
       979: q
       982: 2q
       988: q
       989: q
       990: q
       991: q
       992: 2q
       994: 2q
       996: 2q^2+2q
       998: 2q
       999: 2q
      1000: 2q
      1001: 2q
      1002: 2q
      1004: 2q
      1005: 2q
      1006: 2q
      1007: 2q
      1008: 2q
      1009: 2q
      1010: 2q
      1012: 2q
      1013: 2q
      1014: q^2+2q
      1016: 2q
      1017: 2q
      1020: q^2+2q
      1024: q^2+2q
      1026: q
      1027: q
      1030: q^2+2q
      1032: 2q
      1033: 2q
      1036: q^2+2q
      1042: q^2+2q
      1044: q
      1045: q
      1046: 2q
      1047: 2q
      1050: 2q
      1052: q
      1053: q
      1058: q
      1059: q
      1060: q
      1062: q
      1063: q
      1064: q
      1065: q
      1066: q+2
      1068: q+2
      1070: q+2
      1072: q+2
      1073: q+2
      1074: q^2+4q
      1075: 2
      1076: 2q
      1077: q^2+4q
      1078: 2q
      1079: 2
      1080: 2q
      1081: q^2+4q
      1082: 2q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1091: q
      1098: q
      1102: q
      1110: q
      1112: q
      1114: q
      1116: q
      1118: q
      1120: q
      1122: q
      1124: q
      1126: q
      1127: q
      1130: q
      1131: q
      1132: q
      1133: q
      1134: q
      1135: q
      1136: q
      1137: q
      1138: 2q
      1144: q
      1146: q
      1164: q
      1166: q
      1184: q
      1185: q
      1188: 2q
      1194: q
      1195: q
      1196: q
      1197: q
      1210: q+2
      1212: q+2
      1214: 2q
      1216: 2q
      1217: 2q
      1218: 2q
      1219: 2q
      1222: 2q
      1224: 2q
      1225: 2q
      1226: 2
      1228: 1
      1229: 1
      1234: q
      1235: q
      1236: q^2+2q
      1240: q
      1241: q
      1244: 2
      1246: 1
      1247: 1
      1250: q
      1251: q
      1252: q^2+2q
      1260: q
      1261: q
      1263: 2
      1272: q
      1274: q
      1276: q
      1277: q
      1278: q
      1280: q
      1281: q
      1282: q+2
      1283: 2q
      1284: 2
      1285: 2q
      1286: 2
      1287: q
      1288: 2q
      1289: q
      1290: q
      1295: q
      1302: q
      1307: q
      1314: q
      1316: q
      1318: q
      1320: q
      1322: q
      1323: q
      1326: q
      1327: q
      1328: q
      1329: q
      1334: 2q
      1340: 1
      1342: 1
      1372: 1
      1374: 1
      1407: 2
      1411: 1
      1412: 1
      1430: q
      1438: q+2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1445: 2
      1452: 2
      1454: q
      1455: q
      1458: 2
      1460: q
      1461: q
      1472: q
      1480: q
      1482: q
      1483: q
      1484: q
      1485: 2
      1486: 2
      1487: q
      1488: 1
      1489: q
      1494: q
      1528: 1
      1529: 1
      1541: 1
      1543: 1
      1545: 1
      1547: 1
      1550: 1
      1551: 1
      1556: 2
      1631: q
      1640: 2
      1643: 2
      1647: 1
      1648: 1
      1651: 2
      1653: 1
      1654: 1
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1678: 1
      1679: 1
      1726: 2
      1734: 1
      1735: 1
      1745: 1
      1747: 1
      1761: 1
      1763: 1
      1804: 1
      1826: 1
      1827: 1
      1833: 1
      1837: 1
      1838: 1
      1929: 1
      1956: 1
      1961: 1
      2029: 1

2030:    0: q^2+2q+2
         1: q^2+2q+2
         2: q^2+2q+2
         3: q^2+2q+2
         4: q^2+2q+2
         5: q^2+2q+2
         6: q^2+2q+2
         7: q^2+2q+2
         8: q^2+2q+2
         9: q^2+2q+2
        10: q^2+2q+2
        11: q^2+2q+2
        12: q^2+2q+2
        13: q^2+2q+2
        14: q^2+2q+2
        15: q^2+2q+2
        16: q^2+2q+2
        17: q^2+2q+2
        18: q^2+2q+2
        19: q^2+2q+2
        20: q^2+2q+2
        21: q^2+2q+2
        22: 2q+2
        23: 2q+2
        24: 2q+2
        25: 2q+2
        26: 2q+2
        27: 2q+2
        28: q^2+2q+2
        29: q^2+2q+2
        30: q^2+2q+2
        31: 2q+2
        32: 2q+2
        33: 2q+2
        34: 2q+2
        35: 2q+2
        36: 2q+2
        38: 2q+2
        40: 2q+2
        42: 2q+2
        43: q^2+2q+2
        44: q^2+2q+2
        45: q^2+2q+2
        46: q^2+2q+2
        47: q^2+2q+2
        48: q^2+2q+2
        49: q^2+2q+2
        50: q^2+2q+2
        51: q^2+2q+2
        52: 2q+2
        53: 2q+2
        54: 2q+2
        55: 2q+2
        56: 2q+2
        57: 2q+2
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 2q+2
        65: 2q+2
        67: 2q+2
        68: q^2+2q+2
        69: q^2+2q+2
        70: q^2+2q+2
        71: q^2+2q+2
        72: 2q+2
        73: 2q+2
        75: 2q+2
        77: 2q+2
        79: 2q+2
        80: 2q+2
        81: 2q+2
        82: 2q+2
        83: 2q+2
        84: 2q+2
        85: 2q+2
        86: 2q+2
        87: 2q+2
        88: q^2+2q+2
        89: q^2+2q+2
        90: q^2+2q+2
        91: q^2+2q+2
        92: q^2+2q+2
        93: q^2+2q+2
        94: 2q+2
        95: 2q+2
        96: 2q+2
        97: 2q+2
        98: 2q+2
        99: 2q+2
       100: q+2
       101: q+2
       102: q+2
       104: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+2
       114: 2q+2
       116: 2q+2
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       122: 2q+2
       124: 2q+2
       125: q^2+2q+2
       126: q^2+2q+2
       128: 2q+2
       130: 2q+2
       132: 2q+2
       133: q^2+2q+2
       134: q^2+2q+2
       135: 2q+2
       136: 2q+2
       137: 2q+2
       138: 2q+2
       139: 2q+2
       140: 2
       141: 2q+2
       142: 2q+2
       143: 2q+2
       144: 2q+2
       145: 2q+2
       146: 2q+2
       147: 2q+2
       148: 2
       149: q+2
       150: q+2
       152: q+2
       154: q+2
       156: q+2
       157: q^2+2q+2
       158: q^2+2q+2
       159: q^2+2q+2
       160: 2q+2
       161: 2q+2
       162: 2q+2
       163: 2q+2
       164: 2q+2
       165: 2q+2
       166: q+2
       167: q+2
       168: q+2
       170: q+1
       171: q+1
       174: q+1
       175: q+1
       178: 2q+2
       180: 2q+2
       182: 2q+2
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       188: 2q+2
       190: 2q+2
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       206: 2
       208: 2q+2
       210: q+2
       212: q+2
       214: 2q+2
       216: 2q+2
       218: 2q+2
       219: q^2+2q+2
       220: q^2+2q+2
       221: q^2+2q+2
       222: 2q+2
       223: 2q+2
       224: 2q+2
       225: 2q+2
       226: 2q+2
       227: 2q+2
       228: 2q+2
       229: 2
       230: 2q+2
       231: 2q+2
       232: 2q+2
       233: 2q+2
       234: 2q+2
       235: 2
       236: q+2
       238: q+2
       240: q+2
       242: q+2
       243: q+2
       244: 2
       245: 2
       246: q+2
       247: q+2
       248: q+2
       249: q+2
       250: 2q+2
       251: 2q+2
       252: 2q+2
       253: 2q+2
       254: 2q+2
       255: 2q+2
       256: q+2
       257: q+2
       258: q+2
       260: q+1
       261: q+1
       264: q+1
       265: q+1
       268: 1
       270: 1
       272: 1
       274: 1
       276: q+1
       277: q+1
       280: 2q+2
       282: 2q+2
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: 2q+2
       290: 2q+2
       292: 2q+2
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       298: 2q+2
       299: 1
       300: 1
       302: 2
       303: q+1
       304: q+1
       306: 2
       307: q+1
       308: q+1
       309: 1
       310: 1
       312: 2
       314: 2
       316: q+2
       318: q+2
       319: 1
       320: 1
       321: 1
       322: 1
       324: 2
       326: q+2
       328: 2q+2
       330: 2q+2
       332: 2q+2
       333: q^2+2q+2
       334: 2q+2
       335: 2q+2
       336: q+2
       337: q+2
       339: q+2
       341: q+2
       343: q+2
       344: 2q+2
       345: 2q+2
       346: 2q+2
       347: 2
       348: 2
       349: 2q+2
       350: 2q+2
       351: 2
       352: 2q+2
       353: 2q+2
       354: 2q+2
       355: 2q+2
       356: 2q+2
       357: 2
       358: 2
       359: 2
       361: q+2
       363: q+2
       365: q+2
       366: q+2
       367: q+2
       368: q+2
       369: 2
       370: 2
       371: q+2
       372: q+2
       373: q+2
       374: q+2
       375: q+2
       376: q+2
       378: q+1
       379: q+1
       382: q+1
       383: q+1
       386: q+1
       387: q+1
       390: 1
       392: 1
       394: 1
       395: 1
       398: 1
       400: 1
       402: 1
       403: 1
       407: 1
       408: 1
       410: 2q+2
       412: 2q+2
       414: 2q+2
       416: 2q+2
       418: 2q+2
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       424: 2q+2
       426: q+2
       428: q+2
       429: 1
       430: 1
       431: q+1
       432: q+1
       434: 2
       436: 2
       437: 1
       438: 1
       439: q+1
       440: q+1
       442: 2
       443: 1
       444: 1
       446: 2
       447: q+1
       448: q+1
       449: 1
       450: 1
       452: 2
       453: q+1
       454: q+1
       456: 2
       457: 1
       458: 1
       460: 2
       461: 1
       462: 1
       464: 2
       466: q+2
       468: q+2
       470: q+2
       471: 1
       472: 1
       473: 1
       474: 1
       476: 2
       478: 2
       480: 2
       481: 2q+2
       482: 2q+2
       483: q+2
       484: q+2
       486: q+2
       488: q+2
       490: q+2
       491: q+2
       492: 2q+2
       493: 2
       494: 2q+2
       495: 2
       496: 2
       497: 2q+2
       498: 2q+2
       499: 2
       500: 2
       501: 2
       503: q+2
       505: q+2
       507: q+2
       508: q+2
       509: q+2
       510: q+2
       511: 2
       512: 2
       513: 2
       514: 2
       515: q+2
       516: q+2
       517: q+2
       518: q+2
       519: q+2
       520: q+2
       522: q+1
       523: q+1
       526: q+1
       527: q+1
       530: q+1
       531: q+1
       534: 1
       535: 1
       538: 1
       540: 1
       542: 1
       544: 1
       546: 1
       548: 1
       550: 1
       551: 1
       554: 1
       556: 1
       558: 1
       560: 1
       562: 1
       564: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       576: 1
       581: 2
       584: 2q+2
       586: 2q+2
       588: 2q+2
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: q+1
       596: q+1
       598: q+2
       600: q+2
       602: q+2
       603: 1
       604: 1
       606: 2
       607: q+1
       608: q+1
       610: 2
       612: 2
       614: 2
       615: 1
       616: 1
       618: 2
       619: q+1
       620: q+1
       621: 1
       622: 1
       624: 2
       626: 2
       628: 2
       630: 2
       631: 1
       632: 1
       634: 2
       636: q+2
       638: q+2
       640: q+2
       641: 1
       642: 1
       643: 1
       644: 1
       646: 2
       647: 1
       648: 1
       649: 1
       650: 1
       652: 2
       654: 2
       656: 2
       657: q+2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q+2
       667: q+2
       669: q+2
       671: q+2
       672: q+2
       673: q+2
       674: 2
       675: 2
       676: 2q+2
       677: 2
       678: 2
       679: 2
       680: 2
       681: 2q+2
       682: 2
       683: 2
       684: 2
       685: 2
       686: q+2
       687: 2
       688: 2
       689: 1
       690: q+2
       691: q+2
       692: q+2
       699: 1
       700: 1
       706: q+1
       707: q+1
       710: q+1
       711: q+1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       724: 1
       726: 1
       728: 1
       730: 1
       732: 1
       734: 1
       736: 1
       738: 1
       740: 1
       742: 1
       744: 1
       746: 1
       748: 1
       750: 1
       752: 1
       754: 1
       755: 1
       759: 1
       760: 1
       763: 1
       764: 1
       766: 1
       767: 1
       773: 2
       776: q+2
       778: 2q+2
       780: q+2
       782: q+2
       784: q+2
       785: 1
       786: 1
       787: 1
       788: 1
       790: q+2
       792: 2
       793: 1
       794: 1
       796: 2
       798: 2
       800: 2
       801: 1
       802: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       810: 2
       812: 2
       814: 2
       815: 1
       816: 1
       817: 1
       818: 1
       820: 2
       822: 2
       824: 2
       825: q+1
       826: q+1
       827: 1
       828: 1
       831: 1
       832: 1
       834: 2
       836: 2
       838: 2
       839: 1
       840: 1
       842: q+2
       844: 2
       845: 1
       846: 1
       847: 1
       848: 1
       850: 2
       852: 2
       854: 2
       856: 1
       858: 2
       860: q+2
       862: q+2
       864: q+2
       865: q+2
       866: q+2
       867: q+2
       868: q+2
       869: 2
       870: 2
       871: 2
       872: 2
       873: 2
       874: 2
       875: 2
       876: 2
       877: 2
       878: 2
       879: 1
       880: 1
       881: q+2
       882: q+2
       883: q+2
       890: 1
       891: 1
       897: q+1
       898: q+1
       901: 1
       903: 1
       905: 1
       907: 1
       909: 1
       910: 1
       913: 1
       915: 1
       917: 1
       919: 1
       921: 1
       923: 1
       929: 1
       931: 1
       933: 1
       935: 1
       937: 1
       939: 1
       941: 1
       943: 1
       945: 1
       947: 1
       949: 1
       951: 1
       957: 1
       959: 1
       962: 1
       963: 1
       965: 1
       966: 1
       972: 2
       976: 1
       977: 1
       980: 1
       981: 1
       986: 2
       989: 1
       990: 1
       993: q+2
       995: q+2
       997: q+2
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: q+2
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1009: 2
      1011: 2
      1013: 2
      1015: 2
      1016: 1
      1017: 1
      1019: 2
      1021: 2
      1023: 2
      1025: 2
      1026: 1
      1027: 1
      1031: 2
      1032: 1
      1033: 1
      1035: 2
      1037: 2
      1039: 2
      1043: 2
      1044: 1
      1045: 1
      1047: 2
      1049: 2
      1051: 2
      1052: 1
      1053: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+2
      1069: q+2
      1071: q+2
      1072: q+2
      1073: q+2
      1074: q+2
      1075: 2
      1076: 2
      1077: 2
      1078: 2
      1079: 2
      1080: 2
      1081: 2
      1082: 2
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1104: 1
      1105: 1
      1111: 1
      1113: 1
      1115: 1
      1117: 1
      1119: 1
      1121: 1
      1123: 1
      1125: 1
      1128: 1
      1129: 1
      1131: 1
      1132: 1
      1136: 1
      1137: 1
      1142: 2
      1145: 1
      1147: 1
      1149: 1
      1151: 1
      1157: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1171: 1
      1173: 1
      1175: 1
      1186: 1
      1187: 1
      1192: 2
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1211: q+2
      1213: q+2
      1215: q+2
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1221: 2
      1223: 2
      1225: 2
      1227: 2
      1228: 1
      1229: 1
      1231: 2
      1234: 1
      1235: 1
      1237: 2
      1239: 2
      1240: 1
      1241: 1
      1245: 2
      1246: 1
      1247: 1
      1249: 2
      1250: 1
      1251: 1
      1253: 2
      1257: 2
      1260: 1
      1261: 1
      1263: 2
      1265: 2
      1267: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+2
      1283: 2
      1284: 2
      1285: 2
      1286: 2
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1297: 1
      1308: 1
      1309: 1
      1315: 1
      1317: 1
      1319: 1
      1321: 1
      1324: 1
      1325: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1338: 2
      1341: 1
      1343: 1
      1353: 1
      1355: 1
      1357: 1
      1359: 1
      1373: 1
      1375: 1
      1377: 1
      1379: 1
      1381: 1
      1383: 1
      1408: 2
      1411: 1
      1412: 1
      1416: 1
      1417: 1
      1434: 1
      1437: 2
      1439: q+2
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1445: 2
      1447: 2
      1449: 2
      1453: 2
      1454: 1
      1455: 1
      1457: 2
      1459: 2
      1460: 1
      1461: 1
      1465: 1
      1471: 1
      1473: 1
      1475: 1
      1481: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 2
      1487: 1
      1488: 1
      1495: 1
      1496: 1
      1531: 1
      1532: 1
      1539: 1
      1540: 1
      1542: 1
      1544: 1
      1546: 1
      1548: 1
      1550: 1
      1551: 1
      1557: 2
      1561: 1
      1562: 1
      1568: 1
      1570: 1
      1584: 1
      1586: 1
      1635: 1
      1638: 2
      1640: 2
      1642: 1
      1644: 2
      1647: 1
      1648: 1
      1652: 2
      1653: 1
      1654: 1
      1660: 1
      1662: 1
      1668: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1681: 1
      1682: 1
      1727: 2
      1731: 1
      1732: 1
      1734: 1
      1735: 1
      1746: 1
      1748: 1
      1762: 1
      1764: 1
      1805: 1
      1816: 1
      1818: 1
      1824: 1
      1826: 1
      1828: 1
      1833: 1
      1840: 1
      1841: 1
      1930: 1
      1957: 1
      1959: 1
      1961: 1
      2030: 1

2031:    0: q^5+3q^4+5q^3+4q^2+2q
         1: q^5+3q^4+5q^3+4q^2+2q
         2: q^5+3q^4+5q^3+4q^2+2q
         3: q^5+3q^4+5q^3+4q^2+2q
         4: q^5+3q^4+5q^3+4q^2+2q
         5: q^5+3q^4+5q^3+4q^2+2q
         6: q^5+3q^4+5q^3+4q^2+2q
         7: q^5+3q^4+5q^3+4q^2+2q
         8: q^5+3q^4+5q^3+4q^2+2q
         9: q^6+2q^5+3q^4+4q^3+3q^2+2q
        10: 2q^4+4q^3+4q^2+2q
        11: 2q^4+4q^3+4q^2+2q
        12: 2q^4+4q^3+4q^2+2q
        13: q^5+3q^4+5q^3+4q^2+2q
        14: q^5+3q^4+5q^3+4q^2+2q
        15: q^5+3q^4+5q^3+4q^2+2q
        16: 2q^4+4q^3+4q^2+2q
        17: 2q^4+4q^3+4q^2+2q
        18: q^5+2q^4+4q^3+3q^2+2q
        19: q^5+3q^4+5q^3+4q^2+2q
        20: q^5+3q^4+5q^3+4q^2+2q
        21: q^5+3q^4+5q^3+4q^2+2q
        22: 2q^4+4q^3+4q^2+2q
        23: 2q^4+4q^3+4q^2+2q
        24: 2q^4+4q^3+4q^2+2q
        25: 2q^4+4q^3+4q^2+2q
        26: 2q^4+4q^3+4q^2+2q
        27: 2q^4+4q^3+4q^2+2q
        28: q^4+3q^3+4q^2+2q
        29: 2q^4+4q^3+4q^2+2q
        30: q^5+3q^4+5q^3+4q^2+2q
        31: q^4+3q^3+4q^2+2q
        32: 2q^4+4q^3+4q^2+2q
        33: q^4+3q^3+4q^2+2q
        34: q^4+3q^3+4q^2+2q
        35: 2q^4+4q^3+4q^2+2q
        36: q^4+3q^3+4q^2+2q
        38: 2q^4+4q^3+4q^2+2q
        40: 2q^4+4q^3+4q^2+2q
        42: 2q^4+4q^3+4q^2+2q
        43: 2q^4+4q^3+4q^2+2q
        44: 2q^4+4q^3+4q^2+2q
        45: 2q^4+4q^3+4q^2+2q
        46: 2q^4+4q^3+4q^2+2q
        47: 2q^4+4q^3+4q^2+2q
        48: q^5+2q^4+4q^3+3q^2+2q
        49: 2q^4+4q^3+4q^2+2q
        50: 2q^4+4q^3+4q^2+2q
        51: q^5+2q^4+4q^3+3q^2+2q
        52: 2q^4+4q^3+4q^2+2q
        53: 2q^4+4q^3+4q^2+2q
        54: 2q^4+4q^3+4q^2+2q
        55: 2q^4+4q^3+4q^2+2q
        56: 2q^4+4q^3+4q^2+2q
        57: 2q^4+4q^3+4q^2+2q
        58: q^3+2q^2+q
        59: q^3+2q^2+q
        60: q^3+2q^2+q
        61: q^3+2q^2+q
        63: q^4+3q^3+4q^2+2q
        65: 2q^4+4q^3+4q^2+2q
        67: q^4+3q^3+4q^2+2q
        68: q^4+3q^3+4q^2+2q
        69: q^4+3q^3+3q^2+2q
        70: 2q^4+4q^3+4q^2+2q
        71: q^4+3q^3+4q^2+2q
        72: q^4+3q^3+4q^2+2q
        73: q^4+3q^3+4q^2+2q
        75: 2q^4+4q^3+4q^2+2q
        77: 2q^4+4q^3+4q^2+2q
        79: 2q^4+4q^3+4q^2+2q
        80: q^4+3q^3+4q^2+2q
        81: q^4+3q^3+4q^2+2q
        82: q^4+3q^3+4q^2+2q
        83: 2q^4+4q^3+4q^2+2q
        84: q^4+3q^3+4q^2+2q
        85: q^4+3q^3+4q^2+2q
        86: q^4+3q^3+4q^2+2q
        87: 2q^4+4q^3+4q^2+2q
        88: 3q^3+4q^2+2q
        89: 3q^3+4q^2+2q
        90: q^4+3q^3+3q^2+2q
        91: 2q^4+4q^3+4q^2+2q
        92: 2q^4+4q^3+4q^2+2q
        93: q^5+2q^4+4q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: q^4+3q^3+3q^2+2q
       101: q^4+3q^3+3q^2+2q
       102: q^4+3q^3+3q^2+2q
       104: q^3+2q^2+q
       105: q^3+2q^2+q
       107: q^3+2q^2+q
       108: q^3+2q^2+q
       109: q^3+2q^2+q
       110: q^3+2q^2+q
       112: q^4+3q^3+4q^2+2q
       114: q^4+3q^3+4q^2+2q
       116: 2q^4+4q^3+4q^2+2q
       117: q^3+2q^2+q
       118: q^3+2q^2+q
       119: q^3+2q^2+q
       120: q^3+2q^2+q
       122: q^4+3q^3+4q^2+2q
       124: q^4+3q^3+4q^2+2q
       125: 3q^3+4q^2+2q
       126: 2q^3+3q^2+2q
       128: 3q^3+4q^2+2q
       130: 3q^3+4q^2+2q
       132: q^4+3q^3+3q^2+2q
       133: q^4+3q^3+4q^2+2q
       134: q^4+3q^3+3q^2+2q
       135: q^4+3q^3+4q^2+2q
       136: q^4+3q^3+4q^2+2q
       137: 2q^3+4q^2+2q
       138: 2q^3+3q^2+2q
       139: 2q^3+4q^2+2q
       140: q^3+2q^2+2q
       141: q^4+3q^3+4q^2+2q
       142: 3q^3+4q^2+2q
       143: 2q^3+4q^2+2q
       144: 2q^3+3q^2+2q
       145: 2q^3+4q^2+2q
       146: q^4+3q^3+4q^2+2q
       147: 3q^3+4q^2+2q
       148: q^3+2q^2+2q
       149: q^4+2q^3+3q^2+2q
       150: q^4+3q^3+3q^2+2q
       152: q^4+3q^3+3q^2+2q
       154: q^4+3q^3+3q^2+2q
       156: q^4+3q^3+3q^2+2q
       157: 3q^3+4q^2+2q
       158: 3q^3+4q^2+2q
       159: q^4+3q^3+3q^2+2q
       160: 3q^3+4q^2+2q
       161: 3q^3+4q^2+2q
       162: q^4+3q^3+3q^2+2q
       163: 3q^3+4q^2+2q
       164: 3q^3+4q^2+2q
       165: q^4+3q^3+3q^2+2q
       166: q^3+3q^2+2q
       167: q^3+3q^2+2q
       168: 2q^3+2q^2+2q
       170: q^3+2q^2+q
       171: q^3+2q^2+q
       174: q^3+2q^2+q
       175: q^3+2q^2+q
       178: 2q^3+3q^2+2q
       180: 2q^3+4q^2+2q
       182: 3q^3+4q^2+2q
       183: q^3+2q^2+q
       184: q^3+2q^2+q
       185: q^3+2q^2+q
       186: q^3+2q^2+q
       188: q^4+3q^3+4q^2+2q
       190: q^4+3q^3+4q^2+2q
       191: q^3+2q^2+q
       192: q^3+2q^2+q
       193: q^2+q
       194: q^2+q
       195: q^3+2q^2+q
       196: q^3+2q^2+q
       198: q^3+2q^2+2q
       199: q^3+2q^2+q
       200: q^3+2q^2+q
       201: q^3+2q^2+q
       202: q^3+2q^2+q
       203: q^2+q
       204: q^2+q
       206: q^3+2q^2+2q
       208: 2q^3+4q^2+2q
       210: q^4+2q^3+3q^2+2q
       212: q^4+3q^3+3q^2+2q
       214: 3q^3+4q^2+2q
       216: 3q^3+4q^2+2q
       218: q^4+3q^3+3q^2+2q
       219: 2q^3+3q^2+2q
       220: 3q^3+4q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+4q^2+2q
       223: 2q^3+3q^2+2q
       224: 2q^3+4q^2+2q
       225: 2q^3+3q^2+2q
       226: q^3+3q^2+2q
       227: 2q^3+4q^2+2q
       228: 2q^3+3q^2+2q
       229: q^3+2q^2+2q
       230: 3q^3+4q^2+2q
       231: q^3+3q^2+2q
       232: 2q^3+4q^2+2q
       233: 2q^3+3q^2+2q
       234: 3q^3+4q^2+2q
       235: q^3+2q^2+2q
       236: q^3+2q^2+2q
       238: q^3+3q^2+2q
       240: q^3+3q^2+2q
       242: 2q^3+2q^2+2q
       243: q^3+3q^2+2q
       244: 2q^2+2q
       245: 2q^2+2q
       246: q^4+2q^3+3q^2+2q
       247: q^3+3q^2+2q
       248: q^3+3q^2+2q
       249: 2q^3+2q^2+2q
       250: 4q^2+2q
       251: 4q^2+2q
       252: q^3+3q^2+2q
       253: 4q^2+2q
       254: 4q^2+2q
       255: q^3+3q^2+2q
       256: q^3+3q^2+2q
       257: q^3+3q^2+2q
       258: 2q^3+2q^2+2q
       260: q^3+2q^2+q
       261: q^3+2q^2+q
       264: q^3+2q^2+q
       265: q^3+2q^2+q
       268: q^2+q
       270: q^2+q
       272: q^2+q
       274: q^2+q
       276: q^3+2q^2+q
       277: q^3+2q^2+q
       280: 2q^3+4q^2+2q
       282: 2q^3+3q^2+2q
       283: q^2+q
       284: q^2+q
       285: q^2+q
       286: q^2+q
       288: q^3+3q^2+2q
       290: 3q^3+4q^2+2q
       292: 2q^3+3q^2+2q
       293: q^3+2q^2+q
       294: q^3+2q^2+q
       295: q^3+2q^2+q
       296: q^3+2q^2+q
       298: 2q^3+4q^2+2q
       299: q^2+q
       300: q^2+q
       302: 2q^2+2q
       303: q^3+2q^2+q
       304: q^3+2q^2+q
       306: q^3+2q^2+2q
       307: q^3+2q^2+q
       308: q^3+2q^2+q
       309: q^2+q
       310: q^2+q
       312: 2q^2+2q
       314: q^3+2q^2+2q
       316: q^3+2q^2+2q
       318: q^3+3q^2+2q
       319: q^2+q
       320: q^2+q
       321: q^2+q
       322: q^2+q
       324: 2q^2+2q
       326: q^4+2q^3+3q^2+2q
       328: 4q^2+2q
       330: 4q^2+2q
       332: q^3+3q^2+2q
       333: 2q^3+3q^2+2q
       334: q^3+3q^2+2q
       335: q^3+3q^2+2q
       336: q^3+2q^2+2q
       337: q^3+3q^2+2q
       339: q^3+3q^2+2q
       341: q^3+3q^2+2q
       343: 2q^3+2q^2+2q
       344: q^3+3q^2+2q
       345: 4q^2+2q
       346: 3q^2+2q
       347: 2q^2+2q
       348: q^2+2q
       349: 4q^2+2q
       350: 2q^3+3q^2+2q
       351: 2q^2+2q
       352: q^3+3q^2+2q
       353: 4q^2+2q
       354: 3q^2+2q
       355: 4q^2+2q
       356: 2q^3+3q^2+2q
       357: 2q^2+2q
       358: q^2+2q
       359: 2q^2+2q
       361: q^3+3q^2+2q
       363: q^3+3q^2+2q
       365: 2q^3+2q^2+2q
       366: q^3+2q^2+2q
       367: q^3+3q^2+2q
       368: q^3+2q^2+2q
       369: 2q^2+2q
       370: 2q^2+2q
       371: q^3+3q^2+2q
       372: q^3+3q^2+2q
       373: 2q^3+2q^2+2q
       374: q^2+2q
       375: q^2+2q
       376: q^2+2q
       378: q^2+q
       379: q^2+q
       382: q^3+2q^2+q
       383: q^3+2q^2+q
       386: q^3+2q^2+q
       387: q^3+2q^2+q
       390: q^2+q
       392: q^2+q
       394: q^2+q
       395: q^2+q
       398: q^2+q
       400: q^2+q
       402: q^2+q
       403: q^2+q
       407: q^2+q
       408: q^2+q
       410: 4q^2+2q
       412: 3q^2+2q
       414: q^3+3q^2+2q
       416: 4q^2+2q
       418: 2q^3+3q^2+2q
       419: q^2+q
       420: q^2+q
       421: q^2+q
       422: q^2+q
       424: q^3+3q^2+2q
       426: q^3+2q^2+2q
       428: q^3+3q^2+2q
       429: q
       430: q
       431: q^2+q
       432: q^2+q
       434: q^2+2q
       436: 2q^2+2q
       437: q^2+q
       438: q^2+q
       439: 2q^2+q
       440: 2q^2+q
       442: 2q^2+2q
       443: q^2+q
       444: q^2+q
       446: 2q^2+2q
       447: q^2+q
       448: q^2+q
       449: q
       450: q
       452: q^2+2q
       453: 2q^2+q
       454: 2q^2+q
       456: 2q^2+2q
       457: q^2+q
       458: q^2+q
       460: 2q^2+2q
       461: q^2+q
       462: q^2+q
       464: 2q^2+2q
       466: q^3+3q^2+2q
       468: q^3+2q^2+2q
       470: q^3+2q^2+2q
       471: q^2+q
       472: q^2+q
       473: q^2+q
       474: q^2+q
       476: 2q^2+2q
       478: 3q^2+2q
       480: 2q^2+2q
       481: q^3+3q^2+2q
       482: q^3+3q^2+2q
       483: q^3+2q^2+2q
       484: q^3+3q^2+2q
       486: q^3+3q^2+2q
       488: q^3+3q^2+2q
       490: 2q^3+2q^2+2q
       491: q^3+2q^2+2q
       492: 3q^2+2q
       493: q^2+2q
       494: 3q^2+2q
       495: q^2+2q
       496: 2q^2+2q
       497: 3q^2+2q
       498: 3q^2+2q
       499: q^2+2q
       500: q^2+2q
       501: 2q^2+2q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: q^3+2q^2+2q
       509: q^2+2q
       510: q^2+2q
       511: 2q
       512: q^2+2q
       513: 2q
       514: q^2+2q
       515: q^2+2q
       516: q^2+2q
       517: q^2+2q
       518: q^2+2q
       519: q^2+2q
       520: q^2+2q
       522: q^2+q
       523: q^2+q
       526: 2q^2+q
       527: 2q^2+q
       530: q^2+q
       531: q^2+q
       534: q
       535: q
       538: q^2+q
       540: q^2+q
       542: q^2+q
       544: q^2+q
       546: q^2+q
       548: q^2+q
       550: q
       551: q
       554: q^2+q
       556: q^2+q
       558: q^2+q
       560: q^2+q
       562: q^2+q
       564: q^2+q
       566: q^2+q
       567: q^2+q
       571: q^2+q
       572: q^2+q
       574: q^2+q
       576: q^2+q
       581: 2q^2+2q
       582: q^2
       584: 3q^2+2q
       586: q^3+3q^2+2q
       588: 3q^2+2q
       589: q^2+q
       590: q^2+q
       591: q
       592: q
       593: q
       594: q
       595: q^2+q
       596: q^2+q
       598: q^3+2q^2+2q
       600: q^3+2q^2+2q
       602: q^3+3q^2+2q
       603: q
       604: q
       606: q^2+2q
       607: q^2+q
       608: q^2+q
       610: q^2+2q
       612: 2q
       614: q^2+2q
       615: q^2+q
       616: q^2+q
       618: 2q^2+2q
       619: q^2+q
       620: q^2+q
       621: q
       622: q
       624: q^2+2q
       626: q^2+2q
       628: 2q
       630: q^2+2q
       631: q^2+q
       632: q^2+q
       634: 2q^2+2q
       636: q^2+2q
       638: q^2+2q
       640: q^3+2q^2+2q
       641: q
       642: q
       643: q
       644: q
       646: q^2+2q
       647: q
       648: q
       649: q
       650: q
       652: 3q^2+2q
       654: 2q
       656: 2q^2+2q
       657: q^2+2q
       659: q^2+2q
       661: q^2+2q
       663: q^2+2q
       664: q^2+2q
       665: q^3+2q^2+2q
       667: q^2+2q
       669: q^2+2q
       671: q^2+2q
       672: q^2+2q
       673: q^2+2q
       674: 2q
       675: q^2+2q
       676: 3q^2+2q
       677: q^2+2q
       678: 2q
       679: q^2+2q
       680: 2q
       681: 3q^2+2q
       682: q^2+2q
       683: q^2+2q
       684: 2q
       685: q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q
       689: q
       699: q^2+q
       700: q^2+q
       706: q^2+q
       707: q^2+q
       710: q^2+q
       711: q^2+q
       714: q
       715: q
       718: q
       719: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: q^2+q
       736: q^2+q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: q^2+q
       752: q^2+q
       754: q
       755: q
       759: q^2+q
       760: q^2+q
       763: q
       764: q
       766: q^2+q
       767: q^2+q
       773: 2q^2+2q
       774: q^2
       776: q^2+2q
       778: 3q^2+2q
       780: q^2+2q
       782: q^3+2q^2+2q
       784: q^2+2q
       785: q
       786: q
       787: q
       788: q
       790: q^2+2q
       792: q^2+2q
       793: q
       794: q
       796: 2q
       798: q^2+2q
       800: 2q
       801: q
       802: q
       805: q
       806: q
       807: q^2+q
       808: q^2+q
       810: q^2+2q
       812: q^2+2q
       814: 2q
       815: q
       816: q
       817: q
       818: q
       820: 2q
       822: q^2+2q
       824: 2q
       825: q^2+q
       826: q^2+q
       827: q
       828: q
       831: q
       832: q
       834: q^2+2q
       836: q^2+2q
       838: 2q
       839: q
       840: q
       842: q^2+2q
       844: 2q
       845: q
       846: q
       847: q
       848: q
       850: q^2+2q
       852: 2q
       854: 4q
       856: q
       858: 2q
       866: q^2+2q
       868: q^2+2q
       870: 2q
       871: q^2+2q
       872: 2q
       874: 2q
       875: q^2+2q
       876: 2q
       877: 2q
       878: 2q
       879: q
       880: q
       890: q^2+q
       891: q^2+q
       897: q^2+q
       898: q^2+q
       901: q
       903: q
       905: q
       907: q
       909: q
       910: q
       913: q
       915: q
       917: q
       919: q
       921: q
       923: q
       929: q
       931: q
       933: q
       935: q
       937: q
       939: q
       941: q
       943: q
       945: q
       947: q
       949: q
       951: q
       957: q
       959: q
       962: q
       963: q
       965: q
       966: q
       972: 2q
       976: q
       977: q
       980: 2q
       981: 2q
       986: 2q
       987: 2q
       989: q
       990: q
       995: q^2+2q
       998: q
       999: q
      1000: q
      1001: q
      1003: q^2+2q
      1004: q
      1005: q
      1006: q
      1007: q
      1009: 2q
      1011: q^2+2q
      1013: 2q
      1019: 2q
      1021: 2q
      1023: q^2+2q
      1025: 2q
      1026: q
      1027: q
      1035: 2q
      1037: 2q
      1039: q^2+2q
      1043: 2q
      1044: q
      1045: q
      1049: 2q
      1051: 3q
      1052: q
      1053: q
      1058: q
      1059: q
      1061: q
      1063: q
      1065: q
      1076: 2q
      1078: 2q
      1080: 2q
      1082: 2q
      1083: q
      1084: q
      1085: q
      1092: q
      1093: q
      1104: q
      1105: q
      1108: q
      1109: q
      1111: q
      1113: q
      1115: q
      1117: q
      1119: q
      1121: q
      1123: q
      1125: q
      1128: q
      1129: q
      1131: q
      1132: q
      1136: q
      1137: q
      1142: 2q
      1149: q
      1151: q
      1157: q
      1159: q
      1169: q
      1171: q
      1173: q
      1175: q
      1186: q
      1187: q
      1193: q
      1200: q
      1201: q
      1221: 2q
      1223: 3q
      1231: 2q
      1234: q
      1235: q
      1239: 2q
      1240: q
      1241: q
      1249: 2q
      1250: q
      1251: q
      1257: 2q
      1260: q
      1261: q
      1265: 3q
      1267: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1287: q
      1289: q
      1296: q
      1297: q
      1324: q
      1325: q
      1332: q
      1333: q
      1339: q
      1353: q
      1355: q
      1357: q
      1359: q
      1377: q
      1379: q
      1381: q
      1383: q
      1409: q
      1416: q
      1417: q
      1434: q
      1447: 3q
      1465: q
      1471: q
      1475: q
      1481: q
      1484: q
      1558: q
      1561: q
      1562: q
      1638: 2
      1642: q
      1672: q
      1728: 2
      1731: 1
      1732: 1
      1824: 1
      1844: 1
      1845: 1
      1931: 1
      1959: 1
      2031: 1

2032:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: 2q^2+q+1
        61: 2q
        62: 2q^2+2q+1
        63: q^2+q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q^2+q+1
       104: q^2
       105: q
       106: q
       107: 2q^2+q+1
       108: 2q
       109: 2q^2+2q+1
       110: q^2+q
       111: q^2+2q+1
       112: q^2+q
       113: 2q^2+2q+1
       114: q^2+q
       115: 2q^2+2q+1
       116: q^2+q
       117: 2q^2+2q+1
       118: q^2+q
       119: 2q^2+q+1
       120: 2q
       121: 2q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q^2+q+1
       170: q^2
       171: q
       172: q
       173: q^2+q+1
       174: q^2
       175: q
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q^2+q+1
       184: 2q
       185: 2q^2+2q+1
       186: q^2+q
       187: q^2+2q+1
       188: q^2+q
       189: 2q^2+2q+1
       190: q^2+q
       191: 2q^2+2q+1
       192: q^2+q
       193: 2q^2+q+1
       194: 2q
       195: 2q^2+2q+1
       196: q^2+q
       197: q^2+2q+1
       198: q^2+q
       199: 2q^2+q+1
       200: 2q
       201: q^2+q+1
       202: 2q
       203: 2q+1
       205: q+1
       206: q
       207: q^2+2q+1
       208: q^2+q
       209: 2q^2+2q+1
       210: q^2+q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 2q^2+3q+1
       223: q^2+2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^2+2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 2q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q+1
       262: q
       263: q^2+q+1
       264: q^2
       265: q
       266: q
       267: q^2+q+1
       268: q^2
       269: q
       270: q
       271: q+1
       272: q
       275: q^2+q+1
       276: q^2
       277: q
       278: q
       279: 2q+1
       281: q+1
       283: q^2+1
       284: q
       285: q^2+q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q^2+q+1
       294: 2q
       295: 2q^2+2q+1
       296: q^2+q
       297: q^2+2q+1
       298: q^2+q
       299: 2q^2+q+1
       300: 2q
       301: 2q+1
       303: 2q^2+2q+1
       304: q^2+q
       305: q^2+2q+1
       306: q^2+q
       307: q^2+q+1
       308: 2q
       309: 2q+1
       311: q+1
       313: q+1
       314: q
       315: q+1
       317: 2q+1
       319: q^2+q+1
       320: 2q
       321: 2q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: 2q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: 2q^2+3q+1
       348: q^2+2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: q^2+2q+1
       353: q^2+3q+1
       354: q^2+2q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 2q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       377: 1
       381: q+1
       384: q
       385: q^2+q+1
       386: q^2
       387: q
       388: q
       389: q+1
       391: q
       393: q^2+q+1
       394: q^2
       395: q
       396: q
       397: q+1
       401: q+1
       402: q
       405: q+1
       408: q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q^2+1
       420: q
       421: q^2+q+1
       423: q+1
       425: q+1
       427: 2q+1
       429: q^2+1
       430: q
       431: q^2+q+1
       433: q+1
       435: 2q+1
       437: 2q^2+q+1
       438: 2q
       439: 2q^2+2q+1
       440: q^2+q
       441: q^2+2q+1
       442: q^2+q
       443: q^2+q+1
       444: 2q
       445: 2q+1
       447: q^2+1
       448: q
       449: q+1
       451: 1
       453: q^2+q+1
       454: 2q
       455: q+1
       457: 2q+1
       459: q+1
       460: q
       461: 2q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: q^2+q+1
       472: 2q
       473: 2q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: q^2+3q+1
       512: q^2+2q+1
       513: 2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       521: 1
       525: q+1
       528: q
       529: 1
       533: 1
       537: q+1
       539: q
       541: q^2+q+1
       542: q^2
       543: q
       544: q
       545: q+1
       547: q
       549: 1
       553: q+1
       557: q+1
       558: q
       561: q+1
       565: q+1
       567: q
       569: q+1
       573: q+1
       576: q
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+1
       590: q
       591: q+1
       593: q^2+1
       594: q
       595: q^2+q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: q^2+1
       604: q
       605: q+1
       607: q^2+q+1
       609: q+1
       611: 2q+1
       613: q+1
       615: q^2+q+1
       616: 2q
       617: 2q+1
       619: q^2+1
       620: q
       621: q+1
       623: 1
       625: 1
       627: q+1
       629: 1
       631: 2q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: q^2+1
       642: q
       643: q+1
       645: 1
       647: q^2+q+1
       648: 2q
       649: 2q+1
       651: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q^2+2q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: q+2
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q^2+2q+1
       678: q^2+3q+1
       679: q^2+2q+1
       680: 2
       681: q^2+2q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q+1
       731: q
       733: q+1
       735: q
       737: 1
       741: 1
       745: q+1
       749: q+1
       753: 1
       757: q+1
       761: q+1
       764: q
       765: q+1
       767: q
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: q^2+1
       786: q
       787: q+1
       789: 2q+1
       791: 1
       793: 1
       794: 1
       795: q+2
       797: q+1
       799: q+1
       801: q^2+1
       802: q
       803: q+1
       805: q^2+1
       806: q
       807: q^2+q+1
       809: q+1
       811: q+1
       813: 2q+1
       815: q^2+q+1
       816: 2q
       817: 2
       819: 2
       821: 1
       823: 1
       825: q^2+1
       826: q
       827: q+1
       831: q+1
       833: 1
       835: 1
       837: q+1
       839: 2q+1
       841: q+1
       843: 1
       844: 1
       845: q^2+1
       846: q
       847: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: q+2
       870: q+2
       871: q^2+2q+1
       872: q^2+2q+1
       873: 2
       874: 2
       875: q+1
       876: q+1
       877: q^2+2q+1
       878: q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       918: 1
       920: 1
       924: 1
       928: 1
       932: q+1
       934: q
       936: 1
       940: 2
       944: 1
       948: 1
       956: q+1
       960: 1
       964: 1
       966: 1
       968: 1
       971: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
       990: q
       992: 2
       994: 2
       996: q+2
       998: 2
      1000: 1
      1001: 1
      1002: q+1
      1004: q^2+1
      1005: q
      1006: q+1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: q+1
      1020: q+2
      1022: q+1
      1024: q+1
      1026: q^2+1
      1027: q
      1028: q+1
      1030: 2
      1032: 2
      1034: 1
      1036: 2
      1038: 1
      1042: 1
      1044: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q^2+1
      1053: q
      1054: q+1
      1058: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+2
      1068: q+2
      1070: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 2
      1077: q+2
      1078: q^2+2q+1
      1079: 2
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: q+1
      1086: 1
      1090: 1
      1098: q+1
      1110: 1
      1114: 2
      1118: 1
      1122: 1
      1124: 1
      1126: 1
      1130: 1
      1132: 1
      1134: 1
      1138: 1
      1141: 1
      1144: 1
      1146: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1164: 2
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1196: 1
      1198: 1
      1202: 1
      1210: 2
      1212: q+2
      1214: 2
      1216: 2
      1218: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: q+2
      1228: 1
      1229: 1
      1230: 2
      1232: 2
      1234: 1
      1235: 1
      1236: q+2
      1238: q+1
      1240: q^2+1
      1241: q
      1242: q+1
      1244: 2
      1246: 2
      1248: 1
      1250: 1
      1252: 2
      1256: 1
      1260: q+1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1270: q+1
      1272: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1294: 1
      1302: 1
      1306: 1
      1314: 2
      1318: 1
      1320: 1
      1322: 1
      1326: 1
      1328: 1
      1330: 1
      1334: 1
      1337: 1
      1340: 1
      1342: 1
      1344: 1
      1348: 2
      1352: 1
      1356: 1
      1358: 1
      1360: 1
      1364: 1
      1365: 1
      1368: 1
      1372: 2
      1376: 1
      1380: 1
      1404: 1
      1407: 1
      1410: 1
      1412: 1
      1414: 1
      1418: 1
      1430: 1
      1433: 1
      1438: 2
      1440: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1448: 2
      1450: 2
      1452: q+2
      1454: 1
      1455: 1
      1456: 1
      1458: 2
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 2
      1474: 1
      1478: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1489: 1
      1493: 1
      1501: 1
      1504: 1
      1525: 1
      1529: 1
      1541: 2
      1545: 1
      1547: 1
      1549: 1
      1551: 1
      1553: 1
      1556: 1
      1559: 1
      1563: 2
      1567: 1
      1569: 1
      1571: 1
      1575: 1
      1576: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1634: 1
      1641: 1
      1643: 2
      1645: 2
      1647: 1
      1648: 1
      1649: 1
      1651: 1
      1653: 1
      1661: 1
      1663: 1
      1667: 2
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1679: 1
      1687: 1
      1690: 1
      1737: 2
      1745: 1
      1747: 1
      1749: 1
      1750: 1
      1753: 1
      1757: 1
      1761: 1
      1785: 1
      1801: 1
      1804: 1
      1815: 1
      1819: 1
      1827: 1
      1829: 1
      1833: 1
      1846: 1
      1849: 1
      1902: 1
      1932: 1
      1956: 1
      1962: 1
      2032: 1

2033:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: 2q^2+2q+1
        59: q^2+q
        60: 2q
        61: 2q^2+q+1
        62: q^2+q
        63: 2q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q
       105: q^2+q+1
       106: q^2
       107: 2q
       108: 2q^2+q+1
       109: 2q^2+2q+1
       110: q^2+q
       111: q^2+q
       112: q^2+2q+1
       113: q^2+q
       114: 2q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: q^2+q
       119: 2q
       120: 2q^2+q+1
       121: q^2+q
       122: 2q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q
       171: q^2+q+1
       172: q^2
       173: q
       174: q
       175: q^2+q+1
       176: q^2
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q
       184: 2q^2+q+1
       185: 2q^2+2q+1
       186: q^2+q
       187: q^2+q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: 2q^2+2q+1
       192: q^2+q
       193: 2q
       194: 2q^2+q+1
       195: 2q^2+2q+1
       196: q^2+q
       197: q^2+q
       198: q^2+2q+1
       199: 2q
       200: 2q^2+q+1
       201: 2q
       202: q^2+q+1
       203: 2q+1
       205: q
       206: q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+q
       210: 2q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 2q^2+3q+1
       223: q^2+2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^2+2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 2q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q
       261: q+1
       263: q
       264: q
       265: q^2+q+1
       266: q^2
       267: q
       268: q
       269: q^2
       270: q^2+q+1
       271: q
       272: q+1
       275: q
       276: q
       277: q^2+q+1
       278: q^2
       280: 2q+1
       282: q+1
       283: q
       284: q^2+1
       285: q^2+q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q
       294: 2q^2+q+1
       295: 2q^2+2q+1
       296: q^2+q
       297: q^2+q
       298: q^2+2q+1
       299: 2q
       300: 2q^2+q+1
       302: 2q+1
       303: 2q^2+2q+1
       304: q^2+q
       305: q^2+q
       306: q^2+2q+1
       307: 2q
       308: q^2+q+1
       309: 2q+1
       312: q+1
       313: q
       314: q+1
       316: q+1
       318: 2q+1
       319: 2q
       320: q^2+q+1
       321: 2q+1
       323: q
       324: q+1
       325: q^2+q
       326: 2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: 2q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: 2q^2+3q+1
       348: q^2+2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: q^2+2q+1
       353: q^2+3q+1
       354: q^2+2q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 2q+1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       379: 1
       382: q
       383: q+1
       385: q
       386: q
       387: q^2+q+1
       388: q^2
       390: q
       392: q+1
       393: q
       394: q
       395: q^2+q+1
       396: q^2
       398: q+1
       401: q
       402: q+1
       405: q
       408: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q
       420: q^2+1
       421: q^2+q+1
       424: q+1
       426: q+1
       428: 2q+1
       429: q
       430: q^2+1
       431: q^2+q+1
       434: q+1
       436: 2q+1
       437: 2q
       438: 2q^2+q+1
       439: 2q^2+2q+1
       440: q^2+q
       441: q^2+q
       442: q^2+2q+1
       443: 2q
       444: q^2+q+1
       446: 2q+1
       447: q
       448: q^2+1
       449: q+1
       452: 1
       453: 2q
       454: q^2+q+1
       456: q+1
       457: 2q+1
       459: q
       460: q+1
       461: 2q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 2q
       472: q^2+q+1
       473: 2q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 2q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: q^2+3q+1
       512: q^2+2q+1
       513: 2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       523: 1
       526: q
       527: q+1
       531: 1
       535: 1
       538: q
       540: q+1
       541: q
       542: q
       543: q^2
       544: q^2+q+1
       546: q
       548: q+1
       550: 1
       554: q+1
       557: q
       558: q+1
       562: q+1
       565: q
       567: q+1
       572: q+1
       573: q
       576: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: q^2+1
       591: q+1
       593: q
       594: q^2+1
       595: q^2+q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q
       604: q^2+1
       606: q+1
       607: q^2+q+1
       610: q+1
       612: 2q+1
       614: q+1
       615: 2q
       616: q^2+q+1
       618: 2q+1
       619: q
       620: q^2+1
       621: q+1
       624: 1
       626: 1
       628: q+1
       630: 1
       631: 2q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: q
       642: q^2+1
       643: q+1
       646: 1
       647: 2q
       648: q^2+q+1
       649: 2q+1
       652: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q^2+2q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: q+2
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q^2+2q+1
       678: q^2+3q+1
       679: q^2+2q+1
       680: 2
       681: q^2+2q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       700: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       730: q
       732: q+1
       734: q
       736: q+1
       738: 1
       742: 1
       746: q+1
       750: q+1
       755: 1
       760: q+1
       761: q
       764: q+1
       765: q
       767: q+1
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: q
       786: q^2+1
       787: q+1
       790: 2q+1
       792: 1
       793: 1
       794: 1
       796: q+2
       798: q+1
       800: q+1
       801: q
       802: q^2+1
       803: q+1
       805: q
       806: q^2+1
       807: q^2+q+1
       810: q+1
       812: q+1
       814: 2q+1
       815: 2q
       816: q^2+q+1
       817: 2
       820: 2
       822: 1
       824: 1
       825: q
       826: q^2+1
       827: q+1
       831: q+1
       834: 1
       836: 1
       838: q+1
       839: 2q+1
       842: q+1
       843: 1
       844: 1
       845: q
       846: q^2+1
       847: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q
       858: q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: q+2
       870: q+2
       871: q^2+2q+1
       872: q^2+2q+1
       873: 2
       874: 2
       875: q+1
       876: q+1
       877: q^2+2q+1
       878: q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       917: 1
       919: 1
       923: 1
       925: 1
       931: 1
       933: q
       935: q+1
       937: 1
       941: 2
       945: 1
       949: 1
       957: q+1
       963: 1
       964: 1
       966: 1
       969: 1
       972: 1
       977: 1
       981: q+1
       986: q+1
       988: q
       990: q+1
       993: 2
       995: 2
       997: q+2
       998: 2
      1000: 1
      1001: 1
      1003: q+1
      1004: q
      1005: q^2+1
      1006: q+1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: q+1
      1021: q+2
      1023: q+1
      1025: q+1
      1026: q
      1027: q^2+1
      1028: q+1
      1031: 2
      1032: 2
      1035: 1
      1037: 2
      1039: 1
      1043: 1
      1044: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: q^2+1
      1054: q+1
      1058: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+2
      1069: q+2
      1071: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 2
      1077: q+2
      1078: q^2+2q+1
      1079: 2
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: q+1
      1087: 1
      1093: 1
      1105: q+1
      1111: 1
      1115: 2
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1137: 1
      1139: 1
      1142: 1
      1145: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1165: 2
      1169: 1
      1173: 1
      1187: 1
      1189: 1
      1192: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1211: 2
      1213: q+2
      1215: 2
      1216: 2
      1218: 1
      1219: 1
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1227: q+2
      1228: 1
      1229: 1
      1231: 2
      1232: 2
      1234: 1
      1235: 1
      1237: q+2
      1239: q+1
      1240: q
      1241: q^2+1
      1242: q+1
      1245: 2
      1246: 2
      1249: 1
      1250: 1
      1253: 2
      1257: 1
      1260: q+1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1270: q+1
      1273: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1297: 1
      1303: 1
      1309: 1
      1315: 2
      1319: 1
      1321: 1
      1325: 1
      1326: 1
      1328: 1
      1333: 1
      1335: 1
      1338: 1
      1341: 1
      1343: 1
      1345: 1
      1349: 2
      1355: 1
      1357: 1
      1359: 1
      1362: 1
      1364: 1
      1365: 1
      1370: 1
      1373: 2
      1377: 1
      1381: 1
      1405: 1
      1408: 1
      1410: 1
      1412: 1
      1417: 1
      1419: 1
      1431: 1
      1434: 1
      1439: 2
      1440: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1449: 2
      1450: 2
      1453: q+2
      1454: 1
      1455: 1
      1457: 1
      1459: 2
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 2
      1475: 1
      1478: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1490: 1
      1496: 1
      1502: 1
      1507: 1
      1526: 1
      1532: 1
      1542: 2
      1546: 1
      1548: 1
      1549: 1
      1551: 1
      1554: 1
      1557: 1
      1562: 1
      1564: 2
      1568: 1
      1570: 1
      1573: 1
      1575: 1
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1632: 1
      1635: 1
      1642: 1
      1644: 2
      1645: 2
      1647: 1
      1648: 1
      1649: 1
      1652: 1
      1653: 1
      1662: 1
      1663: 1
      1668: 2
      1669: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1682: 1
      1688: 1
      1693: 1
      1738: 2
      1746: 1
      1748: 1
      1749: 1
      1750: 1
      1755: 1
      1758: 1
      1762: 1
      1786: 1
      1802: 1
      1805: 1
      1816: 1
      1819: 1
      1828: 1
      1829: 1
      1833: 1
      1847: 1
      1852: 1
      1903: 1
      1933: 1
      1957: 1
      1962: 1
      2033: 1

2034:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: 2q
        61: 2q^2+q+1
        62: 2q^2+2q+1
        63: q^2+q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q
       105: q^2
       106: q^2+q+1
       107: 2q
       108: 2q^2+q+1
       109: q^2+q
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q^2+q
       113: 2q^2+2q+1
       114: q^2+q
       115: 2q^2+2q+1
       116: q^2+q
       117: q^2+q
       118: 2q^2+2q+1
       119: 2q
       120: 2q^2+q+1
       121: 2q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q
       171: q^2
       172: q^2+q+1
       173: q
       174: q
       175: q^2
       176: q^2+q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q
       184: 2q^2+q+1
       185: q^2+q
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+q
       189: 2q^2+2q+1
       190: q^2+q
       191: q^2+q
       192: 2q^2+2q+1
       193: 2q
       194: 2q^2+q+1
       195: q^2+q
       196: 2q^2+2q+1
       197: q^2+2q+1
       198: q^2+q
       199: 2q
       200: 2q^2+q+1
       201: 2q
       202: q^2+q+1
       204: 2q+1
       205: q+1
       206: q
       207: q^2+2q+1
       208: q^2+q
       209: 2q^2+2q+1
       210: q^2+q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 2q^2+3q+1
       223: q^2+2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^2+2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 2q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q
       262: q+1
       263: q
       264: q
       265: q^2
       266: q^2+q+1
       267: q
       268: q
       269: q^2+q+1
       270: q^2
       273: q+1
       274: q
       275: q
       276: q
       277: q^2
       278: q^2+q+1
       279: 2q+1
       281: q+1
       283: q
       284: q^2+1
       286: q^2+q+1
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q
       294: 2q^2+q+1
       295: q^2+q
       296: 2q^2+2q+1
       297: q^2+2q+1
       298: q^2+q
       299: 2q
       300: 2q^2+q+1
       301: 2q+1
       303: q^2+q
       304: 2q^2+2q+1
       305: q^2+2q+1
       306: q^2+q
       307: 2q
       308: q^2+q+1
       310: 2q+1
       311: q+1
       313: q+1
       314: q
       315: q+1
       317: 2q+1
       319: 2q
       320: q^2+q+1
       322: 2q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: 2q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: 2q^2+3q+1
       348: q^2+2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: q^2+2q+1
       353: q^2+3q+1
       354: q^2+2q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 2q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       380: 1
       381: q
       384: q+1
       385: q
       386: q
       387: q^2
       388: q^2+q+1
       389: q
       391: q+1
       393: q
       394: q
       395: q^2
       396: q^2+q+1
       399: q+1
       403: q
       404: q+1
       406: q+1
       407: q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q
       420: q^2+1
       422: q^2+q+1
       423: q+1
       425: q+1
       427: 2q+1
       429: q
       430: q^2+1
       432: q^2+q+1
       433: q+1
       435: 2q+1
       437: 2q
       438: 2q^2+q+1
       439: q^2+q
       440: 2q^2+2q+1
       441: q^2+2q+1
       442: q^2+q
       443: 2q
       444: q^2+q+1
       445: 2q+1
       447: q
       448: q^2+1
       450: q+1
       451: 1
       453: 2q
       454: q^2+q+1
       455: q+1
       458: 2q+1
       459: q+1
       460: q
       462: 2q+1
       463: q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 2q
       472: q^2+q+1
       474: 2q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: q^2+3q+1
       512: q^2+2q+1
       513: 2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       524: 1
       525: q
       528: q+1
       532: 1
       536: 1
       537: q
       539: q+1
       541: q
       542: q
       543: q^2+q+1
       544: q^2
       545: q
       547: q+1
       552: 1
       555: q+1
       559: q+1
       560: q
       563: q+1
       566: q
       568: q+1
       570: q+1
       574: q
       575: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: q^2+1
       592: q+1
       593: q
       594: q^2+1
       596: q^2+q+1
       597: q+1
       599: q+1
       601: 2q+1
       603: q
       604: q^2+1
       605: q+1
       608: q^2+q+1
       609: q+1
       611: 2q+1
       613: q+1
       615: 2q
       616: q^2+q+1
       617: 2q+1
       619: q
       620: q^2+1
       622: q+1
       623: 1
       625: 1
       627: q+1
       629: 1
       632: 2q+1
       633: q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: q
       642: q^2+1
       644: q+1
       645: 1
       647: 2q
       648: q^2+q+1
       650: 2q+1
       651: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q^2+2q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: q+2
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q^2+2q+1
       678: q^2+3q+1
       679: q^2+2q+1
       680: 2
       681: q^2+2q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       729: q
       731: q+1
       733: q
       735: q+1
       739: 1
       743: 1
       747: q+1
       751: q+1
       756: 1
       758: q+1
       762: q+1
       763: q
       766: q
       768: q+1
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: q
       786: q^2+1
       788: q+1
       789: 2q+1
       791: 1
       793: 1
       794: 1
       795: q+2
       797: q+1
       799: q+1
       801: q
       802: q^2+1
       804: q+1
       805: q
       806: q^2+1
       808: q^2+q+1
       809: q+1
       811: q+1
       813: 2q+1
       815: 2q
       816: q^2+q+1
       818: 2
       819: 2
       821: 1
       823: 1
       825: q
       826: q^2+1
       828: q+1
       832: q+1
       833: 1
       835: 1
       837: q+1
       840: 2q+1
       841: q+1
       843: 1
       844: 1
       845: q
       846: q^2+1
       848: q+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: q+2
       870: q+2
       871: q^2+2q+1
       872: q^2+2q+1
       873: 2
       874: 2
       875: q+1
       876: q+1
       877: q^2+2q+1
       878: q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       916: 1
       918: 1
       922: 1
       927: 1
       930: 1
       932: q
       934: q+1
       938: 1
       942: 2
       946: 1
       950: 1
       958: q+1
       961: 1
       965: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: q+1
       982: q+1
       989: q
       991: q+1
       992: 2
       994: 2
       996: q+2
       999: 2
      1000: 1
      1001: 1
      1002: q+1
      1004: q
      1005: q^2+1
      1007: q+1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1014: q+2
      1016: 1
      1017: 1
      1018: q+1
      1020: q+2
      1022: q+1
      1024: q+1
      1026: q
      1027: q^2+1
      1029: q+1
      1030: 2
      1033: 2
      1034: 1
      1036: 2
      1038: 1
      1042: 1
      1045: q+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q
      1053: q^2+1
      1055: q+1
      1059: q+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+2
      1068: q+2
      1070: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 2
      1077: q+2
      1078: q^2+2q+1
      1079: 2
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: q+1
      1089: 1
      1091: 1
      1102: q+1
      1112: 1
      1116: 2
      1120: 1
      1122: 1
      1124: 1
      1127: 1
      1131: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1144: 1
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: 2
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1191: 1
      1195: 1
      1197: 1
      1199: 1
      1204: 1
      1210: 2
      1212: q+2
      1214: 2
      1217: 2
      1218: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: q+2
      1228: 1
      1229: 1
      1230: 2
      1233: 2
      1234: 1
      1235: 1
      1236: q+2
      1238: q+1
      1240: q
      1241: q^2+1
      1243: q+1
      1244: 2
      1247: 2
      1248: 1
      1251: 1
      1252: 2
      1256: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1271: q+1
      1272: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 1
      1288: 2
      1289: q+1
      1293: 1
      1295: 1
      1305: 1
      1307: 1
      1316: 2
      1318: 1
      1320: 1
      1323: 1
      1327: 1
      1329: 1
      1331: 1
      1334: 1
      1337: 1
      1340: 1
      1342: 1
      1346: 1
      1350: 2
      1354: 1
      1356: 1
      1358: 1
      1361: 1
      1366: 1
      1367: 1
      1369: 1
      1374: 2
      1378: 1
      1382: 1
      1404: 1
      1407: 1
      1411: 1
      1413: 1
      1415: 1
      1420: 1
      1430: 1
      1433: 1
      1438: 2
      1441: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1448: 2
      1451: 2
      1452: q+2
      1454: 1
      1455: 1
      1456: 1
      1458: 2
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 2
      1474: 1
      1479: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1492: 1
      1494: 1
      1505: 1
      1506: 1
      1528: 1
      1530: 1
      1543: 2
      1545: 1
      1547: 1
      1550: 1
      1552: 1
      1553: 1
      1556: 1
      1560: 1
      1565: 2
      1567: 1
      1569: 1
      1572: 1
      1577: 1
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1634: 1
      1641: 1
      1643: 2
      1646: 2
      1647: 1
      1648: 1
      1650: 1
      1651: 1
      1654: 1
      1661: 1
      1664: 1
      1667: 2
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1674: 1
      1678: 1
      1680: 1
      1691: 1
      1692: 1
      1739: 2
      1745: 1
      1747: 1
      1751: 1
      1752: 1
      1754: 1
      1759: 1
      1763: 1
      1787: 1
      1801: 1
      1804: 1
      1815: 1
      1820: 1
      1827: 1
      1830: 1
      1833: 1
      1850: 1
      1851: 1
      1904: 1
      1934: 1
      1956: 1
      1963: 1
      2034: 1

2035:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: q^3+4q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^2+q
        59: 2q^2+2q+1
        60: 2q^2+q+1
        61: 2q
        62: q^2+q
        63: 2q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^2+3q+1
        73: 3q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: q^3+4q^2+3q+1
        81: 3q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: 2q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q^2
       104: q^2+q+1
       105: q
       106: q
       107: 2q^2+q+1
       108: 2q
       109: q^2+q
       110: 2q^2+2q+1
       111: q^2+q
       112: q^2+2q+1
       113: q^2+q
       114: 2q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: q^2+q
       118: 2q^2+2q+1
       119: 2q^2+q+1
       120: 2q
       121: q^2+q
       122: 2q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 2q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: 2q^2+2q+1
       139: 3q^2+3q+1
       140: 2q^2+3q+1
       141: q^3+4q^2+3q+1
       142: 3q^2+3q+1
       143: 2q^2+3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 3q^2+3q+1
       147: q^2+3q+1
       148: 2q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: q^3+3q^2+2q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q^2
       170: q^2+q+1
       171: q
       172: q
       173: q^2
       174: q^2+q+1
       175: q
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q^2+q+1
       184: 2q
       185: q^2+q
       186: 2q^2+2q+1
       187: q^2+q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: q^2+q
       192: 2q^2+2q+1
       193: 2q^2+q+1
       194: 2q
       195: q^2+q
       196: 2q^2+2q+1
       197: q^2+q
       198: q^2+2q+1
       199: 2q^2+q+1
       200: 2q
       201: q^2+q+1
       202: 2q
       204: 2q+1
       205: q
       206: q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+q
       210: 2q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 2q^2+3q+1
       223: q^2+2q+1
       224: 3q^2+3q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 3q^2+3q+1
       228: 2q^2+2q+1
       229: 2q^2+3q+1
       230: 3q^2+3q+1
       231: q^2+2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: 2q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: q^3+3q^2+2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 2q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q+1
       261: q
       263: q^2
       264: q^2+q+1
       265: q
       266: q
       267: q^2
       268: q^2+q+1
       269: q
       270: q
       273: q
       274: q+1
       275: q^2
       276: q^2+q+1
       277: q
       278: q
       280: 2q+1
       282: q+1
       283: q^2+1
       284: q
       286: q^2+q+1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q^2+q+1
       294: 2q
       295: q^2+q
       296: 2q^2+2q+1
       297: q^2+q
       298: q^2+2q+1
       299: 2q^2+q+1
       300: 2q
       302: 2q+1
       303: q^2+q
       304: 2q^2+2q+1
       305: q^2+q
       306: q^2+2q+1
       307: q^2+q+1
       308: 2q
       310: 2q+1
       312: q+1
       313: q
       314: q+1
       316: q+1
       318: 2q+1
       319: q^2+q+1
       320: 2q
       322: 2q+1
       323: q
       324: q+1
       325: q^2+q
       326: 2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: 2q^2+2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: 2q^2+2q+1
       345: 3q^2+3q+1
       346: 2q^2+2q+1
       347: 2q^2+3q+1
       348: q^2+2q+1
       349: 3q^2+3q+1
       350: 2q^2+2q+1
       351: q^2+3q+1
       352: q^2+2q+1
       353: q^2+3q+1
       354: q^2+2q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 2q+1
       358: q+1
       359: 2q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       378: 1
       382: q+1
       383: q
       385: q^2
       386: q^2+q+1
       387: q
       388: q
       390: q+1
       392: q
       393: q^2
       394: q^2+q+1
       395: q
       396: q
       400: q+1
       403: q+1
       404: q
       406: q
       407: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q^2+1
       420: q
       422: q^2+q+1
       424: q+1
       426: q+1
       428: 2q+1
       429: q^2+1
       430: q
       432: q^2+q+1
       434: q+1
       436: 2q+1
       437: 2q^2+q+1
       438: 2q
       439: q^2+q
       440: 2q^2+2q+1
       441: q^2+q
       442: q^2+2q+1
       443: q^2+q+1
       444: 2q
       446: 2q+1
       447: q^2+1
       448: q
       450: q+1
       452: 1
       453: q^2+q+1
       454: 2q
       456: q+1
       458: 2q+1
       459: q
       460: q+1
       462: 2q+1
       464: q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: q^2+q+1
       472: 2q
       474: 2q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: q^2+2q+1
       482: 2q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: 2q^2+2q+1
       493: q^2+2q+1
       494: 2q^2+2q+1
       495: q^2+2q+1
       496: q^2+3q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 2q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: q^2+3q+1
       512: q^2+2q+1
       513: 2q+1
       514: q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       522: 1
       526: q+1
       527: q
       530: 1
       534: 1
       538: q+1
       540: q
       541: q^2
       542: q^2+q+1
       543: q
       544: q
       546: q+1
       548: q
       551: 1
       556: q+1
       559: q
       560: q+1
       564: q+1
       566: q+1
       568: q
       571: q+1
       574: q+1
       575: q
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+1
       590: q
       592: q+1
       593: q^2+1
       594: q
       596: q^2+q+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q^2+1
       604: q
       606: q+1
       608: q^2+q+1
       610: q+1
       612: 2q+1
       614: q+1
       615: q^2+q+1
       616: 2q
       618: 2q+1
       619: q^2+1
       620: q
       622: q+1
       624: 1
       626: 1
       628: q+1
       630: 1
       632: 2q+1
       634: q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: q^2+1
       642: q
       644: q+1
       646: 1
       647: q^2+q+1
       648: 2q
       650: 2q+1
       652: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q^2+2q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: q+2
       675: q^2+2q+1
       676: 2q^2+2q+1
       677: q^2+2q+1
       678: q^2+3q+1
       679: q^2+2q+1
       680: 2
       681: q^2+2q+1
       682: q+1
       683: q+1
       684: 2q+1
       685: q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       699: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q+1
       732: q
       734: q+1
       736: q
       740: 1
       744: 1
       748: q+1
       752: q+1
       754: 1
       759: q+1
       762: q
       763: q+1
       766: q+1
       768: q
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: q^2+1
       786: q
       788: q+1
       790: 2q+1
       792: 1
       793: 1
       794: 1
       796: q+2
       798: q+1
       800: q+1
       801: q^2+1
       802: q
       804: q+1
       805: q^2+1
       806: q
       808: q^2+q+1
       810: q+1
       812: q+1
       814: 2q+1
       815: q^2+q+1
       816: 2q
       818: 2
       820: 2
       822: 1
       824: 1
       825: q^2+1
       826: q
       828: q+1
       832: q+1
       834: 1
       836: 1
       838: q+1
       840: 2q+1
       842: q+1
       843: 1
       844: 1
       845: q^2+1
       846: q
       848: q+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q
       858: q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: q+2
       870: q+2
       871: q^2+2q+1
       872: q^2+2q+1
       873: 2
       874: 2
       875: q+1
       876: q+1
       877: q^2+2q+1
       878: q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       919: 1
       921: 1
       926: 1
       929: 1
       933: q+1
       935: q
       939: 1
       943: 2
       947: 1
       951: 1
       959: q+1
       962: 1
       965: 1
       967: 1
       969: 1
       972: 1
       976: 1
       980: q+1
       986: q+1
       989: q+1
       991: q
       993: 2
       995: 2
       997: q+2
       999: 2
      1000: 1
      1001: 1
      1003: q+1
      1004: q^2+1
      1005: q
      1007: q+1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1015: q+2
      1016: 1
      1017: 1
      1019: q+1
      1021: q+2
      1023: q+1
      1025: q+1
      1026: q^2+1
      1027: q
      1029: q+1
      1031: 2
      1033: 2
      1035: 1
      1037: 2
      1039: 1
      1043: 1
      1045: q+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q^2+1
      1053: q
      1055: q+1
      1059: q+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+2
      1069: q+2
      1071: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: q+2
      1076: 2
      1077: q+2
      1078: q^2+2q+1
      1079: 2
      1080: 1
      1081: 2
      1082: q+1
      1083: q+1
      1084: 2
      1085: q+1
      1092: 1
      1094: 1
      1104: q+1
      1113: 1
      1117: 2
      1119: 1
      1123: 1
      1125: 1
      1128: 1
      1131: 1
      1133: 1
      1136: 1
      1139: 1
      1142: 1
      1145: 1
      1147: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1167: 2
      1171: 1
      1175: 1
      1186: 1
      1189: 1
      1192: 1
      1195: 1
      1197: 1
      1200: 1
      1205: 1
      1211: 2
      1213: q+2
      1215: 2
      1217: 2
      1218: 1
      1219: 1
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1227: q+2
      1228: 1
      1229: 1
      1231: 2
      1233: 2
      1234: 1
      1235: 1
      1237: q+2
      1239: q+1
      1240: q^2+1
      1241: q
      1243: q+1
      1245: 2
      1247: 2
      1249: 1
      1251: 1
      1253: 2
      1257: 1
      1261: q+1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1271: q+1
      1273: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 2
      1284: q+2
      1285: 1
      1286: 2
      1287: 1
      1288: 2
      1289: q+1
      1296: 1
      1298: 1
      1308: 1
      1310: 1
      1317: 2
      1319: 1
      1321: 1
      1324: 1
      1327: 1
      1329: 1
      1332: 1
      1335: 1
      1338: 1
      1341: 1
      1343: 1
      1347: 1
      1351: 2
      1353: 1
      1357: 1
      1359: 1
      1363: 1
      1366: 1
      1367: 1
      1371: 1
      1375: 2
      1379: 1
      1383: 1
      1405: 1
      1408: 1
      1411: 1
      1413: 1
      1416: 1
      1421: 1
      1431: 1
      1434: 1
      1439: 2
      1441: 2
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1449: 2
      1451: 2
      1453: q+2
      1454: 1
      1455: 1
      1457: 1
      1459: 2
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 2
      1475: 1
      1479: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 2
      1486: 1
      1487: 1
      1488: 2
      1495: 1
      1497: 1
      1508: 1
      1509: 1
      1531: 1
      1533: 1
      1544: 2
      1546: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1557: 1
      1561: 1
      1566: 2
      1568: 1
      1570: 1
      1574: 1
      1577: 1
      1578: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1632: 1
      1635: 1
      1642: 1
      1644: 2
      1646: 2
      1647: 1
      1648: 1
      1650: 1
      1652: 1
      1654: 1
      1662: 1
      1664: 1
      1668: 2
      1669: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1681: 1
      1683: 1
      1694: 1
      1695: 1
      1740: 2
      1746: 1
      1748: 1
      1751: 1
      1752: 1
      1756: 1
      1760: 1
      1764: 1
      1788: 1
      1802: 1
      1805: 1
      1816: 1
      1820: 1
      1828: 1
      1830: 1
      1833: 1
      1853: 1
      1854: 1
      1905: 1
      1935: 1
      1957: 1
      1963: 1
      2035: 1

2036:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: q^4+2q^3+q^2+q+1
        23: q^4+2q^3+q^2+q+1
        24: q^5+q^4+q^3+q^2+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: q^4+2q^3+q^2+q+1
        32: q^3+q^2+q+1
        33: q^4+2q^3+q^2+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: q^4+2q^3+q^2+q+1
        53: q^4+2q^3+q^2+q+1
        54: q^5+q^4+q^3+q^2+q+1
        55: 2q^3+q+1
        56: 2q^3+q+1
        57: q^4+q^3+q+1
        58: q^4+q^3+q^2+1
        59: q^3+q
        60: q^3+1
        61: q^3+q
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: 2q^3+q+1
        73: q^4+2q^3+q^2+q+1
        74: 2q^3+q+1
        76: 2q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q^2+q+1
        81: q^3+q^2+q+1
        82: q^4+2q^3+q^2+q+1
        83: q^3+q^2+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: 2q^3+q+1
        87: q^3+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q^4+2q^3+q^2+q+1
        95: q^4+2q^3+q^2+q+1
        96: q^5+q^4+q^3+q^2+q+1
        97: 2q^3+q+1
        98: 2q^3+q+1
        99: q^4+q^3+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       103: q^3+1
       106: q^3+q
       107: q^3+1
       108: q^3+q
       109: q^4+q^3+q^2+1
       110: q^3+q
       111: 2q^3+q+1
       113: 2q^3+q+1
       115: q^3+q+1
       117: q^2+1
       118: q
       119: 1
       120: q
       121: q^3+q+1
       123: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       127: 2q^3+q+1
       129: 2q^3+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: q^3+q^2+q+1
       139: q^4+2q^3+q^2+q+1
       140: 2q^3+q+1
       141: q^3+q^2+q+1
       142: q^4+2q^3+q^2+q+1
       143: q^3+q+1
       144: q^3+q+1
       145: 2q^3+q+1
       146: q^3+q+1
       147: 2q^3+q+1
       148: q^3+1
       149: 2q^3+q+1
       150: q^3+q+1
       151: 2q^3+q+1
       153: 2q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q^3+q^2+q+1
       161: q^3+q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       169: q^3+1
       172: q^3+q
       173: 1
       176: q
       177: q^3+q+1
       179: 2q^3+q+1
       181: 2q^3+q+1
       183: 1
       184: q
       185: q^2+1
       186: q
       187: q^3+q+1
       189: q^3+q+1
       191: q^2+1
       192: q
       193: q^3+1
       194: q^3+q
       195: q^4+q^3+q^2+1
       196: q^3+q
       197: 2q^3+q+1
       199: 1
       200: q
       201: q^3+1
       202: q^3+q
       203: q^3+1
       205: q^3+1
       207: q^3+q+1
       209: 2q^3+q+1
       211: q^3+q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q+1
       223: q^3+q+1
       224: q^3+q^2+q+1
       225: q^3+q^2+q+1
       226: q^3+q^2+q+1
       227: q^2+q+1
       228: q^3+q^2+q+1
       229: q^3+q+1
       230: q^3+q^2+q+1
       231: q^3+q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q^3+q+1
       237: 2q^3+q+1
       239: 2q^3+q+1
       241: q^4+q^3+q+1
       243: 2q^3+q+1
       244: 2q^3+q+1
       245: q^3+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q^3+q^2+q+1
       251: q^3+q^2+q+1
       252: q^3+q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^3+1
       262: q^3+q
       263: 1
       266: q
       267: q^3+1
       269: q^3+q
       271: q^3+1
       275: 1
       278: q
       279: q+1
       281: q+1
       283: 1
       284: q
       285: q^2+1
       286: q
       287: q^3+q+1
       289: q+1
       291: q^3+q+1
       293: 1
       294: q
       295: q^2+1
       296: q
       297: q^3+q+1
       299: 1
       300: q
       301: 2q^3+q+1
       303: q^2+1
       304: q
       305: q^3+q+1
       307: 1
       308: q
       309: 1
       311: q^3+1
       313: 1
       315: q^3+q+1
       317: 2q^3+q+1
       319: q^3+1
       320: q^3+q
       321: q^3+1
       323: q^3+1
       325: q^3+q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^3+q+1
       335: q^3+q^2+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       338: 2q^3+q+1
       340: 2q^3+q+1
       342: q^4+q^3+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^3+q^2+q+1
       347: q^3+q+1
       348: q^3+q+1
       349: q^3+q^2+q+1
       350: q^3+q^2+q+1
       351: 2q^3+q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q^3+1
       360: q+1
       362: q+1
       364: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       380: q
       381: 1
       384: q
       385: 1
       388: q
       389: q^3+1
       391: q^3+q
       393: 1
       396: q
       397: q^3+1
       401: 1
       405: q^3+1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: 1
       420: q
       421: q^2+1
       422: q
       423: q^3+q+1
       425: q^3+q+1
       427: 2q^3+q+1
       429: 1
       430: q
       431: q^2+1
       432: q
       433: q^3+q+1
       435: q+1
       437: 1
       438: q
       439: q^2+1
       440: q
       441: q^3+q+1
       443: q^3+1
       444: q^3+q
       445: 2q^3+q+1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: q^3+1
       463: q^3+1
       465: q+1
       467: q+1
       469: q^3+q+1
       471: 1
       472: q
       473: 1
       475: 1
       477: q^3+1
       479: q^3+1
       481: q+1
       482: q^2+q+1
       483: q^3+q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+q+1
       493: q^3+q+1
       494: q^3+q^2+q+1
       495: q^3+q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       525: 1
       528: q
       529: 1
       532: q
       533: 1
       536: q
       537: 1
       539: q
       541: 1
       543: q
       545: q^3+1
       547: q^3+q
       549: 1
       553: 1
       557: 1
       561: q^3+1
       565: 1
       569: q^3+1
       573: q^3+1
       577: q^3+1
       583: q+1
       585: q+1
       587: q+1
       589: 1
       590: q
       591: 1
       593: 1
       594: q
       595: q^2+1
       596: q
       597: q+1
       599: q^3+q+1
       601: q+1
       603: 1
       604: q
       605: q+1
       607: q^2+1
       608: q
       609: q^3+q+1
       611: q+1
       613: q^3+q+1
       615: 1
       616: q
       617: q+1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       642: q
       643: 1
       645: 1
       647: 1
       648: q
       649: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q^3+q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q^3+1
       705: 1
       708: q
       709: 1
       712: q
       713: 1
       717: 1
       720: q
       721: 1
       723: q
       725: 1
       727: q
       729: 1
       731: q
       733: 1
       735: q
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       786: q
       787: 1
       789: q+1
       791: 1
       793: 1
       794: q
       795: q+1
       797: q+1
       799: q+1
       801: 1
       802: q
       803: 1
       805: 1
       806: q
       807: q^2+1
       808: q
       809: q+1
       811: q^3+q+1
       813: q+1
       815: 1
       816: q
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: 1
       846: q
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       884: 1
       896: 1
       899: q
       900: 1
       904: 1
       906: q
       908: 1
       912: 1
       914: q
       916: 1
       918: q
       920: 1
       922: q
       924: 1
       928: 1
       930: q
       932: 1
       934: q
       936: 1
       940: 1
       944: 1
       948: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1001: q
      1002: q+1
      1004: 1
      1005: q
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: 1
      1017: q
      1018: q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: 1
      1027: q
      1028: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1120: q
      1122: 1
      1124: q
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1146: q
      1148: 1
      1150: q
      1152: 1
      1156: 1
      1158: q
      1160: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1202: 1
      1214: q+1
      1216: 1
      1218: 1
      1219: q
      1220: 1
      1222: 1
      1224: 1
      1230: q+1
      1232: 1
      1234: 1
      1235: q
      1236: q+1
      1238: q+1
      1240: 1
      1241: q
      1242: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1320: q
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1344: 1
      1348: 1
      1352: 1
      1354: q
      1356: 1
      1358: q
      1360: 1
      1364: 1
      1368: 1
      1376: 1
      1380: 1
      1414: 1
      1418: 1
      1430: 1
      1436: 1
      1446: 1
      1448: q+1
      1450: 1
      1454: 1
      1455: q
      1456: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1474: 1
      1478: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1489: 1
      1501: 1
      1537: 1
      1559: 1
      1563: 1
      1567: 1
      1569: q
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1637: 1
      1641: 1
      1649: 1
      1659: 1
      1661: 1
      1663: 1
      1671: 1
      1673: 1
      1687: 1
      1729: 1
      1741: 1
      1753: 1
      1757: 1
      1785: 1
      1815: 1
      1817: 1
      1819: 1
      1823: 1
      1894: 1
      1902: 1
      1906: 1
      1958: 1
      2036: 1

2037:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: q^4+2q^3+q^2+q+1
        23: q^4+2q^3+q^2+q+1
        24: q^5+q^4+q^3+q^2+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: q^4+2q^3+q^2+q+1
        32: q^3+q^2+q+1
        33: q^4+2q^3+q^2+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: q^4+2q^3+q^2+q+1
        53: q^4+2q^3+q^2+q+1
        54: q^5+q^4+q^3+q^2+q+1
        55: 2q^3+q+1
        56: 2q^3+q+1
        57: q^4+q^3+q+1
        58: q^3+q
        59: q^4+q^3+q^2+1
        60: q^3+q
        61: q^3+1
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: 2q^3+q+1
        73: q^4+2q^3+q^2+q+1
        74: 2q^3+q+1
        76: 2q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q^2+q+1
        81: q^3+q^2+q+1
        82: q^4+2q^3+q^2+q+1
        83: q^3+q^2+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: 2q^3+q+1
        87: q^3+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q^4+2q^3+q^2+q+1
        95: q^4+2q^3+q^2+q+1
        96: q^5+q^4+q^3+q^2+q+1
        97: 2q^3+q+1
        98: 2q^3+q+1
        99: q^4+q^3+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       103: q^3+q
       106: q^3+1
       107: q^3+q
       108: q^3+1
       109: q^3+q
       110: q^4+q^3+q^2+1
       111: 2q^3+q+1
       113: 2q^3+q+1
       115: q^3+q+1
       117: q
       118: q^2+1
       119: q
       120: 1
       121: q^3+q+1
       123: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       127: 2q^3+q+1
       129: 2q^3+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: q^3+q^2+q+1
       139: q^4+2q^3+q^2+q+1
       140: 2q^3+q+1
       141: q^3+q^2+q+1
       142: q^4+2q^3+q^2+q+1
       143: q^3+q+1
       144: q^3+q+1
       145: 2q^3+q+1
       146: q^3+q+1
       147: 2q^3+q+1
       148: q^3+1
       149: 2q^3+q+1
       150: q^3+q+1
       151: 2q^3+q+1
       153: 2q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q^3+q^2+q+1
       161: q^3+q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       169: q^3+q
       172: q^3+1
       173: q
       176: 1
       177: q^3+q+1
       179: 2q^3+q+1
       181: 2q^3+q+1
       183: q
       184: 1
       185: q
       186: q^2+1
       187: q^3+q+1
       189: q^3+q+1
       191: q
       192: q^2+1
       193: q^3+q
       194: q^3+1
       195: q^3+q
       196: q^4+q^3+q^2+1
       197: 2q^3+q+1
       199: q
       200: 1
       201: q^3+q
       202: q^3+1
       204: q^3+1
       205: q^3+1
       207: q^3+q+1
       209: 2q^3+q+1
       211: q^3+q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q+1
       223: q^3+q+1
       224: q^3+q^2+q+1
       225: q^3+q^2+q+1
       226: q^3+q^2+q+1
       227: q^2+q+1
       228: q^3+q^2+q+1
       229: q^3+q+1
       230: q^3+q^2+q+1
       231: q^3+q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q^3+q+1
       237: 2q^3+q+1
       239: 2q^3+q+1
       241: q^4+q^3+q+1
       243: 2q^3+q+1
       244: 2q^3+q+1
       245: q^3+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q^3+q^2+q+1
       251: q^3+q^2+q+1
       252: q^3+q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^3+q
       262: q^3+1
       263: q
       266: 1
       267: q^3+q
       269: q^3+1
       273: q^3+1
       275: q
       278: 1
       279: q+1
       281: q+1
       283: q
       284: 1
       285: q
       286: q^2+1
       287: q^3+q+1
       289: q+1
       291: q^3+q+1
       293: q
       294: 1
       295: q
       296: q^2+1
       297: q^3+q+1
       299: q
       300: 1
       301: 2q^3+q+1
       303: q
       304: q^2+1
       305: q^3+q+1
       307: q
       308: 1
       310: 1
       311: q^3+1
       313: 1
       315: q^3+q+1
       317: 2q^3+q+1
       319: q^3+q
       320: q^3+1
       322: q^3+1
       323: q^3+1
       325: q^3+q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^3+q+1
       335: q^3+q^2+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       338: 2q^3+q+1
       340: 2q^3+q+1
       342: q^4+q^3+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^3+q^2+q+1
       347: q^3+q+1
       348: q^3+q+1
       349: q^3+q^2+q+1
       350: q^3+q^2+q+1
       351: 2q^3+q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q^3+1
       360: q+1
       362: q+1
       364: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: 1
       381: q
       384: 1
       385: q
       388: 1
       389: q^3+q
       391: q^3+1
       393: q
       396: 1
       399: q^3+1
       404: 1
       406: q^3+1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q
       420: 1
       421: q
       422: q^2+1
       423: q^3+q+1
       425: q^3+q+1
       427: 2q^3+q+1
       429: q
       430: 1
       431: q
       432: q^2+1
       433: q^3+q+1
       435: q+1
       437: q
       438: 1
       439: q
       440: q^2+1
       441: q^3+q+1
       443: q^3+q
       444: q^3+1
       445: 2q^3+q+1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: q^3+1
       463: q^3+1
       465: q+1
       467: q+1
       469: q^3+q+1
       471: q
       472: 1
       474: 1
       475: 1
       477: q^3+1
       479: q^3+1
       481: q+1
       482: q^2+q+1
       483: q^3+q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+q+1
       493: q^3+q+1
       494: q^3+q^2+q+1
       495: q^3+q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       525: q
       528: 1
       529: q
       532: 1
       533: q
       536: 1
       537: q
       539: 1
       541: q
       543: 1
       545: q^3+q
       547: q^3+1
       552: 1
       555: 1
       559: 1
       563: q^3+1
       568: 1
       570: q^3+1
       575: q^3+1
       577: q^3+1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: 1
       592: 1
       593: q
       594: 1
       595: q
       596: q^2+1
       597: q+1
       599: q^3+q+1
       601: q+1
       603: q
       604: 1
       605: q+1
       607: q
       608: q^2+1
       609: q^3+q+1
       611: q+1
       613: q^3+q+1
       615: q
       616: 1
       617: q+1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: q
       642: 1
       644: 1
       645: 1
       647: q
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q^3+q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q^3+1
       705: q
       708: 1
       709: q
       712: 1
       716: 1
       717: q
       720: 1
       721: q
       723: 1
       725: q
       727: 1
       729: q
       731: 1
       733: q
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: q
       786: 1
       788: 1
       789: q+1
       791: 1
       793: q
       794: 1
       795: q+1
       797: q+1
       799: q+1
       801: q
       802: 1
       804: 1
       805: q
       806: 1
       807: q
       808: q^2+1
       809: q+1
       811: q^3+q+1
       813: q+1
       815: q
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: q+1
       843: 1
       845: q
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       889: 1
       896: q
       899: 1
       902: 1
       904: q
       906: 1
       911: 1
       912: q
       914: 1
       916: q
       918: 1
       920: q
       922: 1
       927: 1
       928: q
       930: 1
       932: q
       934: 1
       938: 1
       942: 1
       946: 1
       950: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       999: 1
      1000: q
      1001: 1
      1002: q+1
      1004: q
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: q
      1017: 1
      1018: q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: q
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1118: q
      1120: 1
      1122: q
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1144: q
      1146: 1
      1148: q
      1150: 1
      1154: 1
      1156: q
      1158: 1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1204: 1
      1214: q+1
      1217: 1
      1218: q
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1230: q+1
      1233: 1
      1234: q
      1235: 1
      1236: q+1
      1238: q+1
      1240: q
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1318: q
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1346: 1
      1350: 1
      1352: q
      1354: 1
      1356: q
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1378: 1
      1382: 1
      1415: 1
      1420: 1
      1430: 1
      1436: 1
      1446: 1
      1448: q+1
      1451: 1
      1454: q
      1455: 1
      1456: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1474: 1
      1479: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1494: 1
      1506: 1
      1538: 1
      1560: 1
      1565: 1
      1567: q
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1637: 1
      1641: 1
      1650: 1
      1659: 1
      1661: 1
      1664: 1
      1671: 1
      1673: 1
      1692: 1
      1730: 1
      1742: 1
      1754: 1
      1759: 1
      1787: 1
      1815: 1
      1817: 1
      1820: 1
      1823: 1
      1895: 1
      1904: 1
      1907: 1
      1958: 1
      2037: 1

2038:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: q^4+2q^3+q^2+q+1
        23: q^4+2q^3+q^2+q+1
        24: q^5+q^4+q^3+q^2+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: q^4+2q^3+q^2+q+1
        32: q^3+q^2+q+1
        33: q^4+2q^3+q^2+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: q^4+2q^3+q^2+q+1
        53: q^4+2q^3+q^2+q+1
        54: q^5+q^4+q^3+q^2+q+1
        55: 2q^3+q+1
        56: 2q^3+q+1
        57: q^4+q^3+q+1
        58: q^4+q^3+q^2+1
        59: q^3+q
        60: q^3+q
        61: q^3+1
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: 2q^3+q+1
        73: q^4+2q^3+q^2+q+1
        75: 2q^3+q+1
        77: 2q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q^2+q+1
        81: q^3+q^2+q+1
        82: q^4+2q^3+q^2+q+1
        83: q^3+q^2+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: 2q^3+q+1
        87: q^3+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q^4+2q^3+q^2+q+1
        95: q^4+2q^3+q^2+q+1
        96: q^5+q^4+q^3+q^2+q+1
        97: 2q^3+q+1
        98: 2q^3+q+1
        99: q^4+q^3+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       104: q^3+q
       105: q^3+1
       107: q^3+q
       108: q^3+1
       109: q^4+q^3+q^2+1
       110: q^3+q
       112: 2q^3+q+1
       114: 2q^3+q+1
       116: q^3+q+1
       117: q^2+1
       118: q
       119: q
       120: 1
       122: q^3+q+1
       124: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       128: 2q^3+q+1
       130: 2q^3+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: q^3+q^2+q+1
       139: q^4+2q^3+q^2+q+1
       140: 2q^3+q+1
       141: q^3+q^2+q+1
       142: q^4+2q^3+q^2+q+1
       143: q^3+q+1
       144: q^3+q+1
       145: 2q^3+q+1
       146: q^3+q+1
       147: 2q^3+q+1
       148: q^3+1
       149: 2q^3+q+1
       150: q^3+q+1
       152: 2q^3+q+1
       154: 2q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q^3+q^2+q+1
       161: q^3+q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       170: q^3+q
       171: q^3+1
       174: q
       175: 1
       178: q^3+q+1
       180: 2q^3+q+1
       182: 2q^3+q+1
       183: q
       184: 1
       185: q^2+1
       186: q
       188: q^3+q+1
       190: q^3+q+1
       191: q^2+1
       192: q
       193: q^3+q
       194: q^3+1
       195: q^4+q^3+q^2+1
       196: q^3+q
       198: 2q^3+q+1
       199: q
       200: 1
       201: q^3+q
       202: q^3+1
       203: q^3+1
       206: q^3+1
       208: q^3+q+1
       210: 2q^3+q+1
       212: q^3+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q+1
       223: q^3+q+1
       224: q^3+q^2+q+1
       225: q^3+q^2+q+1
       226: q^3+q^2+q+1
       227: q^2+q+1
       228: q^3+q^2+q+1
       229: q^3+q+1
       230: q^3+q^2+q+1
       231: q^3+q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q^3+q+1
       238: 2q^3+q+1
       240: 2q^3+q+1
       242: q^4+q^3+q+1
       243: 2q^3+q+1
       244: 2q^3+q+1
       245: q^3+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q^3+q^2+q+1
       251: q^3+q^2+q+1
       252: q^3+q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^3+q
       261: q^3+1
       264: q
       265: 1
       268: q^3+q
       270: q^3+1
       272: q^3+1
       276: q
       277: 1
       280: q+1
       282: q+1
       283: q
       284: 1
       285: q^2+1
       286: q
       288: q^3+q+1
       290: q+1
       292: q^3+q+1
       293: q
       294: 1
       295: q^2+1
       296: q
       298: q^3+q+1
       299: q
       300: 1
       302: 2q^3+q+1
       303: q^2+1
       304: q
       306: q^3+q+1
       307: q
       308: 1
       309: 1
       312: q^3+1
       314: 1
       316: q^3+q+1
       318: 2q^3+q+1
       319: q^3+q
       320: q^3+1
       321: q^3+1
       324: q^3+1
       326: q^3+q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^3+q+1
       335: q^3+q^2+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       339: 2q^3+q+1
       341: 2q^3+q+1
       343: q^4+q^3+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^3+q^2+q+1
       347: q^3+q+1
       348: q^3+q+1
       349: q^3+q^2+q+1
       350: q^3+q^2+q+1
       351: 2q^3+q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q^3+1
       361: q+1
       363: q+1
       365: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       382: q
       383: 1
       386: q
       387: 1
       390: q^3+q
       392: q^3+1
       394: q
       395: 1
       398: q^3+1
       402: 1
       408: q^3+1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q
       420: 1
       421: q^2+1
       422: q
       424: q^3+q+1
       426: q^3+q+1
       428: 2q^3+q+1
       429: q
       430: 1
       431: q^2+1
       432: q
       434: q^3+q+1
       436: q+1
       437: q
       438: 1
       439: q^2+1
       440: q
       442: q^3+q+1
       443: q^3+q
       444: q^3+1
       446: 2q^3+q+1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: q^3+1
       464: q^3+1
       466: q+1
       468: q+1
       470: q^3+q+1
       471: q
       472: 1
       473: 1
       476: 1
       478: q^3+1
       480: q^3+1
       481: q+1
       482: q^2+q+1
       483: q^3+q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+q+1
       493: q^3+q+1
       494: q^3+q^2+q+1
       495: q^3+q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       526: q
       527: 1
       530: q
       531: 1
       534: q
       535: 1
       538: q
       540: 1
       542: q
       544: 1
       546: q^3+q
       548: q^3+1
       550: 1
       554: 1
       558: 1
       562: q^3+1
       567: 1
       572: q^3+1
       576: q^3+1
       581: q^3+1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: 1
       591: 1
       593: q
       594: 1
       595: q^2+1
       596: q
       598: q+1
       600: q^3+q+1
       602: q+1
       603: q
       604: 1
       606: q+1
       607: q^2+1
       608: q
       610: q^3+q+1
       612: q+1
       614: q^3+q+1
       615: q
       616: 1
       618: q+1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: q
       642: 1
       643: 1
       646: 1
       647: q
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q^3+q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q^3+1
       706: q
       707: 1
       710: q
       711: 1
       714: 1
       718: q
       719: 1
       722: q
       724: 1
       726: q
       728: 1
       730: q
       732: 1
       734: q
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: q
       786: 1
       787: 1
       790: q+1
       792: 1
       793: q
       794: 1
       796: q+1
       798: q+1
       800: q+1
       801: q
       802: 1
       803: 1
       805: q
       806: 1
       807: q^2+1
       808: q
       810: q+1
       812: q^3+q+1
       814: q+1
       815: q
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: q+1
       844: 1
       845: q
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       891: 1
       897: q
       898: 1
       901: 1
       905: q
       907: 1
       910: 1
       913: q
       915: 1
       917: q
       919: 1
       921: q
       923: 1
       925: 1
       929: q
       931: 1
       933: q
       935: 1
       937: 1
       941: 1
       945: 1
       949: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
      1000: q
      1001: 1
      1003: q+1
      1004: q
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: q
      1017: 1
      1019: q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: q
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1119: q
      1121: 1
      1123: q
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1145: q
      1147: 1
      1149: q
      1151: 1
      1153: 1
      1157: q
      1159: 1
      1161: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1203: 1
      1215: q+1
      1216: 1
      1218: q
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1231: q+1
      1232: 1
      1234: q
      1235: 1
      1237: q+1
      1239: q+1
      1240: q
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1319: q
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1345: 1
      1349: 1
      1353: q
      1355: 1
      1357: q
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1377: 1
      1381: 1
      1417: 1
      1419: 1
      1434: 1
      1437: 1
      1447: 1
      1449: q+1
      1450: 1
      1454: q
      1455: 1
      1457: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1475: 1
      1478: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1496: 1
      1507: 1
      1540: 1
      1562: 1
      1564: 1
      1568: q
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1635: 1
      1638: 1
      1642: 1
      1649: 1
      1660: 1
      1662: 1
      1663: 1
      1672: 1
      1673: 1
      1693: 1
      1732: 1
      1743: 1
      1755: 1
      1758: 1
      1786: 1
      1816: 1
      1818: 1
      1819: 1
      1824: 1
      1896: 1
      1903: 1
      1908: 1
      1959: 1
      2038: 1

2039:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: q^4+2q^3+q^2+q+1
        23: q^4+2q^3+q^2+q+1
        24: q^5+q^4+q^3+q^2+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: q^4+2q^3+q^2+q+1
        32: q^3+q^2+q+1
        33: q^4+2q^3+q^2+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: q^4+2q^3+q^2+q+1
        53: q^4+2q^3+q^2+q+1
        54: q^5+q^4+q^3+q^2+q+1
        55: 2q^3+q+1
        56: 2q^3+q+1
        57: q^4+q^3+q+1
        58: q^3+q
        59: q^4+q^3+q^2+1
        60: q^3+1
        61: q^3+q
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: 2q^3+q+1
        73: q^4+2q^3+q^2+q+1
        75: 2q^3+q+1
        77: 2q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q^2+q+1
        81: q^3+q^2+q+1
        82: q^4+2q^3+q^2+q+1
        83: q^3+q^2+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: 2q^3+q+1
        87: q^3+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q^4+2q^3+q^2+q+1
        95: q^4+2q^3+q^2+q+1
        96: q^5+q^4+q^3+q^2+q+1
        97: 2q^3+q+1
        98: 2q^3+q+1
        99: q^4+q^3+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       104: q^3+1
       105: q^3+q
       107: q^3+1
       108: q^3+q
       109: q^3+q
       110: q^4+q^3+q^2+1
       112: 2q^3+q+1
       114: 2q^3+q+1
       116: q^3+q+1
       117: q
       118: q^2+1
       119: 1
       120: q
       122: q^3+q+1
       124: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       128: 2q^3+q+1
       130: 2q^3+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: q^3+q^2+q+1
       139: q^4+2q^3+q^2+q+1
       140: 2q^3+q+1
       141: q^3+q^2+q+1
       142: q^4+2q^3+q^2+q+1
       143: q^3+q+1
       144: q^3+q+1
       145: 2q^3+q+1
       146: q^3+q+1
       147: 2q^3+q+1
       148: q^3+1
       149: 2q^3+q+1
       150: q^3+q+1
       152: 2q^3+q+1
       154: 2q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q^3+q^2+q+1
       161: q^3+q^2+q+1
       162: q^3+q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       170: q^3+1
       171: q^3+q
       174: 1
       175: q
       178: q^3+q+1
       180: 2q^3+q+1
       182: 2q^3+q+1
       183: 1
       184: q
       185: q
       186: q^2+1
       188: q^3+q+1
       190: q^3+q+1
       191: q
       192: q^2+1
       193: q^3+1
       194: q^3+q
       195: q^3+q
       196: q^4+q^3+q^2+1
       198: 2q^3+q+1
       199: 1
       200: q
       201: q^3+1
       202: q^3+q
       204: q^3+1
       206: q^3+1
       208: q^3+q+1
       210: 2q^3+q+1
       212: q^3+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q+1
       223: q^3+q+1
       224: q^3+q^2+q+1
       225: q^3+q^2+q+1
       226: q^3+q^2+q+1
       227: q^2+q+1
       228: q^3+q^2+q+1
       229: q^3+q+1
       230: q^3+q^2+q+1
       231: q^3+q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q^3+q+1
       238: 2q^3+q+1
       240: 2q^3+q+1
       242: q^4+q^3+q+1
       243: 2q^3+q+1
       244: 2q^3+q+1
       245: q^3+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q^3+q^2+q+1
       251: q^3+q^2+q+1
       252: q^3+q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^3+1
       261: q^3+q
       264: 1
       265: q
       268: q^3+1
       270: q^3+q
       274: q^3+1
       276: 1
       277: q
       280: q+1
       282: q+1
       283: 1
       284: q
       285: q
       286: q^2+1
       288: q^3+q+1
       290: q+1
       292: q^3+q+1
       293: 1
       294: q
       295: q
       296: q^2+1
       298: q^3+q+1
       299: 1
       300: q
       302: 2q^3+q+1
       303: q
       304: q^2+1
       306: q^3+q+1
       307: 1
       308: q
       310: 1
       312: q^3+1
       314: 1
       316: q^3+q+1
       318: 2q^3+q+1
       319: q^3+1
       320: q^3+q
       322: q^3+1
       324: q^3+1
       326: q^3+q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^3+q+1
       335: q^3+q^2+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       339: 2q^3+q+1
       341: 2q^3+q+1
       343: q^4+q^3+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^3+q^2+q+1
       347: q^3+q+1
       348: q^3+q+1
       349: q^3+q^2+q+1
       350: q^3+q^2+q+1
       351: 2q^3+q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: q^3+1
       361: q+1
       363: q+1
       365: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       382: 1
       383: q
       386: 1
       387: q
       390: q^3+1
       392: q^3+q
       394: 1
       395: q
       400: q^3+1
       403: 1
       407: q^3+1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: 1
       420: q
       421: q
       422: q^2+1
       424: q^3+q+1
       426: q^3+q+1
       428: 2q^3+q+1
       429: 1
       430: q
       431: q
       432: q^2+1
       434: q^3+q+1
       436: q+1
       437: 1
       438: q
       439: q
       440: q^2+1
       442: q^3+q+1
       443: q^3+1
       444: q^3+q
       446: 2q^3+q+1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: q^3+1
       464: q^3+1
       466: q+1
       468: q+1
       470: q^3+q+1
       471: 1
       472: q
       474: 1
       476: 1
       478: q^3+1
       480: q^3+1
       481: q+1
       482: q^2+q+1
       483: q^3+q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+q+1
       493: q^3+q+1
       494: q^3+q^2+q+1
       495: q^3+q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       526: 1
       527: q
       530: 1
       531: q
       534: 1
       535: q
       538: 1
       540: q
       542: 1
       544: q
       546: q^3+1
       548: q^3+q
       551: 1
       556: 1
       560: 1
       564: q^3+1
       566: 1
       571: q^3+1
       574: q^3+1
       581: q^3+1
       584: q+1
       586: q+1
       588: q+1
       589: 1
       590: q
       592: 1
       593: 1
       594: q
       595: q
       596: q^2+1
       598: q+1
       600: q^3+q+1
       602: q+1
       603: 1
       604: q
       606: q+1
       607: q
       608: q^2+1
       610: q^3+q+1
       612: q+1
       614: q^3+q+1
       615: 1
       616: q
       618: q+1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       642: q
       644: 1
       646: 1
       647: 1
       648: q
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q^3+q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q^3+1
       706: 1
       707: q
       710: 1
       711: q
       715: 1
       718: 1
       719: q
       722: 1
       724: q
       726: 1
       728: q
       730: 1
       732: q
       734: 1
       736: q
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       786: q
       788: 1
       790: q+1
       792: 1
       793: 1
       794: q
       796: q+1
       798: q+1
       800: q+1
       801: 1
       802: q
       804: 1
       805: 1
       806: q
       807: q
       808: q^2+1
       810: q+1
       812: q^3+q+1
       814: q+1
       815: 1
       816: q
       818: 1
       820: 1
       822: 1
       824: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: 1
       846: q
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       890: 1
       897: 1
       898: q
       903: 1
       905: 1
       907: q
       909: 1
       913: 1
       915: q
       917: 1
       919: q
       921: 1
       923: q
       926: 1
       929: 1
       931: q
       933: 1
       935: q
       939: 1
       943: 1
       947: 1
       951: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1001: q
      1003: q+1
      1004: 1
      1005: q
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: 1
      1017: q
      1019: q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: 1
      1027: q
      1029: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1074: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1121: q
      1123: 1
      1125: q
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1147: q
      1149: 1
      1151: q
      1155: 1
      1157: 1
      1159: q
      1162: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1205: 1
      1215: q+1
      1217: 1
      1218: 1
      1219: q
      1221: 1
      1223: 1
      1225: 1
      1231: q+1
      1233: 1
      1234: 1
      1235: q
      1237: q+1
      1239: q+1
      1240: 1
      1241: q
      1243: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: q+1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1321: q
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1347: 1
      1351: 1
      1353: 1
      1355: q
      1357: 1
      1359: q
      1363: 1
      1366: 1
      1371: 1
      1379: 1
      1383: 1
      1416: 1
      1421: 1
      1434: 1
      1437: 1
      1447: 1
      1449: q+1
      1451: 1
      1454: 1
      1455: q
      1457: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1475: 1
      1479: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1508: 1
      1539: 1
      1561: 1
      1566: 1
      1568: 1
      1570: q
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1635: 1
      1638: 1
      1642: 1
      1650: 1
      1660: 1
      1662: 1
      1664: 1
      1672: 1
      1673: 1
      1694: 1
      1731: 1
      1744: 1
      1756: 1
      1760: 1
      1788: 1
      1816: 1
      1818: 1
      1820: 1
      1824: 1
      1897: 1
      1905: 1
      1909: 1
      1959: 1
      2039: 1

2040:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: 2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+q
        39: q+1
        40: q^2+q
        41: q+1
        42: q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: 1
        61: 2q
        62: q+1
        63: q
        64: q+1
        65: q^2+q
        66: q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q+1
        75: q^2+q
        76: q+1
        77: q^2+q
        78: q+1
        79: q^2+q
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 1
       105: q
       106: q
       107: 1
       108: 2q
       109: q^2+q+1
       110: q
       111: q+1
       112: q^2+q
       113: q+1
       114: q
       115: q+1
       116: q^2+q
       117: q^2+q+1
       118: q
       119: 1
       120: 2q
       121: q+1
       122: q
       123: q+1
       124: q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+q
       129: q+1
       130: q^2+q
       131: q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^2+2q+1
       138: q^3+2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^3+2q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+q
       153: q+1
       154: q^2+q
       155: q+1
       156: q^2+q
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: q^3+2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       171: q
       172: q
       173: 1
       175: q
       176: q
       177: q+1
       178: q^2+q
       179: q+1
       180: q
       181: q+1
       182: q^2+q
       183: 1
       184: 2q
       185: q^2+q+1
       186: q
       187: q+1
       188: q^2+q
       189: q+1
       190: q
       191: q^2+q+1
       192: q
       193: 1
       194: 2q
       195: q^2+q+1
       196: q
       197: q+1
       198: q^2+q
       199: 1
       200: 2q
       201: 1
       202: 2q
       203: q+1
       205: 1
       206: q
       207: q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q^2+q
       213: q+1
       214: q^2+q
       215: q+1
       216: q^2+q
       217: q+1
       218: q^2+q
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^3+2q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^3+2q^2+2q+1
       229: q^2+2q+1
       230: q^3+2q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+q
       239: q+1
       240: q^2+q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       261: q
       262: q
       263: 1
       265: q
       266: q
       267: 1
       269: q
       270: q
       271: 1
       272: q
       275: 1
       277: q
       278: q
       279: q+1
       280: q
       281: q+1
       282: q^2+q
       283: 1
       284: 2q
       285: q^2+q+1
       286: q
       287: q+1
       288: q
       289: q+1
       290: q^2+q
       291: q+1
       292: q^2+q
       293: 1
       294: 2q
       295: q^2+q+1
       296: q
       297: q+1
       298: q
       299: 1
       300: 2q
       301: q+1
       302: q^2+q
       303: q^2+q+1
       304: q
       305: q+1
       306: q^2+q
       307: 1
       308: 2q
       309: q+1
       311: 1
       312: q
       313: 1
       314: q
       315: q+1
       316: q^2+q
       317: q+1
       318: q
       319: 1
       320: 2q
       321: q+1
       323: 1
       324: q
       325: q+1
       326: q
       333: q^2+2q+1
       334: 2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q+1
       339: q^2+q
       340: q+1
       341: q^2+q
       342: q+1
       343: q^2+q
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+2q^2+2q+1
       351: q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       361: q^2+q
       362: q+1
       363: q^2+q
       364: q+1
       365: q^2+q
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       379: q
       380: q
       381: 1
       383: q
       384: q
       385: 1
       387: q
       388: q
       389: 1
       391: q
       392: q
       393: 1
       395: q
       396: q
       397: 1
       398: q
       401: 1
       402: q
       405: 1
       408: q
       413: q+1
       414: q
       417: q+1
       418: q^2+q
       419: 1
       420: 2q
       421: q^2+q+1
       422: q
       423: q+1
       424: q
       425: q+1
       426: q^2+q
       427: q+1
       428: q
       429: 1
       430: 2q
       431: q^2+q+1
       432: q
       433: q+1
       434: q^2+q
       435: q+1
       436: q^2+q
       437: 1
       438: 2q
       439: q^2+q+1
       440: q
       441: q+1
       442: q
       443: 1
       444: 2q
       445: q+1
       446: q^2+q
       447: 1
       448: 2q
       449: q+1
       451: 1
       452: q
       453: 1
       454: q
       455: 1
       456: q
       457: 1
       459: 1
       461: q+1
       463: 1
       464: q
       465: q+1
       466: q
       467: q+1
       468: q^2+q
       469: q+1
       470: q
       471: 1
       472: 2q
       473: q+1
       475: 1
       476: q
       477: 1
       478: q
       479: 1
       480: q
       481: 2q+1
       482: q^2+2q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+q
       487: q+1
       488: q^2+q
       489: q+1
       490: q^2+q
       491: q^2+2q+1
       492: q^2+2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       523: q
       524: q
       529: 1
       531: q
       532: q
       533: 1
       535: q
       536: q
       537: 1
       539: q
       540: q
       541: 1
       543: q
       544: q
       545: 1
       547: q
       548: q
       549: 1
       550: q
       553: 1
       554: q
       557: 1
       561: 1
       562: q
       565: 1
       567: q
       569: 1
       572: q
       573: 1
       576: q
       577: 1
       581: q
       585: q+1
       586: q
       589: 1
       590: 2q
       591: q+1
       593: 1
       594: 2q
       595: q^2+q+1
       596: q
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: q+1
       602: q
       603: 1
       604: 2q
       605: q+1
       606: q^2+q
       607: q^2+q+1
       608: q
       609: q+1
       610: q
       613: q+1
       614: q^2+q
       615: 1
       616: 2q
       617: q+1
       618: q^2+q
       619: 1
       620: q
       621: 1
       623: 1
       624: q
       625: 1
       629: 1
       630: q
       631: q+1
       633: 1
       634: q
       639: q+1
       640: q
       641: 1
       642: 2q
       643: q+1
       645: 1
       646: q
       647: 1
       648: q
       649: 1
       651: 1
       652: q
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       659: q^2+q
       660: q+1
       661: q^2+q
       662: q+1
       663: q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       700: q
       709: 1
       711: q
       712: q
       713: 1
       714: q
       717: 1
       719: q
       720: q
       721: 1
       723: q
       724: q
       725: 1
       727: q
       728: q
       733: 1
       735: q
       736: q
       737: 1
       738: q
       741: 1
       749: 1
       750: q
       753: 1
       755: q
       757: 1
       760: q
       761: 1
       765: 1
       767: q
       769: 1
       773: q
       775: q+1
       776: q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       785: 1
       786: 2q
       787: q+1
       791: 1
       792: q
       793: 1
       794: 2q
       795: q+1
       796: q^2+q
       797: q+1
       798: q
       801: 1
       802: 2q
       803: q+1
       805: 1
       806: 2q
       807: q^2+q+1
       808: q
       809: q+1
       810: q^2+q
       811: q+1
       812: q
       815: 1
       816: q
       817: q+1
       819: 1
       820: q
       821: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       834: q
       835: 1
       839: 1
       843: 1
       844: q
       845: 1
       846: q
       847: 1
       849: 1
       850: q
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       891: q
       900: 1
       901: q
       904: 1
       906: q
       907: q
       908: 1
       910: q
       916: 1
       918: q
       919: q
       920: 1
       922: q
       923: q
       924: 1
       925: q
       928: 1
       930: q
       931: q
       940: 1
       941: q
       944: 1
       948: 1
       960: 1
       963: q
       964: 1
       966: q
       968: 1
       972: q
       974: 1
       988: 1
       994: q+1
       995: q
       998: q+1
      1000: 1
      1001: 2q
      1004: 1
      1005: q
      1006: 1
      1008: 1
      1010: 1
      1011: q
      1012: 1
      1013: q
      1016: 1
      1017: q
      1020: q+1
      1021: q^2+q
      1022: q+1
      1023: q
      1026: 1
      1027: 2q
      1028: q+1
      1032: 1
      1036: 1
      1037: q
      1038: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1065: q
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1093: q
      1114: 1
      1115: q
      1122: 1
      1124: q
      1125: q
      1126: 1
      1129: q
      1130: 1
      1132: q
      1134: 1
      1138: 1
      1142: q
      1152: 1
      1153: q
      1156: 1
      1158: q
      1159: q
      1160: 1
      1161: q
      1172: 1
      1194: 1
      1198: 1
      1202: 1
      1216: 1
      1218: 1
      1219: q
      1220: 1
      1224: 1
      1228: 1
      1229: q
      1230: q+1
      1231: q
      1232: q+1
      1234: 1
      1235: 2q
      1240: 1
      1241: q
      1242: 1
      1246: 1
      1248: 1
      1250: 1
      1260: 1
      1262: 1
      1266: 1
      1270: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1279: q
      1280: 1
      1281: q
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1297: q
      1326: 1
      1330: 1
      1348: 1
      1349: q
      1356: 1
      1358: q
      1359: q
      1360: 1
      1362: q
      1364: 1
      1365: q
      1368: 1
      1380: 1
      1410: 1
      1418: 1
      1430: 1
      1434: q
      1436: 1
      1440: 1
      1442: 1
      1443: q
      1444: 1
      1450: 1
      1454: 1
      1455: q
      1460: 1
      1464: 1
      1466: 1
      1474: 1
      1478: 1
      1482: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1501: 1
      1507: q
      1537: 1
      1549: 1
      1575: 1
      1579: 1
      1607: 1
      1639: 1
      1641: 1
      1645: 1
      1647: 1
      1648: q
      1649: 1
      1653: 1
      1659: 1
      1663: 1
      1669: 1
      1673: 1
      1674: 1
      1733: 1
      1741: 1
      1749: 1
      1757: 1
      1817: 1
      1819: 1
      1825: 1
      1829: 1
      1833: 1
      1898: 1
      1906: 1
      1960: 1
      1962: 1
      2040: 1

2041:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: 2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+q
        38: q+1
        39: q^2+q
        40: q+1
        41: q^2+q
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+q+1
        59: q
        60: 2q
        61: 1
        62: q
        63: q+1
        64: q^2+q
        65: q+1
        66: q^2+q
        67: q+1
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q^2+q
        75: q+1
        76: q^2+q
        77: q+1
        78: q^2+q
        79: q+1
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       105: 1
       107: 2q
       108: 1
       109: q^2+q+1
       110: q
       111: q^2+q
       112: q+1
       113: q
       114: q+1
       115: q^2+q
       116: q+1
       117: q^2+q+1
       118: q
       119: 2q
       120: 1
       121: q
       122: q+1
       123: q^2+q
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q
       128: q+1
       129: q^2+q
       130: q+1
       131: q^2+q
       132: q+1
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^2+2q+1
       138: q^3+2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^3+2q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+q
       152: q+1
       153: q^2+q
       154: q+1
       155: q^2+q
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: q^3+2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q
       170: q
       171: 1
       173: q
       174: q
       175: 1
       177: q^2+q
       178: q+1
       179: q
       180: q+1
       181: q^2+q
       182: q+1
       183: 2q
       184: 1
       185: q^2+q+1
       186: q
       187: q^2+q
       188: q+1
       189: q
       190: q+1
       191: q^2+q+1
       192: q
       193: 2q
       194: 1
       195: q^2+q+1
       196: q
       197: q^2+q
       198: q+1
       199: 2q
       200: 1
       201: 2q
       202: 1
       203: q+1
       205: q
       206: 1
       207: q
       208: q+1
       209: q
       210: q+1
       211: q^2+q
       212: q+1
       213: q^2+q
       214: q+1
       215: q^2+q
       216: q+1
       217: q^2+q
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^3+2q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^3+2q^2+2q+1
       229: q^2+2q+1
       230: q^3+2q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+q
       238: q+1
       239: q^2+q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       260: q
       261: 1
       263: q
       264: q
       265: 1
       267: q
       268: q
       270: 1
       271: q
       272: 1
       275: q
       276: q
       277: 1
       279: q
       280: q+1
       281: q^2+q
       282: q+1
       283: 2q
       284: 1
       285: q^2+q+1
       286: q
       287: q
       288: q+1
       289: q^2+q
       290: q+1
       291: q^2+q
       292: q+1
       293: 2q
       294: 1
       295: q^2+q+1
       296: q
       297: q
       298: q+1
       299: 2q
       300: 1
       301: q^2+q
       302: q+1
       303: q^2+q+1
       304: q
       305: q^2+q
       306: q+1
       307: 2q
       308: 1
       309: q+1
       311: q
       312: 1
       313: q
       314: 1
       315: q^2+q
       316: q+1
       317: q
       318: q+1
       319: 2q
       320: 1
       321: q+1
       323: q
       324: 1
       325: q
       326: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q^2+q
       339: q+1
       340: q^2+q
       341: q+1
       342: q^2+q
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+2q^2+2q+1
       351: q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q+1
       360: q^2+q
       361: q+1
       362: q^2+q
       363: q+1
       364: q^2+q
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       379: 1
       381: q
       382: q
       383: 1
       385: q
       386: q
       387: 1
       389: q
       390: q
       392: 1
       393: q
       394: q
       395: 1
       397: q
       398: 1
       401: q
       402: 1
       405: q
       408: 1
       413: q
       414: q+1
       417: q^2+q
       418: q+1
       419: 2q
       420: 1
       421: q^2+q+1
       422: q
       423: q
       424: q+1
       425: q^2+q
       426: q+1
       427: q
       428: q+1
       429: 2q
       430: 1
       431: q^2+q+1
       432: q
       433: q^2+q
       434: q+1
       435: q^2+q
       436: q+1
       437: 2q
       438: 1
       439: q^2+q+1
       440: q
       441: q
       442: q+1
       443: 2q
       444: 1
       445: q^2+q
       446: q+1
       447: 2q
       448: 1
       449: q+1
       451: q
       452: 1
       453: q
       454: 1
       455: q
       456: 1
       457: 1
       460: 1
       461: q+1
       463: q
       464: 1
       465: q
       466: q+1
       467: q^2+q
       468: q+1
       469: q
       470: q+1
       471: 2q
       472: 1
       473: q+1
       475: q
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 2q+1
       482: q^2+2q+1
       483: 2q+1
       484: 2q+1
       485: q^2+q
       486: q+1
       487: q^2+q
       488: q+1
       489: q^2+q
       490: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: q
       523: 1
       529: q
       530: q
       531: 1
       533: q
       534: q
       535: 1
       537: q
       538: q
       540: 1
       541: q
       542: q
       544: 1
       545: q
       546: q
       548: 1
       549: q
       550: 1
       553: q
       554: 1
       558: 1
       561: q
       562: 1
       565: q
       567: 1
       569: q
       572: 1
       573: q
       576: 1
       577: q
       581: 1
       585: q
       586: q+1
       589: 2q
       590: 1
       591: q+1
       593: 2q
       594: 1
       595: q^2+q+1
       596: q
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q
       602: q+1
       603: 2q
       604: 1
       605: q^2+q
       606: q+1
       607: q^2+q+1
       608: q
       609: q
       610: q+1
       613: q^2+q
       614: q+1
       615: 2q
       616: 1
       617: q^2+q
       618: q+1
       619: q
       620: 1
       621: 1
       623: q
       624: 1
       626: 1
       629: q
       630: 1
       631: q+1
       633: q
       634: 1
       639: q
       640: q+1
       641: 2q
       642: 1
       643: q+1
       645: q
       646: 1
       647: q
       648: 1
       649: 1
       651: q
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       658: q^2+q
       659: q+1
       660: q^2+q
       661: q+1
       662: q^2+q
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       700: 1
       709: q
       710: q
       711: 1
       713: q
       714: 1
       717: q
       718: q
       719: 1
       721: q
       722: q
       724: 1
       725: q
       726: q
       728: 1
       733: q
       734: q
       736: 1
       737: q
       738: 1
       742: 1
       749: q
       750: 1
       753: q
       755: 1
       757: q
       760: 1
       764: 1
       765: q
       767: 1
       769: q
       773: 1
       775: q
       776: q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       785: 2q
       786: 1
       787: q+1
       791: q
       792: 1
       793: 2q
       794: 1
       795: q^2+q
       796: q+1
       797: q
       798: q+1
       801: 2q
       802: 1
       803: q+1
       805: 2q
       806: 1
       807: q^2+q+1
       808: q
       809: q^2+q
       810: q+1
       811: q
       812: q+1
       815: q
       816: 1
       817: q+1
       819: q
       820: 1
       822: 1
       825: q
       826: 1
       827: 1
       831: 1
       833: q
       834: 1
       836: 1
       839: 1
       843: q
       844: 1
       845: q
       846: 1
       847: 1
       849: q
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       891: 1
       900: q
       901: 1
       904: q
       905: q
       907: 1
       908: q
       910: 1
       916: q
       917: q
       919: 1
       920: q
       921: q
       923: 1
       924: q
       925: 1
       928: q
       929: q
       931: 1
       940: q
       941: 1
       945: 1
       949: 1
       960: q
       963: 1
       964: q
       966: 1
       968: q
       972: 1
       977: 1
       990: 1
       994: q
       995: q+1
       998: q+1
      1000: 2q
      1001: 1
      1004: q
      1005: 1
      1006: 1
      1009: 1
      1010: q
      1011: 1
      1012: q
      1013: 1
      1016: q
      1017: 1
      1020: q^2+q
      1021: q+1
      1022: q
      1023: q+1
      1026: 2q
      1027: 1
      1028: q+1
      1032: 1
      1036: q
      1037: 1
      1039: 1
      1044: 1
      1047: 1
      1049: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1060: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1093: 1
      1114: q
      1115: 1
      1122: q
      1123: q
      1125: 1
      1126: q
      1129: 1
      1130: q
      1132: 1
      1137: 1
      1138: q
      1142: 1
      1152: q
      1153: 1
      1156: q
      1157: q
      1159: 1
      1160: q
      1161: 1
      1173: 1
      1196: 1
      1201: 1
      1203: 1
      1216: 1
      1218: q
      1219: 1
      1221: 1
      1225: 1
      1228: q
      1229: 1
      1230: q
      1231: q+1
      1232: q+1
      1234: 2q
      1235: 1
      1240: q
      1241: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1260: 1
      1263: 1
      1267: 1
      1270: 1
      1274: q
      1275: 1
      1277: 1
      1278: q
      1279: 1
      1280: q
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: q
      1297: 1
      1328: 1
      1333: 1
      1348: q
      1349: 1
      1356: q
      1357: q
      1359: 1
      1360: q
      1362: 1
      1364: q
      1365: 1
      1370: 1
      1381: 1
      1412: 1
      1419: 1
      1430: q
      1434: 1
      1437: 1
      1440: 1
      1442: q
      1443: 1
      1445: 1
      1450: 1
      1454: q
      1455: 1
      1460: 1
      1465: 1
      1466: 1
      1475: 1
      1478: 1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1501: q
      1507: 1
      1540: 1
      1551: 1
      1576: 1
      1581: 1
      1608: 1
      1640: 1
      1642: 1
      1645: 1
      1647: q
      1648: 1
      1649: 1
      1653: 1
      1660: 1
      1663: 1
      1670: 1
      1673: 1
      1674: 1
      1735: 1
      1743: 1
      1750: 1
      1758: 1
      1818: 1
      1819: 1
      1826: 1
      1829: 1
      1833: 1
      1899: 1
      1908: 1
      1961: 1
      1962: 1
      2041: 1

2042:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: 2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+q
        39: q+1
        40: q^2+q
        41: q+1
        42: q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: 2q
        61: 1
        62: q+1
        63: q
        64: q+1
        65: q^2+q
        66: q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q+1
        75: q^2+q
        76: q+1
        77: q^2+q
        78: q+1
        79: q^2+q
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: q
       106: 1
       107: 2q
       108: 1
       109: q
       110: q^2+q+1
       111: q+1
       112: q^2+q
       113: q+1
       114: q
       115: q+1
       116: q^2+q
       117: q
       118: q^2+q+1
       119: 2q
       120: 1
       121: q+1
       122: q
       123: q+1
       124: q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+q
       129: q+1
       130: q^2+q
       131: q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^2+2q+1
       138: q^3+2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^3+2q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+q
       153: q+1
       154: q^2+q
       155: q+1
       156: q^2+q
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: q^3+2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q
       170: q
       172: 1
       173: q
       174: q
       176: 1
       177: q+1
       178: q^2+q
       179: q+1
       180: q
       181: q+1
       182: q^2+q
       183: 2q
       184: 1
       185: q
       186: q^2+q+1
       187: q+1
       188: q^2+q
       189: q+1
       190: q
       191: q
       192: q^2+q+1
       193: 2q
       194: 1
       195: q
       196: q^2+q+1
       197: q+1
       198: q^2+q
       199: 2q
       200: 1
       201: 2q
       202: 1
       204: q+1
       205: 1
       206: q
       207: q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q^2+q
       213: q+1
       214: q^2+q
       215: q+1
       216: q^2+q
       217: q+1
       218: q^2+q
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^3+2q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^3+2q^2+2q+1
       229: q^2+2q+1
       230: q^3+2q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+q
       239: q+1
       240: q^2+q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       260: q
       262: 1
       263: q
       264: q
       266: 1
       267: q
       268: q
       269: 1
       273: 1
       274: q
       275: q
       276: q
       278: 1
       279: q+1
       280: q
       281: q+1
       282: q^2+q
       283: 2q
       284: 1
       285: q
       286: q^2+q+1
       287: q+1
       288: q
       289: q+1
       290: q^2+q
       291: q+1
       292: q^2+q
       293: 2q
       294: 1
       295: q
       296: q^2+q+1
       297: q+1
       298: q
       299: 2q
       300: 1
       301: q+1
       302: q^2+q
       303: q
       304: q^2+q+1
       305: q+1
       306: q^2+q
       307: 2q
       308: 1
       310: q+1
       311: 1
       312: q
       313: 1
       314: q
       315: q+1
       316: q^2+q
       317: q+1
       318: q
       319: 2q
       320: 1
       322: q+1
       323: 1
       324: q
       325: q+1
       326: q
       333: q^2+2q+1
       334: 2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q+1
       339: q^2+q
       340: q+1
       341: q^2+q
       342: q+1
       343: q^2+q
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+2q^2+2q+1
       351: q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       361: q^2+q
       362: q+1
       363: q^2+q
       364: q+1
       365: q^2+q
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: q
       380: 1
       381: q
       382: q
       384: 1
       385: q
       386: q
       388: 1
       389: q
       390: q
       391: 1
       393: q
       394: q
       396: 1
       399: 1
       400: q
       403: q
       404: 1
       406: 1
       407: q
       413: q+1
       414: q
       417: q+1
       418: q^2+q
       419: 2q
       420: 1
       421: q
       422: q^2+q+1
       423: q+1
       424: q
       425: q+1
       426: q^2+q
       427: q+1
       428: q
       429: 2q
       430: 1
       431: q
       432: q^2+q+1
       433: q+1
       434: q^2+q
       435: q+1
       436: q^2+q
       437: 2q
       438: 1
       439: q
       440: q^2+q+1
       441: q+1
       442: q
       443: 2q
       444: 1
       445: q+1
       446: q^2+q
       447: 2q
       448: 1
       450: q+1
       451: 1
       452: q
       453: q
       454: 1
       455: 1
       456: q
       458: 1
       459: 1
       462: q+1
       463: 1
       464: q
       465: q+1
       466: q
       467: q+1
       468: q^2+q
       469: q+1
       470: q
       471: 2q
       472: 1
       474: q+1
       475: 1
       476: q
       477: 1
       478: q
       479: 1
       480: q
       481: 2q+1
       482: q^2+2q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+q
       487: q+1
       488: q^2+q
       489: q+1
       490: q^2+q
       491: q^2+2q+1
       492: q^2+2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: q
       524: 1
       529: q
       530: q
       532: 1
       533: q
       534: q
       536: 1
       537: q
       538: q
       539: 1
       541: q
       542: q
       543: 1
       545: q
       546: q
       547: 1
       551: q
       552: 1
       555: 1
       556: q
       559: 1
       563: 1
       564: q
       566: q
       568: 1
       570: 1
       571: q
       574: q
       575: 1
       577: 1
       581: q
       585: q+1
       586: q
       589: 2q
       590: 1
       592: q+1
       593: 2q
       594: 1
       595: q
       596: q^2+q+1
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: q+1
       602: q
       603: 2q
       604: 1
       605: q+1
       606: q^2+q
       607: q
       608: q^2+q+1
       609: q+1
       610: q
       613: q+1
       614: q^2+q
       615: 2q
       616: 1
       617: q+1
       618: q^2+q
       619: q
       620: 1
       622: 1
       623: 1
       624: q
       625: 1
       629: 1
       630: q
       632: q+1
       633: 1
       634: q
       639: q+1
       640: q
       641: 2q
       642: 1
       644: q+1
       645: 1
       646: q
       647: q
       648: 1
       650: 1
       651: 1
       652: q
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       659: q^2+q
       660: q+1
       661: q^2+q
       662: q+1
       663: q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       699: q
       709: q
       710: q
       712: 1
       715: q
       716: 1
       717: q
       718: q
       720: 1
       721: q
       722: q
       723: 1
       725: q
       726: q
       727: 1
       733: q
       734: q
       735: 1
       739: 1
       740: q
       743: 1
       751: 1
       752: q
       754: q
       756: 1
       758: 1
       759: q
       762: 1
       766: q
       768: 1
       769: 1
       773: q
       775: q+1
       776: q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       785: 2q
       786: 1
       788: q+1
       791: 1
       792: q
       793: 2q
       794: 1
       795: q+1
       796: q^2+q
       797: q+1
       798: q
       801: 2q
       802: 1
       804: q+1
       805: 2q
       806: 1
       807: q
       808: q^2+q+1
       809: q+1
       810: q^2+q
       811: q+1
       812: q
       815: q
       816: 1
       818: q+1
       819: 1
       820: q
       821: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       834: q
       835: 1
       840: 1
       843: 1
       844: q
       845: q
       846: 1
       848: 1
       849: 1
       850: q
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       890: q
       902: 1
       903: q
       904: q
       905: q
       906: 1
       909: q
       911: 1
       916: q
       917: q
       918: 1
       920: q
       921: q
       922: 1
       926: q
       927: 1
       928: q
       929: q
       930: 1
       942: 1
       943: q
       946: 1
       950: 1
       961: 1
       962: q
       965: q
       967: 1
       968: 1
       972: q
       975: 1
       991: 1
       994: q+1
       995: q
       999: q+1
      1000: 2q
      1001: 1
      1004: q
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1011: q
      1012: 1
      1013: q
      1016: q
      1017: 1
      1020: q+1
      1021: q^2+q
      1022: q+1
      1023: q
      1026: 2q
      1027: 1
      1029: q+1
      1033: 1
      1036: 1
      1037: q
      1038: 1
      1045: 1
      1046: 1
      1048: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1065: q
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: 1
      1092: q
      1116: 1
      1117: q
      1122: q
      1123: q
      1124: 1
      1127: 1
      1128: q
      1131: q
      1133: 1
      1135: 1
      1138: 1
      1142: q
      1154: 1
      1155: q
      1156: q
      1157: q
      1158: 1
      1162: q
      1163: 1
      1174: 1
      1197: 1
      1199: 1
      1204: 1
      1217: 1
      1218: q
      1219: 1
      1220: 1
      1224: 1
      1228: q
      1229: 1
      1230: q+1
      1231: q
      1233: q+1
      1234: 2q
      1235: 1
      1240: q
      1241: 1
      1243: 1
      1247: 1
      1248: 1
      1251: 1
      1261: 1
      1262: 1
      1266: 1
      1271: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1279: q
      1280: 1
      1281: q
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1296: q
      1329: 1
      1331: 1
      1350: 1
      1351: q
      1356: q
      1357: q
      1358: 1
      1361: 1
      1363: q
      1366: q
      1367: 1
      1369: 1
      1382: 1
      1413: 1
      1420: 1
      1430: 1
      1434: q
      1436: 1
      1441: 1
      1442: q
      1443: 1
      1444: 1
      1451: 1
      1454: q
      1455: 1
      1461: 1
      1464: 1
      1467: 1
      1474: 1
      1479: 1
      1482: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1506: 1
      1508: q
      1538: 1
      1552: 1
      1578: 1
      1580: 1
      1609: 1
      1639: 1
      1641: 1
      1646: 1
      1647: q
      1648: 1
      1650: 1
      1654: 1
      1659: 1
      1664: 1
      1669: 1
      1673: 1
      1674: 1
      1736: 1
      1742: 1
      1752: 1
      1759: 1
      1817: 1
      1820: 1
      1825: 1
      1830: 1
      1833: 1
      1900: 1
      1907: 1
      1960: 1
      1963: 1
      2042: 1

2043:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: 2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+q
        38: q+1
        39: q^2+q
        40: q+1
        41: q^2+q
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^3+2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q
        59: q^2+q+1
        60: 1
        61: 2q
        62: q
        63: q+1
        64: q^2+q
        65: q+1
        66: q^2+q
        67: q+1
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q^2+q
        75: q+1
        76: q^2+q
        77: q+1
        78: q^2+q
        79: q+1
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: 1
       105: q
       106: q
       107: 1
       108: 2q
       109: q
       110: q^2+q+1
       111: q^2+q
       112: q+1
       113: q
       114: q+1
       115: q^2+q
       116: q+1
       117: q
       118: q^2+q+1
       119: 1
       120: 2q
       121: q
       122: q+1
       123: q^2+q
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q
       128: q+1
       129: q^2+q
       130: q+1
       131: q^2+q
       132: q+1
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^2+2q+1
       138: q^3+2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^3+2q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+q
       152: q+1
       153: q^2+q
       154: q+1
       155: q^2+q
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: q^3+2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: 1
       171: q
       172: q
       174: 1
       175: q
       176: q
       177: q^2+q
       178: q+1
       179: q
       180: q+1
       181: q^2+q
       182: q+1
       183: 1
       184: 2q
       185: q
       186: q^2+q+1
       187: q^2+q
       188: q+1
       189: q
       190: q+1
       191: q
       192: q^2+q+1
       193: 1
       194: 2q
       195: q
       196: q^2+q+1
       197: q^2+q
       198: q+1
       199: 1
       200: 2q
       201: 1
       202: 2q
       204: q+1
       205: q
       206: 1
       207: q
       208: q+1
       209: q
       210: q+1
       211: q^2+q
       212: q+1
       213: q^2+q
       214: q+1
       215: q^2+q
       216: q+1
       217: q^2+q
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^3+2q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^3+2q^2+2q+1
       229: q^2+2q+1
       230: q^3+2q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+q
       238: q+1
       239: q^2+q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: 1
       261: q
       262: q
       264: 1
       265: q
       266: q
       268: 1
       269: q
       270: q
       273: q
       274: 1
       276: 1
       277: q
       278: q
       279: q
       280: q+1
       281: q^2+q
       282: q+1
       283: 1
       284: 2q
       285: q
       286: q^2+q+1
       287: q
       288: q+1
       289: q^2+q
       290: q+1
       291: q^2+q
       292: q+1
       293: 1
       294: 2q
       295: q
       296: q^2+q+1
       297: q
       298: q+1
       299: 1
       300: 2q
       301: q^2+q
       302: q+1
       303: q
       304: q^2+q+1
       305: q^2+q
       306: q+1
       307: 1
       308: 2q
       310: q+1
       311: q
       312: 1
       313: q
       314: 1
       315: q^2+q
       316: q+1
       317: q
       318: q+1
       319: 1
       320: 2q
       322: q+1
       323: q
       324: 1
       325: q
       326: q+1
       333: q^2+2q+1
       334: 2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q^2+q
       339: q+1
       340: q^2+q
       341: q+1
       342: q^2+q
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^3+2q^2+2q+1
       351: q^2+2q+1
       352: 2q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: 1
       358: q+1
       359: q+1
       360: q^2+q
       361: q+1
       362: q^2+q
       363: q+1
       364: q^2+q
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       380: q
       382: 1
       383: q
       384: q
       386: 1
       387: q
       388: q
       390: 1
       391: q
       392: q
       394: 1
       395: q
       396: q
       399: q
       400: 1
       403: 1
       404: q
       406: q
       407: 1
       413: q
       414: q+1
       417: q^2+q
       418: q+1
       419: 1
       420: 2q
       421: q
       422: q^2+q+1
       423: q
       424: q+1
       425: q^2+q
       426: q+1
       427: q
       428: q+1
       429: 1
       430: 2q
       431: q
       432: q^2+q+1
       433: q^2+q
       434: q+1
       435: q^2+q
       436: q+1
       437: 1
       438: 2q
       439: q
       440: q^2+q+1
       441: q
       442: q+1
       443: 1
       444: 2q
       445: q^2+q
       446: q+1
       447: 1
       448: 2q
       450: q+1
       451: q
       452: 1
       453: 1
       454: q
       455: q
       456: 1
       458: 1
       460: 1
       462: q+1
       463: q
       464: 1
       465: q
       466: q+1
       467: q^2+q
       468: q+1
       469: q
       470: q+1
       471: 1
       472: 2q
       474: q+1
       475: q
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: 2q+1
       482: q^2+2q+1
       483: 2q+1
       484: 2q+1
       485: q^2+q
       486: q+1
       487: q^2+q
       488: q+1
       489: q^2+q
       490: q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 1
       500: q+1
       501: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: q^2+2q+1
       513: 1
       514: q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       524: q
       530: 1
       531: q
       532: q
       534: 1
       535: q
       536: q
       538: 1
       539: q
       540: q
       542: 1
       543: q
       544: q
       546: 1
       547: q
       548: q
       551: 1
       552: q
       555: q
       556: 1
       560: 1
       563: q
       564: 1
       566: 1
       568: q
       570: q
       571: 1
       574: 1
       575: q
       577: q
       581: 1
       585: q
       586: q+1
       589: 1
       590: 2q
       592: q+1
       593: 1
       594: 2q
       595: q
       596: q^2+q+1
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q
       602: q+1
       603: 1
       604: 2q
       605: q^2+q
       606: q+1
       607: q
       608: q^2+q+1
       609: q
       610: q+1
       613: q^2+q
       614: q+1
       615: 1
       616: 2q
       617: q^2+q
       618: q+1
       619: 1
       620: q
       622: 1
       623: q
       624: 1
       626: 1
       629: q
       630: 1
       632: q+1
       633: q
       634: 1
       639: q
       640: q+1
       641: 1
       642: 2q
       644: q+1
       645: q
       646: 1
       647: 1
       648: q
       650: 1
       651: q
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       658: q^2+q
       659: q+1
       660: q^2+q
       661: q+1
       662: q^2+q
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: 2q+1
       676: q^2+2q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       680: q+1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       699: 1
       710: 1
       711: q
       712: q
       715: 1
       716: q
       718: 1
       719: q
       720: q
       722: 1
       723: q
       724: q
       726: 1
       727: q
       728: q
       734: 1
       735: q
       736: q
       739: q
       740: 1
       744: 1
       751: q
       752: 1
       754: 1
       756: q
       758: q
       759: 1
       763: 1
       766: 1
       768: q
       769: q
       773: 1
       775: q
       776: q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       785: 1
       786: 2q
       788: q+1
       791: q
       792: 1
       793: 1
       794: 2q
       795: q^2+q
       796: q+1
       797: q
       798: q+1
       801: 1
       802: 2q
       804: q+1
       805: 1
       806: 2q
       807: q
       808: q^2+q+1
       809: q^2+q
       810: q+1
       811: q
       812: q+1
       815: 1
       816: q
       818: q+1
       819: q
       820: 1
       822: 1
       825: 1
       826: q
       828: 1
       832: 1
       833: q
       834: 1
       836: 1
       840: 1
       843: q
       844: 1
       845: 1
       846: q
       848: 1
       849: q
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: q+1
       870: q^2+2q+1
       871: 2q+1
       872: q+1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q
       890: 1
       902: q
       903: 1
       905: 1
       906: q
       907: q
       909: 1
       911: q
       917: 1
       918: q
       919: q
       921: 1
       922: q
       923: q
       926: 1
       927: q
       929: 1
       930: q
       931: q
       942: q
       943: 1
       947: 1
       951: 1
       961: q
       962: 1
       965: 1
       967: q
       968: q
       972: 1
       976: 1
       989: 1
       994: q
       995: q+1
       999: q+1
      1000: 1
      1001: 2q
      1004: 1
      1005: q
      1007: 1
      1009: 1
      1010: q
      1011: 1
      1012: q
      1013: 1
      1016: 1
      1017: q
      1020: q^2+q
      1021: q+1
      1022: q
      1023: q+1
      1026: 1
      1027: 2q
      1029: q+1
      1033: 1
      1036: q
      1037: 1
      1039: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1060: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: 1
      1091: q
      1092: 1
      1116: q
      1117: 1
      1123: 1
      1124: q
      1125: q
      1127: q
      1128: 1
      1131: 1
      1133: q
      1136: 1
      1138: q
      1142: 1
      1154: q
      1155: 1
      1157: 1
      1158: q
      1159: q
      1162: 1
      1163: q
      1175: 1
      1195: 1
      1200: 1
      1205: 1
      1217: 1
      1218: 1
      1219: q
      1221: 1
      1225: 1
      1228: 1
      1229: q
      1230: q
      1231: q+1
      1233: q+1
      1234: 1
      1235: 2q
      1240: 1
      1241: q
      1243: 1
      1247: 1
      1249: 1
      1251: 1
      1261: 1
      1263: 1
      1267: 1
      1271: 1
      1274: q
      1275: 1
      1277: 1
      1278: q
      1279: 1
      1280: q
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: q
      1296: 1
      1327: 1
      1332: 1
      1350: q
      1351: 1
      1357: 1
      1358: q
      1359: q
      1361: q
      1363: 1
      1366: 1
      1367: q
      1371: 1
      1383: 1
      1411: 1
      1421: 1
      1430: q
      1434: 1
      1437: 1
      1441: 1
      1442: 1
      1443: q
      1445: 1
      1451: 1
      1454: 1
      1455: q
      1461: 1
      1465: 1
      1467: 1
      1475: 1
      1479: 1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1506: q
      1508: 1
      1539: 1
      1550: 1
      1577: 1
      1582: 1
      1610: 1
      1640: 1
      1642: 1
      1646: 1
      1647: 1
      1648: q
      1650: 1
      1654: 1
      1660: 1
      1664: 1
      1670: 1
      1673: 1
      1674: 1
      1734: 1
      1744: 1
      1751: 1
      1760: 1
      1818: 1
      1820: 1
      1826: 1
      1830: 1
      1833: 1
      1901: 1
      1909: 1
      1961: 1
      1963: 1
      2043: 1

2044:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q^2+q+1
        59: 2q
        60: 2q^2+2q+1
        61: q^2+q
        62: 2q^2+2q+1
        63: q^2+q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: 3q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q^2+q+1
       104: q
       105: q^2
       106: q
       107: 2q^2+2q+1
       108: q^2+q
       109: 2q^2+q+1
       110: 2q
       111: q^2+2q+1
       112: q^2+q
       113: 2q^2+2q+1
       114: q^2+q
       115: 2q^2+2q+1
       116: q^2+q
       117: 2q^2+q+1
       118: 2q
       119: 2q^2+2q+1
       120: q^2+q
       121: 2q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: q^2+3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q^2+q+1
       170: q
       171: q^2
       172: q
       173: q^2+q+1
       174: q
       175: q^2
       176: q
       177: q+1
       179: 2q+1
       181: 2q+1
       183: 2q^2+2q+1
       184: q^2+q
       185: 2q^2+q+1
       186: 2q
       187: q^2+2q+1
       188: q^2+q
       189: 2q^2+2q+1
       190: q^2+q
       191: 2q^2+q+1
       192: 2q
       193: 2q+1
       195: q^2+q+1
       196: 2q
       197: q+1
       198: q
       199: 2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       203: 2q^2+q+1
       204: 2q
       205: q^2+2q+1
       206: q^2+q
       207: q^2+2q+1
       208: q^2+q
       209: 2q^2+2q+1
       210: q^2+q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+3q+1
       244: 2q+1
       245: q^2+3q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q+1
       262: q
       263: q^2+q+1
       264: q
       265: q^2
       266: q
       267: q+1
       268: q
       271: q^2+q+1
       272: q^2
       273: q
       274: q
       275: q^2+q+1
       276: q
       277: q^2
       278: q
       279: 2q+1
       281: q+1
       283: q^2+q+1
       285: q^2+1
       286: q
       287: q+1
       289: 2q+1
       291: q+1
       293: 2q^2+2q+1
       294: q^2+q
       295: 2q^2+q+1
       296: 2q
       297: q^2+2q+1
       298: q^2+q
       299: 2q+1
       301: q+1
       303: q^2+q+1
       304: 2q
       305: q+1
       306: q
       307: 2q^2+2q+1
       308: q^2+q
       309: 2q^2+q+1
       310: 2q
       311: 2q+1
       313: q^2+2q+1
       314: q^2+q
       315: q+1
       317: 2q+1
       319: 2q+1
       321: q^2+q+1
       322: 2q
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^2+2q+1
       345: q^2+3q+1
       346: q^2+2q+1
       347: 2q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: 2q^2+3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       377: 1
       381: q+1
       384: q
       385: q^2+q+1
       386: q
       387: q^2
       388: q
       389: q+1
       393: q+1
       394: q
       397: q+1
       399: q
       401: q^2+q+1
       402: q^2
       403: q
       404: q
       405: q+1
       407: q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       419: q^2+q+1
       421: q^2+1
       422: q
       423: q+1
       425: q+1
       427: 2q+1
       429: q+1
       431: q^2+1
       432: q
       433: 1
       435: q+1
       437: 2q+1
       439: q^2+q+1
       440: 2q
       441: q+1
       442: q
       443: 2q+1
       445: q+1
       447: q^2+q+1
       449: q^2+1
       450: q
       451: q+1
       453: 2q^2+2q+1
       454: q^2+q
       455: 2q+1
       457: 2q^2+q+1
       458: 2q
       459: q^2+2q+1
       460: q^2+q
       461: q^2+q+1
       462: 2q
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       471: 2q+1
       473: q^2+q+1
       474: 2q
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: 2q+1
       512: q+1
       513: q^2+3q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       521: 1
       525: q+1
       528: q
       529: 1
       533: 1
       537: q+1
       541: q+1
       542: q
       545: q+1
       549: 1
       553: q+1
       555: q
       557: q^2+q+1
       558: q^2
       559: q
       560: q
       561: q+1
       563: q
       565: q+1
       566: q
       569: q+1
       573: q+1
       574: q
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+q+1
       591: q^2+1
       592: q
       593: q+1
       595: q^2+1
       596: q
       597: q+1
       599: q+1
       601: 2q+1
       603: q+1
       605: 1
       607: q^2+1
       608: q
       609: 1
       611: q+1
       613: 1
       615: 2q+1
       617: q+1
       619: q^2+q+1
       621: q^2+1
       622: q
       623: q+1
       625: q+1
       627: 2q+1
       629: q+1
       631: q^2+q+1
       632: 2q
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       641: q+1
       643: q^2+1
       644: q
       645: 1
       647: 2q+1
       649: q^2+q+1
       650: 2q
       651: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q^2+2q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: 2
       675: q+1
       676: q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+2
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q^2+2q+1
       684: q^2+3q+1
       685: q^2+2q+1
       686: q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       693: q+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q+1
       733: q+1
       737: 1
       741: 1
       745: q+1
       747: q
       749: q+1
       751: q
       753: 1
       757: q+1
       761: q+1
       763: q
       765: q+1
       766: q
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       785: q+1
       787: q^2+1
       788: q
       789: 2q+1
       791: 1
       793: 2
       795: 2
       797: 1
       799: 1
       801: q+1
       805: q+1
       807: q^2+1
       808: q
       809: 1
       811: 1
       813: q+1
       815: 2q+1
       817: 1
       818: 1
       819: q+2
       821: q+1
       823: q+1
       825: q^2+q+1
       827: q^2+1
       828: q
       829: q+1
       831: q^2+1
       832: q
       833: q+1
       835: q+1
       837: 2q+1
       839: q^2+q+1
       840: 2q
       841: q+1
       843: 1
       844: 1
       845: q+1
       847: q^2+1
       848: q
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: 2
       870: 2
       871: q+1
       872: q+1
       873: q+2
       874: q+2
       875: q^2+2q+1
       876: q^2+2q+1
       877: q+1
       878: q^2+2q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       884: q+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 2
       920: 1
       928: 1
       932: q+1
       936: 1
       940: 1
       942: 1
       944: 1
       948: 1
       952: 1
       956: q+1
       958: q
       960: 1
       964: 1
       965: 1
       968: 1
       971: 1
       974: 1
       978: q+1
       982: q+1
       988: q+1
       989: q
       992: 2
       994: 2
       996: q+2
       998: 1
       999: 1
      1000: 2
      1002: q+1
      1004: q+1
      1006: q^2+1
      1007: q
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1014: 2
      1016: 2
      1018: 1
      1020: 2
      1022: 1
      1024: 1
      1026: q+1
      1030: q+2
      1032: 1
      1033: 1
      1034: q+1
      1036: q+2
      1038: q+1
      1040: q+1
      1042: q+1
      1044: q^2+1
      1045: q
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1052: q+1
      1056: q+1
      1058: q^2+1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1066: q+2
      1068: q+2
      1070: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 1
      1077: 2
      1078: q+1
      1079: q+2
      1080: 2
      1081: q+2
      1082: q^2+2q+1
      1083: q+1
      1084: 2
      1085: q+1
      1086: 1
      1089: 1
      1098: q+1
      1110: 1
      1114: 1
      1116: 1
      1118: 1
      1122: 2
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1138: 1
      1141: 1
      1144: 2
      1148: 1
      1156: 1
      1164: 1
      1166: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1191: 1
      1194: 1
      1195: 1
      1198: 1
      1206: 1
      1210: 2
      1212: q+2
      1214: 2
      1216: 1
      1217: 1
      1218: 2
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 2
      1228: 2
      1230: 1
      1234: 1
      1236: 2
      1238: 1
      1240: q+1
      1244: q+2
      1246: 1
      1247: 1
      1248: 2
      1250: 1
      1251: 1
      1252: q+2
      1254: 2
      1256: q+1
      1258: q+1
      1260: q^2+1
      1261: q
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1268: q+1
      1272: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 1
      1288: 2
      1289: q+1
      1290: 1
      1293: 1
      1302: 1
      1305: 1
      1314: 1
      1316: 1
      1318: 2
      1322: 1
      1326: 1
      1327: 1
      1330: 1
      1334: 1
      1337: 1
      1340: 2
      1352: 1
      1356: 1
      1372: 1
      1374: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1388: 2
      1392: 1
      1396: 1
      1397: 1
      1400: 1
      1404: 1
      1407: 1
      1410: 1
      1411: 1
      1414: 1
      1422: 1
      1430: 1
      1433: 1
      1438: 2
      1440: 1
      1441: 1
      1442: 2
      1444: 1
      1445: 1
      1446: 1
      1448: 1
      1452: 2
      1454: 1
      1456: 2
      1458: q+2
      1460: 1
      1461: 1
      1462: 2
      1464: 1
      1468: 1
      1470: 1
      1472: 2
      1474: 1
      1476: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1489: 1
      1492: 1
      1513: 1
      1516: 1
      1525: 1
      1528: 1
      1541: 1
      1543: 1
      1545: 2
      1549: 1
      1550: 1
      1553: 1
      1556: 1
      1559: 1
      1567: 1
      1583: 1
      1585: 1
      1587: 2
      1591: 1
      1595: 1
      1596: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1634: 1
      1641: 1
      1643: 1
      1647: 1
      1651: 2
      1653: 1
      1654: 1
      1655: 2
      1657: 1
      1661: 1
      1665: 1
      1667: 2
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1678: 1
      1699: 1
      1702: 1
      1745: 1
      1761: 1
      1763: 1
      1765: 2
      1773: 1
      1774: 1
      1777: 1
      1781: 1
      1789: 1
      1801: 1
      1804: 1
      1815: 1
      1821: 1
      1827: 1
      1831: 1
      1833: 1
      1858: 1
      1861: 1
      1918: 1
      1936: 1
      1956: 1
      1964: 1
      2044: 1

2045:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: 2q^2+q+1
        60: 2q^2+2q+1
        61: q^2+q
        62: q^2+q
        63: 2q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 3q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q^2+q+1
       105: q
       106: q^2
       107: 2q^2+2q+1
       108: q^2+q
       109: 2q
       110: 2q^2+q+1
       111: q^2+q
       112: q^2+2q+1
       113: q^2+q
       114: 2q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: 2q
       118: 2q^2+q+1
       119: 2q^2+2q+1
       120: q^2+q
       121: q^2+q
       122: 2q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: q^2+3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q^2+q+1
       171: q
       172: q^2
       173: q
       174: q^2+q+1
       175: q
       176: q^2
       178: q+1
       180: 2q+1
       182: 2q+1
       183: 2q^2+2q+1
       184: q^2+q
       185: 2q
       186: 2q^2+q+1
       187: q^2+q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: 2q
       192: 2q^2+q+1
       193: 2q+1
       195: 2q
       196: q^2+q+1
       197: q
       198: q+1
       199: 2q^2+2q+1
       200: q^2+q
       201: 2q^2+2q+1
       202: q^2+q
       203: 2q
       204: 2q^2+q+1
       205: q^2+q
       206: q^2+2q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+q
       210: 2q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+3q+1
       244: 2q+1
       245: q^2+3q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q+1
       261: q
       263: q
       264: q^2+q+1
       265: q
       266: q^2
       267: q
       268: q+1
       271: q
       272: q
       273: q^2
       274: q^2+q+1
       275: q
       276: q^2+q+1
       277: q
       278: q^2
       280: 2q+1
       282: q+1
       283: q^2+q+1
       285: q
       286: q^2+1
       288: q+1
       290: 2q+1
       292: q+1
       293: 2q^2+2q+1
       294: q^2+q
       295: 2q
       296: 2q^2+q+1
       297: q^2+q
       298: q^2+2q+1
       299: 2q+1
       302: q+1
       303: 2q
       304: q^2+q+1
       305: q
       306: q+1
       307: 2q^2+2q+1
       308: q^2+q
       309: 2q
       310: 2q^2+q+1
       312: 2q+1
       313: q^2+q
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       319: 2q+1
       321: 2q
       322: q^2+q+1
       323: q
       324: q+1
       325: q^2+q
       326: 2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^2+2q+1
       345: q^2+3q+1
       346: q^2+2q+1
       347: 2q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: 2q^2+3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       378: 1
       382: q+1
       383: q
       385: q
       386: q^2+q+1
       387: q
       388: q^2
       390: q+1
       393: q
       394: q+1
       398: q
       400: q+1
       401: q
       402: q
       403: q^2+q+1
       404: q^2
       405: q
       407: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       419: q^2+q+1
       421: q
       422: q^2+1
       424: q+1
       426: q+1
       428: 2q+1
       429: q+1
       431: q
       432: q^2+1
       434: 1
       436: q+1
       437: 2q+1
       439: 2q
       440: q^2+q+1
       441: q
       442: q+1
       443: 2q+1
       446: q+1
       447: q^2+q+1
       449: q
       450: q^2+1
       452: q+1
       453: 2q^2+2q+1
       454: q^2+q
       456: 2q+1
       457: 2q
       458: 2q^2+q+1
       459: q^2+q
       460: q^2+2q+1
       461: 2q
       462: q^2+q+1
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       471: 2q+1
       473: 2q
       474: q^2+q+1
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: 2q+1
       512: q+1
       513: q^2+3q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       522: 1
       526: q+1
       527: q
       530: 1
       534: 1
       538: q+1
       541: q
       542: q+1
       546: q+1
       551: 1
       554: q
       556: q+1
       557: q
       558: q
       559: q^2
       560: q^2+q+1
       562: q
       564: q+1
       565: q
       566: q+1
       571: q+1
       573: q
       574: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+q+1
       591: q
       592: q^2+1
       593: q+1
       595: q
       596: q^2+1
       598: q+1
       600: q+1
       602: 2q+1
       603: q+1
       606: 1
       607: q
       608: q^2+1
       610: 1
       612: q+1
       614: 1
       615: 2q+1
       618: q+1
       619: q^2+q+1
       621: q
       622: q^2+1
       624: q+1
       626: q+1
       628: 2q+1
       630: q+1
       631: 2q
       632: q^2+q+1
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       641: q+1
       643: q
       644: q^2+1
       646: 1
       647: 2q+1
       649: 2q
       650: q^2+q+1
       652: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q^2+2q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: 2
       675: q+1
       676: q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+2
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q^2+2q+1
       684: q^2+3q+1
       685: q^2+2q+1
       686: q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       699: q+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q+1
       734: q+1
       740: 1
       744: 1
       746: q
       748: q+1
       750: q
       752: q+1
       754: 1
       759: q+1
       761: q
       763: q+1
       765: q
       766: q+1
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       785: q+1
       787: q
       788: q^2+1
       790: 2q+1
       792: 1
       793: 2
       796: 2
       798: 1
       800: 1
       801: q+1
       805: q+1
       807: q
       808: q^2+1
       810: 1
       812: 1
       814: q+1
       815: 2q+1
       817: 1
       818: 1
       820: q+2
       822: q+1
       824: q+1
       825: q^2+q+1
       827: q
       828: q^2+1
       829: q+1
       831: q
       832: q^2+1
       834: q+1
       836: q+1
       838: 2q+1
       839: 2q
       840: q^2+q+1
       842: q+1
       843: 1
       844: 1
       845: q+1
       847: q
       848: q^2+1
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q
       858: q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: 2
       870: 2
       871: q+1
       872: q+1
       873: q+2
       874: q+2
       875: q^2+2q+1
       876: q^2+2q+1
       877: q+1
       878: q^2+2q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       890: q+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 2
       921: 1
       929: 1
       933: q+1
       939: 1
       941: 1
       943: 1
       947: 1
       951: 1
       953: 1
       957: q
       959: q+1
       962: 1
       964: 1
       965: 1
       969: 1
       972: 1
       976: 1
       980: q+1
       986: q+1
       988: q
       989: q+1
       993: 2
       995: 2
       997: q+2
       998: 1
       999: 1
      1000: 2
      1003: q+1
      1004: q+1
      1006: q
      1007: q^2+1
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 2
      1016: 2
      1019: 1
      1021: 2
      1023: 1
      1025: 1
      1026: q+1
      1031: q+2
      1032: 1
      1033: 1
      1035: q+1
      1037: q+2
      1039: q+1
      1040: q+1
      1043: q+1
      1044: q
      1045: q^2+1
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q+1
      1056: q+1
      1058: q
      1059: q^2+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+2
      1069: q+2
      1071: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 1
      1077: 2
      1078: q+1
      1079: q+2
      1080: 2
      1081: q+2
      1082: q^2+2q+1
      1083: q+1
      1084: 2
      1085: q+1
      1087: 1
      1092: 1
      1104: q+1
      1113: 1
      1115: 1
      1117: 1
      1119: 1
      1123: 2
      1128: 1
      1130: 1
      1131: 1
      1136: 1
      1139: 1
      1142: 1
      1145: 2
      1149: 1
      1157: 1
      1165: 1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1189: 1
      1192: 1
      1194: 1
      1195: 1
      1200: 1
      1207: 1
      1211: 2
      1213: q+2
      1215: 2
      1216: 1
      1217: 1
      1218: 2
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 2
      1228: 2
      1231: 1
      1234: 1
      1237: 2
      1239: 1
      1240: q+1
      1245: q+2
      1246: 1
      1247: 1
      1249: 2
      1250: 1
      1251: 1
      1253: q+2
      1254: 2
      1257: q+1
      1258: q+1
      1260: q
      1261: q^2+1
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1268: q+1
      1273: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 1
      1288: 2
      1289: q+1
      1291: 1
      1296: 1
      1303: 1
      1308: 1
      1315: 1
      1317: 1
      1319: 2
      1324: 1
      1326: 1
      1327: 1
      1332: 1
      1335: 1
      1338: 1
      1341: 2
      1353: 1
      1357: 1
      1373: 1
      1375: 1
      1379: 1
      1381: 1
      1383: 1
      1385: 1
      1389: 2
      1394: 1
      1396: 1
      1397: 1
      1402: 1
      1405: 1
      1408: 1
      1410: 1
      1411: 1
      1416: 1
      1423: 1
      1431: 1
      1434: 1
      1439: 2
      1440: 1
      1441: 1
      1442: 2
      1444: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 2
      1454: 1
      1457: 2
      1459: q+2
      1460: 1
      1461: 1
      1462: 2
      1465: 1
      1468: 1
      1471: 1
      1473: 2
      1475: 1
      1476: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1490: 1
      1495: 1
      1514: 1
      1519: 1
      1526: 1
      1531: 1
      1542: 1
      1544: 1
      1546: 2
      1549: 1
      1550: 1
      1554: 1
      1557: 1
      1561: 1
      1568: 1
      1584: 1
      1586: 1
      1588: 2
      1593: 1
      1595: 1
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1632: 1
      1635: 1
      1642: 1
      1644: 1
      1647: 1
      1652: 2
      1653: 1
      1654: 1
      1655: 2
      1657: 1
      1662: 1
      1665: 1
      1668: 2
      1669: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1681: 1
      1700: 1
      1705: 1
      1746: 1
      1762: 1
      1764: 1
      1766: 2
      1773: 1
      1774: 1
      1779: 1
      1782: 1
      1790: 1
      1802: 1
      1805: 1
      1816: 1
      1821: 1
      1828: 1
      1831: 1
      1833: 1
      1859: 1
      1864: 1
      1919: 1
      1937: 1
      1957: 1
      1964: 1
      2045: 1

2046:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+2q+1
        38: q^2+q
        39: 2q^2+2q+1
        40: q^2+q
        41: 2q^2+2q+1
        42: q^2+q
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q
        59: 2q^2+q+1
        60: q^2+q
        61: 2q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+q
        64: 2q^2+2q+1
        65: q^2+q
        66: q^2+2q+1
        67: q^2+q
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q+1
        75: q^2+q
        76: 2q^2+2q+1
        77: q^2+q
        78: 2q^2+2q+1
        79: q^2+q
        80: 3q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q
       104: q^2
       105: q
       106: q^2+q+1
       107: q^2+q
       108: 2q^2+2q+1
       109: 2q
       110: 2q^2+q+1
       111: q^2+2q+1
       112: q^2+q
       113: 2q^2+2q+1
       114: q^2+q
       115: 2q^2+2q+1
       116: q^2+q
       117: 2q
       118: 2q^2+q+1
       119: q^2+q
       120: 2q^2+2q+1
       121: 2q^2+2q+1
       122: q^2+q
       123: q^2+2q+1
       124: q^2+q
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       127: 2q+1
       129: 2q+1
       131: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: q^2+3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+2q+1
       152: q^2+q
       153: 2q^2+2q+1
       154: q^2+q
       155: 2q^2+2q+1
       156: q^2+q
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q
       170: q^2
       171: q
       172: q^2+q+1
       173: q
       174: q^2
       175: q
       176: q^2+q+1
       177: q+1
       179: 2q+1
       181: 2q+1
       183: q^2+q
       184: 2q^2+2q+1
       185: 2q
       186: 2q^2+q+1
       187: q^2+2q+1
       188: q^2+q
       189: 2q^2+2q+1
       190: q^2+q
       191: 2q
       192: 2q^2+q+1
       194: 2q+1
       195: 2q
       196: q^2+q+1
       197: q+1
       198: q
       199: q^2+q
       200: 2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: 2q
       204: 2q^2+q+1
       205: q^2+2q+1
       206: q^2+q
       207: q^2+2q+1
       208: q^2+q
       209: 2q^2+2q+1
       210: q^2+q
       211: 2q^2+2q+1
       212: q^2+q
       213: 2q+1
       215: 2q+1
       217: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q+1
       239: 2q+1
       241: q^2+q+1
       243: q^2+3q+1
       244: 2q+1
       245: q^2+3q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       259: q
       262: q+1
       263: q
       264: q^2
       265: q
       266: q^2+q+1
       269: q+1
       270: q
       271: q
       272: q
       273: q^2+q+1
       274: q^2
       275: q
       276: q^2
       277: q
       278: q^2+q+1
       279: 2q+1
       281: q+1
       284: q^2+q+1
       285: q
       286: q^2+1
       287: q+1
       289: 2q+1
       291: q+1
       293: q^2+q
       294: 2q^2+2q+1
       295: 2q
       296: 2q^2+q+1
       297: q^2+2q+1
       298: q^2+q
       300: 2q+1
       301: q+1
       303: 2q
       304: q^2+q+1
       305: q+1
       306: q
       307: q^2+q
       308: 2q^2+2q+1
       309: 2q
       310: 2q^2+q+1
       311: 2q+1
       313: q^2+2q+1
       314: q^2+q
       315: q+1
       317: 2q+1
       320: 2q+1
       321: 2q
       322: q^2+q+1
       323: q+1
       324: q
       325: 2q^2+2q+1
       326: q^2+q
       327: 2q+1
       329: 2q+1
       331: q^2+q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q+1
       340: 2q+1
       342: q^2+q+1
       344: q^2+2q+1
       345: q^2+3q+1
       346: q^2+2q+1
       347: 2q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: 2q^2+3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       360: 2q+1
       362: 2q+1
       364: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       380: 1
       381: q
       384: q+1
       385: q
       386: q^2
       387: q
       388: q^2+q+1
       391: q+1
       395: q
       396: q+1
       397: q
       399: q+1
       401: q
       402: q
       403: q^2
       404: q^2+q+1
       406: q+1
       408: q
       409: 2q+1
       411: q+1
       413: q+1
       415: 2q+1
       417: q+1
       420: q^2+q+1
       421: q
       422: q^2+1
       423: q+1
       425: q+1
       427: 2q+1
       430: q+1
       431: q
       432: q^2+1
       433: 1
       435: q+1
       438: 2q+1
       439: 2q
       440: q^2+q+1
       441: q+1
       442: q
       444: 2q+1
       445: q+1
       448: q^2+q+1
       449: q
       450: q^2+1
       451: q+1
       453: q^2+q
       454: 2q^2+2q+1
       455: 2q+1
       457: 2q
       458: 2q^2+q+1
       459: q^2+2q+1
       460: q^2+q
       461: 2q
       462: q^2+q+1
       463: 2q+1
       465: 2q+1
       467: q+1
       469: q+1
       472: 2q+1
       473: 2q
       474: q^2+q+1
       475: q+1
       476: q
       477: q+1
       479: q+1
       480: q
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       485: 2q+1
       487: 2q+1
       489: q^2+q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       502: 2q+1
       504: 2q+1
       506: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: 2q+1
       512: q+1
       513: q^2+3q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       524: 1
       525: q
       528: q+1
       532: 1
       536: 1
       539: q+1
       543: q+1
       544: q
       547: q+1
       552: 1
       553: q
       555: q+1
       557: q
       558: q
       559: q^2+q+1
       560: q^2
       561: q
       563: q+1
       567: q
       568: q+1
       570: q+1
       575: q+1
       576: q
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       590: q^2+q+1
       591: q
       592: q^2+1
       594: q+1
       595: q
       596: q^2+1
       597: q+1
       599: q+1
       601: 2q+1
       604: q+1
       605: 1
       607: q
       608: q^2+1
       609: 1
       611: q+1
       613: 1
       616: 2q+1
       617: q+1
       620: q^2+q+1
       621: q
       622: q^2+1
       623: q+1
       625: q+1
       627: 2q+1
       629: q+1
       631: 2q
       632: q^2+q+1
       633: 2q+1
       635: 2q+1
       637: q+1
       639: q+1
       642: q+1
       643: q
       644: q^2+1
       645: 1
       648: 2q+1
       649: 2q
       650: q^2+q+1
       651: q+1
       653: q+1
       654: q
       655: q+1
       656: q
       657: 2
       658: q+2
       660: q+2
       662: q+2
       664: q+2
       665: q^2+2q+1
       666: 2q+1
       668: 2q+1
       670: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: 2
       675: q+1
       676: q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+2
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q^2+2q+1
       684: q^2+3q+1
       685: q^2+2q+1
       686: q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       697: q+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: q+1
       735: q+1
       739: 1
       743: 1
       745: q
       747: q+1
       749: q
       751: q+1
       756: 1
       758: q+1
       762: q+1
       764: q
       767: q
       768: q+1
       769: q+1
       775: 2
       777: q+1
       779: q+2
       781: q+1
       783: q+1
       786: q+1
       787: q
       788: q^2+1
       789: 2q+1
       791: 1
       794: 2
       795: 2
       797: 1
       799: 1
       802: q+1
       806: q+1
       807: q
       808: q^2+1
       809: 1
       811: 1
       813: q+1
       816: 2q+1
       817: 1
       818: 1
       819: q+2
       821: q+1
       823: q+1
       826: q^2+q+1
       827: q
       828: q^2+1
       830: q+1
       831: q
       832: q^2+1
       833: q+1
       835: q+1
       837: 2q+1
       839: 2q
       840: q^2+q+1
       841: q+1
       843: 1
       844: 1
       846: q+1
       847: q
       848: q^2+1
       849: 1
       851: 1
       853: q+1
       855: 1
       857: q+1
       858: q
       859: q+2
       861: q+2
       863: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: 2
       870: 2
       871: q+1
       872: q+1
       873: q+2
       874: q+2
       875: q^2+2q+1
       876: q^2+2q+1
       877: q+1
       878: q^2+2q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       889: q+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 2
       922: 1
       930: 1
       934: q+1
       938: 1
       940: 1
       942: 1
       946: 1
       950: 1
       955: 1
       956: q
       958: q+1
       961: 1
       966: 1
       967: 1
       968: 1
       971: 1
       975: 1
       979: q+1
       982: q+1
       990: q
       991: q+1
       992: 2
       994: 2
       996: q+2
       998: 1
       999: 1
      1001: 2
      1002: q+1
      1005: q+1
      1006: q
      1007: q^2+1
      1008: 1
      1010: 1
      1012: 1
      1013: 1
      1014: 2
      1017: 2
      1018: 1
      1020: 2
      1022: 1
      1024: 1
      1027: q+1
      1030: q+2
      1032: 1
      1033: 1
      1034: q+1
      1036: q+2
      1038: q+1
      1041: q+1
      1042: q+1
      1044: q
      1045: q^2+1
      1046: 1
      1047: 1
      1048: 1
      1050: 1
      1053: q+1
      1057: q+1
      1058: q
      1059: q^2+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+2
      1068: q+2
      1070: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 1
      1077: 2
      1078: q+1
      1079: q+2
      1080: 2
      1081: q+2
      1082: q^2+2q+1
      1083: q+1
      1084: 2
      1085: q+1
      1090: 1
      1091: 1
      1102: q+1
      1112: 1
      1114: 1
      1116: 1
      1120: 1
      1124: 2
      1127: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1146: 2
      1150: 1
      1158: 1
      1164: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1191: 1
      1196: 1
      1197: 1
      1199: 1
      1208: 1
      1210: 2
      1212: q+2
      1214: 2
      1216: 1
      1217: 1
      1219: 2
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 2
      1229: 2
      1230: 1
      1235: 1
      1236: 2
      1238: 1
      1241: q+1
      1244: q+2
      1246: 1
      1247: 1
      1248: 2
      1250: 1
      1251: 1
      1252: q+2
      1255: 2
      1256: q+1
      1259: q+1
      1260: q
      1261: q^2+1
      1262: 1
      1263: 1
      1264: 1
      1266: 1
      1269: q+1
      1272: 1
      1274: 2
      1276: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 1
      1288: 2
      1289: q+1
      1294: 1
      1295: 1
      1306: 1
      1307: 1
      1314: 1
      1316: 1
      1320: 2
      1323: 1
      1328: 1
      1329: 1
      1331: 1
      1334: 1
      1337: 1
      1342: 2
      1354: 1
      1358: 1
      1372: 1
      1374: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1390: 2
      1393: 1
      1398: 1
      1399: 1
      1401: 1
      1404: 1
      1407: 1
      1412: 1
      1413: 1
      1415: 1
      1424: 1
      1430: 1
      1433: 1
      1438: 2
      1440: 1
      1441: 1
      1443: 2
      1444: 1
      1445: 1
      1446: 1
      1448: 1
      1452: 2
      1455: 1
      1456: 2
      1458: q+2
      1460: 1
      1461: 1
      1463: 2
      1464: 1
      1469: 1
      1470: 1
      1472: 2
      1474: 1
      1477: q+1
      1480: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1493: 1
      1494: 1
      1517: 1
      1518: 1
      1529: 1
      1530: 1
      1541: 1
      1543: 1
      1547: 2
      1551: 1
      1552: 1
      1553: 1
      1556: 1
      1560: 1
      1569: 1
      1583: 1
      1585: 1
      1589: 2
      1592: 1
      1597: 1
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1634: 1
      1641: 1
      1643: 1
      1648: 1
      1651: 2
      1653: 1
      1654: 1
      1656: 2
      1658: 1
      1661: 1
      1666: 1
      1667: 2
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1674: 1
      1679: 1
      1680: 1
      1703: 1
      1704: 1
      1747: 1
      1761: 1
      1763: 1
      1767: 2
      1775: 1
      1776: 1
      1778: 1
      1783: 1
      1791: 1
      1801: 1
      1804: 1
      1815: 1
      1822: 1
      1827: 1
      1832: 1
      1833: 1
      1862: 1
      1863: 1
      1920: 1
      1938: 1
      1956: 1
      1965: 1
      2046: 1

2047:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^4+2q^3+3q^2+2q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^3+3q^2+2q+1
        19: q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: q^3+4q^2+3q+1
        28: 3q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 2q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 3q^2+3q+1
        37: q^2+q
        38: 2q^2+2q+1
        39: q^2+q
        40: 2q^2+2q+1
        41: q^2+q
        42: 2q^2+2q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: q^3+3q^2+2q+1
        49: 3q^2+3q+1
        50: 3q^2+3q+1
        51: q^3+3q^2+2q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^3+4q^2+3q+1
        58: 2q^2+q+1
        59: 2q
        60: q^2+q
        61: 2q^2+2q+1
        62: q^2+q
        63: 2q^2+2q+1
        64: q^2+q
        65: 2q^2+2q+1
        66: q^2+q
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+2q+1
        70: q^3+4q^2+3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+q
        75: 2q^2+2q+1
        76: q^2+q
        77: 2q^2+2q+1
        78: q^2+q
        79: 2q^2+2q+1
        80: 3q^2+3q+1
        81: 2q^2+3q+1
        82: 3q^2+3q+1
        83: 3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: 3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 3q^2+3q+1
        89: 3q^2+3q+1
        90: q^3+3q^2+2q+1
        91: 3q^2+3q+1
        92: 3q^2+3q+1
        93: q^3+3q^2+2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+2q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: q^3+3q^2+2q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: q^2
       104: q
       105: q^2+q+1
       106: q
       107: q^2+q
       108: 2q^2+2q+1
       109: 2q^2+q+1
       110: 2q
       111: q^2+q
       112: q^2+2q+1
       113: q^2+q
       114: 2q^2+2q+1
       115: q^2+q
       116: 2q^2+2q+1
       117: 2q^2+q+1
       118: 2q
       119: q^2+q
       120: 2q^2+2q+1
       121: q^2+q
       122: 2q^2+2q+1
       123: q^2+q
       124: q^2+2q+1
       125: 3q^2+3q+1
       126: 2q^2+2q+1
       128: 2q+1
       130: 2q+1
       132: q^2+q+1
       133: 3q^2+3q+1
       134: 2q^2+2q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: q^2+3q+1
       143: 3q^2+3q+1
       144: 2q^2+2q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: q^2+q
       152: 2q^2+2q+1
       153: q^2+q
       154: 2q^2+2q+1
       155: q^2+q
       156: 2q^2+2q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^3+3q^2+2q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 2q^2+2q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: q^3+3q^2+2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+2q+1
       169: q^2
       170: q
       171: q^2+q+1
       172: q
       173: q^2
       174: q
       175: q^2+q+1
       176: q
       178: q+1
       180: 2q+1
       182: 2q+1
       183: q^2+q
       184: 2q^2+2q+1
       185: 2q^2+q+1
       186: 2q
       187: q^2+q
       188: q^2+2q+1
       189: q^2+q
       190: 2q^2+2q+1
       191: 2q^2+q+1
       192: 2q
       194: 2q+1
       195: q^2+q+1
       196: 2q
       197: q
       198: q+1
       199: q^2+q
       200: 2q^2+2q+1
       201: q^2+q
       202: 2q^2+2q+1
       203: 2q^2+q+1
       204: 2q
       205: q^2+q
       206: q^2+2q+1
       207: q^2+q
       208: q^2+2q+1
       209: q^2+q
       210: 2q^2+2q+1
       211: q^2+q
       212: 2q^2+2q+1
       214: 2q+1
       216: 2q+1
       218: q^2+q+1
       219: 2q^2+2q+1
       220: 3q^2+3q+1
       221: 2q^2+2q+1
       222: 3q^2+3q+1
       223: 2q^2+2q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q+1
       230: q^2+3q+1
       231: 2q^2+2q+1
       232: 3q^2+3q+1
       233: 2q^2+2q+1
       234: 3q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       238: 2q+1
       240: 2q+1
       242: q^2+q+1
       243: q^2+3q+1
       244: 2q+1
       245: q^2+3q+1
       246: 3q^2+3q+1
       247: q^2+3q+1
       248: q^2+3q+1
       249: 2q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q^2+2q+1
       253: 3q^2+3q+1
       254: 3q^2+3q+1
       255: q^3+3q^2+2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q^2+2q+1
       260: q
       261: q+1
       263: q^2
       264: q
       265: q^2+q+1
       266: q
       269: q
       270: q+1
       271: q^2
       272: q^2+q+1
       273: q
       274: q
       275: q^2
       276: q
       277: q^2+q+1
       278: q
       280: 2q+1
       282: q+1
       284: q^2+q+1
       285: q^2+1
       286: q
       288: q+1
       290: 2q+1
       292: q+1
       293: q^2+q
       294: 2q^2+2q+1
       295: 2q^2+q+1
       296: 2q
       297: q^2+q
       298: q^2+2q+1
       300: 2q+1
       302: q+1
       303: q^2+q+1
       304: 2q
       305: q
       306: q+1
       307: q^2+q
       308: 2q^2+2q+1
       309: 2q^2+q+1
       310: 2q
       312: 2q+1
       313: q^2+q
       314: q^2+2q+1
       316: q+1
       318: 2q+1
       320: 2q+1
       321: q^2+q+1
       322: 2q
       323: q
       324: q+1
       325: q^2+q
       326: 2q^2+2q+1
       328: 2q+1
       330: 2q+1
       332: q^2+q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       339: 2q+1
       341: 2q+1
       343: q^2+q+1
       344: q^2+2q+1
       345: q^2+3q+1
       346: q^2+2q+1
       347: 2q+1
       348: q+1
       349: q^2+3q+1
       350: q^2+2q+1
       351: 2q+1
       352: 2q^2+2q+1
       353: 3q^2+3q+1
       354: 2q^2+2q+1
       355: 3q^2+3q+1
       356: 2q^2+2q+1
       357: 2q^2+3q+1
       358: q^2+2q+1
       359: q^2+3q+1
       361: 2q+1
       363: 2q+1
       365: q^2+q+1
       366: q^2+2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: 2q^2+2q+1
       374: q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+2q+1
       379: 1
       382: q
       383: q+1
       385: q^2
       386: q
       387: q^2+q+1
       388: q
       392: q+1
       395: q+1
       396: q
       398: q+1
       400: q
       401: q^2
       402: q^2+q+1
       403: q
       404: q
       406: q
       408: q+1
       410: 2q+1
       412: q+1
       414: q+1
       416: 2q+1
       418: q+1
       420: q^2+q+1
       421: q^2+1
       422: q
       424: q+1
       426: q+1
       428: 2q+1
       430: q+1
       431: q^2+1
       432: q
       434: 1
       436: q+1
       438: 2q+1
       439: q^2+q+1
       440: 2q
       441: q
       442: q+1
       444: 2q+1
       446: q+1
       448: q^2+q+1
       449: q^2+1
       450: q
       452: q+1
       453: q^2+q
       454: 2q^2+2q+1
       456: 2q+1
       457: 2q^2+q+1
       458: 2q
       459: q^2+q
       460: q^2+2q+1
       461: q^2+q+1
       462: 2q
       464: 2q+1
       466: 2q+1
       468: q+1
       470: q+1
       472: 2q+1
       473: q^2+q+1
       474: 2q
       475: q
       476: q+1
       478: q+1
       479: q
       480: q+1
       481: 2q^2+2q+1
       482: q^2+2q+1
       483: q^2+2q+1
       484: q^2+3q+1
       486: 2q+1
       488: 2q+1
       490: q^2+q+1
       491: q^2+2q+1
       492: q^2+2q+1
       493: q+1
       494: q^2+2q+1
       495: q+1
       496: 2q+1
       497: 2q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: q^2+3q+1
       503: 2q+1
       505: 2q+1
       507: q^2+q+1
       508: q^2+2q+1
       509: q^2+3q+1
       510: q^2+2q+1
       511: 2q+1
       512: q+1
       513: q^2+3q+1
       514: q^2+2q+1
       515: q+2
       516: q+2
       517: q+2
       518: q^2+3q+1
       519: q^2+3q+1
       520: 2q^2+2q+1
       523: 1
       526: q
       527: q+1
       531: 1
       535: 1
       540: q+1
       543: q
       544: q+1
       548: q+1
       550: 1
       554: q+1
       556: q
       557: q^2
       558: q^2+q+1
       559: q
       560: q
       562: q+1
       564: q
       567: q+1
       568: q
       572: q+1
       575: q
       576: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       590: q^2+q+1
       591: q^2+1
       592: q
       594: q+1
       595: q^2+1
       596: q
       598: q+1
       600: q+1
       602: 2q+1
       604: q+1
       606: 1
       607: q^2+1
       608: q
       610: 1
       612: q+1
       614: 1
       616: 2q+1
       618: q+1
       620: q^2+q+1
       621: q^2+1
       622: q
       624: q+1
       626: q+1
       628: 2q+1
       630: q+1
       631: q^2+q+1
       632: 2q
       634: 2q+1
       636: 2q+1
       638: q+1
       640: q+1
       642: q+1
       643: q^2+1
       644: q
       646: 1
       648: 2q+1
       649: q^2+q+1
       650: 2q
       652: q+1
       653: q
       654: q+1
       655: q
       656: q+1
       657: 2
       659: q+2
       661: q+2
       663: q+2
       664: q+2
       665: q^2+2q+1
       667: 2q+1
       669: 2q+1
       671: q^2+q+1
       672: q^2+3q+1
       673: q^2+2q+1
       674: 2
       675: q+1
       676: q^2+2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+2
       681: 2q^2+2q+1
       682: q^2+2q+1
       683: q^2+2q+1
       684: q^2+3q+1
       685: q^2+2q+1
       686: q^2+2q+1
       687: q+1
       688: q^2+2q+1
       689: q+1
       690: q+2
       691: q+2
       692: q+2
       700: q+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: q+1
       736: q+1
       738: 1
       742: 1
       746: q+1
       748: q
       750: q+1
       752: q
       755: 1
       760: q+1
       762: q
       764: q+1
       767: q+1
       768: q
       773: q+1
       776: 2
       778: q+1
       780: q+2
       782: q+1
       784: q+1
       786: q+1
       787: q^2+1
       788: q
       790: 2q+1
       792: 1
       794: 2
       796: 2
       798: 1
       800: 1
       802: q+1
       806: q+1
       807: q^2+1
       808: q
       810: 1
       812: 1
       814: q+1
       816: 2q+1
       817: 1
       818: 1
       820: q+2
       822: q+1
       824: q+1
       826: q^2+q+1
       827: q^2+1
       828: q
       830: q+1
       831: q^2+1
       832: q
       834: q+1
       836: q+1
       838: 2q+1
       839: q^2+q+1
       840: 2q
       842: q+1
       843: 1
       844: 1
       846: q+1
       847: q^2+1
       848: q
       850: 1
       852: 1
       854: q+1
       856: 1
       857: q
       858: q+1
       860: q+2
       862: q+2
       864: q+2
       865: 2
       866: 2
       867: q+2
       868: q^2+2q+1
       869: 2
       870: 2
       871: q+1
       872: q+1
       873: q+2
       874: q+2
       875: q^2+2q+1
       876: q^2+2q+1
       877: q+1
       878: q^2+2q+1
       879: q+1
       880: q+1
       881: q+2
       882: q+2
       883: q+2
       891: q+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 2
       923: 1
       931: 1
       935: q+1
       937: 1
       941: 1
       943: 1
       945: 1
       949: 1
       954: 1
       957: q+1
       959: q
       963: 1
       966: 1
       967: 1
       969: 1
       972: 1
       977: 1
       981: q+1
       986: q+1
       990: q+1
       991: q
       993: 2
       995: 2
       997: q+2
       998: 1
       999: 1
      1001: 2
      1003: q+1
      1005: q+1
      1006: q^2+1
      1007: q
      1009: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 2
      1017: 2
      1019: 1
      1021: 2
      1023: 1
      1025: 1
      1027: q+1
      1031: q+2
      1032: 1
      1033: 1
      1035: q+1
      1037: q+2
      1039: q+1
      1041: q+1
      1043: q+1
      1044: q^2+1
      1045: q
      1046: 1
      1047: 1
      1049: 1
      1051: 1
      1053: q+1
      1057: q+1
      1058: q^2+1
      1059: q
      1061: 1
      1063: 1
      1065: 1
      1067: q+2
      1069: q+2
      1071: q+2
      1072: 2
      1073: q+2
      1074: 2
      1075: 2
      1076: 1
      1077: 2
      1078: q+1
      1079: q+2
      1080: 2
      1081: q+2
      1082: q^2+2q+1
      1083: q+1
      1084: 2
      1085: q+1
      1093: 1
      1094: 1
      1105: q+1
      1111: 1
      1115: 1
      1117: 1
      1121: 1
      1125: 2
      1129: 1
      1132: 1
      1133: 1
      1137: 1
      1139: 1
      1142: 1
      1147: 2
      1151: 1
      1159: 1
      1165: 1
      1167: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1189: 1
      1192: 1
      1196: 1
      1197: 1
      1201: 1
      1209: 1
      1211: 2
      1213: q+2
      1215: 2
      1216: 1
      1217: 1
      1219: 2
      1221: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 2
      1229: 2
      1231: 1
      1235: 1
      1237: 2
      1239: 1
      1241: q+1
      1245: q+2
      1246: 1
      1247: 1
      1249: 2
      1250: 1
      1251: 1
      1253: q+2
      1255: 2
      1257: q+1
      1259: q+1
      1260: q^2+1
      1261: q
      1262: 1
      1263: 1
      1265: 1
      1267: 1
      1269: q+1
      1273: 1
      1275: 2
      1277: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 2
      1283: 1
      1284: 2
      1285: 2
      1286: q+2
      1287: 1
      1288: 2
      1289: q+1
      1297: 1
      1298: 1
      1309: 1
      1310: 1
      1315: 1
      1317: 1
      1321: 2
      1325: 1
      1328: 1
      1329: 1
      1333: 1
      1335: 1
      1338: 1
      1343: 2
      1355: 1
      1359: 1
      1373: 1
      1375: 1
      1377: 1
      1381: 1
      1383: 1
      1387: 1
      1391: 2
      1395: 1
      1398: 1
      1399: 1
      1403: 1
      1405: 1
      1408: 1
      1412: 1
      1413: 1
      1417: 1
      1425: 1
      1431: 1
      1434: 1
      1439: 2
      1440: 1
      1441: 1
      1443: 2
      1444: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 2
      1455: 1
      1457: 2
      1459: q+2
      1460: 1
      1461: 1
      1463: 2
      1465: 1
      1469: 1
      1471: 1
      1473: 2
      1475: 1
      1477: q+1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 2
      1487: 1
      1488: 2
      1496: 1
      1497: 1
      1520: 1
      1521: 1
      1532: 1
      1533: 1
      1542: 1
      1544: 1
      1548: 2
      1551: 1
      1552: 1
      1554: 1
      1557: 1
      1562: 1
      1570: 1
      1584: 1
      1586: 1
      1590: 2
      1594: 1
      1597: 1
      1598: 1
      1602: 1
      1614: 1
      1618: 1
      1632: 1
      1635: 1
      1642: 1
      1644: 1
      1648: 1
      1652: 2
      1653: 1
      1654: 1
      1656: 2
      1658: 1
      1662: 1
      1666: 1
      1668: 2
      1669: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1682: 1
      1683: 1
      1706: 1
      1707: 1
      1748: 1
      1762: 1
      1764: 1
      1768: 2
      1775: 1
      1776: 1
      1780: 1
      1784: 1
      1792: 1
      1802: 1
      1805: 1
      1816: 1
      1822: 1
      1828: 1
      1832: 1
      1833: 1
      1865: 1
      1866: 1
      1921: 1
      1939: 1
      1957: 1
      1965: 1
      2047: 1

2048:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: q^4+2q^3+q^2+q+1
        26: q^4+2q^3+q^2+q+1
        27: q^5+q^4+q^3+q^2+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: q^4+2q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^4+2q^3+q^2+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: 2q^3+q+1
        53: 2q^3+q+1
        54: q^4+q^3+q+1
        55: q^4+2q^3+q^2+q+1
        56: q^4+2q^3+q^2+q+1
        57: q^5+q^4+q^3+q^2+q+1
        58: q^3+1
        59: q^3+q
        60: q^4+q^3+q^2+1
        61: q^3+q
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: q^4+2q^3+q^2+q+1
        73: 2q^3+q+1
        74: 2q^3+q+1
        76: 2q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: 2q^3+q+1
        83: q^3+q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^4+2q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^3+q+1
        95: 2q^3+q+1
        96: q^4+q^3+q+1
        97: q^4+2q^3+q^2+q+1
        98: q^4+2q^3+q^2+q+1
        99: q^5+q^4+q^3+q^2+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       103: q^3+1
       106: q^3+q
       107: q^4+q^3+q^2+1
       108: q^3+q
       109: q^3+1
       110: q^3+q
       111: 2q^3+q+1
       113: 2q^3+q+1
       115: q^3+q+1
       117: 1
       118: q
       119: q^2+1
       120: q
       121: q^3+q+1
       123: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       127: 2q^3+q+1
       129: 2q^3+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q^2+q+1
       136: q^3+q+1
       137: q^3+q+1
       138: q^3+q+1
       139: 2q^3+q+1
       140: q^3+1
       141: q^3+q+1
       142: 2q^3+q+1
       143: q^3+q^2+q+1
       144: q^3+q^2+q+1
       145: q^4+2q^3+q^2+q+1
       146: q^3+q^2+q+1
       147: q^4+2q^3+q^2+q+1
       148: 2q^3+q+1
       149: 2q^3+q+1
       150: q^3+q+1
       151: 2q^3+q+1
       153: 2q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^3+q^2+q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       169: q^3+1
       172: q^3+q
       173: 1
       176: q
       177: q^3+q+1
       179: 2q^3+q+1
       181: 2q^3+q+1
       183: q^2+1
       184: q
       185: 1
       186: q
       187: q^3+q+1
       189: q^3+q+1
       191: 1
       192: q
       193: q^3+1
       195: q^3+1
       196: q^3+q
       197: q^3+1
       199: q^2+1
       200: q
       201: q^4+q^3+q^2+1
       202: q^3+q
       203: q^3+1
       204: q^3+q
       205: 2q^3+q+1
       207: q^3+q+1
       209: 2q^3+q+1
       211: q^3+q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q^2+q+1
       223: q^3+q^2+q+1
       224: q^3+q+1
       225: q^3+q+1
       226: q^3+q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^3+q^2+q+1
       232: q^2+q+1
       233: q^3+q^2+q+1
       234: q^3+q^2+q+1
       235: q^3+q+1
       236: q^3+q+1
       237: 2q^3+q+1
       239: 2q^3+q+1
       241: q^4+q^3+q+1
       243: 2q^3+q+1
       244: q^3+1
       245: 2q^3+q+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^3+q^2+q+1
       254: q^3+q^2+q+1
       255: q^3+q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^3+1
       262: q^3+q
       263: 1
       266: q
       267: q^3+1
       271: q^3+1
       273: q^3+q
       275: 1
       278: q
       279: q+1
       281: q+1
       283: q^2+1
       284: q
       285: 1
       286: q
       287: q^3+q+1
       289: q+1
       291: q^3+q+1
       293: q^2+1
       294: q
       295: 1
       296: q
       297: q^3+q+1
       299: 1
       301: q^3+1
       303: 1
       304: q
       305: 1
       307: q^2+1
       308: q
       309: 1
       310: q
       311: 2q^3+q+1
       313: q^3+q+1
       315: q^3+q+1
       317: 2q^3+q+1
       319: q^3+1
       321: q^3+1
       322: q^3+q
       323: q^3+1
       325: q^3+q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^3+q^2+q+1
       335: q^3+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       338: 2q^3+q+1
       340: 2q^3+q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q^3+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^3+q^2+q+1
       355: q^3+q^2+q+1
       356: q^3+q^2+q+1
       357: q^3+q+1
       358: q^3+q+1
       359: 2q^3+q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       380: q
       381: 1
       384: q
       385: 1
       388: q
       389: q^3+1
       393: 1
       397: q^3+1
       399: q^3+q
       401: 1
       404: q
       405: q^3+1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q^2+1
       420: q
       421: 1
       422: q
       423: q^3+q+1
       425: q^3+q+1
       427: 2q^3+q+1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: q^3+1
       445: q^3+1
       447: q^2+1
       448: q
       449: 1
       450: q
       451: q^3+q+1
       453: q^2+1
       454: q
       455: q+1
       457: 1
       458: q
       459: q^3+q+1
       461: q^3+1
       462: q^3+q
       463: 2q^3+q+1
       465: q+1
       467: q+1
       469: q^3+q+1
       471: 1
       473: 1
       474: q
       475: 1
       477: q^3+1
       479: q^3+1
       481: q^2+q+1
       482: q+1
       483: q^3+q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^3+q^2+q+1
       499: q^3+q+1
       500: q^3+q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       525: 1
       528: q
       529: 1
       532: q
       533: 1
       537: 1
       541: 1
       545: q^3+1
       549: 1
       552: q
       553: 1
       555: q
       557: 1
       559: q
       561: q^3+1
       563: q^3+q
       565: 1
       569: q^3+1
       573: q^3+1
       577: q^3+1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+1
       590: q
       591: 1
       592: q
       593: 1
       595: 1
       596: q
       597: q+1
       599: q^3+q+1
       601: q+1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q^2+1
       620: q
       621: 1
       622: q
       623: q+1
       625: q^3+q+1
       627: q+1
       629: q^3+q+1
       631: 1
       632: q
       633: q+1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       644: q
       645: 1
       647: 1
       649: 1
       650: q
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q^3+q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q^3+1
       705: 1
       708: q
       709: 1
       712: q
       713: 1
       716: q
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       739: q
       741: 1
       743: q
       745: 1
       747: q
       749: 1
       751: q
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       788: q
       789: q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       818: q
       819: q+1
       821: q+1
       823: q+1
       825: q^2+1
       826: q
       827: 1
       828: q
       829: 1
       831: 1
       832: q
       833: q+1
       835: q^3+q+1
       837: q+1
       839: 1
       840: q
       841: q+1
       843: 1
       845: 1
       847: 1
       848: q
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       884: 1
       896: 1
       899: q
       900: 1
       902: q
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: 1
       936: 1
       938: q
       940: 1
       942: q
       944: 1
       946: q
       948: 1
       950: q
       952: 1
       956: 1
       958: q
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
       999: q
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1007: q
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: q+1
      1032: 1
      1033: q
      1034: q+1
      1036: q+1
      1038: q+1
      1040: 1
      1042: q+1
      1044: 1
      1045: q
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1112: q
      1114: 1
      1116: q
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1166: q
      1168: 1
      1170: q
      1172: 1
      1174: q
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1206: 1
      1214: q+1
      1216: 1
      1217: q
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1248: q+1
      1250: 1
      1251: q
      1252: q+1
      1254: 1
      1256: q+1
      1258: 1
      1260: 1
      1261: q
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1316: q
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1352: 1
      1356: 1
      1376: 1
      1378: q
      1380: 1
      1382: q
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1414: 1
      1422: 1
      1430: 1
      1436: 1
      1446: 1
      1448: 1
      1454: 1
      1456: q+1
      1460: 1
      1461: q
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1489: 1
      1513: 1
      1537: 1
      1559: 1
      1567: 1
      1583: 1
      1585: q
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1637: 1
      1641: 1
      1657: 1
      1659: 1
      1661: 1
      1665: 1
      1671: 1
      1673: 1
      1699: 1
      1729: 1
      1769: 1
      1777: 1
      1781: 1
      1789: 1
      1815: 1
      1817: 1
      1821: 1
      1823: 1
      1910: 1
      1918: 1
      1922: 1
      1958: 1
      2048: 1

2049:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: q^4+2q^3+q^2+q+1
        26: q^4+2q^3+q^2+q+1
        27: q^5+q^4+q^3+q^2+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: q^4+2q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^4+2q^3+q^2+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: 2q^3+q+1
        53: 2q^3+q+1
        54: q^4+q^3+q+1
        55: q^4+2q^3+q^2+q+1
        56: q^4+2q^3+q^2+q+1
        57: q^5+q^4+q^3+q^2+q+1
        58: q^3+q
        59: q^3+1
        60: q^3+q
        61: q^4+q^3+q^2+1
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: q^4+2q^3+q^2+q+1
        73: 2q^3+q+1
        74: 2q^3+q+1
        76: 2q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: 2q^3+q+1
        83: q^3+q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^4+2q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^3+q+1
        95: 2q^3+q+1
        96: q^4+q^3+q+1
        97: q^4+2q^3+q^2+q+1
        98: q^4+2q^3+q^2+q+1
        99: q^5+q^4+q^3+q^2+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       103: q^3+q
       106: q^3+1
       107: q^3+q
       108: q^4+q^3+q^2+1
       109: q^3+q
       110: q^3+1
       111: 2q^3+q+1
       113: 2q^3+q+1
       115: q^3+q+1
       117: q
       118: 1
       119: q
       120: q^2+1
       121: q^3+q+1
       123: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       127: 2q^3+q+1
       129: 2q^3+q+1
       131: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q^2+q+1
       136: q^3+q+1
       137: q^3+q+1
       138: q^3+q+1
       139: 2q^3+q+1
       140: q^3+1
       141: q^3+q+1
       142: 2q^3+q+1
       143: q^3+q^2+q+1
       144: q^3+q^2+q+1
       145: q^4+2q^3+q^2+q+1
       146: q^3+q^2+q+1
       147: q^4+2q^3+q^2+q+1
       148: 2q^3+q+1
       149: 2q^3+q+1
       150: q^3+q+1
       151: 2q^3+q+1
       153: 2q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^3+q^2+q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       169: q^3+q
       172: q^3+1
       173: q
       176: 1
       177: q^3+q+1
       179: 2q^3+q+1
       181: 2q^3+q+1
       183: q
       184: q^2+1
       185: q
       186: 1
       187: q^3+q+1
       189: q^3+q+1
       191: q
       192: 1
       194: q^3+1
       195: q^3+q
       196: q^3+1
       197: q^3+1
       199: q
       200: q^2+1
       201: q^3+q
       202: q^4+q^3+q^2+1
       203: q^3+q
       204: q^3+1
       205: 2q^3+q+1
       207: q^3+q+1
       209: 2q^3+q+1
       211: q^3+q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q^2+q+1
       223: q^3+q^2+q+1
       224: q^3+q+1
       225: q^3+q+1
       226: q^3+q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^3+q^2+q+1
       232: q^2+q+1
       233: q^3+q^2+q+1
       234: q^3+q^2+q+1
       235: q^3+q+1
       236: q^3+q+1
       237: 2q^3+q+1
       239: 2q^3+q+1
       241: q^4+q^3+q+1
       243: 2q^3+q+1
       244: q^3+1
       245: 2q^3+q+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^3+q^2+q+1
       254: q^3+q^2+q+1
       255: q^3+q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^3+q
       262: q^3+1
       263: q
       266: 1
       269: q^3+1
       271: q^3+q
       273: q^3+1
       275: q
       278: 1
       279: q+1
       281: q+1
       283: q
       284: q^2+1
       285: q
       286: 1
       287: q^3+q+1
       289: q+1
       291: q^3+q+1
       293: q
       294: q^2+1
       295: q
       296: 1
       297: q^3+q+1
       300: 1
       301: q^3+1
       303: q
       304: 1
       305: 1
       307: q
       308: q^2+1
       309: q
       310: 1
       311: 2q^3+q+1
       313: q^3+q+1
       315: q^3+q+1
       317: 2q^3+q+1
       320: q^3+1
       321: q^3+q
       322: q^3+1
       323: q^3+1
       325: q^3+q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^3+q^2+q+1
       335: q^3+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       338: 2q^3+q+1
       340: 2q^3+q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q^3+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^3+q^2+q+1
       355: q^3+q^2+q+1
       356: q^3+q^2+q+1
       357: q^3+q+1
       358: q^3+q+1
       359: 2q^3+q+1
       360: q+1
       362: q+1
       364: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: 1
       381: q
       384: 1
       385: q
       388: 1
       391: q^3+1
       396: 1
       397: q^3+q
       399: q^3+1
       401: q
       404: 1
       406: q^3+1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q
       420: q^2+1
       421: q
       422: 1
       423: q^3+q+1
       425: q^3+q+1
       427: 2q^3+q+1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: q^3+1
       445: q^3+1
       447: q
       448: q^2+1
       449: q
       450: 1
       451: q^3+q+1
       453: q
       454: q^2+1
       455: q+1
       457: q
       458: 1
       459: q^3+q+1
       461: q^3+q
       462: q^3+1
       463: 2q^3+q+1
       465: q+1
       467: q+1
       469: q^3+q+1
       472: 1
       473: q
       474: 1
       475: 1
       477: q^3+1
       479: q^3+1
       481: q^2+q+1
       482: q+1
       483: q^3+q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^3+q^2+q+1
       499: q^3+q+1
       500: q^3+q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       525: q
       528: 1
       529: q
       532: 1
       536: 1
       539: 1
       543: 1
       547: q^3+1
       549: q
       552: 1
       553: q
       555: 1
       557: q
       559: 1
       561: q^3+q
       563: q^3+1
       568: 1
       570: q^3+1
       575: q^3+1
       577: q^3+1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: q^2+1
       591: q
       592: 1
       594: 1
       595: q
       596: 1
       597: q+1
       599: q^3+q+1
       601: q+1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       619: q
       620: q^2+1
       621: q
       622: 1
       623: q+1
       625: q^3+q+1
       627: q+1
       629: q^3+q+1
       631: q
       632: 1
       633: q+1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       643: q
       644: 1
       645: 1
       648: 1
       649: q
       650: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q^3+q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: q^3+1
       705: q
       708: 1
       709: q
       712: 1
       713: q
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       737: q
       739: 1
       741: q
       743: 1
       745: q
       747: 1
       749: q
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       787: q
       788: 1
       789: q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       817: q
       818: 1
       819: q+1
       821: q+1
       823: q+1
       825: q
       826: q^2+1
       827: q
       828: 1
       830: 1
       831: q
       832: 1
       833: q+1
       835: q^3+q+1
       837: q+1
       839: q
       840: 1
       841: q+1
       843: 1
       846: 1
       847: q
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       889: 1
       896: q
       899: 1
       900: q
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: 1
       936: q
       938: 1
       940: q
       942: 1
       944: q
       946: 1
       948: q
       950: 1
       955: 1
       956: q
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       998: q
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1006: q
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: q+1
      1032: q
      1033: 1
      1034: q+1
      1036: q+1
      1038: q+1
      1041: 1
      1042: q+1
      1044: q
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1110: q
      1112: 1
      1114: q
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1158: 1
      1164: q
      1166: 1
      1168: q
      1170: 1
      1172: q
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1208: 1
      1214: q+1
      1216: q
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1248: q+1
      1250: q
      1251: 1
      1252: q+1
      1255: 1
      1256: q+1
      1259: 1
      1260: q
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1314: q
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1354: 1
      1358: 1
      1376: q
      1378: 1
      1380: q
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1415: 1
      1424: 1
      1430: 1
      1436: 1
      1446: 1
      1448: 1
      1455: 1
      1456: q+1
      1460: q
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1494: 1
      1518: 1
      1538: 1
      1560: 1
      1569: 1
      1583: q
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1637: 1
      1641: 1
      1658: 1
      1659: 1
      1661: 1
      1666: 1
      1671: 1
      1673: 1
      1704: 1
      1730: 1
      1770: 1
      1778: 1
      1783: 1
      1791: 1
      1815: 1
      1817: 1
      1822: 1
      1823: 1
      1911: 1
      1920: 1
      1923: 1
      1958: 1
      2049: 1

2050:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: q^4+2q^3+q^2+q+1
        26: q^4+2q^3+q^2+q+1
        27: q^5+q^4+q^3+q^2+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: q^4+2q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^4+2q^3+q^2+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: 2q^3+q+1
        53: 2q^3+q+1
        54: q^4+q^3+q+1
        55: q^4+2q^3+q^2+q+1
        56: q^4+2q^3+q^2+q+1
        57: q^5+q^4+q^3+q^2+q+1
        58: q^3+q
        59: q^3+1
        60: q^4+q^3+q^2+1
        61: q^3+q
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: q^4+2q^3+q^2+q+1
        73: 2q^3+q+1
        75: 2q^3+q+1
        77: 2q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: 2q^3+q+1
        83: q^3+q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^4+2q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^3+q+1
        95: 2q^3+q+1
        96: q^4+q^3+q+1
        97: q^4+2q^3+q^2+q+1
        98: q^4+2q^3+q^2+q+1
        99: q^5+q^4+q^3+q^2+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       104: q^3+1
       105: q^3+q
       107: q^4+q^3+q^2+1
       108: q^3+q
       109: q^3+q
       110: q^3+1
       112: 2q^3+q+1
       114: 2q^3+q+1
       116: q^3+q+1
       117: q
       118: 1
       119: q^2+1
       120: q
       122: q^3+q+1
       124: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       128: 2q^3+q+1
       130: 2q^3+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q^2+q+1
       136: q^3+q+1
       137: q^3+q+1
       138: q^3+q+1
       139: 2q^3+q+1
       140: q^3+1
       141: q^3+q+1
       142: 2q^3+q+1
       143: q^3+q^2+q+1
       144: q^3+q^2+q+1
       145: q^4+2q^3+q^2+q+1
       146: q^3+q^2+q+1
       147: q^4+2q^3+q^2+q+1
       148: 2q^3+q+1
       149: 2q^3+q+1
       150: q^3+q+1
       152: 2q^3+q+1
       154: 2q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^3+q^2+q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       170: q^3+1
       171: q^3+q
       174: 1
       175: q
       178: q^3+q+1
       180: 2q^3+q+1
       182: 2q^3+q+1
       183: q^2+1
       184: q
       185: q
       186: 1
       188: q^3+q+1
       190: q^3+q+1
       191: q
       192: 1
       193: q^3+1
       195: q^3+q
       196: q^3+1
       198: q^3+1
       199: q^2+1
       200: q
       201: q^4+q^3+q^2+1
       202: q^3+q
       203: q^3+q
       204: q^3+1
       206: 2q^3+q+1
       208: q^3+q+1
       210: 2q^3+q+1
       212: q^3+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q^2+q+1
       223: q^3+q^2+q+1
       224: q^3+q+1
       225: q^3+q+1
       226: q^3+q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^3+q^2+q+1
       232: q^2+q+1
       233: q^3+q^2+q+1
       234: q^3+q^2+q+1
       235: q^3+q+1
       236: q^3+q+1
       238: 2q^3+q+1
       240: 2q^3+q+1
       242: q^4+q^3+q+1
       243: 2q^3+q+1
       244: q^3+1
       245: 2q^3+q+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^3+q^2+q+1
       254: q^3+q^2+q+1
       255: q^3+q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^3+1
       261: q^3+q
       264: 1
       265: q
       268: q^3+1
       272: q^3+q
       274: q^3+1
       276: 1
       277: q
       280: q+1
       282: q+1
       283: q^2+1
       284: q
       285: q
       286: 1
       288: q^3+q+1
       290: q+1
       292: q^3+q+1
       293: q^2+1
       294: q
       295: q
       296: 1
       298: q^3+q+1
       299: 1
       302: q^3+1
       303: q
       304: 1
       306: 1
       307: q^2+1
       308: q
       309: q
       310: 1
       312: 2q^3+q+1
       314: q^3+q+1
       316: q^3+q+1
       318: 2q^3+q+1
       319: q^3+1
       321: q^3+q
       322: q^3+1
       324: q^3+1
       326: q^3+q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^3+q^2+q+1
       335: q^3+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       339: 2q^3+q+1
       341: 2q^3+q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q^3+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^3+q^2+q+1
       355: q^3+q^2+q+1
       356: q^3+q^2+q+1
       357: q^3+q+1
       358: q^3+q+1
       359: 2q^3+q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       382: 1
       383: q
       386: 1
       387: q
       390: q^3+1
       394: 1
       398: q^3+q
       400: q^3+1
       402: q
       403: 1
       407: q^3+1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q^2+1
       420: q
       421: q
       422: 1
       424: q^3+q+1
       426: q^3+q+1
       428: 2q^3+q+1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: q^3+1
       446: q^3+1
       447: q^2+1
       448: q
       449: q
       450: 1
       452: q^3+q+1
       453: q^2+1
       454: q
       456: q+1
       457: q
       458: 1
       460: q^3+q+1
       461: q^3+q
       462: q^3+1
       464: 2q^3+q+1
       466: q+1
       468: q+1
       470: q^3+q+1
       471: 1
       473: q
       474: 1
       476: 1
       478: q^3+1
       480: q^3+1
       481: q^2+q+1
       482: q+1
       483: q^3+q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^3+q^2+q+1
       499: q^3+q+1
       500: q^3+q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       526: 1
       527: q
       530: 1
       531: q
       534: 1
       538: 1
       542: 1
       546: q^3+1
       550: q
       551: 1
       554: q
       556: 1
       558: q
       560: 1
       562: q^3+q
       564: q^3+1
       566: 1
       571: q^3+1
       574: q^3+1
       581: q^3+1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+1
       590: q
       591: q
       592: 1
       593: 1
       595: q
       596: 1
       598: q+1
       600: q^3+q+1
       602: q+1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q^2+1
       620: q
       621: q
       622: 1
       624: q+1
       626: q^3+q+1
       628: q+1
       630: q^3+q+1
       631: q
       632: 1
       634: q+1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       643: q
       644: 1
       646: 1
       647: 1
       649: q
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q^3+q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: q^3+1
       706: 1
       707: q
       710: 1
       711: q
       714: q
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       738: q
       740: 1
       742: q
       744: 1
       746: q
       748: 1
       750: q
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       787: q
       788: 1
       790: q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       817: q
       818: 1
       820: q+1
       822: q+1
       824: q+1
       825: q^2+1
       826: q
       827: q
       828: 1
       829: 1
       831: q
       832: 1
       834: q+1
       836: q^3+q+1
       838: q+1
       839: q
       840: 1
       842: q+1
       844: 1
       845: 1
       847: q
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       890: 1
       897: 1
       898: q
       901: q
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: 1
       937: q
       939: 1
       941: q
       943: 1
       945: q
       947: 1
       949: q
       951: 1
       953: 1
       957: q
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       998: q
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1006: q
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: q+1
      1032: q
      1033: 1
      1035: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1043: q+1
      1044: q
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1111: q
      1113: 1
      1115: q
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1157: 1
      1165: q
      1167: 1
      1169: q
      1171: 1
      1173: q
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1207: 1
      1215: q+1
      1216: q
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1249: q+1
      1250: q
      1251: 1
      1253: q+1
      1254: 1
      1257: q+1
      1258: 1
      1260: q
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1315: q
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1353: 1
      1357: 1
      1377: q
      1379: 1
      1381: q
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1416: 1
      1423: 1
      1434: 1
      1437: 1
      1447: 1
      1449: 1
      1454: 1
      1457: q+1
      1460: q
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1519: 1
      1539: 1
      1561: 1
      1568: 1
      1584: q
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1635: 1
      1638: 1
      1642: 1
      1657: 1
      1660: 1
      1662: 1
      1665: 1
      1672: 1
      1673: 1
      1705: 1
      1731: 1
      1771: 1
      1779: 1
      1782: 1
      1790: 1
      1816: 1
      1818: 1
      1821: 1
      1824: 1
      1912: 1
      1919: 1
      1924: 1
      1959: 1
      2050: 1

2051:    0: q^4+2q^3+q^2+q+1
         1: q^4+2q^3+q^2+q+1
         2: q^5+q^4+q^3+q^2+q+1
         3: q^4+2q^3+q^2+q+1
         4: q^4+2q^3+q^2+q+1
         5: q^4+2q^3+q^2+q+1
         6: q^4+2q^3+q^2+q+1
         7: q^5+q^4+q^3+q^2+q+1
         8: q^5+q^4+q^3+q^2+q+1
         9: q^5+q^4+q^3+q^2+q+1
        10: q^4+2q^3+q^2+q+1
        11: q^4+2q^3+q^2+q+1
        12: q^4+2q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^4+2q^3+q^2+q+1
        17: q^4+2q^3+q^2+q+1
        18: q^5+q^4+q^3+q^2+q+1
        19: q^4+2q^3+q^2+q+1
        20: q^4+2q^3+q^2+q+1
        21: q^5+q^4+q^3+q^2+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: q^4+2q^3+q^2+q+1
        26: q^4+2q^3+q^2+q+1
        27: q^5+q^4+q^3+q^2+q+1
        28: q^4+2q^3+q^2+q+1
        29: q^4+2q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: q^4+2q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^4+2q^3+q^2+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^4+2q^3+q^2+q+1
        50: q^4+2q^3+q^2+q+1
        51: q^5+q^4+q^3+q^2+q+1
        52: 2q^3+q+1
        53: 2q^3+q+1
        54: q^4+q^3+q+1
        55: q^4+2q^3+q^2+q+1
        56: q^4+2q^3+q^2+q+1
        57: q^5+q^4+q^3+q^2+q+1
        58: q^3+1
        59: q^3+q
        60: q^3+q
        61: q^4+q^3+q^2+1
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^4+2q^3+q^2+q+1
        72: q^4+2q^3+q^2+q+1
        73: 2q^3+q+1
        75: 2q^3+q+1
        77: 2q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: 2q^3+q+1
        83: q^3+q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^4+2q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q^3+q^2+q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: 2q^3+q+1
        95: 2q^3+q+1
        96: q^4+q^3+q+1
        97: q^4+2q^3+q^2+q+1
        98: q^4+2q^3+q^2+q+1
        99: q^5+q^4+q^3+q^2+q+1
       100: 2q^3+q+1
       101: 2q^3+q+1
       102: q^4+q^3+q+1
       104: q^3+q
       105: q^3+1
       107: q^3+q
       108: q^4+q^3+q^2+1
       109: q^3+1
       110: q^3+q
       112: 2q^3+q+1
       114: 2q^3+q+1
       116: q^3+q+1
       117: 1
       118: q
       119: q
       120: q^2+1
       122: q^3+q+1
       124: q^3+q+1
       125: q^2+q+1
       126: q^3+q^2+q+1
       128: 2q^3+q+1
       130: 2q^3+q+1
       132: q^4+q^3+q+1
       133: q^2+q+1
       134: q^3+q^2+q+1
       135: q^3+q^2+q+1
       136: q^3+q+1
       137: q^3+q+1
       138: q^3+q+1
       139: 2q^3+q+1
       140: q^3+1
       141: q^3+q+1
       142: 2q^3+q+1
       143: q^3+q^2+q+1
       144: q^3+q^2+q+1
       145: q^4+2q^3+q^2+q+1
       146: q^3+q^2+q+1
       147: q^4+2q^3+q^2+q+1
       148: 2q^3+q+1
       149: 2q^3+q+1
       150: q^3+q+1
       152: 2q^3+q+1
       154: 2q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^3+q^2+q+1
       166: 2q^3+q+1
       167: 2q^3+q+1
       168: q^4+q^3+q+1
       170: q^3+q
       171: q^3+1
       174: q
       175: 1
       178: q^3+q+1
       180: 2q^3+q+1
       182: 2q^3+q+1
       183: q
       184: q^2+1
       185: 1
       186: q
       188: q^3+q+1
       190: q^3+q+1
       191: 1
       192: q
       194: q^3+1
       195: q^3+1
       196: q^3+q
       198: q^3+1
       199: q
       200: q^2+1
       201: q^3+q
       202: q^4+q^3+q^2+1
       203: q^3+1
       204: q^3+q
       206: 2q^3+q+1
       208: q^3+q+1
       210: 2q^3+q+1
       212: q^3+q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^3+q^2+q+1
       222: q^3+q^2+q+1
       223: q^3+q^2+q+1
       224: q^3+q+1
       225: q^3+q+1
       226: q^3+q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^3+q^2+q+1
       232: q^2+q+1
       233: q^3+q^2+q+1
       234: q^3+q^2+q+1
       235: q^3+q+1
       236: q^3+q+1
       238: 2q^3+q+1
       240: 2q^3+q+1
       242: q^4+q^3+q+1
       243: 2q^3+q+1
       244: q^3+1
       245: 2q^3+q+1
       246: q^3+q+1
       247: 2q^3+q+1
       248: 2q^3+q+1
       249: q^4+q^3+q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^3+q^2+q+1
       254: q^3+q^2+q+1
       255: q^3+q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: q^3+q
       261: q^3+1
       264: q
       265: 1
       270: q^3+1
       272: q^3+1
       274: q^3+q
       276: q
       277: 1
       280: q+1
       282: q+1
       283: q
       284: q^2+1
       285: 1
       286: q
       288: q^3+q+1
       290: q+1
       292: q^3+q+1
       293: q
       294: q^2+1
       295: 1
       296: q
       298: q^3+q+1
       300: 1
       302: q^3+1
       303: 1
       304: q
       306: 1
       307: q
       308: q^2+1
       309: 1
       310: q
       312: 2q^3+q+1
       314: q^3+q+1
       316: q^3+q+1
       318: 2q^3+q+1
       320: q^3+1
       321: q^3+1
       322: q^3+q
       324: q^3+1
       326: q^3+q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^3+q^2+q+1
       335: q^3+q+1
       336: q^3+q+1
       337: 2q^3+q+1
       339: 2q^3+q+1
       341: 2q^3+q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: q^3+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^3+q^2+q+1
       355: q^3+q^2+q+1
       356: q^3+q^2+q+1
       357: q^3+q+1
       358: q^3+q+1
       359: 2q^3+q+1
       361: q+1
       363: q+1
       365: q+1
       366: q^3+q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       382: q
       383: 1
       386: q
       387: 1
       392: q^3+1
       395: 1
       398: q^3+1
       400: q^3+q
       402: 1
       403: q
       408: q^3+1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q
       420: q^2+1
       421: 1
       422: q
       424: q^3+q+1
       426: q^3+q+1
       428: 2q^3+q+1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: q^3+1
       446: q^3+1
       447: q
       448: q^2+1
       449: 1
       450: q
       452: q^3+q+1
       453: q
       454: q^2+1
       456: q+1
       457: 1
       458: q
       460: q^3+q+1
       461: q^3+1
       462: q^3+q
       464: 2q^3+q+1
       466: q+1
       468: q+1
       470: q^3+q+1
       472: 1
       473: 1
       474: q
       476: 1
       478: q^3+1
       480: q^3+1
       481: q^2+q+1
       482: q+1
       483: q^3+q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^3+q^2+q+1
       499: q^3+q+1
       500: q^3+q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       526: q
       527: 1
       530: q
       531: 1
       535: 1
       540: 1
       544: 1
       548: q^3+1
       550: 1
       551: q
       554: 1
       556: q
       558: 1
       560: q
       562: q^3+1
       564: q^3+q
       567: 1
       572: q^3+1
       576: q^3+1
       581: q^3+1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: q^2+1
       591: 1
       592: q
       594: 1
       595: 1
       596: q
       598: q+1
       600: q^3+q+1
       602: q+1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       619: q
       620: q^2+1
       621: 1
       622: q
       624: q+1
       626: q^3+q+1
       628: q+1
       630: q^3+q+1
       631: 1
       632: q
       634: q+1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       644: q
       646: 1
       648: 1
       649: 1
       650: q
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q^3+q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: q^3+1
       706: q
       707: 1
       710: q
       711: 1
       714: 1
       715: q
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       740: q
       742: 1
       744: q
       746: 1
       748: q
       750: 1
       752: q
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       788: q
       790: q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       818: q
       820: q+1
       822: q+1
       824: q+1
       825: q
       826: q^2+1
       827: 1
       828: q
       830: 1
       831: 1
       832: q
       834: q+1
       836: q^3+q+1
       838: q+1
       839: 1
       840: q
       842: q+1
       844: 1
       846: 1
       847: 1
       848: q
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       891: 1
       897: q
       898: 1
       901: 1
       903: q
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: 1
       937: 1
       939: q
       941: 1
       943: q
       945: 1
       947: q
       949: 1
       951: q
       954: 1
       957: 1
       959: q
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
       999: q
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1007: q
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: q+1
      1032: 1
      1033: q
      1035: q+1
      1037: q+1
      1039: q+1
      1041: 1
      1043: q+1
      1044: 1
      1045: q
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1065: 1
      1074: q+1
      1076: 1
      1077: 1
      1078: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1113: q
      1115: 1
      1117: q
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1167: q
      1169: 1
      1171: q
      1173: 1
      1175: q
      1179: 1
      1182: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1209: 1
      1215: q+1
      1216: 1
      1217: q
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1249: q+1
      1250: 1
      1251: q
      1253: q+1
      1255: 1
      1257: q+1
      1259: 1
      1260: 1
      1261: q
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1317: q
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1355: 1
      1359: 1
      1377: 1
      1379: q
      1381: 1
      1383: q
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1417: 1
      1425: 1
      1434: 1
      1437: 1
      1447: 1
      1449: 1
      1455: 1
      1457: q+1
      1460: 1
      1461: q
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1496: 1
      1520: 1
      1540: 1
      1562: 1
      1570: 1
      1584: 1
      1586: q
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1614: 1
      1618: 1
      1635: 1
      1638: 1
      1642: 1
      1658: 1
      1660: 1
      1662: 1
      1666: 1
      1672: 1
      1673: 1
      1706: 1
      1732: 1
      1772: 1
      1780: 1
      1784: 1
      1792: 1
      1816: 1
      1818: 1
      1822: 1
      1824: 1
      1913: 1
      1921: 1
      1925: 1
      1959: 1
      2051: 1

2052:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q+1
        38: q^2+q
        39: q+1
        40: q^2+q
        41: q+1
        42: q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 1
        59: 2q
        60: q^2+q+1
        61: q
        62: q+1
        63: q
        64: q+1
        65: q^2+q
        66: q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+q
        76: q+1
        77: q^2+q
        78: q+1
        79: q^2+q
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 1
       104: q
       106: q
       107: q^2+q+1
       108: q
       109: 1
       110: 2q
       111: q+1
       112: q^2+q
       113: q+1
       114: q
       115: q+1
       116: q^2+q
       117: 1
       118: 2q
       119: q^2+q+1
       120: q
       121: q+1
       122: q
       123: q+1
       124: q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+q
       129: q+1
       130: q^2+q
       131: q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^3+2q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^3+2q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+q
       153: q+1
       154: q^2+q
       155: q+1
       156: q^2+q
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+2q^2+2q+1
       164: q^3+2q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       170: q
       172: q
       173: 1
       174: q
       176: q
       177: q+1
       178: q^2+q
       179: q+1
       180: q
       181: q+1
       182: q^2+q
       183: q^2+q+1
       184: q
       185: 1
       186: 2q
       187: q+1
       188: q^2+q
       189: q+1
       190: q
       191: 1
       192: 2q
       193: q+1
       195: 1
       196: 2q
       197: 1
       198: q
       199: q^2+q+1
       200: q
       201: q^2+q+1
       202: q
       203: 1
       204: 2q
       205: q+1
       206: q^2+q
       207: q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q^2+q
       213: q+1
       214: q^2+q
       215: q+1
       216: q^2+q
       217: q+1
       218: q^2+q
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^3+2q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^3+2q^2+2q+1
       234: q^3+2q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+q
       239: q+1
       240: q^2+q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 1
       260: q
       262: q
       263: 1
       264: q
       266: q
       267: 1
       268: q
       271: 1
       273: q
       274: q
       275: 1
       276: q
       278: q
       279: q+1
       280: q
       281: q+1
       282: q^2+q
       283: q^2+q+1
       284: q
       285: 1
       286: 2q
       287: q+1
       288: q
       289: q+1
       290: q^2+q
       291: q+1
       292: q^2+q
       293: q^2+q+1
       294: q
       295: 1
       296: 2q
       297: q+1
       298: q
       299: q+1
       301: 1
       302: q
       303: 1
       304: 2q
       305: 1
       306: q
       307: q^2+q+1
       308: q
       309: 1
       310: 2q
       311: q+1
       312: q^2+q
       313: q+1
       314: q^2+q
       315: q+1
       316: q^2+q
       317: q+1
       318: q
       319: q+1
       321: 1
       322: 2q
       323: 1
       324: q
       325: q+1
       326: q
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q+1
       339: q^2+q
       340: q+1
       341: q^2+q
       342: q+1
       343: q^2+q
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+2q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: q+1
       361: q^2+q
       362: q+1
       363: q^2+q
       364: q+1
       365: q^2+q
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q
       380: q
       381: 1
       382: q
       384: q
       385: 1
       386: q
       388: q
       389: 1
       390: q
       393: 1
       394: q
       397: 1
       399: q
       400: q
       401: 1
       403: q
       404: q
       405: 1
       407: q
       413: q+1
       414: q
       417: q+1
       418: q^2+q
       419: q^2+q+1
       420: q
       421: 1
       422: 2q
       423: q+1
       424: q
       425: q+1
       426: q^2+q
       427: q+1
       428: q
       429: q+1
       431: 1
       432: 2q
       433: 1
       434: q
       435: 1
       436: q
       437: 1
       439: 1
       440: q
       441: 1
       443: q+1
       445: 1
       446: q
       447: q^2+q+1
       448: q
       449: 1
       450: 2q
       451: q+1
       452: q^2+q
       453: q^2+q+1
       454: q
       455: q+1
       456: q^2+q
       457: 1
       458: 2q
       459: q+1
       460: q
       461: 1
       462: 2q
       463: q+1
       464: q^2+q
       465: q+1
       466: q
       467: q+1
       468: q^2+q
       469: q+1
       470: q
       471: q+1
       473: 1
       474: 2q
       475: 1
       476: q
       477: 1
       478: q
       479: 1
       480: q
       481: q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+q
       487: q+1
       488: q^2+q
       489: q+1
       490: q^2+q
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q
       524: q
       529: 1
       530: q
       532: q
       533: 1
       534: q
       537: 1
       538: q
       541: 1
       545: 1
       546: q
       549: 1
       551: q
       552: q
       553: 1
       555: q
       556: q
       557: 1
       559: q
       560: q
       561: 1
       563: q
       564: q
       565: 1
       566: q
       569: 1
       571: q
       573: 1
       574: q
       577: 1
       581: q
       585: q+1
       586: q
       589: q^2+q+1
       590: q
       591: 1
       592: 2q
       593: q+1
       595: 1
       596: 2q
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: q+1
       602: q
       603: 1
       605: 1
       606: q
       607: 1
       608: q
       609: 1
       613: 1
       614: q
       615: q+1
       617: 1
       618: q
       619: q^2+q+1
       620: q
       621: 1
       622: 2q
       623: q+1
       624: q^2+q
       625: q+1
       626: q
       629: q+1
       630: q^2+q
       631: 1
       632: 2q
       633: q+1
       634: q^2+q
       639: q+1
       640: q
       641: q+1
       643: 1
       644: 2q
       645: 1
       646: q
       647: 1
       649: 1
       650: q
       651: 1
       652: q
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       659: q^2+q
       660: q+1
       661: q^2+q
       662: q+1
       663: q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       699: q
       709: 1
       710: q
       712: q
       713: 1
       715: q
       716: q
       717: 1
       718: q
       721: 1
       722: q
       725: 1
       733: 1
       734: q
       737: 1
       739: q
       740: q
       741: 1
       743: q
       744: q
       749: 1
       751: q
       752: q
       753: 1
       754: q
       757: 1
       759: q
       761: 1
       765: 1
       766: q
       769: 1
       773: q
       775: q+1
       776: q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       785: q+1
       787: 1
       788: 2q
       791: 1
       792: q
       793: q+1
       795: 1
       796: q
       797: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       810: q
       811: 1
       815: 1
       817: 1
       818: 2q
       819: q+1
       820: q^2+q
       821: q+1
       822: q
       825: q^2+q+1
       826: q
       827: 1
       828: 2q
       829: q+1
       831: 1
       832: 2q
       833: q+1
       834: q^2+q
       835: q+1
       836: q
       839: 1
       840: q
       843: 1
       844: q
       845: 1
       847: 1
       848: q
       849: 1
       850: q
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       890: q
       900: 1
       902: q
       903: q
       904: 1
       905: q
       908: 1
       909: q
       916: 1
       917: q
       920: 1
       928: 1
       940: 1
       942: q
       943: q
       944: 1
       946: q
       947: q
       948: 1
       950: q
       951: q
       952: 1
       953: q
       960: 1
       962: q
       964: 1
       965: q
       968: 1
       972: q
       974: 1
       988: 1
       994: q+1
       995: q
       998: 1
       999: 2q
      1000: q+1
      1004: 1
      1006: 1
      1007: q
      1008: 1
      1010: 1
      1011: q
      1012: 1
      1013: q
      1016: 1
      1020: 1
      1021: q
      1022: 1
      1026: 1
      1032: 1
      1033: q
      1036: q+1
      1037: q^2+q
      1038: q+1
      1039: q
      1040: q+1
      1044: 1
      1045: 2q
      1046: 1
      1048: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1065: q
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: 1
      1092: q
      1114: 1
      1116: q
      1117: q
      1122: 1
      1123: q
      1126: 1
      1128: q
      1130: 1
      1131: q
      1134: 1
      1138: 1
      1142: q
      1156: 1
      1172: 1
      1174: q
      1175: q
      1176: 1
      1177: q
      1180: 1
      1181: q
      1194: 1
      1198: 1
      1206: 1
      1216: 1
      1217: q
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1230: 1
      1234: 1
      1240: 1
      1246: 1
      1247: q
      1248: q+1
      1249: q
      1250: 1
      1251: 2q
      1254: q+1
      1258: 1
      1260: 1
      1261: q
      1262: 1
      1266: 1
      1268: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1279: q
      1280: 1
      1281: q
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1296: q
      1326: 1
      1330: 1
      1356: 1
      1380: 1
      1382: q
      1383: q
      1388: 1
      1389: q
      1392: 1
      1394: q
      1396: 1
      1397: q
      1400: 1
      1410: 1
      1422: 1
      1430: 1
      1434: q
      1436: 1
      1440: 1
      1441: q
      1442: 1
      1444: 1
      1454: 1
      1460: 1
      1461: q
      1462: 1
      1464: 1
      1468: 1
      1474: 1
      1476: 1
      1482: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1513: 1
      1519: q
      1537: 1
      1549: 1
      1595: 1
      1599: 1
      1615: 1
      1639: 1
      1641: 1
      1647: 1
      1653: 1
      1654: q
      1655: 1
      1657: 1
      1659: 1
      1665: 1
      1669: 1
      1673: 1
      1674: 1
      1733: 1
      1769: 1
      1773: 1
      1781: 1
      1817: 1
      1821: 1
      1825: 1
      1831: 1
      1833: 1
      1914: 1
      1922: 1
      1960: 1
      1964: 1
      2052: 1

2053:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^2+q
        38: q+1
        39: q^2+q
        40: q+1
        41: q^2+q
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 2q
        59: 1
        60: q^2+q+1
        61: q
        62: q
        63: q+1
        64: q^2+q
        65: q+1
        66: q^2+q
        67: q+1
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q^2+q
        75: q+1
        76: q^2+q
        77: q+1
        78: q^2+q
        79: q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       104: 1
       105: q
       107: q^2+q+1
       108: q
       109: 2q
       110: 1
       111: q^2+q
       112: q+1
       113: q
       114: q+1
       115: q^2+q
       116: q+1
       117: 2q
       118: 1
       119: q^2+q+1
       120: q
       121: q
       122: q+1
       123: q^2+q
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q
       128: q+1
       129: q^2+q
       130: q+1
       131: q^2+q
       132: q+1
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^3+2q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^3+2q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+q
       152: q+1
       153: q^2+q
       154: q+1
       155: q^2+q
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+2q^2+2q+1
       164: q^3+2q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q
       170: 1
       171: q
       173: q
       174: 1
       175: q
       177: q^2+q
       178: q+1
       179: q
       180: q+1
       181: q^2+q
       182: q+1
       183: q^2+q+1
       184: q
       185: 2q
       186: 1
       187: q^2+q
       188: q+1
       189: q
       190: q+1
       191: 2q
       192: 1
       193: q+1
       195: 2q
       196: 1
       197: q
       198: 1
       199: q^2+q+1
       200: q
       201: q^2+q+1
       202: q
       203: 2q
       204: 1
       205: q^2+q
       206: q+1
       207: q
       208: q+1
       209: q
       210: q+1
       211: q^2+q
       212: q+1
       213: q^2+q
       214: q+1
       215: q^2+q
       216: q+1
       217: q^2+q
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^3+2q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^3+2q^2+2q+1
       234: q^3+2q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: q^2+q
       238: q+1
       239: q^2+q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       260: 1
       261: q
       263: q
       264: 1
       265: q
       267: q
       268: 1
       271: q
       272: q
       274: 1
       275: q
       276: 1
       277: q
       279: q
       280: q+1
       281: q^2+q
       282: q+1
       283: q^2+q+1
       284: q
       285: 2q
       286: 1
       287: q
       288: q+1
       289: q^2+q
       290: q+1
       291: q^2+q
       292: q+1
       293: q^2+q+1
       294: q
       295: 2q
       296: 1
       297: q
       298: q+1
       299: q+1
       301: q
       302: 1
       303: 2q
       304: 1
       305: q
       306: 1
       307: q^2+q+1
       308: q
       309: 2q
       310: 1
       311: q^2+q
       312: q+1
       313: q^2+q
       314: q+1
       315: q^2+q
       316: q+1
       317: q
       318: q+1
       319: q+1
       321: 2q
       322: 1
       323: q
       324: 1
       325: q
       326: q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q^2+q
       339: q+1
       340: q^2+q
       341: q+1
       342: q^2+q
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+2q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: q^2+q
       361: q+1
       362: q^2+q
       363: q+1
       364: q^2+q
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       378: 1
       379: q
       381: q
       382: 1
       383: q
       385: q
       386: 1
       387: q
       389: q
       390: 1
       393: q
       394: 1
       397: q
       398: q
       400: 1
       401: q
       402: q
       403: 1
       405: q
       407: 1
       413: q
       414: q+1
       417: q^2+q
       418: q+1
       419: q^2+q+1
       420: q
       421: 2q
       422: 1
       423: q
       424: q+1
       425: q^2+q
       426: q+1
       427: q
       428: q+1
       429: q+1
       431: 2q
       432: 1
       433: q
       434: 1
       435: q
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: q+1
       445: q
       446: 1
       447: q^2+q+1
       448: q
       449: 2q
       450: 1
       451: q^2+q
       452: q+1
       453: q^2+q+1
       454: q
       455: q^2+q
       456: q+1
       457: 2q
       458: 1
       459: q
       460: q+1
       461: 2q
       462: 1
       463: q^2+q
       464: q+1
       465: q
       466: q+1
       467: q^2+q
       468: q+1
       469: q
       470: q+1
       471: q+1
       473: 2q
       474: 1
       475: q
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q^2+q
       486: q+1
       487: q^2+q
       488: q+1
       489: q^2+q
       490: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       522: 1
       523: q
       529: q
       530: 1
       531: q
       533: q
       534: 1
       537: q
       538: 1
       542: 1
       545: q
       546: 1
       549: q
       550: q
       551: 1
       553: q
       554: q
       556: 1
       557: q
       558: q
       560: 1
       561: q
       562: q
       564: 1
       565: q
       566: 1
       569: q
       571: 1
       573: q
       574: 1
       577: q
       581: 1
       585: q
       586: q+1
       589: q^2+q+1
       590: q
       591: 2q
       592: 1
       593: q+1
       595: 2q
       596: 1
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q
       602: q+1
       603: 1
       605: q
       606: 1
       607: q
       608: 1
       610: 1
       613: q
       614: 1
       615: q+1
       617: q
       618: 1
       619: q^2+q+1
       620: q
       621: 2q
       622: 1
       623: q^2+q
       624: q+1
       625: q
       626: q+1
       629: q^2+q
       630: q+1
       631: 2q
       632: 1
       633: q^2+q
       634: q+1
       639: q
       640: q+1
       641: q+1
       643: 2q
       644: 1
       645: q
       646: 1
       647: 1
       649: q
       650: 1
       651: q
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       658: q^2+q
       659: q+1
       660: q^2+q
       661: q+1
       662: q^2+q
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       699: 1
       709: q
       710: 1
       711: q
       713: q
       714: q
       715: 1
       717: q
       718: 1
       721: q
       722: 1
       726: 1
       733: q
       734: 1
       737: q
       738: q
       740: 1
       741: q
       742: q
       744: 1
       749: q
       750: q
       752: 1
       753: q
       754: 1
       757: q
       759: 1
       763: 1
       765: q
       766: 1
       769: q
       773: 1
       775: q
       776: q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       785: q+1
       787: 2q
       788: 1
       791: q
       792: 1
       793: q+1
       795: q
       796: 1
       798: 1
       801: 1
       805: 1
       807: q
       808: 1
       809: q
       810: 1
       812: 1
       815: 1
       817: 2q
       818: 1
       819: q^2+q
       820: q+1
       821: q
       822: q+1
       825: q^2+q+1
       826: q
       827: 2q
       828: 1
       829: q+1
       831: 2q
       832: 1
       833: q^2+q
       834: q+1
       835: q
       836: q+1
       839: q
       840: 1
       843: q
       844: 1
       845: 1
       847: q
       848: 1
       849: q
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       890: 1
       900: q
       901: q
       903: 1
       904: q
       905: 1
       908: q
       909: 1
       916: q
       917: 1
       921: 1
       929: 1
       940: q
       941: q
       943: 1
       944: q
       945: q
       947: 1
       948: q
       949: q
       951: 1
       952: q
       953: 1
       960: q
       962: 1
       964: q
       965: 1
       968: q
       972: 1
       976: 1
       989: 1
       994: q
       995: q+1
       998: 2q
       999: 1
      1000: q+1
      1004: 1
      1006: q
      1007: 1
      1009: 1
      1010: q
      1011: 1
      1012: q
      1013: 1
      1016: 1
      1020: q
      1021: 1
      1023: 1
      1026: 1
      1032: q
      1033: 1
      1036: q^2+q
      1037: q+1
      1038: q
      1039: q+1
      1040: q+1
      1044: 2q
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1060: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1086: q
      1092: 1
      1114: q
      1115: q
      1117: 1
      1122: q
      1123: 1
      1126: q
      1128: 1
      1130: q
      1131: 1
      1136: 1
      1138: q
      1142: 1
      1157: 1
      1172: q
      1173: q
      1175: 1
      1176: q
      1177: 1
      1180: q
      1181: 1
      1195: 1
      1200: 1
      1207: 1
      1216: q
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1231: 1
      1234: 1
      1240: 1
      1246: q
      1247: 1
      1248: q
      1249: q+1
      1250: 2q
      1251: 1
      1254: q+1
      1258: 1
      1260: q
      1261: 1
      1263: 1
      1267: 1
      1268: 1
      1274: q
      1275: 1
      1277: 1
      1278: q
      1279: 1
      1280: q
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: q
      1296: 1
      1327: 1
      1332: 1
      1357: 1
      1380: q
      1381: q
      1383: 1
      1388: q
      1389: 1
      1392: q
      1394: 1
      1396: q
      1397: 1
      1402: 1
      1411: 1
      1423: 1
      1430: q
      1434: 1
      1437: 1
      1440: q
      1441: 1
      1442: 1
      1445: 1
      1454: 1
      1460: q
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1475: 1
      1476: 1
      1483: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1513: q
      1519: 1
      1539: 1
      1550: 1
      1596: 1
      1601: 1
      1616: 1
      1640: 1
      1642: 1
      1647: 1
      1653: q
      1654: 1
      1655: 1
      1657: 1
      1660: 1
      1665: 1
      1670: 1
      1673: 1
      1674: 1
      1734: 1
      1771: 1
      1774: 1
      1782: 1
      1818: 1
      1821: 1
      1826: 1
      1831: 1
      1833: 1
      1915: 1
      1924: 1
      1961: 1
      1964: 1
      2053: 1

2054:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q+1
        38: q^2+q
        39: q+1
        40: q^2+q
        41: q+1
        42: q^2+q
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 2q
        59: 1
        60: q
        61: q^2+q+1
        62: q+1
        63: q
        64: q+1
        65: q^2+q
        66: q+1
        67: q^2+q
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+q
        76: q+1
        77: q^2+q
        78: q+1
        79: q^2+q
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q
       105: q
       106: 1
       107: q
       108: q^2+q+1
       109: 2q
       110: 1
       111: q+1
       112: q^2+q
       113: q+1
       114: q
       115: q+1
       116: q^2+q
       117: 2q
       118: 1
       119: q
       120: q^2+q+1
       121: q+1
       122: q
       123: q+1
       124: q^2+q
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+q
       129: q+1
       130: q^2+q
       131: q+1
       132: q^2+q
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^3+2q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^3+2q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+q
       153: q+1
       154: q^2+q
       155: q+1
       156: q^2+q
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+2q^2+2q+1
       164: q^3+2q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q
       171: q
       172: 1
       173: q
       175: q
       176: 1
       177: q+1
       178: q^2+q
       179: q+1
       180: q
       181: q+1
       182: q^2+q
       183: q
       184: q^2+q+1
       185: 2q
       186: 1
       187: q+1
       188: q^2+q
       189: q+1
       190: q
       191: 2q
       192: 1
       194: q+1
       195: 2q
       196: 1
       197: 1
       198: q
       199: q
       200: q^2+q+1
       201: q
       202: q^2+q+1
       203: 2q
       204: 1
       205: q+1
       206: q^2+q
       207: q+1
       208: q
       209: q+1
       210: q
       211: q+1
       212: q^2+q
       213: q+1
       214: q^2+q
       215: q+1
       216: q^2+q
       217: q+1
       218: q^2+q
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^3+2q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^3+2q^2+2q+1
       234: q^3+2q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+q
       239: q+1
       240: q^2+q
       241: q+1
       242: q^2+q
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q
       261: q
       262: 1
       263: q
       265: q
       266: 1
       269: 1
       270: q
       271: q
       272: q
       273: 1
       275: q
       277: q
       278: 1
       279: q+1
       280: q
       281: q+1
       282: q^2+q
       283: q
       284: q^2+q+1
       285: 2q
       286: 1
       287: q+1
       288: q
       289: q+1
       290: q^2+q
       291: q+1
       292: q^2+q
       293: q
       294: q^2+q+1
       295: 2q
       296: 1
       297: q+1
       298: q
       300: q+1
       301: 1
       302: q
       303: 2q
       304: 1
       305: 1
       306: q
       307: q
       308: q^2+q+1
       309: 2q
       310: 1
       311: q+1
       312: q^2+q
       313: q+1
       314: q^2+q
       315: q+1
       316: q^2+q
       317: q+1
       318: q
       320: q+1
       321: 2q
       322: 1
       323: 1
       324: q
       325: q+1
       326: q
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q+1
       339: q^2+q
       340: q+1
       341: q^2+q
       342: q+1
       343: q^2+q
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+2q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: q+1
       361: q^2+q
       362: q+1
       363: q^2+q
       364: q+1
       365: q^2+q
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       379: q
       380: 1
       381: q
       383: q
       384: 1
       385: q
       387: q
       388: 1
       391: 1
       392: q
       395: q
       396: 1
       397: q
       398: q
       399: 1
       401: q
       402: q
       404: 1
       406: 1
       408: q
       413: q+1
       414: q
       417: q+1
       418: q^2+q
       419: q
       420: q^2+q+1
       421: 2q
       422: 1
       423: q+1
       424: q
       425: q+1
       426: q^2+q
       427: q+1
       428: q
       430: q+1
       431: 2q
       432: 1
       433: 1
       434: q
       435: 1
       436: q
       438: 1
       439: q
       440: 1
       441: 1
       444: q+1
       445: 1
       446: q
       447: q
       448: q^2+q+1
       449: 2q
       450: 1
       451: q+1
       452: q^2+q
       453: q
       454: q^2+q+1
       455: q+1
       456: q^2+q
       457: 2q
       458: 1
       459: q+1
       460: q
       461: 2q
       462: 1
       463: q+1
       464: q^2+q
       465: q+1
       466: q
       467: q+1
       468: q^2+q
       469: q+1
       470: q
       472: q+1
       473: 2q
       474: 1
       475: 1
       476: q
       477: 1
       478: q
       479: 1
       480: q
       481: q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+q
       487: q+1
       488: q^2+q
       489: q+1
       490: q^2+q
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       523: q
       524: 1
       529: q
       531: q
       532: 1
       535: q
       536: 1
       539: 1
       540: q
       543: 1
       547: 1
       548: q
       549: q
       550: q
       552: 1
       553: q
       554: q
       555: 1
       557: q
       558: q
       559: 1
       561: q
       562: q
       563: 1
       567: q
       568: 1
       570: 1
       572: q
       575: 1
       576: q
       577: 1
       581: q
       585: q+1
       586: q
       589: q
       590: q^2+q+1
       591: 2q
       592: 1
       594: q+1
       595: 2q
       596: 1
       597: q+1
       598: q^2+q
       599: q+1
       600: q
       601: q+1
       602: q
       604: 1
       605: 1
       606: q
       607: q
       608: 1
       609: 1
       613: 1
       614: q
       616: q+1
       617: 1
       618: q
       619: q
       620: q^2+q+1
       621: 2q
       622: 1
       623: q+1
       624: q^2+q
       625: q+1
       626: q
       629: q+1
       630: q^2+q
       631: 2q
       632: 1
       633: q+1
       634: q^2+q
       639: q+1
       640: q
       642: q+1
       643: 2q
       644: 1
       645: 1
       646: q
       648: 1
       649: q
       650: 1
       651: 1
       652: q
       653: 1
       655: 1
       656: q
       657: 2q+1
       658: q+1
       659: q^2+q
       660: q+1
       661: q^2+q
       662: q+1
       663: q^2+q
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       700: q
       709: q
       711: q
       712: 1
       713: q
       714: q
       716: 1
       719: q
       720: 1
       723: 1
       724: q
       727: 1
       735: 1
       736: q
       737: q
       738: q
       739: 1
       741: q
       742: q
       743: 1
       749: q
       750: q
       751: 1
       755: q
       756: 1
       758: 1
       760: q
       762: 1
       767: q
       768: 1
       769: 1
       773: q
       775: q+1
       776: q
       779: q+1
       780: q^2+q
       781: q+1
       782: q
       786: q+1
       787: 2q
       788: 1
       791: 1
       792: q
       794: q+1
       795: 1
       796: q
       797: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       810: q
       811: 1
       816: 1
       817: 2q
       818: 1
       819: q+1
       820: q^2+q
       821: q+1
       822: q
       825: q
       826: q^2+q+1
       827: 2q
       828: 1
       830: q+1
       831: 2q
       832: 1
       833: q+1
       834: q^2+q
       835: q+1
       836: q
       839: q
       840: 1
       843: 1
       844: q
       846: 1
       847: q
       848: 1
       849: 1
       850: q
       851: 1
       855: 1
       856: q
       857: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       891: q
       900: q
       901: q
       902: 1
       906: 1
       907: q
       910: q
       911: 1
       918: 1
       919: q
       922: 1
       930: 1
       940: q
       941: q
       942: 1
       944: q
       945: q
       946: 1
       948: q
       949: q
       950: 1
       954: q
       955: 1
       961: 1
       963: q
       966: q
       967: 1
       968: 1
       972: q
       975: 1
       991: 1
       994: q+1
       995: q
       998: 2q
       999: 1
      1001: q+1
      1005: 1
      1006: q
      1007: 1
      1008: 1
      1010: 1
      1011: q
      1012: 1
      1013: q
      1017: 1
      1020: 1
      1021: q
      1022: 1
      1027: 1
      1032: q
      1033: 1
      1036: q+1
      1037: q^2+q
      1038: q+1
      1039: q
      1041: q+1
      1044: 2q
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1061: q
      1062: 1
      1064: 1
      1065: q
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1091: 1
      1093: q
      1114: q
      1115: q
      1116: 1
      1124: 1
      1125: q
      1127: 1
      1129: q
      1132: q
      1133: 1
      1135: 1
      1138: 1
      1142: q
      1158: 1
      1172: q
      1173: q
      1174: 1
      1178: 1
      1179: q
      1182: q
      1183: 1
      1197: 1
      1199: 1
      1208: 1
      1216: q
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1230: 1
      1235: 1
      1241: 1
      1246: q
      1247: 1
      1248: q+1
      1249: q
      1250: 2q
      1251: 1
      1255: q+1
      1259: 1
      1260: q
      1261: 1
      1262: 1
      1266: 1
      1269: 1
      1274: 1
      1275: q
      1276: 1
      1278: 1
      1279: q
      1280: 1
      1281: q
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1297: q
      1329: 1
      1331: 1
      1358: 1
      1380: q
      1381: q
      1382: 1
      1390: 1
      1391: q
      1393: 1
      1395: q
      1398: q
      1399: 1
      1401: 1
      1413: 1
      1424: 1
      1430: 1
      1434: q
      1436: 1
      1440: q
      1441: 1
      1443: 1
      1444: 1
      1455: 1
      1460: q
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1474: 1
      1477: 1
      1482: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1518: 1
      1520: q
      1538: 1
      1552: 1
      1598: 1
      1600: 1
      1617: 1
      1639: 1
      1641: 1
      1648: 1
      1653: q
      1654: 1
      1656: 1
      1658: 1
      1659: 1
      1666: 1
      1669: 1
      1673: 1
      1674: 1
      1736: 1
      1770: 1
      1776: 1
      1783: 1
      1817: 1
      1822: 1
      1825: 1
      1832: 1
      1833: 1
      1916: 1
      1923: 1
      1960: 1
      1965: 1
      2054: 1

2055:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^2+q
        38: q+1
        39: q^2+q
        40: q+1
        41: q^2+q
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^3+2q^2+2q+1
        58: 1
        59: 2q
        60: q
        61: q^2+q+1
        62: q
        63: q+1
        64: q^2+q
        65: q+1
        66: q^2+q
        67: q+1
        68: q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q^2+q
        75: q+1
        76: q^2+q
        77: q+1
        78: q^2+q
        79: q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       104: q
       105: 1
       106: q
       107: q
       108: q^2+q+1
       109: 1
       110: 2q
       111: q^2+q
       112: q+1
       113: q
       114: q+1
       115: q^2+q
       116: q+1
       117: 1
       118: 2q
       119: q
       120: q^2+q+1
       121: q
       122: q+1
       123: q^2+q
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+q
       128: q+1
       129: q^2+q
       130: q+1
       131: q^2+q
       132: q+1
       133: q^2+2q+1
       134: q^3+2q^2+2q+1
       135: q^3+2q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^3+2q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+q
       152: q+1
       153: q^2+q
       154: q+1
       155: q^2+q
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^3+2q^2+2q+1
       164: q^3+2q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       170: q
       171: 1
       172: q
       174: q
       175: 1
       176: q
       177: q^2+q
       178: q+1
       179: q
       180: q+1
       181: q^2+q
       182: q+1
       183: q
       184: q^2+q+1
       185: 1
       186: 2q
       187: q^2+q
       188: q+1
       189: q
       190: q+1
       191: 1
       192: 2q
       194: q+1
       195: 1
       196: 2q
       197: q
       198: 1
       199: q
       200: q^2+q+1
       201: q
       202: q^2+q+1
       203: 1
       204: 2q
       205: q^2+q
       206: q+1
       207: q
       208: q+1
       209: q
       210: q+1
       211: q^2+q
       212: q+1
       213: q^2+q
       214: q+1
       215: q^2+q
       216: q+1
       217: q^2+q
       218: q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^3+2q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^3+2q^2+2q+1
       234: q^3+2q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: q^2+q
       238: q+1
       239: q^2+q
       240: q+1
       241: q^2+q
       242: q+1
       243: 2q+1
       244: q+1
       245: q^2+2q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       260: q
       261: 1
       262: q
       264: q
       265: 1
       266: q
       269: q
       270: 1
       272: 1
       273: q
       274: q
       276: q
       277: 1
       278: q
       279: q
       280: q+1
       281: q^2+q
       282: q+1
       283: q
       284: q^2+q+1
       285: 1
       286: 2q
       287: q
       288: q+1
       289: q^2+q
       290: q+1
       291: q^2+q
       292: q+1
       293: q
       294: q^2+q+1
       295: 1
       296: 2q
       297: q
       298: q+1
       300: q+1
       301: q
       302: 1
       303: 1
       304: 2q
       305: q
       306: 1
       307: q
       308: q^2+q+1
       309: 1
       310: 2q
       311: q^2+q
       312: q+1
       313: q^2+q
       314: q+1
       315: q^2+q
       316: q+1
       317: q
       318: q+1
       320: q+1
       321: 1
       322: 2q
       323: q
       324: 1
       325: q
       326: q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q^2+2q+1
       337: 2q+1
       338: q^2+q
       339: q+1
       340: q^2+q
       341: q+1
       342: q^2+q
       343: q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q^2+2q+1
       351: q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q^3+2q^2+2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: q^2+q
       361: q+1
       362: q^2+q
       363: q+1
       364: q^2+q
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       380: q
       382: q
       383: 1
       384: q
       386: q
       387: 1
       388: q
       391: q
       392: 1
       395: 1
       396: q
       398: 1
       399: q
       400: q
       402: 1
       403: q
       404: q
       406: q
       408: 1
       413: q
       414: q+1
       417: q^2+q
       418: q+1
       419: q
       420: q^2+q+1
       421: 1
       422: 2q
       423: q
       424: q+1
       425: q^2+q
       426: q+1
       427: q
       428: q+1
       430: q+1
       431: 1
       432: 2q
       433: q
       434: 1
       435: q
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: q+1
       445: q
       446: 1
       447: q
       448: q^2+q+1
       449: 1
       450: 2q
       451: q^2+q
       452: q+1
       453: q
       454: q^2+q+1
       455: q^2+q
       456: q+1
       457: 1
       458: 2q
       459: q
       460: q+1
       461: 1
       462: 2q
       463: q^2+q
       464: q+1
       465: q
       466: q+1
       467: q^2+q
       468: q+1
       469: q
       470: q+1
       472: q+1
       473: 1
       474: 2q
       475: q
       476: 1
       477: q
       478: 1
       479: q
       480: 1
       481: q^2+2q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q^2+q
       486: q+1
       487: q^2+q
       488: q+1
       489: q^2+q
       490: q+1
       491: q^2+2q+1
       492: q+1
       493: 1
       494: q+1
       495: q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: q^2+2q+1
       501: q^2+2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q^2+2q+1
       515: q^2+2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       524: q
       530: q
       531: 1
       532: q
       535: 1
       536: q
       539: q
       540: 1
       544: 1
       547: q
       548: 1
       550: 1
       551: q
       552: q
       554: 1
       555: q
       556: q
       558: 1
       559: q
       560: q
       562: 1
       563: q
       564: q
       567: 1
       568: q
       570: q
       572: 1
       575: q
       576: 1
       577: q
       581: 1
       585: q
       586: q+1
       589: q
       590: q^2+q+1
       591: 1
       592: 2q
       594: q+1
       595: 1
       596: 2q
       597: q^2+q
       598: q+1
       599: q
       600: q+1
       601: q
       602: q+1
       604: 1
       605: q
       606: 1
       607: 1
       608: q
       610: 1
       613: q
       614: 1
       616: q+1
       617: q
       618: 1
       619: q
       620: q^2+q+1
       621: 1
       622: 2q
       623: q^2+q
       624: q+1
       625: q
       626: q+1
       629: q^2+q
       630: q+1
       631: 1
       632: 2q
       633: q^2+q
       634: q+1
       639: q
       640: q+1
       642: q+1
       643: 1
       644: 2q
       645: q
       646: 1
       648: 1
       649: 1
       650: q
       651: q
       652: 1
       654: 1
       655: q
       656: 1
       657: 2q+1
       658: q^2+q
       659: q+1
       660: q^2+q
       661: q+1
       662: q^2+q
       663: q+1
       664: q^2+2q+1
       665: 2q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: 2q+1
       683: 2q+1
       684: q+1
       685: q^2+2q+1
       686: q+1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       697: q
       700: 1
       710: q
       711: 1
       712: q
       714: 1
       715: q
       716: q
       719: 1
       720: q
       723: q
       724: 1
       728: 1
       735: q
       736: 1
       738: 1
       739: q
       740: q
       742: 1
       743: q
       744: q
       750: 1
       751: q
       752: q
       755: 1
       756: q
       758: q
       760: 1
       764: 1
       767: 1
       768: q
       769: q
       773: 1
       775: q
       776: q+1
       779: q^2+q
       780: q+1
       781: q
       782: q+1
       786: q+1
       787: 1
       788: 2q
       791: q
       792: 1
       794: q+1
       795: q
       796: 1
       798: 1
       802: 1
       806: 1
       807: 1
       808: q
       809: q
       810: 1
       812: 1
       816: 1
       817: 1
       818: 2q
       819: q^2+q
       820: q+1
       821: q
       822: q+1
       825: q
       826: q^2+q+1
       827: 1
       828: 2q
       830: q+1
       831: 1
       832: 2q
       833: q^2+q
       834: q+1
       835: q
       836: q+1
       839: 1
       840: q
       843: q
       844: 1
       846: 1
       847: 1
       848: q
       849: q
       850: 1
       852: 1
       855: q
       856: 1
       858: 1
       865: q+1
       866: 2q+1
       867: q+1
       868: q+1
       869: 1
       870: q+1
       871: 1
       872: 1
       873: q+1
       874: q^2+2q+1
       875: 2q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       889: q
       891: 1
       901: 1
       902: q
       903: q
       906: q
       907: 1
       910: 1
       911: q
       918: q
       919: 1
       923: 1
       931: 1
       941: 1
       942: q
       943: q
       945: 1
       946: q
       947: q
       949: 1
       950: q
       951: q
       954: 1
       955: q
       961: q
       963: 1
       966: 1
       967: q
       968: q
       972: 1
       977: 1
       990: 1
       994: q
       995: q+1
       998: 1
       999: 2q
      1001: q+1
      1005: 1
      1006: 1
      1007: q
      1009: 1
      1010: q
      1011: 1
      1012: q
      1013: 1
      1017: 1
      1020: q
      1021: 1
      1023: 1
      1027: 1
      1032: 1
      1033: q
      1036: q^2+q
      1037: q+1
      1038: q
      1039: q+1
      1041: q+1
      1044: 1
      1045: 2q
      1047: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1060: q
      1061: 1
      1063: 1
      1064: q
      1065: 1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: 2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: 1
      1091: q
      1093: 1
      1115: 1
      1116: q
      1117: q
      1124: q
      1125: 1
      1127: q
      1129: 1
      1132: 1
      1133: q
      1137: 1
      1138: q
      1142: 1
      1159: 1
      1173: 1
      1174: q
      1175: q
      1178: q
      1179: 1
      1182: 1
      1183: q
      1196: 1
      1201: 1
      1209: 1
      1216: 1
      1217: q
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1231: 1
      1235: 1
      1241: 1
      1246: 1
      1247: q
      1248: q
      1249: q+1
      1250: 1
      1251: 2q
      1255: q+1
      1259: 1
      1260: 1
      1261: q
      1263: 1
      1267: 1
      1269: 1
      1274: q
      1275: 1
      1277: 1
      1278: q
      1279: 1
      1280: q
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: q
      1297: 1
      1328: 1
      1333: 1
      1359: 1
      1381: 1
      1382: q
      1383: q
      1390: q
      1391: 1
      1393: q
      1395: 1
      1398: 1
      1399: q
      1403: 1
      1412: 1
      1425: 1
      1430: q
      1434: 1
      1437: 1
      1440: 1
      1441: q
      1443: 1
      1445: 1
      1455: 1
      1460: 1
      1461: q
      1463: 1
      1465: 1
      1469: 1
      1475: 1
      1477: 1
      1483: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1518: q
      1520: 1
      1540: 1
      1551: 1
      1597: 1
      1602: 1
      1618: 1
      1640: 1
      1642: 1
      1648: 1
      1653: 1
      1654: q
      1656: 1
      1658: 1
      1660: 1
      1666: 1
      1670: 1
      1673: 1
      1674: 1
      1735: 1
      1772: 1
      1775: 1
      1784: 1
      1818: 1
      1822: 1
      1826: 1
      1832: 1
      1833: 1
      1917: 1
      1925: 1
      1961: 1
      1965: 1
      2055: 1

2056:    0: 2q^3+q+1
         1: 2q^3+q+1
         2: q^4+q^3+q+1
         3: 2q^3+q+1
         4: q^4+q^3+q+1
         5: 2q^3+q+1
         6: q^4+q^3+q+1
         7: q^5+2q^4+q^3+q+1
         8: q^4+q^3+q+1
         9: q^5+2q^4+q^3+q+1
        10: 2q^3+q+1
        11: 2q^3+q+1
        12: q^4+q^3+q+1
        13: q^3+q+1
        14: q^4+q^3+q+1
        15: q^3+q+1
        16: 2q^3+q+1
        17: 2q^3+q+1
        18: q^5+2q^4+q^3+q+1
        19: q^3+q+1
        20: q^3+q+1
        21: q^4+q^3+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: 2q^3+q+1
        29: q^3+q+1
        30: q^3+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q+1
        44: q^4+q^3+q+1
        45: q^3+q+1
        46: q^3+q+1
        47: q^3+q+1
        48: q^4+q^3+q+1
        49: q^3+q+1
        50: q^3+q+1
        51: q^4+q^3+q+1
        52: q^3+q+1
        53: q^3+q+1
        54: q^4+q^3+q+1
        55: q^3+q+1
        56: q^3+q+1
        57: q^4+q^3+q+1
        58: q^3+q+1
        59: q^3
        60: q^3+q+1
        61: q^3
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q+1
        69: q^3+q+1
        70: q^3+q+1
        71: q^3+q+1
        72: q+1
        73: q+1
        74: q^3+q+1
        76: q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: q^3+q+1
        83: q^3+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: q^3+q+1
        87: q^3+q+1
        88: q^3+q+1
        89: q^3+q+1
        90: q^4+q^3+q+1
        91: q^3+q+1
        92: q+1
        93: q^3+q+1
        94: q^3+q+1
        95: q^3+q+1
        96: q^4+q^3+q+1
        97: q^3+q+1
        98: q^3+q+1
        99: q^4+q^3+q+1
       100: q^3+q+1
       101: q^3+q+1
       102: q^4+q^3+q+1
       103: q^3+q+1
       106: q^3
       107: q+1
       109: q+1
       111: q+1
       113: q^3+q+1
       115: q^3+q+1
       117: q+1
       119: q+1
       121: q^3+q+1
       123: q^3+q+1
       125: q+1
       126: q^3+q+1
       127: q^3+q+1
       129: q^3+q+1
       131: q^4+q^3+q+1
       133: q+1
       134: q^3+q+1
       135: q+1
       136: q+1
       137: q^3+q+1
       138: q^3+q+1
       139: q^3+q+1
       140: q+1
       141: q^3+q+1
       142: q+1
       143: q^3+q+1
       144: q^3+q+1
       145: q^3+q+1
       146: q^3+q+1
       147: q+1
       148: q+1
       149: q^3+q+1
       150: q^3+q+1
       151: q^3+q+1
       153: q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: q^3+q+1
       161: q+1
       162: q^3+q+1
       163: q^3+q+1
       164: q+1
       165: q^3+q+1
       166: q^3+q+1
       167: q^3+q+1
       168: q^4+q^3+q+1
       169: q+1
       173: q+1
       177: q^3+q+1
       179: q^3+q+1
       181: q+1
       183: q+1
       185: q+1
       187: q+1
       189: q^3+q+1
       191: q+1
       193: q+1
       195: q+1
       197: q+1
       199: q+1
       201: q+1
       203: q+1
       205: q+1
       207: q^3+q+1
       209: q^3+q+1
       211: q^3+q+1
       213: q^3+q+1
       215: q+1
       217: q^3+q+1
       219: q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q^3+q+1
       227: q+1
       228: q^3+q+1
       229: q+1
       230: q+1
       231: q^3+q+1
       232: q+1
       233: q^3+q+1
       234: q+1
       235: q+1
       236: q^3+q+1
       237: q^3+q+1
       239: q^3+q+1
       241: q^4+q^3+q+1
       243: q^3+q+1
       244: q+1
       245: q+1
       246: q^3+q+1
       247: q+1
       248: q+1
       249: q^4+q^3+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: q^3+q+1
       257: q+1
       258: q^3+q+1
       259: q+1
       263: q+1
       267: q+1
       271: q+1
       275: q+1
       279: q+1
       281: q^3+q+1
       283: q+1
       285: q+1
       287: q^3+q+1
       289: q+1
       291: q+1
       293: q+1
       295: q+1
       297: q+1
       299: q+1
       301: q+1
       303: q+1
       305: q+1
       307: q+1
       309: q+1
       311: q+1
       313: q+1
       315: q^3+q+1
       317: q^3+q+1
       319: q+1
       321: q+1
       323: q+1
       325: q^3+q+1
       327: q^3+q+1
       329: q+1
       331: q^3+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q^3+q+1
       362: q+1
       364: q^3+q+1
       366: q^3+q+1
       367: q+1
       368: q^3+q+1
       369: q+1
       370: q+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       377: q+1
       381: q+1
       385: q+1
       389: q+1
       393: q+1
       397: q+1
       401: q+1
       405: q+1
       409: q+1
       411: q^3+q+1
       413: q+1
       415: q+1
       417: q+1
       419: q+1
       421: q+1
       423: q+1
       425: q+1
       427: q+1
       429: q+1
       431: q+1
       433: q+1
       435: q+1
       437: q+1
       439: q+1
       441: q+1
       443: q+1
       445: q+1
       447: q+1
       449: q+1
       451: q+1
       453: q+1
       455: q+1
       457: q+1
       459: q+1
       461: q+1
       463: q+1
       465: q+1
       467: q^3+q+1
       469: q^3+q+1
       471: q+1
       473: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: q^3+q+1
       504: q+1
       506: q^3+q+1
       508: q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       521: q+1
       525: q+1
       529: q+1
       533: q+1
       537: q+1
       541: q+1
       545: q+1
       549: q+1
       553: q+1
       557: q+1
       561: q+1
       565: q+1
       569: q+1
       573: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: 1
       599: q+1
       601: 1
       603: q+1
       605: q+1
       607: q+1
       609: q+1
       611: q+1
       613: q+1
       615: 1
       617: 1
       619: q+1
       621: q+1
       623: q+1
       625: q+1
       627: q+1
       629: q+1
       631: 1
       633: 1
       635: q+1
       637: q^3+q+1
       639: q+1
       641: q+1
       643: q+1
       645: q+1
       647: q+1
       649: q+1
       651: q+1
       653: q+1
       655: 1
       657: 1
       658: 1
       660: 1
       662: q^3+1
       664: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       674: 1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q^3+1
       693: q+1
       705: q+1
       709: q+1
       713: q+1
       717: q+1
       721: q+1
       725: q+1
       729: q+1
       733: 1
       737: q+1
       741: q+1
       745: q+1
       749: 1
       753: q+1
       757: q+1
       761: q+1
       765: 1
       769: 1
       775: 1
       777: q+1
       779: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       797: q+1
       799: q+1
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: 1
       811: q+1
       813: 1
       815: 1
       817: 1
       819: 1
       821: q+1
       823: q+1
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: 1
       835: q+1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: q+1
       847: q+1
       849: q+1
       851: q+1
       853: q+1
       855: q+1
       857: 1
       859: 1
       861: 1
       863: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       884: 1
       896: q+1
       900: 1
       904: 1
       908: 1
       912: q+1
       916: 1
       920: q+1
       924: q+1
       928: q+1
       932: 1
       936: q+1
       940: 1
       944: q+1
       948: q+1
       952: q+1
       956: 1
       960: q+1
       964: 1
       968: 1
       974: q+1
       978: q+1
       982: 1
       988: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 1
      1016: 1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1034: q+1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1044: 1
      1046: 1
      1048: q+1
      1050: q+1
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 2
      1130: 1
      1134: 1
      1138: 1
      1140: 1
      1144: 1
      1148: q+1
      1152: 1
      1156: 1
      1160: 1
      1164: 1
      1168: q+1
      1172: 1
      1176: 1
      1180: 1
      1184: q+1
      1188: 1
      1194: 1
      1198: q+1
      1202: q+1
      1206: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1260: 1
      1264: q+1
      1266: 1
      1268: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1292: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 2
      1326: 1
      1330: 1
      1334: 1
      1336: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 2
      1364: 1
      1368: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 2
      1396: 1
      1400: 1
      1414: q+1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: 1
      1450: 1
      1454: 1
      1456: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1478: 1
      1480: 2
      1482: 1
      1487: 1
      1489: 1
      1491: 1
      1501: 1
      1503: 1
      1513: 1
      1515: 1
      1537: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 2
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 2
      1595: 1
      1599: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 2
      1623: 1
      1627: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1663: 1
      1665: 1
      1671: 1
      1687: 1
      1689: 1
      1699: 1
      1701: 1
      1711: 1
      1713: 1
      1729: 1
      1741: 1
      1753: 1
      1769: 1
      1777: 1
      1785: 1
      1789: 1
      1793: 2
      1797: 1
      1807: 1
      1823: 1
      1870: 1
      1872: 1
      1894: 1
      1910: 1
      1944: 1
      1948: 1
      2056: 1

2057:    0: 2q^3+q+1
         1: 2q^3+q+1
         2: q^4+q^3+q+1
         3: 2q^3+q+1
         4: q^4+q^3+q+1
         5: 2q^3+q+1
         6: q^4+q^3+q+1
         7: q^5+2q^4+q^3+q+1
         8: q^4+q^3+q+1
         9: q^5+2q^4+q^3+q+1
        10: 2q^3+q+1
        11: 2q^3+q+1
        12: q^4+q^3+q+1
        13: q^3+q+1
        14: q^4+q^3+q+1
        15: q^3+q+1
        16: 2q^3+q+1
        17: 2q^3+q+1
        18: q^5+2q^4+q^3+q+1
        19: q^3+q+1
        20: q^3+q+1
        21: q^4+q^3+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: 2q^3+q+1
        29: q^3+q+1
        30: q^3+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        37: 2q^3+q+1
        39: 2q^3+q+1
        41: q^4+q^3+q+1
        43: q^3+q+1
        44: q^4+q^3+q+1
        45: q^3+q+1
        46: q^3+q+1
        47: q^3+q+1
        48: q^4+q^3+q+1
        49: q^3+q+1
        50: q^3+q+1
        51: q^4+q^3+q+1
        52: q^3+q+1
        53: q^3+q+1
        54: q^4+q^3+q+1
        55: q^3+q+1
        56: q^3+q+1
        57: q^4+q^3+q+1
        58: q^3
        59: q^3+q+1
        60: q^3
        61: q^3+q+1
        62: 2q^3+q+1
        64: q^3+q+1
        66: 2q^3+q+1
        68: q+1
        69: q^3+q+1
        70: q^3+q+1
        71: q^3+q+1
        72: q+1
        73: q+1
        74: q^3+q+1
        76: q^3+q+1
        78: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: q^3+q+1
        83: q^3+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: q^3+q+1
        87: q^3+q+1
        88: q^3+q+1
        89: q^3+q+1
        90: q^4+q^3+q+1
        91: q^3+q+1
        92: q+1
        93: q^3+q+1
        94: q^3+q+1
        95: q^3+q+1
        96: q^4+q^3+q+1
        97: q^3+q+1
        98: q^3+q+1
        99: q^4+q^3+q+1
       100: q^3+q+1
       101: q^3+q+1
       102: q^4+q^3+q+1
       103: q^3
       106: q^3+q+1
       108: q+1
       110: q+1
       111: q+1
       113: q^3+q+1
       115: q^3+q+1
       118: q+1
       120: q+1
       121: q^3+q+1
       123: q^3+q+1
       125: q+1
       126: q^3+q+1
       127: q^3+q+1
       129: q^3+q+1
       131: q^4+q^3+q+1
       133: q+1
       134: q^3+q+1
       135: q+1
       136: q+1
       137: q^3+q+1
       138: q^3+q+1
       139: q^3+q+1
       140: q+1
       141: q^3+q+1
       142: q+1
       143: q^3+q+1
       144: q^3+q+1
       145: q^3+q+1
       146: q^3+q+1
       147: q+1
       148: q+1
       149: q^3+q+1
       150: q^3+q+1
       151: q^3+q+1
       153: q^3+q+1
       155: q^4+q^3+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: q^3+q+1
       161: q+1
       162: q^3+q+1
       163: q^3+q+1
       164: q+1
       165: q^3+q+1
       166: q^3+q+1
       167: q^3+q+1
       168: q^4+q^3+q+1
       172: q+1
       176: q+1
       177: q^3+q+1
       179: q^3+q+1
       181: q+1
       184: q+1
       186: q+1
       187: q+1
       189: q^3+q+1
       192: q+1
       194: q+1
       196: q+1
       197: q+1
       200: q+1
       202: q+1
       204: q+1
       205: q+1
       207: q^3+q+1
       209: q^3+q+1
       211: q^3+q+1
       213: q^3+q+1
       215: q+1
       217: q^3+q+1
       219: q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q^3+q+1
       227: q+1
       228: q^3+q+1
       229: q+1
       230: q+1
       231: q^3+q+1
       232: q+1
       233: q^3+q+1
       234: q+1
       235: q+1
       236: q^3+q+1
       237: q^3+q+1
       239: q^3+q+1
       241: q^4+q^3+q+1
       243: q^3+q+1
       244: q+1
       245: q+1
       246: q^3+q+1
       247: q+1
       248: q+1
       249: q^4+q^3+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: q^3+q+1
       257: q+1
       258: q^3+q+1
       262: q+1
       266: q+1
       269: q+1
       273: q+1
       278: q+1
       279: q+1
       281: q^3+q+1
       284: q+1
       286: q+1
       287: q^3+q+1
       289: q+1
       291: q+1
       294: q+1
       296: q+1
       297: q+1
       300: q+1
       301: q+1
       304: q+1
       305: q+1
       308: q+1
       310: q+1
       311: q+1
       313: q+1
       315: q^3+q+1
       317: q^3+q+1
       320: q+1
       322: q+1
       323: q+1
       325: q^3+q+1
       327: q^3+q+1
       329: q+1
       331: q^3+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q^3+q+1
       362: q+1
       364: q^3+q+1
       366: q^3+q+1
       367: q+1
       368: q^3+q+1
       369: q+1
       370: q+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       380: q+1
       384: q+1
       388: q+1
       391: q+1
       396: q+1
       399: q+1
       404: q+1
       406: q+1
       409: q+1
       411: q^3+q+1
       413: q+1
       415: q+1
       417: q+1
       420: q+1
       422: q+1
       423: q+1
       425: q+1
       427: q+1
       430: q+1
       432: q+1
       433: q+1
       435: q+1
       438: q+1
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       448: q+1
       450: q+1
       451: q+1
       454: q+1
       455: q+1
       458: q+1
       459: q+1
       462: q+1
       463: q+1
       465: q+1
       467: q^3+q+1
       469: q^3+q+1
       472: q+1
       474: q+1
       475: q+1
       477: q+1
       479: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: q^3+q+1
       504: q+1
       506: q^3+q+1
       508: q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       524: q+1
       528: q+1
       532: q+1
       536: q+1
       539: q+1
       543: q+1
       547: q+1
       552: q+1
       555: q+1
       559: q+1
       563: q+1
       568: q+1
       570: q+1
       575: q+1
       577: q+1
       583: q+1
       585: q+1
       587: q+1
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: 1
       599: q+1
       601: 1
       604: q+1
       605: q+1
       608: q+1
       609: q+1
       611: q+1
       613: q+1
       616: 1
       617: 1
       620: q+1
       622: q+1
       623: q+1
       625: q+1
       627: q+1
       629: q+1
       632: 1
       633: 1
       635: q+1
       637: q^3+q+1
       639: q+1
       642: q+1
       644: q+1
       645: q+1
       648: q+1
       650: q+1
       651: q+1
       653: q+1
       655: 1
       657: 1
       658: 1
       660: 1
       662: q^3+1
       664: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       674: 1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q^3+1
       697: q+1
       708: q+1
       712: q+1
       716: q+1
       720: q+1
       723: q+1
       727: q+1
       731: q+1
       735: 1
       739: q+1
       743: q+1
       747: q+1
       751: 1
       756: q+1
       758: q+1
       762: q+1
       768: 1
       769: 1
       775: 1
       777: q+1
       779: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       797: q+1
       799: q+1
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: 1
       811: q+1
       813: 1
       816: 1
       818: 1
       819: 1
       821: q+1
       823: q+1
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: 1
       835: q+1
       837: 1
       840: 1
       841: q+1
       843: 1
       846: q+1
       848: q+1
       849: q+1
       851: q+1
       853: q+1
       855: q+1
       857: 1
       859: 1
       861: 1
       863: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       889: 1
       899: q+1
       902: 1
       906: 1
       911: 1
       914: q+1
       918: 1
       922: q+1
       927: q+1
       930: q+1
       934: 1
       938: q+1
       942: 1
       946: q+1
       950: q+1
       955: q+1
       958: 1
       961: q+1
       967: 1
       968: 1
       975: q+1
       979: q+1
       982: 1
       991: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 2
      1012: 1
      1014: 1
      1017: 1
      1018: q+1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: q+1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1045: 1
      1046: 1
      1048: q+1
      1050: q+1
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: 1
      1062: q+1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 2
      1133: 1
      1135: 1
      1138: 1
      1140: 1
      1146: 1
      1150: q+1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1170: q+1
      1174: 1
      1178: 1
      1183: 1
      1185: q+1
      1188: 1
      1197: 1
      1199: q+1
      1204: q+1
      1208: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 2
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1264: q+1
      1266: 1
      1269: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 2
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1299: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 2
      1329: 1
      1331: 1
      1334: 1
      1336: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 2
      1367: 1
      1369: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 2
      1399: 1
      1401: 1
      1415: q+1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1432: 1
      1436: 1
      1446: 1
      1448: 1
      1451: 1
      1455: 1
      1456: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1479: 1
      1480: 2
      1482: 1
      1487: 1
      1494: 1
      1498: 1
      1506: 1
      1510: 1
      1518: 1
      1522: 1
      1538: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 2
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 2
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 2
      1626: 1
      1630: 1
      1631: 1
      1633: 1
      1637: 1
      1659: 1
      1661: 1
      1664: 1
      1666: 1
      1671: 1
      1692: 1
      1696: 1
      1704: 1
      1708: 1
      1718: 1
      1722: 1
      1730: 1
      1742: 1
      1754: 1
      1770: 1
      1778: 1
      1787: 1
      1791: 1
      1796: 2
      1800: 1
      1808: 1
      1823: 1
      1877: 1
      1881: 1
      1895: 1
      1911: 1
      1945: 1
      1949: 1
      2057: 1

2058:    0: 2q^3+q+1
         1: 2q^3+q+1
         2: q^4+q^3+q+1
         3: 2q^3+q+1
         4: q^4+q^3+q+1
         5: 2q^3+q+1
         6: q^4+q^3+q+1
         7: q^5+2q^4+q^3+q+1
         8: q^4+q^3+q+1
         9: q^5+2q^4+q^3+q+1
        10: 2q^3+q+1
        11: 2q^3+q+1
        12: q^4+q^3+q+1
        13: q^3+q+1
        14: q^4+q^3+q+1
        15: q^3+q+1
        16: 2q^3+q+1
        17: 2q^3+q+1
        18: q^5+2q^4+q^3+q+1
        19: q^3+q+1
        20: q^3+q+1
        21: q^4+q^3+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: 2q^3+q+1
        29: q^3+q+1
        30: q^3+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q+1
        44: q^4+q^3+q+1
        45: q^3+q+1
        46: q^3+q+1
        47: q^3+q+1
        48: q^4+q^3+q+1
        49: q^3+q+1
        50: q^3+q+1
        51: q^4+q^3+q+1
        52: q^3+q+1
        53: q^3+q+1
        54: q^4+q^3+q+1
        55: q^3+q+1
        56: q^3+q+1
        57: q^4+q^3+q+1
        58: q^3
        59: q^3+q+1
        60: q^3+q+1
        61: q^3
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q+1
        69: q^3+q+1
        70: q^3+q+1
        71: q^3+q+1
        72: q+1
        73: q+1
        75: q^3+q+1
        77: q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: q^3+q+1
        83: q^3+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: q^3+q+1
        87: q^3+q+1
        88: q^3+q+1
        89: q^3+q+1
        90: q^4+q^3+q+1
        91: q^3+q+1
        92: q+1
        93: q^3+q+1
        94: q^3+q+1
        95: q^3+q+1
        96: q^4+q^3+q+1
        97: q^3+q+1
        98: q^3+q+1
        99: q^4+q^3+q+1
       100: q^3+q+1
       101: q^3+q+1
       102: q^4+q^3+q+1
       104: q^3+q+1
       105: q^3
       107: q+1
       110: q+1
       112: q+1
       114: q^3+q+1
       116: q^3+q+1
       118: q+1
       119: q+1
       122: q^3+q+1
       124: q^3+q+1
       125: q+1
       126: q^3+q+1
       128: q^3+q+1
       130: q^3+q+1
       132: q^4+q^3+q+1
       133: q+1
       134: q^3+q+1
       135: q+1
       136: q+1
       137: q^3+q+1
       138: q^3+q+1
       139: q^3+q+1
       140: q+1
       141: q^3+q+1
       142: q+1
       143: q^3+q+1
       144: q^3+q+1
       145: q^3+q+1
       146: q^3+q+1
       147: q+1
       148: q+1
       149: q^3+q+1
       150: q^3+q+1
       152: q^3+q+1
       154: q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: q^3+q+1
       161: q+1
       162: q^3+q+1
       163: q^3+q+1
       164: q+1
       165: q^3+q+1
       166: q^3+q+1
       167: q^3+q+1
       168: q^4+q^3+q+1
       170: q+1
       174: q+1
       178: q^3+q+1
       180: q^3+q+1
       182: q+1
       183: q+1
       186: q+1
       188: q+1
       190: q^3+q+1
       192: q+1
       193: q+1
       196: q+1
       198: q+1
       199: q+1
       201: q+1
       204: q+1
       206: q+1
       208: q^3+q+1
       210: q^3+q+1
       212: q^3+q+1
       214: q^3+q+1
       216: q+1
       218: q^3+q+1
       219: q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q^3+q+1
       227: q+1
       228: q^3+q+1
       229: q+1
       230: q+1
       231: q^3+q+1
       232: q+1
       233: q^3+q+1
       234: q+1
       235: q+1
       236: q^3+q+1
       238: q^3+q+1
       240: q^3+q+1
       242: q^4+q^3+q+1
       243: q^3+q+1
       244: q+1
       245: q+1
       246: q^3+q+1
       247: q+1
       248: q+1
       249: q^4+q^3+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: q^3+q+1
       257: q+1
       258: q^3+q+1
       260: q+1
       264: q+1
       268: q+1
       274: q+1
       276: q+1
       280: q+1
       282: q^3+q+1
       283: q+1
       286: q+1
       288: q^3+q+1
       290: q+1
       292: q+1
       293: q+1
       296: q+1
       298: q+1
       299: q+1
       302: q+1
       304: q+1
       306: q+1
       307: q+1
       310: q+1
       312: q+1
       314: q+1
       316: q^3+q+1
       318: q^3+q+1
       319: q+1
       322: q+1
       324: q+1
       326: q^3+q+1
       328: q^3+q+1
       330: q+1
       332: q^3+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       361: q^3+q+1
       363: q+1
       365: q^3+q+1
       366: q^3+q+1
       367: q+1
       368: q^3+q+1
       369: q+1
       370: q+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       378: q+1
       382: q+1
       386: q+1
       390: q+1
       394: q+1
       400: q+1
       403: q+1
       407: q+1
       410: q+1
       412: q^3+q+1
       414: q+1
       416: q+1
       418: q+1
       419: q+1
       422: q+1
       424: q+1
       426: q+1
       428: q+1
       429: q+1
       432: q+1
       434: q+1
       436: q+1
       437: q+1
       440: q+1
       442: q+1
       443: q+1
       446: q+1
       447: q+1
       450: q+1
       452: q+1
       453: q+1
       456: q+1
       458: q+1
       460: q+1
       462: q+1
       464: q+1
       466: q+1
       468: q^3+q+1
       470: q^3+q+1
       471: q+1
       474: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       503: q^3+q+1
       505: q+1
       507: q^3+q+1
       508: q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       522: q+1
       526: q+1
       530: q+1
       534: q+1
       538: q+1
       542: q+1
       546: q+1
       551: q+1
       556: q+1
       560: q+1
       564: q+1
       566: q+1
       571: q+1
       574: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       598: 1
       600: q+1
       602: 1
       603: q+1
       606: q+1
       608: q+1
       610: q+1
       612: q+1
       614: q+1
       615: 1
       618: 1
       619: q+1
       622: q+1
       624: q+1
       626: q+1
       628: q+1
       630: q+1
       632: 1
       634: 1
       636: q+1
       638: q^3+q+1
       640: q+1
       641: q+1
       644: q+1
       646: q+1
       647: q+1
       650: q+1
       652: q+1
       654: q+1
       656: 1
       657: 1
       659: 1
       661: 1
       663: q^3+1
       664: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       674: 1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q^3+1
       699: q+1
       706: q+1
       710: q+1
       715: q+1
       718: q+1
       722: q+1
       726: q+1
       730: q+1
       734: 1
       740: q+1
       744: q+1
       748: q+1
       752: 1
       754: q+1
       759: q+1
       763: q+1
       766: 1
       773: 1
       776: 1
       778: q+1
       780: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: 1
       798: q+1
       800: q+1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       810: 1
       812: q+1
       814: 1
       815: 1
       818: 1
       820: 1
       822: q+1
       824: q+1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       834: 1
       836: q+1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: q+1
       848: q+1
       850: q+1
       852: q+1
       854: q+1
       856: q+1
       858: 1
       860: 1
       862: 1
       864: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       890: 1
       897: q+1
       903: 1
       905: 1
       909: 1
       913: q+1
       917: 1
       921: q+1
       926: q+1
       929: q+1
       933: 1
       939: q+1
       943: 1
       947: q+1
       951: q+1
       953: q+1
       959: 1
       962: q+1
       965: 1
       972: 1
       976: q+1
       980: q+1
       986: 1
       989: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 1
      1016: 1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1029: 1
      1031: 1
      1033: 1
      1035: q+1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1045: 1
      1047: 1
      1049: q+1
      1051: q+1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 2
      1131: 1
      1136: 1
      1142: 1
      1143: 1
      1145: 1
      1149: q+1
      1155: 1
      1157: 1
      1162: 1
      1167: 1
      1171: q+1
      1175: 1
      1177: 1
      1181: 1
      1186: q+1
      1192: 1
      1195: 1
      1200: q+1
      1205: q+1
      1207: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1261: 1
      1265: q+1
      1267: 1
      1268: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1300: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 2
      1327: 1
      1332: 1
      1338: 1
      1339: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 2
      1366: 1
      1371: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 2
      1397: 1
      1402: 1
      1416: q+1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: 1
      1451: 1
      1454: 1
      1457: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1479: 1
      1481: 2
      1483: 1
      1487: 1
      1495: 1
      1499: 1
      1508: 1
      1512: 1
      1519: 1
      1523: 1
      1539: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 2
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 2
      1596: 1
      1601: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 2
      1624: 1
      1628: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1664: 1
      1665: 1
      1672: 1
      1694: 1
      1698: 1
      1705: 1
      1709: 1
      1716: 1
      1719: 1
      1731: 1
      1744: 1
      1756: 1
      1771: 1
      1779: 1
      1788: 1
      1790: 1
      1794: 2
      1798: 1
      1809: 1
      1824: 1
      1875: 1
      1878: 1
      1897: 1
      1912: 1
      1946: 1
      1950: 1
      2058: 1

2059:    0: 2q^3+q+1
         1: 2q^3+q+1
         2: q^4+q^3+q+1
         3: 2q^3+q+1
         4: q^4+q^3+q+1
         5: 2q^3+q+1
         6: q^4+q^3+q+1
         7: q^5+2q^4+q^3+q+1
         8: q^4+q^3+q+1
         9: q^5+2q^4+q^3+q+1
        10: 2q^3+q+1
        11: 2q^3+q+1
        12: q^4+q^3+q+1
        13: q^3+q+1
        14: q^4+q^3+q+1
        15: q^3+q+1
        16: 2q^3+q+1
        17: 2q^3+q+1
        18: q^5+2q^4+q^3+q+1
        19: q^3+q+1
        20: q^3+q+1
        21: q^4+q^3+q+1
        22: 2q^3+q+1
        23: 2q^3+q+1
        24: q^4+q^3+q+1
        25: 2q^3+q+1
        26: 2q^3+q+1
        27: q^4+q^3+q+1
        28: 2q^3+q+1
        29: q^3+q+1
        30: q^3+q+1
        31: 2q^3+q+1
        32: q^3+q+1
        33: 2q^3+q+1
        34: 2q^3+q+1
        35: q^3+q+1
        36: 2q^3+q+1
        38: 2q^3+q+1
        40: 2q^3+q+1
        42: q^4+q^3+q+1
        43: q^3+q+1
        44: q^4+q^3+q+1
        45: q^3+q+1
        46: q^3+q+1
        47: q^3+q+1
        48: q^4+q^3+q+1
        49: q^3+q+1
        50: q^3+q+1
        51: q^4+q^3+q+1
        52: q^3+q+1
        53: q^3+q+1
        54: q^4+q^3+q+1
        55: q^3+q+1
        56: q^3+q+1
        57: q^4+q^3+q+1
        58: q^3+q+1
        59: q^3
        60: q^3
        61: q^3+q+1
        63: 2q^3+q+1
        65: q^3+q+1
        67: 2q^3+q+1
        68: q+1
        69: q^3+q+1
        70: q^3+q+1
        71: q^3+q+1
        72: q+1
        73: q+1
        75: q^3+q+1
        77: q^3+q+1
        79: q^4+q^3+q+1
        80: q^3+q+1
        81: q^3+q+1
        82: q^3+q+1
        83: q^3+q+1
        84: q^3+q+1
        85: q^3+q+1
        86: q^3+q+1
        87: q^3+q+1
        88: q^3+q+1
        89: q^3+q+1
        90: q^4+q^3+q+1
        91: q^3+q+1
        92: q+1
        93: q^3+q+1
        94: q^3+q+1
        95: q^3+q+1
        96: q^4+q^3+q+1
        97: q^3+q+1
        98: q^3+q+1
        99: q^4+q^3+q+1
       100: q^3+q+1
       101: q^3+q+1
       102: q^4+q^3+q+1
       104: q^3
       105: q^3+q+1
       108: q+1
       109: q+1
       112: q+1
       114: q^3+q+1
       116: q^3+q+1
       117: q+1
       120: q+1
       122: q^3+q+1
       124: q^3+q+1
       125: q+1
       126: q^3+q+1
       128: q^3+q+1
       130: q^3+q+1
       132: q^4+q^3+q+1
       133: q+1
       134: q^3+q+1
       135: q+1
       136: q+1
       137: q^3+q+1
       138: q^3+q+1
       139: q^3+q+1
       140: q+1
       141: q^3+q+1
       142: q+1
       143: q^3+q+1
       144: q^3+q+1
       145: q^3+q+1
       146: q^3+q+1
       147: q+1
       148: q+1
       149: q^3+q+1
       150: q^3+q+1
       152: q^3+q+1
       154: q^3+q+1
       156: q^4+q^3+q+1
       157: q^3+q+1
       158: q+1
       159: q^3+q+1
       160: q^3+q+1
       161: q+1
       162: q^3+q+1
       163: q^3+q+1
       164: q+1
       165: q^3+q+1
       166: q^3+q+1
       167: q^3+q+1
       168: q^4+q^3+q+1
       171: q+1
       175: q+1
       178: q^3+q+1
       180: q^3+q+1
       182: q+1
       184: q+1
       185: q+1
       188: q+1
       190: q^3+q+1
       191: q+1
       194: q+1
       195: q+1
       198: q+1
       200: q+1
       202: q+1
       203: q+1
       206: q+1
       208: q^3+q+1
       210: q^3+q+1
       212: q^3+q+1
       214: q^3+q+1
       216: q+1
       218: q^3+q+1
       219: q+1
       220: q+1
       221: q^3+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q^3+q+1
       227: q+1
       228: q^3+q+1
       229: q+1
       230: q+1
       231: q^3+q+1
       232: q+1
       233: q^3+q+1
       234: q+1
       235: q+1
       236: q^3+q+1
       238: q^3+q+1
       240: q^3+q+1
       242: q^4+q^3+q+1
       243: q^3+q+1
       244: q+1
       245: q+1
       246: q^3+q+1
       247: q+1
       248: q+1
       249: q^4+q^3+q+1
       250: q^3+q+1
       251: q+1
       252: q^3+q+1
       253: q^3+q+1
       254: q+1
       255: q^3+q+1
       256: q^3+q+1
       257: q+1
       258: q^3+q+1
       261: q+1
       265: q+1
       270: q+1
       272: q+1
       277: q+1
       280: q+1
       282: q^3+q+1
       284: q+1
       285: q+1
       288: q^3+q+1
       290: q+1
       292: q+1
       294: q+1
       295: q+1
       298: q+1
       300: q+1
       302: q+1
       303: q+1
       306: q+1
       308: q+1
       309: q+1
       312: q+1
       314: q+1
       316: q^3+q+1
       318: q^3+q+1
       320: q+1
       321: q+1
       324: q+1
       326: q^3+q+1
       328: q^3+q+1
       330: q+1
       332: q^3+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q^4+q^3+q+1
       344: q+1
       345: q+1
       346: q^3+q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^3+q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       361: q^3+q+1
       363: q+1
       365: q^3+q+1
       366: q^3+q+1
       367: q+1
       368: q^3+q+1
       369: q+1
       370: q+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q+1
       375: q+1
       376: q^3+q+1
       379: q+1
       383: q+1
       387: q+1
       392: q+1
       395: q+1
       398: q+1
       402: q+1
       408: q+1
       410: q+1
       412: q^3+q+1
       414: q+1
       416: q+1
       418: q+1
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       428: q+1
       430: q+1
       431: q+1
       434: q+1
       436: q+1
       438: q+1
       439: q+1
       442: q+1
       444: q+1
       446: q+1
       448: q+1
       449: q+1
       452: q+1
       454: q+1
       456: q+1
       457: q+1
       460: q+1
       461: q+1
       464: q+1
       466: q+1
       468: q^3+q+1
       470: q^3+q+1
       472: q+1
       473: q+1
       476: q+1
       478: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       503: q^3+q+1
       505: q+1
       507: q^3+q+1
       508: q+1
       509: q+1
       510: q^3+q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       523: q+1
       527: q+1
       531: q+1
       535: q+1
       540: q+1
       544: q+1
       548: q+1
       550: q+1
       554: q+1
       558: q+1
       562: q+1
       567: q+1
       572: q+1
       576: q+1
       581: q+1
       584: q+1
       586: q+1
       588: q+1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       598: 1
       600: q+1
       602: 1
       604: q+1
       606: q+1
       607: q+1
       610: q+1
       612: q+1
       614: q+1
       616: 1
       618: 1
       620: q+1
       621: q+1
       624: q+1
       626: q+1
       628: q+1
       630: q+1
       631: 1
       634: 1
       636: q+1
       638: q^3+q+1
       640: q+1
       642: q+1
       643: q+1
       646: q+1
       648: q+1
       649: q+1
       652: q+1
       654: q+1
       656: 1
       657: 1
       659: 1
       661: 1
       663: q^3+1
       664: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       674: 1
       675: q+1
       676: q+1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q^3+1
       700: q+1
       707: q+1
       711: q+1
       714: q+1
       719: q+1
       724: q+1
       728: q+1
       732: q+1
       736: 1
       738: q+1
       742: q+1
       746: q+1
       750: 1
       755: q+1
       760: q+1
       764: q+1
       767: 1
       773: 1
       776: 1
       778: q+1
       780: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: 1
       798: q+1
       800: q+1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       810: 1
       812: q+1
       814: 1
       816: 1
       817: 1
       820: 1
       822: q+1
       824: q+1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       834: 1
       836: q+1
       838: 1
       839: 1
       842: q+1
       844: 1
       846: q+1
       847: q+1
       850: q+1
       852: q+1
       854: q+1
       856: q+1
       858: 1
       860: 1
       862: 1
       864: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       891: 1
       898: q+1
       901: 1
       907: 1
       910: 1
       915: q+1
       919: 1
       923: q+1
       925: q+1
       931: q+1
       935: 1
       937: q+1
       941: 1
       945: q+1
       949: q+1
       954: q+1
       957: 1
       963: q+1
       966: 1
       972: 1
       977: q+1
       981: q+1
       986: 1
       990: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 2
      1013: 1
      1015: 1
      1017: 1
      1019: q+1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1044: 1
      1047: 1
      1049: q+1
      1051: q+1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1061: 1
      1063: q+1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 2
      1132: 1
      1137: 1
      1142: 1
      1143: 1
      1147: 1
      1151: q+1
      1153: 1
      1159: 1
      1161: 1
      1165: 1
      1169: q+1
      1173: 1
      1179: 1
      1182: 1
      1187: q+1
      1192: 1
      1196: 1
      1201: q+1
      1203: q+1
      1209: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 2
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1260: 1
      1265: q+1
      1267: 1
      1269: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 2
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1301: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 2
      1328: 1
      1333: 1
      1338: 1
      1339: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 2
      1365: 1
      1370: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 2
      1398: 1
      1403: 1
      1417: q+1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1435: 1
      1437: 1
      1447: 1
      1449: 1
      1450: 1
      1455: 1
      1457: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1478: 1
      1481: 2
      1483: 1
      1487: 1
      1496: 1
      1500: 1
      1507: 1
      1511: 1
      1520: 1
      1524: 1
      1540: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 2
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 2
      1597: 1
      1602: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 2
      1625: 1
      1629: 1
      1635: 1
      1636: 1
      1638: 1
      1660: 1
      1662: 1
      1663: 1
      1666: 1
      1672: 1
      1693: 1
      1697: 1
      1706: 1
      1710: 1
      1717: 1
      1721: 1
      1732: 1
      1743: 1
      1755: 1
      1772: 1
      1780: 1
      1786: 1
      1792: 1
      1795: 2
      1799: 1
      1810: 1
      1824: 1
      1876: 1
      1880: 1
      1896: 1
      1913: 1
      1947: 1
      1951: 1
      2059: 1

2060:    0: 5q^4+5q^3+2q^2+1
         1: 5q^4+5q^3+2q^2+1
         2: 5q^4+5q^3+2q^2+1
         3: 5q^4+5q^3+2q^2+1
         4: 3q^5+4q^4+3q^3+2q^2+1
         5: 5q^4+5q^3+2q^2+1
         6: q^6+4q^5+5q^4+3q^3+2q^2+1
         7: 3q^5+4q^4+3q^3+2q^2+1
         8: 5q^4+5q^3+2q^2+1
         9: 3q^5+4q^4+3q^3+2q^2+1
        10: 5q^3+q^2+1
        11: 5q^3+q^2+1
        12: q^5+2q^4+3q^3+q^2+1
        13: 5q^4+5q^3+2q^2+1
        14: 3q^5+4q^4+3q^3+2q^2+1
        15: 5q^4+5q^3+2q^2+1
        16: 5q^4+5q^3+2q^2+1
        17: 5q^4+5q^3+2q^2+1
        18: 3q^5+4q^4+3q^3+2q^2+1
        19: 2q^4+3q^3+2q^2+1
        20: 3q^4+3q^3+2q^2+1
        21: 2q^4+3q^3+2q^2+1
        22: 5q^4+5q^3+2q^2+1
        23: 5q^4+5q^3+2q^2+1
        24: 5q^4+5q^3+2q^2+1
        25: 5q^4+5q^3+2q^2+1
        26: 5q^4+5q^3+2q^2+1
        27: 5q^4+5q^3+2q^2+1
        28: 5q^3+q^2+1
        29: 3q^3+q^2+1
        30: 2q^4+3q^3+2q^2+1
        31: 5q^3+q^2+1
        32: 5q^4+5q^3+2q^2+1
        33: 5q^4+5q^3+2q^2+1
        34: 5q^3+q^2+1
        35: 5q^4+5q^3+2q^2+1
        36: 5q^4+5q^3+2q^2+1
        37: 2q^4+3q^3+q^2+1
        38: 3q^4+2q^3+q^2
        39: 2q^4+3q^3+q^2+1
        40: 3q^4+2q^3+q^2
        41: 2q^4+3q^3+q^2+1
        42: 3q^4+2q^3+q^2
        43: 5q^3+q^2+1
        44: q^5+2q^4+3q^3+q^2+1
        45: 5q^3+q^2+1
        46: 5q^4+5q^3+2q^2+1
        47: 5q^4+5q^3+2q^2+1
        48: 3q^5+4q^4+3q^3+2q^2+1
        49: 2q^4+3q^3+2q^2+1
        50: 3q^4+3q^3+2q^2+1
        51: 2q^4+3q^3+2q^2+1
        52: 2q^4+3q^3+2q^2+1
        53: 3q^4+3q^3+2q^2+1
        54: 2q^4+3q^3+2q^2+1
        55: 2q^4+3q^3+2q^2+1
        56: 3q^4+3q^3+2q^2+1
        57: 2q^4+3q^3+2q^2+1
        58: 3q^3+q^2+1
        59: 2q^3
        60: 3q^3+q^2+1
        61: 2q^3
        62: 3q^3+q^2+1
        63: 2q^3
        64: 2q^4+3q^3+q^2+1
        65: 3q^4+2q^3+q^2
        66: 2q^4+3q^3+q^2+1
        67: 3q^4+2q^3+q^2
        68: 5q^3+q^2+1
        69: 2q^4+3q^3+2q^2+1
        70: 3q^3+q^2+1
        71: 3q^3+q^2+1
        72: q^4+q^3+2q^2+1
        73: q^4+q^3+2q^2+1
        74: q^3+q^2+1
        75: q^3+q^2
        76: q^3+q^2+1
        77: q^4+q^3+q^2
        78: q^3+q^2+1
        79: q^3+q^2
        80: 5q^3+q^2+1
        81: 5q^4+5q^3+2q^2+1
        82: 3q^3+q^2+1
        83: 2q^4+3q^3+2q^2+1
        84: 5q^3+q^2+1
        85: 5q^4+5q^3+2q^2+1
        86: 3q^3+q^2+1
        87: 2q^4+3q^3+2q^2+1
        88: 5q^3+q^2+1
        89: 5q^3+q^2+1
        90: q^5+2q^4+3q^3+q^2+1
        91: 2q^4+3q^3+2q^2+1
        92: 3q^4+3q^3+2q^2+1
        93: 2q^4+3q^3+2q^2+1
        94: 2q^4+3q^3+2q^2+1
        95: 3q^4+3q^3+2q^2+1
        96: 2q^4+3q^3+2q^2+1
        97: 2q^4+3q^3+2q^2+1
        98: 3q^4+3q^3+2q^2+1
        99: 2q^4+3q^3+2q^2+1
       100: 2q^4+3q^3+2q^2+1
       101: 3q^4+3q^3+2q^2+1
       102: 2q^4+3q^3+2q^2+1
       103: 2q^3+q^2+1
       104: q^3
       105: q^3
       106: q^3
       107: q^3+q^2+1
       109: q^3+q^2+1
       111: q^2+1
       112: q^2
       113: q^3+q^2+1
       114: q^3
       115: q^3+q^2+1
       116: q^3+q^2
       117: 3q^3+q^2+1
       118: 2q^3
       119: 3q^3+q^2+1
       120: 2q^3
       121: 3q^3+q^2+1
       122: 2q^3
       123: 2q^4+3q^3+q^2+1
       124: 3q^4+2q^3+q^2
       125: 5q^3+q^2+1
       126: 3q^3+q^2+1
       127: q^3+q^2+1
       128: q^3+q^2
       129: q^3+q^2+1
       130: q^4+q^3+q^2
       131: q^3+q^2+1
       132: q^3+q^2
       133: 3q^3+q^2+1
       134: 2q^4+3q^3+2q^2+1
       135: q^4+q^3+2q^2+1
       136: q^4+q^3+2q^2+1
       137: 5q^3+q^2+1
       138: 2q^4+3q^3+2q^2+1
       139: 3q^3+q^2+1
       140: q^4+q^3+2q^2+1
       141: 3q^3+q^2+1
       142: q^4+q^3+2q^2+1
       143: 5q^3+q^2+1
       144: 2q^4+3q^3+2q^2+1
       145: 3q^3+q^2+1
       146: 3q^3+q^2+1
       147: q^4+q^3+2q^2+1
       148: q^4+q^3+2q^2+1
       149: 3q^3+q^2+1
       150: 2q^4+3q^3+2q^2+1
       151: q^3+q^2+1
       152: q^3+q^2
       153: q^3+q^2+1
       154: q^4+q^3+q^2
       155: q^3+q^2+1
       156: q^3+q^2
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: 2q^4+3q^3+2q^2+1
       161: 3q^4+3q^3+2q^2+1
       162: 2q^4+3q^3+2q^2+1
       163: 2q^4+3q^3+2q^2+1
       164: 3q^4+3q^3+2q^2+1
       165: 2q^4+3q^3+2q^2+1
       166: 2q^4+3q^3+2q^2+1
       167: 3q^4+3q^3+2q^2+1
       168: 2q^4+3q^3+2q^2+1
       169: q^2+1
       173: 2q^3+q^2+1
       174: q^3
       175: q^3
       176: q^3
       177: q^3+q^2+1
       178: q^3+q^2
       179: q^3+q^2+1
       180: q^3
       181: q^2+1
       182: q^2
       183: q^3+q^2+1
       185: q^3+q^2+1
       187: q^2+1
       188: q^2
       189: q^3+q^2+1
       190: q^3
       191: 3q^3+q^2+1
       192: 2q^3
       193: q^3+q^2+1
       195: q^3+q^2+1
       197: q^2+1
       198: q^2
       199: 3q^3+q^2+1
       200: 2q^3
       201: q^3+q^2+1
       203: q^3+q^2+1
       205: q^2+1
       206: q^2
       207: 3q^3+q^2+1
       208: 2q^3
       209: q^3+q^2+1
       210: q^3
       211: q^3+q^2+1
       212: q^3+q^2
       213: q^3+q^2+1
       214: q^3+q^2
       215: q^3+q^2+1
       216: q^4+q^3+q^2
       217: q^3+q^2+1
       218: q^3+q^2
       219: 3q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^4+q^3+2q^2+1
       224: q^2+1
       225: q^4+q^3+2q^2+1
       226: 3q^3+q^2+1
       227: 3q^3+q^2+1
       228: 2q^4+3q^3+2q^2+1
       229: q^4+q^3+2q^2+1
       230: q^4+q^3+2q^2+1
       231: 3q^3+q^2+1
       232: 3q^3+q^2+1
       233: 2q^4+3q^3+2q^2+1
       234: q^4+q^3+2q^2+1
       235: q^4+q^3+2q^2+1
       236: 2q^4+3q^3+2q^2+1
       237: q^3+q^2+1
       238: q^3+q^2
       239: q^3+q^2+1
       240: q^4+q^3+q^2
       241: q^3+q^2+1
       242: q^3+q^2
       243: 3q^3+q^2+1
       244: q^4+q^3+2q^2+1
       245: q^4+q^3+2q^2+1
       246: 3q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: 2q^4+3q^3+2q^2+1
       257: 3q^4+3q^3+2q^2+1
       258: 2q^4+3q^3+2q^2+1
       259: q^2+1
       263: q^2+1
       267: q^2+1
       271: q^2+1
       275: 2q^3+q^2+1
       276: q^3
       277: q^3
       278: q^3
       279: q^3+q^2+1
       280: q^3
       281: q^3+q^2+1
       282: q^3+q^2
       283: q^3+q^2+1
       285: q^3+q^2+1
       287: q^3+q^2+1
       288: q^3
       289: q^2+1
       290: q^2
       291: q^2+1
       292: q^2
       293: q^2+1
       295: q^2+1
       297: q^2+1
       299: q^3+q^2+1
       301: q^2+1
       302: q^2
       303: q^3+q^2+1
       305: q^2+1
       306: q^2
       307: q^3+q^2+1
       309: q^3+q^2+1
       311: q^2+1
       312: q^2
       313: q^2+1
       314: q^2
       315: q^3+q^2+1
       316: q^3+q^2
       317: q^3+q^2+1
       318: q^3
       319: q^3+q^2+1
       321: q^3+q^2+1
       323: q^2+1
       324: q^2
       325: q^3+q^2+1
       326: q^3
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: q^2+1
       337: q^2+1
       338: 1
       339: 2q^2
       340: 1
       341: 2q^2
       342: q^3+1
       343: q^3+q^2
       344: 3q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^4+q^3+2q^2+1
       349: q^2+1
       350: q^4+q^3+2q^2+1
       351: 2q^2+1
       352: 3q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^4+q^3+2q^2+1
       357: q^2+1
       358: q^4+q^3+2q^2+1
       359: 2q^2+1
       360: q^3+q^2+1
       361: q^3+q^2
       362: q^3+q^2+1
       363: q^4+q^3+q^2
       364: q^3+q^2+1
       365: q^3+q^2
       366: 3q^3+q^2+1
       367: 3q^3+q^2+1
       368: 2q^4+3q^3+2q^2+1
       369: q^4+q^3+2q^2+1
       370: q^4+q^3+2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       377: q^2+1
       381: q^2+1
       385: q^2+1
       389: q^2+1
       393: q^2+1
       397: q^2+1
       401: q^2+1
       405: q^2+1
       413: q^3+q^2+1
       414: q^3
       417: q^2+1
       418: q^2
       419: q^2+1
       421: q^2+1
       423: q^2+1
       425: 1
       426: q^2
       427: 1
       428: q^2
       429: q^3+q^2+1
       431: q^3+q^2+1
       433: q^2+1
       434: q^2
       435: q^2+1
       436: q^2
       437: q^2+1
       439: q^2+1
       441: q^2+1
       443: q^2+1
       445: 1
       446: 2q^2
       447: q^3+q^2+1
       449: q^3+q^2+1
       451: q^2+1
       452: q^2
       453: q^2+1
       455: q^2+1
       456: q^2
       457: q^2+1
       459: q^2+1
       461: q^2+1
       463: 1
       464: 2q^2
       465: q^3+q^2+1
       466: q^3
       467: q^3+q^2+1
       468: q^3+q^2
       469: q^3+q^2+1
       470: q^3
       471: q^3+q^2+1
       473: q^3+q^2+1
       475: q^2+1
       476: q^2
       477: q^2+1
       478: q^2
       479: q^2+1
       480: q^2
       481: q^2+1
       482: q^2+1
       483: 1
       484: q^2+1
       485: 1
       486: 2q^2
       487: 1
       488: 2q^2
       489: q^3+1
       490: q^3+q^2
       491: q^2+1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: 2q^2+1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 2q^2+1
       508: 3q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^4+q^3+2q^2+1
       513: q^2+1
       514: q^4+q^3+2q^2+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       521: q^2+1
       529: q^2+1
       533: q^2+1
       537: q^2+1
       541: q^2+1
       545: 1
       546: q^2
       549: q^2+1
       553: q^2+1
       557: q^2+1
       561: 1
       562: q^2
       565: q^2+1
       569: q^2+1
       573: q^2+1
       577: 1
       578: q^2
       581: q^2
       585: q^2+1
       589: q^2+1
       591: 1
       593: 1
       595: q^2+1
       597: 1
       598: q^2
       599: 1
       601: 1
       602: q^2
       603: q^2+1
       605: q^2+1
       606: q^2
       607: q^2+1
       609: q^2+1
       613: 1
       614: q^2
       615: q^2+1
       617: 1
       618: 2q^2
       619: q^2+1
       621: q^2+1
       623: q^2+1
       624: q^2
       625: q^2+1
       629: 1
       630: q^2
       631: q^2+1
       633: 1
       634: 2q^2
       639: q^3+q^2+1
       640: q^3
       641: q^3+q^2+1
       643: q^3+q^2+1
       645: q^2+1
       646: q^2
       647: q^2+1
       649: q^2+1
       651: q^2+1
       652: q^2
       653: q^2+1
       655: q^2+1
       656: q^2
       657: q^2+1
       658: 1
       659: 2q^2
       660: 1
       661: 2q^2
       662: q^3+1
       663: q^3+q^2
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: q^2+1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: q^2+1
       690: 1
       691: 1
       692: q^3+1
       693: 1
       694: q^2
       709: q^2+1
       713: 1
       717: 1
       721: q^2+1
       725: q^2+1
       733: 1
       734: q^2
       737: q^2+1
       741: q^2+1
       749: 1
       750: q^2
       753: q^2+1
       757: q^2+1
       761: q^2+1
       765: q^2+1
       769: 1
       770: q^2
       773: q^2
       775: 1
       776: q^2
       779: 1
       780: q^2
       781: 1
       785: 1
       787: 1
       791: 1
       793: q^2+1
       795: 1
       796: 2q^2
       797: q^2+1
       801: q^2+1
       803: 1
       805: 1
       807: q^2+1
       809: 1
       810: q^2
       811: 1
       815: 1
       817: q^2+1
       819: 1
       820: 2q^2
       821: q^2+1
       825: q^2+1
       827: 1
       829: 1
       831: q^2+1
       833: 1
       834: q^2
       835: 1
       839: 1
       843: q^2+1
       844: q^2
       845: q^2+1
       847: q^2+1
       849: q^2+1
       850: q^2
       851: q^2+1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: q^3+1
       884: 1
       885: q^2
       900: 1
       904: 1
       908: 1
       916: 1
       917: q^2
       920: q^2+1
       924: 1
       928: 1
       940: 1
       941: q^2
       944: q^2+1
       948: 1
       952: 1
       960: q^2+1
       964: q^2+1
       968: 1
       969: q^2
       972: q^2
       974: q^2+1
       988: 1
       994: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1016: 1
      1020: 1
      1021: q^2
      1022: 1
      1026: 1
      1028: 1
      1032: 1
      1036: 1
      1037: q^2
      1038: 1
      1040: 1
      1044: 1
      1046: 1
      1048: q^2+1
      1052: q^2+1
      1054: 1
      1056: 1
      1058: q^2+1
      1060: 1
      1061: q^2
      1062: 1
      1064: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1086: 1
      1087: q^2
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1194: 1
      1198: q^2+1
      1202: 1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1230: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1246: 1
      1248: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1262: 1
      1266: 1
      1268: 1
      1270: 1
      1274: 1
      1275: q^2
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1410: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1474: 1
      1476: 1
      1478: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1501: 1
      1513: 1
      1537: 1
      1549: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1639: 1
      1645: 1
      1647: 1
      1653: 1
      1655: 1
      1659: 1
      1663: 1
      1665: 1
      1669: 1
      1674: 1
      1711: 1
      1733: 1
      1741: 1
      1749: 1
      1769: 1
      1773: 1
      1797: 1
      1807: 1
      1825: 1
      1829: 1
      1831: 1
      1898: 1
      1914: 1
      1940: 1
      1944: 1
      2060: 1

2061:    0: 5q^4+5q^3+2q^2+1
         1: 5q^4+5q^3+2q^2+1
         2: 5q^4+5q^3+2q^2+1
         3: 5q^4+5q^3+2q^2+1
         4: 3q^5+4q^4+3q^3+2q^2+1
         5: 5q^4+5q^3+2q^2+1
         6: q^6+4q^5+5q^4+3q^3+2q^2+1
         7: 3q^5+4q^4+3q^3+2q^2+1
         8: 5q^4+5q^3+2q^2+1
         9: 3q^5+4q^4+3q^3+2q^2+1
        10: 5q^3+q^2+1
        11: 5q^3+q^2+1
        12: q^5+2q^4+3q^3+q^2+1
        13: 5q^4+5q^3+2q^2+1
        14: 3q^5+4q^4+3q^3+2q^2+1
        15: 5q^4+5q^3+2q^2+1
        16: 5q^4+5q^3+2q^2+1
        17: 5q^4+5q^3+2q^2+1
        18: 3q^5+4q^4+3q^3+2q^2+1
        19: 2q^4+3q^3+2q^2+1
        20: 3q^4+3q^3+2q^2+1
        21: 2q^4+3q^3+2q^2+1
        22: 5q^4+5q^3+2q^2+1
        23: 5q^4+5q^3+2q^2+1
        24: 5q^4+5q^3+2q^2+1
        25: 5q^4+5q^3+2q^2+1
        26: 5q^4+5q^3+2q^2+1
        27: 5q^4+5q^3+2q^2+1
        28: 5q^3+q^2+1
        29: 3q^3+q^2+1
        30: 2q^4+3q^3+2q^2+1
        31: 5q^3+q^2+1
        32: 5q^4+5q^3+2q^2+1
        33: 5q^4+5q^3+2q^2+1
        34: 5q^3+q^2+1
        35: 5q^4+5q^3+2q^2+1
        36: 5q^4+5q^3+2q^2+1
        37: 3q^4+2q^3+q^2
        38: 2q^4+3q^3+q^2+1
        39: 3q^4+2q^3+q^2
        40: 2q^4+3q^3+q^2+1
        41: 3q^4+2q^3+q^2
        42: 2q^4+3q^3+q^2+1
        43: 5q^3+q^2+1
        44: q^5+2q^4+3q^3+q^2+1
        45: 5q^3+q^2+1
        46: 5q^4+5q^3+2q^2+1
        47: 5q^4+5q^3+2q^2+1
        48: 3q^5+4q^4+3q^3+2q^2+1
        49: 2q^4+3q^3+2q^2+1
        50: 3q^4+3q^3+2q^2+1
        51: 2q^4+3q^3+2q^2+1
        52: 2q^4+3q^3+2q^2+1
        53: 3q^4+3q^3+2q^2+1
        54: 2q^4+3q^3+2q^2+1
        55: 2q^4+3q^3+2q^2+1
        56: 3q^4+3q^3+2q^2+1
        57: 2q^4+3q^3+2q^2+1
        58: 2q^3
        59: 3q^3+q^2+1
        60: 3q^3+q^2+1
        61: 2q^3
        62: 2q^3
        63: 3q^3+q^2+1
        64: 3q^4+2q^3+q^2
        65: 2q^4+3q^3+q^2+1
        66: 3q^4+2q^3+q^2
        67: 2q^4+3q^3+q^2+1
        68: 5q^3+q^2+1
        69: 2q^4+3q^3+2q^2+1
        70: 3q^3+q^2+1
        71: 3q^3+q^2+1
        72: q^4+q^3+2q^2+1
        73: q^4+q^3+2q^2+1
        74: q^3+q^2
        75: q^3+q^2+1
        76: q^4+q^3+q^2
        77: q^3+q^2+1
        78: q^3+q^2
        79: q^3+q^2+1
        80: 5q^3+q^2+1
        81: 5q^4+5q^3+2q^2+1
        82: 3q^3+q^2+1
        83: 2q^4+3q^3+2q^2+1
        84: 5q^3+q^2+1
        85: 5q^4+5q^3+2q^2+1
        86: 3q^3+q^2+1
        87: 2q^4+3q^3+2q^2+1
        88: 5q^3+q^2+1
        89: 5q^3+q^2+1
        90: q^5+2q^4+3q^3+q^2+1
        91: 2q^4+3q^3+2q^2+1
        92: 3q^4+3q^3+2q^2+1
        93: 2q^4+3q^3+2q^2+1
        94: 2q^4+3q^3+2q^2+1
        95: 3q^4+3q^3+2q^2+1
        96: 2q^4+3q^3+2q^2+1
        97: 2q^4+3q^3+2q^2+1
        98: 3q^4+3q^3+2q^2+1
        99: 2q^4+3q^3+2q^2+1
       100: 2q^4+3q^3+2q^2+1
       101: 3q^4+3q^3+2q^2+1
       102: 2q^4+3q^3+2q^2+1
       103: q^3
       104: 2q^3+q^2+1
       105: q^3
       106: q^3
       107: q^3+q^2+1
       110: q^3+q^2+1
       111: q^2
       112: q^2+1
       113: q^3
       114: q^3+q^2+1
       115: q^3+q^2
       116: q^3+q^2+1
       117: 2q^3
       118: 3q^3+q^2+1
       119: 3q^3+q^2+1
       120: 2q^3
       121: 2q^3
       122: 3q^3+q^2+1
       123: 3q^4+2q^3+q^2
       124: 2q^4+3q^3+q^2+1
       125: 5q^3+q^2+1
       126: 3q^3+q^2+1
       127: q^3+q^2
       128: q^3+q^2+1
       129: q^4+q^3+q^2
       130: q^3+q^2+1
       131: q^3+q^2
       132: q^3+q^2+1
       133: 3q^3+q^2+1
       134: 2q^4+3q^3+2q^2+1
       135: q^4+q^3+2q^2+1
       136: q^4+q^3+2q^2+1
       137: 5q^3+q^2+1
       138: 2q^4+3q^3+2q^2+1
       139: 3q^3+q^2+1
       140: q^4+q^3+2q^2+1
       141: 3q^3+q^2+1
       142: q^4+q^3+2q^2+1
       143: 5q^3+q^2+1
       144: 2q^4+3q^3+2q^2+1
       145: 3q^3+q^2+1
       146: 3q^3+q^2+1
       147: q^4+q^3+2q^2+1
       148: q^4+q^3+2q^2+1
       149: 3q^3+q^2+1
       150: 2q^4+3q^3+2q^2+1
       151: q^3+q^2
       152: q^3+q^2+1
       153: q^4+q^3+q^2
       154: q^3+q^2+1
       155: q^3+q^2
       156: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: 2q^4+3q^3+2q^2+1
       161: 3q^4+3q^3+2q^2+1
       162: 2q^4+3q^3+2q^2+1
       163: 2q^4+3q^3+2q^2+1
       164: 3q^4+3q^3+2q^2+1
       165: 2q^4+3q^3+2q^2+1
       166: 2q^4+3q^3+2q^2+1
       167: 3q^4+3q^3+2q^2+1
       168: 2q^4+3q^3+2q^2+1
       170: q^2+1
       173: q^3
       174: 2q^3+q^2+1
       175: q^3
       176: q^3
       177: q^3+q^2
       178: q^3+q^2+1
       179: q^3
       180: q^3+q^2+1
       181: q^2
       182: q^2+1
       183: q^3+q^2+1
       186: q^3+q^2+1
       187: q^2
       188: q^2+1
       189: q^3
       190: q^3+q^2+1
       191: 2q^3
       192: 3q^3+q^2+1
       193: q^3+q^2+1
       196: q^3+q^2+1
       197: q^2
       198: q^2+1
       199: 3q^3+q^2+1
       200: 2q^3
       201: q^3+q^2+1
       204: q^3+q^2+1
       205: q^2
       206: q^2+1
       207: 2q^3
       208: 3q^3+q^2+1
       209: q^3
       210: q^3+q^2+1
       211: q^3+q^2
       212: q^3+q^2+1
       213: q^3+q^2
       214: q^3+q^2+1
       215: q^4+q^3+q^2
       216: q^3+q^2+1
       217: q^3+q^2
       218: q^3+q^2+1
       219: 3q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^4+q^3+2q^2+1
       224: q^2+1
       225: q^4+q^3+2q^2+1
       226: 3q^3+q^2+1
       227: 3q^3+q^2+1
       228: 2q^4+3q^3+2q^2+1
       229: q^4+q^3+2q^2+1
       230: q^4+q^3+2q^2+1
       231: 3q^3+q^2+1
       232: 3q^3+q^2+1
       233: 2q^4+3q^3+2q^2+1
       234: q^4+q^3+2q^2+1
       235: q^4+q^3+2q^2+1
       236: 2q^4+3q^3+2q^2+1
       237: q^3+q^2
       238: q^3+q^2+1
       239: q^4+q^3+q^2
       240: q^3+q^2+1
       241: q^3+q^2
       242: q^3+q^2+1
       243: 3q^3+q^2+1
       244: q^4+q^3+2q^2+1
       245: q^4+q^3+2q^2+1
       246: 3q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: 2q^4+3q^3+2q^2+1
       257: 3q^4+3q^3+2q^2+1
       258: 2q^4+3q^3+2q^2+1
       260: q^2+1
       264: q^2+1
       268: q^2+1
       274: q^2+1
       275: q^3
       276: 2q^3+q^2+1
       277: q^3
       278: q^3
       279: q^3
       280: q^3+q^2+1
       281: q^3+q^2
       282: q^3+q^2+1
       283: q^3+q^2+1
       286: q^3+q^2+1
       287: q^3
       288: q^3+q^2+1
       289: q^2
       290: q^2+1
       291: q^2
       292: q^2+1
       293: q^2+1
       296: q^2+1
       298: q^2+1
       299: q^3+q^2+1
       301: q^2
       302: q^2+1
       304: q^3+q^2+1
       305: q^2
       306: q^2+1
       307: q^3+q^2+1
       310: q^3+q^2+1
       311: q^2
       312: q^2+1
       313: q^2
       314: q^2+1
       315: q^3+q^2
       316: q^3+q^2+1
       317: q^3
       318: q^3+q^2+1
       319: q^3+q^2+1
       322: q^3+q^2+1
       323: q^2
       324: q^2+1
       325: q^3
       326: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: q^2+1
       337: q^2+1
       338: 2q^2
       339: 1
       340: 2q^2
       341: 1
       342: q^3+q^2
       343: q^3+1
       344: 3q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^4+q^3+2q^2+1
       349: q^2+1
       350: q^4+q^3+2q^2+1
       351: 2q^2+1
       352: 3q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^4+q^3+2q^2+1
       357: q^2+1
       358: q^4+q^3+2q^2+1
       359: 2q^2+1
       360: q^3+q^2
       361: q^3+q^2+1
       362: q^4+q^3+q^2
       363: q^3+q^2+1
       364: q^3+q^2
       365: q^3+q^2+1
       366: 3q^3+q^2+1
       367: 3q^3+q^2+1
       368: 2q^4+3q^3+2q^2+1
       369: q^4+q^3+2q^2+1
       370: q^4+q^3+2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       378: q^2+1
       382: q^2+1
       386: q^2+1
       390: q^2+1
       394: q^2+1
       400: q^2+1
       403: q^2+1
       407: q^2+1
       413: q^3
       414: q^3+q^2+1
       417: q^2
       418: q^2+1
       419: q^2+1
       422: q^2+1
       424: q^2+1
       425: q^2
       426: 1
       427: q^2
       428: 1
       429: q^3+q^2+1
       432: q^3+q^2+1
       433: q^2
       434: q^2+1
       435: q^2
       436: q^2+1
       437: q^2+1
       440: q^2+1
       442: q^2+1
       443: q^2+1
       445: 2q^2
       446: 1
       447: q^3+q^2+1
       450: q^3+q^2+1
       451: q^2
       452: q^2+1
       453: q^2+1
       455: q^2
       456: q^2+1
       458: q^2+1
       460: q^2+1
       462: q^2+1
       463: 2q^2
       464: 1
       465: q^3
       466: q^3+q^2+1
       467: q^3+q^2
       468: q^3+q^2+1
       469: q^3
       470: q^3+q^2+1
       471: q^3+q^2+1
       474: q^3+q^2+1
       475: q^2
       476: q^2+1
       477: q^2
       478: q^2+1
       479: q^2
       480: q^2+1
       481: q^2+1
       482: q^2+1
       483: 1
       484: q^2+1
       485: 2q^2
       486: 1
       487: 2q^2
       488: 1
       489: q^3+q^2
       490: q^3+1
       491: q^2+1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: 2q^2+1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 2q^2+1
       508: 3q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^4+q^3+2q^2+1
       513: q^2+1
       514: q^4+q^3+2q^2+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       522: q^2+1
       530: q^2+1
       534: q^2+1
       538: q^2+1
       542: q^2+1
       545: q^2
       546: 1
       551: q^2+1
       556: q^2+1
       560: q^2+1
       563: q^2
       564: 1
       566: q^2+1
       571: q^2+1
       574: q^2+1
       577: q^2
       580: q^2
       581: 1
       586: q^2+1
       589: q^2+1
       592: 1
       593: 1
       596: q^2+1
       597: q^2
       598: 1
       600: 1
       601: q^2
       602: 1
       603: q^2+1
       605: q^2
       606: q^2+1
       608: q^2+1
       610: q^2+1
       613: q^2
       614: 1
       615: q^2+1
       617: 2q^2
       618: 1
       619: q^2+1
       622: q^2+1
       623: q^2
       624: q^2+1
       626: q^2+1
       629: q^2
       630: 1
       632: q^2+1
       633: 2q^2
       634: 1
       639: q^3
       640: q^3+q^2+1
       641: q^3+q^2+1
       644: q^3+q^2+1
       645: q^2
       646: q^2+1
       647: q^2+1
       650: q^2+1
       651: q^2
       652: q^2+1
       654: q^2+1
       655: q^2
       656: q^2+1
       657: q^2+1
       658: 2q^2
       659: 1
       660: 2q^2
       661: 1
       662: q^3+q^2
       663: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: q^2+1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: q^2+1
       690: 1
       691: 1
       692: q^3+1
       696: q^2
       699: 1
       710: q^2+1
       715: 1
       718: 1
       722: q^2+1
       726: q^2+1
       733: q^2
       734: 1
       740: q^2+1
       744: q^2+1
       751: q^2
       752: 1
       754: q^2+1
       759: q^2+1
       763: q^2+1
       766: q^2+1
       769: q^2
       772: q^2
       773: 1
       775: q^2
       776: 1
       779: q^2
       780: 1
       782: 1
       785: 1
       788: 1
       792: 1
       793: q^2+1
       795: 2q^2
       796: 1
       798: q^2+1
       801: q^2+1
       804: 1
       805: 1
       808: q^2+1
       809: q^2
       810: 1
       812: 1
       815: 1
       818: q^2+1
       819: 2q^2
       820: 1
       822: q^2+1
       825: q^2+1
       828: 1
       829: 1
       832: q^2+1
       833: q^2
       834: 1
       836: 1
       840: 1
       843: q^2
       844: q^2+1
       845: q^2+1
       848: q^2+1
       849: q^2
       850: q^2+1
       852: q^2+1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: q^3+1
       887: q^2
       890: 1
       903: 1
       905: 1
       909: 1
       916: q^2
       917: 1
       921: q^2+1
       926: 1
       929: 1
       942: q^2
       943: 1
       947: q^2+1
       951: 1
       953: 1
       962: q^2+1
       965: q^2+1
       968: q^2
       971: q^2
       972: 1
       976: q^2+1
       989: 1
       995: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1016: 1
      1020: q^2
      1021: 1
      1023: 1
      1026: 1
      1029: 1
      1033: 1
      1036: q^2
      1037: 1
      1039: 1
      1040: 1
      1045: 1
      1047: 1
      1049: q^2+1
      1052: q^2+1
      1055: 1
      1056: 1
      1059: q^2+1
      1060: q^2
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1089: q^2
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1195: 1
      1200: q^2+1
      1205: 1
      1207: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1231: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1247: 1
      1249: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1263: 1
      1267: 1
      1268: 1
      1271: 1
      1274: q^2
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1411: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1437: 1
      1441: 1
      1442: 1
      1445: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1475: 1
      1476: 1
      1479: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1508: 1
      1519: 1
      1539: 1
      1550: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1610: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1640: 1
      1646: 1
      1647: 1
      1654: 1
      1655: 1
      1660: 1
      1664: 1
      1665: 1
      1670: 1
      1674: 1
      1716: 1
      1734: 1
      1744: 1
      1751: 1
      1771: 1
      1774: 1
      1798: 1
      1809: 1
      1826: 1
      1830: 1
      1831: 1
      1901: 1
      1915: 1
      1941: 1
      1946: 1
      2061: 1

2062:    0: 5q^4+5q^3+2q^2+1
         1: 5q^4+5q^3+2q^2+1
         2: 5q^4+5q^3+2q^2+1
         3: 5q^4+5q^3+2q^2+1
         4: 3q^5+4q^4+3q^3+2q^2+1
         5: 5q^4+5q^3+2q^2+1
         6: q^6+4q^5+5q^4+3q^3+2q^2+1
         7: 3q^5+4q^4+3q^3+2q^2+1
         8: 5q^4+5q^3+2q^2+1
         9: 3q^5+4q^4+3q^3+2q^2+1
        10: 5q^3+q^2+1
        11: 5q^3+q^2+1
        12: q^5+2q^4+3q^3+q^2+1
        13: 5q^4+5q^3+2q^2+1
        14: 3q^5+4q^4+3q^3+2q^2+1
        15: 5q^4+5q^3+2q^2+1
        16: 5q^4+5q^3+2q^2+1
        17: 5q^4+5q^3+2q^2+1
        18: 3q^5+4q^4+3q^3+2q^2+1
        19: 2q^4+3q^3+2q^2+1
        20: 3q^4+3q^3+2q^2+1
        21: 2q^4+3q^3+2q^2+1
        22: 5q^4+5q^3+2q^2+1
        23: 5q^4+5q^3+2q^2+1
        24: 5q^4+5q^3+2q^2+1
        25: 5q^4+5q^3+2q^2+1
        26: 5q^4+5q^3+2q^2+1
        27: 5q^4+5q^3+2q^2+1
        28: 5q^3+q^2+1
        29: 3q^3+q^2+1
        30: 2q^4+3q^3+2q^2+1
        31: 5q^3+q^2+1
        32: 5q^4+5q^3+2q^2+1
        33: 5q^4+5q^3+2q^2+1
        34: 5q^3+q^2+1
        35: 5q^4+5q^3+2q^2+1
        36: 5q^4+5q^3+2q^2+1
        37: 3q^4+2q^3+q^2
        38: 2q^4+3q^3+q^2+1
        39: 3q^4+2q^3+q^2
        40: 2q^4+3q^3+q^2+1
        41: 3q^4+2q^3+q^2
        42: 2q^4+3q^3+q^2+1
        43: 5q^3+q^2+1
        44: q^5+2q^4+3q^3+q^2+1
        45: 5q^3+q^2+1
        46: 5q^4+5q^3+2q^2+1
        47: 5q^4+5q^3+2q^2+1
        48: 3q^5+4q^4+3q^3+2q^2+1
        49: 2q^4+3q^3+2q^2+1
        50: 3q^4+3q^3+2q^2+1
        51: 2q^4+3q^3+2q^2+1
        52: 2q^4+3q^3+2q^2+1
        53: 3q^4+3q^3+2q^2+1
        54: 2q^4+3q^3+2q^2+1
        55: 2q^4+3q^3+2q^2+1
        56: 3q^4+3q^3+2q^2+1
        57: 2q^4+3q^3+2q^2+1
        58: 3q^3+q^2+1
        59: 2q^3
        60: 2q^3
        61: 3q^3+q^2+1
        62: 2q^3
        63: 3q^3+q^2+1
        64: 3q^4+2q^3+q^2
        65: 2q^4+3q^3+q^2+1
        66: 3q^4+2q^3+q^2
        67: 2q^4+3q^3+q^2+1
        68: 5q^3+q^2+1
        69: 2q^4+3q^3+2q^2+1
        70: 3q^3+q^2+1
        71: 3q^3+q^2+1
        72: q^4+q^3+2q^2+1
        73: q^4+q^3+2q^2+1
        74: q^3+q^2
        75: q^3+q^2+1
        76: q^4+q^3+q^2
        77: q^3+q^2+1
        78: q^3+q^2
        79: q^3+q^2+1
        80: 5q^3+q^2+1
        81: 5q^4+5q^3+2q^2+1
        82: 3q^3+q^2+1
        83: 2q^4+3q^3+2q^2+1
        84: 5q^3+q^2+1
        85: 5q^4+5q^3+2q^2+1
        86: 3q^3+q^2+1
        87: 2q^4+3q^3+2q^2+1
        88: 5q^3+q^2+1
        89: 5q^3+q^2+1
        90: q^5+2q^4+3q^3+q^2+1
        91: 2q^4+3q^3+2q^2+1
        92: 3q^4+3q^3+2q^2+1
        93: 2q^4+3q^3+2q^2+1
        94: 2q^4+3q^3+2q^2+1
        95: 3q^4+3q^3+2q^2+1
        96: 2q^4+3q^3+2q^2+1
        97: 2q^4+3q^3+2q^2+1
        98: 3q^4+3q^3+2q^2+1
        99: 2q^4+3q^3+2q^2+1
       100: 2q^4+3q^3+2q^2+1
       101: 3q^4+3q^3+2q^2+1
       102: 2q^4+3q^3+2q^2+1
       103: q^3
       104: q^3
       105: 2q^3+q^2+1
       106: q^3
       108: q^3+q^2+1
       109: q^3+q^2+1
       111: q^2
       112: q^2+1
       113: q^3
       114: q^3+q^2+1
       115: q^3+q^2
       116: q^3+q^2+1
       117: 3q^3+q^2+1
       118: 2q^3
       119: 2q^3
       120: 3q^3+q^2+1
       121: 2q^3
       122: 3q^3+q^2+1
       123: 3q^4+2q^3+q^2
       124: 2q^4+3q^3+q^2+1
       125: 5q^3+q^2+1
       126: 3q^3+q^2+1
       127: q^3+q^2
       128: q^3+q^2+1
       129: q^4+q^3+q^2
       130: q^3+q^2+1
       131: q^3+q^2
       132: q^3+q^2+1
       133: 3q^3+q^2+1
       134: 2q^4+3q^3+2q^2+1
       135: q^4+q^3+2q^2+1
       136: q^4+q^3+2q^2+1
       137: 5q^3+q^2+1
       138: 2q^4+3q^3+2q^2+1
       139: 3q^3+q^2+1
       140: q^4+q^3+2q^2+1
       141: 3q^3+q^2+1
       142: q^4+q^3+2q^2+1
       143: 5q^3+q^2+1
       144: 2q^4+3q^3+2q^2+1
       145: 3q^3+q^2+1
       146: 3q^3+q^2+1
       147: q^4+q^3+2q^2+1
       148: q^4+q^3+2q^2+1
       149: 3q^3+q^2+1
       150: 2q^4+3q^3+2q^2+1
       151: q^3+q^2
       152: q^3+q^2+1
       153: q^4+q^3+q^2
       154: q^3+q^2+1
       155: q^3+q^2
       156: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: 2q^4+3q^3+2q^2+1
       161: 3q^4+3q^3+2q^2+1
       162: 2q^4+3q^3+2q^2+1
       163: 2q^4+3q^3+2q^2+1
       164: 3q^4+3q^3+2q^2+1
       165: 2q^4+3q^3+2q^2+1
       166: 2q^4+3q^3+2q^2+1
       167: 3q^4+3q^3+2q^2+1
       168: 2q^4+3q^3+2q^2+1
       171: q^2+1
       173: q^3
       174: q^3
       175: 2q^3+q^2+1
       176: q^3
       177: q^3+q^2
       178: q^3+q^2+1
       179: q^3
       180: q^3+q^2+1
       181: q^2
       182: q^2+1
       184: q^3+q^2+1
       185: q^3+q^2+1
       187: q^2
       188: q^2+1
       189: q^3
       190: q^3+q^2+1
       191: 3q^3+q^2+1
       192: 2q^3
       194: q^3+q^2+1
       195: q^3+q^2+1
       197: q^2
       198: q^2+1
       199: 2q^3
       200: 3q^3+q^2+1
       202: q^3+q^2+1
       203: q^3+q^2+1
       205: q^2
       206: q^2+1
       207: 2q^3
       208: 3q^3+q^2+1
       209: q^3
       210: q^3+q^2+1
       211: q^3+q^2
       212: q^3+q^2+1
       213: q^3+q^2
       214: q^3+q^2+1
       215: q^4+q^3+q^2
       216: q^3+q^2+1
       217: q^3+q^2
       218: q^3+q^2+1
       219: 3q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^4+q^3+2q^2+1
       224: q^2+1
       225: q^4+q^3+2q^2+1
       226: 3q^3+q^2+1
       227: 3q^3+q^2+1
       228: 2q^4+3q^3+2q^2+1
       229: q^4+q^3+2q^2+1
       230: q^4+q^3+2q^2+1
       231: 3q^3+q^2+1
       232: 3q^3+q^2+1
       233: 2q^4+3q^3+2q^2+1
       234: q^4+q^3+2q^2+1
       235: q^4+q^3+2q^2+1
       236: 2q^4+3q^3+2q^2+1
       237: q^3+q^2
       238: q^3+q^2+1
       239: q^4+q^3+q^2
       240: q^3+q^2+1
       241: q^3+q^2
       242: q^3+q^2+1
       243: 3q^3+q^2+1
       244: q^4+q^3+2q^2+1
       245: q^4+q^3+2q^2+1
       246: 3q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: 2q^4+3q^3+2q^2+1
       257: 3q^4+3q^3+2q^2+1
       258: 2q^4+3q^3+2q^2+1
       261: q^2+1
       265: q^2+1
       270: q^2+1
       272: q^2+1
       275: q^3
       276: q^3
       277: 2q^3+q^2+1
       278: q^3
       279: q^3
       280: q^3+q^2+1
       281: q^3+q^2
       282: q^3+q^2+1
       284: q^3+q^2+1
       285: q^3+q^2+1
       287: q^3
       288: q^3+q^2+1
       289: q^2
       290: q^2+1
       291: q^2
       292: q^2+1
       294: q^2+1
       295: q^2+1
       298: q^2+1
       300: q^3+q^2+1
       301: q^2
       302: q^2+1
       303: q^3+q^2+1
       305: q^2
       306: q^2+1
       308: q^3+q^2+1
       309: q^3+q^2+1
       311: q^2
       312: q^2+1
       313: q^2
       314: q^2+1
       315: q^3+q^2
       316: q^3+q^2+1
       317: q^3
       318: q^3+q^2+1
       320: q^3+q^2+1
       321: q^3+q^2+1
       323: q^2
       324: q^2+1
       325: q^3
       326: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: q^2+1
       337: q^2+1
       338: 2q^2
       339: 1
       340: 2q^2
       341: 1
       342: q^3+q^2
       343: q^3+1
       344: 3q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^4+q^3+2q^2+1
       349: q^2+1
       350: q^4+q^3+2q^2+1
       351: 2q^2+1
       352: 3q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^4+q^3+2q^2+1
       357: q^2+1
       358: q^4+q^3+2q^2+1
       359: 2q^2+1
       360: q^3+q^2
       361: q^3+q^2+1
       362: q^4+q^3+q^2
       363: q^3+q^2+1
       364: q^3+q^2
       365: q^3+q^2+1
       366: 3q^3+q^2+1
       367: 3q^3+q^2+1
       368: 2q^4+3q^3+2q^2+1
       369: q^4+q^3+2q^2+1
       370: q^4+q^3+2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       379: q^2+1
       383: q^2+1
       387: q^2+1
       392: q^2+1
       395: q^2+1
       398: q^2+1
       402: q^2+1
       408: q^2+1
       413: q^3
       414: q^3+q^2+1
       417: q^2
       418: q^2+1
       420: q^2+1
       421: q^2+1
       424: q^2+1
       425: q^2
       426: 1
       427: q^2
       428: 1
       430: q^3+q^2+1
       431: q^3+q^2+1
       433: q^2
       434: q^2+1
       435: q^2
       436: q^2+1
       438: q^2+1
       439: q^2+1
       442: q^2+1
       444: q^2+1
       445: 2q^2
       446: 1
       448: q^3+q^2+1
       449: q^3+q^2+1
       451: q^2
       452: q^2+1
       454: q^2+1
       455: q^2
       456: q^2+1
       457: q^2+1
       460: q^2+1
       461: q^2+1
       463: 2q^2
       464: 1
       465: q^3
       466: q^3+q^2+1
       467: q^3+q^2
       468: q^3+q^2+1
       469: q^3
       470: q^3+q^2+1
       472: q^3+q^2+1
       473: q^3+q^2+1
       475: q^2
       476: q^2+1
       477: q^2
       478: q^2+1
       479: q^2
       480: q^2+1
       481: q^2+1
       482: q^2+1
       483: 1
       484: q^2+1
       485: 2q^2
       486: 1
       487: 2q^2
       488: 1
       489: q^3+q^2
       490: q^3+1
       491: q^2+1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: 2q^2+1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 2q^2+1
       508: 3q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^4+q^3+2q^2+1
       513: q^2+1
       514: q^4+q^3+2q^2+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       523: q^2+1
       531: q^2+1
       535: q^2+1
       540: q^2+1
       544: q^2+1
       547: q^2
       548: 1
       550: q^2+1
       554: q^2+1
       558: q^2+1
       561: q^2
       562: 1
       567: q^2+1
       572: q^2+1
       576: q^2+1
       577: q^2
       580: q^2
       581: 1
       586: q^2+1
       590: q^2+1
       591: 1
       594: 1
       595: q^2+1
       597: q^2
       598: 1
       600: 1
       601: q^2
       602: 1
       604: q^2+1
       605: q^2
       606: q^2+1
       607: q^2+1
       610: q^2+1
       613: q^2
       614: 1
       616: q^2+1
       617: 2q^2
       618: 1
       620: q^2+1
       621: q^2+1
       623: q^2
       624: q^2+1
       626: q^2+1
       629: q^2
       630: 1
       631: q^2+1
       633: 2q^2
       634: 1
       639: q^3
       640: q^3+q^2+1
       642: q^3+q^2+1
       643: q^3+q^2+1
       645: q^2
       646: q^2+1
       648: q^2+1
       649: q^2+1
       651: q^2
       652: q^2+1
       654: q^2+1
       655: q^2
       656: q^2+1
       657: q^2+1
       658: 2q^2
       659: 1
       660: 2q^2
       661: 1
       662: q^3+q^2
       663: q^3+1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: q^2+1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: q^2+1
       690: 1
       691: 1
       692: q^3+1
       698: q^2
       700: 1
       711: q^2+1
       714: 1
       719: 1
       724: q^2+1
       728: q^2+1
       735: q^2
       736: 1
       738: q^2+1
       742: q^2+1
       749: q^2
       750: 1
       755: q^2+1
       760: q^2+1
       764: q^2+1
       767: q^2+1
       769: q^2
       772: q^2
       773: 1
       775: q^2
       776: 1
       779: q^2
       780: 1
       782: 1
       786: 1
       787: 1
       792: 1
       794: q^2+1
       795: 2q^2
       796: 1
       798: q^2+1
       802: q^2+1
       803: 1
       806: 1
       807: q^2+1
       809: q^2
       810: 1
       812: 1
       816: 1
       817: q^2+1
       819: 2q^2
       820: 1
       822: q^2+1
       826: q^2+1
       827: 1
       830: 1
       831: q^2+1
       833: q^2
       834: 1
       836: 1
       839: 1
       843: q^2
       844: q^2+1
       846: q^2+1
       847: q^2+1
       849: q^2
       850: q^2+1
       852: q^2+1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: q^3+1
       888: q^2
       891: 1
       901: 1
       907: 1
       910: 1
       918: q^2
       919: 1
       923: q^2+1
       925: 1
       931: 1
       940: q^2
       941: 1
       945: q^2+1
       949: 1
       954: 1
       963: q^2+1
       966: q^2+1
       968: q^2
       971: q^2
       972: 1
       977: q^2+1
       990: 1
       995: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1017: 1
      1020: q^2
      1021: 1
      1023: 1
      1027: 1
      1028: 1
      1032: 1
      1036: q^2
      1037: 1
      1039: 1
      1041: 1
      1044: 1
      1047: 1
      1049: q^2+1
      1053: q^2+1
      1054: 1
      1057: 1
      1058: q^2+1
      1060: q^2
      1061: 1
      1063: 1
      1065: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1090: q^2
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1196: 1
      1201: q^2+1
      1203: 1
      1209: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1231: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1263: 1
      1267: 1
      1269: 1
      1270: 1
      1274: q^2
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1412: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1437: 1
      1440: 1
      1443: 1
      1445: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1475: 1
      1477: 1
      1478: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1507: 1
      1520: 1
      1540: 1
      1551: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1608: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1640: 1
      1645: 1
      1648: 1
      1653: 1
      1656: 1
      1660: 1
      1663: 1
      1666: 1
      1670: 1
      1674: 1
      1717: 1
      1735: 1
      1743: 1
      1750: 1
      1772: 1
      1775: 1
      1799: 1
      1810: 1
      1826: 1
      1829: 1
      1832: 1
      1899: 1
      1917: 1
      1942: 1
      1947: 1
      2062: 1

2063:    0: 5q^4+5q^3+2q^2+1
         1: 5q^4+5q^3+2q^2+1
         2: 5q^4+5q^3+2q^2+1
         3: 5q^4+5q^3+2q^2+1
         4: 3q^5+4q^4+3q^3+2q^2+1
         5: 5q^4+5q^3+2q^2+1
         6: q^6+4q^5+5q^4+3q^3+2q^2+1
         7: 3q^5+4q^4+3q^3+2q^2+1
         8: 5q^4+5q^3+2q^2+1
         9: 3q^5+4q^4+3q^3+2q^2+1
        10: 5q^3+q^2+1
        11: 5q^3+q^2+1
        12: q^5+2q^4+3q^3+q^2+1
        13: 5q^4+5q^3+2q^2+1
        14: 3q^5+4q^4+3q^3+2q^2+1
        15: 5q^4+5q^3+2q^2+1
        16: 5q^4+5q^3+2q^2+1
        17: 5q^4+5q^3+2q^2+1
        18: 3q^5+4q^4+3q^3+2q^2+1
        19: 2q^4+3q^3+2q^2+1
        20: 3q^4+3q^3+2q^2+1
        21: 2q^4+3q^3+2q^2+1
        22: 5q^4+5q^3+2q^2+1
        23: 5q^4+5q^3+2q^2+1
        24: 5q^4+5q^3+2q^2+1
        25: 5q^4+5q^3+2q^2+1
        26: 5q^4+5q^3+2q^2+1
        27: 5q^4+5q^3+2q^2+1
        28: 5q^3+q^2+1
        29: 3q^3+q^2+1
        30: 2q^4+3q^3+2q^2+1
        31: 5q^3+q^2+1
        32: 5q^4+5q^3+2q^2+1
        33: 5q^4+5q^3+2q^2+1
        34: 5q^3+q^2+1
        35: 5q^4+5q^3+2q^2+1
        36: 5q^4+5q^3+2q^2+1
        37: 2q^4+3q^3+q^2+1
        38: 3q^4+2q^3+q^2
        39: 2q^4+3q^3+q^2+1
        40: 3q^4+2q^3+q^2
        41: 2q^4+3q^3+q^2+1
        42: 3q^4+2q^3+q^2
        43: 5q^3+q^2+1
        44: q^5+2q^4+3q^3+q^2+1
        45: 5q^3+q^2+1
        46: 5q^4+5q^3+2q^2+1
        47: 5q^4+5q^3+2q^2+1
        48: 3q^5+4q^4+3q^3+2q^2+1
        49: 2q^4+3q^3+2q^2+1
        50: 3q^4+3q^3+2q^2+1
        51: 2q^4+3q^3+2q^2+1
        52: 2q^4+3q^3+2q^2+1
        53: 3q^4+3q^3+2q^2+1
        54: 2q^4+3q^3+2q^2+1
        55: 2q^4+3q^3+2q^2+1
        56: 3q^4+3q^3+2q^2+1
        57: 2q^4+3q^3+2q^2+1
        58: 2q^3
        59: 3q^3+q^2+1
        60: 2q^3
        61: 3q^3+q^2+1
        62: 3q^3+q^2+1
        63: 2q^3
        64: 2q^4+3q^3+q^2+1
        65: 3q^4+2q^3+q^2
        66: 2q^4+3q^3+q^2+1
        67: 3q^4+2q^3+q^2
        68: 5q^3+q^2+1
        69: 2q^4+3q^3+2q^2+1
        70: 3q^3+q^2+1
        71: 3q^3+q^2+1
        72: q^4+q^3+2q^2+1
        73: q^4+q^3+2q^2+1
        74: q^3+q^2+1
        75: q^3+q^2
        76: q^3+q^2+1
        77: q^4+q^3+q^2
        78: q^3+q^2+1
        79: q^3+q^2
        80: 5q^3+q^2+1
        81: 5q^4+5q^3+2q^2+1
        82: 3q^3+q^2+1
        83: 2q^4+3q^3+2q^2+1
        84: 5q^3+q^2+1
        85: 5q^4+5q^3+2q^2+1
        86: 3q^3+q^2+1
        87: 2q^4+3q^3+2q^2+1
        88: 5q^3+q^2+1
        89: 5q^3+q^2+1
        90: q^5+2q^4+3q^3+q^2+1
        91: 2q^4+3q^3+2q^2+1
        92: 3q^4+3q^3+2q^2+1
        93: 2q^4+3q^3+2q^2+1
        94: 2q^4+3q^3+2q^2+1
        95: 3q^4+3q^3+2q^2+1
        96: 2q^4+3q^3+2q^2+1
        97: 2q^4+3q^3+2q^2+1
        98: 3q^4+3q^3+2q^2+1
        99: 2q^4+3q^3+2q^2+1
       100: 2q^4+3q^3+2q^2+1
       101: 3q^4+3q^3+2q^2+1
       102: 2q^4+3q^3+2q^2+1
       103: q^3
       104: q^3
       105: q^3
       106: 2q^3+q^2+1
       108: q^3+q^2+1
       110: q^3+q^2+1
       111: q^2+1
       112: q^2
       113: q^3+q^2+1
       114: q^3
       115: q^3+q^2+1
       116: q^3+q^2
       117: 2q^3
       118: 3q^3+q^2+1
       119: 2q^3
       120: 3q^3+q^2+1
       121: 3q^3+q^2+1
       122: 2q^3
       123: 2q^4+3q^3+q^2+1
       124: 3q^4+2q^3+q^2
       125: 5q^3+q^2+1
       126: 3q^3+q^2+1
       127: q^3+q^2+1
       128: q^3+q^2
       129: q^3+q^2+1
       130: q^4+q^3+q^2
       131: q^3+q^2+1
       132: q^3+q^2
       133: 3q^3+q^2+1
       134: 2q^4+3q^3+2q^2+1
       135: q^4+q^3+2q^2+1
       136: q^4+q^3+2q^2+1
       137: 5q^3+q^2+1
       138: 2q^4+3q^3+2q^2+1
       139: 3q^3+q^2+1
       140: q^4+q^3+2q^2+1
       141: 3q^3+q^2+1
       142: q^4+q^3+2q^2+1
       143: 5q^3+q^2+1
       144: 2q^4+3q^3+2q^2+1
       145: 3q^3+q^2+1
       146: 3q^3+q^2+1
       147: q^4+q^3+2q^2+1
       148: q^4+q^3+2q^2+1
       149: 3q^3+q^2+1
       150: 2q^4+3q^3+2q^2+1
       151: q^3+q^2+1
       152: q^3+q^2
       153: q^3+q^2+1
       154: q^4+q^3+q^2
       155: q^3+q^2+1
       156: q^3+q^2
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: 2q^4+3q^3+2q^2+1
       161: 3q^4+3q^3+2q^2+1
       162: 2q^4+3q^3+2q^2+1
       163: 2q^4+3q^3+2q^2+1
       164: 3q^4+3q^3+2q^2+1
       165: 2q^4+3q^3+2q^2+1
       166: 2q^4+3q^3+2q^2+1
       167: 3q^4+3q^3+2q^2+1
       168: 2q^4+3q^3+2q^2+1
       172: q^2+1
       173: q^3
       174: q^3
       175: q^3
       176: 2q^3+q^2+1
       177: q^3+q^2+1
       178: q^3+q^2
       179: q^3+q^2+1
       180: q^3
       181: q^2+1
       182: q^2
       184: q^3+q^2+1
       186: q^3+q^2+1
       187: q^2+1
       188: q^2
       189: q^3+q^2+1
       190: q^3
       191: 2q^3
       192: 3q^3+q^2+1
       194: q^3+q^2+1
       196: q^3+q^2+1
       197: q^2+1
       198: q^2
       199: 2q^3
       200: 3q^3+q^2+1
       202: q^3+q^2+1
       204: q^3+q^2+1
       205: q^2+1
       206: q^2
       207: 3q^3+q^2+1
       208: 2q^3
       209: q^3+q^2+1
       210: q^3
       211: q^3+q^2+1
       212: q^3+q^2
       213: q^3+q^2+1
       214: q^3+q^2
       215: q^3+q^2+1
       216: q^4+q^3+q^2
       217: q^3+q^2+1
       218: q^3+q^2
       219: 3q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^4+q^3+2q^2+1
       224: q^2+1
       225: q^4+q^3+2q^2+1
       226: 3q^3+q^2+1
       227: 3q^3+q^2+1
       228: 2q^4+3q^3+2q^2+1
       229: q^4+q^3+2q^2+1
       230: q^4+q^3+2q^2+1
       231: 3q^3+q^2+1
       232: 3q^3+q^2+1
       233: 2q^4+3q^3+2q^2+1
       234: q^4+q^3+2q^2+1
       235: q^4+q^3+2q^2+1
       236: 2q^4+3q^3+2q^2+1
       237: q^3+q^2+1
       238: q^3+q^2
       239: q^3+q^2+1
       240: q^4+q^3+q^2
       241: q^3+q^2+1
       242: q^3+q^2
       243: 3q^3+q^2+1
       244: q^4+q^3+2q^2+1
       245: q^4+q^3+2q^2+1
       246: 3q^3+q^2+1
       247: 2q^2+1
       248: 2q^2+1
       249: 2q^3+q^2+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: 2q^4+3q^3+2q^2+1
       257: 3q^4+3q^3+2q^2+1
       258: 2q^4+3q^3+2q^2+1
       262: q^2+1
       266: q^2+1
       269: q^2+1
       273: q^2+1
       275: q^3
       276: q^3
       277: q^3
       278: 2q^3+q^2+1
       279: q^3+q^2+1
       280: q^3
       281: q^3+q^2+1
       282: q^3+q^2
       284: q^3+q^2+1
       286: q^3+q^2+1
       287: q^3+q^2+1
       288: q^3
       289: q^2+1
       290: q^2
       291: q^2+1
       292: q^2
       294: q^2+1
       296: q^2+1
       297: q^2+1
       300: q^3+q^2+1
       301: q^2+1
       302: q^2
       304: q^3+q^2+1
       305: q^2+1
       306: q^2
       308: q^3+q^2+1
       310: q^3+q^2+1
       311: q^2+1
       312: q^2
       313: q^2+1
       314: q^2
       315: q^3+q^2+1
       316: q^3+q^2
       317: q^3+q^2+1
       318: q^3
       320: q^3+q^2+1
       322: q^3+q^2+1
       323: q^2+1
       324: q^2
       325: q^3+q^2+1
       326: q^3
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: q^2+1
       337: q^2+1
       338: 1
       339: 2q^2
       340: 1
       341: 2q^2
       342: q^3+1
       343: q^3+q^2
       344: 3q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^4+q^3+2q^2+1
       349: q^2+1
       350: q^4+q^3+2q^2+1
       351: 2q^2+1
       352: 3q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^4+q^3+2q^2+1
       357: q^2+1
       358: q^4+q^3+2q^2+1
       359: 2q^2+1
       360: q^3+q^2+1
       361: q^3+q^2
       362: q^3+q^2+1
       363: q^4+q^3+q^2
       364: q^3+q^2+1
       365: q^3+q^2
       366: 3q^3+q^2+1
       367: 3q^3+q^2+1
       368: 2q^4+3q^3+2q^2+1
       369: q^4+q^3+2q^2+1
       370: q^4+q^3+2q^2+1
       371: 2q^2+1
       372: 2q^2+1
       373: 2q^3+q^2+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       380: q^2+1
       384: q^2+1
       388: q^2+1
       391: q^2+1
       396: q^2+1
       399: q^2+1
       404: q^2+1
       406: q^2+1
       413: q^3+q^2+1
       414: q^3
       417: q^2+1
       418: q^2
       420: q^2+1
       422: q^2+1
       423: q^2+1
       425: 1
       426: q^2
       427: 1
       428: q^2
       430: q^3+q^2+1
       432: q^3+q^2+1
       433: q^2+1
       434: q^2
       435: q^2+1
       436: q^2
       438: q^2+1
       440: q^2+1
       441: q^2+1
       444: q^2+1
       445: 1
       446: 2q^2
       448: q^3+q^2+1
       450: q^3+q^2+1
       451: q^2+1
       452: q^2
       454: q^2+1
       455: q^2+1
       456: q^2
       458: q^2+1
       459: q^2+1
       462: q^2+1
       463: 1
       464: 2q^2
       465: q^3+q^2+1
       466: q^3
       467: q^3+q^2+1
       468: q^3+q^2
       469: q^3+q^2+1
       470: q^3
       472: q^3+q^2+1
       474: q^3+q^2+1
       475: q^2+1
       476: q^2
       477: q^2+1
       478: q^2
       479: q^2+1
       480: q^2
       481: q^2+1
       482: q^2+1
       483: 1
       484: q^2+1
       485: 1
       486: 2q^2
       487: 1
       488: 2q^2
       489: q^3+1
       490: q^3+q^2
       491: q^2+1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: 2q^2+1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 2q^2+1
       508: 3q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^4+q^3+2q^2+1
       513: q^2+1
       514: q^4+q^3+2q^2+1
       515: 2q^2+1
       516: 2q^2+1
       517: 2q^3+q^2+1
       518: 1
       519: 1
       520: q^3+1
       524: q^2+1
       532: q^2+1
       536: q^2+1
       539: q^2+1
       543: q^2+1
       547: 1
       548: q^2
       552: q^2+1
       555: q^2+1
       559: q^2+1
       563: 1
       564: q^2
       568: q^2+1
       570: q^2+1
       575: q^2+1
       577: 1
       578: q^2
       581: q^2
       585: q^2+1
       590: q^2+1
       592: 1
       594: 1
       596: q^2+1
       597: 1
       598: q^2
       599: 1
       601: 1
       602: q^2
       604: q^2+1
       605: q^2+1
       606: q^2
       608: q^2+1
       609: q^2+1
       613: 1
       614: q^2
       616: q^2+1
       617: 1
       618: 2q^2
       620: q^2+1
       622: q^2+1
       623: q^2+1
       624: q^2
       625: q^2+1
       629: 1
       630: q^2
       632: q^2+1
       633: 1
       634: 2q^2
       639: q^3+q^2+1
       640: q^3
       642: q^3+q^2+1
       644: q^3+q^2+1
       645: q^2+1
       646: q^2
       648: q^2+1
       650: q^2+1
       651: q^2+1
       652: q^2
       653: q^2+1
       655: q^2+1
       656: q^2
       657: q^2+1
       658: 1
       659: 2q^2
       660: 1
       661: 2q^2
       662: q^3+1
       663: q^3+q^2
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: 2q^2+1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: q^2+1
       680: 2q^2+1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: q^2+1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: q^2+1
       690: 1
       691: 1
       692: q^3+1
       697: 1
       701: q^2
       712: q^2+1
       716: 1
       720: 1
       723: q^2+1
       727: q^2+1
       735: 1
       736: q^2
       739: q^2+1
       743: q^2+1
       751: 1
       752: q^2
       756: q^2+1
       758: q^2+1
       762: q^2+1
       768: q^2+1
       769: 1
       770: q^2
       773: q^2
       775: 1
       776: q^2
       779: 1
       780: q^2
       781: 1
       786: 1
       788: 1
       791: 1
       794: q^2+1
       795: 1
       796: 2q^2
       797: q^2+1
       802: q^2+1
       804: 1
       806: 1
       808: q^2+1
       809: 1
       810: q^2
       811: 1
       816: 1
       818: q^2+1
       819: 1
       820: 2q^2
       821: q^2+1
       826: q^2+1
       828: 1
       830: 1
       832: q^2+1
       833: 1
       834: q^2
       835: 1
       840: 1
       843: q^2+1
       844: q^2
       846: q^2+1
       848: q^2+1
       849: q^2+1
       850: q^2
       851: q^2+1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: q^3+1
       889: 1
       892: q^2
       902: 1
       906: 1
       911: 1
       918: 1
       919: q^2
       922: q^2+1
       927: 1
       930: 1
       942: 1
       943: q^2
       946: q^2+1
       950: 1
       955: 1
       961: q^2+1
       967: q^2+1
       968: 1
       969: q^2
       972: q^2
       975: q^2+1
       991: 1
       994: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1017: 1
      1020: 1
      1021: q^2
      1022: 1
      1027: 1
      1029: 1
      1033: 1
      1036: 1
      1037: q^2
      1038: 1
      1041: 1
      1045: 1
      1046: 1
      1048: q^2+1
      1053: q^2+1
      1055: 1
      1057: 1
      1059: q^2+1
      1060: 1
      1061: q^2
      1062: 1
      1064: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1091: 1
      1094: q^2
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1197: 1
      1199: q^2+1
      1204: 1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1247: 1
      1248: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1262: 1
      1266: 1
      1269: 1
      1271: 1
      1274: 1
      1275: q^2
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1413: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1474: 1
      1477: 1
      1479: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1506: 1
      1518: 1
      1538: 1
      1552: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1639: 1
      1646: 1
      1648: 1
      1654: 1
      1656: 1
      1659: 1
      1664: 1
      1666: 1
      1669: 1
      1674: 1
      1718: 1
      1736: 1
      1742: 1
      1752: 1
      1770: 1
      1776: 1
      1800: 1
      1808: 1
      1825: 1
      1830: 1
      1832: 1
      1900: 1
      1916: 1
      1943: 1
      1945: 1
      2063: 1

2064:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+3q^2+3q+1
        36: 2q^2+3q+1
        37: q^3+q^2+q+1
        38: 2q^2+2q
        39: q^3+q^2+q+1
        40: 2q^2+2q
        41: q^3+q^2+q+1
        42: 2q^2+2q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q^2+2q+1
        61: q
        62: q^2+q+1
        63: q^2+2q
        64: q^3+q^2+q+1
        65: 2q^2+2q
        66: q^2+q+1
        67: q^2+2q
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q^3+q^2+q+1
        75: 2q^2+2q
        76: q^3+q^2+q+1
        77: 2q^2+2q
        78: q^3+q^2+q+1
        79: 2q^2+2q
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^3+3q^2+3q+1
       101: q^3+3q^2+3q+1
       102: q^3+3q^2+3q+1
       103: q^2+q+1
       104: q
       105: q
       107: q^2+2q+1
       108: q
       109: q^2+2q+1
       110: q
       111: q^2+q+1
       112: q^2+2q
       113: q^2+q+1
       114: q^2+2q
       115: q^3+q^2+q+1
       116: 2q^2+2q
       117: q^2+2q+1
       118: q
       119: q^2+2q+1
       120: q
       121: q^2+q+1
       122: q^2+2q
       123: q^2+q+1
       124: q^2+2q
       125: 3q+1
       126: 2q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+q^2+q+1
       152: 2q^2+2q
       153: q^3+q^2+q+1
       154: 2q^2+2q
       155: q^3+q^2+q+1
       156: 2q^2+2q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^3+2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q^3+2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^3+2q^2+2q+1
       169: q^2+q+1
       170: q
       171: q
       173: q^2+q+1
       174: q
       175: q
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       183: q^2+2q+1
       184: q
       185: q^2+2q+1
       186: q
       187: q^2+q+1
       188: q^2+2q
       189: q^2+q+1
       190: q^2+2q
       191: 2q+1
       192: q
       193: q^2+2q+1
       194: q
       195: q^2+2q+1
       196: q
       197: q^2+q+1
       198: q^2+2q
       199: 2q+1
       200: q
       201: q^2+2q+1
       202: q
       203: q^2+2q+1
       204: q
       205: q^2+q+1
       206: q^2+2q
       207: q+1
       208: 2q
       209: q^2+q+1
       210: q^2+2q
       211: q^3+q^2+q+1
       212: 2q^2+2q
       213: q^2+1
       214: 2q
       215: q^2+1
       216: 2q
       217: q^3+1
       218: q^2+q
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: q^2+3q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q^3+2q^2+2q+1
       259: q^2+1
       260: q
       261: q
       263: q^2+q+1
       264: q
       265: q
       267: q^2+q+1
       268: q
       270: q
       271: q^2+q+1
       272: q
       274: q
       275: q+1
       276: q
       277: q
       279: q^2+1
       280: 2q
       281: 1
       282: q
       283: q+1
       285: q+1
       287: 1
       288: q
       289: q^2+1
       290: 2q
       291: 1
       292: q
       293: 2q+1
       294: q
       295: 2q+1
       296: q
       297: q+1
       298: 2q
       299: q^2+2q+1
       300: q
       301: q^2+1
       302: 2q
       303: q^2+2q+1
       304: q
       305: q^2+q+1
       306: q^2+2q
       307: q^2+2q+1
       308: q
       309: q^2+2q+1
       310: q
       311: q^2+1
       312: 2q
       313: q^2+q+1
       314: q^2+2q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: q^2+2q+1
       320: q
       321: q^2+2q+1
       322: q
       323: q^2+q+1
       324: q^2+2q
       325: q^2+q+1
       326: q^2+2q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: q^2+2q+1
       351: 2q^2+3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: 2q^2+3q+1
       360: q^2+1
       361: 2q
       362: q^2+1
       363: 2q
       364: q^3+1
       365: q^2+q
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q^2+3q+1
       372: 2q^2+3q+1
       373: q^3+2q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       377: 1
       381: q^2+1
       382: q
       383: q
       385: q+1
       386: q
       387: q
       389: q^2+1
       390: q
       392: q
       393: q^2+q+1
       394: q
       395: q
       397: q^2+1
       398: q
       400: q
       401: q^2+q+1
       402: q
       403: q
       405: q^2+q+1
       407: q
       408: q
       413: 1
       414: q
       417: 1
       418: q
       419: q+1
       421: q+1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       429: q+1
       431: q+1
       433: 1
       434: q
       435: q^2+1
       436: 2q
       437: 2q+1
       438: q
       439: 2q+1
       440: q
       441: q+1
       442: 2q
       443: q^2+2q+1
       444: q
       445: q^2+1
       446: 2q
       447: q+1
       449: q+1
       451: 1
       452: q
       453: 2q+1
       454: q
       455: q^2+1
       456: 2q
       457: 2q+1
       458: q
       459: q+1
       460: 2q
       461: q^2+2q+1
       462: q
       463: q^2+1
       464: 2q
       465: q^2+1
       466: 2q
       467: 1
       468: q
       469: 1
       470: q
       471: q^2+2q+1
       472: q
       473: q^2+2q+1
       474: q
       475: q^2+q+1
       476: q^2+2q
       477: q^2+1
       478: 2q
       479: q^2+q+1
       480: q^2+2q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: q^2+1
       486: 2q
       487: q^2+1
       488: 2q
       489: q^3+1
       490: q^2+q
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+3q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+2q+1
       513: 3q+1
       514: q^2+2q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       521: 1
       529: 1
       533: 1
       537: q^2+1
       538: q
       540: q
       541: q+1
       542: q
       544: q
       545: q^2+1
       546: q
       548: q
       549: 1
       553: q^2+1
       554: q
       556: q
       557: q+1
       558: q
       560: q
       561: q^2+1
       562: q
       564: q
       565: q^2+q+1
       566: q
       567: q
       569: q^2+1
       571: q
       572: q
       573: q^2+q+1
       574: q
       576: q
       577: q^2+1
       581: 2q
       585: 1
       586: q
       589: q+1
       591: q+1
       593: q+1
       595: q+1
       597: 1
       598: q
       599: 1
       600: q
       601: q^2+1
       602: 2q
       603: q+1
       605: 1
       606: q
       607: q+1
       609: 1
       610: q
       613: 1
       614: q
       615: q^2+2q+1
       616: q
       617: q^2+1
       618: 2q
       619: q+1
       621: q+1
       623: 1
       624: q
       625: 1
       626: q
       629: 1
       630: q
       631: q^2+2q+1
       632: q
       633: q^2+1
       634: 2q
       639: 1
       640: q
       641: q+1
       643: q+1
       645: 1
       646: q
       647: 2q+1
       648: q
       649: 2q+1
       650: q
       651: q^2+1
       652: 2q
       653: q+1
       654: 2q
       655: q^2+q+1
       656: q^2+2q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 2q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 3q+1
       679: q^2+2q+1
       680: 2q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: q^2+2q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: q^2+2q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+1
       699: q
       700: q
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: q^2+1
       734: q
       736: q
       737: 1
       741: 1
       749: q^2+1
       750: q
       752: q
       753: 1
       757: q^2+1
       759: q
       760: q
       761: q+1
       763: q
       764: q
       765: q^2+q+1
       766: q
       767: q
       769: q^2+1
       773: 2q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 1
       782: q
       785: q+1
       787: q+1
       791: 1
       792: q
       793: 2
       795: q+1
       796: q+1
       797: 1
       798: q
       801: q+1
       803: q+1
       805: q+1
       807: q+1
       809: 1
       810: q
       811: 1
       812: q
       815: 2q+1
       816: q
       817: 2
       819: q+1
       820: q+1
       821: 1
       822: q
       825: q+1
       827: q+1
       829: q+1
       831: q+1
       833: 1
       834: q
       835: 1
       836: q
       839: 2q+1
       840: q
       843: 2
       844: 2q
       845: q+1
       847: q+1
       849: 1
       850: q
       851: 1
       852: q
       855: 1
       856: q
       857: q+1
       858: 2q
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 2q+1
       872: 2q+1
       873: q+1
       874: 2q+2
       875: 2q+1
       876: 2q+1
       877: 2q+1
       878: 2q+1
       879: 2q+1
       880: q^2+2q+1
       881: q+1
       882: q+1
       883: q+1
       884: q^2+1
       890: q
       891: q
       900: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       928: 1
       940: 1
       941: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 2
       968: 1
       969: 1
       971: q
       972: q
       974: 1
       988: q+1
       989: q
       990: q
       994: 1
       995: 1
       998: 2
      1000: 2
      1004: q+1
      1006: q+1
      1008: 1
      1009: q
      1010: 1
      1011: q
      1012: 2
      1013: 2q
      1016: 1
      1020: q+1
      1021: q+1
      1022: 1
      1023: q
      1026: q+1
      1028: q+1
      1032: 1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q
      1040: q+1
      1044: q+1
      1046: 1
      1047: q
      1048: 1
      1049: q
      1052: q+1
      1054: q+1
      1056: q+1
      1058: q+1
      1060: 1
      1061: q
      1062: 1
      1063: q
      1064: 1
      1065: q
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+2
      1085: 2q+1
      1086: 1
      1087: 1
      1114: 1
      1115: 1
      1122: 1
      1123: 1
      1126: 1
      1130: 2
      1134: 1
      1138: 1
      1139: 1
      1141: q
      1142: q
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1194: 1
      1198: 1
      1202: 1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1221: q
      1224: 1
      1225: q
      1228: 1
      1230: 1
      1231: 1
      1232: 2
      1234: 2
      1240: q+1
      1242: q+1
      1246: 1
      1248: 1
      1249: 1
      1250: 2
      1254: 2
      1258: q+1
      1260: q+1
      1262: 1
      1263: q
      1266: 1
      1267: q
      1268: q+1
      1270: q+1
      1274: q+1
      1275: q+1
      1276: 1
      1277: q
      1278: 1
      1279: q
      1280: 2
      1281: 2q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1290: 1
      1291: 1
      1326: 1
      1330: 1
      1348: 1
      1349: 1
      1356: 1
      1357: 1
      1360: 1
      1364: 2
      1368: 1
      1380: 1
      1381: 1
      1388: 1
      1389: 1
      1392: 1
      1396: 2
      1400: 1
      1410: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1431: 1
      1433: q
      1434: q
      1440: 1
      1442: 1
      1444: 1
      1445: q
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1465: 1
      1466: 2
      1468: 2
      1474: 1
      1475: q
      1476: q+1
      1478: q+1
      1482: 1
      1483: q
      1484: 2
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1501: 1
      1502: 1
      1513: 1
      1514: 1
      1549: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1608: 1
      1615: 1
      1616: 1
      1619: 1
      1623: 2
      1627: 1
      1641: 1
      1642: 1
      1645: 1
      1647: 1
      1649: 2
      1653: 1
      1655: 1
      1657: 2
      1663: 1
      1665: 1
      1669: 1
      1670: q
      1673: 1
      1674: 1
      1711: 1
      1712: 1
      1749: 1
      1757: 1
      1758: 1
      1773: 1
      1781: 1
      1782: 1
      1797: 1
      1807: 1
      1811: 2
      1819: 1
      1821: 1
      1829: 1
      1831: 1
      1833: 1
      1882: 1
      1883: 1
      1940: 1
      1952: 1
      1962: 1
      1964: 1
      2064: 1

2065:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q
        38: q^3+q^2+q+1
        39: 2q^2+2q
        40: q^3+q^2+q+1
        41: 2q^2+2q
        42: q^3+q^2+q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q^2+2q+1
        61: q
        62: q^2+2q
        63: q^2+q+1
        64: 2q^2+2q
        65: q^3+q^2+q+1
        66: q^2+2q
        67: q^2+q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q
        75: q^3+q^2+q+1
        76: 2q^2+2q
        77: q^3+q^2+q+1
        78: 2q^2+2q
        79: q^3+q^2+q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^3+3q^2+3q+1
       101: q^3+3q^2+3q+1
       102: q^3+3q^2+3q+1
       103: q
       104: q^2+q+1
       106: q
       107: q^2+2q+1
       108: q
       109: q
       110: q^2+2q+1
       111: q^2+2q
       112: q^2+q+1
       113: q^2+2q
       114: q^2+q+1
       115: 2q^2+2q
       116: q^3+q^2+q+1
       117: q
       118: q^2+2q+1
       119: q^2+2q+1
       120: q
       121: q^2+2q
       122: q^2+q+1
       123: q^2+2q
       124: q^2+q+1
       125: 3q+1
       126: 2q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: q^3+3q^2+3q+1
       151: 2q^2+2q
       152: q^3+q^2+q+1
       153: 2q^2+2q
       154: q^3+q^2+q+1
       155: 2q^2+2q
       156: q^3+q^2+q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^3+2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q^3+2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^3+2q^2+2q+1
       169: q
       170: q^2+q+1
       172: q
       173: q
       174: q^2+q+1
       176: q
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       183: q^2+2q+1
       184: q
       185: q
       186: q^2+2q+1
       187: q^2+2q
       188: q^2+q+1
       189: q^2+2q
       190: q^2+q+1
       191: q
       192: 2q+1
       193: q^2+2q+1
       194: q
       195: q
       196: q^2+2q+1
       197: q^2+2q
       198: q^2+q+1
       199: 2q+1
       200: q
       201: q^2+2q+1
       202: q
       203: q
       204: q^2+2q+1
       205: q^2+2q
       206: q^2+q+1
       207: 2q
       208: q+1
       209: q^2+2q
       210: q^2+q+1
       211: 2q^2+2q
       212: q^3+q^2+q+1
       213: 2q
       214: q^2+1
       215: 2q
       216: q^2+1
       217: q^2+q
       218: q^3+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: q^2+3q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q^3+2q^2+2q+1
       259: q
       260: q^2+1
       262: q
       263: q
       264: q^2+q+1
       266: q
       267: q
       268: q^2+q+1
       269: q
       271: q
       273: q
       274: q^2+q+1
       275: q
       276: q+1
       278: q
       279: 2q
       280: q^2+1
       281: q
       282: 1
       283: q+1
       286: q+1
       287: q
       288: 1
       289: 2q
       290: q^2+1
       291: q
       292: 1
       293: 2q+1
       294: q
       295: q
       296: 2q+1
       297: 2q
       298: q+1
       299: q^2+2q+1
       300: q
       301: 2q
       302: q^2+1
       303: q
       304: q^2+2q+1
       305: q^2+2q
       306: q^2+q+1
       307: q^2+2q+1
       308: q
       309: q
       310: q^2+2q+1
       311: 2q
       312: q^2+1
       313: q^2+2q
       314: q^2+q+1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: q^2+2q+1
       320: q
       321: q
       322: q^2+2q+1
       323: q^2+2q
       324: q^2+q+1
       325: q^2+2q
       326: q^2+q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: q^2+2q+1
       351: 2q^2+3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: 2q^2+3q+1
       360: 2q
       361: q^2+1
       362: 2q
       363: q^2+1
       364: q^2+q
       365: q^3+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q^2+3q+1
       372: 2q^2+3q+1
       373: q^3+2q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       378: 1
       381: q
       382: q^2+1
       384: q
       385: q
       386: q+1
       388: q
       389: q
       390: q^2+1
       391: q
       393: q
       394: q^2+q+1
       396: q
       397: q
       399: q
       400: q^2+1
       401: q
       403: q^2+q+1
       404: q
       405: q
       406: q
       407: q^2+q+1
       413: q
       414: 1
       417: q
       418: 1
       419: q+1
       422: q+1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       429: q+1
       432: q+1
       433: q
       434: 1
       435: 2q
       436: q^2+1
       437: 2q+1
       438: q
       439: q
       440: 2q+1
       441: 2q
       442: q+1
       443: q^2+2q+1
       444: q
       445: 2q
       446: q^2+1
       447: q+1
       450: q+1
       451: q
       452: 1
       453: 2q+1
       454: q
       455: 2q
       456: q^2+1
       457: q
       458: 2q+1
       459: 2q
       460: q+1
       461: q
       462: q^2+2q+1
       463: 2q
       464: q^2+1
       465: 2q
       466: q^2+1
       467: q
       468: 1
       469: q
       470: 1
       471: q^2+2q+1
       472: q
       473: q
       474: q^2+2q+1
       475: q^2+2q
       476: q^2+q+1
       477: 2q
       478: q^2+1
       479: q^2+2q
       480: q^2+q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: 2q
       486: q^2+1
       487: 2q
       488: q^2+1
       489: q^2+q
       490: q^3+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+3q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+2q+1
       513: 3q+1
       514: q^2+2q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       522: 1
       530: 1
       534: 1
       537: q
       538: q^2+1
       539: q
       541: q
       542: q+1
       543: q
       545: q
       546: q^2+1
       547: q
       551: 1
       553: q
       555: q
       556: q^2+1
       557: q
       559: q
       560: q+1
       561: q
       563: q
       564: q^2+1
       565: q
       566: q^2+q+1
       568: q
       569: q
       570: q
       571: q^2+1
       573: q
       574: q^2+q+1
       575: q
       577: 2q
       581: q^2+1
       585: q
       586: 1
       589: q+1
       592: q+1
       593: q+1
       596: q+1
       597: q
       598: 1
       599: q
       600: 1
       601: 2q
       602: q^2+1
       603: q+1
       605: q
       606: 1
       608: q+1
       609: q
       610: 1
       613: q
       614: 1
       615: q^2+2q+1
       616: q
       617: 2q
       618: q^2+1
       619: q+1
       622: q+1
       623: q
       624: 1
       625: q
       626: 1
       629: q
       630: 1
       631: q
       632: q^2+2q+1
       633: 2q
       634: q^2+1
       639: q
       640: 1
       641: q+1
       644: q+1
       645: q
       646: 1
       647: 2q+1
       648: q
       649: q
       650: 2q+1
       651: 2q
       652: q^2+1
       653: 2q
       654: q+1
       655: q^2+2q
       656: q^2+q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 2q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 3q+1
       679: q^2+2q+1
       680: 2q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: q^2+2q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: q^2+2q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       699: q^2+1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       733: q
       734: q^2+1
       735: q
       740: 1
       744: 1
       749: q
       751: q
       752: q^2+1
       754: 1
       757: q
       758: q
       759: q^2+1
       761: q
       762: q
       763: q+1
       765: q
       766: q^2+q+1
       768: q
       769: 2q
       773: q^2+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 1
       785: q+1
       788: q+1
       791: q
       792: 1
       793: 2
       795: q+1
       796: q+1
       797: q
       798: 1
       801: q+1
       804: q+1
       805: q+1
       808: q+1
       809: q
       810: 1
       811: q
       812: 1
       815: 2q+1
       816: q
       818: 2
       819: q+1
       820: q+1
       821: q
       822: 1
       825: q+1
       828: q+1
       829: q+1
       832: q+1
       833: q
       834: 1
       835: q
       836: 1
       839: q
       840: 2q+1
       843: 2q
       844: 2
       845: q+1
       848: q+1
       849: q
       850: 1
       851: q
       852: 1
       855: q
       856: 1
       857: 2q
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 2q+1
       872: 2q+1
       873: q+1
       874: 2q+2
       875: 2q+1
       876: 2q+1
       877: 2q+1
       878: 2q+1
       879: 2q+1
       880: q^2+2q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       889: q
       890: q^2+1
       903: 1
       905: 1
       909: 1
       916: 1
       917: 1
       921: 1
       926: 1
       929: 1
       942: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       965: 2
       968: q
       969: q
       971: 1
       972: 1
       976: 1
       988: q
       989: q+1
       991: q
       994: 1
       995: 1
       999: 2
      1000: 2
      1004: q+1
      1007: q+1
      1008: q
      1009: 1
      1010: q
      1011: 1
      1012: 2q
      1013: 2
      1016: 1
      1020: q+1
      1021: q+1
      1022: q
      1023: 1
      1026: q+1
      1029: q+1
      1033: 1
      1036: q+1
      1037: q+1
      1038: q
      1039: 1
      1040: q+1
      1045: q+1
      1046: q
      1047: 1
      1048: q
      1049: 1
      1052: q+1
      1055: q+1
      1056: q+1
      1059: q+1
      1060: q
      1061: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+2
      1085: 2q+1
      1089: 1
      1092: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1128: 1
      1131: 2
      1136: 1
      1138: q
      1139: q
      1141: 1
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1195: 1
      1200: 1
      1205: 1
      1207: 1
      1217: 1
      1218: 1
      1220: q
      1221: 1
      1224: q
      1225: 1
      1228: 1
      1230: 1
      1231: 1
      1233: 2
      1234: 2
      1240: q+1
      1243: q+1
      1247: 1
      1248: 1
      1249: 1
      1251: 2
      1254: 2
      1258: q+1
      1261: q+1
      1262: q
      1263: 1
      1266: q
      1267: 1
      1268: q+1
      1271: q+1
      1274: q+1
      1275: q+1
      1276: q
      1277: 1
      1278: q
      1279: 1
      1280: 2q
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1293: 1
      1296: 1
      1327: 1
      1332: 1
      1350: 1
      1351: 1
      1356: 1
      1357: 1
      1363: 1
      1366: 2
      1371: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1394: 1
      1397: 2
      1402: 1
      1411: 1
      1421: 1
      1423: 1
      1427: 1
      1430: q
      1431: q
      1433: 1
      1434: 1
      1441: 1
      1442: 1
      1444: q
      1445: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1464: 1
      1465: 1
      1467: 2
      1468: 2
      1474: q
      1475: 1
      1476: q+1
      1479: q+1
      1482: q
      1483: 1
      1484: 2
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1505: 1
      1508: 1
      1516: 1
      1519: 1
      1550: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1609: 1
      1610: 1
      1615: 1
      1616: 1
      1620: 1
      1624: 2
      1628: 1
      1641: 1
      1642: 1
      1646: 1
      1647: 1
      1650: 2
      1654: 1
      1655: 1
      1657: 2
      1664: 1
      1665: 1
      1669: q
      1670: 1
      1673: 1
      1674: 1
      1714: 1
      1716: 1
      1751: 1
      1759: 1
      1760: 1
      1774: 1
      1781: 1
      1782: 1
      1798: 1
      1809: 1
      1812: 2
      1820: 1
      1821: 1
      1830: 1
      1831: 1
      1833: 1
      1884: 1
      1887: 1
      1941: 1
      1953: 1
      1963: 1
      1964: 1
      2065: 1

2066:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+3q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+2q
        38: q^3+q^2+q+1
        39: 2q^2+2q
        40: q^3+q^2+q+1
        41: 2q^2+2q
        42: q^3+q^2+q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q^2+2q+1
        59: q
        60: q
        61: q^2+2q+1
        62: q^2+2q
        63: q^2+q+1
        64: 2q^2+2q
        65: q^3+q^2+q+1
        66: q^2+2q
        67: q^2+q+1
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+2q
        75: q^3+q^2+q+1
        76: 2q^2+2q
        77: q^3+q^2+q+1
        78: 2q^2+2q
        79: q^3+q^2+q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^3+3q^2+3q+1
       101: q^3+3q^2+3q+1
       102: q^3+3q^2+3q+1
       103: q
       105: q^2+q+1
       106: q
       107: q
       108: q^2+2q+1
       109: q^2+2q+1
       110: q
       111: q^2+2q
       112: q^2+q+1
       113: q^2+2q
       114: q^2+q+1
       115: 2q^2+2q
       116: q^3+q^2+q+1
       117: q^2+2q+1
       118: q
       119: q
       120: q^2+2q+1
       121: q^2+2q
       122: q^2+q+1
       123: q^2+2q
       124: q^2+q+1
       125: 3q+1
       126: 2q+1
       127: 2q
       128: q^2+1
       129: 2q
       130: q^2+1
       131: q^2+q
       132: q^3+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: q^3+3q^2+3q+1
       151: 2q^2+2q
       152: q^3+q^2+q+1
       153: 2q^2+2q
       154: q^3+q^2+q+1
       155: 2q^2+2q
       156: q^3+q^2+q+1
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^3+2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q^3+2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^3+2q^2+2q+1
       169: q
       171: q^2+q+1
       172: q
       173: q
       175: q^2+q+1
       176: q
       177: q
       178: 1
       179: 2q
       180: q^2+1
       181: 2q
       182: q^2+1
       183: q
       184: q^2+2q+1
       185: q^2+2q+1
       186: q
       187: q^2+2q
       188: q^2+q+1
       189: q^2+2q
       190: q^2+q+1
       191: 2q+1
       192: q
       193: q
       194: q^2+2q+1
       195: q^2+2q+1
       196: q
       197: q^2+2q
       198: q^2+q+1
       199: q
       200: 2q+1
       201: q
       202: q^2+2q+1
       203: q^2+2q+1
       204: q
       205: q^2+2q
       206: q^2+q+1
       207: 2q
       208: q+1
       209: q^2+2q
       210: q^2+q+1
       211: 2q^2+2q
       212: q^3+q^2+q+1
       213: 2q
       214: q^2+1
       215: 2q
       216: q^2+1
       217: q^2+q
       218: q^3+1
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: 2q
       238: q^2+1
       239: 2q
       240: q^2+1
       241: q^2+q
       242: q^3+1
       243: q^2+3q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q^3+2q^2+2q+1
       259: q
       261: q^2+1
       262: q
       263: q
       265: q^2+q+1
       266: q
       267: q
       269: q
       270: q^2+q+1
       271: q
       272: q^2+q+1
       273: q
       275: q
       277: q+1
       278: q
       279: 2q
       280: q^2+1
       281: q
       282: 1
       284: q+1
       285: q+1
       287: q
       288: 1
       289: 2q
       290: q^2+1
       291: q
       292: 1
       293: q
       294: 2q+1
       295: 2q+1
       296: q
       297: 2q
       298: q+1
       299: q
       300: q^2+2q+1
       301: 2q
       302: q^2+1
       303: q^2+2q+1
       304: q
       305: q^2+2q
       306: q^2+q+1
       307: q
       308: q^2+2q+1
       309: q^2+2q+1
       310: q
       311: 2q
       312: q^2+1
       313: q^2+2q
       314: q^2+q+1
       315: q
       316: 1
       317: 2q
       318: q^2+1
       319: q
       320: q^2+2q+1
       321: q^2+2q+1
       322: q
       323: q^2+2q
       324: q^2+q+1
       325: q^2+2q
       326: q^2+q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q
       339: q^2+1
       340: 2q
       341: q^2+1
       342: q^2+q
       343: q^3+1
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: q^2+2q+1
       351: 2q^2+3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: 2q^2+3q+1
       360: 2q
       361: q^2+1
       362: 2q
       363: q^2+1
       364: q^2+q
       365: q^3+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q^2+3q+1
       372: 2q^2+3q+1
       373: q^3+2q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       379: 1
       381: q
       383: q^2+1
       384: q
       385: q
       387: q+1
       388: q
       389: q
       391: q
       392: q^2+1
       393: q
       395: q^2+q+1
       396: q
       397: q
       398: q^2+1
       399: q
       401: q
       402: q^2+q+1
       404: q
       405: q
       406: q
       408: q^2+q+1
       413: q
       414: 1
       417: q
       418: 1
       420: q+1
       421: q+1
       423: q
       424: 1
       425: q
       426: 1
       427: 2q
       428: q^2+1
       430: q+1
       431: q+1
       433: q
       434: 1
       435: 2q
       436: q^2+1
       437: q
       438: 2q+1
       439: 2q+1
       440: q
       441: 2q
       442: q+1
       443: q
       444: q^2+2q+1
       445: 2q
       446: q^2+1
       448: q+1
       449: q+1
       451: q
       452: 1
       453: q
       454: 2q+1
       455: 2q
       456: q^2+1
       457: 2q+1
       458: q
       459: 2q
       460: q+1
       461: q^2+2q+1
       462: q
       463: 2q
       464: q^2+1
       465: 2q
       466: q^2+1
       467: q
       468: 1
       469: q
       470: 1
       471: q
       472: q^2+2q+1
       473: q^2+2q+1
       474: q
       475: q^2+2q
       476: q^2+q+1
       477: 2q
       478: q^2+1
       479: q^2+2q
       480: q^2+q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: 2q
       486: q^2+1
       487: 2q
       488: q^2+1
       489: q^2+q
       490: q^3+1
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+3q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+2q+1
       513: 3q+1
       514: q^2+2q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       523: 1
       531: 1
       535: 1
       537: q
       539: q
       540: q^2+1
       541: q
       543: q
       544: q+1
       545: q
       547: q
       548: q^2+1
       550: 1
       553: q
       554: q^2+1
       555: q
       557: q
       558: q+1
       559: q
       561: q
       562: q^2+1
       563: q
       565: q
       567: q^2+q+1
       568: q
       569: q
       570: q
       572: q^2+1
       573: q
       575: q
       576: q^2+q+1
       577: 2q
       581: q^2+1
       585: q
       586: 1
       590: q+1
       591: q+1
       594: q+1
       595: q+1
       597: q
       598: 1
       599: q
       600: 1
       601: 2q
       602: q^2+1
       604: q+1
       605: q
       606: 1
       607: q+1
       609: q
       610: 1
       613: q
       614: 1
       615: q
       616: q^2+2q+1
       617: 2q
       618: q^2+1
       620: q+1
       621: q+1
       623: q
       624: 1
       625: q
       626: 1
       629: q
       630: 1
       631: q^2+2q+1
       632: q
       633: 2q
       634: q^2+1
       639: q
       640: 1
       642: q+1
       643: q+1
       645: q
       646: 1
       647: q
       648: 2q+1
       649: 2q+1
       650: q
       651: 2q
       652: q^2+1
       653: 2q
       654: q+1
       655: q^2+2q
       656: q^2+q+1
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 2q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 3q+1
       679: q^2+2q+1
       680: 2q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: q^2+2q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: q^2+2q+1
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       700: q^2+1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       733: q
       735: q
       736: q^2+1
       738: 1
       742: 1
       749: q
       750: q^2+1
       751: q
       755: 1
       757: q
       758: q
       760: q^2+1
       761: q
       762: q
       764: q+1
       765: q
       767: q^2+q+1
       768: q
       769: 2q
       773: q^2+1
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: q
       782: 1
       786: q+1
       787: q+1
       791: q
       792: 1
       794: 2
       795: q+1
       796: q+1
       797: q
       798: 1
       802: q+1
       803: q+1
       806: q+1
       807: q+1
       809: q
       810: 1
       811: q
       812: 1
       815: q
       816: 2q+1
       817: 2
       819: q+1
       820: q+1
       821: q
       822: 1
       826: q+1
       827: q+1
       830: q+1
       831: q+1
       833: q
       834: 1
       835: q
       836: 1
       839: 2q+1
       840: q
       843: 2q
       844: 2
       846: q+1
       847: q+1
       849: q
       850: 1
       851: q
       852: 1
       855: q
       856: 1
       857: 2q
       858: q+1
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 2q+1
       872: 2q+1
       873: q+1
       874: 2q+2
       875: 2q+1
       876: 2q+1
       877: 2q+1
       878: 2q+1
       879: 2q+1
       880: q^2+2q+1
       881: q+1
       882: q+1
       883: q+1
       884: q
       889: q
       891: q^2+1
       901: 1
       907: 1
       910: 1
       918: 1
       919: 1
       923: 1
       925: 1
       931: 1
       940: 1
       941: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 2
       968: q
       969: q
       971: 1
       972: 1
       977: 1
       988: q
       990: q+1
       991: q
       994: 1
       995: 1
       998: 2
      1001: 2
      1005: q+1
      1006: q+1
      1008: q
      1009: 1
      1010: q
      1011: 1
      1012: 2q
      1013: 2
      1017: 1
      1020: q+1
      1021: q+1
      1022: q
      1023: 1
      1027: q+1
      1028: q+1
      1032: 1
      1036: q+1
      1037: q+1
      1038: q
      1039: 1
      1041: q+1
      1044: q+1
      1046: q
      1047: 1
      1048: q
      1049: 1
      1053: q+1
      1054: q+1
      1057: q+1
      1058: q+1
      1060: q
      1061: 1
      1062: q
      1063: 1
      1064: q
      1065: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+2
      1085: 2q+1
      1090: 1
      1093: 1
      1114: 1
      1115: 1
      1124: 1
      1125: 1
      1129: 1
      1132: 2
      1137: 1
      1138: q
      1139: q
      1141: 1
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1196: 1
      1201: 1
      1203: 1
      1209: 1
      1216: 1
      1219: 1
      1220: q
      1221: 1
      1224: q
      1225: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 2
      1235: 2
      1241: q+1
      1242: q+1
      1246: 1
      1248: 1
      1249: 1
      1250: 2
      1255: 2
      1259: q+1
      1260: q+1
      1262: q
      1263: 1
      1266: q
      1267: 1
      1269: q+1
      1270: q+1
      1274: q+1
      1275: q+1
      1276: q
      1277: 1
      1278: q
      1279: 1
      1280: 2q
      1281: 2
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1294: 1
      1297: 1
      1328: 1
      1333: 1
      1348: 1
      1349: 1
      1358: 1
      1359: 1
      1362: 1
      1365: 2
      1370: 1
      1380: 1
      1381: 1
      1390: 1
      1391: 1
      1395: 1
      1398: 2
      1403: 1
      1412: 1
      1419: 1
      1425: 1
      1428: 1
      1430: q
      1431: q
      1433: 1
      1434: 1
      1440: 1
      1443: 1
      1444: q
      1445: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 2
      1469: 2
      1474: q
      1475: 1
      1477: q+1
      1478: q+1
      1482: q
      1483: 1
      1484: 2
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1504: 1
      1507: 1
      1517: 1
      1520: 1
      1551: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1607: 1
      1608: 1
      1617: 1
      1618: 1
      1621: 1
      1625: 2
      1629: 1
      1641: 1
      1642: 1
      1645: 1
      1648: 1
      1649: 2
      1653: 1
      1656: 1
      1658: 2
      1663: 1
      1666: 1
      1669: q
      1670: 1
      1673: 1
      1674: 1
      1715: 1
      1717: 1
      1750: 1
      1757: 1
      1758: 1
      1775: 1
      1783: 1
      1784: 1
      1799: 1
      1810: 1
      1813: 2
      1819: 1
      1822: 1
      1829: 1
      1832: 1
      1833: 1
      1885: 1
      1888: 1
      1942: 1
      1954: 1
      1962: 1
      1965: 1
      2066: 1

2067:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^4+2q^3+2q^2+2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+2q^2+2q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+3q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^3+3q^2+3q+1
        36: 2q^2+3q+1
        37: q^3+q^2+q+1
        38: 2q^2+2q
        39: q^3+q^2+q+1
        40: 2q^2+2q
        41: q^3+q^2+q+1
        42: 2q^2+2q
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+2q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: q^3+3q^2+3q+1
        56: q^3+3q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q
        59: q^2+2q+1
        60: q
        61: q^2+2q+1
        62: q^2+q+1
        63: q^2+2q
        64: q^3+q^2+q+1
        65: 2q^2+2q
        66: q^2+q+1
        67: q^2+2q
        68: q^2+3q+1
        69: q^2+2q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q^3+q^2+q+1
        75: 2q^2+2q
        76: q^3+q^2+q+1
        77: 2q^2+2q
        78: q^3+q^2+q+1
        79: 2q^2+2q
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 3q+1
        89: 3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^3+2q^2+2q+1
       100: q^3+3q^2+3q+1
       101: q^3+3q^2+3q+1
       102: q^3+3q^2+3q+1
       104: q
       105: q
       106: q^2+q+1
       107: q
       108: q^2+2q+1
       109: q
       110: q^2+2q+1
       111: q^2+q+1
       112: q^2+2q
       113: q^2+q+1
       114: q^2+2q
       115: q^3+q^2+q+1
       116: 2q^2+2q
       117: q
       118: q^2+2q+1
       119: q
       120: q^2+2q+1
       121: q^2+q+1
       122: q^2+2q
       123: q^2+q+1
       124: q^2+2q
       125: 3q+1
       126: 2q+1
       127: q^2+1
       128: 2q
       129: q^2+1
       130: 2q
       131: q^3+1
       132: q^2+q
       133: q^2+3q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 3q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 3q+1
       144: q^2+2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+q^2+q+1
       152: 2q^2+2q
       153: q^3+q^2+q+1
       154: 2q^2+2q
       155: q^3+q^2+q+1
       156: 2q^2+2q
       157: 3q+1
       158: 3q+1
       159: q^2+2q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^3+2q^2+2q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q^3+2q^2+2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^3+2q^2+2q+1
       170: q
       171: q
       172: q^2+q+1
       174: q
       175: q
       176: q^2+q+1
       177: 1
       178: q
       179: q^2+1
       180: 2q
       181: q^2+1
       182: 2q
       183: q
       184: q^2+2q+1
       185: q
       186: q^2+2q+1
       187: q^2+q+1
       188: q^2+2q
       189: q^2+q+1
       190: q^2+2q
       191: q
       192: 2q+1
       193: q
       194: q^2+2q+1
       195: q
       196: q^2+2q+1
       197: q^2+q+1
       198: q^2+2q
       199: q
       200: 2q+1
       201: q
       202: q^2+2q+1
       203: q
       204: q^2+2q+1
       205: q^2+q+1
       206: q^2+2q
       207: q+1
       208: 2q
       209: q^2+q+1
       210: q^2+2q
       211: q^3+q^2+q+1
       212: 2q^2+2q
       213: q^2+1
       214: 2q
       215: q^2+1
       216: 2q
       217: q^3+1
       218: q^2+q
       219: 2q+1
       220: 3q+1
       221: 2q+1
       222: 3q+1
       223: q^2+2q+1
       224: 3q+1
       225: q^2+2q+1
       226: 2q+1
       227: q^2+3q+1
       228: q^2+2q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+2q+1
       237: q^2+1
       238: 2q
       239: q^2+1
       240: 2q
       241: q^3+1
       242: q^2+q
       243: q^2+3q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^3+2q^2+2q+1
       250: 3q+1
       251: 3q+1
       252: q^2+2q+1
       253: 3q+1
       254: 3q+1
       255: q^2+2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q^3+2q^2+2q+1
       260: q
       261: q
       262: q^2+1
       264: q
       265: q
       266: q^2+q+1
       268: q
       269: q^2+q+1
       270: q
       272: q
       273: q^2+q+1
       274: q
       276: q
       277: q
       278: q+1
       279: q^2+1
       280: 2q
       281: 1
       282: q
       284: q+1
       286: q+1
       287: 1
       288: q
       289: q^2+1
       290: 2q
       291: 1
       292: q
       293: q
       294: 2q+1
       295: q
       296: 2q+1
       297: q+1
       298: 2q
       299: q
       300: q^2+2q+1
       301: q^2+1
       302: 2q
       303: q
       304: q^2+2q+1
       305: q^2+q+1
       306: q^2+2q
       307: q
       308: q^2+2q+1
       309: q
       310: q^2+2q+1
       311: q^2+1
       312: 2q
       313: q^2+q+1
       314: q^2+2q
       315: 1
       316: q
       317: q^2+1
       318: 2q
       319: q
       320: q^2+2q+1
       321: q
       322: q^2+2q+1
       323: q^2+q+1
       324: q^2+2q
       325: q^2+q+1
       326: q^2+2q
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: q^2+1
       339: 2q
       340: q^2+1
       341: 2q
       342: q^3+1
       343: q^2+q
       344: 2q+1
       345: 3q+1
       346: 2q+1
       347: 3q+1
       348: q^2+2q+1
       349: 3q+1
       350: q^2+2q+1
       351: 2q^2+3q+1
       352: 2q+1
       353: 3q+1
       354: 2q+1
       355: 3q+1
       356: q^2+2q+1
       357: 3q+1
       358: q^2+2q+1
       359: 2q^2+3q+1
       360: q^2+1
       361: 2q
       362: q^2+1
       363: 2q
       364: q^3+1
       365: q^2+q
       366: 2q+1
       367: q^2+3q+1
       368: q^2+2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 2q^2+3q+1
       372: 2q^2+3q+1
       373: q^3+2q^2+2q+1
       374: 3q+1
       375: 3q+1
       376: q^2+2q+1
       380: 1
       382: q
       383: q
       384: q^2+1
       386: q
       387: q
       388: q+1
       390: q
       391: q^2+1
       392: q
       394: q
       395: q
       396: q^2+q+1
       398: q
       399: q^2+1
       400: q
       402: q
       403: q
       404: q^2+q+1
       406: q^2+q+1
       407: q
       408: q
       413: 1
       414: q
       417: 1
       418: q
       420: q+1
       422: q+1
       423: 1
       424: q
       425: 1
       426: q
       427: q^2+1
       428: 2q
       430: q+1
       432: q+1
       433: 1
       434: q
       435: q^2+1
       436: 2q
       437: q
       438: 2q+1
       439: q
       440: 2q+1
       441: q+1
       442: 2q
       443: q
       444: q^2+2q+1
       445: q^2+1
       446: 2q
       448: q+1
       450: q+1
       451: 1
       452: q
       453: q
       454: 2q+1
       455: q^2+1
       456: 2q
       457: q
       458: 2q+1
       459: q+1
       460: 2q
       461: q
       462: q^2+2q+1
       463: q^2+1
       464: 2q
       465: q^2+1
       466: 2q
       467: 1
       468: q
       469: 1
       470: q
       471: q
       472: q^2+2q+1
       473: q
       474: q^2+2q+1
       475: q^2+q+1
       476: q^2+2q
       477: q^2+1
       478: 2q
       479: q^2+q+1
       480: q^2+2q
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: q^2+1
       486: 2q
       487: q^2+1
       488: 2q
       489: q^3+1
       490: q^2+q
       491: q^2+2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q^2+3q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 2q^2+3q+1
       508: 2q+1
       509: 3q+1
       510: 2q+1
       511: 3q+1
       512: q^2+2q+1
       513: 3q+1
       514: q^2+2q+1
       515: 2q+2
       516: 2q+2
       517: 2q+2
       518: 3q+1
       519: 3q+1
       520: q^2+2q+1
       524: 1
       532: 1
       536: 1
       538: q
       539: q^2+1
       540: q
       542: q
       543: q+1
       544: q
       546: q
       547: q^2+1
       548: q
       552: 1
       554: q
       555: q^2+1
       556: q
       558: q
       559: q+1
       560: q
       562: q
       563: q^2+1
       564: q
       566: q
       567: q
       568: q^2+q+1
       570: q^2+1
       571: q
       572: q
       574: q
       575: q^2+q+1
       576: q
       577: q^2+1
       581: 2q
       585: 1
       586: q
       590: q+1
       592: q+1
       594: q+1
       596: q+1
       597: 1
       598: q
       599: 1
       600: q
       601: q^2+1
       602: 2q
       604: q+1
       605: 1
       606: q
       608: q+1
       609: 1
       610: q
       613: 1
       614: q
       615: q
       616: q^2+2q+1
       617: q^2+1
       618: 2q
       620: q+1
       622: q+1
       623: 1
       624: q
       625: 1
       626: q
       629: 1
       630: q
       631: q
       632: q^2+2q+1
       633: q^2+1
       634: 2q
       639: 1
       640: q
       642: q+1
       644: q+1
       645: 1
       646: q
       647: q
       648: 2q+1
       649: q
       650: 2q+1
       651: q^2+1
       652: 2q
       653: q+1
       654: 2q
       655: q^2+q+1
       656: q^2+2q
       657: 2
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 2q+2
       665: 2q+1
       672: 3q+1
       673: 2q+1
       674: 2q+2
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: 3q+1
       679: q^2+2q+1
       680: 2q+2
       681: 2q+1
       682: 2q+1
       683: 2q+1
       684: 3q+1
       685: q^2+2q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: q^2+2q+1
       690: q+1
       691: q+1
       692: q+1
       697: q^2+1
       699: q
       700: q
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       734: q
       735: q^2+1
       736: q
       739: 1
       743: 1
       750: q
       751: q^2+1
       752: q
       756: 1
       758: q^2+1
       759: q
       760: q
       762: q+1
       763: q
       764: q
       766: q
       767: q
       768: q^2+q+1
       769: q^2+1
       773: 2q
       775: 1
       776: 1
       779: q+1
       780: q+1
       781: 1
       782: q
       786: q+1
       788: q+1
       791: 1
       792: q
       794: 2
       795: q+1
       796: q+1
       797: 1
       798: q
       802: q+1
       804: q+1
       806: q+1
       808: q+1
       809: 1
       810: q
       811: 1
       812: q
       815: q
       816: 2q+1
       818: 2
       819: q+1
       820: q+1
       821: 1
       822: q
       826: q+1
       828: q+1
       830: q+1
       832: q+1
       833: 1
       834: q
       835: 1
       836: q
       839: q
       840: 2q+1
       843: 2
       844: 2q
       846: q+1
       848: q+1
       849: 1
       850: q
       851: 1
       852: q
       855: 1
       856: q
       857: q+1
       858: 2q
       865: 1
       866: 2
       867: q+1
       868: 2q+1
       869: q+1
       870: 2q+2
       871: 2q+1
       872: 2q+1
       873: q+1
       874: 2q+2
       875: 2q+1
       876: 2q+1
       877: 2q+1
       878: 2q+1
       879: 2q+1
       880: q^2+2q+1
       881: q+1
       882: q+1
       883: q+1
       889: q^2+1
       890: q
       891: q
       902: 1
       906: 1
       911: 1
       918: 1
       919: 1
       922: 1
       927: 1
       930: 1
       942: 1
       943: 1
       946: 1
       950: 1
       955: 1
       961: 1
       967: 2
       968: 1
       969: 1
       971: q
       972: q
       975: 1
       989: q
       990: q
       991: q+1
       994: 1
       995: 1
       999: 2
      1001: 2
      1005: q+1
      1007: q+1
      1008: 1
      1009: q
      1010: 1
      1011: q
      1012: 2
      1013: 2q
      1017: 1
      1020: q+1
      1021: q+1
      1022: 1
      1023: q
      1027: q+1
      1029: q+1
      1033: 1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q
      1041: q+1
      1045: q+1
      1046: 1
      1047: q
      1048: 1
      1049: q
      1053: q+1
      1055: q+1
      1057: q+1
      1059: q+1
      1060: 1
      1061: q
      1062: 1
      1063: q
      1064: 1
      1065: q
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 2
      1077: q+1
      1078: 2q+1
      1079: q+1
      1080: 2
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+2
      1085: 2q+1
      1091: 1
      1094: 1
      1116: 1
      1117: 1
      1124: 1
      1125: 1
      1127: 1
      1133: 2
      1135: 1
      1138: 1
      1139: 1
      1141: q
      1142: q
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1221: q
      1224: 1
      1225: q
      1229: 1
      1230: 1
      1231: 1
      1233: 2
      1235: 2
      1241: q+1
      1243: q+1
      1247: 1
      1248: 1
      1249: 1
      1251: 2
      1255: 2
      1259: q+1
      1261: q+1
      1262: 1
      1263: q
      1266: 1
      1267: q
      1269: q+1
      1271: q+1
      1274: q+1
      1275: q+1
      1276: 1
      1277: q
      1278: 1
      1279: q
      1280: 2
      1281: 2q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 2
      1288: q+1
      1289: 2q+1
      1295: 1
      1298: 1
      1329: 1
      1331: 1
      1350: 1
      1351: 1
      1358: 1
      1359: 1
      1361: 1
      1367: 2
      1369: 1
      1382: 1
      1383: 1
      1390: 1
      1391: 1
      1393: 1
      1399: 2
      1401: 1
      1413: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1431: 1
      1433: q
      1434: q
      1441: 1
      1443: 1
      1444: 1
      1445: q
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 2
      1469: 2
      1474: 1
      1475: q
      1477: q+1
      1479: q+1
      1482: 1
      1483: q
      1484: 2
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1506: 1
      1509: 1
      1518: 1
      1521: 1
      1552: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1610: 1
      1617: 1
      1618: 1
      1622: 1
      1626: 2
      1630: 1
      1641: 1
      1642: 1
      1646: 1
      1648: 1
      1650: 2
      1654: 1
      1656: 1
      1658: 2
      1664: 1
      1666: 1
      1669: 1
      1670: q
      1673: 1
      1674: 1
      1718: 1
      1720: 1
      1752: 1
      1759: 1
      1760: 1
      1776: 1
      1783: 1
      1784: 1
      1800: 1
      1808: 1
      1814: 2
      1820: 1
      1822: 1
      1830: 1
      1832: 1
      1833: 1
      1889: 1
      1890: 1
      1943: 1
      1955: 1
      1963: 1
      1965: 1
      2067: 1

2068:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+1
        59: q
        60: 1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       106: q
       107: 1
       108: q
       109: q^2+1
       110: q
       111: q+1
       113: q+1
       115: q+1
       117: q^2+1
       118: q
       119: 1
       120: q
       121: q+1
       123: q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       172: q
       173: 1
       176: q
       177: q+1
       179: q+1
       181: q+1
       183: 1
       184: q
       185: q^2+1
       186: q
       187: q+1
       189: q+1
       191: q^2+1
       192: q
       193: 1
       194: q
       195: q^2+1
       196: q
       197: q+1
       199: 1
       200: q
       201: 1
       202: q
       203: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       262: q
       263: 1
       266: q
       267: 1
       269: q
       271: 1
       275: 1
       278: q
       279: q+1
       281: q+1
       283: 1
       284: q
       285: q^2+1
       286: q
       287: q+1
       289: q+1
       291: q+1
       293: 1
       294: q
       295: q^2+1
       296: q
       297: q+1
       299: 1
       300: q
       301: q+1
       303: q^2+1
       304: q
       305: q+1
       307: 1
       308: q
       309: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: 1
       320: q
       321: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       380: q
       381: 1
       384: q
       385: 1
       388: q
       389: 1
       391: q
       393: 1
       396: q
       397: 1
       401: 1
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: 1
       420: q
       421: q^2+1
       422: q
       423: q+1
       425: q+1
       427: q+1
       429: 1
       430: q
       431: q^2+1
       432: q
       433: q+1
       435: q+1
       437: 1
       438: q
       439: q^2+1
       440: q
       441: q+1
       443: 1
       444: q
       445: q+1
       447: 1
       448: q
       449: 1
       451: 1
       453: 1
       454: q
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       472: q
       473: 1
       475: 1
       477: 1
       479: 1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       525: 1
       528: q
       529: 1
       532: q
       533: 1
       536: q
       537: 1
       539: q
       541: 1
       543: q
       545: 1
       547: q
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: q+1
       585: q+1
       587: q+1
       589: 1
       590: q
       591: 1
       593: 1
       594: q
       595: q^2+1
       596: q
       597: q+1
       599: q+1
       601: q+1
       603: 1
       604: q
       605: q+1
       607: q^2+1
       608: q
       609: q+1
       611: q+1
       613: q+1
       615: 1
       616: q
       617: q+1
       619: 1
       620: q
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       642: q
       643: 1
       645: 1
       647: 1
       648: q
       649: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       705: 1
       708: q
       709: 1
       712: q
       713: 1
       717: 1
       720: q
       721: 1
       723: q
       725: 1
       727: q
       729: 1
       731: q
       733: 1
       735: q
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       786: q
       787: 1
       789: q+1
       791: 1
       793: 1
       794: q
       795: q+1
       797: q+1
       799: q+1
       801: 1
       802: q
       803: 1
       805: 1
       806: q
       807: q^2+1
       808: q
       809: q+1
       811: q+1
       813: q+1
       815: 1
       816: q
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       826: q
       827: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: q+1
       843: 1
       845: 1
       846: q
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       896: 1
       899: q
       900: 1
       904: 1
       906: q
       908: 1
       912: 1
       914: q
       916: 1
       918: q
       920: 1
       922: q
       924: 1
       928: 1
       930: q
       932: 1
       934: q
       936: 1
       940: 1
       944: 1
       948: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
      1000: 1
      1001: q
      1002: q+1
      1004: 1
      1005: q
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: 1
      1017: q
      1018: q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: 1
      1027: q
      1028: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1053: q
      1054: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1120: q
      1122: 1
      1124: q
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1146: q
      1148: 1
      1150: q
      1152: 1
      1156: 1
      1158: q
      1160: 1
      1164: 1
      1168: 1
      1172: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1202: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1216: 1
      1218: 1
      1219: q
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1228: 1
      1229: q
      1230: q+1
      1232: 1
      1234: 1
      1235: q
      1236: q+1
      1238: q+1
      1240: 1
      1241: q
      1242: 1
      1244: 1
      1246: 1
      1248: 1
      1250: 1
      1252: 1
      1256: 1
      1260: 1
      1262: 1
      1264: 1
      1266: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1320: q
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1342: q
      1344: 1
      1348: 1
      1352: 1
      1354: q
      1356: 1
      1358: q
      1360: 1
      1364: 1
      1368: 1
      1372: 1
      1376: 1
      1380: 1
      1404: 1
      1410: 1
      1414: 1
      1418: 1
      1430: 1
      1436: 1
      1438: q+1
      1440: 1
      1442: 1
      1443: q
      1444: 1
      1446: 1
      1448: q+1
      1450: 1
      1452: q+1
      1454: 1
      1455: q
      1456: 1
      1458: 1
      1460: 1
      1464: 1
      1466: 1
      1470: 1
      1472: 1
      1474: 1
      1478: 1
      1480: 1
      1482: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1501: 1
      1525: 1
      1537: 1
      1541: 1
      1545: 1
      1547: q
      1549: 1
      1553: 1
      1559: 1
      1563: 1
      1567: 1
      1569: q
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1603: 1
      1607: 1
      1631: 1
      1637: 1
      1639: 1
      1641: 1
      1643: q+1
      1645: 1
      1647: 1
      1648: q
      1649: 1
      1651: 1
      1653: 1
      1659: 1
      1661: 1
      1663: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1687: 1
      1723: 1
      1729: 1
      1733: 1
      1737: 1
      1741: 1
      1745: 1
      1747: q
      1749: 1
      1753: 1
      1757: 1
      1761: 1
      1785: 1
      1801: 1
      1815: 1
      1817: 1
      1819: 1
      1823: 1
      1825: 1
      1827: 1
      1829: 1
      1833: 1
      1834: 1
      1846: 1
      1894: 1
      1898: 1
      1902: 1
      1906: 1
      1926: 1
      1932: 1
      1956: 1
      1958: 1
      1960: 1
      1962: 1
      1966: 1
      2026: 1
      2032: 1
      2036: 1
      2040: 1
      2068: 1

2069:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 3q^3+4q^2+2q
        23: 3q^3+4q^2+2q
        24: q^4+3q^3+3q^2+2q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 3q^3+4q^2+2q
        32: 2q^3+3q^2+2q
        33: 3q^3+4q^2+2q
        34: 4q^2+2q
        35: 3q^2+2q
        36: 4q^2+2q
        37: q^2+q
        38: 3q^2+q
        39: q^2+q
        40: 3q^2+q
        41: q^2+q
        42: q^3+2q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 3q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^4+3q^3+3q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: q^3+3q^2+2q
        58: 2q^3+2q^2+2q
        59: q^3+2q^2
        60: q^2+q
        61: 3q^2+q
        62: q^2+q
        63: 3q^2+q
        64: q^2+q
        65: 2q^2+q
        66: q^2+q
        67: 3q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 4q^2+2q
        73: 3q^3+4q^2+2q
        74: q^2+q
        75: 3q^2+q
        76: q^2+q
        77: 3q^2+q
        78: q^2+q
        79: q^3+2q^2+q
        80: 2q^3+3q^2+2q
        81: 2q^3+3q^2+2q
        82: 3q^3+4q^2+2q
        83: 2q^3+3q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 4q^2+2q
        87: 3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q
       104: q^2
       105: 2q^2+q
       106: q^2
       107: q^2+q
       108: 3q^2+q
       109: 2q^3+2q^2+2q
       110: q^3+2q^2
       111: q^2+q
       112: 3q^2+q
       113: q^2+q
       114: 3q^2+q
       115: q^2+q
       116: 2q^2+q
       117: q^3+q^2+2q
       118: q^2
       119: q
       120: 2q^2+q
       121: q^2+q
       122: 2q^2+q
       123: q^2+q
       124: 2q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: q^2+q
       128: 3q^2+q
       129: q^2+q
       130: 3q^2+q
       131: q^2+q
       132: q^3+2q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 3q^2+2q
       136: 2q^3+3q^2+2q
       137: 2q^3+3q^2+2q
       138: 2q^3+3q^2+2q
       139: 3q^3+4q^2+2q
       140: 4q^2+2q
       141: 2q^3+3q^2+2q
       142: 3q^3+4q^2+2q
       143: 3q^2+2q
       144: 3q^2+2q
       145: 4q^2+2q
       146: 3q^2+2q
       147: 4q^2+2q
       148: q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: q^2+q
       152: 3q^2+q
       153: q^2+q
       154: 3q^2+q
       155: q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^3+3q^2+2q
       161: 2q^3+3q^2+2q
       162: 2q^3+3q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q
       170: q^2
       171: 2q^2+q
       172: q^2
       173: q
       175: q^2+q
       176: q^2
       177: q^2+q
       178: 2q^2+q
       179: q^2+q
       180: 3q^2+q
       181: q^2+q
       182: 3q^2+q
       183: q
       184: 2q^2+q
       185: q^3+q^2+2q
       186: q^2
       187: q^2+q
       188: 2q^2+q
       189: q^2+q
       190: 2q^2+q
       191: q^3+q^2+2q
       192: q^2
       193: q^2+q
       194: 3q^2+q
       195: 2q^3+2q^2+2q
       196: q^3+2q^2
       197: q^2+q
       198: 3q^2+q
       199: q
       200: 2q^2+q
       201: q^2+q
       202: 3q^2+q
       203: q^2+2q
       205: q
       206: q^2+q
       207: q^2+q
       208: 2q^2+q
       209: q^2+q
       210: 3q^2+q
       211: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 3q^2+2q
       223: 3q^2+2q
       224: 2q^3+3q^2+2q
       225: 2q^3+3q^2+2q
       226: 2q^3+3q^2+2q
       227: q^3+2q^2+2q
       228: 2q^3+3q^2+2q
       229: 3q^2+2q
       230: 2q^3+3q^2+2q
       231: 3q^2+2q
       232: q^2+2q
       233: 2q^2+2q
       234: 2q^2+2q
       235: 2q
       236: 3q^2+2q
       237: q^2+q
       238: 3q^2+q
       239: q^2+q
       240: 3q^2+q
       241: q^2+q
       242: q^3+2q^2+q
       243: 4q^2+2q
       244: 4q^2+2q
       245: q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^3+3q^2+2q
       251: 2q^3+3q^2+2q
       252: 2q^3+3q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q
       260: q^2
       261: 2q^2+q
       262: q^2
       263: q
       265: q^2+q
       266: q^2
       267: q
       268: q^2
       269: q^2
       270: 2q^2+q
       271: q
       272: q^2+q
       275: q
       277: q^2+q
       278: q^2
       280: q
       282: q^2+q
       283: q
       284: 2q^2+q
       285: q^3+q^2+2q
       286: q^2
       287: q^2+q
       288: 2q^2+q
       290: q^2+q
       291: q^2+q
       292: 2q^2+q
       293: q
       294: 2q^2+q
       295: q^3+q^2+2q
       296: q^2
       297: q^2+q
       298: 2q^2+q
       299: q
       300: 2q^2+q
       301: q^2+q
       302: 3q^2+q
       303: q^3+q^2+2q
       304: q^2
       305: q^2+q
       306: 2q^2+q
       307: q
       308: q^2+q
       309: 2q
       311: q
       312: q^2+q
       313: q
       314: q
       315: q^2+q
       316: 2q^2+q
       317: q^2+q
       318: 3q^2+q
       319: q^2+q
       320: 3q^2+q
       321: q^2+2q
       323: q
       324: q^2+q
       325: q^2+q
       326: 2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+2q
       334: 3q^2+2q
       335: 2q^3+3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: q^2+q
       339: 3q^2+q
       340: q^2+q
       341: 3q^2+q
       342: q^2+q
       343: q^3+2q^2+q
       344: q^3+2q^2+2q
       345: q^3+2q^2+2q
       346: 2q^3+3q^2+2q
       347: 3q^2+2q
       348: 3q^2+2q
       349: 2q^3+3q^2+2q
       350: 2q^3+3q^2+2q
       351: 4q^2+2q
       352: q^2+2q
       353: q^2+2q
       354: 2q^2+2q
       355: 2q^2+2q
       356: 2q^2+2q
       357: 2q
       358: 2q
       359: q^2+2q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q^2+2q
       370: 2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q
       379: q^2+q
       380: q^2
       383: q
       385: q
       387: q^2+q
       388: q^2
       389: q
       390: q^2
       391: q^2
       392: 2q^2+q
       393: q
       395: q^2+q
       396: q^2
       397: q
       398: q^2+q
       401: q
       402: q
       405: q
       408: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q
       420: 2q^2+q
       421: q^3+q^2+2q
       422: q^2
       423: q^2+q
       424: 2q^2+q
       425: q^2+q
       426: 2q^2+q
       427: q^2+q
       428: 3q^2+q
       429: q
       430: 2q^2+q
       431: q^3+q^2+2q
       432: q^2
       433: q^2+q
       434: 2q^2+q
       436: q^2+q
       437: q
       438: 2q^2+q
       439: q^3+q^2+2q
       440: q^2
       441: q^2+q
       442: 2q^2+q
       443: q^2+q
       444: 3q^2+q
       445: q^2+q
       446: 3q^2+q
       447: q
       448: q^2+q
       449: 2q
       451: q
       452: q
       453: q
       454: q^2+q
       456: q
       457: 2q
       459: q
       460: q
       461: q^2+2q
       463: q
       464: q^2+q
       466: q
       468: q^2+q
       469: q^2+q
       470: 2q^2+q
       471: q
       472: q^2+q
       473: 2q
       475: q
       476: q
       477: q
       478: q^2+q
       479: q
       480: q^2+q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: 2q^2+2q
       492: q^3+2q^2+2q
       493: 3q^2+2q
       494: 2q^3+3q^2+2q
       495: 3q^2+2q
       496: 2q^2+2q
       497: q^2+2q
       498: 2q^2+2q
       499: 2q
       500: 2q
       501: 2q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: 2q
       514: 2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       523: q
       527: q
       529: q
       531: q^2+q
       532: q^2
       533: q
       535: q^2+q
       536: q^2
       540: q
       541: q
       543: q^2
       544: q^2+q
       545: q
       546: q^2
       547: q^2
       548: 2q^2+q
       549: q
       550: q
       554: q
       557: q
       558: q
       561: q
       562: q^2+q
       565: q
       567: q
       569: q
       572: q^2+q
       573: q
       576: q^2+q
       577: q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q
       590: q^2+q
       591: 2q
       593: q
       594: 2q^2+q
       595: q^3+q^2+2q
       596: q^2
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q
       603: q
       604: 2q^2+q
       606: q^2+q
       607: q^3+q^2+2q
       608: q^2
       609: q^2+q
       610: 2q^2+q
       612: q^2+q
       613: q^2+q
       614: 2q^2+q
       615: q
       616: q^2+q
       618: q^2+q
       619: q
       620: q^2+q
       621: 2q
       624: q
       625: q
       626: q
       628: q
       629: q
       630: q
       631: 2q
       634: q
       636: q
       638: q^2+q
       640: q
       641: q
       642: q^2+q
       643: 2q
       645: q
       646: q
       647: q
       648: q^2+q
       649: 2q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q^2+2q
       675: q^2+2q
       676: q^3+2q^2+2q
       677: 3q^2+2q
       678: 2q^2+2q
       679: 2q^2+2q
       680: 2q
       681: q^2+2q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+2q
       687: 2q^2+2q
       688: 2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       693: q
       700: q^2+q
       707: q
       711: q
       713: q
       714: q
       717: q
       719: q^2+q
       720: q^2
       724: q
       725: q
       727: q^2
       728: q^2+q
       732: q
       736: q
       738: q
       741: q
       742: q
       746: q
       750: q
       753: q
       755: q
       760: q
       761: q
       764: q
       765: q
       767: q
       773: q
       776: q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: q
       786: q^2+q
       787: 2q
       790: q
       791: q
       792: q
       793: q
       794: q^2+q
       796: q^2+q
       798: q
       800: q^2+q
       801: q
       802: q^2+q
       803: 2q
       805: q
       806: 2q^2+q
       807: q^3+q^2+2q
       808: q^2
       810: q^2+q
       811: q^2+q
       812: 2q^2+q
       814: q^2+q
       815: q
       816: q^2+q
       817: 2q
       820: q
       824: q
       825: q
       826: q^2+q
       827: 2q
       831: q
       834: q
       835: q
       836: q
       838: q
       839: 2q
       842: q
       843: q
       844: q
       845: q
       846: q^2+q
       847: 2q
       850: q
       851: q
       852: q
       854: q
       855: q
       856: q
       857: q
       858: q
       860: q^2+q
       862: q^2+q
       864: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q^2+2q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q^2+2q
       878: q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       891: q
       898: q
       901: q
       907: q
       908: q
       910: q
       915: q
       919: q
       923: q
       924: q
       925: q
       928: q
       930: q^2
       931: q^2+q
       935: q
       937: q
       941: q
       948: q
       949: q
       957: q
       963: q
       964: q
       966: q
       972: q
       974: q
       977: q
       981: q
       986: q
       988: q
       990: q
       993: q
       995: q
       997: q^2+q
       998: 2q
      1000: q
      1001: q^2+q
      1003: q
      1004: q
      1005: q^2+q
      1006: 2q
      1008: q
      1009: q
      1011: q
      1012: q
      1013: q
      1015: q^2+q
      1016: q
      1017: q^2+q
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1026: q
      1027: q^2+q
      1028: 2q
      1031: q
      1032: 2q
      1037: q
      1043: q
      1044: q
      1046: q
      1047: q
      1051: q
      1052: q
      1053: q^2+q
      1054: 2q
      1058: q
      1061: q
      1062: q
      1063: q
      1064: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1093: q
      1105: q
      1111: q
      1115: q
      1121: q
      1125: q
      1129: q
      1130: q
      1132: q
      1134: q
      1137: q
      1142: q
      1147: q
      1151: q
      1153: q
      1159: q
      1160: q
      1161: q
      1165: q
      1187: q
      1192: q
      1194: q
      1196: q
      1202: q
      1203: q
      1211: q+1
      1213: q+1
      1215: q
      1216: 2q
      1218: q
      1219: q^2+q
      1223: q
      1224: q
      1225: q
      1227: q+1
      1228: 1
      1229: q
      1231: q
      1232: 2q
      1234: q
      1235: q^2+q
      1237: q^2+q
      1239: q
      1240: q
      1241: q^2+q
      1242: 2q
      1245: 1
      1246: 1
      1250: q
      1253: q
      1260: q
      1262: 1
      1270: q
      1273: q
      1275: q
      1276: q
      1277: q
      1279: q
      1280: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1297: q
      1309: q
      1315: q
      1321: q
      1325: q
      1326: q
      1328: q
      1338: q
      1341: 1
      1343: q
      1345: q
      1349: q
      1355: q
      1359: q
      1362: q
      1364: q
      1365: q
      1368: q
      1370: q
      1373: 1
      1405: 1
      1410: 1
      1434: q
      1439: q+1
      1440: 1
      1442: 1
      1443: q
      1444: 1
      1449: q
      1450: 2q
      1453: q+1
      1454: q
      1455: q^2+q
      1459: 1
      1460: q
      1466: q
      1473: q
      1478: q
      1481: q
      1482: q
      1483: q
      1484: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1496: q
      1507: q
      1526: 1
      1542: 1
      1546: 1
      1548: q
      1549: 1
      1554: 1
      1564: q
      1570: q
      1573: q
      1575: q
      1576: q
      1635: q
      1639: 1
      1644: q+1
      1645: 1
      1647: 1
      1648: q
      1649: q
      1652: 1
      1653: 1
      1663: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1676: 1
      1693: q
      1724: 1
      1733: 1
      1738: 1
      1746: 1
      1748: q
      1749: 1
      1762: 1
      1802: 1
      1819: q
      1825: 1
      1828: 1
      1829: 1
      1833: 1
      1835: 1
      1847: 1
      1898: 1
      1927: 1
      1933: 1
      1957: 1
      1960: 1
      1962: 1
      1967: 1
      2027: 1
      2033: 1
      2040: 1
      2069: 1

2070:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: q^5+3q^4+3q^3+q^2+q
        23: q^5+3q^4+3q^3+q^2+q
        24: q^5+3q^4+3q^3+q^2+q
        25: 2q^4+2q^3+q^2+q
        26: 2q^4+2q^3+q^2+q
        27: 2q^4+2q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: 2q^4+3q^3+q^2+q
        32: q^5+3q^4+3q^3+q^2+q
        33: 2q^4+3q^3+q^2+q
        34: q^4+2q^3+q^2+q
        35: 2q^4+2q^3+q^2+q
        36: q^4+2q^3+q^2+q
        37: 2q^4+2q^3+q^2+q
        39: 2q^4+2q^3+q^2+q
        41: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^5+3q^4+3q^3+q^2+q
        53: q^5+3q^4+3q^3+q^2+q
        54: q^5+3q^4+3q^3+q^2+q
        55: 2q^4+2q^3+q^2+q
        56: 2q^4+2q^3+q^2+q
        57: 2q^4+2q^3+q^2+q
        58: q^4+2q^3+q
        59: q^3+q^2
        60: q^3+q
        61: q^3+q^2
        62: q^4+2q^3+q^2+q
        64: 2q^4+2q^3+q^2+q
        66: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: q^4+2q^3+q^2+q
        73: 2q^4+3q^3+q^2+q
        74: 2q^4+2q^3+q^2+q
        76: 2q^4+2q^3+q^2+q
        78: 2q^4+2q^3+q^2+q
        80: 2q^4+3q^3+q^2+q
        81: 2q^4+3q^3+q^2+q
        82: 2q^4+3q^3+q^2+q
        83: q^5+3q^4+3q^3+q^2+q
        84: q^4+2q^3+q^2+q
        85: q^4+2q^3+q^2+q
        86: q^4+2q^3+q^2+q
        87: 2q^4+2q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^4+3q^3+q^2+q
        95: 2q^4+3q^3+q^2+q
        96: q^5+2q^4+2q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       103: q^3+q
       106: q^3+q^2
       107: q^3+q
       108: q^3+q^2
       109: q^4+2q^3+q
       110: q^3+q^2
       111: q^4+2q^3+q^2+q
       113: q^4+2q^3+q^2+q
       115: 2q^4+2q^3+q^2+q
       117: q^4+2q^3+q
       118: q^3+q^2
       119: q^3+q
       120: q^3+q^2
       121: q^4+2q^3+q^2+q
       123: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: 2q^4+3q^3+q^2+q
       137: 3q^3+q^2+q
       138: q^4+2q^3+q^2+q
       139: q^4+3q^3+q^2+q
       140: q^4+2q^3+q^2+q
       141: 2q^4+3q^3+q^2+q
       142: 2q^4+3q^3+q^2+q
       143: 2q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^4+2q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^3+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       151: 2q^4+2q^3+q^2+q
       153: 2q^4+2q^3+q^2+q
       155: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^4+3q^3+q^2+q
       161: 2q^4+3q^3+q^2+q
       162: q^5+2q^4+2q^3+q^2+q
       163: 2q^3+q^2+q
       164: 2q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3+q
       172: q^3+q^2
       173: q^3+q
       176: q^3+q^2
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^3+q
       184: q^3+q^2
       185: q^4+2q^3+q
       186: q^3+q^2
       187: q^4+2q^3+q^2+q
       189: q^4+2q^3+q^2+q
       191: 2q^3+q
       192: q^3+q^2
       193: q^3+q
       194: q^3+q^2
       195: q^4+2q^3+q
       196: q^3+q^2
       197: q^4+2q^3+q^2+q
       199: q^3+q
       200: q^3+q^2
       201: q^3+q
       202: q^3+q^2
       203: q^3+q
       205: q^3+q
       207: 2q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: 2q^4+2q^3+q^2+q
       213: 2q^3+q^2+q
       215: 2q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 2q^3+q^2+q
       223: q^3+q^2+q
       224: 3q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^4+3q^3+q^2+q
       228: q^4+2q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: 2q^4+3q^3+q^2+q
       231: q^3+q^2+q
       232: 2q^3+q^2+q
       233: q^3+q^2+q
       234: 2q^3+q^2+q
       235: q^3+q
       236: q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: 2q^3+q^2+q
       245: q^3+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: q^3+q
       262: q^3+q^2
       263: q^3+q
       266: q^3+q^2
       267: q^3+q
       269: q^3+q^2
       271: q^3+q
       275: q^3+q
       278: q^3+q^2
       279: 2q^3+q^2+q
       281: q^3+q^2+q
       283: q
       284: q^2
       285: q^3+q
       286: q^2
       287: q^3+q^2+q
       289: 2q^3+q^2+q
       291: q^3+q^2+q
       293: q^3+q
       294: q^3+q^2
       295: 2q^3+q
       296: q^3+q^2
       297: 2q^3+q^2+q
       299: q^3+q
       300: q^3+q^2
       301: 2q^3+q^2+q
       303: q^4+2q^3+q
       304: q^3+q^2
       305: q^4+2q^3+q^2+q
       307: q^3+q
       308: q^3+q^2
       309: q^3+q
       311: q^3+q
       313: q^3+q
       315: q^3+q^2+q
       317: 2q^3+q^2+q
       319: q^3+q
       320: q^3+q^2
       321: q^3+q
       323: q^3+q
       325: q^4+2q^3+q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: 2q^3+q^2+q
       334: q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       338: 2q^3+q^2+q
       340: 2q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: 2q^3+q^2+q
       348: q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: 2q^3+q^2+q
       352: q^3+q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+q^2+q
       357: q
       358: q
       359: q^3+q
       360: 2q^3+q^2+q
       362: 2q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: 2q^3+q^2+q
       370: q^3+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q
       380: q^2
       381: q^3+q
       384: q^3+q^2
       385: q^3+q
       388: q^3+q^2
       389: q^3+q
       391: q^3+q^2
       393: q^3+q
       396: q^3+q^2
       397: q^3+q
       401: q^3+q
       405: q^3+q
       409: q^2+q
       411: q^2+q
       413: q^3+q^2+q
       415: q^2+q
       417: q^3+q^2+q
       419: q
       420: q^2
       421: q^3+q
       422: q^2
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: 2q^3+q^2+q
       429: q
       430: q^2
       431: q^3+q
       432: q^2
       433: q^3+q^2+q
       435: 2q^3+q^2+q
       437: q^3+q
       438: q^3+q^2
       439: 2q^3+q
       440: q^3+q^2
       441: 2q^3+q^2+q
       443: q^3+q
       444: q^3+q^2
       445: 2q^3+q^2+q
       447: q
       448: q^2
       449: q
       451: q
       453: q
       454: q^2
       455: q^3+q
       457: q
       459: q
       461: q^3+q
       463: q^3+q
       465: 2q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       471: q^3+q
       472: q^3+q^2
       473: q^3+q
       475: q^3+q
       477: q^3+q
       479: q^3+q
       481: q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       485: 2q^3+q^2+q
       487: 2q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^3+q^2+q
       494: 2q^3+q^2+q
       495: q^3+q^2+q
       496: 2q^3+q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^3+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+q^2+q
       513: q
       514: q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       521: q
       524: q^2
       525: q
       528: q^2
       529: q
       532: q^2
       533: q
       536: q^2
       537: q^3+q
       539: q^3+q^2
       541: q^3+q
       543: q^3+q^2
       545: q^3+q
       547: q^3+q^2
       549: q
       553: q^3+q
       557: q
       561: q^3+q
       565: q^3+q
       569: q^3+q
       573: q^3+q
       577: q^3+q
       583: q^2+q
       585: q^3+q^2+q
       587: q^2+q
       589: q
       590: q^2
       591: q
       593: q
       594: q^2
       595: q^3+q
       596: q^2
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: 2q^3+q^2+q
       603: q
       604: q^2
       605: q^3+q^2+q
       607: q^3+q
       608: q^2
       609: q^3+q^2+q
       611: q^2+q
       613: q^3+q^2+q
       615: q^3+q
       616: q^3+q^2
       617: 2q^3+q^2+q
       619: q
       620: q^2
       621: q
       623: q
       625: q
       627: q
       629: q
       631: q^3+q
       633: q^3+q
       635: q^2+q
       637: q^2+q
       639: q^3+q^2+q
       641: q
       642: q^2
       643: q
       645: q
       647: q
       648: q^2
       649: q
       651: q^3+q
       653: q
       655: q^3+q
       657: q^2+q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+q
       673: q^2+q
       674: q^2+q
       675: q^3+q^2+q
       676: 2q^3+q^2+q
       677: q^3+q^2+q
       678: q^2+q
       679: q^3+q^2+q
       680: q
       681: q^2+q
       682: q
       683: q
       684: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       693: q^3+q
       705: q
       708: q^2
       709: q
       712: q^2
       713: q
       717: q
       720: q^2
       721: q
       723: q^2
       725: q
       727: q^2
       729: q
       731: q^2
       733: q^3+q
       735: q^3+q^2
       737: q
       741: q
       745: q
       749: q^3+q
       753: q
       757: q^3+q
       761: q
       765: q^3+q
       769: q^3+q
       775: q^2+q
       777: q^2+q
       779: q^2+q
       781: q^3+q^2+q
       783: q^2+q
       785: q
       786: q^2
       787: q
       789: q^2+q
       791: q
       793: q
       794: q^2
       795: q^2+q
       797: q^3+q^2+q
       799: q^2+q
       801: q
       802: q^2
       803: q
       805: q
       806: q^2
       807: q^3+q
       808: q^2
       809: q^3+q^2+q
       811: q^3+q^2+q
       813: q^2+q
       815: q
       816: q^2
       817: q
       819: q
       821: q
       823: q
       825: q
       826: q^2
       827: q
       831: q
       833: q
       835: q
       837: q
       839: q
       841: q^2+q
       843: q
       845: q
       846: q^2
       847: q
       849: q
       851: q
       853: q
       855: q
       857: q
       866: q^2+q
       868: q^2+q
       870: q^2+q
       871: q^3+q^2+q
       872: q^2+q
       874: q
       875: q
       876: q
       877: q^2+q
       878: q
       879: q
       880: q
       884: q^3+q
       896: q
       899: q^2
       900: q
       904: q
       906: q^2
       908: q
       912: q
       914: q^2
       916: q
       918: q^2
       920: q
       922: q^2
       924: q
       928: q
       930: q^2
       932: q
       934: q^2
       936: q
       940: q
       944: q
       948: q
       956: q
       960: q
       964: q
       968: q
       974: q
       978: q
       982: q
       988: q
       994: q^2+q
       998: q
      1000: q
      1001: q^2
      1002: q^2+q
      1004: q
      1005: q^2
      1006: q
      1008: q
      1010: q
      1012: q
      1018: q^2+q
      1020: q^2+q
      1022: q^3+q^2+q
      1024: q^2+q
      1026: q
      1027: q^2
      1028: q
      1034: q
      1036: q
      1038: q
      1042: q
      1044: q
      1048: q
      1050: q
      1052: q
      1053: q^2
      1054: q
      1058: q
      1060: q
      1062: q
      1064: q
      1076: q^2+q
      1078: q^2+q
      1080: q
      1082: q
      1083: q
      1084: q
      1085: q
      1086: q
      1098: q
      1110: q
      1114: q
      1118: q
      1120: q^2
      1122: q
      1124: q^2
      1126: q
      1130: q
      1134: q
      1138: q
      1148: q
      1150: q^2
      1152: q
      1156: q
      1158: q^2
      1160: q
      1168: q
      1172: q
      1184: q
      1198: q
      1202: q
      1220: q
      1222: q
      1230: q^2+q
      1232: q
      1234: q
      1235: q^2
      1238: q^2+q
      1240: q
      1241: q^2
      1242: q
      1248: q
      1250: q
      1256: q
      1260: q
      1264: q
      1266: q
      1270: q
      1272: q
      1274: q
      1276: q
      1278: q
      1280: q
      1287: q
      1289: q
      1290: q
      1322: q
      1330: q
      1344: q
      1348: q
      1352: q
      1354: q^2
      1356: q
      1358: q^2
      1360: q
      1364: q
      1368: q
      1376: q
      1380: q
      1414: q
      1418: q
      1430: q
      1446: q
      1464: q
      1466: q
      1470: q
      1474: q
      1478: q
      1480: q
      1484: q
      1501: q
      1559: q
      1571: q
      1579: q
      1603: q
      1607: q
      1637: 1
      1641: q
      1649: q
      1671: q
      1725: 1
      1729: 1
      1753: q
      1757: q
      1823: 1
      1836: 1
      1894: 1
      1928: 1
      1958: 1
      1968: 1
      2028: 1
      2036: 1
      2070: 1

2071:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 3q^3+4q^2+2q
        23: 3q^3+4q^2+2q
        24: q^4+3q^3+3q^2+2q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 3q^3+4q^2+2q
        32: 2q^3+3q^2+2q
        33: 3q^3+4q^2+2q
        34: 4q^2+2q
        35: 3q^2+2q
        36: 4q^2+2q
        37: 3q^2+q
        38: q^2+q
        39: 3q^2+q
        40: q^2+q
        41: q^3+2q^2+q
        42: q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 3q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^4+3q^3+3q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: q^3+3q^2+2q
        58: 2q^3+2q^2+2q
        59: q^3+2q^2
        60: 3q^2+q
        61: q^2+q
        62: 3q^2+q
        63: q^2+q
        64: 2q^2+q
        65: q^2+q
        66: 3q^2+q
        67: q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 4q^2+2q
        73: 3q^3+4q^2+2q
        74: 3q^2+q
        75: q^2+q
        76: 3q^2+q
        77: q^2+q
        78: q^3+2q^2+q
        79: q^2+q
        80: 2q^3+3q^2+2q
        81: 2q^3+3q^2+2q
        82: 3q^3+4q^2+2q
        83: 2q^3+3q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 4q^2+2q
        87: 3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: 2q^2+q
       104: q^2
       105: q
       106: q^2
       107: 3q^2+q
       108: q^2+q
       109: 2q^3+2q^2+2q
       110: q^3+2q^2
       111: 3q^2+q
       112: q^2+q
       113: 3q^2+q
       114: q^2+q
       115: 2q^2+q
       116: q^2+q
       117: q^3+q^2+2q
       118: q^2
       119: 2q^2+q
       120: q
       121: 2q^2+q
       122: q^2+q
       123: 2q^2+q
       124: q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: 3q^2+q
       128: q^2+q
       129: 3q^2+q
       130: q^2+q
       131: q^3+2q^2+q
       132: q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 3q^2+2q
       136: 2q^3+3q^2+2q
       137: 2q^3+3q^2+2q
       138: 2q^3+3q^2+2q
       139: 3q^3+4q^2+2q
       140: 4q^2+2q
       141: 2q^3+3q^2+2q
       142: 3q^3+4q^2+2q
       143: 3q^2+2q
       144: 3q^2+2q
       145: 4q^2+2q
       146: 3q^2+2q
       147: 4q^2+2q
       148: q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: 3q^2+q
       152: q^2+q
       153: 3q^2+q
       154: q^2+q
       155: q^3+2q^2+q
       156: q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^3+3q^2+2q
       161: 2q^3+3q^2+2q
       162: 2q^3+3q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: 2q^2+q
       170: q^2
       171: q
       172: q^2
       173: q^2+q
       174: q^2
       175: q
       177: 2q^2+q
       178: q^2+q
       179: 3q^2+q
       180: q^2+q
       181: 3q^2+q
       182: q^2+q
       183: 2q^2+q
       184: q
       185: q^3+q^2+2q
       186: q^2
       187: 2q^2+q
       188: q^2+q
       189: 2q^2+q
       190: q^2+q
       191: q^3+q^2+2q
       192: q^2
       193: 3q^2+q
       194: q^2+q
       195: 2q^3+2q^2+2q
       196: q^3+2q^2
       197: 3q^2+q
       198: q^2+q
       199: 2q^2+q
       200: q
       201: 3q^2+q
       202: q^2+q
       203: q^2+2q
       205: q^2+q
       206: q
       207: 2q^2+q
       208: q^2+q
       209: 3q^2+q
       210: q^2+q
       211: 2q^2+q
       212: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 3q^2+2q
       223: 3q^2+2q
       224: 2q^3+3q^2+2q
       225: 2q^3+3q^2+2q
       226: 2q^3+3q^2+2q
       227: q^3+2q^2+2q
       228: 2q^3+3q^2+2q
       229: 3q^2+2q
       230: 2q^3+3q^2+2q
       231: 3q^2+2q
       232: q^2+2q
       233: 2q^2+2q
       234: 2q^2+2q
       235: 2q
       236: 3q^2+2q
       237: 3q^2+q
       238: q^2+q
       239: 3q^2+q
       240: q^2+q
       241: q^3+2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: 4q^2+2q
       245: q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^3+3q^2+2q
       251: 2q^3+3q^2+2q
       252: 2q^3+3q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: 2q^2+q
       260: q^2
       261: q
       262: q^2
       263: q^2+q
       264: q^2
       265: q
       267: 2q^2+q
       268: q^2
       269: q^2
       270: q
       271: q^2+q
       272: q
       275: q^2+q
       276: q^2
       277: q
       279: q
       281: q^2+q
       283: 2q^2+q
       284: q
       285: q^3+q^2+2q
       286: q^2
       287: 2q^2+q
       288: q^2+q
       289: q^2+q
       291: 2q^2+q
       292: q^2+q
       293: 2q^2+q
       294: q
       295: q^3+q^2+2q
       296: q^2
       297: 2q^2+q
       298: q^2+q
       299: 2q^2+q
       300: q
       301: 3q^2+q
       302: q^2+q
       303: q^3+q^2+2q
       304: q^2
       305: 2q^2+q
       306: q^2+q
       307: q^2+q
       308: q
       309: 2q
       311: q^2+q
       312: q
       313: q
       314: q
       315: 2q^2+q
       316: q^2+q
       317: 3q^2+q
       318: q^2+q
       319: 3q^2+q
       320: q^2+q
       321: q^2+2q
       323: q^2+q
       324: q
       325: 2q^2+q
       326: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+2q
       334: 3q^2+2q
       335: 2q^3+3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: 3q^2+q
       339: q^2+q
       340: 3q^2+q
       341: q^2+q
       342: q^3+2q^2+q
       343: q^2+q
       344: q^3+2q^2+2q
       345: q^3+2q^2+2q
       346: 2q^3+3q^2+2q
       347: 3q^2+2q
       348: 3q^2+2q
       349: 2q^3+3q^2+2q
       350: 2q^3+3q^2+2q
       351: 4q^2+2q
       352: q^2+2q
       353: q^2+2q
       354: 2q^2+2q
       355: 2q^2+2q
       356: 2q^2+2q
       357: 2q
       358: 2q
       359: q^2+2q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q^2+2q
       370: 2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q^2+q
       378: q^2
       379: q
       381: q
       385: q^2+q
       386: q^2
       387: q
       389: 2q^2+q
       390: q^2
       391: q^2
       392: q
       393: q^2+q
       394: q^2
       395: q
       397: q^2+q
       398: q
       401: q
       402: q
       405: q^2+q
       408: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: 2q^2+q
       420: q
       421: q^3+q^2+2q
       422: q^2
       423: 2q^2+q
       424: q^2+q
       425: 2q^2+q
       426: q^2+q
       427: 3q^2+q
       428: q^2+q
       429: 2q^2+q
       430: q
       431: q^3+q^2+2q
       432: q^2
       433: 2q^2+q
       434: q^2+q
       435: q^2+q
       437: 2q^2+q
       438: q
       439: q^3+q^2+2q
       440: q^2
       441: 2q^2+q
       442: q^2+q
       443: 3q^2+q
       444: q^2+q
       445: 3q^2+q
       446: q^2+q
       447: q^2+q
       448: q
       449: 2q
       451: q
       452: q
       453: q^2+q
       454: q
       455: q
       457: 2q
       459: q
       460: q
       461: q^2+2q
       463: q^2+q
       464: q
       465: q
       467: q^2+q
       469: 2q^2+q
       470: q^2+q
       471: q^2+q
       472: q
       473: 2q
       475: q
       476: q
       477: q^2+q
       478: q
       479: q^2+q
       480: q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: 2q^2+2q
       492: q^3+2q^2+2q
       493: 3q^2+2q
       494: 2q^3+3q^2+2q
       495: 3q^2+2q
       496: 2q^2+2q
       497: q^2+2q
       498: 2q^2+2q
       499: 2q
       500: 2q
       501: 2q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: 2q
       514: 2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       521: q
       525: q
       529: q^2+q
       530: q^2
       531: q
       533: q^2+q
       534: q^2
       535: q
       537: q
       541: q^2+q
       542: q^2
       544: q
       545: 2q^2+q
       546: q^2
       547: q^2
       548: q
       549: q
       550: q
       553: q
       557: q
       558: q
       561: q^2+q
       562: q
       565: q
       567: q
       569: q^2+q
       572: q
       573: q^2+q
       576: q
       577: q^2+q
       581: q
       583: q
       585: q
       587: q^2+q
       589: q^2+q
       590: q
       591: 2q
       593: 2q^2+q
       594: q
       595: q^3+q^2+2q
       596: q^2
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q
       603: 2q^2+q
       604: q
       605: q^2+q
       607: q^3+q^2+2q
       608: q^2
       609: 2q^2+q
       610: q^2+q
       611: q^2+q
       613: 2q^2+q
       614: q^2+q
       615: q^2+q
       616: q
       617: q^2+q
       619: q^2+q
       620: q
       621: 2q
       623: q
       625: q
       626: q
       627: q
       629: q
       630: q
       631: 2q
       633: q
       635: q
       637: q^2+q
       639: q
       641: q^2+q
       642: q
       643: 2q
       645: q
       646: q
       647: q^2+q
       648: q
       649: 2q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q^2+2q
       675: q^2+2q
       676: q^3+2q^2+2q
       677: 3q^2+2q
       678: 2q^2+2q
       679: 2q^2+2q
       680: 2q
       681: q^2+2q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+2q
       687: 2q^2+2q
       688: 2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       693: q^2+q
       700: q
       705: q
       709: q
       713: q
       714: q
       717: q^2+q
       718: q^2
       719: q
       721: q
       725: q^2+q
       726: q^2
       728: q
       729: q
       733: q
       737: q
       741: q
       742: q
       745: q
       749: q
       753: q
       755: q
       757: q
       761: q
       764: q
       765: q
       767: q
       769: q
       775: q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: q^2+q
       786: q
       787: 2q
       789: q
       791: q
       792: q
       793: q^2+q
       794: q
       795: q^2+q
       797: q
       799: q^2+q
       801: q^2+q
       802: q
       803: 2q
       805: 2q^2+q
       806: q
       807: q^3+q^2+2q
       808: q^2
       809: q^2+q
       811: 2q^2+q
       812: q^2+q
       813: q^2+q
       815: q^2+q
       816: q
       817: 2q
       819: q
       823: q
       825: q^2+q
       826: q
       827: 2q
       831: q
       833: q
       835: q
       836: q
       837: q
       839: 2q
       841: q
       843: q
       844: q
       845: q^2+q
       846: q
       847: 2q
       849: q
       851: q
       852: q
       853: q
       855: q
       856: q
       857: q
       858: q
       859: q^2+q
       861: q^2+q
       863: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q^2+2q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q^2+2q
       878: q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       884: q
       896: q
       900: q
       904: q
       908: q
       910: q
       912: q
       916: q
       920: q
       924: q
       925: q
       928: q^2+q
       929: q^2
       931: q
       932: q
       936: q
       940: q
       948: q
       949: q
       956: q
       960: q
       964: q
       966: q
       968: q
       974: q
       977: q
       978: q
       982: q
       988: q
       990: q
       992: q
       994: q
       996: q^2+q
       998: 2q
      1000: q^2+q
      1001: q
      1002: q
      1004: q^2+q
      1005: q
      1006: 2q
      1008: q
      1009: q
      1010: q
      1012: q
      1013: q
      1014: q^2+q
      1016: q^2+q
      1017: q
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1026: q^2+q
      1027: q
      1028: 2q
      1030: q
      1032: 2q
      1036: q
      1042: q
      1044: q
      1046: q
      1047: q
      1050: q
      1052: q^2+q
      1053: q
      1054: 2q
      1058: q
      1060: q
      1062: q
      1063: q
      1064: q
      1065: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1098: q
      1110: q
      1114: q
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      1126: q
      1130: q
      1132: q
      1134: q
      1137: q
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      1152: q
      1156: q
      1160: q
      1161: q
      1164: q
      1184: q
      1188: q
      1194: q
      1196: q
      1202: q
      1203: q
      1210: q+1
      1212: q+1
      1214: q
      1216: 2q
      1218: q^2+q
      1219: q
      1222: q
      1224: q
      1225: q
      1226: q+1
      1228: q
      1229: 1
      1230: q
      1232: 2q
      1234: q^2+q
      1235: q
      1236: q^2+q
      1238: q
      1240: q^2+q
      1241: q
      1242: 2q
      1244: 1
      1246: 1
      1250: q
      1252: q
      1260: q
      1263: 1
      1270: q
      1272: q
      1274: q
      1276: q
      1277: q
      1278: q
      1280: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1290: q
      1302: q
      1314: q
      1318: q
      1322: q
      1326: q
      1328: q
      1334: q
      1340: q
      1342: 1
      1344: q
      1348: q
      1352: q
      1356: q
      1360: q
      1364: q
      1365: q
      1368: q
      1370: q
      1372: 1
      1407: 1
      1412: 1
      1430: q
      1438: q+1
      1440: 1
      1442: q
      1443: 1
      1445: 1
      1448: q
      1450: 2q
      1452: q+1
      1454: q^2+q
      1455: q
      1458: 1
      1460: q
      1466: q
      1472: q
      1478: q
      1480: q
      1482: q
      1483: q
      1484: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1489: q
      1501: q
      1529: 1
      1541: 1
      1545: q
      1547: 1
      1551: 1
      1556: 1
      1563: q
      1567: q
      1571: q
      1575: q
      1576: q
      1631: q
      1640: 1
      1643: q+1
      1645: 1
      1647: q
      1648: 1
      1649: q
      1651: 1
      1653: 1
      1663: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1679: 1
      1687: q
      1726: 1
      1735: 1
      1737: 1
      1745: q
      1747: 1
      1750: 1
      1761: 1
      1804: 1
      1819: q
      1826: 1
      1827: 1
      1829: 1
      1833: 1
      1838: 1
      1849: 1
      1899: 1
      1929: 1
      1932: 1
      1956: 1
      1961: 1
      1962: 1
      1969: 1
      2029: 1
      2032: 1
      2041: 1
      2071: 1

2072:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+1
        60: q
        61: 1
        62: q+1
        64: q+1
        66: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        76: q+1
        78: q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: 1
       107: q
       108: 1
       109: q
       110: q^2+1
       111: q+1
       113: q+1
       115: q+1
       117: q
       118: q^2+1
       119: q
       120: 1
       121: q+1
       123: q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q
       172: 1
       173: q
       176: 1
       177: q+1
       179: q+1
       181: q+1
       183: q
       184: 1
       185: q
       186: q^2+1
       187: q+1
       189: q+1
       191: q
       192: q^2+1
       193: q
       194: 1
       195: q
       196: q^2+1
       197: q+1
       199: q
       200: 1
       201: q
       202: 1
       204: 1
       205: 1
       207: q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 1
       263: q
       266: 1
       267: q
       269: 1
       273: 1
       275: q
       278: 1
       279: q+1
       281: q+1
       283: q
       284: 1
       285: q
       286: q^2+1
       287: q+1
       289: q+1
       291: q+1
       293: q
       294: 1
       295: q
       296: q^2+1
       297: q+1
       299: q
       300: 1
       301: q+1
       303: q
       304: q^2+1
       305: q+1
       307: q
       308: 1
       310: 1
       311: 1
       313: 1
       315: q+1
       317: q+1
       319: q
       320: 1
       322: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: 1
       381: q
       384: 1
       385: q
       388: 1
       389: q
       391: 1
       393: q
       396: 1
       399: 1
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q
       420: 1
       421: q
       422: q^2+1
       423: q+1
       425: q+1
       427: q+1
       429: q
       430: 1
       431: q
       432: q^2+1
       433: q+1
       435: q+1
       437: q
       438: 1
       439: q
       440: q^2+1
       441: q+1
       443: q
       444: 1
       445: q+1
       447: q
       448: 1
       450: 1
       451: 1
       453: q
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: q+1
       467: q+1
       469: q+1
       471: q
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       525: q
       528: 1
       529: q
       532: 1
       533: q
       536: 1
       537: q
       539: 1
       541: q
       543: 1
       545: q
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: 1
       592: 1
       593: q
       594: 1
       595: q
       596: q^2+1
       597: q+1
       599: q+1
       601: q+1
       603: q
       604: 1
       605: q+1
       607: q
       608: q^2+1
       609: q+1
       611: q+1
       613: q+1
       615: q
       616: 1
       617: q+1
       619: q
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: q+1
       637: q+1
       639: q+1
       641: q
       642: 1
       644: 1
       645: 1
       647: q
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       705: q
       708: 1
       709: q
       712: 1
       716: 1
       717: q
       720: 1
       721: q
       723: 1
       725: q
       727: 1
       729: q
       731: 1
       733: q
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: q
       786: 1
       788: 1
       789: q+1
       791: 1
       793: q
       794: 1
       795: q+1
       797: q+1
       799: q+1
       801: q
       802: 1
       804: 1
       805: q
       806: 1
       807: q
       808: q^2+1
       809: q+1
       811: q+1
       813: q+1
       815: q
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       825: q
       826: 1
       828: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: q+1
       843: 1
       845: q
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       896: q
       899: 1
       902: 1
       904: q
       906: 1
       911: 1
       912: q
       914: 1
       916: q
       918: 1
       920: q
       922: 1
       927: 1
       928: q
       930: 1
       932: q
       934: 1
       938: 1
       942: 1
       946: 1
       950: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       999: 1
      1000: q
      1001: 1
      1002: q+1
      1004: q
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: q+1
      1016: q
      1017: 1
      1018: q+1
      1020: q+1
      1022: q+1
      1024: q+1
      1026: q
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1052: q
      1053: 1
      1055: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1118: q
      1120: 1
      1122: q
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1144: q
      1146: 1
      1148: q
      1150: 1
      1154: 1
      1156: q
      1158: 1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1204: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1217: 1
      1218: q
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: q+1
      1228: q
      1229: 1
      1230: q+1
      1233: 1
      1234: q
      1235: 1
      1236: q+1
      1238: q+1
      1240: q
      1241: 1
      1243: 1
      1244: 1
      1247: 1
      1248: 1
      1251: 1
      1252: 1
      1256: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1318: q
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1340: q
      1342: 1
      1346: 1
      1350: 1
      1352: q
      1354: 1
      1356: q
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: 1
      1378: 1
      1382: 1
      1404: 1
      1413: 1
      1415: 1
      1420: 1
      1430: 1
      1436: 1
      1438: q+1
      1441: 1
      1442: q
      1443: 1
      1444: 1
      1446: 1
      1448: q+1
      1451: 1
      1452: q+1
      1454: q
      1455: 1
      1456: 1
      1458: 1
      1461: 1
      1464: 1
      1467: 1
      1470: 1
      1472: 1
      1474: 1
      1479: 1
      1480: 1
      1482: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1494: 1
      1506: 1
      1530: 1
      1538: 1
      1543: 1
      1545: q
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1567: q
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1605: 1
      1609: 1
      1631: 1
      1637: 1
      1639: 1
      1641: 1
      1643: q+1
      1646: 1
      1647: q
      1648: 1
      1650: 1
      1651: 1
      1654: 1
      1659: 1
      1661: 1
      1664: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1680: 1
      1692: 1
      1723: 1
      1730: 1
      1736: 1
      1739: 1
      1742: 1
      1745: q
      1747: 1
      1752: 1
      1754: 1
      1759: 1
      1763: 1
      1787: 1
      1801: 1
      1815: 1
      1817: 1
      1820: 1
      1823: 1
      1825: 1
      1827: 1
      1830: 1
      1833: 1
      1839: 1
      1851: 1
      1895: 1
      1900: 1
      1904: 1
      1907: 1
      1926: 1
      1934: 1
      1956: 1
      1958: 1
      1960: 1
      1963: 1
      1970: 1
      2026: 1
      2034: 1
      2037: 1
      2042: 1
      2072: 1

2073:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+1
        59: q
        60: q
        61: 1
        63: q+1
        65: q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: 1
       107: q
       108: 1
       109: q^2+1
       110: q
       112: q+1
       114: q+1
       116: q+1
       117: q^2+1
       118: q
       119: q
       120: 1
       122: q+1
       124: q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: q
       171: 1
       174: q
       175: 1
       178: q+1
       180: q+1
       182: q+1
       183: q
       184: 1
       185: q^2+1
       186: q
       188: q+1
       190: q+1
       191: q^2+1
       192: q
       193: q
       194: 1
       195: q^2+1
       196: q
       198: q+1
       199: q
       200: 1
       201: q
       202: 1
       203: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 1
       264: q
       265: 1
       268: q
       270: 1
       272: 1
       276: q
       277: 1
       280: q+1
       282: q+1
       283: q
       284: 1
       285: q^2+1
       286: q
       288: q+1
       290: q+1
       292: q+1
       293: q
       294: 1
       295: q^2+1
       296: q
       298: q+1
       299: q
       300: 1
       302: q+1
       303: q^2+1
       304: q
       306: q+1
       307: q
       308: 1
       309: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: q
       320: 1
       321: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       382: q
       383: 1
       386: q
       387: 1
       390: q
       392: 1
       394: q
       395: 1
       398: 1
       402: 1
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q
       420: 1
       421: q^2+1
       422: q
       424: q+1
       426: q+1
       428: q+1
       429: q
       430: 1
       431: q^2+1
       432: q
       434: q+1
       436: q+1
       437: q
       438: 1
       439: q^2+1
       440: q
       442: q+1
       443: q
       444: 1
       446: q+1
       447: q
       448: 1
       449: 1
       452: 1
       453: q
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: q
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       526: q
       527: 1
       530: q
       531: 1
       534: q
       535: 1
       538: q
       540: 1
       542: q
       544: 1
       546: q
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: 1
       591: 1
       593: q
       594: 1
       595: q^2+1
       596: q
       598: q+1
       600: q+1
       602: q+1
       603: q
       604: 1
       606: q+1
       607: q^2+1
       608: q
       610: q+1
       612: q+1
       614: q+1
       615: q
       616: 1
       618: q+1
       619: q
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: q
       642: 1
       643: 1
       646: 1
       647: q
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: 1
       706: q
       707: 1
       710: q
       711: 1
       714: 1
       718: q
       719: 1
       722: q
       724: 1
       726: q
       728: 1
       730: q
       732: 1
       734: q
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: q
       786: 1
       787: 1
       790: q+1
       792: 1
       793: q
       794: 1
       796: q+1
       798: q+1
       800: q+1
       801: q
       802: 1
       803: 1
       805: q
       806: 1
       807: q^2+1
       808: q
       810: q+1
       812: q+1
       814: q+1
       815: q
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       825: q
       826: 1
       827: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: q+1
       844: 1
       845: q
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       891: 1
       897: q
       898: 1
       901: 1
       905: q
       907: 1
       910: 1
       913: q
       915: 1
       917: q
       919: 1
       921: q
       923: 1
       925: 1
       929: q
       931: 1
       933: q
       935: 1
       937: 1
       941: 1
       945: 1
       949: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
      1000: q
      1001: 1
      1003: q+1
      1004: q
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: q
      1017: 1
      1019: q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: q
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1052: q
      1053: 1
      1054: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1119: q
      1121: 1
      1123: q
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1145: q
      1147: 1
      1149: q
      1151: 1
      1153: 1
      1157: q
      1159: 1
      1161: 1
      1165: 1
      1169: 1
      1173: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1203: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1216: 1
      1218: q
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1228: q
      1229: 1
      1231: q+1
      1232: 1
      1234: q
      1235: 1
      1237: q+1
      1239: q+1
      1240: q
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1253: 1
      1257: 1
      1260: 1
      1263: 1
      1265: 1
      1267: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1319: q
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1341: q
      1343: 1
      1345: 1
      1349: 1
      1353: q
      1355: 1
      1357: q
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: 1
      1377: 1
      1381: 1
      1408: 1
      1412: 1
      1417: 1
      1419: 1
      1434: 1
      1437: 1
      1439: q+1
      1440: 1
      1442: q
      1443: 1
      1445: 1
      1447: 1
      1449: q+1
      1450: 1
      1453: q+1
      1454: q
      1455: 1
      1457: 1
      1459: 1
      1460: 1
      1465: 1
      1466: 1
      1471: 1
      1473: 1
      1475: 1
      1478: 1
      1481: 1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1496: 1
      1507: 1
      1532: 1
      1540: 1
      1542: 1
      1546: q
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1564: 1
      1568: q
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1604: 1
      1608: 1
      1635: 1
      1638: 1
      1640: 1
      1642: 1
      1644: q+1
      1645: 1
      1647: q
      1648: 1
      1649: 1
      1652: 1
      1653: 1
      1660: 1
      1662: 1
      1663: 1
      1668: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1682: 1
      1693: 1
      1727: 1
      1732: 1
      1735: 1
      1738: 1
      1743: 1
      1746: q
      1748: 1
      1750: 1
      1755: 1
      1758: 1
      1762: 1
      1786: 1
      1805: 1
      1816: 1
      1818: 1
      1819: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1833: 1
      1841: 1
      1852: 1
      1896: 1
      1899: 1
      1903: 1
      1908: 1
      1930: 1
      1933: 1
      1957: 1
      1959: 1
      1961: 1
      1962: 1
      1971: 1
      2030: 1
      2033: 1
      2038: 1
      2041: 1
      2073: 1

2074:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 3q^3+4q^2+2q
        23: 3q^3+4q^2+2q
        24: q^4+3q^3+3q^2+2q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 3q^3+4q^2+2q
        32: 2q^3+3q^2+2q
        33: 3q^3+4q^2+2q
        34: 4q^2+2q
        35: 3q^2+2q
        36: 4q^2+2q
        37: q^2+q
        38: 3q^2+q
        39: q^2+q
        40: 3q^2+q
        41: q^2+q
        42: q^3+2q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 3q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^4+3q^3+3q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: q^3+3q^2+2q
        58: q^3+2q^2
        59: 2q^3+2q^2+2q
        60: 3q^2+q
        61: q^2+q
        62: q^2+q
        63: 3q^2+q
        64: q^2+q
        65: 2q^2+q
        66: q^2+q
        67: 3q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 4q^2+2q
        73: 3q^3+4q^2+2q
        74: q^2+q
        75: 3q^2+q
        76: q^2+q
        77: 3q^2+q
        78: q^2+q
        79: q^3+2q^2+q
        80: 2q^3+3q^2+2q
        81: 2q^3+3q^2+2q
        82: 3q^3+4q^2+2q
        83: 2q^3+3q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 4q^2+2q
        87: 3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q^2
       104: 2q^2+q
       105: q^2
       106: q
       107: 3q^2+q
       108: q^2+q
       109: q^3+2q^2
       110: 2q^3+2q^2+2q
       111: q^2+q
       112: 3q^2+q
       113: q^2+q
       114: 3q^2+q
       115: q^2+q
       116: 2q^2+q
       117: q^2
       118: q^3+q^2+2q
       119: 2q^2+q
       120: q
       121: q^2+q
       122: 2q^2+q
       123: q^2+q
       124: 2q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: q^2+q
       128: 3q^2+q
       129: q^2+q
       130: 3q^2+q
       131: q^2+q
       132: q^3+2q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 3q^2+2q
       136: 2q^3+3q^2+2q
       137: 2q^3+3q^2+2q
       138: 2q^3+3q^2+2q
       139: 3q^3+4q^2+2q
       140: 4q^2+2q
       141: 2q^3+3q^2+2q
       142: 3q^3+4q^2+2q
       143: 3q^2+2q
       144: 3q^2+2q
       145: 4q^2+2q
       146: 3q^2+2q
       147: 4q^2+2q
       148: q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: q^2+q
       152: 3q^2+q
       153: q^2+q
       154: 3q^2+q
       155: q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^3+3q^2+2q
       161: 2q^3+3q^2+2q
       162: 2q^3+3q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q^2
       170: 2q^2+q
       171: q^2
       172: q
       173: q^2
       174: q^2+q
       176: q
       177: q^2+q
       178: 2q^2+q
       179: q^2+q
       180: 3q^2+q
       181: q^2+q
       182: 3q^2+q
       183: 2q^2+q
       184: q
       185: q^2
       186: q^3+q^2+2q
       187: q^2+q
       188: 2q^2+q
       189: q^2+q
       190: 2q^2+q
       191: q^2
       192: q^3+q^2+2q
       193: 3q^2+q
       194: q^2+q
       195: q^3+2q^2
       196: 2q^3+2q^2+2q
       197: q^2+q
       198: 3q^2+q
       199: 2q^2+q
       200: q
       201: 3q^2+q
       202: q^2+q
       204: q^2+2q
       205: q
       206: q^2+q
       207: q^2+q
       208: 2q^2+q
       209: q^2+q
       210: 3q^2+q
       211: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 3q^2+2q
       223: 3q^2+2q
       224: 2q^3+3q^2+2q
       225: 2q^3+3q^2+2q
       226: 2q^3+3q^2+2q
       227: q^3+2q^2+2q
       228: 2q^3+3q^2+2q
       229: 3q^2+2q
       230: 2q^3+3q^2+2q
       231: 3q^2+2q
       232: q^2+2q
       233: 2q^2+2q
       234: 2q^2+2q
       235: 2q
       236: 3q^2+2q
       237: q^2+q
       238: 3q^2+q
       239: q^2+q
       240: 3q^2+q
       241: q^2+q
       242: q^3+2q^2+q
       243: 4q^2+2q
       244: 4q^2+2q
       245: q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^3+3q^2+2q
       251: 2q^3+3q^2+2q
       252: 2q^3+3q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q^2
       260: 2q^2+q
       261: q^2
       262: q
       263: q^2
       264: q^2+q
       266: q
       267: q^2
       268: 2q^2+q
       269: q
       270: q^2
       273: q
       274: q^2+q
       275: q^2
       276: q^2+q
       278: q
       280: q
       282: q^2+q
       283: 2q^2+q
       284: q
       285: q^2
       286: q^3+q^2+2q
       287: q^2+q
       288: 2q^2+q
       290: q^2+q
       291: q^2+q
       292: 2q^2+q
       293: 2q^2+q
       294: q
       295: q^2
       296: q^3+q^2+2q
       297: q^2+q
       298: 2q^2+q
       299: 2q^2+q
       300: q
       301: q^2+q
       302: 3q^2+q
       303: q^2
       304: q^3+q^2+2q
       305: q^2+q
       306: 2q^2+q
       307: q^2+q
       308: q
       310: 2q
       311: q
       312: q^2+q
       313: q
       314: q
       315: q^2+q
       316: 2q^2+q
       317: q^2+q
       318: 3q^2+q
       319: 3q^2+q
       320: q^2+q
       322: q^2+2q
       323: q
       324: q^2+q
       325: q^2+q
       326: 2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+2q
       334: 3q^2+2q
       335: 2q^3+3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: q^2+q
       339: 3q^2+q
       340: q^2+q
       341: 3q^2+q
       342: q^2+q
       343: q^3+2q^2+q
       344: q^3+2q^2+2q
       345: q^3+2q^2+2q
       346: 2q^3+3q^2+2q
       347: 3q^2+2q
       348: 3q^2+2q
       349: 2q^3+3q^2+2q
       350: 2q^3+3q^2+2q
       351: 4q^2+2q
       352: q^2+2q
       353: q^2+2q
       354: 2q^2+2q
       355: 2q^2+2q
       356: 2q^2+2q
       357: 2q
       358: 2q
       359: q^2+2q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q^2+2q
       370: 2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q^2
       378: q^2+q
       380: q
       382: q
       385: q^2
       386: q^2+q
       388: q
       389: q^2
       390: 2q^2+q
       391: q
       392: q^2
       393: q^2
       394: q^2+q
       396: q
       399: q
       400: q^2+q
       403: q
       404: q
       406: q
       407: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: 2q^2+q
       420: q
       421: q^2
       422: q^3+q^2+2q
       423: q^2+q
       424: 2q^2+q
       425: q^2+q
       426: 2q^2+q
       427: q^2+q
       428: 3q^2+q
       429: 2q^2+q
       430: q
       431: q^2
       432: q^3+q^2+2q
       433: q^2+q
       434: 2q^2+q
       436: q^2+q
       437: 2q^2+q
       438: q
       439: q^2
       440: q^3+q^2+2q
       441: q^2+q
       442: 2q^2+q
       443: 3q^2+q
       444: q^2+q
       445: q^2+q
       446: 3q^2+q
       447: q^2+q
       448: q
       450: 2q
       451: q
       452: q
       453: q^2+q
       454: q
       456: q
       458: 2q
       459: q
       460: q
       462: q^2+2q
       463: q
       464: q^2+q
       466: q
       468: q^2+q
       469: q^2+q
       470: 2q^2+q
       471: q^2+q
       472: q
       474: 2q
       475: q
       476: q
       477: q
       478: q^2+q
       479: q
       480: q^2+q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: 2q^2+2q
       492: q^3+2q^2+2q
       493: 3q^2+2q
       494: 2q^3+3q^2+2q
       495: 3q^2+2q
       496: 2q^2+2q
       497: q^2+2q
       498: 2q^2+2q
       499: 2q
       500: 2q
       501: 2q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: 2q
       514: 2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       522: q
       526: q
       529: q^2
       530: q^2+q
       532: q
       533: q^2
       534: q^2+q
       536: q
       538: q
       541: q^2
       542: q^2+q
       543: q
       545: q^2
       546: 2q^2+q
       547: q
       548: q^2
       551: q
       552: q
       556: q
       559: q
       560: q
       563: q
       564: q^2+q
       566: q
       568: q
       570: q
       571: q^2+q
       574: q^2+q
       575: q
       577: q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q^2+q
       590: q
       592: 2q
       593: 2q^2+q
       594: q
       595: q^2
       596: q^3+q^2+2q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q
       603: 2q^2+q
       604: q
       606: q^2+q
       607: q^2
       608: q^3+q^2+2q
       609: q^2+q
       610: 2q^2+q
       612: q^2+q
       613: q^2+q
       614: 2q^2+q
       615: q^2+q
       616: q
       618: q^2+q
       619: q^2+q
       620: q
       622: 2q
       624: q
       625: q
       626: q
       628: q
       629: q
       630: q
       632: 2q
       634: q
       636: q
       638: q^2+q
       640: q
       641: q^2+q
       642: q
       644: 2q
       645: q
       646: q
       647: q^2+q
       648: q
       650: 2q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q^2+2q
       675: q^2+2q
       676: q^3+2q^2+2q
       677: 3q^2+2q
       678: 2q^2+2q
       679: 2q^2+2q
       680: 2q
       681: q^2+2q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+2q
       687: 2q^2+2q
       688: 2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       697: q
       699: q^2+q
       706: q
       710: q
       715: q
       716: q
       717: q^2
       718: q^2+q
       720: q
       722: q
       725: q^2
       726: q^2+q
       727: q
       730: q
       734: q
       740: q
       743: q
       744: q
       748: q
       752: q
       754: q
       756: q
       759: q
       762: q
       763: q
       766: q
       768: q
       773: q
       776: q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: q^2+q
       786: q
       788: 2q
       790: q
       791: q
       792: q
       793: q^2+q
       794: q
       796: q^2+q
       798: q
       800: q^2+q
       801: q^2+q
       802: q
       804: 2q
       805: 2q^2+q
       806: q
       807: q^2
       808: q^3+q^2+2q
       810: q^2+q
       811: q^2+q
       812: 2q^2+q
       814: q^2+q
       815: q^2+q
       816: q
       818: 2q
       820: q
       824: q
       825: q^2+q
       826: q
       828: 2q
       832: q
       834: q
       835: q
       836: q
       838: q
       840: 2q
       842: q
       843: q
       844: q
       845: q^2+q
       846: q
       848: 2q
       850: q
       851: q
       852: q
       854: q
       855: q
       856: q
       857: q
       858: q
       860: q^2+q
       862: q^2+q
       864: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q^2+2q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q^2+2q
       878: q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       890: q
       897: q
       903: q
       905: q
       909: q
       911: q
       913: q
       917: q
       921: q
       926: q
       927: q
       928: q^2
       929: q^2+q
       930: q
       933: q
       939: q
       943: q
       950: q
       951: q
       959: q
       962: q
       965: q
       967: q
       972: q
       975: q
       976: q
       980: q
       986: q
       989: q
       991: q
       993: q
       995: q
       997: q^2+q
       999: 2q
      1000: q^2+q
      1001: q
      1003: q
      1004: q^2+q
      1005: q
      1007: 2q
      1008: q
      1009: q
      1011: q
      1012: q
      1013: q
      1015: q^2+q
      1016: q^2+q
      1017: q
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1026: q^2+q
      1027: q
      1029: 2q
      1031: q
      1033: 2q
      1037: q
      1043: q
      1045: q
      1046: q
      1047: q
      1051: q
      1052: q^2+q
      1053: q
      1055: 2q
      1059: q
      1061: q
      1062: q
      1063: q
      1064: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1092: q
      1104: q
      1113: q
      1117: q
      1119: q
      1123: q
      1128: q
      1131: q
      1133: q
      1135: q
      1136: q
      1142: q
      1145: q
      1149: q
      1155: q
      1157: q
      1162: q
      1163: q
      1167: q
      1186: q
      1192: q
      1195: q
      1197: q
      1204: q
      1205: q
      1211: q+1
      1213: q+1
      1215: q
      1217: 2q
      1218: q^2+q
      1219: q
      1223: q
      1224: q
      1225: q
      1227: q+1
      1228: q
      1229: 1
      1231: q
      1233: 2q
      1234: q^2+q
      1235: q
      1237: q^2+q
      1239: q
      1240: q^2+q
      1241: q
      1243: 2q
      1245: 1
      1247: 1
      1251: q
      1253: q
      1261: q
      1262: 1
      1271: q
      1273: q
      1275: q
      1276: q
      1277: q
      1279: q
      1280: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1296: q
      1308: q
      1317: q
      1319: q
      1324: q
      1327: q
      1329: q
      1338: q
      1341: q
      1343: 1
      1347: q
      1351: q
      1353: q
      1357: q
      1363: q
      1366: q
      1367: q
      1369: q
      1371: q
      1375: 1
      1405: 1
      1413: 1
      1434: q
      1439: q+1
      1441: 1
      1442: q
      1443: 1
      1444: 1
      1449: q
      1451: 2q
      1453: q+1
      1454: q^2+q
      1455: q
      1459: 1
      1461: q
      1467: q
      1473: q
      1479: q
      1481: q
      1482: q
      1483: q
      1484: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1495: q
      1508: q
      1533: 1
      1544: 1
      1546: q
      1548: 1
      1552: 1
      1554: 1
      1566: q
      1568: q
      1574: q
      1577: q
      1578: q
      1635: q
      1639: 1
      1644: q+1
      1646: 1
      1647: q
      1648: 1
      1650: q
      1652: 1
      1654: 1
      1664: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1683: 1
      1694: q
      1724: 1
      1736: 1
      1740: 1
      1746: q
      1748: 1
      1752: 1
      1764: 1
      1802: 1
      1820: q
      1825: 1
      1828: 1
      1830: 1
      1833: 1
      1842: 1
      1854: 1
      1900: 1
      1927: 1
      1935: 1
      1957: 1
      1960: 1
      1963: 1
      1972: 1
      2027: 1
      2035: 1
      2042: 1
      2074: 1

2075:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: q^5+3q^4+3q^3+q^2+q
        23: q^5+3q^4+3q^3+q^2+q
        24: q^5+3q^4+3q^3+q^2+q
        25: 2q^4+2q^3+q^2+q
        26: 2q^4+2q^3+q^2+q
        27: 2q^4+2q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: 2q^4+3q^3+q^2+q
        32: q^5+3q^4+3q^3+q^2+q
        33: 2q^4+3q^3+q^2+q
        34: q^4+2q^3+q^2+q
        35: 2q^4+2q^3+q^2+q
        36: q^4+2q^3+q^2+q
        37: 2q^4+2q^3+q^2+q
        39: 2q^4+2q^3+q^2+q
        41: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^5+3q^4+3q^3+q^2+q
        53: q^5+3q^4+3q^3+q^2+q
        54: q^5+3q^4+3q^3+q^2+q
        55: 2q^4+2q^3+q^2+q
        56: 2q^4+2q^3+q^2+q
        57: 2q^4+2q^3+q^2+q
        58: q^3+q^2
        59: q^4+2q^3+q
        60: q^3+q^2
        61: q^3+q
        62: q^4+2q^3+q^2+q
        64: 2q^4+2q^3+q^2+q
        66: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: q^4+2q^3+q^2+q
        73: 2q^4+3q^3+q^2+q
        74: 2q^4+2q^3+q^2+q
        76: 2q^4+2q^3+q^2+q
        78: 2q^4+2q^3+q^2+q
        80: 2q^4+3q^3+q^2+q
        81: 2q^4+3q^3+q^2+q
        82: 2q^4+3q^3+q^2+q
        83: q^5+3q^4+3q^3+q^2+q
        84: q^4+2q^3+q^2+q
        85: q^4+2q^3+q^2+q
        86: q^4+2q^3+q^2+q
        87: 2q^4+2q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^4+3q^3+q^2+q
        95: 2q^4+3q^3+q^2+q
        96: q^5+2q^4+2q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       103: q^3+q^2
       106: q^3+q
       107: q^3+q^2
       108: q^3+q
       109: q^3+q^2
       110: q^4+2q^3+q
       111: q^4+2q^3+q^2+q
       113: q^4+2q^3+q^2+q
       115: 2q^4+2q^3+q^2+q
       117: q^3+q^2
       118: q^4+2q^3+q
       119: q^3+q^2
       120: q^3+q
       121: q^4+2q^3+q^2+q
       123: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: 2q^4+3q^3+q^2+q
       137: 3q^3+q^2+q
       138: q^4+2q^3+q^2+q
       139: q^4+3q^3+q^2+q
       140: q^4+2q^3+q^2+q
       141: 2q^4+3q^3+q^2+q
       142: 2q^4+3q^3+q^2+q
       143: 2q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^4+2q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^3+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       151: 2q^4+2q^3+q^2+q
       153: 2q^4+2q^3+q^2+q
       155: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^4+3q^3+q^2+q
       161: 2q^4+3q^3+q^2+q
       162: q^5+2q^4+2q^3+q^2+q
       163: 2q^3+q^2+q
       164: 2q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3+q^2
       172: q^3+q
       173: q^3+q^2
       176: q^3+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^3+q^2
       184: q^3+q
       185: q^3+q^2
       186: q^4+2q^3+q
       187: q^4+2q^3+q^2+q
       189: q^4+2q^3+q^2+q
       191: q^3+q^2
       192: 2q^3+q
       193: q^3+q^2
       194: q^3+q
       195: q^3+q^2
       196: q^4+2q^3+q
       197: q^4+2q^3+q^2+q
       199: q^3+q^2
       200: q^3+q
       201: q^3+q^2
       202: q^3+q
       204: q^3+q
       205: q^3+q
       207: 2q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: 2q^4+2q^3+q^2+q
       213: 2q^3+q^2+q
       215: 2q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 2q^3+q^2+q
       223: q^3+q^2+q
       224: 3q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^4+3q^3+q^2+q
       228: q^4+2q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: 2q^4+3q^3+q^2+q
       231: q^3+q^2+q
       232: 2q^3+q^2+q
       233: q^3+q^2+q
       234: 2q^3+q^2+q
       235: q^3+q
       236: q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: 2q^3+q^2+q
       245: q^3+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: q^3+q^2
       262: q^3+q
       263: q^3+q^2
       266: q^3+q
       267: q^3+q^2
       269: q^3+q
       273: q^3+q
       275: q^3+q^2
       278: q^3+q
       279: 2q^3+q^2+q
       281: q^3+q^2+q
       283: q^2
       284: q
       285: q^2
       286: q^3+q
       287: q^3+q^2+q
       289: 2q^3+q^2+q
       291: q^3+q^2+q
       293: q^3+q^2
       294: q^3+q
       295: q^3+q^2
       296: 2q^3+q
       297: 2q^3+q^2+q
       299: q^3+q^2
       300: q^3+q
       301: 2q^3+q^2+q
       303: q^3+q^2
       304: q^4+2q^3+q
       305: q^4+2q^3+q^2+q
       307: q^3+q^2
       308: q^3+q
       310: q^3+q
       311: q^3+q
       313: q^3+q
       315: q^3+q^2+q
       317: 2q^3+q^2+q
       319: q^3+q^2
       320: q^3+q
       322: q^3+q
       323: q^3+q
       325: q^4+2q^3+q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: 2q^3+q^2+q
       334: q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       338: 2q^3+q^2+q
       340: 2q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: 2q^3+q^2+q
       348: q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: 2q^3+q^2+q
       352: q^3+q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+q^2+q
       357: q
       358: q
       359: q^3+q
       360: 2q^3+q^2+q
       362: 2q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: 2q^3+q^2+q
       370: q^3+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2
       380: q
       381: q^3+q^2
       384: q^3+q
       385: q^3+q^2
       388: q^3+q
       389: q^3+q^2
       391: q^3+q
       393: q^3+q^2
       396: q^3+q
       399: q^3+q
       404: q^3+q
       406: q^3+q
       409: q^2+q
       411: q^2+q
       413: q^3+q^2+q
       415: q^2+q
       417: q^3+q^2+q
       419: q^2
       420: q
       421: q^2
       422: q^3+q
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: 2q^3+q^2+q
       429: q^2
       430: q
       431: q^2
       432: q^3+q
       433: q^3+q^2+q
       435: 2q^3+q^2+q
       437: q^3+q^2
       438: q^3+q
       439: q^3+q^2
       440: 2q^3+q
       441: 2q^3+q^2+q
       443: q^3+q^2
       444: q^3+q
       445: 2q^3+q^2+q
       447: q^2
       448: q
       450: q
       451: q
       453: q^2
       454: q
       455: q^3+q
       458: q
       459: q
       462: q^3+q
       463: q^3+q
       465: 2q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       471: q^3+q^2
       472: q^3+q
       474: q^3+q
       475: q^3+q
       477: q^3+q
       479: q^3+q
       481: q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       485: 2q^3+q^2+q
       487: 2q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^3+q^2+q
       494: 2q^3+q^2+q
       495: q^3+q^2+q
       496: 2q^3+q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^3+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+q^2+q
       513: q
       514: q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       521: q^2
       524: q
       525: q^2
       528: q
       529: q^2
       532: q
       533: q^2
       536: q
       537: q^3+q^2
       539: q^3+q
       541: q^3+q^2
       543: q^3+q
       545: q^3+q^2
       547: q^3+q
       552: q
       555: q^3+q
       559: q
       563: q^3+q
       568: q^3+q
       570: q^3+q
       575: q^3+q
       577: q^3+q
       583: q^2+q
       585: q^3+q^2+q
       587: q^2+q
       589: q^2
       590: q
       592: q
       593: q^2
       594: q
       595: q^2
       596: q^3+q
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: 2q^3+q^2+q
       603: q^2
       604: q
       605: q^3+q^2+q
       607: q^2
       608: q^3+q
       609: q^3+q^2+q
       611: q^2+q
       613: q^3+q^2+q
       615: q^3+q^2
       616: q^3+q
       617: 2q^3+q^2+q
       619: q^2
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       632: q^3+q
       633: q^3+q
       635: q^2+q
       637: q^2+q
       639: q^3+q^2+q
       641: q^2
       642: q
       644: q
       645: q
       647: q^2
       648: q
       650: q
       651: q^3+q
       653: q
       655: q^3+q
       657: q^2+q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+q
       673: q^2+q
       674: q^2+q
       675: q^3+q^2+q
       676: 2q^3+q^2+q
       677: q^3+q^2+q
       678: q^2+q
       679: q^3+q^2+q
       680: q
       681: q^2+q
       682: q
       683: q
       684: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       697: q^3+q
       705: q^2
       708: q
       709: q^2
       712: q
       716: q
       717: q^2
       720: q
       721: q^2
       723: q
       725: q^2
       727: q
       729: q^2
       731: q
       733: q^3+q^2
       735: q^3+q
       739: q
       743: q
       747: q
       751: q^3+q
       756: q
       758: q^3+q
       762: q
       768: q^3+q
       769: q^3+q
       775: q^2+q
       777: q^2+q
       779: q^2+q
       781: q^3+q^2+q
       783: q^2+q
       785: q^2
       786: q
       788: q
       789: q^2+q
       791: q
       793: q^2
       794: q
       795: q^2+q
       797: q^3+q^2+q
       799: q^2+q
       801: q^2
       802: q
       804: q
       805: q^2
       806: q
       807: q^2
       808: q^3+q
       809: q^3+q^2+q
       811: q^3+q^2+q
       813: q^2+q
       815: q^2
       816: q
       818: q
       819: q
       821: q
       823: q
       825: q^2
       826: q
       828: q
       832: q
       833: q
       835: q
       837: q
       840: q
       841: q^2+q
       843: q
       845: q^2
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       857: q
       866: q^2+q
       868: q^2+q
       870: q^2+q
       871: q^3+q^2+q
       872: q^2+q
       874: q
       875: q
       876: q
       877: q^2+q
       878: q
       879: q
       880: q
       889: q^3+q
       896: q^2
       899: q
       902: q
       904: q^2
       906: q
       911: q
       912: q^2
       914: q
       916: q^2
       918: q
       920: q^2
       922: q
       927: q
       928: q^2
       930: q
       932: q^2
       934: q
       938: q
       942: q
       946: q
       950: q
       958: q
       961: q
       967: q
       968: q
       975: q
       979: q
       982: q
       991: q
       994: q^2+q
       999: q
      1000: q^2
      1001: q
      1002: q^2+q
      1004: q^2
      1005: q
      1007: q
      1008: q
      1010: q
      1012: q
      1018: q^2+q
      1020: q^2+q
      1022: q^3+q^2+q
      1024: q^2+q
      1026: q^2
      1027: q
      1029: q
      1034: q
      1036: q
      1038: q
      1042: q
      1045: q
      1048: q
      1050: q
      1052: q^2
      1053: q
      1055: q
      1059: q
      1060: q
      1062: q
      1064: q
      1076: q^2+q
      1078: q^2+q
      1080: q
      1082: q
      1083: q
      1084: q
      1085: q
      1091: q
      1102: q
      1112: q
      1116: q
      1118: q^2
      1120: q
      1122: q^2
      1124: q
      1127: q
      1133: q
      1135: q
      1138: q
      1148: q^2
      1150: q
      1154: q
      1156: q^2
      1158: q
      1163: q
      1170: q
      1174: q
      1185: q
      1199: q
      1204: q
      1220: q
      1222: q
      1230: q^2+q
      1233: q
      1234: q^2
      1235: q
      1238: q^2+q
      1240: q^2
      1241: q
      1243: q
      1248: q
      1251: q
      1256: q
      1261: q
      1264: q
      1266: q
      1271: q
      1272: q
      1274: q
      1276: q
      1278: q
      1280: q
      1287: q
      1289: q
      1295: q
      1323: q
      1331: q
      1346: q
      1350: q
      1352: q^2
      1354: q
      1356: q^2
      1358: q
      1361: q
      1367: q
      1369: q
      1378: q
      1382: q
      1415: q
      1420: q
      1430: q
      1446: q
      1464: q
      1467: q
      1470: q
      1474: q
      1479: q
      1480: q
      1484: q
      1506: q
      1560: q
      1572: q
      1580: q
      1605: q
      1609: q
      1637: 1
      1641: q
      1650: q
      1671: q
      1725: 1
      1730: 1
      1754: q
      1759: q
      1823: 1
      1843: 1
      1895: 1
      1928: 1
      1958: 1
      1973: 1
      2028: 1
      2037: 1
      2075: 1

2076:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 3q^3+4q^2+2q
        23: 3q^3+4q^2+2q
        24: q^4+3q^3+3q^2+2q
        25: 4q^2+2q
        26: 4q^2+2q
        27: q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 3q^3+4q^2+2q
        32: 2q^3+3q^2+2q
        33: 3q^3+4q^2+2q
        34: 4q^2+2q
        35: 3q^2+2q
        36: 4q^2+2q
        37: 3q^2+q
        38: q^2+q
        39: 3q^2+q
        40: q^2+q
        41: q^3+2q^2+q
        42: q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 3q^3+4q^2+2q
        53: 3q^3+4q^2+2q
        54: q^4+3q^3+3q^2+2q
        55: 4q^2+2q
        56: 4q^2+2q
        57: q^3+3q^2+2q
        58: q^3+2q^2
        59: 2q^3+2q^2+2q
        60: q^2+q
        61: 3q^2+q
        62: 3q^2+q
        63: q^2+q
        64: 2q^2+q
        65: q^2+q
        66: 3q^2+q
        67: q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 4q^2+2q
        73: 3q^3+4q^2+2q
        74: 3q^2+q
        75: q^2+q
        76: 3q^2+q
        77: q^2+q
        78: q^3+2q^2+q
        79: q^2+q
        80: 2q^3+3q^2+2q
        81: 2q^3+3q^2+2q
        82: 3q^3+4q^2+2q
        83: 2q^3+3q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 4q^2+2q
        87: 3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 3q^3+4q^2+2q
        95: 3q^3+4q^2+2q
        96: q^4+3q^3+3q^2+2q
        97: 4q^2+2q
        98: 4q^2+2q
        99: q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q^2
       104: q
       105: q^2
       106: 2q^2+q
       107: q^2+q
       108: 3q^2+q
       109: q^3+2q^2
       110: 2q^3+2q^2+2q
       111: 3q^2+q
       112: q^2+q
       113: 3q^2+q
       114: q^2+q
       115: 2q^2+q
       116: q^2+q
       117: q^2
       118: q^3+q^2+2q
       119: q
       120: 2q^2+q
       121: 2q^2+q
       122: q^2+q
       123: 2q^2+q
       124: q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: 3q^2+q
       128: q^2+q
       129: 3q^2+q
       130: q^2+q
       131: q^3+2q^2+q
       132: q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 3q^2+2q
       136: 2q^3+3q^2+2q
       137: 2q^3+3q^2+2q
       138: 2q^3+3q^2+2q
       139: 3q^3+4q^2+2q
       140: 4q^2+2q
       141: 2q^3+3q^2+2q
       142: 3q^3+4q^2+2q
       143: 3q^2+2q
       144: 3q^2+2q
       145: 4q^2+2q
       146: 3q^2+2q
       147: 4q^2+2q
       148: q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: 3q^2+q
       152: q^2+q
       153: 3q^2+q
       154: q^2+q
       155: q^3+2q^2+q
       156: q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^3+3q^2+2q
       161: 2q^3+3q^2+2q
       162: 2q^3+3q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q^2
       170: q
       171: q^2
       172: 2q^2+q
       174: q
       175: q^2
       176: q^2+q
       177: 2q^2+q
       178: q^2+q
       179: 3q^2+q
       180: q^2+q
       181: 3q^2+q
       182: q^2+q
       183: q
       184: 2q^2+q
       185: q^2
       186: q^3+q^2+2q
       187: 2q^2+q
       188: q^2+q
       189: 2q^2+q
       190: q^2+q
       191: q^2
       192: q^3+q^2+2q
       193: q^2+q
       194: 3q^2+q
       195: q^3+2q^2
       196: 2q^3+2q^2+2q
       197: 3q^2+q
       198: q^2+q
       199: q
       200: 2q^2+q
       201: q^2+q
       202: 3q^2+q
       204: q^2+2q
       205: q^2+q
       206: q
       207: 2q^2+q
       208: q^2+q
       209: 3q^2+q
       210: q^2+q
       211: 2q^2+q
       212: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 3q^2+2q
       223: 3q^2+2q
       224: 2q^3+3q^2+2q
       225: 2q^3+3q^2+2q
       226: 2q^3+3q^2+2q
       227: q^3+2q^2+2q
       228: 2q^3+3q^2+2q
       229: 3q^2+2q
       230: 2q^3+3q^2+2q
       231: 3q^2+2q
       232: q^2+2q
       233: 2q^2+2q
       234: 2q^2+2q
       235: 2q
       236: 3q^2+2q
       237: 3q^2+q
       238: q^2+q
       239: 3q^2+q
       240: q^2+q
       241: q^3+2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: 4q^2+2q
       245: q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^3+3q^2+2q
       251: 2q^3+3q^2+2q
       252: 2q^3+3q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q^2
       260: q
       261: q^2
       262: 2q^2+q
       264: q
       265: q^2
       266: q^2+q
       267: q^2
       268: q
       269: 2q^2+q
       270: q^2
       273: q^2+q
       274: q
       276: q
       277: q^2
       278: q^2+q
       279: q
       281: q^2+q
       283: q
       284: 2q^2+q
       285: q^2
       286: q^3+q^2+2q
       287: 2q^2+q
       288: q^2+q
       289: q^2+q
       291: 2q^2+q
       292: q^2+q
       293: q
       294: 2q^2+q
       295: q^2
       296: q^3+q^2+2q
       297: 2q^2+q
       298: q^2+q
       299: q
       300: 2q^2+q
       301: 3q^2+q
       302: q^2+q
       303: q^2
       304: q^3+q^2+2q
       305: 2q^2+q
       306: q^2+q
       307: q
       308: q^2+q
       310: 2q
       311: q^2+q
       312: q
       313: q
       314: q
       315: 2q^2+q
       316: q^2+q
       317: 3q^2+q
       318: q^2+q
       319: q^2+q
       320: 3q^2+q
       322: q^2+2q
       323: q^2+q
       324: q
       325: 2q^2+q
       326: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+2q
       334: 3q^2+2q
       335: 2q^3+3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: 3q^2+q
       339: q^2+q
       340: 3q^2+q
       341: q^2+q
       342: q^3+2q^2+q
       343: q^2+q
       344: q^3+2q^2+2q
       345: q^3+2q^2+2q
       346: 2q^3+3q^2+2q
       347: 3q^2+2q
       348: 3q^2+2q
       349: 2q^3+3q^2+2q
       350: 2q^3+3q^2+2q
       351: 4q^2+2q
       352: q^2+2q
       353: q^2+2q
       354: 2q^2+2q
       355: 2q^2+2q
       356: 2q^2+2q
       357: 2q
       358: 2q
       359: q^2+2q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q^2+2q
       370: 2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       378: q
       379: q^2
       380: q^2+q
       384: q
       386: q
       387: q^2
       388: q^2+q
       389: q^2
       390: q
       391: 2q^2+q
       392: q^2
       394: q
       395: q^2
       396: q^2+q
       399: q^2+q
       400: q
       403: q
       404: q
       406: q^2+q
       407: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q
       420: 2q^2+q
       421: q^2
       422: q^3+q^2+2q
       423: 2q^2+q
       424: q^2+q
       425: 2q^2+q
       426: q^2+q
       427: 3q^2+q
       428: q^2+q
       429: q
       430: 2q^2+q
       431: q^2
       432: q^3+q^2+2q
       433: 2q^2+q
       434: q^2+q
       435: q^2+q
       437: q
       438: 2q^2+q
       439: q^2
       440: q^3+q^2+2q
       441: 2q^2+q
       442: q^2+q
       443: q^2+q
       444: 3q^2+q
       445: 3q^2+q
       446: q^2+q
       447: q
       448: q^2+q
       450: 2q
       451: q
       452: q
       453: q
       454: q^2+q
       455: q
       458: 2q
       459: q
       460: q
       462: q^2+2q
       463: q^2+q
       464: q
       465: q
       467: q^2+q
       469: 2q^2+q
       470: q^2+q
       471: q
       472: q^2+q
       474: 2q
       475: q
       476: q
       477: q^2+q
       478: q
       479: q^2+q
       480: q
       481: q^2+2q
       482: q^3+2q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: 2q^2+2q
       492: q^3+2q^2+2q
       493: 3q^2+2q
       494: 2q^3+3q^2+2q
       495: 3q^2+2q
       496: 2q^2+2q
       497: q^2+2q
       498: 2q^2+2q
       499: 2q
       500: 2q
       501: 2q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q^2+2q
       512: 2q^2+2q
       513: 2q
       514: 2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       524: q
       528: q
       530: q
       531: q^2
       532: q^2+q
       534: q
       535: q^2
       536: q^2+q
       539: q
       542: q
       543: q^2+q
       544: q^2
       545: q^2
       546: q
       547: 2q^2+q
       548: q^2
       551: q
       552: q
       555: q
       559: q
       560: q
       563: q^2+q
       564: q
       566: q
       568: q
       570: q^2+q
       571: q
       574: q
       575: q^2+q
       577: q^2+q
       581: q
       583: q
       585: q
       587: q^2+q
       589: q
       590: q^2+q
       592: 2q
       593: q
       594: 2q^2+q
       595: q^2
       596: q^3+q^2+2q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q
       603: q
       604: 2q^2+q
       605: q^2+q
       607: q^2
       608: q^3+q^2+2q
       609: 2q^2+q
       610: q^2+q
       611: q^2+q
       613: 2q^2+q
       614: q^2+q
       615: q
       616: q^2+q
       617: q^2+q
       619: q
       620: q^2+q
       622: 2q
       623: q
       625: q
       626: q
       627: q
       629: q
       630: q
       632: 2q
       633: q
       635: q
       637: q^2+q
       639: q
       641: q
       642: q^2+q
       644: 2q
       645: q
       646: q
       647: q
       648: q^2+q
       650: 2q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q^2+2q
       675: q^2+2q
       676: q^3+2q^2+2q
       677: 3q^2+2q
       678: 2q^2+2q
       679: 2q^2+2q
       680: 2q
       681: q^2+2q
       682: q
       683: 2q
       684: 2q
       685: 2q
       686: q^2+2q
       687: 2q^2+2q
       688: 2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       697: q^2+q
       699: q
       708: q
       712: q
       715: q
       716: q
       718: q
       719: q^2
       720: q^2+q
       723: q
       726: q
       727: q^2+q
       728: q^2
       731: q
       735: q
       739: q
       743: q
       744: q
       747: q
       751: q
       754: q
       756: q
       758: q
       762: q
       763: q
       766: q
       768: q
       769: q
       775: q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: q
       786: q^2+q
       788: 2q
       789: q
       791: q
       792: q
       793: q
       794: q^2+q
       795: q^2+q
       797: q
       799: q^2+q
       801: q
       802: q^2+q
       804: 2q
       805: q
       806: 2q^2+q
       807: q^2
       808: q^3+q^2+2q
       809: q^2+q
       811: 2q^2+q
       812: q^2+q
       813: q^2+q
       815: q
       816: q^2+q
       818: 2q
       819: q
       823: q
       825: q
       826: q^2+q
       828: 2q
       832: q
       833: q
       835: q
       836: q
       837: q
       840: 2q
       841: q
       843: q
       844: q
       845: q
       846: q^2+q
       848: 2q
       849: q
       851: q
       852: q
       853: q
       855: q
       856: q
       857: q
       858: q
       859: q^2+q
       861: q^2+q
       863: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q^2+2q
       870: 2q^2+2q
       871: q^2+2q
       872: 2q^2+2q
       873: 2q
       874: 2q
       875: q
       876: 2q
       877: q^2+2q
       878: q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       889: q
       899: q
       902: q
       906: q
       909: q
       911: q
       914: q
       918: q
       922: q
       926: q
       927: q
       929: q
       930: q^2+q
       931: q^2
       934: q
       938: q
       942: q
       950: q
       951: q
       958: q
       961: q
       965: q
       967: q
       968: q
       975: q
       976: q
       979: q
       982: q
       989: q
       991: q
       992: q
       994: q
       996: q^2+q
       999: 2q
      1000: q
      1001: q^2+q
      1002: q
      1004: q
      1005: q^2+q
      1007: 2q
      1008: q
      1009: q
      1010: q
      1012: q
      1013: q
      1014: q^2+q
      1016: q
      1017: q^2+q
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1026: q
      1027: q^2+q
      1029: 2q
      1030: q
      1033: 2q
      1036: q
      1042: q
      1045: q
      1046: q
      1047: q
      1050: q
      1052: q
      1053: q^2+q
      1055: 2q
      1059: q
      1060: q
      1062: q
      1063: q
      1064: q
      1065: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: q+1
      1076: q^2+2q
      1077: 2q^2+2q
      1078: q^2+2q
      1079: 1
      1080: q
      1081: 2q
      1082: q
      1083: q
      1084: 2q
      1085: 2q
      1091: q
      1102: q
      1112: q
      1116: q
      1120: q
      1124: q
      1127: q
      1131: q
      1133: q
      1135: q
      1136: q
      1138: q
      1146: q
      1150: q
      1154: q
      1158: q
      1162: q
      1163: q
      1166: q
      1185: q
      1188: q
      1195: q
      1197: q
      1204: q
      1205: q
      1210: q+1
      1212: q+1
      1214: q
      1217: 2q
      1218: q
      1219: q^2+q
      1222: q
      1224: q
      1225: q
      1226: q+1
      1228: 1
      1229: q
      1230: q
      1233: 2q
      1234: q
      1235: q^2+q
      1236: q^2+q
      1238: q
      1240: q
      1241: q^2+q
      1243: 2q
      1244: 1
      1247: 1
      1251: q
      1252: q
      1261: q
      1263: 1
      1271: q
      1272: q
      1274: q
      1276: q
      1277: q
      1278: q
      1280: q
      1281: q
      1282: q+1
      1283: q^2+2q
      1284: q+1
      1285: q
      1286: 1
      1287: q
      1288: 2q
      1289: q
      1295: q
      1307: q
      1316: q
      1320: q
      1323: q
      1327: q
      1329: q
      1334: q
      1340: 1
      1342: q
      1346: q
      1350: q
      1354: q
      1358: q
      1361: q
      1366: q
      1367: q
      1369: q
      1371: q
      1374: 1
      1407: 1
      1411: 1
      1430: q
      1438: q+1
      1441: 1
      1442: 1
      1443: q
      1445: 1
      1448: q
      1451: 2q
      1452: q+1
      1454: q
      1455: q^2+q
      1458: 1
      1461: q
      1467: q
      1472: q
      1479: q
      1480: q
      1482: q
      1483: q
      1484: q
      1485: q+1
      1486: 1
      1487: q
      1488: 1
      1494: q
      1506: q
      1528: 1
      1543: 1
      1545: 1
      1547: q
      1550: 1
      1556: 1
      1565: q
      1569: q
      1572: q
      1577: q
      1578: q
      1631: q
      1640: 1
      1643: q+1
      1646: 1
      1647: 1
      1648: q
      1650: q
      1651: 1
      1654: 1
      1664: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1678: 1
      1692: q
      1726: 1
      1734: 1
      1739: 1
      1745: 1
      1747: q
      1751: 1
      1763: 1
      1804: 1
      1820: q
      1826: 1
      1827: 1
      1830: 1
      1833: 1
      1837: 1
      1850: 1
      1901: 1
      1929: 1
      1934: 1
      1956: 1
      1961: 1
      1963: 1
      1974: 1
      2029: 1
      2034: 1
      2043: 1
      2076: 1

2077:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: q^5+3q^4+3q^3+q^2+q
        23: q^5+3q^4+3q^3+q^2+q
        24: q^5+3q^4+3q^3+q^2+q
        25: 2q^4+2q^3+q^2+q
        26: 2q^4+2q^3+q^2+q
        27: 2q^4+2q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: 2q^4+3q^3+q^2+q
        32: q^5+3q^4+3q^3+q^2+q
        33: 2q^4+3q^3+q^2+q
        34: q^4+2q^3+q^2+q
        35: 2q^4+2q^3+q^2+q
        36: q^4+2q^3+q^2+q
        38: 2q^4+2q^3+q^2+q
        40: 2q^4+2q^3+q^2+q
        42: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^5+3q^4+3q^3+q^2+q
        53: q^5+3q^4+3q^3+q^2+q
        54: q^5+3q^4+3q^3+q^2+q
        55: 2q^4+2q^3+q^2+q
        56: 2q^4+2q^3+q^2+q
        57: 2q^4+2q^3+q^2+q
        58: q^4+2q^3+q
        59: q^3+q^2
        60: q^3+q^2
        61: q^3+q
        63: q^4+2q^3+q^2+q
        65: 2q^4+2q^3+q^2+q
        67: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: q^4+2q^3+q^2+q
        73: 2q^4+3q^3+q^2+q
        75: 2q^4+2q^3+q^2+q
        77: 2q^4+2q^3+q^2+q
        79: 2q^4+2q^3+q^2+q
        80: 2q^4+3q^3+q^2+q
        81: 2q^4+3q^3+q^2+q
        82: 2q^4+3q^3+q^2+q
        83: q^5+3q^4+3q^3+q^2+q
        84: q^4+2q^3+q^2+q
        85: q^4+2q^3+q^2+q
        86: q^4+2q^3+q^2+q
        87: 2q^4+2q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^4+3q^3+q^2+q
        95: 2q^4+3q^3+q^2+q
        96: q^5+2q^4+2q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       104: q^3+q^2
       105: q^3+q
       107: q^3+q^2
       108: q^3+q
       109: q^4+2q^3+q
       110: q^3+q^2
       112: q^4+2q^3+q^2+q
       114: q^4+2q^3+q^2+q
       116: 2q^4+2q^3+q^2+q
       117: q^4+2q^3+q
       118: q^3+q^2
       119: q^3+q^2
       120: q^3+q
       122: q^4+2q^3+q^2+q
       124: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: 2q^4+3q^3+q^2+q
       137: 3q^3+q^2+q
       138: q^4+2q^3+q^2+q
       139: q^4+3q^3+q^2+q
       140: q^4+2q^3+q^2+q
       141: 2q^4+3q^3+q^2+q
       142: 2q^4+3q^3+q^2+q
       143: 2q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^4+2q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^3+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       152: 2q^4+2q^3+q^2+q
       154: 2q^4+2q^3+q^2+q
       156: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^4+3q^3+q^2+q
       161: 2q^4+3q^3+q^2+q
       162: q^5+2q^4+2q^3+q^2+q
       163: 2q^3+q^2+q
       164: 2q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3+q^2
       171: q^3+q
       174: q^3+q^2
       175: q^3+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^3+q^2
       184: q^3+q
       185: q^4+2q^3+q
       186: q^3+q^2
       188: q^4+2q^3+q^2+q
       190: q^4+2q^3+q^2+q
       191: 2q^3+q
       192: q^3+q^2
       193: q^3+q^2
       194: q^3+q
       195: q^4+2q^3+q
       196: q^3+q^2
       198: q^4+2q^3+q^2+q
       199: q^3+q^2
       200: q^3+q
       201: q^3+q^2
       202: q^3+q
       203: q^3+q
       206: q^3+q
       208: 2q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: 2q^4+2q^3+q^2+q
       214: 2q^3+q^2+q
       216: 2q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 2q^3+q^2+q
       223: q^3+q^2+q
       224: 3q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^4+3q^3+q^2+q
       228: q^4+2q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: 2q^4+3q^3+q^2+q
       231: q^3+q^2+q
       232: 2q^3+q^2+q
       233: q^3+q^2+q
       234: 2q^3+q^2+q
       235: q^3+q
       236: q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: 2q^3+q^2+q
       245: q^3+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: q^3+q^2
       261: q^3+q
       264: q^3+q^2
       265: q^3+q
       268: q^3+q^2
       270: q^3+q
       272: q^3+q
       276: q^3+q^2
       277: q^3+q
       280: 2q^3+q^2+q
       282: q^3+q^2+q
       283: q^2
       284: q
       285: q^3+q
       286: q^2
       288: q^3+q^2+q
       290: 2q^3+q^2+q
       292: q^3+q^2+q
       293: q^3+q^2
       294: q^3+q
       295: 2q^3+q
       296: q^3+q^2
       298: 2q^3+q^2+q
       299: q^3+q^2
       300: q^3+q
       302: 2q^3+q^2+q
       303: q^4+2q^3+q
       304: q^3+q^2
       306: q^4+2q^3+q^2+q
       307: q^3+q^2
       308: q^3+q
       309: q^3+q
       312: q^3+q
       314: q^3+q
       316: q^3+q^2+q
       318: 2q^3+q^2+q
       319: q^3+q^2
       320: q^3+q
       321: q^3+q
       324: q^3+q
       326: q^4+2q^3+q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: 2q^3+q^2+q
       334: q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       339: 2q^3+q^2+q
       341: 2q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: 2q^3+q^2+q
       348: q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: 2q^3+q^2+q
       352: q^3+q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+q^2+q
       357: q
       358: q
       359: q^3+q
       361: 2q^3+q^2+q
       363: 2q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: 2q^3+q^2+q
       370: q^3+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2
       379: q
       382: q^3+q^2
       383: q^3+q
       386: q^3+q^2
       387: q^3+q
       390: q^3+q^2
       392: q^3+q
       394: q^3+q^2
       395: q^3+q
       398: q^3+q
       402: q^3+q
       408: q^3+q
       410: q^2+q
       412: q^2+q
       414: q^3+q^2+q
       416: q^2+q
       418: q^3+q^2+q
       419: q^2
       420: q
       421: q^3+q
       422: q^2
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: 2q^3+q^2+q
       429: q^2
       430: q
       431: q^3+q
       432: q^2
       434: q^3+q^2+q
       436: 2q^3+q^2+q
       437: q^3+q^2
       438: q^3+q
       439: 2q^3+q
       440: q^3+q^2
       442: 2q^3+q^2+q
       443: q^3+q^2
       444: q^3+q
       446: 2q^3+q^2+q
       447: q^2
       448: q
       449: q
       452: q
       453: q^2
       454: q
       456: q^3+q
       457: q
       460: q
       461: q^3+q
       464: q^3+q
       466: 2q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       471: q^3+q^2
       472: q^3+q
       473: q^3+q
       476: q^3+q
       478: q^3+q
       480: q^3+q
       481: q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       486: 2q^3+q^2+q
       488: 2q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^3+q^2+q
       494: 2q^3+q^2+q
       495: q^3+q^2+q
       496: 2q^3+q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^3+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+q^2+q
       513: q
       514: q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       522: q^2
       523: q
       526: q^2
       527: q
       530: q^2
       531: q
       534: q^2
       535: q
       538: q^3+q^2
       540: q^3+q
       542: q^3+q^2
       544: q^3+q
       546: q^3+q^2
       548: q^3+q
       550: q
       554: q^3+q
       558: q
       562: q^3+q
       567: q^3+q
       572: q^3+q
       576: q^3+q
       581: q^3+q
       584: q^2+q
       586: q^3+q^2+q
       588: q^2+q
       589: q^2
       590: q
       591: q
       593: q^2
       594: q
       595: q^3+q
       596: q^2
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: 2q^3+q^2+q
       603: q^2
       604: q
       606: q^3+q^2+q
       607: q^3+q
       608: q^2
       610: q^3+q^2+q
       612: q^2+q
       614: q^3+q^2+q
       615: q^3+q^2
       616: q^3+q
       618: 2q^3+q^2+q
       619: q^2
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       631: q^3+q
       634: q^3+q
       636: q^2+q
       638: q^2+q
       640: q^3+q^2+q
       641: q^2
       642: q
       643: q
       646: q
       647: q^2
       648: q
       649: q
       652: q^3+q
       654: q
       656: q^3+q
       657: q^2+q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+q
       673: q^2+q
       674: q^2+q
       675: q^3+q^2+q
       676: 2q^3+q^2+q
       677: q^3+q^2+q
       678: q^2+q
       679: q^3+q^2+q
       680: q
       681: q^2+q
       682: q
       683: q
       684: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       700: q^3+q
       706: q^2
       707: q
       710: q^2
       711: q
       714: q
       718: q^2
       719: q
       722: q^2
       724: q
       726: q^2
       728: q
       730: q^2
       732: q
       734: q^3+q^2
       736: q^3+q
       738: q
       742: q
       746: q
       750: q^3+q
       755: q
       760: q^3+q
       764: q
       767: q^3+q
       773: q^3+q
       776: q^2+q
       778: q^2+q
       780: q^2+q
       782: q^3+q^2+q
       784: q^2+q
       785: q^2
       786: q
       787: q
       790: q^2+q
       792: q
       793: q^2
       794: q
       796: q^2+q
       798: q^3+q^2+q
       800: q^2+q
       801: q^2
       802: q
       803: q
       805: q^2
       806: q
       807: q^3+q
       808: q^2
       810: q^3+q^2+q
       812: q^3+q^2+q
       814: q^2+q
       815: q^2
       816: q
       817: q
       820: q
       822: q
       824: q
       825: q^2
       826: q
       827: q
       831: q
       834: q
       836: q
       838: q
       839: q
       842: q^2+q
       844: q
       845: q^2
       846: q
       847: q
       850: q
       852: q
       854: q
       856: q
       858: q
       866: q^2+q
       868: q^2+q
       870: q^2+q
       871: q^3+q^2+q
       872: q^2+q
       874: q
       875: q
       876: q
       877: q^2+q
       878: q
       879: q
       880: q
       891: q^3+q
       897: q^2
       898: q
       901: q
       905: q^2
       907: q
       910: q
       913: q^2
       915: q
       917: q^2
       919: q
       921: q^2
       923: q
       925: q
       929: q^2
       931: q
       933: q^2
       935: q
       937: q
       941: q
       945: q
       949: q
       957: q
       963: q
       966: q
       972: q
       977: q
       981: q
       986: q
       990: q
       995: q^2+q
       998: q
      1000: q^2
      1001: q
      1003: q^2+q
      1004: q^2
      1005: q
      1006: q
      1009: q
      1011: q
      1013: q
      1019: q^2+q
      1021: q^2+q
      1023: q^3+q^2+q
      1025: q^2+q
      1026: q^2
      1027: q
      1028: q
      1035: q
      1037: q
      1039: q
      1043: q
      1044: q
      1049: q
      1051: q
      1052: q^2
      1053: q
      1054: q
      1058: q
      1061: q
      1063: q
      1065: q
      1076: q^2+q
      1078: q^2+q
      1080: q
      1082: q
      1083: q
      1084: q
      1085: q
      1093: q
      1105: q
      1111: q
      1115: q
      1119: q^2
      1121: q
      1123: q^2
      1125: q
      1129: q
      1132: q
      1137: q
      1142: q
      1149: q^2
      1151: q
      1153: q
      1157: q^2
      1159: q
      1161: q
      1169: q
      1173: q
      1187: q
      1201: q
      1203: q
      1221: q
      1223: q
      1231: q^2+q
      1232: q
      1234: q^2
      1235: q
      1239: q^2+q
      1240: q^2
      1241: q
      1242: q
      1249: q
      1250: q
      1257: q
      1260: q
      1265: q
      1267: q
      1270: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1287: q
      1289: q
      1297: q
      1325: q
      1333: q
      1345: q
      1349: q
      1353: q^2
      1355: q
      1357: q^2
      1359: q
      1362: q
      1365: q
      1370: q
      1377: q
      1381: q
      1417: q
      1419: q
      1434: q
      1447: q
      1465: q
      1466: q
      1471: q
      1475: q
      1478: q
      1481: q
      1484: q
      1507: q
      1562: q
      1573: q
      1581: q
      1604: q
      1608: q
      1638: 1
      1642: q
      1649: q
      1672: q
      1728: 1
      1732: 1
      1755: q
      1758: q
      1824: 1
      1845: 1
      1896: 1
      1931: 1
      1959: 1
      1975: 1
      2031: 1
      2038: 1
      2077: 1

2078:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q
        59: q^2+1
        60: 1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q^2+q+1
        75: q+1
        77: q+1
        79: q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: q
       107: 1
       108: q
       109: q
       110: q^2+1
       112: q+1
       114: q+1
       116: q+1
       117: q
       118: q^2+1
       119: 1
       120: q
       122: q+1
       124: q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       171: q
       174: 1
       175: q
       178: q+1
       180: q+1
       182: q+1
       183: 1
       184: q
       185: q
       186: q^2+1
       188: q+1
       190: q+1
       191: q
       192: q^2+1
       193: 1
       194: q
       195: q
       196: q^2+1
       198: q+1
       199: 1
       200: q
       201: 1
       202: q
       204: 1
       206: 1
       208: q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       261: q
       264: 1
       265: q
       268: 1
       270: q
       274: 1
       276: 1
       277: q
       280: q+1
       282: q+1
       283: 1
       284: q
       285: q
       286: q^2+1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       294: q
       295: q
       296: q^2+1
       298: q+1
       299: 1
       300: q
       302: q+1
       303: q
       304: q^2+1
       306: q+1
       307: 1
       308: q
       310: 1
       312: 1
       314: 1
       316: q+1
       318: q+1
       319: 1
       320: q
       322: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: 1
       358: 1
       359: 1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       382: 1
       383: q
       386: 1
       387: q
       390: 1
       392: q
       394: 1
       395: q
       400: 1
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: 1
       420: q
       421: q
       422: q^2+1
       424: q+1
       426: q+1
       428: q+1
       429: 1
       430: q
       431: q
       432: q^2+1
       434: q+1
       436: q+1
       437: 1
       438: q
       439: q
       440: q^2+1
       442: q+1
       443: 1
       444: q
       446: q+1
       447: 1
       448: q
       450: 1
       452: 1
       453: 1
       454: q
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       472: q
       474: 1
       476: 1
       478: 1
       480: 1
       481: q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       526: 1
       527: q
       530: 1
       531: q
       534: 1
       535: q
       538: 1
       540: q
       542: 1
       544: q
       546: 1
       548: q
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: q+1
       586: q+1
       588: q+1
       589: 1
       590: q
       592: 1
       593: 1
       594: q
       595: q
       596: q^2+1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       604: q
       606: q+1
       607: q
       608: q^2+1
       610: q+1
       612: q+1
       614: q+1
       615: 1
       616: q
       618: q+1
       619: 1
       620: q
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       642: q
       644: 1
       646: 1
       647: 1
       648: q
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: 1
       706: 1
       707: q
       710: 1
       711: q
       715: 1
       718: 1
       719: q
       722: 1
       724: q
       726: 1
       728: q
       730: 1
       732: q
       734: 1
       736: q
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       786: q
       788: 1
       790: q+1
       792: 1
       793: 1
       794: q
       796: q+1
       798: q+1
       800: q+1
       801: 1
       802: q
       804: 1
       805: 1
       806: q
       807: q
       808: q^2+1
       810: q+1
       812: q+1
       814: q+1
       815: 1
       816: q
       818: 1
       820: 1
       822: 1
       824: 1
       825: 1
       826: q
       828: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: q+1
       844: 1
       845: 1
       846: q
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       890: 1
       897: 1
       898: q
       903: 1
       905: 1
       907: q
       909: 1
       913: 1
       915: q
       917: 1
       919: q
       921: 1
       923: q
       926: 1
       929: 1
       931: q
       933: 1
       935: q
       939: 1
       943: 1
       947: 1
       951: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       999: 1
      1000: 1
      1001: q
      1003: q+1
      1004: 1
      1005: q
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: q+1
      1016: 1
      1017: q
      1019: q+1
      1021: q+1
      1023: q+1
      1025: q+1
      1026: 1
      1027: q
      1029: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q
      1055: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1121: q
      1123: 1
      1125: q
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1147: q
      1149: 1
      1151: q
      1155: 1
      1157: 1
      1159: q
      1162: 1
      1167: 1
      1171: 1
      1175: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1205: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1217: 1
      1218: 1
      1219: q
      1221: 1
      1223: 1
      1225: 1
      1227: q+1
      1228: 1
      1229: q
      1231: q+1
      1233: 1
      1234: 1
      1235: q
      1237: q+1
      1239: q+1
      1240: 1
      1241: q
      1243: 1
      1245: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1257: 1
      1261: 1
      1263: 1
      1265: 1
      1267: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1321: q
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1343: q
      1347: 1
      1351: 1
      1353: 1
      1355: q
      1357: 1
      1359: q
      1363: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1383: 1
      1408: 1
      1411: 1
      1416: 1
      1421: 1
      1434: 1
      1437: 1
      1439: q+1
      1441: 1
      1442: 1
      1443: q
      1445: 1
      1447: 1
      1449: q+1
      1451: 1
      1453: q+1
      1454: 1
      1455: q
      1457: 1
      1459: 1
      1461: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1475: 1
      1479: 1
      1481: 1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1495: 1
      1508: 1
      1531: 1
      1539: 1
      1544: 1
      1546: 1
      1548: q
      1550: 1
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1570: q
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1606: 1
      1610: 1
      1635: 1
      1638: 1
      1640: 1
      1642: 1
      1644: q+1
      1646: 1
      1647: 1
      1648: q
      1650: 1
      1652: 1
      1654: 1
      1660: 1
      1662: 1
      1664: 1
      1668: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1681: 1
      1694: 1
      1727: 1
      1731: 1
      1734: 1
      1740: 1
      1744: 1
      1746: 1
      1748: q
      1751: 1
      1756: 1
      1760: 1
      1764: 1
      1788: 1
      1805: 1
      1816: 1
      1818: 1
      1820: 1
      1824: 1
      1826: 1
      1828: 1
      1830: 1
      1833: 1
      1840: 1
      1853: 1
      1897: 1
      1901: 1
      1905: 1
      1909: 1
      1930: 1
      1935: 1
      1957: 1
      1959: 1
      1961: 1
      1963: 1
      1976: 1
      2030: 1
      2035: 1
      2039: 1
      2043: 1
      2078: 1

2079:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: q^5+3q^4+3q^3+q^2+q
        23: q^5+3q^4+3q^3+q^2+q
        24: q^5+3q^4+3q^3+q^2+q
        25: 2q^4+2q^3+q^2+q
        26: 2q^4+2q^3+q^2+q
        27: 2q^4+2q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: 2q^4+3q^3+q^2+q
        32: q^5+3q^4+3q^3+q^2+q
        33: 2q^4+3q^3+q^2+q
        34: q^4+2q^3+q^2+q
        35: 2q^4+2q^3+q^2+q
        36: q^4+2q^3+q^2+q
        38: 2q^4+2q^3+q^2+q
        40: 2q^4+2q^3+q^2+q
        42: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^5+3q^4+3q^3+q^2+q
        53: q^5+3q^4+3q^3+q^2+q
        54: q^5+3q^4+3q^3+q^2+q
        55: 2q^4+2q^3+q^2+q
        56: 2q^4+2q^3+q^2+q
        57: 2q^4+2q^3+q^2+q
        58: q^3+q^2
        59: q^4+2q^3+q
        60: q^3+q
        61: q^3+q^2
        63: q^4+2q^3+q^2+q
        65: 2q^4+2q^3+q^2+q
        67: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: q^4+2q^3+q^2+q
        73: 2q^4+3q^3+q^2+q
        75: 2q^4+2q^3+q^2+q
        77: 2q^4+2q^3+q^2+q
        79: 2q^4+2q^3+q^2+q
        80: 2q^4+3q^3+q^2+q
        81: 2q^4+3q^3+q^2+q
        82: 2q^4+3q^3+q^2+q
        83: q^5+3q^4+3q^3+q^2+q
        84: q^4+2q^3+q^2+q
        85: q^4+2q^3+q^2+q
        86: q^4+2q^3+q^2+q
        87: 2q^4+2q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^4+3q^3+q^2+q
        95: 2q^4+3q^3+q^2+q
        96: q^5+2q^4+2q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       104: q^3+q
       105: q^3+q^2
       107: q^3+q
       108: q^3+q^2
       109: q^3+q^2
       110: q^4+2q^3+q
       112: q^4+2q^3+q^2+q
       114: q^4+2q^3+q^2+q
       116: 2q^4+2q^3+q^2+q
       117: q^3+q^2
       118: q^4+2q^3+q
       119: q^3+q
       120: q^3+q^2
       122: q^4+2q^3+q^2+q
       124: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: 2q^4+3q^3+q^2+q
       137: 3q^3+q^2+q
       138: q^4+2q^3+q^2+q
       139: q^4+3q^3+q^2+q
       140: q^4+2q^3+q^2+q
       141: 2q^4+3q^3+q^2+q
       142: 2q^4+3q^3+q^2+q
       143: 2q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^4+2q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^3+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       152: 2q^4+2q^3+q^2+q
       154: 2q^4+2q^3+q^2+q
       156: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^4+3q^3+q^2+q
       161: 2q^4+3q^3+q^2+q
       162: q^5+2q^4+2q^3+q^2+q
       163: 2q^3+q^2+q
       164: 2q^3+q^2+q
       165: q^4+q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3+q
       171: q^3+q^2
       174: q^3+q
       175: q^3+q^2
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^3+q
       184: q^3+q^2
       185: q^3+q^2
       186: q^4+2q^3+q
       188: q^4+2q^3+q^2+q
       190: q^4+2q^3+q^2+q
       191: q^3+q^2
       192: 2q^3+q
       193: q^3+q
       194: q^3+q^2
       195: q^3+q^2
       196: q^4+2q^3+q
       198: q^4+2q^3+q^2+q
       199: q^3+q
       200: q^3+q^2
       201: q^3+q
       202: q^3+q^2
       204: q^3+q
       206: q^3+q
       208: 2q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: 2q^4+2q^3+q^2+q
       214: 2q^3+q^2+q
       216: 2q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 2q^3+q^2+q
       223: q^3+q^2+q
       224: 3q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 2q^3+q^2+q
       227: q^4+3q^3+q^2+q
       228: q^4+2q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: 2q^4+3q^3+q^2+q
       231: q^3+q^2+q
       232: 2q^3+q^2+q
       233: q^3+q^2+q
       234: 2q^3+q^2+q
       235: q^3+q
       236: q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: 2q^3+q^2+q
       245: q^3+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: q^3+q
       261: q^3+q^2
       264: q^3+q
       265: q^3+q^2
       268: q^3+q
       270: q^3+q^2
       274: q^3+q
       276: q^3+q
       277: q^3+q^2
       280: 2q^3+q^2+q
       282: q^3+q^2+q
       283: q
       284: q^2
       285: q^2
       286: q^3+q
       288: q^3+q^2+q
       290: 2q^3+q^2+q
       292: q^3+q^2+q
       293: q^3+q
       294: q^3+q^2
       295: q^3+q^2
       296: 2q^3+q
       298: 2q^3+q^2+q
       299: q^3+q
       300: q^3+q^2
       302: 2q^3+q^2+q
       303: q^3+q^2
       304: q^4+2q^3+q
       306: q^4+2q^3+q^2+q
       307: q^3+q
       308: q^3+q^2
       310: q^3+q
       312: q^3+q
       314: q^3+q
       316: q^3+q^2+q
       318: 2q^3+q^2+q
       319: q^3+q
       320: q^3+q^2
       322: q^3+q
       324: q^3+q
       326: q^4+2q^3+q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: 2q^3+q^2+q
       334: q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       339: 2q^3+q^2+q
       341: 2q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: 2q^3+q^2+q
       348: q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: 2q^3+q^2+q
       352: q^3+q^2+q
       353: q^2+q
       354: q^2+q
       355: q^2+q
       356: q^3+q^2+q
       357: q
       358: q
       359: q^3+q
       361: 2q^3+q^2+q
       363: 2q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: 2q^3+q^2+q
       370: q^3+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q
       379: q^2
       382: q^3+q
       383: q^3+q^2
       386: q^3+q
       387: q^3+q^2
       390: q^3+q
       392: q^3+q^2
       394: q^3+q
       395: q^3+q^2
       400: q^3+q
       403: q^3+q
       407: q^3+q
       410: q^2+q
       412: q^2+q
       414: q^3+q^2+q
       416: q^2+q
       418: q^3+q^2+q
       419: q
       420: q^2
       421: q^2
       422: q^3+q
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: 2q^3+q^2+q
       429: q
       430: q^2
       431: q^2
       432: q^3+q
       434: q^3+q^2+q
       436: 2q^3+q^2+q
       437: q^3+q
       438: q^3+q^2
       439: q^3+q^2
       440: 2q^3+q
       442: 2q^3+q^2+q
       443: q^3+q
       444: q^3+q^2
       446: 2q^3+q^2+q
       447: q
       448: q^2
       450: q
       452: q
       453: q
       454: q^2
       456: q^3+q
       458: q
       460: q
       462: q^3+q
       464: q^3+q
       466: 2q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       471: q^3+q
       472: q^3+q^2
       474: q^3+q
       476: q^3+q
       478: q^3+q
       480: q^3+q
       481: q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       486: 2q^3+q^2+q
       488: 2q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^3+q^2+q
       494: 2q^3+q^2+q
       495: q^3+q^2+q
       496: 2q^3+q^2+q
       497: q^2+q
       498: q^2+q
       499: q
       500: q
       501: q^3+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q^2+q
       512: q^3+q^2+q
       513: q
       514: q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       522: q
       523: q^2
       526: q
       527: q^2
       530: q
       531: q^2
       534: q
       535: q^2
       538: q^3+q
       540: q^3+q^2
       542: q^3+q
       544: q^3+q^2
       546: q^3+q
       548: q^3+q^2
       551: q
       556: q^3+q
       560: q
       564: q^3+q
       566: q^3+q
       571: q^3+q
       574: q^3+q
       581: q^3+q
       584: q^2+q
       586: q^3+q^2+q
       588: q^2+q
       589: q
       590: q^2
       592: q
       593: q
       594: q^2
       595: q^2
       596: q^3+q
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: 2q^3+q^2+q
       603: q
       604: q^2
       606: q^3+q^2+q
       607: q^2
       608: q^3+q
       610: q^3+q^2+q
       612: q^2+q
       614: q^3+q^2+q
       615: q^3+q
       616: q^3+q^2
       618: 2q^3+q^2+q
       619: q
       620: q^2
       622: q
       624: q
       626: q
       628: q
       630: q
       632: q^3+q
       634: q^3+q
       636: q^2+q
       638: q^2+q
       640: q^3+q^2+q
       641: q
       642: q^2
       644: q
       646: q
       647: q
       648: q^2
       650: q
       652: q^3+q
       654: q
       656: q^3+q
       657: q^2+q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+q
       673: q^2+q
       674: q^2+q
       675: q^3+q^2+q
       676: 2q^3+q^2+q
       677: q^3+q^2+q
       678: q^2+q
       679: q^3+q^2+q
       680: q
       681: q^2+q
       682: q
       683: q
       684: q
       685: q
       686: q^2+q
       687: q^2+q
       688: q
       689: q
       699: q^3+q
       706: q
       707: q^2
       710: q
       711: q^2
       715: q
       718: q
       719: q^2
       722: q
       724: q^2
       726: q
       728: q^2
       730: q
       732: q^2
       734: q^3+q
       736: q^3+q^2
       740: q
       744: q
       748: q
       752: q^3+q
       754: q
       759: q^3+q
       763: q
       766: q^3+q
       773: q^3+q
       776: q^2+q
       778: q^2+q
       780: q^2+q
       782: q^3+q^2+q
       784: q^2+q
       785: q
       786: q^2
       788: q
       790: q^2+q
       792: q
       793: q
       794: q^2
       796: q^2+q
       798: q^3+q^2+q
       800: q^2+q
       801: q
       802: q^2
       804: q
       805: q
       806: q^2
       807: q^2
       808: q^3+q
       810: q^3+q^2+q
       812: q^3+q^2+q
       814: q^2+q
       815: q
       816: q^2
       818: q
       820: q
       822: q
       824: q
       825: q
       826: q^2
       828: q
       832: q
       834: q
       836: q
       838: q
       840: q
       842: q^2+q
       844: q
       845: q
       846: q^2
       848: q
       850: q
       852: q
       854: q
       856: q
       858: q
       866: q^2+q
       868: q^2+q
       870: q^2+q
       871: q^3+q^2+q
       872: q^2+q
       874: q
       875: q
       876: q
       877: q^2+q
       878: q
       879: q
       880: q
       890: q^3+q
       897: q
       898: q^2
       903: q
       905: q
       907: q^2
       909: q
       913: q
       915: q^2
       917: q
       919: q^2
       921: q
       923: q^2
       926: q
       929: q
       931: q^2
       933: q
       935: q^2
       939: q
       943: q
       947: q
       951: q
       959: q
       962: q
       965: q
       972: q
       976: q
       980: q
       986: q
       989: q
       995: q^2+q
       999: q
      1000: q
      1001: q^2
      1003: q^2+q
      1004: q
      1005: q^2
      1007: q
      1009: q
      1011: q
      1013: q
      1019: q^2+q
      1021: q^2+q
      1023: q^3+q^2+q
      1025: q^2+q
      1026: q
      1027: q^2
      1029: q
      1035: q
      1037: q
      1039: q
      1043: q
      1045: q
      1049: q
      1051: q
      1052: q
      1053: q^2
      1055: q
      1059: q
      1061: q
      1063: q
      1065: q
      1076: q^2+q
      1078: q^2+q
      1080: q
      1082: q
      1083: q
      1084: q
      1085: q
      1092: q
      1104: q
      1113: q
      1117: q
      1119: q
      1121: q^2
      1123: q
      1125: q^2
      1128: q
      1131: q
      1136: q
      1142: q
      1149: q
      1151: q^2
      1155: q
      1157: q
      1159: q^2
      1162: q
      1171: q
      1175: q
      1186: q
      1200: q
      1205: q
      1221: q
      1223: q
      1231: q^2+q
      1233: q
      1234: q
      1235: q^2
      1239: q^2+q
      1240: q
      1241: q^2
      1243: q
      1249: q
      1251: q
      1257: q
      1261: q
      1265: q
      1267: q
      1271: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1287: q
      1289: q
      1296: q
      1324: q
      1332: q
      1347: q
      1351: q
      1353: q
      1355: q^2
      1357: q
      1359: q^2
      1363: q
      1366: q
      1371: q
      1379: q
      1383: q
      1416: q
      1421: q
      1434: q
      1447: q
      1465: q
      1467: q
      1471: q
      1475: q
      1479: q
      1481: q
      1484: q
      1508: q
      1561: q
      1574: q
      1582: q
      1606: q
      1610: q
      1638: 1
      1642: q
      1650: q
      1672: q
      1728: 1
      1731: 1
      1756: q
      1760: q
      1824: 1
      1844: 1
      1897: 1
      1931: 1
      1959: 1
      1977: 1
      2031: 1
      2039: 1
      2079: 1

2080:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        59: q
        60: q^2+1
        61: q
        62: q+1
        64: q+1
        66: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       106: q
       107: q^2+1
       108: q
       109: 1
       110: q
       111: q+1
       113: q+1
       115: q+1
       117: 1
       118: q
       119: q^2+1
       120: q
       121: q+1
       123: q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       172: q
       173: 1
       176: q
       177: q+1
       179: q+1
       181: q+1
       183: q^2+1
       184: q
       185: 1
       186: q
       187: q+1
       189: q+1
       191: 1
       192: q
       193: 1
       195: 1
       196: q
       197: 1
       199: q^2+1
       200: q
       201: q^2+1
       202: q
       203: 1
       204: q
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       262: q
       263: 1
       266: q
       267: 1
       271: 1
       273: q
       275: 1
       278: q
       279: q+1
       281: q+1
       283: q^2+1
       284: q
       285: 1
       286: q
       287: q+1
       289: q+1
       291: q+1
       293: q^2+1
       294: q
       295: 1
       296: q
       297: q+1
       299: 1
       301: 1
       303: 1
       304: q
       305: 1
       307: q^2+1
       308: q
       309: 1
       310: q
       311: q+1
       313: q+1
       315: q+1
       317: q+1
       319: 1
       321: 1
       322: q
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       380: q
       381: 1
       384: q
       385: 1
       388: q
       389: 1
       393: 1
       397: 1
       399: q
       401: 1
       404: q
       405: 1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q^2+1
       420: q
       421: 1
       422: q
       423: q+1
       425: q+1
       427: q+1
       429: 1
       431: 1
       432: q
       433: 1
       435: 1
       437: 1
       439: 1
       440: q
       441: 1
       443: 1
       445: 1
       447: q^2+1
       448: q
       449: 1
       450: q
       451: q+1
       453: q^2+1
       454: q
       455: q+1
       457: 1
       458: q
       459: q+1
       461: 1
       462: q
       463: q+1
       465: q+1
       467: q+1
       469: q+1
       471: 1
       473: 1
       474: q
       475: 1
       477: 1
       479: 1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       524: q
       525: 1
       528: q
       529: 1
       532: q
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       552: q
       553: 1
       555: q
       557: 1
       559: q
       561: 1
       563: q
       565: 1
       569: 1
       573: 1
       577: 1
       583: q+1
       585: q+1
       587: q+1
       589: q^2+1
       590: q
       591: 1
       592: q
       593: 1
       595: 1
       596: q
       597: q+1
       599: q+1
       601: q+1
       603: 1
       605: 1
       607: 1
       608: q
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: q^2+1
       620: q
       621: 1
       622: q
       623: q+1
       625: q+1
       627: q+1
       629: q+1
       631: 1
       632: q
       633: q+1
       635: q+1
       637: q+1
       639: q+1
       641: 1
       643: 1
       644: q
       645: 1
       647: 1
       649: 1
       650: q
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: 1
       705: 1
       708: q
       709: 1
       712: q
       713: 1
       716: q
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       739: q
       741: 1
       743: q
       745: 1
       747: q
       749: 1
       751: q
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       785: 1
       787: 1
       788: q
       789: q+1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       805: 1
       807: 1
       808: q
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       818: q
       819: q+1
       821: q+1
       823: q+1
       825: q^2+1
       826: q
       827: 1
       828: q
       829: 1
       831: 1
       832: q
       833: q+1
       835: q+1
       837: q+1
       839: 1
       840: q
       841: q+1
       843: 1
       845: 1
       847: 1
       848: q
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       884: 1
       896: 1
       899: q
       900: 1
       902: q
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       928: 1
       932: 1
       936: 1
       938: q
       940: 1
       942: q
       944: 1
       946: q
       948: 1
       950: q
       952: 1
       956: 1
       958: q
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: q+1
       994: q+1
       996: q+1
       998: 1
       999: q
      1000: 1
      1002: q+1
      1004: 1
      1006: 1
      1007: q
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1030: q+1
      1032: 1
      1033: q
      1034: q+1
      1036: q+1
      1038: q+1
      1040: 1
      1042: q+1
      1044: 1
      1045: q
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1056: 1
      1058: 1
      1059: q
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1112: q
      1114: 1
      1116: q
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1156: 1
      1164: 1
      1166: q
      1168: 1
      1170: q
      1172: 1
      1174: q
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1206: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1216: 1
      1217: q
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1228: 1
      1230: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1244: q+1
      1246: 1
      1247: q
      1248: q+1
      1250: 1
      1251: q
      1252: q+1
      1254: 1
      1256: q+1
      1258: 1
      1260: 1
      1261: q
      1262: 1
      1264: 1
      1266: 1
      1268: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1316: q
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1352: 1
      1356: 1
      1372: 1
      1374: q
      1376: 1
      1378: q
      1380: 1
      1382: q
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: 1
      1410: 1
      1414: 1
      1422: 1
      1430: 1
      1436: 1
      1438: q+1
      1440: 1
      1441: q
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1454: 1
      1456: q+1
      1458: q+1
      1460: 1
      1461: q
      1462: 1
      1464: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1480: 1
      1482: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1489: 1
      1513: 1
      1525: 1
      1537: 1
      1541: 1
      1543: q
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1567: 1
      1583: 1
      1585: q
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1611: 1
      1615: 1
      1631: 1
      1637: 1
      1639: 1
      1641: 1
      1643: 1
      1647: 1
      1651: q+1
      1653: 1
      1654: q
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1665: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1699: 1
      1723: 1
      1729: 1
      1733: 1
      1745: 1
      1761: 1
      1763: q
      1765: 1
      1769: 1
      1773: 1
      1777: 1
      1781: 1
      1789: 1
      1801: 1
      1815: 1
      1817: 1
      1821: 1
      1823: 1
      1825: 1
      1827: 1
      1831: 1
      1833: 1
      1834: 1
      1858: 1
      1910: 1
      1914: 1
      1918: 1
      1922: 1
      1926: 1
      1936: 1
      1956: 1
      1958: 1
      1960: 1
      1964: 1
      1978: 1
      2026: 1
      2044: 1
      2048: 1
      2052: 1
      2080: 1

2081:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+3q^2+2q
        25: 3q^3+4q^2+2q
        26: 3q^3+4q^2+2q
        27: q^4+3q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 4q^2+2q
        32: 3q^2+2q
        33: 4q^2+2q
        34: 3q^3+4q^2+2q
        35: 2q^3+3q^2+2q
        36: 3q^3+4q^2+2q
        37: q^2+q
        38: 3q^2+q
        39: q^2+q
        40: 3q^2+q
        41: q^2+q
        42: q^3+2q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: q^3+3q^2+2q
        55: 3q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^4+3q^3+3q^2+2q
        58: q^2+q
        59: 3q^2+q
        60: 2q^3+2q^2+2q
        61: q^3+2q^2
        62: q^2+q
        63: 3q^2+q
        64: q^2+q
        65: 2q^2+q
        66: q^2+q
        67: 3q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 3q^3+4q^2+2q
        73: 4q^2+2q
        74: q^2+q
        75: 3q^2+q
        76: q^2+q
        77: 3q^2+q
        78: q^2+q
        79: q^3+2q^2+q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 4q^2+2q
        83: 3q^2+2q
        84: 2q^3+3q^2+2q
        85: 2q^3+3q^2+2q
        86: 3q^3+4q^2+2q
        87: 2q^3+3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q
       104: 2q^2+q
       105: q^2
       106: q^2
       107: 2q^3+2q^2+2q
       108: q^3+2q^2
       109: q^2+q
       110: 3q^2+q
       111: q^2+q
       112: 3q^2+q
       113: q^2+q
       114: 3q^2+q
       115: q^2+q
       116: 2q^2+q
       117: q
       118: 2q^2+q
       119: q^3+q^2+2q
       120: q^2
       121: q^2+q
       122: 2q^2+q
       123: q^2+q
       124: 2q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: q^2+q
       128: 3q^2+q
       129: q^2+q
       130: 3q^2+q
       131: q^2+q
       132: q^3+2q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+2q
       136: 3q^2+2q
       137: 3q^2+2q
       138: 3q^2+2q
       139: 4q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 4q^2+2q
       143: 2q^3+3q^2+2q
       144: 2q^3+3q^2+2q
       145: 3q^3+4q^2+2q
       146: 2q^3+3q^2+2q
       147: 3q^3+4q^2+2q
       148: 4q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: q^2+q
       152: 3q^2+q
       153: q^2+q
       154: 3q^2+q
       155: q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^3+3q^2+2q
       164: 2q^3+3q^2+2q
       165: 2q^3+3q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q
       170: 2q^2+q
       171: q^2
       172: q^2
       173: q
       174: q^2+q
       176: q^2
       177: q^2+q
       178: 2q^2+q
       179: q^2+q
       180: 3q^2+q
       181: q^2+q
       182: 3q^2+q
       183: q^3+q^2+2q
       184: q^2
       185: q
       186: 2q^2+q
       187: q^2+q
       188: 2q^2+q
       189: q^2+q
       190: 2q^2+q
       191: q
       192: 2q^2+q
       193: q^2+2q
       195: q^2+q
       196: 3q^2+q
       197: q
       198: q^2+q
       199: q^3+q^2+2q
       200: q^2
       201: 2q^3+2q^2+2q
       202: q^3+2q^2
       203: q^2+q
       204: 3q^2+q
       205: q^2+q
       206: 3q^2+q
       207: q^2+q
       208: 2q^2+q
       209: q^2+q
       210: 3q^2+q
       211: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+3q^2+2q
       223: 2q^3+3q^2+2q
       224: 3q^2+2q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+2q
       228: 2q^2+2q
       229: 2q
       230: 2q^2+2q
       231: 2q^3+3q^2+2q
       232: q^3+2q^2+2q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+2q
       235: 3q^2+2q
       236: 3q^2+2q
       237: q^2+q
       238: 3q^2+q
       239: q^2+q
       240: 3q^2+q
       241: q^2+q
       242: q^3+2q^2+q
       243: 4q^2+2q
       244: q^2+2q
       245: 4q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^3+3q^2+2q
       254: 2q^3+3q^2+2q
       255: 2q^3+3q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q
       260: 2q^2+q
       261: q^2
       262: q^2
       263: q
       264: q^2+q
       266: q^2
       267: q
       268: q^2+q
       271: q
       272: q^2
       273: q^2
       274: 2q^2+q
       275: q
       276: q^2+q
       278: q^2
       280: q
       282: q^2+q
       283: q^3+q^2+2q
       284: q^2
       285: q
       286: 2q^2+q
       287: q^2+q
       288: 2q^2+q
       290: q^2+q
       291: q^2+q
       292: 2q^2+q
       293: q^3+q^2+2q
       294: q^2
       295: q
       296: 2q^2+q
       297: q^2+q
       298: 2q^2+q
       299: 2q
       301: q
       302: q^2+q
       303: q
       304: q^2+q
       305: q
       306: q
       307: q^3+q^2+2q
       308: q^2
       309: q
       310: 2q^2+q
       311: q^2+q
       312: 3q^2+q
       313: q^2+q
       314: 2q^2+q
       315: q^2+q
       316: 2q^2+q
       317: q^2+q
       318: 3q^2+q
       319: q^2+2q
       321: q^2+q
       322: 3q^2+q
       323: q
       324: q^2+q
       325: q^2+q
       326: 2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+2q
       334: 2q^3+3q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: q^2+q
       339: 3q^2+q
       340: q^2+q
       341: 3q^2+q
       342: q^2+q
       343: q^3+2q^2+q
       344: q^2+2q
       345: q^2+2q
       346: 2q^2+2q
       347: 2q
       348: 2q
       349: 2q^2+2q
       350: 2q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: q^3+2q^2+2q
       354: 2q^3+3q^2+2q
       355: 2q^3+3q^2+2q
       356: 2q^3+3q^2+2q
       357: 3q^2+2q
       358: 3q^2+2q
       359: 4q^2+2q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q
       370: 2q^2+2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q
       378: q^2+q
       380: q^2
       382: q
       385: q
       386: q^2+q
       388: q^2
       389: q
       390: q^2+q
       393: q
       394: q
       397: q
       398: q^2
       399: q^2
       400: 2q^2+q
       401: q
       403: q^2+q
       404: q^2
       405: q
       407: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q^3+q^2+2q
       420: q^2
       421: q
       422: 2q^2+q
       423: q^2+q
       424: 2q^2+q
       425: q^2+q
       426: 2q^2+q
       427: q^2+q
       428: 3q^2+q
       429: 2q
       431: q
       432: q^2+q
       433: q
       434: q
       436: q
       437: 2q
       439: q
       440: q^2+q
       441: q
       442: q
       443: q^2+2q
       445: q
       446: q^2+q
       447: q^3+q^2+2q
       448: q^2
       449: q
       450: 2q^2+q
       451: q^2+q
       452: 2q^2+q
       453: q^3+q^2+2q
       454: q^2
       456: q^2+q
       457: q
       458: 2q^2+q
       459: q^2+q
       460: 2q^2+q
       461: q^2+q
       462: 3q^2+q
       463: q^2+q
       464: 3q^2+q
       466: q
       468: q^2+q
       469: q^2+q
       470: 2q^2+q
       471: 2q
       473: q
       474: q^2+q
       475: q
       476: q
       477: q
       478: q^2+q
       479: q
       480: q^2+q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: 2q^2+2q
       492: q^2+2q
       493: 2q
       494: 2q^2+2q
       495: 2q
       496: 2q
       497: q^3+2q^2+2q
       498: 2q^3+3q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+2q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q
       512: 2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       522: q
       526: q
       529: q
       530: q^2+q
       532: q^2
       533: q
       534: q
       538: q
       541: q
       542: q
       545: q
       546: q^2+q
       549: q
       551: q^2+q
       552: q^2
       556: q
       557: q
       559: q^2
       560: q^2+q
       561: q
       562: q^2
       563: q^2
       564: 2q^2+q
       565: q
       566: q
       569: q
       571: q^2+q
       573: q
       574: q^2+q
       577: q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q^3+q^2+2q
       590: q^2
       591: q
       592: 2q^2+q
       593: 2q
       595: q
       596: q^2+q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q
       603: 2q
       606: q
       607: q
       608: q^2+q
       609: q
       610: q
       612: q
       613: q
       614: q
       615: 2q
       618: q
       619: q^3+q^2+2q
       620: q^2
       621: q
       622: 2q^2+q
       624: q^2+q
       625: q^2+q
       626: 2q^2+q
       628: q^2+q
       629: q^2+q
       630: 2q^2+q
       631: q
       632: q^2+q
       634: q^2+q
       636: q
       638: q^2+q
       640: q
       641: 2q
       643: q
       644: q^2+q
       645: q
       646: q
       647: 2q
       649: q
       650: q^2+q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q
       675: q
       676: q^2+2q
       677: 2q
       678: 2q
       679: 2q
       680: 2q^2+2q
       681: q^3+2q^2+2q
       682: q^2+2q
       683: 3q^2+2q
       684: 2q^2+2q
       685: 2q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q^2+2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       693: q
       699: q^2+q
       706: q
       710: q
       713: q
       715: q^2+q
       716: q^2
       717: q
       718: q
       722: q
       725: q
       726: q
       730: q
       734: q
       740: q
       741: q
       743: q^2
       744: q^2+q
       748: q
       752: q
       753: q
       754: q
       759: q
       761: q
       763: q
       765: q
       766: q
       773: q
       776: q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: 2q
       787: q
       788: q^2+q
       790: q
       791: q
       792: q
       793: 2q
       796: q
       800: q
       801: q
       805: 2q
       807: q
       808: q^2+q
       810: q
       811: q
       812: q
       814: q
       815: 2q
       817: q
       818: q^2+q
       820: q^2+q
       822: q
       824: q^2+q
       825: q^3+q^2+2q
       826: q^2
       827: q
       828: 2q^2+q
       829: 2q
       831: q
       832: q^2+q
       834: q^2+q
       835: q^2+q
       836: 2q^2+q
       838: q^2+q
       839: q
       840: q^2+q
       842: q
       843: q
       844: q
       845: 2q
       847: q
       848: q^2+q
       850: q
       851: q
       852: q
       854: q
       855: q
       856: q
       857: q
       858: q
       860: q^2+q
       862: q^2+q
       864: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q^2+2q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q
       878: q^2+2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       890: q
       897: q
       903: q
       905: q
       908: q
       909: q
       913: q
       917: q
       928: q
       929: q
       933: q
       939: q
       943: q
       947: q
       948: q
       950: q^2
       951: q^2+q
       952: q
       953: q
       959: q
       962: q
       964: q
       965: q
       972: q
       974: q
       976: q
       980: q
       986: q
       988: q
       989: q
       993: q
       995: q
       997: q^2+q
       998: q
       999: q^2+q
      1000: 2q
      1003: q
      1004: 2q
      1006: q
      1007: q^2+q
      1008: q
      1009: q
      1011: q
      1012: q
      1013: q
      1015: q
      1016: 2q
      1021: q
      1025: q
      1026: q
      1031: q^2+q
      1032: q
      1033: q^2+q
      1035: q
      1037: q^2+q
      1039: q
      1040: 2q
      1043: q^2+q
      1044: q
      1045: q^2+q
      1046: q
      1047: q
      1051: q
      1052: q
      1056: 2q
      1058: q
      1059: q^2+q
      1061: q
      1062: q
      1063: q
      1064: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1092: q
      1104: q
      1113: q
      1117: q
      1119: q
      1123: q
      1128: q
      1130: q
      1131: q
      1134: q
      1136: q
      1142: q
      1145: q
      1167: q
      1171: q
      1175: q
      1177: q
      1180: q
      1181: q
      1186: q
      1192: q
      1194: q
      1195: q
      1206: q
      1207: q
      1211: q+1
      1213: q+1
      1215: q
      1216: q
      1217: q^2+q
      1218: 2q
      1223: q
      1224: q
      1225: q
      1227: 1
      1228: 1
      1234: q
      1237: q
      1240: q
      1245: q+1
      1246: 1
      1247: q
      1249: q
      1250: q
      1251: q^2+q
      1253: q^2+q
      1254: 2q
      1257: q
      1258: 2q
      1260: q
      1261: q^2+q
      1262: 1
      1268: q
      1273: q
      1275: q
      1276: q
      1277: q
      1279: q
      1280: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1296: q
      1308: q
      1317: q
      1319: q
      1324: q
      1326: q
      1327: q
      1338: q
      1341: 1
      1373: 1
      1375: q
      1379: q
      1383: q
      1385: q
      1389: q
      1394: q
      1396: q
      1397: q
      1400: q
      1402: q
      1405: 1
      1410: 1
      1434: q
      1439: q+1
      1440: 1
      1441: q
      1442: 1
      1444: 1
      1453: 1
      1454: q
      1457: q
      1459: q+1
      1460: q
      1461: q^2+q
      1462: 2q
      1468: q
      1473: q
      1476: q
      1481: q
      1482: q
      1483: q
      1484: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1495: q
      1519: q
      1526: 1
      1542: 1
      1544: q
      1546: 1
      1549: 1
      1554: 1
      1586: q
      1588: q
      1593: q
      1595: q
      1596: q
      1635: q
      1639: 1
      1644: 1
      1647: 1
      1652: q+1
      1653: 1
      1654: q
      1655: 1
      1657: q
      1665: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1676: 1
      1705: q
      1724: 1
      1733: 1
      1746: 1
      1762: 1
      1764: q
      1766: 1
      1773: 1
      1802: 1
      1821: q
      1825: 1
      1828: 1
      1831: 1
      1833: 1
      1835: 1
      1859: 1
      1914: 1
      1927: 1
      1937: 1
      1957: 1
      1960: 1
      1964: 1
      1979: 1
      2027: 1
      2045: 1
      2052: 1
      2081: 1

2082:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: 2q^4+2q^3+q^2+q
        23: 2q^4+2q^3+q^2+q
        24: 2q^4+2q^3+q^2+q
        25: q^5+3q^4+3q^3+q^2+q
        26: q^5+3q^4+3q^3+q^2+q
        27: q^5+3q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: q^4+2q^3+q^2+q
        32: 2q^4+2q^3+q^2+q
        33: q^4+2q^3+q^2+q
        34: 2q^4+3q^3+q^2+q
        35: q^5+3q^4+3q^3+q^2+q
        36: 2q^4+3q^3+q^2+q
        37: 2q^4+2q^3+q^2+q
        39: 2q^4+2q^3+q^2+q
        41: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: 2q^4+2q^3+q^2+q
        53: 2q^4+2q^3+q^2+q
        54: 2q^4+2q^3+q^2+q
        55: q^5+3q^4+3q^3+q^2+q
        56: q^5+3q^4+3q^3+q^2+q
        57: q^5+3q^4+3q^3+q^2+q
        58: q^3+q
        59: q^3+q^2
        60: q^4+2q^3+q
        61: q^3+q^2
        62: q^4+2q^3+q^2+q
        64: 2q^4+2q^3+q^2+q
        66: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 2q^4+3q^3+q^2+q
        73: q^4+2q^3+q^2+q
        74: 2q^4+2q^3+q^2+q
        76: 2q^4+2q^3+q^2+q
        78: 2q^4+2q^3+q^2+q
        80: q^4+2q^3+q^2+q
        81: q^4+2q^3+q^2+q
        82: q^4+2q^3+q^2+q
        83: 2q^4+2q^3+q^2+q
        84: 2q^4+3q^3+q^2+q
        85: 2q^4+3q^3+q^2+q
        86: 2q^4+3q^3+q^2+q
        87: q^5+3q^4+3q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^4+3q^3+q^2+q
        98: 2q^4+3q^3+q^2+q
        99: q^5+2q^4+2q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       103: q^3+q
       106: q^3+q^2
       107: q^4+2q^3+q
       108: q^3+q^2
       109: q^3+q
       110: q^3+q^2
       111: q^4+2q^3+q^2+q
       113: q^4+2q^3+q^2+q
       115: 2q^4+2q^3+q^2+q
       117: q^3+q
       118: q^3+q^2
       119: q^4+2q^3+q
       120: q^3+q^2
       121: q^4+2q^3+q^2+q
       123: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 2q^4+3q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 2q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^3+q
       141: q^4+2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: q^4+2q^3+q^2+q
       145: q^4+3q^3+q^2+q
       146: 2q^4+3q^3+q^2+q
       147: 2q^4+3q^3+q^2+q
       148: q^4+2q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       151: 2q^4+2q^3+q^2+q
       153: 2q^4+2q^3+q^2+q
       155: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^3+q^2+q
       161: 2q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: 2q^4+3q^3+q^2+q
       164: 2q^4+3q^3+q^2+q
       165: q^5+2q^4+2q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3+q
       172: q^3+q^2
       173: q^3+q
       176: q^3+q^2
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^4+2q^3+q
       184: q^3+q^2
       185: q^3+q
       186: q^3+q^2
       187: q^4+2q^3+q^2+q
       189: q^4+2q^3+q^2+q
       191: q^3+q
       192: q^3+q^2
       193: q^3+q
       195: q^3+q
       196: q^3+q^2
       197: q^3+q
       199: 2q^3+q
       200: q^3+q^2
       201: q^4+2q^3+q
       202: q^3+q^2
       203: q^3+q
       204: q^3+q^2
       205: q^4+2q^3+q^2+q
       207: 2q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: 2q^4+2q^3+q^2+q
       213: 2q^3+q^2+q
       215: 2q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 3q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: 2q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: 2q^3+q^2+q
       228: q^3+q^2+q
       229: q^3+q
       230: 2q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^4+3q^3+q^2+q
       233: q^4+2q^3+q^2+q
       234: 2q^4+3q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: q^3+q
       245: 2q^3+q^2+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: q^3+q
       262: q^3+q^2
       263: q^3+q
       266: q^3+q^2
       267: q^3+q
       271: q^3+q
       273: q^3+q^2
       275: q^3+q
       278: q^3+q^2
       279: 2q^3+q^2+q
       281: q^3+q^2+q
       283: q^3+q
       284: q^2
       285: q
       286: q^2
       287: q^3+q^2+q
       289: 2q^3+q^2+q
       291: q^3+q^2+q
       293: 2q^3+q
       294: q^3+q^2
       295: q^3+q
       296: q^3+q^2
       297: 2q^3+q^2+q
       299: q^3+q
       301: q^3+q
       303: q^3+q
       304: q^3+q^2
       305: q^3+q
       307: q^4+2q^3+q
       308: q^3+q^2
       309: q^3+q
       310: q^3+q^2
       311: 2q^3+q^2+q
       313: q^4+2q^3+q^2+q
       315: q^3+q^2+q
       317: 2q^3+q^2+q
       319: q^3+q
       321: q^3+q
       322: q^3+q^2
       323: q^3+q
       325: q^4+2q^3+q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: 2q^3+q^2+q
       334: 2q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       338: 2q^3+q^2+q
       340: 2q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^3+q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^3+q^2+q
       351: q^3+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: 2q^3+q^2+q
       358: q^3+q^2+q
       359: 2q^3+q^2+q
       360: 2q^3+q^2+q
       362: 2q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: q^3+q
       370: 2q^3+q^2+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q
       380: q^2
       381: q^3+q
       384: q^3+q^2
       385: q^3+q
       388: q^3+q^2
       389: q^3+q
       393: q^3+q
       397: q^3+q
       399: q^3+q^2
       401: q^3+q
       404: q^3+q^2
       405: q^3+q
       409: q^2+q
       411: q^2+q
       413: q^3+q^2+q
       415: q^2+q
       417: q^3+q^2+q
       419: q^3+q
       420: q^2
       421: q
       422: q^2
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: 2q^3+q^2+q
       429: q
       431: q
       432: q^2
       433: q
       435: q^3+q
       437: q
       439: q
       440: q^2
       441: q
       443: q^3+q
       445: q^3+q
       447: q^3+q
       448: q^2
       449: q
       450: q^2
       451: q^3+q^2+q
       453: 2q^3+q
       454: q^3+q^2
       455: 2q^3+q^2+q
       457: q^3+q
       458: q^3+q^2
       459: 2q^3+q^2+q
       461: q^3+q
       462: q^3+q^2
       463: 2q^3+q^2+q
       465: 2q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       471: q^3+q
       473: q^3+q
       474: q^3+q^2
       475: q^3+q
       477: q^3+q
       479: q^3+q
       481: 2q^3+q^2+q
       482: q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       485: 2q^3+q^2+q
       487: 2q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^3+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^3+q^2+q
       500: q^3+q^2+q
       501: 2q^3+q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^3+q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       521: q
       524: q^2
       525: q
       528: q^2
       529: q
       532: q^2
       533: q
       537: q^3+q
       541: q
       545: q^3+q
       549: q
       552: q^2
       553: q^3+q
       555: q^3+q^2
       557: q^3+q
       559: q^3+q^2
       561: q^3+q
       563: q^3+q^2
       565: q^3+q
       569: q^3+q
       573: q^3+q
       577: q^3+q
       583: q^2+q
       585: q^3+q^2+q
       587: q^2+q
       589: q^3+q
       590: q^2
       591: q
       592: q^2
       593: q
       595: q
       596: q^2
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: 2q^3+q^2+q
       603: q
       605: q
       607: q
       608: q^2
       609: q
       611: q
       613: q
       615: q^3+q
       617: q^3+q
       619: q^3+q
       620: q^2
       621: q
       622: q^2
       623: q^3+q^2+q
       625: q^3+q^2+q
       627: q^2+q
       629: q^3+q^2+q
       631: q^3+q
       632: q^3+q^2
       633: 2q^3+q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+q^2+q
       641: q
       643: q
       644: q^2
       645: q
       647: q
       649: q
       650: q^2
       651: q^3+q
       653: q
       655: q^3+q
       657: q^2+q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+q
       673: q^2+q
       674: q
       675: q
       676: q^2+q
       677: q
       678: q
       679: q
       680: q^2+q
       681: 2q^3+q^2+q
       682: q^3+q^2+q
       683: q^3+q^2+q
       684: q^2+q
       685: q^3+q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       693: q^3+q
       705: q
       708: q^2
       709: q
       712: q^2
       713: q
       716: q^2
       717: q
       721: q
       725: q
       729: q
       733: q^3+q
       737: q
       739: q^2
       741: q
       743: q^2
       745: q
       747: q^2
       749: q^3+q
       751: q^3+q^2
       753: q
       757: q^3+q
       761: q
       765: q^3+q
       769: q^3+q
       775: q^2+q
       777: q^2+q
       779: q^2+q
       781: q^3+q^2+q
       783: q^2+q
       785: q
       787: q
       788: q^2
       789: q^2+q
       791: q
       793: q
       795: q
       797: q
       799: q
       801: q
       805: q
       807: q
       808: q^2
       809: q
       811: q
       813: q
       815: q
       817: q
       818: q^2
       819: q^2+q
       821: q^3+q^2+q
       823: q^2+q
       825: q^3+q
       826: q^2
       827: q
       828: q^2
       829: q
       831: q
       832: q^2
       833: q^3+q^2+q
       835: q^3+q^2+q
       837: q^2+q
       839: q
       840: q^2
       841: q^2+q
       843: q
       845: q
       847: q
       848: q^2
       849: q
       851: q
       853: q
       855: q
       857: q
       866: q^2+q
       868: q^2+q
       870: q
       871: q
       872: q
       874: q^2+q
       875: q^3+q^2+q
       876: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       884: q^3+q
       896: q
       899: q^2
       900: q
       902: q^2
       904: q
       908: q
       912: q
       916: q
       920: q
       928: q
       932: q
       936: q
       938: q^2
       940: q
       942: q^2
       944: q
       946: q^2
       948: q
       950: q^2
       952: q
       956: q
       958: q^2
       960: q
       964: q
       968: q
       974: q
       978: q
       982: q
       988: q
       994: q^2+q
       998: q
       999: q^2
      1000: q
      1002: q^2+q
      1004: q
      1006: q
      1007: q^2
      1008: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1024: q
      1026: q
      1034: q^2+q
      1036: q^2+q
      1038: q^3+q^2+q
      1040: q
      1042: q^2+q
      1044: q
      1045: q^2
      1048: q
      1050: q
      1052: q
      1056: q
      1058: q
      1059: q^2
      1060: q
      1062: q
      1064: q
      1076: q
      1078: q
      1080: q^2+q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1086: q
      1098: q
      1110: q
      1112: q^2
      1114: q
      1116: q^2
      1118: q
      1122: q
      1126: q
      1130: q
      1134: q
      1138: q
      1148: q
      1156: q
      1168: q
      1170: q^2
      1172: q
      1174: q^2
      1176: q
      1180: q
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      1206: q
      1220: q
      1222: q
      1230: q
      1234: q
      1238: q
      1240: q
      1248: q^2+q
      1250: q
      1251: q^2
      1254: q
      1256: q^2+q
      1258: q
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      1261: q^2
      1264: q
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      1287: q
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      1290: q
      1322: q
      1330: q
      1352: q
      1356: q
      1376: q
      1378: q^2
      1380: q
      1382: q^2
      1384: q
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      1400: q
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      1513: q
      1559: q
      1591: q
      1599: q
      1611: q
      1615: q
      1637: 1
      1641: q
      1657: q
      1671: q
      1725: 1
      1729: 1
      1777: q
      1781: q
      1823: 1
      1836: 1
      1910: 1
      1928: 1
      1958: 1
      1980: 1
      2028: 1
      2048: 1
      2082: 1

2083:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+3q^2+2q
        25: 3q^3+4q^2+2q
        26: 3q^3+4q^2+2q
        27: q^4+3q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 4q^2+2q
        32: 3q^2+2q
        33: 4q^2+2q
        34: 3q^3+4q^2+2q
        35: 2q^3+3q^2+2q
        36: 3q^3+4q^2+2q
        37: 3q^2+q
        38: q^2+q
        39: 3q^2+q
        40: q^2+q
        41: q^3+2q^2+q
        42: q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: q^3+3q^2+2q
        55: 3q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^4+3q^3+3q^2+2q
        58: 3q^2+q
        59: q^2+q
        60: 2q^3+2q^2+2q
        61: q^3+2q^2
        62: 3q^2+q
        63: q^2+q
        64: 2q^2+q
        65: q^2+q
        66: 3q^2+q
        67: q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 3q^3+4q^2+2q
        73: 4q^2+2q
        74: 3q^2+q
        75: q^2+q
        76: 3q^2+q
        77: q^2+q
        78: q^3+2q^2+q
        79: q^2+q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 4q^2+2q
        83: 3q^2+2q
        84: 2q^3+3q^2+2q
        85: 2q^3+3q^2+2q
        86: 3q^3+4q^2+2q
        87: 2q^3+3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: 2q^2+q
       104: q
       105: q^2
       106: q^2
       107: 2q^3+2q^2+2q
       108: q^3+2q^2
       109: 3q^2+q
       110: q^2+q
       111: 3q^2+q
       112: q^2+q
       113: 3q^2+q
       114: q^2+q
       115: 2q^2+q
       116: q^2+q
       117: 2q^2+q
       118: q
       119: q^3+q^2+2q
       120: q^2
       121: 2q^2+q
       122: q^2+q
       123: 2q^2+q
       124: q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: 3q^2+q
       128: q^2+q
       129: 3q^2+q
       130: q^2+q
       131: q^3+2q^2+q
       132: q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+2q
       136: 3q^2+2q
       137: 3q^2+2q
       138: 3q^2+2q
       139: 4q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 4q^2+2q
       143: 2q^3+3q^2+2q
       144: 2q^3+3q^2+2q
       145: 3q^3+4q^2+2q
       146: 2q^3+3q^2+2q
       147: 3q^3+4q^2+2q
       148: 4q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: 3q^2+q
       152: q^2+q
       153: 3q^2+q
       154: q^2+q
       155: q^3+2q^2+q
       156: q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^3+3q^2+2q
       164: 2q^3+3q^2+2q
       165: 2q^3+3q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: 2q^2+q
       170: q
       171: q^2
       172: q^2
       173: q^2+q
       174: q
       175: q^2
       177: 2q^2+q
       178: q^2+q
       179: 3q^2+q
       180: q^2+q
       181: 3q^2+q
       182: q^2+q
       183: q^3+q^2+2q
       184: q^2
       185: 2q^2+q
       186: q
       187: 2q^2+q
       188: q^2+q
       189: 2q^2+q
       190: q^2+q
       191: 2q^2+q
       192: q
       193: q^2+2q
       195: 3q^2+q
       196: q^2+q
       197: q^2+q
       198: q
       199: q^3+q^2+2q
       200: q^2
       201: 2q^3+2q^2+2q
       202: q^3+2q^2
       203: 3q^2+q
       204: q^2+q
       205: 3q^2+q
       206: q^2+q
       207: 2q^2+q
       208: q^2+q
       209: 3q^2+q
       210: q^2+q
       211: 2q^2+q
       212: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+3q^2+2q
       223: 2q^3+3q^2+2q
       224: 3q^2+2q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+2q
       228: 2q^2+2q
       229: 2q
       230: 2q^2+2q
       231: 2q^3+3q^2+2q
       232: q^3+2q^2+2q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+2q
       235: 3q^2+2q
       236: 3q^2+2q
       237: 3q^2+q
       238: q^2+q
       239: 3q^2+q
       240: q^2+q
       241: q^3+2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: q^2+2q
       245: 4q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^3+3q^2+2q
       254: 2q^3+3q^2+2q
       255: 2q^3+3q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: 2q^2+q
       260: q
       261: q^2
       262: q^2
       263: q^2+q
       264: q
       265: q^2
       267: q^2+q
       268: q
       271: 2q^2+q
       272: q^2
       273: q^2
       274: q
       275: q^2+q
       276: q
       277: q^2
       279: q
       281: q^2+q
       283: q^3+q^2+2q
       284: q^2
       285: 2q^2+q
       286: q
       287: 2q^2+q
       288: q^2+q
       289: q^2+q
       291: 2q^2+q
       292: q^2+q
       293: q^3+q^2+2q
       294: q^2
       295: 2q^2+q
       296: q
       297: 2q^2+q
       298: q^2+q
       299: 2q
       301: q^2+q
       302: q
       303: q^2+q
       304: q
       305: q
       306: q
       307: q^3+q^2+2q
       308: q^2
       309: 2q^2+q
       310: q
       311: 3q^2+q
       312: q^2+q
       313: 2q^2+q
       314: q^2+q
       315: 2q^2+q
       316: q^2+q
       317: 3q^2+q
       318: q^2+q
       319: q^2+2q
       321: 3q^2+q
       322: q^2+q
       323: q^2+q
       324: q
       325: 2q^2+q
       326: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+2q
       334: 2q^3+3q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: 3q^2+q
       339: q^2+q
       340: 3q^2+q
       341: q^2+q
       342: q^3+2q^2+q
       343: q^2+q
       344: q^2+2q
       345: q^2+2q
       346: 2q^2+2q
       347: 2q
       348: 2q
       349: 2q^2+2q
       350: 2q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: q^3+2q^2+2q
       354: 2q^3+3q^2+2q
       355: 2q^3+3q^2+2q
       356: 2q^3+3q^2+2q
       357: 3q^2+2q
       358: 3q^2+2q
       359: 4q^2+2q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q
       370: 2q^2+2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q^2+q
       378: q
       379: q^2
       381: q
       385: q^2+q
       386: q
       387: q^2
       389: q^2+q
       390: q
       393: q
       394: q
       397: 2q^2+q
       398: q^2
       399: q^2
       400: q
       401: q^2+q
       402: q^2
       403: q
       405: q^2+q
       407: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q^3+q^2+2q
       420: q^2
       421: 2q^2+q
       422: q
       423: 2q^2+q
       424: q^2+q
       425: 2q^2+q
       426: q^2+q
       427: 3q^2+q
       428: q^2+q
       429: 2q
       431: q^2+q
       432: q
       433: q
       434: q
       435: q
       437: 2q
       439: q^2+q
       440: q
       441: q
       442: q
       443: q^2+2q
       445: q^2+q
       446: q
       447: q^3+q^2+2q
       448: q^2
       449: 2q^2+q
       450: q
       451: 2q^2+q
       452: q^2+q
       453: q^3+q^2+2q
       454: q^2
       455: q^2+q
       457: 2q^2+q
       458: q
       459: 2q^2+q
       460: q^2+q
       461: 3q^2+q
       462: q^2+q
       463: 3q^2+q
       464: q^2+q
       465: q
       467: q^2+q
       469: 2q^2+q
       470: q^2+q
       471: 2q
       473: q^2+q
       474: q
       475: q
       476: q
       477: q^2+q
       478: q
       479: q^2+q
       480: q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: 2q^2+2q
       492: q^2+2q
       493: 2q
       494: 2q^2+2q
       495: 2q
       496: 2q
       497: q^3+2q^2+2q
       498: 2q^3+3q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+2q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q
       512: 2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       521: q
       525: q
       529: q^2+q
       530: q
       531: q^2
       533: q
       534: q
       537: q
       541: q
       542: q
       545: q^2+q
       546: q
       549: q^2+q
       550: q^2
       551: q
       553: q
       557: q^2+q
       558: q^2
       560: q
       561: 2q^2+q
       562: q^2
       563: q^2
       564: q
       565: q
       566: q
       569: q^2+q
       571: q
       573: q^2+q
       574: q
       577: q^2+q
       581: q
       583: q
       585: q
       587: q^2+q
       589: q^3+q^2+2q
       590: q^2
       591: 2q^2+q
       592: q
       593: 2q
       595: q^2+q
       596: q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q
       603: 2q
       605: q
       607: q^2+q
       608: q
       609: q
       610: q
       611: q
       613: q
       614: q
       615: 2q
       617: q
       619: q^3+q^2+2q
       620: q^2
       621: 2q^2+q
       622: q
       623: q^2+q
       625: 2q^2+q
       626: q^2+q
       627: q^2+q
       629: 2q^2+q
       630: q^2+q
       631: q^2+q
       632: q
       633: q^2+q
       635: q
       637: q^2+q
       639: q
       641: 2q
       643: q^2+q
       644: q
       645: q
       646: q
       647: 2q
       649: q^2+q
       650: q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q
       675: q
       676: q^2+2q
       677: 2q
       678: 2q
       679: 2q
       680: 2q^2+2q
       681: q^3+2q^2+2q
       682: q^2+2q
       683: 3q^2+2q
       684: 2q^2+2q
       685: 2q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q^2+2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       693: q^2+q
       699: q
       705: q
       709: q
       713: q^2+q
       714: q^2
       715: q
       717: q
       718: q
       721: q
       725: q
       726: q
       729: q
       733: q
       737: q
       741: q^2+q
       742: q^2
       744: q
       745: q
       749: q
       753: q
       754: q
       757: q
       761: q
       763: q
       765: q
       766: q
       769: q
       775: q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: 2q
       787: q^2+q
       788: q
       789: q
       791: q
       792: q
       793: 2q
       795: q
       799: q
       801: q
       805: 2q
       807: q^2+q
       808: q
       809: q
       811: q
       812: q
       813: q
       815: 2q
       817: q^2+q
       818: q
       819: q^2+q
       821: q
       823: q^2+q
       825: q^3+q^2+2q
       826: q^2
       827: 2q^2+q
       828: q
       829: 2q
       831: q^2+q
       832: q
       833: q^2+q
       835: 2q^2+q
       836: q^2+q
       837: q^2+q
       839: q^2+q
       840: q
       841: q
       843: q
       844: q
       845: 2q
       847: q^2+q
       848: q
       849: q
       851: q
       852: q
       853: q
       855: q
       856: q
       857: q
       858: q
       859: q^2+q
       861: q^2+q
       863: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q^2+2q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q
       878: q^2+2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       884: q
       896: q
       900: q
       904: q
       908: q
       909: q
       912: q
       916: q
       928: q
       929: q
       932: q
       936: q
       940: q
       944: q
       948: q^2+q
       949: q^2
       951: q
       952: q
       953: q
       956: q
       960: q
       964: q
       965: q
       968: q
       974: q
       976: q
       978: q
       982: q
       988: q
       989: q
       992: q
       994: q
       996: q^2+q
       998: q^2+q
       999: q
      1000: 2q
      1002: q
      1004: 2q
      1006: q^2+q
      1007: q
      1008: q
      1009: q
      1010: q
      1012: q
      1013: q
      1014: q
      1016: 2q
      1020: q
      1024: q
      1026: q
      1030: q^2+q
      1032: q^2+q
      1033: q
      1034: q
      1036: q^2+q
      1038: q
      1040: 2q
      1042: q^2+q
      1044: q^2+q
      1045: q
      1046: q
      1047: q
      1050: q
      1052: q
      1056: 2q
      1058: q^2+q
      1059: q
      1060: q
      1062: q
      1063: q
      1064: q
      1065: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1086: q
      1098: q
      1110: q
      1114: q
      1118: q
      1122: q
      1126: q
      1130: q
      1131: q
      1134: q
      1136: q
      1138: q
      1144: q
      1164: q
      1168: q
      1172: q
      1176: q
      1180: q
      1181: q
      1184: q
      1188: q
      1194: q
      1195: q
      1206: q
      1207: q
      1210: q+1
      1212: q+1
      1214: q
      1216: q^2+q
      1217: q
      1218: 2q
      1222: q
      1224: q
      1225: q
      1226: 1
      1228: 1
      1234: q
      1236: q
      1240: q
      1244: q+1
      1246: q
      1247: 1
      1248: q
      1250: q^2+q
      1251: q
      1252: q^2+q
      1254: 2q
      1256: q
      1258: 2q
      1260: q^2+q
      1261: q
      1263: 1
      1268: q
      1272: q
      1274: q
      1276: q
      1277: q
      1278: q
      1280: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1290: q
      1302: q
      1314: q
      1318: q
      1322: q
      1326: q
      1327: q
      1334: q
      1340: 1
      1372: q
      1374: 1
      1376: q
      1380: q
      1384: q
      1388: q
      1392: q
      1396: q
      1397: q
      1400: q
      1402: q
      1407: 1
      1411: 1
      1430: q
      1438: q+1
      1440: q
      1441: 1
      1442: 1
      1445: 1
      1452: 1
      1454: q
      1456: q
      1458: q+1
      1460: q^2+q
      1461: q
      1462: 2q
      1468: q
      1472: q
      1476: q
      1480: q
      1482: q
      1483: q
      1484: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1489: q
      1513: q
      1528: 1
      1541: q
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1583: q
      1587: q
      1591: q
      1595: q
      1596: q
      1631: q
      1640: 1
      1643: 1
      1647: 1
      1651: q+1
      1653: q
      1654: 1
      1655: 1
      1657: q
      1665: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1678: 1
      1699: q
      1726: 1
      1734: 1
      1745: 1
      1761: q
      1763: 1
      1765: 1
      1774: 1
      1804: 1
      1821: q
      1826: 1
      1827: 1
      1831: 1
      1833: 1
      1837: 1
      1861: 1
      1915: 1
      1929: 1
      1936: 1
      1956: 1
      1961: 1
      1964: 1
      1981: 1
      2029: 1
      2044: 1
      2053: 1
      2083: 1

2084:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q+1
        39: q+1
        41: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q
        59: 1
        60: q
        61: q^2+1
        62: q+1
        64: q+1
        66: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        76: q+1
        78: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       103: q
       106: 1
       107: q
       108: q^2+1
       109: q
       110: 1
       111: q+1
       113: q+1
       115: q+1
       117: q
       118: 1
       119: q
       120: q^2+1
       121: q+1
       123: q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       129: q+1
       131: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       153: q+1
       155: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       169: q
       172: 1
       173: q
       176: 1
       177: q+1
       179: q+1
       181: q+1
       183: q
       184: q^2+1
       185: q
       186: 1
       187: q+1
       189: q+1
       191: q
       192: 1
       194: 1
       195: q
       196: 1
       197: 1
       199: q
       200: q^2+1
       201: q
       202: q^2+1
       203: q
       204: 1
       205: q+1
       207: q+1
       209: q+1
       211: q+1
       213: q+1
       215: q+1
       217: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       237: q+1
       239: q+1
       241: q+1
       243: q+1
       244: 1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       259: q
       262: 1
       263: q
       266: 1
       269: 1
       271: q
       273: 1
       275: q
       278: 1
       279: q+1
       281: q+1
       283: q
       284: q^2+1
       285: q
       286: 1
       287: q+1
       289: q+1
       291: q+1
       293: q
       294: q^2+1
       295: q
       296: 1
       297: q+1
       300: 1
       301: 1
       303: q
       304: 1
       305: 1
       307: q
       308: q^2+1
       309: q
       310: 1
       311: q+1
       313: q+1
       315: q+1
       317: q+1
       320: 1
       321: q
       322: 1
       323: 1
       325: q+1
       327: q+1
       329: q+1
       331: q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       340: q+1
       342: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       364: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q
       380: 1
       381: q
       384: 1
       385: q
       388: 1
       391: 1
       396: 1
       397: q
       399: 1
       401: q
       404: 1
       406: 1
       409: q+1
       411: q+1
       413: q+1
       415: q+1
       417: q+1
       419: q
       420: q^2+1
       421: q
       422: 1
       423: q+1
       425: q+1
       427: q+1
       430: 1
       431: q
       432: 1
       433: 1
       435: 1
       438: 1
       439: q
       440: 1
       441: 1
       444: 1
       445: 1
       447: q
       448: q^2+1
       449: q
       450: 1
       451: q+1
       453: q
       454: q^2+1
       455: q+1
       457: q
       458: 1
       459: q+1
       461: q
       462: 1
       463: q+1
       465: q+1
       467: q+1
       469: q+1
       472: 1
       473: q
       474: 1
       475: 1
       477: 1
       479: 1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       487: q+1
       489: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       504: q+1
       506: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q
       524: 1
       525: q
       528: 1
       529: q
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       549: q
       552: 1
       553: q
       555: 1
       557: q
       559: 1
       561: q
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: q+1
       585: q+1
       587: q+1
       589: q
       590: q^2+1
       591: q
       592: 1
       594: 1
       595: q
       596: 1
       597: q+1
       599: q+1
       601: q+1
       604: 1
       605: 1
       607: q
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       619: q
       620: q^2+1
       621: q
       622: 1
       623: q+1
       625: q+1
       627: q+1
       629: q+1
       631: q
       632: 1
       633: q+1
       635: q+1
       637: q+1
       639: q+1
       642: 1
       643: q
       644: 1
       645: 1
       648: 1
       649: q
       650: 1
       651: 1
       653: 1
       655: 1
       657: q+1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: q+1
       666: q+1
       668: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       697: 1
       705: q
       708: 1
       709: q
       712: 1
       713: q
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       737: q
       739: 1
       741: q
       743: 1
       745: q
       747: 1
       749: q
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: q+1
       777: q+1
       779: q+1
       781: q+1
       783: q+1
       786: 1
       787: q
       788: 1
       789: q+1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       806: 1
       807: q
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       817: q
       818: 1
       819: q+1
       821: q+1
       823: q+1
       825: q
       826: q^2+1
       827: q
       828: 1
       830: 1
       831: q
       832: 1
       833: q+1
       835: q+1
       837: q+1
       839: q
       840: 1
       841: q+1
       843: 1
       846: 1
       847: q
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: q+1
       861: q+1
       863: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       889: 1
       896: q
       899: 1
       900: q
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       930: 1
       934: 1
       936: q
       938: 1
       940: q
       942: 1
       944: q
       946: 1
       948: q
       950: 1
       955: 1
       956: q
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: q+1
       994: q+1
       996: q+1
       998: q
       999: 1
      1001: 1
      1002: q+1
      1005: 1
      1006: q
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1030: q+1
      1032: q
      1033: 1
      1034: q+1
      1036: q+1
      1038: q+1
      1041: 1
      1042: q+1
      1044: q
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1057: 1
      1058: q
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1110: q
      1112: 1
      1114: q
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1158: 1
      1164: q
      1166: 1
      1168: q
      1170: 1
      1172: q
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1208: 1
      1210: q+1
      1212: q+1
      1214: q+1
      1216: q
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1244: q+1
      1246: q
      1247: 1
      1248: q+1
      1250: q
      1251: 1
      1252: q+1
      1255: 1
      1256: q+1
      1259: 1
      1260: q
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1269: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1314: q
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1354: 1
      1358: 1
      1372: q
      1374: 1
      1376: q
      1378: 1
      1380: q
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: 1
      1413: 1
      1415: 1
      1424: 1
      1430: 1
      1436: 1
      1438: q+1
      1440: q
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1452: 1
      1455: 1
      1456: q+1
      1458: q+1
      1460: q
      1461: 1
      1463: 1
      1464: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1480: 1
      1482: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1494: 1
      1518: 1
      1530: 1
      1538: 1
      1541: q
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1569: 1
      1583: q
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1613: 1
      1617: 1
      1631: 1
      1637: 1
      1639: 1
      1641: 1
      1643: 1
      1648: 1
      1651: q+1
      1653: q
      1654: 1
      1656: 1
      1658: 1
      1659: 1
      1661: 1
      1666: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1680: 1
      1704: 1
      1723: 1
      1730: 1
      1736: 1
      1747: 1
      1761: q
      1763: 1
      1767: 1
      1770: 1
      1776: 1
      1778: 1
      1783: 1
      1791: 1
      1801: 1
      1815: 1
      1817: 1
      1822: 1
      1823: 1
      1825: 1
      1827: 1
      1832: 1
      1833: 1
      1839: 1
      1863: 1
      1911: 1
      1916: 1
      1920: 1
      1923: 1
      1926: 1
      1938: 1
      1956: 1
      1958: 1
      1960: 1
      1965: 1
      1982: 1
      2026: 1
      2046: 1
      2049: 1
      2054: 1
      2084: 1

2085:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q
        59: 1
        60: q^2+1
        61: q
        63: q+1
        65: q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: q
       107: q^2+1
       108: q
       109: q
       110: 1
       112: q+1
       114: q+1
       116: q+1
       117: q
       118: 1
       119: q^2+1
       120: q
       122: q+1
       124: q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       170: 1
       171: q
       174: 1
       175: q
       178: q+1
       180: q+1
       182: q+1
       183: q^2+1
       184: q
       185: q
       186: 1
       188: q+1
       190: q+1
       191: q
       192: 1
       193: 1
       195: q
       196: 1
       198: 1
       199: q^2+1
       200: q
       201: q^2+1
       202: q
       203: q
       204: 1
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: 1
       261: q
       264: 1
       265: q
       268: 1
       272: q
       274: 1
       276: 1
       277: q
       280: q+1
       282: q+1
       283: q^2+1
       284: q
       285: q
       286: 1
       288: q+1
       290: q+1
       292: q+1
       293: q^2+1
       294: q
       295: q
       296: 1
       298: q+1
       299: 1
       302: 1
       303: q
       304: 1
       306: 1
       307: q^2+1
       308: q
       309: q
       310: 1
       312: q+1
       314: q+1
       316: q+1
       318: q+1
       319: 1
       321: q
       322: 1
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: 1
       379: q
       382: 1
       383: q
       386: 1
       387: q
       390: 1
       394: 1
       398: q
       400: 1
       402: q
       403: 1
       407: 1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q^2+1
       420: q
       421: q
       422: 1
       424: q+1
       426: q+1
       428: q+1
       429: 1
       431: q
       432: 1
       434: 1
       436: 1
       437: 1
       439: q
       440: 1
       442: 1
       443: 1
       446: 1
       447: q^2+1
       448: q
       449: q
       450: 1
       452: q+1
       453: q^2+1
       454: q
       456: q+1
       457: q
       458: 1
       460: q+1
       461: q
       462: 1
       464: q+1
       466: q+1
       468: q+1
       470: q+1
       471: 1
       473: q
       474: 1
       476: 1
       478: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 1
       523: q
       526: 1
       527: q
       530: 1
       531: q
       534: 1
       538: 1
       542: 1
       546: 1
       550: q
       551: 1
       554: q
       556: 1
       558: q
       560: 1
       562: q
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: q+1
       586: q+1
       588: q+1
       589: q^2+1
       590: q
       591: q
       592: 1
       593: 1
       595: q
       596: 1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       606: 1
       607: q
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: q^2+1
       620: q
       621: q
       622: 1
       624: q+1
       626: q+1
       628: q+1
       630: q+1
       631: q
       632: 1
       634: q+1
       636: q+1
       638: q+1
       640: q+1
       641: 1
       643: q
       644: 1
       646: 1
       647: 1
       649: q
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       699: 1
       706: 1
       707: q
       710: 1
       711: q
       714: q
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       738: q
       740: 1
       742: q
       744: 1
       746: q
       748: 1
       750: q
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       785: 1
       787: q
       788: 1
       790: q+1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       805: 1
       807: q
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       817: q
       818: 1
       820: q+1
       822: q+1
       824: q+1
       825: q^2+1
       826: q
       827: q
       828: 1
       829: 1
       831: q
       832: 1
       834: q+1
       836: q+1
       838: q+1
       839: q
       840: 1
       842: q+1
       844: 1
       845: 1
       847: q
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       890: 1
       897: 1
       898: q
       901: q
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       929: 1
       933: 1
       937: q
       939: 1
       941: q
       943: 1
       945: q
       947: 1
       949: q
       951: 1
       953: 1
       957: q
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: q+1
       995: q+1
       997: q+1
       998: q
       999: 1
      1000: 1
      1003: q+1
      1004: 1
      1006: q
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1031: q+1
      1032: q
      1033: 1
      1035: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1043: q+1
      1044: q
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1056: 1
      1058: q
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1111: q
      1113: 1
      1115: q
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1157: 1
      1165: q
      1167: 1
      1169: q
      1171: 1
      1173: q
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1207: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1216: q
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1245: q+1
      1246: q
      1247: 1
      1249: q+1
      1250: q
      1251: 1
      1253: q+1
      1254: 1
      1257: q+1
      1258: 1
      1260: q
      1261: 1
      1263: 1
      1265: 1
      1267: 1
      1268: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1315: q
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1353: 1
      1357: 1
      1373: q
      1375: 1
      1377: q
      1379: 1
      1381: q
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1408: 1
      1411: 1
      1416: 1
      1423: 1
      1434: 1
      1437: 1
      1439: q+1
      1440: q
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1454: 1
      1457: q+1
      1459: q+1
      1460: q
      1461: 1
      1462: 1
      1465: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1481: 1
      1483: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1495: 1
      1519: 1
      1531: 1
      1539: 1
      1542: q
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1568: 1
      1584: q
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1612: 1
      1616: 1
      1635: 1
      1638: 1
      1640: 1
      1642: 1
      1644: 1
      1647: 1
      1652: q+1
      1653: q
      1654: 1
      1655: 1
      1657: 1
      1660: 1
      1662: 1
      1665: 1
      1668: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1681: 1
      1705: 1
      1727: 1
      1731: 1
      1734: 1
      1746: 1
      1762: q
      1764: 1
      1766: 1
      1771: 1
      1774: 1
      1779: 1
      1782: 1
      1790: 1
      1805: 1
      1816: 1
      1818: 1
      1821: 1
      1824: 1
      1826: 1
      1828: 1
      1831: 1
      1833: 1
      1840: 1
      1864: 1
      1912: 1
      1915: 1
      1919: 1
      1924: 1
      1930: 1
      1937: 1
      1957: 1
      1959: 1
      1961: 1
      1964: 1
      1983: 1
      2030: 1
      2045: 1
      2050: 1
      2053: 1
      2085: 1

2086:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+3q^2+2q
        25: 3q^3+4q^2+2q
        26: 3q^3+4q^2+2q
        27: q^4+3q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 4q^2+2q
        32: 3q^2+2q
        33: 4q^2+2q
        34: 3q^3+4q^2+2q
        35: 2q^3+3q^2+2q
        36: 3q^3+4q^2+2q
        37: q^2+q
        38: 3q^2+q
        39: q^2+q
        40: 3q^2+q
        41: q^2+q
        42: q^3+2q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: q^3+3q^2+2q
        55: 3q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^4+3q^3+3q^2+2q
        58: 3q^2+q
        59: q^2+q
        60: q^3+2q^2
        61: 2q^3+2q^2+2q
        62: q^2+q
        63: 3q^2+q
        64: q^2+q
        65: 2q^2+q
        66: q^2+q
        67: 3q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 3q^3+4q^2+2q
        73: 4q^2+2q
        74: q^2+q
        75: 3q^2+q
        76: q^2+q
        77: 3q^2+q
        78: q^2+q
        79: q^3+2q^2+q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 4q^2+2q
        83: 3q^2+2q
        84: 2q^3+3q^2+2q
        85: 2q^3+3q^2+2q
        86: 3q^3+4q^2+2q
        87: 2q^3+3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q^2
       104: q^2
       105: 2q^2+q
       106: q
       107: q^3+2q^2
       108: 2q^3+2q^2+2q
       109: 3q^2+q
       110: q^2+q
       111: q^2+q
       112: 3q^2+q
       113: q^2+q
       114: 3q^2+q
       115: q^2+q
       116: 2q^2+q
       117: 2q^2+q
       118: q
       119: q^2
       120: q^3+q^2+2q
       121: q^2+q
       122: 2q^2+q
       123: q^2+q
       124: 2q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: q^2+q
       128: 3q^2+q
       129: q^2+q
       130: 3q^2+q
       131: q^2+q
       132: q^3+2q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+2q
       136: 3q^2+2q
       137: 3q^2+2q
       138: 3q^2+2q
       139: 4q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 4q^2+2q
       143: 2q^3+3q^2+2q
       144: 2q^3+3q^2+2q
       145: 3q^3+4q^2+2q
       146: 2q^3+3q^2+2q
       147: 3q^3+4q^2+2q
       148: 4q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: q^2+q
       152: 3q^2+q
       153: q^2+q
       154: 3q^2+q
       155: q^2+q
       156: q^3+2q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^3+3q^2+2q
       164: 2q^3+3q^2+2q
       165: 2q^3+3q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q^2
       170: q^2
       171: 2q^2+q
       172: q
       173: q^2
       175: q^2+q
       176: q
       177: q^2+q
       178: 2q^2+q
       179: q^2+q
       180: 3q^2+q
       181: q^2+q
       182: 3q^2+q
       183: q^2
       184: q^3+q^2+2q
       185: 2q^2+q
       186: q
       187: q^2+q
       188: 2q^2+q
       189: q^2+q
       190: 2q^2+q
       191: 2q^2+q
       192: q
       194: q^2+2q
       195: 3q^2+q
       196: q^2+q
       197: q
       198: q^2+q
       199: q^2
       200: q^3+q^2+2q
       201: q^3+2q^2
       202: 2q^3+2q^2+2q
       203: 3q^2+q
       204: q^2+q
       205: q^2+q
       206: 3q^2+q
       207: q^2+q
       208: 2q^2+q
       209: q^2+q
       210: 3q^2+q
       211: q^2+q
       212: 2q^2+q
       214: q^2+q
       216: q^2+q
       218: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+3q^2+2q
       223: 2q^3+3q^2+2q
       224: 3q^2+2q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+2q
       228: 2q^2+2q
       229: 2q
       230: 2q^2+2q
       231: 2q^3+3q^2+2q
       232: q^3+2q^2+2q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+2q
       235: 3q^2+2q
       236: 3q^2+2q
       237: q^2+q
       238: 3q^2+q
       239: q^2+q
       240: 3q^2+q
       241: q^2+q
       242: q^3+2q^2+q
       243: 4q^2+2q
       244: q^2+2q
       245: 4q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^3+3q^2+2q
       254: 2q^3+3q^2+2q
       255: 2q^3+3q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q^2
       260: q^2
       261: 2q^2+q
       262: q
       263: q^2
       265: q^2+q
       266: q
       269: q
       270: q^2+q
       271: q^2
       272: 2q^2+q
       273: q
       274: q^2
       275: q^2
       277: q^2+q
       278: q
       280: q
       282: q^2+q
       283: q^2
       284: q^3+q^2+2q
       285: 2q^2+q
       286: q
       287: q^2+q
       288: 2q^2+q
       290: q^2+q
       291: q^2+q
       292: 2q^2+q
       293: q^2
       294: q^3+q^2+2q
       295: 2q^2+q
       296: q
       297: q^2+q
       298: 2q^2+q
       300: 2q
       301: q
       302: q^2+q
       303: q^2+q
       304: q
       305: q
       306: q
       307: q^2
       308: q^3+q^2+2q
       309: 2q^2+q
       310: q
       311: q^2+q
       312: 3q^2+q
       313: q^2+q
       314: 2q^2+q
       315: q^2+q
       316: 2q^2+q
       317: q^2+q
       318: 3q^2+q
       320: q^2+2q
       321: 3q^2+q
       322: q^2+q
       323: q
       324: q^2+q
       325: q^2+q
       326: 2q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: q^3+2q^2+2q
       334: 2q^3+3q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: q^2+q
       339: 3q^2+q
       340: q^2+q
       341: 3q^2+q
       342: q^2+q
       343: q^3+2q^2+q
       344: q^2+2q
       345: q^2+2q
       346: 2q^2+2q
       347: 2q
       348: 2q
       349: 2q^2+2q
       350: 2q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: q^3+2q^2+2q
       354: 2q^3+3q^2+2q
       355: 2q^3+3q^2+2q
       356: 2q^3+3q^2+2q
       357: 3q^2+2q
       358: 3q^2+2q
       359: 4q^2+2q
       361: q^2+q
       363: q^2+q
       365: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q
       370: 2q^2+2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q^2
       379: q^2+q
       380: q
       383: q
       385: q^2
       387: q^2+q
       388: q
       391: q
       392: q^2+q
       395: q
       396: q
       397: q^2
       398: 2q^2+q
       399: q
       400: q^2
       401: q^2
       402: q^2+q
       404: q
       406: q
       408: q^2+q
       410: q
       412: q^2+q
       414: q
       416: q^2+q
       418: q^2+q
       419: q^2
       420: q^3+q^2+2q
       421: 2q^2+q
       422: q
       423: q^2+q
       424: 2q^2+q
       425: q^2+q
       426: 2q^2+q
       427: q^2+q
       428: 3q^2+q
       430: 2q
       431: q^2+q
       432: q
       433: q
       434: q
       436: q
       438: 2q
       439: q^2+q
       440: q
       441: q
       442: q
       444: q^2+2q
       445: q
       446: q^2+q
       447: q^2
       448: q^3+q^2+2q
       449: 2q^2+q
       450: q
       451: q^2+q
       452: 2q^2+q
       453: q^2
       454: q^3+q^2+2q
       456: q^2+q
       457: 2q^2+q
       458: q
       459: q^2+q
       460: 2q^2+q
       461: 3q^2+q
       462: q^2+q
       463: q^2+q
       464: 3q^2+q
       466: q
       468: q^2+q
       469: q^2+q
       470: 2q^2+q
       472: 2q
       473: q^2+q
       474: q
       475: q
       476: q
       477: q
       478: q^2+q
       479: q
       480: q^2+q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       486: q^2+q
       488: q^2+q
       490: q^2+q
       491: 2q^2+2q
       492: q^2+2q
       493: 2q
       494: 2q^2+2q
       495: 2q
       496: 2q
       497: q^3+2q^2+2q
       498: 2q^3+3q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+2q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q
       512: 2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       523: q
       527: q
       529: q^2
       531: q^2+q
       532: q
       535: q
       536: q
       540: q
       543: q
       544: q
       547: q
       548: q^2+q
       549: q^2
       550: q^2+q
       552: q
       554: q
       557: q^2
       558: q^2+q
       559: q
       561: q^2
       562: 2q^2+q
       563: q
       564: q^2
       567: q
       568: q
       570: q
       572: q^2+q
       575: q
       576: q^2+q
       577: q
       581: q^2+q
       584: q
       586: q
       588: q^2+q
       589: q^2
       590: q^3+q^2+2q
       591: 2q^2+q
       592: q
       594: 2q
       595: q^2+q
       596: q
       598: q^2+q
       599: q^2+q
       600: 2q^2+q
       602: q
       604: 2q
       606: q
       607: q^2+q
       608: q
       609: q
       610: q
       612: q
       613: q
       614: q
       616: 2q
       618: q
       619: q^2
       620: q^3+q^2+2q
       621: 2q^2+q
       622: q
       624: q^2+q
       625: q^2+q
       626: 2q^2+q
       628: q^2+q
       629: q^2+q
       630: 2q^2+q
       631: q^2+q
       632: q
       634: q^2+q
       636: q
       638: q^2+q
       640: q
       642: 2q
       643: q^2+q
       644: q
       645: q
       646: q
       648: 2q
       649: q^2+q
       650: q
       652: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q
       675: q
       676: q^2+2q
       677: 2q
       678: 2q
       679: 2q
       680: 2q^2+2q
       681: q^3+2q^2+2q
       682: q^2+2q
       683: 3q^2+2q
       684: 2q^2+2q
       685: 2q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q^2+2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       697: q
       700: q^2+q
       707: q
       711: q
       713: q^2
       714: q^2+q
       716: q
       719: q
       720: q
       724: q
       727: q
       728: q
       732: q
       736: q
       738: q
       741: q^2
       742: q^2+q
       743: q
       746: q
       750: q
       755: q
       756: q
       760: q
       762: q
       764: q
       767: q
       768: q
       773: q
       776: q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       786: 2q
       787: q^2+q
       788: q
       790: q
       791: q
       792: q
       794: 2q
       796: q
       800: q
       802: q
       806: 2q
       807: q^2+q
       808: q
       810: q
       811: q
       812: q
       814: q
       816: 2q
       817: q^2+q
       818: q
       820: q^2+q
       822: q
       824: q^2+q
       825: q^2
       826: q^3+q^2+2q
       827: 2q^2+q
       828: q
       830: 2q
       831: q^2+q
       832: q
       834: q^2+q
       835: q^2+q
       836: 2q^2+q
       838: q^2+q
       839: q^2+q
       840: q
       842: q
       843: q
       844: q
       846: 2q
       847: q^2+q
       848: q
       850: q
       851: q
       852: q
       854: q
       855: q
       856: q
       857: q
       858: q
       860: q^2+q
       862: q^2+q
       864: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q^2+2q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q
       878: q^2+2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       891: q
       898: q
       901: q
       907: q
       910: q
       911: q
       915: q
       919: q
       930: q
       931: q
       935: q
       937: q
       941: q
       945: q
       948: q^2
       949: q^2+q
       950: q
       954: q
       955: q
       957: q
       963: q
       966: q
       967: q
       972: q
       975: q
       977: q
       981: q
       986: q
       990: q
       991: q
       993: q
       995: q
       997: q^2+q
       998: q^2+q
       999: q
      1001: 2q
      1003: q
      1005: 2q
      1006: q^2+q
      1007: q
      1008: q
      1009: q
      1011: q
      1012: q
      1013: q
      1015: q
      1017: 2q
      1021: q
      1025: q
      1027: q
      1031: q^2+q
      1032: q^2+q
      1033: q
      1035: q
      1037: q^2+q
      1039: q
      1041: 2q
      1043: q^2+q
      1044: q^2+q
      1045: q
      1046: q
      1047: q
      1051: q
      1053: q
      1057: 2q
      1058: q^2+q
      1059: q
      1061: q
      1062: q
      1063: q
      1064: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1093: q
      1105: q
      1111: q
      1115: q
      1121: q
      1125: q
      1129: q
      1132: q
      1133: q
      1135: q
      1137: q
      1142: q
      1147: q
      1165: q
      1169: q
      1173: q
      1179: q
      1182: q
      1183: q
      1187: q
      1192: q
      1196: q
      1197: q
      1208: q
      1209: q
      1211: q+1
      1213: q+1
      1215: q
      1216: q^2+q
      1217: q
      1219: 2q
      1223: q
      1224: q
      1225: q
      1227: 1
      1229: 1
      1235: q
      1237: q
      1241: q
      1245: q+1
      1246: q
      1247: 1
      1249: q
      1250: q^2+q
      1251: q
      1253: q^2+q
      1255: 2q
      1257: q
      1259: 2q
      1260: q^2+q
      1261: q
      1262: 1
      1269: q
      1273: q
      1275: q
      1276: q
      1277: q
      1279: q
      1280: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1297: q
      1309: q
      1315: q
      1321: q
      1325: q
      1328: q
      1329: q
      1338: q
      1343: 1
      1373: q
      1375: 1
      1377: q
      1381: q
      1387: q
      1391: q
      1395: q
      1398: q
      1399: q
      1401: q
      1403: q
      1405: 1
      1413: 1
      1434: q
      1439: q+1
      1440: q
      1441: 1
      1443: 1
      1444: 1
      1453: 1
      1455: q
      1457: q
      1459: q+1
      1460: q^2+q
      1461: q
      1463: 2q
      1469: q
      1473: q
      1477: q
      1481: q
      1482: q
      1483: q
      1484: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1496: q
      1520: q
      1533: 1
      1542: q
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1584: q
      1590: q
      1594: q
      1597: q
      1598: q
      1635: q
      1639: 1
      1644: 1
      1648: 1
      1652: q+1
      1653: q
      1654: 1
      1656: 1
      1658: q
      1666: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1683: 1
      1706: q
      1724: 1
      1736: 1
      1748: 1
      1762: q
      1764: 1
      1768: 1
      1776: 1
      1802: 1
      1822: q
      1825: 1
      1828: 1
      1832: 1
      1833: 1
      1842: 1
      1866: 1
      1916: 1
      1927: 1
      1939: 1
      1957: 1
      1960: 1
      1965: 1
      1984: 1
      2027: 1
      2047: 1
      2054: 1
      2086: 1

2087:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: 2q^4+2q^3+q^2+q
        23: 2q^4+2q^3+q^2+q
        24: 2q^4+2q^3+q^2+q
        25: q^5+3q^4+3q^3+q^2+q
        26: q^5+3q^4+3q^3+q^2+q
        27: q^5+3q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: q^4+2q^3+q^2+q
        32: 2q^4+2q^3+q^2+q
        33: q^4+2q^3+q^2+q
        34: 2q^4+3q^3+q^2+q
        35: q^5+3q^4+3q^3+q^2+q
        36: 2q^4+3q^3+q^2+q
        37: 2q^4+2q^3+q^2+q
        39: 2q^4+2q^3+q^2+q
        41: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: 2q^4+2q^3+q^2+q
        53: 2q^4+2q^3+q^2+q
        54: 2q^4+2q^3+q^2+q
        55: q^5+3q^4+3q^3+q^2+q
        56: q^5+3q^4+3q^3+q^2+q
        57: q^5+3q^4+3q^3+q^2+q
        58: q^3+q^2
        59: q^3+q
        60: q^3+q^2
        61: q^4+2q^3+q
        62: q^4+2q^3+q^2+q
        64: 2q^4+2q^3+q^2+q
        66: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 2q^4+3q^3+q^2+q
        73: q^4+2q^3+q^2+q
        74: 2q^4+2q^3+q^2+q
        76: 2q^4+2q^3+q^2+q
        78: 2q^4+2q^3+q^2+q
        80: q^4+2q^3+q^2+q
        81: q^4+2q^3+q^2+q
        82: q^4+2q^3+q^2+q
        83: 2q^4+2q^3+q^2+q
        84: 2q^4+3q^3+q^2+q
        85: 2q^4+3q^3+q^2+q
        86: 2q^4+3q^3+q^2+q
        87: q^5+3q^4+3q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^4+3q^3+q^2+q
        98: 2q^4+3q^3+q^2+q
        99: q^5+2q^4+2q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       103: q^3+q^2
       106: q^3+q
       107: q^3+q^2
       108: q^4+2q^3+q
       109: q^3+q^2
       110: q^3+q
       111: q^4+2q^3+q^2+q
       113: q^4+2q^3+q^2+q
       115: 2q^4+2q^3+q^2+q
       117: q^3+q^2
       118: q^3+q
       119: q^3+q^2
       120: q^4+2q^3+q
       121: q^4+2q^3+q^2+q
       123: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 2q^4+3q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 2q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^3+q
       141: q^4+2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: q^4+2q^3+q^2+q
       145: q^4+3q^3+q^2+q
       146: 2q^4+3q^3+q^2+q
       147: 2q^4+3q^3+q^2+q
       148: q^4+2q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       151: 2q^4+2q^3+q^2+q
       153: 2q^4+2q^3+q^2+q
       155: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^3+q^2+q
       161: 2q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: 2q^4+3q^3+q^2+q
       164: 2q^4+3q^3+q^2+q
       165: q^5+2q^4+2q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3+q^2
       172: q^3+q
       173: q^3+q^2
       176: q^3+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^3+q^2
       184: q^4+2q^3+q
       185: q^3+q^2
       186: q^3+q
       187: q^4+2q^3+q^2+q
       189: q^4+2q^3+q^2+q
       191: q^3+q^2
       192: q^3+q
       194: q^3+q
       195: q^3+q^2
       196: q^3+q
       197: q^3+q
       199: q^3+q^2
       200: 2q^3+q
       201: q^3+q^2
       202: q^4+2q^3+q
       203: q^3+q^2
       204: q^3+q
       205: q^4+2q^3+q^2+q
       207: 2q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: 2q^4+2q^3+q^2+q
       213: 2q^3+q^2+q
       215: 2q^3+q^2+q
       217: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 3q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: 2q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: 2q^3+q^2+q
       228: q^3+q^2+q
       229: q^3+q
       230: 2q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^4+3q^3+q^2+q
       233: q^4+2q^3+q^2+q
       234: 2q^4+3q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: q^3+q^2+q
       237: 2q^3+q^2+q
       239: 2q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: q^3+q
       245: 2q^3+q^2+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: q^3+q^2
       262: q^3+q
       263: q^3+q^2
       266: q^3+q
       269: q^3+q
       271: q^3+q^2
       273: q^3+q
       275: q^3+q^2
       278: q^3+q
       279: 2q^3+q^2+q
       281: q^3+q^2+q
       283: q^2
       284: q^3+q
       285: q^2
       286: q
       287: q^3+q^2+q
       289: 2q^3+q^2+q
       291: q^3+q^2+q
       293: q^3+q^2
       294: 2q^3+q
       295: q^3+q^2
       296: q^3+q
       297: 2q^3+q^2+q
       300: q^3+q
       301: q^3+q
       303: q^3+q^2
       304: q^3+q
       305: q^3+q
       307: q^3+q^2
       308: q^4+2q^3+q
       309: q^3+q^2
       310: q^3+q
       311: 2q^3+q^2+q
       313: q^4+2q^3+q^2+q
       315: q^3+q^2+q
       317: 2q^3+q^2+q
       320: q^3+q
       321: q^3+q^2
       322: q^3+q
       323: q^3+q
       325: q^4+2q^3+q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: 2q^3+q^2+q
       334: 2q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       338: 2q^3+q^2+q
       340: 2q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^3+q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^3+q^2+q
       351: q^3+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: 2q^3+q^2+q
       358: q^3+q^2+q
       359: 2q^3+q^2+q
       360: 2q^3+q^2+q
       362: 2q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: q^3+q
       370: 2q^3+q^2+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q^2
       380: q
       381: q^3+q^2
       384: q^3+q
       385: q^3+q^2
       388: q^3+q
       391: q^3+q
       396: q^3+q
       397: q^3+q^2
       399: q^3+q
       401: q^3+q^2
       404: q^3+q
       406: q^3+q
       409: q^2+q
       411: q^2+q
       413: q^3+q^2+q
       415: q^2+q
       417: q^3+q^2+q
       419: q^2
       420: q^3+q
       421: q^2
       422: q
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: 2q^3+q^2+q
       430: q
       431: q^2
       432: q
       433: q
       435: q^3+q
       438: q
       439: q^2
       440: q
       441: q
       444: q^3+q
       445: q^3+q
       447: q^2
       448: q^3+q
       449: q^2
       450: q
       451: q^3+q^2+q
       453: q^3+q^2
       454: 2q^3+q
       455: 2q^3+q^2+q
       457: q^3+q^2
       458: q^3+q
       459: 2q^3+q^2+q
       461: q^3+q^2
       462: q^3+q
       463: 2q^3+q^2+q
       465: 2q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       472: q^3+q
       473: q^3+q^2
       474: q^3+q
       475: q^3+q
       477: q^3+q
       479: q^3+q
       481: 2q^3+q^2+q
       482: q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       485: 2q^3+q^2+q
       487: 2q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^3+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^3+q^2+q
       500: q^3+q^2+q
       501: 2q^3+q^2+q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^3+q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       521: q^2
       524: q
       525: q^2
       528: q
       529: q^2
       532: q
       536: q
       539: q^3+q
       543: q
       547: q^3+q
       549: q^2
       552: q
       553: q^3+q^2
       555: q^3+q
       557: q^3+q^2
       559: q^3+q
       561: q^3+q^2
       563: q^3+q
       568: q^3+q
       570: q^3+q
       575: q^3+q
       577: q^3+q
       583: q^2+q
       585: q^3+q^2+q
       587: q^2+q
       589: q^2
       590: q^3+q
       591: q^2
       592: q
       594: q
       595: q^2
       596: q
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: 2q^3+q^2+q
       604: q
       605: q
       607: q^2
       608: q
       609: q
       611: q
       613: q
       616: q^3+q
       617: q^3+q
       619: q^2
       620: q^3+q
       621: q^2
       622: q
       623: q^3+q^2+q
       625: q^3+q^2+q
       627: q^2+q
       629: q^3+q^2+q
       631: q^3+q^2
       632: q^3+q
       633: 2q^3+q^2+q
       635: q^2+q
       637: q^2+q
       639: q^3+q^2+q
       642: q
       643: q^2
       644: q
       645: q
       648: q
       649: q^2
       650: q
       651: q^3+q
       653: q
       655: q^3+q
       657: q^2+q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+q
       673: q^2+q
       674: q
       675: q
       676: q^2+q
       677: q
       678: q
       679: q
       680: q^2+q
       681: 2q^3+q^2+q
       682: q^3+q^2+q
       683: q^3+q^2+q
       684: q^2+q
       685: q^3+q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       697: q^3+q
       705: q^2
       708: q
       709: q^2
       712: q
       713: q^2
       716: q
       720: q
       723: q
       727: q
       731: q
       735: q^3+q
       737: q^2
       739: q
       741: q^2
       743: q
       745: q^2
       747: q
       749: q^3+q^2
       751: q^3+q
       756: q
       758: q^3+q
       762: q
       768: q^3+q
       769: q^3+q
       775: q^2+q
       777: q^2+q
       779: q^2+q
       781: q^3+q^2+q
       783: q^2+q
       786: q
       787: q^2
       788: q
       789: q^2+q
       791: q
       794: q
       795: q
       797: q
       799: q
       802: q
       806: q
       807: q^2
       808: q
       809: q
       811: q
       813: q
       816: q
       817: q^2
       818: q
       819: q^2+q
       821: q^3+q^2+q
       823: q^2+q
       825: q^2
       826: q^3+q
       827: q^2
       828: q
       830: q
       831: q^2
       832: q
       833: q^3+q^2+q
       835: q^3+q^2+q
       837: q^2+q
       839: q^2
       840: q
       841: q^2+q
       843: q
       846: q
       847: q^2
       848: q
       849: q
       851: q
       853: q
       855: q
       857: q
       866: q^2+q
       868: q^2+q
       870: q
       871: q
       872: q
       874: q^2+q
       875: q^3+q^2+q
       876: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       889: q^3+q
       896: q^2
       899: q
       900: q^2
       902: q
       906: q
       911: q
       914: q
       918: q
       922: q
       930: q
       934: q
       936: q^2
       938: q
       940: q^2
       942: q
       944: q^2
       946: q
       948: q^2
       950: q
       955: q
       956: q^2
       958: q
       961: q
       967: q
       968: q
       975: q
       979: q
       982: q
       991: q
       994: q^2+q
       998: q^2
       999: q
      1001: q
      1002: q^2+q
      1005: q
      1006: q^2
      1007: q
      1008: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1024: q
      1027: q
      1034: q^2+q
      1036: q^2+q
      1038: q^3+q^2+q
      1041: q
      1042: q^2+q
      1044: q^2
      1045: q
      1048: q
      1050: q
      1053: q
      1057: q
      1058: q^2
      1059: q
      1060: q
      1062: q
      1064: q
      1076: q
      1078: q
      1080: q^2+q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1091: q
      1102: q
      1110: q^2
      1112: q
      1114: q^2
      1116: q
      1120: q
      1124: q
      1127: q
      1133: q
      1135: q
      1138: q
      1150: q
      1158: q
      1168: q^2
      1170: q
      1172: q^2
      1174: q
      1178: q
      1183: q
      1185: q
      1199: q
      1208: q
      1220: q
      1222: q
      1230: q
      1235: q
      1238: q
      1241: q
      1248: q^2+q
      1250: q^2
      1251: q
      1255: q
      1256: q^2+q
      1259: q
      1260: q^2
      1261: q
      1264: q
      1266: q
      1269: q
      1272: q
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      1278: q
      1280: q
      1287: q
      1289: q
      1295: q
      1323: q
      1331: q
      1354: q
      1358: q
      1376: q^2
      1378: q
      1380: q^2
      1382: q
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      1390: q
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      1399: q
      1401: q
      1415: q
      1424: q
      1430: q
      1446: q
      1464: q
      1469: q
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      1474: q
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      1480: q
      1484: q
      1518: q
      1560: q
      1592: q
      1600: q
      1613: q
      1617: q
      1637: 1
      1641: q
      1658: q
      1671: q
      1725: 1
      1730: 1
      1778: q
      1783: q
      1823: 1
      1843: 1
      1911: 1
      1928: 1
      1958: 1
      1985: 1
      2028: 1
      2049: 1
      2087: 1

2088:    0: 3q^3+4q^2+2q
         1: 3q^3+4q^2+2q
         2: q^4+3q^3+3q^2+2q
         3: 3q^3+4q^2+2q
         4: 3q^3+4q^2+2q
         5: 3q^3+4q^2+2q
         6: 3q^3+4q^2+2q
         7: q^4+3q^3+3q^2+2q
         8: q^4+3q^3+3q^2+2q
         9: q^4+3q^3+3q^2+2q
        10: 3q^3+4q^2+2q
        11: 3q^3+4q^2+2q
        12: 3q^3+4q^2+2q
        13: 2q^3+3q^2+2q
        14: 2q^3+3q^2+2q
        15: 2q^3+3q^2+2q
        16: 3q^3+4q^2+2q
        17: 3q^3+4q^2+2q
        18: q^4+3q^3+3q^2+2q
        19: 3q^3+4q^2+2q
        20: 3q^3+4q^2+2q
        21: q^4+3q^3+3q^2+2q
        22: 4q^2+2q
        23: 4q^2+2q
        24: q^3+3q^2+2q
        25: 3q^3+4q^2+2q
        26: 3q^3+4q^2+2q
        27: q^4+3q^3+3q^2+2q
        28: 3q^3+4q^2+2q
        29: 3q^3+4q^2+2q
        30: 2q^3+3q^2+2q
        31: 4q^2+2q
        32: 3q^2+2q
        33: 4q^2+2q
        34: 3q^3+4q^2+2q
        35: 2q^3+3q^2+2q
        36: 3q^3+4q^2+2q
        37: 3q^2+q
        38: q^2+q
        39: 3q^2+q
        40: q^2+q
        41: q^3+2q^2+q
        42: q^2+q
        43: 2q^3+3q^2+2q
        44: 2q^3+3q^2+2q
        45: 2q^3+3q^2+2q
        46: 2q^3+3q^2+2q
        47: 2q^3+3q^2+2q
        48: 2q^3+3q^2+2q
        49: 3q^3+4q^2+2q
        50: 3q^3+4q^2+2q
        51: q^4+3q^3+3q^2+2q
        52: 4q^2+2q
        53: 4q^2+2q
        54: q^3+3q^2+2q
        55: 3q^3+4q^2+2q
        56: 3q^3+4q^2+2q
        57: q^4+3q^3+3q^2+2q
        58: q^2+q
        59: 3q^2+q
        60: q^3+2q^2
        61: 2q^3+2q^2+2q
        62: 3q^2+q
        63: q^2+q
        64: 2q^2+q
        65: q^2+q
        66: 3q^2+q
        67: q^2+q
        68: q^3+2q^2+2q
        69: 2q^3+3q^2+2q
        70: 2q^3+3q^2+2q
        71: 3q^3+4q^2+2q
        72: 3q^3+4q^2+2q
        73: 4q^2+2q
        74: 3q^2+q
        75: q^2+q
        76: 3q^2+q
        77: q^2+q
        78: q^3+2q^2+q
        79: q^2+q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 4q^2+2q
        83: 3q^2+2q
        84: 2q^3+3q^2+2q
        85: 2q^3+3q^2+2q
        86: 3q^3+4q^2+2q
        87: 2q^3+3q^2+2q
        88: 2q^3+3q^2+2q
        89: 2q^3+3q^2+2q
        90: 2q^3+3q^2+2q
        91: 2q^3+3q^2+2q
        92: 2q^3+3q^2+2q
        93: 2q^3+3q^2+2q
        94: 4q^2+2q
        95: 4q^2+2q
        96: q^3+3q^2+2q
        97: 3q^3+4q^2+2q
        98: 3q^3+4q^2+2q
        99: q^4+3q^3+3q^2+2q
       100: 4q^2+2q
       101: 4q^2+2q
       102: q^3+3q^2+2q
       103: q^2
       104: q^2
       105: q
       106: 2q^2+q
       107: q^3+2q^2
       108: 2q^3+2q^2+2q
       109: q^2+q
       110: 3q^2+q
       111: 3q^2+q
       112: q^2+q
       113: 3q^2+q
       114: q^2+q
       115: 2q^2+q
       116: q^2+q
       117: q
       118: 2q^2+q
       119: q^2
       120: q^3+q^2+2q
       121: 2q^2+q
       122: q^2+q
       123: 2q^2+q
       124: q^2+q
       125: q^3+2q^2+2q
       126: 2q^3+3q^2+2q
       127: 3q^2+q
       128: q^2+q
       129: 3q^2+q
       130: q^2+q
       131: q^3+2q^2+q
       132: q^2+q
       133: q^3+2q^2+2q
       134: 2q^3+3q^2+2q
       135: 2q^3+3q^2+2q
       136: 3q^2+2q
       137: 3q^2+2q
       138: 3q^2+2q
       139: 4q^2+2q
       140: q^2+2q
       141: 3q^2+2q
       142: 4q^2+2q
       143: 2q^3+3q^2+2q
       144: 2q^3+3q^2+2q
       145: 3q^3+4q^2+2q
       146: 2q^3+3q^2+2q
       147: 3q^3+4q^2+2q
       148: 4q^2+2q
       149: 4q^2+2q
       150: 3q^2+2q
       151: 3q^2+q
       152: q^2+q
       153: 3q^2+q
       154: q^2+q
       155: q^3+2q^2+q
       156: q^2+q
       157: 2q^3+3q^2+2q
       158: 2q^3+3q^2+2q
       159: 2q^3+3q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^3+3q^2+2q
       164: 2q^3+3q^2+2q
       165: 2q^3+3q^2+2q
       166: 4q^2+2q
       167: 4q^2+2q
       168: q^3+3q^2+2q
       169: q^2
       170: q^2
       171: q
       172: 2q^2+q
       174: q^2
       175: q
       176: q^2+q
       177: 2q^2+q
       178: q^2+q
       179: 3q^2+q
       180: q^2+q
       181: 3q^2+q
       182: q^2+q
       183: q^2
       184: q^3+q^2+2q
       185: q
       186: 2q^2+q
       187: 2q^2+q
       188: q^2+q
       189: 2q^2+q
       190: q^2+q
       191: q
       192: 2q^2+q
       194: q^2+2q
       195: q^2+q
       196: 3q^2+q
       197: q^2+q
       198: q
       199: q^2
       200: q^3+q^2+2q
       201: q^3+2q^2
       202: 2q^3+2q^2+2q
       203: q^2+q
       204: 3q^2+q
       205: 3q^2+q
       206: q^2+q
       207: 2q^2+q
       208: q^2+q
       209: 3q^2+q
       210: q^2+q
       211: 2q^2+q
       212: q^2+q
       213: q^2+q
       215: q^2+q
       217: q^2+q
       219: q^3+2q^2+2q
       220: q^3+2q^2+2q
       221: 2q^3+3q^2+2q
       222: 2q^3+3q^2+2q
       223: 2q^3+3q^2+2q
       224: 3q^2+2q
       225: 3q^2+2q
       226: 3q^2+2q
       227: q^2+2q
       228: 2q^2+2q
       229: 2q
       230: 2q^2+2q
       231: 2q^3+3q^2+2q
       232: q^3+2q^2+2q
       233: 2q^3+3q^2+2q
       234: 2q^3+3q^2+2q
       235: 3q^2+2q
       236: 3q^2+2q
       237: 3q^2+q
       238: q^2+q
       239: 3q^2+q
       240: q^2+q
       241: q^3+2q^2+q
       242: q^2+q
       243: 4q^2+2q
       244: q^2+2q
       245: 4q^2+2q
       246: 3q^2+2q
       247: 4q^2+2q
       248: 4q^2+2q
       249: q^3+3q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^3+3q^2+2q
       254: 2q^3+3q^2+2q
       255: 2q^3+3q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q^2
       260: q^2
       261: q
       262: 2q^2+q
       264: q^2
       265: q
       266: q^2+q
       269: q^2+q
       270: q
       271: q^2
       272: q
       273: 2q^2+q
       274: q^2
       276: q^2
       277: q
       278: q^2+q
       279: q
       281: q^2+q
       283: q^2
       284: q^3+q^2+2q
       285: q
       286: 2q^2+q
       287: 2q^2+q
       288: q^2+q
       289: q^2+q
       291: 2q^2+q
       292: q^2+q
       293: q^2
       294: q^3+q^2+2q
       295: q
       296: 2q^2+q
       297: 2q^2+q
       298: q^2+q
       300: 2q
       301: q^2+q
       302: q
       303: q
       304: q^2+q
       305: q
       306: q
       307: q^2
       308: q^3+q^2+2q
       309: q
       310: 2q^2+q
       311: 3q^2+q
       312: q^2+q
       313: 2q^2+q
       314: q^2+q
       315: 2q^2+q
       316: q^2+q
       317: 3q^2+q
       318: q^2+q
       320: q^2+2q
       321: q^2+q
       322: 3q^2+q
       323: q^2+q
       324: q
       325: 2q^2+q
       326: q^2+q
       327: q^2+q
       329: q^2+q
       331: q^2+q
       333: q^3+2q^2+2q
       334: 2q^3+3q^2+2q
       335: 3q^2+2q
       336: 3q^2+2q
       337: 4q^2+2q
       338: 3q^2+q
       339: q^2+q
       340: 3q^2+q
       341: q^2+q
       342: q^3+2q^2+q
       343: q^2+q
       344: q^2+2q
       345: q^2+2q
       346: 2q^2+2q
       347: 2q
       348: 2q
       349: 2q^2+2q
       350: 2q^2+2q
       351: q^2+2q
       352: q^3+2q^2+2q
       353: q^3+2q^2+2q
       354: 2q^3+3q^2+2q
       355: 2q^3+3q^2+2q
       356: 2q^3+3q^2+2q
       357: 3q^2+2q
       358: 3q^2+2q
       359: 4q^2+2q
       360: q^2+q
       362: q^2+q
       364: q^2+q
       366: 3q^2+2q
       367: q^2+2q
       368: 2q^2+2q
       369: 2q
       370: 2q^2+2q
       371: 2q^2+2q
       372: 2q^2+2q
       373: 2q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       378: q^2
       379: q
       380: q^2+q
       384: q
       386: q^2
       387: q
       388: q^2+q
       391: q^2+q
       392: q
       395: q
       396: q
       397: q^2
       398: q
       399: 2q^2+q
       400: q^2
       402: q
       403: q^2
       404: q^2+q
       406: q^2+q
       408: q
       409: q
       411: q^2+q
       413: q
       415: q^2+q
       417: q^2+q
       419: q^2
       420: q^3+q^2+2q
       421: q
       422: 2q^2+q
       423: 2q^2+q
       424: q^2+q
       425: 2q^2+q
       426: q^2+q
       427: 3q^2+q
       428: q^2+q
       430: 2q
       431: q
       432: q^2+q
       433: q
       434: q
       435: q
       438: 2q
       439: q
       440: q^2+q
       441: q
       442: q
       444: q^2+2q
       445: q^2+q
       446: q
       447: q^2
       448: q^3+q^2+2q
       449: q
       450: 2q^2+q
       451: 2q^2+q
       452: q^2+q
       453: q^2
       454: q^3+q^2+2q
       455: q^2+q
       457: q
       458: 2q^2+q
       459: 2q^2+q
       460: q^2+q
       461: q^2+q
       462: 3q^2+q
       463: 3q^2+q
       464: q^2+q
       465: q
       467: q^2+q
       469: 2q^2+q
       470: q^2+q
       472: 2q
       473: q
       474: q^2+q
       475: q
       476: q
       477: q^2+q
       478: q
       479: q^2+q
       480: q
       481: q^3+2q^2+2q
       482: q^2+2q
       483: 3q^2+2q
       484: q^2+2q
       485: q^2+q
       487: q^2+q
       489: q^2+q
       491: 2q^2+2q
       492: q^2+2q
       493: 2q
       494: 2q^2+2q
       495: 2q
       496: 2q
       497: q^3+2q^2+2q
       498: 2q^3+3q^2+2q
       499: 3q^2+2q
       500: 3q^2+2q
       501: 2q^2+2q
       502: q^2+q
       504: q^2+q
       506: q^2+q
       508: q^2+2q
       509: q^2+2q
       510: 2q^2+2q
       511: 2q
       512: 2q
       513: 2q^2+2q
       514: 2q^2+2q
       515: 2q^2+2q
       516: 2q^2+2q
       517: 2q^2+2q
       518: 2q^2+2q
       519: 2q^2+2q
       520: 2q^2+2q
       524: q
       528: q
       530: q^2
       531: q
       532: q^2+q
       535: q
       536: q
       539: q
       543: q
       544: q
       547: q^2+q
       548: q
       550: q
       551: q^2
       552: q^2+q
       555: q
       558: q
       559: q^2+q
       560: q^2
       561: q^2
       562: q
       563: 2q^2+q
       564: q^2
       567: q
       568: q
       570: q^2+q
       572: q
       575: q^2+q
       576: q
       577: q^2+q
       581: q
       583: q
       585: q
       587: q^2+q
       589: q^2
       590: q^3+q^2+2q
       591: q
       592: 2q^2+q
       594: 2q
       595: q
       596: q^2+q
       597: q^2+q
       599: 2q^2+q
       600: q^2+q
       601: q
       604: 2q
       605: q
       607: q
       608: q^2+q
       609: q
       610: q
       611: q
       613: q
       614: q
       616: 2q
       617: q
       619: q^2
       620: q^3+q^2+2q
       621: q
       622: 2q^2+q
       623: q^2+q
       625: 2q^2+q
       626: q^2+q
       627: q^2+q
       629: 2q^2+q
       630: q^2+q
       631: q
       632: q^2+q
       633: q^2+q
       635: q
       637: q^2+q
       639: q
       642: 2q
       643: q
       644: q^2+q
       645: q
       646: q
       648: 2q
       649: q
       650: q^2+q
       651: q
       653: q
       654: q
       655: q
       656: q
       657: q^2+2q
       658: q^2+q
       660: q^2+q
       662: q^2+q
       664: 2q^2+2q
       665: q^2+2q
       666: q^2+q
       668: q^2+q
       670: q^2+q
       672: q^2+2q
       673: 2q^2+2q
       674: 2q
       675: q
       676: q^2+2q
       677: 2q
       678: 2q
       679: 2q
       680: 2q^2+2q
       681: q^3+2q^2+2q
       682: q^2+2q
       683: 3q^2+2q
       684: 2q^2+2q
       685: 2q^2+2q
       686: q^2+2q
       687: 2q
       688: 2q^2+2q
       689: 2q
       690: 2q^2+2q
       691: 2q^2+2q
       692: 2q^2+2q
       697: q^2+q
       700: q
       708: q
       712: q
       714: q
       715: q^2
       716: q^2+q
       719: q
       720: q
       723: q
       727: q
       728: q
       731: q
       735: q
       739: q
       742: q
       743: q^2+q
       744: q^2
       747: q
       751: q
       755: q
       756: q
       758: q
       762: q
       764: q
       767: q
       768: q
       769: q
       775: q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       786: 2q
       787: q
       788: q^2+q
       789: q
       791: q
       792: q
       794: 2q
       795: q
       799: q
       802: q
       806: 2q
       807: q
       808: q^2+q
       809: q
       811: q
       812: q
       813: q
       816: 2q
       817: q
       818: q^2+q
       819: q^2+q
       821: q
       823: q^2+q
       825: q^2
       826: q^3+q^2+2q
       827: q
       828: 2q^2+q
       830: 2q
       831: q
       832: q^2+q
       833: q^2+q
       835: 2q^2+q
       836: q^2+q
       837: q^2+q
       839: q
       840: q^2+q
       841: q
       843: q
       844: q
       846: 2q
       847: q
       848: q^2+q
       849: q
       851: q
       852: q
       853: q
       855: q
       856: q
       857: q
       858: q
       859: q^2+q
       861: q^2+q
       863: q^2+q
       865: q^2+2q
       866: q^2+2q
       867: 2q^2+2q
       868: q^2+2q
       869: 2q
       870: 2q
       871: q
       872: 2q
       873: 2q^2+2q
       874: 2q^2+2q
       875: q^2+2q
       876: 2q^2+2q
       877: q
       878: q^2+2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       889: q
       899: q
       902: q
       906: q
       910: q
       911: q
       914: q
       918: q
       930: q
       931: q
       934: q
       938: q
       942: q
       946: q
       949: q
       950: q^2+q
       951: q^2
       954: q
       955: q
       958: q
       961: q
       966: q
       967: q
       968: q
       975: q
       977: q
       979: q
       982: q
       990: q
       991: q
       992: q
       994: q
       996: q^2+q
       998: q
       999: q^2+q
      1001: 2q
      1002: q
      1005: 2q
      1006: q
      1007: q^2+q
      1008: q
      1009: q
      1010: q
      1012: q
      1013: q
      1014: q
      1017: 2q
      1020: q
      1024: q
      1027: q
      1030: q^2+q
      1032: q
      1033: q^2+q
      1034: q
      1036: q^2+q
      1038: q
      1041: 2q
      1042: q^2+q
      1044: q
      1045: q^2+q
      1046: q
      1047: q
      1050: q
      1053: q
      1057: 2q
      1058: q
      1059: q^2+q
      1060: q
      1062: q
      1063: q
      1064: q
      1065: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q^2+2q
      1075: 1
      1076: q
      1077: 2q
      1078: q
      1079: q+1
      1080: q^2+2q
      1081: 2q^2+2q
      1082: q^2+2q
      1083: q
      1084: 2q
      1085: 2q
      1091: q
      1102: q
      1112: q
      1116: q
      1120: q
      1124: q
      1127: q
      1132: q
      1133: q
      1135: q
      1137: q
      1138: q
      1146: q
      1166: q
      1170: q
      1174: q
      1178: q
      1182: q
      1183: q
      1185: q
      1188: q
      1196: q
      1197: q
      1208: q
      1209: q
      1210: q+1
      1212: q+1
      1214: q
      1216: q
      1217: q^2+q
      1219: 2q
      1222: q
      1224: q
      1225: q
      1226: 1
      1229: 1
      1235: q
      1236: q
      1241: q
      1244: q+1
      1246: 1
      1247: q
      1248: q
      1250: q
      1251: q^2+q
      1252: q^2+q
      1255: 2q
      1256: q
      1259: 2q
      1260: q
      1261: q^2+q
      1263: 1
      1269: q
      1272: q
      1274: q
      1276: q
      1277: q
      1278: q
      1280: q
      1281: q
      1282: q+1
      1283: q
      1284: 1
      1285: q^2+2q
      1286: q+1
      1287: q
      1288: 2q
      1289: q
      1295: q
      1307: q
      1316: q
      1320: q
      1323: q
      1328: q
      1329: q
      1334: q
      1342: 1
      1372: 1
      1374: q
      1378: q
      1382: q
      1386: q
      1390: q
      1393: q
      1398: q
      1399: q
      1401: q
      1403: q
      1407: 1
      1412: 1
      1430: q
      1438: q+1
      1440: 1
      1441: q
      1443: 1
      1445: 1
      1452: 1
      1455: q
      1456: q
      1458: q+1
      1460: q
      1461: q^2+q
      1463: 2q
      1469: q
      1472: q
      1477: q
      1480: q
      1482: q
      1483: q
      1484: q
      1485: 1
      1486: q+1
      1487: q
      1488: 1
      1494: q
      1518: q
      1529: 1
      1541: 1
      1543: q
      1547: 1
      1551: 1
      1556: 1
      1585: q
      1589: q
      1592: q
      1597: q
      1598: q
      1631: q
      1640: 1
      1643: 1
      1648: 1
      1651: q+1
      1653: 1
      1654: q
      1656: 1
      1658: q
      1666: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1679: 1
      1704: q
      1726: 1
      1735: 1
      1747: 1
      1761: 1
      1763: q
      1767: 1
      1775: 1
      1804: 1
      1822: q
      1826: 1
      1827: 1
      1832: 1
      1833: 1
      1838: 1
      1862: 1
      1917: 1
      1929: 1
      1938: 1
      1956: 1
      1961: 1
      1965: 1
      1986: 1
      2029: 1
      2046: 1
      2055: 1
      2088: 1

2089:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: 2q^4+2q^3+q^2+q
        23: 2q^4+2q^3+q^2+q
        24: 2q^4+2q^3+q^2+q
        25: q^5+3q^4+3q^3+q^2+q
        26: q^5+3q^4+3q^3+q^2+q
        27: q^5+3q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: q^4+2q^3+q^2+q
        32: 2q^4+2q^3+q^2+q
        33: q^4+2q^3+q^2+q
        34: 2q^4+3q^3+q^2+q
        35: q^5+3q^4+3q^3+q^2+q
        36: 2q^4+3q^3+q^2+q
        38: 2q^4+2q^3+q^2+q
        40: 2q^4+2q^3+q^2+q
        42: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: 2q^4+2q^3+q^2+q
        53: 2q^4+2q^3+q^2+q
        54: 2q^4+2q^3+q^2+q
        55: q^5+3q^4+3q^3+q^2+q
        56: q^5+3q^4+3q^3+q^2+q
        57: q^5+3q^4+3q^3+q^2+q
        58: q^3+q^2
        59: q^3+q
        60: q^4+2q^3+q
        61: q^3+q^2
        63: q^4+2q^3+q^2+q
        65: 2q^4+2q^3+q^2+q
        67: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 2q^4+3q^3+q^2+q
        73: q^4+2q^3+q^2+q
        75: 2q^4+2q^3+q^2+q
        77: 2q^4+2q^3+q^2+q
        79: 2q^4+2q^3+q^2+q
        80: q^4+2q^3+q^2+q
        81: q^4+2q^3+q^2+q
        82: q^4+2q^3+q^2+q
        83: 2q^4+2q^3+q^2+q
        84: 2q^4+3q^3+q^2+q
        85: 2q^4+3q^3+q^2+q
        86: 2q^4+3q^3+q^2+q
        87: q^5+3q^4+3q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^4+3q^3+q^2+q
        98: 2q^4+3q^3+q^2+q
        99: q^5+2q^4+2q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       104: q^3+q
       105: q^3+q^2
       107: q^4+2q^3+q
       108: q^3+q^2
       109: q^3+q^2
       110: q^3+q
       112: q^4+2q^3+q^2+q
       114: q^4+2q^3+q^2+q
       116: 2q^4+2q^3+q^2+q
       117: q^3+q^2
       118: q^3+q
       119: q^4+2q^3+q
       120: q^3+q^2
       122: q^4+2q^3+q^2+q
       124: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 2q^4+3q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 2q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^3+q
       141: q^4+2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: q^4+2q^3+q^2+q
       145: q^4+3q^3+q^2+q
       146: 2q^4+3q^3+q^2+q
       147: 2q^4+3q^3+q^2+q
       148: q^4+2q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       152: 2q^4+2q^3+q^2+q
       154: 2q^4+2q^3+q^2+q
       156: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^3+q^2+q
       161: 2q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: 2q^4+3q^3+q^2+q
       164: 2q^4+3q^3+q^2+q
       165: q^5+2q^4+2q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3+q
       171: q^3+q^2
       174: q^3+q
       175: q^3+q^2
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^4+2q^3+q
       184: q^3+q^2
       185: q^3+q^2
       186: q^3+q
       188: q^4+2q^3+q^2+q
       190: q^4+2q^3+q^2+q
       191: q^3+q^2
       192: q^3+q
       193: q^3+q
       195: q^3+q^2
       196: q^3+q
       198: q^3+q
       199: 2q^3+q
       200: q^3+q^2
       201: q^4+2q^3+q
       202: q^3+q^2
       203: q^3+q^2
       204: q^3+q
       206: q^4+2q^3+q^2+q
       208: 2q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: 2q^4+2q^3+q^2+q
       214: 2q^3+q^2+q
       216: 2q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 3q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: 2q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: 2q^3+q^2+q
       228: q^3+q^2+q
       229: q^3+q
       230: 2q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^4+3q^3+q^2+q
       233: q^4+2q^3+q^2+q
       234: 2q^4+3q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: q^3+q
       245: 2q^3+q^2+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: q^3+q
       261: q^3+q^2
       264: q^3+q
       265: q^3+q^2
       268: q^3+q
       272: q^3+q^2
       274: q^3+q
       276: q^3+q
       277: q^3+q^2
       280: 2q^3+q^2+q
       282: q^3+q^2+q
       283: q^3+q
       284: q^2
       285: q^2
       286: q
       288: q^3+q^2+q
       290: 2q^3+q^2+q
       292: q^3+q^2+q
       293: 2q^3+q
       294: q^3+q^2
       295: q^3+q^2
       296: q^3+q
       298: 2q^3+q^2+q
       299: q^3+q
       302: q^3+q
       303: q^3+q^2
       304: q^3+q
       306: q^3+q
       307: q^4+2q^3+q
       308: q^3+q^2
       309: q^3+q^2
       310: q^3+q
       312: 2q^3+q^2+q
       314: q^4+2q^3+q^2+q
       316: q^3+q^2+q
       318: 2q^3+q^2+q
       319: q^3+q
       321: q^3+q^2
       322: q^3+q
       324: q^3+q
       326: q^4+2q^3+q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: 2q^3+q^2+q
       334: 2q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       339: 2q^3+q^2+q
       341: 2q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^3+q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^3+q^2+q
       351: q^3+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: 2q^3+q^2+q
       358: q^3+q^2+q
       359: 2q^3+q^2+q
       361: 2q^3+q^2+q
       363: 2q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: q^3+q
       370: 2q^3+q^2+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q
       379: q^2
       382: q^3+q
       383: q^3+q^2
       386: q^3+q
       387: q^3+q^2
       390: q^3+q
       394: q^3+q
       398: q^3+q^2
       400: q^3+q
       402: q^3+q^2
       403: q^3+q
       407: q^3+q
       410: q^2+q
       412: q^2+q
       414: q^3+q^2+q
       416: q^2+q
       418: q^3+q^2+q
       419: q^3+q
       420: q^2
       421: q^2
       422: q
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: 2q^3+q^2+q
       429: q
       431: q^2
       432: q
       434: q
       436: q^3+q
       437: q
       439: q^2
       440: q
       442: q
       443: q^3+q
       446: q^3+q
       447: q^3+q
       448: q^2
       449: q^2
       450: q
       452: q^3+q^2+q
       453: 2q^3+q
       454: q^3+q^2
       456: 2q^3+q^2+q
       457: q^3+q^2
       458: q^3+q
       460: 2q^3+q^2+q
       461: q^3+q^2
       462: q^3+q
       464: 2q^3+q^2+q
       466: 2q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       471: q^3+q
       473: q^3+q^2
       474: q^3+q
       476: q^3+q
       478: q^3+q
       480: q^3+q
       481: 2q^3+q^2+q
       482: q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       486: 2q^3+q^2+q
       488: 2q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^3+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^3+q^2+q
       500: q^3+q^2+q
       501: 2q^3+q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^3+q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       522: q
       523: q^2
       526: q
       527: q^2
       530: q
       531: q^2
       534: q
       538: q^3+q
       542: q
       546: q^3+q
       550: q^2
       551: q
       554: q^3+q^2
       556: q^3+q
       558: q^3+q^2
       560: q^3+q
       562: q^3+q^2
       564: q^3+q
       566: q^3+q
       571: q^3+q
       574: q^3+q
       581: q^3+q
       584: q^2+q
       586: q^3+q^2+q
       588: q^2+q
       589: q^3+q
       590: q^2
       591: q^2
       592: q
       593: q
       595: q^2
       596: q
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: 2q^3+q^2+q
       603: q
       606: q
       607: q^2
       608: q
       610: q
       612: q
       614: q
       615: q^3+q
       618: q^3+q
       619: q^3+q
       620: q^2
       621: q^2
       622: q
       624: q^3+q^2+q
       626: q^3+q^2+q
       628: q^2+q
       630: q^3+q^2+q
       631: q^3+q^2
       632: q^3+q
       634: 2q^3+q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+q^2+q
       641: q
       643: q^2
       644: q
       646: q
       647: q
       649: q^2
       650: q
       652: q^3+q
       654: q
       656: q^3+q
       657: q^2+q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+q
       673: q^2+q
       674: q
       675: q
       676: q^2+q
       677: q
       678: q
       679: q
       680: q^2+q
       681: 2q^3+q^2+q
       682: q^3+q^2+q
       683: q^3+q^2+q
       684: q^2+q
       685: q^3+q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       699: q^3+q
       706: q
       707: q^2
       710: q
       711: q^2
       714: q^2
       715: q
       718: q
       722: q
       726: q
       730: q
       734: q^3+q
       738: q^2
       740: q
       742: q^2
       744: q
       746: q^2
       748: q
       750: q^3+q^2
       752: q^3+q
       754: q
       759: q^3+q
       763: q
       766: q^3+q
       773: q^3+q
       776: q^2+q
       778: q^2+q
       780: q^2+q
       782: q^3+q^2+q
       784: q^2+q
       785: q
       787: q^2
       788: q
       790: q^2+q
       792: q
       793: q
       796: q
       798: q
       800: q
       801: q
       805: q
       807: q^2
       808: q
       810: q
       812: q
       814: q
       815: q
       817: q^2
       818: q
       820: q^2+q
       822: q^3+q^2+q
       824: q^2+q
       825: q^3+q
       826: q^2
       827: q^2
       828: q
       829: q
       831: q^2
       832: q
       834: q^3+q^2+q
       836: q^3+q^2+q
       838: q^2+q
       839: q^2
       840: q
       842: q^2+q
       844: q
       845: q
       847: q^2
       848: q
       850: q
       852: q
       854: q
       856: q
       858: q
       866: q^2+q
       868: q^2+q
       870: q
       871: q
       872: q
       874: q^2+q
       875: q^3+q^2+q
       876: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       890: q^3+q
       897: q
       898: q^2
       901: q^2
       903: q
       905: q
       909: q
       913: q
       917: q
       921: q
       929: q
       933: q
       937: q^2
       939: q
       941: q^2
       943: q
       945: q^2
       947: q
       949: q^2
       951: q
       953: q
       957: q^2
       959: q
       962: q
       965: q
       972: q
       976: q
       980: q
       986: q
       989: q
       995: q^2+q
       998: q^2
       999: q
      1000: q
      1003: q^2+q
      1004: q
      1006: q^2
      1007: q
      1009: q
      1011: q
      1013: q
      1019: q
      1021: q
      1023: q
      1025: q
      1026: q
      1035: q^2+q
      1037: q^2+q
      1039: q^3+q^2+q
      1040: q
      1043: q^2+q
      1044: q^2
      1045: q
      1049: q
      1051: q
      1052: q
      1056: q
      1058: q^2
      1059: q
      1061: q
      1063: q
      1065: q
      1076: q
      1078: q
      1080: q^2+q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1092: q
      1104: q
      1111: q^2
      1113: q
      1115: q^2
      1117: q
      1119: q
      1123: q
      1128: q
      1131: q
      1136: q
      1142: q
      1149: q
      1157: q
      1169: q^2
      1171: q
      1173: q^2
      1175: q
      1177: q
      1181: q
      1186: q
      1200: q
      1207: q
      1221: q
      1223: q
      1231: q
      1234: q
      1239: q
      1240: q
      1249: q^2+q
      1250: q^2
      1251: q
      1254: q
      1257: q^2+q
      1258: q
      1260: q^2
      1261: q
      1265: q
      1267: q
      1268: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1287: q
      1289: q
      1296: q
      1324: q
      1332: q
      1353: q
      1357: q
      1377: q^2
      1379: q
      1381: q^2
      1383: q
      1385: q
      1389: q
      1394: q
      1397: q
      1402: q
      1416: q
      1423: q
      1434: q
      1447: q
      1465: q
      1468: q
      1471: q
      1475: q
      1476: q
      1481: q
      1484: q
      1519: q
      1561: q
      1593: q
      1601: q
      1612: q
      1616: q
      1638: 1
      1642: q
      1657: q
      1672: q
      1728: 1
      1731: 1
      1779: q
      1782: q
      1824: 1
      1844: 1
      1912: 1
      1931: 1
      1959: 1
      1987: 1
      2031: 1
      2050: 1
      2089: 1

2090:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        38: q+1
        40: q+1
        42: q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: 1
        59: q
        60: q
        61: q^2+1
        63: q+1
        65: q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        77: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q+1
       101: q+1
       102: q+1
       104: q
       105: 1
       107: q
       108: q^2+1
       109: 1
       110: q
       112: q+1
       114: q+1
       116: q+1
       117: 1
       118: q
       119: q
       120: q^2+1
       122: q+1
       124: q+1
       125: q^2+q+1
       126: q^2+q+1
       128: q+1
       130: q+1
       132: q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q+1
       150: q+1
       152: q+1
       154: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       170: q
       171: 1
       174: q
       175: 1
       178: q+1
       180: q+1
       182: q+1
       183: q
       184: q^2+1
       185: 1
       186: q
       188: q+1
       190: q+1
       191: 1
       192: q
       194: 1
       195: 1
       196: q
       198: 1
       199: q
       200: q^2+1
       201: q
       202: q^2+1
       203: 1
       204: q
       206: q+1
       208: q+1
       210: q+1
       212: q+1
       214: q+1
       216: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q+1
       238: q+1
       240: q+1
       242: q+1
       243: q+1
       244: 1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q+1
       257: q+1
       258: q+1
       260: q
       261: 1
       264: q
       265: 1
       270: 1
       272: 1
       274: q
       276: q
       277: 1
       280: q+1
       282: q+1
       283: q
       284: q^2+1
       285: 1
       286: q
       288: q+1
       290: q+1
       292: q+1
       293: q
       294: q^2+1
       295: 1
       296: q
       298: q+1
       300: 1
       302: 1
       303: 1
       304: q
       306: 1
       307: q
       308: q^2+1
       309: 1
       310: q
       312: q+1
       314: q+1
       316: q+1
       318: q+1
       320: 1
       321: 1
       322: q
       324: 1
       326: q+1
       328: q+1
       330: q+1
       332: q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       339: q+1
       341: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: q+1
       351: 1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       378: q
       379: 1
       382: q
       383: 1
       386: q
       387: 1
       392: 1
       395: 1
       398: 1
       400: q
       402: 1
       403: q
       408: 1
       410: q+1
       412: q+1
       414: q+1
       416: q+1
       418: q+1
       419: q
       420: q^2+1
       421: 1
       422: q
       424: q+1
       426: q+1
       428: q+1
       430: 1
       431: 1
       432: q
       434: 1
       436: 1
       438: 1
       439: 1
       440: q
       442: 1
       444: 1
       446: 1
       447: q
       448: q^2+1
       449: 1
       450: q
       452: q+1
       453: q
       454: q^2+1
       456: q+1
       457: 1
       458: q
       460: q+1
       461: 1
       462: q
       464: q+1
       466: q+1
       468: q+1
       470: q+1
       472: 1
       473: 1
       474: q
       476: 1
       478: 1
       480: 1
       481: q^2+q+1
       482: q+1
       483: q+1
       484: q+1
       486: q+1
       488: q+1
       490: q+1
       491: q+1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: 1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       503: q+1
       505: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q
       523: 1
       526: q
       527: 1
       530: q
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       551: q
       554: 1
       556: q
       558: 1
       560: q
       562: 1
       564: q
       567: 1
       572: 1
       576: 1
       581: 1
       584: q+1
       586: q+1
       588: q+1
       589: q
       590: q^2+1
       591: 1
       592: q
       594: 1
       595: 1
       596: q
       598: q+1
       600: q+1
       602: q+1
       604: 1
       606: 1
       607: 1
       608: q
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       619: q
       620: q^2+1
       621: 1
       622: q
       624: q+1
       626: q+1
       628: q+1
       630: q+1
       631: 1
       632: q
       634: q+1
       636: q+1
       638: q+1
       640: q+1
       642: 1
       643: 1
       644: q
       646: 1
       648: 1
       649: 1
       650: q
       652: 1
       654: 1
       656: 1
       657: q+1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: q+1
       667: q+1
       669: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: q^2+q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       700: 1
       706: q
       707: 1
       710: q
       711: 1
       714: 1
       715: q
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       740: q
       742: 1
       744: q
       746: 1
       748: q
       750: 1
       752: q
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: q+1
       778: q+1
       780: q+1
       782: q+1
       784: q+1
       786: 1
       787: 1
       788: q
       790: q+1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       806: 1
       807: 1
       808: q
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       818: q
       820: q+1
       822: q+1
       824: q+1
       825: q
       826: q^2+1
       827: 1
       828: q
       830: 1
       831: 1
       832: q
       834: q+1
       836: q+1
       838: q+1
       839: 1
       840: q
       842: q+1
       844: 1
       846: 1
       847: 1
       848: q
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: q+1
       862: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 1
       878: q+1
       879: 1
       880: 1
       881: q+1
       882: q+1
       883: q+1
       891: 1
       897: q
       898: 1
       901: 1
       903: q
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       931: 1
       935: 1
       937: 1
       939: q
       941: 1
       943: q
       945: 1
       947: q
       949: 1
       951: q
       954: 1
       957: 1
       959: q
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: q+1
       995: q+1
       997: q+1
       998: 1
       999: q
      1001: 1
      1003: q+1
      1005: 1
      1006: 1
      1007: q
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1031: q+1
      1032: 1
      1033: q
      1035: q+1
      1037: q+1
      1039: q+1
      1041: 1
      1043: q+1
      1044: 1
      1045: q
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1057: 1
      1058: 1
      1059: q
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1113: q
      1115: 1
      1117: q
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1159: 1
      1165: 1
      1167: q
      1169: 1
      1171: q
      1173: 1
      1175: q
      1179: 1
      1182: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1209: 1
      1211: q+1
      1213: q+1
      1215: q+1
      1216: 1
      1217: q
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1229: 1
      1231: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1245: q+1
      1246: 1
      1247: q
      1249: q+1
      1250: 1
      1251: q
      1253: q+1
      1255: 1
      1257: q+1
      1259: 1
      1260: 1
      1261: q
      1263: 1
      1265: 1
      1267: 1
      1269: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1317: q
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1355: 1
      1359: 1
      1373: 1
      1375: q
      1377: 1
      1379: q
      1381: 1
      1383: q
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1408: 1
      1412: 1
      1417: 1
      1425: 1
      1434: 1
      1437: 1
      1439: q+1
      1440: 1
      1441: q
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1453: 1
      1455: 1
      1457: q+1
      1459: q+1
      1460: 1
      1461: q
      1463: 1
      1465: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1481: 1
      1483: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1496: 1
      1520: 1
      1532: 1
      1540: 1
      1542: 1
      1544: q
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1570: 1
      1584: 1
      1586: q
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1614: 1
      1618: 1
      1635: 1
      1638: 1
      1640: 1
      1642: 1
      1644: 1
      1648: 1
      1652: q+1
      1653: 1
      1654: q
      1656: 1
      1658: 1
      1660: 1
      1662: 1
      1666: 1
      1668: 1
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1682: 1
      1706: 1
      1727: 1
      1732: 1
      1735: 1
      1748: 1
      1762: 1
      1764: q
      1768: 1
      1772: 1
      1775: 1
      1780: 1
      1784: 1
      1792: 1
      1805: 1
      1816: 1
      1818: 1
      1822: 1
      1824: 1
      1826: 1
      1828: 1
      1832: 1
      1833: 1
      1841: 1
      1865: 1
      1913: 1
      1917: 1
      1921: 1
      1925: 1
      1930: 1
      1939: 1
      1957: 1
      1959: 1
      1961: 1
      1965: 1
      1988: 1
      2030: 1
      2047: 1
      2051: 1
      2055: 1
      2090: 1

2091:    0: q^5+3q^4+3q^3+q^2+q
         1: q^5+3q^4+3q^3+q^2+q
         2: q^5+3q^4+3q^3+q^2+q
         3: q^5+3q^4+3q^3+q^2+q
         4: q^5+3q^4+3q^3+q^2+q
         5: q^5+3q^4+3q^3+q^2+q
         6: q^5+3q^4+3q^3+q^2+q
         7: q^5+3q^4+3q^3+q^2+q
         8: q^5+3q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: 2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: 2q^4+3q^3+q^2+q
        13: q^5+3q^4+3q^3+q^2+q
        14: q^5+3q^4+3q^3+q^2+q
        15: q^5+3q^4+3q^3+q^2+q
        16: 2q^4+3q^3+q^2+q
        17: 2q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+3q^4+3q^3+q^2+q
        20: q^5+3q^4+3q^3+q^2+q
        21: q^5+3q^4+3q^3+q^2+q
        22: 2q^4+2q^3+q^2+q
        23: 2q^4+2q^3+q^2+q
        24: 2q^4+2q^3+q^2+q
        25: q^5+3q^4+3q^3+q^2+q
        26: q^5+3q^4+3q^3+q^2+q
        27: q^5+3q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: 2q^4+3q^3+q^2+q
        30: q^5+3q^4+3q^3+q^2+q
        31: q^4+2q^3+q^2+q
        32: 2q^4+2q^3+q^2+q
        33: q^4+2q^3+q^2+q
        34: 2q^4+3q^3+q^2+q
        35: q^5+3q^4+3q^3+q^2+q
        36: 2q^4+3q^3+q^2+q
        38: 2q^4+2q^3+q^2+q
        40: 2q^4+2q^3+q^2+q
        42: 2q^4+2q^3+q^2+q
        43: 2q^4+3q^3+q^2+q
        44: 2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: 2q^4+3q^3+q^2+q
        47: 2q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: 2q^4+3q^3+q^2+q
        50: 2q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: 2q^4+2q^3+q^2+q
        53: 2q^4+2q^3+q^2+q
        54: 2q^4+2q^3+q^2+q
        55: q^5+3q^4+3q^3+q^2+q
        56: q^5+3q^4+3q^3+q^2+q
        57: q^5+3q^4+3q^3+q^2+q
        58: q^3+q
        59: q^3+q^2
        60: q^3+q^2
        61: q^4+2q^3+q
        63: q^4+2q^3+q^2+q
        65: 2q^4+2q^3+q^2+q
        67: q^4+2q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: 2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 2q^4+3q^3+q^2+q
        73: q^4+2q^3+q^2+q
        75: 2q^4+2q^3+q^2+q
        77: 2q^4+2q^3+q^2+q
        79: 2q^4+2q^3+q^2+q
        80: q^4+2q^3+q^2+q
        81: q^4+2q^3+q^2+q
        82: q^4+2q^3+q^2+q
        83: 2q^4+2q^3+q^2+q
        84: 2q^4+3q^3+q^2+q
        85: 2q^4+3q^3+q^2+q
        86: 2q^4+3q^3+q^2+q
        87: q^5+3q^4+3q^3+q^2+q
        88: 3q^3+q^2+q
        89: 3q^3+q^2+q
        90: q^4+2q^3+q^2+q
        91: 2q^4+3q^3+q^2+q
        92: 2q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^4+3q^3+q^2+q
        98: 2q^4+3q^3+q^2+q
        99: q^5+2q^4+2q^3+q^2+q
       100: 2q^4+2q^3+q^2+q
       101: 2q^4+2q^3+q^2+q
       102: 2q^4+2q^3+q^2+q
       104: q^3+q^2
       105: q^3+q
       107: q^3+q^2
       108: q^4+2q^3+q
       109: q^3+q
       110: q^3+q^2
       112: q^4+2q^3+q^2+q
       114: q^4+2q^3+q^2+q
       116: 2q^4+2q^3+q^2+q
       117: q^3+q
       118: q^3+q^2
       119: q^3+q^2
       120: q^4+2q^3+q
       122: q^4+2q^3+q^2+q
       124: q^4+2q^3+q^2+q
       125: 3q^3+q^2+q
       126: 2q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 2q^4+3q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 2q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^3+q
       141: q^4+2q^3+q^2+q
       142: 2q^3+q^2+q
       143: 3q^3+q^2+q
       144: q^4+2q^3+q^2+q
       145: q^4+3q^3+q^2+q
       146: 2q^4+3q^3+q^2+q
       147: 2q^4+3q^3+q^2+q
       148: q^4+2q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: 2q^4+2q^3+q^2+q
       152: 2q^4+2q^3+q^2+q
       154: 2q^4+2q^3+q^2+q
       156: 2q^4+2q^3+q^2+q
       157: 3q^3+q^2+q
       158: 3q^3+q^2+q
       159: q^4+2q^3+q^2+q
       160: 2q^3+q^2+q
       161: 2q^3+q^2+q
       162: q^4+q^3+q^2+q
       163: 2q^4+3q^3+q^2+q
       164: 2q^4+3q^3+q^2+q
       165: q^5+2q^4+2q^3+q^2+q
       166: 2q^3+q^2+q
       167: 2q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3+q^2
       171: q^3+q
       174: q^3+q^2
       175: q^3+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^3+q^2
       184: q^4+2q^3+q
       185: q^3+q
       186: q^3+q^2
       188: q^4+2q^3+q^2+q
       190: q^4+2q^3+q^2+q
       191: q^3+q
       192: q^3+q^2
       194: q^3+q
       195: q^3+q
       196: q^3+q^2
       198: q^3+q
       199: q^3+q^2
       200: 2q^3+q
       201: q^3+q^2
       202: q^4+2q^3+q
       203: q^3+q
       204: q^3+q^2
       206: q^4+2q^3+q^2+q
       208: 2q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: 2q^4+2q^3+q^2+q
       214: 2q^3+q^2+q
       216: 2q^3+q^2+q
       218: q^4+q^3+q^2+q
       219: 2q^3+q^2+q
       220: 3q^3+q^2+q
       221: 2q^3+q^2+q
       222: 3q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: 2q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: 2q^3+q^2+q
       228: q^3+q^2+q
       229: q^3+q
       230: 2q^3+q^2+q
       231: 2q^3+q^2+q
       232: q^4+3q^3+q^2+q
       233: q^4+2q^3+q^2+q
       234: 2q^4+3q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: q^3+q^2+q
       238: 2q^3+q^2+q
       240: 2q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: 2q^3+q^2+q
       244: q^3+q
       245: 2q^3+q^2+q
       246: q^4+2q^3+q^2+q
       247: 2q^3+q^2+q
       248: 2q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^3+q^2+q
       257: 2q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: q^3+q^2
       261: q^3+q
       264: q^3+q^2
       265: q^3+q
       270: q^3+q
       272: q^3+q
       274: q^3+q^2
       276: q^3+q^2
       277: q^3+q
       280: 2q^3+q^2+q
       282: q^3+q^2+q
       283: q^2
       284: q^3+q
       285: q
       286: q^2
       288: q^3+q^2+q
       290: 2q^3+q^2+q
       292: q^3+q^2+q
       293: q^3+q^2
       294: 2q^3+q
       295: q^3+q
       296: q^3+q^2
       298: 2q^3+q^2+q
       300: q^3+q
       302: q^3+q
       303: q^3+q
       304: q^3+q^2
       306: q^3+q
       307: q^3+q^2
       308: q^4+2q^3+q
       309: q^3+q
       310: q^3+q^2
       312: 2q^3+q^2+q
       314: q^4+2q^3+q^2+q
       316: q^3+q^2+q
       318: 2q^3+q^2+q
       320: q^3+q
       321: q^3+q
       322: q^3+q^2
       324: q^3+q
       326: q^4+2q^3+q^2+q
       328: q^2+q
       330: q^2+q
       332: q^2+q
       333: 2q^3+q^2+q
       334: 2q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: 2q^3+q^2+q
       339: 2q^3+q^2+q
       341: 2q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^3+q^2+q
       345: q^2+q
       346: q^2+q
       347: q
       348: q
       349: q^2+q
       350: q^3+q^2+q
       351: q^3+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: 2q^3+q^2+q
       358: q^3+q^2+q
       359: 2q^3+q^2+q
       361: 2q^3+q^2+q
       363: 2q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: 2q^3+q^2+q
       368: q^3+q^2+q
       369: q^3+q
       370: 2q^3+q^2+q
       371: 2q^3+q^2+q
       372: 2q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q^2
       379: q
       382: q^3+q^2
       383: q^3+q
       386: q^3+q^2
       387: q^3+q
       392: q^3+q
       395: q^3+q
       398: q^3+q
       400: q^3+q^2
       402: q^3+q
       403: q^3+q^2
       408: q^3+q
       410: q^2+q
       412: q^2+q
       414: q^3+q^2+q
       416: q^2+q
       418: q^3+q^2+q
       419: q^2
       420: q^3+q
       421: q
       422: q^2
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: 2q^3+q^2+q
       430: q
       431: q
       432: q^2
       434: q
       436: q^3+q
       438: q
       439: q
       440: q^2
       442: q
       444: q^3+q
       446: q^3+q
       447: q^2
       448: q^3+q
       449: q
       450: q^2
       452: q^3+q^2+q
       453: q^3+q^2
       454: 2q^3+q
       456: 2q^3+q^2+q
       457: q^3+q
       458: q^3+q^2
       460: 2q^3+q^2+q
       461: q^3+q
       462: q^3+q^2
       464: 2q^3+q^2+q
       466: 2q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       472: q^3+q
       473: q^3+q
       474: q^3+q^2
       476: q^3+q
       478: q^3+q
       480: q^3+q
       481: 2q^3+q^2+q
       482: q^3+q^2+q
       483: q^3+q^2+q
       484: 2q^3+q^2+q
       486: 2q^3+q^2+q
       488: 2q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: q^2+q
       493: q
       494: q^2+q
       495: q
       496: q^3+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^3+q^2+q
       500: q^3+q^2+q
       501: 2q^3+q^2+q
       503: q^2+q
       505: q^2+q
       507: q^2+q
       508: q^3+q^2+q
       509: q^2+q
       510: q^2+q
       511: q
       512: q
       513: q^2+q
       514: q^3+q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       522: q^2
       523: q
       526: q^2
       527: q
       530: q^2
       531: q
       535: q
       540: q^3+q
       544: q
       548: q^3+q
       550: q
       551: q^2
       554: q^3+q
       556: q^3+q^2
       558: q^3+q
       560: q^3+q^2
       562: q^3+q
       564: q^3+q^2
       567: q^3+q
       572: q^3+q
       576: q^3+q
       581: q^3+q
       584: q^2+q
       586: q^3+q^2+q
       588: q^2+q
       589: q^2
       590: q^3+q
       591: q
       592: q^2
       594: q
       595: q
       596: q^2
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: 2q^3+q^2+q
       604: q
       606: q
       607: q
       608: q^2
       610: q
       612: q
       614: q
       616: q^3+q
       618: q^3+q
       619: q^2
       620: q^3+q
       621: q
       622: q^2
       624: q^3+q^2+q
       626: q^3+q^2+q
       628: q^2+q
       630: q^3+q^2+q
       631: q^3+q
       632: q^3+q^2
       634: 2q^3+q^2+q
       636: q^2+q
       638: q^2+q
       640: q^3+q^2+q
       642: q
       643: q
       644: q^2
       646: q
       648: q
       649: q
       650: q^2
       652: q^3+q
       654: q
       656: q^3+q
       657: q^2+q
       659: q^2+q
       661: q^2+q
       663: q^2+q
       664: q^2+q
       665: q^3+q^2+q
       667: q^2+q
       669: q^2+q
       671: q^2+q
       672: q^2+q
       673: q^2+q
       674: q
       675: q
       676: q^2+q
       677: q
       678: q
       679: q
       680: q^2+q
       681: 2q^3+q^2+q
       682: q^3+q^2+q
       683: q^3+q^2+q
       684: q^2+q
       685: q^3+q^2+q
       686: q^2+q
       687: q
       688: q^2+q
       689: q
       700: q^3+q
       706: q^2
       707: q
       710: q^2
       711: q
       714: q
       715: q^2
       719: q
       724: q
       728: q
       732: q
       736: q^3+q
       738: q
       740: q^2
       742: q
       744: q^2
       746: q
       748: q^2
       750: q^3+q
       752: q^3+q^2
       755: q
       760: q^3+q
       764: q
       767: q^3+q
       773: q^3+q
       776: q^2+q
       778: q^2+q
       780: q^2+q
       782: q^3+q^2+q
       784: q^2+q
       786: q
       787: q
       788: q^2
       790: q^2+q
       792: q
       794: q
       796: q
       798: q
       800: q
       802: q
       806: q
       807: q
       808: q^2
       810: q
       812: q
       814: q
       816: q
       817: q
       818: q^2
       820: q^2+q
       822: q^3+q^2+q
       824: q^2+q
       825: q^2
       826: q^3+q
       827: q
       828: q^2
       830: q
       831: q
       832: q^2
       834: q^3+q^2+q
       836: q^3+q^2+q
       838: q^2+q
       839: q
       840: q^2
       842: q^2+q
       844: q
       846: q
       847: q
       848: q^2
       850: q
       852: q
       854: q
       856: q
       858: q
       866: q^2+q
       868: q^2+q
       870: q
       871: q
       872: q
       874: q^2+q
       875: q^3+q^2+q
       876: q^2+q
       877: q
       878: q^2+q
       879: q
       880: q
       891: q^3+q
       897: q^2
       898: q
       901: q
       903: q^2
       907: q
       910: q
       915: q
       919: q
       923: q
       931: q
       935: q
       937: q
       939: q^2
       941: q
       943: q^2
       945: q
       947: q^2
       949: q
       951: q^2
       954: q
       957: q
       959: q^2
       963: q
       966: q
       972: q
       977: q
       981: q
       986: q
       990: q
       995: q^2+q
       998: q
       999: q^2
      1001: q
      1003: q^2+q
      1005: q
      1006: q
      1007: q^2
      1009: q
      1011: q
      1013: q
      1019: q
      1021: q
      1023: q
      1025: q
      1027: q
      1035: q^2+q
      1037: q^2+q
      1039: q^3+q^2+q
      1041: q
      1043: q^2+q
      1044: q
      1045: q^2
      1049: q
      1051: q
      1053: q
      1057: q
      1058: q
      1059: q^2
      1061: q
      1063: q
      1065: q
      1076: q
      1078: q
      1080: q^2+q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1093: q
      1105: q
      1111: q
      1113: q^2
      1115: q
      1117: q^2
      1121: q
      1125: q
      1129: q
      1132: q
      1137: q
      1142: q
      1151: q
      1159: q
      1169: q
      1171: q^2
      1173: q
      1175: q^2
      1179: q
      1182: q
      1187: q
      1201: q
      1209: q
      1221: q
      1223: q
      1231: q
      1235: q
      1239: q
      1241: q
      1249: q^2+q
      1250: q
      1251: q^2
      1255: q
      1257: q^2+q
      1259: q
      1260: q
      1261: q^2
      1265: q
      1267: q
      1269: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1287: q
      1289: q
      1297: q
      1325: q
      1333: q
      1355: q
      1359: q
      1377: q
      1379: q^2
      1381: q
      1383: q^2
      1387: q
      1391: q
      1395: q
      1398: q
      1403: q
      1417: q
      1425: q
      1434: q
      1447: q
      1465: q
      1469: q
      1471: q
      1475: q
      1477: q
      1481: q
      1484: q
      1520: q
      1562: q
      1594: q
      1602: q
      1614: q
      1618: q
      1638: 1
      1642: q
      1658: q
      1672: q
      1728: 1
      1732: 1
      1780: q
      1784: q
      1824: 1
      1845: 1
      1913: 1
      1931: 1
      1959: 1
      1989: 1
      2031: 1
      2051: 1
      2091: 1

2092:    0: 2q^3+q^2+1
         1: 2q^3+q^2+1
         2: 2q^3+q^2+1
         3: 2q^3+q^2+1
         4: q^5+q^4+q^3+q^2+1
         5: 2q^3+q^2+1
         6: q^5+q^4+q^3+q^2+1
         7: q^5+q^4+q^3+q^2+1
         8: 2q^3+q^2+1
         9: q^5+q^4+q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: q^5+q^4+q^3+q^2+1
        13: 2q^3+q^2+1
        14: q^5+q^4+q^3+q^2+1
        15: 2q^3+q^2+1
        16: 2q^3+q^2+1
        17: 2q^3+q^2+1
        18: q^5+q^4+q^3+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^3+q^2+1
        22: 2q^3+q^2+1
        23: 2q^3+q^2+1
        24: 2q^3+q^2+1
        25: 2q^3+q^2+1
        26: 2q^3+q^2+1
        27: 2q^3+q^2+1
        28: 2q^3+q^2+1
        29: q^3+q^2+1
        30: q^3+q^2+1
        31: 2q^3+q^2+1
        32: 2q^3+q^2+1
        33: 2q^3+q^2+1
        34: 2q^3+q^2+1
        35: 2q^3+q^2+1
        36: 2q^3+q^2+1
        37: 2q^3+q^2+1
        39: 2q^3+q^2+1
        41: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: q^5+q^4+q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^3+q^2+1
        47: 2q^3+q^2+1
        48: q^5+q^4+q^3+q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^3+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^3+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^3+q^2+1
        58: q^3+q^2+1
        59: q^3
        60: q^3+q^2+1
        61: q^3
        62: 2q^3+q^2+1
        64: 2q^3+q^2+1
        66: 2q^3+q^2+1
        68: 2q^3+q^2+1
        69: q^3+q^2+1
        70: q^3+q^2+1
        71: q^3+q^2+1
        72: q^2+1
        73: q^2+1
        74: q^3+q^2+1
        76: q^3+q^2+1
        78: q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^3+q^2+1
        82: q^3+q^2+1
        83: q^3+q^2+1
        84: 2q^3+q^2+1
        85: 2q^3+q^2+1
        86: q^3+q^2+1
        87: q^3+q^2+1
        88: 2q^3+q^2+1
        89: 2q^3+q^2+1
        90: q^5+q^4+q^3+q^2+1
        91: q^3+q^2+1
        92: q^3+q^2+1
        93: q^3+q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^3+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^3+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^3+q^2+1
       103: q^3+q^2+1
       106: q^3
       107: q^2+1
       109: q^2+1
       111: q^2+1
       113: q^3+q^2+1
       115: q^3+q^2+1
       117: q^3+q^2+1
       118: q^3
       119: q^3+q^2+1
       120: q^3
       121: 2q^3+q^2+1
       123: 2q^3+q^2+1
       125: 2q^3+q^2+1
       126: q^3+q^2+1
       127: q^3+q^2+1
       129: q^3+q^2+1
       131: q^3+q^2+1
       133: q^3+q^2+1
       134: q^3+q^2+1
       135: q^2+1
       136: q^2+1
       137: 2q^3+q^2+1
       138: q^3+q^2+1
       139: q^3+q^2+1
       140: q^2+1
       141: q^3+q^2+1
       142: q^2+1
       143: 2q^3+q^2+1
       144: q^3+q^2+1
       145: q^3+q^2+1
       146: q^3+q^2+1
       147: q^2+1
       148: q^2+1
       149: q^3+q^2+1
       150: q^3+q^2+1
       151: q^3+q^2+1
       153: q^3+q^2+1
       155: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: q^3+q^2+1
       161: q^3+q^2+1
       162: q^3+q^2+1
       163: q^3+q^2+1
       164: q^3+q^2+1
       165: q^3+q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^3+q^2+1
       169: q^2+1
       173: q^3+q^2+1
       176: q^3
       177: q^3+q^2+1
       179: q^3+q^2+1
       181: q^2+1
       183: q^2+1
       185: q^2+1
       187: q^2+1
       189: q^3+q^2+1
       191: q^3+q^2+1
       192: q^3
       193: q^2+1
       195: q^2+1
       197: q^2+1
       199: q^3+q^2+1
       200: q^3
       201: q^2+1
       203: q^2+1
       205: q^2+1
       207: 2q^3+q^2+1
       209: q^3+q^2+1
       211: q^3+q^2+1
       213: q^3+q^2+1
       215: q^3+q^2+1
       217: q^3+q^2+1
       219: q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: q^3+q^2+1
       227: q^3+q^2+1
       228: q^3+q^2+1
       229: q^2+1
       230: q^2+1
       231: q^3+q^2+1
       232: q^3+q^2+1
       233: q^3+q^2+1
       234: q^2+1
       235: q^2+1
       236: q^3+q^2+1
       237: q^3+q^2+1
       239: q^3+q^2+1
       241: q^3+q^2+1
       243: q^3+q^2+1
       244: q^2+1
       245: q^2+1
       246: q^3+q^2+1
       247: 1
       248: 1
       249: q^3+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: q^3+q^2+1
       257: q^3+q^2+1
       258: q^3+q^2+1
       259: q^2+1
       263: q^2+1
       267: q^2+1
       271: q^2+1
       275: q^3+q^2+1
       278: q^3
       279: q^3+q^2+1
       281: q^3+q^2+1
       283: q^2+1
       285: q^2+1
       287: q^3+q^2+1
       289: q^2+1
       291: q^2+1
       293: q^2+1
       295: q^2+1
       297: q^2+1
       299: q^2+1
       301: q^2+1
       303: q^2+1
       305: q^2+1
       307: q^2+1
       309: q^2+1
       311: q^2+1
       313: q^2+1
       315: q^3+q^2+1
       317: q^3+q^2+1
       319: q^2+1
       321: q^2+1
       323: q^2+1
       325: q^3+q^2+1
       327: q^3+q^2+1
       329: q^3+q^2+1
       331: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^3+1
       344: q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       352: q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^2+1
       357: q^2+1
       358: q^2+1
       359: 1
       360: q^3+q^2+1
       362: q^3+q^2+1
       364: q^3+q^2+1
       366: q^3+q^2+1
       367: q^3+q^2+1
       368: q^3+q^2+1
       369: q^2+1
       370: q^2+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       377: q^2+1
       381: q^2+1
       385: q^2+1
       389: q^2+1
       393: q^2+1
       397: q^2+1
       401: q^2+1
       405: q^2+1
       409: q^3+q^2+1
       411: q^3+q^2+1
       413: q^3+q^2+1
       415: q^2+1
       417: q^2+1
       419: q^2+1
       421: q^2+1
       423: q^2+1
       425: 1
       427: 1
       429: q^2+1
       431: q^2+1
       433: q^2+1
       435: q^2+1
       437: q^2+1
       439: q^2+1
       441: q^2+1
       443: 1
       445: 1
       447: q^2+1
       449: q^2+1
       451: q^2+1
       453: q^2+1
       455: q^2+1
       457: q^2+1
       459: q^2+1
       461: 1
       463: 1
       465: q^3+q^2+1
       467: q^3+q^2+1
       469: q^3+q^2+1
       471: q^2+1
       473: q^2+1
       475: q^2+1
       477: q^2+1
       479: 1
       481: q^2+1
       482: q^2+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: 1
       496: 1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: 1
       501: 1
       502: q^3+q^2+1
       504: q^3+q^2+1
       506: q^3+q^2+1
       508: q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: q^2+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       521: q^2+1
       525: q^2+1
       529: q^2+1
       533: q^2+1
       537: q^2+1
       541: q^2+1
       545: 1
       549: q^2+1
       553: q^2+1
       557: q^2+1
       561: 1
       565: q^2+1
       569: q^2+1
       573: 1
       577: 1
       583: q^3+q^2+1
       585: q^2+1
       587: q^2+1
       589: q^2+1
       591: 1
       593: 1
       595: q^2+1
       597: 1
       599: 1
       601: 1
       603: q^2+1
       605: q^2+1
       607: q^2+1
       609: q^2+1
       611: q^2+1
       613: 1
       615: 1
       617: 1
       619: q^2+1
       621: q^2+1
       623: q^2+1
       625: q^2+1
       627: q^2+1
       629: 1
       631: 1
       633: 1
       635: q^3+q^2+1
       637: q^3+q^2+1
       639: q^3+q^2+1
       641: q^2+1
       643: q^2+1
       645: q^2+1
       647: q^2+1
       649: q^2+1
       651: q^2+1
       653: q^2+1
       655: 1
       657: 1
       658: 1
       660: 1
       662: q^3+1
       664: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       674: 1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: 1
       690: 1
       691: 1
       692: q^3+1
       693: 1
       705: q^2+1
       709: q^2+1
       713: 1
       717: 1
       721: q^2+1
       725: q^2+1
       729: q^2+1
       733: 1
       737: q^2+1
       741: q^2+1
       745: q^2+1
       749: 1
       753: q^2+1
       757: q^2+1
       761: q^2+1
       765: 1
       769: 1
       775: 1
       777: q^2+1
       779: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       797: q^2+1
       799: q^2+1
       801: q^2+1
       803: 1
       805: 1
       807: q^2+1
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: 1
       821: q^2+1
       823: q^2+1
       825: q^2+1
       827: 1
       829: 1
       831: q^2+1
       833: 1
       835: 1
       837: 1
       839: 1
       841: q^3+q^2+1
       843: 1
       845: q^2+1
       847: q^2+1
       849: q^2+1
       851: q^2+1
       853: q^2+1
       855: 1
       857: 1
       859: 1
       861: 1
       863: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: q^3+1
       884: 1
       896: q^2+1
       900: 1
       904: 1
       908: 1
       912: q^2+1
       916: 1
       920: q^2+1
       924: 1
       928: 1
       932: 1
       936: q^2+1
       940: 1
       944: q^2+1
       948: 1
       952: 1
       956: 1
       960: q^2+1
       964: 1
       968: 1
       974: q^2+1
       978: q^2+1
       982: 1
       988: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: q^2+1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1034: q^2+1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1044: 1
      1046: 1
      1048: q^2+1
      1050: q^2+1
      1052: q^2+1
      1054: 1
      1056: 1
      1058: q^2+1
      1060: 1
      1062: 1
      1064: 1
      1066: 1
      1068: 1
      1070: q^3+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: q^2+1
      1152: 1
      1156: 1
      1160: 1
      1164: 1
      1168: q^2+1
      1172: 1
      1176: 1
      1180: 1
      1184: q^2+1
      1188: 1
      1194: 1
      1198: q^2+1
      1202: 1
      1206: 1
      1210: 1
      1212: 1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1228: 1
      1230: 1
      1232: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1242: 1
      1244: 1
      1246: 1
      1248: 1
      1250: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1260: 1
      1262: 1
      1264: q^2+1
      1266: 1
      1268: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1340: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1372: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: 1
      1410: 1
      1414: q^2+1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1436: 1
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1446: 1
      1448: 1
      1450: 1
      1452: 1
      1454: 1
      1456: 1
      1458: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1478: 1
      1480: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1501: 1
      1513: 1
      1525: 1
      1537: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1631: 1
      1637: 1
      1639: 1
      1643: 1
      1645: 1
      1647: 1
      1651: 1
      1653: 1
      1655: 1
      1659: 1
      1661: 1
      1663: 1
      1665: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1675: 1
      1687: 1
      1699: 1
      1711: 1
      1723: 1
      1729: 1
      1733: 1
      1737: 1
      1741: 1
      1745: 1
      1749: 1
      1753: 1
      1761: 1
      1765: 1
      1769: 1
      1773: 1
      1777: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1801: 1
      1807: 1
      1823: 1
      1825: 1
      1827: 1
      1829: 1
      1831: 1
      1834: 1
      1846: 1
      1858: 1
      1870: 1
      1894: 1
      1898: 1
      1910: 1
      1914: 1
      1926: 1
      1932: 1
      1936: 1
      1940: 1
      1944: 1
      1948: 1
      1966: 1
      1978: 1
      1990: 1
      2056: 1
      2060: 1
      2092: 1

2093:    0: 15q^4+4q^3+2q^2+q
         1: 15q^4+4q^3+2q^2+q
         2: 5q^5+10q^4+5q^3+q^2+q
         3: 15q^4+4q^3+2q^2+q
         4: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         5: 15q^4+4q^3+2q^2+q
         6: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         7: 3q^6+6q^5+6q^4+4q^3+q^2+q
         8: 5q^5+10q^4+5q^3+q^2+q
         9: 3q^6+6q^5+6q^4+4q^3+q^2+q
        10: 15q^4+4q^3+2q^2+q
        11: 15q^4+4q^3+2q^2+q
        12: 2q^6+7q^5+9q^4+3q^3+2q^2+q
        13: 10q^4+4q^3+q^2+q
        14: q^6+4q^5+6q^4+3q^3+q^2+q
        15: 10q^4+4q^3+q^2+q
        16: 15q^4+4q^3+2q^2+q
        17: 15q^4+4q^3+2q^2+q
        18: 3q^6+6q^5+6q^4+4q^3+q^2+q
        19: 8q^4+3q^3+2q^2+q
        20: 8q^4+3q^3+2q^2+q
        21: 2q^5+5q^4+4q^3+q^2+q
        22: 15q^4+4q^3+2q^2+q
        23: 15q^4+4q^3+2q^2+q
        24: 5q^5+10q^4+5q^3+q^2+q
        25: 15q^4+4q^3+2q^2+q
        26: 15q^4+4q^3+2q^2+q
        27: 5q^5+10q^4+5q^3+q^2+q
        28: 15q^4+4q^3+2q^2+q
        29: 8q^4+3q^3+2q^2+q
        30: 5q^4+3q^3+q^2+q
        31: 15q^4+4q^3+2q^2+q
        32: 10q^4+4q^3+q^2+q
        33: 15q^4+4q^3+2q^2+q
        34: 15q^4+4q^3+2q^2+q
        35: 10q^4+4q^3+q^2+q
        36: 15q^4+4q^3+2q^2+q
        37: 7q^4+2q^3+q
        38: 8q^4+2q^3+2q^2
        39: 7q^4+2q^3+q
        40: 8q^4+2q^3+2q^2
        41: 2q^5+5q^4+2q^3+q
        42: 3q^5+5q^4+3q^3+q^2
        43: 10q^4+4q^3+q^2+q
        44: q^6+4q^5+6q^4+3q^3+q^2+q
        45: 10q^4+4q^3+q^2+q
        46: 10q^4+4q^3+q^2+q
        47: 10q^4+4q^3+q^2+q
        48: q^6+4q^5+6q^4+3q^3+q^2+q
        49: 8q^4+3q^3+2q^2+q
        50: 8q^4+3q^3+2q^2+q
        51: 2q^5+5q^4+4q^3+q^2+q
        52: 8q^4+3q^3+2q^2+q
        53: 8q^4+3q^3+2q^2+q
        54: 2q^5+5q^4+4q^3+q^2+q
        55: 8q^4+3q^3+2q^2+q
        56: 8q^4+3q^3+2q^2+q
        57: 2q^5+5q^4+4q^3+q^2+q
        58: 8q^4+3q^3+q^2+q
        59: 7q^4+q^3+q^2
        60: 8q^4+3q^3+q^2+q
        61: 7q^4+q^3+q^2
        62: 7q^4+2q^3+q
        63: 8q^4+2q^3+2q^2
        64: 5q^4+2q^3+q
        65: 5q^4+2q^3+q^2
        66: 7q^4+2q^3+q
        67: 8q^4+2q^3+2q^2
        68: 5q^4+4q^3+q
        69: 5q^4+3q^3+q^2+q
        70: 5q^4+3q^3+q^2+q
        71: 8q^4+3q^3+2q^2+q
        72: 3q^4+2q^3+2q^2+q
        73: 3q^4+2q^3+2q^2+q
        74: q^4+q^3+q
        75: 2q^4+q^3+2q^2
        76: q^4+q^3+q
        77: 2q^4+q^3+2q^2
        78: q^4+q^3+q
        79: q^4+2q^3+q^2
        80: 10q^4+4q^3+q^2+q
        81: 10q^4+4q^3+q^2+q
        82: 8q^4+3q^3+2q^2+q
        83: 5q^4+3q^3+q^2+q
        84: 10q^4+4q^3+q^2+q
        85: 10q^4+4q^3+q^2+q
        86: 8q^4+3q^3+2q^2+q
        87: 5q^4+3q^3+q^2+q
        88: 10q^4+4q^3+q^2+q
        89: 10q^4+4q^3+q^2+q
        90: q^6+4q^5+6q^4+3q^3+q^2+q
        91: 3q^4+3q^3+q^2+q
        92: 4q^4+3q^3+q^2+q
        93: 3q^4+3q^3+q^2+q
        94: 8q^4+3q^3+2q^2+q
        95: 8q^4+3q^3+2q^2+q
        96: 2q^5+5q^4+4q^3+q^2+q
        97: 8q^4+3q^3+2q^2+q
        98: 8q^4+3q^3+2q^2+q
        99: 2q^5+5q^4+4q^3+q^2+q
       100: 8q^4+3q^3+2q^2+q
       101: 8q^4+3q^3+2q^2+q
       102: 2q^5+5q^4+4q^3+q^2+q
       103: 4q^4+2q^3+q
       104: 4q^4+q^3+q^2
       105: 4q^4+q^3+q^2
       106: 3q^4
       107: 2q^4+2q^3+q^2+q
       108: q^4+q^2
       109: 2q^4+2q^3+q^2+q
       110: q^4+q^2
       111: q^3+q
       112: 2q^2
       113: q^4+q^3+q
       114: 2q^4+q^3+2q^2
       115: q^4+q^3+q
       116: q^4+q^3+q^2
       117: 3q^4+3q^3+q
       118: 2q^4+q^3
       119: 3q^4+3q^3+q
       120: 2q^4+q^3
       121: 5q^4+2q^3+q
       122: 5q^4+2q^3+q^2
       123: 5q^4+2q^3+q
       124: 5q^4+2q^3+q^2
       125: 5q^4+4q^3+q
       126: 5q^4+3q^3+q^2+q
       127: q^4+q^3+q
       128: 2q^4+q^3+2q^2
       129: q^4+q^3+q
       130: 2q^4+q^3+2q^2
       131: q^4+q^3+q
       132: q^4+2q^3+q^2
       133: q^4+3q^3+q
       134: 3q^4+3q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 10q^4+4q^3+q^2+q
       138: 5q^4+3q^3+q^2+q
       139: 8q^4+3q^3+2q^2+q
       140: 3q^4+2q^3+2q^2+q
       141: 5q^4+3q^3+q^2+q
       142: 3q^4+2q^3+2q^2+q
       143: 10q^4+4q^3+q^2+q
       144: 5q^4+3q^3+q^2+q
       145: 8q^4+3q^3+2q^2+q
       146: 5q^4+3q^3+q^2+q
       147: 3q^4+2q^3+2q^2+q
       148: 3q^4+2q^3+2q^2+q
       149: 8q^4+3q^3+2q^2+q
       150: 5q^4+3q^3+q^2+q
       151: q^4+q^3+q
       152: 2q^4+q^3+2q^2
       153: q^4+q^3+q
       154: 2q^4+q^3+2q^2
       155: q^4+q^3+q
       156: q^4+2q^3+q^2
       157: 3q^4+3q^3+q^2+q
       158: 4q^4+3q^3+q^2+q
       159: 3q^4+3q^3+q^2+q
       160: 3q^4+3q^3+q^2+q
       161: 4q^4+3q^3+q^2+q
       162: 3q^4+3q^3+q^2+q
       163: 3q^4+3q^3+q^2+q
       164: 4q^4+3q^3+q^2+q
       165: 3q^4+3q^3+q^2+q
       166: 8q^4+3q^3+2q^2+q
       167: 8q^4+3q^3+2q^2+q
       168: 2q^5+5q^4+4q^3+q^2+q
       169: q^3+q
       170: q^2
       171: q^2
       173: 2q^4+2q^3+q
       174: q^4+q^3
       175: q^4+q^3
       176: q^4
       177: q^4+q^3+q
       178: q^4+q^3+q^2
       179: q^4+q^3+q
       180: 2q^4+q^3+2q^2
       181: q^3+q
       182: 2q^2
       183: 2q^3+q
       185: 2q^3+q
       187: q^3+q
       188: q^2
       189: q^4+q^3+q
       190: q^4+q^3+q^2
       191: 3q^4+3q^3+q
       192: 2q^4+q^3
       193: 2q^4+2q^3+q^2+q
       194: q^4+q^2
       195: 2q^4+2q^3+q^2+q
       196: q^4+q^2
       197: q^3+q
       198: 2q^2
       199: 3q^4+3q^3+q
       200: 2q^4+q^3
       201: 2q^4+2q^3+q^2+q
       202: q^4+q^2
       203: 2q^4+2q^3+q^2+q
       204: q^4+q^2
       205: q^3+q
       206: 2q^2
       207: 5q^4+2q^3+q
       208: 5q^4+2q^3+q^2
       209: q^4+q^3+q
       210: 2q^4+q^3+2q^2
       211: q^4+q^3+q
       212: q^4+q^3+q^2
       214: q^3+q^2
       216: q^4+q^3+q^2
       218: q^3+q^2
       219: q^4+3q^3+q
       220: q^4+3q^3+q
       221: 3q^4+3q^3+q^2+q
       222: q^4+2q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: q^4+2q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 5q^4+3q^3+q^2+q
       227: q^4+3q^3+q
       228: 3q^4+3q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: q^4+2q^3+q^2+q
       231: 5q^4+3q^3+q^2+q
       232: q^4+3q^3+q
       233: 3q^4+3q^3+q^2+q
       234: q^4+2q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: 5q^4+3q^3+q^2+q
       237: q^4+q^3+q
       238: 2q^4+q^3+2q^2
       239: q^4+q^3+q
       240: 2q^4+q^3+2q^2
       241: q^4+q^3+q
       242: q^4+2q^3+q^2
       243: 8q^4+3q^3+2q^2+q
       244: 3q^4+2q^3+2q^2+q
       245: 3q^4+2q^3+2q^2+q
       246: 5q^4+3q^3+q^2+q
       247: q^3+3q^2+q
       248: q^3+3q^2+q
       249: 2q^4+2q^3+q^2+q
       250: 3q^4+3q^3+q^2+q
       251: 4q^4+3q^3+q^2+q
       252: 3q^4+3q^3+q^2+q
       253: 3q^4+3q^3+q^2+q
       254: 4q^4+3q^3+q^2+q
       255: 3q^4+3q^3+q^2+q
       256: 3q^4+3q^3+q^2+q
       257: 4q^4+3q^3+q^2+q
       258: 3q^4+3q^3+q^2+q
       259: q^3+q
       260: q^2
       261: q^2
       263: q^3+q
       267: q^3+q
       268: q^2
       270: q^2
       271: q^3+q
       272: q^2
       274: q^2
       275: 2q^4+2q^3+q
       276: q^4+q^3
       277: q^4+q^3
       278: q^4
       280: q^3
       282: q^3+q^2
       283: 2q^3+q
       285: 2q^3+q
       287: q^4+q^3+q
       288: q^4+q^3+q^2
       290: q^2
       291: q^3+q
       292: q^2
       293: 2q^3+q
       295: 2q^3+q
       297: q^3+q
       298: q^2
       299: 2q^3+q
       301: q^3+q
       302: 2q^2
       303: 2q^3+q
       305: q^3+q
       306: q^2
       307: 2q^3+q
       309: 2q^3+q
       311: q^3+q
       312: 2q^2
       313: q^3+q
       314: q^2
       315: q^4+q^3+q
       316: q^4+q^3+q^2
       317: q^4+q^3+q
       318: 2q^4+q^3+2q^2
       319: 2q^4+2q^3+q^2+q
       320: q^4+q^2
       321: 2q^4+2q^3+q^2+q
       322: q^4+q^2
       323: q^3+q
       324: 2q^2
       325: q^4+q^3+q
       326: q^4+q^3+q^2
       328: q^3+q^2
       330: q^4+q^3+q^2
       332: q^3+q^2
       333: q^4+3q^3+q
       334: q^4+2q^3+q^2+q
       335: q^4+2q^3+q^2+q
       336: q^2+q
       337: q^3+3q^2+q
       338: q
       339: q^3+3q^2
       340: q
       341: q^3+3q^2
       342: q^4+q
       343: q^4+2q^3+q^2
       344: q^4+3q^3+q
       345: q^4+3q^3+q
       346: 3q^4+3q^3+q^2+q
       347: q^4+2q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: q^4+2q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: q^3+3q^2+q
       352: q^4+3q^3+q
       353: q^4+3q^3+q
       354: 3q^4+3q^3+q^2+q
       355: q^4+2q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: q^4+2q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^3+3q^2+q
       361: q^3+q^2
       363: q^4+q^3+q^2
       365: q^3+q^2
       366: 5q^4+3q^3+q^2+q
       367: q^4+3q^3+q
       368: 3q^4+3q^3+q^2+q
       369: q^4+2q^3+q^2+q
       370: q^4+2q^3+q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^4+q^3+q^2+q
       374: 3q^4+3q^3+q^2+q
       375: 4q^4+3q^3+q^2+q
       376: 3q^4+3q^3+q^2+q
       377: q^3+q
       385: q^3+q
       389: q^3+q
       390: q^2
       392: q^2
       393: q^3+q
       397: q^3+q
       398: q^2
       400: q^2
       401: q^3+q
       405: q^3+q
       407: q^2
       408: q^2
       410: q^3
       412: q^3+q^2
       414: q^3
       416: q^2
       418: q^2
       419: 2q^3+q
       421: 2q^3+q
       423: q^3+q
       424: q^2
       425: q
       426: q^2
       427: q
       428: q^3+3q^2
       429: 2q^3+q
       431: 2q^3+q
       433: q^3+q
       434: q^2
       436: q^2
       437: 2q^3+q
       439: 2q^3+q
       441: q^3+q
       442: q^2
       443: q^3+2q^2+q
       444: q^2
       445: q
       446: q^3+3q^2
       447: 2q^3+q
       449: 2q^3+q
       451: q^3+q
       452: q^2
       453: 2q^3+q
       456: q^2
       457: 2q^3+q
       459: q^3+q
       460: q^2
       461: q^3+2q^2+q
       462: q^2
       463: q
       464: q^3+3q^2
       466: q^3
       468: q^3+q^2
       469: q^4+q^3+q
       470: q^4+q^3+q^2
       471: 2q^3+q
       473: 2q^3+q
       475: q^3+q
       476: q^2
       477: q^3+q
       478: 2q^2
       479: q^3+q^2+q
       480: 2q^2
       481: q^3+q
       482: q^3+q
       483: q^2+q
       484: q^2+q
       486: 2q^2
       488: 2q^2
       490: q^3+q^2
       491: q^2+q
       492: q^4+3q^3+q
       493: q^4+2q^3+q^2+q
       494: q^4+2q^3+q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^4+3q^3+q
       498: q^4+2q^3+q^2+q
       499: q^4+2q^3+q^2+q
       500: q^2+q
       501: 2q^2+q
       503: q^3+q^2
       505: q^4+q^3+q^2
       507: q^3+q^2
       508: q^4+3q^3+q
       509: q^4+3q^3+q
       510: 3q^4+3q^3+q^2+q
       511: q^4+2q^3+q^2+q
       512: q^4+2q^3+q^2+q
       513: q^4+2q^3+q^2+q
       514: q^4+2q^3+q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^4+q^3+q^2+q
       518: 2q^2+q
       519: 2q^2+q
       520: q^4+q^3+q^2+q
       529: q^3+q
       533: q^3+q
       541: q^3+q
       545: q
       546: q^3+2q^2
       548: q^2
       549: q^3+q
       557: q^3+q
       561: q
       562: q^3+2q^2
       564: q^2
       565: q^3+q
       569: q^3+q
       571: q^2
       572: q^2
       573: q^3+q^2+q
       574: q^2
       576: q^2
       577: q
       578: q^3+q^2
       581: 2q^2
       584: q^3
       588: q^2
       589: q^3+q
       591: q
       593: q
       595: q^3+q
       598: q^2
       599: q
       600: q^2
       602: q^2
       603: 2q^3+q
       606: q^2
       607: 2q^3+q
       609: q^3+q
       610: q^2
       612: q^2
       613: q
       614: q^2
       615: q^2+q
       618: 2q^2
       619: 2q^3+q
       621: 2q^3+q
       624: q^2
       625: q^3+q
       626: q^2
       628: q^2
       629: q
       630: q^2
       631: q^2+q
       634: 2q^2
       636: q^3
       638: q^3+q^2
       640: q^3
       641: 2q^3+q
       643: 2q^3+q
       645: q^3+q
       646: q^2
       647: 2q^3+q
       649: 2q^3+q
       652: q^2
       653: q^3+q
       654: q^2
       655: q^2+q
       656: q^2
       657: q^2+q
       659: 2q^2
       661: 2q^2
       663: q^3+q^2
       664: q^2+q
       665: q
       667: 2q^2
       669: 2q^2
       671: q^3+q^2
       672: q^2+q
       673: q^2+q
       674: 2q^2+q
       675: q^3+q
       676: q^3+q
       677: q^2+q
       678: 2q^2+q
       679: q^2+q
       680: 2q^2+q
       681: q^3+q
       682: q^3+q
       683: q^2+q
       684: 2q^2+q
       685: q^2+q
       686: q^4+3q^3+q
       687: q^4+2q^3+q^2+q
       688: q^4+2q^3+q^2+q
       689: q^2+q
       690: 2q^2+q
       691: 2q^2+q
       692: q^4+q^3+q^2+q
       693: q
       694: q^3+q^2
       699: q^2
       700: q^2
       713: q
       717: q
       725: q^3+q
       734: q^2
       741: q^3+q
       750: q^2
       753: q^3+q
       761: q^3+q
       765: q^2+q
       770: q^2
       773: q^2
       776: q^2
       780: q^2
       784: q^2
       785: q
       787: q
       790: q^2
       791: q
       793: q^2+q
       796: 2q^2
       800: q^2
       801: q^3+q
       803: q
       805: q
       807: q^3+q
       810: q^2
       811: q
       812: q^2
       814: 2q^2
       815: q^2+q
       817: q^2+q
       820: 2q^2
       824: q^2
       825: q^3+q
       827: q
       829: q
       831: q^3+q
       834: q^2
       835: q
       836: q^2
       838: 2q^2
       839: q^2+q
       842: q^3
       843: q^2+q
       844: q^2
       845: 2q^3+q
       847: 2q^3+q
       850: q^2
       851: q^3+q
       852: q^2
       854: q^2
       855: q
       856: q^2
       857: q^2+q
       858: q^2
       860: 2q^2
       862: 2q^2
       864: q^3+q^2
       865: q^2+q
       866: q
       867: q^2+q
       868: q
       869: 2q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: 2q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q^3+q
       878: q^3+q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: q^3+1
       885: q^2
       908: q
       917: q^2
       924: q
       928: q
       933: q^2
       941: q^2
       948: q
       952: q
       957: q^2
       964: q^2+q
       969: q^2
       972: q^2
       974: q^3+q
       983: q^2
       986: q^2
       988: q^2+q
       993: q^2
       997: q^2
       998: q
      1000: q
      1004: q
      1006: q
      1008: q
      1012: q
      1015: 2q^2
      1016: q^2+q
      1021: q^2
      1025: q^2
      1026: q
      1028: q
      1031: 2q^2
      1032: q^2+q
      1037: q^2
      1040: q
      1043: q^2
      1044: q
      1046: q^2+q
      1047: q^2
      1051: q^2
      1052: q^3+q
      1054: q
      1056: q
      1058: q^3+q
      1061: q^2
      1062: q
      1063: q^2
      1064: q
      1067: 1
      1069: 1
      1071: q^3+1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1087: q^2
      1099: q^2
      1130: q
      1134: q
      1145: q^2
      1160: q
      1165: q^2
      1180: q
      1189: q^2
      1192: q^2
      1194: q^2+q
      1202: q
      1206: q
      1211: 1
      1213: 1
      1216: q
      1218: q
      1224: q
      1227: 1
      1228: 1
      1232: q
      1234: q
      1237: q^2
      1240: q
      1242: q
      1245: 1
      1246: 1
      1250: q
      1253: q^2
      1254: q
      1258: q
      1260: q
      1262: 1
      1268: q
      1270: q
      1273: q^2
      1275: q^2
      1276: q
      1280: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1303: q^2
      1326: q
      1341: 1
      1364: q
      1368: q
      1373: 1
      1396: q
      1400: q
      1405: 1
      1410: 1
      1426: q
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1450: q
      1453: 1
      1454: q
      1459: 1
      1460: q
      1462: q
      1466: q
      1468: q
      1473: q^2
      1476: q
      1478: q
      1482: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1575: q
      1595: q
      1623: q
      1627: q
      1639: 1
      1644: 1
      1645: 1
      1647: 1
      1652: 1
      1653: 1
      1655: 1
      1663: q
      1665: q
      1668: 1
      1669: 1
      1674: 1
      1676: 1
      1724: 1
      1733: 1
      1738: 1
      1746: 1
      1749: 1
      1762: 1
      1766: 1
      1773: 1
      1797: q
      1802: 1
      1825: 1
      1828: 1
      1829: 1
      1831: 1
      1835: 1
      1847: 1
      1859: 1
      1898: 1
      1914: 1
      1927: 1
      1933: 1
      1937: 1
      1940: 1
      1967: 1
      1979: 1
      1991: 1
      2060: 1
      2093: 1

2094:    0: q^4+q
         1: q^4+q
         2: q^4+q
         3: q^4+q
         4: q^5+q^4+q
         5: q^4+q
         6: q
         7: q^5+q^4+q
         8: q^4+q
         9: q^5+q^4+q
        10: q
        11: q
        12: q
        13: q^4+q
        14: q^5+q^4+q
        15: q^4+q
        16: q^4+q
        17: q^4+q
        18: q^5+q^4+q
        19: q^4+q
        20: q
        21: q^4+q
        22: q^4+q
        23: q^4+q
        24: q^4+q
        25: q^4+q
        26: q^4+q
        27: q^4+q
        28: q
        29: q
        30: q^4+q
        31: q
        32: q^4+q
        33: q^4+q
        34: q
        35: q^4+q
        36: q^4+q
        37: q^4+q
        39: q^4+q
        41: q^4+q
        43: q
        44: q
        45: q
        46: q^4+q
        47: q^4+q
        48: q^5+q^4+q
        49: q^4+q
        50: q
        51: q^4+q
        52: q^4+q
        53: q
        54: q^4+q
        55: q^4+q
        56: q
        57: q^4+q
        58: q
        60: q
        62: q
        64: q^4+q
        66: q^4+q
        68: q
        69: q^4+q
        70: q
        71: q
        72: q
        73: q
        74: q^4+q
        76: q
        78: q^4+q
        80: q
        81: q^4+q
        82: q
        83: q^4+q
        84: q
        85: q^4+q
        86: q
        87: q^4+q
        88: q
        89: q
        90: q
        91: q^4+q
        92: q
        93: q^4+q
        94: q^4+q
        95: q
        96: q^4+q
        97: q^4+q
        98: q
        99: q^4+q
       100: q^4+q
       101: q
       102: q^4+q
       103: q
       107: q
       109: q
       111: q
       113: q
       115: q^4+q
       117: q
       119: q
       121: q
       123: q^4+q
       125: q
       126: q
       127: q^4+q
       129: q
       131: q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q^4+q
       151: q^4+q
       153: q
       155: q^4+q
       157: q
       158: q
       159: q
       160: q^4+q
       161: q
       162: q^4+q
       163: q^4+q
       164: q
       165: q^4+q
       166: q^4+q
       167: q
       168: q^4+q
       169: q
       173: q
       177: q^4+q
       179: q
       181: q
       183: q
       185: q
       187: q
       189: q
       191: q
       193: q
       195: q
       197: q
       199: q
       201: q
       203: q
       205: q
       207: q
       209: q
       211: q^4+q
       213: q^4+q
       215: q
       217: q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       237: q^4+q
       239: q
       241: q^4+q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q^4+q
       257: q
       258: q^4+q
       259: q
       263: q
       267: q
       271: q
       275: q
       279: q
       281: q^4+q
       283: q
       285: q
       287: q
       289: q
       291: q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q^4+q
       317: q
       319: q
       321: q
       323: q
       325: q
       327: q
       329: q
       331: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^4+q
       362: q
       364: q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q
       413: q
       415: q
       417: q
       419: q
       421: q
       423: q
       425: q
       427: q
       429: q
       431: q
       433: q
       435: q
       437: q
       439: q
       441: q
       443: q
       445: q
       447: q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       461: q
       463: q
       465: q
       467: q^4+q
       469: q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       502: q
       504: q
       506: q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       515: q
       516: q
       517: q^4+q
       521: q
       525: q
       529: q
       533: q
       537: q
       541: q
       545: q
       549: q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       583: q
       585: q
       587: q
       589: q
       591: q
       593: q
       595: q
       597: q
       599: q
       601: q
       603: q
       605: q
       607: q
       609: q
       611: q
       613: q
       615: q
       617: q
       619: q
       621: q
       623: q
       625: q
       627: q
       629: q
       631: q
       633: q
       635: q
       637: q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       655: q
       657: q
       658: q
       660: q
       662: q^4+q
       664: q
       665: q
       674: q
       675: q
       676: q
       677: q
       679: q
       680: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       693: q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q
       729: q
       733: q
       737: q
       741: q
       745: q
       749: q
       753: q
       757: q
       761: q
       765: q
       769: q
       775: q
       777: q
       779: q
       781: q
       785: q
       787: q
       791: q
       793: q
       795: q
       797: q
       799: q
       801: q
       803: q
       805: q
       807: q
       809: q
       811: q
       817: q
       819: q
       821: q
       823: q
       825: q
       827: q
       829: q
       831: q
       833: q
       835: q
       841: q
       843: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       866: q
       870: q
       871: q
       874: q
       875: q
       877: q
       878: q
       879: q
       880: q
       884: q
       896: q
       900: q
       904: q
       908: q
       912: q
       916: q
       920: q
       924: q
       928: q
       936: q
       940: q
       944: q
       948: q
       952: q
       960: q
       964: q
       968: q
       974: q
       978: q
       994: q
       998: q
      1000: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1026: q
      1028: q
      1034: q
      1036: q
      1038: q
      1040: q
      1044: q
      1048: q
      1050: q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q
      1076: q
      1080: q
      1083: q
      1084: q
      1086: q
      1114: q
      1122: q
      1126: q
      1130: q
      1138: q
      1148: q
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: q
      1198: q
      1202: q
      1206: q
      1222: 1
      1230: q
      1232: q
      1234: q
      1248: q
      1250: q
      1254: q
      1264: q
      1266: q
      1268: q
      1270: q
      1274: q
      1278: q
      1280: q
      1287: q
      1290: q
      1322: 1
      1336: 1
      1348: q
      1356: q
      1360: q
      1364: q
      1380: q
      1388: q
      1392: q
      1396: q
      1414: q
      1418: q
      1422: q
      1426: q
      1430: q
      1446: 1
      1464: q
      1466: q
      1468: q
      1480: 1
      1491: 1
      1501: q
      1513: q
      1555: 1
      1559: 1
      1571: 1
      1591: 1
      1607: q
      1615: q
      1619: q
      1623: q
      1633: 1
      1637: 1
      1671: 1
      1677: 1
      1689: 1
      1701: 1
      1711: q
      1725: 1
      1729: 1
      1753: 1
      1777: 1
      1793: 1
      1803: 1
      1823: 1
      1836: 1
      1848: 1
      1860: 1
      1872: 1
      1894: 1
      1910: 1
      1928: 1
      1948: 1
      1968: 1
      1980: 1
      1992: 1
      2056: 1
      2094: 1

2095:    0: 15q^4+4q^3+2q^2+q
         1: 15q^4+4q^3+2q^2+q
         2: 5q^5+10q^4+5q^3+q^2+q
         3: 15q^4+4q^3+2q^2+q
         4: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         5: 15q^4+4q^3+2q^2+q
         6: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         7: 3q^6+6q^5+6q^4+4q^3+q^2+q
         8: 5q^5+10q^4+5q^3+q^2+q
         9: 3q^6+6q^5+6q^4+4q^3+q^2+q
        10: 15q^4+4q^3+2q^2+q
        11: 15q^4+4q^3+2q^2+q
        12: 2q^6+7q^5+9q^4+3q^3+2q^2+q
        13: 10q^4+4q^3+q^2+q
        14: q^6+4q^5+6q^4+3q^3+q^2+q
        15: 10q^4+4q^3+q^2+q
        16: 15q^4+4q^3+2q^2+q
        17: 15q^4+4q^3+2q^2+q
        18: 3q^6+6q^5+6q^4+4q^3+q^2+q
        19: 8q^4+3q^3+2q^2+q
        20: 8q^4+3q^3+2q^2+q
        21: 2q^5+5q^4+4q^3+q^2+q
        22: 15q^4+4q^3+2q^2+q
        23: 15q^4+4q^3+2q^2+q
        24: 5q^5+10q^4+5q^3+q^2+q
        25: 15q^4+4q^3+2q^2+q
        26: 15q^4+4q^3+2q^2+q
        27: 5q^5+10q^4+5q^3+q^2+q
        28: 15q^4+4q^3+2q^2+q
        29: 8q^4+3q^3+2q^2+q
        30: 5q^4+3q^3+q^2+q
        31: 15q^4+4q^3+2q^2+q
        32: 10q^4+4q^3+q^2+q
        33: 15q^4+4q^3+2q^2+q
        34: 15q^4+4q^3+2q^2+q
        35: 10q^4+4q^3+q^2+q
        36: 15q^4+4q^3+2q^2+q
        37: 8q^4+2q^3+2q^2
        38: 7q^4+2q^3+q
        39: 8q^4+2q^3+2q^2
        40: 7q^4+2q^3+q
        41: 3q^5+5q^4+3q^3+q^2
        42: 2q^5+5q^4+2q^3+q
        43: 10q^4+4q^3+q^2+q
        44: q^6+4q^5+6q^4+3q^3+q^2+q
        45: 10q^4+4q^3+q^2+q
        46: 10q^4+4q^3+q^2+q
        47: 10q^4+4q^3+q^2+q
        48: q^6+4q^5+6q^4+3q^3+q^2+q
        49: 8q^4+3q^3+2q^2+q
        50: 8q^4+3q^3+2q^2+q
        51: 2q^5+5q^4+4q^3+q^2+q
        52: 8q^4+3q^3+2q^2+q
        53: 8q^4+3q^3+2q^2+q
        54: 2q^5+5q^4+4q^3+q^2+q
        55: 8q^4+3q^3+2q^2+q
        56: 8q^4+3q^3+2q^2+q
        57: 2q^5+5q^4+4q^3+q^2+q
        58: 7q^4+q^3+q^2
        59: 8q^4+3q^3+q^2+q
        60: 8q^4+3q^3+q^2+q
        61: 7q^4+q^3+q^2
        62: 8q^4+2q^3+2q^2
        63: 7q^4+2q^3+q
        64: 5q^4+2q^3+q^2
        65: 5q^4+2q^3+q
        66: 8q^4+2q^3+2q^2
        67: 7q^4+2q^3+q
        68: 5q^4+4q^3+q
        69: 5q^4+3q^3+q^2+q
        70: 5q^4+3q^3+q^2+q
        71: 8q^4+3q^3+2q^2+q
        72: 3q^4+2q^3+2q^2+q
        73: 3q^4+2q^3+2q^2+q
        74: 2q^4+q^3+2q^2
        75: q^4+q^3+q
        76: 2q^4+q^3+2q^2
        77: q^4+q^3+q
        78: q^4+2q^3+q^2
        79: q^4+q^3+q
        80: 10q^4+4q^3+q^2+q
        81: 10q^4+4q^3+q^2+q
        82: 8q^4+3q^3+2q^2+q
        83: 5q^4+3q^3+q^2+q
        84: 10q^4+4q^3+q^2+q
        85: 10q^4+4q^3+q^2+q
        86: 8q^4+3q^3+2q^2+q
        87: 5q^4+3q^3+q^2+q
        88: 10q^4+4q^3+q^2+q
        89: 10q^4+4q^3+q^2+q
        90: q^6+4q^5+6q^4+3q^3+q^2+q
        91: 3q^4+3q^3+q^2+q
        92: 4q^4+3q^3+q^2+q
        93: 3q^4+3q^3+q^2+q
        94: 8q^4+3q^3+2q^2+q
        95: 8q^4+3q^3+2q^2+q
        96: 2q^5+5q^4+4q^3+q^2+q
        97: 8q^4+3q^3+2q^2+q
        98: 8q^4+3q^3+2q^2+q
        99: 2q^5+5q^4+4q^3+q^2+q
       100: 8q^4+3q^3+2q^2+q
       101: 8q^4+3q^3+2q^2+q
       102: 2q^5+5q^4+4q^3+q^2+q
       103: 4q^4+q^3+q^2
       104: 4q^4+2q^3+q
       105: 3q^4
       106: 4q^4+q^3+q^2
       107: 2q^4+2q^3+q^2+q
       108: q^4+q^2
       109: q^4+q^2
       110: 2q^4+2q^3+q^2+q
       111: 2q^2
       112: q^3+q
       113: 2q^4+q^3+2q^2
       114: q^4+q^3+q
       115: q^4+q^3+q^2
       116: q^4+q^3+q
       117: 2q^4+q^3
       118: 3q^4+3q^3+q
       119: 3q^4+3q^3+q
       120: 2q^4+q^3
       121: 5q^4+2q^3+q^2
       122: 5q^4+2q^3+q
       123: 5q^4+2q^3+q^2
       124: 5q^4+2q^3+q
       125: 5q^4+4q^3+q
       126: 5q^4+3q^3+q^2+q
       127: 2q^4+q^3+2q^2
       128: q^4+q^3+q
       129: 2q^4+q^3+2q^2
       130: q^4+q^3+q
       131: q^4+2q^3+q^2
       132: q^4+q^3+q
       133: q^4+3q^3+q
       134: 3q^4+3q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 10q^4+4q^3+q^2+q
       138: 5q^4+3q^3+q^2+q
       139: 8q^4+3q^3+2q^2+q
       140: 3q^4+2q^3+2q^2+q
       141: 5q^4+3q^3+q^2+q
       142: 3q^4+2q^3+2q^2+q
       143: 10q^4+4q^3+q^2+q
       144: 5q^4+3q^3+q^2+q
       145: 8q^4+3q^3+2q^2+q
       146: 5q^4+3q^3+q^2+q
       147: 3q^4+2q^3+2q^2+q
       148: 3q^4+2q^3+2q^2+q
       149: 8q^4+3q^3+2q^2+q
       150: 5q^4+3q^3+q^2+q
       151: 2q^4+q^3+2q^2
       152: q^4+q^3+q
       153: 2q^4+q^3+2q^2
       154: q^4+q^3+q
       155: q^4+2q^3+q^2
       156: q^4+q^3+q
       157: 3q^4+3q^3+q^2+q
       158: 4q^4+3q^3+q^2+q
       159: 3q^4+3q^3+q^2+q
       160: 3q^4+3q^3+q^2+q
       161: 4q^4+3q^3+q^2+q
       162: 3q^4+3q^3+q^2+q
       163: 3q^4+3q^3+q^2+q
       164: 4q^4+3q^3+q^2+q
       165: 3q^4+3q^3+q^2+q
       166: 8q^4+3q^3+2q^2+q
       167: 8q^4+3q^3+2q^2+q
       168: 2q^5+5q^4+4q^3+q^2+q
       169: q^2
       170: q^3+q
       172: q^2
       173: q^4+q^3
       174: 2q^4+2q^3+q
       175: q^4
       176: q^4+q^3
       177: q^4+q^3+q^2
       178: q^4+q^3+q
       179: 2q^4+q^3+2q^2
       180: q^4+q^3+q
       181: 2q^2
       182: q^3+q
       183: 2q^3+q
       186: 2q^3+q
       187: q^2
       188: q^3+q
       189: q^4+q^3+q^2
       190: q^4+q^3+q
       191: 2q^4+q^3
       192: 3q^4+3q^3+q
       193: 2q^4+2q^3+q^2+q
       194: q^4+q^2
       195: q^4+q^2
       196: 2q^4+2q^3+q^2+q
       197: 2q^2
       198: q^3+q
       199: 3q^4+3q^3+q
       200: 2q^4+q^3
       201: 2q^4+2q^3+q^2+q
       202: q^4+q^2
       203: q^4+q^2
       204: 2q^4+2q^3+q^2+q
       205: 2q^2
       206: q^3+q
       207: 5q^4+2q^3+q^2
       208: 5q^4+2q^3+q
       209: 2q^4+q^3+2q^2
       210: q^4+q^3+q
       211: q^4+q^3+q^2
       212: q^4+q^3+q
       213: q^3+q^2
       215: q^4+q^3+q^2
       217: q^3+q^2
       219: q^4+3q^3+q
       220: q^4+3q^3+q
       221: 3q^4+3q^3+q^2+q
       222: q^4+2q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: q^4+2q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 5q^4+3q^3+q^2+q
       227: q^4+3q^3+q
       228: 3q^4+3q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: q^4+2q^3+q^2+q
       231: 5q^4+3q^3+q^2+q
       232: q^4+3q^3+q
       233: 3q^4+3q^3+q^2+q
       234: q^4+2q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: 5q^4+3q^3+q^2+q
       237: 2q^4+q^3+2q^2
       238: q^4+q^3+q
       239: 2q^4+q^3+2q^2
       240: q^4+q^3+q
       241: q^4+2q^3+q^2
       242: q^4+q^3+q
       243: 8q^4+3q^3+2q^2+q
       244: 3q^4+2q^3+2q^2+q
       245: 3q^4+2q^3+2q^2+q
       246: 5q^4+3q^3+q^2+q
       247: q^3+3q^2+q
       248: q^3+3q^2+q
       249: 2q^4+2q^3+q^2+q
       250: 3q^4+3q^3+q^2+q
       251: 4q^4+3q^3+q^2+q
       252: 3q^4+3q^3+q^2+q
       253: 3q^4+3q^3+q^2+q
       254: 4q^4+3q^3+q^2+q
       255: 3q^4+3q^3+q^2+q
       256: 3q^4+3q^3+q^2+q
       257: 4q^4+3q^3+q^2+q
       258: 3q^4+3q^3+q^2+q
       259: q^2
       260: q^3+q
       262: q^2
       264: q^3+q
       267: q^2
       268: q^3+q
       269: q^2
       271: q^2
       273: q^2
       274: q^3+q
       275: q^4+q^3
       276: 2q^4+2q^3+q
       277: q^4
       278: q^4+q^3
       279: q^3
       281: q^3+q^2
       283: 2q^3+q
       286: 2q^3+q
       287: q^4+q^3+q^2
       288: q^4+q^3+q
       289: q^2
       291: q^2
       292: q^3+q
       293: 2q^3+q
       296: 2q^3+q
       297: q^2
       298: q^3+q
       299: 2q^3+q
       301: 2q^2
       302: q^3+q
       304: 2q^3+q
       305: q^2
       306: q^3+q
       307: 2q^3+q
       310: 2q^3+q
       311: 2q^2
       312: q^3+q
       313: q^2
       314: q^3+q
       315: q^4+q^3+q^2
       316: q^4+q^3+q
       317: 2q^4+q^3+2q^2
       318: q^4+q^3+q
       319: 2q^4+2q^3+q^2+q
       320: q^4+q^2
       321: q^4+q^2
       322: 2q^4+2q^3+q^2+q
       323: 2q^2
       324: q^3+q
       325: q^4+q^3+q^2
       326: q^4+q^3+q
       327: q^3+q^2
       329: q^4+q^3+q^2
       331: q^3+q^2
       333: q^4+3q^3+q
       334: q^4+2q^3+q^2+q
       335: q^4+2q^3+q^2+q
       336: q^2+q
       337: q^3+3q^2+q
       338: q^3+3q^2
       339: q
       340: q^3+3q^2
       341: q
       342: q^4+2q^3+q^2
       343: q^4+q
       344: q^4+3q^3+q
       345: q^4+3q^3+q
       346: 3q^4+3q^3+q^2+q
       347: q^4+2q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: q^4+2q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: q^3+3q^2+q
       352: q^4+3q^3+q
       353: q^4+3q^3+q
       354: 3q^4+3q^3+q^2+q
       355: q^4+2q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: q^4+2q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^3+3q^2+q
       360: q^3+q^2
       362: q^4+q^3+q^2
       364: q^3+q^2
       366: 5q^4+3q^3+q^2+q
       367: q^4+3q^3+q
       368: 3q^4+3q^3+q^2+q
       369: q^4+2q^3+q^2+q
       370: q^4+2q^3+q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^4+q^3+q^2+q
       374: 3q^4+3q^3+q^2+q
       375: 4q^4+3q^3+q^2+q
       376: 3q^4+3q^3+q^2+q
       378: q^3+q
       386: q^3+q
       389: q^2
       390: q^3+q
       391: q^2
       394: q^3+q
       397: q^2
       399: q^2
       400: q^3+q
       403: q^3+q
       405: q^2
       406: q^2
       407: q^3+q
       409: q^3
       411: q^3+q^2
       413: q^3
       415: q^2
       417: q^2
       419: 2q^3+q
       422: 2q^3+q
       423: q^2
       424: q^3+q
       425: q^2
       426: q
       427: q^3+3q^2
       428: q
       429: 2q^3+q
       432: 2q^3+q
       433: q^2
       434: q^3+q
       435: q^2
       437: 2q^3+q
       440: 2q^3+q
       441: q^2
       442: q^3+q
       443: q^3+2q^2+q
       444: q^2
       445: q^3+3q^2
       446: q
       447: 2q^3+q
       450: 2q^3+q
       451: q^2
       452: q^3+q
       453: 2q^3+q
       455: q^2
       458: 2q^3+q
       459: q^2
       460: q^3+q
       461: q^2
       462: q^3+2q^2+q
       463: q^3+3q^2
       464: q
       465: q^3
       467: q^3+q^2
       469: q^4+q^3+q^2
       470: q^4+q^3+q
       471: 2q^3+q
       474: 2q^3+q
       475: q^2
       476: q^3+q
       477: 2q^2
       478: q^3+q
       479: 2q^2
       480: q^3+q^2+q
       481: q^3+q
       482: q^3+q
       483: q^2+q
       484: q^2+q
       485: 2q^2
       487: 2q^2
       489: q^3+q^2
       491: q^2+q
       492: q^4+3q^3+q
       493: q^4+2q^3+q^2+q
       494: q^4+2q^3+q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^4+3q^3+q
       498: q^4+2q^3+q^2+q
       499: q^4+2q^3+q^2+q
       500: q^2+q
       501: 2q^2+q
       502: q^3+q^2
       504: q^4+q^3+q^2
       506: q^3+q^2
       508: q^4+3q^3+q
       509: q^4+3q^3+q
       510: 3q^4+3q^3+q^2+q
       511: q^4+2q^3+q^2+q
       512: q^4+2q^3+q^2+q
       513: q^4+2q^3+q^2+q
       514: q^4+2q^3+q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^4+q^3+q^2+q
       518: 2q^2+q
       519: 2q^2+q
       520: q^4+q^3+q^2+q
       530: q^3+q
       534: q^3+q
       542: q^3+q
       545: q^3+2q^2
       546: q
       547: q^2
       551: q^3+q
       560: q^3+q
       561: q^2
       563: q^3+2q^2
       564: q
       566: q^3+q
       569: q^2
       570: q^2
       571: q^3+q
       573: q^2
       574: q^3+q^2+q
       575: q^2
       577: 2q^2
       580: q^3+q^2
       581: q
       583: q^3
       587: q^2
       589: q^3+q
       592: q
       593: q
       596: q^3+q
       597: q^2
       599: q^2
       600: q
       601: q^2
       603: 2q^3+q
       605: q^2
       608: 2q^3+q
       609: q^2
       610: q^3+q
       611: q^2
       613: q^2
       614: q
       615: q^2+q
       617: 2q^2
       619: 2q^3+q
       622: 2q^3+q
       623: q^2
       625: q^2
       626: q^3+q
       627: q^2
       629: q^2
       630: q
       632: q^2+q
       633: 2q^2
       635: q^3
       637: q^3+q^2
       639: q^3
       641: 2q^3+q
       644: 2q^3+q
       645: q^2
       646: q^3+q
       647: 2q^3+q
       650: 2q^3+q
       651: q^2
       653: q^2
       654: q^3+q
       655: q^2
       656: q^2+q
       657: q^2+q
       658: 2q^2
       660: 2q^2
       662: q^3+q^2
       664: q^2+q
       665: q
       666: 2q^2
       668: 2q^2
       670: q^3+q^2
       672: q^2+q
       673: q^2+q
       674: 2q^2+q
       675: q^3+q
       676: q^3+q
       677: q^2+q
       678: 2q^2+q
       679: q^2+q
       680: 2q^2+q
       681: q^3+q
       682: q^3+q
       683: q^2+q
       684: 2q^2+q
       685: q^2+q
       686: q^4+3q^3+q
       687: q^4+2q^3+q^2+q
       688: q^4+2q^3+q^2+q
       689: q^2+q
       690: 2q^2+q
       691: 2q^2+q
       692: q^4+q^3+q^2+q
       693: q^2
       696: q^3+q^2
       697: q^2
       699: q
       715: q
       718: q
       726: q^3+q
       733: q^2
       744: q^3+q
       751: q^2
       754: q^3+q
       763: q^3+q
       766: q^2+q
       769: q^2
       772: q^2
       775: q^2
       779: q^2
       783: q^2
       785: q
       788: q
       789: q^2
       792: q
       793: q^2+q
       795: 2q^2
       799: q^2
       801: q^3+q
       804: q
       805: q
       808: q^3+q
       809: q^2
       811: q^2
       812: q
       813: 2q^2
       815: q^2+q
       818: q^2+q
       819: 2q^2
       823: q^2
       825: q^3+q
       828: q
       829: q
       832: q^3+q
       833: q^2
       835: q^2
       836: q
       837: 2q^2
       840: q^2+q
       841: q^3
       843: q^2
       844: q^2+q
       845: 2q^3+q
       848: 2q^3+q
       849: q^2
       851: q^2
       852: q^3+q
       853: q^2
       855: q^2
       856: q
       857: q^2
       858: q^2+q
       859: 2q^2
       861: 2q^2
       863: q^3+q^2
       865: q^2+q
       866: q
       867: q^2+q
       868: q
       869: 2q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: 2q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q^3+q
       878: q^3+q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: q^3+1
       887: q^2
       909: q
       916: q^2
       926: q
       929: q
       932: q^2
       942: q^2
       951: q
       953: q
       958: q^2
       965: q^2+q
       968: q^2
       971: q^2
       976: q^3+q
       982: q^2
       985: q^2
       989: q^2+q
       992: q^2
       996: q^2
       999: q
      1000: q
      1004: q
      1007: q
      1009: q
      1013: q
      1014: 2q^2
      1016: q^2+q
      1020: q^2
      1024: q^2
      1026: q
      1029: q
      1030: 2q^2
      1033: q^2+q
      1036: q^2
      1040: q
      1042: q^2
      1045: q
      1046: q^2
      1047: q^2+q
      1050: q^2
      1052: q^3+q
      1055: q
      1056: q
      1059: q^3+q
      1060: q^2
      1062: q^2
      1063: q
      1065: q
      1066: 1
      1068: 1
      1070: q^3+1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1089: q^2
      1101: q^2
      1131: q
      1136: q
      1144: q^2
      1162: q
      1166: q^2
      1181: q
      1188: q^2
      1191: q^2
      1195: q^2+q
      1205: q
      1207: q
      1210: 1
      1212: 1
      1217: q
      1218: q
      1225: q
      1226: 1
      1228: 1
      1233: q
      1234: q
      1236: q^2
      1240: q
      1243: q
      1244: 1
      1247: 1
      1251: q
      1252: q^2
      1254: q
      1258: q
      1261: q
      1263: 1
      1268: q
      1271: q
      1272: q^2
      1274: q^2
      1277: q
      1281: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1305: q^2
      1327: q
      1340: 1
      1366: q
      1371: q
      1374: 1
      1397: q
      1402: q
      1407: 1
      1411: 1
      1427: q
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1451: q
      1452: 1
      1454: q
      1458: 1
      1461: q
      1462: q
      1467: q
      1468: q
      1472: q^2
      1476: q
      1479: q
      1483: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1577: q
      1596: q
      1624: q
      1628: q
      1640: 1
      1643: 1
      1646: 1
      1647: 1
      1651: 1
      1654: 1
      1655: 1
      1664: q
      1665: q
      1667: 1
      1670: 1
      1674: 1
      1678: 1
      1726: 1
      1734: 1
      1739: 1
      1745: 1
      1751: 1
      1763: 1
      1765: 1
      1774: 1
      1798: q
      1804: 1
      1826: 1
      1827: 1
      1830: 1
      1831: 1
      1837: 1
      1850: 1
      1861: 1
      1901: 1
      1915: 1
      1929: 1
      1934: 1
      1936: 1
      1941: 1
      1974: 1
      1981: 1
      1993: 1
      2061: 1
      2095: 1

2096:    0: 15q^4+4q^3+2q^2+q
         1: 15q^4+4q^3+2q^2+q
         2: 5q^5+10q^4+5q^3+q^2+q
         3: 15q^4+4q^3+2q^2+q
         4: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         5: 15q^4+4q^3+2q^2+q
         6: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         7: 3q^6+6q^5+6q^4+4q^3+q^2+q
         8: 5q^5+10q^4+5q^3+q^2+q
         9: 3q^6+6q^5+6q^4+4q^3+q^2+q
        10: 15q^4+4q^3+2q^2+q
        11: 15q^4+4q^3+2q^2+q
        12: 2q^6+7q^5+9q^4+3q^3+2q^2+q
        13: 10q^4+4q^3+q^2+q
        14: q^6+4q^5+6q^4+3q^3+q^2+q
        15: 10q^4+4q^3+q^2+q
        16: 15q^4+4q^3+2q^2+q
        17: 15q^4+4q^3+2q^2+q
        18: 3q^6+6q^5+6q^4+4q^3+q^2+q
        19: 8q^4+3q^3+2q^2+q
        20: 8q^4+3q^3+2q^2+q
        21: 2q^5+5q^4+4q^3+q^2+q
        22: 15q^4+4q^3+2q^2+q
        23: 15q^4+4q^3+2q^2+q
        24: 5q^5+10q^4+5q^3+q^2+q
        25: 15q^4+4q^3+2q^2+q
        26: 15q^4+4q^3+2q^2+q
        27: 5q^5+10q^4+5q^3+q^2+q
        28: 15q^4+4q^3+2q^2+q
        29: 8q^4+3q^3+2q^2+q
        30: 5q^4+3q^3+q^2+q
        31: 15q^4+4q^3+2q^2+q
        32: 10q^4+4q^3+q^2+q
        33: 15q^4+4q^3+2q^2+q
        34: 15q^4+4q^3+2q^2+q
        35: 10q^4+4q^3+q^2+q
        36: 15q^4+4q^3+2q^2+q
        37: 8q^4+2q^3+2q^2
        38: 7q^4+2q^3+q
        39: 8q^4+2q^3+2q^2
        40: 7q^4+2q^3+q
        41: 3q^5+5q^4+3q^3+q^2
        42: 2q^5+5q^4+2q^3+q
        43: 10q^4+4q^3+q^2+q
        44: q^6+4q^5+6q^4+3q^3+q^2+q
        45: 10q^4+4q^3+q^2+q
        46: 10q^4+4q^3+q^2+q
        47: 10q^4+4q^3+q^2+q
        48: q^6+4q^5+6q^4+3q^3+q^2+q
        49: 8q^4+3q^3+2q^2+q
        50: 8q^4+3q^3+2q^2+q
        51: 2q^5+5q^4+4q^3+q^2+q
        52: 8q^4+3q^3+2q^2+q
        53: 8q^4+3q^3+2q^2+q
        54: 2q^5+5q^4+4q^3+q^2+q
        55: 8q^4+3q^3+2q^2+q
        56: 8q^4+3q^3+2q^2+q
        57: 2q^5+5q^4+4q^3+q^2+q
        58: 8q^4+3q^3+q^2+q
        59: 7q^4+q^3+q^2
        60: 7q^4+q^3+q^2
        61: 8q^4+3q^3+q^2+q
        62: 8q^4+2q^3+2q^2
        63: 7q^4+2q^3+q
        64: 5q^4+2q^3+q^2
        65: 5q^4+2q^3+q
        66: 8q^4+2q^3+2q^2
        67: 7q^4+2q^3+q
        68: 5q^4+4q^3+q
        69: 5q^4+3q^3+q^2+q
        70: 5q^4+3q^3+q^2+q
        71: 8q^4+3q^3+2q^2+q
        72: 3q^4+2q^3+2q^2+q
        73: 3q^4+2q^3+2q^2+q
        74: 2q^4+q^3+2q^2
        75: q^4+q^3+q
        76: 2q^4+q^3+2q^2
        77: q^4+q^3+q
        78: q^4+2q^3+q^2
        79: q^4+q^3+q
        80: 10q^4+4q^3+q^2+q
        81: 10q^4+4q^3+q^2+q
        82: 8q^4+3q^3+2q^2+q
        83: 5q^4+3q^3+q^2+q
        84: 10q^4+4q^3+q^2+q
        85: 10q^4+4q^3+q^2+q
        86: 8q^4+3q^3+2q^2+q
        87: 5q^4+3q^3+q^2+q
        88: 10q^4+4q^3+q^2+q
        89: 10q^4+4q^3+q^2+q
        90: q^6+4q^5+6q^4+3q^3+q^2+q
        91: 3q^4+3q^3+q^2+q
        92: 4q^4+3q^3+q^2+q
        93: 3q^4+3q^3+q^2+q
        94: 8q^4+3q^3+2q^2+q
        95: 8q^4+3q^3+2q^2+q
        96: 2q^5+5q^4+4q^3+q^2+q
        97: 8q^4+3q^3+2q^2+q
        98: 8q^4+3q^3+2q^2+q
        99: 2q^5+5q^4+4q^3+q^2+q
       100: 8q^4+3q^3+2q^2+q
       101: 8q^4+3q^3+2q^2+q
       102: 2q^5+5q^4+4q^3+q^2+q
       103: 4q^4+q^3+q^2
       104: 3q^4
       105: 4q^4+2q^3+q
       106: 4q^4+q^3+q^2
       107: q^4+q^2
       108: 2q^4+2q^3+q^2+q
       109: 2q^4+2q^3+q^2+q
       110: q^4+q^2
       111: 2q^2
       112: q^3+q
       113: 2q^4+q^3+2q^2
       114: q^4+q^3+q
       115: q^4+q^3+q^2
       116: q^4+q^3+q
       117: 3q^4+3q^3+q
       118: 2q^4+q^3
       119: 2q^4+q^3
       120: 3q^4+3q^3+q
       121: 5q^4+2q^3+q^2
       122: 5q^4+2q^3+q
       123: 5q^4+2q^3+q^2
       124: 5q^4+2q^3+q
       125: 5q^4+4q^3+q
       126: 5q^4+3q^3+q^2+q
       127: 2q^4+q^3+2q^2
       128: q^4+q^3+q
       129: 2q^4+q^3+2q^2
       130: q^4+q^3+q
       131: q^4+2q^3+q^2
       132: q^4+q^3+q
       133: q^4+3q^3+q
       134: 3q^4+3q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 10q^4+4q^3+q^2+q
       138: 5q^4+3q^3+q^2+q
       139: 8q^4+3q^3+2q^2+q
       140: 3q^4+2q^3+2q^2+q
       141: 5q^4+3q^3+q^2+q
       142: 3q^4+2q^3+2q^2+q
       143: 10q^4+4q^3+q^2+q
       144: 5q^4+3q^3+q^2+q
       145: 8q^4+3q^3+2q^2+q
       146: 5q^4+3q^3+q^2+q
       147: 3q^4+2q^3+2q^2+q
       148: 3q^4+2q^3+2q^2+q
       149: 8q^4+3q^3+2q^2+q
       150: 5q^4+3q^3+q^2+q
       151: 2q^4+q^3+2q^2
       152: q^4+q^3+q
       153: 2q^4+q^3+2q^2
       154: q^4+q^3+q
       155: q^4+2q^3+q^2
       156: q^4+q^3+q
       157: 3q^4+3q^3+q^2+q
       158: 4q^4+3q^3+q^2+q
       159: 3q^4+3q^3+q^2+q
       160: 3q^4+3q^3+q^2+q
       161: 4q^4+3q^3+q^2+q
       162: 3q^4+3q^3+q^2+q
       163: 3q^4+3q^3+q^2+q
       164: 4q^4+3q^3+q^2+q
       165: 3q^4+3q^3+q^2+q
       166: 8q^4+3q^3+2q^2+q
       167: 8q^4+3q^3+2q^2+q
       168: 2q^5+5q^4+4q^3+q^2+q
       169: q^2
       171: q^3+q
       172: q^2
       173: q^4+q^3
       174: q^4
       175: 2q^4+2q^3+q
       176: q^4+q^3
       177: q^4+q^3+q^2
       178: q^4+q^3+q
       179: 2q^4+q^3+2q^2
       180: q^4+q^3+q
       181: 2q^2
       182: q^3+q
       184: 2q^3+q
       185: 2q^3+q
       187: q^2
       188: q^3+q
       189: q^4+q^3+q^2
       190: q^4+q^3+q
       191: 3q^4+3q^3+q
       192: 2q^4+q^3
       193: q^4+q^2
       194: 2q^4+2q^3+q^2+q
       195: 2q^4+2q^3+q^2+q
       196: q^4+q^2
       197: 2q^2
       198: q^3+q
       199: 2q^4+q^3
       200: 3q^4+3q^3+q
       201: q^4+q^2
       202: 2q^4+2q^3+q^2+q
       203: 2q^4+2q^3+q^2+q
       204: q^4+q^2
       205: 2q^2
       206: q^3+q
       207: 5q^4+2q^3+q^2
       208: 5q^4+2q^3+q
       209: 2q^4+q^3+2q^2
       210: q^4+q^3+q
       211: q^4+q^3+q^2
       212: q^4+q^3+q
       213: q^3+q^2
       215: q^4+q^3+q^2
       217: q^3+q^2
       219: q^4+3q^3+q
       220: q^4+3q^3+q
       221: 3q^4+3q^3+q^2+q
       222: q^4+2q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: q^4+2q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 5q^4+3q^3+q^2+q
       227: q^4+3q^3+q
       228: 3q^4+3q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: q^4+2q^3+q^2+q
       231: 5q^4+3q^3+q^2+q
       232: q^4+3q^3+q
       233: 3q^4+3q^3+q^2+q
       234: q^4+2q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: 5q^4+3q^3+q^2+q
       237: 2q^4+q^3+2q^2
       238: q^4+q^3+q
       239: 2q^4+q^3+2q^2
       240: q^4+q^3+q
       241: q^4+2q^3+q^2
       242: q^4+q^3+q
       243: 8q^4+3q^3+2q^2+q
       244: 3q^4+2q^3+2q^2+q
       245: 3q^4+2q^3+2q^2+q
       246: 5q^4+3q^3+q^2+q
       247: q^3+3q^2+q
       248: q^3+3q^2+q
       249: 2q^4+2q^3+q^2+q
       250: 3q^4+3q^3+q^2+q
       251: 4q^4+3q^3+q^2+q
       252: 3q^4+3q^3+q^2+q
       253: 3q^4+3q^3+q^2+q
       254: 4q^4+3q^3+q^2+q
       255: 3q^4+3q^3+q^2+q
       256: 3q^4+3q^3+q^2+q
       257: 4q^4+3q^3+q^2+q
       258: 3q^4+3q^3+q^2+q
       259: q^2
       261: q^3+q
       262: q^2
       265: q^3+q
       267: q^2
       269: q^2
       270: q^3+q
       271: q^2
       272: q^3+q
       273: q^2
       275: q^4+q^3
       276: q^4
       277: 2q^4+2q^3+q
       278: q^4+q^3
       279: q^3
       281: q^3+q^2
       284: 2q^3+q
       285: 2q^3+q
       287: q^4+q^3+q^2
       288: q^4+q^3+q
       289: q^2
       291: q^2
       292: q^3+q
       294: 2q^3+q
       295: 2q^3+q
       297: q^2
       298: q^3+q
       300: 2q^3+q
       301: 2q^2
       302: q^3+q
       303: 2q^3+q
       305: q^2
       306: q^3+q
       308: 2q^3+q
       309: 2q^3+q
       311: 2q^2
       312: q^3+q
       313: q^2
       314: q^3+q
       315: q^4+q^3+q^2
       316: q^4+q^3+q
       317: 2q^4+q^3+2q^2
       318: q^4+q^3+q
       319: q^4+q^2
       320: 2q^4+2q^3+q^2+q
       321: 2q^4+2q^3+q^2+q
       322: q^4+q^2
       323: 2q^2
       324: q^3+q
       325: q^4+q^3+q^2
       326: q^4+q^3+q
       327: q^3+q^2
       329: q^4+q^3+q^2
       331: q^3+q^2
       333: q^4+3q^3+q
       334: q^4+2q^3+q^2+q
       335: q^4+2q^3+q^2+q
       336: q^2+q
       337: q^3+3q^2+q
       338: q^3+3q^2
       339: q
       340: q^3+3q^2
       341: q
       342: q^4+2q^3+q^2
       343: q^4+q
       344: q^4+3q^3+q
       345: q^4+3q^3+q
       346: 3q^4+3q^3+q^2+q
       347: q^4+2q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: q^4+2q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: q^3+3q^2+q
       352: q^4+3q^3+q
       353: q^4+3q^3+q
       354: 3q^4+3q^3+q^2+q
       355: q^4+2q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: q^4+2q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^3+3q^2+q
       360: q^3+q^2
       362: q^4+q^3+q^2
       364: q^3+q^2
       366: 5q^4+3q^3+q^2+q
       367: q^4+3q^3+q
       368: 3q^4+3q^3+q^2+q
       369: q^4+2q^3+q^2+q
       370: q^4+2q^3+q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^4+q^3+q^2+q
       374: 3q^4+3q^3+q^2+q
       375: 4q^4+3q^3+q^2+q
       376: 3q^4+3q^3+q^2+q
       379: q^3+q
       387: q^3+q
       389: q^2
       391: q^2
       392: q^3+q
       395: q^3+q
       397: q^2
       398: q^3+q
       399: q^2
       402: q^3+q
       405: q^2
       406: q^2
       408: q^3+q
       409: q^3
       411: q^3+q^2
       413: q^3
       415: q^2
       417: q^2
       420: 2q^3+q
       421: 2q^3+q
       423: q^2
       424: q^3+q
       425: q^2
       426: q
       427: q^3+3q^2
       428: q
       430: 2q^3+q
       431: 2q^3+q
       433: q^2
       434: q^3+q
       435: q^2
       438: 2q^3+q
       439: 2q^3+q
       441: q^2
       442: q^3+q
       443: q^2
       444: q^3+2q^2+q
       445: q^3+3q^2
       446: q
       448: 2q^3+q
       449: 2q^3+q
       451: q^2
       452: q^3+q
       454: 2q^3+q
       455: q^2
       457: 2q^3+q
       459: q^2
       460: q^3+q
       461: q^3+2q^2+q
       462: q^2
       463: q^3+3q^2
       464: q
       465: q^3
       467: q^3+q^2
       469: q^4+q^3+q^2
       470: q^4+q^3+q
       472: 2q^3+q
       473: 2q^3+q
       475: q^2
       476: q^3+q
       477: 2q^2
       478: q^3+q
       479: 2q^2
       480: q^3+q^2+q
       481: q^3+q
       482: q^3+q
       483: q^2+q
       484: q^2+q
       485: 2q^2
       487: 2q^2
       489: q^3+q^2
       491: q^2+q
       492: q^4+3q^3+q
       493: q^4+2q^3+q^2+q
       494: q^4+2q^3+q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^4+3q^3+q
       498: q^4+2q^3+q^2+q
       499: q^4+2q^3+q^2+q
       500: q^2+q
       501: 2q^2+q
       502: q^3+q^2
       504: q^4+q^3+q^2
       506: q^3+q^2
       508: q^4+3q^3+q
       509: q^4+3q^3+q
       510: 3q^4+3q^3+q^2+q
       511: q^4+2q^3+q^2+q
       512: q^4+2q^3+q^2+q
       513: q^4+2q^3+q^2+q
       514: q^4+2q^3+q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^4+q^3+q^2+q
       518: 2q^2+q
       519: 2q^2+q
       520: q^4+q^3+q^2+q
       531: q^3+q
       535: q^3+q
       544: q^3+q
       545: q^2
       547: q^3+2q^2
       548: q
       550: q^3+q
       558: q^3+q
       561: q^3+2q^2
       562: q
       563: q^2
       567: q^3+q
       569: q^2
       570: q^2
       572: q^3+q
       573: q^2
       575: q^2
       576: q^3+q^2+q
       577: 2q^2
       580: q^3+q^2
       581: q
       583: q^3
       587: q^2
       590: q^3+q
       591: q
       594: q
       595: q^3+q
       597: q^2
       599: q^2
       600: q
       601: q^2
       604: 2q^3+q
       605: q^2
       607: 2q^3+q
       609: q^2
       610: q^3+q
       611: q^2
       613: q^2
       614: q
       616: q^2+q
       617: 2q^2
       620: 2q^3+q
       621: 2q^3+q
       623: q^2
       625: q^2
       626: q^3+q
       627: q^2
       629: q^2
       630: q
       631: q^2+q
       633: 2q^2
       635: q^3
       637: q^3+q^2
       639: q^3
       642: 2q^3+q
       643: 2q^3+q
       645: q^2
       646: q^3+q
       648: 2q^3+q
       649: 2q^3+q
       651: q^2
       653: q^2
       654: q^3+q
       655: q^2
       656: q^2+q
       657: q^2+q
       658: 2q^2
       660: 2q^2
       662: q^3+q^2
       664: q^2+q
       665: q
       666: 2q^2
       668: 2q^2
       670: q^3+q^2
       672: q^2+q
       673: q^2+q
       674: 2q^2+q
       675: q^3+q
       676: q^3+q
       677: q^2+q
       678: 2q^2+q
       679: q^2+q
       680: 2q^2+q
       681: q^3+q
       682: q^3+q
       683: q^2+q
       684: 2q^2+q
       685: q^2+q
       686: q^4+3q^3+q
       687: q^4+2q^3+q^2+q
       688: q^4+2q^3+q^2+q
       689: q^2+q
       690: 2q^2+q
       691: 2q^2+q
       692: q^4+q^3+q^2+q
       693: q^2
       697: q^2
       698: q^3+q^2
       700: q
       714: q
       719: q
       728: q^3+q
       735: q^2
       742: q^3+q
       749: q^2
       755: q^3+q
       764: q^3+q
       767: q^2+q
       769: q^2
       772: q^2
       775: q^2
       779: q^2
       783: q^2
       786: q
       787: q
       789: q^2
       792: q
       794: q^2+q
       795: 2q^2
       799: q^2
       802: q^3+q
       803: q
       806: q
       807: q^3+q
       809: q^2
       811: q^2
       812: q
       813: 2q^2
       816: q^2+q
       817: q^2+q
       819: 2q^2
       823: q^2
       826: q^3+q
       827: q
       830: q
       831: q^3+q
       833: q^2
       835: q^2
       836: q
       837: 2q^2
       839: q^2+q
       841: q^3
       843: q^2
       844: q^2+q
       846: 2q^3+q
       847: 2q^3+q
       849: q^2
       851: q^2
       852: q^3+q
       853: q^2
       855: q^2
       856: q
       857: q^2
       858: q^2+q
       859: 2q^2
       861: 2q^2
       863: q^3+q^2
       865: q^2+q
       866: q
       867: q^2+q
       868: q
       869: 2q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: 2q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q^3+q
       878: q^3+q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: q^3+1
       888: q^2
       910: q
       918: q^2
       925: q
       931: q
       934: q^2
       940: q^2
       949: q
       954: q
       956: q^2
       966: q^2+q
       968: q^2
       971: q^2
       977: q^3+q
       982: q^2
       985: q^2
       990: q^2+q
       992: q^2
       996: q^2
       998: q
      1001: q
      1005: q
      1006: q
      1009: q
      1013: q
      1014: 2q^2
      1017: q^2+q
      1020: q^2
      1024: q^2
      1027: q
      1028: q
      1030: 2q^2
      1032: q^2+q
      1036: q^2
      1041: q
      1042: q^2
      1044: q
      1046: q^2
      1047: q^2+q
      1050: q^2
      1053: q^3+q
      1054: q
      1057: q
      1058: q^3+q
      1060: q^2
      1062: q^2
      1063: q
      1065: q
      1066: 1
      1068: 1
      1070: q^3+1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1090: q^2
      1103: q^2
      1132: q
      1137: q
      1146: q^2
      1161: q
      1164: q^2
      1182: q
      1188: q^2
      1191: q^2
      1196: q^2+q
      1203: q
      1209: q
      1210: 1
      1212: 1
      1216: q
      1219: q
      1225: q
      1226: 1
      1229: 1
      1232: q
      1235: q
      1236: q^2
      1241: q
      1242: q
      1244: 1
      1246: 1
      1250: q
      1252: q^2
      1255: q
      1259: q
      1260: q
      1263: 1
      1269: q
      1270: q
      1272: q^2
      1274: q^2
      1277: q
      1281: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1306: q^2
      1328: q
      1342: 1
      1365: q
      1370: q
      1372: 1
      1398: q
      1403: q
      1407: 1
      1412: 1
      1428: q
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1450: q
      1452: 1
      1455: q
      1458: 1
      1460: q
      1463: q
      1466: q
      1469: q
      1472: q^2
      1477: q
      1478: q
      1483: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1576: q
      1597: q
      1625: q
      1629: q
      1640: 1
      1643: 1
      1645: 1
      1648: 1
      1651: 1
      1653: 1
      1656: 1
      1663: q
      1666: q
      1667: 1
      1670: 1
      1674: 1
      1679: 1
      1726: 1
      1735: 1
      1737: 1
      1747: 1
      1750: 1
      1761: 1
      1767: 1
      1775: 1
      1799: q
      1804: 1
      1826: 1
      1827: 1
      1829: 1
      1832: 1
      1838: 1
      1849: 1
      1862: 1
      1899: 1
      1917: 1
      1929: 1
      1932: 1
      1938: 1
      1942: 1
      1969: 1
      1986: 1
      1994: 1
      2062: 1
      2096: 1

2097:    0: 2q^3+q^2+1
         1: 2q^3+q^2+1
         2: 2q^3+q^2+1
         3: 2q^3+q^2+1
         4: q^5+q^4+q^3+q^2+1
         5: 2q^3+q^2+1
         6: q^5+q^4+q^3+q^2+1
         7: q^5+q^4+q^3+q^2+1
         8: 2q^3+q^2+1
         9: q^5+q^4+q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: q^5+q^4+q^3+q^2+1
        13: 2q^3+q^2+1
        14: q^5+q^4+q^3+q^2+1
        15: 2q^3+q^2+1
        16: 2q^3+q^2+1
        17: 2q^3+q^2+1
        18: q^5+q^4+q^3+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^3+q^2+1
        22: 2q^3+q^2+1
        23: 2q^3+q^2+1
        24: 2q^3+q^2+1
        25: 2q^3+q^2+1
        26: 2q^3+q^2+1
        27: 2q^3+q^2+1
        28: 2q^3+q^2+1
        29: q^3+q^2+1
        30: q^3+q^2+1
        31: 2q^3+q^2+1
        32: 2q^3+q^2+1
        33: 2q^3+q^2+1
        34: 2q^3+q^2+1
        35: 2q^3+q^2+1
        36: 2q^3+q^2+1
        37: 2q^3+q^2+1
        39: 2q^3+q^2+1
        41: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: q^5+q^4+q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^3+q^2+1
        47: 2q^3+q^2+1
        48: q^5+q^4+q^3+q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^3+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^3+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^3+q^2+1
        58: q^3
        59: q^3+q^2+1
        60: q^3
        61: q^3+q^2+1
        62: 2q^3+q^2+1
        64: 2q^3+q^2+1
        66: 2q^3+q^2+1
        68: 2q^3+q^2+1
        69: q^3+q^2+1
        70: q^3+q^2+1
        71: q^3+q^2+1
        72: q^2+1
        73: q^2+1
        74: q^3+q^2+1
        76: q^3+q^2+1
        78: q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^3+q^2+1
        82: q^3+q^2+1
        83: q^3+q^2+1
        84: 2q^3+q^2+1
        85: 2q^3+q^2+1
        86: q^3+q^2+1
        87: q^3+q^2+1
        88: 2q^3+q^2+1
        89: 2q^3+q^2+1
        90: q^5+q^4+q^3+q^2+1
        91: q^3+q^2+1
        92: q^3+q^2+1
        93: q^3+q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^3+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^3+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^3+q^2+1
       103: q^3
       106: q^3+q^2+1
       108: q^2+1
       110: q^2+1
       111: q^2+1
       113: q^3+q^2+1
       115: q^3+q^2+1
       117: q^3
       118: q^3+q^2+1
       119: q^3
       120: q^3+q^2+1
       121: 2q^3+q^2+1
       123: 2q^3+q^2+1
       125: 2q^3+q^2+1
       126: q^3+q^2+1
       127: q^3+q^2+1
       129: q^3+q^2+1
       131: q^3+q^2+1
       133: q^3+q^2+1
       134: q^3+q^2+1
       135: q^2+1
       136: q^2+1
       137: 2q^3+q^2+1
       138: q^3+q^2+1
       139: q^3+q^2+1
       140: q^2+1
       141: q^3+q^2+1
       142: q^2+1
       143: 2q^3+q^2+1
       144: q^3+q^2+1
       145: q^3+q^2+1
       146: q^3+q^2+1
       147: q^2+1
       148: q^2+1
       149: q^3+q^2+1
       150: q^3+q^2+1
       151: q^3+q^2+1
       153: q^3+q^2+1
       155: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: q^3+q^2+1
       161: q^3+q^2+1
       162: q^3+q^2+1
       163: q^3+q^2+1
       164: q^3+q^2+1
       165: q^3+q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^3+q^2+1
       172: q^2+1
       173: q^3
       176: q^3+q^2+1
       177: q^3+q^2+1
       179: q^3+q^2+1
       181: q^2+1
       184: q^2+1
       186: q^2+1
       187: q^2+1
       189: q^3+q^2+1
       191: q^3
       192: q^3+q^2+1
       194: q^2+1
       196: q^2+1
       197: q^2+1
       199: q^3
       200: q^3+q^2+1
       202: q^2+1
       204: q^2+1
       205: q^2+1
       207: 2q^3+q^2+1
       209: q^3+q^2+1
       211: q^3+q^2+1
       213: q^3+q^2+1
       215: q^3+q^2+1
       217: q^3+q^2+1
       219: q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: q^3+q^2+1
       227: q^3+q^2+1
       228: q^3+q^2+1
       229: q^2+1
       230: q^2+1
       231: q^3+q^2+1
       232: q^3+q^2+1
       233: q^3+q^2+1
       234: q^2+1
       235: q^2+1
       236: q^3+q^2+1
       237: q^3+q^2+1
       239: q^3+q^2+1
       241: q^3+q^2+1
       243: q^3+q^2+1
       244: q^2+1
       245: q^2+1
       246: q^3+q^2+1
       247: 1
       248: 1
       249: q^3+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: q^3+q^2+1
       257: q^3+q^2+1
       258: q^3+q^2+1
       262: q^2+1
       266: q^2+1
       269: q^2+1
       273: q^2+1
       275: q^3
       278: q^3+q^2+1
       279: q^3+q^2+1
       281: q^3+q^2+1
       284: q^2+1
       286: q^2+1
       287: q^3+q^2+1
       289: q^2+1
       291: q^2+1
       294: q^2+1
       296: q^2+1
       297: q^2+1
       300: q^2+1
       301: q^2+1
       304: q^2+1
       305: q^2+1
       308: q^2+1
       310: q^2+1
       311: q^2+1
       313: q^2+1
       315: q^3+q^2+1
       317: q^3+q^2+1
       320: q^2+1
       322: q^2+1
       323: q^2+1
       325: q^3+q^2+1
       327: q^3+q^2+1
       329: q^3+q^2+1
       331: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^3+1
       344: q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       352: q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^2+1
       357: q^2+1
       358: q^2+1
       359: 1
       360: q^3+q^2+1
       362: q^3+q^2+1
       364: q^3+q^2+1
       366: q^3+q^2+1
       367: q^3+q^2+1
       368: q^3+q^2+1
       369: q^2+1
       370: q^2+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       380: q^2+1
       384: q^2+1
       388: q^2+1
       391: q^2+1
       396: q^2+1
       399: q^2+1
       404: q^2+1
       406: q^2+1
       409: q^3+q^2+1
       411: q^3+q^2+1
       413: q^3+q^2+1
       415: q^2+1
       417: q^2+1
       420: q^2+1
       422: q^2+1
       423: q^2+1
       425: 1
       427: 1
       430: q^2+1
       432: q^2+1
       433: q^2+1
       435: q^2+1
       438: q^2+1
       440: q^2+1
       441: q^2+1
       444: 1
       445: 1
       448: q^2+1
       450: q^2+1
       451: q^2+1
       454: q^2+1
       455: q^2+1
       458: q^2+1
       459: q^2+1
       462: 1
       463: 1
       465: q^3+q^2+1
       467: q^3+q^2+1
       469: q^3+q^2+1
       472: q^2+1
       474: q^2+1
       475: q^2+1
       477: q^2+1
       479: 1
       481: q^2+1
       482: q^2+1
       483: 1
       484: 1
       485: 1
       487: 1
       489: q^3+1
       491: 1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: 1
       496: 1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: 1
       501: 1
       502: q^3+q^2+1
       504: q^3+q^2+1
       506: q^3+q^2+1
       508: q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: q^2+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       524: q^2+1
       528: q^2+1
       532: q^2+1
       536: q^2+1
       539: q^2+1
       543: q^2+1
       547: 1
       552: q^2+1
       555: q^2+1
       559: q^2+1
       563: 1
       568: q^2+1
       570: q^2+1
       575: 1
       577: 1
       583: q^3+q^2+1
       585: q^2+1
       587: q^2+1
       590: q^2+1
       592: 1
       594: 1
       596: q^2+1
       597: 1
       599: 1
       601: 1
       604: q^2+1
       605: q^2+1
       608: q^2+1
       609: q^2+1
       611: q^2+1
       613: 1
       616: 1
       617: 1
       620: q^2+1
       622: q^2+1
       623: q^2+1
       625: q^2+1
       627: q^2+1
       629: 1
       632: 1
       633: 1
       635: q^3+q^2+1
       637: q^3+q^2+1
       639: q^3+q^2+1
       642: q^2+1
       644: q^2+1
       645: q^2+1
       648: q^2+1
       650: q^2+1
       651: q^2+1
       653: q^2+1
       655: 1
       657: 1
       658: 1
       660: 1
       662: q^3+1
       664: 1
       665: 1
       666: 1
       668: 1
       670: q^3+1
       672: 1
       673: 1
       674: 1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: 1
       690: 1
       691: 1
       692: q^3+1
       697: 1
       708: q^2+1
       712: q^2+1
       716: 1
       720: 1
       723: q^2+1
       727: q^2+1
       731: q^2+1
       735: 1
       739: q^2+1
       743: q^2+1
       747: q^2+1
       751: 1
       756: q^2+1
       758: q^2+1
       762: q^2+1
       768: 1
       769: 1
       775: 1
       777: q^2+1
       779: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       797: q^2+1
       799: q^2+1
       802: q^2+1
       804: 1
       806: 1
       808: q^2+1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: 1
       821: q^2+1
       823: q^2+1
       826: q^2+1
       828: 1
       830: 1
       832: q^2+1
       833: 1
       835: 1
       837: 1
       840: 1
       841: q^3+q^2+1
       843: 1
       846: q^2+1
       848: q^2+1
       849: q^2+1
       851: q^2+1
       853: q^2+1
       855: 1
       857: 1
       859: 1
       861: 1
       863: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: q^3+1
       889: 1
       899: q^2+1
       902: 1
       906: 1
       911: 1
       914: q^2+1
       918: 1
       922: q^2+1
       927: 1
       930: 1
       934: 1
       938: q^2+1
       942: 1
       946: q^2+1
       950: 1
       955: 1
       958: 1
       961: q^2+1
       967: 1
       968: 1
       975: q^2+1
       979: q^2+1
       982: 1
       991: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: q^2+1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: q^2+1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1045: 1
      1046: 1
      1048: q^2+1
      1050: q^2+1
      1053: q^2+1
      1055: 1
      1057: 1
      1059: q^2+1
      1060: 1
      1062: 1
      1064: 1
      1066: 1
      1068: 1
      1070: q^3+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: q^2+1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1170: q^2+1
      1174: 1
      1178: 1
      1183: 1
      1185: q^2+1
      1188: 1
      1197: 1
      1199: q^2+1
      1204: 1
      1208: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1243: 1
      1244: 1
      1247: 1
      1248: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1262: 1
      1264: q^2+1
      1266: 1
      1269: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: 1
      1413: 1
      1415: q^2+1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1436: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1451: 1
      1452: 1
      1455: 1
      1456: 1
      1458: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1479: 1
      1480: 1
      1482: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1494: 1
      1506: 1
      1518: 1
      1530: 1
      1538: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1637: 1
      1639: 1
      1643: 1
      1646: 1
      1648: 1
      1651: 1
      1654: 1
      1656: 1
      1659: 1
      1661: 1
      1664: 1
      1666: 1
      1667: 1
      1669: 1
      1671: 1
      1674: 1
      1680: 1
      1692: 1
      1704: 1
      1718: 1
      1723: 1
      1730: 1
      1736: 1
      1739: 1
      1742: 1
      1747: 1
      1752: 1
      1754: 1
      1763: 1
      1767: 1
      1770: 1
      1776: 1
      1778: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1801: 1
      1808: 1
      1823: 1
      1825: 1
      1827: 1
      1830: 1
      1832: 1
      1839: 1
      1851: 1
      1863: 1
      1877: 1
      1895: 1
      1900: 1
      1911: 1
      1916: 1
      1926: 1
      1934: 1
      1938: 1
      1943: 1
      1945: 1
      1949: 1
      1970: 1
      1982: 1
      1997: 1
      2057: 1
      2063: 1
      2097: 1

2098:    0: 2q^3+q^2+1
         1: 2q^3+q^2+1
         2: 2q^3+q^2+1
         3: 2q^3+q^2+1
         4: q^5+q^4+q^3+q^2+1
         5: 2q^3+q^2+1
         6: q^5+q^4+q^3+q^2+1
         7: q^5+q^4+q^3+q^2+1
         8: 2q^3+q^2+1
         9: q^5+q^4+q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: q^5+q^4+q^3+q^2+1
        13: 2q^3+q^2+1
        14: q^5+q^4+q^3+q^2+1
        15: 2q^3+q^2+1
        16: 2q^3+q^2+1
        17: 2q^3+q^2+1
        18: q^5+q^4+q^3+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^3+q^2+1
        22: 2q^3+q^2+1
        23: 2q^3+q^2+1
        24: 2q^3+q^2+1
        25: 2q^3+q^2+1
        26: 2q^3+q^2+1
        27: 2q^3+q^2+1
        28: 2q^3+q^2+1
        29: q^3+q^2+1
        30: q^3+q^2+1
        31: 2q^3+q^2+1
        32: 2q^3+q^2+1
        33: 2q^3+q^2+1
        34: 2q^3+q^2+1
        35: 2q^3+q^2+1
        36: 2q^3+q^2+1
        38: 2q^3+q^2+1
        40: 2q^3+q^2+1
        42: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: q^5+q^4+q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^3+q^2+1
        47: 2q^3+q^2+1
        48: q^5+q^4+q^3+q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^3+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^3+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^3+q^2+1
        58: q^3
        59: q^3+q^2+1
        60: q^3+q^2+1
        61: q^3
        63: 2q^3+q^2+1
        65: 2q^3+q^2+1
        67: 2q^3+q^2+1
        68: 2q^3+q^2+1
        69: q^3+q^2+1
        70: q^3+q^2+1
        71: q^3+q^2+1
        72: q^2+1
        73: q^2+1
        75: q^3+q^2+1
        77: q^3+q^2+1
        79: q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^3+q^2+1
        82: q^3+q^2+1
        83: q^3+q^2+1
        84: 2q^3+q^2+1
        85: 2q^3+q^2+1
        86: q^3+q^2+1
        87: q^3+q^2+1
        88: 2q^3+q^2+1
        89: 2q^3+q^2+1
        90: q^5+q^4+q^3+q^2+1
        91: q^3+q^2+1
        92: q^3+q^2+1
        93: q^3+q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^3+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^3+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^3+q^2+1
       104: q^3+q^2+1
       105: q^3
       107: q^2+1
       110: q^2+1
       112: q^2+1
       114: q^3+q^2+1
       116: q^3+q^2+1
       117: q^3
       118: q^3+q^2+1
       119: q^3+q^2+1
       120: q^3
       122: 2q^3+q^2+1
       124: 2q^3+q^2+1
       125: 2q^3+q^2+1
       126: q^3+q^2+1
       128: q^3+q^2+1
       130: q^3+q^2+1
       132: q^3+q^2+1
       133: q^3+q^2+1
       134: q^3+q^2+1
       135: q^2+1
       136: q^2+1
       137: 2q^3+q^2+1
       138: q^3+q^2+1
       139: q^3+q^2+1
       140: q^2+1
       141: q^3+q^2+1
       142: q^2+1
       143: 2q^3+q^2+1
       144: q^3+q^2+1
       145: q^3+q^2+1
       146: q^3+q^2+1
       147: q^2+1
       148: q^2+1
       149: q^3+q^2+1
       150: q^3+q^2+1
       152: q^3+q^2+1
       154: q^3+q^2+1
       156: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: q^3+q^2+1
       161: q^3+q^2+1
       162: q^3+q^2+1
       163: q^3+q^2+1
       164: q^3+q^2+1
       165: q^3+q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^3+q^2+1
       170: q^2+1
       174: q^3+q^2+1
       175: q^3
       178: q^3+q^2+1
       180: q^3+q^2+1
       182: q^2+1
       183: q^2+1
       186: q^2+1
       188: q^2+1
       190: q^3+q^2+1
       191: q^3
       192: q^3+q^2+1
       193: q^2+1
       196: q^2+1
       198: q^2+1
       199: q^3+q^2+1
       200: q^3
       201: q^2+1
       204: q^2+1
       206: q^2+1
       208: 2q^3+q^2+1
       210: q^3+q^2+1
       212: q^3+q^2+1
       214: q^3+q^2+1
       216: q^3+q^2+1
       218: q^3+q^2+1
       219: q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: q^3+q^2+1
       227: q^3+q^2+1
       228: q^3+q^2+1
       229: q^2+1
       230: q^2+1
       231: q^3+q^2+1
       232: q^3+q^2+1
       233: q^3+q^2+1
       234: q^2+1
       235: q^2+1
       236: q^3+q^2+1
       238: q^3+q^2+1
       240: q^3+q^2+1
       242: q^3+q^2+1
       243: q^3+q^2+1
       244: q^2+1
       245: q^2+1
       246: q^3+q^2+1
       247: 1
       248: 1
       249: q^3+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: q^3+q^2+1
       257: q^3+q^2+1
       258: q^3+q^2+1
       260: q^2+1
       264: q^2+1
       268: q^2+1
       274: q^2+1
       276: q^3+q^2+1
       277: q^3
       280: q^3+q^2+1
       282: q^3+q^2+1
       283: q^2+1
       286: q^2+1
       288: q^3+q^2+1
       290: q^2+1
       292: q^2+1
       293: q^2+1
       296: q^2+1
       298: q^2+1
       299: q^2+1
       302: q^2+1
       304: q^2+1
       306: q^2+1
       307: q^2+1
       310: q^2+1
       312: q^2+1
       314: q^2+1
       316: q^3+q^2+1
       318: q^3+q^2+1
       319: q^2+1
       322: q^2+1
       324: q^2+1
       326: q^3+q^2+1
       328: q^3+q^2+1
       330: q^3+q^2+1
       332: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^3+1
       344: q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       352: q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^2+1
       357: q^2+1
       358: q^2+1
       359: 1
       361: q^3+q^2+1
       363: q^3+q^2+1
       365: q^3+q^2+1
       366: q^3+q^2+1
       367: q^3+q^2+1
       368: q^3+q^2+1
       369: q^2+1
       370: q^2+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       378: q^2+1
       382: q^2+1
       386: q^2+1
       390: q^2+1
       394: q^2+1
       400: q^2+1
       403: q^2+1
       407: q^2+1
       410: q^3+q^2+1
       412: q^3+q^2+1
       414: q^3+q^2+1
       416: q^2+1
       418: q^2+1
       419: q^2+1
       422: q^2+1
       424: q^2+1
       426: 1
       428: 1
       429: q^2+1
       432: q^2+1
       434: q^2+1
       436: q^2+1
       437: q^2+1
       440: q^2+1
       442: q^2+1
       443: 1
       446: 1
       447: q^2+1
       450: q^2+1
       452: q^2+1
       453: q^2+1
       456: q^2+1
       458: q^2+1
       460: q^2+1
       462: 1
       464: 1
       466: q^3+q^2+1
       468: q^3+q^2+1
       470: q^3+q^2+1
       471: q^2+1
       474: q^2+1
       476: q^2+1
       478: q^2+1
       480: 1
       481: q^2+1
       482: q^2+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: 1
       496: 1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: 1
       501: 1
       503: q^3+q^2+1
       505: q^3+q^2+1
       507: q^3+q^2+1
       508: q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: q^2+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       522: q^2+1
       526: q^2+1
       530: q^2+1
       534: q^2+1
       538: q^2+1
       542: q^2+1
       546: 1
       551: q^2+1
       556: q^2+1
       560: q^2+1
       564: 1
       566: q^2+1
       571: q^2+1
       574: 1
       581: 1
       584: q^3+q^2+1
       586: q^2+1
       588: q^2+1
       589: q^2+1
       592: 1
       593: 1
       596: q^2+1
       598: 1
       600: 1
       602: 1
       603: q^2+1
       606: q^2+1
       608: q^2+1
       610: q^2+1
       612: q^2+1
       614: 1
       615: 1
       618: 1
       619: q^2+1
       622: q^2+1
       624: q^2+1
       626: q^2+1
       628: q^2+1
       630: 1
       632: 1
       634: 1
       636: q^3+q^2+1
       638: q^3+q^2+1
       640: q^3+q^2+1
       641: q^2+1
       644: q^2+1
       646: q^2+1
       647: q^2+1
       650: q^2+1
       652: q^2+1
       654: q^2+1
       656: 1
       657: 1
       659: 1
       661: 1
       663: q^3+1
       664: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       674: 1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: 1
       690: 1
       691: 1
       692: q^3+1
       699: 1
       706: q^2+1
       710: q^2+1
       715: 1
       718: 1
       722: q^2+1
       726: q^2+1
       730: q^2+1
       734: 1
       740: q^2+1
       744: q^2+1
       748: q^2+1
       752: 1
       754: q^2+1
       759: q^2+1
       763: q^2+1
       766: 1
       773: 1
       776: 1
       778: q^2+1
       780: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: 1
       798: q^2+1
       800: q^2+1
       801: q^2+1
       804: 1
       805: 1
       808: q^2+1
       810: 1
       812: 1
       814: 1
       815: 1
       818: 1
       820: 1
       822: q^2+1
       824: q^2+1
       825: q^2+1
       828: 1
       829: 1
       832: q^2+1
       834: 1
       836: 1
       838: 1
       840: 1
       842: q^3+q^2+1
       844: 1
       845: q^2+1
       848: q^2+1
       850: q^2+1
       852: q^2+1
       854: q^2+1
       856: 1
       858: 1
       860: 1
       862: 1
       864: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: q^3+1
       890: 1
       897: q^2+1
       903: 1
       905: 1
       909: 1
       913: q^2+1
       917: 1
       921: q^2+1
       926: 1
       929: 1
       933: 1
       939: q^2+1
       943: 1
       947: q^2+1
       951: 1
       953: 1
       959: 1
       962: q^2+1
       965: 1
       972: 1
       976: q^2+1
       980: q^2+1
       986: 1
       989: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: q^2+1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1029: 1
      1031: 1
      1033: 1
      1035: q^2+1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1045: 1
      1047: 1
      1049: q^2+1
      1051: q^2+1
      1052: q^2+1
      1055: 1
      1056: 1
      1059: q^2+1
      1061: 1
      1063: 1
      1065: 1
      1067: 1
      1069: 1
      1071: q^3+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: q^2+1
      1155: 1
      1157: 1
      1162: 1
      1167: 1
      1171: q^2+1
      1175: 1
      1177: 1
      1181: 1
      1186: q^2+1
      1192: 1
      1195: 1
      1200: q^2+1
      1205: 1
      1207: 1
      1211: 1
      1213: 1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1233: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1243: 1
      1245: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1261: 1
      1263: 1
      1265: q^2+1
      1267: 1
      1268: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1341: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1408: 1
      1411: 1
      1416: q^2+1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1437: 1
      1439: 1
      1441: 1
      1442: 1
      1445: 1
      1447: 1
      1449: 1
      1451: 1
      1453: 1
      1454: 1
      1457: 1
      1459: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1495: 1
      1508: 1
      1519: 1
      1531: 1
      1539: 1
      1544: 1
      1546: 1
      1550: 1
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1635: 1
      1638: 1
      1640: 1
      1644: 1
      1646: 1
      1647: 1
      1652: 1
      1654: 1
      1655: 1
      1660: 1
      1662: 1
      1664: 1
      1665: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1681: 1
      1694: 1
      1705: 1
      1716: 1
      1727: 1
      1731: 1
      1734: 1
      1740: 1
      1744: 1
      1746: 1
      1751: 1
      1756: 1
      1764: 1
      1766: 1
      1771: 1
      1774: 1
      1779: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1805: 1
      1809: 1
      1824: 1
      1826: 1
      1828: 1
      1830: 1
      1831: 1
      1840: 1
      1853: 1
      1864: 1
      1875: 1
      1897: 1
      1901: 1
      1912: 1
      1915: 1
      1930: 1
      1935: 1
      1937: 1
      1941: 1
      1946: 1
      1950: 1
      1976: 1
      1983: 1
      1995: 1
      2058: 1
      2061: 1
      2098: 1

2099:    0: 2q^3+q^2+1
         1: 2q^3+q^2+1
         2: 2q^3+q^2+1
         3: 2q^3+q^2+1
         4: q^5+q^4+q^3+q^2+1
         5: 2q^3+q^2+1
         6: q^5+q^4+q^3+q^2+1
         7: q^5+q^4+q^3+q^2+1
         8: 2q^3+q^2+1
         9: q^5+q^4+q^3+q^2+1
        10: 2q^3+q^2+1
        11: 2q^3+q^2+1
        12: q^5+q^4+q^3+q^2+1
        13: 2q^3+q^2+1
        14: q^5+q^4+q^3+q^2+1
        15: 2q^3+q^2+1
        16: 2q^3+q^2+1
        17: 2q^3+q^2+1
        18: q^5+q^4+q^3+q^2+1
        19: q^3+q^2+1
        20: q^3+q^2+1
        21: q^3+q^2+1
        22: 2q^3+q^2+1
        23: 2q^3+q^2+1
        24: 2q^3+q^2+1
        25: 2q^3+q^2+1
        26: 2q^3+q^2+1
        27: 2q^3+q^2+1
        28: 2q^3+q^2+1
        29: q^3+q^2+1
        30: q^3+q^2+1
        31: 2q^3+q^2+1
        32: 2q^3+q^2+1
        33: 2q^3+q^2+1
        34: 2q^3+q^2+1
        35: 2q^3+q^2+1
        36: 2q^3+q^2+1
        38: 2q^3+q^2+1
        40: 2q^3+q^2+1
        42: 2q^3+q^2+1
        43: 2q^3+q^2+1
        44: q^5+q^4+q^3+q^2+1
        45: 2q^3+q^2+1
        46: 2q^3+q^2+1
        47: 2q^3+q^2+1
        48: q^5+q^4+q^3+q^2+1
        49: q^3+q^2+1
        50: q^3+q^2+1
        51: q^3+q^2+1
        52: q^3+q^2+1
        53: q^3+q^2+1
        54: q^3+q^2+1
        55: q^3+q^2+1
        56: q^3+q^2+1
        57: q^3+q^2+1
        58: q^3+q^2+1
        59: q^3
        60: q^3
        61: q^3+q^2+1
        63: 2q^3+q^2+1
        65: 2q^3+q^2+1
        67: 2q^3+q^2+1
        68: 2q^3+q^2+1
        69: q^3+q^2+1
        70: q^3+q^2+1
        71: q^3+q^2+1
        72: q^2+1
        73: q^2+1
        75: q^3+q^2+1
        77: q^3+q^2+1
        79: q^3+q^2+1
        80: 2q^3+q^2+1
        81: 2q^3+q^2+1
        82: q^3+q^2+1
        83: q^3+q^2+1
        84: 2q^3+q^2+1
        85: 2q^3+q^2+1
        86: q^3+q^2+1
        87: q^3+q^2+1
        88: 2q^3+q^2+1
        89: 2q^3+q^2+1
        90: q^5+q^4+q^3+q^2+1
        91: q^3+q^2+1
        92: q^3+q^2+1
        93: q^3+q^2+1
        94: q^3+q^2+1
        95: q^3+q^2+1
        96: q^3+q^2+1
        97: q^3+q^2+1
        98: q^3+q^2+1
        99: q^3+q^2+1
       100: q^3+q^2+1
       101: q^3+q^2+1
       102: q^3+q^2+1
       104: q^3
       105: q^3+q^2+1
       108: q^2+1
       109: q^2+1
       112: q^2+1
       114: q^3+q^2+1
       116: q^3+q^2+1
       117: q^3+q^2+1
       118: q^3
       119: q^3
       120: q^3+q^2+1
       122: 2q^3+q^2+1
       124: 2q^3+q^2+1
       125: 2q^3+q^2+1
       126: q^3+q^2+1
       128: q^3+q^2+1
       130: q^3+q^2+1
       132: q^3+q^2+1
       133: q^3+q^2+1
       134: q^3+q^2+1
       135: q^2+1
       136: q^2+1
       137: 2q^3+q^2+1
       138: q^3+q^2+1
       139: q^3+q^2+1
       140: q^2+1
       141: q^3+q^2+1
       142: q^2+1
       143: 2q^3+q^2+1
       144: q^3+q^2+1
       145: q^3+q^2+1
       146: q^3+q^2+1
       147: q^2+1
       148: q^2+1
       149: q^3+q^2+1
       150: q^3+q^2+1
       152: q^3+q^2+1
       154: q^3+q^2+1
       156: q^3+q^2+1
       157: q^3+q^2+1
       158: q^3+q^2+1
       159: q^3+q^2+1
       160: q^3+q^2+1
       161: q^3+q^2+1
       162: q^3+q^2+1
       163: q^3+q^2+1
       164: q^3+q^2+1
       165: q^3+q^2+1
       166: q^3+q^2+1
       167: q^3+q^2+1
       168: q^3+q^2+1
       171: q^2+1
       174: q^3
       175: q^3+q^2+1
       178: q^3+q^2+1
       180: q^3+q^2+1
       182: q^2+1
       184: q^2+1
       185: q^2+1
       188: q^2+1
       190: q^3+q^2+1
       191: q^3+q^2+1
       192: q^3
       194: q^2+1
       195: q^2+1
       198: q^2+1
       199: q^3
       200: q^3+q^2+1
       202: q^2+1
       203: q^2+1
       206: q^2+1
       208: 2q^3+q^2+1
       210: q^3+q^2+1
       212: q^3+q^2+1
       214: q^3+q^2+1
       216: q^3+q^2+1
       218: q^3+q^2+1
       219: q^3+q^2+1
       220: q^3+q^2+1
       221: q^3+q^2+1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: q^3+q^2+1
       227: q^3+q^2+1
       228: q^3+q^2+1
       229: q^2+1
       230: q^2+1
       231: q^3+q^2+1
       232: q^3+q^2+1
       233: q^3+q^2+1
       234: q^2+1
       235: q^2+1
       236: q^3+q^2+1
       238: q^3+q^2+1
       240: q^3+q^2+1
       242: q^3+q^2+1
       243: q^3+q^2+1
       244: q^2+1
       245: q^2+1
       246: q^3+q^2+1
       247: 1
       248: 1
       249: q^3+1
       250: q^3+q^2+1
       251: q^3+q^2+1
       252: q^3+q^2+1
       253: q^3+q^2+1
       254: q^3+q^2+1
       255: q^3+q^2+1
       256: q^3+q^2+1
       257: q^3+q^2+1
       258: q^3+q^2+1
       261: q^2+1
       265: q^2+1
       270: q^2+1
       272: q^2+1
       276: q^3
       277: q^3+q^2+1
       280: q^3+q^2+1
       282: q^3+q^2+1
       284: q^2+1
       285: q^2+1
       288: q^3+q^2+1
       290: q^2+1
       292: q^2+1
       294: q^2+1
       295: q^2+1
       298: q^2+1
       300: q^2+1
       302: q^2+1
       303: q^2+1
       306: q^2+1
       308: q^2+1
       309: q^2+1
       312: q^2+1
       314: q^2+1
       316: q^3+q^2+1
       318: q^3+q^2+1
       320: q^2+1
       321: q^2+1
       324: q^2+1
       326: q^3+q^2+1
       328: q^3+q^2+1
       330: q^3+q^2+1
       332: q^3+q^2+1
       333: q^3+q^2+1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^3+1
       344: q^3+q^2+1
       345: q^3+q^2+1
       346: q^3+q^2+1
       347: q^2+1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       352: q^3+q^2+1
       353: q^3+q^2+1
       354: q^3+q^2+1
       355: q^2+1
       356: q^2+1
       357: q^2+1
       358: q^2+1
       359: 1
       361: q^3+q^2+1
       363: q^3+q^2+1
       365: q^3+q^2+1
       366: q^3+q^2+1
       367: q^3+q^2+1
       368: q^3+q^2+1
       369: q^2+1
       370: q^2+1
       371: 1
       372: 1
       373: q^3+1
       374: q^3+q^2+1
       375: q^3+q^2+1
       376: q^3+q^2+1
       379: q^2+1
       383: q^2+1
       387: q^2+1
       392: q^2+1
       395: q^2+1
       398: q^2+1
       402: q^2+1
       408: q^2+1
       410: q^3+q^2+1
       412: q^3+q^2+1
       414: q^3+q^2+1
       416: q^2+1
       418: q^2+1
       420: q^2+1
       421: q^2+1
       424: q^2+1
       426: 1
       428: 1
       430: q^2+1
       431: q^2+1
       434: q^2+1
       436: q^2+1
       438: q^2+1
       439: q^2+1
       442: q^2+1
       444: 1
       446: 1
       448: q^2+1
       449: q^2+1
       452: q^2+1
       454: q^2+1
       456: q^2+1
       457: q^2+1
       460: q^2+1
       461: 1
       464: 1
       466: q^3+q^2+1
       468: q^3+q^2+1
       470: q^3+q^2+1
       472: q^2+1
       473: q^2+1
       476: q^2+1
       478: q^2+1
       480: 1
       481: q^2+1
       482: q^2+1
       483: 1
       484: 1
       486: 1
       488: 1
       490: q^3+1
       491: 1
       492: q^3+q^2+1
       493: q^2+1
       494: q^2+1
       495: 1
       496: 1
       497: q^3+q^2+1
       498: q^2+1
       499: q^2+1
       500: 1
       501: 1
       503: q^3+q^2+1
       505: q^3+q^2+1
       507: q^3+q^2+1
       508: q^3+q^2+1
       509: q^3+q^2+1
       510: q^3+q^2+1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: q^2+1
       515: 1
       516: 1
       517: q^3+1
       518: 1
       519: 1
       520: q^3+1
       523: q^2+1
       527: q^2+1
       531: q^2+1
       535: q^2+1
       540: q^2+1
       544: q^2+1
       548: 1
       550: q^2+1
       554: q^2+1
       558: q^2+1
       562: 1
       567: q^2+1
       572: q^2+1
       576: 1
       581: 1
       584: q^3+q^2+1
       586: q^2+1
       588: q^2+1
       590: q^2+1
       591: 1
       594: 1
       595: q^2+1
       598: 1
       600: 1
       602: 1
       604: q^2+1
       606: q^2+1
       607: q^2+1
       610: q^2+1
       612: q^2+1
       614: 1
       616: 1
       618: 1
       620: q^2+1
       621: q^2+1
       624: q^2+1
       626: q^2+1
       628: q^2+1
       630: 1
       631: 1
       634: 1
       636: q^3+q^2+1
       638: q^3+q^2+1
       640: q^3+q^2+1
       642: q^2+1
       643: q^2+1
       646: q^2+1
       648: q^2+1
       649: q^2+1
       652: q^2+1
       654: q^2+1
       656: 1
       657: 1
       659: 1
       661: 1
       663: q^3+1
       664: 1
       665: 1
       667: 1
       669: 1
       671: q^3+1
       672: 1
       673: 1
       674: 1
       675: q^2+1
       676: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: q^2+1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q^3+q^2+1
       687: q^2+1
       688: q^2+1
       689: 1
       690: 1
       691: 1
       692: q^3+1
       700: 1
       707: q^2+1
       711: q^2+1
       714: 1
       719: 1
       724: q^2+1
       728: q^2+1
       732: q^2+1
       736: 1
       738: q^2+1
       742: q^2+1
       746: q^2+1
       750: 1
       755: q^2+1
       760: q^2+1
       764: q^2+1
       767: 1
       773: 1
       776: 1
       778: q^2+1
       780: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: 1
       798: q^2+1
       800: q^2+1
       802: q^2+1
       803: 1
       806: 1
       807: q^2+1
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       820: 1
       822: q^2+1
       824: q^2+1
       826: q^2+1
       827: 1
       830: 1
       831: q^2+1
       834: 1
       836: 1
       838: 1
       839: 1
       842: q^3+q^2+1
       844: 1
       846: q^2+1
       847: q^2+1
       850: q^2+1
       852: q^2+1
       854: q^2+1
       856: 1
       858: 1
       860: 1
       862: 1
       864: q^3+1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q^2+1
       878: q^2+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: q^3+1
       891: 1
       898: q^2+1
       901: 1
       907: 1
       910: 1
       915: q^2+1
       919: 1
       923: q^2+1
       925: 1
       931: 1
       935: 1
       937: q^2+1
       941: 1
       945: q^2+1
       949: 1
       954: 1
       957: 1
       963: q^2+1
       966: 1
       972: 1
       977: q^2+1
       981: q^2+1
       986: 1
       990: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: q^2+1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1035: q^2+1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1044: 1
      1047: 1
      1049: q^2+1
      1051: q^2+1
      1053: q^2+1
      1054: 1
      1057: 1
      1058: q^2+1
      1061: 1
      1063: 1
      1065: 1
      1067: 1
      1069: 1
      1071: q^3+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: q^2+1
      1153: 1
      1159: 1
      1161: 1
      1165: 1
      1169: q^2+1
      1173: 1
      1179: 1
      1182: 1
      1187: q^2+1
      1192: 1
      1196: 1
      1201: q^2+1
      1203: 1
      1209: 1
      1211: 1
      1213: 1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1227: 1
      1229: 1
      1231: 1
      1232: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1260: 1
      1263: 1
      1265: q^2+1
      1267: 1
      1269: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1343: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1408: 1
      1412: 1
      1417: q^2+1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1437: 1
      1439: 1
      1440: 1
      1443: 1
      1445: 1
      1447: 1
      1449: 1
      1450: 1
      1453: 1
      1455: 1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1478: 1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1496: 1
      1507: 1
      1520: 1
      1532: 1
      1540: 1
      1542: 1
      1548: 1
      1551: 1
      1557: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1635: 1
      1638: 1
      1640: 1
      1644: 1
      1645: 1
      1648: 1
      1652: 1
      1653: 1
      1656: 1
      1660: 1
      1662: 1
      1663: 1
      1666: 1
      1668: 1
      1670: 1
      1672: 1
      1674: 1
      1682: 1
      1693: 1
      1706: 1
      1717: 1
      1727: 1
      1732: 1
      1735: 1
      1738: 1
      1743: 1
      1748: 1
      1750: 1
      1755: 1
      1762: 1
      1768: 1
      1772: 1
      1775: 1
      1780: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1805: 1
      1810: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1832: 1
      1841: 1
      1852: 1
      1865: 1
      1876: 1
      1896: 1
      1899: 1
      1913: 1
      1917: 1
      1930: 1
      1933: 1
      1939: 1
      1942: 1
      1947: 1
      1951: 1
      1971: 1
      1988: 1
      1996: 1
      2059: 1
      2062: 1
      2099: 1

2100:    0: 15q^4+4q^3+2q^2+q
         1: 15q^4+4q^3+2q^2+q
         2: 5q^5+10q^4+5q^3+q^2+q
         3: 15q^4+4q^3+2q^2+q
         4: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         5: 15q^4+4q^3+2q^2+q
         6: 2q^6+7q^5+9q^4+3q^3+2q^2+q
         7: 3q^6+6q^5+6q^4+4q^3+q^2+q
         8: 5q^5+10q^4+5q^3+q^2+q
         9: 3q^6+6q^5+6q^4+4q^3+q^2+q
        10: 15q^4+4q^3+2q^2+q
        11: 15q^4+4q^3+2q^2+q
        12: 2q^6+7q^5+9q^4+3q^3+2q^2+q
        13: 10q^4+4q^3+q^2+q
        14: q^6+4q^5+6q^4+3q^3+q^2+q
        15: 10q^4+4q^3+q^2+q
        16: 15q^4+4q^3+2q^2+q
        17: 15q^4+4q^3+2q^2+q
        18: 3q^6+6q^5+6q^4+4q^3+q^2+q
        19: 8q^4+3q^3+2q^2+q
        20: 8q^4+3q^3+2q^2+q
        21: 2q^5+5q^4+4q^3+q^2+q
        22: 15q^4+4q^3+2q^2+q
        23: 15q^4+4q^3+2q^2+q
        24: 5q^5+10q^4+5q^3+q^2+q
        25: 15q^4+4q^3+2q^2+q
        26: 15q^4+4q^3+2q^2+q
        27: 5q^5+10q^4+5q^3+q^2+q
        28: 15q^4+4q^3+2q^2+q
        29: 8q^4+3q^3+2q^2+q
        30: 5q^4+3q^3+q^2+q
        31: 15q^4+4q^3+2q^2+q
        32: 10q^4+4q^3+q^2+q
        33: 15q^4+4q^3+2q^2+q
        34: 15q^4+4q^3+2q^2+q
        35: 10q^4+4q^3+q^2+q
        36: 15q^4+4q^3+2q^2+q
        37: 7q^4+2q^3+q
        38: 8q^4+2q^3+2q^2
        39: 7q^4+2q^3+q
        40: 8q^4+2q^3+2q^2
        41: 2q^5+5q^4+2q^3+q
        42: 3q^5+5q^4+3q^3+q^2
        43: 10q^4+4q^3+q^2+q
        44: q^6+4q^5+6q^4+3q^3+q^2+q
        45: 10q^4+4q^3+q^2+q
        46: 10q^4+4q^3+q^2+q
        47: 10q^4+4q^3+q^2+q
        48: q^6+4q^5+6q^4+3q^3+q^2+q
        49: 8q^4+3q^3+2q^2+q
        50: 8q^4+3q^3+2q^2+q
        51: 2q^5+5q^4+4q^3+q^2+q
        52: 8q^4+3q^3+2q^2+q
        53: 8q^4+3q^3+2q^2+q
        54: 2q^5+5q^4+4q^3+q^2+q
        55: 8q^4+3q^3+2q^2+q
        56: 8q^4+3q^3+2q^2+q
        57: 2q^5+5q^4+4q^3+q^2+q
        58: 7q^4+q^3+q^2
        59: 8q^4+3q^3+q^2+q
        60: 7q^4+q^3+q^2
        61: 8q^4+3q^3+q^2+q
        62: 7q^4+2q^3+q
        63: 8q^4+2q^3+2q^2
        64: 5q^4+2q^3+q
        65: 5q^4+2q^3+q^2
        66: 7q^4+2q^3+q
        67: 8q^4+2q^3+2q^2
        68: 5q^4+4q^3+q
        69: 5q^4+3q^3+q^2+q
        70: 5q^4+3q^3+q^2+q
        71: 8q^4+3q^3+2q^2+q
        72: 3q^4+2q^3+2q^2+q
        73: 3q^4+2q^3+2q^2+q
        74: q^4+q^3+q
        75: 2q^4+q^3+2q^2
        76: q^4+q^3+q
        77: 2q^4+q^3+2q^2
        78: q^4+q^3+q
        79: q^4+2q^3+q^2
        80: 10q^4+4q^3+q^2+q
        81: 10q^4+4q^3+q^2+q
        82: 8q^4+3q^3+2q^2+q
        83: 5q^4+3q^3+q^2+q
        84: 10q^4+4q^3+q^2+q
        85: 10q^4+4q^3+q^2+q
        86: 8q^4+3q^3+2q^2+q
        87: 5q^4+3q^3+q^2+q
        88: 10q^4+4q^3+q^2+q
        89: 10q^4+4q^3+q^2+q
        90: q^6+4q^5+6q^4+3q^3+q^2+q
        91: 3q^4+3q^3+q^2+q
        92: 4q^4+3q^3+q^2+q
        93: 3q^4+3q^3+q^2+q
        94: 8q^4+3q^3+2q^2+q
        95: 8q^4+3q^3+2q^2+q
        96: 2q^5+5q^4+4q^3+q^2+q
        97: 8q^4+3q^3+2q^2+q
        98: 8q^4+3q^3+2q^2+q
        99: 2q^5+5q^4+4q^3+q^2+q
       100: 8q^4+3q^3+2q^2+q
       101: 8q^4+3q^3+2q^2+q
       102: 2q^5+5q^4+4q^3+q^2+q
       103: 3q^4
       104: 4q^4+q^3+q^2
       105: 4q^4+q^3+q^2
       106: 4q^4+2q^3+q
       107: q^4+q^2
       108: 2q^4+2q^3+q^2+q
       109: q^4+q^2
       110: 2q^4+2q^3+q^2+q
       111: q^3+q
       112: 2q^2
       113: q^4+q^3+q
       114: 2q^4+q^3+2q^2
       115: q^4+q^3+q
       116: q^4+q^3+q^2
       117: 2q^4+q^3
       118: 3q^4+3q^3+q
       119: 2q^4+q^3
       120: 3q^4+3q^3+q
       121: 5q^4+2q^3+q
       122: 5q^4+2q^3+q^2
       123: 5q^4+2q^3+q
       124: 5q^4+2q^3+q^2
       125: 5q^4+4q^3+q
       126: 5q^4+3q^3+q^2+q
       127: q^4+q^3+q
       128: 2q^4+q^3+2q^2
       129: q^4+q^3+q
       130: 2q^4+q^3+2q^2
       131: q^4+q^3+q
       132: q^4+2q^3+q^2
       133: q^4+3q^3+q
       134: 3q^4+3q^3+q^2+q
       135: q^4+2q^3+q^2+q
       136: q^4+2q^3+q^2+q
       137: 10q^4+4q^3+q^2+q
       138: 5q^4+3q^3+q^2+q
       139: 8q^4+3q^3+2q^2+q
       140: 3q^4+2q^3+2q^2+q
       141: 5q^4+3q^3+q^2+q
       142: 3q^4+2q^3+2q^2+q
       143: 10q^4+4q^3+q^2+q
       144: 5q^4+3q^3+q^2+q
       145: 8q^4+3q^3+2q^2+q
       146: 5q^4+3q^3+q^2+q
       147: 3q^4+2q^3+2q^2+q
       148: 3q^4+2q^3+2q^2+q
       149: 8q^4+3q^3+2q^2+q
       150: 5q^4+3q^3+q^2+q
       151: q^4+q^3+q
       152: 2q^4+q^3+2q^2
       153: q^4+q^3+q
       154: 2q^4+q^3+2q^2
       155: q^4+q^3+q
       156: q^4+2q^3+q^2
       157: 3q^4+3q^3+q^2+q
       158: 4q^4+3q^3+q^2+q
       159: 3q^4+3q^3+q^2+q
       160: 3q^4+3q^3+q^2+q
       161: 4q^4+3q^3+q^2+q
       162: 3q^4+3q^3+q^2+q
       163: 3q^4+3q^3+q^2+q
       164: 4q^4+3q^3+q^2+q
       165: 3q^4+3q^3+q^2+q
       166: 8q^4+3q^3+2q^2+q
       167: 8q^4+3q^3+2q^2+q
       168: 2q^5+5q^4+4q^3+q^2+q
       170: q^2
       171: q^2
       172: q^3+q
       173: q^4
       174: q^4+q^3
       175: q^4+q^3
       176: 2q^4+2q^3+q
       177: q^4+q^3+q
       178: q^4+q^3+q^2
       179: q^4+q^3+q
       180: 2q^4+q^3+2q^2
       181: q^3+q
       182: 2q^2
       184: 2q^3+q
       186: 2q^3+q
       187: q^3+q
       188: q^2
       189: q^4+q^3+q
       190: q^4+q^3+q^2
       191: 2q^4+q^3
       192: 3q^4+3q^3+q
       193: q^4+q^2
       194: 2q^4+2q^3+q^2+q
       195: q^4+q^2
       196: 2q^4+2q^3+q^2+q
       197: q^3+q
       198: 2q^2
       199: 2q^4+q^3
       200: 3q^4+3q^3+q
       201: q^4+q^2
       202: 2q^4+2q^3+q^2+q
       203: q^4+q^2
       204: 2q^4+2q^3+q^2+q
       205: q^3+q
       206: 2q^2
       207: 5q^4+2q^3+q
       208: 5q^4+2q^3+q^2
       209: q^4+q^3+q
       210: 2q^4+q^3+2q^2
       211: q^4+q^3+q
       212: q^4+q^3+q^2
       214: q^3+q^2
       216: q^4+q^3+q^2
       218: q^3+q^2
       219: q^4+3q^3+q
       220: q^4+3q^3+q
       221: 3q^4+3q^3+q^2+q
       222: q^4+2q^3+q^2+q
       223: q^4+2q^3+q^2+q
       224: q^4+2q^3+q^2+q
       225: q^4+2q^3+q^2+q
       226: 5q^4+3q^3+q^2+q
       227: q^4+3q^3+q
       228: 3q^4+3q^3+q^2+q
       229: q^4+2q^3+q^2+q
       230: q^4+2q^3+q^2+q
       231: 5q^4+3q^3+q^2+q
       232: q^4+3q^3+q
       233: 3q^4+3q^3+q^2+q
       234: q^4+2q^3+q^2+q
       235: q^4+2q^3+q^2+q
       236: 5q^4+3q^3+q^2+q
       237: q^4+q^3+q
       238: 2q^4+q^3+2q^2
       239: q^4+q^3+q
       240: 2q^4+q^3+2q^2
       241: q^4+q^3+q
       242: q^4+2q^3+q^2
       243: 8q^4+3q^3+2q^2+q
       244: 3q^4+2q^3+2q^2+q
       245: 3q^4+2q^3+2q^2+q
       246: 5q^4+3q^3+q^2+q
       247: q^3+3q^2+q
       248: q^3+3q^2+q
       249: 2q^4+2q^3+q^2+q
       250: 3q^4+3q^3+q^2+q
       251: 4q^4+3q^3+q^2+q
       252: 3q^4+3q^3+q^2+q
       253: 3q^4+3q^3+q^2+q
       254: 4q^4+3q^3+q^2+q
       255: 3q^4+3q^3+q^2+q
       256: 3q^4+3q^3+q^2+q
       257: 4q^4+3q^3+q^2+q
       258: 3q^4+3q^3+q^2+q
       260: q^2
       261: q^2
       262: q^3+q
       266: q^3+q
       268: q^2
       269: q^3+q
       270: q^2
       272: q^2
       273: q^3+q
       274: q^2
       275: q^4
       276: q^4+q^3
       277: q^4+q^3
       278: 2q^4+2q^3+q
       280: q^3
       282: q^3+q^2
       284: 2q^3+q
       286: 2q^3+q
       287: q^4+q^3+q
       288: q^4+q^3+q^2
       290: q^2
       291: q^3+q
       292: q^2
       294: 2q^3+q
       296: 2q^3+q
       297: q^3+q
       298: q^2
       300: 2q^3+q
       301: q^3+q
       302: 2q^2
       304: 2q^3+q
       305: q^3+q
       306: q^2
       308: 2q^3+q
       310: 2q^3+q
       311: q^3+q
       312: 2q^2
       313: q^3+q
       314: q^2
       315: q^4+q^3+q
       316: q^4+q^3+q^2
       317: q^4+q^3+q
       318: 2q^4+q^3+2q^2
       319: q^4+q^2
       320: 2q^4+2q^3+q^2+q
       321: q^4+q^2
       322: 2q^4+2q^3+q^2+q
       323: q^3+q
       324: 2q^2
       325: q^4+q^3+q
       326: q^4+q^3+q^2
       328: q^3+q^2
       330: q^4+q^3+q^2
       332: q^3+q^2
       333: q^4+3q^3+q
       334: q^4+2q^3+q^2+q
       335: q^4+2q^3+q^2+q
       336: q^2+q
       337: q^3+3q^2+q
       338: q
       339: q^3+3q^2
       340: q
       341: q^3+3q^2
       342: q^4+q
       343: q^4+2q^3+q^2
       344: q^4+3q^3+q
       345: q^4+3q^3+q
       346: 3q^4+3q^3+q^2+q
       347: q^4+2q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: q^4+2q^3+q^2+q
       350: q^4+2q^3+q^2+q
       351: q^3+3q^2+q
       352: q^4+3q^3+q
       353: q^4+3q^3+q
       354: 3q^4+3q^3+q^2+q
       355: q^4+2q^3+q^2+q
       356: q^4+2q^3+q^2+q
       357: q^4+2q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^3+3q^2+q
       361: q^3+q^2
       363: q^4+q^3+q^2
       365: q^3+q^2
       366: 5q^4+3q^3+q^2+q
       367: q^4+3q^3+q
       368: 3q^4+3q^3+q^2+q
       369: q^4+2q^3+q^2+q
       370: q^4+2q^3+q^2+q
       371: 2q^2+q
       372: 2q^2+q
       373: q^4+q^3+q^2+q
       374: 3q^4+3q^3+q^2+q
       375: 4q^4+3q^3+q^2+q
       376: 3q^4+3q^3+q^2+q
       380: q^3+q
       388: q^3+q
       390: q^2
       391: q^3+q
       392: q^2
       396: q^3+q
       398: q^2
       399: q^3+q
       400: q^2
       404: q^3+q
       406: q^3+q
       407: q^2
       408: q^2
       410: q^3
       412: q^3+q^2
       414: q^3
       416: q^2
       418: q^2
       420: 2q^3+q
       422: 2q^3+q
       423: q^3+q
       424: q^2
       425: q
       426: q^2
       427: q
       428: q^3+3q^2
       430: 2q^3+q
       432: 2q^3+q
       433: q^3+q
       434: q^2
       436: q^2
       438: 2q^3+q
       440: 2q^3+q
       441: q^3+q
       442: q^2
       443: q^2
       444: q^3+2q^2+q
       445: q
       446: q^3+3q^2
       448: 2q^3+q
       450: 2q^3+q
       451: q^3+q
       452: q^2
       454: 2q^3+q
       456: q^2
       458: 2q^3+q
       459: q^3+q
       460: q^2
       461: q^2
       462: q^3+2q^2+q
       463: q
       464: q^3+3q^2
       466: q^3
       468: q^3+q^2
       469: q^4+q^3+q
       470: q^4+q^3+q^2
       472: 2q^3+q
       474: 2q^3+q
       475: q^3+q
       476: q^2
       477: q^3+q
       478: 2q^2
       479: q^3+q^2+q
       480: 2q^2
       481: q^3+q
       482: q^3+q
       483: q^2+q
       484: q^2+q
       486: 2q^2
       488: 2q^2
       490: q^3+q^2
       491: q^2+q
       492: q^4+3q^3+q
       493: q^4+2q^3+q^2+q
       494: q^4+2q^3+q^2+q
       495: q^2+q
       496: 2q^2+q
       497: q^4+3q^3+q
       498: q^4+2q^3+q^2+q
       499: q^4+2q^3+q^2+q
       500: q^2+q
       501: 2q^2+q
       503: q^3+q^2
       505: q^4+q^3+q^2
       507: q^3+q^2
       508: q^4+3q^3+q
       509: q^4+3q^3+q
       510: 3q^4+3q^3+q^2+q
       511: q^4+2q^3+q^2+q
       512: q^4+2q^3+q^2+q
       513: q^4+2q^3+q^2+q
       514: q^4+2q^3+q^2+q
       515: 2q^2+q
       516: 2q^2+q
       517: q^4+q^3+q^2+q
       518: 2q^2+q
       519: 2q^2+q
       520: q^4+q^3+q^2+q
       532: q^3+q
       536: q^3+q
       543: q^3+q
       546: q^2
       547: q
       548: q^3+2q^2
       552: q^3+q
       559: q^3+q
       562: q^2
       563: q
       564: q^3+2q^2
       568: q^3+q
       570: q^3+q
       571: q^2
       572: q^2
       574: q^2
       575: q^3+q^2+q
       576: q^2
       577: q
       578: q^3+q^2
       581: 2q^2
       584: q^3
       588: q^2
       590: q^3+q
       592: q
       594: q
       596: q^3+q
       598: q^2
       599: q
       600: q^2
       602: q^2
       604: 2q^3+q
       606: q^2
       608: 2q^3+q
       609: q^3+q
       610: q^2
       612: q^2
       613: q
       614: q^2
       616: q^2+q
       618: 2q^2
       620: 2q^3+q
       622: 2q^3+q
       624: q^2
       625: q^3+q
       626: q^2
       628: q^2
       629: q
       630: q^2
       632: q^2+q
       634: 2q^2
       636: q^3
       638: q^3+q^2
       640: q^3
       642: 2q^3+q
       644: 2q^3+q
       645: q^3+q
       646: q^2
       648: 2q^3+q
       650: 2q^3+q
       652: q^2
       653: q^3+q
       654: q^2
       655: q^2+q
       656: q^2
       657: q^2+q
       659: 2q^2
       661: 2q^2
       663: q^3+q^2
       664: q^2+q
       665: q
       667: 2q^2
       669: 2q^2
       671: q^3+q^2
       672: q^2+q
       673: q^2+q
       674: 2q^2+q
       675: q^3+q
       676: q^3+q
       677: q^2+q
       678: 2q^2+q
       679: q^2+q
       680: 2q^2+q
       681: q^3+q
       682: q^3+q
       683: q^2+q
       684: 2q^2+q
       685: q^2+q
       686: q^4+3q^3+q
       687: q^4+2q^3+q^2+q
       688: q^4+2q^3+q^2+q
       689: q^2+q
       690: 2q^2+q
       691: 2q^2+q
       692: q^4+q^3+q^2+q
       697: q
       699: q^2
       700: q^2
       701: q^3+q^2
       716: q
       720: q
       727: q^3+q
       736: q^2
       743: q^3+q
       752: q^2
       756: q^3+q
       762: q^3+q
       768: q^2+q
       770: q^2
       773: q^2
       776: q^2
       780: q^2
       784: q^2
       786: q
       788: q
       790: q^2
       791: q
       794: q^2+q
       796: 2q^2
       800: q^2
       802: q^3+q
       804: q
       806: q
       808: q^3+q
       810: q^2
       811: q
       812: q^2
       814: 2q^2
       816: q^2+q
       818: q^2+q
       820: 2q^2
       824: q^2
       826: q^3+q
       828: q
       830: q
       832: q^3+q
       834: q^2
       835: q
       836: q^2
       838: 2q^2
       840: q^2+q
       842: q^3
       843: q^2+q
       844: q^2
       846: 2q^3+q
       848: 2q^3+q
       850: q^2
       851: q^3+q
       852: q^2
       854: q^2
       855: q
       856: q^2
       857: q^2+q
       858: q^2
       860: 2q^2
       862: 2q^2
       864: q^3+q^2
       865: q^2+q
       866: q
       867: q^2+q
       868: q
       869: 2q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: 2q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q^3+q
       878: q^3+q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: q^3+1
       892: q^2
       911: q
       919: q^2
       927: q
       930: q
       935: q^2
       943: q^2
       950: q
       955: q
       959: q^2
       967: q^2+q
       969: q^2
       972: q^2
       975: q^3+q
       983: q^2
       986: q^2
       991: q^2+q
       993: q^2
       997: q^2
       999: q
      1001: q
      1005: q
      1007: q
      1008: q
      1012: q
      1015: 2q^2
      1017: q^2+q
      1021: q^2
      1025: q^2
      1027: q
      1029: q
      1031: 2q^2
      1033: q^2+q
      1037: q^2
      1041: q
      1043: q^2
      1045: q
      1046: q^2+q
      1047: q^2
      1051: q^2
      1053: q^3+q
      1055: q
      1057: q
      1059: q^3+q
      1061: q^2
      1062: q
      1063: q^2
      1064: q
      1067: 1
      1069: 1
      1071: q^3+1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1094: q^2
      1106: q^2
      1133: q
      1135: q
      1147: q^2
      1163: q
      1167: q^2
      1183: q
      1189: q^2
      1192: q^2
      1197: q^2+q
      1204: q
      1208: q
      1211: 1
      1213: 1
      1217: q
      1219: q
      1224: q
      1227: 1
      1229: 1
      1233: q
      1235: q
      1237: q^2
      1241: q
      1243: q
      1245: 1
      1247: 1
      1251: q
      1253: q^2
      1255: q
      1259: q
      1261: q
      1262: 1
      1269: q
      1271: q
      1273: q^2
      1275: q^2
      1276: q
      1280: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1310: q^2
      1329: q
      1343: 1
      1367: q
      1369: q
      1375: 1
      1399: q
      1401: q
      1405: 1
      1413: 1
      1429: q
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1451: q
      1453: 1
      1455: q
      1459: 1
      1461: q
      1463: q
      1467: q
      1469: q
      1473: q^2
      1477: q
      1479: q
      1482: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1578: q
      1598: q
      1626: q
      1630: q
      1639: 1
      1644: 1
      1646: 1
      1648: 1
      1652: 1
      1654: 1
      1656: 1
      1664: q
      1666: q
      1668: 1
      1669: 1
      1674: 1
      1683: 1
      1724: 1
      1736: 1
      1740: 1
      1748: 1
      1752: 1
      1764: 1
      1768: 1
      1776: 1
      1800: q
      1802: 1
      1825: 1
      1828: 1
      1830: 1
      1832: 1
      1842: 1
      1854: 1
      1866: 1
      1900: 1
      1916: 1
      1927: 1
      1935: 1
      1939: 1
      1943: 1
      1972: 1
      1984: 1
      1998: 1
      2063: 1
      2100: 1

2101:    0: q^4+q
         1: q^4+q
         2: q^4+q
         3: q^4+q
         4: q^5+q^4+q
         5: q^4+q
         6: q
         7: q^5+q^4+q
         8: q^4+q
         9: q^5+q^4+q
        10: q
        11: q
        12: q
        13: q^4+q
        14: q^5+q^4+q
        15: q^4+q
        16: q^4+q
        17: q^4+q
        18: q^5+q^4+q
        19: q^4+q
        20: q
        21: q^4+q
        22: q^4+q
        23: q^4+q
        24: q^4+q
        25: q^4+q
        26: q^4+q
        27: q^4+q
        28: q
        29: q
        30: q^4+q
        31: q
        32: q^4+q
        33: q^4+q
        34: q
        35: q^4+q
        36: q^4+q
        37: q^4+q
        39: q^4+q
        41: q^4+q
        43: q
        44: q
        45: q
        46: q^4+q
        47: q^4+q
        48: q^5+q^4+q
        49: q^4+q
        50: q
        51: q^4+q
        52: q^4+q
        53: q
        54: q^4+q
        55: q^4+q
        56: q
        57: q^4+q
        59: q
        61: q
        62: q
        64: q^4+q
        66: q^4+q
        68: q
        69: q^4+q
        70: q
        71: q
        72: q
        73: q
        74: q^4+q
        76: q
        78: q^4+q
        80: q
        81: q^4+q
        82: q
        83: q^4+q
        84: q
        85: q^4+q
        86: q
        87: q^4+q
        88: q
        89: q
        90: q
        91: q^4+q
        92: q
        93: q^4+q
        94: q^4+q
        95: q
        96: q^4+q
        97: q^4+q
        98: q
        99: q^4+q
       100: q^4+q
       101: q
       102: q^4+q
       106: q
       108: q
       110: q
       111: q
       113: q
       115: q^4+q
       118: q
       120: q
       121: q
       123: q^4+q
       125: q
       126: q
       127: q^4+q
       129: q
       131: q^4+q
       133: q
       134: q^4+q
       135: q
       136: q
       137: q
       138: q^4+q
       139: q
       140: q
       141: q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q^4+q
       151: q^4+q
       153: q
       155: q^4+q
       157: q
       158: q
       159: q
       160: q^4+q
       161: q
       162: q^4+q
       163: q^4+q
       164: q
       165: q^4+q
       166: q^4+q
       167: q
       168: q^4+q
       172: q
       176: q
       177: q^4+q
       179: q
       181: q
       184: q
       186: q
       187: q
       189: q
       192: q
       194: q
       196: q
       197: q
       200: q
       202: q
       204: q
       205: q
       207: q
       209: q
       211: q^4+q
       213: q^4+q
       215: q
       217: q^4+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q^4+q
       229: q
       230: q
       231: q
       232: q
       233: q^4+q
       234: q
       235: q
       236: q^4+q
       237: q^4+q
       239: q
       241: q^4+q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q
       249: q^4+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q^4+q
       257: q
       258: q^4+q
       262: q
       266: q
       269: q
       273: q
       278: q
       279: q
       281: q^4+q
       284: q
       286: q
       287: q
       289: q
       291: q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q^4+q
       317: q
       320: q
       322: q
       323: q
       325: q
       327: q
       329: q
       331: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q^4+q
       362: q
       364: q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
       375: q
       376: q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
       409: q
       411: q
       413: q
       415: q
       417: q
       420: q
       422: q
       423: q
       425: q
       427: q
       430: q
       432: q
       433: q
       435: q
       438: q
       440: q
       441: q
       444: q
       445: q
       448: q
       450: q
       451: q
       454: q
       455: q
       458: q
       459: q
       462: q
       463: q
       465: q
       467: q^4+q
       469: q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       502: q
       504: q
       506: q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       515: q
       516: q
       517: q^4+q
       524: q
       528: q
       532: q
       536: q
       539: q
       543: q
       547: q
       552: q
       555: q
       559: q
       563: q
       568: q
       570: q
       575: q
       577: q
       583: q
       585: q
       587: q
       590: q
       592: q
       594: q
       596: q
       597: q
       599: q
       601: q
       604: q
       605: q
       608: q
       609: q
       611: q
       613: q
       616: q
       617: q
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       632: q
       633: q
       635: q
       637: q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: q
       653: q
       655: q
       657: q
       658: q
       660: q
       662: q^4+q
       664: q
       665: q
       674: q
       675: q
       676: q
       677: q
       679: q
       680: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       697: q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q
       731: q
       735: q
       739: q
       743: q
       747: q
       751: q
       756: q
       758: q
       762: q
       768: q
       769: q
       775: q
       777: q
       779: q
       781: q
       786: q
       788: q
       791: q
       794: q
       795: q
       797: q
       799: q
       802: q
       804: q
       806: q
       808: q
       809: q
       811: q
       818: q
       819: q
       821: q
       823: q
       826: q
       828: q
       830: q
       832: q
       833: q
       835: q
       841: q
       843: q
       846: q
       848: q
       849: q
       851: q
       853: q
       855: q
       866: q
       870: q
       871: q
       874: q
       875: q
       877: q
       878: q
       879: q
       880: q
       889: q
       899: q
       902: q
       906: q
       911: q
       914: q
       918: q
       922: q
       927: q
       930: q
       938: q
       942: q
       946: q
       950: q
       955: q
       961: q
       967: q
       968: q
       975: q
       979: q
       994: q
       999: q
      1001: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1027: q
      1029: q
      1034: q
      1036: q
      1038: q
      1041: q
      1045: q
      1048: q
      1050: q
      1053: q
      1055: q
      1057: q
      1059: q
      1060: q
      1062: q
      1064: q
      1076: q
      1080: q
      1083: q
      1084: q
      1091: q
      1116: q
      1124: q
      1127: q
      1133: q
      1138: q
      1150: q
      1154: q
      1158: q
      1163: q
      1170: q
      1174: q
      1178: q
      1183: q
      1185: q
      1199: q
      1204: q
      1208: q
      1222: 1
      1230: q
      1233: q
      1235: q
      1248: q
      1251: q
      1255: q
      1264: q
      1266: q
      1269: q
      1271: q
      1274: q
      1278: q
      1280: q
      1287: q
      1295: q
      1323: 1
      1336: 1
      1350: q
      1358: q
      1361: q
      1367: q
      1382: q
      1390: q
      1393: q
      1399: q
      1415: q
      1420: q
      1424: q
      1429: q
      1430: q
      1446: 1
      1464: q
      1467: q
      1469: q
      1480: 1
      1498: 1
      1506: q
      1518: q
      1555: 1
      1560: 1
      1572: 1
      1592: 1
      1609: q
      1617: q
      1622: q
      1626: q
      1633: 1
      1637: 1
      1671: 1
      1684: 1
      1696: 1
      1708: 1
      1718: q
      1725: 1
      1730: 1
      1754: 1
      1778: 1
      1796: 1
      1803: 1
      1823: 1
      1843: 1
      1855: 1
      1867: 1
      1881: 1
      1895: 1
      1911: 1
      1928: 1
      1949: 1
      1973: 1
      1985: 1
      1999: 1
      2057: 1
      2101: 1

2102:    0: q^4+q
         1: q^4+q
         2: q^4+q
         3: q^4+q
         4: q^5+q^4+q
         5: q^4+q
         6: q
         7: q^5+q^4+q
         8: q^4+q
         9: q^5+q^4+q
        10: q
        11: q
        12: q
        13: q^4+q
        14: q^5+q^4+q
        15: q^4+q
        16: q^4+q
        17: q^4+q
        18: q^5+q^4+q
        19: q^4+q
        20: q
        21: q^4+q
        22: q^4+q
        23: q^4+q
        24: q^4+q
        25: q^4+q
        26: q^4+q
        27: q^4+q
        28: q
        29: q
        30: q^4+q
        31: q
        32: q^4+q
        33: q^4+q
        34: q
        35: q^4+q
        36: q^4+q
        38: q^4+q
        40: q^4+q
        42: q^4+q
        43: q
        44: q
        45: q
        46: q^4+q
        47: q^4+q
        48: q^5+q^4+q
        49: q^4+q
        50: q
        51: q^4+q
        52: q^4+q
        53: q
        54: q^4+q
        55: q^4+q
        56: q
        57: q^4+q
        59: q
        60: q
        63: q
        65: q^4+q
        67: q^4+q
        68: q
        69: q^4+q
        70: q
        71: q
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        75: q^4+q
        77: q
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        80: q
        81: q^4+q
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        84: q
        85: q^4+q
        86: q
        87: q^4+q
        88: q
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        90: q
        91: q^4+q
        92: q
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        95: q
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        98: q
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       104: q
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       133: q
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       135: q
       136: q
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       139: q
       140: q
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       143: q
       144: q^4+q
       145: q
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       148: q
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       150: q^4+q
       152: q^4+q
       154: q
       156: q^4+q
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       160: q^4+q
       161: q
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       170: q
       174: q
       178: q^4+q
       180: q
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       204: q
       206: q
       208: q
       210: q
       212: q^4+q
       214: q^4+q
       216: q
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       219: q
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       222: q
       223: q
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       228: q^4+q
       229: q
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       234: q
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       240: q
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       243: q
       244: q
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       249: q^4+q
       250: q
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       254: q
       255: q
       256: q^4+q
       257: q
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       260: q
       264: q
       268: q
       274: q
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       282: q^4+q
       283: q
       286: q
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       302: q
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       310: q
       312: q
       314: q
       316: q^4+q
       318: q
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       322: q
       324: q
       326: q
       328: q
       330: q
       332: q
       333: q
       334: q
       335: q
       336: q
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       341: q
       343: q^4+q
       344: q
       345: q
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       352: q
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       354: q
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       361: q^4+q
       363: q
       365: q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
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       378: q
       382: q
       386: q
       390: q
       394: q
       400: q
       403: q
       407: q
       410: q
       412: q
       414: q
       416: q
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       432: q
       434: q
       436: q
       437: q
       440: q
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       450: q
       452: q
       453: q
       456: q
       458: q
       460: q
       462: q
       464: q
       466: q
       468: q^4+q
       470: q
       471: q
       474: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       484: q
       486: q
       488: q
       490: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       503: q
       505: q
       507: q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       515: q
       516: q
       517: q^4+q
       522: q
       526: q
       530: q
       534: q
       538: q
       542: q
       546: q
       551: q
       556: q
       560: q
       564: q
       566: q
       571: q
       574: q
       581: q
       584: q
       586: q
       588: q
       589: q
       592: q
       593: q
       596: q
       598: q
       600: q
       602: q
       603: q
       606: q
       608: q
       610: q
       612: q
       614: q
       615: q
       618: q
       619: q
       622: q
       624: q
       626: q
       628: q
       630: q
       632: q
       634: q
       636: q
       638: q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: q
       654: q
       656: q
       657: q
       659: q
       661: q
       663: q^4+q
       664: q
       665: q
       674: q
       675: q
       676: q
       677: q
       679: q
       680: q
       681: q
       682: q
       683: q
       685: q
       686: q
       687: q
       688: q
       689: q
       699: q
       706: q
       710: q
       715: q
       718: q
       722: q
       726: q
       730: q
       734: q
       740: q
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       748: q
       752: q
       754: q
       759: q
       763: q
       766: q
       773: q
       776: q
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       780: q
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       785: q
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       792: q
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       800: q
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       804: q
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       818: q
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       822: q
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       825: q
       828: q
       829: q
       832: q
       834: q
       836: q
       842: q
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       874: q
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      1076: q
      1080: q
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      1084: q
      1092: q
      1117: q
      1123: q
      1128: q
      1131: q
      1142: q
      1149: q
      1155: q
      1157: q
      1162: q
      1171: q
      1175: q
      1177: q
      1181: q
      1186: q
      1200: q
      1205: q
      1207: q
      1223: 1
      1231: q
      1233: q
      1234: q
      1249: q
      1251: q
      1254: q
      1265: q
      1267: q
      1268: q
      1271: q
      1275: q
      1279: q
      1281: q
      1287: q
      1296: q
      1324: 1
      1339: 1
      1351: q
      1357: q
      1363: q
      1366: q
      1383: q
      1389: q
      1394: q
      1397: q
      1416: q
      1421: q
      1423: q
      1427: q
      1434: q
      1447: 1
      1465: q
      1467: q
      1468: q
      1481: 1
      1499: 1
      1508: q
      1519: q
      1558: 1
      1561: 1
      1574: 1
      1593: 1
      1610: q
      1616: q
      1620: q
      1624: q
      1636: 1
      1638: 1
      1672: 1
      1685: 1
      1698: 1
      1709: 1
      1716: q
      1728: 1
      1731: 1
      1756: 1
      1779: 1
      1794: 1
      1806: 1
      1824: 1
      1844: 1
      1857: 1
      1868: 1
      1878: 1
      1897: 1
      1912: 1
      1931: 1
      1950: 1
      1977: 1
      1987: 1
      2000: 1
      2058: 1
      2102: 1

2103:    0: q^4+q
         1: q^4+q
         2: q^4+q
         3: q^4+q
         4: q^5+q^4+q
         5: q^4+q
         6: q
         7: q^5+q^4+q
         8: q^4+q
         9: q^5+q^4+q
        10: q
        11: q
        12: q
        13: q^4+q
        14: q^5+q^4+q
        15: q^4+q
        16: q^4+q
        17: q^4+q
        18: q^5+q^4+q
        19: q^4+q
        20: q
        21: q^4+q
        22: q^4+q
        23: q^4+q
        24: q^4+q
        25: q^4+q
        26: q^4+q
        27: q^4+q
        28: q
        29: q
        30: q^4+q
        31: q
        32: q^4+q
        33: q^4+q
        34: q
        35: q^4+q
        36: q^4+q
        38: q^4+q
        40: q^4+q
        42: q^4+q
        43: q
        44: q
        45: q
        46: q^4+q
        47: q^4+q
        48: q^5+q^4+q
        49: q^4+q
        50: q
        51: q^4+q
        52: q^4+q
        53: q
        54: q^4+q
        55: q^4+q
        56: q
        57: q^4+q
        58: q
        61: q
        63: q
        65: q^4+q
        67: q^4+q
        68: q
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        70: q
        71: q
        72: q
        73: q
        75: q^4+q
        77: q
        79: q^4+q
        80: q
        81: q^4+q
        82: q
        83: q^4+q
        84: q
        85: q^4+q
        86: q
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        88: q
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        90: q
        91: q^4+q
        92: q
        93: q^4+q
        94: q^4+q
        95: q
        96: q^4+q
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        98: q
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       100: q^4+q
       101: q
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       105: q
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       112: q
       114: q
       116: q^4+q
       117: q
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       122: q
       124: q^4+q
       125: q
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       128: q^4+q
       130: q
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       133: q
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       135: q
       136: q
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       138: q^4+q
       139: q
       140: q
       141: q
       142: q
       143: q
       144: q^4+q
       145: q
       146: q
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       150: q^4+q
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       154: q
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       157: q
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       160: q^4+q
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       171: q
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       180: q
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       206: q
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       212: q^4+q
       214: q^4+q
       216: q
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       219: q
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       222: q
       223: q
       224: q
       225: q
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       228: q^4+q
       229: q
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       233: q^4+q
       234: q
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       240: q
       242: q^4+q
       243: q
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       249: q^4+q
       250: q
       251: q
       252: q
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       254: q
       255: q
       256: q^4+q
       257: q
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       261: q
       265: q
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       277: q
       280: q
       282: q^4+q
       284: q
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       288: q
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       298: q
       300: q
       302: q
       303: q
       306: q
       308: q
       309: q
       312: q
       314: q
       316: q^4+q
       318: q
       320: q
       321: q
       324: q
       326: q
       328: q
       330: q
       332: q
       333: q
       334: q
       335: q
       336: q
       337: q
       339: q
       341: q
       343: q^4+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       361: q^4+q
       363: q
       365: q^4+q
       366: q
       367: q
       368: q^4+q
       369: q
       370: q
       371: q
       372: q
       373: q^4+q
       374: q
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       379: q
       383: q
       387: q
       392: q
       395: q
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       402: q
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       412: q
       414: q
       416: q
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       420: q
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       428: q
       430: q
       431: q
       434: q
       436: q
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       448: q
       449: q
       452: q
       454: q
       456: q
       457: q
       460: q
       461: q
       464: q
       466: q
       468: q^4+q
       470: q
       472: q
       473: q
       476: q
       478: q
       480: q
       481: q
       482: q
       483: q
       484: q
       486: q
       488: q
       490: q^4+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       503: q
       505: q
       507: q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       515: q
       516: q
       517: q^4+q
       523: q
       527: q
       531: q
       535: q
       540: q
       544: q
       548: q
       550: q
       554: q
       558: q
       562: q
       567: q
       572: q
       576: q
       581: q
       584: q
       586: q
       588: q
       590: q
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       594: q
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       598: q
       600: q
       602: q
       604: q
       606: q
       607: q
       610: q
       612: q
       614: q
       616: q
       618: q
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       631: q
       634: q
       636: q
       638: q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       656: q
       657: q
       659: q
       661: q
       663: q^4+q
       664: q
       665: q
       674: q
       675: q
       676: q
       677: q
       679: q
       680: q
       681: q
       682: q
       683: q
       685: q
       686: q
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       688: q
       689: q
       700: q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q
       732: q
       736: q
       738: q
       742: q
       746: q
       750: q
       755: q
       760: q
       764: q
       767: q
       773: q
       776: q
       778: q
       780: q
       782: q
       786: q
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       792: q
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       812: q
       817: q
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       824: q
       826: q
       827: q
       830: q
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       941: q
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      1013: q
      1019: q
      1021: q
      1023: q
      1027: q
      1028: q
      1035: q
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      1039: q
      1041: q
      1044: q
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      1051: q
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      1057: q
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      1061: q
      1063: q
      1065: q
      1076: q
      1080: q
      1083: q
      1084: q
      1093: q
      1115: q
      1125: q
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      1132: q
      1142: q
      1151: q
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      1169: q
      1173: q
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      1187: q
      1201: q
      1203: q
      1209: q
      1223: 1
      1231: q
      1232: q
      1235: q
      1249: q
      1250: q
      1255: q
      1265: q
      1267: q
      1269: q
      1270: q
      1275: q
      1279: q
      1281: q
      1287: q
      1297: q
      1325: 1
      1339: 1
      1349: q
      1359: q
      1362: q
      1365: q
      1381: q
      1391: q
      1395: q
      1398: q
      1417: q
      1419: q
      1425: q
      1428: q
      1434: q
      1447: 1
      1465: q
      1466: q
      1469: q
      1481: 1
      1500: 1
      1507: q
      1520: q
      1558: 1
      1562: 1
      1573: 1
      1594: 1
      1608: q
      1618: q
      1621: q
      1625: q
      1636: 1
      1638: 1
      1672: 1
      1686: 1
      1697: 1
      1710: 1
      1717: q
      1728: 1
      1732: 1
      1755: 1
      1780: 1
      1795: 1
      1806: 1
      1824: 1
      1845: 1
      1856: 1
      1869: 1
      1880: 1
      1896: 1
      1913: 1
      1931: 1
      1951: 1
      1975: 1
      1989: 1
      2001: 1
      2059: 1
      2103: 1

2104:    0: 3q^3+4q^2+1
         1: 3q^3+4q^2+1
         2: 3q^3+4q^2+1
         3: 3q^3+4q^2+1
         4: 3q^3+4q^2+1
         5: 3q^3+4q^2+1
         6: 3q^3+4q^2+1
         7: 3q^3+4q^2+1
         8: 3q^3+4q^2+1
         9: q^5+2q^4+2q^3+2q^2+1
        10: 3q^3+4q^2+1
        11: 3q^3+4q^2+1
        12: 3q^3+4q^2+1
        13: 3q^3+4q^2+1
        14: 3q^3+4q^2+1
        15: 3q^3+4q^2+1
        16: 4q^2+1
        17: 4q^2+1
        18: 2q^3+2q^2+1
        19: 3q^3+4q^2+1
        20: 3q^3+4q^2+1
        21: 3q^3+4q^2+1
        22: 3q^3+4q^2+1
        23: 3q^3+4q^2+1
        24: 3q^3+4q^2+1
        25: 3q^3+4q^2+1
        26: 3q^3+4q^2+1
        27: 3q^3+4q^2+1
        28: 4q^2+1
        29: 3q^3+4q^2+1
        30: 3q^3+4q^2+1
        31: 3q^3+4q^2+1
        32: 3q^3+4q^2+1
        33: 4q^2+1
        34: 3q^3+4q^2+1
        35: 3q^3+4q^2+1
        36: 4q^2+1
        37: 2q^3+2q^2+1
        38: q^3+2q^2
        39: 2q^3+2q^2+1
        40: q^3+2q^2
        41: 2q^3+2q^2+1
        42: q^3+2q^2
        43: 3q^3+4q^2+1
        44: 3q^3+4q^2+1
        45: 3q^3+4q^2+1
        46: 4q^2+1
        47: 4q^2+1
        48: 2q^3+2q^2+1
        49: 4q^2+1
        50: 4q^2+1
        51: 2q^3+2q^2+1
        52: 3q^3+4q^2+1
        53: 3q^3+4q^2+1
        54: 3q^3+4q^2+1
        55: 3q^3+4q^2+1
        56: 3q^3+4q^2+1
        57: 3q^3+4q^2+1
        58: 3q^2+1
        59: q^2
        60: 3q^2+1
        61: q^2
        62: 2q^3+2q^2+1
        63: q^3+2q^2
        64: 2q^3+2q^2+1
        65: q^3+2q^2
        66: 2q^2+1
        67: 2q^2
        68: 4q^2+1
        69: 2q^2+1
        70: 3q^3+4q^2+1
        71: 4q^2+1
        72: 4q^2+1
        73: 4q^2+1
        74: 2q^3+2q^2+1
        75: q^3+2q^2
        76: 2q^3+2q^2+1
        77: q^3+2q^2
        78: 2q^3+2q^2+1
        79: q^3+2q^2
        80: 3q^3+4q^2+1
        81: 4q^2+1
        82: 3q^3+4q^2+1
        83: 3q^3+4q^2+1
        84: 3q^3+4q^2+1
        85: 4q^2+1
        86: 3q^3+4q^2+1
        87: 3q^3+4q^2+1
        88: 4q^2+1
        89: 4q^2+1
        90: 2q^3+2q^2+1
        91: 4q^2+1
        92: 4q^2+1
        93: 2q^3+2q^2+1
        94: 4q^2+1
        95: 4q^2+1
        96: 2q^3+2q^2+1
        97: 4q^2+1
        98: 4q^2+1
        99: 2q^3+2q^2+1
       100: 3q^3+4q^2+1
       101: 3q^3+4q^2+1
       102: 3q^3+4q^2+1
       103: 2q^2+1
       104: q^2
       105: q^2
       107: 3q^2+1
       108: q^2
       109: 3q^2+1
       110: q^2
       111: 2q^2+1
       112: 2q^2
       113: 2q^3+2q^2+1
       114: q^3+2q^2
       115: 2q^3+2q^2+1
       116: q^3+2q^2
       117: 3q^2+1
       118: q^2
       119: 3q^2+1
       120: q^2
       121: 2q^3+2q^2+1
       122: q^3+2q^2
       123: 2q^2+1
       124: 2q^2
       125: 4q^2+1
       126: 2q^2+1
       127: q^2+1
       129: q^2+1
       131: q^3+1
       133: 4q^2+1
       134: 2q^2+1
       135: 4q^2+1
       136: 4q^2+1
       137: 4q^2+1
       138: 2q^2+1
       139: 4q^2+1
       140: 4q^2+1
       141: 3q^3+4q^2+1
       142: 4q^2+1
       143: 4q^2+1
       144: 2q^2+1
       145: 4q^2+1
       146: 3q^3+4q^2+1
       147: 4q^2+1
       148: 4q^2+1
       149: 3q^3+4q^2+1
       150: 3q^3+4q^2+1
       151: 2q^3+2q^2+1
       152: q^3+2q^2
       153: 2q^3+2q^2+1
       154: q^3+2q^2
       155: 2q^3+2q^2+1
       156: q^3+2q^2
       157: 4q^2+1
       158: 4q^2+1
       159: 2q^3+2q^2+1
       160: 4q^2+1
       161: 4q^2+1
       162: 2q^3+2q^2+1
       163: 4q^2+1
       164: 4q^2+1
       165: 2q^3+2q^2+1
       166: 4q^2+1
       167: 4q^2+1
       168: 2q^3+2q^2+1
       169: 2q^2+1
       170: q^2
       171: q^2
       173: 2q^2+1
       174: q^2
       175: q^2
       177: 1
       179: q^2+1
       181: q^2+1
       183: 3q^2+1
       184: q^2
       185: 3q^2+1
       186: q^2
       187: 2q^2+1
       188: 2q^2
       189: 2q^3+2q^2+1
       190: q^3+2q^2
       191: 3q^2+1
       192: q^2
       193: 3q^2+1
       194: q^2
       195: 3q^2+1
       196: q^2
       197: 2q^2+1
       198: 2q^2
       199: 3q^2+1
       200: q^2
       201: 3q^2+1
       202: q^2
       203: 3q^2+1
       204: q^2
       205: 2q^2+1
       206: 2q^2
       207: 2q^2+1
       208: 2q^2
       209: 2q^3+2q^2+1
       210: q^3+2q^2
       211: 2q^3+2q^2+1
       212: q^3+2q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: 2q^2+1
       220: 4q^2+1
       221: 2q^2+1
       222: 4q^2+1
       223: 2q^2+1
       224: 4q^2+1
       225: 2q^2+1
       226: 2q^2+1
       227: 4q^2+1
       228: 2q^2+1
       229: 4q^2+1
       230: 4q^2+1
       231: 2q^2+1
       232: 4q^2+1
       233: 2q^2+1
       234: 4q^2+1
       235: 4q^2+1
       236: 2q^2+1
       237: q^2+1
       239: q^2+1
       241: q^3+1
       243: 4q^2+1
       244: 4q^2+1
       245: 4q^2+1
       246: 3q^3+4q^2+1
       247: 4q^2+1
       248: 4q^2+1
       249: 2q^3+2q^2+1
       250: 4q^2+1
       251: 4q^2+1
       252: 2q^3+2q^2+1
       253: 4q^2+1
       254: 4q^2+1
       255: 2q^3+2q^2+1
       256: 4q^2+1
       257: 4q^2+1
       258: 2q^3+2q^2+1
       259: q^2+1
       263: 2q^2+1
       264: q^2
       265: q^2
       267: 2q^2+1
       268: q^2
       270: q^2
       271: 2q^2+1
       272: q^2
       274: q^2
       275: 2q^2+1
       276: q^2
       277: q^2
       279: q^2+1
       281: 1
       283: q^2+1
       285: q^2+1
       287: 1
       289: q^2+1
       291: 1
       293: 3q^2+1
       294: q^2
       295: 3q^2+1
       296: q^2
       297: 2q^2+1
       298: 2q^2
       299: 3q^2+1
       300: q^2
       301: q^2+1
       303: 3q^2+1
       304: q^2
       305: 2q^2+1
       306: 2q^2
       307: 3q^2+1
       308: q^2
       309: 3q^2+1
       310: q^2
       311: q^2+1
       313: 2q^2+1
       314: 2q^2
       315: 1
       317: q^2+1
       319: 3q^2+1
       320: q^2
       321: 3q^2+1
       322: q^2
       323: 2q^2+1
       324: 2q^2
       325: 2q^3+2q^2+1
       326: q^3+2q^2
       327: q^2+1
       329: q^2+1
       331: q^3+1
       333: 2q^2+1
       334: 2q^2+1
       335: 2q^2+1
       336: 2q^2+1
       337: 4q^2+1
       338: q^2+1
       340: q^2+1
       342: q^3+1
       344: 2q^2+1
       345: 4q^2+1
       346: 2q^2+1
       347: 4q^2+1
       348: 2q^2+1
       349: 4q^2+1
       350: 2q^2+1
       351: 4q^2+1
       352: 2q^2+1
       353: 4q^2+1
       354: 2q^2+1
       355: 4q^2+1
       356: 2q^2+1
       357: 4q^2+1
       358: 2q^2+1
       359: 4q^2+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: 2q^2+1
       367: 4q^2+1
       368: 2q^2+1
       369: 4q^2+1
       370: 4q^2+1
       371: 4q^2+1
       372: 4q^2+1
       373: 2q^3+2q^2+1
       374: 4q^2+1
       375: 4q^2+1
       376: 2q^3+2q^2+1
       377: 1
       381: q^2+1
       385: 2q^2+1
       386: q^2
       387: q^2
       389: q^2+1
       393: 2q^2+1
       394: q^2
       395: q^2
       397: q^2+1
       401: 2q^2+1
       402: q^2
       403: q^2
       405: 2q^2+1
       407: q^2
       408: q^2
       409: q^2+1
       411: 1
       413: 1
       415: q^2+1
       417: 1
       419: q^2+1
       421: q^2+1
       423: 1
       425: 1
       427: q^2+1
       429: q^2+1
       431: q^2+1
       433: 1
       435: q^2+1
       437: 3q^2+1
       438: q^2
       439: 3q^2+1
       440: q^2
       441: 2q^2+1
       442: 2q^2
       443: 3q^2+1
       444: q^2
       445: q^2+1
       447: q^2+1
       449: q^2+1
       451: 1
       453: 3q^2+1
       454: q^2
       455: q^2+1
       457: 3q^2+1
       458: q^2
       459: 2q^2+1
       460: 2q^2
       461: 3q^2+1
       462: q^2
       463: q^2+1
       465: q^2+1
       467: 1
       469: 1
       471: 3q^2+1
       472: q^2
       473: 3q^2+1
       474: q^2
       475: 2q^2+1
       476: 2q^2
       477: q^2+1
       479: 2q^2+1
       480: 2q^2
       481: 2q^2+1
       482: 2q^2+1
       483: 2q^2+1
       484: 4q^2+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: 2q^2+1
       492: 2q^2+1
       493: 2q^2+1
       494: 2q^2+1
       495: 2q^2+1
       496: 4q^2+1
       497: 2q^2+1
       498: 2q^2+1
       499: 2q^2+1
       500: 2q^2+1
       501: 4q^2+1
       502: q^2+1
       504: q^2+1
       506: q^3+1
       508: 2q^2+1
       509: 4q^2+1
       510: 2q^2+1
       511: 4q^2+1
       512: 2q^2+1
       513: 4q^2+1
       514: 2q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 4q^2+1
       519: 4q^2+1
       520: 2q^3+2q^2+1
       521: 1
       525: q^2+1
       529: 1
       533: 1
       537: q^2+1
       541: 2q^2+1
       542: q^2
       544: q^2
       545: q^2+1
       549: 1
       553: q^2+1
       557: 2q^2+1
       558: q^2
       560: q^2
       561: q^2+1
       565: 2q^2+1
       566: q^2
       567: q^2
       569: q^2+1
       573: 2q^2+1
       574: q^2
       576: q^2
       577: q^2+1
       583: 1
       585: 1
       587: 1
       589: q^2+1
       591: q^2+1
       593: q^2+1
       595: q^2+1
       597: 1
       599: 1
       601: q^2+1
       603: q^2+1
       605: 1
       607: q^2+1
       609: 1
       611: q^2+1
       613: 1
       615: 3q^2+1
       616: q^2
       617: q^2+1
       619: q^2+1
       621: q^2+1
       623: 1
       625: 1
       627: q^2+1
       629: 1
       631: 3q^2+1
       632: q^2
       633: q^2+1
       635: q^2+1
       637: 1
       639: 1
       641: q^2+1
       643: q^2+1
       645: 1
       647: 3q^2+1
       648: q^2
       649: 3q^2+1
       650: q^2
       651: q^2+1
       653: 2q^2+1
       654: 2q^2
       655: 2q^2+1
       656: 2q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q^2+1
       666: q^2+1
       668: q^2+1
       670: q^3+1
       672: 4q^2+1
       673: 2q^2+1
       674: q+1
       675: 2q^2+1
       676: 2q^2+1
       677: 2q^2+1
       678: 4q^2+1
       679: 2q^2+1
       680: q+1
       681: 2q^2+1
       682: 2q^2+1
       683: 2q^2+1
       684: 4q^2+1
       685: 2q^2+1
       686: 2q^2+1
       687: 2q^2+1
       688: 2q^2+1
       689: 2q^2+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: q^2+1
       733: q^2+1
       737: 1
       741: 1
       745: q^2+1
       749: q^2+1
       753: 1
       757: q^2+1
       761: 2q^2+1
       763: q^2
       764: q^2
       765: 2q^2+1
       766: q^2
       767: q^2
       769: q^2+1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: 1
       785: q^2+1
       787: q^2+1
       789: q^2+1
       791: 1
       793: 1
       795: q+1
       797: 1
       799: 1
       801: q^2+1
       803: q^2+1
       805: q^2+1
       807: q^2+1
       809: 1
       811: 1
       813: q^2+1
       815: 3q^2+1
       816: q^2
       817: 1
       819: q+1
       821: 1
       823: 1
       825: q^2+1
       827: q^2+1
       829: q^2+1
       831: q^2+1
       833: 1
       835: 1
       837: q^2+1
       839: 3q^2+1
       840: q^2
       841: 1
       843: 1
       844: q
       845: q^2+1
       847: q^2+1
       849: 1
       851: 1
       853: q^2+1
       855: 1
       857: 2q^2+1
       858: 2q^2
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q^2+1
       869: q+1
       870: q+1
       871: 2q^2+1
       872: 2q^2+1
       873: q+1
       874: q+1
       875: 2q^2+1
       876: 2q^2+1
       877: 2q^2+1
       878: 2q^2+1
       879: 2q^2+1
       880: 2q^2+1
       881: q+1
       882: q+1
       883: q+1
       884: q^2+1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       924: 1
       928: 1
       932: q^2+1
       936: 1
       940: 1
       944: 1
       948: 1
       952: 1
       956: q^2+1
       960: 1
       964: 1
       968: 1
       971: q
       974: 1
       978: q^2+1
       982: q^2+1
       988: 2q^2+1
       989: q^2
       990: q^2
       992: 1
       994: 1
       996: q+1
       998: 1
      1000: 1
      1002: 1
      1004: q^2+1
      1006: q^2+1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1014: q+1
      1016: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: 1
      1026: q^2+1
      1028: q^2+1
      1030: q+1
      1032: 1
      1034: 1
      1036: q+1
      1038: 1
      1040: q^2+1
      1042: 1
      1044: q^2+1
      1046: 1
      1047: q
      1048: 1
      1050: 1
      1052: q^2+1
      1054: q^2+1
      1056: q^2+1
      1058: q^2+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q^2+1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q^2+1
      1083: 2q^2+1
      1084: q+1
      1085: 2q^2+1
      1086: 1
      1098: q^2+1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1141: q
      1144: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1164: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1191: q
      1194: 1
      1198: 1
      1202: 1
      1206: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: q
      1226: q+1
      1228: 1
      1230: 1
      1232: 1
      1234: 1
      1236: q+1
      1238: 1
      1240: q^2+1
      1242: q^2+1
      1244: q+1
      1246: 1
      1248: 1
      1250: 1
      1252: q+1
      1254: 1
      1256: 1
      1258: q^2+1
      1260: q^2+1
      1262: 1
      1263: q
      1264: 1
      1266: 1
      1268: q^2+1
      1270: q^2+1
      1272: 1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q^2+1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1337: q
      1340: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1372: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1404: 1
      1407: q
      1410: 1
      1414: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1433: q
      1438: 1
      1440: 1
      1442: 1
      1444: 1
      1445: q
      1446: 1
      1448: 1
      1450: 1
      1452: q+1
      1454: 1
      1456: 1
      1458: q+1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: q+1
      1474: 1
      1476: q^2+1
      1478: q^2+1
      1480: 1
      1482: 1
      1483: q
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1489: 1
      1501: 1
      1513: 1
      1525: 1
      1541: 1
      1545: 1
      1549: 1
      1553: 1
      1556: q
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1631: 1
      1634: q
      1641: 1
      1643: 1
      1645: 1
      1647: 1
      1649: 1
      1651: 1
      1653: 1
      1655: 1
      1657: 1
      1661: 1
      1663: 1
      1665: 1
      1667: q+1
      1669: 1
      1670: q
      1671: 1
      1673: 1
      1674: 1
      1675: 1
      1687: 1
      1699: 1
      1711: 1
      1737: 1
      1745: 1
      1749: 1
      1753: 1
      1757: 1
      1761: 1
      1765: 1
      1773: 1
      1777: 1
      1781: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1801: 1
      1804: q
      1807: 1
      1811: 1
      1815: 1
      1819: 1
      1821: 1
      1827: 1
      1829: 1
      1831: 1
      1833: 1
      1846: 1
      1858: 1
      1870: 1
      1882: 1
      1902: 1
      1918: 1
      1932: 1
      1936: 1
      1940: 1
      1948: 1
      1952: 1
      1956: 1
      1962: 1
      1964: 1
      1990: 1
      2002: 1
      2032: 1
      2044: 1
      2064: 1
      2104: 1

2105:    0: q^2+3q
         1: q^2+3q
         2: q^2+3q
         3: q^2+3q
         4: q^2+3q
         5: q^2+3q
         6: q^2+3q
         7: q^2+3q
         8: q^2+3q
         9: q^3+q^2+2q
        10: q^2+3q
        11: q^2+3q
        12: q^2+3q
        13: q^2+3q
        14: q^2+3q
        15: q^2+3q
        16: 3q
        17: 3q
        18: q^2+2q
        19: q^2+3q
        20: q^2+3q
        21: q^2+3q
        22: q^2+3q
        23: q^2+3q
        24: q^2+3q
        25: q^2+3q
        26: q^2+3q
        27: q^2+3q
        28: 3q
        29: q^2+3q
        30: q^2+3q
        31: q^2+3q
        32: q^2+3q
        33: 3q
        34: q^2+3q
        35: q^2+3q
        36: 3q
        37: q
        38: q^2+2q
        39: q
        40: q^2+2q
        41: q
        42: q^2+2q
        43: q^2+3q
        44: q^2+3q
        45: q^2+3q
        46: 3q
        47: 3q
        48: q^2+2q
        49: 3q
        50: 3q
        51: q^2+2q
        52: q^2+3q
        53: q^2+3q
        54: q^2+3q
        55: q^2+3q
        56: q^2+3q
        57: q^2+3q
        58: 2q
        59: q
        60: 2q
        61: q
        62: q
        63: q^2+2q
        64: q
        65: q^2+2q
        66: q
        67: 2q
        68: 3q
        69: 2q
        70: q^2+3q
        71: 3q
        72: 3q
        73: 3q
        74: q
        75: q^2+2q
        76: q
        77: q^2+2q
        78: q
        79: q^2+2q
        80: q^2+3q
        81: 3q
        82: q^2+3q
        83: q^2+3q
        84: q^2+3q
        85: 3q
        86: q^2+3q
        87: q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 3q
        92: 3q
        93: q^2+2q
        94: 3q
        95: 3q
        96: q^2+2q
        97: 3q
        98: 3q
        99: q^2+2q
       100: q^2+3q
       101: q^2+3q
       102: q^2+3q
       103: q
       104: q
       105: q
       107: 2q
       108: q
       109: 2q
       110: q
       111: q
       112: 2q
       113: q
       114: q^2+2q
       115: q
       116: q^2+2q
       117: 2q
       118: q
       119: 2q
       120: q
       121: q
       122: q^2+2q
       123: q
       124: 2q
       125: 3q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       133: 3q
       134: 2q
       135: 3q
       136: 3q
       137: 3q
       138: 2q
       139: 3q
       140: 3q
       141: q^2+3q
       142: 3q
       143: 3q
       144: 2q
       145: 3q
       146: q^2+3q
       147: 3q
       148: 3q
       149: q^2+3q
       150: q^2+3q
       151: q
       152: q^2+2q
       153: q
       154: q^2+2q
       155: q
       156: q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q
       161: 3q
       162: q^2+2q
       163: 3q
       164: 3q
       165: q^2+2q
       166: 3q
       167: 3q
       168: q^2+2q
       169: q
       170: q
       171: q
       173: q
       174: q
       175: q
       178: q
       180: 2q
       182: 2q
       183: 2q
       184: q
       185: 2q
       186: q
       187: q
       188: 2q
       189: q
       190: q^2+2q
       191: 2q
       192: q
       193: 2q
       194: q
       195: 2q
       196: q
       197: q
       198: 2q
       199: 2q
       200: q
       201: 2q
       202: q
       203: 2q
       204: q
       205: q
       206: 2q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q
       212: q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: 2q
       224: 3q
       225: 2q
       226: 2q
       227: 3q
       228: 2q
       229: 3q
       230: 3q
       231: 2q
       232: 3q
       233: 2q
       234: 3q
       235: 3q
       236: 2q
       238: 2q
       240: 2q
       242: q^2+q
       243: 3q
       244: 3q
       245: 3q
       246: q^2+3q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 3q
       257: 3q
       258: q^2+2q
       260: q
       261: q
       263: q
       264: q
       265: q
       267: q
       268: q
       270: q
       271: q
       272: q
       274: q
       275: q
       276: q
       277: q
       280: 2q
       282: q
       283: q
       285: q
       288: q
       290: 2q
       292: q
       293: 2q
       294: q
       295: 2q
       296: q
       297: q
       298: 2q
       299: 2q
       300: q
       302: 2q
       303: 2q
       304: q
       305: q
       306: 2q
       307: 2q
       308: q
       309: 2q
       310: q
       312: 2q
       313: q
       314: 2q
       316: q
       318: 2q
       319: 2q
       320: q
       321: 2q
       322: q
       323: q
       324: 2q
       325: q
       326: q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       339: 2q
       341: 2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: 2q
       349: 3q
       350: 2q
       351: 3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: 2q
       357: 3q
       358: 2q
       359: 3q
       361: 2q
       363: 2q
       365: q^2+q
       366: 2q
       367: 3q
       368: 2q
       369: 3q
       370: 3q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
       383: q
       385: q
       386: q
       387: q
       390: q
       392: q
       393: q
       394: q
       395: q
       398: q
       400: q
       401: q
       402: q
       403: q
       405: q
       407: q
       408: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       419: q
       421: q
       424: q
       426: q
       428: 2q
       429: q
       431: q
       434: q
       436: 2q
       437: 2q
       438: q
       439: 2q
       440: q
       441: q
       442: 2q
       443: 2q
       444: q
       446: 2q
       447: q
       449: q
       452: q
       453: 2q
       454: q
       456: 2q
       457: 2q
       458: q
       459: q
       460: 2q
       461: 2q
       462: q
       464: 2q
       466: 2q
       468: q
       470: q
       471: 2q
       472: q
       473: 2q
       474: q
       475: q
       476: 2q
       478: 2q
       479: q
       480: 2q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: 2q
       488: 2q
       490: q^2+q
       491: 2q
       492: 2q
       493: 2q
       494: 2q
       495: 2q
       496: 3q
       497: 2q
       498: 2q
       499: 2q
       500: 2q
       501: 3q
       503: 2q
       505: 2q
       507: q^2+q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: 2q
       513: 3q
       514: 2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       526: q
       527: q
       538: q
       540: q
       541: q
       542: q
       544: q
       546: q
       548: q
       554: q
       556: q
       557: q
       558: q
       560: q
       562: q
       564: q
       565: q
       566: q
       567: q
       571: q
       572: q
       573: q
       574: q
       576: q
       581: 2q
       584: q
       586: q
       588: q
       589: q
       591: q
       593: q
       595: q
       598: q
       600: q
       602: 2q
       603: q
       606: q
       607: q
       610: q
       612: 2q
       614: q
       615: 2q
       616: q
       618: 2q
       619: q
       621: q
       624: q
       626: q
       628: 2q
       630: q
       631: 2q
       632: q
       634: 2q
       636: 2q
       638: q
       640: q
       641: q
       643: q
       646: q
       647: 2q
       648: q
       649: 2q
       650: q
       652: 2q
       653: q
       654: 2q
       655: q
       656: 2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: 2q
       669: 2q
       671: q^2+q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: 2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q
       687: 2q
       688: 2q
       689: 2q
       690: q+1
       691: q+1
       692: q+1
       699: q
       700: q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q
       766: q
       767: q
       773: 2q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       785: q
       787: q
       790: 2q
       792: q
       793: 1
       796: q+1
       798: q
       800: q
       801: q
       803: q
       805: q
       807: q
       810: q
       812: q
       814: 2q
       815: 2q
       816: q
       817: 1
       820: q+1
       822: q
       824: q
       825: q
       827: q
       829: q
       831: q
       834: q
       836: q
       838: 2q
       839: 2q
       840: q
       842: q
       843: 1
       844: q
       845: q
       847: q
       850: q
       852: q
       854: 2q
       856: q
       857: q
       858: 2q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: 2q
       873: q+1
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       890: q
       891: q
       917: 1
       933: q
       935: q
       941: 1
       957: q
       959: q
       964: 1
       969: 1
       972: q
       980: q
       981: q
       986: 2q
       988: q
       989: q
       990: q
       993: 1
       995: 1
       997: q+1
       998: 1
      1000: 1
      1003: q
      1004: q
      1006: q
      1009: q
      1011: q
      1012: 1
      1013: q
      1015: q+1
      1016: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1026: q
      1028: q
      1031: q+1
      1032: 1
      1035: q
      1037: q+1
      1039: q
      1040: q
      1043: q
      1044: q
      1046: 1
      1047: q
      1049: q
      1051: q
      1052: q
      1054: q
      1056: q
      1058: q
      1061: q
      1063: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1087: 1
      1104: q
      1105: q
      1115: 1
      1123: 1
      1130: 1
      1139: 1
      1142: q
      1145: 1
      1165: 1
      1189: 1
      1192: q
      1194: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1218: 1
      1221: q
      1223: q
      1224: 1
      1225: q
      1227: q+1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1237: q+1
      1239: q
      1240: q
      1242: q
      1245: q+1
      1246: 1
      1249: 1
      1250: 1
      1253: q+1
      1254: 1
      1257: q
      1258: q
      1260: q
      1262: 1
      1263: q
      1265: q
      1267: q
      1268: q
      1270: q
      1273: q
      1275: q+1
      1277: q
      1279: q
      1280: 1
      1281: q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1291: 1
      1303: 1
      1315: 1
      1319: 1
      1326: 1
      1335: 1
      1338: q
      1341: 1
      1349: 1
      1357: 1
      1364: 1
      1373: 1
      1381: 1
      1389: 1
      1396: 1
      1405: 1
      1408: q
      1410: 1
      1431: 1
      1434: q
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1445: q
      1447: q
      1449: 1
      1450: 1
      1453: q+1
      1454: 1
      1457: 1
      1459: q+1
      1460: 1
      1462: 1
      1465: 1
      1466: 1
      1468: 1
      1471: q
      1473: q+1
      1475: q
      1476: q
      1478: q
      1481: q
      1482: 1
      1483: q
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1490: 1
      1502: 1
      1514: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1557: q
      1564: 1
      1568: 1
      1575: 1
      1584: 1
      1588: 1
      1595: 1
      1608: 1
      1616: 1
      1623: 1
      1632: 1
      1635: q
      1642: 1
      1644: 1
      1645: 1
      1647: 1
      1649: 1
      1652: 1
      1653: 1
      1655: 1
      1657: 1
      1662: 1
      1663: 1
      1665: 1
      1668: q+1
      1669: 1
      1670: q
      1672: q
      1673: 1
      1674: 1
      1676: 1
      1688: 1
      1700: 1
      1712: 1
      1738: 1
      1746: 1
      1749: 1
      1758: 1
      1762: 1
      1766: 1
      1773: 1
      1782: 1
      1786: 1
      1790: 1
      1797: 1
      1802: 1
      1805: q
      1811: 1
      1816: 1
      1819: 1
      1821: 1
      1828: 1
      1829: 1
      1831: 1
      1833: 1
      1847: 1
      1859: 1
      1871: 1
      1883: 1
      1903: 1
      1919: 1
      1933: 1
      1937: 1
      1940: 1
      1952: 1
      1957: 1
      1962: 1
      1964: 1
      1991: 1
      2003: 1
      2033: 1
      2045: 1
      2064: 1
      2105: 1

2106:    0: q^2+3q
         1: q^2+3q
         2: q^2+3q
         3: q^2+3q
         4: q^2+3q
         5: q^2+3q
         6: q^2+3q
         7: q^2+3q
         8: q^2+3q
         9: q^3+q^2+2q
        10: q^2+3q
        11: q^2+3q
        12: q^2+3q
        13: q^2+3q
        14: q^2+3q
        15: q^2+3q
        16: 3q
        17: 3q
        18: q^2+2q
        19: q^2+3q
        20: q^2+3q
        21: q^2+3q
        22: q^2+3q
        23: q^2+3q
        24: q^2+3q
        25: q^2+3q
        26: q^2+3q
        27: q^2+3q
        28: 3q
        29: q^2+3q
        30: q^2+3q
        31: q^2+3q
        32: q^2+3q
        33: 3q
        34: q^2+3q
        35: q^2+3q
        36: 3q
        37: q^2+2q
        38: q
        39: q^2+2q
        40: q
        41: q^2+2q
        42: q
        43: q^2+3q
        44: q^2+3q
        45: q^2+3q
        46: 3q
        47: 3q
        48: q^2+2q
        49: 3q
        50: 3q
        51: q^2+2q
        52: q^2+3q
        53: q^2+3q
        54: q^2+3q
        55: q^2+3q
        56: q^2+3q
        57: q^2+3q
        58: q
        59: 2q
        60: 2q
        61: q
        62: q^2+2q
        63: q
        64: q^2+2q
        65: q
        66: 2q
        67: q
        68: 3q
        69: 2q
        70: q^2+3q
        71: 3q
        72: 3q
        73: 3q
        74: q^2+2q
        75: q
        76: q^2+2q
        77: q
        78: q^2+2q
        79: q
        80: q^2+3q
        81: 3q
        82: q^2+3q
        83: q^2+3q
        84: q^2+3q
        85: 3q
        86: q^2+3q
        87: q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 3q
        92: 3q
        93: q^2+2q
        94: 3q
        95: 3q
        96: q^2+2q
        97: 3q
        98: 3q
        99: q^2+2q
       100: q^2+3q
       101: q^2+3q
       102: q^2+3q
       103: q
       104: q
       106: q
       107: 2q
       108: q
       109: q
       110: 2q
       111: 2q
       112: q
       113: q^2+2q
       114: q
       115: q^2+2q
       116: q
       117: q
       118: 2q
       119: 2q
       120: q
       121: q^2+2q
       122: q
       123: 2q
       124: q
       125: 3q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       133: 3q
       134: 2q
       135: 3q
       136: 3q
       137: 3q
       138: 2q
       139: 3q
       140: 3q
       141: q^2+3q
       142: 3q
       143: 3q
       144: 2q
       145: 3q
       146: q^2+3q
       147: 3q
       148: 3q
       149: q^2+3q
       150: q^2+3q
       151: q^2+2q
       152: q
       153: q^2+2q
       154: q
       155: q^2+2q
       156: q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q
       161: 3q
       162: q^2+2q
       163: 3q
       164: 3q
       165: q^2+2q
       166: 3q
       167: 3q
       168: q^2+2q
       169: q
       170: q
       172: q
       173: q
       174: q
       176: q
       177: q
       179: 2q
       181: 2q
       183: 2q
       184: q
       185: q
       186: 2q
       187: 2q
       188: q
       189: q^2+2q
       190: q
       191: q
       192: 2q
       193: 2q
       194: q
       195: q
       196: 2q
       197: 2q
       198: q
       199: 2q
       200: q
       201: 2q
       202: q
       203: q
       204: 2q
       205: 2q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: 2q
       224: 3q
       225: 2q
       226: 2q
       227: 3q
       228: 2q
       229: 3q
       230: 3q
       231: 2q
       232: 3q
       233: 2q
       234: 3q
       235: 3q
       236: 2q
       237: 2q
       239: 2q
       241: q^2+q
       243: 3q
       244: 3q
       245: 3q
       246: q^2+3q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 3q
       257: 3q
       258: q^2+2q
       259: q
       262: q
       263: q
       264: q
       266: q
       267: q
       268: q
       269: q
       271: q
       273: q
       274: q
       275: q
       276: q
       278: q
       279: 2q
       281: q
       283: q
       286: q
       287: q
       289: 2q
       291: q
       293: 2q
       294: q
       295: q
       296: 2q
       297: 2q
       298: q
       299: 2q
       300: q
       301: 2q
       303: q
       304: 2q
       305: 2q
       306: q
       307: 2q
       308: q
       309: q
       310: 2q
       311: 2q
       313: 2q
       314: q
       315: q
       317: 2q
       319: 2q
       320: q
       321: q
       322: 2q
       323: 2q
       324: q
       325: q^2+2q
       326: q
       327: 2q
       329: 2q
       331: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       338: 2q
       340: 2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: 2q
       349: 3q
       350: 2q
       351: 3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: 2q
       357: 3q
       358: 2q
       359: 3q
       360: 2q
       362: 2q
       364: q^2+q
       366: 2q
       367: 3q
       368: 2q
       369: 3q
       370: 3q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       386: q
       388: q
       389: q
       391: q
       393: q
       394: q
       396: q
       397: q
       399: q
       401: q
       403: q
       404: q
       405: q
       406: q
       407: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       419: q
       422: q
       423: q
       425: q
       427: 2q
       429: q
       432: q
       433: q
       435: 2q
       437: 2q
       438: q
       439: q
       440: 2q
       441: 2q
       442: q
       443: 2q
       444: q
       445: 2q
       447: q
       450: q
       451: q
       453: 2q
       454: q
       455: 2q
       457: q
       458: 2q
       459: 2q
       460: q
       461: q
       462: 2q
       463: 2q
       465: 2q
       467: q
       469: q
       471: 2q
       472: q
       473: q
       474: 2q
       475: 2q
       476: q
       477: 2q
       479: 2q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: 2q
       487: 2q
       489: q^2+q
       491: 2q
       492: 2q
       493: 2q
       494: 2q
       495: 2q
       496: 3q
       497: 2q
       498: 2q
       499: 2q
       500: 2q
       501: 3q
       502: 2q
       504: 2q
       506: q^2+q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: 2q
       513: 3q
       514: 2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       542: q
       543: q
       545: q
       547: q
       553: q
       555: q
       557: q
       559: q
       560: q
       561: q
       563: q
       565: q
       566: q
       568: q
       569: q
       570: q
       573: q
       574: q
       575: q
       577: 2q
       583: q
       585: q
       587: q
       589: q
       592: q
       593: q
       596: q
       597: q
       599: q
       601: 2q
       603: q
       605: q
       608: q
       609: q
       611: 2q
       613: q
       615: 2q
       616: q
       617: 2q
       619: q
       622: q
       623: q
       625: q
       627: 2q
       629: q
       631: q
       632: 2q
       633: 2q
       635: 2q
       637: q
       639: q
       641: q
       644: q
       645: q
       647: 2q
       648: q
       649: q
       650: 2q
       651: 2q
       653: 2q
       654: q
       655: 2q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: 2q
       668: 2q
       670: q^2+q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: 2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q
       687: 2q
       688: 2q
       689: 2q
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       763: q
       765: q
       766: q
       768: q
       769: 2q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       785: q
       788: q
       789: 2q
       791: q
       793: 1
       795: q+1
       797: q
       799: q
       801: q
       804: q
       805: q
       808: q
       809: q
       811: q
       813: 2q
       815: 2q
       816: q
       818: 1
       819: q+1
       821: q
       823: q
       825: q
       828: q
       829: q
       832: q
       833: q
       835: q
       837: 2q
       839: q
       840: 2q
       841: q
       843: q
       844: 1
       845: q
       848: q
       849: q
       851: q
       853: 2q
       855: q
       857: 2q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: 2q
       873: q+1
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       884: q
       889: q
       916: 1
       932: q
       934: q
       942: 1
       956: q
       958: q
       965: 1
       968: q
       971: 1
       978: q
       979: q
       982: 2q
       988: q
       989: q
       991: q
       992: 1
       994: 1
       996: q+1
       999: 1
      1000: 1
      1002: q
      1004: q
      1007: q
      1008: q
      1010: q
      1012: q
      1013: 1
      1014: q+1
      1016: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1026: q
      1029: q
      1030: q+1
      1033: 1
      1034: q
      1036: q+1
      1038: q
      1040: q
      1042: q
      1045: q
      1046: q
      1047: 1
      1048: q
      1050: q
      1052: q
      1055: q
      1056: q
      1059: q
      1060: q
      1062: q
      1064: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1089: 1
      1098: q
      1102: q
      1116: 1
      1122: 1
      1131: 1
      1138: q
      1141: 1
      1144: 1
      1166: 1
      1188: q
      1191: 1
      1195: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1218: 1
      1220: q
      1222: q
      1224: q
      1225: 1
      1226: q+1
      1228: 1
      1230: 1
      1233: 1
      1234: 1
      1236: q+1
      1238: q
      1240: q
      1243: q
      1244: q+1
      1247: 1
      1248: 1
      1251: 1
      1252: q+1
      1254: 1
      1256: q
      1258: q
      1261: q
      1262: q
      1263: 1
      1264: q
      1266: q
      1268: q
      1271: q
      1272: q
      1274: q+1
      1276: q
      1278: q
      1280: q
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1293: 1
      1305: 1
      1316: 1
      1318: 1
      1327: 1
      1334: q
      1337: 1
      1340: 1
      1350: 1
      1356: 1
      1366: 1
      1374: 1
      1382: 1
      1388: 1
      1397: 1
      1404: q
      1407: 1
      1411: 1
      1430: q
      1433: 1
      1438: 1
      1441: 1
      1442: 1
      1444: q
      1445: 1
      1446: q
      1448: 1
      1451: 1
      1452: q+1
      1454: 1
      1456: 1
      1458: q+1
      1461: 1
      1462: 1
      1464: 1
      1467: 1
      1468: 1
      1470: q
      1472: q+1
      1474: q
      1476: q
      1479: q
      1480: q
      1482: q
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1492: 1
      1505: 1
      1516: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1553: q
      1556: 1
      1565: 1
      1567: 1
      1577: 1
      1585: 1
      1587: 1
      1596: 1
      1609: 1
      1615: 1
      1624: 1
      1631: q
      1634: 1
      1641: 1
      1643: 1
      1646: 1
      1647: 1
      1650: 1
      1651: 1
      1654: 1
      1655: 1
      1657: 1
      1661: 1
      1664: 1
      1665: 1
      1667: q+1
      1669: q
      1670: 1
      1671: q
      1673: 1
      1674: 1
      1678: 1
      1691: 1
      1702: 1
      1714: 1
      1739: 1
      1745: 1
      1751: 1
      1759: 1
      1763: 1
      1765: 1
      1774: 1
      1781: 1
      1787: 1
      1789: 1
      1798: 1
      1801: q
      1804: 1
      1812: 1
      1815: 1
      1820: 1
      1821: 1
      1827: 1
      1830: 1
      1831: 1
      1833: 1
      1850: 1
      1861: 1
      1873: 1
      1884: 1
      1904: 1
      1918: 1
      1934: 1
      1936: 1
      1941: 1
      1953: 1
      1956: 1
      1963: 1
      1964: 1
      1993: 1
      2004: 1
      2034: 1
      2044: 1
      2065: 1
      2106: 1

2107:    0: q^2+3q
         1: q^2+3q
         2: q^2+3q
         3: q^2+3q
         4: q^2+3q
         5: q^2+3q
         6: q^2+3q
         7: q^2+3q
         8: q^2+3q
         9: q^3+q^2+2q
        10: q^2+3q
        11: q^2+3q
        12: q^2+3q
        13: q^2+3q
        14: q^2+3q
        15: q^2+3q
        16: 3q
        17: 3q
        18: q^2+2q
        19: q^2+3q
        20: q^2+3q
        21: q^2+3q
        22: q^2+3q
        23: q^2+3q
        24: q^2+3q
        25: q^2+3q
        26: q^2+3q
        27: q^2+3q
        28: 3q
        29: q^2+3q
        30: q^2+3q
        31: q^2+3q
        32: q^2+3q
        33: 3q
        34: q^2+3q
        35: q^2+3q
        36: 3q
        37: q^2+2q
        38: q
        39: q^2+2q
        40: q
        41: q^2+2q
        42: q
        43: q^2+3q
        44: q^2+3q
        45: q^2+3q
        46: 3q
        47: 3q
        48: q^2+2q
        49: 3q
        50: 3q
        51: q^2+2q
        52: q^2+3q
        53: q^2+3q
        54: q^2+3q
        55: q^2+3q
        56: q^2+3q
        57: q^2+3q
        58: 2q
        59: q
        60: q
        61: 2q
        62: q^2+2q
        63: q
        64: q^2+2q
        65: q
        66: 2q
        67: q
        68: 3q
        69: 2q
        70: q^2+3q
        71: 3q
        72: 3q
        73: 3q
        74: q^2+2q
        75: q
        76: q^2+2q
        77: q
        78: q^2+2q
        79: q
        80: q^2+3q
        81: 3q
        82: q^2+3q
        83: q^2+3q
        84: q^2+3q
        85: 3q
        86: q^2+3q
        87: q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 3q
        92: 3q
        93: q^2+2q
        94: 3q
        95: 3q
        96: q^2+2q
        97: 3q
        98: 3q
        99: q^2+2q
       100: q^2+3q
       101: q^2+3q
       102: q^2+3q
       103: q
       105: q
       106: q
       107: q
       108: 2q
       109: 2q
       110: q
       111: 2q
       112: q
       113: q^2+2q
       114: q
       115: q^2+2q
       116: q
       117: 2q
       118: q
       119: q
       120: 2q
       121: q^2+2q
       122: q
       123: 2q
       124: q
       125: 3q
       126: 2q
       127: 2q
       129: 2q
       131: q^2+q
       133: 3q
       134: 2q
       135: 3q
       136: 3q
       137: 3q
       138: 2q
       139: 3q
       140: 3q
       141: q^2+3q
       142: 3q
       143: 3q
       144: 2q
       145: 3q
       146: q^2+3q
       147: 3q
       148: 3q
       149: q^2+3q
       150: q^2+3q
       151: q^2+2q
       152: q
       153: q^2+2q
       154: q
       155: q^2+2q
       156: q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q
       161: 3q
       162: q^2+2q
       163: 3q
       164: 3q
       165: q^2+2q
       166: 3q
       167: 3q
       168: q^2+2q
       169: q
       171: q
       172: q
       173: q
       175: q
       176: q
       177: q
       179: 2q
       181: 2q
       183: q
       184: 2q
       185: 2q
       186: q
       187: 2q
       188: q
       189: q^2+2q
       190: q
       191: 2q
       192: q
       193: q
       194: 2q
       195: 2q
       196: q
       197: 2q
       198: q
       199: q
       200: 2q
       201: q
       202: 2q
       203: 2q
       204: q
       205: 2q
       206: q
       207: 2q
       208: q
       209: q^2+2q
       210: q
       211: q^2+2q
       212: q
       213: 2q
       215: 2q
       217: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: 2q
       224: 3q
       225: 2q
       226: 2q
       227: 3q
       228: 2q
       229: 3q
       230: 3q
       231: 2q
       232: 3q
       233: 2q
       234: 3q
       235: 3q
       236: 2q
       237: 2q
       239: 2q
       241: q^2+q
       243: 3q
       244: 3q
       245: 3q
       246: q^2+3q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 3q
       257: 3q
       258: q^2+2q
       259: q
       262: q
       263: q
       265: q
       266: q
       267: q
       269: q
       270: q
       271: q
       272: q
       273: q
       275: q
       277: q
       278: q
       279: 2q
       281: q
       284: q
       285: q
       287: q
       289: 2q
       291: q
       293: q
       294: 2q
       295: 2q
       296: q
       297: 2q
       298: q
       299: q
       300: 2q
       301: 2q
       303: 2q
       304: q
       305: 2q
       306: q
       307: q
       308: 2q
       309: 2q
       310: q
       311: 2q
       313: 2q
       314: q
       315: q
       317: 2q
       319: q
       320: 2q
       321: 2q
       322: q
       323: 2q
       324: q
       325: q^2+2q
       326: q
       327: 2q
       329: 2q
       331: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       338: 2q
       340: 2q
       342: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: 2q
       349: 3q
       350: 2q
       351: 3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: 2q
       357: 3q
       358: 2q
       359: 3q
       360: 2q
       362: 2q
       364: q^2+q
       366: 2q
       367: 3q
       368: 2q
       369: 3q
       370: 3q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       381: q
       384: q
       385: q
       387: q
       388: q
       389: q
       391: q
       393: q
       395: q
       396: q
       397: q
       399: q
       401: q
       402: q
       404: q
       405: q
       406: q
       408: q
       409: 2q
       411: q
       413: q
       415: 2q
       417: q
       420: q
       421: q
       423: q
       425: q
       427: 2q
       430: q
       431: q
       433: q
       435: 2q
       437: q
       438: 2q
       439: 2q
       440: q
       441: 2q
       442: q
       443: q
       444: 2q
       445: 2q
       448: q
       449: q
       451: q
       453: q
       454: 2q
       455: 2q
       457: 2q
       458: q
       459: 2q
       460: q
       461: 2q
       462: q
       463: 2q
       465: 2q
       467: q
       469: q
       471: q
       472: 2q
       473: 2q
       474: q
       475: 2q
       476: q
       477: 2q
       479: 2q
       480: q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       485: 2q
       487: 2q
       489: q^2+q
       491: 2q
       492: 2q
       493: 2q
       494: 2q
       495: 2q
       496: 3q
       497: 2q
       498: 2q
       499: 2q
       500: 2q
       501: 3q
       502: 2q
       504: 2q
       506: q^2+q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: 2q
       513: 3q
       514: 2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       525: q
       528: q
       537: q
       539: q
       541: q
       543: q
       544: q
       545: q
       547: q
       553: q
       555: q
       557: q
       558: q
       559: q
       561: q
       563: q
       565: q
       567: q
       568: q
       569: q
       570: q
       573: q
       575: q
       576: q
       577: 2q
       583: q
       585: q
       587: q
       590: q
       591: q
       594: q
       595: q
       597: q
       599: q
       601: 2q
       604: q
       605: q
       607: q
       609: q
       611: 2q
       613: q
       615: q
       616: 2q
       617: 2q
       620: q
       621: q
       623: q
       625: q
       627: 2q
       629: q
       631: 2q
       632: q
       633: 2q
       635: 2q
       637: q
       639: q
       642: q
       643: q
       645: q
       647: q
       648: 2q
       649: 2q
       650: q
       651: 2q
       653: 2q
       654: q
       655: 2q
       656: q
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q
       666: 2q
       668: 2q
       670: q^2+q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: 2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q
       687: 2q
       688: 2q
       689: 2q
       690: q+1
       691: q+1
       692: q+1
       693: q
       697: q
       729: q
       731: q
       733: q
       735: q
       745: q
       747: q
       749: q
       751: q
       757: q
       758: q
       761: q
       762: q
       764: q
       765: q
       767: q
       768: q
       769: 2q
       775: 1
       777: q
       779: q+1
       781: q
       783: q
       786: q
       787: q
       789: 2q
       791: q
       794: 1
       795: q+1
       797: q
       799: q
       802: q
       803: q
       806: q
       807: q
       809: q
       811: q
       813: 2q
       815: q
       816: 2q
       817: 1
       819: q+1
       821: q
       823: q
       826: q
       827: q
       830: q
       831: q
       833: q
       835: q
       837: 2q
       839: 2q
       840: q
       841: q
       843: q
       844: 1
       846: q
       847: q
       849: q
       851: q
       853: 2q
       855: q
       857: 2q
       858: q
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: 2q
       873: q+1
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       884: q
       889: q
       918: 1
       932: q
       934: q
       940: 1
       956: q
       958: q
       966: 1
       968: q
       971: 1
       978: q
       979: q
       982: 2q
       988: q
       990: q
       991: q
       992: 1
       994: 1
       996: q+1
       998: 1
      1001: 1
      1002: q
      1005: q
      1006: q
      1008: q
      1010: q
      1012: q
      1013: 1
      1014: q+1
      1017: 1
      1018: q
      1020: q+1
      1022: q
      1024: q
      1027: q
      1028: q
      1030: q+1
      1032: 1
      1034: q
      1036: q+1
      1038: q
      1041: q
      1042: q
      1044: q
      1046: q
      1047: 1
      1048: q
      1050: q
      1053: q
      1054: q
      1057: q
      1058: q
      1060: q
      1062: q
      1064: q
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1090: 1
      1098: q
      1102: q
      1114: 1
      1124: 1
      1132: 1
      1138: q
      1141: 1
      1146: 1
      1164: 1
      1188: q
      1191: 1
      1196: 1
      1210: 1
      1212: q+1
      1214: 1
      1216: 1
      1219: 1
      1220: q
      1222: q
      1224: q
      1225: 1
      1226: q+1
      1229: 1
      1230: 1
      1232: 1
      1235: 1
      1236: q+1
      1238: q
      1241: q
      1242: q
      1244: q+1
      1246: 1
      1248: 1
      1250: 1
      1252: q+1
      1255: 1
      1256: q
      1259: q
      1260: q
      1262: q
      1263: 1
      1264: q
      1266: q
      1269: q
      1270: q
      1272: q
      1274: q+1
      1276: q
      1278: q
      1280: q
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1294: 1
      1306: 1
      1314: 1
      1320: 1
      1328: 1
      1334: q
      1337: 1
      1342: 1
      1348: 1
      1358: 1
      1365: 1
      1372: 1
      1380: 1
      1390: 1
      1398: 1
      1404: q
      1407: 1
      1412: 1
      1430: q
      1433: 1
      1438: 1
      1440: 1
      1443: 1
      1444: q
      1445: 1
      1446: q
      1448: 1
      1450: 1
      1452: q+1
      1455: 1
      1456: 1
      1458: q+1
      1460: 1
      1463: 1
      1464: 1
      1466: 1
      1469: 1
      1470: q
      1472: q+1
      1474: q
      1477: q
      1478: q
      1480: q
      1482: q
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1493: 1
      1504: 1
      1517: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1553: q
      1556: 1
      1563: 1
      1569: 1
      1576: 1
      1583: 1
      1589: 1
      1597: 1
      1607: 1
      1617: 1
      1625: 1
      1631: q
      1634: 1
      1641: 1
      1643: 1
      1645: 1
      1648: 1
      1649: 1
      1651: 1
      1653: 1
      1656: 1
      1658: 1
      1661: 1
      1663: 1
      1666: 1
      1667: q+1
      1669: q
      1670: 1
      1671: q
      1673: 1
      1674: 1
      1679: 1
      1690: 1
      1703: 1
      1715: 1
      1737: 1
      1747: 1
      1750: 1
      1757: 1
      1761: 1
      1767: 1
      1775: 1
      1783: 1
      1785: 1
      1791: 1
      1799: 1
      1801: q
      1804: 1
      1813: 1
      1815: 1
      1819: 1
      1822: 1
      1827: 1
      1829: 1
      1832: 1
      1833: 1
      1849: 1
      1862: 1
      1874: 1
      1885: 1
      1902: 1
      1920: 1
      1932: 1
      1938: 1
      1942: 1
      1954: 1
      1956: 1
      1962: 1
      1965: 1
      1994: 1
      2005: 1
      2032: 1
      2046: 1
      2066: 1
      2107: 1

2108:    0: 3q^3+4q^2+1
         1: 3q^3+4q^2+1
         2: 3q^3+4q^2+1
         3: 3q^3+4q^2+1
         4: 3q^3+4q^2+1
         5: 3q^3+4q^2+1
         6: 3q^3+4q^2+1
         7: 3q^3+4q^2+1
         8: 3q^3+4q^2+1
         9: q^5+2q^4+2q^3+2q^2+1
        10: 3q^3+4q^2+1
        11: 3q^3+4q^2+1
        12: 3q^3+4q^2+1
        13: 3q^3+4q^2+1
        14: 3q^3+4q^2+1
        15: 3q^3+4q^2+1
        16: 4q^2+1
        17: 4q^2+1
        18: 2q^3+2q^2+1
        19: 3q^3+4q^2+1
        20: 3q^3+4q^2+1
        21: 3q^3+4q^2+1
        22: 3q^3+4q^2+1
        23: 3q^3+4q^2+1
        24: 3q^3+4q^2+1
        25: 3q^3+4q^2+1
        26: 3q^3+4q^2+1
        27: 3q^3+4q^2+1
        28: 4q^2+1
        29: 3q^3+4q^2+1
        30: 3q^3+4q^2+1
        31: 3q^3+4q^2+1
        32: 3q^3+4q^2+1
        33: 4q^2+1
        34: 3q^3+4q^2+1
        35: 3q^3+4q^2+1
        36: 4q^2+1
        37: q^3+2q^2
        38: 2q^3+2q^2+1
        39: q^3+2q^2
        40: 2q^3+2q^2+1
        41: q^3+2q^2
        42: 2q^3+2q^2+1
        43: 3q^3+4q^2+1
        44: 3q^3+4q^2+1
        45: 3q^3+4q^2+1
        46: 4q^2+1
        47: 4q^2+1
        48: 2q^3+2q^2+1
        49: 4q^2+1
        50: 4q^2+1
        51: 2q^3+2q^2+1
        52: 3q^3+4q^2+1
        53: 3q^3+4q^2+1
        54: 3q^3+4q^2+1
        55: 3q^3+4q^2+1
        56: 3q^3+4q^2+1
        57: 3q^3+4q^2+1
        58: q^2
        59: 3q^2+1
        60: 3q^2+1
        61: q^2
        62: q^3+2q^2
        63: 2q^3+2q^2+1
        64: q^3+2q^2
        65: 2q^3+2q^2+1
        66: 2q^2
        67: 2q^2+1
        68: 4q^2+1
        69: 2q^2+1
        70: 3q^3+4q^2+1
        71: 4q^2+1
        72: 4q^2+1
        73: 4q^2+1
        74: q^3+2q^2
        75: 2q^3+2q^2+1
        76: q^3+2q^2
        77: 2q^3+2q^2+1
        78: q^3+2q^2
        79: 2q^3+2q^2+1
        80: 3q^3+4q^2+1
        81: 4q^2+1
        82: 3q^3+4q^2+1
        83: 3q^3+4q^2+1
        84: 3q^3+4q^2+1
        85: 4q^2+1
        86: 3q^3+4q^2+1
        87: 3q^3+4q^2+1
        88: 4q^2+1
        89: 4q^2+1
        90: 2q^3+2q^2+1
        91: 4q^2+1
        92: 4q^2+1
        93: 2q^3+2q^2+1
        94: 4q^2+1
        95: 4q^2+1
        96: 2q^3+2q^2+1
        97: 4q^2+1
        98: 4q^2+1
        99: 2q^3+2q^2+1
       100: 3q^3+4q^2+1
       101: 3q^3+4q^2+1
       102: 3q^3+4q^2+1
       103: q^2
       104: 2q^2+1
       106: q^2
       107: 3q^2+1
       108: q^2
       109: q^2
       110: 3q^2+1
       111: 2q^2
       112: 2q^2+1
       113: q^3+2q^2
       114: 2q^3+2q^2+1
       115: q^3+2q^2
       116: 2q^3+2q^2+1
       117: q^2
       118: 3q^2+1
       119: 3q^2+1
       120: q^2
       121: q^3+2q^2
       122: 2q^3+2q^2+1
       123: 2q^2
       124: 2q^2+1
       125: 4q^2+1
       126: 2q^2+1
       128: q^2+1
       130: q^2+1
       132: q^3+1
       133: 4q^2+1
       134: 2q^2+1
       135: 4q^2+1
       136: 4q^2+1
       137: 4q^2+1
       138: 2q^2+1
       139: 4q^2+1
       140: 4q^2+1
       141: 3q^3+4q^2+1
       142: 4q^2+1
       143: 4q^2+1
       144: 2q^2+1
       145: 4q^2+1
       146: 3q^3+4q^2+1
       147: 4q^2+1
       148: 4q^2+1
       149: 3q^3+4q^2+1
       150: 3q^3+4q^2+1
       151: q^3+2q^2
       152: 2q^3+2q^2+1
       153: q^3+2q^2
       154: 2q^3+2q^2+1
       155: q^3+2q^2
       156: 2q^3+2q^2+1
       157: 4q^2+1
       158: 4q^2+1
       159: 2q^3+2q^2+1
       160: 4q^2+1
       161: 4q^2+1
       162: 2q^3+2q^2+1
       163: 4q^2+1
       164: 4q^2+1
       165: 2q^3+2q^2+1
       166: 4q^2+1
       167: 4q^2+1
       168: 2q^3+2q^2+1
       169: q^2
       170: 2q^2+1
       172: q^2
       173: q^2
       174: 2q^2+1
       176: q^2
       178: 1
       180: q^2+1
       182: q^2+1
       183: 3q^2+1
       184: q^2
       185: q^2
       186: 3q^2+1
       187: 2q^2
       188: 2q^2+1
       189: q^3+2q^2
       190: 2q^3+2q^2+1
       191: q^2
       192: 3q^2+1
       193: 3q^2+1
       194: q^2
       195: q^2
       196: 3q^2+1
       197: 2q^2
       198: 2q^2+1
       199: 3q^2+1
       200: q^2
       201: 3q^2+1
       202: q^2
       203: q^2
       204: 3q^2+1
       205: 2q^2
       206: 2q^2+1
       207: 2q^2
       208: 2q^2+1
       209: q^3+2q^2
       210: 2q^3+2q^2+1
       211: q^3+2q^2
       212: 2q^3+2q^2+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: 2q^2+1
       220: 4q^2+1
       221: 2q^2+1
       222: 4q^2+1
       223: 2q^2+1
       224: 4q^2+1
       225: 2q^2+1
       226: 2q^2+1
       227: 4q^2+1
       228: 2q^2+1
       229: 4q^2+1
       230: 4q^2+1
       231: 2q^2+1
       232: 4q^2+1
       233: 2q^2+1
       234: 4q^2+1
       235: 4q^2+1
       236: 2q^2+1
       238: q^2+1
       240: q^2+1
       242: q^3+1
       243: 4q^2+1
       244: 4q^2+1
       245: 4q^2+1
       246: 3q^3+4q^2+1
       247: 4q^2+1
       248: 4q^2+1
       249: 2q^3+2q^2+1
       250: 4q^2+1
       251: 4q^2+1
       252: 2q^3+2q^2+1
       253: 4q^2+1
       254: 4q^2+1
       255: 2q^3+2q^2+1
       256: 4q^2+1
       257: 4q^2+1
       258: 2q^3+2q^2+1
       260: q^2+1
       263: q^2
       264: 2q^2+1
       266: q^2
       267: q^2
       268: 2q^2+1
       269: q^2
       271: q^2
       273: q^2
       274: 2q^2+1
       275: q^2
       276: 2q^2+1
       278: q^2
       280: q^2+1
       282: 1
       283: q^2+1
       286: q^2+1
       288: 1
       290: q^2+1
       292: 1
       293: 3q^2+1
       294: q^2
       295: q^2
       296: 3q^2+1
       297: 2q^2
       298: 2q^2+1
       299: 3q^2+1
       300: q^2
       302: q^2+1
       303: q^2
       304: 3q^2+1
       305: 2q^2
       306: 2q^2+1
       307: 3q^2+1
       308: q^2
       309: q^2
       310: 3q^2+1
       312: q^2+1
       313: 2q^2
       314: 2q^2+1
       316: 1
       318: q^2+1
       319: 3q^2+1
       320: q^2
       321: q^2
       322: 3q^2+1
       323: 2q^2
       324: 2q^2+1
       325: q^3+2q^2
       326: 2q^3+2q^2+1
       328: q^2+1
       330: q^2+1
       332: q^3+1
       333: 2q^2+1
       334: 2q^2+1
       335: 2q^2+1
       336: 2q^2+1
       337: 4q^2+1
       339: q^2+1
       341: q^2+1
       343: q^3+1
       344: 2q^2+1
       345: 4q^2+1
       346: 2q^2+1
       347: 4q^2+1
       348: 2q^2+1
       349: 4q^2+1
       350: 2q^2+1
       351: 4q^2+1
       352: 2q^2+1
       353: 4q^2+1
       354: 2q^2+1
       355: 4q^2+1
       356: 2q^2+1
       357: 4q^2+1
       358: 2q^2+1
       359: 4q^2+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: 2q^2+1
       367: 4q^2+1
       368: 2q^2+1
       369: 4q^2+1
       370: 4q^2+1
       371: 4q^2+1
       372: 4q^2+1
       373: 2q^3+2q^2+1
       374: 4q^2+1
       375: 4q^2+1
       376: 2q^3+2q^2+1
       378: 1
       382: q^2+1
       385: q^2
       386: 2q^2+1
       388: q^2
       390: q^2+1
       393: q^2
       394: 2q^2+1
       396: q^2
       400: q^2+1
       401: q^2
       403: 2q^2+1
       404: q^2
       405: q^2
       406: q^2
       407: 2q^2+1
       410: q^2+1
       412: 1
       414: 1
       416: q^2+1
       418: 1
       419: q^2+1
       422: q^2+1
       424: 1
       426: 1
       428: q^2+1
       429: q^2+1
       432: q^2+1
       434: 1
       436: q^2+1
       437: 3q^2+1
       438: q^2
       439: q^2
       440: 3q^2+1
       441: 2q^2
       442: 2q^2+1
       443: 3q^2+1
       444: q^2
       446: q^2+1
       447: q^2+1
       450: q^2+1
       452: 1
       453: 3q^2+1
       454: q^2
       456: q^2+1
       457: q^2
       458: 3q^2+1
       459: 2q^2
       460: 2q^2+1
       461: q^2
       462: 3q^2+1
       464: q^2+1
       466: q^2+1
       468: 1
       470: 1
       471: 3q^2+1
       472: q^2
       473: q^2
       474: 3q^2+1
       475: 2q^2
       476: 2q^2+1
       478: q^2+1
       479: 2q^2
       480: 2q^2+1
       481: 2q^2+1
       482: 2q^2+1
       483: 2q^2+1
       484: 4q^2+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: 2q^2+1
       492: 2q^2+1
       493: 2q^2+1
       494: 2q^2+1
       495: 2q^2+1
       496: 4q^2+1
       497: 2q^2+1
       498: 2q^2+1
       499: 2q^2+1
       500: 2q^2+1
       501: 4q^2+1
       503: q^2+1
       505: q^2+1
       507: q^3+1
       508: 2q^2+1
       509: 4q^2+1
       510: 2q^2+1
       511: 4q^2+1
       512: 2q^2+1
       513: 4q^2+1
       514: 2q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 4q^2+1
       519: 4q^2+1
       520: 2q^3+2q^2+1
       522: 1
       526: q^2+1
       530: 1
       534: 1
       538: q^2+1
       541: q^2
       542: 2q^2+1
       543: q^2
       546: q^2+1
       551: 1
       556: q^2+1
       557: q^2
       559: q^2
       560: 2q^2+1
       564: q^2+1
       565: q^2
       566: 2q^2+1
       568: q^2
       571: q^2+1
       573: q^2
       574: 2q^2+1
       575: q^2
       581: q^2+1
       584: 1
       586: 1
       588: 1
       589: q^2+1
       592: q^2+1
       593: q^2+1
       596: q^2+1
       598: 1
       600: 1
       602: q^2+1
       603: q^2+1
       606: 1
       608: q^2+1
       610: 1
       612: q^2+1
       614: 1
       615: 3q^2+1
       616: q^2
       618: q^2+1
       619: q^2+1
       622: q^2+1
       624: 1
       626: 1
       628: q^2+1
       630: 1
       631: q^2
       632: 3q^2+1
       634: q^2+1
       636: q^2+1
       638: 1
       640: 1
       641: q^2+1
       644: q^2+1
       646: 1
       647: 3q^2+1
       648: q^2
       649: q^2
       650: 3q^2+1
       652: q^2+1
       653: 2q^2
       654: 2q^2+1
       655: 2q^2
       656: 2q^2+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q^2+1
       667: q^2+1
       669: q^2+1
       671: q^3+1
       672: 4q^2+1
       673: 2q^2+1
       674: q+1
       675: 2q^2+1
       676: 2q^2+1
       677: 2q^2+1
       678: 4q^2+1
       679: 2q^2+1
       680: q+1
       681: 2q^2+1
       682: 2q^2+1
       683: 2q^2+1
       684: 4q^2+1
       685: 2q^2+1
       686: 2q^2+1
       687: 2q^2+1
       688: 2q^2+1
       689: 2q^2+1
       690: q+1
       691: q+1
       692: q+1
       699: q^2+1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: q^2+1
       734: q^2+1
       740: 1
       744: 1
       748: q^2+1
       752: q^2+1
       754: 1
       759: q^2+1
       761: q^2
       762: q^2
       763: 2q^2+1
       765: q^2
       766: 2q^2+1
       768: q^2
       773: q^2+1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: 1
       785: q^2+1
       788: q^2+1
       790: q^2+1
       792: 1
       793: 1
       796: q+1
       798: 1
       800: 1
       801: q^2+1
       804: q^2+1
       805: q^2+1
       808: q^2+1
       810: 1
       812: 1
       814: q^2+1
       815: 3q^2+1
       816: q^2
       818: 1
       820: q+1
       822: 1
       824: 1
       825: q^2+1
       828: q^2+1
       829: q^2+1
       832: q^2+1
       834: 1
       836: 1
       838: q^2+1
       839: q^2
       840: 3q^2+1
       842: 1
       843: q
       844: 1
       845: q^2+1
       848: q^2+1
       850: 1
       852: 1
       854: q^2+1
       856: 1
       857: 2q^2
       858: 2q^2+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q^2+1
       869: q+1
       870: q+1
       871: 2q^2+1
       872: 2q^2+1
       873: q+1
       874: q+1
       875: 2q^2+1
       876: 2q^2+1
       877: 2q^2+1
       878: 2q^2+1
       879: 2q^2+1
       880: 2q^2+1
       881: q+1
       882: q+1
       883: q+1
       890: q^2+1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       926: 1
       929: 1
       933: q^2+1
       939: 1
       943: 1
       947: 1
       951: 1
       953: 1
       959: q^2+1
       962: 1
       965: 1
       969: q
       972: 1
       976: 1
       980: q^2+1
       986: q^2+1
       988: q^2
       989: 2q^2+1
       991: q^2
       993: 1
       995: 1
       997: q+1
       999: 1
      1000: 1
      1003: 1
      1004: q^2+1
      1007: q^2+1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1015: q+1
      1016: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: 1
      1026: q^2+1
      1029: q^2+1
      1031: q+1
      1033: 1
      1035: 1
      1037: q+1
      1039: 1
      1040: q^2+1
      1043: 1
      1045: q^2+1
      1046: q
      1047: 1
      1049: 1
      1051: 1
      1052: q^2+1
      1055: q^2+1
      1056: q^2+1
      1059: q^2+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q^2+1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q^2+1
      1083: 2q^2+1
      1084: q+1
      1085: 2q^2+1
      1092: 1
      1104: q^2+1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1139: q
      1142: 1
      1145: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1189: q
      1192: 1
      1195: 1
      1200: 1
      1205: 1
      1207: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1224: q
      1225: 1
      1227: q+1
      1228: 1
      1231: 1
      1233: 1
      1234: 1
      1237: q+1
      1239: 1
      1240: q^2+1
      1243: q^2+1
      1245: q+1
      1247: 1
      1249: 1
      1251: 1
      1253: q+1
      1254: 1
      1257: 1
      1258: q^2+1
      1261: q^2+1
      1262: q
      1263: 1
      1265: 1
      1267: 1
      1268: q^2+1
      1271: q^2+1
      1273: 1
      1275: q+1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q^2+1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1335: q
      1338: 1
      1341: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1405: q
      1408: 1
      1411: 1
      1416: 1
      1421: 1
      1423: 1
      1427: 1
      1431: q
      1434: 1
      1439: 1
      1441: 1
      1442: 1
      1444: q
      1445: 1
      1447: 1
      1449: 1
      1451: 1
      1453: q+1
      1454: 1
      1457: 1
      1459: q+1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: q+1
      1475: 1
      1476: q^2+1
      1479: q^2+1
      1481: 1
      1482: q
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1495: 1
      1508: 1
      1519: 1
      1531: 1
      1544: 1
      1546: 1
      1550: 1
      1554: q
      1557: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1632: q
      1635: 1
      1642: 1
      1644: 1
      1646: 1
      1647: 1
      1650: 1
      1652: 1
      1654: 1
      1655: 1
      1657: 1
      1662: 1
      1664: 1
      1665: 1
      1668: q+1
      1669: q
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1681: 1
      1694: 1
      1705: 1
      1716: 1
      1740: 1
      1746: 1
      1751: 1
      1756: 1
      1760: 1
      1764: 1
      1766: 1
      1774: 1
      1779: 1
      1782: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1802: q
      1805: 1
      1809: 1
      1812: 1
      1816: 1
      1820: 1
      1821: 1
      1828: 1
      1830: 1
      1831: 1
      1833: 1
      1853: 1
      1864: 1
      1875: 1
      1887: 1
      1905: 1
      1919: 1
      1935: 1
      1937: 1
      1941: 1
      1950: 1
      1953: 1
      1957: 1
      1963: 1
      1964: 1
      1995: 1
      2007: 1
      2035: 1
      2045: 1
      2065: 1
      2108: 1

2109:    0: 3q^3+4q^2+1
         1: 3q^3+4q^2+1
         2: 3q^3+4q^2+1
         3: 3q^3+4q^2+1
         4: 3q^3+4q^2+1
         5: 3q^3+4q^2+1
         6: 3q^3+4q^2+1
         7: 3q^3+4q^2+1
         8: 3q^3+4q^2+1
         9: q^5+2q^4+2q^3+2q^2+1
        10: 3q^3+4q^2+1
        11: 3q^3+4q^2+1
        12: 3q^3+4q^2+1
        13: 3q^3+4q^2+1
        14: 3q^3+4q^2+1
        15: 3q^3+4q^2+1
        16: 4q^2+1
        17: 4q^2+1
        18: 2q^3+2q^2+1
        19: 3q^3+4q^2+1
        20: 3q^3+4q^2+1
        21: 3q^3+4q^2+1
        22: 3q^3+4q^2+1
        23: 3q^3+4q^2+1
        24: 3q^3+4q^2+1
        25: 3q^3+4q^2+1
        26: 3q^3+4q^2+1
        27: 3q^3+4q^2+1
        28: 4q^2+1
        29: 3q^3+4q^2+1
        30: 3q^3+4q^2+1
        31: 3q^3+4q^2+1
        32: 3q^3+4q^2+1
        33: 4q^2+1
        34: 3q^3+4q^2+1
        35: 3q^3+4q^2+1
        36: 4q^2+1
        37: q^3+2q^2
        38: 2q^3+2q^2+1
        39: q^3+2q^2
        40: 2q^3+2q^2+1
        41: q^3+2q^2
        42: 2q^3+2q^2+1
        43: 3q^3+4q^2+1
        44: 3q^3+4q^2+1
        45: 3q^3+4q^2+1
        46: 4q^2+1
        47: 4q^2+1
        48: 2q^3+2q^2+1
        49: 4q^2+1
        50: 4q^2+1
        51: 2q^3+2q^2+1
        52: 3q^3+4q^2+1
        53: 3q^3+4q^2+1
        54: 3q^3+4q^2+1
        55: 3q^3+4q^2+1
        56: 3q^3+4q^2+1
        57: 3q^3+4q^2+1
        58: 3q^2+1
        59: q^2
        60: q^2
        61: 3q^2+1
        62: q^3+2q^2
        63: 2q^3+2q^2+1
        64: q^3+2q^2
        65: 2q^3+2q^2+1
        66: 2q^2
        67: 2q^2+1
        68: 4q^2+1
        69: 2q^2+1
        70: 3q^3+4q^2+1
        71: 4q^2+1
        72: 4q^2+1
        73: 4q^2+1
        74: q^3+2q^2
        75: 2q^3+2q^2+1
        76: q^3+2q^2
        77: 2q^3+2q^2+1
        78: q^3+2q^2
        79: 2q^3+2q^2+1
        80: 3q^3+4q^2+1
        81: 4q^2+1
        82: 3q^3+4q^2+1
        83: 3q^3+4q^2+1
        84: 3q^3+4q^2+1
        85: 4q^2+1
        86: 3q^3+4q^2+1
        87: 3q^3+4q^2+1
        88: 4q^2+1
        89: 4q^2+1
        90: 2q^3+2q^2+1
        91: 4q^2+1
        92: 4q^2+1
        93: 2q^3+2q^2+1
        94: 4q^2+1
        95: 4q^2+1
        96: 2q^3+2q^2+1
        97: 4q^2+1
        98: 4q^2+1
        99: 2q^3+2q^2+1
       100: 3q^3+4q^2+1
       101: 3q^3+4q^2+1
       102: 3q^3+4q^2+1
       103: q^2
       105: 2q^2+1
       106: q^2
       107: q^2
       108: 3q^2+1
       109: 3q^2+1
       110: q^2
       111: 2q^2
       112: 2q^2+1
       113: q^3+2q^2
       114: 2q^3+2q^2+1
       115: q^3+2q^2
       116: 2q^3+2q^2+1
       117: 3q^2+1
       118: q^2
       119: q^2
       120: 3q^2+1
       121: q^3+2q^2
       122: 2q^3+2q^2+1
       123: 2q^2
       124: 2q^2+1
       125: 4q^2+1
       126: 2q^2+1
       128: q^2+1
       130: q^2+1
       132: q^3+1
       133: 4q^2+1
       134: 2q^2+1
       135: 4q^2+1
       136: 4q^2+1
       137: 4q^2+1
       138: 2q^2+1
       139: 4q^2+1
       140: 4q^2+1
       141: 3q^3+4q^2+1
       142: 4q^2+1
       143: 4q^2+1
       144: 2q^2+1
       145: 4q^2+1
       146: 3q^3+4q^2+1
       147: 4q^2+1
       148: 4q^2+1
       149: 3q^3+4q^2+1
       150: 3q^3+4q^2+1
       151: q^3+2q^2
       152: 2q^3+2q^2+1
       153: q^3+2q^2
       154: 2q^3+2q^2+1
       155: q^3+2q^2
       156: 2q^3+2q^2+1
       157: 4q^2+1
       158: 4q^2+1
       159: 2q^3+2q^2+1
       160: 4q^2+1
       161: 4q^2+1
       162: 2q^3+2q^2+1
       163: 4q^2+1
       164: 4q^2+1
       165: 2q^3+2q^2+1
       166: 4q^2+1
       167: 4q^2+1
       168: 2q^3+2q^2+1
       169: q^2
       171: 2q^2+1
       172: q^2
       173: q^2
       175: 2q^2+1
       176: q^2
       178: 1
       180: q^2+1
       182: q^2+1
       183: q^2
       184: 3q^2+1
       185: 3q^2+1
       186: q^2
       187: 2q^2
       188: 2q^2+1
       189: q^3+2q^2
       190: 2q^3+2q^2+1
       191: 3q^2+1
       192: q^2
       193: q^2
       194: 3q^2+1
       195: 3q^2+1
       196: q^2
       197: 2q^2
       198: 2q^2+1
       199: q^2
       200: 3q^2+1
       201: q^2
       202: 3q^2+1
       203: 3q^2+1
       204: q^2
       205: 2q^2
       206: 2q^2+1
       207: 2q^2
       208: 2q^2+1
       209: q^3+2q^2
       210: 2q^3+2q^2+1
       211: q^3+2q^2
       212: 2q^3+2q^2+1
       214: q^2+1
       216: q^2+1
       218: q^3+1
       219: 2q^2+1
       220: 4q^2+1
       221: 2q^2+1
       222: 4q^2+1
       223: 2q^2+1
       224: 4q^2+1
       225: 2q^2+1
       226: 2q^2+1
       227: 4q^2+1
       228: 2q^2+1
       229: 4q^2+1
       230: 4q^2+1
       231: 2q^2+1
       232: 4q^2+1
       233: 2q^2+1
       234: 4q^2+1
       235: 4q^2+1
       236: 2q^2+1
       238: q^2+1
       240: q^2+1
       242: q^3+1
       243: 4q^2+1
       244: 4q^2+1
       245: 4q^2+1
       246: 3q^3+4q^2+1
       247: 4q^2+1
       248: 4q^2+1
       249: 2q^3+2q^2+1
       250: 4q^2+1
       251: 4q^2+1
       252: 2q^3+2q^2+1
       253: 4q^2+1
       254: 4q^2+1
       255: 2q^3+2q^2+1
       256: 4q^2+1
       257: 4q^2+1
       258: 2q^3+2q^2+1
       261: q^2+1
       263: q^2
       265: 2q^2+1
       266: q^2
       267: q^2
       269: q^2
       270: 2q^2+1
       271: q^2
       272: 2q^2+1
       273: q^2
       275: q^2
       277: 2q^2+1
       278: q^2
       280: q^2+1
       282: 1
       284: q^2+1
       285: q^2+1
       288: 1
       290: q^2+1
       292: 1
       293: q^2
       294: 3q^2+1
       295: 3q^2+1
       296: q^2
       297: 2q^2
       298: 2q^2+1
       299: q^2
       300: 3q^2+1
       302: q^2+1
       303: 3q^2+1
       304: q^2
       305: 2q^2
       306: 2q^2+1
       307: q^2
       308: 3q^2+1
       309: 3q^2+1
       310: q^2
       312: q^2+1
       313: 2q^2
       314: 2q^2+1
       316: 1
       318: q^2+1
       319: q^2
       320: 3q^2+1
       321: 3q^2+1
       322: q^2
       323: 2q^2
       324: 2q^2+1
       325: q^3+2q^2
       326: 2q^3+2q^2+1
       328: q^2+1
       330: q^2+1
       332: q^3+1
       333: 2q^2+1
       334: 2q^2+1
       335: 2q^2+1
       336: 2q^2+1
       337: 4q^2+1
       339: q^2+1
       341: q^2+1
       343: q^3+1
       344: 2q^2+1
       345: 4q^2+1
       346: 2q^2+1
       347: 4q^2+1
       348: 2q^2+1
       349: 4q^2+1
       350: 2q^2+1
       351: 4q^2+1
       352: 2q^2+1
       353: 4q^2+1
       354: 2q^2+1
       355: 4q^2+1
       356: 2q^2+1
       357: 4q^2+1
       358: 2q^2+1
       359: 4q^2+1
       361: q^2+1
       363: q^2+1
       365: q^3+1
       366: 2q^2+1
       367: 4q^2+1
       368: 2q^2+1
       369: 4q^2+1
       370: 4q^2+1
       371: 4q^2+1
       372: 4q^2+1
       373: 2q^3+2q^2+1
       374: 4q^2+1
       375: 4q^2+1
       376: 2q^3+2q^2+1
       379: 1
       383: q^2+1
       385: q^2
       387: 2q^2+1
       388: q^2
       392: q^2+1
       393: q^2
       395: 2q^2+1
       396: q^2
       398: q^2+1
       401: q^2
       402: 2q^2+1
       404: q^2
       405: q^2
       406: q^2
       408: 2q^2+1
       410: q^2+1
       412: 1
       414: 1
       416: q^2+1
       418: 1
       420: q^2+1
       421: q^2+1
       424: 1
       426: 1
       428: q^2+1
       430: q^2+1
       431: q^2+1
       434: 1
       436: q^2+1
       437: q^2
       438: 3q^2+1
       439: 3q^2+1
       440: q^2
       441: 2q^2
       442: 2q^2+1
       443: q^2
       444: 3q^2+1
       446: q^2+1
       448: q^2+1
       449: q^2+1
       452: 1
       453: q^2
       454: 3q^2+1
       456: q^2+1
       457: 3q^2+1
       458: q^2
       459: 2q^2
       460: 2q^2+1
       461: 3q^2+1
       462: q^2
       464: q^2+1
       466: q^2+1
       468: 1
       470: 1
       471: q^2
       472: 3q^2+1
       473: 3q^2+1
       474: q^2
       475: 2q^2
       476: 2q^2+1
       478: q^2+1
       479: 2q^2
       480: 2q^2+1
       481: 2q^2+1
       482: 2q^2+1
       483: 2q^2+1
       484: 4q^2+1
       486: q^2+1
       488: q^2+1
       490: q^3+1
       491: 2q^2+1
       492: 2q^2+1
       493: 2q^2+1
       494: 2q^2+1
       495: 2q^2+1
       496: 4q^2+1
       497: 2q^2+1
       498: 2q^2+1
       499: 2q^2+1
       500: 2q^2+1
       501: 4q^2+1
       503: q^2+1
       505: q^2+1
       507: q^3+1
       508: 2q^2+1
       509: 4q^2+1
       510: 2q^2+1
       511: 4q^2+1
       512: 2q^2+1
       513: 4q^2+1
       514: 2q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 4q^2+1
       519: 4q^2+1
       520: 2q^3+2q^2+1
       523: 1
       527: q^2+1
       531: 1
       535: 1
       540: q^2+1
       541: q^2
       543: q^2
       544: 2q^2+1
       548: q^2+1
       550: 1
       554: q^2+1
       557: q^2
       558: 2q^2+1
       559: q^2
       562: q^2+1
       565: q^2
       567: 2q^2+1
       568: q^2
       572: q^2+1
       573: q^2
       575: q^2
       576: 2q^2+1
       581: q^2+1
       584: 1
       586: 1
       588: 1
       590: q^2+1
       591: q^2+1
       594: q^2+1
       595: q^2+1
       598: 1
       600: 1
       602: q^2+1
       604: q^2+1
       606: 1
       607: q^2+1
       610: 1
       612: q^2+1
       614: 1
       615: q^2
       616: 3q^2+1
       618: q^2+1
       620: q^2+1
       621: q^2+1
       624: 1
       626: 1
       628: q^2+1
       630: 1
       631: 3q^2+1
       632: q^2
       634: q^2+1
       636: q^2+1
       638: 1
       640: 1
       642: q^2+1
       643: q^2+1
       646: 1
       647: q^2
       648: 3q^2+1
       649: 3q^2+1
       650: q^2
       652: q^2+1
       653: 2q^2
       654: 2q^2+1
       655: 2q^2
       656: 2q^2+1
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q^2+1
       667: q^2+1
       669: q^2+1
       671: q^3+1
       672: 4q^2+1
       673: 2q^2+1
       674: q+1
       675: 2q^2+1
       676: 2q^2+1
       677: 2q^2+1
       678: 4q^2+1
       679: 2q^2+1
       680: q+1
       681: 2q^2+1
       682: 2q^2+1
       683: 2q^2+1
       684: 4q^2+1
       685: 2q^2+1
       686: 2q^2+1
       687: 2q^2+1
       688: 2q^2+1
       689: 2q^2+1
       690: q+1
       691: q+1
       692: q+1
       700: q^2+1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: q^2+1
       736: q^2+1
       738: 1
       742: 1
       746: q^2+1
       750: q^2+1
       755: 1
       760: q^2+1
       761: q^2
       762: q^2
       764: 2q^2+1
       765: q^2
       767: 2q^2+1
       768: q^2
       773: q^2+1
       776: 1
       778: 1
       780: q+1
       782: 1
       784: 1
       786: q^2+1
       787: q^2+1
       790: q^2+1
       792: 1
       794: 1
       796: q+1
       798: 1
       800: 1
       802: q^2+1
       803: q^2+1
       806: q^2+1
       807: q^2+1
       810: 1
       812: 1
       814: q^2+1
       815: q^2
       816: 3q^2+1
       817: 1
       820: q+1
       822: 1
       824: 1
       826: q^2+1
       827: q^2+1
       830: q^2+1
       831: q^2+1
       834: 1
       836: 1
       838: q^2+1
       839: 3q^2+1
       840: q^2
       842: 1
       843: q
       844: 1
       846: q^2+1
       847: q^2+1
       850: 1
       852: 1
       854: q^2+1
       856: 1
       857: 2q^2
       858: 2q^2+1
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q^2+1
       869: q+1
       870: q+1
       871: 2q^2+1
       872: 2q^2+1
       873: q+1
       874: q+1
       875: 2q^2+1
       876: 2q^2+1
       877: 2q^2+1
       878: 2q^2+1
       879: 2q^2+1
       880: 2q^2+1
       881: q+1
       882: q+1
       883: q+1
       891: q^2+1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       925: 1
       931: 1
       935: q^2+1
       937: 1
       941: 1
       945: 1
       949: 1
       954: 1
       957: q^2+1
       963: 1
       966: 1
       969: q
       972: 1
       977: 1
       981: q^2+1
       986: q^2+1
       988: q^2
       990: 2q^2+1
       991: q^2
       993: 1
       995: 1
       997: q+1
       998: 1
      1001: 1
      1003: 1
      1005: q^2+1
      1006: q^2+1
      1009: 1
      1011: 1
      1012: q
      1013: 1
      1015: q+1
      1017: 1
      1019: 1
      1021: q+1
      1023: 1
      1025: 1
      1027: q^2+1
      1028: q^2+1
      1031: q+1
      1032: 1
      1035: 1
      1037: q+1
      1039: 1
      1041: q^2+1
      1043: 1
      1044: q^2+1
      1046: q
      1047: 1
      1049: 1
      1051: 1
      1053: q^2+1
      1054: q^2+1
      1057: q^2+1
      1058: q^2+1
      1061: 1
      1063: 1
      1065: 1
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q^2+1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q^2+1
      1083: 2q^2+1
      1084: q+1
      1085: 2q^2+1
      1093: 1
      1105: q^2+1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1139: q
      1142: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1165: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1189: q
      1192: 1
      1196: 1
      1201: 1
      1203: 1
      1209: 1
      1211: 1
      1213: q+1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1224: q
      1225: 1
      1227: q+1
      1229: 1
      1231: 1
      1232: 1
      1235: 1
      1237: q+1
      1239: 1
      1241: q^2+1
      1242: q^2+1
      1245: q+1
      1246: 1
      1249: 1
      1250: 1
      1253: q+1
      1255: 1
      1257: 1
      1259: q^2+1
      1260: q^2+1
      1262: q
      1263: 1
      1265: 1
      1267: 1
      1269: q^2+1
      1270: q^2+1
      1273: 1
      1275: q+1
      1277: 1
      1279: 1
      1280: q
      1281: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q^2+1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1335: q
      1338: 1
      1343: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1373: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1405: q
      1408: 1
      1412: 1
      1417: 1
      1419: 1
      1425: 1
      1428: 1
      1431: q
      1434: 1
      1439: 1
      1440: 1
      1443: 1
      1444: q
      1445: 1
      1447: 1
      1449: 1
      1450: 1
      1453: q+1
      1455: 1
      1457: 1
      1459: q+1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: q+1
      1475: 1
      1477: q^2+1
      1478: q^2+1
      1481: 1
      1482: q
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1496: 1
      1507: 1
      1520: 1
      1532: 1
      1542: 1
      1548: 1
      1551: 1
      1554: q
      1557: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1632: q
      1635: 1
      1642: 1
      1644: 1
      1645: 1
      1648: 1
      1649: 1
      1652: 1
      1653: 1
      1656: 1
      1658: 1
      1662: 1
      1663: 1
      1666: 1
      1668: q+1
      1669: q
      1670: 1
      1672: 1
      1673: 1
      1674: 1
      1682: 1
      1693: 1
      1706: 1
      1717: 1
      1738: 1
      1748: 1
      1750: 1
      1755: 1
      1758: 1
      1762: 1
      1768: 1
      1775: 1
      1780: 1
      1784: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1802: q
      1805: 1
      1810: 1
      1813: 1
      1816: 1
      1819: 1
      1822: 1
      1828: 1
      1829: 1
      1832: 1
      1833: 1
      1852: 1
      1865: 1
      1876: 1
      1888: 1
      1903: 1
      1921: 1
      1933: 1
      1939: 1
      1942: 1
      1951: 1
      1954: 1
      1957: 1
      1962: 1
      1965: 1
      1996: 1
      2008: 1
      2033: 1
      2047: 1
      2066: 1
      2109: 1

2110:    0: 3q^5+q^4+q^2
         1: q^6+2q^5+q^4+q^2
         2: 3q^5+q^4+q^2
         3: q^7+2q^6+3q^5+q^4+q^2
         4: 3q^5+q^4+q^2
         5: q^6+2q^5+q^4+q^2
         6: q^6+2q^5+q^4+q^2
         7: 3q^5+q^4+q^2
         8: q^6+2q^5+q^4+q^2
         9: q^7+q^6+2q^5+q^4+q^2
        10: 2q^5+q^2
        11: q^6+2q^5+q^2
        12: 2q^5+q^2
        13: 3q^5+q^4+q^2
        14: 3q^5+q^4+q^2
        15: q^6+2q^5+q^4+q^2
        16: 2q^5+q^4+q^2
        17: q^5+q^4+q^2
        18: 2q^5+q^4+q^2
        19: 3q^5+q^4+q^2
        20: q^6+2q^5+q^4+q^2
        21: 3q^5+q^4+q^2
        22: 2q^5+q^4+q^2
        23: q^6+2q^5+q^4+q^2
        24: 2q^5+q^4+q^2
        25: 2q^5+q^4+q^2
        26: q^6+2q^5+q^4+q^2
        27: 2q^5+q^4+q^2
        28: q^5+q^2
        29: 2q^5+q^2
        30: 3q^5+q^4+q^2
        31: 2q^5+q^2
        32: 2q^5+q^4+q^2
        33: q^5+q^4+q^2
        34: 2q^5+q^2
        35: 2q^5+q^4+q^2
        36: q^5+q^4+q^2
        37: 2q^5+q^4+q^2
        39: q^6+2q^5+q^4+q^2
        41: 2q^5+q^4+q^2
        43: 2q^5+q^2
        44: 2q^5+q^2
        45: q^6+2q^5+q^2
        46: 2q^5+q^4+q^2
        47: q^5+q^4+q^2
        48: 2q^5+q^4+q^2
        49: 2q^5+q^4+q^2
        50: q^5+q^4+q^2
        51: 2q^5+q^4+q^2
        52: 2q^5+q^4+q^2
        53: q^6+2q^5+q^4+q^2
        54: 2q^5+q^4+q^2
        55: 2q^5+q^4+q^2
        56: q^6+2q^5+q^4+q^2
        57: 2q^5+q^4+q^2
        58: q^5+q^2
        60: q^5+q^2
        62: 2q^5+q^2
        64: 2q^5+q^4+q^2
        66: q^5+q^4+q^2
        68: q^5+q^2
        69: q^5+q^4+q^2
        70: 2q^5+q^2
        71: q^5+q^2
        72: q^5+q^4+q^2
        73: q^5+q^4+q^2
        74: 2q^5+q^4+q^2
        76: q^6+2q^5+q^4+q^2
        78: 2q^5+q^4+q^2
        80: 2q^5+q^2
        81: q^5+q^4+q^2
        82: 2q^5+q^2
        83: 2q^5+q^4+q^2
        84: 2q^5+q^2
        85: q^5+q^4+q^2
        86: 2q^5+q^2
        87: 2q^5+q^4+q^2
        88: q^2
        89: q^2
        90: q^5+q^2
        91: 2q^5+q^4+q^2
        92: q^5+q^4+q^2
        93: 2q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^5+q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^5+q^4+q^2
       100: q^5+q^4+q^2
       101: q^5+q^2
       102: q^5+q^4+q^2
       103: q^5+q^2
       107: q^5+q^2
       109: q^5+q^2
       111: q^5+q^4+q^2
       113: 2q^5+q^2
       115: 2q^5+q^4+q^2
       117: q^5+q^2
       119: q^5+q^2
       121: 2q^5+q^2
       123: q^5+q^4+q^2
       125: q^2
       126: q^2
       127: q^4+q^2
       129: q^4+q^2
       131: q^5+q^4+q^2
       133: q^5+q^2
       134: q^5+q^4+q^2
       135: q^5+q^4+q^2
       136: q^5+q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: 2q^5+q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: 2q^5+q^2
       147: q^4+q^2
       148: q^2
       149: q^5+q^2
       150: q^5+q^4+q^2
       151: q^5+q^4+q^2
       153: q^5+q^2
       155: q^5+q^4+q^2
       157: q^2
       158: q^2
       159: q^5+q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^5+q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^5+q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       169: q^5+q^2
       173: q^5+q^2
       177: q^4+q^2
       179: q^2
       181: q^4+q^2
       183: q^5+q^2
       185: q^5+q^2
       187: q^5+q^4+q^2
       189: 2q^5+q^2
       191: q^2
       193: q^2
       195: q^2
       197: q^2
       199: q^2
       201: q^2
       203: q^2
       205: q^2
       207: q^2
       209: q^5+q^2
       211: q^5+q^4+q^2
       213: q^4+q^2
       215: q^4+q^2
       217: q^5+q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       237: q^4+q^2
       239: q^2
       241: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^5+q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^5+q^2
       253: q^2
       254: q^2
       255: q^5+q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       259: q^2
       263: q^5+q^2
       267: q^2
       271: q^2
       275: q^2
       279: q^2
       281: q^4+q^2
       283: q^2
       285: q^2
       287: q^2
       289: q^4+q^2
       291: q^4+q^2
       293: q^2
       295: q^2
       297: q^2
       299: q^2
       301: q^2
       303: q^2
       305: q^2
       307: q^2
       309: q^2
       311: q^2
       313: q^2
       315: q^4+q^2
       317: q^2
       319: q^2
       321: q^2
       323: q^2
       325: q^5+q^2
       327: q^2
       329: q^2
       331: q^5+q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       338: q^4+q^2
       340: q^2
       342: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       360: q^4+q^2
       362: q^2
       364: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       377: q^2
       381: q^2
       385: q^2
       389: q^2
       393: q^2
       397: q^2
       401: q^2
       405: q^2
       409: q^2
       411: q^2
       413: q^2
       415: q^2
       417: q^4+q^2
       419: q^2
       421: q^2
       423: q^2
       425: q^4+q^2
       427: q^2
       429: q^2
       431: q^2
       433: q^2
       435: q^2
       437: q^2
       439: q^2
       441: q^2
       443: q^2
       445: q^2
       447: q^2
       449: q^2
       451: q^2
       453: q^2
       455: q^2
       457: q^2
       459: q^2
       461: q^2
       463: q^2
       465: q^2
       467: q^4+q^2
       469: q^2
       471: q^2
       473: q^2
       475: q^2
       477: q^2
       479: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       485: q^4+q^2
       487: q^2
       489: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       521: q^2
       525: q^2
       529: q^2
       533: q^2
       537: q^2
       541: q^2
       545: q^2
       549: q^2
       553: q^2
       557: q^2
       561: q^2
       565: q^2
       569: q^2
       573: q^2
       577: q^2
       583: q^2
       585: q^2
       587: q^2
       589: q^2
       591: q^2
       593: q^2
       595: q^2
       597: q^4+q^2
       599: q^2
       601: q^2
       603: q^2
       605: q^2
       607: q^2
       609: q^2
       613: q^2
       615: q^2
       617: q^2
       619: q^2
       621: q^2
       623: q^2
       625: q^2
       629: q^2
       631: q^2
       633: q^2
       639: q^2
       641: q^2
       643: q^2
       645: q^2
       651: q^2
       655: q^2
       665: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       693: q^2
       705: q^2
       709: q^2
       713: q^2
       717: q^2
       721: q^2
       725: q^2
       733: q^2
       737: q^2
       741: q^2
       749: q^2
       753: q^2
       757: q^2
       765: q^2
       769: q^2
       777: q^2
       781: q^2
       785: q^2
       787: q^2
       791: q^2
       797: q^2
       801: q^2
       803: q^2
       805: q^2
       807: q^2
       809: q^2
       811: q^2
       821: q^2
       825: q^2
       827: q^2
       829: q^2
       831: q^2
       833: q^2
       835: q^2
       849: q^2
       853: q
       855: q^2
       871: q^2
       875: q^2
       880: q^2
       884: q^2
       896: q^2
       900: q^2
       904: q^2
       908: q^2
       920: q^2
       924: q^2
       928: q^2
       944: q^2
       948: q^2
       952: q^2
       960: q^2
       978: q
       984: q
      1010: q^2
      1022: q^2
      1026: q^2
      1028: q^2
      1038: q^2
      1040: q^2
      1044: q^2
      1050: q
      1060: q^2
      1064: q^2
      1100: q
      1126: q^2
      1152: q^2
      1156: q^2
      1160: q^2
      1172: q^2
      1176: q^2
      1180: q^2
      1184: q
      1190: q
      1222: q
      1264: q
      1278: q^2
      1304: q
      1322: q
      1336: q
      1360: q^2
      1392: q^2
      1406: q
      1414: q
      1446: q
      1491: q
      1527: q
      1555: q
      1559: q
      1677: q
      1793: 1
      1872: 1
      1948: 1
      1992: 1
      2006: 1
      2110: 1

2111:    0: 3q^3+4q^2+1
         1: 3q^3+4q^2+1
         2: 3q^3+4q^2+1
         3: 3q^3+4q^2+1
         4: 3q^3+4q^2+1
         5: 3q^3+4q^2+1
         6: 3q^3+4q^2+1
         7: 3q^3+4q^2+1
         8: 3q^3+4q^2+1
         9: q^5+2q^4+2q^3+2q^2+1
        10: 3q^3+4q^2+1
        11: 3q^3+4q^2+1
        12: 3q^3+4q^2+1
        13: 3q^3+4q^2+1
        14: 3q^3+4q^2+1
        15: 3q^3+4q^2+1
        16: 4q^2+1
        17: 4q^2+1
        18: 2q^3+2q^2+1
        19: 3q^3+4q^2+1
        20: 3q^3+4q^2+1
        21: 3q^3+4q^2+1
        22: 3q^3+4q^2+1
        23: 3q^3+4q^2+1
        24: 3q^3+4q^2+1
        25: 3q^3+4q^2+1
        26: 3q^3+4q^2+1
        27: 3q^3+4q^2+1
        28: 4q^2+1
        29: 3q^3+4q^2+1
        30: 3q^3+4q^2+1
        31: 3q^3+4q^2+1
        32: 3q^3+4q^2+1
        33: 4q^2+1
        34: 3q^3+4q^2+1
        35: 3q^3+4q^2+1
        36: 4q^2+1
        37: 2q^3+2q^2+1
        38: q^3+2q^2
        39: 2q^3+2q^2+1
        40: q^3+2q^2
        41: 2q^3+2q^2+1
        42: q^3+2q^2
        43: 3q^3+4q^2+1
        44: 3q^3+4q^2+1
        45: 3q^3+4q^2+1
        46: 4q^2+1
        47: 4q^2+1
        48: 2q^3+2q^2+1
        49: 4q^2+1
        50: 4q^2+1
        51: 2q^3+2q^2+1
        52: 3q^3+4q^2+1
        53: 3q^3+4q^2+1
        54: 3q^3+4q^2+1
        55: 3q^3+4q^2+1
        56: 3q^3+4q^2+1
        57: 3q^3+4q^2+1
        58: q^2
        59: 3q^2+1
        60: q^2
        61: 3q^2+1
        62: 2q^3+2q^2+1
        63: q^3+2q^2
        64: 2q^3+2q^2+1
        65: q^3+2q^2
        66: 2q^2+1
        67: 2q^2
        68: 4q^2+1
        69: 2q^2+1
        70: 3q^3+4q^2+1
        71: 4q^2+1
        72: 4q^2+1
        73: 4q^2+1
        74: 2q^3+2q^2+1
        75: q^3+2q^2
        76: 2q^3+2q^2+1
        77: q^3+2q^2
        78: 2q^3+2q^2+1
        79: q^3+2q^2
        80: 3q^3+4q^2+1
        81: 4q^2+1
        82: 3q^3+4q^2+1
        83: 3q^3+4q^2+1
        84: 3q^3+4q^2+1
        85: 4q^2+1
        86: 3q^3+4q^2+1
        87: 3q^3+4q^2+1
        88: 4q^2+1
        89: 4q^2+1
        90: 2q^3+2q^2+1
        91: 4q^2+1
        92: 4q^2+1
        93: 2q^3+2q^2+1
        94: 4q^2+1
        95: 4q^2+1
        96: 2q^3+2q^2+1
        97: 4q^2+1
        98: 4q^2+1
        99: 2q^3+2q^2+1
       100: 3q^3+4q^2+1
       101: 3q^3+4q^2+1
       102: 3q^3+4q^2+1
       104: q^2
       105: q^2
       106: 2q^2+1
       107: q^2
       108: 3q^2+1
       109: q^2
       110: 3q^2+1
       111: 2q^2+1
       112: 2q^2
       113: 2q^3+2q^2+1
       114: q^3+2q^2
       115: 2q^3+2q^2+1
       116: q^3+2q^2
       117: q^2
       118: 3q^2+1
       119: q^2
       120: 3q^2+1
       121: 2q^3+2q^2+1
       122: q^3+2q^2
       123: 2q^2+1
       124: 2q^2
       125: 4q^2+1
       126: 2q^2+1
       127: q^2+1
       129: q^2+1
       131: q^3+1
       133: 4q^2+1
       134: 2q^2+1
       135: 4q^2+1
       136: 4q^2+1
       137: 4q^2+1
       138: 2q^2+1
       139: 4q^2+1
       140: 4q^2+1
       141: 3q^3+4q^2+1
       142: 4q^2+1
       143: 4q^2+1
       144: 2q^2+1
       145: 4q^2+1
       146: 3q^3+4q^2+1
       147: 4q^2+1
       148: 4q^2+1
       149: 3q^3+4q^2+1
       150: 3q^3+4q^2+1
       151: 2q^3+2q^2+1
       152: q^3+2q^2
       153: 2q^3+2q^2+1
       154: q^3+2q^2
       155: 2q^3+2q^2+1
       156: q^3+2q^2
       157: 4q^2+1
       158: 4q^2+1
       159: 2q^3+2q^2+1
       160: 4q^2+1
       161: 4q^2+1
       162: 2q^3+2q^2+1
       163: 4q^2+1
       164: 4q^2+1
       165: 2q^3+2q^2+1
       166: 4q^2+1
       167: 4q^2+1
       168: 2q^3+2q^2+1
       170: q^2
       171: q^2
       172: 2q^2+1
       174: q^2
       175: q^2
       176: 2q^2+1
       177: 1
       179: q^2+1
       181: q^2+1
       183: q^2
       184: 3q^2+1
       185: q^2
       186: 3q^2+1
       187: 2q^2+1
       188: 2q^2
       189: 2q^3+2q^2+1
       190: q^3+2q^2
       191: q^2
       192: 3q^2+1
       193: q^2
       194: 3q^2+1
       195: q^2
       196: 3q^2+1
       197: 2q^2+1
       198: 2q^2
       199: q^2
       200: 3q^2+1
       201: q^2
       202: 3q^2+1
       203: q^2
       204: 3q^2+1
       205: 2q^2+1
       206: 2q^2
       207: 2q^2+1
       208: 2q^2
       209: 2q^3+2q^2+1
       210: q^3+2q^2
       211: 2q^3+2q^2+1
       212: q^3+2q^2
       213: q^2+1
       215: q^2+1
       217: q^3+1
       219: 2q^2+1
       220: 4q^2+1
       221: 2q^2+1
       222: 4q^2+1
       223: 2q^2+1
       224: 4q^2+1
       225: 2q^2+1
       226: 2q^2+1
       227: 4q^2+1
       228: 2q^2+1
       229: 4q^2+1
       230: 4q^2+1
       231: 2q^2+1
       232: 4q^2+1
       233: 2q^2+1
       234: 4q^2+1
       235: 4q^2+1
       236: 2q^2+1
       237: q^2+1
       239: q^2+1
       241: q^3+1
       243: 4q^2+1
       244: 4q^2+1
       245: 4q^2+1
       246: 3q^3+4q^2+1
       247: 4q^2+1
       248: 4q^2+1
       249: 2q^3+2q^2+1
       250: 4q^2+1
       251: 4q^2+1
       252: 2q^3+2q^2+1
       253: 4q^2+1
       254: 4q^2+1
       255: 2q^3+2q^2+1
       256: 4q^2+1
       257: 4q^2+1
       258: 2q^3+2q^2+1
       262: q^2+1
       264: q^2
       265: q^2
       266: 2q^2+1
       268: q^2
       269: 2q^2+1
       270: q^2
       272: q^2
       273: 2q^2+1
       274: q^2
       276: q^2
       277: q^2
       278: 2q^2+1
       279: q^2+1
       281: 1
       284: q^2+1
       286: q^2+1
       287: 1
       289: q^2+1
       291: 1
       293: q^2
       294: 3q^2+1
       295: q^2
       296: 3q^2+1
       297: 2q^2+1
       298: 2q^2
       299: q^2
       300: 3q^2+1
       301: q^2+1
       303: q^2
       304: 3q^2+1
       305: 2q^2+1
       306: 2q^2
       307: q^2
       308: 3q^2+1
       309: q^2
       310: 3q^2+1
       311: q^2+1
       313: 2q^2+1
       314: 2q^2
       315: 1
       317: q^2+1
       319: q^2
       320: 3q^2+1
       321: q^2
       322: 3q^2+1
       323: 2q^2+1
       324: 2q^2
       325: 2q^3+2q^2+1
       326: q^3+2q^2
       327: q^2+1
       329: q^2+1
       331: q^3+1
       333: 2q^2+1
       334: 2q^2+1
       335: 2q^2+1
       336: 2q^2+1
       337: 4q^2+1
       338: q^2+1
       340: q^2+1
       342: q^3+1
       344: 2q^2+1
       345: 4q^2+1
       346: 2q^2+1
       347: 4q^2+1
       348: 2q^2+1
       349: 4q^2+1
       350: 2q^2+1
       351: 4q^2+1
       352: 2q^2+1
       353: 4q^2+1
       354: 2q^2+1
       355: 4q^2+1
       356: 2q^2+1
       357: 4q^2+1
       358: 2q^2+1
       359: 4q^2+1
       360: q^2+1
       362: q^2+1
       364: q^3+1
       366: 2q^2+1
       367: 4q^2+1
       368: 2q^2+1
       369: 4q^2+1
       370: 4q^2+1
       371: 4q^2+1
       372: 4q^2+1
       373: 2q^3+2q^2+1
       374: 4q^2+1
       375: 4q^2+1
       376: 2q^3+2q^2+1
       380: 1
       384: q^2+1
       386: q^2
       387: q^2
       388: 2q^2+1
       391: q^2+1
       394: q^2
       395: q^2
       396: 2q^2+1
       399: q^2+1
       402: q^2
       403: q^2
       404: 2q^2+1
       406: 2q^2+1
       407: q^2
       408: q^2
       409: q^2+1
       411: 1
       413: 1
       415: q^2+1
       417: 1
       420: q^2+1
       422: q^2+1
       423: 1
       425: 1
       427: q^2+1
       430: q^2+1
       432: q^2+1
       433: 1
       435: q^2+1
       437: q^2
       438: 3q^2+1
       439: q^2
       440: 3q^2+1
       441: 2q^2+1
       442: 2q^2
       443: q^2
       444: 3q^2+1
       445: q^2+1
       448: q^2+1
       450: q^2+1
       451: 1
       453: q^2
       454: 3q^2+1
       455: q^2+1
       457: q^2
       458: 3q^2+1
       459: 2q^2+1
       460: 2q^2
       461: q^2
       462: 3q^2+1
       463: q^2+1
       465: q^2+1
       467: 1
       469: 1
       471: q^2
       472: 3q^2+1
       473: q^2
       474: 3q^2+1
       475: 2q^2+1
       476: 2q^2
       477: q^2+1
       479: 2q^2+1
       480: 2q^2
       481: 2q^2+1
       482: 2q^2+1
       483: 2q^2+1
       484: 4q^2+1
       485: q^2+1
       487: q^2+1
       489: q^3+1
       491: 2q^2+1
       492: 2q^2+1
       493: 2q^2+1
       494: 2q^2+1
       495: 2q^2+1
       496: 4q^2+1
       497: 2q^2+1
       498: 2q^2+1
       499: 2q^2+1
       500: 2q^2+1
       501: 4q^2+1
       502: q^2+1
       504: q^2+1
       506: q^3+1
       508: 2q^2+1
       509: 4q^2+1
       510: 2q^2+1
       511: 4q^2+1
       512: 2q^2+1
       513: 4q^2+1
       514: 2q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: 4q^2+1
       519: 4q^2+1
       520: 2q^3+2q^2+1
       524: 1
       528: q^2+1
       532: 1
       536: 1
       539: q^2+1
       542: q^2
       543: 2q^2+1
       544: q^2
       547: q^2+1
       552: 1
       555: q^2+1
       558: q^2
       559: 2q^2+1
       560: q^2
       563: q^2+1
       566: q^2
       567: q^2
       568: 2q^2+1
       570: q^2+1
       574: q^2
       575: 2q^2+1
       576: q^2
       577: q^2+1
       583: 1
       585: 1
       587: 1
       590: q^2+1
       592: q^2+1
       594: q^2+1
       596: q^2+1
       597: 1
       599: 1
       601: q^2+1
       604: q^2+1
       605: 1
       608: q^2+1
       609: 1
       611: q^2+1
       613: 1
       615: q^2
       616: 3q^2+1
       617: q^2+1
       620: q^2+1
       622: q^2+1
       623: 1
       625: 1
       627: q^2+1
       629: 1
       631: q^2
       632: 3q^2+1
       633: q^2+1
       635: q^2+1
       637: 1
       639: 1
       642: q^2+1
       644: q^2+1
       645: 1
       647: q^2
       648: 3q^2+1
       649: q^2
       650: 3q^2+1
       651: q^2+1
       653: 2q^2+1
       654: 2q^2
       655: 2q^2+1
       656: 2q^2
       657: 1
       658: q+1
       660: q+1
       662: q+1
       664: q+1
       665: 2q^2+1
       666: q^2+1
       668: q^2+1
       670: q^3+1
       672: 4q^2+1
       673: 2q^2+1
       674: q+1
       675: 2q^2+1
       676: 2q^2+1
       677: 2q^2+1
       678: 4q^2+1
       679: 2q^2+1
       680: q+1
       681: 2q^2+1
       682: 2q^2+1
       683: 2q^2+1
       684: 4q^2+1
       685: 2q^2+1
       686: 2q^2+1
       687: 2q^2+1
       688: 2q^2+1
       689: 2q^2+1
       690: q+1
       691: q+1
       692: q+1
       697: q^2+1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: q^2+1
       735: q^2+1
       739: 1
       743: 1
       747: q^2+1
       751: q^2+1
       756: 1
       758: q^2+1
       762: 2q^2+1
       763: q^2
       764: q^2
       766: q^2
       767: q^2
       768: 2q^2+1
       769: q^2+1
       775: 1
       777: 1
       779: q+1
       781: 1
       783: 1
       786: q^2+1
       788: q^2+1
       789: q^2+1
       791: 1
       794: 1
       795: q+1
       797: 1
       799: 1
       802: q^2+1
       804: q^2+1
       806: q^2+1
       808: q^2+1
       809: 1
       811: 1
       813: q^2+1
       815: q^2
       816: 3q^2+1
       818: 1
       819: q+1
       821: 1
       823: 1
       826: q^2+1
       828: q^2+1
       830: q^2+1
       832: q^2+1
       833: 1
       835: 1
       837: q^2+1
       839: q^2
       840: 3q^2+1
       841: 1
       843: 1
       844: q
       846: q^2+1
       848: q^2+1
       849: 1
       851: 1
       853: q^2+1
       855: 1
       857: 2q^2+1
       858: 2q^2
       859: q+1
       861: q+1
       863: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q^2+1
       869: q+1
       870: q+1
       871: 2q^2+1
       872: 2q^2+1
       873: q+1
       874: q+1
       875: 2q^2+1
       876: 2q^2+1
       877: 2q^2+1
       878: 2q^2+1
       879: 2q^2+1
       880: 2q^2+1
       881: q+1
       882: q+1
       883: q+1
       889: q^2+1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       927: 1
       930: 1
       934: q^2+1
       938: 1
       942: 1
       946: 1
       950: 1
       955: 1
       958: q^2+1
       961: 1
       967: 1
       968: 1
       971: q
       975: 1
       979: q^2+1
       982: q^2+1
       989: q^2
       990: q^2
       991: 2q^2+1
       992: 1
       994: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1005: q^2+1
      1007: q^2+1
      1008: 1
      1010: 1
      1012: 1
      1013: q
      1014: q+1
      1017: 1
      1018: 1
      1020: q+1
      1022: 1
      1024: 1
      1027: q^2+1
      1029: q^2+1
      1030: q+1
      1033: 1
      1034: 1
      1036: q+1
      1038: 1
      1041: q^2+1
      1042: 1
      1045: q^2+1
      1046: 1
      1047: q
      1048: 1
      1050: 1
      1053: q^2+1
      1055: q^2+1
      1057: q^2+1
      1059: q^2+1
      1060: 1
      1062: 1
      1064: 1
      1066: q+1
      1068: q+1
      1070: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q^2+1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q^2+1
      1083: 2q^2+1
      1084: q+1
      1085: 2q^2+1
      1091: 1
      1102: q^2+1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1141: q
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1191: q
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1210: 1
      1212: q+1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1225: q
      1226: q+1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1236: q+1
      1238: 1
      1241: q^2+1
      1243: q^2+1
      1244: q+1
      1247: 1
      1248: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1259: q^2+1
      1261: q^2+1
      1262: 1
      1263: q
      1264: 1
      1266: 1
      1269: q^2+1
      1271: q^2+1
      1272: 1
      1274: q+1
      1276: 1
      1278: 1
      1280: 1
      1281: q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q^2+1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1337: q
      1342: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: 1
      1407: q
      1413: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1433: q
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1445: q
      1446: 1
      1448: 1
      1451: 1
      1452: q+1
      1455: 1
      1456: 1
      1458: q+1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: q+1
      1474: 1
      1477: q^2+1
      1479: q^2+1
      1480: 1
      1482: 1
      1483: q
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1494: 1
      1506: 1
      1518: 1
      1530: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1556: q
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1634: q
      1641: 1
      1643: 1
      1646: 1
      1648: 1
      1650: 1
      1651: 1
      1654: 1
      1656: 1
      1658: 1
      1661: 1
      1664: 1
      1666: 1
      1667: q+1
      1669: 1
      1670: q
      1671: 1
      1673: 1
      1674: 1
      1680: 1
      1692: 1
      1704: 1
      1718: 1
      1739: 1
      1747: 1
      1752: 1
      1754: 1
      1759: 1
      1763: 1
      1767: 1
      1776: 1
      1778: 1
      1783: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1801: 1
      1804: q
      1808: 1
      1814: 1
      1815: 1
      1820: 1
      1822: 1
      1827: 1
      1830: 1
      1832: 1
      1833: 1
      1851: 1
      1863: 1
      1877: 1
      1889: 1
      1904: 1
      1920: 1
      1934: 1
      1938: 1
      1943: 1
      1949: 1
      1955: 1
      1956: 1
      1963: 1
      1965: 1
      1997: 1
      2009: 1
      2034: 1
      2046: 1
      2067: 1
      2111: 1

2112:    0: q^2+3q
         1: q^2+3q
         2: q^2+3q
         3: q^2+3q
         4: q^2+3q
         5: q^2+3q
         6: q^2+3q
         7: q^2+3q
         8: q^2+3q
         9: q^3+q^2+2q
        10: q^2+3q
        11: q^2+3q
        12: q^2+3q
        13: q^2+3q
        14: q^2+3q
        15: q^2+3q
        16: 3q
        17: 3q
        18: q^2+2q
        19: q^2+3q
        20: q^2+3q
        21: q^2+3q
        22: q^2+3q
        23: q^2+3q
        24: q^2+3q
        25: q^2+3q
        26: q^2+3q
        27: q^2+3q
        28: 3q
        29: q^2+3q
        30: q^2+3q
        31: q^2+3q
        32: q^2+3q
        33: 3q
        34: q^2+3q
        35: q^2+3q
        36: 3q
        37: q
        38: q^2+2q
        39: q
        40: q^2+2q
        41: q
        42: q^2+2q
        43: q^2+3q
        44: q^2+3q
        45: q^2+3q
        46: 3q
        47: 3q
        48: q^2+2q
        49: 3q
        50: 3q
        51: q^2+2q
        52: q^2+3q
        53: q^2+3q
        54: q^2+3q
        55: q^2+3q
        56: q^2+3q
        57: q^2+3q
        58: q
        59: 2q
        60: q
        61: 2q
        62: q
        63: q^2+2q
        64: q
        65: q^2+2q
        66: q
        67: 2q
        68: 3q
        69: 2q
        70: q^2+3q
        71: 3q
        72: 3q
        73: 3q
        74: q
        75: q^2+2q
        76: q
        77: q^2+2q
        78: q
        79: q^2+2q
        80: q^2+3q
        81: 3q
        82: q^2+3q
        83: q^2+3q
        84: q^2+3q
        85: 3q
        86: q^2+3q
        87: q^2+3q
        88: 3q
        89: 3q
        90: q^2+2q
        91: 3q
        92: 3q
        93: q^2+2q
        94: 3q
        95: 3q
        96: q^2+2q
        97: 3q
        98: 3q
        99: q^2+2q
       100: q^2+3q
       101: q^2+3q
       102: q^2+3q
       104: q
       105: q
       106: q
       107: q
       108: 2q
       109: q
       110: 2q
       111: q
       112: 2q
       113: q
       114: q^2+2q
       115: q
       116: q^2+2q
       117: q
       118: 2q
       119: q
       120: 2q
       121: q
       122: q^2+2q
       123: q
       124: 2q
       125: 3q
       126: 2q
       128: 2q
       130: 2q
       132: q^2+q
       133: 3q
       134: 2q
       135: 3q
       136: 3q
       137: 3q
       138: 2q
       139: 3q
       140: 3q
       141: q^2+3q
       142: 3q
       143: 3q
       144: 2q
       145: 3q
       146: q^2+3q
       147: 3q
       148: 3q
       149: q^2+3q
       150: q^2+3q
       151: q
       152: q^2+2q
       153: q
       154: q^2+2q
       155: q
       156: q^2+2q
       157: 3q
       158: 3q
       159: q^2+2q
       160: 3q
       161: 3q
       162: q^2+2q
       163: 3q
       164: 3q
       165: q^2+2q
       166: 3q
       167: 3q
       168: q^2+2q
       170: q
       171: q
       172: q
       174: q
       175: q
       176: q
       178: q
       180: 2q
       182: 2q
       183: q
       184: 2q
       185: q
       186: 2q
       187: q
       188: 2q
       189: q
       190: q^2+2q
       191: q
       192: 2q
       193: q
       194: 2q
       195: q
       196: 2q
       197: q
       198: 2q
       199: q
       200: 2q
       201: q
       202: 2q
       203: q
       204: 2q
       205: q
       206: 2q
       207: q
       208: 2q
       209: q
       210: q^2+2q
       211: q
       212: q^2+2q
       214: 2q
       216: 2q
       218: q^2+q
       219: 2q
       220: 3q
       221: 2q
       222: 3q
       223: 2q
       224: 3q
       225: 2q
       226: 2q
       227: 3q
       228: 2q
       229: 3q
       230: 3q
       231: 2q
       232: 3q
       233: 2q
       234: 3q
       235: 3q
       236: 2q
       238: 2q
       240: 2q
       242: q^2+q
       243: 3q
       244: 3q
       245: 3q
       246: q^2+3q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 3q
       251: 3q
       252: q^2+2q
       253: 3q
       254: 3q
       255: q^2+2q
       256: 3q
       257: 3q
       258: q^2+2q
       260: q
       261: q
       264: q
       265: q
       266: q
       268: q
       269: q
       270: q
       272: q
       273: q
       274: q
       276: q
       277: q
       278: q
       280: 2q
       282: q
       284: q
       286: q
       288: q
       290: 2q
       292: q
       293: q
       294: 2q
       295: q
       296: 2q
       297: q
       298: 2q
       299: q
       300: 2q
       302: 2q
       303: q
       304: 2q
       305: q
       306: 2q
       307: q
       308: 2q
       309: q
       310: 2q
       312: 2q
       313: q
       314: 2q
       316: q
       318: 2q
       319: q
       320: 2q
       321: q
       322: 2q
       323: q
       324: 2q
       325: q
       326: q^2+2q
       328: 2q
       330: 2q
       332: q^2+q
       333: 2q
       334: 2q
       335: 2q
       336: 2q
       337: 3q
       339: 2q
       341: 2q
       343: q^2+q
       344: 2q
       345: 3q
       346: 2q
       347: 3q
       348: 2q
       349: 3q
       350: 2q
       351: 3q
       352: 2q
       353: 3q
       354: 2q
       355: 3q
       356: 2q
       357: 3q
       358: 2q
       359: 3q
       361: 2q
       363: 2q
       365: q^2+q
       366: 2q
       367: 3q
       368: 2q
       369: 3q
       370: 3q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 3q
       375: 3q
       376: q^2+2q
       382: q
       383: q
       386: q
       387: q
       388: q
       390: q
       392: q
       394: q
       395: q
       396: q
       398: q
       400: q
       402: q
       403: q
       404: q
       406: q
       407: q
       408: q
       410: 2q
       412: q
       414: q
       416: 2q
       418: q
       420: q
       422: q
       424: q
       426: q
       428: 2q
       430: q
       432: q
       434: q
       436: 2q
       437: q
       438: 2q
       439: q
       440: 2q
       441: q
       442: 2q
       443: q
       444: 2q
       446: 2q
       448: q
       450: q
       452: q
       453: q
       454: 2q
       456: 2q
       457: q
       458: 2q
       459: q
       460: 2q
       461: q
       462: 2q
       464: 2q
       466: 2q
       468: q
       470: q
       471: q
       472: 2q
       473: q
       474: 2q
       475: q
       476: 2q
       478: 2q
       479: q
       480: 2q
       481: 2q
       482: 2q
       483: 2q
       484: 3q
       486: 2q
       488: 2q
       490: q^2+q
       491: 2q
       492: 2q
       493: 2q
       494: 2q
       495: 2q
       496: 3q
       497: 2q
       498: 2q
       499: 2q
       500: 2q
       501: 3q
       503: 2q
       505: 2q
       507: q^2+q
       508: 2q
       509: 3q
       510: 2q
       511: 3q
       512: 2q
       513: 3q
       514: 2q
       515: q+1
       516: q+1
       517: q+1
       518: 3q
       519: 3q
       520: q^2+2q
       526: q
       527: q
       538: q
       540: q
       542: q
       543: q
       544: q
       546: q
       548: q
       554: q
       556: q
       558: q
       559: q
       560: q
       562: q
       564: q
       566: q
       567: q
       568: q
       571: q
       572: q
       574: q
       575: q
       576: q
       581: 2q
       584: q
       586: q
       588: q
       590: q
       592: q
       594: q
       596: q
       598: q
       600: q
       602: 2q
       604: q
       606: q
       608: q
       610: q
       612: 2q
       614: q
       615: q
       616: 2q
       618: 2q
       620: q
       622: q
       624: q
       626: q
       628: 2q
       630: q
       631: q
       632: 2q
       634: 2q
       636: 2q
       638: q
       640: q
       642: q
       644: q
       646: q
       647: q
       648: 2q
       649: q
       650: 2q
       652: 2q
       653: q
       654: 2q
       655: q
       656: 2q
       657: 1
       659: q+1
       661: q+1
       663: q+1
       664: q+1
       665: 2q
       667: 2q
       669: 2q
       671: q^2+q
       672: 3q
       673: 2q
       674: q+1
       675: 2q
       676: 2q
       677: 2q
       678: 3q
       679: 2q
       680: q+1
       681: 2q
       682: 2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q
       687: 2q
       688: 2q
       689: 2q
       690: q+1
       691: q+1
       692: q+1
       699: q
       700: q
       730: q
       732: q
       734: q
       736: q
       746: q
       748: q
       750: q
       752: q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q
       773: 2q
       776: 1
       778: q
       780: q+1
       782: q
       784: q
       786: q
       788: q
       790: 2q
       792: q
       794: 1
       796: q+1
       798: q
       800: q
       802: q
       804: q
       806: q
       808: q
       810: q
       812: q
       814: 2q
       815: q
       816: 2q
       818: 1
       820: q+1
       822: q
       824: q
       826: q
       828: q
       830: q
       832: q
       834: q
       836: q
       838: 2q
       839: q
       840: 2q
       842: q
       843: 1
       844: q
       846: q
       848: q
       850: q
       852: q
       854: 2q
       856: q
       857: q
       858: 2q
       860: q+1
       862: q+1
       864: q+1
       865: 1
       866: 1
       867: q+1
       868: 2q
       869: q+1
       870: q+1
       871: 2q
       872: 2q
       873: q+1
       874: q+1
       875: 2q
       876: 2q
       877: 2q
       878: 2q
       879: 2q
       880: 2q
       881: q+1
       882: q+1
       883: q+1
       890: q
       891: q
       919: 1
       933: q
       935: q
       943: 1
       957: q
       959: q
       967: 1
       969: 1
       972: q
       980: q
       981: q
       986: 2q
       989: q
       990: q
       991: q
       993: 1
       995: 1
       997: q+1
       999: 1
      1001: 1
      1003: q
      1005: q
      1007: q
      1009: q
      1011: q
      1012: 1
      1013: q
      1015: q+1
      1017: 1
      1019: q
      1021: q+1
      1023: q
      1025: q
      1027: q
      1029: q
      1031: q+1
      1033: 1
      1035: q
      1037: q+1
      1039: q
      1041: q
      1043: q
      1045: q
      1046: 1
      1047: q
      1049: q
      1051: q
      1053: q
      1055: q
      1057: q
      1059: q
      1061: q
      1063: q
      1065: q
      1067: q+1
      1069: q+1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: q+1
      1076: 1
      1077: q+1
      1078: 2q
      1079: q+1
      1080: 1
      1081: q+1
      1082: 2q
      1083: 2q
      1084: q+1
      1085: 2q
      1094: 1
      1104: q
      1105: q
      1117: 1
      1125: 1
      1133: 1
      1139: 1
      1142: q
      1147: 1
      1167: 1
      1189: 1
      1192: q
      1197: 1
      1211: 1
      1213: q+1
      1215: 1
      1217: 1
      1219: 1
      1221: q
      1223: q
      1224: 1
      1225: q
      1227: q+1
      1229: 1
      1231: 1
      1233: 1
      1235: 1
      1237: q+1
      1239: q
      1241: q
      1243: q
      1245: q+1
      1247: 1
      1249: 1
      1251: 1
      1253: q+1
      1255: 1
      1257: q
      1259: q
      1261: q
      1262: 1
      1263: q
      1265: q
      1267: q
      1269: q
      1271: q
      1273: q
      1275: q+1
      1277: q
      1279: q
      1280: 1
      1281: q
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 2q
      1298: 1
      1310: 1
      1317: 1
      1321: 1
      1329: 1
      1335: 1
      1338: q
      1343: 1
      1351: 1
      1359: 1
      1367: 1
      1375: 1
      1383: 1
      1391: 1
      1399: 1
      1405: 1
      1408: q
      1413: 1
      1431: 1
      1434: q
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1445: q
      1447: q
      1449: 1
      1451: 1
      1453: q+1
      1455: 1
      1457: 1
      1459: q+1
      1461: 1
      1463: 1
      1465: 1
      1467: 1
      1469: 1
      1471: q
      1473: q+1
      1475: q
      1477: q
      1479: q
      1481: q
      1482: 1
      1483: q
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: q+1
      1497: 1
      1509: 1
      1521: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1557: q
      1566: 1
      1570: 1
      1578: 1
      1586: 1
      1590: 1
      1598: 1
      1610: 1
      1618: 1
      1626: 1
      1632: 1
      1635: q
      1642: 1
      1644: 1
      1646: 1
      1648: 1
      1650: 1
      1652: 1
      1654: 1
      1656: 1
      1658: 1
      1662: 1
      1664: 1
      1666: 1
      1668: q+1
      1669: 1
      1670: q
      1672: q
      1673: 1
      1674: 1
      1683: 1
      1695: 1
      1707: 1
      1720: 1
      1740: 1
      1748: 1
      1752: 1
      1760: 1
      1764: 1
      1768: 1
      1776: 1
      1784: 1
      1788: 1
      1792: 1
      1800: 1
      1802: 1
      1805: q
      1814: 1
      1816: 1
      1820: 1
      1822: 1
      1828: 1
      1830: 1
      1832: 1
      1833: 1
      1854: 1
      1866: 1
      1879: 1
      1890: 1
      1905: 1
      1921: 1
      1935: 1
      1939: 1
      1943: 1
      1955: 1
      1957: 1
      1963: 1
      1965: 1
      1998: 1
      2010: 1
      2035: 1
      2047: 1
      2067: 1
      2112: 1

2113:    0: 3q^5+q^4+q^2
         1: q^6+2q^5+q^4+q^2
         2: 3q^5+q^4+q^2
         3: q^7+2q^6+3q^5+q^4+q^2
         4: 3q^5+q^4+q^2
         5: q^6+2q^5+q^4+q^2
         6: q^6+2q^5+q^4+q^2
         7: 3q^5+q^4+q^2
         8: q^6+2q^5+q^4+q^2
         9: q^7+q^6+2q^5+q^4+q^2
        10: 2q^5+q^2
        11: q^6+2q^5+q^2
        12: 2q^5+q^2
        13: 3q^5+q^4+q^2
        14: 3q^5+q^4+q^2
        15: q^6+2q^5+q^4+q^2
        16: 2q^5+q^4+q^2
        17: q^5+q^4+q^2
        18: 2q^5+q^4+q^2
        19: 3q^5+q^4+q^2
        20: q^6+2q^5+q^4+q^2
        21: 3q^5+q^4+q^2
        22: 2q^5+q^4+q^2
        23: q^6+2q^5+q^4+q^2
        24: 2q^5+q^4+q^2
        25: 2q^5+q^4+q^2
        26: q^6+2q^5+q^4+q^2
        27: 2q^5+q^4+q^2
        28: q^5+q^2
        29: 2q^5+q^2
        30: 3q^5+q^4+q^2
        31: 2q^5+q^2
        32: 2q^5+q^4+q^2
        33: q^5+q^4+q^2
        34: 2q^5+q^2
        35: 2q^5+q^4+q^2
        36: q^5+q^4+q^2
        37: 2q^5+q^4+q^2
        39: q^6+2q^5+q^4+q^2
        41: 2q^5+q^4+q^2
        43: 2q^5+q^2
        44: 2q^5+q^2
        45: q^6+2q^5+q^2
        46: 2q^5+q^4+q^2
        47: q^5+q^4+q^2
        48: 2q^5+q^4+q^2
        49: 2q^5+q^4+q^2
        50: q^5+q^4+q^2
        51: 2q^5+q^4+q^2
        52: 2q^5+q^4+q^2
        53: q^6+2q^5+q^4+q^2
        54: 2q^5+q^4+q^2
        55: 2q^5+q^4+q^2
        56: q^6+2q^5+q^4+q^2
        57: 2q^5+q^4+q^2
        59: q^5+q^2
        61: q^5+q^2
        62: 2q^5+q^2
        64: 2q^5+q^4+q^2
        66: q^5+q^4+q^2
        68: q^5+q^2
        69: q^5+q^4+q^2
        70: 2q^5+q^2
        71: q^5+q^2
        72: q^5+q^4+q^2
        73: q^5+q^4+q^2
        74: 2q^5+q^4+q^2
        76: q^6+2q^5+q^4+q^2
        78: 2q^5+q^4+q^2
        80: 2q^5+q^2
        81: q^5+q^4+q^2
        82: 2q^5+q^2
        83: 2q^5+q^4+q^2
        84: 2q^5+q^2
        85: q^5+q^4+q^2
        86: 2q^5+q^2
        87: 2q^5+q^4+q^2
        88: q^2
        89: q^2
        90: q^5+q^2
        91: 2q^5+q^4+q^2
        92: q^5+q^4+q^2
        93: 2q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^5+q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^5+q^4+q^2
       100: q^5+q^4+q^2
       101: q^5+q^2
       102: q^5+q^4+q^2
       106: q^5+q^2
       108: q^5+q^2
       110: q^5+q^2
       111: q^5+q^4+q^2
       113: 2q^5+q^2
       115: 2q^5+q^4+q^2
       118: q^5+q^2
       120: q^5+q^2
       121: 2q^5+q^2
       123: q^5+q^4+q^2
       125: q^2
       126: q^2
       127: q^4+q^2
       129: q^4+q^2
       131: q^5+q^4+q^2
       133: q^5+q^2
       134: q^5+q^4+q^2
       135: q^5+q^4+q^2
       136: q^5+q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: 2q^5+q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: 2q^5+q^2
       147: q^4+q^2
       148: q^2
       149: q^5+q^2
       150: q^5+q^4+q^2
       151: q^5+q^4+q^2
       153: q^5+q^2
       155: q^5+q^4+q^2
       157: q^2
       158: q^2
       159: q^5+q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^5+q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^5+q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       172: q^5+q^2
       176: q^5+q^2
       177: q^4+q^2
       179: q^2
       181: q^4+q^2
       184: q^5+q^2
       186: q^5+q^2
       187: q^5+q^4+q^2
       189: 2q^5+q^2
       192: q^2
       194: q^2
       196: q^2
       197: q^2
       200: q^2
       202: q^2
       204: q^2
       205: q^2
       207: q^2
       209: q^5+q^2
       211: q^5+q^4+q^2
       213: q^4+q^2
       215: q^4+q^2
       217: q^5+q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       237: q^4+q^2
       239: q^2
       241: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^5+q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^5+q^2
       253: q^2
       254: q^2
       255: q^5+q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       262: q^2
       266: q^5+q^2
       269: q^2
       273: q^2
       278: q^2
       279: q^2
       281: q^4+q^2
       284: q^2
       286: q^2
       287: q^2
       289: q^4+q^2
       291: q^4+q^2
       294: q^2
       296: q^2
       297: q^2
       300: q^2
       301: q^2
       304: q^2
       305: q^2
       308: q^2
       310: q^2
       311: q^2
       313: q^2
       315: q^4+q^2
       317: q^2
       320: q^2
       322: q^2
       323: q^2
       325: q^5+q^2
       327: q^2
       329: q^2
       331: q^5+q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       338: q^4+q^2
       340: q^2
       342: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       360: q^4+q^2
       362: q^2
       364: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       380: q^2
       384: q^2
       388: q^2
       391: q^2
       396: q^2
       399: q^2
       404: q^2
       406: q^2
       409: q^2
       411: q^2
       413: q^2
       415: q^2
       417: q^4+q^2
       420: q^2
       422: q^2
       423: q^2
       425: q^4+q^2
       427: q^2
       430: q^2
       432: q^2
       433: q^2
       435: q^2
       438: q^2
       440: q^2
       441: q^2
       444: q^2
       445: q^2
       448: q^2
       450: q^2
       451: q^2
       454: q^2
       455: q^2
       458: q^2
       459: q^2
       462: q^2
       463: q^2
       465: q^2
       467: q^4+q^2
       469: q^2
       472: q^2
       474: q^2
       475: q^2
       477: q^2
       479: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       485: q^4+q^2
       487: q^2
       489: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       524: q^2
       528: q^2
       532: q^2
       536: q^2
       539: q^2
       543: q^2
       547: q^2
       552: q^2
       555: q^2
       559: q^2
       563: q^2
       568: q^2
       570: q^2
       575: q^2
       577: q^2
       583: q^2
       585: q^2
       587: q^2
       590: q^2
       592: q^2
       594: q^2
       596: q^2
       597: q^4+q^2
       599: q^2
       601: q^2
       604: q^2
       605: q^2
       608: q^2
       609: q^2
       613: q^2
       616: q^2
       617: q^2
       620: q^2
       622: q^2
       623: q^2
       625: q^2
       629: q^2
       632: q^2
       633: q^2
       639: q^2
       642: q^2
       644: q^2
       645: q^2
       651: q^2
       655: q^2
       665: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       697: q^2
       708: q^2
       712: q^2
       716: q^2
       720: q^2
       723: q^2
       727: q^2
       735: q^2
       739: q^2
       743: q^2
       751: q^2
       756: q^2
       758: q^2
       768: q^2
       769: q^2
       777: q^2
       781: q^2
       786: q^2
       788: q^2
       791: q^2
       797: q^2
       802: q^2
       804: q^2
       806: q^2
       808: q^2
       809: q^2
       811: q^2
       821: q^2
       826: q^2
       828: q^2
       830: q^2
       832: q^2
       833: q^2
       835: q^2
       849: q^2
       853: q
       855: q^2
       871: q^2
       875: q^2
       880: q^2
       889: q^2
       899: q^2
       902: q^2
       906: q^2
       911: q^2
       922: q^2
       927: q^2
       930: q^2
       946: q^2
       950: q^2
       955: q^2
       961: q^2
       979: q
       984: q
      1010: q^2
      1022: q^2
      1027: q^2
      1029: q^2
      1038: q^2
      1041: q^2
      1045: q^2
      1050: q
      1060: q^2
      1064: q^2
      1107: q
      1127: q^2
      1154: q^2
      1158: q^2
      1163: q^2
      1174: q^2
      1178: q^2
      1183: q^2
      1185: q
      1190: q
      1222: q
      1264: q
      1278: q^2
      1311: q
      1323: q
      1336: q
      1361: q^2
      1393: q^2
      1406: q
      1415: q
      1446: q
      1498: q
      1534: q
      1555: q
      1560: q
      1684: q
      1796: 1
      1881: 1
      1949: 1
      1999: 1
      2011: 1
      2113: 1

2114:    0: 3q^5+q^4+q^2
         1: q^6+2q^5+q^4+q^2
         2: 3q^5+q^4+q^2
         3: q^7+2q^6+3q^5+q^4+q^2
         4: 3q^5+q^4+q^2
         5: q^6+2q^5+q^4+q^2
         6: q^6+2q^5+q^4+q^2
         7: 3q^5+q^4+q^2
         8: q^6+2q^5+q^4+q^2
         9: q^7+q^6+2q^5+q^4+q^2
        10: 2q^5+q^2
        11: q^6+2q^5+q^2
        12: 2q^5+q^2
        13: 3q^5+q^4+q^2
        14: 3q^5+q^4+q^2
        15: q^6+2q^5+q^4+q^2
        16: 2q^5+q^4+q^2
        17: q^5+q^4+q^2
        18: 2q^5+q^4+q^2
        19: 3q^5+q^4+q^2
        20: q^6+2q^5+q^4+q^2
        21: 3q^5+q^4+q^2
        22: 2q^5+q^4+q^2
        23: q^6+2q^5+q^4+q^2
        24: 2q^5+q^4+q^2
        25: 2q^5+q^4+q^2
        26: q^6+2q^5+q^4+q^2
        27: 2q^5+q^4+q^2
        28: q^5+q^2
        29: 2q^5+q^2
        30: 3q^5+q^4+q^2
        31: 2q^5+q^2
        32: 2q^5+q^4+q^2
        33: q^5+q^4+q^2
        34: 2q^5+q^2
        35: 2q^5+q^4+q^2
        36: q^5+q^4+q^2
        38: 2q^5+q^4+q^2
        40: q^6+2q^5+q^4+q^2
        42: 2q^5+q^4+q^2
        43: 2q^5+q^2
        44: 2q^5+q^2
        45: q^6+2q^5+q^2
        46: 2q^5+q^4+q^2
        47: q^5+q^4+q^2
        48: 2q^5+q^4+q^2
        49: 2q^5+q^4+q^2
        50: q^5+q^4+q^2
        51: 2q^5+q^4+q^2
        52: 2q^5+q^4+q^2
        53: q^6+2q^5+q^4+q^2
        54: 2q^5+q^4+q^2
        55: 2q^5+q^4+q^2
        56: q^6+2q^5+q^4+q^2
        57: 2q^5+q^4+q^2
        59: q^5+q^2
        60: q^5+q^2
        63: 2q^5+q^2
        65: 2q^5+q^4+q^2
        67: q^5+q^4+q^2
        68: q^5+q^2
        69: q^5+q^4+q^2
        70: 2q^5+q^2
        71: q^5+q^2
        72: q^5+q^4+q^2
        73: q^5+q^4+q^2
        75: 2q^5+q^4+q^2
        77: q^6+2q^5+q^4+q^2
        79: 2q^5+q^4+q^2
        80: 2q^5+q^2
        81: q^5+q^4+q^2
        82: 2q^5+q^2
        83: 2q^5+q^4+q^2
        84: 2q^5+q^2
        85: q^5+q^4+q^2
        86: 2q^5+q^2
        87: 2q^5+q^4+q^2
        88: q^2
        89: q^2
        90: q^5+q^2
        91: 2q^5+q^4+q^2
        92: q^5+q^4+q^2
        93: 2q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^5+q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^5+q^4+q^2
       100: q^5+q^4+q^2
       101: q^5+q^2
       102: q^5+q^4+q^2
       104: q^5+q^2
       107: q^5+q^2
       110: q^5+q^2
       112: q^5+q^4+q^2
       114: 2q^5+q^2
       116: 2q^5+q^4+q^2
       118: q^5+q^2
       119: q^5+q^2
       122: 2q^5+q^2
       124: q^5+q^4+q^2
       125: q^2
       126: q^2
       128: q^4+q^2
       130: q^4+q^2
       132: q^5+q^4+q^2
       133: q^5+q^2
       134: q^5+q^4+q^2
       135: q^5+q^4+q^2
       136: q^5+q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: 2q^5+q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: 2q^5+q^2
       147: q^4+q^2
       148: q^2
       149: q^5+q^2
       150: q^5+q^4+q^2
       152: q^5+q^4+q^2
       154: q^5+q^2
       156: q^5+q^4+q^2
       157: q^2
       158: q^2
       159: q^5+q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^5+q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^5+q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       170: q^5+q^2
       174: q^5+q^2
       178: q^4+q^2
       180: q^2
       182: q^4+q^2
       183: q^5+q^2
       186: q^5+q^2
       188: q^5+q^4+q^2
       190: 2q^5+q^2
       192: q^2
       193: q^2
       196: q^2
       198: q^2
       199: q^2
       201: q^2
       204: q^2
       206: q^2
       208: q^2
       210: q^5+q^2
       212: q^5+q^4+q^2
       214: q^4+q^2
       216: q^4+q^2
       218: q^5+q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       238: q^4+q^2
       240: q^2
       242: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^5+q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^5+q^2
       253: q^2
       254: q^2
       255: q^5+q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       260: q^2
       264: q^5+q^2
       268: q^2
       274: q^2
       276: q^2
       280: q^2
       282: q^4+q^2
       283: q^2
       286: q^2
       288: q^2
       290: q^4+q^2
       292: q^4+q^2
       293: q^2
       296: q^2
       298: q^2
       299: q^2
       302: q^2
       304: q^2
       306: q^2
       307: q^2
       310: q^2
       312: q^2
       314: q^2
       316: q^4+q^2
       318: q^2
       319: q^2
       322: q^2
       324: q^2
       326: q^5+q^2
       328: q^2
       330: q^2
       332: q^5+q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       339: q^4+q^2
       341: q^2
       343: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       361: q^4+q^2
       363: q^2
       365: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       378: q^2
       382: q^2
       386: q^2
       390: q^2
       394: q^2
       400: q^2
       403: q^2
       407: q^2
       410: q^2
       412: q^2
       414: q^2
       416: q^2
       418: q^4+q^2
       419: q^2
       422: q^2
       424: q^2
       426: q^4+q^2
       428: q^2
       429: q^2
       432: q^2
       434: q^2
       436: q^2
       437: q^2
       440: q^2
       442: q^2
       443: q^2
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       447: q^2
       450: q^2
       452: q^2
       453: q^2
       456: q^2
       458: q^2
       460: q^2
       462: q^2
       464: q^2
       466: q^2
       468: q^4+q^2
       470: q^2
       471: q^2
       474: q^2
       476: q^2
       478: q^2
       480: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       486: q^4+q^2
       488: q^2
       490: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       522: q^2
       526: q^2
       530: q^2
       534: q^2
       538: q^2
       542: q^2
       546: q^2
       551: q^2
       556: q^2
       560: q^2
       564: q^2
       566: q^2
       571: q^2
       574: q^2
       581: q^2
       584: q^2
       586: q^2
       588: q^2
       589: q^2
       592: q^2
       593: q^2
       596: q^2
       598: q^4+q^2
       600: q^2
       602: q^2
       603: q^2
       606: q^2
       608: q^2
       610: q^2
       614: q^2
       615: q^2
       618: q^2
       619: q^2
       622: q^2
       624: q^2
       626: q^2
       630: q^2
       632: q^2
       634: q^2
       640: q^2
       641: q^2
       644: q^2
       646: q^2
       652: q^2
       656: q^2
       665: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       699: q^2
       706: q^2
       710: q^2
       715: q^2
       718: q^2
       722: q^2
       726: q^2
       734: q^2
       740: q^2
       744: q^2
       752: q^2
       754: q^2
       759: q^2
       766: q^2
       773: q^2
       778: q^2
       782: q^2
       785: q^2
       788: q^2
       792: q^2
       798: q^2
       801: q^2
       804: q^2
       805: q^2
       808: q^2
       810: q^2
       812: q^2
       822: q^2
       825: q^2
       828: q^2
       829: q^2
       832: q^2
       834: q^2
       836: q^2
       850: q^2
       854: q
       856: q^2
       871: q^2
       875: q^2
       880: q^2
       890: q^2
       897: q^2
       903: q^2
       905: q^2
       909: q^2
       921: q^2
       926: q^2
       929: q^2
       947: q^2
       951: q^2
       953: q^2
       962: q^2
       980: q
       987: q
      1011: q^2
      1023: q^2
      1026: q^2
      1029: q^2
      1039: q^2
      1040: q^2
      1045: q^2
      1051: q
      1061: q^2
      1065: q^2
      1108: q
      1128: q^2
      1155: q^2
      1157: q^2
      1162: q^2
      1175: q^2
      1177: q^2
      1181: q^2
      1186: q
      1193: q
      1223: q
      1265: q
      1279: q^2
      1312: q
      1324: q
      1339: q
      1363: q^2
      1394: q^2
      1409: q
      1416: q
      1447: q
      1499: q
      1535: q
      1558: q
      1561: q
      1685: q
      1794: 1
      1878: 1
      1950: 1
      2000: 1
      2012: 1
      2114: 1

2115:    0: 3q^5+q^4+q^2
         1: q^6+2q^5+q^4+q^2
         2: 3q^5+q^4+q^2
         3: q^7+2q^6+3q^5+q^4+q^2
         4: 3q^5+q^4+q^2
         5: q^6+2q^5+q^4+q^2
         6: q^6+2q^5+q^4+q^2
         7: 3q^5+q^4+q^2
         8: q^6+2q^5+q^4+q^2
         9: q^7+q^6+2q^5+q^4+q^2
        10: 2q^5+q^2
        11: q^6+2q^5+q^2
        12: 2q^5+q^2
        13: 3q^5+q^4+q^2
        14: 3q^5+q^4+q^2
        15: q^6+2q^5+q^4+q^2
        16: 2q^5+q^4+q^2
        17: q^5+q^4+q^2
        18: 2q^5+q^4+q^2
        19: 3q^5+q^4+q^2
        20: q^6+2q^5+q^4+q^2
        21: 3q^5+q^4+q^2
        22: 2q^5+q^4+q^2
        23: q^6+2q^5+q^4+q^2
        24: 2q^5+q^4+q^2
        25: 2q^5+q^4+q^2
        26: q^6+2q^5+q^4+q^2
        27: 2q^5+q^4+q^2
        28: q^5+q^2
        29: 2q^5+q^2
        30: 3q^5+q^4+q^2
        31: 2q^5+q^2
        32: 2q^5+q^4+q^2
        33: q^5+q^4+q^2
        34: 2q^5+q^2
        35: 2q^5+q^4+q^2
        36: q^5+q^4+q^2
        38: 2q^5+q^4+q^2
        40: q^6+2q^5+q^4+q^2
        42: 2q^5+q^4+q^2
        43: 2q^5+q^2
        44: 2q^5+q^2
        45: q^6+2q^5+q^2
        46: 2q^5+q^4+q^2
        47: q^5+q^4+q^2
        48: 2q^5+q^4+q^2
        49: 2q^5+q^4+q^2
        50: q^5+q^4+q^2
        51: 2q^5+q^4+q^2
        52: 2q^5+q^4+q^2
        53: q^6+2q^5+q^4+q^2
        54: 2q^5+q^4+q^2
        55: 2q^5+q^4+q^2
        56: q^6+2q^5+q^4+q^2
        57: 2q^5+q^4+q^2
        58: q^5+q^2
        61: q^5+q^2
        63: 2q^5+q^2
        65: 2q^5+q^4+q^2
        67: q^5+q^4+q^2
        68: q^5+q^2
        69: q^5+q^4+q^2
        70: 2q^5+q^2
        71: q^5+q^2
        72: q^5+q^4+q^2
        73: q^5+q^4+q^2
        75: 2q^5+q^4+q^2
        77: q^6+2q^5+q^4+q^2
        79: 2q^5+q^4+q^2
        80: 2q^5+q^2
        81: q^5+q^4+q^2
        82: 2q^5+q^2
        83: 2q^5+q^4+q^2
        84: 2q^5+q^2
        85: q^5+q^4+q^2
        86: 2q^5+q^2
        87: 2q^5+q^4+q^2
        88: q^2
        89: q^2
        90: q^5+q^2
        91: 2q^5+q^4+q^2
        92: q^5+q^4+q^2
        93: 2q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^5+q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^5+q^4+q^2
       100: q^5+q^4+q^2
       101: q^5+q^2
       102: q^5+q^4+q^2
       105: q^5+q^2
       108: q^5+q^2
       109: q^5+q^2
       112: q^5+q^4+q^2
       114: 2q^5+q^2
       116: 2q^5+q^4+q^2
       117: q^5+q^2
       120: q^5+q^2
       122: 2q^5+q^2
       124: q^5+q^4+q^2
       125: q^2
       126: q^2
       128: q^4+q^2
       130: q^4+q^2
       132: q^5+q^4+q^2
       133: q^5+q^2
       134: q^5+q^4+q^2
       135: q^5+q^4+q^2
       136: q^5+q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: 2q^5+q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: 2q^5+q^2
       147: q^4+q^2
       148: q^2
       149: q^5+q^2
       150: q^5+q^4+q^2
       152: q^5+q^4+q^2
       154: q^5+q^2
       156: q^5+q^4+q^2
       157: q^2
       158: q^2
       159: q^5+q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^5+q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^5+q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       171: q^5+q^2
       175: q^5+q^2
       178: q^4+q^2
       180: q^2
       182: q^4+q^2
       184: q^5+q^2
       185: q^5+q^2
       188: q^5+q^4+q^2
       190: 2q^5+q^2
       191: q^2
       194: q^2
       195: q^2
       198: q^2
       200: q^2
       202: q^2
       203: q^2
       206: q^2
       208: q^2
       210: q^5+q^2
       212: q^5+q^4+q^2
       214: q^4+q^2
       216: q^4+q^2
       218: q^5+q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       238: q^4+q^2
       240: q^2
       242: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^5+q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^5+q^2
       253: q^2
       254: q^2
       255: q^5+q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       261: q^2
       265: q^5+q^2
       270: q^2
       272: q^2
       277: q^2
       280: q^2
       282: q^4+q^2
       284: q^2
       285: q^2
       288: q^2
       290: q^4+q^2
       292: q^4+q^2
       294: q^2
       295: q^2
       298: q^2
       300: q^2
       302: q^2
       303: q^2
       306: q^2
       308: q^2
       309: q^2
       312: q^2
       314: q^2
       316: q^4+q^2
       318: q^2
       320: q^2
       321: q^2
       324: q^2
       326: q^5+q^2
       328: q^2
       330: q^2
       332: q^5+q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       339: q^4+q^2
       341: q^2
       343: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       361: q^4+q^2
       363: q^2
       365: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       379: q^2
       383: q^2
       387: q^2
       392: q^2
       395: q^2
       398: q^2
       402: q^2
       408: q^2
       410: q^2
       412: q^2
       414: q^2
       416: q^2
       418: q^4+q^2
       420: q^2
       421: q^2
       424: q^2
       426: q^4+q^2
       428: q^2
       430: q^2
       431: q^2
       434: q^2
       436: q^2
       438: q^2
       439: q^2
       442: q^2
       444: q^2
       446: q^2
       448: q^2
       449: q^2
       452: q^2
       454: q^2
       456: q^2
       457: q^2
       460: q^2
       461: q^2
       464: q^2
       466: q^2
       468: q^4+q^2
       470: q^2
       472: q^2
       473: q^2
       476: q^2
       478: q^2
       480: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       486: q^4+q^2
       488: q^2
       490: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       523: q^2
       527: q^2
       531: q^2
       535: q^2
       540: q^2
       544: q^2
       548: q^2
       550: q^2
       554: q^2
       558: q^2
       562: q^2
       567: q^2
       572: q^2
       576: q^2
       581: q^2
       584: q^2
       586: q^2
       588: q^2
       590: q^2
       591: q^2
       594: q^2
       595: q^2
       598: q^4+q^2
       600: q^2
       602: q^2
       604: q^2
       606: q^2
       607: q^2
       610: q^2
       614: q^2
       616: q^2
       618: q^2
       620: q^2
       621: q^2
       624: q^2
       626: q^2
       630: q^2
       631: q^2
       634: q^2
       640: q^2
       642: q^2
       643: q^2
       646: q^2
       652: q^2
       656: q^2
       665: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       700: q^2
       707: q^2
       711: q^2
       714: q^2
       719: q^2
       724: q^2
       728: q^2
       736: q^2
       738: q^2
       742: q^2
       750: q^2
       755: q^2
       760: q^2
       767: q^2
       773: q^2
       778: q^2
       782: q^2
       786: q^2
       787: q^2
       792: q^2
       798: q^2
       802: q^2
       803: q^2
       806: q^2
       807: q^2
       810: q^2
       812: q^2
       822: q^2
       826: q^2
       827: q^2
       830: q^2
       831: q^2
       834: q^2
       836: q^2
       850: q^2
       854: q
       856: q^2
       871: q^2
       875: q^2
       880: q^2
       891: q^2
       898: q^2
       901: q^2
       907: q^2
       910: q^2
       923: q^2
       925: q^2
       931: q^2
       945: q^2
       949: q^2
       954: q^2
       963: q^2
       981: q
       987: q
      1011: q^2
      1023: q^2
      1027: q^2
      1028: q^2
      1039: q^2
      1041: q^2
      1044: q^2
      1051: q
      1061: q^2
      1065: q^2
      1109: q
      1129: q^2
      1153: q^2
      1159: q^2
      1161: q^2
      1173: q^2
      1179: q^2
      1182: q^2
      1187: q
      1193: q
      1223: q
      1265: q
      1279: q^2
      1313: q
      1325: q
      1339: q
      1362: q^2
      1395: q^2
      1409: q
      1417: q
      1447: q
      1500: q
      1536: q
      1558: q
      1562: q
      1686: q
      1795: 1
      1880: 1
      1951: 1
      2001: 1
      2013: 1
      2115: 1

2116:    0: 1
         1: 1
         2: q^5+1
         3: 1
         4: 1
         5: 1
         6: 1
         7: q^5+1
         8: q^5+1
         9: q^5+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: q^5+1
        19: 1
        20: 1
        21: q^5+1
        22: 1
        23: 1
        24: q^5+1
        25: 1
        26: 1
        27: q^5+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q^5+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^5+1
        52: 1
        53: 1
        54: q^5+1
        55: 1
        56: 1
        57: q^5+1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q^5+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q^5+1
        97: 1
        98: 1
        99: q^5+1
       100: 1
       101: 1
       102: q^5+1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^5+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: q^5+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q^5+1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: q^5+1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q^5+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^5+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: 1
       585: 1
       587: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       884: 1
       896: 1
       900: 1
       904: 1
       908: 1
       912: 1
       916: 1
       920: 1
       924: 1
       928: 1
       932: 1
       936: 1
       940: 1
       944: 1
       948: 1
       952: 1
       956: 1
       960: 1
       964: 1
       968: 1
       974: 1
       978: 1
       982: 1
       988: 1
       992: 1
       994: 1
       996: 1
       998: 1
      1000: 1
      1002: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1016: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1034: 1
      1036: 1
      1038: 1
      1040: 1
      1042: 1
      1044: 1
      1046: 1
      1048: 1
      1050: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1098: 1
      1110: 1
      1114: 1
      1118: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1144: 1
      1148: 1
      1152: 1
      1156: 1
      1160: 1
      1164: 1
      1168: 1
      1172: 1
      1176: 1
      1180: 1
      1184: 1
      1188: 1
      1194: 1
      1198: 1
      1202: 1
      1206: 1
      1214: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1234: 1
      1236: 1
      1238: 1
      1240: 1
      1242: 1
      1248: 1
      1250: 1
      1252: 1
      1254: 1
      1256: 1
      1258: 1
      1260: 1
      1264: 1
      1266: 1
      1268: 1
      1270: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1302: 1
      1314: 1
      1318: 1
      1322: 1
      1326: 1
      1330: 1
      1334: 1
      1344: 1
      1348: 1
      1352: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1376: 1
      1380: 1
      1384: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1414: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1436: 1
      1446: 1
      1448: 1
      1450: 1
      1454: 1
      1456: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1470: 1
      1472: 1
      1474: 1
      1476: 1
      1478: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1489: 1
      1501: 1
      1513: 1
      1537: 1
      1559: 1
      1563: 1
      1567: 1
      1571: 1
      1575: 1
      1579: 1
      1583: 1
      1587: 1
      1591: 1
      1595: 1
      1599: 1
      1603: 1
      1607: 1
      1611: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1631: 1
      1637: 1
      1641: 1
      1649: 1
      1657: 1
      1659: 1
      1661: 1
      1663: 1
      1665: 1
      1671: 1
      1673: 1
      1687: 1
      1699: 1
      1711: 1
      1729: 1
      1741: 1
      1753: 1
      1757: 1
      1769: 1
      1777: 1
      1781: 1
      1785: 1
      1789: 1
      1793: 1
      1797: 1
      1807: 1
      1811: 1
      1815: 1
      1817: 1
      1819: 1
      1821: 1
      1823: 1
      1870: 1
      1882: 1
      1894: 1
      1902: 1
      1906: 1
      1910: 1
      1918: 1
      1922: 1
      1944: 1
      1948: 1
      1952: 1
      1958: 1
      2002: 1
      2014: 1
      2036: 1
      2048: 1
      2056: 1
      2116: 1

2117:    0: q^4+2q^3+q^2+q
         1: q^4+2q^3+q^2+q
         2: q^5+2q^4+q^3+q^2+q
         3: q^4+2q^3+q^2+q
         4: q^4+2q^3+q^2+q
         5: q^4+2q^3+q^2+q
         6: q^4+2q^3+q^2+q
         7: q^5+2q^4+q^3+q^2+q
         8: q^4+q^3+q^2+q
         9: q^5+2q^4+q^3+q^2+q
        10: q^4+2q^3+q^2+q
        11: q^4+2q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: q^4+q^3+q^2+q
        14: q^4+q^3+q^2+q
        15: q^3+q^2+q
        16: q^4+2q^3+q^2+q
        17: q^4+2q^3+q^2+q
        18: q^5+2q^4+q^3+q^2+q
        19: q^4+2q^3+q^2+q
        20: q^4+2q^3+q^2+q
        21: q^5+2q^4+q^3+q^2+q
        22: 2q^3+q^2+q
        23: 2q^3+q^2+q
        24: q^4+q^3+q^2+q
        25: 2q^3+q^2+q
        26: 2q^3+q^2+q
        27: q^4+q^3+q^2+q
        28: q^4+2q^3+q^2+q
        29: q^4+2q^3+q^2+q
        30: q^4+q^3+q^2+q
        31: 2q^3+q^2+q
        32: q^3+q^2+q
        33: 2q^3+q^2+q
        34: 2q^3+q^2+q
        35: q^3+q^2+q
        36: 2q^3+q^2+q
        37: 2q^3+q^2+q
        39: 2q^3+q^2+q
        41: q^4+q^3+q^2+q
        43: q^4+q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: q^4+q^3+q^2+q
        47: q^3+q^2+q
        48: q^4+q^3+q^2+q
        49: q^4+2q^3+q^2+q
        50: q^4+2q^3+q^2+q
        51: q^5+2q^4+q^3+q^2+q
        52: 2q^3+q^2+q
        53: 2q^3+q^2+q
        54: q^4+q^3+q^2+q
        55: 2q^3+q^2+q
        56: 2q^3+q^2+q
        57: q^4+q^3+q^2+q
        58: q^3+q^2+q
        59: q^3
        60: q^3+q^2+q
        61: q^3
        62: 2q^3+q^2+q
        64: q^3+q^2+q
        66: 2q^3+q^2+q
        68: q^2+q
        69: q^4+q^3+q^2+q
        70: q^4+q^3+q^2+q
        71: q^4+2q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        74: 2q^3+q^2+q
        76: 2q^3+q^2+q
        78: q^4+q^3+q^2+q
        80: q^3+q^2+q
        81: q^3+q^2+q
        82: 2q^3+q^2+q
        83: q^3+q^2+q
        84: q^3+q^2+q
        85: q^3+q^2+q
        86: 2q^3+q^2+q
        87: q^3+q^2+q
        88: q^4+q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: q^4+q^3+q^2+q
        92: q^3+q^2+q
        93: q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: q^3+q^2+q
       101: q^3+q^2+q
       102: q^4+q^3+q^2+q
       103: q^3+q^2+q
       106: q^3
       107: q^3+q^2+q
       108: q^3
       109: q^3+q^2+q
       110: q^3
       111: 2q^3+q^2+q
       113: 2q^3+q^2+q
       115: q^3+q^2+q
       117: q^2+q
       119: q^2+q
       121: q^3+q^2+q
       123: q^3+q^2+q
       125: q^2+q
       126: q^4+q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^2+q
       134: q^4+q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^3+q^2+q
       150: q^3+q^2+q
       151: q^3+q^2+q
       153: q^3+q^2+q
       155: q^4+q^3+q^2+q
       157: q^4+q^3+q^2+q
       158: q^3+q^2+q
       159: q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3+q^2+q
       172: q^3
       173: q^2+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       183: q^2+q
       185: q^2+q
       187: q^3+q^2+q
       189: q^3+q^2+q
       191: q^2+q
       193: q^2+q
       195: q^3+q^2+q
       196: q^3
       197: q^2+q
       199: q^2+q
       201: q^3+q^2+q
       202: q^3
       203: q^2+q
       205: q^2+q
       207: q^3+q^2+q
       209: q^3+q^2+q
       211: q^3+q^2+q
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^3+q^2+q
       219: q^2+q
       220: q^2+q
       221: q^4+q^3+q^2+q
       222: q^3+q^2+q
       223: q^3+q^2+q
       224: q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
       230: q^3+q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: q^3+q^2+q
       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       259: q^3+q^2+q
       262: q^3
       263: q^2+q
       267: q^2+q
       271: q^2+q
       275: q^2+q
       279: q^2+q
       281: q^3+q^2+q
       283: q^2+q
       285: q^2+q
       287: q^3+q^2+q
       289: q^3+q^2+q
       291: q^3+q^2+q
       293: q^2+q
       295: q^2+q
       297: q^3+q^2+q
       299: q^2+q
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       311: q^2+q
       313: q^2+q
       315: q^3+q^2+q
       317: q^3+q^2+q
       319: q^2+q
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       323: q^2+q
       325: q^3+q^2+q
       327: q^3+q^2+q
       329: q^3+q^2+q
       331: q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       377: q^2+q
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       385: q^2+q
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       393: q^2+q
       397: q^2+q
       401: q^2+q
       405: q^2+q
       409: q^2+q
       411: q^3+q^2+q
       413: q^2+q
       415: q^3+q^2+q
       417: q^3+q^2+q
       419: q^2+q
       421: q^2+q
       423: q^3+q^2+q
       425: q^3+q^2+q
       427: q^3+q^2+q
       429: q^2+q
       431: q^2+q
       433: q^2+q
       435: q
       437: q^2+q
       439: q^2+q
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       447: q^2+q
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       455: q
       457: q^2+q
       459: q^2+q
       461: q^2+q
       463: q^2+q
       465: q
       467: q^3+q
       469: q^3+q^2+q
       471: q
       473: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       485: q^3+q
       487: q
       489: q^3+q
       491: q^3+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: q^2+q
       496: q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q
       502: q^3+q
       504: q
       506: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
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       513: q
       514: q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q
       519: q
       520: q^3+q
       521: q^2+q
       525: q^2+q
       529: q^2+q
       533: q^2+q
       537: q
       541: q^2+q
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       549: q^2+q
       553: q
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       561: q^2+q
       565: q
       569: q^2+q
       573: q^2+q
       577: q^2+q
       583: q^2+q
       585: q^2+q
       587: q^3+q^2+q
       589: q^2+q
       591: q^2+q
       593: q^2+q
       595: q^2+q
       597: q^3+q
       599: q^3+q^2+q
       601: q
       603: q^2+q
       605: q
       607: q^2+q
       609: q^2+q
       611: q
       613: q^2+q
       615: q
       617: q
       619: q^2+q
       621: q^2+q
       623: q
       625: q^2+q
       627: q
       629: q^2+q
       631: q
       633: q
       635: q
       637: q^3+q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: 2q
       653: q
       655: q
       657: q
       658: q^3+q
       660: q
       662: q^3+q
       664: q^3+q
       665: q
       666: q^3+q
       668: q
       670: q^3+q
       672: q
       673: q^3+q
       674: q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q
       680: q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       693: q^2+q
       705: q^2+q
       709: q^2+q
       713: q^2+q
       717: q^2+q
       721: q
       725: q^2+q
       729: q
       733: q
       737: q
       741: q^2+q
       745: q
       749: q
       753: q
       757: 2q
       761: q
       765: q
       769: q
       771: q
       775: q
       777: q^2+q
       779: q^3+q
       781: q
       783: q^3+q
       785: q
       787: q
       789: q
       791: q
       793: q
       795: q
       797: q
       799: q
       801: q
       803: q
       805: q^2+q
       807: q^2+q
       809: q
       811: q^2+q
       813: q
       815: q
       817: q
       819: q
       821: q
       823: q
       825: q^2+q
       827: q^2+q
       829: q
       831: q
       833: q
       835: q^2+q
       837: q
       839: q
       841: q
       843: q
       845: q
       847: q
       849: 2q
       851: q
       853: 2q
       855: q
       857: q
       859: q^3+q
       861: q
       863: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q
       869: q
       870: q
       871: q
       872: q
       873: q
       874: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       884: q
       886: q
       896: q^2+q
       900: q
       904: q
       908: q
       912: q
       916: q
       920: q
       924: q
       928: q^2+q
       932: q
       936: q
       940: q
       944: q
       948: q^2+q
       952: q
       956: q
       960: 2q
       964: q
       968: q
       970: q
       974: q
       978: 2q
       982: q
       984: q
       988: q
       992: q
       994: q
       996: q^3+q
       998: q
      1000: q
      1002: q
      1004: q
      1006: q
      1008: q
      1010: 2q
      1012: q
      1014: q
      1016: q
      1018: q
      1020: q
      1022: q
      1024: q
      1026: q
      1028: q
      1030: q
      1032: q
      1034: q
      1036: q
      1038: q
      1040: q
      1042: q
      1044: q
      1046: q
      1048: q
      1050: 2q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q
      1074: q
      1076: q
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      1081: q
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      1088: q
      1098: q
      1100: q
      1110: q
      1114: q
      1118: q
      1122: q
      1126: 2q
      1130: q
      1134: q
      1138: q
      1140: q
      1144: q
      1148: q
      1152: q
      1156: q
      1160: q
      1164: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: 2q
      1188: q
      1190: q
      1194: q
      1198: q
      1202: q
      1206: q
      1214: q
      1216: q
      1218: q
      1220: q
      1222: 2q
      1224: q
      1230: q
      1232: q
      1234: q
      1236: q
      1238: q
      1240: q
      1242: q
      1248: q
      1250: q
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      1285: q
      1288: q
      1290: q
      1292: q
      1302: q
      1304: q
      1314: q
      1318: q
      1322: 2q
      1326: q
      1330: q
      1334: q
      1336: q
      1344: q
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      1352: q
      1356: q
      1360: q
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      1563: q
      1567: q
      1571: q
      1575: q
      1583: q
      1587: q
      1591: q
      1595: q
      1619: 1
      1631: q
      1637: q
      1687: q
      1699: q
      1713: 1
      1729: q
      1793: 1
      1807: 1
      1872: 1
      1886: 1
      1944: 1
      1948: 1
      2006: 1
      2015: 1
      2056: 1
      2117: 1

2118:    0: 3q^4+2q^3+3q^2+2q
         1: 3q^4+2q^3+3q^2+2q
         2: 2q^5+2q^4+q^3+3q^2+2q
         3: 3q^4+2q^3+3q^2+2q
         4: q^5+2q^4+3q^3+2q^2+2q
         5: 3q^4+2q^3+3q^2+2q
         6: q^5+2q^4+3q^3+2q^2+2q
         7: q^6+q^5+2q^4+2q^3+2q^2+2q
         8: 2q^5+2q^4+q^3+3q^2+2q
         9: q^6+q^5+2q^4+2q^3+2q^2+2q
        10: 3q^4+2q^3+3q^2+2q
        11: 3q^4+2q^3+3q^2+2q
        12: q^5+2q^4+3q^3+2q^2+2q
        13: q^4+q^3+3q^2+2q
        14: q^4+2q^3+2q^2+2q
        15: q^4+q^3+3q^2+2q
        16: 3q^4+2q^3+3q^2+2q
        17: 3q^4+2q^3+3q^2+2q
        18: q^6+q^5+2q^4+2q^3+2q^2+2q
        19: 2q^4+2q^3+2q^2+2q
        20: 2q^4+2q^3+2q^2+2q
        21: q^5+2q^4+q^3+2q^2+2q
        22: 3q^4+2q^3+3q^2+2q
        23: 3q^4+2q^3+3q^2+2q
        24: 2q^5+2q^4+q^3+3q^2+2q
        25: 3q^4+2q^3+3q^2+2q
        26: 3q^4+2q^3+3q^2+2q
        27: 2q^5+2q^4+q^3+3q^2+2q
        28: 3q^4+2q^3+3q^2+2q
        29: 2q^4+2q^3+2q^2+2q
        30: q^4+q^3+2q^2+2q
        31: 3q^4+2q^3+3q^2+2q
        32: q^4+q^3+3q^2+2q
        33: 3q^4+2q^3+3q^2+2q
        34: 3q^4+2q^3+3q^2+2q
        35: q^4+q^3+3q^2+2q
        36: 3q^4+2q^3+3q^2+2q
        37: 2q^4+2q^3+2q^2+2q
        38: q^4+q^2
        39: 2q^4+2q^3+2q^2+2q
        40: q^4+q^2
        41: q^5+2q^4+q^3+2q^2+2q
        42: q^5+q^2
        43: q^4+q^3+3q^2+2q
        44: q^4+2q^3+2q^2+2q
        45: q^4+q^3+3q^2+2q
        46: q^4+q^3+3q^2+2q
        47: q^4+q^3+3q^2+2q
        48: q^4+2q^3+2q^2+2q
        49: 2q^4+2q^3+2q^2+2q
        50: 2q^4+2q^3+2q^2+2q
        51: q^5+2q^4+q^3+2q^2+2q
        52: 2q^4+2q^3+2q^2+2q
        53: 2q^4+2q^3+2q^2+2q
        54: q^5+2q^4+q^3+2q^2+2q
        55: 2q^4+2q^3+2q^2+2q
        56: 2q^4+2q^3+2q^2+2q
        57: q^5+2q^4+q^3+2q^2+2q
        58: q^4+q^3+q^2+q
        59: 2q^4+q^3+2q^2+q
        60: 2q^4+q^3+2q^2+q
        61: q^4+q^3+q^2+q
        62: 2q^4+2q^3+2q^2+2q
        63: q^4+q^2
        64: q^4+q^3+2q^2+2q
        65: q^2
        66: 2q^4+2q^3+2q^2+2q
        67: q^4+q^2
        68: 3q^2+2q
        69: q^4+q^3+2q^2+2q
        70: q^4+q^3+2q^2+2q
        71: 2q^4+2q^3+2q^2+2q
        72: q^4+2q^3+q^2+2q
        73: q^4+2q^3+q^2+2q
        74: q^4+2q^3+q^2+2q
        76: q^4+2q^3+q^2+2q
        78: 2q^4+q^3+q^2+2q
        80: q^4+q^3+3q^2+2q
        81: q^4+q^3+3q^2+2q
        82: 2q^4+2q^3+2q^2+2q
        83: q^4+q^3+2q^2+2q
        84: q^4+q^3+3q^2+2q
        85: q^4+q^3+3q^2+2q
        86: 2q^4+2q^3+2q^2+2q
        87: q^4+q^3+2q^2+2q
        88: q^4+q^3+3q^2+2q
        89: q^4+q^3+3q^2+2q
        90: q^4+2q^3+2q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: 2q^4+2q^3+2q^2+2q
        95: 2q^4+2q^3+2q^2+2q
        96: q^5+2q^4+q^3+2q^2+2q
        97: 2q^4+2q^3+2q^2+2q
        98: 2q^4+2q^3+2q^2+2q
        99: q^5+2q^4+q^3+2q^2+2q
       100: 2q^4+2q^3+2q^2+2q
       101: 2q^4+2q^3+2q^2+2q
       102: q^5+2q^4+q^3+2q^2+2q
       103: q^4+q^3+q^2+q
       104: q^4+q^2
       106: q^4+q^3+q^2+q
       107: q^4+q^3+q^2+q
       108: q^3+q
       109: q^3+q
       110: q^4+q^3+q^2+q
       111: 2q^3+2q
       113: q^4+2q^3+q^2+2q
       115: q^4+q^3+q^2+2q
       117: q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: q^2+q
       121: q^4+q^3+2q^2+2q
       122: q^2
       123: q^4+q^3+2q^2+2q
       124: q^2
       125: 3q^2+2q
       126: q^4+q^3+2q^2+2q
       127: q^4+2q^3+q^2+2q
       129: q^4+2q^3+q^2+2q
       131: 2q^4+q^3+q^2+2q
       133: 2q^2+2q
       134: q^3+2q^2+2q
       135: q^3+q^2+2q
       136: q^3+q^2+2q
       137: q^4+q^3+3q^2+2q
       138: q^4+q^3+2q^2+2q
       139: 2q^4+2q^3+2q^2+2q
       140: q^4+2q^3+q^2+2q
       141: q^4+q^3+2q^2+2q
       142: q^4+2q^3+q^2+2q
       143: q^4+q^3+3q^2+2q
       144: q^4+q^3+2q^2+2q
       145: 2q^4+2q^3+2q^2+2q
       146: q^4+q^3+2q^2+2q
       147: q^4+2q^3+q^2+2q
       148: q^4+2q^3+q^2+2q
       149: 2q^4+2q^3+2q^2+2q
       150: q^4+q^3+2q^2+2q
       151: q^4+2q^3+q^2+2q
       153: q^4+2q^3+q^2+2q
       155: 2q^4+q^3+q^2+2q
       157: q^3+2q^2+2q
       158: q^3+2q^2+2q
       159: q^3+2q^2+2q
       160: q^3+2q^2+2q
       161: q^3+2q^2+2q
       162: q^3+2q^2+2q
       163: q^3+2q^2+2q
       164: q^3+2q^2+2q
       165: q^3+2q^2+2q
       166: 2q^4+2q^3+2q^2+2q
       167: 2q^4+2q^3+2q^2+2q
       168: q^5+2q^4+q^3+2q^2+2q
       169: q^3+q
       172: q^3+q
       173: q^2+q
       174: q^2
       176: q^2+q
       177: q^4+q^3+q^2+2q
       179: q^4+2q^3+q^2+2q
       181: 2q^3+2q
       183: q^2+q
       184: q
       185: q
       186: q^2+q
       187: q^3+2q
       189: q^4+q^3+q^2+2q
       191: q^2+q
       192: 2q^2+q
       193: q^4+q^3+q^2+q
       194: q^3+q
       195: q^3+q
       196: q^4+q^3+q^2+q
       197: 2q^3+2q
       199: 2q^2+q
       200: q^2+q
       201: q^4+q^3+q^2+q
       202: q^3+q
       203: q^3+q
       204: q^4+q^3+q^2+q
       205: 2q^3+2q
       207: q^4+q^3+2q^2+2q
       208: q^2
       209: q^4+2q^3+q^2+2q
       211: q^4+q^3+q^2+2q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: q^3+2q^2+2q
       222: q^3+q^2+2q
       223: q^3+q^2+2q
       224: q^3+q^2+2q
       225: q^3+q^2+2q
       226: q^4+q^3+2q^2+2q
       227: 2q^2+2q
       228: q^3+2q^2+2q
       229: q^3+q^2+2q
       230: q^3+q^2+2q
       231: q^4+q^3+2q^2+2q
       232: 2q^2+2q
       233: q^3+2q^2+2q
       234: q^3+q^2+2q
       235: q^3+q^2+2q
       236: q^4+q^3+2q^2+2q
       237: q^4+2q^3+q^2+2q
       239: q^4+2q^3+q^2+2q
       241: 2q^4+q^3+q^2+2q
       243: 2q^4+2q^3+2q^2+2q
       244: q^4+2q^3+q^2+2q
       245: q^4+2q^3+q^2+2q
       246: q^4+q^3+2q^2+2q
       247: 3q^3+3q
       248: 3q^3+3q
       249: 2q^4+q^3+q^2+2q
       250: q^3+2q^2+2q
       251: q^3+2q^2+2q
       252: q^3+2q^2+2q
       253: q^3+2q^2+2q
       254: q^3+2q^2+2q
       255: q^3+2q^2+2q
       256: q^3+2q^2+2q
       257: q^3+2q^2+2q
       258: q^3+2q^2+2q
       259: q^3+q
       262: q^3+q
       263: q
       266: q
       267: q^3+q
       269: q^3+q
       271: q^3+q
       273: q^3+q
       275: q^2+q
       276: q^2
       278: q^2+q
       279: q^2+2q
       281: q^2+2q
       283: q^2+q
       284: q
       285: q
       286: q^2+q
       287: q^4+q^3+q^2+2q
       289: 2q
       291: q^3+2q
       293: q^2+q
       294: q
       295: q
       296: q^2+q
       297: q^3+2q
       299: q^2+q
       300: q
       301: 2q^3+2q
       303: q
       304: q^2+q
       305: q^3+2q
       307: q^2+q
       308: q
       309: q
       310: q^2+q
       311: 2q^3+2q
       313: q^3+2q
       315: q^4+q^3+q^2+2q
       317: q^4+2q^3+q^2+2q
       319: q^4+q^3+q^2+q
       320: q^3+q
       321: q^3+q
       322: q^4+q^3+q^2+q
       323: 2q^3+2q
       325: q^4+q^3+q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: 2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: q^3+2q
       337: 3q^3+3q
       338: 3q^3+3q
       340: 3q^3+3q
       342: 2q^4+q^3+q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: q^3+2q^2+2q
       347: q^3+q^2+2q
       348: q^3+q^2+2q
       349: q^3+q^2+2q
       350: q^3+q^2+2q
       351: 3q^3+3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: q^3+2q^2+2q
       355: q^3+q^2+2q
       356: q^3+q^2+2q
       357: q^3+q^2+2q
       358: q^3+q^2+2q
       359: 3q^3+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: q^4+q^3+2q^2+2q
       367: 2q^2+2q
       368: q^3+2q^2+2q
       369: q^3+q^2+2q
       370: q^3+q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: q^3+2q^2+2q
       375: q^3+2q^2+2q
       376: q^3+2q^2+2q
       377: q
       380: q
       381: q
       384: q
       385: q
       388: q
       389: q^3+q
       391: q^3+q
       393: q
       396: q
       397: q^3+q
       399: q^3+q
       401: q
       404: q
       405: q^3+q
       406: q^3+q
       409: q^2+2q
       411: q^2+2q
       413: q^2+2q
       415: 2q
       417: 2q
       419: q^2+q
       420: q
       421: q
       422: q^2+q
       423: q^3+2q
       425: q^3+2q
       427: 3q^3+3q
       429: q^2+q
       430: q
       431: q
       432: q^2+q
       433: q^3+2q
       435: 2q
       437: q^2+q
       438: q
       439: q
       440: q^2+q
       441: q^3+2q
       443: 2q^3+2q
       444: q^3+q
       445: 3q^3+3q
       447: q^2+q
       448: q
       449: q
       450: q^2+q
       451: q^3+2q
       453: q^2+q
       454: q
       455: 2q
       457: q
       458: q^2+q
       459: q^3+2q
       461: q^3+q
       462: 2q^3+2q
       463: 3q^3+3q
       465: q^2+2q
       467: q^2+2q
       469: q^4+q^3+q^2+2q
       471: q^2+q
       472: q
       473: q
       474: q^2+q
       475: q^3+2q
       477: 2q^3+2q
       479: 2q^3+2q
       480: q^3+q
       481: q^2+2q
       482: q^2+2q
       483: q^3+2q
       484: 3q
       485: 3q
       487: 3q
       489: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: q^3+2q
       496: 3q
       497: 2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: q^3+2q
       501: 3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: q^3+2q^2+2q
       511: q^3+q^2+2q
       512: q^3+q^2+2q
       513: q^3+q^2+2q
       514: q^3+q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       525: q
       528: q
       529: q
       532: q
       533: q
       536: q
       537: q
       539: q
       541: q
       543: q
       545: 2q^3+2q
       547: q^3+q
       549: q
       552: q
       553: q
       555: q
       557: q
       559: q
       561: q^3+q
       563: 2q^3+2q
       565: q
       568: q
       569: q^3+q
       570: q^3+q
       573: q^3+q
       574: q^3+q
       575: q^3+q
       577: 2q^3+2q
       580: q^3+q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q^2+q
       590: q
       592: q
       593: q
       595: q
       596: q^2+q
       597: 2q
       599: q^3+2q
       601: 3q
       603: q^2+q
       604: q
       605: 2q
       607: q
       608: q^2+q
       609: q^3+2q
       611: 2q
       613: q^3+2q
       615: 2q
       616: q
       617: 3q
       619: q^2+q
       620: q
       621: q
       622: q^2+q
       623: 2q
       625: q^3+2q
       627: 2q
       629: q^3+2q
       631: q
       632: 2q
       633: 3q
       635: q^2+2q
       637: q^2+2q
       639: q^2+2q
       641: q^2+q
       642: q
       643: q
       644: q^2+q
       645: q^3+2q
       647: q^2+q
       648: q
       649: q
       650: q^2+q
       651: 2q
       653: q^3+2q
       655: 2q
       656: q
       657: 3q
       658: 3q
       660: 3q
       662: q^2+2q
       664: 2q
       665: 2q
       666: 3q
       668: 3q
       670: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: q^3+2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: q^3+2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: q^3+2q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^3+q
       696: q^3+q
       697: q^3+q
       705: q
       708: q
       709: q
       712: q
       716: q
       717: q
       721: q
       723: q
       725: q
       727: q
       729: q
       731: q
       733: 2q
       735: q
       737: q
       739: q
       741: q
       743: q
       745: q
       747: q
       749: q
       751: 2q
       753: q
       756: q
       757: q
       758: q
       761: q
       762: q
       765: q
       766: q
       768: q
       769: 2q
       772: q
       775: 3q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       785: q
       788: q
       789: 3q
       791: q
       793: 2q
       794: q
       795: 3q
       797: 2q
       799: 2q
       801: q^2+q
       802: q
       804: q
       805: q
       807: q
       808: q^2+q
       809: 2q
       811: q^3+2q
       813: 3q
       815: 2q
       816: q
       817: q
       818: 2q
       819: 3q
       821: 2q
       823: 2q
       825: q^2+q
       826: q
       828: q
       829: q
       831: q
       832: q^2+q
       833: 2q
       835: q^3+2q
       837: 3q
       839: q
       840: 2q
       841: q^2+2q
       843: 2q
       844: q
       845: q^2+q
       846: q
       847: q
       848: q^2+q
       849: 2q
       851: q^3+2q
       853: 2q
       855: q^3+2q
       857: 2q
       858: q
       859: 3q
       861: 3q
       863: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: q^3+2q
       880: 2q
       884: q
       887: q
       889: q
       896: q
       899: q
       902: q
       904: q
       912: q
       914: q
       916: 2q
       918: q
       920: q
       922: q
       927: q
       928: q
       932: 2q
       934: q
       936: q
       938: q
       940: q
       942: 2q
       944: q
       946: q
       950: q
       952: q
       956: q
       958: 2q
       960: q
       961: q
       964: q
       965: q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       978: q
       979: q
       982: 2q
       985: q
       988: q
       989: q
       991: q
       992: 3q
       994: 2q
       996: 2q
       999: q
      1000: q
      1002: 2q
      1004: q
      1007: q
      1008: q
      1010: q
      1012: q
      1014: 3q
      1016: 2q
      1017: q
      1018: 2q
      1020: 2q
      1022: 2q
      1024: 2q
      1026: q
      1029: q
      1030: 3q
      1032: q
      1033: 2q
      1034: 2q
      1036: 2q
      1038: 2q
      1040: q
      1042: 2q
      1045: q
      1046: 2q
      1047: q
      1048: 2q
      1050: 2q
      1052: q^2+q
      1053: q
      1055: q
      1056: q
      1058: q
      1059: q^2+q
      1060: 2q
      1062: q^3+2q
      1064: q
      1074: 2q
      1076: 2q
      1077: 2q
      1078: 2q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1086: q
      1089: q
      1091: q
      1098: q
      1101: q
      1102: q
      1112: q
      1116: q
      1118: q
      1122: q
      1138: q
      1144: 2q
      1146: q
      1148: q
      1150: q
      1154: q
      1156: q
      1164: q
      1166: 2q
      1168: q
      1170: q
      1174: q
      1176: q
      1184: q
      1185: q
      1188: 2q
      1191: q
      1194: q
      1195: q
      1197: q
      1198: q
      1199: q
      1204: q
      1206: q
      1214: 2q
      1217: q
      1218: q
      1220: q
      1222: q
      1224: q
      1230: 2q
      1233: q
      1234: q
      1236: 2q
      1238: 2q
      1240: q
      1243: q
      1248: 2q
      1251: q
      1252: 2q
      1254: q
      1256: 2q
      1258: q
      1261: q
      1264: 2q
      1266: 2q
      1268: q
      1271: q
      1272: 2q
      1274: 2q
      1276: q
      1278: q
      1280: q
      1283: 2q
      1285: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1302: q
      1305: q
      1307: q
      1316: q
      1318: q
      1334: q
      1346: q
      1350: q
      1352: q
      1356: q
      1378: q
      1382: q
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      1388: q
      1414: q
      1415: q
      1420: q
      1422: q
      1430: q
      1436: q
      1446: q
      1448: 2q
      1451: q
      1454: q
      1456: 2q
      1461: q
      1462: q
      1464: 2q
      1467: q
      1468: q
      1470: 2q
      1472: 2q
      1474: q
      1476: q
      1479: q
      1480: q
      1482: q
      1484: 1
      1487: 2q
      1565: q
      1567: q
      1585: q
      1587: q
      1605: q
      1609: q
      1611: q
      1615: q
      1631: q
      1637: q
      1641: 1
      1650: 1
      1657: 1
      1659: q
      1661: 2q
      1664: q
      1665: q
      1671: q
      1673: 1
      1759: 1
      1781: 1
      1787: q
      1789: q
      1812: 1
      1815: 1
      1817: 1
      1820: 1
      1821: 1
      1823: q
      1884: 1
      1904: 1
      1907: 1
      1918: 1
      1922: 1
      1953: 1
      1958: 1
      2004: 1
      2016: 1
      2037: 1
      2048: 1
      2118: 1

2119:    0: 3q^4+2q^3+3q^2+2q
         1: 3q^4+2q^3+3q^2+2q
         2: 2q^5+2q^4+q^3+3q^2+2q
         3: 3q^4+2q^3+3q^2+2q
         4: q^5+2q^4+3q^3+2q^2+2q
         5: 3q^4+2q^3+3q^2+2q
         6: q^5+2q^4+3q^3+2q^2+2q
         7: q^6+q^5+2q^4+2q^3+2q^2+2q
         8: 2q^5+2q^4+q^3+3q^2+2q
         9: q^6+q^5+2q^4+2q^3+2q^2+2q
        10: 3q^4+2q^3+3q^2+2q
        11: 3q^4+2q^3+3q^2+2q
        12: q^5+2q^4+3q^3+2q^2+2q
        13: q^4+q^3+3q^2+2q
        14: q^4+2q^3+2q^2+2q
        15: q^4+q^3+3q^2+2q
        16: 3q^4+2q^3+3q^2+2q
        17: 3q^4+2q^3+3q^2+2q
        18: q^6+q^5+2q^4+2q^3+2q^2+2q
        19: 2q^4+2q^3+2q^2+2q
        20: 2q^4+2q^3+2q^2+2q
        21: q^5+2q^4+q^3+2q^2+2q
        22: 3q^4+2q^3+3q^2+2q
        23: 3q^4+2q^3+3q^2+2q
        24: 2q^5+2q^4+q^3+3q^2+2q
        25: 3q^4+2q^3+3q^2+2q
        26: 3q^4+2q^3+3q^2+2q
        27: 2q^5+2q^4+q^3+3q^2+2q
        28: 3q^4+2q^3+3q^2+2q
        29: 2q^4+2q^3+2q^2+2q
        30: q^4+q^3+2q^2+2q
        31: 3q^4+2q^3+3q^2+2q
        32: q^4+q^3+3q^2+2q
        33: 3q^4+2q^3+3q^2+2q
        34: 3q^4+2q^3+3q^2+2q
        35: q^4+q^3+3q^2+2q
        36: 3q^4+2q^3+3q^2+2q
        37: 2q^4+2q^3+2q^2+2q
        38: q^4+q^2
        39: 2q^4+2q^3+2q^2+2q
        40: q^4+q^2
        41: q^5+2q^4+q^3+2q^2+2q
        42: q^5+q^2
        43: q^4+q^3+3q^2+2q
        44: q^4+2q^3+2q^2+2q
        45: q^4+q^3+3q^2+2q
        46: q^4+q^3+3q^2+2q
        47: q^4+q^3+3q^2+2q
        48: q^4+2q^3+2q^2+2q
        49: 2q^4+2q^3+2q^2+2q
        50: 2q^4+2q^3+2q^2+2q
        51: q^5+2q^4+q^3+2q^2+2q
        52: 2q^4+2q^3+2q^2+2q
        53: 2q^4+2q^3+2q^2+2q
        54: q^5+2q^4+q^3+2q^2+2q
        55: 2q^4+2q^3+2q^2+2q
        56: 2q^4+2q^3+2q^2+2q
        57: q^5+2q^4+q^3+2q^2+2q
        58: 2q^4+q^3+2q^2+q
        59: q^4+q^3+q^2+q
        60: q^4+q^3+q^2+q
        61: 2q^4+q^3+2q^2+q
        62: 2q^4+2q^3+2q^2+2q
        63: q^4+q^2
        64: q^4+q^3+2q^2+2q
        65: q^2
        66: 2q^4+2q^3+2q^2+2q
        67: q^4+q^2
        68: 3q^2+2q
        69: q^4+q^3+2q^2+2q
        70: q^4+q^3+2q^2+2q
        71: 2q^4+2q^3+2q^2+2q
        72: q^4+2q^3+q^2+2q
        73: q^4+2q^3+q^2+2q
        74: q^4+2q^3+q^2+2q
        76: q^4+2q^3+q^2+2q
        78: 2q^4+q^3+q^2+2q
        80: q^4+q^3+3q^2+2q
        81: q^4+q^3+3q^2+2q
        82: 2q^4+2q^3+2q^2+2q
        83: q^4+q^3+2q^2+2q
        84: q^4+q^3+3q^2+2q
        85: q^4+q^3+3q^2+2q
        86: 2q^4+2q^3+2q^2+2q
        87: q^4+q^3+2q^2+2q
        88: q^4+q^3+3q^2+2q
        89: q^4+q^3+3q^2+2q
        90: q^4+2q^3+2q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: 2q^4+2q^3+2q^2+2q
        95: 2q^4+2q^3+2q^2+2q
        96: q^5+2q^4+q^3+2q^2+2q
        97: 2q^4+2q^3+2q^2+2q
        98: 2q^4+2q^3+2q^2+2q
        99: q^5+2q^4+q^3+2q^2+2q
       100: 2q^4+2q^3+2q^2+2q
       101: 2q^4+2q^3+2q^2+2q
       102: q^5+2q^4+q^3+2q^2+2q
       103: q^4+q^3+q^2+q
       105: q^4+q^2
       106: q^4+q^3+q^2+q
       107: q^3+q
       108: q^4+q^3+q^2+q
       109: q^4+q^3+q^2+q
       110: q^3+q
       111: 2q^3+2q
       113: q^4+2q^3+q^2+2q
       115: q^4+q^3+q^2+2q
       117: 2q^2+q
       118: q^2+q
       119: q^2+q
       120: 2q^2+q
       121: q^4+q^3+2q^2+2q
       122: q^2
       123: q^4+q^3+2q^2+2q
       124: q^2
       125: 3q^2+2q
       126: q^4+q^3+2q^2+2q
       127: q^4+2q^3+q^2+2q
       129: q^4+2q^3+q^2+2q
       131: 2q^4+q^3+q^2+2q
       133: 2q^2+2q
       134: q^3+2q^2+2q
       135: q^3+q^2+2q
       136: q^3+q^2+2q
       137: q^4+q^3+3q^2+2q
       138: q^4+q^3+2q^2+2q
       139: 2q^4+2q^3+2q^2+2q
       140: q^4+2q^3+q^2+2q
       141: q^4+q^3+2q^2+2q
       142: q^4+2q^3+q^2+2q
       143: q^4+q^3+3q^2+2q
       144: q^4+q^3+2q^2+2q
       145: 2q^4+2q^3+2q^2+2q
       146: q^4+q^3+2q^2+2q
       147: q^4+2q^3+q^2+2q
       148: q^4+2q^3+q^2+2q
       149: 2q^4+2q^3+2q^2+2q
       150: q^4+q^3+2q^2+2q
       151: q^4+2q^3+q^2+2q
       153: q^4+2q^3+q^2+2q
       155: 2q^4+q^3+q^2+2q
       157: q^3+2q^2+2q
       158: q^3+2q^2+2q
       159: q^3+2q^2+2q
       160: q^3+2q^2+2q
       161: q^3+2q^2+2q
       162: q^3+2q^2+2q
       163: q^3+2q^2+2q
       164: q^3+2q^2+2q
       165: q^3+2q^2+2q
       166: 2q^4+2q^3+2q^2+2q
       167: 2q^4+2q^3+2q^2+2q
       168: q^5+2q^4+q^3+2q^2+2q
       169: q^3+q
       172: q^3+q
       173: q^2+q
       175: q^2
       176: q^2+q
       177: q^4+q^3+q^2+2q
       179: q^4+2q^3+q^2+2q
       181: 2q^3+2q
       183: q
       184: q^2+q
       185: q^2+q
       186: q
       187: q^3+2q
       189: q^4+q^3+q^2+2q
       191: 2q^2+q
       192: q^2+q
       193: q^3+q
       194: q^4+q^3+q^2+q
       195: q^4+q^3+q^2+q
       196: q^3+q
       197: 2q^3+2q
       199: q^2+q
       200: 2q^2+q
       201: q^3+q
       202: q^4+q^3+q^2+q
       203: q^4+q^3+q^2+q
       204: q^3+q
       205: 2q^3+2q
       207: q^4+q^3+2q^2+2q
       208: q^2
       209: q^4+2q^3+q^2+2q
       211: q^4+q^3+q^2+2q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: q^3+2q^2+2q
       222: q^3+q^2+2q
       223: q^3+q^2+2q
       224: q^3+q^2+2q
       225: q^3+q^2+2q
       226: q^4+q^3+2q^2+2q
       227: 2q^2+2q
       228: q^3+2q^2+2q
       229: q^3+q^2+2q
       230: q^3+q^2+2q
       231: q^4+q^3+2q^2+2q
       232: 2q^2+2q
       233: q^3+2q^2+2q
       234: q^3+q^2+2q
       235: q^3+q^2+2q
       236: q^4+q^3+2q^2+2q
       237: q^4+2q^3+q^2+2q
       239: q^4+2q^3+q^2+2q
       241: 2q^4+q^3+q^2+2q
       243: 2q^4+2q^3+2q^2+2q
       244: q^4+2q^3+q^2+2q
       245: q^4+2q^3+q^2+2q
       246: q^4+q^3+2q^2+2q
       247: 3q^3+3q
       248: 3q^3+3q
       249: 2q^4+q^3+q^2+2q
       250: q^3+2q^2+2q
       251: q^3+2q^2+2q
       252: q^3+2q^2+2q
       253: q^3+2q^2+2q
       254: q^3+2q^2+2q
       255: q^3+2q^2+2q
       256: q^3+2q^2+2q
       257: q^3+2q^2+2q
       258: q^3+2q^2+2q
       259: q^3+q
       262: q^3+q
       263: q
       266: q
       267: q^3+q
       269: q^3+q
       271: q^3+q
       273: q^3+q
       275: q^2+q
       277: q^2
       278: q^2+q
       279: q^2+2q
       281: q^2+2q
       283: q
       284: q^2+q
       285: q^2+q
       286: q
       287: q^4+q^3+q^2+2q
       289: 2q
       291: q^3+2q
       293: q
       294: q^2+q
       295: q^2+q
       296: q
       297: q^3+2q
       299: q
       300: q^2+q
       301: 2q^3+2q
       303: q^2+q
       304: q
       305: q^3+2q
       307: q
       308: q^2+q
       309: q^2+q
       310: q
       311: 2q^3+2q
       313: q^3+2q
       315: q^4+q^3+q^2+2q
       317: q^4+2q^3+q^2+2q
       319: q^3+q
       320: q^4+q^3+q^2+q
       321: q^4+q^3+q^2+q
       322: q^3+q
       323: 2q^3+2q
       325: q^4+q^3+q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: 2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: q^3+2q
       337: 3q^3+3q
       338: 3q^3+3q
       340: 3q^3+3q
       342: 2q^4+q^3+q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: q^3+2q^2+2q
       347: q^3+q^2+2q
       348: q^3+q^2+2q
       349: q^3+q^2+2q
       350: q^3+q^2+2q
       351: 3q^3+3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: q^3+2q^2+2q
       355: q^3+q^2+2q
       356: q^3+q^2+2q
       357: q^3+q^2+2q
       358: q^3+q^2+2q
       359: 3q^3+3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: q^4+q^3+2q^2+2q
       367: 2q^2+2q
       368: q^3+2q^2+2q
       369: q^3+q^2+2q
       370: q^3+q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: q^3+2q^2+2q
       375: q^3+2q^2+2q
       376: q^3+2q^2+2q
       377: q
       380: q
       381: q
       384: q
       385: q
       388: q
       389: q^3+q
       391: q^3+q
       393: q
       396: q
       397: q^3+q
       399: q^3+q
       401: q
       404: q
       405: q^3+q
       406: q^3+q
       409: q^2+2q
       411: q^2+2q
       413: q^2+2q
       415: 2q
       417: 2q
       419: q
       420: q^2+q
       421: q^2+q
       422: q
       423: q^3+2q
       425: q^3+2q
       427: 3q^3+3q
       429: q
       430: q^2+q
       431: q^2+q
       432: q
       433: q^3+2q
       435: 2q
       437: q
       438: q^2+q
       439: q^2+q
       440: q
       441: q^3+2q
       443: q^3+q
       444: 2q^3+2q
       445: 3q^3+3q
       447: q
       448: q^2+q
       449: q^2+q
       450: q
       451: q^3+2q
       453: q
       454: q^2+q
       455: 2q
       457: q^2+q
       458: q
       459: q^3+2q
       461: 2q^3+2q
       462: q^3+q
       463: 3q^3+3q
       465: q^2+2q
       467: q^2+2q
       469: q^4+q^3+q^2+2q
       471: q
       472: q^2+q
       473: q^2+q
       474: q
       475: q^3+2q
       477: 2q^3+2q
       479: 2q^3+2q
       480: q^3+q
       481: q^2+2q
       482: q^2+2q
       483: q^3+2q
       484: 3q
       485: 3q
       487: 3q
       489: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: q^3+2q
       496: 3q
       497: 2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: q^3+2q
       501: 3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: q^3+2q^2+2q
       511: q^3+q^2+2q
       512: q^3+q^2+2q
       513: q^3+q^2+2q
       514: q^3+q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       525: q
       528: q
       529: q
       532: q
       533: q
       536: q
       537: q
       539: q
       541: q
       543: q
       545: q^3+q
       547: 2q^3+2q
       549: q
       552: q
       553: q
       555: q
       557: q
       559: q
       561: 2q^3+2q
       563: q^3+q
       565: q
       568: q
       569: q^3+q
       570: q^3+q
       573: q^3+q
       575: q^3+q
       576: q^3+q
       577: 2q^3+2q
       580: q^3+q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       596: q
       597: 2q
       599: q^3+2q
       601: 3q
       603: q
       604: q^2+q
       605: 2q
       607: q^2+q
       608: q
       609: q^3+2q
       611: 2q
       613: q^3+2q
       615: q
       616: 2q
       617: 3q
       619: q
       620: q^2+q
       621: q^2+q
       622: q
       623: 2q
       625: q^3+2q
       627: 2q
       629: q^3+2q
       631: 2q
       632: q
       633: 3q
       635: q^2+2q
       637: q^2+2q
       639: q^2+2q
       641: q
       642: q^2+q
       643: q^2+q
       644: q
       645: q^3+2q
       647: q
       648: q^2+q
       649: q^2+q
       650: q
       651: 2q
       653: q^3+2q
       655: 2q
       656: q
       657: 3q
       658: 3q
       660: 3q
       662: q^2+2q
       664: 2q
       665: 2q
       666: 3q
       668: 3q
       670: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: q^3+2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: q^3+2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: q^3+2q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^3+q
       697: q^3+q
       698: q^3+q
       705: q
       708: q
       709: q
       712: q
       713: q
       720: q
       721: q
       723: q
       725: q
       727: q
       729: q
       731: q
       733: q
       735: 2q
       737: q
       739: q
       741: q
       743: q
       745: q
       747: q
       749: 2q
       751: q
       753: q
       756: q
       757: q
       758: q
       761: q
       762: q
       765: q
       767: q
       768: q
       769: 2q
       772: q
       775: 3q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       786: q
       787: q
       789: 3q
       791: q
       793: q
       794: 2q
       795: 3q
       797: 2q
       799: 2q
       801: q
       802: q^2+q
       803: q
       806: q
       807: q^2+q
       808: q
       809: 2q
       811: q^3+2q
       813: 3q
       815: q
       816: 2q
       817: 2q
       818: q
       819: 3q
       821: 2q
       823: 2q
       825: q
       826: q^2+q
       827: q
       830: q
       831: q^2+q
       832: q
       833: 2q
       835: q^3+2q
       837: 3q
       839: 2q
       840: q
       841: q^2+2q
       843: 2q
       844: q
       845: q
       846: q^2+q
       847: q^2+q
       848: q
       849: 2q
       851: q^3+2q
       853: 2q
       855: q^3+2q
       857: 2q
       858: q
       859: 3q
       861: 3q
       863: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: q^3+2q
       880: 2q
       884: q
       888: q
       889: q
       896: q
       899: q
       900: q
       906: q
       912: q
       914: q
       916: q
       918: 2q
       920: q
       922: q
       924: q
       930: q
       932: q
       934: 2q
       936: q
       938: q
       940: 2q
       942: q
       944: q
       946: q
       948: q
       955: q
       956: 2q
       958: q
       960: q
       961: q
       964: q
       966: q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       978: q
       979: q
       982: 2q
       985: q
       988: q
       990: q
       991: q
       992: 3q
       994: 2q
       996: 2q
       998: q
      1001: q
      1002: 2q
      1005: q
      1006: q
      1008: q
      1010: q
      1012: q
      1014: 3q
      1016: q
      1017: 2q
      1018: 2q
      1020: 2q
      1022: 2q
      1024: 2q
      1027: q
      1028: q
      1030: 3q
      1032: 2q
      1033: q
      1034: 2q
      1036: 2q
      1038: 2q
      1041: q
      1042: 2q
      1044: q
      1046: 2q
      1047: q
      1048: 2q
      1050: 2q
      1052: q
      1053: q^2+q
      1054: q
      1057: q
      1058: q^2+q
      1059: q
      1060: 2q
      1062: q^3+2q
      1064: q
      1074: 2q
      1076: 2q
      1077: 2q
      1078: 2q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1086: q
      1090: q
      1091: q
      1098: q
      1102: q
      1103: q
      1110: q
      1114: q
      1120: q
      1124: q
      1138: q
      1144: q
      1146: 2q
      1148: q
      1150: q
      1152: q
      1158: q
      1164: 2q
      1166: q
      1168: q
      1170: q
      1172: q
      1178: q
      1184: q
      1185: q
      1188: 2q
      1191: q
      1194: q
      1196: q
      1197: q
      1198: q
      1199: q
      1202: q
      1208: q
      1214: 2q
      1216: q
      1219: q
      1220: q
      1222: q
      1224: q
      1230: 2q
      1232: q
      1235: q
      1236: 2q
      1238: 2q
      1241: q
      1242: q
      1248: 2q
      1250: q
      1252: 2q
      1255: q
      1256: 2q
      1259: q
      1260: q
      1264: 2q
      1266: 2q
      1269: q
      1270: q
      1272: 2q
      1274: 2q
      1276: q
      1278: q
      1280: q
      1283: 2q
      1285: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1302: q
      1306: q
      1307: q
      1314: q
      1320: q
      1334: q
      1344: q
      1348: q
      1354: q
      1358: q
      1376: q
      1380: q
      1386: q
      1390: q
      1414: q
      1415: q
      1418: q
      1424: q
      1430: q
      1436: q
      1446: q
      1448: 2q
      1450: q
      1455: q
      1456: 2q
      1460: q
      1463: q
      1464: 2q
      1466: q
      1469: q
      1470: 2q
      1472: 2q
      1474: q
      1477: q
      1478: q
      1480: q
      1482: q
      1484: 1
      1487: 2q
      1563: q
      1569: q
      1583: q
      1589: q
      1603: q
      1607: q
      1613: q
      1617: q
      1631: q
      1637: q
      1641: 1
      1649: 1
      1658: 1
      1659: q
      1661: 2q
      1663: q
      1666: q
      1671: q
      1673: 1
      1757: 1
      1783: 1
      1785: q
      1791: q
      1813: 1
      1815: 1
      1817: 1
      1819: 1
      1822: 1
      1823: q
      1885: 1
      1902: 1
      1906: 1
      1920: 1
      1923: 1
      1954: 1
      1958: 1
      2005: 1
      2017: 1
      2036: 1
      2049: 1
      2119: 1

2120:    0: 3q^4+2q^3+3q^2+2q
         1: 3q^4+2q^3+3q^2+2q
         2: 2q^5+2q^4+q^3+3q^2+2q
         3: 3q^4+2q^3+3q^2+2q
         4: q^5+2q^4+3q^3+2q^2+2q
         5: 3q^4+2q^3+3q^2+2q
         6: q^5+2q^4+3q^3+2q^2+2q
         7: q^6+q^5+2q^4+2q^3+2q^2+2q
         8: 2q^5+2q^4+q^3+3q^2+2q
         9: q^6+q^5+2q^4+2q^3+2q^2+2q
        10: 3q^4+2q^3+3q^2+2q
        11: 3q^4+2q^3+3q^2+2q
        12: q^5+2q^4+3q^3+2q^2+2q
        13: q^4+q^3+3q^2+2q
        14: q^4+2q^3+2q^2+2q
        15: q^4+q^3+3q^2+2q
        16: 3q^4+2q^3+3q^2+2q
        17: 3q^4+2q^3+3q^2+2q
        18: q^6+q^5+2q^4+2q^3+2q^2+2q
        19: 2q^4+2q^3+2q^2+2q
        20: 2q^4+2q^3+2q^2+2q
        21: q^5+2q^4+q^3+2q^2+2q
        22: 3q^4+2q^3+3q^2+2q
        23: 3q^4+2q^3+3q^2+2q
        24: 2q^5+2q^4+q^3+3q^2+2q
        25: 3q^4+2q^3+3q^2+2q
        26: 3q^4+2q^3+3q^2+2q
        27: 2q^5+2q^4+q^3+3q^2+2q
        28: 3q^4+2q^3+3q^2+2q
        29: 2q^4+2q^3+2q^2+2q
        30: q^4+q^3+2q^2+2q
        31: 3q^4+2q^3+3q^2+2q
        32: q^4+q^3+3q^2+2q
        33: 3q^4+2q^3+3q^2+2q
        34: 3q^4+2q^3+3q^2+2q
        35: q^4+q^3+3q^2+2q
        36: 3q^4+2q^3+3q^2+2q
        37: q^4+q^2
        38: 2q^4+2q^3+2q^2+2q
        39: q^4+q^2
        40: 2q^4+2q^3+2q^2+2q
        41: q^5+q^2
        42: q^5+2q^4+q^3+2q^2+2q
        43: q^4+q^3+3q^2+2q
        44: q^4+2q^3+2q^2+2q
        45: q^4+q^3+3q^2+2q
        46: q^4+q^3+3q^2+2q
        47: q^4+q^3+3q^2+2q
        48: q^4+2q^3+2q^2+2q
        49: 2q^4+2q^3+2q^2+2q
        50: 2q^4+2q^3+2q^2+2q
        51: q^5+2q^4+q^3+2q^2+2q
        52: 2q^4+2q^3+2q^2+2q
        53: 2q^4+2q^3+2q^2+2q
        54: q^5+2q^4+q^3+2q^2+2q
        55: 2q^4+2q^3+2q^2+2q
        56: 2q^4+2q^3+2q^2+2q
        57: q^5+2q^4+q^3+2q^2+2q
        58: 2q^4+q^3+2q^2+q
        59: q^4+q^3+q^2+q
        60: 2q^4+q^3+2q^2+q
        61: q^4+q^3+q^2+q
        62: q^4+q^2
        63: 2q^4+2q^3+2q^2+2q
        64: q^2
        65: q^4+q^3+2q^2+2q
        66: q^4+q^2
        67: 2q^4+2q^3+2q^2+2q
        68: 3q^2+2q
        69: q^4+q^3+2q^2+2q
        70: q^4+q^3+2q^2+2q
        71: 2q^4+2q^3+2q^2+2q
        72: q^4+2q^3+q^2+2q
        73: q^4+2q^3+q^2+2q
        75: q^4+2q^3+q^2+2q
        77: q^4+2q^3+q^2+2q
        79: 2q^4+q^3+q^2+2q
        80: q^4+q^3+3q^2+2q
        81: q^4+q^3+3q^2+2q
        82: 2q^4+2q^3+2q^2+2q
        83: q^4+q^3+2q^2+2q
        84: q^4+q^3+3q^2+2q
        85: q^4+q^3+3q^2+2q
        86: 2q^4+2q^3+2q^2+2q
        87: q^4+q^3+2q^2+2q
        88: q^4+q^3+3q^2+2q
        89: q^4+q^3+3q^2+2q
        90: q^4+2q^3+2q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: 2q^4+2q^3+2q^2+2q
        95: 2q^4+2q^3+2q^2+2q
        96: q^5+2q^4+q^3+2q^2+2q
        97: 2q^4+2q^3+2q^2+2q
        98: 2q^4+2q^3+2q^2+2q
        99: q^5+2q^4+q^3+2q^2+2q
       100: 2q^4+2q^3+2q^2+2q
       101: 2q^4+2q^3+2q^2+2q
       102: q^5+2q^4+q^3+2q^2+2q
       103: q^4+q^2
       104: q^4+q^3+q^2+q
       105: q^4+q^3+q^2+q
       107: q^4+q^3+q^2+q
       108: q^3+q
       109: q^4+q^3+q^2+q
       110: q^3+q
       112: 2q^3+2q
       114: q^4+2q^3+q^2+2q
       116: q^4+q^3+q^2+2q
       117: 2q^2+q
       118: q^2+q
       119: 2q^2+q
       120: q^2+q
       121: q^2
       122: q^4+q^3+2q^2+2q
       123: q^2
       124: q^4+q^3+2q^2+2q
       125: 3q^2+2q
       126: q^4+q^3+2q^2+2q
       128: q^4+2q^3+q^2+2q
       130: q^4+2q^3+q^2+2q
       132: 2q^4+q^3+q^2+2q
       133: 2q^2+2q
       134: q^3+2q^2+2q
       135: q^3+q^2+2q
       136: q^3+q^2+2q
       137: q^4+q^3+3q^2+2q
       138: q^4+q^3+2q^2+2q
       139: 2q^4+2q^3+2q^2+2q
       140: q^4+2q^3+q^2+2q
       141: q^4+q^3+2q^2+2q
       142: q^4+2q^3+q^2+2q
       143: q^4+q^3+3q^2+2q
       144: q^4+q^3+2q^2+2q
       145: 2q^4+2q^3+2q^2+2q
       146: q^4+q^3+2q^2+2q
       147: q^4+2q^3+q^2+2q
       148: q^4+2q^3+q^2+2q
       149: 2q^4+2q^3+2q^2+2q
       150: q^4+q^3+2q^2+2q
       152: q^4+2q^3+q^2+2q
       154: q^4+2q^3+q^2+2q
       156: 2q^4+q^3+q^2+2q
       157: q^3+2q^2+2q
       158: q^3+2q^2+2q
       159: q^3+2q^2+2q
       160: q^3+2q^2+2q
       161: q^3+2q^2+2q
       162: q^3+2q^2+2q
       163: q^3+2q^2+2q
       164: q^3+2q^2+2q
       165: q^3+2q^2+2q
       166: 2q^4+2q^3+2q^2+2q
       167: 2q^4+2q^3+2q^2+2q
       168: q^5+2q^4+q^3+2q^2+2q
       170: q^3+q
       171: q^3+q
       173: q^2
       174: q^2+q
       175: q^2+q
       178: q^4+q^3+q^2+2q
       180: q^4+2q^3+q^2+2q
       182: 2q^3+2q
       183: q^2+q
       184: q
       185: q^2+q
       186: q
       188: q^3+2q
       190: q^4+q^3+q^2+2q
       191: 2q^2+q
       192: q^2+q
       193: q^4+q^3+q^2+q
       194: q^3+q
       195: q^4+q^3+q^2+q
       196: q^3+q
       198: 2q^3+2q
       199: 2q^2+q
       200: q^2+q
       201: q^4+q^3+q^2+q
       202: q^3+q
       203: q^4+q^3+q^2+q
       204: q^3+q
       206: 2q^3+2q
       207: q^2
       208: q^4+q^3+2q^2+2q
       210: q^4+2q^3+q^2+2q
       212: q^4+q^3+q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: q^3+2q^2+2q
       222: q^3+q^2+2q
       223: q^3+q^2+2q
       224: q^3+q^2+2q
       225: q^3+q^2+2q
       226: q^4+q^3+2q^2+2q
       227: 2q^2+2q
       228: q^3+2q^2+2q
       229: q^3+q^2+2q
       230: q^3+q^2+2q
       231: q^4+q^3+2q^2+2q
       232: 2q^2+2q
       233: q^3+2q^2+2q
       234: q^3+q^2+2q
       235: q^3+q^2+2q
       236: q^4+q^3+2q^2+2q
       238: q^4+2q^3+q^2+2q
       240: q^4+2q^3+q^2+2q
       242: 2q^4+q^3+q^2+2q
       243: 2q^4+2q^3+2q^2+2q
       244: q^4+2q^3+q^2+2q
       245: q^4+2q^3+q^2+2q
       246: q^4+q^3+2q^2+2q
       247: 3q^3+3q
       248: 3q^3+3q
       249: 2q^4+q^3+q^2+2q
       250: q^3+2q^2+2q
       251: q^3+2q^2+2q
       252: q^3+2q^2+2q
       253: q^3+2q^2+2q
       254: q^3+2q^2+2q
       255: q^3+2q^2+2q
       256: q^3+2q^2+2q
       257: q^3+2q^2+2q
       258: q^3+2q^2+2q
       260: q^3+q
       261: q^3+q
       264: q
       265: q
       268: q^3+q
       270: q^3+q
       272: q^3+q
       274: q^3+q
       275: q^2
       276: q^2+q
       277: q^2+q
       280: q^2+2q
       282: q^2+2q
       283: q^2+q
       284: q
       285: q^2+q
       286: q
       288: q^4+q^3+q^2+2q
       290: 2q
       292: q^3+2q
       293: q^2+q
       294: q
       295: q^2+q
       296: q
       298: q^3+2q
       299: q^2+q
       300: q
       302: 2q^3+2q
       303: q^2+q
       304: q
       306: q^3+2q
       307: q^2+q
       308: q
       309: q^2+q
       310: q
       312: 2q^3+2q
       314: q^3+2q
       316: q^4+q^3+q^2+2q
       318: q^4+2q^3+q^2+2q
       319: q^4+q^3+q^2+q
       320: q^3+q
       321: q^4+q^3+q^2+q
       322: q^3+q
       324: 2q^3+2q
       326: q^4+q^3+q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: 2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: q^3+2q
       337: 3q^3+3q
       339: 3q^3+3q
       341: 3q^3+3q
       343: 2q^4+q^3+q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: q^3+2q^2+2q
       347: q^3+q^2+2q
       348: q^3+q^2+2q
       349: q^3+q^2+2q
       350: q^3+q^2+2q
       351: 3q^3+3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: q^3+2q^2+2q
       355: q^3+q^2+2q
       356: q^3+q^2+2q
       357: q^3+q^2+2q
       358: q^3+q^2+2q
       359: 3q^3+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: q^4+q^3+2q^2+2q
       367: 2q^2+2q
       368: q^3+2q^2+2q
       369: q^3+q^2+2q
       370: q^3+q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: q^3+2q^2+2q
       375: q^3+2q^2+2q
       376: q^3+2q^2+2q
       378: q
       379: q
       382: q
       383: q
       386: q
       387: q
       390: q^3+q
       392: q^3+q
       394: q
       395: q
       398: q^3+q
       400: q^3+q
       402: q
       403: q
       407: q^3+q
       408: q^3+q
       410: q^2+2q
       412: q^2+2q
       414: q^2+2q
       416: 2q
       418: 2q
       419: q^2+q
       420: q
       421: q^2+q
       422: q
       424: q^3+2q
       426: q^3+2q
       428: 3q^3+3q
       429: q^2+q
       430: q
       431: q^2+q
       432: q
       434: q^3+2q
       436: 2q
       437: q^2+q
       438: q
       439: q^2+q
       440: q
       442: q^3+2q
       443: 2q^3+2q
       444: q^3+q
       446: 3q^3+3q
       447: q^2+q
       448: q
       449: q^2+q
       450: q
       452: q^3+2q
       453: q^2+q
       454: q
       456: 2q
       457: q^2+q
       458: q
       460: q^3+2q
       461: 2q^3+2q
       462: q^3+q
       464: 3q^3+3q
       466: q^2+2q
       468: q^2+2q
       470: q^4+q^3+q^2+2q
       471: q^2+q
       472: q
       473: q^2+q
       474: q
       476: q^3+2q
       478: 2q^3+2q
       479: q^3+q
       480: 2q^3+2q
       481: q^2+2q
       482: q^2+2q
       483: q^3+2q
       484: 3q
       486: 3q
       488: 3q
       490: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: q^3+2q
       496: 3q
       497: 2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: q^3+2q
       501: 3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: q^3+2q^2+2q
       511: q^3+q^2+2q
       512: q^3+q^2+2q
       513: q^3+q^2+2q
       514: q^3+q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: 2q^3+2q
       548: q^3+q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: 2q^3+2q
       564: q^3+q
       566: q
       567: q
       571: q^3+q
       572: q^3+q
       573: q^3+q
       574: q^3+q
       576: q^3+q
       578: q^3+q
       581: 2q^3+2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q^2+q
       590: q
       591: q
       593: q
       595: q^2+q
       596: q
       598: 2q
       600: q^3+2q
       602: 3q
       603: q^2+q
       604: q
       606: 2q
       607: q^2+q
       608: q
       610: q^3+2q
       612: 2q
       614: q^3+2q
       615: 2q
       616: q
       618: 3q
       619: q^2+q
       620: q
       621: q^2+q
       622: q
       624: 2q
       626: q^3+2q
       628: 2q
       630: q^3+2q
       631: 2q
       632: q
       634: 3q
       636: q^2+2q
       638: q^2+2q
       640: q^2+2q
       641: q^2+q
       642: q
       643: q^2+q
       644: q
       646: q^3+2q
       647: q^2+q
       648: q
       649: q^2+q
       650: q
       652: 2q
       654: q^3+2q
       655: q
       656: 2q
       657: 3q
       659: 3q
       661: 3q
       663: q^2+2q
       664: 2q
       665: 2q
       667: 3q
       669: 3q
       671: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: q^3+2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: q^3+2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: q^3+2q
       690: 3q
       691: 3q
       692: q^2+2q
       694: q^3+q
       699: q^3+q
       700: q^3+q
       706: q
       707: q
       710: q
       711: q
       714: q
       718: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: 2q
       736: q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: 2q
       752: q
       754: q
       755: q
       759: q
       760: q
       763: q
       764: q
       765: q
       766: q
       767: q
       770: q
       773: 2q
       776: 3q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       785: q
       787: q
       790: 3q
       792: q
       793: 2q
       794: q
       796: 3q
       798: 2q
       800: 2q
       801: q^2+q
       802: q
       803: q
       805: q
       807: q^2+q
       808: q
       810: 2q
       812: q^3+2q
       814: 3q
       815: 2q
       816: q
       817: 2q
       818: q
       820: 3q
       822: 2q
       824: 2q
       825: q^2+q
       826: q
       827: q
       829: q
       831: q^2+q
       832: q
       834: 2q
       836: q^3+2q
       838: 3q
       839: 2q
       840: q
       842: q^2+2q
       843: q
       844: 2q
       845: q^2+q
       846: q
       847: q^2+q
       848: q
       850: 2q
       852: q^3+2q
       854: 2q
       856: q^3+2q
       857: q
       858: 2q
       860: 3q
       862: 3q
       864: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: q^3+2q
       880: 2q
       885: q
       890: q
       891: q
       897: q
       898: q
       901: q
       905: q
       913: q
       915: q
       917: 2q
       919: q
       921: q
       923: q
       925: q
       929: q
       933: 2q
       935: q
       937: q
       939: q
       941: 2q
       943: q
       945: q
       947: q
       949: q
       953: q
       957: 2q
       959: q
       962: q
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       964: q
       965: q
       966: q
       969: q
       972: 2q
       976: q
       977: q
       980: q
       981: q
       983: q
       986: 2q
       988: q
       989: q
       990: q
       993: 3q
       995: 2q
       997: 2q
       998: q
      1000: q
      1003: 2q
      1004: q
      1006: q
      1009: q
      1011: q
      1013: q
      1015: 3q
      1016: 2q
      1017: q
      1019: 2q
      1021: 2q
      1023: 2q
      1025: 2q
      1026: q
      1028: q
      1031: 3q
      1032: 2q
      1033: q
      1035: 2q
      1037: 2q
      1039: 2q
      1040: q
      1043: 2q
      1044: q
      1046: q
      1047: 2q
      1049: 2q
      1051: 2q
      1052: q^2+q
      1053: q
      1054: q
      1056: q
      1058: q^2+q
      1059: q
      1061: 2q
      1063: q^3+2q
      1065: q
      1074: 2q
      1076: 2q
      1077: 2q
      1078: 2q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1087: q
      1092: q
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      1099: q
      1104: q
      1105: q
      1111: q
      1115: q
      1119: q
      1123: q
      1142: q
      1145: 2q
      1147: q
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      1151: q
      1153: q
      1157: q
      1165: 2q
      1167: q
      1169: q
      1171: q
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      1177: q
      1186: q
      1187: q
      1189: q
      1192: 2q
      1194: q
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      1196: q
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      1201: q
      1203: q
      1207: q
      1215: 2q
      1216: q
      1218: q
      1221: q
      1223: q
      1225: q
      1231: 2q
      1232: q
      1234: q
      1237: 2q
      1239: 2q
      1240: q
      1242: q
      1249: 2q
      1250: q
      1253: 2q
      1254: q
      1257: 2q
      1258: q
      1260: q
      1265: 2q
      1267: 2q
      1268: q
      1270: q
      1273: 2q
      1275: 2q
      1277: q
      1279: q
      1281: q
      1283: 2q
      1285: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1303: q
      1308: q
      1309: q
      1315: q
      1319: q
      1338: q
      1345: q
      1349: q
      1353: q
      1357: q
      1377: q
      1381: q
      1385: q
      1389: q
      1416: q
      1417: q
      1419: q
      1423: q
      1434: q
      1437: q
      1447: q
      1449: 2q
      1450: q
      1454: q
      1457: 2q
      1460: q
      1462: q
      1465: 2q
      1466: q
      1468: q
      1471: 2q
      1473: 2q
      1475: q
      1476: q
      1478: q
      1481: q
      1483: q
      1484: 1
      1487: 2q
      1564: q
      1568: q
      1584: q
      1588: q
      1604: q
      1608: q
      1612: q
      1616: q
      1635: q
      1638: q
      1642: 1
      1649: 1
      1657: 1
      1660: q
      1662: 2q
      1663: q
      1665: q
      1672: q
      1673: 1
      1758: 1
      1782: 1
      1786: q
      1790: q
      1811: 1
      1816: 1
      1818: 1
      1819: 1
      1821: 1
      1824: q
      1883: 1
      1903: 1
      1908: 1
      1919: 1
      1924: 1
      1952: 1
      1959: 1
      2003: 1
      2018: 1
      2038: 1
      2050: 1
      2120: 1

2121:    0: 1
         1: 1
         2: q^5+1
         3: 1
         4: 1
         5: 1
         6: 1
         7: q^5+1
         8: q^5+1
         9: q^5+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: q^5+1
        19: 1
        20: 1
        21: q^5+1
        22: 1
        23: 1
        24: q^5+1
        25: 1
        26: 1
        27: q^5+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q^5+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^5+1
        52: 1
        53: 1
        54: q^5+1
        55: 1
        56: 1
        57: q^5+1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q^5+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q^5+1
        97: 1
        98: 1
        99: q^5+1
       100: 1
       101: 1
       102: q^5+1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: q^5+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: q^5+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q^5+1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: q^5+1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q^5+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: q^5+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: 1
       585: 1
       587: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       697: 1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       927: 1
       930: 1
       934: 1
       938: 1
       942: 1
       946: 1
       950: 1
       955: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1230: 1
      1233: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1243: 1
      1248: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1264: 1
      1266: 1
      1269: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1436: 1
      1446: 1
      1448: 1
      1451: 1
      1455: 1
      1456: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1479: 1
      1480: 1
      1482: 1
      1484: 1
      1487: 1
      1494: 1
      1506: 1
      1518: 1
      1538: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1637: 1
      1641: 1
      1650: 1
      1658: 1
      1659: 1
      1661: 1
      1664: 1
      1666: 1
      1671: 1
      1673: 1
      1692: 1
      1704: 1
      1718: 1
      1730: 1
      1742: 1
      1754: 1
      1759: 1
      1770: 1
      1778: 1
      1783: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1808: 1
      1814: 1
      1815: 1
      1817: 1
      1820: 1
      1822: 1
      1823: 1
      1877: 1
      1889: 1
      1895: 1
      1904: 1
      1907: 1
      1911: 1
      1920: 1
      1923: 1
      1945: 1
      1949: 1
      1955: 1
      1958: 1
      2009: 1
      2019: 1
      2037: 1
      2049: 1
      2057: 1
      2121: 1

2122:    0: 1
         1: 1
         2: q^5+1
         3: 1
         4: 1
         5: 1
         6: 1
         7: q^5+1
         8: q^5+1
         9: q^5+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: q^5+1
        19: 1
        20: 1
        21: q^5+1
        22: 1
        23: 1
        24: q^5+1
        25: 1
        26: 1
        27: q^5+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: q^5+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^5+1
        52: 1
        53: 1
        54: q^5+1
        55: 1
        56: 1
        57: q^5+1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: q^5+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q^5+1
        97: 1
        98: 1
        99: q^5+1
       100: 1
       101: 1
       102: q^5+1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^5+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: q^5+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q^5+1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: q^5+1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q^5+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^5+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: 1
       586: 1
       588: 1
       589: 1
       592: 1
       593: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       606: 1
       608: 1
       610: 1
       612: 1
       614: 1
       615: 1
       618: 1
       619: 1
       622: 1
       624: 1
       626: 1
       628: 1
       630: 1
       632: 1
       634: 1
       636: 1
       638: 1
       640: 1
       641: 1
       644: 1
       646: 1
       647: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       699: 1
       706: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       730: 1
       734: 1
       740: 1
       744: 1
       748: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       773: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       785: 1
       788: 1
       790: 1
       792: 1
       793: 1
       796: 1
       798: 1
       800: 1
       801: 1
       804: 1
       805: 1
       808: 1
       810: 1
       812: 1
       814: 1
       815: 1
       818: 1
       820: 1
       822: 1
       824: 1
       825: 1
       828: 1
       829: 1
       832: 1
       834: 1
       836: 1
       838: 1
       840: 1
       842: 1
       844: 1
       845: 1
       848: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       890: 1
       897: 1
       903: 1
       905: 1
       909: 1
       913: 1
       917: 1
       921: 1
       926: 1
       929: 1
       933: 1
       939: 1
       943: 1
       947: 1
       951: 1
       953: 1
       959: 1
       962: 1
       965: 1
       972: 1
       976: 1
       980: 1
       986: 1
       989: 1
       993: 1
       995: 1
       997: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1016: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1026: 1
      1029: 1
      1031: 1
      1033: 1
      1035: 1
      1037: 1
      1039: 1
      1040: 1
      1043: 1
      1045: 1
      1047: 1
      1049: 1
      1051: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1092: 1
      1104: 1
      1113: 1
      1117: 1
      1119: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1142: 1
      1145: 1
      1149: 1
      1155: 1
      1157: 1
      1162: 1
      1167: 1
      1171: 1
      1175: 1
      1177: 1
      1181: 1
      1186: 1
      1192: 1
      1195: 1
      1200: 1
      1205: 1
      1207: 1
      1215: 1
      1217: 1
      1218: 1
      1221: 1
      1223: 1
      1225: 1
      1231: 1
      1233: 1
      1234: 1
      1237: 1
      1239: 1
      1240: 1
      1243: 1
      1249: 1
      1251: 1
      1253: 1
      1254: 1
      1257: 1
      1258: 1
      1261: 1
      1265: 1
      1267: 1
      1268: 1
      1271: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1308: 1
      1317: 1
      1319: 1
      1324: 1
      1327: 1
      1332: 1
      1338: 1
      1347: 1
      1351: 1
      1353: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1379: 1
      1383: 1
      1385: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1416: 1
      1421: 1
      1423: 1
      1427: 1
      1434: 1
      1437: 1
      1447: 1
      1449: 1
      1451: 1
      1454: 1
      1457: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1471: 1
      1473: 1
      1475: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1495: 1
      1508: 1
      1519: 1
      1539: 1
      1561: 1
      1566: 1
      1568: 1
      1574: 1
      1577: 1
      1582: 1
      1586: 1
      1588: 1
      1593: 1
      1596: 1
      1601: 1
      1606: 1
      1610: 1
      1612: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1635: 1
      1638: 1
      1642: 1
      1650: 1
      1657: 1
      1660: 1
      1662: 1
      1664: 1
      1665: 1
      1672: 1
      1673: 1
      1694: 1
      1705: 1
      1716: 1
      1731: 1
      1744: 1
      1756: 1
      1760: 1
      1771: 1
      1779: 1
      1782: 1
      1788: 1
      1790: 1
      1794: 1
      1798: 1
      1809: 1
      1812: 1
      1816: 1
      1818: 1
      1820: 1
      1821: 1
      1824: 1
      1875: 1
      1887: 1
      1897: 1
      1905: 1
      1909: 1
      1912: 1
      1919: 1
      1924: 1
      1946: 1
      1950: 1
      1953: 1
      1959: 1
      2007: 1
      2020: 1
      2039: 1
      2050: 1
      2058: 1
      2122: 1

2123:    0: 1
         1: 1
         2: q^5+1
         3: 1
         4: 1
         5: 1
         6: 1
         7: q^5+1
         8: q^5+1
         9: q^5+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: q^5+1
        19: 1
        20: 1
        21: q^5+1
        22: 1
        23: 1
        24: q^5+1
        25: 1
        26: 1
        27: q^5+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: q^5+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^5+1
        52: 1
        53: 1
        54: q^5+1
        55: 1
        56: 1
        57: q^5+1
        58: 1
        61: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: q^5+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: q^5+1
        97: 1
        98: 1
        99: q^5+1
       100: 1
       101: 1
       102: q^5+1
       105: 1
       108: 1
       109: 1
       112: 1
       114: 1
       116: 1
       117: 1
       120: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: q^5+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: q^5+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: q^5+1
       171: 1
       175: 1
       178: 1
       180: 1
       182: 1
       184: 1
       185: 1
       188: 1
       190: 1
       191: 1
       194: 1
       195: 1
       198: 1
       200: 1
       202: 1
       203: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: q^5+1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q^5+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       288: 1
       290: 1
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       306: 1
       308: 1
       309: 1
       312: 1
       314: 1
       316: 1
       318: 1
       320: 1
       321: 1
       324: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: q^5+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       428: 1
       430: 1
       431: 1
       434: 1
       436: 1
       438: 1
       439: 1
       442: 1
       444: 1
       446: 1
       448: 1
       449: 1
       452: 1
       454: 1
       456: 1
       457: 1
       460: 1
       461: 1
       464: 1
       466: 1
       468: 1
       470: 1
       472: 1
       473: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       523: 1
       527: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       581: 1
       584: 1
       586: 1
       588: 1
       590: 1
       591: 1
       594: 1
       595: 1
       598: 1
       600: 1
       602: 1
       604: 1
       606: 1
       607: 1
       610: 1
       612: 1
       614: 1
       616: 1
       618: 1
       620: 1
       621: 1
       624: 1
       626: 1
       628: 1
       630: 1
       631: 1
       634: 1
       636: 1
       638: 1
       640: 1
       642: 1
       643: 1
       646: 1
       648: 1
       649: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       663: 1
       664: 1
       665: 1
       667: 1
       669: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       700: 1
       707: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       732: 1
       736: 1
       738: 1
       742: 1
       746: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       773: 1
       776: 1
       778: 1
       780: 1
       782: 1
       784: 1
       786: 1
       787: 1
       790: 1
       792: 1
       794: 1
       796: 1
       798: 1
       800: 1
       802: 1
       803: 1
       806: 1
       807: 1
       810: 1
       812: 1
       814: 1
       816: 1
       817: 1
       820: 1
       822: 1
       824: 1
       826: 1
       827: 1
       830: 1
       831: 1
       834: 1
       836: 1
       838: 1
       839: 1
       842: 1
       844: 1
       846: 1
       847: 1
       850: 1
       852: 1
       854: 1
       856: 1
       858: 1
       860: 1
       862: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       891: 1
       898: 1
       901: 1
       907: 1
       910: 1
       915: 1
       919: 1
       923: 1
       925: 1
       931: 1
       935: 1
       937: 1
       941: 1
       945: 1
       949: 1
       954: 1
       957: 1
       963: 1
       966: 1
       972: 1
       977: 1
       981: 1
       986: 1
       990: 1
       993: 1
       995: 1
       997: 1
       998: 1
      1001: 1
      1003: 1
      1005: 1
      1006: 1
      1009: 1
      1011: 1
      1013: 1
      1015: 1
      1017: 1
      1019: 1
      1021: 1
      1023: 1
      1025: 1
      1027: 1
      1028: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1039: 1
      1041: 1
      1043: 1
      1044: 1
      1047: 1
      1049: 1
      1051: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1061: 1
      1063: 1
      1065: 1
      1074: 1
      1076: 1
      1077: 1
      1078: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1093: 1
      1105: 1
      1111: 1
      1115: 1
      1121: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1142: 1
      1147: 1
      1151: 1
      1153: 1
      1159: 1
      1161: 1
      1165: 1
      1169: 1
      1173: 1
      1179: 1
      1182: 1
      1187: 1
      1192: 1
      1196: 1
      1201: 1
      1203: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1221: 1
      1223: 1
      1225: 1
      1231: 1
      1232: 1
      1235: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1249: 1
      1250: 1
      1253: 1
      1255: 1
      1257: 1
      1259: 1
      1260: 1
      1265: 1
      1267: 1
      1269: 1
      1270: 1
      1273: 1
      1275: 1
      1277: 1
      1279: 1
      1281: 1
      1283: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1309: 1
      1315: 1
      1321: 1
      1325: 1
      1328: 1
      1333: 1
      1338: 1
      1345: 1
      1349: 1
      1355: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1377: 1
      1381: 1
      1387: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1417: 1
      1419: 1
      1425: 1
      1428: 1
      1434: 1
      1437: 1
      1447: 1
      1449: 1
      1450: 1
      1455: 1
      1457: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1471: 1
      1473: 1
      1475: 1
      1477: 1
      1478: 1
      1481: 1
      1483: 1
      1484: 1
      1487: 1
      1496: 1
      1507: 1
      1520: 1
      1540: 1
      1562: 1
      1564: 1
      1570: 1
      1573: 1
      1576: 1
      1581: 1
      1584: 1
      1590: 1
      1594: 1
      1597: 1
      1602: 1
      1604: 1
      1608: 1
      1614: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1635: 1
      1638: 1
      1642: 1
      1649: 1
      1658: 1
      1660: 1
      1662: 1
      1663: 1
      1666: 1
      1672: 1
      1673: 1
      1693: 1
      1706: 1
      1717: 1
      1732: 1
      1743: 1
      1755: 1
      1758: 1
      1772: 1
      1780: 1
      1784: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1810: 1
      1813: 1
      1816: 1
      1818: 1
      1819: 1
      1822: 1
      1824: 1
      1876: 1
      1888: 1
      1896: 1
      1903: 1
      1908: 1
      1913: 1
      1921: 1
      1925: 1
      1947: 1
      1951: 1
      1954: 1
      1959: 1
      2008: 1
      2021: 1
      2038: 1
      2051: 1
      2059: 1
      2123: 1

2124:    0: q^4+2q^3+q^2+q
         1: q^4+2q^3+q^2+q
         2: q^5+2q^4+q^3+q^2+q
         3: q^4+2q^3+q^2+q
         4: q^4+2q^3+q^2+q
         5: q^4+2q^3+q^2+q
         6: q^4+2q^3+q^2+q
         7: q^5+2q^4+q^3+q^2+q
         8: q^4+q^3+q^2+q
         9: q^5+2q^4+q^3+q^2+q
        10: q^4+2q^3+q^2+q
        11: q^4+2q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: q^4+q^3+q^2+q
        14: q^4+q^3+q^2+q
        15: q^3+q^2+q
        16: q^4+2q^3+q^2+q
        17: q^4+2q^3+q^2+q
        18: q^5+2q^4+q^3+q^2+q
        19: q^4+2q^3+q^2+q
        20: q^4+2q^3+q^2+q
        21: q^5+2q^4+q^3+q^2+q
        22: 2q^3+q^2+q
        23: 2q^3+q^2+q
        24: q^4+q^3+q^2+q
        25: 2q^3+q^2+q
        26: 2q^3+q^2+q
        27: q^4+q^3+q^2+q
        28: q^4+2q^3+q^2+q
        29: q^4+2q^3+q^2+q
        30: q^4+q^3+q^2+q
        31: 2q^3+q^2+q
        32: q^3+q^2+q
        33: 2q^3+q^2+q
        34: 2q^3+q^2+q
        35: q^3+q^2+q
        36: 2q^3+q^2+q
        37: 2q^3+q^2+q
        39: 2q^3+q^2+q
        41: q^4+q^3+q^2+q
        43: q^4+q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: q^4+q^3+q^2+q
        47: q^3+q^2+q
        48: q^4+q^3+q^2+q
        49: q^4+2q^3+q^2+q
        50: q^4+2q^3+q^2+q
        51: q^5+2q^4+q^3+q^2+q
        52: 2q^3+q^2+q
        53: 2q^3+q^2+q
        54: q^4+q^3+q^2+q
        55: 2q^3+q^2+q
        56: 2q^3+q^2+q
        57: q^4+q^3+q^2+q
        58: q^3
        59: q^3+q^2+q
        60: q^3
        61: q^3+q^2+q
        62: 2q^3+q^2+q
        64: q^3+q^2+q
        66: 2q^3+q^2+q
        68: q^2+q
        69: q^4+q^3+q^2+q
        70: q^4+q^3+q^2+q
        71: q^4+2q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        74: 2q^3+q^2+q
        76: 2q^3+q^2+q
        78: q^4+q^3+q^2+q
        80: q^3+q^2+q
        81: q^3+q^2+q
        82: 2q^3+q^2+q
        83: q^3+q^2+q
        84: q^3+q^2+q
        85: q^3+q^2+q
        86: 2q^3+q^2+q
        87: q^3+q^2+q
        88: q^4+q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: q^4+q^3+q^2+q
        92: q^3+q^2+q
        93: q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: q^3+q^2+q
       101: q^3+q^2+q
       102: q^4+q^3+q^2+q
       103: q^3
       106: q^3+q^2+q
       107: q^3
       108: q^3+q^2+q
       109: q^3
       110: q^3+q^2+q
       111: 2q^3+q^2+q
       113: 2q^3+q^2+q
       115: q^3+q^2+q
       118: q^2+q
       120: q^2+q
       121: q^3+q^2+q
       123: q^3+q^2+q
       125: q^2+q
       126: q^4+q^3+q^2+q
       127: 2q^3+q^2+q
       129: 2q^3+q^2+q
       131: q^4+q^3+q^2+q
       133: q^2+q
       134: q^4+q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^3+q^2+q
       150: q^3+q^2+q
       151: q^3+q^2+q
       153: q^3+q^2+q
       155: q^4+q^3+q^2+q
       157: q^4+q^3+q^2+q
       158: q^3+q^2+q
       159: q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3
       172: q^3+q^2+q
       176: q^2+q
       177: q^3+q^2+q
       179: 2q^3+q^2+q
       181: 2q^3+q^2+q
       184: q^2+q
       186: q^2+q
       187: q^3+q^2+q
       189: q^3+q^2+q
       192: q^2+q
       194: q^2+q
       195: q^3
       196: q^3+q^2+q
       197: q^2+q
       200: q^2+q
       201: q^3
       202: q^3+q^2+q
       204: q^2+q
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       211: q^3+q^2+q
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       215: q^3+q^2+q
       217: q^3+q^2+q
       219: q^2+q
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       221: q^4+q^3+q^2+q
       222: q^3+q^2+q
       223: q^3+q^2+q
       224: q^3+q^2+q
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       226: q^3+q^2+q
       227: q^2+q
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       231: q^3+q^2+q
       232: q^2+q
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       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       259: q^3
       262: q^3+q^2+q
       266: q^2+q
       269: q^2+q
       273: q^2+q
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       331: q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
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       336: q^3+q^2+q
       337: q^3+q^2+q
       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
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       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q
       362: q
       364: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
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       376: q^3+q
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       411: q^3+q^2+q
       413: q^2+q
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       417: q^3+q^2+q
       420: q^2+q
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       425: q^3+q^2+q
       427: q^3+q^2+q
       430: q^2+q
       432: q^2+q
       433: q^2+q
       435: q
       438: q^2+q
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       441: q^2+q
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       450: q^2+q
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       454: q^2+q
       455: q
       458: q^2+q
       459: q^2+q
       462: q^2+q
       463: q^2+q
       465: q
       467: q^3+q
       469: q^3+q^2+q
       472: q
       474: q
       475: q
       477: q^2+q
       479: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       485: q^3+q
       487: q
       489: q^3+q
       491: q^3+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: q^2+q
       496: q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q
       502: q^3+q
       504: q
       506: q^3+q
       508: q
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       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       515: q^3+q
       516: q
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       518: q^3+q
       519: q
       520: q^3+q
       524: q^2+q
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       536: q^2+q
       539: q
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       555: q
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       563: q^2+q
       568: q
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       583: q^2+q
       585: q^2+q
       587: q^3+q^2+q
       590: q^2+q
       592: q^2+q
       594: q^2+q
       596: q^2+q
       597: q^3+q
       599: q^3+q^2+q
       601: q
       604: q^2+q
       605: q
       608: q^2+q
       609: q^2+q
       611: q
       613: q^2+q
       616: q
       617: q
       620: q^2+q
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       623: q
       625: q^2+q
       627: q
       629: q^2+q
       632: q
       633: q
       635: q
       637: q^3+q
       639: q
       642: q
       644: q
       645: q
       648: q
       650: q
       651: 2q
       653: q
       655: q
       657: q
       658: q^3+q
       660: q
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       664: q^3+q
       665: q
       666: q^3+q
       668: q
       670: q^3+q
       672: q
       673: q^3+q
       674: q
       675: q
       676: q^2+q
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       678: q
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       680: q
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       682: q
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       686: q
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       688: q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       697: q^2+q
       708: q^2+q
       712: q^2+q
       716: q^2+q
       720: q^2+q
       723: q
       727: q^2+q
       731: q
       735: q
       739: q
       743: q^2+q
       747: q
       751: q
       756: q
       758: 2q
       762: q
       768: q
       769: q
       771: q
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       777: q^2+q
       779: q^3+q
       781: q
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       802: q
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       849: 2q
       851: q
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       899: q^2+q
       902: q
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       922: q
       927: q
       930: q^2+q
       934: q
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       950: q^2+q
       955: q
       958: q
       961: 2q
       967: q
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       970: q
       975: q
       979: 2q
       982: q
       984: q
       991: q
       992: q
       994: q
       996: q^3+q
       999: q
      1001: q
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      1005: q
      1007: q
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      1010: 2q
      1012: q
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      1027: q
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      1048: q
      1050: 2q
      1053: q
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      1091: q
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      1102: q
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      1120: q
      1124: q
      1127: 2q
      1133: q
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      1163: q
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      1185: 2q
      1188: q
      1190: q
      1197: q
      1199: q
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      1217: q
      1219: q
      1220: q
      1222: 2q
      1224: q
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      1323: 2q
      1329: q
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      1598: q
      1622: 1
      1631: q
      1637: q
      1692: q
      1704: q
      1722: 1
      1730: q
      1796: 1
      1808: 1
      1881: 1
      1891: 1
      1945: 1
      1949: 1
      2011: 1
      2022: 1
      2057: 1
      2124: 1

2125:    0: q^4+2q^3+q^2+q
         1: q^4+2q^3+q^2+q
         2: q^5+2q^4+q^3+q^2+q
         3: q^4+2q^3+q^2+q
         4: q^4+2q^3+q^2+q
         5: q^4+2q^3+q^2+q
         6: q^4+2q^3+q^2+q
         7: q^5+2q^4+q^3+q^2+q
         8: q^4+q^3+q^2+q
         9: q^5+2q^4+q^3+q^2+q
        10: q^4+2q^3+q^2+q
        11: q^4+2q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: q^4+q^3+q^2+q
        14: q^4+q^3+q^2+q
        15: q^3+q^2+q
        16: q^4+2q^3+q^2+q
        17: q^4+2q^3+q^2+q
        18: q^5+2q^4+q^3+q^2+q
        19: q^4+2q^3+q^2+q
        20: q^4+2q^3+q^2+q
        21: q^5+2q^4+q^3+q^2+q
        22: 2q^3+q^2+q
        23: 2q^3+q^2+q
        24: q^4+q^3+q^2+q
        25: 2q^3+q^2+q
        26: 2q^3+q^2+q
        27: q^4+q^3+q^2+q
        28: q^4+2q^3+q^2+q
        29: q^4+2q^3+q^2+q
        30: q^4+q^3+q^2+q
        31: 2q^3+q^2+q
        32: q^3+q^2+q
        33: 2q^3+q^2+q
        34: 2q^3+q^2+q
        35: q^3+q^2+q
        36: 2q^3+q^2+q
        38: 2q^3+q^2+q
        40: 2q^3+q^2+q
        42: q^4+q^3+q^2+q
        43: q^4+q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: q^4+q^3+q^2+q
        47: q^3+q^2+q
        48: q^4+q^3+q^2+q
        49: q^4+2q^3+q^2+q
        50: q^4+2q^3+q^2+q
        51: q^5+2q^4+q^3+q^2+q
        52: 2q^3+q^2+q
        53: 2q^3+q^2+q
        54: q^4+q^3+q^2+q
        55: 2q^3+q^2+q
        56: 2q^3+q^2+q
        57: q^4+q^3+q^2+q
        58: q^3
        59: q^3+q^2+q
        60: q^3+q^2+q
        61: q^3
        63: 2q^3+q^2+q
        65: q^3+q^2+q
        67: 2q^3+q^2+q
        68: q^2+q
        69: q^4+q^3+q^2+q
        70: q^4+q^3+q^2+q
        71: q^4+2q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        75: 2q^3+q^2+q
        77: 2q^3+q^2+q
        79: q^4+q^3+q^2+q
        80: q^3+q^2+q
        81: q^3+q^2+q
        82: 2q^3+q^2+q
        83: q^3+q^2+q
        84: q^3+q^2+q
        85: q^3+q^2+q
        86: 2q^3+q^2+q
        87: q^3+q^2+q
        88: q^4+q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: q^4+q^3+q^2+q
        92: q^3+q^2+q
        93: q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: q^3+q^2+q
       101: q^3+q^2+q
       102: q^4+q^3+q^2+q
       104: q^3+q^2+q
       105: q^3
       107: q^3+q^2+q
       108: q^3
       109: q^3
       110: q^3+q^2+q
       112: 2q^3+q^2+q
       114: 2q^3+q^2+q
       116: q^3+q^2+q
       118: q^2+q
       119: q^2+q
       122: q^3+q^2+q
       124: q^3+q^2+q
       125: q^2+q
       126: q^4+q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^2+q
       134: q^4+q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^3+q^2+q
       150: q^3+q^2+q
       152: q^3+q^2+q
       154: q^3+q^2+q
       156: q^4+q^3+q^2+q
       157: q^4+q^3+q^2+q
       158: q^3+q^2+q
       159: q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3+q^2+q
       171: q^3
       174: q^2+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       183: q^2+q
       186: q^2+q
       188: q^3+q^2+q
       190: q^3+q^2+q
       192: q^2+q
       193: q^2+q
       195: q^3
       196: q^3+q^2+q
       198: q^2+q
       199: q^2+q
       201: q^3+q^2+q
       202: q^3
       204: q^2+q
       206: q^2+q
       208: q^3+q^2+q
       210: q^3+q^2+q
       212: q^3+q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: q^2+q
       220: q^2+q
       221: q^4+q^3+q^2+q
       222: q^3+q^2+q
       223: q^3+q^2+q
       224: q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
       230: q^3+q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: q^3+q^2+q
       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       260: q^3+q^2+q
       261: q^3
       264: q^2+q
       268: q^2+q
       274: q^2+q
       276: q^2+q
       280: q^2+q
       282: q^3+q^2+q
       283: q^2+q
       286: q^2+q
       288: q^3+q^2+q
       290: q^3+q^2+q
       292: q^3+q^2+q
       293: q^2+q
       296: q^2+q
       298: q^3+q^2+q
       299: q^2+q
       302: q^2+q
       304: q^2+q
       306: q^2+q
       307: q^2+q
       310: q^2+q
       312: q^2+q
       314: q^2+q
       316: q^3+q^2+q
       318: q^3+q^2+q
       319: q^2+q
       322: q^2+q
       324: q^2+q
       326: q^3+q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       378: q^2+q
       382: q^2+q
       386: q^2+q
       390: q^2+q
       394: q^2+q
       400: q^2+q
       403: q^2+q
       407: q^2+q
       410: q^2+q
       412: q^3+q^2+q
       414: q^2+q
       416: q^3+q^2+q
       418: q^3+q^2+q
       419: q^2+q
       422: q^2+q
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: q^3+q^2+q
       429: q^2+q
       432: q^2+q
       434: q^2+q
       436: q
       437: q^2+q
       440: q^2+q
       442: q^2+q
       443: q^2+q
       446: q^2+q
       447: q^2+q
       450: q^2+q
       452: q^2+q
       453: q^2+q
       456: q
       458: q^2+q
       460: q^2+q
       462: q^2+q
       464: q^2+q
       466: q
       468: q^3+q
       470: q^3+q^2+q
       471: q
       474: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       486: q^3+q
       488: q
       490: q^3+q
       491: q^3+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: q^2+q
       496: q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q
       503: q^3+q
       505: q
       507: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q
       519: q
       520: q^3+q
       522: q^2+q
       526: q^2+q
       530: q^2+q
       534: q^2+q
       538: q
       542: q^2+q
       546: q^2+q
       551: q^2+q
       556: q
       560: q^2+q
       564: q^2+q
       566: q
       571: q^2+q
       574: q^2+q
       581: q^2+q
       584: q^2+q
       586: q^2+q
       588: q^3+q^2+q
       589: q^2+q
       592: q^2+q
       593: q^2+q
       596: q^2+q
       598: q^3+q
       600: q^3+q^2+q
       602: q
       603: q^2+q
       606: q
       608: q^2+q
       610: q^2+q
       612: q
       614: q^2+q
       615: q
       618: q
       619: q^2+q
       622: q^2+q
       624: q
       626: q^2+q
       628: q
       630: q^2+q
       632: q
       634: q
       636: q
       638: q^3+q
       640: q
       641: q
       644: q
       646: q
       647: q
       650: q
       652: 2q
       654: q
       656: q
       657: q
       659: q^3+q
       661: q
       663: q^3+q
       664: q^3+q
       665: q
       667: q^3+q
       669: q
       671: q^3+q
       672: q
       673: q^3+q
       674: q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q
       680: q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       699: q^2+q
       706: q^2+q
       710: q^2+q
       715: q^2+q
       718: q^2+q
       722: q
       726: q^2+q
       730: q
       734: q
       740: q
       744: q^2+q
       748: q
       752: q
       754: q
       759: 2q
       763: q
       766: q
       773: q
       774: q
       776: q
       778: q^2+q
       780: q^3+q
       782: q
       784: q^3+q
       785: q
       788: q
       790: q
       792: q
       793: q
       796: q
       798: q
       800: q
       801: q
       804: q
       805: q^2+q
       808: q^2+q
       810: q
       812: q^2+q
       814: q
       815: q
       818: q
       820: q
       822: q
       824: q
       825: q^2+q
       828: q^2+q
       829: q
       832: q
       834: q
       836: q^2+q
       838: q
       840: q
       842: q
       844: q
       845: q
       848: q
       850: 2q
       852: q
       854: 2q
       856: q
       858: q
       860: q^3+q
       862: q
       864: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q
       869: q
       870: q
       871: q
       872: q
       873: q
       874: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       890: q
       894: q
       897: q^2+q
       903: q
       905: q
       909: q
       913: q
       917: q
       921: q
       926: q
       929: q^2+q
       933: q
       939: q
       943: q
       947: q
       951: q^2+q
       953: q
       959: q
       962: 2q
       965: q
       972: q
       973: q
       976: q
       980: 2q
       986: q
       987: q
       989: q
       993: q
       995: q
       997: q^3+q
       999: q
      1000: q
      1003: q
      1004: q
      1007: q
      1009: q
      1011: 2q
      1013: q
      1015: q
      1016: q
      1019: q
      1021: q
      1023: q
      1025: q
      1026: q
      1029: q
      1031: q
      1033: q
      1035: q
      1037: q
      1039: q
      1040: q
      1043: q
      1045: q
      1047: q
      1049: q
      1051: 2q
      1052: q
      1055: q
      1056: q
      1059: q
      1061: q
      1063: q
      1065: q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q
      1085: q
      1092: q
      1096: q
      1104: q
      1108: q
      1113: q
      1117: q
      1119: q
      1123: q
      1128: 2q
      1131: q
      1136: q
      1142: q
      1143: q
      1145: q
      1149: q
      1155: q
      1157: q
      1162: q
      1167: q
      1171: q
      1175: q
      1177: q
      1181: q
      1186: 2q
      1192: q
      1193: q
      1195: q
      1200: q
      1205: q
      1207: q
      1215: q
      1217: q
      1218: q
      1221: q
      1223: 2q
      1225: q
      1231: q
      1233: q
      1234: q
      1237: q
      1239: q
      1240: q
      1243: q
      1249: q
      1251: q
      1253: q
      1254: q
      1257: q
      1258: q
      1261: q
      1265: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1283: q
      1285: q
      1288: q
      1296: q
      1300: q
      1308: q
      1312: q
      1317: q
      1319: q
      1324: 2q
      1327: q
      1332: q
      1338: q
      1339: q
      1347: q
      1351: q
      1353: q
      1357: q
      1363: q
      1366: q
      1371: q
      1379: q
      1383: q
      1385: q
      1389: q
      1394: q
      1397: q
      1402: q
      1416: q
      1434: q
      1437: q
      1447: q
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      1451: q
      1454: q
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      1462: q
      1473: q
      1481: q
      1483: q
      1495: q
      1499: q
      1508: q
      1519: q
      1539: q
      1561: q
      1566: q
      1568: q
      1574: q
      1577: q
      1586: q
      1588: q
      1593: q
      1596: q
      1620: 1
      1635: q
      1638: q
      1694: q
      1705: q
      1719: 1
      1731: q
      1794: 1
      1809: 1
      1878: 1
      1892: 1
      1946: 1
      1950: 1
      2012: 1
      2023: 1
      2058: 1
      2125: 1

2126:    0: 3q^4+2q^3+3q^2+2q
         1: 3q^4+2q^3+3q^2+2q
         2: 2q^5+2q^4+q^3+3q^2+2q
         3: 3q^4+2q^3+3q^2+2q
         4: q^5+2q^4+3q^3+2q^2+2q
         5: 3q^4+2q^3+3q^2+2q
         6: q^5+2q^4+3q^3+2q^2+2q
         7: q^6+q^5+2q^4+2q^3+2q^2+2q
         8: 2q^5+2q^4+q^3+3q^2+2q
         9: q^6+q^5+2q^4+2q^3+2q^2+2q
        10: 3q^4+2q^3+3q^2+2q
        11: 3q^4+2q^3+3q^2+2q
        12: q^5+2q^4+3q^3+2q^2+2q
        13: q^4+q^3+3q^2+2q
        14: q^4+2q^3+2q^2+2q
        15: q^4+q^3+3q^2+2q
        16: 3q^4+2q^3+3q^2+2q
        17: 3q^4+2q^3+3q^2+2q
        18: q^6+q^5+2q^4+2q^3+2q^2+2q
        19: 2q^4+2q^3+2q^2+2q
        20: 2q^4+2q^3+2q^2+2q
        21: q^5+2q^4+q^3+2q^2+2q
        22: 3q^4+2q^3+3q^2+2q
        23: 3q^4+2q^3+3q^2+2q
        24: 2q^5+2q^4+q^3+3q^2+2q
        25: 3q^4+2q^3+3q^2+2q
        26: 3q^4+2q^3+3q^2+2q
        27: 2q^5+2q^4+q^3+3q^2+2q
        28: 3q^4+2q^3+3q^2+2q
        29: 2q^4+2q^3+2q^2+2q
        30: q^4+q^3+2q^2+2q
        31: 3q^4+2q^3+3q^2+2q
        32: q^4+q^3+3q^2+2q
        33: 3q^4+2q^3+3q^2+2q
        34: 3q^4+2q^3+3q^2+2q
        35: q^4+q^3+3q^2+2q
        36: 3q^4+2q^3+3q^2+2q
        37: q^4+q^2
        38: 2q^4+2q^3+2q^2+2q
        39: q^4+q^2
        40: 2q^4+2q^3+2q^2+2q
        41: q^5+q^2
        42: q^5+2q^4+q^3+2q^2+2q
        43: q^4+q^3+3q^2+2q
        44: q^4+2q^3+2q^2+2q
        45: q^4+q^3+3q^2+2q
        46: q^4+q^3+3q^2+2q
        47: q^4+q^3+3q^2+2q
        48: q^4+2q^3+2q^2+2q
        49: 2q^4+2q^3+2q^2+2q
        50: 2q^4+2q^3+2q^2+2q
        51: q^5+2q^4+q^3+2q^2+2q
        52: 2q^4+2q^3+2q^2+2q
        53: 2q^4+2q^3+2q^2+2q
        54: q^5+2q^4+q^3+2q^2+2q
        55: 2q^4+2q^3+2q^2+2q
        56: 2q^4+2q^3+2q^2+2q
        57: q^5+2q^4+q^3+2q^2+2q
        58: q^4+q^3+q^2+q
        59: 2q^4+q^3+2q^2+q
        60: q^4+q^3+q^2+q
        61: 2q^4+q^3+2q^2+q
        62: q^4+q^2
        63: 2q^4+2q^3+2q^2+2q
        64: q^2
        65: q^4+q^3+2q^2+2q
        66: q^4+q^2
        67: 2q^4+2q^3+2q^2+2q
        68: 3q^2+2q
        69: q^4+q^3+2q^2+2q
        70: q^4+q^3+2q^2+2q
        71: 2q^4+2q^3+2q^2+2q
        72: q^4+2q^3+q^2+2q
        73: q^4+2q^3+q^2+2q
        75: q^4+2q^3+q^2+2q
        77: q^4+2q^3+q^2+2q
        79: 2q^4+q^3+q^2+2q
        80: q^4+q^3+3q^2+2q
        81: q^4+q^3+3q^2+2q
        82: 2q^4+2q^3+2q^2+2q
        83: q^4+q^3+2q^2+2q
        84: q^4+q^3+3q^2+2q
        85: q^4+q^3+3q^2+2q
        86: 2q^4+2q^3+2q^2+2q
        87: q^4+q^3+2q^2+2q
        88: q^4+q^3+3q^2+2q
        89: q^4+q^3+3q^2+2q
        90: q^4+2q^3+2q^2+2q
        91: q^3+2q^2+2q
        92: q^3+2q^2+2q
        93: q^3+2q^2+2q
        94: 2q^4+2q^3+2q^2+2q
        95: 2q^4+2q^3+2q^2+2q
        96: q^5+2q^4+q^3+2q^2+2q
        97: 2q^4+2q^3+2q^2+2q
        98: 2q^4+2q^3+2q^2+2q
        99: q^5+2q^4+q^3+2q^2+2q
       100: 2q^4+2q^3+2q^2+2q
       101: 2q^4+2q^3+2q^2+2q
       102: q^5+2q^4+q^3+2q^2+2q
       104: q^4+q^3+q^2+q
       105: q^4+q^3+q^2+q
       106: q^4+q^2
       107: q^3+q
       108: q^4+q^3+q^2+q
       109: q^3+q
       110: q^4+q^3+q^2+q
       112: 2q^3+2q
       114: q^4+2q^3+q^2+2q
       116: q^4+q^3+q^2+2q
       117: q^2+q
       118: 2q^2+q
       119: q^2+q
       120: 2q^2+q
       121: q^2
       122: q^4+q^3+2q^2+2q
       123: q^2
       124: q^4+q^3+2q^2+2q
       125: 3q^2+2q
       126: q^4+q^3+2q^2+2q
       128: q^4+2q^3+q^2+2q
       130: q^4+2q^3+q^2+2q
       132: 2q^4+q^3+q^2+2q
       133: 2q^2+2q
       134: q^3+2q^2+2q
       135: q^3+q^2+2q
       136: q^3+q^2+2q
       137: q^4+q^3+3q^2+2q
       138: q^4+q^3+2q^2+2q
       139: 2q^4+2q^3+2q^2+2q
       140: q^4+2q^3+q^2+2q
       141: q^4+q^3+2q^2+2q
       142: q^4+2q^3+q^2+2q
       143: q^4+q^3+3q^2+2q
       144: q^4+q^3+2q^2+2q
       145: 2q^4+2q^3+2q^2+2q
       146: q^4+q^3+2q^2+2q
       147: q^4+2q^3+q^2+2q
       148: q^4+2q^3+q^2+2q
       149: 2q^4+2q^3+2q^2+2q
       150: q^4+q^3+2q^2+2q
       152: q^4+2q^3+q^2+2q
       154: q^4+2q^3+q^2+2q
       156: 2q^4+q^3+q^2+2q
       157: q^3+2q^2+2q
       158: q^3+2q^2+2q
       159: q^3+2q^2+2q
       160: q^3+2q^2+2q
       161: q^3+2q^2+2q
       162: q^3+2q^2+2q
       163: q^3+2q^2+2q
       164: q^3+2q^2+2q
       165: q^3+2q^2+2q
       166: 2q^4+2q^3+2q^2+2q
       167: 2q^4+2q^3+2q^2+2q
       168: q^5+2q^4+q^3+2q^2+2q
       170: q^3+q
       171: q^3+q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q^4+q^3+q^2+2q
       180: q^4+2q^3+q^2+2q
       182: 2q^3+2q
       183: q
       184: q^2+q
       185: q
       186: q^2+q
       188: q^3+2q
       190: q^4+q^3+q^2+2q
       191: q^2+q
       192: 2q^2+q
       193: q^3+q
       194: q^4+q^3+q^2+q
       195: q^3+q
       196: q^4+q^3+q^2+q
       198: 2q^3+2q
       199: q^2+q
       200: 2q^2+q
       201: q^3+q
       202: q^4+q^3+q^2+q
       203: q^3+q
       204: q^4+q^3+q^2+q
       206: 2q^3+2q
       207: q^2
       208: q^4+q^3+2q^2+2q
       210: q^4+2q^3+q^2+2q
       212: q^4+q^3+q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: q^3+2q^2+2q
       222: q^3+q^2+2q
       223: q^3+q^2+2q
       224: q^3+q^2+2q
       225: q^3+q^2+2q
       226: q^4+q^3+2q^2+2q
       227: 2q^2+2q
       228: q^3+2q^2+2q
       229: q^3+q^2+2q
       230: q^3+q^2+2q
       231: q^4+q^3+2q^2+2q
       232: 2q^2+2q
       233: q^3+2q^2+2q
       234: q^3+q^2+2q
       235: q^3+q^2+2q
       236: q^4+q^3+2q^2+2q
       238: q^4+2q^3+q^2+2q
       240: q^4+2q^3+q^2+2q
       242: 2q^4+q^3+q^2+2q
       243: 2q^4+2q^3+2q^2+2q
       244: q^4+2q^3+q^2+2q
       245: q^4+2q^3+q^2+2q
       246: q^4+q^3+2q^2+2q
       247: 3q^3+3q
       248: 3q^3+3q
       249: 2q^4+q^3+q^2+2q
       250: q^3+2q^2+2q
       251: q^3+2q^2+2q
       252: q^3+2q^2+2q
       253: q^3+2q^2+2q
       254: q^3+2q^2+2q
       255: q^3+2q^2+2q
       256: q^3+2q^2+2q
       257: q^3+2q^2+2q
       258: q^3+2q^2+2q
       260: q^3+q
       261: q^3+q
       264: q
       265: q
       268: q^3+q
       270: q^3+q
       272: q^3+q
       274: q^3+q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: q^2+2q
       282: q^2+2q
       283: q
       284: q^2+q
       285: q
       286: q^2+q
       288: q^4+q^3+q^2+2q
       290: 2q
       292: q^3+2q
       293: q
       294: q^2+q
       295: q
       296: q^2+q
       298: q^3+2q
       299: q
       300: q^2+q
       302: 2q^3+2q
       303: q
       304: q^2+q
       306: q^3+2q
       307: q
       308: q^2+q
       309: q
       310: q^2+q
       312: 2q^3+2q
       314: q^3+2q
       316: q^4+q^3+q^2+2q
       318: q^4+2q^3+q^2+2q
       319: q^3+q
       320: q^4+q^3+q^2+q
       321: q^3+q
       322: q^4+q^3+q^2+q
       324: 2q^3+2q
       326: q^4+q^3+q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: 2q^2+2q
       334: q^3+q^2+2q
       335: q^3+q^2+2q
       336: q^3+2q
       337: 3q^3+3q
       339: 3q^3+3q
       341: 3q^3+3q
       343: 2q^4+q^3+q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: q^3+2q^2+2q
       347: q^3+q^2+2q
       348: q^3+q^2+2q
       349: q^3+q^2+2q
       350: q^3+q^2+2q
       351: 3q^3+3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: q^3+2q^2+2q
       355: q^3+q^2+2q
       356: q^3+q^2+2q
       357: q^3+q^2+2q
       358: q^3+q^2+2q
       359: 3q^3+3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: q^4+q^3+2q^2+2q
       367: 2q^2+2q
       368: q^3+2q^2+2q
       369: q^3+q^2+2q
       370: q^3+q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: q^3+2q^2+2q
       375: q^3+2q^2+2q
       376: q^3+2q^2+2q
       378: q
       379: q
       382: q
       383: q
       386: q
       387: q
       390: q^3+q
       392: q^3+q
       394: q
       395: q
       398: q^3+q
       400: q^3+q
       402: q
       403: q
       407: q^3+q
       408: q^3+q
       410: q^2+2q
       412: q^2+2q
       414: q^2+2q
       416: 2q
       418: 2q
       419: q
       420: q^2+q
       421: q
       422: q^2+q
       424: q^3+2q
       426: q^3+2q
       428: 3q^3+3q
       429: q
       430: q^2+q
       431: q
       432: q^2+q
       434: q^3+2q
       436: 2q
       437: q
       438: q^2+q
       439: q
       440: q^2+q
       442: q^3+2q
       443: q^3+q
       444: 2q^3+2q
       446: 3q^3+3q
       447: q
       448: q^2+q
       449: q
       450: q^2+q
       452: q^3+2q
       453: q
       454: q^2+q
       456: 2q
       457: q
       458: q^2+q
       460: q^3+2q
       461: q^3+q
       462: 2q^3+2q
       464: 3q^3+3q
       466: q^2+2q
       468: q^2+2q
       470: q^4+q^3+q^2+2q
       471: q
       472: q^2+q
       473: q
       474: q^2+q
       476: q^3+2q
       478: 2q^3+2q
       479: q^3+q
       480: 2q^3+2q
       481: q^2+2q
       482: q^2+2q
       483: q^3+2q
       484: 3q
       486: 3q
       488: 3q
       490: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^3+q^2+2q
       494: q^3+q^2+2q
       495: q^3+2q
       496: 3q
       497: 2q^2+2q
       498: q^3+q^2+2q
       499: q^3+q^2+2q
       500: q^3+2q
       501: 3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: q^3+2q^2+2q
       511: q^3+q^2+2q
       512: q^3+q^2+2q
       513: q^3+q^2+2q
       514: q^3+q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: q^3+q
       548: 2q^3+2q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: q^3+q
       564: 2q^3+2q
       566: q
       567: q
       571: q^3+q
       572: q^3+q
       574: q^3+q
       575: q^3+q
       576: q^3+q
       578: q^3+q
       581: 2q^3+2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q
       590: q^2+q
       592: q
       594: q
       595: q
       596: q^2+q
       598: 2q
       600: q^3+2q
       602: 3q
       603: q
       604: q^2+q
       606: 2q
       607: q
       608: q^2+q
       610: q^3+2q
       612: 2q
       614: q^3+2q
       615: q
       616: 2q
       618: 3q
       619: q
       620: q^2+q
       621: q
       622: q^2+q
       624: 2q
       626: q^3+2q
       628: 2q
       630: q^3+2q
       631: q
       632: 2q
       634: 3q
       636: q^2+2q
       638: q^2+2q
       640: q^2+2q
       641: q
       642: q^2+q
       643: q
       644: q^2+q
       646: q^3+2q
       647: q
       648: q^2+q
       649: q
       650: q^2+q
       652: 2q
       654: q^3+2q
       655: q
       656: 2q
       657: 3q
       659: 3q
       661: 3q
       663: q^2+2q
       664: 2q
       665: 2q
       667: 3q
       669: 3q
       671: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: q^3+2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: q^3+2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^3+q^2+2q
       688: q^3+q^2+2q
       689: q^3+2q
       690: 3q
       691: 3q
       692: q^2+2q
       699: q^3+q
       700: q^3+q
       701: q^3+q
       706: q
       707: q
       710: q
       711: q
       715: q
       719: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: q
       736: 2q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: q
       752: 2q
       754: q
       755: q
       759: q
       760: q
       763: q
       764: q
       766: q
       767: q
       768: q
       770: q
       773: 2q
       776: 3q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       786: q
       788: q
       790: 3q
       792: q
       793: q
       794: 2q
       796: 3q
       798: 2q
       800: 2q
       801: q
       802: q^2+q
       804: q
       806: q
       807: q
       808: q^2+q
       810: 2q
       812: q^3+2q
       814: 3q
       815: q
       816: 2q
       817: q
       818: 2q
       820: 3q
       822: 2q
       824: 2q
       825: q
       826: q^2+q
       828: q
       830: q
       831: q
       832: q^2+q
       834: 2q
       836: q^3+2q
       838: 3q
       839: q
       840: 2q
       842: q^2+2q
       843: q
       844: 2q
       845: q
       846: q^2+q
       847: q
       848: q^2+q
       850: 2q
       852: q^3+2q
       854: 2q
       856: q^3+2q
       857: q
       858: 2q
       860: 3q
       862: 3q
       864: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: q^3+2q
       880: 2q
       890: q
       891: q
       892: q
       897: q
       898: q
       903: q
       907: q
       913: q
       915: q
       917: q
       919: 2q
       921: q
       923: q
       926: q
       931: q
       933: q
       935: 2q
       937: q
       939: q
       941: q
       943: 2q
       945: q
       947: q
       951: q
       954: q
       957: q
       959: 2q
       962: q
       963: q
       965: q
       966: q
       967: q
       969: q
       972: 2q
       976: q
       977: q
       980: q
       981: q
       983: q
       986: 2q
       989: q
       990: q
       991: q
       993: 3q
       995: 2q
       997: 2q
       999: q
      1001: q
      1003: 2q
      1005: q
      1007: q
      1009: q
      1011: q
      1013: q
      1015: 3q
      1016: q
      1017: 2q
      1019: 2q
      1021: 2q
      1023: 2q
      1025: 2q
      1027: q
      1029: q
      1031: 3q
      1032: q
      1033: 2q
      1035: 2q
      1037: 2q
      1039: 2q
      1041: q
      1043: 2q
      1045: q
      1046: q
      1047: 2q
      1049: 2q
      1051: 2q
      1052: q
      1053: q^2+q
      1055: q
      1057: q
      1058: q
      1059: q^2+q
      1061: 2q
      1063: q^3+2q
      1065: q
      1074: 2q
      1076: 2q
      1077: 2q
      1078: 2q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1092: q
      1093: q
      1094: q
      1104: q
      1105: q
      1106: q
      1113: q
      1117: q
      1121: q
      1125: q
      1142: q
      1145: q
      1147: 2q
      1149: q
      1151: q
      1155: q
      1159: q
      1165: q
      1167: 2q
      1169: q
      1171: q
      1175: q
      1179: q
      1186: q
      1187: q
      1189: q
      1192: 2q
      1195: q
      1196: q
      1197: q
      1200: q
      1201: q
      1205: q
      1209: q
      1215: 2q
      1217: q
      1219: q
      1221: q
      1223: q
      1225: q
      1231: 2q
      1233: q
      1235: q
      1237: 2q
      1239: 2q
      1241: q
      1243: q
      1249: 2q
      1251: q
      1253: 2q
      1255: q
      1257: 2q
      1259: q
      1261: q
      1265: 2q
      1267: 2q
      1269: q
      1271: q
      1273: 2q
      1275: 2q
      1277: q
      1279: q
      1281: q
      1283: 2q
      1285: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1308: q
      1309: q
      1310: q
      1317: q
      1321: q
      1338: q
      1347: q
      1351: q
      1355: q
      1359: q
      1379: q
      1383: q
      1387: q
      1391: q
      1416: q
      1417: q
      1421: q
      1425: q
      1434: q
      1437: q
      1447: q
      1449: 2q
      1451: q
      1455: q
      1457: 2q
      1461: q
      1463: q
      1465: 2q
      1467: q
      1469: q
      1471: 2q
      1473: 2q
      1475: q
      1477: q
      1479: q
      1481: q
      1483: q
      1484: 1
      1487: 2q
      1566: q
      1570: q
      1586: q
      1590: q
      1606: q
      1610: q
      1614: q
      1618: q
      1635: q
      1638: q
      1642: 1
      1650: 1
      1658: 1
      1660: q
      1662: 2q
      1664: q
      1666: q
      1672: q
      1673: 1
      1760: 1
      1784: 1
      1788: q
      1792: q
      1814: 1
      1816: 1
      1818: 1
      1820: 1
      1822: 1
      1824: q
      1890: 1
      1905: 1
      1909: 1
      1921: 1
      1925: 1
      1955: 1
      1959: 1
      2010: 1
      2024: 1
      2039: 1
      2051: 1
      2126: 1

2127:    0: q^4+2q^3+q^2+q
         1: q^4+2q^3+q^2+q
         2: q^5+2q^4+q^3+q^2+q
         3: q^4+2q^3+q^2+q
         4: q^4+2q^3+q^2+q
         5: q^4+2q^3+q^2+q
         6: q^4+2q^3+q^2+q
         7: q^5+2q^4+q^3+q^2+q
         8: q^4+q^3+q^2+q
         9: q^5+2q^4+q^3+q^2+q
        10: q^4+2q^3+q^2+q
        11: q^4+2q^3+q^2+q
        12: q^4+2q^3+q^2+q
        13: q^4+q^3+q^2+q
        14: q^4+q^3+q^2+q
        15: q^3+q^2+q
        16: q^4+2q^3+q^2+q
        17: q^4+2q^3+q^2+q
        18: q^5+2q^4+q^3+q^2+q
        19: q^4+2q^3+q^2+q
        20: q^4+2q^3+q^2+q
        21: q^5+2q^4+q^3+q^2+q
        22: 2q^3+q^2+q
        23: 2q^3+q^2+q
        24: q^4+q^3+q^2+q
        25: 2q^3+q^2+q
        26: 2q^3+q^2+q
        27: q^4+q^3+q^2+q
        28: q^4+2q^3+q^2+q
        29: q^4+2q^3+q^2+q
        30: q^4+q^3+q^2+q
        31: 2q^3+q^2+q
        32: q^3+q^2+q
        33: 2q^3+q^2+q
        34: 2q^3+q^2+q
        35: q^3+q^2+q
        36: 2q^3+q^2+q
        38: 2q^3+q^2+q
        40: 2q^3+q^2+q
        42: q^4+q^3+q^2+q
        43: q^4+q^3+q^2+q
        44: q^4+q^3+q^2+q
        45: q^3+q^2+q
        46: q^4+q^3+q^2+q
        47: q^3+q^2+q
        48: q^4+q^3+q^2+q
        49: q^4+2q^3+q^2+q
        50: q^4+2q^3+q^2+q
        51: q^5+2q^4+q^3+q^2+q
        52: 2q^3+q^2+q
        53: 2q^3+q^2+q
        54: q^4+q^3+q^2+q
        55: 2q^3+q^2+q
        56: 2q^3+q^2+q
        57: q^4+q^3+q^2+q
        58: q^3+q^2+q
        59: q^3
        60: q^3
        61: q^3+q^2+q
        63: 2q^3+q^2+q
        65: q^3+q^2+q
        67: 2q^3+q^2+q
        68: q^2+q
        69: q^4+q^3+q^2+q
        70: q^4+q^3+q^2+q
        71: q^4+2q^3+q^2+q
        72: 2q^3+q^2+q
        73: 2q^3+q^2+q
        75: 2q^3+q^2+q
        77: 2q^3+q^2+q
        79: q^4+q^3+q^2+q
        80: q^3+q^2+q
        81: q^3+q^2+q
        82: 2q^3+q^2+q
        83: q^3+q^2+q
        84: q^3+q^2+q
        85: q^3+q^2+q
        86: 2q^3+q^2+q
        87: q^3+q^2+q
        88: q^4+q^3+q^2+q
        89: q^3+q^2+q
        90: q^4+q^3+q^2+q
        91: q^4+q^3+q^2+q
        92: q^3+q^2+q
        93: q^4+q^3+q^2+q
        94: 2q^3+q^2+q
        95: 2q^3+q^2+q
        96: q^4+q^3+q^2+q
        97: 2q^3+q^2+q
        98: 2q^3+q^2+q
        99: q^4+q^3+q^2+q
       100: q^3+q^2+q
       101: q^3+q^2+q
       102: q^4+q^3+q^2+q
       104: q^3
       105: q^3+q^2+q
       107: q^3
       108: q^3+q^2+q
       109: q^3+q^2+q
       110: q^3
       112: 2q^3+q^2+q
       114: 2q^3+q^2+q
       116: q^3+q^2+q
       117: q^2+q
       120: q^2+q
       122: q^3+q^2+q
       124: q^3+q^2+q
       125: q^2+q
       126: q^4+q^3+q^2+q
       128: 2q^3+q^2+q
       130: 2q^3+q^2+q
       132: q^4+q^3+q^2+q
       133: q^2+q
       134: q^4+q^3+q^2+q
       135: q^3+q^2+q
       136: q^3+q^2+q
       137: q^3+q^2+q
       138: q^3+q^2+q
       139: 2q^3+q^2+q
       140: q^2+q
       141: q^3+q^2+q
       142: 2q^3+q^2+q
       143: q^3+q^2+q
       144: q^3+q^2+q
       145: 2q^3+q^2+q
       146: q^3+q^2+q
       147: 2q^3+q^2+q
       148: q^2+q
       149: q^3+q^2+q
       150: q^3+q^2+q
       152: q^3+q^2+q
       154: q^3+q^2+q
       156: q^4+q^3+q^2+q
       157: q^4+q^3+q^2+q
       158: q^3+q^2+q
       159: q^4+q^3+q^2+q
       160: q^3+q^2+q
       161: q^3+q^2+q
       162: q^3+q^2+q
       163: q^3+q^2+q
       164: q^3+q^2+q
       165: q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3
       171: q^3+q^2+q
       175: q^2+q
       178: q^3+q^2+q
       180: 2q^3+q^2+q
       182: 2q^3+q^2+q
       184: q^2+q
       185: q^2+q
       188: q^3+q^2+q
       190: q^3+q^2+q
       191: q^2+q
       194: q^2+q
       195: q^3+q^2+q
       196: q^3
       198: q^2+q
       200: q^2+q
       201: q^3
       202: q^3+q^2+q
       203: q^2+q
       206: q^2+q
       208: q^3+q^2+q
       210: q^3+q^2+q
       212: q^3+q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: q^2+q
       220: q^2+q
       221: q^4+q^3+q^2+q
       222: q^3+q^2+q
       223: q^3+q^2+q
       224: q^3+q^2+q
       225: q^3+q^2+q
       226: q^3+q^2+q
       227: q^2+q
       228: q^3+q^2+q
       229: q^2+q
       230: q^3+q^2+q
       231: q^3+q^2+q
       232: q^2+q
       233: q^3+q^2+q
       234: q^3+q^2+q
       235: q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: q^3+q^2+q
       251: q^3+q^2+q
       252: q^3+q^2+q
       253: q^3+q^2+q
       254: q^3+q^2+q
       255: q^3+q^2+q
       256: q^3+q
       257: q
       258: q^3+q
       260: q^3
       261: q^3+q^2+q
       265: q^2+q
       270: q^2+q
       272: q^2+q
       277: q^2+q
       280: q^2+q
       282: q^3+q^2+q
       284: q^2+q
       285: q^2+q
       288: q^3+q^2+q
       290: q^3+q^2+q
       292: q^3+q^2+q
       294: q^2+q
       295: q^2+q
       298: q^3+q^2+q
       300: q^2+q
       302: q^2+q
       303: q^2+q
       306: q^2+q
       308: q^2+q
       309: q^2+q
       312: q^2+q
       314: q^2+q
       316: q^3+q^2+q
       318: q^3+q^2+q
       320: q^2+q
       321: q^2+q
       324: q^2+q
       326: q^3+q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^3+q^2+q
       333: q^2+q
       334: q^3+q^2+q
       335: q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: q^2+q
       345: q^2+q
       346: q^3+q^2+q
       347: q^2+q
       348: q^2+q
       349: q^3+q^2+q
       350: q^3+q^2+q
       351: q^2+q
       352: q^2+q
       353: q^2+q
       354: q^3+q^2+q
       355: q^3+q^2+q
       356: q^3+q^2+q
       357: q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q
       363: q
       365: q^3+q
       366: q^3+q^2+q
       367: q
       368: q^3+q
       369: q
       370: q
       371: q^3+q
       372: q
       373: q^3+q
       374: q^3+q
       375: q
       376: q^3+q
       379: q^2+q
       383: q^2+q
       387: q^2+q
       392: q^2+q
       395: q^2+q
       398: q^2+q
       402: q^2+q
       408: q^2+q
       410: q^2+q
       412: q^3+q^2+q
       414: q^2+q
       416: q^3+q^2+q
       418: q^3+q^2+q
       420: q^2+q
       421: q^2+q
       424: q^3+q^2+q
       426: q^3+q^2+q
       428: q^3+q^2+q
       430: q^2+q
       431: q^2+q
       434: q^2+q
       436: q
       438: q^2+q
       439: q^2+q
       442: q^2+q
       444: q^2+q
       446: q^2+q
       448: q^2+q
       449: q^2+q
       452: q^2+q
       454: q^2+q
       456: q
       457: q^2+q
       460: q^2+q
       461: q^2+q
       464: q^2+q
       466: q
       468: q^3+q
       470: q^3+q^2+q
       472: q
       473: q
       476: q
       478: q^2+q
       480: q^2+q
       481: q^2+q
       482: q^2+q
       483: q^3+q^2+q
       484: q
       486: q^3+q
       488: q
       490: q^3+q
       491: q^3+q
       492: q^2+q
       493: q^2+q
       494: q^3+q^2+q
       495: q^2+q
       496: q
       497: q^2+q
       498: q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q
       503: q^3+q
       505: q
       507: q^3+q
       508: q
       509: q
       510: q^3+q
       511: q
       512: q
       513: q
       514: q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q
       519: q
       520: q^3+q
       523: q^2+q
       527: q^2+q
       531: q^2+q
       535: q^2+q
       540: q
       544: q^2+q
       548: q^2+q
       550: q^2+q
       554: q
       558: q^2+q
       562: q^2+q
       567: q
       572: q^2+q
       576: q^2+q
       581: q^2+q
       584: q^2+q
       586: q^2+q
       588: q^3+q^2+q
       590: q^2+q
       591: q^2+q
       594: q^2+q
       595: q^2+q
       598: q^3+q
       600: q^3+q^2+q
       602: q
       604: q^2+q
       606: q
       607: q^2+q
       610: q^2+q
       612: q
       614: q^2+q
       616: q
       618: q
       620: q^2+q
       621: q^2+q
       624: q
       626: q^2+q
       628: q
       630: q^2+q
       631: q
       634: q
       636: q
       638: q^3+q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: 2q
       654: q
       656: q
       657: q
       659: q^3+q
       661: q
       663: q^3+q
       664: q^3+q
       665: q
       667: q^3+q
       669: q
       671: q^3+q
       672: q
       673: q^3+q
       674: q
       675: q
       676: q^2+q
       677: q^2+q
       678: q
       679: q
       680: q
       681: q^2+q
       682: q
       683: q^2+q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       700: q^2+q
       707: q^2+q
       711: q^2+q
       714: q^2+q
       719: q^2+q
       724: q
       728: q^2+q
       732: q
       736: q
       738: q
       742: q^2+q
       746: q
       750: q
       755: q
       760: 2q
       764: q
       767: q
       773: q
       774: q
       776: q
       778: q^2+q
       780: q^3+q
       782: q
       784: q^3+q
       786: q
       787: q
       790: q
       792: q
       794: q
       796: q
       798: q
       800: q
       802: q
       803: q
       806: q^2+q
       807: q^2+q
       810: q
       812: q^2+q
       814: q
       816: q
       817: q
       820: q
       822: q
       824: q
       826: q^2+q
       827: q^2+q
       830: q
       831: q
       834: q
       836: q^2+q
       838: q
       839: q
       842: q
       844: q
       846: q
       847: q
       850: 2q
       852: q
       854: 2q
       856: q
       858: q
       860: q^3+q
       862: q
       864: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q
       869: q
       870: q
       871: q
       872: q
       873: q
       874: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       891: q
       895: q
       898: q^2+q
       901: q
       907: q
       910: q
       915: q
       919: q
       923: q
       925: q
       931: q^2+q
       935: q
       937: q
       941: q
       945: q
       949: q^2+q
       954: q
       957: q
       963: 2q
       966: q
       972: q
       973: q
       977: q
       981: 2q
       986: q
       987: q
       990: q
       993: q
       995: q
       997: q^3+q
       998: q
      1001: q
      1003: q
      1005: q
      1006: q
      1009: q
      1011: 2q
      1013: q
      1015: q
      1017: q
      1019: q
      1021: q
      1023: q
      1025: q
      1027: q
      1028: q
      1031: q
      1032: q
      1035: q
      1037: q
      1039: q
      1041: q
      1043: q
      1044: q
      1047: q
      1049: q
      1051: 2q
      1053: q
      1054: q
      1057: q
      1058: q
      1061: q
      1063: q
      1065: q
      1074: q
      1076: q
      1077: q
      1078: q
      1080: q
      1081: q
      1082: q
      1084: q
      1085: q
      1093: q
      1097: q
      1105: q
      1109: q
      1111: q
      1115: q
      1121: q
      1125: q
      1129: 2q
      1132: q
      1137: q
      1142: q
      1143: q
      1147: q
      1151: q
      1153: q
      1159: q
      1161: q
      1165: q
      1169: q
      1173: q
      1179: q
      1182: q
      1187: 2q
      1192: q
      1193: q
      1196: q
      1201: q
      1203: q
      1209: q
      1215: q
      1216: q
      1219: q
      1221: q
      1223: 2q
      1225: q
      1231: q
      1232: q
      1235: q
      1237: q
      1239: q
      1241: q
      1242: q
      1249: q
      1250: q
      1253: q
      1255: q
      1257: q
      1259: q
      1260: q
      1265: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1283: q
      1285: q
      1288: q
      1297: q
      1301: q
      1309: q
      1313: q
      1315: q
      1321: q
      1325: 2q
      1328: q
      1333: q
      1338: q
      1339: q
      1345: q
      1349: q
      1355: q
      1359: q
      1362: q
      1365: q
      1370: q
      1377: q
      1381: q
      1387: q
      1391: q
      1395: q
      1398: q
      1403: q
      1417: q
      1434: q
      1437: q
      1447: q
      1449: q
      1450: q
      1455: q
      1457: q
      1460: q
      1463: q
      1473: q
      1481: q
      1483: q
      1496: q
      1500: q
      1507: q
      1520: q
      1540: q
      1562: q
      1564: q
      1570: q
      1573: q
      1576: q
      1584: q
      1590: q
      1594: q
      1597: q
      1621: 1
      1635: q
      1638: q
      1693: q
      1706: q
      1721: 1
      1732: q
      1795: 1
      1810: 1
      1880: 1
      1893: 1
      1947: 1
      1951: 1
      2013: 1
      2025: 1
      2059: 1
      2127: 1

2128:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: 1
        11: 1
        12: 1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: 1
        38: q^2
        39: 1
        40: q^2
        41: 1
        42: q^2
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        58: 1
        60: 1
        62: 1
        64: 1
        65: q^2
        66: 1
        67: q^2
        68: 1
        69: q^2+1
        70: 1
        71: 1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2
        76: 1
        77: q^2
        78: 1
        79: q^2
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        85: q^2+1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: 1
       107: 1
       109: 1
       111: 1
       112: q^2
       113: 1
       115: 1
       116: q^2
       117: 1
       119: 1
       121: 1
       123: 1
       124: q^2
       125: 1
       126: 1
       127: 1
       128: q^2
       129: 1
       130: q^2
       131: 1
       132: q^2
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: 1
       140: q^2+1
       141: 1
       142: q^2+1
       143: 1
       144: q^2+1
       145: 1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: 1
       152: q^2
       153: 1
       154: q^2
       155: 1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: q^2+1
       169: 1
       173: 1
       177: 1
       178: q^2
       179: 1
       181: 1
       182: q^2
       183: 1
       185: 1
       187: 1
       188: q^2
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       198: q^2
       199: 1
       201: 1
       203: 1
       205: 1
       206: q^2
       207: 1
       209: 1
       211: 1
       212: q^2
       213: 1
       214: q^2
       215: 1
       216: q^2
       217: 1
       218: q^2
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: 1
       238: q^2
       239: 1
       240: q^2
       241: 1
       242: q^2
       243: 1
       244: q^2+1
       245: q^2+1
       246: 1
       247: q^2+1
       248: q^2+1
       249: q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       282: q^2
       283: 1
       285: 1
       287: 1
       289: 1
       290: q^2
       291: 1
       292: q^2
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       302: q^2
       303: 1
       305: 1
       306: q^2
       307: 1
       309: 1
       311: 1
       312: q^2
       313: 1
       314: q^2
       315: 1
       316: q^2
       317: 1
       319: 1
       321: 1
       323: 1
       324: q^2
       325: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: 1
       338: 1
       339: q^2
       340: 1
       341: q^2
       342: 1
       343: q^2
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^2+1
       360: 1
       361: q^2
       362: 1
       363: q^2
       364: 1
       365: q^2
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       413: 1
       417: 1
       418: q^2
       419: 1
       421: 1
       423: 1
       425: 1
       426: q^2
       427: 1
       429: 1
       431: 1
       433: 1
       434: q^2
       435: 1
       436: q^2
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       446: q^2
       447: 1
       449: 1
       451: 1
       452: q^2
       453: 1
       455: 1
       456: q^2
       457: 1
       459: 1
       461: 1
       463: 1
       464: q^2
       465: 1
       467: 1
       468: q^2
       469: 1
       471: 1
       473: 1
       475: 1
       476: q^2
       477: 1
       478: q^2
       479: 1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q^2
       487: 1
       488: q^2
       489: 1
       490: q^2
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       521: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       581: q^2
       585: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       598: q^2
       599: 1
       601: 1
       603: 1
       605: 1
       606: q^2
       607: 1
       609: 1
       613: 1
       614: q^2
       615: 1
       617: 1
       618: q^2
       619: 1
       621: 1
       623: 1
       624: q^2
       625: 1
       629: 1
       630: q^2
       631: 1
       633: 1
       634: q^2
       639: 1
       641: 1
       643: 1
       645: 1
       646: q^2
       647: 1
       649: 1
       651: 1
       652: q^2
       653: 1
       655: 1
       656: q^2
       657: 1
       658: 1
       659: q^2
       660: 1
       661: q^2
       662: 1
       663: q^2
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       693: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       733: 1
       737: 1
       741: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       773: q^2
       775: 1
       779: 1
       780: q^2
       781: 1
       785: 1
       787: 1
       791: 1
       792: q^2
       793: 1
       795: 1
       796: q^2
       797: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       810: q^2
       811: 1
       815: 1
       817: 1
       819: 1
       820: q^2
       821: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       834: q^2
       835: 1
       839: 1
       843: 1
       844: q^2
       845: 1
       847: 1
       849: 1
       850: q^2
       851: 1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: 1
       884: 1
       900: 1
       904: 1
       908: 1
       916: 1
       920: 1
       924: 1
       928: 1
       940: 1
       944: 1
       948: 1
       952: 1
       960: 1
       964: 1
       968: 1
       972: q^2
       974: 1
       988: 1
       994: 1
       998: 1
      1000: 1
      1004: 1
      1006: 1
      1008: 1
      1010: 1
      1011: q^2
      1012: 1
      1013: q^2
      1016: 1
      1020: 1
      1021: q^2
      1022: 1
      1026: 1
      1028: 1
      1032: 1
      1036: 1
      1037: q^2
      1038: 1
      1040: 1
      1044: 1
      1046: 1
      1048: 1
      1052: 1
      1054: 1
      1056: 1
      1058: 1
      1060: 1
      1061: q^2
      1062: 1
      1064: 1
      1065: q^2
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1086: 1
      1114: 1
      1122: 1
      1126: 1
      1130: 1
      1134: 1
      1138: 1
      1142: q^2
      1152: 1
      1156: 1
      1160: 1
      1172: 1
      1176: 1
      1180: 1
      1194: 1
      1198: 1
      1202: 1
      1206: 1
      1216: 1
      1218: 1
      1220: 1
      1224: 1
      1228: 1
      1230: 1
      1232: 1
      1234: 1
      1240: 1
      1242: 1
      1246: 1
      1248: 1
      1250: 1
      1254: 1
      1258: 1
      1260: 1
      1262: 1
      1266: 1
      1268: 1
      1270: 1
      1274: 1
      1275: q^2
      1276: 1
      1278: 1
      1279: q^2
      1280: 1
      1281: q^2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1326: 1
      1330: 1
      1348: 1
      1356: 1
      1360: 1
      1364: 1
      1368: 1
      1380: 1
      1388: 1
      1392: 1
      1396: 1
      1400: 1
      1410: 1
      1418: 1
      1422: 1
      1426: 1
      1430: 1
      1434: q^2
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1450: 1
      1454: 1
      1460: 1
      1462: 1
      1464: 1
      1466: 1
      1468: 1
      1474: 1
      1476: 1
      1478: 1
      1482: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1501: 1
      1513: 1
      1537: 1
      1549: 1
      1575: 1
      1579: 1
      1595: 1
      1599: 1
      1607: 1
      1615: 1
      1619: 1
      1623: 1
      1627: 1
      1639: 1
      1641: 1
      1645: 1
      1647: 1
      1649: 1
      1653: 1
      1655: 1
      1657: 1
      1659: 1
      1663: 1
      1665: 1
      1669: 1
      1673: 1
      1674: 1
      1711: 1
      1733: 1
      1741: 1
      1749: 1
      1757: 1
      1769: 1
      1773: 1
      1781: 1
      1797: 1
      1807: 1
      1811: 1
      1817: 1
      1819: 1
      1821: 1
      1825: 1
      1829: 1
      1831: 1
      1833: 1
      1882: 1
      1898: 1
      1906: 1
      1914: 1
      1922: 1
      1940: 1
      1944: 1
      1952: 1
      1960: 1
      1962: 1
      1964: 1
      2014: 1
      2040: 1
      2052: 1
      2060: 1
      2064: 1
      2128: 1

2129:    0: 3q^3+4q^2+3q
         1: 3q^3+4q^2+3q
         2: 3q^3+4q^2+3q
         3: 3q^3+4q^2+3q
         4: q^4+3q^3+3q^2+3q
         5: 3q^3+4q^2+3q
         6: q^4+3q^3+3q^2+3q
         7: q^4+3q^3+3q^2+3q
         8: 3q^3+4q^2+3q
         9: q^4+3q^3+3q^2+3q
        10: 4q^2+3q
        11: 4q^2+3q
        12: q^3+3q^2+3q
        13: 3q^3+4q^2+3q
        14: q^4+3q^3+3q^2+3q
        15: 3q^3+4q^2+3q
        16: 3q^3+4q^2+3q
        17: 3q^3+4q^2+3q
        18: q^4+3q^3+3q^2+3q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 3q^3+4q^2+3q
        23: 3q^3+4q^2+3q
        24: 3q^3+4q^2+3q
        25: 3q^3+4q^2+3q
        26: 3q^3+4q^2+3q
        27: 3q^3+4q^2+3q
        28: 4q^2+3q
        29: 3q^2+3q
        30: 2q^3+3q^2+3q
        31: 4q^2+3q
        32: 3q^3+4q^2+3q
        33: 3q^3+4q^2+3q
        34: 4q^2+3q
        35: 3q^3+4q^2+3q
        36: 3q^3+4q^2+3q
        37: 2q^3+2q^2+q
        38: q^3+2q^2+2q
        39: 2q^3+2q^2+q
        40: q^3+2q^2+2q
        41: 2q^3+2q^2+q
        42: q^3+2q^2+2q
        43: 4q^2+3q
        44: q^3+3q^2+3q
        45: 4q^2+3q
        46: 3q^3+4q^2+3q
        47: 3q^3+4q^2+3q
        48: q^4+3q^3+3q^2+3q
        49: 2q^3+3q^2+3q
        50: 2q^3+3q^2+3q
        51: 2q^3+3q^2+3q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: 3q^2+2q
        59: q^2+q
        60: 3q^2+2q
        61: q^2+q
        62: 2q^2+q
        63: 2q^2+2q
        64: 2q^3+2q^2+q
        65: q^3+2q^2+2q
        66: 2q^3+2q^2+q
        67: q^3+2q^2+2q
        68: 4q^2+3q
        69: 2q^3+3q^2+3q
        70: 3q^2+3q
        71: 3q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^3+q^2+q
        75: q^2+2q
        76: q^3+q^2+q
        77: q^2+2q
        78: q^3+q^2+q
        79: q^2+2q
        80: 4q^2+3q
        81: 3q^3+4q^2+3q
        82: 3q^2+3q
        83: 2q^3+3q^2+3q
        84: 4q^2+3q
        85: 3q^3+4q^2+3q
        86: 3q^2+3q
        87: 2q^3+3q^2+3q
        88: 4q^2+3q
        89: 4q^2+3q
        90: q^3+3q^2+3q
        91: 2q^3+3q^2+3q
        92: 2q^3+3q^2+3q
        93: 2q^3+3q^2+3q
        94: 2q^3+3q^2+3q
        95: 2q^3+3q^2+3q
        96: 2q^3+3q^2+3q
        97: 2q^3+3q^2+3q
        98: 2q^3+3q^2+3q
        99: 2q^3+3q^2+3q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: 2q^2+q
       104: q^2+q
       105: q^2+q
       107: 2q^2+2q
       108: q
       109: 2q^2+2q
       110: q
       111: q^2+q
       112: 2q
       113: q^2+q
       114: q^2+2q
       115: q^3+q^2+q
       116: q^2+2q
       117: 3q^2+2q
       118: q^2+q
       119: 3q^2+2q
       120: q^2+q
       121: 2q^2+q
       122: 2q^2+2q
       123: 2q^3+2q^2+q
       124: q^3+2q^2+2q
       125: 4q^2+3q
       126: 3q^2+3q
       127: q^3+q^2+q
       128: q^2+2q
       129: q^3+q^2+q
       130: q^2+2q
       131: q^3+q^2+q
       132: q^2+2q
       133: 3q^2+3q
       134: 2q^3+3q^2+3q
       135: q^3+2q^2+3q
       136: q^3+2q^2+3q
       137: 4q^2+3q
       138: 2q^3+3q^2+3q
       139: 3q^2+3q
       140: q^3+2q^2+3q
       141: 3q^2+3q
       142: q^3+2q^2+3q
       143: 4q^2+3q
       144: 2q^3+3q^2+3q
       145: 3q^2+3q
       146: 3q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: 3q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+q^2+q
       152: q^2+2q
       153: q^3+q^2+q
       154: q^2+2q
       155: q^3+q^2+q
       156: q^2+2q
       157: 2q^2+3q
       158: 2q^2+3q
       159: 2q^2+3q
       160: 2q^3+3q^2+3q
       161: 2q^3+3q^2+3q
       162: 2q^3+3q^2+3q
       163: 2q^3+3q^2+3q
       164: 2q^3+3q^2+3q
       165: 2q^3+3q^2+3q
       166: 2q^3+3q^2+3q
       167: 2q^3+3q^2+3q
       168: 2q^3+3q^2+3q
       169: q^2+q
       170: q
       171: q
       173: 2q^2+q
       174: q^2+q
       175: q^2+q
       177: q^3+q^2+q
       178: q^2+2q
       179: q^2+q
       180: q^2+2q
       181: q^2+q
       182: 2q
       183: 2q^2+2q
       184: q
       185: 2q^2+2q
       186: q
       187: q^2+q
       188: 2q
       189: q^2+q
       190: q^2+2q
       191: 3q^2+2q
       192: q^2+q
       193: 2q^2+2q
       194: q
       195: 2q^2+2q
       196: q
       197: q^2+q
       198: 2q
       199: 3q^2+2q
       200: q^2+q
       201: 2q^2+2q
       202: q
       203: 2q^2+2q
       204: q
       205: q^2+q
       206: 2q
       207: 2q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: q^2+2q
       211: q^3+q^2+q
       212: q^2+2q
       213: q^3+q^2+q
       214: q^2+2q
       215: q^3+q^2+q
       216: q^2+2q
       217: q^3+q^2+q
       218: q^2+2q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 2q^2+3q
       222: q^2+3q
       223: q^3+2q^2+3q
       224: q^2+3q
       225: q^3+2q^2+3q
       226: 3q^2+3q
       227: 3q^2+3q
       228: 2q^3+3q^2+3q
       229: q^3+2q^2+3q
       230: q^3+2q^2+3q
       231: 3q^2+3q
       232: 3q^2+3q
       233: 2q^3+3q^2+3q
       234: q^3+2q^2+3q
       235: q^3+2q^2+3q
       236: 2q^3+3q^2+3q
       237: q^3+q^2+q
       238: q^2+2q
       239: q^3+q^2+q
       240: q^2+2q
       241: q^3+q^2+q
       242: q^2+2q
       243: 3q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: 3q^2+3q
       247: 2q^2+4q
       248: 2q^2+4q
       249: q^3+2q^2+3q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+3q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+3q
       256: 2q^3+3q^2+3q
       257: 2q^3+3q^2+3q
       258: 2q^3+3q^2+3q
       259: q^2+q
       260: q
       261: q
       263: q^2+q
       264: q
       265: q
       267: q^2+q
       268: q
       270: q
       271: q^2+q
       272: q
       274: q
       275: 2q^2+q
       276: q^2+q
       277: q^2+q
       279: q^2+q
       280: q^2+2q
       281: q^3+q^2+q
       282: q^2+2q
       283: 2q^2+2q
       284: q
       285: 2q^2+2q
       286: q
       287: q^2+q
       288: q^2+2q
       289: q^2+q
       290: 2q
       291: q^2+q
       292: 2q
       293: q^2+2q
       294: q
       295: q^2+2q
       296: q
       297: q
       298: 2q
       299: 2q^2+2q
       300: q
       301: q^2+q
       302: 2q
       303: 2q^2+2q
       304: q
       305: q^2+q
       306: 2q
       307: 2q^2+2q
       308: q
       309: 2q^2+2q
       310: q
       311: q^2+q
       312: 2q
       313: q^2+q
       314: 2q
       315: q^3+q^2+q
       316: q^2+2q
       317: q^2+q
       318: q^2+2q
       319: 2q^2+2q
       320: q
       321: 2q^2+2q
       322: q
       323: q^2+q
       324: 2q
       325: q^2+q
       326: q^2+2q
       333: 2q^2+3q
       334: q^2+3q
       335: q^2+3q
       336: q^2+3q
       337: q^2+4q
       338: 2q^2+q
       339: 3q
       340: 2q^2+q
       341: 3q
       342: q^3+q^2+q
       343: q^2+2q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 2q^2+3q
       347: q^2+3q
       348: q^3+2q^2+3q
       349: q^2+3q
       350: q^3+2q^2+3q
       351: 2q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 2q^2+3q
       355: q^2+3q
       356: q^3+2q^2+3q
       357: q^2+3q
       358: q^3+2q^2+3q
       359: 2q^2+4q
       360: q^3+q^2+q
       361: q^2+2q
       362: q^3+q^2+q
       363: q^2+2q
       364: q^3+q^2+q
       365: q^2+2q
       366: 3q^2+3q
       367: 3q^2+3q
       368: 2q^3+3q^2+3q
       369: q^3+2q^2+3q
       370: q^3+2q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+3q
       377: q^2+q
       378: q
       379: q
       381: q^2+q
       382: q
       383: q
       385: q
       386: q
       387: q
       389: q^2+q
       390: q
       392: q
       393: q^2+q
       394: q
       395: q
       397: q^2+q
       398: q
       400: q
       401: q^2+q
       402: q
       403: q
       405: q^2+q
       407: q
       408: q
       413: q^2+q
       414: q^2+2q
       417: q^2+q
       418: 2q
       419: q^2+2q
       420: q
       421: q^2+2q
       422: q
       423: q
       424: 2q
       425: q^2+q
       426: 2q
       427: q^2+q
       428: 3q
       429: 2q^2+2q
       430: q
       431: 2q^2+2q
       432: q
       433: q^2+q
       434: 2q
       435: q^2+q
       436: 2q
       437: q^2+2q
       438: q
       439: q^2+2q
       440: q
       441: q
       442: 2q
       443: q^2+3q
       444: q
       445: 2q^2+q
       446: 3q
       447: 2q^2+2q
       448: q
       449: 2q^2+2q
       450: q
       451: q^2+q
       452: 2q
       453: q^2+2q
       454: q
       455: q^2+q
       456: 2q
       457: q^2+2q
       458: q
       459: q
       460: 2q
       461: q^2+3q
       462: q
       463: 2q^2+q
       464: 3q
       465: q^2+q
       466: q^2+2q
       467: q^3+q^2+q
       468: q^2+2q
       469: q^2+q
       470: q^2+2q
       471: 2q^2+2q
       472: q
       473: 2q^2+2q
       474: q
       475: q^2+q
       476: 2q
       477: q^2+q
       478: 2q
       479: q^2+2q
       480: q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: 3q
       484: q^2+4q
       485: 2q^2+q
       486: 3q
       487: 2q^2+q
       488: 3q
       489: q^3+q^2+q
       490: q^2+2q
       491: q^2+3q
       492: 2q^2+3q
       493: q^2+3q
       494: q^2+3q
       495: q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: q^2+3q
       499: q^2+3q
       500: q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 2q^2+3q
       511: q^2+3q
       512: q^3+2q^2+3q
       513: q^2+3q
       514: q^3+2q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q^2+q
       522: q
       523: q
       529: q
       530: q
       531: q
       533: q^2+q
       534: q
       535: q
       537: q^2+q
       538: q
       540: q
       541: q
       542: q
       544: q
       545: q^2+q
       546: 2q
       548: q
       549: q^2+q
       550: q
       551: q
       553: q^2+q
       554: q
       556: q
       557: q
       558: q
       560: q
       561: q^2+q
       562: 2q
       564: q
       565: q^2+q
       566: q
       567: q
       569: q^2+q
       571: q
       572: q
       573: q^2+2q
       574: q
       576: q
       577: q^2+q
       578: q
       580: q^2
       581: 2q
       585: q
       586: 2q
       589: q^2+2q
       590: q
       591: 2q
       593: 2q
       595: q^2+2q
       596: q
       597: q^2+q
       598: 2q
       599: q
       600: 2q
       601: q^2+q
       602: 3q
       603: q^2+2q
       604: q
       605: q^2+q
       606: 2q
       607: q^2+2q
       608: q
       609: q
       610: 2q
       613: q^2+q
       614: 2q
       615: q^2+3q
       616: q
       617: 2q^2+q
       618: 3q
       619: q^2+2q
       620: q
       621: q^2+2q
       622: q
       623: q^2+q
       624: 2q
       625: q
       626: 2q
       629: q^2+q
       630: 2q
       631: q^2+3q
       632: q
       633: 2q^2+q
       634: 3q
       639: q^2+q
       640: q^2+2q
       641: 2q^2+2q
       642: q
       643: 2q^2+2q
       644: q
       645: q^2+q
       646: 2q
       647: q^2+2q
       648: q
       649: q^2+2q
       650: q
       651: q^2+q
       652: 2q
       653: q
       654: 2q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 2q^2+q
       659: 3q
       660: 2q^2+q
       661: 3q
       662: q^3+q^2+q
       663: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: 3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: 3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: q^2+3q
       688: q^2+3q
       689: q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q^2+q
       694: q
       699: q
       700: q
       709: q
       710: q
       711: q
       713: q
       714: q
       717: q
       718: q
       721: q^2+q
       722: q
       724: q
       725: q
       726: q
       728: q
       733: q^2+q
       734: 2q
       736: q
       737: q^2+q
       738: q
       740: q
       741: q
       742: q
       744: q
       749: q^2+q
       750: 2q
       752: q
       753: q^2+q
       754: q
       755: q
       757: q^2+q
       759: q
       760: q
       761: q
       763: q
       764: q
       765: q^2+2q
       766: q
       767: q
       769: q^2+q
       770: q
       772: q^2
       773: 2q
       775: q^2+q
       776: 3q
       779: q^2+q
       780: 2q
       781: q
       782: 2q
       785: 2q
       787: 2q
       791: q
       792: q
       793: q^2+3q
       794: q
       795: 2q^2+q
       796: 3q
       797: q
       798: 2q
       801: q^2+2q
       802: q
       803: 2q
       805: 2q
       807: q^2+2q
       808: q
       809: q^2+q
       810: 2q
       811: q
       812: 2q
       815: 2q
       816: q
       817: q^2+3q
       818: q
       819: 2q^2+q
       820: 3q
       821: q
       822: 2q
       825: q^2+2q
       826: q
       827: 2q
       829: 2q
       831: q^2+2q
       832: q
       833: q^2+q
       834: 2q
       835: q
       836: 2q
       839: 2q
       840: q
       843: q^2+2q
       844: q^2+2q
       845: q^2+2q
       846: q
       847: q^2+2q
       848: q
       849: q^2+q
       850: 2q
       851: q
       852: 2q
       855: q^2+q
       856: 2q
       857: q
       858: 2q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: 3q
       880: q^2+3q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q^2+q
       885: q
       890: q
       891: q
       900: q
       901: q
       904: q
       905: q
       908: q
       916: q^2+q
       917: 2q
       919: q
       920: q
       921: q
       923: q
       924: q
       925: q
       928: q
       929: q
       940: q^2+q
       941: 2q
       943: q
       944: q
       945: q
       947: q
       948: q
       949: q
       952: q
       953: q
       960: q^2+q
       962: q
       963: q
       964: q^2+2q
       965: q
       966: q
       968: q^2+q
       969: q
       971: q^2
       972: 2q
       974: q
       976: q
       977: q
       988: q
       989: q
       990: q
       994: q
       995: 2q
       998: 2q
      1000: 2q
      1004: q
      1006: q
      1009: q
      1010: q
      1011: q
      1012: q
      1013: q
      1016: 2q
      1017: q
      1020: q^2+q
      1021: 2q
      1022: q
      1023: 2q
      1026: 2q
      1028: 2q
      1032: 2q
      1033: q
      1036: q^2+q
      1037: 2q
      1038: q
      1039: 2q
      1040: 2q
      1044: 2q
      1046: q
      1047: 2q
      1048: q
      1049: 2q
      1052: q^2+2q
      1053: q
      1054: 2q
      1056: 2q
      1058: q^2+2q
      1059: q
      1060: q^2+q
      1061: 2q
      1062: q
      1063: 2q
      1064: q
      1065: q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 3q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1086: q^2+q
      1087: q
      1092: q
      1093: q
      1114: q
      1115: q
      1122: q
      1123: q
      1126: q
      1130: q
      1138: q
      1142: q
      1152: q
      1153: q
      1156: q
      1157: q
      1160: q
      1172: q
      1173: q
      1176: q
      1177: q
      1180: q
      1194: q
      1195: q
      1196: q
      1198: q
      1200: q
      1201: q
      1202: q
      1203: q
      1206: q
      1207: q
      1216: q
      1218: q
      1221: q
      1225: q
      1228: 2q
      1229: q
      1230: q
      1231: 2q
      1232: 2q
      1234: 2q
      1240: q
      1242: q
      1246: 2q
      1247: q
      1248: q
      1249: 2q
      1250: 2q
      1254: 2q
      1258: q
      1260: q
      1262: q
      1263: 2q
      1266: q
      1267: 2q
      1268: 2q
      1270: 2q
      1274: q^2+q
      1275: 2q
      1277: q
      1278: q
      1279: q
      1280: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1290: q
      1348: q
      1349: q
      1356: q
      1357: q
      1360: q
      1364: q
      1380: q
      1381: q
      1388: q
      1389: q
      1392: q
      1396: q
      1410: q
      1411: q
      1412: q
      1418: q
      1419: q
      1422: q
      1423: q
      1426: q
      1430: q
      1434: q
      1437: q
      1440: q
      1442: q
      1445: q
      1450: q
      1454: q
      1460: q
      1462: q
      1464: q
      1465: 2q
      1466: 2q
      1468: 2q
      1475: q
      1476: q
      1478: q
      1483: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1501: q
      1513: q
      1607: q
      1608: q
      1615: q
      1616: q
      1619: q
      1623: q
      1640: q
      1642: 1
      1645: q
      1647: q
      1649: 1
      1653: q
      1655: q
      1657: 1
      1660: q
      1663: q
      1665: q
      1670: q
      1673: 1
      1674: 2q
      1711: q
      1758: 1
      1782: 1
      1811: 1
      1818: 1
      1819: 1
      1821: 1
      1826: q
      1829: q
      1831: q
      1833: 1
      1883: 1
      1908: 1
      1924: 1
      1952: 1
      1961: 1
      1962: 1
      1964: 1
      2018: 1
      2041: 1
      2053: 1
      2064: 1
      2129: 1

2130:    0: 5q^5+10q^4+7q^3+q^2+q
         1: q^6+7q^5+10q^4+7q^3+q^2+q
         2: 5q^5+10q^4+7q^3+q^2+q
         3: 5q^5+10q^4+7q^3+q^2+q
         4: 5q^5+10q^4+7q^3+q^2+q
         5: 5q^5+10q^4+7q^3+q^2+q
         6: q^6+7q^5+10q^4+7q^3+q^2+q
         7: 5q^5+10q^4+7q^3+q^2+q
         8: 5q^5+10q^4+7q^3+q^2+q
         9: 3q^6+7q^5+7q^4+5q^3+q^2+q
        10: q^5+5q^4+6q^3+q^2+q
        11: 5q^4+6q^3+q^2+q
        12: q^5+5q^4+6q^3+q^2+q
        13: 5q^5+10q^4+7q^3+q^2+q
        14: 5q^5+10q^4+7q^3+q^2+q
        15: 5q^5+10q^4+7q^3+q^2+q
        16: 2q^5+8q^4+7q^3+q^2+q
        17: 3q^5+8q^4+7q^3+q^2+q
        18: 5q^5+7q^4+5q^3+q^2+q
        19: 5q^5+10q^4+7q^3+q^2+q
        20: q^6+7q^5+10q^4+7q^3+q^2+q
        21: 5q^5+10q^4+7q^3+q^2+q
        22: 2q^5+8q^4+7q^3+q^2+q
        23: 3q^5+8q^4+7q^3+q^2+q
        24: 2q^5+8q^4+7q^3+q^2+q
        25: 2q^5+8q^4+7q^3+q^2+q
        26: 3q^5+8q^4+7q^3+q^2+q
        27: 2q^5+8q^4+7q^3+q^2+q
        28: 3q^4+6q^3+q^2+q
        29: q^5+5q^4+6q^3+q^2+q
        30: 5q^5+10q^4+7q^3+q^2+q
        31: 3q^4+6q^3+q^2+q
        32: 2q^5+8q^4+7q^3+q^2+q
        33: q^5+6q^4+7q^3+q^2+q
        34: 3q^4+6q^3+q^2+q
        35: 2q^5+8q^4+7q^3+q^2+q
        36: q^5+6q^4+7q^3+q^2+q
        37: 3q^4+4q^3+q^2+q
        38: 4q^4+3q^3
        39: 3q^4+4q^3+q^2+q
        40: q^5+4q^4+3q^3
        41: 3q^4+4q^3+q^2+q
        42: 4q^4+3q^3
        43: q^5+5q^4+6q^3+q^2+q
        44: q^5+5q^4+6q^3+q^2+q
        45: 5q^4+6q^3+q^2+q
        46: 2q^5+8q^4+7q^3+q^2+q
        47: 3q^5+8q^4+7q^3+q^2+q
        48: 5q^5+7q^4+5q^3+q^2+q
        49: 2q^5+8q^4+7q^3+q^2+q
        50: 3q^5+8q^4+7q^3+q^2+q
        51: 5q^5+7q^4+5q^3+q^2+q
        52: 2q^5+8q^4+7q^3+q^2+q
        53: 3q^5+8q^4+7q^3+q^2+q
        54: 2q^5+8q^4+7q^3+q^2+q
        55: 2q^5+8q^4+7q^3+q^2+q
        56: 3q^5+8q^4+7q^3+q^2+q
        57: 2q^5+8q^4+7q^3+q^2+q
        58: q^4+4q^3+q^2+q
        59: 2q^3
        60: q^4+4q^3+q^2+q
        61: 2q^3
        62: q^4+4q^3+q^2+q
        63: q^4+2q^3
        64: 3q^4+4q^3+q^2+q
        65: 4q^4+3q^3
        66: 2q^4+4q^3+q^2+q
        67: 3q^4+3q^3
        68: 3q^4+6q^3+q^2+q
        69: 2q^5+5q^4+5q^3+q^2+q
        70: q^5+5q^4+6q^3+q^2+q
        71: 3q^4+6q^3+q^2+q
        72: q^5+6q^4+7q^3+q^2+q
        73: q^5+6q^4+7q^3+q^2+q
        74: 3q^4+4q^3+q^2+q
        75: 4q^4+3q^3
        76: 3q^4+4q^3+q^2+q
        77: q^5+4q^4+3q^3
        78: 3q^4+4q^3+q^2+q
        79: 4q^4+3q^3
        80: 3q^4+6q^3+q^2+q
        81: q^5+6q^4+7q^3+q^2+q
        82: 3q^4+6q^3+q^2+q
        83: 2q^5+8q^4+7q^3+q^2+q
        84: 3q^4+6q^3+q^2+q
        85: q^5+6q^4+7q^3+q^2+q
        86: 3q^4+6q^3+q^2+q
        87: 2q^5+8q^4+7q^3+q^2+q
        88: q^4+6q^3+q^2+q
        89: q^4+6q^3+q^2+q
        90: q^5+3q^4+4q^3+q^2+q
        91: 2q^5+8q^4+7q^3+q^2+q
        92: 3q^5+8q^4+7q^3+q^2+q
        93: 5q^5+7q^4+5q^3+q^2+q
        94: q^5+5q^4+7q^3+q^2+q
        95: q^5+5q^4+7q^3+q^2+q
        96: 2q^5+5q^4+5q^3+q^2+q
        97: q^5+5q^4+7q^3+q^2+q
        98: q^5+5q^4+7q^3+q^2+q
        99: 2q^5+5q^4+5q^3+q^2+q
       100: 6q^4+6q^3+q^2+q
       101: q^5+7q^4+6q^3+q^2+q
       102: 6q^4+6q^3+q^2+q
       103: 3q^3+q^2+q
       104: q^3
       105: q^3
       106: q^3
       107: q^4+4q^3+q^2+q
       108: 2q^3
       109: q^4+4q^3+q^2+q
       110: 2q^3
       111: 2q^4+4q^3+q^2+q
       112: 3q^4+3q^3
       113: q^4+4q^3+q^2+q
       114: q^4+2q^3
       115: 3q^4+4q^3+q^2+q
       116: 4q^4+3q^3
       117: q^4+4q^3+q^2+q
       118: 2q^3
       119: q^4+4q^3+q^2+q
       120: 2q^3
       121: q^4+4q^3+q^2+q
       122: q^4+2q^3
       123: 2q^4+4q^3+q^2+q
       124: 3q^4+3q^3
       125: q^4+6q^3+q^2+q
       126: q^4+4q^3+q^2+q
       127: 3q^3+q^2+q
       128: q^4+3q^3
       129: 3q^3+q^2+q
       130: q^4+3q^3
       131: q^4+2q^3+q^2+q
       132: q^4+2q^3
       133: 3q^4+6q^3+q^2+q
       134: 2q^5+5q^4+5q^3+q^2+q
       135: q^5+6q^4+7q^3+q^2+q
       136: q^5+6q^4+7q^3+q^2+q
       137: 6q^3+q^2+q
       138: q^5+3q^4+5q^3+q^2+q
       139: q^4+6q^3+q^2+q
       140: 2q^4+4q^3+q^2+q
       141: 3q^4+6q^3+q^2+q
       142: q^5+5q^4+7q^3+q^2+q
       143: 6q^3+q^2+q
       144: q^5+3q^4+5q^3+q^2+q
       145: q^4+6q^3+q^2+q
       146: 3q^4+6q^3+q^2+q
       147: q^5+5q^4+7q^3+q^2+q
       148: 2q^4+4q^3+q^2+q
       149: 2q^4+5q^3+q^2+q
       150: 6q^4+6q^3+q^2+q
       151: 3q^4+3q^3+q^2+q
       152: 3q^4+3q^3
       153: 3q^4+3q^3+q^2+q
       154: q^5+4q^4+3q^3
       155: 3q^4+3q^3+q^2+q
       156: 3q^4+3q^3
       157: q^4+6q^3+q^2+q
       158: q^4+6q^3+q^2+q
       159: q^5+3q^4+4q^3+q^2+q
       160: q^5+5q^4+7q^3+q^2+q
       161: q^5+5q^4+7q^3+q^2+q
       162: 2q^5+5q^4+5q^3+q^2+q
       163: q^5+5q^4+7q^3+q^2+q
       164: q^5+5q^4+7q^3+q^2+q
       165: 2q^5+5q^4+5q^3+q^2+q
       166: 2q^4+5q^3+q^2+q
       167: 3q^4+5q^3+q^2+q
       168: 4q^4+4q^3+q^2+q
       169: 3q^3+q^2+q
       170: q^3
       171: q^3
       172: q^3
       173: 3q^3+q^2+q
       174: q^3
       175: q^3
       176: q^3
       177: 2q^3+q^2+q
       178: 2q^3
       179: 3q^3+q^2+q
       180: 2q^3
       181: 3q^3+q^2+q
       182: q^4+3q^3
       183: q^4+4q^3+q^2+q
       184: 2q^3
       185: q^4+4q^3+q^2+q
       186: 2q^3
       187: 2q^4+4q^3+q^2+q
       188: 3q^4+3q^3
       189: q^4+4q^3+q^2+q
       190: q^4+2q^3
       191: 4q^3+q^2+q
       192: 2q^3
       193: 3q^3+q^2+q
       195: q^4+4q^3+q^2+q
       196: 2q^3
       197: q^4+2q^3+q^2+q
       198: q^4+2q^3
       199: 4q^3+q^2+q
       200: 2q^3
       201: q^4+4q^3+q^2+q
       202: 2q^3
       203: 3q^3+q^2+q
       205: q^4+2q^3+q^2+q
       206: q^4+2q^3
       207: 4q^3+q^2+q
       208: 2q^3
       209: q^4+3q^3+q^2+q
       210: q^4+2q^3
       211: 3q^4+3q^3+q^2+q
       212: 3q^4+3q^3
       213: 3q^3+q^2+q
       214: q^4+3q^3
       215: 3q^3+q^2+q
       216: q^4+3q^3
       217: q^4+2q^3+q^2+q
       218: q^4+2q^3
       219: q^4+4q^3+q^2+q
       220: q^4+6q^3+q^2+q
       221: q^4+4q^3+q^2+q
       222: 6q^3+q^2+q
       223: q^5+3q^4+5q^3+q^2+q
       224: 6q^3+q^2+q
       225: q^5+3q^4+5q^3+q^2+q
       226: 4q^3+q^2+q
       227: q^4+6q^3+q^2+q
       228: q^5+3q^4+5q^3+q^2+q
       229: 2q^4+4q^3+q^2+q
       230: q^5+5q^4+7q^3+q^2+q
       231: 4q^3+q^2+q
       232: q^4+6q^3+q^2+q
       233: q^5+3q^4+5q^3+q^2+q
       234: q^5+5q^4+7q^3+q^2+q
       235: 2q^4+4q^3+q^2+q
       236: 2q^4+4q^3+q^2+q
       237: q^3+q^2+q
       238: 3q^3
       239: q^3+q^2+q
       240: q^4+3q^3
       241: q^4+q^3+q^2+q
       242: q^4+2q^3
       243: 4q^3+q^2+q
       244: q^4+3q^3+q^2+q
       245: q^4+3q^3+q^2+q
       246: 2q^4+5q^3+q^2+q
       247: 2q^4+5q^3+q^2+q
       248: 3q^4+5q^3+q^2+q
       249: 4q^4+4q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^4+5q^3+q^2+q
       257: 3q^4+5q^3+q^2+q
       258: 4q^4+4q^3+q^2+q
       259: 2q^3+q^2+q
       260: q^3
       261: q^3
       262: q^3
       263: 3q^3+q^2+q
       264: q^3
       265: q^3
       266: q^3
       267: 2q^3+q^2+q
       268: q^3
       271: 2q^3+q^2+q
       272: q^3
       275: 3q^3+q^2+q
       276: q^3
       277: q^3
       278: q^3
       279: 3q^3+q^2+q
       280: 2q^3
       281: 2q^3+q^2+q
       282: 2q^3
       283: 2q^3+q^2+q
       285: 2q^3+q^2+q
       287: 2q^3+q^2+q
       288: q^3
       289: 3q^3+q^2+q
       290: q^4+3q^3
       291: 2q^3+q^2+q
       292: 2q^3
       293: 4q^3+q^2+q
       294: 2q^3
       295: 4q^3+q^2+q
       296: 2q^3
       297: 4q^3+q^2+q
       298: 2q^3
       299: 3q^3+q^2+q
       301: q^2+q
       302: 2q^3
       303: q^4+4q^3+q^2+q
       304: 2q^3
       305: q^4+2q^3+q^2+q
       306: q^4+2q^3
       307: q^4+4q^3+q^2+q
       308: 2q^3
       309: 3q^3+q^2+q
       311: q^2+q
       312: 2q^3
       313: q^4+2q^3+q^2+q
       314: q^4+2q^3
       315: q^3+q^2+q
       316: 2q^3
       317: q^3+q^2+q
       318: 2q^3
       319: 2q^3+q^2+q
       321: 2q^3+q^2+q
       323: q^3+q^2+q
       324: q^3
       325: q^4+3q^3+q^2+q
       326: q^4+2q^3
       333: q^4+4q^3+q^2+q
       334: 4q^3+q^2+q
       335: 4q^3+q^2+q
       336: 2q^4+4q^3+q^2+q
       337: 4q^3+q^2+q
       338: q^3+q^2+q
       339: 3q^3
       340: q^3+q^2+q
       341: q^4+3q^3
       342: q^4+q^3+q^2+q
       343: q^4+2q^3
       344: 4q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^5+3q^4+5q^3+q^2+q
       351: q^4+3q^3+q^2+q
       352: 4q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^5+3q^4+5q^3+q^2+q
       357: q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^4+3q^3+q^2+q
       360: q^3+q^2+q
       361: 3q^3
       362: q^3+q^2+q
       363: q^4+3q^3
       364: q^4+q^3+q^2+q
       365: q^4+2q^3
       366: 3q^3+q^2+q
       367: 4q^3+q^2+q
       368: 2q^4+4q^3+q^2+q
       369: q^4+3q^3+q^2+q
       370: q^4+3q^3+q^2+q
       371: 2q^4+5q^3+q^2+q
       372: 3q^4+5q^3+q^2+q
       373: 4q^4+4q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       377: q^3+q^2+q
       381: 2q^3+q^2+q
       382: q^3
       383: q^3
       384: q^3
       385: 3q^3+q^2+q
       386: q^3
       387: q^3
       388: q^3
       389: q^2+q
       390: q^3
       393: 2q^3+q^2+q
       394: q^3
       397: q^2+q
       398: q^3
       401: 2q^3+q^2+q
       402: q^3
       405: q^3+q^2+q
       413: 2q^3+q^2+q
       414: q^3
       417: 2q^3+q^2+q
       418: 2q^3
       419: 2q^3+q^2+q
       421: 2q^3+q^2+q
       423: 2q^3+q^2+q
       424: q^3
       425: q^3+q^2+q
       426: 2q^3
       427: q^3+q^2+q
       428: 2q^3
       429: q^3+q^2+q
       431: 2q^3+q^2+q
       433: q^2+q
       434: q^3
       435: q^2+q
       436: 2q^3
       437: q^3+q^2+q
       439: 2q^3+q^2+q
       440: q^3
       441: q^3+q^2+q
       443: 2q^3+q^2+q
       445: q^2+q
       446: 2q^3
       447: 2q^3+q^2+q
       449: q^3+q^2+q
       451: q^2+q
       452: q^3
       453: 2q^3+q^2+q
       454: q^3
       455: q^2+q
       456: 2q^3
       457: q^3+q^2+q
       459: q^3+q^2+q
       461: 2q^3+q^2+q
       463: q^2+q
       464: 2q^3
       465: q^3+q^2+q
       466: 2q^3
       467: q^3+q^2+q
       468: 2q^3
       469: q^3+q^2+q
       470: q^3
       471: 2q^3+q^2+q
       473: 2q^3+q^2+q
       475: q^3+q^2+q
       476: q^3
       477: 2q^2+q
       478: q^3
       479: q^3+q^2+q
       480: q^3
       481: 4q^3+q^2+q
       482: 4q^3+q^2+q
       483: 3q^3+q^2+q
       484: 4q^3+q^2+q
       485: q^3+q^2+q
       486: 3q^3
       487: q^3+q^2+q
       488: q^4+3q^3
       489: q^4+q^3+q^2+q
       490: q^4+2q^3
       491: 2q^4+4q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^4+2q^3+q^2+q
       496: q^4+3q^3+q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^4+2q^3+q^2+q
       501: q^4+3q^3+q^2+q
       508: 3q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^4+2q^3+q^2+q
       513: q^2+q
       514: q^4+2q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       521: q^3+q^2+q
       529: q^3+q^2+q
       533: q^2+q
       537: q^2+q
       538: q^3
       541: q^3+q^2+q
       545: q^2+q
       546: q^3
       549: q^2+q
       553: q^2+q
       554: q^3
       557: q^3+q^2+q
       561: q^2+q
       562: q^3
       565: q^3+q^2+q
       569: 2q^2+q
       573: q^3+q^2+q
       577: q^2+q
       579: q^2
       581: q^3
       585: 2q^3+q^2+q
       586: q^3
       589: 2q^3+q^2+q
       591: q^3+q^2+q
       593: q^3+q^2+q
       595: 2q^3+q^2+q
       597: q^3+q^2+q
       598: 2q^3
       599: q^3+q^2+q
       600: q^3
       601: q^3+q^2+q
       602: 2q^3
       603: q^2+q
       605: q^2+q
       606: q^3
       607: q^3+q^2+q
       609: q^2+q
       613: q^2+q
       614: q^3
       615: 2q^3+q^2+q
       617: q^2+q
       618: 2q^3
       619: q^3+q^2+q
       621: q^2+q
       623: q^2+q
       624: q^3
       625: q^2+q
       629: q^2+q
       630: q^3
       631: 2q^3+q^2+q
       633: q^2+q
       634: 2q^3
       639: q^3+q^2+q
       640: q^3
       641: q^3+q^2+q
       643: q^3+q^2+q
       645: q^2+q
       647: q^2+q
       649: q^2+q
       651: 2q^2+q
       652: q^3
       653: q^2+q
       655: q^3+q^2+q
       656: q^3
       657: q^2+q
       658: q^3+q
       659: 2q^3+q^2
       660: q
       661: 2q^3+q^2
       662: q^3+q
       663: 2q^3+q^2
       664: 3q^3+q^2+q
       665: 3q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q^3+q^2+q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^4+2q^3+q^2+q
       680: q^3+q^2+q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^4+2q^3+q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q^3+q
       690: q^3+q
       691: q
       692: q^3+q
       693: q^2+q
       695: q^2
       709: q^3+q^2+q
       713: q^2+q
       717: q^2+q
       721: q^2+q
       725: q^2+q
       733: q^2+q
       734: q^3
       737: q^2+q
       741: q^2+q
       749: q^2+q
       750: q^3
       753: q^2+q
       757: 2q^2+q
       761: q^2+q
       765: q^3+q^2+q
       769: q^2+q
       771: q^2
       773: q^3
       775: q
       776: q^2
       779: q^3+q
       780: 2q^3+q^2
       781: q^3+q^2+q
       782: q^3
       785: q^3+q^2+q
       787: q^3+q^2+q
       791: q^2+q
       793: q^2+q
       795: q
       796: q^3+q^2
       797: q^2+q
       801: q^2+q
       803: q
       805: q^2+q
       807: q^3+q^2+q
       809: q^2+q
       810: q^3
       811: q^2+q
       815: q^2+q
       817: q^2+q
       819: q
       820: q^3+q^2
       821: q^2+q
       825: q^3+q^2+q
       827: q^2+q
       829: q
       831: q^2+q
       833: q^2+q
       834: q^3
       835: q^2+q
       839: q^2+q
       843: q^2+q
       845: q^2+q
       847: q^2+q
       849: q^2+q
       851: q^2+q
       855: q
       857: q^2+q
       865: q
       866: q^2+q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q^3+q^2+q
       871: q^2+q
       872: q^2+q
       873: q
       874: q^3+q^2+q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q^3+q
       881: q^3+q
       882: q
       883: q^3+q
       884: q^2+q
       886: q^2
       900: q^2+q
       904: q^2+q
       908: q^2+q
       916: q
       917: q^2
       920: q^2+q
       924: q
       928: q^2+q
       940: q
       941: q^2
       944: q^2+q
       948: q^2+q
       952: q
       960: q^2+q
       964: q^2+q
       968: q
       969: q^2
       974: q^2+q
       988: q^2+q
       994: q
       995: q^2
       998: q^2+q
      1000: q^2+q
      1004: q^2+q
      1006: q^2+q
      1008: q^2+q
      1010: q^2+q
      1012: q^2+q
      1016: q
      1020: q
      1021: q^3+q^2
      1022: q^2+q
      1026: q^2+q
      1028: q
      1032: q
      1036: q
      1037: q^3+q^2
      1038: q^2+q
      1040: q
      1044: q^2+q
      1046: q
      1048: q^2+q
      1052: q^2+q
      1054: q
      1056: q
      1058: q^2+q
      1060: q
      1062: q
      1064: q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q^2+q
      1085: q
      1086: q
      1087: q^2
      1114: q
      1115: q^2
      1122: q
      1123: q^2
      1126: q^2+q
      1130: q^2+q
      1134: q^2+q
      1138: q
      1139: q^2
      1152: q
      1156: q^2+q
      1160: q
      1172: q^2+q
      1176: q
      1180: q
      1194: q
      1198: q^2+q
      1202: q
      1206: q
      1216: q
      1218: q
      1220: q^2+q
      1224: q
      1228: q
      1230: q
      1232: q
      1234: q
      1240: q^2+q
      1242: q
      1246: q
      1248: q
      1250: q
      1254: q
      1258: q
      1260: q^2+q
      1262: q
      1266: q
      1268: q
      1270: q
      1274: q
      1275: q^2
      1276: q
      1278: q
      1280: q^2+q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1290: q
      1291: q^2
      1326: q
      1330: q^2+q
      1348: q
      1356: q
      1360: q
      1364: q
      1368: q
      1380: q
      1388: q
      1392: q
      1396: q
      1400: q
      1410: q
      1418: q
      1422: q
      1426: q
      1430: q
      1431: q^2
      1436: q
      1440: q
      1442: q
      1444: q
      1450: q
      1454: q
      1460: q
      1462: q
      1474: q
      1476: q
      1478: q
      1482: q
      1485: q
      1486: q
      1488: q
      1501: q
      1513: q
      1537: q
      1549: q
      1575: q
      1579: q
      1595: q
      1599: q
      1619: q
      1627: q
      1639: q
      1645: q
      1647: q
      1653: q
      1655: q
      1669: q
      1733: q
      1749: q
      1773: q
      1807: q
      1944: 1
      2015: 1
      2060: 1
      2130: 1

2131:    0: 3q^3+4q^2+3q
         1: 3q^3+4q^2+3q
         2: 3q^3+4q^2+3q
         3: 3q^3+4q^2+3q
         4: q^4+3q^3+3q^2+3q
         5: 3q^3+4q^2+3q
         6: q^4+3q^3+3q^2+3q
         7: q^4+3q^3+3q^2+3q
         8: 3q^3+4q^2+3q
         9: q^4+3q^3+3q^2+3q
        10: 4q^2+3q
        11: 4q^2+3q
        12: q^3+3q^2+3q
        13: 3q^3+4q^2+3q
        14: q^4+3q^3+3q^2+3q
        15: 3q^3+4q^2+3q
        16: 3q^3+4q^2+3q
        17: 3q^3+4q^2+3q
        18: q^4+3q^3+3q^2+3q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 3q^3+4q^2+3q
        23: 3q^3+4q^2+3q
        24: 3q^3+4q^2+3q
        25: 3q^3+4q^2+3q
        26: 3q^3+4q^2+3q
        27: 3q^3+4q^2+3q
        28: 4q^2+3q
        29: 3q^2+3q
        30: 2q^3+3q^2+3q
        31: 4q^2+3q
        32: 3q^3+4q^2+3q
        33: 3q^3+4q^2+3q
        34: 4q^2+3q
        35: 3q^3+4q^2+3q
        36: 3q^3+4q^2+3q
        37: q^3+2q^2+2q
        38: 2q^3+2q^2+q
        39: q^3+2q^2+2q
        40: 2q^3+2q^2+q
        41: q^3+2q^2+2q
        42: 2q^3+2q^2+q
        43: 4q^2+3q
        44: q^3+3q^2+3q
        45: 4q^2+3q
        46: 3q^3+4q^2+3q
        47: 3q^3+4q^2+3q
        48: q^4+3q^3+3q^2+3q
        49: 2q^3+3q^2+3q
        50: 2q^3+3q^2+3q
        51: 2q^3+3q^2+3q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q^2+q
        59: 3q^2+2q
        60: 3q^2+2q
        61: q^2+q
        62: 2q^2+2q
        63: 2q^2+q
        64: q^3+2q^2+2q
        65: 2q^3+2q^2+q
        66: q^3+2q^2+2q
        67: 2q^3+2q^2+q
        68: 4q^2+3q
        69: 2q^3+3q^2+3q
        70: 3q^2+3q
        71: 3q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^2+2q
        75: q^3+q^2+q
        76: q^2+2q
        77: q^3+q^2+q
        78: q^2+2q
        79: q^3+q^2+q
        80: 4q^2+3q
        81: 3q^3+4q^2+3q
        82: 3q^2+3q
        83: 2q^3+3q^2+3q
        84: 4q^2+3q
        85: 3q^3+4q^2+3q
        86: 3q^2+3q
        87: 2q^3+3q^2+3q
        88: 4q^2+3q
        89: 4q^2+3q
        90: q^3+3q^2+3q
        91: 2q^3+3q^2+3q
        92: 2q^3+3q^2+3q
        93: 2q^3+3q^2+3q
        94: 2q^3+3q^2+3q
        95: 2q^3+3q^2+3q
        96: 2q^3+3q^2+3q
        97: 2q^3+3q^2+3q
        98: 2q^3+3q^2+3q
        99: 2q^3+3q^2+3q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: q^2+q
       104: 2q^2+q
       106: q^2+q
       107: 2q^2+2q
       108: q
       109: q
       110: 2q^2+2q
       111: 2q
       112: q^2+q
       113: q^2+2q
       114: q^2+q
       115: q^2+2q
       116: q^3+q^2+q
       117: q^2+q
       118: 3q^2+2q
       119: 3q^2+2q
       120: q^2+q
       121: 2q^2+2q
       122: 2q^2+q
       123: q^3+2q^2+2q
       124: 2q^3+2q^2+q
       125: 4q^2+3q
       126: 3q^2+3q
       127: q^2+2q
       128: q^3+q^2+q
       129: q^2+2q
       130: q^3+q^2+q
       131: q^2+2q
       132: q^3+q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+3q
       135: q^3+2q^2+3q
       136: q^3+2q^2+3q
       137: 4q^2+3q
       138: 2q^3+3q^2+3q
       139: 3q^2+3q
       140: q^3+2q^2+3q
       141: 3q^2+3q
       142: q^3+2q^2+3q
       143: 4q^2+3q
       144: 2q^3+3q^2+3q
       145: 3q^2+3q
       146: 3q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: 3q^2+3q
       150: 2q^3+3q^2+3q
       151: q^2+2q
       152: q^3+q^2+q
       153: q^2+2q
       154: q^3+q^2+q
       155: q^2+2q
       156: q^3+q^2+q
       157: 2q^2+3q
       158: 2q^2+3q
       159: 2q^2+3q
       160: 2q^3+3q^2+3q
       161: 2q^3+3q^2+3q
       162: 2q^3+3q^2+3q
       163: 2q^3+3q^2+3q
       164: 2q^3+3q^2+3q
       165: 2q^3+3q^2+3q
       166: 2q^3+3q^2+3q
       167: 2q^3+3q^2+3q
       168: 2q^3+3q^2+3q
       169: q
       170: q^2+q
       172: q
       173: q^2+q
       174: 2q^2+q
       176: q^2+q
       177: q^2+2q
       178: q^3+q^2+q
       179: q^2+2q
       180: q^2+q
       181: 2q
       182: q^2+q
       183: 2q^2+2q
       184: q
       185: q
       186: 2q^2+2q
       187: 2q
       188: q^2+q
       189: q^2+2q
       190: q^2+q
       191: q^2+q
       192: 3q^2+2q
       193: 2q^2+2q
       194: q
       195: q
       196: 2q^2+2q
       197: 2q
       198: q^2+q
       199: 3q^2+2q
       200: q^2+q
       201: 2q^2+2q
       202: q
       203: q
       204: 2q^2+2q
       205: 2q
       206: q^2+q
       207: 2q^2+2q
       208: 2q^2+q
       209: q^2+2q
       210: q^2+q
       211: q^2+2q
       212: q^3+q^2+q
       213: q^2+2q
       214: q^3+q^2+q
       215: q^2+2q
       216: q^3+q^2+q
       217: q^2+2q
       218: q^3+q^2+q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 2q^2+3q
       222: q^2+3q
       223: q^3+2q^2+3q
       224: q^2+3q
       225: q^3+2q^2+3q
       226: 3q^2+3q
       227: 3q^2+3q
       228: 2q^3+3q^2+3q
       229: q^3+2q^2+3q
       230: q^3+2q^2+3q
       231: 3q^2+3q
       232: 3q^2+3q
       233: 2q^3+3q^2+3q
       234: q^3+2q^2+3q
       235: q^3+2q^2+3q
       236: 2q^3+3q^2+3q
       237: q^2+2q
       238: q^3+q^2+q
       239: q^2+2q
       240: q^3+q^2+q
       241: q^2+2q
       242: q^3+q^2+q
       243: 3q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: 3q^2+3q
       247: 2q^2+4q
       248: 2q^2+4q
       249: q^3+2q^2+3q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+3q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+3q
       256: 2q^3+3q^2+3q
       257: 2q^3+3q^2+3q
       258: 2q^3+3q^2+3q
       259: q
       260: q^2+q
       262: q
       263: q
       264: q^2+q
       266: q
       267: q
       268: q^2+q
       269: q
       271: q
       273: q
       274: q^2+q
       275: q^2+q
       276: 2q^2+q
       278: q^2+q
       279: q^2+2q
       280: q^2+q
       281: q^2+2q
       282: q^3+q^2+q
       283: 2q^2+2q
       284: q
       285: q
       286: 2q^2+2q
       287: q^2+2q
       288: q^2+q
       289: 2q
       290: q^2+q
       291: 2q
       292: q^2+q
       293: q^2+2q
       294: q
       295: q
       296: q^2+2q
       297: 2q
       298: q
       299: 2q^2+2q
       300: q
       301: 2q
       302: q^2+q
       303: q
       304: 2q^2+2q
       305: 2q
       306: q^2+q
       307: 2q^2+2q
       308: q
       309: q
       310: 2q^2+2q
       311: 2q
       312: q^2+q
       313: 2q
       314: q^2+q
       315: q^2+2q
       316: q^3+q^2+q
       317: q^2+2q
       318: q^2+q
       319: 2q^2+2q
       320: q
       321: q
       322: 2q^2+2q
       323: 2q
       324: q^2+q
       325: q^2+2q
       326: q^2+q
       333: 2q^2+3q
       334: q^2+3q
       335: q^2+3q
       336: q^2+3q
       337: q^2+4q
       338: 3q
       339: 2q^2+q
       340: 3q
       341: 2q^2+q
       342: q^2+2q
       343: q^3+q^2+q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 2q^2+3q
       347: q^2+3q
       348: q^3+2q^2+3q
       349: q^2+3q
       350: q^3+2q^2+3q
       351: 2q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 2q^2+3q
       355: q^2+3q
       356: q^3+2q^2+3q
       357: q^2+3q
       358: q^3+2q^2+3q
       359: 2q^2+4q
       360: q^2+2q
       361: q^3+q^2+q
       362: q^2+2q
       363: q^3+q^2+q
       364: q^2+2q
       365: q^3+q^2+q
       366: 3q^2+3q
       367: 3q^2+3q
       368: 2q^3+3q^2+3q
       369: q^3+2q^2+3q
       370: q^3+2q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+3q
       377: q
       378: q^2+q
       380: q
       381: q
       382: q^2+q
       384: q
       385: q
       386: q
       388: q
       389: q
       390: q^2+q
       391: q
       393: q
       394: q^2+q
       396: q
       397: q
       399: q
       400: q^2+q
       401: q
       403: q^2+q
       404: q
       405: q
       406: q
       407: q^2+q
       413: q^2+2q
       414: q^2+q
       417: 2q
       418: q^2+q
       419: q^2+2q
       420: q
       421: q
       422: q^2+2q
       423: 2q
       424: q
       425: 2q
       426: q^2+q
       427: 3q
       428: q^2+q
       429: 2q^2+2q
       430: q
       431: q
       432: 2q^2+2q
       433: 2q
       434: q^2+q
       435: 2q
       436: q^2+q
       437: q^2+2q
       438: q
       439: q
       440: q^2+2q
       441: 2q
       442: q
       443: q^2+3q
       444: q
       445: 3q
       446: 2q^2+q
       447: 2q^2+2q
       448: q
       449: q
       450: 2q^2+2q
       451: 2q
       452: q^2+q
       453: q^2+2q
       454: q
       455: 2q
       456: q^2+q
       457: q
       458: q^2+2q
       459: 2q
       460: q
       461: q
       462: q^2+3q
       463: 3q
       464: 2q^2+q
       465: q^2+2q
       466: q^2+q
       467: q^2+2q
       468: q^3+q^2+q
       469: q^2+2q
       470: q^2+q
       471: 2q^2+2q
       472: q
       473: q
       474: 2q^2+2q
       475: 2q
       476: q^2+q
       477: 2q
       478: q^2+q
       479: q^2+2q
       480: q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: 3q
       484: q^2+4q
       485: 3q
       486: 2q^2+q
       487: 3q
       488: 2q^2+q
       489: q^2+2q
       490: q^3+q^2+q
       491: q^2+3q
       492: 2q^2+3q
       493: q^2+3q
       494: q^2+3q
       495: q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: q^2+3q
       499: q^2+3q
       500: q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 2q^2+3q
       511: q^2+3q
       512: q^3+2q^2+3q
       513: q^2+3q
       514: q^3+2q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       522: q^2+q
       524: q
       529: q
       530: q
       532: q
       533: q
       534: q^2+q
       536: q
       537: q
       538: q^2+q
       539: q
       541: q
       542: q
       543: q
       545: 2q
       546: q^2+q
       547: q
       549: q
       551: q^2+q
       552: q
       553: q
       555: q
       556: q^2+q
       557: q
       559: q
       560: q
       561: q
       563: 2q
       564: q^2+q
       565: q
       566: q^2+q
       568: q
       569: q
       570: q
       571: q^2+q
       573: q
       574: q^2+2q
       575: q
       577: 2q
       578: q^2
       580: q
       581: q^2+q
       585: 2q
       586: q
       589: q^2+2q
       590: q
       592: 2q
       593: 2q
       595: q
       596: q^2+2q
       597: 2q
       598: q^2+q
       599: 2q
       600: q
       601: 3q
       602: q^2+q
       603: q^2+2q
       604: q
       605: 2q
       606: q^2+q
       607: q
       608: q^2+2q
       609: 2q
       610: q
       613: 2q
       614: q^2+q
       615: q^2+3q
       616: q
       617: 3q
       618: 2q^2+q
       619: q^2+2q
       620: q
       621: q
       622: q^2+2q
       623: 2q
       624: q^2+q
       625: 2q
       626: q
       629: 2q
       630: q^2+q
       631: q
       632: q^2+3q
       633: 3q
       634: 2q^2+q
       639: q^2+2q
       640: q^2+q
       641: 2q^2+2q
       642: q
       643: q
       644: 2q^2+2q
       645: 2q
       646: q^2+q
       647: q^2+2q
       648: q
       649: q
       650: q^2+2q
       651: 2q
       652: q^2+q
       653: 2q
       654: q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 3q
       659: 2q^2+q
       660: 3q
       661: 2q^2+q
       662: q^2+2q
       663: q^3+q^2+q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: 3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: 3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: q^2+3q
       688: q^2+3q
       689: q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q
       696: q
       697: q
       699: q^2+q
       709: q
       710: q
       712: q
       715: q
       716: q
       717: q
       718: q
       721: q
       722: q^2+q
       723: q
       725: q
       726: q
       727: q
       733: 2q
       734: q^2+q
       735: q
       737: q
       739: q
       740: q^2+q
       741: q
       743: q
       744: q
       749: q
       751: 2q
       752: q^2+q
       753: q
       754: q^2+q
       756: q
       757: q
       758: q
       759: q^2+q
       761: q
       762: q
       763: q
       765: q
       766: q^2+2q
       768: q
       769: 2q
       770: q^2
       772: q
       773: q^2+q
       775: 3q
       776: q^2+q
       779: 2q
       780: q^2+q
       781: 2q
       782: q
       785: 2q
       788: 2q
       791: q
       792: q
       793: q^2+3q
       794: q
       795: 3q
       796: 2q^2+q
       797: 2q
       798: q
       801: q^2+2q
       802: q
       804: 2q
       805: 2q
       807: q
       808: q^2+2q
       809: 2q
       810: q^2+q
       811: 2q
       812: q
       815: 2q
       816: q
       817: q
       818: q^2+3q
       819: 3q
       820: 2q^2+q
       821: 2q
       822: q
       825: q^2+2q
       826: q
       828: 2q
       829: 2q
       831: q
       832: q^2+2q
       833: 2q
       834: q^2+q
       835: 2q
       836: q
       839: q
       840: 2q
       843: q^2+2q
       844: q^2+2q
       845: q^2+2q
       846: q
       847: q
       848: q^2+2q
       849: 2q
       850: q^2+q
       851: 2q
       852: q
       855: 2q
       856: q^2+q
       857: 2q
       858: q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: 3q
       880: q^2+3q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q
       887: q
       889: q
       890: q^2+q
       902: q
       903: q
       904: q
       905: q
       909: q
       916: 2q
       917: q^2+q
       918: q
       920: q
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       922: q
       926: q
       927: q
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       940: q
       942: 2q
       943: q^2+q
       944: q
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       960: q
       961: q
       962: q^2+q
       964: q
       965: q^2+2q
       967: q
       968: 2q
       969: q^2
       971: q
       972: q^2+q
       974: q
       975: q
       976: q
       988: q
       989: q
       991: q
       994: 2q
       995: q
       999: 2q
      1000: 2q
      1004: q
      1007: q
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      1010: q
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      1012: q
      1013: q
      1016: 2q
      1017: q
      1020: 2q
      1021: q^2+q
      1022: 2q
      1023: q
      1026: 2q
      1029: 2q
      1032: q
      1033: 2q
      1036: 2q
      1037: q^2+q
      1038: 2q
      1039: q
      1040: 2q
      1045: 2q
      1046: 2q
      1047: q
      1048: 2q
      1049: q
      1052: q^2+2q
      1053: q
      1055: 2q
      1056: 2q
      1058: q
      1059: q^2+2q
      1060: 2q
      1061: q^2+q
      1062: 2q
      1063: q
      1064: q
      1065: q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 3q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1086: q
      1089: q
      1091: q
      1092: q^2+q
      1116: q
      1117: q
      1122: q
      1123: q
      1128: q
      1131: q
      1138: q
      1142: q
      1154: q
      1155: q
      1156: q
      1157: q
      1162: q
      1174: q
      1175: q
      1176: q
      1177: q
      1181: q
      1194: q
      1195: q
      1197: q
      1198: q
      1199: q
      1200: q
      1204: q
      1205: q
      1206: q
      1207: q
      1217: q
      1218: q
      1220: q
      1224: q
      1228: 2q
      1229: q
      1230: 2q
      1231: q
      1233: 2q
      1234: 2q
      1240: q
      1243: q
      1246: q
      1247: 2q
      1248: 2q
      1249: q
      1251: 2q
      1254: 2q
      1258: q
      1261: q
      1262: 2q
      1263: q
      1266: 2q
      1267: q
      1268: 2q
      1271: 2q
      1274: 2q
      1275: q^2+q
      1276: q
      1278: q
      1279: q
      1280: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1296: q
      1350: q
      1351: q
      1356: q
      1357: q
      1363: q
      1366: q
      1382: q
      1383: q
      1388: q
      1389: q
      1394: q
      1397: q
      1410: q
      1411: q
      1413: q
      1420: q
      1421: q
      1422: q
      1423: q
      1427: q
      1430: q
      1434: q
      1436: q
      1441: q
      1442: q
      1444: q
      1451: q
      1454: q
      1461: q
      1462: q
      1464: 2q
      1465: q
      1467: 2q
      1468: 2q
      1474: q
      1476: q
      1479: q
      1482: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1508: q
      1519: q
      1609: q
      1610: q
      1615: q
      1616: q
      1620: q
      1624: q
      1639: q
      1641: 1
      1646: q
      1647: q
      1650: 1
      1654: q
      1655: q
      1657: 1
      1659: q
      1664: q
      1665: q
      1669: q
      1673: 1
      1674: 2q
      1716: q
      1759: 1
      1781: 1
      1812: 1
      1817: 1
      1820: 1
      1821: 1
      1825: q
      1830: q
      1831: q
      1833: 1
      1884: 1
      1907: 1
      1922: 1
      1953: 1
      1960: 1
      1963: 1
      1964: 1
      2016: 1
      2042: 1
      2052: 1
      2065: 1
      2131: 1

2132:    0: 3q^3+4q^2+3q
         1: 3q^3+4q^2+3q
         2: 3q^3+4q^2+3q
         3: 3q^3+4q^2+3q
         4: q^4+3q^3+3q^2+3q
         5: 3q^3+4q^2+3q
         6: q^4+3q^3+3q^2+3q
         7: q^4+3q^3+3q^2+3q
         8: 3q^3+4q^2+3q
         9: q^4+3q^3+3q^2+3q
        10: 4q^2+3q
        11: 4q^2+3q
        12: q^3+3q^2+3q
        13: 3q^3+4q^2+3q
        14: q^4+3q^3+3q^2+3q
        15: 3q^3+4q^2+3q
        16: 3q^3+4q^2+3q
        17: 3q^3+4q^2+3q
        18: q^4+3q^3+3q^2+3q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 3q^3+4q^2+3q
        23: 3q^3+4q^2+3q
        24: 3q^3+4q^2+3q
        25: 3q^3+4q^2+3q
        26: 3q^3+4q^2+3q
        27: 3q^3+4q^2+3q
        28: 4q^2+3q
        29: 3q^2+3q
        30: 2q^3+3q^2+3q
        31: 4q^2+3q
        32: 3q^3+4q^2+3q
        33: 3q^3+4q^2+3q
        34: 4q^2+3q
        35: 3q^3+4q^2+3q
        36: 3q^3+4q^2+3q
        37: q^3+2q^2+2q
        38: 2q^3+2q^2+q
        39: q^3+2q^2+2q
        40: 2q^3+2q^2+q
        41: q^3+2q^2+2q
        42: 2q^3+2q^2+q
        43: 4q^2+3q
        44: q^3+3q^2+3q
        45: 4q^2+3q
        46: 3q^3+4q^2+3q
        47: 3q^3+4q^2+3q
        48: q^4+3q^3+3q^2+3q
        49: 2q^3+3q^2+3q
        50: 2q^3+3q^2+3q
        51: 2q^3+3q^2+3q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: 3q^2+2q
        59: q^2+q
        60: q^2+q
        61: 3q^2+2q
        62: 2q^2+2q
        63: 2q^2+q
        64: q^3+2q^2+2q
        65: 2q^3+2q^2+q
        66: q^3+2q^2+2q
        67: 2q^3+2q^2+q
        68: 4q^2+3q
        69: 2q^3+3q^2+3q
        70: 3q^2+3q
        71: 3q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^2+2q
        75: q^3+q^2+q
        76: q^2+2q
        77: q^3+q^2+q
        78: q^2+2q
        79: q^3+q^2+q
        80: 4q^2+3q
        81: 3q^3+4q^2+3q
        82: 3q^2+3q
        83: 2q^3+3q^2+3q
        84: 4q^2+3q
        85: 3q^3+4q^2+3q
        86: 3q^2+3q
        87: 2q^3+3q^2+3q
        88: 4q^2+3q
        89: 4q^2+3q
        90: q^3+3q^2+3q
        91: 2q^3+3q^2+3q
        92: 2q^3+3q^2+3q
        93: 2q^3+3q^2+3q
        94: 2q^3+3q^2+3q
        95: 2q^3+3q^2+3q
        96: 2q^3+3q^2+3q
        97: 2q^3+3q^2+3q
        98: 2q^3+3q^2+3q
        99: 2q^3+3q^2+3q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       103: q^2+q
       105: 2q^2+q
       106: q^2+q
       107: q
       108: 2q^2+2q
       109: 2q^2+2q
       110: q
       111: 2q
       112: q^2+q
       113: q^2+2q
       114: q^2+q
       115: q^2+2q
       116: q^3+q^2+q
       117: 3q^2+2q
       118: q^2+q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+2q
       122: 2q^2+q
       123: q^3+2q^2+2q
       124: 2q^3+2q^2+q
       125: 4q^2+3q
       126: 3q^2+3q
       127: q^2+2q
       128: q^3+q^2+q
       129: q^2+2q
       130: q^3+q^2+q
       131: q^2+2q
       132: q^3+q^2+q
       133: 3q^2+3q
       134: 2q^3+3q^2+3q
       135: q^3+2q^2+3q
       136: q^3+2q^2+3q
       137: 4q^2+3q
       138: 2q^3+3q^2+3q
       139: 3q^2+3q
       140: q^3+2q^2+3q
       141: 3q^2+3q
       142: q^3+2q^2+3q
       143: 4q^2+3q
       144: 2q^3+3q^2+3q
       145: 3q^2+3q
       146: 3q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: 3q^2+3q
       150: 2q^3+3q^2+3q
       151: q^2+2q
       152: q^3+q^2+q
       153: q^2+2q
       154: q^3+q^2+q
       155: q^2+2q
       156: q^3+q^2+q
       157: 2q^2+3q
       158: 2q^2+3q
       159: 2q^2+3q
       160: 2q^3+3q^2+3q
       161: 2q^3+3q^2+3q
       162: 2q^3+3q^2+3q
       163: 2q^3+3q^2+3q
       164: 2q^3+3q^2+3q
       165: 2q^3+3q^2+3q
       166: 2q^3+3q^2+3q
       167: 2q^3+3q^2+3q
       168: 2q^3+3q^2+3q
       169: q
       171: q^2+q
       172: q
       173: q^2+q
       175: 2q^2+q
       176: q^2+q
       177: q^2+2q
       178: q^3+q^2+q
       179: q^2+2q
       180: q^2+q
       181: 2q
       182: q^2+q
       183: q
       184: 2q^2+2q
       185: 2q^2+2q
       186: q
       187: 2q
       188: q^2+q
       189: q^2+2q
       190: q^2+q
       191: 3q^2+2q
       192: q^2+q
       193: q
       194: 2q^2+2q
       195: 2q^2+2q
       196: q
       197: 2q
       198: q^2+q
       199: q^2+q
       200: 3q^2+2q
       201: q
       202: 2q^2+2q
       203: 2q^2+2q
       204: q
       205: 2q
       206: q^2+q
       207: 2q^2+2q
       208: 2q^2+q
       209: q^2+2q
       210: q^2+q
       211: q^2+2q
       212: q^3+q^2+q
       213: q^2+2q
       214: q^3+q^2+q
       215: q^2+2q
       216: q^3+q^2+q
       217: q^2+2q
       218: q^3+q^2+q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 2q^2+3q
       222: q^2+3q
       223: q^3+2q^2+3q
       224: q^2+3q
       225: q^3+2q^2+3q
       226: 3q^2+3q
       227: 3q^2+3q
       228: 2q^3+3q^2+3q
       229: q^3+2q^2+3q
       230: q^3+2q^2+3q
       231: 3q^2+3q
       232: 3q^2+3q
       233: 2q^3+3q^2+3q
       234: q^3+2q^2+3q
       235: q^3+2q^2+3q
       236: 2q^3+3q^2+3q
       237: q^2+2q
       238: q^3+q^2+q
       239: q^2+2q
       240: q^3+q^2+q
       241: q^2+2q
       242: q^3+q^2+q
       243: 3q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: 3q^2+3q
       247: 2q^2+4q
       248: 2q^2+4q
       249: q^3+2q^2+3q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+3q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+3q
       256: 2q^3+3q^2+3q
       257: 2q^3+3q^2+3q
       258: 2q^3+3q^2+3q
       259: q
       261: q^2+q
       262: q
       263: q
       265: q^2+q
       266: q
       267: q
       269: q
       270: q^2+q
       271: q
       272: q^2+q
       273: q
       275: q^2+q
       277: 2q^2+q
       278: q^2+q
       279: q^2+2q
       280: q^2+q
       281: q^2+2q
       282: q^3+q^2+q
       283: q
       284: 2q^2+2q
       285: 2q^2+2q
       286: q
       287: q^2+2q
       288: q^2+q
       289: 2q
       290: q^2+q
       291: 2q
       292: q^2+q
       293: q
       294: q^2+2q
       295: q^2+2q
       296: q
       297: 2q
       298: q
       299: q
       300: 2q^2+2q
       301: 2q
       302: q^2+q
       303: 2q^2+2q
       304: q
       305: 2q
       306: q^2+q
       307: q
       308: 2q^2+2q
       309: 2q^2+2q
       310: q
       311: 2q
       312: q^2+q
       313: 2q
       314: q^2+q
       315: q^2+2q
       316: q^3+q^2+q
       317: q^2+2q
       318: q^2+q
       319: q
       320: 2q^2+2q
       321: 2q^2+2q
       322: q
       323: 2q
       324: q^2+q
       325: q^2+2q
       326: q^2+q
       333: 2q^2+3q
       334: q^2+3q
       335: q^2+3q
       336: q^2+3q
       337: q^2+4q
       338: 3q
       339: 2q^2+q
       340: 3q
       341: 2q^2+q
       342: q^2+2q
       343: q^3+q^2+q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 2q^2+3q
       347: q^2+3q
       348: q^3+2q^2+3q
       349: q^2+3q
       350: q^3+2q^2+3q
       351: 2q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 2q^2+3q
       355: q^2+3q
       356: q^3+2q^2+3q
       357: q^2+3q
       358: q^3+2q^2+3q
       359: 2q^2+4q
       360: q^2+2q
       361: q^3+q^2+q
       362: q^2+2q
       363: q^3+q^2+q
       364: q^2+2q
       365: q^3+q^2+q
       366: 3q^2+3q
       367: 3q^2+3q
       368: 2q^3+3q^2+3q
       369: q^3+2q^2+3q
       370: q^3+2q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+3q
       377: q
       379: q^2+q
       380: q
       381: q
       383: q^2+q
       384: q
       385: q
       387: q
       388: q
       389: q
       391: q
       392: q^2+q
       393: q
       395: q^2+q
       396: q
       397: q
       398: q^2+q
       399: q
       401: q
       402: q^2+q
       404: q
       405: q
       406: q
       408: q^2+q
       413: q^2+2q
       414: q^2+q
       417: 2q
       418: q^2+q
       419: q
       420: q^2+2q
       421: q^2+2q
       422: q
       423: 2q
       424: q
       425: 2q
       426: q^2+q
       427: 3q
       428: q^2+q
       429: q
       430: 2q^2+2q
       431: 2q^2+2q
       432: q
       433: 2q
       434: q^2+q
       435: 2q
       436: q^2+q
       437: q
       438: q^2+2q
       439: q^2+2q
       440: q
       441: 2q
       442: q
       443: q
       444: q^2+3q
       445: 3q
       446: 2q^2+q
       447: q
       448: 2q^2+2q
       449: 2q^2+2q
       450: q
       451: 2q
       452: q^2+q
       453: q
       454: q^2+2q
       455: 2q
       456: q^2+q
       457: q^2+2q
       458: q
       459: 2q
       460: q
       461: q^2+3q
       462: q
       463: 3q
       464: 2q^2+q
       465: q^2+2q
       466: q^2+q
       467: q^2+2q
       468: q^3+q^2+q
       469: q^2+2q
       470: q^2+q
       471: q
       472: 2q^2+2q
       473: 2q^2+2q
       474: q
       475: 2q
       476: q^2+q
       477: 2q
       478: q^2+q
       479: q^2+2q
       480: q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: 3q
       484: q^2+4q
       485: 3q
       486: 2q^2+q
       487: 3q
       488: 2q^2+q
       489: q^2+2q
       490: q^3+q^2+q
       491: q^2+3q
       492: 2q^2+3q
       493: q^2+3q
       494: q^2+3q
       495: q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: q^2+3q
       499: q^2+3q
       500: q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 2q^2+3q
       511: q^2+3q
       512: q^3+2q^2+3q
       513: q^2+3q
       514: q^3+2q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       523: q^2+q
       524: q
       529: q
       531: q
       532: q
       533: q
       535: q^2+q
       536: q
       537: q
       539: q
       540: q^2+q
       541: q
       543: q
       544: q
       545: q
       547: 2q
       548: q^2+q
       549: q
       550: q^2+q
       552: q
       553: q
       554: q^2+q
       555: q
       557: q
       558: q
       559: q
       561: 2q
       562: q^2+q
       563: q
       565: q
       567: q^2+q
       568: q
       569: q
       570: q
       572: q^2+q
       573: q
       575: q
       576: q^2+2q
       577: 2q
       578: q^2
       580: q
       581: q^2+q
       585: 2q
       586: q
       589: q
       590: q^2+2q
       591: 2q
       594: 2q
       595: q^2+2q
       596: q
       597: 2q
       598: q^2+q
       599: 2q
       600: q
       601: 3q
       602: q^2+q
       603: q
       604: q^2+2q
       605: 2q
       606: q^2+q
       607: q^2+2q
       608: q
       609: 2q
       610: q
       613: 2q
       614: q^2+q
       615: q
       616: q^2+3q
       617: 3q
       618: 2q^2+q
       619: q
       620: q^2+2q
       621: q^2+2q
       622: q
       623: 2q
       624: q^2+q
       625: 2q
       626: q
       629: 2q
       630: q^2+q
       631: q^2+3q
       632: q
       633: 3q
       634: 2q^2+q
       639: q^2+2q
       640: q^2+q
       641: q
       642: 2q^2+2q
       643: 2q^2+2q
       644: q
       645: 2q
       646: q^2+q
       647: q
       648: q^2+2q
       649: q^2+2q
       650: q
       651: 2q
       652: q^2+q
       653: 2q
       654: q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 3q
       659: 2q^2+q
       660: 3q
       661: 2q^2+q
       662: q^2+2q
       663: q^3+q^2+q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: 3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: 3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: q^2+3q
       688: q^2+3q
       689: q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q
       697: q
       698: q
       700: q^2+q
       709: q
       711: q
       712: q
       713: q
       714: q
       719: q
       720: q
       721: q
       723: q
       724: q^2+q
       725: q
       727: q
       728: q
       733: q
       735: 2q
       736: q^2+q
       737: q
       738: q^2+q
       739: q
       741: q
       742: q
       743: q
       749: 2q
       750: q^2+q
       751: q
       753: q
       755: q^2+q
       756: q
       757: q
       758: q
       760: q^2+q
       761: q
       762: q
       764: q
       765: q
       767: q^2+2q
       768: q
       769: 2q
       770: q^2
       772: q
       773: q^2+q
       775: 3q
       776: q^2+q
       779: 2q
       780: q^2+q
       781: 2q
       782: q
       786: 2q
       787: 2q
       791: q
       792: q
       793: q
       794: q^2+3q
       795: 3q
       796: 2q^2+q
       797: 2q
       798: q
       801: q
       802: q^2+2q
       803: 2q
       806: 2q
       807: q^2+2q
       808: q
       809: 2q
       810: q^2+q
       811: 2q
       812: q
       815: q
       816: 2q
       817: q^2+3q
       818: q
       819: 3q
       820: 2q^2+q
       821: 2q
       822: q
       825: q
       826: q^2+2q
       827: 2q
       830: 2q
       831: q^2+2q
       832: q
       833: 2q
       834: q^2+q
       835: 2q
       836: q
       839: 2q
       840: q
       843: q^2+2q
       844: q^2+2q
       845: q
       846: q^2+2q
       847: q^2+2q
       848: q
       849: 2q
       850: q^2+q
       851: 2q
       852: q
       855: 2q
       856: q^2+q
       857: 2q
       858: q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: 3q
       880: q^2+3q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q
       888: q
       889: q
       891: q^2+q
       900: q
       901: q
       906: q
       907: q
       910: q
       916: q
       918: 2q
       919: q^2+q
       920: q
       922: q
       923: q
       924: q
       925: q
       930: q
       931: q
       940: 2q
       941: q^2+q
       942: q
       944: q
       945: q
       946: q
       948: q
       949: q
       954: q
       955: q
       960: q
       961: q
       963: q^2+q
       964: q
       966: q^2+2q
       967: q
       968: 2q
       969: q^2
       971: q
       972: q^2+q
       974: q
       975: q
       977: q
       988: q
       990: q
       991: q
       994: 2q
       995: q
       998: 2q
      1001: 2q
      1005: q
      1006: q
      1008: q
      1010: q
      1011: q
      1012: q
      1013: q
      1016: q
      1017: 2q
      1020: 2q
      1021: q^2+q
      1022: 2q
      1023: q
      1027: 2q
      1028: 2q
      1032: 2q
      1033: q
      1036: 2q
      1037: q^2+q
      1038: 2q
      1039: q
      1041: 2q
      1044: 2q
      1046: 2q
      1047: q
      1048: 2q
      1049: q
      1052: q
      1053: q^2+2q
      1054: 2q
      1057: 2q
      1058: q^2+2q
      1059: q
      1060: 2q
      1061: q^2+q
      1062: 2q
      1063: q
      1064: q
      1065: q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 3q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1086: q
      1090: q
      1091: q
      1093: q^2+q
      1114: q
      1115: q
      1124: q
      1125: q
      1129: q
      1132: q
      1138: q
      1142: q
      1152: q
      1153: q
      1158: q
      1159: q
      1161: q
      1172: q
      1173: q
      1178: q
      1179: q
      1182: q
      1194: q
      1196: q
      1197: q
      1198: q
      1199: q
      1201: q
      1202: q
      1203: q
      1208: q
      1209: q
      1216: q
      1219: q
      1220: q
      1224: q
      1228: q
      1229: 2q
      1230: 2q
      1231: q
      1232: 2q
      1235: 2q
      1241: q
      1242: q
      1246: 2q
      1247: q
      1248: 2q
      1249: q
      1250: 2q
      1255: 2q
      1259: q
      1260: q
      1262: 2q
      1263: q
      1266: 2q
      1267: q
      1269: 2q
      1270: 2q
      1274: 2q
      1275: q^2+q
      1276: q
      1278: q
      1279: q
      1280: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1297: q
      1348: q
      1349: q
      1358: q
      1359: q
      1362: q
      1365: q
      1380: q
      1381: q
      1390: q
      1391: q
      1395: q
      1398: q
      1410: q
      1412: q
      1413: q
      1418: q
      1419: q
      1424: q
      1425: q
      1428: q
      1430: q
      1434: q
      1436: q
      1440: q
      1443: q
      1444: q
      1450: q
      1455: q
      1460: q
      1463: q
      1464: 2q
      1465: q
      1466: 2q
      1469: 2q
      1474: q
      1477: q
      1478: q
      1482: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1507: q
      1520: q
      1607: q
      1608: q
      1617: q
      1618: q
      1621: q
      1625: q
      1639: q
      1641: 1
      1645: q
      1648: q
      1649: 1
      1653: q
      1656: q
      1658: 1
      1659: q
      1663: q
      1666: q
      1669: q
      1673: 1
      1674: 2q
      1717: q
      1757: 1
      1783: 1
      1813: 1
      1817: 1
      1819: 1
      1822: 1
      1825: q
      1829: q
      1832: q
      1833: 1
      1885: 1
      1906: 1
      1923: 1
      1954: 1
      1960: 1
      1962: 1
      1965: 1
      2017: 1
      2040: 1
      2054: 1
      2066: 1
      2132: 1

2133:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: 1
        11: 1
        12: 1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: q^2
        38: 1
        39: q^2
        40: 1
        41: q^2
        42: 1
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        59: 1
        60: 1
        63: 1
        64: q^2
        65: 1
        66: q^2
        67: 1
        68: 1
        69: q^2+1
        70: 1
        71: 1
        72: q^2+1
        73: q^2+1
        74: q^2
        75: 1
        76: q^2
        77: 1
        78: q^2
        79: 1
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        85: q^2+1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       104: 1
       107: 1
       110: 1
       111: q^2
       112: 1
       114: 1
       115: q^2
       116: 1
       118: 1
       119: 1
       122: 1
       123: q^2
       124: 1
       125: 1
       126: 1
       127: q^2
       128: 1
       129: q^2
       130: 1
       131: q^2
       132: 1
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: 1
       140: q^2+1
       141: 1
       142: q^2+1
       143: 1
       144: q^2+1
       145: 1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2
       152: 1
       153: q^2
       154: 1
       155: q^2
       156: 1
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: q^2+1
       170: 1
       174: 1
       177: q^2
       178: 1
       180: 1
       181: q^2
       182: 1
       183: 1
       186: 1
       187: q^2
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       197: q^2
       198: 1
       199: 1
       201: 1
       204: 1
       205: q^2
       206: 1
       208: 1
       210: 1
       211: q^2
       212: 1
       213: q^2
       214: 1
       215: q^2
       216: 1
       217: q^2
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^2
       238: 1
       239: q^2
       240: 1
       241: q^2
       242: 1
       243: 1
       244: q^2+1
       245: q^2+1
       246: 1
       247: q^2+1
       248: q^2+1
       249: q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       281: q^2
       282: 1
       283: 1
       286: 1
       288: 1
       289: q^2
       290: 1
       291: q^2
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       301: q^2
       302: 1
       304: 1
       305: q^2
       306: 1
       307: 1
       310: 1
       311: q^2
       312: 1
       313: q^2
       314: 1
       315: q^2
       316: 1
       318: 1
       319: 1
       322: 1
       323: q^2
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: 1
       338: q^2
       339: 1
       340: q^2
       341: 1
       342: q^2
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^2+1
       360: q^2
       361: 1
       362: q^2
       363: 1
       364: q^2
       365: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       414: 1
       417: q^2
       418: 1
       419: 1
       422: 1
       424: 1
       425: q^2
       426: 1
       428: 1
       429: 1
       432: 1
       433: q^2
       434: 1
       435: q^2
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       445: q^2
       446: 1
       447: 1
       450: 1
       451: q^2
       452: 1
       453: 1
       455: q^2
       456: 1
       458: 1
       460: 1
       462: 1
       463: q^2
       464: 1
       466: 1
       467: q^2
       468: 1
       470: 1
       471: 1
       474: 1
       475: q^2
       476: 1
       477: q^2
       478: 1
       479: q^2
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2
       486: 1
       487: q^2
       488: 1
       489: q^2
       490: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       522: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       577: q^2
       581: 1
       586: 1
       589: 1
       592: 1
       593: 1
       596: 1
       597: q^2
       598: 1
       600: 1
       602: 1
       603: 1
       605: q^2
       606: 1
       608: 1
       610: 1
       613: q^2
       614: 1
       615: 1
       617: q^2
       618: 1
       619: 1
       622: 1
       623: q^2
       624: 1
       626: 1
       629: q^2
       630: 1
       632: 1
       633: q^2
       634: 1
       640: 1
       641: 1
       644: 1
       645: q^2
       646: 1
       647: 1
       650: 1
       651: q^2
       652: 1
       654: 1
       655: q^2
       656: 1
       657: 1
       658: q^2
       659: 1
       660: q^2
       661: 1
       662: q^2
       663: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       699: 1
       710: 1
       715: 1
       718: 1
       722: 1
       726: 1
       734: 1
       740: 1
       744: 1
       752: 1
       754: 1
       759: 1
       763: 1
       766: 1
       769: q^2
       773: 1
       776: 1
       779: q^2
       780: 1
       782: 1
       785: 1
       788: 1
       791: q^2
       792: 1
       793: 1
       795: q^2
       796: 1
       798: 1
       801: 1
       804: 1
       805: 1
       808: 1
       809: q^2
       810: 1
       812: 1
       815: 1
       818: 1
       819: q^2
       820: 1
       822: 1
       825: 1
       828: 1
       829: 1
       832: 1
       833: q^2
       834: 1
       836: 1
       840: 1
       843: q^2
       844: 1
       845: 1
       848: 1
       849: q^2
       850: 1
       852: 1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: 1
       890: 1
       903: 1
       905: 1
       909: 1
       917: 1
       921: 1
       926: 1
       929: 1
       943: 1
       947: 1
       951: 1
       953: 1
       962: 1
       965: 1
       968: q^2
       972: 1
       976: 1
       989: 1
       995: 1
       999: 1
      1000: 1
      1004: 1
      1007: 1
      1009: 1
      1010: q^2
      1011: 1
      1012: q^2
      1013: 1
      1016: 1
      1020: q^2
      1021: 1
      1023: 1
      1026: 1
      1029: 1
      1033: 1
      1036: q^2
      1037: 1
      1039: 1
      1040: 1
      1045: 1
      1047: 1
      1049: 1
      1052: 1
      1055: 1
      1056: 1
      1059: 1
      1060: q^2
      1061: 1
      1063: 1
      1064: q^2
      1065: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1092: 1
      1117: 1
      1123: 1
      1128: 1
      1131: 1
      1136: 1
      1138: q^2
      1142: 1
      1155: 1
      1157: 1
      1162: 1
      1175: 1
      1177: 1
      1181: 1
      1195: 1
      1200: 1
      1205: 1
      1207: 1
      1217: 1
      1218: 1
      1221: 1
      1225: 1
      1228: 1
      1231: 1
      1233: 1
      1234: 1
      1240: 1
      1243: 1
      1247: 1
      1249: 1
      1251: 1
      1254: 1
      1258: 1
      1261: 1
      1263: 1
      1267: 1
      1268: 1
      1271: 1
      1274: q^2
      1275: 1
      1277: 1
      1278: q^2
      1279: 1
      1280: q^2
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1296: 1
      1327: 1
      1332: 1
      1351: 1
      1357: 1
      1363: 1
      1366: 1
      1371: 1
      1383: 1
      1389: 1
      1394: 1
      1397: 1
      1402: 1
      1411: 1
      1421: 1
      1423: 1
      1427: 1
      1430: q^2
      1434: 1
      1437: 1
      1441: 1
      1442: 1
      1445: 1
      1451: 1
      1454: 1
      1461: 1
      1462: 1
      1465: 1
      1467: 1
      1468: 1
      1475: 1
      1476: 1
      1479: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1508: 1
      1519: 1
      1539: 1
      1550: 1
      1577: 1
      1582: 1
      1596: 1
      1601: 1
      1610: 1
      1616: 1
      1620: 1
      1624: 1
      1628: 1
      1640: 1
      1642: 1
      1646: 1
      1647: 1
      1650: 1
      1654: 1
      1655: 1
      1657: 1
      1660: 1
      1664: 1
      1665: 1
      1670: 1
      1673: 1
      1674: 1
      1716: 1
      1734: 1
      1744: 1
      1751: 1
      1760: 1
      1771: 1
      1774: 1
      1782: 1
      1798: 1
      1809: 1
      1812: 1
      1818: 1
      1820: 1
      1821: 1
      1826: 1
      1830: 1
      1831: 1
      1833: 1
      1887: 1
      1901: 1
      1909: 1
      1915: 1
      1924: 1
      1941: 1
      1946: 1
      1953: 1
      1961: 1
      1963: 1
      1964: 1
      2020: 1
      2043: 1
      2053: 1
      2061: 1
      2065: 1
      2133: 1

2134:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: 1
        11: 1
        12: 1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: q^2
        38: 1
        39: q^2
        40: 1
        41: q^2
        42: 1
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        58: 1
        61: 1
        63: 1
        64: q^2
        65: 1
        66: q^2
        67: 1
        68: 1
        69: q^2+1
        70: 1
        71: 1
        72: q^2+1
        73: q^2+1
        74: q^2
        75: 1
        76: q^2
        77: 1
        78: q^2
        79: 1
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        85: q^2+1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       105: 1
       108: 1
       109: 1
       111: q^2
       112: 1
       114: 1
       115: q^2
       116: 1
       117: 1
       120: 1
       122: 1
       123: q^2
       124: 1
       125: 1
       126: 1
       127: q^2
       128: 1
       129: q^2
       130: 1
       131: q^2
       132: 1
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: 1
       140: q^2+1
       141: 1
       142: q^2+1
       143: 1
       144: q^2+1
       145: 1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2
       152: 1
       153: q^2
       154: 1
       155: q^2
       156: 1
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: q^2+1
       171: 1
       175: 1
       177: q^2
       178: 1
       180: 1
       181: q^2
       182: 1
       184: 1
       185: 1
       187: q^2
       188: 1
       190: 1
       191: 1
       194: 1
       195: 1
       197: q^2
       198: 1
       200: 1
       202: 1
       203: 1
       205: q^2
       206: 1
       208: 1
       210: 1
       211: q^2
       212: 1
       213: q^2
       214: 1
       215: q^2
       216: 1
       217: q^2
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^2
       238: 1
       239: q^2
       240: 1
       241: q^2
       242: 1
       243: 1
       244: q^2+1
       245: q^2+1
       246: 1
       247: q^2+1
       248: q^2+1
       249: q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       261: 1
       265: 1
       270: 1
       272: 1
       277: 1
       280: 1
       281: q^2
       282: 1
       284: 1
       285: 1
       288: 1
       289: q^2
       290: 1
       291: q^2
       292: 1
       294: 1
       295: 1
       298: 1
       300: 1
       301: q^2
       302: 1
       303: 1
       305: q^2
       306: 1
       308: 1
       309: 1
       311: q^2
       312: 1
       313: q^2
       314: 1
       315: q^2
       316: 1
       318: 1
       320: 1
       321: 1
       323: q^2
       324: 1
       326: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: 1
       338: q^2
       339: 1
       340: q^2
       341: 1
       342: q^2
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^2+1
       360: q^2
       361: 1
       362: q^2
       363: 1
       364: q^2
       365: 1
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       379: 1
       383: 1
       387: 1
       392: 1
       395: 1
       398: 1
       402: 1
       408: 1
       414: 1
       417: q^2
       418: 1
       420: 1
       421: 1
       424: 1
       425: q^2
       426: 1
       428: 1
       430: 1
       431: 1
       433: q^2
       434: 1
       435: q^2
       436: 1
       438: 1
       439: 1
       442: 1
       444: 1
       445: q^2
       446: 1
       448: 1
       449: 1
       451: q^2
       452: 1
       454: 1
       455: q^2
       456: 1
       457: 1
       460: 1
       461: 1
       463: q^2
       464: 1
       466: 1
       467: q^2
       468: 1
       470: 1
       472: 1
       473: 1
       475: q^2
       476: 1
       477: q^2
       478: 1
       479: q^2
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2
       486: 1
       487: q^2
       488: 1
       489: q^2
       490: 1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       523: 1
       531: 1
       535: 1
       540: 1
       544: 1
       548: 1
       550: 1
       554: 1
       558: 1
       562: 1
       567: 1
       572: 1
       576: 1
       577: q^2
       581: 1
       586: 1
       590: 1
       591: 1
       594: 1
       595: 1
       597: q^2
       598: 1
       600: 1
       602: 1
       604: 1
       605: q^2
       606: 1
       607: 1
       610: 1
       613: q^2
       614: 1
       616: 1
       617: q^2
       618: 1
       620: 1
       621: 1
       623: q^2
       624: 1
       626: 1
       629: q^2
       630: 1
       631: 1
       633: q^2
       634: 1
       640: 1
       642: 1
       643: 1
       645: q^2
       646: 1
       648: 1
       649: 1
       651: q^2
       652: 1
       654: 1
       655: q^2
       656: 1
       657: 1
       658: q^2
       659: 1
       660: q^2
       661: 1
       662: q^2
       663: 1
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       700: 1
       711: 1
       714: 1
       719: 1
       724: 1
       728: 1
       736: 1
       738: 1
       742: 1
       750: 1
       755: 1
       760: 1
       764: 1
       767: 1
       769: q^2
       773: 1
       776: 1
       779: q^2
       780: 1
       782: 1
       786: 1
       787: 1
       791: q^2
       792: 1
       794: 1
       795: q^2
       796: 1
       798: 1
       802: 1
       803: 1
       806: 1
       807: 1
       809: q^2
       810: 1
       812: 1
       816: 1
       817: 1
       819: q^2
       820: 1
       822: 1
       826: 1
       827: 1
       830: 1
       831: 1
       833: q^2
       834: 1
       836: 1
       839: 1
       843: q^2
       844: 1
       846: 1
       847: 1
       849: q^2
       850: 1
       852: 1
       855: q^2
       856: 1
       858: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: 1
       891: 1
       901: 1
       907: 1
       910: 1
       919: 1
       923: 1
       925: 1
       931: 1
       941: 1
       945: 1
       949: 1
       954: 1
       963: 1
       966: 1
       968: q^2
       972: 1
       977: 1
       990: 1
       995: 1
       998: 1
      1001: 1
      1005: 1
      1006: 1
      1009: 1
      1010: q^2
      1011: 1
      1012: q^2
      1013: 1
      1017: 1
      1020: q^2
      1021: 1
      1023: 1
      1027: 1
      1028: 1
      1032: 1
      1036: q^2
      1037: 1
      1039: 1
      1041: 1
      1044: 1
      1047: 1
      1049: 1
      1053: 1
      1054: 1
      1057: 1
      1058: 1
      1060: q^2
      1061: 1
      1063: 1
      1064: q^2
      1065: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1093: 1
      1115: 1
      1125: 1
      1129: 1
      1132: 1
      1137: 1
      1138: q^2
      1142: 1
      1153: 1
      1159: 1
      1161: 1
      1173: 1
      1179: 1
      1182: 1
      1196: 1
      1201: 1
      1203: 1
      1209: 1
      1216: 1
      1219: 1
      1221: 1
      1225: 1
      1229: 1
      1231: 1
      1232: 1
      1235: 1
      1241: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1255: 1
      1259: 1
      1260: 1
      1263: 1
      1267: 1
      1269: 1
      1270: 1
      1274: q^2
      1275: 1
      1277: 1
      1278: q^2
      1279: 1
      1280: q^2
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1297: 1
      1328: 1
      1333: 1
      1349: 1
      1359: 1
      1362: 1
      1365: 1
      1370: 1
      1381: 1
      1391: 1
      1395: 1
      1398: 1
      1403: 1
      1412: 1
      1419: 1
      1425: 1
      1428: 1
      1430: q^2
      1434: 1
      1437: 1
      1440: 1
      1443: 1
      1445: 1
      1450: 1
      1455: 1
      1460: 1
      1463: 1
      1465: 1
      1466: 1
      1469: 1
      1475: 1
      1477: 1
      1478: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1507: 1
      1520: 1
      1540: 1
      1551: 1
      1576: 1
      1581: 1
      1597: 1
      1602: 1
      1608: 1
      1618: 1
      1621: 1
      1625: 1
      1629: 1
      1640: 1
      1642: 1
      1645: 1
      1648: 1
      1649: 1
      1653: 1
      1656: 1
      1658: 1
      1660: 1
      1663: 1
      1666: 1
      1670: 1
      1673: 1
      1674: 1
      1717: 1
      1735: 1
      1743: 1
      1750: 1
      1758: 1
      1772: 1
      1775: 1
      1784: 1
      1799: 1
      1810: 1
      1813: 1
      1818: 1
      1819: 1
      1822: 1
      1826: 1
      1829: 1
      1832: 1
      1833: 1
      1888: 1
      1899: 1
      1908: 1
      1917: 1
      1925: 1
      1942: 1
      1947: 1
      1954: 1
      1961: 1
      1962: 1
      1965: 1
      2021: 1
      2041: 1
      2055: 1
      2062: 1
      2066: 1
      2134: 1

2135:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: 1
        11: 1
        12: 1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: 1
        38: q^2
        39: 1
        40: q^2
        41: 1
        42: q^2
        43: 1
        44: 1
        45: 1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        59: 1
        61: 1
        62: 1
        64: 1
        65: q^2
        66: 1
        67: q^2
        68: 1
        69: q^2+1
        70: 1
        71: 1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2
        76: 1
        77: q^2
        78: 1
        79: q^2
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        85: q^2+1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       106: 1
       108: 1
       110: 1
       111: 1
       112: q^2
       113: 1
       115: 1
       116: q^2
       118: 1
       120: 1
       121: 1
       123: 1
       124: q^2
       125: 1
       126: 1
       127: 1
       128: q^2
       129: 1
       130: q^2
       131: 1
       132: q^2
       133: 1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: 1
       138: q^2+1
       139: 1
       140: q^2+1
       141: 1
       142: q^2+1
       143: 1
       144: q^2+1
       145: 1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: 1
       152: q^2
       153: 1
       154: q^2
       155: 1
       156: q^2
       157: 1
       158: 1
       159: 1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: q^2+1
       172: 1
       176: 1
       177: 1
       178: q^2
       179: 1
       181: 1
       182: q^2
       184: 1
       186: 1
       187: 1
       188: q^2
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       198: q^2
       200: 1
       202: 1
       204: 1
       205: 1
       206: q^2
       207: 1
       209: 1
       211: 1
       212: q^2
       213: 1
       214: q^2
       215: 1
       216: q^2
       217: 1
       218: q^2
       219: 1
       220: 1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: 1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: 1
       232: 1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: 1
       238: q^2
       239: 1
       240: q^2
       241: 1
       242: q^2
       243: 1
       244: q^2+1
       245: q^2+1
       246: 1
       247: q^2+1
       248: q^2+1
       249: q^2+1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       282: q^2
       284: 1
       286: 1
       287: 1
       289: 1
       290: q^2
       291: 1
       292: q^2
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: q^2
       304: 1
       305: 1
       306: q^2
       308: 1
       310: 1
       311: 1
       312: q^2
       313: 1
       314: q^2
       315: 1
       316: q^2
       317: 1
       320: 1
       322: 1
       323: 1
       324: q^2
       325: 1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: 1
       338: 1
       339: q^2
       340: 1
       341: q^2
       342: 1
       343: q^2
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: 1
       350: q^2+1
       351: q^2+1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q^2+1
       357: 1
       358: q^2+1
       359: q^2+1
       360: 1
       361: q^2
       362: 1
       363: q^2
       364: 1
       365: q^2
       366: 1
       367: 1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       413: 1
       417: 1
       418: q^2
       420: 1
       422: 1
       423: 1
       425: 1
       426: q^2
       427: 1
       430: 1
       432: 1
       433: 1
       434: q^2
       435: 1
       436: q^2
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: q^2
       448: 1
       450: 1
       451: 1
       452: q^2
       454: 1
       455: 1
       456: q^2
       458: 1
       459: 1
       462: 1
       463: 1
       464: q^2
       465: 1
       467: 1
       468: q^2
       469: 1
       472: 1
       474: 1
       475: 1
       476: q^2
       477: 1
       478: q^2
       479: 1
       480: q^2
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q^2
       487: 1
       488: q^2
       489: 1
       490: q^2
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: q^2+1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       508: 1
       509: 1
       510: 1
       511: 1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: 1
       519: 1
       520: 1
       524: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       581: q^2
       585: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       598: q^2
       599: 1
       601: 1
       604: 1
       605: 1
       606: q^2
       608: 1
       609: 1
       613: 1
       614: q^2
       616: 1
       617: 1
       618: q^2
       620: 1
       622: 1
       623: 1
       624: q^2
       625: 1
       629: 1
       630: q^2
       632: 1
       633: 1
       634: q^2
       639: 1
       642: 1
       644: 1
       645: 1
       646: q^2
       648: 1
       650: 1
       651: 1
       652: q^2
       653: 1
       655: 1
       656: q^2
       657: 1
       658: 1
       659: q^2
       660: 1
       661: q^2
       662: 1
       663: q^2
       664: q^2+1
       665: 1
       672: 1
       673: 1
       674: q^2+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q^2+1
       680: q^2+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: 1
       692: 1
       697: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       735: 1
       739: 1
       743: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       773: q^2
       775: 1
       779: 1
       780: q^2
       781: 1
       786: 1
       788: 1
       791: 1
       792: q^2
       794: 1
       795: 1
       796: q^2
       797: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       810: q^2
       811: 1
       816: 1
       818: 1
       819: 1
       820: q^2
       821: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       834: q^2
       835: 1
       840: 1
       843: 1
       844: q^2
       846: 1
       848: 1
       849: 1
       850: q^2
       851: 1
       855: 1
       856: q^2
       857: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: q^2+1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q^2+1
       881: 1
       882: 1
       883: 1
       889: 1
       902: 1
       906: 1
       911: 1
       918: 1
       922: 1
       927: 1
       930: 1
       942: 1
       946: 1
       950: 1
       955: 1
       961: 1
       967: 1
       968: 1
       972: q^2
       975: 1
       991: 1
       994: 1
       999: 1
      1001: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1011: q^2
      1012: 1
      1013: q^2
      1017: 1
      1020: 1
      1021: q^2
      1022: 1
      1027: 1
      1029: 1
      1033: 1
      1036: 1
      1037: q^2
      1038: 1
      1041: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1061: q^2
      1062: 1
      1064: 1
      1065: q^2
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: 1
      1091: 1
      1116: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1142: q^2
      1154: 1
      1158: 1
      1163: 1
      1174: 1
      1178: 1
      1183: 1
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1217: 1
      1219: 1
      1220: 1
      1224: 1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1241: 1
      1243: 1
      1247: 1
      1248: 1
      1251: 1
      1255: 1
      1259: 1
      1261: 1
      1262: 1
      1266: 1
      1269: 1
      1271: 1
      1274: 1
      1275: q^2
      1276: 1
      1278: 1
      1279: q^2
      1280: 1
      1281: q^2
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1329: 1
      1331: 1
      1350: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1382: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1413: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1434: q^2
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1451: 1
      1455: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1474: 1
      1477: 1
      1479: 1
      1482: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1506: 1
      1518: 1
      1538: 1
      1552: 1
      1578: 1
      1580: 1
      1598: 1
      1600: 1
      1609: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1639: 1
      1641: 1
      1646: 1
      1648: 1
      1650: 1
      1654: 1
      1656: 1
      1658: 1
      1659: 1
      1664: 1
      1666: 1
      1669: 1
      1673: 1
      1674: 1
      1718: 1
      1736: 1
      1742: 1
      1752: 1
      1759: 1
      1770: 1
      1776: 1
      1783: 1
      1800: 1
      1808: 1
      1814: 1
      1817: 1
      1820: 1
      1822: 1
      1825: 1
      1830: 1
      1832: 1
      1833: 1
      1889: 1
      1900: 1
      1907: 1
      1916: 1
      1923: 1
      1943: 1
      1945: 1
      1955: 1
      1960: 1
      1963: 1
      1965: 1
      2019: 1
      2042: 1
      2054: 1
      2063: 1
      2067: 1
      2135: 1

2136:    0: 5q^5+10q^4+7q^3+q^2+q
         1: q^6+7q^5+10q^4+7q^3+q^2+q
         2: 5q^5+10q^4+7q^3+q^2+q
         3: 5q^5+10q^4+7q^3+q^2+q
         4: 5q^5+10q^4+7q^3+q^2+q
         5: 5q^5+10q^4+7q^3+q^2+q
         6: q^6+7q^5+10q^4+7q^3+q^2+q
         7: 5q^5+10q^4+7q^3+q^2+q
         8: 5q^5+10q^4+7q^3+q^2+q
         9: 3q^6+7q^5+7q^4+5q^3+q^2+q
        10: q^5+5q^4+6q^3+q^2+q
        11: 5q^4+6q^3+q^2+q
        12: q^5+5q^4+6q^3+q^2+q
        13: 5q^5+10q^4+7q^3+q^2+q
        14: 5q^5+10q^4+7q^3+q^2+q
        15: 5q^5+10q^4+7q^3+q^2+q
        16: 2q^5+8q^4+7q^3+q^2+q
        17: 3q^5+8q^4+7q^3+q^2+q
        18: 5q^5+7q^4+5q^3+q^2+q
        19: 5q^5+10q^4+7q^3+q^2+q
        20: q^6+7q^5+10q^4+7q^3+q^2+q
        21: 5q^5+10q^4+7q^3+q^2+q
        22: 2q^5+8q^4+7q^3+q^2+q
        23: 3q^5+8q^4+7q^3+q^2+q
        24: 2q^5+8q^4+7q^3+q^2+q
        25: 2q^5+8q^4+7q^3+q^2+q
        26: 3q^5+8q^4+7q^3+q^2+q
        27: 2q^5+8q^4+7q^3+q^2+q
        28: 3q^4+6q^3+q^2+q
        29: q^5+5q^4+6q^3+q^2+q
        30: 5q^5+10q^4+7q^3+q^2+q
        31: 3q^4+6q^3+q^2+q
        32: 2q^5+8q^4+7q^3+q^2+q
        33: q^5+6q^4+7q^3+q^2+q
        34: 3q^4+6q^3+q^2+q
        35: 2q^5+8q^4+7q^3+q^2+q
        36: q^5+6q^4+7q^3+q^2+q
        37: 4q^4+3q^3
        38: 3q^4+4q^3+q^2+q
        39: q^5+4q^4+3q^3
        40: 3q^4+4q^3+q^2+q
        41: 4q^4+3q^3
        42: 3q^4+4q^3+q^2+q
        43: q^5+5q^4+6q^3+q^2+q
        44: q^5+5q^4+6q^3+q^2+q
        45: 5q^4+6q^3+q^2+q
        46: 2q^5+8q^4+7q^3+q^2+q
        47: 3q^5+8q^4+7q^3+q^2+q
        48: 5q^5+7q^4+5q^3+q^2+q
        49: 2q^5+8q^4+7q^3+q^2+q
        50: 3q^5+8q^4+7q^3+q^2+q
        51: 5q^5+7q^4+5q^3+q^2+q
        52: 2q^5+8q^4+7q^3+q^2+q
        53: 3q^5+8q^4+7q^3+q^2+q
        54: 2q^5+8q^4+7q^3+q^2+q
        55: 2q^5+8q^4+7q^3+q^2+q
        56: 3q^5+8q^4+7q^3+q^2+q
        57: 2q^5+8q^4+7q^3+q^2+q
        58: 2q^3
        59: q^4+4q^3+q^2+q
        60: q^4+4q^3+q^2+q
        61: 2q^3
        62: q^4+2q^3
        63: q^4+4q^3+q^2+q
        64: 4q^4+3q^3
        65: 3q^4+4q^3+q^2+q
        66: 3q^4+3q^3
        67: 2q^4+4q^3+q^2+q
        68: 3q^4+6q^3+q^2+q
        69: 2q^5+5q^4+5q^3+q^2+q
        70: q^5+5q^4+6q^3+q^2+q
        71: 3q^4+6q^3+q^2+q
        72: q^5+6q^4+7q^3+q^2+q
        73: q^5+6q^4+7q^3+q^2+q
        74: 4q^4+3q^3
        75: 3q^4+4q^3+q^2+q
        76: q^5+4q^4+3q^3
        77: 3q^4+4q^3+q^2+q
        78: 4q^4+3q^3
        79: 3q^4+4q^3+q^2+q
        80: 3q^4+6q^3+q^2+q
        81: q^5+6q^4+7q^3+q^2+q
        82: 3q^4+6q^3+q^2+q
        83: 2q^5+8q^4+7q^3+q^2+q
        84: 3q^4+6q^3+q^2+q
        85: q^5+6q^4+7q^3+q^2+q
        86: 3q^4+6q^3+q^2+q
        87: 2q^5+8q^4+7q^3+q^2+q
        88: q^4+6q^3+q^2+q
        89: q^4+6q^3+q^2+q
        90: q^5+3q^4+4q^3+q^2+q
        91: 2q^5+8q^4+7q^3+q^2+q
        92: 3q^5+8q^4+7q^3+q^2+q
        93: 5q^5+7q^4+5q^3+q^2+q
        94: q^5+5q^4+7q^3+q^2+q
        95: q^5+5q^4+7q^3+q^2+q
        96: 2q^5+5q^4+5q^3+q^2+q
        97: q^5+5q^4+7q^3+q^2+q
        98: q^5+5q^4+7q^3+q^2+q
        99: 2q^5+5q^4+5q^3+q^2+q
       100: 6q^4+6q^3+q^2+q
       101: q^5+7q^4+6q^3+q^2+q
       102: 6q^4+6q^3+q^2+q
       103: q^3
       104: 3q^3+q^2+q
       105: q^3
       106: q^3
       107: q^4+4q^3+q^2+q
       108: 2q^3
       109: 2q^3
       110: q^4+4q^3+q^2+q
       111: 3q^4+3q^3
       112: 2q^4+4q^3+q^2+q
       113: q^4+2q^3
       114: q^4+4q^3+q^2+q
       115: 4q^4+3q^3
       116: 3q^4+4q^3+q^2+q
       117: 2q^3
       118: q^4+4q^3+q^2+q
       119: q^4+4q^3+q^2+q
       120: 2q^3
       121: q^4+2q^3
       122: q^4+4q^3+q^2+q
       123: 3q^4+3q^3
       124: 2q^4+4q^3+q^2+q
       125: q^4+6q^3+q^2+q
       126: q^4+4q^3+q^2+q
       127: q^4+3q^3
       128: 3q^3+q^2+q
       129: q^4+3q^3
       130: 3q^3+q^2+q
       131: q^4+2q^3
       132: q^4+2q^3+q^2+q
       133: 3q^4+6q^3+q^2+q
       134: 2q^5+5q^4+5q^3+q^2+q
       135: q^5+6q^4+7q^3+q^2+q
       136: q^5+6q^4+7q^3+q^2+q
       137: 6q^3+q^2+q
       138: q^5+3q^4+5q^3+q^2+q
       139: q^4+6q^3+q^2+q
       140: 2q^4+4q^3+q^2+q
       141: 3q^4+6q^3+q^2+q
       142: q^5+5q^4+7q^3+q^2+q
       143: 6q^3+q^2+q
       144: q^5+3q^4+5q^3+q^2+q
       145: q^4+6q^3+q^2+q
       146: 3q^4+6q^3+q^2+q
       147: q^5+5q^4+7q^3+q^2+q
       148: 2q^4+4q^3+q^2+q
       149: 2q^4+5q^3+q^2+q
       150: 6q^4+6q^3+q^2+q
       151: 3q^4+3q^3
       152: 3q^4+3q^3+q^2+q
       153: q^5+4q^4+3q^3
       154: 3q^4+3q^3+q^2+q
       155: 3q^4+3q^3
       156: 3q^4+3q^3+q^2+q
       157: q^4+6q^3+q^2+q
       158: q^4+6q^3+q^2+q
       159: q^5+3q^4+4q^3+q^2+q
       160: q^5+5q^4+7q^3+q^2+q
       161: q^5+5q^4+7q^3+q^2+q
       162: 2q^5+5q^4+5q^3+q^2+q
       163: q^5+5q^4+7q^3+q^2+q
       164: q^5+5q^4+7q^3+q^2+q
       165: 2q^5+5q^4+5q^3+q^2+q
       166: 2q^4+5q^3+q^2+q
       167: 3q^4+5q^3+q^2+q
       168: 4q^4+4q^3+q^2+q
       169: q^3
       170: 3q^3+q^2+q
       171: q^3
       172: q^3
       173: q^3
       174: 3q^3+q^2+q
       175: q^3
       176: q^3
       177: 2q^3
       178: 2q^3+q^2+q
       179: 2q^3
       180: 3q^3+q^2+q
       181: q^4+3q^3
       182: 3q^3+q^2+q
       183: q^4+4q^3+q^2+q
       184: 2q^3
       185: 2q^3
       186: q^4+4q^3+q^2+q
       187: 3q^4+3q^3
       188: 2q^4+4q^3+q^2+q
       189: q^4+2q^3
       190: q^4+4q^3+q^2+q
       191: 2q^3
       192: 4q^3+q^2+q
       193: 3q^3+q^2+q
       195: 2q^3
       196: q^4+4q^3+q^2+q
       197: q^4+2q^3
       198: q^4+2q^3+q^2+q
       199: 4q^3+q^2+q
       200: 2q^3
       201: q^4+4q^3+q^2+q
       202: 2q^3
       204: 3q^3+q^2+q
       205: q^4+2q^3
       206: q^4+2q^3+q^2+q
       207: 2q^3
       208: 4q^3+q^2+q
       209: q^4+2q^3
       210: q^4+3q^3+q^2+q
       211: 3q^4+3q^3
       212: 3q^4+3q^3+q^2+q
       213: q^4+3q^3
       214: 3q^3+q^2+q
       215: q^4+3q^3
       216: 3q^3+q^2+q
       217: q^4+2q^3
       218: q^4+2q^3+q^2+q
       219: q^4+4q^3+q^2+q
       220: q^4+6q^3+q^2+q
       221: q^4+4q^3+q^2+q
       222: 6q^3+q^2+q
       223: q^5+3q^4+5q^3+q^2+q
       224: 6q^3+q^2+q
       225: q^5+3q^4+5q^3+q^2+q
       226: 4q^3+q^2+q
       227: q^4+6q^3+q^2+q
       228: q^5+3q^4+5q^3+q^2+q
       229: 2q^4+4q^3+q^2+q
       230: q^5+5q^4+7q^3+q^2+q
       231: 4q^3+q^2+q
       232: q^4+6q^3+q^2+q
       233: q^5+3q^4+5q^3+q^2+q
       234: q^5+5q^4+7q^3+q^2+q
       235: 2q^4+4q^3+q^2+q
       236: 2q^4+4q^3+q^2+q
       237: 3q^3
       238: q^3+q^2+q
       239: q^4+3q^3
       240: q^3+q^2+q
       241: q^4+2q^3
       242: q^4+q^3+q^2+q
       243: 4q^3+q^2+q
       244: q^4+3q^3+q^2+q
       245: q^4+3q^3+q^2+q
       246: 2q^4+5q^3+q^2+q
       247: 2q^4+5q^3+q^2+q
       248: 3q^4+5q^3+q^2+q
       249: 4q^4+4q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^4+5q^3+q^2+q
       257: 3q^4+5q^3+q^2+q
       258: 4q^4+4q^3+q^2+q
       259: q^3
       260: 2q^3+q^2+q
       261: q^3
       262: q^3
       263: q^3
       264: 3q^3+q^2+q
       265: q^3
       266: q^3
       267: q^3
       268: 2q^3+q^2+q
       273: q^3
       274: 2q^3+q^2+q
       275: q^3
       276: 3q^3+q^2+q
       277: q^3
       278: q^3
       279: 2q^3
       280: 3q^3+q^2+q
       281: 2q^3
       282: 2q^3+q^2+q
       283: 2q^3+q^2+q
       286: 2q^3+q^2+q
       287: q^3
       288: 2q^3+q^2+q
       289: q^4+3q^3
       290: 3q^3+q^2+q
       291: 2q^3
       292: 2q^3+q^2+q
       293: 4q^3+q^2+q
       294: 2q^3
       295: 2q^3
       296: 4q^3+q^2+q
       297: 2q^3
       298: 4q^3+q^2+q
       299: 3q^3+q^2+q
       301: 2q^3
       302: q^2+q
       303: 2q^3
       304: q^4+4q^3+q^2+q
       305: q^4+2q^3
       306: q^4+2q^3+q^2+q
       307: q^4+4q^3+q^2+q
       308: 2q^3
       310: 3q^3+q^2+q
       311: 2q^3
       312: q^2+q
       313: q^4+2q^3
       314: q^4+2q^3+q^2+q
       315: 2q^3
       316: q^3+q^2+q
       317: 2q^3
       318: q^3+q^2+q
       319: 2q^3+q^2+q
       322: 2q^3+q^2+q
       323: q^3
       324: q^3+q^2+q
       325: q^4+2q^3
       326: q^4+3q^3+q^2+q
       333: q^4+4q^3+q^2+q
       334: 4q^3+q^2+q
       335: 4q^3+q^2+q
       336: 2q^4+4q^3+q^2+q
       337: 4q^3+q^2+q
       338: 3q^3
       339: q^3+q^2+q
       340: q^4+3q^3
       341: q^3+q^2+q
       342: q^4+2q^3
       343: q^4+q^3+q^2+q
       344: 4q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^5+3q^4+5q^3+q^2+q
       351: q^4+3q^3+q^2+q
       352: 4q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^5+3q^4+5q^3+q^2+q
       357: q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^4+3q^3+q^2+q
       360: 3q^3
       361: q^3+q^2+q
       362: q^4+3q^3
       363: q^3+q^2+q
       364: q^4+2q^3
       365: q^4+q^3+q^2+q
       366: 3q^3+q^2+q
       367: 4q^3+q^2+q
       368: 2q^4+4q^3+q^2+q
       369: q^4+3q^3+q^2+q
       370: q^4+3q^3+q^2+q
       371: 2q^4+5q^3+q^2+q
       372: 3q^4+5q^3+q^2+q
       373: 4q^4+4q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       378: q^3+q^2+q
       381: q^3
       382: 2q^3+q^2+q
       383: q^3
       384: q^3
       385: q^3
       386: 3q^3+q^2+q
       387: q^3
       388: q^3
       389: q^3
       390: q^2+q
       393: q^3
       394: 2q^3+q^2+q
       399: q^3
       400: q^2+q
       403: 2q^3+q^2+q
       404: q^3
       407: q^3+q^2+q
       413: q^3
       414: 2q^3+q^2+q
       417: 2q^3
       418: 2q^3+q^2+q
       419: 2q^3+q^2+q
       422: 2q^3+q^2+q
       423: q^3
       424: 2q^3+q^2+q
       425: 2q^3
       426: q^3+q^2+q
       427: 2q^3
       428: q^3+q^2+q
       429: q^3+q^2+q
       432: 2q^3+q^2+q
       433: q^3
       434: q^2+q
       435: 2q^3
       436: q^2+q
       437: q^3+q^2+q
       439: q^3
       440: 2q^3+q^2+q
       442: q^3+q^2+q
       443: 2q^3+q^2+q
       445: 2q^3
       446: q^2+q
       447: 2q^3+q^2+q
       450: q^3+q^2+q
       451: q^3
       452: q^2+q
       453: 2q^3+q^2+q
       454: q^3
       455: 2q^3
       456: q^2+q
       458: q^3+q^2+q
       460: q^3+q^2+q
       462: 2q^3+q^2+q
       463: 2q^3
       464: q^2+q
       465: 2q^3
       466: q^3+q^2+q
       467: 2q^3
       468: q^3+q^2+q
       469: q^3
       470: q^3+q^2+q
       471: 2q^3+q^2+q
       474: 2q^3+q^2+q
       475: q^3
       476: q^3+q^2+q
       477: q^3
       478: 2q^2+q
       479: q^3
       480: q^3+q^2+q
       481: 4q^3+q^2+q
       482: 4q^3+q^2+q
       483: 3q^3+q^2+q
       484: 4q^3+q^2+q
       485: 3q^3
       486: q^3+q^2+q
       487: q^4+3q^3
       488: q^3+q^2+q
       489: q^4+2q^3
       490: q^4+q^3+q^2+q
       491: 2q^4+4q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^4+2q^3+q^2+q
       496: q^4+3q^3+q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^4+2q^3+q^2+q
       501: q^4+3q^3+q^2+q
       508: 3q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^4+2q^3+q^2+q
       513: q^2+q
       514: q^4+2q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       522: q^3+q^2+q
       530: q^3+q^2+q
       534: q^2+q
       537: q^3
       538: q^2+q
       542: q^3+q^2+q
       545: q^3
       546: q^2+q
       551: q^2+q
       555: q^3
       556: q^2+q
       560: q^3+q^2+q
       563: q^3
       564: q^2+q
       566: q^3+q^2+q
       571: 2q^2+q
       574: q^3+q^2+q
       577: q^3
       581: q^2+q
       582: q^2
       585: q^3
       586: 2q^3+q^2+q
       589: 2q^3+q^2+q
       592: q^3+q^2+q
       593: q^3+q^2+q
       596: 2q^3+q^2+q
       597: 2q^3
       598: q^3+q^2+q
       599: q^3
       600: q^3+q^2+q
       601: 2q^3
       602: q^3+q^2+q
       603: q^2+q
       605: q^3
       606: q^2+q
       608: q^3+q^2+q
       610: q^2+q
       613: q^3
       614: q^2+q
       615: 2q^3+q^2+q
       617: 2q^3
       618: q^2+q
       619: q^3+q^2+q
       622: q^2+q
       623: q^3
       624: q^2+q
       626: q^2+q
       629: q^3
       630: q^2+q
       632: 2q^3+q^2+q
       633: 2q^3
       634: q^2+q
       639: q^3
       640: q^3+q^2+q
       641: q^3+q^2+q
       644: q^3+q^2+q
       646: q^2+q
       647: q^2+q
       650: q^2+q
       651: q^3
       652: 2q^2+q
       654: q^2+q
       655: q^3
       656: q^3+q^2+q
       657: q^2+q
       658: 2q^3+q^2
       659: q^3+q
       660: 2q^3+q^2
       661: q
       662: 2q^3+q^2
       663: q^3+q
       664: 3q^3+q^2+q
       665: 3q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q^3+q^2+q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^4+2q^3+q^2+q
       680: q^3+q^2+q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^4+2q^3+q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q^3+q
       690: q^3+q
       691: q
       692: q^3+q
       699: q^2+q
       703: q^2
       710: q^3+q^2+q
       715: q^2+q
       718: q^2+q
       722: q^2+q
       726: q^2+q
       733: q^3
       734: q^2+q
       740: q^2+q
       744: q^2+q
       751: q^3
       752: q^2+q
       754: q^2+q
       759: 2q^2+q
       763: q^2+q
       766: q^3+q^2+q
       769: q^3
       773: q^2+q
       774: q^2
       775: q^2
       776: q
       779: 2q^3+q^2
       780: q^3+q
       781: q^3
       782: q^3+q^2+q
       785: q^3+q^2+q
       788: q^3+q^2+q
       792: q^2+q
       793: q^2+q
       795: q^3+q^2
       796: q
       798: q^2+q
       801: q^2+q
       804: q
       805: q^2+q
       808: q^3+q^2+q
       809: q^3
       810: q^2+q
       812: q^2+q
       815: q^2+q
       818: q^2+q
       819: q^3+q^2
       820: q
       822: q^2+q
       825: q^3+q^2+q
       828: q^2+q
       829: q
       832: q^2+q
       833: q^3
       834: q^2+q
       836: q^2+q
       840: q^2+q
       844: q^2+q
       845: q^2+q
       848: q^2+q
       850: q^2+q
       852: q^2+q
       856: q
       858: q^2+q
       865: q
       866: q^2+q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q^3+q^2+q
       871: q^2+q
       872: q^2+q
       873: q
       874: q^3+q^2+q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q^3+q
       881: q^3+q
       882: q
       883: q^3+q
       890: q^2+q
       894: q^2
       903: q^2+q
       905: q^2+q
       909: q^2+q
       916: q^2
       917: q
       921: q^2+q
       926: q
       929: q^2+q
       942: q^2
       943: q
       947: q^2+q
       951: q^2+q
       953: q
       962: q^2+q
       965: q^2+q
       971: q^2
       972: q
       976: q^2+q
       989: q^2+q
       994: q^2
       995: q
       999: q^2+q
      1000: q^2+q
      1004: q^2+q
      1007: q^2+q
      1009: q^2+q
      1011: q^2+q
      1013: q^2+q
      1016: q
      1020: q^3+q^2
      1021: q
      1023: q^2+q
      1026: q^2+q
      1029: q
      1033: q
      1036: q^3+q^2
      1037: q
      1039: q^2+q
      1040: q
      1045: q^2+q
      1047: q
      1049: q^2+q
      1052: q^2+q
      1055: q
      1056: q
      1059: q^2+q
      1061: q
      1063: q
      1065: q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q^2+q
      1085: q
      1089: q^2
      1092: q
      1116: q^2
      1117: q
      1122: q^2
      1123: q
      1128: q^2+q
      1131: q^2+q
      1136: q^2+q
      1141: q^2
      1142: q
      1155: q
      1157: q^2+q
      1162: q
      1175: q^2+q
      1177: q
      1181: q
      1195: q
      1200: q^2+q
      1205: q
      1207: q
      1217: q
      1218: q
      1221: q^2+q
      1225: q
      1228: q
      1231: q
      1233: q
      1234: q
      1240: q^2+q
      1243: q
      1247: q
      1249: q
      1251: q
      1254: q
      1258: q
      1261: q^2+q
      1263: q
      1267: q
      1268: q
      1271: q
      1274: q^2
      1275: q
      1277: q
      1279: q
      1281: q^2+q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1293: q^2
      1296: q
      1327: q
      1332: q^2+q
      1351: q
      1357: q
      1363: q
      1366: q
      1371: q
      1383: q
      1389: q
      1394: q
      1397: q
      1402: q
      1411: q
      1421: q
      1423: q
      1427: q
      1433: q^2
      1434: q
      1437: q
      1441: q
      1442: q
      1445: q
      1451: q
      1454: q
      1461: q
      1462: q
      1475: q
      1476: q
      1479: q
      1483: q
      1485: q
      1486: q
      1488: q
      1508: q
      1519: q
      1539: q
      1550: q
      1577: q
      1582: q
      1596: q
      1601: q
      1620: q
      1628: q
      1640: q
      1646: q
      1647: q
      1654: q
      1655: q
      1670: q
      1734: q
      1751: q
      1774: q
      1809: q
      1946: 1
      2023: 1
      2061: 1
      2136: 1

2137:    0: 3q^3+4q^2+3q
         1: 3q^3+4q^2+3q
         2: 3q^3+4q^2+3q
         3: 3q^3+4q^2+3q
         4: q^4+3q^3+3q^2+3q
         5: 3q^3+4q^2+3q
         6: q^4+3q^3+3q^2+3q
         7: q^4+3q^3+3q^2+3q
         8: 3q^3+4q^2+3q
         9: q^4+3q^3+3q^2+3q
        10: 4q^2+3q
        11: 4q^2+3q
        12: q^3+3q^2+3q
        13: 3q^3+4q^2+3q
        14: q^4+3q^3+3q^2+3q
        15: 3q^3+4q^2+3q
        16: 3q^3+4q^2+3q
        17: 3q^3+4q^2+3q
        18: q^4+3q^3+3q^2+3q
        19: 2q^3+3q^2+3q
        20: 2q^3+3q^2+3q
        21: 2q^3+3q^2+3q
        22: 3q^3+4q^2+3q
        23: 3q^3+4q^2+3q
        24: 3q^3+4q^2+3q
        25: 3q^3+4q^2+3q
        26: 3q^3+4q^2+3q
        27: 3q^3+4q^2+3q
        28: 4q^2+3q
        29: 3q^2+3q
        30: 2q^3+3q^2+3q
        31: 4q^2+3q
        32: 3q^3+4q^2+3q
        33: 3q^3+4q^2+3q
        34: 4q^2+3q
        35: 3q^3+4q^2+3q
        36: 3q^3+4q^2+3q
        37: 2q^3+2q^2+q
        38: q^3+2q^2+2q
        39: 2q^3+2q^2+q
        40: q^3+2q^2+2q
        41: 2q^3+2q^2+q
        42: q^3+2q^2+2q
        43: 4q^2+3q
        44: q^3+3q^2+3q
        45: 4q^2+3q
        46: 3q^3+4q^2+3q
        47: 3q^3+4q^2+3q
        48: q^4+3q^3+3q^2+3q
        49: 2q^3+3q^2+3q
        50: 2q^3+3q^2+3q
        51: 2q^3+3q^2+3q
        52: 2q^3+3q^2+3q
        53: 2q^3+3q^2+3q
        54: 2q^3+3q^2+3q
        55: 2q^3+3q^2+3q
        56: 2q^3+3q^2+3q
        57: 2q^3+3q^2+3q
        58: q^2+q
        59: 3q^2+2q
        60: q^2+q
        61: 3q^2+2q
        62: 2q^2+q
        63: 2q^2+2q
        64: 2q^3+2q^2+q
        65: q^3+2q^2+2q
        66: 2q^3+2q^2+q
        67: q^3+2q^2+2q
        68: 4q^2+3q
        69: 2q^3+3q^2+3q
        70: 3q^2+3q
        71: 3q^2+3q
        72: q^3+2q^2+3q
        73: q^3+2q^2+3q
        74: q^3+q^2+q
        75: q^2+2q
        76: q^3+q^2+q
        77: q^2+2q
        78: q^3+q^2+q
        79: q^2+2q
        80: 4q^2+3q
        81: 3q^3+4q^2+3q
        82: 3q^2+3q
        83: 2q^3+3q^2+3q
        84: 4q^2+3q
        85: 3q^3+4q^2+3q
        86: 3q^2+3q
        87: 2q^3+3q^2+3q
        88: 4q^2+3q
        89: 4q^2+3q
        90: q^3+3q^2+3q
        91: 2q^3+3q^2+3q
        92: 2q^3+3q^2+3q
        93: 2q^3+3q^2+3q
        94: 2q^3+3q^2+3q
        95: 2q^3+3q^2+3q
        96: 2q^3+3q^2+3q
        97: 2q^3+3q^2+3q
        98: 2q^3+3q^2+3q
        99: 2q^3+3q^2+3q
       100: 2q^3+3q^2+3q
       101: 2q^3+3q^2+3q
       102: 2q^3+3q^2+3q
       104: q^2+q
       105: q^2+q
       106: 2q^2+q
       107: q
       108: 2q^2+2q
       109: q
       110: 2q^2+2q
       111: q^2+q
       112: 2q
       113: q^2+q
       114: q^2+2q
       115: q^3+q^2+q
       116: q^2+2q
       117: q^2+q
       118: 3q^2+2q
       119: q^2+q
       120: 3q^2+2q
       121: 2q^2+q
       122: 2q^2+2q
       123: 2q^3+2q^2+q
       124: q^3+2q^2+2q
       125: 4q^2+3q
       126: 3q^2+3q
       127: q^3+q^2+q
       128: q^2+2q
       129: q^3+q^2+q
       130: q^2+2q
       131: q^3+q^2+q
       132: q^2+2q
       133: 3q^2+3q
       134: 2q^3+3q^2+3q
       135: q^3+2q^2+3q
       136: q^3+2q^2+3q
       137: 4q^2+3q
       138: 2q^3+3q^2+3q
       139: 3q^2+3q
       140: q^3+2q^2+3q
       141: 3q^2+3q
       142: q^3+2q^2+3q
       143: 4q^2+3q
       144: 2q^3+3q^2+3q
       145: 3q^2+3q
       146: 3q^2+3q
       147: q^3+2q^2+3q
       148: q^3+2q^2+3q
       149: 3q^2+3q
       150: 2q^3+3q^2+3q
       151: q^3+q^2+q
       152: q^2+2q
       153: q^3+q^2+q
       154: q^2+2q
       155: q^3+q^2+q
       156: q^2+2q
       157: 2q^2+3q
       158: 2q^2+3q
       159: 2q^2+3q
       160: 2q^3+3q^2+3q
       161: 2q^3+3q^2+3q
       162: 2q^3+3q^2+3q
       163: 2q^3+3q^2+3q
       164: 2q^3+3q^2+3q
       165: 2q^3+3q^2+3q
       166: 2q^3+3q^2+3q
       167: 2q^3+3q^2+3q
       168: 2q^3+3q^2+3q
       170: q
       171: q
       172: q^2+q
       174: q^2+q
       175: q^2+q
       176: 2q^2+q
       177: q^3+q^2+q
       178: q^2+2q
       179: q^2+q
       180: q^2+2q
       181: q^2+q
       182: 2q
       183: q
       184: 2q^2+2q
       185: q
       186: 2q^2+2q
       187: q^2+q
       188: 2q
       189: q^2+q
       190: q^2+2q
       191: q^2+q
       192: 3q^2+2q
       193: q
       194: 2q^2+2q
       195: q
       196: 2q^2+2q
       197: q^2+q
       198: 2q
       199: q^2+q
       200: 3q^2+2q
       201: q
       202: 2q^2+2q
       203: q
       204: 2q^2+2q
       205: q^2+q
       206: 2q
       207: 2q^2+q
       208: 2q^2+2q
       209: q^2+q
       210: q^2+2q
       211: q^3+q^2+q
       212: q^2+2q
       213: q^3+q^2+q
       214: q^2+2q
       215: q^3+q^2+q
       216: q^2+2q
       217: q^3+q^2+q
       218: q^2+2q
       219: 3q^2+3q
       220: 2q^2+3q
       221: 2q^2+3q
       222: q^2+3q
       223: q^3+2q^2+3q
       224: q^2+3q
       225: q^3+2q^2+3q
       226: 3q^2+3q
       227: 3q^2+3q
       228: 2q^3+3q^2+3q
       229: q^3+2q^2+3q
       230: q^3+2q^2+3q
       231: 3q^2+3q
       232: 3q^2+3q
       233: 2q^3+3q^2+3q
       234: q^3+2q^2+3q
       235: q^3+2q^2+3q
       236: 2q^3+3q^2+3q
       237: q^3+q^2+q
       238: q^2+2q
       239: q^3+q^2+q
       240: q^2+2q
       241: q^3+q^2+q
       242: q^2+2q
       243: 3q^2+3q
       244: q^3+2q^2+3q
       245: q^3+2q^2+3q
       246: 3q^2+3q
       247: 2q^2+4q
       248: 2q^2+4q
       249: q^3+2q^2+3q
       250: 2q^2+3q
       251: 2q^2+3q
       252: 2q^2+3q
       253: 2q^2+3q
       254: 2q^2+3q
       255: 2q^2+3q
       256: 2q^3+3q^2+3q
       257: 2q^3+3q^2+3q
       258: 2q^3+3q^2+3q
       260: q
       261: q
       262: q^2+q
       264: q
       265: q
       266: q^2+q
       268: q
       269: q^2+q
       270: q
       272: q
       273: q^2+q
       274: q
       276: q^2+q
       277: q^2+q
       278: 2q^2+q
       279: q^2+q
       280: q^2+2q
       281: q^3+q^2+q
       282: q^2+2q
       283: q
       284: 2q^2+2q
       285: q
       286: 2q^2+2q
       287: q^2+q
       288: q^2+2q
       289: q^2+q
       290: 2q
       291: q^2+q
       292: 2q
       293: q
       294: q^2+2q
       295: q
       296: q^2+2q
       297: q
       298: 2q
       299: q
       300: 2q^2+2q
       301: q^2+q
       302: 2q
       303: q
       304: 2q^2+2q
       305: q^2+q
       306: 2q
       307: q
       308: 2q^2+2q
       309: q
       310: 2q^2+2q
       311: q^2+q
       312: 2q
       313: q^2+q
       314: 2q
       315: q^3+q^2+q
       316: q^2+2q
       317: q^2+q
       318: q^2+2q
       319: q
       320: 2q^2+2q
       321: q
       322: 2q^2+2q
       323: q^2+q
       324: 2q
       325: q^2+q
       326: q^2+2q
       333: 2q^2+3q
       334: q^2+3q
       335: q^2+3q
       336: q^2+3q
       337: q^2+4q
       338: 2q^2+q
       339: 3q
       340: 2q^2+q
       341: 3q
       342: q^3+q^2+q
       343: q^2+2q
       344: 3q^2+3q
       345: 2q^2+3q
       346: 2q^2+3q
       347: q^2+3q
       348: q^3+2q^2+3q
       349: q^2+3q
       350: q^3+2q^2+3q
       351: 2q^2+4q
       352: 3q^2+3q
       353: 2q^2+3q
       354: 2q^2+3q
       355: q^2+3q
       356: q^3+2q^2+3q
       357: q^2+3q
       358: q^3+2q^2+3q
       359: 2q^2+4q
       360: q^3+q^2+q
       361: q^2+2q
       362: q^3+q^2+q
       363: q^2+2q
       364: q^3+q^2+q
       365: q^2+2q
       366: 3q^2+3q
       367: 3q^2+3q
       368: 2q^3+3q^2+3q
       369: q^3+2q^2+3q
       370: q^3+2q^2+3q
       371: 2q^2+4q
       372: 2q^2+4q
       373: q^3+2q^2+3q
       374: 2q^2+3q
       375: 2q^2+3q
       376: 2q^2+3q
       378: q
       379: q
       380: q^2+q
       382: q
       383: q
       384: q^2+q
       386: q
       387: q
       388: q
       390: q
       391: q^2+q
       392: q
       394: q
       395: q
       396: q^2+q
       398: q
       399: q^2+q
       400: q
       402: q
       403: q
       404: q^2+q
       406: q^2+q
       407: q
       408: q
       413: q^2+q
       414: q^2+2q
       417: q^2+q
       418: 2q
       419: q
       420: q^2+2q
       421: q
       422: q^2+2q
       423: q
       424: 2q
       425: q^2+q
       426: 2q
       427: q^2+q
       428: 3q
       429: q
       430: 2q^2+2q
       431: q
       432: 2q^2+2q
       433: q^2+q
       434: 2q
       435: q^2+q
       436: 2q
       437: q
       438: q^2+2q
       439: q
       440: q^2+2q
       441: q
       442: 2q
       443: q
       444: q^2+3q
       445: 2q^2+q
       446: 3q
       447: q
       448: 2q^2+2q
       449: q
       450: 2q^2+2q
       451: q^2+q
       452: 2q
       453: q
       454: q^2+2q
       455: q^2+q
       456: 2q
       457: q
       458: q^2+2q
       459: q
       460: 2q
       461: q
       462: q^2+3q
       463: 2q^2+q
       464: 3q
       465: q^2+q
       466: q^2+2q
       467: q^3+q^2+q
       468: q^2+2q
       469: q^2+q
       470: q^2+2q
       471: q
       472: 2q^2+2q
       473: q
       474: 2q^2+2q
       475: q^2+q
       476: 2q
       477: q^2+q
       478: 2q
       479: q^2+2q
       480: q^2+2q
       481: q^2+3q
       482: q^2+3q
       483: 3q
       484: q^2+4q
       485: 2q^2+q
       486: 3q
       487: 2q^2+q
       488: 3q
       489: q^3+q^2+q
       490: q^2+2q
       491: q^2+3q
       492: 2q^2+3q
       493: q^2+3q
       494: q^2+3q
       495: q^2+3q
       496: 2q^2+4q
       497: 2q^2+3q
       498: q^2+3q
       499: q^2+3q
       500: q^2+3q
       501: 2q^2+4q
       508: 3q^2+3q
       509: 2q^2+3q
       510: 2q^2+3q
       511: q^2+3q
       512: q^3+2q^2+3q
       513: q^2+3q
       514: q^3+2q^2+3q
       515: 2q^2+4q
       516: 2q^2+4q
       517: q^3+2q^2+3q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       524: q^2+q
       530: q
       531: q
       532: q
       534: q
       535: q
       536: q^2+q
       538: q
       539: q^2+q
       540: q
       542: q
       543: q
       544: q
       546: q
       547: q^2+q
       548: 2q
       550: q
       551: q
       552: q^2+q
       554: q
       555: q^2+q
       556: q
       558: q
       559: q
       560: q
       562: q
       563: q^2+q
       564: 2q
       566: q
       567: q
       568: q^2+q
       570: q^2+q
       571: q
       572: q
       574: q
       575: q^2+2q
       576: q
       577: q^2+q
       578: q
       580: q^2
       581: 2q
       585: q
       586: 2q
       589: q
       590: q^2+2q
       592: 2q
       594: 2q
       595: q
       596: q^2+2q
       597: q^2+q
       598: 2q
       599: q
       600: 2q
       601: q^2+q
       602: 3q
       603: q
       604: q^2+2q
       605: q^2+q
       606: 2q
       607: q
       608: q^2+2q
       609: q
       610: 2q
       613: q^2+q
       614: 2q
       615: q
       616: q^2+3q
       617: 2q^2+q
       618: 3q
       619: q
       620: q^2+2q
       621: q
       622: q^2+2q
       623: q^2+q
       624: 2q
       625: q
       626: 2q
       629: q^2+q
       630: 2q
       631: q
       632: q^2+3q
       633: 2q^2+q
       634: 3q
       639: q^2+q
       640: q^2+2q
       641: q
       642: 2q^2+2q
       643: q
       644: 2q^2+2q
       645: q^2+q
       646: 2q
       647: q
       648: q^2+2q
       649: q
       650: q^2+2q
       651: q^2+q
       652: 2q
       653: q
       654: 2q
       655: q^2+2q
       656: q^2+2q
       657: q^2+4q
       658: 2q^2+q
       659: 3q
       660: 2q^2+q
       661: 3q
       662: q^3+q^2+q
       663: q^2+2q
       664: q^2+3q
       665: 3q
       672: 3q
       673: 2q
       674: 2q^2+4q
       675: q^2+3q
       676: q^2+3q
       677: 3q
       678: 3q
       679: q^2+3q
       680: 2q^2+4q
       681: q^2+3q
       682: q^2+3q
       683: 3q
       684: 3q
       685: q^2+3q
       686: 2q^2+3q
       687: q^2+3q
       688: q^2+3q
       689: q^2+3q
       690: 3q
       691: 3q
       692: q^2+2q
       697: q^2+q
       699: q
       700: q
       701: q
       710: q
       711: q
       712: q
       715: q
       716: q
       719: q
       720: q
       722: q
       723: q^2+q
       724: q
       726: q
       727: q
       728: q
       734: q
       735: q^2+q
       736: 2q
       738: q
       739: q^2+q
       740: q
       742: q
       743: q
       744: q
       750: q
       751: q^2+q
       752: 2q
       754: q
       755: q
       756: q^2+q
       758: q^2+q
       759: q
       760: q
       762: q
       763: q
       764: q
       766: q
       767: q
       768: q^2+2q
       769: q^2+q
       770: q
       772: q^2
       773: 2q
       775: q^2+q
       776: 3q
       779: q^2+q
       780: 2q
       781: q
       782: 2q
       786: 2q
       788: 2q
       791: q
       792: q
       793: q
       794: q^2+3q
       795: 2q^2+q
       796: 3q
       797: q
       798: 2q
       801: q
       802: q^2+2q
       804: 2q
       806: 2q
       807: q
       808: q^2+2q
       809: q^2+q
       810: 2q
       811: q
       812: 2q
       815: q
       816: 2q
       817: q
       818: q^2+3q
       819: 2q^2+q
       820: 3q
       821: q
       822: 2q
       825: q
       826: q^2+2q
       828: 2q
       830: 2q
       831: q
       832: q^2+2q
       833: q^2+q
       834: 2q
       835: q
       836: 2q
       839: q
       840: 2q
       843: q^2+2q
       844: q^2+2q
       845: q
       846: q^2+2q
       847: q
       848: q^2+2q
       849: q^2+q
       850: 2q
       851: q
       852: 2q
       855: q^2+q
       856: 2q
       857: q
       858: 2q
       865: 3q
       866: 3q
       867: 2q
       868: 2q
       869: 3q
       870: q^2+3q
       871: 3q
       872: 2q
       873: 3q
       874: q^2+3q
       875: 3q
       876: 2q
       877: q^2+3q
       878: q^2+3q
       879: 3q
       880: q^2+3q
       881: 3q
       882: 3q
       883: q^2+2q
       889: q^2+q
       890: q
       891: q
       892: q
       902: q
       903: q
       906: q
       907: q
       911: q
       917: q
       918: q^2+q
       919: 2q
       921: q
       922: q
       923: q
       926: q
       927: q
       930: q
       931: q
       941: q
       942: q^2+q
       943: 2q
       945: q
       946: q
       947: q
       950: q
       951: q
       954: q
       955: q
       961: q^2+q
       962: q
       963: q
       965: q
       966: q
       967: q^2+2q
       968: q^2+q
       969: q
       971: q^2
       972: 2q
       975: q
       976: q
       977: q
       989: q
       990: q
       991: q
       994: q
       995: 2q
       999: 2q
      1001: 2q
      1005: q
      1007: q
      1009: q
      1010: q
      1011: q
      1012: q
      1013: q
      1016: q
      1017: 2q
      1020: q^2+q
      1021: 2q
      1022: q
      1023: 2q
      1027: 2q
      1029: 2q
      1032: q
      1033: 2q
      1036: q^2+q
      1037: 2q
      1038: q
      1039: 2q
      1041: 2q
      1045: 2q
      1046: q
      1047: 2q
      1048: q
      1049: 2q
      1052: q
      1053: q^2+2q
      1055: 2q
      1057: 2q
      1058: q
      1059: q^2+2q
      1060: q^2+q
      1061: 2q
      1062: q
      1063: 2q
      1064: q
      1065: q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 3q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 3q
      1081: 2q
      1082: 2q
      1083: 3q
      1084: q^2+3q
      1085: 2q
      1091: q^2+q
      1092: q
      1093: q
      1094: q
      1116: q
      1117: q
      1124: q
      1125: q
      1127: q
      1133: q
      1138: q
      1142: q
      1154: q
      1155: q
      1158: q
      1159: q
      1163: q
      1174: q
      1175: q
      1178: q
      1179: q
      1183: q
      1195: q
      1196: q
      1197: q
      1199: q
      1200: q
      1201: q
      1204: q
      1205: q
      1208: q
      1209: q
      1217: q
      1219: q
      1221: q
      1225: q
      1228: q
      1229: 2q
      1230: q
      1231: 2q
      1233: 2q
      1235: 2q
      1241: q
      1243: q
      1246: q
      1247: 2q
      1248: q
      1249: 2q
      1251: 2q
      1255: 2q
      1259: q
      1261: q
      1262: q
      1263: 2q
      1266: q
      1267: 2q
      1269: 2q
      1271: 2q
      1274: q^2+q
      1275: 2q
      1277: q
      1278: q
      1279: q
      1280: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 3q
      1288: 2q
      1289: 2q
      1295: q
      1350: q
      1351: q
      1358: q
      1359: q
      1361: q
      1367: q
      1382: q
      1383: q
      1390: q
      1391: q
      1393: q
      1399: q
      1411: q
      1412: q
      1413: q
      1420: q
      1421: q
      1424: q
      1425: q
      1429: q
      1430: q
      1434: q
      1437: q
      1441: q
      1443: q
      1445: q
      1451: q
      1455: q
      1461: q
      1463: q
      1464: q
      1465: 2q
      1467: 2q
      1469: 2q
      1475: q
      1477: q
      1479: q
      1483: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1506: q
      1518: q
      1609: q
      1610: q
      1617: q
      1618: q
      1622: q
      1626: q
      1640: q
      1642: 1
      1646: q
      1648: q
      1650: 1
      1654: q
      1656: q
      1658: 1
      1660: q
      1664: q
      1666: q
      1670: q
      1673: 1
      1674: 2q
      1718: q
      1760: 1
      1784: 1
      1814: 1
      1818: 1
      1820: 1
      1822: 1
      1826: q
      1830: q
      1832: q
      1833: 1
      1890: 1
      1909: 1
      1925: 1
      1955: 1
      1961: 1
      1963: 1
      1965: 1
      2024: 1
      2043: 1
      2055: 1
      2067: 1
      2137: 1

2138:    0: 5q^5+10q^4+7q^3+q^2+q
         1: q^6+7q^5+10q^4+7q^3+q^2+q
         2: 5q^5+10q^4+7q^3+q^2+q
         3: 5q^5+10q^4+7q^3+q^2+q
         4: 5q^5+10q^4+7q^3+q^2+q
         5: 5q^5+10q^4+7q^3+q^2+q
         6: q^6+7q^5+10q^4+7q^3+q^2+q
         7: 5q^5+10q^4+7q^3+q^2+q
         8: 5q^5+10q^4+7q^3+q^2+q
         9: 3q^6+7q^5+7q^4+5q^3+q^2+q
        10: q^5+5q^4+6q^3+q^2+q
        11: 5q^4+6q^3+q^2+q
        12: q^5+5q^4+6q^3+q^2+q
        13: 5q^5+10q^4+7q^3+q^2+q
        14: 5q^5+10q^4+7q^3+q^2+q
        15: 5q^5+10q^4+7q^3+q^2+q
        16: 2q^5+8q^4+7q^3+q^2+q
        17: 3q^5+8q^4+7q^3+q^2+q
        18: 5q^5+7q^4+5q^3+q^2+q
        19: 5q^5+10q^4+7q^3+q^2+q
        20: q^6+7q^5+10q^4+7q^3+q^2+q
        21: 5q^5+10q^4+7q^3+q^2+q
        22: 2q^5+8q^4+7q^3+q^2+q
        23: 3q^5+8q^4+7q^3+q^2+q
        24: 2q^5+8q^4+7q^3+q^2+q
        25: 2q^5+8q^4+7q^3+q^2+q
        26: 3q^5+8q^4+7q^3+q^2+q
        27: 2q^5+8q^4+7q^3+q^2+q
        28: 3q^4+6q^3+q^2+q
        29: q^5+5q^4+6q^3+q^2+q
        30: 5q^5+10q^4+7q^3+q^2+q
        31: 3q^4+6q^3+q^2+q
        32: 2q^5+8q^4+7q^3+q^2+q
        33: q^5+6q^4+7q^3+q^2+q
        34: 3q^4+6q^3+q^2+q
        35: 2q^5+8q^4+7q^3+q^2+q
        36: q^5+6q^4+7q^3+q^2+q
        37: 4q^4+3q^3
        38: 3q^4+4q^3+q^2+q
        39: q^5+4q^4+3q^3
        40: 3q^4+4q^3+q^2+q
        41: 4q^4+3q^3
        42: 3q^4+4q^3+q^2+q
        43: q^5+5q^4+6q^3+q^2+q
        44: q^5+5q^4+6q^3+q^2+q
        45: 5q^4+6q^3+q^2+q
        46: 2q^5+8q^4+7q^3+q^2+q
        47: 3q^5+8q^4+7q^3+q^2+q
        48: 5q^5+7q^4+5q^3+q^2+q
        49: 2q^5+8q^4+7q^3+q^2+q
        50: 3q^5+8q^4+7q^3+q^2+q
        51: 5q^5+7q^4+5q^3+q^2+q
        52: 2q^5+8q^4+7q^3+q^2+q
        53: 3q^5+8q^4+7q^3+q^2+q
        54: 2q^5+8q^4+7q^3+q^2+q
        55: 2q^5+8q^4+7q^3+q^2+q
        56: 3q^5+8q^4+7q^3+q^2+q
        57: 2q^5+8q^4+7q^3+q^2+q
        58: q^4+4q^3+q^2+q
        59: 2q^3
        60: 2q^3
        61: q^4+4q^3+q^2+q
        62: q^4+2q^3
        63: q^4+4q^3+q^2+q
        64: 4q^4+3q^3
        65: 3q^4+4q^3+q^2+q
        66: 3q^4+3q^3
        67: 2q^4+4q^3+q^2+q
        68: 3q^4+6q^3+q^2+q
        69: 2q^5+5q^4+5q^3+q^2+q
        70: q^5+5q^4+6q^3+q^2+q
        71: 3q^4+6q^3+q^2+q
        72: q^5+6q^4+7q^3+q^2+q
        73: q^5+6q^4+7q^3+q^2+q
        74: 4q^4+3q^3
        75: 3q^4+4q^3+q^2+q
        76: q^5+4q^4+3q^3
        77: 3q^4+4q^3+q^2+q
        78: 4q^4+3q^3
        79: 3q^4+4q^3+q^2+q
        80: 3q^4+6q^3+q^2+q
        81: q^5+6q^4+7q^3+q^2+q
        82: 3q^4+6q^3+q^2+q
        83: 2q^5+8q^4+7q^3+q^2+q
        84: 3q^4+6q^3+q^2+q
        85: q^5+6q^4+7q^3+q^2+q
        86: 3q^4+6q^3+q^2+q
        87: 2q^5+8q^4+7q^3+q^2+q
        88: q^4+6q^3+q^2+q
        89: q^4+6q^3+q^2+q
        90: q^5+3q^4+4q^3+q^2+q
        91: 2q^5+8q^4+7q^3+q^2+q
        92: 3q^5+8q^4+7q^3+q^2+q
        93: 5q^5+7q^4+5q^3+q^2+q
        94: q^5+5q^4+7q^3+q^2+q
        95: q^5+5q^4+7q^3+q^2+q
        96: 2q^5+5q^4+5q^3+q^2+q
        97: q^5+5q^4+7q^3+q^2+q
        98: q^5+5q^4+7q^3+q^2+q
        99: 2q^5+5q^4+5q^3+q^2+q
       100: 6q^4+6q^3+q^2+q
       101: q^5+7q^4+6q^3+q^2+q
       102: 6q^4+6q^3+q^2+q
       103: q^3
       104: q^3
       105: 3q^3+q^2+q
       106: q^3
       107: 2q^3
       108: q^4+4q^3+q^2+q
       109: q^4+4q^3+q^2+q
       110: 2q^3
       111: 3q^4+3q^3
       112: 2q^4+4q^3+q^2+q
       113: q^4+2q^3
       114: q^4+4q^3+q^2+q
       115: 4q^4+3q^3
       116: 3q^4+4q^3+q^2+q
       117: q^4+4q^3+q^2+q
       118: 2q^3
       119: 2q^3
       120: q^4+4q^3+q^2+q
       121: q^4+2q^3
       122: q^4+4q^3+q^2+q
       123: 3q^4+3q^3
       124: 2q^4+4q^3+q^2+q
       125: q^4+6q^3+q^2+q
       126: q^4+4q^3+q^2+q
       127: q^4+3q^3
       128: 3q^3+q^2+q
       129: q^4+3q^3
       130: 3q^3+q^2+q
       131: q^4+2q^3
       132: q^4+2q^3+q^2+q
       133: 3q^4+6q^3+q^2+q
       134: 2q^5+5q^4+5q^3+q^2+q
       135: q^5+6q^4+7q^3+q^2+q
       136: q^5+6q^4+7q^3+q^2+q
       137: 6q^3+q^2+q
       138: q^5+3q^4+5q^3+q^2+q
       139: q^4+6q^3+q^2+q
       140: 2q^4+4q^3+q^2+q
       141: 3q^4+6q^3+q^2+q
       142: q^5+5q^4+7q^3+q^2+q
       143: 6q^3+q^2+q
       144: q^5+3q^4+5q^3+q^2+q
       145: q^4+6q^3+q^2+q
       146: 3q^4+6q^3+q^2+q
       147: q^5+5q^4+7q^3+q^2+q
       148: 2q^4+4q^3+q^2+q
       149: 2q^4+5q^3+q^2+q
       150: 6q^4+6q^3+q^2+q
       151: 3q^4+3q^3
       152: 3q^4+3q^3+q^2+q
       153: q^5+4q^4+3q^3
       154: 3q^4+3q^3+q^2+q
       155: 3q^4+3q^3
       156: 3q^4+3q^3+q^2+q
       157: q^4+6q^3+q^2+q
       158: q^4+6q^3+q^2+q
       159: q^5+3q^4+4q^3+q^2+q
       160: q^5+5q^4+7q^3+q^2+q
       161: q^5+5q^4+7q^3+q^2+q
       162: 2q^5+5q^4+5q^3+q^2+q
       163: q^5+5q^4+7q^3+q^2+q
       164: q^5+5q^4+7q^3+q^2+q
       165: 2q^5+5q^4+5q^3+q^2+q
       166: 2q^4+5q^3+q^2+q
       167: 3q^4+5q^3+q^2+q
       168: 4q^4+4q^3+q^2+q
       169: q^3
       170: q^3
       171: 3q^3+q^2+q
       172: q^3
       173: q^3
       174: q^3
       175: 3q^3+q^2+q
       176: q^3
       177: 2q^3
       178: 2q^3+q^2+q
       179: 2q^3
       180: 3q^3+q^2+q
       181: q^4+3q^3
       182: 3q^3+q^2+q
       183: 2q^3
       184: q^4+4q^3+q^2+q
       185: q^4+4q^3+q^2+q
       186: 2q^3
       187: 3q^4+3q^3
       188: 2q^4+4q^3+q^2+q
       189: q^4+2q^3
       190: q^4+4q^3+q^2+q
       191: 4q^3+q^2+q
       192: 2q^3
       194: 3q^3+q^2+q
       195: q^4+4q^3+q^2+q
       196: 2q^3
       197: q^4+2q^3
       198: q^4+2q^3+q^2+q
       199: 2q^3
       200: 4q^3+q^2+q
       201: 2q^3
       202: q^4+4q^3+q^2+q
       203: 3q^3+q^2+q
       205: q^4+2q^3
       206: q^4+2q^3+q^2+q
       207: 2q^3
       208: 4q^3+q^2+q
       209: q^4+2q^3
       210: q^4+3q^3+q^2+q
       211: 3q^4+3q^3
       212: 3q^4+3q^3+q^2+q
       213: q^4+3q^3
       214: 3q^3+q^2+q
       215: q^4+3q^3
       216: 3q^3+q^2+q
       217: q^4+2q^3
       218: q^4+2q^3+q^2+q
       219: q^4+4q^3+q^2+q
       220: q^4+6q^3+q^2+q
       221: q^4+4q^3+q^2+q
       222: 6q^3+q^2+q
       223: q^5+3q^4+5q^3+q^2+q
       224: 6q^3+q^2+q
       225: q^5+3q^4+5q^3+q^2+q
       226: 4q^3+q^2+q
       227: q^4+6q^3+q^2+q
       228: q^5+3q^4+5q^3+q^2+q
       229: 2q^4+4q^3+q^2+q
       230: q^5+5q^4+7q^3+q^2+q
       231: 4q^3+q^2+q
       232: q^4+6q^3+q^2+q
       233: q^5+3q^4+5q^3+q^2+q
       234: q^5+5q^4+7q^3+q^2+q
       235: 2q^4+4q^3+q^2+q
       236: 2q^4+4q^3+q^2+q
       237: 3q^3
       238: q^3+q^2+q
       239: q^4+3q^3
       240: q^3+q^2+q
       241: q^4+2q^3
       242: q^4+q^3+q^2+q
       243: 4q^3+q^2+q
       244: q^4+3q^3+q^2+q
       245: q^4+3q^3+q^2+q
       246: 2q^4+5q^3+q^2+q
       247: 2q^4+5q^3+q^2+q
       248: 3q^4+5q^3+q^2+q
       249: 4q^4+4q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^4+5q^3+q^2+q
       257: 3q^4+5q^3+q^2+q
       258: 4q^4+4q^3+q^2+q
       259: q^3
       260: q^3
       261: 2q^3+q^2+q
       262: q^3
       263: q^3
       264: q^3
       265: 3q^3+q^2+q
       266: q^3
       269: q^3
       270: 2q^3+q^2+q
       271: q^3
       272: 2q^3+q^2+q
       275: q^3
       276: q^3
       277: 3q^3+q^2+q
       278: q^3
       279: 2q^3
       280: 3q^3+q^2+q
       281: 2q^3
       282: 2q^3+q^2+q
       284: 2q^3+q^2+q
       285: 2q^3+q^2+q
       287: q^3
       288: 2q^3+q^2+q
       289: q^4+3q^3
       290: 3q^3+q^2+q
       291: 2q^3
       292: 2q^3+q^2+q
       293: 2q^3
       294: 4q^3+q^2+q
       295: 4q^3+q^2+q
       296: 2q^3
       297: 2q^3
       298: 4q^3+q^2+q
       300: 3q^3+q^2+q
       301: 2q^3
       302: q^2+q
       303: q^4+4q^3+q^2+q
       304: 2q^3
       305: q^4+2q^3
       306: q^4+2q^3+q^2+q
       307: 2q^3
       308: q^4+4q^3+q^2+q
       309: 3q^3+q^2+q
       311: 2q^3
       312: q^2+q
       313: q^4+2q^3
       314: q^4+2q^3+q^2+q
       315: 2q^3
       316: q^3+q^2+q
       317: 2q^3
       318: q^3+q^2+q
       320: 2q^3+q^2+q
       321: 2q^3+q^2+q
       323: q^3
       324: q^3+q^2+q
       325: q^4+2q^3
       326: q^4+3q^3+q^2+q
       333: q^4+4q^3+q^2+q
       334: 4q^3+q^2+q
       335: 4q^3+q^2+q
       336: 2q^4+4q^3+q^2+q
       337: 4q^3+q^2+q
       338: 3q^3
       339: q^3+q^2+q
       340: q^4+3q^3
       341: q^3+q^2+q
       342: q^4+2q^3
       343: q^4+q^3+q^2+q
       344: 4q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^5+3q^4+5q^3+q^2+q
       351: q^4+3q^3+q^2+q
       352: 4q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^5+3q^4+5q^3+q^2+q
       357: q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^4+3q^3+q^2+q
       360: 3q^3
       361: q^3+q^2+q
       362: q^4+3q^3
       363: q^3+q^2+q
       364: q^4+2q^3
       365: q^4+q^3+q^2+q
       366: 3q^3+q^2+q
       367: 4q^3+q^2+q
       368: 2q^4+4q^3+q^2+q
       369: q^4+3q^3+q^2+q
       370: q^4+3q^3+q^2+q
       371: 2q^4+5q^3+q^2+q
       372: 3q^4+5q^3+q^2+q
       373: 4q^4+4q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       379: q^3+q^2+q
       381: q^3
       382: q^3
       383: 2q^3+q^2+q
       384: q^3
       385: q^3
       386: q^3
       387: 3q^3+q^2+q
       388: q^3
       391: q^3
       392: q^2+q
       395: 2q^3+q^2+q
       396: q^3
       397: q^3
       398: q^2+q
       401: q^3
       402: 2q^3+q^2+q
       408: q^3+q^2+q
       413: q^3
       414: 2q^3+q^2+q
       417: 2q^3
       418: 2q^3+q^2+q
       420: 2q^3+q^2+q
       421: 2q^3+q^2+q
       423: q^3
       424: 2q^3+q^2+q
       425: 2q^3
       426: q^3+q^2+q
       427: 2q^3
       428: q^3+q^2+q
       430: q^3+q^2+q
       431: 2q^3+q^2+q
       433: q^3
       434: q^2+q
       435: 2q^3
       436: q^2+q
       438: q^3+q^2+q
       439: 2q^3+q^2+q
       440: q^3
       442: q^3+q^2+q
       444: 2q^3+q^2+q
       445: 2q^3
       446: q^2+q
       448: 2q^3+q^2+q
       449: q^3+q^2+q
       451: q^3
       452: q^2+q
       453: q^3
       454: 2q^3+q^2+q
       455: 2q^3
       456: q^2+q
       457: q^3+q^2+q
       460: q^3+q^2+q
       461: 2q^3+q^2+q
       463: 2q^3
       464: q^2+q
       465: 2q^3
       466: q^3+q^2+q
       467: 2q^3
       468: q^3+q^2+q
       469: q^3
       470: q^3+q^2+q
       472: 2q^3+q^2+q
       473: 2q^3+q^2+q
       475: q^3
       476: q^3+q^2+q
       477: q^3
       478: 2q^2+q
       479: q^3
       480: q^3+q^2+q
       481: 4q^3+q^2+q
       482: 4q^3+q^2+q
       483: 3q^3+q^2+q
       484: 4q^3+q^2+q
       485: 3q^3
       486: q^3+q^2+q
       487: q^4+3q^3
       488: q^3+q^2+q
       489: q^4+2q^3
       490: q^4+q^3+q^2+q
       491: 2q^4+4q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^4+2q^3+q^2+q
       496: q^4+3q^3+q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^4+2q^3+q^2+q
       501: q^4+3q^3+q^2+q
       508: 3q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^4+2q^3+q^2+q
       513: q^2+q
       514: q^4+2q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       523: q^3+q^2+q
       531: q^3+q^2+q
       535: q^2+q
       539: q^3
       540: q^2+q
       544: q^3+q^2+q
       547: q^3
       548: q^2+q
       550: q^2+q
       553: q^3
       554: q^2+q
       558: q^3+q^2+q
       561: q^3
       562: q^2+q
       567: q^3+q^2+q
       572: 2q^2+q
       576: q^3+q^2+q
       577: q^3
       581: q^2+q
       582: q^2
       585: q^3
       586: 2q^3+q^2+q
       590: 2q^3+q^2+q
       591: q^3+q^2+q
       594: q^3+q^2+q
       595: 2q^3+q^2+q
       597: 2q^3
       598: q^3+q^2+q
       599: q^3
       600: q^3+q^2+q
       601: 2q^3
       602: q^3+q^2+q
       604: q^2+q
       605: q^3
       606: q^2+q
       607: q^3+q^2+q
       610: q^2+q
       613: q^3
       614: q^2+q
       616: 2q^3+q^2+q
       617: 2q^3
       618: q^2+q
       620: q^3+q^2+q
       621: q^2+q
       623: q^3
       624: q^2+q
       626: q^2+q
       629: q^3
       630: q^2+q
       631: 2q^3+q^2+q
       633: 2q^3
       634: q^2+q
       639: q^3
       640: q^3+q^2+q
       642: q^3+q^2+q
       643: q^3+q^2+q
       646: q^2+q
       648: q^2+q
       649: q^2+q
       651: q^3
       652: 2q^2+q
       654: q^2+q
       655: q^3
       656: q^3+q^2+q
       657: q^2+q
       658: 2q^3+q^2
       659: q^3+q
       660: 2q^3+q^2
       661: q
       662: 2q^3+q^2
       663: q^3+q
       664: 3q^3+q^2+q
       665: 3q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q^3+q^2+q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^4+2q^3+q^2+q
       680: q^3+q^2+q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^4+2q^3+q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q^3+q
       690: q^3+q
       691: q
       692: q^3+q
       700: q^2+q
       704: q^2
       711: q^3+q^2+q
       714: q^2+q
       719: q^2+q
       724: q^2+q
       728: q^2+q
       735: q^3
       736: q^2+q
       738: q^2+q
       742: q^2+q
       749: q^3
       750: q^2+q
       755: q^2+q
       760: 2q^2+q
       764: q^2+q
       767: q^3+q^2+q
       769: q^3
       773: q^2+q
       774: q^2
       775: q^2
       776: q
       779: 2q^3+q^2
       780: q^3+q
       781: q^3
       782: q^3+q^2+q
       786: q^3+q^2+q
       787: q^3+q^2+q
       792: q^2+q
       794: q^2+q
       795: q^3+q^2
       796: q
       798: q^2+q
       802: q^2+q
       803: q
       806: q^2+q
       807: q^3+q^2+q
       809: q^3
       810: q^2+q
       812: q^2+q
       816: q^2+q
       817: q^2+q
       819: q^3+q^2
       820: q
       822: q^2+q
       826: q^3+q^2+q
       827: q^2+q
       830: q
       831: q^2+q
       833: q^3
       834: q^2+q
       836: q^2+q
       839: q^2+q
       844: q^2+q
       846: q^2+q
       847: q^2+q
       850: q^2+q
       852: q^2+q
       856: q
       858: q^2+q
       865: q
       866: q^2+q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q^3+q^2+q
       871: q^2+q
       872: q^2+q
       873: q
       874: q^3+q^2+q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q^3+q
       881: q^3+q
       882: q
       883: q^3+q
       891: q^2+q
       895: q^2
       901: q^2+q
       907: q^2+q
       910: q^2+q
       918: q^2
       919: q
       923: q^2+q
       925: q
       931: q^2+q
       940: q^2
       941: q
       945: q^2+q
       949: q^2+q
       954: q
       963: q^2+q
       966: q^2+q
       971: q^2
       972: q
       977: q^2+q
       990: q^2+q
       994: q^2
       995: q
       998: q^2+q
      1001: q^2+q
      1005: q^2+q
      1006: q^2+q
      1009: q^2+q
      1011: q^2+q
      1013: q^2+q
      1017: q
      1020: q^3+q^2
      1021: q
      1023: q^2+q
      1027: q^2+q
      1028: q
      1032: q
      1036: q^3+q^2
      1037: q
      1039: q^2+q
      1041: q
      1044: q^2+q
      1047: q
      1049: q^2+q
      1053: q^2+q
      1054: q
      1057: q
      1058: q^2+q
      1061: q
      1063: q
      1065: q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q^2+q
      1085: q
      1090: q^2
      1093: q
      1114: q^2
      1115: q
      1124: q^2
      1125: q
      1129: q^2+q
      1132: q^2+q
      1137: q^2+q
      1141: q^2
      1142: q
      1153: q
      1159: q^2+q
      1161: q
      1173: q^2+q
      1179: q
      1182: q
      1196: q
      1201: q^2+q
      1203: q
      1209: q
      1216: q
      1219: q
      1221: q^2+q
      1225: q
      1229: q
      1231: q
      1232: q
      1235: q
      1241: q^2+q
      1242: q
      1246: q
      1249: q
      1250: q
      1255: q
      1259: q
      1260: q^2+q
      1263: q
      1267: q
      1269: q
      1270: q
      1274: q^2
      1275: q
      1277: q
      1279: q
      1281: q^2+q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1294: q^2
      1297: q
      1328: q
      1333: q^2+q
      1349: q
      1359: q
      1362: q
      1365: q
      1370: q
      1381: q
      1391: q
      1395: q
      1398: q
      1403: q
      1412: q
      1419: q
      1425: q
      1428: q
      1433: q^2
      1434: q
      1437: q
      1440: q
      1443: q
      1445: q
      1450: q
      1455: q
      1460: q
      1463: q
      1475: q
      1477: q
      1478: q
      1483: q
      1485: q
      1486: q
      1488: q
      1507: q
      1520: q
      1540: q
      1551: q
      1576: q
      1581: q
      1597: q
      1602: q
      1621: q
      1629: q
      1640: q
      1645: q
      1648: q
      1653: q
      1656: q
      1670: q
      1735: q
      1750: q
      1775: q
      1810: q
      1947: 1
      2025: 1
      2062: 1
      2138: 1

2139:    0: 5q^5+10q^4+7q^3+q^2+q
         1: q^6+7q^5+10q^4+7q^3+q^2+q
         2: 5q^5+10q^4+7q^3+q^2+q
         3: 5q^5+10q^4+7q^3+q^2+q
         4: 5q^5+10q^4+7q^3+q^2+q
         5: 5q^5+10q^4+7q^3+q^2+q
         6: q^6+7q^5+10q^4+7q^3+q^2+q
         7: 5q^5+10q^4+7q^3+q^2+q
         8: 5q^5+10q^4+7q^3+q^2+q
         9: 3q^6+7q^5+7q^4+5q^3+q^2+q
        10: q^5+5q^4+6q^3+q^2+q
        11: 5q^4+6q^3+q^2+q
        12: q^5+5q^4+6q^3+q^2+q
        13: 5q^5+10q^4+7q^3+q^2+q
        14: 5q^5+10q^4+7q^3+q^2+q
        15: 5q^5+10q^4+7q^3+q^2+q
        16: 2q^5+8q^4+7q^3+q^2+q
        17: 3q^5+8q^4+7q^3+q^2+q
        18: 5q^5+7q^4+5q^3+q^2+q
        19: 5q^5+10q^4+7q^3+q^2+q
        20: q^6+7q^5+10q^4+7q^3+q^2+q
        21: 5q^5+10q^4+7q^3+q^2+q
        22: 2q^5+8q^4+7q^3+q^2+q
        23: 3q^5+8q^4+7q^3+q^2+q
        24: 2q^5+8q^4+7q^3+q^2+q
        25: 2q^5+8q^4+7q^3+q^2+q
        26: 3q^5+8q^4+7q^3+q^2+q
        27: 2q^5+8q^4+7q^3+q^2+q
        28: 3q^4+6q^3+q^2+q
        29: q^5+5q^4+6q^3+q^2+q
        30: 5q^5+10q^4+7q^3+q^2+q
        31: 3q^4+6q^3+q^2+q
        32: 2q^5+8q^4+7q^3+q^2+q
        33: q^5+6q^4+7q^3+q^2+q
        34: 3q^4+6q^3+q^2+q
        35: 2q^5+8q^4+7q^3+q^2+q
        36: q^5+6q^4+7q^3+q^2+q
        37: 3q^4+4q^3+q^2+q
        38: 4q^4+3q^3
        39: 3q^4+4q^3+q^2+q
        40: q^5+4q^4+3q^3
        41: 3q^4+4q^3+q^2+q
        42: 4q^4+3q^3
        43: q^5+5q^4+6q^3+q^2+q
        44: q^5+5q^4+6q^3+q^2+q
        45: 5q^4+6q^3+q^2+q
        46: 2q^5+8q^4+7q^3+q^2+q
        47: 3q^5+8q^4+7q^3+q^2+q
        48: 5q^5+7q^4+5q^3+q^2+q
        49: 2q^5+8q^4+7q^3+q^2+q
        50: 3q^5+8q^4+7q^3+q^2+q
        51: 5q^5+7q^4+5q^3+q^2+q
        52: 2q^5+8q^4+7q^3+q^2+q
        53: 3q^5+8q^4+7q^3+q^2+q
        54: 2q^5+8q^4+7q^3+q^2+q
        55: 2q^5+8q^4+7q^3+q^2+q
        56: 3q^5+8q^4+7q^3+q^2+q
        57: 2q^5+8q^4+7q^3+q^2+q
        58: 2q^3
        59: q^4+4q^3+q^2+q
        60: 2q^3
        61: q^4+4q^3+q^2+q
        62: q^4+4q^3+q^2+q
        63: q^4+2q^3
        64: 3q^4+4q^3+q^2+q
        65: 4q^4+3q^3
        66: 2q^4+4q^3+q^2+q
        67: 3q^4+3q^3
        68: 3q^4+6q^3+q^2+q
        69: 2q^5+5q^4+5q^3+q^2+q
        70: q^5+5q^4+6q^3+q^2+q
        71: 3q^4+6q^3+q^2+q
        72: q^5+6q^4+7q^3+q^2+q
        73: q^5+6q^4+7q^3+q^2+q
        74: 3q^4+4q^3+q^2+q
        75: 4q^4+3q^3
        76: 3q^4+4q^3+q^2+q
        77: q^5+4q^4+3q^3
        78: 3q^4+4q^3+q^2+q
        79: 4q^4+3q^3
        80: 3q^4+6q^3+q^2+q
        81: q^5+6q^4+7q^3+q^2+q
        82: 3q^4+6q^3+q^2+q
        83: 2q^5+8q^4+7q^3+q^2+q
        84: 3q^4+6q^3+q^2+q
        85: q^5+6q^4+7q^3+q^2+q
        86: 3q^4+6q^3+q^2+q
        87: 2q^5+8q^4+7q^3+q^2+q
        88: q^4+6q^3+q^2+q
        89: q^4+6q^3+q^2+q
        90: q^5+3q^4+4q^3+q^2+q
        91: 2q^5+8q^4+7q^3+q^2+q
        92: 3q^5+8q^4+7q^3+q^2+q
        93: 5q^5+7q^4+5q^3+q^2+q
        94: q^5+5q^4+7q^3+q^2+q
        95: q^5+5q^4+7q^3+q^2+q
        96: 2q^5+5q^4+5q^3+q^2+q
        97: q^5+5q^4+7q^3+q^2+q
        98: q^5+5q^4+7q^3+q^2+q
        99: 2q^5+5q^4+5q^3+q^2+q
       100: 6q^4+6q^3+q^2+q
       101: q^5+7q^4+6q^3+q^2+q
       102: 6q^4+6q^3+q^2+q
       103: q^3
       104: q^3
       105: q^3
       106: 3q^3+q^2+q
       107: 2q^3
       108: q^4+4q^3+q^2+q
       109: 2q^3
       110: q^4+4q^3+q^2+q
       111: 2q^4+4q^3+q^2+q
       112: 3q^4+3q^3
       113: q^4+4q^3+q^2+q
       114: q^4+2q^3
       115: 3q^4+4q^3+q^2+q
       116: 4q^4+3q^3
       117: 2q^3
       118: q^4+4q^3+q^2+q
       119: 2q^3
       120: q^4+4q^3+q^2+q
       121: q^4+4q^3+q^2+q
       122: q^4+2q^3
       123: 2q^4+4q^3+q^2+q
       124: 3q^4+3q^3
       125: q^4+6q^3+q^2+q
       126: q^4+4q^3+q^2+q
       127: 3q^3+q^2+q
       128: q^4+3q^3
       129: 3q^3+q^2+q
       130: q^4+3q^3
       131: q^4+2q^3+q^2+q
       132: q^4+2q^3
       133: 3q^4+6q^3+q^2+q
       134: 2q^5+5q^4+5q^3+q^2+q
       135: q^5+6q^4+7q^3+q^2+q
       136: q^5+6q^4+7q^3+q^2+q
       137: 6q^3+q^2+q
       138: q^5+3q^4+5q^3+q^2+q
       139: q^4+6q^3+q^2+q
       140: 2q^4+4q^3+q^2+q
       141: 3q^4+6q^3+q^2+q
       142: q^5+5q^4+7q^3+q^2+q
       143: 6q^3+q^2+q
       144: q^5+3q^4+5q^3+q^2+q
       145: q^4+6q^3+q^2+q
       146: 3q^4+6q^3+q^2+q
       147: q^5+5q^4+7q^3+q^2+q
       148: 2q^4+4q^3+q^2+q
       149: 2q^4+5q^3+q^2+q
       150: 6q^4+6q^3+q^2+q
       151: 3q^4+3q^3+q^2+q
       152: 3q^4+3q^3
       153: 3q^4+3q^3+q^2+q
       154: q^5+4q^4+3q^3
       155: 3q^4+3q^3+q^2+q
       156: 3q^4+3q^3
       157: q^4+6q^3+q^2+q
       158: q^4+6q^3+q^2+q
       159: q^5+3q^4+4q^3+q^2+q
       160: q^5+5q^4+7q^3+q^2+q
       161: q^5+5q^4+7q^3+q^2+q
       162: 2q^5+5q^4+5q^3+q^2+q
       163: q^5+5q^4+7q^3+q^2+q
       164: q^5+5q^4+7q^3+q^2+q
       165: 2q^5+5q^4+5q^3+q^2+q
       166: 2q^4+5q^3+q^2+q
       167: 3q^4+5q^3+q^2+q
       168: 4q^4+4q^3+q^2+q
       169: q^3
       170: q^3
       171: q^3
       172: 3q^3+q^2+q
       173: q^3
       174: q^3
       175: q^3
       176: 3q^3+q^2+q
       177: 2q^3+q^2+q
       178: 2q^3
       179: 3q^3+q^2+q
       180: 2q^3
       181: 3q^3+q^2+q
       182: q^4+3q^3
       183: 2q^3
       184: q^4+4q^3+q^2+q
       185: 2q^3
       186: q^4+4q^3+q^2+q
       187: 2q^4+4q^3+q^2+q
       188: 3q^4+3q^3
       189: q^4+4q^3+q^2+q
       190: q^4+2q^3
       191: 2q^3
       192: 4q^3+q^2+q
       194: 3q^3+q^2+q
       195: 2q^3
       196: q^4+4q^3+q^2+q
       197: q^4+2q^3+q^2+q
       198: q^4+2q^3
       199: 2q^3
       200: 4q^3+q^2+q
       201: 2q^3
       202: q^4+4q^3+q^2+q
       204: 3q^3+q^2+q
       205: q^4+2q^3+q^2+q
       206: q^4+2q^3
       207: 4q^3+q^2+q
       208: 2q^3
       209: q^4+3q^3+q^2+q
       210: q^4+2q^3
       211: 3q^4+3q^3+q^2+q
       212: 3q^4+3q^3
       213: 3q^3+q^2+q
       214: q^4+3q^3
       215: 3q^3+q^2+q
       216: q^4+3q^3
       217: q^4+2q^3+q^2+q
       218: q^4+2q^3
       219: q^4+4q^3+q^2+q
       220: q^4+6q^3+q^2+q
       221: q^4+4q^3+q^2+q
       222: 6q^3+q^2+q
       223: q^5+3q^4+5q^3+q^2+q
       224: 6q^3+q^2+q
       225: q^5+3q^4+5q^3+q^2+q
       226: 4q^3+q^2+q
       227: q^4+6q^3+q^2+q
       228: q^5+3q^4+5q^3+q^2+q
       229: 2q^4+4q^3+q^2+q
       230: q^5+5q^4+7q^3+q^2+q
       231: 4q^3+q^2+q
       232: q^4+6q^3+q^2+q
       233: q^5+3q^4+5q^3+q^2+q
       234: q^5+5q^4+7q^3+q^2+q
       235: 2q^4+4q^3+q^2+q
       236: 2q^4+4q^3+q^2+q
       237: q^3+q^2+q
       238: 3q^3
       239: q^3+q^2+q
       240: q^4+3q^3
       241: q^4+q^3+q^2+q
       242: q^4+2q^3
       243: 4q^3+q^2+q
       244: q^4+3q^3+q^2+q
       245: q^4+3q^3+q^2+q
       246: 2q^4+5q^3+q^2+q
       247: 2q^4+5q^3+q^2+q
       248: 3q^4+5q^3+q^2+q
       249: 4q^4+4q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: 2q^4+5q^3+q^2+q
       257: 3q^4+5q^3+q^2+q
       258: 4q^4+4q^3+q^2+q
       259: q^3
       260: q^3
       261: q^3
       262: 2q^3+q^2+q
       263: q^3
       264: q^3
       265: q^3
       266: 3q^3+q^2+q
       269: 2q^3+q^2+q
       270: q^3
       273: 2q^3+q^2+q
       274: q^3
       275: q^3
       276: q^3
       277: q^3
       278: 3q^3+q^2+q
       279: 3q^3+q^2+q
       280: 2q^3
       281: 2q^3+q^2+q
       282: 2q^3
       284: 2q^3+q^2+q
       286: 2q^3+q^2+q
       287: 2q^3+q^2+q
       288: q^3
       289: 3q^3+q^2+q
       290: q^4+3q^3
       291: 2q^3+q^2+q
       292: 2q^3
       293: 2q^3
       294: 4q^3+q^2+q
       295: 2q^3
       296: 4q^3+q^2+q
       297: 4q^3+q^2+q
       298: 2q^3
       300: 3q^3+q^2+q
       301: q^2+q
       302: 2q^3
       303: 2q^3
       304: q^4+4q^3+q^2+q
       305: q^4+2q^3+q^2+q
       306: q^4+2q^3
       307: 2q^3
       308: q^4+4q^3+q^2+q
       310: 3q^3+q^2+q
       311: q^2+q
       312: 2q^3
       313: q^4+2q^3+q^2+q
       314: q^4+2q^3
       315: q^3+q^2+q
       316: 2q^3
       317: q^3+q^2+q
       318: 2q^3
       320: 2q^3+q^2+q
       322: 2q^3+q^2+q
       323: q^3+q^2+q
       324: q^3
       325: q^4+3q^3+q^2+q
       326: q^4+2q^3
       333: q^4+4q^3+q^2+q
       334: 4q^3+q^2+q
       335: 4q^3+q^2+q
       336: 2q^4+4q^3+q^2+q
       337: 4q^3+q^2+q
       338: q^3+q^2+q
       339: 3q^3
       340: q^3+q^2+q
       341: q^4+3q^3
       342: q^4+q^3+q^2+q
       343: q^4+2q^3
       344: 4q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^4+2q^3+q^2+q
       349: 3q^3+q^2+q
       350: q^5+3q^4+5q^3+q^2+q
       351: q^4+3q^3+q^2+q
       352: 4q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: q^5+3q^4+5q^3+q^2+q
       357: q^3+q^2+q
       358: q^4+2q^3+q^2+q
       359: q^4+3q^3+q^2+q
       360: q^3+q^2+q
       361: 3q^3
       362: q^3+q^2+q
       363: q^4+3q^3
       364: q^4+q^3+q^2+q
       365: q^4+2q^3
       366: 3q^3+q^2+q
       367: 4q^3+q^2+q
       368: 2q^4+4q^3+q^2+q
       369: q^4+3q^3+q^2+q
       370: q^4+3q^3+q^2+q
       371: 2q^4+5q^3+q^2+q
       372: 3q^4+5q^3+q^2+q
       373: 4q^4+4q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       380: q^3+q^2+q
       381: q^3
       382: q^3
       383: q^3
       384: 2q^3+q^2+q
       385: q^3
       386: q^3
       387: q^3
       388: 3q^3+q^2+q
       391: q^2+q
       392: q^3
       395: q^3
       396: 2q^3+q^2+q
       399: q^2+q
       400: q^3
       403: q^3
       404: 2q^3+q^2+q
       406: q^3+q^2+q
       413: 2q^3+q^2+q
       414: q^3
       417: 2q^3+q^2+q
       418: 2q^3
       420: 2q^3+q^2+q
       422: 2q^3+q^2+q
       423: 2q^3+q^2+q
       424: q^3
       425: q^3+q^2+q
       426: 2q^3
       427: q^3+q^2+q
       428: 2q^3
       430: q^3+q^2+q
       432: 2q^3+q^2+q
       433: q^2+q
       434: q^3
       435: q^2+q
       436: 2q^3
       438: q^3+q^2+q
       439: q^3
       440: 2q^3+q^2+q
       441: q^3+q^2+q
       444: 2q^3+q^2+q
       445: q^2+q
       446: 2q^3
       448: 2q^3+q^2+q
       450: q^3+q^2+q
       451: q^2+q
       452: q^3
       453: q^3
       454: 2q^3+q^2+q
       455: q^2+q
       456: 2q^3
       458: q^3+q^2+q
       459: q^3+q^2+q
       462: 2q^3+q^2+q
       463: q^2+q
       464: 2q^3
       465: q^3+q^2+q
       466: 2q^3
       467: q^3+q^2+q
       468: 2q^3
       469: q^3+q^2+q
       470: q^3
       472: 2q^3+q^2+q
       474: 2q^3+q^2+q
       475: q^3+q^2+q
       476: q^3
       477: 2q^2+q
       478: q^3
       479: q^3+q^2+q
       480: q^3
       481: 4q^3+q^2+q
       482: 4q^3+q^2+q
       483: 3q^3+q^2+q
       484: 4q^3+q^2+q
       485: q^3+q^2+q
       486: 3q^3
       487: q^3+q^2+q
       488: q^4+3q^3
       489: q^4+q^3+q^2+q
       490: q^4+2q^3
       491: 2q^4+4q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^4+2q^3+q^2+q
       496: q^4+3q^3+q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^4+2q^3+q^2+q
       501: q^4+3q^3+q^2+q
       508: 3q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^4+2q^3+q^2+q
       513: q^2+q
       514: q^4+2q^3+q^2+q
       515: 3q^3+q^2+q
       516: 2q^3+q^2+q
       517: 3q^3+q^2+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       524: q^3+q^2+q
       532: q^3+q^2+q
       536: q^2+q
       539: q^2+q
       540: q^3
       543: q^3+q^2+q
       547: q^2+q
       548: q^3
       552: q^2+q
       555: q^2+q
       556: q^3
       559: q^3+q^2+q
       563: q^2+q
       564: q^3
       568: q^3+q^2+q
       570: 2q^2+q
       575: q^3+q^2+q
       577: q^2+q
       579: q^2
       581: q^3
       585: 2q^3+q^2+q
       586: q^3
       590: 2q^3+q^2+q
       592: q^3+q^2+q
       594: q^3+q^2+q
       596: 2q^3+q^2+q
       597: q^3+q^2+q
       598: 2q^3
       599: q^3+q^2+q
       600: q^3
       601: q^3+q^2+q
       602: 2q^3
       604: q^2+q
       605: q^2+q
       606: q^3
       608: q^3+q^2+q
       609: q^2+q
       613: q^2+q
       614: q^3
       616: 2q^3+q^2+q
       617: q^2+q
       618: 2q^3
       620: q^3+q^2+q
       622: q^2+q
       623: q^2+q
       624: q^3
       625: q^2+q
       629: q^2+q
       630: q^3
       632: 2q^3+q^2+q
       633: q^2+q
       634: 2q^3
       639: q^3+q^2+q
       640: q^3
       642: q^3+q^2+q
       644: q^3+q^2+q
       645: q^2+q
       648: q^2+q
       650: q^2+q
       651: 2q^2+q
       652: q^3
       653: q^2+q
       655: q^3+q^2+q
       656: q^3
       657: q^2+q
       658: q^3+q
       659: 2q^3+q^2
       660: q
       661: 2q^3+q^2
       662: q^3+q
       663: 2q^3+q^2
       664: 3q^3+q^2+q
       665: 3q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q^3+q^2+q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^4+2q^3+q^2+q
       680: q^3+q^2+q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^4+2q^3+q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q^3+q
       690: q^3+q
       691: q
       692: q^3+q
       697: q^2+q
       702: q^2
       712: q^3+q^2+q
       716: q^2+q
       720: q^2+q
       723: q^2+q
       727: q^2+q
       735: q^2+q
       736: q^3
       739: q^2+q
       743: q^2+q
       751: q^2+q
       752: q^3
       756: q^2+q
       758: 2q^2+q
       762: q^2+q
       768: q^3+q^2+q
       769: q^2+q
       771: q^2
       773: q^3
       775: q
       776: q^2
       779: q^3+q
       780: 2q^3+q^2
       781: q^3+q^2+q
       782: q^3
       786: q^3+q^2+q
       788: q^3+q^2+q
       791: q^2+q
       794: q^2+q
       795: q
       796: q^3+q^2
       797: q^2+q
       802: q^2+q
       804: q
       806: q^2+q
       808: q^3+q^2+q
       809: q^2+q
       810: q^3
       811: q^2+q
       816: q^2+q
       818: q^2+q
       819: q
       820: q^3+q^2
       821: q^2+q
       826: q^3+q^2+q
       828: q^2+q
       830: q
       832: q^2+q
       833: q^2+q
       834: q^3
       835: q^2+q
       840: q^2+q
       843: q^2+q
       846: q^2+q
       848: q^2+q
       849: q^2+q
       851: q^2+q
       855: q
       857: q^2+q
       865: q
       866: q^2+q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q^3+q^2+q
       871: q^2+q
       872: q^2+q
       873: q
       874: q^3+q^2+q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q^3+q
       881: q^3+q
       882: q
       883: q^3+q
       889: q^2+q
       893: q^2
       902: q^2+q
       906: q^2+q
       911: q^2+q
       918: q
       919: q^2
       922: q^2+q
       927: q
       930: q^2+q
       942: q
       943: q^2
       946: q^2+q
       950: q^2+q
       955: q
       961: q^2+q
       967: q^2+q
       968: q
       969: q^2
       975: q^2+q
       991: q^2+q
       994: q
       995: q^2
       999: q^2+q
      1001: q^2+q
      1005: q^2+q
      1007: q^2+q
      1008: q^2+q
      1010: q^2+q
      1012: q^2+q
      1017: q
      1020: q
      1021: q^3+q^2
      1022: q^2+q
      1027: q^2+q
      1029: q
      1033: q
      1036: q
      1037: q^3+q^2
      1038: q^2+q
      1041: q
      1045: q^2+q
      1046: q
      1048: q^2+q
      1053: q^2+q
      1055: q
      1057: q
      1059: q^2+q
      1060: q
      1062: q
      1064: q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q^2+q
      1085: q
      1091: q
      1094: q^2
      1116: q
      1117: q^2
      1124: q
      1125: q^2
      1127: q^2+q
      1133: q^2+q
      1135: q^2+q
      1138: q
      1139: q^2
      1154: q
      1158: q^2+q
      1163: q
      1174: q^2+q
      1178: q
      1183: q
      1197: q
      1199: q^2+q
      1204: q
      1208: q
      1217: q
      1219: q
      1220: q^2+q
      1224: q
      1229: q
      1230: q
      1233: q
      1235: q
      1241: q^2+q
      1243: q
      1247: q
      1248: q
      1251: q
      1255: q
      1259: q
      1261: q^2+q
      1262: q
      1266: q
      1269: q
      1271: q
      1274: q
      1275: q^2
      1276: q
      1278: q
      1280: q^2+q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1295: q
      1298: q^2
      1329: q
      1331: q^2+q
      1350: q
      1358: q
      1361: q
      1367: q
      1369: q
      1382: q
      1390: q
      1393: q
      1399: q
      1401: q
      1413: q
      1420: q
      1424: q
      1429: q
      1430: q
      1431: q^2
      1436: q
      1441: q
      1443: q
      1444: q
      1451: q
      1455: q
      1461: q
      1463: q
      1474: q
      1477: q
      1479: q
      1482: q
      1485: q
      1486: q
      1488: q
      1506: q
      1518: q
      1538: q
      1552: q
      1578: q
      1580: q
      1598: q
      1600: q
      1622: q
      1630: q
      1639: q
      1646: q
      1648: q
      1654: q
      1656: q
      1669: q
      1736: q
      1752: q
      1776: q
      1808: q
      1945: 1
      2022: 1
      2063: 1
      2139: 1

2140:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        60: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: 1
       111: 1
       113: 1
       115: 1
       117: 1
       119: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       173: 1
       177: 1
       179: 1
       181: 1
       183: 1
       185: 1
       187: 1
       189: 1
       191: 1
       193: 1
       195: 1
       197: 1
       199: 1
       201: 1
       203: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       263: 1
       267: 1
       271: 1
       275: 1
       279: 1
       281: 1
       283: 1
       285: 1
       287: 1
       289: 1
       291: 1
       293: 1
       295: 1
       297: 1
       299: 1
       301: 1
       303: 1
       305: 1
       307: 1
       309: 1
       311: 1
       313: 1
       315: 1
       317: 1
       319: 1
       321: 1
       323: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       381: 1
       385: 1
       389: 1
       393: 1
       397: 1
       401: 1
       405: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       419: 1
       421: 1
       423: 1
       425: 1
       427: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       439: 1
       441: 1
       443: 1
       445: 1
       447: 1
       449: 1
       451: 1
       453: 1
       455: 1
       457: 1
       459: 1
       461: 1
       463: 1
       465: 1
       467: 1
       469: 1
       471: 1
       473: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       525: 1
       529: 1
       533: 1
       537: 1
       541: 1
       545: 1
       549: 1
       553: 1
       557: 1
       561: 1
       565: 1
       569: 1
       573: 1
       577: 1
       583: 1
       585: 1
       587: 1
       589: 1
       591: 1
       593: 1
       595: 1
       597: 1
       599: 1
       601: 1
       603: 1
       605: 1
       607: 1
       609: 1
       611: 1
       613: 1
       615: 1
       617: 1
       619: 1
       621: 1
       623: 1
       625: 1
       627: 1
       629: 1
       631: 1
       633: 1
       635: 1
       637: 1
       639: 1
       641: 1
       643: 1
       645: 1
       647: 1
       649: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       705: 1
       709: 1
       713: 1
       717: 1
       721: 1
       725: 1
       729: 1
       733: 1
       737: 1
       741: 1
       745: 1
       749: 1
       753: 1
       757: 1
       761: 1
       765: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       785: 1
       787: 1
       789: 1
       791: 1
       793: 1
       795: 1
       797: 1
       799: 1
       801: 1
       803: 1
       805: 1
       807: 1
       809: 1
       811: 1
       813: 1
       815: 1
       817: 1
       819: 1
       821: 1
       823: 1
       825: 1
       827: 1
       829: 1
       831: 1
       833: 1
       835: 1
       837: 1
       839: 1
       841: 1
       843: 1
       845: 1
       847: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: 1
       861: 1
       863: 1
       865: 1
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      1932: 1
      1936: 1
      1940: 1
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2141:    0: 2q^2+q
         1: 2q^2+q
         2: q^3+q^2+q
         3: 2q^2+q
         4: 2q^2+q
         5: 2q^2+q
         6: 2q^2+q
         7: q^3+q^2+q
         8: q^3+q^2+q
         9: q^3+q^2+q
        10: 2q^2+q
        11: 2q^2+q
        12: 2q^2+q
        13: q^2+q
        14: q^2+q
        15: q^2+q
        16: 2q^2+q
        17: 2q^2+q
        18: q^3+q^2+q
        19: 2q^2+q
        20: 2q^2+q
        21: q^3+q^2+q
        22: 2q^2+q
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        24: q^3+q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^3+q^2+q
        28: 2q^2+q
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        30: q^2+q
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        32: q^2+q
        33: 2q^2+q
        34: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        37: q
        38: 2q^2
        39: q
        40: 2q^2
        41: q
        42: q^3+q^2
        43: q^2+q
        44: q^2+q
        45: q^2+q
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        48: q^2+q
        49: 2q^2+q
        50: 2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^3+q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^3+q^2+q
        58: q^2+q
        59: q^2
        60: q^2+q
        61: q^2
        62: q
        63: 2q^2
        64: q
        65: q^2
        66: q
        67: 2q^2
        68: q
        69: q^2+q
        70: q^2+q
        71: 2q^2+q
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        73: 2q^2+q
        74: q
        75: 2q^2
        76: q
        77: 2q^2
        78: q
        79: q^3+q^2
        80: q^2+q
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        94: 2q^2+q
        95: 2q^2+q
        96: q^3+q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^3+q^2+q
       100: 2q^2+q
       101: 2q^2+q
       102: q^3+q^2+q
       103: q
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       126: q^2+q
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       131: q
       132: q^3+q^2
       133: q
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       146: q^2+q
       147: 2q^2+q
       148: 2q^2+q
       149: 2q^2+q
       150: q^2+q
       151: q
       152: 2q^2
       153: q
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       155: q
       156: q^3+q^2
       157: q^2+q
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       168: q^3+q^2+q
       169: q
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       179: q
       180: 2q^2
       181: q
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       183: q
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       193: q^2+q
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       198: 2q^2
       199: q
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       204: q^2
       205: q
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       237: q
       238: 2q^2
       239: q
       240: 2q^2
       241: q
       242: q^3+q^2
       243: 2q^2+q
       244: 2q^2+q
       245: 2q^2+q
       246: q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
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       259: q
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       290: q^2
       291: q
       292: q^2
       293: q
       295: q
       297: q
       298: q^2
       299: q
       301: q
       302: 2q^2
       303: q
       305: q
       306: q^2
       307: q
       309: q
       311: q
       312: 2q^2
       313: q
       314: q^2
       315: q
       316: q^2
       317: q
       318: 2q^2
       319: q^2+q
       320: q^2
       321: q^2+q
       322: q^2
       323: q
       324: 2q^2
       325: q
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       328: q^2
       330: q^2
       332: q^2
       333: q
       334: q^2+q
       335: q^2+q
       336: q^2+q
       337: 2q^2+q
       338: q
       339: 2q^2
       340: q
       341: 2q^2
       342: q
       343: q^3+q^2
       344: q
       345: q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: q^2+q
       350: q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q^2+q
       358: q^2+q
       359: 2q^2+q
       361: q^2
       363: q^2
       365: q^2
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q^2+q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       377: q
       385: q
       389: q
       390: q^2
       392: q^2
       393: q
       397: q
       398: q^2
       400: q^2
       401: q
       405: q
       407: q^2
       408: q^2
       412: q^2
       416: q^2
       418: q^2
       419: q
       421: q
       423: q
       424: q^2
       425: q
       426: q^2
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       428: 2q^2
       429: q
       431: q
       433: q
       434: q^2
       436: q^2
       437: q
       439: q
       441: q
       442: q^2
       443: q^2+q
       444: q^2
       445: q
       446: 2q^2
       447: q
       449: q
       451: q
       452: q^2
       453: q
       456: q^2
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       459: q
       460: q^2
       461: q^2+q
       462: q^2
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       464: 2q^2
       468: q^2
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       478: 2q^2
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       483: q^2+q
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       494: q^2+q
       495: q^2+q
       496: q^2+q
       497: q
       498: q^2+q
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       500: q^2+q
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       503: q^2
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       507: q^2
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
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       514: q^2+q
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       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       529: q
       533: q
       541: q
       545: q
       546: q^2
       548: q^2
       549: q
       557: q
       561: q
       562: q^2
       564: q^2
       565: q
       569: q
       571: q^2
       572: q^2
       573: q
       574: q^2
       576: q^2
       577: q
       581: 2q^2
       588: q^2
       589: q
       591: q
       593: q
       595: q
       598: q^2
       599: q
       600: q^2
       603: q
       606: q^2
       607: q
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       610: q^2
       612: q^2
       613: q
       614: q^2
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       618: q^2
       619: q
       621: q
       624: q^2
       625: q
       626: q^2
       628: q^2
       629: q
       630: q^2
       631: q
       634: q^2
       638: q^2
       641: q
       643: q
       645: q
       646: q^2
       647: q
       649: q
       652: q^2
       653: q
       654: q^2
       655: q
       656: q^2
       657: q
       659: q^2
       661: q^2
       663: q^2
       664: q^2+q
       665: q
       667: q^2
       669: q^2
       671: q^2
       672: q
       673: q^2+q
       674: q^2+q
       675: q
       676: q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q^2+q
       681: q
       682: q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q
       687: q^2+q
       688: q^2+q
       689: q^2+q
       690: q^2+q
       691: q^2+q
       692: q^2+q
       693: q
       699: q^2
       700: q^2
       713: q
       717: q
       725: q
       741: q
       753: q
       761: q
       765: q
       773: q^2
       780: q^2
       784: q^2
       785: q
       787: q
       791: q
       792: q^2
       793: q
       796: q^2
       800: q^2
       801: q
       803: q
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       810: q^2
       811: q
       812: q^2
       814: q^2
       815: q
       817: q
       820: q^2
       824: q^2
       825: q
       827: q
       829: q
       831: q
       834: q^2
       835: q
       836: q^2
       838: q^2
       839: q
       843: q
       844: q^2
       845: q
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       850: q^2
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       854: q^2
       855: q
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       860: q^2
       862: q^2
       864: q^2
       865: q
       866: q
       867: q^2+q
       868: q
       869: q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q
       878: q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: 1
       908: q
       924: q
       928: q
       948: q
       952: q
       964: q
       972: q^2
       974: q
       986: q^2
       988: q
       997: q^2
       998: q
      1000: q
      1004: q
      1006: q
      1008: q
      1009: q^2
      1011: q^2
      1012: q
      1013: q^2
      1015: q^2
      1016: q
      1021: q^2
      1025: q^2
      1026: q
      1028: q
      1031: q^2
      1032: q
      1037: q^2
      1040: q
      1043: q^2
      1044: q
      1046: q
      1047: q^2
      1051: q^2
      1052: q
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      1056: q
      1058: q
      1061: q^2
      1062: q
      1063: q^2
      1064: q
      1065: q^2
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1130: q
      1134: q
      1142: q^2
      1160: q
      1180: q
      1192: q^2
      1194: q
      1202: q
      1206: q
      1211: 1
      1213: 1
      1216: q
      1218: q
      1223: q^2
      1224: q
      1225: q^2
      1227: 1
      1228: 1
      1232: q
      1234: q
      1237: q^2
      1240: q
      1242: q
      1245: 1
      1246: 1
      1250: q
      1253: q^2
      1254: q
      1258: q
      1260: q
      1262: 1
      1268: q
      1270: q
      1273: q^2
      1275: q^2
      1276: q
      1277: q^2
      1279: q^2
      1280: q
      1281: q^2
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1326: q
      1338: q^2
      1341: 1
      1364: q
      1368: q
      1373: 1
      1396: q
      1400: q
      1405: 1
      1410: 1
      1426: q
      1434: q^2
      1439: 1
      1440: 1
      1442: 1
      1444: 1
      1450: q
      1453: 1
      1454: q
      1459: 1
      1460: q
      1462: q
      1466: q
      1468: q
      1473: q^2
      1476: q
      1478: q
      1481: q^2
      1482: q
      1483: q^2
      1484: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1526: 1
      1542: 1
      1546: 1
      1549: 1
      1554: 1
      1575: q
      1595: q
      1623: q
      1627: q
      1635: q^2
      1639: 1
      1644: 1
      1645: 1
      1647: 1
      1649: q
      1652: 1
      1653: 1
      1655: 1
      1657: q
      1663: q
      1665: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1676: 1
      1724: 1
      1733: 1
      1738: 1
      1746: 1
      1749: 1
      1762: 1
      1766: 1
      1773: 1
      1797: q
      1802: 1
      1811: q
      1819: q
      1821: q
      1825: 1
      1828: 1
      1829: 1
      1831: 1
      1833: 1
      1835: 1
      1847: 1
      1859: 1
      1898: 1
      1914: 1
      1927: 1
      1933: 1
      1937: 1
      1940: 1
      1952: q
      1957: 1
      1960: 1
      1962: 1
      1964: 1
      1967: 1
      1979: 1
      1991: 1
      2027: 1
      2033: 1
      2040: 1
      2045: 1
      2052: 1
      2060: 1
      2064: 1
      2069: 1
      2081: 1
      2093: 1
      2105: 1
      2128: 1
      2141: 1

2142:    0: q^5+q
         1: q
         2: q^5+q
         3: q
         4: q^5+q
         5: q^5+q
         6: q
         7: q^5+q
         8: q^5+q
         9: q^6+q^5+q
        10: q
        11: q
        12: q
        13: q^5+q
        14: q^5+q
        15: q^5+q
        16: q
        17: q
        18: q^5+q
        19: q^5+q
        20: q
        21: q^5+q
        22: q^5+q
        23: q
        24: q^5+q
        25: q^5+q
        26: q
        27: q^5+q
        28: q
        29: q
        30: q^5+q
        31: q
        32: q^5+q
        33: q
        34: q
        35: q^5+q
        36: q
        37: q^5+q
        39: q
        41: q^5+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q^5+q
        49: q
        50: q
        51: q^5+q
        52: q^5+q
        53: q
        54: q^5+q
        55: q^5+q
        56: q
        57: q^5+q
        58: q
        60: q
        62: q
        64: q^5+q
        66: q
        68: q
        69: q
        70: q
        71: q
        72: q
        73: q
        74: q^5+q
        76: q
        78: q^5+q
        80: q
        81: q
        82: q
        83: q^5+q
        84: q
        85: q
        86: q
        87: q^5+q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q^5+q
        94: q
        95: q
        96: q^5+q
        97: q
        98: q
        99: q^5+q
       100: q^5+q
       101: q
       102: q^5+q
       103: q
       107: q
       109: q
       111: q
       113: q
       115: q^5+q
       117: q
       119: q
       121: q
       123: q
       125: q
       126: q
       127: q
       129: q
       131: q^5+q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q
       140: q
       141: q
       142: q
       143: q
       144: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q^5+q
       151: q^5+q
       153: q
       155: q^5+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q^5+q
       163: q
       164: q
       165: q^5+q
       166: q
       167: q
       168: q^5+q
       169: q
       173: q
       177: q
       179: q
       181: q
       183: q
       185: q
       187: q
       189: q
       191: q
       193: q
       195: q
       197: q
       199: q
       201: q
       203: q
       205: q
       207: q
       209: q
       211: q^5+q
       213: q
       215: q
       217: q^5+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q
       241: q^5+q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q
       249: q^5+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q
       257: q
       258: q^5+q
       259: q
       263: q
       267: q
       271: q
       275: q
       279: q
       281: q
       283: q
       285: q
       287: q
       289: q
       291: q
       293: q
       295: q
       297: q
       299: q
       301: q
       303: q
       305: q
       307: q
       309: q
       311: q
       313: q
       315: q
       317: q
       319: q
       321: q
       323: q
       325: q
       327: q
       329: q
       331: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^5+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q
       362: q
       364: q^5+q
       366: q
       367: q
       368: q
       369: q
       370: q
       371: q
       372: q
       373: q^5+q
       374: q
       375: q
       376: q
       377: q
       381: q
       385: q
       389: q
       393: q
       397: q
       401: q
       405: q
       409: q
       411: q
       413: q
       415: q
       417: q
       419: q
       421: q
       423: q
       425: q
       427: q
       429: q
       431: q
       433: q
       435: q
       437: q
       439: q
       441: q
       443: q
       445: q
       447: q
       449: q
       451: q
       453: q
       455: q
       457: q
       459: q
       461: q
       463: q
       465: q
       467: q
       469: q
       471: q
       473: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^5+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
       502: q
       504: q
       506: q
       508: q
       509: q
       510: q
       511: q
       512: q
       513: q
       514: q
       515: q
       516: q
       517: q
       518: q
       519: q
       520: q
       521: q
       525: q
       529: q
       533: q
       537: q
       541: q
       545: q
       549: q
       553: q
       557: q
       561: q
       565: q
       569: q
       573: q
       577: q
       583: q
       585: q
       587: q
       589: q
       591: q
       593: q
       595: q
       597: q
       599: q
       601: q
       603: q
       605: q
       607: q
       609: q
       611: q
       613: q
       615: q
       617: q
       619: q
       621: q
       623: q
       625: q
       627: q
       629: q
       631: q
       633: q
       635: q
       637: q
       639: q
       641: q
       643: q
       645: q
       647: q
       649: q
       651: q
       653: q
       655: q
       657: q
       658: q
       660: q
       662: q
       664: q
       665: q
       666: q
       668: q
       670: q
       672: q
       673: q
       674: q
       675: q
       676: q
       677: q
       678: q
       679: q
       680: q
       681: q
       682: q
       683: q
       684: q
       685: q
       686: q
       687: q
       688: q
       689: q
       693: q
       705: q
       709: q
       713: q
       717: q
       721: q
       725: q
       729: q
       733: q
       737: q
       741: q
       745: q
       749: q
       753: q
       757: q
       761: q
       765: q
       769: q
       775: q
       777: q
       779: q
       781: q
       783: q
       785: q
       787: q
       789: q
       791: q
       793: q
       795: q
       797: q
       799: q
       801: q
       803: q
       805: q
       807: q
       809: q
       811: q
       813: q
       815: q
       817: q
       819: q
       821: q
       823: q
       825: q
       827: q
       829: q
       831: q
       833: q
       835: q
       837: q
       839: q
       841: q
       843: q
       845: q
       847: q
       849: q
       851: q
       853: q
       855: q
       857: q
       866: q
       868: q
       870: q
       871: q
       872: q
       874: q
       875: q
       876: q
       877: q
       878: q
       879: q
       880: q
       884: q
       896: q
       900: q
       904: q
       908: q
       912: q
       916: q
       920: q
       924: q
       928: q
       932: q
       936: q
       940: q
       944: q
       948: q
       952: q
       956: q
       960: q
       964: q
       968: q
       974: q
       978: q
       982: q
       988: q
       994: q
       998: q
      1000: q
      1002: q
      1004: q
      1006: q
      1008: q
      1010: q
      1012: q
      1018: q
      1020: q
      1022: q
      1024: q
      1026: q
      1028: q
      1034: q
      1036: q
      1038: q
      1040: q
      1042: q
      1044: q
      1048: q
      1050: q
      1052: q
      1054: q
      1056: q
      1058: q
      1060: q
      1062: q
      1064: q
      1076: q
      1078: q
      1080: q
      1082: q
      1083: q
      1084: q
      1085: q
      1086: q
      1098: q
      1110: q
      1114: q
      1118: q
      1122: q
      1126: q
      1130: q
      1134: q
      1138: q
      1148: q
      1152: q
      1156: q
      1160: q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: q
      1198: q
      1202: q
      1206: q
      1220: q
      1222: q
      1230: q
      1232: q
      1234: q
      1238: q
      1240: q
      1242: q
      1248: q
      1250: q
      1254: q
      1256: q
      1258: q
      1260: q
      1264: q
      1266: q
      1268: q
      1270: q
      1272: q
      1274: q
      1276: q
      1278: q
      1280: q
      1287: q
      1289: q
      1290: q
      1322: q
      1330: q
      1344: q
      1348: q
      1352: q
      1356: q
      1360: q
      1364: q
      1368: q
      1376: q
      1380: q
      1384: q
      1388: q
      1392: q
      1396: q
      1400: q
      1414: q
      1418: q
      1422: q
      1426: q
      1430: q
      1446: q
      1464: q
      1466: q
      1468: q
      1470: q
      1474: q
      1476: q
      1478: q
      1480: q
      1484: q
      1501: q
      1513: q
      1559: q
      1571: q
      1579: q
      1591: q
      1599: q
      1603: q
      1607: q
      1611: q
      1615: q
      1619: q
      1623: q
      1627: q
      1637: 1
      1641: q
      1649: q
      1657: q
      1671: q
      1711: q
      1725: 1
      1729: 1
      1753: q
      1757: q
      1777: q
      1781: q
      1793: q
      1807: q
      1811: q
      1823: 1
      1836: 1
      1882: q
      1894: 1
      1910: 1
      1928: 1
      1948: q
      1958: 1
      1968: 1
      1980: 1
      2028: 1
      2036: 1
      2048: 1
      2056: 1
      2070: 1
      2082: 1
      2094: 1
      2116: 1
      2142: 1

2143:    0: 10q^3+4q^2+q
         1: 10q^3+4q^2+q
         2: 3q^4+7q^3+4q^2+q
         3: 10q^3+4q^2+q
         4: 3q^4+7q^3+4q^2+q
         5: 10q^3+4q^2+q
         6: 3q^4+7q^3+4q^2+q
         7: q^5+4q^4+5q^3+4q^2+q
         8: 3q^4+7q^3+4q^2+q
         9: q^5+4q^4+5q^3+4q^2+q
        10: 10q^3+4q^2+q
        11: 10q^3+4q^2+q
        12: 3q^4+7q^3+4q^2+q
        13: 7q^3+4q^2+q
        14: 2q^4+5q^3+4q^2+q
        15: 7q^3+4q^2+q
        16: 10q^3+4q^2+q
        17: 10q^3+4q^2+q
        18: q^5+4q^4+5q^3+4q^2+q
        19: 7q^3+4q^2+q
        20: 7q^3+4q^2+q
        21: 2q^4+5q^3+4q^2+q
        22: 10q^3+4q^2+q
        23: 10q^3+4q^2+q
        24: 3q^4+7q^3+4q^2+q
        25: 10q^3+4q^2+q
        26: 10q^3+4q^2+q
        27: 3q^4+7q^3+4q^2+q
        28: 10q^3+4q^2+q
        29: 7q^3+4q^2+q
        30: 5q^3+4q^2+q
        31: 10q^3+4q^2+q
        32: 7q^3+4q^2+q
        33: 10q^3+4q^2+q
        34: 10q^3+4q^2+q
        35: 7q^3+4q^2+q
        36: 10q^3+4q^2+q
        37: 6q^3+2q^2+q
        38: 4q^3+2q^2
        39: 6q^3+2q^2+q
        40: 4q^3+2q^2
        41: 2q^4+4q^3+2q^2+q
        42: q^4+3q^3+2q^2
        43: 7q^3+4q^2+q
        44: 2q^4+5q^3+4q^2+q
        45: 7q^3+4q^2+q
        46: 7q^3+4q^2+q
        47: 7q^3+4q^2+q
        48: 2q^4+5q^3+4q^2+q
        49: 7q^3+4q^2+q
        50: 7q^3+4q^2+q
        51: 2q^4+5q^3+4q^2+q
        52: 7q^3+4q^2+q
        53: 7q^3+4q^2+q
        54: 2q^4+5q^3+4q^2+q
        55: 7q^3+4q^2+q
        56: 7q^3+4q^2+q
        57: 2q^4+5q^3+4q^2+q
        58: 6q^3+3q^2+q
        59: 4q^3+q^2
        60: 6q^3+3q^2+q
        61: 4q^3+q^2
        62: 6q^3+2q^2+q
        63: 4q^3+2q^2
        64: 4q^3+2q^2+q
        65: 3q^3+2q^2
        66: 6q^3+2q^2+q
        67: 4q^3+2q^2
        68: 4q^3+4q^2+q
        69: 5q^3+4q^2+q
        70: 5q^3+4q^2+q
        71: 7q^3+4q^2+q
        72: 4q^3+4q^2+q
        73: 4q^3+4q^2+q
        74: 3q^3+2q^2+q
        75: q^3+2q^2
        76: 3q^3+2q^2+q
        77: q^3+2q^2
        78: q^4+2q^3+2q^2+q
        79: q^3+2q^2
        80: 7q^3+4q^2+q
        81: 7q^3+4q^2+q
        82: 7q^3+4q^2+q
        83: 5q^3+4q^2+q
        84: 7q^3+4q^2+q
        85: 7q^3+4q^2+q
        86: 7q^3+4q^2+q
        87: 5q^3+4q^2+q
        88: 7q^3+4q^2+q
        89: 7q^3+4q^2+q
        90: 2q^4+5q^3+4q^2+q
        91: 4q^3+4q^2+q
        92: 4q^3+4q^2+q
        93: 4q^3+4q^2+q
        94: 7q^3+4q^2+q
        95: 7q^3+4q^2+q
        96: 2q^4+5q^3+4q^2+q
        97: 7q^3+4q^2+q
        98: 7q^3+4q^2+q
        99: 2q^4+5q^3+4q^2+q
       100: 7q^3+4q^2+q
       101: 7q^3+4q^2+q
       102: 2q^4+5q^3+4q^2+q
       103: 4q^3+2q^2+q
       104: 2q^3+q^2
       105: 2q^3+q^2
       106: 2q^3
       107: 3q^3+3q^2+q
       108: q^3+q^2
       109: 3q^3+3q^2+q
       110: q^3+q^2
       111: q^3+2q^2+q
       112: 2q^2
       113: 3q^3+2q^2+q
       114: q^3+2q^2
       115: 2q^3+2q^2+q
       116: q^3+2q^2
       117: 3q^3+3q^2+q
       118: q^3+q^2
       119: 3q^3+3q^2+q
       120: q^3+q^2
       121: 4q^3+2q^2+q
       122: 3q^3+2q^2
       123: 4q^3+2q^2+q
       124: 3q^3+2q^2
       125: 4q^3+4q^2+q
       126: 5q^3+4q^2+q
       127: 3q^3+2q^2+q
       128: q^3+2q^2
       129: 3q^3+2q^2+q
       130: q^3+2q^2
       131: q^4+2q^3+2q^2+q
       132: q^3+2q^2
       133: 2q^3+4q^2+q
       134: 4q^3+4q^2+q
       135: 2q^3+4q^2+q
       136: 2q^3+4q^2+q
       137: 7q^3+4q^2+q
       138: 5q^3+4q^2+q
       139: 7q^3+4q^2+q
       140: 4q^3+4q^2+q
       141: 5q^3+4q^2+q
       142: 4q^3+4q^2+q
       143: 7q^3+4q^2+q
       144: 5q^3+4q^2+q
       145: 7q^3+4q^2+q
       146: 5q^3+4q^2+q
       147: 4q^3+4q^2+q
       148: 4q^3+4q^2+q
       149: 7q^3+4q^2+q
       150: 5q^3+4q^2+q
       151: 3q^3+2q^2+q
       152: q^3+2q^2
       153: 3q^3+2q^2+q
       154: q^3+2q^2
       155: q^4+2q^3+2q^2+q
       156: q^3+2q^2
       157: 4q^3+4q^2+q
       158: 4q^3+4q^2+q
       159: 4q^3+4q^2+q
       160: 4q^3+4q^2+q
       161: 4q^3+4q^2+q
       162: 4q^3+4q^2+q
       163: 4q^3+4q^2+q
       164: 4q^3+4q^2+q
       165: 4q^3+4q^2+q
       166: 7q^3+4q^2+q
       167: 7q^3+4q^2+q
       168: 2q^4+5q^3+4q^2+q
       169: q^3+2q^2+q
       170: q^2
       171: q^2
       173: 2q^3+2q^2+q
       174: q^3+q^2
       175: q^3+q^2
       177: 2q^3+2q^2+q
       178: q^3+2q^2
       179: 3q^3+2q^2+q
       180: q^3+2q^2
       181: q^3+2q^2+q
       182: 2q^2
       183: q^3+3q^2+q
       184: q^2
       185: q^3+3q^2+q
       186: q^2
       187: 2q^2+q
       188: 2q^2
       189: 2q^3+2q^2+q
       190: q^3+2q^2
       191: 3q^3+3q^2+q
       192: q^3+q^2
       193: 3q^3+3q^2+q
       194: q^3+q^2
       195: 3q^3+3q^2+q
       196: q^3+q^2
       197: q^3+2q^2+q
       198: 2q^2
       199: 3q^3+3q^2+q
       200: q^3+q^2
       201: 3q^3+3q^2+q
       202: q^3+q^2
       203: 3q^3+3q^2+q
       204: q^3+q^2
       205: q^3+2q^2+q
       206: 2q^2
       207: 4q^3+2q^2+q
       208: 3q^3+2q^2
       209: 3q^3+2q^2+q
       210: q^3+2q^2
       211: 2q^3+2q^2+q
       212: q^3+2q^2
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^3+q^2+q
       219: 2q^3+4q^2+q
       220: 2q^3+4q^2+q
       221: 4q^3+4q^2+q
       222: 2q^3+4q^2+q
       223: 2q^3+4q^2+q
       224: 2q^3+4q^2+q
       225: 2q^3+4q^2+q
       226: 5q^3+4q^2+q
       227: 2q^3+4q^2+q
       228: 4q^3+4q^2+q
       229: 2q^3+4q^2+q
       230: 2q^3+4q^2+q
       231: 5q^3+4q^2+q
       232: 2q^3+4q^2+q
       233: 4q^3+4q^2+q
       234: 2q^3+4q^2+q
       235: 2q^3+4q^2+q
       236: 5q^3+4q^2+q
       237: 3q^3+2q^2+q
       238: q^3+2q^2
       239: 3q^3+2q^2+q
       240: q^3+2q^2
       241: q^4+2q^3+2q^2+q
       242: q^3+2q^2
       243: 7q^3+4q^2+q
       244: 4q^3+4q^2+q
       245: 4q^3+4q^2+q
       246: 5q^3+4q^2+q
       247: q^3+7q^2+q
       248: q^3+7q^2+q
       249: q^4+3q^3+4q^2+q
       250: 4q^3+4q^2+q
       251: 4q^3+4q^2+q
       252: 4q^3+4q^2+q
       253: 4q^3+4q^2+q
       254: 4q^3+4q^2+q
       255: 4q^3+4q^2+q
       256: 4q^3+4q^2+q
       257: 4q^3+4q^2+q
       258: 4q^3+4q^2+q
       259: q^3+2q^2+q
       260: q^2
       261: q^2
       263: 2q^2+q
       264: q^2
       265: q^2
       267: q^3+2q^2+q
       268: q^2
       270: q^2
       271: q^3+2q^2+q
       272: q^2
       274: q^2
       275: 2q^3+2q^2+q
       276: q^3+q^2
       277: q^3+q^2
       279: q^2+q
       281: q^3+q^2+q
       283: q^3+3q^2+q
       284: q^2
       285: q^3+3q^2+q
       286: q^2
       287: 2q^3+2q^2+q
       288: q^3+2q^2
       289: q^2+q
       291: 2q^2+q
       292: 2q^2
       293: q^3+3q^2+q
       294: q^2
       295: q^3+3q^2+q
       296: q^2
       297: 2q^2+q
       298: 2q^2
       299: q^3+3q^2+q
       300: q^2
       301: q^3+2q^2+q
       302: 2q^2
       303: q^3+3q^2+q
       304: q^2
       305: 2q^2+q
       306: 2q^2
       307: q^3+3q^2+q
       308: q^2
       309: q^3+3q^2+q
       310: q^2
       311: q^3+2q^2+q
       312: 2q^2
       313: 2q^2+q
       314: 2q^2
       315: 2q^3+2q^2+q
       316: q^3+2q^2
       317: 3q^3+2q^2+q
       318: q^3+2q^2
       319: 3q^3+3q^2+q
       320: q^3+q^2
       321: 3q^3+3q^2+q
       322: q^3+q^2
       323: q^3+2q^2+q
       324: 2q^2
       325: 2q^3+2q^2+q
       326: q^3+2q^2
       327: q^3+q^2+q
       329: q^3+q^2+q
       331: q^3+q^2+q
       333: 2q^3+4q^2+q
       334: 2q^3+4q^2+q
       335: 2q^3+4q^2+q
       336: 4q^2+q
       337: q^3+7q^2+q
       338: q^3+4q^2+q
       339: 3q^2
       340: q^3+4q^2+q
       341: 3q^2
       342: q^4+2q^3+2q^2+q
       343: q^3+2q^2
       344: 2q^3+4q^2+q
       345: 2q^3+4q^2+q
       346: 4q^3+4q^2+q
       347: 2q^3+4q^2+q
       348: 2q^3+4q^2+q
       349: 2q^3+4q^2+q
       350: 2q^3+4q^2+q
       351: q^3+7q^2+q
       352: 2q^3+4q^2+q
       353: 2q^3+4q^2+q
       354: 4q^3+4q^2+q
       355: 2q^3+4q^2+q
       356: 2q^3+4q^2+q
       357: 2q^3+4q^2+q
       358: 2q^3+4q^2+q
       359: q^3+7q^2+q
       360: q^3+q^2+q
       362: q^3+q^2+q
       364: q^3+q^2+q
       366: 5q^3+4q^2+q
       367: 2q^3+4q^2+q
       368: 4q^3+4q^2+q
       369: 2q^3+4q^2+q
       370: 2q^3+4q^2+q
       371: 5q^2+q
       372: 5q^2+q
       373: 2q^3+3q^2+q
       374: 4q^3+4q^2+q
       375: 4q^3+4q^2+q
       376: 4q^3+4q^2+q
       377: 2q^2+q
       378: q^2
       379: q^2
       381: q^2+q
       385: 2q^2+q
       386: q^2
       387: q^2
       389: q^3+2q^2+q
       390: q^2
       392: q^2
       393: 2q^2+q
       394: q^2
       395: q^2
       397: q^3+2q^2+q
       398: q^2
       400: q^2
       401: 2q^2+q
       402: q^2
       403: q^2
       405: q^3+2q^2+q
       407: q^2
       408: q^2
       409: q^2+q
       411: q^3+q^2+q
       413: q^2+q
       415: q^2+q
       417: q^2+q
       419: q^3+3q^2+q
       420: q^2
       421: q^3+3q^2+q
       422: q^2
       423: 2q^2+q
       424: 2q^2
       425: 2q^2+q
       426: 2q^2
       427: q^3+4q^2+q
       428: 3q^2
       429: q^3+3q^2+q
       430: q^2
       431: q^3+3q^2+q
       432: q^2
       433: 2q^2+q
       434: 2q^2
       435: q^2+q
       437: q^3+3q^2+q
       438: q^2
       439: q^3+3q^2+q
       440: q^2
       441: 2q^2+q
       442: 2q^2
       443: q^3+5q^2+q
       444: 2q^2
       445: q^3+4q^2+q
       446: 3q^2
       447: q^3+3q^2+q
       448: q^2
       449: q^3+3q^2+q
       450: q^2
       451: 2q^2+q
       452: 2q^2
       453: q^3+3q^2+q
       454: q^2
       455: q^2+q
       457: q^3+3q^2+q
       458: q^2
       459: 2q^2+q
       460: 2q^2
       461: q^3+5q^2+q
       462: 2q^2
       463: q^3+4q^2+q
       464: 3q^2
       465: q^2+q
       467: q^3+q^2+q
       469: 2q^3+2q^2+q
       470: q^3+2q^2
       471: q^3+3q^2+q
       472: q^2
       473: q^3+3q^2+q
       474: q^2
       475: 2q^2+q
       476: 2q^2
       477: q^3+2q^2+q
       478: 2q^2
       479: q^3+3q^2+q
       480: 4q^2
       481: q^3+3q^2+q
       482: q^3+3q^2+q
       483: 4q^2+q
       484: 4q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: 3q^2+q
       492: 2q^3+4q^2+q
       493: 2q^3+4q^2+q
       494: 2q^3+4q^2+q
       495: 4q^2+q
       496: 5q^2+q
       497: 2q^3+4q^2+q
       498: 2q^3+4q^2+q
       499: 2q^3+4q^2+q
       500: 4q^2+q
       501: 5q^2+q
       502: q^3+q^2+q
       504: q^3+q^2+q
       506: q^3+q^2+q
       508: 2q^3+4q^2+q
       509: 2q^3+4q^2+q
       510: 4q^3+4q^2+q
       511: 2q^3+4q^2+q
       512: 2q^3+4q^2+q
       513: 2q^3+4q^2+q
       514: 2q^3+4q^2+q
       515: 5q^2+q
       516: 5q^2+q
       517: 2q^3+3q^2+q
       518: 5q^2+q
       519: 5q^2+q
       520: 2q^3+3q^2+q
       521: q^2+q
       525: q^2+q
       529: 2q^2+q
       530: q^2
       531: q^2
       533: 2q^2+q
       534: q^2
       535: q^2
       537: q^2+q
       541: 2q^2+q
       542: q^2
       544: q^2
       545: q^3+3q^2+q
       546: 2q^2
       547: q^2
       548: q^2
       549: 2q^2+q
       550: q^2
       551: q^2
       553: q^2+q
       557: 2q^2+q
       558: q^2
       560: q^2
       561: q^3+3q^2+q
       562: 2q^2
       563: q^2
       564: q^2
       565: 2q^2+q
       566: q^2
       567: q^2
       569: q^3+2q^2+q
       571: q^2
       572: q^2
       573: q^3+3q^2+q
       574: 2q^2
       576: 2q^2
       577: q^3+2q^2+q
       578: q^2
       580: 2q^2
       581: 2q^2
       583: q^2+q
       585: q
       587: q^2+q
       589: q^3+2q^2+q
       590: q^2
       591: 2q^2+q
       593: 2q^2+q
       595: q^3+2q^2+q
       596: q^2
       597: q^2+q
       599: 2q^2+q
       600: 2q^2
       601: q^2+q
       603: q^3+3q^2+q
       604: q^2
       605: q^2+q
       607: q^3+3q^2+q
       608: q^2
       609: 2q^2+q
       610: 2q^2
       611: q^2+q
       613: 2q^2+q
       614: 2q^2
       615: 3q^2+q
       616: q^2
       617: 2q^2+q
       619: q^3+3q^2+q
       620: q^2
       621: q^3+3q^2+q
       622: q^2
       623: q^2+q
       625: 2q^2+q
       626: 2q^2
       627: q^2+q
       629: 2q^2+q
       630: 2q^2
       631: 3q^2+q
       632: q^2
       633: 2q^2+q
       635: q^2+q
       637: q^3+q^2+q
       639: q^2+q
       641: q^3+3q^2+q
       642: q^2
       643: q^3+3q^2+q
       644: q^2
       645: 2q^2+q
       646: 2q^2
       647: q^3+3q^2+q
       648: q^2
       649: q^3+3q^2+q
       650: q^2
       651: q^2+q
       653: 2q^2+q
       654: 2q^2
       655: 2q^2+q
       656: 3q^2
       657: 4q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: 3q^2+q
       665: 2q^2+q
       666: 2q^2+q
       668: 2q^2+q
       670: q^3+q^2+q
       672: 4q^2+q
       673: 3q^2+q
       674: 5q^2+q
       675: q^3+3q^2+q
       676: q^3+3q^2+q
       677: 4q^2+q
       678: 5q^2+q
       679: 3q^2+q
       680: 5q^2+q
       681: q^3+3q^2+q
       682: q^3+3q^2+q
       683: 4q^2+q
       684: 5q^2+q
       685: 3q^2+q
       686: 2q^3+4q^2+q
       687: 2q^3+4q^2+q
       688: 2q^3+4q^2+q
       689: 4q^2+q
       690: 5q^2+q
       691: 5q^2+q
       692: 2q^3+3q^2+q
       693: q^3+2q^2+q
       694: q^2
       696: q^2
       698: q^2
       699: q^2
       700: q^2
       705: q^2+q
       709: q
       713: q^2+q
       714: q^2
       717: q^2+q
       718: q^2
       721: q^2+q
       725: 2q^2+q
       726: q^2
       728: q^2
       729: q^2+q
       733: q^2+q
       737: q^2+q
       741: 2q^2+q
       742: q^2
       744: q^2
       745: q^2+q
       749: q^2+q
       753: 2q^2+q
       754: q^2
       755: q^2
       757: q^2+q
       761: 2q^2+q
       763: q^2
       764: q^2
       765: 2q^2+q
       766: q^2
       767: q^2
       769: q^2+q
       772: q^2
       775: q^2+q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       785: q^2+q
       787: q^2+q
       789: q^2+q
       791: q
       792: q^2
       793: 3q^2+q
       794: q^2
       795: 2q^2+q
       797: q
       799: q^2+q
       801: q^3+2q^2+q
       802: q^2
       803: 2q^2+q
       805: 2q^2+q
       807: q^3+2q^2+q
       808: q^2
       809: q^2+q
       811: 2q^2+q
       812: 2q^2
       813: 2q^2+q
       815: 3q^2+q
       816: q^2
       817: 3q^2+q
       818: q^2
       819: 2q^2+q
       821: q
       823: q^2+q
       825: q^3+2q^2+q
       826: q^2
       827: 2q^2+q
       829: 2q^2+q
       831: q^3+2q^2+q
       832: q^2
       833: q^2+q
       835: 2q^2+q
       836: 2q^2
       837: 2q^2+q
       839: 3q^2+q
       840: q^2
       841: q^2+q
       843: 2q^2+q
       844: 3q^2
       845: q^3+3q^2+q
       846: q^2
       847: q^3+3q^2+q
       848: q^2
       849: q^2+q
       851: 2q^2+q
       852: 2q^2
       853: q^2+q
       855: 2q^2+q
       856: 2q^2
       857: 2q^2+q
       858: 3q^2
       859: 2q^2+q
       861: 2q^2+q
       863: q^3+q^2+q
       865: 4q^2+q
       866: 2q^2+q
       867: 3q^2+q
       868: 2q^2+q
       869: 5q^2+q
       870: 3q^2+q
       871: 2q^2+q
       872: 3q^2+q
       873: 5q^2+q
       874: 3q^2+q
       875: 2q^2+q
       876: 3q^2+q
       877: q^3+3q^2+q
       878: q^3+3q^2+q
       879: 4q^2+q
       880: 3q^2+q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q^2+q
       896: q
       900: q
       904: q
       908: q
       912: q^2+q
       916: q^2+q
       920: q
       924: q^2+q
       925: q^2
       928: q^2+q
       929: q^2
       932: q^2+q
       936: q^2+q
       940: q^2+q
       944: q
       948: q^2+q
       949: q^2
       952: q^2+q
       953: q^2
       956: q^2+q
       960: q^2+q
       964: 2q^2+q
       965: q^2
       966: q^2
       968: q^2+q
       971: q^2
       974: 2q^2+q
       976: q^2
       977: q^2
       978: q^2+q
       982: q^2+q
       985: q^2
       988: 2q^2+q
       989: q^2
       990: q^2
       992: q^2+q
       994: q
       996: q^2+q
       998: q^2+q
      1000: q^2+q
      1002: q
      1004: q^2+q
      1006: q^2+q
      1008: q
      1009: q^2
      1010: q
      1012: q
      1013: q^2
      1014: 2q^2+q
      1016: 3q^2+q
      1017: q^2
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1026: q^2+q
      1028: q^2+q
      1030: 2q^2+q
      1032: 3q^2+q
      1033: q^2
      1034: q
      1036: q^2+q
      1038: q
      1040: q^2+q
      1042: q^2+q
      1044: q^2+q
      1046: 2q^2+q
      1047: 3q^2
      1048: q
      1050: q^2+q
      1052: q^3+2q^2+q
      1053: q^2
      1054: 2q^2+q
      1056: 2q^2+q
      1058: q^3+2q^2+q
      1059: q^2
      1060: q^2+q
      1062: 2q^2+q
      1063: 2q^2
      1064: q
      1065: q^2
      1066: 3q
      1068: 3q
      1070: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q^2+q
      1075: 3q
      1076: 2q^2+q
      1077: 3q^2+q
      1078: 2q^2+q
      1079: 3q
      1080: 2q^2+q
      1081: 3q^2+q
      1082: 2q^2+q
      1083: 2q^2+q
      1084: 3q^2+q
      1085: 3q^2+q
      1086: q^2+q
      1098: q^2+q
      1110: q
      1114: q
      1118: q
      1122: q
      1126: q
      1130: q
      1134: q
      1138: q
      1144: q^2+q
      1148: q
      1152: q
      1156: q
      1160: q
      1164: q^2+q
      1168: q
      1172: q
      1176: q
      1180: q
      1184: q^2+q
      1188: q^2+q
      1191: q^2
      1194: 2q^2+q
      1195: q^2
      1196: q^2
      1198: q
      1202: q^2+q
      1203: q^2
      1206: q^2+q
      1207: q^2
      1210: 3q
      1212: 2q
      1214: q
      1216: q^2+q
      1218: q^2+q
      1222: q
      1224: q
      1225: q^2
      1226: 3q
      1228: 2q
      1229: q
      1230: q
      1232: q^2+q
      1234: q^2+q
      1236: q^2+q
      1238: q
      1240: q^2+q
      1242: q^2+q
      1244: 3q
      1246: 2q
      1247: q
      1248: q
      1250: q^2+q
      1252: q^2+q
      1254: q^2+q
      1256: q
      1258: q^2+q
      1260: q^2+q
      1262: q
      1263: 2q
      1264: q
      1266: q
      1268: q^2+q
      1270: q^2+q
      1272: q^2+q
      1274: q^2+q
      1276: q
      1277: q^2
      1278: q
      1280: q
      1281: q^2
      1282: 2q
      1283: 2q^2+q
      1284: 2q
      1285: 2q^2+q
      1286: 2q
      1287: 2q^2+q
      1288: 3q^2+q
      1289: 2q^2+q
      1290: q
      1302: q^2+q
      1314: q
      1318: q
      1322: q
      1326: q
      1334: q
      1340: 2q
      1342: q
      1344: q
      1348: q
      1352: q
      1356: q
      1360: q
      1364: q
      1368: q
      1372: 2q
      1374: q
      1376: q
      1380: q
      1384: q
      1388: q
      1392: q
      1396: q
      1400: q
      1404: q
      1407: 2q
      1410: q
      1411: q
      1412: q
      1414: q
      1418: q
      1422: q
      1426: q
      1430: q
      1438: 2q
      1440: q
      1442: q
      1445: q
      1448: q
      1450: q^2+q
      1452: 2q
      1454: q^2+q
      1456: q
      1458: 2q
      1460: q^2+q
      1462: q^2+q
      1464: q
      1466: q^2+q
      1468: q^2+q
      1470: q
      1472: q^2+q
      1476: q^2+q
      1478: q^2+q
      1480: q
      1482: q
      1483: q^2
      1484: q
      1485: 2q
      1486: 2q
      1487: 2q^2+q
      1488: 2q
      1489: q
      1501: q
      1513: q
      1525: q
      1528: q
      1529: q
      1541: q
      1545: q
      1556: q
      1563: q
      1567: q
      1571: q
      1575: q
      1583: q
      1587: q
      1591: q
      1595: q
      1603: q
      1607: q
      1611: q
      1615: q
      1619: q
      1623: q
      1627: q
      1631: q
      1640: q
      1643: 2q
      1645: q
      1647: q
      1649: q
      1651: 2q
      1653: q
      1655: q
      1657: q
      1661: q
      1663: q^2+q
      1665: q^2+q
      1667: 2q
      1670: q
      1673: q
      1674: 2q
      1687: q
      1699: q
      1711: q
      1726: q
      1737: q
      1745: q
      1761: q
      1765: q
      1785: q
      1789: q
      1793: q
      1797: q
      1804: q
      1811: q
      1819: q
      1821: q
      1826: q
      1827: 2q
      1829: q
      1831: q
      1833: 1
      1870: q
      1929: q
      1932: q
      1936: q
      1952: q
      1956: 1
      1961: 1
      1962: 1
      1964: 1
      2029: 1
      2032: 1
      2041: 1
      2044: 1
      2053: 1
      2064: 1
      2071: 1
      2083: 1
      2104: 1
      2129: 1
      2143: 1

2144:    0: q^5+2q^4+3q^3+q^2+q
         1: q^5+2q^4+3q^3+q^2+q
         2: q^5+2q^4+3q^3+q^2+q
         3: 2q^4+3q^3+q^2+q
         4: q^5+2q^4+3q^3+q^2+q
         5: 2q^4+3q^3+q^2+q
         6: q^5+2q^4+3q^3+q^2+q
         7: q^5+2q^4+3q^3+q^2+q
         8: 2q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: q^5+2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: q^5+2q^4+3q^3+q^2+q
        13: q^5+2q^4+3q^3+q^2+q
        14: q^5+2q^4+3q^3+q^2+q
        15: 2q^4+3q^3+q^2+q
        16: q^4+3q^3+q^2+q
        17: q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+2q^4+3q^3+q^2+q
        20: q^5+2q^4+3q^3+q^2+q
        21: q^5+2q^4+3q^3+q^2+q
        22: q^4+3q^3+q^2+q
        23: q^4+3q^3+q^2+q
        24: q^4+3q^3+q^2+q
        25: q^4+3q^3+q^2+q
        26: q^4+3q^3+q^2+q
        27: q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: q^5+2q^4+3q^3+q^2+q
        30: q^5+2q^4+3q^3+q^2+q
        31: q^4+3q^3+q^2+q
        32: q^4+3q^3+q^2+q
        33: 3q^3+q^2+q
        34: q^4+3q^3+q^2+q
        35: q^4+3q^3+q^2+q
        36: 3q^3+q^2+q
        37: q^4+3q^3+q^2+q
        39: q^4+3q^3+q^2+q
        41: q^4+3q^3+q^2+q
        43: q^5+2q^4+3q^3+q^2+q
        44: q^5+2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: q^4+3q^3+q^2+q
        47: q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: q^4+3q^3+q^2+q
        50: q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^4+3q^3+q^2+q
        53: q^4+3q^3+q^2+q
        54: q^4+3q^3+q^2+q
        55: q^4+3q^3+q^2+q
        56: q^4+3q^3+q^2+q
        57: q^4+3q^3+q^2+q
        58: 2q^3+q^2+q
        59: q^3
        60: 2q^3+q^2+q
        61: q^3
        62: q^4+3q^3+q^2+q
        64: q^4+3q^3+q^2+q
        66: 3q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: q^5+2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 3q^3+q^2+q
        73: 3q^3+q^2+q
        74: q^4+3q^3+q^2+q
        76: q^4+3q^3+q^2+q
        78: q^4+3q^3+q^2+q
        80: q^4+3q^3+q^2+q
        81: 3q^3+q^2+q
        82: q^4+3q^3+q^2+q
        83: q^4+3q^3+q^2+q
        84: q^4+3q^3+q^2+q
        85: 3q^3+q^2+q
        86: q^4+3q^3+q^2+q
        87: q^4+3q^3+q^2+q
        88: q^4+3q^3+q^2+q
        89: q^4+3q^3+q^2+q
        90: q^5+2q^4+2q^3+q^2+q
        91: q^4+3q^3+q^2+q
        92: q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 3q^3+q^2+q
        95: 3q^3+q^2+q
        96: q^4+2q^3+q^2+q
        97: 3q^3+q^2+q
        98: 3q^3+q^2+q
        99: q^4+2q^3+q^2+q
       100: q^4+2q^3+q^2+q
       101: q^4+2q^3+q^2+q
       102: q^4+2q^3+q^2+q
       103: 2q^3+q^2+q
       106: q^3
       107: 2q^3+q^2+q
       108: q^3
       109: 2q^3+q^2+q
       110: q^3
       111: 3q^3+q^2+q
       113: q^4+3q^3+q^2+q
       115: q^4+3q^3+q^2+q
       117: 2q^3+q^2+q
       118: q^3
       119: 2q^3+q^2+q
       120: q^3
       121: q^4+3q^3+q^2+q
       123: 3q^3+q^2+q
       125: q^4+3q^3+q^2+q
       126: q^4+2q^3+q^2+q
       127: 3q^3+q^2+q
       129: 3q^3+q^2+q
       131: q^4+2q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 3q^3+q^2+q
       136: 3q^3+q^2+q
       137: 3q^3+q^2+q
       138: 2q^3+q^2+q
       139: 3q^3+q^2+q
       140: q^3+q^2+q
       141: q^4+3q^3+q^2+q
       142: 3q^3+q^2+q
       143: 3q^3+q^2+q
       144: 2q^3+q^2+q
       145: 3q^3+q^2+q
       146: q^4+3q^3+q^2+q
       147: 3q^3+q^2+q
       148: q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: q^4+2q^3+q^2+q
       151: q^4+2q^3+q^2+q
       153: q^4+2q^3+q^2+q
       155: q^4+2q^3+q^2+q
       157: q^4+3q^3+q^2+q
       158: q^4+3q^3+q^2+q
       159: q^5+2q^4+2q^3+q^2+q
       160: 3q^3+q^2+q
       161: 3q^3+q^2+q
       162: q^4+2q^3+q^2+q
       163: 3q^3+q^2+q
       164: 3q^3+q^2+q
       165: q^4+2q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: 2q^3+q^2+q
       172: q^3
       173: 2q^3+q^2+q
       176: q^3
       177: 2q^3+q^2+q
       179: 3q^3+q^2+q
       181: 3q^3+q^2+q
       183: 2q^3+q^2+q
       184: q^3
       185: 2q^3+q^2+q
       186: q^3
       187: 3q^3+q^2+q
       189: q^4+3q^3+q^2+q
       191: 2q^3+q^2+q
       192: q^3
       193: q^3+q^2+q
       195: 2q^3+q^2+q
       196: q^3
       197: q^3+q^2+q
       199: 2q^3+q^2+q
       200: q^3
       201: 2q^3+q^2+q
       202: q^3
       203: q^3+q^2+q
       205: q^3+q^2+q
       207: 3q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: q^4+2q^3+q^2+q
       213: 3q^3+q^2+q
       215: 3q^3+q^2+q
       217: q^4+2q^3+q^2+q
       219: q^4+2q^3+q^2+q
       220: q^4+3q^3+q^2+q
       221: q^4+2q^3+q^2+q
       222: 3q^3+q^2+q
       223: 2q^3+q^2+q
       224: 3q^3+q^2+q
       225: 2q^3+q^2+q
       226: 2q^3+q^2+q
       227: 3q^3+q^2+q
       228: 2q^3+q^2+q
       229: q^3+q^2+q
       230: 3q^3+q^2+q
       231: 2q^3+q^2+q
       232: 3q^3+q^2+q
       233: 2q^3+q^2+q
       234: 3q^3+q^2+q
       235: q^3+q^2+q
       236: q^3+q^2+q
       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+2q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: q^3+q^2+q
       257: q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: 2q^3+q^2+q
       262: q^3
       263: 2q^3+q^2+q
       266: q^3
       267: q^3+q^2+q
       271: q^3+q^2+q
       275: 2q^3+q^2+q
       278: q^3
       279: 3q^3+q^2+q
       281: 2q^3+q^2+q
       283: q^3+q^2+q
       285: q^3+q^2+q
       287: 2q^3+q^2+q
       289: 3q^3+q^2+q
       291: 2q^3+q^2+q
       293: 2q^3+q^2+q
       294: q^3
       295: 2q^3+q^2+q
       296: q^3
       297: 3q^3+q^2+q
       299: q^3+q^2+q
       301: q^2+q
       303: 2q^3+q^2+q
       304: q^3
       305: q^3+q^2+q
       307: 2q^3+q^2+q
       308: q^3
       309: q^3+q^2+q
       311: q^2+q
       313: q^3+q^2+q
       315: q^3+q^2+q
       317: q^3+q^2+q
       319: q^2+q
       321: q^2+q
       323: q^2+q
       325: q^4+2q^3+q^2+q
       327: 3q^3+q^2+q
       329: 3q^3+q^2+q
       331: q^4+2q^3+q^2+q
       333: q^4+2q^3+q^2+q
       334: 2q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^2+q
       349: 3q^3+q^2+q
       350: 2q^3+q^2+q
       351: q^2+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: 2q^3+q^2+q
       357: q^3+q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q^2+q
       362: q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: q^3+q^2+q
       368: q^3+q^2+q
       369: q^2+q
       370: q^2+q
       371: q^3+q^2+q
       372: q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       377: q^3+q^2+q
       381: 2q^3+q^2+q
       384: q^3
       385: 2q^3+q^2+q
       388: q^3
       389: q^2+q
       393: q^3+q^2+q
       397: q^2+q
       401: q^3+q^2+q
       405: q^2+q
       409: 3q^3+q^2+q
       411: 2q^3+q^2+q
       413: 2q^3+q^2+q
       415: 3q^3+q^2+q
       417: 2q^3+q^2+q
       419: q^3+q^2+q
       421: q^3+q^2+q
       423: 2q^3+q^2+q
       425: q^3+q^2+q
       427: q^3+q^2+q
       429: q^2+q
       431: q^3+q^2+q
       433: q^2+q
       435: q^2+q
       437: q^3+q^2+q
       439: 2q^3+q^2+q
       440: q^3
       441: q^3+q^2+q
       443: q^2+q
       445: q^2+q
       447: q^3+q^2+q
       449: q^2+q
       451: q^2+q
       453: 2q^3+q^2+q
       454: q^3
       455: q^2+q
       457: q^3+q^2+q
       459: q^3+q^2+q
       461: q^2+q
       463: q^2+q
       465: q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       471: q^2+q
       473: q^2+q
       475: q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: q^3+q^2+q
       485: q^3+q^2+q
       487: q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^2+q
       496: q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       502: q^3+q^2+q
       504: q^3+q^2+q
       506: q^4+q^3+q^2+q
       508: q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       521: q^3+q^2+q
       525: 2q^3+q^2+q
       528: q^3
       529: q^3+q^2+q
       533: q^2+q
       537: q^2+q
       541: q^3+q^2+q
       545: q^2+q
       549: q^2+q
       553: q^2+q
       557: q^3+q^2+q
       561: q^2+q
       565: q^2+q
       569: 2q^2+q
       573: q^2+q
       577: q^2+q
       579: q^2
       583: 2q^3+q^2+q
       585: 2q^3+q^2+q
       587: 2q^3+q^2+q
       589: q^3+q^2+q
       591: q^2+q
       593: q^2+q
       595: q^3+q^2+q
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: q^3+q^2+q
       603: q^2+q
       605: q^2+q
       607: q^3+q^2+q
       609: q^2+q
       611: q^2+q
       613: q^2+q
       615: q^2+q
       617: q^2+q
       619: q^3+q^2+q
       621: q^2+q
       623: q^2+q
       625: q^2+q
       627: q^2+q
       629: q^2+q
       631: q^2+q
       633: q^2+q
       635: q^3+q^2+q
       637: q^3+q^2+q
       639: q^3+q^2+q
       641: q^2+q
       643: q^2+q
       645: q^2+q
       647: q^2+q
       649: q^2+q
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       657: q
       658: q^3+q
       660: q
       662: q^3+q
       664: q^3+q
       665: q^3+q^2+q
       666: q^3+q^2+q
       668: q^3+q^2+q
       670: q^4+q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       693: q^2+q
       695: q^2
       705: q^3+q^2+q
       709: q^3+q^2+q
       713: q^2+q
       717: q^2+q
       721: q^2+q
       725: q^2+q
       729: q^2+q
       733: q^2+q
       737: q^2+q
       741: q^2+q
       745: q^2+q
       749: q^2+q
       753: q^2+q
       757: 2q^2+q
       761: q^2+q
       765: q^2+q
       769: q^2+q
       771: q^2
       775: q
       777: 2q^3+q^2+q
       779: q^3+q
       781: q^3+q^2+q
       783: q^3+q^2+q
       785: q^2+q
       787: q^2+q
       789: q^3+q^2+q
       791: q^2+q
       793: q
       795: q
       797: q^2+q
       799: q^2+q
       801: q^2+q
       803: q
       805: q^2+q
       807: q^3+q^2+q
       809: q^2+q
       811: q^2+q
       813: q^2+q
       815: q^2+q
       817: q
       819: q
       821: q^2+q
       823: q^2+q
       825: q^3+q^2+q
       827: q^2+q
       829: q
       831: q^2+q
       833: q^2+q
       835: q^2+q
       837: q^2+q
       839: q^2+q
       841: q^3+q^2+q
       843: q
       845: q^2+q
       847: q^2+q
       849: q^2+q
       851: q^2+q
       853: 2q^2+q
       855: q
       857: q^2+q
       859: q^3+q
       861: q
       863: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q
       871: q^2+q
       872: q^2+q
       873: q
       874: q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q
       881: q^3+q
       882: q
       883: q^3+q
       884: q^2+q
       886: q^2
       896: q^3+q^2+q
       900: q^2+q
       904: q^2+q
       908: q^2+q
       912: q^2+q
       916: q
       920: q^2+q
       924: q
       928: q^2+q
       932: q^2+q
       936: q^2+q
       940: q
       944: q^2+q
       948: q^2+q
       952: q
       956: q^2+q
       960: q^2+q
       964: q
       968: q
       974: q^2+q
       978: 2q^2+q
       982: q^2+q
       984: q^2
       988: q^2+q
       992: q
       994: q
       996: q^3+q
       998: q
      1000: q
      1002: q^3+q^2+q
      1004: q^2+q
      1006: q^2+q
      1008: q^2+q
      1010: q^2+q
      1012: q
      1014: q
      1016: q
      1018: q^2+q
      1020: q
      1022: q^2+q
      1024: q^2+q
      1026: q^2+q
      1028: q
      1030: q
      1032: q
      1034: q^2+q
      1036: q
      1038: q^2+q
      1040: q
      1042: q^2+q
      1044: q^2+q
      1046: q
      1048: q^2+q
      1050: q^2+q
      1052: q^2+q
      1054: q
      1056: q
      1058: q^2+q
      1060: q
      1062: q
      1064: q
      1066: q^3+q
      1068: q
      1070: q^3+q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1086: q
      1098: q^2+q
      1100: q^2
      1110: q^2+q
      1114: q
      1118: q^2+q
      1122: q
      1126: q^2+q
      1130: q
      1134: q^2+q
      1138: q
      1144: q
      1148: q^2+q
      1152: q
      1156: q^2+q
      1160: q
      1164: q
      1168: q^2+q
      1172: q^2+q
      1176: q
      1180: q
      1184: q^2+q
      1188: q
      1194: q
      1198: q^2+q
      1202: q
      1206: q
      1210: q
      1212: q^3+q
      1214: q
      1216: q
      1218: q
      1220: q^2+q
      1222: q^2+q
      1224: q
      1226: q
      1228: q
      1230: q
      1232: q
      1234: q
      1236: q
      1238: q^2+q
      1240: q^2+q
      1242: q
      1244: q
      1246: q
      1248: q
      1250: q
      1252: q
      1254: q
      1256: q^2+q
      1258: q
      1260: q^2+q
      1262: q
      1264: q^2+q
      1266: q
      1268: q
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      1290: q
      1302: q
      1314: q
      1318: q
      1322: q^2+q
      1326: q
      1330: q^2+q
      1334: q
      1340: q
      1344: q
      1348: q
      1352: q^2+q
      1356: q
      1360: q
      1364: q
      1368: q
      1372: q
      1376: q^2+q
      1380: q
      1384: q
      1388: q
      1392: q
      1396: q
      1400: q
      1404: q
      1410: q
      1414: q^2+q
      1418: q
      1422: q
      1426: q
      1430: q
      1436: q
      1438: q
      1440: q
      1442: q
      1444: q
      1446: q^2+q
      1448: q
      1450: q
      1452: q
      1454: q
      1456: q
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      1470: q
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      1501: q
      1513: q
      1525: q
      1537: q
      1541: q
      1545: q
      1549: q
      1553: q
      1559: q^2+q
      1563: q
      1567: q
      1571: q
      1575: q
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      1745: q
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      1761: q
      1765: q
      1773: q
      1777: q
      1793: q
      1801: q
      1807: q
      1834: q
      1846: q
      1858: q
      1944: 1
      1948: q
      2015: 1
      2056: 1
      2060: 1
      2092: 1
      2117: 1
      2130: 1
      2144: 1

2145:    0: 3q^2+2q
         1: 3q^2+2q
         2: 3q^2+2q
         3: 3q^2+2q
         4: q^3+2q^2+2q
         5: 3q^2+2q
         6: q^3+2q^2+2q
         7: q^3+2q^2+2q
         8: 3q^2+2q
         9: q^3+2q^2+2q
        10: 3q^2+2q
        11: 3q^2+2q
        12: q^3+2q^2+2q
        13: 3q^2+2q
        14: q^3+2q^2+2q
        15: 3q^2+2q
        16: 3q^2+2q
        17: 3q^2+2q
        18: q^3+2q^2+2q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+2q
        23: 3q^2+2q
        24: 3q^2+2q
        25: 3q^2+2q
        26: 3q^2+2q
        27: 3q^2+2q
        28: 3q^2+2q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+2q
        32: 3q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 3q^2+2q
        36: 3q^2+2q
        37: 2q^2+2q
        38: q^2
        39: 2q^2+2q
        40: q^2
        41: 2q^2+2q
        42: q^2
        43: 3q^2+2q
        44: q^3+2q^2+2q
        45: 3q^2+2q
        46: 3q^2+2q
        47: 3q^2+2q
        48: q^3+2q^2+2q
        49: 2q^2+2q
        50: 2q^2+2q
        51: 2q^2+2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: q^2+q
        59: 2q^2+q
        60: 2q^2+q
        61: q^2+q
        62: 2q^2+2q
        63: q^2
        64: 2q^2+2q
        65: q^2
        66: 2q^2+2q
        67: q^2
        68: 3q^2+2q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 2q^2+2q
        72: q^2+2q
        73: q^2+2q
        74: q^2+2q
        76: q^2+2q
        78: q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q^2+2q
        89: 3q^2+2q
        90: q^3+2q^2+2q
        91: 2q^2+2q
        92: 2q^2+2q
        93: 2q^2+2q
        94: 2q^2+2q
        95: 2q^2+2q
        96: 2q^2+2q
        97: 2q^2+2q
        98: 2q^2+2q
        99: 2q^2+2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q^2+q
       104: q^2
       106: q^2+q
       107: q^2+q
       108: q
       109: q
       110: q^2+q
       111: 2q
       113: q^2+2q
       115: q^2+2q
       117: q^2+q
       118: 2q^2+q
       119: 2q^2+q
       120: q^2+q
       121: 2q^2+2q
       122: q^2
       123: 2q^2+2q
       124: q^2
       125: 3q^2+2q
       126: 2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+2q
       133: 2q^2+2q
       134: 2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 3q^2+2q
       138: 2q^2+2q
       139: 2q^2+2q
       140: q^2+2q
       141: 2q^2+2q
       142: q^2+2q
       143: 3q^2+2q
       144: 2q^2+2q
       145: 2q^2+2q
       146: 2q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 2q^2+2q
       151: q^2+2q
       153: q^2+2q
       155: q^2+2q
       157: 2q^2+2q
       158: 2q^2+2q
       159: 2q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 2q^2+2q
       167: 2q^2+2q
       168: 2q^2+2q
       169: q
       172: q
       173: q^2+q
       174: q^2
       176: q^2+q
       177: q^2+2q
       179: q^2+2q
       181: 2q
       183: q^2+q
       184: q
       185: q
       186: q^2+q
       187: 2q
       189: q^2+2q
       191: q^2+q
       192: 2q^2+q
       193: q^2+q
       194: q
       195: q
       196: q^2+q
       197: 2q
       199: 2q^2+q
       200: q^2+q
       201: q^2+q
       202: q
       203: q
       204: q^2+q
       205: 2q
       207: 2q^2+2q
       208: q^2
       209: q^2+2q
       211: q^2+2q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: 2q^2+2q
       222: q^2+2q
       223: q^2+2q
       224: q^2+2q
       225: q^2+2q
       226: 2q^2+2q
       227: 2q^2+2q
       228: 2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: 2q^2+2q
       232: 2q^2+2q
       233: 2q^2+2q
       234: q^2+2q
       235: q^2+2q
       236: 2q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       266: q
       267: q
       269: q
       271: q
       273: q
       275: q^2+q
       276: q^2
       278: q^2+q
       279: q^2+2q
       281: q^2+2q
       283: q^2+q
       284: q
       285: q
       286: q^2+q
       287: q^2+2q
       289: 2q
       291: 2q
       293: q^2+q
       294: q
       295: q
       296: q^2+q
       297: 2q
       299: q^2+q
       300: q
       301: 2q
       303: q
       304: q^2+q
       305: 2q
       307: q^2+q
       308: q
       309: q
       310: q^2+q
       311: 2q
       313: 2q
       315: q^2+2q
       317: q^2+2q
       319: q^2+q
       320: q
       321: q
       322: q^2+q
       323: 2q
       325: q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: 3q
       338: 3q
       340: 3q
       342: q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: 2q^2+2q
       347: q^2+2q
       348: q^2+2q
       349: q^2+2q
       350: q^2+2q
       351: 3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: 2q^2+2q
       355: q^2+2q
       356: q^2+2q
       357: q^2+2q
       358: q^2+2q
       359: 3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q
       380: q
       381: q
       384: q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: q^2+2q
       411: q^2+2q
       413: q^2+2q
       415: 2q
       417: 2q
       419: q^2+q
       420: q
       421: q
       422: q^2+q
       423: 2q
       425: 2q
       427: 3q
       429: q^2+q
       430: q
       431: q
       432: q^2+q
       433: 2q
       435: 2q
       437: q^2+q
       438: q
       439: q
       440: q^2+q
       441: 2q
       443: 2q
       444: q
       445: 3q
       447: q^2+q
       448: q
       449: q
       450: q^2+q
       451: 2q
       453: q^2+q
       454: q
       455: 2q
       457: q
       458: q^2+q
       459: 2q
       461: q
       462: 2q
       463: 3q
       465: q^2+2q
       467: q^2+2q
       469: q^2+2q
       471: q^2+q
       472: q
       473: q
       474: q^2+q
       475: 2q
       477: 2q
       479: 2q
       480: q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: 3q
       485: 3q
       487: 3q
       489: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^2+2q
       494: q^2+2q
       495: 2q
       496: 3q
       497: 2q^2+2q
       498: q^2+2q
       499: q^2+2q
       500: 2q
       501: 3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: 2q^2+2q
       511: q^2+2q
       512: q^2+2q
       513: q^2+2q
       514: q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       525: q
       528: q
       529: q
       532: q
       533: q
       536: q
       537: q
       539: q
       541: q
       543: q
       545: 2q
       547: q
       549: q
       552: q
       553: q
       555: q
       557: q
       559: q
       561: q
       563: 2q
       565: q
       568: q
       569: q
       570: q
       573: q
       574: q
       575: q
       577: 2q
       580: q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q^2+q
       590: q
       592: q
       593: q
       595: q
       596: q^2+q
       597: 2q
       599: 2q
       601: 3q
       603: q^2+q
       604: q
       605: 2q
       607: q
       608: q^2+q
       609: 2q
       611: 2q
       613: 2q
       615: 2q
       616: q
       617: 3q
       619: q^2+q
       620: q
       621: q
       622: q^2+q
       623: 2q
       625: 2q
       627: 2q
       629: 2q
       631: q
       632: 2q
       633: 3q
       635: q^2+2q
       637: q^2+2q
       639: q^2+2q
       641: q^2+q
       642: q
       643: q
       644: q^2+q
       645: 2q
       647: q^2+q
       648: q
       649: q
       650: q^2+q
       651: 2q
       653: 2q
       655: 2q
       656: q
       657: 3q
       658: 3q
       660: 3q
       662: q^2+2q
       664: 2q
       665: 2q
       666: 3q
       668: 3q
       670: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: 2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^2+2q
       688: q^2+2q
       689: 2q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q
       696: q
       697: q
       705: q
       708: q
       709: q
       712: q
       716: q
       717: q
       721: q
       723: q
       725: q
       727: q
       729: q
       731: q
       733: 2q
       735: q
       737: q
       739: q
       741: q
       743: q
       745: q
       747: q
       749: q
       751: 2q
       753: q
       756: q
       757: q
       758: q
       761: q
       762: q
       765: q
       766: q
       768: q
       769: 2q
       772: q
       775: 3q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       785: q
       788: q
       789: 3q
       791: q
       793: 2q
       794: q
       795: 3q
       797: 2q
       799: 2q
       801: q^2+q
       802: q
       804: q
       805: q
       807: q
       808: q^2+q
       809: 2q
       811: 2q
       813: 3q
       815: 2q
       816: q
       817: q
       818: 2q
       819: 3q
       821: 2q
       823: 2q
       825: q^2+q
       826: q
       828: q
       829: q
       831: q
       832: q^2+q
       833: 2q
       835: 2q
       837: 3q
       839: q
       840: 2q
       841: q^2+2q
       843: 2q
       844: q
       845: q^2+q
       846: q
       847: q
       848: q^2+q
       849: 2q
       851: 2q
       853: 2q
       855: 2q
       857: 2q
       858: q
       859: 3q
       861: 3q
       863: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: 2q
       880: 2q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q
       887: q
       889: q
       896: q
       899: q
       902: q
       904: q
       912: q
       914: q
       916: 2q
       918: q
       920: q
       922: q
       927: q
       928: q
       932: 2q
       934: q
       936: q
       938: q
       940: q
       942: 2q
       944: q
       946: q
       950: q
       952: q
       956: q
       958: 2q
       960: q
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       964: q
       965: q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       978: q
       979: q
       982: 2q
       985: q
       988: q
       989: q
       991: q
       992: 3q
       994: 2q
       996: 2q
       999: q
      1000: q
      1002: 2q
      1004: q
      1007: q
      1008: q
      1010: q
      1012: q
      1014: 3q
      1016: 2q
      1017: q
      1018: 2q
      1020: 2q
      1022: 2q
      1024: 2q
      1026: q
      1029: q
      1030: 3q
      1032: q
      1033: 2q
      1034: 2q
      1036: 2q
      1038: 2q
      1040: q
      1042: 2q
      1045: q
      1046: 2q
      1047: q
      1048: 2q
      1050: 2q
      1052: q^2+q
      1053: q
      1055: q
      1056: q
      1058: q
      1059: q^2+q
      1060: 2q
      1062: 2q
      1064: q
      1066: 3q
      1068: 3q
      1070: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 2q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1086: q
      1089: q
      1091: q
      1098: q
      1101: q
      1102: q
      1112: q
      1116: q
      1118: q
      1122: q
      1138: q
      1144: 2q
      1146: q
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      1150: q
      1154: q
      1156: q
      1164: q
      1166: 2q
      1168: q
      1170: q
      1174: q
      1176: q
      1184: q
      1185: q
      1188: 2q
      1191: q
      1194: q
      1195: q
      1197: q
      1198: q
      1199: q
      1204: q
      1206: q
      1210: 3q
      1212: 2q
      1214: 2q
      1217: q
      1218: q
      1220: q
      1222: q
      1224: q
      1226: 3q
      1228: 2q
      1229: q
      1230: 2q
      1233: q
      1234: q
      1236: 2q
      1238: 2q
      1240: q
      1243: q
      1244: 3q
      1246: q
      1247: 2q
      1248: 2q
      1251: q
      1252: 2q
      1254: q
      1256: 2q
      1258: q
      1261: q
      1262: 2q
      1263: q
      1264: 2q
      1266: 2q
      1268: q
      1271: q
      1272: 2q
      1274: 2q
      1276: q
      1278: q
      1280: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1302: q
      1305: q
      1307: q
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      1334: q
      1340: 2q
      1342: q
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      1350: q
      1352: q
      1356: q
      1372: q
      1374: 2q
      1378: q
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      1388: q
      1404: 2q
      1407: q
      1410: q
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      1413: q
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      1422: q
      1430: q
      1436: q
      1438: 2q
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      1448: 2q
      1451: q
      1452: 2q
      1454: q
      1456: 2q
      1458: 2q
      1461: q
      1462: q
      1464: 2q
      1467: q
      1468: q
      1470: 2q
      1472: 2q
      1474: q
      1476: q
      1479: q
      1480: q
      1482: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1525: q
      1528: q
      1530: q
      1543: q
      1545: q
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      1565: q
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      1605: q
      1609: q
      1611: q
      1615: q
      1631: q
      1637: q
      1639: q
      1641: 1
      1643: 2q
      1646: q
      1647: q
      1650: 1
      1651: 2q
      1654: q
      1655: q
      1657: 1
      1659: q
      1661: 2q
      1664: q
      1665: q
      1667: 2q
      1669: q
      1671: q
      1673: 1
      1674: 2q
      1723: q
      1739: q
      1745: q
      1759: 1
      1763: q
      1765: q
      1781: 1
      1787: q
      1789: q
      1801: q
      1812: 1
      1815: 1
      1817: 1
      1820: 1
      1821: 1
      1823: q
      1825: q
      1827: 2q
      1830: q
      1831: q
      1833: 1
      1884: 1
      1904: 1
      1907: 1
      1918: 1
      1922: 1
      1926: q
      1934: q
      1936: q
      1953: 1
      1956: 1
      1958: 1
      1960: 1
      1963: 1
      1964: 1
      2004: 1
      2016: 1
      2026: 1
      2034: 1
      2037: 1
      2042: 1
      2044: 1
      2048: 1
      2052: 1
      2065: 1
      2072: 1
      2080: 1
      2106: 1
      2118: 1
      2131: 1
      2145: 1

2146:    0: 3q^2+2q
         1: 3q^2+2q
         2: 3q^2+2q
         3: 3q^2+2q
         4: q^3+2q^2+2q
         5: 3q^2+2q
         6: q^3+2q^2+2q
         7: q^3+2q^2+2q
         8: 3q^2+2q
         9: q^3+2q^2+2q
        10: 3q^2+2q
        11: 3q^2+2q
        12: q^3+2q^2+2q
        13: 3q^2+2q
        14: q^3+2q^2+2q
        15: 3q^2+2q
        16: 3q^2+2q
        17: 3q^2+2q
        18: q^3+2q^2+2q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+2q
        23: 3q^2+2q
        24: 3q^2+2q
        25: 3q^2+2q
        26: 3q^2+2q
        27: 3q^2+2q
        28: 3q^2+2q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+2q
        32: 3q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 3q^2+2q
        36: 3q^2+2q
        37: 2q^2+2q
        38: q^2
        39: 2q^2+2q
        40: q^2
        41: 2q^2+2q
        42: q^2
        43: 3q^2+2q
        44: q^3+2q^2+2q
        45: 3q^2+2q
        46: 3q^2+2q
        47: 3q^2+2q
        48: q^3+2q^2+2q
        49: 2q^2+2q
        50: 2q^2+2q
        51: 2q^2+2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: 2q^2+q
        59: q^2+q
        60: q^2+q
        61: 2q^2+q
        62: 2q^2+2q
        63: q^2
        64: 2q^2+2q
        65: q^2
        66: 2q^2+2q
        67: q^2
        68: 3q^2+2q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 2q^2+2q
        72: q^2+2q
        73: q^2+2q
        74: q^2+2q
        76: q^2+2q
        78: q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q^2+2q
        89: 3q^2+2q
        90: q^3+2q^2+2q
        91: 2q^2+2q
        92: 2q^2+2q
        93: 2q^2+2q
        94: 2q^2+2q
        95: 2q^2+2q
        96: 2q^2+2q
        97: 2q^2+2q
        98: 2q^2+2q
        99: 2q^2+2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q^2+q
       105: q^2
       106: q^2+q
       107: q
       108: q^2+q
       109: q^2+q
       110: q
       111: 2q
       113: q^2+2q
       115: q^2+2q
       117: 2q^2+q
       118: q^2+q
       119: q^2+q
       120: 2q^2+q
       121: 2q^2+2q
       122: q^2
       123: 2q^2+2q
       124: q^2
       125: 3q^2+2q
       126: 2q^2+2q
       127: q^2+2q
       129: q^2+2q
       131: q^2+2q
       133: 2q^2+2q
       134: 2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 3q^2+2q
       138: 2q^2+2q
       139: 2q^2+2q
       140: q^2+2q
       141: 2q^2+2q
       142: q^2+2q
       143: 3q^2+2q
       144: 2q^2+2q
       145: 2q^2+2q
       146: 2q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 2q^2+2q
       151: q^2+2q
       153: q^2+2q
       155: q^2+2q
       157: 2q^2+2q
       158: 2q^2+2q
       159: 2q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 2q^2+2q
       167: 2q^2+2q
       168: 2q^2+2q
       169: q
       172: q
       173: q^2+q
       175: q^2
       176: q^2+q
       177: q^2+2q
       179: q^2+2q
       181: 2q
       183: q
       184: q^2+q
       185: q^2+q
       186: q
       187: 2q
       189: q^2+2q
       191: 2q^2+q
       192: q^2+q
       193: q
       194: q^2+q
       195: q^2+q
       196: q
       197: 2q
       199: q^2+q
       200: 2q^2+q
       201: q
       202: q^2+q
       203: q^2+q
       204: q
       205: 2q
       207: 2q^2+2q
       208: q^2
       209: q^2+2q
       211: q^2+2q
       213: q^2+2q
       215: q^2+2q
       217: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: 2q^2+2q
       222: q^2+2q
       223: q^2+2q
       224: q^2+2q
       225: q^2+2q
       226: 2q^2+2q
       227: 2q^2+2q
       228: 2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: 2q^2+2q
       232: 2q^2+2q
       233: 2q^2+2q
       234: q^2+2q
       235: q^2+2q
       236: 2q^2+2q
       237: q^2+2q
       239: q^2+2q
       241: q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       259: q
       262: q
       263: q
       266: q
       267: q
       269: q
       271: q
       273: q
       275: q^2+q
       277: q^2
       278: q^2+q
       279: q^2+2q
       281: q^2+2q
       283: q
       284: q^2+q
       285: q^2+q
       286: q
       287: q^2+2q
       289: 2q
       291: 2q
       293: q
       294: q^2+q
       295: q^2+q
       296: q
       297: 2q
       299: q
       300: q^2+q
       301: 2q
       303: q^2+q
       304: q
       305: 2q
       307: q
       308: q^2+q
       309: q^2+q
       310: q
       311: 2q
       313: 2q
       315: q^2+2q
       317: q^2+2q
       319: q
       320: q^2+q
       321: q^2+q
       322: q
       323: 2q
       325: q^2+2q
       327: q^2+2q
       329: q^2+2q
       331: q^2+2q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: 3q
       338: 3q
       340: 3q
       342: q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: 2q^2+2q
       347: q^2+2q
       348: q^2+2q
       349: q^2+2q
       350: q^2+2q
       351: 3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: 2q^2+2q
       355: q^2+2q
       356: q^2+2q
       357: q^2+2q
       358: q^2+2q
       359: 3q
       360: q^2+2q
       362: q^2+2q
       364: q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       377: q
       380: q
       381: q
       384: q
       385: q
       388: q
       389: q
       391: q
       393: q
       396: q
       397: q
       399: q
       401: q
       404: q
       405: q
       406: q
       409: q^2+2q
       411: q^2+2q
       413: q^2+2q
       415: 2q
       417: 2q
       419: q
       420: q^2+q
       421: q^2+q
       422: q
       423: 2q
       425: 2q
       427: 3q
       429: q
       430: q^2+q
       431: q^2+q
       432: q
       433: 2q
       435: 2q
       437: q
       438: q^2+q
       439: q^2+q
       440: q
       441: 2q
       443: q
       444: 2q
       445: 3q
       447: q
       448: q^2+q
       449: q^2+q
       450: q
       451: 2q
       453: q
       454: q^2+q
       455: 2q
       457: q^2+q
       458: q
       459: 2q
       461: 2q
       462: q
       463: 3q
       465: q^2+2q
       467: q^2+2q
       469: q^2+2q
       471: q
       472: q^2+q
       473: q^2+q
       474: q
       475: 2q
       477: 2q
       479: 2q
       480: q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: 3q
       485: 3q
       487: 3q
       489: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^2+2q
       494: q^2+2q
       495: 2q
       496: 3q
       497: 2q^2+2q
       498: q^2+2q
       499: q^2+2q
       500: 2q
       501: 3q
       502: q^2+2q
       504: q^2+2q
       506: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: 2q^2+2q
       511: q^2+2q
       512: q^2+2q
       513: q^2+2q
       514: q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       521: q
       524: q
       525: q
       528: q
       529: q
       532: q
       533: q
       536: q
       537: q
       539: q
       541: q
       543: q
       545: q
       547: 2q
       549: q
       552: q
       553: q
       555: q
       557: q
       559: q
       561: 2q
       563: q
       565: q
       568: q
       569: q
       570: q
       573: q
       575: q
       576: q
       577: 2q
       580: q
       583: q^2+2q
       585: 2q
       587: 2q
       589: q
       590: q^2+q
       591: q
       594: q
       595: q^2+q
       596: q
       597: 2q
       599: 2q
       601: 3q
       603: q
       604: q^2+q
       605: 2q
       607: q^2+q
       608: q
       609: 2q
       611: 2q
       613: 2q
       615: q
       616: 2q
       617: 3q
       619: q
       620: q^2+q
       621: q^2+q
       622: q
       623: 2q
       625: 2q
       627: 2q
       629: 2q
       631: 2q
       632: q
       633: 3q
       635: q^2+2q
       637: q^2+2q
       639: q^2+2q
       641: q
       642: q^2+q
       643: q^2+q
       644: q
       645: 2q
       647: q
       648: q^2+q
       649: q^2+q
       650: q
       651: 2q
       653: 2q
       655: 2q
       656: q
       657: 3q
       658: 3q
       660: 3q
       662: q^2+2q
       664: 2q
       665: 2q
       666: 3q
       668: 3q
       670: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: 2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^2+2q
       688: q^2+2q
       689: 2q
       690: 3q
       691: 3q
       692: q^2+2q
       693: q
       697: q
       698: q
       705: q
       708: q
       709: q
       712: q
       713: q
       720: q
       721: q
       723: q
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       729: q
       731: q
       733: q
       735: 2q
       737: q
       739: q
       741: q
       743: q
       745: q
       747: q
       749: 2q
       751: q
       753: q
       756: q
       757: q
       758: q
       761: q
       762: q
       765: q
       767: q
       768: q
       769: 2q
       772: q
       775: 3q
       777: 2q
       779: 2q
       781: 2q
       783: 2q
       786: q
       787: q
       789: 3q
       791: q
       793: q
       794: 2q
       795: 3q
       797: 2q
       799: 2q
       801: q
       802: q^2+q
       803: q
       806: q
       807: q^2+q
       808: q
       809: 2q
       811: 2q
       813: 3q
       815: q
       816: 2q
       817: 2q
       818: q
       819: 3q
       821: 2q
       823: 2q
       825: q
       826: q^2+q
       827: q
       830: q
       831: q^2+q
       832: q
       833: 2q
       835: 2q
       837: 3q
       839: 2q
       840: q
       841: q^2+2q
       843: 2q
       844: q
       845: q
       846: q^2+q
       847: q^2+q
       848: q
       849: 2q
       851: 2q
       853: 2q
       855: 2q
       857: 2q
       858: q
       859: 3q
       861: 3q
       863: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: 2q
       880: 2q
       881: 3q
       882: 3q
       883: q^2+2q
       884: q
       888: q
       889: q
       896: q
       899: q
       900: q
       906: q
       912: q
       914: q
       916: q
       918: 2q
       920: q
       922: q
       924: q
       930: q
       932: q
       934: 2q
       936: q
       938: q
       940: 2q
       942: q
       944: q
       946: q
       948: q
       955: q
       956: 2q
       958: q
       960: q
       961: q
       964: q
       966: q
       967: q
       968: 2q
       971: q
       974: q
       975: q
       978: q
       979: q
       982: 2q
       985: q
       988: q
       990: q
       991: q
       992: 3q
       994: 2q
       996: 2q
       998: q
      1001: q
      1002: 2q
      1005: q
      1006: q
      1008: q
      1010: q
      1012: q
      1014: 3q
      1016: q
      1017: 2q
      1018: 2q
      1020: 2q
      1022: 2q
      1024: 2q
      1027: q
      1028: q
      1030: 3q
      1032: 2q
      1033: q
      1034: 2q
      1036: 2q
      1038: 2q
      1041: q
      1042: 2q
      1044: q
      1046: 2q
      1047: q
      1048: 2q
      1050: 2q
      1052: q
      1053: q^2+q
      1054: q
      1057: q
      1058: q^2+q
      1059: q
      1060: 2q
      1062: 2q
      1064: q
      1066: 3q
      1068: 3q
      1070: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 2q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1086: q
      1090: q
      1091: q
      1098: q
      1102: q
      1103: q
      1110: q
      1114: q
      1120: q
      1124: q
      1138: q
      1144: q
      1146: 2q
      1148: q
      1150: q
      1152: q
      1158: q
      1164: 2q
      1166: q
      1168: q
      1170: q
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      1178: q
      1184: q
      1185: q
      1188: 2q
      1191: q
      1194: q
      1196: q
      1197: q
      1198: q
      1199: q
      1202: q
      1208: q
      1210: 3q
      1212: 2q
      1214: 2q
      1216: q
      1219: q
      1220: q
      1222: q
      1224: q
      1226: 3q
      1228: q
      1229: 2q
      1230: 2q
      1232: q
      1235: q
      1236: 2q
      1238: 2q
      1241: q
      1242: q
      1244: 3q
      1246: 2q
      1247: q
      1248: 2q
      1250: q
      1252: 2q
      1255: q
      1256: 2q
      1259: q
      1260: q
      1262: 2q
      1263: q
      1264: 2q
      1266: 2q
      1269: q
      1270: q
      1272: 2q
      1274: 2q
      1276: q
      1278: q
      1280: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1302: q
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      1314: q
      1320: q
      1334: q
      1340: q
      1342: 2q
      1344: q
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      1354: q
      1358: q
      1372: 2q
      1374: q
      1376: q
      1380: q
      1386: q
      1390: q
      1404: 2q
      1407: q
      1410: q
      1412: q
      1413: q
      1414: q
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      1418: q
      1424: q
      1430: q
      1436: q
      1438: 2q
      1440: q
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      1446: q
      1448: 2q
      1450: q
      1452: 2q
      1455: q
      1456: 2q
      1458: 2q
      1460: q
      1463: q
      1464: 2q
      1466: q
      1469: q
      1470: 2q
      1472: 2q
      1474: q
      1477: q
      1478: q
      1480: q
      1482: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1525: q
      1529: q
      1530: q
      1541: q
      1547: q
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      1563: q
      1569: q
      1583: q
      1589: q
      1603: q
      1607: q
      1613: q
      1617: q
      1631: q
      1637: q
      1639: q
      1641: 1
      1643: 2q
      1645: q
      1648: q
      1649: 1
      1651: 2q
      1653: q
      1656: q
      1658: 1
      1659: q
      1661: 2q
      1663: q
      1666: q
      1667: 2q
      1669: q
      1671: q
      1673: 1
      1674: 2q
      1723: q
      1737: q
      1747: q
      1757: 1
      1761: q
      1767: q
      1783: 1
      1785: q
      1791: q
      1801: q
      1813: 1
      1815: 1
      1817: 1
      1819: 1
      1822: 1
      1823: q
      1825: q
      1827: 2q
      1829: q
      1832: q
      1833: 1
      1885: 1
      1902: 1
      1906: 1
      1920: 1
      1923: 1
      1926: q
      1932: q
      1938: q
      1954: 1
      1956: 1
      1958: 1
      1960: 1
      1962: 1
      1965: 1
      2005: 1
      2017: 1
      2026: 1
      2032: 1
      2036: 1
      2040: 1
      2046: 1
      2049: 1
      2054: 1
      2066: 1
      2068: 1
      2084: 1
      2107: 1
      2119: 1
      2132: 1
      2146: 1

2147:    0: 3q^2+2q
         1: 3q^2+2q
         2: 3q^2+2q
         3: 3q^2+2q
         4: q^3+2q^2+2q
         5: 3q^2+2q
         6: q^3+2q^2+2q
         7: q^3+2q^2+2q
         8: 3q^2+2q
         9: q^3+2q^2+2q
        10: 3q^2+2q
        11: 3q^2+2q
        12: q^3+2q^2+2q
        13: 3q^2+2q
        14: q^3+2q^2+2q
        15: 3q^2+2q
        16: 3q^2+2q
        17: 3q^2+2q
        18: q^3+2q^2+2q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+2q
        23: 3q^2+2q
        24: 3q^2+2q
        25: 3q^2+2q
        26: 3q^2+2q
        27: 3q^2+2q
        28: 3q^2+2q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+2q
        32: 3q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 3q^2+2q
        36: 3q^2+2q
        37: q^2
        38: 2q^2+2q
        39: q^2
        40: 2q^2+2q
        41: q^2
        42: 2q^2+2q
        43: 3q^2+2q
        44: q^3+2q^2+2q
        45: 3q^2+2q
        46: 3q^2+2q
        47: 3q^2+2q
        48: q^3+2q^2+2q
        49: 2q^2+2q
        50: 2q^2+2q
        51: 2q^2+2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: 2q^2+q
        59: q^2+q
        60: 2q^2+q
        61: q^2+q
        62: q^2
        63: 2q^2+2q
        64: q^2
        65: 2q^2+2q
        66: q^2
        67: 2q^2+2q
        68: 3q^2+2q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 2q^2+2q
        72: q^2+2q
        73: q^2+2q
        75: q^2+2q
        77: q^2+2q
        79: q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q^2+2q
        89: 3q^2+2q
        90: q^3+2q^2+2q
        91: 2q^2+2q
        92: 2q^2+2q
        93: 2q^2+2q
        94: 2q^2+2q
        95: 2q^2+2q
        96: 2q^2+2q
        97: 2q^2+2q
        98: 2q^2+2q
        99: 2q^2+2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       103: q^2
       104: q^2+q
       105: q^2+q
       107: q^2+q
       108: q
       109: q^2+q
       110: q
       112: 2q
       114: q^2+2q
       116: q^2+2q
       117: 2q^2+q
       118: q^2+q
       119: 2q^2+q
       120: q^2+q
       121: q^2
       122: 2q^2+2q
       123: q^2
       124: 2q^2+2q
       125: 3q^2+2q
       126: 2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+2q
       133: 2q^2+2q
       134: 2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 3q^2+2q
       138: 2q^2+2q
       139: 2q^2+2q
       140: q^2+2q
       141: 2q^2+2q
       142: q^2+2q
       143: 3q^2+2q
       144: 2q^2+2q
       145: 2q^2+2q
       146: 2q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 2q^2+2q
       152: q^2+2q
       154: q^2+2q
       156: q^2+2q
       157: 2q^2+2q
       158: 2q^2+2q
       159: 2q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 2q^2+2q
       167: 2q^2+2q
       168: 2q^2+2q
       170: q
       171: q
       173: q^2
       174: q^2+q
       175: q^2+q
       178: q^2+2q
       180: q^2+2q
       182: 2q
       183: q^2+q
       184: q
       185: q^2+q
       186: q
       188: 2q
       190: q^2+2q
       191: 2q^2+q
       192: q^2+q
       193: q^2+q
       194: q
       195: q^2+q
       196: q
       198: 2q
       199: 2q^2+q
       200: q^2+q
       201: q^2+q
       202: q
       203: q^2+q
       204: q
       206: 2q
       207: q^2
       208: 2q^2+2q
       210: q^2+2q
       212: q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: 2q^2+2q
       222: q^2+2q
       223: q^2+2q
       224: q^2+2q
       225: q^2+2q
       226: 2q^2+2q
       227: 2q^2+2q
       228: 2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: 2q^2+2q
       232: 2q^2+2q
       233: 2q^2+2q
       234: q^2+2q
       235: q^2+2q
       236: 2q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       260: q
       261: q
       264: q
       265: q
       268: q
       270: q
       272: q
       274: q
       275: q^2
       276: q^2+q
       277: q^2+q
       280: q^2+2q
       282: q^2+2q
       283: q^2+q
       284: q
       285: q^2+q
       286: q
       288: q^2+2q
       290: 2q
       292: 2q
       293: q^2+q
       294: q
       295: q^2+q
       296: q
       298: 2q
       299: q^2+q
       300: q
       302: 2q
       303: q^2+q
       304: q
       306: 2q
       307: q^2+q
       308: q
       309: q^2+q
       310: q
       312: 2q
       314: 2q
       316: q^2+2q
       318: q^2+2q
       319: q^2+q
       320: q
       321: q^2+q
       322: q
       324: 2q
       326: q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: 3q
       339: 3q
       341: 3q
       343: q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: 2q^2+2q
       347: q^2+2q
       348: q^2+2q
       349: q^2+2q
       350: q^2+2q
       351: 3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: 2q^2+2q
       355: q^2+2q
       356: q^2+2q
       357: q^2+2q
       358: q^2+2q
       359: 3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       378: q
       379: q
       382: q
       383: q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: q^2+2q
       412: q^2+2q
       414: q^2+2q
       416: 2q
       418: 2q
       419: q^2+q
       420: q
       421: q^2+q
       422: q
       424: 2q
       426: 2q
       428: 3q
       429: q^2+q
       430: q
       431: q^2+q
       432: q
       434: 2q
       436: 2q
       437: q^2+q
       438: q
       439: q^2+q
       440: q
       442: 2q
       443: 2q
       444: q
       446: 3q
       447: q^2+q
       448: q
       449: q^2+q
       450: q
       452: 2q
       453: q^2+q
       454: q
       456: 2q
       457: q^2+q
       458: q
       460: 2q
       461: 2q
       462: q
       464: 3q
       466: q^2+2q
       468: q^2+2q
       470: q^2+2q
       471: q^2+q
       472: q
       473: q^2+q
       474: q
       476: 2q
       478: 2q
       479: q
       480: 2q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: 3q
       486: 3q
       488: 3q
       490: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^2+2q
       494: q^2+2q
       495: 2q
       496: 3q
       497: 2q^2+2q
       498: q^2+2q
       499: q^2+2q
       500: 2q
       501: 3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: 2q^2+2q
       511: q^2+2q
       512: q^2+2q
       513: q^2+2q
       514: q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: 2q
       548: q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: 2q
       564: q
       566: q
       567: q
       571: q
       572: q
       573: q
       574: q
       576: q
       578: q
       581: 2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q^2+q
       590: q
       591: q
       593: q
       595: q^2+q
       596: q
       598: 2q
       600: 2q
       602: 3q
       603: q^2+q
       604: q
       606: 2q
       607: q^2+q
       608: q
       610: 2q
       612: 2q
       614: 2q
       615: 2q
       616: q
       618: 3q
       619: q^2+q
       620: q
       621: q^2+q
       622: q
       624: 2q
       626: 2q
       628: 2q
       630: 2q
       631: 2q
       632: q
       634: 3q
       636: q^2+2q
       638: q^2+2q
       640: q^2+2q
       641: q^2+q
       642: q
       643: q^2+q
       644: q
       646: 2q
       647: q^2+q
       648: q
       649: q^2+q
       650: q
       652: 2q
       654: 2q
       655: q
       656: 2q
       657: 3q
       659: 3q
       661: 3q
       663: q^2+2q
       664: 2q
       665: 2q
       667: 3q
       669: 3q
       671: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: 2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^2+2q
       688: q^2+2q
       689: 2q
       690: 3q
       691: 3q
       692: q^2+2q
       694: q
       699: q
       700: q
       706: q
       707: q
       710: q
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       714: q
       718: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: 2q
       736: q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: 2q
       752: q
       754: q
       755: q
       759: q
       760: q
       763: q
       764: q
       765: q
       766: q
       767: q
       770: q
       773: 2q
       776: 3q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       785: q
       787: q
       790: 3q
       792: q
       793: 2q
       794: q
       796: 3q
       798: 2q
       800: 2q
       801: q^2+q
       802: q
       803: q
       805: q
       807: q^2+q
       808: q
       810: 2q
       812: 2q
       814: 3q
       815: 2q
       816: q
       817: 2q
       818: q
       820: 3q
       822: 2q
       824: 2q
       825: q^2+q
       826: q
       827: q
       829: q
       831: q^2+q
       832: q
       834: 2q
       836: 2q
       838: 3q
       839: 2q
       840: q
       842: q^2+2q
       843: q
       844: 2q
       845: q^2+q
       846: q
       847: q^2+q
       848: q
       850: 2q
       852: 2q
       854: 2q
       856: 2q
       857: q
       858: 2q
       860: 3q
       862: 3q
       864: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: 2q
       880: 2q
       881: 3q
       882: 3q
       883: q^2+2q
       885: q
       890: q
       891: q
       897: q
       898: q
       901: q
       905: q
       913: q
       915: q
       917: 2q
       919: q
       921: q
       923: q
       925: q
       929: q
       933: 2q
       935: q
       937: q
       939: q
       941: 2q
       943: q
       945: q
       947: q
       949: q
       953: q
       957: 2q
       959: q
       962: q
       963: q
       964: q
       965: q
       966: q
       969: q
       972: 2q
       976: q
       977: q
       980: q
       981: q
       983: q
       986: 2q
       988: q
       989: q
       990: q
       993: 3q
       995: 2q
       997: 2q
       998: q
      1000: q
      1003: 2q
      1004: q
      1006: q
      1009: q
      1011: q
      1013: q
      1015: 3q
      1016: 2q
      1017: q
      1019: 2q
      1021: 2q
      1023: 2q
      1025: 2q
      1026: q
      1028: q
      1031: 3q
      1032: 2q
      1033: q
      1035: 2q
      1037: 2q
      1039: 2q
      1040: q
      1043: 2q
      1044: q
      1046: q
      1047: 2q
      1049: 2q
      1051: 2q
      1052: q^2+q
      1053: q
      1054: q
      1056: q
      1058: q^2+q
      1059: q
      1061: 2q
      1063: 2q
      1065: q
      1067: 3q
      1069: 3q
      1071: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 2q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1087: q
      1092: q
      1093: q
      1099: q
      1104: q
      1105: q
      1111: q
      1115: q
      1119: q
      1123: q
      1142: q
      1145: 2q
      1147: q
      1149: q
      1151: q
      1153: q
      1157: q
      1165: 2q
      1167: q
      1169: q
      1171: q
      1173: q
      1177: q
      1186: q
      1187: q
      1189: q
      1192: 2q
      1194: q
      1195: q
      1196: q
      1200: q
      1201: q
      1203: q
      1207: q
      1211: 3q
      1213: 2q
      1215: 2q
      1216: q
      1218: q
      1221: q
      1223: q
      1225: q
      1227: 3q
      1228: 2q
      1229: q
      1231: 2q
      1232: q
      1234: q
      1237: 2q
      1239: 2q
      1240: q
      1242: q
      1245: 3q
      1246: 2q
      1247: q
      1249: 2q
      1250: q
      1253: 2q
      1254: q
      1257: 2q
      1258: q
      1260: q
      1262: q
      1263: 2q
      1265: 2q
      1267: 2q
      1268: q
      1270: q
      1273: 2q
      1275: 2q
      1277: q
      1279: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1303: q
      1308: q
      1309: q
      1315: q
      1319: q
      1338: q
      1341: 2q
      1343: q
      1345: q
      1349: q
      1353: q
      1357: q
      1373: 2q
      1375: q
      1377: q
      1381: q
      1385: q
      1389: q
      1405: q
      1408: 2q
      1410: q
      1411: q
      1412: q
      1416: q
      1417: q
      1419: q
      1423: q
      1434: q
      1437: q
      1439: 2q
      1440: q
      1442: q
      1445: q
      1447: q
      1449: 2q
      1450: q
      1453: 2q
      1454: q
      1457: 2q
      1459: 2q
      1460: q
      1462: q
      1465: 2q
      1466: q
      1468: q
      1471: 2q
      1473: 2q
      1475: q
      1476: q
      1478: q
      1481: q
      1483: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1526: q
      1531: q
      1532: q
      1542: q
      1546: q
      1557: q
      1564: q
      1568: q
      1584: q
      1588: q
      1604: q
      1608: q
      1612: q
      1616: q
      1635: q
      1638: q
      1640: q
      1642: 1
      1644: 2q
      1645: q
      1647: q
      1649: 1
      1652: 2q
      1653: q
      1655: q
      1657: 1
      1660: q
      1662: 2q
      1663: q
      1665: q
      1668: 2q
      1670: q
      1672: q
      1673: 1
      1674: 2q
      1727: q
      1738: q
      1746: q
      1758: 1
      1762: q
      1766: q
      1782: 1
      1786: q
      1790: q
      1805: q
      1811: 1
      1816: 1
      1818: 1
      1819: 1
      1821: 1
      1824: q
      1826: q
      1828: 2q
      1829: q
      1831: q
      1833: 1
      1883: 1
      1903: 1
      1908: 1
      1919: 1
      1924: 1
      1930: q
      1933: q
      1937: q
      1952: 1
      1957: 1
      1959: 1
      1961: 1
      1962: 1
      1964: 1
      2003: 1
      2018: 1
      2030: 1
      2033: 1
      2038: 1
      2041: 1
      2045: 1
      2050: 1
      2053: 1
      2064: 1
      2073: 1
      2085: 1
      2105: 1
      2120: 1
      2129: 1
      2147: 1

2148:    0: 2q^6+15q^5+19q^4+6q^3+q^2
         1: 2q^6+15q^5+19q^4+6q^3+q^2
         2: 5q^6+14q^5+15q^4+5q^3+q^2
         3: 15q^5+19q^4+6q^3+q^2
         4: 2q^6+15q^5+19q^4+6q^3+q^2
         5: 15q^5+19q^4+6q^3+q^2
         6: 2q^6+15q^5+19q^4+6q^3+q^2
         7: 5q^6+14q^5+15q^4+5q^3+q^2
         8: 5q^6+15q^5+15q^4+5q^3+q^2
         9: 3q^7+9q^6+12q^5+10q^4+4q^3+q^2
        10: 2q^6+15q^5+19q^4+6q^3+q^2
        11: 15q^5+19q^4+6q^3+q^2
        12: 2q^6+15q^5+19q^4+6q^3+q^2
        13: q^6+9q^5+14q^4+5q^3+q^2
        14: q^6+9q^5+14q^4+5q^3+q^2
        15: 10q^5+14q^4+5q^3+q^2
        16: 8q^5+18q^4+6q^3+q^2
        17: 8q^5+18q^4+6q^3+q^2
        18: 5q^6+11q^5+10q^4+4q^3+q^2
        19: 2q^6+15q^5+19q^4+6q^3+q^2
        20: 2q^6+15q^5+19q^4+6q^3+q^2
        21: 5q^6+14q^5+15q^4+5q^3+q^2
        22: 8q^5+18q^4+6q^3+q^2
        23: 8q^5+18q^4+6q^3+q^2
        24: 2q^6+10q^5+14q^4+5q^3+q^2
        25: 8q^5+18q^4+6q^3+q^2
        26: 8q^5+18q^4+6q^3+q^2
        27: 2q^6+10q^5+14q^4+5q^3+q^2
        28: 8q^5+18q^4+6q^3+q^2
        29: 2q^6+15q^5+19q^4+6q^3+q^2
        30: q^6+9q^5+14q^4+5q^3+q^2
        31: 8q^5+18q^4+6q^3+q^2
        32: 5q^5+13q^4+5q^3+q^2
        33: 3q^5+17q^4+6q^3+q^2
        34: 8q^5+18q^4+6q^3+q^2
        35: 5q^5+13q^4+5q^3+q^2
        36: 3q^5+17q^4+6q^3+q^2
        37: q^5+8q^4+2q^3+q^2
        38: 2q^5+9q^4+4q^3
        39: q^5+8q^4+2q^3+q^2
        40: 2q^5+9q^4+4q^3
        41: 3q^5+6q^4+2q^3+q^2
        42: 4q^5+7q^4+3q^3
        43: q^6+9q^5+14q^4+5q^3+q^2
        44: q^6+9q^5+14q^4+5q^3+q^2
        45: 10q^5+14q^4+5q^3+q^2
        46: 3q^5+13q^4+5q^3+q^2
        47: 4q^5+13q^4+5q^3+q^2
        48: q^6+7q^5+9q^4+4q^3+q^2
        49: 8q^5+18q^4+6q^3+q^2
        50: 8q^5+18q^4+6q^3+q^2
        51: 5q^6+11q^5+10q^4+4q^3+q^2
        52: 8q^5+18q^4+6q^3+q^2
        53: 8q^5+18q^4+6q^3+q^2
        54: 2q^6+10q^5+14q^4+5q^3+q^2
        55: 8q^5+18q^4+6q^3+q^2
        56: 8q^5+18q^4+6q^3+q^2
        57: 2q^6+10q^5+14q^4+5q^3+q^2
        58: 2q^5+10q^4+4q^3+q^2
        59: q^5+7q^4+2q^3
        60: 2q^5+10q^4+4q^3+q^2
        61: q^5+7q^4+2q^3
        62: q^5+8q^4+2q^3+q^2
        63: 2q^5+9q^4+4q^3
        64: q^5+6q^4+2q^3+q^2
        65: q^5+6q^4+3q^3
        66: 8q^4+2q^3+q^2
        67: 8q^4+4q^3
        68: q^5+8q^4+4q^3+q^2
        69: 3q^5+8q^4+4q^3+q^2
        70: q^6+9q^5+14q^4+5q^3+q^2
        71: 8q^5+18q^4+6q^3+q^2
        72: 3q^5+17q^4+6q^3+q^2
        73: 3q^5+17q^4+6q^3+q^2
        74: q^5+8q^4+2q^3+q^2
        75: 2q^5+9q^4+4q^3
        76: q^5+8q^4+2q^3+q^2
        77: 2q^5+9q^4+4q^3
        78: 3q^5+6q^4+2q^3+q^2
        79: 4q^5+7q^4+3q^3
        80: 5q^5+13q^4+5q^3+q^2
        81: q^5+12q^4+5q^3+q^2
        82: 8q^5+18q^4+6q^3+q^2
        83: 5q^5+13q^4+5q^3+q^2
        84: 5q^5+13q^4+5q^3+q^2
        85: q^5+12q^4+5q^3+q^2
        86: 8q^5+18q^4+6q^3+q^2
        87: 5q^5+13q^4+5q^3+q^2
        88: 3q^5+13q^4+5q^3+q^2
        89: 4q^5+13q^4+5q^3+q^2
        90: q^6+7q^5+9q^4+4q^3+q^2
        91: 3q^5+13q^4+5q^3+q^2
        92: 4q^5+13q^4+5q^3+q^2
        93: q^6+7q^5+9q^4+4q^3+q^2
        94: 3q^5+15q^4+6q^3+q^2
        95: 3q^5+15q^4+6q^3+q^2
        96: 2q^6+7q^5+9q^4+4q^3+q^2
        97: 3q^5+15q^4+6q^3+q^2
        98: 3q^5+15q^4+6q^3+q^2
        99: 2q^6+7q^5+9q^4+4q^3+q^2
       100: 3q^5+15q^4+6q^3+q^2
       101: 3q^5+15q^4+6q^3+q^2
       102: 6q^5+11q^4+5q^3+q^2
       103: 5q^4+2q^3+q^2
       104: 4q^4+2q^3
       105: 4q^4+2q^3
       106: 3q^4
       107: 2q^5+10q^4+4q^3+q^2
       108: q^5+7q^4+2q^3
       109: 2q^5+10q^4+4q^3+q^2
       110: q^5+7q^4+2q^3
       111: 8q^4+2q^3+q^2
       112: 8q^4+4q^3
       113: q^5+8q^4+2q^3+q^2
       114: 2q^5+9q^4+4q^3
       115: q^5+6q^4+2q^3+q^2
       116: q^5+6q^4+3q^3
       117: 5q^4+3q^3+q^2
       118: 2q^4+q^3
       119: 5q^4+3q^3+q^2
       120: 2q^4+q^3
       121: q^5+6q^4+2q^3+q^2
       122: q^5+6q^4+3q^3
       123: 6q^4+2q^3+q^2
       124: 5q^4+3q^3
       125: q^5+8q^4+4q^3+q^2
       126: 3q^5+8q^4+4q^3+q^2
       127: 3q^4+q^3+q^2
       128: 4q^4+4q^3
       129: 3q^4+q^3+q^2
       130: 4q^4+4q^3
       131: q^5+2q^4+q^3+q^2
       132: q^5+3q^4+2q^3
       133: q^5+8q^4+4q^3+q^2
       134: 3q^5+8q^4+4q^3+q^2
       135: q^5+12q^4+5q^3+q^2
       136: q^5+12q^4+5q^3+q^2
       137: q^5+12q^4+5q^3+q^2
       138: q^5+7q^4+4q^3+q^2
       139: 3q^5+15q^4+6q^3+q^2
       140: 7q^4+5q^3+q^2
       141: 5q^5+13q^4+5q^3+q^2
       142: 3q^5+15q^4+6q^3+q^2
       143: q^5+12q^4+5q^3+q^2
       144: q^5+7q^4+4q^3+q^2
       145: 3q^5+15q^4+6q^3+q^2
       146: 5q^5+13q^4+5q^3+q^2
       147: 3q^5+15q^4+6q^3+q^2
       148: 7q^4+5q^3+q^2
       149: 3q^5+15q^4+6q^3+q^2
       150: 2q^5+10q^4+5q^3+q^2
       151: q^5+7q^4+2q^3+q^2
       152: 2q^5+8q^4+4q^3
       153: q^5+7q^4+2q^3+q^2
       154: 2q^5+8q^4+4q^3
       155: 3q^5+5q^4+2q^3+q^2
       156: 3q^5+6q^4+3q^3
       157: 3q^5+13q^4+5q^3+q^2
       158: 4q^5+13q^4+5q^3+q^2
       159: q^6+7q^5+9q^4+4q^3+q^2
       160: q^5+8q^4+5q^3+q^2
       161: q^5+8q^4+5q^3+q^2
       162: 3q^5+6q^4+4q^3+q^2
       163: q^5+8q^4+5q^3+q^2
       164: q^5+8q^4+5q^3+q^2
       165: 3q^5+6q^4+4q^3+q^2
       166: 9q^4+6q^3+q^2
       167: 9q^4+6q^3+q^2
       168: 4q^5+7q^4+4q^3+q^2
       169: 5q^4+2q^3+q^2
       170: 4q^4+2q^3
       171: 4q^4+2q^3
       172: 3q^4
       173: 3q^4+2q^3+q^2
       174: q^4+q^3
       175: q^4+q^3
       176: q^4
       177: 2q^4+q^3+q^2
       178: q^4+2q^3
       179: 3q^4+q^3+q^2
       180: 4q^4+4q^3
       181: 3q^4+q^3+q^2
       182: 4q^4+4q^3
       183: 5q^4+3q^3+q^2
       184: 2q^4+q^3
       185: 5q^4+3q^3+q^2
       186: 2q^4+q^3
       187: 6q^4+2q^3+q^2
       188: 5q^4+3q^3
       189: q^5+6q^4+2q^3+q^2
       190: q^5+6q^4+3q^3
       191: 5q^4+3q^3+q^2
       192: 2q^4+q^3
       193: 5q^4+4q^3+q^2
       194: 2q^4+q^3
       195: 2q^5+9q^4+4q^3+q^2
       196: q^5+6q^4+2q^3
       197: 4q^4+2q^3+q^2
       198: 3q^4+3q^3
       199: 5q^4+3q^3+q^2
       200: 2q^4+q^3
       201: 2q^5+9q^4+4q^3+q^2
       202: q^5+6q^4+2q^3
       203: 5q^4+4q^3+q^2
       204: 2q^4+q^3
       205: 4q^4+2q^3+q^2
       206: 3q^4+3q^3
       207: 6q^4+2q^3+q^2
       208: 5q^4+3q^3
       209: q^5+7q^4+2q^3+q^2
       210: 2q^5+8q^4+4q^3
       211: q^5+5q^4+2q^3+q^2
       212: q^5+5q^4+3q^3
       214: q^4+3q^3
       216: q^4+3q^3
       218: q^4+2q^3
       219: q^5+4q^4+3q^3+q^2
       220: q^5+8q^4+4q^3+q^2
       221: 3q^5+8q^4+4q^3+q^2
       222: q^5+12q^4+5q^3+q^2
       223: q^5+7q^4+4q^3+q^2
       224: q^5+12q^4+5q^3+q^2
       225: q^5+7q^4+4q^3+q^2
       226: q^5+7q^4+4q^3+q^2
       227: 4q^4+4q^3+q^2
       228: q^5+5q^4+4q^3+q^2
       229: 3q^4+4q^3+q^2
       230: q^5+8q^4+5q^3+q^2
       231: q^5+7q^4+4q^3+q^2
       232: 4q^4+4q^3+q^2
       233: q^5+5q^4+4q^3+q^2
       234: q^5+8q^4+5q^3+q^2
       235: 3q^4+4q^3+q^2
       236: 5q^4+4q^3+q^2
       237: q^4+q^3+q^2
       238: 3q^4+4q^3
       239: q^4+q^3+q^2
       240: 3q^4+4q^3
       241: q^5+q^4+q^3+q^2
       242: q^5+3q^4+2q^3
       243: 9q^4+6q^3+q^2
       244: 4q^4+5q^3+q^2
       245: 4q^4+5q^3+q^2
       246: 2q^5+10q^4+5q^3+q^2
       247: 9q^4+6q^3+q^2
       248: 9q^4+6q^3+q^2
       249: 4q^5+7q^4+4q^3+q^2
       250: q^5+8q^4+5q^3+q^2
       251: q^5+8q^4+5q^3+q^2
       252: 3q^5+6q^4+4q^3+q^2
       253: q^5+8q^4+5q^3+q^2
       254: q^5+8q^4+5q^3+q^2
       255: 3q^5+6q^4+4q^3+q^2
       256: 3q^4+5q^3+q^2
       257: 4q^4+5q^3+q^2
       258: q^5+4q^4+4q^3+q^2
       259: 2q^4+q^3+q^2
       260: 2q^4+2q^3
       261: 2q^4+2q^3
       262: q^4
       263: 3q^4+2q^3+q^2
       264: q^4+q^3
       265: q^4+q^3
       266: q^4
       267: 3q^4+2q^3+q^2
       268: 2q^4+2q^3
       269: q^4
       270: q^4+q^3
       271: 3q^4+2q^3+q^2
       272: 2q^4+2q^3
       273: q^4
       274: q^4+q^3
       275: 3q^4+2q^3+q^2
       276: q^4+q^3
       277: q^4+q^3
       278: q^4
       280: 2q^3
       282: 2q^3
       283: 2q^4+2q^3+q^2
       285: 2q^4+2q^3+q^2
       287: 2q^4+q^3+q^2
       288: q^4+2q^3
       290: q^4+3q^3
       291: 2q^4+q^3+q^2
       292: q^4+2q^3
       293: 5q^4+3q^3+q^2
       294: 2q^4+q^3
       295: 5q^4+3q^3+q^2
       296: 2q^4+q^3
       297: 6q^4+2q^3+q^2
       298: 5q^4+3q^3
       299: q^4+3q^3+q^2
       301: q^3+q^2
       302: q^4+3q^3
       303: 3q^4+3q^3+q^2
       304: q^4+q^3
       305: 2q^4+2q^3+q^2
       306: q^4+2q^3
       307: 3q^4+3q^3+q^2
       308: q^4+q^3
       309: q^4+3q^3+q^2
       311: q^3+q^2
       312: q^4+3q^3
       313: 2q^4+2q^3+q^2
       314: q^4+2q^3
       315: q^4+q^3+q^2
       316: q^4+2q^3
       317: q^4+q^3+q^2
       318: 3q^4+4q^3
       319: 3q^4+4q^3+q^2
       320: q^4+q^3
       321: 3q^4+4q^3+q^2
       322: q^4+q^3
       323: q^4+2q^3+q^2
       324: 2q^3
       325: q^5+5q^4+2q^3+q^2
       326: q^5+5q^4+3q^3
       328: q^4+3q^3
       330: q^4+3q^3
       332: q^4+2q^3
       333: q^5+4q^4+3q^3+q^2
       334: q^5+7q^4+4q^3+q^2
       335: q^5+7q^4+4q^3+q^2
       336: 5q^4+4q^3+q^2
       337: 9q^4+6q^3+q^2
       338: q^4+q^3+q^2
       339: 3q^4+4q^3
       340: q^4+q^3+q^2
       341: 3q^4+4q^3
       342: q^5+q^4+q^3+q^2
       343: q^5+3q^4+2q^3
       344: 2q^4+3q^3+q^2
       345: 4q^4+4q^3+q^2
       346: q^5+5q^4+4q^3+q^2
       347: 3q^4+4q^3+q^2
       348: q^4+3q^3+q^2
       349: q^5+8q^4+5q^3+q^2
       350: q^5+5q^4+4q^3+q^2
       351: 4q^4+5q^3+q^2
       352: 2q^4+3q^3+q^2
       353: 4q^4+4q^3+q^2
       354: q^5+5q^4+4q^3+q^2
       355: q^5+8q^4+5q^3+q^2
       356: q^5+5q^4+4q^3+q^2
       357: 3q^4+4q^3+q^2
       358: q^4+3q^3+q^2
       359: 4q^4+5q^3+q^2
       361: 3q^3
       363: q^4+3q^3
       365: q^4+2q^3
       366: 5q^4+4q^3+q^2
       367: q^4+4q^3+q^2
       368: 3q^4+4q^3+q^2
       369: q^4+4q^3+q^2
       370: q^4+4q^3+q^2
       371: 3q^4+5q^3+q^2
       372: 4q^4+5q^3+q^2
       373: q^5+4q^4+4q^3+q^2
       374: 3q^4+5q^3+q^2
       375: 4q^4+5q^3+q^2
       376: q^5+4q^4+4q^3+q^2
       377: q^4+q^3+q^2
       382: q^3
       383: q^3
       385: 3q^4+2q^3+q^2
       386: q^4+q^3
       387: q^4+q^3
       388: q^4
       389: q^3+q^2
       390: q^4+2q^3
       392: q^3
       393: q^4+2q^3+q^2
       394: q^3
       397: q^3+q^2
       398: q^4+2q^3
       400: q^3
       401: q^4+2q^3+q^2
       402: q^3
       405: q^4+2q^3+q^2
       407: q^3
       408: q^3
       410: 2q^3
       412: 2q^3
       414: q^3
       416: q^4+3q^3
       418: 2q^3
       419: 2q^4+2q^3+q^2
       421: 2q^4+2q^3+q^2
       423: 2q^4+q^3+q^2
       424: q^4+2q^3
       425: q^4+q^3+q^2
       426: q^4+2q^3
       427: q^4+q^3+q^2
       428: 3q^4+4q^3
       429: 2q^3+q^2
       431: q^4+2q^3+q^2
       433: q^3+q^2
       434: q^3
       436: 2q^3
       437: q^4+3q^3+q^2
       439: 3q^4+3q^3+q^2
       440: q^4+q^3
       441: 2q^4+2q^3+q^2
       442: q^4+2q^3
       443: 3q^4+4q^3+q^2
       444: q^4+q^3
       445: q^3+q^2
       446: q^4+3q^3
       447: q^4+2q^3+q^2
       449: 2q^3+q^2
       451: q^3+q^2
       452: q^3
       453: 3q^4+3q^3+q^2
       454: q^4+q^3
       456: 2q^3
       457: q^4+3q^3+q^2
       459: 2q^4+2q^3+q^2
       460: q^4+2q^3
       461: 3q^4+4q^3+q^2
       462: q^4+q^3
       463: q^3+q^2
       464: q^4+3q^3
       466: 2q^3
       468: 2q^3
       469: q^4+q^3+q^2
       470: q^4+2q^3
       471: 3q^3+q^2
       473: 3q^3+q^2
       475: 2q^3+q^2
       476: q^3
       477: 2q^3+q^2
       478: 2q^3
       479: q^4+2q^3+q^2
       480: 2q^3
       481: 2q^4+3q^3+q^2
       482: 2q^4+3q^3+q^2
       483: 5q^4+4q^3+q^2
       484: q^4+4q^3+q^2
       486: 3q^3
       488: q^4+3q^3
       490: q^4+2q^3
       491: 3q^4+4q^3+q^2
       492: 2q^4+3q^3+q^2
       493: q^4+3q^3+q^2
       494: q^5+5q^4+4q^3+q^2
       495: q^4+3q^3+q^2
       496: q^4+4q^3+q^2
       497: 2q^4+3q^3+q^2
       498: q^5+5q^4+4q^3+q^2
       499: q^4+3q^3+q^2
       500: q^4+3q^3+q^2
       501: q^4+4q^3+q^2
       503: 3q^3
       505: q^4+3q^3
       507: q^4+2q^3
       508: q^4+3q^3+q^2
       509: q^4+4q^3+q^2
       510: 3q^4+4q^3+q^2
       511: q^4+4q^3+q^2
       512: q^4+3q^3+q^2
       513: q^4+4q^3+q^2
       514: q^4+3q^3+q^2
       515: q^4+2q^3+2q^2
       516: 2q^3+2q^2
       517: q^4+2q^3+2q^2
       518: 3q^4+5q^3+q^2
       519: 4q^4+5q^3+q^2
       520: q^5+4q^4+4q^3+q^2
       526: q^3
       527: q^3
       529: q^4+q^3+q^2
       533: q^3+q^2
       538: q^3
       541: q^4+2q^3+q^2
       542: q^3
       545: q^3+q^2
       546: q^4+2q^3
       548: q^3
       549: q^3+q^2
       554: q^3
       557: q^4+2q^3+q^2
       558: q^3
       561: q^3+q^2
       562: q^4+2q^3
       564: q^3
       565: 2q^3+q^2
       569: 2q^3+q^2
       571: q^3
       572: q^3
       573: q^4+2q^3+q^2
       574: q^3
       576: q^3
       577: q^3+q^2
       579: q^3
       581: 2q^3
       584: q^3
       586: q^3
       588: 2q^3
       589: q^4+2q^3+q^2
       591: 2q^3+q^2
       593: 2q^3+q^2
       595: q^4+2q^3+q^2
       598: 2q^3
       599: q^4+q^3+q^2
       600: q^4+2q^3
       602: 2q^3
       603: 2q^3+q^2
       606: q^3
       607: q^4+2q^3+q^2
       609: q^3+q^2
       610: q^3
       612: 2q^3
       613: q^3+q^2
       614: q^3
       615: 3q^3+q^2
       618: 2q^3
       619: q^4+2q^3+q^2
       621: 2q^3+q^2
       624: q^3
       625: q^3+q^2
       626: q^3
       628: 2q^3
       629: q^3+q^2
       630: q^3
       631: 3q^3+q^2
       634: 2q^3
       636: 2q^3
       638: 2q^3
       640: q^3
       641: 2q^3+q^2
       643: 2q^3+q^2
       645: q^3+q^2
       647: 3q^3+q^2
       649: 3q^3+q^2
       652: q^3
       653: 2q^3+q^2
       654: q^3
       655: 2q^3+q^2
       656: q^3
       657: 2q^2
       659: 2q^3+q^2
       661: 2q^3+q^2
       663: 2q^3+q^2
       664: q^4+2q^3+2q^2
       665: q^4+3q^3+q^2
       667: 3q^3
       669: q^4+3q^3
       671: q^4+2q^3
       672: q^4+4q^3+q^2
       673: 3q^4+4q^3+q^2
       674: q^3+2q^2
       675: q^3+q^2
       676: 2q^4+3q^3+q^2
       677: q^4+3q^3+q^2
       678: q^4+4q^3+q^2
       679: q^4+3q^3+q^2
       680: q^3+2q^2
       681: 2q^4+3q^3+q^2
       682: q^3+q^2
       683: q^4+3q^3+q^2
       684: q^4+4q^3+q^2
       685: q^4+3q^3+q^2
       686: q^4+3q^3+q^2
       687: q^4+3q^3+q^2
       688: q^4+3q^3+q^2
       689: q^3+q^2
       690: q^4+2q^3+2q^2
       691: 2q^3+2q^2
       692: q^4+2q^3+2q^2
       693: q^3+q^2
       695: q^3
       699: q^3
       700: q^3
       713: q^3+q^2
       717: q^3+q^2
       725: q^3+q^2
       730: q^3
       734: q^3
       741: q^3+q^2
       746: q^3
       750: q^3
       753: q^3+q^2
       761: 2q^3+q^2
       765: 2q^3+q^2
       773: q^3
       776: q^2
       778: q^3
       780: 2q^3+q^2
       782: q^3
       784: 2q^3
       785: 2q^3+q^2
       787: 2q^3+q^2
       790: 2q^3
       791: q^3+q^2
       793: 2q^2
       796: q^3+q^2
       800: q^3
       801: q^3+q^2
       803: q^2
       805: 2q^3+q^2
       807: q^4+2q^3+q^2
       810: q^3
       811: q^3+q^2
       812: q^3
       814: 2q^3
       815: 3q^3+q^2
       817: 2q^2
       820: q^3+q^2
       824: q^3
       825: q^4+2q^3+q^2
       827: 2q^3+q^2
       829: q^2
       831: q^3+q^2
       834: q^3
       835: q^3+q^2
       836: q^3
       838: 2q^3
       839: 3q^3+q^2
       842: q^3
       843: 2q^2
       845: 2q^3+q^2
       847: 2q^3+q^2
       851: q^3+q^2
       854: q^3
       855: q^2
       857: 2q^3+q^2
       858: q^3
       860: 2q^3+q^2
       862: 2q^3+q^2
       864: 2q^3+q^2
       865: 2q^2
       866: 2q^2
       867: q^4+2q^3+2q^2
       868: q^4+3q^3+q^2
       869: q^3+2q^2
       870: q^3+2q^2
       871: q^3+q^2
       872: q^4+3q^3+q^2
       873: q^3+2q^2
       874: q^3+2q^2
       875: q^3+q^2
       876: q^4+3q^3+q^2
       877: q^3+q^2
       878: q^3+q^2
       879: q^3+q^2
       880: q^3+q^2
       881: q^3+q
       882: q
       883: q^3+q
       908: q^3+q^2
       917: q^2
       924: q^2
       928: q^3+q^2
       933: q^3
       941: q^2
       948: q^3+q^2
       952: q^2
       957: q^3
       964: 2q^2
       969: q^2
       974: q^3+q^2
       986: q^3
       988: 2q^3+q^2
       993: q^2
       995: q^2
       997: 2q^3+q^2
       998: 2q^2
      1000: 2q^2
      1003: q^3
      1004: 2q^3+q^2
      1006: 2q^3+q^2
      1008: q^3+q^2
      1012: 2q^2
      1015: q^3+q^2
      1016: 2q^2
      1021: q^3+q^2
      1025: q^3
      1026: q^3+q^2
      1028: q^2
      1031: q^3+q^2
      1032: 2q^2
      1037: q^3+q^2
      1040: q^2
      1043: q^3
      1044: q^3+q^2
      1046: 2q^2
      1052: q^3+q^2
      1054: q^2
      1056: q^2
      1058: q^3+q^2
      1062: q^2
      1064: q^2
      1067: q^3+q
      1069: q
      1071: q^3+q
      1072: q
      1073: q^3+q
      1074: 2q^2
      1075: q
      1076: q^2
      1077: q^3+2q^2
      1078: q^3+q^2
      1079: q
      1080: q^2
      1081: q^3+2q^2
      1082: q^3+q^2
      1083: q^2
      1084: 2q^2
      1085: q^3+q^2
      1087: q^2
      1115: q^2
      1123: q^2
      1130: 2q^2
      1134: q^3+q^2
      1139: q^2
      1145: q^2
      1160: q^2
      1165: q^2
      1180: q^2
      1189: q^2
      1194: 2q^2
      1202: q^2
      1206: q^2
      1211: q
      1213: q^3+q
      1215: q^2
      1216: 2q^2
      1218: 2q^2
      1224: 2q^2
      1227: q
      1228: q
      1232: q^2
      1234: q^2
      1237: q^3+q^2
      1240: q^3+q^2
      1242: q^2
      1245: q
      1246: q
      1250: q^2
      1253: q^3+q^2
      1254: q^2
      1258: q^2
      1260: q^3+q^2
      1262: q
      1268: q^2
      1270: q^2
      1275: q^2
      1276: q^2
      1280: 2q^2
      1282: q
      1283: q^2
      1284: q
      1285: q^2
      1286: q
      1288: 2q^2
      1289: q^2
      1291: q^2
      1303: q^2
      1315: q^2
      1319: q^2
      1326: 2q^2
      1335: q^2
      1341: q
      1364: q^2
      1368: q^2
      1373: q
      1396: q^2
      1400: q^2
      1405: q
      1410: q
      1426: q^2
      1431: q^2
      1439: q
      1440: q
      1442: q
      1444: q
      1450: q^2
      1453: q
      1454: q^2
      1459: q
      1460: q^2
      1462: q^2
      1473: q^2
      1476: q^2
      1478: q^2
      1482: 2q^2
      1485: q
      1486: q
      1488: q
      1490: q^2
      1526: q
      1542: q
      1546: q
      1549: q
      1554: q
      1575: q^2
      1595: q^2
      1627: q^2
      1632: q^2
      1639: q
      1644: q
      1645: q
      1647: q
      1652: q
      1653: q
      1655: q
      1668: q
      1669: q
      1676: q
      1724: q
      1733: q
      1738: q
      1746: q
      1749: q
      1762: q
      1766: q
      1773: q
      1802: q
      1835: q
      1847: q
      1859: q
      2060: 1
      2093: 1
      2130: 1
      2148: 1

2149:    0: 10q^3+4q^2+q
         1: 10q^3+4q^2+q
         2: 3q^4+7q^3+4q^2+q
         3: 10q^3+4q^2+q
         4: 3q^4+7q^3+4q^2+q
         5: 10q^3+4q^2+q
         6: 3q^4+7q^3+4q^2+q
         7: q^5+4q^4+5q^3+4q^2+q
         8: 3q^4+7q^3+4q^2+q
         9: q^5+4q^4+5q^3+4q^2+q
        10: 10q^3+4q^2+q
        11: 10q^3+4q^2+q
        12: 3q^4+7q^3+4q^2+q
        13: 7q^3+4q^2+q
        14: 2q^4+5q^3+4q^2+q
        15: 7q^3+4q^2+q
        16: 10q^3+4q^2+q
        17: 10q^3+4q^2+q
        18: q^5+4q^4+5q^3+4q^2+q
        19: 7q^3+4q^2+q
        20: 7q^3+4q^2+q
        21: 2q^4+5q^3+4q^2+q
        22: 10q^3+4q^2+q
        23: 10q^3+4q^2+q
        24: 3q^4+7q^3+4q^2+q
        25: 10q^3+4q^2+q
        26: 10q^3+4q^2+q
        27: 3q^4+7q^3+4q^2+q
        28: 10q^3+4q^2+q
        29: 7q^3+4q^2+q
        30: 5q^3+4q^2+q
        31: 10q^3+4q^2+q
        32: 7q^3+4q^2+q
        33: 10q^3+4q^2+q
        34: 10q^3+4q^2+q
        35: 7q^3+4q^2+q
        36: 10q^3+4q^2+q
        37: 4q^3+2q^2
        38: 6q^3+2q^2+q
        39: 4q^3+2q^2
        40: 6q^3+2q^2+q
        41: q^4+3q^3+2q^2
        42: 2q^4+4q^3+2q^2+q
        43: 7q^3+4q^2+q
        44: 2q^4+5q^3+4q^2+q
        45: 7q^3+4q^2+q
        46: 7q^3+4q^2+q
        47: 7q^3+4q^2+q
        48: 2q^4+5q^3+4q^2+q
        49: 7q^3+4q^2+q
        50: 7q^3+4q^2+q
        51: 2q^4+5q^3+4q^2+q
        52: 7q^3+4q^2+q
        53: 7q^3+4q^2+q
        54: 2q^4+5q^3+4q^2+q
        55: 7q^3+4q^2+q
        56: 7q^3+4q^2+q
        57: 2q^4+5q^3+4q^2+q
        58: 4q^3+q^2
        59: 6q^3+3q^2+q
        60: 6q^3+3q^2+q
        61: 4q^3+q^2
        62: 4q^3+2q^2
        63: 6q^3+2q^2+q
        64: 3q^3+2q^2
        65: 4q^3+2q^2+q
        66: 4q^3+2q^2
        67: 6q^3+2q^2+q
        68: 4q^3+4q^2+q
        69: 5q^3+4q^2+q
        70: 5q^3+4q^2+q
        71: 7q^3+4q^2+q
        72: 4q^3+4q^2+q
        73: 4q^3+4q^2+q
        74: q^3+2q^2
        75: 3q^3+2q^2+q
        76: q^3+2q^2
        77: 3q^3+2q^2+q
        78: q^3+2q^2
        79: q^4+2q^3+2q^2+q
        80: 7q^3+4q^2+q
        81: 7q^3+4q^2+q
        82: 7q^3+4q^2+q
        83: 5q^3+4q^2+q
        84: 7q^3+4q^2+q
        85: 7q^3+4q^2+q
        86: 7q^3+4q^2+q
        87: 5q^3+4q^2+q
        88: 7q^3+4q^2+q
        89: 7q^3+4q^2+q
        90: 2q^4+5q^3+4q^2+q
        91: 4q^3+4q^2+q
        92: 4q^3+4q^2+q
        93: 4q^3+4q^2+q
        94: 7q^3+4q^2+q
        95: 7q^3+4q^2+q
        96: 2q^4+5q^3+4q^2+q
        97: 7q^3+4q^2+q
        98: 7q^3+4q^2+q
        99: 2q^4+5q^3+4q^2+q
       100: 7q^3+4q^2+q
       101: 7q^3+4q^2+q
       102: 2q^4+5q^3+4q^2+q
       103: 2q^3+q^2
       104: 4q^3+2q^2+q
       105: 2q^3
       106: 2q^3+q^2
       107: 3q^3+3q^2+q
       108: q^3+q^2
       109: q^3+q^2
       110: 3q^3+3q^2+q
       111: 2q^2
       112: q^3+2q^2+q
       113: q^3+2q^2
       114: 3q^3+2q^2+q
       115: q^3+2q^2
       116: 2q^3+2q^2+q
       117: q^3+q^2
       118: 3q^3+3q^2+q
       119: 3q^3+3q^2+q
       120: q^3+q^2
       121: 3q^3+2q^2
       122: 4q^3+2q^2+q
       123: 3q^3+2q^2
       124: 4q^3+2q^2+q
       125: 4q^3+4q^2+q
       126: 5q^3+4q^2+q
       127: q^3+2q^2
       128: 3q^3+2q^2+q
       129: q^3+2q^2
       130: 3q^3+2q^2+q
       131: q^3+2q^2
       132: q^4+2q^3+2q^2+q
       133: 2q^3+4q^2+q
       134: 4q^3+4q^2+q
       135: 2q^3+4q^2+q
       136: 2q^3+4q^2+q
       137: 7q^3+4q^2+q
       138: 5q^3+4q^2+q
       139: 7q^3+4q^2+q
       140: 4q^3+4q^2+q
       141: 5q^3+4q^2+q
       142: 4q^3+4q^2+q
       143: 7q^3+4q^2+q
       144: 5q^3+4q^2+q
       145: 7q^3+4q^2+q
       146: 5q^3+4q^2+q
       147: 4q^3+4q^2+q
       148: 4q^3+4q^2+q
       149: 7q^3+4q^2+q
       150: 5q^3+4q^2+q
       151: q^3+2q^2
       152: 3q^3+2q^2+q
       153: q^3+2q^2
       154: 3q^3+2q^2+q
       155: q^3+2q^2
       156: q^4+2q^3+2q^2+q
       157: 4q^3+4q^2+q
       158: 4q^3+4q^2+q
       159: 4q^3+4q^2+q
       160: 4q^3+4q^2+q
       161: 4q^3+4q^2+q
       162: 4q^3+4q^2+q
       163: 4q^3+4q^2+q
       164: 4q^3+4q^2+q
       165: 4q^3+4q^2+q
       166: 7q^3+4q^2+q
       167: 7q^3+4q^2+q
       168: 2q^4+5q^3+4q^2+q
       169: q^2
       170: q^3+2q^2+q
       172: q^2
       173: q^3+q^2
       174: 2q^3+2q^2+q
       176: q^3+q^2
       177: q^3+2q^2
       178: 2q^3+2q^2+q
       179: q^3+2q^2
       180: 3q^3+2q^2+q
       181: 2q^2
       182: q^3+2q^2+q
       183: q^3+3q^2+q
       184: q^2
       185: q^2
       186: q^3+3q^2+q
       187: 2q^2
       188: 2q^2+q
       189: q^3+2q^2
       190: 2q^3+2q^2+q
       191: q^3+q^2
       192: 3q^3+3q^2+q
       193: 3q^3+3q^2+q
       194: q^3+q^2
       195: q^3+q^2
       196: 3q^3+3q^2+q
       197: 2q^2
       198: q^3+2q^2+q
       199: 3q^3+3q^2+q
       200: q^3+q^2
       201: 3q^3+3q^2+q
       202: q^3+q^2
       203: q^3+q^2
       204: 3q^3+3q^2+q
       205: 2q^2
       206: q^3+2q^2+q
       207: 3q^3+2q^2
       208: 4q^3+2q^2+q
       209: q^3+2q^2
       210: 3q^3+2q^2+q
       211: q^3+2q^2
       212: 2q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: 2q^3+4q^2+q
       220: 2q^3+4q^2+q
       221: 4q^3+4q^2+q
       222: 2q^3+4q^2+q
       223: 2q^3+4q^2+q
       224: 2q^3+4q^2+q
       225: 2q^3+4q^2+q
       226: 5q^3+4q^2+q
       227: 2q^3+4q^2+q
       228: 4q^3+4q^2+q
       229: 2q^3+4q^2+q
       230: 2q^3+4q^2+q
       231: 5q^3+4q^2+q
       232: 2q^3+4q^2+q
       233: 4q^3+4q^2+q
       234: 2q^3+4q^2+q
       235: 2q^3+4q^2+q
       236: 5q^3+4q^2+q
       237: q^3+2q^2
       238: 3q^3+2q^2+q
       239: q^3+2q^2
       240: 3q^3+2q^2+q
       241: q^3+2q^2
       242: q^4+2q^3+2q^2+q
       243: 7q^3+4q^2+q
       244: 4q^3+4q^2+q
       245: 4q^3+4q^2+q
       246: 5q^3+4q^2+q
       247: q^3+7q^2+q
       248: q^3+7q^2+q
       249: q^4+3q^3+4q^2+q
       250: 4q^3+4q^2+q
       251: 4q^3+4q^2+q
       252: 4q^3+4q^2+q
       253: 4q^3+4q^2+q
       254: 4q^3+4q^2+q
       255: 4q^3+4q^2+q
       256: 4q^3+4q^2+q
       257: 4q^3+4q^2+q
       258: 4q^3+4q^2+q
       259: q^2
       260: q^3+2q^2+q
       262: q^2
       263: q^2
       264: 2q^2+q
       266: q^2
       267: q^2
       268: q^3+2q^2+q
       269: q^2
       271: q^2
       273: q^2
       274: q^3+2q^2+q
       275: q^3+q^2
       276: 2q^3+2q^2+q
       278: q^3+q^2
       280: q^2+q
       282: q^3+q^2+q
       283: q^3+3q^2+q
       284: q^2
       285: q^2
       286: q^3+3q^2+q
       287: q^3+2q^2
       288: 2q^3+2q^2+q
       290: q^2+q
       291: 2q^2
       292: 2q^2+q
       293: q^3+3q^2+q
       294: q^2
       295: q^2
       296: q^3+3q^2+q
       297: 2q^2
       298: 2q^2+q
       299: q^3+3q^2+q
       300: q^2
       301: 2q^2
       302: q^3+2q^2+q
       303: q^2
       304: q^3+3q^2+q
       305: 2q^2
       306: 2q^2+q
       307: q^3+3q^2+q
       308: q^2
       309: q^2
       310: q^3+3q^2+q
       311: 2q^2
       312: q^3+2q^2+q
       313: 2q^2
       314: 2q^2+q
       315: q^3+2q^2
       316: 2q^3+2q^2+q
       317: q^3+2q^2
       318: 3q^3+2q^2+q
       319: 3q^3+3q^2+q
       320: q^3+q^2
       321: q^3+q^2
       322: 3q^3+3q^2+q
       323: 2q^2
       324: q^3+2q^2+q
       325: q^3+2q^2
       326: 2q^3+2q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^3+q^2+q
       333: 2q^3+4q^2+q
       334: 2q^3+4q^2+q
       335: 2q^3+4q^2+q
       336: 4q^2+q
       337: q^3+7q^2+q
       338: 3q^2
       339: q^3+4q^2+q
       340: 3q^2
       341: q^3+4q^2+q
       342: q^3+2q^2
       343: q^4+2q^3+2q^2+q
       344: 2q^3+4q^2+q
       345: 2q^3+4q^2+q
       346: 4q^3+4q^2+q
       347: 2q^3+4q^2+q
       348: 2q^3+4q^2+q
       349: 2q^3+4q^2+q
       350: 2q^3+4q^2+q
       351: q^3+7q^2+q
       352: 2q^3+4q^2+q
       353: 2q^3+4q^2+q
       354: 4q^3+4q^2+q
       355: 2q^3+4q^2+q
       356: 2q^3+4q^2+q
       357: 2q^3+4q^2+q
       358: 2q^3+4q^2+q
       359: q^3+7q^2+q
       361: q^3+q^2+q
       363: q^3+q^2+q
       365: q^3+q^2+q
       366: 5q^3+4q^2+q
       367: 2q^3+4q^2+q
       368: 4q^3+4q^2+q
       369: 2q^3+4q^2+q
       370: 2q^3+4q^2+q
       371: 5q^2+q
       372: 5q^2+q
       373: 2q^3+3q^2+q
       374: 4q^3+4q^2+q
       375: 4q^3+4q^2+q
       376: 4q^3+4q^2+q
       377: q^2
       378: 2q^2+q
       380: q^2
       382: q^2+q
       385: q^2
       386: 2q^2+q
       388: q^2
       389: q^2
       390: q^3+2q^2+q
       391: q^2
       393: q^2
       394: 2q^2+q
       396: q^2
       397: q^2
       399: q^2
       400: q^3+2q^2+q
       401: q^2
       403: 2q^2+q
       404: q^2
       405: q^2
       406: q^2
       407: q^3+2q^2+q
       410: q^2+q
       412: q^3+q^2+q
       414: q^2+q
       416: q^2+q
       418: q^2+q
       419: q^3+3q^2+q
       420: q^2
       421: q^2
       422: q^3+3q^2+q
       423: 2q^2
       424: 2q^2+q
       425: 2q^2
       426: 2q^2+q
       427: 3q^2
       428: q^3+4q^2+q
       429: q^3+3q^2+q
       430: q^2
       431: q^2
       432: q^3+3q^2+q
       433: 2q^2
       434: 2q^2+q
       436: q^2+q
       437: q^3+3q^2+q
       438: q^2
       439: q^2
       440: q^3+3q^2+q
       441: 2q^2
       442: 2q^2+q
       443: q^3+5q^2+q
       444: 2q^2
       445: 3q^2
       446: q^3+4q^2+q
       447: q^3+3q^2+q
       448: q^2
       449: q^2
       450: q^3+3q^2+q
       451: 2q^2
       452: 2q^2+q
       453: q^3+3q^2+q
       454: q^2
       456: q^2+q
       457: q^2
       458: q^3+3q^2+q
       459: 2q^2
       460: 2q^2+q
       461: 2q^2
       462: q^3+5q^2+q
       463: 3q^2
       464: q^3+4q^2+q
       466: q^2+q
       468: q^3+q^2+q
       469: q^3+2q^2
       470: 2q^3+2q^2+q
       471: q^3+3q^2+q
       472: q^2
       473: q^2
       474: q^3+3q^2+q
       475: 2q^2
       476: 2q^2+q
       477: 2q^2
       478: q^3+2q^2+q
       479: 4q^2
       480: q^3+3q^2+q
       481: q^3+3q^2+q
       482: q^3+3q^2+q
       483: 4q^2+q
       484: 4q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: 3q^2+q
       492: 2q^3+4q^2+q
       493: 2q^3+4q^2+q
       494: 2q^3+4q^2+q
       495: 4q^2+q
       496: 5q^2+q
       497: 2q^3+4q^2+q
       498: 2q^3+4q^2+q
       499: 2q^3+4q^2+q
       500: 4q^2+q
       501: 5q^2+q
       503: q^3+q^2+q
       505: q^3+q^2+q
       507: q^3+q^2+q
       508: 2q^3+4q^2+q
       509: 2q^3+4q^2+q
       510: 4q^3+4q^2+q
       511: 2q^3+4q^2+q
       512: 2q^3+4q^2+q
       513: 2q^3+4q^2+q
       514: 2q^3+4q^2+q
       515: 5q^2+q
       516: 5q^2+q
       517: 2q^3+3q^2+q
       518: 5q^2+q
       519: 5q^2+q
       520: 2q^3+3q^2+q
       522: q^2+q
       526: q^2+q
       529: q^2
       530: 2q^2+q
       532: q^2
       533: q^2
       534: 2q^2+q
       536: q^2
       538: q^2+q
       541: q^2
       542: 2q^2+q
       543: q^2
       545: 2q^2
       546: q^3+3q^2+q
       547: q^2
       548: q^2
       549: q^2
       551: 2q^2+q
       552: q^2
       556: q^2+q
       557: q^2
       559: q^2
       560: 2q^2+q
       561: q^2
       562: q^2
       563: 2q^2
       564: q^3+3q^2+q
       565: q^2
       566: 2q^2+q
       568: q^2
       569: q^2
       570: q^2
       571: q^3+2q^2+q
       573: 2q^2
       574: q^3+3q^2+q
       575: 2q^2
       577: 2q^2
       578: 2q^2
       580: q^2
       581: q^3+2q^2+q
       584: q^2+q
       586: q
       588: q^2+q
       589: q^3+2q^2+q
       590: q^2
       592: 2q^2+q
       593: 2q^2+q
       595: q^2
       596: q^3+2q^2+q
       598: q^2+q
       599: 2q^2
       600: 2q^2+q
       602: q^2+q
       603: q^3+3q^2+q
       604: q^2
       606: q^2+q
       607: q^2
       608: q^3+3q^2+q
       609: 2q^2
       610: 2q^2+q
       612: q^2+q
       613: 2q^2
       614: 2q^2+q
       615: 3q^2+q
       616: q^2
       618: 2q^2+q
       619: q^3+3q^2+q
       620: q^2
       621: q^2
       622: q^3+3q^2+q
       624: q^2+q
       625: 2q^2
       626: 2q^2+q
       628: q^2+q
       629: 2q^2
       630: 2q^2+q
       631: q^2
       632: 3q^2+q
       634: 2q^2+q
       636: q^2+q
       638: q^3+q^2+q
       640: q^2+q
       641: q^3+3q^2+q
       642: q^2
       643: q^2
       644: q^3+3q^2+q
       645: 2q^2
       646: 2q^2+q
       647: q^3+3q^2+q
       648: q^2
       649: q^2
       650: q^3+3q^2+q
       652: q^2+q
       653: 2q^2
       654: 2q^2+q
       655: 3q^2
       656: 2q^2+q
       657: 4q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: 3q^2+q
       665: 2q^2+q
       667: 2q^2+q
       669: 2q^2+q
       671: q^3+q^2+q
       672: 4q^2+q
       673: 3q^2+q
       674: 5q^2+q
       675: q^3+3q^2+q
       676: q^3+3q^2+q
       677: 4q^2+q
       678: 5q^2+q
       679: 3q^2+q
       680: 5q^2+q
       681: q^3+3q^2+q
       682: q^3+3q^2+q
       683: 4q^2+q
       684: 5q^2+q
       685: 3q^2+q
       686: 2q^3+4q^2+q
       687: 2q^3+4q^2+q
       688: 2q^3+4q^2+q
       689: 4q^2+q
       690: 5q^2+q
       691: 5q^2+q
       692: 2q^3+3q^2+q
       693: q^2
       694: q^2
       696: q^2
       697: q^2
       699: q^3+2q^2+q
       701: q^2
       706: q^2+q
       710: q
       715: q^2+q
       716: q^2
       717: q^2
       718: q^2+q
       722: q^2+q
       725: q^2
       726: 2q^2+q
       727: q^2
       730: q^2+q
       734: q^2+q
       740: q^2+q
       741: q^2
       743: q^2
       744: 2q^2+q
       748: q^2+q
       752: q^2+q
       753: q^2
       754: 2q^2+q
       756: q^2
       759: q^2+q
       761: q^2
       762: q^2
       763: 2q^2+q
       765: q^2
       766: 2q^2+q
       768: q^2
       770: q^2
       773: q^2+q
       776: q^2+q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       785: q^2+q
       788: q^2+q
       790: q^2+q
       791: q^2
       792: q
       793: 3q^2+q
       794: q^2
       796: 2q^2+q
       798: q
       800: q^2+q
       801: q^3+2q^2+q
       802: q^2
       804: 2q^2+q
       805: 2q^2+q
       807: q^2
       808: q^3+2q^2+q
       810: q^2+q
       811: 2q^2
       812: 2q^2+q
       814: 2q^2+q
       815: 3q^2+q
       816: q^2
       817: q^2
       818: 3q^2+q
       820: 2q^2+q
       822: q
       824: q^2+q
       825: q^3+2q^2+q
       826: q^2
       828: 2q^2+q
       829: 2q^2+q
       831: q^2
       832: q^3+2q^2+q
       834: q^2+q
       835: 2q^2
       836: 2q^2+q
       838: 2q^2+q
       839: q^2
       840: 3q^2+q
       842: q^2+q
       843: 3q^2
       844: 2q^2+q
       845: q^3+3q^2+q
       846: q^2
       847: q^2
       848: q^3+3q^2+q
       850: q^2+q
       851: 2q^2
       852: 2q^2+q
       854: q^2+q
       855: 2q^2
       856: 2q^2+q
       857: 3q^2
       858: 2q^2+q
       860: 2q^2+q
       862: 2q^2+q
       864: q^3+q^2+q
       865: 4q^2+q
       866: 2q^2+q
       867: 3q^2+q
       868: 2q^2+q
       869: 5q^2+q
       870: 3q^2+q
       871: 2q^2+q
       872: 3q^2+q
       873: 5q^2+q
       874: 3q^2+q
       875: 2q^2+q
       876: 3q^2+q
       877: q^3+3q^2+q
       878: q^3+3q^2+q
       879: 4q^2+q
       880: 3q^2+q
       881: 3q
       882: 3q
       883: q^2+2q
       890: q^2+q
       897: q
       903: q
       905: q
       909: q
       913: q^2+q
       917: q^2+q
       921: q
       926: q^2+q
       927: q^2
       928: q^2
       929: q^2+q
       933: q^2+q
       939: q^2+q
       943: q^2+q
       947: q
       950: q^2
       951: q^2+q
       952: q^2
       953: q^2+q
       959: q^2+q
       962: q^2+q
       964: q^2
       965: 2q^2+q
       967: q^2
       969: q^2
       972: q^2+q
       974: q^2
       975: q^2
       976: 2q^2+q
       980: q^2+q
       983: q^2
       986: q^2+q
       988: q^2
       989: 2q^2+q
       991: q^2
       993: q^2+q
       995: q
       997: q^2+q
       999: q^2+q
      1000: q^2+q
      1003: q
      1004: q^2+q
      1007: q^2+q
      1008: q^2
      1009: q
      1011: q
      1012: q^2
      1013: q
      1015: 2q^2+q
      1016: 3q^2+q
      1017: q^2
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1026: q^2+q
      1029: q^2+q
      1031: 2q^2+q
      1032: q^2
      1033: 3q^2+q
      1035: q
      1037: q^2+q
      1039: q
      1040: q^2+q
      1043: q^2+q
      1045: q^2+q
      1046: 3q^2
      1047: 2q^2+q
      1049: q
      1051: q^2+q
      1052: q^3+2q^2+q
      1053: q^2
      1055: 2q^2+q
      1056: 2q^2+q
      1058: q^2
      1059: q^3+2q^2+q
      1061: q^2+q
      1062: 2q^2
      1063: 2q^2+q
      1064: q^2
      1065: q
      1067: 3q
      1069: 3q
      1071: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q^2+q
      1075: 3q
      1076: 2q^2+q
      1077: 3q^2+q
      1078: 2q^2+q
      1079: 3q
      1080: 2q^2+q
      1081: 3q^2+q
      1082: 2q^2+q
      1083: 2q^2+q
      1084: 3q^2+q
      1085: 3q^2+q
      1092: q^2+q
      1104: q^2+q
      1113: q
      1117: q
      1119: q
      1123: q
      1128: q
      1131: q
      1136: q
      1142: q
      1145: q^2+q
      1149: q
      1155: q
      1157: q
      1162: q
      1167: q^2+q
      1171: q
      1175: q
      1177: q
      1181: q
      1186: q^2+q
      1189: q^2
      1192: q^2+q
      1194: q^2
      1195: 2q^2+q
      1197: q^2
      1200: q
      1204: q^2
      1205: q^2+q
      1206: q^2
      1207: q^2+q
      1211: 3q
      1213: 2q
      1215: q
      1217: q^2+q
      1218: q^2+q
      1223: q
      1224: q^2
      1225: q
      1227: 3q
      1228: 2q
      1229: q
      1231: q
      1233: q^2+q
      1234: q^2+q
      1237: q^2+q
      1239: q
      1240: q^2+q
      1243: q^2+q
      1245: 3q
      1246: q
      1247: 2q
      1249: q
      1251: q^2+q
      1253: q^2+q
      1254: q^2+q
      1257: q
      1258: q^2+q
      1261: q^2+q
      1262: 2q
      1263: q
      1265: q
      1267: q
      1268: q^2+q
      1271: q^2+q
      1273: q^2+q
      1275: q^2+q
      1276: q^2
      1277: q
      1279: q
      1280: q^2
      1281: q
      1282: 2q
      1283: 2q^2+q
      1284: 2q
      1285: 2q^2+q
      1286: 2q
      1287: 2q^2+q
      1288: 3q^2+q
      1289: 2q^2+q
      1296: q
      1308: q^2+q
      1317: q
      1319: q
      1324: q
      1327: q
      1338: q
      1341: 2q
      1343: q
      1347: q
      1351: q
      1353: q
      1357: q
      1363: q
      1366: q
      1371: q
      1373: q
      1375: 2q
      1379: q
      1383: q
      1385: q
      1389: q
      1394: q
      1397: q
      1402: q
      1405: 2q
      1408: q
      1410: q
      1411: q
      1413: q
      1416: q
      1421: q
      1423: q
      1427: q
      1434: q
      1439: 2q
      1441: q
      1442: q
      1444: q
      1449: q
      1451: q^2+q
      1453: 2q
      1454: q^2+q
      1457: q
      1459: 2q
      1461: q^2+q
      1462: q^2+q
      1465: q
      1467: q^2+q
      1468: q^2+q
      1471: q
      1473: q^2+q
      1476: q^2+q
      1479: q^2+q
      1481: q
      1482: q^2
      1483: q
      1484: q
      1485: 2q
      1486: 2q
      1487: 2q^2+q
      1488: 2q
      1495: q
      1508: q
      1519: q
      1526: q
      1531: q
      1533: q
      1544: q
      1546: q
      1554: q
      1566: q
      1568: q
      1574: q
      1577: q
      1586: q
      1588: q
      1593: q
      1596: q
      1606: q
      1610: q
      1612: q
      1616: q
      1620: q
      1624: q
      1628: q
      1635: q
      1639: q
      1644: 2q
      1646: q
      1647: q
      1650: q
      1652: 2q
      1654: q
      1655: q
      1657: q
      1662: q
      1664: q^2+q
      1665: q^2+q
      1668: 2q
      1669: q
      1673: q
      1674: 2q
      1694: q
      1705: q
      1716: q
      1724: q
      1740: q
      1746: q
      1764: q
      1766: q
      1788: q
      1790: q
      1794: q
      1798: q
      1802: q
      1812: q
      1820: q
      1821: q
      1825: q
      1828: 2q
      1830: q
      1831: q
      1833: 1
      1875: q
      1927: q
      1935: q
      1937: q
      1953: q
      1957: 1
      1960: 1
      1963: 1
      1964: 1
      2027: 1
      2035: 1
      2042: 1
      2045: 1
      2052: 1
      2065: 1
      2074: 1
      2081: 1
      2108: 1
      2131: 1
      2149: 1

2150:    0: 10q^3+4q^2+q
         1: 10q^3+4q^2+q
         2: 3q^4+7q^3+4q^2+q
         3: 10q^3+4q^2+q
         4: 3q^4+7q^3+4q^2+q
         5: 10q^3+4q^2+q
         6: 3q^4+7q^3+4q^2+q
         7: q^5+4q^4+5q^3+4q^2+q
         8: 3q^4+7q^3+4q^2+q
         9: q^5+4q^4+5q^3+4q^2+q
        10: 10q^3+4q^2+q
        11: 10q^3+4q^2+q
        12: 3q^4+7q^3+4q^2+q
        13: 7q^3+4q^2+q
        14: 2q^4+5q^3+4q^2+q
        15: 7q^3+4q^2+q
        16: 10q^3+4q^2+q
        17: 10q^3+4q^2+q
        18: q^5+4q^4+5q^3+4q^2+q
        19: 7q^3+4q^2+q
        20: 7q^3+4q^2+q
        21: 2q^4+5q^3+4q^2+q
        22: 10q^3+4q^2+q
        23: 10q^3+4q^2+q
        24: 3q^4+7q^3+4q^2+q
        25: 10q^3+4q^2+q
        26: 10q^3+4q^2+q
        27: 3q^4+7q^3+4q^2+q
        28: 10q^3+4q^2+q
        29: 7q^3+4q^2+q
        30: 5q^3+4q^2+q
        31: 10q^3+4q^2+q
        32: 7q^3+4q^2+q
        33: 10q^3+4q^2+q
        34: 10q^3+4q^2+q
        35: 7q^3+4q^2+q
        36: 10q^3+4q^2+q
        37: 4q^3+2q^2
        38: 6q^3+2q^2+q
        39: 4q^3+2q^2
        40: 6q^3+2q^2+q
        41: q^4+3q^3+2q^2
        42: 2q^4+4q^3+2q^2+q
        43: 7q^3+4q^2+q
        44: 2q^4+5q^3+4q^2+q
        45: 7q^3+4q^2+q
        46: 7q^3+4q^2+q
        47: 7q^3+4q^2+q
        48: 2q^4+5q^3+4q^2+q
        49: 7q^3+4q^2+q
        50: 7q^3+4q^2+q
        51: 2q^4+5q^3+4q^2+q
        52: 7q^3+4q^2+q
        53: 7q^3+4q^2+q
        54: 2q^4+5q^3+4q^2+q
        55: 7q^3+4q^2+q
        56: 7q^3+4q^2+q
        57: 2q^4+5q^3+4q^2+q
        58: 6q^3+3q^2+q
        59: 4q^3+q^2
        60: 4q^3+q^2
        61: 6q^3+3q^2+q
        62: 4q^3+2q^2
        63: 6q^3+2q^2+q
        64: 3q^3+2q^2
        65: 4q^3+2q^2+q
        66: 4q^3+2q^2
        67: 6q^3+2q^2+q
        68: 4q^3+4q^2+q
        69: 5q^3+4q^2+q
        70: 5q^3+4q^2+q
        71: 7q^3+4q^2+q
        72: 4q^3+4q^2+q
        73: 4q^3+4q^2+q
        74: q^3+2q^2
        75: 3q^3+2q^2+q
        76: q^3+2q^2
        77: 3q^3+2q^2+q
        78: q^3+2q^2
        79: q^4+2q^3+2q^2+q
        80: 7q^3+4q^2+q
        81: 7q^3+4q^2+q
        82: 7q^3+4q^2+q
        83: 5q^3+4q^2+q
        84: 7q^3+4q^2+q
        85: 7q^3+4q^2+q
        86: 7q^3+4q^2+q
        87: 5q^3+4q^2+q
        88: 7q^3+4q^2+q
        89: 7q^3+4q^2+q
        90: 2q^4+5q^3+4q^2+q
        91: 4q^3+4q^2+q
        92: 4q^3+4q^2+q
        93: 4q^3+4q^2+q
        94: 7q^3+4q^2+q
        95: 7q^3+4q^2+q
        96: 2q^4+5q^3+4q^2+q
        97: 7q^3+4q^2+q
        98: 7q^3+4q^2+q
        99: 2q^4+5q^3+4q^2+q
       100: 7q^3+4q^2+q
       101: 7q^3+4q^2+q
       102: 2q^4+5q^3+4q^2+q
       103: 2q^3+q^2
       104: 2q^3
       105: 4q^3+2q^2+q
       106: 2q^3+q^2
       107: q^3+q^2
       108: 3q^3+3q^2+q
       109: 3q^3+3q^2+q
       110: q^3+q^2
       111: 2q^2
       112: q^3+2q^2+q
       113: q^3+2q^2
       114: 3q^3+2q^2+q
       115: q^3+2q^2
       116: 2q^3+2q^2+q
       117: 3q^3+3q^2+q
       118: q^3+q^2
       119: q^3+q^2
       120: 3q^3+3q^2+q
       121: 3q^3+2q^2
       122: 4q^3+2q^2+q
       123: 3q^3+2q^2
       124: 4q^3+2q^2+q
       125: 4q^3+4q^2+q
       126: 5q^3+4q^2+q
       127: q^3+2q^2
       128: 3q^3+2q^2+q
       129: q^3+2q^2
       130: 3q^3+2q^2+q
       131: q^3+2q^2
       132: q^4+2q^3+2q^2+q
       133: 2q^3+4q^2+q
       134: 4q^3+4q^2+q
       135: 2q^3+4q^2+q
       136: 2q^3+4q^2+q
       137: 7q^3+4q^2+q
       138: 5q^3+4q^2+q
       139: 7q^3+4q^2+q
       140: 4q^3+4q^2+q
       141: 5q^3+4q^2+q
       142: 4q^3+4q^2+q
       143: 7q^3+4q^2+q
       144: 5q^3+4q^2+q
       145: 7q^3+4q^2+q
       146: 5q^3+4q^2+q
       147: 4q^3+4q^2+q
       148: 4q^3+4q^2+q
       149: 7q^3+4q^2+q
       150: 5q^3+4q^2+q
       151: q^3+2q^2
       152: 3q^3+2q^2+q
       153: q^3+2q^2
       154: 3q^3+2q^2+q
       155: q^3+2q^2
       156: q^4+2q^3+2q^2+q
       157: 4q^3+4q^2+q
       158: 4q^3+4q^2+q
       159: 4q^3+4q^2+q
       160: 4q^3+4q^2+q
       161: 4q^3+4q^2+q
       162: 4q^3+4q^2+q
       163: 4q^3+4q^2+q
       164: 4q^3+4q^2+q
       165: 4q^3+4q^2+q
       166: 7q^3+4q^2+q
       167: 7q^3+4q^2+q
       168: 2q^4+5q^3+4q^2+q
       169: q^2
       171: q^3+2q^2+q
       172: q^2
       173: q^3+q^2
       175: 2q^3+2q^2+q
       176: q^3+q^2
       177: q^3+2q^2
       178: 2q^3+2q^2+q
       179: q^3+2q^2
       180: 3q^3+2q^2+q
       181: 2q^2
       182: q^3+2q^2+q
       183: q^2
       184: q^3+3q^2+q
       185: q^3+3q^2+q
       186: q^2
       187: 2q^2
       188: 2q^2+q
       189: q^3+2q^2
       190: 2q^3+2q^2+q
       191: 3q^3+3q^2+q
       192: q^3+q^2
       193: q^3+q^2
       194: 3q^3+3q^2+q
       195: 3q^3+3q^2+q
       196: q^3+q^2
       197: 2q^2
       198: q^3+2q^2+q
       199: q^3+q^2
       200: 3q^3+3q^2+q
       201: q^3+q^2
       202: 3q^3+3q^2+q
       203: 3q^3+3q^2+q
       204: q^3+q^2
       205: 2q^2
       206: q^3+2q^2+q
       207: 3q^3+2q^2
       208: 4q^3+2q^2+q
       209: q^3+2q^2
       210: 3q^3+2q^2+q
       211: q^3+2q^2
       212: 2q^3+2q^2+q
       214: q^3+q^2+q
       216: q^3+q^2+q
       218: q^3+q^2+q
       219: 2q^3+4q^2+q
       220: 2q^3+4q^2+q
       221: 4q^3+4q^2+q
       222: 2q^3+4q^2+q
       223: 2q^3+4q^2+q
       224: 2q^3+4q^2+q
       225: 2q^3+4q^2+q
       226: 5q^3+4q^2+q
       227: 2q^3+4q^2+q
       228: 4q^3+4q^2+q
       229: 2q^3+4q^2+q
       230: 2q^3+4q^2+q
       231: 5q^3+4q^2+q
       232: 2q^3+4q^2+q
       233: 4q^3+4q^2+q
       234: 2q^3+4q^2+q
       235: 2q^3+4q^2+q
       236: 5q^3+4q^2+q
       237: q^3+2q^2
       238: 3q^3+2q^2+q
       239: q^3+2q^2
       240: 3q^3+2q^2+q
       241: q^3+2q^2
       242: q^4+2q^3+2q^2+q
       243: 7q^3+4q^2+q
       244: 4q^3+4q^2+q
       245: 4q^3+4q^2+q
       246: 5q^3+4q^2+q
       247: q^3+7q^2+q
       248: q^3+7q^2+q
       249: q^4+3q^3+4q^2+q
       250: 4q^3+4q^2+q
       251: 4q^3+4q^2+q
       252: 4q^3+4q^2+q
       253: 4q^3+4q^2+q
       254: 4q^3+4q^2+q
       255: 4q^3+4q^2+q
       256: 4q^3+4q^2+q
       257: 4q^3+4q^2+q
       258: 4q^3+4q^2+q
       259: q^2
       261: q^3+2q^2+q
       262: q^2
       263: q^2
       265: 2q^2+q
       266: q^2
       267: q^2
       269: q^2
       270: q^3+2q^2+q
       271: q^2
       272: q^3+2q^2+q
       273: q^2
       275: q^3+q^2
       277: 2q^3+2q^2+q
       278: q^3+q^2
       280: q^2+q
       282: q^3+q^2+q
       283: q^2
       284: q^3+3q^2+q
       285: q^3+3q^2+q
       286: q^2
       287: q^3+2q^2
       288: 2q^3+2q^2+q
       290: q^2+q
       291: 2q^2
       292: 2q^2+q
       293: q^2
       294: q^3+3q^2+q
       295: q^3+3q^2+q
       296: q^2
       297: 2q^2
       298: 2q^2+q
       299: q^2
       300: q^3+3q^2+q
       301: 2q^2
       302: q^3+2q^2+q
       303: q^3+3q^2+q
       304: q^2
       305: 2q^2
       306: 2q^2+q
       307: q^2
       308: q^3+3q^2+q
       309: q^3+3q^2+q
       310: q^2
       311: 2q^2
       312: q^3+2q^2+q
       313: 2q^2
       314: 2q^2+q
       315: q^3+2q^2
       316: 2q^3+2q^2+q
       317: q^3+2q^2
       318: 3q^3+2q^2+q
       319: q^3+q^2
       320: 3q^3+3q^2+q
       321: 3q^3+3q^2+q
       322: q^3+q^2
       323: 2q^2
       324: q^3+2q^2+q
       325: q^3+2q^2
       326: 2q^3+2q^2+q
       328: q^3+q^2+q
       330: q^3+q^2+q
       332: q^3+q^2+q
       333: 2q^3+4q^2+q
       334: 2q^3+4q^2+q
       335: 2q^3+4q^2+q
       336: 4q^2+q
       337: q^3+7q^2+q
       338: 3q^2
       339: q^3+4q^2+q
       340: 3q^2
       341: q^3+4q^2+q
       342: q^3+2q^2
       343: q^4+2q^3+2q^2+q
       344: 2q^3+4q^2+q
       345: 2q^3+4q^2+q
       346: 4q^3+4q^2+q
       347: 2q^3+4q^2+q
       348: 2q^3+4q^2+q
       349: 2q^3+4q^2+q
       350: 2q^3+4q^2+q
       351: q^3+7q^2+q
       352: 2q^3+4q^2+q
       353: 2q^3+4q^2+q
       354: 4q^3+4q^2+q
       355: 2q^3+4q^2+q
       356: 2q^3+4q^2+q
       357: 2q^3+4q^2+q
       358: 2q^3+4q^2+q
       359: q^3+7q^2+q
       361: q^3+q^2+q
       363: q^3+q^2+q
       365: q^3+q^2+q
       366: 5q^3+4q^2+q
       367: 2q^3+4q^2+q
       368: 4q^3+4q^2+q
       369: 2q^3+4q^2+q
       370: 2q^3+4q^2+q
       371: 5q^2+q
       372: 5q^2+q
       373: 2q^3+3q^2+q
       374: 4q^3+4q^2+q
       375: 4q^3+4q^2+q
       376: 4q^3+4q^2+q
       377: q^2
       379: 2q^2+q
       380: q^2
       383: q^2+q
       385: q^2
       387: 2q^2+q
       388: q^2
       389: q^2
       391: q^2
       392: q^3+2q^2+q
       393: q^2
       395: 2q^2+q
       396: q^2
       397: q^2
       398: q^3+2q^2+q
       399: q^2
       401: q^2
       402: 2q^2+q
       404: q^2
       405: q^2
       406: q^2
       408: q^3+2q^2+q
       410: q^2+q
       412: q^3+q^2+q
       414: q^2+q
       416: q^2+q
       418: q^2+q
       419: q^2
       420: q^3+3q^2+q
       421: q^3+3q^2+q
       422: q^2
       423: 2q^2
       424: 2q^2+q
       425: 2q^2
       426: 2q^2+q
       427: 3q^2
       428: q^3+4q^2+q
       429: q^2
       430: q^3+3q^2+q
       431: q^3+3q^2+q
       432: q^2
       433: 2q^2
       434: 2q^2+q
       436: q^2+q
       437: q^2
       438: q^3+3q^2+q
       439: q^3+3q^2+q
       440: q^2
       441: 2q^2
       442: 2q^2+q
       443: 2q^2
       444: q^3+5q^2+q
       445: 3q^2
       446: q^3+4q^2+q
       447: q^2
       448: q^3+3q^2+q
       449: q^3+3q^2+q
       450: q^2
       451: 2q^2
       452: 2q^2+q
       453: q^2
       454: q^3+3q^2+q
       456: q^2+q
       457: q^3+3q^2+q
       458: q^2
       459: 2q^2
       460: 2q^2+q
       461: q^3+5q^2+q
       462: 2q^2
       463: 3q^2
       464: q^3+4q^2+q
       466: q^2+q
       468: q^3+q^2+q
       469: q^3+2q^2
       470: 2q^3+2q^2+q
       471: q^2
       472: q^3+3q^2+q
       473: q^3+3q^2+q
       474: q^2
       475: 2q^2
       476: 2q^2+q
       477: 2q^2
       478: q^3+2q^2+q
       479: 4q^2
       480: q^3+3q^2+q
       481: q^3+3q^2+q
       482: q^3+3q^2+q
       483: 4q^2+q
       484: 4q^2+q
       486: 2q^2+q
       488: 2q^2+q
       490: q^3+q^2+q
       491: 3q^2+q
       492: 2q^3+4q^2+q
       493: 2q^3+4q^2+q
       494: 2q^3+4q^2+q
       495: 4q^2+q
       496: 5q^2+q
       497: 2q^3+4q^2+q
       498: 2q^3+4q^2+q
       499: 2q^3+4q^2+q
       500: 4q^2+q
       501: 5q^2+q
       503: q^3+q^2+q
       505: q^3+q^2+q
       507: q^3+q^2+q
       508: 2q^3+4q^2+q
       509: 2q^3+4q^2+q
       510: 4q^3+4q^2+q
       511: 2q^3+4q^2+q
       512: 2q^3+4q^2+q
       513: 2q^3+4q^2+q
       514: 2q^3+4q^2+q
       515: 5q^2+q
       516: 5q^2+q
       517: 2q^3+3q^2+q
       518: 5q^2+q
       519: 5q^2+q
       520: 2q^3+3q^2+q
       523: q^2+q
       527: q^2+q
       529: q^2
       531: 2q^2+q
       532: q^2
       533: q^2
       535: 2q^2+q
       536: q^2
       540: q^2+q
       541: q^2
       543: q^2
       544: 2q^2+q
       545: q^2
       546: q^2
       547: 2q^2
       548: q^3+3q^2+q
       549: q^2
       550: 2q^2+q
       552: q^2
       554: q^2+q
       557: q^2
       558: 2q^2+q
       559: q^2
       561: 2q^2
       562: q^3+3q^2+q
       563: q^2
       564: q^2
       565: q^2
       567: 2q^2+q
       568: q^2
       569: q^2
       570: q^2
       572: q^3+2q^2+q
       573: 2q^2
       575: 2q^2
       576: q^3+3q^2+q
       577: 2q^2
       578: 2q^2
       580: q^2
       581: q^3+2q^2+q
       584: q^2+q
       586: q
       588: q^2+q
       589: q^2
       590: q^3+2q^2+q
       591: 2q^2+q
       594: 2q^2+q
       595: q^3+2q^2+q
       596: q^2
       598: q^2+q
       599: 2q^2
       600: 2q^2+q
       602: q^2+q
       603: q^2
       604: q^3+3q^2+q
       606: q^2+q
       607: q^3+3q^2+q
       608: q^2
       609: 2q^2
       610: 2q^2+q
       612: q^2+q
       613: 2q^2
       614: 2q^2+q
       615: q^2
       616: 3q^2+q
       618: 2q^2+q
       619: q^2
       620: q^3+3q^2+q
       621: q^3+3q^2+q
       622: q^2
       624: q^2+q
       625: 2q^2
       626: 2q^2+q
       628: q^2+q
       629: 2q^2
       630: 2q^2+q
       631: 3q^2+q
       632: q^2
       634: 2q^2+q
       636: q^2+q
       638: q^3+q^2+q
       640: q^2+q
       641: q^2
       642: q^3+3q^2+q
       643: q^3+3q^2+q
       644: q^2
       645: 2q^2
       646: 2q^2+q
       647: q^2
       648: q^3+3q^2+q
       649: q^3+3q^2+q
       650: q^2
       652: q^2+q
       653: 2q^2
       654: 2q^2+q
       655: 3q^2
       656: 2q^2+q
       657: 4q^2+q
       659: 2q^2+q
       661: 2q^2+q
       663: q^3+q^2+q
       664: 3q^2+q
       665: 2q^2+q
       667: 2q^2+q
       669: 2q^2+q
       671: q^3+q^2+q
       672: 4q^2+q
       673: 3q^2+q
       674: 5q^2+q
       675: q^3+3q^2+q
       676: q^3+3q^2+q
       677: 4q^2+q
       678: 5q^2+q
       679: 3q^2+q
       680: 5q^2+q
       681: q^3+3q^2+q
       682: q^3+3q^2+q
       683: 4q^2+q
       684: 5q^2+q
       685: 3q^2+q
       686: 2q^3+4q^2+q
       687: 2q^3+4q^2+q
       688: 2q^3+4q^2+q
       689: 4q^2+q
       690: 5q^2+q
       691: 5q^2+q
       692: 2q^3+3q^2+q
       693: q^2
       694: q^2
       697: q^2
       698: q^2
       700: q^3+2q^2+q
       701: q^2
       707: q^2+q
       711: q
       713: q^2
       714: q^2+q
       719: q^2+q
       720: q^2
       724: q^2+q
       725: q^2
       727: q^2
       728: 2q^2+q
       732: q^2+q
       736: q^2+q
       738: q^2+q
       741: q^2
       742: 2q^2+q
       743: q^2
       746: q^2+q
       750: q^2+q
       753: q^2
       755: 2q^2+q
       756: q^2
       760: q^2+q
       761: q^2
       762: q^2
       764: 2q^2+q
       765: q^2
       767: 2q^2+q
       768: q^2
       770: q^2
       773: q^2+q
       776: q^2+q
       778: q
       780: q^2+q
       782: q
       784: q^2+q
       786: q^2+q
       787: q^2+q
       790: q^2+q
       791: q^2
       792: q
       793: q^2
       794: 3q^2+q
       796: 2q^2+q
       798: q
       800: q^2+q
       801: q^2
       802: q^3+2q^2+q
       803: 2q^2+q
       806: 2q^2+q
       807: q^3+2q^2+q
       808: q^2
       810: q^2+q
       811: 2q^2
       812: 2q^2+q
       814: 2q^2+q
       815: q^2
       816: 3q^2+q
       817: 3q^2+q
       818: q^2
       820: 2q^2+q
       822: q
       824: q^2+q
       825: q^2
       826: q^3+2q^2+q
       827: 2q^2+q
       830: 2q^2+q
       831: q^3+2q^2+q
       832: q^2
       834: q^2+q
       835: 2q^2
       836: 2q^2+q
       838: 2q^2+q
       839: 3q^2+q
       840: q^2
       842: q^2+q
       843: 3q^2
       844: 2q^2+q
       845: q^2
       846: q^3+3q^2+q
       847: q^3+3q^2+q
       848: q^2
       850: q^2+q
       851: 2q^2
       852: 2q^2+q
       854: q^2+q
       855: 2q^2
       856: 2q^2+q
       857: 3q^2
       858: 2q^2+q
       860: 2q^2+q
       862: 2q^2+q
       864: q^3+q^2+q
       865: 4q^2+q
       866: 2q^2+q
       867: 3q^2+q
       868: 2q^2+q
       869: 5q^2+q
       870: 3q^2+q
       871: 2q^2+q
       872: 3q^2+q
       873: 5q^2+q
       874: 3q^2+q
       875: 2q^2+q
       876: 3q^2+q
       877: q^3+3q^2+q
       878: q^3+3q^2+q
       879: 4q^2+q
       880: 3q^2+q
       881: 3q
       882: 3q
       883: q^2+2q
       891: q^2+q
       898: q
       901: q
       907: q
       910: q
       915: q^2+q
       919: q^2+q
       923: q
       924: q^2
       925: q^2+q
       930: q^2
       931: q^2+q
       935: q^2+q
       937: q^2+q
       941: q^2+q
       945: q
       948: q^2
       949: q^2+q
       954: q^2+q
       955: q^2
       957: q^2+q
       963: q^2+q
       964: q^2
       966: 2q^2+q
       967: q^2
       969: q^2
       972: q^2+q
       974: q^2
       975: q^2
       977: 2q^2+q
       981: q^2+q
       983: q^2
       986: q^2+q
       988: q^2
       990: 2q^2+q
       991: q^2
       993: q^2+q
       995: q
       997: q^2+q
       998: q^2+q
      1001: q^2+q
      1003: q
      1005: q^2+q
      1006: q^2+q
      1008: q^2
      1009: q
      1011: q
      1012: q^2
      1013: q
      1015: 2q^2+q
      1016: q^2
      1017: 3q^2+q
      1019: q
      1021: q^2+q
      1023: q
      1025: q^2+q
      1027: q^2+q
      1028: q^2+q
      1031: 2q^2+q
      1032: 3q^2+q
      1033: q^2
      1035: q
      1037: q^2+q
      1039: q
      1041: q^2+q
      1043: q^2+q
      1044: q^2+q
      1046: 3q^2
      1047: 2q^2+q
      1049: q
      1051: q^2+q
      1052: q^2
      1053: q^3+2q^2+q
      1054: 2q^2+q
      1057: 2q^2+q
      1058: q^3+2q^2+q
      1059: q^2
      1061: q^2+q
      1062: 2q^2
      1063: 2q^2+q
      1064: q^2
      1065: q
      1067: 3q
      1069: 3q
      1071: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q^2+q
      1075: 3q
      1076: 2q^2+q
      1077: 3q^2+q
      1078: 2q^2+q
      1079: 3q
      1080: 2q^2+q
      1081: 3q^2+q
      1082: 2q^2+q
      1083: 2q^2+q
      1084: 3q^2+q
      1085: 3q^2+q
      1093: q^2+q
      1105: q^2+q
      1111: q
      1115: q
      1121: q
      1125: q
      1129: q
      1132: q
      1137: q
      1142: q
      1147: q^2+q
      1151: q
      1153: q
      1159: q
      1161: q
      1165: q^2+q
      1169: q
      1173: q
      1179: q
      1182: q
      1187: q^2+q
      1189: q^2
      1192: q^2+q
      1194: q^2
      1196: 2q^2+q
      1197: q^2
      1201: q
      1202: q^2
      1203: q^2+q
      1208: q^2
      1209: q^2+q
      1211: 3q
      1213: 2q
      1215: q
      1216: q^2+q
      1219: q^2+q
      1223: q
      1224: q^2
      1225: q
      1227: 3q
      1228: q
      1229: 2q
      1231: q
      1232: q^2+q
      1235: q^2+q
      1237: q^2+q
      1239: q
      1241: q^2+q
      1242: q^2+q
      1245: 3q
      1246: 2q
      1247: q
      1249: q
      1250: q^2+q
      1253: q^2+q
      1255: q^2+q
      1257: q
      1259: q^2+q
      1260: q^2+q
      1262: 2q
      1263: q
      1265: q
      1267: q
      1269: q^2+q
      1270: q^2+q
      1273: q^2+q
      1275: q^2+q
      1276: q^2
      1277: q
      1279: q
      1280: q^2
      1281: q
      1282: 2q
      1283: 2q^2+q
      1284: 2q
      1285: 2q^2+q
      1286: 2q
      1287: 2q^2+q
      1288: 3q^2+q
      1289: 2q^2+q
      1297: q
      1309: q^2+q
      1315: q
      1321: q
      1325: q
      1328: q
      1338: q
      1341: q
      1343: 2q
      1345: q
      1349: q
      1355: q
      1359: q
      1362: q
      1365: q
      1370: q
      1373: 2q
      1375: q
      1377: q
      1381: q
      1387: q
      1391: q
      1395: q
      1398: q
      1403: q
      1405: 2q
      1408: q
      1410: q
      1412: q
      1413: q
      1417: q
      1419: q
      1425: q
      1428: q
      1434: q
      1439: 2q
      1440: q
      1443: q
      1444: q
      1449: q
      1450: q^2+q
      1453: 2q
      1455: q^2+q
      1457: q
      1459: 2q
      1460: q^2+q
      1463: q^2+q
      1465: q
      1466: q^2+q
      1469: q^2+q
      1471: q
      1473: q^2+q
      1477: q^2+q
      1478: q^2+q
      1481: q
      1482: q^2
      1483: q
      1484: q
      1485: 2q
      1486: 2q
      1487: 2q^2+q
      1488: 2q
      1496: q
      1507: q
      1520: q
      1526: q
      1532: q
      1533: q
      1542: q
      1548: q
      1554: q
      1564: q
      1570: q
      1573: q
      1576: q
      1584: q
      1590: q
      1594: q
      1597: q
      1604: q
      1608: q
      1614: q
      1618: q
      1621: q
      1625: q
      1629: q
      1635: q
      1639: q
      1644: 2q
      1645: q
      1648: q
      1649: q
      1652: 2q
      1653: q
      1656: q
      1658: q
      1662: q
      1663: q^2+q
      1666: q^2+q
      1668: 2q
      1669: q
      1673: q
      1674: 2q
      1693: q
      1706: q
      1717: q
      1724: q
      1738: q
      1748: q
      1762: q
      1768: q
      1786: q
      1792: q
      1795: q
      1799: q
      1802: q
      1813: q
      1819: q
      1822: q
      1825: q
      1828: 2q
      1829: q
      1832: q
      1833: 1
      1876: q
      1927: q
      1933: q
      1939: q
      1954: q
      1957: 1
      1960: 1
      1962: 1
      1965: 1
      2027: 1
      2033: 1
      2040: 1
      2047: 1
      2054: 1
      2066: 1
      2069: 1
      2086: 1
      2109: 1
      2132: 1
      2150: 1

2151:    0: q^5+q^4+q^2
         1: q^4+q^2
         2: q^5+q^4+q^2
         3: q^5+q^4+q^2
         4: q^5+q^4+q^2
         5: q^4+q^2
         6: q^4+q^2
         7: q^5+q^4+q^2
         8: q^4+q^2
         9: q^5+q^4+q^2
        10: q^2
        11: q^2
        12: q^2
        13: q^5+q^4+q^2
        14: q^5+q^4+q^2
        15: q^4+q^2
        16: q^5+q^4+q^2
        17: q^4+q^2
        18: q^5+q^4+q^2
        19: q^5+q^4+q^2
        20: q^4+q^2
        21: q^5+q^4+q^2
        22: q^4+q^2
        23: q^4+q^2
        24: q^4+q^2
        25: q^4+q^2
        26: q^4+q^2
        27: q^4+q^2
        28: q^2
        29: q^2
        30: q^5+q^4+q^2
        31: q^2
        32: q^4+q^2
        33: q^4+q^2
        34: q^2
        35: q^4+q^2
        36: q^4+q^2
        37: q^4+q^2
        39: q^4+q^2
        41: q^4+q^2
        43: q^2
        44: q^2
        45: q^2
        46: q^5+q^4+q^2
        47: q^4+q^2
        48: q^5+q^4+q^2
        49: q^5+q^4+q^2
        50: q^4+q^2
        51: q^5+q^4+q^2
        52: q^4+q^2
        53: q^4+q^2
        54: q^4+q^2
        55: q^4+q^2
        56: q^4+q^2
        57: q^4+q^2
        58: q^2
        60: q^2
        62: q^2
        64: q^4+q^2
        66: q^4+q^2
        68: q^2
        69: q^5+q^4+q^2
        70: q^2
        71: q^2
        72: q^4+q^2
        73: q^4+q^2
        74: q^4+q^2
        76: q^4+q^2
        78: q^4+q^2
        80: q^2
        81: q^4+q^2
        82: q^2
        83: q^4+q^2
        84: q^2
        85: q^4+q^2
        86: q^2
        87: q^4+q^2
        88: q^2
        89: q^2
        90: q^2
        91: q^5+q^4+q^2
        92: q^4+q^2
        93: q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^4+q^2
       100: q^4+q^2
       101: q^2
       102: q^4+q^2
       103: q^2
       107: q^2
       109: q^2
       111: q^4+q^2
       113: q^2
       115: q^4+q^2
       117: q^2
       119: q^2
       121: q^2
       123: q^4+q^2
       125: q^2
       126: q^2
       127: q^4+q^2
       129: q^4+q^2
       131: q^4+q^2
       133: q^2
       134: q^5+q^4+q^2
       135: q^4+q^2
       136: q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: q^2
       147: q^4+q^2
       148: q^2
       149: q^2
       150: q^4+q^2
       151: q^4+q^2
       153: q^2
       155: q^4+q^2
       157: q^2
       158: q^2
       159: q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       169: q^2
       173: q^2
       177: q^4+q^2
       179: q^2
       181: q^4+q^2
       183: q^2
       185: q^2
       187: q^4+q^2
       189: q^2
       191: q^2
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       199: q^2
       201: q^2
       203: q^2
       205: q^2
       207: q^2
       209: q^2
       211: q^4+q^2
       213: q^4+q^2
       215: q^4+q^2
       217: q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       237: q^4+q^2
       239: q^2
       241: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
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       255: q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       259: q^2
       263: q^2
       267: q^2
       271: q^2
       275: q^2
       279: q^2
       281: q^4+q^2
       283: q^2
       285: q^2
       287: q^2
       289: q^4+q^2
       291: q^4+q^2
       293: q^2
       295: q^2
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       311: q^2
       313: q^2
       315: q^4+q^2
       317: q^2
       319: q^2
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       325: q^2
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       331: q^2
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       335: q^2
       336: q^4+q^2
       337: q^2
       338: q^4+q^2
       340: q^2
       342: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
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       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       360: q^4+q^2
       362: q^2
       364: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       377: q^2
       381: q^2
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       397: q^2
       401: q^2
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       415: q^2
       417: q^4+q^2
       419: q^2
       421: q^2
       423: q^2
       425: q^4+q^2
       427: q^2
       429: q^2
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       463: q^2
       465: q^2
       467: q^4+q^2
       469: q^2
       471: q^2
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       475: q^2
       477: q^2
       479: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       485: q^4+q^2
       487: q^2
       489: q^4+q^2
       491: q^4+q^2
       492: q^2
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       501: q^2
       508: q^2
       512: q^2
       514: q^2
       515: q^4+q^2
       516: q^2
       517: q^4+q^2
       521: q^2
       525: q^2
       529: q^2
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       537: q^2
       541: q^2
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       569: q^2
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       583: q^2
       585: q^2
       587: q^2
       589: q^2
       591: q^2
       593: q^2
       595: q^2
       597: q^4+q^2
       599: q^2
       601: q^2
       603: q^2
       605: q^2
       607: q^2
       609: q^2
       613: q^2
       615: q^2
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       619: q^2
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       629: q^2
       631: q^2
       633: q^2
       639: q^2
       641: q^2
       643: q^2
       645: q^2
       651: q^2
       655: q^2
       657: q^2
       658: q^4+q^2
       660: q^2
       662: q^4+q^2
       664: q^4+q^2
       665: q^2
       674: q^2
       675: q^2
       676: q^2
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       693: q^2
       705: q^2
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       713: q^2
       717: q^2
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       733: q^2
       737: q^2
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       749: q^2
       753: q^2
       757: q^2
       765: q^2
       769: q^2
       775: q^2
       777: q^2
       779: q^4+q^2
       781: q^2
       785: q^2
       787: q^2
       791: q^2
       793: q^2
       795: q^2
       797: q^2
       801: q^2
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       833: q^2
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       849: q^2
       853: q
       855: q^2
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       940: q^2
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       952: q^2
       960: q^2
       964: q^2
       968: q^2
       978: q
       984: q
       994: q^2
       998: q^2
      1000: q^2
      1010: q^2
      1012: q^2
      1020: q^2
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      1026: q^2
      1028: q^2
      1036: q^2
      1038: q^2
      1040: q^2
      1044: q^2
      1050: q
      1060: q^2
      1064: q^2
      1076: q^2
      1080: q^2
      1084: q^2
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      1100: q
      1114: q^2
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      1130: q^2
      1138: q^2
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      1160: q^2
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      1180: q^2
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      1190: q
      1222: q
      1230: q^2
      1232: q^2
      1234: q^2
      1248: q^2
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      1264: q
      1274: q^2
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      1348: q^2
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      1380: q^2
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      1392: q^2
      1396: q^2
      1406: q
      1414: q
      1430: q^2
      1446: q
      1491: q
      1501: q^2
      1513: q^2
      1527: q
      1555: q
      1559: q
      1637: q
      1677: q
      1725: q
      1729: q
      1793: 1
      1836: q
      1872: 1
      1948: 1
      1992: 1
      2006: 1
      2056: 1
      2094: 1
      2110: 1
      2117: 1
      2151: 1

2152:    0: 3q^5+5q^4+5q^3+2q^2
         1: 3q^5+5q^4+5q^3+2q^2
         2: 3q^5+5q^4+5q^3+2q^2
         3: 3q^5+5q^4+5q^3+2q^2
         4: q^6+3q^5+5q^4+4q^3+2q^2
         5: 3q^5+5q^4+5q^3+2q^2
         6: q^6+3q^5+5q^4+4q^3+2q^2
         7: q^6+3q^5+5q^4+4q^3+2q^2
         8: 3q^5+5q^4+5q^3+2q^2
         9: q^7+2q^6+3q^5+4q^4+3q^3+2q^2
        10: q^5+4q^4+5q^3+2q^2
        11: q^5+4q^4+5q^3+2q^2
        12: 2q^5+4q^4+4q^3+2q^2
        13: 3q^5+5q^4+5q^3+2q^2
        14: q^6+3q^5+5q^4+4q^3+2q^2
        15: 3q^5+5q^4+5q^3+2q^2
        16: q^5+4q^4+5q^3+2q^2
        17: q^5+4q^4+5q^3+2q^2
        18: q^6+2q^5+4q^4+3q^3+2q^2
        19: 2q^5+4q^4+4q^3+2q^2
        20: 2q^5+4q^4+4q^3+2q^2
        21: 2q^5+4q^4+4q^3+2q^2
        22: 3q^5+5q^4+5q^3+2q^2
        23: 3q^5+5q^4+5q^3+2q^2
        24: 3q^5+5q^4+5q^3+2q^2
        25: 3q^5+5q^4+5q^3+2q^2
        26: 3q^5+5q^4+5q^3+2q^2
        27: 3q^5+5q^4+5q^3+2q^2
        28: 3q^4+5q^3+2q^2
        29: q^5+3q^4+4q^3+2q^2
        30: 2q^5+4q^4+4q^3+2q^2
        31: q^5+4q^4+5q^3+2q^2
        32: 3q^5+5q^4+5q^3+2q^2
        33: q^5+4q^4+5q^3+2q^2
        34: q^5+4q^4+5q^3+2q^2
        35: 3q^5+5q^4+5q^3+2q^2
        36: q^5+4q^4+5q^3+2q^2
        37: 2q^5+4q^4+4q^3+2q^2
        38: q^5+q^4+q^3
        39: 2q^5+4q^4+4q^3+2q^2
        40: q^5+q^4+q^3
        41: 2q^5+4q^4+4q^3+2q^2
        42: q^5+q^4+q^3
        43: q^5+4q^4+5q^3+2q^2
        44: 2q^5+4q^4+4q^3+2q^2
        45: q^5+4q^4+5q^3+2q^2
        46: q^5+4q^4+5q^3+2q^2
        47: q^5+4q^4+5q^3+2q^2
        48: q^6+2q^5+4q^4+3q^3+2q^2
        49: 3q^4+4q^3+2q^2
        50: 3q^4+4q^3+2q^2
        51: q^5+3q^4+3q^3+2q^2
        52: 2q^5+4q^4+4q^3+2q^2
        53: 2q^5+4q^4+4q^3+2q^2
        54: 2q^5+4q^4+4q^3+2q^2
        55: 2q^5+4q^4+4q^3+2q^2
        56: 2q^5+4q^4+4q^3+2q^2
        57: 2q^5+4q^4+4q^3+2q^2
        58: q^4+2q^3+q^2
        59: 2q^4+3q^3+q^2
        60: 2q^4+3q^3+q^2
        61: q^4+2q^3+q^2
        62: q^5+3q^4+4q^3+2q^2
        63: q^4+q^3
        64: 2q^5+4q^4+4q^3+2q^2
        65: q^5+q^4+q^3
        66: q^5+3q^4+4q^3+2q^2
        67: q^4+q^3
        68: 3q^4+5q^3+2q^2
        69: 2q^4+3q^3+2q^2
        70: q^5+3q^4+4q^3+2q^2
        71: 2q^4+4q^3+2q^2
        72: 2q^4+3q^3+2q^2
        73: 2q^4+3q^3+2q^2
        74: q^5+3q^4+3q^3+2q^2
        76: q^5+3q^4+3q^3+2q^2
        78: q^5+3q^4+3q^3+2q^2
        80: q^5+4q^4+5q^3+2q^2
        81: q^5+4q^4+5q^3+2q^2
        82: q^5+3q^4+4q^3+2q^2
        83: 2q^5+4q^4+4q^3+2q^2
        84: q^5+4q^4+5q^3+2q^2
        85: q^5+4q^4+5q^3+2q^2
        86: q^5+3q^4+4q^3+2q^2
        87: 2q^5+4q^4+4q^3+2q^2
        88: 2q^4+5q^3+2q^2
        89: 2q^4+5q^3+2q^2
        90: q^5+3q^4+3q^3+2q^2
        91: 3q^4+4q^3+2q^2
        92: 3q^4+4q^3+2q^2
        93: q^5+3q^4+3q^3+2q^2
        94: 3q^4+4q^3+2q^2
        95: 3q^4+4q^3+2q^2
        96: q^5+3q^4+3q^3+2q^2
        97: 3q^4+4q^3+2q^2
        98: 3q^4+4q^3+2q^2
        99: q^5+3q^4+3q^3+2q^2
       100: 2q^5+4q^4+4q^3+2q^2
       101: 2q^5+4q^4+4q^3+2q^2
       102: 2q^5+4q^4+4q^3+2q^2
       103: q^4+2q^3+q^2
       104: q^4+q^3
       106: q^4+2q^3+q^2
       107: q^4+2q^3+q^2
       108: q^3+q^2
       109: q^3+q^2
       110: q^4+2q^3+q^2
       111: q^4+2q^3+2q^2
       113: q^5+2q^4+3q^3+2q^2
       115: q^5+3q^4+3q^3+2q^2
       117: q^4+2q^3+q^2
       118: 2q^4+3q^3+q^2
       119: 2q^4+3q^3+q^2
       120: q^4+2q^3+q^2
       121: q^5+3q^4+4q^3+2q^2
       122: q^4+q^3
       123: q^5+3q^4+4q^3+2q^2
       124: q^4+q^3
       125: 2q^4+5q^3+2q^2
       126: q^4+3q^3+2q^2
       127: q^4+3q^3+2q^2
       129: q^4+3q^3+2q^2
       131: 2q^4+2q^3+2q^2
       133: 2q^4+4q^3+2q^2
       134: 2q^4+3q^3+2q^2
       135: 2q^4+3q^3+2q^2
       136: 2q^4+3q^3+2q^2
       137: 2q^4+5q^3+2q^2
       138: 2q^4+3q^3+2q^2
       139: 2q^4+4q^3+2q^2
       140: 2q^4+3q^3+2q^2
       141: q^5+3q^4+4q^3+2q^2
       142: 2q^4+3q^3+2q^2
       143: 2q^4+5q^3+2q^2
       144: 2q^4+3q^3+2q^2
       145: 2q^4+4q^3+2q^2
       146: q^5+3q^4+4q^3+2q^2
       147: 2q^4+3q^3+2q^2
       148: 2q^4+3q^3+2q^2
       149: q^5+3q^4+4q^3+2q^2
       150: 2q^5+4q^4+4q^3+2q^2
       151: q^5+3q^4+3q^3+2q^2
       153: q^5+3q^4+3q^3+2q^2
       155: q^5+3q^4+3q^3+2q^2
       157: 4q^3+2q^2
       158: 4q^3+2q^2
       159: q^4+3q^3+2q^2
       160: 3q^4+4q^3+2q^2
       161: 3q^4+4q^3+2q^2
       162: q^5+3q^4+3q^3+2q^2
       163: 3q^4+4q^3+2q^2
       164: 3q^4+4q^3+2q^2
       165: q^5+3q^4+3q^3+2q^2
       166: 3q^4+4q^3+2q^2
       167: 3q^4+4q^3+2q^2
       168: q^5+3q^4+3q^3+2q^2
       169: q^3+q^2
       172: q^3+q^2
       173: q^4+2q^3+q^2
       174: q^4+q^3
       176: q^4+2q^3+q^2
       177: q^4+2q^3+2q^2
       179: q^4+3q^3+2q^2
       181: 2q^3+2q^2
       183: q^4+2q^3+q^2
       184: q^3+q^2
       185: q^3+q^2
       186: q^4+2q^3+q^2
       187: q^4+2q^3+2q^2
       189: q^5+2q^4+3q^3+2q^2
       191: q^4+2q^3+q^2
       192: q^4+3q^3+q^2
       193: q^4+2q^3+q^2
       194: q^3+q^2
       195: q^3+q^2
       196: q^4+2q^3+q^2
       197: q^4+2q^3+2q^2
       199: q^4+3q^3+q^2
       200: q^4+2q^3+q^2
       201: q^4+2q^3+q^2
       202: q^3+q^2
       203: q^3+q^2
       204: q^4+2q^3+q^2
       205: q^4+2q^3+2q^2
       207: 2q^4+4q^3+2q^2
       208: q^3
       209: q^5+2q^4+3q^3+2q^2
       211: q^5+3q^4+3q^3+2q^2
       213: q^4+3q^3+2q^2
       215: q^4+3q^3+2q^2
       217: 2q^4+2q^3+2q^2
       219: q^4+3q^3+2q^2
       220: 4q^3+2q^2
       221: 3q^3+2q^2
       222: 3q^3+2q^2
       223: q^4+2q^3+2q^2
       224: 3q^3+2q^2
       225: q^4+2q^3+2q^2
       226: q^4+3q^3+2q^2
       227: 2q^4+4q^3+2q^2
       228: 2q^4+3q^3+2q^2
       229: 2q^4+3q^3+2q^2
       230: 2q^4+3q^3+2q^2
       231: q^4+3q^3+2q^2
       232: 2q^4+4q^3+2q^2
       233: 2q^4+3q^3+2q^2
       234: 2q^4+3q^3+2q^2
       235: 2q^4+3q^3+2q^2
       236: 2q^4+3q^3+2q^2
       237: q^4+3q^3+2q^2
       239: q^4+3q^3+2q^2
       241: 2q^4+2q^3+2q^2
       243: 2q^4+4q^3+2q^2
       244: 2q^4+3q^3+2q^2
       245: 2q^4+3q^3+2q^2
       246: q^5+3q^4+4q^3+2q^2
       247: 3q^3+3q^2
       248: 3q^3+3q^2
       249: 2q^4+2q^3+2q^2
       250: 4q^3+2q^2
       251: 4q^3+2q^2
       252: q^4+3q^3+2q^2
       253: 4q^3+2q^2
       254: 4q^3+2q^2
       255: q^4+3q^3+2q^2
       256: 3q^4+4q^3+2q^2
       257: 3q^4+4q^3+2q^2
       258: q^5+3q^4+3q^3+2q^2
       259: q^3+q^2
       262: q^3+q^2
       263: q^3+q^2
       266: q^3+q^2
       267: q^3+q^2
       269: q^3+q^2
       271: q^3+q^2
       273: q^3+q^2
       275: q^4+2q^3+q^2
       276: q^3
       278: q^4+2q^3+q^2
       279: q^4+3q^3+2q^2
       281: q^4+2q^3+2q^2
       283: q^3+q^2
       284: q^2
       285: q^2
       286: q^3+q^2
       287: q^4+2q^3+2q^2
       289: 2q^3+2q^2
       291: q^3+2q^2
       293: 2q^3+q^2
       294: q^3+q^2
       295: q^3+q^2
       296: 2q^3+q^2
       297: 2q^3+2q^2
       299: q^4+2q^3+q^2
       300: q^3+q^2
       301: 2q^3+2q^2
       303: q^3+q^2
       304: q^4+2q^3+q^2
       305: q^4+2q^3+2q^2
       307: q^4+2q^3+q^2
       308: q^3+q^2
       309: q^3+q^2
       310: q^4+2q^3+q^2
       311: 2q^3+2q^2
       313: q^4+2q^3+2q^2
       315: q^4+2q^3+2q^2
       317: q^4+3q^3+2q^2
       319: q^4+2q^3+q^2
       320: q^3+q^2
       321: q^3+q^2
       322: q^4+2q^3+q^2
       323: q^4+2q^3+2q^2
       325: q^5+2q^4+3q^3+2q^2
       327: q^3+2q^2
       329: q^3+2q^2
       331: q^3+2q^2
       333: 3q^3+2q^2
       334: 2q^3+2q^2
       335: 2q^3+2q^2
       336: q^3+2q^2
       337: 3q^3+3q^2
       338: 3q^3+3q^2
       340: 3q^3+3q^2
       342: 2q^4+2q^3+2q^2
       344: q^4+3q^3+2q^2
       345: 4q^3+2q^2
       346: 3q^3+2q^2
       347: 3q^3+2q^2
       348: q^4+2q^3+2q^2
       349: 3q^3+2q^2
       350: q^4+2q^3+2q^2
       351: 3q^3+3q^2
       352: q^4+3q^3+2q^2
       353: 4q^3+2q^2
       354: 3q^3+2q^2
       355: 3q^3+2q^2
       356: q^4+2q^3+2q^2
       357: 3q^3+2q^2
       358: q^4+2q^3+2q^2
       359: 3q^3+3q^2
       360: q^4+3q^3+2q^2
       362: q^4+3q^3+2q^2
       364: 2q^4+2q^3+2q^2
       366: q^4+3q^3+2q^2
       367: 2q^4+4q^3+2q^2
       368: 2q^4+3q^3+2q^2
       369: 2q^4+3q^3+2q^2
       370: 2q^4+3q^3+2q^2
       371: 3q^3+3q^2
       372: 3q^3+3q^2
       373: 2q^4+2q^3+2q^2
       374: 4q^3+2q^2
       375: 4q^3+2q^2
       376: q^4+3q^3+2q^2
       377: q^2
       380: q^2
       381: q^3+q^2
       384: q^3+q^2
       385: q^3+q^2
       388: q^3+q^2
       389: q^3+q^2
       391: q^3+q^2
       393: q^3+q^2
       396: q^3+q^2
       397: q^3+q^2
       399: q^3+q^2
       401: q^3+q^2
       404: q^3+q^2
       405: q^3+q^2
       406: q^3+q^2
       409: q^3+2q^2
       411: q^3+2q^2
       413: q^4+2q^3+2q^2
       415: 2q^2
       417: q^3+2q^2
       419: q^3+q^2
       420: q^2
       421: q^2
       422: q^3+q^2
       423: q^3+2q^2
       425: q^3+2q^2
       427: 3q^3+3q^2
       429: q^3+q^2
       430: q^2
       431: q^2
       432: q^3+q^2
       433: q^3+2q^2
       435: 2q^3+2q^2
       437: 2q^3+q^2
       438: q^3+q^2
       439: q^3+q^2
       440: 2q^3+q^2
       441: 2q^3+2q^2
       443: 2q^3+2q^2
       444: q^3+q^2
       445: 3q^3+3q^2
       447: q^3+q^2
       448: q^2
       449: q^2
       450: q^3+q^2
       451: q^3+2q^2
       453: 2q^3+q^2
       454: q^3+q^2
       455: 2q^3+2q^2
       457: q^3+q^2
       458: 2q^3+q^2
       459: 2q^3+2q^2
       461: q^3+q^2
       462: 2q^3+2q^2
       463: 3q^3+3q^2
       465: q^4+3q^3+2q^2
       467: q^4+2q^3+2q^2
       469: q^4+2q^3+2q^2
       471: q^4+2q^3+q^2
       472: q^3+q^2
       473: q^3+q^2
       474: q^4+2q^3+q^2
       475: q^4+2q^3+2q^2
       477: 2q^3+2q^2
       479: 2q^3+2q^2
       480: q^3+q^2
       481: 2q^3+2q^2
       482: 2q^3+2q^2
       483: q^3+2q^2
       484: 3q^3+3q^2
       485: 3q^3+3q^2
       487: 3q^3+3q^2
       489: 2q^4+2q^3+2q^2
       491: q^3+2q^2
       492: 3q^3+2q^2
       493: 2q^3+2q^2
       494: 2q^3+2q^2
       495: q^3+2q^2
       496: 3q^3+3q^2
       497: 3q^3+2q^2
       498: 2q^3+2q^2
       499: 2q^3+2q^2
       500: q^3+2q^2
       501: 3q^3+3q^2
       502: q^3+2q^2
       504: q^3+2q^2
       506: q^3+2q^2
       508: q^4+3q^3+2q^2
       509: 4q^3+2q^2
       510: 3q^3+2q^2
       511: 3q^3+2q^2
       512: q^4+2q^3+2q^2
       513: 3q^3+2q^2
       514: q^4+2q^3+2q^2
       515: 3q^2
       516: 3q^2
       517: q^3+2q^2
       518: 3q^2
       519: 3q^2
       520: q^3+2q^2
       521: q^2
       524: q^2
       525: q^2
       528: q^2
       529: q^2
       532: q^2
       533: q^2
       536: q^2
       537: q^3+q^2
       539: q^3+q^2
       541: q^3+q^2
       543: q^3+q^2
       545: 2q^3+2q^2
       547: q^3+q^2
       549: q^2
       552: q^2
       553: q^3+q^2
       555: q^3+q^2
       557: q^3+q^2
       559: q^3+q^2
       561: q^3+q^2
       563: 2q^3+2q^2
       565: q^3+q^2
       568: q^3+q^2
       569: q^3+q^2
       570: q^3+q^2
       573: q^3+q^2
       574: q^3+q^2
       575: q^3+q^2
       577: 2q^3+2q^2
       580: q^3+q^2
       583: q^3+2q^2
       585: q^3+2q^2
       587: 2q^2
       589: q^3+q^2
       590: q^2
       592: q^2
       593: q^2
       595: q^2
       596: q^3+q^2
       597: q^3+2q^2
       599: q^3+2q^2
       601: 3q^3+3q^2
       603: q^3+q^2
       604: q^2
       605: q^3+2q^2
       607: q^2
       608: q^3+q^2
       609: q^3+2q^2
       611: 2q^2
       613: q^3+2q^2
       615: 2q^3+2q^2
       616: q^3+q^2
       617: 3q^3+3q^2
       619: q^3+q^2
       620: q^2
       621: q^2
       622: q^3+q^2
       623: q^3+2q^2
       625: q^3+2q^2
       627: 2q^2
       629: q^3+2q^2
       631: q^3+q^2
       632: 2q^3+2q^2
       633: 3q^3+3q^2
       635: q^3+2q^2
       637: q^3+2q^2
       639: q^4+2q^3+2q^2
       641: q^3+q^2
       642: q^2
       643: q^2
       644: q^3+q^2
       645: q^3+2q^2
       647: 2q^3+q^2
       648: q^3+q^2
       649: q^3+q^2
       650: 2q^3+q^2
       651: 2q^3+2q^2
       653: 2q^3+2q^2
       655: 2q^3+2q^2
       656: q^3+q^2
       657: 3q^2
       658: 3q^2
       660: 3q^2
       662: q^3+2q^2
       664: 2q^2
       665: q^3+2q^2
       666: 3q^2
       668: 3q^2
       670: q^3+2q^2
       672: 3q^2
       673: 2q^2
       674: 3q^2
       675: 2q^3+2q^2
       676: 2q^3+2q^2
       677: q^3+2q^2
       678: 3q^2
       679: q^3+2q^2
       680: 3q^2
       681: 2q^3+2q^2
       682: 2q^3+2q^2
       683: q^3+2q^2
       684: 3q^2
       685: q^3+2q^2
       686: 3q^3+2q^2
       687: 2q^3+2q^2
       688: 2q^3+2q^2
       689: q^3+2q^2
       693: q^3+q^2
       696: q^3+q^2
       697: q^3+q^2
       705: q^2
       708: q^2
       709: q^2
       712: q^2
       716: q^2
       717: q^2
       721: q^2
       723: q^2
       725: q^2
       727: q^2
       729: q^2
       731: q^2
       733: 2q^3+2q^2
       735: q^3+q^2
       737: q^2
       739: q^2
       741: q^2
       743: q^2
       745: q^2
       747: q^2
       749: q^3+q^2
       751: 2q^3+2q^2
       753: q^2
       756: q^2
       757: q^3+q^2
       758: q^3+q^2
       761: q^3+q^2
       762: q^3+q^2
       765: q^3+q^2
       766: q^3+q^2
       768: q^3+q^2
       769: 2q^3+2q^2
       772: q^3+q^2
       775: 3q^2
       777: 2q^2
       779: 2q^2
       781: q^3+2q^2
       783: 2q^2
       785: q^2
       788: q^2
       789: 3q^2
       791: q^2
       793: 2q^2
       794: q^2
       795: 3q^2
       797: q^3+2q^2
       799: 2q^2
       801: q^3+q^2
       802: q^2
       804: q^2
       805: q^2
       807: q^2
       808: q^3+q^2
       809: q^3+2q^2
       811: q^3+2q^2
       813: 3q^2
       815: 2q^2
       816: q^2
       817: q^2
       818: 2q^2
       819: 3q^2
       821: q^3+2q^2
       823: 2q^2
       825: q^3+q^2
       826: q^2
       828: q^2
       829: q^2
       831: q^2
       832: q^3+q^2
       833: q^3+2q^2
       835: q^3+2q^2
       837: 3q^2
       839: q^2
       840: 2q^2
       841: q^3+2q^2
       843: 2q^2
       844: q^2
       845: q^3+q^2
       846: q^2
       847: q^2
       848: q^3+q^2
       849: q^3+2q^2
       851: q^3+2q^2
       853: 2q^2
       855: q^3+2q^2
       857: 2q^2
       858: q^2
       866: 2q^2
       868: 2q^2
       870: 2q^2
       871: q^3+2q^2
       872: 2q^2
       874: 2q^2
       875: q^3+2q^2
       876: 2q^2
       877: 2q^3+2q^2
       878: 2q^3+2q^2
       879: q^3+2q^2
       880: q^3+2q^2
       884: q^3+q^2
       887: q^3+q^2
       889: q^3+q^2
       896: q^2
       899: q^2
       902: q^2
       904: q^2
       912: q^2
       914: q^2
       916: 2q^2
       918: q^2
       920: q^2
       922: q^2
       927: q^2
       928: q^2
       932: 2q^2
       934: q^2
       936: q^2
       938: q^2
       940: q^2
       942: 2q^2
       944: q^2
       946: q^2
       950: q^2
       952: q^2
       956: q^2
       958: 2q^2
       960: q^2
       961: q^2
       964: q^2
       965: q^2
       967: q^2
       968: 2q^2
       971: q^2
       974: q^2
       975: q^2
       978: q^2
       979: q^2
       982: 2q^2
       985: q^2
       988: q^2
       989: q^2
       991: q^2
       994: 2q^2
       999: q^2
      1000: q^2
      1002: 2q^2
      1004: q^2
      1007: q^2
      1008: q^2
      1010: q^2
      1012: q^2
      1018: 2q^2
      1020: 2q^2
      1022: q^3+2q^2
      1024: 2q^2
      1026: q^2
      1029: q^2
      1034: 2q^2
      1036: 2q^2
      1038: q^3+2q^2
      1040: q^2
      1042: 2q^2
      1045: q^2
      1048: q^3+2q^2
      1050: 2q^2
      1052: q^3+q^2
      1053: q^2
      1055: q^2
      1056: q^2
      1058: q^2
      1059: q^3+q^2
      1060: q^3+2q^2
      1062: q^3+2q^2
      1064: q^2
      1076: 2q^2
      1078: 2q^2
      1080: 2q^2
      1082: 2q^2
      1083: q^3+2q^2
      1084: 2q^2
      1085: 2q^2
      1086: q^2
      1089: q^2
      1091: q^2
      1098: q^2
      1101: q^2
      1102: q^2
      1112: q^2
      1116: q^2
      1118: q^2
      1122: q^2
      1138: q^2
      1148: q^2
      1150: q^2
      1154: q^2
      1156: q^2
      1168: q^2
      1170: q^2
      1174: q^2
      1176: q^2
      1184: q^2
      1185: q^2
      1198: q^2
      1199: q^2
      1204: q^2
      1206: q^2
      1220: q^2
      1222: q^2
      1230: 2q^2
      1233: q^2
      1234: q^2
      1238: 2q^2
      1240: q^2
      1243: q^2
      1248: 2q^2
      1251: q^2
      1254: q^2
      1256: 2q^2
      1258: q^2
      1261: q^2
      1264: 2q^2
      1266: q^3+2q^2
      1268: q^2
      1271: q^2
      1272: 2q^2
      1274: 2q^2
      1276: q^2
      1278: q^2
      1280: q^2
      1287: 2q^2
      1289: 2q^2
      1346: q^2
      1350: q^2
      1352: q^2
      1356: q^2
      1378: q^2
      1382: q^2
      1384: q^2
      1388: q^2
      1414: q^2
      1415: q^2
      1420: q^2
      1422: q^2
      1430: q^2
      1446: q^2
      1464: 2q^2
      1467: q^2
      1468: q^2
      1470: 2q^2
      1474: q^2
      1476: q^2
      1479: q^2
      1480: q^2
      1484: q
      1605: q^2
      1609: q^2
      1611: q^2
      1615: q^2
      1637: q
      1641: q
      1650: q
      1657: q
      1671: q^2
      1725: q
      1759: q
      1781: q
      1812: q
      1823: q
      1884: q
      1928: q
      1958: 1
      2028: 1
      2037: 1
      2048: 1
      2075: 1
      2082: 1
      2118: 1
      2152: 1

2153:    0: 3q^5+5q^4+5q^3+2q^2
         1: 3q^5+5q^4+5q^3+2q^2
         2: 3q^5+5q^4+5q^3+2q^2
         3: 3q^5+5q^4+5q^3+2q^2
         4: q^6+3q^5+5q^4+4q^3+2q^2
         5: 3q^5+5q^4+5q^3+2q^2
         6: q^6+3q^5+5q^4+4q^3+2q^2
         7: q^6+3q^5+5q^4+4q^3+2q^2
         8: 3q^5+5q^4+5q^3+2q^2
         9: q^7+2q^6+3q^5+4q^4+3q^3+2q^2
        10: q^5+4q^4+5q^3+2q^2
        11: q^5+4q^4+5q^3+2q^2
        12: 2q^5+4q^4+4q^3+2q^2
        13: 3q^5+5q^4+5q^3+2q^2
        14: q^6+3q^5+5q^4+4q^3+2q^2
        15: 3q^5+5q^4+5q^3+2q^2
        16: q^5+4q^4+5q^3+2q^2
        17: q^5+4q^4+5q^3+2q^2
        18: q^6+2q^5+4q^4+3q^3+2q^2
        19: 2q^5+4q^4+4q^3+2q^2
        20: 2q^5+4q^4+4q^3+2q^2
        21: 2q^5+4q^4+4q^3+2q^2
        22: 3q^5+5q^4+5q^3+2q^2
        23: 3q^5+5q^4+5q^3+2q^2
        24: 3q^5+5q^4+5q^3+2q^2
        25: 3q^5+5q^4+5q^3+2q^2
        26: 3q^5+5q^4+5q^3+2q^2
        27: 3q^5+5q^4+5q^3+2q^2
        28: 3q^4+5q^3+2q^2
        29: q^5+3q^4+4q^3+2q^2
        30: 2q^5+4q^4+4q^3+2q^2
        31: q^5+4q^4+5q^3+2q^2
        32: 3q^5+5q^4+5q^3+2q^2
        33: q^5+4q^4+5q^3+2q^2
        34: q^5+4q^4+5q^3+2q^2
        35: 3q^5+5q^4+5q^3+2q^2
        36: q^5+4q^4+5q^3+2q^2
        37: 2q^5+4q^4+4q^3+2q^2
        38: q^5+q^4+q^3
        39: 2q^5+4q^4+4q^3+2q^2
        40: q^5+q^4+q^3
        41: 2q^5+4q^4+4q^3+2q^2
        42: q^5+q^4+q^3
        43: q^5+4q^4+5q^3+2q^2
        44: 2q^5+4q^4+4q^3+2q^2
        45: q^5+4q^4+5q^3+2q^2
        46: q^5+4q^4+5q^3+2q^2
        47: q^5+4q^4+5q^3+2q^2
        48: q^6+2q^5+4q^4+3q^3+2q^2
        49: 3q^4+4q^3+2q^2
        50: 3q^4+4q^3+2q^2
        51: q^5+3q^4+3q^3+2q^2
        52: 2q^5+4q^4+4q^3+2q^2
        53: 2q^5+4q^4+4q^3+2q^2
        54: 2q^5+4q^4+4q^3+2q^2
        55: 2q^5+4q^4+4q^3+2q^2
        56: 2q^5+4q^4+4q^3+2q^2
        57: 2q^5+4q^4+4q^3+2q^2
        58: 2q^4+3q^3+q^2
        59: q^4+2q^3+q^2
        60: q^4+2q^3+q^2
        61: 2q^4+3q^3+q^2
        62: q^5+3q^4+4q^3+2q^2
        63: q^4+q^3
        64: 2q^5+4q^4+4q^3+2q^2
        65: q^5+q^4+q^3
        66: q^5+3q^4+4q^3+2q^2
        67: q^4+q^3
        68: 3q^4+5q^3+2q^2
        69: 2q^4+3q^3+2q^2
        70: q^5+3q^4+4q^3+2q^2
        71: 2q^4+4q^3+2q^2
        72: 2q^4+3q^3+2q^2
        73: 2q^4+3q^3+2q^2
        74: q^5+3q^4+3q^3+2q^2
        76: q^5+3q^4+3q^3+2q^2
        78: q^5+3q^4+3q^3+2q^2
        80: q^5+4q^4+5q^3+2q^2
        81: q^5+4q^4+5q^3+2q^2
        82: q^5+3q^4+4q^3+2q^2
        83: 2q^5+4q^4+4q^3+2q^2
        84: q^5+4q^4+5q^3+2q^2
        85: q^5+4q^4+5q^3+2q^2
        86: q^5+3q^4+4q^3+2q^2
        87: 2q^5+4q^4+4q^3+2q^2
        88: 2q^4+5q^3+2q^2
        89: 2q^4+5q^3+2q^2
        90: q^5+3q^4+3q^3+2q^2
        91: 3q^4+4q^3+2q^2
        92: 3q^4+4q^3+2q^2
        93: q^5+3q^4+3q^3+2q^2
        94: 3q^4+4q^3+2q^2
        95: 3q^4+4q^3+2q^2
        96: q^5+3q^4+3q^3+2q^2
        97: 3q^4+4q^3+2q^2
        98: 3q^4+4q^3+2q^2
        99: q^5+3q^4+3q^3+2q^2
       100: 2q^5+4q^4+4q^3+2q^2
       101: 2q^5+4q^4+4q^3+2q^2
       102: 2q^5+4q^4+4q^3+2q^2
       103: q^4+2q^3+q^2
       105: q^4+q^3
       106: q^4+2q^3+q^2
       107: q^3+q^2
       108: q^4+2q^3+q^2
       109: q^4+2q^3+q^2
       110: q^3+q^2
       111: q^4+2q^3+2q^2
       113: q^5+2q^4+3q^3+2q^2
       115: q^5+3q^4+3q^3+2q^2
       117: 2q^4+3q^3+q^2
       118: q^4+2q^3+q^2
       119: q^4+2q^3+q^2
       120: 2q^4+3q^3+q^2
       121: q^5+3q^4+4q^3+2q^2
       122: q^4+q^3
       123: q^5+3q^4+4q^3+2q^2
       124: q^4+q^3
       125: 2q^4+5q^3+2q^2
       126: q^4+3q^3+2q^2
       127: q^4+3q^3+2q^2
       129: q^4+3q^3+2q^2
       131: 2q^4+2q^3+2q^2
       133: 2q^4+4q^3+2q^2
       134: 2q^4+3q^3+2q^2
       135: 2q^4+3q^3+2q^2
       136: 2q^4+3q^3+2q^2
       137: 2q^4+5q^3+2q^2
       138: 2q^4+3q^3+2q^2
       139: 2q^4+4q^3+2q^2
       140: 2q^4+3q^3+2q^2
       141: q^5+3q^4+4q^3+2q^2
       142: 2q^4+3q^3+2q^2
       143: 2q^4+5q^3+2q^2
       144: 2q^4+3q^3+2q^2
       145: 2q^4+4q^3+2q^2
       146: q^5+3q^4+4q^3+2q^2
       147: 2q^4+3q^3+2q^2
       148: 2q^4+3q^3+2q^2
       149: q^5+3q^4+4q^3+2q^2
       150: 2q^5+4q^4+4q^3+2q^2
       151: q^5+3q^4+3q^3+2q^2
       153: q^5+3q^4+3q^3+2q^2
       155: q^5+3q^4+3q^3+2q^2
       157: 4q^3+2q^2
       158: 4q^3+2q^2
       159: q^4+3q^3+2q^2
       160: 3q^4+4q^3+2q^2
       161: 3q^4+4q^3+2q^2
       162: q^5+3q^4+3q^3+2q^2
       163: 3q^4+4q^3+2q^2
       164: 3q^4+4q^3+2q^2
       165: q^5+3q^4+3q^3+2q^2
       166: 3q^4+4q^3+2q^2
       167: 3q^4+4q^3+2q^2
       168: q^5+3q^4+3q^3+2q^2
       169: q^3+q^2
       172: q^3+q^2
       173: q^4+2q^3+q^2
       175: q^4+q^3
       176: q^4+2q^3+q^2
       177: q^4+2q^3+2q^2
       179: q^4+3q^3+2q^2
       181: 2q^3+2q^2
       183: q^3+q^2
       184: q^4+2q^3+q^2
       185: q^4+2q^3+q^2
       186: q^3+q^2
       187: q^4+2q^3+2q^2
       189: q^5+2q^4+3q^3+2q^2
       191: q^4+3q^3+q^2
       192: q^4+2q^3+q^2
       193: q^3+q^2
       194: q^4+2q^3+q^2
       195: q^4+2q^3+q^2
       196: q^3+q^2
       197: q^4+2q^3+2q^2
       199: q^4+2q^3+q^2
       200: q^4+3q^3+q^2
       201: q^3+q^2
       202: q^4+2q^3+q^2
       203: q^4+2q^3+q^2
       204: q^3+q^2
       205: q^4+2q^3+2q^2
       207: 2q^4+4q^3+2q^2
       208: q^3
       209: q^5+2q^4+3q^3+2q^2
       211: q^5+3q^4+3q^3+2q^2
       213: q^4+3q^3+2q^2
       215: q^4+3q^3+2q^2
       217: 2q^4+2q^3+2q^2
       219: q^4+3q^3+2q^2
       220: 4q^3+2q^2
       221: 3q^3+2q^2
       222: 3q^3+2q^2
       223: q^4+2q^3+2q^2
       224: 3q^3+2q^2
       225: q^4+2q^3+2q^2
       226: q^4+3q^3+2q^2
       227: 2q^4+4q^3+2q^2
       228: 2q^4+3q^3+2q^2
       229: 2q^4+3q^3+2q^2
       230: 2q^4+3q^3+2q^2
       231: q^4+3q^3+2q^2
       232: 2q^4+4q^3+2q^2
       233: 2q^4+3q^3+2q^2
       234: 2q^4+3q^3+2q^2
       235: 2q^4+3q^3+2q^2
       236: 2q^4+3q^3+2q^2
       237: q^4+3q^3+2q^2
       239: q^4+3q^3+2q^2
       241: 2q^4+2q^3+2q^2
       243: 2q^4+4q^3+2q^2
       244: 2q^4+3q^3+2q^2
       245: 2q^4+3q^3+2q^2
       246: q^5+3q^4+4q^3+2q^2
       247: 3q^3+3q^2
       248: 3q^3+3q^2
       249: 2q^4+2q^3+2q^2
       250: 4q^3+2q^2
       251: 4q^3+2q^2
       252: q^4+3q^3+2q^2
       253: 4q^3+2q^2
       254: 4q^3+2q^2
       255: q^4+3q^3+2q^2
       256: 3q^4+4q^3+2q^2
       257: 3q^4+4q^3+2q^2
       258: q^5+3q^4+3q^3+2q^2
       259: q^3+q^2
       262: q^3+q^2
       263: q^3+q^2
       266: q^3+q^2
       267: q^3+q^2
       269: q^3+q^2
       271: q^3+q^2
       273: q^3+q^2
       275: q^4+2q^3+q^2
       277: q^3
       278: q^4+2q^3+q^2
       279: q^4+3q^3+2q^2
       281: q^4+2q^3+2q^2
       283: q^2
       284: q^3+q^2
       285: q^3+q^2
       286: q^2
       287: q^4+2q^3+2q^2
       289: 2q^3+2q^2
       291: q^3+2q^2
       293: q^3+q^2
       294: 2q^3+q^2
       295: 2q^3+q^2
       296: q^3+q^2
       297: 2q^3+2q^2
       299: q^3+q^2
       300: q^4+2q^3+q^2
       301: 2q^3+2q^2
       303: q^4+2q^3+q^2
       304: q^3+q^2
       305: q^4+2q^3+2q^2
       307: q^3+q^2
       308: q^4+2q^3+q^2
       309: q^4+2q^3+q^2
       310: q^3+q^2
       311: 2q^3+2q^2
       313: q^4+2q^3+2q^2
       315: q^4+2q^3+2q^2
       317: q^4+3q^3+2q^2
       319: q^3+q^2
       320: q^4+2q^3+q^2
       321: q^4+2q^3+q^2
       322: q^3+q^2
       323: q^4+2q^3+2q^2
       325: q^5+2q^4+3q^3+2q^2
       327: q^3+2q^2
       329: q^3+2q^2
       331: q^3+2q^2
       333: 3q^3+2q^2
       334: 2q^3+2q^2
       335: 2q^3+2q^2
       336: q^3+2q^2
       337: 3q^3+3q^2
       338: 3q^3+3q^2
       340: 3q^3+3q^2
       342: 2q^4+2q^3+2q^2
       344: q^4+3q^3+2q^2
       345: 4q^3+2q^2
       346: 3q^3+2q^2
       347: 3q^3+2q^2
       348: q^4+2q^3+2q^2
       349: 3q^3+2q^2
       350: q^4+2q^3+2q^2
       351: 3q^3+3q^2
       352: q^4+3q^3+2q^2
       353: 4q^3+2q^2
       354: 3q^3+2q^2
       355: 3q^3+2q^2
       356: q^4+2q^3+2q^2
       357: 3q^3+2q^2
       358: q^4+2q^3+2q^2
       359: 3q^3+3q^2
       360: q^4+3q^3+2q^2
       362: q^4+3q^3+2q^2
       364: 2q^4+2q^3+2q^2
       366: q^4+3q^3+2q^2
       367: 2q^4+4q^3+2q^2
       368: 2q^4+3q^3+2q^2
       369: 2q^4+3q^3+2q^2
       370: 2q^4+3q^3+2q^2
       371: 3q^3+3q^2
       372: 3q^3+3q^2
       373: 2q^4+2q^3+2q^2
       374: 4q^3+2q^2
       375: 4q^3+2q^2
       376: q^4+3q^3+2q^2
       377: q^2
       380: q^2
       381: q^3+q^2
       384: q^3+q^2
       385: q^3+q^2
       388: q^3+q^2
       389: q^3+q^2
       391: q^3+q^2
       393: q^3+q^2
       396: q^3+q^2
       397: q^3+q^2
       399: q^3+q^2
       401: q^3+q^2
       404: q^3+q^2
       405: q^3+q^2
       406: q^3+q^2
       409: q^3+2q^2
       411: q^3+2q^2
       413: q^4+2q^3+2q^2
       415: 2q^2
       417: q^3+2q^2
       419: q^2
       420: q^3+q^2
       421: q^3+q^2
       422: q^2
       423: q^3+2q^2
       425: q^3+2q^2
       427: 3q^3+3q^2
       429: q^2
       430: q^3+q^2
       431: q^3+q^2
       432: q^2
       433: q^3+2q^2
       435: 2q^3+2q^2
       437: q^3+q^2
       438: 2q^3+q^2
       439: 2q^3+q^2
       440: q^3+q^2
       441: 2q^3+2q^2
       443: q^3+q^2
       444: 2q^3+2q^2
       445: 3q^3+3q^2
       447: q^2
       448: q^3+q^2
       449: q^3+q^2
       450: q^2
       451: q^3+2q^2
       453: q^3+q^2
       454: 2q^3+q^2
       455: 2q^3+2q^2
       457: 2q^3+q^2
       458: q^3+q^2
       459: 2q^3+2q^2
       461: 2q^3+2q^2
       462: q^3+q^2
       463: 3q^3+3q^2
       465: q^4+3q^3+2q^2
       467: q^4+2q^3+2q^2
       469: q^4+2q^3+2q^2
       471: q^3+q^2
       472: q^4+2q^3+q^2
       473: q^4+2q^3+q^2
       474: q^3+q^2
       475: q^4+2q^3+2q^2
       477: 2q^3+2q^2
       479: 2q^3+2q^2
       480: q^3+q^2
       481: 2q^3+2q^2
       482: 2q^3+2q^2
       483: q^3+2q^2
       484: 3q^3+3q^2
       485: 3q^3+3q^2
       487: 3q^3+3q^2
       489: 2q^4+2q^3+2q^2
       491: q^3+2q^2
       492: 3q^3+2q^2
       493: 2q^3+2q^2
       494: 2q^3+2q^2
       495: q^3+2q^2
       496: 3q^3+3q^2
       497: 3q^3+2q^2
       498: 2q^3+2q^2
       499: 2q^3+2q^2
       500: q^3+2q^2
       501: 3q^3+3q^2
       502: q^3+2q^2
       504: q^3+2q^2
       506: q^3+2q^2
       508: q^4+3q^3+2q^2
       509: 4q^3+2q^2
       510: 3q^3+2q^2
       511: 3q^3+2q^2
       512: q^4+2q^3+2q^2
       513: 3q^3+2q^2
       514: q^4+2q^3+2q^2
       515: 3q^2
       516: 3q^2
       517: q^3+2q^2
       518: 3q^2
       519: 3q^2
       520: q^3+2q^2
       521: q^2
       524: q^2
       525: q^2
       528: q^2
       529: q^2
       532: q^2
       533: q^2
       536: q^2
       537: q^3+q^2
       539: q^3+q^2
       541: q^3+q^2
       543: q^3+q^2
       545: q^3+q^2
       547: 2q^3+2q^2
       549: q^2
       552: q^2
       553: q^3+q^2
       555: q^3+q^2
       557: q^3+q^2
       559: q^3+q^2
       561: 2q^3+2q^2
       563: q^3+q^2
       565: q^3+q^2
       568: q^3+q^2
       569: q^3+q^2
       570: q^3+q^2
       573: q^3+q^2
       575: q^3+q^2
       576: q^3+q^2
       577: 2q^3+2q^2
       580: q^3+q^2
       583: q^3+2q^2
       585: q^3+2q^2
       587: 2q^2
       589: q^2
       590: q^3+q^2
       591: q^2
       594: q^2
       595: q^3+q^2
       596: q^2
       597: q^3+2q^2
       599: q^3+2q^2
       601: 3q^3+3q^2
       603: q^2
       604: q^3+q^2
       605: q^3+2q^2
       607: q^3+q^2
       608: q^2
       609: q^3+2q^2
       611: 2q^2
       613: q^3+2q^2
       615: q^3+q^2
       616: 2q^3+2q^2
       617: 3q^3+3q^2
       619: q^2
       620: q^3+q^2
       621: q^3+q^2
       622: q^2
       623: q^3+2q^2
       625: q^3+2q^2
       627: 2q^2
       629: q^3+2q^2
       631: 2q^3+2q^2
       632: q^3+q^2
       633: 3q^3+3q^2
       635: q^3+2q^2
       637: q^3+2q^2
       639: q^4+2q^3+2q^2
       641: q^2
       642: q^3+q^2
       643: q^3+q^2
       644: q^2
       645: q^3+2q^2
       647: q^3+q^2
       648: 2q^3+q^2
       649: 2q^3+q^2
       650: q^3+q^2
       651: 2q^3+2q^2
       653: 2q^3+2q^2
       655: 2q^3+2q^2
       656: q^3+q^2
       657: 3q^2
       658: 3q^2
       660: 3q^2
       662: q^3+2q^2
       664: 2q^2
       665: q^3+2q^2
       666: 3q^2
       668: 3q^2
       670: q^3+2q^2
       672: 3q^2
       673: 2q^2
       674: 3q^2
       675: 2q^3+2q^2
       676: 2q^3+2q^2
       677: q^3+2q^2
       678: 3q^2
       679: q^3+2q^2
       680: 3q^2
       681: 2q^3+2q^2
       682: 2q^3+2q^2
       683: q^3+2q^2
       684: 3q^2
       685: q^3+2q^2
       686: 3q^3+2q^2
       687: 2q^3+2q^2
       688: 2q^3+2q^2
       689: q^3+2q^2
       693: q^3+q^2
       697: q^3+q^2
       698: q^3+q^2
       705: q^2
       708: q^2
       709: q^2
       712: q^2
       713: q^2
       720: q^2
       721: q^2
       723: q^2
       725: q^2
       727: q^2
       729: q^2
       731: q^2
       733: q^3+q^2
       735: 2q^3+2q^2
       737: q^2
       739: q^2
       741: q^2
       743: q^2
       745: q^2
       747: q^2
       749: 2q^3+2q^2
       751: q^3+q^2
       753: q^2
       756: q^2
       757: q^3+q^2
       758: q^3+q^2
       761: q^3+q^2
       762: q^3+q^2
       765: q^3+q^2
       767: q^3+q^2
       768: q^3+q^2
       769: 2q^3+2q^2
       772: q^3+q^2
       775: 3q^2
       777: 2q^2
       779: 2q^2
       781: q^3+2q^2
       783: 2q^2
       786: q^2
       787: q^2
       789: 3q^2
       791: q^2
       793: q^2
       794: 2q^2
       795: 3q^2
       797: q^3+2q^2
       799: 2q^2
       801: q^2
       802: q^3+q^2
       803: q^2
       806: q^2
       807: q^3+q^2
       808: q^2
       809: q^3+2q^2
       811: q^3+2q^2
       813: 3q^2
       815: q^2
       816: 2q^2
       817: 2q^2
       818: q^2
       819: 3q^2
       821: q^3+2q^2
       823: 2q^2
       825: q^2
       826: q^3+q^2
       827: q^2
       830: q^2
       831: q^3+q^2
       832: q^2
       833: q^3+2q^2
       835: q^3+2q^2
       837: 3q^2
       839: 2q^2
       840: q^2
       841: q^3+2q^2
       843: 2q^2
       844: q^2
       845: q^2
       846: q^3+q^2
       847: q^3+q^2
       848: q^2
       849: q^3+2q^2
       851: q^3+2q^2
       853: 2q^2
       855: q^3+2q^2
       857: 2q^2
       858: q^2
       866: 2q^2
       868: 2q^2
       870: 2q^2
       871: q^3+2q^2
       872: 2q^2
       874: 2q^2
       875: q^3+2q^2
       876: 2q^2
       877: 2q^3+2q^2
       878: 2q^3+2q^2
       879: q^3+2q^2
       880: q^3+2q^2
       884: q^3+q^2
       888: q^3+q^2
       889: q^3+q^2
       896: q^2
       899: q^2
       900: q^2
       906: q^2
       912: q^2
       914: q^2
       916: q^2
       918: 2q^2
       920: q^2
       922: q^2
       924: q^2
       930: q^2
       932: q^2
       934: 2q^2
       936: q^2
       938: q^2
       940: 2q^2
       942: q^2
       944: q^2
       946: q^2
       948: q^2
       955: q^2
       956: 2q^2
       958: q^2
       960: q^2
       961: q^2
       964: q^2
       966: q^2
       967: q^2
       968: 2q^2
       971: q^2
       974: q^2
       975: q^2
       978: q^2
       979: q^2
       982: 2q^2
       985: q^2
       988: q^2
       990: q^2
       991: q^2
       994: 2q^2
       998: q^2
      1001: q^2
      1002: 2q^2
      1005: q^2
      1006: q^2
      1008: q^2
      1010: q^2
      1012: q^2
      1018: 2q^2
      1020: 2q^2
      1022: q^3+2q^2
      1024: 2q^2
      1027: q^2
      1028: q^2
      1034: 2q^2
      1036: 2q^2
      1038: q^3+2q^2
      1041: q^2
      1042: 2q^2
      1044: q^2
      1048: q^3+2q^2
      1050: 2q^2
      1052: q^2
      1053: q^3+q^2
      1054: q^2
      1057: q^2
      1058: q^3+q^2
      1059: q^2
      1060: q^3+2q^2
      1062: q^3+2q^2
      1064: q^2
      1076: 2q^2
      1078: 2q^2
      1080: 2q^2
      1082: 2q^2
      1083: q^3+2q^2
      1084: 2q^2
      1085: 2q^2
      1086: q^2
      1090: q^2
      1091: q^2
      1098: q^2
      1102: q^2
      1103: q^2
      1110: q^2
      1114: q^2
      1120: q^2
      1124: q^2
      1138: q^2
      1148: q^2
      1150: q^2
      1152: q^2
      1158: q^2
      1168: q^2
      1170: q^2
      1172: q^2
      1178: q^2
      1184: q^2
      1185: q^2
      1198: q^2
      1199: q^2
      1202: q^2
      1208: q^2
      1220: q^2
      1222: q^2
      1230: 2q^2
      1232: q^2
      1235: q^2
      1238: 2q^2
      1241: q^2
      1242: q^2
      1248: 2q^2
      1250: q^2
      1255: q^2
      1256: 2q^2
      1259: q^2
      1260: q^2
      1264: 2q^2
      1266: q^3+2q^2
      1269: q^2
      1270: q^2
      1272: 2q^2
      1274: 2q^2
      1276: q^2
      1278: q^2
      1280: q^2
      1287: 2q^2
      1289: 2q^2
      1344: q^2
      1348: q^2
      1354: q^2
      1358: q^2
      1376: q^2
      1380: q^2
      1386: q^2
      1390: q^2
      1414: q^2
      1415: q^2
      1418: q^2
      1424: q^2
      1430: q^2
      1446: q^2
      1464: 2q^2
      1466: q^2
      1469: q^2
      1470: 2q^2
      1474: q^2
      1477: q^2
      1478: q^2
      1480: q^2
      1484: q
      1603: q^2
      1607: q^2
      1613: q^2
      1617: q^2
      1637: q
      1641: q
      1649: q
      1658: q
      1671: q^2
      1725: q
      1757: q
      1783: q
      1813: q
      1823: q
      1885: q
      1928: q
      1958: 1
      2028: 1
      2036: 1
      2049: 1
      2070: 1
      2087: 1
      2119: 1
      2153: 1

2154:    0: 2q^2+q
         1: 2q^2+q
         2: q^3+q^2+q
         3: 2q^2+q
         4: 2q^2+q
         5: 2q^2+q
         6: 2q^2+q
         7: q^3+q^2+q
         8: q^3+q^2+q
         9: q^3+q^2+q
        10: 2q^2+q
        11: 2q^2+q
        12: 2q^2+q
        13: q^2+q
        14: q^2+q
        15: q^2+q
        16: 2q^2+q
        17: 2q^2+q
        18: q^3+q^2+q
        19: 2q^2+q
        20: 2q^2+q
        21: q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^3+q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^3+q^2+q
        28: 2q^2+q
        29: 2q^2+q
        30: q^2+q
        31: 2q^2+q
        32: q^2+q
        33: 2q^2+q
        34: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2
        38: q
        39: 2q^2
        40: q
        41: q^3+q^2
        42: q
        43: q^2+q
        44: q^2+q
        45: q^2+q
        46: q^2+q
        47: q^2+q
        48: q^2+q
        49: 2q^2+q
        50: 2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^3+q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^3+q^2+q
        58: q^2
        59: q^2+q
        60: q^2+q
        61: q^2
        62: 2q^2
        63: q
        64: q^2
        65: q
        66: 2q^2
        67: q
        68: q
        69: q^2+q
        70: q^2+q
        71: 2q^2+q
        72: 2q^2+q
        73: 2q^2+q
        74: 2q^2
        75: q
        76: 2q^2
        77: q
        78: q^3+q^2
        79: q
        80: q^2+q
        81: q^2+q
        82: 2q^2+q
        83: q^2+q
        84: q^2+q
        85: q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^2+q
        89: q^2+q
        90: q^2+q
        91: q^2+q
        92: q^2+q
        93: q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^3+q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^3+q^2+q
       100: 2q^2+q
       101: 2q^2+q
       102: q^3+q^2+q
       103: q^2
       104: q
       106: q^2
       107: q^2+q
       108: q^2
       109: q^2
       110: q^2+q
       111: 2q^2
       112: q
       113: 2q^2
       114: q
       115: q^2
       116: q
       118: q
       119: q
       121: q^2
       122: q
       123: q^2
       124: q
       125: q
       126: q^2+q
       127: 2q^2
       128: q
       129: 2q^2
       130: q
       131: q^3+q^2
       132: q
       133: q
       134: q^2+q
       135: q^2+q
       136: q^2+q
       137: q^2+q
       138: q^2+q
       139: 2q^2+q
       140: 2q^2+q
       141: q^2+q
       142: 2q^2+q
       143: q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: 2q^2+q
       148: 2q^2+q
       149: 2q^2+q
       150: q^2+q
       151: 2q^2
       152: q
       153: 2q^2
       154: q
       155: q^3+q^2
       156: q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: 2q^2+q
       168: q^3+q^2+q
       169: q^2
       170: q
       172: q^2
       174: q
       177: q^2
       178: q
       179: 2q^2
       180: q
       181: 2q^2
       182: q
       183: q
       186: q
       187: q^2
       188: q
       189: q^2
       190: q
       192: q
       193: q^2+q
       194: q^2
       195: q^2
       196: q^2+q
       197: 2q^2
       198: q
       199: q
       201: q^2+q
       202: q^2
       203: q^2
       204: q^2+q
       205: 2q^2
       206: q
       207: q^2
       208: q
       209: 2q^2
       210: q
       211: q^2
       212: q
       213: q^2
       215: q^2
       217: q^2
       219: q
       220: q
       221: q^2+q
       222: q^2+q
       223: q^2+q
       224: q^2+q
       225: q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q^2+q
       230: q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q^2+q
       236: q^2+q
       237: 2q^2
       238: q
       239: 2q^2
       240: q
       241: q^3+q^2
       242: q
       243: 2q^2+q
       244: 2q^2+q
       245: 2q^2+q
       246: q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2
       260: q
       262: q^2
       264: q
       267: q^2
       268: q
       269: q^2
       271: q^2
       273: q^2
       274: q
       276: q
       281: q^2
       283: q
       286: q
       287: q^2
       288: q
       289: q^2
       291: q^2
       292: q
       293: q
       296: q
       297: q^2
       298: q
       299: q
       301: 2q^2
       302: q
       304: q
       305: q^2
       306: q
       307: q
       310: q
       311: 2q^2
       312: q
       313: q^2
       314: q
       315: q^2
       316: q
       317: 2q^2
       318: q
       319: q^2+q
       320: q^2
       321: q^2
       322: q^2+q
       323: 2q^2
       324: q
       325: q^2
       326: q
       327: q^2
       329: q^2
       331: q^2
       333: q
       334: q^2+q
       335: q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2
       339: q
       340: 2q^2
       341: q
       342: q^3+q^2
       343: q
       344: q
       345: q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: q^2+q
       350: q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q^2+q
       358: q^2+q
       359: 2q^2+q
       360: q^2
       362: q^2
       364: q^2
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q^2+q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       378: q
       386: q
       389: q^2
       390: q
       391: q^2
       394: q
       397: q^2
       399: q^2
       400: q
       403: q
       405: q^2
       406: q^2
       407: q
       411: q^2
       415: q^2
       417: q^2
       419: q
       422: q
       423: q^2
       424: q
       425: q^2
       426: q
       427: 2q^2
       428: q
       429: q
       432: q
       433: q^2
       434: q
       435: q^2
       437: q
       440: q
       441: q^2
       442: q
       443: q^2+q
       444: q^2
       445: 2q^2
       446: q
       447: q
       450: q
       451: q^2
       452: q
       453: q
       455: q^2
       458: q
       459: q^2
       460: q
       461: q^2
       462: q^2+q
       463: 2q^2
       464: q
       467: q^2
       469: q^2
       470: q
       471: q
       474: q
       475: q^2
       476: q
       477: 2q^2
       478: q
       479: 2q^2
       480: q
       481: q
       482: q
       483: q^2+q
       484: q
       485: q^2
       487: q^2
       489: q^2
       491: q^2+q
       492: q
       493: q^2+q
       494: q^2+q
       495: q^2+q
       496: q^2+q
       497: q
       498: q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       502: q^2
       504: q^2
       506: q^2
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       530: q
       534: q
       542: q
       545: q^2
       546: q
       547: q^2
       551: q
       560: q
       561: q^2
       563: q^2
       564: q
       566: q
       569: q^2
       570: q^2
       571: q
       573: q^2
       574: q
       575: q^2
       577: 2q^2
       581: q
       587: q^2
       589: q
       592: q
       593: q
       596: q
       597: q^2
       599: q^2
       600: q
       603: q
       605: q^2
       608: q
       609: q^2
       610: q
       611: q^2
       613: q^2
       614: q
       615: q
       617: q^2
       619: q
       622: q
       623: q^2
       625: q^2
       626: q
       627: q^2
       629: q^2
       630: q
       632: q
       633: q^2
       637: q^2
       641: q
       644: q
       645: q^2
       646: q
       647: q
       650: q
       651: q^2
       653: q^2
       654: q
       655: q^2
       656: q
       657: q
       658: q^2
       660: q^2
       662: q^2
       664: q^2+q
       665: q
       666: q^2
       668: q^2
       670: q^2
       672: q
       673: q^2+q
       674: q^2+q
       675: q
       676: q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q^2+q
       681: q
       682: q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q
       687: q^2+q
       688: q^2+q
       689: q^2+q
       690: q^2+q
       691: q^2+q
       692: q^2+q
       693: q^2
       697: q^2
       699: q
       715: q
       718: q
       726: q
       744: q
       754: q
       763: q
       766: q
       769: q^2
       779: q^2
       783: q^2
       785: q
       788: q
       791: q^2
       792: q
       793: q
       795: q^2
       799: q^2
       801: q
       804: q
       805: q
       808: q
       809: q^2
       811: q^2
       812: q
       813: q^2
       815: q
       818: q
       819: q^2
       823: q^2
       825: q
       828: q
       829: q
       832: q
       833: q^2
       835: q^2
       836: q
       837: q^2
       840: q
       843: q^2
       844: q
       845: q
       848: q
       849: q^2
       851: q^2
       852: q
       853: q^2
       855: q^2
       856: q
       857: q^2
       858: q
       859: q^2
       861: q^2
       863: q^2
       865: q
       866: q
       867: q^2+q
       868: q
       869: q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q
       878: q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: 1
       909: q
       926: q
       929: q
       951: q
       953: q
       965: q
       968: q^2
       976: q
       982: q^2
       989: q
       996: q^2
       999: q
      1000: q
      1004: q
      1007: q
      1008: q^2
      1009: q
      1010: q^2
      1012: q^2
      1013: q
      1014: q^2
      1016: q
      1020: q^2
      1024: q^2
      1026: q
      1029: q
      1030: q^2
      1033: q
      1036: q^2
      1040: q
      1042: q^2
      1045: q
      1046: q^2
      1047: q
      1050: q^2
      1052: q
      1055: q
      1056: q
      1059: q
      1060: q^2
      1062: q^2
      1063: q
      1064: q^2
      1065: q
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1131: q
      1136: q
      1138: q^2
      1162: q
      1181: q
      1188: q^2
      1195: q
      1205: q
      1207: q
      1210: 1
      1212: 1
      1217: q
      1218: q
      1222: q^2
      1224: q^2
      1225: q
      1226: 1
      1228: 1
      1233: q
      1234: q
      1236: q^2
      1240: q
      1243: q
      1244: 1
      1247: 1
      1251: q
      1252: q^2
      1254: q
      1258: q
      1261: q
      1263: 1
      1268: q
      1271: q
      1272: q^2
      1274: q^2
      1276: q^2
      1277: q
      1278: q^2
      1280: q^2
      1281: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1327: q
      1334: q^2
      1340: 1
      1366: q
      1371: q
      1374: 1
      1397: q
      1402: q
      1407: 1
      1411: 1
      1427: q
      1430: q^2
      1438: 1
      1441: 1
      1442: 1
      1445: 1
      1451: q
      1452: 1
      1454: q
      1458: 1
      1461: q
      1462: q
      1467: q
      1468: q
      1472: q^2
      1476: q
      1479: q
      1480: q^2
      1482: q^2
      1483: q
      1484: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1528: 1
      1543: 1
      1545: 1
      1550: 1
      1556: 1
      1577: q
      1596: q
      1624: q
      1628: q
      1631: q^2
      1640: 1
      1643: 1
      1646: 1
      1647: 1
      1650: q
      1651: 1
      1654: 1
      1655: 1
      1657: q
      1664: q
      1665: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1678: 1
      1726: 1
      1734: 1
      1739: 1
      1745: 1
      1751: 1
      1763: 1
      1765: 1
      1774: 1
      1798: q
      1804: 1
      1812: q
      1820: q
      1821: q
      1826: 1
      1827: 1
      1830: 1
      1831: 1
      1833: 1
      1837: 1
      1850: 1
      1861: 1
      1901: 1
      1915: 1
      1929: 1
      1934: 1
      1936: 1
      1941: 1
      1953: q
      1956: 1
      1961: 1
      1963: 1
      1964: 1
      1974: 1
      1981: 1
      1993: 1
      2029: 1
      2034: 1
      2043: 1
      2044: 1
      2053: 1
      2061: 1
      2065: 1
      2076: 1
      2083: 1
      2095: 1
      2106: 1
      2133: 1
      2154: 1

2155:    0: 2q^2+q
         1: 2q^2+q
         2: q^3+q^2+q
         3: 2q^2+q
         4: 2q^2+q
         5: 2q^2+q
         6: 2q^2+q
         7: q^3+q^2+q
         8: q^3+q^2+q
         9: q^3+q^2+q
        10: 2q^2+q
        11: 2q^2+q
        12: 2q^2+q
        13: q^2+q
        14: q^2+q
        15: q^2+q
        16: 2q^2+q
        17: 2q^2+q
        18: q^3+q^2+q
        19: 2q^2+q
        20: 2q^2+q
        21: q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^3+q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^3+q^2+q
        28: 2q^2+q
        29: 2q^2+q
        30: q^2+q
        31: 2q^2+q
        32: q^2+q
        33: 2q^2+q
        34: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        37: 2q^2
        38: q
        39: 2q^2
        40: q
        41: q^3+q^2
        42: q
        43: q^2+q
        44: q^2+q
        45: q^2+q
        46: q^2+q
        47: q^2+q
        48: q^2+q
        49: 2q^2+q
        50: 2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^3+q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^3+q^2+q
        58: q^2+q
        59: q^2
        60: q^2
        61: q^2+q
        62: 2q^2
        63: q
        64: q^2
        65: q
        66: 2q^2
        67: q
        68: q
        69: q^2+q
        70: q^2+q
        71: 2q^2+q
        72: 2q^2+q
        73: 2q^2+q
        74: 2q^2
        75: q
        76: 2q^2
        77: q
        78: q^3+q^2
        79: q
        80: q^2+q
        81: q^2+q
        82: 2q^2+q
        83: q^2+q
        84: q^2+q
        85: q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^2+q
        89: q^2+q
        90: q^2+q
        91: q^2+q
        92: q^2+q
        93: q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^3+q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^3+q^2+q
       100: 2q^2+q
       101: 2q^2+q
       102: q^3+q^2+q
       103: q^2
       105: q
       106: q^2
       107: q^2
       108: q^2+q
       109: q^2+q
       110: q^2
       111: 2q^2
       112: q
       113: 2q^2
       114: q
       115: q^2
       116: q
       117: q
       120: q
       121: q^2
       122: q
       123: q^2
       124: q
       125: q
       126: q^2+q
       127: 2q^2
       128: q
       129: 2q^2
       130: q
       131: q^3+q^2
       132: q
       133: q
       134: q^2+q
       135: q^2+q
       136: q^2+q
       137: q^2+q
       138: q^2+q
       139: 2q^2+q
       140: 2q^2+q
       141: q^2+q
       142: 2q^2+q
       143: q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: 2q^2+q
       148: 2q^2+q
       149: 2q^2+q
       150: q^2+q
       151: 2q^2
       152: q
       153: 2q^2
       154: q
       155: q^3+q^2
       156: q
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: 2q^2+q
       168: q^3+q^2+q
       169: q^2
       171: q
       172: q^2
       175: q
       177: q^2
       178: q
       179: 2q^2
       180: q
       181: 2q^2
       182: q
       184: q
       185: q
       187: q^2
       188: q
       189: q^2
       190: q
       191: q
       193: q^2
       194: q^2+q
       195: q^2+q
       196: q^2
       197: 2q^2
       198: q
       200: q
       201: q^2
       202: q^2+q
       203: q^2+q
       204: q^2
       205: 2q^2
       206: q
       207: q^2
       208: q
       209: 2q^2
       210: q
       211: q^2
       212: q
       213: q^2
       215: q^2
       217: q^2
       219: q
       220: q
       221: q^2+q
       222: q^2+q
       223: q^2+q
       224: q^2+q
       225: q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q^2+q
       230: q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q^2+q
       236: q^2+q
       237: 2q^2
       238: q
       239: 2q^2
       240: q
       241: q^3+q^2
       242: q
       243: 2q^2+q
       244: 2q^2+q
       245: 2q^2+q
       246: q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       259: q^2
       261: q
       262: q^2
       265: q
       267: q^2
       269: q^2
       270: q
       271: q^2
       272: q
       273: q^2
       277: q
       281: q^2
       284: q
       285: q
       287: q^2
       288: q
       289: q^2
       291: q^2
       292: q
       294: q
       295: q
       297: q^2
       298: q
       300: q
       301: 2q^2
       302: q
       303: q
       305: q^2
       306: q
       308: q
       309: q
       311: 2q^2
       312: q
       313: q^2
       314: q
       315: q^2
       316: q
       317: 2q^2
       318: q
       319: q^2
       320: q^2+q
       321: q^2+q
       322: q^2
       323: 2q^2
       324: q
       325: q^2
       326: q
       327: q^2
       329: q^2
       331: q^2
       333: q
       334: q^2+q
       335: q^2+q
       336: q^2+q
       337: 2q^2+q
       338: 2q^2
       339: q
       340: 2q^2
       341: q
       342: q^3+q^2
       343: q
       344: q
       345: q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: q^2+q
       350: q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q^2+q
       358: q^2+q
       359: 2q^2+q
       360: q^2
       362: q^2
       364: q^2
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q^2+q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       379: q
       387: q
       389: q^2
       391: q^2
       392: q
       395: q
       397: q^2
       398: q
       399: q^2
       402: q
       405: q^2
       406: q^2
       408: q
       411: q^2
       415: q^2
       417: q^2
       420: q
       421: q
       423: q^2
       424: q
       425: q^2
       426: q
       427: 2q^2
       428: q
       430: q
       431: q
       433: q^2
       434: q
       435: q^2
       438: q
       439: q
       441: q^2
       442: q
       443: q^2
       444: q^2+q
       445: 2q^2
       446: q
       448: q
       449: q
       451: q^2
       452: q
       454: q
       455: q^2
       457: q
       459: q^2
       460: q
       461: q^2+q
       462: q^2
       463: 2q^2
       464: q
       467: q^2
       469: q^2
       470: q
       472: q
       473: q
       475: q^2
       476: q
       477: 2q^2
       478: q
       479: 2q^2
       480: q
       481: q
       482: q
       483: q^2+q
       484: q
       485: q^2
       487: q^2
       489: q^2
       491: q^2+q
       492: q
       493: q^2+q
       494: q^2+q
       495: q^2+q
       496: q^2+q
       497: q
       498: q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       502: q^2
       504: q^2
       506: q^2
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       531: q
       535: q
       544: q
       545: q^2
       547: q^2
       548: q
       550: q
       558: q
       561: q^2
       562: q
       563: q^2
       567: q
       569: q^2
       570: q^2
       572: q
       573: q^2
       575: q^2
       576: q
       577: 2q^2
       581: q
       587: q^2
       590: q
       591: q
       594: q
       595: q
       597: q^2
       599: q^2
       600: q
       604: q
       605: q^2
       607: q
       609: q^2
       610: q
       611: q^2
       613: q^2
       614: q
       616: q
       617: q^2
       620: q
       621: q
       623: q^2
       625: q^2
       626: q
       627: q^2
       629: q^2
       630: q
       631: q
       633: q^2
       637: q^2
       642: q
       643: q
       645: q^2
       646: q
       648: q
       649: q
       651: q^2
       653: q^2
       654: q
       655: q^2
       656: q
       657: q
       658: q^2
       660: q^2
       662: q^2
       664: q^2+q
       665: q
       666: q^2
       668: q^2
       670: q^2
       672: q
       673: q^2+q
       674: q^2+q
       675: q
       676: q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q^2+q
       681: q
       682: q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q
       687: q^2+q
       688: q^2+q
       689: q^2+q
       690: q^2+q
       691: q^2+q
       692: q^2+q
       693: q^2
       697: q^2
       700: q
       714: q
       719: q
       728: q
       742: q
       755: q
       764: q
       767: q
       769: q^2
       779: q^2
       783: q^2
       786: q
       787: q
       791: q^2
       792: q
       794: q
       795: q^2
       799: q^2
       802: q
       803: q
       806: q
       807: q
       809: q^2
       811: q^2
       812: q
       813: q^2
       816: q
       817: q
       819: q^2
       823: q^2
       826: q
       827: q
       830: q
       831: q
       833: q^2
       835: q^2
       836: q
       837: q^2
       839: q
       843: q^2
       844: q
       846: q
       847: q
       849: q^2
       851: q^2
       852: q
       853: q^2
       855: q^2
       856: q
       857: q^2
       858: q
       859: q^2
       861: q^2
       863: q^2
       865: q
       866: q
       867: q^2+q
       868: q
       869: q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q
       878: q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: 1
       910: q
       925: q
       931: q
       949: q
       954: q
       966: q
       968: q^2
       977: q
       982: q^2
       990: q
       996: q^2
       998: q
      1001: q
      1005: q
      1006: q
      1008: q^2
      1009: q
      1010: q^2
      1012: q^2
      1013: q
      1014: q^2
      1017: q
      1020: q^2
      1024: q^2
      1027: q
      1028: q
      1030: q^2
      1032: q
      1036: q^2
      1041: q
      1042: q^2
      1044: q
      1046: q^2
      1047: q
      1050: q^2
      1053: q
      1054: q
      1057: q
      1058: q
      1060: q^2
      1062: q^2
      1063: q
      1064: q^2
      1065: q
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1132: q
      1137: q
      1138: q^2
      1161: q
      1182: q
      1188: q^2
      1196: q
      1203: q
      1209: q
      1210: 1
      1212: 1
      1216: q
      1219: q
      1222: q^2
      1224: q^2
      1225: q
      1226: 1
      1229: 1
      1232: q
      1235: q
      1236: q^2
      1241: q
      1242: q
      1244: 1
      1246: 1
      1250: q
      1252: q^2
      1255: q
      1259: q
      1260: q
      1263: 1
      1269: q
      1270: q
      1272: q^2
      1274: q^2
      1276: q^2
      1277: q
      1278: q^2
      1280: q^2
      1281: q
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1328: q
      1334: q^2
      1342: 1
      1365: q
      1370: q
      1372: 1
      1398: q
      1403: q
      1407: 1
      1412: 1
      1428: q
      1430: q^2
      1438: 1
      1440: 1
      1443: 1
      1445: 1
      1450: q
      1452: 1
      1455: q
      1458: 1
      1460: q
      1463: q
      1466: q
      1469: q
      1472: q^2
      1477: q
      1478: q
      1480: q^2
      1482: q^2
      1483: q
      1484: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1529: 1
      1541: 1
      1547: 1
      1551: 1
      1556: 1
      1576: q
      1597: q
      1625: q
      1629: q
      1631: q^2
      1640: 1
      1643: 1
      1645: 1
      1648: 1
      1649: q
      1651: 1
      1653: 1
      1656: 1
      1658: q
      1663: q
      1666: q
      1667: 1
      1670: 1
      1673: q
      1674: 1
      1679: 1
      1726: 1
      1735: 1
      1737: 1
      1747: 1
      1750: 1
      1761: 1
      1767: 1
      1775: 1
      1799: q
      1804: 1
      1813: q
      1819: q
      1822: q
      1826: 1
      1827: 1
      1829: 1
      1832: 1
      1833: 1
      1838: 1
      1849: 1
      1862: 1
      1899: 1
      1917: 1
      1929: 1
      1932: 1
      1938: 1
      1942: 1
      1954: q
      1956: 1
      1961: 1
      1962: 1
      1965: 1
      1969: 1
      1986: 1
      1994: 1
      2029: 1
      2032: 1
      2041: 1
      2046: 1
      2055: 1
      2062: 1
      2066: 1
      2071: 1
      2088: 1
      2096: 1
      2107: 1
      2134: 1
      2155: 1

2156:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        61: 1
        62: 1
        64: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       106: 1
       108: 1
       110: 1
       111: 1
       113: 1
       115: 1
       118: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       127: 1
       129: 1
       131: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       172: 1
       176: 1
       177: 1
       179: 1
       181: 1
       184: 1
       186: 1
       187: 1
       189: 1
       192: 1
       194: 1
       196: 1
       197: 1
       200: 1
       202: 1
       204: 1
       205: 1
       207: 1
       209: 1
       211: 1
       213: 1
       215: 1
       217: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       262: 1
       266: 1
       269: 1
       273: 1
       278: 1
       279: 1
       281: 1
       284: 1
       286: 1
       287: 1
       289: 1
       291: 1
       294: 1
       296: 1
       297: 1
       300: 1
       301: 1
       304: 1
       305: 1
       308: 1
       310: 1
       311: 1
       313: 1
       315: 1
       317: 1
       320: 1
       322: 1
       323: 1
       325: 1
       327: 1
       329: 1
       331: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       340: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       364: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       380: 1
       384: 1
       388: 1
       391: 1
       396: 1
       399: 1
       404: 1
       406: 1
       409: 1
       411: 1
       413: 1
       415: 1
       417: 1
       420: 1
       422: 1
       423: 1
       425: 1
       427: 1
       430: 1
       432: 1
       433: 1
       435: 1
       438: 1
       440: 1
       441: 1
       444: 1
       445: 1
       448: 1
       450: 1
       451: 1
       454: 1
       455: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       467: 1
       469: 1
       472: 1
       474: 1
       475: 1
       477: 1
       479: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       487: 1
       489: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       504: 1
       506: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       524: 1
       528: 1
       532: 1
       536: 1
       539: 1
       543: 1
       547: 1
       552: 1
       555: 1
       559: 1
       563: 1
       568: 1
       570: 1
       575: 1
       577: 1
       583: 1
       585: 1
       587: 1
       590: 1
       592: 1
       594: 1
       596: 1
       597: 1
       599: 1
       601: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       613: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       625: 1
       627: 1
       629: 1
       632: 1
       633: 1
       635: 1
       637: 1
       639: 1
       642: 1
       644: 1
       645: 1
       648: 1
       650: 1
       651: 1
       653: 1
       655: 1
       657: 1
       658: 1
       660: 1
       662: 1
       664: 1
       665: 1
       666: 1
       668: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       697: 1
       708: 1
       712: 1
       716: 1
       720: 1
       723: 1
       727: 1
       731: 1
       735: 1
       739: 1
       743: 1
       747: 1
       751: 1
       756: 1
       758: 1
       762: 1
       768: 1
       769: 1
       775: 1
       777: 1
       779: 1
       781: 1
       783: 1
       786: 1
       788: 1
       789: 1
       791: 1
       794: 1
       795: 1
       797: 1
       799: 1
       802: 1
       804: 1
       806: 1
       808: 1
       809: 1
       811: 1
       813: 1
       816: 1
       818: 1
       819: 1
       821: 1
       823: 1
       826: 1
       828: 1
       830: 1
       832: 1
       833: 1
       835: 1
       837: 1
       840: 1
       841: 1
       843: 1
       846: 1
       848: 1
       849: 1
       851: 1
       853: 1
       855: 1
       857: 1
       859: 1
       861: 1
       863: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       889: 1
       899: 1
       902: 1
       906: 1
       911: 1
       914: 1
       918: 1
       922: 1
       927: 1
       930: 1
       934: 1
       938: 1
       942: 1
       946: 1
       950: 1
       955: 1
       958: 1
       961: 1
       967: 1
       968: 1
       975: 1
       979: 1
       982: 1
       991: 1
       992: 1
       994: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1005: 1
      1007: 1
      1008: 1
      1010: 1
      1012: 1
      1014: 1
      1017: 1
      1018: 1
      1020: 1
      1022: 1
      1024: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1036: 1
      1038: 1
      1041: 1
      1042: 1
      1045: 1
      1046: 1
      1048: 1
      1050: 1
      1053: 1
      1055: 1
      1057: 1
      1059: 1
      1060: 1
      1062: 1
      1064: 1
      1066: 1
      1068: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1091: 1
      1102: 1
      1112: 1
      1116: 1
      1120: 1
      1124: 1
      1127: 1
      1133: 1
      1135: 1
      1138: 1
      1146: 1
      1150: 1
      1154: 1
      1158: 1
      1163: 1
      1166: 1
      1170: 1
      1174: 1
      1178: 1
      1183: 1
      1185: 1
      1188: 1
      1197: 1
      1199: 1
      1204: 1
      1208: 1
      1210: 1
      1212: 1
      1214: 1
      1217: 1
      1219: 1
      1220: 1
      1222: 1
      1224: 1
      1226: 1
      1229: 1
      1230: 1
      1233: 1
      1235: 1
      1236: 1
      1238: 1
      1241: 1
      1243: 1
      1244: 1
      1247: 1
      1248: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1259: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1269: 1
      1271: 1
      1272: 1
      1274: 1
      1276: 1
      1278: 1
      1280: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1295: 1
      1307: 1
      1316: 1
      1320: 1
      1323: 1
      1329: 1
      1331: 1
      1334: 1
      1342: 1
      1346: 1
      1350: 1
      1354: 1
      1358: 1
      1361: 1
      1367: 1
      1369: 1
      1374: 1
      1378: 1
      1382: 1
      1386: 1
      1390: 1
      1393: 1
      1399: 1
      1401: 1
      1404: 1
      1413: 1
      1415: 1
      1420: 1
      1424: 1
      1429: 1
      1430: 1
      1436: 1
      1438: 1
      1441: 1
      1443: 1
      1444: 1
      1446: 1
      1448: 1
      1451: 1
      1452: 1
      1455: 1
      1456: 1
      1458: 1
      1461: 1
      1463: 1
      1464: 1
      1467: 1
      1469: 1
      1470: 1
      1472: 1
      1474: 1
      1477: 1
      1479: 1
      1480: 1
      1482: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1494: 1
      1506: 1
      1518: 1
      1530: 1
      1538: 1
      1543: 1
      1547: 1
      1552: 1
      1553: 1
      1560: 1
      1565: 1
      1569: 1
      1572: 1
      1578: 1
      1580: 1
      1585: 1
      1589: 1
      1592: 1
      1598: 1
      1600: 1
      1605: 1
      1609: 1
      1613: 1
      1617: 1
      1622: 1
      1626: 1
      1630: 1
      1631: 1
      1637: 1
      1639: 1
      1641: 1
      1643: 1
      1646: 1
      1648: 1
      1650: 1
      1651: 1
      1654: 1
      1656: 1
      1658: 1
      1659: 1
      1661: 1
      1664: 1
      1666: 1
      1667: 1
      1669: 1
      1671: 1
      1673: 1
      1674: 1
      1680: 1
      1692: 1
      1704: 1
      1718: 1
      1723: 1
      1730: 1
      1736: 1
      1739: 1
      1742: 1
      1747: 1
      1752: 1
      1754: 1
      1759: 1
      1763: 1
      1767: 1
      1770: 1
      1776: 1
      1778: 1
      1783: 1
      1787: 1
      1791: 1
      1796: 1
      1800: 1
      1801: 1
      1808: 1
      1814: 1
      1815: 1
      1817: 1
      1820: 1
      1822: 1
      1823: 1
      1825: 1
      1827: 1
      1830: 1
      1832: 1
      1833: 1
      1839: 1
      1851: 1
      1863: 1
      1877: 1
      1889: 1
      1895: 1
      1900: 1
      1904: 1
      1907: 1
      1911: 1
      1916: 1
      1920: 1
      1923: 1
      1926: 1
      1934: 1
      1938: 1
      1943: 1
      1945: 1
      1949: 1
      1955: 1
      1956: 1
      1958: 1
      1960: 1
      1963: 1
      1965: 1
      1970: 1
      1982: 1
      1997: 1
      2009: 1
      2019: 1
      2026: 1
      2034: 1
      2037: 1
      2042: 1
      2046: 1
      2049: 1
      2054: 1
      2057: 1
      2063: 1
      2067: 1
      2072: 1
      2084: 1
      2097: 1
      2111: 1
      2121: 1
      2135: 1
      2156: 1

2157:    0: 3q^5+5q^4+5q^3+2q^2
         1: 3q^5+5q^4+5q^3+2q^2
         2: 3q^5+5q^4+5q^3+2q^2
         3: 3q^5+5q^4+5q^3+2q^2
         4: q^6+3q^5+5q^4+4q^3+2q^2
         5: 3q^5+5q^4+5q^3+2q^2
         6: q^6+3q^5+5q^4+4q^3+2q^2
         7: q^6+3q^5+5q^4+4q^3+2q^2
         8: 3q^5+5q^4+5q^3+2q^2
         9: q^7+2q^6+3q^5+4q^4+3q^3+2q^2
        10: q^5+4q^4+5q^3+2q^2
        11: q^5+4q^4+5q^3+2q^2
        12: 2q^5+4q^4+4q^3+2q^2
        13: 3q^5+5q^4+5q^3+2q^2
        14: q^6+3q^5+5q^4+4q^3+2q^2
        15: 3q^5+5q^4+5q^3+2q^2
        16: q^5+4q^4+5q^3+2q^2
        17: q^5+4q^4+5q^3+2q^2
        18: q^6+2q^5+4q^4+3q^3+2q^2
        19: 2q^5+4q^4+4q^3+2q^2
        20: 2q^5+4q^4+4q^3+2q^2
        21: 2q^5+4q^4+4q^3+2q^2
        22: 3q^5+5q^4+5q^3+2q^2
        23: 3q^5+5q^4+5q^3+2q^2
        24: 3q^5+5q^4+5q^3+2q^2
        25: 3q^5+5q^4+5q^3+2q^2
        26: 3q^5+5q^4+5q^3+2q^2
        27: 3q^5+5q^4+5q^3+2q^2
        28: 3q^4+5q^3+2q^2
        29: q^5+3q^4+4q^3+2q^2
        30: 2q^5+4q^4+4q^3+2q^2
        31: q^5+4q^4+5q^3+2q^2
        32: 3q^5+5q^4+5q^3+2q^2
        33: q^5+4q^4+5q^3+2q^2
        34: q^5+4q^4+5q^3+2q^2
        35: 3q^5+5q^4+5q^3+2q^2
        36: q^5+4q^4+5q^3+2q^2
        37: q^5+q^4+q^3
        38: 2q^5+4q^4+4q^3+2q^2
        39: q^5+q^4+q^3
        40: 2q^5+4q^4+4q^3+2q^2
        41: q^5+q^4+q^3
        42: 2q^5+4q^4+4q^3+2q^2
        43: q^5+4q^4+5q^3+2q^2
        44: 2q^5+4q^4+4q^3+2q^2
        45: q^5+4q^4+5q^3+2q^2
        46: q^5+4q^4+5q^3+2q^2
        47: q^5+4q^4+5q^3+2q^2
        48: q^6+2q^5+4q^4+3q^3+2q^2
        49: 3q^4+4q^3+2q^2
        50: 3q^4+4q^3+2q^2
        51: q^5+3q^4+3q^3+2q^2
        52: 2q^5+4q^4+4q^3+2q^2
        53: 2q^5+4q^4+4q^3+2q^2
        54: 2q^5+4q^4+4q^3+2q^2
        55: 2q^5+4q^4+4q^3+2q^2
        56: 2q^5+4q^4+4q^3+2q^2
        57: 2q^5+4q^4+4q^3+2q^2
        58: 2q^4+3q^3+q^2
        59: q^4+2q^3+q^2
        60: 2q^4+3q^3+q^2
        61: q^4+2q^3+q^2
        62: q^4+q^3
        63: q^5+3q^4+4q^3+2q^2
        64: q^5+q^4+q^3
        65: 2q^5+4q^4+4q^3+2q^2
        66: q^4+q^3
        67: q^5+3q^4+4q^3+2q^2
        68: 3q^4+5q^3+2q^2
        69: 2q^4+3q^3+2q^2
        70: q^5+3q^4+4q^3+2q^2
        71: 2q^4+4q^3+2q^2
        72: 2q^4+3q^3+2q^2
        73: 2q^4+3q^3+2q^2
        75: q^5+3q^4+3q^3+2q^2
        77: q^5+3q^4+3q^3+2q^2
        79: q^5+3q^4+3q^3+2q^2
        80: q^5+4q^4+5q^3+2q^2
        81: q^5+4q^4+5q^3+2q^2
        82: q^5+3q^4+4q^3+2q^2
        83: 2q^5+4q^4+4q^3+2q^2
        84: q^5+4q^4+5q^3+2q^2
        85: q^5+4q^4+5q^3+2q^2
        86: q^5+3q^4+4q^3+2q^2
        87: 2q^5+4q^4+4q^3+2q^2
        88: 2q^4+5q^3+2q^2
        89: 2q^4+5q^3+2q^2
        90: q^5+3q^4+3q^3+2q^2
        91: 3q^4+4q^3+2q^2
        92: 3q^4+4q^3+2q^2
        93: q^5+3q^4+3q^3+2q^2
        94: 3q^4+4q^3+2q^2
        95: 3q^4+4q^3+2q^2
        96: q^5+3q^4+3q^3+2q^2
        97: 3q^4+4q^3+2q^2
        98: 3q^4+4q^3+2q^2
        99: q^5+3q^4+3q^3+2q^2
       100: 2q^5+4q^4+4q^3+2q^2
       101: 2q^5+4q^4+4q^3+2q^2
       102: 2q^5+4q^4+4q^3+2q^2
       103: q^4+q^3
       104: q^4+2q^3+q^2
       105: q^4+2q^3+q^2
       107: q^4+2q^3+q^2
       108: q^3+q^2
       109: q^4+2q^3+q^2
       110: q^3+q^2
       112: q^4+2q^3+2q^2
       114: q^5+2q^4+3q^3+2q^2
       116: q^5+3q^4+3q^3+2q^2
       117: 2q^4+3q^3+q^2
       118: q^4+2q^3+q^2
       119: 2q^4+3q^3+q^2
       120: q^4+2q^3+q^2
       121: q^4+q^3
       122: q^5+3q^4+4q^3+2q^2
       123: q^4+q^3
       124: q^5+3q^4+4q^3+2q^2
       125: 2q^4+5q^3+2q^2
       126: q^4+3q^3+2q^2
       128: q^4+3q^3+2q^2
       130: q^4+3q^3+2q^2
       132: 2q^4+2q^3+2q^2
       133: 2q^4+4q^3+2q^2
       134: 2q^4+3q^3+2q^2
       135: 2q^4+3q^3+2q^2
       136: 2q^4+3q^3+2q^2
       137: 2q^4+5q^3+2q^2
       138: 2q^4+3q^3+2q^2
       139: 2q^4+4q^3+2q^2
       140: 2q^4+3q^3+2q^2
       141: q^5+3q^4+4q^3+2q^2
       142: 2q^4+3q^3+2q^2
       143: 2q^4+5q^3+2q^2
       144: 2q^4+3q^3+2q^2
       145: 2q^4+4q^3+2q^2
       146: q^5+3q^4+4q^3+2q^2
       147: 2q^4+3q^3+2q^2
       148: 2q^4+3q^3+2q^2
       149: q^5+3q^4+4q^3+2q^2
       150: 2q^5+4q^4+4q^3+2q^2
       152: q^5+3q^4+3q^3+2q^2
       154: q^5+3q^4+3q^3+2q^2
       156: q^5+3q^4+3q^3+2q^2
       157: 4q^3+2q^2
       158: 4q^3+2q^2
       159: q^4+3q^3+2q^2
       160: 3q^4+4q^3+2q^2
       161: 3q^4+4q^3+2q^2
       162: q^5+3q^4+3q^3+2q^2
       163: 3q^4+4q^3+2q^2
       164: 3q^4+4q^3+2q^2
       165: q^5+3q^4+3q^3+2q^2
       166: 3q^4+4q^3+2q^2
       167: 3q^4+4q^3+2q^2
       168: q^5+3q^4+3q^3+2q^2
       170: q^3+q^2
       171: q^3+q^2
       173: q^4+q^3
       174: q^4+2q^3+q^2
       175: q^4+2q^3+q^2
       178: q^4+2q^3+2q^2
       180: q^4+3q^3+2q^2
       182: 2q^3+2q^2
       183: q^4+2q^3+q^2
       184: q^3+q^2
       185: q^4+2q^3+q^2
       186: q^3+q^2
       188: q^4+2q^3+2q^2
       190: q^5+2q^4+3q^3+2q^2
       191: q^4+3q^3+q^2
       192: q^4+2q^3+q^2
       193: q^4+2q^3+q^2
       194: q^3+q^2
       195: q^4+2q^3+q^2
       196: q^3+q^2
       198: q^4+2q^3+2q^2
       199: q^4+3q^3+q^2
       200: q^4+2q^3+q^2
       201: q^4+2q^3+q^2
       202: q^3+q^2
       203: q^4+2q^3+q^2
       204: q^3+q^2
       206: q^4+2q^3+2q^2
       207: q^3
       208: 2q^4+4q^3+2q^2
       210: q^5+2q^4+3q^3+2q^2
       212: q^5+3q^4+3q^3+2q^2
       214: q^4+3q^3+2q^2
       216: q^4+3q^3+2q^2
       218: 2q^4+2q^3+2q^2
       219: q^4+3q^3+2q^2
       220: 4q^3+2q^2
       221: 3q^3+2q^2
       222: 3q^3+2q^2
       223: q^4+2q^3+2q^2
       224: 3q^3+2q^2
       225: q^4+2q^3+2q^2
       226: q^4+3q^3+2q^2
       227: 2q^4+4q^3+2q^2
       228: 2q^4+3q^3+2q^2
       229: 2q^4+3q^3+2q^2
       230: 2q^4+3q^3+2q^2
       231: q^4+3q^3+2q^2
       232: 2q^4+4q^3+2q^2
       233: 2q^4+3q^3+2q^2
       234: 2q^4+3q^3+2q^2
       235: 2q^4+3q^3+2q^2
       236: 2q^4+3q^3+2q^2
       238: q^4+3q^3+2q^2
       240: q^4+3q^3+2q^2
       242: 2q^4+2q^3+2q^2
       243: 2q^4+4q^3+2q^2
       244: 2q^4+3q^3+2q^2
       245: 2q^4+3q^3+2q^2
       246: q^5+3q^4+4q^3+2q^2
       247: 3q^3+3q^2
       248: 3q^3+3q^2
       249: 2q^4+2q^3+2q^2
       250: 4q^3+2q^2
       251: 4q^3+2q^2
       252: q^4+3q^3+2q^2
       253: 4q^3+2q^2
       254: 4q^3+2q^2
       255: q^4+3q^3+2q^2
       256: 3q^4+4q^3+2q^2
       257: 3q^4+4q^3+2q^2
       258: q^5+3q^4+3q^3+2q^2
       260: q^3+q^2
       261: q^3+q^2
       264: q^3+q^2
       265: q^3+q^2
       268: q^3+q^2
       270: q^3+q^2
       272: q^3+q^2
       274: q^3+q^2
       275: q^3
       276: q^4+2q^3+q^2
       277: q^4+2q^3+q^2
       280: q^4+3q^3+2q^2
       282: q^4+2q^3+2q^2
       283: q^3+q^2
       284: q^2
       285: q^3+q^2
       286: q^2
       288: q^4+2q^3+2q^2
       290: 2q^3+2q^2
       292: q^3+2q^2
       293: 2q^3+q^2
       294: q^3+q^2
       295: 2q^3+q^2
       296: q^3+q^2
       298: 2q^3+2q^2
       299: q^4+2q^3+q^2
       300: q^3+q^2
       302: 2q^3+2q^2
       303: q^4+2q^3+q^2
       304: q^3+q^2
       306: q^4+2q^3+2q^2
       307: q^4+2q^3+q^2
       308: q^3+q^2
       309: q^4+2q^3+q^2
       310: q^3+q^2
       312: 2q^3+2q^2
       314: q^4+2q^3+2q^2
       316: q^4+2q^3+2q^2
       318: q^4+3q^3+2q^2
       319: q^4+2q^3+q^2
       320: q^3+q^2
       321: q^4+2q^3+q^2
       322: q^3+q^2
       324: q^4+2q^3+2q^2
       326: q^5+2q^4+3q^3+2q^2
       328: q^3+2q^2
       330: q^3+2q^2
       332: q^3+2q^2
       333: 3q^3+2q^2
       334: 2q^3+2q^2
       335: 2q^3+2q^2
       336: q^3+2q^2
       337: 3q^3+3q^2
       339: 3q^3+3q^2
       341: 3q^3+3q^2
       343: 2q^4+2q^3+2q^2
       344: q^4+3q^3+2q^2
       345: 4q^3+2q^2
       346: 3q^3+2q^2
       347: 3q^3+2q^2
       348: q^4+2q^3+2q^2
       349: 3q^3+2q^2
       350: q^4+2q^3+2q^2
       351: 3q^3+3q^2
       352: q^4+3q^3+2q^2
       353: 4q^3+2q^2
       354: 3q^3+2q^2
       355: 3q^3+2q^2
       356: q^4+2q^3+2q^2
       357: 3q^3+2q^2
       358: q^4+2q^3+2q^2
       359: 3q^3+3q^2
       361: q^4+3q^3+2q^2
       363: q^4+3q^3+2q^2
       365: 2q^4+2q^3+2q^2
       366: q^4+3q^3+2q^2
       367: 2q^4+4q^3+2q^2
       368: 2q^4+3q^3+2q^2
       369: 2q^4+3q^3+2q^2
       370: 2q^4+3q^3+2q^2
       371: 3q^3+3q^2
       372: 3q^3+3q^2
       373: 2q^4+2q^3+2q^2
       374: 4q^3+2q^2
       375: 4q^3+2q^2
       376: q^4+3q^3+2q^2
       378: q^2
       379: q^2
       382: q^3+q^2
       383: q^3+q^2
       386: q^3+q^2
       387: q^3+q^2
       390: q^3+q^2
       392: q^3+q^2
       394: q^3+q^2
       395: q^3+q^2
       398: q^3+q^2
       400: q^3+q^2
       402: q^3+q^2
       403: q^3+q^2
       407: q^3+q^2
       408: q^3+q^2
       410: q^3+2q^2
       412: q^3+2q^2
       414: q^4+2q^3+2q^2
       416: 2q^2
       418: q^3+2q^2
       419: q^3+q^2
       420: q^2
       421: q^3+q^2
       422: q^2
       424: q^3+2q^2
       426: q^3+2q^2
       428: 3q^3+3q^2
       429: q^3+q^2
       430: q^2
       431: q^3+q^2
       432: q^2
       434: q^3+2q^2
       436: 2q^3+2q^2
       437: 2q^3+q^2
       438: q^3+q^2
       439: 2q^3+q^2
       440: q^3+q^2
       442: 2q^3+2q^2
       443: 2q^3+2q^2
       444: q^3+q^2
       446: 3q^3+3q^2
       447: q^3+q^2
       448: q^2
       449: q^3+q^2
       450: q^2
       452: q^3+2q^2
       453: 2q^3+q^2
       454: q^3+q^2
       456: 2q^3+2q^2
       457: 2q^3+q^2
       458: q^3+q^2
       460: 2q^3+2q^2
       461: 2q^3+2q^2
       462: q^3+q^2
       464: 3q^3+3q^2
       466: q^4+3q^3+2q^2
       468: q^4+2q^3+2q^2
       470: q^4+2q^3+2q^2
       471: q^4+2q^3+q^2
       472: q^3+q^2
       473: q^4+2q^3+q^2
       474: q^3+q^2
       476: q^4+2q^3+2q^2
       478: 2q^3+2q^2
       479: q^3+q^2
       480: 2q^3+2q^2
       481: 2q^3+2q^2
       482: 2q^3+2q^2
       483: q^3+2q^2
       484: 3q^3+3q^2
       486: 3q^3+3q^2
       488: 3q^3+3q^2
       490: 2q^4+2q^3+2q^2
       491: q^3+2q^2
       492: 3q^3+2q^2
       493: 2q^3+2q^2
       494: 2q^3+2q^2
       495: q^3+2q^2
       496: 3q^3+3q^2
       497: 3q^3+2q^2
       498: 2q^3+2q^2
       499: 2q^3+2q^2
       500: q^3+2q^2
       501: 3q^3+3q^2
       503: q^3+2q^2
       505: q^3+2q^2
       507: q^3+2q^2
       508: q^4+3q^3+2q^2
       509: 4q^3+2q^2
       510: 3q^3+2q^2
       511: 3q^3+2q^2
       512: q^4+2q^3+2q^2
       513: 3q^3+2q^2
       514: q^4+2q^3+2q^2
       515: 3q^2
       516: 3q^2
       517: q^3+2q^2
       518: 3q^2
       519: 3q^2
       520: q^3+2q^2
       522: q^2
       523: q^2
       526: q^2
       527: q^2
       530: q^2
       531: q^2
       534: q^2
       535: q^2
       538: q^3+q^2
       540: q^3+q^2
       542: q^3+q^2
       544: q^3+q^2
       546: 2q^3+2q^2
       548: q^3+q^2
       550: q^2
       551: q^2
       554: q^3+q^2
       556: q^3+q^2
       558: q^3+q^2
       560: q^3+q^2
       562: 2q^3+2q^2
       564: q^3+q^2
       566: q^3+q^2
       567: q^3+q^2
       571: q^3+q^2
       572: q^3+q^2
       573: q^3+q^2
       574: q^3+q^2
       576: q^3+q^2
       578: q^3+q^2
       581: 2q^3+2q^2
       584: q^3+2q^2
       586: q^3+2q^2
       588: 2q^2
       589: q^3+q^2
       590: q^2
       591: q^2
       593: q^2
       595: q^3+q^2
       596: q^2
       598: q^3+2q^2
       600: q^3+2q^2
       602: 3q^3+3q^2
       603: q^3+q^2
       604: q^2
       606: q^3+2q^2
       607: q^3+q^2
       608: q^2
       610: q^3+2q^2
       612: 2q^2
       614: q^3+2q^2
       615: 2q^3+2q^2
       616: q^3+q^2
       618: 3q^3+3q^2
       619: q^3+q^2
       620: q^2
       621: q^3+q^2
       622: q^2
       624: q^3+2q^2
       626: q^3+2q^2
       628: 2q^2
       630: q^3+2q^2
       631: 2q^3+2q^2
       632: q^3+q^2
       634: 3q^3+3q^2
       636: q^3+2q^2
       638: q^3+2q^2
       640: q^4+2q^3+2q^2
       641: q^3+q^2
       642: q^2
       643: q^3+q^2
       644: q^2
       646: q^3+2q^2
       647: 2q^3+q^2
       648: q^3+q^2
       649: 2q^3+q^2
       650: q^3+q^2
       652: 2q^3+2q^2
       654: 2q^3+2q^2
       655: q^3+q^2
       656: 2q^3+2q^2
       657: 3q^2
       659: 3q^2
       661: 3q^2
       663: q^3+2q^2
       664: 2q^2
       665: q^3+2q^2
       667: 3q^2
       669: 3q^2
       671: q^3+2q^2
       672: 3q^2
       673: 2q^2
       674: 3q^2
       675: 2q^3+2q^2
       676: 2q^3+2q^2
       677: q^3+2q^2
       678: 3q^2
       679: q^3+2q^2
       680: 3q^2
       681: 2q^3+2q^2
       682: 2q^3+2q^2
       683: q^3+2q^2
       684: 3q^2
       685: q^3+2q^2
       686: 3q^3+2q^2
       687: 2q^3+2q^2
       688: 2q^3+2q^2
       689: q^3+2q^2
       694: q^3+q^2
       699: q^3+q^2
       700: q^3+q^2
       706: q^2
       707: q^2
       710: q^2
       711: q^2
       714: q^2
       718: q^2
       722: q^2
       724: q^2
       726: q^2
       728: q^2
       730: q^2
       732: q^2
       734: 2q^3+2q^2
       736: q^3+q^2
       738: q^2
       740: q^2
       742: q^2
       744: q^2
       746: q^2
       748: q^2
       750: 2q^3+2q^2
       752: q^3+q^2
       754: q^2
       755: q^2
       759: q^3+q^2
       760: q^3+q^2
       763: q^3+q^2
       764: q^3+q^2
       765: q^3+q^2
       766: q^3+q^2
       767: q^3+q^2
       770: q^3+q^2
       773: 2q^3+2q^2
       776: 3q^2
       778: 2q^2
       780: 2q^2
       782: q^3+2q^2
       784: 2q^2
       785: q^2
       787: q^2
       790: 3q^2
       792: q^2
       793: 2q^2
       794: q^2
       796: 3q^2
       798: q^3+2q^2
       800: 2q^2
       801: q^3+q^2
       802: q^2
       803: q^2
       805: q^2
       807: q^3+q^2
       808: q^2
       810: q^3+2q^2
       812: q^3+2q^2
       814: 3q^2
       815: 2q^2
       816: q^2
       817: 2q^2
       818: q^2
       820: 3q^2
       822: q^3+2q^2
       824: 2q^2
       825: q^3+q^2
       826: q^2
       827: q^2
       829: q^2
       831: q^3+q^2
       832: q^2
       834: q^3+2q^2
       836: q^3+2q^2
       838: 3q^2
       839: 2q^2
       840: q^2
       842: q^3+2q^2
       843: q^2
       844: 2q^2
       845: q^3+q^2
       846: q^2
       847: q^3+q^2
       848: q^2
       850: q^3+2q^2
       852: q^3+2q^2
       854: 2q^2
       856: q^3+2q^2
       857: q^2
       858: 2q^2
       866: 2q^2
       868: 2q^2
       870: 2q^2
       871: q^3+2q^2
       872: 2q^2
       874: 2q^2
       875: q^3+2q^2
       876: 2q^2
       877: 2q^3+2q^2
       878: 2q^3+2q^2
       879: q^3+2q^2
       880: q^3+2q^2
       885: q^3+q^2
       890: q^3+q^2
       891: q^3+q^2
       897: q^2
       898: q^2
       901: q^2
       905: q^2
       913: q^2
       915: q^2
       917: 2q^2
       919: q^2
       921: q^2
       923: q^2
       925: q^2
       929: q^2
       933: 2q^2
       935: q^2
       937: q^2
       939: q^2
       941: 2q^2
       943: q^2
       945: q^2
       947: q^2
       949: q^2
       953: q^2
       957: 2q^2
       959: q^2
       962: q^2
       963: q^2
       964: q^2
       965: q^2
       966: q^2
       969: q^2
       972: 2q^2
       976: q^2
       977: q^2
       980: q^2
       981: q^2
       983: q^2
       986: 2q^2
       988: q^2
       989: q^2
       990: q^2
       995: 2q^2
       998: q^2
      1000: q^2
      1003: 2q^2
      1004: q^2
      1006: q^2
      1009: q^2
      1011: q^2
      1013: q^2
      1019: 2q^2
      1021: 2q^2
      1023: q^3+2q^2
      1025: 2q^2
      1026: q^2
      1028: q^2
      1035: 2q^2
      1037: 2q^2
      1039: q^3+2q^2
      1040: q^2
      1043: 2q^2
      1044: q^2
      1049: q^3+2q^2
      1051: 2q^2
      1052: q^3+q^2
      1053: q^2
      1054: q^2
      1056: q^2
      1058: q^3+q^2
      1059: q^2
      1061: q^3+2q^2
      1063: q^3+2q^2
      1065: q^2
      1076: 2q^2
      1078: 2q^2
      1080: 2q^2
      1082: 2q^2
      1083: q^3+2q^2
      1084: 2q^2
      1085: 2q^2
      1087: q^2
      1092: q^2
      1093: q^2
      1099: q^2
      1104: q^2
      1105: q^2
      1111: q^2
      1115: q^2
      1119: q^2
      1123: q^2
      1142: q^2
      1149: q^2
      1151: q^2
      1153: q^2
      1157: q^2
      1169: q^2
      1171: q^2
      1173: q^2
      1177: q^2
      1186: q^2
      1187: q^2
      1200: q^2
      1201: q^2
      1203: q^2
      1207: q^2
      1221: q^2
      1223: q^2
      1231: 2q^2
      1232: q^2
      1234: q^2
      1239: 2q^2
      1240: q^2
      1242: q^2
      1249: 2q^2
      1250: q^2
      1254: q^2
      1257: 2q^2
      1258: q^2
      1260: q^2
      1265: 2q^2
      1267: q^3+2q^2
      1268: q^2
      1270: q^2
      1273: 2q^2
      1275: 2q^2
      1277: q^2
      1279: q^2
      1281: q^2
      1287: 2q^2
      1289: 2q^2
      1345: q^2
      1349: q^2
      1353: q^2
      1357: q^2
      1377: q^2
      1381: q^2
      1385: q^2
      1389: q^2
      1416: q^2
      1417: q^2
      1419: q^2
      1423: q^2
      1434: q^2
      1447: q^2
      1465: 2q^2
      1466: q^2
      1468: q^2
      1471: 2q^2
      1475: q^2
      1476: q^2
      1478: q^2
      1481: q^2
      1484: q
      1604: q^2
      1608: q^2
      1612: q^2
      1616: q^2
      1638: q
      1642: q
      1649: q
      1657: q
      1672: q^2
      1728: q
      1758: q
      1782: q
      1811: q
      1824: q
      1883: q
      1931: q
      1959: 1
      2031: 1
      2038: 1
      2050: 1
      2077: 1
      2089: 1
      2120: 1
      2157: 1

2158:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        59: 1
        60: 1
        63: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       107: 1
       110: 1
       112: 1
       114: 1
       116: 1
       118: 1
       119: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       188: 1
       190: 1
       192: 1
       193: 1
       196: 1
       198: 1
       199: 1
       201: 1
       204: 1
       206: 1
       208: 1
       210: 1
       212: 1
       214: 1
       216: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       240: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       260: 1
       264: 1
       268: 1
       274: 1
       276: 1
       280: 1
       282: 1
       283: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       296: 1
       298: 1
       299: 1
       302: 1
       304: 1
       306: 1
       307: 1
       310: 1
       312: 1
       314: 1
       316: 1
       318: 1
       319: 1
       322: 1
       324: 1
       326: 1
       328: 1
       330: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       339: 1
       341: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       378: 1
       382: 1
       386: 1
       390: 1
       394: 1
       400: 1
       403: 1
       407: 1
       410: 1
       412: 1
       414: 1
       416: 1
       418: 1
       419: 1
       422: 1
       424: 1
       426: 1
       428: 1
       429: 1
       432: 1
       434: 1
       436: 1
       437: 1
       440: 1
       442: 1
       443: 1
       446: 1
       447: 1
       450: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       462: 1
       464: 1
       466: 1
       468: 1
       470: 1
       471: 1
       474: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       486: 1
       488: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       503: 1
       505: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       526: 1
       530: 1
       534: 1
       538: 1
       542: 1
       546: 1
       551: 1
       556: 1
       560: 1
       564: 1
       566: 1
       571: 1
       574: 1
       581: 1
       584: 1
       586: 1
       588: 1
       589: 1
       592: 1
       593: 1
       596: 1
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      1772: 1
      1775: 1
      1780: 1
      1784: 1
      1786: 1
      1792: 1
      1795: 1
      1799: 1
      1805: 1
      1810: 1
      1813: 1
      1816: 1
      1818: 1
      1819: 1
      1822: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1832: 1
      1833: 1
      1841: 1
      1852: 1
      1865: 1
      1876: 1
      1888: 1
      1896: 1
      1899: 1
      1903: 1
      1908: 1
      1913: 1
      1917: 1
      1921: 1
      1925: 1
      1930: 1
      1933: 1
      1939: 1
      1942: 1
      1947: 1
      1951: 1
      1954: 1
      1957: 1
      1959: 1
      1961: 1
      1962: 1
      1965: 1
      1971: 1
      1988: 1
      1996: 1
      2008: 1
      2021: 1
      2030: 1
      2033: 1
      2038: 1
      2041: 1
      2047: 1
      2051: 1
      2055: 1
      2059: 1
      2062: 1
      2066: 1
      2073: 1
      2090: 1
      2099: 1
      2109: 1
      2123: 1
      2134: 1
      2159: 1

2160:    0: 2q^2+q
         1: 2q^2+q
         2: q^3+q^2+q
         3: 2q^2+q
         4: 2q^2+q
         5: 2q^2+q
         6: 2q^2+q
         7: q^3+q^2+q
         8: q^3+q^2+q
         9: q^3+q^2+q
        10: 2q^2+q
        11: 2q^2+q
        12: 2q^2+q
        13: q^2+q
        14: q^2+q
        15: q^2+q
        16: 2q^2+q
        17: 2q^2+q
        18: q^3+q^2+q
        19: 2q^2+q
        20: 2q^2+q
        21: q^3+q^2+q
        22: 2q^2+q
        23: 2q^2+q
        24: q^3+q^2+q
        25: 2q^2+q
        26: 2q^2+q
        27: q^3+q^2+q
        28: 2q^2+q
        29: 2q^2+q
        30: q^2+q
        31: 2q^2+q
        32: q^2+q
        33: 2q^2+q
        34: 2q^2+q
        35: q^2+q
        36: 2q^2+q
        37: q
        38: 2q^2
        39: q
        40: 2q^2
        41: q
        42: q^3+q^2
        43: q^2+q
        44: q^2+q
        45: q^2+q
        46: q^2+q
        47: q^2+q
        48: q^2+q
        49: 2q^2+q
        50: 2q^2+q
        51: q^3+q^2+q
        52: 2q^2+q
        53: 2q^2+q
        54: q^3+q^2+q
        55: 2q^2+q
        56: 2q^2+q
        57: q^3+q^2+q
        58: q^2
        59: q^2+q
        60: q^2
        61: q^2+q
        62: q
        63: 2q^2
        64: q
        65: q^2
        66: q
        67: 2q^2
        68: q
        69: q^2+q
        70: q^2+q
        71: 2q^2+q
        72: 2q^2+q
        73: 2q^2+q
        74: q
        75: 2q^2
        76: q
        77: 2q^2
        78: q
        79: q^3+q^2
        80: q^2+q
        81: q^2+q
        82: 2q^2+q
        83: q^2+q
        84: q^2+q
        85: q^2+q
        86: 2q^2+q
        87: q^2+q
        88: q^2+q
        89: q^2+q
        90: q^2+q
        91: q^2+q
        92: q^2+q
        93: q^2+q
        94: 2q^2+q
        95: 2q^2+q
        96: q^3+q^2+q
        97: 2q^2+q
        98: 2q^2+q
        99: q^3+q^2+q
       100: 2q^2+q
       101: 2q^2+q
       102: q^3+q^2+q
       104: q^2
       105: q^2
       106: q
       107: q^2
       108: q^2+q
       109: q^2
       110: q^2+q
       111: q
       112: 2q^2
       113: q
       114: 2q^2
       115: q
       116: q^2
       118: q
       120: q
       121: q
       122: q^2
       123: q
       124: q^2
       125: q
       126: q^2+q
       127: q
       128: 2q^2
       129: q
       130: 2q^2
       131: q
       132: q^3+q^2
       133: q
       134: q^2+q
       135: q^2+q
       136: q^2+q
       137: q^2+q
       138: q^2+q
       139: 2q^2+q
       140: 2q^2+q
       141: q^2+q
       142: 2q^2+q
       143: q^2+q
       144: q^2+q
       145: 2q^2+q
       146: q^2+q
       147: 2q^2+q
       148: 2q^2+q
       149: 2q^2+q
       150: q^2+q
       151: q
       152: 2q^2
       153: q
       154: 2q^2
       155: q
       156: q^3+q^2
       157: q^2+q
       158: q^2+q
       159: q^2+q
       160: q^2+q
       161: q^2+q
       162: q^2+q
       163: q^2+q
       164: q^2+q
       165: q^2+q
       166: 2q^2+q
       167: 2q^2+q
       168: q^3+q^2+q
       170: q^2
       171: q^2
       172: q
       176: q
       177: q
       178: q^2
       179: q
       180: 2q^2
       181: q
       182: 2q^2
       184: q
       186: q
       187: q
       188: q^2
       189: q
       190: q^2
       192: q
       193: q^2
       194: q^2+q
       195: q^2
       196: q^2+q
       197: q
       198: 2q^2
       200: q
       201: q^2
       202: q^2+q
       203: q^2
       204: q^2+q
       205: q
       206: 2q^2
       207: q
       208: q^2
       209: q
       210: 2q^2
       211: q
       212: q^2
       214: q^2
       216: q^2
       218: q^2
       219: q
       220: q
       221: q^2+q
       222: q^2+q
       223: q^2+q
       224: q^2+q
       225: q^2+q
       226: q^2+q
       227: q
       228: q^2+q
       229: q^2+q
       230: q^2+q
       231: q^2+q
       232: q
       233: q^2+q
       234: q^2+q
       235: q^2+q
       236: q^2+q
       237: q
       238: 2q^2
       239: q
       240: 2q^2
       241: q
       242: q^3+q^2
       243: 2q^2+q
       244: 2q^2+q
       245: 2q^2+q
       246: q^2+q
       247: 2q^2+q
       248: 2q^2+q
       249: q^3+q^2+q
       250: q^2+q
       251: q^2+q
       252: q^2+q
       253: q^2+q
       254: q^2+q
       255: q^2+q
       256: q^2+q
       257: q^2+q
       258: q^2+q
       260: q^2
       261: q^2
       262: q
       266: q
       268: q^2
       269: q
       270: q^2
       272: q^2
       273: q
       274: q^2
       278: q
       282: q^2
       284: q
       286: q
       287: q
       288: q^2
       290: q^2
       291: q
       292: q^2
       294: q
       296: q
       297: q
       298: q^2
       300: q
       301: q
       302: 2q^2
       304: q
       305: q
       306: q^2
       308: q
       310: q
       311: q
       312: 2q^2
       313: q
       314: q^2
       315: q
       316: q^2
       317: q
       318: 2q^2
       319: q^2
       320: q^2+q
       321: q^2
       322: q^2+q
       323: q
       324: 2q^2
       325: q
       326: q^2
       328: q^2
       330: q^2
       332: q^2
       333: q
       334: q^2+q
       335: q^2+q
       336: q^2+q
       337: 2q^2+q
       338: q
       339: 2q^2
       340: q
       341: 2q^2
       342: q
       343: q^3+q^2
       344: q
       345: q
       346: q^2+q
       347: q^2+q
       348: q^2+q
       349: q^2+q
       350: q^2+q
       351: 2q^2+q
       352: q
       353: q
       354: q^2+q
       355: q^2+q
       356: q^2+q
       357: q^2+q
       358: q^2+q
       359: 2q^2+q
       361: q^2
       363: q^2
       365: q^2
       366: q^2+q
       367: q
       368: q^2+q
       369: q^2+q
       370: q^2+q
       371: q^2+q
       372: q^2+q
       373: q^2+q
       374: q^2+q
       375: q^2+q
       376: q^2+q
       380: q
       388: q
       390: q^2
       391: q
       392: q^2
       396: q
       398: q^2
       399: q
       400: q^2
       404: q
       406: q
       407: q^2
       408: q^2
       412: q^2
       416: q^2
       418: q^2
       420: q
       422: q
       423: q
       424: q^2
       425: q
       426: q^2
       427: q
       428: 2q^2
       430: q
       432: q
       433: q
       434: q^2
       436: q^2
       438: q
       440: q
       441: q
       442: q^2
       443: q^2
       444: q^2+q
       445: q
       446: 2q^2
       448: q
       450: q
       451: q
       452: q^2
       454: q
       456: q^2
       458: q
       459: q
       460: q^2
       461: q^2
       462: q^2+q
       463: q
       464: 2q^2
       468: q^2
       469: q
       470: q^2
       472: q
       474: q
       475: q
       476: q^2
       477: q
       478: 2q^2
       479: q
       480: 2q^2
       481: q
       482: q
       483: q^2+q
       484: q
       486: q^2
       488: q^2
       490: q^2
       491: q^2+q
       492: q
       493: q^2+q
       494: q^2+q
       495: q^2+q
       496: q^2+q
       497: q
       498: q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       503: q^2
       505: q^2
       507: q^2
       508: q
       509: q
       510: q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^2+q
       516: q^2+q
       517: q^2+q
       518: q^2+q
       519: q^2+q
       520: q^2+q
       532: q
       536: q
       543: q
       546: q^2
       547: q
       548: q^2
       552: q
       559: q
       562: q^2
       563: q
       564: q^2
       568: q
       570: q
       571: q^2
       572: q^2
       574: q^2
       575: q
       576: q^2
       577: q
       581: 2q^2
       588: q^2
       590: q
       592: q
       594: q
       596: q
       598: q^2
       599: q
       600: q^2
       604: q
       606: q^2
       608: q
       609: q
       610: q^2
       612: q^2
       613: q
       614: q^2
       616: q
       618: q^2
       620: q
       622: q
       624: q^2
       625: q
       626: q^2
       628: q^2
       629: q
       630: q^2
       632: q
       634: q^2
       638: q^2
       642: q
       644: q
       645: q
       646: q^2
       648: q
       650: q
       652: q^2
       653: q
       654: q^2
       655: q
       656: q^2
       657: q
       659: q^2
       661: q^2
       663: q^2
       664: q^2+q
       665: q
       667: q^2
       669: q^2
       671: q^2
       672: q
       673: q^2+q
       674: q^2+q
       675: q
       676: q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q^2+q
       681: q
       682: q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q
       687: q^2+q
       688: q^2+q
       689: q^2+q
       690: q^2+q
       691: q^2+q
       692: q^2+q
       697: q
       699: q^2
       700: q^2
       716: q
       720: q
       727: q
       743: q
       756: q
       762: q
       768: q
       773: q^2
       780: q^2
       784: q^2
       786: q
       788: q
       791: q
       792: q^2
       794: q
       796: q^2
       800: q^2
       802: q
       804: q
       806: q
       808: q
       810: q^2
       811: q
       812: q^2
       814: q^2
       816: q
       818: q
       820: q^2
       824: q^2
       826: q
       828: q
       830: q
       832: q
       834: q^2
       835: q
       836: q^2
       838: q^2
       840: q
       843: q
       844: q^2
       846: q
       848: q
       850: q^2
       851: q
       852: q^2
       854: q^2
       855: q
       856: q^2
       857: q
       858: q^2
       860: q^2
       862: q^2
       864: q^2
       865: q
       866: q
       867: q^2+q
       868: q
       869: q^2+q
       870: q^2+q
       871: q
       872: q^2+q
       873: q^2+q
       874: q^2+q
       875: q
       876: q^2+q
       877: q
       878: q
       879: q^2+q
       880: q^2+q
       881: 1
       882: 1
       883: 1
       911: q
       927: q
       930: q
       950: q
       955: q
       967: q
       972: q^2
       975: q
       986: q^2
       991: q
       997: q^2
       999: q
      1001: q
      1005: q
      1007: q
      1008: q
      1009: q^2
      1011: q^2
      1012: q
      1013: q^2
      1015: q^2
      1017: q
      1021: q^2
      1025: q^2
      1027: q
      1029: q
      1031: q^2
      1033: q
      1037: q^2
      1041: q
      1043: q^2
      1045: q
      1046: q
      1047: q^2
      1051: q^2
      1053: q
      1055: q
      1057: q
      1059: q
      1061: q^2
      1062: q
      1063: q^2
      1064: q
      1065: q^2
      1067: 1
      1069: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q
      1075: 1
      1076: q
      1077: q^2+q
      1078: q
      1079: 1
      1080: q
      1081: q^2+q
      1082: q
      1083: q
      1084: q^2+q
      1085: q^2+q
      1133: q
      1135: q
      1142: q^2
      1163: q
      1183: q
      1192: q^2
      1197: q
      1204: q
      1208: q
      1211: 1
      1213: 1
      1217: q
      1219: q
      1223: q^2
      1224: q
      1225: q^2
      1227: 1
      1229: 1
      1233: q
      1235: q
      1237: q^2
      1241: q
      1243: q
      1245: 1
      1247: 1
      1251: q
      1253: q^2
      1255: q
      1259: q
      1261: q
      1262: 1
      1269: q
      1271: q
      1273: q^2
      1275: q^2
      1276: q
      1277: q^2
      1279: q^2
      1280: q
      1281: q^2
      1282: 1
      1283: q
      1284: 1
      1285: q
      1286: 1
      1287: q
      1288: q^2+q
      1289: q
      1329: q
      1338: q^2
      1343: 1
      1367: q
      1369: q
      1375: 1
      1399: q
      1401: q
      1405: 1
      1413: 1
      1429: q
      1434: q^2
      1439: 1
      1441: 1
      1443: 1
      1444: 1
      1451: q
      1453: 1
      1455: q
      1459: 1
      1461: q
      1463: q
      1467: q
      1469: q
      1473: q^2
      1477: q
      1479: q
      1481: q^2
      1482: q
      1483: q^2
      1484: q
      1485: 1
      1486: 1
      1487: q
      1488: 1
      1533: 1
      1544: 1
      1548: 1
      1552: 1
      1554: 1
      1578: q
      1598: q
      1626: q
      1630: q
      1635: q^2
      1639: 1
      1644: 1
      1646: 1
      1648: 1
      1650: q
      1652: 1
      1654: 1
      1656: 1
      1658: q
      1664: q
      1666: q
      1668: 1
      1669: 1
      1673: q
      1674: 1
      1683: 1
      1724: 1
      1736: 1
      1740: 1
      1748: 1
      1752: 1
      1764: 1
      1768: 1
      1776: 1
      1800: q
      1802: 1
      1814: q
      1820: q
      1822: q
      1825: 1
      1828: 1
      1830: 1
      1832: 1
      1833: 1
      1842: 1
      1854: 1
      1866: 1
      1900: 1
      1916: 1
      1927: 1
      1935: 1
      1939: 1
      1943: 1
      1955: q
      1957: 1
      1960: 1
      1963: 1
      1965: 1
      1972: 1
      1984: 1
      1998: 1
      2027: 1
      2035: 1
      2042: 1
      2047: 1
      2054: 1
      2063: 1
      2067: 1
      2074: 1
      2086: 1
      2100: 1
      2112: 1
      2135: 1
      2160: 1

2161:    0: q^7+4q^6+4q^5+q^3
         1: 3q^6+4q^5+q^3
         2: 3q^6+3q^5+q^3
         3: q^7+4q^6+4q^5+q^3
         4: 3q^6+3q^5+q^3
         5: 3q^6+4q^5+q^3
         6: q^7+3q^6+3q^5+q^3
         7: q^7+3q^6+3q^5+q^3
         8: q^7+3q^6+3q^5+q^3
         9: q^7+3q^6+3q^5+q^3
        10: 2q^6+3q^5+q^3
        11: 2q^6+3q^5+q^3
        12: 2q^6+2q^5+q^3
        13: 2q^6+3q^5+q^3
        14: 2q^6+3q^5+q^3
        15: 2q^6+3q^5+q^3
        16: q^7+4q^6+4q^5+q^3
        17: 3q^6+4q^5+q^3
        18: q^7+3q^6+3q^5+q^3
        19: 2q^6+3q^5+q^3
        20: 2q^6+3q^5+q^3
        21: 2q^6+3q^5+q^3
        22: 2q^6+4q^5+q^3
        23: 2q^6+4q^5+q^3
        24: 2q^6+3q^5+q^3
        25: 2q^6+4q^5+q^3
        26: 2q^6+4q^5+q^3
        27: 2q^6+3q^5+q^3
        28: 2q^6+3q^5+q^3
        29: q^6+2q^5+q^3
        30: q^6+3q^5+q^3
        31: q^6+3q^5+q^3
        32: q^6+3q^5+q^3
        33: 2q^6+4q^5+q^3
        34: q^6+3q^5+q^3
        35: q^6+3q^5+q^3
        36: 2q^6+4q^5+q^3
        37: 2q^6+4q^5+q^3
        39: 2q^6+4q^5+q^3
        41: 2q^6+3q^5+q^3
        43: 2q^5+q^3
        44: q^6+2q^5+q^3
        45: q^6+2q^5+q^3
        46: 2q^6+3q^5+q^3
        47: 2q^6+3q^5+q^3
        48: 2q^6+3q^5+q^3
        49: 2q^6+3q^5+q^3
        50: 2q^6+3q^5+q^3
        51: 2q^6+3q^5+q^3
        52: 3q^5+q^3
        53: q^6+3q^5+q^3
        54: q^6+3q^5+q^3
        55: 3q^5+q^3
        56: q^6+3q^5+q^3
        57: q^6+3q^5+q^3
        58: q^6+2q^5+q^3
        59: q^5
        60: q^6+2q^5+q^3
        61: q^5
        62: q^6+3q^5+q^3
        64: q^6+3q^5+q^3
        66: 2q^6+4q^5+q^3
        68: q^5+q^3
        69: q^6+3q^5+q^3
        70: 2q^5+q^3
        71: q^6+2q^5+q^3
        72: 2q^5+q^3
        73: 2q^5+q^3
        74: 3q^5+q^3
        76: q^6+3q^5+q^3
        78: q^6+3q^5+q^3
        80: 2q^5+q^3
        81: q^6+3q^5+q^3
        82: 2q^5+q^3
        83: 3q^5+q^3
        84: 2q^5+q^3
        85: q^6+3q^5+q^3
        86: 2q^5+q^3
        87: 3q^5+q^3
        88: 2q^5+q^3
        89: q^6+2q^5+q^3
        90: q^6+2q^5+q^3
        91: q^6+3q^5+q^3
        92: q^6+2q^5+q^3
        93: q^6+3q^5+q^3
        94: 3q^5+q^3
        95: q^6+3q^5+q^3
        96: q^6+3q^5+q^3
        97: 3q^5+q^3
        98: q^6+3q^5+q^3
        99: q^6+3q^5+q^3
       100: 2q^5+q^3
       101: q^5+q^3
       102: 2q^5+q^3
       103: q^6+2q^5+q^3
       106: q^5
       107: q^5+q^3
       109: q^5+q^3
       111: 2q^5+q^3
       113: 2q^5+q^3
       115: 3q^5+q^3
       117: q^5+q^3
       119: q^5+q^3
       121: 2q^5+q^3
       123: q^6+3q^5+q^3
       125: q^5+q^3
       126: 2q^5+q^3
       127: 3q^5+q^3
       129: q^6+3q^5+q^3
       131: q^6+3q^5+q^3
       133: q^5+q^3
       134: q^6+3q^5+q^3
       135: 2q^5+q^3
       136: 2q^5+q^3
       137: 2q^5+q^3
       138: 3q^5+q^3
       139: 2q^5+q^3
       140: q^3
       141: 2q^5+q^3
       142: 2q^5+q^3
       143: 2q^5+q^3
       144: 3q^5+q^3
       145: 2q^5+q^3
       146: 2q^5+q^3
       147: 2q^5+q^3
       148: q^3
       149: q^5+q^3
       150: 2q^5+q^3
       151: 2q^5+q^3
       153: q^5+q^3
       155: 2q^5+q^3
       157: q^5+q^3
       158: q^3
       159: q^5+q^3
       160: 2q^5+q^3
       161: q^5+q^3
       162: 2q^5+q^3
       163: 2q^5+q^3
       164: q^5+q^3
       165: 2q^5+q^3
       166: 2q^5+q^3
       167: q^5+q^3
       168: 2q^5+q^3
       169: q^5+q^3
       173: q^5+q^3
       177: 3q^5+q^3
       179: 2q^5+q^3
       181: 2q^5+q^3
       183: q^5+q^3
       185: q^5+q^3
       187: 2q^5+q^3
       189: 2q^5+q^3
       191: q^5+q^3
       193: q^3
       195: q^5+q^3
       197: q^3
       199: q^5+q^3
       201: q^5+q^3
       203: q^3
       205: q^3
       207: 2q^5+q^3
       209: q^5+q^3
       211: 2q^5+q^3
       213: 2q^5+q^3
       215: q^5+q^3
       217: 2q^5+q^3
       219: q^5+q^3
       220: q^3
       221: q^5+q^3
       222: q^3
       223: 2q^5+q^3
       224: q^3
       225: 2q^5+q^3
       226: 2q^5+q^3
       227: q^3
       228: 2q^5+q^3
       229: q^3
       230: q^5+q^3
       231: 2q^5+q^3
       232: q^3
       233: 2q^5+q^3
       234: q^5+q^3
       235: q^3
       236: 2q^5+q^3
       237: 2q^5+q^3
       239: q^5+q^3
       241: 2q^5+q^3
       243: q^5+q^3
       244: q^3
       245: q^3
       246: q^5+q^3
       247: q^5+q^3
       248: q^3
       249: q^5+q^3
       250: q^5+q^3
       251: q^3
       252: q^5+q^3
       253: q^5+q^3
       254: q^3
       255: q^5+q^3
       256: q^5+q^3
       257: q^3
       258: q^5+q^3
       259: q^5+q^3
       263: q^5+q^3
       267: q^3
       271: q^3
       275: q^5+q^3
       279: q^3
       281: 2q^5+q^3
       283: q^5+q^3
       285: q^5+q^3
       287: 2q^5+q^3
       289: q^5+q^3
       291: 2q^5+q^3
       293: q^3
       295: q^3
       297: q^3
       299: q^3
       301: q^3
       303: q^3
       305: q^3
       307: q^3
       309: q^3
       311: q^3
       313: q^3
       315: 2q^5+q^3
       317: q^5+q^3
       319: q^3
       321: q^3
       323: q^3
       325: q^5+q^3
       327: q^5+q^3
       329: q^3
       331: q^5+q^3
       333: q^3
       334: q^3
       335: q^3
       336: q^5+q^3
       337: q^3
       338: q^5+q^3
       340: q^3
       342: q^5+q^3
       344: q^3
       345: q^3
       346: q^5+q^3
       347: q^3
       348: q^3
       349: q^3
       350: q^5+q^3
       351: q^3
       352: q^3
       353: q^3
       354: q^5+q^3
       355: q^3
       356: q^5+q^3
       357: q^3
       358: q^3
       359: q^3
       360: q^5+q^3
       362: q^3
       364: q^5+q^3
       366: q^5+q^3
       367: q^3
       368: q^5+q^3
       369: q^3
       370: q^3
       377: q^5+q^3
       381: q^3
       385: q^3
       389: q^3
       393: q^3
       397: q^3
       401: q^3
       405: q^3
       409: q^3
       411: q^5+q^3
       413: q^3
       415: q^3
       417: q^5+q^3
       419: q^3
       421: q^3
       423: q^3
       425: q^5+q^3
       427: q^3
       429: q^3
       431: q^3
       433: q^3
       435: q^3
       437: q^3
       439: q^3
       441: q^3
       443: q^3
       445: q^3
       447: q^3
       449: q^3
       451: q^3
       453: q^3
       455: q^3
       457: q^3
       459: q^3
       461: q^3
       463: q^3
       465: q^3
       467: q^5+q^3
       469: q^5+q^3
       471: q^3
       473: q^3
       475: q^3
       477: q^3
       479: q^3
       481: q^3
       482: q^3
       483: q^3
       492: q^3
       493: q^3
       494: q^3
       495: q^3
       497: q^3
       498: q^3
       499: q^3
       500: q^3
       508: q^3
       512: q^3
       514: q^3
       521: q^3
       525: q^3
       529: q^3
       533: q^3
       537: q^3
       541: q^3
       545: q^3
       549: q^3
       553: q^3
       557: q^3
       561: q^3
       565: q^3
       569: q^3
       573: q^3
       577: q^3
       583: q^3
       585: q^3
       587: q^3
       589: q^3
       591: q^3
       593: q^3
       595: q^3
       599: q^3
       603: q^3
       605: q^3
       607: q^3
       609: q^3
       613: q^3
       619: q^3
       621: q^3
       623: q^3
       625: q^3
       629: q^3
       639: q^3
       641: q^3
       643: q^3
       645: q^3
       651: q^3
       675: q^3
       676: q^3
       677: q^3
       681: q^3
       682: q^3
       683: q^3
       689: q^3
       693: q^3
       705: q^3
       709: q^3
       713: q^3
       717: q^3
       721: q^3
       725: q^3
       737: q^3
       741: q^3
       753: q^3
       757: q^3
       777: q^3
       797: q^3
       801: q^3
       803: q^3
       805: q^3
       807: q^3
       811: q^3
       821: q^3
       825: q^3
       827: q^3
       829: q^3
       831: q^3
       835: q^3
       849: q^3
       853: q^2
       855: q^3
       896: q^3
       920: q^3
       924: q^3
       928: q^3
       944: q^3
       948: q^3
       952: q^3
       960: q^3
       978: q^2
       984: q^2
      1010: q^2
      1050: q^2
      1100: q^2
      1126: q^2
      1140: q^2
      1184: q^2
      1190: q^2
      1222: q^2
      1264: q^2
      1278: q^2
      1292: q^2
      1304: q^2
      1322: q^2
      1336: q^2
      1360: q^2
      1392: q^2
      1406: q^2
      1414: q^2
      1432: q^2
      1491: q^2
      1503: q^2
      1515: q^2
      1527: q^2
      1793: q
      1872: q
      2110: 1
      2161: 1

2162:    0: q^5+q
         1: q
         2: q^5+q
         3: q
         4: q^5+q
         5: q^5+q
         6: q
         7: q^5+q
         8: q^5+q
         9: q^6+q^5+q
        10: q
        11: q
        12: q
        13: q^5+q
        14: q^5+q
        15: q^5+q
        16: q
        17: q
        18: q^5+q
        19: q^5+q
        20: q
        21: q^5+q
        22: q^5+q
        23: q
        24: q^5+q
        25: q^5+q
        26: q
        27: q^5+q
        28: q
        29: q
        30: q^5+q
        31: q
        32: q^5+q
        33: q
        34: q
        35: q^5+q
        36: q
        37: q^5+q
        39: q
        41: q^5+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q^5+q
        49: q
        50: q
        51: q^5+q
        52: q^5+q
        53: q
        54: q^5+q
        55: q^5+q
        56: q
        57: q^5+q
        59: q
        61: q
        62: q
        64: q^5+q
        66: q
        68: q
        69: q
        70: q
        71: q
        72: q
        73: q
        74: q^5+q
        76: q
        78: q^5+q
        80: q
        81: q
        82: q
        83: q^5+q
        84: q
        85: q
        86: q
        87: q^5+q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q^5+q
        94: q
        95: q
        96: q^5+q
        97: q
        98: q
        99: q^5+q
       100: q^5+q
       101: q
       102: q^5+q
       106: q
       108: q
       110: q
       111: q
       113: q
       115: q^5+q
       118: q
       120: q
       121: q
       123: q
       125: q
       126: q
       127: q
       129: q
       131: q^5+q
       133: q
       134: q
       135: q
       136: q
       137: q
       138: q
       139: q
       140: q
       141: q
       142: q
       143: q
       144: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q^5+q
       151: q^5+q
       153: q
       155: q^5+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q^5+q
       163: q
       164: q
       165: q^5+q
       166: q
       167: q
       168: q^5+q
       172: q
       176: q
       177: q
       179: q
       181: q
       184: q
       186: q
       187: q
       189: q
       192: q
       194: q
       196: q
       197: q
       200: q
       202: q
       204: q
       205: q
       207: q
       209: q
       211: q^5+q
       213: q
       215: q
       217: q^5+q
       219: q
       220: q
       221: q
       222: q
       223: q
       224: q
       225: q
       226: q
       227: q
       228: q
       229: q
       230: q
       231: q
       232: q
       233: q
       234: q
       235: q
       236: q
       237: q
       239: q
       241: q^5+q
       243: q
       244: q
       245: q
       246: q
       247: q
       248: q
       249: q^5+q
       250: q
       251: q
       252: q
       253: q
       254: q
       255: q
       256: q
       257: q
       258: q^5+q
       262: q
       266: q
       269: q
       273: q
       278: q
       279: q
       281: q
       284: q
       286: q
       287: q
       289: q
       291: q
       294: q
       296: q
       297: q
       300: q
       301: q
       304: q
       305: q
       308: q
       310: q
       311: q
       313: q
       315: q
       317: q
       320: q
       322: q
       323: q
       325: q
       327: q
       329: q
       331: q
       333: q
       334: q
       335: q
       336: q
       337: q
       338: q
       340: q
       342: q^5+q
       344: q
       345: q
       346: q
       347: q
       348: q
       349: q
       350: q
       351: q
       352: q
       353: q
       354: q
       355: q
       356: q
       357: q
       358: q
       359: q
       360: q
       362: q
       364: q^5+q
       366: q
       367: q
       368: q
       369: q
       370: q
       371: q
       372: q
       373: q^5+q
       374: q
       375: q
       376: q
       380: q
       384: q
       388: q
       391: q
       396: q
       399: q
       404: q
       406: q
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       411: q
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       415: q
       417: q
       420: q
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       423: q
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       427: q
       430: q
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       433: q
       435: q
       438: q
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       441: q
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       450: q
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       454: q
       455: q
       458: q
       459: q
       462: q
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       465: q
       467: q
       469: q
       472: q
       474: q
       475: q
       477: q
       479: q
       481: q
       482: q
       483: q
       484: q
       485: q
       487: q
       489: q^5+q
       491: q
       492: q
       493: q
       494: q
       495: q
       496: q
       497: q
       498: q
       499: q
       500: q
       501: q
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       515: q
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       524: q
       528: q
       532: q
       536: q
       539: q
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       552: q
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       559: q
       563: q
       568: q
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       583: q
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       599: q
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       604: q
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       608: q
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       611: q
       613: q
       616: q
       617: q
       620: q
       622: q
       623: q
       625: q
       627: q
       629: q
       632: q
       633: q
       635: q
       637: q
       639: q
       642: q
       644: q
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       648: q
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       655: q
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       664: q
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       672: q
       673: q
       674: q
       675: q
       676: q
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       689: q
       697: q
       708: q
       712: q
       716: q
       720: q
       723: q
       727: q
       731: q
       735: q
       739: q
       743: q
       747: q
       751: q
       756: q
       758: q
       762: q
       768: q
       769: q
       775: q
       777: q
       779: q
       781: q
       783: q
       786: q
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       791: q
       794: q
       795: q
       797: q
       799: q
       802: q
       804: q
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       811: q
       813: q
       816: q
       818: q
       819: q
       821: q
       823: q
       826: q
       828: q
       830: q
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       991: q
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      1622: q
      1626: q
      1630: q
      1637: 1
      1641: q
      1650: q
      1658: q
      1671: q
      1718: q
      1725: 1
      1730: 1
      1754: q
      1759: q
      1778: q
      1783: q
      1796: q
      1808: q
      1814: q
      1823: 1
      1843: 1
      1889: q
      1895: 1
      1911: 1
      1928: 1
      1949: q
      1958: 1
      1973: 1
      1985: 1
      2028: 1
      2037: 1
      2049: 1
      2057: 1
      2075: 1
      2087: 1
      2101: 1
      2121: 1
      2162: 1

2163:    0: 2q^6+15q^5+19q^4+6q^3+q^2
         1: 2q^6+15q^5+19q^4+6q^3+q^2
         2: 5q^6+14q^5+15q^4+5q^3+q^2
         3: 15q^5+19q^4+6q^3+q^2
         4: 2q^6+15q^5+19q^4+6q^3+q^2
         5: 15q^5+19q^4+6q^3+q^2
         6: 2q^6+15q^5+19q^4+6q^3+q^2
         7: 5q^6+14q^5+15q^4+5q^3+q^2
         8: 5q^6+15q^5+15q^4+5q^3+q^2
         9: 3q^7+9q^6+12q^5+10q^4+4q^3+q^2
        10: 2q^6+15q^5+19q^4+6q^3+q^2
        11: 15q^5+19q^4+6q^3+q^2
        12: 2q^6+15q^5+19q^4+6q^3+q^2
        13: q^6+9q^5+14q^4+5q^3+q^2
        14: q^6+9q^5+14q^4+5q^3+q^2
        15: 10q^5+14q^4+5q^3+q^2
        16: 8q^5+18q^4+6q^3+q^2
        17: 8q^5+18q^4+6q^3+q^2
        18: 5q^6+11q^5+10q^4+4q^3+q^2
        19: 2q^6+15q^5+19q^4+6q^3+q^2
        20: 2q^6+15q^5+19q^4+6q^3+q^2
        21: 5q^6+14q^5+15q^4+5q^3+q^2
        22: 8q^5+18q^4+6q^3+q^2
        23: 8q^5+18q^4+6q^3+q^2
        24: 2q^6+10q^5+14q^4+5q^3+q^2
        25: 8q^5+18q^4+6q^3+q^2
        26: 8q^5+18q^4+6q^3+q^2
        27: 2q^6+10q^5+14q^4+5q^3+q^2
        28: 8q^5+18q^4+6q^3+q^2
        29: 2q^6+15q^5+19q^4+6q^3+q^2
        30: q^6+9q^5+14q^4+5q^3+q^2
        31: 8q^5+18q^4+6q^3+q^2
        32: 5q^5+13q^4+5q^3+q^2
        33: 3q^5+17q^4+6q^3+q^2
        34: 8q^5+18q^4+6q^3+q^2
        35: 5q^5+13q^4+5q^3+q^2
        36: 3q^5+17q^4+6q^3+q^2
        37: 2q^5+9q^4+4q^3
        38: q^5+8q^4+2q^3+q^2
        39: 2q^5+9q^4+4q^3
        40: q^5+8q^4+2q^3+q^2
        41: 4q^5+7q^4+3q^3
        42: 3q^5+6q^4+2q^3+q^2
        43: q^6+9q^5+14q^4+5q^3+q^2
        44: q^6+9q^5+14q^4+5q^3+q^2
        45: 10q^5+14q^4+5q^3+q^2
        46: 3q^5+13q^4+5q^3+q^2
        47: 4q^5+13q^4+5q^3+q^2
        48: q^6+7q^5+9q^4+4q^3+q^2
        49: 8q^5+18q^4+6q^3+q^2
        50: 8q^5+18q^4+6q^3+q^2
        51: 5q^6+11q^5+10q^4+4q^3+q^2
        52: 8q^5+18q^4+6q^3+q^2
        53: 8q^5+18q^4+6q^3+q^2
        54: 2q^6+10q^5+14q^4+5q^3+q^2
        55: 8q^5+18q^4+6q^3+q^2
        56: 8q^5+18q^4+6q^3+q^2
        57: 2q^6+10q^5+14q^4+5q^3+q^2
        58: q^5+7q^4+2q^3
        59: 2q^5+10q^4+4q^3+q^2
        60: 2q^5+10q^4+4q^3+q^2
        61: q^5+7q^4+2q^3
        62: 2q^5+9q^4+4q^3
        63: q^5+8q^4+2q^3+q^2
        64: q^5+6q^4+3q^3
        65: q^5+6q^4+2q^3+q^2
        66: 8q^4+4q^3
        67: 8q^4+2q^3+q^2
        68: q^5+8q^4+4q^3+q^2
        69: 3q^5+8q^4+4q^3+q^2
        70: q^6+9q^5+14q^4+5q^3+q^2
        71: 8q^5+18q^4+6q^3+q^2
        72: 3q^5+17q^4+6q^3+q^2
        73: 3q^5+17q^4+6q^3+q^2
        74: 2q^5+9q^4+4q^3
        75: q^5+8q^4+2q^3+q^2
        76: 2q^5+9q^4+4q^3
        77: q^5+8q^4+2q^3+q^2
        78: 4q^5+7q^4+3q^3
        79: 3q^5+6q^4+2q^3+q^2
        80: 5q^5+13q^4+5q^3+q^2
        81: q^5+12q^4+5q^3+q^2
        82: 8q^5+18q^4+6q^3+q^2
        83: 5q^5+13q^4+5q^3+q^2
        84: 5q^5+13q^4+5q^3+q^2
        85: q^5+12q^4+5q^3+q^2
        86: 8q^5+18q^4+6q^3+q^2
        87: 5q^5+13q^4+5q^3+q^2
        88: 3q^5+13q^4+5q^3+q^2
        89: 4q^5+13q^4+5q^3+q^2
        90: q^6+7q^5+9q^4+4q^3+q^2
        91: 3q^5+13q^4+5q^3+q^2
        92: 4q^5+13q^4+5q^3+q^2
        93: q^6+7q^5+9q^4+4q^3+q^2
        94: 3q^5+15q^4+6q^3+q^2
        95: 3q^5+15q^4+6q^3+q^2
        96: 2q^6+7q^5+9q^4+4q^3+q^2
        97: 3q^5+15q^4+6q^3+q^2
        98: 3q^5+15q^4+6q^3+q^2
        99: 2q^6+7q^5+9q^4+4q^3+q^2
       100: 3q^5+15q^4+6q^3+q^2
       101: 3q^5+15q^4+6q^3+q^2
       102: 6q^5+11q^4+5q^3+q^2
       103: 4q^4+2q^3
       104: 5q^4+2q^3+q^2
       105: 3q^4
       106: 4q^4+2q^3
       107: 2q^5+10q^4+4q^3+q^2
       108: q^5+7q^4+2q^3
       109: q^5+7q^4+2q^3
       110: 2q^5+10q^4+4q^3+q^2
       111: 8q^4+4q^3
       112: 8q^4+2q^3+q^2
       113: 2q^5+9q^4+4q^3
       114: q^5+8q^4+2q^3+q^2
       115: q^5+6q^4+3q^3
       116: q^5+6q^4+2q^3+q^2
       117: 2q^4+q^3
       118: 5q^4+3q^3+q^2
       119: 5q^4+3q^3+q^2
       120: 2q^4+q^3
       121: q^5+6q^4+3q^3
       122: q^5+6q^4+2q^3+q^2
       123: 5q^4+3q^3
       124: 6q^4+2q^3+q^2
       125: q^5+8q^4+4q^3+q^2
       126: 3q^5+8q^4+4q^3+q^2
       127: 4q^4+4q^3
       128: 3q^4+q^3+q^2
       129: 4q^4+4q^3
       130: 3q^4+q^3+q^2
       131: q^5+3q^4+2q^3
       132: q^5+2q^4+q^3+q^2
       133: q^5+8q^4+4q^3+q^2
       134: 3q^5+8q^4+4q^3+q^2
       135: q^5+12q^4+5q^3+q^2
       136: q^5+12q^4+5q^3+q^2
       137: q^5+12q^4+5q^3+q^2
       138: q^5+7q^4+4q^3+q^2
       139: 3q^5+15q^4+6q^3+q^2
       140: 7q^4+5q^3+q^2
       141: 5q^5+13q^4+5q^3+q^2
       142: 3q^5+15q^4+6q^3+q^2
       143: q^5+12q^4+5q^3+q^2
       144: q^5+7q^4+4q^3+q^2
       145: 3q^5+15q^4+6q^3+q^2
       146: 5q^5+13q^4+5q^3+q^2
       147: 3q^5+15q^4+6q^3+q^2
       148: 7q^4+5q^3+q^2
       149: 3q^5+15q^4+6q^3+q^2
       150: 2q^5+10q^4+5q^3+q^2
       151: 2q^5+8q^4+4q^3
       152: q^5+7q^4+2q^3+q^2
       153: 2q^5+8q^4+4q^3
       154: q^5+7q^4+2q^3+q^2
       155: 3q^5+6q^4+3q^3
       156: 3q^5+5q^4+2q^3+q^2
       157: 3q^5+13q^4+5q^3+q^2
       158: 4q^5+13q^4+5q^3+q^2
       159: q^6+7q^5+9q^4+4q^3+q^2
       160: q^5+8q^4+5q^3+q^2
       161: q^5+8q^4+5q^3+q^2
       162: 3q^5+6q^4+4q^3+q^2
       163: q^5+8q^4+5q^3+q^2
       164: q^5+8q^4+5q^3+q^2
       165: 3q^5+6q^4+4q^3+q^2
       166: 9q^4+6q^3+q^2
       167: 9q^4+6q^3+q^2
       168: 4q^5+7q^4+4q^3+q^2
       169: 4q^4+2q^3
       170: 5q^4+2q^3+q^2
       171: 3q^4
       172: 4q^4+2q^3
       173: q^4+q^3
       174: 3q^4+2q^3+q^2
       175: q^4
       176: q^4+q^3
       177: q^4+2q^3
       178: 2q^4+q^3+q^2
       179: 4q^4+4q^3
       180: 3q^4+q^3+q^2
       181: 4q^4+4q^3
       182: 3q^4+q^3+q^2
       183: 5q^4+3q^3+q^2
       184: 2q^4+q^3
       185: 2q^4+q^3
       186: 5q^4+3q^3+q^2
       187: 5q^4+3q^3
       188: 6q^4+2q^3+q^2
       189: q^5+6q^4+3q^3
       190: q^5+6q^4+2q^3+q^2
       191: 2q^4+q^3
       192: 5q^4+3q^3+q^2
       193: 5q^4+4q^3+q^2
       194: 2q^4+q^3
       195: q^5+6q^4+2q^3
       196: 2q^5+9q^4+4q^3+q^2
       197: 3q^4+3q^3
       198: 4q^4+2q^3+q^2
       199: 5q^4+3q^3+q^2
       200: 2q^4+q^3
       201: 2q^5+9q^4+4q^3+q^2
       202: q^5+6q^4+2q^3
       203: 2q^4+q^3
       204: 5q^4+4q^3+q^2
       205: 3q^4+3q^3
       206: 4q^4+2q^3+q^2
       207: 5q^4+3q^3
       208: 6q^4+2q^3+q^2
       209: 2q^5+8q^4+4q^3
       210: q^5+7q^4+2q^3+q^2
       211: q^5+5q^4+3q^3
       212: q^5+5q^4+2q^3+q^2
       213: q^4+3q^3
       215: q^4+3q^3
       217: q^4+2q^3
       219: q^5+4q^4+3q^3+q^2
       220: q^5+8q^4+4q^3+q^2
       221: 3q^5+8q^4+4q^3+q^2
       222: q^5+12q^4+5q^3+q^2
       223: q^5+7q^4+4q^3+q^2
       224: q^5+12q^4+5q^3+q^2
       225: q^5+7q^4+4q^3+q^2
       226: q^5+7q^4+4q^3+q^2
       227: 4q^4+4q^3+q^2
       228: q^5+5q^4+4q^3+q^2
       229: 3q^4+4q^3+q^2
       230: q^5+8q^4+5q^3+q^2
       231: q^5+7q^4+4q^3+q^2
       232: 4q^4+4q^3+q^2
       233: q^5+5q^4+4q^3+q^2
       234: q^5+8q^4+5q^3+q^2
       235: 3q^4+4q^3+q^2
       236: 5q^4+4q^3+q^2
       237: 3q^4+4q^3
       238: q^4+q^3+q^2
       239: 3q^4+4q^3
       240: q^4+q^3+q^2
       241: q^5+3q^4+2q^3
       242: q^5+q^4+q^3+q^2
       243: 9q^4+6q^3+q^2
       244: 4q^4+5q^3+q^2
       245: 4q^4+5q^3+q^2
       246: 2q^5+10q^4+5q^3+q^2
       247: 9q^4+6q^3+q^2
       248: 9q^4+6q^3+q^2
       249: 4q^5+7q^4+4q^3+q^2
       250: q^5+8q^4+5q^3+q^2
       251: q^5+8q^4+5q^3+q^2
       252: 3q^5+6q^4+4q^3+q^2
       253: q^5+8q^4+5q^3+q^2
       254: q^5+8q^4+5q^3+q^2
       255: 3q^5+6q^4+4q^3+q^2
       256: 3q^4+5q^3+q^2
       257: 4q^4+5q^3+q^2
       258: q^5+4q^4+4q^3+q^2
       259: 2q^4+2q^3
       260: 2q^4+q^3+q^2
       261: q^4
       262: 2q^4+2q^3
       263: q^4+q^3
       264: 3q^4+2q^3+q^2
       265: q^4
       266: q^4+q^3
       267: 2q^4+2q^3
       268: 3q^4+2q^3+q^2
       269: q^4+q^3
       270: q^4
       271: q^4+q^3
       272: q^4
       273: 2q^4+2q^3
       274: 3q^4+2q^3+q^2
       275: q^4+q^3
       276: 3q^4+2q^3+q^2
       277: q^4
       278: q^4+q^3
       279: 2q^3
       281: 2q^3
       283: 2q^4+2q^3+q^2
       286: 2q^4+2q^3+q^2
       287: q^4+2q^3
       288: 2q^4+q^3+q^2
       289: q^4+3q^3
       291: q^4+2q^3
       292: 2q^4+q^3+q^2
       293: 5q^4+3q^3+q^2
       294: 2q^4+q^3
       295: 2q^4+q^3
       296: 5q^4+3q^3+q^2
       297: 5q^4+3q^3
       298: 6q^4+2q^3+q^2
       299: q^4+3q^3+q^2
       301: q^4+3q^3
       302: q^3+q^2
       303: q^4+q^3
       304: 3q^4+3q^3+q^2
       305: q^4+2q^3
       306: 2q^4+2q^3+q^2
       307: 3q^4+3q^3+q^2
       308: q^4+q^3
       310: q^4+3q^3+q^2
       311: q^4+3q^3
       312: q^3+q^2
       313: q^4+2q^3
       314: 2q^4+2q^3+q^2
       315: q^4+2q^3
       316: q^4+q^3+q^2
       317: 3q^4+4q^3
       318: q^4+q^3+q^2
       319: 3q^4+4q^3+q^2
       320: q^4+q^3
       321: q^4+q^3
       322: 3q^4+4q^3+q^2
       323: 2q^3
       324: q^4+2q^3+q^2
       325: q^5+5q^4+3q^3
       326: q^5+5q^4+2q^3+q^2
       327: q^4+3q^3
       329: q^4+3q^3
       331: q^4+2q^3
       333: q^5+4q^4+3q^3+q^2
       334: q^5+7q^4+4q^3+q^2
       335: q^5+7q^4+4q^3+q^2
       336: 5q^4+4q^3+q^2
       337: 9q^4+6q^3+q^2
       338: 3q^4+4q^3
       339: q^4+q^3+q^2
       340: 3q^4+4q^3
       341: q^4+q^3+q^2
       342: q^5+3q^4+2q^3
       343: q^5+q^4+q^3+q^2
       344: 2q^4+3q^3+q^2
       345: 4q^4+4q^3+q^2
       346: q^5+5q^4+4q^3+q^2
       347: 3q^4+4q^3+q^2
       348: q^4+3q^3+q^2
       349: q^5+8q^4+5q^3+q^2
       350: q^5+5q^4+4q^3+q^2
       351: 4q^4+5q^3+q^2
       352: 2q^4+3q^3+q^2
       353: 4q^4+4q^3+q^2
       354: q^5+5q^4+4q^3+q^2
       355: q^5+8q^4+5q^3+q^2
       356: q^5+5q^4+4q^3+q^2
       357: 3q^4+4q^3+q^2
       358: q^4+3q^3+q^2
       359: 4q^4+5q^3+q^2
       360: 3q^3
       362: q^4+3q^3
       364: q^4+2q^3
       366: 5q^4+4q^3+q^2
       367: q^4+4q^3+q^2
       368: 3q^4+4q^3+q^2
       369: q^4+4q^3+q^2
       370: q^4+4q^3+q^2
       371: 3q^4+5q^3+q^2
       372: 4q^4+5q^3+q^2
       373: q^5+4q^4+4q^3+q^2
       374: 3q^4+5q^3+q^2
       375: 4q^4+5q^3+q^2
       376: q^5+4q^4+4q^3+q^2
       378: q^4+q^3+q^2
       381: q^3
       384: q^3
       385: q^4+q^3
       386: 3q^4+2q^3+q^2
       387: q^4
       388: q^4+q^3
       389: q^4+2q^3
       390: q^3+q^2
       391: q^3
       393: q^3
       394: q^4+2q^3+q^2
       397: q^3
       399: q^4+2q^3
       400: q^3+q^2
       403: q^4+2q^3+q^2
       404: q^3
       405: q^3
       406: q^3
       407: q^4+2q^3+q^2
       409: 2q^3
       411: 2q^3
       413: q^3
       415: q^4+3q^3
       417: 2q^3
       419: 2q^4+2q^3+q^2
       422: 2q^4+2q^3+q^2
       423: q^4+2q^3
       424: 2q^4+q^3+q^2
       425: q^4+2q^3
       426: q^4+q^3+q^2
       427: 3q^4+4q^3
       428: q^4+q^3+q^2
       429: 2q^3+q^2
       432: q^4+2q^3+q^2
       433: q^3
       434: q^3+q^2
       435: 2q^3
       437: q^4+3q^3+q^2
       439: q^4+q^3
       440: 3q^4+3q^3+q^2
       441: q^4+2q^3
       442: 2q^4+2q^3+q^2
       443: 3q^4+4q^3+q^2
       444: q^4+q^3
       445: q^4+3q^3
       446: q^3+q^2
       447: q^4+2q^3+q^2
       450: 2q^3+q^2
       451: q^3
       452: q^3+q^2
       453: 3q^4+3q^3+q^2
       454: q^4+q^3
       455: 2q^3
       458: q^4+3q^3+q^2
       459: q^4+2q^3
       460: 2q^4+2q^3+q^2
       461: q^4+q^3
       462: 3q^4+4q^3+q^2
       463: q^4+3q^3
       464: q^3+q^2
       465: 2q^3
       467: 2q^3
       469: q^4+2q^3
       470: q^4+q^3+q^2
       471: 3q^3+q^2
       474: 3q^3+q^2
       475: q^3
       476: 2q^3+q^2
       477: 2q^3
       478: 2q^3+q^2
       479: 2q^3
       480: q^4+2q^3+q^2
       481: 2q^4+3q^3+q^2
       482: 2q^4+3q^3+q^2
       483: 5q^4+4q^3+q^2
       484: q^4+4q^3+q^2
       485: 3q^3
       487: q^4+3q^3
       489: q^4+2q^3
       491: 3q^4+4q^3+q^2
       492: 2q^4+3q^3+q^2
       493: q^4+3q^3+q^2
       494: q^5+5q^4+4q^3+q^2
       495: q^4+3q^3+q^2
       496: q^4+4q^3+q^2
       497: 2q^4+3q^3+q^2
       498: q^5+5q^4+4q^3+q^2
       499: q^4+3q^3+q^2
       500: q^4+3q^3+q^2
       501: q^4+4q^3+q^2
       502: 3q^3
       504: q^4+3q^3
       506: q^4+2q^3
       508: q^4+3q^3+q^2
       509: q^4+4q^3+q^2
       510: 3q^4+4q^3+q^2
       511: q^4+4q^3+q^2
       512: q^4+3q^3+q^2
       513: q^4+4q^3+q^2
       514: q^4+3q^3+q^2
       515: q^4+2q^3+2q^2
       516: 2q^3+2q^2
       517: q^4+2q^3+2q^2
       518: 3q^4+5q^3+q^2
       519: 4q^4+5q^3+q^2
       520: q^5+4q^4+4q^3+q^2
       525: q^3
       528: q^3
       530: q^4+q^3+q^2
       534: q^3+q^2
       537: q^3
       541: q^3
       542: q^4+2q^3+q^2
       545: q^4+2q^3
       546: q^3+q^2
       547: q^3
       551: q^3+q^2
       555: q^3
       559: q^3
       560: q^4+2q^3+q^2
       561: q^3
       563: q^4+2q^3
       564: q^3+q^2
       566: 2q^3+q^2
       569: q^3
       570: q^3
       571: 2q^3+q^2
       573: q^3
       574: q^4+2q^3+q^2
       575: q^3
       577: 2q^3
       581: q^3+q^2
       582: q^3
       583: q^3
       585: q^3
       587: 2q^3
       589: q^4+2q^3+q^2
       592: 2q^3+q^2
       593: 2q^3+q^2
       596: q^4+2q^3+q^2
       597: 2q^3
       599: q^4+2q^3
       600: q^4+q^3+q^2
       601: 2q^3
       603: 2q^3+q^2
       605: q^3
       608: q^4+2q^3+q^2
       609: q^3
       610: q^3+q^2
       611: 2q^3
       613: q^3
       614: q^3+q^2
       615: 3q^3+q^2
       617: 2q^3
       619: q^4+2q^3+q^2
       622: 2q^3+q^2
       623: q^3
       625: q^3
       626: q^3+q^2
       627: 2q^3
       629: q^3
       630: q^3+q^2
       632: 3q^3+q^2
       633: 2q^3
       635: 2q^3
       637: 2q^3
       639: q^3
       641: 2q^3+q^2
       644: 2q^3+q^2
       646: q^3+q^2
       647: 3q^3+q^2
       650: 3q^3+q^2
       651: q^3
       653: q^3
       654: 2q^3+q^2
       655: q^3
       656: 2q^3+q^2
       657: 2q^2
       658: 2q^3+q^2
       660: 2q^3+q^2
       662: 2q^3+q^2
       664: q^4+2q^3+2q^2
       665: q^4+3q^3+q^2
       666: 3q^3
       668: q^4+3q^3
       670: q^4+2q^3
       672: q^4+4q^3+q^2
       673: 3q^4+4q^3+q^2
       674: q^3+2q^2
       675: q^3+q^2
       676: 2q^4+3q^3+q^2
       677: q^4+3q^3+q^2
       678: q^4+4q^3+q^2
       679: q^4+3q^3+q^2
       680: q^3+2q^2
       681: 2q^4+3q^3+q^2
       682: q^3+q^2
       683: q^4+3q^3+q^2
       684: q^4+4q^3+q^2
       685: q^4+3q^3+q^2
       686: q^4+3q^3+q^2
       687: q^4+3q^3+q^2
       688: q^4+3q^3+q^2
       689: q^3+q^2
       690: q^4+2q^3+2q^2
       691: 2q^3+2q^2
       692: q^4+2q^3+2q^2
       693: q^3
       697: q^3
       699: q^3+q^2
       703: q^3
       715: q^3+q^2
       718: q^3+q^2
       726: q^3+q^2
       729: q^3
       733: q^3
       744: q^3+q^2
       747: q^3
       751: q^3
       754: q^3+q^2
       763: 2q^3+q^2
       766: 2q^3+q^2
       769: q^3
       775: q^2
       777: q^3
       779: 2q^3+q^2
       781: q^3
       783: 2q^3
       785: 2q^3+q^2
       788: 2q^3+q^2
       789: 2q^3
       792: q^3+q^2
       793: 2q^2
       795: q^3+q^2
       799: q^3
       801: q^3+q^2
       804: q^2
       805: 2q^3+q^2
       808: q^4+2q^3+q^2
       809: q^3
       811: q^3
       812: q^3+q^2
       813: 2q^3
       815: 3q^3+q^2
       818: 2q^2
       819: q^3+q^2
       823: q^3
       825: q^4+2q^3+q^2
       828: 2q^3+q^2
       829: q^2
       832: q^3+q^2
       833: q^3
       835: q^3
       836: q^3+q^2
       837: 2q^3
       840: 3q^3+q^2
       841: q^3
       844: 2q^2
       845: 2q^3+q^2
       848: 2q^3+q^2
       852: q^3+q^2
       853: q^3
       856: q^2
       857: q^3
       858: 2q^3+q^2
       859: 2q^3+q^2
       861: 2q^3+q^2
       863: 2q^3+q^2
       865: 2q^2
       866: 2q^2
       867: q^4+2q^3+2q^2
       868: q^4+3q^3+q^2
       869: q^3+2q^2
       870: q^3+2q^2
       871: q^3+q^2
       872: q^4+3q^3+q^2
       873: q^3+2q^2
       874: q^3+2q^2
       875: q^3+q^2
       876: q^4+3q^3+q^2
       877: q^3+q^2
       878: q^3+q^2
       879: q^3+q^2
       880: q^3+q^2
       881: q^3+q
       882: q
       883: q^3+q
       909: q^3+q^2
       916: q^2
       926: q^2
       929: q^3+q^2
       932: q^3
       942: q^2
       951: q^3+q^2
       953: q^2
       958: q^3
       965: 2q^2
       971: q^2
       976: q^3+q^2
       982: q^3
       989: 2q^3+q^2
       992: q^2
       994: q^2
       996: 2q^3+q^2
       999: 2q^2
      1000: 2q^2
      1002: q^3
      1004: 2q^3+q^2
      1007: 2q^3+q^2
      1009: q^3+q^2
      1013: 2q^2
      1014: q^3+q^2
      1016: 2q^2
      1020: q^3+q^2
      1024: q^3
      1026: q^3+q^2
      1029: q^2
      1030: q^3+q^2
      1033: 2q^2
      1036: q^3+q^2
      1040: q^2
      1042: q^3
      1045: q^3+q^2
      1047: 2q^2
      1052: q^3+q^2
      1055: q^2
      1056: q^2
      1059: q^3+q^2
      1063: q^2
      1065: q^2
      1066: q^3+q
      1068: q
      1070: q^3+q
      1072: q
      1073: q^3+q
      1074: 2q^2
      1075: q
      1076: q^2
      1077: q^3+2q^2
      1078: q^3+q^2
      1079: q
      1080: q^2
      1081: q^3+2q^2
      1082: q^3+q^2
      1083: q^2
      1084: 2q^2
      1085: q^3+q^2
      1089: q^2
      1116: q^2
      1122: q^2
      1131: 2q^2
      1136: q^3+q^2
      1141: q^2
      1144: q^2
      1162: q^2
      1166: q^2
      1181: q^2
      1191: q^2
      1195: 2q^2
      1205: q^2
      1207: q^2
      1210: q
      1212: q^3+q
      1214: q^2
      1217: 2q^2
      1218: 2q^2
      1225: 2q^2
      1226: q
      1228: q
      1233: q^2
      1234: q^2
      1236: q^3+q^2
      1240: q^3+q^2
      1243: q^2
      1244: q
      1247: q
      1251: q^2
      1252: q^3+q^2
      1254: q^2
      1258: q^2
      1261: q^3+q^2
      1263: q
      1268: q^2
      1271: q^2
      1274: q^2
      1277: q^2
      1281: 2q^2
      1282: q
      1283: q^2
      1284: q
      1285: q^2
      1286: q
      1288: 2q^2
      1289: q^2
      1293: q^2
      1305: q^2
      1316: q^2
      1318: q^2
      1327: 2q^2
      1337: q^2
      1340: q
      1366: q^2
      1371: q^2
      1374: q
      1397: q^2
      1402: q^2
      1407: q
      1411: q
      1427: q^2
      1433: q^2
      1438: q
      1441: q
      1442: q
      1445: q
      1451: q^2
      1452: q
      1454: q^2
      1458: q
      1461: q^2
      1462: q^2
      1472: q^2
      1476: q^2
      1479: q^2
      1483: 2q^2
      1485: q
      1486: q
      1488: q
      1492: q^2
      1528: q
      1543: q
      1545: q
      1550: q
      1556: q
      1577: q^2
      1596: q^2
      1628: q^2
      1634: q^2
      1640: q
      1643: q
      1646: q
      1647: q
      1651: q
      1654: q
      1655: q
      1667: q
      1670: q
      1678: q
      1726: q
      1734: q
      1739: q
      1745: q
      1751: q
      1763: q
      1765: q
      1774: q
      1804: q
      1837: q
      1850: q
      1861: q
      2061: 1
      2095: 1
      2136: 1
      2163: 1

2164:    0: 10q^3+4q^2+q
         1: 10q^3+4q^2+q
         2: 3q^4+7q^3+4q^2+q
         3: 10q^3+4q^2+q
         4: 3q^4+7q^3+4q^2+q
         5: 10q^3+4q^2+q
         6: 3q^4+7q^3+4q^2+q
         7: q^5+4q^4+5q^3+4q^2+q
         8: 3q^4+7q^3+4q^2+q
         9: q^5+4q^4+5q^3+4q^2+q
        10: 10q^3+4q^2+q
        11: 10q^3+4q^2+q
        12: 3q^4+7q^3+4q^2+q
        13: 7q^3+4q^2+q
        14: 2q^4+5q^3+4q^2+q
        15: 7q^3+4q^2+q
        16: 10q^3+4q^2+q
        17: 10q^3+4q^2+q
        18: q^5+4q^4+5q^3+4q^2+q
        19: 7q^3+4q^2+q
        20: 7q^3+4q^2+q
        21: 2q^4+5q^3+4q^2+q
        22: 10q^3+4q^2+q
        23: 10q^3+4q^2+q
        24: 3q^4+7q^3+4q^2+q
        25: 10q^3+4q^2+q
        26: 10q^3+4q^2+q
        27: 3q^4+7q^3+4q^2+q
        28: 10q^3+4q^2+q
        29: 7q^3+4q^2+q
        30: 5q^3+4q^2+q
        31: 10q^3+4q^2+q
        32: 7q^3+4q^2+q
        33: 10q^3+4q^2+q
        34: 10q^3+4q^2+q
        35: 7q^3+4q^2+q
        36: 10q^3+4q^2+q
        37: 6q^3+2q^2+q
        38: 4q^3+2q^2
        39: 6q^3+2q^2+q
        40: 4q^3+2q^2
        41: 2q^4+4q^3+2q^2+q
        42: q^4+3q^3+2q^2
        43: 7q^3+4q^2+q
        44: 2q^4+5q^3+4q^2+q
        45: 7q^3+4q^2+q
        46: 7q^3+4q^2+q
        47: 7q^3+4q^2+q
        48: 2q^4+5q^3+4q^2+q
        49: 7q^3+4q^2+q
        50: 7q^3+4q^2+q
        51: 2q^4+5q^3+4q^2+q
        52: 7q^3+4q^2+q
        53: 7q^3+4q^2+q
        54: 2q^4+5q^3+4q^2+q
        55: 7q^3+4q^2+q
        56: 7q^3+4q^2+q
        57: 2q^4+5q^3+4q^2+q
        58: 4q^3+q^2
        59: 6q^3+3q^2+q
        60: 4q^3+q^2
        61: 6q^3+3q^2+q
        62: 6q^3+2q^2+q
        63: 4q^3+2q^2
        64: 4q^3+2q^2+q
        65: 3q^3+2q^2
        66: 6q^3+2q^2+q
        67: 4q^3+2q^2
        68: 4q^3+4q^2+q
        69: 5q^3+4q^2+q
        70: 5q^3+4q^2+q
        71: 7q^3+4q^2+q
        72: 4q^3+4q^2+q
        73: 4q^3+4q^2+q
        74: 3q^3+2q^2+q
        75: q^3+2q^2
        76: 3q^3+2q^2+q
        77: q^3+2q^2
        78: q^4+2q^3+2q^2+q
        79: q^3+2q^2
        80: 7q^3+4q^2+q
        81: 7q^3+4q^2+q
        82: 7q^3+4q^2+q
        83: 5q^3+4q^2+q
        84: 7q^3+4q^2+q
        85: 7q^3+4q^2+q
        86: 7q^3+4q^2+q
        87: 5q^3+4q^2+q
        88: 7q^3+4q^2+q
        89: 7q^3+4q^2+q
        90: 2q^4+5q^3+4q^2+q
        91: 4q^3+4q^2+q
        92: 4q^3+4q^2+q
        93: 4q^3+4q^2+q
        94: 7q^3+4q^2+q
        95: 7q^3+4q^2+q
        96: 2q^4+5q^3+4q^2+q
        97: 7q^3+4q^2+q
        98: 7q^3+4q^2+q
        99: 2q^4+5q^3+4q^2+q
       100: 7q^3+4q^2+q
       101: 7q^3+4q^2+q
       102: 2q^4+5q^3+4q^2+q
       103: 2q^3
       104: 2q^3+q^2
       105: 2q^3+q^2
       106: 4q^3+2q^2+q
       107: q^3+q^2
       108: 3q^3+3q^2+q
       109: q^3+q^2
       110: 3q^3+3q^2+q
       111: q^3+2q^2+q
       112: 2q^2
       113: 3q^3+2q^2+q
       114: q^3+2q^2
       115: 2q^3+2q^2+q
       116: q^3+2q^2
       117: q^3+q^2
       118: 3q^3+3q^2+q
       119: q^3+q^2
       120: 3q^3+3q^2+q
       121: 4q^3+2q^2+q
       122: 3q^3+2q^2
       123: 4q^3+2q^2+q
       124: 3q^3+2q^2
       125: 4q^3+4q^2+q
       126: 5q^3+4q^2+q
       127: 3q^3+2q^2+q
       128: q^3+2q^2
       129: 3q^3+2q^2+q
       130: q^3+2q^2
       131: q^4+2q^3+2q^2+q
       132: q^3+2q^2
       133: 2q^3+4q^2+q
       134: 4q^3+4q^2+q
       135: 2q^3+4q^2+q
       136: 2q^3+4q^2+q
       137: 7q^3+4q^2+q
       138: 5q^3+4q^2+q
       139: 7q^3+4q^2+q
       140: 4q^3+4q^2+q
       141: 5q^3+4q^2+q
       142: 4q^3+4q^2+q
       143: 7q^3+4q^2+q
       144: 5q^3+4q^2+q
       145: 7q^3+4q^2+q
       146: 5q^3+4q^2+q
       147: 4q^3+4q^2+q
       148: 4q^3+4q^2+q
       149: 7q^3+4q^2+q
       150: 5q^3+4q^2+q
       151: 3q^3+2q^2+q
       152: q^3+2q^2
       153: 3q^3+2q^2+q
       154: q^3+2q^2
       155: q^4+2q^3+2q^2+q
       156: q^3+2q^2
       157: 4q^3+4q^2+q
       158: 4q^3+4q^2+q
       159: 4q^3+4q^2+q
       160: 4q^3+4q^2+q
       161: 4q^3+4q^2+q
       162: 4q^3+4q^2+q
       163: 4q^3+4q^2+q
       164: 4q^3+4q^2+q
       165: 4q^3+4q^2+q
       166: 7q^3+4q^2+q
       167: 7q^3+4q^2+q
       168: 2q^4+5q^3+4q^2+q
       170: q^2
       171: q^2
       172: q^3+2q^2+q
       174: q^3+q^2
       175: q^3+q^2
       176: 2q^3+2q^2+q
       177: 2q^3+2q^2+q
       178: q^3+2q^2
       179: 3q^3+2q^2+q
       180: q^3+2q^2
       181: q^3+2q^2+q
       182: 2q^2
       183: q^2
       184: q^3+3q^2+q
       185: q^2
       186: q^3+3q^2+q
       187: 2q^2+q
       188: 2q^2
       189: 2q^3+2q^2+q
       190: q^3+2q^2
       191: q^3+q^2
       192: 3q^3+3q^2+q
       193: q^3+q^2
       194: 3q^3+3q^2+q
       195: q^3+q^2
       196: 3q^3+3q^2+q
       197: q^3+2q^2+q
       198: 2q^2
       199: q^3+q^2
       200: 3q^3+3q^2+q
       201: q^3+q^2
       202: 3q^3+3q^2+q
       203: q^3+q^2
       204: 3q^3+3q^2+q
       205: q^3+2q^2+q
       206: 2q^2
       207: 4q^3+2q^2+q
       208: 3q^3+2q^2
       209: 3q^3+2q^2+q
       210: q^3+2q^2
       211: 2q^3+2q^2+q
       212: q^3+2q^2
       213: q^3+q^2+q
       215: q^3+q^2+q
       217: q^3+q^2+q
       219: 2q^3+4q^2+q
       220: 2q^3+4q^2+q
       221: 4q^3+4q^2+q
       222: 2q^3+4q^2+q
       223: 2q^3+4q^2+q
       224: 2q^3+4q^2+q
       225: 2q^3+4q^2+q
       226: 5q^3+4q^2+q
       227: 2q^3+4q^2+q
       228: 4q^3+4q^2+q
       229: 2q^3+4q^2+q
       230: 2q^3+4q^2+q
       231: 5q^3+4q^2+q
       232: 2q^3+4q^2+q
       233: 4q^3+4q^2+q
       234: 2q^3+4q^2+q
       235: 2q^3+4q^2+q
       236: 5q^3+4q^2+q
       237: 3q^3+2q^2+q
       238: q^3+2q^2
       239: 3q^3+2q^2+q
       240: q^3+2q^2
       241: q^4+2q^3+2q^2+q
       242: q^3+2q^2
       243: 7q^3+4q^2+q
       244: 4q^3+4q^2+q
       245: 4q^3+4q^2+q
       246: 5q^3+4q^2+q
       247: q^3+7q^2+q
       248: q^3+7q^2+q
       249: q^4+3q^3+4q^2+q
       250: 4q^3+4q^2+q
       251: 4q^3+4q^2+q
       252: 4q^3+4q^2+q
       253: 4q^3+4q^2+q
       254: 4q^3+4q^2+q
       255: 4q^3+4q^2+q
       256: 4q^3+4q^2+q
       257: 4q^3+4q^2+q
       258: 4q^3+4q^2+q
       260: q^2
       261: q^2
       262: q^3+2q^2+q
       264: q^2
       265: q^2
       266: 2q^2+q
       268: q^2
       269: q^3+2q^2+q
       270: q^2
       272: q^2
       273: q^3+2q^2+q
       274: q^2
       276: q^3+q^2
       277: q^3+q^2
       278: 2q^3+2q^2+q
       279: q^2+q
       281: q^3+q^2+q
       283: q^2
       284: q^3+3q^2+q
       285: q^2
       286: q^3+3q^2+q
       287: 2q^3+2q^2+q
       288: q^3+2q^2
       289: q^2+q
       291: 2q^2+q
       292: 2q^2
       293: q^2
       294: q^3+3q^2+q
       295: q^2
       296: q^3+3q^2+q
       297: 2q^2+q
       298: 2q^2
       299: q^2
       300: q^3+3q^2+q
       301: q^3+2q^2+q
       302: 2q^2
       303: q^2
       304: q^3+3q^2+q
       305: 2q^2+q
       306: 2q^2
       307: q^2
       308: q^3+3q^2+q
       309: q^2
       310: q^3+3q^2+q
       311: q^3+2q^2+q
       312: 2q^2
       313: 2q^2+q
       314: 2q^2
       315: 2q^3+2q^2+q
       316: q^3+2q^2
       317: 3q^3+2q^2+q
       318: q^3+2q^2
       319: q^3+q^2
       320: 3q^3+3q^2+q
       321: q^3+q^2
       322: 3q^3+3q^2+q
       323: q^3+2q^2+q
       324: 2q^2
       325: 2q^3+2q^2+q
       326: q^3+2q^2
       327: q^3+q^2+q
       329: q^3+q^2+q
       331: q^3+q^2+q
       333: 2q^3+4q^2+q
       334: 2q^3+4q^2+q
       335: 2q^3+4q^2+q
       336: 4q^2+q
       337: q^3+7q^2+q
       338: q^3+4q^2+q
       339: 3q^2
       340: q^3+4q^2+q
       341: 3q^2
       342: q^4+2q^3+2q^2+q
       343: q^3+2q^2
       344: 2q^3+4q^2+q
       345: 2q^3+4q^2+q
       346: 4q^3+4q^2+q
       347: 2q^3+4q^2+q
       348: 2q^3+4q^2+q
       349: 2q^3+4q^2+q
       350: 2q^3+4q^2+q
       351: q^3+7q^2+q
       352: 2q^3+4q^2+q
       353: 2q^3+4q^2+q
       354: 4q^3+4q^2+q
       355: 2q^3+4q^2+q
       356: 2q^3+4q^2+q
       357: 2q^3+4q^2+q
       358: 2q^3+4q^2+q
       359: q^3+7q^2+q
       360: q^3+q^2+q
       362: q^3+q^2+q
       364: q^3+q^2+q
       366: 5q^3+4q^2+q
       367: 2q^3+4q^2+q
       368: 4q^3+4q^2+q
       369: 2q^3+4q^2+q
       370: 2q^3+4q^2+q
       371: 5q^2+q
       372: 5q^2+q
       373: 2q^3+3q^2+q
       374: 4q^3+4q^2+q
       375: 4q^3+4q^2+q
       376: 4q^3+4q^2+q
       378: q^2
       379: q^2
       380: 2q^2+q
       384: q^2+q
       386: q^2
       387: q^2
       388: 2q^2+q
       390: q^2
       391: q^3+2q^2+q
       392: q^2
       394: q^2
       395: q^2
       396: 2q^2+q
       398: q^2
       399: q^3+2q^2+q
       400: q^2
       402: q^2
       403: q^2
       404: 2q^2+q
       406: q^3+2q^2+q
       407: q^2
       408: q^2
       409: q^2+q
       411: q^3+q^2+q
       413: q^2+q
       415: q^2+q
       417: q^2+q
       419: q^2
       420: q^3+3q^2+q
       421: q^2
       422: q^3+3q^2+q
       423: 2q^2+q
       424: 2q^2
       425: 2q^2+q
       426: 2q^2
       427: q^3+4q^2+q
       428: 3q^2
       429: q^2
       430: q^3+3q^2+q
       431: q^2
       432: q^3+3q^2+q
       433: 2q^2+q
       434: 2q^2
       435: q^2+q
       437: q^2
       438: q^3+3q^2+q
       439: q^2
       440: q^3+3q^2+q
       441: 2q^2+q
       442: 2q^2
       443: 2q^2
       444: q^3+5q^2+q
       445: q^3+4q^2+q
       446: 3q^2
       447: q^2
       448: q^3+3q^2+q
       449: q^2
       450: q^3+3q^2+q
       451: 2q^2+q
       452: 2q^2
       453: q^2
       454: q^3+3q^2+q
       455: q^2+q
       457: q^2
       458: q^3+3q^2+q
       459: 2q^2+q
       460: 2q^2
       461: 2q^2
       462: q^3+5q^2+q
       463: q^3+4q^2+q
       464: 3q^2
       465: q^2+q
       467: q^3+q^2+q
       469: 2q^3+2q^2+q
       470: q^3+2q^2
       471: q^2
       472: q^3+3q^2+q
       473: q^2
       474: q^3+3q^2+q
       475: 2q^2+q
       476: 2q^2
       477: q^3+2q^2+q
       478: 2q^2
       479: q^3+3q^2+q
       480: 4q^2
       481: q^3+3q^2+q
       482: q^3+3q^2+q
       483: 4q^2+q
       484: 4q^2+q
       485: 2q^2+q
       487: 2q^2+q
       489: q^3+q^2+q
       491: 3q^2+q
       492: 2q^3+4q^2+q
       493: 2q^3+4q^2+q
       494: 2q^3+4q^2+q
       495: 4q^2+q
       496: 5q^2+q
       497: 2q^3+4q^2+q
       498: 2q^3+4q^2+q
       499: 2q^3+4q^2+q
       500: 4q^2+q
       501: 5q^2+q
       502: q^3+q^2+q
       504: q^3+q^2+q
       506: q^3+q^2+q
       508: 2q^3+4q^2+q
       509: 2q^3+4q^2+q
       510: 4q^3+4q^2+q
       511: 2q^3+4q^2+q
       512: 2q^3+4q^2+q
       513: 2q^3+4q^2+q
       514: 2q^3+4q^2+q
       515: 5q^2+q
       516: 5q^2+q
       517: 2q^3+3q^2+q
       518: 5q^2+q
       519: 5q^2+q
       520: 2q^3+3q^2+q
       524: q^2+q
       528: q^2+q
       530: q^2
       531: q^2
       532: 2q^2+q
       534: q^2
       535: q^2
       536: 2q^2+q
       539: q^2+q
       542: q^2
       543: 2q^2+q
       544: q^2
       545: q^2
       546: q^2
       547: q^3+3q^2+q
       548: 2q^2
       550: q^2
       551: q^2
       552: 2q^2+q
       555: q^2+q
       558: q^2
       559: 2q^2+q
       560: q^2
       561: q^2
       562: q^2
       563: q^3+3q^2+q
       564: 2q^2
       566: q^2
       567: q^2
       568: 2q^2+q
       570: q^3+2q^2+q
       571: q^2
       572: q^2
       574: 2q^2
       575: q^3+3q^2+q
       576: 2q^2
       577: q^3+2q^2+q
       578: q^2
       580: 2q^2
       581: 2q^2
       583: q^2+q
       585: q
       587: q^2+q
       589: q^2
       590: q^3+2q^2+q
       592: 2q^2+q
       594: 2q^2+q
       595: q^2
       596: q^3+2q^2+q
       597: q^2+q
       599: 2q^2+q
       600: 2q^2
       601: q^2+q
       603: q^2
       604: q^3+3q^2+q
       605: q^2+q
       607: q^2
       608: q^3+3q^2+q
       609: 2q^2+q
       610: 2q^2
       611: q^2+q
       613: 2q^2+q
       614: 2q^2
       615: q^2
       616: 3q^2+q
       617: 2q^2+q
       619: q^2
       620: q^3+3q^2+q
       621: q^2
       622: q^3+3q^2+q
       623: q^2+q
       625: 2q^2+q
       626: 2q^2
       627: q^2+q
       629: 2q^2+q
       630: 2q^2
       631: q^2
       632: 3q^2+q
       633: 2q^2+q
       635: q^2+q
       637: q^3+q^2+q
       639: q^2+q
       641: q^2
       642: q^3+3q^2+q
       643: q^2
       644: q^3+3q^2+q
       645: 2q^2+q
       646: 2q^2
       647: q^2
       648: q^3+3q^2+q
       649: q^2
       650: q^3+3q^2+q
       651: q^2+q
       653: 2q^2+q
       654: 2q^2
       655: 2q^2+q
       656: 3q^2
       657: 4q^2+q
       658: 2q^2+q
       660: 2q^2+q
       662: q^3+q^2+q
       664: 3q^2+q
       665: 2q^2+q
       666: 2q^2+q
       668: 2q^2+q
       670: q^3+q^2+q
       672: 4q^2+q
       673: 3q^2+q
       674: 5q^2+q
       675: q^3+3q^2+q
       676: q^3+3q^2+q
       677: 4q^2+q
       678: 5q^2+q
       679: 3q^2+q
       680: 5q^2+q
       681: q^3+3q^2+q
       682: q^3+3q^2+q
       683: 4q^2+q
       684: 5q^2+q
       685: 3q^2+q
       686: 2q^3+4q^2+q
       687: 2q^3+4q^2+q
       688: 2q^3+4q^2+q
       689: 4q^2+q
       690: 5q^2+q
       691: 5q^2+q
       692: 2q^3+3q^2+q
       696: q^2
       697: q^3+2q^2+q
       698: q^2
       699: q^2
       700: q^2
       701: q^2
       708: q^2+q
       712: q
       715: q^2
       716: q^2+q
       719: q^2
       720: q^2+q
       723: q^2+q
       726: q^2
       727: 2q^2+q
       728: q^2
       731: q^2+q
       735: q^2+q
       739: q^2+q
       742: q^2
       743: 2q^2+q
       744: q^2
       747: q^2+q
       751: q^2+q
       754: q^2
       755: q^2
       756: 2q^2+q
       758: q^2+q
       762: 2q^2+q
       763: q^2
       764: q^2
       766: q^2
       767: q^2
       768: 2q^2+q
       769: q^2+q
       772: q^2
       775: q^2+q
       777: q
       779: q^2+q
       781: q
       783: q^2+q
       786: q^2+q
       788: q^2+q
       789: q^2+q
       791: q
       792: q^2
       793: q^2
       794: 3q^2+q
       795: 2q^2+q
       797: q
       799: q^2+q
       801: q^2
       802: q^3+2q^2+q
       804: 2q^2+q
       806: 2q^2+q
       807: q^2
       808: q^3+2q^2+q
       809: q^2+q
       811: 2q^2+q
       812: 2q^2
       813: 2q^2+q
       815: q^2
       816: 3q^2+q
       817: q^2
       818: 3q^2+q
       819: 2q^2+q
       821: q
       823: q^2+q
       825: q^2
       826: q^3+2q^2+q
       828: 2q^2+q
       830: 2q^2+q
       831: q^2
       832: q^3+2q^2+q
       833: q^2+q
       835: 2q^2+q
       836: 2q^2
       837: 2q^2+q
       839: q^2
       840: 3q^2+q
       841: q^2+q
       843: 2q^2+q
       844: 3q^2
       845: q^2
       846: q^3+3q^2+q
       847: q^2
       848: q^3+3q^2+q
       849: q^2+q
       851: 2q^2+q
       852: 2q^2
       853: q^2+q
       855: 2q^2+q
       856: 2q^2
       857: 2q^2+q
       858: 3q^2
       859: 2q^2+q
       861: 2q^2+q
       863: q^3+q^2+q
       865: 4q^2+q
       866: 2q^2+q
       867: 3q^2+q
       868: 2q^2+q
       869: 5q^2+q
       870: 3q^2+q
       871: 2q^2+q
       872: 3q^2+q
       873: 5q^2+q
       874: 3q^2+q
       875: 2q^2+q
       876: 3q^2+q
       877: q^3+3q^2+q
       878: q^3+3q^2+q
       879: 4q^2+q
       880: 3q^2+q
       881: 3q
       882: 3q
       883: q^2+2q
       889: q^2+q
       899: q
       902: q
       906: q
       911: q
       914: q^2+q
       918: q^2+q
       922: q
       926: q^2
       927: q^2+q
       930: q^2+q
       931: q^2
       934: q^2+q
       938: q^2+q
       942: q^2+q
       946: q
       950: q^2+q
       951: q^2
       954: q^2
       955: q^2+q
       958: q^2+q
       961: q^2+q
       965: q^2
       966: q^2
       967: 2q^2+q
       968: q^2+q
       971: q^2
       975: 2q^2+q
       976: q^2
       977: q^2
       979: q^2+q
       982: q^2+q
       985: q^2
       989: q^2
       990: q^2
       991: 2q^2+q
       992: q^2+q
       994: q
       996: q^2+q
       999: q^2+q
      1001: q^2+q
      1002: q
      1005: q^2+q
      1007: q^2+q
      1008: q
      1009: q^2
      1010: q
      1012: q
      1013: q^2
      1014: 2q^2+q
      1016: q^2
      1017: 3q^2+q
      1018: q
      1020: q^2+q
      1022: q
      1024: q^2+q
      1027: q^2+q
      1029: q^2+q
      1030: 2q^2+q
      1032: q^2
      1033: 3q^2+q
      1034: q
      1036: q^2+q
      1038: q
      1041: q^2+q
      1042: q^2+q
      1045: q^2+q
      1046: 2q^2+q
      1047: 3q^2
      1048: q
      1050: q^2+q
      1052: q^2
      1053: q^3+2q^2+q
      1055: 2q^2+q
      1057: 2q^2+q
      1058: q^2
      1059: q^3+2q^2+q
      1060: q^2+q
      1062: 2q^2+q
      1063: 2q^2
      1064: q
      1065: q^2
      1066: 3q
      1068: 3q
      1070: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q^2+q
      1075: 3q
      1076: 2q^2+q
      1077: 3q^2+q
      1078: 2q^2+q
      1079: 3q
      1080: 2q^2+q
      1081: 3q^2+q
      1082: 2q^2+q
      1083: 2q^2+q
      1084: 3q^2+q
      1085: 3q^2+q
      1091: q^2+q
      1102: q^2+q
      1112: q
      1116: q
      1120: q
      1124: q
      1127: q
      1133: q
      1135: q
      1138: q
      1146: q^2+q
      1150: q
      1154: q
      1158: q
      1163: q
      1166: q^2+q
      1170: q
      1174: q
      1178: q
      1183: q
      1185: q^2+q
      1188: q^2+q
      1191: q^2
      1195: q^2
      1196: q^2
      1197: 2q^2+q
      1199: q
      1204: q^2+q
      1205: q^2
      1208: q^2+q
      1209: q^2
      1210: 3q
      1212: 2q
      1214: q
      1217: q^2+q
      1219: q^2+q
      1222: q
      1224: q
      1225: q^2
      1226: 3q
      1228: q
      1229: 2q
      1230: q
      1233: q^2+q
      1235: q^2+q
      1236: q^2+q
      1238: q
      1241: q^2+q
      1243: q^2+q
      1244: 3q
      1246: q
      1247: 2q
      1248: q
      1251: q^2+q
      1252: q^2+q
      1255: q^2+q
      1256: q
      1259: q^2+q
      1261: q^2+q
      1262: q
      1263: 2q
      1264: q
      1266: q
      1269: q^2+q
      1271: q^2+q
      1272: q^2+q
      1274: q^2+q
      1276: q
      1277: q^2
      1278: q
      1280: q
      1281: q^2
      1282: 2q
      1283: 2q^2+q
      1284: 2q
      1285: 2q^2+q
      1286: 2q
      1287: 2q^2+q
      1288: 3q^2+q
      1289: 2q^2+q
      1295: q
      1307: q^2+q
      1316: q
      1320: q
      1323: q
      1329: q
      1334: q
      1340: q
      1342: 2q
      1346: q
      1350: q
      1354: q
      1358: q
      1361: q
      1367: q
      1369: q
      1372: q
      1374: 2q
      1378: q
      1382: q
      1386: q
      1390: q
      1393: q
      1399: q
      1401: q
      1404: q
      1407: 2q
      1411: q
      1412: q
      1413: q
      1415: q
      1420: q
      1424: q
      1429: q
      1430: q
      1438: 2q
      1441: q
      1443: q
      1445: q
      1448: q
      1451: q^2+q
      1452: 2q
      1455: q^2+q
      1456: q
      1458: 2q
      1461: q^2+q
      1463: q^2+q
      1464: q
      1467: q^2+q
      1469: q^2+q
      1470: q
      1472: q^2+q
      1477: q^2+q
      1479: q^2+q
      1480: q
      1482: q
      1483: q^2
      1484: q
      1485: 2q
      1486: 2q
      1487: 2q^2+q
      1488: 2q
      1494: q
      1506: q
      1518: q
      1528: q
      1529: q
      1530: q
      1543: q
      1547: q
      1556: q
      1565: q
      1569: q
      1572: q
      1578: q
      1585: q
      1589: q
      1592: q
      1598: q
      1605: q
      1609: q
      1613: q
      1617: q
      1622: q
      1626: q
      1630: q
      1631: q
      1640: q
      1643: 2q
      1646: q
      1648: q
      1650: q
      1651: 2q
      1654: q
      1656: q
      1658: q
      1661: q
      1664: q^2+q
      1666: q^2+q
      1667: 2q
      1670: q
      1673: q
      1674: 2q
      1692: q
      1704: q
      1718: q
      1726: q
      1739: q
      1747: q
      1763: q
      1767: q
      1787: q
      1791: q
      1796: q
      1800: q
      1804: q
      1814: q
      1820: q
      1822: q
      1826: q
      1827: 2q
      1830: q
      1832: q
      1833: 1
      1877: q
      1929: q
      1934: q
      1938: q
      1955: q
      1956: 1
      1961: 1
      1963: 1
      1965: 1
      2029: 1
      2034: 1
      2043: 1
      2046: 1
      2055: 1
      2067: 1
      2076: 1
      2088: 1
      2111: 1
      2137: 1
      2164: 1

2165:    0: 2q^6+15q^5+19q^4+6q^3+q^2
         1: 2q^6+15q^5+19q^4+6q^3+q^2
         2: 5q^6+14q^5+15q^4+5q^3+q^2
         3: 15q^5+19q^4+6q^3+q^2
         4: 2q^6+15q^5+19q^4+6q^3+q^2
         5: 15q^5+19q^4+6q^3+q^2
         6: 2q^6+15q^5+19q^4+6q^3+q^2
         7: 5q^6+14q^5+15q^4+5q^3+q^2
         8: 5q^6+15q^5+15q^4+5q^3+q^2
         9: 3q^7+9q^6+12q^5+10q^4+4q^3+q^2
        10: 2q^6+15q^5+19q^4+6q^3+q^2
        11: 15q^5+19q^4+6q^3+q^2
        12: 2q^6+15q^5+19q^4+6q^3+q^2
        13: q^6+9q^5+14q^4+5q^3+q^2
        14: q^6+9q^5+14q^4+5q^3+q^2
        15: 10q^5+14q^4+5q^3+q^2
        16: 8q^5+18q^4+6q^3+q^2
        17: 8q^5+18q^4+6q^3+q^2
        18: 5q^6+11q^5+10q^4+4q^3+q^2
        19: 2q^6+15q^5+19q^4+6q^3+q^2
        20: 2q^6+15q^5+19q^4+6q^3+q^2
        21: 5q^6+14q^5+15q^4+5q^3+q^2
        22: 8q^5+18q^4+6q^3+q^2
        23: 8q^5+18q^4+6q^3+q^2
        24: 2q^6+10q^5+14q^4+5q^3+q^2
        25: 8q^5+18q^4+6q^3+q^2
        26: 8q^5+18q^4+6q^3+q^2
        27: 2q^6+10q^5+14q^4+5q^3+q^2
        28: 8q^5+18q^4+6q^3+q^2
        29: 2q^6+15q^5+19q^4+6q^3+q^2
        30: q^6+9q^5+14q^4+5q^3+q^2
        31: 8q^5+18q^4+6q^3+q^2
        32: 5q^5+13q^4+5q^3+q^2
        33: 3q^5+17q^4+6q^3+q^2
        34: 8q^5+18q^4+6q^3+q^2
        35: 5q^5+13q^4+5q^3+q^2
        36: 3q^5+17q^4+6q^3+q^2
        37: 2q^5+9q^4+4q^3
        38: q^5+8q^4+2q^3+q^2
        39: 2q^5+9q^4+4q^3
        40: q^5+8q^4+2q^3+q^2
        41: 4q^5+7q^4+3q^3
        42: 3q^5+6q^4+2q^3+q^2
        43: q^6+9q^5+14q^4+5q^3+q^2
        44: q^6+9q^5+14q^4+5q^3+q^2
        45: 10q^5+14q^4+5q^3+q^2
        46: 3q^5+13q^4+5q^3+q^2
        47: 4q^5+13q^4+5q^3+q^2
        48: q^6+7q^5+9q^4+4q^3+q^2
        49: 8q^5+18q^4+6q^3+q^2
        50: 8q^5+18q^4+6q^3+q^2
        51: 5q^6+11q^5+10q^4+4q^3+q^2
        52: 8q^5+18q^4+6q^3+q^2
        53: 8q^5+18q^4+6q^3+q^2
        54: 2q^6+10q^5+14q^4+5q^3+q^2
        55: 8q^5+18q^4+6q^3+q^2
        56: 8q^5+18q^4+6q^3+q^2
        57: 2q^6+10q^5+14q^4+5q^3+q^2
        58: 2q^5+10q^4+4q^3+q^2
        59: q^5+7q^4+2q^3
        60: q^5+7q^4+2q^3
        61: 2q^5+10q^4+4q^3+q^2
        62: 2q^5+9q^4+4q^3
        63: q^5+8q^4+2q^3+q^2
        64: q^5+6q^4+3q^3
        65: q^5+6q^4+2q^3+q^2
        66: 8q^4+4q^3
        67: 8q^4+2q^3+q^2
        68: q^5+8q^4+4q^3+q^2
        69: 3q^5+8q^4+4q^3+q^2
        70: q^6+9q^5+14q^4+5q^3+q^2
        71: 8q^5+18q^4+6q^3+q^2
        72: 3q^5+17q^4+6q^3+q^2
        73: 3q^5+17q^4+6q^3+q^2
        74: 2q^5+9q^4+4q^3
        75: q^5+8q^4+2q^3+q^2
        76: 2q^5+9q^4+4q^3
        77: q^5+8q^4+2q^3+q^2
        78: 4q^5+7q^4+3q^3
        79: 3q^5+6q^4+2q^3+q^2
        80: 5q^5+13q^4+5q^3+q^2
        81: q^5+12q^4+5q^3+q^2
        82: 8q^5+18q^4+6q^3+q^2
        83: 5q^5+13q^4+5q^3+q^2
        84: 5q^5+13q^4+5q^3+q^2
        85: q^5+12q^4+5q^3+q^2
        86: 8q^5+18q^4+6q^3+q^2
        87: 5q^5+13q^4+5q^3+q^2
        88: 3q^5+13q^4+5q^3+q^2
        89: 4q^5+13q^4+5q^3+q^2
        90: q^6+7q^5+9q^4+4q^3+q^2
        91: 3q^5+13q^4+5q^3+q^2
        92: 4q^5+13q^4+5q^3+q^2
        93: q^6+7q^5+9q^4+4q^3+q^2
        94: 3q^5+15q^4+6q^3+q^2
        95: 3q^5+15q^4+6q^3+q^2
        96: 2q^6+7q^5+9q^4+4q^3+q^2
        97: 3q^5+15q^4+6q^3+q^2
        98: 3q^5+15q^4+6q^3+q^2
        99: 2q^6+7q^5+9q^4+4q^3+q^2
       100: 3q^5+15q^4+6q^3+q^2
       101: 3q^5+15q^4+6q^3+q^2
       102: 6q^5+11q^4+5q^3+q^2
       103: 4q^4+2q^3
       104: 3q^4
       105: 5q^4+2q^3+q^2
       106: 4q^4+2q^3
       107: q^5+7q^4+2q^3
       108: 2q^5+10q^4+4q^3+q^2
       109: 2q^5+10q^4+4q^3+q^2
       110: q^5+7q^4+2q^3
       111: 8q^4+4q^3
       112: 8q^4+2q^3+q^2
       113: 2q^5+9q^4+4q^3
       114: q^5+8q^4+2q^3+q^2
       115: q^5+6q^4+3q^3
       116: q^5+6q^4+2q^3+q^2
       117: 5q^4+3q^3+q^2
       118: 2q^4+q^3
       119: 2q^4+q^3
       120: 5q^4+3q^3+q^2
       121: q^5+6q^4+3q^3
       122: q^5+6q^4+2q^3+q^2
       123: 5q^4+3q^3
       124: 6q^4+2q^3+q^2
       125: q^5+8q^4+4q^3+q^2
       126: 3q^5+8q^4+4q^3+q^2
       127: 4q^4+4q^3
       128: 3q^4+q^3+q^2
       129: 4q^4+4q^3
       130: 3q^4+q^3+q^2
       131: q^5+3q^4+2q^3
       132: q^5+2q^4+q^3+q^2
       133: q^5+8q^4+4q^3+q^2
       134: 3q^5+8q^4+4q^3+q^2
       135: q^5+12q^4+5q^3+q^2
       136: q^5+12q^4+5q^3+q^2
       137: q^5+12q^4+5q^3+q^2
       138: q^5+7q^4+4q^3+q^2
       139: 3q^5+15q^4+6q^3+q^2
       140: 7q^4+5q^3+q^2
       141: 5q^5+13q^4+5q^3+q^2
       142: 3q^5+15q^4+6q^3+q^2
       143: q^5+12q^4+5q^3+q^2
       144: q^5+7q^4+4q^3+q^2
       145: 3q^5+15q^4+6q^3+q^2
       146: 5q^5+13q^4+5q^3+q^2
       147: 3q^5+15q^4+6q^3+q^2
       148: 7q^4+5q^3+q^2
       149: 3q^5+15q^4+6q^3+q^2
       150: 2q^5+10q^4+5q^3+q^2
       151: 2q^5+8q^4+4q^3
       152: q^5+7q^4+2q^3+q^2
       153: 2q^5+8q^4+4q^3
       154: q^5+7q^4+2q^3+q^2
       155: 3q^5+6q^4+3q^3
       156: 3q^5+5q^4+2q^3+q^2
       157: 3q^5+13q^4+5q^3+q^2
       158: 4q^5+13q^4+5q^3+q^2
       159: q^6+7q^5+9q^4+4q^3+q^2
       160: q^5+8q^4+5q^3+q^2
       161: q^5+8q^4+5q^3+q^2
       162: 3q^5+6q^4+4q^3+q^2
       163: q^5+8q^4+5q^3+q^2
       164: q^5+8q^4+5q^3+q^2
       165: 3q^5+6q^4+4q^3+q^2
       166: 9q^4+6q^3+q^2
       167: 9q^4+6q^3+q^2
       168: 4q^5+7q^4+4q^3+q^2
       169: 4q^4+2q^3
       170: 3q^4
       171: 5q^4+2q^3+q^2
       172: 4q^4+2q^3
       173: q^4+q^3
       174: q^4
       175: 3q^4+2q^3+q^2
       176: q^4+q^3
       177: q^4+2q^3
       178: 2q^4+q^3+q^2
       179: 4q^4+4q^3
       180: 3q^4+q^3+q^2
       181: 4q^4+4q^3
       182: 3q^4+q^3+q^2
       183: 2q^4+q^3
       184: 5q^4+3q^3+q^2
       185: 5q^4+3q^3+q^2
       186: 2q^4+q^3
       187: 5q^4+3q^3
       188: 6q^4+2q^3+q^2
       189: q^5+6q^4+3q^3
       190: q^5+6q^4+2q^3+q^2
       191: 5q^4+3q^3+q^2
       192: 2q^4+q^3
       193: 2q^4+q^3
       194: 5q^4+4q^3+q^2
       195: 2q^5+9q^4+4q^3+q^2
       196: q^5+6q^4+2q^3
       197: 3q^4+3q^3
       198: 4q^4+2q^3+q^2
       199: 2q^4+q^3
       200: 5q^4+3q^3+q^2
       201: q^5+6q^4+2q^3
       202: 2q^5+9q^4+4q^3+q^2
       203: 5q^4+4q^3+q^2
       204: 2q^4+q^3
       205: 3q^4+3q^3
       206: 4q^4+2q^3+q^2
       207: 5q^4+3q^3
       208: 6q^4+2q^3+q^2
       209: 2q^5+8q^4+4q^3
       210: q^5+7q^4+2q^3+q^2
       211: q^5+5q^4+3q^3
       212: q^5+5q^4+2q^3+q^2
       213: q^4+3q^3
       215: q^4+3q^3
       217: q^4+2q^3
       219: q^5+4q^4+3q^3+q^2
       220: q^5+8q^4+4q^3+q^2
       221: 3q^5+8q^4+4q^3+q^2
       222: q^5+12q^4+5q^3+q^2
       223: q^5+7q^4+4q^3+q^2
       224: q^5+12q^4+5q^3+q^2
       225: q^5+7q^4+4q^3+q^2
       226: q^5+7q^4+4q^3+q^2
       227: 4q^4+4q^3+q^2
       228: q^5+5q^4+4q^3+q^2
       229: 3q^4+4q^3+q^2
       230: q^5+8q^4+5q^3+q^2
       231: q^5+7q^4+4q^3+q^2
       232: 4q^4+4q^3+q^2
       233: q^5+5q^4+4q^3+q^2
       234: q^5+8q^4+5q^3+q^2
       235: 3q^4+4q^3+q^2
       236: 5q^4+4q^3+q^2
       237: 3q^4+4q^3
       238: q^4+q^3+q^2
       239: 3q^4+4q^3
       240: q^4+q^3+q^2
       241: q^5+3q^4+2q^3
       242: q^5+q^4+q^3+q^2
       243: 9q^4+6q^3+q^2
       244: 4q^4+5q^3+q^2
       245: 4q^4+5q^3+q^2
       246: 2q^5+10q^4+5q^3+q^2
       247: 9q^4+6q^3+q^2
       248: 9q^4+6q^3+q^2
       249: 4q^5+7q^4+4q^3+q^2
       250: q^5+8q^4+5q^3+q^2
       251: q^5+8q^4+5q^3+q^2
       252: 3q^5+6q^4+4q^3+q^2
       253: q^5+8q^4+5q^3+q^2
       254: q^5+8q^4+5q^3+q^2
       255: 3q^5+6q^4+4q^3+q^2
       256: 3q^4+5q^3+q^2
       257: 4q^4+5q^3+q^2
       258: q^5+4q^4+4q^3+q^2
       259: 2q^4+2q^3
       260: q^4
       261: 2q^4+q^3+q^2
       262: 2q^4+2q^3
       263: q^4+q^3
       264: q^4
       265: 3q^4+2q^3+q^2
       266: q^4+q^3
       267: q^4+q^3
       268: q^4
       269: 2q^4+2q^3
       270: 3q^4+2q^3+q^2
       271: 2q^4+2q^3
       272: 3q^4+2q^3+q^2
       273: q^4+q^3
       274: q^4
       275: q^4+q^3
       276: q^4
       277: 3q^4+2q^3+q^2
       278: q^4+q^3
       279: 2q^3
       281: 2q^3
       284: 2q^4+2q^3+q^2
       285: 2q^4+2q^3+q^2
       287: q^4+2q^3
       288: 2q^4+q^3+q^2
       289: q^4+3q^3
       291: q^4+2q^3
       292: 2q^4+q^3+q^2
       293: 2q^4+q^3
       294: 5q^4+3q^3+q^2
       295: 5q^4+3q^3+q^2
       296: 2q^4+q^3
       297: 5q^4+3q^3
       298: 6q^4+2q^3+q^2
       300: q^4+3q^3+q^2
       301: q^4+3q^3
       302: q^3+q^2
       303: 3q^4+3q^3+q^2
       304: q^4+q^3
       305: q^4+2q^3
       306: 2q^4+2q^3+q^2
       307: q^4+q^3
       308: 3q^4+3q^3+q^2
       309: q^4+3q^3+q^2
       311: q^4+3q^3
       312: q^3+q^2
       313: q^4+2q^3
       314: 2q^4+2q^3+q^2
       315: q^4+2q^3
       316: q^4+q^3+q^2
       317: 3q^4+4q^3
       318: q^4+q^3+q^2
       319: q^4+q^3
       320: 3q^4+4q^3+q^2
       321: 3q^4+4q^3+q^2
       322: q^4+q^3
       323: 2q^3
       324: q^4+2q^3+q^2
       325: q^5+5q^4+3q^3
       326: q^5+5q^4+2q^3+q^2
       327: q^4+3q^3
       329: q^4+3q^3
       331: q^4+2q^3
       333: q^5+4q^4+3q^3+q^2
       334: q^5+7q^4+4q^3+q^2
       335: q^5+7q^4+4q^3+q^2
       336: 5q^4+4q^3+q^2
       337: 9q^4+6q^3+q^2
       338: 3q^4+4q^3
       339: q^4+q^3+q^2
       340: 3q^4+4q^3
       341: q^4+q^3+q^2
       342: q^5+3q^4+2q^3
       343: q^5+q^4+q^3+q^2
       344: 2q^4+3q^3+q^2
       345: 4q^4+4q^3+q^2
       346: q^5+5q^4+4q^3+q^2
       347: 3q^4+4q^3+q^2
       348: q^4+3q^3+q^2
       349: q^5+8q^4+5q^3+q^2
       350: q^5+5q^4+4q^3+q^2
       351: 4q^4+5q^3+q^2
       352: 2q^4+3q^3+q^2
       353: 4q^4+4q^3+q^2
       354: q^5+5q^4+4q^3+q^2
       355: q^5+8q^4+5q^3+q^2
       356: q^5+5q^4+4q^3+q^2
       357: 3q^4+4q^3+q^2
       358: q^4+3q^3+q^2
       359: 4q^4+5q^3+q^2
       360: 3q^3
       362: q^4+3q^3
       364: q^4+2q^3
       366: 5q^4+4q^3+q^2
       367: q^4+4q^3+q^2
       368: 3q^4+4q^3+q^2
       369: q^4+4q^3+q^2
       370: q^4+4q^3+q^2
       371: 3q^4+5q^3+q^2
       372: 4q^4+5q^3+q^2
       373: q^5+4q^4+4q^3+q^2
       374: 3q^4+5q^3+q^2
       375: 4q^4+5q^3+q^2
       376: q^5+4q^4+4q^3+q^2
       379: q^4+q^3+q^2
       381: q^3
       384: q^3
       385: q^4+q^3
       386: q^4
       387: 3q^4+2q^3+q^2
       388: q^4+q^3
       389: q^3
       391: q^4+2q^3
       392: q^3+q^2
       395: q^4+2q^3+q^2
       396: q^3
       397: q^4+2q^3
       398: q^3+q^2
       399: q^3
       401: q^3
       402: q^4+2q^3+q^2
       405: q^3
       406: q^3
       408: q^4+2q^3+q^2
       409: 2q^3
       411: 2q^3
       413: q^3
       415: q^4+3q^3
       417: 2q^3
       420: 2q^4+2q^3+q^2
       421: 2q^4+2q^3+q^2
       423: q^4+2q^3
       424: 2q^4+q^3+q^2
       425: q^4+2q^3
       426: q^4+q^3+q^2
       427: 3q^4+4q^3
       428: q^4+q^3+q^2
       430: 2q^3+q^2
       431: q^4+2q^3+q^2
       433: q^3
       434: q^3+q^2
       435: 2q^3
       438: q^4+3q^3+q^2
       439: 3q^4+3q^3+q^2
       440: q^4+q^3
       441: q^4+2q^3
       442: 2q^4+2q^3+q^2
       443: q^4+q^3
       444: 3q^4+4q^3+q^2
       445: q^4+3q^3
       446: q^3+q^2
       448: q^4+2q^3+q^2
       449: 2q^3+q^2
       451: q^3
       452: q^3+q^2
       453: q^4+q^3
       454: 3q^4+3q^3+q^2
       455: 2q^3
       457: q^4+3q^3+q^2
       459: q^4+2q^3
       460: 2q^4+2q^3+q^2
       461: 3q^4+4q^3+q^2
       462: q^4+q^3
       463: q^4+3q^3
       464: q^3+q^2
       465: 2q^3
       467: 2q^3
       469: q^4+2q^3
       470: q^4+q^3+q^2
       472: 3q^3+q^2
       473: 3q^3+q^2
       475: q^3
       476: 2q^3+q^2
       477: 2q^3
       478: 2q^3+q^2
       479: 2q^3
       480: q^4+2q^3+q^2
       481: 2q^4+3q^3+q^2
       482: 2q^4+3q^3+q^2
       483: 5q^4+4q^3+q^2
       484: q^4+4q^3+q^2
       485: 3q^3
       487: q^4+3q^3
       489: q^4+2q^3
       491: 3q^4+4q^3+q^2
       492: 2q^4+3q^3+q^2
       493: q^4+3q^3+q^2
       494: q^5+5q^4+4q^3+q^2
       495: q^4+3q^3+q^2
       496: q^4+4q^3+q^2
       497: 2q^4+3q^3+q^2
       498: q^5+5q^4+4q^3+q^2
       499: q^4+3q^3+q^2
       500: q^4+3q^3+q^2
       501: q^4+4q^3+q^2
       502: 3q^3
       504: q^4+3q^3
       506: q^4+2q^3
       508: q^4+3q^3+q^2
       509: q^4+4q^3+q^2
       510: 3q^4+4q^3+q^2
       511: q^4+4q^3+q^2
       512: q^4+3q^3+q^2
       513: q^4+4q^3+q^2
       514: q^4+3q^3+q^2
       515: q^4+2q^3+2q^2
       516: 2q^3+2q^2
       517: q^4+2q^3+2q^2
       518: 3q^4+5q^3+q^2
       519: 4q^4+5q^3+q^2
       520: q^5+4q^4+4q^3+q^2
       525: q^3
       528: q^3
       531: q^4+q^3+q^2
       535: q^3+q^2
       539: q^3
       543: q^3
       544: q^4+2q^3+q^2
       545: q^3
       547: q^4+2q^3
       548: q^3+q^2
       550: q^3+q^2
       553: q^3
       557: q^3
       558: q^4+2q^3+q^2
       561: q^4+2q^3
       562: q^3+q^2
       563: q^3
       567: 2q^3+q^2
       569: q^3
       570: q^3
       572: 2q^3+q^2
       573: q^3
       575: q^3
       576: q^4+2q^3+q^2
       577: 2q^3
       581: q^3+q^2
       582: q^3
       583: q^3
       585: q^3
       587: 2q^3
       590: q^4+2q^3+q^2
       591: 2q^3+q^2
       594: 2q^3+q^2
       595: q^4+2q^3+q^2
       597: 2q^3
       599: q^4+2q^3
       600: q^4+q^3+q^2
       601: 2q^3
       604: 2q^3+q^2
       605: q^3
       607: q^4+2q^3+q^2
       609: q^3
       610: q^3+q^2
       611: 2q^3
       613: q^3
       614: q^3+q^2
       616: 3q^3+q^2
       617: 2q^3
       620: q^4+2q^3+q^2
       621: 2q^3+q^2
       623: q^3
       625: q^3
       626: q^3+q^2
       627: 2q^3
       629: q^3
       630: q^3+q^2
       631: 3q^3+q^2
       633: 2q^3
       635: 2q^3
       637: 2q^3
       639: q^3
       642: 2q^3+q^2
       643: 2q^3+q^2
       646: q^3+q^2
       648: 3q^3+q^2
       649: 3q^3+q^2
       651: q^3
       653: q^3
       654: 2q^3+q^2
       655: q^3
       656: 2q^3+q^2
       657: 2q^2
       658: 2q^3+q^2
       660: 2q^3+q^2
       662: 2q^3+q^2
       664: q^4+2q^3+2q^2
       665: q^4+3q^3+q^2
       666: 3q^3
       668: q^4+3q^3
       670: q^4+2q^3
       672: q^4+4q^3+q^2
       673: 3q^4+4q^3+q^2
       674: q^3+2q^2
       675: q^3+q^2
       676: 2q^4+3q^3+q^2
       677: q^4+3q^3+q^2
       678: q^4+4q^3+q^2
       679: q^4+3q^3+q^2
       680: q^3+2q^2
       681: 2q^4+3q^3+q^2
       682: q^3+q^2
       683: q^4+3q^3+q^2
       684: q^4+4q^3+q^2
       685: q^4+3q^3+q^2
       686: q^4+3q^3+q^2
       687: q^4+3q^3+q^2
       688: q^4+3q^3+q^2
       689: q^3+q^2
       690: q^4+2q^3+2q^2
       691: 2q^3+2q^2
       692: q^4+2q^3+2q^2
       693: q^3
       697: q^3
       700: q^3+q^2
       704: q^3
       714: q^3+q^2
       719: q^3+q^2
       728: q^3+q^2
       731: q^3
       735: q^3
       742: q^3+q^2
       745: q^3
       749: q^3
       755: q^3+q^2
       764: 2q^3+q^2
       767: 2q^3+q^2
       769: q^3
       775: q^2
       777: q^3
       779: 2q^3+q^2
       781: q^3
       783: 2q^3
       786: 2q^3+q^2
       787: 2q^3+q^2
       789: 2q^3
       792: q^3+q^2
       794: 2q^2
       795: q^3+q^2
       799: q^3
       802: q^3+q^2
       803: q^2
       806: 2q^3+q^2
       807: q^4+2q^3+q^2
       809: q^3
       811: q^3
       812: q^3+q^2
       813: 2q^3
       816: 3q^3+q^2
       817: 2q^2
       819: q^3+q^2
       823: q^3
       826: q^4+2q^3+q^2
       827: 2q^3+q^2
       830: q^2
       831: q^3+q^2
       833: q^3
       835: q^3
       836: q^3+q^2
       837: 2q^3
       839: 3q^3+q^2
       841: q^3
       844: 2q^2
       846: 2q^3+q^2
       847: 2q^3+q^2
       852: q^3+q^2
       853: q^3
       856: q^2
       857: q^3
       858: 2q^3+q^2
       859: 2q^3+q^2
       861: 2q^3+q^2
       863: 2q^3+q^2
       865: 2q^2
       866: 2q^2
       867: q^4+2q^3+2q^2
       868: q^4+3q^3+q^2
       869: q^3+2q^2
       870: q^3+2q^2
       871: q^3+q^2
       872: q^4+3q^3+q^2
       873: q^3+2q^2
       874: q^3+2q^2
       875: q^3+q^2
       876: q^4+3q^3+q^2
       877: q^3+q^2
       878: q^3+q^2
       879: q^3+q^2
       880: q^3+q^2
       881: q^3+q
       882: q
       883: q^3+q
       910: q^3+q^2
       918: q^2
       925: q^2
       931: q^3+q^2
       934: q^3
       940: q^2
       949: q^3+q^2
       954: q^2
       956: q^3
       966: 2q^2
       971: q^2
       977: q^3+q^2
       982: q^3
       990: 2q^3+q^2
       992: q^2
       994: q^2
       996: 2q^3+q^2
       998: 2q^2
      1001: 2q^2
      1002: q^3
      1005: 2q^3+q^2
      1006: 2q^3+q^2
      1009: q^3+q^2
      1013: 2q^2
      1014: q^3+q^2
      1017: 2q^2
      1020: q^3+q^2
      1024: q^3
      1027: q^3+q^2
      1028: q^2
      1030: q^3+q^2
      1032: 2q^2
      1036: q^3+q^2
      1041: q^2
      1042: q^3
      1044: q^3+q^2
      1047: 2q^2
      1053: q^3+q^2
      1054: q^2
      1057: q^2
      1058: q^3+q^2
      1063: q^2
      1065: q^2
      1066: q^3+q
      1068: q
      1070: q^3+q
      1072: q
      1073: q^3+q
      1074: 2q^2
      1075: q
      1076: q^2
      1077: q^3+2q^2
      1078: q^3+q^2
      1079: q
      1080: q^2
      1081: q^3+2q^2
      1082: q^3+q^2
      1083: q^2
      1084: 2q^2
      1085: q^3+q^2
      1090: q^2
      1114: q^2
      1124: q^2
      1132: 2q^2
      1137: q^3+q^2
      1141: q^2
      1146: q^2
      1161: q^2
      1164: q^2
      1182: q^2
      1191: q^2
      1196: 2q^2
      1203: q^2
      1209: q^2
      1210: q
      1212: q^3+q
      1214: q^2
      1216: 2q^2
      1219: 2q^2
      1225: 2q^2
      1226: q
      1229: q
      1232: q^2
      1235: q^2
      1236: q^3+q^2
      1241: q^3+q^2
      1242: q^2
      1244: q
      1246: q
      1250: q^2
      1252: q^3+q^2
      1255: q^2
      1259: q^2
      1260: q^3+q^2
      1263: q
      1269: q^2
      1270: q^2
      1274: q^2
      1277: q^2
      1281: 2q^2
      1282: q
      1283: q^2
      1284: q
      1285: q^2
      1286: q
      1288: 2q^2
      1289: q^2
      1294: q^2
      1306: q^2
      1314: q^2
      1320: q^2
      1328: 2q^2
      1337: q^2
      1342: q
      1365: q^2
      1370: q^2
      1372: q
      1398: q^2
      1403: q^2
      1407: q
      1412: q
      1428: q^2
      1433: q^2
      1438: q
      1440: q
      1443: q
      1445: q
      1450: q^2
      1452: q
      1455: q^2
      1458: q
      1460: q^2
      1463: q^2
      1472: q^2
      1477: q^2
      1478: q^2
      1483: 2q^2
      1485: q
      1486: q
      1488: q
      1493: q^2
      1529: q
      1541: q
      1547: q
      1551: q
      1556: q
      1576: q^2
      1597: q^2
      1629: q^2
      1634: q^2
      1640: q
      1643: q
      1645: q
      1648: q
      1651: q
      1653: q
      1656: q
      1667: q
      1670: q
      1679: q
      1726: q
      1735: q
      1737: q
      1747: q
      1750: q
      1761: q
      1767: q
      1775: q
      1804: q
      1838: q
      1849: q
      1862: q
      2062: 1
      2096: 1
      2138: 1
      2165: 1

2166:    0: q^5+2q^4+3q^3+q^2+q
         1: q^5+2q^4+3q^3+q^2+q
         2: q^5+2q^4+3q^3+q^2+q
         3: 2q^4+3q^3+q^2+q
         4: q^5+2q^4+3q^3+q^2+q
         5: 2q^4+3q^3+q^2+q
         6: q^5+2q^4+3q^3+q^2+q
         7: q^5+2q^4+3q^3+q^2+q
         8: 2q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: q^5+2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: q^5+2q^4+3q^3+q^2+q
        13: q^5+2q^4+3q^3+q^2+q
        14: q^5+2q^4+3q^3+q^2+q
        15: 2q^4+3q^3+q^2+q
        16: q^4+3q^3+q^2+q
        17: q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+2q^4+3q^3+q^2+q
        20: q^5+2q^4+3q^3+q^2+q
        21: q^5+2q^4+3q^3+q^2+q
        22: q^4+3q^3+q^2+q
        23: q^4+3q^3+q^2+q
        24: q^4+3q^3+q^2+q
        25: q^4+3q^3+q^2+q
        26: q^4+3q^3+q^2+q
        27: q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: q^5+2q^4+3q^3+q^2+q
        30: q^5+2q^4+3q^3+q^2+q
        31: q^4+3q^3+q^2+q
        32: q^4+3q^3+q^2+q
        33: 3q^3+q^2+q
        34: q^4+3q^3+q^2+q
        35: q^4+3q^3+q^2+q
        36: 3q^3+q^2+q
        37: q^4+3q^3+q^2+q
        39: q^4+3q^3+q^2+q
        41: q^4+3q^3+q^2+q
        43: q^5+2q^4+3q^3+q^2+q
        44: q^5+2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: q^4+3q^3+q^2+q
        47: q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: q^4+3q^3+q^2+q
        50: q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^4+3q^3+q^2+q
        53: q^4+3q^3+q^2+q
        54: q^4+3q^3+q^2+q
        55: q^4+3q^3+q^2+q
        56: q^4+3q^3+q^2+q
        57: q^4+3q^3+q^2+q
        58: q^3
        59: 2q^3+q^2+q
        60: q^3
        61: 2q^3+q^2+q
        62: q^4+3q^3+q^2+q
        64: q^4+3q^3+q^2+q
        66: 3q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: q^5+2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 3q^3+q^2+q
        73: 3q^3+q^2+q
        74: q^4+3q^3+q^2+q
        76: q^4+3q^3+q^2+q
        78: q^4+3q^3+q^2+q
        80: q^4+3q^3+q^2+q
        81: 3q^3+q^2+q
        82: q^4+3q^3+q^2+q
        83: q^4+3q^3+q^2+q
        84: q^4+3q^3+q^2+q
        85: 3q^3+q^2+q
        86: q^4+3q^3+q^2+q
        87: q^4+3q^3+q^2+q
        88: q^4+3q^3+q^2+q
        89: q^4+3q^3+q^2+q
        90: q^5+2q^4+2q^3+q^2+q
        91: q^4+3q^3+q^2+q
        92: q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 3q^3+q^2+q
        95: 3q^3+q^2+q
        96: q^4+2q^3+q^2+q
        97: 3q^3+q^2+q
        98: 3q^3+q^2+q
        99: q^4+2q^3+q^2+q
       100: q^4+2q^3+q^2+q
       101: q^4+2q^3+q^2+q
       102: q^4+2q^3+q^2+q
       103: q^3
       106: 2q^3+q^2+q
       107: q^3
       108: 2q^3+q^2+q
       109: q^3
       110: 2q^3+q^2+q
       111: 3q^3+q^2+q
       113: q^4+3q^3+q^2+q
       115: q^4+3q^3+q^2+q
       117: q^3
       118: 2q^3+q^2+q
       119: q^3
       120: 2q^3+q^2+q
       121: q^4+3q^3+q^2+q
       123: 3q^3+q^2+q
       125: q^4+3q^3+q^2+q
       126: q^4+2q^3+q^2+q
       127: 3q^3+q^2+q
       129: 3q^3+q^2+q
       131: q^4+2q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 3q^3+q^2+q
       136: 3q^3+q^2+q
       137: 3q^3+q^2+q
       138: 2q^3+q^2+q
       139: 3q^3+q^2+q
       140: q^3+q^2+q
       141: q^4+3q^3+q^2+q
       142: 3q^3+q^2+q
       143: 3q^3+q^2+q
       144: 2q^3+q^2+q
       145: 3q^3+q^2+q
       146: q^4+3q^3+q^2+q
       147: 3q^3+q^2+q
       148: q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: q^4+2q^3+q^2+q
       151: q^4+2q^3+q^2+q
       153: q^4+2q^3+q^2+q
       155: q^4+2q^3+q^2+q
       157: q^4+3q^3+q^2+q
       158: q^4+3q^3+q^2+q
       159: q^5+2q^4+2q^3+q^2+q
       160: 3q^3+q^2+q
       161: 3q^3+q^2+q
       162: q^4+2q^3+q^2+q
       163: 3q^3+q^2+q
       164: 3q^3+q^2+q
       165: q^4+2q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       169: q^3
       172: 2q^3+q^2+q
       173: q^3
       176: 2q^3+q^2+q
       177: 2q^3+q^2+q
       179: 3q^3+q^2+q
       181: 3q^3+q^2+q
       183: q^3
       184: 2q^3+q^2+q
       185: q^3
       186: 2q^3+q^2+q
       187: 3q^3+q^2+q
       189: q^4+3q^3+q^2+q
       191: q^3
       192: 2q^3+q^2+q
       194: q^3+q^2+q
       195: q^3
       196: 2q^3+q^2+q
       197: q^3+q^2+q
       199: q^3
       200: 2q^3+q^2+q
       201: q^3
       202: 2q^3+q^2+q
       204: q^3+q^2+q
       205: q^3+q^2+q
       207: 3q^3+q^2+q
       209: q^4+2q^3+q^2+q
       211: q^4+2q^3+q^2+q
       213: 3q^3+q^2+q
       215: 3q^3+q^2+q
       217: q^4+2q^3+q^2+q
       219: q^4+2q^3+q^2+q
       220: q^4+3q^3+q^2+q
       221: q^4+2q^3+q^2+q
       222: 3q^3+q^2+q
       223: 2q^3+q^2+q
       224: 3q^3+q^2+q
       225: 2q^3+q^2+q
       226: 2q^3+q^2+q
       227: 3q^3+q^2+q
       228: 2q^3+q^2+q
       229: q^3+q^2+q
       230: 3q^3+q^2+q
       231: 2q^3+q^2+q
       232: 3q^3+q^2+q
       233: 2q^3+q^2+q
       234: 3q^3+q^2+q
       235: q^3+q^2+q
       236: q^3+q^2+q
       237: q^3+q^2+q
       239: q^3+q^2+q
       241: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+2q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: q^3+q^2+q
       257: q^3+q^2+q
       258: q^4+q^3+q^2+q
       259: q^3
       262: 2q^3+q^2+q
       263: q^3
       266: 2q^3+q^2+q
       269: q^3+q^2+q
       273: q^3+q^2+q
       275: q^3
       278: 2q^3+q^2+q
       279: 3q^3+q^2+q
       281: 2q^3+q^2+q
       284: q^3+q^2+q
       286: q^3+q^2+q
       287: 2q^3+q^2+q
       289: 3q^3+q^2+q
       291: 2q^3+q^2+q
       293: q^3
       294: 2q^3+q^2+q
       295: q^3
       296: 2q^3+q^2+q
       297: 3q^3+q^2+q
       300: q^3+q^2+q
       301: q^2+q
       303: q^3
       304: 2q^3+q^2+q
       305: q^3+q^2+q
       307: q^3
       308: 2q^3+q^2+q
       310: q^3+q^2+q
       311: q^2+q
       313: q^3+q^2+q
       315: q^3+q^2+q
       317: q^3+q^2+q
       320: q^2+q
       322: q^2+q
       323: q^2+q
       325: q^4+2q^3+q^2+q
       327: 3q^3+q^2+q
       329: 3q^3+q^2+q
       331: q^4+2q^3+q^2+q
       333: q^4+2q^3+q^2+q
       334: 2q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       338: q^3+q^2+q
       340: q^3+q^2+q
       342: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^2+q
       349: 3q^3+q^2+q
       350: 2q^3+q^2+q
       351: q^2+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: 2q^3+q^2+q
       357: q^3+q^2+q
       358: q^2+q
       359: q^2+q
       360: q^3+q^2+q
       362: q^3+q^2+q
       364: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: q^3+q^2+q
       368: q^3+q^2+q
       369: q^2+q
       370: q^2+q
       371: q^3+q^2+q
       372: q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       380: q^3+q^2+q
       381: q^3
       384: 2q^3+q^2+q
       385: q^3
       388: 2q^3+q^2+q
       391: q^2+q
       396: q^3+q^2+q
       399: q^2+q
       404: q^3+q^2+q
       406: q^2+q
       409: 3q^3+q^2+q
       411: 2q^3+q^2+q
       413: 2q^3+q^2+q
       415: 3q^3+q^2+q
       417: 2q^3+q^2+q
       420: q^3+q^2+q
       422: q^3+q^2+q
       423: 2q^3+q^2+q
       425: q^3+q^2+q
       427: q^3+q^2+q
       430: q^2+q
       432: q^3+q^2+q
       433: q^2+q
       435: q^2+q
       438: q^3+q^2+q
       439: q^3
       440: 2q^3+q^2+q
       441: q^3+q^2+q
       444: q^2+q
       445: q^2+q
       448: q^3+q^2+q
       450: q^2+q
       451: q^2+q
       453: q^3
       454: 2q^3+q^2+q
       455: q^2+q
       458: q^3+q^2+q
       459: q^3+q^2+q
       462: q^2+q
       463: q^2+q
       465: q^3+q^2+q
       467: q^3+q^2+q
       469: q^3+q^2+q
       472: q^2+q
       474: q^2+q
       475: q^2+q
       477: 2q^2+q
       479: q^2+q
       481: 2q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: q^3+q^2+q
       485: q^3+q^2+q
       487: q^3+q^2+q
       489: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^2+q
       496: q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       502: q^3+q^2+q
       504: q^3+q^2+q
       506: q^4+q^3+q^2+q
       508: q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       524: q^3+q^2+q
       525: q^3
       528: 2q^3+q^2+q
       532: q^3+q^2+q
       536: q^2+q
       539: q^2+q
       543: q^3+q^2+q
       547: q^2+q
       552: q^2+q
       555: q^2+q
       559: q^3+q^2+q
       563: q^2+q
       568: q^2+q
       570: 2q^2+q
       575: q^2+q
       577: q^2+q
       579: q^2
       583: 2q^3+q^2+q
       585: 2q^3+q^2+q
       587: 2q^3+q^2+q
       590: q^3+q^2+q
       592: q^2+q
       594: q^2+q
       596: q^3+q^2+q
       597: q^3+q^2+q
       599: q^3+q^2+q
       601: q^3+q^2+q
       604: q^2+q
       605: q^2+q
       608: q^3+q^2+q
       609: q^2+q
       611: q^2+q
       613: q^2+q
       616: q^2+q
       617: q^2+q
       620: q^3+q^2+q
       622: q^2+q
       623: q^2+q
       625: q^2+q
       627: q^2+q
       629: q^2+q
       632: q^2+q
       633: q^2+q
       635: q^3+q^2+q
       637: q^3+q^2+q
       639: q^3+q^2+q
       642: q^2+q
       644: q^2+q
       645: q^2+q
       648: q^2+q
       650: q^2+q
       651: 2q^2+q
       653: q^2+q
       655: q^2+q
       657: q
       658: q^3+q
       660: q
       662: q^3+q
       664: q^3+q
       665: q^3+q^2+q
       666: q^3+q^2+q
       668: q^3+q^2+q
       670: q^4+q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       697: q^2+q
       702: q^2
       708: q^3+q^2+q
       712: q^3+q^2+q
       716: q^2+q
       720: q^2+q
       723: q^2+q
       727: q^2+q
       731: q^2+q
       735: q^2+q
       739: q^2+q
       743: q^2+q
       747: q^2+q
       751: q^2+q
       756: q^2+q
       758: 2q^2+q
       762: q^2+q
       768: q^2+q
       769: q^2+q
       771: q^2
       775: q
       777: 2q^3+q^2+q
       779: q^3+q
       781: q^3+q^2+q
       783: q^3+q^2+q
       786: q^2+q
       788: q^2+q
       789: q^3+q^2+q
       791: q^2+q
       794: q
       795: q
       797: q^2+q
       799: q^2+q
       802: q^2+q
       804: q
       806: q^2+q
       808: q^3+q^2+q
       809: q^2+q
       811: q^2+q
       813: q^2+q
       816: q^2+q
       818: q
       819: q
       821: q^2+q
       823: q^2+q
       826: q^3+q^2+q
       828: q^2+q
       830: q
       832: q^2+q
       833: q^2+q
       835: q^2+q
       837: q^2+q
       840: q^2+q
       841: q^3+q^2+q
       843: q
       846: q^2+q
       848: q^2+q
       849: q^2+q
       851: q^2+q
       853: 2q^2+q
       855: q
       857: q^2+q
       859: q^3+q
       861: q
       863: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q
       871: q^2+q
       872: q^2+q
       873: q
       874: q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q
       881: q^3+q
       882: q
       883: q^3+q
       889: q^2+q
       893: q^2
       899: q^3+q^2+q
       902: q^2+q
       906: q^2+q
       911: q^2+q
       914: q^2+q
       918: q
       922: q^2+q
       927: q
       930: q^2+q
       934: q^2+q
       938: q^2+q
       942: q
       946: q^2+q
       950: q^2+q
       955: q
       958: q^2+q
       961: q^2+q
       967: q
       968: q
       975: q^2+q
       979: 2q^2+q
       982: q^2+q
       984: q^2
       991: q^2+q
       992: q
       994: q
       996: q^3+q
       999: q
      1001: q
      1002: q^3+q^2+q
      1005: q^2+q
      1007: q^2+q
      1008: q^2+q
      1010: q^2+q
      1012: q
      1014: q
      1017: q
      1018: q^2+q
      1020: q
      1022: q^2+q
      1024: q^2+q
      1027: q^2+q
      1029: q
      1030: q
      1033: q
      1034: q^2+q
      1036: q
      1038: q^2+q
      1041: q
      1042: q^2+q
      1045: q^2+q
      1046: q
      1048: q^2+q
      1050: q^2+q
      1053: q^2+q
      1055: q
      1057: q
      1059: q^2+q
      1060: q
      1062: q
      1064: q
      1066: q^3+q
      1068: q
      1070: q^3+q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1091: q
      1102: q^2+q
      1107: q^2
      1112: q^2+q
      1116: q
      1120: q^2+q
      1124: q
      1127: q^2+q
      1133: q
      1135: q^2+q
      1138: q
      1146: q
      1150: q^2+q
      1154: q
      1158: q^2+q
      1163: q
      1166: q
      1170: q^2+q
      1174: q^2+q
      1178: q
      1183: q
      1185: q^2+q
      1188: q
      1197: q
      1199: q^2+q
      1204: q
      1208: q
      1210: q
      1212: q^3+q
      1214: q
      1217: q
      1219: q
      1220: q^2+q
      1222: q^2+q
      1224: q
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      1229: q
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      1233: q
      1235: q
      1236: q
      1238: q^2+q
      1241: q^2+q
      1243: q
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      1248: q
      1251: q
      1252: q
      1255: q
      1256: q^2+q
      1259: q
      1261: q^2+q
      1262: q
      1264: q^2+q
      1266: q
      1269: q
      1271: q
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      1280: q
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      1295: q
      1307: q
      1316: q
      1320: q
      1323: q^2+q
      1329: q
      1331: q^2+q
      1334: q
      1342: q
      1346: q
      1350: q
      1354: q^2+q
      1358: q
      1361: q
      1367: q
      1369: q
      1374: q
      1378: q^2+q
      1382: q
      1386: q
      1390: q
      1393: q
      1399: q
      1401: q
      1404: q
      1413: q
      1415: q^2+q
      1420: q
      1424: q
      1429: q
      1430: q
      1436: q
      1438: q
      1441: q
      1443: q
      1444: q
      1446: q^2+q
      1448: q
      1451: q
      1452: q
      1455: q
      1456: q
      1458: q
      1461: q
      1463: q
      1470: q
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      1506: q
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      1530: q
      1538: q
      1543: q
      1547: q
      1552: q
      1553: q
      1560: q^2+q
      1565: q
      1569: q
      1572: q
      1578: q
      1580: q
      1585: q
      1589: q
      1592: q
      1598: q
      1600: q
      1605: q
      1613: q
      1622: q
      1630: q
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      1637: q
      1639: q
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      1667: q
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      1680: q
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      1723: q
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      1736: q
      1739: q
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      1752: q
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      1763: q
      1767: q
      1776: q
      1778: q
      1796: q
      1801: q
      1808: q
      1839: q
      1851: q
      1863: q
      1945: 1
      1949: q
      2022: 1
      2057: 1
      2063: 1
      2097: 1
      2124: 1
      2139: 1
      2166: 1

2167:    0: q^5+q
         1: q
         2: q^5+q
         3: q
         4: q^5+q
         5: q^5+q
         6: q
         7: q^5+q
         8: q^5+q
         9: q^6+q^5+q
        10: q
        11: q
        12: q
        13: q^5+q
        14: q^5+q
        15: q^5+q
        16: q
        17: q
        18: q^5+q
        19: q^5+q
        20: q
        21: q^5+q
        22: q^5+q
        23: q
        24: q^5+q
        25: q^5+q
        26: q
        27: q^5+q
        28: q
        29: q
        30: q^5+q
        31: q
        32: q^5+q
        33: q
        34: q
        35: q^5+q
        36: q
        38: q^5+q
        40: q
        42: q^5+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q^5+q
        49: q
        50: q
        51: q^5+q
        52: q^5+q
        53: q
        54: q^5+q
        55: q^5+q
        56: q
        57: q^5+q
        59: q
        60: q
        63: q
        65: q^5+q
        67: q
        68: q
        69: q
        70: q
        71: q
        72: q
        73: q
        75: q^5+q
        77: q
        79: q^5+q
        80: q
        81: q
        82: q
        83: q^5+q
        84: q
        85: q
        86: q
        87: q^5+q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q^5+q
        94: q
        95: q
        96: q^5+q
        97: q
        98: q
        99: q^5+q
       100: q^5+q
       101: q
       102: q^5+q
       104: q
       107: q
       110: q
       112: q
       114: q
       116: q^5+q
       118: q
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       122: q
       124: q
       125: q
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       128: q
       130: q
       132: q^5+q
       133: q
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       136: q
       137: q
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       142: q
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       145: q
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       149: q
       150: q^5+q
       152: q^5+q
       154: q
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       157: q
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       160: q
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       162: q^5+q
       163: q
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       170: q
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       243: q
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       249: q^5+q
       250: q
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       256: q
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       258: q^5+q
       260: q
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       343: q^5+q
       344: q
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       363: q
       365: q^5+q
       366: q
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       373: q^5+q
       374: q
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       429: q
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       490: q^5+q
       491: q
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       634: q
       636: q
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       644: q
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      1620: q
      1624: q
      1628: q
      1638: 1
      1642: q
      1650: q
      1657: q
      1672: q
      1716: q
      1728: 1
      1731: 1
      1756: q
      1760: q
      1779: q
      1782: q
      1794: q
      1809: q
      1812: q
      1824: 1
      1844: 1
      1887: q
      1897: 1
      1912: 1
      1931: 1
      1950: q
      1959: 1
      1977: 1
      1987: 1
      2031: 1
      2039: 1
      2050: 1
      2058: 1
      2079: 1
      2089: 1
      2102: 1
      2122: 1
      2167: 1

2168:    0: q^5+q
         1: q
         2: q^5+q
         3: q
         4: q^5+q
         5: q^5+q
         6: q
         7: q^5+q
         8: q^5+q
         9: q^6+q^5+q
        10: q
        11: q
        12: q
        13: q^5+q
        14: q^5+q
        15: q^5+q
        16: q
        17: q
        18: q^5+q
        19: q^5+q
        20: q
        21: q^5+q
        22: q^5+q
        23: q
        24: q^5+q
        25: q^5+q
        26: q
        27: q^5+q
        28: q
        29: q
        30: q^5+q
        31: q
        32: q^5+q
        33: q
        34: q
        35: q^5+q
        36: q
        38: q^5+q
        40: q
        42: q^5+q
        43: q
        44: q
        45: q
        46: q
        47: q
        48: q^5+q
        49: q
        50: q
        51: q^5+q
        52: q^5+q
        53: q
        54: q^5+q
        55: q^5+q
        56: q
        57: q^5+q
        58: q
        61: q
        63: q
        65: q^5+q
        67: q
        68: q
        69: q
        70: q
        71: q
        72: q
        73: q
        75: q^5+q
        77: q
        79: q^5+q
        80: q
        81: q
        82: q
        83: q^5+q
        84: q
        85: q
        86: q
        87: q^5+q
        88: q
        89: q
        90: q
        91: q
        92: q
        93: q^5+q
        94: q
        95: q
        96: q^5+q
        97: q
        98: q
        99: q^5+q
       100: q^5+q
       101: q
       102: q^5+q
       105: q
       108: q
       109: q
       112: q
       114: q
       116: q^5+q
       117: q
       120: q
       122: q
       124: q
       125: q
       126: q
       128: q
       130: q
       132: q^5+q
       133: q
       134: q
       135: q
       136: q
       137: q
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       139: q
       140: q
       141: q
       142: q
       143: q
       144: q
       145: q
       146: q
       147: q
       148: q
       149: q
       150: q^5+q
       152: q^5+q
       154: q
       156: q^5+q
       157: q
       158: q
       159: q
       160: q
       161: q
       162: q^5+q
       163: q
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       165: q^5+q
       166: q
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       168: q^5+q
       171: q
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       212: q^5+q
       214: q
       216: q
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       219: q
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       240: q
       242: q^5+q
       243: q
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       248: q
       249: q^5+q
       250: q
       251: q
       252: q
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       254: q
       255: q
       256: q
       257: q
       258: q^5+q
       261: q
       265: q
       270: q
       272: q
       277: q
       280: q
       282: q
       284: q
       285: q
       288: q
       290: q
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       330: q
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       335: q
       336: q
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       341: q
       343: q^5+q
       344: q
       345: q
       346: q
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       351: q
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       353: q
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       363: q
       365: q^5+q
       366: q
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       372: q
       373: q^5+q
       374: q
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       392: q
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       473: q
       476: q
       478: q
       480: q
       481: q
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       483: q
       484: q
       486: q
       488: q
       490: q^5+q
       491: q
       492: q
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       495: q
       496: q
       497: q
       498: q
       499: q
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       527: q
       531: q
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       567: q
       572: q
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       581: q
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       594: q
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       600: q
       602: q
       604: q
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       607: q
       610: q
       612: q
       614: q
       616: q
       618: q
       620: q
       621: q
       624: q
       626: q
       628: q
       630: q
       631: q
       634: q
       636: q
       638: q
       640: q
       642: q
       643: q
       646: q
       648: q
       649: q
       652: q
       654: q
       656: q
       657: q
       659: q
       661: q
       663: q
       664: q
       665: q
       667: q
       669: q
       671: q
       672: q
       673: q
       674: q
       675: q
       676: q
       677: q
       678: q
       679: q
       680: q
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       682: q
       683: q
       684: q
       685: q
       686: q
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       688: q
       689: q
       700: q
       707: q
       711: q
       714: q
       719: q
       724: q
       728: q
       732: q
       736: q
       738: q
       742: q
       746: q
       750: q
       755: q
       760: q
       764: q
       767: q
       773: q
       776: q
       778: q
       780: q
       782: q
       784: q
       786: q
       787: q
       790: q
       792: q
       794: q
       796: q
       798: q
       800: q
       802: q
       803: q
       806: q
       807: q
       810: q
       812: q
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       817: q
       820: q
       822: q
       824: q
       826: q
       827: q
       830: q
       831: q
       834: q
       836: q
       838: q
       839: q
       842: q
       844: q
       846: q
       847: q
       850: q
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       854: q
       856: q
       858: q
       866: q
       868: q
       870: q
       871: q
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      1035: q
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      1076: q
      1078: q
      1080: q
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      1105: q
      1111: q
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      1132: q
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      1169: q
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      1221: q
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      1231: q
      1232: q
      1235: q
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      1250: q
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      1265: q
      1267: q
      1269: q
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      1273: q
      1275: q
      1277: q
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      1281: q
      1287: q
      1289: q
      1297: q
      1325: q
      1333: q
      1345: q
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      1355: q
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      1362: q
      1365: q
      1370: q
      1377: q
      1381: q
      1387: q
      1391: q
      1395: q
      1398: q
      1403: q
      1417: q
      1419: q
      1425: q
      1428: q
      1434: q
      1447: q
      1465: q
      1466: q
      1469: q
      1471: q
      1475: q
      1477: q
      1478: q
      1481: q
      1484: q
      1507: q
      1520: q
      1562: q
      1573: q
      1581: q
      1594: q
      1602: q
      1604: q
      1608: q
      1614: q
      1618: q
      1621: q
      1625: q
      1629: q
      1638: 1
      1642: q
      1649: q
      1658: q
      1672: q
      1717: q
      1728: 1
      1732: 1
      1755: q
      1758: q
      1780: q
      1784: q
      1795: q
      1810: q
      1813: q
      1824: 1
      1845: 1
      1888: q
      1896: 1
      1913: 1
      1931: 1
      1951: q
      1959: 1
      1975: 1
      1989: 1
      2031: 1
      2038: 1
      2051: 1
      2059: 1
      2077: 1
      2091: 1
      2103: 1
      2123: 1
      2168: 1

2169:    0: q^5+2q^4+3q^3+q^2+q
         1: q^5+2q^4+3q^3+q^2+q
         2: q^5+2q^4+3q^3+q^2+q
         3: 2q^4+3q^3+q^2+q
         4: q^5+2q^4+3q^3+q^2+q
         5: 2q^4+3q^3+q^2+q
         6: q^5+2q^4+3q^3+q^2+q
         7: q^5+2q^4+3q^3+q^2+q
         8: 2q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: q^5+2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: q^5+2q^4+3q^3+q^2+q
        13: q^5+2q^4+3q^3+q^2+q
        14: q^5+2q^4+3q^3+q^2+q
        15: 2q^4+3q^3+q^2+q
        16: q^4+3q^3+q^2+q
        17: q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+2q^4+3q^3+q^2+q
        20: q^5+2q^4+3q^3+q^2+q
        21: q^5+2q^4+3q^3+q^2+q
        22: q^4+3q^3+q^2+q
        23: q^4+3q^3+q^2+q
        24: q^4+3q^3+q^2+q
        25: q^4+3q^3+q^2+q
        26: q^4+3q^3+q^2+q
        27: q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: q^5+2q^4+3q^3+q^2+q
        30: q^5+2q^4+3q^3+q^2+q
        31: q^4+3q^3+q^2+q
        32: q^4+3q^3+q^2+q
        33: 3q^3+q^2+q
        34: q^4+3q^3+q^2+q
        35: q^4+3q^3+q^2+q
        36: 3q^3+q^2+q
        38: q^4+3q^3+q^2+q
        40: q^4+3q^3+q^2+q
        42: q^4+3q^3+q^2+q
        43: q^5+2q^4+3q^3+q^2+q
        44: q^5+2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: q^4+3q^3+q^2+q
        47: q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: q^4+3q^3+q^2+q
        50: q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^4+3q^3+q^2+q
        53: q^4+3q^3+q^2+q
        54: q^4+3q^3+q^2+q
        55: q^4+3q^3+q^2+q
        56: q^4+3q^3+q^2+q
        57: q^4+3q^3+q^2+q
        58: q^3
        59: 2q^3+q^2+q
        60: 2q^3+q^2+q
        61: q^3
        63: q^4+3q^3+q^2+q
        65: q^4+3q^3+q^2+q
        67: 3q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: q^5+2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 3q^3+q^2+q
        73: 3q^3+q^2+q
        75: q^4+3q^3+q^2+q
        77: q^4+3q^3+q^2+q
        79: q^4+3q^3+q^2+q
        80: q^4+3q^3+q^2+q
        81: 3q^3+q^2+q
        82: q^4+3q^3+q^2+q
        83: q^4+3q^3+q^2+q
        84: q^4+3q^3+q^2+q
        85: 3q^3+q^2+q
        86: q^4+3q^3+q^2+q
        87: q^4+3q^3+q^2+q
        88: q^4+3q^3+q^2+q
        89: q^4+3q^3+q^2+q
        90: q^5+2q^4+2q^3+q^2+q
        91: q^4+3q^3+q^2+q
        92: q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 3q^3+q^2+q
        95: 3q^3+q^2+q
        96: q^4+2q^3+q^2+q
        97: 3q^3+q^2+q
        98: 3q^3+q^2+q
        99: q^4+2q^3+q^2+q
       100: q^4+2q^3+q^2+q
       101: q^4+2q^3+q^2+q
       102: q^4+2q^3+q^2+q
       104: 2q^3+q^2+q
       105: q^3
       107: 2q^3+q^2+q
       108: q^3
       109: q^3
       110: 2q^3+q^2+q
       112: 3q^3+q^2+q
       114: q^4+3q^3+q^2+q
       116: q^4+3q^3+q^2+q
       117: q^3
       118: 2q^3+q^2+q
       119: 2q^3+q^2+q
       120: q^3
       122: q^4+3q^3+q^2+q
       124: 3q^3+q^2+q
       125: q^4+3q^3+q^2+q
       126: q^4+2q^3+q^2+q
       128: 3q^3+q^2+q
       130: 3q^3+q^2+q
       132: q^4+2q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 3q^3+q^2+q
       136: 3q^3+q^2+q
       137: 3q^3+q^2+q
       138: 2q^3+q^2+q
       139: 3q^3+q^2+q
       140: q^3+q^2+q
       141: q^4+3q^3+q^2+q
       142: 3q^3+q^2+q
       143: 3q^3+q^2+q
       144: 2q^3+q^2+q
       145: 3q^3+q^2+q
       146: q^4+3q^3+q^2+q
       147: 3q^3+q^2+q
       148: q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: q^4+2q^3+q^2+q
       152: q^4+2q^3+q^2+q
       154: q^4+2q^3+q^2+q
       156: q^4+2q^3+q^2+q
       157: q^4+3q^3+q^2+q
       158: q^4+3q^3+q^2+q
       159: q^5+2q^4+2q^3+q^2+q
       160: 3q^3+q^2+q
       161: 3q^3+q^2+q
       162: q^4+2q^3+q^2+q
       163: 3q^3+q^2+q
       164: 3q^3+q^2+q
       165: q^4+2q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: 2q^3+q^2+q
       171: q^3
       174: 2q^3+q^2+q
       175: q^3
       178: 2q^3+q^2+q
       180: 3q^3+q^2+q
       182: 3q^3+q^2+q
       183: 2q^3+q^2+q
       184: q^3
       185: q^3
       186: 2q^3+q^2+q
       188: 3q^3+q^2+q
       190: q^4+3q^3+q^2+q
       191: q^3
       192: 2q^3+q^2+q
       193: q^3+q^2+q
       195: q^3
       196: 2q^3+q^2+q
       198: q^3+q^2+q
       199: 2q^3+q^2+q
       200: q^3
       201: 2q^3+q^2+q
       202: q^3
       204: q^3+q^2+q
       206: q^3+q^2+q
       208: 3q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: q^4+2q^3+q^2+q
       214: 3q^3+q^2+q
       216: 3q^3+q^2+q
       218: q^4+2q^3+q^2+q
       219: q^4+2q^3+q^2+q
       220: q^4+3q^3+q^2+q
       221: q^4+2q^3+q^2+q
       222: 3q^3+q^2+q
       223: 2q^3+q^2+q
       224: 3q^3+q^2+q
       225: 2q^3+q^2+q
       226: 2q^3+q^2+q
       227: 3q^3+q^2+q
       228: 2q^3+q^2+q
       229: q^3+q^2+q
       230: 3q^3+q^2+q
       231: 2q^3+q^2+q
       232: 3q^3+q^2+q
       233: 2q^3+q^2+q
       234: 3q^3+q^2+q
       235: q^3+q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+2q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: q^3+q^2+q
       257: q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: 2q^3+q^2+q
       261: q^3
       264: 2q^3+q^2+q
       265: q^3
       268: q^3+q^2+q
       274: q^3+q^2+q
       276: 2q^3+q^2+q
       277: q^3
       280: 3q^3+q^2+q
       282: 2q^3+q^2+q
       283: q^3+q^2+q
       286: q^3+q^2+q
       288: 2q^3+q^2+q
       290: 3q^3+q^2+q
       292: 2q^3+q^2+q
       293: 2q^3+q^2+q
       294: q^3
       295: q^3
       296: 2q^3+q^2+q
       298: 3q^3+q^2+q
       299: q^3+q^2+q
       302: q^2+q
       303: q^3
       304: 2q^3+q^2+q
       306: q^3+q^2+q
       307: 2q^3+q^2+q
       308: q^3
       310: q^3+q^2+q
       312: q^2+q
       314: q^3+q^2+q
       316: q^3+q^2+q
       318: q^3+q^2+q
       319: q^2+q
       322: q^2+q
       324: q^2+q
       326: q^4+2q^3+q^2+q
       328: 3q^3+q^2+q
       330: 3q^3+q^2+q
       332: q^4+2q^3+q^2+q
       333: q^4+2q^3+q^2+q
       334: 2q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^2+q
       349: 3q^3+q^2+q
       350: 2q^3+q^2+q
       351: q^2+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: 2q^3+q^2+q
       357: q^3+q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q^2+q
       363: q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: q^3+q^2+q
       368: q^3+q^2+q
       369: q^2+q
       370: q^2+q
       371: q^3+q^2+q
       372: q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       378: q^3+q^2+q
       382: 2q^3+q^2+q
       383: q^3
       386: 2q^3+q^2+q
       387: q^3
       390: q^2+q
       394: q^3+q^2+q
       400: q^2+q
       403: q^3+q^2+q
       407: q^2+q
       410: 3q^3+q^2+q
       412: 2q^3+q^2+q
       414: 2q^3+q^2+q
       416: 3q^3+q^2+q
       418: 2q^3+q^2+q
       419: q^3+q^2+q
       422: q^3+q^2+q
       424: 2q^3+q^2+q
       426: q^3+q^2+q
       428: q^3+q^2+q
       429: q^2+q
       432: q^3+q^2+q
       434: q^2+q
       436: q^2+q
       437: q^3+q^2+q
       439: q^3
       440: 2q^3+q^2+q
       442: q^3+q^2+q
       443: q^2+q
       446: q^2+q
       447: q^3+q^2+q
       450: q^2+q
       452: q^2+q
       453: 2q^3+q^2+q
       454: q^3
       456: q^2+q
       458: q^3+q^2+q
       460: q^3+q^2+q
       462: q^2+q
       464: q^2+q
       466: q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       471: q^2+q
       474: q^2+q
       476: q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: q^3+q^2+q
       486: q^3+q^2+q
       488: q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^2+q
       496: q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       503: q^3+q^2+q
       505: q^3+q^2+q
       507: q^4+q^3+q^2+q
       508: q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       522: q^3+q^2+q
       526: 2q^3+q^2+q
       527: q^3
       530: q^3+q^2+q
       534: q^2+q
       538: q^2+q
       542: q^3+q^2+q
       546: q^2+q
       551: q^2+q
       556: q^2+q
       560: q^3+q^2+q
       564: q^2+q
       566: q^2+q
       571: 2q^2+q
       574: q^2+q
       581: q^2+q
       582: q^2
       584: 2q^3+q^2+q
       586: 2q^3+q^2+q
       588: 2q^3+q^2+q
       589: q^3+q^2+q
       592: q^2+q
       593: q^2+q
       596: q^3+q^2+q
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: q^3+q^2+q
       603: q^2+q
       606: q^2+q
       608: q^3+q^2+q
       610: q^2+q
       612: q^2+q
       614: q^2+q
       615: q^2+q
       618: q^2+q
       619: q^3+q^2+q
       622: q^2+q
       624: q^2+q
       626: q^2+q
       628: q^2+q
       630: q^2+q
       632: q^2+q
       634: q^2+q
       636: q^3+q^2+q
       638: q^3+q^2+q
       640: q^3+q^2+q
       641: q^2+q
       644: q^2+q
       646: q^2+q
       647: q^2+q
       650: q^2+q
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       657: q
       659: q^3+q
       661: q
       663: q^3+q
       664: q^3+q
       665: q^3+q^2+q
       667: q^3+q^2+q
       669: q^3+q^2+q
       671: q^4+q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       699: q^2+q
       703: q^2
       706: q^3+q^2+q
       710: q^3+q^2+q
       715: q^2+q
       718: q^2+q
       722: q^2+q
       726: q^2+q
       730: q^2+q
       734: q^2+q
       740: q^2+q
       744: q^2+q
       748: q^2+q
       752: q^2+q
       754: q^2+q
       759: 2q^2+q
       763: q^2+q
       766: q^2+q
       773: q^2+q
       774: q^2
       776: q
       778: 2q^3+q^2+q
       780: q^3+q
       782: q^3+q^2+q
       784: q^3+q^2+q
       785: q^2+q
       788: q^2+q
       790: q^3+q^2+q
       792: q^2+q
       793: q
       796: q
       798: q^2+q
       800: q^2+q
       801: q^2+q
       804: q
       805: q^2+q
       808: q^3+q^2+q
       810: q^2+q
       812: q^2+q
       814: q^2+q
       815: q^2+q
       818: q
       820: q
       822: q^2+q
       824: q^2+q
       825: q^3+q^2+q
       828: q^2+q
       829: q
       832: q^2+q
       834: q^2+q
       836: q^2+q
       838: q^2+q
       840: q^2+q
       842: q^3+q^2+q
       844: q
       845: q^2+q
       848: q^2+q
       850: q^2+q
       852: q^2+q
       854: 2q^2+q
       856: q
       858: q^2+q
       860: q^3+q
       862: q
       864: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q
       871: q^2+q
       872: q^2+q
       873: q
       874: q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q
       881: q^3+q
       882: q
       883: q^3+q
       890: q^2+q
       894: q^2
       897: q^3+q^2+q
       903: q^2+q
       905: q^2+q
       909: q^2+q
       913: q^2+q
       917: q
       921: q^2+q
       926: q
       929: q^2+q
       933: q^2+q
       939: q^2+q
       943: q
       947: q^2+q
       951: q^2+q
       953: q
       959: q^2+q
       962: q^2+q
       965: q
       972: q
       976: q^2+q
       980: 2q^2+q
       986: q^2+q
       987: q^2
       989: q^2+q
       993: q
       995: q
       997: q^3+q
       999: q
      1000: q
      1003: q^3+q^2+q
      1004: q^2+q
      1007: q^2+q
      1009: q^2+q
      1011: q^2+q
      1013: q
      1015: q
      1016: q
      1019: q^2+q
      1021: q
      1023: q^2+q
      1025: q^2+q
      1026: q^2+q
      1029: q
      1031: q
      1033: q
      1035: q^2+q
      1037: q
      1039: q^2+q
      1040: q
      1043: q^2+q
      1045: q^2+q
      1047: q
      1049: q^2+q
      1051: q^2+q
      1052: q^2+q
      1055: q
      1056: q
      1059: q^2+q
      1061: q
      1063: q
      1065: q
      1067: q^3+q
      1069: q
      1071: q^3+q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1092: q
      1104: q^2+q
      1108: q^2
      1113: q^2+q
      1117: q
      1119: q^2+q
      1123: q
      1128: q^2+q
      1131: q
      1136: q^2+q
      1142: q
      1145: q
      1149: q^2+q
      1155: q
      1157: q^2+q
      1162: q
      1167: q
      1171: q^2+q
      1175: q^2+q
      1177: q
      1181: q
      1186: q^2+q
      1192: q
      1195: q
      1200: q^2+q
      1205: q
      1207: q
      1211: q
      1213: q^3+q
      1215: q
      1217: q
      1218: q
      1221: q^2+q
      1223: q^2+q
      1225: q
      1227: q
      1228: q
      1231: q
      1233: q
      1234: q
      1237: q
      1239: q^2+q
      1240: q^2+q
      1243: q
      1245: q
      1247: q
      1249: q
      1251: q
      1253: q
      1254: q
      1257: q^2+q
      1258: q
      1261: q^2+q
      1263: q
      1265: q^2+q
      1267: q
      1268: q
      1271: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1296: q
      1308: q
      1317: q
      1319: q
      1324: q^2+q
      1327: q
      1332: q^2+q
      1338: q
      1341: q
      1347: q
      1351: q
      1353: q^2+q
      1357: q
      1363: q
      1366: q
      1371: q
      1375: q
      1379: q^2+q
      1383: q
      1385: q
      1389: q
      1394: q
      1397: q
      1402: q
      1408: q
      1411: q
      1416: q^2+q
      1421: q
      1423: q
      1427: q
      1434: q
      1437: q
      1439: q
      1441: q
      1442: q
      1445: q
      1447: q^2+q
      1449: q
      1451: q
      1453: q
      1454: q
      1457: q
      1459: q
      1461: q
      1462: q
      1471: q
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      1508: q
      1519: q
      1531: q
      1539: q
      1544: q
      1546: q
      1550: q
      1557: q
      1561: q^2+q
      1566: q
      1568: q
      1574: q
      1577: q
      1582: q
      1586: q
      1588: q
      1593: q
      1596: q
      1601: q
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      1774: q
      1779: q
      1794: q
      1805: q
      1809: q
      1840: q
      1853: q
      1864: q
      1946: 1
      1950: q
      2023: 1
      2058: 1
      2061: 1
      2098: 1
      2125: 1
      2136: 1
      2169: 1

2170:    0: 3q^2+2q
         1: 3q^2+2q
         2: 3q^2+2q
         3: 3q^2+2q
         4: q^3+2q^2+2q
         5: 3q^2+2q
         6: q^3+2q^2+2q
         7: q^3+2q^2+2q
         8: 3q^2+2q
         9: q^3+2q^2+2q
        10: 3q^2+2q
        11: 3q^2+2q
        12: q^3+2q^2+2q
        13: 3q^2+2q
        14: q^3+2q^2+2q
        15: 3q^2+2q
        16: 3q^2+2q
        17: 3q^2+2q
        18: q^3+2q^2+2q
        19: 2q^2+2q
        20: 2q^2+2q
        21: 2q^2+2q
        22: 3q^2+2q
        23: 3q^2+2q
        24: 3q^2+2q
        25: 3q^2+2q
        26: 3q^2+2q
        27: 3q^2+2q
        28: 3q^2+2q
        29: 2q^2+2q
        30: 2q^2+2q
        31: 3q^2+2q
        32: 3q^2+2q
        33: 3q^2+2q
        34: 3q^2+2q
        35: 3q^2+2q
        36: 3q^2+2q
        37: q^2
        38: 2q^2+2q
        39: q^2
        40: 2q^2+2q
        41: q^2
        42: 2q^2+2q
        43: 3q^2+2q
        44: q^3+2q^2+2q
        45: 3q^2+2q
        46: 3q^2+2q
        47: 3q^2+2q
        48: q^3+2q^2+2q
        49: 2q^2+2q
        50: 2q^2+2q
        51: 2q^2+2q
        52: 2q^2+2q
        53: 2q^2+2q
        54: 2q^2+2q
        55: 2q^2+2q
        56: 2q^2+2q
        57: 2q^2+2q
        58: q^2+q
        59: 2q^2+q
        60: q^2+q
        61: 2q^2+q
        62: q^2
        63: 2q^2+2q
        64: q^2
        65: 2q^2+2q
        66: q^2
        67: 2q^2+2q
        68: 3q^2+2q
        69: 2q^2+2q
        70: 2q^2+2q
        71: 2q^2+2q
        72: q^2+2q
        73: q^2+2q
        75: q^2+2q
        77: q^2+2q
        79: q^2+2q
        80: 3q^2+2q
        81: 3q^2+2q
        82: 2q^2+2q
        83: 2q^2+2q
        84: 3q^2+2q
        85: 3q^2+2q
        86: 2q^2+2q
        87: 2q^2+2q
        88: 3q^2+2q
        89: 3q^2+2q
        90: q^3+2q^2+2q
        91: 2q^2+2q
        92: 2q^2+2q
        93: 2q^2+2q
        94: 2q^2+2q
        95: 2q^2+2q
        96: 2q^2+2q
        97: 2q^2+2q
        98: 2q^2+2q
        99: 2q^2+2q
       100: 2q^2+2q
       101: 2q^2+2q
       102: 2q^2+2q
       104: q^2+q
       105: q^2+q
       106: q^2
       107: q
       108: q^2+q
       109: q
       110: q^2+q
       112: 2q
       114: q^2+2q
       116: q^2+2q
       117: q^2+q
       118: 2q^2+q
       119: q^2+q
       120: 2q^2+q
       121: q^2
       122: 2q^2+2q
       123: q^2
       124: 2q^2+2q
       125: 3q^2+2q
       126: 2q^2+2q
       128: q^2+2q
       130: q^2+2q
       132: q^2+2q
       133: 2q^2+2q
       134: 2q^2+2q
       135: q^2+2q
       136: q^2+2q
       137: 3q^2+2q
       138: 2q^2+2q
       139: 2q^2+2q
       140: q^2+2q
       141: 2q^2+2q
       142: q^2+2q
       143: 3q^2+2q
       144: 2q^2+2q
       145: 2q^2+2q
       146: 2q^2+2q
       147: q^2+2q
       148: q^2+2q
       149: 2q^2+2q
       150: 2q^2+2q
       152: q^2+2q
       154: q^2+2q
       156: q^2+2q
       157: 2q^2+2q
       158: 2q^2+2q
       159: 2q^2+2q
       160: 2q^2+2q
       161: 2q^2+2q
       162: 2q^2+2q
       163: 2q^2+2q
       164: 2q^2+2q
       165: 2q^2+2q
       166: 2q^2+2q
       167: 2q^2+2q
       168: 2q^2+2q
       170: q
       171: q
       174: q^2+q
       175: q^2+q
       176: q^2
       178: q^2+2q
       180: q^2+2q
       182: 2q
       183: q
       184: q^2+q
       185: q
       186: q^2+q
       188: 2q
       190: q^2+2q
       191: q^2+q
       192: 2q^2+q
       193: q
       194: q^2+q
       195: q
       196: q^2+q
       198: 2q
       199: q^2+q
       200: 2q^2+q
       201: q
       202: q^2+q
       203: q
       204: q^2+q
       206: 2q
       207: q^2
       208: 2q^2+2q
       210: q^2+2q
       212: q^2+2q
       214: q^2+2q
       216: q^2+2q
       218: q^2+2q
       219: 2q^2+2q
       220: 2q^2+2q
       221: 2q^2+2q
       222: q^2+2q
       223: q^2+2q
       224: q^2+2q
       225: q^2+2q
       226: 2q^2+2q
       227: 2q^2+2q
       228: 2q^2+2q
       229: q^2+2q
       230: q^2+2q
       231: 2q^2+2q
       232: 2q^2+2q
       233: 2q^2+2q
       234: q^2+2q
       235: q^2+2q
       236: 2q^2+2q
       238: q^2+2q
       240: q^2+2q
       242: q^2+2q
       243: 2q^2+2q
       244: q^2+2q
       245: q^2+2q
       246: 2q^2+2q
       247: 3q
       248: 3q
       249: q^2+2q
       250: 2q^2+2q
       251: 2q^2+2q
       252: 2q^2+2q
       253: 2q^2+2q
       254: 2q^2+2q
       255: 2q^2+2q
       256: 2q^2+2q
       257: 2q^2+2q
       258: 2q^2+2q
       260: q
       261: q
       264: q
       265: q
       268: q
       270: q
       272: q
       274: q
       276: q^2+q
       277: q^2+q
       278: q^2
       280: q^2+2q
       282: q^2+2q
       283: q
       284: q^2+q
       285: q
       286: q^2+q
       288: q^2+2q
       290: 2q
       292: 2q
       293: q
       294: q^2+q
       295: q
       296: q^2+q
       298: 2q
       299: q
       300: q^2+q
       302: 2q
       303: q
       304: q^2+q
       306: 2q
       307: q
       308: q^2+q
       309: q
       310: q^2+q
       312: 2q
       314: 2q
       316: q^2+2q
       318: q^2+2q
       319: q
       320: q^2+q
       321: q
       322: q^2+q
       324: 2q
       326: q^2+2q
       328: q^2+2q
       330: q^2+2q
       332: q^2+2q
       333: 2q^2+2q
       334: q^2+2q
       335: q^2+2q
       336: 2q
       337: 3q
       339: 3q
       341: 3q
       343: q^2+2q
       344: 2q^2+2q
       345: 2q^2+2q
       346: 2q^2+2q
       347: q^2+2q
       348: q^2+2q
       349: q^2+2q
       350: q^2+2q
       351: 3q
       352: 2q^2+2q
       353: 2q^2+2q
       354: 2q^2+2q
       355: q^2+2q
       356: q^2+2q
       357: q^2+2q
       358: q^2+2q
       359: 3q
       361: q^2+2q
       363: q^2+2q
       365: q^2+2q
       366: 2q^2+2q
       367: 2q^2+2q
       368: 2q^2+2q
       369: q^2+2q
       370: q^2+2q
       371: 3q
       372: 3q
       373: q^2+2q
       374: 2q^2+2q
       375: 2q^2+2q
       376: 2q^2+2q
       378: q
       379: q
       382: q
       383: q
       386: q
       387: q
       390: q
       392: q
       394: q
       395: q
       398: q
       400: q
       402: q
       403: q
       407: q
       408: q
       410: q^2+2q
       412: q^2+2q
       414: q^2+2q
       416: 2q
       418: 2q
       419: q
       420: q^2+q
       421: q
       422: q^2+q
       424: 2q
       426: 2q
       428: 3q
       429: q
       430: q^2+q
       431: q
       432: q^2+q
       434: 2q
       436: 2q
       437: q
       438: q^2+q
       439: q
       440: q^2+q
       442: 2q
       443: q
       444: 2q
       446: 3q
       447: q
       448: q^2+q
       449: q
       450: q^2+q
       452: 2q
       453: q
       454: q^2+q
       456: 2q
       457: q
       458: q^2+q
       460: 2q
       461: q
       462: 2q
       464: 3q
       466: q^2+2q
       468: q^2+2q
       470: q^2+2q
       471: q
       472: q^2+q
       473: q
       474: q^2+q
       476: 2q
       478: 2q
       479: q
       480: 2q
       481: q^2+2q
       482: q^2+2q
       483: 2q
       484: 3q
       486: 3q
       488: 3q
       490: q^2+2q
       491: 2q
       492: 2q^2+2q
       493: q^2+2q
       494: q^2+2q
       495: 2q
       496: 3q
       497: 2q^2+2q
       498: q^2+2q
       499: q^2+2q
       500: 2q
       501: 3q
       503: q^2+2q
       505: q^2+2q
       507: q^2+2q
       508: 2q^2+2q
       509: 2q^2+2q
       510: 2q^2+2q
       511: q^2+2q
       512: q^2+2q
       513: q^2+2q
       514: q^2+2q
       515: 3q
       516: 3q
       517: q^2+2q
       518: 3q
       519: 3q
       520: q^2+2q
       522: q
       523: q
       526: q
       527: q
       530: q
       531: q
       534: q
       535: q
       538: q
       540: q
       542: q
       544: q
       546: q
       548: 2q
       550: q
       551: q
       554: q
       556: q
       558: q
       560: q
       562: q
       564: 2q
       566: q
       567: q
       571: q
       572: q
       574: q
       575: q
       576: q
       578: q
       581: 2q
       584: q^2+2q
       586: 2q
       588: 2q
       589: q
       590: q^2+q
       592: q
       594: q
       595: q
       596: q^2+q
       598: 2q
       600: 2q
       602: 3q
       603: q
       604: q^2+q
       606: 2q
       607: q
       608: q^2+q
       610: 2q
       612: 2q
       614: 2q
       615: q
       616: 2q
       618: 3q
       619: q
       620: q^2+q
       621: q
       622: q^2+q
       624: 2q
       626: 2q
       628: 2q
       630: 2q
       631: q
       632: 2q
       634: 3q
       636: q^2+2q
       638: q^2+2q
       640: q^2+2q
       641: q
       642: q^2+q
       643: q
       644: q^2+q
       646: 2q
       647: q
       648: q^2+q
       649: q
       650: q^2+q
       652: 2q
       654: 2q
       655: q
       656: 2q
       657: 3q
       659: 3q
       661: 3q
       663: q^2+2q
       664: 2q
       665: 2q
       667: 3q
       669: 3q
       671: q^2+2q
       672: 3q
       673: 2q
       674: 3q
       675: q^2+2q
       676: q^2+2q
       677: 2q
       678: 3q
       679: 2q
       680: 3q
       681: q^2+2q
       682: q^2+2q
       683: 2q
       684: 3q
       685: 2q
       686: 2q^2+2q
       687: q^2+2q
       688: q^2+2q
       689: 2q
       690: 3q
       691: 3q
       692: q^2+2q
       699: q
       700: q
       701: q
       706: q
       707: q
       710: q
       711: q
       715: q
       719: q
       722: q
       724: q
       726: q
       728: q
       730: q
       732: q
       734: q
       736: 2q
       738: q
       740: q
       742: q
       744: q
       746: q
       748: q
       750: q
       752: 2q
       754: q
       755: q
       759: q
       760: q
       763: q
       764: q
       766: q
       767: q
       768: q
       770: q
       773: 2q
       776: 3q
       778: 2q
       780: 2q
       782: 2q
       784: 2q
       786: q
       788: q
       790: 3q
       792: q
       793: q
       794: 2q
       796: 3q
       798: 2q
       800: 2q
       801: q
       802: q^2+q
       804: q
       806: q
       807: q
       808: q^2+q
       810: 2q
       812: 2q
       814: 3q
       815: q
       816: 2q
       817: q
       818: 2q
       820: 3q
       822: 2q
       824: 2q
       825: q
       826: q^2+q
       828: q
       830: q
       831: q
       832: q^2+q
       834: 2q
       836: 2q
       838: 3q
       839: q
       840: 2q
       842: q^2+2q
       843: q
       844: 2q
       845: q
       846: q^2+q
       847: q
       848: q^2+q
       850: 2q
       852: 2q
       854: 2q
       856: 2q
       857: q
       858: 2q
       860: 3q
       862: 3q
       864: q^2+2q
       865: 3q
       866: 2q
       867: 2q
       868: 2q
       869: 3q
       870: 2q
       871: 2q
       872: 2q
       873: 3q
       874: 2q
       875: 2q
       876: 2q
       877: q^2+2q
       878: q^2+2q
       879: 2q
       880: 2q
       881: 3q
       882: 3q
       883: q^2+2q
       890: q
       891: q
       892: q
       897: q
       898: q
       903: q
       907: q
       913: q
       915: q
       917: q
       919: 2q
       921: q
       923: q
       926: q
       931: q
       933: q
       935: 2q
       937: q
       939: q
       941: q
       943: 2q
       945: q
       947: q
       951: q
       954: q
       957: q
       959: 2q
       962: q
       963: q
       965: q
       966: q
       967: q
       969: q
       972: 2q
       976: q
       977: q
       980: q
       981: q
       983: q
       986: 2q
       989: q
       990: q
       991: q
       993: 3q
       995: 2q
       997: 2q
       999: q
      1001: q
      1003: 2q
      1005: q
      1007: q
      1009: q
      1011: q
      1013: q
      1015: 3q
      1016: q
      1017: 2q
      1019: 2q
      1021: 2q
      1023: 2q
      1025: 2q
      1027: q
      1029: q
      1031: 3q
      1032: q
      1033: 2q
      1035: 2q
      1037: 2q
      1039: 2q
      1041: q
      1043: 2q
      1045: q
      1046: q
      1047: 2q
      1049: 2q
      1051: 2q
      1052: q
      1053: q^2+q
      1055: q
      1057: q
      1058: q
      1059: q^2+q
      1061: 2q
      1063: 2q
      1065: q
      1067: 3q
      1069: 3q
      1071: q^2+2q
      1072: 3q
      1073: 2q
      1074: 2q
      1075: 3q
      1076: 2q
      1077: 2q
      1078: 2q
      1079: 3q
      1080: 2q
      1081: 2q
      1082: 2q
      1083: 2q
      1084: 2q
      1085: 2q
      1092: q
      1093: q
      1094: q
      1104: q
      1105: q
      1106: q
      1113: q
      1117: q
      1121: q
      1125: q
      1142: q
      1145: q
      1147: 2q
      1149: q
      1151: q
      1155: q
      1159: q
      1165: q
      1167: 2q
      1169: q
      1171: q
      1175: q
      1179: q
      1186: q
      1187: q
      1189: q
      1192: 2q
      1195: q
      1196: q
      1197: q
      1200: q
      1201: q
      1205: q
      1209: q
      1211: 3q
      1213: 2q
      1215: 2q
      1217: q
      1219: q
      1221: q
      1223: q
      1225: q
      1227: 3q
      1228: q
      1229: 2q
      1231: 2q
      1233: q
      1235: q
      1237: 2q
      1239: 2q
      1241: q
      1243: q
      1245: 3q
      1246: q
      1247: 2q
      1249: 2q
      1251: q
      1253: 2q
      1255: q
      1257: 2q
      1259: q
      1261: q
      1262: q
      1263: 2q
      1265: 2q
      1267: 2q
      1269: q
      1271: q
      1273: 2q
      1275: 2q
      1277: q
      1279: q
      1281: q
      1282: 2q
      1283: 2q
      1284: 2q
      1285: 2q
      1286: 2q
      1287: 2q
      1288: 2q
      1289: 2q
      1308: q
      1309: q
      1310: q
      1317: q
      1321: q
      1338: q
      1341: q
      1343: 2q
      1347: q
      1351: q
      1355: q
      1359: q
      1373: q
      1375: 2q
      1379: q
      1383: q
      1387: q
      1391: q
      1405: q
      1408: 2q
      1411: q
      1412: q
      1413: q
      1416: q
      1417: q
      1421: q
      1425: q
      1434: q
      1437: q
      1439: 2q
      1441: q
      1443: q
      1445: q
      1447: q
      1449: 2q
      1451: q
      1453: 2q
      1455: q
      1457: 2q
      1459: 2q
      1461: q
      1463: q
      1465: 2q
      1467: q
      1469: q
      1471: 2q
      1473: 2q
      1475: q
      1477: q
      1479: q
      1481: q
      1483: q
      1484: 1
      1485: 2q
      1486: 2q
      1487: 2q
      1488: 2q
      1531: q
      1532: q
      1533: q
      1544: q
      1548: q
      1557: q
      1566: q
      1570: q
      1586: q
      1590: q
      1606: q
      1610: q
      1614: q
      1618: q
      1635: q
      1638: q
      1640: q
      1642: 1
      1644: 2q
      1646: q
      1648: q
      1650: 1
      1652: 2q
      1654: q
      1656: q
      1658: 1
      1660: q
      1662: 2q
      1664: q
      1666: q
      1668: 2q
      1670: q
      1672: q
      1673: 1
      1674: 2q
      1727: q
      1740: q
      1748: q
      1760: 1
      1764: q
      1768: q
      1784: 1
      1788: q
      1792: q
      1805: q
      1814: 1
      1816: 1
      1818: 1
      1820: 1
      1822: 1
      1824: q
      1826: q
      1828: 2q
      1830: q
      1832: q
      1833: 1
      1890: 1
      1905: 1
      1909: 1
      1921: 1
      1925: 1
      1930: q
      1935: q
      1939: q
      1955: 1
      1957: 1
      1959: 1
      1961: 1
      1963: 1
      1965: 1
      2010: 1
      2024: 1
      2030: 1
      2035: 1
      2039: 1
      2043: 1
      2047: 1
      2051: 1
      2055: 1
      2067: 1
      2078: 1
      2090: 1
      2112: 1
      2126: 1
      2137: 1
      2170: 1

2171:    0: q^5+2q^4+3q^3+q^2+q
         1: q^5+2q^4+3q^3+q^2+q
         2: q^5+2q^4+3q^3+q^2+q
         3: 2q^4+3q^3+q^2+q
         4: q^5+2q^4+3q^3+q^2+q
         5: 2q^4+3q^3+q^2+q
         6: q^5+2q^4+3q^3+q^2+q
         7: q^5+2q^4+3q^3+q^2+q
         8: 2q^4+3q^3+q^2+q
         9: q^6+2q^5+2q^4+2q^3+q^2+q
        10: q^5+2q^4+3q^3+q^2+q
        11: 2q^4+3q^3+q^2+q
        12: q^5+2q^4+3q^3+q^2+q
        13: q^5+2q^4+3q^3+q^2+q
        14: q^5+2q^4+3q^3+q^2+q
        15: 2q^4+3q^3+q^2+q
        16: q^4+3q^3+q^2+q
        17: q^4+3q^3+q^2+q
        18: q^5+2q^4+2q^3+q^2+q
        19: q^5+2q^4+3q^3+q^2+q
        20: q^5+2q^4+3q^3+q^2+q
        21: q^5+2q^4+3q^3+q^2+q
        22: q^4+3q^3+q^2+q
        23: q^4+3q^3+q^2+q
        24: q^4+3q^3+q^2+q
        25: q^4+3q^3+q^2+q
        26: q^4+3q^3+q^2+q
        27: q^4+3q^3+q^2+q
        28: q^4+3q^3+q^2+q
        29: q^5+2q^4+3q^3+q^2+q
        30: q^5+2q^4+3q^3+q^2+q
        31: q^4+3q^3+q^2+q
        32: q^4+3q^3+q^2+q
        33: 3q^3+q^2+q
        34: q^4+3q^3+q^2+q
        35: q^4+3q^3+q^2+q
        36: 3q^3+q^2+q
        38: q^4+3q^3+q^2+q
        40: q^4+3q^3+q^2+q
        42: q^4+3q^3+q^2+q
        43: q^5+2q^4+3q^3+q^2+q
        44: q^5+2q^4+3q^3+q^2+q
        45: 2q^4+3q^3+q^2+q
        46: q^4+3q^3+q^2+q
        47: q^4+3q^3+q^2+q
        48: q^5+2q^4+2q^3+q^2+q
        49: q^4+3q^3+q^2+q
        50: q^4+3q^3+q^2+q
        51: q^5+2q^4+2q^3+q^2+q
        52: q^4+3q^3+q^2+q
        53: q^4+3q^3+q^2+q
        54: q^4+3q^3+q^2+q
        55: q^4+3q^3+q^2+q
        56: q^4+3q^3+q^2+q
        57: q^4+3q^3+q^2+q
        58: 2q^3+q^2+q
        59: q^3
        60: q^3
        61: 2q^3+q^2+q
        63: q^4+3q^3+q^2+q
        65: q^4+3q^3+q^2+q
        67: 3q^3+q^2+q
        68: q^4+3q^3+q^2+q
        69: q^4+2q^3+q^2+q
        70: q^5+2q^4+3q^3+q^2+q
        71: q^4+3q^3+q^2+q
        72: 3q^3+q^2+q
        73: 3q^3+q^2+q
        75: q^4+3q^3+q^2+q
        77: q^4+3q^3+q^2+q
        79: q^4+3q^3+q^2+q
        80: q^4+3q^3+q^2+q
        81: 3q^3+q^2+q
        82: q^4+3q^3+q^2+q
        83: q^4+3q^3+q^2+q
        84: q^4+3q^3+q^2+q
        85: 3q^3+q^2+q
        86: q^4+3q^3+q^2+q
        87: q^4+3q^3+q^2+q
        88: q^4+3q^3+q^2+q
        89: q^4+3q^3+q^2+q
        90: q^5+2q^4+2q^3+q^2+q
        91: q^4+3q^3+q^2+q
        92: q^4+3q^3+q^2+q
        93: q^5+2q^4+2q^3+q^2+q
        94: 3q^3+q^2+q
        95: 3q^3+q^2+q
        96: q^4+2q^3+q^2+q
        97: 3q^3+q^2+q
        98: 3q^3+q^2+q
        99: q^4+2q^3+q^2+q
       100: q^4+2q^3+q^2+q
       101: q^4+2q^3+q^2+q
       102: q^4+2q^3+q^2+q
       104: q^3
       105: 2q^3+q^2+q
       107: q^3
       108: 2q^3+q^2+q
       109: 2q^3+q^2+q
       110: q^3
       112: 3q^3+q^2+q
       114: q^4+3q^3+q^2+q
       116: q^4+3q^3+q^2+q
       117: 2q^3+q^2+q
       118: q^3
       119: q^3
       120: 2q^3+q^2+q
       122: q^4+3q^3+q^2+q
       124: 3q^3+q^2+q
       125: q^4+3q^3+q^2+q
       126: q^4+2q^3+q^2+q
       128: 3q^3+q^2+q
       130: 3q^3+q^2+q
       132: q^4+2q^3+q^2+q
       133: q^4+3q^3+q^2+q
       134: q^4+2q^3+q^2+q
       135: 3q^3+q^2+q
       136: 3q^3+q^2+q
       137: 3q^3+q^2+q
       138: 2q^3+q^2+q
       139: 3q^3+q^2+q
       140: q^3+q^2+q
       141: q^4+3q^3+q^2+q
       142: 3q^3+q^2+q
       143: 3q^3+q^2+q
       144: 2q^3+q^2+q
       145: 3q^3+q^2+q
       146: q^4+3q^3+q^2+q
       147: 3q^3+q^2+q
       148: q^3+q^2+q
       149: q^4+2q^3+q^2+q
       150: q^4+2q^3+q^2+q
       152: q^4+2q^3+q^2+q
       154: q^4+2q^3+q^2+q
       156: q^4+2q^3+q^2+q
       157: q^4+3q^3+q^2+q
       158: q^4+3q^3+q^2+q
       159: q^5+2q^4+2q^3+q^2+q
       160: 3q^3+q^2+q
       161: 3q^3+q^2+q
       162: q^4+2q^3+q^2+q
       163: 3q^3+q^2+q
       164: 3q^3+q^2+q
       165: q^4+2q^3+q^2+q
       166: q^3+q^2+q
       167: q^3+q^2+q
       168: q^4+q^3+q^2+q
       170: q^3
       171: 2q^3+q^2+q
       174: q^3
       175: 2q^3+q^2+q
       178: 2q^3+q^2+q
       180: 3q^3+q^2+q
       182: 3q^3+q^2+q
       183: q^3
       184: 2q^3+q^2+q
       185: 2q^3+q^2+q
       186: q^3
       188: 3q^3+q^2+q
       190: q^4+3q^3+q^2+q
       191: 2q^3+q^2+q
       192: q^3
       194: q^3+q^2+q
       195: 2q^3+q^2+q
       196: q^3
       198: q^3+q^2+q
       199: q^3
       200: 2q^3+q^2+q
       201: q^3
       202: 2q^3+q^2+q
       203: q^3+q^2+q
       206: q^3+q^2+q
       208: 3q^3+q^2+q
       210: q^4+2q^3+q^2+q
       212: q^4+2q^3+q^2+q
       214: 3q^3+q^2+q
       216: 3q^3+q^2+q
       218: q^4+2q^3+q^2+q
       219: q^4+2q^3+q^2+q
       220: q^4+3q^3+q^2+q
       221: q^4+2q^3+q^2+q
       222: 3q^3+q^2+q
       223: 2q^3+q^2+q
       224: 3q^3+q^2+q
       225: 2q^3+q^2+q
       226: 2q^3+q^2+q
       227: 3q^3+q^2+q
       228: 2q^3+q^2+q
       229: q^3+q^2+q
       230: 3q^3+q^2+q
       231: 2q^3+q^2+q
       232: 3q^3+q^2+q
       233: 2q^3+q^2+q
       234: 3q^3+q^2+q
       235: q^3+q^2+q
       236: q^3+q^2+q
       238: q^3+q^2+q
       240: q^3+q^2+q
       242: q^4+q^3+q^2+q
       243: q^3+q^2+q
       244: q^2+q
       245: q^2+q
       246: q^4+2q^3+q^2+q
       247: q^3+q^2+q
       248: q^3+q^2+q
       249: q^4+q^3+q^2+q
       250: 3q^3+q^2+q
       251: 3q^3+q^2+q
       252: q^4+2q^3+q^2+q
       253: 3q^3+q^2+q
       254: 3q^3+q^2+q
       255: q^4+2q^3+q^2+q
       256: q^3+q^2+q
       257: q^3+q^2+q
       258: q^4+q^3+q^2+q
       260: q^3
       261: 2q^3+q^2+q
       264: q^3
       265: 2q^3+q^2+q
       270: q^3+q^2+q
       272: q^3+q^2+q
       276: q^3
       277: 2q^3+q^2+q
       280: 3q^3+q^2+q
       282: 2q^3+q^2+q
       284: q^3+q^2+q
       285: q^3+q^2+q
       288: 2q^3+q^2+q
       290: 3q^3+q^2+q
       292: 2q^3+q^2+q
       293: q^3
       294: 2q^3+q^2+q
       295: 2q^3+q^2+q
       296: q^3
       298: 3q^3+q^2+q
       300: q^3+q^2+q
       302: q^2+q
       303: 2q^3+q^2+q
       304: q^3
       306: q^3+q^2+q
       307: q^3
       308: 2q^3+q^2+q
       309: q^3+q^2+q
       312: q^2+q
       314: q^3+q^2+q
       316: q^3+q^2+q
       318: q^3+q^2+q
       320: q^2+q
       321: q^2+q
       324: q^2+q
       326: q^4+2q^3+q^2+q
       328: 3q^3+q^2+q
       330: 3q^3+q^2+q
       332: q^4+2q^3+q^2+q
       333: q^4+2q^3+q^2+q
       334: 2q^3+q^2+q
       335: 2q^3+q^2+q
       336: q^3+q^2+q
       337: q^3+q^2+q
       339: q^3+q^2+q
       341: q^3+q^2+q
       343: q^4+q^3+q^2+q
       344: 2q^3+q^2+q
       345: 3q^3+q^2+q
       346: 2q^3+q^2+q
       347: q^3+q^2+q
       348: q^2+q
       349: 3q^3+q^2+q
       350: 2q^3+q^2+q
       351: q^2+q
       352: 2q^3+q^2+q
       353: 3q^3+q^2+q
       354: 2q^3+q^2+q
       355: 3q^3+q^2+q
       356: 2q^3+q^2+q
       357: q^3+q^2+q
       358: q^2+q
       359: q^2+q
       361: q^3+q^2+q
       363: q^3+q^2+q
       365: q^4+q^3+q^2+q
       366: q^3+q^2+q
       367: q^3+q^2+q
       368: q^3+q^2+q
       369: q^2+q
       370: q^2+q
       371: q^3+q^2+q
       372: q^3+q^2+q
       373: q^4+q^3+q^2+q
       374: q^3+q^2+q
       375: q^3+q^2+q
       376: q^4+q^3+q^2+q
       379: q^3+q^2+q
       382: q^3
       383: 2q^3+q^2+q
       386: q^3
       387: 2q^3+q^2+q
       392: q^2+q
       395: q^3+q^2+q
       398: q^2+q
       402: q^3+q^2+q
       408: q^2+q
       410: 3q^3+q^2+q
       412: 2q^3+q^2+q
       414: 2q^3+q^2+q
       416: 3q^3+q^2+q
       418: 2q^3+q^2+q
       420: q^3+q^2+q
       421: q^3+q^2+q
       424: 2q^3+q^2+q
       426: q^3+q^2+q
       428: q^3+q^2+q
       430: q^2+q
       431: q^3+q^2+q
       434: q^2+q
       436: q^2+q
       438: q^3+q^2+q
       439: 2q^3+q^2+q
       440: q^3
       442: q^3+q^2+q
       444: q^2+q
       446: q^2+q
       448: q^3+q^2+q
       449: q^2+q
       452: q^2+q
       453: q^3
       454: 2q^3+q^2+q
       456: q^2+q
       457: q^3+q^2+q
       460: q^3+q^2+q
       461: q^2+q
       464: q^2+q
       466: q^3+q^2+q
       468: q^3+q^2+q
       470: q^3+q^2+q
       472: q^2+q
       473: q^2+q
       476: q^2+q
       478: 2q^2+q
       480: q^2+q
       481: 2q^3+q^2+q
       482: 2q^3+q^2+q
       483: q^3+q^2+q
       484: q^3+q^2+q
       486: q^3+q^2+q
       488: q^3+q^2+q
       490: q^4+q^3+q^2+q
       491: q^3+q^2+q
       492: 2q^3+q^2+q
       493: q^2+q
       494: 2q^3+q^2+q
       495: q^2+q
       496: q^2+q
       497: 2q^3+q^2+q
       498: 2q^3+q^2+q
       499: q^2+q
       500: q^2+q
       501: q^2+q
       503: q^3+q^2+q
       505: q^3+q^2+q
       507: q^4+q^3+q^2+q
       508: q^3+q^2+q
       509: q^3+q^2+q
       510: q^3+q^2+q
       511: q^2+q
       512: q^2+q
       513: q^2+q
       514: q^2+q
       515: q^3+q
       516: q
       517: q^3+q
       518: q^3+q^2+q
       519: q^3+q^2+q
       520: q^4+q^3+q^2+q
       523: q^3+q^2+q
       526: q^3
       527: 2q^3+q^2+q
       531: q^3+q^2+q
       535: q^2+q
       540: q^2+q
       544: q^3+q^2+q
       548: q^2+q
       550: q^2+q
       554: q^2+q
       558: q^3+q^2+q
       562: q^2+q
       567: q^2+q
       572: 2q^2+q
       576: q^2+q
       581: q^2+q
       582: q^2
       584: 2q^3+q^2+q
       586: 2q^3+q^2+q
       588: 2q^3+q^2+q
       590: q^3+q^2+q
       591: q^2+q
       594: q^2+q
       595: q^3+q^2+q
       598: q^3+q^2+q
       600: q^3+q^2+q
       602: q^3+q^2+q
       604: q^2+q
       606: q^2+q
       607: q^3+q^2+q
       610: q^2+q
       612: q^2+q
       614: q^2+q
       616: q^2+q
       618: q^2+q
       620: q^3+q^2+q
       621: q^2+q
       624: q^2+q
       626: q^2+q
       628: q^2+q
       630: q^2+q
       631: q^2+q
       634: q^2+q
       636: q^3+q^2+q
       638: q^3+q^2+q
       640: q^3+q^2+q
       642: q^2+q
       643: q^2+q
       646: q^2+q
       648: q^2+q
       649: q^2+q
       652: 2q^2+q
       654: q^2+q
       656: q^2+q
       657: q
       659: q^3+q
       661: q
       663: q^3+q
       664: q^3+q
       665: q^3+q^2+q
       667: q^3+q^2+q
       669: q^3+q^2+q
       671: q^4+q^3+q^2+q
       672: q^3+q^2+q
       673: q^3+q^2+q
       674: q
       675: q^2+q
       676: 2q^3+q^2+q
       677: q^2+q
       678: q^2+q
       679: q^2+q
       680: q
       681: 2q^3+q^2+q
       682: q^2+q
       683: q^2+q
       684: q^2+q
       685: q^2+q
       686: q^3+q^2+q
       687: q^2+q
       688: q^2+q
       689: q
       690: q^3+q
       691: q
       692: q^3+q
       700: q^2+q
       704: q^2
       707: q^3+q^2+q
       711: q^3+q^2+q
       714: q^2+q
       719: q^2+q
       724: q^2+q
       728: q^2+q
       732: q^2+q
       736: q^2+q
       738: q^2+q
       742: q^2+q
       746: q^2+q
       750: q^2+q
       755: q^2+q
       760: 2q^2+q
       764: q^2+q
       767: q^2+q
       773: q^2+q
       774: q^2
       776: q
       778: 2q^3+q^2+q
       780: q^3+q
       782: q^3+q^2+q
       784: q^3+q^2+q
       786: q^2+q
       787: q^2+q
       790: q^3+q^2+q
       792: q^2+q
       794: q
       796: q
       798: q^2+q
       800: q^2+q
       802: q^2+q
       803: q
       806: q^2+q
       807: q^3+q^2+q
       810: q^2+q
       812: q^2+q
       814: q^2+q
       816: q^2+q
       817: q
       820: q
       822: q^2+q
       824: q^2+q
       826: q^3+q^2+q
       827: q^2+q
       830: q
       831: q^2+q
       834: q^2+q
       836: q^2+q
       838: q^2+q
       839: q^2+q
       842: q^3+q^2+q
       844: q
       846: q^2+q
       847: q^2+q
       850: q^2+q
       852: q^2+q
       854: 2q^2+q
       856: q
       858: q^2+q
       860: q^3+q
       862: q
       864: q^3+q
       865: q
       866: q
       867: q^3+q
       868: q^3+q^2+q
       869: q
       870: q
       871: q^2+q
       872: q^2+q
       873: q
       874: q
       875: q^2+q
       876: q^2+q
       877: q^2+q
       878: q^2+q
       879: q
       880: q
       881: q^3+q
       882: q
       883: q^3+q
       891: q^2+q
       895: q^2
       898: q^3+q^2+q
       901: q^2+q
       907: q^2+q
       910: q^2+q
       915: q^2+q
       919: q
       923: q^2+q
       925: q
       931: q^2+q
       935: q^2+q
       937: q^2+q
       941: q
       945: q^2+q
       949: q^2+q
       954: q
       957: q^2+q
       963: q^2+q
       966: q
       972: q
       977: q^2+q
       981: 2q^2+q
       986: q^2+q
       987: q^2
       990: q^2+q
       993: q
       995: q
       997: q^3+q
       998: q
      1001: q
      1003: q^3+q^2+q
      1005: q^2+q
      1006: q^2+q
      1009: q^2+q
      1011: q^2+q
      1013: q
      1015: q
      1017: q
      1019: q^2+q
      1021: q
      1023: q^2+q
      1025: q^2+q
      1027: q^2+q
      1028: q
      1031: q
      1032: q
      1035: q^2+q
      1037: q
      1039: q^2+q
      1041: q
      1043: q^2+q
      1044: q^2+q
      1047: q
      1049: q^2+q
      1051: q^2+q
      1053: q^2+q
      1054: q
      1057: q
      1058: q^2+q
      1061: q
      1063: q
      1065: q
      1067: q^3+q
      1069: q
      1071: q^3+q
      1072: q
      1073: q^3+q
      1074: q
      1075: q
      1076: q
      1077: q
      1078: q^2+q
      1079: q
      1080: q
      1081: q
      1082: q^2+q
      1083: q
      1084: q
      1085: q
      1093: q
      1105: q^2+q
      1109: q^2
      1111: q^2+q
      1115: q
      1121: q^2+q
      1125: q
      1129: q^2+q
      1132: q
      1137: q^2+q
      1142: q
      1147: q
      1151: q^2+q
      1153: q
      1159: q^2+q
      1161: q
      1165: q
      1169: q^2+q
      1173: q^2+q
      1179: q
      1182: q
      1187: q^2+q
      1192: q
      1196: q
      1201: q^2+q
      1203: q
      1209: q
      1211: q
      1213: q^3+q
      1215: q
      1216: q
      1219: q
      1221: q^2+q
      1223: q^2+q
      1225: q
      1227: q
      1229: q
      1231: q
      1232: q
      1235: q
      1237: q
      1239: q^2+q
      1241: q^2+q
      1242: q
      1245: q
      1246: q
      1249: q
      1250: q
      1253: q
      1255: q
      1257: q^2+q
      1259: q
      1260: q^2+q
      1263: q
      1265: q^2+q
      1267: q
      1269: q
      1270: q
      1273: q
      1275: q
      1277: q
      1279: q
      1281: q
      1282: q
      1283: q
      1284: q
      1285: q
      1286: q
      1288: q
      1289: q
      1297: q
      1309: q
      1315: q
      1321: q
      1325: q^2+q
      1328: q
      1333: q^2+q
      1338: q
      1343: q
      1345: q
      1349: q
      1355: q^2+q
      1359: q
      1362: q
      1365: q
      1370: q
      1373: q
      1377: q^2+q
      1381: q
      1387: q
      1391: q
      1395: q
      1398: q
      1403: q
      1408: q
      1412: q
      1417: q^2+q
      1419: q
      1425: q
      1428: q
      1434: q
      1437: q
      1439: q
      1440: q
      1443: q
      1445: q
      1447: q^2+q
      1449: q
      1450: q
      1453: q
      1455: q
      1457: q
      1459: q
      1460: q
      1463: q
      1471: q
      1473: q
      1475: q
      1477: q
      1478: q
      1481: q
      1483: q
      1485: q
      1486: q
      1488: q
      1496: q
      1507: q
      1520: q
      1532: q
      1540: q
      1542: q
      1548: q
      1551: q
      1557: q
      1562: q^2+q
      1564: q
      1570: q
      1573: q
      1576: q
      1581: q
      1584: q
      1590: q
      1594: q
      1597: q
      1602: q
      1604: q
      1614: q
      1621: q
      1629: q
      1635: q
      1638: q
      1640: q
      1644: q
      1645: q
      1648: q
      1652: q
      1653: q
      1656: q
      1668: q
      1670: q
      1672: q
      1682: q
      1693: q
      1706: q
      1727: q
      1732: q
      1735: q
      1738: q
      1748: q
      1750: q
      1755: q
      1762: q
      1768: q
      1775: q
      1780: q
      1795: q
      1805: q
      1810: q
      1841: q
      1852: q
      1865: q
      1947: 1
      1951: q
      2025: 1
      2059: 1
      2062: 1
      2099: 1
      2127: 1
      2138: 1
      2171: 1

2172:    0: 2q^6+15q^5+19q^4+6q^3+q^2
         1: 2q^6+15q^5+19q^4+6q^3+q^2
         2: 5q^6+14q^5+15q^4+5q^3+q^2
         3: 15q^5+19q^4+6q^3+q^2
         4: 2q^6+15q^5+19q^4+6q^3+q^2
         5: 15q^5+19q^4+6q^3+q^2
         6: 2q^6+15q^5+19q^4+6q^3+q^2
         7: 5q^6+14q^5+15q^4+5q^3+q^2
         8: 5q^6+15q^5+15q^4+5q^3+q^2
         9: 3q^7+9q^6+12q^5+10q^4+4q^3+q^2
        10: 2q^6+15q^5+19q^4+6q^3+q^2
        11: 15q^5+19q^4+6q^3+q^2
        12: 2q^6+15q^5+19q^4+6q^3+q^2
        13: q^6+9q^5+14q^4+5q^3+q^2
        14: q^6+9q^5+14q^4+5q^3+q^2
        15: 10q^5+14q^4+5q^3+q^2
        16: 8q^5+18q^4+6q^3+q^2
        17: 8q^5+18q^4+6q^3+q^2
        18: 5q^6+11q^5+10q^4+4q^3+q^2
        19: 2q^6+15q^5+19q^4+6q^3+q^2
        20: 2q^6+15q^5+19q^4+6q^3+q^2
        21: 5q^6+14q^5+15q^4+5q^3+q^2
        22: 8q^5+18q^4+6q^3+q^2
        23: 8q^5+18q^4+6q^3+q^2
        24: 2q^6+10q^5+14q^4+5q^3+q^2
        25: 8q^5+18q^4+6q^3+q^2
        26: 8q^5+18q^4+6q^3+q^2
        27: 2q^6+10q^5+14q^4+5q^3+q^2
        28: 8q^5+18q^4+6q^3+q^2
        29: 2q^6+15q^5+19q^4+6q^3+q^2
        30: q^6+9q^5+14q^4+5q^3+q^2
        31: 8q^5+18q^4+6q^3+q^2
        32: 5q^5+13q^4+5q^3+q^2
        33: 3q^5+17q^4+6q^3+q^2
        34: 8q^5+18q^4+6q^3+q^2
        35: 5q^5+13q^4+5q^3+q^2
        36: 3q^5+17q^4+6q^3+q^2
        37: q^5+8q^4+2q^3+q^2
        38: 2q^5+9q^4+4q^3
        39: q^5+8q^4+2q^3+q^2
        40: 2q^5+9q^4+4q^3
        41: 3q^5+6q^4+2q^3+q^2
        42: 4q^5+7q^4+3q^3
        43: q^6+9q^5+14q^4+5q^3+q^2
        44: q^6+9q^5+14q^4+5q^3+q^2
        45: 10q^5+14q^4+5q^3+q^2
        46: 3q^5+13q^4+5q^3+q^2
        47: 4q^5+13q^4+5q^3+q^2
        48: q^6+7q^5+9q^4+4q^3+q^2
        49: 8q^5+18q^4+6q^3+q^2
        50: 8q^5+18q^4+6q^3+q^2
        51: 5q^6+11q^5+10q^4+4q^3+q^2
        52: 8q^5+18q^4+6q^3+q^2
        53: 8q^5+18q^4+6q^3+q^2
        54: 2q^6+10q^5+14q^4+5q^3+q^2
        55: 8q^5+18q^4+6q^3+q^2
        56: 8q^5+18q^4+6q^3+q^2
        57: 2q^6+10q^5+14q^4+5q^3+q^2
        58: q^5+7q^4+2q^3
        59: 2q^5+10q^4+4q^3+q^2
        60: q^5+7q^4+2q^3
        61: 2q^5+10q^4+4q^3+q^2
        62: q^5+8q^4+2q^3+q^2
        63: 2q^5+9q^4+4q^3
        64: q^5+6q^4+2q^3+q^2
        65: q^5+6q^4+3q^3
        66: 8q^4+2q^3+q^2
        67: 8q^4+4q^3
        68: q^5+8q^4+4q^3+q^2
        69: 3q^5+8q^4+4q^3+q^2
        70: q^6+9q^5+14q^4+5q^3+q^2
        71: 8q^5+18q^4+6q^3+q^2
        72: 3q^5+17q^4+6q^3+q^2
        73: 3q^5+17q^4+6q^3+q^2
        74: q^5+8q^4+2q^3+q^2
        75: 2q^5+9q^4+4q^3
        76: q^5+8q^4+2q^3+q^2
        77: 2q^5+9q^4+4q^3
        78: 3q^5+6q^4+2q^3+q^2
        79: 4q^5+7q^4+3q^3
        80: 5q^5+13q^4+5q^3+q^2
        81: q^5+12q^4+5q^3+q^2
        82: 8q^5+18q^4+6q^3+q^2
        83: 5q^5+13q^4+5q^3+q^2
        84: 5q^5+13q^4+5q^3+q^2
        85: q^5+12q^4+5q^3+q^2
        86: 8q^5+18q^4+6q^3+q^2
        87: 5q^5+13q^4+5q^3+q^2
        88: 3q^5+13q^4+5q^3+q^2
        89: 4q^5+13q^4+5q^3+q^2
        90: q^6+7q^5+9q^4+4q^3+q^2
        91: 3q^5+13q^4+5q^3+q^2
        92: 4q^5+13q^4+5q^3+q^2
        93: q^6+7q^5+9q^4+4q^3+q^2
        94: 3q^5+15q^4+6q^3+q^2
        95: 3q^5+15q^4+6q^3+q^2
        96: 2q^6+7q^5+9q^4+4q^3+q^2
        97: 3q^5+15q^4+6q^3+q^2
        98: 3q^5+15q^4+6q^3+q^2
        99: 2q^6+7q^5+9q^4+4q^3+q^2
       100: 3q^5+15q^4+6q^3+q^2
       101: 3q^5+15q^4+6q^3+q^2
       102: 6q^5+11q^4+5q^3+q^2
       103: 3q^4
       104: 4q^4+2q^3
       105: 4q^4+2q^3
       106: 5q^4+2q^3+q^2
       107: q^5+7q^4+2q^3
       108: 2q^5+10q^4+4q^3+q^2
       109: q^5+7q^4+2q^3
       110: 2q^5+10q^4+4q^3+q^2
       111: 8q^4+2q^3+q^2
       112: 8q^4+4q^3
       113: q^5+8q^4+2q^3+q^2
       114: 2q^5+9q^4+4q^3
       115: q^5+6q^4+2q^3+q^2
       116: q^5+6q^4+3q^3
       117: 2q^4+q^3
       118: 5q^4+3q^3+q^2
       119: 2q^4+q^3
       120: 5q^4+3q^3+q^2
       121: q^5+6q^4+2q^3+q^2
       122: q^5+6q^4+3q^3
       123: 6q^4+2q^3+q^2
       124: 5q^4+3q^3
       125: q^5+8q^4+4q^3+q^2
       126: 3q^5+8q^4+4q^3+q^2
       127: 3q^4+q^3+q^2
       128: 4q^4+4q^3
       129: 3q^4+q^3+q^2
       130: 4q^4+4q^3
       131: q^5+2q^4+q^3+q^2
       132: q^5+3q^4+2q^3
       133: q^5+8q^4+4q^3+q^2
       134: 3q^5+8q^4+4q^3+q^2
       135: q^5+12q^4+5q^3+q^2
       136: q^5+12q^4+5q^3+q^2
       137: q^5+12q^4+5q^3+q^2
       138: q^5+7q^4+4q^3+q^2
       139: 3q^5+15q^4+6q^3+q^2
       140: 7q^4+5q^3+q^2
       141: 5q^5+13q^4+5q^3+q^2
       142: 3q^5+15q^4+6q^3+q^2
       143: q^5+12q^4+5q^3+q^2
       144: q^5+7q^4+4q^3+q^2
       145: 3q^5+15q^4+6q^3+q^2
       146: 5q^5+13q^4+5q^3+q^2
       147: 3q^5+15q^4+6q^3+q^2
       148: 7q^4+5q^3+q^2
       149: 3q^5+15q^4+6q^3+q^2
       150: 2q^5+10q^4+5q^3+q^2
       151: q^5+7q^4+2q^3+q^2
       152: 2q^5+8q^4+4q^3
       153: q^5+7q^4+2q^3+q^2
       154: 2q^5+8q^4+4q^3
       155: 3q^5+5q^4+2q^3+q^2
       156: 3q^5+6q^4+3q^3
       157: 3q^5+13q^4+5q^3+q^2
       158: 4q^5+13q^4+5q^3+q^2
       159: q^6+7q^5+9q^4+4q^3+q^2
       160: q^5+8q^4+5q^3+q^2
       161: q^5+8q^4+5q^3+q^2
       162: 3q^5+6q^4+4q^3+q^2
       163: q^5+8q^4+5q^3+q^2
       164: q^5+8q^4+5q^3+q^2
       165: 3q^5+6q^4+4q^3+q^2
       166: 9q^4+6q^3+q^2
       167: 9q^4+6q^3+q^2
       168: 4q^5+7q^4+4q^3+q^2
       169: 3q^4
       170: 4q^4+2q^3
       171: 4q^4+2q^3
       172: 5q^4+2q^3+q^2
       173: q^4
       174: q^4+q^3
       175: q^4+q^3
       176: 3q^4+2q^3+q^2
       177: 2q^4+q^3+q^2
       178: q^4+2q^3
       179: 3q^4+q^3+q^2
       180: 4q^4+4q^3
       181: 3q^4+q^3+q^2
       182: 4q^4+4q^3
       183: 2q^4+q^3
       184: 5q^4+3q^3+q^2
       185: 2q^4+q^3
       186: 5q^4+3q^3+q^2
       187: 6q^4+2q^3+q^2
       188: 5q^4+3q^3
       189: q^5+6q^4+2q^3+q^2
       190: q^5+6q^4+3q^3
       191: 2q^4+q^3
       192: 5q^4+3q^3+q^2
       193: 2q^4+q^3
       194: 5q^4+4q^3+q^2
       195: q^5+6q^4+2q^3
       196: 2q^5+9q^4+4q^3+q^2
       197: 4q^4+2q^3+q^2
       198: 3q^4+3q^3
       199: 2q^4+q^3
       200: 5q^4+3q^3+q^2
       201: q^5+6q^4+2q^3
       202: 2q^5+9q^4+4q^3+q^2
       203: 2q^4+q^3
       204: 5q^4+4q^3+q^2
       205: 4q^4+2q^3+q^2
       206: 3q^4+3q^3
       207: 6q^4+2q^3+q^2
       208: 5q^4+3q^3
       209: q^5+7q^4+2q^3+q^2
       210: 2q^5+8q^4+4q^3
       211: q^5+5q^4+2q^3+q^2
       212: q^5+5q^4+3q^3
       214: q^4+3q^3
       216: q^4+3q^3
       218: q^4+2q^3
       219: q^5+4q^4+3q^3+q^2
       220: q^5+8q^4+4q^3+q^2
       221: 3q^5+8q^4+4q^3+q^2
       222: q^5+12q^4+5q^3+q^2
       223: q^5+7q^4+4q^3+q^2
       224: q^5+12q^4+5q^3+q^2
       225: q^5+7q^4+4q^3+q^2
       226: q^5+7q^4+4q^3+q^2
       227: 4q^4+4q^3+q^2
       228: q^5+5q^4+4q^3+q^2
       229: 3q^4+4q^3+q^2
       230: q^5+8q^4+5q^3+q^2
       231: q^5+7q^4+4q^3+q^2
       232: 4q^4+4q^3+q^2
       233: q^5+5q^4+4q^3+q^2
       234: q^5+8q^4+5q^3+q^2
       235: 3q^4+4q^3+q^2
       236: 5q^4+4q^3+q^2
       237: q^4+q^3+q^2
       238: 3q^4+4q^3
       239: q^4+q^3+q^2
       240: 3q^4+4q^3
       241: q^5+q^4+q^3+q^2
       242: q^5+3q^4+2q^3
       243: 9q^4+6q^3+q^2
       244: 4q^4+5q^3+q^2
       245: 4q^4+5q^3+q^2
       246: 2q^5+10q^4+5q^3+q^2
       247: 9q^4+6q^3+q^2
       248: 9q^4+6q^3+q^2
       249: 4q^5+7q^4+4q^3+q^2
       250: q^5+8q^4+5q^3+q^2
       251: q^5+8q^4+5q^3+q^2
       252: 3q^5+6q^4+4q^3+q^2
       253: q^5+8q^4+5q^3+q^2
       254: q^5+8q^4+5q^3+q^2
       255: 3q^5+6q^4+4q^3+q^2
       256: 3q^4+5q^3+q^2
       257: 4q^4+5q^3+q^2
       258: q^5+4q^4+4q^3+q^2
       259: q^4
       260: 2q^4+2q^3
       261: 2q^4+2q^3
       262: 2q^4+q^3+q^2
       263: q^4
       264: q^4+q^3
       265: q^4+q^3
       266: 3q^4+2q^3+q^2
       267: q^4
       268: q^4+q^3
       269: 3q^4+2q^3+q^2
       270: 2q^4+2q^3
       271: q^4
       272: q^4+q^3
       273: 3q^4+2q^3+q^2
       274: 2q^4+2q^3
       275: q^4
       276: q^4+q^3
       277: q^4+q^3
       278: 3q^4+2q^3+q^2
       280: 2q^3
       282: 2q^3
       284: 2q^4+2q^3+q^2
       286: 2q^4+2q^3+q^2
       287: 2q^4+q^3+q^2
       288: q^4+2q^3
       290: q^4+3q^3
       291: 2q^4+q^3+q^2
       292: q^4+2q^3
       293: 2q^4+q^3
       294: 5q^4+3q^3+q^2
       295: 2q^4+q^3
       296: 5q^4+3q^3+q^2
       297: 6q^4+2q^3+q^2
       298: 5q^4+3q^3
       300: q^4+3q^3+q^2
       301: q^3+q^2
       302: q^4+3q^3
       303: q^4+q^3
       304: 3q^4+3q^3+q^2
       305: 2q^4+2q^3+q^2
       306: q^4+2q^3
       307: q^4+q^3
       308: 3q^4+3q^3+q^2
       310: q^4+3q^3+q^2
       311: q^3+q^2
       312: q^4+3q^3
       313: 2q^4+2q^3+q^2
       314: q^4+2q^3
       315: q^4+q^3+q^2
       316: q^4+2q^3
       317: q^4+q^3+q^2
       318: 3q^4+4q^3
       319: q^4+q^3
       320: 3q^4+4q^3+q^2
       321: q^4+q^3
       322: 3q^4+4q^3+q^2
       323: q^4+2q^3+q^2
       324: 2q^3
       325: q^5+5q^4+2q^3+q^2
       326: q^5+5q^4+3q^3
       328: q^4+3q^3
       330: q^4+3q^3
       332: q^4+2q^3
       333: q^5+4q^4+3q^3+q^2
       334: q^5+7q^4+4q^3+q^2
       335: q^5+7q^4+4q^3+q^2
       336: 5q^4+4q^3+q^2
       337: 9q^4+6q^3+q^2
       338: q^4+q^3+q^2
       339: 3q^4+4q^3
       340: q^4+q^3+q^2
       341: 3q^4+4q^3
       342: q^5+q^4+q^3+q^2
       343: q^5+3q^4+2q^3
       344: 2q^4+3q^3+q^2
       345: 4q^4+4q^3+q^2
       346: q^5+5q^4+4q^3+q^2
       347: 3q^4+4q^3+q^2
       348: q^4+3q^3+q^2
       349: q^5+8q^4+5q^3+q^2
       350: q^5+5q^4+4q^3+q^2
       351: 4q^4+5q^3+q^2
       352: 2q^4+3q^3+q^2
       353: 4q^4+4q^3+q^2
       354: q^5+5q^4+4q^3+q^2
       355: q^5+8q^4+5q^3+q^2
       356: q^5+5q^4+4q^3+q^2
       357: 3q^4+4q^3+q^2
       358: q^4+3q^3+q^2
       359: 4q^4+5q^3+q^2
       361: 3q^3
       363: q^4+3q^3
       365: q^4+2q^3
       366: 5q^4+4q^3+q^2
       367: q^4+4q^3+q^2
       368: 3q^4+4q^3+q^2
       369: q^4+4q^3+q^2
       370: q^4+4q^3+q^2
       371: 3q^4+5q^3+q^2
       372: 4q^4+5q^3+q^2
       373: q^5+4q^4+4q^3+q^2
       374: 3q^4+5q^3+q^2
       375: 4q^4+5q^3+q^2
       376: q^5+4q^4+4q^3+q^2
       380: q^4+q^3+q^2
       382: q^3
       383: q^3
       385: q^4
       386: q^4+q^3
       387: q^4+q^3
       388: 3q^4+2q^3+q^2
       390: q^3
       391: q^3+q^2
       392: q^4+2q^3
       395: q^3
       396: q^4+2q^3+q^2
       398: q^3
       399: q^3+q^2
       400: q^4+2q^3
       403: q^3
       404: q^4+2q^3+q^2
       406: q^4+2q^3+q^2
       407: q^3
       408: q^3
       410: 2q^3
       412: 2q^3
       414: q^3
       416: q^4+3q^3
       418: 2q^3
       420: 2q^4+2q^3+q^2
       422: 2q^4+2q^3+q^2
       423: 2q^4+q^3+q^2
       424: q^4+2q^3
       425: q^4+q^3+q^2
       426: q^4+2q^3
       427: q^4+q^3+q^2
       428: 3q^4+4q^3
       430: 2q^3+q^2
       432: q^4+2q^3+q^2
       433: q^3+q^2
       434: q^3
       436: 2q^3
       438: q^4+3q^3+q^2
       439: q^4+q^3
       440: 3q^4+3q^3+q^2
       441: 2q^4+2q^3+q^2
       442: q^4+2q^3
       443: q^4+q^3
       444: 3q^4+4q^3+q^2
       445: q^3+q^2
       446: q^4+3q^3
       448: q^4+2q^3+q^2
       450: 2q^3+q^2
       451: q^3+q^2
       452: q^3
       453: q^4+q^3
       454: 3q^4+3q^3+q^2
       456: 2q^3
       458: q^4+3q^3+q^2
       459: 2q^4+2q^3+q^2
       460: q^4+2q^3
       461: q^4+q^3
       462: 3q^4+4q^3+q^2
       463: q^3+q^2
       464: q^4+3q^3
       466: 2q^3
       468: 2q^3
       469: q^4+q^3+q^2
       470: q^4+2q^3
       472: 3q^3+q^2
       474: 3q^3+q^2
       475: 2q^3+q^2
       476: q^3
       477: 2q^3+q^2
       478: 2q^3
       479: q^4+2q^3+q^2
       480: 2q^3
       481: 2q^4+3q^3+q^2
       482: 2q^4+3q^3+q^2
       483: 5q^4+4q^3+q^2
       484: q^4+4q^3+q^2
       486: 3q^3
       488: q^4+3q^3
       490: q^4+2q^3
       491: 3q^4+4q^3+q^2
       492: 2q^4+3q^3+q^2
       493: q^4+3q^3+q^2
       494: q^5+5q^4+4q^3+q^2
       495: q^4+3q^3+q^2
       496: q^4+4q^3+q^2
       497: 2q^4+3q^3+q^2
       498: q^5+5q^4+4q^3+q^2
       499: q^4+3q^3+q^2
       500: q^4+3q^3+q^2
       501: q^4+4q^3+q^2
       503: 3q^3
       505: q^4+3q^3
       507: q^4+2q^3
       508: q^4+3q^3+q^2
       509: q^4+4q^3+q^2
       510: 3q^4+4q^3+q^2
       511: q^4+4q^3+q^2
       512: q^4+3q^3+q^2
       513: q^4+4q^3+q^2
       514: q^4+3q^3+q^2
       515: q^4+2q^3+2q^2
       516: 2q^3+2q^2
       517: q^4+2q^3+2q^2
       518: 3q^4+5q^3+q^2
       519: 4q^4+5q^3+q^2
       520: q^5+4q^4+4q^3+q^2
       526: q^3
       527: q^3
       532: q^4+q^3+q^2
       536: q^3+q^2
       540: q^3
       543: q^4+2q^3+q^2
       544: q^3
       546: q^3
       547: q^3+q^2
       548: q^4+2q^3
       552: q^3+q^2
       556: q^3
       559: q^4+2q^3+q^2
       560: q^3
       562: q^3
       563: q^3+q^2
       564: q^4+2q^3
       568: 2q^3+q^2
       570: 2q^3+q^2
       571: q^3
       572: q^3
       574: q^3
       575: q^4+2q^3+q^2
       576: q^3
       577: q^3+q^2
       579: q^3
       581: 2q^3
       584: q^3
       586: q^3
       588: 2q^3
       590: q^4+2q^3+q^2
       592: 2q^3+q^2
       594: 2q^3+q^2
       596: q^4+2q^3+q^2
       598: 2q^3
       599: q^4+q^3+q^2
       600: q^4+2q^3
       602: 2q^3
       604: 2q^3+q^2
       606: q^3
       608: q^4+2q^3+q^2
       609: q^3+q^2
       610: q^3
       612: 2q^3
       613: q^3+q^2
       614: q^3
       616: 3q^3+q^2
       618: 2q^3
       620: q^4+2q^3+q^2
       622: 2q^3+q^2
       624: q^3
       625: q^3+q^2
       626: q^3
       628: 2q^3
       629: q^3+q^2
       630: q^3
       632: 3q^3+q^2
       634: 2q^3
       636: 2q^3
       638: 2q^3
       640: q^3
       642: 2q^3+q^2
       644: 2q^3+q^2
       645: q^3+q^2
       648: 3q^3+q^2
       650: 3q^3+q^2
       652: q^3
       653: 2q^3+q^2
       654: q^3
       655: 2q^3+q^2
       656: q^3
       657: 2q^2
       659: 2q^3+q^2
       661: 2q^3+q^2
       663: 2q^3+q^2
       664: q^4+2q^3+2q^2
       665: q^4+3q^3+q^2
       667: 3q^3
       669: q^4+3q^3
       671: q^4+2q^3
       672: q^4+4q^3+q^2
       673: 3q^4+4q^3+q^2
       674: q^3+2q^2
       675: q^3+q^2
       676: 2q^4+3q^3+q^2
       677: q^4+3q^3+q^2
       678: q^4+4q^3+q^2
       679: q^4+3q^3+q^2
       680: q^3+2q^2
       681: 2q^4+3q^3+q^2
       682: q^3+q^2
       683: q^4+3q^3+q^2
       684: q^4+4q^3+q^2
       685: q^4+3q^3+q^2
       686: q^4+3q^3+q^2
       687: q^4+3q^3+q^2
       688: q^4+3q^3+q^2
       689: q^3+q^2
       690: q^4+2q^3+2q^2
       691: 2q^3+2q^2
       692: q^4+2q^3+2q^2
       697: q^3+q^2
       699: q^3
       700: q^3
       702: q^3
       716: q^3+q^2
       720: q^3+q^2
       727: q^3+q^2
       732: q^3
       736: q^3
       743: q^3+q^2
       748: q^3
       752: q^3
       756: q^3+q^2
       762: 2q^3+q^2
       768: 2q^3+q^2
       773: q^3
       776: q^2
       778: q^3
       780: 2q^3+q^2
       782: q^3
       784: 2q^3
       786: 2q^3+q^2
       788: 2q^3+q^2
       790: 2q^3
       791: q^3+q^2
       794: 2q^2
       796: q^3+q^2
       800: q^3
       802: q^3+q^2
       804: q^2
       806: 2q^3+q^2
       808: q^4+2q^3+q^2
       810: q^3
       811: q^3+q^2
       812: q^3
       814: 2q^3
       816: 3q^3+q^2
       818: 2q^2
       820: q^3+q^2
       824: q^3
       826: q^4+2q^3+q^2
       828: 2q^3+q^2
       830: q^2
       832: q^3+q^2
       834: q^3
       835: q^3+q^2
       836: q^3
       838: 2q^3
       840: 3q^3+q^2
       842: q^3
       843: 2q^2
       846: 2q^3+q^2
       848: 2q^3+q^2
       851: q^3+q^2
       854: q^3
       855: q^2
       857: 2q^3+q^2
       858: q^3
       860: 2q^3+q^2
       862: 2q^3+q^2
       864: 2q^3+q^2
       865: 2q^2
       866: 2q^2
       867: q^4+2q^3+2q^2
       868: q^4+3q^3+q^2
       869: q^3+2q^2
       870: q^3+2q^2
       871: q^3+q^2
       872: q^4+3q^3+q^2
       873: q^3+2q^2
       874: q^3+2q^2
       875: q^3+q^2
       876: q^4+3q^3+q^2
       877: q^3+q^2
       878: q^3+q^2
       879: q^3+q^2
       880: q^3+q^2
       881: q^3+q
       882: q
       883: q^3+q
       911: q^3+q^2
       919: q^2
       927: q^2
       930: q^3+q^2
       935: q^3
       943: q^2
       950: q^3+q^2
       955: q^2
       959: q^3
       967: 2q^2
       969: q^2
       975: q^3+q^2
       986: q^3
       991: 2q^3+q^2
       993: q^2
       995: q^2
       997: 2q^3+q^2
       999: 2q^2
      1001: 2q^2
      1003: q^3
      1005: 2q^3+q^2
      1007: 2q^3+q^2
      1008: q^3+q^2
      1012: 2q^2
      1015: q^3+q^2
      1017: 2q^2
      1021: q^3+q^2
      1025: q^3
      1027: q^3+q^2
      1029: q^2
      1031: q^3+q^2
      1033: 2q^2
      1037: q^3+q^2
      1041: q^2
      1043: q^3
      1045: q^3+q^2
      1046: 2q^2
      1053: q^3+q^2
      1055: q^2
      1057: q^2
      1059: q^3+q^2
      1062: q^2
      1064: q^2
      1067: q^3+q
      1069: q
      1071: q^3+q
      1072: q
      1073: q^3+q
      1074: 2q^2
      1075: q
      1076: q^2
      1077: q^3+2q^2
      1078: q^3+q^2
      1079: q
      1080: q^2
      1081: q^3+2q^2
      1082: q^3+q^2
      1083: q^2
      1084: 2q^2
      1085: q^3+q^2
      1094: q^2
      1117: q^2
      1125: q^2
      1133: 2q^2
      1135: q^3+q^2
      1139: q^2
      1147: q^2
      1163: q^2
      1167: q^2
      1183: q^2
      1189: q^2
      1197: 2q^2
      1204: q^2
      1208: q^2
      1211: q
      1213: q^3+q
      1215: q^2
      1217: 2q^2
      1219: 2q^2
      1224: 2q^2
      1227: q
      1229: q
      1233: q^2
      1235: q^2
      1237: q^3+q^2
      1241: q^3+q^2
      1243: q^2
      1245: q
      1247: q
      1251: q^2
      1253: q^3+q^2
      1255: q^2
      1259: q^2
      1261: q^3+q^2
      1262: q
      1269: q^2
      1271: q^2
      1275: q^2
      1276: q^2
      1280: 2q^2
      1282: q
      1283: q^2
      1284: q
      1285: q^2
      1286: q
      1288: 2q^2
      1289: q^2
      1298: q^2
      1310: q^2
      1317: q^2
      1321: q^2
      1329: 2q^2
      1335: q^2
      1343: q
      1367: q^2
      1369: q^2
      1375: q
      1399: q^2
      1401: q^2
      1405: q
      1413: q
      1429: q^2
      1431: q^2
      1439: q
      1441: q
      1443: q
      1444: q
      1451: q^2
      1453: q
      1455: q^2
      1459: q
      1461: q^2
      1463: q^2
      1473: q^2
      1477: q^2
      1479: q^2
      1482: 2q^2
      1485: q
      1486: q
      1488: q
      1497: q^2
      1533: q
      1544: q
      1548: q
      1552: q
      1554: q
      1578: q^2
      1598: q^2
      1630: q^2
      1632: q^2
      1639: q
      1644: q
      1646: q
      1648: q
      1652: q
      1654: q
      1656: q
      1668: q
      1669: q
      1683: q
      1724: q
      1736: q
      1740: q
      1748: q
      1752: q
      1764: q
      1768: q
      1776: q
      1802: q
      1842: q
      1854: q
      1866: q
      2063: 1
      2100: 1
      2139: 1
      2172: 1

2173:    0: q^5+q^4+q^2
         1: q^4+q^2
         2: q^5+q^4+q^2
         3: q^5+q^4+q^2
         4: q^5+q^4+q^2
         5: q^4+q^2
         6: q^4+q^2
         7: q^5+q^4+q^2
         8: q^4+q^2
         9: q^5+q^4+q^2
        10: q^2
        11: q^2
        12: q^2
        13: q^5+q^4+q^2
        14: q^5+q^4+q^2
        15: q^4+q^2
        16: q^5+q^4+q^2
        17: q^4+q^2
        18: q^5+q^4+q^2
        19: q^5+q^4+q^2
        20: q^4+q^2
        21: q^5+q^4+q^2
        22: q^4+q^2
        23: q^4+q^2
        24: q^4+q^2
        25: q^4+q^2
        26: q^4+q^2
        27: q^4+q^2
        28: q^2
        29: q^2
        30: q^5+q^4+q^2
        31: q^2
        32: q^4+q^2
        33: q^4+q^2
        34: q^2
        35: q^4+q^2
        36: q^4+q^2
        37: q^4+q^2
        39: q^4+q^2
        41: q^4+q^2
        43: q^2
        44: q^2
        45: q^2
        46: q^5+q^4+q^2
        47: q^4+q^2
        48: q^5+q^4+q^2
        49: q^5+q^4+q^2
        50: q^4+q^2
        51: q^5+q^4+q^2
        52: q^4+q^2
        53: q^4+q^2
        54: q^4+q^2
        55: q^4+q^2
        56: q^4+q^2
        57: q^4+q^2
        59: q^2
        61: q^2
        62: q^2
        64: q^4+q^2
        66: q^4+q^2
        68: q^2
        69: q^5+q^4+q^2
        70: q^2
        71: q^2
        72: q^4+q^2
        73: q^4+q^2
        74: q^4+q^2
        76: q^4+q^2
        78: q^4+q^2
        80: q^2
        81: q^4+q^2
        82: q^2
        83: q^4+q^2
        84: q^2
        85: q^4+q^2
        86: q^2
        87: q^4+q^2
        88: q^2
        89: q^2
        90: q^2
        91: q^5+q^4+q^2
        92: q^4+q^2
        93: q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^4+q^2
       100: q^4+q^2
       101: q^2
       102: q^4+q^2
       106: q^2
       108: q^2
       110: q^2
       111: q^4+q^2
       113: q^2
       115: q^4+q^2
       118: q^2
       120: q^2
       121: q^2
       123: q^4+q^2
       125: q^2
       126: q^2
       127: q^4+q^2
       129: q^4+q^2
       131: q^4+q^2
       133: q^2
       134: q^5+q^4+q^2
       135: q^4+q^2
       136: q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: q^2
       147: q^4+q^2
       148: q^2
       149: q^2
       150: q^4+q^2
       151: q^4+q^2
       153: q^2
       155: q^4+q^2
       157: q^2
       158: q^2
       159: q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       172: q^2
       176: q^2
       177: q^4+q^2
       179: q^2
       181: q^4+q^2
       184: q^2
       186: q^2
       187: q^4+q^2
       189: q^2
       192: q^2
       194: q^2
       196: q^2
       197: q^2
       200: q^2
       202: q^2
       204: q^2
       205: q^2
       207: q^2
       209: q^2
       211: q^4+q^2
       213: q^4+q^2
       215: q^4+q^2
       217: q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       237: q^4+q^2
       239: q^2
       241: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^2
       253: q^2
       254: q^2
       255: q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       262: q^2
       266: q^2
       269: q^2
       273: q^2
       278: q^2
       279: q^2
       281: q^4+q^2
       284: q^2
       286: q^2
       287: q^2
       289: q^4+q^2
       291: q^4+q^2
       294: q^2
       296: q^2
       297: q^2
       300: q^2
       301: q^2
       304: q^2
       305: q^2
       308: q^2
       310: q^2
       311: q^2
       313: q^2
       315: q^4+q^2
       317: q^2
       320: q^2
       322: q^2
       323: q^2
       325: q^2
       327: q^2
       329: q^2
       331: q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       338: q^4+q^2
       340: q^2
       342: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       360: q^4+q^2
       362: q^2
       364: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       380: q^2
       384: q^2
       388: q^2
       391: q^2
       396: q^2
       399: q^2
       404: q^2
       406: q^2
       409: q^2
       411: q^2
       413: q^2
       415: q^2
       417: q^4+q^2
       420: q^2
       422: q^2
       423: q^2
       425: q^4+q^2
       427: q^2
       430: q^2
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       435: q^2
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       450: q^2
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       454: q^2
       455: q^2
       458: q^2
       459: q^2
       462: q^2
       463: q^2
       465: q^2
       467: q^4+q^2
       469: q^2
       472: q^2
       474: q^2
       475: q^2
       477: q^2
       479: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       485: q^4+q^2
       487: q^2
       489: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       515: q^4+q^2
       516: q^2
       517: q^4+q^2
       524: q^2
       528: q^2
       532: q^2
       536: q^2
       539: q^2
       543: q^2
       547: q^2
       552: q^2
       555: q^2
       559: q^2
       563: q^2
       568: q^2
       570: q^2
       575: q^2
       577: q^2
       583: q^2
       585: q^2
       587: q^2
       590: q^2
       592: q^2
       594: q^2
       596: q^2
       597: q^4+q^2
       599: q^2
       601: q^2
       604: q^2
       605: q^2
       608: q^2
       609: q^2
       613: q^2
       616: q^2
       617: q^2
       620: q^2
       622: q^2
       623: q^2
       625: q^2
       629: q^2
       632: q^2
       633: q^2
       639: q^2
       642: q^2
       644: q^2
       645: q^2
       651: q^2
       655: q^2
       657: q^2
       658: q^4+q^2
       660: q^2
       662: q^4+q^2
       664: q^4+q^2
       665: q^2
       674: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       680: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       697: q^2
       708: q^2
       712: q^2
       716: q^2
       720: q^2
       723: q^2
       727: q^2
       735: q^2
       739: q^2
       743: q^2
       751: q^2
       756: q^2
       758: q^2
       768: q^2
       769: q^2
       775: q^2
       777: q^2
       779: q^4+q^2
       781: q^2
       786: q^2
       788: q^2
       791: q^2
       794: q^2
       795: q^2
       797: q^2
       802: q^2
       804: q^2
       806: q^2
       808: q^2
       809: q^2
       811: q^2
       818: q^2
       819: q^2
       821: q^2
       826: q^2
       828: q^2
       830: q^2
       832: q^2
       833: q^2
       835: q^2
       843: q^2
       849: q^2
       853: q
       855: q^2
       866: q^2
       870: q^2
       871: q^2
       874: q^2
       875: q^2
       880: q^2
       889: q^2
       899: q^2
       902: q^2
       906: q^2
       911: q^2
       918: q^2
       922: q^2
       927: q^2
       930: q^2
       942: q^2
       946: q^2
       950: q^2
       955: q^2
       961: q^2
       967: q^2
       968: q^2
       979: q
       984: q
       994: q^2
       999: q^2
      1001: q^2
      1010: q^2
      1012: q^2
      1020: q^2
      1022: q^2
      1027: q^2
      1029: q^2
      1036: q^2
      1038: q^2
      1041: q^2
      1045: q^2
      1050: q
      1060: q^2
      1064: q^2
      1076: q^2
      1080: q^2
      1084: q^2
      1091: q^2
      1107: q
      1116: q^2
      1124: q^2
      1127: q^2
      1133: q^2
      1138: q^2
      1154: q^2
      1158: q^2
      1163: q^2
      1174: q^2
      1178: q^2
      1183: q^2
      1185: q
      1190: q
      1222: q
      1230: q^2
      1233: q^2
      1235: q^2
      1248: q^2
      1251: q^2
      1255: q^2
      1264: q
      1274: q^2
      1278: q^2
      1280: q^2
      1295: q^2
      1311: q
      1323: q
      1336: q
      1350: q^2
      1358: q^2
      1361: q^2
      1367: q^2
      1382: q^2
      1390: q^2
      1393: q^2
      1399: q^2
      1406: q
      1415: q
      1430: q^2
      1446: q
      1498: q
      1506: q^2
      1518: q^2
      1534: q
      1555: q
      1560: q
      1637: q
      1684: q
      1725: q
      1730: q
      1796: 1
      1843: q
      1881: 1
      1949: 1
      1999: 1
      2011: 1
      2057: 1
      2101: 1
      2113: 1
      2124: 1
      2173: 1

2174:    0: q^5+q^4+q^2
         1: q^4+q^2
         2: q^5+q^4+q^2
         3: q^5+q^4+q^2
         4: q^5+q^4+q^2
         5: q^4+q^2
         6: q^4+q^2
         7: q^5+q^4+q^2
         8: q^4+q^2
         9: q^5+q^4+q^2
        10: q^2
        11: q^2
        12: q^2
        13: q^5+q^4+q^2
        14: q^5+q^4+q^2
        15: q^4+q^2
        16: q^5+q^4+q^2
        17: q^4+q^2
        18: q^5+q^4+q^2
        19: q^5+q^4+q^2
        20: q^4+q^2
        21: q^5+q^4+q^2
        22: q^4+q^2
        23: q^4+q^2
        24: q^4+q^2
        25: q^4+q^2
        26: q^4+q^2
        27: q^4+q^2
        28: q^2
        29: q^2
        30: q^5+q^4+q^2
        31: q^2
        32: q^4+q^2
        33: q^4+q^2
        34: q^2
        35: q^4+q^2
        36: q^4+q^2
        38: q^4+q^2
        40: q^4+q^2
        42: q^4+q^2
        43: q^2
        44: q^2
        45: q^2
        46: q^5+q^4+q^2
        47: q^4+q^2
        48: q^5+q^4+q^2
        49: q^5+q^4+q^2
        50: q^4+q^2
        51: q^5+q^4+q^2
        52: q^4+q^2
        53: q^4+q^2
        54: q^4+q^2
        55: q^4+q^2
        56: q^4+q^2
        57: q^4+q^2
        59: q^2
        60: q^2
        63: q^2
        65: q^4+q^2
        67: q^4+q^2
        68: q^2
        69: q^5+q^4+q^2
        70: q^2
        71: q^2
        72: q^4+q^2
        73: q^4+q^2
        75: q^4+q^2
        77: q^4+q^2
        79: q^4+q^2
        80: q^2
        81: q^4+q^2
        82: q^2
        83: q^4+q^2
        84: q^2
        85: q^4+q^2
        86: q^2
        87: q^4+q^2
        88: q^2
        89: q^2
        90: q^2
        91: q^5+q^4+q^2
        92: q^4+q^2
        93: q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^4+q^2
       100: q^4+q^2
       101: q^2
       102: q^4+q^2
       104: q^2
       107: q^2
       110: q^2
       112: q^4+q^2
       114: q^2
       116: q^4+q^2
       118: q^2
       119: q^2
       122: q^2
       124: q^4+q^2
       125: q^2
       126: q^2
       128: q^4+q^2
       130: q^4+q^2
       132: q^4+q^2
       133: q^2
       134: q^5+q^4+q^2
       135: q^4+q^2
       136: q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: q^2
       147: q^4+q^2
       148: q^2
       149: q^2
       150: q^4+q^2
       152: q^4+q^2
       154: q^2
       156: q^4+q^2
       157: q^2
       158: q^2
       159: q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       170: q^2
       174: q^2
       178: q^4+q^2
       180: q^2
       182: q^4+q^2
       183: q^2
       186: q^2
       188: q^4+q^2
       190: q^2
       192: q^2
       193: q^2
       196: q^2
       198: q^2
       199: q^2
       201: q^2
       204: q^2
       206: q^2
       208: q^2
       210: q^2
       212: q^4+q^2
       214: q^4+q^2
       216: q^4+q^2
       218: q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       238: q^4+q^2
       240: q^2
       242: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^2
       253: q^2
       254: q^2
       255: q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       260: q^2
       264: q^2
       268: q^2
       274: q^2
       276: q^2
       280: q^2
       282: q^4+q^2
       283: q^2
       286: q^2
       288: q^2
       290: q^4+q^2
       292: q^4+q^2
       293: q^2
       296: q^2
       298: q^2
       299: q^2
       302: q^2
       304: q^2
       306: q^2
       307: q^2
       310: q^2
       312: q^2
       314: q^2
       316: q^4+q^2
       318: q^2
       319: q^2
       322: q^2
       324: q^2
       326: q^2
       328: q^2
       330: q^2
       332: q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       339: q^4+q^2
       341: q^2
       343: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       361: q^4+q^2
       363: q^2
       365: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       378: q^2
       382: q^2
       386: q^2
       390: q^2
       394: q^2
       400: q^2
       403: q^2
       407: q^2
       410: q^2
       412: q^2
       414: q^2
       416: q^2
       418: q^4+q^2
       419: q^2
       422: q^2
       424: q^2
       426: q^4+q^2
       428: q^2
       429: q^2
       432: q^2
       434: q^2
       436: q^2
       437: q^2
       440: q^2
       442: q^2
       443: q^2
       446: q^2
       447: q^2
       450: q^2
       452: q^2
       453: q^2
       456: q^2
       458: q^2
       460: q^2
       462: q^2
       464: q^2
       466: q^2
       468: q^4+q^2
       470: q^2
       471: q^2
       474: q^2
       476: q^2
       478: q^2
       480: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       486: q^4+q^2
       488: q^2
       490: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       515: q^4+q^2
       516: q^2
       517: q^4+q^2
       522: q^2
       526: q^2
       530: q^2
       534: q^2
       538: q^2
       542: q^2
       546: q^2
       551: q^2
       556: q^2
       560: q^2
       564: q^2
       566: q^2
       571: q^2
       574: q^2
       581: q^2
       584: q^2
       586: q^2
       588: q^2
       589: q^2
       592: q^2
       593: q^2
       596: q^2
       598: q^4+q^2
       600: q^2
       602: q^2
       603: q^2
       606: q^2
       608: q^2
       610: q^2
       614: q^2
       615: q^2
       618: q^2
       619: q^2
       622: q^2
       624: q^2
       626: q^2
       630: q^2
       632: q^2
       634: q^2
       640: q^2
       641: q^2
       644: q^2
       646: q^2
       652: q^2
       656: q^2
       657: q^2
       659: q^4+q^2
       661: q^2
       663: q^4+q^2
       664: q^4+q^2
       665: q^2
       674: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       680: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       699: q^2
       706: q^2
       710: q^2
       715: q^2
       718: q^2
       722: q^2
       726: q^2
       734: q^2
       740: q^2
       744: q^2
       752: q^2
       754: q^2
       759: q^2
       766: q^2
       773: q^2
       776: q^2
       778: q^2
       780: q^4+q^2
       782: q^2
       785: q^2
       788: q^2
       792: q^2
       793: q^2
       796: q^2
       798: q^2
       801: q^2
       804: q^2
       805: q^2
       808: q^2
       810: q^2
       812: q^2
       818: q^2
       820: q^2
       822: q^2
       825: q^2
       828: q^2
       829: q^2
       832: q^2
       834: q^2
       836: q^2
       844: q^2
       850: q^2
       854: q
       856: q^2
       866: q^2
       870: q^2
       871: q^2
       874: q^2
       875: q^2
       880: q^2
       890: q^2
       897: q^2
       903: q^2
       905: q^2
       909: q^2
       917: q^2
       921: q^2
       926: q^2
       929: q^2
       943: q^2
       947: q^2
       951: q^2
       953: q^2
       962: q^2
       965: q^2
       972: q^2
       980: q
       987: q
       995: q^2
       999: q^2
      1000: q^2
      1011: q^2
      1013: q^2
      1021: q^2
      1023: q^2
      1026: q^2
      1029: q^2
      1037: q^2
      1039: q^2
      1040: q^2
      1045: q^2
      1051: q
      1061: q^2
      1065: q^2
      1076: q^2
      1080: q^2
      1084: q^2
      1092: q^2
      1108: q
      1117: q^2
      1123: q^2
      1128: q^2
      1131: q^2
      1142: q^2
      1155: q^2
      1157: q^2
      1162: q^2
      1175: q^2
      1177: q^2
      1181: q^2
      1186: q
      1193: q
      1223: q
      1231: q^2
      1233: q^2
      1234: q^2
      1249: q^2
      1251: q^2
      1254: q^2
      1265: q
      1275: q^2
      1279: q^2
      1281: q^2
      1296: q^2
      1312: q
      1324: q
      1339: q
      1351: q^2
      1357: q^2
      1363: q^2
      1366: q^2
      1383: q^2
      1389: q^2
      1394: q^2
      1397: q^2
      1409: q
      1416: q
      1434: q^2
      1447: q
      1499: q
      1508: q^2
      1519: q^2
      1535: q
      1558: q
      1561: q
      1638: q
      1685: q
      1728: q
      1731: q
      1794: 1
      1844: q
      1878: 1
      1950: 1
      2000: 1
      2012: 1
      2058: 1
      2102: 1
      2114: 1
      2125: 1
      2174: 1

2175:    0: 3q^5+5q^4+5q^3+2q^2
         1: 3q^5+5q^4+5q^3+2q^2
         2: 3q^5+5q^4+5q^3+2q^2
         3: 3q^5+5q^4+5q^3+2q^2
         4: q^6+3q^5+5q^4+4q^3+2q^2
         5: 3q^5+5q^4+5q^3+2q^2
         6: q^6+3q^5+5q^4+4q^3+2q^2
         7: q^6+3q^5+5q^4+4q^3+2q^2
         8: 3q^5+5q^4+5q^3+2q^2
         9: q^7+2q^6+3q^5+4q^4+3q^3+2q^2
        10: q^5+4q^4+5q^3+2q^2
        11: q^5+4q^4+5q^3+2q^2
        12: 2q^5+4q^4+4q^3+2q^2
        13: 3q^5+5q^4+5q^3+2q^2
        14: q^6+3q^5+5q^4+4q^3+2q^2
        15: 3q^5+5q^4+5q^3+2q^2
        16: q^5+4q^4+5q^3+2q^2
        17: q^5+4q^4+5q^3+2q^2
        18: q^6+2q^5+4q^4+3q^3+2q^2
        19: 2q^5+4q^4+4q^3+2q^2
        20: 2q^5+4q^4+4q^3+2q^2
        21: 2q^5+4q^4+4q^3+2q^2
        22: 3q^5+5q^4+5q^3+2q^2
        23: 3q^5+5q^4+5q^3+2q^2
        24: 3q^5+5q^4+5q^3+2q^2
        25: 3q^5+5q^4+5q^3+2q^2
        26: 3q^5+5q^4+5q^3+2q^2
        27: 3q^5+5q^4+5q^3+2q^2
        28: 3q^4+5q^3+2q^2
        29: q^5+3q^4+4q^3+2q^2
        30: 2q^5+4q^4+4q^3+2q^2
        31: q^5+4q^4+5q^3+2q^2
        32: 3q^5+5q^4+5q^3+2q^2
        33: q^5+4q^4+5q^3+2q^2
        34: q^5+4q^4+5q^3+2q^2
        35: 3q^5+5q^4+5q^3+2q^2
        36: q^5+4q^4+5q^3+2q^2
        37: q^5+q^4+q^3
        38: 2q^5+4q^4+4q^3+2q^2
        39: q^5+q^4+q^3
        40: 2q^5+4q^4+4q^3+2q^2
        41: q^5+q^4+q^3
        42: 2q^5+4q^4+4q^3+2q^2
        43: q^5+4q^4+5q^3+2q^2
        44: 2q^5+4q^4+4q^3+2q^2
        45: q^5+4q^4+5q^3+2q^2
        46: q^5+4q^4+5q^3+2q^2
        47: q^5+4q^4+5q^3+2q^2
        48: q^6+2q^5+4q^4+3q^3+2q^2
        49: 3q^4+4q^3+2q^2
        50: 3q^4+4q^3+2q^2
        51: q^5+3q^4+3q^3+2q^2
        52: 2q^5+4q^4+4q^3+2q^2
        53: 2q^5+4q^4+4q^3+2q^2
        54: 2q^5+4q^4+4q^3+2q^2
        55: 2q^5+4q^4+4q^3+2q^2
        56: 2q^5+4q^4+4q^3+2q^2
        57: 2q^5+4q^4+4q^3+2q^2
        58: q^4+2q^3+q^2
        59: 2q^4+3q^3+q^2
        60: q^4+2q^3+q^2
        61: 2q^4+3q^3+q^2
        62: q^4+q^3
        63: q^5+3q^4+4q^3+2q^2
        64: q^5+q^4+q^3
        65: 2q^5+4q^4+4q^3+2q^2
        66: q^4+q^3
        67: q^5+3q^4+4q^3+2q^2
        68: 3q^4+5q^3+2q^2
        69: 2q^4+3q^3+2q^2
        70: q^5+3q^4+4q^3+2q^2
        71: 2q^4+4q^3+2q^2
        72: 2q^4+3q^3+2q^2
        73: 2q^4+3q^3+2q^2
        75: q^5+3q^4+3q^3+2q^2
        77: q^5+3q^4+3q^3+2q^2
        79: q^5+3q^4+3q^3+2q^2
        80: q^5+4q^4+5q^3+2q^2
        81: q^5+4q^4+5q^3+2q^2
        82: q^5+3q^4+4q^3+2q^2
        83: 2q^5+4q^4+4q^3+2q^2
        84: q^5+4q^4+5q^3+2q^2
        85: q^5+4q^4+5q^3+2q^2
        86: q^5+3q^4+4q^3+2q^2
        87: 2q^5+4q^4+4q^3+2q^2
        88: 2q^4+5q^3+2q^2
        89: 2q^4+5q^3+2q^2
        90: q^5+3q^4+3q^3+2q^2
        91: 3q^4+4q^3+2q^2
        92: 3q^4+4q^3+2q^2
        93: q^5+3q^4+3q^3+2q^2
        94: 3q^4+4q^3+2q^2
        95: 3q^4+4q^3+2q^2
        96: q^5+3q^4+3q^3+2q^2
        97: 3q^4+4q^3+2q^2
        98: 3q^4+4q^3+2q^2
        99: q^5+3q^4+3q^3+2q^2
       100: 2q^5+4q^4+4q^3+2q^2
       101: 2q^5+4q^4+4q^3+2q^2
       102: 2q^5+4q^4+4q^3+2q^2
       104: q^4+2q^3+q^2
       105: q^4+2q^3+q^2
       106: q^4+q^3
       107: q^3+q^2
       108: q^4+2q^3+q^2
       109: q^3+q^2
       110: q^4+2q^3+q^2
       112: q^4+2q^3+2q^2
       114: q^5+2q^4+3q^3+2q^2
       116: q^5+3q^4+3q^3+2q^2
       117: q^4+2q^3+q^2
       118: 2q^4+3q^3+q^2
       119: q^4+2q^3+q^2
       120: 2q^4+3q^3+q^2
       121: q^4+q^3
       122: q^5+3q^4+4q^3+2q^2
       123: q^4+q^3
       124: q^5+3q^4+4q^3+2q^2
       125: 2q^4+5q^3+2q^2
       126: q^4+3q^3+2q^2
       128: q^4+3q^3+2q^2
       130: q^4+3q^3+2q^2
       132: 2q^4+2q^3+2q^2
       133: 2q^4+4q^3+2q^2
       134: 2q^4+3q^3+2q^2
       135: 2q^4+3q^3+2q^2
       136: 2q^4+3q^3+2q^2
       137: 2q^4+5q^3+2q^2
       138: 2q^4+3q^3+2q^2
       139: 2q^4+4q^3+2q^2
       140: 2q^4+3q^3+2q^2
       141: q^5+3q^4+4q^3+2q^2
       142: 2q^4+3q^3+2q^2
       143: 2q^4+5q^3+2q^2
       144: 2q^4+3q^3+2q^2
       145: 2q^4+4q^3+2q^2
       146: q^5+3q^4+4q^3+2q^2
       147: 2q^4+3q^3+2q^2
       148: 2q^4+3q^3+2q^2
       149: q^5+3q^4+4q^3+2q^2
       150: 2q^5+4q^4+4q^3+2q^2
       152: q^5+3q^4+3q^3+2q^2
       154: q^5+3q^4+3q^3+2q^2
       156: q^5+3q^4+3q^3+2q^2
       157: 4q^3+2q^2
       158: 4q^3+2q^2
       159: q^4+3q^3+2q^2
       160: 3q^4+4q^3+2q^2
       161: 3q^4+4q^3+2q^2
       162: q^5+3q^4+3q^3+2q^2
       163: 3q^4+4q^3+2q^2
       164: 3q^4+4q^3+2q^2
       165: q^5+3q^4+3q^3+2q^2
       166: 3q^4+4q^3+2q^2
       167: 3q^4+4q^3+2q^2
       168: q^5+3q^4+3q^3+2q^2
       170: q^3+q^2
       171: q^3+q^2
       174: q^4+2q^3+q^2
       175: q^4+2q^3+q^2
       176: q^4+q^3
       178: q^4+2q^3+2q^2
       180: q^4+3q^3+2q^2
       182: 2q^3+2q^2
       183: q^3+q^2
       184: q^4+2q^3+q^2
       185: q^3+q^2
       186: q^4+2q^3+q^2
       188: q^4+2q^3+2q^2
       190: q^5+2q^4+3q^3+2q^2
       191: q^4+2q^3+q^2
       192: q^4+3q^3+q^2
       193: q^3+q^2
       194: q^4+2q^3+q^2
       195: q^3+q^2
       196: q^4+2q^3+q^2
       198: q^4+2q^3+2q^2
       199: q^4+2q^3+q^2
       200: q^4+3q^3+q^2
       201: q^3+q^2
       202: q^4+2q^3+q^2
       203: q^3+q^2
       204: q^4+2q^3+q^2
       206: q^4+2q^3+2q^2
       207: q^3
       208: 2q^4+4q^3+2q^2
       210: q^5+2q^4+3q^3+2q^2
       212: q^5+3q^4+3q^3+2q^2
       214: q^4+3q^3+2q^2
       216: q^4+3q^3+2q^2
       218: 2q^4+2q^3+2q^2
       219: q^4+3q^3+2q^2
       220: 4q^3+2q^2
       221: 3q^3+2q^2
       222: 3q^3+2q^2
       223: q^4+2q^3+2q^2
       224: 3q^3+2q^2
       225: q^4+2q^3+2q^2
       226: q^4+3q^3+2q^2
       227: 2q^4+4q^3+2q^2
       228: 2q^4+3q^3+2q^2
       229: 2q^4+3q^3+2q^2
       230: 2q^4+3q^3+2q^2
       231: q^4+3q^3+2q^2
       232: 2q^4+4q^3+2q^2
       233: 2q^4+3q^3+2q^2
       234: 2q^4+3q^3+2q^2
       235: 2q^4+3q^3+2q^2
       236: 2q^4+3q^3+2q^2
       238: q^4+3q^3+2q^2
       240: q^4+3q^3+2q^2
       242: 2q^4+2q^3+2q^2
       243: 2q^4+4q^3+2q^2
       244: 2q^4+3q^3+2q^2
       245: 2q^4+3q^3+2q^2
       246: q^5+3q^4+4q^3+2q^2
       247: 3q^3+3q^2
       248: 3q^3+3q^2
       249: 2q^4+2q^3+2q^2
       250: 4q^3+2q^2
       251: 4q^3+2q^2
       252: q^4+3q^3+2q^2
       253: 4q^3+2q^2
       254: 4q^3+2q^2
       255: q^4+3q^3+2q^2
       256: 3q^4+4q^3+2q^2
       257: 3q^4+4q^3+2q^2
       258: q^5+3q^4+3q^3+2q^2
       260: q^3+q^2
       261: q^3+q^2
       264: q^3+q^2
       265: q^3+q^2
       268: q^3+q^2
       270: q^3+q^2
       272: q^3+q^2
       274: q^3+q^2
       276: q^4+2q^3+q^2
       277: q^4+2q^3+q^2
       278: q^3
       280: q^4+3q^3+2q^2
       282: q^4+2q^3+2q^2
       283: q^2
       284: q^3+q^2
       285: q^2
       286: q^3+q^2
       288: q^4+2q^3+2q^2
       290: 2q^3+2q^2
       292: q^3+2q^2
       293: q^3+q^2
       294: 2q^3+q^2
       295: q^3+q^2
       296: 2q^3+q^2
       298: 2q^3+2q^2
       299: q^3+q^2
       300: q^4+2q^3+q^2
       302: 2q^3+2q^2
       303: q^3+q^2
       304: q^4+2q^3+q^2
       306: q^4+2q^3+2q^2
       307: q^3+q^2
       308: q^4+2q^3+q^2
       309: q^3+q^2
       310: q^4+2q^3+q^2
       312: 2q^3+2q^2
       314: q^4+2q^3+2q^2
       316: q^4+2q^3+2q^2
       318: q^4+3q^3+2q^2
       319: q^3+q^2
       320: q^4+2q^3+q^2
       321: q^3+q^2
       322: q^4+2q^3+q^2
       324: q^4+2q^3+2q^2
       326: q^5+2q^4+3q^3+2q^2
       328: q^3+2q^2
       330: q^3+2q^2
       332: q^3+2q^2
       333: 3q^3+2q^2
       334: 2q^3+2q^2
       335: 2q^3+2q^2
       336: q^3+2q^2
       337: 3q^3+3q^2
       339: 3q^3+3q^2
       341: 3q^3+3q^2
       343: 2q^4+2q^3+2q^2
       344: q^4+3q^3+2q^2
       345: 4q^3+2q^2
       346: 3q^3+2q^2
       347: 3q^3+2q^2
       348: q^4+2q^3+2q^2
       349: 3q^3+2q^2
       350: q^4+2q^3+2q^2
       351: 3q^3+3q^2
       352: q^4+3q^3+2q^2
       353: 4q^3+2q^2
       354: 3q^3+2q^2
       355: 3q^3+2q^2
       356: q^4+2q^3+2q^2
       357: 3q^3+2q^2
       358: q^4+2q^3+2q^2
       359: 3q^3+3q^2
       361: q^4+3q^3+2q^2
       363: q^4+3q^3+2q^2
       365: 2q^4+2q^3+2q^2
       366: q^4+3q^3+2q^2
       367: 2q^4+4q^3+2q^2
       368: 2q^4+3q^3+2q^2
       369: 2q^4+3q^3+2q^2
       370: 2q^4+3q^3+2q^2
       371: 3q^3+3q^2
       372: 3q^3+3q^2
       373: 2q^4+2q^3+2q^2
       374: 4q^3+2q^2
       375: 4q^3+2q^2
       376: q^4+3q^3+2q^2
       378: q^2
       379: q^2
       382: q^3+q^2
       383: q^3+q^2
       386: q^3+q^2
       387: q^3+q^2
       390: q^3+q^2
       392: q^3+q^2
       394: q^3+q^2
       395: q^3+q^2
       398: q^3+q^2
       400: q^3+q^2
       402: q^3+q^2
       403: q^3+q^2
       407: q^3+q^2
       408: q^3+q^2
       410: q^3+2q^2
       412: q^3+2q^2
       414: q^4+2q^3+2q^2
       416: 2q^2
       418: q^3+2q^2
       419: q^2
       420: q^3+q^2
       421: q^2
       422: q^3+q^2
       424: q^3+2q^2
       426: q^3+2q^2
       428: 3q^3+3q^2
       429: q^2
       430: q^3+q^2
       431: q^2
       432: q^3+q^2
       434: q^3+2q^2
       436: 2q^3+2q^2
       437: q^3+q^2
       438: 2q^3+q^2
       439: q^3+q^2
       440: 2q^3+q^2
       442: 2q^3+2q^2
       443: q^3+q^2
       444: 2q^3+2q^2
       446: 3q^3+3q^2
       447: q^2
       448: q^3+q^2
       449: q^2
       450: q^3+q^2
       452: q^3+2q^2
       453: q^3+q^2
       454: 2q^3+q^2
       456: 2q^3+2q^2
       457: q^3+q^2
       458: 2q^3+q^2
       460: 2q^3+2q^2
       461: q^3+q^2
       462: 2q^3+2q^2
       464: 3q^3+3q^2
       466: q^4+3q^3+2q^2
       468: q^4+2q^3+2q^2
       470: q^4+2q^3+2q^2
       471: q^3+q^2
       472: q^4+2q^3+q^2
       473: q^3+q^2
       474: q^4+2q^3+q^2
       476: q^4+2q^3+2q^2
       478: 2q^3+2q^2
       479: q^3+q^2
       480: 2q^3+2q^2
       481: 2q^3+2q^2
       482: 2q^3+2q^2
       483: q^3+2q^2
       484: 3q^3+3q^2
       486: 3q^3+3q^2
       488: 3q^3+3q^2
       490: 2q^4+2q^3+2q^2
       491: q^3+2q^2
       492: 3q^3+2q^2
       493: 2q^3+2q^2
       494: 2q^3+2q^2
       495: q^3+2q^2
       496: 3q^3+3q^2
       497: 3q^3+2q^2
       498: 2q^3+2q^2
       499: 2q^3+2q^2
       500: q^3+2q^2
       501: 3q^3+3q^2
       503: q^3+2q^2
       505: q^3+2q^2
       507: q^3+2q^2
       508: q^4+3q^3+2q^2
       509: 4q^3+2q^2
       510: 3q^3+2q^2
       511: 3q^3+2q^2
       512: q^4+2q^3+2q^2
       513: 3q^3+2q^2
       514: q^4+2q^3+2q^2
       515: 3q^2
       516: 3q^2
       517: q^3+2q^2
       518: 3q^2
       519: 3q^2
       520: q^3+2q^2
       522: q^2
       523: q^2
       526: q^2
       527: q^2
       530: q^2
       531: q^2
       534: q^2
       535: q^2
       538: q^3+q^2
       540: q^3+q^2
       542: q^3+q^2
       544: q^3+q^2
       546: q^3+q^2
       548: 2q^3+2q^2
       550: q^2
       551: q^2
       554: q^3+q^2
       556: q^3+q^2
       558: q^3+q^2
       560: q^3+q^2
       562: q^3+q^2
       564: 2q^3+2q^2
       566: q^3+q^2
       567: q^3+q^2
       571: q^3+q^2
       572: q^3+q^2
       574: q^3+q^2
       575: q^3+q^2
       576: q^3+q^2
       578: q^3+q^2
       581: 2q^3+2q^2
       584: q^3+2q^2
       586: q^3+2q^2
       588: 2q^2
       589: q^2
       590: q^3+q^2
       592: q^2
       594: q^2
       595: q^2
       596: q^3+q^2
       598: q^3+2q^2
       600: q^3+2q^2
       602: 3q^3+3q^2
       603: q^2
       604: q^3+q^2
       606: q^3+2q^2
       607: q^2
       608: q^3+q^2
       610: q^3+2q^2
       612: 2q^2
       614: q^3+2q^2
       615: q^3+q^2
       616: 2q^3+2q^2
       618: 3q^3+3q^2
       619: q^2
       620: q^3+q^2
       621: q^2
       622: q^3+q^2
       624: q^3+2q^2
       626: q^3+2q^2
       628: 2q^2
       630: q^3+2q^2
       631: q^3+q^2
       632: 2q^3+2q^2
       634: 3q^3+3q^2
       636: q^3+2q^2
       638: q^3+2q^2
       640: q^4+2q^3+2q^2
       641: q^2
       642: q^3+q^2
       643: q^2
       644: q^3+q^2
       646: q^3+2q^2
       647: q^3+q^2
       648: 2q^3+q^2
       649: q^3+q^2
       650: 2q^3+q^2
       652: 2q^3+2q^2
       654: 2q^3+2q^2
       655: q^3+q^2
       656: 2q^3+2q^2
       657: 3q^2
       659: 3q^2
       661: 3q^2
       663: q^3+2q^2
       664: 2q^2
       665: q^3+2q^2
       667: 3q^2
       669: 3q^2
       671: q^3+2q^2
       672: 3q^2
       673: 2q^2
       674: 3q^2
       675: 2q^3+2q^2
       676: 2q^3+2q^2
       677: q^3+2q^2
       678: 3q^2
       679: q^3+2q^2
       680: 3q^2
       681: 2q^3+2q^2
       682: 2q^3+2q^2
       683: q^3+2q^2
       684: 3q^2
       685: q^3+2q^2
       686: 3q^3+2q^2
       687: 2q^3+2q^2
       688: 2q^3+2q^2
       689: q^3+2q^2
       699: q^3+q^2
       700: q^3+q^2
       701: q^3+q^2
       706: q^2
       707: q^2
       710: q^2
       711: q^2
       715: q^2
       719: q^2
       722: q^2
       724: q^2
       726: q^2
       728: q^2
       730: q^2
       732: q^2
       734: q^3+q^2
       736: 2q^3+2q^2
       738: q^2
       740: q^2
       742: q^2
       744: q^2
       746: q^2
       748: q^2
       750: q^3+q^2
       752: 2q^3+2q^2
       754: q^2
       755: q^2
       759: q^3+q^2
       760: q^3+q^2
       763: q^3+q^2
       764: q^3+q^2
       766: q^3+q^2
       767: q^3+q^2
       768: q^3+q^2
       770: q^3+q^2
       773: 2q^3+2q^2
       776: 3q^2
       778: 2q^2
       780: 2q^2
       782: q^3+2q^2
       784: 2q^2
       786: q^2
       788: q^2
       790: 3q^2
       792: q^2
       793: q^2
       794: 2q^2
       796: 3q^2
       798: q^3+2q^2
       800: 2q^2
       801: q^2
       802: q^3+q^2
       804: q^2
       806: q^2
       807: q^2
       808: q^3+q^2
       810: q^3+2q^2
       812: q^3+2q^2
       814: 3q^2
       815: q^2
       816: 2q^2
       817: q^2
       818: 2q^2
       820: 3q^2
       822: q^3+2q^2
       824: 2q^2
       825: q^2
       826: q^3+q^2
       828: q^2
       830: q^2
       831: q^2
       832: q^3+q^2
       834: q^3+2q^2
       836: q^3+2q^2
       838: 3q^2
       839: q^2
       840: 2q^2
       842: q^3+2q^2
       843: q^2
       844: 2q^2
       845: q^2
       846: q^3+q^2
       847: q^2
       848: q^3+q^2
       850: q^3+2q^2
       852: q^3+2q^2
       854: 2q^2
       856: q^3+2q^2
       857: q^2
       858: 2q^2
       866: 2q^2
       868: 2q^2
       870: 2q^2
       871: q^3+2q^2
       872: 2q^2
       874: 2q^2
       875: q^3+2q^2
       876: 2q^2
       877: 2q^3+2q^2
       878: 2q^3+2q^2
       879: q^3+2q^2
       880: q^3+2q^2
       890: q^3+q^2
       891: q^3+q^2
       892: q^3+q^2
       897: q^2
       898: q^2
       903: q^2
       907: q^2
       913: q^2
       915: q^2
       917: q^2
       919: 2q^2
       921: q^2
       923: q^2
       926: q^2
       931: q^2
       933: q^2
       935: 2q^2
       937: q^2
       939: q^2
       941: q^2
       943: 2q^2
       945: q^2
       947: q^2
       951: q^2
       954: q^2
       957: q^2
       959: 2q^2
       962: q^2
       963: q^2
       965: q^2
       966: q^2
       967: q^2
       969: q^2
       972: 2q^2
       976: q^2
       977: q^2
       980: q^2
       981: q^2
       983: q^2
       986: 2q^2
       989: q^2
       990: q^2
       991: q^2
       995: 2q^2
       999: q^2
      1001: q^2
      1003: 2q^2
      1005: q^2
      1007: q^2
      1009: q^2
      1011: q^2
      1013: q^2
      1019: 2q^2
      1021: 2q^2
      1023: q^3+2q^2
      1025: 2q^2
      1027: q^2
      1029: q^2
      1035: 2q^2
      1037: 2q^2
      1039: q^3+2q^2
      1041: q^2
      1043: 2q^2
      1045: q^2
      1049: q^3+2q^2
      1051: 2q^2
      1052: q^2
      1053: q^3+q^2
      1055: q^2
      1057: q^2
      1058: q^2
      1059: q^3+q^2
      1061: q^3+2q^2
      1063: q^3+2q^2
      1065: q^2
      1076: 2q^2
      1078: 2q^2
      1080: 2q^2
      1082: 2q^2
      1083: q^3+2q^2
      1084: 2q^2
      1085: 2q^2
      1092: q^2
      1093: q^2
      1094: q^2
      1104: q^2
      1105: q^2
      1106: q^2
      1113: q^2
      1117: q^2
      1121: q^2
      1125: q^2
      1142: q^2
      1149: q^2
      1151: q^2
      1155: q^2
      1159: q^2
      1169: q^2
      1171: q^2
      1175: q^2
      1179: q^2
      1186: q^2
      1187: q^2
      1200: q^2
      1201: q^2
      1205: q^2
      1209: q^2
      1221: q^2
      1223: q^2
      1231: 2q^2
      1233: q^2
      1235: q^2
      1239: 2q^2
      1241: q^2
      1243: q^2
      1249: 2q^2
      1251: q^2
      1255: q^2
      1257: 2q^2
      1259: q^2
      1261: q^2
      1265: 2q^2
      1267: q^3+2q^2
      1269: q^2
      1271: q^2
      1273: 2q^2
      1275: 2q^2
      1277: q^2
      1279: q^2
      1281: q^2
      1287: 2q^2
      1289: 2q^2
      1347: q^2
      1351: q^2
      1355: q^2
      1359: q^2
      1379: q^2
      1383: q^2
      1387: q^2
      1391: q^2
      1416: q^2
      1417: q^2
      1421: q^2
      1425: q^2
      1434: q^2
      1447: q^2
      1465: 2q^2
      1467: q^2
      1469: q^2
      1471: 2q^2
      1475: q^2
      1477: q^2
      1479: q^2
      1481: q^2
      1484: q
      1606: q^2
      1610: q^2
      1614: q^2
      1618: q^2
      1638: q
      1642: q
      1650: q
      1658: q
      1672: q^2
      1728: q
      1760: q
      1784: q
      1814: q
      1824: q
      1890: q
      1931: q
      1959: 1
      2031: 1
      2039: 1
      2051: 1
      2079: 1
      2091: 1
      2126: 1
      2175: 1

2176:    0: q^5+q^4+q^2
         1: q^4+q^2
         2: q^5+q^4+q^2
         3: q^5+q^4+q^2
         4: q^5+q^4+q^2
         5: q^4+q^2
         6: q^4+q^2
         7: q^5+q^4+q^2
         8: q^4+q^2
         9: q^5+q^4+q^2
        10: q^2
        11: q^2
        12: q^2
        13: q^5+q^4+q^2
        14: q^5+q^4+q^2
        15: q^4+q^2
        16: q^5+q^4+q^2
        17: q^4+q^2
        18: q^5+q^4+q^2
        19: q^5+q^4+q^2
        20: q^4+q^2
        21: q^5+q^4+q^2
        22: q^4+q^2
        23: q^4+q^2
        24: q^4+q^2
        25: q^4+q^2
        26: q^4+q^2
        27: q^4+q^2
        28: q^2
        29: q^2
        30: q^5+q^4+q^2
        31: q^2
        32: q^4+q^2
        33: q^4+q^2
        34: q^2
        35: q^4+q^2
        36: q^4+q^2
        38: q^4+q^2
        40: q^4+q^2
        42: q^4+q^2
        43: q^2
        44: q^2
        45: q^2
        46: q^5+q^4+q^2
        47: q^4+q^2
        48: q^5+q^4+q^2
        49: q^5+q^4+q^2
        50: q^4+q^2
        51: q^5+q^4+q^2
        52: q^4+q^2
        53: q^4+q^2
        54: q^4+q^2
        55: q^4+q^2
        56: q^4+q^2
        57: q^4+q^2
        58: q^2
        61: q^2
        63: q^2
        65: q^4+q^2
        67: q^4+q^2
        68: q^2
        69: q^5+q^4+q^2
        70: q^2
        71: q^2
        72: q^4+q^2
        73: q^4+q^2
        75: q^4+q^2
        77: q^4+q^2
        79: q^4+q^2
        80: q^2
        81: q^4+q^2
        82: q^2
        83: q^4+q^2
        84: q^2
        85: q^4+q^2
        86: q^2
        87: q^4+q^2
        88: q^2
        89: q^2
        90: q^2
        91: q^5+q^4+q^2
        92: q^4+q^2
        93: q^5+q^4+q^2
        94: q^4+q^2
        95: q^4+q^2
        96: q^4+q^2
        97: q^4+q^2
        98: q^4+q^2
        99: q^4+q^2
       100: q^4+q^2
       101: q^2
       102: q^4+q^2
       105: q^2
       108: q^2
       109: q^2
       112: q^4+q^2
       114: q^2
       116: q^4+q^2
       117: q^2
       120: q^2
       122: q^2
       124: q^4+q^2
       125: q^2
       126: q^2
       128: q^4+q^2
       130: q^4+q^2
       132: q^4+q^2
       133: q^2
       134: q^5+q^4+q^2
       135: q^4+q^2
       136: q^4+q^2
       137: q^2
       138: q^4+q^2
       139: q^2
       140: q^2
       141: q^2
       142: q^4+q^2
       143: q^2
       144: q^4+q^2
       145: q^2
       146: q^2
       147: q^4+q^2
       148: q^2
       149: q^2
       150: q^4+q^2
       152: q^4+q^2
       154: q^2
       156: q^4+q^2
       157: q^2
       158: q^2
       159: q^2
       160: q^4+q^2
       161: q^4+q^2
       162: q^4+q^2
       163: q^4+q^2
       164: q^4+q^2
       165: q^4+q^2
       166: q^4+q^2
       167: q^2
       168: q^4+q^2
       171: q^2
       175: q^2
       178: q^4+q^2
       180: q^2
       182: q^4+q^2
       184: q^2
       185: q^2
       188: q^4+q^2
       190: q^2
       191: q^2
       194: q^2
       195: q^2
       198: q^2
       200: q^2
       202: q^2
       203: q^2
       206: q^2
       208: q^2
       210: q^2
       212: q^4+q^2
       214: q^4+q^2
       216: q^4+q^2
       218: q^4+q^2
       219: q^2
       220: q^2
       221: q^2
       222: q^2
       223: q^4+q^2
       224: q^2
       225: q^4+q^2
       226: q^2
       227: q^2
       228: q^4+q^2
       229: q^2
       230: q^4+q^2
       231: q^2
       232: q^2
       233: q^4+q^2
       234: q^4+q^2
       235: q^2
       236: q^4+q^2
       238: q^4+q^2
       240: q^2
       242: q^4+q^2
       243: q^2
       244: q^2
       245: q^2
       246: q^2
       247: q^4+q^2
       248: q^2
       249: q^4+q^2
       250: q^2
       251: q^2
       252: q^2
       253: q^2
       254: q^2
       255: q^2
       256: q^4+q^2
       257: q^2
       258: q^4+q^2
       261: q^2
       265: q^2
       270: q^2
       272: q^2
       277: q^2
       280: q^2
       282: q^4+q^2
       284: q^2
       285: q^2
       288: q^2
       290: q^4+q^2
       292: q^4+q^2
       294: q^2
       295: q^2
       298: q^2
       300: q^2
       302: q^2
       303: q^2
       306: q^2
       308: q^2
       309: q^2
       312: q^2
       314: q^2
       316: q^4+q^2
       318: q^2
       320: q^2
       321: q^2
       324: q^2
       326: q^2
       328: q^2
       330: q^2
       332: q^2
       333: q^2
       334: q^2
       335: q^2
       336: q^4+q^2
       337: q^2
       339: q^4+q^2
       341: q^2
       343: q^4+q^2
       344: q^2
       345: q^2
       346: q^2
       347: q^2
       348: q^2
       349: q^2
       350: q^4+q^2
       351: q^2
       352: q^2
       353: q^2
       354: q^2
       355: q^2
       356: q^4+q^2
       357: q^2
       358: q^2
       359: q^2
       361: q^4+q^2
       363: q^2
       365: q^4+q^2
       366: q^2
       367: q^2
       368: q^4+q^2
       369: q^2
       370: q^2
       371: q^4+q^2
       372: q^2
       373: q^4+q^2
       379: q^2
       383: q^2
       387: q^2
       392: q^2
       395: q^2
       398: q^2
       402: q^2
       408: q^2
       410: q^2
       412: q^2
       414: q^2
       416: q^2
       418: q^4+q^2
       420: q^2
       421: q^2
       424: q^2
       426: q^4+q^2
       428: q^2
       430: q^2
       431: q^2
       434: q^2
       436: q^2
       438: q^2
       439: q^2
       442: q^2
       444: q^2
       446: q^2
       448: q^2
       449: q^2
       452: q^2
       454: q^2
       456: q^2
       457: q^2
       460: q^2
       461: q^2
       464: q^2
       466: q^2
       468: q^4+q^2
       470: q^2
       472: q^2
       473: q^2
       476: q^2
       478: q^2
       480: q^2
       481: q^2
       482: q^2
       483: q^2
       484: q^2
       486: q^4+q^2
       488: q^2
       490: q^4+q^2
       491: q^4+q^2
       492: q^2
       493: q^2
       494: q^2
       495: q^2
       496: q^2
       497: q^2
       498: q^2
       499: q^2
       500: q^2
       501: q^2
       508: q^2
       512: q^2
       514: q^2
       515: q^4+q^2
       516: q^2
       517: q^4+q^2
       523: q^2
       527: q^2
       531: q^2
       535: q^2
       540: q^2
       544: q^2
       548: q^2
       550: q^2
       554: q^2
       558: q^2
       562: q^2
       567: q^2
       572: q^2
       576: q^2
       581: q^2
       584: q^2
       586: q^2
       588: q^2
       590: q^2
       591: q^2
       594: q^2
       595: q^2
       598: q^4+q^2
       600: q^2
       602: q^2
       604: q^2
       606: q^2
       607: q^2
       610: q^2
       614: q^2
       616: q^2
       618: q^2
       620: q^2
       621: q^2
       624: q^2
       626: q^2
       630: q^2
       631: q^2
       634: q^2
       640: q^2
       642: q^2
       643: q^2
       646: q^2
       652: q^2
       656: q^2
       657: q^2
       659: q^4+q^2
       661: q^2
       663: q^4+q^2
       664: q^4+q^2
       665: q^2
       674: q^2
       675: q^2
       676: q^2
       677: q^2
       679: q^2
       680: q^2
       681: q^2
       682: q^2
       683: q^2
       685: q^2
       689: q^2
       700: q^2
       707: q^2
       711: q^2
       714: q^2
       719: q^2
       724: q^2
       728: q^2
       736: q^2
       738: q^2
       742: q^2
       750: q^2
       755: q^2
       760: q^2
       767: q^2
       773: q^2
       776: q^2
       778: q^2
       780: q^4+q^2
       782: q^2
       786: q^2
       787: q^2
       792: q^2
       794: q^2
       796: q^2
       798: q^2
       802: q^2
       803: q^2
       806: q^2
       807: q^2
       810: q^2
       812: q^2
       817: q^2
       820: q^2
       822: q^2
       826: q^2
       827: q^2
       830: q^2
       831: q^2
       834: q^2
       836: q^2
       844: q^2
       850: q^2
       854: q
       856: q^2
       866: q^2
       870: q^2
       871: q^2
       874: q^2
       875: q^2
       880: q^2
       891: q^2
       898: q^2
       901: q^2
       907: q^2
       910: q^2
       919: q^2
       923: q^2
       925: q^2
       931: q^2
       941: q^2
       945: q^2
       949: q^2
       954: q^2
       963: q^2
       966: q^2
       972: q^2
       981: q
       987: q
       995: q^2
       998: q^2
      1001: q^2
      1011: q^2
      1013: q^2
      1021: q^2
      1023: q^2
      1027: q^2
      1028: q^2
      1037: q^2
      1039: q^2
      1041: q^2
      1044: q^2
      1051: q
      1061: q^2
      1065: q^2
      1076: q^2
      1080: q^2
      1084: q^2
      1093: q^2
      1109: q
      1115: q^2
      1125: q^2
      1129: q^2
      1132: q^2
      1142: q^2
      1153: q^2
      1159: q^2
      1161: q^2
      1173: q^2
      1179: q^2
      1182: q^2
      1187: q
      1193: q
      1223: q
      1231: q^2
      1232: q^2
      1235: q^2
      1249: q^2
      1250: q^2
      1255: q^2
      1265: q
      1275: q^2
      1279: q^2
      1281: q^2
      1297: q^2
      1313: q
      1325: q
      1339: q
      1349: q^2
      1359: q^2
      1362: q^2
      1365: q^2
      1381: q^2
      1391: q^2
      1395: q^2
      1398: q^2
      1409: q
      1417: q
      1434: q^2
      1447: q
      1500: q
      1507: q^2
      1520: q^2
      1536: q
      1558: q
      1562: q
      1638: q
      1686: q
      1728: q
      1732: q
      1795: 1
      1845: q
      1880: 1
      1951: 1
      2001: 1
      2013: 1
      2059: 1
      2103: 1
      2115: 1
      2127: 1
      2176: 1

2177:    0: q^7+4q^6+4q^5+q^3
         1: 3q^6+4q^5+q^3
         2: 3q^6+3q^5+q^3
         3: q^7+4q^6+4q^5+q^3
         4: 3q^6+3q^5+q^3
         5: 3q^6+4q^5+q^3
         6: q^7+3q^6+3q^5+q^3
         7: q^7+3q^6+3q^5+q^3
         8: q^7+3q^6+3q^5+q^3
         9: q^7+3q^6+3q^5+q^3
        10: 2q^6+3q^5+q^3
        11: 2q^6+3q^5+q^3
        12: 2q^6+2q^5+q^3
        13: 2q^6+3q^5+q^3
        14: 2q^6+3q^5+q^3
        15: 2q^6+3q^5+q^3
        16: q^7+4q^6+4q^5+q^3
        17: 3q^6+4q^5+q^3
        18: q^7+3q^6+3q^5+q^3
        19: 2q^6+3q^5+q^3
        20: 2q^6+3q^5+q^3
        21: 2q^6+3q^5+q^3
        22: 2q^6+4q^5+q^3
        23: 2q^6+4q^5+q^3
        24: 2q^6+3q^5+q^3
        25: 2q^6+4q^5+q^3
        26: 2q^6+4q^5+q^3
        27: 2q^6+3q^5+q^3
        28: 2q^6+3q^5+q^3
        29: q^6+2q^5+q^3
        30: q^6+3q^5+q^3
        31: q^6+3q^5+q^3
        32: q^6+3q^5+q^3
        33: 2q^6+4q^5+q^3
        34: q^6+3q^5+q^3
        35: q^6+3q^5+q^3
        36: 2q^6+4q^5+q^3
        37: 2q^6+4q^5+q^3
        39: 2q^6+4q^5+q^3
        41: 2q^6+3q^5+q^3
        43: 2q^5+q^3
        44: q^6+2q^5+q^3
        45: q^6+2q^5+q^3
        46: 2q^6+3q^5+q^3
        47: 2q^6+3q^5+q^3
        48: 2q^6+3q^5+q^3
        49: 2q^6+3q^5+q^3
        50: 2q^6+3q^5+q^3
        51: 2q^6+3q^5+q^3
        52: 3q^5+q^3
        53: q^6+3q^5+q^3
        54: q^6+3q^5+q^3
        55: 3q^5+q^3
        56: q^6+3q^5+q^3
        57: q^6+3q^5+q^3
        58: q^5
        59: q^6+2q^5+q^3
        60: q^5
        61: q^6+2q^5+q^3
        62: q^6+3q^5+q^3
        64: q^6+3q^5+q^3
        66: 2q^6+4q^5+q^3
        68: q^5+q^3
        69: q^6+3q^5+q^3
        70: 2q^5+q^3
        71: q^6+2q^5+q^3
        72: 2q^5+q^3
        73: 2q^5+q^3
        74: 3q^5+q^3
        76: q^6+3q^5+q^3
        78: q^6+3q^5+q^3
        80: 2q^5+q^3
        81: q^6+3q^5+q^3
        82: 2q^5+q^3
        83: 3q^5+q^3
        84: 2q^5+q^3
        85: q^6+3q^5+q^3
        86: 2q^5+q^3
        87: 3q^5+q^3
        88: 2q^5+q^3
        89: q^6+2q^5+q^3
        90: q^6+2q^5+q^3
        91: q^6+3q^5+q^3
        92: q^6+2q^5+q^3
        93: q^6+3q^5+q^3
        94: 3q^5+q^3
        95: q^6+3q^5+q^3
        96: q^6+3q^5+q^3
        97: 3q^5+q^3
        98: q^6+3q^5+q^3
        99: q^6+3q^5+q^3
       100: 2q^5+q^3
       101: q^5+q^3
       102: 2q^5+q^3
       103: q^5
       106: q^6+2q^5+q^3
       108: q^5+q^3
       110: q^5+q^3
       111: 2q^5+q^3
       113: 2q^5+q^3
       115: 3q^5+q^3
       118: q^5+q^3
       120: q^5+q^3
       121: 2q^5+q^3
       123: q^6+3q^5+q^3
       125: q^5+q^3
       126: 2q^5+q^3
       127: 3q^5+q^3
       129: q^6+3q^5+q^3
       131: q^6+3q^5+q^3
       133: q^5+q^3
       134: q^6+3q^5+q^3
       135: 2q^5+q^3
       136: 2q^5+q^3
       137: 2q^5+q^3
       138: 3q^5+q^3
       139: 2q^5+q^3
       140: q^3
       141: 2q^5+q^3
       142: 2q^5+q^3
       143: 2q^5+q^3
       144: 3q^5+q^3
       145: 2q^5+q^3
       146: 2q^5+q^3
       147: 2q^5+q^3
       148: q^3
       149: q^5+q^3
       150: 2q^5+q^3
       151: 2q^5+q^3
       153: q^5+q^3
       155: 2q^5+q^3
       157: q^5+q^3
       158: q^3
       159: q^5+q^3
       160: 2q^5+q^3
       161: q^5+q^3
       162: 2q^5+q^3
       163: 2q^5+q^3
       164: q^5+q^3
       165: 2q^5+q^3
       166: 2q^5+q^3
       167: q^5+q^3
       168: 2q^5+q^3
       172: q^5+q^3
       176: q^5+q^3
       177: 3q^5+q^3
       179: 2q^5+q^3
       181: 2q^5+q^3
       184: q^5+q^3
       186: q^5+q^3
       187: 2q^5+q^3
       189: 2q^5+q^3
       192: q^5+q^3
       194: q^3
       196: q^5+q^3
       197: q^3
       200: q^5+q^3
       202: q^5+q^3
       204: q^3
       205: q^3
       207: 2q^5+q^3
       209: q^5+q^3
       211: 2q^5+q^3
       213: 2q^5+q^3
       215: q^5+q^3
       217: 2q^5+q^3
       219: q^5+q^3
       220: q^3
       221: q^5+q^3
       222: q^3
       223: 2q^5+q^3
       224: q^3
       225: 2q^5+q^3
       226: 2q^5+q^3
       227: q^3
       228: 2q^5+q^3
       229: q^3
       230: q^5+q^3
       231: 2q^5+q^3
       232: q^3
       233: 2q^5+q^3
       234: q^5+q^3
       235: q^3
       236: 2q^5+q^3
       237: 2q^5+q^3
       239: q^5+q^3
       241: 2q^5+q^3
       243: q^5+q^3
       244: q^3
       245: q^3
       246: q^5+q^3
       247: q^5+q^3
       248: q^3
       249: q^5+q^3
       250: q^5+q^3
       251: q^3
       252: q^5+q^3
       253: q^5+q^3
       254: q^3
       255: q^5+q^3
       256: q^5+q^3
       257: q^3
       258: q^5+q^3
       262: q^5+q^3
       266: q^5+q^3
       269: q^3
       273: q^3
       278: q^5+q^3
       279: q^3
       281: 2q^5+q^3
       284: q^5+q^3
       286: q^5+q^3
       287: 2q^5+q^3
       289: q^5+q^3
       291: 2q^5+q^3
       294: q^3
       296: q^3
       297: q^3
       300: q^3
       301: q^3
       304: q^3
       305: q^3
       308: q^3
       310: q^3
       311: q^3
       313: q^3
       315: 2q^5+q^3
       317: q^5+q^3
       320: q^3
       322: q^3
       323: q^3
       325: q^5+q^3
       327: q^5+q^3
       329: q^3
       331: q^5+q^3
       333: q^3
       334: q^3
       335: q^3
       336: q^5+q^3
       337: q^3
       338: q^5+q^3
       340: q^3
       342: q^5+q^3
       344: q^3
       345: q^3
       346: q^5+q^3
       347: q^3
       348: q^3
       349: q^3
       350: q^5+q^3
       351: q^3
       352: q^3
       353: q^3
       354: q^5+q^3
       355: q^3
       356: q^5+q^3
       357: q^3
       358: q^3
       359: q^3
       360: q^5+q^3
       362: q^3
       364: q^5+q^3
       366: q^5+q^3
       367: q^3
       368: q^5+q^3
       369: q^3
       370: q^3
       380: q^5+q^3
       384: q^3
       388: q^3
       391: q^3
       396: q^3
       399: q^3
       404: q^3
       406: q^3
       409: q^3
       411: q^5+q^3
       413: q^3
       415: q^3
       417: q^5+q^3
       420: q^3
       422: q^3
       423: q^3
       425: q^5+q^3
       427: q^3
       430: q^3
       432: q^3
       433: q^3
       435: q^3
       438: q^3
       440: q^3
       441: q^3
       444: q^3
       445: q^3
       448: q^3
       450: q^3
       451: q^3
       454: q^3
       455: q^3
       458: q^3
       459: q^3
       462: q^3
       463: q^3
       465: q^3
       467: q^5+q^3
       469: q^5+q^3
       472: q^3
       474: q^3
       475: q^3
       477: q^3
       479: q^3
       481: q^3
       482: q^3
       483: q^3
       492: q^3
       493: q^3
       494: q^3
       495: q^3
       497: q^3
       498: q^3
       499: q^3
       500: q^3
       508: q^3
       512: q^3
       514: q^3
       524: q^3
       528: q^3
       532: q^3
       536: q^3
       539: q^3
       543: q^3
       547: q^3
       552: q^3
       555: q^3
       559: q^3
       563: q^3
       568: q^3
       570: q^3
       575: q^3
       577: q^3
       583: q^3
       585: q^3
       587: q^3
       590: q^3
       592: q^3
       594: q^3
       596: q^3
       599: q^3
       604: q^3
       605: q^3
       608: q^3
       609: q^3
       613: q^3
       620: q^3
       622: q^3
       623: q^3
       625: q^3
       629: q^3
       639: q^3
       642: q^3
       644: q^3
       645: q^3
       651: q^3
       675: q^3
       676: q^3
       677: q^3
       681: q^3
       682: q^3
       683: q^3
       689: q^3
       697: q^3
       708: q^3
       712: q^3
       716: q^3
       720: q^3
       723: q^3
       727: q^3
       739: q^3
       743: q^3
       756: q^3
       758: q^3
       777: q^3
       797: q^3
       802: q^3
       804: q^3
       806: q^3
       808: q^3
       811: q^3
       821: q^3
       826: q^3
       828: q^3
       830: q^3
       832: q^3
       835: q^3
       849: q^3
       853: q^2
       855: q^3
       899: q^3
       922: q^3
       927: q^3
       930: q^3
       946: q^3
       950: q^3
       955: q^3
       961: q^3
       979: q^2
       984: q^2
      1010: q^2
      1050: q^2
      1107: q^2
      1127: q^2
      1140: q^2
      1185: q^2
      1190: q^2
      1222: q^2
      1264: q^2
      1278: q^2
      1299: q^2
      1311: q^2
      1323: q^2
      1336: q^2
      1361: q^2
      1393: q^2
      1406: q^2
      1415: q^2
      1432: q^2
      1498: q^2
      1510: q^2
      1522: q^2
      1534: q^2
      1796: q
      1881: q
      2113: 1
      2177: 1

2178:    0: q^7+4q^6+4q^5+q^3
         1: 3q^6+4q^5+q^3
         2: 3q^6+3q^5+q^3
         3: q^7+4q^6+4q^5+q^3
         4: 3q^6+3q^5+q^3
         5: 3q^6+4q^5+q^3
         6: q^7+3q^6+3q^5+q^3
         7: q^7+3q^6+3q^5+q^3
         8: q^7+3q^6+3q^5+q^3
         9: q^7+3q^6+3q^5+q^3
        10: 2q^6+3q^5+q^3
        11: 2q^6+3q^5+q^3
        12: 2q^6+2q^5+q^3
        13: 2q^6+3q^5+q^3
        14: 2q^6+3q^5+q^3
        15: 2q^6+3q^5+q^3
        16: q^7+4q^6+4q^5+q^3
        17: 3q^6+4q^5+q^3
        18: q^7+3q^6+3q^5+q^3
        19: 2q^6+3q^5+q^3
        20: 2q^6+3q^5+q^3
        21: 2q^6+3q^5+q^3
        22: 2q^6+4q^5+q^3
        23: 2q^6+4q^5+q^3
        24: 2q^6+3q^5+q^3
        25: 2q^6+4q^5+q^3
        26: 2q^6+4q^5+q^3
        27: 2q^6+3q^5+q^3
        28: 2q^6+3q^5+q^3
        29: q^6+2q^5+q^3
        30: q^6+3q^5+q^3
        31: q^6+3q^5+q^3
        32: q^6+3q^5+q^3
        33: 2q^6+4q^5+q^3
        34: q^6+3q^5+q^3
        35: q^6+3q^5+q^3
        36: 2q^6+4q^5+q^3
        38: 2q^6+4q^5+q^3
        40: 2q^6+4q^5+q^3
        42: 2q^6+3q^5+q^3
        43: 2q^5+q^3
        44: q^6+2q^5+q^3
        45: q^6+2q^5+q^3
        46: 2q^6+3q^5+q^3
        47: 2q^6+3q^5+q^3
        48: 2q^6+3q^5+q^3
        49: 2q^6+3q^5+q^3
        50: 2q^6+3q^5+q^3
        51: 2q^6+3q^5+q^3
        52: 3q^5+q^3
        53: q^6+3q^5+q^3
        54: q^6+3q^5+q^3
        55: 3q^5+q^3
        56: q^6+3q^5+q^3
        57: q^6+3q^5+q^3
        58: q^5
        59: q^6+2q^5+q^3
        60: q^6+2q^5+q^3
        61: q^5
        63: q^6+3q^5+q^3
        65: q^6+3q^5+q^3
        67: 2q^6+4q^5+q^3
        68: q^5+q^3
        69: q^6+3q^5+q^3
        70: 2q^5+q^3
        71: q^6+2q^5+q^3
        72: 2q^5+q^3
        73: 2q^5+q^3
        75: 3q^5+q^3
        77: q^6+3q^5+q^3
        79: q^6+3q^5+q^3
        80: 2q^5+q^3
        81: q^6+3q^5+q^3
        82: 2q^5+q^3
        83: 3q^5+q^3
        84: 2q^5+q^3
        85: q^6+3q^5+q^3
        86: 2q^5+q^3
        87: 3q^5+q^3
        88: 2q^5+q^3
        89: q^6+2q^5+q^3
        90: q^6+2q^5+q^3
        91: q^6+3q^5+q^3
        92: q^6+2q^5+q^3
        93: q^6+3q^5+q^3
        94: 3q^5+q^3
        95: q^6+3q^5+q^3
        96: q^6+3q^5+q^3
        97: 3q^5+q^3
        98: q^6+3q^5+q^3
        99: q^6+3q^5+q^3
       100: 2q^5+q^3
       101: q^5+q^3
       102: 2q^5+q^3
       104: q^6+2q^5+q^3
       105: q^5
       107: q^5+q^3
       110: q^5+q^3
       112: 2q^5+q^3
       114: 2q^5+q^3
       116: 3q^5+q^3
       118: q^5+q^3
       119: q^5+q^3
       122: 2q^5+q^3
       124: q^6+3q^5+q^3
       125: q^5+q^3
       126: 2q^5+q^3
       128: 3q^5+q^3
       130: q^6+3q^5+q^3
       132: q^6+3q^5+q^3
       133: q^5+q^3
       134: q^6+3q^5+q^3
       135: 2q^5+q^3
       136: 2q^5+q^3
       137: 2q^5+q^3
       138: 3q^5+q^3
       139: 2q^5+q^3
       140: q^3
       141: 2q^5+q^3
       142: 2q^5+q^3
       143: 2q^5+q^3
       144: 3q^5+q^3
       145: 2q^5+q^3
       146: 2q^5+q^3
       147: 2q^5+q^3
       148: q^3
       149: q^5+q^3
       150: 2q^5+q^3
       152: 2q^5+q^3
       154: q^5+q^3
       156: 2q^5+q^3
       157: q^5+q^3
       158: q^3
       159: q^5+q^3
       160: 2q^5+q^3
       161: q^5+q^3
       162: 2q^5+q^3
       163: 2q^5+q^3
       164: q^5+q^3
       165: 2q^5+q^3
       166: 2q^5+q^3
       167: q^5+q^3
       168: 2q^5+q^3
       170: q^5+q^3
       174: q^5+q^3
       178: 3q^5+q^3
       180: 2q^5+q^3
       182: 2q^5+q^3
       183: q^5+q^3
       186: q^5+q^3
       188: 2q^5+q^3
       190: 2q^5+q^3
       192: q^5+q^3
       193: q^3
       196: q^5+q^3
       198: q^3
       199: q^5+q^3
       201: q^5+q^3
       204: q^3
       206: q^3
       208: 2q^5+q^3
       210: q^5+q^3
       212: 2q^5+q^3
       214: 2q^5+q^3
       216: q^5+q^3
       218: 2q^5+q^3
       219: q^5+q^3
       220: q^3
       221: q^5+q^3
       222: q^3
       223: 2q^5+q^3
       224: q^3
       225: 2q^5+q^3
       226: 2q^5+q^3
       227: q^3
       228: 2q^5+q^3
       229: q^3
       230: q^5+q^3
       231: 2q^5+q^3
       232: q^3
       233: 2q^5+q^3
       234: q^5+q^3
       235: q^3
       236: 2q^5+q^3
       238: 2q^5+q^3
       240: q^5+q^3
       242: 2q^5+q^3
       243: q^5+q^3
       244: q^3
       245: q^3
       246: q^5+q^3
       247: q^5+q^3
       248: q^3
       249: q^5+q^3
       250: q^5+q^3
       251: q^3
       252: q^5+q^3
       253: q^5+q^3
       254: q^3
       255: q^5+q^3
       256: q^5+q^3
       257: q^3
       258: q^5+q^3
       260: q^5+q^3
       264: q^5+q^3
       268: q^3
       274: q^3
       276: q^5+q^3
       280: q^3
       282: 2q^5+q^3
       283: q^5+q^3
       286: q^5+q^3
       288: 2q^5+q^3
       290: q^5+q^3
       292: 2q^5+q^3
       293: q^3
       296: q^3
       298: q^3
       299: q^3
       302: q^3
       304: q^3
       306: q^3
       307: q^3
       310: q^3
       312: q^3
       314: q^3
       316: 2q^5+q^3
       318: q^5+q^3
       319: q^3
       322: q^3
       324: q^3
       326: q^5+q^3
       328: q^5+q^3
       330: q^3
       332: q^5+q^3
       333: q^3
       334: q^3
       335: q^3
       336: q^5+q^3
       337: q^3
       339: q^5+q^3
       341: q^3
       343: q^5+q^3
       344: q^3
       345: q^3
       346: q^5+q^3
       347: q^3
       348: q^3
       349: q^3
       350: q^5+q^3
       351: q^3
       352: q^3
       353: q^3
       354: q^5+q^3
       355: q^3
       356: q^5+q^3
       357: q^3
       358: q^3
       359: q^3
       361: q^5+q^3
       363: q^3
       365: q^5+q^3
       366: q^5+q^3
       367: q^3
       368: q^5+q^3
       369: q^3
       370: q^3
       378: q^5+q^3
       382: q^3
       386: q^3
       390: q^3
       394: q^3
       400: q^3
       403: q^3
       407: q^3
       410: q^3
       412: q^5+q^3
       414: q^3
       416: q^3
       418: q^5+q^3
       419: q^3
       422: q^3
       424: q^3
       426: q^5+q^3
       428: q^3
       429: q^3
       432: q^3
       434: q^3
       436: q^3
       437: q^3
       440: q^3
       442: q^3
       443: q^3
       446: q^3
       447: q^3
       450: q^3
       452: q^3
       453: q^3
       456: q^3
       458: q^3
       460: q^3
       462: q^3
       464: q^3
       466: q^3
       468: q^5+q^3
       470: q^5+q^3
       471: q^3
       474: q^3
       476: q^3
       478: q^3
       480: q^3
       481: q^3
       482: q^3
       483: q^3
       492: q^3
       493: q^3
       494: q^3
       495: q^3
       497: q^3
       498: q^3
       499: q^3
       500: q^3
       508: q^3
       512: q^3
       514: q^3
       522: q^3
       526: q^3
       530: q^3
       534: q^3
       538: q^3
       542: q^3
       546: q^3
       551: q^3
       556: q^3
       560: q^3
       564: q^3
       566: q^3
       571: q^3
       574: q^3
       581: q^3
       584: q^3
       586: q^3
       588: q^3
       589: q^3
       592: q^3
       593: q^3
       596: q^3
       600: q^3
       603: q^3
       606: q^3
       608: q^3
       610: q^3
       614: q^3
       619: q^3
       622: q^3
       624: q^3
       626: q^3
       630: q^3
       640: q^3
       641: q^3
       644: q^3
       646: q^3
       652: q^3
       675: q^3
       676: q^3
       677: q^3
       681: q^3
       682: q^3
       683: q^3
       689: q^3
       699: q^3
       706: q^3
       710: q^3
       715: q^3
       718: q^3
       722: q^3
       726: q^3
       740: q^3
       744: q^3
       754: q^3
       759: q^3
       778: q^3
       798: q^3
       801: q^3
       804: q^3
       805: q^3
       808: q^3
       812: q^3
       822: q^3
       825: q^3
       828: q^3
       829: q^3
       832: q^3
       836: q^3
       850: q^3
       854: q^2
       856: q^3
       897: q^3
       921: q^3
       926: q^3
       929: q^3
       947: q^3
       951: q^3
       953: q^3
       962: q^3
       980: q^2
       987: q^2
      1011: q^2
      1051: q^2
      1108: q^2
      1128: q^2
      1143: q^2
      1186: q^2
      1193: q^2
      1223: q^2
      1265: q^2
      1279: q^2
      1300: q^2
      1312: q^2
      1324: q^2
      1339: q^2
      1363: q^2
      1394: q^2
      1409: q^2
      1416: q^2
      1435: q^2
      1499: q^2
      1512: q^2
      1523: q^2
      1535: q^2
      1794: q
      1878: q
      2114: 1
      2178: 1

2179:    0: q^7+4q^6+4q^5+q^3
         1: 3q^6+4q^5+q^3
         2: 3q^6+3q^5+q^3
         3: q^7+4q^6+4q^5+q^3
         4: 3q^6+3q^5+q^3
         5: 3q^6+4q^5+q^3
         6: q^7+3q^6+3q^5+q^3
         7: q^7+3q^6+3q^5+q^3
         8: q^7+3q^6+3q^5+q^3
         9: q^7+3q^6+3q^5+q^3
        10: 2q^6+3q^5+q^3
        11: 2q^6+3q^5+q^3
        12: 2q^6+2q^5+q^3
        13: 2q^6+3q^5+q^3
        14: 2q^6+3q^5+q^3
        15: 2q^6+3q^5+q^3
        16: q^7+4q^6+4q^5+q^3
        17: 3q^6+4q^5+q^3
        18: q^7+3q^6+3q^5+q^3
        19: 2q^6+3q^5+q^3
        20: 2q^6+3q^5+q^3
        21: 2q^6+3q^5+q^3
        22: 2q^6+4q^5+q^3
        23: 2q^6+4q^5+q^3
        24: 2q^6+3q^5+q^3
        25: 2q^6+4q^5+q^3
        26: 2q^6+4q^5+q^3
        27: 2q^6+3q^5+q^3
        28: 2q^6+3q^5+q^3
        29: q^6+2q^5+q^3
        30: q^6+3q^5+q^3
        31: q^6+3q^5+q^3
        32: q^6+3q^5+q^3
        33: 2q^6+4q^5+q^3
        34: q^6+3q^5+q^3
        35: q^6+3q^5+q^3
        36: 2q^6+4q^5+q^3
        38: 2q^6+4q^5+q^3
        40: 2q^6+4q^5+q^3
        42: 2q^6+3q^5+q^3
        43: 2q^5+q^3
        44: q^6+2q^5+q^3
        45: q^6+2q^5+q^3
        46: 2q^6+3q^5+q^3
        47: 2q^6+3q^5+q^3
        48: 2q^6+3q^5+q^3
        49: 2q^6+3q^5+q^3
        50: 2q^6+3q^5+q^3
        51: 2q^6+3q^5+q^3
        52: 3q^5+q^3
        53: q^6+3q^5+q^3
        54: q^6+3q^5+q^3
        55: 3q^5+q^3
        56: q^6+3q^5+q^3
        57: q^6+3q^5+q^3
        58: q^6+2q^5+q^3
        59: q^5
        60: q^5
        61: q^6+2q^5+q^3
        63: q^6+3q^5+q^3
        65: q^6+3q^5+q^3
        67: 2q^6+4q^5+q^3
        68: q^5+q^3
        69: q^6+3q^5+q^3
        70: 2q^5+q^3
        71: q^6+2q^5+q^3
        72: 2q^5+q^3
        73: 2q^5+q^3
        75: 3q^5+q^3
        77: q^6+3q^5+q^3
        79: q^6+3q^5+q^3
        80: 2q^5+q^3
        81: q^6+3q^5+q^3
        82: 2q^5+q^3
        83: 3q^5+q^3
        84: 2q^5+q^3
        85: q^6+3q^5+q^3
        86: 2q^5+q^3
        87: 3q^5+q^3
        88: 2q^5+q^3
        89: q^6+2q^5+q^3
        90: q^6+2q^5+q^3
        91: q^6+3q^5+q^3
        92: q^6+2q^5+q^3
        93: q^6+3q^5+q^3
        94: 3q^5+q^3
        95: q^6+3q^5+q^3
        96: q^6+3q^5+q^3
        97: 3q^5+q^3
        98: q^6+3q^5+q^3
        99: q^6+3q^5+q^3
       100: 2q^5+q^3
       101: q^5+q^3
       102: 2q^5+q^3
       104: q^5
       105: q^6+2q^5+q^3
       108: q^5+q^3
       109: q^5+q^3
       112: 2q^5+q^3
       114: 2q^5+q^3
       116: 3q^5+q^3
       117: q^5+q^3
       120: q^5+q^3
       122: 2q^5+q^3
       124: q^6+3q^5+q^3
       125: q^5+q^3
       126: 2q^5+q^3
       128: 3q^5+q^3
       130: q^6+3q^5+q^3
       132: q^6+3q^5+q^3
       133: q^5+q^3
       134: q^6+3q^5+q^3
       135: 2q^5+q^3
       136: 2q^5+q^3
       137: 2q^5+q^3
       138: 3q^5+q^3
       139: 2q^5+q^3
       140: q^3
       141: 2q^5+q^3
       142: 2q^5+q^3
       143: 2q^5+q^3
       144: 3q^5+q^3
       145: 2q^5+q^3
       146: 2q^5+q^3
       147: 2q^5+q^3
       148: q^3
       149: q^5+q^3
       150: 2q^5+q^3
       152: 2q^5+q^3
       154: q^5+q^3
       156: 2q^5+q^3
       157: q^5+q^3
       158: q^3
       159: q^5+q^3
       160: 2q^5+q^3
       161: q^5+q^3
       162: 2q^5+q^3
       163: 2q^5+q^3
       164: q^5+q^3
       165: 2q^5+q^3
       166: 2q^5+q^3
       167: q^5+q^3
       168: 2q^5+q^3
       171: q^5+q^3
       175: q^5+q^3
       178: 3q^5+q^3
       180: 2q^5+q^3
       182: 2q^5+q^3
       184: q^5+q^3
       185: q^5+q^3
       188: 2q^5+q^3
       190: 2q^5+q^3
       191: q^5+q^3
       194: q^3
       195: q^5+q^3
       198: q^3
       200: q^5+q^3
       202: q^5+q^3
       203: q^3
       206: q^3
       208: 2q^5+q^3
       210: q^5+q^3
       212: 2q^5+q^3
       214: 2q^5+q^3
       216: q^5+q^3
       218: 2q^5+q^3
       219: q^5+q^3
       220: q^3
       221: q^5+q^3
       222: q^3
       223: 2q^5+q^3
       224: q^3
       225: 2q^5+q^3
       226: 2q^5+q^3
       227: q^3
       228: 2q^5+q^3
       229: q^3
       230: q^5+q^3
       231: 2q^5+q^3
       232: q^3
       233: 2q^5+q^3
       234: q^5+q^3
       235: q^3
       236: 2q^5+q^3
       238: 2q^5+q^3
       240: q^5+q^3
       242: 2q^5+q^3
       243: q^5+q^3
       244: q^3
       245: q^3
       246: q^5+q^3
       247: q^5+q^3
       248: q^3
       249: q^5+q^3
       250: q^5+q^3
       251: q^3
       252: q^5+q^3
       253: q^5+q^3
       254: q^3
       255: q^5+q^3
       256: q^5+q^3
       257: q^3
       258: q^5+q^3
       261: q^5+q^3
       265: q^5+q^3
       270: q^3
       272: q^3
       277: q^5+q^3
       280: q^3
       282: 2q^5+q^3
       284: q^5+q^3
       285: q^5+q^3
       288: 2q^5+q^3
       290: q^5+q^3
       292: 2q^5+q^3
       294: q^3
       295: q^3
       298: q^3
       300: q^3
       302: q^3
       303: q^3
       306: q^3
       308: q^3
       309: q^3
       312: q^3
       314: q^3
       316: 2q^5+q^3
       318: q^5+q^3
       320: q^3
       321: q^3
       324: q^3
       326: q^5+q^3
       328: q^5+q^3
       330: q^3
       332: q^5+q^3
       333: q^3
       334: q^3
       335: q^3
       336: q^5+q^3
       337: q^3
       339: q^5+q^3
       341: q^3
       343: q^5+q^3
       344: q^3
       345: q^3
       346: q^5+q^3
       347: q^3
       348: q^3
       349: q^3
       350: q^5+q^3
       351: q^3
       352: q^3
       353: q^3
       354: q^5+q^3
       355: q^3
       356: q^5+q^3
       357: q^3
       358: q^3
       359: q^3
       361: q^5+q^3
       363: q^3
       365: q^5+q^3
       366: q^5+q^3
       367: q^3
       368: q^5+q^3
       369: q^3
       370: q^3
       379: q^5+q^3
       383: q^3
       387: q^3
       392: q^3
       395: q^3
       398: q^3
       402: q^3
       408: q^3
       410: q^3
       412: q^5+q^3
       414: q^3
       416: q^3
       418: q^5+q^3
       420: q^3
       421: q^3
       424: q^3
       426: q^5+q^3
       428: q^3
       430: q^3
       431: q^3
       434: q^3
       436: q^3
       438: q^3
       439: q^3
       442: q^3
       444: q^3
       446: q^3
       448: q^3
       449: q^3
       452: q^3
       454: q^3
       456: q^3
       457: q^3
       460: q^3
       461: q^3
       464: q^3
       466: q^3
       468: q^5+q^3
       470: q^5+q^3
       472: q^3
       473: q^3
       476: q^3
       478: q^3
       480: q^3
       481: q^3
       482: q^3
       483: q^3
       492: q^3
       493: q^3
       494: q^3
       495: q^3
       497: q^3
       498: q^3
       499: q^3
       500: q^3
       508: q^3
       512: q^3
       514: q^3
       523: q^3
       527: q^3
       531: q^3
       535: q^3
       540: q^3
       544: q^3
       548: q^3
       550: q^3
       554: q^3
       558: q^3
       562: q^3
       567: q^3
       572: q^3
       576: q^3
       581: q^3
       584: q^3
       586: q^3
       588: q^3
       590: q^3
       591: q^3
       594: q^3
       595: q^3
       600: q^3
       604: q^3
       606: q^3
       607: q^3
       610: q^3
       614: q^3
       620: q^3
       621: q^3
       624: q^3
       626: q^3
       630: q^3
       640: q^3
       642: q^3
       643: q^3
       646: q^3
       652: q^3
       675: q^3
       676: q^3
       677: q^3
       681: q^3
       682: q^3
       683: q^3
       689: q^3
       700: q^3
       707: q^3
       711: q^3
       714: q^3
       719: q^3
       724: q^3
       728: q^3
       738: q^3
       742: q^3
       755: q^3
       760: q^3
       778: q^3
       798: q^3
       802: q^3
       803: q^3
       806: q^3
       807: q^3
       812: q^3
       822: q^3
       826: q^3
       827: q^3
       830: q^3
       831: q^3
       836: q^3
       850: q^3
       854: q^2
       856: q^3
       898: q^3
       923: q^3
       925: q^3
       931: q^3
       945: q^3
       949: q^3
       954: q^3
       963: q^3
       981: q^2
       987: q^2
      1011: q^2
      1051: q^2
      1109: q^2
      1129: q^2
      1143: q^2
      1187: q^2
      1193: q^2
      1223: q^2
      1265: q^2
      1279: q^2
      1301: q^2
      1313: q^2
      1325: q^2
      1339: q^2
      1362: q^2
      1395: q^2
      1409: q^2
      1417: q^2
      1435: q^2
      1500: q^2
      1511: q^2
      1524: q^2
      1536: q^2
      1795: q
      1880: q
      2115: 1
      2179: 1

806332 nonzero polynomials, and 213838 zero polynomials,
 at 1020170 Bruhat-comparable pairs.